Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [41,4,Mod(4,41)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(41, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("41.4");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 41 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 41.f (of order \(10\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.41907831024\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 23.6 | ||
Character | \(\chi\) | \(=\) | 41.23 |
Dual form | 41.4.f.a.25.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/41\mathbb{Z}\right)^\times\).
\(n\) | \(6\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.239215 | + | 0.736229i | 0.0845754 | + | 0.260296i | 0.984397 | − | 0.175962i | \(-0.0563035\pi\) |
−0.899822 | + | 0.436258i | \(0.856303\pi\) | |||||||
\(3\) | 6.90238i | 1.32836i | 0.747571 | + | 0.664182i | \(0.231220\pi\) | ||||
−0.747571 | + | 0.664182i | \(0.768780\pi\) | |||||||
\(4\) | 5.98733 | − | 4.35005i | 0.748416 | − | 0.543756i | ||||
\(5\) | −13.1428 | + | 9.54883i | −1.17553 | + | 0.854074i | −0.991661 | − | 0.128877i | \(-0.958863\pi\) |
−0.183871 | + | 0.982950i | \(0.558863\pi\) | |||||||
\(6\) | −5.08173 | + | 1.65116i | −0.345768 | + | 0.112347i | ||||
\(7\) | 5.83421 | + | 1.89565i | 0.315018 | + | 0.102356i | 0.462259 | − | 0.886745i | \(-0.347039\pi\) |
−0.147241 | + | 0.989101i | \(0.547039\pi\) | |||||||
\(8\) | 9.64508 | + | 7.00756i | 0.426256 | + | 0.309693i | ||||
\(9\) | −20.6429 | −0.764551 | ||||||||
\(10\) | −10.1741 | − | 7.39191i | −0.321733 | − | 0.233753i | ||||
\(11\) | −14.9430 | + | 20.5673i | −0.409591 | + | 0.563753i | −0.963119 | − | 0.269077i | \(-0.913281\pi\) |
0.553528 | + | 0.832831i | \(0.313281\pi\) | |||||||
\(12\) | 30.0257 | + | 41.3268i | 0.722306 | + | 0.994169i | ||||
\(13\) | 73.9579 | − | 24.0304i | 1.57786 | − | 0.512679i | 0.616359 | − | 0.787465i | \(-0.288607\pi\) |
0.961505 | + | 0.274786i | \(0.0886069\pi\) | |||||||
\(14\) | 4.74879i | 0.0906548i | ||||||||
\(15\) | −65.9097 | − | 90.7169i | −1.13452 | − | 1.56153i | ||||
\(16\) | 15.4437 | − | 47.5309i | 0.241308 | − | 0.742670i | ||||
\(17\) | 44.9458 | − | 61.8625i | 0.641232 | − | 0.882581i | −0.357448 | − | 0.933933i | \(-0.616353\pi\) |
0.998681 | + | 0.0513523i | \(0.0163531\pi\) | |||||||
\(18\) | −4.93809 | − | 15.1979i | −0.0646622 | − | 0.199010i | ||||
\(19\) | −29.5808 | − | 9.61137i | −0.357173 | − | 0.116053i | 0.124933 | − | 0.992165i | \(-0.460128\pi\) |
−0.482107 | + | 0.876112i | \(0.660128\pi\) | |||||||
\(20\) | −37.1526 | + | 114.344i | −0.415379 | + | 1.27840i | ||||
\(21\) | −13.0845 | + | 40.2700i | −0.135965 | + | 0.418459i | ||||
\(22\) | −18.7169 | − | 6.08148i | −0.181384 | − | 0.0589353i | ||||
\(23\) | −34.1778 | − | 105.189i | −0.309851 | − | 0.953623i | −0.977822 | − | 0.209436i | \(-0.932837\pi\) |
0.667971 | − | 0.744187i | \(-0.267163\pi\) | |||||||
\(24\) | −48.3689 | + | 66.5740i | −0.411386 | + | 0.566224i | ||||
\(25\) | 42.9269 | − | 132.115i | 0.343415 | − | 1.05692i | ||||
\(26\) | 35.3837 | + | 48.7016i | 0.266897 | + | 0.367352i | ||||
\(27\) | 43.8793i | 0.312762i | ||||||||
\(28\) | 43.1775 | − | 14.0292i | 0.291421 | − | 0.0946884i | ||||
\(29\) | 47.0508 | + | 64.7599i | 0.301280 | + | 0.414676i | 0.932637 | − | 0.360816i | \(-0.117502\pi\) |
−0.631357 | + | 0.775492i | \(0.717502\pi\) | |||||||
\(30\) | 51.0218 | − | 70.2255i | 0.310509 | − | 0.427379i | ||||
\(31\) | 147.970 | + | 107.506i | 0.857295 | + | 0.622861i | 0.927148 | − | 0.374696i | \(-0.122253\pi\) |
−0.0698526 | + | 0.997557i | \(0.522253\pi\) | |||||||
\(32\) | 134.064 | 0.740605 | ||||||||
\(33\) | −141.964 | − | 103.143i | −0.748870 | − | 0.544086i | ||||
\(34\) | 56.2967 | + | 18.2919i | 0.283965 | + | 0.0922658i | ||||
\(35\) | −94.7794 | + | 30.7957i | −0.457733 | + | 0.148726i | ||||
\(36\) | −123.596 | + | 89.7975i | −0.572202 | + | 0.415729i | ||||
\(37\) | −356.892 | + | 259.297i | −1.58575 | + | 1.15211i | −0.676040 | + | 0.736865i | \(0.736305\pi\) |
−0.909708 | + | 0.415249i | \(0.863695\pi\) | |||||||
\(38\) | − | 24.0774i | − | 0.102786i | ||||||
\(39\) | 165.867 | + | 510.486i | 0.681025 | + | 2.09598i | ||||
\(40\) | −193.678 | −0.765579 | ||||||||
\(41\) | −57.2776 | − | 256.204i | −0.218177 | − | 0.975909i | ||||
\(42\) | −32.7779 | −0.120423 | ||||||||
\(43\) | −49.7936 | − | 153.249i | −0.176592 | − | 0.543494i | 0.823111 | − | 0.567881i | \(-0.192237\pi\) |
−0.999703 | + | 0.0243870i | \(0.992237\pi\) | |||||||
\(44\) | 188.146i | 0.644639i | ||||||||
\(45\) | 271.306 | − | 197.115i | 0.898753 | − | 0.652983i | ||||
\(46\) | 69.2670 | − | 50.3254i | 0.222019 | − | 0.161306i | ||||
\(47\) | −54.5050 | + | 17.7098i | −0.169157 | + | 0.0549624i | −0.392371 | − | 0.919807i | \(-0.628345\pi\) |
0.223214 | + | 0.974769i | \(0.428345\pi\) | |||||||
\(48\) | 328.076 | + | 106.598i | 0.986536 | + | 0.320545i | ||||
\(49\) | −247.048 | − | 179.491i | −0.720257 | − | 0.523298i | ||||
\(50\) | 107.536 | 0.304158 | ||||||||
\(51\) | 426.999 | + | 310.233i | 1.17239 | + | 0.851790i | ||||
\(52\) | 338.277 | − | 465.598i | 0.902127 | − | 1.24167i | ||||
\(53\) | −295.876 | − | 407.238i | −0.766824 | − | 1.05544i | −0.996616 | − | 0.0822025i | \(-0.973805\pi\) |
0.229792 | − | 0.973240i | \(-0.426195\pi\) | |||||||
\(54\) | −32.3052 | + | 10.4966i | −0.0814109 | + | 0.0264520i | ||||
\(55\) | − | 413.002i | − | 1.01253i | ||||||
\(56\) | 42.9876 | + | 59.1673i | 0.102580 | + | 0.141189i | ||||
\(57\) | 66.3414 | − | 204.178i | 0.154160 | − | 0.474456i | ||||
\(58\) | −36.4228 | + | 50.1317i | −0.0824578 | + | 0.113493i | ||||
\(59\) | 229.265 | + | 705.604i | 0.505893 | + | 1.55698i | 0.799264 | + | 0.600981i | \(0.205223\pi\) |
−0.293370 | + | 0.955999i | \(0.594777\pi\) | |||||||
\(60\) | −789.246 | − | 256.441i | −1.69819 | − | 0.551774i | ||||
\(61\) | 76.1086 | − | 234.238i | 0.159749 | − | 0.491658i | −0.838862 | − | 0.544345i | \(-0.816778\pi\) |
0.998611 | + | 0.0526866i | \(0.0167784\pi\) | |||||||
\(62\) | −43.7526 | + | 134.657i | −0.0896224 | + | 0.275830i | ||||
\(63\) | −120.435 | − | 39.1317i | −0.240847 | − | 0.0782560i | ||||
\(64\) | −91.4797 | − | 281.545i | −0.178671 | − | 0.549893i | ||||
\(65\) | −742.555 | + | 1022.04i | −1.41696 | + | 1.95028i | ||||
\(66\) | 41.9767 | − | 129.191i | 0.0782875 | − | 0.240944i | ||||
\(67\) | −296.940 | − | 408.703i | −0.541449 | − | 0.745240i | 0.447372 | − | 0.894348i | \(-0.352360\pi\) |
−0.988821 | + | 0.149108i | \(0.952360\pi\) | |||||||
\(68\) | − | 565.907i | − | 1.00921i | ||||||
\(69\) | 726.052 | − | 235.909i | 1.26676 | − | 0.411595i | ||||
\(70\) | −45.3454 | − | 62.4126i | −0.0774258 | − | 0.106568i | ||||
\(71\) | −106.041 | + | 145.953i | −0.177250 | + | 0.243964i | −0.888393 | − | 0.459083i | \(-0.848178\pi\) |
0.711143 | + | 0.703047i | \(0.248178\pi\) | |||||||
\(72\) | −199.102 | − | 144.656i | −0.325895 | − | 0.236776i | ||||
\(73\) | 1062.74 | 1.70390 | 0.851948 | − | 0.523626i | \(-0.175421\pi\) | ||||
0.851948 | + | 0.523626i | \(0.175421\pi\) | |||||||
\(74\) | −276.276 | − | 200.726i | −0.434006 | − | 0.315324i | ||||
\(75\) | 911.911 | + | 296.298i | 1.40398 | + | 0.456181i | ||||
\(76\) | −218.920 | + | 71.1313i | −0.330418 | + | 0.107359i | ||||
\(77\) | −126.169 | + | 91.6675i | −0.186732 | + | 0.135669i | ||||
\(78\) | −336.157 | + | 244.232i | −0.487978 | + | 0.354536i | ||||
\(79\) | − | 49.6847i | − | 0.0707591i | −0.999374 | − | 0.0353795i | \(-0.988736\pi\) | ||
0.999374 | − | 0.0353795i | \(-0.0112640\pi\) | |||||||
\(80\) | 250.890 | + | 772.160i | 0.350630 | + | 1.07913i | ||||
\(81\) | −860.229 | −1.18001 | ||||||||
\(82\) | 174.923 | − | 103.457i | 0.235573 | − | 0.139329i | ||||
\(83\) | 1334.93 | 1.76540 | 0.882698 | − | 0.469940i | \(-0.155725\pi\) | ||||
0.882698 | + | 0.469940i | \(0.155725\pi\) | |||||||
\(84\) | 96.8351 | + | 298.028i | 0.125781 | + | 0.387113i | ||||
\(85\) | 1242.23i | 1.58516i | ||||||||
\(86\) | 100.915 | − | 73.3190i | 0.126534 | − | 0.0919324i | ||||
\(87\) | −446.997 | + | 324.763i | −0.550841 | + | 0.400209i | ||||
\(88\) | −288.254 | + | 93.6594i | −0.349181 | + | 0.113456i | ||||
\(89\) | −392.073 | − | 127.392i | −0.466963 | − | 0.151725i | 0.0660789 | − | 0.997814i | \(-0.478951\pi\) |
−0.533042 | + | 0.846089i | \(0.678951\pi\) | |||||||
\(90\) | 210.023 | + | 152.590i | 0.245981 | + | 0.178716i | ||||
\(91\) | 477.040 | 0.549531 | ||||||||
\(92\) | −662.209 | − | 481.123i | −0.750436 | − | 0.545223i | ||||
\(93\) | −742.050 | + | 1021.34i | −0.827387 | + | 1.13880i | ||||
\(94\) | −26.0769 | − | 35.8917i | −0.0286130 | − | 0.0393825i | ||||
\(95\) | 480.553 | − | 156.141i | 0.518986 | − | 0.168629i | ||||
\(96\) | 925.360i | 0.983793i | ||||||||
\(97\) | −774.515 | − | 1066.03i | −0.810723 | − | 1.11586i | −0.991211 | − | 0.132287i | \(-0.957768\pi\) |
0.180488 | − | 0.983577i | \(-0.442232\pi\) | |||||||
\(98\) | 73.0488 | − | 224.821i | 0.0752964 | − | 0.231738i | ||||
\(99\) | 308.467 | − | 424.569i | 0.313153 | − | 0.431018i | ||||
\(100\) | −317.691 | − | 977.753i | −0.317691 | − | 0.977753i | ||||
\(101\) | −275.089 | − | 89.3819i | −0.271014 | − | 0.0880577i | 0.170357 | − | 0.985382i | \(-0.445508\pi\) |
−0.441371 | + | 0.897325i | \(0.645508\pi\) | |||||||
\(102\) | −126.258 | + | 388.581i | −0.122563 | + | 0.377209i | ||||
\(103\) | −131.977 | + | 406.184i | −0.126253 | + | 0.388568i | −0.994127 | − | 0.108217i | \(-0.965486\pi\) |
0.867874 | + | 0.496784i | \(0.165486\pi\) | |||||||
\(104\) | 881.725 | + | 286.490i | 0.831349 | + | 0.270122i | ||||
\(105\) | −212.564 | − | 654.204i | −0.197563 | − | 0.608036i | ||||
\(106\) | 229.042 | − | 315.250i | 0.209873 | − | 0.288866i | ||||
\(107\) | 180.069 | − | 554.195i | 0.162691 | − | 0.500711i | −0.836168 | − | 0.548474i | \(-0.815209\pi\) |
0.998859 | + | 0.0477626i | \(0.0152091\pi\) | |||||||
\(108\) | 190.877 | + | 262.720i | 0.170066 | + | 0.234076i | ||||
\(109\) | 601.564i | 0.528618i | 0.964438 | + | 0.264309i | \(0.0851439\pi\) | ||||
