Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.a (trivial) |
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: | yes |
Analytic conductor: | \(47.9182262530\) |
Analytic rank: | \(1\) |
Dimension: | \(114\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.79736 | −1.97803 | −0.989016 | − | 0.147811i | \(-0.952777\pi\) | ||||
−0.989016 | + | 0.147811i | \(0.952777\pi\) | |||||||
\(3\) | 1.48474 | 0.857212 | 0.428606 | − | 0.903491i | \(-0.359005\pi\) | ||||
0.428606 | + | 0.903491i | \(0.359005\pi\) | |||||||
\(4\) | 5.82522 | 2.91261 | ||||||||
\(5\) | 0.639507 | 0.285996 | 0.142998 | − | 0.989723i | \(-0.454326\pi\) | ||||
0.142998 | + | 0.989723i | \(0.454326\pi\) | |||||||
\(6\) | −4.15334 | −1.69559 | ||||||||
\(7\) | 0.101329 | 0.0382986 | 0.0191493 | − | 0.999817i | \(-0.493904\pi\) | ||||
0.0191493 | + | 0.999817i | \(0.493904\pi\) | |||||||
\(8\) | −10.7005 | −3.78320 | ||||||||
\(9\) | −0.795561 | −0.265187 | ||||||||
\(10\) | −1.78893 | −0.565710 | ||||||||
\(11\) | −3.15797 | −0.952162 | −0.476081 | − | 0.879401i | \(-0.657943\pi\) | ||||
−0.476081 | + | 0.879401i | \(0.657943\pi\) | |||||||
\(12\) | 8.64890 | 2.49672 | ||||||||
\(13\) | −1.87733 | −0.520677 | −0.260338 | − | 0.965517i | \(-0.583834\pi\) | ||||
−0.260338 | + | 0.965517i | \(0.583834\pi\) | |||||||
\(14\) | −0.283453 | −0.0757559 | ||||||||
\(15\) | 0.949499 | 0.245160 | ||||||||
\(16\) | 18.2827 | 4.57068 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 2.22547 | 0.524549 | ||||||||
\(19\) | 3.76627 | 0.864041 | 0.432020 | − | 0.901864i | \(-0.357801\pi\) | ||||
0.432020 | + | 0.901864i | \(0.357801\pi\) | |||||||
\(20\) | 3.72527 | 0.832995 | ||||||||
\(21\) | 0.150446 | 0.0328301 | ||||||||
\(22\) | 8.83396 | 1.88341 | ||||||||
\(23\) | 4.51994 | 0.942472 | 0.471236 | − | 0.882007i | \(-0.343808\pi\) | ||||
0.471236 | + | 0.882007i | \(0.343808\pi\) | |||||||
\(24\) | −15.8874 | −3.24300 | ||||||||
\(25\) | −4.59103 | −0.918206 | ||||||||
\(26\) | 5.25155 | 1.02991 | ||||||||
\(27\) | −5.63540 | −1.08453 | ||||||||
\(28\) | 0.590261 | 0.111549 | ||||||||
\(29\) | 3.83813 | 0.712722 | 0.356361 | − | 0.934348i | \(-0.384017\pi\) | ||||
0.356361 | + | 0.934348i | \(0.384017\pi\) | |||||||
\(30\) | −2.65609 | −0.484933 | ||||||||
\(31\) | 2.57699 | 0.462841 | 0.231421 | − | 0.972854i | \(-0.425663\pi\) | ||||
0.231421 | + | 0.972854i | \(0.425663\pi\) | |||||||
\(32\) | −29.7423 | −5.25774 | ||||||||
\(33\) | −4.68874 | −0.816205 | ||||||||
\(34\) | −2.79736 | −0.479743 | ||||||||
\(35\) | 0.0648004 | 0.0109533 | ||||||||
\(36\) | −4.63432 | −0.772386 | ||||||||
\(37\) | −1.98047 | −0.325588 | −0.162794 | − | 0.986660i | \(-0.552051\pi\) | ||||
−0.162794 | + | 0.986660i | \(0.552051\pi\) | |||||||
\(38\) | −10.5356 | −1.70910 | ||||||||
\(39\) | −2.78733 | −0.446330 | ||||||||
\(40\) | −6.84305 | −1.08198 | ||||||||
\(41\) | −3.78408 | −0.590975 | −0.295487 | − | 0.955347i | \(-0.595482\pi\) | ||||
−0.295487 | + | 0.955347i | \(0.595482\pi\) | |||||||
\(42\) | −0.420852 | −0.0649389 | ||||||||
\(43\) | 3.02029 | 0.460591 | 0.230295 | − | 0.973121i | \(-0.426031\pi\) | ||||
0.230295 | + | 0.973121i | \(0.426031\pi\) | |||||||
\(44\) | −18.3958 | −2.77328 | ||||||||
\(45\) | −0.508767 | −0.0758426 | ||||||||
\(46\) | −12.6439 | −1.86424 | ||||||||
\(47\) | 8.87393 | 1.29440 | 0.647198 | − | 0.762322i | \(-0.275941\pi\) | ||||
0.647198 | + | 0.762322i | \(0.275941\pi\) | |||||||
\(48\) | 27.1450 | 3.91804 | ||||||||
\(49\) | −6.98973 | −0.998533 | ||||||||
\(50\) | 12.8428 | 1.81624 | ||||||||
\(51\) | 1.48474 | 0.207905 | ||||||||
\(52\) | −10.9358 | −1.51653 | ||||||||
\(53\) | −7.39587 | −1.01590 | −0.507951 | − | 0.861386i | \(-0.669597\pi\) | ||||
−0.507951 | + | 0.861386i | \(0.669597\pi\) | |||||||
\(54\) | 15.7642 | 2.14524 | ||||||||
\(55\) | −2.01954 | −0.272315 | ||||||||
\(56\) | −1.08427 | −0.144891 | ||||||||
\(57\) | 5.59191 | 0.740666 | ||||||||
\(58\) | −10.7366 | −1.40979 | ||||||||
\(59\) | −7.61184 | −0.990977 | −0.495488 | − | 0.868615i | \(-0.665011\pi\) | ||||
−0.495488 | + | 0.868615i | \(0.665011\pi\) | |||||||
\(60\) | 5.53104 | 0.714054 | ||||||||
\(61\) | −1.42549 | −0.182515 | −0.0912577 | − | 0.995827i | \(-0.529089\pi\) | ||||
−0.0912577 | + | 0.995827i | \(0.529089\pi\) | |||||||
\(62\) | −7.20877 | −0.915514 | ||||||||
\(63\) | −0.0806132 | −0.0101563 | ||||||||
\(64\) | 46.6344 | 5.82931 | ||||||||
\(65\) | −1.20056 | −0.148912 | ||||||||
\(66\) | 13.1161 | 1.61448 | ||||||||
\(67\) | 6.79364 | 0.829975 | 0.414987 | − | 0.909827i | \(-0.363786\pi\) | ||||
0.414987 | + | 0.909827i | \(0.363786\pi\) | |||||||
\(68\) | 5.82522 | 0.706411 | ||||||||
\(69\) | 6.71091 | 0.807899 | ||||||||
\(70\) | −0.181270 | −0.0216659 | ||||||||
\(71\) | 3.66082 | 0.434459 | 0.217230 | − | 0.976121i | \(-0.430298\pi\) | ||||
0.217230 | + | 0.976121i | \(0.430298\pi\) | |||||||
\(72\) | 8.51291 | 1.00326 | ||||||||
\(73\) | 4.12875 | 0.483234 | 0.241617 | − | 0.970372i | \(-0.422322\pi\) | ||||
0.241617 | + | 0.970372i | \(0.422322\pi\) | |||||||
\(74\) | 5.54010 | 0.644023 | ||||||||
\(75\) | −6.81646 | −0.787097 | ||||||||
\(76\) | 21.9393 | 2.51661 | ||||||||
\(77\) | −0.319992 | −0.0364665 | ||||||||
\(78\) | 7.79717 | 0.882855 | ||||||||
\(79\) | 15.2849 | 1.71968 | 0.859842 | − | 0.510561i | \(-0.170562\pi\) | ||||
0.859842 | + | 0.510561i | \(0.170562\pi\) | |||||||
\(80\) | 11.6919 | 1.30720 | ||||||||
\(81\) | −5.98040 | −0.664489 | ||||||||
\(82\) | 10.5854 | 1.16897 | ||||||||
\(83\) | −4.12323 | −0.452583 | −0.226292 | − | 0.974060i | \(-0.572660\pi\) | ||||
−0.226292 | + | 0.974060i | \(0.572660\pi\) | |||||||
\(84\) | 0.876382 | 0.0956211 | ||||||||
\(85\) | 0.639507 | 0.0693643 | ||||||||
\(86\) | −8.44885 | −0.911063 | ||||||||
\(87\) | 5.69860 | 0.610954 | ||||||||
\(88\) | 33.7918 | 3.60222 | ||||||||
\(89\) | −17.2913 | −1.83287 | −0.916437 | − | 0.400179i | \(-0.868948\pi\) | ||||
−0.916437 | + | 0.400179i | \(0.868948\pi\) | |||||||
\(90\) | 1.42320 | 0.150019 | ||||||||
\(91\) | −0.190227 | −0.0199412 | ||||||||
\(92\) | 26.3296 | 2.74505 | ||||||||
\(93\) | 3.82615 | 0.396753 | ||||||||
\(94\) | −24.8236 | −2.56036 | ||||||||
\(95\) | 2.40856 | 0.247113 | ||||||||
\(96\) | −44.1594 | −4.50700 | ||||||||
\(97\) | −6.63908 | −0.674096 | −0.337048 | − | 0.941487i | \(-0.609429\pi\) | ||||
−0.337048 | + | 0.941487i | \(0.609429\pi\) | |||||||
\(98\) | 19.5528 | 1.97513 | ||||||||
\(99\) | 2.51236 | 0.252501 | ||||||||
\(100\) | −26.7437 | −2.67437 | ||||||||
\(101\) | −14.8755 | −1.48017 | −0.740084 | − | 0.672515i | \(-0.765214\pi\) | ||||
−0.740084 | + | 0.672515i | \(0.765214\pi\) | |||||||
\(102\) | −4.15334 | −0.411242 | ||||||||
\(103\) | 18.2938 | 1.80254 | 0.901270 | − | 0.433258i | \(-0.142636\pi\) | ||||
0.901270 | + | 0.433258i | \(0.142636\pi\) | |||||||
\(104\) | 20.0883 | 1.96982 | ||||||||
\(105\) | 0.0962115 | 0.00938928 | ||||||||
\(106\) | 20.6889 | 2.00948 | ||||||||
\(107\) | 4.22880 | 0.408814 | 0.204407 | − | 0.978886i | \(-0.434473\pi\) | ||||
0.204407 | + | 0.978886i | \(0.434473\pi\) | |||||||
\(108\) | −32.8274 | −3.15882 | ||||||||
