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lfunc_lfunctions • Show schema
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{'Lhash': '1467357755671011262056540532909', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-45.0, -67.34983296193094], 'a4': [0.0, 0.0], 'a5': [0.0, 224.4994432064365], 'a6': [0.0, 0.0], 'a7': [1750.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-2511.0, 6061.484966573785], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 19.554173282934112, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [45.0, 67.34983296193094]]]], 'bad_primes': [2, 3], 'central_character': '48.17', 'coefficient_field': 'CDF', 'conductor': 48, 'conductor_radical': 6, 'conjugate': '1036083342924444564935480850025', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [45.0, 67.34983296193094]], [[1.0, 0], [0, -224.4994432064365], [-390625.0, 0]], [[1.0, 0], [-1750.0, 0], [5764801.0, 0]], [[1.0, 0], [0, -6959.482739399531], [-214358881.0, 0]], [[1.0, 0], [-25730.0, 0], [815730721.0, 0]], [[1.0, 0], [0, 74893.0142536672], 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'positive_zeros': ['1.15754116742170621321686701466121', '3.61288252650347321324123224000225', '4.98065529848868112208831702534081', '6.17716237888234916682840836212755', '8.172804267250429017577728294864750', '9.310256699504618723072463268847476', '10.76121746546170846429735256890089', '11.46640651235785166298089456403100', '12.86274930643841808110116366316620', '14.27448520457435243076198718688646'], 'prelabel': '2-48-3.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.422010095299886, 'root_angle': 0.31250561891173007, 'root_number': '0.5555555555555556 + 0.8314794192830981*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.156252809456', 'prec': 47}, 'spectral_label': 'c8-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.15754116742170621321686701466', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.61288252650347321324123224000', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.98065529848868112208831702534', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 19.554173282934112, 'bad_primes': [2, 3], 'central_character': '3.2', 'conductor': 48, 'conductor_radical': 6, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/48/9/e/b/17/1'], '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': '2-48-3.2-c8-0-8', 'motivic_weight': 8, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [8], 'order_of_vanishing': 0, 'prelabel': '2-48-3.2-c8-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.422010095299886, 'root_angle': 0.15625280945586503, 'self_dual': False, 'spectral_label': 'c8-0', 'z1': {'__RealLiteral__': 0, 'data': '1.15754116742170621321686701466', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1467357755671011262056540532909', 'Lhash_array': ['1467357755671011262056540532909'], 'label': '2-48-3.2-c8-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/48/9/e/b/17/1'}