Newspace parameters
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.a (trivial) |
Newform invariants
Self dual: | yes |
Analytic conductor: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-expansion
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.959867 | 0.678728 | 0.339364 | − | 0.940655i | \(-0.389788\pi\) | ||||
0.339364 | + | 0.940655i | \(0.389788\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.07866 | −0.539328 | ||||||||
\(5\) | 2.40466 | 1.07540 | 0.537698 | − | 0.843138i | \(-0.319294\pi\) | ||||
0.537698 | + | 0.843138i | \(0.319294\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −2.95510 | −1.04479 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.30815 | 0.729901 | ||||||||
\(11\) | 4.25741 | 1.28366 | 0.641829 | − | 0.766848i | \(-0.278176\pi\) | ||||
0.641829 | + | 0.766848i | \(0.278176\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.54385 | 0.982886 | 0.491443 | − | 0.870910i | \(-0.336470\pi\) | ||||
0.491443 | + | 0.870910i | \(0.336470\pi\) | |||||||
\(14\) | −0.959867 | −0.256535 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.679190 | −0.169797 | ||||||||
\(17\) | 0.302404 | 0.0733436 | 0.0366718 | − | 0.999327i | \(-0.488324\pi\) | ||||
0.0366718 | + | 0.999327i | \(0.488324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.75953 | −1.55074 | −0.775371 | − | 0.631506i | \(-0.782437\pi\) | ||||
−0.775371 | + | 0.631506i | \(0.782437\pi\) | |||||||
\(20\) | −2.59380 | −0.579991 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.08655 | 0.871255 | ||||||||
\(23\) | −6.51256 | −1.35796 | −0.678981 | − | 0.734155i | \(-0.737578\pi\) | ||||
−0.678981 | + | 0.734155i | \(0.737578\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.782373 | 0.156475 | ||||||||
\(26\) | 3.40162 | 0.667113 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.07866 | 0.203847 | ||||||||
\(29\) | −3.90770 | −0.725641 | −0.362820 | − | 0.931859i | \(-0.618186\pi\) | ||||
−0.362820 | + | 0.931859i | \(0.618186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.48700 | −0.985495 | −0.492748 | − | 0.870172i | \(-0.664007\pi\) | ||||
−0.492748 | + | 0.870172i | \(0.664007\pi\) | |||||||
\(32\) | 5.25827 | 0.929539 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.290267 | 0.0497804 | ||||||||
\(35\) | −2.40466 | −0.406461 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.55479 | −1.07760 | −0.538800 | − | 0.842434i | \(-0.681122\pi\) | ||||
−0.538800 | + | 0.842434i | \(0.681122\pi\) | |||||||
\(38\) | −6.48825 | −1.05253 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.10600 | −1.12356 | ||||||||
\(41\) | −2.17456 | −0.339609 | −0.169805 | − | 0.985478i | \(-0.554314\pi\) | ||||
−0.169805 | + | 0.985478i | \(0.554314\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.47361 | 1.44471 | 0.722356 | − | 0.691521i | \(-0.243059\pi\) | ||||
0.722356 | + | 0.691521i | \(0.243059\pi\) | |||||||
\(44\) | −4.59228 | −0.692313 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.25119 | −0.921688 | ||||||||
\(47\) | −1.43429 | −0.209212 | −0.104606 | − | 0.994514i | \(-0.533358\pi\) | ||||
−0.104606 | + | 0.994514i | \(0.533358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.750974 | 0.106204 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.82259 | −0.530098 | ||||||||
\(53\) | −10.5740 | −1.45246 | −0.726228 | − | 0.687454i | \(-0.758728\pi\) | ||||
−0.726228 | + | 0.687454i | \(0.758728\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.2376 | 1.38044 | ||||||||
\(56\) | 2.95510 | 0.394892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.75087 | −0.492513 | ||||||||
\(59\) | 7.97145 | 1.03779 | 0.518897 | − | 0.854837i | \(-0.326343\pi\) | ||||
0.518897 | + | 0.854837i | \(0.326343\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.05914 | 0.135608 | 0.0678042 | − | 0.997699i | \(-0.478401\pi\) | ||||
0.0678042 | + | 0.997699i | \(0.478401\pi\) | |||||||
\(62\) | −5.26679 | −0.668883 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.40561 | 0.800702 | ||||||||
\(65\) | 8.52173 | 1.05699 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.72133 | −0.576802 | −0.288401 | − | 0.957510i | \(-0.593124\pi\) | ||||
−0.288401 | + | 0.957510i | \(0.593124\pi\) | |||||||
\(68\) | −0.326189 | −0.0395563 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.30815 | −0.275877 | ||||||||
\(71\) | −6.25244 | −0.742028 | −0.371014 | − | 0.928627i | \(-0.620990\pi\) | ||||
−0.371014 | + | 0.928627i | \(0.620990\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.4772 | −1.34330 | −0.671652 | − | 0.740867i | \(-0.734415\pi\) | ||||
−0.671652 | + | 0.740867i | \(0.734415\pi\) | |||||||
\(74\) | −6.29172 | −0.731398 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.29120 | 0.836358 | ||||||||
\(77\) | −4.25741 | −0.485177 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.55627 | 0.512620 | 0.256310 | − | 0.966595i | \(-0.417493\pi\) | ||||
0.256310 | + | 0.966595i | \(0.417493\pi\) | |||||||
\(80\) | −1.63322 | −0.182599 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.08729 | −0.230502 | ||||||||
\(83\) | −10.1365 | −1.11263 | −0.556315 | − | 0.830972i | \(-0.687785\pi\) | ||||
−0.556315 | + | 0.830972i | \(0.687785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.727177 | 0.0788734 | ||||||||
\(86\) | 9.09340 | 0.980567 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.5811 | −1.34115 | ||||||||
\(89\) | −8.24382 | −0.873844 | −0.436922 | − | 0.899499i | \(-0.643931\pi\) | ||||
−0.436922 | + | 0.899499i | \(0.643931\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.54385 | −0.371496 | ||||||||
\(92\) | 7.02481 | 0.732387 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.37672 | −0.141998 | ||||||||
\(95\) | −16.2543 | −1.66766 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.74407 | 0.177084 | 0.0885419 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885419 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(98\) | 0.959867 | 0.0969612 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.843912 | −0.0843912 | ||||||||
\(101\) | 3.61578 | 0.359783 | 0.179892 | − | 0.983686i | \(-0.442425\pi\) | ||||
0.179892 | + | 0.983686i | \(0.442425\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.92884 | 0.584186 | 0.292093 | − | 0.956390i | \(-0.405648\pi\) | ||||
0.292093 | + | 0.956390i | \(0.405648\pi\) | |||||||
\(104\) | −10.4724 | −1.02690 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1497 | −0.985823 | ||||||||
\(107\) | −6.45523 | −0.624050 | −0.312025 | − | 0.950074i | \(-0.601007\pi\) | ||||
−0.312025 | + | 0.950074i | \(0.601007\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.5285 | 1.96628 | 0.983138 | − | 0.182865i | \(-0.0585371\pi\) | ||||