\(109\) | −1.26827 | −0.121478 | −0.0607389 | − | 0.998154i | \(-0.519346\pi\) | ||||
−0.0607389 | + | 0.998154i | \(0.519346\pi\) | |||||||
\(110\) | 5.64938 | 0.538648 | ||||||||
\(111\) | −2.94048 | −0.279098 | ||||||||
\(112\) | 1.85256 | 0.175051 | ||||||||
\(113\) | −5.59199 | −0.526050 | −0.263025 | − | 0.964789i | \(-0.584720\pi\) | ||||
−0.263025 | + | 0.964789i | \(0.584720\pi\) | |||||||
\(114\) | −15.6426 | −1.46506 | ||||||||
\(115\) | 2.89053 | 0.269544 | ||||||||
\(116\) | 22.3579 | 2.07588 | ||||||||
\(117\) | 1.49353 | 0.138077 | ||||||||
\(118\) | 21.2930 | 1.96018 | ||||||||
\(119\) | 0.101329 | 0.00928878 | ||||||||
\(120\) | −10.1601 | −0.927487 | ||||||||
\(121\) | −1.02725 | −0.0933866 | ||||||||
\(122\) | 3.98761 | 0.361021 | ||||||||
\(123\) | −5.61836 | −0.506591 | ||||||||
\(124\) | 15.0115 | 1.34807 | ||||||||
\(125\) | −6.13353 | −0.548600 | ||||||||
\(126\) | 0.225504 | 0.0200895 | ||||||||
\(127\) | 1.30542 | 0.115837 | 0.0579184 | − | 0.998321i | \(-0.481554\pi\) | ||||
0.0579184 | + | 0.998321i | \(0.481554\pi\) | |||||||
\(128\) | −70.9687 | −6.27281 | ||||||||
\(129\) | 4.48434 | 0.394824 | ||||||||
\(130\) | 3.35841 | 0.294552 | ||||||||
\(131\) | −12.0900 | −1.05631 | −0.528155 | − | 0.849148i | \(-0.677116\pi\) | ||||
−0.528155 | + | 0.849148i | \(0.677116\pi\) | |||||||
\(132\) | −27.3129 | −2.37729 | ||||||||
\(133\) | 0.381631 | 0.0330916 | ||||||||
\(134\) | −19.0042 | −1.64172 | ||||||||
\(135\) | −3.60388 | −0.310173 | ||||||||
\(136\) | −10.7005 | −0.917560 | ||||||||
\(137\) | −13.1154 | −1.12052 | −0.560262 | − | 0.828315i | \(-0.689300\pi\) | ||||
−0.560262 | + | 0.828315i | \(0.689300\pi\) | |||||||
\(138\) | −18.7728 | −1.59805 | ||||||||
\(139\) | 8.02261 | 0.680469 | 0.340234 | − | 0.940341i | \(-0.389494\pi\) | ||||
0.340234 | + | 0.940341i | \(0.389494\pi\) | |||||||
\(140\) | 0.377476 | 0.0319026 | ||||||||
\(141\) | 13.1754 | 1.10957 | ||||||||
\(142\) | −10.2406 | −0.859374 | ||||||||
\(143\) | 5.92853 | 0.495769 | ||||||||
\(144\) | −14.5450 | −1.21208 | ||||||||
\(145\) | 2.45451 | 0.203836 | ||||||||
\(146\) | −11.5496 | −0.955852 | ||||||||
\(147\) | −10.3779 | −0.855955 | ||||||||
\(148\) | −11.5367 | −0.948310 | ||||||||
\(149\) | 6.49004 | 0.531685 | 0.265842 | − | 0.964017i | \(-0.414350\pi\) | ||||
0.265842 | + | 0.964017i | \(0.414350\pi\) | |||||||
\(150\) | 19.0681 | 1.55690 | ||||||||
\(151\) | −6.29066 | −0.511926 | −0.255963 | − | 0.966687i | \(-0.582393\pi\) | ||||
−0.255963 | + | 0.966687i | \(0.582393\pi\) | |||||||
\(152\) | −40.3009 | −3.26884 | ||||||||
\(153\) | −0.795561 | −0.0643173 | ||||||||
\(154\) | 0.895134 | 0.0721319 | ||||||||
\(155\) | 1.64800 | 0.132371 | ||||||||
\(156\) | −16.2368 | −1.29999 | ||||||||
\(157\) | −4.61294 | −0.368153 | −0.184076 | − | 0.982912i | \(-0.558929\pi\) | ||||
−0.184076 | + | 0.982912i | \(0.558929\pi\) | |||||||
\(158\) | −42.7573 | −3.40159 | ||||||||
\(159\) | −10.9809 | −0.870843 | ||||||||
\(160\) | −19.0204 | −1.50370 | ||||||||
\(161\) | 0.457999 | 0.0360954 | ||||||||
\(162\) | 16.7293 | 1.31438 | ||||||||
\(163\) | −14.3112 | −1.12094 | −0.560469 | − | 0.828175i | \(-0.689379\pi\) | ||||
−0.560469 | + | 0.828175i | \(0.689379\pi\) | |||||||
\(164\) | −22.0431 | −1.72128 | ||||||||
\(165\) | −2.99849 | −0.233432 | ||||||||
\(166\) | 11.5342 | 0.895224 | ||||||||
\(167\) | 13.7503 | 1.06403 | 0.532014 | − | 0.846735i | \(-0.321435\pi\) | ||||
0.532014 | + | 0.846735i | \(0.321435\pi\) | |||||||
\(168\) | −1.60985 | −0.124203 | ||||||||
\(169\) | −9.47565 | −0.728896 | ||||||||
\(170\) | −1.78893 | −0.137205 | ||||||||
\(171\) | −2.99630 | −0.229133 | ||||||||
\(172\) | 17.5939 | 1.34152 | ||||||||
\(173\) | −2.84904 | −0.216608 | −0.108304 | − | 0.994118i | \(-0.534542\pi\) | ||||
−0.108304 | + | 0.994118i | \(0.534542\pi\) | |||||||
\(174\) | −15.9410 | −1.20849 | ||||||||
\(175\) | −0.465203 | −0.0351660 | ||||||||
\(176\) | −57.7362 | −4.35203 | ||||||||
\(177\) | −11.3016 | −0.849478 | ||||||||
\(178\) | 48.3700 | 3.62548 | ||||||||
\(179\) | −16.7721 | −1.25361 | −0.626804 | − | 0.779177i | \(-0.715637\pi\) | ||||
−0.626804 | + | 0.779177i | \(0.715637\pi\) | |||||||
\(180\) | −2.96368 | −0.220900 | ||||||||
\(181\) | 8.92632 | 0.663488 | 0.331744 | − | 0.943369i | \(-0.392363\pi\) | ||||
0.331744 | + | 0.943369i | \(0.392363\pi\) | |||||||
\(182\) | 0.532133 | 0.0394443 | ||||||||
\(183\) | −2.11648 | −0.156454 | ||||||||
\(184\) | −48.3656 | −3.56556 | ||||||||
\(185\) | −1.26653 | −0.0931170 | ||||||||
\(186\) | −10.7031 | −0.784790 | ||||||||
\(187\) | −3.15797 | −0.230933 | ||||||||
\(188\) | 51.6926 | 3.77007 | ||||||||
\(189\) | −0.571028 | −0.0415362 | ||||||||
\(190\) | −6.73759 | −0.488796 | ||||||||
\(191\) | −11.9926 | −0.867754 | −0.433877 | − | 0.900972i | \(-0.642855\pi\) | ||||
−0.433877 | + | 0.900972i | \(0.642855\pi\) | |||||||
\(192\) | 69.2398 | 4.99695 | ||||||||
\(193\) | −6.64884 | −0.478594 | −0.239297 | − | 0.970946i | \(-0.576917\pi\) | ||||
−0.239297 | + | 0.970946i | \(0.576917\pi\) | |||||||
\(194\) | 18.5719 | 1.33338 | ||||||||
\(195\) | −1.78252 | −0.127649 | ||||||||
\(196\) | −40.7167 | −2.90834 | ||||||||
\(197\) | 11.5746 | 0.824654 | 0.412327 | − | 0.911036i | \(-0.364716\pi\) | ||||
0.412327 | + | 0.911036i | \(0.364716\pi\) | |||||||
\(198\) | −7.02796 | −0.499455 | ||||||||
\(199\) | −15.4792 | −1.09729 | −0.548644 | − | 0.836056i | \(-0.684856\pi\) | ||||
−0.548644 | + | 0.836056i | \(0.684856\pi\) | |||||||
\(200\) | 49.1263 | 3.47376 | ||||||||
\(201\) | 10.0868 | 0.711465 | ||||||||
\(202\) | 41.6121 | 2.92782 | ||||||||
\(203\) | 0.388912 | 0.0272963 | ||||||||
\(204\) | 8.64890 | 0.605544 | ||||||||
\(205\) | −2.41995 | −0.169017 | ||||||||
\(206\) | −51.1743 | −3.56548 | ||||||||
\(207\) | −3.59589 | −0.249931 | ||||||||
\(208\) | −34.3226 | −2.37984 | ||||||||
\(209\) | −11.8937 | −0.822707 | ||||||||
\(210\) | −0.269138 | −0.0185723 | ||||||||
\(211\) | 12.0398 | 0.828856 | 0.414428 | − | 0.910082i | \(-0.363982\pi\) | ||||
0.414428 | + | 0.910082i | \(0.363982\pi\) | |||||||
\(212\) | −43.0825 | −2.95892 | ||||||||
\(213\) | 5.43535 | 0.372424 | ||||||||
\(214\) | −11.8295 | −0.808646 | ||||||||
\(215\) | 1.93150 | 0.131727 | ||||||||
\(216\) | 60.3016 | 4.10301 | ||||||||
\(217\) | 0.261123 | 0.0177262 | ||||||||
\(218\) | 3.54779 | 0.240287 | ||||||||
\(219\) | 6.13011 | 0.414234 | ||||||||
\(220\) | −11.7643 | −0.793147 | ||||||||
\(221\) | −1.87733 | −0.126283 | ||||||||
\(222\) | 8.22558 | 0.552065 | ||||||||
\(223\) | −14.7568 | −0.988185 | −0.494093 | − | 0.869409i | \(-0.664500\pi\) | ||||
−0.494093 | + | 0.869409i | \(0.664500\pi\) | |||||||
\(224\) | −3.01375 | −0.201364 | ||||||||
\(225\) | 3.65245 | 0.243496 | ||||||||
\(226\) | 15.6428 | 1.04054 | ||||||||
\(227\) | −22.6487 | −1.50325 | −0.751625 | − | 0.659591i | \(-0.770730\pi\) | ||||
−0.751625 | + | 0.659591i | \(0.770730\pi\) | |||||||
\(228\) | 32.5741 | 2.15727 | ||||||||
\(229\) | 8.72949 | 0.576861 | 0.288430 | − | 0.957501i | \(-0.406867\pi\) | ||||
0.288430 | + | 0.957501i | \(0.406867\pi\) | |||||||
\(230\) | −8.08586 | −0.533166 | ||||||||
\(231\) | −0.475104 | −0.0312596 | ||||||||
