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lfunc_lfunctions • Show schema
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{'Lhash': '2118204188979798215599327922391', 'a10': [0.5345342951887144, -1.5746872552977889], 'a2': [0.6087614290087207, -0.7933533402912352], 'a3': [0.0, 0.0], 'a4': [-0.25881904510252074, -0.9659258262890683], 'a5': [1.5746872552977889, -0.5345342951887144], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [-0.9238795325112867, -0.3826834323650898], 'a9': [0.9914448613738104, -0.1305261922200516], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.6628846220931641, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.6087614290087207, 0.7933533402912352]]], [7, [[1.0, 0], [0, 0]]], [17, [[1.0, 0], [-0.9914448613738104, -0.1305261922200516]]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.2579', 'coefficient_field': 'CDF', 'conductor': 3332, 'conductor_radical': 238, 'conjugate': '1673160272305510218914033815564', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.6087614290087207, 0.7933533402912352]], [[1.0, 0], [0, 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'4.72514025068184660637238381207954', '5.35870789255967555539216356582125', '5.85177288685282521084676760122196', '6.88204261696370832228427210806766', '7.17455044995273549527328838392534', '8.042000406890544837980758582650755', '9.005031086838998283917851650280405'], 'prelabel': '2-3332-476.199-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.5254817251991404, 'root_number': '-0.079967724391049143882102642692369 + 0.99679745337541728885684757109566*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2627408625995702', 'prec': 60}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.67096847396154277911218242612', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.74084307522887046437466154344', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44527533878281614325521235279', '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': '476.199', 'conductor': 3332, 'conductor_radical': 238, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/ce/b/2579/1'], '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': '2-3332-476.199-c0-0-3', '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': '2-3332-476.199-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2895288372476066, 'root_angle': 0.2627408625995702, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.67096847396154277911218242612', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2118204188979798215599327922391', 'Lhash_array': ['2118204188979798215599327922391'], 'label': '2-3332-476.199-c0-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/ce/b/2579/1'}