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lfunc_lfunctions • Show schema
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{'Lhash': '2472340974850926608270353888377', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.2928932188134525, -1.7071067811865475], 'a4': [0.0, 0.0], 'a5': [-0.7071067811865476, 2.1213203435596424], 'a6': [0.0, 0.0], 'a7': [-1.0, -1.0], 'a8': [0.0, 0.0], 'a9': [-2.8284271247461903, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.665638594042921, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.2928932188134525, 1.7071067811865475]]], [5, [[1.0, 0], [0.7071067811865476, -2.1213203435596424]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.257', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '258789992061754727001587872416', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.2928932188134525, 1.7071067811865475]], [[1.0, 0], [0.7071067811865476, -2.1213203435596424]], [[1.0, 0], [1.0, 1.0], [0, 7.0]], [[1.0, 0], [0, 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'5.21170507379327805897836170796625', '5.77971823397591661707713077093293', '7.18418168116567936861454056583771', '8.209684779455155106840401339325512', '8.852066666520139752078336198561556', '9.609159076809507427011314821272509', '10.16423732328131222046756948721083'], 'prelabel': '2-960-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.9802949151594798, 'root_number': '-0.9980844756861901 + 0.06186581765581963*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.49014745758', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.95033313943590074673392815114', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.44324479722191991400280460006', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.16881072783887814163433241579', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.665638594042921, 'bad_primes': [2, 3, 5], 'central_character': '15.2', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/2/v/k/257/1'], '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': '2-960-15.2-c1-0-38', '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': '2-960-15.2-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.768688966648822, 'root_angle': 0.4901474575797399, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.95033313943590074673392815114', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2472340974850926608270353888377', 'Lhash_array': ['2472340974850926608270353888377'], 'label': '2-960-15.2-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/2/v/k/257/1'}