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  • lfunc_lfunctions • Show schema
    {'Lhash': '1092155989090304042679829328479,1693941707906220828163736429927', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -78, 'a6': 0, 'a7': -98, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 26136.183442385598, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, 98, 2401]]], 'bad_primes': [2, 3, 7], 'central_character': '1008.1', 'coefficient_field': '1.1.1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'euler_factors': [[1], [1], [1, 78, 3226, 243750, 9765625], [1, 98, 2401], [1, -174, 216046, -28022874, 25937424601], [1, -208, 589782, -77228944, 137858491849], [1, 1482, 1748050, 2104228074, 2015993900449], [1, 352, -907146, 871586848, 6131066257801], [1, -3354, 13680670, -21587494422, 41426511213649], [1, 276, -4408658, 5661077124, 420707233300201], [1, 6520, 61995582, 186662064520, 819628286980801], [1, -13864, 182650038, -961384619848, 4808584372417849], [1, 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'label': '4-1008e2-1.1-c5e2-0-11', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'origin': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 27}, 'plot_values': [1.274064628574569e-120, 0.014781001422194184, 0.05871689352012772, 0.13059558190352896, 0.22842953288654752, 0.34950187613034217, 0.4904324069644838, 0.6472576331008523, 0.8155265165049764, 0.9904071228643017, 1.1668082976269274, 1.339494519628919, 1.5032358863084645, 1.6529076241870484, 1.7836656380529743, 1.8910188838314335, 1.971007351294563, 2.0202576712898384, 2.036124120210028, 2.01674409246517, 1.961114325302881, 1.869141658549657, 1.74166039116607, 1.5804438627027693, 1.3881949093485144, 1.1684832519914699, 0.9257289965803716, 0.6650648742347498, 0.39229954131823314, 0.11374206814539609, -0.16388836618223548, -0.4336295190645228, -0.6884333704746237, 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'8.051104124478749091926629119294199', '8.673426650838941802186296450483149', '9.019304493183041706347359607186040'], 'prelabel': '4-1008e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e2-0', 'trace_hash': 371613173061737622, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.861559162196326740773649012234', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '1.33628438909052813276167543332', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.21441376989172694708514872592', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 26136.183442385598, 'bad_primes': [2, 3, 7], 'central_character': '1.1', 'conductor': 1016064, 'conductor_radical': 42, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -78, 0, -98, 0, 0, 0, 174, 0, 208, 0, 0, 0, -1482, 0, -352, 0, 0, 0, 3354, 0, 2858, 0, 0, 0, -276, 0, -6520, 0, 0, 0, 7644, 0, 13864, 0, 0, 0, 12930, 0, -12712, 0, 0, 0, -28116, 0, 7203, 0, 0, 0, 46992, 0, -13572, 0, 0, 0, -65556, 0, -13148, 0, 0, 0, -16224, 0, 75236, 0, 0, 0, -66042, 0, 60496, 0, 0, 0, -17052, 0, 34916, 0, 0, 0, -82488, 0, 115596, 0, 0, 0, -42510, 0, -20384, 0, 0, 0, 27456, 0, 213256, 0, 0, 0], 'euler11': [1, -174, 216046, -28022874, 25937424601], 'euler13': [1, -208, 589782, -77228944, 137858491849], 'euler17': [1, 1482, 1748050, 2104228074, 2015993900449], 'euler19': [1, 352, -907146, 871586848, 6131066257801], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, -3354, 13680670, -21587494422, 41426511213649], 'euler29': [1, 276, -4408658, 5661077124, 420707233300201], 'euler3': [1, 0, 0, 0, 0], 'euler31': [1, 6520, 61995582, 186662064520, 819628286980801], 'euler37': [1, -13864, 182650038, -961384619848, 4808584372417849], 'euler41': [1, -12930, 272958682, -1498020678930, 13422659310152401], 'euler43': [1, 12712, 268967622, 1868771327416, 21611482313284249], 'euler47': [1, 28116, 641027998, 6448264216812, 52599132235830049], 'euler5': [1, 78, 3226, 243750, 9765625], 'euler53': [1, -46992, 1329386182, -19651842607056, 174887470365513049], 'euler59': [1, 65556, 2467431382, 46867577345244, 511116753300641401], 'euler61': [1, 13148, 1323360078, 11104752165548, 713342911662882601], 'euler67': [1, -75236, 4068077958, -101578012550252, 1822837804551761449], 'euler7': [1, 98, 2401, 0, 0], 'euler71': [1, 66042, 4539911038, 119154914798742, 3255243551009881201], 'euler73': [1, -60496, 4988928270, -125412539090128, 4297625829703557649], 'euler79': [1, -34916, 3983487582, -107438501227484, 9468276082626847201], 'euler83': [1, 82488, 9550060822, 324923584559784, 15516041187205853449], 'euler89': [1, 42510, 4392793978, 237378367176990, 31181719929966183601], 'euler97': [1, -213256, 28472054478, -1831301833846792, 73742412689492826049], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, 0, 0, 0], [1, 78, 3226, 243750, 9765625], [1, 98, 2401, 0, 0], [1, -174, 216046, -28022874, 25937424601], [1, -208, 589782, -77228944, 137858491849], [1, 1482, 1748050, 2104228074, 2015993900449], [1, 352, -907146, 871586848, 6131066257801], [1, -3354, 13680670, -21587494422, 41426511213649], [1, 276, -4408658, 5661077124, 420707233300201], [1, 6520, 61995582, 186662064520, 819628286980801], [1, -13864, 182650038, -961384619848, 4808584372417849], [1, -12930, 272958682, -1498020678930, 13422659310152401], [1, 12712, 268967622, 1868771327416, 21611482313284249], [1, 28116, 641027998, 6448264216812, 52599132235830049], [1, -46992, 1329386182, -19651842607056, 174887470365513049], [1, 65556, 2467431382, 46867577345244, 511116753300641401], [1, 13148, 1323360078, 11104752165548, 713342911662882601], [1, -75236, 4068077958, -101578012550252, 1822837804551761449], [1, 66042, 4539911038, 119154914798742, 3255243551009881201], [1, -60496, 4988928270, -125412539090128, 4297625829703557649], [1, -34916, 3983487582, -107438501227484, 9468276082626847201], [1, 82488, 9550060822, 324923584559784, 15516041187205853449], [1, 42510, 4392793978, 237378367176990, 31181719929966183601], [1, -213256, 28472054478, -1831301833846792, 73742412689492826049]], 'index': 11, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1008/6/a/bf'], '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': '4-1008e2-1.1-c5e2-0-11', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [5, 5], 'order_of_vanishing': 2, 'prelabel': '4-1008e2-1.1-c5e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 12.714829545514345, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e2-0', 'trace_hash': 371613173061737622, 'z1': {'__RealLiteral__': 0, 'data': '0.861559162196326740773649012234', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '1092155989090304042679829328479,1693941707906220828163736429927', 'Lhash_array': ['1092155989090304042679829328479', '1693941707906220828163736429927'], 'factors': ['2-1008-1.1-c5-0-31', '2-1008-1.1-c5-0-61'], 'label': '4-1008e2-1.1-c5e2-0-11', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1008/6/a/bf'}