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hmf_forms • Show schema
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{'deg': 3, 'dimension': 5, 'disc': 1849, 'field_bad_primes': [43], 'field_label': '3.3.1849.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.1849.1-8.9-b', 'label_nsuffix': 1, 'label_suffix': 'b', 'level_bad_primes': [2], 'level_ideal': '[8,8,w^2 - 2*w - 11]', 'level_label': '8.9', 'level_norm': 8, 'parallel_weight': 2, 'short_label': '8.9-b', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[2,2,w + 3]', 1]], 'hecke_eigenvalues': ['e', '-e^2 + 2', 0, 'e^3 - 3*e', '2*e^4 + e^3 - 9*e^2 - 5*e + 5', '-e^4 - e^3 + 5*e^2 + 5*e - 4', '-2*e^3 + 2*e^2 + 8*e - 2', '-3*e^4 - 3*e^3 + 14*e^2 + 7*e - 9', '3*e^4 + e^3 - 16*e^2 - 7*e + 11', '-e^4 - e^3 + 4*e^2 + 5*e - 3', '-2*e^4 + 10*e^2 - 2*e - 8', '-e^4 + 3*e^3 + 2*e^2 - 11*e + 5', '-e^4 - e^3 + 2*e^2 + 5*e - 1', '-5*e^4 - 3*e^3 + 22*e^2 + 11*e - 11', 'e^4 - 2*e^2 - 9', '3*e^4 - 2*e^3 - 11*e^2 + 4*e - 4', '-4*e^4 - 4*e^3 + 17*e^2 + 10*e - 9', 'e^4 - e^3 - 4*e^2 + e + 3', '-5*e^4 - e^3 + 24*e^2 + 5*e - 19', '-3*e^4 + e^3 + 14*e^2 - 3*e - 9', '4*e^4 + 2*e^3 - 17*e^2 - 4*e + 3', 'e^4 - 8*e^2 + 4*e + 11', '-e^4 - 2*e^3 + 5*e^2 + 4*e - 12', '6*e^4 + 2*e^3 - 32*e^2 - 6*e + 20', '-8*e^3 + 28*e', '2*e^4 + 4*e^3 - 10*e^2 - 14*e - 2', 'e^4 + 5*e^3 - 4*e^2 - 21*e + 7', '-e^4 - 2*e^3 + 3*e^2 + 4*e - 8', '2*e^4 + 4*e^3 - 5*e^2 - 14*e - 1', '-e^4 + 4*e^3 + 6*e^2 - 16*e - 9', '6*e^4 + 3*e^3 - 24*e^2 - 7*e + 4', '-e^4 + 5*e^3 + 5*e^2 - 19*e + 2', 'e^3 + e^2 + e - 7', '3*e^4 + 7*e^3 - 9*e^2 - 25*e + 6', '-7*e^3 + 23*e + 4', '-2*e^4 + e^3 + 7*e^2 - e - 3', '-4*e^4 + 3*e^3 + 14*e^2 - 15*e - 4', '-7*e^4 - 9*e^3 + 29*e^2 + 31*e - 18', '2*e^4 - e^3 - 13*e^2 + 7*e + 13', '-5*e^4 - 3*e^3 + 22*e^2 + 19*e - 11', '5*e^4 + 3*e^3 - 22*e^2 - 9*e + 9', 'e^4 - e^3 - 2*e^2 + e - 7', '5*e^4 - 25*e^2 - 6*e + 20', '-3*e^4 + 18*e^2 + 6*e - 25', '6*e^4 + 2*e^3 - 27*e^2 - 12*e + 15', '6*e^4 + 4*e^3 - 28*e^2 - 12*e + 6', '-4*e^4 + 2*e^3 + 18*e^2 - 6*e - 12', '-4*e^4 + 14*e^2 - 4*e + 6', '4*e^4 + 3*e^3 - 16*e^2 - 5*e + 14', '-6*e^4 - e^3 + 37*e^2 + e - 27', '3*e^4 + 3*e^3 - 21*e^2 - 11*e + 18', '3*e^4 + 5*e^3 - 16*e^2 - 15*e + 11', '-e^4 + 5*e^3 + 2*e^2 - 19*e + 13', '3*e^4 + 3*e^3 - 14*e^2 - 9*e - 1', '5*e^4 + 12*e^3 - 21*e^2 - 34*e + 10', '-9*e^4 - 4*e^3 + 40*e^2 + 16*e - 19', '-6*e^4 + 2*e^3 + 23*e^2 - 10*e - 1', '-2*e^4 - 5*e^3 + 11*e^2 + 19*e - 1', '-2*e^4 - 5*e^3 + 12*e^2 + 25*e - 14', '-e^4 + 5*e^3 + e^2 - 11*e + 12', '-3*e^4 - 2*e^3 + 8*e^2 + 6*e - 9', '4*e^3 + 7*e^2 - 8*e - 31', '3*e^4 - 2*e^3 - 5*e^2 + 8*e - 20', '4*e^4 - e^3 - 6*e^2 + 9*e - 18', 'e^4 + 9*e^3 - 3*e^2 - 35*e + 6', '-6*e^4 - e^3 + 25*e^2 - 5*e - 15', '6*e^4 + 4*e^3 - 30*e^2 + 2*e + 22', '-6*e^4 - 3*e^3 + 26*e^2 - e - 18', '3*e^4 + e^3 - 3*e^2 + e - 12', '-7*e^3 - e^2 + 21*e + 3', '6*e^4 + 3*e^3 - 27*e^2 - 13*e + 7', '-7*e^4 + 9*e^3 + 35*e^2 - 35*e - 30', '-9*e^3 - 10*e^2 + 29*e + 16', '3*e^4 - e^3 - 21*e^2 + 3*e + 14', '2*e^4 + 5*e^3 - 9*e^2 - 13*e + 21', '-12*e^4 - 11*e^3 + 56*e^2 + 47*e - 28', '-4*e^4 - 9*e^3 + 24*e^2 + 23*e - 24', '11*e^4 + 11*e^3 - 55*e^2 - 37*e + 28', '-4*e^4 - e^3 + 17*e^2 - e - 13', '6*e^3 + 9*e^2 - 20*e - 21', 'e^4 + 4*e^3 - 9*e^2 - 26*e + 20', '5*e^4 + 2*e^3 - 20*e^2 - 14*e + 9', '8*e^4 - 2*e^3 - 34*e^2 - 2*e - 6', '-2*e^4 + 2*e^3 + 6*e^2 + 2*e + 16', '-8*e^4 - 10*e^3 + 36*e^2 + 42*e - 16', '4*e^4 + 3*e^3 - 13*e^2 - 5*e - 7', '2*e^4 + 15*e^3 - 18*e^2 - 65*e + 16', '-7*e^4 - 13*e^3 + 29*e^2 + 51*e - 