-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '537985855265183840375540607775,767223352456623318071586517606,1201304953311751461322578670522,1233521614204113403861319026618,1312771273997126419549516529904', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 7, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 254964898.63999012, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [167, [1, -5, 10, -10, 5, -1]]], 'bad_primes': [2, 3, 167], 'central_character': '6012.1', 'coefficient_field': '1.1.1.1', 'conductor': 7854071662702328832, 'conductor_radical': 1002, 'degree': 10, 'euler_factors': [[1], [1], [1, -7, 36, -134, 394, -981, 1970, -3350, 4500, -4375, 3125], [1, 2, 24, 41, 286, 405, 2002, 2009, 8232, 4802, 16807], [1, -5, 36, -136, 628, -2025, 6908, -16456, 47916, -73205, 161051], [1, 8, 64, 292, 1433, 4915, 18629, 49348, 140608, 228488, 371293], [1, -7, 79, -402, 2557, -9625, 43469, -116178, 388127, -584647, 1419857], [1, -2, 50, -86, 1389, -2425, 26391, -31046, 342950, -260642, 2476099], [1, -13, 144, -1052, 6778, -34395, 155894, -556508, 1752048, -3637933, 6436343], [1, -11, 166, -1174, 9958, -49617, 288782, -987334, 4048574, -7780091, 20511149], [1, 12, 153, 1291, 9382, 57399, 290842, 1240651, 4558023, 11082252, 28629151], [1, 7, 178, 920, 12752, 48883, 471824, 1259480, 9016234, 13119127, 69343957], [1, -12, 193, -1363, 13060, -69271, 535460, -2291203, 13301753, -33909132, 115856201], [1, 0, 107, -197, 6754, -10885, 290422, -364253, 8507249, 0, 147008443], [1, -19, 168, -1313, 12955, -108573, 608885, -2900417, 17442264, -92713939, 229345007], [1, -21, 350, -4071, 40465, -314151, 2144645, -11435439, 52106950, -165700101, 418195493], [1, -7, 196, -789, 15775, -43795, 930725, -2746509, 40254284, -84821527, 714924299], [1, 6, 158, 1262, 14037, 105179, 856257, 4695902, 35862998, 83075046, 844596301], [1, -10, 142, -236, -205, 59767, -13735, -1059404, 42708346, -201511210, 1350125107], [1, -35, 763, -11235, 130765, -1205501, 9284315, -56635635, 273086093, -889408835, 1804229351], [1, 8, 312, 2092, 42635, 220341, 3112355, 11148268, 121373304, 227185928, 2073071593], [1, 0, 197, 805, 17746, 119621, 1401934, 5024005, 97128683, 0, 3077056399], [1, -11, 326, -2557, 45301, -272481, 3759983, -17615173, 186402562, -522041531, 3939040643], [1, -32, 606, -7762, 78409, -741105, 6978401, -61482802, 427211214, -2007751712, 5584059449], [1, -11, 505, -4153, 99605, -598793, 9661685, -39075577, 460899865, -973822091, 8587340257], [1, -8, 234, -2119, 24592, -261393, 2483792, -21615919, 241090434, -832483208, 10510100501], [1, -9, 174, 352, -572, 201333, -58916, 3734368, 190134498, -1012957929, 11592740743], [1, -20, 526, -7827, 111946, -1221767, 11978222, -89611323, 644372618, -2621592020, 14025517307], [1, 22, 266, 2317, 36528, 451829, 3981552, 27528277, 344477714, 3105479542, 15386239549], [1, 1, 482, 267, 100471, 36103, 11353223, 3409323, 695476354, 163047361, 18424351793]], 'euler_factors_factorization': [[1], [1], [[[1, -7, 36, -134, 394, -981, 1970, -3350, 4500, -4375, 3125], 1]], [[[1, 2, 24, 41, 286, 405, 2002, 2009, 8232, 4802, 16807], 1]], [[[1, -5, 36, -136, 628, -2025, 6908, -16456, 47916, -73205, 161051], 1]], [[[1, 8, 64, 292, 1433, 4915, 18629, 49348, 140608, 228488, 371293], 1]], [[[1, -7, 79, -402, 2557, -9625, 43469, -116178, 388127, -584647, 1419857], 1]], [[[1, -2, 50, -86, 1389, -2425, 26391, -31046, 342950, -260642, 2476099], 1]], [[[1, -13, 144, -1052, 6778, -34395, 155894, -556508, 1752048, -3637933, 6436343], 1]], [[[1, -11, 166, -1174, 9958, -49617, 288782, -987334, 4048574, -7780091, 20511149], 1]], [[[1, 12, 153, 1291, 9382, 57399, 290842, 1240651, 4558023, 11082252, 28629151], 1]], [[[1, 7, 178, 920, 12752, 48883, 471824, 1259480, 9016234, 13119127, 69343957], 1]], [[[1, -12, 193, -1363, 13060, -69271, 535460, -2291203, 13301753, -33909132, 115856201], 1]], [[[1, 0, 107, -197, 6754, -10885, 290422, -364253, 8507249, 0, 147008443], 1]], [[[1, -19, 168, -1313, 12955, -108573, 608885, -2900417, 17442264, -92713939, 229345007], 1]], [[[1, -21, 350, -4071, 40465, -314151, 2144645, -11435439, 52106950, -165700101, 418195493], 1]], [[[1, -7, 196, -789, 15775, -43795, 930725, -2746509, 40254284, -84821527, 714924299], 1]], [[[1, 6, 158, 1262, 14037, 105179, 856257, 4695902, 35862998, 83075046, 844596301], 1]], [[[1, -10, 142, -236, -205, 59767, -13735, -1059404, 42708346, -201511210, 1350125107], 1]], [[[1, -35, 763, -11235, 130765, -1205501, 9284315, -56635635, 273086093, -889408835, 1804229351], 1]], [[[1, 8, 312, 2092, 42635, 220341, 3112355, 11148268, 121373304, 227185928, 2073071593], 1]], [[[1, 0, 197, 805, 17746, 119621, 1401934, 5024005, 97128683, 0, 3077056399], 1]], [[[1, -11, 326, -2557, 45301, -272481, 3759983, -17615173, 