0.983138 | + | 0.182865i | \(0.0585371\pi\) | |||||||
\(110\) | 9.82675 | 0.936943 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.679190 | 0.0641774 | ||||||||
\(113\) | 15.2547 | 1.43504 | 0.717520 | − | 0.696538i | \(-0.245277\pi\) | ||||
0.717520 | + | 0.696538i | \(0.245277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.6605 | −1.46035 | ||||||||
\(116\) | 4.21506 | 0.391358 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.65153 | 0.704380 | ||||||||
\(119\) | −0.302404 | −0.0277213 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.12556 | 0.647778 | ||||||||
\(122\) | 1.01663 | 0.0920412 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.91859 | 0.531505 | ||||||||
\(125\) | −10.1419 | −0.907123 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −4.36800 | −0.386080 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.17973 | 0.717410 | ||||||||
\(131\) | 5.94653 | 0.519551 | 0.259775 | − | 0.965669i | \(-0.416352\pi\) | ||||
0.259775 | + | 0.965669i | \(0.416352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.75953 | 0.586125 | ||||||||
\(134\) | −4.53185 | −0.391492 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.893633 | −0.0766284 | ||||||||
\(137\) | −1.37243 | −0.117255 | −0.0586273 | − | 0.998280i | \(-0.518672\pi\) | ||||
−0.0586273 | + | 0.998280i | \(0.518672\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.13422 | 0.265841 | 0.132921 | − | 0.991127i | \(-0.457564\pi\) | ||||
0.132921 | + | 0.991127i | \(0.457564\pi\) | |||||||
\(140\) | 2.59380 | 0.219216 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00151 | −0.503635 | ||||||||
\(143\) | 15.0876 | 1.26169 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.39666 | −0.780351 | ||||||||
\(146\) | −11.0166 | −0.911738 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.07036 | 0.581180 | ||||||||
\(149\) | −13.3703 | −1.09534 | −0.547670 | − | 0.836694i | \(-0.684485\pi\) | ||||
−0.547670 | + | 0.836694i | \(0.684485\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.2915 | −0.837513 | −0.418757 | − | 0.908098i | \(-0.637534\pi\) | ||||
−0.418757 | + | 0.908098i | \(0.637534\pi\) | |||||||
\(152\) | 19.9751 | 1.62019 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.08655 | −0.329303 | ||||||||
\(155\) | −13.1944 | −1.05980 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.70342 | 0.614800 | 0.307400 | − | 0.951580i | \(-0.400541\pi\) | ||||
0.307400 | + | 0.951580i | \(0.400541\pi\) | |||||||
\(158\) | 4.37341 | 0.347930 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6443 | 0.999622 | ||||||||
\(161\) | 6.51256 | 0.513262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.54115 | 0.512342 | 0.256171 | − | 0.966631i | \(-0.417539\pi\) | ||||
0.256171 | + | 0.966631i | \(0.417539\pi\) | |||||||
\(164\) | 2.34560 | 0.183161 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.72973 | −0.755173 | ||||||||
\(167\) | −2.06466 | −0.159769 | −0.0798843 | − | 0.996804i | \(-0.525455\pi\) | ||||
−0.0798843 | + | 0.996804i | \(0.525455\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.441156 | −0.0339351 | ||||||||
\(170\) | 0.697993 | 0.0535336 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.2188 | −0.779174 | ||||||||
\(173\) | 11.0221 | 0.837991 | 0.418996 | − | 0.907988i | \(-0.362382\pi\) | ||||
0.418996 | + | 0.907988i | \(0.362382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.782373 | −0.0591419 | ||||||||
\(176\) | −2.89159 | −0.217962 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.91297 | −0.593102 | ||||||||
\(179\) | −23.6676 | −1.76900 | −0.884501 | − | 0.466537i | \(-0.845501\pi\) | ||||
−0.884501 | + | 0.466537i | \(0.845501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1437 | −1.12563 | −0.562813 | − | 0.826584i | \(-0.690281\pi\) | ||||
−0.562813 | + | 0.826584i | \(0.690281\pi\) | |||||||
\(182\) | −3.40162 | −0.252145 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 19.2453 | 1.41878 | ||||||||
\(185\) | −15.7620 | −1.15885 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.28746 | 0.0941482 | ||||||||
\(188\) | 1.54710 | 0.112834 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −15.6020 | −1.13189 | ||||||||
\(191\) | −11.4808 | −0.830722 | −0.415361 | − | 0.909657i | \(-0.636345\pi\) | ||||
−0.415361 | + | 0.909657i | \(0.636345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.41906 | −0.606017 | −0.303009 | − | 0.952988i | \(-0.597991\pi\) | ||||
−0.303009 | + | 0.952988i | \(0.597991\pi\) | |||||||
\(194\) | 1.67408 | 0.120192 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.07866 | −0.0770468 | ||||||||
\(197\) | −6.10162 | −0.434723 | −0.217361 | − | 0.976091i | \(-0.569745\pi\) | ||||
−0.217361 | + | 0.976091i | \(0.569745\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.7103 | −0.759231 | −0.379616 | − | 0.925144i | \(-0.623944\pi\) | ||||
−0.379616 | + | 0.925144i | \(0.623944\pi\) | |||||||
\(200\) | −2.31199 | −0.163482 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.47066 | 0.244195 | ||||||||
\(203\) | 3.90770 | 0.274266 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.22907 | −0.365214 | ||||||||
\(206\) | 5.69089 | 0.396503 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.40694 | −0.166891 | ||||||||
\(209\) | −28.7781 | −1.99062 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8349 | −0.952436 | −0.476218 | − | 0.879327i | \(-0.657993\pi\) | ||||
−0.476218 | + | 0.879327i | \(0.657993\pi\) | |||||||
\(212\) | 11.4057 | 0.783350 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.19616 | −0.423561 | ||||||||
\(215\) | 22.7808 | 1.55364 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.48700 | 0.372482 | ||||||||
\(218\) | 19.7046 | 1.33457 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.0429 | −0.744510 | ||||||||
\(221\) | 1.07167 | 0.0720884 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.00800 | −0.335360 | −0.167680 | − | 0.985841i | \(-0.553628\pi\) | ||||
−0.167680 | + | 0.985841i | \(0.553628\pi\) | |||||||
\(224\) | −5.25827 | −0.351333 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.6425 | 0.974002 | ||||||||
\(227\) | 23.4386 | 1.55567 | 0.777837 | − | 0.628467i | \(-0.216317\pi\) | ||||
0.777837 | + | 0.628467i | \(0.216317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.95298 | −0.261220 | −0.130610 | − | 0.991434i | \(-0.541694\pi\) | ||||
−0.130610 | + | 0.991434i | \(0.541694\pi\) | |||||||
\(230\) | −15.0320 | −0.991179 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 11.5476 | 0.758139 | ||||||||
\(233\) | −1.27357 | −0.0834346 | −0.0417173 | − | 0.999129i | \(-0.513283\pi\) | ||||
