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lfunc_lfunctions • Show schema
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{'Lhash': '1353314954791712131996362202669', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.4142135623730951, -1.4142135623730951], 'a4': [0, 0], 'a5': [1.4142135623730951, 1.4142135623730951], 'a6': [0, 0], 'a7': [0, 4.0], 'a8': [0, 0], 'a9': [0, -1.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.176681166979115, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]]], 'bad_primes': [2], 'central_character': '1024.769', 'coefficient_field': 'CDF', 'conductor': 1024, 'conductor_radical': 2, 'conjugate': '2075800131098969426990735265381', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -3.0]], [[1.0, 0], [-1.4142135623730951, -1.4142135623730951], [0, 5.0]], [[1.0, 0], [0, -4.0], [-7.0, 0]], [[1.0, 0], [1.4142135623730951, 1.4142135623730951], [0, 11.0]], [[1.0, 0], [-1.4142135623730951, 1.4142135623730951], [0, -13.0]], [[1.0, 0], [-2.0, 0], [17.0, 0]], 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['1.06757726028612270039533786595031', '2.56983300073975949157135885651231', '3.83788875370598494527992325939772', '4.37316585694665343858710972663634', '5.35633980321687366441404325790500', '6.62333895088324518299342854291463', '7.45948193348215694965451488622686', '8.474509505206986133625904796929504', '9.105151362839531963921654237869455', '9.936203449858407066101766210083194'], 'prelabel': '2-2e10-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': -0.12500000000000003, 'root_number': '0.92387953251128675612818318939678828682241662586364248612 - 0.38268343236508977172845998403039886676134456248562704143*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0625', 'prec': 24}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.06757726028612270039533786595', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.56983300073975949157135885651', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83788875370598494527992325940', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.176681166979115, 'bad_primes': [2], 'central_character': '16.5', 'conductor': 1024, 'conductor_radical': 2, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1024/2/e/m/769/2'], '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': '2-2e10-16.5-c1-0-11', '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': '2-2e10-16.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8594896689757623, 'root_angle': -0.06250000000000001, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.06757726028612270039533786595', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1353314954791712131996362202669', 'Lhash_array': ['1353314954791712131996362202669'], 'label': '2-2e10-16.5-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1024/2/e/m/769/2'}