−0.964438 | + | 0.264309i | \(0.914856\pi\) | |||||||
\(110\) | 304.064 | − | 98.7964i | 0.263558 | − | 0.0856352i | ||||
\(111\) | −1789.77 | − | 2463.40i | −1.53043 | − | 2.10645i | ||||
\(112\) | 180.204 | − | 248.029i | 0.152033 | − | 0.209255i | ||||
\(113\) | 48.0074 | + | 34.8794i | 0.0399660 | + | 0.0290370i | 0.607589 | − | 0.794252i | \(-0.292137\pi\) |
−0.567623 | + | 0.823289i | \(0.692137\pi\) | |||||||
\(114\) | 166.191 | 0.136537 | ||||||||
\(115\) | 1453.62 | + | 1056.12i | 1.17870 | + | 0.856379i | ||||
\(116\) | 563.417 | + | 183.065i | 0.450965 | + | 0.146527i | ||||
\(117\) | −1526.70 | + | 496.056i | −1.20636 | + | 0.391969i | ||||
\(118\) | −464.642 | + | 337.583i | −0.362490 | + | 0.263364i | ||||
\(119\) | 379.493 | − | 275.718i | 0.292337 | − | 0.212395i | ||||
\(120\) | − | 1336.84i | − | 1.01697i | ||||||
\(121\) | 211.581 | + | 651.179i | 0.158964 | + | 0.489240i | ||||
\(122\) | 190.659 | 0.141488 | ||||||||
\(123\) | 1768.41 | − | 395.352i | 1.29636 | − | 0.289818i | ||||
\(124\) | 1353.60 | 0.980298 | ||||||||
\(125\) | 69.8521 | + | 214.983i | 0.0499821 | + | 0.153829i | ||||
\(126\) | − | 98.0286i | − | 0.0693102i | ||||||
\(127\) | −1177.58 | + | 855.562i | −0.822782 | + | 0.597786i | −0.917508 | − | 0.397717i | \(-0.869803\pi\) |
0.0947258 | + | 0.995503i | \(0.469803\pi\) | |||||||
\(128\) | 1053.08 | − | 765.106i | 0.727186 | − | 0.528332i | ||||
\(129\) | 1057.78 | − | 343.694i | 0.721958 | − | 0.234578i | ||||
\(130\) | −930.086 | − | 302.203i | −0.627492 | − | 0.203884i | ||||
\(131\) | −973.263 | − | 707.117i | −0.649118 | − | 0.471612i | 0.213853 | − | 0.976866i | \(-0.431399\pi\) |
−0.862971 | + | 0.505254i | \(0.831399\pi\) | |||||||
\(132\) | −1298.66 | −0.856316 | ||||||||
\(133\) | −154.361 | − | 112.150i | −0.100637 | − | 0.0731173i | ||||
\(134\) | 229.867 | − | 316.384i | 0.148190 | − | 0.203966i | ||||
\(135\) | −418.996 | − | 576.699i | −0.267122 | − | 0.367662i | ||||
\(136\) | 867.011 | − | 281.709i | 0.546659 | − | 0.177620i | ||||
\(137\) | − | 2083.88i | − | 1.29955i | −0.760128 | − | 0.649774i | \(-0.774864\pi\) | ||
0.760128 | − | 0.649774i | \(-0.225136\pi\) | |||||||
\(138\) | 347.365 | + | 478.108i | 0.214273 | + | 0.294922i | ||||
\(139\) | −383.139 | + | 1179.18i | −0.233794 | + | 0.719544i | 0.763485 | + | 0.645826i | \(0.223487\pi\) |
−0.997279 | + | 0.0737188i | \(0.976513\pi\) | |||||||
\(140\) | −433.513 | + | 596.679i | −0.261704 | + | 0.360204i | ||||
\(141\) | −122.240 | − | 376.215i | −0.0730101 | − | 0.224702i | ||||
\(142\) | −132.822 | − | 43.1564i | −0.0784939 | − | 0.0255042i | ||||
\(143\) | −610.916 | + | 1880.21i | −0.357254 | + | 1.09952i | ||||
\(144\) | −318.803 | + | 981.174i | −0.184492 | + | 0.567809i | ||||
\(145\) | −1236.76 | − | 401.848i | −0.708328 | − | 0.230150i | ||||
\(146\) | 254.224 | + | 782.421i | 0.144108 | + | 0.443518i | ||||
\(147\) | 1238.92 | − | 1705.22i | 0.695130 | − | 0.956764i | ||||
\(148\) | −1008.87 | + | 3104.99i | −0.560330 | + | 1.72452i | ||||
\(149\) | −418.665 | − | 576.243i | −0.230191 | − | 0.316830i | 0.678260 | − | 0.734822i | \(-0.262734\pi\) |
−0.908451 | + | 0.417992i | \(0.862734\pi\) | |||||||
\(150\) | 742.255i | 0.404032i | ||||||||
\(151\) | −1045.53 | + | 339.713i | −0.563469 | + | 0.183082i | −0.576882 | − | 0.816828i | \(-0.695731\pi\) |
0.0134123 | + | 0.999910i | \(0.495731\pi\) | |||||||
\(152\) | −217.957 | − | 299.992i | −0.116307 | − | 0.160082i | ||||
\(153\) | −927.810 | + | 1277.02i | −0.490255 | + | 0.674778i | ||||
\(154\) | −97.6699 | − | 70.9614i | −0.0511069 | − | 0.0371314i | ||||
\(155\) | −2971.30 | −1.53975 | ||||||||
\(156\) | 3213.74 | + | 2334.92i | 1.64939 | + | 1.19835i | ||||
\(157\) | 1618.87 | + | 526.004i | 0.822930 | + | 0.267386i | 0.690065 | − | 0.723748i | \(-0.257582\pi\) |
0.132866 | + | 0.991134i | \(0.457582\pi\) | |||||||
\(158\) | 36.5793 | − | 11.8853i | 0.0184183 | − | 0.00598448i | ||||
\(159\) | 2810.91 | − | 2042.25i | 1.40201 | − | 1.01862i | ||||
\(160\) | −1761.98 | + | 1280.15i | −0.870604 | + | 0.632531i | ||||
\(161\) | − | 678.482i | − | 0.332123i | ||||||
\(162\) | −205.780 | − | 633.326i | −0.0998001 | − | 0.307153i | ||||
\(163\) | 1940.23 | 0.932334 | 0.466167 | − | 0.884697i | \(-0.345635\pi\) | ||||
0.466167 | + | 0.884697i | \(0.345635\pi\) | |||||||
\(164\) | −1457.44 | − | 1284.81i | −0.693943 | − | 0.611751i | ||||
\(165\) | 2850.70 | 1.34501 | ||||||||
\(166\) | 319.336 | + | 982.816i | 0.149309 | + | 0.459526i | ||||
\(167\) | 2594.41i | 1.20216i | 0.799187 | + | 0.601082i | \(0.205263\pi\) | ||||
−0.799187 | + | 0.601082i | \(0.794737\pi\) | |||||||
\(168\) | −408.396 | + | 296.717i | −0.187550 | + | 0.136263i | ||||
\(169\) | 3114.91 | − | 2263.11i | 1.41780 | − | 1.03009i | ||||
\(170\) | −914.565 | + | 297.160i | −0.412611 | + | 0.134066i | ||||
\(171\) | 610.632 | + | 198.406i | 0.273077 | + | 0.0887281i | ||||
\(172\) | −964.770 | − | 700.947i | −0.427692 | − | 0.310737i | ||||
\(173\) | −1625.84 | −0.714509 | −0.357255 | − | 0.934007i | \(-0.616287\pi\) | ||||
−0.357255 | + | 0.934007i | \(0.616287\pi\) | |||||||
\(174\) | −346.028 | − | 251.404i | −0.150761 | − | 0.109534i | ||||
\(175\) | 500.890 | − | 689.416i | 0.216364 | − | 0.297800i | ||||
\(176\) | 746.808 | + | 1027.89i | 0.319845 | + | 0.440229i | ||||
\(177\) | −4870.35 | + | 1582.47i | −2.06824 | + | 0.672010i | ||||
\(178\) | − | 319.130i | − | 0.134381i | ||||||
\(179\) | 1144.58 | + | 1575.37i | 0.477931 | + | 0.657816i | 0.978106 | − | 0.208109i | \(-0.0667308\pi\) |
−0.500174 | + | 0.865925i | \(0.666731\pi\) | |||||||
\(180\) | 766.936 | − | 2360.39i | 0.317578 | − | 0.977405i | ||||
\(181\) | −2466.62 | + | 3395.01i | −1.01294 | + | 1.39419i | −0.0959027 | + | 0.995391i | \(0.530574\pi\) |
−0.917037 | + | 0.398802i | \(0.869426\pi\) | |||||||
\(182\) | 114.115 | + | 351.211i | 0.0464768 | + | 0.143041i | ||||
\(183\) | 1616.80 | + | 525.331i | 0.653101 | + | 0.212205i | ||||
\(184\) | 407.468 | − | 1254.06i | 0.163255 | − | 0.502447i | ||||
\(185\) | 2214.59 | − | 6815.80i | 0.880107 | − | 2.70869i | ||||
\(186\) | −929.453 | − | 301.997i | −0.366402 | − | 0.119051i | ||||
\(187\) | 600.721 | + | 1848.83i | 0.234915 | + | 0.722994i | ||||
\(188\) | −249.301 | + | 343.134i | −0.0967136 | + | 0.133115i | ||||
\(189\) | −83.1799 | + | 256.001i | −0.0320130 | + | 0.0985257i | ||||
\(190\) | 229.911 | + | 316.446i | 0.0877869 | + | 0.120828i | ||||
\(191\) | 1762.14i | 0.667561i | 0.942651 | + | 0.333781i | \(0.108324\pi\) | ||||
−0.942651 | + | 0.333781i | \(0.891676\pi\) | |||||||
\(192\) | 1943.33 | − | 631.427i | 0.730459 | − | 0.237340i | ||||
\(193\) | −1077.95 | − | 1483.68i | −0.402036 | − | 0.553355i | 0.559218 | − | 0.829021i | \(-0.311102\pi\) |
−0.961253 | + | 0.275666i | \(0.911102\pi\) | |||||||
\(194\) | 599.566 | − | 825.231i | 0.221888 | − | 0.305403i | ||||
\(195\) | −7054.51 | − | 5125.40i | −2.59069 | − | 1.88224i | ||||
\(196\) | −2259.95 | −0.823598 | ||||||||
\(197\) | −1380.89 | − | 1003.27i | −0.499412 | − | 0.362844i | 0.309380 | − | 0.950938i | \(-0.399878\pi\) |
−0.808792 | + | 0.588094i | \(0.799878\pi\) | |||||||
\(198\) | 386.370 | + | 125.539i | 0.138677 | + | 0.0450590i | ||||
\(199\) | −2004.66 | + | 651.353i | −0.714103 | + | 0.232026i | −0.643464 | − | 0.765476i | \(-0.722504\pi\) |
−0.0706382 | + | 0.997502i | \(0.522504\pi\) | |||||||
\(200\) | 1339.84 | − | 973.452i | 0.473705 | − | 0.344167i | ||||
\(201\) | 2821.03 | − | 2049.60i | 0.989950 | − | 0.719241i | ||||
\(202\) | − | 223.910i | − | 0.0779914i | ||||||
\(203\) | 151.742 | + | 467.015i | 0.0524641 | + | 0.161468i | ||||
\(204\) | 3906.11 | 1.34060 | ||||||||
\(205\) | 3199.23 | + | 2820.31i | 1.08997 | + | 0.960873i | ||||
\(206\) | −330.615 | −0.111821 | ||||||||
\(207\) | 705.529 | + | 2171.39i | 0.236897 | + | 0.729093i | ||||
\(208\) | − | 3886.41i | − | 1.29555i | ||||||
\(209\) | 639.707 | − | 464.774i | 0.211720 | − | 0.153824i | ||||
\(210\) | 430.795 | − | 312.991i | 0.141560 | − | 0.102850i | ||||
\(211\) | 995.002 | − | 323.296i | 0.324639 | − | 0.105481i | −0.142164 | − | 0.989843i | \(-0.545406\pi\) |
0.466802 | + | 0.884362i | \(0.345406\pi\) | |||||||
\(212\) | −3543.01 | − | 1151.19i | −1.14781 | − | 0.372945i | ||||
\(213\) | −1007.42 | − | 731.936i | −0.324073 | − | 0.235453i | ||||
\(214\) | 451.090 | 0.144093 | ||||||||
\(215\) | 2117.78 | + | 1538.66i | 0.671773 | + | 0.488072i | ||||
\(216\) | −307.487 | + | 423.220i | −0.0968604 | + | 0.133317i | ||||
\(217\) | 659.493 | + | 907.714i | 0.206310 | + | 0.283961i | ||||
\(218\) | −442.889 | + | 143.903i | −0.137597 | + | 0.0447081i | ||||
\(219\) | 7335.44i | 2.26339i | ||||||||
\(220\) | −1796.58 | − | 2472.78i | −0.550569 | − | 0.757794i | ||||
\(221\) | 1837.52 | − | 5655.29i | 0.559297 | − | 1.72134i | ||||
\(222\) | 1385.49 | − | 1906.96i | 0.418865 | − | 0.576518i | ||||
\(223\) | 1018.69 | + | 3135.19i | 0.305902 | + | 0.941471i | 0.979339 | + | 0.202226i | \(0.0648174\pi\) |
−0.673437 | + | 0.739245i | \(0.735183\pi\) | |||||||
\(224\) | 782.157 | + | 254.138i | 0.233304 | + | 0.0758050i | ||||
\(225\) | −886.135 | + | 2727.24i | −0.262558 | + | 0.808072i | ||||
\(226\) | −14.1951 | + | 43.6882i | −0.00417808 | + | 0.0128588i | ||||
\(227\) | −3939.96 | − | 1280.17i | −1.15200 | − | 0.374308i | −0.330105 | − | 0.943944i | \(-0.607084\pi\) |
−0.821897 | + | 0.569636i | \(0.807084\pi\) | |||||||
\(228\) | −490.975 | − | 1511.07i | −0.142612 | − | 0.438916i | ||||
\(229\) | −668.145 | + | 919.622i | −0.192805 | + | 0.265373i | −0.894464 | − | 0.447140i | \(-0.852443\pi\) |
0.701660 | + | 0.712512i | \(0.252443\pi\) | |||||||
\(230\) | −429.816 | + | 1322.84i | −0.123223 | + | 0.379241i | ||||
\(231\) | −632.724 | − | 870.870i | −0.180217 | − | 0.248048i | ||||
\(232\) | 954.326i | 0.270063i | ||||||||
\(233\) | −1040.66 | + | 338.132i | −0.292601 | + | 0.0950719i | −0.451639 | − | 0.892201i | \(-0.649161\pi\) |
0.159038 | + | 0.987272i | \(0.449161\pi\) | |||||||
