label dictionary

290 days ago by andrew.ohana

K.<a> = NumberField(x**2-x-1) sqrt5 = K.ideal(2*a-1) custom_hash = lambda self: str(self.pari_hnf()).__hash__() sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal.__hash__ = custom_hash eta = lambda alpha: (alpha*alpha).trace() def find_small(alpha): while True: plus=a*alpha minus=alpha/a if eta(plus)<eta(alpha): alpha=plus continue if eta(minus)<eta(alpha): alpha=minus continue return alpha sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal.eta = lambda self: eta(find_small(self.gens_reduced()[0])) def custom_cmp(self, other): if cmp(self.norm(),other.norm()): return cmp(self.norm(), other.norm()) if cmp(self.eta(), other.eta()): return cmp(self.eta(), other.eta()) return cmp(other.integral_basis()[1][0],self.integral_basis()[1][0]) sage.rings.number_field.number_field_ideal.NumberFieldFractionalIdeal.__cmp__ = custom_cmp 
       
def ideals_of_given_norm(n): pta = [] for p,e in factor(n): t = p%5 if t == 2 or t == 3: if e%2: pta = [] break q = K.ideal(p^(e/2)) if pta: for i in range(len(pta)): pta[i] *= q else: pta.append(q) elif t == 0: if pta: for i in range(len(pta)): pta[i] *= sqrt5^e else: pta.append(sqrt5^e) else: q1,q2 = K.primes_above(p) if pta: new_pta = [] for v in pta: for i in range(e+1): new_pta.append(v*q1^(e-i)*q2^i) del v del pta pta = new_pta else: for i in range(e+1): pta.append(q1^(e-i)*q2^i) pta.sort() return pta 
       
d = {} for N in range(1,2000): t = 97 for I in ideals_of_given_norm(N): d[I] = str(N)+chr(t) t += 1 
       
