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hmf_forms • Show schema
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{'deg': 4, 'dimension': 5, 'disc': 17417, 'field_bad_primes': [17417], 'field_label': '4.4.17417.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '4.4.17417.1-20.2-a', 'label_nsuffix': 0, 'label_suffix': 'a', 'level_bad_primes': [2, 5], 'level_ideal': '[20, 20, w^3 - 2*w^2 - 3*w]', 'level_label': '20.2', 'level_norm': 20, 'parallel_weight': 2, 'short_label': '20.2-a', 'weight': '[2, 2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2, 2, w^3 - 3*w^2 - w + 2]', -1], ['[5, 5, w^2 - 2*w - 3]', -1]], 'hecke_eigenvalues': [0, 1, 'e', '-e^3 + e^2 + 5*e + 1', 'e^4 - 3*e^3 - 3*e^2 + 9*e + 2', '-e^3 + 6*e + 4', '-e^4 + 3*e^3 + 3*e^2 - 10*e', '-e^4 + 3*e^3 + 5*e^2 - 12*e - 6', 'e^4 - 2*e^3 - 4*e^2 + 6*e + 2', 'e^4 - 3*e^3 - 5*e^2 + 14*e + 6', '2*e^3 - 3*e^2 - 7*e + 4', 'e^4 - 3*e^3 - 3*e^2 + 8*e + 6', '2*e^4 - 6*e^3 - 10*e^2 + 22*e + 16', '-2*e^4 + 7*e^3 + 6*e^2 - 23*e - 6', '-e^4 + 3*e^3 + 4*e^2 - 10*e - 4', '2*e^4 - 8*e^3 - 4*e^2 + 30*e + 6', '-3*e^2 + 7*e + 14', '-3*e^3 + 3*e^2 + 14*e', '-2*e^4 + 3*e^3 + 14*e^2 - 13*e - 14', '-2*e^4 + 4*e^3 + 13*e^2 - 15*e - 16', '3*e^3 + 2*e^2 - 23*e - 14', '2*e^4 - 5*e^3 - 8*e^2 + 14*e + 10', '2*e^3 - e^2 - 13*e - 2', '3*e^4 - 8*e^3 - 8*e^2 + 20*e - 2', '-4*e^2 + 2*e + 16', 'e^3 - 2*e^2 - 7*e + 8', '2*e^4 - 5*e^3 - 12*e^2 + 18*e + 18', '-e^4 + e^3 + 2*e^2 + 14', 'e^4 - 3*e^3 - 3*e^2 + 14*e + 8', '-3*e^4 + 8*e^3 + 12*e^2 - 24*e - 18', 'e^4 - 6*e^3 + 4*e^2 + 14*e - 14', 'e^4 - 3*e^3 - 3*e^2 + 7*e + 14', '-e^4 + 6*e^3 + e^2 - 26*e - 12', '2*e^4 - 3*e^3 - 17*e^2 + 16*e + 28', '2*e^4 - 3*e^3 - 12*e^2 + 11*e + 6', '-2*e^4 + 10*e^3 - 36*e', '-e^4 + 5*e^3 - 6*e^2 - 12*e + 20', 'e^4 + e^3 - 11*e^2 + 12', '-2*e^4 + 8*e^3 + 2*e^2 - 30*e + 2', 'e^4 - 5*e^3 - 4*e^2 + 28*e + 16', '-6*e^3 + 10*e^2 + 25*e - 16', '2*e^4 - 5*e^3 - 7*e^2 + 10*e + 8', '-e^4 + 5*e^3 + 4*e^2 - 18*e - 10', 'e^4 + 3*e^3 - 8*e^2 - 22*e - 2', '-5*e^4 + 13*e^3 + 25*e^2 - 49*e - 36', '2*e^4 - 5*e^3 - 5*e^2 + 16*e - 10', '-4*e^4 + 12*e^3 + 14*e^2 - 36*e - 10', '2*e^4 - 7*e^3 - 4*e^2 + 20*e', '2*e^4 - 6*e^3 - 15*e^2 + 29*e + 38', '6*e^3 - 13*e^2 - 22*e + 18', '-2*e^4 + 10*e^3 - e^2 - 34*e + 8', '3*e^4 - 5*e^3 - 16*e^2 + 12*e + 18', '-e^4 + 8*e^3 + e^2 - 36*e - 10', '2*e^3 + 2*e^2 - 14*e - 18', '6*e^4 - 20*e^3 - 27*e^2 + 76*e + 50', '-5*e^4 + 15*e^3 + 19*e^2 - 49*e - 26', '4*e^3 + 2*e^2 - 29*e - 26', '4*e^4 - 13*e^3 - 14*e^2 + 41*e + 20', 'e^3 - 4*e^2 + e + 20', '-8*e^4 + 19*e^3 + 40*e^2 - 61*e - 50', '-e^4 + e^3 + 12*e^2 - 10*e - 18', '-3*e^4 + 13*e^3 + 11*e^2 - 58*e - 40', '6*e^4 - 19*e^3 - 23*e^2 + 68*e + 36', 'e^4 + 4*e^3 - 12*e^2 - 20*e + 2', '3*e^4 - 10*e^3 - 18*e^2 + 52*e + 36', '3*e^4 - 13*e^3 - 11*e^2 + 48*e + 42', '7*e^4 - 13*e^3 - 35*e^2 + 32*e + 34', '7*e^3 - 11*e^2 - 32*e + 22', '-e^4 + 3*e^3 - e^2 - 6*e + 20', '-4*e^4 + 6*e^3 + 22*e^2 - 21*e - 10', 'e^4 + 2*e^3 - 5*e^2 - 14*e - 10', '3*e^4 - 4*e^3 - 14*e^2 + 12*e - 4', 'e^4 - 2*e^3 + 8*e - 16', '2*e^4 - 3*e^3 - 8*e^2 + 3*e - 8', '3*e^4 - 11*e^3 - 4*e^2 + 40*e - 4', 'e^4 - 9*e^3 + e^2 + 39*e + 16', '-6*e^3 + 12*e^2 + 26*e - 26', '4*e^4 - 13*e^3 - 16*e^2 + 44*e + 28', '-4*e^4 + 10*e^3 + 17*e^2 - 35*e - 10', 'e^4 - 12*e^2 + 8*e + 10', 'e^3 - 11*e^2 + 36', '3*e^4 - 14*e^3 - 18*e^2 + 72*e + 48', '5*e^4 - 19*e^3 - 19*e^2 + 77*e + 48', '-4*e^4 + 15*e^3 + 12*e^2 - 54*e - 12', '9*e^2 - 16*e - 32', '2*e^4 - 2*e^3 - 12*e^2 + 2*e + 12', '-4*e^4 + 5*e^3 + 26*e^2 - 16*e - 30', 'e^4 + 5*e^3 - 5*e^2 - 42*e - 8', '3*e^4 - 6*e^3 - 11*e^2 + 14*e - 10', 'e^4 - 3*e^3 - 13*e^2 + 15*e + 36', '-5*e^4 + 17*e^3 + 17*e^2 - 67*e - 30', '-e^4 + 9*e^3 + 7*e^2 - 52*e - 32', '4*e^3 - 4*e^2 - 18*e + 18', 'e^4 - 3*e^3 + 9*e^2 - 6*e - 44', '4*e^4 - 12*e^3 - 14*e^2 + 32*e + 24', '-3*e^4 + 9*e^3 + 16*e^2 - 38*e - 16', '11*e^3 - 8*e^2 - 54*e - 18', '2*e^4 - 5*e^3 - 9*e^2 + 10*e - 6', '6*e^4 - 18*e^3 - 22*e^2 + 52*e + 28', '-e^4 - 5*e^3 + 14*e^2 + 24*e - 10', '-4*e^4 + 6*e^3 + 28*e^2 - 22*e - 50', '8*e^4 - 19*e^3 - 34*e^2 + 56*e + 38', '4*e^4 - 14*e^3 - 14*e^2 + 60*e + 22', '-4*e^4 + 10*e^3 + 8*e^2 - 24*e + 18', '-2*e^4 + 9*e^2 + 17*e + 10', '-3*e^4 + 9*e^3 + 13*e^2 - 25*e - 36', '-7*e^4 + 13*e^3 + 35*e^2 - 36*e - 32', '-3*e^4 + 8*e^3 + 6*e^2 - 24*e + 24', '-8*e^3 + 2*e^2 + 42*e + 32', 'e^4 - 10*e^3 + 10*e^2 + 44*e - 26', '6*e^4 - 16*e^3 - 24*e^2 + 57*e + 26', '4*e^4 - 11*e^3 - 22*e^2 + 34*e + 40', '4*e^4 - 14*e^3 - 18*e^2 + 58*e + 24', '-5*e^4 + 20*e^3 + 16*e^2 - 76*e - 26', '-6*e^4 + 13*e^3 + 26*e^2 - 43*e - 20', '-3*e^4 + 8*e^3 + 14*e^2 - 36*e - 16', '-2*e^3 + 6*e^2 + e - 14', '-6*e^4 + 12*e^3 + 26*e^2 - 29*e - 18', '-e^4 - e^3 + 11*e^2 + 8*e - 6', '4*e^4 - 8*e^3 - 20*e^2 + 29*e - 2', '6*e^4 - 16*e^3 - 20*e^2 + 40*e + 2', '-3*e^4 + 15*e^3 + 3*e^2 - 48*e - 10', '2*e^3 + 5*e^2 - 27*e - 24', '-5*e^4 + 13*e^3 + 24*e^2 - 44*e - 22', '-6*e^4 + 23*e^3 + 25*e^2 - 94*e - 62', '-3*e^4 + 8*e^3 + 18*e^2 - 44*e - 24', '2*e^4 - 11*e^3 - e^2 + 32*e + 4', '-4*e^4 + 9*e^3 + 21*e^2 - 26*e - 22', '-2*e^4 - 6*e^3 + 24*e^2 + 30*e - 14', '2*e^4 - 6*e^3 + 4*e^2 + 19*e - 44', '-e^4 + 7*e^3 + 4*e^2 - 28*e - 12', '5*e^4 - 9*e^3 - 23*e^2 + 25*e + 6', '-4*e^4 + 19*e^3 + e^2 - 62*e + 22', '2*e^4 + 6*e^3 - 27*e^2 - 27*e + 46', '-2*e^3 + 5*e^2 + 10*e - 4', '-e^4 + 9*e^3 - 5*e^2 - 38*e + 16', '2*e^4 + 2*e^3 - 14*e^2 - 23*e + 22', '-5*e^4 + 2*e^3 + 34*e^2 + 8*e - 22', '-4*e^4 + 9*e^3 + 21*e^2 - 42*e - 30', '4*e^4 - 13*e^3 - 14*e^2 + 45*e + 44', '-4*e^4 + 23*e^3 + 3*e^2 - 88*e - 24', '-3*e^4 + 23*e^3 - 6*e^2 - 92*e - 4', 'e^4 - 6*e^3 - 2*e^2 + 18*e + 