Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8023,2,Mod(1,8023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8023, 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("8023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8023 = 71 \cdot 113 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8023.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: | \(64.0639775417\) |
Analytic rank: | \(1\) |
Dimension: | \(158\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 8023.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65311 | −1.87603 | −0.938017 | − | 0.346589i | \(-0.887340\pi\) | ||||
−0.938017 | + | 0.346589i | \(0.887340\pi\) | |||||||
\(3\) | 3.18762 | 1.84037 | 0.920187 | − | 0.391480i | \(-0.128037\pi\) | ||||
0.920187 | + | 0.391480i | \(0.128037\pi\) | |||||||
\(4\) | 5.03901 | 2.51950 | ||||||||
\(5\) | 1.63340 | 0.730478 | 0.365239 | − | 0.930914i | \(-0.380987\pi\) | ||||
0.365239 | + | 0.930914i | \(0.380987\pi\) | |||||||
\(6\) | −8.45712 | −3.45260 | ||||||||
\(7\) | −4.20358 | −1.58880 | −0.794402 | − | 0.607392i | \(-0.792216\pi\) | ||||
−0.794402 | + | 0.607392i | \(0.792216\pi\) | |||||||
\(8\) | −8.06283 | −2.85064 | ||||||||
\(9\) | 7.16092 | 2.38697 | ||||||||
\(10\) | −4.33359 | −1.37040 | ||||||||
\(11\) | 2.16758 | 0.653551 | 0.326775 | − | 0.945102i | \(-0.394038\pi\) | ||||
0.326775 | + | 0.945102i | \(0.394038\pi\) | |||||||
\(12\) | 16.0624 | 4.63683 | ||||||||
\(13\) | −5.03410 | −1.39621 | −0.698103 | − | 0.715997i | \(-0.745972\pi\) | ||||
−0.698103 | + | 0.715997i | \(0.745972\pi\) | |||||||
\(14\) | 11.1526 | 2.98065 | ||||||||
\(15\) | 5.20666 | 1.34435 | ||||||||
\(16\) | 11.3136 | 2.82840 | ||||||||
\(17\) | −3.71761 | −0.901652 | −0.450826 | − | 0.892612i | \(-0.648870\pi\) | ||||
−0.450826 | + | 0.892612i | \(0.648870\pi\) | |||||||
\(18\) | −18.9987 | −4.47805 | ||||||||
\(19\) | −3.68579 | −0.845578 | −0.422789 | − | 0.906228i | \(-0.638949\pi\) | ||||
−0.422789 | + | 0.906228i | \(0.638949\pi\) | |||||||
\(20\) | 8.23071 | 1.84044 | ||||||||
\(21\) | −13.3994 | −2.92399 | ||||||||
\(22\) | −5.75084 | −1.22608 | ||||||||
\(23\) | 8.32475 | 1.73583 | 0.867915 | − | 0.496713i | \(-0.165460\pi\) | ||||
0.867915 | + | 0.496713i | \(0.165460\pi\) | |||||||
\(24\) | −25.7012 | −5.24624 | ||||||||
\(25\) | −2.33201 | −0.466402 | ||||||||
\(26\) | 13.3560 | 2.61933 | ||||||||
\(27\) | 13.2634 | 2.55255 | ||||||||
\(28\) | −21.1819 | −4.00300 | ||||||||
\(29\) | 1.34136 | 0.249085 | 0.124542 | − | 0.992214i | \(-0.460254\pi\) | ||||
0.124542 | + | 0.992214i | \(0.460254\pi\) | |||||||
\(30\) | −13.8138 | −2.52205 | ||||||||
\(31\) | −5.07756 | −0.911958 | −0.455979 | − | 0.889991i | \(-0.650711\pi\) | ||||
−0.455979 | + | 0.889991i | \(0.650711\pi\) | |||||||
