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lfunc_lfunctions • Show schema
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{'Lhash': '1010680803588310497936558339726', 'a10': [2985811.9685437214, -6910775.322304755], 'a2': [0.0, 43.09396690763303], 'a3': [0.0, 6725.99057612346], 'a4': [30910.91001616383, 0.0], 'a5': [-160365.26266233993, -69286.07837248928], 'a6': [-289849.615308516, 0.0], 'a7': [0.0, 1297165.373298072], 'a8': [0.0, 2744176.8409507056], 'a9': [-30890042.230101593, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.134675254996026, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '7.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [160365.26266233993, 69286.07837248928]]]], 'bad_primes': [5], 'central_character': '5.4', 'coefficient_field': 'CDF', 'conductor': 5, 'conductor_radical': 5, 'conjugate': '4276470942984702454965216142492', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -43.09396690763303], [-32768.0, 0]], [[1.0, 0], [0, -6725.99057612346], [-14348907.0, 0]], [[1.0, 0], [160365.26266233993, 69286.07837248928]], [[1.0, 0], [0, -1297165.373298072], 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'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5/16/b/a/4/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [1.464916923349022, 1.1300139410653567, 0.7933790427547059, 0.4651177184182123, 0.15516756493585016, -0.12695231884029945, -0.37238904263341877, -0.5731969535842701, -0.7225676922284282, -0.8150444122256829, -0.846714706566882, -0.8153762236908463, -0.7206684964514406, -0.5641642151136785, -0.34941312531159147, -0.08193199520832625, 0.23086526006064423, 0.5798021272606325, 0.9541419876289134, 1.3418597643207237, 1.7299813847551047, 2.1049867143590784, 2.453268238934031, 2.7616341346275326, 3.0178406253219547, 3.2111348849509693, 3.3327864298051493, 3.376582223328064, 3.3392588584587206, 3.22084446501942, 3.024883667222422, 2.7585212029203423, 2.432423860616226, 2.060526252502986, 1.659593570804183, 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'rational': False, 'root_analytic_conductor': 2.671081289477358, 'root_angle': -0.8701842280728109, 'root_number': '-0.9179843290690586 - 0.3966166557062757*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.435092114036', 'prec': 50}, 'spectral_label': 'c15-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.797286573608174255919263181731', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.68510038089086795817311505079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.78719957234729993419978858596', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.134675254996026, 'bad_primes': [5], 'central_character': '5.4', 'conductor': 5, 'conductor_radical': 5, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5/16/b/a/4/4'], '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': '2-5-5.4-c15-0-1', 'motivic_weight': 15, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [15], 'order_of_vanishing': 0, 'prelabel': '2-5-5.4-c15-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.671081289477358, 'root_angle': -0.43509211403640546, 'self_dual': False, 'spectral_label': 'c15-0', 'z1': {'__RealLiteral__': 0, 'data': '0.797286573608174255919263181731', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1010680803588310497936558339726', 'Lhash_array': ['1010680803588310497936558339726'], 'label': '2-5-5.4-c15-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5/16/b/a/4/4'}