14', '-2*e^4 + 4*e^3 + 8*e^2 - 18*e - 14', '-4*e^4 + 8*e^3 + 24*e^2 - 26*e - 26', '-7*e^4 + 19*e^3 + 31*e^2 - 64*e - 52', '6*e^4 - 20*e^3 - 28*e^2 + 75*e + 68', '-2*e^4 - 4*e^3 + 12*e^2 + 33*e + 10', 'e^4 - 3*e^3 - 15*e^2 + 18*e + 24', 'e^3 - 2*e^2 + 3*e + 12', '-e^4 - e^3 + 19*e^2 + 12*e - 46', '-4*e^2 + 18*e + 12', '-2*e^2 - 4*e - 10', '5*e^3 - 17*e^2 - 12*e + 40', '6*e^4 - 12*e^3 - 37*e^2 + 33*e + 44', '-6*e^4 + 20*e^3 + 26*e^2 - 82*e - 54', '4*e^4 - 22*e^3 - 8*e^2 + 92*e + 44', '4*e^4 - 21*e^3 - 6*e^2 + 81*e + 32', '-e^4 + 3*e^3 + 9*e^2 - 14*e - 36', '-6*e^4 + 15*e^3 + 34*e^2 - 68*e - 52', '4*e^4 - 20*e^3 - 6*e^2 + 74*e + 2', '7*e^4 - 21*e^3 - 31*e^2 + 80*e + 38', '-e^4 + 9*e^3 - 15*e^2 - 16*e + 54', 'e^4 - 5*e^3 - 7*e^2 + 24*e + 58', '-6*e^4 + 14*e^3 + 30*e^2 - 40*e - 38', '4*e^4 - 24*e^3 - 8*e^2 + 94*e + 50', 'e^4 + 7*e^3 - 11*e^2 - 35*e - 24', '2*e^4 - 4*e^3 - 20*e^2 + 18*e + 40', '-7*e^4 + 25*e^3 + 23*e^2 - 92*e - 46', '-3*e^4 + 2*e^3 + 22*e^2 - 18*e - 4', '2*e^4 - 7*e^3 - 20*e^2 + 36*e + 58', '-9*e^4 + 29*e^3 + 39*e^2 - 103*e - 86', '-2*e^4 + 10*e^3 + 4*e^2 - 34*e - 30'], 'hecke_polynomial': 'x^5 - 2*x^4 - 8*x^3 + 8*x^2 + 20*x + 4', 'label': '4.4.17417.1-20.2-a'}
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hmf_fields • Show schema
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{'degree': 4, 'discriminant': 17417, 'ideals': ['[1, 1, 1]', '[2, 2, w^3 - 3*w^2 - w + 2]', '[4, 4, w]', '[5, 5, w^2 - 2*w - 3]', '[5, 5, w^3 - 3*w^2 - 3*w + 5]', '[8, 2, w^3 - 2*w^2 - 3*w + 3]', '[8, 8, -w^2 + w + 4]', '[10, 10, -w^3 + 3*w^2 + 2*w - 6]', '[10, 10, -w + 2]', '[13, 13, -w^2 + w + 3]', '[16, 2, 2]', '[16, 16, w^3 - 2*w^2 - 4*w]', '[17, 17, -w^2 + 3*w + 1]', '[20, 20, -2*w^3 + 5*w^2 + 7*w - 8]', '[20, 20, w^3 - 2*w^2 - 3*w]', '[23, 23, w^2 - 3]', '[25, 5, -w^3 + 2*w^2 + 4*w - 3]', '[25, 5, -w^2 + 2*w + 1]', '[25, 25, w^3 - 4*w^2 + 2*w + 3]', '[25, 25, w^3 - 3*w^2 - 2*w + 3]', '[26, 26, w^2 - 3*w - 2]', '[32, 4, 2*w^3 - 6*w^2 - 2*w + 4]', '[32, 32, 2*w^3 - 5*w^2 - 6*w + 8]', '[34, 34, w^3 - 2*w^2 - 3*w + 2]', '[37, 37, w^3 - 4*w^2 - 2*w + 9]', '[40, 10, -w^3 + 2*w^2 + 5*w - 1]', '[40, 10, w^3 - 2*w^2 - 3*w + 1]', '[40, 40, w^3 - 3*w^2 - 3*w + 4]', '[40, 40, -w^2 + 2*w]', '[41, 41, w^2 - w - 5]', '[46, 46, -w^3 + 3*w^2 + 2*w - 2]', '[49, 7, -w^3 + 2*w^2 + 2*w - 1]', '[49, 7, w^2 + w - 3]', '[50, 10, -w^2 + 2*w + 6]', '[50, 10, -w^3 + 4*w^2 - w - 6]', '[50, 50, w^3 - 2*w^2 - 2*w + 2]', '[50, 50, -w^3 + 4*w^2 + w - 10]', '[52, 52, w^3 - 2*w^2 - 4*w + 4]', '[59, 59, w^3 - 3*w^2 - 4*w + 5]', '[64, 4, -w^3 + 2*w^2 + 5*w - 3]', '[64, 8, 2*w]', '[64, 64, w^2 - 3*w - 4]', '[65, 65, -2*w + 1]', '[65, 65, -2*w^2 + 4*w + 5]', '[67, 67, -w^3 + 3*w^2 + w - 5]', '[68, 68, -w^3 + 3*w^2 + w]', '[71, 71, 2*w - 3]', '[71, 71, w^3 - 4*w^2 + 2*w + 5]', '[74, 74, w^3 - 2*w^2 - 5*w + 2]', '[79, 79, -w^3 + 5*w^2 - 4*w - 5]', '[79, 79, -2*w^3 + 7*w^2 + 5*w - 15]', '[80, 10, 2*w^2 - 4*w - 6]', '[80, 10, 2*w^3 - 6*w^2 - 6*w + 10]', '[80, 80, -w^3 + 3*w^2]', '[80, 80, w^3 - 3*w^2 - 2*w + 8]', '[81, 3, -3]', '[82, 82, -2*w^3 + 5*w^2 + 5*w - 2]', '[83, 83, -2*w^3 + 6*w^2 + 2*w - 5]', '[85, 85, w + 3]', '[85, 85, -2*w^3 + 6*w^2 + w - 3]', '[92, 92, -2*w^3 + 5*w^2 + 5*w - 8]', '[97, 97, w^3 - w^2 - 7*w - 3]', '[98, 14, -2*w^3 + 7*w^2 + w - 6]', '[98, 14, 3*w^3 - 10*w^2 - w + 6]', '[100, 20, 2*w^3 - 4*w^2 - 7*w]', '[100, 20, -w^2 + 4]', '[100, 100, -w^3 + 3*w^2 + w - 8]', '[100, 100, -w^3 + 3*w^2 - 4]', '[101, 101, -w^3 + 3*w^2 + 3*w - 3]', '[104, 26, w^3 - 2*w^2 - 3*w - 3]', '[104, 104, w^3 - 3*w^2 - 2*w]', '[107, 107, -w^3 + 4*w^2 - 7]', '[113, 113, w^3 - 3*w^2 - 5*w + 3]', '[115, 115, -w^2 + 3*w + 5]', '[115, 115, w^3 - 2*w^2 - 2*w - 1]', '[118, 118, w^3 - 4*w^2 + 6]', '[121, 11, -w^3 + 3*w^2 + 4*w - 3]', '[121, 11, 2*w^3 - 6*w^2 - 3*w + 5]', '[125, 5, -w^3 + 4*w^2 + 2*w - 7]', '[125, 5, 2*w^3 - 5*w^2 - 5*w + 1]', '[125, 25, w^2 + 1]', '[125, 25, -2*w^2 + 5*w + 3]', '[125, 125, -2*w^3 + 4*w^2 + 9*w - 3]', '[125, 125, 2*w^3 - 6*w^2 - 6*w + 13]', '[127, 127, -2*w^3 + 6*w^2 + 5*w - 9]', '[128, 4, 2*w^3 - 4*w^2 - 6*w + 6]', '[128, 16, -2*w^2 + 2*w + 8]', '[128, 128, -w^3 + 4*w^2 + 2*w - 8]', '[130, 130, -w^3 + 4*w^2 + 2*w - 10]', '[130, 130, w^3 - 3*w^2 - w + 6]', '[134, 134, 2*w^3 - 8*w^2 + 3*w + 6]', '[136, 34, -w^3 + 4*w^2 + w - 9]', '[136, 136, w^3 - 3*w^2 - 4*w + 8]', '[137, 137, -w^3 + 5*w^2 + 3*w - 9]', '[139, 139, w^3 - w^2 - 4*w + 1]', '[142, 142, -5*w^3 + 17*w^2 + w - 14]', '[142, 142, -7*w^3 + 26*w^2 - 5*w - 22]', '[148, 148, w^3 - 5*w^2 + 3*w + 8]', '[149, 149, w^3 - 3*w^2 - w + 9]', '[157, 157, w^2 - 4*w + 1]', '[158, 158, -w^3 + 3*w^2 + 3*w - 2]', '[158, 158, -2*w^3 + 5*w^2 + 7*w - 6]', '[160, 20, -2*w^3 + 6*w^2 + 4*w - 12]', '[160, 20, -2*w + 4]', '[160, 160, 2*w^3 - 5*w^2 - 5*w + 4]', '[160, 160, -w^3 + 2*w^2 + w - 4]', '[162, 6, -3*w^3 + 9*w^2 + 3*w - 6]', '[163, 163, -3*w^3 + 7*w^2 + 9*w - 13]', '[163, 163, w^3 - 3*w^2 - w + 7]', '[164, 164, w^3 - w^2 - 5*w]', '[166, 166, w^3 - 4*w^2 + 10]', '[169, 169, -2*w^3 + 6*w^2 + 4*w - 13]', '[170, 170, 2*w^3 - 5*w^2 - 4*w + 2]', '[170, 170, -w^3 + w^2 + 7*w + 2]', '[179, 179, -2*w^3 + 3*w^2 + 5*w - 5]', '[179, 179, -2*w^3 + 4*w^2 + 5*w - 9]', '[181, 181, -w^2 + 3*w - 3]', '[181, 181, 2*w^3 - 4*w^2 - 8*w + 5]', '[184, 46, w^3 - 4*w^2 + w + 7]', '[184, 184, w^3 - 3*w^2 + w + 4]', '[185, 185, -2*w^2 + 3*w + 7]', '[185, 185, 2*w^2 - 4*w - 11]', '[191, 191, 2*w - 5]', '[193, 193, -2*w^3 + 4*w^2 + 7*w + 3]', '[193, 193, -2*w^3 + 5*w^2 + 5*w - 7]', '[194, 194, -4*w^2 + 9*w + 10]', '[196, 28, w^3 - 4*w^2 - w + 8]', '[196, 28, -3*w^2 + 2*w + 