Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8018,2,Mod(1,8018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8018, 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("8018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8018 = 2 \cdot 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8018.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: | \(64.0240523407\) |
Analytic rank: | \(0\) |
Dimension: | \(47\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
Character | \(\chi\) | \(=\) | 8018.1 |
$q$-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 | ||||||||
\(3\) | 0.295377 | 0.170536 | 0.0852681 | − | 0.996358i | \(-0.472825\pi\) | ||||
0.0852681 | + | 0.996358i | \(0.472825\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.172140 | 0.0769835 | 0.0384918 | − | 0.999259i | \(-0.487745\pi\) | ||||
0.0384918 | + | 0.999259i | \(0.487745\pi\) | |||||||
\(6\) | 0.295377 | 0.120587 | ||||||||
\(7\) | −3.30669 | −1.24981 | −0.624905 | − | 0.780700i | \(-0.714862\pi\) | ||||
−0.624905 | + | 0.780700i | \(0.714862\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.91275 | −0.970917 | ||||||||
\(10\) | 0.172140 | 0.0544356 | ||||||||
\(11\) | −2.45188 | −0.739269 | −0.369635 | − | 0.929177i | \(-0.620517\pi\) | ||||
−0.369635 | + | 0.929177i | \(0.620517\pi\) | |||||||
\(12\) | 0.295377 | 0.0852681 | ||||||||
\(13\) | −2.40163 | −0.666093 | −0.333046 | − | 0.942910i | \(-0.608077\pi\) | ||||
−0.333046 | + | 0.942910i | \(0.608077\pi\) | |||||||
\(14\) | −3.30669 | −0.883750 | ||||||||
\(15\) | 0.0508464 | 0.0131285 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.737190 | −0.178795 | −0.0893975 | − | 0.995996i | \(-0.528494\pi\) | ||||
−0.0893975 | + | 0.995996i | \(0.528494\pi\) | |||||||
\(18\) | −2.91275 | −0.686542 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0.172140 | 0.0384918 | ||||||||
\(21\) | −0.976721 | −0.213138 | ||||||||
\(22\) | −2.45188 | −0.522742 | ||||||||
\(23\) | −1.13177 | −0.235990 | −0.117995 | − | 0.993014i | \(-0.537647\pi\) | ||||
−0.117995 | + | 0.993014i | \(0.537647\pi\) | |||||||
\(24\) | 0.295377 | 0.0602937 | ||||||||
\(25\) | −4.97037 | −0.994074 | ||||||||
\(26\) | −2.40163 | −0.470999 | ||||||||
\(27\) | −1.74649 | −0.336113 | ||||||||
\(28\) | −3.30669 | −0.624905 | ||||||||
\(29\) | 3.37680 | 0.627056 | 0.313528 | − | 0.949579i | \(-0.398489\pi\) | ||||
0.313528 | + | 0.949579i | \(0.398489\pi\) | |||||||
\(30\) | 0.0508464 | 0.00928324 | ||||||||
\(31\) | 2.23204 | 0.400887 | 0.200444 | − | 0.979705i | \(-0.435762\pi\) | ||||
0.200444 | + | 0.979705i | \(0.435762\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.724229 | −0.126072 | ||||||||
\(34\) | −0.737190 | −0.126427 | ||||||||
\(35\) | −0.569215 | −0.0962149 | ||||||||
\(36\) | −2.91275 | −0.485459 | ||||||||
\(37\) | 8.49904 | 1.39723 | 0.698617 | − | 0.715496i | \(-0.253799\pi\) | ||||
0.698617 | + | 0.715496i | \(0.253799\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −0.709388 | −0.113593 | ||||||||
\(40\) | 0.172140 | 0.0272178 | ||||||||
\(41\) | 8.47459 | 1.32351 | 0.661754 | − | 0.749721i | \(-0.269812\pi\) | ||||
0.661754 | + | 0.749721i | \(0.269812\pi\) | |||||||
\(42\) | −0.976721 | −0.150711 | ||||||||
\(43\) | −10.7373 | −1.63742 | −0.818710 | − | 0.574207i | \(-0.805310\pi\) | ||||
−0.818710 | + | 0.574207i | \(0.805310\pi\) | |||||||
\(44\) | −2.45188 | −0.369635 | ||||||||
\(45\) | −0.501402 | −0.0747446 | ||||||||
\(46\) | −1.13177 | −0.166870 | ||||||||
\(47\) | 10.8454 | 1.58197 | 0.790985 | − | 0.611836i | \(-0.209569\pi\) | ||||
0.790985 | + | 0.611836i | \(0.209569\pi\) | |||||||
\(48\) | 0.295377 | 0.0426341 | ||||||||
\(49\) | 3.93419 | 0.562027 | ||||||||
\(50\) | −4.97037 | −0.702916 | ||||||||
\(51\) | −0.217749 | −0.0304910 | ||||||||
\(52\) | −2.40163 | −0.333046 | ||||||||
\(53\) | 11.0578 | 1.51891 | 0.759453 | − | 0.650562i | \(-0.225467\pi\) | ||||
0.759453 | + | 0.650562i | \(0.225467\pi\) | |||||||
\(54\) | −1.74649 | −0.237668 | ||||||||
\(55\) | −0.422067 | −0.0569115 | ||||||||
\(56\) | −3.30669 | −0.441875 | ||||||||
\(57\) | −0.295377 | −0.0391237 | ||||||||
\(58\) | 3.37680 | 0.443395 | ||||||||
\(59\) | −2.36963 | −0.308499 | −0.154249 | − | 0.988032i | \(-0.549296\pi\) | ||||
−0.154249 | + | 0.988032i | \(0.549296\pi\) | |||||||
\(60\) | 0.0508464 | 0.00656424 | ||||||||
\(61\) | 7.18189 | 0.919547 | 0.459774 | − | 0.888036i | \(-0.347931\pi\) | ||||
0.459774 | + | 0.888036i | \(0.347931\pi\) | |||||||
\(62\) | 2.23204 | 0.283470 | ||||||||
\(63\) | 9.63157 | 1.21346 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.413418 | −0.0512782 | ||||||||
\(66\) | −0.724229 | −0.0891465 | ||||||||
\(67\) | −0.726963 | −0.0888127 | −0.0444063 | − | 0.999014i | \(-0.514140\pi\) | ||||
−0.0444063 | + | 0.999014i | \(0.514140\pi\) | |||||||
\(68\) | −0.737190 | −0.0893975 | ||||||||
\(69\) | −0.334298 | −0.0402448 | ||||||||
\(70\) | −0.569215 | −0.0680342 | ||||||||
\(71\) | 10.2530 | 1.21681 | 0.608406 | − | 0.793626i | \(-0.291809\pi\) | ||||
0.608406 | + | 0.793626i | \(0.291809\pi\) | |||||||
\(72\) | −2.91275 | −0.343271 | ||||||||
\(73\) | −3.97307 | −0.465013 | −0.232506 | − | 0.972595i | \(-0.574693\pi\) | ||||
−0.232506 | + | 0.972595i | \(0.574693\pi\) | |||||||
\(74\) | 8.49904 | 0.987994 | ||||||||
\(75\) | −1.46813 | −0.169526 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 8.10760 | 0.923947 | ||||||||
\(78\) | −0.709388 | −0.0803223 | ||||||||
\(79\) | 5.35217 | 0.602167 | 0.301083 | − | 0.953598i | \(-0.402652\pi\) | ||||
0.301083 | + | 0.953598i | \(0.402652\pi\) | |||||||
\(80\) | 0.172140 | 0.0192459 | ||||||||
\(81\) | 8.22238 | 0.913598 | ||||||||
\(82\) | 8.47459 | 0.935862 | ||||||||
\(83\) | 2.06586 | 0.226758 | 0.113379 | − | 0.993552i | \(-0.463833\pi\) | ||||
0.113379 | + | 0.993552i | \(0.463833\pi\) | |||||||
\(84\) | −0.976721 | −0.106569 | ||||||||
\(85\) | −0.126900 | −0.0137643 | ||||||||
\(86\) | −10.7373 | −1.15783 | ||||||||
\(87\) | 0.997430 | 0.106936 | ||||||||
\(88\) | −2.45188 | −0.261371 | ||||||||
\(89\) | 3.34314 | 0.354372 | 0.177186 | − | 0.984177i | \(-0.443301\pi\) | ||||
0.177186 | + | 0.984177i | \(0.443301\pi\) | |||||||
\(90\) | −0.501402 | −0.0528524 | ||||||||
\(91\) | 7.94145 | 0.832490 | ||||||||
\(92\) | −1.13177 | −0.117995 | ||||||||
\(93\) | 0.659296 | 0.0683658 | ||||||||
\(94\) | 10.8454 | 1.11862 | ||||||||
\(95\) | −0.172140 | −0.0176612 | ||||||||
\(96\) | 0.295377 | 0.0301468 | ||||||||
\(97\) | 6.07568 | 0.616892 | 0.308446 | − | 0.951242i | \(-0.400191\pi\) | ||||
0.308446 | + | 0.951242i | \(0.400191\pi\) | |||||||
\(98\) | 3.93419 | 0.397413 | ||||||||
\(99\) | 7.14171 | 0.717769 | ||||||||
\(100\) | −4.97037 | −0.497037 | ||||||||
\(101\) | 6.68046 | 0.664730 | 0.332365 | − | 0.943151i | \(-0.392153\pi\) | ||||
0.332365 | + | 0.943151i | \(0.392153\pi\) | |||||||
\(102\) | −0.217749 | −0.0215604 | ||||||||
\(103\) | −6.72207 | −0.662345 | −0.331173 | − | 0.943570i | \(-0.607444\pi\) | ||||
−0.331173 | + | 0.943570i | \(0.607444\pi\) | |||||||
\(104\) | −2.40163 | −0.235499 | ||||||||
\(105\) | −0.168133 | −0.0164081 | ||||||||
\(106\) | 11.0578 | 1.07403 | ||||||||
\(107\) | −1.11875 | −0.108154 | −0.0540769 | − | 0.998537i | \(-0.517222\pi\) | ||||