\(32\) | −13.8906 | −2.45553 | ||||||||
\(33\) | 6.90943 | 1.20278 | ||||||||
\(34\) | 9.86323 | 1.69153 | ||||||||
\(35\) | −6.86613 | −1.16059 | ||||||||
\(36\) | 36.0839 | 6.01399 | ||||||||
\(37\) | −8.50610 | −1.39839 | −0.699197 | − | 0.714929i | \(-0.746459\pi\) | ||||
−0.699197 | + | 0.714929i | \(0.746459\pi\) | |||||||
\(38\) | 9.77882 | 1.58633 | ||||||||
\(39\) | −16.0468 | −2.56954 | ||||||||
\(40\) | −13.1698 | −2.08233 | ||||||||
\(41\) | 4.79784 | 0.749297 | 0.374648 | − | 0.927167i | \(-0.377763\pi\) | ||||
0.374648 | + | 0.927167i | \(0.377763\pi\) | |||||||
\(42\) | 35.5502 | 5.48551 | ||||||||
\(43\) | 5.13540 | 0.783141 | 0.391570 | − | 0.920148i | \(-0.371932\pi\) | ||||
0.391570 | + | 0.920148i | \(0.371932\pi\) | |||||||
\(44\) | 10.9225 | 1.64662 | ||||||||
\(45\) | 11.6966 | 1.74363 | ||||||||
\(46\) | −22.0865 | −3.25648 | ||||||||
\(47\) | 8.84448 | 1.29010 | 0.645050 | − | 0.764141i | \(-0.276837\pi\) | ||||
0.645050 | + | 0.764141i | \(0.276837\pi\) | |||||||
\(48\) | 36.0634 | 5.20530 | ||||||||
\(49\) | 10.6701 | 1.52430 | ||||||||
\(50\) | 6.18708 | 0.874985 | ||||||||
\(51\) | −11.8503 | −1.65938 | ||||||||
\(52\) | −25.3668 | −3.51775 | ||||||||
\(53\) | −1.62659 | −0.223429 | −0.111715 | − | 0.993740i | \(-0.535634\pi\) | ||||
−0.111715 | + | 0.993740i | \(0.535634\pi\) | |||||||
\(54\) | −35.1894 | −4.78867 | ||||||||
\(55\) | 3.54053 | 0.477405 | ||||||||
\(56\) | 33.8928 | 4.52911 | ||||||||
\(57\) | −11.7489 | −1.55618 | ||||||||
\(58\) | −3.55879 | −0.467291 | ||||||||
\(59\) | −6.82868 | −0.889019 | −0.444509 | − | 0.895774i | \(-0.646622\pi\) | ||||
−0.444509 | + | 0.895774i | \(0.646622\pi\) | |||||||
\(60\) | 26.2364 | 3.38710 | ||||||||
\(61\) | 10.3494 | 1.32510 | 0.662552 | − | 0.749016i | \(-0.269473\pi\) | ||||
0.662552 | + | 0.749016i | \(0.269473\pi\) | |||||||
\(62\) | 13.4714 | 1.71086 | ||||||||
\(63\) | −30.1015 | −3.79244 | ||||||||
\(64\) | 14.2260 | 1.77825 | ||||||||
\(65\) | −8.22269 | −1.01990 | ||||||||
\(66\) | −18.3315 | −2.25645 | ||||||||
\(67\) | −12.2664 | −1.49858 | −0.749288 | − | 0.662245i | \(-0.769604\pi\) | ||||
−0.749288 | + | 0.662245i | \(0.769604\pi\) | |||||||
\(68\) | −18.7330 | −2.27172 | ||||||||
\(69\) | 26.5361 | 3.19457 | ||||||||
\(70\) | 18.2166 | 2.17730 | ||||||||
\(71\) | −1.00000 | −0.118678 | ||||||||
\(72\) | −57.7373 | −6.80441 | ||||||||
\(73\) | −15.9852 | −1.87093 | −0.935465 | − | 0.353420i | \(-0.885018\pi\) | ||||
−0.935465 | + | 0.353420i | \(0.885018\pi\) | |||||||
\(74\) | 22.5676 | 2.62344 | ||||||||
\(75\) | −7.43356 | −0.858353 | ||||||||
\(76\) | −18.5727 | −2.13044 | ||||||||
\(77\) | −9.11161 | −1.03836 | ||||||||
\(78\) | 42.5739 | 4.82055 | ||||||||