186402562, -522041531, 3939040643], 1]], [[[1, -32, 606, -7762, 78409, -741105, 6978401, -61482802, 427211214, -2007751712, 5584059449], 1]], [[[1, -11, 505, -4153, 99605, -598793, 9661685, -39075577, 460899865, -973822091, 8587340257], 1]], [[[1, -8, 234, -2119, 24592, -261393, 2483792, -21615919, 241090434, -832483208, 10510100501], 1]], [[[1, -9, 174, 352, -572, 201333, -58916, 3734368, 190134498, -1012957929, 11592740743], 1]], [[[1, -20, 526, -7827, 111946, -1221767, 11978222, -89611323, 644372618, -2621592020, 14025517307], 1]], [[[1, 22, 266, 2317, 36528, 451829, 3981552, 27528277, 344477714, 3105479542, 15386239549], 1]], [[[1, 1, 482, 267, 100471, 36103, 11353223, 3409323, 695476354, 163047361, 18424351793], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '10-6012e5-1.1-c1e5-0-1', 'leading_term': '28.845562179870514523615138941130501279759118921887464363096663198689040085685428103596961', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/6012/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01015625', 'prec': 34}, 'plot_values': [28.84556217987052, 28.744778916256948, 28.626170515050237, 28.47189255347253, 28.26444037746759, 27.986917537581817, 27.62878644455836, 27.19414815962235, 26.690132393128795, 26.1240331694264, 25.50306418867185, 24.832633302348412, 24.11525789655269, 23.35313278138392, 22.5487621384517, 21.705072224060313, 20.825707033814968, 19.91514266829146, 18.978119324780526, 18.01945495532704, 17.043971196710412, 16.05644922260018, 15.061567459897425, 14.063979105658353, 13.068320367004144, 12.079197883914931, 11.101152524563775, 10.138657223432956, 9.196040990382539, 8.277450570682229, 7.386824601887444, 6.527866771954349, 5.704034295663017, 4.918496924873787, 4.174116753214773, 3.473423274502774, 2.8185987722825736, 2.2114805088111056, 1.653525852518107, 1.145798551772064, 0.688958727922819, 0.2832665716965525, -0.07140432142331132, -0.3755813567070611, -0.6301908183004592, -0.836543976514807, -0.9963155182830177, -1.11151741029413, -1.18449322551878, -1.217891580225067, -1.214631560382209, -1.1778661714818586, -1.110947670460254, -1.0174003278742851, -0.9008730878720391, -0.7650945852378955, -0.6138292801389736, -0.4508413115571887, -0.27984986481503, -0.10447883310163243, 0.0717862824139872, 0.24563653812332598, 0.413971237148803, 0.5739418469456063, 0.722986667770324, 0.8588583535358509, 0.9796430622990521, 1.0837802138019021, 1.170082007958463, 1.2377407307997803, 1.2863292590951072, 1.3157942707778076, 1.326452137800591, 1.3189730510002258, 1.2943573422134649, 1.2539064190184768, 1.1991903828157668, 1.1320151062191564, 1.0543771210385458, 0.9684161114143469, 0.8763659623791666, 0.7805051682766542, 0.6831069361718315, 0.5863834508034488, 0.4924329445103438, 0.4031899092270628, 0.3203775153297449, 0.24546427076713187, 0.17962228971698785, 0.12369271764498482, 0.07815773662210344, 0.04311921103587198, 0.0182852076525224, 0.002963728361806385, -0.003934535299766695, -0.0038848209969826113, 0.001271817288770471, 0.009357125751532431, 0.017892490555316606, 0.0241435812868524, 0.025172207857122753, 0.017894492875775235, -0.0008557162176391465, -0.03425914108947284, -0.08544026101362381, -0.157394563962431, -0.2529156750340837, -0.3745255526700821, -0.5244058148532779, -0.7043321319202217, -0.9156135616117167, -1.159040747215422, -1.4348513075815397, -1.7426942172825086, -2.081600222990888, -2.4499655974894896, -2.8455542363772963, -3.2655373405462242, -3.7065045530316287, -4.164485988003987, -4.6349949220307005, -5.11309897417939, -5.593546134326995, -6.070802394210126, -6.539117128858269, -6.99261041257565, -7.425403957898159, -7.831794419909895, -8.206279701864709, -8.543631978796327, -8.838993356832304, -9.088025299685794, -9.287057474424714, -9.433065694265144, -9.523703972389447, -9.557371011513348, -9.533306634262365, -9.45166696144523, -9.313427137341664, -9.12034107253154, -8.874952727880864, -8.580582346613213, -8.241328025614086, -7.861892510129486, -7.4474801560472965, -7.003741210102805, -6.536666111026635, -6.052540614347492, -5.557739125152173, -5.0586042707183205, -4.561344562328481, -4.071919096278849, -3.595986193347399, -3.138734544907988, -2.7047969771097886, -2.2981687837491758, -1.9221555024057164, -1.5793613948525147, -1.2716172929724132, -0.9999670026838464, -0.764669673600895, -0.5652352441093981, -0.4004793281477253, -0.2685584761207539, -0.16703857521986049, -0.09298176399558852, -0.04304646943370469, -0.01359139464792629, -0.0007761177045638607, -0.0006726729824906897, -0.009378227022311184, -0.02312237690666241, -0.03836566220120618, -0.05189270595351594, -0.060894383611859934, -0.06303519486250032, -0.056504563190331196, -0.04005278000426436, -0.01301125459774963, 0.024707706651855874, 0.07262896059559107, 