predicting torsion

317 days ago by Jonathan_Bober

curves = """145 11*a-8 [-2, 3, '?', 8, 5, -2, -8, -1, '?', '?', -3, -10, 7, 0, 4, -3, -8, 13, -12, 2, -4, 10, 6, 13] 179 -12*a+5 [1, 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8, -11, -10, 10, 12, 0, 12, 4, 4] 199 3*a+13 [0, 0, 1, 5, -3, 2, 0, 5, 0, 0, 2, -8, -3, -8, 10, -5, 7, 2, 2, -3, -10, 10, -10, 0] 205 13*a-9 [3, -4, '?', 4, 0, -2, 4, -4, -6, -8, -6, 10, '?', '?', 4, 12, 2, 6, 4, -2, -4, -16, -8, -6] 209 a-15 [-2, 2, 4, -12, '?', '?', '?', '?', 7, 1, -5, -2, -11, -3, -3, 10, 8, -2, 12, -13, 4, -10, -14, 10] 239 a+15 [1, -1, 1, -6, -5, 3, -2, 5, -2, 0, -4, 1, 9, -2, 11, 14, -14, 5, -8, -6, 2, -3, 9, -4] 244 14*a-6 ['?', 5, 0, 8, -4, 3, 6, -6, 9, -8, -3, 0, 0, -10, 1, -10, '?', '?', -10, -7, 8, -13, 13, -4] 284 2*a+16 ['?', 2, 0, -2, -2, 4, 2, 6, 0, 4, -8, -8, -10, -6, 0, 2, 8, -10, '?', '?', 4, 12, -6, -10] 324 18 ['?', '?', 4, 10, -2, -2, 0, 0, 0, 0, -8, -8, -2, -2, 10, 10, 2, 2, -12, -12, 0, 0, -10, -10] 380 -4*a-18 ['?', 2, '?', 0, 2, 4, '?', '?', 4, -2, 4, 0, -12, 2, -4, 0, -2, 6, 0, -8, -6, -16, 6, -14] 395 2*a+19 [1, 4, '?', 4, 2, -2, 0, 0, 6, -4, -4, 0, -6, 2, 4, 12, -10, -14, -6, 4, '?', '?', 0, 0] 396 18*a-6 ['?', '?', 3, 11, '?', '?', -1, -1, 0, -9, 5, -10, 9, -6, 9, -12, -1, 8, 3, 12, 14, -10, -6, 9] 396 18*a-12 ['?', '?', 3, -11, '?', '?', -7, 7, -7, 0, 6, -1, 2, -5, 4, 11, -12, -5, 12, 5, -14, -14, -11, 10] 400 20 ['?', 2, '?', 10, 0, 0, 4, 4, -6, -6, -4, -4, 6, 6, -12, -12, 2, 2, -12, -12, -8, -8, 6, 6] 404 18*a-10 ['?', 0, 1, -10, -3, 2, 5, -5, 5, 0, 7, -8, -3, -8, 10, 0, -8, -3, 12, 2, 0, 10, -15, 0] 404 18*a-10 ['?', 4, 2, -4, -2, -1, -2, 0, 0, 3, -1, 5, -1, -6, -9, 14, 7, -10, -4, -8, -10, -8, 17, 0] 404 18*a-8 ['?', 0, -2, -4, -1, 6, 4, 2, 9, -4, -5, -11, -2, 3, 6, -5, -6, 1, -16, -12, -8, 6, 12, 9] 404 18*a-8 ['?', 0, 1, -10, 2, -3, -5, 5, 0, 5, -8, 7, -8, -3, 0, 10, -3, -8, 2, 12, 10, 0, 0, -15] 405 18*a-9 [-3, '?', '?', -14, 4, 4, 4, 4, 2, 2, 0, 0, -10, -10, 4, 4, -2, -2, 8, 8, 0, 0, 6, 6] 431 -19*a+5 [2, -5, 0, -4, 6, 0, 5, -1, -9, 9, -4, 2, -9, 9, -12, -12, 8, -4, -6, 3, -4, -1, -6, 15] 445 -19*a+7 [1, 2, '?', -6, 0, 0, -8, 4, -10, -2, 0, 4, 10, 2, 0, 4, 14, -2, -16, 8, -12, -4, '?', '?'] 451 19*a-10 [3, 1, -1, 4, '?', '?', -6, 1, -6, 2, 4, 0, '?', '?', -1, 2, -3, 6, -6, -12, 11, 14, -3, -16] 464 4*a+20 ['?', 0, 4, 2, -4, 0, -6, 4, '?', '?', -2, -8, -12, 6, 0, 6, 6, -4, 10, 16, -4, 4, 6, -6] 484 22 ['?', 5, -4, 5, '?', '?', 5, 5, -5, -5, 7, 7, -8, -8, 0, 0, -13, -13, -3, -3, 0, 0, 15, 15] 495 -3*a+24 [3, '?', '?', -2, '?', '?', 4, 0, -2, 2, 4, -8, -10, 2, 0, 4, -6, -10, -8, 0, -16, 4, 14, -10] 505 a+22 [0, 1, '?', 9, 5, -6, 7, 8, -6, 0, 2, -8, 0, -9, 5, -14, -5, 0, -1, 13, -6, -8, -1, -18] 539 21*a-14 [-3, -1, -1, '?', '?', '?', -6, -3, -1, -4, -4, -4, 5, 8, 11, -7, 13, -14, 4, -2, 5, -10, -9, 6] 539 21*a-14 [3, -1, -1, '?', '?', '?', -6, 3, -1, 8, -4, -4, 5, -4, 5, -1, -11, -2, -8, 10, -13, 14, -9, 6] 539 21*a-7 [-3, 2, 2, '?', '?', '?', 6, 6, 2, 2, 8, -10, 8, -10, 8, 2, 4, -14, -8, -8, -4, -4, 12, 0] 545 21*a-8 [1, 2, '?', 2, 0, 2, 6, 0, 2, 2, -8, -4, 2, -2, 6, 0, 2, 2, -2, -10, -14, -8, -6, 2] 549 21*a-12 [3, '?', -1, 3, -3, 3, -2, 7, -6, 1, 3, -5, -2, 6, 6, -14, '?', '?', -8, -5, 14, 0, -1, -10] 580 22*a-6 ['?', 3, '?', -4, 1, -4, 2, 7, '?', '?', -10, 3, -12, -5, 6, -14, 10, 13, 2, -6, -14, -7, 7, -18] 580 22*a-6 ['?', 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3, 4, 13, -8, 2, -12, 10, -4, 13, 6] 599 a+24 [-1, 2, 2, 8, -4, 6, 6, -4, -2, 2, 2, 0, -8, 