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hmf_forms • Show schema
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{'deg': 3, 'dimension': 4, 'disc': 473, 'field_bad_primes': [11, 43], 'field_label': '3.3.473.1', 'is_CM': 'no', 'is_base_change': 'no', 'label': '3.3.473.1-11.1-c', 'label_nsuffix': 2, 'label_suffix': 'c', 'level_bad_primes': [11], 'level_ideal': '[11, 11, -w^2 + 3]', 'level_label': '11.1', 'level_norm': 11, 'parallel_weight': 2, 'short_label': '11.1-c', 'weight': '[2, 2, 2]'}
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hmf_hecke • Show schema
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{'AL_eigenvalues': [['[11, 11, -w^2 + 3]', -1]], 'hecke_eigenvalues': ['e', '-e^3 + e^2 + 8*e - 3', 'e^3 - 2*e^2 - 7*e + 5', '-e^3 + e^2 + 9*e - 3', 1, 'e^3 - 2*e^2 - 7*e + 8', '-e^3 + 2*e^2 + 7*e - 7', '3*e^3 - 4*e^2 - 25*e + 15', '3*e^3 - 4*e^2 - 22*e + 11', '-e^2 + e', '-3*e^3 + 4*e^2 + 27*e - 13', '2*e^3 - 2*e^2 - 14*e + 4', '-2*e + 2', 'e^2 + 2*e - 2', '-2*e^3 + 4*e^2 + 14*e - 18', 'e^3 - 2*e^2 - 11*e + 11', '-e^3 + 2*e^2 + 7*e + 3', '2*e^3 - 2*e^2 - 16*e - 2', '-4*e^3 + 6*e^2 + 28*e - 18', 'e^3 - e^2 - 10*e + 7', '-7*e^3 + 10*e^2 + 49*e - 31', '3*e^3 - 4*e^2 - 23*e + 18', 'e^3 - 2*e^2 - 9*e + 8', 4, '2*e^3 - 4*e^2 - 16*e + 8', 'e^3 - 4*e^2 - 9*e + 21', '-e^3 + 3*e^2 + 3*e - 7', '6*e^3 - 8*e^2 - 50*e + 22', '-e^3 - e^2 + 8*e + 11', '-8*e^3 + 12*e^2 + 60*e - 30', '-5*e^3 + 8*e^2 + 35*e - 23', '-2*e^3 + 4*e^2 + 10*e - 26', 'e^3 - 2*e^2 - 5*e + 13', 'e^3 + 2*e^2 - 12*e - 15', 'e^3 - 2*e^2 - 5*e + 2', '-8*e^3 + 12*e^2 + 56*e - 36', '6*e^3 - 8*e^2 - 46*e + 23', '-e^3 - 2*e^2 + 7*e + 17', '6*e^3 - 9*e^2 - 50*e + 40', '4*e^3 - 9*e^2 - 25*e + 30', 'e^3 - 9*e - 9', '-3*e^3 + 4*e^2 + 27*e - 7', 'e^3 - 15*e - 4', '-8*e^3 + 12*e^2 + 54*e - 34', '2*e^3 - 2*e^2 - 8*e - 2', '6*e^3 - 10*e^2 - 46*e + 22', '4*e^3 - 4*e^2 - 31*e + 6', '2*e^3 - 4*e^2 - 12*e + 24', '-2*e^3 + 6*e^2 + 10*e - 25', '4*e^3 - 6*e^2 - 26*e + 16', 'e^3 + 4*e^2 - 13*e - 23', '-e^3 - 2*e^2 + 11*e + 5', '5*e^3 - 10*e^2 - 35*e + 33', '-4*e^3 + 8*e^2 + 34*e - 26', '-8*e^3 + 12*e^2 + 60*e - 36', '6*e^3 - 10*e^2 - 36*e + 35', '3*e^3 - 2*e^2 - 21*e - 7', '-2*e^3 + 2*e^2 + 18*e - 18', '5*e^3 - 8*e^2 - 37*e + 18', '-2*e^3 + 22*e + 2', '13*e^3 - 18*e^2 - 99*e + 64', '-7*e^3 + 11*e^2 + 47*e - 27', '-9*e^3 + 11*e^2 + 73*e - 49', '-8*e^3 + 11*e^2 + 59*e - 32', '-e^3 + 14*e + 1', '10*e^3 - 16*e^2 - 75*e + 48', '-10*e^3 + 14*e^2 + 78*e - 58', '-2*e^3 + 2*e^2 + 22*e + 2', '5*e^3 - 6*e^2 - 36*e - 1', '-8*e^3 + 11*e^2 + 58*e - 42', '-13*e^3 + 19*e^2 + 90*e - 53', '6*e^3 - 8*e^2 - 44*e + 30', '6*e^3 - 9*e^2 - 52*e + 36', '-6*e^3 + 11*e^2 + 42*e - 42', '8*e^3 - 7*e^2 - 64*e + 24', '-7*e^3 + 14*e^2 + 51*e - 31', '-10*e^3 + 16*e^2 + 74*e - 38', '3*e^3 - 4*e^2 - 21*e + 5', '-8*e^3 + 11*e^2 + 58*e - 12', '-15*e^3 + 23*e^2 + 119*e - 69', '13*e^3 - 18*e^2 - 93*e + 63', '7*e^3 - 6*e^2 - 59*e + 19', '-8*e^3 + 12*e^2 + 64*e - 26', '3*e^3 - 8*e^2 - 17*e + 24', '-11*e^3 + 18*e^2 + 87*e - 60', '-2*e^3 + 16*e - 4', '-4*e^3 + 8*e^2 + 39*e - 44', '4*e^3 - 2*e^2 - 30*e - 14', '-13*e^3 + 21*e^2 + 95*e - 59', '6*e^3 - 8*e^2 - 56*e + 26', '-8*e^3 + 10*e^2 + 64*e - 46', '-4*e^3 + 8*e^2 + 26*e - 18', '4*e^3 - 8*e^2 - 24*e + 30', '6*e^3 - 9*e^2 - 43*e + 46', '4*e^3 - 4*e^2 - 33*e + 8', '-2*e^2 + 2*e + 4', '8*e^3 - 12*e^2 - 64*e + 36', '2*e^3 - 5*e^2 - 18*e + 34', '8*e^3 - 16*e^2 - 59*e + 40', '6*e^3 - 11*e^2 - 45*e + 32', '-6*e^3 + 12*e^2 + 55*e - 56', '2*e + 16', '-4*e^3 + 6*e^2 + 38*e - 18', '4*e^2 - 4*e - 24', '3*e^3 + 2*e^2 - 23*e - 15', '-2*e^3 + 4*e^2 + 8*e - 20', '-5*e^3 + 8*e^2 + 39*e - 31', '-2*e^3 + 4*e^2 + 8*e - 4', '-13*e^3 + 18*e^2 + 101*e - 65', '10*e^3 - 14*e^2 - 85*e + 52', '-7*e^3 + 12*e^2 + 57*e - 34', '3*e^3 - 27*e + 5', '-6*e^3 + 7*e^2 + 55*e - 16', '3*e^3 - 13*e^2 - 18*e + 55', '-18*e^3 + 23*e^2 + 139*e - 78', '-2*e^3 + 3*e^2 + 5*e + 4', '-2*e^3 + 7*e^2 + 7*e - 18', '12*e^3 - 15*e^2 - 93*e + 42', '-6*e^3 + 7*e^2 + 38*e - 26', '-2*e^3 + 24*e - 8', '-15*e^3 + 22*e^2 + 102*e - 63', '-7*e^3 + 13*e^2 + 54*e - 39', '-3*e^2 + 10', '8*e^3 - 8*e^2 - 60*e + 34', '-7*e^3 + 14*e^2 + 57*e - 51', '13*e^3 - 22*e^2 - 97*e + 61', '3*e^3 - 6*e^2 - 35*e + 28', '-7*e^3 + 6*e^2 + 47*e - 2', '-6*e^3 + 8*e^2 + 54*e - 26', '-12*e^3 + 18*e^2 + 99*e - 74', '-3*e^3 + 4*e^2 + 23*e + 13', 'e^3 + e^2 + 6*e - 19', '-4*e^3 + 6*e^2 + 27*e + 12', '-13*e^3 + 21*e^2 + 101*e - 73', '-10*e^3 + 12*e^2 + 79*e - 48', '-6*e^3 + 8*e^2 + 43*e - 46', '8*e^3 - 14*e^2 - 63*e + 34', '-4*e^3 + 7*e^2 + 28*e + 10', '-16*e^3 + 21*e^2 + 112*e - 58', '4*e^3 - 6*e^2 - 38*e + 25', '-7*e^3 + 8*e^2 + 59*e - 21', '2*e^3 - 8*e^2 - 20*e + 29', '14*e^3 - 14*e^2 - 106*e + 40', '-2*e^2 + 8*e + 10', '3*e^3 - 6*e^2 - 7*e + 29', '8*e^3 - 11*e^2 - 68*e + 60', '-10*e^3 + 18*e^2 + 79*e - 40', '10*e^3 - 9*e^2 - 77*e + 36', '8*e^3 - 10*e^2 - 48*e + 18', 'e^3 - e^2 - 14*e + 13', '14*e^3 - 23*e^2 - 118*e + 84', '6*e^3 - 2*e^2 - 48*e - 6', '5*e^3 - 16*e^2 - 33*e + 51', '-2*e^3 + e^2 + 22*e - 16', '3*e^3 - 6*e^2 - 13*e + 20', '7*e^3 - 2*e^2 - 65*e - 3', '19*e^3 - 20*e^2 - 153*e + 78', '-12*e^3 + 18*e^2 + 104*e - 66', '22*e^3 - 30*e^2 - 170*e + 107', '12*e^3 - 16*e^2 - 80*e + 50', '-4*e^2 - 12*e + 30', '-8*e^3 + 11*e^2 + 64*e - 48', '22*e^3 - 28*e^2 - 169*e + 88', '8*e^3 - 13*e^2 - 71*e + 52', '-8*e^2 + 19*e + 36', '14*e^3 - 16*e^2 - 114*e + 58'], 'hecke_polynomial': 'x^4 - 2*x^3 - 7*x^2 + 9*x - 2', 'label': '3.3.473.1-11.1-c'}