−0.0540769 | + | 0.998537i | \(0.517222\pi\) | |||||||
\(108\) | −1.74649 | −0.168056 | ||||||||
\(109\) | −2.84306 | −0.272315 | −0.136158 | − | 0.990687i | \(-0.543475\pi\) | ||||
−0.136158 | + | 0.990687i | \(0.543475\pi\) | |||||||
\(110\) | −0.422067 | −0.0402425 | ||||||||
\(111\) | 2.51042 | 0.238279 | ||||||||
\(112\) | −3.30669 | −0.312453 | ||||||||
\(113\) | −8.42912 | −0.792945 | −0.396473 | − | 0.918047i | \(-0.629766\pi\) | ||||
−0.396473 | + | 0.918047i | \(0.629766\pi\) | |||||||
\(114\) | −0.295377 | −0.0276646 | ||||||||
\(115\) | −0.194823 | −0.0181673 | ||||||||
\(116\) | 3.37680 | 0.313528 | ||||||||
\(117\) | 6.99536 | 0.646721 | ||||||||
\(118\) | −2.36963 | −0.218142 | ||||||||
\(119\) | 2.43766 | 0.223460 | ||||||||
\(120\) | 0.0508464 | 0.00464162 | ||||||||
\(121\) | −4.98829 | −0.453481 | ||||||||
\(122\) | 7.18189 | 0.650218 | ||||||||
\(123\) | 2.50320 | 0.225706 | ||||||||
\(124\) | 2.23204 | 0.200444 | ||||||||
\(125\) | −1.71630 | −0.153511 | ||||||||
\(126\) | 9.63157 | 0.858048 | ||||||||
\(127\) | 6.68152 | 0.592889 | 0.296445 | − | 0.955050i | \(-0.404199\pi\) | ||||
0.296445 | + | 0.955050i | \(0.404199\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.17155 | −0.279239 | ||||||||
\(130\) | −0.413418 | −0.0362591 | ||||||||
\(131\) | 4.29041 | 0.374855 | 0.187427 | − | 0.982278i | \(-0.439985\pi\) | ||||
0.187427 | + | 0.982278i | \(0.439985\pi\) | |||||||
\(132\) | −0.724229 | −0.0630361 | ||||||||
\(133\) | 3.30669 | 0.286726 | ||||||||
\(134\) | −0.726963 | −0.0628001 | ||||||||
\(135\) | −0.300642 | −0.0258752 | ||||||||
\(136\) | −0.737190 | −0.0632135 | ||||||||
\(137\) | 16.0219 | 1.36884 | 0.684420 | − | 0.729088i | \(-0.260056\pi\) | ||||
0.684420 | + | 0.729088i | \(0.260056\pi\) | |||||||
\(138\) | −0.334298 | −0.0284574 | ||||||||
\(139\) | −12.8331 | −1.08849 | −0.544243 | − | 0.838928i | \(-0.683183\pi\) | ||||
−0.544243 | + | 0.838928i | \(0.683183\pi\) | |||||||
\(140\) | −0.569215 | −0.0481074 | ||||||||
\(141\) | 3.20350 | 0.269783 | ||||||||
\(142\) | 10.2530 | 0.860417 | ||||||||
\(143\) | 5.88851 | 0.492422 | ||||||||
\(144\) | −2.91275 | −0.242729 | ||||||||
\(145\) | 0.581283 | 0.0482730 | ||||||||
\(146\) | −3.97307 | −0.328814 | ||||||||
\(147\) | 1.16207 | 0.0958460 | ||||||||
\(148\) | 8.49904 | 0.698617 | ||||||||
\(149\) | 17.3940 | 1.42497 | 0.712486 | − | 0.701686i | \(-0.247569\pi\) | ||||
0.712486 | + | 0.701686i | \(0.247569\pi\) | |||||||
\(150\) | −1.46813 | −0.119873 | ||||||||
\(151\) | −20.5050 | −1.66867 | −0.834335 | − | 0.551258i | \(-0.814148\pi\) | ||||
−0.834335 | + | 0.551258i | \(0.814148\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 2.14725 | 0.173595 | ||||||||
\(154\) | 8.10760 | 0.653329 | ||||||||
\(155\) | 0.384225 | 0.0308617 | ||||||||
\(156\) | −0.709388 | −0.0567965 | ||||||||
\(157\) | 16.3390 | 1.30400 | 0.651999 | − | 0.758220i | \(-0.273931\pi\) | ||||
0.651999 | + | 0.758220i | \(0.273931\pi\) | |||||||
\(158\) | 5.35217 | 0.425796 | ||||||||
\(159\) | 3.26623 | 0.259029 | ||||||||
\(160\) | 0.172140 | 0.0136089 | ||||||||
\(161\) | 3.74240 | 0.294942 | ||||||||
\(162\) | 8.22238 | 0.646011 | ||||||||
\(163\) | 16.2441 | 1.27234 | 0.636170 | − | 0.771549i | \(-0.280518\pi\) | ||||
0.636170 | + | 0.771549i | \(0.280518\pi\) | |||||||
\(164\) | 8.47459 | 0.661754 | ||||||||
\(165\) | −0.124669 | −0.00970548 | ||||||||
\(166\) | 2.06586 | 0.160342 | ||||||||
\(167\) | −1.51083 | −0.116912 | −0.0584559 | − | 0.998290i | \(-0.518618\pi\) | ||||
−0.0584559 | + | 0.998290i | \(0.518618\pi\) | |||||||
\(168\) | −0.976721 | −0.0753557 | ||||||||
\(169\) | −7.23217 | −0.556321 | ||||||||
\(170\) | −0.126900 | −0.00973280 | ||||||||
\(171\) | 2.91275 | 0.222744 | ||||||||
\(172\) | −10.7373 | −0.818710 | ||||||||
\(173\) | −20.1631 | −1.53297 | −0.766485 | − | 0.642262i | \(-0.777996\pi\) | ||||
−0.766485 | + | 0.642262i | \(0.777996\pi\) | |||||||
\(174\) | 0.997430 | 0.0756150 | ||||||||
\(175\) | 16.4355 | 1.24240 | ||||||||
\(176\) | −2.45188 | −0.184817 | ||||||||
\(177\) | −0.699934 | −0.0526102 | ||||||||
\(178\) | 3.34314 | 0.250579 | ||||||||
\(179\) | −2.74253 | −0.204987 | −0.102493 | − | 0.994734i | \(-0.532682\pi\) | ||||
−0.102493 | + | 0.994734i | \(0.532682\pi\) | |||||||
\(180\) | −0.501402 | −0.0373723 | ||||||||
\(181\) | −0.968669 | −0.0720006 | −0.0360003 | − | 0.999352i | \(-0.511462\pi\) | ||||
−0.0360003 | + | 0.999352i | \(0.511462\pi\) | |||||||
\(182\) | 7.94145 | 0.588659 | ||||||||
\(183\) | 2.12137 | 0.156816 | ||||||||
\(184\) | −1.13177 | −0.0834349 | ||||||||
\(185\) | 1.46303 | 0.107564 | ||||||||
\(186\) | 0.659296 | 0.0483419 | ||||||||
\(187\) | 1.80750 | 0.132178 | ||||||||
\(188\) | 10.8454 | 0.790985 | ||||||||
\(189\) | 5.77511 | 0.420077 | ||||||||
\(190\) | −0.172140 | −0.0124884 | ||||||||
\(191\) | −3.85353 | −0.278832 | −0.139416 | − | 0.990234i | \(-0.544522\pi\) | ||||
−0.139416 | + | 0.990234i | \(0.544522\pi\) | |||||||
\(192\) | 0.295377 | 0.0213170 | ||||||||
\(193\) | −6.61520 | −0.476173 | −0.238086 | − | 0.971244i | \(-0.576520\pi\) | ||||
−0.238086 | + | 0.971244i | \(0.576520\pi\) | |||||||
\(194\) | 6.07568 | 0.436209 | ||||||||
\(195\) | −0.122114 | −0.00874478 | ||||||||
\(196\) | 3.93419 | 0.281014 | ||||||||
\(197\) | −5.86335 | −0.417746 | −0.208873 | − | 0.977943i | \(-0.566980\pi\) | ||||
−0.208873 | + | 0.977943i | \(0.566980\pi\) | |||||||
\(198\) | 7.14171 | 0.507540 | ||||||||
\(199\) | −19.8599 | −1.40783 | −0.703916 | − | 0.710284i | \(-0.748567\pi\) | ||||
−0.703916 | + | 0.710284i | \(0.748567\pi\) | |||||||
\(200\) | −4.97037 | −0.351458 | ||||||||
\(201\) | −0.214729 | −0.0151458 | ||||||||
\(202\) | 6.68046 | 0.470035 | ||||||||
\(203\) | −11.1660 | −0.783701 | ||||||||
\(204\) | −0.217749 | −0.0152455 | ||||||||
\(205\) | 1.45882 | 0.101888 | ||||||||
\(206\) | −6.72207 | −0.468349 | ||||||||
\(207\) | 3.29656 | 0.229126 | ||||||||
\(208\) | −2.40163 | −0.166523 | ||||||||
\(209\) | 2.45188 | 0.169600 | ||||||||
\(210\) | −0.168133 | −0.0116023 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | 11.0578 | 0.759453 | ||||||||
\(213\) | 3.02852 | 0.207511 | ||||||||
\(214\) | −1.11875 | −0.0764762 | ||||||||
\(215\) | −1.84832 | −0.126054 | ||||||||
\(216\) | −1.74649 | −0.118834 | ||||||||
\(217\) | −7.38068 | −0.501033 | ||||||||
\(218\) | −2.84306 | −0.192556 | ||||||||
\(219\) | −1.17356 | −0.0793015 | ||||||||
\(220\) | −0.422067 | −0.0284558 | ||||||||
\(221\) | 1.77046 | 0.119094 | ||||||||
\(222\) | 2.51042 | 0.168489 | ||||||||
\(223\) | 12.8030 | 0.857354 | 0.428677 | − | 0.903458i | \(-0.358980\pi\) | ||||
0.428677 | + | 0.903458i | \(0.358980\pi\) | |||||||
\(224\) | −3.30669 | −0.220937 | ||||||||
\(225\) | 14.4774 | 0.965163 | ||||||||
\(226\) | −8.42912 | −0.560697 | ||||||||
\(227\) | 22.1849 | 1.47247 | 0.736233 | − | 0.676728i | \(-0.236603\pi\) | ||||
0.736233 | + | 0.676728i | \(0.236603\pi\) | |||||||
\(228\) | −0.295377 | −0.0195618 | ||||||||
\(229\) | −1.61219 | −0.106536 | −0.0532682 | − | 0.998580i | \(-0.516964\pi\) | ||||
−0.0532682 | + | 0.998580i | \(0.516964\pi\) | |||||||
\(230\) | −0.194823 | −0.0128462 | ||||||||
\(231\) | 2.39480 | 0.157566 | ||||||||