0.12974898748273134, 0.1945843564322927, 0.26523789868829456, 0.3394772853376135, 0.4148230147003969, 0.48864296801708446, 0.5582513607126378, 0.6210113527520703, 0.6744348470920837, 0.7162769527491916, 0.7446224570037687, 0.7579621822136412, 0.7552562158877005, 0.7359817076326804, 0.7001629091963933, 0.6483823344228139, 0.5817766002512655, 0.5020117073478362, 0.4112402348162968, 0.3120365405691869, 0.20732119468561014, 0.10027724902786157, -0.005748077364158438, -0.107351723513281, -0.20119531865334203, -0.2841074438974189, -0.353186368899213, -0.4059009899289116, -0.44019072902776846, -0.4545477025446169, -0.4480648903984072, -0.42047384942070043, -0.3721724513063691, -0.304237906938853, -0.2183997480650782, -0.11699114250938993, -0.0028754430245382743, 0.12062295220982978, 0.2498152650009161, 0.38076125797576027, 0.5093925990405748, 0.6316618677523506, 0.7436633602180667, 0.8417609125441567, 0.9226953718436766, 0.9837003908686751, 1.0226311315333334, 1.038043414328879, 1.0292245317059843, 0.9962122380743242, 0.9398127135558281, 0.8616269330865991, 0.7639978443244694, 0.6498973715434949, 0.5228330106360521, 0.38674845897353044, 0.24593559863368852, 0.10485701808478444, -0.03203171330983219, -0.16042789601508498, -0.2763184260536591, -0.37611391880448986, -0.45681247601942826, -0.5161113189382593, -0.5524871422693194, -0.5652499978795309, -0.5546040412651292, -0.5216484515775017, -0.46833321497197045, -0.39738911640912383, -0.3122357850852844, -0.21688751126190992, -0.11577837044110224, -0.01357953225891474, 0.08498758821883869, 0.1753389037888287, 0.25321549936207105, 0.314899547135245, 0.3574002012416581, 0.3786121182502131, 0.3774489441224843, 0.35395101049600336, 0.3093588932833782, 0.24613592072054494, 0.16794516368652365, 0.07958403168803665, -0.013122534414720425, -0.1034836536744216, -0.18414460745980293, -0.2473226151245875, -0.2850707339992391, -0.2895650879156838, -0.2534112533429788, -0.1699506395832887, -0.03355834809424131, 0.16007543388208484, 0.4136859764000541, 0.7282161049239306, 1.1026465428713967, 1.5338796055199633, 2.016683915203754, 2.5437068876890567, 3.1055521609376466, 3.690925886459938, 4.28684986135702, 4.878947851667999, 5.451810034560517, 5.989356768656878, 6.475254991641764, 6.893374523752648, 7.228279702902014, 7.465745185864059, 7.593140719569172, 7.5998602918735925, 7.4777229017019184, 7.221338253222853, 6.828366888744134, 6.299625993349979, 5.639225367681236, 4.854605513016832, 3.9564533157420554, 2.958402831155582, 1.8768051717413785, 0.7304313840336484, -0.45992169986477727, -1.6720754107409603, -2.8831428774793553, -4.069912182649378, -5.209386223496049, -6.279388883417905, -7.259485653340506, -8.131454606340878, -8.879531243558866, -9.49077348969978, -9.955555997901275, -10.26811762064517, -10.426449542780272, -10.43213424969302, -10.29024142359581, -10.009467295147028, -9.601829478211672, -9.082101172711365, -8.467213875542159, -7.7757872592564246, -7.027843675447701, -6.243944048731063, -5.444549344570507, -4.649339271798898, -3.87677971390086, -3.143660835321408, -2.464453564149996, -1.8509846915143249, -1.312157120757074, -0.8538967361885775, -0.47902504184825573, -0.18727808402221588, 0.024492715851471336, 0.16202164850595308, 0.23324139633786956, 0.24788221628535903, 0.21695854027619746, 0.15221597844671164, 0.06556242926176001, -0.03147731168211567, -0.12828822027928038, -0.21564360376739813, -0.2861125772664764, -0.3343646374967105, -0.3573815490267121, -0.3545535217929865, -0.3276522539510997, -0.2806853889297626, -0.21962060418546275, -0.1520074365212551, -0.08649998135423435, -0.032301937428961106, 0.0014459097957818167, 0.0063165118783656, -0.024749842380845027, -0.09681562350438348, -0.21236697632050128, -0.3708112905666908, -0.5680803497714698, -0.7963611199992783, -1.0439725747625803, -1.295404921775764, -1.5315269743657765, -1.7299559213194133, -1.8655985600885665, -1.9113553716158227, -1.838968024445596, -1.6199398357879367, -1.2265676433594865, -0.6330524956853936, 0.18335799372264622, 1.241288067272309, 2.5543720648694426, 4.130261552184, 5.969750563694336, 8.066113042277426, 10.404763135418632, 12.963492666738524, 15.712243641574009, 18.61322278053944, 21.621466043878737, 24.685761628388093, 27.75051063909196, 30.756308555663132, 33.641114130724155, 36.34180448427017, 38.79595980553919, 40.94482822794876, 42.733892124841276, 44.11425042656637, 45.043926673849946, 45.48948361800831, 45.42874377152375, 44.85024076497377, 43.75348271159595, 42.14888323959985, 40.05821265579601, 37.51585789285335, 34.566637852305576, 31.26423756562508, 27.66974516228518, 23.850716180085996, 19.88081691210755, 15.836532538484017, 11.794635336426285, 7.830289445579942, 4.0155983691343105, 