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lfunc_lfunctions • Show schema
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{'Lhash': '900967577350783894535795046009', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.0, 0.0], 'a4': [0.0, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.8587460420735726, 0.0], 'a8': [0.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 63.722062806199894, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.1', 'coefficient_field': 'CDF', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [3.8587460420735726, 0], [343.0, 0]], [[1.0, 0], [-42.27833497578869, 0], [1331.0, 0]], [[1.0, 0], [-4.967000985473213, 0], [2197.0, 0]], [[1.0, 0], [25.887572116536194, 0], [4913.0, 0]], [[1.0, 0], [-28.995827059935834, 0], [6859.0, 0]], [[1.0, 0], [191.46889520251202, 0], [12167.0, 0]], 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'3.36987185654270255202751829042518', '4.12463576321131943517577708272345', '5.11395257140662274878112368258352', '6.37605361929033029909593553927118', '6.77869701818573832443564971793862', '8.016135375957208348443834637786289', '8.554788506479603047017022812724853', '9.568827125993691358247551415874690'], 'prelabel': '2-1080-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.982610024684902, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.71073809864372135639065978957', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.01104205526282171519443229088', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.36987185654270255202751829043', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 63.722062806199894, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1080, 'conductor_radical': 30, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/4/a/d/1/2'], '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': '2-1080-1.1-c3-0-12', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-1080-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.982610024684902, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.71073809864372135639065978957', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '900967577350783894535795046009', 'Lhash_array': ['900967577350783894535795046009'], 'label': '2-1080-1.1-c3-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/4/a/d/1/2'}