Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(0\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.25 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.22439 | −0.706902 | −0.353451 | − | 0.935453i | \(-0.614992\pi\) | ||||
−0.353451 | + | 0.935453i | \(0.614992\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.248249 | −0.111020 | −0.0555102 | − | 0.998458i | \(-0.517679\pi\) | ||||
−0.0555102 | + | 0.998458i | \(0.517679\pi\) | |||||||
\(6\) | 1.22439 | 0.499855 | ||||||||
\(7\) | 4.32372 | 1.63421 | 0.817107 | − | 0.576486i | \(-0.195577\pi\) | ||||
0.817107 | + | 0.576486i | \(0.195577\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.50087 | −0.500289 | ||||||||
\(10\) | 0.248249 | 0.0785032 | ||||||||
\(11\) | −3.72248 | −1.12237 | −0.561185 | − | 0.827690i | \(-0.689655\pi\) | ||||
−0.561185 | + | 0.827690i | \(0.689655\pi\) | |||||||
\(12\) | −1.22439 | −0.353451 | ||||||||
\(13\) | 3.31452 | 0.919282 | 0.459641 | − | 0.888105i | \(-0.347978\pi\) | ||||
0.459641 | + | 0.888105i | \(0.347978\pi\) | |||||||
\(14\) | −4.32372 | −1.15556 | ||||||||
\(15\) | 0.303954 | 0.0784805 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.48677 | 1.08820 | 0.544101 | − | 0.839020i | \(-0.316871\pi\) | ||||
0.544101 | + | 0.839020i | \(0.316871\pi\) | |||||||
\(18\) | 1.50087 | 0.353758 | ||||||||
\(19\) | −1.51739 | −0.348112 | −0.174056 | − | 0.984736i | \(-0.555687\pi\) | ||||
−0.174056 | + | 0.984736i | \(0.555687\pi\) | |||||||
\(20\) | −0.248249 | −0.0555102 | ||||||||
\(21\) | −5.29393 | −1.15523 | ||||||||
\(22\) | 3.72248 | 0.793636 | ||||||||
\(23\) | 6.11286 | 1.27462 | 0.637310 | − | 0.770608i | \(-0.280047\pi\) | ||||
0.637310 | + | 0.770608i | \(0.280047\pi\) | |||||||
\(24\) | 1.22439 | 0.249928 | ||||||||
\(25\) | −4.93837 | −0.987674 | ||||||||
\(26\) | −3.31452 | −0.650030 | ||||||||
\(27\) | 5.51082 | 1.06056 | ||||||||
\(28\) | 4.32372 | 0.817107 | ||||||||
\(29\) | 7.04693 | 1.30858 | 0.654291 | − | 0.756243i | \(-0.272967\pi\) | ||||
0.654291 | + | 0.756243i | \(0.272967\pi\) | |||||||
\(30\) | −0.303954 | −0.0554941 | ||||||||
\(31\) | 1.22406 | 0.219848 | 0.109924 | − | 0.993940i | \(-0.464939\pi\) | ||||
0.109924 | + | 0.993940i | \(0.464939\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 4.55777 | 0.793407 | ||||||||
\(34\) | −4.48677 | −0.769475 | ||||||||
\(35\) | −1.07336 | −0.181431 | ||||||||
\(36\) | −1.50087 | −0.250145 | ||||||||
\(37\) | 4.45284 | 0.732043 | 0.366022 | − | 0.930606i | \(-0.380720\pi\) | ||||
0.366022 | + | 0.930606i | \(0.380720\pi\) | |||||||
\(38\) | 1.51739 | 0.246153 | ||||||||
\(39\) | −4.05826 | −0.649842 | ||||||||
\(40\) | 0.248249 | 0.0392516 | ||||||||
\(41\) | 1.02518 | 0.160107 | 0.0800533 | − | 0.996791i | \(-0.474491\pi\) | ||||
0.0800533 | + | 0.996791i | \(0.474491\pi\) | |||||||
\(42\) | 5.29393 | 0.816871 | ||||||||
\(43\) | −12.1218 | −1.84856 | −0.924281 | − | 0.381713i | \(-0.875334\pi\) | ||||
−0.924281 | + | 0.381713i | \(0.875334\pi\) | |||||||
\(44\) | −3.72248 | −0.561185 | ||||||||
\(45\) | 0.372589 | 0.0555423 | ||||||||
\(46\) | −6.11286 | −0.901292 | ||||||||
\(47\) | 11.9160 | 1.73813 | 0.869064 | − | 0.494700i | \(-0.164722\pi\) | ||||
0.869064 | + | 0.494700i | \(0.164722\pi\) | |||||||
\(48\) | −1.22439 | −0.176726 | ||||||||
\(49\) | 11.6946 | 1.67065 | ||||||||
\(50\) | 4.93837 | 0.698391 | ||||||||
\(51\) | −5.49356 | −0.769252 | ||||||||
\(52\) | 3.31452 | 0.459641 | ||||||||
\(53\) | −8.22284 | −1.12949 | −0.564747 | − | 0.825264i | \(-0.691026\pi\) | ||||
−0.564747 | + | 0.825264i | \(0.691026\pi\) | |||||||
\(54\) | −5.51082 | −0.749928 | ||||||||
\(55\) | 0.924103 | 0.124606 | ||||||||
\(56\) | −4.32372 | −0.577782 | ||||||||
\(57\) | 1.85787 | 0.246081 | ||||||||
\(58\) | −7.04693 | −0.925308 | ||||||||
\(59\) | 5.21389 | 0.678791 | 0.339395 | − | 0.940644i | \(-0.389778\pi\) | ||||
0.339395 | + | 0.940644i | \(0.389778\pi\) | |||||||
\(60\) | 0.303954 | 0.0392403 | ||||||||
\(61\) | −9.22447 | −1.18107 | −0.590536 | − | 0.807011i | \(-0.701084\pi\) | ||||
−0.590536 | + | 0.807011i | \(0.701084\pi\) | |||||||
\(62\) | −1.22406 | −0.155456 | ||||||||
\(63\) | −6.48934 | −0.817580 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.822825 | −0.102059 | ||||||||
\(66\) | −4.55777 | −0.561023 | ||||||||
\(67\) | −8.76845 | −1.07124 | −0.535618 | − | 0.844460i | \(-0.679921\pi\) | ||||
−0.535618 | + | 0.844460i | \(0.679921\pi\) | |||||||
\(68\) | 4.48677 | 0.544101 | ||||||||
\(69\) | −7.48453 | −0.901032 | ||||||||
\(70\) | 1.07336 | 0.128291 | ||||||||
\(71\) | 5.36999 | 0.637300 | 0.318650 | − | 0.947872i | \(-0.396770\pi\) | ||||
0.318650 | + | 0.947872i | \(0.396770\pi\) | |||||||
\(72\) | 1.50087 | 0.176879 | ||||||||
\(73\) | −0.386914 | −0.0452849 | −0.0226424 | − | 0.999744i | \(-0.507208\pi\) | ||||
−0.0226424 | + | 0.999744i | \(0.507208\pi\) | |||||||
\(74\) | −4.45284 | −0.517633 | ||||||||
\(75\) | 6.04650 | 0.698189 | ||||||||
\(76\) | −1.51739 | −0.174056 | ||||||||
\(77\) | −16.0950 | −1.83419 | ||||||||
\(78\) | 4.05826 | 0.459508 | ||||||||
\(79\) | 1.57570 | 0.177280 | 0.0886398 | − | 0.996064i | \(-0.471748\pi\) | ||||
0.0886398 | + | 0.996064i | \(0.471748\pi\) | |||||||
\(80\) | −0.248249 | −0.0277551 | ||||||||
\(81\) | −2.24479 | −0.249421 | ||||||||
\(82\) | −1.02518 | −0.113212 | ||||||||
\(83\) | −1.96103 | −0.215251 | −0.107625 | − | 0.994192i | \(-0.534325\pi\) | ||||
−0.107625 | + | 0.994192i | \(0.534325\pi\) | |||||||
\(84\) | −5.29393 | −0.577615 | ||||||||
\(85\) | −1.11384 | −0.120812 | ||||||||
\(86\) | 12.1218 | 1.30713 | ||||||||
\(87\) | −8.62820 | −0.925040 | ||||||||
\(88\) | 3.72248 | 0.396818 | ||||||||
\(89\) | 0.276183 | 0.0292754 | 0.0146377 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146377 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(90\) | −0.372589 | −0.0392743 | ||||||||
\(91\) | 14.3311 | 1.50230 | ||||||||
\(92\) | 6.11286 | 0.637310 | ||||||||
\(93\) | −1.49873 | −0.155411 | ||||||||
\(94\) | −11.9160 | −1.22904 | ||||||||
\(95\) | 0.376690 | 0.0386475 | ||||||||
\(96\) | 1.22439 | 0.124964 | ||||||||
\(97\) | −1.72988 | −0.175643 | −0.0878216 | − | 0.996136i | \(-0.527991\pi\) | ||||
−0.0878216 | + | 0.996136i | \(0.527991\pi\) | |||||||
\(98\) | −11.6946 | −1.18133 | ||||||||
\(99\) | 5.58695 | 0.561510 | ||||||||
\(100\) | −4.93837 | −0.493837 | ||||||||
\(101\) | 16.4714 | 1.63897 | 0.819484 | − | 0.573102i | \(-0.194260\pi\) | ||||
0.819484 | + | 0.573102i | \(0.194260\pi\) | |||||||
\(102\) | 5.49356 | 0.543943 | ||||||||
\(103\) | 13.3695 | 1.31733 | 0.658667 | − | 0.752435i | \(-0.271121\pi\) | ||||
0.658667 | + | 0.752435i | \(0.271121\pi\) | |||||||
\(104\) | −3.31452 | −0.325015 | ||||||||
\(105\) | 1.31421 | 0.128254 | ||||||||
\(106\) | 8.22284 | 0.798673 | ||||||||
\(107\) | −11.6495 | −1.12620 | −0.563098 | − | 0.826390i | \(-0.690390\pi\) | ||||
−0.563098 | + | 0.826390i | \(0.690390\pi\) | |||||||
\(108\) | 5.51082 | 0.530279 | ||||||||
\(109\) | 11.4514 | 1.09685 | 0.548423 | − | 0.836201i | \(-0.315228\pi\) | ||||
0.548423 | + | 0.836201i | \(0.315228\pi\) | |||||||
\(110\) | −0.924103 | −0.0881097 | ||||||||
