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lfunc_lfunctions • Show schema
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{'Lhash': '1408134057992907765322532852831', 'a10': [-4.851734646010501, 0.0], 'a2': [-1.5365232820979118, 0.0], 'a3': [0.0, 0.0], 'a4': [0.36090379642893916, 0.0], 'a5': [3.1576056819562943, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [2.5185094783852335, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.6926245622462, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '3969.1', 'coefficient_field': 'CDF', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5365232820979118, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1576056819562943, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-5.749161724537352, 0], [11.0, 0]], [[1.0, 0], [-0.36090379642893916, 0], [13.0, 0]], [[1.0, 0], [-2.7768403533410235, 0], [17.0, 0]], [[1.0, 0], [-7.230652246152118, 0], [19.0, 0]], [[1.0, 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[109.0, 0]], [[1.0, 0], [4.686636364561065, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 84, 'label': '2-63e2-1.1-c1-0-84', 'leading_term': '1.7743525080336599032948293524999', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3969/2/a/t/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [1.77435250803366, 1.7696486649470478, 1.7555093547553737, 1.7318568606018356, 1.698579994323469, 1.655560205915036, 1.6027054911431746, 1.539989782078839, 1.4674952439217948, 1.3854548374127238, 1.2942926054997528, 1.1946593600646194, 1.0874617336306793, 0.9738828845173998, 0.8553934765143273, 0.7337518827498359, 0.6109928848022709, 0.4894044553337687, 0.37149253150958755, 0.25993401303373065, 0.15751855660722786, 0.0670800887043888, 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'5.57563035463830511352757176982900', '6.47179518133398942922048421530360', '6.94610348365603553891516947972598', '7.950412597388767987837210143703010', '8.607841460881679186299435000034199'], 'prelabel': '2-63e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.629620285796032, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.11082190766082195375261712101', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.43650366893265572994786448288', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.69671159140971554176645505054', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.6926245622462, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 3969, 'conductor_radical': 21, 'degree': 2, 'index': 84, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3969/2/a/t/1/2'], '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': '2-63e2-1.1-c1-0-84', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-63e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.629620285796032, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11082190766082195375261712101', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1408134057992907765322532852831', 'Lhash_array': ['1408134057992907765322532852831'], 'label': '2-63e2-1.1-c1-0-84', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3969/2/a/t/1/2'}