Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [143,4,Mod(100,143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(143, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("143.100");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 143 = 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 143.e (of order \(3\), degree \(2\), 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: | \(8.43727313082\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 133.2 | ||
Character | \(\chi\) | \(=\) | 143.133 |
Dual form | 143.4.e.b.100.2 |
$q$-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 \(\left(\mathbb{Z}/143\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.09541 | − | 3.62936i | −0.740841 | − | 1.28317i | −0.952113 | − | 0.305747i | \(-0.901094\pi\) |
0.211272 | − | 0.977427i | \(-0.432239\pi\) | |||||||
\(3\) | −2.35272 | − | 4.07503i | −0.452781 | − | 0.784240i | 0.545777 | − | 0.837931i | \(-0.316235\pi\) |
−0.998558 | + | 0.0536910i | \(0.982901\pi\) | |||||||
\(4\) | −4.78153 | + | 8.28185i | −0.597691 | + | 1.03523i | ||||
\(5\) | 14.4259 | 1.29029 | 0.645147 | − | 0.764058i | \(-0.276796\pi\) | ||||
0.645147 | + | 0.764058i | \(0.276796\pi\) | |||||||
\(6\) | −9.85985 | + | 17.0778i | −0.670878 | + | 1.16199i | ||||
\(7\) | 17.3506 | − | 30.0521i | 0.936844 | − | 1.62266i | 0.165531 | − | 0.986205i | \(-0.447066\pi\) |
0.771312 | − | 0.636457i | \(-0.219601\pi\) | |||||||
\(8\) | 6.55048 | 0.289493 | ||||||||
\(9\) | 2.42942 | − | 4.20788i | 0.0899786 | − | 0.155848i | ||||
\(10\) | −30.2283 | − | 52.3570i | −0.955903 | − | 1.65567i | ||||
\(11\) | −5.50000 | − | 9.52628i | −0.150756 | − | 0.261116i | ||||
\(12\) | 44.9984 | 1.08249 | ||||||||
\(13\) | 40.3094 | − | 23.9197i | 0.859986 | − | 0.510318i | ||||
\(14\) | −145.427 | −2.77621 | ||||||||
\(15\) | −33.9402 | − | 58.7861i | −0.584221 | − | 1.01190i | ||||
\(16\) | 24.5262 | + | 42.4807i | 0.383222 | + | 0.663761i | ||||
\(17\) | 37.6196 | − | 65.1590i | 0.536711 | − | 0.929611i | −0.462367 | − | 0.886689i | \(-0.653000\pi\) |
0.999078 | − | 0.0429226i | \(-0.0136669\pi\) | |||||||
\(18\) | −20.3626 | −0.266639 | ||||||||
\(19\) | −25.2778 | + | 43.7824i | −0.305217 | + | 0.528652i | −0.977310 | − | 0.211816i | \(-0.932062\pi\) |
0.672093 | + | 0.740467i | \(0.265396\pi\) | |||||||
\(20\) | −68.9779 | + | 119.473i | −0.771197 | + | 1.33575i | ||||
\(21\) | −163.284 | −1.69674 | ||||||||
\(22\) | −23.0496 | + | 39.9230i | −0.223372 | + | 0.386892i | ||||
\(23\) | 85.1614 | + | 147.504i | 0.772060 | + | 1.33725i | 0.936432 | + | 0.350848i | \(0.114107\pi\) |
−0.164372 | + | 0.986398i | \(0.552560\pi\) | |||||||
\(24\) | −15.4114 | − | 26.6934i | −0.131077 | − | 0.227032i | ||||
\(25\) | 83.1074 | 0.664859 | ||||||||
\(26\) | −171.278 | − | 96.1758i | −1.29194 | − | 0.725447i | ||||
\(27\) | −149.910 | −1.06852 | ||||||||
\(28\) | 165.925 | + | 287.390i | 1.11989 | + | 1.93970i | ||||
\(29\) | 132.876 | + | 230.149i | 0.850846 | + | 1.47371i | 0.880446 | + | 0.474147i | \(0.157243\pi\) |
−0.0295999 | + | 0.999562i | \(0.509423\pi\) | |||||||
\(30\) | −142.237 | + | 246.362i | −0.865629 | + | 1.49931i | ||||
\(31\) | −134.471 | −0.779088 | −0.389544 | − | 0.921008i | \(-0.627367\pi\) | ||||
−0.389544 | + | 0.921008i | \(0.627367\pi\) | |||||||
\(32\) | 128.987 | − | 223.412i | 0.712560 | − | 1.23419i | ||||
\(33\) | −25.8799 | + | 44.8253i | −0.136519 | + | 0.236457i | ||||
\(34\) | −315.315 | −1.59047 | ||||||||
\(35\) | 250.298 | − | 433.530i | 1.20880 | − | 2.09371i | ||||
\(36\) | 23.2327 | + | 40.2402i | 0.107559 | + | 0.186297i | ||||
\(37\) | 3.68075 | + | 6.37524i | 0.0163544 | + | 0.0283266i | 0.874087 | − | 0.485770i | \(-0.161461\pi\) |
−0.857732 | + | 0.514096i | \(0.828127\pi\) | |||||||
\(38\) | 211.870 | 0.904469 | ||||||||
\(39\) | −192.310 | − | 107.986i | −0.789597 | − | 0.443373i | ||||
\(40\) | 94.4968 | 0.373531 | ||||||||
\(41\) | −53.3593 | − | 92.4211i | −0.203252 | − | 0.352043i | 0.746322 | − | 0.665585i | \(-0.231818\pi\) |
−0.949574 | + | 0.313542i | \(0.898484\pi\) | |||||||
\(42\) | 342.148 | + | 592.618i | 1.25702 | + | 2.17721i | ||||
\(43\) | −218.702 | + | 378.803i | −0.775621 | + | 1.34342i | 0.158823 | + | 0.987307i | \(0.449230\pi\) |
−0.934445 | + | 0.356108i | \(0.884103\pi\) | |||||||
\(44\) | 105.194 | 0.360421 | ||||||||
\(45\) | 35.0467 | − | 60.7026i | 0.116099 | − | 0.201089i | ||||
\(46\) | 356.897 | − | 618.163i | 1.14395 | − | 1.98137i | ||||
\(47\) | −374.024 | −1.16079 | −0.580393 | − | 0.814337i | \(-0.697101\pi\) | ||||
−0.580393 | + | 0.814337i | \(0.697101\pi\) | |||||||
\(48\) | 115.407 | − | 199.890i | 0.347032 | − | 0.601076i | ||||
\(49\) | −430.586 | − | 745.797i | −1.25535 | − | 2.17434i | ||||
\(50\) | −174.144 | − | 301.627i | −0.492555 | − | 0.853130i | ||||
\(51\) | −354.033 | −0.972051 | ||||||||
\(52\) | 5.35896 | + | 448.209i | 0.0142914 | + | 1.19530i | ||||
\(53\) | 650.058 | 1.68476 | 0.842381 | − | 0.538882i | \(-0.181153\pi\) | ||||
0.842381 | + | 0.538882i | \(0.181153\pi\) | |||||||
\(54\) | 314.123 | + | 544.078i | 0.791607 | + | 1.37110i | ||||
\(55\) | −79.3426 | − | 137.425i | −0.194519 | − | 0.336917i | ||||
\(56\) | 113.655 | − | 196.856i | 0.271210 | − | 0.469749i | ||||
\(57\) | 237.886 | 0.552786 | ||||||||
\(58\) | 556.862 | − | 964.514i | 1.26068 | − | 2.18357i | ||||
\(59\) | −139.299 | + | 241.272i | −0.307375 | + | 0.532390i | −0.977787 | − | 0.209599i | \(-0.932784\pi\) |
0.670412 | + | 0.741989i | \(0.266117\pi\) | |||||||
\(60\) | 649.143 | 1.39673 | ||||||||
\(61\) | −26.2898 | + | 45.5353i | −0.0551815 | + | 0.0955771i | −0.892297 | − | 0.451450i | \(-0.850907\pi\) |
0.837115 | + | 0.547027i | \(0.184240\pi\) | |||||||
\(62\) | 281.773 | + | 488.045i | 0.577180 | + | 0.999705i | ||||
\(63\) | −84.3038 | − | 146.019i | −0.168592 | − | 0.292010i | ||||
\(64\) | −688.707 | −1.34513 | ||||||||
\(65\) | 581.500 | − | 345.064i | 1.10963 | − | 0.658460i | ||||
\(66\) | 216.917 | 0.404554 | ||||||||
\(67\) | 42.5053 | + | 73.6213i | 0.0775051 | + | 0.134243i | 0.902173 | − | 0.431375i | \(-0.141971\pi\) |
−0.824668 | + | 0.565617i | \(0.808638\pi\) | |||||||
\(68\) | 359.758 | + | 623.119i | 0.641575 | + | 1.11124i | ||||
\(69\) | 400.722 | − | 694.070i | 0.699148 | − | 1.21096i | ||||
\(70\) | −2097.92 | −3.58213 | ||||||||
\(71\) | −132.378 | + | 229.286i | −0.221273 | + | 0.383257i | −0.955195 | − | 0.295978i | \(-0.904355\pi\) |
0.733921 | + | 0.679234i | \(0.237688\pi\) | |||||||
\(72\) | 15.9139 | − | 27.5637i | 0.0260482 | − | 0.0451168i | ||||
\(73\) | 269.190 | 0.431593 | 0.215796 | − | 0.976438i | \(-0.430765\pi\) | ||||
0.215796 | + | 0.976438i | \(0.430765\pi\) | |||||||
\(74\) | 15.4254 | − | 26.7176i | 0.0242320 | − | 0.0419710i | ||||
\(75\) | −195.528 | − | 338.665i | −0.301036 | − | 0.521409i | ||||
\(76\) | −241.733 | − | 418.694i | −0.364851 | − | 0.631940i | ||||
\(77\) | −381.713 | −0.564938 | ||||||||
\(78\) | 11.0506 | + | 924.239i | 0.0160414 | + | 1.34166i | ||||
\(79\) | 214.784 | 0.305887 | 0.152943 | − | 0.988235i | \(-0.451125\pi\) | ||||
0.152943 | + | 0.988235i | \(0.451125\pi\) | |||||||
\(80\) | 353.814 | + | 612.823i | 0.494470 | + | 0.856446i | ||||
\(81\) | 287.101 | + | 497.274i | 0.393829 | + | 0.682132i | ||||
\(82\) | −223.620 | + | 387.321i | −0.301155 | + | 0.521615i | ||||
\(83\) | 1129.86 | 1.49419 | 0.747095 | − | 0.664717i | \(-0.231448\pi\) | ||||
0.747095 | + | 0.664717i | \(0.231448\pi\) | |||||||
\(84\) | 780.748 | − | 1352.30i | 1.01413 | − | 1.75652i | ||||
\(85\) | 542.697 | − | 939.980i | 0.692515 | − | 1.19947i | ||||
\(86\) | 1833.08 | 2.29845 | ||||||||
\(87\) | 625.242 | − | 1082.95i | 0.770494 | − | 1.33453i | ||||
\(88\) | −36.0277 | − | 62.4017i | −0.0436427 | − | 0.0755914i | ||||
\(89\) | 436.827 | + | 756.606i | 0.520264 | + | 0.901124i | 0.999722 | + | 0.0235594i | \(0.00749988\pi\) |
−0.479458 | + | 0.877565i | \(0.659167\pi\) | |||||||
\(90\) | −293.749 | −0.344043 | ||||||||
\(91\) | −19.4459 | − | 1626.40i | −0.0224010 | − | 1.87355i | ||||
\(92\) | −1628.81 | −1.84581 | ||||||||
\(93\) | 316.373 | + | 547.974i | 0.352756 | + | 0.610992i | ||||
\(94\) | 783.734 | + | 1357.47i | 0.859958 | + | 1.48949i | ||||
\(95\) | −364.656 | + | 631.602i | −0.393820 | + | 0.682116i | ||||
\(96\) | −1213.88 | −1.29054 | ||||||||
\(97\) | 260.296 | − | 450.847i | 0.272465 | − | 0.471923i | −0.697027 | − | 0.717044i | \(-0.745494\pi\) |
0.969492 | + | 0.245121i | \(0.0788278\pi\) | |||||||
\(98\) | −1804.51 | + | 3125.51i | −1.86003 | + | 3.22167i | ||||
\(99\) | −53.4473 | −0.0542591 | ||||||||
\(100\) | −397.380 | + | 688.283i | −0.397380 | + | 0.688283i | ||||
\(101\) | 207.101 | + | 358.709i | 0.204033 | + | 0.353395i | 0.949824 | − | 0.312785i | \(-0.101262\pi\) |
−0.745792 | + | 0.666179i | \(0.767928\pi\) | |||||||
\(102\) | 741.847 | + | 1284.92i | 0.720135 | + | 1.24731i | ||||
\(103\) | −1396.04 | −1.33549 | −0.667746 | − | 0.744389i | \(-0.732741\pi\) | ||||
−0.667746 | + | 0.744389i | \(0.732741\pi\) | |||||||
\(104\) | 264.046 | − | 156.686i | 0.248960 | − | 0.147734i | ||||
\(105\) | −2355.53 | −2.18929 | ||||||||
\(106\) | −1362.14 | − | 2359.30i | −1.24814 | − | 2.16184i | ||||
\(107\) | −164.717 | − | 285.299i | −0.148821 | − | 0.257765i | 0.781971 | − | 0.623315i | \(-0.214214\pi\) |
−0.930792 | + | 0.365550i | \(0.880881\pi\) | |||||||
\(108\) | 716.798 | − | 1241.53i | 0.638647 | − | 1.10617i | ||||
\(109\) | −726.701 | −0.638581 | −0.319290 | − | 0.947657i | \(-0.603445\pi\) | ||||
−0.319290 | + | 0.947657i | \(0.603445\pi\) | |||||||
