Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(104,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.104");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.g (of order \(2\), degree \(1\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 104.15 | ||
Character | \(\chi\) | \(=\) | 105.104 |
Dual form | 105.4.g.b.104.16 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.24438 | −0.793509 | −0.396754 | − | 0.917925i | \(-0.629864\pi\) | ||||
−0.396754 | + | 0.917925i | \(0.629864\pi\) | |||||||
\(3\) | 1.06702 | − | 5.08542i | 0.205347 | − | 0.978689i | ||||
\(4\) | −2.96275 | −0.370344 | ||||||||
\(5\) | −8.51335 | − | 7.24727i | −0.761457 | − | 0.648215i | ||||
\(6\) | −2.39479 | + | 11.4136i | −0.162945 | + | 0.776599i | ||||
\(7\) | −12.2768 | + | 13.8665i | −0.662886 | + | 0.748721i | ||||
\(8\) | 24.6046 | 1.08738 | ||||||||
\(9\) | −24.7230 | − | 10.8524i | −0.915665 | − | 0.401943i | ||||
\(10\) | 19.1072 | + | 16.2656i | 0.604223 | + | 0.514365i | ||||
\(11\) | 25.7488i | 0.705779i | 0.935665 | + | 0.352889i | \(0.114801\pi\) | ||||
−0.935665 | + | 0.352889i | \(0.885199\pi\) | |||||||
\(12\) | −3.16130 | + | 15.0668i | −0.0760491 | + | 0.362451i | ||||
\(13\) | 68.2910 | 1.45696 | 0.728481 | − | 0.685066i | \(-0.240227\pi\) | ||||
0.728481 | + | 0.685066i | \(0.240227\pi\) | |||||||
\(14\) | 27.5539 | − | 31.1217i | 0.526006 | − | 0.594116i | ||||
\(15\) | −45.9393 | + | 35.5610i | −0.790764 | + | 0.612121i | ||||
\(16\) | −31.5201 | −0.492502 | ||||||||
\(17\) | − | 30.6502i | − | 0.437281i | −0.975806 | − | 0.218640i | \(-0.929838\pi\) | ||
0.975806 | − | 0.218640i | \(-0.0701621\pi\) | |||||||
\(18\) | 55.4878 | + | 24.3570i | 0.726588 | + | 0.318945i | ||||
\(19\) | 109.632i | 1.32375i | 0.749615 | + | 0.661874i | \(0.230239\pi\) | ||||
−0.749615 | + | 0.661874i | \(0.769761\pi\) | |||||||
\(20\) | 25.2229 | + | 21.4718i | 0.282001 | + | 0.240062i | ||||
\(21\) | 57.4174 | + | 77.2285i | 0.596643 | + | 0.802507i | ||||
\(22\) | − | 57.7902i | − | 0.560042i | ||||||
\(23\) | −152.265 | −1.38041 | −0.690206 | − | 0.723613i | \(-0.742480\pi\) | ||||
−0.690206 | + | 0.723613i | \(0.742480\pi\) | |||||||
\(24\) | 26.2535 | − | 125.125i | 0.223291 | − | 1.06421i | ||||
\(25\) | 19.9543 | + | 123.397i | 0.159634 | + | 0.987176i | ||||
\(26\) | −153.271 | −1.15611 | ||||||||
\(27\) | −81.5690 | + | 114.147i | −0.581406 | + | 0.813613i | ||||
\(28\) | 36.3731 | − | 41.0829i | 0.245495 | − | 0.277284i | ||||
\(29\) | 191.763i | 1.22791i | 0.789340 | + | 0.613956i | \(0.210423\pi\) | ||||
−0.789340 | + | 0.613956i | \(0.789577\pi\) | |||||||
\(30\) | 103.105 | − | 79.8125i | 0.627479 | − | 0.485723i | ||||
\(31\) | 16.4683i | 0.0954130i | 0.998861 | + | 0.0477065i | \(0.0151912\pi\) | ||||
−0.998861 | + | 0.0477065i | \(0.984809\pi\) | |||||||
\(32\) | −126.094 | −0.696575 | ||||||||
\(33\) | 130.944 | + | 27.4744i | 0.690738 | + | 0.144930i | ||||
\(34\) | 68.7908i | 0.346986i | ||||||||
\(35\) | 205.011 | − | 29.0770i | 0.990091 | − | 0.140426i | ||||
\(36\) | 73.2479 | + | 32.1531i | 0.339111 | + | 0.148857i | ||||
\(37\) | − | 81.9337i | − | 0.364049i | −0.983294 | − | 0.182025i | \(-0.941735\pi\) | ||
0.983294 | − | 0.182025i | \(-0.0582651\pi\) | |||||||
\(38\) | − | 246.055i | − | 1.05041i | ||||||
\(39\) | 72.8676 | − | 347.288i | 0.299183 | − | 1.42591i | ||||
\(40\) | −209.468 | − | 178.316i | −0.827993 | − | 0.704856i | ||||
\(41\) | −372.656 | −1.41949 | −0.709745 | − | 0.704459i | \(-0.751190\pi\) | ||||
−0.709745 | + | 0.704459i | \(0.751190\pi\) | |||||||
\(42\) | −128.867 | − | 173.330i | −0.473441 | − | 0.636796i | ||||
\(43\) | − | 192.593i | − | 0.683028i | −0.939877 | − | 0.341514i | \(-0.889060\pi\) | ||
0.939877 | − | 0.341514i | \(-0.110940\pi\) | |||||||
\(44\) | − | 76.2873i | − | 0.261381i | ||||||
\(45\) | 131.825 | + | 271.565i | 0.436694 | + | 0.899610i | ||||
\(46\) | 341.741 | 1.09537 | ||||||||
\(47\) | 0.366739i | 0.00113818i | 1.00000 | 0.000569089i | \(0.000181147\pi\) | |||||
−1.00000 | 0.000569089i | \(0.999819\pi\) | ||||||||
\(48\) | −33.6325 | + | 160.293i | −0.101134 | + | 0.482006i | ||||
\(49\) | −41.5595 | − | 340.473i | −0.121165 | − | 0.992632i | ||||
\(50\) | −44.7850 | − | 276.950i | −0.126671 | − | 0.783333i | ||||
\(51\) | −155.869 | − | 32.7043i | −0.427962 | − | 0.0897944i | ||||
\(52\) | −202.329 | −0.539576 | ||||||||
\(53\) | 5.95065 | 0.0154223 | 0.00771117 | − | 0.999970i | \(-0.497545\pi\) | ||||
0.00771117 | + | 0.999970i | \(0.497545\pi\) | |||||||
\(54\) | 183.072 | − | 256.189i | 0.461351 | − | 0.645610i | ||||
\(55\) | 186.609 | − | 219.209i | 0.457497 | − | 0.537420i | ||||
\(56\) | −302.066 | + | 341.180i | −0.720809 | + | 0.814144i | ||||
\(57\) | 557.523 | + | 116.979i | 1.29554 | + | 0.271828i | ||||
\(58\) | − | 430.389i | − | 0.974359i | ||||||
\(59\) | 198.813 | 0.438699 | 0.219349 | − | 0.975646i | \(-0.429607\pi\) | ||||
0.219349 | + | 0.975646i | \(0.429607\pi\) | |||||||
\(60\) | 136.106 | − | 105.358i | 0.292855 | − | 0.226695i | ||||
\(61\) | 83.5752i | 0.175421i | 0.996146 | + | 0.0877107i | \(0.0279551\pi\) | ||||
−0.996146 | + | 0.0877107i | \(0.972045\pi\) | |||||||
\(62\) | − | 36.9613i | − | 0.0757110i | ||||||
\(63\) | 454.005 | − | 209.587i | 0.907924 | − | 0.419135i | ||||
\(64\) | 535.163 | 1.04524 | ||||||||
\(65\) | −581.385 | − | 494.923i | −1.10941 | − | 0.944425i | ||||
\(66\) | −293.887 | − | 61.6631i | −0.548107 | − | 0.115003i | ||||
\(67\) | 1080.15i | 1.96958i | 0.173757 | + | 0.984789i | \(0.444409\pi\) | ||||
−0.173757 | + | 0.984789i | \(0.555591\pi\) | |||||||
\(68\) | 90.8089i | 0.161944i | ||||||||
\(69\) | −162.469 | + | 774.332i | −0.283464 | + | 1.35099i | ||||
\(70\) | −460.123 | + | 65.2599i | −0.785646 | + | 0.111429i | ||||
\(71\) | 773.288i | 1.29257i | 0.763097 | + | 0.646284i | \(0.223678\pi\) | ||||
−0.763097 | + | 0.646284i | \(0.776322\pi\) | |||||||
\(72\) | −608.298 | − | 267.020i | −0.995676 | − | 0.437064i | ||||
\(73\) | −448.111 | −0.718459 | −0.359229 | − | 0.933249i | \(-0.616960\pi\) | ||||
−0.359229 | + | 0.933249i | \(0.616960\pi\) | |||||||
\(74\) | 183.891i | 0.288876i | ||||||||
\(75\) | 648.817 | + | 30.1909i | 0.998919 | + | 0.0464820i | ||||
\(76\) | − | 324.811i | − | 0.490242i | ||||||
\(77\) | −357.046 | − | 316.114i | −0.528431 | − | 0.467851i | ||||
\(78\) | −163.543 | + | 779.447i | −0.237405 | + | 1.13147i | ||||
\(79\) | −1270.27 | −1.80908 | −0.904538 | − | 0.426393i | \(-0.859784\pi\) | ||||
−0.904538 | + | 0.426393i | \(0.859784\pi\) | |||||||
\(80\) | 268.342 | + | 228.435i | 0.375019 | + | 0.319247i | ||||
\(81\) | 493.449 | + | 536.609i | 0.676884 | + | 0.736089i | ||||
\(82\) | 836.382 | 1.12638 | ||||||||
\(83\) | − | 429.749i | − | 0.568327i | −0.958776 | − | 0.284163i | \(-0.908284\pi\) | ||
0.958776 | − | 0.284163i | \(-0.0917158\pi\) | |||||||
\(84\) | −170.113 | − | 228.809i | −0.220963 | − | 0.297203i | ||||
\(85\) | −222.130 | + | 260.936i | −0.283452 | + | 0.332971i | ||||
\(86\) | 432.253i | 0.541989i | ||||||||
\(87\) | 975.193 | + | 204.614i | 1.20174 | + | 0.252148i | ||||
\(88\) | 633.540i | 0.767450i | ||||||||
\(89\) | −5.29611 | −0.00630772 | −0.00315386 | − | 0.999995i | \(-0.501004\pi\) | ||||
−0.00315386 | + | 0.999995i | \(0.501004\pi\) | |||||||
\(90\) | −295.865 | − | 609.495i | −0.346521 | − | 0.713849i | ||||
\(91\) | −838.395 | + | 946.956i | −0.965799 | + | 1.09086i | ||||
\(92\) | 451.123 | 0.511227 | ||||||||
\(93\) | 83.7484 | + | 17.5720i | 0.0933796 | + | 0.0195928i | ||||
\(94\) | − | 0.823102i | − | 0.000903154i | ||||||
\(95\) | 794.530 | − | 933.333i | 0.858074 | − | 1.00798i | ||||
\(96\) | −134.544 | + | 641.238i | −0.143040 | + | 0.681730i | ||||
\(97\) | 435.169 | 0.455513 | 0.227757 | − | 0.973718i | \(-0.426861\pi\) | ||||
0.227757 | + | 0.973718i | \(0.426861\pi\) | |||||||
\(98\) | 93.2755 | + | 764.151i | 0.0961454 | + | 0.787663i | ||||
\(99\) | 279.438 | − | 636.587i | 0.283682 | − | 0.646257i | ||||
\(100\) | −59.1194 | − | 365.594i | −0.0591194 | − | 0.365594i | ||||
\(101\) | −1122.41 | −1.10578 | −0.552891 | − | 0.833254i | \(-0.686475\pi\) | ||||
−0.552891 | + | 0.833254i | \(0.686475\pi\) | |||||||
\(102\) | 349.830 | + | 73.4009i | 0.339592 | + | 0.0712527i | ||||
\(103\) | −625.230 | −0.598114 | −0.299057 | − | 0.954235i | \(-0.596672\pi\) | ||||
−0.299057 | + | 0.954235i | \(0.596672\pi\) | |||||||
\(104\) | 1680.27 | 1.58427 | ||||||||
\(105\) | 70.8815 | − | 1073.59i | 0.0658793 | − | 0.997828i | ||||
\(106\) | −13.3555 | −0.0122378 | ||||||||
\(107\) | 988.994 | 0.893548 | 0.446774 | − | 0.894647i | \(-0.352573\pi\) | ||||
0.446774 | + | 0.894647i | \(0.352573\pi\) | |||||||
\(108\) | 241.669 | − | 338.188i | 0.215320 | − | 0.301317i | ||||
\(109\) | 810.973 | 0.712634 | 0.356317 | − | 0.934365i | \(-0.384032\pi\) | ||||
0.356317 | + | 0.934365i | \(0.384032\pi\) | |||||||
\(110\) | −418.821 | + | 491.988i | −0.363028 | + | 0.426448i | ||||
\(111\) | −416.667 | − | 87.4246i | −0.356291 | − | 0.0747566i | ||||
\(112\) | 386.967 | − | 437.074i | 0.326473 | − | 0.368746i | ||||
\(113\) | −107.711 | −0.0896687 | −0.0448343 | − | 0.998994i | \(-0.514276\pi\) | ||||
−0.0448343 | + | 0.998994i | \(0.514276\pi\) | |||||||