−0.0417173 | + | 0.999129i | \(0.513283\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.44897 | −0.224986 | ||||||||
\(236\) | −8.59845 | −0.559712 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.290267 | −0.0188152 | ||||||||
\(239\) | −8.13559 | −0.526248 | −0.263124 | − | 0.964762i | \(-0.584753\pi\) | ||||
−0.263124 | + | 0.964762i | \(0.584753\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4833 | 1.25503 | 0.627513 | − | 0.778606i | \(-0.284073\pi\) | ||||
0.627513 | + | 0.778606i | \(0.284073\pi\) | |||||||
\(242\) | 6.83959 | 0.439665 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.14244 | −0.0731374 | ||||||||
\(245\) | 2.40466 | 0.153628 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.9547 | −1.52420 | ||||||||
\(248\) | 16.2146 | 1.02963 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −9.73491 | −0.615690 | ||||||||
\(251\) | −2.25176 | −0.142130 | −0.0710650 | − | 0.997472i | \(-0.522640\pi\) | ||||
−0.0710650 | + | 0.997472i | \(0.522640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −27.7267 | −1.74316 | ||||||||
\(254\) | −0.959867 | −0.0602274 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −17.0039 | −1.06275 | ||||||||
\(257\) | −15.5072 | −0.967310 | −0.483655 | − | 0.875259i | \(-0.660691\pi\) | ||||
−0.483655 | + | 0.875259i | \(0.660691\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.55479 | 0.407295 | ||||||||
\(260\) | −9.19202 | −0.570065 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.70787 | 0.352634 | ||||||||
\(263\) | −3.83687 | −0.236591 | −0.118296 | − | 0.992978i | \(-0.537743\pi\) | ||||
−0.118296 | + | 0.992978i | \(0.537743\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.4269 | −1.56196 | ||||||||
\(266\) | 6.48825 | 0.397820 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.09269 | 0.311086 | ||||||||
\(269\) | −15.6381 | −0.953470 | −0.476735 | − | 0.879047i | \(-0.658180\pi\) | ||||
−0.476735 | + | 0.879047i | \(0.658180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.4561 | 1.42485 | 0.712427 | − | 0.701746i | \(-0.247596\pi\) | ||||
0.712427 | + | 0.701746i | \(0.247596\pi\) | |||||||
\(272\) | −0.205389 | −0.0124536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.31735 | −0.0795840 | ||||||||
\(275\) | 3.33089 | 0.200860 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8299 | 1.61205 | 0.806025 | − | 0.591881i | \(-0.201615\pi\) | ||||
0.806025 | + | 0.591881i | \(0.201615\pi\) | |||||||
\(278\) | 3.00844 | 0.180434 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.10600 | 0.424665 | ||||||||
\(281\) | 20.9721 | 1.25109 | 0.625545 | − | 0.780188i | \(-0.284877\pi\) | ||||
0.625545 | + | 0.780188i | \(0.284877\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.5527 | −0.983959 | −0.491979 | − | 0.870607i | \(-0.663726\pi\) | ||||
−0.491979 | + | 0.870607i | \(0.663726\pi\) | |||||||
\(284\) | 6.74423 | 0.400196 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.4821 | 0.856344 | ||||||||
\(287\) | 2.17456 | 0.128360 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9086 | −0.994621 | ||||||||
\(290\) | −9.01955 | −0.529646 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.3799 | 0.724481 | ||||||||
\(293\) | 16.6113 | 0.970443 | 0.485221 | − | 0.874391i | \(-0.338739\pi\) | ||||
0.485221 | + | 0.874391i | \(0.338739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1686 | 1.11604 | ||||||||
\(296\) | 19.3701 | 1.12586 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.8337 | −0.743439 | ||||||||
\(299\) | −23.0795 | −1.33472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.47361 | −0.546050 | ||||||||
\(302\) | −9.87850 | −0.568444 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.59100 | 0.263312 | ||||||||
\(305\) | 2.54686 | 0.145833 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.6493 | −1.46388 | −0.731942 | − | 0.681367i | \(-0.761386\pi\) | ||||
−0.731942 | + | 0.681367i | \(0.761386\pi\) | |||||||
\(308\) | 4.59228 | 0.261670 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −12.6648 | −0.719314 | ||||||||
\(311\) | −6.28790 | −0.356554 | −0.178277 | − | 0.983980i | \(-0.557052\pi\) | ||||
−0.178277 | + | 0.983980i | \(0.557052\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.0220 | −1.35781 | −0.678903 | − | 0.734228i | \(-0.737544\pi\) | ||||
−0.678903 | + | 0.734228i | \(0.737544\pi\) | |||||||
\(314\) | 7.39425 | 0.417282 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.91464 | −0.276470 | ||||||||
\(317\) | 11.7159 | 0.658031 | 0.329016 | − | 0.944324i | \(-0.393283\pi\) | ||||
0.329016 | + | 0.944324i | \(0.393283\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.6367 | −0.931475 | ||||||||
\(320\) | 15.4033 | 0.861071 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.25119 | 0.348365 | ||||||||
\(323\) | −2.04411 | −0.113737 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.77261 | 0.153797 | ||||||||
\(326\) | 6.27863 | 0.347741 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.42604 | 0.354819 | ||||||||
\(329\) | 1.43429 | 0.0790748 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.4126 | −0.792187 | −0.396094 | − | 0.918210i | \(-0.629634\pi\) | ||||
−0.396094 | + | 0.918210i | \(0.629634\pi\) | |||||||
\(332\) | 10.9338 | 0.600072 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.98180 | −0.108439 | ||||||||
\(335\) | −11.3532 | −0.620290 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.1181 | −0.769061 | −0.384531 | − | 0.923112i | \(-0.625637\pi\) | ||||
−0.384531 | + | 0.923112i | \(0.625637\pi\) | |||||||
\(338\) | −0.423451 | −0.0230327 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.784373 | −0.0425386 | ||||||||
\(341\) | −23.3604 | −1.26504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −27.9955 | −1.50941 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5797 | 0.568768 | ||||||||
\(347\) | 28.8833 | 1.55053 | 0.775267 | − | 0.631633i | \(-0.217615\pi\) | ||||
0.775267 | + | 0.631633i | \(0.217615\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3596 | 1.30394 | 0.651971 | − | 0.758244i | \(-0.273943\pi\) | ||||
0.651971 | + | 0.758244i | \(0.273943\pi\) | |||||||
\(350\) | −0.750974 | −0.0401413 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.3866 | 1.19321 | ||||||||
\(353\) | −22.1309 | −1.17791 | −0.588955 | − | 0.808166i | \(-0.700461\pi\) | ||||
−0.588955 | + | 0.808166i | \(0.700461\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0350 | −0.797973 | ||||||||
\(356\) | 8.89225 | 0.471288 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −22.7178 | −1.20067 | ||||||||
\(359\) | −34.4554 | −1.81848 | −0.909242 | − | 0.416268i | \(-0.863338\pi\) | ||||