\(232\) | 3.37680 | 0.221698 | ||||||||
\(233\) | −22.0222 | −1.44272 | −0.721361 | − | 0.692559i | \(-0.756483\pi\) | ||||
−0.721361 | + | 0.692559i | \(0.756483\pi\) | |||||||
\(234\) | 6.99536 | 0.457301 | ||||||||
\(235\) | 1.86694 | 0.121786 | ||||||||
\(236\) | −2.36963 | −0.154249 | ||||||||
\(237\) | 1.58091 | 0.102691 | ||||||||
\(238\) | 2.43766 | 0.158010 | ||||||||
\(239\) | 22.7925 | 1.47433 | 0.737163 | − | 0.675715i | \(-0.236165\pi\) | ||||
0.737163 | + | 0.675715i | \(0.236165\pi\) | |||||||
\(240\) | 0.0508464 | 0.00328212 | ||||||||
\(241\) | −3.70087 | −0.238394 | −0.119197 | − | 0.992871i | \(-0.538032\pi\) | ||||
−0.119197 | + | 0.992871i | \(0.538032\pi\) | |||||||
\(242\) | −4.98829 | −0.320660 | ||||||||
\(243\) | 7.66819 | 0.491914 | ||||||||
\(244\) | 7.18189 | 0.459774 | ||||||||
\(245\) | 0.677233 | 0.0432669 | ||||||||
\(246\) | 2.50320 | 0.159598 | ||||||||
\(247\) | 2.40163 | 0.152812 | ||||||||
\(248\) | 2.23204 | 0.141735 | ||||||||
\(249\) | 0.610208 | 0.0386704 | ||||||||
\(250\) | −1.71630 | −0.108549 | ||||||||
\(251\) | −23.2800 | −1.46942 | −0.734710 | − | 0.678382i | \(-0.762682\pi\) | ||||
−0.734710 | + | 0.678382i | \(0.762682\pi\) | |||||||
\(252\) | 9.63157 | 0.606732 | ||||||||
\(253\) | 2.77495 | 0.174460 | ||||||||
\(254\) | 6.68152 | 0.419236 | ||||||||
\(255\) | −0.0374835 | −0.00234731 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.83805 | 0.488924 | 0.244462 | − | 0.969659i | \(-0.421389\pi\) | ||||
0.244462 | + | 0.969659i | \(0.421389\pi\) | |||||||
\(258\) | −3.17155 | −0.197452 | ||||||||
\(259\) | −28.1037 | −1.74628 | ||||||||
\(260\) | −0.413418 | −0.0256391 | ||||||||
\(261\) | −9.83578 | −0.608819 | ||||||||
\(262\) | 4.29041 | 0.265062 | ||||||||
\(263\) | 6.33785 | 0.390809 | 0.195404 | − | 0.980723i | \(-0.437398\pi\) | ||||
0.195404 | + | 0.980723i | \(0.437398\pi\) | |||||||
\(264\) | −0.724229 | −0.0445732 | ||||||||
\(265\) | 1.90350 | 0.116931 | ||||||||
\(266\) | 3.30669 | 0.202746 | ||||||||
\(267\) | 0.987488 | 0.0604333 | ||||||||
\(268\) | −0.726963 | −0.0444063 | ||||||||
\(269\) | 5.60736 | 0.341887 | 0.170944 | − | 0.985281i | \(-0.445318\pi\) | ||||
0.170944 | + | 0.985281i | \(0.445318\pi\) | |||||||
\(270\) | −0.300642 | −0.0182965 | ||||||||
\(271\) | 26.3981 | 1.60357 | 0.801786 | − | 0.597612i | \(-0.203883\pi\) | ||||
0.801786 | + | 0.597612i | \(0.203883\pi\) | |||||||
\(272\) | −0.737190 | −0.0446987 | ||||||||
\(273\) | 2.34572 | 0.141970 | ||||||||
\(274\) | 16.0219 | 0.967916 | ||||||||
\(275\) | 12.1867 | 0.734888 | ||||||||
\(276\) | −0.334298 | −0.0201224 | ||||||||
\(277\) | −12.5493 | −0.754017 | −0.377008 | − | 0.926210i | \(-0.623047\pi\) | ||||
−0.377008 | + | 0.926210i | \(0.623047\pi\) | |||||||
\(278\) | −12.8331 | −0.769676 | ||||||||
\(279\) | −6.50139 | −0.389228 | ||||||||
\(280\) | −0.569215 | −0.0340171 | ||||||||
\(281\) | 10.8646 | 0.648127 | 0.324064 | − | 0.946035i | \(-0.394951\pi\) | ||||
0.324064 | + | 0.946035i | \(0.394951\pi\) | |||||||
\(282\) | 3.20350 | 0.190765 | ||||||||
\(283\) | 7.01506 | 0.417002 | 0.208501 | − | 0.978022i | \(-0.433142\pi\) | ||||
0.208501 | + | 0.978022i | \(0.433142\pi\) | |||||||
\(284\) | 10.2530 | 0.608406 | ||||||||
\(285\) | −0.0508464 | −0.00301188 | ||||||||
\(286\) | 5.88851 | 0.348195 | ||||||||
\(287\) | −28.0228 | −1.65414 | ||||||||
\(288\) | −2.91275 | −0.171636 | ||||||||
\(289\) | −16.4566 | −0.968032 | ||||||||
\(290\) | 0.581283 | 0.0341341 | ||||||||
\(291\) | 1.79462 | 0.105202 | ||||||||
\(292\) | −3.97307 | −0.232506 | ||||||||
\(293\) | 17.7179 | 1.03509 | 0.517546 | − | 0.855655i | \(-0.326846\pi\) | ||||
0.517546 | + | 0.855655i | \(0.326846\pi\) | |||||||
\(294\) | 1.16207 | 0.0677734 | ||||||||
\(295\) | −0.407908 | −0.0237493 | ||||||||
\(296\) | 8.49904 | 0.493997 | ||||||||
\(297\) | 4.28219 | 0.248478 | ||||||||
\(298\) | 17.3940 | 1.00761 | ||||||||
\(299\) | 2.71809 | 0.157191 | ||||||||
\(300\) | −1.46813 | −0.0847628 | ||||||||
\(301\) | 35.5048 | 2.04647 | ||||||||
\(302\) | −20.5050 | −1.17993 | ||||||||
\(303\) | 1.97326 | 0.113361 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 1.23629 | 0.0707900 | ||||||||
\(306\) | 2.14725 | 0.122750 | ||||||||
\(307\) | −17.9338 | −1.02354 | −0.511769 | − | 0.859123i | \(-0.671010\pi\) | ||||
−0.511769 | + | 0.859123i | \(0.671010\pi\) | |||||||
\(308\) | 8.10760 | 0.461973 | ||||||||
\(309\) | −1.98555 | −0.112954 | ||||||||
\(310\) | 0.384225 | 0.0218225 | ||||||||
\(311\) | −26.3427 | −1.49376 | −0.746878 | − | 0.664961i | \(-0.768448\pi\) | ||||
−0.746878 | + | 0.664961i | \(0.768448\pi\) | |||||||
\(312\) | −0.709388 | −0.0401612 | ||||||||
\(313\) | 11.0123 | 0.622452 | 0.311226 | − | 0.950336i | \(-0.399260\pi\) | ||||
0.311226 | + | 0.950336i | \(0.399260\pi\) | |||||||
\(314\) | 16.3390 | 0.922065 | ||||||||
\(315\) | 1.65798 | 0.0934167 | ||||||||
\(316\) | 5.35217 | 0.301083 | ||||||||
\(317\) | −0.0614134 | −0.00344932 | −0.00172466 | − | 0.999999i | \(-0.500549\pi\) | ||||
−0.00172466 | + | 0.999999i | \(0.500549\pi\) | |||||||
\(318\) | 3.26623 | 0.183161 | ||||||||
\(319\) | −8.27950 | −0.463563 | ||||||||
\(320\) | 0.172140 | 0.00962294 | ||||||||
\(321\) | −0.330454 | −0.0184441 | ||||||||
\(322\) | 3.74240 | 0.208556 | ||||||||
\(323\) | 0.737190 | 0.0410184 | ||||||||
\(324\) | 8.22238 | 0.456799 | ||||||||
\(325\) | 11.9370 | 0.662145 | ||||||||
\(326\) | 16.2441 | 0.899680 | ||||||||
\(327\) | −0.839774 | −0.0464396 | ||||||||
\(328\) | 8.47459 | 0.467931 | ||||||||
\(329\) | −35.8625 | −1.97716 | ||||||||
\(330\) | −0.124669 | −0.00686281 | ||||||||
\(331\) | −7.06512 | −0.388334 | −0.194167 | − | 0.980968i | \(-0.562200\pi\) | ||||
−0.194167 | + | 0.980968i | \(0.562200\pi\) | |||||||
\(332\) | 2.06586 | 0.113379 | ||||||||
\(333\) | −24.7556 | −1.35660 | ||||||||
\(334\) | −1.51083 | −0.0826691 | ||||||||
\(335\) | −0.125140 | −0.00683711 | ||||||||
\(336\) | −0.976721 | −0.0532845 | ||||||||
\(337\) | −30.0402 | −1.63640 | −0.818198 | − | 0.574937i | \(-0.805026\pi\) | ||||
−0.818198 | + | 0.574937i | \(0.805026\pi\) | |||||||
\(338\) | −7.23217 | −0.393378 | ||||||||
\(339\) | −2.48977 | −0.135226 | ||||||||
\(340\) | −0.126900 | −0.00688213 | ||||||||
\(341\) | −5.47270 | −0.296363 | ||||||||
\(342\) | 2.91275 | 0.157504 | ||||||||
\(343\) | 10.1377 | 0.547383 | ||||||||
\(344\) | −10.7373 | −0.578915 | ||||||||
\(345\) | −0.0575462 | −0.00309819 | ||||||||
\(346\) | −20.1631 | −1.08397 | ||||||||
\(347\) | 13.2232 | 0.709858 | 0.354929 | − | 0.934893i | \(-0.384505\pi\) | ||||
0.354929 | + | 0.934893i | \(0.384505\pi\) | |||||||
\(348\) | 0.997430 | 0.0534679 | ||||||||
\(349\) | 21.7286 | 1.16310 | 0.581552 | − | 0.813509i | \(-0.302446\pi\) | ||||
0.581552 | + | 0.813509i | \(0.302446\pi\) | |||||||
\(350\) | 16.4355 | 0.878512 | ||||||||
\(351\) | 4.19443 | 0.223882 | ||||||||
\(352\) | −2.45188 | −0.130686 | ||||||||
\(353\) | 5.47856 | 0.291594 | 0.145797 | − | 0.989315i | \(-0.453425\pi\) | ||||
0.145797 | + | 0.989315i | \(0.453425\pi\) | |||||||
\(354\) | −0.699934 | −0.0372011 | ||||||||
\(355\) | 1.76496 | 0.0936746 | ||||||||
\(356\) | 3.34314 | 0.177186 | ||||||||
\(357\) | 0.720029 | 0.0381080 | ||||||||
