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lfunc_lfunctions • Show schema
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{'Lhash': '5615094580508813408467595792013', 'a10': [2.944212466820662, 4.685687298507825], 'a2': [0.29312774158576466, -2.601580662097162], 'a3': [0.07828347718834139, -0.12458744023339591], 'a4': [-2.782586419783444, -0.6351071922422215], 'a5': [-1.6526002539480458, 1.3179047249838696], 'a6': [-0.3011772163796895, -0.24018081540048006], 'a7': [0.7479873939953909, 3.277146897601165], 'a8': [0.9908024405027924, -2.8315506943833473], 'a9': [3.8955599245948105, 8.089213535050842], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7901927666448612, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[29, [[1.0, 0], [-12.664398847991073, -26.088560746407655]]]], 'bad_primes': [29], 'central_character': '29.27', 'coefficient_field': 'CDF', 'conductor': 29, 'conductor_radical': 29, 'conjugate': '3106554128360427634567902611899', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.29312774158576466, 2.601580662097162], [-3.8997116487272945, 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.219903007935', 'prec': 47}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '4.42952859368178009667574778504', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '6.27837703960268647104166312972', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.53101644713485027683921518924', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7901927666448612, 'bad_primes': [29], 'central_character': '29.27', 'conductor': 29, 'conductor_radical': 29, 'degree': 2, 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/29/3/f/a/27/4'], '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': '2-29-29.27-c2-0-3', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-29-29.27-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8889278748272332, 'root_angle': 0.21990300793531667, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '4.42952859368178009667574778504', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '5615094580508813408467595792013', 'Lhash_array': ['5615094580508813408467595792013'], 'label': '2-29-29.27-c2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/29/3/f/a/27/4'}