\(111\) | −5.45202 | −0.517483 | ||||||||
\(112\) | 4.32372 | 0.408553 | ||||||||
\(113\) | 16.3565 | 1.53869 | 0.769344 | − | 0.638835i | \(-0.220583\pi\) | ||||
0.769344 | + | 0.638835i | \(0.220583\pi\) | |||||||
\(114\) | −1.85787 | −0.174006 | ||||||||
\(115\) | −1.51751 | −0.141509 | ||||||||
\(116\) | 7.04693 | 0.654291 | ||||||||
\(117\) | −4.97465 | −0.459907 | ||||||||
\(118\) | −5.21389 | −0.479978 | ||||||||
\(119\) | 19.3996 | 1.77835 | ||||||||
\(120\) | −0.303954 | −0.0277470 | ||||||||
\(121\) | 2.85688 | 0.259716 | ||||||||
\(122\) | 9.22447 | 0.835144 | ||||||||
\(123\) | −1.25522 | −0.113180 | ||||||||
\(124\) | 1.22406 | 0.109924 | ||||||||
\(125\) | 2.46719 | 0.220672 | ||||||||
\(126\) | 6.48934 | 0.578116 | ||||||||
\(127\) | 15.0082 | 1.33176 | 0.665882 | − | 0.746057i | \(-0.268055\pi\) | ||||
0.665882 | + | 0.746057i | \(0.268055\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 14.8419 | 1.30675 | ||||||||
\(130\) | 0.822825 | 0.0721666 | ||||||||
\(131\) | 5.86352 | 0.512298 | 0.256149 | − | 0.966637i | \(-0.417546\pi\) | ||||
0.256149 | + | 0.966637i | \(0.417546\pi\) | |||||||
\(132\) | 4.55777 | 0.396703 | ||||||||
\(133\) | −6.56076 | −0.568890 | ||||||||
\(134\) | 8.76845 | 0.757479 | ||||||||
\(135\) | −1.36806 | −0.117743 | ||||||||
\(136\) | −4.48677 | −0.384737 | ||||||||
\(137\) | −15.9745 | −1.36479 | −0.682395 | − | 0.730983i | \(-0.739062\pi\) | ||||
−0.682395 | + | 0.730983i | \(0.739062\pi\) | |||||||
\(138\) | 7.48453 | 0.637126 | ||||||||
\(139\) | −15.9939 | −1.35658 | −0.678291 | − | 0.734793i | \(-0.737279\pi\) | ||||
−0.678291 | + | 0.734793i | \(0.737279\pi\) | |||||||
\(140\) | −1.07336 | −0.0907155 | ||||||||
\(141\) | −14.5898 | −1.22869 | ||||||||
\(142\) | −5.36999 | −0.450639 | ||||||||
\(143\) | −12.3382 | −1.03177 | ||||||||
\(144\) | −1.50087 | −0.125072 | ||||||||
\(145\) | −1.74939 | −0.145279 | ||||||||
\(146\) | 0.386914 | 0.0320212 | ||||||||
\(147\) | −14.3187 | −1.18099 | ||||||||
\(148\) | 4.45284 | 0.366022 | ||||||||
\(149\) | −22.3966 | −1.83480 | −0.917399 | − | 0.397968i | \(-0.869716\pi\) | ||||
−0.917399 | + | 0.397968i | \(0.869716\pi\) | |||||||
\(150\) | −6.04650 | −0.493694 | ||||||||
\(151\) | 19.1383 | 1.55745 | 0.778727 | − | 0.627363i | \(-0.215866\pi\) | ||||
0.778727 | + | 0.627363i | \(0.215866\pi\) | |||||||
\(152\) | 1.51739 | 0.123076 | ||||||||
\(153\) | −6.73405 | −0.544416 | ||||||||
\(154\) | 16.0950 | 1.29697 | ||||||||
\(155\) | −0.303872 | −0.0244076 | ||||||||
\(156\) | −4.05826 | −0.324921 | ||||||||
\(157\) | −23.6945 | −1.89102 | −0.945512 | − | 0.325588i | \(-0.894438\pi\) | ||||
−0.945512 | + | 0.325588i | \(0.894438\pi\) | |||||||
\(158\) | −1.57570 | −0.125356 | ||||||||
\(159\) | 10.0680 | 0.798442 | ||||||||
\(160\) | 0.248249 | 0.0196258 | ||||||||
\(161\) | 26.4303 | 2.08300 | ||||||||
\(162\) | 2.24479 | 0.176368 | ||||||||
\(163\) | −0.879204 | −0.0688646 | −0.0344323 | − | 0.999407i | \(-0.510962\pi\) | ||||
−0.0344323 | + | 0.999407i | \(0.510962\pi\) | |||||||
\(164\) | 1.02518 | 0.0800533 | ||||||||
\(165\) | −1.13146 | −0.0880842 | ||||||||
\(166\) | 1.96103 | 0.152205 | ||||||||
\(167\) | −11.6716 | −0.903177 | −0.451588 | − | 0.892226i | \(-0.649142\pi\) | ||||
−0.451588 | + | 0.892226i | \(0.649142\pi\) | |||||||
\(168\) | 5.29393 | 0.408435 | ||||||||
\(169\) | −2.01398 | −0.154921 | ||||||||
\(170\) | 1.11384 | 0.0854273 | ||||||||
\(171\) | 2.27740 | 0.174157 | ||||||||
\(172\) | −12.1218 | −0.924281 | ||||||||
\(173\) | 7.76573 | 0.590417 | 0.295209 | − | 0.955433i | \(-0.404611\pi\) | ||||
0.295209 | + | 0.955433i | \(0.404611\pi\) | |||||||
\(174\) | 8.62820 | 0.654102 | ||||||||
\(175\) | −21.3522 | −1.61407 | ||||||||
\(176\) | −3.72248 | −0.280593 | ||||||||
\(177\) | −6.38384 | −0.479839 | ||||||||
\(178\) | −0.276183 | −0.0207008 | ||||||||
\(179\) | 17.2220 | 1.28723 | 0.643616 | − | 0.765348i | \(-0.277433\pi\) | ||||
0.643616 | + | 0.765348i | \(0.277433\pi\) | |||||||
\(180\) | 0.372589 | 0.0277711 | ||||||||
\(181\) | −11.3054 | −0.840321 | −0.420161 | − | 0.907450i | \(-0.638026\pi\) | ||||
−0.420161 | + | 0.907450i | \(0.638026\pi\) | |||||||
\(182\) | −14.3311 | −1.06229 | ||||||||
\(183\) | 11.2943 | 0.834902 | ||||||||
\(184\) | −6.11286 | −0.450646 | ||||||||
\(185\) | −1.10541 | −0.0812716 | ||||||||
\(186\) | 1.49873 | 0.109892 | ||||||||
\(187\) | −16.7019 | −1.22137 | ||||||||
\(188\) | 11.9160 | 0.869064 | ||||||||
\(189\) | 23.8273 | 1.73318 | ||||||||
\(190\) | −0.376690 | −0.0273279 | ||||||||
\(191\) | 8.44189 | 0.610834 | 0.305417 | − | 0.952219i | \(-0.401204\pi\) | ||||
0.305417 | + | 0.952219i | \(0.401204\pi\) | |||||||
\(192\) | −1.22439 | −0.0883628 | ||||||||
\(193\) | 4.44258 | 0.319784 | 0.159892 | − | 0.987135i | \(-0.448885\pi\) | ||||
0.159892 | + | 0.987135i | \(0.448885\pi\) | |||||||
\(194\) | 1.72988 | 0.124198 | ||||||||
\(195\) | 1.00746 | 0.0721457 | ||||||||
\(196\) | 11.6946 | 0.835327 | ||||||||
\(197\) | 6.69132 | 0.476736 | 0.238368 | − | 0.971175i | \(-0.423387\pi\) | ||||
0.238368 | + | 0.971175i | \(0.423387\pi\) | |||||||
\(198\) | −5.58695 | −0.397048 | ||||||||
\(199\) | −12.3570 | −0.875964 | −0.437982 | − | 0.898984i | \(-0.644307\pi\) | ||||
−0.437982 | + | 0.898984i | \(0.644307\pi\) | |||||||
\(200\) | 4.93837 | 0.349196 | ||||||||
\(201\) | 10.7360 | 0.757260 | ||||||||
\(202\) | −16.4714 | −1.15893 | ||||||||
\(203\) | 30.4690 | 2.13850 | ||||||||
\(204\) | −5.49356 | −0.384626 | ||||||||
\(205\) | −0.254500 | −0.0177751 | ||||||||
\(206\) | −13.3695 | −0.931495 | ||||||||
\(207\) | −9.17460 | −0.637679 | ||||||||
\(208\) | 3.31452 | 0.229820 | ||||||||
\(209\) | 5.64844 | 0.390711 | ||||||||
\(210\) | −1.31421 | −0.0906892 | ||||||||
\(211\) | 10.2881 | 0.708261 | 0.354131 | − | 0.935196i | \(-0.384777\pi\) | ||||
0.354131 | + | 0.935196i | \(0.384777\pi\) | |||||||
\(212\) | −8.22284 | −0.564747 | ||||||||
\(213\) | −6.57496 | −0.450509 | ||||||||
\(214\) | 11.6495 | 0.796340 | ||||||||
\(215\) | 3.00923 | 0.205228 | ||||||||
\(216\) | −5.51082 | −0.374964 | ||||||||
\(217\) | 5.29251 | 0.359279 | ||||||||
\(218\) | −11.4514 | −0.775587 | ||||||||
\(219\) | 0.473734 | 0.0320120 | ||||||||
\(220\) | 0.924103 | 0.0623030 | ||||||||
\(221\) | 14.8715 | 1.00036 | ||||||||
\(222\) | 5.45202 | 0.365916 | ||||||||
\(223\) | 11.2371 | 0.752490 | 0.376245 | − | 0.926520i | \(-0.377215\pi\) | ||||
0.376245 | + | 0.926520i | \(0.377215\pi\) | |||||||
\(224\) | −4.32372 | −0.288891 | ||||||||
\(225\) | 7.41184 | 0.494123 | ||||||||
\(226\) | −16.3565 | −1.08802 | ||||||||
\(227\) | −5.84329 | −0.387833 | −0.193916 | − | 0.981018i | \(-0.562119\pi\) | ||||
−0.193916 | + | 0.981018i | \(0.562119\pi\) | |||||||
\(228\) | 1.85787 | 0.123041 | ||||||||
\(229\) | 24.3768 | 1.61087 | 0.805433 | − | 0.592687i | \(-0.201933\pi\) | ||||
0.805433 | + | 0.592687i | \(0.201933\pi\) | |||||||
\(230\) | 1.51751 | 0.100062 | ||||||||
\(231\) | 19.7066 | 1.29660 | ||||||||
\(232\) | −7.04693 | −0.462654 | ||||||||
\(233\) | −0.658244 | −0.0431230 | −0.0215615 | − | 0.999768i | \(-0.506864\pi\) | ||||
−0.0215615 | + | 0.999768i | \(0.506864\pi\) | |||||||