\(358\) | −2.74253 | −0.144947 | ||||||||
\(359\) | 28.8807 | 1.52426 | 0.762132 | − | 0.647422i | \(-0.224153\pi\) | ||||
0.762132 | + | 0.647422i | \(0.224153\pi\) | |||||||
\(360\) | −0.501402 | −0.0264262 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −0.968669 | −0.0509121 | ||||||||
\(363\) | −1.47343 | −0.0773350 | ||||||||
\(364\) | 7.94145 | 0.416245 | ||||||||
\(365\) | −0.683926 | −0.0357983 | ||||||||
\(366\) | 2.12137 | 0.110886 | ||||||||
\(367\) | 28.7707 | 1.50182 | 0.750910 | − | 0.660405i | \(-0.229615\pi\) | ||||
0.750910 | + | 0.660405i | \(0.229615\pi\) | |||||||
\(368\) | −1.13177 | −0.0589974 | ||||||||
\(369\) | −24.6844 | −1.28502 | ||||||||
\(370\) | 1.46303 | 0.0760592 | ||||||||
\(371\) | −36.5647 | −1.89835 | ||||||||
\(372\) | 0.659296 | 0.0341829 | ||||||||
\(373\) | −27.5792 | −1.42800 | −0.713999 | − | 0.700146i | \(-0.753118\pi\) | ||||
−0.713999 | + | 0.700146i | \(0.753118\pi\) | |||||||
\(374\) | 1.80750 | 0.0934636 | ||||||||
\(375\) | −0.506957 | −0.0261792 | ||||||||
\(376\) | 10.8454 | 0.559311 | ||||||||
\(377\) | −8.10982 | −0.417677 | ||||||||
\(378\) | 5.77511 | 0.297040 | ||||||||
\(379\) | 22.5703 | 1.15936 | 0.579680 | − | 0.814844i | \(-0.303178\pi\) | ||||
0.579680 | + | 0.814844i | \(0.303178\pi\) | |||||||
\(380\) | −0.172140 | −0.00883062 | ||||||||
\(381\) | 1.97357 | 0.101109 | ||||||||
\(382\) | −3.85353 | −0.197164 | ||||||||
\(383\) | 24.5709 | 1.25552 | 0.627758 | − | 0.778409i | \(-0.283973\pi\) | ||||
0.627758 | + | 0.778409i | \(0.283973\pi\) | |||||||
\(384\) | 0.295377 | 0.0150734 | ||||||||
\(385\) | 1.39565 | 0.0711287 | ||||||||
\(386\) | −6.61520 | −0.336705 | ||||||||
\(387\) | 31.2750 | 1.58980 | ||||||||
\(388\) | 6.07568 | 0.308446 | ||||||||
\(389\) | 17.2012 | 0.872135 | 0.436067 | − | 0.899914i | \(-0.356371\pi\) | ||||
0.436067 | + | 0.899914i | \(0.356371\pi\) | |||||||
\(390\) | −0.122114 | −0.00618350 | ||||||||
\(391\) | 0.834327 | 0.0421937 | ||||||||
\(392\) | 3.93419 | 0.198707 | ||||||||
\(393\) | 1.26729 | 0.0639263 | ||||||||
\(394\) | −5.86335 | −0.295391 | ||||||||
\(395\) | 0.921325 | 0.0463569 | ||||||||
\(396\) | 7.14171 | 0.358885 | ||||||||
\(397\) | 25.7587 | 1.29279 | 0.646395 | − | 0.763003i | \(-0.276276\pi\) | ||||
0.646395 | + | 0.763003i | \(0.276276\pi\) | |||||||
\(398\) | −19.8599 | −0.995487 | ||||||||
\(399\) | 0.976721 | 0.0488972 | ||||||||
\(400\) | −4.97037 | −0.248518 | ||||||||
\(401\) | −9.53177 | −0.475994 | −0.237997 | − | 0.971266i | \(-0.576491\pi\) | ||||
−0.237997 | + | 0.971266i | \(0.576491\pi\) | |||||||
\(402\) | −0.214729 | −0.0107097 | ||||||||
\(403\) | −5.36055 | −0.267028 | ||||||||
\(404\) | 6.68046 | 0.332365 | ||||||||
\(405\) | 1.41540 | 0.0703320 | ||||||||
\(406\) | −11.1660 | −0.554160 | ||||||||
\(407\) | −20.8386 | −1.03293 | ||||||||
\(408\) | −0.217749 | −0.0107802 | ||||||||
\(409\) | −20.5341 | −1.01534 | −0.507672 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507672 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(410\) | 1.45882 | 0.0720460 | ||||||||
\(411\) | 4.73250 | 0.233437 | ||||||||
\(412\) | −6.72207 | −0.331173 | ||||||||
\(413\) | 7.83561 | 0.385565 | ||||||||
\(414\) | 3.29656 | 0.162017 | ||||||||
\(415\) | 0.355618 | 0.0174566 | ||||||||
\(416\) | −2.40163 | −0.117750 | ||||||||
\(417\) | −3.79060 | −0.185626 | ||||||||
\(418\) | 2.45188 | 0.119925 | ||||||||
\(419\) | −27.3905 | −1.33811 | −0.669057 | − | 0.743211i | \(-0.733302\pi\) | ||||
−0.669057 | + | 0.743211i | \(0.733302\pi\) | |||||||
\(420\) | −0.168133 | −0.00820406 | ||||||||
\(421\) | −20.3757 | −0.993053 | −0.496527 | − | 0.868021i | \(-0.665391\pi\) | ||||
−0.496527 | + | 0.868021i | \(0.665391\pi\) | |||||||
\(422\) | −1.00000 | −0.0486792 | ||||||||
\(423\) | −31.5901 | −1.53596 | ||||||||
\(424\) | 11.0578 | 0.537015 | ||||||||
\(425\) | 3.66411 | 0.177735 | ||||||||
\(426\) | 3.02852 | 0.146732 | ||||||||
\(427\) | −23.7483 | −1.14926 | ||||||||
\(428\) | −1.11875 | −0.0540769 | ||||||||
\(429\) | 1.73933 | 0.0839757 | ||||||||
\(430\) | −1.84832 | −0.0891339 | ||||||||
\(431\) | 5.25951 | 0.253342 | 0.126671 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126671 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(432\) | −1.74649 | −0.0840282 | ||||||||
\(433\) | 34.9253 | 1.67840 | 0.839202 | − | 0.543820i | \(-0.183022\pi\) | ||||
0.839202 | + | 0.543820i | \(0.183022\pi\) | |||||||
\(434\) | −7.38068 | −0.354284 | ||||||||
\(435\) | 0.171698 | 0.00823229 | ||||||||
\(436\) | −2.84306 | −0.136158 | ||||||||
\(437\) | 1.13177 | 0.0541397 | ||||||||
\(438\) | −1.17356 | −0.0560746 | ||||||||
\(439\) | −14.4547 | −0.689885 | −0.344943 | − | 0.938624i | \(-0.612102\pi\) | ||||
−0.344943 | + | 0.938624i | \(0.612102\pi\) | |||||||
\(440\) | −0.422067 | −0.0201213 | ||||||||
\(441\) | −11.4593 | −0.545682 | ||||||||
\(442\) | 1.77046 | 0.0842122 | ||||||||
\(443\) | 1.17908 | 0.0560200 | 0.0280100 | − | 0.999608i | \(-0.491083\pi\) | ||||
0.0280100 | + | 0.999608i | \(0.491083\pi\) | |||||||
\(444\) | 2.51042 | 0.119139 | ||||||||
\(445\) | 0.575489 | 0.0272808 | ||||||||
\(446\) | 12.8030 | 0.606241 | ||||||||
\(447\) | 5.13780 | 0.243009 | ||||||||
\(448\) | −3.30669 | −0.156226 | ||||||||
\(449\) | −27.3337 | −1.28996 | −0.644978 | − | 0.764201i | \(-0.723134\pi\) | ||||
−0.644978 | + | 0.764201i | \(0.723134\pi\) | |||||||
\(450\) | 14.4774 | 0.682474 | ||||||||
\(451\) | −20.7787 | −0.978429 | ||||||||
\(452\) | −8.42912 | −0.396473 | ||||||||
\(453\) | −6.05670 | −0.284569 | ||||||||
\(454\) | 22.1849 | 1.04119 | ||||||||
\(455\) | 1.36704 | 0.0640880 | ||||||||
\(456\) | −0.295377 | −0.0138323 | ||||||||
\(457\) | 28.6036 | 1.33802 | 0.669009 | − | 0.743254i | \(-0.266719\pi\) | ||||
0.669009 | + | 0.743254i | \(0.266719\pi\) | |||||||
\(458\) | −1.61219 | −0.0753326 | ||||||||
\(459\) | 1.28750 | 0.0600953 | ||||||||
\(460\) | −0.194823 | −0.00908366 | ||||||||
\(461\) | 14.9798 | 0.697681 | 0.348841 | − | 0.937182i | \(-0.386575\pi\) | ||||
0.348841 | + | 0.937182i | \(0.386575\pi\) | |||||||
\(462\) | 2.39480 | 0.111416 | ||||||||
\(463\) | −32.3245 | −1.50225 | −0.751123 | − | 0.660162i | \(-0.770488\pi\) | ||||
−0.751123 | + | 0.660162i | \(0.770488\pi\) | |||||||
\(464\) | 3.37680 | 0.156764 | ||||||||
\(465\) | 0.113491 | 0.00526304 | ||||||||
\(466\) | −22.0222 | −1.02016 | ||||||||
\(467\) | 2.71335 | 0.125559 | 0.0627795 | − | 0.998027i | \(-0.480004\pi\) | ||||
0.0627795 | + | 0.998027i | \(0.480004\pi\) | |||||||
\(468\) | 6.99536 | 0.323360 | ||||||||
\(469\) | 2.40384 | 0.110999 | ||||||||
\(470\) | 1.86694 | 0.0861154 | ||||||||
\(471\) | 4.82618 | 0.222379 | ||||||||
\(472\) | −2.36963 | −0.109071 | ||||||||
\(473\) | 26.3265 | 1.21049 | ||||||||
\(474\) | 1.58091 | 0.0726137 | ||||||||
\(475\) | 4.97037 | 0.228056 | ||||||||
\(476\) | 2.43766 | 0.111730 | ||||||||
\(477\) | −32.2086 | −1.47473 | ||||||||
\(478\) | 22.7925 | 1.04251 | ||||||||
\(479\) | 27.1385 | 1.23999 | 0.619995 | − | 0.784605i | \(-0.287134\pi\) | ||||
0.619995 | + | 0.784605i | \(0.287134\pi\) | |||||||
\(480\) | 0.0508464 | 0.00232081 | ||||||||
\(481\) | −20.4116 | −0.930687 | ||||||||
\(482\) | −3.70087 | −0.168570 | ||||||||