\(234\) | −730.422 | − | 1005.34i | −0.204056 | − | 0.280859i | ||||
\(235\) | 547.243 | − | 753.216i | 0.151907 | − | 0.209083i | ||||
\(236\) | 4442.09 | + | 3227.37i | 1.22524 | + | 0.890186i | ||||
\(237\) | 342.943 | 0.0939938 | ||||||||
\(238\) | 293.772 | + | 213.438i | 0.0800101 | + | 0.0581308i | ||||
\(239\) | 1321.97 | + | 429.534i | 0.357787 | + | 0.116252i | 0.482394 | − | 0.875954i | \(-0.339767\pi\) |
−0.124608 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(240\) | −5329.75 | + | 1731.74i | −1.43347 | + | 0.465764i | ||||
\(241\) | −718.023 | + | 521.674i | −0.191917 | + | 0.139436i | −0.679594 | − | 0.733588i | \(-0.737844\pi\) |
0.487678 | + | 0.873024i | \(0.337844\pi\) | |||||||
\(242\) | −428.803 | + | 311.544i | −0.113903 | + | 0.0827554i | ||||
\(243\) | − | 4752.89i | − | 1.25472i | ||||||
\(244\) | −563.260 | − | 1733.54i | −0.147783 | − | 0.454829i | ||||
\(245\) | 4960.85 | 1.29362 | ||||||||
\(246\) | 714.101 | + | 1207.38i | 0.185079 | + | 0.312927i | ||||
\(247\) | −2418.70 | −0.623069 | ||||||||
\(248\) | 673.823 | + | 2073.81i | 0.172532 | + | 0.530997i | ||||
\(249\) | 9214.22i | 2.34509i | ||||||||
\(250\) | −141.567 | + | 102.854i | −0.0358139 | + | 0.0260203i | ||||
\(251\) | 1411.40 | − | 1025.44i | 0.354927 | − | 0.257870i | −0.396006 | − | 0.918248i | \(-0.629604\pi\) |
0.750933 | + | 0.660378i | \(0.229604\pi\) | |||||||
\(252\) | −891.308 | + | 289.604i | −0.222806 | + | 0.0723941i | ||||
\(253\) | 2674.17 | + | 868.891i | 0.664520 | + | 0.215916i | ||||
\(254\) | −911.585 | − | 662.305i | −0.225189 | − | 0.163609i | ||||
\(255\) | −8574.34 | −2.10567 | ||||||||
\(256\) | −1100.77 | − | 799.756i | −0.268742 | − | 0.195253i | ||||
\(257\) | −822.973 | + | 1132.73i | −0.199750 | + | 0.274932i | −0.897127 | − | 0.441772i | \(-0.854350\pi\) |
0.697378 | + | 0.716704i | \(0.254350\pi\) | |||||||
\(258\) | 506.076 | + | 696.553i | 0.122120 | + | 0.168083i | ||||
\(259\) | −2573.72 | + | 836.253i | −0.617464 | + | 0.200626i | ||||
\(260\) | 9349.43i | 2.23011i | ||||||||
\(261\) | −971.263 | − | 1336.83i | −0.230344 | − | 0.317041i | ||||
\(262\) | 287.781 | − | 885.698i | 0.0678594 | − | 0.208850i | ||||
\(263\) | 4455.45 | − | 6132.40i | 1.04462 | − | 1.43780i | 0.151237 | − | 0.988498i | \(-0.451674\pi\) |
0.893382 | − | 0.449298i | \(-0.148326\pi\) | |||||||
\(264\) | −646.473 | − | 1989.64i | −0.150711 | − | 0.463840i | ||||
\(265\) | 7777.29 | + | 2527.00i | 1.80285 | + | 0.585782i | ||||
\(266\) | 45.6424 | − | 140.473i | 0.0105207 | − | 0.0323795i | ||||
\(267\) | 879.311 | − | 2706.24i | 0.201547 | − | 0.620297i | ||||
\(268\) | −3555.76 | − | 1155.34i | −0.810457 | − | 0.263334i | ||||
\(269\) | 1264.67 | + | 3892.24i | 0.286647 | + | 0.882209i | 0.985900 | + | 0.167335i | \(0.0535161\pi\) |
−0.699253 | + | 0.714874i | \(0.746484\pi\) | |||||||
\(270\) | 324.352 | − | 446.433i | 0.0731091 | − | 0.100626i | ||||
\(271\) | −397.710 | + | 1224.03i | −0.0891483 | + | 0.274370i | −0.985685 | − | 0.168600i | \(-0.946075\pi\) |
0.896536 | + | 0.442970i | \(0.146075\pi\) | |||||||
\(272\) | −2246.25 | − | 3091.70i | −0.500732 | − | 0.689198i | ||||
\(273\) | 3292.71i | 0.729978i | ||||||||
\(274\) | 1534.21 | − | 498.496i | 0.338267 | − | 0.109910i | ||||
\(275\) | 2075.81 | + | 2857.10i | 0.455185 | + | 0.626508i | ||||
\(276\) | 3320.90 | − | 4570.82i | 0.724255 | − | 0.996852i | ||||
\(277\) | 1757.32 | + | 1276.77i | 0.381181 | + | 0.276944i | 0.761832 | − | 0.647775i | \(-0.224300\pi\) |
−0.380651 | + | 0.924719i | \(0.624300\pi\) | |||||||
\(278\) | −959.799 | −0.207068 | ||||||||
\(279\) | −3054.52 | − | 2219.24i | −0.655446 | − | 0.476209i | ||||
\(280\) | −1129.96 | − | 367.146i | −0.241171 | − | 0.0783612i | ||||
\(281\) | −1723.59 | + | 560.030i | −0.365911 | + | 0.118892i | −0.486201 | − | 0.873847i | \(-0.661618\pi\) |
0.120290 | + | 0.992739i | \(0.461618\pi\) | |||||||
\(282\) | 247.739 | − | 179.993i | 0.0523142 | − | 0.0380085i | ||||
\(283\) | 7093.11 | − | 5153.44i | 1.48990 | − | 1.08248i | 0.515704 | − | 0.856767i | \(-0.327530\pi\) |
0.974195 | − | 0.225709i | \(-0.0724697\pi\) | |||||||
\(284\) | 1335.15i | 0.278967i | ||||||||
\(285\) | 1077.74 | + | 3316.96i | 0.224000 | + | 0.689402i | ||||
\(286\) | −1530.40 | −0.316415 | ||||||||
\(287\) | 151.503 | − | 1603.33i | 0.0311601 | − | 0.329761i | ||||
\(288\) | −2767.46 | −0.566230 | ||||||||
\(289\) | −288.652 | − | 888.378i | −0.0587526 | − | 0.180822i | ||||
\(290\) | − | 1006.67i | − | 0.203840i | ||||||
\(291\) | 7358.14 | − | 5346.00i | 1.48227 | − | 1.07694i | ||||
\(292\) | 6362.98 | − | 4622.97i | 1.27522 | − | 0.926504i | ||||
\(293\) | −3925.26 | + | 1275.39i | −0.782649 | + | 0.254298i | −0.672971 | − | 0.739669i | \(-0.734982\pi\) |
−0.109678 | + | 0.993967i | \(0.534982\pi\) | |||||||
\(294\) | 1551.80 | + | 504.211i | 0.307833 | + | 0.100021i | ||||
\(295\) | −9750.88 | − | 7084.43i | −1.92447 | − | 1.39821i | ||||
\(296\) | −5259.29 | −1.03274 | ||||||||
\(297\) | −902.481 | − | 655.691i | −0.176321 | − | 0.128105i | ||||
\(298\) | 324.096 | − | 446.080i | 0.0630012 | − | 0.0867138i | ||||
\(299\) | −5055.45 | − | 6958.22i | −0.977806 | − | 1.34583i | ||||
\(300\) | 6748.82 | − | 2192.83i | 1.29881 | − | 0.422009i | ||||
\(301\) | − | 988.478i | − | 0.189285i | ||||||
\(302\) | −500.213 | − | 688.484i | −0.0953113 | − | 0.131185i | ||||
\(303\) | 616.948 | − | 1898.77i | 0.116973 | − | 0.360005i | ||||
\(304\) | −913.674 | + | 1257.56i | −0.172378 | + | 0.237257i | ||||
\(305\) | 1236.42 | + | 3805.30i | 0.232122 | + | 0.714397i | ||||
\(306\) | −1162.13 | − | 377.598i | −0.217106 | − | 0.0705419i | ||||
\(307\) | −2776.55 | + | 8545.33i | −0.516176 | + | 1.58863i | 0.264957 | + | 0.964260i | \(0.414642\pi\) |
−0.781133 | + | 0.624365i | \(0.785358\pi\) | |||||||
\(308\) | −356.660 | + | 1097.69i | −0.0659824 | + | 0.203073i | ||||
\(309\) | −2803.64 | − | 910.957i | −0.516160 | − | 0.167710i | ||||
\(310\) | −710.781 | − | 2187.56i | −0.130225 | − | 0.400790i | ||||
\(311\) | −5195.10 | + | 7150.44i | −0.947225 | + | 1.30374i | 0.00552349 | + | 0.999985i | \(0.498242\pi\) |
−0.952749 | + | 0.303759i | \(0.901758\pi\) | |||||||
\(312\) | −1977.46 | + | 6086.00i | −0.358820 | + | 1.10433i | ||||
\(313\) | −1827.17 | − | 2514.88i | −0.329960 | − | 0.454151i | 0.611515 | − | 0.791232i | \(-0.290560\pi\) |
−0.941475 | + | 0.337082i | \(0.890560\pi\) | |||||||
\(314\) | 1317.69i | 0.236820i | ||||||||
\(315\) | 1956.52 | − | 635.712i | 0.349960 | − | 0.113709i | ||||
\(316\) | −216.131 | − | 297.479i | −0.0384757 | − | 0.0529572i | ||||
\(317\) | 3244.46 | − | 4465.61i | 0.574848 | − | 0.791211i | −0.418270 | − | 0.908323i | \(-0.637364\pi\) |
0.993119 | + | 0.117112i | \(0.0373636\pi\) | |||||||
\(318\) | 2175.98 | + | 1580.94i | 0.383719 | + | 0.278788i | ||||
\(319\) | −2035.02 | −0.357176 | ||||||||
\(320\) | 3890.73 | + | 2826.78i | 0.679683 | + | 0.493819i | ||||
\(321\) | 3825.27 | + | 1242.90i | 0.665127 | + | 0.216113i | ||||
\(322\) | 499.518 | − | 162.303i | 0.0864505 | − | 0.0280895i | ||||
\(323\) | −1924.11 | + | 1397.95i | −0.331457 | + | 0.240818i | ||||
\(324\) | −5150.47 | + | 3742.04i | −0.883140 | + | 0.641639i | ||||
\(325\) | − | 10802.5i | − | 1.84374i | ||||||
\(326\) | 464.133 | + | 1428.45i | 0.0788525 | + | 0.242683i | ||||
\(327\) | −4152.23 | −0.702198 | ||||||||
\(328\) | 1242.92 | − | 2872.48i | 0.209233 | − | 0.483556i | ||||
\(329\) | −351.566 | −0.0589132 | ||||||||
\(330\) | 681.930 | + | 2098.77i | 0.113755 | + | 0.350101i | ||||
\(331\) | − | 6735.97i | − | 1.11856i | −0.828980 | − | 0.559279i | \(-0.811078\pi\) | ||
0.828980 | − | 0.559279i | \(-0.188922\pi\) | |||||||
\(332\) | 7992.68 | − | 5807.02i | 1.32125 | − | 0.959945i | ||||
\(333\) | 7367.27 | − | 5352.64i | 1.21238 | − | 0.880849i | ||||
\(334\) | −1910.08 | + | 620.622i | −0.312919 | + | 0.101673i | ||||
\(335\) | 7805.28 | + | 2536.09i | 1.27298 | + | 0.413616i | ||||
\(336\) | 1711.99 | + | 1243.84i | 0.277967 | + | 0.201955i | ||||
\(337\) | 7485.43 | 1.20996 | 0.604981 | − | 0.796240i | \(-0.293181\pi\) | ||||
0.604981 | + | 0.796240i | \(0.293181\pi\) | |||||||
\(338\) | 2411.30 | + | 1751.91i | 0.388040 | + | 0.281928i | ||||
\(339\) | −240.751 | + | 331.366i | −0.0385717 | + | 0.0530894i | ||||
\(340\) | 5403.76 | + | 7437.63i | 0.861941 | + | 1.18636i | ||||
\(341\) | −4422.24 | + | 1436.87i | −0.702280 | + | 0.228185i | ||||
\(342\) | 497.027i | 0.0785852i | ||||||||
\(343\) | −2337.85 | − | 3217.77i | −0.368023 | − | 0.506541i | ||||
\(344\) | 593.638 | − | 1827.03i | 0.0930431 | − | 0.286357i | ||||
\(345\) | −7289.73 | + | 10033.5i | −1.13758 | + | 1.56575i | ||||
\(346\) | −388.925 | − | 1196.99i | −0.0604299 | − | 0.185984i | ||||
\(347\) | 3470.33 | + | 1127.58i | 0.536879 | + | 0.174443i | 0.564892 | − | 0.825165i | \(-0.308918\pi\) |
−0.0280129 | + | 0.999608i | \(0.508918\pi\) | |||||||
\(348\) | −1263.59 | + | 3888.92i | −0.194642 | + | 0.599046i | ||||
\(349\) | −547.491 | + | 1685.00i | −0.0839728 | + | 0.258442i | −0.984223 | − | 0.176930i | \(-0.943383\pi\) |
0.900251 | + | 0.435372i | \(0.143383\pi\) | |||||||
\(350\) | 627.388 | + | 203.851i | 0.0958152 | + | 0.0311322i | ||||
\(351\) | 1054.44 | + | 3245.23i | 0.160347 | + | 0.493497i | ||||
\(352\) | −2003.32 | + | 2757.34i | −0.303345 | + | 0.417519i | ||||
\(353\) | 363.011 | − | 1117.23i | 0.0547341 | − | 0.168454i | −0.919953 | − | 0.392030i | \(-0.871773\pi\) |
0.974687 | + | 0.223576i | \(0.0717730\pi\) | |||||||
\(354\) | −2330.12 | − | 3207.14i | −0.349844 | − | 0.481518i | ||||
\(355\) | − | 2930.81i | − | 0.438172i | ||||||
\(356\) | −2901.63 | + | 942.798i | −0.431984 | + | 0.140360i | ||||
\(357\) | 1903.11 | + | 2619.41i | 0.282138 | + | 0.388330i | ||||
\(358\) | −886.036 | + | 1219.52i | −0.130806 | + | 0.180039i | ||||
\(359\) | −3786.09 | − | 2750.75i | −0.556608 | − | 0.404399i | 0.273608 | − | 0.961841i | \(-0.411783\pi\) |
−0.830216 | + | 0.557442i | \(0.811783\pi\) | |||||||
\(360\) | 3998.07 | 0.585324 | ||||||||
