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lfunc_lfunctions • Show schema
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{'Lhash': '3038162249201121471436591316641', 'a10': [4690.071250580217, -6429.7420281844925], 'a2': [4.0267378641323806, 4.0267378641323806], 'a3': [130.18618304349178, 52.2929990014577], 'a4': [0.0, -479.5707643471252], 'a5': [-216.01490291932785, -1380.7471027370484], 'a6': [313.6554335398907, 734.7958317563036], 'a7': [17.280019853694835, -17.280019853694835], 'a8': [3992.7955417632547, -3992.7955417632547], 'a9': [14213.884510867088, 13615.651879793808], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.725537542458099, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '4.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-130.18618304349178, -52.2929990014577]]], [5, [[1.0, 0], [216.01490291932785, 1380.7471027370484]]]], 'bad_primes': [3, 5], 'central_character': '15.8', 'coefficient_field': 'CDF', 'conductor': 15, 'conductor_radical': 15, 'conjugate': '1626433076594208341383623449175', 'degree': 2, 'euler_factors': [[[1.0, 0], [-4.0267378641323806, 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[1392136356.1715415, -1392136356.1715415], [0, -3004041937984268300]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 11, 'label': '2-15-15.8-c9-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/15/10/e/a/8/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.17578125', 'prec': 34}, 'plot_values': [2.39472979398997, 2.5364917280019084, 2.616014859910618, 2.6316695272802466, 2.5835345241390586, 2.4734644142842797, 2.305147208295608, 2.0841428608025923, 1.81789000168466, 1.5156660552560073, 1.188484715363443, 0.8489149104144635, 0.5108071578782509, 0.18891676223014317, -0.1015812463276042, -0.345683227145815, -0.5292429046272604, -0.6397307147757971, -0.6670340158435589, -0.6042547156937786, -0.4484510034797024, -0.2012622362754345, 0.13064814403562008, 0.5353962914638308, 0.9959866366625137, 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'12.01574092905133933592118838610385', '13.17552184857874914909197896667496', '14.53062678048916572529381642375442', '15.69071774352223932558891140085496', '17.72791702883448145426428414959043'], 'prelabel': '2-15-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77948512182708, 'root_angle': 0.24838900507185419, 'root_number': '0.7106764407283948 + 0.7035190094045934*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.124194502536', 'prec': 47}, 'spectral_label': 'c9-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.39668742211310193480209892455', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.80286312376229969073215396079', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '7.05665021416247457618843862189', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 7.725537542458099, 'bad_primes': [3, 5], 'central_character': '15.8', 'conductor': 15, 'conductor_radical': 15, 'degree': 2, 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/15/10/e/a/8/9'], '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': '2-15-15.8-c9-0-11', 'motivic_weight': 9, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [9], 'order_of_vanishing': 0, 'prelabel': '2-15-15.8-c9-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.77948512182708, 'root_angle': 0.12419450253592709, 'self_dual': False, 'spectral_label': 'c9-0', 'z1': {'__RealLiteral__': 0, 'data': '2.39668742211310193480209892455', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3038162249201121471436591316641', 'Lhash_array': ['3038162249201121471436591316641'], 'label': '2-15-15.8-c9-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/15/10/e/a/8/9'}