\(234\) | 4.97465 | 0.325203 | ||||||||
\(235\) | −2.95814 | −0.192967 | ||||||||
\(236\) | 5.21389 | 0.339395 | ||||||||
\(237\) | −1.92927 | −0.125319 | ||||||||
\(238\) | −19.3996 | −1.25749 | ||||||||
\(239\) | 20.6017 | 1.33261 | 0.666305 | − | 0.745679i | \(-0.267875\pi\) | ||||
0.666305 | + | 0.745679i | \(0.267875\pi\) | |||||||
\(240\) | 0.303954 | 0.0196201 | ||||||||
\(241\) | −10.4957 | −0.676090 | −0.338045 | − | 0.941130i | \(-0.609766\pi\) | ||||
−0.338045 | + | 0.941130i | \(0.609766\pi\) | |||||||
\(242\) | −2.85688 | −0.183647 | ||||||||
\(243\) | −13.7840 | −0.884241 | ||||||||
\(244\) | −9.22447 | −0.590536 | ||||||||
\(245\) | −2.90317 | −0.185477 | ||||||||
\(246\) | 1.25522 | 0.0800301 | ||||||||
\(247\) | −5.02940 | −0.320013 | ||||||||
\(248\) | −1.22406 | −0.0777281 | ||||||||
\(249\) | 2.40106 | 0.152161 | ||||||||
\(250\) | −2.46719 | −0.156039 | ||||||||
\(251\) | −27.7384 | −1.75083 | −0.875416 | − | 0.483369i | \(-0.839413\pi\) | ||||
−0.875416 | + | 0.483369i | \(0.839413\pi\) | |||||||
\(252\) | −6.48934 | −0.408790 | ||||||||
\(253\) | −22.7550 | −1.43060 | ||||||||
\(254\) | −15.0082 | −0.941699 | ||||||||
\(255\) | 1.36377 | 0.0854026 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.7192 | −1.23005 | −0.615024 | − | 0.788509i | \(-0.710854\pi\) | ||||
−0.615024 | + | 0.788509i | \(0.710854\pi\) | |||||||
\(258\) | −14.8419 | −0.924013 | ||||||||
\(259\) | 19.2529 | 1.19631 | ||||||||
\(260\) | −0.822825 | −0.0510295 | ||||||||
\(261\) | −10.5765 | −0.654670 | ||||||||
\(262\) | −5.86352 | −0.362250 | ||||||||
\(263\) | −21.9558 | −1.35385 | −0.676925 | − | 0.736052i | \(-0.736688\pi\) | ||||
−0.676925 | + | 0.736052i | \(0.736688\pi\) | |||||||
\(264\) | −4.55777 | −0.280512 | ||||||||
\(265\) | 2.04131 | 0.125397 | ||||||||
\(266\) | 6.56076 | 0.402266 | ||||||||
\(267\) | −0.338156 | −0.0206948 | ||||||||
\(268\) | −8.76845 | −0.535618 | ||||||||
\(269\) | 22.8909 | 1.39568 | 0.697842 | − | 0.716252i | \(-0.254144\pi\) | ||||
0.697842 | + | 0.716252i | \(0.254144\pi\) | |||||||
\(270\) | 1.36806 | 0.0832572 | ||||||||
\(271\) | −10.7632 | −0.653820 | −0.326910 | − | 0.945056i | \(-0.606007\pi\) | ||||
−0.326910 | + | 0.945056i | \(0.606007\pi\) | |||||||
\(272\) | 4.48677 | 0.272050 | ||||||||
\(273\) | −17.5468 | −1.06198 | ||||||||
\(274\) | 15.9745 | 0.965053 | ||||||||
\(275\) | 18.3830 | 1.10854 | ||||||||
\(276\) | −7.48453 | −0.450516 | ||||||||
\(277\) | 1.48199 | 0.0890444 | 0.0445222 | − | 0.999008i | \(-0.485823\pi\) | ||||
0.0445222 | + | 0.999008i | \(0.485823\pi\) | |||||||
\(278\) | 15.9939 | 0.959248 | ||||||||
\(279\) | −1.83716 | −0.109988 | ||||||||
\(280\) | 1.07336 | 0.0641455 | ||||||||
\(281\) | 18.5237 | 1.10503 | 0.552515 | − | 0.833503i | \(-0.313668\pi\) | ||||
0.552515 | + | 0.833503i | \(0.313668\pi\) | |||||||
\(282\) | 14.5898 | 0.868813 | ||||||||
\(283\) | −7.04766 | −0.418940 | −0.209470 | − | 0.977815i | \(-0.567174\pi\) | ||||
−0.209470 | + | 0.977815i | \(0.567174\pi\) | |||||||
\(284\) | 5.36999 | 0.318650 | ||||||||
\(285\) | −0.461215 | −0.0273200 | ||||||||
\(286\) | 12.3382 | 0.729575 | ||||||||
\(287\) | 4.43260 | 0.261648 | ||||||||
\(288\) | 1.50087 | 0.0884395 | ||||||||
\(289\) | 3.13111 | 0.184183 | ||||||||
\(290\) | 1.74939 | 0.102728 | ||||||||
\(291\) | 2.11805 | 0.124163 | ||||||||
\(292\) | −0.386914 | −0.0226424 | ||||||||
\(293\) | 24.4395 | 1.42777 | 0.713886 | − | 0.700262i | \(-0.246933\pi\) | ||||
0.713886 | + | 0.700262i | \(0.246933\pi\) | |||||||
\(294\) | 14.3187 | 0.835086 | ||||||||
\(295\) | −1.29434 | −0.0753596 | ||||||||
\(296\) | −4.45284 | −0.258816 | ||||||||
\(297\) | −20.5139 | −1.19034 | ||||||||
\(298\) | 22.3966 | 1.29740 | ||||||||
\(299\) | 20.2612 | 1.17173 | ||||||||
\(300\) | 6.04650 | 0.349095 | ||||||||
\(301\) | −52.4114 | −3.02094 | ||||||||
\(302\) | −19.1383 | −1.10129 | ||||||||
\(303\) | −20.1675 | −1.15859 | ||||||||
\(304\) | −1.51739 | −0.0870281 | ||||||||
\(305\) | 2.28996 | 0.131123 | ||||||||
\(306\) | 6.73405 | 0.384960 | ||||||||
\(307\) | −13.4958 | −0.770246 | −0.385123 | − | 0.922865i | \(-0.625841\pi\) | ||||
−0.385123 | + | 0.922865i | \(0.625841\pi\) | |||||||
\(308\) | −16.0950 | −0.917097 | ||||||||
\(309\) | −16.3695 | −0.931226 | ||||||||
\(310\) | 0.303872 | 0.0172588 | ||||||||
\(311\) | −14.1036 | −0.799739 | −0.399870 | − | 0.916572i | \(-0.630945\pi\) | ||||
−0.399870 | + | 0.916572i | \(0.630945\pi\) | |||||||
\(312\) | 4.05826 | 0.229754 | ||||||||
\(313\) | 17.1577 | 0.969812 | 0.484906 | − | 0.874566i | \(-0.338854\pi\) | ||||
0.484906 | + | 0.874566i | \(0.338854\pi\) | |||||||
\(314\) | 23.6945 | 1.33716 | ||||||||
\(315\) | 1.61097 | 0.0907679 | ||||||||
\(316\) | 1.57570 | 0.0886398 | ||||||||
\(317\) | −5.02832 | −0.282419 | −0.141209 | − | 0.989980i | \(-0.545099\pi\) | ||||
−0.141209 | + | 0.989980i | \(0.545099\pi\) | |||||||
\(318\) | −10.0680 | −0.564583 | ||||||||
\(319\) | −26.2321 | −1.46871 | ||||||||
\(320\) | −0.248249 | −0.0138775 | ||||||||
\(321\) | 14.2635 | 0.796110 | ||||||||
\(322\) | −26.4303 | −1.47290 | ||||||||
\(323\) | −6.80816 | −0.378816 | ||||||||
\(324\) | −2.24479 | −0.124711 | ||||||||
\(325\) | −16.3683 | −0.907951 | ||||||||
\(326\) | 0.879204 | 0.0486946 | ||||||||
\(327\) | −14.0210 | −0.775363 | ||||||||
\(328\) | −1.02518 | −0.0566062 | ||||||||
\(329\) | 51.5215 | 2.84047 | ||||||||
\(330\) | 1.13146 | 0.0622850 | ||||||||
\(331\) | −10.9441 | −0.601543 | −0.300771 | − | 0.953696i | \(-0.597244\pi\) | ||||
−0.300771 | + | 0.953696i | \(0.597244\pi\) | |||||||
\(332\) | −1.96103 | −0.107625 | ||||||||
\(333\) | −6.68313 | −0.366233 | ||||||||
\(334\) | 11.6716 | 0.638642 | ||||||||
\(335\) | 2.17676 | 0.118929 | ||||||||
\(336\) | −5.29393 | −0.288807 | ||||||||
\(337\) | 8.73457 | 0.475802 | 0.237901 | − | 0.971289i | \(-0.423541\pi\) | ||||
0.237901 | + | 0.971289i | \(0.423541\pi\) | |||||||
\(338\) | 2.01398 | 0.109546 | ||||||||
\(339\) | −20.0267 | −1.08770 | ||||||||
\(340\) | −1.11384 | −0.0604062 | ||||||||
\(341\) | −4.55655 | −0.246751 | ||||||||
\(342\) | −2.27740 | −0.123147 | ||||||||
\(343\) | 20.2981 | 1.09599 | ||||||||
\(344\) | 12.1218 | 0.653565 | ||||||||
\(345\) | 1.85803 | 0.100033 | ||||||||
\(346\) | −7.76573 | −0.417488 | ||||||||
\(347\) | 29.6761 | 1.59309 | 0.796547 | − | 0.604577i | \(-0.206658\pi\) | ||||
0.796547 | + | 0.604577i | \(0.206658\pi\) | |||||||
\(348\) | −8.62820 | −0.462520 | ||||||||
\(349\) | 1.27149 | 0.0680610 | 0.0340305 | − | 0.999421i | \(-0.489166\pi\) | ||||
0.0340305 | + | 0.999421i | \(0.489166\pi\) | |||||||
\(350\) | 21.3522 | 1.14132 | ||||||||
\(351\) | 18.2657 | 0.974951 | ||||||||
\(352\) | 3.72248 | 0.198409 | ||||||||
\(353\) | −9.27511 | −0.493664 | −0.246832 | − | 0.969058i | \(-0.579390\pi\) | ||||
−0.246832 | + | 0.969058i | \(0.579390\pi\) | |||||||
\(354\) | 6.38384 | 0.339297 | ||||||||
\(355\) | −1.33309 | −0.0707533 | ||||||||
\(356\) | 0.276183 | 0.0146377 | ||||||||
\(357\) | −23.7526 | −1.25712 | ||||||||
\(358\) | −17.2220 | −0.910211 | ||||||||
\(359\) | 17.0690 | 0.900867 | 0.450433 | − | 0.892810i | \(-0.351270\pi\) | ||||