18', '6*e^4 - 2*e^3 - 40*e^2 + 12*e + 48', '4*e^4 + 12*e^3 - 22*e^2 - 36*e + 24', '-14*e^4 - 12*e^3 + 64*e^2 + 32*e - 28', '-8*e^4 - 4*e^3 + 33*e^2 + 6*e - 29', 'e^4 - 2*e^3 + 5*e^2 + 4*e - 22', '5*e^4 + 4*e^3 - 14*e^2 - 8*e + 5', '8*e^4 + 8*e^3 - 33*e^2 - 26*e + 3', '3*e^4 - 2*e^3 - 9*e^2 + 8*e - 8', '-7*e^4 - 6*e^3 + 38*e^2 + 34*e - 33', '7*e^3 + e^2 - 29*e + 7', '5*e^4 - 5*e^3 - 31*e^2 + 25*e + 32', '7*e^3 + 4*e^2 - 15*e - 10', 'e^4 - 3*e^2 + 6*e - 24', '4*e^4 - 2*e^3 - 17*e^2 + 6*e + 13', '7*e^4 + 6*e^3 - 30*e^2 - 30*e + 1', '10*e^4 - 40*e^2 + 12*e + 18', '10*e^4 - 42*e^2 + 4*e + 20', '-4*e^4 - 12*e^3 + 18*e^2 + 48*e - 2', '12*e^4 + e^3 - 50*e^2 + 9*e + 20', '-16*e^4 - 3*e^3 + 71*e^2 + 15*e - 19', '-7*e^4 - 13*e^3 + 31*e^2 + 37*e - 6', '4*e^4 + 9*e^3 - 9*e^2 - 27*e - 11', '-8*e^4 - 15*e^3 + 40*e^2 + 55*e - 12', '5*e^4 - 5*e^3 - 19*e^2 + 27*e + 14', '-5*e^4 - 5*e^3 + 23*e^2 + 23*e - 16', '16*e^4 + 11*e^3 - 77*e^2 - 31*e + 39', '-6*e^4 + 3*e^3 + 20*e^2 - 23*e - 2', '9*e^4 + 5*e^3 - 37*e^2 - 15*e + 16', 'e^3 + 3*e^2 - 7*e - 27', '-6*e^4 + 7*e^3 + 36*e^2 - 25*e - 40', '5*e^4 + 5*e^3 - 23*e^2 - 33*e + 6', '6*e^4 - 5*e^3 - 22*e^2 + 21*e + 2', '8*e^4 + 7*e^3 - 33*e^2 - 21*e + 33', '8*e^4 + 10*e^3 - 27*e^2 - 40*e + 3', '-e^4 - 3*e^2 + 2*e + 6', '-9*e^4 - 14*e^3 + 42*e^2 + 58*e - 21', '4*e^4 + 12*e^3 - 17*e^2 - 30*e + 13', '-17*e^4 - 20*e^3 + 75*e^2 + 72*e - 36', '-3*e^4 + 8*e^3 + 4*e^2 - 32*e + 29', '-13*e^4 - 2*e^3 + 61*e^2 + 20*e - 40', '3*e^4 - 10*e^3 - 8*e^2 + 34*e + 1', '14*e^4 + 14*e^3 - 65*e^2 - 40*e + 15', '-7*e^3 + 19*e^2 + 31*e - 29', '-e^4 + 13*e^3 + 13*e^2 - 35*e - 18', '-12*e^4 - 15*e^3 + 46*e^2 + 51*e - 14', '-20*e^4 - 12*e^3 + 86*e^2 + 44*e - 40', '-16*e^4 - 8*e^3 + 58*e^2 + 22*e - 18', '-6*e^4 - 16*e^3 + 14*e^2 + 56*e + 10', '-4*e^4 - 6*e^3 + 5*e^2 + 16*e + 33', '-15*e^4 - 8*e^3 + 65*e^2 + 18*e - 34', '7*e^4 + 8*e^3 - 36*e^2 - 30*e + 3', 'e^4 + 8*e^3 - 16*e^2 - 42*e + 47', '15*e^4 - 6*e^3 - 75*e^2 + 22*e + 64', '4*e^4 - 8*e^3 - 23*e^2 + 12*e + 13', '-8*e^4 + 45*e^2 + 2*e - 13', '-13*e^4 + 2*e^3 + 58*e^2 - 6*e - 29', '-5*e^4 - 10*e^3 + 29*e^2 + 56*e - 24', '7*e^4 + 15*e^3 - 33*e^2 - 45*e + 22', '-8*e^4 + 5*e^3 + 47*e^2 - 19*e - 57', '2*e^4 + 15*e^3 - 4*e^2 - 45*e - 6', '13*e^4 + 11*e^3 - 61*e^2 - 49*e + 22', '-2*e^4 - 3*e^3 - 8*e^2 + 7*e + 32', '-9*e^3 + 3*e^2 + 43*e + 3', '9*e^4 - 3*e^3 - 46*e^2 + 15*e + 33', '-3*e^4 - 11*e^3 + 18*e^2 + 43*e - 1', '-7*e^4 + 7*e^3 + 42*e^2 - 23*e - 37', '4*e^4 + 5*e^3 - 5*e^2 - 25*e - 13', '-8*e^4 - 7*e^3 + 26*e^2 + 33*e + 2', '-5*e^4 + e^3 + 23*e^2 + 7*e + 20', '-19*e^4 - 4*e^3 + 88*e^2 + 22*e - 51', '18*e^4 + 6*e^3 - 67*e^2 - 22*e + 7', '-e^4 + 2*e^3 + e^2 - 22*e - 6', '-17*e^4 - 22*e^3 + 72*e^2 + 62*e - 23', '13*e^4 + 4*e^3 - 59*e^2 + 2*e + 50', '16*e^4 + 6*e^3 - 69*e^2 - 24*e + 45', '12*e^4 - 3*e^3 - 43*e^2 + 21*e + 13', '19*e^4 + 11*e^3 - 97*e^2 - 33*e + 48', '2*e^4 + 9*e^3 - 26*e^2 - 41*e + 50', '6*e^4 + 4*e^3 - 39*e^2 - 14*e + 25', '5*e^4 - 2*e^3 - 24*e^2 - 14*e + 7', '15*e^4 + 18*e^3 - 69*e^2 - 68*e + 46', '-13*e^4 - 5*e^3 + 59*e^2 + 7*e - 18', '-12*e^4 - 7*e^3 + 48*e^2 + 45*e - 6', '-10*e^4 - 5*e^3 + 35*e^2 + 23*e + 11'], 'hecke_polynomial': 'x^5 + x^4 - 5*x^3 - 4*x^2 + 4*x + 1', 'label': '3.3.1849.1-8.9-b'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 1849, 'ideals': ['[1, 1, 1]', '[2, 2, -1/2*w^2 + 1/2*w + 8]', '[2, 2, 1/2*w^2 - 3/2*w - 1]', '[2, 2, w + 3]', '[4, 2, w^2 - 4*w - 2]', '[4, 2, -3/2*w^2 + 5/2*w + 20]', '[4, 2, 1/2*w^2 + 3/2*w + 1]', '[4, 4, -1/2*w^2 + 1/2*w + 6]', '[4, 