d 
        
WARNING: Output truncated!  
full_output.txt



{Fractional ideal (-39*a + 15): '1881d', Fractional ideal (-40*a + 15):
'1975a', Fractional ideal (-2*a + 35): '1151b', Fractional ideal (-32*a
+ 23): '1231a', Fractional ideal (34*a - 24): '1396b', Fractional ideal
(37*a - 14): '1691a', Fractional ideal (32*a - 14): '1276a', Fractional
ideal (40*a - 12): '1936c', Fractional ideal (32*a - 19): '1271b',
Fractional ideal (-a - 23): '551d', Fractional ideal (33*a - 17):
'1361a', Fractional ideal (-39*a + 25): '1871b', Fractional ideal (23*a
- 16): '641b', Fractional ideal (-28*a + 18): '964b', Fractional ideal
(3*a - 42): '1629a', Fractional ideal (36*a - 14): '1604b', Fractional
ideal (33*a - 25): '1289a', Fractional ideal (3*a + 18): '369b',
Fractional ideal (28*a - 14): '980a', Fractional ideal (4*a + 22):
'556a', Fractional ideal (-3*a + 25): '541b', Fractional ideal (18*a -
12): '396b', Fractional ideal (-21*a + 13): '545b', Fractional ideal
(12*a - 6): '180a', Fractional ideal (32*a - 16): '1280a', Fractional
ideal (35*a - 14): '1519b', Fractional ideal (33*a - 13): '1349b',
Fractional ideal (5*a + 35): '1375b', Fractional ideal (5*a - 2): '31b',
Fractional ideal (2): '4a', Fractional ideal (-24*a + 7): '695a',
Fractional ideal (2*a + 36): '1364b', Fractional ideal (-37*a + 26):
'1655a', Fractional ideal (-28*a + 17): '971a', Fractional ideal (a +
12): '155b', Fractional ideal (-35*a + 11): '1489a', Fractional ideal
(20*a - 8): '496b', Fractional ideal (a - 30): '869a', Fractional ideal
(5*a - 39): '1301a', Fractional ideal (21*a - 9): '549b', Fractional
ideal (5*a - 32): '839a', Fractional ideal (37*a - 25): '1669a',
Fractional ideal (-23*a + 14): '655a', Fractional ideal (-34*a + 19):
'1441a', Fractional ideal (-4*a - 27): '821b', Fractional ideal (14):
'196a', Fractional ideal (16*a - 8): '320a', Fractional ideal (31*a -
15): '1201b', Fractional ideal (6*a - 35): '979c', Fractional ideal
(29*a - 8): '1009a', Fractional ideal (5*a + 25): '725b', Fractional
ideal (-15*a + 4): '269a', Fractional ideal (-32*a + 12): '1264a',
Fractional ideal (2*a + 29): '895a', Fractional ideal (24*a - 12):
'720a', Fractional ideal (3*a + 21): '495b', Fractional ideal (-6*a -
27): '855a', Fractional ideal (-3*a + 18): '261a', Fractional ideal
(18*a - 9): '405a', Fractional ideal (5*a - 35): '1025a', Fractional
ideal (-38*a + 22): '1796a', Fractional ideal (-3*a - 41): '1795b',
Fractional ideal (34*a - 18): '1444b', Fractional ideal (7*a - 3):
'61b', Fractional ideal (4*a - 31): '821a', Fractional ideal (a - 25):
'599a', Fractional ideal (28*a - 15): '979b', Fractional ideal (7*a +
40): '1831a', Fractional ideal (37*a - 21): '1705b', Fractional ideal
(4*a + 28): '880b', Fractional ideal (39*a - 27): '1845a', Fractional
ideal (3*a - 32): '919a', Fractional ideal (-38*a + 11): '1741a',
Fractional ideal (4*a + 30): '1004a', Fractional ideal (-31*a + 9):
'1159c', Fractional ideal (4*a + 42): '1916a', Fractional ideal (-34*a +
10): '1396a', Fractional ideal (6*a - 41): '1399a', Fractional ideal
(10*a - 6): '124a', Fractional ideal (30*a - 21): '1089b', Fractional
ideal (37*a - 17): '1709b', Fractional ideal (-34*a + 13): '1429b',
Fractional ideal (8*a + 41): '1945a', Fractional ideal (7*a - 2): '59b',
Fractional ideal (27): '729a', Fractional ideal (20*a - 6): '484c',
Fractional ideal (38*a - 21): '1801b', Fractional ideal (-22*a + 14):
'596b', Fractional ideal (9*a + 39): '1791a', Fractional ideal (37*a -
19): '1711a', Fractional ideal (3*a - 33): '981a', Fractional ideal (9*a
- 6): '99b', Fractional ideal (-40*a + 29): '1919d', Fractional ideal
(33*a - 14): '1355b', Fractional ideal (3*a - 36): '1179a', Fractional
ideal (-32*a + 11): '1255a', Fractional ideal (2*a + 34): '1220b',
Fractional ideal (a - 18): '305a', Fractional ideal (33*a - 24):
'1305b', Fractional ideal (27*a - 15): '909a', Fractional ideal (5*a +
41): '1861a', Fractional ideal (-33*a + 19): '1355a', Fractional ideal
(-3*a + 22): '409b', Fractional ideal (-2*a + 29): '779d', Fractional
ideal (-4*a + 34): '1004b', Fractional ideal (-a + 8): '55a', Fractional
ideal (4*a - 23): '421a', Fractional ideal (a + 19): '379b', Fractional
ideal (6): '36a', Fractional ideal (6*a - 4): '44b', Fractional ideal (a
+ 26): '701b', Fractional ideal (a + 38): '1481b', Fractional ideal (5*a
- 34): '961b', Fractional ideal (27*a - 18): '891b', Fractional ideal
(-4*a + 27): '605b', Fractional ideal (-17*a + 5): '349a', Fractional
ideal (-a - 14): '209b', Fractional ideal (29*a - 14): '1051b',
Fractional ideal (a + 33): '1121b', Fractional ideal (-4*a - 39):
'1661b', Fractional ideal (2*a + 43): '1931a', Fractional ideal (27*a -
8): '881b', Fractional ideal (-35*a + 26): '1459b', Fractional ideal
(2*a + 41): '1759a', Fractional ideal (3*a - 23): '451c', Fractional
ideal (6*a - 33): '855b', Fractional ideal (24*a - 17): '695b',
Fractional ideal (3*a + 33): '1179b', Fractional ideal (2*a + 13):
'191a', Fractional ideal (a - 14): '181a', Fractional ideal (5*a - 29):
'671c', Fractional ideal (2*a - 42): '1676a', Fractional ideal (25*a -
8): '761b', Fractional ideal (-32*a + 15): '1279a', Fractional ideal
(12*a - 8): '176b', Fractional ideal (31*a - 20): '1181a', Fractional
ideal (4*a + 26): '764a', Fractional ideal (-7*a + 46): '1745b',
Fractional ideal (-6*a + 44): '1636b', Fractional ideal (-24*a + 10):
'716a', Fractional ideal (-6*a + 38): '1180b', Fractional ideal (a +
15): '239b', Fractional ideal (25*a - 11): '779b', Fractional ideal
(-20*a + 13): '491b', Fractional ideal (31*a - 19): '1189d', Fractional
ideal (-23*a + 7): '641a', Fractional ideal (22*a - 7): '589d',
Fractional ideal (-26*a + 9): '829a', Fractional ideal (-20*a + 9):
'499a', Fractional ideal (32): '1024a', Fractional ideal (-4*a + 33):
'941b', Fractional ideal (a - 13): '155a', Fractional ideal (6*a - 40):
'1324a', Fractional ideal (4*a + 37): '1501a', Fractional ideal (18*a -
5): '389b', Fractional ideal (-23*a + 8): '649c', Fractional ideal (-5*a
+ 30): '725a', Fractional ideal (-6*a - 35): '1399b', Fractional ideal
(25*a - 7): '751b', Fractional ideal (a - 29): '811a', Fractional ideal
(-9*a + 48): '1791b', Fractional ideal (3*a + 43): '1969a', Fractional
ideal (30*a - 18): '1116a', Fractional ideal (3*a - 34): '1045d',
Fractional ideal (18*a - 8): '404b', Fractional ideal (35*a - 25):
'1475a', Fractional ideal (23): '529a', Fractional ideal (3*a + 27):
'801b', Fractional ideal (-16*a + 6): '316a', Fractional ideal (-5*a +
40): '1375a', Fractional ideal (41*a - 10): '1991d', Fractional ideal
(30*a - 11): '1109a', Fractional ideal (-31*a + 23): '1145b', Fractional
ideal (-24*a + 18): '684b', Fractional ideal (33*a - 22): '1331d',
Fractional ideal (6*a + 36): '1476b', Fractional ideal (-4*a + 46):
'1916b', Fractional ideal (25*a - 13): '781a', Fractional ideal (4*a +
23): '605c', Fractional ideal (39*a - 17): '1895b', Fractional ideal
(26*a - 19): '809a', Fractional ideal (a + 9): '89b', Fractional ideal
(16*a - 11): '311a', Fractional ideal (a + 21): '461b', Fractional ideal
(27*a - 9): '891a', Fractional ideal (5*a + 36): '1451a', Fractional
ideal (-6*a + 43): '1555b', Fractional ideal (21): '441a', Fractional
ideal (38*a - 20): '1804a', Fractional ideal (-5*a + 31): '781d',
Fractional ideal (-4*a + 1): '19a', Fractional ideal (-5*a - 34):
'1301b', Fractional ideal (39*a - 14): '1871a', Fractional ideal (11):
'121a', Fractional ideal (6*a + 33): '1251a', Fractional ideal (a - 41):
'1639a', Fractional ideal (-40*a + 23): '1991a', Fractional ideal (-9*a
+ 50): '1969d', Fractional ideal (36*a - 18): '1620a', Fractional ideal
(-33*a + 21): '1341b', Fractional ideal (-3*a - 35): '1321b', Fractional
ideal (2*a + 32): '1084b', Fractional ideal (-35*a + 9): '1459a',
Fractional ideal (29): '841a', Fractional ideal (2*a + 22): '524b',
Fractional ideal (33*a - 23): '1319b', Fractional ideal (4*a + 21):
'509a', Fractional ideal (4*a + 34): '1276c', Fractional ideal (3*a -
1): '11a', Fractional ideal (30*a - 17): '1121d', Fractional ideal
(-40*a + 25): '1975b', Fractional ideal (6*a + 25): '739a', Fractional