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hmf_fields • Show schema
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{'degree': 3, 'discriminant': 473, 'ideals': ['[1, 1, 1]', '[3, 3, w + 1]', '[5, 5, w - 1]', '[8, 2, 2]', '[9, 3, -w^2 + w + 4]', '[9, 9, -w^2 + w + 2]', '[11, 11, -w^2 + 3]', '[11, 11, -w^2 - w + 1]', '[13, 13, w + 3]', '[15, 15, w^2 - w - 5]', '[17, 17, -w^2 + 2]', '[24, 6, 2*w + 2]', '[25, 5, w^2 + w - 4]', '[25, 25, 2*w + 3]', '[27, 3, 3]', '[27, 27, -2*w + 1]', '[33, 33, -w^2 + 2*w + 3]', '[33, 33, -w^2 - 2*w + 2]', '[37, 37, w^2 + w - 5]', '[39, 39, -w^2 - w + 6]', '[40, 10, 2*w - 2]', '[41, 41, 2*w^2 + w - 6]', '[43, 43, w^2 - 3*w - 2]', '[43, 43, -w + 4]', '[45, 15, 2*w^2 - 2*w - 5]', '[45, 45, -w - 4]', '[51, 51, -w^2 + w + 8]', '[55, 55, 2*w^2 - 7]', '[55, 55, w^2 - 2*w - 4]', '[64, 4, 4]', '[65, 65, w^2 + 2*w - 3]', '[71, 71, w^2 - 8]', '[72, 6, -2*w^2 + 2*w + 8]', '[72, 18, -2*w^2 + 2*w + 4]', '[73, 73, 3*w + 5]', '[73, 73, w^2 - 2*w - 5]', '[73, 73, w^2 - 2*w - 7]', '[75, 15, 2*w^2 + 2*w - 3]', '[75, 75, -2*w^2 + w + 6]', '[79, 79, 2*w^2 + w - 9]', '[81, 9, -2*w^2 - w + 5]', '[81, 9, 3*w + 3]', '[81, 81, -w^2 + 2*w + 6]', '[83, 83, 3*w^2 - 2*w - 13]', '[85, 85, w^2 - 3*w - 3]', '[88, 22, -2*w^2 + 6]', '[88, 22, -2*w^2 - 2*w + 2]', '[89, 89, -w^2 - 2*w + 9]', '[99, 33, w^2 - w + 2]', '[99, 33, -w^2 - 2*w + 4]', '[99, 99, -2*w^2 - w + 10]', '[99, 99, -w + 5]', '[101, 101, -w - 5]', '[103, 103, 2*w^2 - 2*w - 9]', '[103, 103, 2*w^2 - w - 13]', '[103, 103, 2*w^2 - w - 5]', '[104, 26, 2*w + 6]', '[107, 107, w^2 - 2*w - 10]', '[109, 109, 2*w^2 - 13]', '[111, 111, 2*w^2 + w - 4]', '[113, 113, -w^2 - 2*w - 3]', '[117, 39, -2*w^2 + 2*w + 11]', '[117, 117, -2*w^2 + 5]', '[120, 30, 2*w^2 - 2*w - 10]', '[121, 11, -3*w^2 + 2*w + 10]', '[121, 11, -2*w^2 + w + 4]', '[121, 121, -w^2 + w + 9]', '[123, 123, 3*w^2 + 5*w - 4]', '[125, 5, 5]', '[125, 125, 2*w^2 + w - 3]', '[127, 127, -3*w^2 - w + 10]', '[129, 129, -w^2 + 3*w + 4]', '[129, 129, -2*w^2 - 1]', '[135, 15, 3*w - 3]', '[135, 135, w^2 + 2*w - 8]', '[136, 34, -2*w^2 + 4]', '[137, 137, 2*w^2 + 2*w - 7]', '[139, 139, 2*w^2 - 3]', '[143, 143, -3*w + 4]', '[143, 143, -w^2 + 9]', '[149, 149, -3*w^2 + 11]', '[149, 149, 3*w^2 - w - 11]', '[149, 149, w^2 + 2*w - 