0.4185870366313721, -2.89968909869516, -5.886895785611672, -8.500472179520598, -10.708279422362729, -12.488992498627459, -13.833029197323677, -14.742461121053541, -15.230462974186924, -15.32049458108254, -15.045369808457536, -14.446031469434201, -13.569935941319763, -12.4692932970254, -11.199317812004901, -9.816461556943272, -8.376434299222767, -6.932376352241134, -5.5332125024030265, -4.222249115504457, -3.0359534888891795, -2.0029066483285725, -1.1431301481007838, -0.46775518990854614, 0.0209905676248763, 0.3294878291805307, 0.47214722497429074, 0.4705327711189995, 0.3522433291784853, 0.14960084552741346, -0.10180614301842447, -0.3646684653537044, -0.6015367586983407, -0.7763824274125942, -0.8560625730923614, -0.8116499951478763, -0.6195867325106195, -0.262627667355473, 0.2694738685985512, 0.9795662951592781, 1.8630234211916359, 2.9078792447497532, 4.095251008119628, 5.400007258909041, 6.791685911972726, 8.235751068919107, 9.694737267480768, 11.129553808294794, 12.500791646708944, 13.770154023373081, 14.902070286226826, 15.864693231204338, 16.630834102917305, 17.178790538404435, 17.493150535009, 17.565595375952704, 17.394695506145297, 16.985716609093107, 16.35038277979923, 15.50654495318286, 14.477717446558392, 13.291711678420691, 11.979674259334711, 10.575108413776077, 9.112875414678317, 7.6279785977423975, 6.154224154200379, 4.723378457418359, 3.3643508971118097, 2.102405604132759, 0.9582746336725636, -0.052080837826412915, -0.9175723912989702, -1.6319983168599246, -2.1941305420115236, -2.6075325961510987, -2.8797992381538307, -3.021947019273281, -3.0477981389177877, -2.9735023606285433, -2.816672930136639, -2.595462121274472, -2.32785468957857, -2.031104424234649, -1.7212475448248348, -1.412515465812416, -1.1169359925494433, -0.8441246304845774, -0.6012366305802436, -0.3929568451101723, -0.22159033209653953, -0.08727910122338164, 0.011687310748196216, 0.07850958152548144, 0.11750322806658646, 0.13369679116577954, 0.13243257878274345, 0.1189985973248791, 0.0983099213247684, 0.0746470014537507, 0.051465318729924686, 0.03127805463827371, 0.015617428231441934, 0.005068553279614992, -0.000629939829936136, -0.002429230017251944, -0.0017717274857452525, -0.00036572423141660734, 5.024521696675818e-05, -0.0020632054410453815, -0.007839141978434192, -0.017833949781108447, -0.03190537565562468, -0.04914609099834298, -0.06787902538965906, -0.08571728644452381, -0.09968600668218651, -0.10639312045679729, -0.10224499381464279, -0.083697153687689, -0.047520958751010575, 0.008931834993763888, 0.08748173904816733, 0.1888948850653774, 0.31270272936060645, 0.45711752430112956, 0.6189878817445909, 0.7938041845794338, 0.9757800517664529, 1.158037807883021, 1.3329625732800008, 1.49244011394534, 1.6281521532038625, 1.7319290300834704, 1.7962235630049457, 1.8146101081572759, 1.7819725811906035, 1.6947590434666813, 1.5512364827670664, 1.351837776437288, 1.0992115408463383, 0.7980461755794944, 0.45494408780648793, 0.07831487349731178, -0.32177574055361396, -0.7341516972922705, -1.1470024164370298, -1.5483069213431948, -1.9261639729286677, -2.2692997600867404, -2.567712987642749, -2.8130259721422837, -2.9987453120990537, -3.120427277282305, -3.1759546539410324, -3.1657311825030354, -3.0925241527017753, -2.961239474762398, -2.778673695381294, -2.553256605700399, -2.2947334008644757, -2.0136077645715025, -1.7206298174717247, -1.426334679375814, -1.1406096078180987, -0.8723120604011562, -0.6288527744650124, -0.4159135355893396, -0.23727611492379938, -0.09475542990958707, 0.011764013454234739, 0.08421131116401763, 0.12609660611364595, 0.14218969744895435, 0.13813268664296058, 0.12000845535638639, 0.0938849391447054, 0.06535885140829464, 0.03912643634584991, 0.018605300522659667, 0.005628934203771637, 0.00023301945186512735, 0.0005462348061909997, 0.0027944438049529777, 0.0014225104902921822, -0.010670728206480294, -0.04179599671228443, -0.10104623643482281, -0.1977941932471282, -0.3411446741472019, -0.5394015683318508, -0.7995172877442892, -1.1265634927630763, -1.523258235222543, -1.989625066413557, -2.522880162433565, -3.117250390029132, -3.763928681433043, -4.451190712776604, -5.164797703213557, -5.88867843356907, -6.6052479461825335, -7.295899378275612, -7.941682428526911, -8.524214249053074, -9.026725721204851, -9.434349495877493, -9.73455856195287, -9.917783150645086, -9.977959455098954, -9.91317636476399, -9.725272528413347, -9.419642530111284, -9.005177460663468, -8.493956561479942, -7.9011574541693, -7.243957189962511, -6.540800476750843, -5.810744609917208, -5.072761470051005, -4.345307757591556, -3.6452865730387516, -2.987451942181415, -2.3839402374664878, -1.8439946587335514, -1.373897513056584, -0.9767277649403958, -0.6524548830830185, -0.39819657425764865, -0.2086295900120838, -0.07648398358007878, 0.006976607387057226, 