−0.909242 | + | 0.416268i | \(0.863338\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.6912 | 1.40480 | ||||||||
\(362\) | −14.5360 | −0.763994 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.82259 | 0.200358 | ||||||||
\(365\) | −27.5987 | −1.44458 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.6470 | −1.54756 | −0.773780 | − | 0.633455i | \(-0.781636\pi\) | ||||
−0.773780 | + | 0.633455i | \(0.781636\pi\) | |||||||
\(368\) | 4.42326 | 0.230579 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −15.1294 | −0.786542 | ||||||||
\(371\) | 10.5740 | 0.548977 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.6924 | −1.27852 | −0.639262 | − | 0.768989i | \(-0.720760\pi\) | ||||
−0.639262 | + | 0.768989i | \(0.720760\pi\) | |||||||
\(374\) | 1.23579 | 0.0639010 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.23846 | 0.218582 | ||||||||
\(377\) | −13.8483 | −0.713222 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.1608 | −1.90882 | −0.954412 | − | 0.298493i | \(-0.903516\pi\) | ||||
−0.954412 | + | 0.298493i | \(0.903516\pi\) | |||||||
\(380\) | 17.5328 | 0.899416 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.0200 | −0.563834 | ||||||||
\(383\) | −16.4370 | −0.839894 | −0.419947 | − | 0.907549i | \(-0.637951\pi\) | ||||
−0.419947 | + | 0.907549i | \(0.637951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.2376 | −0.521757 | ||||||||
\(386\) | −8.08118 | −0.411321 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.88125 | −0.0955062 | ||||||||
\(389\) | −3.32747 | −0.168709 | −0.0843547 | − | 0.996436i | \(-0.526883\pi\) | ||||
−0.0843547 | + | 0.996436i | \(0.526883\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.96942 | −0.0995979 | ||||||||
\(392\) | −2.95510 | −0.149255 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.85675 | −0.295059 | ||||||||
\(395\) | 10.9563 | 0.551269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.88603 | 0.245223 | 0.122611 | − | 0.992455i | \(-0.460873\pi\) | ||||
0.122611 | + | 0.992455i | \(0.460873\pi\) | |||||||
\(398\) | −10.2804 | −0.515312 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.531380 | −0.0265690 | ||||||||
\(401\) | 18.0905 | 0.903396 | 0.451698 | − | 0.892171i | \(-0.350818\pi\) | ||||
0.451698 | + | 0.892171i | \(0.350818\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.4451 | −0.968629 | ||||||||
\(404\) | −3.90018 | −0.194041 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.75087 | 0.186152 | ||||||||
\(407\) | −27.9064 | −1.38327 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1826 | 0.651837 | 0.325918 | − | 0.945398i | \(-0.394327\pi\) | ||||
0.325918 | + | 0.945398i | \(0.394327\pi\) | |||||||
\(410\) | −5.01921 | −0.247881 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.39518 | −0.315068 | ||||||||
\(413\) | −7.97145 | −0.392249 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −24.3749 | −1.19652 | ||||||||
\(416\) | 18.6345 | 0.913631 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −27.6231 | −1.35109 | ||||||||
\(419\) | 33.2567 | 1.62470 | 0.812348 | − | 0.583173i | \(-0.198189\pi\) | ||||
0.812348 | + | 0.583173i | \(0.198189\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.43830 | −0.216309 | −0.108155 | − | 0.994134i | \(-0.534494\pi\) | ||||
−0.108155 | + | 0.994134i | \(0.534494\pi\) | |||||||
\(422\) | −13.2797 | −0.646445 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 31.2473 | 1.51750 | ||||||||
\(425\) | 0.236592 | 0.0114764 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.05914 | −0.0512552 | ||||||||
\(428\) | 6.96297 | 0.336568 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.8665 | 1.05450 | ||||||||
\(431\) | 19.7379 | 0.950743 | 0.475371 | − | 0.879785i | \(-0.342314\pi\) | ||||
0.475371 | + | 0.879785i | \(0.342314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 29.6295 | 1.42390 | 0.711952 | − | 0.702228i | \(-0.247811\pi\) | ||||
0.711952 | + | 0.702228i | \(0.247811\pi\) | |||||||
\(434\) | 5.26679 | 0.252814 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −22.1432 | −1.06047 | ||||||||
\(437\) | 44.0218 | 2.10585 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.2017 | −1.96645 | −0.983224 | − | 0.182403i | \(-0.941612\pi\) | ||||
−0.983224 | + | 0.182403i | \(0.941612\pi\) | |||||||
\(440\) | −30.2532 | −1.44226 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.02866 | 0.0489285 | ||||||||
\(443\) | 24.9988 | 1.18773 | 0.593863 | − | 0.804566i | \(-0.297602\pi\) | ||||
0.593863 | + | 0.804566i | \(0.297602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.8236 | −0.939727 | ||||||||
\(446\) | −4.80701 | −0.227619 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.40561 | −0.302637 | ||||||||
\(449\) | −4.39785 | −0.207548 | −0.103774 | − | 0.994601i | \(-0.533092\pi\) | ||||
−0.103774 | + | 0.994601i | \(0.533092\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.25800 | −0.435942 | ||||||||
\(452\) | −16.4545 | −0.773957 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.4979 | 1.05588 | ||||||||
\(455\) | −8.52173 | −0.399505 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.3749 | 0.625653 | 0.312826 | − | 0.949810i | \(-0.398724\pi\) | ||||
0.312826 | + | 0.949810i | \(0.398724\pi\) | |||||||
\(458\) | −3.79433 | −0.177298 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 16.8923 | 0.787606 | ||||||||
\(461\) | 10.2563 | 0.477685 | 0.238842 | − | 0.971058i | \(-0.423232\pi\) | ||||
0.238842 | + | 0.971058i | \(0.423232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.2905 | −0.757084 | −0.378542 | − | 0.925584i | \(-0.623575\pi\) | ||||
−0.378542 | + | 0.925584i | \(0.623575\pi\) | |||||||
\(464\) | 2.65407 | 0.123212 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.22246 | −0.0566294 | ||||||||
\(467\) | 8.99794 | 0.416375 | 0.208188 | − | 0.978089i | \(-0.433244\pi\) | ||||
0.208188 | + | 0.978089i | \(0.433244\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.72133 | 0.218011 | ||||||||
\(470\) | −3.31055 | −0.152704 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −23.5564 | −1.08427 | ||||||||
\(473\) | 40.3331 | 1.85452 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.28847 | −0.242652 | ||||||||
\(476\) | 0.326189 | 0.0149509 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.80908 | −0.357179 | ||||||||
\(479\) | 14.2639 | 0.651733 | 0.325866 | − | 0.945416i | \(-0.394344\pi\) | ||||
0.325866 | + | 0.945416i | \(0.394344\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.2292 | −1.05916 | ||||||||
\(482\) | 18.7013 | 0.851822 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.68603 | −0.349365 | ||||||||