6]', '[153, 51, -w^2 - 2*w + 7]', '[153, 153, w^2 - 2*w + 3]', '[157, 157, -3*w^2 + 3*w + 11]', '[163, 163, w^2 + 3*w - 3]', '[165, 165, 2*w^2 + 3*w - 5]', '[165, 165, -w^2 - w - 3]', '[167, 167, 2*w^2 - 3*w - 7]', '[169, 13, -w^2 + 3*w - 4]', '[169, 169, -w^2 + 3*w + 5]', '[173, 173, -w^2 + 5*w - 1]', '[179, 179, -3*w - 8]', '[185, 185, -w + 6]', '[187, 187, w + 6]', '[187, 187, -3*w^2 + 3*w + 7]', '[191, 191, -w^2 + w - 3]', '[192, 12, 4*w + 4]', '[193, 193, -w^2 - 3]', '[195, 195, 2*w - 7]', '[197, 197, -3*w^2 + 2*w + 9]', '[199, 199, w^2 - 3*w - 6]', '[200, 10, 2*w^2 + 2*w - 8]', '[200, 50, 4*w + 6]', '[205, 205, -w^2 + 3*w + 8]', '[211, 211, 2*w^2 - w - 14]', '[211, 211, -4*w - 5]', '[211, 211, -2*w - 7]', '[213, 213, w^2 - 3*w - 7]', '[215, 215, -w^2 + 5*w - 4]', '[215, 215, -4*w^2 + 6*w + 3]', '[216, 6, 6]', '[216, 54, -4*w + 2]', '[219, 219, -w^2 - 2*w - 4]', '[219, 219, -w^2 - 4*w - 6]', '[219, 219, 3*w^2 + 8*w + 5]', '[221, 221, w^2 - 5*w + 2]', '[223, 223, 3*w^2 - 10]', '[225, 15, 4*w^2 - w - 16]', '[225, 45, 2*w^2 - 3*w - 8]', '[225, 75, -w^2 + w + 10]', '[225, 225, -w^2 - 3*w + 4]', '[237, 237, 3*w^2 + 2*w - 7]', '[239, 239, w^2 - 2*w - 11]', '[243, 9, -3*w^2 + 3*w + 12]', '[243, 27, -3*w^2 + 3*w + 6]', '[243, 243, w^2 + 3*w + 5]', '[249, 249, w^2 - 10]', '[255, 255, 2*w^2 + 2*w - 9]', '[257, 257, 2*w^2 + 3*w - 6]', '[264, 66, -2*w^2 + 4*w + 6]', '[264, 66, -2*w^2 - 4*w + 4]', '[267, 267, -3*w^2 + 2*w + 8]', '[271, 271, -w^2 + 2*w - 4]', '[275, 55, 2*w^2 - 3*w - 13]', '[275, 55, -w^2 - 6*w - 6]', '[275, 275, -3*w^2 + 3*w + 5]', '[275, 275, -2*w^2 + 3*w + 9]', '[277, 277, 4*w^2 - 3*w - 17]', '[277, 277, w^2 + 2*w - 12]', '[277, 277, 4*w - 3]', '[281, 281, 4*w^2 + w - 14]', '[283, 283, w^2 + 3*w - 5]', '[289, 17, 3*w^2 - w - 9]', '[289, 289, w^2 + w + 4]', '[293, 293, -3*w^2 - 2*w + 12]', '[296, 74, 2*w^2 + 2*w - 10]', '[297, 33, -3*w^2 + 9]', '[297, 33, -3*w^2 - 3*w + 3]', '[297, 297, -w^2 + 4*w + 5]', '[297, 297, -3*w^2 - w + 8]', '[303, 303, -w^2 - 6*w - 5]', '[307, 307, w - 7]', '[309, 309, -w - 7]', '[309, 309, w^2 - 4*w - 11]', '[309, 309, w^2 + 4*w - 3]', '[311, 311, 4*w^2 - 15]', '[311, 311, 2*w^2 - 3*w - 10]', '[311, 311, w^2 + w - 11]', '[312, 78, -2*w^2 - 2*w + 12]', '[313, 313, -2*w^2 - 2*w + 17]', '[317, 317, 3*w^2 - 3*w - 13]', '[317, 317, 2*w^2 - 3*w - 12]', '[317, 317, 2*w^2 + 2*w - 11]', '[320, 20, 4*w - 4]', '[321, 321, -w^2 - 7*w - 9]', '[325, 65, 4*w^2 + 4*w - 11]', '[325, 325, w^2 + 4]', '[327, 327, 2*w^2 - 3*w - 11]', '[328, 82, 4*w^2 + 2*w - 12]', '[331, 331, w^2 + 3*w - 6]', '[333, 111, 