ideal (2*a + 17): '319c', Fractional ideal (40*a - 27): '1951a',
Fractional ideal (40*a - 24): '1984a', Fractional ideal (2*a - 22):
'436a', Fractional ideal (3*a + 22): '541a', Fractional ideal (9*a - 4):
'101b', Fractional ideal (5*a - 47): '1949a', Fractional ideal (7*a +
30): '1061b', Fractional ideal (2*a - 18): '284a', Fractional ideal
(33): '1089a', Fractional ideal (32*a - 18): '1276b', Fractional ideal
(22*a - 11): '605a', Fractional ideal (38*a - 26): '1756a', Fractional
ideal (29*a - 7): '995b', Fractional ideal (3*a - 29): '745a',
Fractional ideal (-4*a + 21): '341d', Fractional ideal (25*a - 10):
'775b', Fractional ideal (-26*a + 16): '836c', Fractional ideal (37*a -
18): '1711b', Fractional ideal (a + 28): '811b', Fractional ideal (38*a
- 16): '1796b', Fractional ideal (14*a - 4): '236b', Fractional ideal
(-2*a + 12): '116a', Fractional ideal (10*a - 5): '125a', Fractional
ideal (-21*a + 10): '551b', Fractional ideal (32*a - 17): '1279b',
Fractional ideal (-6*a + 37): '1111d', Fractional ideal (-4*a + 38):
'1276d', Fractional ideal (7*a + 37): '1579b', Fractional ideal (-29*a +
21): '1009b', Fractional ideal (-7*a + 39): '1199d', Fractional ideal
(-3*a + 31): '859b', Fractional ideal (33*a - 9): '1305a', Fractional
ideal (-3*a - 38): '1549b', Fractional ideal (30*a - 9): '1089c',
Fractional ideal (-6*a - 28): '916b', Fractional ideal (5*a - 44):
'1691c', Fractional ideal (a - 21): '419a', Fractional ideal (-2*a -
28): '836b', Fractional ideal (a + 40): '1639b', Fractional ideal (-29*a
+ 12): '1045b', Fractional ideal (33*a - 18): '1359a', Fractional ideal
(4*a + 38): '1580a', Fractional ideal (-8*a - 39): '1769d', Fractional
ideal (39*a - 19): '1901b', Fractional ideal (30*a - 20): '1100b',
Fractional ideal (20*a - 14): '484b', Fractional ideal (a + 36):
'1331b', Fractional ideal (2*a - 28): '724a', Fractional ideal (2*a +
18): '356b', Fractional ideal (4*a + 25): '709a', Fractional ideal (a +
5): '29b', Fractional ideal (-40*a + 10): '1900a', Fractional ideal
(39*a - 18): '1899b', Fractional ideal (37): '1369a', Fractional ideal
(16*a - 9): '319b', Fractional ideal (29*a - 22): '995a', Fractional
ideal (-8*a + 49): '1945b', Fractional ideal (12*a - 7): '179b',
Fractional ideal (-14*a + 9): '241b', Fractional ideal (7): '49a',
Fractional ideal (-7*a - 32): '1199c', Fractional ideal (3*a - 21):
'369a', Fractional ideal (-a + 37): '1331a', Fractional ideal (-2*a +
39): '1439b', Fractional ideal (4*a - 39): '1349c', Fractional ideal
(-7*a + 43): '1499b', Fractional ideal (19*a - 9): '451b', Fractional
ideal (16): '256a', Fractional ideal (-22*a + 8): '596a', Fractional
ideal (3*a + 19): '409a', Fractional ideal (6*a + 38): '1636a',
Fractional ideal (13*a - 6): '211b', Fractional ideal (38*a - 18):
'1804b', Fractional ideal (36*a - 19): '1619b', Fractional ideal (-5*a -
23): '619a', Fractional ideal (-22*a + 9): '601a', Fractional ideal
(24): '576a', Fractional ideal (5): '25a', Fractional ideal (2*a + 37):
'1439a', Fractional ideal (18*a - 10): '404a', Fractional ideal (34*a -
15): '1441b', Fractional ideal (a + 25): '649b', Fractional ideal (-28*a
+ 7): '931a', Fractional ideal (-7*a - 39): '1745a', Fractional ideal (a
- 22): '461a', Fractional ideal (-34*a + 14): '1436a', Fractional ideal
(18*a - 6): '396a', Fractional ideal (a + 18): '341b', Fractional ideal
(3*a + 39): '1629b', Fractional ideal (-6*a + 32): '796b', Fractional
ideal (22*a - 13): '601b', Fractional ideal (19*a - 12): '445a',
Fractional ideal (3*a + 40): '1711c', Fractional ideal (-32*a + 21):
'1255b', Fractional ideal (-3*a - 26): '745b', Fractional ideal (-34*a +
12): '1420a', Fractional ideal (3*a + 28): '859a', Fractional ideal
(-6*a + 39): '1251b', Fractional ideal (3*a + 24): '639b', Fractional
ideal (-35*a + 16): '1529a', Fractional ideal (-2*a + 19): '319d',
Fractional ideal (-37*a + 10): '1639d', Fractional ideal (13*a - 4):
'205b', Fractional ideal (19*a - 10): '451a', Fractional ideal (-3*a -
29): '919b', Fractional ideal (4): '16a', Fractional ideal (3*a - 26):
'589a', Fractional ideal (24*a - 8): '704a', Fractional ideal (-2*a +
16): '220a', Fractional ideal (35*a - 21): '1519a', Fractional ideal
(30): '900a', Fractional ideal (2*a + 38): '1516b', Fractional ideal
(34*a - 17): '1445a', Fractional ideal (-6*a + 48): '1980a', Fractional
ideal (39*a - 11): '1829d', Fractional ideal (29*a - 16): '1049b',
Fractional ideal (16*a - 7): '319a', Fractional ideal (31*a - 16):
'1201a', Fractional ideal (17*a - 10): '359b', Fractional ideal (3*a -
20): '331a', Fractional ideal (-37*a + 13): '1681c', Fractional ideal
(-3*a - 42): '1881b', Fractional ideal (5*a + 21): '521a', Fractional
ideal (-4*a - 35): '1349d', Fractional ideal (-26*a + 17): '829b',
Fractional ideal (a + 30): '929b', Fractional ideal (-5*a + 43):
'1609b', Fractional ideal (5*a + 31): '1091a', Fractional ideal (a + 8):
'71b', Fractional ideal (-36*a + 27): '1539b', Fractional ideal (-31*a +
8): '1145a', Fractional ideal (-2*a + 23): '479b', Fractional ideal
(-37*a + 23): '1691b', Fractional ideal (-3*a - 32): '1111b', Fractional
ideal (6*a + 30): '1044b', Fractional ideal (-17*a + 6): '355a',
Fractional ideal (5*a + 27): '839b', Fractional ideal (-26*a + 10):
'836d', Fractional ideal (2*a - 1): '5a', Fractional ideal (a - 35):
'1189a', Fractional ideal (2*a + 31): '1019a', Fractional ideal (-21*a +
11): '551a', Fractional ideal (5*a + 32): '1159b', Fractional ideal
(-4*a - 18): '380a', Fractional ideal (18): '324a', Fractional ideal
(38): '1444a', Fractional ideal (4*a - 43): '1661a', Fractional ideal (a
- 28): '755a', Fractional ideal (40*a - 16): '1984b', Fractional ideal
(2*a - 14): '164a', Fractional ideal (2*a + 19): '395a', Fractional
ideal (-3*a - 23): '589b', Fractional ideal (40*a - 21): '1999b',
Fractional ideal (31*a - 14): '1199b', Fractional ideal (a + 37):
'1405b', Fractional ideal (15): '225a', Fractional ideal (a + 20):
'419b', Fractional ideal (-7*a - 41): '1919b', Fractional ideal (-40*a +
26): '1964b', Fractional ideal (26*a - 8): '820b', Fractional ideal
(-19*a + 11): '449a', Fractional ideal (-32*a + 24): '1216b', Fractional
ideal (-39*a + 24): '1881c', Fractional ideal (5*a - 3): '31a',
Fractional ideal (2*a - 40): '1516a', Fractional ideal (3*a + 25):
'691a', Fractional ideal (6*a + 39): '1719a', Fractional ideal (14*a -
8): '244a', Fractional ideal (12*a - 4): '176a', Fractional ideal (3*a +
30): '981b', Fractional ideal (29*a - 11): '1039a', Fractional ideal
(-3*a + 24): '495a', Fractional ideal (26*a - 15): '841b', Fractional
ideal (a - 42): '1721a', Fractional ideal (4*a + 33): '1205a',
Fractional ideal (23*a - 13): '659b', Fractional ideal (19): '361a',
Fractional ideal (38*a - 12): '1756b', Fractional ideal (-5*a - 29):
'961c', Fractional ideal (37*a - 12): '1669b', Fractional ideal (36*a -
23): '1595c', Fractional ideal (7*a + 31): '1129b', Fractional ideal
(-5*a - 28): '899c', Fractional ideal (36*a - 12): '1584a', Fractional
ideal (13): '169a', Fractional ideal (28*a - 12): '976b', Fractional
ideal (6*a + 26): '796a', Fractional ideal (a - 16): '239a', Fractional
ideal (2*a + 12): '164b', Fractional ideal (39*a - 20): '1901a',
Fractional ideal (28*a - 19): '955a', Fractional ideal (-39*a + 29):
'1811b', Fractional ideal (-24*a + 11): '719a', Fractional ideal (19*a -
6): '439b', Fractional ideal (3*a + 36): '1395b', Fractional ideal
(-32*a + 20): '1264b', Fractional ideal (26*a - 18): '820a', Fractional
ideal (-3*a + 40): '1471b', Fractional ideal (-3*a + 19): '295b',
Fractional ideal (7*a - 4): '61a', Fractional ideal (12): '144a',
Fractional ideal (2*a - 44): '1844a', Fractional ideal (38*a - 27):
'1741b', Fractional ideal (a - 26): '649a', Fractional ideal (a - 27):
'701a', Fractional ideal (30*a - 12): '1116b', Fractional ideal (39*a -
21): '1899a', Fractional ideal (-8*a + 6): '76b', Fractional ideal (25*a
- 16): '769a', Fractional ideal (-24*a + 9): '711a', Fractional ideal
(23*a - 11): '661b', Fractional ideal (24*a - 16): '704b', Fractional
ideal (2*a + 20): '436b', Fr

...

