-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1850997075470181349791993813580', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.41541501300188644, 0.9096319953545183], 'a4': [0.0, 0.0], 'a5': [-1.2048943600997284, -1.3905222172983402], 'a6': [0.0, 0.0], 'a7': [-0.9213548038943153, -0.5921187785894567], 'a8': [0.0, 0.0], 'a9': [-0.6548607339452851, 0.7557495743542583], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.4077421915746795, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.41541501300188644, -0.9096319953545183]]], [23, [[1.0, 0], [-0.34929299817726994, 4.783094646923091]]]], 'bad_primes': [2, 3, 23], 'central_character': '552.169', 'coefficient_field': 'CDF', 'conductor': 552, 'conductor_radical': 138, 'conjugate': '1223456179504193900265685710340', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.41541501300188644, -0.9096319953545183]], [[1.0, 0], [1.2048943600997284, 1.3905222172983402], [-0.7115741913664257, 4.949107209404664]], [[1.0, 0], [0.9213548038943153, 0.5921187785894567], [2.907905091013205, 6.367423967481629]], [[1.0, 0], [0.11706719413427288, 0.8142202197667313], [-10.554422709759471, 3.0990581252557265]], [[1.0, 0], [-4.257804208827878, 2.7363246134367567], [5.400395169024524, -11.82521593960874]], [[1.0, 0], [-6.776525352854669, 1.9897673736666446], [14.30131005813008, -9.190893896745159]], [[1.0, 0], [-6.404031005431036, -1.8803931647932774], [15.983817123792441, 10.272175531656353]], [[1.0, 0], [-0.34929299817726994, 4.783094646923091]], [[1.0, 0], [7.907345206570976, -2.3218060414584403], [24.396352452104253, -15.67858370621233]], [[1.0, 0], [3.034326732067962, -6.644248747543463], [-20.300682752303835, -23.428236804982006]], [[1.0, 0], [-6.75088791775139, 7.790939975308091], [-5.26564901611155, -36.62339334959451]], [[1.0, 0], [1.36620363120436, 1.5766830399854226], [-5.83490836920469, 40.58267911711824]], [[1.0, 0], [-2.2309761354918325, -4.8851563140461955], [-28.159011559647258, 32.497231697233104]], [[1.0, 0], [-0.43346370800064177, 0], [47.0, 0]], [[1.0, 0], [5.967814774571145, 3.835281674585495], [22.016995689099982, 48.21049575378947]], [[1.0, 0], [-4.384063763701109, 2.817466702348426], [24.5094857671113, -53.668287725916585]], [[1.0, 0], [4.75508624216218, -10.412186491009559], [-39.946504770662386, -46.10072403560976]], [[1.0, 0], [1.3295738373860597, -9.247389160373146], [-64.28602923217133, -18.876081308375788]], [[1.0, 0], [-0.7975510290256023, 5.547089250158204], [-68.12400112662931, -20.003011535741507]], [[1.0, 0], [-3.5102247058572122, -1.0306949698064631], [61.41150789667623, 39.466779674258625]], [[1.0, 0], [-6.05314757748307, 3.890121737089386], [32.817786027149026, -71.86092763300695]], [[1.0, 0], [6.976411520717654, -8.05120808746342], [-11.812131576682667, -82.15517967611741]], [[1.0, 0], [3.910997480096957, 8.56388991803465], [-58.28260532113037, 67.26171211752899]], [[1.0, 0], [-4.703587107682271, -5.428228889451262], [-13.804539312508659, 96.01267986245047]], [[1.0, 0], [-8.77788066612625, 10.130214308606968], [-14.373798665601798, -99.9719656299742]], [[1.0, 0], [-0.062372935458346664, -0.43381329493676773], [-98.82777628229323, 29.01845335466726]], [[1.0, 0], [7.123913222403263, -15.599194050306723], [-70.07009853214551, -80.86520445590564]], [[1.0, 0], [1.9622963961258815, -0.5761822089000386], [91.69663507859875, -58.929849102660135]], [[1.0, 0], [0.7909075538154435, -5.5008828651360595], [-108.4227060184382, -31.835778923081556]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 7, 