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lfunc_lfunctions • Show schema
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{'Lhash': '375733410557336811268045487715', 'a10': [0.0, 0.0], 'a2': [-0.4446478012083381, 0.0], 'a3': [-9.0, 0.0], 'a4': [-31.80228833288059, 0.0], 'a5': [0.0, 0.0], 'a6': [4.001830210875043, 0.0], 'a7': [-205.80442937224376, 0.0], 'a8': [28.369547219275756, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 132.31665134570906, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [9.0, 0]]], [5, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [-121.0, 0]]]], 'bad_primes': [3, 5, 11], 'central_character': '825.1', 'coefficient_field': 'CDF', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.4446478012083381, 0], [32.0, 0]], [[1.0, 0], [9.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [205.80442937224376, 0], [16807.0, 0]], [[1.0, 0], [-121.0, 0]], [[1.0, 0], [-893.0054530620339, 0], [371293.0, 0]], [[1.0, 0], [836.2912805734334, 0], [1419857.0, 0]], [[1.0, 0], 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['0.29640139837403879074750780372890', '1.58725250934802393415173784389060', '3.44828314695527494894901524046242', '3.85078484571128203376809505411264', '5.12795250419173298099979469161341', '6.08702521347582668292518482017931', '6.59871737268540538766697140647072', '7.84117605668804631841892990169570', '8.875408602948382725191898553332849', '9.455709363752049839936242609368626'], 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29640139837403879074750780373', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.58725250934802393415173784389', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.44828314695527494894901524046', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 132.31665134570906, 'bad_primes': [3, 5, 11], 'central_character': '1.1', 'conductor': 825, 'conductor_radical': 165, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/825/6/a/u/1/5'], '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': '2-825-1.1-c5-0-6', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5], 'order_of_vanishing': 0, 'prelabel': '2-825-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.502897519569105, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '0.29640139837403879074750780373', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '375733410557336811268045487715', 'Lhash_array': ['375733410557336811268045487715'], 'label': '2-825-1.1-c5-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/825/6/a/u/1/5'}