\(361\) | −4766.40 | − | 3463.00i | −0.694912 | − | 0.504883i | ||||
\(362\) | −3089.55 | − | 1003.86i | −0.448573 | − | 0.145750i | ||||
\(363\) | −4494.68 | + | 1460.41i | −0.649889 | + | 0.211162i | ||||
\(364\) | 2856.19 | − | 2075.15i | 0.411278 | − | 0.298811i | ||||
\(365\) | −13967.4 | + | 10147.9i | −2.00298 | + | 1.45525i | ||||
\(366\) | 1316.00i | 0.187947i | ||||||||
\(367\) | −72.1109 | − | 221.935i | −0.0102566 | − | 0.0315665i | 0.945797 | − | 0.324758i | \(-0.105283\pi\) |
−0.956054 | + | 0.293191i | \(0.905283\pi\) | |||||||
\(368\) | −5527.54 | −0.782997 | ||||||||
\(369\) | 1182.37 | + | 5288.78i | 0.166807 | + | 0.746132i | ||||
\(370\) | 5547.76 | 0.779498 | ||||||||
\(371\) | −954.221 | − | 2936.79i | −0.133533 | − | 0.410972i | ||||
\(372\) | 9343.07i | 1.30219i | ||||||||
\(373\) | −7641.63 | + | 5551.97i | −1.06077 | + | 0.770697i | −0.974231 | − | 0.225551i | \(-0.927582\pi\) |
−0.0865426 | + | 0.996248i | \(0.527582\pi\) | |||||||
\(374\) | −1217.46 | + | 884.537i | −0.168325 | + | 0.122295i | ||||
\(375\) | −1483.89 | + | 482.146i | −0.204341 | + | 0.0663944i | ||||
\(376\) | −649.808 | − | 211.135i | −0.0891258 | − | 0.0289587i | ||||
\(377\) | 5035.98 | + | 3658.86i | 0.687975 | + | 0.499843i | ||||
\(378\) | −208.374 | −0.0283534 | ||||||||
\(379\) | 6947.23 | + | 5047.46i | 0.941570 | + | 0.684091i | 0.948798 | − | 0.315883i | \(-0.102301\pi\) |
−0.00722773 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(380\) | 2198.00 | − | 3025.29i | 0.296724 | − | 0.408406i | ||||
\(381\) | −5905.42 | − | 8128.11i | −0.794078 | − | 1.09295i | ||||
\(382\) | −1297.34 | + | 421.532i | −0.173764 | + | 0.0564593i | ||||
\(383\) | 4664.68i | 0.622334i | 0.950355 | + | 0.311167i | \(0.100720\pi\) | ||||
−0.950355 | + | 0.311167i | \(0.899280\pi\) | |||||||
\(384\) | 5281.05 | + | 7268.75i | 0.701817 | + | 0.965968i | ||||
\(385\) | 782.908 | − | 2409.54i | 0.103638 | − | 0.318965i | ||||
\(386\) | 834.463 | − | 1148.54i | 0.110034 | − | 0.151449i | ||||
\(387\) | 1027.88 | + | 3163.50i | 0.135013 | + | 0.415529i | ||||
\(388\) | −9274.55 | − | 3013.49i | −1.21352 | − | 0.394295i | ||||
\(389\) | 3169.49 | − | 9754.70i | 0.413110 | − | 1.27142i | −0.500821 | − | 0.865551i | \(-0.666968\pi\) |
0.913931 | − | 0.405871i | \(-0.133032\pi\) | |||||||
\(390\) | 2085.92 | − | 6419.81i | 0.270833 | − | 0.833537i | ||||
\(391\) | −8043.38 | − | 2613.45i | −1.04034 | − | 0.338026i | ||||
\(392\) | −1125.01 | − | 3462.41i | −0.144953 | − | 0.446118i | ||||
\(393\) | 4880.79 | − | 6717.84i | 0.626472 | − | 0.862265i | ||||
\(394\) | 408.310 | − | 1256.65i | 0.0522090 | − | 0.160683i | ||||
\(395\) | 474.431 | + | 652.998i | 0.0604334 | + | 0.0831795i | ||||
\(396\) | − | 3883.88i | − | 0.492860i | ||||||
\(397\) | 10582.6 | − | 3438.49i | 1.33784 | − | 0.434692i | 0.449258 | − | 0.893402i | \(-0.351688\pi\) |
0.888586 | + | 0.458710i | \(0.151688\pi\) | |||||||
\(398\) | −959.090 | − | 1320.07i | −0.120791 | − | 0.166255i | ||||
\(399\) | 774.099 | − | 1065.46i | 0.0971264 | − | 0.133683i | ||||
\(400\) | −5616.61 | − | 4080.71i | −0.702077 | − | 0.510089i | ||||
\(401\) | 3371.22 | 0.419827 | 0.209914 | − | 0.977720i | \(-0.432682\pi\) | ||||
0.209914 | + | 0.977720i | \(0.432682\pi\) | |||||||
\(402\) | 2183.81 | + | 1586.63i | 0.270941 | + | 0.196850i | ||||
\(403\) | 13527.0 | + | 4395.17i | 1.67202 | + | 0.543274i | ||||
\(404\) | −2035.86 | + | 661.492i | −0.250713 | + | 0.0814616i | ||||
\(405\) | 11305.9 | − | 8214.19i | 1.38714 | − | 1.00782i | ||||
\(406\) | −307.531 | + | 223.434i | −0.0375924 | + | 0.0273124i | ||||
\(407\) | − | 11215.0i | − | 1.36587i | ||||||
\(408\) | 1944.46 | + | 5984.44i | 0.235944 | + | 0.726162i | ||||
\(409\) | 6796.37 | 0.821659 | 0.410830 | − | 0.911712i | \(-0.365239\pi\) | ||||
0.410830 | + | 0.911712i | \(0.365239\pi\) | |||||||
\(410\) | −1311.09 | + | 3030.03i | −0.157927 | + | 0.364982i | ||||
\(411\) | 14383.7 | 1.72627 | ||||||||
\(412\) | 976.729 | + | 3006.06i | 0.116796 | + | 0.359461i | ||||
\(413\) | 4551.25i | 0.542258i | ||||||||
\(414\) | −1429.87 | + | 1038.86i | −0.169745 | + | 0.123327i | ||||
\(415\) | −17544.8 | + | 12747.0i | −2.07528 | + | 1.50778i | ||||
\(416\) | 9915.08 | − | 3221.61i | 1.16857 | − | 0.379693i | ||||
\(417\) | −8139.15 | − | 2644.57i | −0.955817 | − | 0.310564i | ||||
\(418\) | 495.208 | + | 359.790i | 0.0579460 | + | 0.0421002i | ||||
\(419\) | −201.792 | −0.0235279 | −0.0117640 | − | 0.999931i | \(-0.503745\pi\) | ||||
−0.0117640 | + | 0.999931i | \(0.503745\pi\) | |||||||
\(420\) | −4118.50 | − | 2992.27i | −0.478482 | − | 0.347638i | ||||
\(421\) | −1921.16 | + | 2644.25i | −0.222403 | + | 0.306112i | −0.905609 | − | 0.424115i | \(-0.860585\pi\) |
0.683205 | + | 0.730226i | \(0.260585\pi\) | |||||||
\(422\) | 476.039 | + | 655.212i | 0.0549129 | + | 0.0755811i | ||||
\(423\) | 1125.14 | − | 365.580i | 0.129329 | − | 0.0420216i | ||||
\(424\) | − | 6001.21i | − | 0.687369i | ||||||
\(425\) | −6243.62 | − | 8593.60i | −0.712611 | − | 0.980825i | ||||
\(426\) | 297.882 | − | 916.785i | 0.0338789 | − | 0.104269i | ||||
\(427\) | 888.068 | − | 1222.32i | 0.100648 | − | 0.138530i | ||||
\(428\) | −1332.64 | − | 4101.46i | −0.150504 | − | 0.463204i | ||||
\(429\) | −12977.9 | − | 4216.77i | −1.46056 | − | 0.474564i | ||||
\(430\) | −626.198 | + | 1927.24i | −0.0702278 | + | 0.216139i | ||||
\(431\) | −4692.47 | + | 14442.0i | −0.524428 | + | 1.61402i | 0.241016 | + | 0.970521i | \(0.422520\pi\) |
−0.765444 | + | 0.643503i | \(0.777480\pi\) | |||||||
\(432\) | 2085.62 | + | 677.660i | 0.232279 | + | 0.0754721i | ||||
\(433\) | 1344.90 | + | 4139.19i | 0.149265 | + | 0.459392i | 0.997535 | − | 0.0701731i | \(-0.0223552\pi\) |
−0.848269 | + | 0.529565i | \(0.822355\pi\) | |||||||
\(434\) | −510.525 | + | 702.677i | −0.0564654 | + | 0.0777179i | ||||
\(435\) | 2773.71 | − | 8536.60i | 0.305722 | − | 0.940917i | ||||
\(436\) | 2616.83 | + | 3601.76i | 0.287439 | + | 0.395626i | ||||
\(437\) | 3440.05i | 0.376568i | ||||||||
\(438\) | −5400.57 | + | 1754.75i | −0.589153 | + | 0.191427i | ||||
\(439\) | −10201.7 | − | 14041.4i | −1.10911 | − | 1.52656i | −0.822717 | − | 0.568451i | \(-0.807543\pi\) |
−0.286396 | − | 0.958111i | \(-0.592457\pi\) | |||||||
\(440\) | 2894.14 | − | 3983.44i | 0.313574 | − | 0.431598i | ||||
\(441\) | 5099.79 | + | 3705.21i | 0.550673 | + | 0.400088i | ||||
\(442\) | 4603.15 | 0.495361 | ||||||||
\(443\) | 1759.44 | + | 1278.31i | 0.188698 | + | 0.137097i | 0.678124 | − | 0.734948i | \(-0.262793\pi\) |
−0.489425 | + | 0.872045i | \(0.662793\pi\) | |||||||
\(444\) | −21431.9 | − | 6963.63i | −2.29079 | − | 0.744323i | ||||
\(445\) | 6369.40 | − | 2069.55i | 0.678514 | − | 0.220463i | ||||
\(446\) | −2064.53 | + | 1499.97i | −0.219189 | + | 0.159250i | ||||
\(447\) | 3977.45 | − | 2889.79i | 0.420866 | − | 0.305777i | ||||
\(448\) | − | 1816.01i | − | 0.191514i | ||||||
\(449\) | 1267.82 | + | 3901.95i | 0.133256 | + | 0.410121i | 0.995315 | − | 0.0966882i | \(-0.0308250\pi\) |
−0.862058 | + | 0.506809i | \(0.830825\pi\) | |||||||
\(450\) | −2219.85 | −0.232544 | ||||||||
\(451\) | 6125.33 | + | 2650.42i | 0.639535 | + | 0.276726i | ||||
\(452\) | 439.163 | 0.0457002 | ||||||||
\(453\) | −2344.83 | − | 7216.63i | −0.243200 | − | 0.748492i | ||||
\(454\) | − | 3206.95i | − | 0.331519i | ||||||
\(455\) | −6269.66 | + | 4555.17i | −0.645991 | + | 0.469340i | ||||
\(456\) | 2070.66 | − | 1504.42i | 0.212648 | − | 0.154498i | ||||
\(457\) | 4496.52 | − | 1461.01i | 0.460259 | − | 0.149547i | −0.0697043 | − | 0.997568i | \(-0.522206\pi\) |
0.529964 | + | 0.848020i | \(0.322206\pi\) | |||||||
\(458\) | −836.883 | − | 271.920i | −0.0853821 | − | 0.0277423i | ||||
\(459\) | 2714.49 | + | 1972.19i | 0.276038 | + | 0.200553i | ||||
\(460\) | 13297.5 | 1.34782 | ||||||||
\(461\) | −8979.75 | − | 6524.17i | −0.907221 | − | 0.659135i | 0.0330896 | − | 0.999452i | \(-0.489465\pi\) |
−0.940310 | + | 0.340318i | \(0.889465\pi\) | |||||||
\(462\) | 489.802 | − | 674.155i | 0.0493240 | − | 0.0678886i | ||||
\(463\) | 2987.44 | + | 4111.86i | 0.299866 | + | 0.412730i | 0.932187 | − | 0.361976i | \(-0.117898\pi\) |
−0.632321 | + | 0.774706i | \(0.717898\pi\) | |||||||
\(464\) | 3804.73 | − | 1236.23i | 0.380669 | − | 0.123687i | ||||
\(465\) | − | 20509.1i | − | 2.04534i | ||||||
\(466\) | −497.885 | − | 685.280i | −0.0494937 | − | 0.0681223i | ||||
\(467\) | −2680.84 | + | 8250.77i | −0.265641 | + | 0.817559i | 0.725904 | + | 0.687796i | \(0.241422\pi\) |
−0.991545 | + | 0.129763i | \(0.958578\pi\) | |||||||
\(468\) | −6983.01 | + | 9611.29i | −0.689722 | + | 0.949320i | ||||
\(469\) | −957.655 | − | 2947.36i | −0.0942866 | − | 0.290184i | ||||
\(470\) | 685.449 | + | 222.716i | 0.0672710 | + | 0.0218577i | ||||
\(471\) | −3630.68 | + | 11174.1i | −0.355186 | + | 1.09315i | ||||
\(472\) | −2733.29 | + | 8412.19i | −0.266546 | + | 0.820344i | ||||
\(473\) | 3895.99 | + | 1265.88i | 0.378727 | + | 0.123056i | ||||
\(474\) | 82.0372 | + | 252.484i | 0.00794956 | + | 0.0244662i | ||||
\(475\) | −2539.62 | + | 3495.49i | −0.245318 | + | 0.337651i | ||||
\(476\) | 1072.76 | − | 3301.63i | 0.103298 | − | 0.317920i | ||||
\(477\) | 6107.72 | + | 8406.56i | 0.586276 | + | 0.806939i | ||||
\(478\) | 1076.02i | 0.102963i | ||||||||
\(479\) | 18968.9 | − | 6163.35i | 1.80941 | − | 0.587914i | 0.809414 | − | 0.587239i | \(-0.199785\pi\) |
1.00000 | 0.000675501i | \(-0.000215019\pi\) | ||||||||
\(480\) | −8836.10 | − | 12161.9i | −0.840232 | − | 1.15648i | ||||
\(481\) | −20164.0 | + | 27753.3i | −1.91143 | + | 2.63086i | ||||
\(482\) | −555.834 | − | 403.837i | −0.0525260 | − | 0.0381624i | ||||
\(483\) | 4683.14 | 0.441181 | ||||||||
\(484\) | 4099.46 | + | 2978.43i | 0.384998 | + | 0.279718i | ||||
\(485\) | 20358.7 | + | 6614.93i | 1.90606 | + | 0.619317i | ||||
\(486\) | 3499.22 | − | 1136.96i | 0.326600 | − | 0.106119i | ||||
\(487\) | −6246.91 | + | 4538.65i | −0.581262 | + | 0.422312i | −0.839179 | − | 0.543855i | \(-0.816964\pi\) |