0.05136261109527885, 0.06654305276611444, 0.06206234473551553, 0.04662584443401997, 0.027668696173401855, 0.011021235545033762, 0.0007043690228103032, -0.00113577622498039, 0.005842870443802543, 0.020379488455390962, 0.03993392426478209, 0.06110907604188065, 0.08014374261637458, 0.0934447704392004, 0.09812754181958068, 0.09252601578392466, 0.0766382301628257, 0.05247553566497727, 0.02428760578374536, -0.0013552593266187728, -0.015636108561605508, -0.007728535491472876, 0.03480819598413585, 0.1254983176819416, 0.2782974887651611, 0.5068412256240022, 0.8236325260003922, 1.2392579631464056, 1.7616400831703722, 2.395306374549863, 3.1407588309406713, 3.9940416998495856, 4.946609439983444, 5.985319204267135, 7.092488468839658, 8.246191082183913, 9.421025449762595, 10.588989489383598, 11.720521892042122, 12.78531249115233, 13.753375558360586, 14.59658119047252, 15.289591934086554, 15.811199869549275, 16.14481435006805, 16.27931783697855, 16.20976187558147, 15.937308291651078, 15.46970400482676, 14.820546930832876, 14.009036093317622, 13.05898302350081, 11.99775991179405, 10.855654278528311, 9.664319558670181, 8.455627948978801, 7.260117229848059, 6.1059512479894105, 5.018188292844154, 4.017741633001772, 3.1206501653765173, 2.337619659314092, 1.6740345162257158, 1.1302286902861858, 0.7017700479115119, 0.3800237677915891, 0.15300305380282758, 0.006363633281888527, -0.07556141125167384, -0.10876627208203346, -0.108571679587837, -0.08872893121389355, -0.06070501574325303, -0.0331898471618315, -0.011837964218607938, 0.000724205255850768, 0.004613573574769806, 0.002148181064736952, -0.0029211610577156957, -0.006365183213865323, -0.004558923216907369, 0.004377566875723522, 0.019454246820826755, 0.035778840575180805, 0.04369587989334359, 0.02816740651357713, -0.031543078835882324, -0.16183693414543818, -0.3943734964734541, -0.7652683275755884, -1.3138995345127176, -2.0813613623973017, -3.108659557018933, -4.434723409081599, -6.094179213794605, -8.115051354412012, -10.516661690188055, -13.307753472713092, -16.485039046855505, -20.031683667910833, -23.9163597129421, -28.093373136173565, -32.50289927402085, -37.0725467467658, -41.7182310586069, -46.34644740280043, -50.8573453377637, -55.14722352462284, -59.11312142301802, -62.65513663332137, -65.68082447752387, -68.10800480382254, -69.86740670468707, -70.90717162312257, -71.19385482983775, -70.71481625049081, -69.47718699536536, -67.50808799872344, -64.85579432310979, -61.587645486720334, -57.787213757186244, -53.549913813833534, -48.98030344583635, -44.19009279995694, -39.293835048820355, -34.40332054221806, -29.623398197131568, -25.049125527759966, -20.763984761593786, -16.836641347887156, -13.318127897681448, -10.241121832669853, -7.620200055706546, -5.453004020760763, -3.7209524670108287, -2.3911567401095137, -1.4193032374695236, -0.7529027746176183, -0.3346808187977223, -0.10585377256584651, -0.009552770954060581, 0.006028300528452928, -0.015031007252059653, -0.03844683933051851, -0.04113534045379397, -0.011839162544519529, 0.04906755705210543, 0.1305736530809813, 0.212777669374932, 0.26932142074212967, 0.2703658520660215, 0.18594725755975583, -0.010462818067309271, -0.3383825856436437, -0.8069466126464642, -1.411929473211397, -2.1333582308498924, -2.933884035823979, -3.7580413992367614, -4.532415935721488, -5.166850713595214, -5.556730919327374, -5.586181697550457, -5.13204974717676, -4.068579373932689, -2.2727725382640673, 0.3699142188139247, 3.959938933827192, 8.578761981509086, 14.28359071763806, 21.102799733267084, 29.032194305520324, 38.032599310390765, 48.03045693703498, 58.91689313651309, 70.5489107609893, 82.75113234185795, 95.32007431102805, 108.03305285733153, 120.65239645469129, 132.9310422850874, 144.61793751258938, 155.46654352765998, 165.24834933326485, 173.7572206760569, 180.81223952026312, 186.26169612870265, 189.98947496524818, 191.92650065437473, 192.04782855917216, 190.36815250506567, 186.94050332268293, 181.8565353950322, 175.2515346798488, 167.29245175329433, 158.16862691446096, 148.08609538725403, 137.263786540225, 125.93270495463916, 114.32195869848279, 102.65074300294854, 91.12329238092384, 79.92616085887828, 69.22632638744246, 59.16364527086691, 49.84836592931568, 41.36083547210486, 33.75280390987264, 27.048830473718198, 21.24666027163171, 16.32001225047169, 12.22235399271392, 8.89100205764098, 6.251137993866797, 4.219579130680268, 2.7088430610734764, 1.6309981647498497, 0.9010239758940791, 0.43963561964108666, 0.17550666969102924, 0.04690325193961449, 0.0026782096545870525, 0.0026421949678613233, 0.017362415470158134, 0.027461277781607615, 0.02250771225145204, -0.0003971159084343051, -0.038235546793583056, -0.0837841489922271, -0.12730231009631673, -0.1581155095038521, -0.1660183908098143, -0.14243677504593752, -0.08129079651860216, 