0, 12, 6, 6, -8, -14, -8, 2, -16, 6, -2] 599 a-25 [-1, 2, 2, 11, -3, 5, 2, 0, 2, 1, -3, -1, 6, -5, -12, 3, 1, -12, -2, 7, 11, 5, -2, -15] 605 4*a+23 [1, -2, '?', -14, '?', '?', 4, 8, 6, 6, 4, -8, -6, -6, 0, -12, -2, -10, 0, 0, -8, -4, -6, 18] 620 2*a-26 ['?', 4, '?', -9, 1, -3, 6, 5, -2, 7, '?', '?', 8, -4, 6, 3, -5, -14, 14, -5, -14, 10, 10, -9] 639 3*a+24 [2, '?', 1, 2, 3, 0, -6, 0, 6, 3, -2, -3, 2, -9, 10, -5, -6, -5, '?', '?', 10, 4, 10, -2] 639 3*a+24 [-1, '?', 4, -4, 0, 0, 6, 0, -6, 6, -2, 0, -10, 0, 4, -2, -12, -2, '?', '?', -14, 16, -2, 10] 639 3*a-27 [-2, '?', -1, 8, -2, 5, 6, 6, 9, 2, -3, 4, -7, 0, -3, -10, -1, 6, '?', '?', -4, -4, -8, 6] 649 -23*a+15 [-2, -1, -2, -4, '?', '?', 0, -5, -9, 0, -6, 3, 0, -3, '?', '?', 7, 5, 10, 2, -1, -6, 10, 2] 649 a+25 [-1, 2, 4, 8, '?', '?', 0, -4, -2, 2, -10, -8, 2, 4, '?', '?', 0, -8, 6, 0, -10, -8, 14, 10] 684 -24*a+18 ['?', '?', 0, -2, 4, -2, '?', '?', 8, 6, -4, 4, 0, 2, -2, 2, -10, -14, -14, 6, 0, 4, 0, -2] 704 24*a-16 ['?', -2, 0, -8, '?', '?', 6, 4, 10, 2, -2, 4, 0, -6, 4, -8, -8, -10, 4, -8, 10, 0, 6, -10] 716 -24*a+10 ['?', 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8, -11, -10, 10, 12, 0, 12, 4, 4] 725 -5*a+30 [2, 5, '?', 6, -3, 0, 6, -7, '?', '?', -7, -8, -5, 8, 4, -9, 6, -7, 0, 6, -8, 4, 14, -1] 725 5*a+25 [-2, 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3, 4, 13, -8, 2, -12, 10, -4, 13, 6] 725 5*a+25 [2, -3, '?', -8, -2, 5, 1, 8, '?', '?', -10, -3, 0, 7, 3, -4, 13, -8, 2, -12, -10, 4, -13, -6] 775 25*a-10 [2, 2, '?', -3, -6, 1, 4, 6, -7, 8, '?', '?', -1, -1, -3, -9, -14, -2, -8, -10, -10, 11, 0, -1] 775 25*a-10 [-1, 2, '?', 6, 0, 4, 4, 0, 2, 2, '?', '?', 2, 2, 12, -12, 10, -2, 16, -4, 8, -16, -18, -10] 781 25*a-13 [1, 2, 2, -2, '?', '?', 8, 4, -2, 6, -4, -8, 10, -2, -12, 0, 2, -2, '?', '?', 4, 8, -6, -6] 784 28 ['?', -3, -4, '?', 3, 3, 8, 8, 1, 1, -2, -2, -6, -6, 10, 10, 0, 0, 0, 0, 7, 7, -8, -8] 796 -6*a+32 ['?', -2, 3, -4, 3, 3, -4, -7, 6, -9, -7, -10, 3, 0, 0, 6, 5, 11, 6, 12, -13, -4, 6, 6] 796 6*a+26 ['?', 0, 1, 5, -3, 2, 0, 5, 0, 0, 2, -8, -3, -8, 10, -5, 7, 2, 2, -3, -10, 10, -10, 0] 820 26*a-18 ['?', 4, '?', 12, 0, -2, 4, 4, 10, -8, 2, 2, '?', '?', -12, 12, 10, -2, -12, -10, -4, 16, -16, 10] 820 26*a-8 ['?', -4, '?', 4, -2, 0, -4, 4, -8, -6, 10, -6, '?', '?', 12, 4, 6, 2, -2, 4, -16, -4, -6, -8] 829 -26*a+17 [-1, -5, 0, -4, -3, -3, 5, -4, 3, 0, -7, 2, 0, 12, -3, -12, 5, 2, 6, 6, -4, 11, -18, -6] 836 -26*a+10 ['?', 4, 0, -4, '?', '?', '?', '?', -6, 6, -4, -4, 0, 0, 12, 6, -10, 8, 6, 0, 8, 8, -6, -18] 836 -26*a+10 ['?', -4, 2, -4, '?', '?', '?', '?', 8, 4, 0, 10, -4, -4, -12, -14, -2, -2, 0, -4, -16, 4, -10, 14] 836 -2*a-28 ['?', 2, 4, -12, '?', '?', '?', '?', 1, 7, -2, -5, -3, -11, 10, -3, -2, 8, -13, 12, -10, 4, 10, -14] 836 -2*a-28 ['?', -5, -3, 2, '?', '?', '?', '?', 8, -7, 5, -5, -10, -4, -4, -10, -2, -6, 1, 12, 11, 11, 3, 0] 836 -2*a-28 ['?', 2, 1, 0, '?', '?', '?', '?', 4, -2, 4, 7, 9, -5, -11, 0, -2, -1, -7, 6, 8, -2, -8, 7] 836 -2*a-28 ['?', 5, 1, 10, '?', '?', '?', '?', 0, -5, -3, -3, 2, 12, 0, -10, 2, 2, -3, 12, -5, -15, 15, 0] 855 6*a-33 [1, '?', '?', 2, 4, 0, '?', '?', -6, -2, 0, 8, -2, 2, -8, 0, 14, -2, -12, 12, -8, -8, -10, -6] 891 27*a-18 [1, '?', 2, 2, '?', '?', -4, 4, 2, -6, 8, -8, -2, 6, -12, -12, -2, -2, 8, -8, 8, 16, 14, -2] 895 -2*a+31 [1, 0, '?', -5, -5, 3, 1, -4, 7, 5, 2, 1, -6, -3, 8, -4, -10, -11, 12, 10, 12, 0, 4, 4] 895 2*a+29 [2, -2, '?', 5, 0, 3, 5, 5, 0, 6, -1, -7, 0, -3, -9, 3, 2, -4, -6, 0, -1, 8, -6, -9] 909 27*a-12 [-1, '?', -1, 2, 2, 3, 