5*w^2 - 2*w - 20]', '[333, 333, 3*w^2 - 4*w - 10]', '[337, 337, 4*w^2 - w - 15]', '[339, 339, -3*w^2 - 10*w - 4]', '[343, 7, -7]', '[344, 86, 2*w^2 - 6*w - 4]', '[344, 86, -2*w + 8]', '[351, 39, 3*w + 9]', '[351, 351, -2*w^2 - 5*w + 3]', '[353, 353, 3*w^2 - w - 8]', '[353, 353, 2*w^2 - 4*w - 7]', '[353, 353, 2*w^2 + 3*w - 7]', '[355, 355, -w^2 - 3*w + 9]', '[359, 359, w^2 - 4*w - 6]', '[360, 30, 4*w^2 - 4*w - 10]', '[360, 90, -2*w - 8]', '[363, 33, -w^2 - 3*w + 7]', '[363, 33, -2*w^2 + w + 15]', '[363, 363, 2*w^2 - 4*w + 3]', '[365, 365, 3*w^2 + 2*w - 5]', '[365, 365, -3*w^2 + 8]', '[365, 365, -3*w^2 + 2*w + 6]', '[367, 367, 3*w^2 - 2*w - 4]', '[367, 367, 2*w^2 - 15]', '[367, 367, 3*w^2 + w - 7]', '[369, 123, 5*w^2 + w - 23]', '[369, 369, w^2 - w - 11]', '[373, 373, w^2 + 3*w - 8]', '[373, 373, -3*w^2 + 3*w + 17]', '[373, 373, 3*w^2 - 3*w - 14]', '[375, 15, -5*w^2 + 20]', '[375, 375, 3*w^2 - 5*w - 8]', '[381, 381, 4*w^2 + 6*w - 7]', '[383, 383, 4*w^2 - 3*w - 12]', '[387, 129, -2*w^2 + 5*w - 4]', '[387, 129, -2*w^2 - 4*w + 5]', '[387, 387, -4*w^2 + 11*w]', '[387, 387, 2*w^2 + 2*w + 3]', '[389, 389, 3*w^2 + 3*w - 10]', '[395, 395, -w^2 + 11]', '[405, 45, 3*w^2 - 3*w - 15]', '[405, 45, w^2 - 4*w - 7]', '[405, 405, 3*w^2 - w - 7]', '[407, 407, 3*w^2 - 3*w - 16]', '[407, 407, -5*w - 7]', '[408, 102, -2*w^2 + 2*w + 16]', '[409, 409, w^2 + 4*w - 13]', '[409, 409, -5*w^2 + 3*w + 18]', '[409, 409, w^2 + 4*w - 4]', '[411, 411, 4*w^2 + 5*w - 5]', '[415, 415, -5*w^2 + 4*w + 16]', '[417, 417, 2*w^2 + 7*w - 1]', '[419, 419, 3*w^2 + w - 6]', '[421, 421, 3*w^2 - 7]', '[425, 85, w^2 - 4*w - 9]', '[425, 425, -4*w^2 + 4*w + 15]', '[429, 429, -3*w^2 + w + 4]', '[429, 429, -w^2 + 4*w + 8]', '[431, 431, -4*w^2 - w + 13]', '[433, 433, -w^2 + 2*w - 5]', '[439, 439, 3*w^2 - w - 6]', '[440, 110, 4*w^2 - 14]', '[440, 110, 2*w^2 - 4*w - 8]', '[445, 445, -w^2 + 6*w - 10]', '[447, 447, -3*w^2 - 4*w + 8]', '[447, 447, 2*w^2 + 3*w - 8]', '[447, 447, 3*w^2 + w - 5]', '[449, 449, 3*w^2 - w - 5]', '[451, 451, -3*w^2 - 10*w - 9]', '[451, 451, 2*w^2 - 4*w - 19]', '[457, 457, 3*w^2 - 4]', '[457, 457, 2*w^2 - 5*w - 6]', '[457, 457, -w^2 - w - 5]', '[459, 51, -3*w^2 + 6]', '[459, 459, -4*w^2 + w + 14]', '[461, 461, -3*w^2 - 5*w + 6]', '[463, 463, 3*w^2 + 2*w - 14]', '[467, 467, 3*w^2 + 2*w - 18]', '[471, 471, -w + 8]', '[473, 473, w^2 + 8*w]', '[473, 473, -2*w^2 + 7*w + 4]', '[473, 473, 5*w - 3]', '[473, 473, -3*w^2 + 5]', '[479, 479, 3*w^2 + w - 21]', '[481, 481, 4*w^2 + 3*w - 14]', '[489, 489, 4*w^2 + 5*w - 2]', '[495, 165, -w^2 + w - 5]', '[495, 165, w^2 + 