0.450433 | + | 0.892810i | \(0.351270\pi\) | |||||||
\(360\) | −0.372589 | −0.0196372 | ||||||||
\(361\) | −16.6975 | −0.878818 | ||||||||
\(362\) | 11.3054 | 0.594197 | ||||||||
\(363\) | −3.49794 | −0.183594 | ||||||||
\(364\) | 14.3311 | 0.751151 | ||||||||
\(365\) | 0.0960510 | 0.00502754 | ||||||||
\(366\) | −11.2943 | −0.590365 | ||||||||
\(367\) | 8.70871 | 0.454591 | 0.227296 | − | 0.973826i | \(-0.427012\pi\) | ||||
0.227296 | + | 0.973826i | \(0.427012\pi\) | |||||||
\(368\) | 6.11286 | 0.318655 | ||||||||
\(369\) | −1.53866 | −0.0800996 | ||||||||
\(370\) | 1.10541 | 0.0574677 | ||||||||
\(371\) | −35.5533 | −1.84583 | ||||||||
\(372\) | −1.49873 | −0.0777056 | ||||||||
\(373\) | 24.9428 | 1.29149 | 0.645745 | − | 0.763553i | \(-0.276547\pi\) | ||||
0.645745 | + | 0.763553i | \(0.276547\pi\) | |||||||
\(374\) | 16.7019 | 0.863636 | ||||||||
\(375\) | −3.02080 | −0.155994 | ||||||||
\(376\) | −11.9160 | −0.614521 | ||||||||
\(377\) | 23.3572 | 1.20296 | ||||||||
\(378\) | −23.8273 | −1.22554 | ||||||||
\(379\) | −23.6900 | −1.21687 | −0.608437 | − | 0.793602i | \(-0.708203\pi\) | ||||
−0.608437 | + | 0.793602i | \(0.708203\pi\) | |||||||
\(380\) | 0.376690 | 0.0193238 | ||||||||
\(381\) | −18.3759 | −0.941427 | ||||||||
\(382\) | −8.44189 | −0.431925 | ||||||||
\(383\) | −4.57618 | −0.233832 | −0.116916 | − | 0.993142i | \(-0.537301\pi\) | ||||
−0.116916 | + | 0.993142i | \(0.537301\pi\) | |||||||
\(384\) | 1.22439 | 0.0624819 | ||||||||
\(385\) | 3.99556 | 0.203633 | ||||||||
\(386\) | −4.44258 | −0.226121 | ||||||||
\(387\) | 18.1933 | 0.924815 | ||||||||
\(388\) | −1.72988 | −0.0878216 | ||||||||
\(389\) | 0.0324068 | 0.00164309 | 0.000821546 | − | 1.00000i | \(-0.499738\pi\) | ||||
0.000821546 | 1.00000i | \(0.499738\pi\) | ||||||||
\(390\) | −1.00746 | −0.0510147 | ||||||||
\(391\) | 27.4270 | 1.38704 | ||||||||
\(392\) | −11.6946 | −0.590666 | ||||||||
\(393\) | −7.17924 | −0.362145 | ||||||||
\(394\) | −6.69132 | −0.337104 | ||||||||
\(395\) | −0.391165 | −0.0196816 | ||||||||
\(396\) | 5.58695 | 0.280755 | ||||||||
\(397\) | −2.85169 | −0.143122 | −0.0715610 | − | 0.997436i | \(-0.522798\pi\) | ||||
−0.0715610 | + | 0.997436i | \(0.522798\pi\) | |||||||
\(398\) | 12.3570 | 0.619400 | ||||||||
\(399\) | 8.03293 | 0.402150 | ||||||||
\(400\) | −4.93837 | −0.246919 | ||||||||
\(401\) | 17.5491 | 0.876362 | 0.438181 | − | 0.898887i | \(-0.355623\pi\) | ||||
0.438181 | + | 0.898887i | \(0.355623\pi\) | |||||||
\(402\) | −10.7360 | −0.535463 | ||||||||
\(403\) | 4.05718 | 0.202102 | ||||||||
\(404\) | 16.4714 | 0.819484 | ||||||||
\(405\) | 0.557268 | 0.0276908 | ||||||||
\(406\) | −30.4690 | −1.51215 | ||||||||
\(407\) | −16.5756 | −0.821624 | ||||||||
\(408\) | 5.49356 | 0.271972 | ||||||||
\(409\) | −2.30656 | −0.114052 | −0.0570259 | − | 0.998373i | \(-0.518162\pi\) | ||||
−0.0570259 | + | 0.998373i | \(0.518162\pi\) | |||||||
\(410\) | 0.254500 | 0.0125689 | ||||||||
\(411\) | 19.5590 | 0.964773 | ||||||||
\(412\) | 13.3695 | 0.658667 | ||||||||
\(413\) | 22.5434 | 1.10929 | ||||||||
\(414\) | 9.17460 | 0.450907 | ||||||||
\(415\) | 0.486823 | 0.0238972 | ||||||||
\(416\) | −3.31452 | −0.162508 | ||||||||
\(417\) | 19.5827 | 0.958971 | ||||||||
\(418\) | −5.64844 | −0.276274 | ||||||||
\(419\) | 11.6974 | 0.571458 | 0.285729 | − | 0.958310i | \(-0.407764\pi\) | ||||
0.285729 | + | 0.958310i | \(0.407764\pi\) | |||||||
\(420\) | 1.31421 | 0.0641270 | ||||||||
\(421\) | −0.852363 | −0.0415416 | −0.0207708 | − | 0.999784i | \(-0.506612\pi\) | ||||
−0.0207708 | + | 0.999784i | \(0.506612\pi\) | |||||||
\(422\) | −10.2881 | −0.500816 | ||||||||
\(423\) | −17.8843 | −0.869567 | ||||||||
\(424\) | 8.22284 | 0.399336 | ||||||||
\(425\) | −22.1573 | −1.07479 | ||||||||
\(426\) | 6.57496 | 0.318558 | ||||||||
\(427\) | −39.8840 | −1.93012 | ||||||||
\(428\) | −11.6495 | −0.563098 | ||||||||
\(429\) | 15.1068 | 0.729364 | ||||||||
\(430\) | −3.00923 | −0.145118 | ||||||||
\(431\) | 13.1994 | 0.635793 | 0.317897 | − | 0.948125i | \(-0.397023\pi\) | ||||
0.317897 | + | 0.948125i | \(0.397023\pi\) | |||||||
\(432\) | 5.51082 | 0.265139 | ||||||||
\(433\) | 0.224106 | 0.0107698 | 0.00538492 | − | 0.999986i | \(-0.498286\pi\) | ||||
0.00538492 | + | 0.999986i | \(0.498286\pi\) | |||||||
\(434\) | −5.29251 | −0.254049 | ||||||||
\(435\) | 2.14194 | 0.102698 | ||||||||
\(436\) | 11.4514 | 0.548423 | ||||||||
\(437\) | −9.27557 | −0.443711 | ||||||||
\(438\) | −0.473734 | −0.0226359 | ||||||||
\(439\) | 0.963307 | 0.0459761 | 0.0229881 | − | 0.999736i | \(-0.492682\pi\) | ||||
0.0229881 | + | 0.999736i | \(0.492682\pi\) | |||||||
\(440\) | −0.924103 | −0.0440549 | ||||||||
\(441\) | −17.5520 | −0.835811 | ||||||||
\(442\) | −14.8715 | −0.707364 | ||||||||
\(443\) | 17.3974 | 0.826575 | 0.413287 | − | 0.910601i | \(-0.364381\pi\) | ||||
0.413287 | + | 0.910601i | \(0.364381\pi\) | |||||||
\(444\) | −5.45202 | −0.258741 | ||||||||
\(445\) | −0.0685622 | −0.00325016 | ||||||||
\(446\) | −11.2371 | −0.532091 | ||||||||
\(447\) | 27.4222 | 1.29702 | ||||||||
\(448\) | 4.32372 | 0.204277 | ||||||||
\(449\) | 26.4577 | 1.24862 | 0.624309 | − | 0.781177i | \(-0.285381\pi\) | ||||
0.624309 | + | 0.781177i | \(0.285381\pi\) | |||||||
\(450\) | −7.41184 | −0.349398 | ||||||||
\(451\) | −3.81622 | −0.179699 | ||||||||
\(452\) | 16.3565 | 0.769344 | ||||||||
\(453\) | −23.4328 | −1.10097 | ||||||||
\(454\) | 5.84329 | 0.274239 | ||||||||
\(455\) | −3.55767 | −0.166786 | ||||||||
\(456\) | −1.85787 | −0.0870029 | ||||||||
\(457\) | −3.63016 | −0.169812 | −0.0849059 | − | 0.996389i | \(-0.527059\pi\) | ||||
−0.0849059 | + | 0.996389i | \(0.527059\pi\) | |||||||
\(458\) | −24.3768 | −1.13905 | ||||||||
\(459\) | 24.7258 | 1.15410 | ||||||||
\(460\) | −1.51751 | −0.0707543 | ||||||||
\(461\) | 15.7254 | 0.732404 | 0.366202 | − | 0.930535i | \(-0.380658\pi\) | ||||
0.366202 | + | 0.930535i | \(0.380658\pi\) | |||||||
\(462\) | −19.7066 | −0.916832 | ||||||||
\(463\) | −23.0730 | −1.07229 | −0.536146 | − | 0.844125i | \(-0.680120\pi\) | ||||
−0.536146 | + | 0.844125i | \(0.680120\pi\) | |||||||
\(464\) | 7.04693 | 0.327146 | ||||||||
\(465\) | 0.372058 | 0.0172538 | ||||||||
\(466\) | 0.658244 | 0.0304926 | ||||||||
\(467\) | −13.1775 | −0.609780 | −0.304890 | − | 0.952387i | \(-0.598620\pi\) | ||||
−0.304890 | + | 0.952387i | \(0.598620\pi\) | |||||||
\(468\) | −4.97465 | −0.229953 | ||||||||
\(469\) | −37.9124 | −1.75063 | ||||||||
\(470\) | 2.95814 | 0.136449 | ||||||||
\(471\) | 29.0113 | 1.33677 | ||||||||
\(472\) | −5.21389 | −0.239989 | ||||||||
\(473\) | 45.1233 | 2.07477 | ||||||||
\(474\) | 1.92927 | 0.0886142 | ||||||||
\(475\) | 7.49342 | 0.343822 | ||||||||
\(476\) | 19.3996 | 0.889177 | ||||||||
\(477\) | 12.3414 | 0.565074 | ||||||||
\(478\) | −20.6017 | −0.942298 | ||||||||
\(479\) | 6.21942 | 0.284173 | 0.142086 | − | 0.989854i | \(-0.454619\pi\) | ||||
0.142086 | + | 0.989854i | \(0.454619\pi\) | |||||||
\(480\) | −0.303954 | −0.0138735 | ||||||||
\(481\) | 14.7590 | 0.672954 | ||||||||
\(482\) | 10.4957 | 0.478068 | ||||||||
\(483\) | −32.3610 | −1.47248 | ||||||||
\(484\) | 2.85688 | 0.129858 | ||||||||
\(485\) | 0.429442 | 0.0195000 | ||||||||