\(110\) | −332.511 | + | 575.927i | −0.288216 | + | 0.499204i | ||||
\(111\) | 17.3195 | − | 29.9983i | 0.0148099 | − | 0.0256515i | ||||
\(112\) | 1702.18 | 1.43608 | ||||||||
\(113\) | −837.170 | + | 1450.02i | −0.696941 | + | 1.20714i | 0.272581 | + | 0.962133i | \(0.412123\pi\) |
−0.969522 | + | 0.245004i | \(0.921211\pi\) | |||||||
\(114\) | −498.470 | − | 863.376i | −0.409527 | − | 0.709321i | ||||
\(115\) | 1228.53 | + | 2127.88i | 0.996184 | + | 1.72544i | ||||
\(116\) | −2541.41 | −2.03417 | ||||||||
\(117\) | −2.72281 | − | 227.728i | −0.00215149 | − | 0.179944i | ||||
\(118\) | 1167.55 | 0.910865 | ||||||||
\(119\) | −1305.44 | − | 2261.10i | −1.00563 | − | 1.74180i | ||||
\(120\) | −222.324 | − | 385.077i | −0.169128 | − | 0.292938i | ||||
\(121\) | −60.5000 | + | 104.789i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 220.352 | 0.163523 | ||||||||
\(123\) | −251.079 | + | 434.882i | −0.184057 | + | 0.318796i | ||||
\(124\) | 642.977 | − | 1113.67i | 0.465654 | − | 0.806536i | ||||
\(125\) | −604.340 | −0.432430 | ||||||||
\(126\) | −353.303 | + | 611.939i | −0.249799 | + | 0.432665i | ||||
\(127\) | −336.909 | − | 583.544i | −0.235400 | − | 0.407726i | 0.723989 | − | 0.689812i | \(-0.242307\pi\) |
−0.959389 | + | 0.282086i | \(0.908973\pi\) | |||||||
\(128\) | 411.229 | + | 712.270i | 0.283968 | + | 0.491846i | ||||
\(129\) | 2058.18 | 1.40475 | ||||||||
\(130\) | −2470.85 | − | 1387.42i | −1.66698 | − | 0.936040i | ||||
\(131\) | 1455.87 | 0.970989 | 0.485495 | − | 0.874240i | \(-0.338640\pi\) | ||||
0.485495 | + | 0.874240i | \(0.338640\pi\) | |||||||
\(132\) | −247.491 | − | 428.667i | −0.163192 | − | 0.282657i | ||||
\(133\) | 877.170 | + | 1519.30i | 0.571882 | + | 0.990528i | ||||
\(134\) | 178.132 | − | 308.534i | 0.114838 | − | 0.198905i | ||||
\(135\) | −2162.59 | −1.37871 | ||||||||
\(136\) | 246.426 | − | 426.823i | 0.155374 | − | 0.269116i | ||||
\(137\) | 1116.45 | − | 1933.75i | 0.696239 | − | 1.20592i | −0.273522 | − | 0.961866i | \(-0.588189\pi\) |
0.969761 | − | 0.244056i | \(-0.0784781\pi\) | |||||||
\(138\) | −3358.71 | −2.07183 | ||||||||
\(139\) | 652.130 | − | 1129.52i | 0.397935 | − | 0.689244i | −0.595536 | − | 0.803329i | \(-0.703060\pi\) |
0.993471 | + | 0.114085i | \(0.0363936\pi\) | |||||||
\(140\) | 2393.62 | + | 4145.87i | 1.44498 | + | 2.50278i | ||||
\(141\) | 879.972 | + | 1524.16i | 0.525582 | + | 0.910335i | ||||
\(142\) | 1109.55 | 0.655714 | ||||||||
\(143\) | −449.568 | − | 252.440i | −0.262900 | − | 0.147623i | ||||
\(144\) | 238.338 | 0.137927 | ||||||||
\(145\) | 1916.87 | + | 3320.11i | 1.09784 | + | 1.90152i | ||||
\(146\) | −564.064 | − | 976.988i | −0.319742 | − | 0.553809i | ||||
\(147\) | −2026.10 | + | 3509.30i | −1.13680 | + | 1.96900i | ||||
\(148\) | −70.3984 | −0.0390994 | ||||||||
\(149\) | 1135.03 | − | 1965.93i | 0.624063 | − | 1.08091i | −0.364659 | − | 0.931141i | \(-0.618814\pi\) |
0.988721 | − | 0.149767i | \(-0.0478523\pi\) | |||||||
\(150\) | −819.426 | + | 1419.29i | −0.446039 | + | 0.772562i | ||||
\(151\) | 1327.17 | 0.715257 | 0.357629 | − | 0.933864i | \(-0.383585\pi\) | ||||
0.357629 | + | 0.933864i | \(0.383585\pi\) | |||||||
\(152\) | −165.582 | + | 286.796i | −0.0883583 | + | 0.153041i | ||||
\(153\) | −182.788 | − | 316.598i | −0.0965851 | − | 0.167290i | ||||
\(154\) | 799.847 | + | 1385.38i | 0.418529 | + | 0.724914i | ||||
\(155\) | −1939.87 | −1.00525 | ||||||||
\(156\) | 1813.86 | − | 1076.35i | 0.930928 | − | 0.552415i | ||||
\(157\) | −554.004 | −0.281620 | −0.140810 | − | 0.990037i | \(-0.544971\pi\) | ||||
−0.140810 | + | 0.990037i | \(0.544971\pi\) | |||||||
\(158\) | −450.061 | − | 779.529i | −0.226613 | − | 0.392506i | ||||
\(159\) | −1529.41 | − | 2649.01i | −0.762828 | − | 1.32126i | ||||
\(160\) | 1860.76 | − | 3222.93i | 0.919412 | − | 1.59247i | ||||
\(161\) | 5910.40 | 2.89320 | ||||||||
\(162\) | 1203.19 | − | 2083.99i | 0.583529 | − | 1.01070i | ||||
\(163\) | 387.250 | − | 670.737i | 0.186084 | − | 0.322308i | −0.757857 | − | 0.652421i | \(-0.773754\pi\) |
0.943941 | + | 0.330113i | \(0.107087\pi\) | |||||||
\(164\) | 1020.56 | 0.485927 | ||||||||
\(165\) | −373.342 | + | 646.647i | −0.176149 | + | 0.305099i | ||||
\(166\) | −2367.52 | − | 4100.66i | −1.10696 | − | 1.91731i | ||||
\(167\) | 325.532 | + | 563.839i | 0.150841 | + | 0.261264i | 0.931537 | − | 0.363647i | \(-0.118468\pi\) |
−0.780696 | + | 0.624911i | \(0.785135\pi\) | |||||||
\(168\) | −1069.59 | −0.491195 | ||||||||
\(169\) | 1052.69 | − | 1928.38i | 0.479151 | − | 0.877733i | ||||
\(170\) | −4548.71 | −2.05218 | ||||||||
\(171\) | 122.821 | + | 212.732i | 0.0549260 | + | 0.0951347i | ||||
\(172\) | −2091.46 | − | 3622.51i | −0.927163 | − | 1.60589i | ||||
\(173\) | −1727.23 | + | 2991.65i | −0.759069 | + | 1.31475i | 0.184257 | + | 0.982878i | \(0.441012\pi\) |
−0.943326 | + | 0.331868i | \(0.892321\pi\) | |||||||
\(174\) | −5240.56 | −2.28325 | ||||||||
\(175\) | 1441.96 | − | 2497.55i | 0.622869 | − | 1.07884i | ||||
\(176\) | 269.789 | − | 467.287i | 0.115546 | − | 0.200131i | ||||
\(177\) | 1310.92 | 0.556695 | ||||||||
\(178\) | 1830.67 | − | 3170.81i | 0.770866 | − | 1.33518i | ||||
\(179\) | 944.081 | + | 1635.20i | 0.394212 | + | 0.682795i | 0.993000 | − | 0.118112i | \(-0.0376843\pi\) |
−0.598788 | + | 0.800907i | \(0.704351\pi\) | |||||||
\(180\) | 335.153 | + | 580.502i | 0.138782 | + | 0.240378i | ||||
\(181\) | −3714.29 | −1.52531 | −0.762654 | − | 0.646807i | \(-0.776104\pi\) | ||||
−0.762654 | + | 0.646807i | \(0.776104\pi\) | |||||||
\(182\) | −5862.06 | + | 3478.57i | −2.38750 | + | 1.41675i | ||||
\(183\) | 247.410 | 0.0999405 | ||||||||
\(184\) | 557.848 | + | 966.221i | 0.223506 | + | 0.387124i | ||||
\(185\) | 53.0982 | + | 91.9688i | 0.0211019 | + | 0.0365496i | ||||
\(186\) | 1325.86 | − | 2296.46i | 0.522673 | − | 0.905295i | ||||
\(187\) | −827.631 | −0.323649 | ||||||||
\(188\) | 1788.40 | − | 3097.61i | 0.693791 | − | 1.20168i | ||||
\(189\) | −2601.02 | + | 4505.11i | −1.00104 | + | 1.73385i | ||||
\(190\) | 3056.42 | 1.16703 | ||||||||
\(191\) | 472.908 | − | 819.101i | 0.179154 | − | 0.310304i | −0.762437 | − | 0.647063i | \(-0.775997\pi\) |
0.941591 | + | 0.336759i | \(0.109331\pi\) | |||||||
\(192\) | 1620.33 | + | 2806.50i | 0.609050 | + | 1.05490i | ||||
\(193\) | 57.9300 | + | 100.338i | 0.0216057 | + | 0.0374221i | 0.876626 | − | 0.481172i | \(-0.159789\pi\) |
−0.855020 | + | 0.518594i | \(0.826456\pi\) | |||||||
\(194\) | −2181.72 | −0.807413 | ||||||||
\(195\) | −2774.25 | − | 1557.79i | −1.01881 | − | 0.572081i | ||||
\(196\) | 8235.43 | 3.00125 | ||||||||
\(197\) | 1257.50 | + | 2178.05i | 0.454787 | + | 0.787715i | 0.998676 | − | 0.0514425i | \(-0.0163819\pi\) |
−0.543889 | + | 0.839157i | \(0.683049\pi\) | |||||||
\(198\) | 111.994 | + | 193.980i | 0.0401974 | + | 0.0696239i | ||||
\(199\) | 398.451 | − | 690.138i | 0.141937 | − | 0.245842i | −0.786289 | − | 0.617859i | \(-0.788000\pi\) |
0.928226 | + | 0.372017i | \(0.121334\pi\) | |||||||
\(200\) | 544.394 | 0.192472 | ||||||||
\(201\) | 200.006 | − | 346.420i | 0.0701857 | − | 0.121565i | ||||
\(202\) | 867.924 | − | 1503.29i | 0.302311 | − | 0.523619i | ||||
\(203\) | 9221.94 | 3.18844 | ||||||||
\(204\) | 1692.82 | − | 2932.05i | 0.580986 | − | 1.00630i | ||||
\(205\) | −769.758 | − | 1333.26i | −0.262255 | − | 0.454239i | ||||
\(206\) | 2925.28 | + | 5066.73i | 0.989388 | + | 1.71367i | ||||
\(207\) | 827.572 | 0.277875 | ||||||||
\(208\) | 2004.76 | + | 1125.71i | 0.668295 | + | 0.375259i | ||||
\(209\) | 556.112 | 0.184053 | ||||||||
\(210\) | 4935.81 | + | 8549.07i | 1.62192 | + | 2.80925i | ||||
\(211\) | −84.7465 | − | 146.785i | −0.0276502 | − | 0.0478915i | 0.851869 | − | 0.523755i | \(-0.175469\pi\) |
−0.879519 | + | 0.475863i | \(0.842136\pi\) | |||||||
\(212\) | −3108.27 | + | 5383.68i | −1.00697 | + | 1.74412i | ||||
\(213\) | 1245.80 | 0.400754 | ||||||||
\(214\) | −690.302 | + | 1195.64i | −0.220505 | + | 0.381926i | ||||
\(215\) | −3154.98 | + | 5464.58i | −1.00078 | + | 1.73340i | ||||
\(216\) | −981.982 | −0.309331 | ||||||||
\(217\) | −2333.15 | + | 4041.14i | −0.729884 | + | 1.26420i | ||||
\(218\) | 1522.74 | + | 2637.46i | 0.473087 | + | 0.819410i | ||||
\(219\) | −633.328 | − | 1096.96i | −0.195417 | − | 0.338472i | ||||
\(220\) | 1517.51 | 0.465049 | ||||||||
\(221\) | −42.1627 | − | 3526.37i | −0.0128333 | − | 1.07335i | ||||
\(222\) | −145.166 | −0.0438871 | ||||||||
\(223\) | 1428.61 | + | 2474.43i | 0.429000 | + | 0.743050i | 0.996785 | − | 0.0801271i | \(-0.0255326\pi\) |
−0.567784 | + | 0.823177i | \(0.692199\pi\) | |||||||
\(224\) | −4476.01 | − | 7752.67i | −1.33512 | − | 2.31249i | ||||
\(225\) | 201.903 | − | 349.706i | 0.0598231 | − | 0.103617i | ||||
\(226\) | 7016.87 | 2.06529 | ||||||||
\(227\) | 147.869 | − | 256.117i | 0.0432354 | − | 0.0748859i | −0.843598 | − | 0.536975i | \(-0.819567\pi\) |
0.886833 | + | 0.462090i | \(0.152900\pi\) | |||||||
\(228\) | −1137.46 | + | 1970.14i | −0.330395 | + | 0.572261i | ||||
\(229\) | −3805.61 | −1.09817 | −0.549087 | − | 0.835765i | \(-0.685024\pi\) | ||||
−0.549087 | + | 0.835765i | \(0.685024\pi\) | |||||||
\(230\) | 5148.57 | − | 8917.58i | 1.47603 | − | 2.55656i | ||||
\(231\) | 898.064 | + | 1555.49i | 0.255793 | + | 0.443047i | ||||
\(232\) | 870.405 | + | 1507.59i | 0.246314 | + | 0.426629i | ||||
\(233\) | −1773.05 | −0.498526 | −0.249263 | − | 0.968436i | \(-0.580188\pi\) | ||||
−0.249263 | + | 0.968436i | \(0.580188\pi\) | |||||||
\(234\) | −820.804 | + | 487.067i | −0.229306 | + | 0.136071i | ||||