\(483\) | 1.10542 | 0.0502984 | ||||||||
\(484\) | −4.98829 | −0.226741 | ||||||||
\(485\) | 1.04587 | 0.0474905 | ||||||||
\(486\) | 7.66819 | 0.347836 | ||||||||
\(487\) | 38.8091 | 1.75861 | 0.879304 | − | 0.476260i | \(-0.158008\pi\) | ||||
0.879304 | + | 0.476260i | \(0.158008\pi\) | |||||||
\(488\) | 7.18189 | 0.325109 | ||||||||
\(489\) | 4.79815 | 0.216980 | ||||||||
\(490\) | 0.677233 | 0.0305943 | ||||||||
\(491\) | −32.8313 | −1.48166 | −0.740828 | − | 0.671694i | \(-0.765567\pi\) | ||||
−0.740828 | + | 0.671694i | \(0.765567\pi\) | |||||||
\(492\) | 2.50320 | 0.112853 | ||||||||
\(493\) | −2.48934 | −0.112114 | ||||||||
\(494\) | 2.40163 | 0.108054 | ||||||||
\(495\) | 1.22938 | 0.0552564 | ||||||||
\(496\) | 2.23204 | 0.100222 | ||||||||
\(497\) | −33.9036 | −1.52079 | ||||||||
\(498\) | 0.610208 | 0.0273441 | ||||||||
\(499\) | 9.63830 | 0.431470 | 0.215735 | − | 0.976452i | \(-0.430785\pi\) | ||||
0.215735 | + | 0.976452i | \(0.430785\pi\) | |||||||
\(500\) | −1.71630 | −0.0767554 | ||||||||
\(501\) | −0.446266 | −0.0199377 | ||||||||
\(502\) | −23.2800 | −1.03904 | ||||||||
\(503\) | −32.7166 | −1.45876 | −0.729381 | − | 0.684108i | \(-0.760192\pi\) | ||||
−0.729381 | + | 0.684108i | \(0.760192\pi\) | |||||||
\(504\) | 9.63157 | 0.429024 | ||||||||
\(505\) | 1.14998 | 0.0511733 | ||||||||
\(506\) | 2.77495 | 0.123362 | ||||||||
\(507\) | −2.13622 | −0.0948728 | ||||||||
\(508\) | 6.68152 | 0.296445 | ||||||||
\(509\) | 11.7606 | 0.521278 | 0.260639 | − | 0.965436i | \(-0.416067\pi\) | ||||
0.260639 | + | 0.965436i | \(0.416067\pi\) | |||||||
\(510\) | −0.0374835 | −0.00165980 | ||||||||
\(511\) | 13.1377 | 0.581178 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.74649 | 0.0771096 | ||||||||
\(514\) | 7.83805 | 0.345721 | ||||||||
\(515\) | −1.15714 | −0.0509897 | ||||||||
\(516\) | −3.17155 | −0.139620 | ||||||||
\(517\) | −26.5917 | −1.16950 | ||||||||
\(518\) | −28.1037 | −1.23481 | ||||||||
\(519\) | −5.95572 | −0.261427 | ||||||||
\(520\) | −0.413418 | −0.0181296 | ||||||||
\(521\) | −19.6619 | −0.861403 | −0.430702 | − | 0.902494i | \(-0.641734\pi\) | ||||
−0.430702 | + | 0.902494i | \(0.641734\pi\) | |||||||
\(522\) | −9.83578 | −0.430500 | ||||||||
\(523\) | −42.5510 | −1.86062 | −0.930312 | − | 0.366768i | \(-0.880464\pi\) | ||||
−0.930312 | + | 0.366768i | \(0.880464\pi\) | |||||||
\(524\) | 4.29041 | 0.187427 | ||||||||
\(525\) | 4.85466 | 0.211875 | ||||||||
\(526\) | 6.33785 | 0.276344 | ||||||||
\(527\) | −1.64544 | −0.0716766 | ||||||||
\(528\) | −0.724229 | −0.0315180 | ||||||||
\(529\) | −21.7191 | −0.944309 | ||||||||
\(530\) | 1.90350 | 0.0826825 | ||||||||
\(531\) | 6.90213 | 0.299527 | ||||||||
\(532\) | 3.30669 | 0.143363 | ||||||||
\(533\) | −20.3528 | −0.881580 | ||||||||
\(534\) | 0.987488 | 0.0427328 | ||||||||
\(535\) | −0.192582 | −0.00832606 | ||||||||
\(536\) | −0.726963 | −0.0314000 | ||||||||
\(537\) | −0.810083 | −0.0349576 | ||||||||
\(538\) | 5.60736 | 0.241751 | ||||||||
\(539\) | −9.64616 | −0.415490 | ||||||||
\(540\) | −0.300642 | −0.0129376 | ||||||||
\(541\) | 20.8524 | 0.896516 | 0.448258 | − | 0.893904i | \(-0.352045\pi\) | ||||
0.448258 | + | 0.893904i | \(0.352045\pi\) | |||||||
\(542\) | 26.3981 | 1.13390 | ||||||||
\(543\) | −0.286123 | −0.0122787 | ||||||||
\(544\) | −0.737190 | −0.0316068 | ||||||||
\(545\) | −0.489405 | −0.0209638 | ||||||||
\(546\) | 2.34572 | 0.100388 | ||||||||
\(547\) | 22.0066 | 0.940936 | 0.470468 | − | 0.882417i | \(-0.344085\pi\) | ||||
0.470468 | + | 0.882417i | \(0.344085\pi\) | |||||||
\(548\) | 16.0219 | 0.684420 | ||||||||
\(549\) | −20.9191 | −0.892805 | ||||||||
\(550\) | 12.1867 | 0.519644 | ||||||||
\(551\) | −3.37680 | −0.143856 | ||||||||
\(552\) | −0.334298 | −0.0142287 | ||||||||
\(553\) | −17.6980 | −0.752594 | ||||||||
\(554\) | −12.5493 | −0.533171 | ||||||||
\(555\) | 0.432146 | 0.0183436 | ||||||||
\(556\) | −12.8331 | −0.544243 | ||||||||
\(557\) | 1.29275 | 0.0547756 | 0.0273878 | − | 0.999625i | \(-0.491281\pi\) | ||||
0.0273878 | + | 0.999625i | \(0.491281\pi\) | |||||||
\(558\) | −6.50139 | −0.275226 | ||||||||
\(559\) | 25.7870 | 1.09067 | ||||||||
\(560\) | −0.569215 | −0.0240537 | ||||||||
\(561\) | 0.533895 | 0.0225411 | ||||||||
\(562\) | 10.8646 | 0.458295 | ||||||||
\(563\) | 1.62339 | 0.0684177 | 0.0342088 | − | 0.999415i | \(-0.489109\pi\) | ||||
0.0342088 | + | 0.999415i | \(0.489109\pi\) | |||||||
\(564\) | 3.20350 | 0.134892 | ||||||||
\(565\) | −1.45099 | −0.0610437 | ||||||||
\(566\) | 7.01506 | 0.294865 | ||||||||
\(567\) | −27.1889 | −1.14182 | ||||||||
\(568\) | 10.2530 | 0.430208 | ||||||||
\(569\) | 30.4307 | 1.27572 | 0.637861 | − | 0.770152i | \(-0.279820\pi\) | ||||
0.637861 | + | 0.770152i | \(0.279820\pi\) | |||||||
\(570\) | −0.0508464 | −0.00212972 | ||||||||
\(571\) | 2.90148 | 0.121423 | 0.0607117 | − | 0.998155i | \(-0.480663\pi\) | ||||
0.0607117 | + | 0.998155i | \(0.480663\pi\) | |||||||
\(572\) | 5.88851 | 0.246211 | ||||||||
\(573\) | −1.13825 | −0.0475509 | ||||||||
\(574\) | −28.0228 | −1.16965 | ||||||||
\(575\) | 5.62530 | 0.234591 | ||||||||
\(576\) | −2.91275 | −0.121365 | ||||||||
\(577\) | −7.52091 | −0.313100 | −0.156550 | − | 0.987670i | \(-0.550037\pi\) | ||||
−0.156550 | + | 0.987670i | \(0.550037\pi\) | |||||||
\(578\) | −16.4566 | −0.684502 | ||||||||
\(579\) | −1.95398 | −0.0812047 | ||||||||
\(580\) | 0.581283 | 0.0241365 | ||||||||
\(581\) | −6.83116 | −0.283404 | ||||||||
\(582\) | 1.79462 | 0.0743894 | ||||||||
\(583\) | −27.1124 | −1.12288 | ||||||||
\(584\) | −3.97307 | −0.164407 | ||||||||
\(585\) | 1.20418 | 0.0497869 | ||||||||
\(586\) | 17.7179 | 0.731920 | ||||||||
\(587\) | −11.8648 | −0.489714 | −0.244857 | − | 0.969559i | \(-0.578741\pi\) | ||||
−0.244857 | + | 0.969559i | \(0.578741\pi\) | |||||||
\(588\) | 1.16207 | 0.0479230 | ||||||||
\(589\) | −2.23204 | −0.0919698 | ||||||||
\(590\) | −0.407908 | −0.0167933 | ||||||||
\(591\) | −1.73190 | −0.0712408 | ||||||||
\(592\) | 8.49904 | 0.349308 | ||||||||
\(593\) | 21.2835 | 0.874008 | 0.437004 | − | 0.899460i | \(-0.356040\pi\) | ||||
0.437004 | + | 0.899460i | \(0.356040\pi\) | |||||||
\(594\) | 4.28219 | 0.175700 | ||||||||
\(595\) | 0.419620 | 0.0172027 | ||||||||
\(596\) | 17.3940 | 0.712486 | ||||||||
\(597\) | −5.86617 | −0.240086 | ||||||||
\(598\) | 2.71809 | 0.111151 | ||||||||
\(599\) | −2.67523 | −0.109307 | −0.0546534 | − | 0.998505i | \(-0.517405\pi\) | ||||
−0.0546534 | + | 0.998505i | \(0.517405\pi\) | |||||||
\(600\) | −1.46813 | −0.0599363 | ||||||||
\(601\) | 42.1168 | 1.71798 | 0.858989 | − | 0.511994i | \(-0.171093\pi\) | ||||
0.858989 | + | 0.511994i | \(0.171093\pi\) | |||||||
\(602\) | 35.5048 | 1.44707 | ||||||||
\(603\) | 2.11746 | 0.0862298 | ||||||||
\(604\) | −20.5050 | −0.834335 | ||||||||
\(605\) | −0.858687 | −0.0349106 | ||||||||
\(606\) | 1.97326 | 0.0801580 | ||||||||
\(607\) | −37.0344 | −1.50318 | −0.751590 | − | 0.659631i | \(-0.770713\pi\) | ||||
−0.751590 | + | 0.659631i | \(0.770713\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | −3.29819 | −0.133649 | ||||||||
\(610\) | 1.23629 | 0.0500561 | ||||||||
\(611\) | −26.0467 | −1.05374 | ||||||||
\(612\) | 2.14725 | 0.0867975 | ||||||||