2*w - 13]', '[495, 495, 4*w^2 + 2*w - 11]', '[495, 495, w^2 + w - 12]', '[499, 499, w^2 - 5*w - 13]', '[501, 501, -w^2 - 5]', '[505, 505, -w^2 - 4*w + 5]', '[507, 39, 2*w^2 - 6*w - 5]', '[507, 507, -4*w^2 - 2*w + 17]', '[509, 509, 4*w^2 + 3*w - 9]', '[509, 509, 3*w^2 - w - 20]', '[509, 509, 2*w^2 + 5*w - 4]', '[512, 8, 8]', '[515, 515, -3*w^2 - 2*w + 15]', '[515, 515, -3*w^2 + 6*w + 7]', '[515, 515, -4*w^2 + 3*w + 11]', '[519, 519, 4*w^2 - w - 2]', '[520, 130, 2*w^2 + 4*w - 6]', '[521, 521, w^2 + 7*w + 5]', '[523, 523, 3*w^2 + 2*w - 17]', '[523, 523, 3*w^2 - 4*w - 20]', '[523, 523, 3*w^2 - 5*w - 9]', '[533, 533, 7*w^2 + 7*w - 16]', '[535, 535, -3*w^2 - 3*w + 11]', '[537, 537, -3*w^2 - 11*w - 8]', '[541, 541, 2*w - 9]', '[545, 545, -2*w^2 - 3*w + 15]', '[547, 547, -4*w^2 + 5*w + 13]', '[555, 555, -6*w^2 + w + 25]', '[557, 557, -2*w - 9]', '[559, 559, -6*w - 5]', '[559, 559, -w^2 + w + 12]', '[561, 561, -w^2 - 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6*w - 28]', '[9769, 9769, 6*w^2 - 11*w - 24]', '[9771, 9771, -2*w^2 - 19*w - 11]', '[9777, 9777, 11*w^2 + 12*w - 17]', '[9783, 3261, 8*w^2 + 7*w - 32]', '[9783, 9783, -2*w^2 - 3*w - 16]', '[9791, 9791, -2*w^2 - 5*w - 17]', '[9792, 204, -4*w^2 - 8*w + 28]', '[9792, 612, 4*w^2 - 8*w + 12]', '[9795, 9795, -25*w^2 + 11*w + 114]', '[9799, 9799, 7*w^2 + 6*w - 35]', '[9801, 99, w^2 + 5*w + 20]', '[9801, 99, -w^2 - 14*w + 7]', '[9801, 99, -3*w^2 - 9*w + 21]', '[9801, 99, -6*w^2 + 3*w + 45]', '[9801, 891, -4*w^2 - 9*w + 19]', '[9801, 891, 5*w^2 - 7*w + 9]', '[9801, 1089, -2*w^2 - 10*w + 23]', '[9801, 1089, 6*w^2 - 12*w + 9]', '[9801, 9801, w^2 - 10*w + 25]', '[9803, 9803, w^2 + w - 25]', '[9803, 9803, 8*w^2 + 8*w - 29]', '[9803, 9803, -w^2 + 14*w - 10]', '[9809, 9809, 10*w^2 + 9*w - 17]', '[9813, 9813, 10*w^2 + 8*w - 5]', '[9816, 2454, -4*w^2 - 8*w + 26]', '[9816, 2454, 10*w^2 + 10*w - 6]', '[9816, 2454, 10*w^2 - 8*w - 24]', '[9819, 3273, w^2 + 8*w - 31]', '[9819, 9819, -5*w^2 + 20*w - 11]', '[9829, 9829, 3*w^2 + 5*w - 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36]', '[9897, 9897, w^2 - 14*w - 15]', '[9903, 9903, -w^2 - 16*w - 15]', '[9907, 9907, 3*w^2 + 3*w - 34]', '[9909, 1101, 9*w^2 - 6*w - 12]', '[9909, 1101, 6*w^2 - 45]', '[9909, 1101, 9*w^2 + 3*w - 21]', '[9909, 9909, w^2 - 15*w - 13]', '[9909, 9909, 2*w^2 + 10*w - 19]', '[9909, 9909, 7*w^2 - 24*w - 10]', '[9915, 9915, -11*w^2 + 3*w + 38]', '[9915, 9915, 17*w^2 + 3*w - 95]', '[9915, 9915, -15*w^2 + 7*w + 58]', '[9921, 9921, 9*w^2 + 23*w - 4]', '[9921, 9921, w^2 - 9*w - 31]', '[9921, 9921, 9*w^2 - 10*w - 