\(486\) | 13.7840 | 0.625253 | ||||||||
\(487\) | 9.26111 | 0.419661 | 0.209830 | − | 0.977738i | \(-0.432709\pi\) | ||||
0.209830 | + | 0.977738i | \(0.432709\pi\) | |||||||
\(488\) | 9.22447 | 0.417572 | ||||||||
\(489\) | 1.07649 | 0.0486805 | ||||||||
\(490\) | 2.90317 | 0.131152 | ||||||||
\(491\) | 39.7962 | 1.79598 | 0.897989 | − | 0.440017i | \(-0.145028\pi\) | ||||
0.897989 | + | 0.440017i | \(0.145028\pi\) | |||||||
\(492\) | −1.25522 | −0.0565898 | ||||||||
\(493\) | 31.6180 | 1.42400 | ||||||||
\(494\) | 5.02940 | 0.226283 | ||||||||
\(495\) | −1.38696 | −0.0623390 | ||||||||
\(496\) | 1.22406 | 0.0549620 | ||||||||
\(497\) | 23.2183 | 1.04149 | ||||||||
\(498\) | −2.40106 | −0.107594 | ||||||||
\(499\) | −6.82565 | −0.305558 | −0.152779 | − | 0.988260i | \(-0.548822\pi\) | ||||
−0.152779 | + | 0.988260i | \(0.548822\pi\) | |||||||
\(500\) | 2.46719 | 0.110336 | ||||||||
\(501\) | 14.2906 | 0.638458 | ||||||||
\(502\) | 27.7384 | 1.23803 | ||||||||
\(503\) | 25.4730 | 1.13579 | 0.567893 | − | 0.823102i | \(-0.307759\pi\) | ||||
0.567893 | + | 0.823102i | \(0.307759\pi\) | |||||||
\(504\) | 6.48934 | 0.289058 | ||||||||
\(505\) | −4.08901 | −0.181959 | ||||||||
\(506\) | 22.7550 | 1.01158 | ||||||||
\(507\) | 2.46590 | 0.109514 | ||||||||
\(508\) | 15.0082 | 0.665882 | ||||||||
\(509\) | 14.7446 | 0.653543 | 0.326772 | − | 0.945103i | \(-0.394039\pi\) | ||||
0.326772 | + | 0.945103i | \(0.394039\pi\) | |||||||
\(510\) | −1.36377 | −0.0603888 | ||||||||
\(511\) | −1.67291 | −0.0740051 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −8.36204 | −0.369193 | ||||||||
\(514\) | 19.7192 | 0.869775 | ||||||||
\(515\) | −3.31896 | −0.146251 | ||||||||
\(516\) | 14.8419 | 0.653376 | ||||||||
\(517\) | −44.3571 | −1.95082 | ||||||||
\(518\) | −19.2529 | −0.845922 | ||||||||
\(519\) | −9.50828 | −0.417367 | ||||||||
\(520\) | 0.822825 | 0.0360833 | ||||||||
\(521\) | 17.1824 | 0.752776 | 0.376388 | − | 0.926462i | \(-0.377166\pi\) | ||||
0.376388 | + | 0.926462i | \(0.377166\pi\) | |||||||
\(522\) | 10.5765 | 0.462921 | ||||||||
\(523\) | 40.1178 | 1.75423 | 0.877115 | − | 0.480281i | \(-0.159465\pi\) | ||||
0.877115 | + | 0.480281i | \(0.159465\pi\) | |||||||
\(524\) | 5.86352 | 0.256149 | ||||||||
\(525\) | 26.1434 | 1.14099 | ||||||||
\(526\) | 21.9558 | 0.957317 | ||||||||
\(527\) | 5.49209 | 0.239239 | ||||||||
\(528\) | 4.55777 | 0.198352 | ||||||||
\(529\) | 14.3671 | 0.624656 | ||||||||
\(530\) | −2.04131 | −0.0886689 | ||||||||
\(531\) | −7.82536 | −0.339592 | ||||||||
\(532\) | −6.56076 | −0.284445 | ||||||||
\(533\) | 3.39798 | 0.147183 | ||||||||
\(534\) | 0.338156 | 0.0146335 | ||||||||
\(535\) | 2.89196 | 0.125031 | ||||||||
\(536\) | 8.76845 | 0.378739 | ||||||||
\(537\) | −21.0865 | −0.909948 | ||||||||
\(538\) | −22.8909 | −0.986897 | ||||||||
\(539\) | −43.5329 | −1.87509 | ||||||||
\(540\) | −1.36806 | −0.0588717 | ||||||||
\(541\) | −7.71991 | −0.331905 | −0.165952 | − | 0.986134i | \(-0.553070\pi\) | ||||
−0.165952 | + | 0.986134i | \(0.553070\pi\) | |||||||
\(542\) | 10.7632 | 0.462320 | ||||||||
\(543\) | 13.8422 | 0.594025 | ||||||||
\(544\) | −4.48677 | −0.192369 | ||||||||
\(545\) | −2.84280 | −0.121772 | ||||||||
\(546\) | 17.5468 | 0.750934 | ||||||||
\(547\) | 29.0251 | 1.24102 | 0.620512 | − | 0.784197i | \(-0.286925\pi\) | ||||
0.620512 | + | 0.784197i | \(0.286925\pi\) | |||||||
\(548\) | −15.9745 | −0.682395 | ||||||||
\(549\) | 13.8447 | 0.590878 | ||||||||
\(550\) | −18.3830 | −0.783854 | ||||||||
\(551\) | −10.6929 | −0.455534 | ||||||||
\(552\) | 7.48453 | 0.318563 | ||||||||
\(553\) | 6.81287 | 0.289713 | ||||||||
\(554\) | −1.48199 | −0.0629639 | ||||||||
\(555\) | 1.35346 | 0.0574511 | ||||||||
\(556\) | −15.9939 | −0.678291 | ||||||||
\(557\) | −14.3046 | −0.606105 | −0.303053 | − | 0.952974i | \(-0.598006\pi\) | ||||
−0.303053 | + | 0.952974i | \(0.598006\pi\) | |||||||
\(558\) | 1.83716 | 0.0777730 | ||||||||
\(559\) | −40.1780 | −1.69935 | ||||||||
\(560\) | −1.07336 | −0.0453577 | ||||||||
\(561\) | 20.4497 | 0.863386 | ||||||||
\(562\) | −18.5237 | −0.781374 | ||||||||
\(563\) | 15.2574 | 0.643022 | 0.321511 | − | 0.946906i | \(-0.395809\pi\) | ||||
0.321511 | + | 0.946906i | \(0.395809\pi\) | |||||||
\(564\) | −14.5898 | −0.614343 | ||||||||
\(565\) | −4.06048 | −0.170826 | ||||||||
\(566\) | 7.04766 | 0.296235 | ||||||||
\(567\) | −9.70586 | −0.407608 | ||||||||
\(568\) | −5.36999 | −0.225320 | ||||||||
\(569\) | −28.0678 | −1.17666 | −0.588332 | − | 0.808619i | \(-0.700215\pi\) | ||||
−0.588332 | + | 0.808619i | \(0.700215\pi\) | |||||||
\(570\) | 0.461215 | 0.0193182 | ||||||||
\(571\) | 8.96499 | 0.375173 | 0.187587 | − | 0.982248i | \(-0.439933\pi\) | ||||
0.187587 | + | 0.982248i | \(0.439933\pi\) | |||||||
\(572\) | −12.3382 | −0.515887 | ||||||||
\(573\) | −10.3362 | −0.431800 | ||||||||
\(574\) | −4.43260 | −0.185013 | ||||||||
\(575\) | −30.1876 | −1.25891 | ||||||||
\(576\) | −1.50087 | −0.0625362 | ||||||||
\(577\) | 12.2395 | 0.509539 | 0.254769 | − | 0.967002i | \(-0.418000\pi\) | ||||
0.254769 | + | 0.967002i | \(0.418000\pi\) | |||||||
\(578\) | −3.13111 | −0.130237 | ||||||||
\(579\) | −5.43945 | −0.226056 | ||||||||
\(580\) | −1.74939 | −0.0726396 | ||||||||
\(581\) | −8.47894 | −0.351766 | ||||||||
\(582\) | −2.11805 | −0.0877962 | ||||||||
\(583\) | 30.6094 | 1.26771 | ||||||||
\(584\) | 0.386914 | 0.0160106 | ||||||||
\(585\) | 1.23495 | 0.0510590 | ||||||||
\(586\) | −24.4395 | −1.00959 | ||||||||
\(587\) | 24.7196 | 1.02029 | 0.510144 | − | 0.860089i | \(-0.329592\pi\) | ||||
0.510144 | + | 0.860089i | \(0.329592\pi\) | |||||||
\(588\) | −14.3187 | −0.590495 | ||||||||
\(589\) | −1.85738 | −0.0765318 | ||||||||
\(590\) | 1.29434 | 0.0532873 | ||||||||
\(591\) | −8.19278 | −0.337006 | ||||||||
\(592\) | 4.45284 | 0.183011 | ||||||||
\(593\) | −40.4198 | −1.65984 | −0.829922 | − | 0.557880i | \(-0.811615\pi\) | ||||
−0.829922 | + | 0.557880i | \(0.811615\pi\) | |||||||
\(594\) | 20.5139 | 0.841697 | ||||||||
\(595\) | −4.81592 | −0.197433 | ||||||||
\(596\) | −22.3966 | −0.917399 | ||||||||
\(597\) | 15.1298 | 0.619221 | ||||||||
\(598\) | −20.2612 | −0.828541 | ||||||||
\(599\) | −15.4101 | −0.629639 | −0.314819 | − | 0.949152i | \(-0.601944\pi\) | ||||
−0.314819 | + | 0.949152i | \(0.601944\pi\) | |||||||
\(600\) | −6.04650 | −0.246847 | ||||||||
\(601\) | −22.2557 | −0.907830 | −0.453915 | − | 0.891045i | \(-0.649973\pi\) | ||||
−0.453915 | + | 0.891045i | \(0.649973\pi\) | |||||||
\(602\) | 52.4114 | 2.13613 | ||||||||
\(603\) | 13.1603 | 0.535928 | ||||||||
\(604\) | 19.1383 | 0.778727 | ||||||||
\(605\) | −0.709218 | −0.0288338 | ||||||||
\(606\) | 20.1675 | 0.819247 | ||||||||
\(607\) | −13.2148 | −0.536370 | −0.268185 | − | 0.963367i | \(-0.586424\pi\) | ||||
−0.268185 | + | 0.963367i | \(0.586424\pi\) | |||||||
\(608\) | 1.51739 | 0.0615381 | ||||||||
\(609\) | −37.3059 | −1.51171 | ||||||||
\(610\) | −2.28996 | −0.0927179 | ||||||||
\(611\) | 39.4958 | 1.59783 | ||||||||
\(612\) | −6.73405 | −0.272208 | ||||||||
\(613\) | 19.7996 | 0.799700 | 0.399850 | − | 0.916581i | \(-0.369062\pi\) | ||||