'1436b', Fractional ideal (a + 41): '1721b', Fractional ideal (13*a -
9): '205a', Fractional ideal (5*a + 37): '1529d', Fractional ideal (7*a
- 44): '1579a', Fractional ideal (39*a - 16): '1889b', Fractional ideal
(-37*a + 15): '1699a', Fractional ideal (-19*a + 14): '431b', Fractional
ideal (39*a - 22): '1895a', Fractional ideal (-3*a + 46): '1969b',
Fractional ideal (30*a - 14): '1124b', Fractional ideal (35*a - 15):
'1525b', Fractional ideal (37*a - 28): '1621a', Fractional ideal (32*a -
10): '1244b', Fractional ideal (9): '81a', Fractional ideal (-30*a +
22): '1076b', Fractional ideal (-29*a + 19): '1031b', Fractional ideal
(8*a - 4): '80a', Fractional ideal (a + 22): '505b', Fractional ideal
(-3*a + 37): '1249b', Fractional ideal (7*a - 38): '1129a', Fractional
ideal (38*a - 15): '1789b', Fractional ideal (a + 13): '181b',
Fractional ideal (a - 44): '1891a', Fractional ideal (30*a - 15):
'1125a', Fractional ideal (-38*a + 14): '1780b', Fractional ideal (-23*a
+ 17): '631b', Fractional ideal (22): '484a', Fractional ideal (18*a -
7): '401b', Fractional ideal (25*a - 15): '775a', Fractional ideal (a +
34): '1189b', Fractional ideal (-29*a + 13): '1049a', Fractional ideal
(2*a + 39): '1595a', Fractional ideal (37*a - 27): '1639c', Fractional
ideal (13*a - 7): '211a', Fractional ideal (-23*a + 6): '631a',
Fractional ideal (23*a - 12): '661a', Fractional ideal (a - 17): '271a',
Fractional ideal (-5*a - 39): '1691d', Fractional ideal (-4*a + 26):
'556b', Fractional ideal (2*a - 36): '1220a', Fractional ideal (-38*a +
25): '1769b', Fractional ideal (6*a - 3): '45a', Fractional ideal (25):
'625a', Fractional ideal (21*a - 6): '531b', Fractional ideal (44):
'1936a', Fractional ideal (37*a - 24): '1681b', Fractional ideal (a -
11): '109a', Fractional ideal (-31*a + 13): '1195a', Fractional ideal
(-3*a - 20): '451d', Fractional ideal (11*a - 5): '151b', Fractional
ideal (-3*a + 43): '1711d', Fractional ideal (2*a - 38): '1364a',
Fractional ideal (39): '1521a', Fractional ideal (31*a - 21): '1171a',
Fractional ideal (-8*a + 2): '76a', Fractional ideal (33*a - 16):
'1361b', Fractional ideal (a + 43): '1891b', Fractional ideal (-35*a +
12): '1501c', Fractional ideal (-29*a + 17): '1045a', Fractional ideal
(-35*a + 23): '1501d', Fractional ideal (-27*a + 7): '869c', Fractional
ideal (21*a - 14): '539b', Fractional ideal (6*a - 34): '916a',
Fractional ideal (40*a - 13): '1951b', Fractional ideal (26): '676a',
Fractional ideal (-35*a + 13): '1511b', Fractional ideal (2*a - 24):
'524a', Fractional ideal (-8*a - 38): '1684b', Fractional ideal (2*a +
42): '1844b', Fractional ideal (-31*a + 18): '1195b', Fractional ideal
(-6*a - 41): '1891d', Fractional ideal (36*a - 24): '1584b', Fractional
ideal (2*a - 32): '956a', Fractional ideal (a - 31): '929a', Fractional
ideal (17*a - 12): '349b', Fractional ideal (-39*a + 28): '1829c',
Fractional ideal (24*a - 14): '716b', Fractional ideal (33*a - 8):
'1289b', Fractional ideal (a + 39): '1559b', Fractional ideal (a - 38):
'1405a', Fractional ideal (2*a + 10): '116b', Fractional ideal (-8*a +
45): '1601a', Fractional ideal (39*a - 26): '1859b', Fractional ideal
(36*a - 21): '1611b', Fractional ideal (-27*a + 20): '869d', Fractional
ideal (35*a - 24): '1489b', Fractional ideal (-20*a + 7): '491a',
Fractional ideal (41): '1681a', Fractional ideal (-6*a - 34): '1324b',
Fractional ideal (27*a - 17): '899a', Fractional ideal (15*a - 7):
'281b', Fractional ideal (-36*a + 15): '1611a', Fractional ideal (30*a -
16): '1124a', Fractional ideal (-40*a + 19): '1999a', Fractional ideal
(-25*a + 9): '769b', Fractional ideal (35*a - 22): '1511a', Fractional
ideal (-9*a - 41): '1969c', Fractional ideal (a + 44): '1979b',
Fractional ideal (-16*a + 10): '316b', Fractional ideal (a - 32):
'991a', Fractional ideal (2*a + 16): '284b', Fractional ideal (-28*a +
13): '979a', Fractional ideal (2*a - 20): '356a', Fractional ideal (-7*a
+ 42): '1421a', Fractional ideal (-16*a + 4): '304a', Fractional ideal
(-8*a - 35): '1441c', Fractional ideal (3*a + 16): '295a', Fractional
ideal (3*a - 44): '1795a', Fractional ideal (a + 32): '1055b',
Fractional ideal (22*a - 12): '604a', Fractional ideal (-4*a + 25):
'509b', Fractional ideal (16*a - 5): '311b', Fractional ideal (-38*a +
17): '1801a', Fractional ideal (-36*a + 17): '1619a', Fractional ideal
(-5*a - 33): '1229a', Fractional ideal (2*a + 26): '724b', Fractional
ideal (41*a - 31): '1991c', Fractional ideal (-4*a + 30): '764b',
Fractional ideal (-25*a + 18): '751a', Fractional ideal (-5*a + 33):
'899d', Fractional ideal (8*a - 47): '1769c', Fractional ideal (17):
'289a', Fractional ideal (10*a - 4): '124b', Fractional ideal (9*a - 5):
'101a', Fractional ideal (25*a - 12): '781b', Fractional ideal (-2*a +
41): '1595b', Fractional ideal (34*a - 11): '1409b', Fractional ideal
(2*a - 26): '620a', Fractional ideal (-25*a + 14): '779a', Fractional
ideal (-32*a + 8): '1216a', Fractional ideal (9*a - 47): '1705c',
Fractional ideal (-5*a - 38): '1609a', Fractional ideal (7*a - 40):
'1271d', Fractional ideal (-28*a + 21): '931b', Fractional ideal (27*a -
14): '911a', Fractional ideal (39*a - 13): '1859a', Fractional ideal
(4*a - 22): '380b', Fractional ideal (-8*a + 43): '1441d', Fractional
ideal (-33*a + 20): '1349a', Fractional ideal (-2*a + 43): '1759b',
Fractional ideal (15*a - 10): '275b', Fractional ideal (28*a - 20):
'944a', Fractional ideal (5*a - 37): '1159a', Fractional ideal (3*a -
35): '1111a', Fractional ideal (a - 34): '1121a', Fractional ideal
(-33*a + 10): '1319a', Fractional ideal (-2*a + 21): '395b', Fractional
ideal (35*a - 18): '1531a', Fractional ideal (11*a - 3): '145a',
Fractional ideal (a - 10): '89a', Fractional ideal (2*a + 27): '779c',
Fractional ideal (2*a + 11): '139a', Fractional ideal (40*a - 28):
'1936b', Fractional ideal (5*a + 42): '1949b', Fractional ideal (3*a -
39): '1395a', Fractional ideal (a + 24): '599b', Fractional ideal (a -
36): '1259a', Fractional ideal (-2*a + 13): '139b', Fractional ideal
(3*a + 13): '199a', Fractional ideal (-20*a + 5): '475a', Fractional
ideal (a + 6): '41b', Fractional ideal (-4*a + 45): '1829b', Fractional
ideal (39*a - 23): '1889a', Fractional ideal (-15*a + 11): '269b',
Fractional ideal (-37*a + 16): '1705a', Fractional ideal (a + 29):
'869b', Fractional ideal (6*a - 46): '1804c', Fractional ideal (15*a -
5): '275a', Fractional ideal (-8*a + 5): '79b', Fractional ideal (19*a -
13): '439a', Fractional ideal (10*a - 3): '121c', Fractional ideal (7*a
- 41): '1345a', Fractional ideal (19*a - 8): '449b', Fractional ideal
(-38*a + 13): '1769a', Fractional ideal (-39*a + 10): '1811a',
Fractional ideal (-27*a + 10): '899b', Fractional ideal (20): '400a',
Fractional ideal (-6*a + 36): '1044a', Fractional ideal (-23*a + 10):
'659a', Fractional ideal (21*a - 12): '549a', Fractional ideal (3*a +
15): '261b', Fractional ideal (a + 27): '755b', Fractional ideal (-3*a +
28): '691b', Fractional ideal (3*a - 38): '1321a', Fractional ideal (6*a
+ 31): '1111c', Fractional ideal (-5*a + 36): '1091b', Fractional ideal
(7*a - 48): '1919a', Fractional ideal (22*a - 6): '580a', Fractional
ideal (40*a - 17): '1991b', Fractional ideal (-24*a + 15): '711b',
Fractional ideal (-4*a + 42): '1580b', Fractional ideal (14*a - 6):
'244b', Fractional ideal (a - 40): '1559a', Fractional ideal (4*a - 40):
'1424a', Fractional ideal (40*a - 11): '1919c', Fractional ideal (29*a -
20): '1021b', Fractional ideal (4*a - 2): '20a', Fractional ideal (2*a +
23): '571a', Fractional ideal (-4*a + 41): '1501b', Fractional ideal
(-6*a + 31): '739b', Fractional ideal (-36*a + 22): '1604a', Fractional
ideal (2*a + 30): '956b', Fractional ideal (14*a - 7): '245a',
Fractional ideal (7*a + 36): '1499a', Fractional ideal (25*a - 17):
'761a', Fractional ideal (-18*a + 11): '401a', Fractional ideal (31*a -
10): '1171b', Fractional ideal (36*a - 16): '1616b', Fractional ideal
(-2*a - 9): '95a', Fractional ideal (7*a + 38): '1661d', Fractional
ideal (35*a - 10): '1475b', Fractional ideal (35): '1225a', Fractional
