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lfunc_lfunctions • Show schema
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{'Lhash': '2704259299100488876765187613265', 'a10': [-3.4415275766754125, -3.3569856548978945], 'a2': [2.1030612325682534, 0.44701946457622665], 'a3': [1.0156205112046632, 1.403037767567352], 'a4': [2.3959492309362824, 1.0667453261557593], 'a5': [-1.890322643653156, -1.1944372327134414], 'a6': [1.5087269324774963, 3.4046764739313478], 'a7': [-0.10733946169607259, 0.1859174013146911], 'a8': [1.083126338755074, 0.7869373483083024], 'a9': [-0.9370299544407572, 2.849907869472407], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0156205112046632, -1.403037767567352]]], [5, [[1.0, 0], [1.890322643653156, 1.1944372327134414]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '3702611811077268550964064194417', 'degree': 2, 'euler_factors': [[[1.0, 0], 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1.3403857823323886, 'root_angle': -0.27124670332859296, 'root_number': '0.6583688900392781 - 0.7526954262040184*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.135623351664', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.13328443864075057126307409750', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.58191266634263940093198417064', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14237762546584046497621935566', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'bad_primes': [3, 5], 'central_character': '225.106', 'conductor': 225, 'conductor_radical': 15, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/25'], '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': '2-15e2-225.106-c1-0-15', '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': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.13562335166429648, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.13328443864075057126307409750', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2704259299100488876765187613265', 'Lhash_array': ['2704259299100488876765187613265'], 'label': '2-15e2-225.106-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/25'}