0.02045560615182687, 0.16253669195477513, 0.3414099707600823, 0.5505545582624338, 0.7810558628630991, 1.0222508336641685, 1.2624587141298564, 1.4897665956937944, 1.69284977559292, 1.861826582837782, 1.98871896257649, 2.0678395835115886, 2.09607555242955, 2.073051037002487, 2.001155928279496, 1.8850867027943363, 1.731480615489917, 1.5484776392719883, 1.3452325922841564, 1.1313108629653679, 0.9160156505020319, 0.7079483093857689, 0.5146079108428334, 0.34204519707174713, 0.1945376549202712, 0.07456419263631171, -0.017123579884683823, -0.0813619254264245, -0.1204216145174166, -0.13773049403179527, -0.13743145817874589, -0.12401827966508945, -0.10200374378269321, -0.07565465415813953, -0.048684243297476955, -0.024028411184173537, -0.003743451915630026, 0.011008321823112814, 0.01990782869798032, 0.0233872535446295, 0.02245648756363578, 0.018490716891218915, 0.01300581013764613, 0.007445193014459399, 0.002988651811464036, 0.0003977040860448237, -8.167153541352325e-05, 0.0012474128605704845, 0.0035640436938897545, 0.005622792100253566, 0.005901778812379522, 0.0027921175963749266, -0.005188105461128299, -0.019174321419403745, -0.03975132389539124, -0.0667822441994635, -0.09928740690236762, -0.1353869586312642, -0.17231955797080373, -0.20654552813133498, -0.23391241128543616, -0.24988186551654212, -0.2498184893024746, -0.229323217986652, -0.18458732674663536, -0.11268952261317844, -0.011869086099315238, 0.11820998993344072, 0.2762746079850083, 0.45938316643364197, 0.6630461064802254, 0.8813168714815699, 1.1069569486946274, 1.3317349991906169, 1.546952680283099, 1.7439629096313598, 1.9144587017482486, 2.0508736178478633, 2.14683201316154, 2.1978161964961376, 2.2013117168707153, 2.156782041765209, 2.065718591353491, 1.931691862120037, 1.7604516142394382, 1.5593113746811942, 1.3366766456735446, 1.101627646752136, 0.863585648475857, 0.6318471047467589, 0.4148683291944253, 0.21984244974786105, 0.05240017526588897, -0.08355677466963327, -0.18608398007726304, -0.2552465123426621, -0.2929679484380146, -0.3027648185366523, -0.28941519148119776, -0.2585960028600861, -0.21639669668366635, -0.16882840596767879, -0.12136844788133834, -0.07856626574222805, -0.043724856429845055, -0.01867037415405099, -0.003659366999506537, 0.002579057862562258, 0.002672669257213921, 0.00031569670838297134, -0.0001238291209100321, 0.005927984803640004, 0.022742877465950957, 0.05377971231835213, 0.101209796384979, 0.16551692283477992, 0.24520776338990452, 0.33665861820321946, 0.4341185932818254, 0.5298793807701954, 0.6146067782794673, 0.6778333978694722, 0.7085660298355552, 0.6959903650525568, 0.6301996219291447, 0.5029582875522713, 0.30841997185461456, 0.04374941034859901, -0.29040817536005115, -0.6897784611082796, -1.1463350499718685, -1.6483882382787187, -2.1808885733975347, -2.7260475577420578, -3.2645023218768214, -3.7760654111636285, -4.24052532891029, -4.63861545242432, -4.953180416569447, -5.170806594202979, -5.282119679460446, -5.282057891933494, -5.170199128349575, -4.951105950265729, -4.634821464285286, -4.235615453267265, -3.7710245548013486, -3.260975251828892, -2.726981037296149, -2.191296067258645, -1.6750731706214488, -1.1971429006081564, -0.7731069247461082, -0.41467974235146193, -0.12919723395597968, 0.08090932498795808, 0.21802868736826064, 0.2889209832110698, 0.30401127523771193, 0.2764421436009484, 0.22098539356310784, 0.15277286838622084, 0.08601946299524156, 0.03281656182328356, 0.0020976469972772203, -0.0011439843936254478, 0.023699345825858715, 0.07279034856454293, 0.13821008605330665, 0.20874165596356184, 0.2710587004296293, 0.3112588158022857, 0.3166617312890825, 0.2777605516458048, 0.19019997695565607, 0.0566503884824728, -0.11156376125363106, -0.29322970870912696, -0.4565270274196128, -0.5589194794797407, -0.5477359951217119, -0.3614807054086326, 0.0681378386937114, 0.8134965634439516, 1.9478248193938732, 3.5414693874331724, 5.6578671487579495, 8.349320723636193, 11.652943268576166, 15.587437235166044, 20.15007794332422, 25.314071003299706, 31.026699064557878, 37.20896938386783, 43.75823395254704, 50.54997309595423, 57.43954193550808, 64.26569302087084, 70.85616715306388, 77.03798952171478, 82.64149551435825, 87.50442229314453, 91.47780734231324, 94.43375313861368, 96.27706194428347, 96.94395770272403, 96.40300318767189, 94.65691094064799, 91.74630306810262, 87.75307247396462, 82.79095131352358, 77.00004738171104, 70.54230873623281, 63.598760877355105, 56.36360002507367, 49.03200056978349, 41.792164984288526, 34.81947885480226, 28.271590508854448, 22.282431012418826, 16.955674679002254, 12.3618610088559, 8.537888821974777, 5.487177908275418, 3.1811196658700873, 1.561696756845823, 0.5461431201271725, 0.032630164835339225, -0.09365665866684804, 