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lfunc_lfunctions • Show schema
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{'Lhash': '1964948983652192861433512602740', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-2.525828583525087, -1.4582878126250602], 'a4': [0, 0], 'a5': [22.121261531942864, -38.31514890084397], 'a6': [0, 0], 'a7': [11.190361468714501, 0], 'a8': [0, 0], 'a9': [-36.246793311098436, -62.78128762627022], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 31.424468777488684, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-255.30823441916456, 255.22285445815567]]]], 'bad_primes': [2, 19], 'central_character': '304.65', 'coefficient_field': 'CDF', 'conductor': 304, 'conductor_radical': 38, 'conjugate': '1096828541004201738520309344544', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [2.525828583525087, 1.4582878126250602], [40.5, 70.14805770653953]], [[1.0, 0], [-22.121261531942864, 38.31514890084397], [-312.5, -541.2658773652742]], [[1.0, 0], [-11.190361468714501, 0], [2401.0, 0]], [[1.0, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 31, 'label': '2-304-19.8-c4-0-31', 'leading_term': '2.406499187137134403443674734677741300960686007963551003', 'load_key': 'CMFs-workshop', 'motivic_weight': 4, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [4], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/304/5/r/d/65/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0703125', 'prec': 30}, 'plot_values': [2.4064991871371344, 2.558488845154296, 2.689726488985876, 2.7979625749893566, 2.881212311099284, 2.93777862587571, 2.966276016586051, 2.965655144659474, 2.9352278241565273, 2.8746918278372746, 2.7841547257032877, 2.6641557819817048, 2.5156847773292212, 2.3401965017110045, 2.1396195871401513, 1.9163583242966136, 1.6732861377386234, 1.4137294842976633, 1.1414410900585776, 0.8605616531060158, 0.5755694101584387, 0.29121729153581516, 0.012457764774370602, -0.2556441153625445, -0.5080084838428812, 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'7.12045179011806536614011025365355', '8.658127210521459437717343630015873', '9.588299151457351519790780288412172', '10.49479466098467638442865909378419', '11.38554963082053504668485007470396'], 'prelabel': '2-304-19.8-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.605753185566475, 'root_angle': 0.5522264761515578, 'root_number': '-0.1633391468890348458687922491368786164904027564532320445 + 0.9865699788122291623053020384333072350703623885500614645*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2761132380757789', 'prec': 60}, 'spectral_label': 'c4-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55007143395697598832389261153', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79455539942626497024035811645', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.07406475727481762659046064779', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 31.424468777488684, 'bad_primes': [2, 19], 'central_character': '19.8', 'conductor': 304, 'conductor_radical': 38, 'degree': 2, 'index': 31, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/304/5/r/d/65/9'], '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': '2-304-19.8-c4-0-31', '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': '2-304-19.8-c4-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.605753185566475, 'root_angle': 0.2761132380757789, 'self_dual': False, 'spectral_label': 'c4-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55007143395697598832389261153', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1964948983652192861433512602740', 'Lhash_array': ['1964948983652192861433512602740'], 'label': '2-304-19.8-c4-0-31', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/304/5/r/d/65/9'}