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lfunc_lfunctions • Show schema
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{'Lhash': '1614093010091566583718266095890', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0.8740320488976422], 'a4': [0, 0], 'a5': [2.23606797749979, 0], 'a6': [0, 0], 'a7': [0, -2.8284271247461903], 'a8': [0, 0], 'a9': [2.23606797749979, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 12.137261107234623, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.23606797749979, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 19], 'central_character': '1520.609', 'coefficient_field': 'CDF', 'conductor': 1520, 'conductor_radical': 190, 'conjugate': '1379883225086088635621773382711', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.8740320488976422], [-3.0, 0]], [[1.0, 0], [-2.23606797749979, 0]], [[1.0, 0], [0, 2.8284271247461903], [-7.0, 0]], [[1.0, 0], [-0.7639320225002103, 0], [11.0, 0]], [[1.0, 0], [0, -5.450523271439116], [-13.0, 0]], [[1.0, 0], [0, 7.404918347287665], 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'4.55380762098603427637189860558718', '5.63888996969578368688672453368760', '6.08678966076541757880115864477299', '6.89199686909356662442319023055420', '8.072531279329500846321863866101576', '8.528384915927602925103755657517263', '9.505311258893448360383406267947418'], 'prelabel': '2-1520-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'root_number': '1', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27329487305174095836253820266', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.19174949254656807452003272147', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.20096910062222297460504201692', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 12.137261107234623, 'bad_primes': [2, 5, 19], 'central_character': '5.4', 'conductor': 1520, 'conductor_radical': 190, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1520/2/d/f/609/3'], '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': '2-1520-5.4-c1-0-33', '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': '2-1520-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.483857216826577, 'root_angle': 0.0, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27329487305174095836253820266', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1614093010091566583718266095890', 'Lhash_array': ['1614093010091566583718266095890'], 'label': '2-1520-5.4-c1-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1520/2/d/f/609/3'}