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lfunc_lfunctions • Show schema
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{'Lhash': '1523524729983080151258091403341', 'a10': [5.536875415790515, 0.09697853840777323], 'a2': [-1.067264903144075, -0.9278715571224652], 'a3': [0.36143406203390965, 2.0497944250034914], 'a4': [0.27810874696626375, 1.9805694950848998], 'a5': [-2.999648215897178, 2.517003711620908], 'a6': [1.5162000556993473, -2.523038034403118], 'a7': [0.010854286600028008, 0.006266725290387518], 'a8': [1.540898396499211, -2.37184150643886], 'a9': [-1.2519447412193363, 0.45567062074994197], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6068630553617312, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.067264903144075, 0.9278715571224652]]], [19, [[1.0, 0], [-3.9609557607218346, -1.8195684822519083]]]], 'bad_primes': [2, 19], 'central_character': '76.15', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '4297004883580246118669735195191', 'degree': 2, 'euler_factors': [[[1.0, 0], 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[41.5, 71.88010851410841]], [[1.0, 0], [-4.868492197119741, -0.8584465297208448], [83.63264324994584, 30.439792755984517]], [[1.0, 0], [1.3502002975117227, -3.7096448291543713], [-74.30631098254086, -62.35039813959431]], [[1.0, 0], [1.113408947022929, -6.314455919050835], [-94.90895469937675, -34.544034475892545]], [[1.0, 0], [1.8162099655616637, 3.1457679375657226], [-51.5, 89.20061658979718]], [[1.0, 0], [2.160975991365904, -3.7429202109822697], [-53.5, -92.66471820493493]], [[1.0, 0], [10.455951206370516, 12.460917414181825], [-18.927651365695407, 107.34404507833068]], [[1.0, 0], [0, 5.684984095154873], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-76-76.15-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/76/2/k/a/15/2', 'plot_delta': {'__RealLiteral__': 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{'__RealLiteral__': 0, 'data': '-0.184503882633', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.20184909762105019397197168795', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.50313483586985032137055263256', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.43165580582090097832045034354', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6068630553617312, 'bad_primes': [2, 19], 'central_character': '76.15', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/2/k/a/15/2'], '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': '2-76-76.15-c1-0-0', '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': '2-76-76.15-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.779014156072745, 'root_angle': -0.18450388263286652, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.20184909762105019397197168795', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1523524729983080151258091403341', 'Lhash_array': ['1523524729983080151258091403341'], 'label': '2-76-76.15-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/2/k/a/15/2'}