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lfunc_lfunctions • Show schema
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{'Lhash': '2362537493594120391602434735522', 'a10': [0.0, 556.5023741605196], 'a2': [5.656854249492381, 0.0], 'a3': [0.0, 29.953875065847583], 'a4': [32.0, 0.0], 'a5': [0.0, 98.37665062882918], 'a6': [0.0, 169.44470545500377], 'a7': [195.79393923933998, -281.62694004150535], 'a8': [181.01933598375618, 0.0], 'a9': [-168.23463146040567, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.2207571706779143, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-5.656854249492381, 0]]], [7, [[1.0, 0], [-195.79393923933998, 281.62694004150535]]]], 'bad_primes': [2, 7], 'central_character': '14.13', 'coefficient_field': 'CDF', 'conductor': 14, 'conductor_radical': 14, 'conjugate': '4362278727153381755515046330528', 'degree': 2, 'euler_factors': [[[1.0, 0], [-5.656854249492381, 0]], [[1.0, 0], [0, -29.953875065847583], [-729.0, 0]], [[1.0, 0], [0, -98.37665062882918], [-15625.0, 0]], [[1.0, 0], [-195.79393923933998, 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'z1': {'__RealLiteral__': 0, 'data': '1.86371346581523819161058772347', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.04012306530305913138641290254', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.97470933455247246630931941210', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.2207571706779143, 'bad_primes': [2, 7], 'central_character': '7.6', 'conductor': 14, 'conductor_radical': 14, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/7/b/a/13/4'], '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': '2-14-7.6-c6-0-1', 'motivic_weight': 6, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [6], 'order_of_vanishing': 0, 'prelabel': '2-14-7.6-c6-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7946468094524657, 'root_angle': -0.15331118961305776, 'self_dual': False, 'spectral_label': 'c6-0', 'z1': {'__RealLiteral__': 0, 'data': '1.86371346581523819161058772347', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2362537493594120391602434735522', 'Lhash_array': ['2362537493594120391602434735522'], 'factors': ['2-14-7.6-c6-0-1'], 'label': '2-14-7.6-c6-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/7/b/a/13/4'}