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lfunc_lfunctions • Show schema
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{'Lhash': '1096782238102653945270921213089', 'a10': [1.4253353773155486, -1.2350601349720505], 'a2': [-2.2876739145676415, -0.1089753397324619], 'a3': [1.5831933226776722, 0.7024947708195642], 'a4': [3.230632469577262, 0.30848799746583416], 'a5': [-0.5959802178636705, 0.568265989925083], 'a6': [-3.5452754596970415, -1.7796079925250552], 'a7': [-0.6453101135680587, 3.3481868047303958], 'a8': [-2.8231032731954206, -0.4059009723916627], 'a9': [2.0130021939423357, 2.2243700607550316], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6529033218405047, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.5831933226776722, -0.7024947708195642]]], [23, [[1.0, 0], [-4.573359009524836, -1.4437407558138722]]]], 'bad_primes': [3, 23], 'central_character': '207.113', 'coefficient_field': 'CDF', 'conductor': 207, 'conductor_radical': 69, 'conjugate': '2689748621255525650306653723900', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'root_analytic_conductor': 1.2856528776619702, 'root_angle': -0.24483772303954693, 'root_number': '0.03242985566852643 - 0.9994740138999706*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.24483772304', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.865208629179986896754823279397', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.63281929800381546449966487114', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38764779604688639698534148498', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6529033218405047, 'bad_primes': [3, 23], 'central_character': '207.113', 'conductor': 207, 'conductor_radical': 69, 'degree': 2, 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/207/2/o/a/113/4'], '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': '2-207-207.113-c1-0-4', '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': '2-207-207.113-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2856528776619702, 'root_angle': -0.24483772303954693, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.865208629179986896754823279397', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1096782238102653945270921213089', 'Lhash_array': ['1096782238102653945270921213089'], 'factors': ['2-207-207.113-c1-0-4'], 'label': '2-207-207.113-c1-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/207/2/o/a/113/4'}