0.257917 | + | 0.966167i | \(0.416964\pi\) | |||||||
\(488\) | 2375.51 | − | 1725.91i | 0.220357 | − | 0.160099i | ||||
\(489\) | 13392.2i | 1.23848i | ||||||||
\(490\) | 1186.71 | + | 3652.32i | 0.109408 | + | 0.336724i | ||||
\(491\) | −6642.42 | −0.610526 | −0.305263 | − | 0.952268i | \(-0.598744\pi\) | ||||
−0.305263 | + | 0.952268i | \(0.598744\pi\) | |||||||
\(492\) | 8868.28 | − | 10059.8i | 0.812628 | − | 0.921809i | ||||
\(493\) | 6120.94 | 0.559175 | ||||||||
\(494\) | −578.590 | − | 1780.72i | −0.0526963 | − | 0.162183i | ||||
\(495\) | 8525.55i | 0.774131i | ||||||||
\(496\) | 7395.07 | − | 5372.84i | 0.669453 | − | 0.486386i | ||||
\(497\) | −895.343 | + | 650.505i | −0.0808081 | + | 0.0587105i | ||||
\(498\) | −6783.77 | + | 2204.18i | −0.610418 | + | 0.198337i | ||||
\(499\) | −20915.5 | − | 6795.86i | −1.87637 | − | 0.609668i | −0.988855 | − | 0.148881i | \(-0.952433\pi\) |
−0.887511 | − | 0.460787i | \(-0.847567\pi\) | |||||||
\(500\) | 1353.41 | + | 983.311i | 0.121053 | + | 0.0879500i | ||||
\(501\) | −17907.6 | −1.59691 | ||||||||
\(502\) | 1092.59 | + | 793.812i | 0.0971407 | + | 0.0705768i | ||||
\(503\) | −7867.05 | + | 10828.1i | −0.697365 | + | 0.959840i | 0.302613 | + | 0.953114i | \(0.402141\pi\) |
−0.999977 | + | 0.00672653i | \(0.997859\pi\) | |||||||
\(504\) | −887.387 | − | 1221.38i | −0.0784273 | − | 0.107946i | ||||
\(505\) | 4468.95 | − | 1452.05i | 0.393793 | − | 0.127951i | ||||
\(506\) | 2176.65i | 0.191233i | ||||||||
\(507\) | 15620.9 | + | 21500.3i | 1.36834 | + | 1.88335i | ||||
\(508\) | −3328.82 | + | 10245.1i | −0.290733 | + | 0.894786i | ||||
\(509\) | 3586.84 | − | 4936.86i | 0.312346 | − | 0.429907i | −0.623765 | − | 0.781612i | \(-0.714398\pi\) |
0.936111 | + | 0.351705i | \(0.114398\pi\) | |||||||
\(510\) | −2051.11 | − | 6312.68i | −0.178088 | − | 0.548098i | ||||
\(511\) | 6200.26 | + | 2014.59i | 0.536758 | + | 0.174403i | ||||
\(512\) | 3543.40 | − | 10905.5i | 0.305855 | − | 0.941325i | ||||
\(513\) | 421.741 | − | 1297.98i | 0.0362969 | − | 0.111710i | ||||
\(514\) | −1030.81 | − | 334.931i | −0.0884576 | − | 0.0287416i | ||||
\(515\) | −2144.03 | − | 6598.64i | −0.183451 | − | 0.564603i | ||||
\(516\) | 4838.20 | − | 6659.21i | 0.412771 | − | 0.568131i | ||||
\(517\) | 450.229 | − | 1385.66i | 0.0382999 | − | 0.117875i | ||||
\(518\) | −1231.35 | − | 1694.80i | −0.104445 | − | 0.143756i | ||||
\(519\) | − | 11222.1i | − | 0.949129i | ||||||
\(520\) | −14324.0 | + | 4654.15i | −1.20798 | + | 0.392496i | ||||
\(521\) | 5211.53 | + | 7173.05i | 0.438236 | + | 0.603181i | 0.969819 | − | 0.243826i | \(-0.0784025\pi\) |
−0.531583 | + | 0.847006i | \(0.678403\pi\) | |||||||
\(522\) | 751.872 | − | 1034.86i | 0.0630432 | − | 0.0867715i | ||||
\(523\) | 10168.0 | + | 7387.51i | 0.850128 | + | 0.617654i | 0.925181 | − | 0.379525i | \(-0.123913\pi\) |
−0.0750531 | + | 0.997180i | \(0.523913\pi\) | |||||||
\(524\) | −8903.24 | −0.742252 | ||||||||
\(525\) | 4758.61 | + | 3457.33i | 0.395586 | + | 0.287410i | ||||
\(526\) | 5580.67 | + | 1813.27i | 0.462602 | + | 0.150308i | ||||
\(527\) | 13301.2 | − | 4321.83i | 1.09945 | − | 0.357233i | ||||
\(528\) | −7094.91 | + | 5154.75i | −0.584785 | + | 0.424871i | ||||
\(529\) | −53.2042 | + | 38.6551i | −0.00437283 | + | 0.00317705i | ||||
\(530\) | 6330.37i | 0.518818i | ||||||||
\(531\) | −4732.68 | − | 14565.7i | −0.386781 | − | 1.19039i | ||||
\(532\) | −1412.06 | −0.115077 | ||||||||
\(533\) | −10392.8 | − | 17571.9i | −0.844582 | − | 1.42800i | ||||
\(534\) | 2202.76 | 0.178507 | ||||||||
\(535\) | 2925.30 | + | 9003.15i | 0.236396 | + | 0.727552i | ||||
\(536\) | − | 6022.81i | − | 0.485346i | ||||||
\(537\) | −10873.8 | + | 7900.31i | −0.873819 | + | 0.634867i | ||||
\(538\) | −2563.06 | + | 1862.17i | −0.205393 | + | 0.149226i | ||||
\(539\) | 7383.31 | − | 2398.98i | 0.590022 | − | 0.191710i | ||||
\(540\) | −5017.34 | − | 1630.23i | −0.399837 | − | 0.129915i | ||||
\(541\) | 3524.71 | + | 2560.85i | 0.280109 | + | 0.203511i | 0.718965 | − | 0.695046i | \(-0.244616\pi\) |
−0.438856 | + | 0.898557i | \(0.644616\pi\) | |||||||
\(542\) | −996.303 | −0.0789573 | ||||||||
\(543\) | −23433.6 | − | 17025.5i | −1.85199 | − | 1.34555i | ||||
\(544\) | 6025.60 | − | 8293.53i | 0.474900 | − | 0.653644i | ||||
\(545\) | −5744.24 | − | 7906.26i | −0.451479 | − | 0.621407i | ||||
\(546\) | −2424.19 | + | 787.667i | −0.190010 | + | 0.0617381i | ||||
\(547\) | − | 16038.6i | − | 1.25368i | −0.779149 | − | 0.626839i | \(-0.784348\pi\) | ||
0.779149 | − | 0.626839i | \(-0.215652\pi\) | |||||||
\(548\) | −9064.98 | − | 12476.9i | −0.706637 | − | 0.972602i | ||||
\(549\) | −1571.10 | + | 4835.35i | −0.122136 | + | 0.375897i | ||||
\(550\) | −1606.92 | + | 2211.73i | −0.124580 | + | 0.171470i | ||||
\(551\) | −769.367 | − | 2367.87i | −0.0594848 | − | 0.183076i | ||||
\(552\) | 8655.97 | + | 2812.50i | 0.667432 | + | 0.216862i | ||||
\(553\) | 94.1849 | − | 289.871i | 0.00724258 | − | 0.0222904i | ||||
\(554\) | −519.616 | + | 1599.21i | −0.0398490 | + | 0.122643i | ||||
\(555\) | 47045.3 | + | 15285.9i | 3.59813 | + | 1.16910i | ||||
\(556\) | 2835.51 | + | 8726.80i | 0.216281 | + | 0.665645i | ||||
\(557\) | 2467.81 | − | 3396.65i | 0.187728 | − | 0.258385i | −0.704771 | − | 0.709435i | \(-0.748950\pi\) |
0.892499 | + | 0.451050i | \(0.148950\pi\) | |||||||
\(558\) | 903.180 | − | 2779.70i | 0.0685209 | − | 0.210886i | ||||
\(559\) | −7365.26 | − | 10137.4i | −0.557276 | − | 0.767025i | ||||
\(560\) | 4980.55i | 0.375833i | ||||||||
\(561\) | −12761.3 | + | 4146.41i | −0.960399 | + | 0.312053i | ||||
\(562\) | −824.620 | − | 1134.99i | −0.0618941 | − | 0.0851900i | ||||
\(563\) | 6319.49 | − | 8698.03i | 0.473064 | − | 0.651116i | −0.504090 | − | 0.863651i | \(-0.668172\pi\) |
0.977153 | + | 0.212535i | \(0.0681720\pi\) | |||||||
\(564\) | −2368.44 | − | 1720.77i | −0.176825 | − | 0.128471i | ||||
\(565\) | −964.012 | −0.0717810 | ||||||||
\(566\) | 5490.90 | + | 3989.37i | 0.407773 | + | 0.296264i | ||||
\(567\) | −5018.76 | − | 1630.69i | −0.371725 | − | 0.120781i | ||||
\(568\) | −2045.55 | + | 664.640i | −0.151108 | + | 0.0490980i | ||||
\(569\) | −2672.06 | + | 1941.37i | −0.196870 | + | 0.143034i | −0.681853 | − | 0.731489i | \(-0.738826\pi\) |
0.484983 | + | 0.874523i | \(0.338826\pi\) | |||||||
\(570\) | −2184.23 | + | 1586.93i | −0.160504 | + | 0.116613i | ||||
\(571\) | 4207.30i | 0.308354i | 0.988043 | + | 0.154177i | \(0.0492726\pi\) | ||||
−0.988043 | + | 0.154177i | \(0.950727\pi\) | |||||||
\(572\) | 4521.23 | + | 13914.9i | 0.330493 | + | 1.01715i | ||||
\(573\) | −12163.0 | −0.886764 | ||||||||
\(574\) | 1216.66 | − | 271.999i | 0.0884708 | − | 0.0197788i | ||||
\(575\) | −15364.2 | −1.11431 | ||||||||
\(576\) | 1888.40 | + | 5811.91i | 0.136603 | + | 0.420421i | ||||
\(577\) | − | 10683.1i | − | 0.770782i | −0.922753 | − | 0.385391i | \(-0.874067\pi\) | ||
0.922753 | − | 0.385391i | \(-0.125933\pi\) | |||||||
\(578\) | 585.000 | − | 425.027i | 0.0420983 | − | 0.0305862i | ||||
\(579\) | 10240.9 | − | 7440.46i | 0.735056 | − | 0.534050i | ||||
\(580\) | −9152.96 | + | 2973.98i | −0.655269 | + | 0.212910i | ||||
\(581\) | 7788.28 | + | 2530.57i | 0.556132 | + | 0.180698i | ||||
\(582\) | 5696.06 | + | 4138.43i | 0.405686 | + | 0.294748i | ||||
\(583\) | 12797.1 | 0.909093 | ||||||||
\(584\) | 10250.2 | + | 7447.23i | 0.726297 | + | 0.527686i | ||||
\(585\) | 15328.5 | − | 21097.8i | 1.08334 | − | 1.49109i | ||||
\(586\) | −1877.97 | − | 2584.80i | −0.132386 | − | 0.182213i | ||||
\(587\) | 6862.54 | − | 2229.77i | 0.482533 | − | 0.156785i | −0.0576415 | − | 0.998337i | \(-0.518358\pi\) |
0.540175 | + | 0.841553i | \(0.318358\pi\) | |||||||
\(588\) | − | 15599.1i | − | 1.09404i | ||||||
\(589\) | −3343.78 | − | 4602.31i | −0.233918 | − | 0.321961i | ||||
\(590\) | 2883.20 | − | 8873.59i | 0.201186 | − | 0.619186i | ||||
\(591\) | 6924.98 | − | 9531.41i | 0.481989 | − | 0.663401i | ||||
\(592\) | 6812.89 | + | 20967.9i | 0.472986 | + | 1.45570i | ||||
\(593\) | −15798.3 | − | 5133.19i | −1.09403 | − | 0.355472i | −0.294227 | − | 0.955736i | \(-0.595062\pi\) |
−0.799802 | + | 0.600264i | \(0.795062\pi\) | |||||||
\(594\) | 266.851 | − | 821.284i | 0.0184327 | − | 0.0567301i | ||||
\(595\) | −2354.83 | + | 7247.43i | −0.162250 | + | 0.499354i | ||||
\(596\) | −5013.37 | − | 1628.94i | −0.344556 | − | 0.111953i | ||||
\(597\) | −4495.89 | − | 13836.9i | −0.308215 | − | 0.948588i | ||||
\(598\) | 3913.51 | − | 5386.48i | 0.267617 | − | 0.368344i | ||||
\(599\) | 1807.00 | − | 5561.38i | 0.123259 | − | 0.379352i | −0.870321 | − | 0.492485i | \(-0.836089\pi\) |
0.993580 | + | 0.113133i | \(0.0360886\pi\) | |||||||
\(600\) | 6719.13 | + | 9248.10i | 0.457179 | + | 0.629253i | ||||
\(601\) | − | 18424.8i | − | 1.25052i | −0.780416 | − | 0.625261i | \(-0.784992\pi\) | ||
0.780416 | − | 0.625261i | \(-0.215008\pi\) | |||||||
\(602\) | 727.746 | − | 236.459i | 0.0492703 | − | 0.0160089i | ||||
\(603\) | 6129.70 | + | 8436.81i | 0.413965 | + | 0.569774i | ||||
\(604\) | −4782.15 | + | 6582.07i | −0.322157 | + | 0.443411i | ||||
\(605\) | −8998.77 | − | 6537.99i | −0.604714 | − | 0.439350i | ||||
\(606\) | 1545.51 | 0.103601 | ||||||||
\(607\) | 791.041 | + | 574.725i | 0.0528952 | + | 0.0384306i | 0.613919 | − | 0.789369i | \(-0.289592\pi\) |
−0.561023 | + | 0.827800i | \(0.689592\pi\) | |||||||
\(608\) | −3965.71 | − | 1288.54i | −0.264524 | − | 0.0859492i | ||||
\(609\) | −3223.51 | + | 1047.38i | −0.214488 | + | 0.0696915i | ||||
\(610\) | −2505.81 | + | 1820.57i | −0.166323 | + | 0.120841i | ||||
\(611\) | −3605.51 | + | 2619.55i | −0.238729 | + | 0.173447i | ||||
\(612\) | 11682.0i | 0.771593i | ||||||||
\(613\) | −2244.04 | − | 6906.43i | −0.147856 | − | 0.455054i | 0.849511 | − | 0.527571i | \(-0.176897\pi\) |
−0.997367 | + | 0.0725165i | \(0.976897\pi\) | |||||||
\(614\) | −6955.52 | −0.457169 | ||||||||
\(615\) | −19466.8 | + | 22082.3i | −1.27639 | + | 1.44788i | ||||
\(616\) | −1859.28 | −0.121611 | ||||||||
