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lfunc_lfunctions • Show schema
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{'Lhash': '3658042295899726641136023403828', 'a10': [0.0, 0.0], 'a2': [1.5388417685876268, 0.5], 'a3': [0.5877852522924731, -0.8090169943749475], 'a4': [0.5, 0.36327126400268045], 'a5': [0.0, 0.0], 'a6': [1.3090169943749475, -0.9510565162951535], 'a7': [0.0, -0.6180339887498949], 'a8': [-1.314327780297834, -1.8090169943749475], 'a9': [0.6180339887498949, 1.902113032590307], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9981300252660052, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]]], 'bad_primes': [5], 'central_character': '125.24', 'coefficient_field': 'CDF', 'conductor': 125, 'conductor_radical': 5, 'conjugate': '3154364976315454758019444629766', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.5388417685876268, -0.5], [1.618033988749895, 1.1755705045849463]], [[1.0, 0], [-0.5877852522924731, 0.8090169943749475], [-0.9270509831248422, -2.853169548885461]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 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'z3': {'__RealLiteral__': 0, 'data': '5.21613428887431790206537603324', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9981300252660052, 'bad_primes': [5], 'central_character': '25.4', 'conductor': 125, 'conductor_radical': 5, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/125/2/e/a/24/2'], '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': '2-5e3-25.4-c1-0-2', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5e3-25.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9990645751231525, 'root_angle': -0.0018959044126083183, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.88568655688020667946843684064', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3658042295899726641136023403828', 'Lhash_array': ['3658042295899726641136023403828'], 'label': '2-5e3-25.4-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/125/2/e/a/24/2'}