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lfunc_lfunctions • Show schema
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{'Lhash': '564991998857642903516776984051', 'a10': [-0.5443759135431903, 0.8791972881047386], 'a2': [-0.6213818060055473, 0.2630083599048781], 'a3': [1.6815486179553174, 0.41520386011279076], 'a4': [-1.0753259404709914, 1.1089666267843836], 'a5': [1.2508579002131432, -0.8854639739656429], 'a6': [-1.1540858033856467, 0.18426121965138192], 'a7': [-4.150826695626892, 1.6080388287168532], 'a8': [0.8640167434804236, -2.2302843067346436], 'a9': [2.655211509094876, 1.3963709542847527], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.4021322673726955, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.6815486179553174, -0.41520386011279076]]], [103, [[1.0, 0], [9.990976533984892, 1.7833642077162062]]]], 'bad_primes': [3, 103], 'central_character': '927.77', 'coefficient_field': 'CDF', 'conductor': 927, 'conductor_radical': 309, 'conjugate': '2415949874350947107585767976560', 'degree': 2, 'euler_factors': [[[1.0, 0], 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-0.8259086972492306, 'root_number': '-0.8541282942047012 - 0.5200623587984112*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.412954348625', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.44570009966146904874578131556', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.03787914775547856968013226578', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.16362917300304087122867938269', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.4021322673726955, 'bad_primes': [3, 103], 'central_character': '927.77', 'conductor': 927, 'conductor_radical': 309, 'degree': 2, 'index': 21, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/927/2/bg/a/77/43'], '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': '2-927-927.77-c1-0-21', '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': '2-927-927.77-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.720685992056543, 'root_angle': -0.4129543486246153, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.44570009966146904874578131556', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '564991998857642903516776984051', 'Lhash_array': ['564991998857642903516776984051'], 'label': '2-927-927.77-c1-0-21', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/927/2/bg/a/77/43'}