\(235\) | −5395.64 | −1.49776 | ||||||||
\(236\) | −1332.12 | − | 2307.30i | −0.367431 | − | 0.636409i | ||||
\(237\) | −505.326 | − | 875.250i | −0.138500 | − | 0.239889i | ||||
\(238\) | −5470.89 | + | 9475.87i | −1.49002 | + | 2.58080i | ||||
\(239\) | 1276.93 | 0.345597 | 0.172799 | − | 0.984957i | \(-0.444719\pi\) | ||||
0.172799 | + | 0.984957i | \(0.444719\pi\) | |||||||
\(240\) | 1664.85 | − | 2883.60i | 0.447773 | − | 0.775565i | ||||
\(241\) | −179.882 | + | 311.564i | −0.0480797 | + | 0.0832765i | −0.889064 | − | 0.457784i | \(-0.848643\pi\) |
0.840984 | + | 0.541060i | \(0.181977\pi\) | |||||||
\(242\) | 507.090 | 0.134698 | ||||||||
\(243\) | −672.845 | + | 1165.40i | −0.177626 | + | 0.307657i | ||||
\(244\) | −251.411 | − | 435.457i | −0.0659629 | − | 0.114251i | ||||
\(245\) | −6211.60 | − | 10758.8i | −1.61977 | − | 2.80553i | ||||
\(246\) | 2104.46 | 0.545429 | ||||||||
\(247\) | 28.3305 | + | 2369.48i | 0.00729807 | + | 0.610391i | ||||
\(248\) | −880.851 | −0.225541 | ||||||||
\(249\) | −2658.23 | − | 4604.20i | −0.676541 | − | 1.17180i | ||||
\(250\) | 1266.34 | + | 2193.37i | 0.320362 | + | 0.554883i | ||||
\(251\) | 600.203 | − | 1039.58i | 0.150934 | − | 0.261426i | −0.780637 | − | 0.624985i | \(-0.785105\pi\) |
0.931571 | + | 0.363559i | \(0.118439\pi\) | |||||||
\(252\) | 1612.40 | 0.403063 | ||||||||
\(253\) | 936.775 | − | 1622.54i | 0.232785 | − | 0.403195i | ||||
\(254\) | −1411.93 | + | 2445.53i | −0.348789 | + | 0.604120i | ||||
\(255\) | −5107.26 | −1.25423 | ||||||||
\(256\) | −1031.44 | + | 1786.50i | −0.251816 | + | 0.436157i | ||||
\(257\) | −2223.57 | − | 3851.33i | −0.539698 | − | 0.934784i | −0.998920 | − | 0.0464625i | \(-0.985205\pi\) |
0.459222 | − | 0.888321i | \(-0.348128\pi\) | |||||||
\(258\) | −4312.73 | − | 7469.87i | −1.04069 | − | 1.80253i | ||||
\(259\) | 255.453 | 0.0612859 | ||||||||
\(260\) | 77.3080 | + | 6465.83i | 0.0184402 | + | 1.54228i | ||||
\(261\) | 1291.25 | 0.306232 | ||||||||
\(262\) | −3050.64 | − | 5283.87i | −0.719349 | − | 1.24595i | ||||
\(263\) | 1263.22 | + | 2187.96i | 0.296173 | + | 0.512986i | 0.975257 | − | 0.221074i | \(-0.0709562\pi\) |
−0.679084 | + | 0.734060i | \(0.737623\pi\) | |||||||
\(264\) | −169.526 | + | 293.628i | −0.0395212 | + | 0.0684528i | ||||
\(265\) | 9377.70 | 2.17384 | ||||||||
\(266\) | 3676.07 | − | 6367.14i | 0.847347 | − | 1.46765i | ||||
\(267\) | 2055.46 | − | 3560.16i | 0.471132 | − | 0.816024i | ||||
\(268\) | −812.960 | −0.185296 | ||||||||
\(269\) | −2043.23 | + | 3538.98i | −0.463115 | + | 0.802138i | −0.999114 | − | 0.0420799i | \(-0.986602\pi\) |
0.535999 | + | 0.844218i | \(0.319935\pi\) | |||||||
\(270\) | 4531.52 | + | 7848.82i | 1.02141 | + | 1.76913i | ||||
\(271\) | −2947.04 | − | 5104.43i | −0.660591 | − | 1.14418i | −0.980461 | − | 0.196715i | \(-0.936973\pi\) |
0.319870 | − | 0.947461i | \(-0.396361\pi\) | |||||||
\(272\) | 3690.67 | 0.822719 | ||||||||
\(273\) | −6581.89 | + | 3905.71i | −1.45917 | + | 0.865877i | ||||
\(274\) | −9357.71 | −2.06321 | ||||||||
\(275\) | −457.091 | − | 791.704i | −0.100231 | − | 0.173606i | ||||
\(276\) | 3832.12 | + | 6637.43i | 0.835749 | + | 1.44756i | ||||
\(277\) | −222.600 | + | 385.555i | −0.0482844 | + | 0.0836309i | −0.889157 | − | 0.457601i | \(-0.848709\pi\) |
0.840873 | + | 0.541232i | \(0.182042\pi\) | |||||||
\(278\) | −5465.93 | −1.17923 | ||||||||
\(279\) | −326.687 | + | 565.839i | −0.0701012 | + | 0.121419i | ||||
\(280\) | 1639.58 | − | 2839.83i | 0.349941 | − | 0.606115i | ||||
\(281\) | 1700.06 | 0.360914 | 0.180457 | − | 0.983583i | \(-0.442242\pi\) | ||||
0.180457 | + | 0.983583i | \(0.442242\pi\) | |||||||
\(282\) | 3687.81 | − | 6387.48i | 0.778745 | − | 1.34883i | ||||
\(283\) | −4031.35 | − | 6982.51i | −0.846781 | − | 1.46667i | −0.884066 | − | 0.467363i | \(-0.845204\pi\) |
0.0372848 | − | 0.999305i | \(-0.488129\pi\) | |||||||
\(284\) | −1265.94 | − | 2192.67i | −0.264506 | − | 0.458138i | ||||
\(285\) | 3431.73 | 0.713257 | ||||||||
\(286\) | 25.8331 | + | 2160.61i | 0.00534107 | + | 0.446712i | ||||
\(287\) | −3703.26 | −0.761661 | ||||||||
\(288\) | −626.729 | − | 1085.53i | −0.128230 | − | 0.222101i | ||||
\(289\) | −373.967 | − | 647.730i | −0.0761179 | − | 0.131840i | ||||
\(290\) | 8033.26 | − | 13914.0i | 1.62665 | − | 2.81744i | ||||
\(291\) | −2449.62 | −0.493468 | ||||||||
\(292\) | −1287.14 | + | 2229.39i | −0.257959 | + | 0.446798i | ||||
\(293\) | 1903.70 | − | 3297.31i | 0.379575 | − | 0.657442i | −0.611426 | − | 0.791302i | \(-0.709404\pi\) |
0.991000 | + | 0.133859i | \(0.0427370\pi\) | |||||||
\(294\) | 16982.0 | 3.36875 | ||||||||
\(295\) | −2009.51 | + | 3480.58i | −0.396605 | + | 0.686939i | ||||
\(296\) | 24.1107 | + | 41.7609i | 0.00473448 | + | 0.00820035i | ||||
\(297\) | 824.504 | + | 1428.08i | 0.161086 | + | 0.279009i | ||||
\(298\) | −9513.44 | −1.84932 | ||||||||
\(299\) | 6961.05 | + | 3908.75i | 1.34638 | + | 0.756017i | ||||
\(300\) | 3739.70 | 0.719705 | ||||||||
\(301\) | 7589.21 | + | 13144.9i | 1.45327 | + | 2.51714i | ||||
\(302\) | −2780.98 | − | 4816.80i | −0.529892 | − | 0.917800i | ||||
\(303\) | 974.499 | − | 1687.88i | 0.184764 | − | 0.320021i | ||||
\(304\) | −2479.88 | −0.467864 | ||||||||
\(305\) | −379.255 | + | 656.889i | −0.0712003 | + | 0.123323i | ||||
\(306\) | −766.032 | + | 1326.81i | −0.143108 | + | 0.247871i | ||||
\(307\) | −7435.92 | −1.38238 | −0.691189 | − | 0.722674i | \(-0.742913\pi\) | ||||
−0.691189 | + | 0.722674i | \(0.742913\pi\) | |||||||
\(308\) | 1825.17 | − | 3161.29i | 0.337658 | − | 0.584841i | ||||
\(309\) | 3284.49 | + | 5688.90i | 0.604686 | + | 1.04735i | ||||
\(310\) | 4064.83 | + | 7040.50i | 0.744732 | + | 1.28991i | ||||
\(311\) | −3396.84 | −0.619347 | −0.309674 | − | 0.950843i | \(-0.600220\pi\) | ||||
−0.309674 | + | 0.950843i | \(0.600220\pi\) | |||||||
\(312\) | −1259.72 | − | 707.358i | −0.228583 | − | 0.128353i | ||||
\(313\) | 1123.70 | 0.202925 | 0.101462 | − | 0.994839i | \(-0.467648\pi\) | ||||
0.101462 | + | 0.994839i | \(0.467648\pi\) | |||||||
\(314\) | 1160.87 | + | 2010.68i | 0.208636 | + | 0.361368i | ||||
\(315\) | −1216.16 | − | 2106.45i | −0.217533 | − | 0.376778i | ||||
\(316\) | −1026.99 | + | 1778.81i | −0.182826 | + | 0.316663i | ||||
\(317\) | −2824.61 | −0.500460 | −0.250230 | − | 0.968186i | \(-0.580506\pi\) | ||||
−0.250230 | + | 0.968186i | \(0.580506\pi\) | |||||||
\(318\) | −6409.48 | + | 11101.5i | −1.13027 | + | 1.95768i | ||||
\(319\) | 1461.64 | − | 2531.64i | 0.256540 | − | 0.444340i | ||||
\(320\) | −9935.24 | −1.73561 | ||||||||
\(321\) | −775.067 | + | 1342.45i | −0.134766 | + | 0.233422i | ||||
\(322\) | −12384.7 | − | 21451.0i | −2.14340 | − | 3.71248i | ||||
\(323\) | 1901.88 | + | 3294.15i | 0.327627 | + | 0.567466i | ||||
\(324\) | −5491.13 | −0.941552 | ||||||||
\(325\) | 3350.01 | − | 1987.91i | 0.571769 | − | 0.339290i | ||||
\(326\) | −3245.80 | −0.551436 | ||||||||
\(327\) | 1709.72 | + | 2961.33i | 0.289137 | + | 0.500801i | ||||
\(328\) | −349.529 | − | 605.403i | −0.0588400 | − | 0.101914i | ||||
\(329\) | −6489.53 | + | 11240.2i | −1.08748 | + | 1.88356i | ||||
\(330\) | 3129.22 | 0.521994 | ||||||||
\(331\) | 816.053 | − | 1413.45i | 0.135512 | − | 0.234713i | −0.790281 | − | 0.612744i | \(-0.790066\pi\) |
0.925793 | + | 0.378031i | \(0.123399\pi\) | |||||||
\(332\) | −5402.44 | + | 9357.29i | −0.893064 | + | 1.54683i | ||||
\(333\) | 35.7684 | 0.00588617 | ||||||||
\(334\) | 1364.25 | − | 2362.95i | 0.223498 | − | 0.387111i | ||||
\(335\) | 613.178 | + | 1062.06i | 0.100004 | + | 0.173213i | ||||
\(336\) | −4004.75 | − | 6936.43i | −0.650229 | − | 1.12623i | ||||
\(337\) | 3066.09 | 0.495609 | 0.247805 | − | 0.968810i | \(-0.420291\pi\) | ||||
0.247805 | + | 0.968810i | \(0.420291\pi\) | |||||||
\(338\) | −9204.62 | + | 220.140i | −1.48126 | + | 0.0354261i | ||||
\(339\) | 7878.50 | 1.26225 | ||||||||
\(340\) | 5189.84 | + | 8989.07i | 0.827820 | + | 1.43383i | ||||
\(341\) | 739.591 | + | 1281.01i | 0.117452 | + | 0.203433i | ||||
\(342\) | 514.722 | − | 891.524i | 0.0813829 | − | 0.140959i | ||||
\(343\) | −17981.2 | −2.83059 | ||||||||
\(344\) | −1432.60 | + | 2481.34i | −0.224537 | + | 0.388910i | ||||
\(345\) | 5780.78 | − | 10012.6i | 0.902107 | − | 1.56249i | ||||
\(346\) | 14477.1 | 2.24940 | ||||||||
\(347\) | 2926.59 | − | 5069.00i | 0.452759 | − | 0.784202i | −0.545797 | − | 0.837917i | \(-0.683773\pi\) |
0.998556 | + | 0.0537154i | \(0.0171064\pi\) | |||||||
\(348\) | 5979.22 | + | 10356.3i | 0.921034 | + | 1.59528i | ||||
\(349\) | 1252.10 | + | 2168.70i | 0.192044 | + | 0.332631i | 0.945928 | − | 0.324378i | \(-0.105155\pi\) |
−0.753883 | + | 0.657008i | \(0.771822\pi\) | |||||||
\(350\) | −12086.0 | −1.84579 | ||||||||
\(351\) | −6042.78 | + | 3585.80i | −0.918916 | + | 0.545287i | ||||
\(352\) | −2837.72 | −0.429690 | ||||||||
\(353\) | 497.326 | + | 861.393i | 0.0749857 | + | 0.129879i | 0.901080 | − | 0.433653i | \(-0.142776\pi\) |
−0.826094 | + | 0.563532i | \(0.809442\pi\) | |||||||
\(354\) | −2746.93 | − | 4757.82i | −0.412422 | − | 0.714337i | ||||
\(355\) | −1909.68 | + | 3307.66i | −0.285508 | + | 0.494514i | ||||
\(356\) | −8354.79 | −1.24383 | ||||||||
\(357\) | −6142.69 | + | 10639.4i | −0.910660 | + | 1.57731i | ||||
\(358\) | 3956.48 | − | 6852.83i | 0.584097 | − | 1.01168i | ||||
\(359\) | −8022.18 | −1.17937 | −0.589686 | − | 0.807633i | \(-0.700749\pi\) | ||||
−0.589686 | + | 0.807633i | \(0.700749\pi\) | |||||||
\(360\) | 229.573 | − | 397.632i | 0.0336098 | − | 0.0582139i | ||||