\(79\) | −3.57000 | −0.401656 | −0.200828 | − | 0.979626i | \(-0.564363\pi\) | ||||
−0.200828 | + | 0.979626i | \(0.564363\pi\) | |||||||
\(80\) | 18.4796 | 2.06608 | ||||||||
\(81\) | 20.7961 | 2.31067 | ||||||||
\(82\) | −12.7292 | −1.40571 | ||||||||
\(83\) | −5.03437 | −0.552594 | −0.276297 | − | 0.961072i | \(-0.589107\pi\) | ||||
−0.276297 | + | 0.961072i | \(0.589107\pi\) | |||||||
\(84\) | −67.5198 | −7.36702 | ||||||||
\(85\) | −6.07233 | −0.658637 | ||||||||
\(86\) | −13.6248 | −1.46920 | ||||||||
\(87\) | 4.27575 | 0.458409 | ||||||||
\(88\) | −17.4769 | −1.86304 | ||||||||
\(89\) | −17.4561 | −1.85034 | −0.925172 | − | 0.379549i | \(-0.876079\pi\) | ||||
−0.925172 | + | 0.379549i | \(0.876079\pi\) | |||||||
\(90\) | −31.0325 | −3.27111 | ||||||||
\(91\) | 21.1612 | 2.21830 | ||||||||
\(92\) | 41.9485 | 4.37343 | ||||||||
\(93\) | −16.1853 | −1.67834 | ||||||||
\(94\) | −23.4654 | −2.42027 | ||||||||
\(95\) | −6.02037 | −0.617677 | ||||||||
\(96\) | −44.2778 | −4.51909 | ||||||||
\(97\) | 10.7728 | 1.09382 | 0.546908 | − | 0.837193i | \(-0.315805\pi\) | ||||
0.546908 | + | 0.837193i | \(0.315805\pi\) | |||||||
\(98\) | −28.3090 | −2.85964 | ||||||||
\(99\) | 15.5219 | 1.56001 | ||||||||
\(100\) | −11.7510 | −1.17510 | ||||||||
\(101\) | 16.4307 | 1.63491 | 0.817457 | − | 0.575990i | \(-0.195383\pi\) | ||||
0.817457 | + | 0.575990i | \(0.195383\pi\) | |||||||
\(102\) | 31.4402 | 3.11305 | ||||||||
\(103\) | −8.18039 | −0.806038 | −0.403019 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403019 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(104\) | 40.5891 | 3.98008 | ||||||||
\(105\) | −21.8866 | −2.13591 | ||||||||
\(106\) | 4.31552 | 0.419161 | ||||||||
\(107\) | −15.2568 | −1.47493 | −0.737467 | − | 0.675383i | \(-0.763978\pi\) | ||||
−0.737467 | + | 0.675383i | \(0.763978\pi\) | |||||||
\(108\) | 66.8346 | 6.43116 | ||||||||
\(109\) | 4.92343 | 0.471580 | 0.235790 | − | 0.971804i | \(-0.424232\pi\) | ||||
0.235790 | + | 0.971804i | \(0.424232\pi\) | |||||||
\(110\) | −9.39342 | −0.895627 | ||||||||
\(111\) | −27.1142 | −2.57357 | ||||||||
\(112\) | −47.5576 | −4.49377 | ||||||||
\(113\) | −1.00000 | −0.0940721 | ||||||||
\(114\) | 31.1712 | 2.91945 | ||||||||
\(115\) | 13.5976 | 1.26799 | ||||||||
\(116\) | 6.75913 | 0.627570 | ||||||||
\(117\) | −36.0488 | −3.33271 | ||||||||
\(118\) | 18.1173 | 1.66783 | ||||||||
\(119\) | 15.6273 | 1.43255 | ||||||||
\(120\) | −41.9804 | −3.83227 | ||||||||
\(121\) | −6.30159 | −0.572871 | ||||||||
\(122\) | −27.4581 | −2.48594 | ||||||||
\(123\) | 15.2937 | 1.37899 | ||||||||
\(124\) | −25.5859 | −2.29768 | ||||||||
\(125\) | −11.9761 | −1.07117 | ||||||||
\(126\) | 79.8628 | 7.11474 | ||||||||
\(127\) | 2.87553 | 0.255162 | 0.127581 | − | 0.991828i | \(-0.459279\pi\) | ||||