0.04605489634335574, 0.3308533620486079, 0.6466192750182946, 0.8918111485794012, 0.9823588304335686, 0.8554769602542047, 0.47214984694800494, -0.18185688682815807, -1.0964266354917118, -2.2388896089934596, -3.5570125196030773, -4.983144119181387, -6.439175081849658, -7.841979172990109, -9.1090602947526, -10.164100696326978, -10.941981896384027, -11.393100384760166, -11.486733739010626, -11.21330874147935, -10.585376674799372, -9.637034224033847, -8.422285884399624, -7.0122943085201195, -5.491550442979512, -3.9530353973038697, -2.492956338957532, -1.2056240497211648, -0.1781747749603226, 0.5144793080461703, 0.814055253807846, 0.6819688461900657, 0.10154551501293312, -0.9206220089769773, -2.3546889286777812, -4.149845852867872, -6.236713670409785, -8.530343686515515, -10.934078735406324, -13.344943358347827, -15.660783683830143, -17.78380367407827, -19.6244905689203, -21.10568598671756, -22.167577884207947, -22.772014822704044, -22.901507164338046, -22.55875931240436, -21.766350784218442, -20.56628786910005, -19.01826865100559, -17.19396758036801, -15.172581105271734, -13.037270364248412, -10.871249646027616, -8.754309404926765, -6.757658734880624, -4.94074788081754, -3.3493349520123803, -2.014135516320433, -0.95065786055489, -0.1589761314236558, 0.37499663839166625, 0.6774091094244933, 0.7837646623501653, 0.7358736327376791, 0.5787668650128932, 0.3574501392872883, 0.11384265038949332, -0.11586227479678532, -0.3032635720737597, -0.42924835306183184, -0.48484490506459, -0.4712291112731403, -0.3989426261078848], 'positive_zeros': ['0.42439600878059316446815568226263', '0.60523250832563126221853186895497', '0.947662512915993581495484390034124', '0.973076977190740593462311448105245', '1.03559393555351406408400121007765', '1.70789573585979855324745199154333', '1.71479057497070911595844381146276', '1.81165033501310444938528462249996', '2.06116010626006796329874322884202', '2.20414976932895680863978180055435', '2.42492235863041341943804309630953', '2.58105470431620863279746074866366', '2.71028360404887738067007013675150', '2.79497242727545626472397138539996', '3.09376458736996657602643132727665', '3.42126363551032204969124764995619', '3.49050390440047606152257497225868', '3.62510106029962839840631464629321', '3.63942655137263077135661495445969', '3.80654779492185920198237424851579', '4.18560860694675874696339415684117', '4.42759416258627250006456211626833', '4.48508890222424990811994495222056', '4.56559163654757471439683260913727', '4.90490666378709603930894278169781', '5.11734530071596428677925369015133', '5.23897108277763268173849182608676', '5.27496677003415711122665753874135', '5.28196737942227455087274558946310', '5.41190140437642900494559634027041', '5.63874689075100056905657896878492', '5.90962816279714972419134685940579', '6.02407451502591836181516925387230', '6.02940751747733801513910619523955', '6.05530212730551832260493574549690', '6.52937010637141820560678951808168', '6.60280662825159296719099004993704', '6.61464871371783242190414027291160', '6.73296641852211256184920743627832', '6.75671173174790749250653123078947', '7.22168300170012175152965035631387', '7.30146685908226046610378113752667', '7.32710114399640974803504918690783', '7.35928790568972555964528322418169', '7.40987447461993647015141522916469', '7.965026030272994598981312998933923', '7.976641428206304868998559703545290', '8.015691554841912529144819243680058', '8.083961385446700354558051812896663', '8.225328134038056356137077093268048'], 'prelabel': '10-6012e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.92864068163401, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e5-0', 'trace_hash': 592084606843794560, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.42439600878059316446815568226', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.60523250832563126221853186895', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.947662512915993581495484390034', 'prec': 107}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 254964898.63999012, 'bad_primes': [2, 3, 167], 'central_character': '1.1', 'conductor': 7854071662702328832, 'conductor_radical': 1002, 'degree': 10, 'dirichlet_coefficients': [1, 0, 0, 0, 7, 0, -2, 0, 0, 0, 5, 0, -8, 0, 0, 0, 7, 0, 2, 0, 0, 0, 13, 0, 13, 0, 0, 0, 11, 0, -12, 0, 0, 0, -14, 0, -7, 0, 0, 0, 12, 0, 0, 0, 0, 0, 19, 0, -20, 0, 0, 0, 21, 0, 35, 0, 0, 0, 7, 0, -6, 0, 0, 0, -56, 0, 10, 0, 0, 0, 35, 0, -8, 0, 0, 0, -10, 0, 0, 0, 0, 0, 11, 0, 49, 0, 0, 0, 32, 0, 16, 0, 0, 0, 14, 0, 11, 0, 0, 0], 'euler11': [1, -5, 36, -136, 628, -2025, 6908, -16456, 47916, -73205, 161051], 'euler13': [1, 8, 64, 292, 1433, 4915, 18629, 49348, 140608, 228488, 371293], 'euler17': [1, -7, 79, -402, 2557, -9625, 43469, -116178, 388127, -584647, 1419857], 'euler19': [1, -2, 50, -86, 