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  • lfunc_lfunctions • Show schema
    {'Lhash': '2434142913652324463802656665548', 'a10': [-3.435861348370356, -1.9836954743798556], 'a2': [-0.7071067811865476, -0.7071067811865476], 'a3': [1.6739774676158747, 0.4447464872422751], 'a4': [0.0, 1.0], 'a5': [3.832205380392495, -1.0268363369063724], 'a6': [-0.8691975618667601, -1.4981640759425783], 'a7': [-1.5517610987237422, 0.4157931332490584], 'a8': [0.7071067811865476, -0.7071067811865476], 'a9': [2.6044011241713134, 1.4889911968897593], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.868499407297962, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0.7071067811865476, 0.7071067811865476]]], [3, [[1.0, 0], [-1.6739774676158747, -0.4447464872422751]]], [13, [[1.0, 0], [1.0390768072815246, 3.4525815542242637]]]], 'bad_primes': [2, 3, 13], 'central_character': '234.149', 'coefficient_field': 'CDF', 'conductor': 234, 'conductor_radical': 78, 'conjugate': '2521743945949593344866687548189', 'degree': 2, 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'6.45940698429993905504441488994823', '7.05621346328667778594614068241180', '8.568454091458252745490078295209877', '9.140805977313498920091908534310291', '10.17267753568737865203088541055197', '10.68117167944282690393444898130901', '12.66829401593755248949645317041808'], 'prelabel': '2-234-117.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.05616781429094224, 'root_number': '0.9383699415356647 + 0.3456325401670873*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0561678142909', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.92020018230108385184546902031', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.11197061608121771681908992683', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.24648075824000802976927669520', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.868499407297962, 'bad_primes': [2, 3, 13], 'central_character': '117.32', 'conductor': 234, 'conductor_radical': 78, 'degree': 2, 'index': 10, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/234/2/y/a/149/7'], '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': '2-234-117.32-c1-0-10', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-234-117.32-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3669306519710362, 'root_angle': 0.05616781429094224, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.92020018230108385184546902031', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2434142913652324463802656665548', 'Lhash_array': ['2434142913652324463802656665548'], 'factors': ['2-234-117.32-c1-0-10'], 'label': '2-234-117.32-c1-0-10', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/234/2/y/a/149/7'}