0.127581 | + | 0.991828i | \(0.459279\pi\) | |||||||
\(128\) | −9.96218 | −0.880541 | ||||||||
\(129\) | 16.3697 | 1.44127 | ||||||||
\(130\) | 21.8157 | 1.91336 | ||||||||
\(131\) | 16.2102 | 1.41629 | 0.708145 | − | 0.706067i | \(-0.249532\pi\) | ||||
0.708145 | + | 0.706067i | \(0.249532\pi\) | |||||||
\(132\) | 34.8167 | 3.03040 | ||||||||
\(133\) | 15.4935 | 1.34346 | ||||||||
\(134\) | 32.5441 | 2.81138 | ||||||||
\(135\) | 21.6645 | 1.86458 | ||||||||
\(136\) | 29.9744 | 2.57029 | ||||||||
\(137\) | −0.210990 | −0.0180261 | −0.00901306 | − | 0.999959i | \(-0.502869\pi\) | ||||
−0.00901306 | + | 0.999959i | \(0.502869\pi\) | |||||||
\(138\) | −70.4033 | −5.99313 | ||||||||
\(139\) | −0.551847 | −0.0468070 | −0.0234035 | − | 0.999726i | \(-0.507450\pi\) | ||||
−0.0234035 | + | 0.999726i | \(0.507450\pi\) | |||||||
\(140\) | −34.5985 | −2.92410 | ||||||||
\(141\) | 28.1928 | 2.37426 | ||||||||
\(142\) | 2.65311 | 0.222644 | ||||||||
\(143\) | −10.9118 | −0.912492 | ||||||||
\(144\) | 81.0157 | 6.75131 | ||||||||
\(145\) | 2.19098 | 0.181951 | ||||||||
\(146\) | 42.4106 | 3.50993 | ||||||||
\(147\) | 34.0123 | 2.80528 | ||||||||
\(148\) | −42.8623 | −3.52326 | ||||||||
\(149\) | −8.87298 | −0.726903 | −0.363452 | − | 0.931613i | \(-0.618402\pi\) | ||||
−0.363452 | + | 0.931613i | \(0.618402\pi\) | |||||||
\(150\) | 19.7221 | 1.61030 | ||||||||
\(151\) | −7.40506 | −0.602615 | −0.301308 | − | 0.953527i | \(-0.597423\pi\) | ||||
−0.301308 | + | 0.953527i | \(0.597423\pi\) | |||||||
\(152\) | 29.7179 | 2.41044 | ||||||||
\(153\) | −26.6215 | −2.15222 | ||||||||
\(154\) | 24.1741 | 1.94801 | ||||||||
\(155\) | −8.29369 | −0.666165 | ||||||||
\(156\) | −80.8599 | −6.47397 | ||||||||
\(157\) | −3.00465 | −0.239797 | −0.119898 | − | 0.992786i | \(-0.538257\pi\) | ||||
−0.119898 | + | 0.992786i | \(0.538257\pi\) | |||||||
\(158\) | 9.47161 | 0.753521 | ||||||||
\(159\) | −5.18495 | −0.411193 | ||||||||
\(160\) | −22.6888 | −1.79371 | ||||||||
\(161\) | −34.9938 | −2.75789 | ||||||||
\(162\) | −55.1743 | −4.33490 | ||||||||
\(163\) | 6.98601 | 0.547186 | 0.273593 | − | 0.961846i | \(-0.411788\pi\) | ||||
0.273593 | + | 0.961846i | \(0.411788\pi\) | |||||||
\(164\) | 24.1764 | 1.88786 | ||||||||
\(165\) | 11.2859 | 0.878603 | ||||||||
\(166\) | 13.3568 | 1.03669 | ||||||||
\(167\) | 15.9892 | 1.23728 | 0.618639 | − | 0.785675i | \(-0.287684\pi\) | ||||
0.618639 | + | 0.785675i | \(0.287684\pi\) | |||||||
\(168\) | 108.037 | 8.33526 | ||||||||
\(169\) | 12.3421 | 0.949394 | ||||||||
\(170\) | 16.1106 | 1.23563 | ||||||||
\(171\) | −26.3937 | −2.01837 | ||||||||
\(172\) | 25.8773 | 1.97313 | ||||||||
\(173\) | −16.1864 | −1.23063 | −0.615314 | − | 0.788282i | \(-0.710971\pi\) | ||||