37]', '[9923, 9923, 5*w^2 - 10*w - 28]', '[9927, 3309, 13*w^2 - 13*w - 46]', '[9927, 9927, 13*w^2 - 17*w - 24]', '[9928, 2482, 4*w^2 + 10*w - 16]', '[9928, 2482, 8*w^2 + 10*w - 24]', '[9928, 2482, -10*w^2 - 18*w + 14]', '[9931, 9931, 8*w^2 - 11*w - 30]', '[9931, 9931, -w^2 - 3*w - 19]', '[9931, 9931, 4*w^2 - 11*w - 22]', '[9935, 9935, 8*w^2 - 13*w + 5]', '[9944, 2486, 18*w^2 + 34*w]', '[9944, 2486, 10*w^2 + 10*w - 14]', '[9945, 3315, w^2 - w - 25]', '[9945, 9945, w^2 + 13*w - 9]', '[9960, 2490, -22*w^2 + 2*w + 120]', '[9963, 369, 15*w^2 + 3*w - 69]', '[9963, 1107, 3*w^2 - 3*w - 33]', '[9963, 9963, 17*w^2 + 24*w - 23]', '[9965, 9965, -3*w^2 - 9*w + 22]', '[9967, 9967, 11*w^2 - 12*w - 22]', '[9969, 9969, -9*w^2 + 4*w + 22]', '[9973, 9973, 3*w^2 + 13*w - 9]', '[9979, 9979, 9*w^2 - w - 24]', '[9981, 3327, 11*w^2 - 5*w - 68]', '[9981, 9981, 7*w^2 + 7*w - 30]', '[9993, 9993, -3*w^2 - w - 13]', '[9995, 9995, -8*w^2 + 9*w + 39]', '[9997, 9997, 9*w^2 + 20*w - 8]', '[9999, 3333, -4*w^2 - 2*w - 11]', '[9999, 3333, 7*w^2 + 11*w - 19]', '[9999, 9999, 11*w^2 + 5*w - 48]', '[9999, 9999, w^2 - 25]'], 'label': '3.3.473.1', 'narrow_class_no': 1, 'primes': ['[3, 3, w + 1]', '[5, 5, w - 1]', '[8, 2, 2]', '[9, 3, -w^2 + w + 4]', '[11, 11, -w^2 + 3]', '[11, 11, -w^2 - w + 1]', '[13, 13, w + 3]', '[17, 17, -w^2 + 2]', '[25, 5, w^2 + w - 4]', '[37, 37, w^2 + w - 5]', '[41, 41, 2*w^2 + w - 6]', '[43, 43, w^2 - 3*w - 2]', '[43, 43, -w + 4]', '[71, 71, w^2 - 8]', '[73, 73, 3*w + 5]', '[73, 73, w^2 - 2*w - 5]', '[73, 73, w^2 - 2*w - 7]', '[79, 79, 2*w^2 + w - 9]', '[83, 83, 3*w^2 - 2*w - 13]', '[89, 89, -w^2 - 2*w + 9]', '[101, 101, -w - 5]', '[103, 103, 2*w^2 - 2*w - 9]', '[103, 103, 2*w^2 - w - 13]', '[103, 103, 2*w^2 - w - 5]', '[107, 107, w^2 - 2*w - 10]', '[109, 109, 2*w^2 - 13]', '[113, 113, -w^2 - 2*w - 3]', '[127, 127, -3*w^2 - w + 10]', '[137, 137, 2*w^2 + 2*w - 7]', '[139, 139, 2*w^2 - 3]', '[149, 149, -3*w^2 + 11]', '[149, 149, 3*w^2 - w - 11]', '[149, 149, w^2 + 2*w - 6]', '[157, 157, -3*w^2 + 3*w + 11]', '[163, 163, w^2 + 3*w - 3]', '[167, 167, 2*w^2 - 3*w - 7]', '[169, 13, -w^2 + 3*w - 4]', '[173, 173, -w^2 + 5*w - 1]', '[179, 179, -3*w - 8]', '[191, 191, -w^2 + w - 3]', '[193, 193, -w^2 - 3]', '[197, 197, -3*w^2 + 2*w + 9]', '[199, 199, w^2 - 3*w - 6]', '[211, 211, 2*w^2 - w - 14]', '[211, 211, -4*w - 5]', '[211, 211, -2*w - 7]', '[223, 223, 3*w^2 - 10]', '[239, 239, w^2 - 2*w - 11]', '[257, 257, 2*w^2 + 3*w - 6]', '[271, 271, -w^2 + 2*w - 4]', '[277, 277, 4*w^2 - 3*w - 17]', '[277, 277, w^2 + 2*w - 12]', '[277, 277, 4*w - 3]', '[281, 