\(617\) | 1155.31 | + | 3555.69i | 0.0753828 | + | 0.232004i | 0.981647 | − | 0.190707i | \(-0.0610782\pi\) |
−0.906264 | + | 0.422712i | \(0.861078\pi\) | |||||||
\(618\) | − | 2282.03i | − | 0.148539i | ||||||
\(619\) | −16372.2 | + | 11895.1i | −1.06309 | + | 0.772381i | −0.974658 | − | 0.223702i | \(-0.928186\pi\) |
−0.0884330 | + | 0.996082i | \(0.528186\pi\) | |||||||
\(620\) | −17790.2 | + | 12925.3i | −1.15237 | + | 0.837246i | ||||
\(621\) | 4615.61 | − | 1499.70i | 0.298257 | − | 0.0969097i | ||||
\(622\) | −6507.11 | − | 2114.29i | −0.419472 | − | 0.136295i | ||||
\(623\) | −2045.95 | − | 1486.47i | −0.131572 | − | 0.0955925i | ||||
\(624\) | 26825.5 | 1.72096 | ||||||||
\(625\) | 11077.1 | + | 8048.01i | 0.708936 | + | 0.515072i | ||||
\(626\) | 1414.44 | − | 1946.81i | 0.0903073 | − | 0.124297i | ||||
\(627\) | 3208.05 | + | 4415.50i | 0.204334 | + | 0.281241i | ||||
\(628\) | 11980.9 | − | 3892.82i | 0.761287 | − | 0.247357i | ||||
\(629\) | 33732.6i | 2.13832i | ||||||||
\(630\) | 936.059 | + | 1288.37i | 0.0591960 | + | 0.0814763i | ||||
\(631\) | −2726.57 | + | 8391.52i | −0.172018 | + | 0.529416i | −0.999485 | − | 0.0320986i | \(-0.989781\pi\) |
0.827467 | + | 0.561514i | \(0.189781\pi\) | |||||||
\(632\) | 348.169 | − | 479.213i | 0.0219136 | − | 0.0301615i | ||||
\(633\) | 2231.51 | + | 6867.88i | 0.140118 | + | 0.431238i | ||||
\(634\) | 4063.84 | + | 1320.42i | 0.254567 | + | 0.0827139i | ||||
\(635\) | 7307.13 | − | 22489.0i | 0.456653 | − | 1.40543i | ||||
\(636\) | 7945.98 | − | 24455.2i | 0.495406 | − | 1.52470i | ||||
\(637\) | −22584.4 | − | 7338.12i | −1.40475 | − | 0.456432i | ||||
\(638\) | −486.808 | − | 1498.24i | −0.0302083 | − | 0.0929717i | ||||
\(639\) | 2188.99 | − | 3012.89i | 0.135517 | − | 0.186523i | ||||
\(640\) | −6534.57 | + | 20111.3i | −0.403596 | + | 1.24214i | ||||
\(641\) | 12720.1 | + | 17507.7i | 0.783795 | + | 1.07880i | 0.994853 | + | 0.101328i | \(0.0323091\pi\) |
−0.211058 | + | 0.977474i | \(0.567691\pi\) | |||||||
\(642\) | 3113.60i | 0.191408i | ||||||||
\(643\) | −13660.6 | + | 4438.61i | −0.837827 | + | 0.272226i | −0.696338 | − | 0.717714i | \(-0.745189\pi\) |
−0.141488 | + | 0.989940i | \(0.545189\pi\) | |||||||
\(644\) | −2951.43 | − | 4062.29i | −0.180594 | − | 0.248566i | ||||
\(645\) | −10620.4 | + | 14617.7i | −0.648337 | + | 0.892359i | ||||
\(646\) | −1489.49 | − | 1082.18i | −0.0907170 | − | 0.0659098i | ||||
\(647\) | −1673.52 | −0.101689 | −0.0508447 | − | 0.998707i | \(-0.516191\pi\) | ||||
−0.0508447 | + | 0.998707i | \(0.516191\pi\) | |||||||
\(648\) | −8296.98 | − | 6028.11i | −0.502988 | − | 0.365442i | ||||
\(649\) | −17938.3 | − | 5828.51i | −1.08496 | − | 0.352525i | ||||
\(650\) | 7953.14 | − | 2584.13i | 0.479920 | − | 0.155935i | ||||
\(651\) | −6265.39 | + | 4552.07i | −0.377204 | + | 0.274055i | ||||
\(652\) | 11616.8 | − | 8440.09i | 0.697774 | − | 0.506962i | ||||
\(653\) | 21298.6i | 1.27639i | 0.769876 | + | 0.638193i | \(0.220318\pi\) | ||||
−0.769876 | + | 0.638193i | \(0.779682\pi\) | |||||||
\(654\) | −993.276 | − | 3056.99i | −0.0593886 | − | 0.182779i | ||||
\(655\) | 19543.6 | 1.16585 | ||||||||
\(656\) | −13062.2 | − | 1234.28i | −0.777427 | − | 0.0734614i | ||||
\(657\) | −21938.0 | −1.30272 | ||||||||
\(658\) | −84.0999 | − | 258.833i | −0.00498261 | − | 0.0153349i | ||||
\(659\) | − | 3519.78i | − | 0.208060i | −0.994574 | − | 0.104030i | \(-0.966826\pi\) | ||
0.994574 | − | 0.104030i | \(-0.0331737\pi\) | |||||||
\(660\) | 17068.1 | − | 12400.7i | 1.00663 | − | 0.731357i | ||||
\(661\) | −6441.33 | + | 4679.90i | −0.379030 | + | 0.275381i | −0.760945 | − | 0.648816i | \(-0.775265\pi\) |
0.381915 | + | 0.924197i | \(0.375265\pi\) | |||||||
\(662\) | 4959.22 | − | 1611.35i | 0.291156 | − | 0.0946024i | ||||
\(663\) | 39035.0 | + | 12683.2i | 2.28657 | + | 0.742950i | ||||
\(664\) | 12875.5 | + | 9354.63i | 0.752512 | + | 0.546732i | ||||
\(665\) | 3099.64 | 0.180750 | ||||||||
\(666\) | 5703.13 | + | 4143.57i | 0.331820 | + | 0.241081i | ||||
\(667\) | 5203.90 | − | 7162.56i | 0.302093 | − | 0.415795i | ||||
\(668\) | 11285.8 | + | 15533.6i | 0.653684 | + | 0.899718i | ||||
\(669\) | −21640.3 | + | 7031.36i | −1.25062 | + | 0.406350i | ||||
\(670\) | 6353.15i | 0.366334i | ||||||||
\(671\) | 3680.36 | + | 5065.58i | 0.211742 | + | 0.291438i | ||||
\(672\) | −1754.16 | + | 5398.75i | −0.100697 | + | 0.309912i | ||||
\(673\) | 16941.5 | − | 23317.9i | 0.970350 | − | 1.33557i | 0.0284805 | − | 0.999594i | \(-0.490933\pi\) |
0.941870 | − | 0.335978i | \(-0.109067\pi\) | |||||||
\(674\) | 1790.63 | + | 5510.99i | 0.102333 | + | 0.314949i | ||||
\(675\) | 5797.14 | + | 1883.60i | 0.330566 | + | 0.107407i | ||||
\(676\) | 8805.32 | − | 27100.0i | 0.500985 | − | 1.54187i | ||||
\(677\) | −1199.26 | + | 3690.95i | −0.0680818 | + | 0.209534i | −0.979309 | − | 0.202369i | \(-0.935136\pi\) |
0.911228 | + | 0.411903i | \(0.135136\pi\) | |||||||
\(678\) | −301.552 | − | 97.9803i | −0.0170812 | − | 0.00555001i | ||||
\(679\) | −2497.87 | − | 7687.65i | −0.141177 | − | 0.434499i | ||||
\(680\) | −8705.00 | + | 11981.4i | −0.490914 | + | 0.675685i | ||||
\(681\) | 8836.23 | − | 27195.1i | 0.497218 | − | 1.53028i | ||||
\(682\) | −2115.73 | − | 2912.06i | −0.118791 | − | 0.163502i | ||||
\(683\) | 7371.34i | 0.412967i | 0.978450 | + | 0.206484i | \(0.0662020\pi\) | ||||
−0.978450 | + | 0.206484i | \(0.933798\pi\) | |||||||
\(684\) | 4519.13 | − | 1468.35i | 0.252622 | − | 0.0820818i | ||||
\(685\) | 19898.6 | + | 27388.1i | 1.10991 | + | 1.52766i | ||||
\(686\) | 1809.77 | − | 2490.93i | 0.100725 | − | 0.138636i | ||||
\(687\) | −6347.58 | − | 4611.79i | −0.352512 | − | 0.256115i | ||||
\(688\) | −8053.05 | −0.446250 | ||||||||
\(689\) | −31668.4 | − | 23008.5i | −1.75105 | − | 1.27221i | ||||
\(690\) | −9130.74 | − | 2966.76i | −0.503770 | − | 0.163685i | ||||
\(691\) | −9536.30 | + | 3098.53i | −0.525004 | + | 0.170584i | −0.559515 | − | 0.828820i | \(-0.689013\pi\) |
0.0345109 | + | 0.999404i | \(0.489013\pi\) | |||||||
\(692\) | −9734.42 | + | 7072.47i | −0.534750 | + | 0.388519i | ||||
\(693\) | 2604.50 | − | 1892.28i | 0.142766 | − | 0.103725i | ||||
\(694\) | 2824.69i | 0.154501i | ||||||||
\(695\) | −6224.26 | − | 19156.3i | −0.339711 | − | 1.04552i | ||||
\(696\) | −6587.12 | −0.358742 | ||||||||
\(697\) | −18423.8 | − | 7971.93i | −1.00122 | − | 0.433226i | ||||
\(698\) | −1371.52 | −0.0743734 | ||||||||
\(699\) | −2333.91 | − | 7183.05i | −0.126290 | − | 0.388681i | ||||
\(700\) | − | 6306.65i | − | 0.340527i | ||||||
\(701\) | −6913.85 | + | 5023.21i | −0.372514 | + | 0.270648i | −0.758253 | − | 0.651961i | \(-0.773947\pi\) |
0.385738 | + | 0.922608i | \(0.373947\pi\) | |||||||
\(702\) | −2136.99 | + | 1552.62i | −0.114894 | + | 0.0834753i | ||||
\(703\) | 13049.3 | − | 4239.99i | 0.700093 | − | 0.227474i | ||||
\(704\) | 7157.63 | + | 2325.65i | 0.383186 | + | 0.124505i | ||||
\(705\) | 5198.98 | + | 3777.28i | 0.277738 | + | 0.201788i | ||||
\(706\) | 909.377 | 0.0484771 | ||||||||
\(707\) | −1435.49 | − | 1042.95i | −0.0763610 | − | 0.0554795i | ||||
\(708\) | −22276.5 | + | 30661.0i | −1.18249 | + | 1.62756i | ||||
\(709\) | 7969.24 | + | 10968.7i | 0.422132 | + | 0.581014i | 0.966125 | − | 0.258075i | \(-0.0830883\pi\) |
−0.543993 | + | 0.839090i | \(0.683088\pi\) | |||||||
\(710\) | 2157.75 | − | 701.094i | 0.114055 | − | 0.0370586i | ||||
\(711\) | 1025.63i | 0.0540989i | ||||||||
\(712\) | −2888.87 | − | 3976.19i | −0.152058 | − | 0.209289i | ||||
\(713\) | 6251.15 | − | 19239.1i | 0.328341 | − | 1.01053i | ||||
\(714\) | −1473.23 | + | 2027.73i | −0.0772188 | + | 0.106283i | ||||
\(715\) | −9924.60 | − | 30544.8i | −0.519103 | − | 1.59764i | ||||
\(716\) | 13705.9 | + | 4453.32i | 0.715383 | + | 0.232442i | ||||
\(717\) | −2964.81 | + | 9124.74i | −0.154425 | + | 0.475271i | ||||
\(718\) | 1119.49 | − | 3445.45i | 0.0581883 | − | 0.179085i | ||||
\(719\) | 3927.03 | + | 1275.97i | 0.203690 | + | 0.0661830i | 0.409085 | − | 0.912496i | \(-0.365848\pi\) |
−0.205395 | + | 0.978679i | \(0.565848\pi\) | |||||||
\(720\) | −5179.09 | − | 15939.6i | −0.268074 | − | 0.825047i | ||||
\(721\) | −1539.97 | + | 2119.58i | −0.0795442 | + | 0.109483i | ||||
\(722\) | 1409.36 | − | 4337.57i | 0.0726468 | − | 0.223584i | ||||
\(723\) | −3600.80 | − | 4956.07i | −0.185221 | − | 0.254935i | ||||
\(724\) | 31056.9i | 1.59423i | ||||||||
\(725\) | 10575.5 | − | 3436.20i | 0.541745 | − | 0.176024i | ||||
\(726\) | −2150.39 | − | 2959.76i | −0.109929 | − | 0.151305i | ||||
\(727\) | 15012.6 | − | 20663.1i | 0.765868 | − | 1.05413i | −0.230835 | − | 0.972993i | \(-0.574146\pi\) |
0.996703 | − | 0.0811340i | \(-0.0258542\pi\) | |||||||
\(728\) | 4601.09 | + | 3342.89i | 0.234241 | + | 0.170186i | ||||
\(729\) | 9580.06 | 0.486718 | ||||||||
\(730\) | −10812.4 | − | 7855.69i | −0.548200 | − | 0.398291i | ||||
\(731\) | −11718.4 | − | 3807.53i | −0.592914 | − | 0.192649i | ||||
\(732\) | 11965.5 | − | 3887.84i | 0.604179 | − | 0.196310i | ||||
\(733\) | 6136.48 | − | 4458.42i | 0.309217 | − | 0.224659i | −0.422343 | − | 0.906436i | \(-0.638792\pi\) |
0.731561 | + | 0.681777i | \(0.238792\pi\) | |||||||
\(734\) | 146.145 | − | 106.180i | 0.00734918 | − | 0.00533949i | ||||
\(735\) | 34241.7i | 1.71840i | ||||||||
\(736\) | −4582.01 | − | 14102.0i | −0.229477 | − | 0.706258i | ||||
\(737\) | 12843.1 | 0.641904 | ||||||||
\(738\) | −3610.91 | + | 2135.65i | −0.180108 | + | 0.106524i | ||||
\(739\) | −6609.79 | −0.329019 | −0.164510 | − | 0.986375i | \(-0.552604\pi\) | ||||
−0.164510 | + | 0.986375i | \(0.552604\pi\) | |||||||
\(740\) | −16389.6 | − | 50442.0i | −0.814181 | − | 2.50579i | ||||
\(741\) | − | 16694.8i | − | 0.827662i | ||||||
\(742\) | 1933.89 | − | 1405.05i | 0.0956809 | − | 0.0695162i | ||||
\(743\) | 16138.8 | − | 11725.5i | 0.796871 | − | 0.578961i | −0.113123 | − | 0.993581i | \(-0.536086\pi\) |
0.909995 | + | 0.414620i | \(0.136086\pi\) | |||||||
\(744\) | −14314.3 | + | 4650.99i | −0.705358 | + | 0.229185i | ||||
\(745\) | 11004.9 | + | 3575.71i | 0.541192 | + | 0.175844i | ||||
