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lfunc_lfunctions • Show schema
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{'Lhash': '2349885169789689246153899928675', 'a10': [1.1584011040905782, 2.006409567828765], 'a2': [0.0, -1.276564082537673], 'a3': [-0.5839625916042501, -1.011452878378156], 'a4': [0.3703841431747494, 0.0], 'a5': [-1.5717264767783825, 0.9074367044604613], 'a6': [-1.291184415716899, 0.7454656699876013], 'a7': [0.0, 0.0], 'a8': [0.0, -3.025947258993722], 'a9': [0.8179753832136956, -1.4167749230667432], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.086470608755563, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-3.583053402592878, 0.4021545898875171]]]], 'bad_primes': [7, 13], 'central_character': '637.459', 'coefficient_field': 'CDF', 'conductor': 637, 'conductor_radical': 91, 'conjugate': '946359039927871029866804246163', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 1.276564082537673], [-2.0, 0]], [[1.0, 0], [0.5839625916042501, 1.011452878378156], [-1.5, 2.598076211353316]], [[1.0, 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'8.963858678057750085071769265744530', '10.27205735268847772830881384448504', '10.80559714721814563923901429153325'], 'prelabel': '2-637-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.8743656876203985, 'root_number': '-0.9231151057921436 + 0.3845237332836031*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.43718284381', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.85373254220572528227519880723', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.81329651604730884510982313762', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.52590097769786824750339231136', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.086470608755563, 'bad_primes': [7, 13], 'central_character': '91.4', 'conductor': 637, 'conductor_radical': 91, 'degree': 2, 'index': 29, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/637/2/k/g/459/2'], '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': '2-637-91.4-c1-0-29', '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': '2-637-91.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2553205113144257, 'root_angle': 0.43718284381019923, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.85373254220572528227519880723', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2349885169789689246153899928675', 'Lhash_array': ['2349885169789689246153899928675'], 'label': '2-637-91.4-c1-0-29', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/637/2/k/g/459/2'}