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{'Lhash': '779191587020379720028195324623,858768664485139560355939980910,1243129389380722561469565335620', 'a10': 0, 'a2': 0, 'a3': 3, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 6, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 241610.12449032863, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -3, 3, -1]], [5, [1]], [13, [1, 3, 3, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '7800.1', 'coefficient_field': '1.1.1.1', 'conductor': 474552000000, 'conductor_radical': 390, 'degree': 6, 'euler_factors': [[1], [1, -3, 3, -1], [1], [1, 2, 16, 20, 112, 98, 343], [1, -2, 4, 36, 44, -242, 1331], [1, 3, 3, 1], [1, 2, 44, 64, 748, 578, 4913], [1, -3, 17, -14, 323, -1083, 6859], [1, 4, 49, 120, 1127, 2116, 12167], [1, -1, 54, -57, 1566, -841, 24389], [1, -14, 128, -768, 3968, -13454, 29791], [1, 1, 87, 94, 3219, 1369, 50653], [1, -5, 107, -346, 4387, -8405, 68921], [1, 6, 101, 508, 4343, 11094, 79507], 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'5.69828887806746847553125071079886', '6.21762979626372457683138029855883', '6.41796797197110059155321250358696', '6.61487731310417875338173927364207', '6.64830092603914128731069642449255', '6.95226843690636668021618399339307', '7.27187203208441415433761563585833', '7.28732819317045322710340979068050', '7.79143995920375914093072240097307', '7.961747712010711864184296710845141', '8.066827691633452624584585035174493'], 'prelabel': '6-7800e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.891977798790283, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e3-0', 'trace_hash': 1799143553152182189, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.61467378067749353879409291721', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.67744902604118656560256861552', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.980656175413720460102212646079', 'prec': 107}}
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{'algebraic': True, 'analytic_conductor': 241610.12449032863, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 474552000000, 'conductor_radical': 390, 'degree': 6, 'dirichlet_coefficients': [1, 0, 3, 0, 0, 0, -2, 0, 6, 0, 2, 0, -3, 0, 0, 0, -2, 0, 3, 0, -6, 0, -4, 0, 0, 0, 10, 0, 1, 0, 14, 0, 6, 0, 0, 0, -1, 0, -9, 0, 5, 0, -6, 0, 0, 0, 5, 0, -12, 0, -6, 0, 15, 0, 0, 0, 9, 0, 8, 0, 18, 0, -12, 0, 0, 0, -3, 0, -12, 0, 23, 0, 8, 0, 0, 0, -4, 0, 7, 0, 15, 0, 8, 0, 0, 0, 3, 0, -14, 0, 6, 0, 42, 0, 0, 0, 0, 0, 12, 0], 'euler11': [1, -2, 4, 36, 44, -242, 1331], 'euler13': [1, 3, 3, 1, 0, 0, 0], 'euler17': [1, 2, 44, 64, 748, 578, 4913], 'euler19': [1, -3, 17, -14, 323, -1083, 6859], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 4, 49, 120, 1127, 2116, 12167], 'euler29': [1, -1, 54, -57, 1566, -841, 24389], 'euler3': [1, -3, 3, -1, 0, 0, 0], 'euler31': [1, -14, 128, -768, 3968, -13454, 29791], 'euler37': [1, 1, 87, 94, 3219, 1369, 50653], 'euler41': [1, -5, 107, -346, 4387, -8405, 68921], 'euler43': [1, 6, 101, 508, 4343, 11094, 79507], 'euler47': [1, -5, 130, -411, 6110, -11045, 103823], 'euler5': [1, 0, 0, 0, 0, 0, 0], 'euler53': [1, -15, 194, -1579, 10282, -42135, 148877], 'euler59': [1, -8, 80, -274, 4720, -27848, 205379], 'euler61': [1, -18, 200, -1532, 12200, -66978, 226981], 'euler67': [1, 3, 14, 341, 938, 13467, 300763], 'euler7': [1, 2, 16, 20, 112, 98, 343], 'euler71': [1, -23, 365, -3502, 25915, -115943, 357911], 'euler73': [1, -8, 207, -1088, 15111, -42632, 389017], 'euler79': [1, -7, 125, -822, 9875, -43687, 493039], 'euler83': [1, -8, 208, -1158, 17264, -55112, 571787], 'euler89': [1, 14, 235, 2364, 20915, 110894, 704969], 'euler97': [1, 0, -9, -272, -873, 0, 912673], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, -3, 3, -1, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, 2, 16, 20, 112, 98, 343], [1, -2, 4, 36, 44, -242, 1331], [1, 3, 3, 1, 0, 0, 0], [1, 2, 44, 64, 748, 578, 4913], [1, -3, 17, -14, 323, -1083, 6859], [1, 4, 49, 120, 1127, 2116, 12167], [1, -1, 54, -57, 1566, -841, 24389], [1, -14, 128, -768, 3968, -13454, 29791], [1, 1, 87, 94, 3219, 1369, 50653], [1, -5, 107, -346, 4387, -8405, 68921], [1, 6, 101, 508, 4343, 11094, 79507], [1, -5, 130, -411, 6110, -11045, 103823], [1, -15, 194, -1579, 10282, -42135, 148877], [1, -8, 80, -274, 4720, -27848, 205379], [1, -18, 200, -1532, 12200, -66978, 226981], [1, 3, 14, 341, 938, 13467, 300763], [1, -23, 365, -3502, 25915, -115943, 357911], [1, -8, 207, -1088, 15111, -42632, 389017], [1, -7, 125, -822, 9875, -43687, 493039], [1, -8, 208, -1158, 17264, -55112, 571787], [1, 14, 235, 2364, 20915, 110894, 704969], [1, 0, -9, -272, -873, 0, 912673]], 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7800/2/a/bn'], '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': '6-7800e3-1.1-c1e3-0-7', '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': '6-7800e3-1.1-c1e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.891977798790283, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e3-0', 'trace_hash': 1799143553152182189, 'z1': {'__RealLiteral__': 0, 'data': '0.61467378067749353879409291721', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '779191587020379720028195324623,858768664485139560355939980910,1243129389380722561469565335620', 'Lhash_array': ['779191587020379720028195324623', '858768664485139560355939980910', '1243129389380722561469565335620'], 'label': '6-7800e3-1.1-c1e3-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7800/2/a/bn'}