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lfunc_lfunctions • Show schema
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{'Lhash': '512235960692231278291218820289', 'a10': [1.0447862785870676, -4.229570986892662], 'a2': [-1.9377027922054404, -0.2036607701469188], 'a3': [-0.500957893459156, 2.3568215891488444], 'a4': [1.7569192001563125, 0.37344470431727117], 'a5': [-0.30638450326961425, 2.2149782247589322], 'a6': [1.4506996088781006, -4.464794303630709], 'a7': [-2.52107144233034, 0.8026199490832626], 'a8': [0.3777005603792172, 0.12272235134541373], 'a9': [-2.5630128191312473, -1.1411268278907303], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0.30638450326961425, -2.2149782247589322]]], [7, [[1.0, 0], [2.52107144233034, -0.8026199490832626]]]], 'bad_primes': [5, 7], 'central_character': '175.109', 'coefficient_field': 'CDF', 'conductor': 175, 'conductor_radical': 35, 'conjugate': '3630994976928236807225985822001', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'-0.9874752986604657 + 0.15777368137754835*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.474784177004', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.40408292363842818713151899360', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.86447933462948192018786262382', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51365107214742066804641230000', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3973820353724073, 'bad_primes': [5, 7], 'central_character': '175.109', 'conductor': 175, 'conductor_radical': 35, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/175/2/t/a/109/4'], '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': '2-175-175.109-c1-0-0', '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': '2-175-175.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.182109146979418, 'root_angle': 0.47478417700381353, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.40408292363842818713151899360', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '512235960692231278291218820289', 'Lhash_array': ['512235960692231278291218820289'], 'factors': ['2-175-175.109-c1-0-0'], 'label': '2-175-175.109-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/175/2/t/a/109/4'}