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  • lfunc_lfunctions • Show schema
    {'Lhash': '462318314274749469226009909041,1428132135619155832906469601450', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': -1, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 428.3750897471616, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '2592.1', 'coefficient_field': '1.1.1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'euler_factors': [[1], [1], [1, 2, -1, 10, 25], [1, 1, -6, 7, 49], [1, 2, -7, 22, 121], [1, 1, -12, 13, 169], [1, -12, 70, -204, 289], [1, 10, 63, 190, 361], [1, -6, 13, -138, 529], [1, 8, 35, 232, 841], [1, 8, 33, 248, 961], [1, 10, 99, 370, 1369], [1, 8, 23, 328, 1681], [1, -4, -27, -172, 1849], [1, 10, 53, 470, 2209], [1, -8, 122, -424, 2809], [1, -14, 137, -826, 3481], [1, 3, -52, 183, 3721], [1, -13, 102, -871, 4489], [1, -8, 158, -568, 5041], [1, -18, 227, -1314, 5329], [1, 11, 42, 869, 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0.09853190519005176, 0.267471159853464], 'positive_zeros': ['0.36470484389903109025466912874178', '1.12659760927974406734232360859449', '1.95127430833541022792962749106127', '2.33222440703395001109327315120455', '3.16654151727281908286106669513165', '3.48690876803487961968732657726352', '3.63425248054337213612292633150097', '4.24486905978201178992458255098403', '4.76250329269470778886795209926648', '5.34872448735191040196449811286342', '5.61512121159976493635059759834100', '5.62744903114759413230907644897017', '6.63316497795641254071546618942463', '6.96244770770211698235830948959359', '7.04505635537817955425168739500600', '7.53447336677812027102722253324197', '8.023205247063217770380306113119581', '8.346812771950802682173692420936026', '8.506280981085827258676944065772108', '8.983209757758252815104287735671564'], 'prelabel': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 252652984753568148, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.36470484389903109025466912874', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.12659760927974406734232360859', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '1.95127430833541022792962749106', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 428.3750897471616, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 6718464, 'conductor_radical': 6, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, -1, 0, 0, 0, -2, 0, -1, 0, 0, 0, 12, 0, -10, 0, 0, 0, 6, 0, 5, 0, 0, 0, -8, 0, -8, 0, 0, 0, 2, 0, -10, 0, 0, 0, -8, 0, 4, 0, 0, 0, -10, 0, 7, 0, 0, 0, 8, 0, 4, 0, 0, 0, 14, 0, -3, 0, 0, 0, 2, 0, 13, 0, 0, 0, 8, 0, 18, 0, 0, 0, 2, 0, -11, 0, 0, 0, -12, 0, -24, 0, 0, 0, -4, 0, 1, 0, 0, 0, 20, 0, -1, 0, 0, 0], 'euler11': [1, 2, -7, 22, 121], 'euler13': [1, 1, -12, 13, 169], 'euler17': [1, -12, 70, -204, 289], 'euler19': [1, 10, 63, 190, 361], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -6, 13, -138, 529], 'euler29': [1, 8, 35, 232, 841], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 8, 33, 248, 961], 'euler37': [1, 10, 99, 370, 1369], 'euler41': [1, 8, 23, 328, 1681], 'euler43': [1, -4, -27, -172, 1849], 'euler47': [1, 10, 53, 470, 2209], 'euler5': [1, 2, -1, 10, 25], 'euler53': [1, -8, 122, -424, 2809], 'euler59': [1, -14, 137, -826, 3481], 'euler61': [1, 3, -52, 183, 3721], 'euler67': [1, -13, 102, -871, 4489], 'euler7': [1, 1, -6, 7, 49], 'euler71': [1, -8, 158, -568, 5041], 'euler73': [1, -18, 227, -1314, 5329], 'euler79': [1, 11, 42, 869, 6241], 'euler83': [1, 12, 61, 996, 6889], 'euler89': [1, 4, 182, 356, 7921], 'euler97': [1, 1, -96, 97, 9409], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 2, -1, 10, 25], [1, 1, -6, 7, 49], [1, 2, -7, 22, 121], [1, 1, -12, 13, 169], [1, -12, 70, -204, 289], [1, 10, 63, 190, 361], [1, -6, 13, -138, 529], [1, 8, 35, 232, 841], [1, 8, 33, 248, 961], [1, 10, 99, 370, 1369], [1, 8, 23, 328, 1681], [1, -4, -27, -172, 1849], [1, 10, 53, 470, 2209], [1, -8, 122, -424, 2809], [1, -14, 137, -826, 3481], [1, 3, -52, 183, 3721], [1, -13, 102, -871, 4489], [1, -8, 158, -568, 5041], [1, -18, 227, -1314, 5329], [1, 11, 42, 869, 6241], [1, 12, 61, 996, 6889], [1, 4, 182, 356, 7921], [1, 1, -96, 97, 9409]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2592/2/i/d'], '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': '4-2592e2-1.1-c1e2-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-2592e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.549420205247685, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 252652984753568148, 'z1': {'__RealLiteral__': 0, 'data': '0.36470484389903109025466912874', 'prec': 97}}
  • lfunc_instances • Show schema
    {'Lhash': '462318314274749469226009909041,1428132135619155832906469601450', 'Lhash_array': ['462318314274749469226009909041', '1428132135619155832906469601450'], 'factors': ['2-2592-9.7-c1-0-6', '2-2592-9.4-c1-0-29'], 'label': '4-2592e2-1.1-c1e2-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2592/2/i/d'}