\(114\) | −1251.29 | − | 262.545i | −1.02802 | − | 0.215698i | ||||
\(115\) | 1296.29 | + | 1103.51i | 1.05112 | + | 0.894804i | ||||
\(116\) | − | 568.145i | − | 0.454749i | ||||||
\(117\) | −1688.35 | − | 741.124i | −1.33409 | − | 0.585615i | ||||
\(118\) | −446.212 | −0.348111 | ||||||||
\(119\) | 425.011 | + | 376.287i | 0.327401 | + | 0.289867i | ||||
\(120\) | −1130.32 | + | 874.964i | −0.859861 | + | 0.665608i | ||||
\(121\) | 667.997 | 0.501876 | ||||||||
\(122\) | − | 187.575i | − | 0.139199i | ||||||
\(123\) | −397.630 | + | 1895.11i | −0.291488 | + | 1.38924i | ||||
\(124\) | − | 48.7916i | − | 0.0353356i | ||||||
\(125\) | 724.414 | − | 1195.14i | 0.518348 | − | 0.855170i | ||||
\(126\) | −1018.96 | + | 470.394i | −0.720446 | + | 0.332587i | ||||
\(127\) | 33.0601i | 0.0230993i | 0.999933 | + | 0.0115496i | \(0.00367645\pi\) | ||||
−0.999933 | + | 0.0115496i | \(0.996324\pi\) | |||||||
\(128\) | −192.362 | −0.132833 | ||||||||
\(129\) | −979.418 | − | 205.500i | −0.668472 | − | 0.140258i | ||||
\(130\) | 1304.85 | + | 1110.80i | 0.880330 | + | 0.749409i | ||||
\(131\) | −997.301 | −0.665150 | −0.332575 | − | 0.943077i | \(-0.607917\pi\) | ||||
−0.332575 | + | 0.943077i | \(0.607917\pi\) | |||||||
\(132\) | −387.953 | − | 81.3998i | −0.255810 | − | 0.0536738i | ||||
\(133\) | −1520.21 | − | 1345.93i | −0.991118 | − | 0.877494i | ||||
\(134\) | − | 2424.28i | − | 1.56288i | ||||||
\(135\) | 1521.68 | − | 380.619i | 0.970113 | − | 0.242655i | ||||
\(136\) | − | 754.136i | − | 0.475490i | ||||||
\(137\) | −1373.30 | −0.856418 | −0.428209 | − | 0.903680i | \(-0.640855\pi\) | ||||
−0.428209 | + | 0.903680i | \(0.640855\pi\) | |||||||
\(138\) | 364.643 | − | 1737.90i | 0.224931 | − | 1.07203i | ||||
\(139\) | − | 1361.65i | − | 0.830891i | −0.909618 | − | 0.415446i | \(-0.863626\pi\) | ||
0.909618 | − | 0.415446i | \(-0.136374\pi\) | |||||||
\(140\) | −607.396 | + | 86.1478i | −0.366674 | + | 0.0520058i | ||||
\(141\) | 1.86502 | + | 0.391316i | 0.00111392 | + | 0.000233722i | ||||
\(142\) | − | 1735.55i | − | 1.02567i | ||||||
\(143\) | 1758.41i | 1.02829i | ||||||||
\(144\) | 779.271 | + | 342.071i | 0.450967 | + | 0.197958i | ||||
\(145\) | 1389.76 | − | 1632.54i | 0.795951 | − | 0.935002i | ||||
\(146\) | 1005.73 | 0.570103 | ||||||||
\(147\) | −1775.79 | − | 151.942i | −0.996359 | − | 0.0852517i | ||||
\(148\) | 242.749i | 0.134823i | ||||||||
\(149\) | 2971.73i | 1.63392i | 0.576697 | + | 0.816958i | \(0.304341\pi\) | ||||
−0.576697 | + | 0.816958i | \(0.695659\pi\) | |||||||
\(150\) | −1456.19 | − | 67.7600i | −0.792651 | − | 0.0368839i | ||||
\(151\) | 1456.31 | 0.784851 | 0.392425 | − | 0.919784i | \(-0.371636\pi\) | ||||
0.392425 | + | 0.919784i | \(0.371636\pi\) | |||||||
\(152\) | 2697.44i | 1.43942i | ||||||||
\(153\) | −332.630 | + | 757.764i | −0.175762 | + | 0.400403i | ||||
\(154\) | 801.348 | + | 709.480i | 0.419315 | + | 0.371244i | ||||
\(155\) | 119.350 | − | 140.201i | 0.0618481 | − | 0.0726529i | ||||
\(156\) | −215.888 | + | 1028.93i | −0.110801 | + | 0.528078i | ||||
\(157\) | −2903.14 | −1.47577 | −0.737885 | − | 0.674927i | \(-0.764175\pi\) | ||||
−0.737885 | + | 0.674927i | \(0.764175\pi\) | |||||||
\(158\) | 2850.98 | 1.43552 | ||||||||
\(159\) | 6.34944 | − | 30.2615i | 0.00316694 | − | 0.0150937i | ||||
\(160\) | 1073.48 | + | 913.834i | 0.530412 | + | 0.451531i | ||||
\(161\) | 1869.33 | − | 2111.38i | 0.915056 | − | 1.03354i | ||||
\(162\) | −1107.49 | − | 1204.36i | −0.537114 | − | 0.584093i | ||||
\(163\) | − | 1666.60i | − | 0.800850i | −0.916330 | − | 0.400425i | \(-0.868863\pi\) | ||
0.916330 | − | 0.400425i | \(-0.131137\pi\) | |||||||
\(164\) | 1104.09 | 0.525699 | ||||||||
\(165\) | −915.654 | − | 1182.88i | −0.432022 | − | 0.558105i | ||||
\(166\) | 964.522i | 0.450972i | ||||||||
\(167\) | 1688.52i | 0.782403i | 0.920305 | + | 0.391201i | \(0.127940\pi\) | ||||
−0.920305 | + | 0.391201i | \(0.872060\pi\) | |||||||
\(168\) | 1412.73 | + | 1900.18i | 0.648777 | + | 0.872630i | ||||
\(169\) | 2466.65 | 1.12274 | ||||||||
\(170\) | 498.545 | − | 585.640i | 0.224922 | − | 0.264215i | ||||
\(171\) | 1189.77 | − | 2710.42i | 0.532071 | − | 1.21211i | ||||
\(172\) | 570.606i | 0.252955i | ||||||||
\(173\) | − | 719.668i | − | 0.316274i | −0.987417 | − | 0.158137i | \(-0.949451\pi\) | ||
0.987417 | − | 0.158137i | \(-0.0505487\pi\) | |||||||
\(174\) | −2188.71 | − | 459.232i | −0.953594 | − | 0.200082i | ||||
\(175\) | −1956.06 | − | 1238.23i | −0.844938 | − | 0.534864i | ||||
\(176\) | − | 811.607i | − | 0.347598i | ||||||
\(177\) | 212.136 | − | 1011.05i | 0.0900856 | − | 0.429350i | ||||
\(178\) | 11.8865 | 0.00500523 | ||||||||
\(179\) | 1130.92i | 0.472231i | 0.971725 | + | 0.236115i | \(0.0758743\pi\) | ||||
−0.971725 | + | 0.236115i | \(0.924126\pi\) | |||||||
\(180\) | −390.563 | − | 804.577i | −0.161727 | − | 0.333165i | ||||
\(181\) | − | 1072.04i | − | 0.440243i | −0.975472 | − | 0.220121i | \(-0.929355\pi\) | ||
0.975472 | − | 0.220121i | \(-0.0706453\pi\) | |||||||
\(182\) | 1881.68 | − | 2125.33i | 0.766370 | − | 0.865605i | ||||
\(183\) | 425.015 | + | 89.1761i | 0.171683 | + | 0.0360223i | ||||
\(184\) | −3746.42 | −1.50103 | ||||||||
\(185\) | −593.796 | + | 697.530i | −0.235982 | + | 0.277208i | ||||
\(186\) | −187.963 | − | 39.4383i | −0.0740976 | − | 0.0155471i | ||||
\(187\) | 789.208 | 0.308623 | ||||||||
\(188\) | − | 1.08655i | − | 0.000421517i | ||||||
\(189\) | −581.409 | − | 2532.44i | −0.223763 | − | 0.974644i | ||||
\(190\) | −1783.23 | + | 2094.75i | −0.680889 | + | 0.799839i | ||||
\(191\) | − | 1611.22i | − | 0.610386i | −0.952291 | − | 0.305193i | \(-0.901279\pi\) | ||
0.952291 | − | 0.305193i | \(-0.0987209\pi\) | |||||||
\(192\) | 571.028 | − | 2721.53i | 0.214637 | − | 1.02297i | ||||
\(193\) | − | 1961.99i | − | 0.731747i | −0.930665 | − | 0.365874i | \(-0.880770\pi\) | ||
0.930665 | − | 0.365874i | \(-0.119230\pi\) | |||||||
\(194\) | −976.687 | −0.361454 | ||||||||
\(195\) | −3137.24 | + | 2428.49i | −1.15211 | + | 0.891836i | ||||
\(196\) | 123.130 | + | 1008.74i | 0.0448726 | + | 0.367615i | ||||
\(197\) | −658.980 | −0.238327 | −0.119163 | − | 0.992875i | \(-0.538021\pi\) | ||||
−0.119163 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(198\) | −627.165 | + | 1428.75i | −0.225105 | + | 0.512811i | ||||
\(199\) | 5062.64i | 1.80342i | 0.432338 | + | 0.901712i | \(0.357689\pi\) | ||||
−0.432338 | + | 0.901712i | \(0.642311\pi\) | |||||||
\(200\) | 490.966 | + | 3036.13i | 0.173583 | + | 1.07344i | ||||
\(201\) | 5493.03 | + | 1152.54i | 1.92760 | + | 0.404447i | ||||
\(202\) | 2519.12 | 0.877447 | ||||||||
\(203\) | −2659.08 | − | 2354.23i | −0.919362 | − | 0.813965i | ||||
\(204\) | 461.801 | + | 96.8946i | 0.158493 | + | 0.0332548i | ||||
\(205\) | 3172.55 | + | 2700.74i | 1.08088 | + | 0.920135i | ||||
\(206\) | 1403.26 | 0.474609 | ||||||||
\(207\) | 3764.44 | + | 1652.45i | 1.26399 | + | 0.554846i | ||||
\(208\) | −2152.54 | −0.717557 | ||||||||
\(209\) | −2822.89 | −0.934274 | ||||||||
\(210\) | −159.085 | + | 2409.55i | −0.0522758 | + | 0.791785i | ||||
\(211\) | −3467.27 | −1.13126 | −0.565631 | − | 0.824658i | \(-0.691368\pi\) | ||||
−0.565631 | + | 0.824658i | \(0.691368\pi\) | |||||||
\(212\) | −17.6303 | −0.00571157 | ||||||||
\(213\) | 3932.49 | + | 825.111i | 1.26502 | + | 0.265426i | ||||
\(214\) | −2219.68 | −0.709038 | ||||||||
\(215\) | −1395.78 | + | 1639.61i | −0.442749 | + | 0.520097i | ||||
\(216\) | −2006.97 | + | 2808.54i | −0.632209 | + | 0.884707i | ||||
\(217\) | −228.358 | − | 202.179i | −0.0714376 | − | 0.0632479i | ||||
\(218\) | −1820.13 | −0.565481 | ||||||||
\(219\) | −478.142 | + | 2278.83i | −0.147534 | + | 0.703148i | ||||
\(220\) | −552.875 | + | 649.461i | −0.169431 | + | 0.199030i | ||||
\(221\) | − | 2093.13i | − | 0.637101i | ||||||
\(222\) | 935.161 | + | 196.214i | 0.282720 | + | 0.0593200i | ||||
\(223\) | 2047.08 | 0.614720 | 0.307360 | − | 0.951593i | \(-0.400555\pi\) | ||||
0.307360 | + | 0.951593i | \(0.400555\pi\) | |||||||
\(224\) | 1548.03 | − | 1748.48i | 0.461750 | − | 0.521540i | ||||
\(225\) | 845.832 | − | 3267.29i | 0.250617 | − | 0.968086i | ||||
\(226\) | 241.744 | 0.0711529 | ||||||||
\(227\) | − | 3998.46i | − | 1.16911i | −0.811355 | − | 0.584553i | \(-0.801270\pi\) | ||
0.811355 | − | 0.584553i | \(-0.198730\pi\) | |||||||
\(228\) | −1651.80 | − | 346.579i | −0.479794 | − | 0.100670i | ||||
\(229\) | − | 3325.60i | − | 0.959659i | −0.877362 | − | 0.479829i | \(-0.840699\pi\) | ||
0.877362 | − | 0.479829i | \(-0.159301\pi\) | |||||||
\(230\) | −2909.36 | − | 2476.69i | −0.834077 | − | 0.710035i | ||||
\(231\) | −1988.54 | + | 1478.43i | −0.566392 | + | 0.421098i | ||||
\(232\) | 4718.24i | 1.33521i | ||||||||
\(233\) | 3464.53 | 0.974116 | 0.487058 | − | 0.873370i | \(-0.338070\pi\) | ||||
0.487058 | + | 0.873370i | \(0.338070\pi\) | |||||||
\(234\) | 3789.31 | + | 1663.37i | 1.05861 | + | 0.464691i | ||||
\(235\) | 2.65785 | − | 3.12217i | 0.000737784 | − | 0.000866673i | ||||
\(236\) | −589.032 | −0.162469 | ||||||||
\(237\) | −1355.40 | + | 6459.88i | −0.371489 | + | 1.77052i | ||||
\(238\) | −953.888 | − | 844.532i | −0.259796 | − | 0.230012i | ||||
\(239\) | 4519.56i | 1.22321i | 0.791165 | + | 0.611603i | \(0.209475\pi\) | ||||
