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lfunc_lfunctions • Show schema
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{'Lhash': '716977853651834925949681801997', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0.5239763970818659], 'a4': [0, 0], 'a5': [0, 0], 'a6': [0, 0], 'a7': [0, 0.47602360291813406], 'a8': [0, 0], 'a9': [2.7254487353011068, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 36.731184929788995, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 5, 23], 'central_character': '4600.4049', 'coefficient_field': 'CDF', 'conductor': 4600, 'conductor_radical': 230, 'conjugate': '1232017322972565850522957652969', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.5239763970818659], [-3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -0.47602360291813406], [-7.0, 0]], [[1.0, 0], [1.6774959411373749, 0], [11.0, 0]], [[1.0, 0], [0, 2.6774959411373747], [-13.0, 0]], [[1.0, 0], [0, -1.6774959411373749], [-17.0, 0]], [[1.0, 0], 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'3.78630080699195349151673022168698', '4.42919763886811375532492091586966', '5.11494389817308811311501058759611', '6.32048935458583879976922409976648', '6.62961224463539028750563335382005', '7.49808677560816723647680434593736', '8.082784173110893796924619425651434'], 'prelabel': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': -0.35241638234956674, 'root_number': '0.4472135954999579392818347337462552470881236719223051449 - 0.8944271909999158785636694674925104941762473438446102897*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.17620819117478337', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.56559579865520462447109211236', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.83690412465453070576025163005', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.51446714722516750308001293744', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 36.731184929788995, 'bad_primes': [2, 5, 23], 'central_character': '5.4', 'conductor': 4600, 'conductor_radical': 230, 'degree': 2, 'index': 28, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4600/2/e/r/4049/4'], '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': '2-4600-5.4-c1-0-28', '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': '2-4600-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.06062578697852, 'root_angle': -0.17620819117478337, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.56559579865520462447109211236', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '716977853651834925949681801997', 'Lhash_array': ['716977853651834925949681801997'], 'label': '2-4600-5.4-c1-0-28', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4600/2/e/r/4049/4'}