'label': '2-552-23.8-c1-0-7', '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/552/2/q/b/169/1', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.4474948764119195, 1.5109651047962873, 1.5603641512469368, 1.5918160155675247, 1.5981804766922367, 1.5702563436733015, 1.4982309947040529, 1.373176552379833, 1.1884809241270813, 0.9411462999631286, 0.6328860455790121, 0.2709277186508027, -0.1315909392018382, -0.555750089754737, -0.9775973602812694, -1.3695717306387956, -1.7025875817581835, -1.9486809403239191, -2.084028174032425, -2.092059220271922, -1.9663163869009082, -1.7126698739634623, -1.350505046032702, -0.9125531317417804, -0.4431496208046916, 0.005131261764258349, 0.3763150444284058, 0.6169679573589969, 0.6826617506419335, 0.5442194991214316, 0.19291098014770428, -0.3562200566662467, -1.0635826434465316, -1.86725500391458, -2.6882751739821313, -3.4386749337626217, -4.031498896215636, -4.391674582932413, -4.466339579313265, -4.233145124457941, -3.7051794874864488, -2.931498685483071, -1.992791745749821, -0.9923827309901513, -0.043491585780174695, 0.7456696060848109, 1.2869129032687512, 1.5249532980384075, 1.4460434882849413, 1.0807569733576716, 0.500120863116339, -0.19468489186526855, -0.8877751424515282, -1.466920817245217, -1.8419434955262335, -1.9600570435091098, -1.8153832446275258, -1.4506930070505712, -0.9506597186695709, -0.42737037242239345, -0.00027737425652171505, 0.226076090193883, 0.18259880254435554, -0.1494360895194264, -0.7322163561556883, -1.4756277883976823, -2.251722284251062, -2.917280488766542, -3.3406450379391024, -3.427929067141622, -3.1435059765337923, -2.520466217976155, -1.6584052821387272, -0.70821854124679, 0.15389058472753817, 0.758722907653679, 0.9767345252216121, 0.7446314352341615, 0.08035958066368803, -0.9170389417207881, -2.0833794017663356, -3.2186198276492473, -4.124179755452186, -4.6411124980471214, -4.681457346148897, -4.246175270223811, -3.425580342889727, -2.3816650595559334, -1.3154893008727775, -0.4260656197938894, 0.13080171550643038, 0.2749802256046656, 0.018629893586254793, -0.5369437044876851, -1.2239220850051329, -1.8455084896255514, -2.220340155032774, -2.223986476014319, -1.8181187778356676, -1.0604650990160964, -0.09285318340184627, 0.8903984980415216, 1.6868742976670401, 2.133200611432284, 2.143957453527311, 1.7330025294892921, 1.011730683558573, 0.16411186977446865, -0.5961050140489574, -1.0761895372392427, -1.1511655854648402, -0.7950383297497583, -0.08849051000263017, 0.7994629808643522, 1.6520468713376704, 2.258094089061975, 2.465298905842045, 2.2200437352930127, 1.5833989825699915, 0.7185207422763201, -0.14829097015762158, -0.783876587820765, -1.0081314077841752, -0.7424180146803864, -0.033716120571515, 0.9525392891023233, 1.9702534111398484, 2.7525767588175567, 3.0794384389168927, 2.8357597987482355, 2.0451926169743397, 0.8699717470657643, -0.42416976786572747, -1.5301757886117207, -2.173933153296273, -2.1821392551515717, -1.5264751021314236, -0.33249171394808186, 1.1495344268299936, 2.604768710830779, 3.729889616652873, 4.305658951469188, 4.24734771228743, 3.6200852332419666, 2.6154270269234625, 1.4957610238429715, 0.5218153401842556, -0.116891876878067, -0.3496342457629468, -0.23713961349597174, 0.05387444985853314, 0.3067424182848991, 0.3251521690781218, -0.002871410838852228, -0.6663203769371844, -1.5298492140309174, -2.370980987998965, -2.94581993984684, -3.064508002105723, -2.6541705866454715, -1.7899986105833634, -0.6837744824503504, 0.36875641696283723, 1.068143043853445, 1.1969640267741835, 