−0.791165 | + | 0.611603i | \(0.790525\pi\) | |||||||
\(240\) | 1448.01 | − | 1120.89i | 0.389453 | − | 0.301471i | ||||
\(241\) | − | 7087.15i | − | 1.89429i | −0.320810 | − | 0.947143i | \(-0.603955\pi\) | ||
0.320810 | − | 0.947143i | \(-0.396045\pi\) | |||||||
\(242\) | −1499.24 | −0.398243 | ||||||||
\(243\) | 3255.40 | − | 1936.82i | 0.859399 | − | 0.511305i | ||||
\(244\) | − | 247.612i | − | 0.0649662i | ||||||
\(245\) | −2113.69 | + | 3199.76i | −0.551178 | + | 0.834388i | ||||
\(246\) | 892.433 | − | 4253.35i | 0.231299 | − | 1.10237i | ||||
\(247\) | 7486.85i | 1.92865i | ||||||||
\(248\) | 405.197i | 0.103750i | ||||||||
\(249\) | −2185.46 | − | 458.550i | −0.556215 | − | 0.116704i | ||||
\(250\) | −1625.86 | + | 2682.34i | −0.411314 | + | 0.678585i | ||||
\(251\) | 4749.21 | 1.19429 | 0.597146 | − | 0.802132i | \(-0.296301\pi\) | ||||
0.597146 | + | 0.802132i | \(0.296301\pi\) | |||||||
\(252\) | −1345.10 | + | 620.954i | −0.336244 | + | 0.155224i | ||||
\(253\) | − | 3920.65i | − | 0.974266i | ||||||
\(254\) | − | 74.1995i | − | 0.0183295i | ||||||
\(255\) | 1089.95 | + | 1408.05i | 0.267669 | + | 0.345786i | ||||
\(256\) | −3849.57 | −0.939837 | ||||||||
\(257\) | 1571.33i | 0.381389i | 0.981649 | + | 0.190695i | \(0.0610740\pi\) | ||||
−0.981649 | + | 0.190695i | \(0.938926\pi\) | |||||||
\(258\) | 2198.19 | + | 461.221i | 0.530439 | + | 0.111296i | ||||
\(259\) | 1136.13 | + | 1005.89i | 0.272571 | + | 0.241323i | ||||
\(260\) | 1722.50 | + | 1466.33i | 0.410864 | + | 0.349762i | ||||
\(261\) | 2081.09 | − | 4740.94i | 0.493550 | − | 1.12436i | ||||
\(262\) | 2238.33 | 0.527802 | ||||||||
\(263\) | −5430.48 | −1.27322 | −0.636612 | − | 0.771184i | \(-0.719665\pi\) | ||||
−0.636612 | + | 0.771184i | \(0.719665\pi\) | |||||||
\(264\) | 3221.81 | + | 675.997i | 0.751095 | + | 0.157594i | ||||
\(265\) | −50.6599 | − | 43.1259i | −0.0117435 | − | 0.00999700i | ||||
\(266\) | 3411.93 | + | 3020.78i | 0.786461 | + | 0.696299i | ||||
\(267\) | −5.65104 | + | 26.9330i | −0.00129527 | + | 0.00617330i | ||||
\(268\) | − | 3200.22i | − | 0.729420i | ||||||
\(269\) | −5118.42 | −1.16013 | −0.580066 | − | 0.814570i | \(-0.696973\pi\) | ||||
−0.580066 | + | 0.814570i | \(0.696973\pi\) | |||||||
\(270\) | −3415.23 | + | 854.255i | −0.769793 | + | 0.192549i | ||||
\(271\) | 6280.28i | 1.40775i | 0.710324 | + | 0.703875i | \(0.248548\pi\) | ||||
−0.710324 | + | 0.703875i | \(0.751452\pi\) | |||||||
\(272\) | 966.099i | 0.215362i | ||||||||
\(273\) | 3921.09 | + | 5274.01i | 0.869286 | + | 1.16922i | ||||
\(274\) | 3082.22 | 0.679575 | ||||||||
\(275\) | −3177.33 | + | 513.799i | −0.696728 | + | 0.112666i | ||||
\(276\) | 481.356 | − | 2294.15i | 0.104979 | − | 0.500332i | ||||
\(277\) | − | 5807.51i | − | 1.25971i | −0.776713 | − | 0.629854i | \(-0.783115\pi\) | ||
0.776713 | − | 0.629854i | \(-0.216885\pi\) | |||||||
\(278\) | 3056.07i | 0.659320i | ||||||||
\(279\) | 178.722 | − | 407.146i | 0.0383505 | − | 0.0873663i | ||||
\(280\) | 5044.21 | − | 715.428i | 1.07661 | − | 0.152696i | ||||
\(281\) | − | 201.056i | − | 0.0426833i | −0.999772 | − | 0.0213416i | \(-0.993206\pi\) | ||
0.999772 | − | 0.0213416i | \(-0.00679377\pi\) | |||||||
\(282\) | −4.18582 | − | 0.878263i | −0.000883907 | − | 0.000185460i | ||||
\(283\) | −4808.75 | −1.01007 | −0.505036 | − | 0.863098i | \(-0.668521\pi\) | ||||
−0.505036 | + | 0.863098i | \(0.668521\pi\) | |||||||
\(284\) | − | 2291.06i | − | 0.478695i | ||||||
\(285\) | −3898.61 | − | 5036.40i | −0.810294 | − | 1.04677i | ||||
\(286\) | − | 3946.55i | − | 0.815959i | ||||||
\(287\) | 4575.03 | − | 5167.43i | 0.940959 | − | 1.06280i | ||||
\(288\) | 3117.40 | + | 1368.42i | 0.637829 | + | 0.279983i | ||||
\(289\) | 3973.56 | 0.808786 | ||||||||
\(290\) | −3119.14 | + | 3664.05i | −0.631594 | + | 0.741932i | ||||
\(291\) | 464.333 | − | 2213.02i | 0.0935384 | − | 0.445806i | ||||
\(292\) | 1327.64 | 0.266076 | ||||||||
\(293\) | − | 6701.42i | − | 1.33618i | −0.744080 | − | 0.668091i | \(-0.767112\pi\) | ||
0.744080 | − | 0.668091i | \(-0.232888\pi\) | |||||||
\(294\) | 3985.56 | + | 341.017i | 0.790620 | + | 0.0676480i | ||||
\(295\) | −1692.56 | − | 1440.85i | −0.334050 | − | 0.284371i | ||||
\(296\) | − | 2015.95i | − | 0.395860i | ||||||
\(297\) | −2939.15 | − | 2100.31i | −0.574231 | − | 0.410344i | ||||
\(298\) | − | 6669.69i | − | 1.29653i | ||||||
\(299\) | −10398.3 | −2.01121 | ||||||||
\(300\) | −1922.28 | − | 89.4482i | −0.369943 | − | 0.0172143i | ||||
\(301\) | 2670.60 | + | 2364.43i | 0.511397 | + | 0.452770i | ||||
\(302\) | −3268.51 | −0.622786 | ||||||||
\(303\) | −1197.63 | + | 5707.92i | −0.227069 | + | 1.08222i | ||||
\(304\) | − | 3455.60i | − | 0.651949i | ||||||
\(305\) | 605.692 | − | 711.505i | 0.113711 | − | 0.133576i | ||||
\(306\) | 746.549 | − | 1700.71i | 0.139468 | − | 0.317723i | ||||
\(307\) | 1476.12 | 0.274419 | 0.137209 | − | 0.990542i | \(-0.456187\pi\) | ||||
0.137209 | + | 0.990542i | \(0.456187\pi\) | |||||||
\(308\) | 1057.84 | + | 936.566i | 0.195701 | + | 0.173266i | ||||
\(309\) | −667.131 | + | 3179.56i | −0.122821 | + | 0.585368i | ||||
\(310\) | −267.868 | + | 314.664i | −0.0490771 | + | 0.0576507i | ||||
\(311\) | −2162.00 | −0.394199 | −0.197100 | − | 0.980383i | \(-0.563152\pi\) | ||||
−0.197100 | + | 0.980383i | \(0.563152\pi\) | |||||||
\(312\) | 1792.88 | − | 8544.88i | 0.325326 | − | 1.55051i | ||||
\(313\) | −1187.83 | −0.214505 | −0.107253 | − | 0.994232i | \(-0.534205\pi\) | ||||
−0.107253 | + | 0.994232i | \(0.534205\pi\) | |||||||
\(314\) | 6515.75 | 1.17104 | ||||||||
\(315\) | −5384.03 | − | 1506.00i | −0.963035 | − | 0.269377i | ||||
\(316\) | 3763.50 | 0.669980 | ||||||||
\(317\) | −4280.71 | −0.758450 | −0.379225 | − | 0.925305i | \(-0.623809\pi\) | ||||
−0.379225 | + | 0.925305i | \(0.623809\pi\) | |||||||
\(318\) | −14.2506 | + | 67.9184i | −0.00251299 | + | 0.0119770i | ||||
\(319\) | −4937.67 | −0.866634 | ||||||||
\(320\) | −4556.03 | − | 3878.47i | −0.795906 | − | 0.677541i | ||||
\(321\) | 1055.27 | − | 5029.45i | 0.183488 | − | 0.874506i | ||||
\(322\) | −4195.49 | + | 4738.75i | −0.726105 | + | 0.820125i | ||||
\(323\) | 3360.23 | 0.578850 | ||||||||
\(324\) | −1461.96 | − | 1589.84i | −0.250680 | − | 0.272606i | ||||
\(325\) | 1362.69 | + | 8426.90i | 0.232581 | + | 1.43828i | ||||
\(326\) | 3740.50i | 0.635481i | ||||||||
\(327\) | 865.321 | − | 4124.13i | 0.146337 | − | 0.697447i | ||||
\(328\) | −9169.05 | −1.54352 | ||||||||
\(329\) | −5.08538 | − | 4.50238i | −0.000852177 | − | 0.000754481i | ||||
\(330\) | 2055.08 | + | 2654.84i | 0.342813 | + | 0.442861i | ||||
\(331\) | 4975.22 | 0.826172 | 0.413086 | − | 0.910692i | \(-0.364451\pi\) | ||||
0.413086 | + | 0.910692i | \(0.364451\pi\) | |||||||
\(332\) | 1273.24i | 0.210476i | ||||||||
\(333\) | −889.181 | + | 2025.64i | −0.146327 | + | 0.333347i | ||||
\(334\) | − | 3789.67i | − | 0.620843i | ||||||
\(335\) | 7828.16 | − | 9195.72i | 1.27671 | − | 1.49975i | ||||
\(336\) | −1809.80 | − | 2434.25i | −0.293848 | − | 0.395236i | ||||
\(337\) | − | 8230.66i | − | 1.33042i | −0.746655 | − | 0.665212i | \(-0.768341\pi\) | ||
0.746655 | − | 0.665212i | \(-0.231659\pi\) | |||||||
\(338\) | −5536.11 | −0.890902 | ||||||||
\(339\) | −114.929 | + | 547.754i | −0.0184132 | + | 0.0877578i | ||||
\(340\) | 658.116 | − | 773.088i | 0.104975 | − | 0.123313i | ||||
\(341\) | −424.041 | −0.0673404 | ||||||||
\(342\) | −2670.30 | + | 6083.21i | −0.422203 | + | 0.961820i | ||||
\(343\) | 5231.39 | + | 3603.64i | 0.823523 | + | 0.567283i | ||||
\(344\) | − | 4738.68i | − | 0.742711i | ||||||
\(345\) | 6994.95 | − | 5414.70i | 1.09158 | − | 0.844979i | ||||
\(346\) | 1615.21i | 0.250966i | ||||||||
\(347\) | −864.297 | −0.133712 | −0.0668558 | − | 0.997763i | \(-0.521297\pi\) | ||||
−0.0668558 | + | 0.997763i | \(0.521297\pi\) | |||||||
\(348\) | −2889.25 | − | 606.219i | −0.445058 | − | 0.0933815i | ||||
\(349\) | 4811.80i | 0.738022i | 0.929425 | + | 0.369011i | \(0.120304\pi\) | ||||
−0.929425 | + | 0.369011i | \(0.879696\pi\) | |||||||
\(350\) | 4390.14 | + | 2779.06i | 0.670466 | + | 0.424419i | ||||
\(351\) | −5570.43 | + | 7795.19i | −0.847086 | + | 1.18540i | ||||
\(352\) | − | 3246.76i | − | 0.491628i | ||||||
\(353\) | 1206.50i | 0.181913i | 0.995855 | + | 0.0909565i | \(0.0289924\pi\) | ||||
−0.995855 | + | 0.0909565i | \(0.971008\pi\) | |||||||
\(354\) | −476.115 | + | 2269.17i | −0.0714837 | + | 0.340693i | ||||
\(355\) | 5604.22 | − | 6583.27i | 0.837863 | − | 0.984236i | ||||
\(356\) | 15.6911 | 0.00233602 | ||||||||
\(357\) | 2367.07 | − | 1759.86i | 0.350921 | − | 0.260900i | ||||
\(358\) | − | 2538.23i | − | 0.374719i | ||||||
\(359\) | − | 7589.54i | − | 1.11577i | −0.829919 | − | 0.557884i | \(-0.811613\pi\) | ||
0.829919 | − | 0.557884i | \(-0.188387\pi\) | |||||||
\(360\) | 3243.49 | + | 6681.74i | 0.474853 | + | 0.978218i | ||||
\(361\) | −5160.10 | −0.752310 | ||||||||
\(362\) | 2406.06i | 0.349337i | ||||||||
\(363\) | 712.764 | − | 3397.05i | 0.103059 | − | 0.491181i | ||||
\(364\) | 2483.95 | − | 2805.59i | 0.357678 | − | 0.403992i | ||||
\(365\) | 3814.93 | + | 3247.58i | 0.547075 | + | 0.465716i | ||||
\(366\) | −953.896 | − | 200.145i | −0.136232 | − | 0.0285840i | ||||
