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lfunc_lfunctions • Show schema
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{'Lhash': '4369775719351796641229397879875', 'a10': [-23.223011226091497, -54.656509313236626], 'a2': [4.2971779820514495, 3.1220825543686352], 'a3': [-1.9377980890182767, -5.963929276941217], 'a4': [6.246203178135205, 19.223836691198464], 'a5': [-9.585447244668963, -5.75492842002993], 'a6': [10.292816269235809, -31.67803118299666], 'a7': [-9.636018005118958, 0.0], 'a8': [-20.046350925632268, 61.69632422425634], 'a9': [-9.969932138430115, 7.24357969989691], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.475047750143516, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [9.585447244668963, 5.75492842002993]]]], 'bad_primes': [5], 'central_character': '25.16', 'coefficient_field': 'CDF', 'conductor': 25, 'conductor_radical': 5, 'conjugate': '4998992667740136870981995115157', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.2971779820514495, -3.1220825543686352], [2.4721359549995796, 7.608452130361228]], [[1.0, 0], 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'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.44714522958065633275445861733', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.47707200632211495859973607277', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.28744435979204827396181593619', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.475047750143516, 'bad_primes': [5], 'central_character': '25.16', 'conductor': 25, 'conductor_radical': 5, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/25/4/d/a/16/7'], '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': '2-5e2-25.16-c3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-5e2-25.16-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2145154384129977, 'root_angle': -0.10788977607942818, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '3.44714522958065633275445861733', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4369775719351796641229397879875', 'Lhash_array': ['4369775719351796641229397879875'], 'label': '2-5e2-25.16-c3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/25/4/d/a/16/7'}