4, w + 1]', '[4, 4, -1/2*w^2 + 3/2*w + 3]', '[8, 2, 2]', '[8, 4, -w]', '[8, 4, -1/2*w^2 + 3/2*w + 2]', '[8, 4, -1/2*w^2 + 1/2*w + 5]', '[8, 4, w + 2]', '[8, 4, -1/2*w^2 + 3/2*w + 4]', '[8, 4, -1/2*w^2 + 1/2*w + 7]', '[8, 8, -1/2*w^2 + 5/2*w + 2]', '[8, 8, -w^2 + 2*w + 11]', '[8, 8, -1/2*w^2 - 1/2*w + 3]', '[11, 11, -w^2 + 3*w + 7]', '[11, 11, -2*w - 1]', '[11, 11, -w^2 + w + 11]', '[16, 4, -w^2 + w + 16]', '[16, 4, -w^2 + 2*w + 12]', '[16, 4, w^2 - 3*w - 2]', '[16, 4, -1/2*w^2 - 1/2*w + 2]', '[16, 4, 1/2*w^2 - 5/2*w - 1]', '[16, 4, 2*w + 6]', '[16, 8, 1/2*w^2 + 5/2*w + 2]', '[16, 8, -1/2*w^2 + 3/2*w + 8]', '[16, 8, -3/2*w^2 + 11/2*w + 5]', '[16, 8, -1/2*w^2 + 1/2*w + 1]', '[16, 8, -w + 4]', '[16, 8, -2*w^2 + 3*w + 26]', '[16, 16, -3/2*w^2 + 11/2*w + 6]', '[16, 16, -2*w^2 + 3*w + 25]', '[16, 16, -1/2*w^2 - 5/2*w - 1]', '[22, 22, -w^2 + 2*w + 13]', '[22, 22, -1/2*w^2 + 3/2*w + 5]', '[22, 22, 1/2*w^2 - 5/2*w]', '[22, 22, 1/2*w^2 - 1/2*w]', '[22, 22, -1/2*w^2 - 1/2*w + 1]', '[22, 22, -1/2*w^2 + 3/2*w + 9]', '[22, 22, -1/2*w^2 + 1/2*w + 4]', '[22, 22, -w + 5]', '[22, 22, -w + 1]', '[27, 3, 3]', '[32, 4, 2*w^2 - 8*w - 4]', '[32, 4, -3*w^2 + 5*w + 40]', '[32, 4, w^2 + 3*w + 2]', '[32, 8, -w^2 + 8]', '[32, 8, -3/2*w^2 + 5/2*w + 18]', '[32, 8, -3/2*w^2 + 7/2*w + 15]', '[32, 8, -w^2 + w + 12]', '[32, 8, 2*w + 2]', '[32, 8, -w^2 + 4*w + 4]', '[32, 8, -w^2 + 3*w + 6]', '[32, 8, 1/2*w^2 - 7/2*w - 2]', '[32, 8, -1/2*w^2 - 3/2*w + 1]', '[32, 16, w + 4]', '[32, 16, -1/2*w^2 + 3/2*w + 6]', '[32, 16, -1/2*w^2 + 1/2*w + 3]', '[32, 16, 1/2*w^2 - 3/2*w]', '[32, 16, -1/2*w^2 + 1/2*w + 9]', '[32, 16, -w + 2]', '[32, 32, -1/2*w^2 + 3/2*w + 7]', '[32, 32, -1/2*w^2 + 1/2*w + 2]', '[32, 32, -w + 3]', '[41, 41, 2*w + 5]', '[41, 41, -w^2 + 3*w + 3]', '[41, 41, -w^2 + w + 15]', '[43, 43, -3*w^2 + 11*w + 11]', '[44, 22, -w^2 - 2*w + 2]', '[44, 22, 3/2*w^2 - 13/2*w - 4]', '[44, 22, -1/2*w^2 + 5/2*w + 3]', '[44, 22, -w^2 + 2*w + 10]', '[44, 22, -1/2*w^2 + 5/2*w + 11]', '[44, 22, -1/2*w^2 - 1/2*w + 4]', '[44, 22, -w^2 + 2*w + 2]', '[44, 22, -5/2*w^2 + 9/2*w + 31]', '[44, 22, -1/2*w^2 - 1/2*w + 12]', '[44, 44, w^2 - 4*w - 1]', '[44, 44, -3/2*w^2 + 13/2*w + 5]', '[44, 44, -3/2*w^2 + 5/2*w + 21]', '[44, 44, -5/2*w^2 + 9/2*w + 30]', '[44, 44, -w^2 + 2*w + 15]', '[44, 44, -w^2 - 2*w + 3]', '[44, 44, 1/2*w^2 + 3/2*w + 2]', '[44, 44, 1/2*w^2 - 5/2*w + 2]', '[44, 44, 1/2*w^2 + 1/2*w + 1]', '[47, 47, -w^2 - w + 5]', '[47, 47, w^2 - 5*w - 3]', '[47, 47, -2*w^2 + 4*w + 23]', '[54, 6, -3/2*w^2 + 3/2*w + 24]', '[54, 6, 3/2*w^2 - 9/2*w - 3]', '[54, 6, 3*w + 9]', '[59, 59, -w^2 + w + 13]', '[59, 59, w^2 - 3*w - 5]', '[59, 59, -2*w - 3]', '[64, 4, 4]', '[64, 8, -2*w]', '[64, 8, -w^2 - 2*w]', '[64, 8, 3/2*w^2 - 13/2*w - 2]', '[64, 8, -5/2*w^2 + 9/2*w + 33]', '[64, 8, -w^2 + 3*w + 4]', '[64, 8, -w^2 + w + 10]', '[64, 8, 2*w + 4]', '[64, 8, -w^2 + 3*w + 8]', '[64, 8, -w^2 + w + 14]', '[64, 16, 5/2*w^2 - 19/2*w - 6]', '[64, 16, -7/2*w^2 + 11/2*w + 47]', '[64, 16, 1/2*w^2 - 7/2*w + 6]', '[64, 16, -3/2*w^2 + 7/2*w + 23]', '[64, 16, -w^2 + 5*w + 4]', '[64, 16, w^2]', '[64, 16, -2*w^2 + 4*w + 22]', '[64, 16, w^2 + 4*w + 4]', '[64, 16, -w^2 - w + 6]', '[64, 32, -3/2*w^2 - 7/2*w + 2]', '[64, 32, -4*w^2 + 7*w + 50]', '[64, 32, -2*w^2 + 3*w + 28]', '[64, 32, 5/2*w^2 - 21/2*w - 7]', '[64, 32, 1/2*w^2 + 5/2*w + 4]', '[64, 32, 3/2*w^2 - 11/2*w - 3]', '[64, 64, -w^2 + 9]', '[64, 64, -1/2*w^2 + 7/2*w + 3]', '[64, 64, -3/2*w^2 + 7/2*w + 14]', '[82, 82, w^2 - 2*w - 1]', '[82, 82, -w^2 - 2*w + 1]', '[82, 