\(361\) | 2151.57 | + | 3726.62i | 0.313685 | + | 0.543318i | ||||
\(362\) | 7782.97 | + | 13480.5i | 1.13001 | + | 1.95724i | ||||
\(363\) | 569.358 | 0.0823238 | ||||||||
\(364\) | 13562.6 | + | 7615.64i | 1.95295 | + | 1.09662i | ||||
\(365\) | 3883.31 | 0.556882 | ||||||||
\(366\) | −518.427 | − | 897.943i | −0.0740400 | − | 0.128241i | ||||
\(367\) | 2336.69 | + | 4047.27i | 0.332355 | + | 0.575656i | 0.982973 | − | 0.183749i | \(-0.0588234\pi\) |
−0.650618 | + | 0.759405i | \(0.725490\pi\) | |||||||
\(368\) | −4177.37 | + | 7235.43i | −0.591741 | + | 1.02493i | ||||
\(369\) | −518.530 | −0.0731533 | ||||||||
\(370\) | 222.526 | − | 385.426i | 0.0312664 | − | 0.0541549i | ||||
\(371\) | 11278.9 | − | 19535.6i | 1.57836 | − | 2.73380i | ||||
\(372\) | −6050.98 | −0.843356 | ||||||||
\(373\) | 2483.97 | − | 4302.36i | 0.344812 | − | 0.597232i | −0.640507 | − | 0.767952i | \(-0.721276\pi\) |
0.985320 | + | 0.170720i | \(0.0546092\pi\) | |||||||
\(374\) | 1734.23 | + | 3003.77i | 0.239772 | + | 0.415298i | ||||
\(375\) | 1421.84 | + | 2462.70i | 0.195796 | + | 0.339129i | ||||
\(376\) | −2450.04 | −0.336040 | ||||||||
\(377\) | 10861.3 | + | 6098.79i | 1.48378 | + | 0.833166i | ||||
\(378\) | 21800.9 | 2.96645 | ||||||||
\(379\) | −1599.33 | − | 2770.11i | −0.216759 | − | 0.375438i | 0.737056 | − | 0.675832i | \(-0.236215\pi\) |
−0.953815 | + | 0.300393i | \(0.902882\pi\) | |||||||
\(380\) | −3487.22 | − | 6040.05i | −0.470765 | − | 0.815389i | ||||
\(381\) | −1585.31 | + | 2745.83i | −0.213170 | + | 0.369221i | ||||
\(382\) | −3963.75 | −0.530899 | ||||||||
\(383\) | −180.575 | + | 312.766i | −0.0240913 | + | 0.0417273i | −0.877820 | − | 0.478991i | \(-0.841003\pi\) |
0.853728 | + | 0.520719i | \(0.174336\pi\) | |||||||
\(384\) | 1935.01 | − | 3351.54i | 0.257150 | − | 0.445397i | ||||
\(385\) | −5506.56 | −0.728936 | ||||||||
\(386\) | 242.775 | − | 420.498i | 0.0320127 | − | 0.0554476i | ||||
\(387\) | 1062.64 | + | 1840.54i | 0.139579 | + | 0.241757i | ||||
\(388\) | 2489.23 | + | 4311.47i | 0.325700 | + | 0.564128i | ||||
\(389\) | −7648.28 | −0.996872 | −0.498436 | − | 0.866927i | \(-0.666092\pi\) | ||||
−0.498436 | + | 0.866927i | \(0.666092\pi\) | |||||||
\(390\) | 159.415 | + | 13333.0i | 0.0206981 | + | 1.73114i | ||||
\(391\) | 12814.9 | 1.65749 | ||||||||
\(392\) | −2820.55 | − | 4885.33i | −0.363416 | − | 0.629455i | ||||
\(393\) | −3425.24 | − | 5932.70i | −0.439646 | − | 0.761488i | ||||
\(394\) | 5269.97 | − | 9127.85i | 0.673850 | − | 1.16714i | ||||
\(395\) | 3098.45 | 0.394684 | ||||||||
\(396\) | 255.560 | − | 442.642i | 0.0324302 | − | 0.0561707i | ||||
\(397\) | 6417.23 | − | 11115.0i | 0.811264 | − | 1.40515i | −0.100717 | − | 0.994915i | \(-0.532114\pi\) |
0.911980 | − | 0.410235i | \(-0.134553\pi\) | |||||||
\(398\) | −3339.68 | −0.420611 | ||||||||
\(399\) | 4127.47 | − | 7148.98i | 0.517874 | − | 0.896985i | ||||
\(400\) | 2038.31 | + | 3530.46i | 0.254789 | + | 0.441307i | ||||
\(401\) | 74.5201 | + | 129.073i | 0.00928020 | + | 0.0160738i | 0.870628 | − | 0.491942i | \(-0.163713\pi\) |
−0.861348 | + | 0.508015i | \(0.830379\pi\) | |||||||
\(402\) | −1676.38 | −0.207986 | ||||||||
\(403\) | −5420.45 | + | 3216.51i | −0.670004 | + | 0.397583i | ||||
\(404\) | −3961.03 | −0.487793 | ||||||||
\(405\) | 4141.70 | + | 7173.64i | 0.508155 | + | 0.880151i | ||||
\(406\) | −19323.8 | − | 33469.8i | −2.36213 | − | 4.09132i | ||||
\(407\) | 40.4882 | − | 70.1277i | 0.00493103 | − | 0.00854079i | ||||
\(408\) | −2319.09 | −0.281402 | ||||||||
\(409\) | 877.721 | − | 1520.26i | 0.106114 | − | 0.183794i | −0.808079 | − | 0.589074i | \(-0.799493\pi\) |
0.914193 | + | 0.405280i | \(0.132826\pi\) | |||||||
\(410\) | −3225.92 | + | 5587.47i | −0.388578 | + | 0.673037i | ||||
\(411\) | −10506.8 | −1.26098 | ||||||||
\(412\) | 6675.19 | − | 11561.8i | 0.798211 | − | 1.38254i | ||||
\(413\) | 4833.83 | + | 8372.44i | 0.575925 | + | 0.997532i | ||||
\(414\) | −1734.11 | − | 3003.56i | −0.205862 | − | 0.356563i | ||||
\(415\) | 16299.2 | 1.92795 | ||||||||
\(416\) | −144.564 | − | 12091.0i | −0.0170381 | − | 1.42502i | ||||
\(417\) | −6137.12 | −0.720710 | ||||||||
\(418\) | −1165.28 | − | 2018.33i | −0.136354 | − | 0.236172i | ||||
\(419\) | 3454.05 | + | 5982.59i | 0.402724 | + | 0.697538i | 0.994054 | − | 0.108892i | \(-0.0347302\pi\) |
−0.591330 | + | 0.806430i | \(0.701397\pi\) | |||||||
\(420\) | 11263.0 | − | 19508.1i | 1.30852 | − | 2.26643i | ||||
\(421\) | 12297.9 | 1.42366 | 0.711831 | − | 0.702350i | \(-0.247866\pi\) | ||||
0.711831 | + | 0.702350i | \(0.247866\pi\) | |||||||
\(422\) | −355.158 | + | 615.152i | −0.0409688 | + | 0.0709600i | ||||
\(423\) | −908.661 | + | 1573.85i | −0.104446 | + | 0.180906i | ||||
\(424\) | 4258.20 | 0.487727 | ||||||||
\(425\) | 3126.47 | − | 5415.20i | 0.356837 | − | 0.618060i | ||||
\(426\) | −2610.46 | − | 4521.45i | −0.296895 | − | 0.514237i | ||||
\(427\) | 912.288 | + | 1580.13i | 0.103393 | + | 0.179082i | ||||
\(428\) | 3150.40 | 0.355795 | ||||||||
\(429\) | 29.0053 | + | 2425.92i | 0.00326431 | + | 0.273018i | ||||
\(430\) | 26443.9 | 2.96567 | ||||||||
\(431\) | −744.496 | − | 1289.50i | −0.0832044 | − | 0.144114i | 0.821420 | − | 0.570323i | \(-0.193182\pi\) |
−0.904625 | + | 0.426209i | \(0.859849\pi\) | |||||||
\(432\) | −3676.72 | − | 6368.27i | −0.409482 | − | 0.709244i | ||||
\(433\) | −5674.97 | + | 9829.34i | −0.629842 | + | 1.09092i | 0.357741 | + | 0.933821i | \(0.383547\pi\) |
−0.987583 | + | 0.157098i | \(0.949786\pi\) | |||||||
\(434\) | 19555.7 | 2.16291 | ||||||||
\(435\) | 9019.69 | − | 15622.6i | 0.994164 | − | 1.72194i | ||||
\(436\) | 3474.74 | − | 6018.42i | 0.381674 | − | 0.661079i | ||||
\(437\) | −8610.77 | −0.942584 | ||||||||
\(438\) | −2654.17 | + | 4597.16i | −0.289546 | + | 0.501508i | ||||
\(439\) | 1619.30 | + | 2804.70i | 0.176047 | + | 0.304923i | 0.940523 | − | 0.339729i | \(-0.110335\pi\) |
−0.764476 | + | 0.644652i | \(0.777002\pi\) | |||||||
\(440\) | −519.732 | − | 900.203i | −0.0563120 | − | 0.0975352i | ||||
\(441\) | −4184.30 | −0.451820 | ||||||||
\(442\) | −12710.1 | + | 7542.23i | −1.36778 | + | 0.811646i | ||||
\(443\) | 10922.8 | 1.17146 | 0.585730 | − | 0.810506i | \(-0.300808\pi\) | ||||
0.585730 | + | 0.810506i | \(0.300808\pi\) | |||||||
\(444\) | 165.628 | + | 286.876i | 0.0177035 | + | 0.0306633i | ||||
\(445\) | 6301.63 | + | 10914.7i | 0.671294 | + | 1.16272i | ||||
\(446\) | 5987.08 | − | 10369.9i | 0.635642 | − | 1.10096i | ||||
\(447\) | −10681.6 | −1.13025 | ||||||||
\(448\) | −11949.5 | + | 20697.1i | −1.26018 | + | 2.18269i | ||||
\(449\) | −6850.47 | + | 11865.4i | −0.720030 | + | 1.24713i | 0.240957 | + | 0.970536i | \(0.422539\pi\) |
−0.960987 | + | 0.276593i | \(0.910795\pi\) | |||||||
\(450\) | −1692.28 | −0.177278 | ||||||||
\(451\) | −586.953 | + | 1016.63i | −0.0612828 | + | 0.106145i | ||||
\(452\) | −8005.90 | − | 13866.6i | −0.833110 | − | 1.44299i | ||||
\(453\) | −3122.47 | − | 5408.27i | −0.323855 | − | 0.560933i | ||||
\(454\) | −1239.39 | −0.128122 | ||||||||
\(455\) | −280.526 | − | 23462.4i | −0.0289038 | − | 2.41744i | ||||
\(456\) | 1558.27 | 0.160028 | ||||||||
\(457\) | −402.806 | − | 697.681i | −0.0412308 | − | 0.0714138i | 0.844674 | − | 0.535282i | \(-0.179795\pi\) |
−0.885904 | + | 0.463868i | \(0.846461\pi\) | |||||||
\(458\) | 7974.33 | + | 13811.9i | 0.813572 | + | 1.40915i | ||||
\(459\) | −5639.55 | + | 9767.98i | −0.573489 | + | 0.993312i | ||||
\(460\) | −23497.0 | −2.38164 | ||||||||
\(461\) | 2587.56 | − | 4481.79i | 0.261420 | − | 0.452793i | −0.705199 | − | 0.709009i | \(-0.749142\pi\) |
0.966620 | + | 0.256216i | \(0.0824758\pi\) | |||||||
\(462\) | 3763.63 | − | 6518.80i | 0.379004 | − | 0.656455i | ||||
\(463\) | 2642.44 | 0.265237 | 0.132618 | − | 0.991167i | \(-0.457662\pi\) | ||||
0.132618 | + | 0.991167i | \(0.457662\pi\) | |||||||
\(464\) | −6517.92 | + | 11289.4i | −0.652126 | + | 1.12952i | ||||
\(465\) | 4563.97 | + | 7905.03i | 0.455159 | + | 0.788359i | ||||
\(466\) | 3715.28 | + | 6435.06i | 0.369329 | + | 0.639696i | ||||
\(467\) | 6618.54 | 0.655823 | 0.327912 | − | 0.944708i | \(-0.393655\pi\) | ||||
0.327912 | + | 0.944708i | \(0.393655\pi\) | |||||||
\(468\) | 1899.03 | + | 1066.34i | 0.187570 | + | 0.105324i | ||||
\(469\) | 2949.97 | 0.290441 | ||||||||
\(470\) | 11306.1 | + | 19582.7i | 1.10960 | + | 1.92188i | ||||
\(471\) | 1303.42 | + | 2257.58i | 0.127512 | + | 0.220858i | ||||
\(472\) | −912.474 | + | 1580.45i | −0.0889831 | + | 0.154123i | ||||
\(473\) | 4811.44 | 0.467717 | ||||||||
\(474\) | −2117.73 | + | 3668.02i | −0.205213 | + | 0.355439i | ||||
\(475\) | −2100.77 | + | 3638.64i | −0.202926 | + | 0.351479i | ||||
\(476\) | 24968.1 | 2.40422 | ||||||||
\(477\) | 1579.27 | − | 2735.37i | 0.151593 | − | 0.262566i | ||||
\(478\) | −2675.70 | − | 4634.44i | −0.256032 | − | 0.443461i | ||||
\(479\) | −7485.77 | − | 12965.7i | −0.714057 | − | 1.23678i | −0.963322 | − | 0.268348i | \(-0.913522\pi\) |
0.249265 | − | 0.968435i | \(-0.419811\pi\) | |||||||
\(480\) | −17511.4 | −1.66517 | ||||||||
\(481\) | 300.863 | + | 168.940i | 0.0285201 | + | 0.0160145i | ||||
\(482\) | 1507.71 | 0.142478 | ||||||||
\(483\) | −13905.5 | − | 24085.1i | −1.30999 | − | 2.26896i | ||||
\(484\) | −578.565 | − | 1002.10i | −0.0543355 | − | 0.0941119i | ||||
\(485\) | 3755.02 | − | 6503.88i | 0.351560 | − | 0.608920i | ||||
\(486\) | 5639.56 | 0.526369 | ||||||||
\(487\) | 43.8445 | − | 75.9409i | 0.00407964 | − | 0.00706614i | −0.863978 | − | 0.503529i | \(-0.832035\pi\) |
0.868058 | + | 0.496463i | \(0.165368\pi\) | |||||||
