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  • lfunc_lfunctions • Show schema
    {'Lhash': '2433218207512279819316311000561', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5, 0.8660254037844386], 'a4': [0.0, 0.0], 'a5': [3.0, 0.0], 'a6': [0.0, 0.0], 'a7': [-2.0, -3.4641016151377544], 'a8': [0.0, 0.0], 'a9': [-0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0.5, -0.8660254037844386]]], [13, [[1.0, 0], [2.5, 2.598076211353316]]]], 'bad_primes': [2, 3, 13], 'central_character': '624.529', 'coefficient_field': 'CDF', 'conductor': 624, 'conductor_radical': 78, 'conjugate': '989937544640190603955100042543', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5, -0.8660254037844386]], [[1.0, 0], [-3.0, 0], [5.0, 0]], [[1.0, 0], [2.0, 3.4641016151377544], [-3.5, 6.06217782649107]], [[1.0, 0], [-2.0, 3.4641016151377544], [-5.5, -9.526279441628825]], [[1.0, 0], [2.5, 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-1.7473206826224017, -1.133853137551377], 'positive_zeros': ['1.91947071777838480588208054129516', '2.46388135250376994776166240556568', '4.36887885855977114378883232237883', '5.54659780721599603499567235342285', '6.36810786646446921750579328786473', '6.74126309742186585395125833202774', '8.290926747982199134972998442251375', '9.180587457514239873106109126043605', '9.801942763502910906073008206897553', '10.54331968385547638521964653801196'], 'prelabel': '2-624-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.17074856945180006, 'root_number': '0.4776267392880571 + 0.8785628593999739*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.170748569452', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.91947071777838480588208054130', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.46388135250376994776166240557', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.36887885855977114378883232238', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 4.9826650861278985, 'bad_primes': [2, 3, 13], 'central_character': '13.9', 'conductor': 624, 'conductor_radical': 78, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/624/2/q/e/529/1'], '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': '2-624-13.9-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-624-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.232188407399317, 'root_angle': 0.17074856945180006, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.91947071777838480588208054130', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '2433218207512279819316311000561', 'Lhash_array': ['2433218207512279819316311000561'], 'factors': ['2-624-13.9-c1-0-11'], 'label': '2-624-13.9-c1-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/624/2/q/e/529/1'}