\(232\) | −41.0699 | −2.69637 | ||||||||
\(233\) | −9.24232 | −0.605485 | −0.302742 | − | 0.953072i | \(-0.597902\pi\) | ||||
−0.302742 | + | 0.953072i | \(0.597902\pi\) | |||||||
\(234\) | −4.17793 | −0.273120 | ||||||||
\(235\) | 5.67494 | 0.370192 | ||||||||
\(236\) | −44.3406 | −2.88633 | ||||||||
\(237\) | 22.6940 | 1.47413 | ||||||||
\(238\) | −0.283453 | −0.0183735 | ||||||||
\(239\) | −12.8169 | −0.829056 | −0.414528 | − | 0.910037i | \(-0.636053\pi\) | ||||
−0.414528 | + | 0.910037i | \(0.636053\pi\) | |||||||
\(240\) | 17.3594 | 1.12055 | ||||||||
\(241\) | −25.0976 | −1.61668 | −0.808340 | − | 0.588717i | \(-0.799633\pi\) | ||||
−0.808340 | + | 0.588717i | \(0.799633\pi\) | |||||||
\(242\) | 2.87360 | 0.184722 | ||||||||
\(243\) | 8.02690 | 0.514926 | ||||||||
\(244\) | −8.30379 | −0.531596 | ||||||||
\(245\) | −4.46999 | −0.285577 | ||||||||
\(246\) | 15.7166 | 1.00205 | ||||||||
\(247\) | −7.07051 | −0.449886 | ||||||||
\(248\) | −27.5751 | −1.75102 | ||||||||
\(249\) | −6.12191 | −0.387960 | ||||||||
\(250\) | 17.1577 | 1.08515 | ||||||||
\(251\) | −15.4669 | −0.976265 | −0.488133 | − | 0.872769i | \(-0.662322\pi\) | ||||
−0.488133 | + | 0.872769i | \(0.662322\pi\) | |||||||
\(252\) | −0.469589 | −0.0295813 | ||||||||
\(253\) | −14.2738 | −0.897387 | ||||||||
\(254\) | −3.65172 | −0.229129 | ||||||||
\(255\) | 0.949499 | 0.0594599 | ||||||||
\(256\) | 105.256 | 6.57850 | ||||||||
\(257\) | −7.82671 | −0.488217 | −0.244109 | − | 0.969748i | \(-0.578495\pi\) | ||||
−0.244109 | + | 0.969748i | \(0.578495\pi\) | |||||||
\(258\) | −12.5443 | −0.780974 | ||||||||
\(259\) | −0.200679 | −0.0124696 | ||||||||
\(260\) | −6.99354 | −0.433721 | ||||||||
\(261\) | −3.05347 | −0.189005 | ||||||||
\(262\) | 33.8201 | 2.08942 | ||||||||
\(263\) | −7.16826 | −0.442014 | −0.221007 | − | 0.975272i | \(-0.570934\pi\) | ||||
−0.221007 | + | 0.975272i | \(0.570934\pi\) | |||||||
\(264\) | 50.1719 | 3.08787 | ||||||||
\(265\) | −4.72971 | −0.290544 | ||||||||
\(266\) | −1.06756 | −0.0654562 | ||||||||
\(267\) | −25.6730 | −1.57116 | ||||||||
\(268\) | 39.5744 | 2.41739 | ||||||||
\(269\) | −3.27187 | −0.199490 | −0.0997449 | − | 0.995013i | \(-0.531803\pi\) | ||||
−0.0997449 | + | 0.995013i | \(0.531803\pi\) | |||||||
\(270\) | 10.0814 | 0.613531 | ||||||||
\(271\) | 10.5903 | 0.643313 | 0.321656 | − | 0.946857i | \(-0.395760\pi\) | ||||
0.321656 | + | 0.946857i | \(0.395760\pi\) | |||||||
\(272\) | 18.2827 | 1.10855 | ||||||||
\(273\) | −0.282437 | −0.0170938 | ||||||||
\(274\) | 36.6885 | 2.21643 | ||||||||
\(275\) | 14.4983 | 0.874281 | ||||||||
\(276\) | 39.0925 | 2.35309 | ||||||||
\(277\) | 24.1277 | 1.44969 | 0.724846 | − | 0.688911i | \(-0.241911\pi\) | ||||
0.724846 | + | 0.688911i | \(0.241911\pi\) | |||||||
\(278\) | −22.4421 | −1.34599 | ||||||||
\(279\) | −2.05015 | −0.122740 | ||||||||
\(280\) | −0.693397 | −0.0414384 | ||||||||
\(281\) | 3.25958 | 0.194450 | 0.0972250 | − | 0.995262i | \(-0.469003\pi\) | ||||
0.0972250 | + | 0.995262i | \(0.469003\pi\) | |||||||
\(282\) | −36.8564 | −2.19477 | ||||||||
\(283\) | 12.9396 | 0.769180 | 0.384590 | − | 0.923088i | \(-0.374343\pi\) | ||||
0.384590 | + | 0.923088i | \(0.374343\pi\) | |||||||
\(284\) | 21.3251 | 1.26541 | ||||||||
\(285\) | 3.57607 | 0.211828 | ||||||||
\(286\) | −16.5842 | −0.980646 | ||||||||
\(287\) | −0.383436 | −0.0226335 | ||||||||
\(288\) | 23.6618 | 1.39429 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −6.86615 | −0.403194 | ||||||||
\(291\) | −9.85728 | −0.577844 | ||||||||
\(292\) | 24.0509 | 1.40747 | ||||||||
\(293\) | −12.5905 | −0.735544 | −0.367772 | − | 0.929916i | \(-0.619879\pi\) | ||||
−0.367772 | + | 0.929916i | \(0.619879\pi\) | |||||||
\(294\) | 29.0307 | 1.69311 | ||||||||
\(295\) | −4.86783 | −0.283416 | ||||||||
\(296\) | 21.1921 | 1.23176 | ||||||||
\(297\) | 17.7964 | 1.03265 | ||||||||
\(298\) | −18.1550 | −1.05169 | ||||||||
\(299\) | −8.48540 | −0.490723 | ||||||||
\(300\) | −39.7074 | −2.29251 | ||||||||
\(301\) | 0.306042 | 0.0176400 | ||||||||
\(302\) | 17.5972 | 1.01261 | ||||||||
\(303\) | −22.0862 | −1.26882 | ||||||||
\(304\) | 68.8576 | 3.94925 | ||||||||
\(305\) | −0.911612 | −0.0521987 | ||||||||
\(306\) | 2.22547 | 0.127222 | ||||||||
\(307\) | −14.4317 | −0.823661 | −0.411830 | − | 0.911261i | \(-0.635110\pi\) | ||||
−0.411830 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(308\) | −1.86403 | −0.106213 | ||||||||
\(309\) | 27.1614 | 1.54516 | ||||||||
\(310\) | −4.61006 | −0.261834 | ||||||||
\(311\) | 5.18238 | 0.293866 | 0.146933 | − | 0.989146i | \(-0.453060\pi\) | ||||
0.146933 | + | 0.989146i | \(0.453060\pi\) | |||||||
\(312\) | 29.8259 | 1.68856 | ||||||||
\(313\) | −25.7190 | −1.45372 | −0.726861 | − | 0.686785i | \(-0.759021\pi\) | ||||
−0.726861 | + | 0.686785i | \(0.759021\pi\) | |||||||
\(314\) | 12.9041 | 0.728218 | ||||||||
\(315\) | −0.0515527 | −0.00290467 | ||||||||
\(316\) | 89.0377 | 5.00876 | ||||||||
\(317\) | −23.5528 | −1.32286 | −0.661429 | − | 0.750007i | \(-0.730050\pi\) | ||||
−0.661429 | + | 0.750007i | \(0.730050\pi\) | |||||||
\(318\) | 30.7175 | 1.72255 | ||||||||
\(319\) | −12.1207 | −0.678627 | ||||||||
\(320\) | 29.8231 | 1.66716 | ||||||||
\(321\) | 6.27865 | 0.350440 | ||||||||
\(322\) | −1.28119 | −0.0713978 | ||||||||
\(323\) | 3.76627 | 0.209561 | ||||||||
\(324\) | −34.8371 | −1.93539 | ||||||||
\(325\) | 8.61886 | 0.478088 | ||||||||
\(326\) | 40.0335 | 2.21725 | ||||||||
\(327\) | −1.88304 | −0.104132 | ||||||||
\(328\) | 40.4916 | 2.23577 | ||||||||
\(329\) | 0.899183 | 0.0495736 | ||||||||
\(330\) | 8.38784 | 0.461735 | ||||||||
\(331\) | −17.8657 | −0.981987 | −0.490994 | − | 0.871163i | \(-0.663366\pi\) | ||||
−0.490994 | + | 0.871163i | \(0.663366\pi\) | |||||||
\(332\) | −24.0187 | −1.31820 | ||||||||
\(333\) | 1.57559 | 0.0863418 | ||||||||
\(334\) | −38.4645 | −2.10468 | ||||||||
\(335\) | 4.34458 | 0.237370 | ||||||||
\(336\) | 2.75056 | 0.150056 | ||||||||
\(337\) | 17.7767 | 0.968356 | 0.484178 | − | 0.874969i | \(-0.339119\pi\) | ||||
0.484178 | + | 0.874969i | \(0.339119\pi\) | |||||||
\(338\) | 26.5068 | 1.44178 | ||||||||
\(339\) | −8.30263 | −0.450937 | ||||||||
\(340\) | 3.72527 | 0.202031 | ||||||||
\(341\) | −8.13805 | −0.440700 | ||||||||
\(342\) | 8.38172 | 0.453231 | ||||||||
\(343\) | −1.41756 | −0.0765411 | ||||||||
\(344\) | −32.3187 | −1.74251 | ||||||||
\(345\) | 4.29168 | 0.231056 | ||||||||
\(346\) | 7.96977 | 0.428458 | ||||||||
\(347\) | 20.7279 | 1.11273 | 0.556365 | − | 0.830938i | \(-0.312196\pi\) | ||||
0.556365 | + | 0.830938i | \(0.312196\pi\) | |||||||
\(348\) | 33.1956 | 1.77947 | ||||||||
\(349\) | −15.1982 | −0.813540 | −0.406770 | − | 0.913531i | \(-0.633345\pi\) | ||||
−0.406770 | + | 0.913531i | \(0.633345\pi\) | |||||||
\(350\) | 1.30134 | 0.0695595 | ||||||||
\(351\) | 10.5795 | 0.564691 | ||||||||
\(352\) | 93.9251 | 5.00623 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 31.6145 | 1.68029 | ||||||||
\(355\) | 2.34112 | 0.124254 | ||||||||
\(356\) | −100.726 | −5.33844 | ||||||||
\(357\) | 0.150446 | 0.00796246 | ||||||||
\(358\) | 46.9176 | 2.47967 | ||||||||
\(359\) | 11.5498 | 0.609575 | 0.304787 | − | 0.952420i | \(-0.401415\pi\) | ||||
