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lfunc_lfunctions • Show schema
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{'Lhash': '1173151275262418368930322275306', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 3.240284586068454], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, -0.8586259247588958], 'a8': [0, 0], 'a9': [-7.499444198712814, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.73866482872497, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 41], 'central_character': '4100.1149', 'coefficient_field': 'CDF', 'conductor': 4100, 'conductor_radical': 410, 'conjugate': '944269102612509796727576637222', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.240284586068454], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0.8586259247588958], [-7.0, 0]], [[1.0, 0], [-6.206943881601213, 0], [11.0, 0]], [[1.0, 0], [0, 1.4149993657767992], [-13.0, 0]], [[1.0, 0], [0, 3.9333185910655186], [-17.0, 0]], [[1.0, 0], [3.825285220291655, 0], 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'3.55286021176547737317131479638576', '4.47061705737293372137325440475832', '5.81296172464417125806273525468151', '6.27061038341598966188331386961551', '6.74603245619807885496443075874660', '7.46257968241262147575232299925559', '8.274614000944226937361056173604853'], 'prelabel': '2-4100-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.721771126908605, 'root_angle': -0.35241638234956674, 'root_number': '0.447213595499957939281834733746255247088123671922305145 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.925453176964695748369816735845', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.67108024071376353396434373532', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.43092277511463363102581008465', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.73866482872497, 'bad_primes': [2, 5, 41], 'central_character': '5.4', 'conductor': 4100, 'conductor_radical': 410, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4100/2/d/c/1149/8'], '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': '2-4100-5.4-c1-0-32', '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': '2-4100-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.721771126908605, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.925453176964695748369816735845', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1173151275262418368930322275306', 'Lhash_array': ['1173151275262418368930322275306'], 'label': '2-4100-5.4-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4100/2/d/c/1149/8'}