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lfunc_lfunctions • Show schema
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{'Lhash': '1944686030561434600678329326486', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.348445480393272, 0.1379593252266736], 'a4': [0.5358267949789967, 0.8443279255020151], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.6265871500319126, -0.5884044992220088], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6862143923703783, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [-0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [-0.8763066800438636, -0.48175367410171527]]]], 'bad_primes': [5, 11], 'central_character': '1375.1286', 'coefficient_field': 'CDF', 'conductor': 1375, 'conductor_radical': 55, 'conjugate': '1909760778718399151111762595407', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0], [-0.5358267949789967, -0.8443279255020151]], [[1.0, 0], [-0.348445480393272, -0.1379593252266736], [0.7289686274214116, 0.6845471059286887]], 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'positive_zeros': ['1.53408678243934952776277110015369', '2.61236435278439496055815234491064', '3.36923559371122185973073482625045', '4.87366628280298513786281417356840', '5.82631661314716290250808884703997', '6.44057779087443568833325492336758', '7.21339590637989932253254989072626', '8.046314869775991540754831587857215', '9.202981874719485476734629644551312', '9.660069335815935025392222887232989'], 'prelabel': '2-1375-1375.1286-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8283805842548329, 'root_angle': -0.048, 'root_number': '0.98865174473791400858000916042905 - 0.15022558912075705501672757501258*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.024', 'prec': 20}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53408678243934952776277110015', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.61236435278439496055815234491', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36923559371122185973073482625', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6862143923703783, 'bad_primes': [5, 11], 'central_character': '1375.1286', 'conductor': 1375, 'conductor_radical': 55, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1375/1/ch/a/1286/1'], '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': '2-1375-1375.1286-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-1375-1375.1286-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8283805842548329, 'root_angle': -0.024, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53408678243934952776277110015', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1944686030561434600678329326486', 'Lhash_array': ['1944686030561434600678329326486'], 'label': '2-1375-1375.1286-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1375/1/ch/a/1286/1'}