0.399850 | + | 0.916581i | \(0.369062\pi\) | |||||||
\(614\) | 13.4958 | 0.544646 | ||||||||
\(615\) | 0.311608 | 0.0125652 | ||||||||
\(616\) | 16.0950 | 0.648486 | ||||||||
\(617\) | −11.9802 | −0.482304 | −0.241152 | − | 0.970487i | \(-0.577525\pi\) | ||||
−0.241152 | + | 0.970487i | \(0.577525\pi\) | |||||||
\(618\) | 16.3695 | 0.658476 | ||||||||
\(619\) | 49.0668 | 1.97216 | 0.986081 | − | 0.166268i | \(-0.0531718\pi\) | ||||
0.986081 | + | 0.166268i | \(0.0531718\pi\) | |||||||
\(620\) | −0.303872 | −0.0122038 | ||||||||
\(621\) | 33.6869 | 1.35181 | ||||||||
\(622\) | 14.1036 | 0.565501 | ||||||||
\(623\) | 1.19414 | 0.0478422 | ||||||||
\(624\) | −4.05826 | −0.162461 | ||||||||
\(625\) | 24.0794 | 0.963175 | ||||||||
\(626\) | −17.1577 | −0.685761 | ||||||||
\(627\) | −6.91590 | −0.276195 | ||||||||
\(628\) | −23.6945 | −0.945512 | ||||||||
\(629\) | 19.9789 | 0.796611 | ||||||||
\(630\) | −1.61097 | −0.0641826 | ||||||||
\(631\) | 3.11727 | 0.124097 | 0.0620484 | − | 0.998073i | \(-0.480237\pi\) | ||||
0.0620484 | + | 0.998073i | \(0.480237\pi\) | |||||||
\(632\) | −1.57570 | −0.0626778 | ||||||||
\(633\) | −12.5966 | −0.500671 | ||||||||
\(634\) | 5.02832 | 0.199700 | ||||||||
\(635\) | −3.72577 | −0.147853 | ||||||||
\(636\) | 10.0680 | 0.399221 | ||||||||
\(637\) | 38.7619 | 1.53580 | ||||||||
\(638\) | 26.2321 | 1.03854 | ||||||||
\(639\) | −8.05964 | −0.318835 | ||||||||
\(640\) | 0.248249 | 0.00981290 | ||||||||
\(641\) | 3.41858 | 0.135026 | 0.0675128 | − | 0.997718i | \(-0.478494\pi\) | ||||
0.0675128 | + | 0.997718i | \(0.478494\pi\) | |||||||
\(642\) | −14.2635 | −0.562935 | ||||||||
\(643\) | 25.2786 | 0.996890 | 0.498445 | − | 0.866921i | \(-0.333905\pi\) | ||||
0.498445 | + | 0.866921i | \(0.333905\pi\) | |||||||
\(644\) | 26.4303 | 1.04150 | ||||||||
\(645\) | −3.68447 | −0.145076 | ||||||||
\(646\) | 6.80816 | 0.267864 | ||||||||
\(647\) | 10.2230 | 0.401910 | 0.200955 | − | 0.979601i | \(-0.435596\pi\) | ||||
0.200955 | + | 0.979601i | \(0.435596\pi\) | |||||||
\(648\) | 2.24479 | 0.0881838 | ||||||||
\(649\) | −19.4086 | −0.761855 | ||||||||
\(650\) | 16.3683 | 0.642018 | ||||||||
\(651\) | −6.48010 | −0.253975 | ||||||||
\(652\) | −0.879204 | −0.0344323 | ||||||||
\(653\) | 45.8179 | 1.79299 | 0.896497 | − | 0.443049i | \(-0.146103\pi\) | ||||
0.896497 | + | 0.443049i | \(0.146103\pi\) | |||||||
\(654\) | 14.0210 | 0.548264 | ||||||||
\(655\) | −1.45561 | −0.0568755 | ||||||||
\(656\) | 1.02518 | 0.0400266 | ||||||||
\(657\) | 0.580707 | 0.0226555 | ||||||||
\(658\) | −51.5215 | −2.00852 | ||||||||
\(659\) | 17.5979 | 0.685519 | 0.342759 | − | 0.939423i | \(-0.388638\pi\) | ||||
0.342759 | + | 0.939423i | \(0.388638\pi\) | |||||||
\(660\) | −1.13146 | −0.0440421 | ||||||||
\(661\) | −40.7498 | −1.58498 | −0.792492 | − | 0.609882i | \(-0.791217\pi\) | ||||
−0.792492 | + | 0.609882i | \(0.791217\pi\) | |||||||
\(662\) | 10.9441 | 0.425355 | ||||||||
\(663\) | −18.2085 | −0.707159 | ||||||||
\(664\) | 1.96103 | 0.0761026 | ||||||||
\(665\) | 1.62870 | 0.0631583 | ||||||||
\(666\) | 6.68313 | 0.258966 | ||||||||
\(667\) | 43.0769 | 1.66795 | ||||||||
\(668\) | −11.6716 | −0.451588 | ||||||||
\(669\) | −13.7586 | −0.531937 | ||||||||
\(670\) | −2.17676 | −0.0840955 | ||||||||
\(671\) | 34.3379 | 1.32560 | ||||||||
\(672\) | 5.29393 | 0.204218 | ||||||||
\(673\) | 49.5901 | 1.91156 | 0.955778 | − | 0.294088i | \(-0.0950158\pi\) | ||||
0.955778 | + | 0.294088i | \(0.0950158\pi\) | |||||||
\(674\) | −8.73457 | −0.336443 | ||||||||
\(675\) | −27.2145 | −1.04749 | ||||||||
\(676\) | −2.01398 | −0.0774607 | ||||||||
\(677\) | −11.7471 | −0.451479 | −0.225740 | − | 0.974188i | \(-0.572480\pi\) | ||||
−0.225740 | + | 0.974188i | \(0.572480\pi\) | |||||||
\(678\) | 20.0267 | 0.769121 | ||||||||
\(679\) | −7.47954 | −0.287038 | ||||||||
\(680\) | 1.11384 | 0.0427137 | ||||||||
\(681\) | 7.15447 | 0.274160 | ||||||||
\(682\) | 4.55655 | 0.174479 | ||||||||
\(683\) | 8.28016 | 0.316831 | 0.158416 | − | 0.987373i | \(-0.449361\pi\) | ||||
0.158416 | + | 0.987373i | \(0.449361\pi\) | |||||||
\(684\) | 2.27740 | 0.0870784 | ||||||||
\(685\) | 3.96564 | 0.151519 | ||||||||
\(686\) | −20.2981 | −0.774984 | ||||||||
\(687\) | −29.8467 | −1.13872 | ||||||||
\(688\) | −12.1218 | −0.462140 | ||||||||
\(689\) | −27.2547 | −1.03832 | ||||||||
\(690\) | −1.85803 | −0.0707339 | ||||||||
\(691\) | 18.3635 | 0.698580 | 0.349290 | − | 0.937015i | \(-0.386423\pi\) | ||||
0.349290 | + | 0.937015i | \(0.386423\pi\) | |||||||
\(692\) | 7.76573 | 0.295209 | ||||||||
\(693\) | 24.1564 | 0.917628 | ||||||||
\(694\) | −29.6761 | −1.12649 | ||||||||
\(695\) | 3.97046 | 0.150608 | ||||||||
\(696\) | 8.62820 | 0.327051 | ||||||||
\(697\) | 4.59976 | 0.174228 | ||||||||
\(698\) | −1.27149 | −0.0481264 | ||||||||
\(699\) | 0.805947 | 0.0304837 | ||||||||
\(700\) | −21.3522 | −0.807036 | ||||||||
\(701\) | 39.5504 | 1.49380 | 0.746899 | − | 0.664938i | \(-0.231542\pi\) | ||||
0.746899 | + | 0.664938i | \(0.231542\pi\) | |||||||
\(702\) | −18.2657 | −0.689395 | ||||||||
\(703\) | −6.75668 | −0.254833 | ||||||||
\(704\) | −3.72248 | −0.140296 | ||||||||
\(705\) | 3.62191 | 0.136409 | ||||||||
\(706\) | 9.27511 | 0.349073 | ||||||||
\(707\) | 71.2179 | 2.67842 | ||||||||
\(708\) | −6.38384 | −0.239919 | ||||||||
\(709\) | −46.4479 | −1.74439 | −0.872193 | − | 0.489162i | \(-0.837303\pi\) | ||||
−0.872193 | + | 0.489162i | \(0.837303\pi\) | |||||||
\(710\) | 1.33309 | 0.0500301 | ||||||||
\(711\) | −2.36491 | −0.0886911 | ||||||||
\(712\) | −0.276183 | −0.0103504 | ||||||||
\(713\) | 7.48253 | 0.280223 | ||||||||
\(714\) | 23.7526 | 0.888920 | ||||||||
\(715\) | 3.06295 | 0.114548 | ||||||||
\(716\) | 17.2220 | 0.643616 | ||||||||
\(717\) | −25.2245 | −0.942026 | ||||||||
\(718\) | −17.0690 | −0.637009 | ||||||||
\(719\) | 7.80352 | 0.291022 | 0.145511 | − | 0.989357i | \(-0.453517\pi\) | ||||
0.145511 | + | 0.989357i | \(0.453517\pi\) | |||||||
\(720\) | 0.372589 | 0.0138856 | ||||||||
\(721\) | 57.8059 | 2.15280 | ||||||||
\(722\) | 16.6975 | 0.621418 | ||||||||
\(723\) | 12.8509 | 0.477930 | ||||||||
\(724\) | −11.3054 | −0.420161 | ||||||||
\(725\) | −34.8004 | −1.29245 | ||||||||
\(726\) | 3.49794 | 0.129821 | ||||||||
\(727\) | −33.7186 | −1.25055 | −0.625277 | − | 0.780403i | \(-0.715014\pi\) | ||||
−0.625277 | + | 0.780403i | \(0.715014\pi\) | |||||||
\(728\) | −14.3311 | −0.531144 | ||||||||
\(729\) | 23.6113 | 0.874494 | ||||||||
\(730\) | −0.0960510 | −0.00355501 | ||||||||
\(731\) | −54.3879 | −2.01161 | ||||||||
\(732\) | 11.2943 | 0.417451 | ||||||||
\(733\) | 3.09009 | 0.114135 | 0.0570675 | − | 0.998370i | \(-0.481825\pi\) | ||||
0.0570675 | + | 0.998370i | \(0.481825\pi\) | |||||||
\(734\) | −8.70871 | −0.321444 | ||||||||
\(735\) | 3.55461 | 0.131114 | ||||||||
\(736\) | −6.11286 | −0.225323 | ||||||||
\(737\) | 32.6404 | 1.20233 | ||||||||
\(738\) | 1.53866 | 0.0566390 | ||||||||
\(739\) | 24.3931 | 0.897313 | 0.448657 | − | 0.893704i | \(-0.351903\pi\) | ||||
0.448657 | + | 0.893704i | \(0.351903\pi\) | |||||||
\(740\) | −1.10541 | −0.0406358 | ||||||||
\(741\) | 6.15795 | 0.226218 | ||||||||
\(742\) | 35.5533 | 1.30520 | ||||||||