3, 7, 2, 9, 4, -1, -12, 5, 4, 10, 1, -10, 0, 14, 0, -4, -6, 3] 956 2*a-32 ['?', -1, 1, -6, 3, -5, 5, -2, 0, -2, 1, -4, -2, 9, 14, 11, 5, -14, -6, -8, -3, 2, -4, 9] 961 31 [2, -3, 3, -3, -6, 6, -1, -4, 8, 8, '?', '?', 9, -6, -13, -4, -4, 8, -8, -5, 10, -14, -10, 14] 961 -5*a-29 [-3, -2, 2, 2, -4, -4, -4, 4, -2, 2, '?', '?', -6, -6, 12, -4, -6, -2, 8, 0, 0, 16, -10, -6] 961 -5*a-29 [0, 5, 1, 5, 4, -1, -5, 5, -5, -5, '?', '?', 9, -6, 0, 5, 9, -11, 4, -3, 0, -5, -5, 15] 976 28*a-12 ['?', 5, 0, 8, -4, 3, 6, -6, 9, -8, -3, 0, 0, -10, 1, -10, '?', '?', -10, -7, 8, -13, 13, -4] 979 -28*a+13 [3, 4, 0, 4, '?', '?', 4, -2, -10, -2, 0, -4, 0, -10, -4, -4, 6, 12, 8, 4, 4, 14, '?', '?'] 979 -6*a-29 [3, -1, 2, 6, '?', '?', -5, 2, 1, -1, 8, -4, -2, 0, -3, 0, -5, -10, 8, 3, 4, 4, '?', '?'] 995 29*a-22 [0, 0, '?', 5, 2, -3, 5, 0, 0, 0, -8, 2, -8, -3, -5, 10, 2, 7, -3, 2, 10, -10, 0, -10]""".split("\n") import psage import psage.modform.hilbert.sqrt5.tables as t #[I for I in t.ideals_of_bounded_norm(100) if I.is_prime()] #[I.norm() for I in t.ideals_of_bounded_norm(100) if I.is_prime()] K.<a> = NumberField(x^2 - x - 1) #prime_norms = [I.norm() for I in t.ideals_of_bounded_norm(100) if I.is_prime()] prime_norms = [4, 9, 5, 49, 11, 11, 19, 19, 29, 29, 31, 31, 41, 41, 59, 59, 61, 61, 71, 71, 79, 79, 89, 89] def list_torsions(): for line in curves: N, n, ap_list = line.split(" ", 2) ap_list = sage_eval(ap_list) point_counts = [] for b, a in zip(prime_norms, ap_list): if a != "?": point_counts.append(ZZ(-a + b + 1)) #print -a + b + 1, torsion = gcd(point_counts) if torsion != 1: print line + "; torsion prediction:", torsion else: print line + "; torsion prediction: none" 
       
list_torsions() 
        
145 11*a-8 [-2, 3, '?', 8, 5, -2, -8, -1, '?', '?', -3, -10, 7, 0, 4,
-3, -8, 13, -12, 2, -4, 10, 6, 13]; torsion prediction: 7
179 -12*a+5 [1, 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8, -11,
-10, 10, 12, 0, 12, 4, 4]; torsion prediction: none
199 3*a+13 [0, 0, 1, 5, -3, 2, 0, 5, 0, 0, 2, -8, -3, -8, 10, -5, 7, 2,
2, -3, -10, 10, -10, 0]; torsion prediction: 5
205 13*a-9 [3, -4, '?', 4, 0, -2, 4, -4, -6, -8, -6, 10, '?', '?', 4,
12, 2, 6, 4, -2, -4, -16, -8, -6]; torsion prediction: 2
209 a-15 [-2, 2, 4, -12, '?', '?', '?', '?', 7, 1, -5, -2, -11, -3, -3,
10, 8, -2, 12, -13, 4, -10, -14, 10]; torsion prediction: none
239 a+15 [1, -1, 1, -6, -5, 3, -2, 5, -2, 0, -4, 1, 9, -2, 11, 14, -14,
5, -8, -6, 2, -3, 9, -4]; torsion prediction: none
244 14*a-6 ['?', 5, 0, 8, -4, 3, 6, -6, 9, -8, -3, 0, 0, -10, 1, -10,
'?', '?', -10, -7, 8, -13, 13, -4]; torsion prediction: none
284 2*a+16 ['?', 2, 0, -2, -2, 4, 2, 6, 0, 4, -8, -8, -10, -6, 0, 2, 8,
-10, '?', '?', 4, 12, -6, -10]; torsion prediction: 2
324 18 ['?', '?', 4, 10, -2, -2, 0, 0, 0, 0, -8, -8, -2, -2, 10, 10, 2,
2, -12, -12, 0, 0, -10, -10]; torsion prediction: 2
380 -4*a-18 ['?', 2, '?', 0, 2, 4, '?', '?', 4, -2, 4, 0, -12, 2, -4, 0,
-2, 6, 0, -8, -6, -16, 6, -14]; torsion prediction: 2
395 2*a+19 [1, 4, '?', 4, 2, -2, 0, 0, 6, -4, -4, 0, -6, 2, 4, 12, -10,
-14, -6, 4, '?', '?', 0, 0]; torsion prediction: 2
396 18*a-6 ['?', '?', 3, 11, '?', '?', -1, -1, 0, -9, 5, -10, 9, -6, 9,
-12, -1, 8, 3, 12, 14, -10, -6, 9]; torsion prediction: 3
396 18*a-12 ['?', '?', 3, -11, '?', '?', -7, 7, -7, 0, 6, -1, 2, -5, 4,
11, -12, -5, 12, 5, -14, -14, -11, 10]; torsion prediction: none
400 20 ['?', 2, '?', 10, 0, 0, 4, 4, -6, -6, -4, -4, 6, 6, -12, -12, 2,
2, -12, -12, -8, -8, 6, 6]; torsion prediction: 4