4]', '[197, 197, -w^3 + 4*w^2 - 11]', '[199, 199, -2*w^3 + 8*w^2 + 6*w - 15]', '[200, 10, -w^3 + 4*w^2 - w - 1]', '[200, 10, -w^3 + 2*w^2 + w - 5]', '[200, 40, 3*w^3 - 8*w^2 - 9*w + 12]', '[200, 40, 2*w^3 - 6*w^2 - 3*w + 4]', '[200, 50, -w^3 + 4*w^2 + w - 7]', '[200, 50, w^3 - 4*w^2 - 3*w + 9]', '[200, 200, -w^3 + w^2 + 6*w]', '[200, 200, 2*w^3 - 4*w^2 - 7*w + 4]', '[202, 202, 2*w^3 - 6*w^2 - w + 2]', '[205, 205, -w^3 - w^2 + 10*w + 11]', '[205, 205, -4*w^3 + 10*w^2 + 12*w - 17]', '[208, 26, -2*w^2 + 2*w + 6]', '[208, 208, w^2 + w - 4]', '[211, 211, -2*w^3 + 3*w^2 + 6*w - 5]', '[211, 211, -4*w^3 + 10*w^2 + 12*w - 19]', '[214, 214, 3*w^3 - 12*w^2 + 5*w + 10]', '[221, 221, -2*w^3 + 4*w^2 + 7*w - 1]', '[226, 226, -2*w^2 + 3*w + 6]', '[229, 229, w^3 - 3*w^2 - 4*w + 9]', '[229, 229, w^2 - 5]', '[230, 230, 3*w^2 - 7*w - 6]', '[230, 230, -w^3 + 2*w^2 + 3*w - 6]', '[233, 233, w^2 - 2*w - 7]', '[236, 236, -4*w^3 + 15*w^2 - 4*w - 12]', '[239, 239, -3*w^3 + 10*w^2 + 2*w - 9]', '[239, 239, -2*w^3 + 5*w^2 + 5*w - 5]', '[242, 22, w^3 - 2*w^2 - 2*w - 2]', '[242, 22, -8*w^3 + 27*w^2 - 18]', '[245, 35, w^3 - 3*w^2 + 5]', '[245, 35, 2*w^2 - 6*w - 5]', '[245, 35, 2*w^3 - 6*w^2 + 3]', '[245, 35, 2*w^2 + w - 5]', '[250, 10, w^3 - 4*w^2 + 3*w + 2]', '[250, 10, 2*w^3 - 5*w^2 - 5*w + 6]', '[250, 50, 5*w^3 - 13*w^2 - 15*w + 22]', '[250, 50, w^3 - 3*w^2 - 4*w + 2]', '[250, 250, -2*w^2 + 3*w + 2]', '[250, 250, -w^2 + 4*w + 2]', '[254, 254, 2*w^3 - 7*w^2 + 2*w + 2]', '[256, 4, 4]', '[256, 32, 2*w^3 - 4*w^2 - 8*w]', '[256, 256, -w^2 + 4*w]', '[257, 257, -2*w^3 + 5*w^2 + 4*w - 9]', '[260, 260, -2*w^3 + 5*w^2 + 6*w - 4]', '[260, 260, -w^3 + 5*w^2 - 4*w - 4]', '[263, 263, w^3 - 2*w^2 - 4*w - 3]', '[263, 263, w^3 - 6*w - 7]', '[268, 268, w^3 - 4*w^2 - 2*w + 4]', '[269, 269, w^3 - 3*w^2 - w - 1]', '[269, 269, w - 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5]', '[1564, 1564, w^3 - w^2 - 2*w - 4]', '[1568, 28, -4*w^3 + 14*w^2 + 2*w - 12]', '[1568, 28, 6*w^3 - 20*w^2 - 2*w + 12]', '[1568, 224, -w^3 + 2*w^2 + 2*w - 8]', '[1568, 224, 3*w^3 - 10*w^2 - w + 4]', '[1570, 1570, -w^3 + 6*w^2 - 9*w + 2]', '[1570, 1570, -6*w^3 + 17*w^2 + 15*w - 26]', '[1571, 1571, -5*w^3 + 12*w^2 + 18*w - 15]', '[1571, 1571, -3*w^3 + 6*w^2 + 6*w - 13]', '[1571, 1571, 3*w^2 - 5*w - 3]', '[1571, 1571, -2*w^3 + 2*w^2 + 7*w - 3]', '[1573, 143, w^3 - 8*w - 1]', '[1573, 143, -3*w^3 + 3*w^2 + 11*w - 1]', '[1574, 1574, -3*w^3 + 8*w^2 + 10*w - 10]', '[1574, 1574, -6*w^3 + 17*w^2 + 9*w - 10]', '[1576, 394, -7*w^3 + 16*w^2 + 23*w - 25]', '[1576, 1576, -w^3 + 9*w^2 - 6*w - 32]', '[1580, 1580, -3*w^3 + 8*w^2 + 5*w - 8]', '[1580, 1580, 8*w^3 - 21*w^2 - 26*w + 36]', '[1580, 1580, 2*w^3 - 5*w^2 - 9*w + 8]', '[1580, 1580, -5*w^3 + 13*w^2 + 14*w - 20]', '[1585, 1585, -5*w^3 + 13*w^2 + 14*w - 19]', '[1585, 1585, 10*w^3 - 24*w^2 - 27*w + 45]', '[1585, 1585, -2*w^3 + 6*w^2 + 2*w - 11]', '[1585, 1585, 2*w^2 - 8*w + 3]', '[1588, 1588, w^3 + 2*w^2 - 11*w - 8]', '[1588, 1588, 8*w^3 - 30*w^2 + 7*w + 24]', '[1592, 398, 3*w^3 - 8*w^2 - 9*w + 19]', '[1592, 1592, w^3 - 3*w + 4]', '[1594, 1594, -3*w^3 + 6*w^2 + 10*w - 6]', '[1600, 20, 3*w^3 - 6*w^2 - 7*w + 9]', '[1600, 20, -w^3 + 2*w^2 + w + 5]', '[1600, 40, 4*w^3 - 8*w^2 - 14*w]', '[1600, 40, -2*w^2 + 8]', '[1600, 100, -w^3 + 6*w^2 - 7*w - 11]', '[1600, 100, -w^3 + 2*w^2 + 5*w + 5]', '[1600, 200, -2*w^3 + 6*w^2 + 2*w - 16]', '[1600, 200, -2*w^3 + 6*w^2 - 8]', '[1600, 320, w^3 - 6*w^2 + 7*w + 4]', '[1600, 320, 3*w^3 - 5*w^2 - 12*w]', '[1600, 1600, -2*w^2 + 7*w + 4]', '[1600, 1600, 3*w^3 - 7*w^2 - 8*w + 16]', '[1601, 1601, -5*w^3 + 13*w^2 + 14*w - 27]', '[1609, 1609, w^3 - 3*w^2 + w + 9]', '[1609, 1609, 3*w^3 - 11*w^2 - w + 13]', '[1616, 202, -2*w^3 + 6*w^2 + 6*w - 6]', '[1616, 1616, w^3 - w^2 - 6*w - 8]', '[1620, 60, 6*w^3 - 15*w^2 - 21*w + 24]', '[1620, 60, -3*w^3 + 6*w^2 + 9*w]', '[1621, 1621, 3*w^3 - 7*w^2 - 8*w + 9]', '[1621, 1621, -5*w^3 + 16*w^2 + 2*w - 7]', '[1621, 1621, -5*w^3 + 14*w^2 + 10*w - 15]', '[1621, 1621, 4*w^3 - 9*w^2 - 9*w + 19]', '[1625, 65, -4*w^3 + 10*w^2 + 10*w - 7]', '[1625, 65, -2*w^3 + 3*w^2 + 4*w - 9]', '[1625, 325, -w^3 + 4*w^2 + 4*w - 11]', '[1625, 325, -3*w^3 + 6*w^2 + 12*w + 1]', '[1625, 1625, 4*w^3 - 11*w^2 - 9*w + 23]', '[1625, 1625, -w^3 + 7*w^2 - 8*w - 9]', '[1630, 1630, -w^3 + 2*w^2 + w + 6]', '[1630, 1630, -7*w^3 + 20*w^2 + 22*w - 38]', '[1630, 1630, -5*w^3 + 12*w^2 + 13*w - 2]', '[1630, 1630, 3*w^3 - 10*w^2 - 6*w + 18]', '[1633, 1633, 2*w^3 - 3*w^2 - 6*w + 9]', '[1633, 1633, 4*w^2 - 4*w - 7]', '[1636, 1636, -w^3 + 6*w^2 - 4*w - 4]', '[1640, 410, 5*w^3 - 8*w^2 - 23*w + 1]', '[1640, 410, -3*w^3 + 6*w^2 + 13*w - 1]', '[1640, 1640, w^3 - 2*w^2 - 7*w + 4]', '[1640, 1640, -4*w^3 + 9*w^2 + 13*w - 12]', '[1649, 1649, 4*w^3 - 6*w^2 - 18*w - 11]', '[1651, 1651, -3*w^3 + 6*w^2 + 10*w - 11]', '[1654, 1654, -8*w^3 + 27*w^2 + 2*w - 26]', '[1654, 1654, -2*w^3 + 7*w^2 + 5*w - 18]', '[1655, 1655, w^3 - 3*w^2 - 2*w + 11]', '[1655, 1655, -2*w^3 + 8*w^2 - 11]', '[1655, 1655, -4*w^2 + 8*w + 17]', '[1655, 1655, 2*w^3 - 4*w^2 - 5*w - 5]', '[1660, 1660, -3*w^2 + 7*w + 16]', '[1660, 1660, w^3 - 5*w - 8]', '[1664, 52, 2*w^3 - 4*w^2 - 6*w - 6]', '[1664, 208, 2*w^3 - 6*w^2 - 4*w]', '[1664, 1664, -w^3 + 7*w^2 - 10*w - 8]', '[1666, 238, -w^3 + 7*w^2 + 4*w - 10]', '[1666, 238, -2*w^2 - w - 2]', '[1669, 1669, -4*w^3 + 13*w^2 + w - 5]', '[1669, 1669, 4*w^3 - 13*w^2 - 10*w + 23]', '[1675, 335, 3*w^3 - 8*w^2 - 4*w + 7]', '[1675, 335, 4*w^3 - 10*w^2 - 11*w + 15]', '[1675, 1675, -w^2 + 6*w - 3]', '[1675, 1675, 6*w^3 - 20*w^2 - 3*w + 17]', '[1676, 1676, -2*w^3 + 6*w^2 + 9*w - 8]', '[1681, 1681, -w^3 + 5*w^2 + 5*w - 5]', '[1684, 1684, 2*w^3 - 11*w^2 + 9*w + 16]', '[1684, 1684, 2*w^3 - 6*w^2 - 3*w]', '[1685, 1685, -4*w^3 + w^2 + 30*w + 19]', '[1685, 1685, w^3 - 3*w^2 - w + 11]', '[1688, 422, 3*w^3 - 8*w^2 - 9*w + 9]', '[1688, 422, 7*w^3 - 20*w^2 - 17*w + 31]', '[1688, 1688, w^3 - 5*w^2 - 3*w + 4]', '[1688, 1688, 3*w^3 - 10*w^2 - 5*w + 12]', '[1690, 1690, -3*w^2 + w + 10]', '[1690, 1690, -2*w^3 + 7*w^2 + w - 2]', '[1693, 1693, -2*w^3 + 9*w^2 - 6*w - 5]', '[1697, 1697, -4*w^3 + 15*w^2 - 5*w - 11]', '[1699, 1699, -3*w^3 + 8*w^2 + 6*w - 17]', '[1700, 340, -w^3 + 9*w]', '[1700, 340, 4*w^3 - 7*w^2 - 16*w + 4]', '[1700, 1700, 5*w^3 - 16*w^2 - 4*w + 12]', '[1700, 1700, 4*w^3 - 9*w^2 - 15*w + 8]', '[1702, 1702, -3*w^3 + 5*w^2 + 11*w - 6]', '[1706, 1706, 5*w^3 - 12*w^2 - 12*w + 26]', '[1712, 214, -2*w^3 + 8*w^2 - 14]', '[1712, 1712, -2*w^3 + w^2 + 15*w + 4]', '[1714, 1714, 7*w^3 - 26*w^2 + 6*w + 18]', '[1714, 1714, -w^2 + w + 10]', '[1717, 1717, 2*w^3 - 8*w^2 + 2*w + 13]', '[1721, 1721, 4*w^2 - 5*w - 15]', '[1721, 1721, -3*w^3 + 8*w^2 + 8*w - 7]', '[1724, 1724, -4*w^3 + 13*w^2 + 4*w - 12]', '[1724, 1724, -w^2 - w + 8]', '[1724, 1724, -2*w^3 + 10*w^2 - 7*w - 16]', '[1724, 1724, w^3 - 7*w^2 + 9*w + 8]', '[1726, 1726, 7*w^3 - 26*w^2 + 7*w + 18]', '[1726, 1726, 2*w^3 - 5*w^2 - 8*w + 2]', '[1735, 1735, -2*w^3 + 4*w^2 + 12*w + 1]', '[1735, 1735, 5*w^3 - 7*w^2 - 22*w - 1]', '[1741, 1741, -3*w^2 + 6*w + 17]', '[1741, 1741, w^3 - 2*w^2 - 3]', '[1742, 1742, -3*w^3 + 9*w^2 + 5*w - 6]', '[1745, 1745, 3*w^3 - 9*w^2 - 5*w + 5]', '[1745, 1745, 3*w^3 - 4*w^2 - 16*w - 1]', '[1745, 1745, -6*w^3 + 11*w^2 + 27*w - 3]', '[1745, 1745, -6*w^3 + 15*w^2 + 20*w - 27]', '[1747, 1747, -2*w^3 + 7*w^2 + 8*w - 9]', '[1754, 1754, -5*w^3 + 17*w^2 + w - 18]', '[1759, 1759, -4*w^3 + 10*w^2 + 15*w - 15]', '[1759, 1759, 4*w^3 - 11*w^2 - 9*w + 21]', '[1762, 1762, 4*w^3 - 13*w^2 - 2*w + 6]', '[1765, 1765, 3*w^3 - 6*w^2 - 14*w + 5]', '[1765, 1765, -11*w^3 + 33*w^2 + 32*w - 63]', '[1768, 442, -w^3 + 4*w^2 - w - 15]', '[1768, 1768, 3*w^3 - 8*w^2 - 6*w + 16]', '[1772, 1772, w^3 - 6*w^2 + w + 8]', '[1772, 1772, 5*w^3 - 13*w^2 - 11*w + 8]', '[1772, 1772, -7*w^3 + 25*w^2 - 3*w - 16]', '[1772, 1772, w^3 - 4*w^2 + 3*w + 8]', '[1775, 355, 3*w^3 - 8*w^2 - 12*w + 17]', '[1775, 355, -2*w^3 + 7*w^2 - 4*w - 3]', '[1775, 355, -6*w^3 + 18*w^2 + 4*w - 11]', '[1775, 355, -3*w^3 + 7*w^2 + 7*w - 3]', '[1775, 1775, -15*w^3 + 51*w^2 + w - 37]', '[1775, 1775, -7*w^3 + 26*w^2 - 6*w - 17]', '[1775, 1775, -4*w^3 + 15*w^2 - 5*w - 13]', '[1775, 1775, -5*w^3 + 15*w^2 + 6*w - 17]', '[1781, 1781, -w^3 + 5*w^2 - 6*w - 3]', '[1783, 1783, 4*w^3 - 11*w^2 - 10*w + 13]', '[1783, 1783, 3*w^3 - 5*w^2 - 16*w - 1]', '[1787, 1787, 4*w^3 - 11*w^2 - 11*w + 15]', '[1787, 1787, 4*w^3 - 15*w^2 - 14*w + 27]', '[1789, 1789, 4*w^3 - 10*w^2 - 11*w + 7]', '[1790, 1790, w^3 - 6*w^2 + 4*w + 10]', '[1790, 1790, -4*w^3 + 13*w^2 + 13*w - 26]', '[1790, 1790, -3*w^3 + 11*w^2 + 9*w - 18]', '[1790, 1790, 2*w^2 - 7*w - 2]', '[1807, 1807, w^3 - 5*w^2 - 7*w + 3]', '[1808, 226, 2*w^3 - 6*w^2 - 10*w + 6]', '[1808, 1808, -w^3 - w^2 + 12*w + 16]', '[1810, 1810, w^3 - 5*w^2 + 9*w - 6]', '[1810, 1810, 4*w^3 - 10*w^2 - 15*w + 18]', '[1810, 1810, 7*w^3 - 20*w^2 - 16*w + 34]', '[1810, 1810, -9*w^3 + 23*w^2 + 28*w - 38]', '[1813, 259, w^2 - 6*w - 3]', '[1813, 259, 4*w^3 - 11*w^2 - 6*w + 1]', '[1814, 1814, -w^3 - 2*w^2 + 14*w + 6]', '[1814, 1814, -6*w^3 + 19*w^2 + 6*w - 18]', '[1817, 1817, -2*w^2 + 7*w + 3]', '[1817, 1817, -3*w^3 + 6*w^2 + 14*w - 7]', '[1819, 1819, 6*w^3 - 17*w^2 - 10*w + 13]', '[1832, 458, 7*w^3 - 20*w^2 - 21*w + 35]', '[1832, 458, -3*w^3 + 10*w^2 + 11*w - 15]', '[1832, 1832, -w^3 + 4*w^2 - 2*w - 16]', '[1832, 1832, 4*w^3 - 12*w^2 - 9*w + 28]', '[1835, 1835, -5*w^3 + 8*w^2 + 26*w + 5]', '[1835, 1835, -3*w^3 + 5*w^2 + 6*w - 13]', '[1835, 1835, 3*w^3 - 3*w^2 - 16*w - 5]', '[1835, 1835, 3*w^3 - 2*w^2 - 18*w - 9]', '[1840, 230, -2*w^2 + 6*w + 10]', '[1840, 230, 2*w^3 - 4*w^2 - 4*w - 2]', '[1840, 1840, 3*w^3 - 12*w^2 + w + 12]', '[1840, 1840, -w^2 + w - 4]', '[1844, 1844, 5*w^3 - 20*w^2 + 6*w + 20]', '[1844, 1844, 3*w^3 - 13*w^2 + 7*w + 16]', '[1846, 1846, 2*w^3 - 9*w^2 + 5*w + 6]', '[1846, 1846, 7*w^3 - 21*w^2 - 8*w + 10]', '[1847, 1847, -w^3 + 6*w^2 - 6*w - 5]', '[1847, 1847, 4*w^3 - 10*w^2 - 11*w + 11]', '[1850, 370, w^3 - w^2 - 3*w - 6]', '[1850, 370, -2*w^3 + 8*w^2 + 3*w - 22]', '[1850, 1850, 2*w^3 - 7*w^2 - w + 14]', '[1850, 1850, 2*w^3 - 6*w^2 - w - 2]', '[1858, 1858, -3*w^2 + 8*w + 2]', '[1858, 1858, -2*w^3 + 8*w^2 + 3*w - 18]', '[1863, 69, -3*w^2 + 9]', '[1864, 466, -5*w^3 + 10*w^2 + 17*w - 13]', '[1864, 1864, w^3 + 4*w^2 - 12*w - 24]', '[1865, 1865, 4*w^3 - 10*w^2 - 9*w + 21]', '[1865, 1865, -4*w^3 + 6*w^2 + 18*w + 5]', '[1867, 1867, -2*w^3 + 3*w^2 + 8*w - 5]', '[1867, 1867, 3*w^3 - 7*w^2 - 6*w - 1]', '[1867, 1867, -4*w^2 + 9*w + 7]', '[1867, 1867, -w^3 + 7*w^2 + 2*w - 15]', '[1871, 1871, -4*w^2 + 11*w + 7]', '[1874, 1874, 9*w^3 - 28*w^2 - 6*w + 14]', '[1877, 1877, 4*w^3 - 11*w^2 - 8*w + 7]', '[1879, 1879, -5*w^2 + 3*w + 15]', '[1882, 1882, 3*w^3 - 14*w^2 + 10*w + 18]', '[1886, 1886, 3*w^3 - 6*w^2 - 10*w + 2]', '[1888, 236, 2*w^3 - 8*w^2 + 12]', '[1888, 1888, w^3 + w^2 - 11*w - 4]', '[1889, 1889, -3*w^3 + 13*w^2 - 7*w - 11]', '[1895, 1895, 6*w^3 - 16*w^2 - 16*w + 33]', '[1895, 1895, -3*w^3 + 3*w^2 + 18*w + 5]', '[1901, 1901, w^3 - 7*w^2 + w + 21]', '[1906, 1906, 3*w^3 - 17*w^2 + 17*w + 22]', '[1906, 1906, -3*w^3 + 8*w^2 + 3*w - 2]', '[1907, 1907, -2*w^3 + 8*w^2 + w - 17]', '[1909, 1909, 2*w^3 - 7*w^2 - 4*w + 7]', '[1910, 1910, -2*w^2 + 9*w - 10]', '[1910, 1910, 7*w^3 - 