0.304787 | + | 0.952420i | \(0.401415\pi\) | |||||||
\(360\) | 5.44407 | 0.286927 | ||||||||
\(361\) | −4.81523 | −0.253433 | ||||||||
\(362\) | −24.9701 | −1.31240 | ||||||||
\(363\) | −1.52520 | −0.0800522 | ||||||||
\(364\) | −1.10811 | −0.0580809 | ||||||||
\(365\) | 2.64037 | 0.138203 | ||||||||
\(366\) | 5.92054 | 0.309472 | ||||||||
\(367\) | 28.3479 | 1.47975 | 0.739873 | − | 0.672746i | \(-0.234885\pi\) | ||||
0.739873 | + | 0.672746i | \(0.234885\pi\) | |||||||
\(368\) | 82.6367 | 4.30774 | ||||||||
\(369\) | 3.01047 | 0.156719 | ||||||||
\(370\) | 3.54293 | 0.184188 | ||||||||
\(371\) | −0.749414 | −0.0389076 | ||||||||
\(372\) | 22.2881 | 1.15559 | ||||||||
\(373\) | 2.18780 | 0.113280 | 0.0566400 | − | 0.998395i | \(-0.481961\pi\) | ||||
0.0566400 | + | 0.998395i | \(0.481961\pi\) | |||||||
\(374\) | 8.83396 | 0.456793 | ||||||||
\(375\) | −9.10667 | −0.470267 | ||||||||
\(376\) | −94.9555 | −4.89696 | ||||||||
\(377\) | −7.20542 | −0.371098 | ||||||||
\(378\) | 1.59737 | 0.0821598 | ||||||||
\(379\) | 8.06008 | 0.414019 | 0.207009 | − | 0.978339i | \(-0.433627\pi\) | ||||
0.207009 | + | 0.978339i | \(0.433627\pi\) | |||||||
\(380\) | 14.0304 | 0.719742 | ||||||||
\(381\) | 1.93820 | 0.0992968 | ||||||||
\(382\) | 33.5476 | 1.71644 | ||||||||
\(383\) | −6.57773 | −0.336106 | −0.168053 | − | 0.985778i | \(-0.553748\pi\) | ||||
−0.168053 | + | 0.985778i | \(0.553748\pi\) | |||||||
\(384\) | −105.370 | −5.37713 | ||||||||
\(385\) | −0.204638 | −0.0104293 | ||||||||
\(386\) | 18.5992 | 0.946673 | ||||||||
\(387\) | −2.40283 | −0.122143 | ||||||||
\(388\) | −38.6741 | −1.96338 | ||||||||
\(389\) | −20.5918 | −1.04404 | −0.522022 | − | 0.852932i | \(-0.674822\pi\) | ||||
−0.522022 | + | 0.852932i | \(0.674822\pi\) | |||||||
\(390\) | 4.98635 | 0.252493 | ||||||||
\(391\) | 4.51994 | 0.228583 | ||||||||
\(392\) | 74.7936 | 3.77765 | ||||||||
\(393\) | −17.9505 | −0.905482 | ||||||||
\(394\) | −32.3782 | −1.63119 | ||||||||
\(395\) | 9.77479 | 0.491823 | ||||||||
\(396\) | 14.6350 | 0.735437 | ||||||||
\(397\) | −9.16305 | −0.459880 | −0.229940 | − | 0.973205i | \(-0.573853\pi\) | ||||
−0.229940 | + | 0.973205i | \(0.573853\pi\) | |||||||
\(398\) | 43.3008 | 2.17047 | ||||||||
\(399\) | 0.566621 | 0.0283665 | ||||||||
\(400\) | −83.9365 | −4.19682 | ||||||||
\(401\) | −8.25806 | −0.412388 | −0.206194 | − | 0.978511i | \(-0.566108\pi\) | ||||
−0.206194 | + | 0.978511i | \(0.566108\pi\) | |||||||
\(402\) | −28.2163 | −1.40730 | ||||||||
\(403\) | −4.83785 | −0.240991 | ||||||||
\(404\) | −86.6530 | −4.31115 | ||||||||
\(405\) | −3.82451 | −0.190041 | ||||||||
\(406\) | −1.08793 | −0.0539929 | ||||||||
\(407\) | 6.25427 | 0.310013 | ||||||||
\(408\) | −15.8874 | −0.786544 | ||||||||
\(409\) | −25.9679 | −1.28403 | −0.642015 | − | 0.766692i | \(-0.721901\pi\) | ||||
−0.642015 | + | 0.766692i | \(0.721901\pi\) | |||||||
\(410\) | 6.76947 | 0.334320 | ||||||||
\(411\) | −19.4729 | −0.960527 | ||||||||
\(412\) | 106.565 | 5.25009 | ||||||||
\(413\) | −0.771297 | −0.0379531 | ||||||||
\(414\) | 10.0590 | 0.494372 | ||||||||
\(415\) | −2.63684 | −0.129437 | ||||||||
\(416\) | 55.8360 | 2.73758 | ||||||||
\(417\) | 11.9115 | 0.583306 | ||||||||
\(418\) | 33.2711 | 1.62734 | ||||||||
\(419\) | −23.0324 | −1.12521 | −0.562603 | − | 0.826727i | \(-0.690200\pi\) | ||||
−0.562603 | + | 0.826727i | \(0.690200\pi\) | |||||||
\(420\) | 0.560453 | 0.0273473 | ||||||||
\(421\) | 0.885951 | 0.0431786 | 0.0215893 | − | 0.999767i | \(-0.493127\pi\) | ||||
0.0215893 | + | 0.999767i | \(0.493127\pi\) | |||||||
\(422\) | −33.6797 | −1.63950 | ||||||||
\(423\) | −7.05976 | −0.343257 | ||||||||
\(424\) | 79.1395 | 3.84336 | ||||||||
\(425\) | −4.59103 | −0.222698 | ||||||||
\(426\) | −15.2046 | −0.736666 | ||||||||
\(427\) | −0.144443 | −0.00699009 | ||||||||
\(428\) | 24.6337 | 1.19071 | ||||||||
\(429\) | 8.80230 | 0.424979 | ||||||||
\(430\) | −5.40310 | −0.260561 | ||||||||
\(431\) | 31.6398 | 1.52404 | 0.762018 | − | 0.647556i | \(-0.224209\pi\) | ||||
0.762018 | + | 0.647556i | \(0.224209\pi\) | |||||||
\(432\) | −103.030 | −4.95705 | ||||||||
\(433\) | 29.4846 | 1.41694 | 0.708469 | − | 0.705742i | \(-0.249386\pi\) | ||||
0.708469 | + | 0.705742i | \(0.249386\pi\) | |||||||
\(434\) | −0.730455 | −0.0350629 | ||||||||
\(435\) | 3.64430 | 0.174731 | ||||||||
\(436\) | −7.38792 | −0.353817 | ||||||||
\(437\) | 17.0233 | 0.814334 | ||||||||
\(438\) | −17.1481 | −0.819368 | ||||||||
\(439\) | −19.6191 | −0.936368 | −0.468184 | − | 0.883631i | \(-0.655091\pi\) | ||||
−0.468184 | + | 0.883631i | \(0.655091\pi\) | |||||||
\(440\) | 21.6101 | 1.03022 | ||||||||
\(441\) | 5.56076 | 0.264798 | ||||||||
\(442\) | 5.25155 | 0.249791 | ||||||||
\(443\) | 34.6408 | 1.64583 | 0.822917 | − | 0.568162i | \(-0.192345\pi\) | ||||
0.822917 | + | 0.568162i | \(0.192345\pi\) | |||||||
\(444\) | −17.1289 | −0.812903 | ||||||||
\(445\) | −11.0579 | −0.524195 | ||||||||
\(446\) | 41.2799 | 1.95466 | ||||||||
\(447\) | 9.63599 | 0.455767 | ||||||||
\(448\) | 4.72541 | 0.223254 | ||||||||
\(449\) | −17.0222 | −0.803329 | −0.401665 | − | 0.915787i | \(-0.631568\pi\) | ||||
−0.401665 | + | 0.915787i | \(0.631568\pi\) | |||||||
\(450\) | −10.2172 | −0.481644 | ||||||||
\(451\) | 11.9500 | 0.562704 | ||||||||
\(452\) | −32.5746 | −1.53218 | ||||||||
\(453\) | −9.33996 | −0.438829 | ||||||||
\(454\) | 63.3567 | 2.97348 | ||||||||
\(455\) | −0.121652 | −0.00570311 | ||||||||
\(456\) | −59.8362 | −2.80209 | ||||||||
\(457\) | 0.0164250 | 0.000768328 0 | 0.000384164 | − | 1.00000i | \(-0.499878\pi\) | ||||
0.000384164 | 1.00000i | \(0.499878\pi\) | ||||||||
\(458\) | −24.4195 | −1.14105 | ||||||||
\(459\) | −5.63540 | −0.263038 | ||||||||
\(460\) | 16.8380 | 0.785075 | ||||||||
\(461\) | 4.13999 | 0.192818 | 0.0964092 | − | 0.995342i | \(-0.469264\pi\) | ||||
0.0964092 | + | 0.995342i | \(0.469264\pi\) | |||||||
\(462\) | 1.32904 | 0.0618324 | ||||||||
\(463\) | −40.9287 | −1.90212 | −0.951059 | − | 0.309009i | \(-0.900003\pi\) | ||||
−0.951059 | + | 0.309009i | \(0.900003\pi\) | |||||||
\(464\) | 70.1714 | 3.25762 | ||||||||
\(465\) | 2.44685 | 0.113470 | ||||||||
\(466\) | 25.8541 | 1.19767 | ||||||||
\(467\) | 24.6218 | 1.13936 | 0.569679 | − | 0.821867i | \(-0.307067\pi\) | ||||
0.569679 | + | 0.821867i | \(0.307067\pi\) | |||||||
\(468\) | 8.70013 | 0.402163 | ||||||||
\(469\) | 0.688390 | 0.0317869 | ||||||||
\(470\) | −15.8749 | −0.732252 | ||||||||
\(471\) | −6.84900 | −0.315585 | ||||||||
\(472\) | 81.4505 | 3.74906 | ||||||||
\(473\) | −9.53799 | −0.438557 | ||||||||
\(474\) | −63.4832 | −2.91588 | ||||||||
\(475\) | −17.2910 | −0.793368 | ||||||||
\(476\) | 0.590261 | 0.0270546 | ||||||||
\(477\) | 5.88387 | 0.269404 | ||||||||
\(478\) | 35.8534 | 1.63990 | ||||||||
\(479\) | −21.3914 | −0.977397 | −0.488698 | − | 0.872453i | \(-0.662528\pi\) | ||||
−0.488698 | + | 0.872453i | \(0.662528\pi\) | |||||||
\(480\) | −28.2403 | −1.28899 | ||||||||
\(481\) | 3.71800 | 0.169526 | ||||||||
\(482\) | 70.2070 | 3.19784 | ||||||||
\(483\) | 0.680008 | 0.0309414 | ||||||||
\(484\) | −5.98397 | −0.271999 | ||||||||
\(485\) | −4.24574 | −0.192789 | ||||||||