\(488\) | −172.211 | + | 298.278i | −0.0159747 | + | 0.0276689i | ||||
\(489\) | −3644.36 | −0.337022 | ||||||||
\(490\) | −26031.8 | + | 45088.3i | −2.39999 | + | 4.15691i | ||||
\(491\) | −8543.16 | − | 14797.2i | −0.785229 | − | 1.36006i | −0.928862 | − | 0.370426i | \(-0.879212\pi\) |
0.143633 | − | 0.989631i | \(-0.454122\pi\) | |||||||
\(492\) | −2401.08 | − | 4158.80i | −0.220019 | − | 0.381083i | ||||
\(493\) | 19995.0 | 1.82663 | ||||||||
\(494\) | 8540.35 | − | 5067.87i | 0.777831 | − | 0.461567i | ||||
\(495\) | −771.027 | −0.0700103 | ||||||||
\(496\) | −3298.07 | − | 5712.42i | −0.298564 | − | 0.517128i | ||||
\(497\) | 4593.68 | + | 7956.49i | 0.414597 | + | 0.718104i | ||||
\(498\) | −11140.2 | + | 19295.4i | −1.00242 | + | 1.73624i | ||||
\(499\) | −1104.76 | −0.0991099 | −0.0495550 | − | 0.998771i | \(-0.515780\pi\) | ||||
−0.0495550 | + | 0.998771i | \(0.515780\pi\) | |||||||
\(500\) | 2889.67 | − | 5005.05i | 0.258460 | − | 0.447665i | ||||
\(501\) | 1531.77 | − | 2653.11i | 0.136596 | − | 0.236591i | ||||
\(502\) | −5030.70 | −0.447273 | ||||||||
\(503\) | 2760.02 | − | 4780.50i | 0.244659 | − | 0.423761i | −0.717377 | − | 0.696685i | \(-0.754657\pi\) |
0.962036 | + | 0.272924i | \(0.0879908\pi\) | |||||||
\(504\) | −552.231 | − | 956.492i | −0.0488062 | − | 0.0845348i | ||||
\(505\) | 2987.62 | + | 5174.71i | 0.263262 | + | 0.455983i | ||||
\(506\) | −7851.73 | −0.689826 | ||||||||
\(507\) | −10334.9 | + | 247.172i | −0.905303 | + | 0.0216514i | ||||
\(508\) | 6443.76 | 0.562787 | ||||||||
\(509\) | −4321.09 | − | 7484.35i | −0.376285 | − | 0.651745i | 0.614233 | − | 0.789124i | \(-0.289465\pi\) |
−0.990518 | + | 0.137380i | \(0.956132\pi\) | |||||||
\(510\) | 10701.8 | + | 18536.1i | 0.929186 | + | 1.60940i | ||||
\(511\) | 4670.60 | − | 8089.72i | 0.404335 | − | 0.700329i | ||||
\(512\) | 15224.8 | 1.31416 | ||||||||
\(513\) | 3789.39 | − | 6563.42i | 0.326132 | − | 0.564877i | ||||
\(514\) | −9318.59 | + | 16140.3i | −0.799660 | + | 1.38505i | ||||
\(515\) | −20139.1 | −1.72318 | ||||||||
\(516\) | −9841.22 | + | 17045.5i | −0.839604 | + | 1.45424i | ||||
\(517\) | 2057.13 | + | 3563.05i | 0.174995 | + | 0.303100i | ||||
\(518\) | −535.279 | − | 927.131i | −0.0454031 | − | 0.0786405i | ||||
\(519\) | 16254.8 | 1.37477 | ||||||||
\(520\) | 3809.11 | − | 2260.34i | 0.321232 | − | 0.190620i | ||||
\(521\) | 1763.72 | 0.148311 | 0.0741553 | − | 0.997247i | \(-0.476374\pi\) | ||||
0.0741553 | + | 0.997247i | \(0.476374\pi\) | |||||||
\(522\) | −2705.71 | − | 4686.42i | −0.226869 | − | 0.392949i | ||||
\(523\) | −10607.1 | − | 18372.1i | −0.886839 | − | 1.53605i | −0.843591 | − | 0.536986i | \(-0.819563\pi\) |
−0.0432477 | − | 0.999064i | \(-0.513770\pi\) | |||||||
\(524\) | −6961.26 | + | 12057.3i | −0.580351 | + | 1.00520i | ||||
\(525\) | −13570.1 | −1.12809 | ||||||||
\(526\) | 5293.94 | − | 9169.37i | 0.438834 | − | 0.760083i | ||||
\(527\) | −5058.75 | + | 8762.01i | −0.418145 | + | 0.724249i | ||||
\(528\) | −2538.95 | −0.209268 | ||||||||
\(529\) | −8421.42 | + | 14586.3i | −0.692153 | + | 1.19884i | ||||
\(530\) | −19650.2 | − | 34035.1i | −1.61047 | − | 2.78941i | ||||
\(531\) | 676.831 | + | 1172.31i | 0.0553144 | + | 0.0958074i | ||||
\(532\) | −16776.8 | −1.36723 | ||||||||
\(533\) | −4361.57 | − | 2449.10i | −0.354447 | − | 0.199029i | ||||
\(534\) | −17228.2 | −1.39613 | ||||||||
\(535\) | −2376.20 | − | 4115.70i | −0.192022 | − | 0.332593i | ||||
\(536\) | 278.430 | + | 482.255i | 0.0224372 | + | 0.0388624i | ||||
\(537\) | 4442.32 | − | 7694.32i | 0.356983 | − | 0.618313i | ||||
\(538\) | 17125.7 | 1.37238 | ||||||||
\(539\) | −4736.45 | + | 8203.77i | −0.378503 | + | 0.655587i | ||||
\(540\) | 10340.5 | − | 17910.2i | 0.824043 | − | 1.42728i | ||||
\(541\) | −7949.82 | −0.631773 | −0.315887 | − | 0.948797i | \(-0.602302\pi\) | ||||
−0.315887 | + | 0.948797i | \(0.602302\pi\) | |||||||
\(542\) | −12350.6 | + | 21391.8i | −0.978785 | + | 1.69531i | ||||
\(543\) | 8738.67 | + | 15135.8i | 0.690630 | + | 1.19621i | ||||
\(544\) | −9704.89 | − | 16809.4i | −0.764878 | − | 1.32481i | ||||
\(545\) | −10483.3 | −0.823957 | ||||||||
\(546\) | 27967.1 | + | 15704.0i | 2.19209 | + | 1.23090i | ||||
\(547\) | −2367.88 | −0.185089 | −0.0925443 | − | 0.995709i | \(-0.529500\pi\) | ||||
−0.0925443 | + | 0.995709i | \(0.529500\pi\) | |||||||
\(548\) | 10676.7 | + | 18492.5i | 0.832272 | + | 1.44154i | ||||
\(549\) | 127.738 | + | 221.249i | 0.00993030 | + | 0.0171998i | ||||
\(550\) | −1915.59 | + | 3317.90i | −0.148511 | + | 0.257228i | ||||
\(551\) | −13435.3 | −1.03877 | ||||||||
\(552\) | 2624.92 | − | 4546.50i | 0.202399 | − | 0.350565i | ||||
\(553\) | 3726.62 | − | 6454.70i | 0.286568 | − | 0.496351i | ||||
\(554\) | 1865.76 | 0.143084 | ||||||||
\(555\) | 249.850 | − | 432.754i | 0.0191091 | − | 0.0330980i | ||||
\(556\) | 6236.36 | + | 10801.7i | 0.475684 | + | 0.823909i | ||||
\(557\) | 6926.22 | + | 11996.6i | 0.526882 | + | 0.912587i | 0.999509 | + | 0.0313241i | \(0.00997240\pi\) |
−0.472627 | + | 0.881262i | \(0.656694\pi\) | |||||||
\(558\) | 2738.18 | 0.207735 | ||||||||
\(559\) | 245.113 | + | 20500.6i | 0.0185459 | + | 1.55113i | ||||
\(560\) | 24555.5 | 1.85296 | ||||||||
\(561\) | 1947.18 | + | 3372.62i | 0.146542 | + | 0.253818i | ||||
\(562\) | −3562.32 | − | 6170.13i | −0.267380 | − | 0.463116i | ||||
\(563\) | −914.505 | + | 1583.97i | −0.0684579 | + | 0.118572i | −0.898223 | − | 0.439541i | \(-0.855141\pi\) |
0.829765 | + | 0.558113i | \(0.188475\pi\) | |||||||
\(564\) | −16830.4 | −1.25654 | ||||||||
\(565\) | −12076.9 | + | 20917.9i | −0.899259 | + | 1.55756i | ||||
\(566\) | −16894.7 | + | 29262.5i | −1.25466 | + | 2.17313i | ||||
\(567\) | 19925.5 | 1.47583 | ||||||||
\(568\) | −867.142 | + | 1501.93i | −0.0640571 | + | 0.110950i | ||||
\(569\) | 669.855 | + | 1160.22i | 0.0493528 | + | 0.0854816i | 0.889646 | − | 0.456650i | \(-0.150951\pi\) |
−0.840294 | + | 0.542132i | \(0.817617\pi\) | |||||||
\(570\) | −7190.90 | − | 12455.0i | −0.528410 | − | 0.915233i | ||||
\(571\) | 11875.5 | 0.870360 | 0.435180 | − | 0.900344i | \(-0.356685\pi\) | ||||
0.435180 | + | 0.900344i | \(0.356685\pi\) | |||||||
\(572\) | 4240.29 | − | 2516.20i | 0.309957 | − | 0.183929i | ||||
\(573\) | −4450.48 | −0.324470 | ||||||||
\(574\) | 7759.87 | + | 13440.5i | 0.564270 | + | 0.977344i | ||||
\(575\) | 7077.54 | + | 12258.7i | 0.513311 | + | 0.889081i | ||||
\(576\) | −1673.16 | + | 2898.00i | −0.121033 | + | 0.209635i | ||||
\(577\) | 18998.0 | 1.37070 | 0.685352 | − | 0.728212i | \(-0.259648\pi\) | ||||
0.685352 | + | 0.728212i | \(0.259648\pi\) | |||||||
\(578\) | −1567.23 | + | 2714.53i | −0.112782 | + | 0.195345i | ||||
\(579\) | 272.586 | − | 472.133i | 0.0195653 | − | 0.0338880i | ||||
\(580\) | −36662.2 | −2.62468 | ||||||||
\(581\) | 19603.7 | − | 33954.6i | 1.39982 | − | 2.42457i | ||||
\(582\) | 5132.97 | + | 8890.56i | 0.365581 | + | 0.633205i | ||||
\(583\) | −3575.32 | − | 6192.64i | −0.253987 | − | 0.439919i | ||||
\(584\) | 1763.32 | 0.124943 | ||||||||
\(585\) | −39.2791 | − | 3285.19i | −0.00277605 | − | 0.232181i | ||||
\(586\) | −15956.2 | −1.12482 | ||||||||
\(587\) | 10599.3 | + | 18358.6i | 0.745284 | + | 1.29087i | 0.950062 | + | 0.312062i | \(0.101020\pi\) |
−0.204778 | + | 0.978809i | \(0.565647\pi\) | |||||||
\(588\) | −19375.7 | − | 33559.6i | −1.35891 | − | 2.35370i | ||||
\(589\) | 3399.13 | − | 5887.47i | 0.237791 | − | 0.411866i | ||||
\(590\) | 16843.1 | 1.17528 | ||||||||
\(591\) | 5917.09 | − | 10248.7i | 0.411838 | − | 0.713325i | ||||
\(592\) | −180.550 | + | 312.721i | −0.0125347 | + | 0.0217108i | ||||
\(593\) | −17808.4 | −1.23323 | −0.616613 | − | 0.787266i | \(-0.711496\pi\) | ||||
−0.616613 | + | 0.787266i | \(0.711496\pi\) | |||||||
\(594\) | 3455.36 | − | 5984.85i | 0.238678 | − | 0.413403i | ||||
\(595\) | −18832.2 | − | 32618.4i | −1.29756 | − | 2.24744i | ||||
\(596\) | 10854.4 | + | 18800.3i | 0.745993 | + | 1.29210i | ||||
\(597\) | −3749.78 | −0.257066 | ||||||||
\(598\) | −399.997 | − | 33454.7i | −0.0273530 | − | 2.28773i | ||||
\(599\) | −3515.70 | −0.239812 | −0.119906 | − | 0.992785i | \(-0.538259\pi\) | ||||
−0.119906 | + | 0.992785i | \(0.538259\pi\) | |||||||
\(600\) | −1280.81 | − | 2218.42i | −0.0871478 | − | 0.150944i | ||||
\(601\) | −4574.71 | − | 7923.63i | −0.310493 | − | 0.537790i | 0.667976 | − | 0.744183i | \(-0.267161\pi\) |
−0.978469 | + | 0.206393i | \(0.933827\pi\) | |||||||
\(602\) | 31805.1 | − | 55088.0i | 2.15329 | − | 3.72960i | ||||
\(603\) | 413.053 | 0.0278952 | ||||||||
\(604\) | −6345.91 | + | 10991.4i | −0.427503 | + | 0.740456i | ||||
\(605\) | −872.769 | + | 1511.68i | −0.0586497 | + | 0.101584i | ||||
\(606\) | −8167.92 | −0.547523 | ||||||||
\(607\) | −12335.0 | + | 21364.8i | −0.824812 | + | 1.42862i | 0.0772508 | + | 0.997012i | \(0.475386\pi\) |
−0.902063 | + | 0.431605i | \(0.857948\pi\) | |||||||
\(608\) | 6521.02 | + | 11294.7i | 0.434971 | + | 0.753392i | ||||
\(609\) | −21696.6 | − | 37579.7i | −1.44367 | − | 2.50050i | ||||
\(610\) | 3178.79 | 0.210992 | ||||||||
\(611\) | −15076.7 | + | 8946.54i | −0.998259 | + | 0.592370i | ||||
\(612\) | 3496.02 | 0.230912 | ||||||||
\(613\) | 7739.26 | + | 13404.8i | 0.509928 | + | 0.883221i | 0.999934 | + | 0.0115017i | \(0.00366120\pi\) |
−0.490006 | + | 0.871719i | \(0.663005\pi\) | |||||||
\(614\) | 15581.3 | + | 26987.7i | 1.02412 | + | 1.77383i | ||||
\(615\) | −3622.05 | + | 6273.57i | −0.237488 | + | 0.411341i | ||||
\(616\) | −2500.40 | −0.163546 | ||||||||
