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lfunc_lfunctions • Show schema
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{'Lhash': '2944523494230558578670967261417', 'a10': [-28.077692325759273, -55.81729126840431], 'a2': [-0.2299980555104296, 3.993382137294329], 'a3': [7.74459030175246, -13.414023886440443], 'a4': [-15.894201788922842, -1.836940252975558], 'a5': [-13.527622454078484, 7.810176465357839], 'a6': [51.78608266722272, 34.012307982132924], 'a7': [43.55437314672147, -22.45031357901595], 'a8': [10.991239898852164, -63.04912882416283], 'a9': [-79.45735788399652, -137.62418089026548], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.788717932695284, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.2299980555104296, -3.993382137294329]]], [7, [[1.0, 0], [-43.55437314672147, 22.45031357901595]]]], 'bad_primes': [2, 7], 'central_character': '56.11', 'coefficient_field': 'CDF', 'conductor': 56, 'conductor_radical': 14, 'conjugate': '1315319794688502177215690067814', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2299980555104296, 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['2.32281946910325517256304020241810', '4.21038817906317688226705322778394', '4.68837959642791898556534458780496', '8.027600421790773724764363646479782', '9.156792849850621432197041651313119', '9.730652536574107171782450260031292', '11.25503540762152828433354989781964', '11.93932612228594654460759370181369', '13.73782234433827970724083259426620', '14.65057652088043689517815821923526'], 'prelabel': '2-56-56.11-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.40597546385978, 'root_angle': 0.25694978845680155, 'root_number': '0.6915009281257689 + 0.7223755715700803*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.128474894228', 'prec': 47}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.32281946910325517256304020242', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.21038817906317688226705322778', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.68837959642791898556534458780', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.788717932695284, 'bad_primes': [2, 7], 'central_character': '56.11', 'conductor': 56, 'conductor_radical': 14, 'degree': 2, 'index': 22, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/56/5/k/a/11/15'], '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': '2-56-56.11-c4-0-22', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'prelabel': '2-56-56.11-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.40597546385978, 'root_angle': 0.12847489422840078, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '2.32281946910325517256304020242', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2944523494230558578670967261417', 'Lhash_array': ['2944523494230558578670967261417'], 'label': '2-56-56.11-c4-0-22', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/56/5/k/a/11/15'}