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lfunc_lfunctions • Show schema
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{'Lhash': '2031054250760603802772039714345', 'a10': [4.375275491477975, 7.578199448350744], 'a2': [1.7075827554916836, 1.8964627783555814], 'a3': [0.3751001528521576, 0.16700534791339708], 'a4': [-0.47167527630029354, 4.487690482767129], 'a5': [3.354045333965522, 0.7129243438730924], 'a6': [0.3237951264885574, 0.996538930211412], 'a7': [0.0, 0.0], 'a8': [-5.187033013031676, 3.768600078135298], 'a9': [-1.8945824806385374, -2.104147013373297], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.303936668947014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [2.8572804783042067, -1.684027395353675]]]], 'bad_primes': [7, 11], 'central_character': '539.471', 'coefficient_field': 'CDF', 'conductor': 539, 'conductor_radical': 77, 'conjugate': '3246290088030415325895404735761', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.7075827554916836, -1.8964627783555814], [-0.20905692653530694, 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{'__RealLiteral__': 0, 'data': '-0.349057381594', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.60221929480799382105095947977', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.38480982146505839838610632663', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.46100867159876642219022796093', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.303936668947014, 'bad_primes': [7, 11], 'central_character': '77.9', 'conductor': 539, 'conductor_radical': 77, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/539/2/q/f/471/4'], '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': '2-539-77.9-c1-0-15', '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': '2-539-77.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0745931333509744, 'root_angle': -0.34905738159373706, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.60221929480799382105095947977', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2031054250760603802772039714345', 'Lhash_array': ['2031054250760603802772039714345'], 'label': '2-539-77.9-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/539/2/q/f/471/4'}