-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2458928173497136464566410915628', 'a10': [1.9289553603049836, -0.47848997601114346], 'a2': [-0.3404858832570231, -1.372614062037354], 'a3': [0.0, 0.15502988636534598], 'a4': [-1.7681387266053696, 0.9347114225675975], 'a5': [0.0, 1.4053151673543687], 'a6': [0.21279620206112695, -0.05278548779034076], 'a7': [-1.0, 0.0], 'a8': [1.885024318612401, 2.1087160354679937], 'a9': [2.9759657343335477, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 5.142365890170459, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.3404858832570231, 1.372614062037354]]], [7, [[1.0, 0], [1.0, 0]]], [23, [[1.0, 0], [2.0203157699076177, 4.349519995340013]]]], 'bad_primes': [2, 7, 23], 'central_character': '644.183', 'coefficient_field': 'CDF', 'conductor': 644, 'conductor_radical': 322, 'conjugate': '28914289976780362315335281601', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.3404858832570231, 1.372614062037354]], [[1.0, 0], [0, -0.15502988636534598], [-3.0, 0]], [[1.0, 0], [0, -1.4053151673543687], [-5.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [3.4206807651234277, 0], [11.0, 0]], [[1.0, 0], [5.810733408455851, 0], [13.0, 0]], [[1.0, 0], [0, 4.219616934904946], [-17.0, 0]], [[1.0, 0], [7.135350246256692, 0], [19.0, 0]], [[1.0, 0], [2.0203157699076177, 4.349519995340013]], [[1.0, 0], [5.128943224405264, 0], [29.0, 0]], [[1.0, 0], [0, 4.8161051916222], [-31.0, 0]], [[1.0, 0], [0, -12.140982470948446], [-37.0, 0]], [[1.0, 0], [2.169205026887229, 0], [41.0, 0]], [[1.0, 0], [5.694556934895216, 0], [43.0, 0]], [[1.0, 0], [0, -1.8079507174539502], [-47.0, 0]], [[1.0, 0], [0, -8.277417008109555], [-53.0, 0]], [[1.0, 0], [0, 5.174014723603435], [-59.0, 0]], [[1.0, 0], [0, 11.406104122745406], [-61.0, 0]], [[1.0, 0], [-8.181074345671465, 0], [67.0, 0]], [[1.0, 0], [0, -11.67988794259708], [-71.0, 0]], [[1.0, 0], [0.10029449092410771, 0], [73.0, 0]], [[1.0, 0], [12.614733802812284, 0], [79.0, 0]], [[1.0, 0], [2.6877196362189477, 0], [83.0, 0]], [[1.0, 0], [0, -3.827948853690979], [-89.0, 0]], [[1.0, 0], [0, 8.453188648567027], [-97.0, 0]], [[1.0, 0], [5.840206441111228, 0], [101.0, 0]], [[1.0, 0], [-0.9547932609084474, 0], [103.0, 0]], [[1.0, 0], [-5.818092163003721, 0], [107.0, 0]], [[1.0, 0], [0, 16.417739740033163], [-109.0, 0]], [[1.0, 0], [0, -8.511947805181025], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 55, 'label': '2-644-92.91-c1-0-55', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/644/2/c/a/183/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.041346623263213, 0.27192992585554304, 0.5119403023081764, 0.7633981099334619, 1.0249696304177518, 1.2908976373296557, 1.5505238907906347, 1.7883806080456293, 1.9848086518854446, 2.117079006658315, 2.16100306908836, 2.092996080877191, 1.8925083450058702, 1.5446720033525918, 1.0429408792033574, 0.39144093578330097, -0.3932878180746235, -1.2814793184394522, -2.23053983145887, -3.1868492997896936, -4.089025070674851, -4.872537977363318, -5.4753812316979396, -5.844305754682655, -5.940978618867232, -5.747322576972915, -5.269279562882752, -4.538327284959422, -3.6102712869384876, -2.5611255192138462, -1.4802561927532871, -0.46135445722874313, 0.4078305370180629, 1.0557842998632565, 1.436188182624746, 1.5342296204681716, 1.369180308656163, 0.992590230187516, 0.48202290408240506, -0.0690895442182753, -0.5642590683362115, -0.9177001094766931, -1.0670240138283629, -0.9828666603823634, -0.6737794544985398, -0.18535194259319038, 0.4065988704724135, 1.0079673050454516, 1.52170531011601, 1.8641609418203717, 1.979663831300374, 1.8507409915998383, 1.50195244640993, 0.9963526991468952, 0.42486028426470274, -0.1098612771299723, -0.5122865756600138, -0.7122600070063241, -0.6790696256940929, -0.42843469567206194, -0.020669501901535662, 0.4500925621674583, 0.8739644924050156, 1.1474414075839787, 1.1953483734661245, 0.9880900092571397, 0.5503443683198819, -0.04115649380878365, -0.6710091748765631, -1.2076077816050967, -1.530546000128429, -1.557434583654595, -1.2643138830873506, -0.6947570437511144, 0.04519657750080236, 0.8063078782856039, 1.4265597993945085, 1.7670144831361254, 1.7457238920399099, 1.3621111613880663, 0.7056681976732471, -0.05430158350051088, -0.6973356447876584, -0.9942802022450195, -0.7556476747072982, 0.12395055679525166, 1.6350157873246733, 3.643532628025971, 5.906027283576123, 8.107823825093053, 9.917989256769362, 11.05053965939595, 11.319592407772056, 10.67682932054594, 9.222876480058803, 7.189426619394991, 4.895068933756029, 2.6835236936544034, 0.8570042186313221, -0.3812286569809533, -0.9628010365131479, -0.9608805371273573, -0.5661898117765845, -0.03786910606579953, 0.35959769243076856, 0.418942988110626, 