21*w^2 - 16*w + 38]', '[1912, 478, -3*w^3 + 4*w^2 + 15*w + 1]', '[1912, 478, -3*w^3 + 8*w^2 + 7*w - 19]', '[1912, 1912, -2*w^3 + 9*w + 4]', '[1912, 1912, -4*w^3 + 9*w^2 + 16*w - 8]', '[1913, 1913, -2*w^3 + 8*w^2 - 19]', '[1915, 1915, 2*w^2 - 6*w - 11]', '[1915, 1915, -7*w^3 + 9*w^2 + 36*w + 15]', '[1915, 1915, -w^3 - 3*w^2 + 10*w + 19]', '[1915, 1915, 4*w^3 - 12*w^2 - 8*w + 27]', '[1916, 1916, w^3 + w^2 - 5*w]', '[1921, 1921, 2*w^2 - 4*w - 13]', '[1924, 1924, -2*w^3 + 3*w^2 + 9*w + 8]', '[1930, 1930, 4*w^2 - 9*w - 14]', '[1930, 1930, -4*w^3 + 11*w^2 + 5*w - 2]', '[1930, 1930, 7*w^3 - 18*w^2 - 22*w + 34]', '[1930, 1930, -5*w^3 + 15*w^2 + 11*w - 22]', '[1933, 1933, w^3 + 2*w^2 - 10*w - 13]', '[1933, 1933, -4*w^3 + 8*w^2 + 14*w - 9]', '[1934, 1934, 2*w^3 - 11*w^2 + 11*w + 14]', '[1936, 22, -2*w^3 + 6*w^2 + 8*w - 6]', '[1936, 22, 4*w^3 - 12*w^2 - 6*w + 10]', '[1936, 176, -3*w^3 + 7*w^2 + 7*w + 4]', '[1936, 176, w^3 - 9*w - 12]', '[1937, 1937, 6*w^2 - 4*w - 19]', '[1940, 1940, -4*w^3 + w^2 + 28*w + 20]', '[1940, 1940, w^3 + 3*w^2 - 13*w - 24]', '[1942, 1942, 3*w^3 - 13*w^2 + 8*w + 14]', '[1942, 1942, 3*w^3 - 10*w^2 - 4*w + 10]', '[1948, 1948, -2*w^3 + 4*w^2 - w]', '[1948, 1948, -4*w^3 + 14*w^2 + w - 8]', '[1954, 1954, -3*w^3 + 6*w^2 + 14*w - 6]', '[1955, 1955, 4*w^3 - 13*w^2 - 2*w + 15]', '[1955, 1955, 4*w^3 - 13*w^2 - 10*w + 25]', '[1960, 70, 3*w^3 - 4*w^2 - 9*w + 7]', '[1960, 70, -w^3 - 2*w^2 + 7*w + 9]', '[1960, 70, -w^3 + 6*w^2 + 3*w - 7]', '[1960, 70, w^3 - 4*w^2 - 3*w - 1]', '[1960, 280, w^3 - w - 4]', '[1960, 280, -4*w^2 + 3*w + 12]', '[1960, 280, -w^2 - w - 4]', '[1960, 280, 3*w^3 - 8*w^2 + 8]', '[1964, 1964, w^3 - 8*w^2 + 8*w + 12]', '[1966, 1966, -4*w^3 + 9*w^2 + 14*w - 6]', '[1970, 1970, -4*w^3 + 13*w^2 + 8*w - 26]', '[1970, 1970, 7*w^3 - 21*w^2 - 17*w + 46]', '[1975, 395, 2*w^3 - 5*w^2 - 3*w - 5]', '[1975, 395, -4*w^2 + 8*w + 19]', '[1975, 395, 3*w^3 - 9*w^2 - 12*w + 13]', '[1975, 395, -3*w^3 + 9*w^2 + 7*w - 11]', '[1975, 1975, -7*w^3 + 17*w^2 + 21*w - 29]', '[1975, 1975, -2*w^3 + 9*w^2 + w - 27]', '[1975, 1975, 4*w^3 - 9*w^2 - 14*w + 15]', '[1975, 1975, w^3 - 6*w + 1]', '[1982, 1982, w^3 - 7*w^2 + 7*w + 14]', '[1982, 1982, 2*w^3 - 3*w^2 - 12*w + 2]', '[1985, 1985, 4*w^3 - 9*w^2 - 17*w + 9]', '[1985, 1985, -3*w^2 + 7*w + 3]', '[1985, 1985, 3*w^3 - 7*w^2 - 11*w + 5]', '[1985, 1985, -3*w^3 + 6*w^2 + 10*w - 5]', '[1987, 1987, -3*w^3 + 7*w^2 + 10*w - 3]', '[1990, 1990, 3*w^3 - 7*w^2 - 8*w + 6]', '[1990, 1990, -8*w^3 + 20*w^2 + 21*w - 38]', '[1993, 1993, w^3 - 2*w^2 - 6*w + 11]', '[1993, 1993, w^3 - 6*w^2 - 4*w + 13]', '[1994, 1994, -4*w^3 + 11*w^2 + 8*w - 14]', '[1997, 1997, -3*w^3 + 9*w^2 + 9*w - 13]', '[1999, 1999, 2*w^3 - 5*w^2 - 2*w - 1]', '[2000, 10, -2*w^3 + 8*w^2 + 4*w - 14]', '[2000, 10, 4*w^3 - 10*w^2 - 10*w + 2]', '[2000, 50, 2*w^2 + 2]', '[2000, 50, -4*w^2 + 10*w + 6]', '[2000, 80, 4*w^3 - 10*w^2 - 15*w + 12]', '[2000, 80, -2*w^3 + 3*w^2 + 9*w - 4]', '[2000, 250, -4*w^3 + 8*w^2 + 18*w - 6]', '[2000, 250, 4*w^3 - 12*w^2 - 12*w + 26]', '[2000, 400, -w^3 + w^2 + 9*w - 4]', '[2000, 400, w^3 - 7*w^2 + 6*w + 8]', '[2000, 2000, 4*w^3 - 11*w^2 - 12*w + 16]', '[2000, 2000, 5*w^3 - 12*w^2 - 16*w + 16]', '[2003, 2003, -4*w^3 + 10*w^2 + 16*w - 11]', '[2006, 2006, -6*w^3 + 18*w^2 + 7*w - 14]', '[2009, 287, 2*w^3 - 5*w^2 - 8*w + 1]', '[2009, 287, 2*w^3 - 4*w^2 - 5*w + 11]', '[2011, 2011, 3*w + 7]', '[2011, 2011, -4*w^3 + 12*w^2 + 8*w - 15]', '[2020, 2020, 5*w^3 - 15*w^2 - 11*w + 32]', '[2020, 2020, 2*w^3 - 3*w^2 - 6*w - 4]', '[2025, 15, 3*w^3 - 6*w^2 - 12*w + 9]', '[2025, 15, 3*w^2 - 6*w - 3]', '[2025, 75, -3*w^3 + 12*w^2 - 6*w - 9]', '[2025, 75, -3*w^3 + 9*w^2 + 6*w - 9]', '[2026, 2026, -w^3 + 4*w^2 - 2*w - 10]', '[2027, 2027, -3*w^3 + 7*w^2 + 7*w - 9]', '[2029, 2029, -3*w^3 + 13*w^2 + 10*w - 25]', '[2029, 2029, -2*w^3 + 2*w^2 + 12*w + 1]', '[2032, 254, -4*w^3 + 12*w^2 + 10*w - 18]', '[2032, 2032, -w^3 + 3*w^2 + 3*w - 12]', '[2036, 2036, -w^3 + 6*w^2 - 4*w - 12]', '[2036, 2036, -5*w^2 + 10*w + 12]', '[2038, 2038, -3*w^3 + 11*w^2 + w - 14]', '[2039, 2039, w^3 - 6*w^2 + 4*w + 11]', '[2039, 2039, w^2 + 2*w - 7]', '[2041, 2041, 3*w^3 - 7*w^2 - 8*w + 7]', '[2042, 2042, w^3 - 2*w^2 - 3*w - 6]', '[2045, 2045, -5*w^3 + 13*w^2 + 12*w - 21]', '[2045, 2045, 3*w^3 - 12*w^2 + 4*w + 15]', '[2048, 8, 4*w^3 - 8*w^2 - 12*w + 12]', '[2048, 32, -4*w^2 + 4*w + 16]', '[2048, 256, -2*w^3 + 8*w^2 + 4*w - 16]', '[2048, 2048, -3*w^3 + 5*w^2 + 13*w - 4]', '[2050, 410, w^3 + 4*w^2 - 13*w - 26]', '[2050, 410, w^3 - 7*w^2 + 6*w + 18]', '[2050, 2050, 3*w^3 - 13*w^2 + 38]', '[2050, 2050, -2*w^3 + 6*w^2 + 7*w - 6]', '[2054, 2054, -4*w^3 + 7*w^2 + 16*w - 6]', '[2054, 2054, 4*w^3 - 10*w^2 - 11*w + 14]', '[2056, 514, -7*w^3 + 14*w^2 + 19*w - 27]', '[2056, 2056, -3*w^3 + 12*w^2 + 8*w - 24]', '[2057, 187, -7*w^3 + 26*w^2 - 4*w - 27]', '[2057, 187, w^3 - 5*w^2 + 3*w + 13]', '[2063, 2063, -w^3 + 2*w^2 + 4*w - 9]', '[2069, 2069, -4*w^3 + 8*w^2 + 18*w - 9]', '[2069, 2069, 3*w^3 - 8*w^2 - 8*w + 1]', '[2075, 415, -2*w^3 + 6*w^2 + 3*w - 17]', '[2075, 415, w^3 - 3*w^2 - 4*w - 3]', '[2075, 2075, -2*w^3 + 7*w^2 + 5*w - 19]', '[2075, 2075, 5*w^3 - 16*w^2 - 12*w + 33]', '[2080, 260, -2*w^3 + 8*w^2 + 4*w - 20]', '[2080, 260, 2*w^3 - 6*w^2 - 2*w + 12]', '[2080, 2080, 2*w^3 - 3*w^2 - 12*w]', '[2080, 2080, 4*w^3 - 13*w^2 - 10*w + 24]', '[2081, 2081, -4*w^3 + 15*w^2 - w - 15]', '[2083, 2083, w^2 + w - 9]', '[2084, 2084, 3*w^2 - 5*w]', '[2084, 2084, w^2 + 4]', '[2087, 2087, -2*w^3 + 6*w^2 + 6*w + 1]', '[2087, 2087, 2*w^3 - 3*w^2 - 5*w + 9]', '[2092, 2092, -4*w^2 + 5*w + 8]', '[2092, 2092, w^3 - 7*w]', '[2092, 2092, -8*w^3 + 27*w^2 + 2*w - 20]', '[2092, 2092, w^3 - 5*w^2 + 6*w + 4]', '[2095, 2095, -w^3 + w^2 + 5*w + 9]', '[2095, 2095, 5*w^3 - 13*w^2 - 13*w + 21]', '[2098, 2098, 2*w^3 - 10*w^2 + 9*w + 10]', '[2099, 2099, -4*w^3 + 9*w^2 + 15*w - 15]', '[2102, 2102, 2*w^3 - 10*w^2 - 5*w + 22]', '[2104, 526, -3*w^3 + 4*w^2 + 11*w - 1]', '[2104, 526, -3*w^3 + 8*w^2 + 15*w - 5]', '[2104, 2104, 3*w^3 - w^2 - 24*w - 24]', '[2104, 2104, 3*w^3 - w^2 - 18*w - 16]', '[2105, 2105, 2*w^3 - w^2 - 15*w - 15]', '[2105, 2105, -6*w^3 + 13*w^2 + 18*w + 1]', '[2105, 2105, -w^3 - 2*w^2 + 10*w + 11]', '[2105, 2105, 3*w^3 - 9*w^2 - 5*w + 17]', '[2106, 78, -3*w^2 + 9*w + 6]', '[2110, 2110, -2*w^3 + 3*w^2 + 7*w + 6]', '[2110, 2110, -10*w^3 + 28*w^2 + 31*w - 54]', '[2110, 2110, -3*w^3 + 10*w^2 + 11*w - 18]', '[2110, 2110, -w^3 + 3*w^2 - 2*w + 6]', '[2111, 2111, 2*w^3 - w^2 - 14*w - 5]', '[2113, 2113, -4*w^3 + 9*w^2 + 13*w - 3]', '[2116, 2116, -3*w^3 + 10*w^2 + 2*w - 4]', '[2119, 2119, w^3 - 9*w^2 + 14*w + 13]', '[2119, 2119, 3*w^3 - 11*w^2 + 17]', '[2122, 2122, 4*w^3 - 11*w^2 - 7*w + 14]', '[2125, 85, 4*w^3 - 11*w^2 - 8*w + 13]', '[2125, 85, -4*w^3 + 10*w^2 + 15*w - 17]', '[2125, 425, -3*w^3 + 5*w^2 + 12*w - 5]', '[2125, 425, w^3 - 5*w^2 + 6*w + 5]', '[2125, 2125, 2*w^3 - 6*w^2 - 6*w + 5]', '[2125, 2125, 3*w^3 - 6*w^2 - 10*w + 3]', '[2126, 2126, -4*w^3 + 8*w^2 + 15*w - 6]', '[2132, 2132, -4*w^3 + 10*w^2 + 15*w - 16]', '[2140, 2140, -4*w^2 + 11*w + 8]', '[2140, 2140, 9*w^3 - 23*w^2 - 28*w + 36]', '[2141, 2141, 5*w^2 - 9*w - 9]', '[2144, 268, 4*w^3 - 16*w^2 + 6*w + 12]', '[2144, 2144, -6*w^3 + 15*w^2 + 19*w - 28]', '[2152, 538, -3*w^3 + 6*w^2 + 9*w - 7]', '[2152, 538, -5*w^3 + 12*w^2 + 15*w - 19]', '[2152, 2152, w^3 + w^2 - 7*w - 12]', '[2152, 2152, -w^3 + 6*w^2 - w - 20]', '[2153, 2153, w^2 - 6*w - 9]', '[2153, 2153, w^3 - 7*w^2 + 7*w + 13]', '[2155, 2155, -w^3 - 3*w^2 + 11*w + 21]', '[2155, 2155, 5*w^3 - 11*w^2 - 17*w + 5]', '[2155, 2155, 3*w^2 - 7*w - 13]', '[2155, 2155, 4*w^3 - 8*w^2 - 13*w + 13]', '[2155, 2155, -10*w^3 + 29*w^2 + 27*w - 55]', '[2155, 2155, 4*w^3 - 8*w^2 - 18*w + 3]', '[2155, 2155, -2*w^3 + 7*w^2 + 6*w - 9]', '[2155, 2155, -2*w^3 + 2*w^2 + 11*w + 1]', '[2158, 2158, -4*w^2 + 5*w + 18]', '[2159, 2159, 5*w^3 - 16*w^2 - 6*w + 23]', '[2161, 2161, 2*w^3 - 3*w^2 - 12*w + 1]', '[2164, 2164, 3*w^3 - 6*w^2 - 10*w + 4]', '[2174, 2174, -8*w^3 + 26*w^2 + 5*w - 22]', '[2176, 68, -2*w^3 + 8*w^2 + 2*w - 18]', '[2176, 272, 2*w^3 - 6*w^2 - 8*w + 16]', '[2176, 2176, 4*w^3 - 10*w^2 - 11*w + 12]', '[2183, 2183, -3*w^3 + 11*w^2 + 3*w - 23]', '[2188, 2188, -4*w^3 + 11*w^2 + 4*w - 4]', '[2188, 2188, 3*w^3 - 7*w^2 - 5*w + 8]', '[2188, 2188, -7*w^3 + 21*w^2 + 6*w - 12]', '[2188, 2188, 2*w^3 - 3*w^2 - 10*w + 4]', '[2192, 274, -2*w^3 + 10*w^2 + 6*w - 18]', '[2192, 2192, -3*w^3 + 5*w^2 + 10*w - 8]', '[2194, 2194, 3*w^3 - 9*w^2 - w + 2]', '[2197, 13, 3*w^3 - 11*w^2 - w + 15]', '[2197, 2197, 3*w^3 - 12*w^2 + 2*w + 13]', '[2203, 2203, -4*w^3 + 10*w^2 + 7*w - 1]', '[2209, 47, 2*w^3 - 7*w^2 + 3*w + 9]', '[2209, 47, w^2 - 5*w - 11]', '[2210, 2210, w^3 - 6*w^2 - w + 10]', '[2210, 2210, -4*w^3 + 11*w^2 + 9*w - 10]', '[2213, 2213, w^3 - 7*w^2 + 8*w + 15]', '[2215, 2215, -3*w^3 + 8*w^2 + 8*w - 19]', '[2215, 2215, -2*w^3 + 8*w^2 + 4*w - 15]', '[2215, 2215, 3*w^2 - 9*w - 5]', '[2215, 2215, -6*w^3 + 12*w^2 + 26*w - 9]', '[2215, 2215, 2*w^2 - 3*w + 3]', '[2215, 2215, 2*w^3 + w^2 - 19*w - 11]', '[2215, 2215, -3*w^3 + 10*w^2 + 10*w - 21]', '[2215, 2215, 4*w^3 - 8*w^2 - 15*w + 5]', '[2218, 2218, 3*w^3 - 16*w^2 + 13*w + 22]', '[2224, 278, 2*w^3 - 2*w^2 - 8*w + 2]', '[2224, 2224, -w^3 - 2*w^2 + 9*w + 12]', '[2231, 2231, -3*w^3 + 2*w^2 + 14*w + 5]', '[2234, 2234, 4*w^3 - 16*w^2 + 7*w + 14]', '[2234, 2234, -w^3 + 6*w - 2]', '[2237, 2237, -4*w^3 + 10*w^2 + 11*w - 13]', '[2248, 562, 7*w^3 - 18*w^2 - 21*w + 29]', '[2248, 2248, 2*w^3 - 9*w^2 - w + 28]', '[2251, 2251, 3*w^3 - 5*w^2 - 15*w + 5]', '[2251, 2251, -w^3 + 6*w^2 - 15]', '[2252, 2252, w^3 - 2*w^2 + 3*w]', '[2252, 2252, 2*w^3 - 5*w^2 - w]', '[2254, 322, -3*w^3 + 7*w^2 + 3*w - 2]', '[2254, 322, 3*w^3 - 6*w^2 - 4*w + 6]', '[2258, 2258, w^3 - 10*w^2 + 17*w + 14]', '[2258, 2258, w^2 - 6*w + 2]', '[2260, 2260, -w^3 + 5*w^2 + w - 16]', '[2260, 2260, 2*w^3 - 7*w^2 + 12]', '[2269, 2269, w^3 - 4*w - 7]', '[2272, 284, -10*w^3 + 34*w^2 + 2*w - 28]', '[2272, 284, -14*w^3 + 52*w^2 - 10*w - 44]', '[2272, 2272, w^3 - 8*w]', '[2272, 2272, -8*w^3 + 23*w^2 + 22*w - 40]', '[2273, 2273, 2*w^3 - 9*w^2 + 2*w + 19]', '[2276, 2276, -2*w^2 - 5*w]', '[2278, 2278, -2*w^3 + 3*w^2 + 8*w - 6]', '[2281, 2281, 4*w^3 - 10*w^2 - 9*w + 15]', '[2281, 2281, -w^3 + 7*w^2 - 5*w - 7]', '[2284, 2284, 2*w^3 - 7*w^2 - 5*w + 8]', '[2290, 2290, 4*w^3 - 13*w^2 - 9*w + 26]', '[2290, 2290, -10*w^3 + 29*w^2 + 26*w - 54]', '[2290, 2290, -w^3 + 2*w^2 + 5*w - 10]', '[2290, 2290, 3*w^3 - 7*w^2 - 14*w + 22]', '[2297, 2297, -3*w^3 + 9*w^2 + 10*w - 21]', '[2300, 460, 7*w^3 - 19*w^2 - 18*w + 36]', '[2300, 460, -3*w^3 + 6*w^2 + 13*w]', '[2300, 2300, 3*w^3 - 5*w^2 - 14*w + 4]', '[2300, 2300, -4*w^3 + 9*w^2 + 12*w - 4]', '[2305, 2305, -4*w^2 + 6*w + 9]', '[2305, 2305, 2*w^3 - 12*w - 13]', '[2305, 2305, -2*w^2 + 7*w + 9]', '[2305, 2305, w^3 - w^2 - 8*w - 9]', '[2308, 2308, w^3 - 5*w^2 - 4*w + 4]', '[2309, 2309, -3*w^2 + 7*w + 15]', '[2311, 2311, -3*w^3 + 11*w^2 + 2*w - 23]', '[2311, 2311, 4*w^3 - 10*w^2 - 9*w + 5]', '[2311, 2311, 2*w^3 - 6*w^2 - 9*w + 5]', '[2311, 2311, -2*w^3 + 3*w^2 + 11*w - 5]', '[2312, 578, -w^3 + 2*w^2 - w + 3]', '[2312, 2312, 3*w^3 - 7*w^2 - 7*w + 4]', '[2323, 2323, 3*w^3 - 4*w^2 - 8*w + 5]', '[2327, 2327, 4*w^3 - 11*w^2 - 7*w + 