\(486\) | −22.4541 | −1.01854 | ||||||||
\(487\) | −8.73761 | −0.395939 | −0.197970 | − | 0.980208i | \(-0.563435\pi\) | ||||
−0.197970 | + | 0.980208i | \(0.563435\pi\) | |||||||
\(488\) | 15.2535 | 0.690492 | ||||||||
\(489\) | −21.2483 | −0.960882 | ||||||||
\(490\) | 12.5042 | 0.564880 | ||||||||
\(491\) | 18.8899 | 0.852491 | 0.426246 | − | 0.904607i | \(-0.359836\pi\) | ||||
0.426246 | + | 0.904607i | \(0.359836\pi\) | |||||||
\(492\) | −32.7282 | −1.47550 | ||||||||
\(493\) | 3.83813 | 0.172861 | ||||||||
\(494\) | 19.7788 | 0.889888 | ||||||||
\(495\) | 1.60667 | 0.0722144 | ||||||||
\(496\) | 47.1144 | 2.11550 | ||||||||
\(497\) | 0.370946 | 0.0166392 | ||||||||
\(498\) | 17.1252 | 0.767397 | ||||||||
\(499\) | 0.776616 | 0.0347661 | 0.0173830 | − | 0.999849i | \(-0.494467\pi\) | ||||
0.0173830 | + | 0.999849i | \(0.494467\pi\) | |||||||
\(500\) | −35.7292 | −1.59786 | ||||||||
\(501\) | 20.4155 | 0.912099 | ||||||||
\(502\) | 43.2666 | 1.93108 | ||||||||
\(503\) | −16.2869 | −0.726196 | −0.363098 | − | 0.931751i | \(-0.618281\pi\) | ||||
−0.363098 | + | 0.931751i | \(0.618281\pi\) | |||||||
\(504\) | 0.862601 | 0.0384233 | ||||||||
\(505\) | −9.51299 | −0.423323 | ||||||||
\(506\) | 39.9290 | 1.77506 | ||||||||
\(507\) | −14.0688 | −0.624818 | ||||||||
\(508\) | 7.60433 | 0.337387 | ||||||||
\(509\) | −7.79334 | −0.345434 | −0.172717 | − | 0.984972i | \(-0.555255\pi\) | ||||
−0.172717 | + | 0.984972i | \(0.555255\pi\) | |||||||
\(510\) | −2.65609 | −0.117614 | ||||||||
\(511\) | 0.418361 | 0.0185072 | ||||||||
\(512\) | −152.501 | −6.73967 | ||||||||
\(513\) | −21.2244 | −0.937082 | ||||||||
\(514\) | 21.8941 | 0.965709 | ||||||||
\(515\) | 11.6990 | 0.515520 | ||||||||
\(516\) | 26.1222 | 1.14997 | ||||||||
\(517\) | −28.0236 | −1.23247 | ||||||||
\(518\) | 0.561371 | 0.0246652 | ||||||||
\(519\) | −4.23006 | −0.185679 | ||||||||
\(520\) | 12.8466 | 0.563362 | ||||||||
\(521\) | 29.3623 | 1.28639 | 0.643194 | − | 0.765703i | \(-0.277609\pi\) | ||||
0.643194 | + | 0.765703i | \(0.277609\pi\) | |||||||
\(522\) | 8.54164 | 0.373857 | ||||||||
\(523\) | −26.8371 | −1.17351 | −0.586753 | − | 0.809766i | \(-0.699594\pi\) | ||||
−0.586753 | + | 0.809766i | \(0.699594\pi\) | |||||||
\(524\) | −70.4270 | −3.07662 | ||||||||
\(525\) | −0.690703 | −0.0301448 | ||||||||
\(526\) | 20.0522 | 0.874317 | ||||||||
\(527\) | 2.57699 | 0.112255 | ||||||||
\(528\) | −85.7229 | −3.73061 | ||||||||
\(529\) | −2.57017 | −0.111746 | ||||||||
\(530\) | 13.2307 | 0.574705 | ||||||||
\(531\) | 6.05568 | 0.262794 | ||||||||
\(532\) | 2.22308 | 0.0963828 | ||||||||
\(533\) | 7.10396 | 0.307707 | ||||||||
\(534\) | 71.8166 | 3.10781 | ||||||||
\(535\) | 2.70435 | 0.116919 | ||||||||
\(536\) | −72.6953 | −3.13996 | ||||||||
\(537\) | −24.9022 | −1.07461 | ||||||||
\(538\) | 9.15261 | 0.394597 | ||||||||
\(539\) | 22.0733 | 0.950766 | ||||||||
\(540\) | −20.9934 | −0.903412 | ||||||||
\(541\) | 40.8138 | 1.75472 | 0.877360 | − | 0.479833i | \(-0.159303\pi\) | ||||
0.877360 | + | 0.479833i | \(0.159303\pi\) | |||||||
\(542\) | −29.6248 | −1.27249 | ||||||||
\(543\) | 13.2532 | 0.568750 | ||||||||
\(544\) | −29.7423 | −1.27519 | ||||||||
\(545\) | −0.811065 | −0.0347422 | ||||||||
\(546\) | 0.790077 | 0.0338122 | ||||||||
\(547\) | 1.53872 | 0.0657909 | 0.0328955 | − | 0.999459i | \(-0.489527\pi\) | ||||
0.0328955 | + | 0.999459i | \(0.489527\pi\) | |||||||
\(548\) | −76.4000 | −3.26365 | ||||||||
\(549\) | 1.13407 | 0.0484007 | ||||||||
\(550\) | −40.5570 | −1.72936 | ||||||||
\(551\) | 14.4554 | 0.615821 | ||||||||
\(552\) | −71.8101 | −3.05644 | ||||||||
\(553\) | 1.54880 | 0.0658615 | ||||||||
\(554\) | −67.4938 | −2.86754 | ||||||||
\(555\) | −1.88046 | −0.0798210 | ||||||||
\(556\) | 46.7334 | 1.98194 | ||||||||
\(557\) | −22.3893 | −0.948666 | −0.474333 | − | 0.880345i | \(-0.657311\pi\) | ||||
−0.474333 | + | 0.880345i | \(0.657311\pi\) | |||||||
\(558\) | 5.73502 | 0.242783 | ||||||||
\(559\) | −5.67008 | −0.239819 | ||||||||
\(560\) | 1.18473 | 0.0500639 | ||||||||
\(561\) | −4.68874 | −0.197959 | ||||||||
\(562\) | −9.11821 | −0.384628 | ||||||||
\(563\) | 10.4811 | 0.441724 | 0.220862 | − | 0.975305i | \(-0.429113\pi\) | ||||
0.220862 | + | 0.975305i | \(0.429113\pi\) | |||||||
\(564\) | 76.7498 | 3.23175 | ||||||||
\(565\) | −3.57612 | −0.150448 | ||||||||
\(566\) | −36.1967 | −1.52146 | ||||||||
\(567\) | −0.605986 | −0.0254490 | ||||||||
\(568\) | −39.1726 | −1.64365 | ||||||||
\(569\) | 9.04933 | 0.379368 | 0.189684 | − | 0.981845i | \(-0.439254\pi\) | ||||
0.189684 | + | 0.981845i | \(0.439254\pi\) | |||||||
\(570\) | −10.0035 | −0.419002 | ||||||||
\(571\) | −18.9933 | −0.794844 | −0.397422 | − | 0.917636i | \(-0.630095\pi\) | ||||
−0.397422 | + | 0.917636i | \(0.630095\pi\) | |||||||
\(572\) | 34.5350 | 1.44398 | ||||||||
\(573\) | −17.8058 | −0.743849 | ||||||||
\(574\) | 1.07261 | 0.0447698 | ||||||||
\(575\) | −20.7512 | −0.865384 | ||||||||
\(576\) | −37.1006 | −1.54586 | ||||||||
\(577\) | −16.8541 | −0.701646 | −0.350823 | − | 0.936442i | \(-0.614098\pi\) | ||||
−0.350823 | + | 0.936442i | \(0.614098\pi\) | |||||||
\(578\) | −2.79736 | −0.116355 | ||||||||
\(579\) | −9.87176 | −0.410256 | ||||||||
\(580\) | 14.2981 | 0.593694 | ||||||||
\(581\) | −0.417801 | −0.0173333 | ||||||||
\(582\) | 27.5743 | 1.14299 | ||||||||
\(583\) | 23.3559 | 0.967303 | ||||||||
\(584\) | −44.1797 | −1.82817 | ||||||||
\(585\) | 0.955122 | 0.0394894 | ||||||||
\(586\) | 35.2201 | 1.45493 | ||||||||
\(587\) | −17.3538 | −0.716269 | −0.358135 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358135 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(588\) | −60.4535 | −2.49306 | ||||||||
\(589\) | 9.70563 | 0.399914 | ||||||||
\(590\) | 13.6171 | 0.560605 | ||||||||
\(591\) | 17.1852 | 0.706904 | ||||||||
\(592\) | −36.2084 | −1.48816 | ||||||||
\(593\) | 30.2476 | 1.24212 | 0.621059 | − | 0.783763i | \(-0.286703\pi\) | ||||
0.621059 | + | 0.783763i | \(0.286703\pi\) | |||||||
\(594\) | −49.7829 | −2.04262 | ||||||||
\(595\) | 0.0648004 | 0.00265656 | ||||||||
\(596\) | 37.8059 | 1.54859 | ||||||||
\(597\) | −22.9825 | −0.940609 | ||||||||
\(598\) | 23.7367 | 0.970666 | ||||||||
\(599\) | −14.7850 | −0.604097 | −0.302048 | − | 0.953293i | \(-0.597670\pi\) | ||||
−0.302048 | + | 0.953293i | \(0.597670\pi\) | |||||||
\(600\) | 72.9396 | 2.97775 | ||||||||
\(601\) | −31.8594 | −1.29957 | −0.649786 | − | 0.760117i | \(-0.725142\pi\) | ||||
−0.649786 | + | 0.760117i | \(0.725142\pi\) | |||||||
\(602\) | −0.856110 | −0.0348925 | ||||||||
\(603\) | −5.40476 | −0.220099 | ||||||||
\(604\) | −36.6444 | −1.49104 | ||||||||
\(605\) | −0.656936 | −0.0267082 | ||||||||
\(606\) | 61.7830 | 2.50976 | ||||||||
\(607\) | −32.7173 | −1.32795 | −0.663977 | − | 0.747753i | \(-0.731133\pi\) | ||||
−0.663977 | + | 0.747753i | \(0.731133\pi\) | |||||||
\(608\) | −112.017 | −4.54291 | ||||||||
\(609\) | 0.577432 | 0.0233987 | ||||||||
\(610\) | 2.55011 | 0.103251 | ||||||||
\(611\) | −16.6593 | −0.673961 | ||||||||
\(612\) | −4.63432 | −0.187331 | ||||||||
\(613\) | 27.3628 | 1.10517 | 0.552587 | − | 0.833455i | \(-0.313641\pi\) | ||||