\(485\) | 4.19390 | 0.190435 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.7755 | −0.488284 | −0.244142 | − | 0.969740i | \(-0.578506\pi\) | ||||
−0.244142 | + | 0.969740i | \(0.578506\pi\) | |||||||
\(488\) | −3.12985 | −0.141682 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.30815 | 0.104272 | ||||||||
\(491\) | 6.80357 | 0.307041 | 0.153520 | − | 0.988145i | \(-0.450939\pi\) | ||||
0.153520 | + | 0.988145i | \(0.450939\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.18170 | −0.0532211 | ||||||||
\(494\) | −22.9933 | −1.03452 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.72672 | 0.167335 | ||||||||
\(497\) | 6.25244 | 0.280460 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.2923 | −1.35607 | −0.678035 | − | 0.735030i | \(-0.737168\pi\) | ||||
−0.678035 | + | 0.735030i | \(0.737168\pi\) | |||||||
\(500\) | 10.9397 | 0.489237 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.16139 | −0.0964677 | ||||||||
\(503\) | −14.4114 | −0.642571 | −0.321286 | − | 0.946982i | \(-0.604115\pi\) | ||||
−0.321286 | + | 0.946982i | \(0.604115\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.69470 | 0.386909 | ||||||||
\(506\) | −26.6139 | −1.18313 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.07866 | 0.0478576 | ||||||||
\(509\) | 0.467272 | 0.0207115 | 0.0103557 | − | 0.999946i | \(-0.496704\pi\) | ||||
0.0103557 | + | 0.999946i | \(0.496704\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.4772 | 0.507721 | ||||||||
\(512\) | −7.58551 | −0.335235 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.8848 | −0.656541 | ||||||||
\(515\) | 14.2568 | 0.628230 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.10635 | −0.268557 | ||||||||
\(518\) | 6.29172 | 0.276442 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −25.1826 | −1.10433 | ||||||||
\(521\) | 34.7244 | 1.52130 | 0.760651 | − | 0.649160i | \(-0.224880\pi\) | ||||
0.760651 | + | 0.649160i | \(0.224880\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.13868 | −0.399607 | −0.199803 | − | 0.979836i | \(-0.564030\pi\) | ||||
−0.199803 | + | 0.979836i | \(0.564030\pi\) | |||||||
\(524\) | −6.41426 | −0.280208 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.68288 | −0.160581 | ||||||||
\(527\) | −1.65929 | −0.0722798 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4134 | 0.844063 | ||||||||
\(530\) | −24.4065 | −1.06015 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.29120 | −0.316114 | ||||||||
\(533\) | −7.70631 | −0.333797 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15.5226 | −0.671101 | ||||||||
\(536\) | 13.9520 | 0.602635 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.0105 | −0.647147 | ||||||||
\(539\) | 4.25741 | 0.183380 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.80281 | 0.378462 | 0.189231 | − | 0.981933i | \(-0.439400\pi\) | ||||
0.189231 | + | 0.981933i | \(0.439400\pi\) | |||||||
\(542\) | 22.5147 | 0.967089 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.59012 | 0.0681758 | ||||||||
\(545\) | 49.3641 | 2.11452 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.47099 | 0.105652 | 0.0528258 | − | 0.998604i | \(-0.483177\pi\) | ||||
0.0528258 | + | 0.998604i | \(0.483177\pi\) | |||||||
\(548\) | 1.48038 | 0.0632386 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.19721 | 0.136329 | ||||||||
\(551\) | 26.4142 | 1.12528 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.55627 | −0.193752 | ||||||||
\(554\) | 25.7531 | 1.09414 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.38075 | −0.143376 | ||||||||
\(557\) | −32.2057 | −1.36460 | −0.682299 | − | 0.731073i | \(-0.739020\pi\) | ||||
−0.682299 | + | 0.731073i | \(0.739020\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 33.5730 | 1.41999 | ||||||||
\(560\) | 1.63322 | 0.0690161 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 20.1304 | 0.849150 | ||||||||
\(563\) | −13.9684 | −0.588696 | −0.294348 | − | 0.955698i | \(-0.595102\pi\) | ||||
−0.294348 | + | 0.955698i | \(0.595102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 36.6823 | 1.54323 | ||||||||
\(566\) | −15.8884 | −0.667841 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 18.4766 | 0.775260 | ||||||||
\(569\) | 18.2780 | 0.766252 | 0.383126 | − | 0.923696i | \(-0.374847\pi\) | ||||
0.383126 | + | 0.923696i | \(0.374847\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 40.3925 | 1.69037 | 0.845187 | − | 0.534470i | \(-0.179489\pi\) | ||||
0.845187 | + | 0.534470i | \(0.179489\pi\) | |||||||
\(572\) | −16.2743 | −0.680464 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.08729 | 0.0871217 | ||||||||
\(575\) | −5.09525 | −0.212487 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.42495 | 0.184213 | 0.0921065 | − | 0.995749i | \(-0.470640\pi\) | ||||
0.0921065 | + | 0.995749i | \(0.470640\pi\) | |||||||
\(578\) | −16.2300 | −0.675077 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.1358 | 0.420865 | ||||||||
\(581\) | 10.1365 | 0.420534 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.0180 | −1.86446 | ||||||||
\(584\) | 33.9162 | 1.40346 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.9446 | 0.658667 | ||||||||
\(587\) | 22.3504 | 0.922500 | 0.461250 | − | 0.887270i | \(-0.347401\pi\) | ||||
0.461250 | + | 0.887270i | \(0.347401\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.0896 | 1.52825 | ||||||||
\(590\) | 18.3993 | 0.757487 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.45194 | 0.182974 | ||||||||
\(593\) | 39.1966 | 1.60961 | 0.804805 | − | 0.593539i | \(-0.202270\pi\) | ||||
0.804805 | + | 0.593539i | \(0.202270\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.727177 | −0.0298113 | ||||||||
\(596\) | 14.4220 | 0.590748 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −22.1533 | −0.905914 | ||||||||
\(599\) | 20.9632 | 0.856534 | 0.428267 | − | 0.903652i | \(-0.359124\pi\) | ||||
0.428267 | + | 0.903652i | \(0.359124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3899 | 1.60675 | 0.803375 | − | 0.595474i | \(-0.203036\pi\) | ||||
0.803375 | + | 0.595474i | \(0.203036\pi\) | |||||||
\(602\) | −9.09340 | −0.370620 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.1010 | 0.451694 | ||||||||
\(605\) | 17.1345 | 0.696618 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.62814 | −0.269028 | −0.134514 | − | 0.990912i | \(-0.542947\pi\) | ||||
−0.134514 | + | 0.990912i | \(0.542947\pi\) | |||||||
\(608\) | −35.5434 | −1.44148 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.44464 | 0.0989807 | ||||||||
\(611\) | −5.08289 | −0.205632 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.9071 | −0.925210 | −0.462605 | − | 0.886565i | \(-0.653085\pi\) | ||||