\(743\) | −9.21427 | −0.338039 | −0.169019 | − | 0.985613i | \(-0.554060\pi\) | ||||
−0.169019 | + | 0.985613i | \(0.554060\pi\) | |||||||
\(744\) | 1.49873 | 0.0549461 | ||||||||
\(745\) | 5.55993 | 0.203700 | ||||||||
\(746\) | −24.9428 | −0.913222 | ||||||||
\(747\) | 2.94324 | 0.107688 | ||||||||
\(748\) | −16.7019 | −0.610683 | ||||||||
\(749\) | −50.3690 | −1.84044 | ||||||||
\(750\) | 3.02080 | 0.110304 | ||||||||
\(751\) | 42.6684 | 1.55699 | 0.778496 | − | 0.627650i | \(-0.215983\pi\) | ||||
0.778496 | + | 0.627650i | \(0.215983\pi\) | |||||||
\(752\) | 11.9160 | 0.434532 | ||||||||
\(753\) | 33.9626 | 1.23767 | ||||||||
\(754\) | −23.3572 | −0.850618 | ||||||||
\(755\) | −4.75106 | −0.172909 | ||||||||
\(756\) | 23.8273 | 0.866589 | ||||||||
\(757\) | 24.8955 | 0.904843 | 0.452422 | − | 0.891804i | \(-0.350560\pi\) | ||||
0.452422 | + | 0.891804i | \(0.350560\pi\) | |||||||
\(758\) | 23.6900 | 0.860459 | ||||||||
\(759\) | 27.8610 | 1.01129 | ||||||||
\(760\) | −0.376690 | −0.0136640 | ||||||||
\(761\) | −0.296409 | −0.0107448 | −0.00537242 | − | 0.999986i | \(-0.501710\pi\) | ||||
−0.00537242 | + | 0.999986i | \(0.501710\pi\) | |||||||
\(762\) | 18.3759 | 0.665689 | ||||||||
\(763\) | 49.5127 | 1.79248 | ||||||||
\(764\) | 8.44189 | 0.305417 | ||||||||
\(765\) | 1.67172 | 0.0604412 | ||||||||
\(766\) | 4.57618 | 0.165344 | ||||||||
\(767\) | 17.2815 | 0.624000 | ||||||||
\(768\) | −1.22439 | −0.0441814 | ||||||||
\(769\) | 38.0258 | 1.37124 | 0.685622 | − | 0.727958i | \(-0.259530\pi\) | ||||
0.685622 | + | 0.727958i | \(0.259530\pi\) | |||||||
\(770\) | −3.99556 | −0.143990 | ||||||||
\(771\) | 24.1440 | 0.869523 | ||||||||
\(772\) | 4.44258 | 0.159892 | ||||||||
\(773\) | −34.7634 | −1.25035 | −0.625177 | − | 0.780483i | \(-0.714973\pi\) | ||||
−0.625177 | + | 0.780483i | \(0.714973\pi\) | |||||||
\(774\) | −18.1933 | −0.653943 | ||||||||
\(775\) | −6.04488 | −0.217138 | ||||||||
\(776\) | 1.72988 | 0.0620992 | ||||||||
\(777\) | −23.5730 | −0.845678 | ||||||||
\(778\) | −0.0324068 | −0.00116184 | ||||||||
\(779\) | −1.55560 | −0.0557351 | ||||||||
\(780\) | 1.00746 | 0.0360728 | ||||||||
\(781\) | −19.9897 | −0.715287 | ||||||||
\(782\) | −27.4270 | −0.980788 | ||||||||
\(783\) | 38.8344 | 1.38783 | ||||||||
\(784\) | 11.6946 | 0.417664 | ||||||||
\(785\) | 5.88212 | 0.209942 | ||||||||
\(786\) | 7.17924 | 0.256075 | ||||||||
\(787\) | 6.82652 | 0.243339 | 0.121670 | − | 0.992571i | \(-0.461175\pi\) | ||||
0.121670 | + | 0.992571i | \(0.461175\pi\) | |||||||
\(788\) | 6.69132 | 0.238368 | ||||||||
\(789\) | 26.8824 | 0.957040 | ||||||||
\(790\) | 0.391165 | 0.0139170 | ||||||||
\(791\) | 70.7208 | 2.51454 | ||||||||
\(792\) | −5.58695 | −0.198524 | ||||||||
\(793\) | −30.5746 | −1.08574 | ||||||||
\(794\) | 2.85169 | 0.101203 | ||||||||
\(795\) | −2.49936 | −0.0886432 | ||||||||
\(796\) | −12.3570 | −0.437982 | ||||||||
\(797\) | 21.5899 | 0.764754 | 0.382377 | − | 0.924006i | \(-0.375106\pi\) | ||||
0.382377 | + | 0.924006i | \(0.375106\pi\) | |||||||
\(798\) | −8.03293 | −0.284363 | ||||||||
\(799\) | 53.4644 | 1.89143 | ||||||||
\(800\) | 4.93837 | 0.174598 | ||||||||
\(801\) | −0.414515 | −0.0146462 | ||||||||
\(802\) | −17.5491 | −0.619681 | ||||||||
\(803\) | 1.44028 | 0.0508264 | ||||||||
\(804\) | 10.7360 | 0.378630 | ||||||||
\(805\) | −6.56130 | −0.231255 | ||||||||
\(806\) | −4.05718 | −0.142908 | ||||||||
\(807\) | −28.0274 | −0.986612 | ||||||||
\(808\) | −16.4714 | −0.579463 | ||||||||
\(809\) | −29.9123 | −1.05166 | −0.525830 | − | 0.850590i | \(-0.676245\pi\) | ||||
−0.525830 | + | 0.850590i | \(0.676245\pi\) | |||||||
\(810\) | −0.557268 | −0.0195804 | ||||||||
\(811\) | −28.7896 | −1.01094 | −0.505470 | − | 0.862844i | \(-0.668681\pi\) | ||||
−0.505470 | + | 0.862844i | \(0.668681\pi\) | |||||||
\(812\) | 30.4690 | 1.06925 | ||||||||
\(813\) | 13.1784 | 0.462187 | ||||||||
\(814\) | 16.5756 | 0.580976 | ||||||||
\(815\) | 0.218262 | 0.00764537 | ||||||||
\(816\) | −5.49356 | −0.192313 | ||||||||
\(817\) | 18.3935 | 0.643507 | ||||||||
\(818\) | 2.30656 | 0.0806469 | ||||||||
\(819\) | −21.5090 | −0.751586 | ||||||||
\(820\) | −0.254500 | −0.00888754 | ||||||||
\(821\) | −22.8651 | −0.797997 | −0.398999 | − | 0.916952i | \(-0.630642\pi\) | ||||
−0.398999 | + | 0.916952i | \(0.630642\pi\) | |||||||
\(822\) | −19.5590 | −0.682198 | ||||||||
\(823\) | −6.57694 | −0.229258 | −0.114629 | − | 0.993408i | \(-0.536568\pi\) | ||||
−0.114629 | + | 0.993408i | \(0.536568\pi\) | |||||||
\(824\) | −13.3695 | −0.465748 | ||||||||
\(825\) | −22.5080 | −0.783627 | ||||||||
\(826\) | −22.5434 | −0.784386 | ||||||||
\(827\) | −25.3271 | −0.880708 | −0.440354 | − | 0.897824i | \(-0.645147\pi\) | ||||
−0.440354 | + | 0.897824i | \(0.645147\pi\) | |||||||
\(828\) | −9.17460 | −0.318839 | ||||||||
\(829\) | −33.7966 | −1.17380 | −0.586901 | − | 0.809658i | \(-0.699652\pi\) | ||||
−0.586901 | + | 0.809658i | \(0.699652\pi\) | |||||||
\(830\) | −0.486823 | −0.0168979 | ||||||||
\(831\) | −1.81454 | −0.0629457 | ||||||||
\(832\) | 3.31452 | 0.114910 | ||||||||
\(833\) | 52.4709 | 1.81801 | ||||||||
\(834\) | −19.5827 | −0.678095 | ||||||||
\(835\) | 2.89747 | 0.100271 | ||||||||
\(836\) | 5.64844 | 0.195356 | ||||||||
\(837\) | 6.74559 | 0.233162 | ||||||||
\(838\) | −11.6974 | −0.404082 | ||||||||
\(839\) | 33.5138 | 1.15703 | 0.578513 | − | 0.815673i | \(-0.303633\pi\) | ||||
0.578513 | + | 0.815673i | \(0.303633\pi\) | |||||||
\(840\) | −1.31421 | −0.0453446 | ||||||||
\(841\) | 20.6593 | 0.712388 | ||||||||
\(842\) | 0.852363 | 0.0293744 | ||||||||
\(843\) | −22.6802 | −0.781148 | ||||||||
\(844\) | 10.2881 | 0.354131 | ||||||||
\(845\) | 0.499968 | 0.0171994 | ||||||||
\(846\) | 17.8843 | 0.614876 | ||||||||
\(847\) | 12.3524 | 0.424432 | ||||||||
\(848\) | −8.22284 | −0.282373 | ||||||||
\(849\) | 8.62909 | 0.296150 | ||||||||
\(850\) | 22.1573 | 0.759991 | ||||||||
\(851\) | 27.2196 | 0.933077 | ||||||||
\(852\) | −6.57496 | −0.225255 | ||||||||
\(853\) | −20.5431 | −0.703382 | −0.351691 | − | 0.936116i | \(-0.614393\pi\) | ||||
−0.351691 | + | 0.936116i | \(0.614393\pi\) | |||||||
\(854\) | 39.8840 | 1.36480 | ||||||||
\(855\) | −0.565361 | −0.0193349 | ||||||||
\(856\) | 11.6495 | 0.398170 | ||||||||
\(857\) | 1.77537 | 0.0606453 | 0.0303227 | − | 0.999540i | \(-0.490347\pi\) | ||||
0.0303227 | + | 0.999540i | \(0.490347\pi\) | |||||||
\(858\) | −15.1068 | −0.515738 | ||||||||
\(859\) | 25.5058 | 0.870245 | 0.435123 | − | 0.900371i | \(-0.356705\pi\) | ||||
0.435123 | + | 0.900371i | \(0.356705\pi\) | |||||||
\(860\) | 3.00923 | 0.102614 | ||||||||
\(861\) | −5.42724 | −0.184960 | ||||||||
\(862\) | −13.1994 | −0.449574 | ||||||||
\(863\) | −31.4835 | −1.07171 | −0.535856 | − | 0.844309i | \(-0.680011\pi\) | ||||
−0.535856 | + | 0.844309i | \(0.680011\pi\) | |||||||
\(864\) | −5.51082 | −0.187482 | ||||||||
\(865\) | −1.92783 | −0.0655483 | ||||||||
\(866\) | −0.224106 | −0.00761543 | ||||||||
\(867\) | −3.83371 | −0.130199 | ||||||||
\(868\) | 5.29251 | 0.179639 | ||||||||
\(869\) | −5.86550 | −0.198973 | ||||||||
\(870\) | −2.14194 | −0.0726186 | ||||||||
\(871\) | −29.0632 | −0.984768 | ||||||||