82, -3*w^2 + 4*w + 37]', '[82, 82, -5/2*w^2 + 9/2*w + 32]', '[82, 82, 1/2*w^2 + 9/2*w + 3]', '[82, 82, -5/2*w^2 + 17/2*w + 12]', '[82, 82, -1/2*w^2 - 1/2*w + 13]', '[82, 82, 3/2*w^2 - 13/2*w - 3]', '[82, 82, -1/2*w^2 + 5/2*w + 12]', '[86, 86, -1/2*w^2 + 5/2*w + 4]', '[86, 86, -1/2*w^2 - 1/2*w + 5]', '[86, 86, -w^2 + 2*w + 9]', '[88, 22, -2*w^2 + 6*w + 14]', '[88, 22, -4*w - 2]', '[88, 22, -2*w^2 + 2*w + 22]', '[88, 44, -4*w^2 + 7*w + 54]', '[88, 44, -1/2*w^2 - 5/2*w]', '[88, 44, 1/2*w^2 + 7/2*w + 5]', '[88, 44, -2*w^2 + 7*w + 6]', '[88, 44, -5/2*w^2 + 7/2*w + 34]', '[88, 44, 1/2*w^2 + 7/2*w + 3]', '[88, 44, -2*w^2 + 7*w + 8]', '[88, 44, -1/2*w^2 + 3/2*w + 10]', '[88, 44, -3/2*w^2 + 11/2*w + 7]', '[88, 44, -2*w^2 + 3*w + 24]', '[88, 44, 3*w + 8]', '[88, 44, 3/2*w^2 + 7/2*w + 2]', '[88, 44, -3/2*w^2 + 3/2*w + 23]', '[88, 44, -3/2*w^2 + 9/2*w + 4]', '[88, 44, 1/2*w^2 - 1/2*w + 1]', '[88, 44, -w + 6]', '[88, 44, -5/2*w^2 + 7/2*w + 32]', '[88, 44, 5/2*w^2 - 21/2*w - 3]', '[88, 88, w + 5]', '[88, 88, 1/2*w^2 - 7/2*w + 5]', '[88, 88, -w^2 + 1]', '[88, 88, -1/2*w^2 + 1/2*w + 10]', '[88, 88, -3/2*w^2 + 5/2*w + 17]', '[88, 88, 1/2*w^2 - 3/2*w + 1]', '[88, 88, -3/2*w^2 + 7/2*w + 22]', '[88, 88, -w^2 + 4*w + 5]', '[88, 88, -1/2*w^2 - 3/2*w + 2]', '[94, 94, -3/2*w^2 - 7/2*w - 1]', '[94, 94, -7/2*w^2 + 11/2*w + 44]', '[94, 94, -w^2 - 4*w - 1]', '[94, 94, -5/2*w^2 + 19/2*w + 9]', '[94, 94, -3/2*w^2 + 3/2*w + 16]', '[94, 94, -3*w - 1]', '[94, 94, -3/2*w^2 + 9/2*w + 11]', '[94, 94, 5/2*w^2 - 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7/2*w + 6]', '[1894, 1894, 7*w^2 - 26*w - 27]', '[1894, 1894, -w^2 - 4*w - 9]', '[1894, 1894, 2*w^2 - 15*w - 11]', '[1894, 1894, 9/2*w^2 - 1/2*w - 40]', '[1894, 1894, -5/2*w^2 + 19/2*w + 1]', '[1894, 1894, 13/2*w^2 - 31/2*w - 61]', '[1894, 1894, 5/2*w^2 + 23/2*w + 4]', '[1894, 1894, 19/2*w^2 - 29/2*w - 119]', '[1894, 1894, 7/2*w^2 - 11/2*w - 52]', '[1903, 1903, 2*w^2 - 2*w - 7]', '[1903, 1903, 2*w^2 - 6*w - 29]', '[1903, 1903, 11*w^2 - 41*w - 37]', '[1903, 1903, 3*w^2 + 7*w - 7]', '[1903, 1903, 8*w^2 - 14*w - 97]', '[1903, 1903, -4*w^2 - 18*w - 11]', '[1903, 1903, 4*w - 13]', '[1903, 1903, 5*w^2 - 21*w - 17]', '[1903, 1903, 15*w^2 - 23*w - 193]', '[1913, 1913, 18*w^2 - 30*w - 235]', '[1913, 1913, -12*w^2 + 48*w + 29]', '[1913, 1913, 6*w^2 + 18*w + 7]', '[1927, 1927, -6*w^2 + 10*w + 83]', '[1927, 1927, -4*w^2 + 10*w + 9]', '[1927, 1927, 4*w^2 - 16*w - 5]', '[1927, 1927, 3*w^2 - 15*w + 5]', '[1927, 1927, 2*w^2 + 6*w + 7]', '[1927, 1927, -3*w^2 - 3*w + 1]', '[1927, 1927, -w^2 + 9*w + 33]', '[1927, 1927, -6*w^2 + 12*w + 83]', '[1927, 1927, -3*w^2 + w + 55]', '[1931, 1931, -8*w - 21]', '[1931, 1931, 4*w^2 - 4*w - 61]', '[1931, 1931, 4*w^2 - 12*w - 11]', '[1933, 1933, 2*w^2 - 2*w - 13]', '[1933, 1933, 2*w^2 - 6*w - 23]', '[1933, 1933, 4*w - 7]', '[1934, 1934, 2*w^2 - 3*w - 11]', '[1934, 1934, 5*w^2 - 8*w - 59]', '[1934, 1934, 4*w^2 - 11*w - 29]', '[1934, 1934, 1/2*w^2 - 17/2*w - 8]', '[1934, 1934, 3/2*w^2 + 11/2*w - 3]', '[1934, 1934, 7/2*w^2 - 5/2*w - 39]', '[1934, 1934, 3/2*w^2 - 11/2*w - 20]', '[1934, 1934, 1/2*w^2 + 5/2*w - 13]', '[1934, 1934, 7/2*w^2 - 27/2*w - 16]', '[1936, 44, -3/2*w^2 - 1/2*w + 35]', '[1936, 44, w^2 - 7*w + 6]', '[1936, 44, w^2 + 11*w + 8]', '[1936, 44, 5*w^2 - 22*w - 4]', '[1936, 44, -17/2*w^2 + 31/2*w + 114]', '[1936, 44, 1/2*w^2 + 11/2*w + 15]', '[1936, 44, -3*w^2 + 7*w + 40]', '[1936, 44, -w^2 + 6*w + 28]', '[1936, 44, -7/2*w^2 - 13/2*w - 1]', '[1936, 44, 5/2*w^2 - 11/2*w - 2]', '[1936, 44, 