\(613\) | −39.7141 | −1.60404 | −0.802018 | − | 0.597300i | \(-0.796240\pi\) | ||||
−0.802018 | + | 0.597300i | \(0.796240\pi\) | |||||||
\(614\) | −17.9338 | −0.723750 | ||||||||
\(615\) | 0.430902 | 0.0173757 | ||||||||
\(616\) | 8.10760 | 0.326664 | ||||||||
\(617\) | 32.3712 | 1.30321 | 0.651607 | − | 0.758557i | \(-0.274095\pi\) | ||||
0.651607 | + | 0.758557i | \(0.274095\pi\) | |||||||
\(618\) | −1.98555 | −0.0798705 | ||||||||
\(619\) | 43.6604 | 1.75486 | 0.877430 | − | 0.479705i | \(-0.159256\pi\) | ||||
0.877430 | + | 0.479705i | \(0.159256\pi\) | |||||||
\(620\) | 0.384225 | 0.0154308 | ||||||||
\(621\) | 1.97662 | 0.0793191 | ||||||||
\(622\) | −26.3427 | −1.05625 | ||||||||
\(623\) | −11.0547 | −0.442898 | ||||||||
\(624\) | −0.709388 | −0.0283982 | ||||||||
\(625\) | 24.5564 | 0.982256 | ||||||||
\(626\) | 11.0123 | 0.440140 | ||||||||
\(627\) | 0.724229 | 0.0289229 | ||||||||
\(628\) | 16.3390 | 0.651999 | ||||||||
\(629\) | −6.26541 | −0.249818 | ||||||||
\(630\) | 1.65798 | 0.0660556 | ||||||||
\(631\) | −26.3425 | −1.04868 | −0.524339 | − | 0.851509i | \(-0.675688\pi\) | ||||
−0.524339 | + | 0.851509i | \(0.675688\pi\) | |||||||
\(632\) | 5.35217 | 0.212898 | ||||||||
\(633\) | −0.295377 | −0.0117402 | ||||||||
\(634\) | −0.0614134 | −0.00243904 | ||||||||
\(635\) | 1.15016 | 0.0456427 | ||||||||
\(636\) | 3.26623 | 0.129514 | ||||||||
\(637\) | −9.44848 | −0.374362 | ||||||||
\(638\) | −8.27950 | −0.327788 | ||||||||
\(639\) | −29.8646 | −1.18142 | ||||||||
\(640\) | 0.172140 | 0.00680445 | ||||||||
\(641\) | 33.1176 | 1.30807 | 0.654034 | − | 0.756465i | \(-0.273075\pi\) | ||||
0.654034 | + | 0.756465i | \(0.273075\pi\) | |||||||
\(642\) | −0.330454 | −0.0130420 | ||||||||
\(643\) | −9.32860 | −0.367884 | −0.183942 | − | 0.982937i | \(-0.558886\pi\) | ||||
−0.183942 | + | 0.982937i | \(0.558886\pi\) | |||||||
\(644\) | 3.74240 | 0.147471 | ||||||||
\(645\) | −0.545952 | −0.0214968 | ||||||||
\(646\) | 0.737190 | 0.0290044 | ||||||||
\(647\) | 8.26257 | 0.324835 | 0.162418 | − | 0.986722i | \(-0.448071\pi\) | ||||
0.162418 | + | 0.986722i | \(0.448071\pi\) | |||||||
\(648\) | 8.22238 | 0.323006 | ||||||||
\(649\) | 5.81003 | 0.228064 | ||||||||
\(650\) | 11.9370 | 0.468207 | ||||||||
\(651\) | −2.18009 | −0.0854443 | ||||||||
\(652\) | 16.2441 | 0.636170 | ||||||||
\(653\) | 38.8783 | 1.52142 | 0.760712 | − | 0.649089i | \(-0.224850\pi\) | ||||
0.760712 | + | 0.649089i | \(0.224850\pi\) | |||||||
\(654\) | −0.839774 | −0.0328378 | ||||||||
\(655\) | 0.738552 | 0.0288576 | ||||||||
\(656\) | 8.47459 | 0.330877 | ||||||||
\(657\) | 11.5726 | 0.451489 | ||||||||
\(658\) | −35.8625 | −1.39807 | ||||||||
\(659\) | −17.2662 | −0.672594 | −0.336297 | − | 0.941756i | \(-0.609175\pi\) | ||||
−0.336297 | + | 0.941756i | \(0.609175\pi\) | |||||||
\(660\) | −0.124669 | −0.00485274 | ||||||||
\(661\) | 46.5289 | 1.80977 | 0.904883 | − | 0.425661i | \(-0.139958\pi\) | ||||
0.904883 | + | 0.425661i | \(0.139958\pi\) | |||||||
\(662\) | −7.06512 | −0.274594 | ||||||||
\(663\) | 0.522954 | 0.0203098 | ||||||||
\(664\) | 2.06586 | 0.0801709 | ||||||||
\(665\) | 0.569215 | 0.0220732 | ||||||||
\(666\) | −24.7556 | −0.959260 | ||||||||
\(667\) | −3.82175 | −0.147979 | ||||||||
\(668\) | −1.51083 | −0.0584559 | ||||||||
\(669\) | 3.78173 | 0.146210 | ||||||||
\(670\) | −0.125140 | −0.00483457 | ||||||||
\(671\) | −17.6091 | −0.679793 | ||||||||
\(672\) | −0.976721 | −0.0376778 | ||||||||
\(673\) | 43.8931 | 1.69195 | 0.845977 | − | 0.533220i | \(-0.179018\pi\) | ||||
0.845977 | + | 0.533220i | \(0.179018\pi\) | |||||||
\(674\) | −30.0402 | −1.15711 | ||||||||
\(675\) | 8.68071 | 0.334121 | ||||||||
\(676\) | −7.23217 | −0.278160 | ||||||||
\(677\) | −4.57794 | −0.175944 | −0.0879722 | − | 0.996123i | \(-0.528039\pi\) | ||||
−0.0879722 | + | 0.996123i | \(0.528039\pi\) | |||||||
\(678\) | −2.48977 | −0.0956191 | ||||||||
\(679\) | −20.0904 | −0.770999 | ||||||||
\(680\) | −0.126900 | −0.00486640 | ||||||||
\(681\) | 6.55293 | 0.251109 | ||||||||
\(682\) | −5.47270 | −0.209561 | ||||||||
\(683\) | 42.0730 | 1.60988 | 0.804939 | − | 0.593358i | \(-0.202198\pi\) | ||||
0.804939 | + | 0.593358i | \(0.202198\pi\) | |||||||
\(684\) | 2.91275 | 0.111372 | ||||||||
\(685\) | 2.75801 | 0.105378 | ||||||||
\(686\) | 10.1377 | 0.387058 | ||||||||
\(687\) | −0.476204 | −0.0181683 | ||||||||
\(688\) | −10.7373 | −0.409355 | ||||||||
\(689\) | −26.5568 | −1.01173 | ||||||||
\(690\) | −0.0575462 | −0.00219075 | ||||||||
\(691\) | 20.8317 | 0.792474 | 0.396237 | − | 0.918148i | \(-0.370316\pi\) | ||||
0.396237 | + | 0.918148i | \(0.370316\pi\) | |||||||
\(692\) | −20.1631 | −0.766485 | ||||||||
\(693\) | −23.6154 | −0.897076 | ||||||||
\(694\) | 13.2232 | 0.501945 | ||||||||
\(695\) | −2.20909 | −0.0837955 | ||||||||
\(696\) | 0.997430 | 0.0378075 | ||||||||
\(697\) | −6.24739 | −0.236637 | ||||||||
\(698\) | 21.7286 | 0.822439 | ||||||||
\(699\) | −6.50486 | −0.246037 | ||||||||
\(700\) | 16.4355 | 0.621202 | ||||||||
\(701\) | 30.5069 | 1.15223 | 0.576116 | − | 0.817368i | \(-0.304568\pi\) | ||||
0.576116 | + | 0.817368i | \(0.304568\pi\) | |||||||
\(702\) | 4.19443 | 0.158309 | ||||||||
\(703\) | −8.49904 | −0.320547 | ||||||||
\(704\) | −2.45188 | −0.0924086 | ||||||||
\(705\) | 0.551451 | 0.0207689 | ||||||||
\(706\) | 5.47856 | 0.206188 | ||||||||
\(707\) | −22.0902 | −0.830787 | ||||||||
\(708\) | −0.699934 | −0.0263051 | ||||||||
\(709\) | −8.31447 | −0.312257 | −0.156128 | − | 0.987737i | \(-0.549901\pi\) | ||||
−0.156128 | + | 0.987737i | \(0.549901\pi\) | |||||||
\(710\) | 1.76496 | 0.0662379 | ||||||||
\(711\) | −15.5896 | −0.584654 | ||||||||
\(712\) | 3.34314 | 0.125289 | ||||||||
\(713\) | −2.52615 | −0.0946052 | ||||||||
\(714\) | 0.720029 | 0.0269464 | ||||||||
\(715\) | 1.01365 | 0.0379084 | ||||||||
\(716\) | −2.74253 | −0.102493 | ||||||||
\(717\) | 6.73240 | 0.251426 | ||||||||
\(718\) | 28.8807 | 1.07782 | ||||||||
\(719\) | 22.4595 | 0.837598 | 0.418799 | − | 0.908079i | \(-0.362451\pi\) | ||||
0.418799 | + | 0.908079i | \(0.362451\pi\) | |||||||
\(720\) | −0.501402 | −0.0186862 | ||||||||
\(721\) | 22.2278 | 0.827806 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −1.09315 | −0.0406548 | ||||||||
\(724\) | −0.968669 | −0.0360003 | ||||||||
\(725\) | −16.7839 | −0.623339 | ||||||||
\(726\) | −1.47343 | −0.0546841 | ||||||||
\(727\) | 5.67953 | 0.210642 | 0.105321 | − | 0.994438i | \(-0.466413\pi\) | ||||
0.105321 | + | 0.994438i | \(0.466413\pi\) | |||||||
\(728\) | 7.94145 | 0.294330 | ||||||||
\(729\) | −22.4021 | −0.829709 | ||||||||
\(730\) | −0.683926 | −0.0253132 | ||||||||
\(731\) | 7.91542 | 0.292762 | ||||||||
\(732\) | 2.12137 | 0.0784081 | ||||||||
\(733\) | 26.8685 | 0.992411 | 0.496206 | − | 0.868205i | \(-0.334726\pi\) | ||||
0.496206 | + | 0.868205i | \(0.334726\pi\) | |||||||
\(734\) | 28.7707 | 1.06195 | ||||||||
\(735\) | 0.200039 | 0.00737857 | ||||||||
\(736\) | −1.13177 | −0.0417175 | ||||||||
\(737\) | 1.78243 | 0.0656565 | ||||||||
\(738\) | −24.6844 | −0.908645 | ||||||||
\(739\) | −42.7357 | −1.57206 | −0.786030 | − | 0.618189i | \(-0.787867\pi\) | ||||
−0.786030 | + | 0.618189i | \(0.787867\pi\) | |||||||
\(740\) | 1.46303 | 0.0537820 | ||||||||
\(741\) | 0.709388 | 0.0260600 | ||||||||