−0.615314 | + | 0.788282i | \(0.710971\pi\) | |||||||
\(174\) | −11.3441 | −0.859991 | ||||||||
\(175\) | 9.80279 | 0.741021 | ||||||||
\(176\) | 24.5231 | 1.84850 | ||||||||
\(177\) | −21.7672 | −1.63613 | ||||||||
\(178\) | 46.3130 | 3.47131 | ||||||||
\(179\) | −22.5409 | −1.68479 | −0.842395 | − | 0.538861i | \(-0.818855\pi\) | ||||
−0.842395 | + | 0.538861i | \(0.818855\pi\) | |||||||
\(180\) | 58.9395 | 4.39309 | ||||||||
\(181\) | 7.21461 | 0.536257 | 0.268129 | − | 0.963383i | \(-0.413595\pi\) | ||||
0.268129 | + | 0.963383i | \(0.413595\pi\) | |||||||
\(182\) | −56.1432 | −4.16161 | ||||||||
\(183\) | 32.9899 | 2.43869 | ||||||||
\(184\) | −67.1210 | −4.94823 | ||||||||
\(185\) | −13.8939 | −1.02150 | ||||||||
\(186\) | 42.9416 | 3.14863 | ||||||||
\(187\) | −8.05822 | −0.589275 | ||||||||
\(188\) | 44.5674 | 3.25041 | ||||||||
\(189\) | −55.7540 | −4.05551 | ||||||||
\(190\) | 15.9727 | 1.15878 | ||||||||
\(191\) | −8.84764 | −0.640193 | −0.320096 | − | 0.947385i | \(-0.603715\pi\) | ||||
−0.320096 | + | 0.947385i | \(0.603715\pi\) | |||||||
\(192\) | 45.3472 | 3.27265 | ||||||||
\(193\) | −0.0801491 | −0.00576926 | −0.00288463 | − | 0.999996i | \(-0.500918\pi\) | ||||
−0.00288463 | + | 0.999996i | \(0.500918\pi\) | |||||||
\(194\) | −28.5815 | −2.05204 | ||||||||
\(195\) | −26.2108 | −1.87699 | ||||||||
\(196\) | 53.7668 | 3.84048 | ||||||||
\(197\) | −20.5025 | −1.46074 | −0.730372 | − | 0.683049i | \(-0.760653\pi\) | ||||
−0.730372 | + | 0.683049i | \(0.760653\pi\) | |||||||
\(198\) | −41.1813 | −2.92663 | ||||||||
\(199\) | −4.29022 | −0.304125 | −0.152063 | − | 0.988371i | \(-0.548592\pi\) | ||||
−0.152063 | + | 0.988371i | \(0.548592\pi\) | |||||||
\(200\) | 18.8026 | 1.32954 | ||||||||
\(201\) | −39.1005 | −2.75794 | ||||||||
\(202\) | −43.5924 | −3.06715 | ||||||||
\(203\) | −5.63853 | −0.395747 | ||||||||
\(204\) | −59.7138 | −4.18080 | ||||||||
\(205\) | 7.83679 | 0.547345 | ||||||||
\(206\) | 21.7035 | 1.51215 | ||||||||
\(207\) | 59.6129 | 4.14338 | ||||||||
\(208\) | −56.9537 | −3.94903 | ||||||||
\(209\) | −7.98926 | −0.552628 | ||||||||
\(210\) | 58.0676 | 4.00705 | ||||||||
\(211\) | −19.5231 | −1.34402 | −0.672012 | − | 0.740540i | \(-0.734570\pi\) | ||||
−0.672012 | + | 0.740540i | \(0.734570\pi\) | |||||||
\(212\) | −8.19639 | −0.562930 | ||||||||
\(213\) | −3.18762 | −0.218412 | ||||||||
\(214\) | 40.4781 | 2.76703 | ||||||||
\(215\) | 8.38815 | 0.572067 | ||||||||
\(216\) | −106.941 | −7.27641 | ||||||||
\(217\) | 21.3440 | 1.44892 | ||||||||
\(218\) | −13.0624 | −0.884699 | ||||||||
\(219\) | −50.9548 | −3.44321 | ||||||||
\(220\) | 17.8407 | 1.20282 | ||||||||
\(221\) | 18.7148 | 1.25889 | ||||||||
\(222\) | 71.9371 | 4.82810 | ||||||||
\(223\) | −7.71790 | −0.516829 | −0.258415 | − | 0.966034i | \(-0.583200\pi\) | ||||