3*w^2 - 10*w - 4]', '[1936, 44, -7*w^2 + 27*w + 24]', '[1936, 44, -3*w^2 - 11*w - 2]', '[1936, 44, -7/2*w^2 + 9/2*w + 54]', '[1936, 44, -7*w^2 + 9*w + 86]', '[1936, 44, -6*w^2 + 20*w + 30]', '[1936, 44, -10*w^2 + 16*w + 126]', '[1936, 44, -2*w^2 + 6]', '[1936, 88, -19/2*w^2 + 33/2*w + 122]', '[1936, 88, -7/2*w^2 + 5/2*w + 34]', '[1936, 88, -1/2*w^2 - 5/2*w + 14]', '[1936, 88, 1/2*w^2 - 17/2*w - 3]', '[1936, 88, 1/2*w^2 - 11/2*w + 4]', '[1936, 88, 5/2*w^2 + 9/2*w + 4]', '[1936, 88, -9/2*w^2 + 43/2*w + 16]', '[1936, 88, -3/2*w^2 + 11/2*w + 21]', '[1936, 88, -7/2*w^2 - 17/2*w + 1]', '[1936, 88, 7/2*w^2 - 31/2*w + 1]', '[1936, 88, -5/2*w^2 + 13/2*w + 29]', '[1936, 88, -6*w^2 + 11*w + 84]', '[1936, 88, -17/2*w^2 + 33/2*w + 97]', '[1936, 88, -2*w^2 + w + 12]', '[1936, 88, -4*w^2 - 5*w + 20]', '[1936, 88, -2*w^2 + 3*w + 10]', '[1936, 88, -4*w^2 + 11*w + 34]', '[1936, 88, 6*w^2 - 25*w - 14]', '[1936, 176, 1/2*w^2 + 15/2*w + 14]', '[1936, 176, -7/2*w^2 + 11/2*w + 38]', '[1936, 176, 3/2*w^2 - 7/2*w + 2]', '[1936, 176, -4*w^2 + 13*w + 13]', '[1936, 176, -w^2 + 25]', '[1936, 176, -w^2 - 4*w + 5]', '[1936, 176, -9/2*w^2 + 11/2*w + 63]', '[1936, 176, -5/2*w^2 + 19/2*w + 15]', '[1936, 176, -1/2*w^2 + 7/2*w + 19]', '[1936, 484, -3*w^2 - 5*w + 8]', '[1936, 484, -7*w^2 + 29*w + 22]', '[1936, 484, -5*w^2 + 6*w + 76]', '[1936, 484, -11/2*w^2 + 39/2*w + 19]', '[1936, 484, -3/2*w^2 - 3/2*w + 14]', '[1936, 484, -7*w^2 + 10*w + 92]', '[1936, 484, -11*w^2 + 19*w + 136]', '[1936, 484, -3*w^2 + 5*w + 6]', '[1936, 484, -7*w^2 + 13*w + 86]', '[1936, 484, -w^2 - 3*w + 32]', '[1936, 484, -3*w^2 + 6*w + 28]', '[1936, 484, -3/2*w^2 + 15/2*w + 11]', '[1936, 484, 1/2*w^2 + 17/2*w + 22]', '[1936, 484, 3/2*w^2 + 19/2*w + 10]', '[1936, 484, 9/2*w^2 - 29/2*w - 9]', '[1936, 484, -2*w^2 + 8*w + 38]', '[1936, 484, 4*w^2 - 18*w - 10]', '[1936, 484, -4*w^2 - 10*w + 6]', '[1936, 968, 3/2*w^2 - 19/2*w - 3]', '[1936, 968, 2*w^2 - 9*w + 4]', '[1936, 968, 3/2*w^2 + 5/2*w + 5]', '[1936, 968, -15/2*w^2 + 53/2*w + 34]', '[1936, 968, -6*w^2 + 17*w + 44]', '[1936, 968, -4*w^2 + 9*w + 44]', '[1936, 968, -4*w^2 + 7*w + 58]', '[1936, 968, -5/2*w^2 - 1/2*w + 16]', '[1936, 968, -3/2*w^2 + 19/2*w + 41]', '[1936, 968, 4*w^2 - 9*w - 6]', '[1936, 968, 3/2*w^2 + 7/2*w + 6]', '[1936, 968, -2*w^2 - 13*w - 6]', '[1936, 968, -5/2*w^2 - 1/2*w + 54]', '[1936, 968, -1/2*w^2 + 25/2*w + 9]', '[1936, 968, -19/2*w^2 + 27/2*w + 117]', '[1936, 968, -7/2*w^2 + 13/2*w + 52]', '[1936, 968, -11/2*w^2 + 9/2*w + 60]', '[1936, 968, 5/2*w^2 - 21/2*w + 1]', '[1936, 1936, 3/2*w^2 - 19/2*w + 10]', '[1936, 1936, -21/2*w^2 + 31/2*w + 131]', '[1936, 1936, -8*w^2 + 29*w + 33]', '[1936, 1936, -5/2*w^2 - 1/2*w + 3]', '[1936, 1936, -19/2*w^2 + 71/2*w + 30]', '[1936, 1936, -4*w^2 + 9*w + 57]', '[1936, 1936, -5/2*w^2 - 27/2*w - 6]', '[1936, 1936, -13*w^2 + 20*w + 169]', '[1936, 1936, 7/2*w^2 + 31/2*w + 11]', '[1951, 1951, 2*w^2 + 10*w + 3]', '[1951, 1951, 8*w^2 - 12*w - 99]', '[1951, 1951, 6*w^2 - 22*w - 25]', '[1979, 1979, 5*w^2 - 17*w - 15]', '[1979, 1979, 6*w^2 - 8*w - 83]', '[1979, 1979, -w^2 - 9*w - 15]', '[1982, 1982, 25/2*w^2 - 103/2*w - 37]', '[1982, 1982, 15/2*w^2 - 43/2*w - 56]', '[1982, 1982, 7*w^2 + 18*w - 7]', '[1982, 1982, 7*w^2 - 6*w - 75]', '[1982, 1982, -7*w - 17]', '[1982, 1982, 7/2*w^2 - 7/2*w - 52]', '[1982, 1982, -1/2*w^2 + 31/2*w + 9]', '[1982, 1982, 7/2*w^2 - 21/2*w - 11]', '[1982, 1982, 39/2*w^2 - 67/2*w - 244]', '[1994, 1994, w^2 + 6*w - 1]', '[1994, 1994, 9/2*w^2 - 13/2*w - 52]', '[1994, 1994, 25/2*w^2 - 95/2*w - 41]', '[1994, 1994, 5*w^2 + 20*w + 9]', '[1994, 1994, 35/2*w^2 - 55/2*w - 224]', '[1994, 1994, 9/2*w^2 + 25/2*w + 3]', '[1994, 1994, 13*w^2 - 22*w - 169]', '[1994, 1994, -17/2*w^2 + 69/2*w + 20]', '[1994, 1994, 7/2*w^2 - 25/2*w - 19]', '[1999, 1999, 2*w^2 - 9]', '[1999, 1999, -3*w^2 + 7*w + 37]', '[1999, 1999, -w^2 + 7*w - 3]', '[2000, 20, 5*w^2 - 5*w - 80]', '[2000, 20, 5*w^2 - 10*w - 60]', '[2000, 20, -5*w^2 + 15*w + 10]', '[2000, 20, 5/2*w^2 + 5/2*w - 10]', '[2000, 20, -5/2*w^2 + 25/2*w + 5]', '[2000, 20, -10*w - 30]', '[2000, 40, -5/2*w^2 - 25/2*w - 10]', '[2000, 40, 5/2*w^2 - 15/2*w - 40]', '[2000, 40, 15/2*w^2 - 55/2*w - 25]', '[2000, 40, 5/2*w^2 - 5/2*w - 5]', '[2000, 40, 5*w - 20]', '[2000, 40, 10*w^2 - 15*w - 130]', '[2000, 80, 15/2*w^2 - 55/2*w - 30]', '[2000, 80, 10*w^2 - 15*w - 125]', '[2000, 80, 5/2*w^2 + 25/2*w + 5]', '[2017, 2017, 6*w^2 - 8*w - 71]', '[2017, 2017, 5*w^2 - 17*w - 27]', '[2017, 2017, 28*w^2 - 46*w - 365]', '[2021, 2021, -w^2 + 3*w + 23]', '[2021, 2021, w^2 - 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27/2*w + 2]', '[9944, 9944, 5/2*w^2 + 1/2*w - 43]', '[9944, 9944, -1/2*w^2 - 31/2*w - 6]', '[9944, 9944, 7/2*w^2 + 19/2*w - 113]', '[9944, 9944, -9/2*w^2 + 23/2*w + 27]', '[9944, 9944, -2*w^2 - 17*w - 35]', '[9944, 9944, 5*w^2 - 8*w - 77]', '[9944, 9944, -3/2*w^2 - 11/2*w - 15]', '[9944, 9944, -1/2*w^2 + 15/2*w - 29]', '[9944, 9944, -14*w^2 + 57*w + 43]', '[9944, 9944, 7/2*w^2 - 19/2*w - 62]', '[9944, 9944, 23/2*w^2 - 31/2*w - 166]', '[9944, 9944, -3/2*w^2 + 19/2*w + 30]', '[9944, 9944, -10*w^2 + 17*w + 15]', '[9944, 9944, 15/2*w^2 + 41/2*w - 6]', '[9944, 9944, 7/2*w^2 - 3/2*w - 46]', '[9944, 9944, 17/2*w^2 - 19/2*w - 95]', '[9944, 9944, 43/2*w^2 - 73/2*w - 269]', '[9944, 9944, 35/2*w^2 - 141/2*w - 41]', '[9944, 9944, w^2 - 10*w - 19]', '[9944, 9944, 8*w^2 - 25*w - 53]', '[9944, 9944, 3*w^2 - 2*w + 3]', '[9949, 9949, -20*w^2 + 80*w + 49]', '[9949, 9949, 30*w^2 - 50*w - 391]', '[9949, 9949, 10*w^2 + 30*w + 11]', '[9974, 9974, -13/2*w^2 - 57/2*w - 19]', '[9974, 9974, 45/2*w^2 - 77/2*w - 296]', '[9974, 9974, -29/2*w^2 + 119/2*w + 29]', '[9974, 9974, 13/2*w^2 - 25/2*w - 96]', '[9974, 9974, 8*w^2 + 21*w + 7]', '[9974, 9974, -3*w^2 - 4*w - 7]', '[9974, 9974, 24*w^2 - 37*w - 311]', '[9974, 9974, 35/2*w^2 - 131/2*w - 56]', '[9974, 9974, -7/2*w^2 + 33/2*w - 9]', '[9977, 9977, 30*w^2 - 50*w - 387]', '[9977, 9977, 10*w^2 + 30*w + 7]', '[9977, 9977, 8*w^2 - 8*w - 9]', '[9977, 9977, 4*w^2 - 8*w - 29]', '[9977, 9977, 2*w^2 + 2*w - 27]', '[9977, 9977, 8*w^2 - 24*w - 135]', '[9977, 9977, -20*w^2 + 80*w + 53]', '[9977, 9977, 2*w^2 - 10*w - 23]', '[9977, 9977, 16*w - 71]', '[9992, 2498, 4*w^2 - 8*w - 14]', '[9992, 2498, 2*w^2 + 2*w - 42]', '[9992, 2498, 2*w^2 - 10*w - 38]', '[9992, 4996, 2*w^2 + 13*w + 2]', '[9992, 4996, -17/2*w^2 + 59/2*w + 18]', '[9992, 4996, -1/2*w^2 - 7/2*w - 19]', '[9992, 4996, -2*w^2 + 7*w - 8]', '[9992, 4996, 15/2*w^2 - 53/2*w - 38]', '[9992, 4996, 17/2*w^2 - 33/2*w - 109]', '[9992, 4996, -2*w^2 - 15*w - 30]', '[9992, 4996, 15/2*w^2 - 7/2*w - 75]', '[9992, 4996, 1/2*w^2 + 13/2*w - 10]', '[9992, 4996, 2*w^2 - 21*w - 16]', '[9992, 4996, -9/2*w^2 + 43/2*w + 4]', '[9992, 4996, 7/2*w^2 - 23/2*w - 33]', '[9992, 4996, 4*w^2 - 5*w - 34]', '[9992, 4996, 19/2*w^2 - 49/2*w - 80]', '[9992, 4996, 21/2*w^2 - 29/2*w - 151]', '[9992, 4996, 4*w^2 + 5*w - 8]', '[9992, 4996, 19/2*w^2 - 27/2*w - 113]', '[9992, 4996, 5/2*w^2 - 7/2*w - 48]', '[9992, 9992, 19/2*w^2 + 23/2*w - 45]', '[9992, 9992, -21/2*w^2 + 101/2*w + 34]', '[9992, 9992, -w^2 + 10*w - 29]', '[9992, 9992, -5/2*w^2 - 33/2*w - 21]', '[9992, 9992, 19/2*w^2 - 67/2*w - 30]', '[9992, 9992, 20*w^2 - 39*w - 231]', '[9992, 9992, 9/2*w^2 - 23/2*w - 75]', '[9992, 9992, -7/2*w^2 + 3/2*w - 2]', '[9992, 9992, 12*w^2 - 17*w - 161]', '[9998, 9998, 41/2*w^2 - 89/2*w - 216]', '[9998, 9998, 31/2*w^2 - 125/2*w - 47]', '[9998, 9998, 47/2*w^2 - 79/2*w - 296]', '[9998, 9998, 9/2*w^2 - 11/2*w - 9]', '[9998, 9998, -17/2*w^2 + 99/2*w + 33]', '[9998, 9998, 1/2*w^2 + 15/2*w - 40]', '[9998, 9998, 4*w^2 - 13*w - 67]', '[9998, 9998, 12*w^2 + 5*w - 85]', '[9998, 9998, 8*w^2 + 23*w - 3]'], 'label': '3.3.1849.1', 'narrow_class_no': 1, 'primes': ['[2, 2, -1/2*w^2 + 1/2*w + 8]', '[2, 2, 1/2*w^2 - 3/2*w - 1]', '[2, 2, w + 3]', '[11, 11, -w^2 + 3*w + 7]', '[11, 11, -2*w - 1]', '[11, 11, -w^2 + w + 11]', '[27, 3, 3]', '[41, 41, 2*w + 5]', '[41, 41, -w^2 + 3*w + 3]', '[41, 41, -w^2 + w + 15]', '[43, 43, -3*w^2 + 11*w + 11]', '[47, 47, -w^2 - w + 5]', '[47, 47, w^2 - 5*w - 3]', '[47, 47, -2*w^2 + 4*w + 23]', '[59, 59, -w^2 + w + 13]', '[59, 59, w^2 - 3*w - 5]', '[59, 59, -2*w - 3]', '[97, 97, 7*w^2 - 11*w - 91]', '[97, 97, -2*w^2 - 8*w - 5]', '[97, 97, 5*w^2 - 19*w - 15]', '[107, 107, w^2 + 3*w - 1]', '[107, 107, -3*w^2 + 5*w + 37]', '[107, 107, w^2 - 5*w - 23]', '[113, 113, w^2 - 3*w - 1]', '[113, 113, w^2 - w - 17]', '[113, 113, -2*w - 7]', '[125, 5, -5]', '[127, 127, -w^2 - w - 1]', '[127, 127, 2*w^2 - 4*w - 29]', '[127, 127, -w^2 + 5*w - 3]', '[131, 131, -w^2 + 5*w - 1]', '[131, 131, 2*w^2 - 4*w - 27]', '[131, 131, w^2 + w - 1]', '[137, 137, 2*w^2 - 6*w - 5]', '[137, 137, -4*w - 11]', '[137, 137, 2*w^2 - 2*w - 31]', '[151, 151, -2*w^2 + 8*w + 3]', '[151, 151, 3*w^2 - 5*w - 41]', '[151, 151, -w^2 - 3*w - 3]', '[173, 173, 2*w^2 - 4*w - 25]', '[173, 173, w^2 + w - 3]', '[173, 173, -w^2 + 5*w + 1]', '[193, 193, -6*w - 17]', '[193, 193, 3*w^2 - 9*w - 7]', '[193, 193, 3*w^2 - 3*w - 47]', '[199, 199, w^2 + w - 7]', '[199, 199, 2*w^2 - 4*w - 21]', '[199, 199, -w^2 + 5*w + 5]', '[211, 211, 2*w - 7]', '[211, 211, w^2 - w - 3]', '[211, 211, -w^2 + 3*w + 15]', '[223, 223, w^2 - w - 7]', '[223, 223, w^2 - 3*w - 11]', '[223, 223, 2*w - 3]', '[257, 257, -2*w^2 - 4*w - 1]', '[257, 257, -3*w^2 + 13*w + 3]', '[257, 257, 5*w^2 - 9*w - 67]', '[269, 269, 2*w - 5]', '[269, 269, w^2 - 3*w - 13]', '[269, 269, w^2 - w - 5]', '[293, 293, -13*w^2 + 51*w + 35]', '[293, 293, -19*w^2 + 31*w + 247]', '[293, 293, 6*w^2 + 20*w + 9]', '[317, 317, 5*w^2 - 19*w - 17]', '[317, 317, 7*w^2 - 11*w - 89]', '[317, 317, 2*w^2 + 8*w + 3]', '[343, 7, -7]', '[379, 379, 3*w^2 - 11*w - 13]', '[379, 379, 4*w^2 - 6*w - 49]', '[379, 379, w^2 + 5*w + 1]', '[383, 383, -4*w - 5]', '[383, 383, -2*w^2 + 2*w + 25]', '[383, 383, 2*w^2 - 6*w - 11]', '[389, 389, 4*w^2 - 18*w - 13]', '[389, 389, -7*w^2 + 13*w + 83]', '[389, 389, 4*w^2 - 14*w - 11]', '[409, 409, 2*w - 11]', '[409, 409, w^2 - 3*w - 19]', '[409, 409, -w^2 + w - 1]', '[419, 419, 10*w^2 - 38*w - 31]', '[419, 419, -14*w^2 + 22*w + 181]', '[419, 419, 4*w^2 - 14*w - 17]', '[431, 431, -4*w^2 + 16*w + 13]', '[431, 431, 2*w^2 + 6*w - 1]', '[431, 431, -6*w^2 + 10*w + 75]', '[457, 457, -2*w^2 + 8*w + 9]', '[457, 457, 3*w^2 - 5*w - 35]', '[457, 457, w^2 + 3*w - 3]', '[557, 557, 5*w^2 - 9*w - 63]', '[557, 557, -3*w^2 + 13*w + 7]', '[557, 557, 2*w^2 + 4*w - 3]', '[563, 563, -9*w^2 + 35*w + 23]', '[563, 563, 13*w^2 - 21*w - 171]', '[563, 563, -4*w^2 - 14*w - 9]', '[601, 601, 5*w^2 - 17*w - 13]', '[601, 601, 6*w^2 - 8*w - 85]', '[601, 