\(746\) | −5915.52 | − | 4297.88i | −0.290325 | − | 0.210934i | ||||
\(747\) | −27556.8 | −1.34974 | ||||||||
\(748\) | 11639.2 | + | 8456.38i | 0.568946 | + | 0.413364i | ||||
\(749\) | 2101.12 | − | 2891.95i | 0.102501 | − | 0.141081i | ||||
\(750\) | −709.939 | − | 977.148i | −0.0345644 | − | 0.0475739i | ||||
\(751\) | 16191.0 | − | 5260.79i | 0.786710 | − | 0.255618i | 0.112008 | − | 0.993707i | \(-0.464272\pi\) |
0.674703 | + | 0.738090i | \(0.264272\pi\) | |||||||
\(752\) | 2864.18i | 0.138891i | ||||||||
\(753\) | 7077.99 | + | 9742.02i | 0.342545 | + | 0.471473i | ||||
\(754\) | −1489.07 | + | 4582.89i | −0.0719215 | + | 0.221352i | ||||
\(755\) | 10497.3 | − | 14448.4i | 0.506010 | − | 0.696463i | ||||
\(756\) | 615.593 | + | 1894.60i | 0.0296150 | + | 0.0911455i | ||||
\(757\) | −11119.1 | − | 3612.83i | −0.533860 | − | 0.173462i | 0.0296662 | − | 0.999560i | \(-0.490556\pi\) |
−0.563526 | + | 0.826098i | \(0.690556\pi\) | |||||||
\(758\) | −2054.20 | + | 6322.18i | −0.0984327 | + | 0.302945i | ||||
\(759\) | −5997.42 | + | 18458.1i | −0.286815 | + | 0.882725i | ||||
\(760\) | 5729.14 | + | 1861.51i | 0.273444 | + | 0.0888474i | ||||
\(761\) | 10998.5 | + | 33849.9i | 0.523910 | + | 1.61243i | 0.766462 | + | 0.642289i | \(0.222015\pi\) |
−0.242553 | + | 0.970138i | \(0.577985\pi\) | |||||||
\(762\) | 4571.48 | − | 6292.11i | 0.217333 | − | 0.299133i | ||||
\(763\) | −1140.36 | + | 3509.65i | −0.0541070 | + | 0.166524i | ||||
\(764\) | 7665.41 | + | 10550.5i | 0.362990 | + | 0.499614i | ||||
\(765\) | − | 25643.2i | − | 1.21194i | ||||||
\(766\) | −3434.27 | + | 1115.86i | −0.161991 | + | 0.0526341i | ||||
\(767\) | 33911.9 | + | 46675.7i | 1.59646 | + | 2.19734i | ||||
\(768\) | 5520.22 | − | 7597.93i | 0.259367 | − | 0.356988i | ||||
\(769\) | 10422.9 | + | 7572.65i | 0.488762 | + | 0.355106i | 0.804708 | − | 0.593671i | \(-0.202322\pi\) |
−0.315946 | + | 0.948777i | \(0.602322\pi\) | |||||||
\(770\) | 1961.26 | 0.0917907 | ||||||||
\(771\) | −7818.50 | − | 5680.47i | −0.365209 | − | 0.265340i | ||||
\(772\) | −12908.1 | − | 4194.11i | −0.601780 | − | 0.195530i | ||||
\(773\) | 36605.5 | − | 11893.8i | 1.70324 | − | 0.553417i | 0.714058 | − | 0.700086i | \(-0.246855\pi\) |
0.989186 | + | 0.146669i | \(0.0468552\pi\) | |||||||
\(774\) | −2083.17 | + | 1513.51i | −0.0967418 | + | 0.0702870i | ||||
\(775\) | 20555.1 | − | 14934.2i | 0.952725 | − | 0.692196i | ||||
\(776\) | − | 15709.4i | − | 0.726720i | ||||||
\(777\) | −5772.14 | − | 17764.8i | −0.266505 | − | 0.820217i | ||||
\(778\) | 7939.89 | 0.365885 | ||||||||
\(779\) | −768.154 | + | 8129.21i | −0.0353299 | + | 0.373889i | ||||
\(780\) | −64533.4 | −2.96239 | ||||||||
\(781\) | −1417.29 | − | 4361.97i | −0.0649355 | − | 0.199851i | ||||
\(782\) | − | 6546.95i | − | 0.299384i | ||||||
\(783\) | −2841.62 | + | 2064.56i | −0.129695 | + | 0.0942289i | ||||
\(784\) | −12346.7 | + | 8970.41i | −0.562441 | + | 0.408638i | ||||
\(785\) | −26299.3 | + | 8545.16i | −1.19575 | + | 0.388522i | ||||
\(786\) | 6113.43 | + | 1986.37i | 0.277428 | + | 0.0901419i | ||||
\(787\) | −21399.6 | − | 15547.7i | −0.969267 | − | 0.704214i | −0.0139829 | − | 0.999902i | \(-0.504451\pi\) |
−0.955284 | + | 0.295688i | \(0.904451\pi\) | |||||||
\(788\) | −12632.1 | −0.571066 | ||||||||
\(789\) | 42328.2 | + | 30753.2i | 1.90992 | + | 1.38763i | ||||
\(790\) | −367.265 | + | 505.497i | −0.0165401 | + | 0.0227655i | ||||
\(791\) | 213.966 | + | 294.499i | 0.00961791 | + | 0.0132379i | ||||
\(792\) | 5950.39 | − | 1933.40i | 0.266967 | − | 0.0867428i | ||||
\(793\) | − | 19152.7i | − | 0.857670i | ||||||
\(794\) | 5063.03 | + | 6968.66i | 0.226297 | + | 0.311472i | ||||
\(795\) | −17442.3 | + | 53681.9i | −0.778131 | + | 2.39484i | ||||
\(796\) | −9169.13 | + | 12620.2i | −0.408280 | + | 0.561950i | ||||
\(797\) | −5133.99 | − | 15800.8i | −0.228175 | − | 0.702249i | −0.997954 | − | 0.0639390i | \(-0.979634\pi\) |
0.769779 | − | 0.638310i | \(-0.220366\pi\) | |||||||
\(798\) | 969.597 | + | 315.041i | 0.0430117 | + | 0.0139754i | ||||
\(799\) | −1354.20 | + | 4167.80i | −0.0599601 | + | 0.184538i | ||||
\(800\) | 5754.95 | − | 17711.9i | 0.254335 | − | 0.782763i | ||||
\(801\) | 8093.52 | + | 2629.74i | 0.357017 | + | 0.116002i | ||||
\(802\) | 806.448 | + | 2481.99i | 0.0355071 | + | 0.109279i | ||||
\(803\) | −15880.6 | + | 21857.8i | −0.697900 | + | 0.960577i | ||||
\(804\) | 7974.57 | − | 24543.2i | 0.349803 | − | 1.07658i | ||||
\(805\) | 6478.71 | + | 8917.18i | 0.283658 | + | 0.390422i | ||||
\(806\) | 11010.3i | 0.481169i | ||||||||
\(807\) | −26865.8 | + | 8729.21i | −1.17189 | + | 0.380772i | ||||
\(808\) | −2026.91 | − | 2789.80i | −0.0882505 | − | 0.121466i | ||||
\(809\) | 1631.22 | − | 2245.18i | 0.0708908 | − | 0.0975728i | −0.772099 | − | 0.635502i | \(-0.780793\pi\) |
0.842990 | + | 0.537929i | \(0.180793\pi\) | |||||||
\(810\) | 8752.06 | + | 6358.74i | 0.379649 | + | 0.275831i | ||||
\(811\) | −2758.75 | −0.119449 | −0.0597243 | − | 0.998215i | \(-0.519022\pi\) | ||||
−0.0597243 | + | 0.998215i | \(0.519022\pi\) | |||||||
\(812\) | 2940.07 | + | 2136.08i | 0.127064 | + | 0.0923175i | ||||
\(813\) | −8448.70 | − | 2745.15i | −0.364464 | − | 0.118421i | ||||
\(814\) | 8256.82 | − | 2682.80i | 0.355530 | − | 0.115519i | ||||
\(815\) | −25500.1 | + | 18526.9i | −1.09599 | + | 0.796282i | ||||
\(816\) | 21340.1 | − | 15504.5i | 0.915506 | − | 0.665154i | ||||
\(817\) | 5011.80i | 0.214615i | ||||||||
\(818\) | 1625.80 | + | 5003.68i | 0.0694922 | + | 0.213875i | ||||
\(819\) | −9847.47 | −0.420145 | ||||||||
\(820\) | 31423.3 | + | 2969.29i | 1.33823 | + | 0.126454i | ||||
\(821\) | −10480.8 | −0.445532 | −0.222766 | − | 0.974872i | \(-0.571509\pi\) | ||||
−0.222766 | + | 0.974872i | \(0.571509\pi\) | |||||||
\(822\) | 3440.81 | + | 10589.7i | 0.146000 | + | 0.449342i | ||||
\(823\) | − | 17073.1i | − | 0.723124i | −0.932348 | − | 0.361562i | \(-0.882244\pi\) | ||
0.932348 | − | 0.361562i | \(-0.117756\pi\) | |||||||
\(824\) | −4119.29 | + | 2992.84i | −0.174153 | + | 0.126530i | ||||
\(825\) | −19720.8 | + | 14328.0i | −0.832230 | + | 0.604651i | ||||
\(826\) | −3350.76 | + | 1088.73i | −0.141148 | + | 0.0458616i | ||||
\(827\) | −7156.21 | − | 2325.19i | −0.300902 | − | 0.0977689i | 0.154675 | − | 0.987965i | \(-0.450567\pi\) |
−0.455577 | + | 0.890196i | \(0.650567\pi\) | |||||||
\(828\) | 13669.9 | + | 9931.76i | 0.573746 | + | 0.416851i | ||||
\(829\) | 19742.1 | 0.827106 | 0.413553 | − | 0.910480i | \(-0.364288\pi\) | ||||
0.413553 | + | 0.910480i | \(0.364288\pi\) | |||||||
\(830\) | −13581.7 | − | 9867.71i | −0.567987 | − | 0.412666i | ||||
\(831\) | −8812.74 | + | 12129.7i | −0.367883 | + | 0.506347i | ||||
\(832\) | −13531.3 | − | 18624.2i | −0.563838 | − | 0.776056i | ||||
\(833\) | −22207.5 | + | 7215.67i | −0.923705 | + | 0.300130i | ||||
\(834\) | − | 6624.90i | − | 0.275062i | ||||||
\(835\) | −24773.6 | − | 34097.9i | −1.02674 | − | 1.41318i | ||||
\(836\) | 1808.34 | − | 5565.51i | 0.0748121 | − | 0.230248i | ||||
\(837\) | −4717.31 | + | 6492.81i | −0.194808 | + | 0.268130i | ||||
\(838\) | −48.2718 | − | 148.565i | −0.00198988 | − | 0.00612423i | ||||
\(839\) | 34900.6 | + | 11339.9i | 1.43612 | + | 0.466623i | 0.920684 | − | 0.390308i | \(-0.127631\pi\) |
0.515432 | + | 0.856930i | \(0.327631\pi\) | |||||||
\(840\) | 2534.18 | − | 7799.40i | 0.104092 | − | 0.320363i | ||||
\(841\) | 5556.55 | − | 17101.3i | 0.227830 | − | 0.701190i | ||||
\(842\) | −2406.35 | − | 781.870i | −0.0984895 | − | 0.0320012i | ||||
\(843\) | −3865.54 | − | 11896.9i | −0.157931 | − | 0.486063i | ||||
\(844\) | 4551.05 | − | 6263.98i | 0.185609 | − | 0.255468i | ||||
\(845\) | −19328.6 | + | 59487.4i | −0.786894 | + | 2.42181i | ||||
\(846\) | 538.302 | + | 740.909i | 0.0218761 | + | 0.0301099i | ||||
\(847\) | 4200.20i | 0.170390i | ||||||||
\(848\) | −23925.8 | + | 7773.97i | −0.968886 | + | 0.314810i | ||||
\(849\) | 35571.0 | + | 48959.3i | 1.43792 | + | 1.97913i | ||||
\(850\) | 4833.29 | − | 6652.45i | 0.195036 | − | 0.268444i | ||||
\(851\) | 39472.9 | + | 28678.7i | 1.59003 | + | 1.15522i | ||||
\(852\) | −9215.73 | −0.370570 | ||||||||
\(853\) | 28075.2 | + | 20397.8i | 1.12694 | + | 0.818766i | 0.985246 | − | 0.171145i | \(-0.0547466\pi\) |
0.141689 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(854\) | 1112.35 | + | 361.424i | 0.0445711 | + | 0.0144820i | ||||
\(855\) | −9919.99 | + | 3223.20i | −0.396791 | + | 0.128925i | ||||
\(856\) | 5620.34 | − | 4083.42i | 0.224415 | − | 0.163047i | ||||
\(857\) | −21793.8 | + | 15834.1i | −0.868682 | + | 0.631135i | −0.930233 | − | 0.366969i | \(-0.880395\pi\) |
0.0615506 | + | 0.998104i | \(0.480395\pi\) | |||||||
\(858\) | − | 10563.4i | − | 0.420314i | ||||||
\(859\) | −10402.8 | − | 32016.4i | −0.413199 | − | 1.27170i | −0.913852 | − | 0.406047i | \(-0.866907\pi\) |
0.500653 | − | 0.865648i | \(-0.333093\pi\) | |||||||
\(860\) | 19373.0 | 0.768157 | ||||||||
\(861\) | 11066.8 | + | 1045.73i | 0.438042 | + | 0.0413919i | ||||
\(862\) | −11755.1 | −0.464478 | ||||||||
\(863\) | −405.570 | − | 1248.22i | −0.0159974 | − | 0.0492350i | 0.942739 | − | 0.333531i | \(-0.108240\pi\) |
−0.958737 | + | 0.284296i | \(0.908240\pi\) | |||||||
\(864\) | 5882.63i | 0.231633i | ||||||||
\(865\) | 21368.1 | − | 15524.8i | 0.839928 | − | 0.610244i | ||||
\(866\) | −2725.67 | + | 1980.31i | −0.106954 | + | 0.0777065i | ||||
\(867\) | 6131.93 | − | 1992.38i | 0.240197 | − | 0.0780449i | ||||
\(868\) | 7897.20 | + | 2565.96i | 0.308811 | + | 0.100339i | ||||
\(869\) | 1021.88 | + | 742.441i | 0.0398907 | + | 0.0289823i | ||||
\(870\) | 6948.41 | 0.270774 | ||||||||
\(871\) | −31782.4 | − | 23091.3i | −1.23640 | − | 0.898298i | ||||
\(872\) | −4215.50 | + | 5802.14i | −0.163710 | + | 0.225327i | ||||
\(873\) | 15988.2 | + | 22005.9i | 0.619839 | + | 0.853135i | ||||
\(874\) | −2532.67 | + | 822.914i | −0.0980192 | + | 0.0318484i | ||||
\(875\) | 1386.67i | 0.0535749i | ||||||||
\(876\) | 31909.5 | + | 43919.7i | 1.23073 | + | 1.69396i | ||||