\(742\) | −36.5647 | −1.34233 | ||||||||
\(743\) | −24.6981 | −0.906084 | −0.453042 | − | 0.891489i | \(-0.649661\pi\) | ||||
−0.453042 | + | 0.891489i | \(0.649661\pi\) | |||||||
\(744\) | 0.659296 | 0.0241709 | ||||||||
\(745\) | 2.99421 | 0.109699 | ||||||||
\(746\) | −27.5792 | −1.00975 | ||||||||
\(747\) | −6.01734 | −0.220163 | ||||||||
\(748\) | 1.80750 | 0.0660888 | ||||||||
\(749\) | 3.69936 | 0.135172 | ||||||||
\(750\) | −0.506957 | −0.0185115 | ||||||||
\(751\) | −31.5967 | −1.15298 | −0.576490 | − | 0.817104i | \(-0.695578\pi\) | ||||
−0.576490 | + | 0.817104i | \(0.695578\pi\) | |||||||
\(752\) | 10.8454 | 0.395492 | ||||||||
\(753\) | −6.87638 | −0.250589 | ||||||||
\(754\) | −8.10982 | −0.295342 | ||||||||
\(755\) | −3.52973 | −0.128460 | ||||||||
\(756\) | 5.77511 | 0.210039 | ||||||||
\(757\) | 42.4597 | 1.54322 | 0.771612 | − | 0.636094i | \(-0.219451\pi\) | ||||
0.771612 | + | 0.636094i | \(0.219451\pi\) | |||||||
\(758\) | 22.5703 | 0.819791 | ||||||||
\(759\) | 0.819659 | 0.0297517 | ||||||||
\(760\) | −0.172140 | −0.00624419 | ||||||||
\(761\) | −24.8255 | −0.899924 | −0.449962 | − | 0.893048i | \(-0.648562\pi\) | ||||
−0.449962 | + | 0.893048i | \(0.648562\pi\) | |||||||
\(762\) | 1.97357 | 0.0714949 | ||||||||
\(763\) | 9.40110 | 0.340343 | ||||||||
\(764\) | −3.85353 | −0.139416 | ||||||||
\(765\) | 0.369629 | 0.0133640 | ||||||||
\(766\) | 24.5709 | 0.887783 | ||||||||
\(767\) | 5.69097 | 0.205489 | ||||||||
\(768\) | 0.295377 | 0.0106585 | ||||||||
\(769\) | 50.3009 | 1.81390 | 0.906948 | − | 0.421243i | \(-0.138406\pi\) | ||||
0.906948 | + | 0.421243i | \(0.138406\pi\) | |||||||
\(770\) | 1.39565 | 0.0502956 | ||||||||
\(771\) | 2.31518 | 0.0833792 | ||||||||
\(772\) | −6.61520 | −0.238086 | ||||||||
\(773\) | 9.73526 | 0.350153 | 0.175077 | − | 0.984555i | \(-0.443983\pi\) | ||||
0.175077 | + | 0.984555i | \(0.443983\pi\) | |||||||
\(774\) | 31.2750 | 1.12416 | ||||||||
\(775\) | −11.0941 | −0.398511 | ||||||||
\(776\) | 6.07568 | 0.218104 | ||||||||
\(777\) | −8.30119 | −0.297804 | ||||||||
\(778\) | 17.2012 | 0.616692 | ||||||||
\(779\) | −8.47459 | −0.303634 | ||||||||
\(780\) | −0.122114 | −0.00437239 | ||||||||
\(781\) | −25.1392 | −0.899552 | ||||||||
\(782\) | 0.834327 | 0.0298355 | ||||||||
\(783\) | −5.89756 | −0.210761 | ||||||||
\(784\) | 3.93419 | 0.140507 | ||||||||
\(785\) | 2.81261 | 0.100386 | ||||||||
\(786\) | 1.26729 | 0.0452027 | ||||||||
\(787\) | −2.85611 | −0.101809 | −0.0509047 | − | 0.998704i | \(-0.516210\pi\) | ||||
−0.0509047 | + | 0.998704i | \(0.516210\pi\) | |||||||
\(788\) | −5.86335 | −0.208873 | ||||||||
\(789\) | 1.87206 | 0.0666471 | ||||||||
\(790\) | 0.921325 | 0.0327793 | ||||||||
\(791\) | 27.8725 | 0.991031 | ||||||||
\(792\) | 7.14171 | 0.253770 | ||||||||
\(793\) | −17.2483 | −0.612504 | ||||||||
\(794\) | 25.7587 | 0.914140 | ||||||||
\(795\) | 0.562249 | 0.0199409 | ||||||||
\(796\) | −19.8599 | −0.703916 | ||||||||
\(797\) | −37.1655 | −1.31647 | −0.658235 | − | 0.752812i | \(-0.728697\pi\) | ||||
−0.658235 | + | 0.752812i | \(0.728697\pi\) | |||||||
\(798\) | 0.976721 | 0.0345756 | ||||||||
\(799\) | −7.99515 | −0.282848 | ||||||||
\(800\) | −4.97037 | −0.175729 | ||||||||
\(801\) | −9.73774 | −0.344066 | ||||||||
\(802\) | −9.53177 | −0.336579 | ||||||||
\(803\) | 9.74149 | 0.343770 | ||||||||
\(804\) | −0.214729 | −0.00757289 | ||||||||
\(805\) | 0.644218 | 0.0227057 | ||||||||
\(806\) | −5.36055 | −0.188817 | ||||||||
\(807\) | 1.65629 | 0.0583041 | ||||||||
\(808\) | 6.68046 | 0.235018 | ||||||||
\(809\) | 44.6198 | 1.56875 | 0.784373 | − | 0.620289i | \(-0.212985\pi\) | ||||
0.784373 | + | 0.620289i | \(0.212985\pi\) | |||||||
\(810\) | 1.41540 | 0.0497322 | ||||||||
\(811\) | −52.2489 | −1.83471 | −0.917354 | − | 0.398072i | \(-0.869680\pi\) | ||||
−0.917354 | + | 0.398072i | \(0.869680\pi\) | |||||||
\(812\) | −11.1660 | −0.391851 | ||||||||
\(813\) | 7.79741 | 0.273467 | ||||||||
\(814\) | −20.8386 | −0.730393 | ||||||||
\(815\) | 2.79627 | 0.0979492 | ||||||||
\(816\) | −0.217749 | −0.00762275 | ||||||||
\(817\) | 10.7373 | 0.375650 | ||||||||
\(818\) | −20.5341 | −0.717957 | ||||||||
\(819\) | −23.1315 | −0.808279 | ||||||||
\(820\) | 1.45882 | 0.0509442 | ||||||||
\(821\) | 1.09622 | 0.0382583 | 0.0191291 | − | 0.999817i | \(-0.493911\pi\) | ||||
0.0191291 | + | 0.999817i | \(0.493911\pi\) | |||||||
\(822\) | 4.73250 | 0.165065 | ||||||||
\(823\) | −45.7684 | −1.59539 | −0.797693 | − | 0.603063i | \(-0.793947\pi\) | ||||
−0.797693 | + | 0.603063i | \(0.793947\pi\) | |||||||
\(824\) | −6.72207 | −0.234174 | ||||||||
\(825\) | 3.59969 | 0.125325 | ||||||||
\(826\) | 7.83561 | 0.272636 | ||||||||
\(827\) | 25.4957 | 0.886572 | 0.443286 | − | 0.896380i | \(-0.353813\pi\) | ||||
0.443286 | + | 0.896380i | \(0.353813\pi\) | |||||||
\(828\) | 3.29656 | 0.114563 | ||||||||
\(829\) | 28.5484 | 0.991528 | 0.495764 | − | 0.868457i | \(-0.334888\pi\) | ||||
0.495764 | + | 0.868457i | \(0.334888\pi\) | |||||||
\(830\) | 0.355618 | 0.0123437 | ||||||||
\(831\) | −3.70679 | −0.128587 | ||||||||
\(832\) | −2.40163 | −0.0832616 | ||||||||
\(833\) | −2.90025 | −0.100488 | ||||||||
\(834\) | −3.79060 | −0.131258 | ||||||||
\(835\) | −0.260076 | −0.00900029 | ||||||||
\(836\) | 2.45188 | 0.0848000 | ||||||||
\(837\) | −3.89825 | −0.134743 | ||||||||
\(838\) | −27.3905 | −0.946189 | ||||||||
\(839\) | 57.2754 | 1.97737 | 0.988684 | − | 0.150015i | \(-0.0479323\pi\) | ||||
0.988684 | + | 0.150015i | \(0.0479323\pi\) | |||||||
\(840\) | −0.168133 | −0.00580115 | ||||||||
\(841\) | −17.5972 | −0.606801 | ||||||||
\(842\) | −20.3757 | −0.702195 | ||||||||
\(843\) | 3.20915 | 0.110529 | ||||||||
\(844\) | −1.00000 | −0.0344214 | ||||||||
\(845\) | −1.24495 | −0.0428275 | ||||||||
\(846\) | −31.5901 | −1.08609 | ||||||||
\(847\) | 16.4947 | 0.566766 | ||||||||
\(848\) | 11.0578 | 0.379727 | ||||||||
\(849\) | 2.07209 | 0.0711140 | ||||||||
\(850\) | 3.66411 | 0.125678 | ||||||||
\(851\) | −9.61893 | −0.329733 | ||||||||
\(852\) | 3.02852 | 0.103755 | ||||||||
\(853\) | 24.5099 | 0.839204 | 0.419602 | − | 0.907708i | \(-0.362170\pi\) | ||||
0.419602 | + | 0.907708i | \(0.362170\pi\) | |||||||
\(854\) | −23.7483 | −0.812650 | ||||||||
\(855\) | 0.501402 | 0.0171476 | ||||||||
\(856\) | −1.11875 | −0.0382381 | ||||||||
\(857\) | 54.1694 | 1.85039 | 0.925196 | − | 0.379490i | \(-0.123900\pi\) | ||||
0.925196 | + | 0.379490i | \(0.123900\pi\) | |||||||
\(858\) | 1.73933 | 0.0593798 | ||||||||
\(859\) | 23.5060 | 0.802013 | 0.401006 | − | 0.916075i | \(-0.368660\pi\) | ||||
0.401006 | + | 0.916075i | \(0.368660\pi\) | |||||||
\(860\) | −1.84832 | −0.0630272 | ||||||||
\(861\) | −8.27731 | −0.282090 | ||||||||
\(862\) | 5.25951 | 0.179140 | ||||||||
\(863\) | −34.1086 | −1.16107 | −0.580534 | − | 0.814236i | \(-0.697156\pi\) | ||||
−0.580534 | + | 0.814236i | \(0.697156\pi\) | |||||||
\(864\) | −1.74649 | −0.0594169 | ||||||||
\(865\) | −3.47088 | −0.118014 | ||||||||
\(866\) | 34.9253 | 1.18681 | ||||||||
\(867\) | −4.86089 | −0.165085 | ||||||||
\(868\) | −7.38068 | −0.250516 | ||||||||
\(869\) | −13.1229 | −0.445163 | ||||||||
\(870\) | 0.171698 | 0.00582111 | ||||||||
\(871\) | 1.74590 | 0.0591575 | ||||||||
