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lfunc_lfunctions • Show schema
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{'Lhash': '1746536045162308805115136251137', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -27.0], 'a4': [0, 0], 'a5': [0, 344.30603743722907], 'a6': [0, 0], 'a7': [1669.7452213467348, 0], 'a8': [0, 0], 'a9': [-729.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 119.95584978590281, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 27.0]]]], 'bad_primes': [2, 3], 'central_character': '384.193', 'coefficient_field': 'CDF', 'conductor': 384, 'conductor_radical': 6, 'conjugate': '303820925991883956746023474474', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 27.0]], [[1.0, 0], [0, -344.30603743722907], [-78125.0, 0]], [[1.0, 0], [-1669.7452213467348, 0], [823543.0, 0]], [[1.0, 0], [0, 2282.143956373077], [-19487171.0, 0]], [[1.0, 0], [0, 11526.909278323796], [-62748517.0, 0]], [[1.0, 0], [17243.893206439658, 0], [410338673.0, 0]], [[1.0, 0], [0, -14550.180418726384], 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1.352786753573147, 1.6857466695384717, 1.925876149771534, 2.0617989021483485, 2.0884924395171587], 'positive_zeros': ['1.37777400558786488045057717934548', '2.02446455628715034609537460341973', '4.04201053557396057561832850916559', '4.76539509637654389676692936518657', '5.19631202689642882923646632471038', '6.79785150636743511945135127503705', '7.984377627800964289495468125575688', '8.805687759330101094139129291724166', '9.275137284103501731356583097699293', '10.60600220562858540037652576811313'], 'prelabel': '2-384-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.952435792366135, 'root_angle': 0.75, 'root_number': '-0.7071067811865475244008443621048490392848359376884740366 + 0.7071067811865475244008443621048490392848359376884740366*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.375', 'prec': 17}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.37777400558786488045057717935', 'prec': 103}, 'z2': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 119.95584978590281, 'bad_primes': [2, 3], 'central_character': '8.5', 'conductor': 384, 'conductor_radical': 6, 'degree': 2, 'index': 50, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/384/8/d/d/193/4'], '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': '2-384-8.5-c7-0-50', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-384-8.5-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 10.952435792366135, 'root_angle': 0.375, 'self_dual': False, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.37777400558786488045057717935', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1746536045162308805115136251137', 'Lhash_array': ['1746536045162308805115136251137'], 'label': '2-384-8.5-c7-0-50', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/384/8/d/d/193/4'}