0.03778225813937716, -0.7595535769592171, -1.8309014477613417, -2.953461134327634, -3.880119580966322, -4.401104267469342, -4.395872942075493, -3.8625511928136778, -2.917790199772346, -1.7672917588009944, -0.6546065638670251, 0.19871017136980793, 0.64632779895409, 0.6502289773059933, 0.28537531246369346, -0.2849022465791534, -0.8559445063839238, -1.2384647005635845, -1.3095814729830306, -1.0444098575008627, -0.5197402234912317, 0.11099331086418265, 0.6642787685816762, 0.9813707349848166, 0.9757035595752238, 0.6591025312814078, 0.13891254162664007, -0.4135625399736404, -0.8145519932255478, -0.9244233575276044, -0.6926449026887175, -0.177239061606848, 0.46808532310411544, 1.0366073226625683, 1.3295920038017572, 1.2181610621024586, 0.6875016530350501, -0.15077322272588706, -1.0835388313477439, -1.8529614363201923, -2.2300227177021705, -2.0837862447716433, -1.4255064681799041, -0.41294759448477203, 0.688775655555703, 1.5808663075231861, 2.019312802298359, 1.8928857411721136, 1.26693270059408, 0.37782201441514707, -0.4236119516370116, -0.7665223544530672, -0.3675395124779594, 0.8787696257381763, 2.853339158307719, 5.225715666663908, 7.526467013765054, 9.261722145466797, 10.04005121538365, 9.67723179765443, 8.249384558886296, 6.078424586503187, 3.6521842404602634, 1.4997959612530554, 0.05575435200108697, -0.45029632501886596, -0.047808704573227605, 0.9911616816423567, 2.2341634263299723, 3.2127637054331935, 3.5538657872530877, 3.0809688027255997, 1.8574115393690611, 0.16068088947217027, -1.6030746917937506, -3.0180356483846356, -3.7757420598551046, -3.7561791426731816, -3.050514485968486, -1.9211603505836965, -0.7138285655443694, 0.24966931390964048, 0.7642206203194268, 0.7918180844886891, 0.45588249855382884, -0.0159019357686933, -0.3792470711142286, -0.46115921087234485, -0.218604298773937, 0.25105931849044877, 0.7502412209766353, 1.0569782763794193, 1.0094887167963806, 0.5695182877764888, -0.15810405175171763, -0.9571684893328174, -1.5726864742058968, -1.7995667546159198, -1.5564484712937623, -0.9183039609621844, -0.09522338785760218, 0.636701357966724, 1.029557567103131, 0.9505972197650389, 0.4313182450869477, -0.3397534990248728, -1.079846678728905, -1.5100464319517544, -1.4553637833707667, -0.9115121641725888, -0.05349829812425446, 0.8193723888100384, 1.3853029958073464, 1.414631962287609, 0.857237261443495, -0.1296115726154391, -1.2258933319069452, -2.0540724126891017, -2.3111566445078187, -1.8826137726528365, -0.8970835554071315, 0.30082788501542673, 1.2552357990297114, 1.5497011253381447, 0.9549657665717559, -0.47701102882067653, -2.4079064955928793, -4.303758518173008, -5.596654235240597, -5.867541187321682, -4.991009546627123, -3.192923060564064, -0.9984664964778904, 0.9168352996504586, 1.9286791640065364, 1.655539094917511, 0.07955389334407513, -2.4421821654025297, -5.28018789359299, -7.716970554605762, -9.155155984133307, -9.284250857949958, -8.155099043401206, -6.14174313508019, -3.8072024520076515, -1.720287370346694, -0.28482253602911156, 0.3639671454580895, 0.3659847659866232, 0.04995115942734483, -0.20995317755221282], 'positive_zeros': ['1.93975230481840024134872560887672', '3.93794191259042032955746598078108', '4.85907051602808999474581364720839', '5.66562508934312071380038454403937', '6.84737338641346143829800389614044', '7.50563659076948026009974726884326', '8.366843594227824513874862789971157', '9.242727899493904684848991874076354', '10.11588380006109878692353568898253', '10.61179498096028346305314377840807'], 'prelabel': '2-644-92.91-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2676785244320805, 'root_angle': -0.7932070106056772, 'root_number': '-0.7962899173947531 - 0.6049151737685684*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.396603505303', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93975230481840024134872560888', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.93794191259042032955746598078', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.85907051602808999474581364721', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 5.142365890170459, 'bad_primes': [2, 7, 23], 'central_character': '92.91', 'conductor': 644, 'conductor_radical': 322, 'degree': 2, 'index': 55, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/644/2/c/a/183/15'], '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': '2-644-92.91-c1-0-55', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-644-92.91-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.2676785244320805, 'root_angle': -0.3966035053028386, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93975230481840024134872560888', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2458928173497136464566410915628', 'Lhash_array': ['2458928173497136464566410915628'], 'label': '2-644-92.91-c1-0-55', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/644/2/c/a/183/15'}