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lfunc_lfunctions • Show schema
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{'Lhash': '1496360829446998240872507762470,2062397894333316370074834340367', 'a10': 0, 'a2': 0, 'a3': -8, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 8, 'a8': 0, 'a9': -197, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4115.675145248425, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]]], 'bad_primes': [2, 5], 'central_character': '400.1', 'coefficient_field': '1.1.1.1', 'conductor': 160000, 'conductor_radical': 10, 'degree': 4, 'euler_factors': [[1], [1, 8, 261, 1944, 59049], [1], [1, -8, 32666, -134456, 282475249], [1, -200, 225821, -32210200, 25937424601], [1, 592, 178538, 219805456, 137858491849], [1, -278, 2797339, -394720246, 2015993900449], [1, -840, 4289677, -2079923160, 6131066257801], [1, -1952, 11510698, -12563741536, 41426511213649], [1, 4680, 41219034, 95992177320, 420707233300201], [1, -5008, 33327162, -143374788208, 819628286980801], [1, -12500, 121294718, -866799462500, 4808584372417849], [1, 5334, 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'prec': 10}, 'spectral_label': 'c5e2-0', 'trace_hash': 144519834608765006, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18042055845482309029156719362', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.62694506984968860545250238413', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.72596894324336354677795325257', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 4115.675145248425, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 160000, 'conductor_radical': 10, 'degree': 4, 'dirichlet_coefficients': [1, 0, -8, 0, 0, 0, 8, 0, -197, 0, 200, 0, -592, 0, 0, 0, 278, 0, 840, 0, -64, 0, 1952, 0, 0, 0, 1720, 0, -4680, 0, 5008, 0, -1600, 0, 0, 0, 12500, 0, 4736, 0, -5334, 0, -224, 0, 0, 0, -26072, 0, -32602, 0, -2224, 0, -46812, 0, 0, 0, -6720, 0, 81776, 0, -46932, 0, -1576, 0, 0, 0, -68808, 0, -15616, 0, -7448, 0, -108822, 0, 0, 0, 1600, 0, 108104, 0, -5840, 0, -27224, 0, 0, 0, 37440, 0, 70990, 0, -4736, 0, -40064, 0, 0, 0, -96852, 0, -39400, 0], 'euler11': [1, -200, 225821, -32210200, 25937424601], 'euler13': [1, 592, 178538, 219805456, 137858491849], 'euler17': [1, -278, 2797339, -394720246, 2015993900449], 'euler19': [1, -840, 4289677, -2079923160, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -1952, 11510698, -12563741536, 41426511213649], 'euler29': [1, 4680, 41219034, 95992177320, 420707233300201], 'euler3': [1, 8, 261, 1944, 59049], 'euler31': [1, -5008, 33327162, -143374788208, 819628286980801], 'euler37': [1, -12500, 121294718, -866799462500, 4808584372417849], 'euler41': [1, 5334, 27686155, 617976976134, 13422659310152401], 'euler43': [1, 224, 15005414, 32929891232, 21611482313284249], 'euler47': [1, 26072, 628627310, 5979483022504, 52599132235830049], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 46812, 1352998222, 19576567418316, 174887470365513049], 'euler59': [1, -81776, 3059970646, -58463649475024, 511116753300641401], 'euler61': [1, 46932, 2239379182, 39638593598532, 713342911662882601], 'euler67': [1, 68808, 3858742141, 92899408362456, 1822837804551761449], 'euler7': [1, -8, 32666, -134456, 282475249], 'euler71': [1, 7448, 3593807902, 13437900206248, 3255243551009881201], 'euler73': [1, 108822, 7105450763, 225595796893446, 4297625829703557649], 'euler79': [1, -108104, 6816153098, -332642104957496, 9468276082626847201], 'euler83': [1, 27224, 4507827109, 107236442465032, 15516041187205853449], 'euler89': [1, -70990, 6345035107, -396412380284510, 31181719929966183601], 'euler97': [1, 96852, 16039717990, 831701078570964, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 8, 261, 1944, 59049], [1, 0, 0, 0, 0], [1, -8, 32666, -134456, 282475249], [1, -200, 225821, -32210200, 25937424601], [1, 592, 178538, 219805456, 137858491849], [1, -278, 2797339, -394720246, 2015993900449], [1, -840, 4289677, -2079923160, 6131066257801], [1, -1952, 11510698, -12563741536, 41426511213649], [1, 4680, 41219034, 95992177320, 420707233300201], [1, -5008, 33327162, -143374788208, 819628286980801], [1, -12500, 121294718, -866799462500, 4808584372417849], [1, 5334, 27686155, 617976976134, 13422659310152401], [1, 224, 15005414, 32929891232, 21611482313284249], [1, 26072, 628627310, 5979483022504, 52599132235830049], [1, 46812, 1352998222, 19576567418316, 174887470365513049], [1, -81776, 3059970646, -58463649475024, 511116753300641401], [1, 46932, 2239379182, 39638593598532, 713342911662882601], [1, 68808, 3858742141, 92899408362456, 1822837804551761449], [1, 7448, 3593807902, 13437900206248, 3255243551009881201], [1, 108822, 7105450763, 225595796893446, 4297625829703557649], [1, -108104, 6816153098, -332642104957496, 9468276082626847201], [1, 27224, 4507827109, 107236442465032, 15516041187205853449], [1, -70990, 6345035107, -396412380284510, 31181719929966183601], [1, 96852, 16039717990, 831701078570964, 73742412689492826049]], 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/400/6/a/r'], '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': '4-20e4-1.1-c5e2-0-18', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-20e4-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.009589747620803, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 144519834608765006, 'z1': {'__RealLiteral__': 0, 'data': '1.18042055845482309029156719362', 'prec': 103}}
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{'Lhash': '1496360829446998240872507762470,2062397894333316370074834340367', 'Lhash_array': ['1496360829446998240872507762470', '2062397894333316370074834340367'], 'label': '4-20e4-1.1-c5e2-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/400/6/a/r'}