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lfunc_lfunctions • Show schema
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{'Lhash': '533480175996425583739779814336,1154771113858453638314472177647,1397258616708113497211176402388', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -4, 'a8': 0, 'a9': -1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 16683.27298019835, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '3200.1', 'coefficient_field': '1.1.1.1', 'conductor': 32768000000, 'conductor_radical': 10, 'degree': 6, 'euler_factors': [[1], [1, -2, 5, -8, 15, -18, 27], [1], [1, 4, 17, 36, 119, 196, 343], [1, 2, 13, 36, 143, 242, 1331], [1, -8, 47, -192, 611, -1352, 2197], [1, -4, 35, -104, 595, -1156, 4913], [1, 2, 21, -28, 399, 722, 6859], [1, 8, 81, 372, 1863, 4232, 12167], [1, 6, 99, 356, 2871, 5046, 24389], [1, -8, 61, -368, 1891, -7688, 29791], [1, -8, 79, -320, 2923, -10952, 50653], [1, -2, 71, 20, 2911, -3362, 68921], [1, -14, 149, -1104, 6407, -25886, 79507], [1, 4, 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171613889700775504, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42084165455400497960245270812', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.910953786201455827732466803708', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.10224269720422118375847820065', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 16683.27298019835, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 32768000000, 'conductor_radical': 10, 'degree': 6, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, -4, 0, -1, 0, -2, 0, 8, 0, 0, 0, 4, 0, -2, 0, -8, 0, -8, 0, 0, 0, -4, 0, -6, 0, 8, 0, -4, 0, 0, 0, 8, 0, 16, 0, 2, 0, 14, 0, 0, 0, -4, 0, -1, 0, 8, 0, 16, 0, 0, 0, -4, 0, 2, 0, -10, 0, 4, 0, 0, 0, 10, 0, -16, 0, -12, 0, 20, 0, 0, 0, 8, 0, 16, 0, -2, 0, 30, 0, 0, 0, -12, 0, -10, 0, -32, 0, 16, 0, 0, 0, 28, 0, 2, 0], 'euler11': [1, 2, 13, 36, 143, 242, 1331], 'euler13': [1, -8, 47, -192, 611, -1352, 2197], 'euler17': [1, -4, 35, -104, 595, -1156, 4913], 'euler19': [1, 2, 21, -28, 399, 722, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 8, 81, 372, 1863, 4232, 12167], 'euler29': [1, 6, 99, 356, 2871, 5046, 24389], 'euler3': [1, -2, 5, -8, 15, -18, 27], 'euler31': [1, -8, 61, -368, 1891, -7688, 29791], 'euler37': [1, -8, 79, -320, 2923, -10952, 50653], 'euler41': [1, -2, 71, 20, 2911, -3362, 68921], 'euler43': [1, -14, 149, -1104, 6407, -25886, 79507], 'euler47': [1, 4, 113, 260, 5311, 8836, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -16, 231, -1776, 12243, -44944, 148877], 'euler59': [1, -2, 141, -132, 8319, -6962, 205379], 'euler61': [1, 10, 155, 1212, 9455, 37210, 226981], 'euler67': [1, -10, 141, -736, 9447, -44890, 300763], 'euler7': [1, 4, 17, 36, 119, 196, 343], 'euler71': [1, 12, 197, 1384, 13987, 60492, 357911], 'euler73': [1, -20, 219, -1736, 15987, -106580, 389017], 'euler79': [1, -16, 269, -2400, 21251, -99856, 493039], 'euler83': [1, -30, 509, -5504, 42247, -206670, 571787], 'euler89': [1, 10, 151, 684, 13439, 79210, 704969], 'euler97': [1, -28, 531, -6040, 51507, -263452, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -2, 5, -8, 15, -18, 27], [1, 0, 0, 0, 0, 0, 0], [1, 4, 17, 36, 119, 196, 343], [1, 2, 13, 36, 143, 242, 1331], [1, -8, 47, -192, 611, -1352, 2197], [1, -4, 35, -104, 595, -1156, 4913], [1, 2, 21, -28, 399, 722, 6859], [1, 8, 81, 372, 1863, 4232, 12167], [1, 6, 99, 356, 2871, 5046, 24389], [1, -8, 61, -368, 1891, -7688, 29791], [1, -8, 79, -320, 2923, -10952, 50653], [1, -2, 71, 20, 2911, -3362, 68921], [1, -14, 149, -1104, 6407, -25886, 79507], [1, 4, 113, 260, 5311, 8836, 103823], [1, -16, 231, -1776, 12243, -44944, 148877], [1, -2, 141, -132, 8319, -6962, 205379], [1, 10, 155, 1212, 9455, 37210, 226981], [1, -10, 141, -736, 9447, -44890, 300763], [1, 12, 197, 1384, 13987, 60492, 357911], [1, -20, 219, -1736, 15987, -106580, 389017], [1, -16, 269, -2400, 21251, -99856, 493039], [1, -30, 509, -5504, 42247, -206670, 571787], [1, 10, 151, 684, 13439, 79210, 704969], [1, -28, 531, -6040, 51507, -263452, 912673]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3200/2/a/bs'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-3200e3-1.1-c1e3-0-0', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '6-3200e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.054911339164094, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 171613889700775504, 'z1': {'__RealLiteral__': 0, 'data': '0.42084165455400497960245270812', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '533480175996425583739779814336,1154771113858453638314472177647,1397258616708113497211176402388', 'Lhash_array': ['533480175996425583739779814336', '1154771113858453638314472177647', '1397258616708113497211176402388'], 'label': '6-3200e3-1.1-c1e3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3200/2/a/bs'}