9]', '[2327, 2327, -2*w^3 + 6*w^2 + 2*w + 1]', '[2329, 2329, 4*w^3 - 10*w^2 - 10*w + 15]', '[2330, 2330, 4*w^3 - 13*w^2 - 7*w + 30]', '[2330, 2330, -w^3 + 4*w^2 + 3*w - 14]', '[2341, 2341, 3*w^3 - 7*w^2 - 8*w - 3]', '[2344, 586, -3*w^3 + 12*w^2 + 13*w - 17]', '[2344, 586, w^3 - 11*w + 5]', '[2344, 2344, -w^3 + 4*w^2 - 5*w - 20]', '[2344, 2344, -w^3 + 6*w^2 - 5*w - 4]', '[2347, 2347, -4*w^3 + 11*w^2 + 6*w - 7]', '[2347, 2347, w^3 - 3*w^2 - 3*w - 3]', '[2351, 2351, -4*w^3 + 9*w^2 + 10*w - 1]', '[2353, 2353, -2*w^3 + 8*w^2 + 3*w - 13]', '[2353, 2353, 4*w^3 - 9*w^2 - 17*w + 7]', '[2360, 590, -7*w^3 + 20*w^2 + 21*w - 41]', '[2360, 590, 3*w^3 - 10*w^2 + w + 11]', '[2360, 2360, -7*w^3 + 18*w^2 + 21*w - 28]', '[2360, 2360, -w^3 + 6*w^2 - 8*w - 8]', '[2363, 2363, w^3 - w^2 - 3*w - 7]', '[2368, 148, -w^3 + 6*w^2 - 7*w - 3]', '[2368, 296, 2*w^3 - 10*w^2 + 6*w + 16]', '[2368, 2368, 6*w^3 - 19*w^2 - 14*w + 40]', '[2371, 2371, -5*w^3 + 13*w^2 + 13*w - 15]', '[2371, 2371, -w^3 + 7*w^2 - 10*w - 9]', '[2372, 2372, w^3 - 4]', '[2374, 2374, -3*w^3 + 8*w^2 + 8*w - 6]', '[2377, 2377, 2*w^3 - 6*w^2 - 2*w + 15]', '[2377, 2377, 3*w^3 - 10*w^2 - 4*w + 25]', '[2381, 2381, -5*w^2 + 9*w + 11]', '[2383, 2383, 2*w^3 - 8*w^2 - 7*w + 17]', '[2384, 298, -2*w^3 + 6*w^2 + 2*w - 18]', '[2384, 2384, -5*w^3 + 9*w^2 + 24*w]', '[2389, 2389, -3*w^3 + 3*w^2 + 8*w - 3]', '[2390, 2390, 4*w^3 - 7*w^2 - 12*w + 10]', '[2390, 2390, 5*w^3 - 12*w^2 - 18*w + 22]', '[2390, 2390, 3*w^3 - w^2 - 23*w - 18]', '[2390, 2390, -5*w^3 + 15*w^2 + 9*w - 18]', '[2392, 598, -w^3 + 5*w + 9]', '[2392, 2392, -2*w^3 + 8*w^2 + w - 12]', '[2393, 2393, 2*w^3 - 3*w^2 - 12*w + 7]', '[2395, 2395, -6*w^3 + 14*w^2 + 16*w - 25]', '[2395, 2395, w^3 - 5*w^2 + 4*w + 11]', '[2399, 2399, -2*w^3 + 5*w^2 + 10*w - 5]', '[2399, 2399, -2*w^3 + 7*w^2 + 7*w - 9]', '[2401, 7, 7]', '[2401, 49, -w^3 + 6*w^2 - 4*w - 21]', '[2401, 49, -4*w^3 + 10*w^2 + 9*w - 23]', '[2402, 2402, w^3 - w^2 - 9*w - 2]', '[2404, 2404, -2*w^3 + 6*w^2 - 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35]', '[5485, 5485, 2*w^3 - w^2 - 14*w - 3]', '[5486, 5486, w^3 + 2*w^2 - 4*w - 10]', '[5486, 5486, -2*w^3 + 7*w^2 + 7*w - 18]', '[5494, 5494, -w^3 + 7*w^2 - 11*w - 6]', '[5497, 5497, 3*w^3 - 9*w^2 - 10*w + 11]', '[5497, 5497, -w^3 - 3*w^2 + 12*w + 15]', '[5498, 5498, 4*w^3 - 17*w^2 + 10*w + 14]', '[5503, 5503, -4*w^3 + 12*w^2 + 7*w - 23]', '[5503, 5503, 3*w^3 - 3*w^2 - 14*w - 11]', '[5503, 5503, 4*w^3 - 10*w^2 - 6*w + 1]', '[5503, 5503, -6*w^3 + 24*w^2 - 10*w - 21]', '[5507, 5507, 3*w^3 - 12*w^2 - 6*w + 29]', '[5507, 5507, 2*w^3 - 11*w^2 + 8*w + 19]', '[5508, 204, 3*w^3 - 9*w^2 - 3*w]', '[5513, 5513, -3*w^2 + 11]', '[5521, 5521, 6*w^2 - 12*w - 19]', '[5525, 1105, w^3 - 7*w^2 + 9*w + 15]', '[5525, 1105, w^3 - 7*w^2 + 6*w + 23]', '[5525, 5525, 2*w^3 - 4*w^2 - 4*w - 7]', '[5525, 5525, 9*w^3 - 23*w^2 - 28*w + 43]', '[5527, 5527, -3*w^3 + 5*w^2 + 11*w - 9]', '[5531, 5531, -w^3 + 5*w^2 - 6*w - 11]', '[5537, 791, 2*w^3 - 8*w^2 - 6*w + 19]', '[5537, 791, -5*w^3 + 18*w^2 + 10*w - 41]', '[5542, 5542, 7*w^3 - 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4]', '[10000, 2000, -4*w^3 + 11*w^2 + w - 4]', '[10000, 10000, -2*w^3 + 6*w^2 - w - 12]', '[10000, 10000, 6*w^3 - 17*w^2 - 11*w + 12]'], 'label': '4.4.17417.1', 'narrow_class_no': 2, 'primes': ['[2, 2, w^3 - 3*w^2 - w + 2]', '[5, 5, w^2 - 2*w - 3]', '[5, 5, w^3 - 3*w^2 - 3*w + 5]', '[8, 2, w^3 - 2*w^2 - 3*w + 3]', '[13, 13, -w^2 + w + 3]', '[17, 17, -w^2 + 3*w + 1]', '[23, 23, w^2 - 3]', '[25, 5, -w^2 + 2*w + 1]', '[37, 37, w^3 - 4*w^2 - 2*w + 9]', '[41, 41, w^2 - w - 5]', '[49, 7, -w^3 + 2*w^2 + 2*w - 1]', '[49, 7, w^2 + w - 3]', '[59, 59, w^3 - 3*w^2 - 4*w + 5]', '[67, 67, -w^3 + 3*w^2 + w - 5]', '[71, 71, 2*w - 3]', '[71, 71, w^3 - 4*w^2 + 2*w + 5]', '[79, 79, -w^3 + 5*w^2 - 4*w - 5]', '[79, 79, -2*w^3 + 7*w^2 + 5*w - 15]', '[81, 3, -3]', '[83, 83, -2*w^3 + 6*w^2 + 2*w - 5]', '[97, 97, w^3 - w^2 - 7*w - 3]', '[101, 101, -w^3 + 3*w^2 + 3*w - 3]', '[107, 107, -w^3 + 4*w^2 - 7]', '[113, 113, w^3 - 3*w^2 - 5*w + 3]', '[121, 11, -w^3 + 3*w^2 + 4*w - 3]', '[121, 11, 2*w^3 - 6*w^2 - 3*w + 5]', '[127, 127, -2*w^3 + 6*w^2 + 5*w - 9]', '[137, 137, -w^3 + 5*w^2 + 3*w - 9]', '[139, 139, w^3 - w^2 - 4*w + 1]', '[149, 149, w^3 - 3*w^2 - w + 9]', '[157, 157, w^2 - 4*w + 1]', '[163, 163, -3*w^3 + 7*w^2 + 9*w - 13]', '[163, 163, w^3 - 3*w^2 - w + 7]', '[179, 179, -2*w^3 + 3*w^2 + 5*w - 5]', '[179, 179, -2*w^3 + 4*w^2 + 5*w - 9]', '[181, 181, -w^2 + 3*w - 3]', '[181, 181, 2*w^3 - 4*w^2 - 8*w + 5]', '[191, 191, 2*w - 5]', '[193, 193, -2*w^3 + 4*w^2 + 7*w + 3]', '[193, 193, -2*w^3 + 5*w^2 + 5*w - 7]', '[197, 197, -w^3 + 4*w^2 - 11]', '[199, 199, -2*w^3 + 8*w^2 + 6*w - 15]', '[211, 211, -2*w^3 + 3*w^2 + 6*w - 5]', '[211, 211, -4*w^3 + 10*w^2 + 12*w - 19]', '[229, 229, w^3 - 3*w^2 - 4*w + 9]', '[229, 229, w^2 - 5]', '[233, 233, w^2 - 2*w - 7]', '[239, 239, -3*w^3 + 10*w^2 + 2*w - 9]', '[239, 239, -2*w^3 + 5*w^2 + 5*w - 5]', '[257, 257, -2*w^3 + 5*w^2 + 4*w - 9]', '[263, 263, w^3 - 2*w^2 - 4*w - 3]', '[263, 263, w^3 - 6*w - 7]', '[269, 269, w^3 - 3*w^2 - w - 1]', '[269, 269, w - 5]', '[281, 281, -2*w + 7]', '[293, 293, 2*w^2 - w - 7]', '[293, 293, -2*w^3 + 6*w^2 + 6*w - 9]', '[307, 307, -2*w^3 + 5*w^2 + 4*w - 11]', '[311, 311, -w^3 + 3*w^2 + 2*w - 9]', '[317, 317, 4*w^3 - 15*w^2 + 3*w + 15]', '[317, 317, w^3 - 4*w^2 - 4*w + 9]', '[331, 331, -w^3 + 4*w^2 + 2*w - 11]', '[331, 331, 2*w^3 - 7*w^2 - 5*w + 13]', '[337, 337, 2*w^3 - 4*w^2 - 8*w - 1]', '[347, 347, -2*w^3 + 7*w^2 + 9*w - 9]', '[349, 349, -w^3 + 5*w^2 - 2*w - 11]', '[349, 349, 4*w^3 - 9*w^2 - 14*w + 13]', '[353, 353, -3*w^3 + 7*w^2 + 9*w - 11]', '[367, 367, 3*w^3 - 5*w^2 - 11*w + 5]', '[367, 367, -w^3 + 3*w^2 + 5*w - 1]', '[373, 373, w^3 - 2*w^2 - 6*w + 1]', '[379, 379, 2*w^3 - 5*w^2 - 7*w + 5]', '[383, 383, 2*w^3 - 3*w^2 - 11*w - 1]', '[383, 383, -2*w^3 + 5*w^2 + 3*w - 13]', '[397, 397, -2*w^3 + 4*w^2 + 7*w - 7]', '[397, 397, 2*w^3 - 3*w^2 - 8*w - 5]', '[409, 409, w^3 - 3*w^2 + w - 1]', '[419, 419, -4*w^3 + 14*w^2 - w - 13]', '[421, 421, -3*w^2 + 2*w + 9]', '[421, 421, 2*w^2 - 6*w - 3]', '[431, 431, -2*w^3 + 4*w^2 + 9*w - 7]', '[431, 431, -2*w^3 + 6*w^2 + 3*w - 15]', '[431, 431, -3*w^3 + 6*w^2 + 10*w - 9]', '[431, 431, -3*w^3 + 11*w^2 + 10*w - 19]', '[443, 443, 3*w^3 - 6*w^2 - 8*w + 13]', '[443, 443, -2*w^3 + 5*w^2 + 4*w - 5]', '[443, 443, -2*w^3 + 5*w^2 + 6*w - 3]', '[443, 443, 5*w^3 - 12*w^2 - 16*w + 19]', '[461, 461, w^3 - 2*w^2 + 7]', '[461, 461, -3*w^2 + w + 7]', '[479, 479, w^2 + w - 5]', '[487, 487, 2*w^2 - 4*w + 1]', '[487, 487, 2*w^3 - 8*w^2 + 4*w + 7]', '[491, 491, -3*w^3 + 7*w^2 + 7*w - 1]', '[509, 509, -2*w^3 + 9*w^2 + 5*w - 19]', '[509, 509, -3*w^3 + 6*w^2 + 10*w + 1]', '[521, 521, w^3 - 2*w^2 - 6*w + 3]', '[521, 521, 3*w - 5]', '[523, 523, -w^3 + 5*w^2 + 4*w - 7]', '[523, 523, -2*w^3 + 4*w^2 + 6*w - 1]', '[523, 523, w^2 - 7]', '[523, 523, -2*w^3 + 8*w^2 + 8*w - 13]', '[541, 541, -w^3 + 5*w^2 - w - 13]', '[547, 547, -2*w^3 + 7*w^2 + 3*w - 11]', '[547, 547, -w^3 + 4*w^2 + 2*w - 13]', '[547, 547, -2*w^3 + 2*w^2 + 6*w - 1]', '[547, 547, -w^3 + 6*w^2 - 6*w - 7]', '[563, 563, 2*w^2 - 5*w - 1]', '[563, 563, w^2 - 2*w + 3]', '[569, 569, -2*w - 5]', '[571, 571, -2*w^3 + 6*w^2 + 3*w - 11]', '[577, 577, -w^3 + 3*w^2 - 7]', '[593, 593, w^3 - w^2 - 5*w + 3]', '[601, 601, 2*w^3 - 6*w^2 - 4*w + 5]', '[607, 607, -6*w^2 + 15*w + 13]', '[607, 607, -w^3 + 4*w^2 - 2*w - 7]', '[613, 613, -2*w^3 + 6*w^2 + 2*w - 9]', '[617, 617, -3*w^3 + 9*w^2 + 5*w - 9]', '[617, 617, 3*w^3 - 6*w^2 - 12*w + 7]', '[619, 619, -2*w^3 + 8*w^2 + 7*w - 13]', '[619, 619, 2*w^3 - 4*w^2 - 5*w + 1]', '[641, 641, 2*w^3 - w^2 - 6*w + 1]', '[641, 641, -2*w^3 + 4*w^2 + 8*w - 7]', '[641, 641, -2*w^3 + 7*w^2 + 4*w - 13]', '[641, 641, -2*w^3 + 3*w^2 + 7*w - 1]', '[647, 647, -2*w^3 + 7*w^2 + 8*w - 11]', '[647, 647, -2*w^3 + 4*w^2 + 6*w - 3]', '[653, 653, -4*w^2 + 3*w + 13]', '[653, 653, 3*w^3 - 7*w^2 - 11*w + 7]', '[659, 659, -5*w^3 + 14*w^2 + 16*w - 25]', '[659, 659, -4*w^3 + 13*w^2 + 11*w - 25]', '[673, 673, 2*w^3 - 7*w^2 - 6*w + 15]', '[677, 677, 3*w^3 - 8*w^2 - 6*w + 11]', '[677, 677, w^3 - 5*w^2 + 2*w + 9]', '[683, 683, 2*w^2 - 5*w - 9]', '[683, 683, w^3 - w^2 - 4*w - 7]', '[709, 709, -2*w^3 + 6*w^2 + 4*w - 3]', '[733, 733, -2*w^3 + 5*w^2 + 3*w + 1]', '[733, 733, 2*w^3 - 2*w^2 - 9*w - 1]', '[739, 739, -w - 5]', '[751, 751, 3*w^3 - 7*w^2 - 7*w + 11]', '[757, 757, -2*w^3 + 3*w^2 + 8*w - 3]', '[757, 757, 2*w^3 - 3*w^2 - 12*w - 3]', '[761, 761, -3*w^3 + 7*w^2 + 12*w - 11]', '[761, 761, -3*w^3 + 9*w^2 + 6*w - 11]', '[787, 787, -3*w^3 + 5*w^2 + 12*w + 3]', '[787, 787, w^2 - w - 9]', '[797, 797, -3*w^3 + 7*w^2 + 6*w - 17]', '[827, 827, -2*w^3 + 4*w^2 + 9*w - 11]', '[827, 827, -6*w^3 + 17*w^2 + 19*w - 29]', '[853, 853, -3*w^3 + 10*w^2 + 6*w - 21]', '[857, 857, 3*w^3 - 12*w^2 + 4*w + 9]', '[857, 857, -3*w^3 + 9*w^2 + 4*w - 13]', '[863, 863, -3*w^3 + 10*w^2 + 4*w - 15]', '[863, 863, -4*w^2 + w + 11]', '[877, 877, -2*w^3 + 4*w^2 + 8*w - 9]', '[881, 881, -2*w^3 + 4*w^2 + 5*w - 3]', '[907, 907, -w^3 + 5*w^2 - 2*w - 15]', '[907, 907, -2*w^3 + 6*w^2 + 7*w - 15]', '[929, 929, -w^2 + 11]', '[929, 929, -2*w^3 + 6*w^2 + 3*w - 13]', '[937, 937, -3*w^3 + 7*w^2 + 8*w - 3]', '[941, 941, w^3 + w^2 - 8*w - 5]', '[953, 953, 4*w^2 - 8*w - 13]', '[953, 953, w^3 - 4*w^2 - 4*w + 3]', '[967, 967, 3*w^2 - 5*w - 9]', '[971, 971, 3*w^2 - 4*w - 7]', '[971, 971, w^3 - 5*w^2 - 4*w + 11]', '[977, 977, -3*w^3 + 11*w^2 + 6*w - 25]', '[983, 983, -2*w^3 + 8*w^2 + 3*w - 21]', '[991, 991, 2*w^3 - 4*w^2 - 10*w + 3]', '[991, 991, 2*w^3 - 8*w^2 - 3*w + 19]', '[997, 997, -4*w^3 + 10*w^2 + 11*w - 21]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [4, 3, -5, -2, 1], 'conductor': 0, 'degree': 4, 'dirichlet_group': [], 'disc_abs': 17417, 'disc_rad': 17417, 'disc_sign': 1, 'frobs': [[2, [[3, 1], [1, 1]]], [3, [[4, 1]]], [5, [[2, 1], [1, 2]]], [7, [[2, 2]]], [11, [[2, 2]]], [13, [[3, 1], [1, 1]]], [17, [[3, 1], [1, 1]]], [19, [[4, 1]]], [23, [[3, 1], [1, 1]]], [29, [[4, 1]]], [31, [[4, 1]]], [37, [[3, 1], [1, 1]]], [41, [[3, 1], [1, 1]]], [43, [[4, 1]]], [47, [[2, 2]]], [53, [[4, 1]]], [59, [[3, 1], [1, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [12], 'galois_label': '4T5', 'galt': 5, 'grd': 131.97348218486925, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '4.4.17417.1', 'local_algs': ['m17417.1.1.0', 'm17417.1.1.0', 'm17417.2.1.1'], 'monogenic': 1, 'num_ram': 1, 'r2': 0, 'ramps': [17417], 'rd': 11.4879711953, 'regulator': {'__RealLiteral__': 0, 'data': '11.0297540098', 'prec': 44}, 'res': {'gal': ['-7104857,541230878,970568429,-2529129614,-3248450651,4658507748,3705206704,-4450013504,-1889348486,2378106518,425977719,-730948894,-20282386,131905418,-8670071,-14084634,1763909,882278,-146011,-31254,6114,568,-126,-4,1'], 'sib': ['-200,-3648,-3906,8031,6075,-4527,-3090,870,617,-51,-47,0,1', '-33187,473874,-193653,-508960,129297,140458,-30849,-13094,2537,480,-85,-6,1', '-9,0,26,0,-13,0,1', '1077004,427217,-408720,-36738,17730,764,-250,-4,1', '567,1527,929,-65,-87,-3,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a + 1 \\)', '\\( a - 1 \\)', '\\( 2 a^{3} - 6 a^{2} - 6 a + 11 \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3']}