\(617\) | 7183.69 | − | 12442.5i | 0.468727 | − | 0.811859i | −0.530634 | − | 0.847601i | \(-0.678046\pi\) |
0.999361 | + | 0.0357422i | \(0.0113795\pi\) | |||||||
\(618\) | 13764.7 | − | 23841.2i | 0.895952 | − | 1.55183i | ||||
\(619\) | −16902.2 | −1.09751 | −0.548755 | − | 0.835983i | \(-0.684898\pi\) | ||||
−0.548755 | + | 0.835983i | \(0.684898\pi\) | |||||||
\(620\) | 9275.54 | − | 16065.7i | 0.600830 | − | 1.04067i | ||||
\(621\) | −12766.5 | − | 22112.3i | −0.824965 | − | 1.42888i | ||||
\(622\) | 7117.78 | + | 12328.4i | 0.458838 | + | 0.794730i | ||||
\(623\) | 30316.8 | 1.94963 | ||||||||
\(624\) | −129.344 | − | 10817.9i | −0.00829790 | − | 0.694014i | ||||
\(625\) | −19106.6 | −1.22282 | ||||||||
\(626\) | −2354.62 | − | 4078.32i | −0.150335 | − | 0.260388i | ||||
\(627\) | −1308.37 | − | 2266.17i | −0.0833356 | − | 0.144342i | ||||
\(628\) | 2648.99 | − | 4588.18i | 0.168322 | − | 0.291542i | ||||
\(629\) | 553.873 | 0.0351103 | ||||||||
\(630\) | −5096.72 | + | 8827.78i | −0.322315 | + | 0.558266i | ||||
\(631\) | −12917.2 | + | 22373.2i | −0.814935 | + | 1.41151i | 0.0944398 | + | 0.995531i | \(0.469894\pi\) |
−0.909375 | + | 0.415978i | \(0.863439\pi\) | |||||||
\(632\) | 1406.94 | 0.0885522 | ||||||||
\(633\) | −398.769 | + | 690.689i | −0.0250390 | + | 0.0433687i | ||||
\(634\) | 5918.72 | + | 10251.5i | 0.370761 | + | 0.642177i | ||||
\(635\) | −4860.23 | − | 8418.16i | −0.303736 | − | 0.526086i | ||||
\(636\) | 29251.6 | 1.82374 | ||||||||
\(637\) | −35195.9 | − | 19763.1i | −2.18919 | − | 1.22927i | ||||
\(638\) | −12251.0 | −0.760221 | ||||||||
\(639\) | 643.206 | + | 1114.06i | 0.0398198 | + | 0.0689698i | ||||
\(640\) | 5932.36 | + | 10275.2i | 0.366402 | + | 0.634627i | ||||
\(641\) | 8436.96 | − | 14613.2i | 0.519875 | − | 0.900450i | −0.479858 | − | 0.877346i | \(-0.659312\pi\) |
0.999733 | − | 0.0231040i | \(-0.00735489\pi\) | |||||||
\(642\) | 6496.34 | 0.399362 | ||||||||
\(643\) | 6957.80 | − | 12051.3i | 0.426732 | − | 0.739121i | −0.569848 | − | 0.821750i | \(-0.692998\pi\) |
0.996580 | + | 0.0826284i | \(0.0263314\pi\) | |||||||
\(644\) | −28260.7 | + | 48949.0i | −1.72924 | + | 2.99513i | ||||
\(645\) | 29691.1 | 1.81254 | ||||||||
\(646\) | 7970.46 | − | 13805.2i | 0.485439 | − | 0.840805i | ||||
\(647\) | −8628.35 | − | 14944.7i | −0.524290 | − | 0.908097i | −0.999600 | − | 0.0282783i | \(-0.990998\pi\) |
0.475310 | − | 0.879818i | \(-0.342336\pi\) | |||||||
\(648\) | 1880.65 | + | 3257.39i | 0.114011 | + | 0.197473i | ||||
\(649\) | 3064.57 | 0.185354 | ||||||||
\(650\) | −14234.5 | − | 7992.92i | −0.858958 | − | 0.482320i | ||||
\(651\) | 21957.0 | 1.32191 | ||||||||
\(652\) | 3703.29 | + | 6414.29i | 0.222442 | + | 0.385281i | ||||
\(653\) | −3336.57 | − | 5779.10i | −0.199954 | − | 0.346330i | 0.748559 | − | 0.663068i | \(-0.230746\pi\) |
−0.948513 | + | 0.316737i | \(0.897413\pi\) | |||||||
\(654\) | 7165.16 | − | 12410.4i | 0.428410 | − | 0.742027i | ||||
\(655\) | 21002.2 | 1.25286 | ||||||||
\(656\) | 2617.41 | − | 4533.48i | 0.155781 | − | 0.269821i | ||||
\(657\) | 653.976 | − | 1132.72i | 0.0388341 | − | 0.0672627i | ||||
\(658\) | 54393.0 | 3.22259 | ||||||||
\(659\) | 10975.5 | − | 19010.1i | 0.648779 | − | 1.12372i | −0.334636 | − | 0.942347i | \(-0.608613\pi\) |
0.983415 | − | 0.181370i | \(-0.0580533\pi\) | |||||||
\(660\) | −3570.29 | − | 6183.92i | −0.210565 | − | 0.364710i | ||||
\(661\) | 10695.8 | + | 18525.7i | 0.629380 | + | 1.09012i | 0.987676 | + | 0.156510i | \(0.0500243\pi\) |
−0.358297 | + | 0.933608i | \(0.616642\pi\) | |||||||
\(662\) | −6839.88 | −0.401570 | ||||||||
\(663\) | −14270.9 | + | 8468.38i | −0.835950 | + | 0.496055i | ||||
\(664\) | 7401.10 | 0.432558 | ||||||||
\(665\) | 12654.0 | + | 21917.3i | 0.737896 | + | 1.27807i | ||||
\(666\) | −74.9496 | − | 129.817i | −0.00436072 | − | 0.00755298i | ||||
\(667\) | −22631.9 | + | 39199.6i | −1.31381 | + | 2.27558i | ||||
\(668\) | −6226.17 | −0.360625 | ||||||||
\(669\) | 6722.25 | − | 11643.3i | 0.388486 | − | 0.672878i | ||||
\(670\) | 2569.72 | − | 4450.89i | 0.148175 | − | 0.256646i | ||||
\(671\) | 578.376 | 0.0332757 | ||||||||
\(672\) | −21061.6 | + | 36479.7i | −1.20903 | + | 2.09410i | ||||
\(673\) | −1108.72 | − | 1920.37i | −0.0635040 | − | 0.109992i | 0.832525 | − | 0.553987i | \(-0.186894\pi\) |
−0.896029 | + | 0.443995i | \(0.853561\pi\) | |||||||
\(674\) | −6424.72 | − | 11127.9i | −0.367168 | − | 0.635953i | ||||
\(675\) | −12458.6 | −0.710418 | ||||||||
\(676\) | 10937.0 | + | 17938.8i | 0.622272 | + | 1.02064i | ||||
\(677\) | −4300.30 | −0.244127 | −0.122063 | − | 0.992522i | \(-0.538951\pi\) | ||||
−0.122063 | + | 0.992522i | \(0.538951\pi\) | |||||||
\(678\) | −16508.7 | − | 28594.0i | −0.935124 | − | 1.61968i | ||||
\(679\) | −9032.60 | − | 15644.9i | −0.510514 | − | 0.884237i | ||||
\(680\) | 3554.93 | − | 6157.32i | 0.200478 | − | 0.347239i | ||||
\(681\) | −1391.58 | −0.0783046 | ||||||||
\(682\) | 3099.50 | − | 5368.49i | 0.174026 | − | 0.301423i | ||||
\(683\) | 6030.07 | − | 10444.4i | 0.337825 | − | 0.585130i | −0.646198 | − | 0.763169i | \(-0.723642\pi\) |
0.984023 | + | 0.178040i | \(0.0569755\pi\) | |||||||
\(684\) | −2349.09 | −0.131315 | ||||||||
\(685\) | 16105.8 | − | 27896.1i | 0.898354 | − | 1.55599i | ||||
\(686\) | 37678.0 | + | 65260.3i | 2.09702 | + | 3.63214i | ||||
\(687\) | 8953.53 | + | 15508.0i | 0.497232 | + | 0.861231i | ||||
\(688\) | −21455.7 | −1.18894 | ||||||||
\(689\) | 26203.5 | − | 15549.2i | 1.44887 | − | 0.859765i | ||||
\(690\) | −48452.5 | −2.67327 | ||||||||
\(691\) | 1145.11 | + | 1983.39i | 0.0630420 | + | 0.109192i | 0.895824 | − | 0.444409i | \(-0.146586\pi\) |
−0.832782 | + | 0.553601i | \(0.813253\pi\) | |||||||
\(692\) | −16517.6 | − | 28609.3i | −0.907377 | − | 1.57162i | ||||
\(693\) | −927.342 | + | 1606.20i | −0.0508324 | + | 0.0880442i | ||||
\(694\) | −24529.7 | −1.34169 | ||||||||
\(695\) | 9407.58 | − | 16294.4i | 0.513453 | − | 0.889327i | ||||
\(696\) | 4095.64 | − | 7093.85i | 0.223053 | − | 0.386339i | ||||
\(697\) | −8029.43 | −0.436350 | ||||||||
\(698\) | 5247.35 | − | 9088.67i | 0.284549 | − | 0.492853i | ||||
\(699\) | 4171.50 | + | 7225.24i | 0.225723 | + | 0.390964i | ||||
\(700\) | 13789.6 | + | 23884.2i | 0.744566 | + | 1.28963i | ||||
\(701\) | −25045.0 | −1.34941 | −0.674705 | − | 0.738087i | \(-0.735729\pi\) | ||||
−0.674705 | + | 0.738087i | \(0.735729\pi\) | |||||||
\(702\) | 25676.3 | + | 14417.7i | 1.38047 | + | 0.775158i | ||||
\(703\) | −372.165 | −0.0199665 | ||||||||
\(704\) | 3787.89 | + | 6560.81i | 0.202786 | + | 0.351236i | ||||
\(705\) | 12694.4 | + | 21987.4i | 0.678155 | + | 1.17460i | ||||
\(706\) | 2084.21 | − | 3609.95i | 0.111105 | − | 0.192440i | ||||
\(707\) | 14373.3 | 0.764587 | ||||||||
\(708\) | −6268.21 | + | 10856.9i | −0.332731 | + | 0.576308i | ||||
\(709\) | 2723.41 | − | 4717.09i | 0.144260 | − | 0.249865i | −0.784837 | − | 0.619702i | \(-0.787253\pi\) |
0.929096 | + | 0.369838i | \(0.120587\pi\) | |||||||
\(710\) | 16006.3 | 0.846064 | ||||||||
\(711\) | 521.800 | − | 903.785i | 0.0275233 | − | 0.0476717i | ||||
\(712\) | 2861.42 | + | 4956.13i | 0.150613 | + | 0.260869i | ||||
\(713\) | −11451.7 | − | 19835.0i | −0.601502 | − | 1.04183i | ||||
\(714\) | 51485.9 | 2.69862 | ||||||||
\(715\) | −6485.43 | − | 3641.68i | −0.339219 | − | 0.190477i | ||||
\(716\) | −18056.6 | −0.942467 | ||||||||
\(717\) | −3004.26 | − | 5203.52i | −0.156480 | − | 0.271031i | ||||
\(718\) | 16809.8 | + | 29115.4i | 0.873727 | + | 1.51334i | ||||
\(719\) | −14265.7 | + | 24709.0i | −0.739947 | + | 1.28163i | 0.212571 | + | 0.977146i | \(0.431816\pi\) |
−0.952519 | + | 0.304481i | \(0.901517\pi\) | |||||||
\(720\) | 3438.25 | 0.177967 | ||||||||
\(721\) | −24222.1 | + | 41953.9i | −1.25115 | + | 2.16705i | ||||
\(722\) | 9016.84 | − | 15617.6i | 0.464781 | − | 0.805025i | ||||
\(723\) | 1692.85 | 0.0870783 | ||||||||
\(724\) | 17760.0 | − | 30761.1i | 0.911662 | − | 1.57905i | ||||
\(725\) | 11043.0 | + | 19127.1i | 0.565693 | + | 0.979809i | ||||
\(726\) | −1193.04 | − | 2066.41i | −0.0609889 | − | 0.105636i | ||||
\(727\) | 863.427 | 0.0440478 | 0.0220239 | − | 0.999757i | \(-0.492989\pi\) | ||||
0.0220239 | + | 0.999757i | \(0.492989\pi\) | |||||||
\(728\) | −127.380 | − | 10653.7i | −0.00648492 | − | 0.542381i | ||||
\(729\) | 21835.5 | 1.10936 | ||||||||
\(730\) | −8137.15 | − | 14094.0i | −0.412561 | − | 0.714576i | ||||
\(731\) | 16454.9 | + | 28500.8i | 0.832569 | + | 1.44205i | ||||
\(732\) | −1183.00 | + | 2049.01i | −0.0597335 | + | 0.103461i | ||||
\(733\) | −1088.81 | −0.0548653 | −0.0274327 | − | 0.999624i | \(-0.508733\pi\) | ||||
−0.0274327 | + | 0.999624i | \(0.508733\pi\) | |||||||
\(734\) | 9792.68 | − | 16961.4i | 0.492445 | − | 0.852939i | ||||
\(735\) | −29228.3 | + | 50624.9i | −1.46681 | + | 2.54058i | ||||
\(736\) | 43938.9 | 2.20056 | ||||||||
\(737\) | 467.558 | − | 809.834i | 0.0233687 | − | 0.0404757i | ||||
\(738\) | 1086.53 | + | 1881.93i | 0.0541950 | + | 0.0938684i | ||||
\(739\) | 4947.45 | + | 8569.24i | 0.246272 | + | 0.426556i | 0.962488 | − | 0.271322i | \(-0.0874610\pi\) |
−0.716216 | + | 0.697878i | \(0.754128\pi\) | |||||||
\(740\) | −1015.56 | −0.0504497 | ||||||||
\(741\) | 9589.05 | − | 5690.17i | 0.475388 | − | 0.282097i | ||||
\(742\) | −94535.9 | −4.67725 | ||||||||
\(743\) | 1104.56 | + | 1913.16i | 0.0545391 | + | 0.0944645i | 0.892006 | − | 0.452024i | \(-0.149298\pi\) |
−0.837467 | + | 0.546488i | \(0.815964\pi\) | |||||||
\(744\) | 2072.39 | + | 3589.49i | 0.102121 | + | 0.176878i | ||||
\(745\) | 16373.9 | − | 28360.4i | 0.805224 | − | 1.39469i | ||||
