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lfunc_lfunctions • Show schema
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{'Lhash': '1170556434315955383073599312936', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.7299560740944864, 0.0], 'a4': [0.0, 0.0], 'a5': [0.138350676076554, 0.0], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.0072519817035917485, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 64.16778306430095, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [0, 0]]], [41, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 7, 41], 'central_character': '8036.1', 'coefficient_field': 'CDF', 'conductor': 8036, 'conductor_radical': 574, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.7299560740944864, 0], [3.0, 0]], [[1.0, 0], [-0.138350676076554, 0], [5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.693153583586227, 0], [11.0, 0]], [[1.0, 0], [-5.050042035387641, 0], [13.0, 0]], [[1.0, 0], [-4.382166565814136, 0], [17.0, 0]], [[1.0, 0], [5.730736823263956, 0], [19.0, 0]], [[1.0, 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'3.89493753788066566140847887959020', '5.03560972686145046602791736507886', '5.81817976844318104677271839459074', '6.54506324689659066376713154842198', '7.10948855146574501898304683327784', '8.151827594122396358102171169031624'], 'prelabel': '2-8036-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.010479577672047, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.923406208386764410315545996406', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.83282893929898172799115342578', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.74520742400250981971648887924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 64.16778306430095, 'bad_primes': [2, 7, 41], 'central_character': '1.1', 'conductor': 8036, 'conductor_radical': 574, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8036/2/a/r/1/11'], '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': '2-8036-1.1-c1-0-67', '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': '2-8036-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.010479577672047, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.923406208386764410315545996406', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1170556434315955383073599312936', 'Lhash_array': ['1170556434315955383073599312936'], 'label': '2-8036-1.1-c1-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8036/2/a/r/1/11'}