404 18*a-10 ['?', 0, 1, -10, -3, 2, 5, -5, 5, 0, 7, -8, -3, -8, 10, 0,
-8, -3, 12, 2, 0, 10, -15, 0]; torsion prediction: 5
404 18*a-10 ['?', 4, 2, -4, -2, -1, -2, 0, 0, 3, -1, 5, -1, -6, -9, 14,
7, -10, -4, -8, -10, -8, 17, 0]; torsion prediction: none
404 18*a-8 ['?', 0, -2, -4, -1, 6, 4, 2, 9, -4, -5, -11, -2, 3, 6, -5,
-6, 1, -16, -12, -8, 6, 12, 9]; torsion prediction: none
404 18*a-8 ['?', 0, 1, -10, 2, -3, -5, 5, 0, 5, -8, 7, -8, -3, 0, 10,
-3, -8, 2, 12, 10, 0, 0, -15]; torsion prediction: 5
405 18*a-9 [-3, '?', '?', -14, 4, 4, 4, 4, 2, 2, 0, 0, -10, -10, 4, 4,
-2, -2, 8, 8, 0, 0, 6, 6]; torsion prediction: 4
431 -19*a+5 [2, -5, 0, -4, 6, 0, 5, -1, -9, 9, -4, 2, -9, 9, -12, -12,
8, -4, -6, 3, -4, -1, -6, 15]; torsion prediction: 3
445 -19*a+7 [1, 2, '?', -6, 0, 0, -8, 4, -10, -2, 0, 4, 10, 2, 0, 4, 14,
-2, -16, 8, -12, -4, '?', '?']; torsion prediction: 4
451 19*a-10 [3, 1, -1, 4, '?', '?', -6, 1, -6, 2, 4, 0, '?', '?', -1, 2,
-3, 6, -6, -12, 11, 14, -3, -16]; torsion prediction: none
464 4*a+20 ['?', 0, 4, 2, -4, 0, -6, 4, '?', '?', -2, -8, -12, 6, 0, 6,
6, -4, 10, 16, -4, 4, 6, -6]; torsion prediction: 2
484 22 ['?', 5, -4, 5, '?', '?', 5, 5, -5, -5, 7, 7, -8, -8, 0, 0, -13,
-13, -3, -3, 0, 0, 15, 15]; torsion prediction: 5
495 -3*a+24 [3, '?', '?', -2, '?', '?', 4, 0, -2, 2, 4, -8, -10, 2, 0,
4, -6, -10, -8, 0, -16, 4, 14, -10]; torsion prediction: 2
505 a+22 [0, 1, '?', 9, 5, -6, 7, 8, -6, 0, 2, -8, 0, -9, 5, -14, -5, 0,
-1, 13, -6, -8, -1, -18]; torsion prediction: none
539 21*a-14 [-3, -1, -1, '?', '?', '?', -6, -3, -1, -4, -4, -4, 5, 8,
11, -7, 13, -14, 4, -2, 5, -10, -9, 6]; torsion prediction: none
539 21*a-14 [3, -1, -1, '?', '?', '?', -6, 3, -1, 8, -4, -4, 5, -4, 5,
-1, -11, -2, -8, 10, -13, 14, -9, 6]; torsion prediction: none
539 21*a-7 [-3, 2, 2, '?', '?', '?', 6, 6, 2, 2, 8, -10, 8, -10, 8, 2,
4, -14, -8, -8, -4, -4, 12, 0]; torsion prediction: 2
545 21*a-8 [1, 2, '?', 2, 0, 2, 6, 0, 2, 2, -8, -4, 2, -2, 6, 0, 2, 2,
-2, -10, -14, -8, -6, 2]; torsion prediction: 2
549 21*a-12 [3, '?', -1, 3, -3, 3, -2, 7, -6, 1, 3, -5, -2, 6, 6, -14,
'?', '?', -8, -5, 14, 0, -1, -10]; torsion prediction: none
580 22*a-6 ['?', 3, '?', -4, 1, -4, 2, 7, '?', '?', -10, 3, -12, -5, 6,
-14, 10, 13, 2, -6, -14, -7, 7, -18]; torsion prediction: none
580 22*a-6 ['?', 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3,
4, 13, -8, 2, -12, 10, -4, 13, 6]; torsion prediction: 7
599 a+24 [-1, 2, 2, 8, -4, 6, 6, -4, -2, 2, 2, 0, -8, 0, 12, 6, 6, -8,
-14, -8, 2, -16, 6, -2]; torsion prediction: 2
599 a-25 [-1, 2, 2, 11, -3, 5, 2, 0, 2, 1, -3, -1, 6, -5, -12, 3, 1,
-12, -2, 7, 11, 5, -2, -15]; torsion prediction: none
605 4*a+23 [1, -2, '?', -14, '?', '?', 4, 8, 6, 6, 4, -8, -6, -6, 0,
-12, -2, -10, 0, 0, -8, -4, -6, 18]; torsion prediction: 4
620 2*a-26 ['?', 4, '?', -9, 1, -3, 6, 5, -2, 7, '?', '?', 8, -4, 6, 3,
-5, -14, 14, -5, -14, 10, 10, -9]; torsion prediction: none
639 3*a+24 [2, '?', 1, 2, 3, 0, -6, 0, 6, 3, -2, -3, 2, -9, 10, -5, -6,
-5, '?', '?', 10, 4, 10, -2]; torsion prediction: none
639 3*a+24 [-1, '?', 4, -4, 0, 0, 6, 0, -6, 6, -2, 0, -10, 0, 4, -2,
-12, -2, '?', '?', -14, 16, -2, 10]; torsion prediction: 2
639 3*a-27 [-2, '?', -1, 8, -2, 5, 6, 6, 9, 2, -3, 4, -7, 0, -3, -10,
-1, 6, '?', '?', -4, -4, -8, 6]; torsion prediction: 7
649 -23*a+15 [-2, -1, -2, -4, '?', '?', 0, -5, -9, 0, -6, 3, 0, -3, '?',
'?', 7, 5, 10, 2, -1, -6, 10, 2]; torsion prediction: none
649 a+25 [-1, 2, 4, 8, '?', '?', 0, -4, -2, 2, -10, -8, 2, 4, '?', '?',
0, -8, 6, 0, -10, -8, 14, 10]; torsion prediction: 2
