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lfunc_lfunctions • Show schema
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{'Lhash': '2270060698755003722877307056732', 'a10': [-7.142883559062792, 0.0], 'a2': [-0.8203518246253879, 0.0], 'a3': [0.13002550592819018, 0.0], 'a4': [-7.327022883833797, 0.0], 'a5': [8.707097789810579, 0.0], 'a6': [-0.10666666103603002, 0.0], 'a7': [11.402367976882132, 0.0], 'a8': [12.57355118882813, 0.0], 'a9': [-26.983093367808117, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17.051551991659046, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[17, [[1.0, 0], [0, 0]]]], 'bad_primes': [17], 'central_character': '289.1', 'coefficient_field': 'CDF', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8203518246253879, 0], [8.0, 0]], [[1.0, 0], [-0.13002550592819018, 0], [27.0, 0]], [[1.0, 0], [-8.707097789810579, 0], [125.0, 0]], [[1.0, 0], [-11.402367976882132, 0], [343.0, 0]], [[1.0, 0], [7.2731636102790524, 0], [1331.0, 0]], [[1.0, 0], [52.146978030544226, 0], [2197.0, 0]], [[1.0, 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'5.39702332383909838719184423683247', '7.16704576104983263877089838831311', '8.145122610647729335881771184147521', '9.158111358158718752664643536259197', '9.691485166832703605977766112964718', '10.80970479432603838388414012836665'], 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79076213772651482353341510891', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.37916915246236202328194421329', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.14357683494766949323042401044', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 17.051551991659046, 'bad_primes': [17], 'central_character': '1.1', 'conductor': 289, 'conductor_radical': 17, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/289/4/a/h/1/6'], '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': '2-17e2-1.1-c3-0-38', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-17e2-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.129352490604193, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79076213772651482353341510891', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2270060698755003722877307056732', 'Lhash_array': ['2270060698755003722877307056732'], 'label': '2-17e2-1.1-c3-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/289/4/a/h/1/6'}