ideal (a - 9): '71a', Fractional ideal (30*a - 10): '1100a', Fractional
ideal (11*a - 6): '151a', Fractional ideal (3*a - 2): '11b', Fractional
ideal (-8*a - 37): '1601b', Fractional ideal (-2*a + 31): '895b',
Fractional ideal (15*a - 6): '279b', Fractional ideal (a - 33): '1055a',
Fractional ideal (a - 24): '551c', Fractional ideal (6*a + 42): '1980b',
Fractional ideal (-6*a - 29): '979d', Fractional ideal (-16*a + 12):
'304b', Fractional ideal (-2*a + 37): '1291b', Fractional ideal (a -
19): '341a', Fractional ideal (7*a - 45): '1661c', Fractional ideal
(-13*a + 8): '209c', Fractional ideal (34*a - 25): '1381a', Fractional
ideal (-23*a + 15): '649d', Fractional ideal (4*a + 17): '341c',
Fractional ideal (8*a + 34): '1364c', Fractional ideal (-38*a + 23):
'1789a', Fractional ideal (-31*a + 17): '1199a', Fractional ideal (a -
45): '1979a', Fractional ideal (4*a + 20): '464b', Fractional ideal (3*a
- 41): '1549a', Fractional ideal (15*a - 8): '281a', Fractional ideal
(7*a + 35): '1421b', Fractional ideal (-8*a + 48): '1856a', Fractional
ideal (-13*a + 5): '209d', Fractional ideal (-5*a + 46): '1861b',
Fractional ideal (28*a - 9): '955b', Fractional ideal (a + 10): '109b',
Fractional ideal (-5*a + 38): '1229b', Fractional ideal (-6*a - 40):
'1804d', Fractional ideal (-29*a + 18): '1039b', Fractional ideal (a +
7): '55b', Fractional ideal (-19*a + 7): '445b', Fractional ideal (4*a +
36): '1424b', Fractional ideal (37*a - 22): '1699b', Fractional ideal
(-31*a + 11): '1181b', Fractional ideal (14*a - 10): '236a', Fractional
ideal (27*a - 16): '905b', Fractional ideal (4*a + 29): '941a',
Fractional ideal (26*a - 14): '844a', Fractional ideal (9*a + 40):
'1879b', Fractional ideal (2*a - 34): '1084a', Fractional ideal (5*a +
30): '1025b', Fractional ideal (4*a - 35): '1069a', Fractional ideal
(21*a - 8): '545a', Fractional ideal (-3*a - 17): '331b', Fractional
ideal (a - 15): '209a', Fractional ideal (22*a - 16): '580b', Fractional
ideal (8*a + 40): '1856b', Fractional ideal (-8*a + 3): '79a',
Fractional ideal (-12*a + 3): '171a', Fractional ideal (21*a - 7):
'539a', Fractional ideal (7*a - 5): '59a', Fractional ideal (2*a + 25):
'671a', Fractional ideal (5*a + 22): '569b', Fractional ideal (-20*a +
15): '475b', Fractional ideal (38*a - 19): '1805a', Fractional ideal
(11*a - 8): '145b', Fractional ideal (3*a + 37): '1471a', Fractional
ideal (5*a + 40): '1775b', Fractional ideal (-2*a + 27): '671b',
Fractional ideal (-27*a + 11): '905a', Fractional ideal (-8*a - 36):
'1520a', Fractional ideal (22*a - 15): '589c', Fractional ideal (-2*a +
45): '1931b', Fractional ideal (a + 16): '271b', Fractional ideal (-4*a
+ 24): '464a', Fractional ideal (28*a - 8): '944b', Fractional ideal
(2*a + 14): '220b', Fractional ideal (36*a - 11): '1571b', Fractional
ideal (-2*a + 33): '1019b', Fractional ideal (36): '1296a', Fractional
ideal (-37*a + 20): '1709a', Fractional ideal (-36*a + 25): '1571a',
Fractional ideal (-5*a - 24): '671d', Fractional ideal (-2*a + 17):
'251b', Fractional ideal (35*a - 20): '1525a', Fractional ideal (-3*a -
31): '1045c', Fractional ideal (36*a - 13): '1595d', Fractional ideal
(40): '1600a', Fractional ideal (-4*a + 32): '880a', Fractional ideal
(-30*a + 19): '1109b', Fractional ideal (-12*a + 9): '171b', Fractional
ideal (21*a - 15): '531a', Fractional ideal (3*a - 30): '801a',
Fractional ideal (5*a - 27): '569a', Fractional ideal (4*a + 41):
'1829a', Fractional ideal (-3*a - 14): '229b', Fractional ideal (-4*a +
37): '1205b', Fractional ideal (39*a - 12): '1845b', Fractional ideal
(-4*a + 29): '709b', Fractional ideal (a + 42): '1805c', Fractional
ideal (10*a - 7): '121b', Fractional ideal (-34*a + 9): '1381b',
Fractional ideal (-33*a + 12): '1341a', Fractional ideal (-14*a + 5):
'241a', Fractional ideal (31*a - 22): '1159d', Fractional ideal (-2*a +
25): '571b', Fractional ideal (-17*a + 7): '359a', Fractional ideal
(-40*a + 14): '1964a', Fractional ideal (24*a - 13): '719b', Fractional
ideal (-38*a + 28): '1724b', Fractional ideal (4*a + 40): '1744b',
Fractional ideal (a + 11): '131b', Fractional ideal (3*a - 45): '1881a',
Fractional ideal (-17*a + 11): '355b', Fractional ideal (-34*a + 22):
'1420b', Fractional ideal (-4*a - 19): '421b', Fractional ideal (2*a +
24): '620b', Fractional ideal (a - 39): '1481a', Fractional ideal (7*a -
47): '1831b', Fractional ideal (42): '1764a', Fractional ideal (37*a -
11): '1655b', Fractional ideal (-12*a + 5): '179a', Fractional ideal
(-27*a + 19): '881a', Fractional ideal (3): '9a', Fractional ideal (a -
23): '505a', Fractional ideal (34*a - 23): '1409a', Fractional ideal
(5*a - 45): '1775a', Fractional ideal (2*a - 11): '95b', Fractional
ideal (35*a - 17): '1531b', Fractional ideal (32*a - 9): '1231b',
Fractional ideal (-5*a + 28): '619b', Fractional ideal (-3*a + 16):
'199b', Fractional ideal (2*a + 33): '1151a', Fractional ideal (a - 20):
'379a', Fractional ideal (2*a + 21): '479a', Fractional ideal (-30*a +
13): '1121c', Fractional ideal (9*a + 38): '1705d', Fractional ideal
(20*a - 11): '499b', Fractional ideal (3*a - 17): '229a', Fractional
ideal (-2*a + 15): '191b', Fractional ideal (4*a - 28): '656a',
Fractional ideal (-38*a + 10): '1724a', Fractional ideal (4*a + 32):
'1136b', Fractional ideal (-29*a + 9): '1021a', Fractional ideal (17*a -
8): '361c', Fractional ideal (a - 12): '131a', Fractional ideal (-29*a +
10): '1031a', Fractional ideal (-7*a - 34): '1345b', Fractional ideal
(9*a - 49): '1879a', Fractional ideal (-a + 6): '29a', Fractional ideal
(5*a - 42): '1529c', Fractional ideal (2*a - 30): '836a', Fractional
ideal (a + 35): '1259b', Fractional ideal (-11*a + 4): '149a',
Fractional ideal (-40*a + 30): '1900b', Fractional ideal (28*a - 16):
'976a', Fractional ideal (-24*a + 6): '684a', Fractional ideal (6*a -
42): '1476a', Fractional ideal (36*a - 20): '1616a', Fractional ideal
(26*a - 13): '845a', Fractional ideal (-36*a + 9): '1539a', Fractional
ideal (-34*a + 21): '1429a', Fractional ideal (6*a + 37): '1555a',
Fractional ideal (3*a - 27): '639a', Fractional ideal (-30*a + 8):
'1076a', Fractional ideal (7*a - 37): '1061a', Fractional ideal (10):
'100a', Fractional ideal (-32*a + 13): '1271a', Fractional ideal (-18*a
+ 13): '389a', Fractional ideal (31*a - 12): '1189c', Fractional ideal
(6*a + 32): '1180a', Fractional ideal (31): '961a', Fractional ideal
(32*a - 22): '1244a', Fractional ideal (8*a - 44): '1520b', Fractional
ideal (9*a - 3): '99a', Fractional ideal (-19*a + 5): '431a', Fractional
ideal (-11*a + 7): '149b', Fractional ideal (20*a - 10): '500a',
Fractional ideal (-4*a - 31): '1069b', Fractional ideal (26*a - 11):
'841c', Fractional ideal (22*a - 10): '604b', Fractional ideal (-4*a +
3): '19b', Fractional ideal (5*a + 26): '781c', Fractional ideal (20*a -
12): '496a', Fractional ideal (43): '1849a', Fractional ideal (8*a -
46): '1684a', Fractional ideal (-5*a + 26): '521b', Fractional ideal
(37*a - 9): '1621b', Fractional ideal (8): '64a', Fractional ideal (33*a
- 11): '1331c', Fractional ideal (a + 31): '991b', Fractional ideal
(-26*a + 7): '809b', Fractional ideal (3*a + 34): '1249a', Fractional
ideal (2*a + 15): '251a', Fractional ideal (-8*a + 42): '1364d',
Fractional ideal (-6*a + 45): '1719b', Fractional ideal (7*a + 33):
'1271c', Fractional ideal (38*a - 24): '1780a', Fractional ideal (2*a +
40): '1676b', Fractional ideal (4*a - 36): '1136a', Fractional ideal
(35*a - 19): '1529b', Fractional ideal (-40*a + 18): '1996a', Fractional
ideal (4*a - 44): '1744a', Fractional ideal (34): '1156a', Fractional
ideal (36*a - 10): '1556b', Fractional ideal (27*a - 12): '909b',
Fractional ideal (6*a - 2): '44a', Fractional ideal (4*a + 24): '656b',
Fractional ideal (26*a - 12): '844b', Fractional ideal (6*a - 47):
'1891c', Fractional ideal (28): '784a', Fractional ideal (-a + 43):
'1805b', Fractional ideal (-36*a + 26): '1556a', Fractional ideal (a +
17): '305b', Fractional ideal (2*a + 35): '1291a', Fractional ideal (a -
7): '41a', Fractional ideal (15*a - 9): '279a'}
WARNING: Output truncated!  
full_output.txt



