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lfunc_lfunctions • Show schema
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{'Lhash': '1582368877998921861138644373484', 'a10': [0.7326258162712896, 0.8353996340690167], 'a2': [0.9914448613738104, 0.1305261922200516], 'a3': [0.0, 0.0], 'a4': [0.9659258262890683, 0.25881904510252074], 'a5': [0.8353996340690167, 0.7326258162712896], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.9238795325112867, 0.3826834323650898], 'a9': [-0.6087614290087207, -0.7933533402912352], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.9914448613738104, -0.1305261922200516]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.7933533402912352, -0.6087614290087207]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.607', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '2223480502397513415698859164048', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.9914448613738104, -0.1305261922200516]], [[1.0, 0], [0, 0], 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'4.23831885762843513765121234881356', '5.12181641146545939122589498297433', '5.45136593535720083868508903079346', '6.07948821270604965305855747784720', '7.25048524690780573808427788860129', '7.79340509341281811360521437593856', '8.643398774171405332026871177876913'], 'prelabel': '2-3332-476.131-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.2551712927090605, 'root_number': '0.69552624916684973136699097640137 - 0.71850068665234639660310887546986*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.12758564635453026', 'prec': 67}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.24826894549178629095598830741', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44690739075334442720094291530', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93743532467631561619264879415', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'bad_primes': [2, 7, 17], 'central_character': '476.131', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/ce/a/607/1'], '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': '2-3332-476.131-c0-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-3332-476.131-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': -0.12758564635453026, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.24826894549178629095598830741', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1582368877998921861138644373484', 'Lhash_array': ['1582368877998921861138644373484'], 'label': '2-3332-476.131-c0-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/ce/a/607/1'}