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lfunc_lfunctions • Show schema
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{'Lhash': '1725282711184722549108179144799', 'a10': [0.20095583884796014, 1.1396771954044627], 'a2': [-0.6984166961369017, 0.3507580481293939], 'a3': [0.29545335679149604, 1.706665554219876], 'a4': [-0.8295625102903292, 1.1142958312741684], 'a5': [0.42467710852290635, -1.4185203292155195], 'a6': [-0.8049762359207079, -1.0883310750474375], 'a7': [-1.5056033430574975, 3.4903808745218985], 'a8': [0.459960807333055, -2.6085673643646388], 'a9': [-2.825414627921274, 1.0084801338293627], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.29545335679149604, -1.706665554219876]]]], 'bad_primes': [3], 'central_character': '81.25', 'coefficient_field': 'CDF', 'conductor': 81, 'conductor_radical': 3, 'conjugate': '4258709477926879074702554944029', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6984166961369017, -0.3507580481293939], [1.1943171834055724, 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'root_number': '-0.08440386662399241 - 0.9964316270065494*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.263449293764', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.36100808130734169910796253745', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77183149691555731189488387005', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.20716105423918308507922175325', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6467882563723715, 'bad_primes': [3], 'central_character': '81.25', 'conductor': 81, 'conductor_radical': 3, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/81/2/g/a/25/4'], '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': '2-3e4-81.25-c1-0-1', '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': '2-3e4-81.25-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8042314693994332, 'root_angle': -0.26344929376370124, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.36100808130734169910796253745', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1725282711184722549108179144799', 'Lhash_array': ['1725282711184722549108179144799'], 'factors': ['2-3e4-81.25-c1-0-1'], 'label': '2-3e4-81.25-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/81/2/g/a/25/4'}