\(877\) | 316.442 | − | 973.908i | 0.0121841 | − | 0.0374989i | −0.944780 | − | 0.327706i | \(-0.893724\pi\) |
0.956964 | + | 0.290207i | \(0.0937243\pi\) | |||||||
\(878\) | 7897.31 | − | 10869.7i | 0.303555 | − | 0.417808i | ||||
\(879\) | −8803.26 | − | 27093.7i | −0.337801 | − | 1.03964i | ||||
\(880\) | −19630.3 | − | 6378.29i | −0.751976 | − | 0.244332i | ||||
\(881\) | 603.439 | − | 1857.20i | 0.0230765 | − | 0.0710221i | −0.938855 | − | 0.344313i | \(-0.888112\pi\) |
0.961932 | + | 0.273290i | \(0.0881120\pi\) | |||||||
\(882\) | −1507.94 | + | 4640.95i | −0.0575679 | + | 0.177176i | ||||
\(883\) | 24829.9 | + | 8067.72i | 0.946310 | + | 0.307475i | 0.741215 | − | 0.671267i | \(-0.234250\pi\) |
0.205095 | + | 0.978742i | \(0.434250\pi\) | |||||||
\(884\) | −13599.0 | − | 41853.4i | −0.517402 | − | 1.59240i | ||||
\(885\) | 48899.4 | − | 67304.3i | 1.85733 | − | 2.55639i | ||||
\(886\) | −520.241 | + | 1601.14i | −0.0197267 | + | 0.0607125i | ||||
\(887\) | −22140.3 | − | 30473.5i | −0.838103 | − | 1.15355i | −0.986360 | − | 0.164601i | \(-0.947366\pi\) |
0.148258 | − | 0.988949i | \(-0.452634\pi\) | |||||||
\(888\) | − | 36301.7i | − | 1.37185i | ||||||
\(889\) | −8492.10 | + | 2759.25i | −0.320378 | + | 0.104097i | ||||
\(890\) | 3047.32 | + | 4194.27i | 0.114771 | + | 0.157969i | ||||
\(891\) | 12854.4 | − | 17692.6i | 0.483322 | − | 0.665236i | ||||
\(892\) | 19737.4 | + | 14340.1i | 0.740872 | + | 0.538275i | ||||
\(893\) | 1782.52 | 0.0667969 | ||||||||
\(894\) | 3079.01 | + | 2237.03i | 0.115187 | + | 0.0836886i | ||||
\(895\) | −30086.0 | − | 9775.53i | −1.12365 | − | 0.365095i | ||||
\(896\) | 7594.26 | − | 2467.52i | 0.283154 | − | 0.0920024i | ||||
\(897\) | 48028.3 | − | 34894.6i | 1.78776 | − | 1.29888i | ||||
\(898\) | −2569.44 | + | 1866.81i | −0.0954827 | + | 0.0693723i | ||||
\(899\) | 14640.8i | 0.543155i | ||||||||
\(900\) | 6558.06 | + | 20183.6i | 0.242891 | + | 0.747542i | ||||
\(901\) | −38491.1 | −1.42323 | ||||||||
\(902\) | −486.041 | + | 5143.67i | −0.0179417 | + | 0.189873i | ||||
\(903\) | 6822.85 | 0.251440 | ||||||||
\(904\) | 218.616 | + | 672.830i | 0.00804320 | + | 0.0247544i | ||||
\(905\) | − | 68173.3i | − | 2.50404i | ||||||
\(906\) | 4752.18 | − | 3452.66i | 0.174261 | − | 0.126608i | ||||
\(907\) | −26176.1 | + | 19018.1i | −0.958284 | + | 0.696234i | −0.952752 | − | 0.303751i | \(-0.901761\pi\) |
−0.00553234 | + | 0.999985i | \(0.501761\pi\) | |||||||
\(908\) | −29158.6 | + | 9474.22i | −1.06571 | + | 0.346270i | ||||
\(909\) | 5678.63 | + | 1845.10i | 0.207204 | + | 0.0673246i | ||||
\(910\) | −4853.45 | − | 3526.24i | −0.176802 | − | 0.128455i | ||||
\(911\) | 26910.1 | 0.978672 | 0.489336 | − | 0.872095i | \(-0.337239\pi\) | ||||
0.489336 | + | 0.872095i | \(0.337239\pi\) | |||||||
\(912\) | −8680.19 | − | 6306.53i | −0.315164 | − | 0.228980i | ||||
\(913\) | −19948.0 | + | 27456.0i | −0.723090 | + | 0.995248i | ||||
\(914\) | 2151.28 | + | 2960.98i | 0.0778532 | + | 0.107156i | ||||
\(915\) | −26265.7 | + | 8534.23i | −0.948979 | + | 0.308342i | ||||
\(916\) | 8412.54i | 0.303448i | ||||||||
\(917\) | −4337.78 | − | 5970.44i | −0.156212 | − | 0.215007i | ||||
\(918\) | −802.637 | + | 2470.26i | −0.0288573 | + | 0.0888135i | ||||
\(919\) | −6830.64 | + | 9401.57i | −0.245182 | + | 0.337464i | −0.913817 | − | 0.406127i | \(-0.866879\pi\) |
0.668635 | + | 0.743591i | \(0.266879\pi\) | |||||||
\(920\) | 6619.49 | + | 20372.7i | 0.237215 | + | 0.730074i | ||||
\(921\) | −58983.1 | − | 19164.8i | −2.11027 | − | 0.685669i | ||||
\(922\) | 2655.19 | − | 8171.84i | 0.0948417 | − | 0.291893i | ||||
\(923\) | −4335.27 | + | 13342.6i | −0.154602 | + | 0.475815i | ||||
\(924\) | −7576.65 | − | 2461.80i | −0.269755 | − | 0.0876487i | ||||
\(925\) | 18936.9 | + | 58281.8i | 0.673126 | + | 2.07167i | ||||
\(926\) | −2312.63 | + | 3183.06i | −0.0820709 | + | 0.112961i | ||||
\(927\) | 2724.39 | − | 8384.80i | 0.0965271 | − | 0.297080i | ||||
\(928\) | 6307.81 | + | 8681.95i | 0.223129 | + | 0.307111i | ||||
\(929\) | − | 38065.6i | − | 1.34434i | −0.740396 | − | 0.672171i | \(-0.765362\pi\) | ||
0.740396 | − | 0.672171i | \(-0.234638\pi\) | |||||||
\(930\) | 15099.4 | − | 4906.08i | 0.532396 | − | 0.172986i | ||||
\(931\) | 5582.72 | + | 7683.96i | 0.196527 | + | 0.270496i | ||||
\(932\) | −4759.90 | + | 6551.44i | −0.167291 | + | 0.230257i | ||||
\(933\) | −49355.1 | − | 35858.6i | −1.73185 | − | 1.25826i | ||||
\(934\) | −6715.76 | −0.235274 | ||||||||
\(935\) | −25549.4 | − | 18562.7i | −0.893640 | − | 0.649267i | ||||
\(936\) | −18201.3 | − | 5913.97i | −0.635608 | − | 0.206522i | ||||
\(937\) | 4742.18 | − | 1540.83i | 0.165337 | − | 0.0537211i | −0.225179 | − | 0.974317i | \(-0.572297\pi\) |
0.390516 | + | 0.920596i | \(0.372297\pi\) | |||||||
\(938\) | 1940.85 | − | 1410.11i | 0.0675596 | − | 0.0490849i | ||||
\(939\) | 17358.6 | − | 12611.8i | 0.603278 | − | 0.438307i | ||||
\(940\) | − | 6890.29i | − | 0.239081i | ||||||
\(941\) | 198.608 | + | 611.251i | 0.00688036 | + | 0.0211756i | 0.954438 | − | 0.298410i | \(-0.0964563\pi\) |
−0.947557 | + | 0.319586i | \(0.896456\pi\) | |||||||
\(942\) | −9095.19 | −0.314583 | ||||||||
\(943\) | −24992.1 | + | 14781.4i | −0.863048 | + | 0.510445i | ||||
\(944\) | 37078.7 | 1.27840 | ||||||||
\(945\) | −1351.29 | − | 4158.86i | −0.0465160 | − | 0.143162i | ||||
\(946\) | 3171.16i | 0.108989i | ||||||||
\(947\) | −25503.0 | + | 18529.0i | −0.875116 | + | 0.635809i | −0.931955 | − | 0.362575i | \(-0.881898\pi\) |
0.0568391 | + | 0.998383i | \(0.481898\pi\) | |||||||
\(948\) | 2053.31 | − | 1491.82i | 0.0703464 | − | 0.0511097i | ||||
\(949\) | 78598.1 | − | 25538.1i | 2.68852 | − | 0.873553i | ||||
\(950\) | −3181.00 | − | 1033.57i | −0.108637 | − | 0.0352983i | ||||
\(951\) | 30823.4 | + | 22394.5i | 1.05102 | + | 0.763608i | ||||
\(952\) | 5592.35 | 0.190388 | ||||||||
\(953\) | −4534.05 | − | 3294.18i | −0.154116 | − | 0.111972i | 0.508055 | − | 0.861325i | \(-0.330365\pi\) |
−0.662171 | + | 0.749353i | \(0.730365\pi\) | |||||||
\(954\) | −4728.09 | + | 6507.66i | −0.160459 | + | 0.220853i | ||||
\(955\) | −16826.4 | − | 23159.6i | −0.570146 | − | 0.784739i | ||||
\(956\) | 9783.55 | − | 3178.87i | 0.330986 | − | 0.107544i | ||||
\(957\) | − | 14046.5i | − | 0.474460i | ||||||
\(958\) | 9075.28 | + | 12491.1i | 0.306064 | + | 0.421261i | ||||
\(959\) | 3950.31 | − | 12157.8i | 0.133016 | − | 0.409381i | ||||
\(960\) | −19511.5 | + | 26855.3i | −0.655971 | + | 0.902866i | ||||
\(961\) | 1131.51 | + | 3482.44i | 0.0379817 | + | 0.116896i | ||||
\(962\) | −25256.4 | − | 8206.29i | −0.846463 | − | 0.275033i | ||||
\(963\) | −3717.14 | + | 11440.2i | −0.124385 | + | 0.382819i | ||||
\(964\) | −2029.73 | + | 6246.87i | −0.0678146 | + | 0.208712i | ||||
\(965\) | 28334.8 | + | 9206.53i | 0.945211 | + | 0.307118i | ||||
\(966\) | 1120.28 | + | 3447.87i | 0.0373130 | + | 0.114838i | ||||
\(967\) | −17646.1 | + | 24287.7i | −0.586824 | + | 0.807694i | −0.994423 | − | 0.105467i | \(-0.966366\pi\) |
0.407599 | + | 0.913161i | \(0.366366\pi\) | |||||||
\(968\) | −2522.46 | + | 7763.34i | −0.0837551 | + | 0.257772i | ||||
\(969\) | −9649.19 | − | 13281.0i | −0.319893 | − | 0.440295i | ||||
\(970\) | 16571.0i | 0.548519i | ||||||||
\(971\) | 9830.86 | − | 3194.24i | 0.324910 | − | 0.105570i | −0.142021 | − | 0.989864i | \(-0.545360\pi\) |
0.466930 | + | 0.884294i | \(0.345360\pi\) | |||||||
\(972\) | −20675.3 | − | 28457.1i | −0.682264 | − | 0.939056i | ||||
\(973\) | −4470.63 | + | 6153.29i | −0.147299 | + | 0.202739i | ||||
\(974\) | −4835.84 | − | 3513.45i | −0.159087 | − | 0.115583i | ||||
\(975\) | 74563.2 | 2.44916 | ||||||||
\(976\) | −9958.15 | − | 7235.02i | −0.326591 | − | 0.237282i | ||||
\(977\) | 13210.6 | + | 4292.38i | 0.432594 | + | 0.140558i | 0.517216 | − | 0.855855i | \(-0.326968\pi\) |
−0.0846222 | + | 0.996413i | \(0.526968\pi\) | |||||||
\(978\) | −9859.73 | + | 3203.62i | −0.322372 | + | 0.104745i | ||||
\(979\) | 8478.89 | − | 6160.28i | 0.276799 | − | 0.201107i | ||||
\(980\) | 29702.2 | − | 21579.9i | 0.968165 | − | 0.703413i | ||||
\(981\) | − | 12418.0i | − | 0.404156i | ||||||
\(982\) | −1588.97 | − | 4890.34i | −0.0516355 | − | 0.158918i | ||||
\(983\) | 46369.0 | 1.50452 | 0.752259 | − | 0.658868i | \(-0.228964\pi\) | ||||
0.752259 | + | 0.658868i | \(0.228964\pi\) | |||||||
\(984\) | 19827.0 | + | 8579.08i | 0.642338 | + | 0.277938i | ||||
\(985\) | 27728.9 | 0.896970 | ||||||||
\(986\) | 1464.22 | + | 4506.42i | 0.0472925 | + | 0.145551i | ||||
\(987\) | − | 2426.64i | − | 0.0782582i | ||||||
\(988\) | −14481.5 | + | 10521.4i | −0.466315 | + | 0.338797i | ||||
\(989\) | −14418.2 | + | 10475.4i | −0.463571 | + | 0.336804i | ||||
\(990\) | −6276.75 | + | 2039.44i | −0.201503 | + | 0.0654724i | ||||
\(991\) | −49000.5 | − | 15921.2i | −1.57069 | − | 0.510347i | −0.611051 | − | 0.791591i | \(-0.709253\pi\) |
−0.959636 | + | 0.281244i | \(0.909253\pi\) | |||||||
\(992\) | 19837.4 | + | 14412.7i | 0.634917 | + | 0.461294i | ||||
\(993\) | 46494.3 | 1.48585 | ||||||||
\(994\) | −693.100 | − | 503.567i | −0.0221165 | − | 0.0160686i | ||||
\(995\) | 20127.2 | − | 27702.8i | 0.641283 | − | 0.882650i | ||||
\(996\) | 40082.3 | + | 55168.5i | 1.27516 | + | 1.75510i | ||||
\(997\) | −32857.0 | + | 10675.9i | −1.04372 | + | 0.339126i | −0.780202 | − | 0.625527i | \(-0.784884\pi\) |
−0.263521 | + | 0.964654i | \(0.584884\pi\) | |||||||
\(998\) | − | 17024.3i | − | 0.539974i | ||||||
\(999\) | −11377.8 | − | 15660.2i | −0.360338 | − | 0.495962i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 41.4.f.a.23.6 | ✓ | 40 | |
41.5 | even | 20 | 1681.4.a.l.1.17 | 40 | |||
41.25 | even | 10 | inner | 41.4.f.a.25.6 | yes | 40 | |
41.36 | even | 20 | 1681.4.a.l.1.18 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.4.f.a.23.6 | ✓ | 40 | 1.1 | even | 1 | trivial | |
41.4.f.a.25.6 | yes | 40 | 41.25 | even | 10 | inner | |
1681.4.a.l.1.17 | 40 | 41.5 | even | 20 | |||
1681.4.a.l.1.18 | 40 | 41.36 | even | 20 |