0.552587 | + | 0.833455i | \(0.313641\pi\) | |||||||
\(614\) | 40.3707 | 1.62923 | ||||||||
\(615\) | −3.59298 | −0.144883 | ||||||||
\(616\) | 3.42408 | 0.137960 | ||||||||
\(617\) | 14.0799 | 0.566836 | 0.283418 | − | 0.958996i | \(-0.408532\pi\) | ||||
0.283418 | + | 0.958996i | \(0.408532\pi\) | |||||||
\(618\) | −75.9802 | −3.05637 | ||||||||
\(619\) | −38.8920 | −1.56320 | −0.781601 | − | 0.623778i | \(-0.785597\pi\) | ||||
−0.781601 | + | 0.623778i | \(0.785597\pi\) | |||||||
\(620\) | 9.59998 | 0.385545 | ||||||||
\(621\) | −25.4717 | −1.02214 | ||||||||
\(622\) | −14.4970 | −0.581276 | ||||||||
\(623\) | −1.75210 | −0.0701966 | ||||||||
\(624\) | −50.9600 | −2.04003 | ||||||||
\(625\) | 19.0327 | 0.761308 | ||||||||
\(626\) | 71.9452 | 2.87551 | ||||||||
\(627\) | −17.6591 | −0.705235 | ||||||||
\(628\) | −26.8714 | −1.07228 | ||||||||
\(629\) | −1.98047 | −0.0789667 | ||||||||
\(630\) | 0.144211 | 0.00574552 | ||||||||
\(631\) | 20.0506 | 0.798202 | 0.399101 | − | 0.916907i | \(-0.369322\pi\) | ||||
0.399101 | + | 0.916907i | \(0.369322\pi\) | |||||||
\(632\) | −163.556 | −6.50590 | ||||||||
\(633\) | 17.8760 | 0.710506 | ||||||||
\(634\) | 65.8857 | 2.61666 | ||||||||
\(635\) | 0.834823 | 0.0331289 | ||||||||
\(636\) | −63.9662 | −2.53642 | ||||||||
\(637\) | 13.1220 | 0.519913 | ||||||||
\(638\) | 33.9059 | 1.34235 | ||||||||
\(639\) | −2.91241 | −0.115213 | ||||||||
\(640\) | −45.3850 | −1.79400 | ||||||||
\(641\) | −4.91583 | −0.194164 | −0.0970819 | − | 0.995276i | \(-0.530951\pi\) | ||||
−0.0970819 | + | 0.995276i | \(0.530951\pi\) | |||||||
\(642\) | −17.5636 | −0.693182 | ||||||||
\(643\) | 10.8734 | 0.428807 | 0.214403 | − | 0.976745i | \(-0.431219\pi\) | ||||
0.214403 | + | 0.976745i | \(0.431219\pi\) | |||||||
\(644\) | 2.66794 | 0.105132 | ||||||||
\(645\) | 2.86777 | 0.112918 | ||||||||
\(646\) | −10.5356 | −0.414518 | ||||||||
\(647\) | 0.0316748 | 0.00124527 | 0.000622633 | − | 1.00000i | \(-0.499802\pi\) | ||||
0.000622633 | 1.00000i | \(0.499802\pi\) | ||||||||
\(648\) | 63.9933 | 2.51389 | ||||||||
\(649\) | 24.0379 | 0.943571 | ||||||||
\(650\) | −24.1100 | −0.945674 | ||||||||
\(651\) | 0.387698 | 0.0151951 | ||||||||
\(652\) | −83.3657 | −3.26485 | ||||||||
\(653\) | 27.6432 | 1.08176 | 0.540881 | − | 0.841099i | \(-0.318091\pi\) | ||||
0.540881 | + | 0.841099i | \(0.318091\pi\) | |||||||
\(654\) | 5.26753 | 0.205977 | ||||||||
\(655\) | −7.73166 | −0.302101 | ||||||||
\(656\) | −69.1833 | −2.70115 | ||||||||
\(657\) | −3.28468 | −0.128147 | ||||||||
\(658\) | −2.51534 | −0.0980581 | ||||||||
\(659\) | 21.9828 | 0.856330 | 0.428165 | − | 0.903701i | \(-0.359160\pi\) | ||||
0.428165 | + | 0.903701i | \(0.359160\pi\) | |||||||
\(660\) | −17.4668 | −0.679895 | ||||||||
\(661\) | −1.79999 | −0.0700114 | −0.0350057 | − | 0.999387i | \(-0.511145\pi\) | ||||
−0.0350057 | + | 0.999387i | \(0.511145\pi\) | |||||||
\(662\) | 49.9767 | 1.94240 | ||||||||
\(663\) | −2.78733 | −0.108251 | ||||||||
\(664\) | 44.1206 | 1.71221 | ||||||||
\(665\) | 0.244056 | 0.00946407 | ||||||||
\(666\) | −4.40749 | −0.170787 | ||||||||
\(667\) | 17.3481 | 0.671721 | ||||||||
\(668\) | 80.0984 | 3.09910 | ||||||||
\(669\) | −21.9099 | −0.847084 | ||||||||
\(670\) | −12.1533 | −0.469525 | ||||||||
\(671\) | 4.50165 | 0.173784 | ||||||||
\(672\) | −4.47462 | −0.172612 | ||||||||
\(673\) | −37.8346 | −1.45842 | −0.729208 | − | 0.684292i | \(-0.760111\pi\) | ||||
−0.729208 | + | 0.684292i | \(0.760111\pi\) | |||||||
\(674\) | −49.7277 | −1.91544 | ||||||||
\(675\) | 25.8723 | 0.995826 | ||||||||
\(676\) | −55.1977 | −2.12299 | ||||||||
\(677\) | −15.4724 | −0.594654 | −0.297327 | − | 0.954776i | \(-0.596095\pi\) | ||||
−0.297327 | + | 0.954776i | \(0.596095\pi\) | |||||||
\(678\) | 23.2254 | 0.891967 | ||||||||
\(679\) | −0.672729 | −0.0258170 | ||||||||
\(680\) | −6.84305 | −0.262419 | ||||||||
\(681\) | −33.6274 | −1.28860 | ||||||||
\(682\) | 22.7650 | 0.871718 | ||||||||
\(683\) | 31.2040 | 1.19399 | 0.596994 | − | 0.802246i | \(-0.296362\pi\) | ||||
0.596994 | + | 0.802246i | \(0.296362\pi\) | |||||||
\(684\) | −17.4541 | −0.667373 | ||||||||
\(685\) | −8.38739 | −0.320466 | ||||||||
\(686\) | 3.96543 | 0.151401 | ||||||||
\(687\) | 12.9610 | 0.494492 | ||||||||
\(688\) | 55.2192 | 2.10521 | ||||||||
\(689\) | 13.8845 | 0.528956 | ||||||||
\(690\) | −12.0054 | −0.457036 | ||||||||
\(691\) | 33.7403 | 1.28354 | 0.641770 | − | 0.766897i | \(-0.278200\pi\) | ||||
0.641770 | + | 0.766897i | \(0.278200\pi\) | |||||||
\(692\) | −16.5962 | −0.630895 | ||||||||
\(693\) | 0.254574 | 0.00967045 | ||||||||
\(694\) | −57.9833 | −2.20101 | ||||||||
\(695\) | 5.13052 | 0.194612 | ||||||||
\(696\) | −60.9779 | −2.31136 | ||||||||
\(697\) | −3.78408 | −0.143332 | ||||||||
\(698\) | 42.5147 | 1.60921 | ||||||||
\(699\) | −13.7224 | −0.519029 | ||||||||
\(700\) | −2.70991 | −0.102425 | ||||||||
\(701\) | 33.8760 | 1.27948 | 0.639740 | − | 0.768591i | \(-0.279042\pi\) | ||||
0.639740 | + | 0.768591i | \(0.279042\pi\) | |||||||
\(702\) | −29.5946 | −1.11698 | ||||||||
\(703\) | −7.45900 | −0.281321 | ||||||||
\(704\) | −147.270 | −5.55045 | ||||||||
\(705\) | 8.42579 | 0.317334 | ||||||||
\(706\) | −2.79736 | −0.105280 | ||||||||
\(707\) | −1.50731 | −0.0566884 | ||||||||
\(708\) | −65.8340 | −2.47420 | ||||||||
\(709\) | −12.6587 | −0.475407 | −0.237704 | − | 0.971338i | \(-0.576395\pi\) | ||||
−0.237704 | + | 0.971338i | \(0.576395\pi\) | |||||||
\(710\) | −6.54895 | −0.245778 | ||||||||
\(711\) | −12.1601 | −0.456038 | ||||||||
\(712\) | 185.026 | 6.93413 | ||||||||
\(713\) | 11.6478 | 0.436215 | ||||||||
\(714\) | −0.420852 | −0.0157500 | ||||||||
\(715\) | 3.79134 | 0.141788 | ||||||||
\(716\) | −97.7012 | −3.65127 | ||||||||
\(717\) | −19.0297 | −0.710677 | ||||||||
\(718\) | −32.3089 | −1.20576 | ||||||||
\(719\) | 43.3953 | 1.61837 | 0.809185 | − | 0.587553i | \(-0.199909\pi\) | ||||
0.809185 | + | 0.587553i | \(0.199909\pi\) | |||||||
\(720\) | −9.30165 | −0.346652 | ||||||||
\(721\) | 1.85368 | 0.0690348 | ||||||||
\(722\) | 13.4699 | 0.501299 | ||||||||
\(723\) | −37.2633 | −1.38584 | ||||||||
\(724\) | 51.9977 | 1.93248 | ||||||||
\(725\) | −17.6210 | −0.654426 | ||||||||
\(726\) | 4.26653 | 0.158346 | ||||||||
\(727\) | −29.4651 | −1.09280 | −0.546399 | − | 0.837525i | \(-0.684002\pi\) | ||||
−0.546399 | + | 0.837525i | \(0.684002\pi\) | |||||||
\(728\) | 2.03552 | 0.0754415 | ||||||||
\(729\) | 29.8590 | 1.10589 | ||||||||
\(730\) | −7.38606 | −0.273370 | ||||||||
\(731\) | 3.02029 | 0.111710 | ||||||||
\(732\) | −12.3289 | −0.455690 | ||||||||
\(733\) | −11.1971 | −0.413574 | −0.206787 | − | 0.978386i | \(-0.566301\pi\) | ||||
−0.206787 | + | 0.978386i | \(0.566301\pi\) | |||||||
\(734\) | −79.2992 | −2.92699 | ||||||||
\(735\) | −6.63674 | −0.244800 | ||||||||
\(736\) | −134.433 | −4.95528 | ||||||||
\(737\) | −21.4541 | −0.790271 | ||||||||
\(738\) | −8.42137 | −0.309995 | ||||||||
\(739\) | −40.5346 | −1.49109 | −0.745544 | − | 0.666456i | \(-0.767810\pi\) | ||||
−0.745544 | + | 0.666456i | \(0.767810\pi\) | |||||||
\(740\) | −7.37780 | −0.271213 | ||||||||
\(741\) | −10.4978 | −0.385648 | ||||||||
\(742\) | 2.09638 | 0.0769605 | ||||||||
