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lfunc_lfunctions • Show schema
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{'Lhash': '277337483463553400984214315404', 'a10': [-12533.676193595436, -839.9735319664426], 'a2': [-6.355819394998424, -6.355819394998424], 'a3': [-140.2956981199847, 0.34218273789954506], 'a4': [0.0, -431.20711963632374], 'a5': [1052.0791179250616, -919.920936616851], 'a6': [893.8689708280183, 889.5192674636671], 'a7': [-7865.99943425172, 7865.99943425172], 'a8': [-5994.8541044851445, 5994.8541044851445], 'a9': [19682.765821947767, -96.01353219644886], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.725537542458099, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [140.2956981199847, -0.34218273789954506]]], [5, [[1.0, 0], [-1052.0791179250616, 919.920936616851]]]], 'bad_primes': [3, 5], 'central_character': '15.8', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '2248614130548872162813988774764', 'degree': 2, 'euler_factors': [[[1.0, 0], [6.355819394998424, 6.355819394998424], 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'12.67204768065423243394151261361790', '13.79073183254233479226081432043202', '16.20034037799159283563974055325922', '16.69924376910559785529676440009636'], 'prelabel': '2-15-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77948512182708, 'root_angle': -0.5532677403472392, 'root_number': '-0.16656556248034993 - 0.9860303815783795*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.276633870174', 'prec': 50}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.21878069825677612834486054859', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.51961274540368439748814843124', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.19897463264964757868351767423', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.725537542458099, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/10/e/a/8/7'], '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': '2-15-15.8-c9-0-0', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-15-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77948512182708, 'root_angle': -0.2766338701736196, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '0.21878069825677612834486054859', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '277337483463553400984214315404', 'Lhash_array': ['277337483463553400984214315404'], 'label': '2-15-15.8-c9-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/10/e/a/8/7'}