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lfunc_lfunctions • Show schema
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{'Lhash': '4291773004503032033751780964182', 'a10': [-2.4558867801028668, 1.554212298030435e-60], 'a2': [0.7589107513125553, -2.335687125499954], 'a3': [-0.8090169943749475, 0.5877852522924731], 'a4': [-3.2614548310185567, -2.369585637903519], 'a5': [-0.30901699437494745, -0.9510565162951535], 'a6': [0.7589107513125553, 2.335687125499954], 'a7': [-2.6591107806106744, -1.931957068791188], 'a8': [-4.036055520673124, 2.9323659811598453], 'a9': [0.30901699437494745, -0.9510565162951535], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.3175316333511269, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0.8090169943749475, -0.5877852522924731]]], [5, [[1.0, 0], [0.30901699437494745, 0.9510565162951535]]], [11, [[1.0, 0], [-2.968127774985622, 1.4799383471479144]]]], 'bad_primes': [3, 5, 11], 'central_character': '165.31', 'coefficient_field': 'CDF', 'conductor': 165, 'conductor_radical': 165, 'conjugate': 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'data': '0.46910239317', 'prec': 44}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.38561193733536342553195425618', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.02056400090550295996883660776', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.03144301687022952365354579795', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.3175316333511269, 'bad_primes': [3, 5, 11], 'central_character': '11.9', 'conductor': 165, 'conductor_radical': 165, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/165/2/m/a/31/2'], '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': '2-165-11.9-c1-0-6', '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': '2-165-11.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.1478378079463696, 'root_angle': 0.4691023931702339, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.38561193733536342553195425618', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4291773004503032033751780964182', 'Lhash_array': ['4291773004503032033751780964182'], 'label': '2-165-11.9-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/165/2/m/a/31/2'}