\(743\) | 39.3921 | 1.44515 | 0.722577 | − | 0.691290i | \(-0.242957\pi\) | ||||
0.722577 | + | 0.691290i | \(0.242957\pi\) | |||||||
\(744\) | −40.9417 | −1.50100 | ||||||||
\(745\) | 4.15043 | 0.152060 | ||||||||
\(746\) | −6.12007 | −0.224072 | ||||||||
\(747\) | 3.28028 | 0.120019 | ||||||||
\(748\) | −18.3958 | −0.672618 | ||||||||
\(749\) | 0.428499 | 0.0156570 | ||||||||
\(750\) | 25.4746 | 0.930202 | ||||||||
\(751\) | −38.6038 | −1.40867 | −0.704337 | − | 0.709866i | \(-0.748756\pi\) | ||||
−0.704337 | + | 0.709866i | \(0.748756\pi\) | |||||||
\(752\) | 162.239 | 5.91626 | ||||||||
\(753\) | −22.9643 | −0.836866 | ||||||||
\(754\) | 20.1561 | 0.734043 | ||||||||
\(755\) | −4.02292 | −0.146409 | ||||||||
\(756\) | −3.32636 | −0.120979 | ||||||||
\(757\) | −21.6946 | −0.788502 | −0.394251 | − | 0.919003i | \(-0.628996\pi\) | ||||
−0.394251 | + | 0.919003i | \(0.628996\pi\) | |||||||
\(758\) | −22.5469 | −0.818942 | ||||||||
\(759\) | −21.1928 | −0.769251 | ||||||||
\(760\) | −25.7728 | −0.934876 | ||||||||
\(761\) | −35.2702 | −1.27854 | −0.639272 | − | 0.768980i | \(-0.720764\pi\) | ||||
−0.639272 | + | 0.768980i | \(0.720764\pi\) | |||||||
\(762\) | −5.42183 | −0.196412 | ||||||||
\(763\) | −0.128512 | −0.00465243 | ||||||||
\(764\) | −69.8595 | −2.52743 | ||||||||
\(765\) | −0.508767 | −0.0183945 | ||||||||
\(766\) | 18.4003 | 0.664829 | ||||||||
\(767\) | 14.2899 | 0.515978 | ||||||||
\(768\) | 156.277 | 5.63917 | ||||||||
\(769\) | −16.7477 | −0.603939 | −0.301969 | − | 0.953318i | \(-0.597644\pi\) | ||||
−0.301969 | + | 0.953318i | \(0.597644\pi\) | |||||||
\(770\) | 0.572445 | 0.0206295 | ||||||||
\(771\) | −11.6206 | −0.418506 | ||||||||
\(772\) | −38.7309 | −1.39396 | ||||||||
\(773\) | 5.05437 | 0.181793 | 0.0908965 | − | 0.995860i | \(-0.471027\pi\) | ||||
0.0908965 | + | 0.995860i | \(0.471027\pi\) | |||||||
\(774\) | 6.72158 | 0.241602 | ||||||||
\(775\) | −11.8310 | −0.424984 | ||||||||
\(776\) | 71.0415 | 2.55024 | ||||||||
\(777\) | −0.297955 | −0.0106891 | ||||||||
\(778\) | 57.6026 | 2.06515 | ||||||||
\(779\) | −14.2519 | −0.510626 | ||||||||
\(780\) | −10.3836 | −0.371791 | ||||||||
\(781\) | −11.5607 | −0.413676 | ||||||||
\(782\) | −12.6439 | −0.452144 | ||||||||
\(783\) | −21.6294 | −0.772971 | ||||||||
\(784\) | −127.791 | −4.56397 | ||||||||
\(785\) | −2.95001 | −0.105290 | ||||||||
\(786\) | 50.2140 | 1.79107 | ||||||||
\(787\) | −6.73811 | −0.240188 | −0.120094 | − | 0.992763i | \(-0.538320\pi\) | ||||
−0.120094 | + | 0.992763i | \(0.538320\pi\) | |||||||
\(788\) | 67.4244 | 2.40189 | ||||||||
\(789\) | −10.6430 | −0.378900 | ||||||||
\(790\) | −27.3436 | −0.972842 | ||||||||
\(791\) | −0.566629 | −0.0201470 | ||||||||
\(792\) | −26.8835 | −0.955262 | ||||||||
\(793\) | 2.67611 | 0.0950315 | ||||||||
\(794\) | 25.6323 | 0.909658 | ||||||||
\(795\) | −7.02237 | −0.249058 | ||||||||
\(796\) | −90.1695 | −3.19597 | ||||||||
\(797\) | 35.9824 | 1.27456 | 0.637281 | − | 0.770631i | \(-0.280059\pi\) | ||||
0.637281 | + | 0.770631i | \(0.280059\pi\) | |||||||
\(798\) | −1.58504 | −0.0561099 | ||||||||
\(799\) | 8.87393 | 0.313937 | ||||||||
\(800\) | 136.548 | 4.82769 | ||||||||
\(801\) | 13.7563 | 0.486055 | ||||||||
\(802\) | 23.1008 | 0.815716 | ||||||||
\(803\) | −13.0385 | −0.460117 | ||||||||
\(804\) | 58.7575 | 2.07222 | ||||||||
\(805\) | 0.292894 | 0.0103232 | ||||||||
\(806\) | 13.5332 | 0.476687 | ||||||||
\(807\) | −4.85787 | −0.171005 | ||||||||
\(808\) | 159.175 | 5.59977 | ||||||||
\(809\) | 47.8332 | 1.68173 | 0.840863 | − | 0.541248i | \(-0.182048\pi\) | ||||
0.840863 | + | 0.541248i | \(0.182048\pi\) | |||||||
\(810\) | 10.6985 | 0.375908 | ||||||||
\(811\) | 0.650276 | 0.0228343 | 0.0114171 | − | 0.999935i | \(-0.496366\pi\) | ||||
0.0114171 | + | 0.999935i | \(0.496366\pi\) | |||||||
\(812\) | 2.26550 | 0.0795034 | ||||||||
\(813\) | 15.7237 | 0.551455 | ||||||||
\(814\) | −17.4954 | −0.613215 | ||||||||
\(815\) | −9.15211 | −0.320584 | ||||||||
\(816\) | 27.1450 | 0.950264 | ||||||||
\(817\) | 11.3752 | 0.397969 | ||||||||
\(818\) | 72.6415 | 2.53985 | ||||||||
\(819\) | 0.151337 | 0.00528815 | ||||||||
\(820\) | −14.0967 | −0.492279 | ||||||||
\(821\) | 12.3551 | 0.431197 | 0.215598 | − | 0.976482i | \(-0.430830\pi\) | ||||
0.215598 | + | 0.976482i | \(0.430830\pi\) | |||||||
\(822\) | 54.4727 | 1.89995 | ||||||||
\(823\) | 15.1516 | 0.528152 | 0.264076 | − | 0.964502i | \(-0.414933\pi\) | ||||
0.264076 | + | 0.964502i | \(0.414933\pi\) | |||||||
\(824\) | −195.753 | −6.81937 | ||||||||
\(825\) | 21.5262 | 0.749445 | ||||||||
\(826\) | 2.15760 | 0.0750723 | ||||||||
\(827\) | −57.4000 | −1.99599 | −0.997997 | − | 0.0632634i | \(-0.979849\pi\) | ||||
−0.997997 | + | 0.0632634i | \(0.979849\pi\) | |||||||
\(828\) | −20.9468 | −0.727952 | ||||||||
\(829\) | 41.3553 | 1.43633 | 0.718164 | − | 0.695874i | \(-0.244983\pi\) | ||||
0.718164 | + | 0.695874i | \(0.244983\pi\) | |||||||
\(830\) | 7.37618 | 0.256031 | ||||||||
\(831\) | 35.8232 | 1.24269 | ||||||||
\(832\) | −87.5481 | −3.03518 | ||||||||
\(833\) | −6.98973 | −0.242180 | ||||||||
\(834\) | −33.3206 | −1.15380 | ||||||||
\(835\) | 8.79341 | 0.304308 | ||||||||
\(836\) | −69.2836 | −2.39622 | ||||||||
\(837\) | −14.5224 | −0.501967 | ||||||||
\(838\) | 64.4299 | 2.22569 | ||||||||
\(839\) | −54.2565 | −1.87314 | −0.936572 | − | 0.350476i | \(-0.886020\pi\) | ||||
−0.936572 | + | 0.350476i | \(0.886020\pi\) | |||||||
\(840\) | −1.02951 | −0.0355215 | ||||||||
\(841\) | −14.2688 | −0.492027 | ||||||||
\(842\) | −2.47832 | −0.0854087 | ||||||||
\(843\) | 4.83961 | 0.166685 | ||||||||
\(844\) | 70.1346 | 2.41413 | ||||||||
\(845\) | −6.05975 | −0.208462 | ||||||||
\(846\) | 19.7487 | 0.678973 | ||||||||
\(847\) | −0.104090 | −0.00357658 | ||||||||
\(848\) | −135.217 | −4.64336 | ||||||||
\(849\) | 19.2119 | 0.659350 | ||||||||
\(850\) | 12.8428 | 0.440503 | ||||||||
\(851\) | −8.95162 | −0.306858 | ||||||||
\(852\) | 31.6621 | 1.08472 | ||||||||
\(853\) | −0.841557 | −0.0288144 | −0.0144072 | − | 0.999896i | \(-0.504586\pi\) | ||||
−0.0144072 | + | 0.999896i | \(0.504586\pi\) | |||||||
\(854\) | 0.404059 | 0.0138266 | ||||||||
\(855\) | −1.91615 | −0.0655311 | ||||||||
\(856\) | −45.2503 | −1.54662 | ||||||||
\(857\) | 27.3452 | 0.934094 | 0.467047 | − | 0.884232i | \(-0.345318\pi\) | ||||
0.467047 | + | 0.884232i | \(0.345318\pi\) | |||||||
\(858\) | −24.6232 | −0.840622 | ||||||||
\(859\) | −32.1697 | −1.09762 | −0.548808 | − | 0.835948i | \(-0.684918\pi\) | ||||
−0.548808 | + | 0.835948i | \(0.684918\pi\) | |||||||
\(860\) | 11.2514 | 0.383670 | ||||||||
\(861\) | −0.569301 | −0.0194017 | ||||||||
\(862\) | −88.5079 | −3.01459 | ||||||||
\(863\) | −23.4200 | −0.797227 | −0.398614 | − | 0.917119i | \(-0.630509\pi\) | ||||
−0.398614 | + | 0.917119i | \(0.630509\pi\) | |||||||
\(864\) | 167.610 | 5.70220 | ||||||||
\(865\) | −1.82198 | −0.0619491 | ||||||||
\(866\) | −82.4789 | −2.80275 | ||||||||
\(867\) | 1.48474 | 0.0504242 | ||||||||
\(868\) | 1.52110 | 0.0516294 | ||||||||
\(869\) | −48.2691 | −1.63742 | ||||||||
\(870\) | −10.1944 | −0.345623 | ||||||||
\(871\) | −12.7539 | −0.432148 | ||||||||