{Fractional ideal (-39*a + 15): '1881d', Fractional ideal (-40*a + 15): '1975a', Fractional ideal (-2*a + 35): '1151b', Fractional ideal (-32*a + 23): '1231a', Fractional ideal (34*a - 24): '1396b', Fractional ideal (37*a - 14): '1691a', Fractional ideal (32*a - 14): '1276a', Fractional ideal (40*a - 12): '1936c', Fractional ideal (32*a - 19): '1271b', Fractional ideal (-a - 23): '551d', Fractional ideal (33*a - 17): '1361a', Fractional ideal (-39*a + 25): '1871b', Fractional ideal (23*a - 16): '641b', Fractional ideal (-28*a + 18): '964b', Fractional ideal (3*a - 42): '1629a', Fractional ideal (36*a - 14): '1604b', Fractional ideal (33*a - 25): '1289a', Fractional ideal (3*a + 18): '369b', Fractional ideal (28*a - 14): '980a', Fractional ideal (4*a + 22): '556a', Fractional ideal (-3*a + 25): '541b', Fractional ideal (18*a - 12): '396b', Fractional ideal (-21*a + 13): '545b', Fractional ideal (12*a - 6): '180a', Fractional ideal (32*a - 16): '1280a', Fractional ideal (35*a - 14): '1519b', Fractional ideal (33*a - 13): '1349b', Fractional ideal (5*a + 35): '1375b', Fractional ideal (5*a - 2): '31b', Fractional ideal (2): '4a', Fractional ideal (-24*a + 7): '695a', Fractional ideal (2*a + 36): '1364b', Fractional ideal (-37*a + 26): '1655a', Fractional ideal (-28*a + 17): '971a', Fractional ideal (a + 12): '155b', Fractional ideal (-35*a + 11): '1489a', Fractional ideal (20*a - 8): '496b', Fractional ideal (a - 30): '869a', Fractional ideal (5*a - 39): '1301a', Fractional ideal (21*a - 9): '549b', Fractional ideal (5*a - 32): '839a', Fractional ideal (37*a - 25): '1669a', Fractional ideal (-23*a + 14): '655a', Fractional ideal (-34*a + 19): '1441a', Fractional ideal (-4*a - 27): '821b', Fractional ideal (14): '196a', Fractional ideal (16*a - 8): '320a', Fractional ideal (31*a - 15): '1201b', Fractional ideal (6*a - 35): '979c', Fractional ideal (29*a - 8): '1009a', Fractional ideal (5*a + 25): '725b', Fractional ideal (-15*a + 4): '269a', Fractional ideal (-32*a + 12): '1264a', Fractional ideal (2*a + 29): '895a', Fractional ideal (24*a - 12): '720a', Fractional ideal (3*a + 21): '495b', Fractional ideal (-6*a - 27): '855a', Fractional ideal (-3*a + 18): '261a', Fractional ideal (18*a - 9): '405a', Fractional ideal (5*a - 35): '1025a', Fractional ideal (-38*a + 22): '1796a', Fractional ideal (-3*a - 41): '1795b', Fractional ideal (34*a - 18): '1444b', Fractional ideal (7*a - 3): '61b', Fractional ideal (4*a - 31): '821a', Fractional ideal (a - 25): '599a', Fractional ideal (28*a - 15): '979b', Fractional ideal (7*a + 40): '1831a', Fractional ideal (37*a - 21): '1705b', Fractional ideal (4*a + 28): '880b', Fractional ideal (39*a - 27): '1845a', Fractional ideal (3*a - 32): '919a', Fractional ideal (-38*a + 11): '1741a', Fractional ideal (4*a + 30): '1004a', Fractional ideal (-31*a + 9): '1159c', Fractional ideal (4*a + 42): '1916a', Fractional ideal (-34*a + 10): '1396a', Fractional ideal (6*a - 41): '1399a', Fractional ideal (10*a - 6): '124a', Fractional ideal (30*a - 21): '1089b', Fractional ideal (37*a - 17): '1709b', Fractional ideal (-34*a + 13): '1429b', Fractional ideal (8*a + 41): '1945a', Fractional ideal (7*a - 2): '59b', Fractional ideal (27): '729a', Fractional ideal (20*a - 6): '484c', Fractional ideal (38*a - 21): '1801b', Fractional ideal (-22*a + 14): '596b', Fractional ideal (9*a + 39): '1791a', Fractional ideal (37*a - 19): '1711a', Fractional ideal (3*a - 33): '981a', Fractional ideal (9*a - 6): '99b', Fractional ideal (-40*a + 29): '1919d', Fractional ideal (33*a - 14): '1355b', Fractional ideal (3*a - 36): '1179a', Fractional ideal (-32*a + 11): '1255a', Fractional ideal (2*a + 34): '1220b', Fractional ideal (a - 18): '305a', Fractional ideal (33*a - 24): '1305b', Fractional ideal (27*a - 15): '909a', Fractional ideal (5*a + 41): '1861a', Fractional ideal (-33*a + 19): '1355a', Fractional ideal (-3*a + 22): '409b', Fractional ideal (-2*a + 29): '779d', Fractional ideal (-4*a + 34): '1004b', Fractional ideal (-a + 8): '55a', Fractional ideal (4*a - 23): '421a', Fractional ideal (a + 19): '379b', Fractional ideal (6): '36a', Fractional ideal (6*a - 4): '44b', Fractional ideal (a + 26): '701b', Fractional ideal (a + 38): '1481b', Fractional ideal (5*a - 34): '961b', Fractional ideal (27*a - 18): '891b', Fractional ideal (-4*a + 27): '605b', Fractional ideal (-17*a + 5): '349a', Fractional ideal (-a - 14): '209b', Fractional ideal (29*a - 14): '1051b', Fractional ideal (a + 33): '1121b', Fractional ideal (-4*a - 39): '1661b', Fractional ideal (2*a + 43): '1931a', Fractional ideal (27*a - 8): '881b', Fractional ideal (-35*a + 26): '1459b', Fractional ideal (2*a + 41): '1759a', Fractional ideal (3*a - 23): '451c', Fractional ideal (6*a - 33): '855b', Fractional ideal (24*a - 17): '695b', Fractional ideal (3*a + 33): '1179b', Fractional ideal (2*a + 13): '191a', Fractional ideal (a - 14): '181a', Fractional ideal (5*a - 29): '671c', Fractional ideal (2*a - 42): '1676a', Fractional ideal (25*a - 8): '761b', Fractional ideal (-32*a + 15): '1279a', Fractional ideal (12*a - 8): '176b', Fractional ideal (31*a - 20): '1181a', Fractional ideal (4*a + 26): '764a', Fractional ideal (-7*a + 46): '1745b', Fractional ideal (-6*a + 44): '1636b', Fractional ideal (-24*a + 10): '716a', Fractional ideal (-6*a + 38): '1180b', Fractional ideal (a + 15): '239b', Fractional ideal (25*a - 11): '779b', Fractional ideal (-20*a + 13): '491b', Fractional ideal (31*a - 19): '1189d', Fractional ideal (-23*a + 7): '641a', Fractional ideal (22*a - 7): '589d', Fractional ideal (-26*a + 9): '829a', Fractional ideal (-20*a + 9): '499a', Fractional ideal (32): '1024a', Fractional ideal (-4*a + 33): '941b', Fractional ideal (a - 13): '155a', Fractional ideal (6*a - 40): '1324a', Fractional ideal (4*a + 37): '1501a', Fractional ideal (18*a - 5): '389b', Fractional ideal (-23*a + 8): '649c', Fractional ideal (-5*a + 30): '725a', Fractional ideal (-6*a - 35): '1399b', Fractional ideal (25*a - 7): '751b', Fractional ideal (a - 29): '811a', Fractional ideal (-9*a + 48): '1791b', Fractional ideal (3*a + 43): '1969a', Fractional ideal (30*a - 18): '1116a', Fractional ideal (3*a - 34): '1045d', Fractional ideal (18*a - 8): '404b', Fractional ideal (35*a - 25): '1475a', Fractional ideal (23): '529a', Fractional ideal (3*a + 27): '801b', Fractional ideal (-16*a + 6): '316a', Fractional ideal (-5*a + 40): '1375a', Fractional ideal (41*a - 10): '1991d', Fractional ideal (30*a - 11): '1109a', Fractional ideal (-31*a + 23): '1145b', Fractional ideal (-24*a + 18): '684b', Fractional ideal (33*a - 22): '1331d', Fractional ideal (6*a + 36): '1476b', Fractional ideal (-4*a + 46): '1916b', Fractional ideal (25*a - 13): '781a', Fractional ideal (4*a + 23): '605c', Fractional ideal (39*a - 17): '1895b', Fractional ideal (26*a - 19): '809a', Fractional ideal (a + 9): '89b', Fractional ideal (16*a - 11): '311a', Fractional ideal (a + 21): '461b', Fractional ideal (27*a - 9): '891a', Fractional ideal (5*a + 36): '1451a', Fractional ideal (-6*a + 43): '1555b', Fractional ideal (21): '441a', Fractional ideal (38*a - 20): '1804a', Fractional ideal (-5*a + 31): '781d', Fractional ideal (-4*a + 1): '19a', Fractional ideal (-5*a - 34): '1301b', Fractional ideal (39*a - 14): '1871a', Fractional ideal (11): '121a', Fractional ideal (6*a + 33): '1251a', Fractional ideal (a - 41): '1639a', Fractional ideal (-40*a + 23): '1991a', Fractional ideal (-9*a + 50): '1969d', Fractional ideal (36*a - 18): '1620a', Fractional ideal (-33*a + 21): '1341b', Fractional ideal (-3*a - 35): '1321b', Fractional ideal (2*a + 32): '1084b', Fractional ideal (-35*a + 9): '1459a', Fractional ideal (29): '841a', Fractional ideal (2*a + 22): '524b', Fractional ideal (33*a - 23): '1319b', Fractional ideal (4*a + 21): '509a', Fractional ideal (4*a + 34): '1276c', Fractional ideal (3*a - 1): '11a', Fractional ideal (30*a - 17): '1121d', Fractional ideal (-40*a + 25): '1975b', Fractional ideal (6*a + 25): '739a', Fractional ideal (2*a + 17): '319c', Fractional ideal (40*a - 27): '1951a', Fractional ideal (40*a - 24): '1984a', Fractional ideal (2*a - 22): '436a', Fractional ideal (3*a + 22): '541a', Fractional ideal (9*a - 4): '101b', Fractional ideal (5*a - 47): '1949a', Fractional ideal (7*a + 30): '1061b', Fractional ideal (2*a - 18): '284a', Fractional ideal (33): '1089a', Fractional ideal (32*a - 18): '1276b', Fractional ideal (22*a - 11): '605a', Fractional ideal (38*a - 26): '1756a', Fractional ideal (29*a - 7): '995b', Fractional ideal (3*a - 29): '745a', Fractional ideal (-4*a + 21): '341d', Fractional ideal (25*a - 10): '775b', Fractional ideal (-26*a + 16): '836c', Fractional ideal (37*a - 18): '1711b', Fractional ideal (a + 28): '811b', Fractional ideal (38*a - 16): '1796b', Fractional ideal (14*a - 4): '236b', Fractional ideal (-2*a + 12): '116a', Fractional ideal (10*a - 5): '125a', Fractional ideal (-21*a + 10): '551b', Fractional ideal (32*a - 17): '1279b', Fractional ideal (-6*a + 37): '1111d', Fractional ideal (-4*a + 38): '1276d', Fractional ideal (7*a + 37): '1579b', Fractional ideal (-29*a + 21): '1009b', Fractional ideal (-7*a + 39): '1199d', Fractional ideal (-3*a + 31): '859b', Fractional ideal (33*a - 9): '1305a', Fractional ideal (-3*a - 38): '1549b', Fractional ideal (30*a - 9): '1089c', Fractional ideal (-6*a - 28): '916b', Fractional ideal (5*a - 44): '1691c', Fractional ideal (a - 21): '419a', Fractional ideal (-2*a - 28): '836b', Fractional ideal (a + 40): '1639b', Fractional ideal (-29*a + 12): '1045b', Fractional ideal (33*a - 18): '1359a', Fractional ideal (4*a + 38): '1580a', Fractional ideal (-8*a - 39): '1769d', Fractional ideal (39*a - 19): '1901b', Fractional ideal (30*a - 20): '1100b', Fractional ideal (20*a - 14): '484b', Fractional ideal (a + 36): '1331b', Fractional ideal (2*a - 28): '724a', Fractional ideal (2*a + 18): '356b', Fractional ideal (4*a + 25): '709a', Fractional ideal (a + 5): '29b', Fractional ideal (-40*a + 10): '1900a', Fractional ideal (39*a - 18): '1899b', Fractional ideal (37): '1369a', Fractional ideal (16*a - 9): '319b', Fractional ideal (29*a - 22): '995a', Fractional ideal (-8*a + 49): '1945b', Fractional ideal (12*a - 7): '179b', Fractional ideal (-14*a + 9): '241b', Fractional ideal (7): '49a', Fractional ideal (-7*a - 32): '1199c', Fractional ideal (3*a - 21): '369a', Fractional ideal (-a + 37): '1331a', Fractional ideal (-2*a + 39): '1439b', Fractional ideal (4*a - 39): '1349c', Fractional ideal (-7*a + 43): '1499b', Fractional ideal (19*a - 9): '451b', Fractional ideal (16): '256a', Fractional ideal (-22*a + 8): '596a', Fractional ideal (3*a + 19): '409a', Fractional ideal (6*a + 38): '1636a', Fractional ideal (13*a - 6): '211b', Fractional ideal (38*a - 18): '1804b', Fractional ideal (36*a - 19): '1619b', Fractional ideal (-5*a - 23): '619a', Fractional ideal (-22*a + 9): '601a', Fractional ideal (24): '576a', Fractional ideal (5): '25a', Fractional ideal (2*a + 37): '1439a', Fractional ideal (18*a - 10): '404a', Fractional ideal (34*a - 15): '1441b', Fractional ideal (a + 25): '649b', Fractional ideal (-28*a + 7): '931a', Fractional ideal (-7*a - 39): '1745a', Fractional ideal (a - 22): '461a', Fractional ideal (-34*a + 14): '1436a', Fractional ideal (18*a - 6): '396a', Fractional ideal (a + 18): '341b', Fractional ideal (3*a + 39): '1629b', Fractional ideal (-6*a + 32): '796b', Fractional ideal (22*a - 13): '601b', Fractional ideal (19*a - 12): '445a', Fractional ideal (3*a + 40): '1711c', Fractional ideal (-32*a + 21): '1255b', Fractional ideal (-3*a - 26): '745b', Fractional ideal (-34*a + 12): '1420a', Fractional ideal (3*a + 28): '859a', Fractional ideal (-6*a + 39): '1251b', Fractional ideal (3*a + 24): '639b', Fractional ideal (-35*a + 16): '1529a', Fractional ideal (-2*a + 19): '319d', Fractional ideal (-37*a + 10): '1639d', Fractional ideal (13*a - 4): '205b', Fractional ideal (19*a - 10): '451a', Fractional ideal (-3*a - 29): '919b', Fractional ideal (4): '16a', Fractional ideal (3*a - 26): '589a', Fractional ideal (24*a - 8): '704a', Fractional ideal (-2*a + 16): '220a', Fractional ideal (35*a - 21): '1519a', Fractional ideal (30): '900a', Fractional ideal (2*a + 38): '1516b', Fractional ideal (34*a - 17): '1445a', Fractional ideal (-6*a + 48): '1980a', Fractional ideal (39*a - 11): '1829d', Fractional ideal (29*a - 16): '1049b', Fractional ideal (16*a - 7): '319a', Fractional ideal (31*a - 16): '1201a', Fractional ideal (17*a - 10): '359b', Fractional ideal (3*a - 20): '331a', Fractional ideal (-37*a + 13): '1681c', Fractional ideal (-3*a - 42): '1881b', Fractional ideal (5*a + 21): '521a', Fractional ideal (-4*a - 35): '1349d', Fractional ideal (-26*a + 17): '829b', Fractional ideal (a + 30): '929b', Fractional ideal (-5*a + 43): '1609b', Fractional ideal (5*a + 31): '1091a', Fractional ideal (a + 8): '71b', Fractional ideal (-36*a + 27): '1539b', Fractional ideal (-31*a + 8): '1145a', Fractional ideal (-2*a + 23): '479b', Fractional ideal (-37*a + 23): '1691b', Fractional ideal (-3*a - 32): '1111b', Fractional ideal (6*a + 30): '1044b', Fractional ideal (-17*a + 6): '355a', Fractional ideal (5*a + 27): '839b', Fractional ideal (-26*a + 10): '836d', Fractional ideal (2*a - 1): '5a', Fractional ideal (a - 35): '1189a', Fractional ideal (2*a + 31): '1019a', Fractional ideal (-21*a + 11): '551a', Fractional ideal (5*a + 32): '1159b', Fractional ideal (-4*a - 18): '380a', Fractional ideal (18): '324a', Fractional ideal (38): '1444a', Fractional ideal (4*a - 43): '1661a', Fractional ideal (a - 28): '755a', Fractional ideal (40*a - 16): '1984b', Fractional ideal (2*a - 14): '164a', Fractional ideal (2*a + 19): '395a', Fractional ideal (-3*a - 23): '589b', Fractional ideal (40*a - 21): '1999b', Fractional ideal (31*a - 14): '1199b', Fractional ideal (a + 37): '1405b', Fractional ideal (15): '225a', Fractional ideal (a + 20): '419b', Fractional ideal (-7*a - 41): '1919b', Fractional ideal (-40*a + 26): '1964b', Fractional ideal (26*a - 8): '820b', Fractional ideal (-19*a + 11): '449a', Fractional ideal (-32*a + 24): '1216b', Fractional ideal (-39*a + 24): '1881c', Fractional ideal (5*a - 3): '31a', Fractional ideal (2*a - 40): '1516a', Fractional ideal (3*a + 25): '691a', Fractional ideal (6*a + 39): '1719a', Fractional ideal (14*a - 8): '244a', Fractional ideal (12*a - 4): '176a', Fractional ideal (3*a + 30): '981b', Fractional ideal (29*a - 11): '1039a', Fractional ideal (-3*a + 24): '495a', Fractional ideal (26*a - 15): '841b', Fractional ideal (a - 42): '1721a', Fractional ideal (4*a + 33): '1205a', Fractional ideal (23*a - 13): '659b', Fractional ideal (19): '361a', Fractional ideal (38*a - 12): '1756b', Fractional ideal (-5*a - 29): '961c', Fractional ideal (37*a - 12): '1669b', Fractional ideal (36*a - 23): '1595c', Fractional ideal (7*a + 31): '1129b', Fractional ideal (-5*a - 28): '899c', Fractional ideal (36*a - 12): '1584a', Fractional ideal (13): '169a', Fractional ideal (28*a - 12): '976b', Fractional ideal (6*a + 26): '796a', Fractional ideal (a - 16): '239a', Fractional ideal (2*a + 12): '164b', Fractional ideal (39*a - 20): '1901a', Fractional ideal (28*a - 19): '955a', Fractional ideal (-39*a + 29): '1811b', Fractional ideal (-24*a + 11): '719a', Fractional ideal (19*a - 6): '439b', Fractional ideal (3*a + 36): '1395b', Fractional ideal (-32*a + 20): '1264b', Fractional ideal (26*a - 18): '820a', Fractional ideal (-3*a + 40): '1471b', Fractional ideal (-3*a + 19): '295b', Fractional ideal (7*a - 4): '61a', Fractional ideal (12): '144a', Fractional ideal (2*a - 44): '1844a', Fractional ideal (38*a - 27): '1741b', Fractional ideal (a - 26): '649a', Fractional ideal (a - 27): '701a', Fractional ideal (30*a - 12): '1116b', Fractional ideal (39*a - 21): '1899a', Fractional ideal (-8*a + 6): '76b', Fractional ideal (25*a - 16): '769a', Fractional ideal (-24*a + 9): '711a', Fractional ideal (23*a - 11): '661b', Fractional ideal (24*a - 16): '704b', Fractional ideal (2*a + 20): '436b', Fr