\(367\) | 6905.34 | 0.982168 | 0.491084 | − | 0.871112i | \(-0.336601\pi\) | ||||
0.491084 | + | 0.871112i | \(0.336601\pi\) | |||||||
\(368\) | 4799.42 | 0.679856 | ||||||||
\(369\) | 9213.15 | + | 4044.23i | 1.29978 | + | 0.570553i | ||||
\(370\) | 1332.70 | − | 1565.52i | 0.187254 | − | 0.219967i | ||||
\(371\) | −73.0550 | + | 82.5146i | −0.0102233 | + | 0.0115470i | ||||
\(372\) | −248.126 | − | 52.0614i | −0.0345825 | − | 0.00725607i | ||||
\(373\) | 11871.0i | 1.64788i | 0.566678 | + | 0.823939i | \(0.308228\pi\) | ||||
−0.566678 | + | 0.823939i | \(0.691772\pi\) | |||||||
\(374\) | −1771.28 | −0.244895 | ||||||||
\(375\) | −5304.80 | − | 4959.18i | −0.730504 | − | 0.682909i | ||||
\(376\) | 9.02346i | 0.00123763i | ||||||||
\(377\) | 13095.7i | 1.78902i | ||||||||
\(378\) | 1304.90 | + | 5683.75i | 0.177558 | + | 0.773388i | ||||
\(379\) | −4071.94 | −0.551877 | −0.275938 | − | 0.961175i | \(-0.588989\pi\) | ||||
−0.275938 | + | 0.961175i | \(0.588989\pi\) | |||||||
\(380\) | −2353.99 | + | 2765.23i | −0.317782 | + | 0.373298i | ||||
\(381\) | 168.124 | + | 35.2757i | 0.0226070 | + | 0.00474338i | ||||
\(382\) | 3616.19i | 0.484346i | ||||||||
\(383\) | 9559.09i | 1.27532i | 0.770319 | + | 0.637659i | \(0.220097\pi\) | ||||
−0.770319 | + | 0.637659i | \(0.779903\pi\) | |||||||
\(384\) | −205.254 | + | 978.243i | −0.0272768 | + | 0.130002i | ||||
\(385\) | 748.699 | + | 5278.80i | 0.0991096 | + | 0.698785i | ||||
\(386\) | 4403.46i | 0.580648i | ||||||||
\(387\) | −2090.11 | + | 4761.48i | −0.274538 | + | 0.625425i | ||||
\(388\) | −1289.30 | −0.168696 | ||||||||
\(389\) | 6559.03i | 0.854899i | 0.904039 | + | 0.427450i | \(0.140588\pi\) | ||||
−0.904039 | + | 0.427450i | \(0.859412\pi\) | |||||||
\(390\) | 7041.16 | − | 5450.47i | 0.914212 | − | 0.707680i | ||||
\(391\) | 4666.96i | 0.603628i | ||||||||
\(392\) | −1022.56 | − | 8377.20i | −0.131752 | − | 1.07937i | ||||
\(393\) | −1064.14 | + | 5071.69i | −0.136587 | + | 0.650975i | ||||
\(394\) | 1479.00 | 0.189115 | ||||||||
\(395\) | 10814.3 | + | 9206.02i | 1.37753 | + | 1.17267i | ||||
\(396\) | −827.904 | + | 1886.05i | −0.105060 | + | 0.239337i | ||||
\(397\) | −3903.80 | −0.493516 | −0.246758 | − | 0.969077i | \(-0.579365\pi\) | ||||
−0.246758 | + | 0.969077i | \(0.579365\pi\) | |||||||
\(398\) | − | 11362.5i | − | 1.43103i | ||||||
\(399\) | −8466.69 | + | 6294.76i | −1.06232 | + | 0.789805i | ||||
\(400\) | −628.961 | − | 3889.49i | −0.0786201 | − | 0.486186i | ||||
\(401\) | 3085.45i | 0.384239i | 0.981372 | + | 0.192120i | \(0.0615362\pi\) | ||||
−0.981372 | + | 0.192120i | \(0.938464\pi\) | |||||||
\(402\) | −12328.5 | − | 2586.74i | −1.52957 | − | 0.320933i | ||||
\(403\) | 1124.64i | 0.139013i | ||||||||
\(404\) | 3325.42 | 0.409519 | ||||||||
\(405\) | −311.953 | − | 8144.50i | −0.0382742 | − | 0.999267i | ||||
\(406\) | 5967.98 | + | 5283.80i | 0.729522 | + | 0.645889i | ||||
\(407\) | 2109.70 | 0.256938 | ||||||||
\(408\) | −3835.10 | − | 804.676i | −0.465357 | − | 0.0976407i | ||||
\(409\) | 254.304i | 0.0307446i | 0.999882 | + | 0.0153723i | \(0.00489335\pi\) | ||||
−0.999882 | + | 0.0153723i | \(0.995107\pi\) | |||||||
\(410\) | −7120.41 | − | 6061.48i | −0.857688 | − | 0.730135i | ||||
\(411\) | −1465.34 | + | 6983.82i | −0.175863 | + | 0.838167i | ||||
\(412\) | 1852.40 | 0.221508 | ||||||||
\(413\) | −2440.79 | + | 2756.84i | −0.290807 | + | 0.328463i | ||||
\(414\) | −8448.85 | − | 3708.73i | −1.00299 | − | 0.440275i | ||||
\(415\) | −3114.51 | + | 3658.61i | −0.368398 | + | 0.432756i | ||||
\(416\) | −8611.05 | −1.01488 | ||||||||
\(417\) | −6924.57 | − | 1452.91i | −0.813184 | − | 0.170621i | ||||
\(418\) | 6335.64 | 0.741355 | ||||||||
\(419\) | 1777.00 | 0.207189 | 0.103594 | − | 0.994620i | \(-0.466966\pi\) | ||||
0.103594 | + | 0.994620i | \(0.466966\pi\) | |||||||
\(420\) | −210.004 | + | 3180.78i | −0.0243980 | + | 0.369539i | ||||
\(421\) | −6856.09 | −0.793695 | −0.396847 | − | 0.917885i | \(-0.629896\pi\) | ||||
−0.396847 | + | 0.917885i | \(0.629896\pi\) | |||||||
\(422\) | 7781.87 | 0.897667 | ||||||||
\(423\) | 3.98001 | − | 9.06686i | 0.000457482 | − | 0.00104219i | ||||
\(424\) | 146.413 | 0.0167699 | ||||||||
\(425\) | 3782.15 | − | 611.602i | 0.431673 | − | 0.0698049i | ||||
\(426\) | −8826.02 | − | 1851.86i | −1.00381 | − | 0.210618i | ||||
\(427\) | −1158.90 | − | 1026.04i | −0.131342 | − | 0.116284i | ||||
\(428\) | −2930.14 | −0.330920 | ||||||||
\(429\) | 8942.26 | + | 1876.25i | 1.00638 | + | 0.211157i | ||||
\(430\) | 3132.65 | − | 3679.92i | 0.351325 | − | 0.412701i | ||||
\(431\) | − | 1425.61i | − | 0.159325i | −0.996822 | − | 0.0796625i | \(-0.974616\pi\) | ||
0.996822 | − | 0.0796625i | \(-0.0253842\pi\) | |||||||
\(432\) | 2571.07 | − | 3597.92i | 0.286344 | − | 0.400706i | ||||
\(433\) | −5863.42 | −0.650757 | −0.325379 | − | 0.945584i | \(-0.605492\pi\) | ||||
−0.325379 | + | 0.945584i | \(0.605492\pi\) | |||||||
\(434\) | 512.523 | + | 453.767i | 0.0566864 | + | 0.0501878i | ||||
\(435\) | −6819.27 | − | 8809.44i | −0.751630 | − | 0.970989i | ||||
\(436\) | −2402.71 | −0.263919 | ||||||||
\(437\) | − | 16693.1i | − | 1.82732i | ||||||
\(438\) | 1073.13 | − | 5114.57i | 0.117069 | − | 0.557954i | ||||
\(439\) | 9688.48i | 1.05332i | 0.850077 | + | 0.526658i | \(0.176555\pi\) | ||||
−0.850077 | + | 0.526658i | \(0.823445\pi\) | |||||||
\(440\) | 4591.43 | − | 5393.55i | 0.497473 | − | 0.584380i | ||||
\(441\) | −2667.49 | + | 8868.52i | −0.288035 | + | 0.957620i | ||||
\(442\) | 4697.79i | 0.505546i | ||||||||
\(443\) | 17681.9 | 1.89637 | 0.948185 | − | 0.317719i | \(-0.102917\pi\) | ||||
0.948185 | + | 0.317719i | \(0.102917\pi\) | |||||||
\(444\) | 1234.48 | + | 259.017i | 0.131950 | + | 0.0276856i | ||||
\(445\) | 45.0877 | + | 38.3824i | 0.00480306 | + | 0.00408876i | ||||
\(446\) | −4594.42 | −0.487785 | ||||||||
\(447\) | 15112.5 | + | 3170.88i | 1.59910 | + | 0.335520i | ||||
\(448\) | −6570.10 | + | 7420.84i | −0.692875 | + | 0.782593i | ||||
\(449\) | − | 5275.90i | − | 0.554533i | −0.960793 | − | 0.277266i | \(-0.910572\pi\) | ||
0.960793 | − | 0.277266i | \(-0.0894285\pi\) | |||||||
\(450\) | −1898.37 | + | 7333.05i | −0.198867 | + | 0.768185i | ||||
\(451\) | − | 9595.45i | − | 1.00185i | ||||||
\(452\) | 319.119 | 0.0332082 | ||||||||
\(453\) | 1553.90 | − | 7405.92i | 0.161167 | − | 0.768125i | ||||
\(454\) | 8974.08i | 0.927697i | ||||||||
\(455\) | 14000.4 | − | 1985.69i | 1.44252 | − | 0.204595i | ||||
\(456\) | 13717.6 | + | 2878.22i | 1.40874 | + | 0.295581i | ||||
\(457\) | 696.329i | 0.0712755i | 0.999365 | + | 0.0356378i | \(0.0113463\pi\) | ||||
−0.999365 | + | 0.0356378i | \(0.988654\pi\) | |||||||
\(458\) | 7463.92i | 0.761498i | ||||||||
\(459\) | 3498.63 | + | 2500.11i | 0.355777 | + | 0.254238i | ||||
\(460\) | −3840.57 | − | 3269.41i | −0.389277 | − | 0.331385i | ||||
\(461\) | −7690.68 | −0.776986 | −0.388493 | − | 0.921452i | \(-0.627004\pi\) | ||||
−0.388493 | + | 0.921452i | \(0.627004\pi\) | |||||||
\(462\) | 4463.05 | − | 3318.16i | 0.449437 | − | 0.334145i | ||||
\(463\) | − | 4517.49i | − | 0.453446i | −0.973959 | − | 0.226723i | \(-0.927199\pi\) | ||
0.973959 | − | 0.226723i | \(-0.0728012\pi\) | |||||||
\(464\) | − | 6044.38i | − | 0.604749i | ||||||
\(465\) | −585.631 | − | 756.544i | −0.0584042 | − | 0.0754492i | ||||
\(466\) | −7775.73 | −0.772970 | ||||||||
\(467\) | 17707.4i | 1.75461i | 0.479934 | + | 0.877304i | \(0.340661\pi\) | ||||
−0.479934 | + | 0.877304i | \(0.659339\pi\) | |||||||
\(468\) | 5002.17 | + | 2195.76i | 0.494071 | + | 0.216879i | ||||
\(469\) | −14977.9 | − | 13260.8i | −1.47466 | − | 1.30560i | ||||
\(470\) | −5.96524 | + | 7.00735i | −0.000585438 | + | 0.000687713i | ||||
\(471\) | −3097.70 | + | 14763.7i | −0.303045 | + | 1.44432i | ||||
\(472\) | 4891.71 | 0.477032 | ||||||||
\(473\) | 4959.05 | 0.482067 | ||||||||
\(474\) | 3042.04 | − | 14498.4i | 0.294780 | − | 1.40493i | ||||
\(475\) | −13528.2 | + | 2187.62i | −1.30677 | + | 0.211315i | ||||
\(476\) | −1259.20 | − | 1114.84i | −0.121251 | − | 0.107350i | ||||
\(477\) | −147.118 | − | 64.5791i | −0.0141217 | − | 0.00619890i | ||||
\(478\) | − | 10143.6i | − | 0.970624i | ||||||
\(479\) | 12707.4 | 1.21214 | 0.606072 | − | 0.795410i | \(-0.292744\pi\) | ||||
0.606072 | + | 0.795410i | \(0.292744\pi\) | |||||||
\(480\) | 5792.65 | − | 4484.01i | 0.550827 | − | 0.426388i | ||||
\(481\) | − | 5595.33i | − | 0.530406i | ||||||
\(482\) | 15906.3i | 1.50313i | ||||||||
\(483\) | −8742.67 | − | 11759.2i | −0.823613 | − | 1.10779i | ||||
\(484\) | −1979.11 | −0.185867 | ||||||||
\(485\) | −3704.75 | − | 3153.79i | −0.346854 | − | 0.295271i | ||||
\(486\) | −7306.36 | + | 4346.97i | −0.681941 | + | 0.405725i | ||||
\(487\) | 224.275i | 0.0208684i | 0.999946 | + | 0.0104342i | \(0.00332136\pi\) | ||||
−0.999946 | + | 0.0104342i | \(0.996679\pi\) | |||||||
\(488\) | 2056.33i | 0.190750i | ||||||||
\(489\) | −8475.38 | − | 1778.29i | −0.783783 | − | 0.164452i | ||||
\(490\) | 4743.92 | − | 7181.48i | 0.437364 | − | 0.662094i | ||||
\(491\) | − | 6605.29i | − | 0.607113i | −0.952813 | − | 0.303557i | \(-0.901826\pi\) | ||
0.952813 | − | 0.303557i | \(-0.0981742\pi\) | |||||||
\(492\) | 1178.08 | − | 5614.74i | 0.107951 | − | 0.514496i | ||||
