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lfunc_lfunctions • Show schema
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{'Lhash': '2365459558012154205384259487245', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [7.998493043435337, 0.0], 'a4': [0.0, 0.0], 'a5': [5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-9.935007713630295, 0.0], 'a8': [0.0, 0.0], 'a9': [36.97589096588348, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 75.52244480734802, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-5.0, 0]]]], 'bad_primes': [2, 5], 'central_character': '1280.1', 'coefficient_field': 'CDF', 'conductor': 1280, 'conductor_radical': 10, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-7.998493043435337, 0], [27.0, 0]], [[1.0, 0], [-5.0, 0]], [[1.0, 0], [9.935007713630295, 0], [343.0, 0]], [[1.0, 0], [60.0131576586571, 0], [1331.0, 0]], [[1.0, 0], [-32.311032803797154, 0], [2197.0, 0]], [[1.0, 0], [-12.524592501471776, 0], [4913.0, 0]], [[1.0, 0], [116.81161728679503, 0], [6859.0, 0]], [[1.0, 0], 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'5.60970228448851984659187746141974', '6.43026726681854179409219500913874', '7.57316100764805992063501550368140', '8.200986196244737107243908700557677', '8.730595572778350580632557505497736'], 'prelabel': '2-1280-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.69036505604615, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.86601856819716245500367849479', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.53555095235012548279964992415', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.43611723294409045982209927708', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 75.52244480734802, 'bad_primes': [2, 5], 'central_character': '1.1', 'conductor': 1280, 'conductor_radical': 10, 'degree': 2, 'index': 93, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1280/4/a/bb/1/6'], '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': '2-1280-1.1-c3-0-93', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-1280-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.69036505604615, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86601856819716245500367849479', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2365459558012154205384259487245', 'Lhash_array': ['2365459558012154205384259487245'], 'label': '2-1280-1.1-c3-0-93', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1280/4/a/bb/1/6'}