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lfunc_lfunctions • Show schema
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{'Lhash': '1331843976316684393906572774885', 'a10': [0, -5.79555495773441], 'a2': [-1.7320508075688772, 0], 'a3': [0, 0], 'a4': [1.0, 0], 'a5': [0, 3.3460652149512318], 'a6': [0, 0], 'a7': [0, 1.035276180410083], 'a8': [1.7320508075688772, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.695708780117439, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 11], 'central_character': '1089.1088', 'coefficient_field': 'CDF', 'conductor': 1089, 'conductor_radical': 33, 'conjugate': '864930283648516060147257159365', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.7320508075688772, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -3.3460652149512318], [-5.0, 0]], [[1.0, 0], [0, -1.035276180410083], [-7.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 6.174492339697422], [-13.0, 0]], [[1.0, 0], [-4.267949192431122, 0], [17.0, 0]], [[1.0, 0], [0, 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'4.61821961762401860156742153419186', '5.57925922923502941948474451950399', '6.81827449628234482064041230438964', '7.76000328763721469962363578617389', '8.361869721447544068278778562491996', '9.054237354203499761264014542463104', '9.760502355358582352762310535608378'], 'prelabel': '2-33e2-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.948848721131255, 'root_angle': 0.021012419874782216, 'root_number': '0.99782196840055497535597709342084173711097949905149182612 + 0.0659645312061100623400871756332933895528400943398610362*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.010506209937391108', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.05063964477033145930900136371', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.75768412606207051868366068912', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.83805922632564112381975736196', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.695708780117439, 'bad_primes': [3, 11], 'central_character': '33.32', 'conductor': 1089, 'conductor_radical': 33, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1089/2/d/e/1088/2'], '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': '2-33e2-33.32-c1-0-16', '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': '2-33e2-33.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.948848721131255, 'root_angle': 0.010506209937391108, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05063964477033145930900136371', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1331843976316684393906572774885', 'Lhash_array': ['1331843976316684393906572774885'], 'label': '2-33e2-33.32-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1089/2/d/e/1088/2'}