...

'1436b', Fractional ideal (a + 41): '1721b', Fractional ideal (13*a - 9): '205a', Fractional ideal (5*a + 37): '1529d', Fractional ideal (7*a - 44): '1579a', Fractional ideal (39*a - 16): '1889b', Fractional ideal (-37*a + 15): '1699a', Fractional ideal (-19*a + 14): '431b', Fractional ideal (39*a - 22): '1895a', Fractional ideal (-3*a + 46): '1969b', Fractional ideal (30*a - 14): '1124b', Fractional ideal (35*a - 15): '1525b', Fractional ideal (37*a - 28): '1621a', Fractional ideal (32*a - 10): '1244b', Fractional ideal (9): '81a', Fractional ideal (-30*a + 22): '1076b', Fractional ideal (-29*a + 19): '1031b', Fractional ideal (8*a - 4): '80a', Fractional ideal (a + 22): '505b', Fractional ideal (-3*a + 37): '1249b', Fractional ideal (7*a - 38): '1129a', Fractional ideal (38*a - 15): '1789b', Fractional ideal (a + 13): '181b', Fractional ideal (a - 44): '1891a', Fractional ideal (30*a - 15): '1125a', Fractional ideal (-38*a + 14): '1780b', Fractional ideal (-23*a + 17): '631b', Fractional ideal (22): '484a', Fractional ideal (18*a - 7): '401b', Fractional ideal (25*a - 15): '775a', Fractional ideal (a + 34): '1189b', Fractional ideal (-29*a + 13): '1049a', Fractional ideal (2*a + 39): '1595a', Fractional ideal (37*a - 27): '1639c', Fractional ideal (13*a - 7): '211a', Fractional ideal (-23*a + 6): '631a', Fractional ideal (23*a - 12): '661a', Fractional ideal (a - 17): '271a', Fractional ideal (-5*a - 39): '1691d', Fractional ideal (-4*a + 26): '556b', Fractional ideal (2*a - 36): '1220a', Fractional ideal (-38*a + 25): '1769b', Fractional ideal (6*a - 3): '45a', Fractional ideal (25): '625a', Fractional ideal (21*a - 6): '531b', Fractional ideal (44): '1936a', Fractional ideal (37*a - 24): '1681b', Fractional ideal (a - 11): '109a', Fractional ideal (-31*a + 13): '1195a', Fractional ideal (-3*a - 20): '451d', Fractional ideal (11*a - 5): '151b', Fractional ideal (-3*a + 43): '1711d', Fractional ideal (2*a - 38): '1364a', Fractional ideal (39): '1521a', Fractional ideal (31*a - 21): '1171a', Fractional ideal (-8*a + 2): '76a', Fractional ideal (33*a - 16): '1361b', Fractional ideal (a + 43): '1891b', Fractional ideal (-35*a + 12): '1501c', Fractional ideal (-29*a + 17): '1045a', Fractional ideal (-35*a + 23): '1501d', Fractional ideal (-27*a + 7): '869c', Fractional ideal (21*a - 14): '539b', Fractional ideal (6*a - 34): '916a', Fractional ideal (40*a - 13): '1951b', Fractional ideal (26): '676a', Fractional ideal (-35*a + 13): '1511b', Fractional ideal (2*a - 24): '524a', Fractional ideal (-8*a - 38): '1684b', Fractional ideal (2*a + 42): '1844b', Fractional ideal (-31*a + 18): '1195b', Fractional ideal (-6*a - 41): '1891d', Fractional ideal (36*a - 24): '1584b', Fractional ideal (2*a - 32): '956a', Fractional ideal (a - 31): '929a', Fractional ideal (17*a - 12): '349b', Fractional ideal (-39*a + 28): '1829c', Fractional ideal (24*a - 14): '716b', Fractional ideal (33*a - 8): '1289b', Fractional ideal (a + 39): '1559b', Fractional ideal (a - 38): '1405a', Fractional ideal (2*a + 10): '116b', Fractional ideal (-8*a + 45): '1601a', Fractional ideal (39*a - 26): '1859b', Fractional ideal (36*a - 21): '1611b', Fractional ideal (-27*a + 20): '869d', Fractional ideal (35*a - 24): '1489b', Fractional ideal (-20*a + 7): '491a', Fractional ideal (41): '1681a', Fractional ideal (-6*a - 34): '1324b', Fractional ideal (27*a - 17): '899a', Fractional ideal (15*a - 7): '281b', Fractional ideal (-36*a + 15): '1611a', Fractional ideal (30*a - 16): '1124a', Fractional ideal (-40*a + 19): '1999a', Fractional ideal (-25*a + 9): '769b', Fractional ideal (35*a - 22): '1511a', Fractional ideal (-9*a - 41): '1969c', Fractional ideal (a + 44): '1979b', Fractional ideal (-16*a + 10): '316b', Fractional ideal (a - 32): '991a', Fractional ideal (2*a + 16): '284b', Fractional ideal (-28*a + 13): '979a', Fractional ideal (2*a - 20): '356a', Fractional ideal (-7*a + 42): '1421a', Fractional ideal (-16*a + 4): '304a', Fractional ideal (-8*a - 35): '1441c', Fractional ideal (3*a + 16): '295a', Fractional ideal (3*a - 44): '1795a', Fractional ideal (a + 32): '1055b', Fractional ideal (22*a - 12): '604a', Fractional ideal (-4*a + 25): '509b', Fractional ideal (16*a - 5): '311b', Fractional ideal (-38*a + 17): '1801a', Fractional ideal (-36*a + 17): '1619a', Fractional ideal (-5*a - 33): '1229a', Fractional ideal (2*a + 26): '724b', Fractional ideal (41*a - 31): '1991c', Fractional ideal (-4*a + 30): '764b', Fractional ideal (-25*a + 18): '751a', Fractional ideal (-5*a + 33): '899d', Fractional ideal (8*a - 47): '1769c', Fractional ideal (17): '289a', Fractional ideal (10*a - 4): '124b', Fractional ideal (9*a - 5): '101a', Fractional ideal (25*a - 12): '781b', Fractional ideal (-2*a + 41): '1595b', Fractional ideal (34*a - 11): '1409b', Fractional ideal (2*a - 26): '620a', Fractional ideal (-25*a + 14): '779a', Fractional ideal (-32*a + 8): '1216a', Fractional ideal (9*a - 47): '1705c', Fractional ideal (-5*a - 38): '1609a', Fractional ideal (7*a - 40): '1271d', Fractional ideal (-28*a + 21): '931b', Fractional ideal (27*a - 14): '911a', Fractional ideal (39*a - 13): '1859a', Fractional ideal (4*a - 22): '380b', Fractional ideal (-8*a + 43): '1441d', Fractional ideal (-33*a + 20): '1349a', Fractional ideal (-2*a + 43): '1759b', Fractional ideal (15*a - 10): '275b', Fractional ideal (28*a - 20): '944a', Fractional ideal (5*a - 37): '1159a', Fractional ideal (3*a - 35): '1111a', Fractional ideal (a - 34): '1121a', Fractional ideal (-33*a + 10): '1319a', Fractional ideal (-2*a + 21): '395b', Fractional ideal (35*a - 18): '1531a', Fractional ideal (11*a - 3): '145a', Fractional ideal (a - 10): '89a', Fractional ideal (2*a + 27): '779c', Fractional ideal (2*a + 11): '139a', Fractional ideal (40*a - 28): '1936b', Fractional ideal (5*a + 42): '1949b', Fractional ideal (3*a - 39): '1395a', Fractional ideal (a + 24): '599b', Fractional ideal (a - 36): '1259a', Fractional ideal (-2*a + 13): '139b', Fractional ideal (3*a + 13): '199a', Fractional ideal (-20*a + 5): '475a', Fractional ideal (a + 6): '41b', Fractional ideal (-4*a + 45): '1829b', Fractional ideal (39*a - 23): '1889a', Fractional ideal (-15*a + 11): '269b', Fractional ideal (-37*a + 16): '1705a', Fractional ideal (a + 29): '869b', Fractional ideal (6*a - 46): '1804c', Fractional ideal (15*a - 5): '275a', Fractional ideal (-8*a + 5): '79b', Fractional ideal (19*a - 13): '439a', Fractional ideal (10*a - 3): '121c', Fractional ideal (7*a - 41): '1345a', Fractional ideal (19*a - 8): '449b', Fractional ideal (-38*a + 13): '1769a', Fractional ideal (-39*a + 10): '1811a', Fractional ideal (-27*a + 10): '899b', Fractional ideal (20): '400a', Fractional ideal (-6*a + 36): '1044a', Fractional ideal (-23*a + 10): '659a', Fractional ideal (21*a - 12): '549a', Fractional ideal (3*a + 15): '261b', Fractional ideal (a + 27): '755b', Fractional ideal (-3*a + 28): '691b', Fractional ideal (3*a - 38): '1321a', Fractional ideal (6*a + 31): '1111c', Fractional ideal (-5*a + 36): '1091b', Fractional ideal (7*a - 48): '1919a', Fractional ideal (22*a - 6): '580a', Fractional ideal (40*a - 17): '1991b', Fractional ideal (-24*a + 15): '711b', Fractional ideal (-4*a + 42): '1580b', Fractional ideal (14*a - 6): '244b', Fractional ideal (a - 40): '1559a', Fractional ideal (4*a - 40): '1424a', Fractional ideal (40*a - 11): '1919c', Fractional ideal (29*a - 20): '1021b', Fractional ideal (4*a - 2): '20a', Fractional ideal (2*a + 23): '571a', Fractional ideal (-4*a + 41): '1501b', Fractional ideal (-6*a + 31): '739b', Fractional ideal (-36*a + 22): '1604a', Fractional ideal (2*a + 30): '956b', Fractional ideal (14*a - 7): '245a', Fractional ideal (7*a + 36): '1499a', Fractional ideal (25*a - 17): '761a', Fractional ideal (-18*a + 11): '401a', Fractional ideal (31*a - 10): '1171b', Fractional ideal (36*a - 16): '1616b', Fractional ideal (-2*a - 9): '95a', Fractional ideal (7*a + 38): '1661d', Fractional ideal (35*a - 10): '1475b', Fractional ideal (35): '1225a', Fractional ideal (a - 9): '71a', Fractional ideal (30*a - 10): '1100a', Fractional ideal (11*a - 6): '151a', Fractional ideal (3*a - 2): '11b', Fractional ideal (-8*a - 37): '1601b', Fractional ideal (-2*a + 31): '895b', Fractional ideal (15*a - 6): '279b', Fractional ideal (a - 33): '1055a', Fractional ideal (a - 24): '551c', Fractional ideal (6*a + 42): '1980b', Fractional ideal (-6*a - 29): '979d', Fractional ideal (-16*a + 12): '304b', Fractional ideal (-2*a + 37): '1291b', Fractional ideal (a - 19): '341a', Fractional ideal (7*a - 45): '1661c', Fractional ideal (-13*a + 8): '209c', Fractional ideal (34*a - 25): '1381a', Fractional ideal (-23*a + 15): '649d', Fractional ideal (4*a + 17): '341c', Fractional ideal (8*a + 34): '1364c', Fractional ideal (-38*a + 23): '1789a', Fractional ideal (-31*a + 17): '1199a', Fractional ideal (a - 45): '1979a', Fractional ideal (4*a + 20): '464b', Fractional ideal (3*a - 41): '1549a', Fractional ideal (15*a - 8): '281a', Fractional ideal (7*a + 35): '1421b', Fractional ideal (-8*a + 48): '1856a', Fractional ideal (-13*a + 5): '209d', Fractional ideal (-5*a + 46): '1861b', Fractional ideal (28*a - 9): '955b', Fractional ideal (a + 10): '109b', Fractional ideal (-5*a + 38): '1229b', Fractional ideal (-6*a - 40): '1804d', Fractional ideal (-29*a + 18): '1039b', Fractional ideal (a + 7): '55b', Fractional ideal (-19*a + 7): '445b', Fractional ideal (4*a + 36): '1424b', Fractional ideal (37*a - 22): '1699b', Fractional ideal (-31*a + 11): '1181b', Fractional ideal (14*a - 10): '236a', Fractional ideal (27*a - 16): '905b', Fractional ideal (4*a + 29): '941a', Fractional ideal (26*a - 14): '844a', Fractional ideal (9*a + 40): '1879b', Fractional ideal (2*a - 34): '1084a', Fractional ideal (5*a + 30): '1025b', Fractional ideal (4*a - 35): '1069a', Fractional ideal (21*a - 8): '545a', Fractional ideal (-3*a - 17): '331b', Fractional ideal (a - 15): '209a', Fractional ideal (22*a - 16): '580b', Fractional ideal (8*a + 40): '1856b', Fractional ideal (-8*a + 3): '79a', Fractional ideal (-12*a + 3): '171a', Fractional ideal (21*a - 7): '539a', Fractional ideal (7*a - 5): '59a', Fractional ideal (2*a + 25): '671a', Fractional ideal (5*a + 22): '569b', Fractional ideal (-20*a + 15): '475b', Fractional ideal (38*a - 19): '1805a', Fractional ideal (11*a - 8): '145b', Fractional ideal (3*a + 37): '1471a', Fractional ideal (5*a + 40): '1775b', Fractional ideal (-2*a + 27): '671b', Fractional ideal (-27*a + 11): '905a', Fractional ideal (-8*a - 36): '1520a', Fractional ideal (22*a - 15): '589c', Fractional ideal (-2*a + 45): '1931b', Fractional ideal (a + 16): '271b', Fractional ideal (-4*a + 24): '464a', Fractional ideal (28*a - 8): '944b', Fractional ideal (2*a + 14): '220b', Fractional ideal (36*a - 11): '1571b', Fractional ideal (-2*a + 33): '1019b', Fractional ideal (36): '1296a', Fractional ideal (-37*a + 20): '1709a', Fractional ideal (-36*a + 25): '1571a', Fractional ideal (-5*a - 24): '671d', Fractional ideal (-2*a + 17): '251b', Fractional ideal (35*a - 20): '1525a', Fractional ideal (-3*a - 31): '1045c', Fractional ideal (36*a - 13): '1595d', Fractional ideal (40): '1600a', Fractional ideal (-4*a + 32): '880a', Fractional ideal (-30*a + 19): '1109b', Fractional ideal (-12*a + 9): '171b', Fractional ideal (21*a - 15): '531a', Fractional ideal (3*a - 30): '801a', Fractional ideal (5*a - 27): '569a', Fractional ideal (4*a + 41): '1829a', Fractional ideal (-3*a - 14): '229b', Fractional ideal (-4*a + 37): '1205b', Fractional ideal (39*a - 12): '1845b', Fractional ideal (-4*a + 29): '709b', Fractional ideal (a + 42): '1805c', Fractional ideal (10*a - 7): '121b', Fractional ideal (-34*a + 9): '1381b', Fractional ideal (-33*a + 12): '1341a', Fractional ideal (-14*a + 5): '241a', Fractional ideal (31*a - 22): '1159d', Fractional ideal (-2*a + 25): '571b', Fractional ideal (-17*a + 7): '359a', Fractional ideal (-40*a + 14): '1964a', Fractional ideal (24*a - 13): '719b', Fractional ideal (-38*a + 28): '1724b', Fractional ideal (4*a + 40): '1744b', Fractional ideal (a + 11): '131b', Fractional ideal (3*a - 45): '1881a', Fractional ideal (-17*a + 11): '355b', Fractional ideal (-34*a + 22): '1420b', Fractional ideal (-4*a - 19): '421b', Fractional ideal (2*a + 24): '620b', Fractional ideal (a - 39): '1481a', Fractional ideal (7*a - 47): '1831b', Fractional ideal (42): '1764a', Fractional ideal (37*a - 11): '1655b', Fractional ideal (-12*a + 5): '179a', Fractional ideal (-27*a + 19): '881a', Fractional ideal (3): '9a', Fractional ideal (a - 23): '505a', Fractional ideal (34*a - 23): '1409a', Fractional ideal (5*a - 45): '1775a', Fractional ideal (2*a - 11): '95b', Fractional ideal (35*a - 17): '1531b', Fractional ideal (32*a - 9): '1231b', Fractional ideal (-5*a + 28): '619b', Fractional ideal (-3*a + 16): '199b', Fractional ideal (2*a + 33): '1151a', Fractional ideal (a - 20): '379a', Fractional ideal (2*a + 21): '479a', Fractional ideal (-30*a + 13): '1121c', Fractional ideal (9*a + 38): '1705d', Fractional ideal (20*a - 11): '499b', Fractional ideal (3*a - 17): '229a', Fractional ideal (-2*a + 15): '191b', Fractional ideal (4*a - 28): '656a', Fractional ideal (-38*a + 10): '1724a', Fractional ideal (4*a + 32): '1136b', Fractional ideal (-29*a + 9): '1021a', Fractional ideal (17*a - 8): '361c', Fractional ideal (a - 12): '131a', Fractional ideal (-29*a + 10): '1031a', Fractional ideal (-7*a - 34): '1345b', Fractional ideal (9*a - 49): '1879a', Fractional ideal (-a + 6): '29a', Fractional ideal (5*a - 42): '1529c', Fractional ideal (2*a - 30): '836a', Fractional ideal (a + 35): '1259b', Fractional ideal (-11*a + 4): '149a', Fractional ideal (-40*a + 30): '1900b', Fractional ideal (28*a - 16): '976a', Fractional ideal (-24*a + 6): '684a', Fractional ideal (6*a - 42): '1476a', Fractional ideal (36*a - 20): '1616a', Fractional ideal (26*a - 13): '845a', Fractional ideal (-36*a + 9): '1539a', Fractional ideal (-34*a + 21): '1429a', Fractional ideal (6*a + 37): '1555a', Fractional ideal (3*a - 27): '639a', Fractional ideal (-30*a + 8): '1076a', Fractional ideal (7*a - 37): '1061a', Fractional ideal (10): '100a', Fractional ideal (-32*a + 13): '1271a', Fractional ideal (-18*a + 13): '389a', Fractional ideal (31*a - 12): '1189c', Fractional ideal (6*a + 32): '1180a', Fractional ideal (31): '961a', Fractional ideal (32*a - 22): '1244a', Fractional ideal (8*a - 44): '1520b', Fractional ideal (9*a - 3): '99a', Fractional ideal (-19*a + 5): '431a', Fractional ideal (-11*a + 7): '149b', Fractional ideal (20*a - 10): '500a', Fractional ideal (-4*a - 31): '1069b', Fractional ideal (26*a - 11): '841c', Fractional ideal (22*a - 10): '604b', Fractional ideal (-4*a + 3): '19b', Fractional ideal (5*a + 26): '781c', Fractional ideal (20*a - 12): '496a', Fractional ideal (43): '1849a', Fractional ideal (8*a - 46): '1684a', Fractional ideal (-5*a + 26): '521b', Fractional ideal (37*a - 9): '1621b', Fractional ideal (8): '64a', Fractional ideal (33*a - 11): '1331c', Fractional ideal (a + 31): '991b', Fractional ideal (-26*a + 7): '809b', Fractional ideal (3*a + 34): '1249a', Fractional ideal (2*a + 15): '251a', Fractional ideal (-8*a + 42): '1364d', Fractional ideal (-6*a + 45): '1719b', Fractional ideal (7*a + 33): '1271c', Fractional ideal (38*a - 24): '1780a', Fractional ideal (2*a + 40): '1676b', Fractional ideal (4*a - 36): '1136a', Fractional ideal (35*a - 19): '1529b', Fractional ideal (-40*a + 18): '1996a', Fractional ideal (4*a - 44): '1744a', Fractional ideal (34): '1156a', Fractional ideal (36*a - 10): '1556b', Fractional ideal (27*a - 12): '909b', Fractional ideal (6*a - 2): '44a', Fractional ideal (4*a + 24): '656b', Fractional ideal (26*a - 12): '844b', Fractional ideal (6*a - 47): '1891c', Fractional ideal (28): '784a', Fractional ideal (-a + 43): '1805b', Fractional ideal (-36*a + 26): '1556a', Fractional ideal (a + 17): '305b', Fractional ideal (2*a + 35): '1291a', Fractional ideal (a - 7): '41a', Fractional ideal (15*a - 9): '279a'}
ideals_of_given_norm(451) 
        
