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lfunc_lfunctions • Show schema
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{'Lhash': '2572801623731148315766783070135', 'a10': [0.0, 0.0], 'a2': [0.8660254037844386, 0.5], 'a3': [0.8660254037844386, -0.5], 'a4': [0.5, 0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [1.0, 0.0], 'a7': [-0.8660254037844386, -0.5], 'a8': [3.9689140359382235e-80, 1.0], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8660254037844386, -0.5]]], [3, [[1.0, 0], [-0.8660254037844386, 0.5]]], [5, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '900.151', 'coefficient_field': 'CDF', 'conductor': 900, 'conductor_radical': 30, 'conjugate': '2526690610670824241131686445877', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.8660254037844386, -0.5]], [[1.0, 0], [-0.8660254037844386, 0.5]], [[1.0, 0], [0, 0]], [[1.0, 0], [0.8660254037844386, 0.5], [0.5, 0.8660254037844386]], [[1.0, 0], [0, 0], [0.5, 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-0.6770199526551399, -0.30894757296094344], 'positive_zeros': ['2.02958261785064266889205810693175', '2.96282099632115777682341682215751', '3.80229274777523275152376534826416', '4.71981590459968416260113368717221', '5.79215999053065059993379423144171', '6.63735453477614437838846371569709', '7.76459623773891057538114256539763', '8.807323760400979211374242548427960', '9.714010054932680819325937152914451', '10.08910766686788402894711233567048'], 'prelabel': '2-30e2-36.7-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': -0.05555555555555555, 'root_number': '0.93969262078590838405410927732446 - 0.34202014332566873304409961468239*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.05555555555555555', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.02958261785064266889205810693', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.96282099632115777682341682216', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.80229274777523275152376534826', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.4491585113697022, 'bad_primes': [2, 3, 5], 'central_character': '36.7', 'conductor': 900, 'conductor_radical': 30, 'degree': 2, 'index': 1, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/900/1/t/a/151/2', 'ArtinRepresentation/2.900.24t65.b.c'], 'is_instance_Artin': True, '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': '2-30e2-36.7-c0-0-1', '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': '2-30e2-36.7-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6701928911661942, 'root_angle': -0.05555555555555555, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.02958261785064266889205810693', 'prec': 103}}
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lfunc_instances • Show schema
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id: 19810737
{'Lhash': '2572801623731148315766783070135', 'Lhash_array': ['2572801623731148315766783070135'], 'factors': ['2-30e2-36.7-c0-0-1'], 'label': '2-30e2-36.7-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/900/1/t/a/151/2'}
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id: 24603816
{'Lhash': '2572801623731148315766783070135', 'Lhash_array': ['2572801623731148315766783070135'], 'factors': ['2-30e2-36.7-c0-0-1'], 'label': '2-30e2-36.7-c0-0-1', 'type': 'Artin', 'url': 'ArtinRepresentation/2.900.24t65.b.c'}