\(872\) | 13.5711 | 0.459575 | ||||||||
\(873\) | 5.28180 | 0.178762 | ||||||||
\(874\) | −47.6203 | −1.61078 | ||||||||
\(875\) | −0.621503 | −0.0210106 | ||||||||
\(876\) | 35.7092 | 1.20650 | ||||||||
\(877\) | −3.77327 | −0.127414 | −0.0637072 | − | 0.997969i | \(-0.520292\pi\) | ||||
−0.0637072 | + | 0.997969i | \(0.520292\pi\) | |||||||
\(878\) | 54.8816 | 1.85216 | ||||||||
\(879\) | −18.6935 | −0.630517 | ||||||||
\(880\) | −36.9227 | −1.24466 | ||||||||
\(881\) | −15.7213 | −0.529665 | −0.264833 | − | 0.964294i | \(-0.585317\pi\) | ||||
−0.264833 | + | 0.964294i | \(0.585317\pi\) | |||||||
\(882\) | −15.5554 | −0.523779 | ||||||||
\(883\) | −31.1139 | −1.04707 | −0.523533 | − | 0.852005i | \(-0.675386\pi\) | ||||
−0.523533 | + | 0.852005i | \(0.675386\pi\) | |||||||
\(884\) | −10.9358 | −0.367812 | ||||||||
\(885\) | −7.22743 | −0.242947 | ||||||||
\(886\) | −96.9027 | −3.25551 | ||||||||
\(887\) | 1.90150 | 0.0638461 | 0.0319230 | − | 0.999490i | \(-0.489837\pi\) | ||||
0.0319230 | + | 0.999490i | \(0.489837\pi\) | |||||||
\(888\) | 31.4646 | 1.05588 | ||||||||
\(889\) | 0.132276 | 0.00443639 | ||||||||
\(890\) | 30.9329 | 1.03687 | ||||||||
\(891\) | 18.8859 | 0.632701 | ||||||||
\(892\) | −85.9613 | −2.87820 | ||||||||
\(893\) | 33.4216 | 1.11841 | ||||||||
\(894\) | −26.9553 | −0.901520 | ||||||||
\(895\) | −10.7259 | −0.358527 | ||||||||
\(896\) | −7.19116 | −0.240240 | ||||||||
\(897\) | −12.5986 | −0.420654 | ||||||||
\(898\) | 47.6173 | 1.58901 | ||||||||
\(899\) | 9.89082 | 0.329877 | ||||||||
\(900\) | 21.2763 | 0.709210 | ||||||||
\(901\) | −7.39587 | −0.246392 | ||||||||
\(902\) | −33.4285 | −1.11305 | ||||||||
\(903\) | 0.454392 | 0.0151212 | ||||||||
\(904\) | 59.8371 | 1.99015 | ||||||||
\(905\) | 5.70845 | 0.189755 | ||||||||
\(906\) | 26.1272 | 0.868018 | ||||||||
\(907\) | 35.8434 | 1.19016 | 0.595080 | − | 0.803667i | \(-0.297120\pi\) | ||||
0.595080 | + | 0.803667i | \(0.297120\pi\) | |||||||
\(908\) | −131.934 | −4.37838 | ||||||||
\(909\) | 11.8344 | 0.392521 | ||||||||
\(910\) | 0.340303 | 0.0112809 | ||||||||
\(911\) | −8.28538 | −0.274507 | −0.137253 | − | 0.990536i | \(-0.543827\pi\) | ||||
−0.137253 | + | 0.990536i | \(0.543827\pi\) | |||||||
\(912\) | 102.235 | 3.38535 | ||||||||
\(913\) | 13.0210 | 0.430933 | ||||||||
\(914\) | −0.0459465 | −0.00151978 | ||||||||
\(915\) | −1.35350 | −0.0447454 | ||||||||
\(916\) | 50.8511 | 1.68017 | ||||||||
\(917\) | −1.22507 | −0.0404553 | ||||||||
\(918\) | 15.7642 | 0.520298 | ||||||||
\(919\) | 38.7336 | 1.27770 | 0.638852 | − | 0.769329i | \(-0.279410\pi\) | ||||
0.638852 | + | 0.769329i | \(0.279410\pi\) | |||||||
\(920\) | −30.9302 | −1.01974 | ||||||||
\(921\) | −21.4273 | −0.706052 | ||||||||
\(922\) | −11.5810 | −0.381401 | ||||||||
\(923\) | −6.87255 | −0.226213 | ||||||||
\(924\) | −2.76758 | −0.0910468 | ||||||||
\(925\) | 9.09242 | 0.298957 | ||||||||
\(926\) | 114.492 | 3.76245 | ||||||||
\(927\) | −14.5538 | −0.478010 | ||||||||
\(928\) | −114.155 | −3.74731 | ||||||||
\(929\) | 40.3157 | 1.32272 | 0.661358 | − | 0.750070i | \(-0.269980\pi\) | ||||
0.661358 | + | 0.750070i | \(0.269980\pi\) | |||||||
\(930\) | −6.84472 | −0.224447 | ||||||||
\(931\) | −26.3252 | −0.862774 | ||||||||
\(932\) | −53.8385 | −1.76354 | ||||||||
\(933\) | 7.69447 | 0.251906 | ||||||||
\(934\) | −68.8759 | −2.25369 | ||||||||
\(935\) | −2.01954 | −0.0660461 | ||||||||
\(936\) | −15.9815 | −0.522372 | ||||||||
\(937\) | −28.0304 | −0.915714 | −0.457857 | − | 0.889026i | \(-0.651383\pi\) | ||||
−0.457857 | + | 0.889026i | \(0.651383\pi\) | |||||||
\(938\) | −1.92567 | −0.0628755 | ||||||||
\(939\) | −38.1858 | −1.24615 | ||||||||
\(940\) | 33.0578 | 1.07823 | ||||||||
\(941\) | −25.3400 | −0.826061 | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413031 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(942\) | 19.1591 | 0.624237 | ||||||||
\(943\) | −17.1038 | −0.556977 | ||||||||
\(944\) | −139.165 | −4.52944 | ||||||||
\(945\) | −0.365177 | −0.0118792 | ||||||||
\(946\) | 26.6812 | 0.867480 | ||||||||
\(947\) | 26.5795 | 0.863718 | 0.431859 | − | 0.901941i | \(-0.357858\pi\) | ||||
0.431859 | + | 0.901941i | \(0.357858\pi\) | |||||||
\(948\) | 132.197 | 4.29357 | ||||||||
\(949\) | −7.75102 | −0.251609 | ||||||||
\(950\) | 48.3693 | 1.56931 | ||||||||
\(951\) | −34.9697 | −1.13397 | ||||||||
\(952\) | −1.08427 | −0.0351413 | ||||||||
\(953\) | 2.22132 | 0.0719557 | 0.0359778 | − | 0.999353i | \(-0.488545\pi\) | ||||
0.0359778 | + | 0.999353i | \(0.488545\pi\) | |||||||
\(954\) | −16.4593 | −0.532889 | ||||||||
\(955\) | −7.66935 | −0.248174 | ||||||||
\(956\) | −74.6611 | −2.41471 | ||||||||
\(957\) | −17.9960 | −0.581728 | ||||||||
\(958\) | 59.8393 | 1.93332 | ||||||||
\(959\) | −1.32897 | −0.0429145 | ||||||||
\(960\) | 44.2794 | 1.42911 | ||||||||
\(961\) | −24.3591 | −0.785778 | ||||||||
\(962\) | −10.4006 | −0.335328 | ||||||||
\(963\) | −3.36427 | −0.108412 | ||||||||
\(964\) | −146.199 | −4.70875 | ||||||||
\(965\) | −4.25198 | −0.136876 | ||||||||
\(966\) | −1.90223 | −0.0612031 | ||||||||
\(967\) | 39.8654 | 1.28198 | 0.640992 | − | 0.767548i | \(-0.278523\pi\) | ||||
0.640992 | + | 0.767548i | \(0.278523\pi\) | |||||||
\(968\) | 10.9921 | 0.353300 | ||||||||
\(969\) | 5.59191 | 0.179638 | ||||||||
\(970\) | 11.8769 | 0.381343 | ||||||||
\(971\) | −32.3206 | −1.03722 | −0.518608 | − | 0.855012i | \(-0.673550\pi\) | ||||
−0.518608 | + | 0.855012i | \(0.673550\pi\) | |||||||
\(972\) | 46.7585 | 1.49978 | ||||||||
\(973\) | 0.812920 | 0.0260610 | ||||||||
\(974\) | 24.4422 | 0.783180 | ||||||||
\(975\) | 12.7967 | 0.409823 | ||||||||
\(976\) | −26.0618 | −0.834219 | ||||||||
\(977\) | 28.1171 | 0.899547 | 0.449773 | − | 0.893143i | \(-0.351505\pi\) | ||||
0.449773 | + | 0.893143i | \(0.351505\pi\) | |||||||
\(978\) | 59.4392 | 1.90066 | ||||||||
\(979\) | 54.6053 | 1.74519 | ||||||||
\(980\) | −26.0386 | −0.831774 | ||||||||
\(981\) | 1.00898 | 0.0322144 | ||||||||
\(982\) | −52.8420 | −1.68625 | ||||||||
\(983\) | 38.9016 | 1.24077 | 0.620385 | − | 0.784298i | \(-0.286977\pi\) | ||||
0.620385 | + | 0.784298i | \(0.286977\pi\) | |||||||
\(984\) | 60.1193 | 1.91653 | ||||||||
\(985\) | 7.40202 | 0.235848 | ||||||||
\(986\) | −10.7366 | −0.341924 | ||||||||
\(987\) | 1.33505 | 0.0424951 | ||||||||
\(988\) | −41.1873 | −1.31034 | ||||||||
\(989\) | 13.6515 | 0.434094 | ||||||||
\(990\) | −4.49443 | −0.142842 | ||||||||
\(991\) | −46.4117 | −1.47431 | −0.737157 | − | 0.675721i | \(-0.763832\pi\) | ||||
−0.737157 | + | 0.675721i | \(0.763832\pi\) | |||||||
\(992\) | −76.6456 | −2.43350 | ||||||||
\(993\) | −26.5258 | −0.841771 | ||||||||
\(994\) | −1.03767 | −0.0329128 | ||||||||
\(995\) | −9.89904 | −0.313821 | ||||||||
\(996\) | −35.6614 | −1.12998 | ||||||||
\(997\) | −1.56609 | −0.0495985 | −0.0247993 | − | 0.999692i | \(-0.507895\pi\) | ||||
−0.0247993 | + | 0.999692i | \(0.507895\pi\) | |||||||
\(998\) | −2.17247 | −0.0687684 | ||||||||
\(999\) | 11.1608 | 0.353111 |
(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 | 6001.2.a.b.1.1 | ✓ | 114 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.b.1.1 | ✓ | 114 | 1.1 | even | 1 | trivial |