\(493\) | 5877.57 | 0.536942 | ||||||||
\(494\) | − | 16803.4i | − | 1.53040i | ||||||
\(495\) | −6992.47 | + | 3394.33i | −0.634926 | + | 0.308210i | ||||
\(496\) | − | 519.084i | − | 0.0469911i | ||||||
\(497\) | −10722.8 | − | 9493.51i | −0.967773 | − | 0.856826i | ||||
\(498\) | 4905.00 | + | 1029.16i | 0.441362 | + | 0.0926060i | ||||
\(499\) | 14083.4 | 1.26344 | 0.631722 | − | 0.775195i | \(-0.282349\pi\) | ||||
0.631722 | + | 0.775195i | \(0.282349\pi\) | |||||||
\(500\) | −2146.26 | + | 3540.89i | −0.191967 | + | 0.316707i | ||||
\(501\) | 8586.81 | + | 1801.67i | 0.765729 | + | 0.160664i | ||||
\(502\) | −10659.0 | −0.947682 | ||||||||
\(503\) | − | 23.1056i | − | 0.00204816i | −0.999999 | − | 0.00102408i | \(-0.999674\pi\) | ||
0.999999 | − | 0.00102408i | \(-0.000325975\pi\) | |||||||
\(504\) | 11170.6 | − | 5156.81i | 0.987258 | − | 0.455759i | ||||
\(505\) | 9555.46 | + | 8134.40i | 0.842005 | + | 0.716784i | ||||
\(506\) | 8799.44i | 0.773088i | ||||||||
\(507\) | 2631.96 | − | 12544.0i | 0.230551 | − | 1.09881i | ||||
\(508\) | − | 97.9487i | − | 0.00855467i | ||||||
\(509\) | −3934.85 | −0.342650 | −0.171325 | − | 0.985215i | \(-0.554805\pi\) | ||||
−0.171325 | + | 0.985215i | \(0.554805\pi\) | |||||||
\(510\) | −2446.27 | − | 3160.20i | −0.212397 | − | 0.274384i | ||||
\(511\) | 5501.38 | − | 6213.74i | 0.476256 | − | 0.537925i | ||||
\(512\) | 10178.8 | 0.878602 | ||||||||
\(513\) | −12514.1 | − | 8942.55i | −1.07702 | − | 0.769636i | ||||
\(514\) | − | 3526.67i | − | 0.302636i | ||||||
\(515\) | 5322.81 | + | 4531.21i | 0.455438 | + | 0.387707i | ||||
\(516\) | 2901.77 | + | 608.845i | 0.247564 | + | 0.0519437i | ||||
\(517\) | −9.44309 | −0.000803301 | ||||||||
\(518\) | −2549.92 | − | 2257.59i | −0.216288 | − | 0.191492i | ||||
\(519\) | −3659.81 | − | 767.897i | −0.309533 | − | 0.0649459i | ||||
\(520\) | −14304.7 | − | 12177.4i | −1.20635 | − | 1.02695i | ||||
\(521\) | 8113.65 | 0.682275 | 0.341138 | − | 0.940013i | \(-0.389188\pi\) | ||||
0.341138 | + | 0.940013i | \(0.389188\pi\) | |||||||
\(522\) | −4670.77 | + | 10640.5i | −0.391636 | + | 0.892186i | ||||
\(523\) | −5518.74 | −0.461410 | −0.230705 | − | 0.973024i | \(-0.574103\pi\) | ||||
−0.230705 | + | 0.973024i | \(0.574103\pi\) | |||||||
\(524\) | 2954.75 | 0.246334 | ||||||||
\(525\) | −8384.05 | + | 8626.17i | −0.696971 | + | 0.717099i | ||||
\(526\) | 12188.1 | 1.01031 | ||||||||
\(527\) | 504.759 | 0.0417223 | ||||||||
\(528\) | −4127.36 | − | 865.998i | −0.340190 | − | 0.0713782i | ||||
\(529\) | 11017.7 | 0.905537 | ||||||||
\(530\) | 113.700 | + | 96.7911i | 0.00931854 | + | 0.00793271i | ||||
\(531\) | −4915.24 | − | 2157.61i | −0.401701 | − | 0.176332i | ||||
\(532\) | 4503.99 | + | 3987.64i | 0.367054 | + | 0.324974i | ||||
\(533\) | −25449.0 | −2.06814 | ||||||||
\(534\) | 12.6831 | − | 60.4478i | 0.00102781 | − | 0.00489857i | ||||
\(535\) | −8419.65 | − | 7167.50i | −0.680398 | − | 0.579211i | ||||
\(536\) | 26576.7i | 2.14168i | ||||||||
\(537\) | 5751.22 | + | 1206.72i | 0.462167 | + | 0.0969713i | ||||
\(538\) | 11487.7 | 0.920575 | ||||||||
\(539\) | 8766.78 | − | 1070.11i | 0.700579 | − | 0.0855156i | ||||
\(540\) | −4508.35 | + | 1127.68i | −0.359275 | + | 0.0898659i | ||||
\(541\) | 3915.43 | 0.311160 | 0.155580 | − | 0.987823i | \(-0.450275\pi\) | ||||
0.155580 | + | 0.987823i | \(0.450275\pi\) | |||||||
\(542\) | − | 14095.4i | − | 1.11706i | ||||||
\(543\) | −5451.76 | − | 1143.88i | −0.430861 | − | 0.0904027i | ||||
\(544\) | 3864.80i | 0.304599i | ||||||||
\(545\) | −6904.09 | − | 5877.33i | −0.542640 | − | 0.461940i | ||||
\(546\) | −8800.42 | − | 11836.9i | −0.689786 | − | 0.927788i | ||||
\(547\) | − | 5022.18i | − | 0.392564i | −0.980547 | − | 0.196282i | \(-0.937113\pi\) | ||
0.980547 | − | 0.196282i | \(-0.0628869\pi\) | |||||||
\(548\) | 4068.75 | 0.317169 | ||||||||
\(549\) | 906.996 | − | 2066.23i | 0.0705093 | − | 0.160627i | ||||
\(550\) | 7131.14 | − | 1153.16i | 0.552860 | − | 0.0894017i | ||||
\(551\) | −21023.3 | −1.62545 | ||||||||
\(552\) | −3997.49 | + | 19052.1i | −0.308233 | + | 1.46904i | ||||
\(553\) | 15594.9 | − | 17614.3i | 1.19921 | − | 1.35449i | ||||
\(554\) | 13034.3i | 0.999590i | ||||||||
\(555\) | 2913.64 | + | 3763.97i | 0.222842 | + | 0.287877i | ||||
\(556\) | 4034.23i | 0.307715i | ||||||||
\(557\) | 13585.5 | 1.03346 | 0.516729 | − | 0.856149i | \(-0.327149\pi\) | ||||
0.516729 | + | 0.856149i | \(0.327149\pi\) | |||||||
\(558\) | −401.120 | + | 913.791i | −0.0304315 | + | 0.0693259i | ||||
\(559\) | − | 13152.4i | − | 0.995146i | ||||||
\(560\) | −6461.98 | + | 916.510i | −0.487622 | + | 0.0691601i | ||||
\(561\) | 842.097 | − | 4013.45i | 0.0633750 | − | 0.302046i | ||||
\(562\) | 451.247i | 0.0338696i | ||||||||
\(563\) | 12293.5i | 0.920267i | 0.887850 | + | 0.460133i | \(0.152198\pi\) | ||||
−0.887850 | + | 0.460133i | \(0.847802\pi\) | |||||||
\(564\) | −5.52558 | − | 1.15937i | −0.000412534 | − | 8.65573e-5i | ||||
\(565\) | 916.978 | + | 780.608i | 0.0682789 | + | 0.0581246i | ||||
\(566\) | 10792.7 | 0.801502 | ||||||||
\(567\) | −13498.9 | + | 254.555i | −0.999822 | + | 0.0188542i | ||||
\(568\) | 19026.4i | 1.40551i | ||||||||
\(569\) | 10764.9i | 0.793123i | 0.918008 | + | 0.396562i | \(0.129797\pi\) | ||||
−0.918008 | + | 0.396562i | \(0.870203\pi\) | |||||||
\(570\) | 8749.97 | + | 11303.6i | 0.642975 | + | 0.830624i | ||||
\(571\) | 14290.9 | 1.04738 | 0.523690 | − | 0.851909i | \(-0.324555\pi\) | ||||
0.523690 | + | 0.851909i | \(0.324555\pi\) | |||||||
\(572\) | − | 5209.73i | − | 0.380822i | ||||||
\(573\) | −8193.72 | − | 1719.20i | −0.597378 | − | 0.125341i | ||||
\(574\) | −10268.1 | + | 11597.7i | −0.746660 | + | 0.843342i | ||||
\(575\) | −3038.34 | − | 18789.1i | −0.220361 | − | 1.36271i | ||||
\(576\) | −13230.8 | − | 5807.83i | −0.957090 | − | 0.420127i | ||||
\(577\) | −25946.6 | −1.87205 | −0.936024 | − | 0.351937i | \(-0.885523\pi\) | ||||
−0.936024 | + | 0.351937i | \(0.885523\pi\) | |||||||
\(578\) | −8918.20 | −0.641779 | ||||||||
\(579\) | −9977.55 | − | 2093.48i | −0.716153 | − | 0.150262i | ||||
\(580\) | −4117.49 | + | 4836.81i | −0.294775 | + | 0.346272i | ||||
\(581\) | 5959.12 | + | 5275.95i | 0.425518 | + | 0.376736i | ||||
\(582\) | −1042.14 | + | 4966.86i | −0.0742236 | + | 0.353751i | ||||
\(583\) | 153.222i | 0.0108848i | ||||||||
\(584\) | −11025.6 | −0.781237 | ||||||||
\(585\) | 9002.42 | + | 18545.4i | 0.636247 | + | 1.31070i | ||||
\(586\) | 15040.6i | 1.06027i | ||||||||
\(587\) | 18044.2i | 1.26876i | 0.773020 | + | 0.634382i | \(0.218745\pi\) | ||||
−0.773020 | + | 0.634382i | \(0.781255\pi\) | |||||||
\(588\) | 5261.22 | + | 450.167i | 0.368995 | + | 0.0315724i | ||||
\(589\) | −1805.45 | −0.126303 | ||||||||
\(590\) | 3798.76 | + | 3233.82i | 0.265072 | + | 0.225651i | ||||
\(591\) | −703.143 | + | 3351.19i | −0.0489398 | + | 0.233248i | ||||
\(592\) | 2582.56i | 0.179295i | ||||||||
\(593\) | − | 14485.3i | − | 1.00310i | −0.865129 | − | 0.501550i | \(-0.832763\pi\) | ||
0.865129 | − | 0.501550i | \(-0.167237\pi\) | |||||||
\(594\) | 6596.57 | + | 4713.89i | 0.455658 | + | 0.325612i | ||||
\(595\) | −891.216 | − | 6283.64i | −0.0614056 | − | 0.432948i | ||||
\(596\) | − | 8804.48i | − | 0.605110i | ||||||
\(597\) | 25745.7 | + | 5401.92i | 1.76499 | + | 0.370328i | ||||
\(598\) | 23337.8 | 1.59591 | ||||||||
\(599\) | − | 2982.21i | − | 0.203422i | −0.994814 | − | 0.101711i | \(-0.967568\pi\) | ||
0.994814 | − | 0.101711i | \(-0.0324317\pi\) | |||||||
\(600\) | 15963.9 | + | 742.836i | 1.08620 | + | 0.0505436i | ||||
\(601\) | 15274.2i | 1.03668i | 0.855174 | + | 0.518341i | \(0.173450\pi\) | ||||
−0.855174 | + | 0.518341i | \(0.826550\pi\) | |||||||
\(602\) | −5993.84 | − | 5306.69i | −0.405798 | − | 0.359277i | ||||
\(603\) | 11722.3 | − | 26704.6i | 0.791657 | − | 1.80347i | ||||
\(604\) | −4314.67 | −0.290664 | ||||||||
\(605\) | −5686.90 | − | 4841.16i | −0.382157 | − | 0.325324i | ||||
\(606\) | 2687.94 | − | 12810.8i | 0.180182 | − | 0.858748i | ||||
\(607\) | 14554.3 | 0.973214 | 0.486607 | − | 0.873621i | \(-0.338234\pi\) | ||||
0.486607 | + | 0.873621i | \(0.338234\pi\) | |||||||
\(608\) | − | 13823.8i | − | 0.922090i | ||||||
\(609\) | −14809.5 | + | 11010.5i | −0.985407 | + | 0.732625i | ||||
\(610\) | −1359.40 | + | 1596.89i | −0.0902306 | + | 0.105994i | ||||
\(611\) | 25.0449i | 0.00165828i | ||||||||
\(612\) | 985.499 | − | 2245.06i | 0.0650922 | − | 0.148287i | ||||
\(613\) | 18176.4i | 1.19761i | 0.800893 | + | 0.598807i | \(0.204358\pi\) | ||||
−0.800893 | + | 0.598807i | \(0.795642\pi\) | |||||||
\(614\) | −3312.98 | −0.217754 | ||||||||
\(615\) | 17119.5 | − | 13252.0i | 1.12248 | − | 0.868899i | ||||
\(616\) | −8784.98 | − | 7777.85i | −0.574605 | − | 0.508731i | ||||
\(617\) | 7001.54 | 0.456842 | 0.228421 | − | 0.973562i | \(-0.426644\pi\) | ||||
0.228421 | + | 0.973562i | \(0.426644\pi\) | |||||||
\(618\) | 1497.30 | − | 7136.14i | 0.0974597 | − | 0.464495i | ||||
\(619\) | − | 382.714i | − | 0.0248507i | −0.999923 | − | 0.0124253i | \(-0.996045\pi\) | ||
0.999923 | − | 0.0124253i | \(-0.00395521\pi\) | |||||||
\(620\) | −353.605 | + | 415.380i | −0.0229051 | + | 0.0269065i | ||||
