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lfunc_lfunctions • Show schema
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{'Lhash': '2022707070208611027138755064973', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.5615528128088303, 0.0], 'a4': [0.0, 0.0], 'a5': [3.4061663888745843, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.504067928786756, 0.0], 'a8': [0.0, 0.0], 'a9': [-0.5615528128088303, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.85490444289385, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 19], 'central_character': '608.1', 'coefficient_field': 'CDF', 'conductor': 608, 'conductor_radical': 38, 'conjugate': '2022707070208611027138755064973', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.5615528128088303, 0], [3.0, 0]], [[1.0, 0], [-3.4061663888745843, 0], [5.0, 0]], [[1.0, 0], [2.504067928786756, 0], [7.0, 0]], [[1.0, 0], [-1.4061663888745846, 0], [11.0, 0]], [[1.0, 0], [-6.221007165529832, 0], [13.0, 0]], [[1.0, 0], [3.163522281507758, 0], [17.0, 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'6.77389117415901392003830991003753', '8.393219105454484635380522827516568', '9.050055381398546220359706494022496', '9.459273231051144528766447910292245', '10.54175949275693305108239912440156'], 'prelabel': '2-608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.203384769597414, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.59563453040170557506753101078', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81979441333074951592183675639', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.66468006284354467491265928533', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.85490444289385, 'bad_primes': [2, 19], 'central_character': '1.1', 'conductor': 608, 'conductor_radical': 38, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/608/2/a/i/1/4'], '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': '2-608-1.1-c1-0-8', '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': '2-608-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.203384769597414, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.59563453040170557506753101078', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2022707070208611027138755064973', 'Lhash_array': ['2022707070208611027138755064973'], 'label': '2-608-1.1-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/608/2/a/i/1/4'}