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lfunc_lfunctions • Show schema
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{'Lhash': '1537064458857051568250773125224', 'a10': [163.97375593618253, -24.715067056964415], 'a2': [3.7393113443488177, -1.1534247948521874], 'a3': [0.0993194667462685, 0.2530618741319391], 'a4': [-13.787580205515884, 9.400213017547921], 'a5': [41.903133386320455, 6.315881133703482], 'a6': [0.6632742489745389, 0.8317196012070891], 'a7': [64.15015905074002, 112.65769877715752], 'a8': [-118.7877506873129, 148.95512796205594], 'a9': [178.07742889898338, -165.23170733754822], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.8588071708360525, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-64.15015905074002, -112.65769877715752]]]], 'bad_primes': [7], 'central_character': '49.25', 'coefficient_field': 'CDF', 'conductor': 49, 'conductor_radical': 7, 'conjugate': '2610659477791214971029203839788', 'degree': 2, 'euler_factors': [[[1.0, 0], [-3.7393113443488177, 1.1534247948521874], [26.439640778111837, 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'0.7691237033492353 - 0.6390999365876651*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.11034649093', 'prec': 47}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.21253006039701835684817270298', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.89749565791239143722011769702', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.23342146430829724144135897211', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.8588071708360525, 'bad_primes': [7], 'central_character': '49.25', 'conductor': 49, 'conductor_radical': 7, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/49/6/g/a/25/14'], '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': '2-7e2-49.25-c5-0-8', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-7e2-49.25-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8033564116672807, 'root_angle': -0.1103464909296981, 'self_dual': False, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '1.21253006039701835684817270298', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1537064458857051568250773125224', 'Lhash_array': ['1537064458857051568250773125224'], 'label': '2-7e2-49.25-c5-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/49/6/g/a/25/14'}