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lfunc_lfunctions • Show schema
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{'Lhash': '1275112430372402726920902940285', 'a10': [0.473019127139251, 1.332761383504347], 'a2': [0.8018454198606244, 1.1649222818061893], 'a3': [1.7099318758529405, 0.27592205410594517], 'a4': [-0.7140878452970779, 1.8681751923197611], 'a5': [0.9659258262890683, 0.25881904510252074], 'a6': [1.0496732940566178, 2.2131845778751327], 'a7': [-1.1984820634366726, 2.0758318258323034], 'a8': [-2.748866975980457, 0.6661308793053046], 'a9': [2.847734040115912, 0.9436158311331507], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.749228945532191, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8018454198606244, -1.1649222818061893]]], [3, [[1.0, 0], [-1.7099318758529405, -0.27592205410594517]]], [5, [[1.0, 0], [-0.9659258262890683, -0.25881904510252074]]]], 'bad_primes': [2, 3, 5], 'central_character': '720.11', 'coefficient_field': 'CDF', 'conductor': 720, 'conductor_radical': 30, 'conjugate': 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['1.00588634608213800252283311728557', '2.68049137405635417912228735336816', '3.01935422513816493153998316806124', '4.57555948451205877737357479523580', '5.11384886025319893282077012546305', '6.75754228960212962743864615983621', '7.31280750083478057129416151581816', '8.622037704545848013980289457837662', '9.701413654101402401878666472302866', '9.810672895931758648092879088020345'], 'prelabel': '2-720-144.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.397754980295566, 'root_angle': -0.7351639447318284, 'root_number': '-0.6733933694211199 - 0.7392843634351203*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.367581972366', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.00588634608213800252283311729', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.68049137405635417912228735337', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.01935422513816493153998316806', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.749228945532191, 'bad_primes': [2, 3, 5], 'central_character': '144.11', 'conductor': 720, 'conductor_radical': 30, 'degree': 2, 'index': 37, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/720/2/cf/a/11/68'], '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': '2-720-144.11-c1-0-37', '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': '2-720-144.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.397754980295566, 'root_angle': -0.3675819723659142, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.00588634608213800252283311729', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1275112430372402726920902940285', 'Lhash_array': ['1275112430372402726920902940285'], 'label': '2-720-144.11-c1-0-37', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/720/2/cf/a/11/68'}