684 -24*a+18 ['?', '?', 0, -2, 4, -2, '?', '?', 8, 6, -4, 4, 0, 2, -2,
2, -10, -14, -14, 6, 0, 4, 0, -2]; torsion prediction: 2
704 24*a-16 ['?', -2, 0, -8, '?', '?', 6, 4, 10, 2, -2, 4, 0, -6, 4, -8,
-8, -10, 4, -8, 10, 0, 6, -10]; torsion prediction: 2
716 -24*a+10 ['?', 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8,
-11, -10, 10, 12, 0, 12, 4, 4]; torsion prediction: none
725 -5*a+30 [2, 5, '?', 6, -3, 0, 6, -7, '?', '?', -7, -8, -5, 8, 4, -9,
6, -7, 0, 6, -8, 4, 14, -1]; torsion prediction: none
725 5*a+25 [-2, 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3,
4, 13, -8, 2, -12, 10, -4, 13, 6]; torsion prediction: 7
725 5*a+25 [2, -3, '?', -8, -2, 5, 1, 8, '?', '?', -10, -3, 0, 7, 3, -4,
13, -8, 2, -12, -10, 4, -13, -6]; torsion prediction: none
775 25*a-10 [2, 2, '?', -3, -6, 1, 4, 6, -7, 8, '?', '?', -1, -1, -3,
-9, -14, -2, -8, -10, -10, 11, 0, -1]; torsion prediction: none
775 25*a-10 [-1, 2, '?', 6, 0, 4, 4, 0, 2, 2, '?', '?', 2, 2, 12, -12,
10, -2, 16, -4, 8, -16, -18, -10]; torsion prediction: 2
781 25*a-13 [1, 2, 2, -2, '?', '?', 8, 4, -2, 6, -4, -8, 10, -2, -12, 0,
2, -2, '?', '?', 4, 8, -6, -6]; torsion prediction: 4
784 28 ['?', -3, -4, '?', 3, 3, 8, 8, 1, 1, -2, -2, -6, -6, 10, 10, 0,
0, 0, 0, 7, 7, -8, -8]; torsion prediction: none
796 -6*a+32 ['?', -2, 3, -4, 3, 3, -4, -7, 6, -9, -7, -10, 3, 0, 0, 6,
5, 11, 6, 12, -13, -4, 6, 6]; torsion prediction: 3
796 6*a+26 ['?', 0, 1, 5, -3, 2, 0, 5, 0, 0, 2, -8, -3, -8, 10, -5, 7,
2, 2, -3, -10, 10, -10, 0]; torsion prediction: 5
820 26*a-18 ['?', 4, '?', 12, 0, -2, 4, 4, 10, -8, 2, 2, '?', '?', -12,
12, 10, -2, -12, -10, -4, 16, -16, 10]; torsion prediction: 2
820 26*a-8 ['?', -4, '?', 4, -2, 0, -4, 4, -8, -6, 10, -6, '?', '?', 12,
4, 6, 2, -2, 4, -16, -4, -6, -8]; torsion prediction: 2
829 -26*a+17 [-1, -5, 0, -4, -3, -3, 5, -4, 3, 0, -7, 2, 0, 12, -3, -12,
5, 2, 6, 6, -4, 11, -18, -6]; torsion prediction: 3
836 -26*a+10 ['?', 4, 0, -4, '?', '?', '?', '?', -6, 6, -4, -4, 0, 0,
12, 6, -10, 8, 6, 0, 8, 8, -6, -18]; torsion prediction: 6
836 -26*a+10 ['?', -4, 2, -4, '?', '?', '?', '?', 8, 4, 0, 10, -4, -4,
-12, -14, -2, -2, 0, -4, -16, 4, -10, 14]; torsion prediction: 2
836 -2*a-28 ['?', 2, 4, -12, '?', '?', '?', '?', 1, 7, -2, -5, -3, -11,
10, -3, -2, 8, -13, 12, -10, 4, 10, -14]; torsion prediction: none
836 -2*a-28 ['?', -5, -3, 2, '?', '?', '?', '?', 8, -7, 5, -5, -10, -4,
-4, -10, -2, -6, 1, 12, 11, 11, 3, 0]; torsion prediction: none
836 -2*a-28 ['?', 2, 1, 0, '?', '?', '?', '?', 4, -2, 4, 7, 9, -5, -11,
0, -2, -1, -7, 6, 8, -2, -8, 7]; torsion prediction: none
836 -2*a-28 ['?', 5, 1, 10, '?', '?', '?', '?', 0, -5, -3, -3, 2, 12, 0,
-10, 2, 2, -3, 12, -5, -15, 15, 0]; torsion prediction: 5
855 6*a-33 [1, '?', '?', 2, 4, 0, '?', '?', -6, -2, 0, 8, -2, 2, -8, 0,
14, -2, -12, 12, -8, -8, -10, -6]; torsion prediction: 4
891 27*a-18 [1, '?', 2, 2, '?', '?', -4, 4, 2, -6, 8, -8, -2, 6, -12,
-12, -2, -2, 8, -8, 8, 16, 14, -2]; torsion prediction: 4
895 -2*a+31 [1, 0, '?', -5, -5, 3, 1, -4, 7, 5, 2, 1, -6, -3, 8, -4,
-10, -11, 12, 10, 12, 0, 4, 4]; torsion prediction: none
895 2*a+29 [2, -2, '?', 5, 0, 3, 5, 5, 0, 6, -1, -7, 0, -3, -9, 3, 2,
-4, -6, 0, -1, 8, -6, -9]; torsion prediction: 3
909 27*a-12 [-1, '?', -1, 2, 2, 3, 3, 7, 2, 9, 4, -1, -12, 5, 4, 10, 1,
-10, 0, 14, 0, -4, -6, 3]; torsion prediction: none
956 2*a-32 ['?', -1, 1, -6, 3, -5, 5, -2, 0, -2, 1, -4, -2, 9, 14, 11,
5, -14, -6, -8, -3, 2, -4, 9]; torsion prediction: none