\(872\) | −2.84306 | −0.0962780 | ||||||||
\(873\) | −17.6970 | −0.598951 | ||||||||
\(874\) | 1.13177 | 0.0382826 | ||||||||
\(875\) | 5.67528 | 0.191859 | ||||||||
\(876\) | −1.17356 | −0.0396508 | ||||||||
\(877\) | −39.6840 | −1.34003 | −0.670016 | − | 0.742346i | \(-0.733713\pi\) | ||||
−0.670016 | + | 0.742346i | \(0.733713\pi\) | |||||||
\(878\) | −14.4547 | −0.487823 | ||||||||
\(879\) | 5.23347 | 0.176521 | ||||||||
\(880\) | −0.422067 | −0.0142279 | ||||||||
\(881\) | −5.91419 | −0.199254 | −0.0996270 | − | 0.995025i | \(-0.531765\pi\) | ||||
−0.0996270 | + | 0.995025i | \(0.531765\pi\) | |||||||
\(882\) | −11.4593 | −0.385856 | ||||||||
\(883\) | 52.2003 | 1.75668 | 0.878340 | − | 0.478036i | \(-0.158651\pi\) | ||||
0.878340 | + | 0.478036i | \(0.158651\pi\) | |||||||
\(884\) | 1.77046 | 0.0595470 | ||||||||
\(885\) | −0.120487 | −0.00405012 | ||||||||
\(886\) | 1.17908 | 0.0396121 | ||||||||
\(887\) | 37.9827 | 1.27533 | 0.637667 | − | 0.770312i | \(-0.279900\pi\) | ||||
0.637667 | + | 0.770312i | \(0.279900\pi\) | |||||||
\(888\) | 2.51042 | 0.0842443 | ||||||||
\(889\) | −22.0937 | −0.741000 | ||||||||
\(890\) | 0.575489 | 0.0192904 | ||||||||
\(891\) | −20.1603 | −0.675395 | ||||||||
\(892\) | 12.8030 | 0.428677 | ||||||||
\(893\) | −10.8454 | −0.362929 | ||||||||
\(894\) | 5.13780 | 0.171834 | ||||||||
\(895\) | −0.472101 | −0.0157806 | ||||||||
\(896\) | −3.30669 | −0.110469 | ||||||||
\(897\) | 0.802861 | 0.0268068 | ||||||||
\(898\) | −27.3337 | −0.912137 | ||||||||
\(899\) | 7.53716 | 0.251378 | ||||||||
\(900\) | 14.4774 | 0.482582 | ||||||||
\(901\) | −8.15171 | −0.271573 | ||||||||
\(902\) | −20.7787 | −0.691854 | ||||||||
\(903\) | 10.4873 | 0.348996 | ||||||||
\(904\) | −8.42912 | −0.280348 | ||||||||
\(905\) | −0.166747 | −0.00554286 | ||||||||
\(906\) | −6.05670 | −0.201220 | ||||||||
\(907\) | −10.9524 | −0.363667 | −0.181833 | − | 0.983329i | \(-0.558203\pi\) | ||||
−0.181833 | + | 0.983329i | \(0.558203\pi\) | |||||||
\(908\) | 22.1849 | 0.736233 | ||||||||
\(909\) | −19.4585 | −0.645398 | ||||||||
\(910\) | 1.36704 | 0.0453171 | ||||||||
\(911\) | 18.1890 | 0.602629 | 0.301314 | − | 0.953525i | \(-0.402575\pi\) | ||||
0.301314 | + | 0.953525i | \(0.402575\pi\) | |||||||
\(912\) | −0.295377 | −0.00978092 | ||||||||
\(913\) | −5.06524 | −0.167635 | ||||||||
\(914\) | 28.6036 | 0.946122 | ||||||||
\(915\) | 0.365173 | 0.0120723 | ||||||||
\(916\) | −1.61219 | −0.0532682 | ||||||||
\(917\) | −14.1870 | −0.468497 | ||||||||
\(918\) | 1.28750 | 0.0424938 | ||||||||
\(919\) | 25.0964 | 0.827855 | 0.413927 | − | 0.910310i | \(-0.364157\pi\) | ||||
0.413927 | + | 0.910310i | \(0.364157\pi\) | |||||||
\(920\) | −0.194823 | −0.00642312 | ||||||||
\(921\) | −5.29725 | −0.174550 | ||||||||
\(922\) | 14.9798 | 0.493335 | ||||||||
\(923\) | −24.6240 | −0.810510 | ||||||||
\(924\) | 2.39480 | 0.0787832 | ||||||||
\(925\) | −42.2434 | −1.38895 | ||||||||
\(926\) | −32.3245 | −1.06225 | ||||||||
\(927\) | 19.5797 | 0.643083 | ||||||||
\(928\) | 3.37680 | 0.110849 | ||||||||
\(929\) | 29.3290 | 0.962255 | 0.481127 | − | 0.876651i | \(-0.340227\pi\) | ||||
0.481127 | + | 0.876651i | \(0.340227\pi\) | |||||||
\(930\) | 0.113491 | 0.00372153 | ||||||||
\(931\) | −3.93419 | −0.128938 | ||||||||
\(932\) | −22.0222 | −0.721361 | ||||||||
\(933\) | −7.78103 | −0.254740 | ||||||||
\(934\) | 2.71335 | 0.0887837 | ||||||||
\(935\) | 0.311144 | 0.0101755 | ||||||||
\(936\) | 6.99536 | 0.228650 | ||||||||
\(937\) | −33.4242 | −1.09192 | −0.545961 | − | 0.837811i | \(-0.683835\pi\) | ||||
−0.545961 | + | 0.837811i | \(0.683835\pi\) | |||||||
\(938\) | 2.40384 | 0.0784882 | ||||||||
\(939\) | 3.25279 | 0.106151 | ||||||||
\(940\) | 1.86694 | 0.0608928 | ||||||||
\(941\) | −7.23354 | −0.235807 | −0.117903 | − | 0.993025i | \(-0.537617\pi\) | ||||
−0.117903 | + | 0.993025i | \(0.537617\pi\) | |||||||
\(942\) | 4.82618 | 0.157246 | ||||||||
\(943\) | −9.59126 | −0.312334 | ||||||||
\(944\) | −2.36963 | −0.0771247 | ||||||||
\(945\) | 0.994130 | 0.0323390 | ||||||||
\(946\) | 26.3265 | 0.855948 | ||||||||
\(947\) | 6.88631 | 0.223775 | 0.111887 | − | 0.993721i | \(-0.464310\pi\) | ||||
0.111887 | + | 0.993721i | \(0.464310\pi\) | |||||||
\(948\) | 1.58091 | 0.0513456 | ||||||||
\(949\) | 9.54185 | 0.309742 | ||||||||
\(950\) | 4.97037 | 0.161260 | ||||||||
\(951\) | −0.0181401 | −0.000588234 0 | ||||||||
\(952\) | 2.43766 | 0.0790050 | ||||||||
\(953\) | 29.2317 | 0.946908 | 0.473454 | − | 0.880819i | \(-0.343007\pi\) | ||||
0.473454 | + | 0.880819i | \(0.343007\pi\) | |||||||
\(954\) | −32.2086 | −1.04279 | ||||||||
\(955\) | −0.663348 | −0.0214654 | ||||||||
\(956\) | 22.7925 | 0.737163 | ||||||||
\(957\) | −2.44558 | −0.0790543 | ||||||||
\(958\) | 27.1385 | 0.876806 | ||||||||
\(959\) | −52.9793 | −1.71079 | ||||||||
\(960\) | 0.0508464 | 0.00164106 | ||||||||
\(961\) | −26.0180 | −0.839290 | ||||||||
\(962\) | −20.4116 | −0.658095 | ||||||||
\(963\) | 3.25864 | 0.105008 | ||||||||
\(964\) | −3.70087 | −0.119197 | ||||||||
\(965\) | −1.13874 | −0.0366575 | ||||||||
\(966\) | 1.10542 | 0.0355663 | ||||||||
\(967\) | −23.8692 | −0.767582 | −0.383791 | − | 0.923420i | \(-0.625382\pi\) | ||||
−0.383791 | + | 0.923420i | \(0.625382\pi\) | |||||||
\(968\) | −4.98829 | −0.160330 | ||||||||
\(969\) | 0.217749 | 0.00699512 | ||||||||
\(970\) | 1.04587 | 0.0335809 | ||||||||
\(971\) | −12.9613 | −0.415947 | −0.207973 | − | 0.978134i | \(-0.566687\pi\) | ||||
−0.207973 | + | 0.978134i | \(0.566687\pi\) | |||||||
\(972\) | 7.66819 | 0.245957 | ||||||||
\(973\) | 42.4349 | 1.36040 | ||||||||
\(974\) | 38.8091 | 1.24352 | ||||||||
\(975\) | 3.52592 | 0.112920 | ||||||||
\(976\) | 7.18189 | 0.229887 | ||||||||
\(977\) | 2.20374 | 0.0705037 | 0.0352519 | − | 0.999378i | \(-0.488777\pi\) | ||||
0.0352519 | + | 0.999378i | \(0.488777\pi\) | |||||||
\(978\) | 4.79815 | 0.153428 | ||||||||
\(979\) | −8.19697 | −0.261976 | ||||||||
\(980\) | 0.677233 | 0.0216334 | ||||||||
\(981\) | 8.28112 | 0.264396 | ||||||||
\(982\) | −32.8313 | −1.04769 | ||||||||
\(983\) | −37.5214 | −1.19675 | −0.598374 | − | 0.801217i | \(-0.704186\pi\) | ||||
−0.598374 | + | 0.801217i | \(0.704186\pi\) | |||||||
\(984\) | 2.50320 | 0.0797992 | ||||||||
\(985\) | −1.00932 | −0.0321596 | ||||||||
\(986\) | −2.48934 | −0.0792768 | ||||||||
\(987\) | −10.5930 | −0.337178 | ||||||||
\(988\) | 2.40163 | 0.0764061 | ||||||||
\(989\) | 12.1521 | 0.386414 | ||||||||
\(990\) | 1.22938 | 0.0390722 | ||||||||
\(991\) | 44.7112 | 1.42030 | 0.710149 | − | 0.704052i | \(-0.248628\pi\) | ||||
0.710149 | + | 0.704052i | \(0.248628\pi\) | |||||||
\(992\) | 2.23204 | 0.0708675 | ||||||||
\(993\) | −2.08688 | −0.0662250 | ||||||||
\(994\) | −33.9036 | −1.07536 | ||||||||
\(995\) | −3.41869 | −0.108380 | ||||||||
\(996\) | 0.610208 | 0.0193352 | ||||||||
\(997\) | −2.87454 | −0.0910377 | −0.0455189 | − | 0.998963i | \(-0.514494\pi\) | ||||
−0.0455189 | + | 0.998963i | \(0.514494\pi\) | |||||||
\(998\) | 9.63830 | 0.305095 | ||||||||
\(999\) | −14.8435 | −0.469628 |
(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 | 8018.2.a.j.1.23 | ✓ | 47 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8018.2.a.j.1.23 | ✓ | 47 | 1.1 | even | 1 | trivial |