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lfunc_lfunctions • Show schema
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{'Lhash': '3407342318603762758786273345022', 'a10': [0.0, 0.0], 'a2': [0.30901699437494745, 0.9510565162951535], 'a3': [-0.5, -0.36327126400268045], 'a4': [-0.8090169943749475, 0.5877852522924731], 'a5': [0.0, 0.0], 'a6': [0.19098300562505258, -0.5877852522924731], 'a7': [0.0, 0.0], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [-0.19098300562505258, -0.5877852522924731], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.043917721111704215, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.30901699437494745, -0.9510565162951535]]], [11, [[1.0, 0], [0.8090169943749475, 0.5877852522924731]]]], 'bad_primes': [2, 11], 'central_character': '88.27', 'coefficient_field': 'CDF', 'conductor': 88, 'conductor_radical': 22, 'conjugate': '4663494867405781313070587947231', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.30901699437494745, -0.9510565162951535]], [[1.0, 0], [0.5, 0.36327126400268045], 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'group': 'GL2', 'index': 0, 'label': '2-88-88.27-c0-0-0', 'leading_term': '0.50206178440910868707292439028519', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/88/1/l/a/27/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.08203125', 'prec': 34}, 'plot_values': [0.5020617844091086, 0.5015408275770993, 0.5144098117596919, 0.538884031751971, 0.5728921915155231, 0.6144136904000023, 0.6616549220939755, 0.7130826213838362, 0.7673794330587423, 0.8233747675588122, 0.8799790098864324, 0.9361314903241553, 0.9907638816154164, 1.0427774139110928, 1.091031573240239, 1.13434217094146, 1.1714871265915967, 1.2012187267075918, 1.2222814288543649, 1.2334344714255596, 1.2334786417244876, 1.2212865714716292, 1.195835889829749, 1.1562444864964696, 1.101807035483682, 1.0320318158401887, 0.9466767492627877, 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'11.19988117789173054107974827316755', '11.86431717417097928868419946549936', '13.27116718676973756489086046972047', '13.87047523104848998121753688517405'], 'prelabel': '2-88-88.27-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20956555325650306, 'root_angle': -0.2854342601392135, 'root_number': '0.62417735821399263386961876627007 - 0.78128267963202737461068725062413*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.1427171300696068', 'prec': 64}, 'spectral_label': 'c0-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.68791914585162550379183914391', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.65735988994615014311933168328', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.47635468920967000080472360694', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.043917721111704215, 'bad_primes': [2, 11], 'central_character': '88.27', 'conductor': 88, 'conductor_radical': 22, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/88/1/l/a/27/1'], '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': '2-88-88.27-c0-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0], 'order_of_vanishing': 0, 'prelabel': '2-88-88.27-c0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.20956555325650306, 'root_angle': -0.14271713006960676, 'self_dual': False, 'spectral_label': 'c0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.68791914585162550379183914391', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3407342318603762758786273345022', 'Lhash_array': ['3407342318603762758786273345022'], 'label': '2-88-88.27-c0-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/88/1/l/a/27/1'}