961 31 [2, -3, 3, -3, -6, 6, -1, -4, 8, 8, '?', '?', 9, -6, -13, -4, -4,
8, -8, -5, 10, -14, -10, 14]; torsion prediction: none
961 -5*a-29 [-3, -2, 2, 2, -4, -4, -4, 4, -2, 2, '?', '?', -6, -6, 12,
-4, -6, -2, 8, 0, 0, 16, -10, -6]; torsion prediction: 4
961 -5*a-29 [0, 5, 1, 5, 4, -1, -5, 5, -5, -5, '?', '?', 9, -6, 0, 5, 9,
-11, 4, -3, 0, -5, -5, 15]; torsion prediction: none
976 28*a-12 ['?', 5, 0, 8, -4, 3, 6, -6, 9, -8, -3, 0, 0, -10, 1, -10,
'?', '?', -10, -7, 8, -13, 13, -4]; torsion prediction: none
979 -28*a+13 [3, 4, 0, 4, '?', '?', 4, -2, -10, -2, 0, -4, 0, -10, -4,
-4, 6, 12, 8, 4, 4, 14, '?', '?']; torsion prediction: 2
979 -6*a-29 [3, -1, 2, 6, '?', '?', -5, 2, 1, -1, 8, -4, -2, 0, -3, 0,
-5, -10, 8, 3, 4, 4, '?', '?']; torsion prediction: none
995 29*a-22 [0, 0, '?', 5, 2, -3, 5, 0, 0, 0, -8, 2, -8, -3, -5, 10, 2,
7, -3, 2, 10, -10, 0, -10]; torsion prediction: 5
145 11*a-8 [-2, 3, '?', 8, 5, -2, -8, -1, '?', '?', -3, -10, 7, 0, 4, -3, -8, 13, -12, 2, -4, 10, 6, 13]; torsion prediction: 7
179 -12*a+5 [1, 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8, -11, -10, 10, 12, 0, 12, 4, 4]; torsion prediction: none
199 3*a+13 [0, 0, 1, 5, -3, 2, 0, 5, 0, 0, 2, -8, -3, -8, 10, -5, 7, 2, 2, -3, -10, 10, -10, 0]; torsion prediction: 5
205 13*a-9 [3, -4, '?', 4, 0, -2, 4, -4, -6, -8, -6, 10, '?', '?', 4, 12, 2, 6, 4, -2, -4, -16, -8, -6]; torsion prediction: 2
209 a-15 [-2, 2, 4, -12, '?', '?', '?', '?', 7, 1, -5, -2, -11, -3, -3, 10, 8, -2, 12, -13, 4, -10, -14, 10]; torsion prediction: none
239 a+15 [1, -1, 1, -6, -5, 3, -2, 5, -2, 0, -4, 1, 9, -2, 11, 14, -14, 5, -8, -6, 2, -3, 9, -4]; torsion prediction: none
244 14*a-6 ['?', 5, 0, 8, -4, 3, 6, -6, 9, -8, -3, 0, 0, -10, 1, -10, '?', '?', -10, -7, 8, -13, 13, -4]; torsion prediction: none
284 2*a+16 ['?', 2, 0, -2, -2, 4, 2, 6, 0, 4, -8, -8, -10, -6, 0, 2, 8, -10, '?', '?', 4, 12, -6, -10]; torsion prediction: 2
324 18 ['?', '?', 4, 10, -2, -2, 0, 0, 0, 0, -8, -8, -2, -2, 10, 10, 2, 2, -12, -12, 0, 0, -10, -10]; torsion prediction: 2
380 -4*a-18 ['?', 2, '?', 0, 2, 4, '?', '?', 4, -2, 4, 0, -12, 2, -4, 0, -2, 6, 0, -8, -6, -16, 6, -14]; torsion prediction: 2
395 2*a+19 [1, 4, '?', 4, 2, -2, 0, 0, 6, -4, -4, 0, -6, 2, 4, 12, -10, -14, -6, 4, '?', '?', 0, 0]; torsion prediction: 2
396 18*a-6 ['?', '?', 3, 11, '?', '?', -1, -1, 0, -9, 5, -10, 9, -6, 9, -12, -1, 8, 3, 12, 14, -10, -6, 9]; torsion prediction: 3
396 18*a-12 ['?', '?', 3, -11, '?', '?', -7, 7, -7, 0, 6, -1, 2, -5, 4, 11, -12, -5, 12, 5, -14, -14, -11, 10]; torsion prediction: none
400 20 ['?', 2, '?', 10, 0, 0, 4, 4, -6, -6, -4, -4, 6, 6, -12, -12, 2, 2, -12, -12, -8, -8, 6, 6]; torsion prediction: 4
404 18*a-10 ['?', 0, 1, -10, -3, 2, 5, -5, 5, 0, 7, -8, -3, -8, 10, 0, -8, -3, 12, 2, 0, 10, -15, 0]; torsion prediction: 5
404 18*a-10 ['?', 4, 2, -4, -2, -1, -2, 0, 0, 3, -1, 5, -1, -6, -9, 14, 7, -10, -4, -8, -10, -8, 17, 0]; torsion prediction: none
404 18*a-8 ['?', 0, -2, -4, -1, 6, 4, 2, 9, -4, -5, -11, -2, 3, 6, -5, -6, 1, -16, -12, -8, 6, 12, 9]; torsion prediction: none
404 18*a-8 ['?', 0, 1, -10, 2, -3, -5, 5, 0, 5, -8, 7, -8, -3, 0, 10, -3, -8, 2, 12, 10, 0, 0, -15]; torsion prediction: 5
405 18*a-9 [-3, '?', '?', -14, 4, 4, 4, 4, 2, 2, 0, 0, -10, -10, 4, 4, -2, -2, 8, 8, 0, 0, 6, 6]; torsion prediction: 4
431 -19*a+5 [2, -5, 0, -4, 6, 0, 5, -1, -9, 9, -4, 2, -9, 9, -12, -12, 8, -4, -6, 3, -4, -1, -6, 15]; torsion prediction: 3
445 -19*a+7 [1, 2, '?', -6, 0, 0, -8, 4, -10, -2, 0, 4, 10, 2, 0, 4, 14, -2, -16, 8, -12, -4, '?', '?']; torsion prediction: 4
