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lfunc_lfunctions • Show schema
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{'Lhash': '1284023146992454857806267576732', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.5264397284942957, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 33.058066436810094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '4140.1', 'coefficient_field': 'CDF', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.5264397284942957, 0], [7.0, 0]], [[1.0, 0], [-3.5982107418842784, 0], [11.0, 0]], [[1.0, 0], [-5.598210741884278, 0], [13.0, 0]], [[1.0, 0], [4.0717710133899825, 0], [17.0, 0]], [[1.0, 0], [1.5982107418842784, 0], [19.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 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'5.57628269647893686768030019779164', '6.35328800989069438960007878872688', '6.67183457801333938463394652085253', '7.82579156835232422114346742314764', '8.537581665840920820538938978246383'], 'prelabel': '2-4140-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01291566206120024120795033286', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.82678201657040856791767364805', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.89498398684534227420128739029', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 33.058066436810094, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 4140, 'conductor_radical': 690, 'degree': 2, 'index': 18, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4140/2/a/s/1/2'], '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': '2-4140-1.1-c1-0-18', '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': '2-4140-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.749614459840772, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01291566206120024120795033286', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1284023146992454857806267576732', 'Lhash_array': ['1284023146992454857806267576732'], 'label': '2-4140-1.1-c1-0-18', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4140/2/a/s/1/2'}