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lfunc_lfunctions • Show schema
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{'Lhash': '1501782975209185014569200961634', 'a10': [0, 0], 'a2': [0, 0], 'a3': [-1.0066736892499974, 1.7436099764237991], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [-1.3440264001724078, 0], 'a8': [0, 0], 'a9': [-0.5267838332564009, -0.9124163638059779], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.17157638404328, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [2.898151681594239, 3.2558742037235535]]]], 'bad_primes': [2, 5, 19], 'central_character': '1900.201', 'coefficient_field': 'CDF', 'conductor': 1900, 'conductor_radical': 190, 'conjugate': '564406303590684412726711876491', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.0066736892499974, -1.7436099764237991], [-1.5, -2.598076211353316]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3440264001724078, 0], [7.0, 0]], [[1.0, 0], [-5.255942642796556, 0], [11.0, 0]], [[1.0, 0], [1.217732903068941, 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'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1900/2/i/g/201/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05859375', 'prec': 34}, 'plot_values': [1.0196686189003392, 1.0982214737710223, 1.164833252778998, 1.2194450510783303, 1.261802512618067, 1.2914732148787011, 1.3078827281642005, 1.3103664241785364, 1.2982333573412246, 1.270838218757491, 1.227657385482026, 1.1683653370305627, 1.0929080692088773, 1.0015705126842855, 0.8950353088547093, 0.7744305921883021, 0.6413646855398675, 0.4979458565581939, 0.34678553753044283, 0.1909837042960978, 0.034095462756998526, -0.11992168316313491, -0.2667799058769292, -0.4019519184276616, -0.5207794369124814, -0.6185973633628443, -0.6908711013436615, -0.7333437088969216, -0.7421889182092068, -0.7141654406497004, -0.6467674626354255, -0.5383658547067459, -0.38833439390824664, 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'9.564361405141748228842860646677384'], 'prelabel': '2-1900-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': 0.20072869905405352, 'root_number': '0.8076692731769431775884969554457241232147253411159723207 + 0.589635773309106759930864697158397833980535546360665099*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.10036434952702676', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.18469787726902202159307723812', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98424126111597573169556672062', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54958803969096594467863004055', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.17157638404328, 'bad_primes': [2, 5, 19], 'central_character': '19.11', 'conductor': 1900, 'conductor_radical': 190, 'degree': 2, 'index': 20, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1900/2/i/g/201/3'], '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': '2-1900-19.11-c1-0-20', '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': '2-1900-19.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.8950707803637252, 'root_angle': 0.10036434952702676, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.18469787726902202159307723812', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1501782975209185014569200961634', 'Lhash_array': ['1501782975209185014569200961634'], 'label': '2-1900-19.11-c1-0-20', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1900/2/i/g/201/3'}