\(621\) | 12420.1 | − | 17380.6i | 0.802580 | − | 1.12312i | ||||
\(622\) | 4852.36 | 0.312801 | ||||||||
\(623\) | 65.0194 | − | 73.4386i | 0.00418130 | − | 0.00472272i | ||||
\(624\) | −2296.80 | + | 10946.6i | −0.147348 | + | 0.702265i | ||||
\(625\) | −14828.7 | + | 4924.59i | −0.949034 | + | 0.315174i | ||||
\(626\) | 2665.95 | 0.170212 | ||||||||
\(627\) | −3012.07 | + | 14355.6i | −0.191851 | + | 0.914364i | ||||
\(628\) | 8601.27 | 0.546542 | ||||||||
\(629\) | −2511.29 | −0.159192 | ||||||||
\(630\) | 12083.8 | + | 3380.05i | 0.764177 | + | 0.213753i | ||||
\(631\) | −20481.5 | −1.29217 | −0.646083 | − | 0.763267i | \(-0.723594\pi\) | ||||
−0.646083 | + | 0.763267i | \(0.723594\pi\) | |||||||
\(632\) | −31254.6 | −1.96715 | ||||||||
\(633\) | −3699.63 | + | 17632.5i | −0.232302 | + | 1.10715i | ||||
\(634\) | 9607.55 | 0.601837 | ||||||||
\(635\) | 239.595 | − | 281.452i | 0.0149733 | − | 0.0175891i | ||||
\(636\) | −18.8118 | + | 89.6573i | −0.00117286 | + | 0.00558985i | ||||
\(637\) | −2838.14 | − | 23251.2i | −0.176533 | − | 1.44623i | ||||
\(638\) | 11082.0 | 0.687682 | ||||||||
\(639\) | 8392.07 | − | 19118.0i | 0.519538 | − | 1.18356i | ||||
\(640\) | 1637.65 | + | 1394.10i | 0.101146 | + | 0.0861042i | ||||
\(641\) | − | 28510.2i | − | 1.75676i | −0.477962 | − | 0.878380i | \(-0.658624\pi\) | ||
0.477962 | − | 0.878380i | \(-0.341376\pi\) | |||||||
\(642\) | −2368.43 | + | 11288.0i | −0.145599 | + | 0.693928i | ||||
\(643\) | −1013.84 | −0.0621802 | −0.0310901 | − | 0.999517i | \(-0.509898\pi\) | ||||
−0.0310901 | + | 0.999517i | \(0.509898\pi\) | |||||||
\(644\) | −5538.36 | + | 6255.50i | −0.338885 | + | 0.382766i | ||||
\(645\) | 6848.81 | + | 8847.60i | 0.418096 | + | 0.540114i | ||||
\(646\) | −7541.65 | −0.459322 | ||||||||
\(647\) | − | 9793.59i | − | 0.595094i | −0.954707 | − | 0.297547i | \(-0.903832\pi\) | ||
0.954707 | − | 0.297547i | \(-0.0961685\pi\) | |||||||
\(648\) | 12141.1 | + | 13203.1i | 0.736031 | + | 0.800409i | ||||
\(649\) | 5119.20i | 0.309624i | ||||||||
\(650\) | −3058.41 | − | 18913.2i | −0.184555 | − | 1.14129i | ||||
\(651\) | −1271.83 | + | 945.569i | −0.0765696 | + | 0.0569275i | ||||
\(652\) | 4937.73i | 0.296590i | ||||||||
\(653\) | 9713.50 | 0.582111 | 0.291056 | − | 0.956706i | \(-0.405994\pi\) | ||||
0.291056 | + | 0.956706i | \(0.405994\pi\) | |||||||
\(654\) | −1942.11 | + | 9256.13i | −0.116120 | + | 0.553430i | ||||
\(655\) | 8490.38 | + | 7227.71i | 0.506483 | + | 0.431160i | ||||
\(656\) | 11746.2 | 0.699101 | ||||||||
\(657\) | 11078.6 | + | 4863.11i | 0.657867 | + | 0.288779i | ||||
\(658\) | 11.4135 | + | 10.1051i | 0.000676210 | + | 0.000598688i | ||||
\(659\) | 14730.6i | 0.870745i | 0.900250 | + | 0.435373i | \(0.143383\pi\) | ||||
−0.900250 | + | 0.435373i | \(0.856617\pi\) | |||||||
\(660\) | 2712.85 | + | 3504.58i | 0.159996 | + | 0.206691i | ||||
\(661\) | 23656.2i | 1.39201i | 0.718036 | + | 0.696006i | \(0.245041\pi\) | ||||
−0.718036 | + | 0.696006i | \(0.754959\pi\) | |||||||
\(662\) | −11166.3 | −0.655575 | ||||||||
\(663\) | −10644.5 | − | 2233.41i | −0.623524 | − | 0.130827i | ||||
\(664\) | − | 10573.8i | − | 0.617987i | ||||||
\(665\) | 3187.76 | + | 22475.7i | 0.185889 | + | 1.31063i | ||||
\(666\) | 1995.66 | − | 4546.32i | 0.116112 | − | 0.264514i | ||||
\(667\) | − | 29198.8i | − | 1.69502i | ||||||
\(668\) | − | 5002.65i | − | 0.289758i | ||||||
\(669\) | 2184.27 | − | 10410.2i | 0.126231 | − | 0.601619i | ||||
\(670\) | −17569.4 | + | 20638.7i | −1.01308 | + | 1.19006i | ||||
\(671\) | −2151.96 | −0.123809 | ||||||||
\(672\) | −7239.96 | − | 9738.02i | −0.415606 | − | 0.559006i | ||||
\(673\) | 23206.9i | 1.32921i | 0.747194 | + | 0.664606i | \(0.231400\pi\) | ||||
−0.747194 | + | 0.664606i | \(0.768600\pi\) | |||||||
\(674\) | 18472.7i | 1.05570i | ||||||||
\(675\) | −15713.0 | − | 7787.66i | −0.895992 | − | 0.444070i | ||||
\(676\) | −7308.08 | −0.415799 | ||||||||
\(677\) | 2008.10i | 0.113999i | 0.998374 | + | 0.0569997i | \(0.0181534\pi\) | ||||
−0.998374 | + | 0.0569997i | \(0.981847\pi\) | |||||||
\(678\) | 257.945 | − | 1229.37i | 0.0146111 | − | 0.0696366i | ||||
\(679\) | −5342.50 | + | 6034.28i | −0.301953 | + | 0.341052i | ||||
\(680\) | −5465.43 | + | 6420.23i | −0.308220 | + | 0.362065i | ||||
\(681\) | −20333.8 | − | 4266.42i | −1.14419 | − | 0.240073i | ||||
\(682\) | 951.709 | 0.0534352 | ||||||||
\(683\) | 9344.15 | 0.523491 | 0.261745 | − | 0.965137i | \(-0.415702\pi\) | ||||
0.261745 | + | 0.965137i | \(0.415702\pi\) | |||||||
\(684\) | −3524.99 | + | 8030.29i | −0.197049 | + | 0.448897i | ||||
\(685\) | 11691.4 | + | 9952.70i | 0.652125 | + | 0.555143i | ||||
\(686\) | −11741.2 | − | 8087.94i | −0.653473 | − | 0.450144i | ||||
\(687\) | −16912.1 | − | 3548.47i | −0.939208 | − | 0.197063i | ||||
\(688\) | 6070.57i | 0.336393i | ||||||||
\(689\) | 406.375 | 0.0224698 | ||||||||
\(690\) | −15699.3 | + | 12152.7i | −0.866179 | + | 0.670498i | ||||
\(691\) | − | 28869.6i | − | 1.58937i | −0.607025 | − | 0.794683i | \(-0.707637\pi\) | ||
0.607025 | − | 0.794683i | \(-0.292363\pi\) | |||||||
\(692\) | 2132.19i | 0.117130i | ||||||||
\(693\) | 5396.63 | + | 11690.1i | 0.295817 | + | 0.640793i | ||||
\(694\) | 1939.81 | 0.106101 | ||||||||
\(695\) | −9868.26 | + | 11592.2i | −0.538596 | + | 0.632688i | ||||
\(696\) | 23994.2 | + | 5034.44i | 1.30675 | + | 0.274181i | ||||
\(697\) | 11422.0i | 0.620715i | ||||||||
\(698\) | − | 10799.5i | − | 0.585627i | ||||||
\(699\) | 3696.71 | − | 17618.6i | 0.200032 | − | 0.953357i | ||||
\(700\) | 5795.31 | + | 3668.56i | 0.312917 | + | 0.198083i | ||||
\(701\) | 3198.20i | 0.172317i | 0.996281 | + | 0.0861585i | \(0.0274592\pi\) | ||||
−0.996281 | + | 0.0861585i | \(0.972541\pi\) | |||||||
\(702\) | 12502.2 | − | 17495.4i | 0.672171 | − | 0.940628i | ||||
\(703\) | 8982.53 | 0.481910 | ||||||||
\(704\) | 13779.8i | 0.737709i | ||||||||
\(705\) | −13.0416 | − | 16.8477i | −0.000696702 | − | 0.000900030i | ||||
\(706\) | − | 2707.84i | − | 0.144350i | ||||||
\(707\) | 13779.6 | − | 15563.9i | 0.733007 | − | 0.827921i | ||||
\(708\) | −628.507 | + | 2995.48i | −0.0333626 | + | 0.159007i | ||||
\(709\) | −5643.25 | −0.298923 | −0.149462 | − | 0.988768i | \(-0.547754\pi\) | ||||
−0.149462 | + | 0.988768i | \(0.547754\pi\) | |||||||
\(710\) | −12578.0 | + | 14775.4i | −0.664852 | + | 0.781000i | ||||
\(711\) | 31404.9 | + | 13785.6i | 1.65651 | + | 0.727145i | ||||
\(712\) | −130.309 | −0.00685889 | ||||||||
\(713\) | − | 2507.55i | − | 0.131709i | ||||||
\(714\) | −5312.61 | + | 3949.79i | −0.278459 | + | 0.207027i | ||||
\(715\) | 12743.7 | − | 14970.0i | 0.666555 | − | 0.783001i | ||||
\(716\) | − | 3350.65i | − | 0.174888i | ||||||
\(717\) | 22983.9 | + | 4822.44i | 1.19714 | + | 0.251182i | ||||
\(718\) | 17033.8i | 0.885372i | ||||||||
\(719\) | 31212.4 | 1.61895 | 0.809475 | − | 0.587154i | \(-0.199752\pi\) | ||||
0.809475 | + | 0.587154i | \(0.199752\pi\) | |||||||
\(720\) | −4155.13 | − | 8559.75i | −0.215073 | − | 0.443060i | ||||
\(721\) | 7675.84 | − | 8669.76i | 0.396482 | − | 0.447821i | ||||
\(722\) | 11581.2 | 0.596965 | ||||||||
\(723\) | −36041.1 | − | 7562.10i | −1.85392 | − | 0.388987i | ||||
\(724\) | 3176.18i | 0.163041i | ||||||||
\(725\) | −23662.9 | + | 3826.48i | −1.21217 | + | 0.196016i | ||||
\(726\) | −1599.71 | + | 7624.27i | −0.0817782 | + | 0.389756i | ||||
\(727\) | −34019.5 | −1.73551 | −0.867753 | − | 0.496995i | \(-0.834437\pi\) | ||||
−0.867753 | + | 0.496995i | \(0.834437\pi\) | |||||||
\(728\) | −20628.4 | + | 23299.5i | −1.05019 | + | 1.18618i | ||||
\(729\) | −6375.99 | − | 18621.7i | −0.323934 | − | 0.946080i | ||||
\(730\) | −8562.16 | − | 7288.82i | −0.434109 | − | 0.369550i | ||||
\(731\) | −5903.03 | −0.298675 | ||||||||
\(732\) | −1259.21 | − | 264.206i | −0.0635817 | − | 0.0133406i | ||||
\(733\) | −7823.52 | −0.394227 | −0.197113 | − | 0.980381i | \(-0.563157\pi\) | ||||
−0.197113 | + | 0.980381i | \(0.563157\pi\) | |||||||
\(734\) | −15498.2 | −0.779359 | ||||||||
\(735\) | 14016.8 | + | 14163.2i | 0.703424 | + | 0.710771i | ||||
\(736\) | 19199.7 | 0.961561 | ||||||||
\(737\) | −27812.7 | −1.39009 | ||||||||
\(738\) | −20677.8 | − | 9076.79i | −1.03138 | − | 0.452739i | ||||
\(739\) | 14767.9 | 0.735107 | 0.367554 | − | 0.930002i | \(-0.380195\pi\) | ||||
0.367554 | + | 0.930002i | \(0.380195\pi\) | |||||||
\(740\) | 1759.27 | − | 2066.61i | 0.0873945 | − | 0.102662i | ||||
\(741\) | 38073.8 | + | 7988.59i | 1.88755 | + | 0.396043i | ||||
\(742\) | 163.963 | − | 185.194i | 0.00811224 | − | 0.00916267i | ||||
\(743\) | −13145.6 | −0.649077 | −0.324539 | − | 0.945872i | \(-0.605209\pi\) | ||||
−0.324539 | + | 0.945872i | \(0.605209\pi\) | |||||||
\(744\) | 2060.60 | + | 432.352i | 0.101539 | + | 0.0213048i | ||||
\(745\) | 21536.9 | − | 25299.4i | 1.05913 | − | 1.24416i | ||||
\(746\) | − | 26643.1i | − | 1.30761i | ||||||
\(747\) | −4663.83 | + | 10624.7i | −0.228435 | + | 0.520397i | ||||
\(748\) | −2338.22 | −0.114297 | ||||||||
\(749\) | −12141.7 | + | 13713.9i | −0.592320 | + | 0.669018i | ||||
\(750\) | 11906.0 | + | 11130.3i | 0.579661 | + | 0.541894i | ||||
\(751\) | 326.336 | 0.0158564 | 0.00792821 | − | 0.999969i | \(-0.497476\pi\) | ||||
0.00792821 | + | 0.999969i | \(0.497476\pi\) | |||||||
