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lfunc_lfunctions • Show schema
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{'Lhash': '1686381402617278019185212935118', 'a10': [-3.3189517275847145, -0.7054649675641869], 'a2': [-0.5527791225252713, 2.6006213037234707], 'a3': [-0.5331222506695099, -0.5920922435274638], 'a4': [-4.630575491795354, -2.061665038433974], 'a5': [0.0, 1.2762149271148266], 'a6': [1.834506552210737, -1.0591528517490012], 'a7': [1.0893295180248854, -2.4466741563832484], 'a8': [4.795781806333883, -6.600827372762543], 'a9': [0.24723149911649872, -2.352250587158178], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.217971201457601, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[13, [[1.0, 0], [-1.5698550203798578, -3.2458520013993484]]], [31, [[1.0, 0], [0.5916854485961924, -5.536235935174686]]]], 'bad_primes': [13, 31], 'central_character': '403.4', 'coefficient_field': 'CDF', 'conductor': 403, 'conductor_radical': 403, 'conjugate': '1160029136644305004890096148139', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.5527791225252713, 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'0.4022186958923027 - 0.9155436203014553*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.184119574062', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.33032035981654550525626217324', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.51964510451631339047015518662', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.98471085950971697516915676645', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.217971201457601, 'bad_primes': [13, 31], 'central_character': '403.4', 'conductor': 403, 'conductor_radical': 403, 'degree': 2, 'index': 14, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/403/2/bs/a/4/1'], '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': '2-403-403.4-c1-0-14', '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': '2-403-403.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7938704528080063, 'root_angle': -0.18411957406179585, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33032035981654550525626217324', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1686381402617278019185212935118', 'Lhash_array': ['1686381402617278019185212935118'], 'label': '2-403-403.4-c1-0-14', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/403/2/bs/a/4/1'}