451 19*a-10 [3, 1, -1, 4, '?', '?', -6, 1, -6, 2, 4, 0, '?', '?', -1, 2, -3, 6, -6, -12, 11, 14, -3, -16]; torsion prediction: none
464 4*a+20 ['?', 0, 4, 2, -4, 0, -6, 4, '?', '?', -2, -8, -12, 6, 0, 6, 6, -4, 10, 16, -4, 4, 6, -6]; torsion prediction: 2
484 22 ['?', 5, -4, 5, '?', '?', 5, 5, -5, -5, 7, 7, -8, -8, 0, 0, -13, -13, -3, -3, 0, 0, 15, 15]; torsion prediction: 5
495 -3*a+24 [3, '?', '?', -2, '?', '?', 4, 0, -2, 2, 4, -8, -10, 2, 0, 4, -6, -10, -8, 0, -16, 4, 14, -10]; torsion prediction: 2
505 a+22 [0, 1, '?', 9, 5, -6, 7, 8, -6, 0, 2, -8, 0, -9, 5, -14, -5, 0, -1, 13, -6, -8, -1, -18]; torsion prediction: none
539 21*a-14 [-3, -1, -1, '?', '?', '?', -6, -3, -1, -4, -4, -4, 5, 8, 11, -7, 13, -14, 4, -2, 5, -10, -9, 6]; torsion prediction: none
539 21*a-14 [3, -1, -1, '?', '?', '?', -6, 3, -1, 8, -4, -4, 5, -4, 5, -1, -11, -2, -8, 10, -13, 14, -9, 6]; torsion prediction: none
539 21*a-7 [-3, 2, 2, '?', '?', '?', 6, 6, 2, 2, 8, -10, 8, -10, 8, 2, 4, -14, -8, -8, -4, -4, 12, 0]; torsion prediction: 2
545 21*a-8 [1, 2, '?', 2, 0, 2, 6, 0, 2, 2, -8, -4, 2, -2, 6, 0, 2, 2, -2, -10, -14, -8, -6, 2]; torsion prediction: 2
549 21*a-12 [3, '?', -1, 3, -3, 3, -2, 7, -6, 1, 3, -5, -2, 6, 6, -14, '?', '?', -8, -5, 14, 0, -1, -10]; torsion prediction: none
580 22*a-6 ['?', 3, '?', -4, 1, -4, 2, 7, '?', '?', -10, 3, -12, -5, 6, -14, 10, 13, 2, -6, -14, -7, 7, -18]; torsion prediction: none
580 22*a-6 ['?', 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3, 4, 13, -8, 2, -12, 10, -4, 13, 6]; torsion prediction: 7
599 a+24 [-1, 2, 2, 8, -4, 6, 6, -4, -2, 2, 2, 0, -8, 0, 12, 6, 6, -8, -14, -8, 2, -16, 6, -2]; torsion prediction: 2
599 a-25 [-1, 2, 2, 11, -3, 5, 2, 0, 2, 1, -3, -1, 6, -5, -12, 3, 1, -12, -2, 7, 11, 5, -2, -15]; torsion prediction: none
605 4*a+23 [1, -2, '?', -14, '?', '?', 4, 8, 6, 6, 4, -8, -6, -6, 0, -12, -2, -10, 0, 0, -8, -4, -6, 18]; torsion prediction: 4
620 2*a-26 ['?', 4, '?', -9, 1, -3, 6, 5, -2, 7, '?', '?', 8, -4, 6, 3, -5, -14, 14, -5, -14, 10, 10, -9]; torsion prediction: none
639 3*a+24 [2, '?', 1, 2, 3, 0, -6, 0, 6, 3, -2, -3, 2, -9, 10, -5, -6, -5, '?', '?', 10, 4, 10, -2]; torsion prediction: none
639 3*a+24 [-1, '?', 4, -4, 0, 0, 6, 0, -6, 6, -2, 0, -10, 0, 4, -2, -12, -2, '?', '?', -14, 16, -2, 10]; torsion prediction: 2
639 3*a-27 [-2, '?', -1, 8, -2, 5, 6, 6, 9, 2, -3, 4, -7, 0, -3, -10, -1, 6, '?', '?', -4, -4, -8, 6]; torsion prediction: 7
649 -23*a+15 [-2, -1, -2, -4, '?', '?', 0, -5, -9, 0, -6, 3, 0, -3, '?', '?', 7, 5, 10, 2, -1, -6, 10, 2]; torsion prediction: none
649 a+25 [-1, 2, 4, 8, '?', '?', 0, -4, -2, 2, -10, -8, 2, 4, '?', '?', 0, -8, 6, 0, -10, -8, 14, 10]; torsion prediction: 2
684 -24*a+18 ['?', '?', 0, -2, 4, -2, '?', '?', 8, 6, -4, 4, 0, 2, -2, 2, -10, -14, -14, 6, 0, 4, 0, -2]; torsion prediction: 2
704 24*a-16 ['?', -2, 0, -8, '?', '?', 6, 4, 10, 2, -2, 4, 0, -6, 4, -8, -8, -10, 4, -8, 10, 0, 6, -10]; torsion prediction: 2
716 -24*a+10 ['?', 0, 0, -5, 3, -5, -4, 1, 5, 7, 1, 2, -3, -6, -4, 8, -11, -10, 10, 12, 0, 12, 4, 4]; torsion prediction: none
725 -5*a+30 [2, 5, '?', 6, -3, 0, 6, -7, '?', '?', -7, -8, -5, 8, 4, -9, 6, -7, 0, 6, -8, 4, 14, -1]; torsion prediction: none
725 5*a+25 [-2, 3, '?', 8, -2, 5, -1, -8, '?', '?', -10, -3, 0, 7, -3, 4, 13, -8, 2, -12, 10, -4, 13, 6]; torsion prediction: 7
725 5*a+25 [2, -3, '?', -8, -2, 5, 1, 8, '?', '?', -10, -3, 0, 7, 3, -4, 13, -8, 2, -12, -10, 4, -13, -6]; torsion prediction: none
775 25*a-10 [2, 2, '?', -3, -6, 1, 4, 6, -7, 8, '?', '?', -1, -1, -3, -9, -14, -2, -8, -10, -10, 11, 0, -1]; torsion prediction: none