\(752\) | − | 11.5596i | − | 0.000560555i | ||||||
\(753\) | 5067.48 | − | 24151.7i | 0.245245 | − | 1.16884i | ||||
\(754\) | − | 29391.7i | − | 1.41960i | ||||||
\(755\) | −12398.0 | − | 10554.2i | −0.597630 | − | 0.508752i | ||||
\(756\) | 1722.57 | + | 7502.97i | 0.0828693 | + | 0.360953i | ||||
\(757\) | − | 361.891i | − | 0.0173754i | −0.999962 | − | 0.00868769i | \(-0.997235\pi\) | ||
0.999962 | − | 0.00868769i | \(-0.00276541\pi\) | |||||||
\(758\) | 9138.98 | 0.437919 | ||||||||
\(759\) | −19938.1 | − | 4183.40i | −0.953503 | − | 0.200063i | ||||
\(760\) | 19549.1 | − | 22964.3i | 0.933052 | − | 1.09605i | ||||
\(761\) | 31708.0 | 1.51040 | 0.755199 | − | 0.655495i | \(-0.227540\pi\) | ||||
0.755199 | + | 0.655495i | \(0.227540\pi\) | |||||||
\(762\) | −377.335 | − | 79.1721i | −0.0179389 | − | 0.00376391i | ||||
\(763\) | −9956.16 | + | 11245.4i | −0.472395 | + | 0.533564i | ||||
\(764\) | 4773.63i | 0.226052i | ||||||||
\(765\) | 8323.51 | − | 4040.45i | 0.393382 | − | 0.190958i | ||||
\(766\) | − | 21454.3i | − | 1.01198i | ||||||
\(767\) | 13577.1 | 0.639167 | ||||||||
\(768\) | −4107.55 | + | 19576.7i | −0.192993 | + | 0.919808i | ||||
\(769\) | − | 4392.75i | − | 0.205990i | −0.994682 | − | 0.102995i | \(-0.967157\pi\) | ||
0.994682 | − | 0.102995i | \(-0.0328426\pi\) | |||||||
\(770\) | −1680.37 | − | 11847.6i | −0.0786444 | − | 0.554492i | ||||
\(771\) | 7990.89 | + | 1676.64i | 0.373262 | + | 0.0783173i | ||||
\(772\) | 5812.89i | 0.270998i | ||||||||
\(773\) | 11252.2i | 0.523563i | 0.965127 | + | 0.261782i | \(0.0843100\pi\) | ||||
−0.965127 | + | 0.261782i | \(0.915690\pi\) | |||||||
\(774\) | 4691.00 | − | 10686.6i | 0.217848 | − | 0.496280i | ||||
\(775\) | −2032.14 | + | 328.613i | −0.0941894 | + | 0.0152312i | ||||
\(776\) | 10707.2 | 0.495316 | ||||||||
\(777\) | 6327.62 | − | 4704.42i | 0.292152 | − | 0.217207i | ||||
\(778\) | − | 14721.0i | − | 0.678370i | ||||||
\(779\) | − | 40854.9i | − | 1.87905i | ||||||
\(780\) | 9294.84 | − | 7195.02i | 0.426678 | − | 0.330286i | ||||
\(781\) | −19911.3 | −0.912268 | ||||||||
\(782\) | − | 10474.4i | − | 0.478984i | ||||||
\(783\) | −21889.1 | − | 15641.9i | −0.999045 | − | 0.713915i | ||||
\(784\) | 1309.96 | + | 10731.8i | 0.0596739 | + | 0.488874i | ||||
\(785\) | 24715.4 | + | 21039.8i | 1.12373 | + | 0.956616i | ||||
\(786\) | 2388.33 | − | 11382.8i | 0.108383 | − | 0.516554i | ||||
\(787\) | −10540.6 | −0.477421 | −0.238711 | − | 0.971091i | \(-0.576725\pi\) | ||||
−0.238711 | + | 0.971091i | \(0.576725\pi\) | |||||||
\(788\) | 1952.39 | 0.0882628 | ||||||||
\(789\) | −5794.41 | + | 27616.3i | −0.261453 | + | 1.24609i | ||||
\(790\) | −24271.4 | − | 20661.8i | −1.09309 | − | 0.930525i | ||||
\(791\) | 1322.34 | − | 1493.57i | 0.0594401 | − | 0.0671368i | ||||
\(792\) | 6875.46 | − | 15663.0i | 0.308471 | − | 0.702727i | ||||
\(793\) | 5707.43i | 0.255582i | ||||||||
\(794\) | 8761.61 | 0.391609 | ||||||||
\(795\) | −273.368 | + | 211.611i | −0.0121954 | + | 0.00944033i | ||||
\(796\) | − | 14999.3i | − | 0.667886i | ||||||
\(797\) | 34322.0i | 1.52540i | 0.646750 | + | 0.762702i | \(0.276128\pi\) | ||||
−0.646750 | + | 0.762702i | \(0.723872\pi\) | |||||||
\(798\) | 19002.5 | − | 14127.9i | 0.842958 | − | 0.626717i | ||||
\(799\) | 11.2406 | 0.000497703 | ||||||||
\(800\) | −2516.10 | − | 15559.6i | −0.111197 | − | 0.687642i | ||||
\(801\) | 130.936 | + | 57.4758i | 0.00577576 | + | 0.00253534i | ||||
\(802\) | − | 6924.93i | − | 0.304897i | ||||||
\(803\) | − | 11538.3i | − | 0.507073i | ||||||
\(804\) | −16274.5 | − | 3414.69i | −0.713876 | − | 0.149785i | ||||
\(805\) | −31216.0 | + | 4427.41i | −1.36673 | + | 0.193846i | ||||
\(806\) | − | 2524.12i | − | 0.110308i | ||||||
\(807\) | −5461.43 | + | 26029.3i | −0.238230 | + | 1.13541i | ||||
\(808\) | −27616.4 | −1.20240 | ||||||||
\(809\) | 32097.4i | 1.39491i | 0.716627 | + | 0.697457i | \(0.245685\pi\) | ||||
−0.716627 | + | 0.697457i | \(0.754315\pi\) | |||||||
\(810\) | 700.141 | + | 18279.4i | 0.0303709 | + | 0.792928i | ||||
\(811\) | − | 15356.6i | − | 0.664910i | −0.943119 | − | 0.332455i | \(-0.892123\pi\) | ||
0.943119 | − | 0.332455i | \(-0.107877\pi\) | |||||||
\(812\) | 7878.18 | + | 6975.01i | 0.340480 | + | 0.301447i | ||||
\(813\) | 31937.9 | + | 6701.16i | 1.37775 | + | 0.289078i | ||||
\(814\) | −4734.97 | −0.203883 | ||||||||
\(815\) | −12078.3 | + | 14188.4i | −0.519123 | + | 0.609813i | ||||
\(816\) | 4913.02 | + | 1030.84i | 0.210772 | + | 0.0442240i | ||||
\(817\) | 21114.3 | 0.904158 | ||||||||
\(818\) | − | 570.756i | − | 0.0243961i | ||||||
\(819\) | 31004.4 | − | 14312.9i | 1.32281 | − | 0.610664i | ||||
\(820\) | −9399.47 | − | 8001.60i | −0.400297 | − | 0.340766i | ||||
\(821\) | − | 38785.8i | − | 1.64876i | −0.566035 | − | 0.824381i | \(-0.691523\pi\) | ||
0.566035 | − | 0.824381i | \(-0.308477\pi\) | |||||||
\(822\) | 3288.78 | − | 15674.4i | 0.139549 | − | 0.665093i | ||||
\(823\) | 21905.2i | 0.927787i | 0.885891 | + | 0.463894i | \(0.153548\pi\) | ||||
−0.885891 | + | 0.463894i | \(0.846452\pi\) | |||||||
\(824\) | −15383.5 | −0.650378 | ||||||||
\(825\) | −777.382 | + | 16706.3i | −0.0328060 | + | 0.705016i | ||||
\(826\) | 5478.06 | − | 6187.40i | 0.230758 | − | 0.260638i | ||||
\(827\) | −14660.5 | −0.616438 | −0.308219 | − | 0.951315i | \(-0.599733\pi\) | ||||
−0.308219 | + | 0.951315i | \(0.599733\pi\) | |||||||
\(828\) | −11153.1 | − | 4895.79i | −0.468112 | − | 0.205484i | ||||
\(829\) | 6485.45i | 0.271712i | 0.990729 | + | 0.135856i | \(0.0433784\pi\) | ||||
−0.990729 | + | 0.135856i | \(0.956622\pi\) | |||||||
\(830\) | 6990.15 | − | 8211.31i | 0.292327 | − | 0.343396i | ||||
\(831\) | −29533.6 | − | 6196.71i | −1.23286 | − | 0.258678i | ||||
\(832\) | 36546.8 | 1.52288 | ||||||||
\(833\) | −10435.6 | + | 1273.81i | −0.434059 | + | 0.0529831i | ||||
\(834\) | 15541.4 | + | 3260.88i | 0.645269 | + | 0.135390i | ||||
\(835\) | 12237.1 | − | 14374.9i | 0.507165 | − | 0.595766i | ||||
\(836\) | 8363.51 | 0.346002 | ||||||||
\(837\) | −1879.81 | − | 1343.31i | −0.0776293 | − | 0.0554737i | ||||
\(838\) | −3988.27 | −0.164406 | ||||||||
\(839\) | 10919.1 | 0.449306 | 0.224653 | − | 0.974439i | \(-0.427875\pi\) | ||||
0.224653 | + | 0.974439i | \(0.427875\pi\) | |||||||
\(840\) | 1744.01 | − | 26415.3i | 0.0716358 | − | 1.08502i | ||||
\(841\) | −12383.9 | −0.507766 | ||||||||
\(842\) | 15387.7 | 0.629804 | ||||||||
\(843\) | −1022.45 | − | 214.530i | −0.0417736 | − | 0.00876490i | ||||
\(844\) | 10272.6 | 0.418956 | ||||||||
\(845\) | −20999.5 | − | 17876.5i | −0.854916 | − | 0.727775i | ||||
\(846\) | −8.93267 | + | 20.3495i | −0.000363016 | + | 0.000826986i | ||||
\(847\) | −8200.88 | + | 9262.78i | −0.332687 | + | 0.375765i | ||||
\(848\) | −187.565 | −0.00759554 | ||||||||
\(849\) | −5131.01 | + | 24454.5i | −0.207416 | + | 0.988547i | ||||
\(850\) | −8488.58 | + | 1372.67i | −0.342536 | + | 0.0553908i | ||||
\(851\) | 12475.7i | 0.502538i | ||||||||
\(852\) | −11651.0 | − | 2444.60i | −0.468493 | − | 0.0982987i | ||||
\(853\) | 33026.1 | 1.32567 | 0.662833 | − | 0.748768i | \(-0.269354\pi\) | ||||
0.662833 | + | 0.748768i | \(0.269354\pi\) | |||||||
\(854\) | 2601.00 | + | 2302.82i | 0.104221 | + | 0.0922727i | ||||
\(855\) | −29772.1 | + | 14452.1i | −1.19086 | + | 0.578074i | ||||
\(856\) | 24333.8 | 0.971626 | ||||||||
\(857\) | − | 25463.0i | − | 1.01494i | −0.861671 | − | 0.507468i | \(-0.830582\pi\) | ||
0.861671 | − | 0.507468i | \(-0.169418\pi\) | |||||||
\(858\) | −20069.9 | − | 4211.03i | −0.798571 | − | 0.167555i | ||||
\(859\) | 16073.2i | 0.638429i | 0.947682 | + | 0.319215i | \(0.103419\pi\) | ||||
−0.947682 | + | 0.319215i | \(0.896581\pi\) | |||||||
\(860\) | 4135.33 | − | 4857.77i | 0.163969 | − | 0.192614i | ||||
\(861\) | −21396.9 | − | 28779.7i | −0.846928 | − | 1.13915i | ||||
\(862\) | 3199.61i | 0.126426i | ||||||||
\(863\) | 17723.7 | 0.699099 | 0.349549 | − | 0.936918i | \(-0.386335\pi\) | ||||
0.349549 | + | 0.936918i | \(0.386335\pi\) | |||||||
\(864\) | 10285.3 | − | 14393.2i | 0.404993 | − | 0.566743i | ||||
\(865\) | −5215.62 | + | 6126.78i | −0.205013 | + | 0.240829i | ||||
\(866\) | 13159.8 | 0.516382 | ||||||||
\(867\) | 4239.86 | − | 20207.2i | 0.166082 | − | 0.791550i | ||||
\(868\) | 676.568 | + | 599.005i | 0.0264565 | + | 0.0234235i | ||||
\(869\) | − | 32708.1i | − | 1.27681i | ||||||
\(870\) | 15305.0 | + | 19771.7i | 0.596425 | + | 0.770488i | ||||
\(871\) | 73764.7i | 2.86960i | ||||||||
\(872\) | 19953.7 | 0.774904 | ||||||||
\(873\) | −10758.7 | − | 4722.65i | −0.417097 | − | 0.183090i | ||||
\(874\) | 37465.6i | 1.44999i | ||||||||
\(875\) | 7678.86 | + | 24717.5i | 0.296677 | + | 0.954978i | ||||
\(876\) | 1416.61 | − | 6751.61i | 0.0546381 | − | 0.260406i | ||||
\(877\) | 24096.5i | 0.927802i | 0.885887 | + | 0.463901i | \(0.153551\pi\) | ||||
−0.885887 | + | 0.463901i | \(0.846449\pi\) | |||||||
\(878\) | − | 21744.6i | − | 0.835816i | ||||||
\(879\) | −34079.5 | − | 7150.53i | −1.30771 | − | 0.274381i | ||||
\(880\) | −5881.93 | + | 6909.49i | −0.225318 | + | 0.264681i | ||||
\(881\) | −22774.5 | −0.870934 | −0.435467 | − | 0.900205i | \(-0.643417\pi\) | ||||
−0.435467 | + | 0.900205i | \(0.643417\pi\) | |||||||