−0.462605 | + | 0.886565i | \(0.653085\pi\) | |||||||
\(614\) | −24.6199 | −0.993579 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 12.5811 | 0.506906 | ||||||||
\(617\) | 40.6908 | 1.63815 | 0.819076 | − | 0.573685i | \(-0.194487\pi\) | ||||
0.819076 | + | 0.573685i | \(0.194487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.2607 | −0.975118 | −0.487559 | − | 0.873090i | \(-0.662113\pi\) | ||||
−0.487559 | + | 0.873090i | \(0.662113\pi\) | |||||||
\(620\) | 14.2322 | 0.571578 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.03554 | −0.242003 | ||||||||
\(623\) | 8.24382 | 0.330282 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.2998 | −1.13199 | ||||||||
\(626\) | −23.0579 | −0.921581 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −8.30933 | −0.331579 | ||||||||
\(629\) | −1.98219 | −0.0790351 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.8846 | −1.46835 | −0.734177 | − | 0.678959i | \(-0.762432\pi\) | ||||
−0.734177 | + | 0.678959i | \(0.762432\pi\) | |||||||
\(632\) | −13.4642 | −0.535578 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.2457 | 0.446624 | ||||||||
\(635\) | −2.40466 | −0.0954259 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.54385 | 0.140412 | ||||||||
\(638\) | −15.9690 | −0.632218 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −10.5035 | −0.415189 | ||||||||
\(641\) | 37.0112 | 1.46186 | 0.730928 | − | 0.682455i | \(-0.239088\pi\) | ||||
0.730928 | + | 0.682455i | \(0.239088\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.7735 | −0.779790 | −0.389895 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389895 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(644\) | −7.02481 | −0.276816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.96207 | −0.0771966 | ||||||||
\(647\) | 8.97670 | 0.352910 | 0.176455 | − | 0.984309i | \(-0.443537\pi\) | ||||
0.176455 | + | 0.984309i | \(0.443537\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 33.9378 | 1.33217 | ||||||||
\(650\) | 2.66134 | 0.104386 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.05565 | −0.276321 | ||||||||
\(653\) | −11.3033 | −0.442331 | −0.221166 | − | 0.975236i | \(-0.570986\pi\) | ||||
−0.221166 | + | 0.975236i | \(0.570986\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.2994 | 0.558722 | ||||||||
\(656\) | 1.47694 | 0.0576648 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.37672 | 0.0536703 | ||||||||
\(659\) | −44.1617 | −1.72029 | −0.860147 | − | 0.510046i | \(-0.829629\pi\) | ||||
−0.860147 | + | 0.510046i | \(0.829629\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.8877 | 1.39587 | 0.697936 | − | 0.716160i | \(-0.254102\pi\) | ||||
0.697936 | + | 0.716160i | \(0.254102\pi\) | |||||||
\(662\) | −13.8342 | −0.537680 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 29.9545 | 1.16246 | ||||||||
\(665\) | 16.2543 | 0.630316 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.4491 | 0.985393 | ||||||||
\(668\) | 2.22706 | 0.0861676 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.8975 | −0.421009 | ||||||||
\(671\) | 4.50918 | 0.174075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0012 | 1.15646 | 0.578230 | − | 0.815873i | \(-0.303743\pi\) | ||||
0.578230 | + | 0.815873i | \(0.303743\pi\) | |||||||
\(674\) | −13.5515 | −0.521984 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.475856 | 0.0183022 | ||||||||
\(677\) | 12.7361 | 0.489488 | 0.244744 | − | 0.969588i | \(-0.421296\pi\) | ||||
0.244744 | + | 0.969588i | \(0.421296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.74407 | −0.0669314 | ||||||||
\(680\) | −2.14888 | −0.0824058 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.4229 | −0.858618 | ||||||||
\(683\) | −21.9682 | −0.840591 | −0.420295 | − | 0.907387i | \(-0.638074\pi\) | ||||
−0.420295 | + | 0.907387i | \(0.638074\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.30022 | −0.126095 | ||||||||
\(686\) | −0.959867 | −0.0366479 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.43438 | −0.245308 | ||||||||
\(689\) | −37.4728 | −1.42760 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.3489 | 1.30669 | 0.653347 | − | 0.757058i | \(-0.273364\pi\) | ||||
0.653347 | + | 0.757058i | \(0.273364\pi\) | |||||||
\(692\) | −11.8890 | −0.451952 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.7241 | 1.05239 | ||||||||
\(695\) | 7.53673 | 0.285884 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.657595 | −0.0249082 | ||||||||
\(698\) | 23.3820 | 0.885022 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.843912 | 0.0318969 | ||||||||
\(701\) | −44.3643 | −1.67562 | −0.837809 | − | 0.545963i | \(-0.816164\pi\) | ||||
−0.837809 | + | 0.545963i | \(0.816164\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.3073 | 1.67108 | ||||||||
\(704\) | 27.2713 | 1.02783 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.2427 | −0.799481 | ||||||||
\(707\) | −3.61578 | −0.135985 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.5449 | 0.996913 | 0.498457 | − | 0.866915i | \(-0.333900\pi\) | ||||
0.498457 | + | 0.866915i | \(0.333900\pi\) | |||||||
\(710\) | −14.4316 | −0.541607 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 24.3613 | 0.912979 | ||||||||
\(713\) | 35.7345 | 1.33827 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 36.2805 | 1.35681 | ||||||||
\(716\) | 25.5292 | 0.954073 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −33.0725 | −1.23426 | ||||||||
\(719\) | −29.8919 | −1.11478 | −0.557389 | − | 0.830251i | \(-0.688197\pi\) | ||||
−0.557389 | + | 0.830251i | \(0.688197\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.92884 | −0.220801 | ||||||||
\(722\) | 25.6200 | 0.953478 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.3349 | 0.607081 | ||||||||
\(725\) | −3.05728 | −0.113544 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.0562 | −1.55978 | −0.779889 | − | 0.625918i | \(-0.784725\pi\) | ||||
−0.779889 | + | 0.625918i | \(0.784725\pi\) | |||||||
\(728\) | 10.4724 | 0.388134 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26.4911 | −0.980478 | ||||||||
\(731\) | 2.86485 | 0.105960 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2662 | 0.416128 | 0.208064 | − | 0.978115i | \(-0.433284\pi\) | ||||
0.208064 | + | 0.978115i | \(0.433284\pi\) | |||||||
\(734\) | −28.4571 | −1.05037 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −34.2448 | −1.26228 | ||||||||
\(737\) | −20.1006 | −0.740417 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3213 | 1.11539 | 0.557694 | − | 0.830046i | \(-0.311686\pi\) | ||||
0.557694 | + | 0.830046i | \(0.311686\pi\) | |||||||
\(740\) | 17.0018 | 0.624998 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.1497 | 0.372606 | ||||||||
