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lfunc_lfunctions • Show schema
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{'Lhash': '1834795940858818115773492560126', 'a10': [-0.17447143858776779, -0.9894766977053552], 'a2': [-0.6959717356613602, -0.4577478115242287], 'a3': [0.0, 0.0], 'a4': [-0.5173159341940483, -1.1992731359971347], 'a5': [0.8277128418764408, 0.8773243574118523], 'a6': [0.0, 0.0], 'a7': [1.3060037868905507, -0.15264994983017216], 'a8': [-0.478229567216428, 2.7121746501581736], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.821094307351343, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]]], 'bad_primes': [3], 'central_character': '729.703', 'coefficient_field': 'CDF', 'conductor': 729, 'conductor_radical': 3, 'conjugate': '950662546879279375585262557903', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.6959717356613602, 0.4577478115242287], [0.7921595320783137, 1.836432213760548]], [[1.0, 0], [0, 0]], [[1.0, 0], [-0.8277128418764408, -0.8773243574118523], [-0.29072414455237916, 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'0.256672096632', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.44739878680172529949079065824', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.99436095791601570557332654044', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.37581457057526528957534418661', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 5.821094307351343, 'bad_primes': [3], 'central_character': '81.52', 'conductor': 729, 'conductor_radical': 3, 'degree': 2, 'index': 17, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/729/2/g/c/703/3'], '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': '2-3e6-81.52-c1-0-17', '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': '2-3e6-81.52-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.4126944081982997, 'root_angle': 0.2566720966323132, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44739878680172529949079065824', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1834795940858818115773492560126', 'Lhash_array': ['1834795940858818115773492560126'], 'label': '2-3e6-81.52-c1-0-17', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/729/2/g/c/703/3'}