\(882\) | 5986.87 | − | 19904.3i | 0.228558 | − | 0.759880i | ||||
\(883\) | − | 739.337i | − | 0.0281774i | −0.999901 | − | 0.0140887i | \(-0.995515\pi\) | ||
0.999901 | − | 0.0140887i | \(-0.00448472\pi\) | |||||||
\(884\) | 6201.43i | 0.235946i | ||||||||
\(885\) | −9133.31 | + | 7069.98i | −0.346907 | + | 0.268536i | ||||
\(886\) | −39684.9 | −1.50479 | ||||||||
\(887\) | 2411.83i | 0.0912979i | 0.998958 | + | 0.0456490i | \(0.0145356\pi\) | ||||
−0.998958 | + | 0.0456490i | \(0.985464\pi\) | |||||||
\(888\) | −10251.9 | − | 2151.05i | −0.387424 | − | 0.0812888i | ||||
\(889\) | −458.428 | − | 405.873i | −0.0172949 | − | 0.0153122i | ||||
\(890\) | −101.194 | − | 86.1447i | −0.00381127 | − | 0.00324447i | ||||
\(891\) | −13817.1 | + | 12705.7i | −0.519516 | + | 0.477731i | ||||
\(892\) | −6064.98 | −0.227657 | ||||||||
\(893\) | −40.2062 | −0.00150666 | ||||||||
\(894\) | −33918.2 | − | 7116.67i | −1.26890 | − | 0.266238i | ||||
\(895\) | 8196.11 | − | 9627.96i | 0.306107 | − | 0.359583i | ||||
\(896\) | 2361.60 | − | 2667.39i | 0.0880529 | − | 0.0994546i | ||||
\(897\) | −11095.2 | + | 52879.9i | −0.412996 | + | 1.96835i | ||||
\(898\) | 11841.1i | 0.440027i | ||||||||
\(899\) | −3158.01 | −0.117159 | ||||||||
\(900\) | −2505.99 | + | 9680.16i | −0.0928143 | + | 0.358525i | ||||
\(901\) | − | 182.389i | − | 0.00674389i | ||||||
\(902\) | 21535.9i | 0.794973i | ||||||||
\(903\) | 14873.7 | − | 11058.2i | 0.548135 | − | 0.407524i | ||||
\(904\) | −2650.18 | −0.0975039 | ||||||||
\(905\) | −7769.34 | + | 9126.63i | −0.285372 | + | 0.335226i | ||||
\(906\) | −3487.55 | + | 16621.7i | −0.127888 | + | 0.609514i | ||||
\(907\) | − | 21835.5i | − | 0.799379i | −0.916651 | − | 0.399690i | \(-0.869118\pi\) | ||
0.916651 | − | 0.399690i | \(-0.130882\pi\) | |||||||
\(908\) | 11846.4i | 0.432971i | ||||||||
\(909\) | 27749.3 | + | 12180.9i | 1.01253 | + | 0.444461i | ||||
\(910\) | −31422.2 | + | 4456.66i | −1.14466 | + | 0.162348i | ||||
\(911\) | 25167.1i | 0.915282i | 0.889137 | + | 0.457641i | \(0.151306\pi\) | ||||
−0.889137 | + | 0.457641i | \(0.848694\pi\) | |||||||
\(912\) | −17573.2 | − | 3687.19i | −0.638055 | − | 0.133876i | ||||
\(913\) | 11065.5 | 0.401113 | ||||||||
\(914\) | − | 1562.83i | − | 0.0565577i | ||||||
\(915\) | −2972.02 | − | 3839.38i | −0.107379 | − | 0.138717i | ||||
\(916\) | 9852.92i | 0.355403i | ||||||||
\(917\) | 12243.7 | − | 13829.1i | 0.440918 | − | 0.498011i | ||||
\(918\) | −7852.25 | − | 5611.20i | −0.282313 | − | 0.201740i | ||||
\(919\) | −30919.9 | −1.10985 | −0.554925 | − | 0.831900i | \(-0.687253\pi\) | ||||
−0.554925 | + | 0.831900i | \(0.687253\pi\) | |||||||
\(920\) | 31894.6 | + | 27151.3i | 1.14297 | + | 0.972992i | ||||
\(921\) | 1575.04 | − | 7506.68i | 0.0563512 | − | 0.268571i | ||||
\(922\) | 17260.8 | 0.616546 | ||||||||
\(923\) | 52808.6i | 1.88322i | ||||||||
\(924\) | 5891.56 | − | 4380.22i | 0.209760 | − | 0.155951i | ||||
\(925\) | 10110.4 | − | 1634.93i | 0.359381 | − | 0.0581146i | ||||
\(926\) | 10139.0i | 0.359813i | ||||||||
\(927\) | 15457.5 | + | 6785.28i | 0.547672 | + | 0.240408i | ||||
\(928\) | − | 24180.0i | − | 0.855332i | ||||||
\(929\) | 27897.3 | 0.985230 | 0.492615 | − | 0.870247i | \(-0.336041\pi\) | ||||
0.492615 | + | 0.870247i | \(0.336041\pi\) | |||||||
\(930\) | 1314.38 | + | 1697.97i | 0.0463443 | + | 0.0598696i | ||||
\(931\) | 37326.6 | − | 4556.24i | 1.31400 | − | 0.160392i | ||||
\(932\) | −10264.5 | −0.360758 | ||||||||
\(933\) | −2306.89 | + | 10994.7i | −0.0809478 | + | 0.385798i | ||||
\(934\) | − | 39742.3i | − | 1.39230i | ||||||
\(935\) | −6718.80 | − | 5719.60i | −0.235004 | − | 0.200054i | ||||
\(936\) | −41541.3 | − | 18235.1i | −1.45066 | − | 0.636786i | ||||
\(937\) | 28956.4 | 1.00957 | 0.504784 | − | 0.863246i | \(-0.331572\pi\) | ||||
0.504784 | + | 0.863246i | \(0.331572\pi\) | |||||||
\(938\) | 33616.2 | + | 29762.4i | 1.17016 | + | 1.03601i | ||||
\(939\) | −1267.43 | + | 6040.61i | −0.0440481 | + | 0.209934i | ||||
\(940\) | −7.87455 | + | 9.25022i | −0.000273233 | + | 0.000320967i | ||||
\(941\) | 38808.0 | 1.34442 | 0.672212 | − | 0.740358i | \(-0.265344\pi\) | ||||
0.672212 | + | 0.740358i | \(0.265344\pi\) | |||||||
\(942\) | 6952.42 | − | 33135.3i | 0.240469 | − | 1.14608i | ||||
\(943\) | 56742.5 | 1.95948 | ||||||||
\(944\) | −6266.61 | −0.216060 | ||||||||
\(945\) | −13403.5 | + | 25773.1i | −0.461393 | + | 0.887196i | ||||
\(946\) | −11130.0 | −0.382524 | ||||||||
\(947\) | 19164.9 | 0.657629 | 0.328814 | − | 0.944395i | \(-0.393351\pi\) | ||||
0.328814 | + | 0.944395i | \(0.393351\pi\) | |||||||
\(948\) | 4015.72 | − | 19139.0i | 0.137579 | − | 0.655702i | ||||
\(949\) | −30602.0 | −1.04677 | ||||||||
\(950\) | 30362.5 | − | 4909.85i | 1.03694 | − | 0.167681i | ||||
\(951\) | −4567.59 | + | 21769.2i | −0.155746 | + | 0.742287i | ||||
\(952\) | 10457.2 | + | 9258.40i | 0.356009 | + | 0.315196i | ||||
\(953\) | 3621.39 | 0.123094 | 0.0615469 | − | 0.998104i | \(-0.480397\pi\) | ||||
0.0615469 | + | 0.998104i | \(0.480397\pi\) | |||||||
\(954\) | 330.188 | + | 144.940i | 0.0112057 | + | 0.00491888i | ||||
\(955\) | −11676.9 | + | 13716.9i | −0.395661 | + | 0.464782i | ||||
\(956\) | − | 13390.3i | − | 0.453006i | ||||||
\(957\) | −5268.57 | + | 25110.1i | −0.177961 | + | 0.848165i | ||||
\(958\) | −28520.3 | −0.961848 | ||||||||
\(959\) | 16859.8 | − | 19042.9i | 0.567707 | − | 0.641217i | ||||
\(960\) | −24585.0 | + | 19030.9i | −0.826539 | + | 0.639813i | ||||
\(961\) | 29519.8 | 0.990896 | ||||||||
\(962\) | 12558.1i | 0.420882i | ||||||||
\(963\) | −24450.8 | − | 10733.0i | −0.818190 | − | 0.359155i | ||||
\(964\) | 20997.4i | 0.701537i | ||||||||
\(965\) | −14219.1 | + | 16703.1i | −0.474330 | + | 0.557194i | ||||
\(966\) | 19621.9 | + | 26392.2i | 0.653544 | + | 0.879041i | ||||
\(967\) | − | 9516.35i | − | 0.316469i | −0.987402 | − | 0.158234i | \(-0.949420\pi\) | ||
0.987402 | − | 0.158234i | \(-0.0505801\pi\) | |||||||
\(968\) | 16435.8 | 0.545730 | ||||||||
\(969\) | 3585.43 | − | 17088.2i | 0.118865 | − | 0.566514i | ||||
\(970\) | 8314.88 | + | 7078.31i | 0.275231 | + | 0.234300i | ||||
\(971\) | −1539.07 | −0.0508661 | −0.0254331 | − | 0.999677i | \(-0.508096\pi\) | ||||
−0.0254331 | + | 0.999677i | \(0.508096\pi\) | |||||||
\(972\) | −9644.93 | + | 5738.32i | −0.318273 | + | 0.189359i | ||||
\(973\) | 18881.4 | + | 16716.8i | 0.622105 | + | 0.550786i | ||||
\(974\) | − | 503.360i | − | 0.0165592i | ||||||
\(975\) | 44308.3 | + | 2061.77i | 1.45539 | + | 0.0677225i | ||||
\(976\) | − | 2634.30i | − | 0.0863954i | ||||||
\(977\) | −20070.0 | −0.657213 | −0.328607 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328607 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(978\) | 19022.0 | + | 3991.17i | 0.621939 | + | 0.130494i | ||||
\(979\) | − | 136.369i | − | 0.00445185i | ||||||
\(980\) | 6262.32 | − | 9480.08i | 0.204125 | − | 0.309010i | ||||
\(981\) | −20049.6 | − | 8801.04i | −0.652534 | − | 0.286438i | ||||
\(982\) | 14824.8i | 0.481750i | ||||||||
\(983\) | − | 7463.49i | − | 0.242165i | −0.992642 | − | 0.121083i | \(-0.961363\pi\) | ||
0.992642 | − | 0.121083i | \(-0.0386366\pi\) | |||||||
\(984\) | −9783.52 | + | 46628.4i | −0.316959 | + | 1.51063i | ||||
\(985\) | 5610.13 | + | 4775.81i | 0.181476 | + | 0.154487i | ||||
\(986\) | −13191.5 | −0.426068 | ||||||||
\(987\) | −28.3227 | + | 21.0572i | −0.000913395 | + | 0.000679085i | ||||
\(988\) | − | 22181.7i | − | 0.714263i | ||||||
\(989\) | 29325.3i | 0.942860i | ||||||||
\(990\) | 15693.8 | − | 7618.17i | 0.503819 | − | 0.244567i | ||||
\(991\) | −21807.0 | −0.699014 | −0.349507 | − | 0.936934i | \(-0.613651\pi\) | ||||
−0.349507 | + | 0.936934i | \(0.613651\pi\) | |||||||
\(992\) | − | 2076.55i | − | 0.0664623i | ||||||
\(993\) | 5308.64 | − | 25301.1i | 0.169652 | − | 0.808566i | ||||
\(994\) | 24066.1 | + | 21307.1i | 0.767936 | + | 0.679899i | ||||
\(995\) | 36690.3 | − | 43100.1i | 1.16901 | − | 1.37323i | ||||
\(996\) | 6474.95 | + | 1358.57i | 0.205991 | + | 0.0432207i | ||||
\(997\) | −34022.7 | −1.08075 | −0.540377 | − | 0.841423i | \(-0.681718\pi\) | ||||
−0.540377 | + | 0.841423i | \(0.681718\pi\) | |||||||
\(998\) | −31608.5 | −1.00255 | ||||||||
\(999\) | 9352.47 | + | 6683.25i | 0.296195 | + | 0.211660i |
(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 | 105.4.g.b.104.15 | yes | 40 | |
3.2 | odd | 2 | inner | 105.4.g.b.104.28 | yes | 40 | |
5.4 | even | 2 | inner | 105.4.g.b.104.26 | yes | 40 | |
7.6 | odd | 2 | inner | 105.4.g.b.104.14 | yes | 40 | |
15.14 | odd | 2 | inner | 105.4.g.b.104.13 | ✓ | 40 | |
21.20 | even | 2 | inner | 105.4.g.b.104.25 | yes | 40 | |
35.34 | odd | 2 | inner | 105.4.g.b.104.27 | yes | 40 | |
105.104 | even | 2 | inner | 105.4.g.b.104.16 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.g.b.104.13 | ✓ | 40 | 15.14 | odd | 2 | inner | |
105.4.g.b.104.14 | yes | 40 | 7.6 | odd | 2 | inner | |
105.4.g.b.104.15 | yes | 40 | 1.1 | even | 1 | trivial | |
105.4.g.b.104.16 | yes | 40 | 105.104 | even | 2 | inner | |
105.4.g.b.104.25 | yes | 40 | 21.20 | even | 2 | inner | |
105.4.g.b.104.26 | yes | 40 | 5.4 | even | 2 | inner | |
105.4.g.b.104.27 | yes | 40 | 35.34 | odd | 2 | inner | |
105.4.g.b.104.28 | yes | 40 | 3.2 | odd | 2 | inner |