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lfunc_lfunctions • Show schema
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{'Lhash': '2142358999227761056659422419344', 'a10': [0, 0], 'a2': [0, 0], 'a3': [2.822694906863802, 1.0160676467465888], 'a4': [0, 0], 'a5': [-1.8117376914898995, -3.138021731648054], 'a6': [0, 0], 'a7': [-1.5942211781576467, -0.9204240263571197], 'a8': [0, 0], 'a9': [6.935213074469699, 5.73609794300137], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 15.694863227153103, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-2.822694906863802, -1.0160676467465888]]]], 'bad_primes': [2, 3], 'central_character': '576.511', 'coefficient_field': 'CDF', 'conductor': 576, 'conductor_radical': 6, 'conjugate': '793502324637664090068345117402', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-2.822694906863802, -1.0160676467465888]], [[1.0, 0], [1.8117376914898995, 3.138021731648054], [-12.5, 21.650635094610966]], [[1.0, 0], [1.5942211781576467, 0.9204240263571197], [24.5, 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'9.717316027509657715273205491468660', '10.57647901535463316521549298093614'], 'prelabel': '2-24e2-36.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.961674295945226, 'root_angle': 0.2210946339635013, 'root_number': '0.1806209724259855809366210067194488769643249841832769813 + 0.9835527765808458925582047366789096520851208205086507980*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.22109463396350132', 'prec': 64}, 'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.69002325943919251853949972081', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.90662138518172555255369149993', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.73528423406373206478794821898', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 15.694863227153103, 'bad_primes': [2, 3], 'central_character': '36.7', 'conductor': 576, 'conductor_radical': 6, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/576/3/o/e/511/4'], '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': '2-24e2-36.7-c2-0-38', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-24e2-36.7-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.961674295945226, 'root_angle': 0.2210946339635013, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '1.69002325943919251853949972081', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2142358999227761056659422419344', 'Lhash_array': ['2142358999227761056659422419344'], 'factors': ['2-24e2-36.7-c2-0-38'], 'label': '2-24e2-36.7-c2-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/576/3/o/e/511/4'}