\(746\) | −20819.8 | −1.02180 | ||||||||
\(747\) | 2744.90 | − | 4754.30i | 0.134445 | − | 0.232866i | ||||
\(748\) | 3957.34 | − | 6854.31i | 0.193442 | − | 0.335051i | ||||
\(749\) | −11431.8 | −0.557687 | ||||||||
\(750\) | 5958.70 | − | 10320.8i | 0.290108 | − | 0.502481i | ||||
\(751\) | 9392.24 | + | 16267.8i | 0.456362 | + | 0.790442i | 0.998765 | − | 0.0496764i | \(-0.0158190\pi\) |
−0.542404 | + | 0.840118i | \(0.682486\pi\) | |||||||
\(752\) | −9173.39 | − | 15888.8i | −0.444839 | − | 0.770484i | ||||
\(753\) | −5648.44 | −0.273361 | ||||||||
\(754\) | −624.112 | − | 52199.0i | −0.0301443 | − | 2.52119i | ||||
\(755\) | 19145.7 | 0.922892 | ||||||||
\(756\) | −24873.7 | − | 43082.6i | −1.19663 | − | 2.07262i | ||||
\(757\) | 19194.6 | + | 33246.1i | 0.921586 | + | 1.59623i | 0.796961 | + | 0.604030i | \(0.206439\pi\) |
0.124625 | + | 0.992204i | \(0.460227\pi\) | |||||||
\(758\) | −6702.50 | + | 11609.1i | −0.321169 | + | 0.556280i | ||||
\(759\) | −8815.88 | −0.421602 | ||||||||
\(760\) | −2388.67 | + | 4137.30i | −0.114008 | + | 0.197468i | ||||
\(761\) | −16669.8 | + | 28873.0i | −0.794062 | + | 1.37536i | 0.129372 | + | 0.991596i | \(0.458704\pi\) |
−0.923433 | + | 0.383759i | \(0.874629\pi\) | |||||||
\(762\) | 13287.5 | 0.631700 | ||||||||
\(763\) | −12608.7 | + | 21838.9i | −0.598251 | + | 1.03620i | ||||
\(764\) | 4522.45 | + | 7833.10i | 0.214157 | + | 0.370932i | ||||
\(765\) | −2636.88 | − | 4567.22i | −0.124623 | − | 0.215854i | ||||
\(766\) | 1513.52 | 0.0713913 | ||||||||
\(767\) | 156.121 | + | 13057.5i | 0.00734968 | + | 0.614707i | ||||
\(768\) | 9706.72 | 0.456069 | ||||||||
\(769\) | −7795.91 | − | 13502.9i | −0.365576 | − | 0.633195i | 0.623293 | − | 0.781989i | \(-0.285794\pi\) |
−0.988868 | + | 0.148793i | \(0.952461\pi\) | |||||||
\(770\) | 11538.5 | + | 19985.3i | 0.540026 | + | 0.935352i | ||||
\(771\) | −10462.9 | + | 18122.2i | −0.488730 | + | 0.846505i | ||||
\(772\) | −1107.97 | −0.0516540 | ||||||||
\(773\) | 8616.89 | − | 14924.9i | 0.400942 | − | 0.694451i | −0.592898 | − | 0.805277i | \(-0.702016\pi\) |
0.993840 | + | 0.110826i | \(0.0353497\pi\) | |||||||
\(774\) | 4453.34 | − | 7713.40i | 0.206811 | − | 0.358207i | ||||
\(775\) | −11175.5 | −0.517984 | ||||||||
\(776\) | 1705.07 | − | 2953.26i | 0.0788768 | − | 0.136619i | ||||
\(777\) | −601.009 | − | 1040.98i | −0.0277491 | − | 0.0480629i | ||||
\(778\) | 16026.3 | + | 27758.4i | 0.738523 | + | 1.27916i | ||||
\(779\) | 5395.23 | 0.248144 | ||||||||
\(780\) | 26166.6 | − | 15527.3i | 1.20117 | − | 0.712778i | ||||
\(781\) | 2912.32 | 0.133433 | ||||||||
\(782\) | −26852.6 | − | 46510.1i | −1.22794 | − | 2.12685i | ||||
\(783\) | −19919.5 | − | 34501.6i | −0.909150 | − | 1.57469i | ||||
\(784\) | 21121.3 | − | 36583.2i | 0.962158 | − | 1.66651i | ||||
\(785\) | −7992.02 | −0.363373 | ||||||||
\(786\) | −14354.6 | + | 24862.9i | −0.651415 | + | 1.12828i | ||||
\(787\) | 19837.4 | − | 34359.4i | 0.898510 | − | 1.55627i | 0.0691108 | − | 0.997609i | \(-0.477984\pi\) |
0.829399 | − | 0.558656i | \(-0.188683\pi\) | |||||||
\(788\) | −24051.1 | −1.08729 | ||||||||
\(789\) | 5944.00 | − | 10295.3i | 0.268203 | − | 0.464541i | ||||
\(790\) | −6492.55 | − | 11245.4i | −0.292398 | − | 0.506448i | ||||
\(791\) | 29050.8 | + | 50317.4i | 1.30585 | + | 2.26180i | ||||
\(792\) | −350.106 | −0.0157077 | ||||||||
\(793\) | 29.4647 | + | 2464.35i | 0.00131945 | + | 0.110355i | ||||
\(794\) | −53787.0 | −2.40407 | ||||||||
\(795\) | −22063.1 | − | 38214.4i | −0.984273 | − | 1.70481i | ||||
\(796\) | 3810.41 | + | 6599.83i | 0.169669 | + | 0.293875i | ||||
\(797\) | −14182.8 | + | 24565.4i | −0.630340 | + | 1.09178i | 0.357142 | + | 0.934050i | \(0.383751\pi\) |
−0.987482 | + | 0.157731i | \(0.949582\pi\) | |||||||
\(798\) | −34595.0 | −1.53465 | ||||||||
\(799\) | −14070.6 | + | 24371.0i | −0.623007 | + | 1.07908i | ||||
\(800\) | 10719.8 | − | 18567.2i | 0.473752 | − | 0.820563i | ||||
\(801\) | 4244.94 | 0.187251 | ||||||||
\(802\) | 312.301 | − | 540.922i | 0.0137503 | − | 0.0238162i | ||||
\(803\) | −1480.54 | − | 2564.38i | −0.0650651 | − | 0.112696i | ||||
\(804\) | 1912.67 | + | 3312.84i | 0.0838987 | + | 0.145317i | ||||
\(805\) | 85263.0 | 3.73308 | ||||||||
\(806\) | 23032.0 | + | 12932.9i | 1.00653 | + | 0.565187i | ||||
\(807\) | 19228.6 | 0.838759 | ||||||||
\(808\) | 1356.61 | + | 2349.72i | 0.0590660 | + | 0.102305i | ||||
\(809\) | −4922.61 | − | 8526.21i | −0.213930 | − | 0.370538i | 0.739011 | − | 0.673694i | \(-0.235293\pi\) |
−0.952941 | + | 0.303155i | \(0.901960\pi\) | |||||||
\(810\) | 17357.2 | − | 30063.5i | 0.752925 | − | 1.30410i | ||||
\(811\) | 30581.9 | 1.32414 | 0.662070 | − | 0.749442i | \(-0.269678\pi\) | ||||
0.662070 | + | 0.749442i | \(0.269678\pi\) | |||||||
\(812\) | −44094.9 | + | 76374.7i | −1.90570 | + | 3.30077i | ||||
\(813\) | −13867.1 | + | 24018.6i | −0.598206 | + | 1.03612i | ||||
\(814\) | −339.359 | −0.0146124 | ||||||||
\(815\) | 5586.44 | − | 9676.00i | 0.240104 | − | 0.415872i | ||||
\(816\) | −8683.10 | − | 15039.6i | −0.372512 | − | 0.645209i | ||||
\(817\) | −11056.6 | − | 19150.6i | −0.473466 | − | 0.820067i | ||||
\(818\) | −7356.76 | −0.314454 | ||||||||
\(819\) | −6890.96 | − | 3869.40i | −0.294004 | − | 0.165089i | ||||
\(820\) | 14722.5 | 0.626989 | ||||||||
\(821\) | −12271.3 | − | 21254.6i | −0.521647 | − | 0.903519i | −0.999683 | − | 0.0251790i | \(-0.991984\pi\) |
0.478036 | − | 0.878340i | \(-0.341349\pi\) | |||||||
\(822\) | 22016.1 | + | 38132.9i | 0.934183 | + | 1.61805i | ||||
\(823\) | 14348.8 | − | 24852.9i | 0.607739 | − | 1.05263i | −0.383874 | − | 0.923386i | \(-0.625410\pi\) |
0.991612 | − | 0.129248i | \(-0.0412565\pi\) | |||||||
\(824\) | −9144.72 | −0.386616 | ||||||||
\(825\) | −2150.81 | + | 3725.32i | −0.0907657 | + | 0.157211i | ||||
\(826\) | 20257.8 | − | 35087.5i | 0.853338 | − | 1.47803i | ||||
\(827\) | 43827.0 | 1.84282 | 0.921412 | − | 0.388587i | \(-0.127037\pi\) | ||||
0.921412 | + | 0.388587i | \(0.127037\pi\) | |||||||
\(828\) | −3957.06 | + | 6853.82i | −0.166084 | + | 0.287665i | ||||
\(829\) | 6467.26 | + | 11201.6i | 0.270949 | + | 0.469298i | 0.969105 | − | 0.246648i | \(-0.0793290\pi\) |
−0.698156 | + | 0.715946i | \(0.745996\pi\) | |||||||
\(830\) | −34153.6 | − | 59155.8i | −1.42830 | − | 2.47389i | ||||
\(831\) | 2094.87 | 0.0874490 | ||||||||
\(832\) | −27761.4 | + | 16473.7i | −1.15679 | + | 0.686444i | ||||
\(833\) | −64793.9 | −2.69505 | ||||||||
\(834\) | 12859.8 | + | 22273.8i | 0.533931 | + | 0.924796i | ||||
\(835\) | 4696.11 | + | 8133.90i | 0.194629 | + | 0.337108i | ||||
\(836\) | −2659.06 | + | 4605.63i | −0.110007 | + | 0.190537i | ||||
\(837\) | 20158.5 | 0.832474 | ||||||||
\(838\) | 14475.3 | − | 25072.0i | 0.596709 | − | 1.03353i | ||||
\(839\) | −9617.52 | + | 16658.0i | −0.395749 | + | 0.685458i | −0.993197 | − | 0.116450i | \(-0.962848\pi\) |
0.597447 | + | 0.801908i | \(0.296182\pi\) | |||||||
\(840\) | −15429.8 | −0.633786 | ||||||||
\(841\) | −23117.8 | + | 40041.2i | −0.947878 | + | 1.64177i | ||||
\(842\) | −25769.2 | − | 44633.5i | −1.05471 | − | 1.82681i | ||||
\(843\) | −3999.76 | − | 6927.78i | −0.163415 | − | 0.283043i | ||||
\(844\) | 1620.87 | 0.0661050 | ||||||||
\(845\) | 15186.1 | − | 27818.6i | 0.618246 | − | 1.13253i | ||||
\(846\) | 7616.09 | 0.309511 | ||||||||
\(847\) | 2099.42 | + | 3636.30i | 0.0851676 | + | 0.147515i | ||||
\(848\) | 15943.5 | + | 27614.9i | 0.645638 | + | 1.11828i | ||||
\(849\) | −18969.3 | + | 32855.8i | −0.766813 | + | 1.32816i | ||||
\(850\) | −26205.0 | −1.05744 | ||||||||
\(851\) | −626.915 | + | 1085.85i | −0.0252531 | + | 0.0437396i | ||||
\(852\) | −5956.81 | + | 10317.5i | −0.239527 | + | 0.414872i | ||||
\(853\) | 12364.7 | 0.496317 | 0.248159 | − | 0.968719i | \(-0.420175\pi\) | ||||
0.248159 | + | 0.968719i | \(0.420175\pi\) | |||||||
\(854\) | 3823.25 | − | 6622.05i | 0.153195 | − | 0.265342i | ||||
\(855\) | 1771.81 | + | 3068.86i | 0.0708707 | + | 0.122752i | ||||
\(856\) | −1078.98 | − | 1868.84i | −0.0430826 | − | 0.0746212i | ||||
\(857\) | −14924.8 | −0.594893 | −0.297446 | − | 0.954739i | \(-0.596135\pi\) | ||||
−0.297446 | + | 0.954739i | \(0.596135\pi\) | |||||||
\(858\) | 8743.78 | − | 5188.58i | 0.347911 | − | 0.206451i | ||||
\(859\) | −43335.2 | −1.72128 | −0.860639 | − | 0.509215i | \(-0.829936\pi\) | ||||
−0.860639 | + | 0.509215i | \(0.829936\pi\) | |||||||
\(860\) | −30171.2 | − | 52258.1i | −1.19631 | − | 2.07208i | ||||
\(861\) | 8712.74 | + | 15090.9i | 0.344866 | + | 0.597325i | ||||
\(862\) | −3120.06 | + | 5404.09i | −0.123283 | + | 0.213532i | ||||
\(863\) | −6338.71 | −0.250026 | −0.125013 | − | 0.992155i | \(-0.539897\pi\) | ||||
−0.125013 | + | 0.992155i | \(0.539897\pi\) | |||||||
\(864\) | −19336.4 | + | 33491.7i | −0.761388 | + | 1.31876i | ||||
\(865\) | −24916.9 | + | 43157.4i | −0.979423 | + | 1.69641i | ||||
\(866\) | 47565.7 | 1.86645 | ||||||||
\(867\) | −1759.68 | + | 3047.85i | −0.0689295 | + | 0.119389i | ||||
\(868\) | −22312.1 | − | 38645.6i | −0.872489 | − | 1.51120i | ||||
\(869\) | −1181.31 | − | 2046.09i | −0.0461142 | − | 0.0798721i | ||||
\(870\) | −75600.0 | −2.94607 | ||||||||
\(871\) | 3474.36 | + | 1950.92i | 0.135160 | + | 0.0758947i | ||||
\(872\) | −4760.24 | −0.184865 | ||||||||
\(873\) | −1264.74 | − | 2190.59i | −0.0490320 | − | 0.0849260i | ||||
\(874\) | 18043.1 | + | 31251.6i | 0.698305 | + | 1.20950i | ||||
\(875\) | −10485.7 | + | 18161.7i | −0.405120 | + | 0.701688i | ||||
\(876\) | 12113.1 | 0.467196 | ||||||||