0.6863990265103157, -0.3564221840785122, -1.669779248347096, -2.9032241252999014, -3.7108059135609017, -3.846118262998932, -3.2323514163165, -1.9869549206956008, -0.3929942237698134, 1.1756528287583605, 2.354786081612071, 2.887920579269572, 2.694090749926822, 1.886079646087748, 0.7339248413481941, -0.4155796218246759, -1.239784129987912, -1.531854416240549, -1.2562895007986532, -0.5521217775702778, 0.3166850490313589, 1.0481870899365078, 1.3999361180543095, 1.2668665274443744, 0.7153808426661697, -0.037175735102837684, -0.6915798826222224, -0.9630689884359307, -0.6749205311306037, 0.18028013540411383, 1.4315059630023947, 2.77602347071358, 3.868224185285365, 4.4233291837540145, 4.303660540589517, 3.560212501284257, 2.4160052090126185, 1.1959626842049988, 0.22510195749550255, -0.2728048672532415, -0.24367303000831242, 0.18363523180986385, 0.7440352932743359, 1.1283709991774, 1.0914061274915503, 0.5403282505077013, -0.4259503212325343, -1.540996364657222, -2.4524218085537117, -2.8357153051643205, -2.503980008529258, -1.4775059256756162, 0.010856809433082306, 1.5783872425646277, 2.805162502787835, 3.361991714322082, 3.1131156620044877, 2.160364402966699, 0.8135821765205192, -0.5044850631559471, -1.389483491333952, -1.5815528672113348, -1.0460489712269587, 0.017090872332804413, 1.2385358766844352, 2.1984746293898736, 2.560995350941832, 2.1806186204539273, 1.1467449419635507, -0.2478972002443719, -1.6037938728756578, -2.5438837398613314, -2.832642652634683, -2.445904914997406, -1.5691309087910834, -0.5260990482495742, 0.33647787695010495, 0.7681396335091298, 0.696455312747685, 0.24345136292890213, -0.3282609379411907, -0.7198193042515009, -0.7130978918744427, -0.2577616692418687, 0.5039331971212302, 1.2849854543862058, 1.7584801004869166, 1.6827019673967416, 1.0013675202395194, -0.1187610609531602, -1.329510932299367, -2.2111225353664796], 'positive_zeros': ['1.46017922851685276557252817555596', '3.12347113735994546113697971478413', '3.79889944343069548405840768445959', '5.50616480685418595685397167121730', '6.34083932822884316564581106478019', '7.50010146042809899515779525842577', '7.83072554985666418576550520664294', '9.225462595822826095010499831052021', '9.761558991706364806337392332861807', '11.21116907118509104809887267051822'], 'prelabel': '2-552-23.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0994623577417815, 'root_angle': 0.14786124424479394, 'root_number': '0.8940367957694227 + 0.44799353545597453*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0739306221224', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46017922851685276557252817556', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.12347113735994546113697971478', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.79889944343069548405840768446', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 4.4077421915746795, 'bad_primes': [2, 3, 23], 'central_character': '23.8', 'conductor': 552, 'conductor_radical': 138, 'degree': 2, 'index': 7, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/552/2/q/b/169/1'], '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': '2-552-23.8-c1-0-7', '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': '2-552-23.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0994623577417815, 'root_angle': 0.07393062212239697, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46017922851685276557252817556', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1850997075470181349791993813580', 'Lhash_array': ['1850997075470181349791993813580'], 'label': '2-552-23.8-c1-0-7', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/552/2/q/b/169/1'}