775 25*a-10 [-1, 2, '?', 6, 0, 4, 4, 0, 2, 2, '?', '?', 2, 2, 12, -12, 10, -2, 16, -4, 8, -16, -18, -10]; torsion prediction: 2
781 25*a-13 [1, 2, 2, -2, '?', '?', 8, 4, -2, 6, -4, -8, 10, -2, -12, 0, 2, -2, '?', '?', 4, 8, -6, -6]; torsion prediction: 4
784 28 ['?', -3, -4, '?', 3, 3, 8, 8, 1, 1, -2, -2, -6, -6, 10, 10, 0, 0, 0, 0, 7, 7, -8, -8]; torsion prediction: none
796 -6*a+32 ['?', -2, 3, -4, 3, 3, -4, -7, 6, -9, -7, -10, 3, 0, 0, 6, 5, 11, 6, 12, -13, -4, 6, 6]; torsion prediction: 3
796 6*a+26 ['?', 0, 1, 5, -3, 2, 0, 5, 0, 0, 2, -8, -3, -8, 10, -5, 7, 2, 2, -3, -10, 10, -10, 0]; torsion prediction: 5
820 26*a-18 ['?', 4, '?', 12, 0, -2, 4, 4, 10, -8, 2, 2, '?', '?', -12, 12, 10, -2, -12, -10, -4, 16, -16, 10]; torsion prediction: 2
820 26*a-8 ['?', -4, '?', 4, -2, 0, -4, 4, -8, -6, 10, -6, '?', '?', 12, 4, 6, 2, -2, 4, -16, -4, -6, -8]; torsion prediction: 2
829 -26*a+17 [-1, -5, 0, -4, -3, -3, 5, -4, 3, 0, -7, 2, 0, 12, -3, -12, 5, 2, 6, 6, -4, 11, -18, -6]; torsion prediction: 3
836 -26*a+10 ['?', 4, 0, -4, '?', '?', '?', '?', -6, 6, -4, -4, 0, 0, 12, 6, -10, 8, 6, 0, 8, 8, -6, -18]; torsion prediction: 6
836 -26*a+10 ['?', -4, 2, -4, '?', '?', '?', '?', 8, 4, 0, 10, -4, -4, -12, -14, -2, -2, 0, -4, -16, 4, -10, 14]; torsion prediction: 2
836 -2*a-28 ['?', 2, 4, -12, '?', '?', '?', '?', 1, 7, -2, -5, -3, -11, 10, -3, -2, 8, -13, 12, -10, 4, 10, -14]; torsion prediction: none
836 -2*a-28 ['?', -5, -3, 2, '?', '?', '?', '?', 8, -7, 5, -5, -10, -4, -4, -10, -2, -6, 1, 12, 11, 11, 3, 0]; torsion prediction: none
836 -2*a-28 ['?', 2, 1, 0, '?', '?', '?', '?', 4, -2, 4, 7, 9, -5, -11, 0, -2, -1, -7, 6, 8, -2, -8, 7]; torsion prediction: none
836 -2*a-28 ['?', 5, 1, 10, '?', '?', '?', '?', 0, -5, -3, -3, 2, 12, 0, -10, 2, 2, -3, 12, -5, -15, 15, 0]; torsion prediction: 5
855 6*a-33 [1, '?', '?', 2, 4, 0, '?', '?', -6, -2, 0, 8, -2, 2, -8, 0, 14, -2, -12, 12, -8, -8, -10, -6]; torsion prediction: 4
891 27*a-18 [1, '?', 2, 2, '?', '?', -4, 4, 2, -6, 8, -8, -2, 6, -12, -12, -2, -2, 8, -8, 8, 16, 14, -2]; torsion prediction: 4
895 -2*a+31 [1, 0, '?', -5, -5, 3, 1, -4, 7, 5, 2, 1, -6, -3, 8, -4, -10, -11, 12, 10, 12, 0, 4, 4]; torsion prediction: none
895 2*a+29 [2, -2, '?', 5, 0, 3, 5, 5, 0, 6, -1, -7, 0, -3, -9, 3, 2, -4, -6, 0, -1, 8, -6, -9]; torsion prediction: 3
909 27*a-12 [-1, '?', -1, 2, 2, 3, 3, 7, 2, 9, 4, -1, -12, 5, 4, 10, 1, -10, 0, 14, 0, -4, -6, 3]; torsion prediction: none
956 2*a-32 ['?', -1, 1, -6, 3, -5, 5, -2, 0, -2, 1, -4, -2, 9, 14, 11, 5, -14, -6, -8, -3, 2, -4, 9]; torsion prediction: none
961 31 [2, -3, 3, -3, -6, 6, -1, -4, 8, 8, '?', '?', 9, -6, -13, -4, -4, 8, -8, -5, 10, -14, -10, 14]; torsion prediction: none
961 -5*a-29 [-3, -2, 2, 2, -4, -4, -4, 4, -2, 2, '?', '?', -6, -6, 12, -4, -6, -2, 8, 0, 0, 16, -10, -6]; torsion prediction: 4
961 -5*a-29 [0, 5, 1, 5, 4, -1, -5, 5, -5, -5, '?', '?', 9, -6, 0, 5, 9, -11, 4, -3, 0, -5, -5, 15]; torsion prediction: none
976 28*a-12 ['?', 5, 0, 8, -4, 3, 6, -6, 9, -8, -3, 0, 0, -10, 1, -10, '?', '?', -10, -7, 8, -13, 13, -4]; torsion prediction: none
979 -28*a+13 [3, 4, 0, 4, '?', '?', 4, -2, -10, -2, 0, -4, 0, -10, -4, -4, 6, 12, 8, 4, 4, 14, '?', '?']; torsion prediction: 2
979 -6*a-29 [3, -1, 2, 6, '?', '?', -5, 2, 1, -1, 8, -4, -2, 0, -3, 0, -5, -10, 8, 3, 4, 4, '?', '?']; torsion prediction: none
995 29*a-22 [0, 0, '?', 5, 2, -3, 5, 0, 0, 0, -8, 2, -8, -3, -5, 10, 2, 7, -3, 2, 10, -10, 0, -10]; torsion prediction: 5