1389, -2425, 26391, -31046, 342950, -260642, 2476099], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -13, 144, -1052, 6778, -34395, 155894, -556508, 1752048, -3637933, 6436343], 'euler29': [1, -11, 166, -1174, 9958, -49617, 288782, -987334, 4048574, -7780091, 20511149], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 12, 153, 1291, 9382, 57399, 290842, 1240651, 4558023, 11082252, 28629151], 'euler37': [1, 7, 178, 920, 12752, 48883, 471824, 1259480, 9016234, 13119127, 69343957], 'euler41': [1, -12, 193, -1363, 13060, -69271, 535460, -2291203, 13301753, -33909132, 115856201], 'euler43': [1, 0, 107, -197, 6754, -10885, 290422, -364253, 8507249, 0, 147008443], 'euler47': [1, -19, 168, -1313, 12955, -108573, 608885, -2900417, 17442264, -92713939, 229345007], 'euler5': [1, -7, 36, -134, 394, -981, 1970, -3350, 4500, -4375, 3125], 'euler53': [1, -21, 350, -4071, 40465, -314151, 2144645, -11435439, 52106950, -165700101, 418195493], 'euler59': [1, -7, 196, -789, 15775, -43795, 930725, -2746509, 40254284, -84821527, 714924299], 'euler61': [1, 6, 158, 1262, 14037, 105179, 856257, 4695902, 35862998, 83075046, 844596301], 'euler67': [1, -10, 142, -236, -205, 59767, -13735, -1059404, 42708346, -201511210, 1350125107], 'euler7': [1, 2, 24, 41, 286, 405, 2002, 2009, 8232, 4802, 16807], 'euler71': [1, -35, 763, -11235, 130765, -1205501, 9284315, -56635635, 273086093, -889408835, 1804229351], 'euler73': [1, 8, 312, 2092, 42635, 220341, 3112355, 11148268, 121373304, 227185928, 2073071593], 'euler79': [1, 0, 197, 805, 17746, 119621, 1401934, 5024005, 97128683, 0, 3077056399], 'euler83': [1, -11, 326, -2557, 45301, -272481, 3759983, -17615173, 186402562, -522041531, 3939040643], 'euler89': [1, -32, 606, -7762, 78409, -741105, 6978401, -61482802, 427211214, -2007751712, 5584059449], 'euler97': [1, -11, 505, -4153, 99605, -598793, 9661685, -39075577, 460899865, -973822091, 8587340257], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -7, 36, -134, 394, -981, 1970, -3350, 4500, -4375, 3125], [1, 2, 24, 41, 286, 405, 2002, 2009, 8232, 4802, 16807], [1, -5, 36, -136, 628, -2025, 6908, -16456, 47916, -73205, 161051], [1, 8, 64, 292, 1433, 4915, 18629, 49348, 140608, 228488, 371293], [1, -7, 79, -402, 2557, -9625, 43469, -116178, 388127, -584647, 1419857], [1, -2, 50, -86, 1389, -2425, 26391, -31046, 342950, -260642, 2476099], [1, -13, 144, -1052, 6778, -34395, 155894, -556508, 1752048, -3637933, 6436343], [1, -11, 166, -1174, 9958, -49617, 288782, -987334, 4048574, -7780091, 20511149], [1, 12, 153, 1291, 9382, 57399, 290842, 1240651, 4558023, 11082252, 28629151], [1, 7, 178, 920, 12752, 48883, 471824, 1259480, 9016234, 13119127, 69343957], [1, -12, 193, -1363, 13060, -69271, 535460, -2291203, 13301753, -33909132, 115856201], [1, 0, 107, -197, 6754, -10885, 290422, -364253, 8507249, 0, 147008443], [1, -19, 168, -1313, 12955, -108573, 608885, -2900417, 17442264, -92713939, 229345007], [1, -21, 350, -4071, 40465, -314151, 2144645, -11435439, 52106950, -165700101, 418195493], [1, -7, 196, -789, 15775, -43795, 930725, -2746509, 40254284, -84821527, 714924299], [1, 6, 158, 1262, 14037, 105179, 856257, 4695902, 35862998, 83075046, 844596301], [1, -10, 142, -236, -205, 59767, -13735, -1059404, 42708346, -201511210, 1350125107], [1, -35, 763, -11235, 130765, -1205501, 9284315, -56635635, 273086093, -889408835, 1804229351], [1, 8, 312, 2092, 42635, 220341, 3112355, 11148268, 121373304, 227185928, 2073071593], [1, 0, 197, 805, 17746, 119621, 1401934, 5024005, 97128683, 0, 3077056399], [1, -11, 326, -2557, 45301, -272481, 3759983, -17615173, 186402562, -522041531, 3939040643], [1, -32, 606, -7762, 78409, -741105, 6978401, -61482802, 427211214, -2007751712, 5584059449], [1, -11, 505, -4153, 99605, -598793, 9661685, -39075577, 460899865, -973822091, 8587340257]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6012/2/a/f'], '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': '10-6012e5-1.1-c1e5-0-1', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '10-6012e5-1.1-c1e5-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.92864068163401, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e5-0', 'trace_hash': 592084606843794560, 'z1': {'__RealLiteral__': 0, 'data': '0.42439600878059316446815568226', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '537985855265183840375540607775,767223352456623318071586517606,1201304953311751461322578670522,1233521614204113403861319026618,1312771273997126419549516529904', 'Lhash_array': ['537985855265183840375540607775', '767223352456623318071586517606', '1201304953311751461322578670522', '1233521614204113403861319026618', '1312771273997126419549516529904'], 'label': '10-6012e5-1.1-c1e5-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6012/2/a/f'}