601, -w^2 - 9*w - 17]', '[613, 613, -2*w^2 + 15]', '[613, 613, 3*w^2 - 7*w - 31]', '[613, 613, 22*w^2 - 36*w - 285]', '[641, 641, 3*w^2 - 5*w - 43]', '[641, 641, -2*w^2 + 8*w + 1]', '[641, 641, -w^2 - 3*w - 5]', '[643, 643, 2*w^2 + 4*w - 1]', '[643, 643, 5*w^2 - 9*w - 65]', '[643, 643, -3*w^2 + 13*w + 5]', '[647, 647, 9*w^2 - 35*w - 27]', '[647, 647, 4*w^2 + 14*w + 5]', '[647, 647, 13*w^2 - 21*w - 167]', '[653, 653, -4*w^2 + 16*w + 7]', '[653, 653, 6*w^2 - 10*w - 81]', '[653, 653, -2*w^2 - 6*w - 5]', '[661, 661, -w^2 - 7*w - 13]', '[661, 661, -4*w^2 + 14*w + 9]', '[661, 661, 5*w^2 - 7*w - 71]', '[677, 677, -12*w^2 + 20*w + 155]', '[677, 677, -4*w^2 - 12*w - 3]', '[677, 677, -8*w^2 + 32*w + 21]', '[709, 709, -2*w^2 + 10*w - 3]', '[709, 709, 19*w^2 - 31*w - 249]', '[709, 709, 4*w^2 - 8*w - 55]', '[727, 727, -w^2 + 5*w + 21]', '[727, 727, -23*w^2 + 37*w + 301]', '[727, 727, -w^2 - w + 23]', '[733, 733, 2*w^2 + 2*w - 9]', '[733, 733, -2*w^2 + 10*w + 5]', '[733, 733, 4*w^2 - 8*w - 47]', '[739, 739, 2*w^2 - 6*w - 17]', '[739, 739, 2*w^2 - 2*w - 19]', '[739, 739, 4*w - 1]', '[773, 773, 8*w^2 - 12*w - 103]', '[773, 773, 6*w^2 - 22*w - 21]', '[773, 773, -2*w^2 - 10*w - 7]', '[809, 809, 4*w^2 + 16*w + 11]', '[809, 809, w^2 - 9*w - 7]', '[809, 809, 3*w^2 - w - 29]', '[821, 821, 3*w^2 + w - 23]', '[821, 821, 2*w^2 - 12*w - 9]', '[821, 821, 5*w^2 - 11*w - 51]', '[839, 839, 2*w^2 + 4*w - 7]', '[839, 839, 5*w^2 - 9*w - 59]', '[839, 839, 3*w^2 - 13*w - 11]', '[859, 859, w^2 + w - 11]', '[859, 859, 2*w^2 - 4*w - 17]', '[859, 859, w^2 - 5*w - 9]', '[881, 881, 4*w^2 - 14*w - 15]', '[881, 881, 5*w^2 - 7*w - 65]', '[881, 881, -w^2 - 7*w - 7]', '[887, 887, 5*w^2 - 7*w - 67]', '[887, 887, 4*w^2 - 14*w - 13]', '[887, 887, -w^2 - 7*w - 9]', '[907, 907, -3*w^2 - 11*w - 9]', '[907, 907, 10*w^2 - 16*w - 133]', '[907, 907, -7*w^2 + 27*w + 17]', '[911, 911, w^2 - 7*w - 7]', '[911, 911, 3*w^2 - 7*w - 27]', '[911, 911, 2*w^2 - 19]', '[919, 919, -3*w^2 - 5*w - 1]', '[919, 919, -4*w^2 + 18*w + 1]', '[919, 919, 7*w^2 - 13*w - 95]', '[947, 947, 4*w^2 - 6*w - 57]', '[947, 947, -3*w^2 + 11*w + 5]', '[947, 947, -w^2 - 5*w - 9]', '[967, 967, 8*w^2 - 30*w - 25]', '[967, 967, -3*w^2 - 13*w - 9]', '[967, 967, 11*w^2 - 17*w - 143]', '[991, 991, 2*w^2 - 8*w - 11]', '[991, 991, w^2 + 3*w - 5]', '[991, 991, 3*w^2 - 5*w - 33]', '[997, 997, 4*w^2 + 2*w - 27]', '[997, 997, 7*w^2 - 15*w - 75]', '[997, 997, -3*w^2 + 17*w + 11]']}
-
nf_fields • Show schema
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-8, -14, -1, 1], 'conductor': 43, 'degree': 3, 'dirichlet_group': [1, 36, 6], 'disc_abs': 1849, 'disc_rad': 43, 'disc_sign': 1, 'frobs': [[2, [[1, 3]]], [3, [[3, 1]]], [5, [[3, 1]]], [7, [[3, 1]]], [11, [[1, 3]]], [13, [[3, 1]]], [17, [[3, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[3, 1]]], [37, [[3, 1]]], [41, [[1, 3]]], [43, [0]], [47, [[1, 3]]], [53, [[3, 1]]], [59, [[1, 3]]]], 'gal_is_abelian': True, 'gal_is_cyclic': True, 'gal_is_solvable': True, 'galois_disc_exponents': [2], 'galois_label': '3T1', 'galt': 1, 'grd': 12.27379796952146, 'index': 2, 'inessentialp': [2], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.1849.1', 'local_algs': ['43.3.2.1'], 'monogenic': -1, 'num_ram': 1, 'r2': 0, 'ramps': [43], 'rd': 12.2737979695, 'regulator': {'__RealLiteral__': 0, 'data': '18.9218643829', 'prec': 44}, 'res': {}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a^{2} - 3 a - 17 \\)', '\\( a^{2} - a - 1 \\)'], 'used_grh': False, 'zk': ['1', 'a', '1/2*a^2 - 1/2*a']}