\(877\) | −16958.3 | + | 29372.7i | −0.652956 | + | 1.13095i | 0.329446 | + | 0.944174i | \(0.393138\pi\) |
−0.982402 | + | 0.186778i | \(0.940195\pi\) | |||||||
\(878\) | 6786.19 | − | 11754.0i | 0.260846 | − | 0.451799i | ||||
\(879\) | −17915.5 | −0.687457 | ||||||||
\(880\) | 3891.95 | − | 6741.05i | 0.149088 | − | 0.258228i | ||||
\(881\) | 8917.77 | + | 15446.0i | 0.341030 | + | 0.590681i | 0.984624 | − | 0.174686i | \(-0.0558909\pi\) |
−0.643594 | + | 0.765367i | \(0.722558\pi\) | |||||||
\(882\) | 8767.85 | + | 15186.4i | 0.334727 | + | 0.579763i | ||||
\(883\) | −6224.35 | −0.237221 | −0.118610 | − | 0.992941i | \(-0.537844\pi\) | ||||
−0.118610 | + | 0.992941i | \(0.537844\pi\) | |||||||
\(884\) | 29406.5 | + | 16512.3i | 1.11883 | + | 0.628243i | ||||
\(885\) | 18911.3 | 0.718300 | ||||||||
\(886\) | −22887.8 | − | 39642.8i | −0.867866 | − | 1.50319i | ||||
\(887\) | 3253.95 | + | 5636.01i | 0.123176 | + | 0.213347i | 0.921018 | − | 0.389519i | \(-0.127359\pi\) |
−0.797843 | + | 0.602866i | \(0.794025\pi\) | |||||||
\(888\) | 113.451 | − | 196.504i | 0.00428736 | − | 0.00742593i | ||||
\(889\) | −23382.3 | −0.882134 | ||||||||
\(890\) | 26409.0 | − | 45741.8i | 0.994644 | − | 1.72277i | ||||
\(891\) | 3158.12 | − | 5470.02i | 0.118744 | − | 0.205671i | ||||
\(892\) | −27323.8 | −1.02564 | ||||||||
\(893\) | 9454.49 | − | 16375.7i | 0.354292 | − | 0.613651i | ||||
\(894\) | 22382.5 | + | 38767.5i | 0.837339 | + | 1.45031i | ||||
\(895\) | 13619.2 | + | 23589.2i | 0.508649 | + | 0.881006i | ||||
\(896\) | 28540.3 | 1.06413 | ||||||||
\(897\) | −449.115 | − | 37562.7i | −0.0167174 | − | 1.39820i | ||||
\(898\) | 57418.3 | 2.13371 | ||||||||
\(899\) | −17868.0 | − | 30948.4i | −0.662884 | − | 1.14815i | ||||
\(900\) | 1930.81 | + | 3344.26i | 0.0715114 | + | 0.123861i | ||||
\(901\) | 24454.9 | − | 42357.2i | 0.904231 | − | 1.56617i | ||||
\(902\) | 4919.64 | 0.181603 | ||||||||
\(903\) | 35710.6 | − | 61852.5i | 1.31603 | − | 2.27943i | ||||
\(904\) | −5483.87 | + | 9498.33i | −0.201760 | + | 0.349458i | ||||
\(905\) | −53582.0 | −1.96810 | ||||||||
\(906\) | −13085.7 | + | 22665.1i | −0.479850 | + | 0.831125i | ||||
\(907\) | 20958.5 | + | 36301.1i | 0.767271 | + | 1.32895i | 0.939038 | + | 0.343814i | \(0.111719\pi\) |
−0.171767 | + | 0.985138i | \(0.554948\pi\) | |||||||
\(908\) | 1414.08 | + | 2449.26i | 0.0516828 | + | 0.0895172i | ||||
\(909\) | 2012.54 | 0.0734343 | ||||||||
\(910\) | −84565.7 | + | 50181.5i | −3.08058 | + | 1.82802i | ||||
\(911\) | −16133.7 | −0.586753 | −0.293377 | − | 0.955997i | \(-0.594779\pi\) | ||||
−0.293377 | + | 0.955997i | \(0.594779\pi\) | |||||||
\(912\) | 5834.45 | + | 10105.6i | 0.211840 | + | 0.366918i | ||||
\(913\) | −6214.21 | − | 10763.3i | −0.225258 | − | 0.390158i | ||||
\(914\) | −1688.09 | + | 2923.86i | −0.0610909 | + | 0.105813i | ||||
\(915\) | 3569.12 | 0.128953 | ||||||||
\(916\) | 18196.6 | − | 31517.5i | 0.656368 | − | 1.13686i | ||||
\(917\) | 25260.1 | − | 43751.8i | 0.909665 | − | 1.57559i | ||||
\(918\) | 47268.8 | 1.69946 | ||||||||
\(919\) | −8288.34 | + | 14355.8i | −0.297505 | + | 0.515294i | −0.975565 | − | 0.219713i | \(-0.929488\pi\) |
0.678059 | + | 0.735007i | \(0.262821\pi\) | |||||||
\(920\) | 8047.48 | + | 13938.6i | 0.288389 | + | 0.499504i | ||||
\(921\) | 17494.6 | + | 30301.6i | 0.625915 | + | 1.08412i | ||||
\(922\) | −21688.1 | −0.774683 | ||||||||
\(923\) | 148.365 | + | 12408.8i | 0.00529089 | + | 0.442515i | ||||
\(924\) | −17176.5 | −0.611541 | ||||||||
\(925\) | 305.897 | + | 529.830i | 0.0108733 | + | 0.0188332i | ||||
\(926\) | −5537.01 | − | 9590.38i | −0.196498 | − | 0.340345i | ||||
\(927\) | −3391.57 | + | 5874.37i | −0.120166 | + | 0.208133i | ||||
\(928\) | 68557.4 | 2.42512 | ||||||||
\(929\) | 25201.6 | − | 43650.5i | 0.890030 | − | 1.54158i | 0.0501933 | − | 0.998740i | \(-0.484016\pi\) |
0.839837 | − | 0.542838i | \(-0.182650\pi\) | |||||||
\(930\) | 19126.8 | − | 33128.6i | 0.674401 | − | 1.16810i | ||||
\(931\) | 43537.1 | 1.53262 | ||||||||
\(932\) | 8477.90 | − | 14684.2i | 0.297964 | − | 0.516089i | ||||
\(933\) | 7991.80 | + | 13842.2i | 0.280429 | + | 0.485717i | ||||
\(934\) | −13868.6 | − | 24021.1i | −0.485861 | − | 0.841535i | ||||
\(935\) | −11939.3 | −0.417602 | ||||||||
\(936\) | −17.8357 | − | 1491.73i | −0.000622841 | − | 0.0520927i | ||||
\(937\) | −29253.1 | −1.01991 | −0.509956 | − | 0.860201i | \(-0.670338\pi\) | ||||
−0.509956 | + | 0.860201i | \(0.670338\pi\) | |||||||
\(938\) | −6181.40 | − | 10706.5i | −0.215170 | − | 0.372686i | ||||
\(939\) | −2643.76 | − | 4579.12i | −0.0918804 | − | 0.159142i | ||||
\(940\) | 25799.4 | − | 44685.8i | 0.895195 | − | 1.55052i | ||||
\(941\) | 27097.4 | 0.938736 | 0.469368 | − | 0.883003i | \(-0.344482\pi\) | ||||
0.469368 | + | 0.883003i | \(0.344482\pi\) | |||||||
\(942\) | 5462.40 | − | 9461.15i | 0.188933 | − | 0.327241i | ||||
\(943\) | 9088.31 | − | 15741.4i | 0.313845 | − | 0.543596i | ||||
\(944\) | −13665.9 | −0.471172 | ||||||||
\(945\) | −37522.2 | + | 64990.3i | −1.29164 | + | 2.23718i | ||||
\(946\) | −10082.0 | − | 17462.5i | −0.346504 | − | 0.600163i | ||||
\(947\) | 14328.4 | + | 24817.4i | 0.491668 | + | 0.851593i | 0.999954 | − | 0.00959491i | \(-0.00305420\pi\) |
−0.508286 | + | 0.861188i | \(0.669721\pi\) | |||||||
\(948\) | 9664.92 | 0.331120 | ||||||||
\(949\) | 10850.9 | − | 6438.94i | 0.371164 | − | 0.220250i | ||||
\(950\) | 17608.0 | 0.601345 | ||||||||
\(951\) | 6645.51 | + | 11510.4i | 0.226599 | + | 0.392481i | ||||
\(952\) | −8551.29 | − | 14811.3i | −0.291123 | − | 0.504240i | ||||
\(953\) | −27408.8 | + | 47473.4i | −0.931644 | + | 1.61365i | −0.151132 | + | 0.988514i | \(0.548292\pi\) |
−0.780512 | + | 0.625141i | \(0.785041\pi\) | |||||||
\(954\) | −13236.9 | −0.449224 | ||||||||
\(955\) | 6822.14 | − | 11816.3i | 0.231161 | − | 0.400383i | ||||
\(956\) | −6105.67 | + | 10575.3i | −0.206560 | + | 0.357773i | ||||
\(957\) | −13755.3 | −0.464625 | ||||||||
\(958\) | −31371.6 | + | 54337.1i | −1.05801 | + | 1.83252i | ||||
\(959\) | −38742.1 | − | 67103.4i | −1.30454 | − | 2.25952i | ||||
\(960\) | 23374.8 | + | 40486.4i | 0.785853 | + | 1.36114i | ||||
\(961\) | −11708.5 | −0.393022 | ||||||||
\(962\) | −17.2882 | − | 1445.94i | −0.000579413 | − | 0.0484605i | ||||
\(963\) | −1600.67 | −0.0535627 | ||||||||
\(964\) | −1720.22 | − | 2979.51i | −0.0574736 | − | 0.0995472i | ||||
\(965\) | 835.694 | + | 1447.46i | 0.0278777 | + | 0.0482855i | ||||
\(966\) | −58275.6 | + | 100936.i | −1.94098 | + | 3.36188i | ||||
\(967\) | −14806.3 | −0.492388 | −0.246194 | − | 0.969221i | \(-0.579180\pi\) | ||||
−0.246194 | + | 0.969221i | \(0.579180\pi\) | |||||||
\(968\) | −396.304 | + | 686.419i | −0.0131588 | + | 0.0227917i | ||||
\(969\) | 8949.19 | − | 15500.4i | 0.296687 | − | 0.513876i | ||||
\(970\) | −31473.3 | −1.04180 | ||||||||
\(971\) | −27308.6 | + | 47299.9i | −0.902549 | + | 1.56326i | −0.0783760 | + | 0.996924i | \(0.524973\pi\) |
−0.824173 | + | 0.566338i | \(0.808360\pi\) | |||||||
\(972\) | −6434.45 | − | 11144.8i | −0.212330 | − | 0.367767i | ||||
\(973\) | −22629.7 | − | 39195.8i | −0.745606 | − | 1.29143i | ||||
\(974\) | −367.489 | −0.0120894 | ||||||||
\(975\) | −15982.4 | − | 8974.40i | −0.524971 | − | 0.294780i | ||||
\(976\) | −2579.16 | −0.0845871 | ||||||||
\(977\) | −475.229 | − | 823.121i | −0.0155618 | − | 0.0269539i | 0.858140 | − | 0.513416i | \(-0.171620\pi\) |
−0.873701 | + | 0.486463i | \(0.838287\pi\) | |||||||
\(978\) | 7636.45 | + | 13226.7i | 0.249680 | + | 0.432458i | ||||
\(979\) | 4805.09 | − | 8322.66i | 0.156866 | − | 0.271699i | ||||
\(980\) | 118804. | 3.87250 | ||||||||
\(981\) | −1765.46 | + | 3057.87i | −0.0574586 | + | 0.0995213i | ||||
\(982\) | −35802.9 | + | 62012.5i | −1.16346 | + | 2.01517i | ||||
\(983\) | −627.901 | −0.0203733 | −0.0101866 | − | 0.999948i | \(-0.503243\pi\) | ||||
−0.0101866 | + | 0.999948i | \(0.503243\pi\) | |||||||
\(984\) | −1644.69 | + | 2848.69i | −0.0532833 | + | 0.0922894i | ||||
\(985\) | 18140.6 | + | 31420.4i | 0.586810 | + | 1.01638i | ||||
\(986\) | −41897.9 | − | 72569.2i | −1.35325 | − | 2.34389i | ||||
\(987\) | 61072.2 | 1.96955 | ||||||||
\(988\) | −19759.1 | − | 11095.1i | −0.636257 | − | 0.357270i | ||||
\(989\) | −74499.8 | −2.39530 | ||||||||
\(990\) | 1615.62 | + | 2798.34i | 0.0518665 | + | 0.0898354i | ||||
\(991\) | −14478.4 | − | 25077.3i | −0.464098 | − | 0.803841i | 0.535062 | − | 0.844813i | \(-0.320288\pi\) |
−0.999160 | + | 0.0409713i | \(0.986955\pi\) | |||||||
\(992\) | −17345.0 | + | 30042.5i | −0.555147 | + | 0.961543i | ||||
\(993\) | −7679.78 | −0.245428 | ||||||||
\(994\) | 19251.3 | − | 33344.3i | 0.614301 | − | 1.06400i | ||||
\(995\) | 5748.03 | − | 9955.88i | 0.183141 | − | 0.317209i | ||||
\(996\) | 50841.7 | 1.61745 | ||||||||
\(997\) | 20006.3 | − | 34651.9i | 0.635512 | − | 1.10074i | −0.350895 | − | 0.936415i | \(-0.614122\pi\) |
0.986406 | − | 0.164324i | \(-0.0525442\pi\) | |||||||
\(998\) | 2314.93 | + | 4009.58i | 0.0734247 | + | 0.127175i | ||||
\(999\) | −551.781 | − | 955.712i | −0.0174750 | − | 0.0302677i |
(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 | 143.4.e.b.133.2 | yes | 34 | |
13.3 | even | 3 | 1859.4.a.g.1.16 | 17 | |||
13.9 | even | 3 | inner | 143.4.e.b.100.2 | ✓ | 34 | |
13.10 | even | 6 | 1859.4.a.h.1.2 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
143.4.e.b.100.2 | ✓ | 34 | 13.9 | even | 3 | inner | |
143.4.e.b.133.2 | yes | 34 | 1.1 | even | 1 | trivial | |
1859.4.a.g.1.16 | 17 | 13.3 | even | 3 | |||
1859.4.a.h.1.2 | 17 | 13.10 | even | 6 |