[Fractional ideal (19*a - 10), Fractional ideal (3*a - 23), Fractional
ideal (-3*a - 20), Fractional ideal (19*a - 9)]
[Fractional ideal (19*a - 10), Fractional ideal (3*a - 23), Fractional ideal (-3*a - 20), Fractional ideal (19*a - 9)]
d.keys()[2].eta() 
        
406802
406802
print d.keys()[2].eta() print K.ideal(19*a-9).eta() 
        
406802
903
406802
903
d.keys()[2].gens_reduced(0) 
        
(19*a - 9,)
(19*a - 9,)
q1,q2 = K.primes_above(11) 
       
print q1 print q2 
        
Fractional ideal (3*a - 1)
Fractional ideal (3*a - 2)
Fractional ideal (3*a - 1)
Fractional ideal (3*a - 2)
(q1*q2).eta() 
        
242
242
(q1*q1).eta() 
        
258
258
(q2*q2).eta() 
        
258
258
E = EllipticCurve(K,[1+a,-1-a,0,a,0]) 
       
E.conductor() 
        
Fractional ideal (4*a + 17)
Fractional ideal (4*a + 17)
cmp((q1*q2).eta(),(q2*q2).eta()) 
        
-1
-1
d[K.ideal(4*a + 17)] 
        
'341c'
'341c'
ids = [] m = 0 for N in range(1,2000): if len(ideals_of_given_norm(N)) > m: m = len(ideals_of_given_norm(N)) 
       
11**2*19**2 
        
43681
43681
K.ideal(209).norm() 
        
43681
43681
ideals_of_given_norm(43681) 
        
[Fractional ideal (209), Fractional ideal (187*a - 99), Fractional ideal
(187*a - 88), Fractional ideal (-29*a + 226), Fractional ideal (29*a +
197), Fractional ideal (190*a - 133), Fractional ideal (190*a - 57),
Fractional ideal (-39*a + 233), Fractional ideal (39*a + 194)]
[Fractional ideal (209), Fractional ideal (187*a - 99), Fractional ideal (187*a - 88), Fractional ideal (-29*a + 226), Fractional ideal (29*a + 197), Fractional ideal (190*a - 133), Fractional ideal (190*a - 57), Fractional ideal (-39*a + 233), Fractional ideal (39*a + 194)]
ids[0] 
       
11*31 
        
341
341
factor(451) 
        
11 * 41
11 * 41
K.ideal(-19*(1-a)+9).integral_basis() 
        
[451, a + 403]
[451, a + 403]
K.ideal(-19*a+9).integral_basis() 
        
[451, a + 47]
[451, a + 47]
d[K.ideal(-19*a+9)] 
        
'451d'
'451d'
from psage.number_fields.sqrt5 import primes_of_bounded_norm 
       
[p.sage_ideal() for p in primes_of_bounded_norm(100)] 
        
[Fractional ideal (2), Fractional ideal (2*a - 1), Fractional ideal (3),
Fractional ideal (3*a - 1), Fractional ideal (3*a - 2), Fractional ideal
(-4*a + 1), Fractional ideal (-4*a + 3), Fractional ideal (-a + 6),
Fractional ideal (a + 5), Fractional ideal (5*a - 3), Fractional ideal
(5*a - 2), Fractional ideal (a - 7), Fractional ideal (a + 6),
Fractional ideal (7), Fractional ideal (7*a - 5), Fractional ideal (7*a
- 2), Fractional ideal (7*a - 4), Fractional ideal (7*a - 3), Fractional
ideal (a - 9), Fractional ideal (a + 8), Fractional ideal (-8*a + 3),
Fractional ideal (-8*a + 5), Fractional ideal (a - 10), Fractional ideal
(a + 9)]
[Fractional ideal (2), Fractional ideal (2*a - 1), Fractional ideal (3), Fractional ideal (3*a - 1), Fractional ideal (3*a - 2), Fractional ideal (-4*a + 1), Fractional ideal (-4*a + 3), Fractional ideal (-a + 6), Fractional ideal (a + 5), Fractional ideal (5*a - 3), Fractional ideal (5*a - 2), Fractional ideal (a - 7), Fractional ideal (a + 6), Fractional ideal (7), Fractional ideal (7*a - 5), Fractional ideal (7*a - 2), Fractional ideal (7*a - 4), Fractional ideal (7*a - 3), Fractional ideal (a - 9), Fractional ideal (a + 8), Fractional ideal (-8*a + 3), Fractional ideal (-8*a + 5), Fractional ideal (a - 10), Fractional ideal (a + 9)]
[ideals_of_given_norm(p) for p in prime_range(100)] 
        
[[], [], [Fractional ideal (2*a - 1)], [], [Fractional ideal (3*a - 1),
Fractional ideal (3*a - 2)], [], [], [Fractional ideal (-4*a + 1),
Fractional ideal (-4*a + 3)], [], [Fractional ideal (-a + 6), Fractional
ideal (a + 5)], [Fractional ideal (5*a - 3), Fractional ideal (5*a -
2)], [], [Fractional ideal (a - 7), Fractional ideal (a + 6)], [], [],
[], [Fractional ideal (7*a - 5), Fractional ideal (7*a - 2)],
[Fractional ideal (7*a - 4), Fractional ideal (7*a - 3)], [],
[Fractional ideal (a - 9), Fractional ideal (a + 8)], [], [Fractional
ideal (-8*a + 3), Fractional ideal (-8*a + 5)], [], [Fractional ideal (a
- 10), Fractional ideal (a + 9)], []]
[[], [], [Fractional ideal (2*a - 1)], [], [Fractional ideal (3*a - 1), Fractional ideal (3*a - 2)], [], [], [Fractional ideal (-4*a + 1), Fractional ideal (-4*a + 3)], [], [Fractional ideal (-a + 6), Fractional ideal (a + 5)], [Fractional ideal (5*a - 3), Fractional ideal (5*a - 2)], [], [Fractional ideal (a - 7), Fractional ideal (a + 6)], [], [], [], [Fractional ideal (7*a - 5), Fractional ideal (7*a - 2)], [Fractional ideal (7*a - 4), Fractional ideal (7*a - 3)], [], [Fractional ideal (a - 9), Fractional ideal (a + 8)], [], [Fractional ideal (-8*a + 3), Fractional ideal (-8*a + 5)], [], [Fractional ideal (a - 10), Fractional ideal (a + 9)], []]