\(743\) | 39.3851 | 1.44490 | 0.722450 | − | 0.691423i | \(-0.243016\pi\) | ||||
0.722450 | + | 0.691423i | \(0.243016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −32.1511 | −1.17792 | ||||||||
\(746\) | −23.7014 | −0.867771 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.38872 | −0.0507767 | ||||||||
\(749\) | 6.45523 | 0.235869 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.95873 | 0.0714751 | 0.0357375 | − | 0.999361i | \(-0.488622\pi\) | ||||
0.0357375 | + | 0.999361i | \(0.488622\pi\) | |||||||
\(752\) | 0.974153 | 0.0355237 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −13.2925 | −0.484084 | ||||||||
\(755\) | −24.7476 | −0.900658 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.2998 | 1.06492 | 0.532460 | − | 0.846455i | \(-0.321268\pi\) | ||||
0.532460 | + | 0.846455i | \(0.321268\pi\) | |||||||
\(758\) | −35.6694 | −1.29557 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.0332 | 1.74235 | ||||||||
\(761\) | 2.27331 | 0.0824075 | 0.0412038 | − | 0.999151i | \(-0.486881\pi\) | ||||
0.0412038 | + | 0.999151i | \(0.486881\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.5285 | −0.743183 | ||||||||
\(764\) | 12.3838 | 0.448031 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.7774 | −0.570060 | ||||||||
\(767\) | 28.2496 | 1.02003 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −37.8564 | −1.36514 | −0.682568 | − | 0.730822i | \(-0.739137\pi\) | ||||
−0.682568 | + | 0.730822i | \(0.739137\pi\) | |||||||
\(770\) | −9.82675 | −0.354131 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.08127 | 0.326842 | ||||||||
\(773\) | −31.5316 | −1.13411 | −0.567056 | − | 0.823679i | \(-0.691918\pi\) | ||||
−0.567056 | + | 0.823679i | \(0.691918\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.29289 | −0.154205 | ||||||||
\(776\) | −5.15391 | −0.185015 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.19393 | −0.114508 | ||||||||
\(779\) | 14.6990 | 0.526646 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.6192 | −0.952510 | ||||||||
\(782\) | −1.89038 | −0.0675999 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.679190 | −0.0242568 | ||||||||
\(785\) | 18.5241 | 0.661152 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.10263 | −0.181889 | −0.0909446 | − | 0.995856i | \(-0.528989\pi\) | ||||
−0.0909446 | + | 0.995856i | \(0.528989\pi\) | |||||||
\(788\) | 6.58155 | 0.234458 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 10.5165 | 0.374162 | ||||||||
\(791\) | −15.2547 | −0.542394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.75341 | 0.133288 | ||||||||
\(794\) | 4.68994 | 0.166440 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.5527 | 0.409475 | ||||||||
\(797\) | 20.3107 | 0.719441 | 0.359720 | − | 0.933060i | \(-0.382872\pi\) | ||||
0.359720 | + | 0.933060i | \(0.382872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.433733 | −0.0153444 | ||||||||
\(800\) | 4.11393 | 0.145449 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.3645 | 0.613161 | ||||||||
\(803\) | −48.8631 | −1.72434 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 15.6605 | 0.551959 | ||||||||
\(806\) | −18.6647 | −0.657436 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.6850 | −0.375896 | ||||||||
\(809\) | 41.8654 | 1.47191 | 0.735955 | − | 0.677030i | \(-0.236733\pi\) | ||||
0.735955 | + | 0.677030i | \(0.236733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.27580 | 0.0447992 | 0.0223996 | − | 0.999749i | \(-0.492869\pi\) | ||||
0.0223996 | + | 0.999749i | \(0.492869\pi\) | |||||||
\(812\) | −4.21506 | −0.147920 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.7865 | −0.938865 | ||||||||
\(815\) | 15.7292 | 0.550970 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −64.0371 | −2.24038 | ||||||||
\(818\) | 12.6535 | 0.442420 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.64037 | 0.196970 | ||||||||
\(821\) | −41.2734 | −1.44045 | −0.720226 | − | 0.693740i | \(-0.755962\pi\) | ||||
−0.720226 | + | 0.693740i | \(0.755962\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.3455 | 1.30178 | 0.650891 | − | 0.759171i | \(-0.274396\pi\) | ||||
0.650891 | + | 0.759171i | \(0.274396\pi\) | |||||||
\(824\) | −17.5203 | −0.610349 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.65153 | −0.266231 | ||||||||
\(827\) | 5.74511 | 0.199777 | 0.0998886 | − | 0.994999i | \(-0.468151\pi\) | ||||
0.0998886 | + | 0.994999i | \(0.468151\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.6365 | 1.61975 | 0.809876 | − | 0.586601i | \(-0.199534\pi\) | ||||
0.809876 | + | 0.586601i | \(0.199534\pi\) | |||||||
\(830\) | −23.3966 | −0.812110 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 22.7005 | 0.786999 | ||||||||
\(833\) | 0.302404 | 0.0104777 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.96481 | −0.171814 | ||||||||
\(836\) | 31.0417 | 1.07360 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 31.9220 | 1.10273 | ||||||||
\(839\) | −31.6074 | −1.09121 | −0.545605 | − | 0.838043i | \(-0.683700\pi\) | ||||
−0.545605 | + | 0.838043i | \(0.683700\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.7299 | −0.473446 | ||||||||
\(842\) | −4.26017 | −0.146815 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.9231 | 0.513675 | ||||||||
\(845\) | −1.06083 | −0.0364937 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.12556 | −0.244837 | ||||||||
\(848\) | 7.18178 | 0.246623 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.227097 | 0.00778937 | ||||||||
\(851\) | 42.6885 | 1.46334 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.7198 | −1.22302 | −0.611512 | − | 0.791235i | \(-0.709438\pi\) | ||||
−0.611512 | + | 0.791235i | \(0.709438\pi\) | |||||||
\(854\) | −1.01663 | −0.0347883 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.0758 | 0.651999 | ||||||||
\(857\) | 11.5668 | 0.395113 | 0.197556 | − | 0.980292i | \(-0.436699\pi\) | ||||
0.197556 | + | 0.980292i | \(0.436699\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.8509 | −1.18910 | −0.594549 | − | 0.804059i | \(-0.702669\pi\) | ||||
−0.594549 | + | 0.804059i | \(0.702669\pi\) | |||||||
\(860\) | −24.5726 | −0.837920 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 18.9458 | 0.645296 | ||||||||
\(863\) | −11.4883 | −0.391068 | −0.195534 | − | 0.980697i | \(-0.562644\pi\) | ||||
−0.195534 | + | 0.980697i | \(0.562644\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.5043 | 0.901172 | ||||||||
\(866\) | 28.4404 | 0.966444 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.91859 | −0.200890 | ||||||||
\(869\) | 19.3979 | 0.658029 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.7317 | −0.566931 | ||||||||