281, 4*w^2 + w - 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7]', '[661, 661, -6*w^2 + 4*w + 21]', '[677, 677, w^2 + 3*w - 15]', '[677, 677, 3*w^2 - 5*w - 10]', '[677, 677, 2*w^2 + 3*w - 13]', '[683, 683, 2*w^2 + 3*w - 12]', '[683, 683, 2*w^2 + 5*w - 5]', '[683, 683, w - 9]', '[691, 691, 5*w^2 - 6*w - 10]', '[701, 701, w^2 + 5*w - 15]', '[709, 709, 4*w^2 - w - 12]', '[709, 709, w^2 - 5*w - 8]', '[709, 709, w^2 + 4*w - 8]', '[719, 719, 4*w^2 + w - 11]', '[719, 719, -w^2 + w - 6]', '[719, 719, 4*w^2 - 2*w - 11]', '[727, 727, -w^2 - 6]', '[751, 751, w^2 - 5*w - 10]', '[757, 757, 5*w^2 - 18]', '[769, 769, w^2 + 6*w - 3]', '[773, 773, 3*w^2 - 4*w - 18]', '[787, 787, 3*w^2 + w - 22]', '[809, 809, 3*w - 11]', '[821, 821, 3*w^2 + 4*w - 10]', '[823, 823, 5*w^2 - 3*w - 16]', '[823, 823, 3*w^2 - 4*w - 17]', '[823, 823, 2*w^2 - w - 17]', '[827, 827, 4*w^2 - 11]', '[829, 829, 2*w^2 - 5*w - 9]', '[839, 839, -w^2 - 4*w + 17]', '[853, 853, 5*w^2 - 4*w - 14]', '[857, 857, 2*w^2 - 6*w - 7]', '[859, 859, -3*w^2 + 5*w - 3]', '[863, 863, -3*w - 11]', '[877, 877, 6*w^2 - 3*w - 22]', '[911, 911, 6*w^2 - 23]', '[919, 919, 2*w^2 + 4*w - 9]', '[929, 929, 4*w^2 - 2*w - 5]', '[941, 941, 5*w^2 + 2*w - 23]', '[967, 967, 6*w^2 - 5*w - 24]', '[971, 971, 6*w^2 - 5*w - 18]', '[971, 971, 4*w^2 - 4*w - 21]', '[971, 971, w^2 - 3*w - 15]', '[983, 983, -3*w^2 + 4*w - 3]', '[991, 991, 6*w - 5]']}
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{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-1, -5, 0, 1], 'conductor': 0, 'degree': 3, 'dirichlet_group': [], 'disc_abs': 473, 'disc_rad': 473, 'disc_sign': 1, 'frobs': [[2, [[3, 1]]], [3, [[2, 1], [1, 1]]], [5, [[2, 1], [1, 1]]], [7, [[3, 1]]], [11, [0]], [13, [[2, 1], [1, 1]]], [17, [[2, 1], [1, 1]]], [19, [[3, 1]]], [23, [[3, 1]]], [29, [[3, 1]]], [31, [[3, 1]]], [37, [[2, 1], [1, 1]]], [41, [[2, 1], [1, 1]]], [43, [0]], [47, [[3, 1]]], [53, [[3, 1]]], [59, [[3, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [3, 3], 'galois_label': '3T2', 'galt': 2, 'grd': 21.748563170931547, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '3.3.473.1', 'local_algs': ['11.1.0.1', '11.2.1.2', '43.1.0.1', '43.2.1.1'], 'monogenic': 1, 'num_ram': 2, 'r2': 0, 'ramps': [11, 43], 'rd': 7.79148753564, 'regulator': {'__RealLiteral__': 0, 'data': '2.84322939957', 'prec': 44}, 'res': {'gal': ['11,-33,-30,67,-22,-2,1']}, 'subfield_mults': [], 'subfields': [], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( a \\)', '\\( a + 2 \\)'], 'unitsGmodule': [[3, 1], [5, 1]], 'used_grh': False, 'zk': ['1', 'a', 'a^2']}