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lfunc_lfunctions • Show schema
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{'Lhash': '1388618471211567079594457418485', 'a10': [-0.9135052345139473, -0.7304021388421196], 'a2': [-0.5116336764673328, -0.10875109510448877], 'a3': [1.1848948907893542, 1.2633384731659543], 'a4': [-1.577148697076148, -0.7021918409352841], 'a5': [1.9986126794915045, 1.0027698426736762], 'a6': [-0.4688426867574858, -0.7752251246055799], 'a7': [-1.6886406073531248, 2.924811327659579], 'a8': [1.5768933860657826, 1.1456801071071672], 'a9': [-0.19204819556256866, 2.9938466043839256], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.7966340454788094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.1848948907893542, -1.2633384731659543]]], [5, [[1.0, 0], [-1.9986126794915045, -1.0027698426736762]]]], 'bad_primes': [3, 5], 'central_character': '225.106', 'coefficient_field': 'CDF', 'conductor': 225, 'conductor_radical': 15, 'conjugate': '2938062467960306272085061224051', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.26486982373545226 - 0.9642841782764822*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.207335505975', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.09542682420657432822763358015', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.09215279227082288418555892057', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.45407199906233043760855243911', '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': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/225/2/q/a/106/13'], '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-c1-0-6', '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': '2-15e2-225.106-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3403857823323886, 'root_angle': -0.2073355059754009, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.09542682420657432822763358015', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1388618471211567079594457418485', 'Lhash_array': ['1388618471211567079594457418485'], 'label': '2-15e2-225.106-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/225/2/q/a/106/13'}