\(872\) | −11.4514 | −0.387793 | ||||||||
\(873\) | 2.59633 | 0.0878724 | ||||||||
\(874\) | 9.27557 | 0.313751 | ||||||||
\(875\) | 10.6674 | 0.360626 | ||||||||
\(876\) | 0.473734 | 0.0160060 | ||||||||
\(877\) | −39.1735 | −1.32279 | −0.661397 | − | 0.750036i | \(-0.730036\pi\) | ||||
−0.661397 | + | 0.750036i | \(0.730036\pi\) | |||||||
\(878\) | −0.963307 | −0.0325100 | ||||||||
\(879\) | −29.9235 | −1.00930 | ||||||||
\(880\) | 0.924103 | 0.0311515 | ||||||||
\(881\) | 34.6580 | 1.16766 | 0.583828 | − | 0.811877i | \(-0.301554\pi\) | ||||
0.583828 | + | 0.811877i | \(0.301554\pi\) | |||||||
\(882\) | 17.5520 | 0.591007 | ||||||||
\(883\) | 39.1964 | 1.31906 | 0.659532 | − | 0.751677i | \(-0.270755\pi\) | ||||
0.659532 | + | 0.751677i | \(0.270755\pi\) | |||||||
\(884\) | 14.8715 | 0.500182 | ||||||||
\(885\) | 1.58478 | 0.0532718 | ||||||||
\(886\) | −17.3974 | −0.584477 | ||||||||
\(887\) | 33.3120 | 1.11851 | 0.559253 | − | 0.828997i | \(-0.311088\pi\) | ||||
0.559253 | + | 0.828997i | \(0.311088\pi\) | |||||||
\(888\) | 5.45202 | 0.182958 | ||||||||
\(889\) | 64.8914 | 2.17639 | ||||||||
\(890\) | 0.0685622 | 0.00229821 | ||||||||
\(891\) | 8.35620 | 0.279943 | ||||||||
\(892\) | 11.2371 | 0.376245 | ||||||||
\(893\) | −18.0812 | −0.605064 | ||||||||
\(894\) | −27.4222 | −0.917134 | ||||||||
\(895\) | −4.27534 | −0.142909 | ||||||||
\(896\) | −4.32372 | −0.144445 | ||||||||
\(897\) | −24.8076 | −0.828302 | ||||||||
\(898\) | −26.4577 | −0.882906 | ||||||||
\(899\) | 8.62589 | 0.287689 | ||||||||
\(900\) | 7.41184 | 0.247061 | ||||||||
\(901\) | −36.8940 | −1.22912 | ||||||||
\(902\) | 3.81622 | 0.127066 | ||||||||
\(903\) | 64.1721 | 2.13551 | ||||||||
\(904\) | −16.3565 | −0.544008 | ||||||||
\(905\) | 2.80655 | 0.0932927 | ||||||||
\(906\) | 23.4328 | 0.778501 | ||||||||
\(907\) | 22.4933 | 0.746878 | 0.373439 | − | 0.927655i | \(-0.378178\pi\) | ||||
0.373439 | + | 0.927655i | \(0.378178\pi\) | |||||||
\(908\) | −5.84329 | −0.193916 | ||||||||
\(909\) | −24.7214 | −0.819958 | ||||||||
\(910\) | 3.55767 | 0.117936 | ||||||||
\(911\) | 12.1245 | 0.401701 | 0.200851 | − | 0.979622i | \(-0.435629\pi\) | ||||
0.200851 | + | 0.979622i | \(0.435629\pi\) | |||||||
\(912\) | 1.85787 | 0.0615203 | ||||||||
\(913\) | 7.29989 | 0.241591 | ||||||||
\(914\) | 3.63016 | 0.120075 | ||||||||
\(915\) | −2.80381 | −0.0926911 | ||||||||
\(916\) | 24.3768 | 0.805433 | ||||||||
\(917\) | 25.3523 | 0.837205 | ||||||||
\(918\) | −24.7258 | −0.816073 | ||||||||
\(919\) | 23.0906 | 0.761689 | 0.380845 | − | 0.924639i | \(-0.375633\pi\) | ||||
0.380845 | + | 0.924639i | \(0.375633\pi\) | |||||||
\(920\) | 1.51751 | 0.0500309 | ||||||||
\(921\) | 16.5241 | 0.544489 | ||||||||
\(922\) | −15.7254 | −0.517888 | ||||||||
\(923\) | 17.7989 | 0.585859 | ||||||||
\(924\) | 19.7066 | 0.648298 | ||||||||
\(925\) | −21.9898 | −0.723020 | ||||||||
\(926\) | 23.0730 | 0.758225 | ||||||||
\(927\) | −20.0658 | −0.659048 | ||||||||
\(928\) | −7.04693 | −0.231327 | ||||||||
\(929\) | 38.6985 | 1.26966 | 0.634828 | − | 0.772654i | \(-0.281071\pi\) | ||||
0.634828 | + | 0.772654i | \(0.281071\pi\) | |||||||
\(930\) | −0.372058 | −0.0122003 | ||||||||
\(931\) | −17.7452 | −0.581575 | ||||||||
\(932\) | −0.658244 | −0.0215615 | ||||||||
\(933\) | 17.2683 | 0.565338 | ||||||||
\(934\) | 13.1775 | 0.431180 | ||||||||
\(935\) | 4.14624 | 0.135596 | ||||||||
\(936\) | 4.97465 | 0.162602 | ||||||||
\(937\) | −33.4369 | −1.09233 | −0.546167 | − | 0.837676i | \(-0.683914\pi\) | ||||
−0.546167 | + | 0.837676i | \(0.683914\pi\) | |||||||
\(938\) | 37.9124 | 1.23788 | ||||||||
\(939\) | −21.0078 | −0.685562 | ||||||||
\(940\) | −2.95814 | −0.0964837 | ||||||||
\(941\) | −1.60120 | −0.0521977 | −0.0260988 | − | 0.999659i | \(-0.508308\pi\) | ||||
−0.0260988 | + | 0.999659i | \(0.508308\pi\) | |||||||
\(942\) | −29.0113 | −0.945238 | ||||||||
\(943\) | 6.26680 | 0.204075 | ||||||||
\(944\) | 5.21389 | 0.169698 | ||||||||
\(945\) | −5.91509 | −0.192418 | ||||||||
\(946\) | −45.1233 | −1.46709 | ||||||||
\(947\) | −22.7702 | −0.739932 | −0.369966 | − | 0.929045i | \(-0.620631\pi\) | ||||
−0.369966 | + | 0.929045i | \(0.620631\pi\) | |||||||
\(948\) | −1.92927 | −0.0626597 | ||||||||
\(949\) | −1.28243 | −0.0416295 | ||||||||
\(950\) | −7.49342 | −0.243119 | ||||||||
\(951\) | 6.15663 | 0.199642 | ||||||||
\(952\) | −19.3996 | −0.628743 | ||||||||
\(953\) | −33.6497 | −1.09002 | −0.545011 | − | 0.838429i | \(-0.683475\pi\) | ||||
−0.545011 | + | 0.838429i | \(0.683475\pi\) | |||||||
\(954\) | −12.3414 | −0.399567 | ||||||||
\(955\) | −2.09569 | −0.0678150 | ||||||||
\(956\) | 20.6017 | 0.666305 | ||||||||
\(957\) | 32.1183 | 1.03824 | ||||||||
\(958\) | −6.21942 | −0.200940 | ||||||||
\(959\) | −69.0692 | −2.23036 | ||||||||
\(960\) | 0.303954 | 0.00981006 | ||||||||
\(961\) | −29.5017 | −0.951667 | ||||||||
\(962\) | −14.7590 | −0.475850 | ||||||||
\(963\) | 17.4843 | 0.563423 | ||||||||
\(964\) | −10.4957 | −0.338045 | ||||||||
\(965\) | −1.10287 | −0.0355025 | ||||||||
\(966\) | 32.3610 | 1.04120 | ||||||||
\(967\) | 22.0176 | 0.708037 | 0.354019 | − | 0.935238i | \(-0.384815\pi\) | ||||
0.354019 | + | 0.935238i | \(0.384815\pi\) | |||||||
\(968\) | −2.85688 | −0.0918236 | ||||||||
\(969\) | 8.33585 | 0.267786 | ||||||||
\(970\) | −0.429442 | −0.0137886 | ||||||||
\(971\) | 44.6273 | 1.43216 | 0.716079 | − | 0.698019i | \(-0.245935\pi\) | ||||
0.716079 | + | 0.698019i | \(0.245935\pi\) | |||||||
\(972\) | −13.7840 | −0.442121 | ||||||||
\(973\) | −69.1530 | −2.21694 | ||||||||
\(974\) | −9.26111 | −0.296745 | ||||||||
\(975\) | 20.0412 | 0.641833 | ||||||||
\(976\) | −9.22447 | −0.295268 | ||||||||
\(977\) | 27.5899 | 0.882678 | 0.441339 | − | 0.897340i | \(-0.354504\pi\) | ||||
0.441339 | + | 0.897340i | \(0.354504\pi\) | |||||||
\(978\) | −1.07649 | −0.0344223 | ||||||||
\(979\) | −1.02809 | −0.0328578 | ||||||||
\(980\) | −2.90317 | −0.0927383 | ||||||||
\(981\) | −17.1870 | −0.548740 | ||||||||
\(982\) | −39.7962 | −1.26995 | ||||||||
\(983\) | 7.57649 | 0.241652 | 0.120826 | − | 0.992674i | \(-0.461446\pi\) | ||||
0.120826 | + | 0.992674i | \(0.461446\pi\) | |||||||
\(984\) | 1.25522 | 0.0400151 | ||||||||
\(985\) | −1.66111 | −0.0529274 | ||||||||
\(986\) | −31.6180 | −1.00692 | ||||||||
\(987\) | −63.0824 | −2.00794 | ||||||||
\(988\) | −5.02940 | −0.160007 | ||||||||
\(989\) | −74.0991 | −2.35621 | ||||||||
\(990\) | 1.38696 | 0.0440803 | ||||||||
\(991\) | 31.2023 | 0.991174 | 0.495587 | − | 0.868558i | \(-0.334953\pi\) | ||||
0.495587 | + | 0.868558i | \(0.334953\pi\) | |||||||
\(992\) | −1.22406 | −0.0388640 | ||||||||
\(993\) | 13.3999 | 0.425232 | ||||||||
\(994\) | −23.2183 | −0.736441 | ||||||||
\(995\) | 3.06761 | 0.0972497 | ||||||||
\(996\) | 2.40106 | 0.0760806 | ||||||||
\(997\) | −5.73538 | −0.181641 | −0.0908207 | − | 0.995867i | \(-0.528949\pi\) | ||||
−0.0908207 | + | 0.995867i | \(0.528949\pi\) | |||||||
\(998\) | 6.82565 | 0.216062 | ||||||||
\(999\) | 24.5388 | 0.776374 |
(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 | 8002.2.a.e.1.25 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.e.1.25 | ✓ | 77 | 1.1 | even | 1 | trivial |