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lfunc_lfunctions • Show schema
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{'Lhash': '594947768175647766480072029972', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.6113934342734688, 0.0], 'a4': [0.0, 0.0], 'a5': [-1.6261980685272936, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.102611491715857, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.6261980685272936, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26.574213792682123, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 13], 'central_character': '3328.1', 'coefficient_field': 'CDF', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.6113934342734688, 0], [3.0, 0]], [[1.0, 0], [1.6261980685272936, 0], [5.0, 0]], [[1.0, 0], [3.102611491715857, 0], [7.0, 0]], [[1.0, 0], [5.319645182188578, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [1.8969162951364875, 0], [17.0, 0]], [[1.0, 0], [0.8855778012431353, 0], [19.0, 0]], [[1.0, 0], 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'4.72131669231216142171524521234712', '5.73254863074653923518114209341912', '6.30770984240382642036891821416604', '7.28988587085818103897772254690771', '7.996811463041136895435663996373800', '8.460502235882901348599436971564725'], 'prelabel': '2-3328-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.15501831157583, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.46933103496226217639687674695', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.45478937191893209061591099051', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.93362146801560989111058666471', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 26.574213792682123, 'bad_primes': [2, 13], 'central_character': '1.1', 'conductor': 3328, 'conductor_radical': 26, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3328/2/a/bp/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': '2-3328-1.1-c1-0-5', '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': '2-3328-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.15501831157583, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.46933103496226217639687674695', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '594947768175647766480072029972', 'Lhash_array': ['594947768175647766480072029972'], 'factors': ['2-3328-1.1-c1-0-5'], 'label': '2-3328-1.1-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3328/2/a/bp/1/4'}