\(872\) | −60.6638 | −2.05434 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 42.2551 | 1.42930 | ||||||||
\(875\) | 10.1419 | 0.342860 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.92650 | −0.267659 | −0.133829 | − | 0.991004i | \(-0.542727\pi\) | ||||
−0.133829 | + | 0.991004i | \(0.542727\pi\) | |||||||
\(878\) | −39.5481 | −1.33468 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.95328 | −0.234395 | ||||||||
\(881\) | 31.4350 | 1.05907 | 0.529536 | − | 0.848287i | \(-0.322366\pi\) | ||||
0.529536 | + | 0.848287i | \(0.322366\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.77775 | 0.0598260 | 0.0299130 | − | 0.999553i | \(-0.490477\pi\) | ||||
0.0299130 | + | 0.999553i | \(0.490477\pi\) | |||||||
\(884\) | −1.15596 | −0.0388793 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.9955 | 0.806144 | ||||||||
\(887\) | −10.3134 | −0.346292 | −0.173146 | − | 0.984896i | \(-0.555393\pi\) | ||||
−0.173146 | + | 0.984896i | \(0.555393\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −19.0280 | −0.637819 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.40191 | 0.180869 | ||||||||
\(893\) | 9.69510 | 0.324434 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −56.9126 | −1.90238 | ||||||||
\(896\) | 4.36800 | 0.145925 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.22135 | −0.140868 | ||||||||
\(899\) | 21.4415 | 0.715115 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.19763 | −0.106528 | ||||||||
\(902\) | −8.88644 | −0.295886 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −45.0791 | −1.49931 | ||||||||
\(905\) | −36.4155 | −1.21049 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.28463 | 0.0758598 | 0.0379299 | − | 0.999280i | \(-0.487924\pi\) | ||||
0.0379299 | + | 0.999280i | \(0.487924\pi\) | |||||||
\(908\) | −25.2822 | −0.839018 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.17973 | −0.271155 | ||||||||
\(911\) | 5.90967 | 0.195796 | 0.0978980 | − | 0.995196i | \(-0.468788\pi\) | ||||
0.0978980 | + | 0.995196i | \(0.468788\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.1554 | −1.42824 | ||||||||
\(914\) | 12.8381 | 0.424648 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.26390 | 0.140883 | ||||||||
\(917\) | −5.94653 | −0.196372 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.1535 | −1.48947 | −0.744737 | − | 0.667358i | \(-0.767425\pi\) | ||||
−0.744737 | + | 0.667358i | \(0.767425\pi\) | |||||||
\(920\) | 46.2783 | 1.52575 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 9.84471 | 0.324218 | ||||||||
\(923\) | −22.1577 | −0.729329 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.12829 | −0.168617 | ||||||||
\(926\) | −15.6367 | −0.513855 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −20.5477 | −0.674511 | ||||||||
\(929\) | −43.7874 | −1.43662 | −0.718309 | − | 0.695724i | \(-0.755084\pi\) | ||||
−0.718309 | + | 0.695724i | \(0.755084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.75953 | −0.221535 | ||||||||
\(932\) | 1.37375 | 0.0449986 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.63683 | 0.282606 | ||||||||
\(935\) | 3.09589 | 0.101246 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.0370 | 1.27528 | 0.637642 | − | 0.770333i | \(-0.279910\pi\) | ||||
0.637642 | + | 0.770333i | \(0.279910\pi\) | |||||||
\(938\) | 4.53185 | 0.147970 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 3.72025 | 0.121341 | ||||||||
\(941\) | −15.5982 | −0.508488 | −0.254244 | − | 0.967140i | \(-0.581827\pi\) | ||||
−0.254244 | + | 0.967140i | \(0.581827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.1620 | 0.461177 | ||||||||
\(944\) | −5.41413 | −0.176215 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 38.7144 | 1.25871 | ||||||||
\(947\) | 51.9065 | 1.68673 | 0.843367 | − | 0.537338i | \(-0.180570\pi\) | ||||
0.843367 | + | 0.537338i | \(0.180570\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.6734 | −1.32031 | ||||||||
\(950\) | −5.07623 | −0.164695 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.893633 | 0.0289628 | ||||||||
\(953\) | 9.02726 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.6074 | −0.893354 | ||||||||
\(956\) | 8.77550 | 0.283820 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.6914 | 0.442349 | ||||||||
\(959\) | 1.37243 | 0.0443180 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.892778 | −0.0287993 | ||||||||
\(962\) | −22.2969 | −0.718881 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.0157 | −0.676871 | ||||||||
\(965\) | −20.2449 | −0.651708 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.81098 | 0.219027 | 0.109513 | − | 0.993985i | \(-0.465071\pi\) | ||||
0.109513 | + | 0.993985i | \(0.465071\pi\) | |||||||
\(968\) | −21.0567 | −0.676789 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.02558 | 0.129254 | ||||||||
\(971\) | −24.2046 | −0.776764 | −0.388382 | − | 0.921499i | \(-0.626966\pi\) | ||||
−0.388382 | + | 0.921499i | \(0.626966\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.13422 | −0.100479 | ||||||||
\(974\) | −10.3430 | −0.331412 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.719354 | −0.0230260 | ||||||||
\(977\) | 25.4883 | 0.815443 | 0.407722 | − | 0.913106i | \(-0.366323\pi\) | ||||
0.407722 | + | 0.913106i | \(0.366323\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.0974 | −1.12172 | ||||||||
\(980\) | −2.59380 | −0.0828558 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.53052 | 0.208397 | ||||||||
\(983\) | 21.3210 | 0.680035 | 0.340017 | − | 0.940419i | \(-0.389567\pi\) | ||||
0.340017 | + | 0.940419i | \(0.389567\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.6723 | −0.467499 | ||||||||
\(986\) | −1.13428 | −0.0361227 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 25.8389 | 0.822045 | ||||||||
\(989\) | −61.6975 | −1.96187 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.5238 | 1.73200 | 0.866002 | − | 0.500040i | \(-0.166681\pi\) | ||||
0.866002 | + | 0.500040i | \(0.166681\pi\) | |||||||
\(992\) | −28.8521 | −0.916056 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00151 | 0.190356 | ||||||||
\(995\) | −25.7545 | −0.816473 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −54.8655 | −1.73761 | −0.868804 | − | 0.495155i | \(-0.835111\pi\) | ||||
−0.868804 | + | 0.495155i | \(0.835111\pi\) | |||||||
\(998\) | −29.0766 | −0.920403 | ||||||||
\(999\) | 0 | 0 |
(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 | 8001.2.a.z.1.22 | yes | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.11 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.11 | ✓ | 32 | 3.2 | odd | 2 | inner | |
8001.2.a.z.1.22 | yes | 32 | 1.1 | even | 1 | trivial |