−0.258415 | + | 0.966034i | \(0.583200\pi\) | |||||||
\(224\) | 58.3901 | 3.90135 | ||||||||
\(225\) | −16.6993 | −1.11329 | ||||||||
\(226\) | 2.65311 | 0.176482 | ||||||||
\(227\) | −23.0036 | −1.52680 | −0.763400 | − | 0.645926i | \(-0.776471\pi\) | ||||
−0.763400 | + | 0.645926i | \(0.776471\pi\) | |||||||
\(228\) | −59.2028 | −3.92080 | ||||||||
\(229\) | 9.96613 | 0.658580 | 0.329290 | − | 0.944229i | \(-0.393191\pi\) | ||||
0.329290 | + | 0.944229i | \(0.393191\pi\) | |||||||
\(230\) | −36.0761 | −2.37878 | ||||||||
\(231\) | −29.0444 | −1.91098 | ||||||||
\(232\) | −10.8152 | −0.710051 | ||||||||
\(233\) | 24.0838 | 1.57778 | 0.788890 | − | 0.614534i | \(-0.210656\pi\) | ||||
0.788890 | + | 0.614534i | \(0.210656\pi\) | |||||||
\(234\) | 95.6415 | 6.25228 | ||||||||
\(235\) | 14.4466 | 0.942390 | ||||||||
\(236\) | −34.4098 | −2.23989 | ||||||||
\(237\) | −11.3798 | −0.739198 | ||||||||
\(238\) | −41.4609 | −2.68751 | ||||||||
\(239\) | −10.7836 | −0.697532 | −0.348766 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348766 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(240\) | 58.9059 | 3.80236 | ||||||||
\(241\) | −1.67148 | −0.107669 | −0.0538347 | − | 0.998550i | \(-0.517144\pi\) | ||||
−0.0538347 | + | 0.998550i | \(0.517144\pi\) | |||||||
\(242\) | 16.7188 | 1.07473 | ||||||||
\(243\) | 26.4996 | 1.69995 | ||||||||
\(244\) | 52.1507 | 3.33860 | ||||||||
\(245\) | 17.4285 | 1.11347 | ||||||||
\(246\) | −40.5759 | −2.58702 | ||||||||
\(247\) | 18.5546 | 1.18060 | ||||||||
\(248\) | 40.9395 | 2.59966 | ||||||||
\(249\) | −16.0477 | −1.01698 | ||||||||
\(250\) | 31.7739 | 2.00956 | ||||||||
\(251\) | −28.8956 | −1.82388 | −0.911938 | − | 0.410328i | \(-0.865414\pi\) | ||||
−0.911938 | + | 0.410328i | \(0.865414\pi\) | |||||||
\(252\) | −151.682 | −9.55506 | ||||||||
\(253\) | 18.0446 | 1.13445 | ||||||||
\(254\) | −7.62909 | −0.478692 | ||||||||
\(255\) | −19.3563 | −1.21214 | ||||||||
\(256\) | −2.02129 | −0.126331 | ||||||||
\(257\) | −0.195501 | −0.0121950 | −0.00609751 | − | 0.999981i | \(-0.501941\pi\) | ||||
−0.00609751 | + | 0.999981i | \(0.501941\pi\) | |||||||
\(258\) | −43.4306 | −2.70387 | ||||||||
\(259\) | 35.7561 | 2.22178 | ||||||||
\(260\) | −41.4342 | −2.56964 | ||||||||
\(261\) | 9.60539 | 0.594559 | ||||||||
\(262\) | −43.0074 | −2.65701 | ||||||||
\(263\) | 6.13642 | 0.378388 | 0.189194 | − | 0.981940i | \(-0.439413\pi\) | ||||
0.189194 | + | 0.981940i | \(0.439413\pi\) | |||||||
\(264\) | −55.7096 | −3.42869 | ||||||||
\(265\) | −2.65687 | −0.163210 | ||||||||
\(266\) | −41.1061 | −2.52038 | ||||||||
\(267\) | −55.6434 | −3.40532 | ||||||||
\(268\) | −61.8103 | −3.77567 | ||||||||
\(269\) | −9.97582 | −0.608237 | −0.304118 | − | 0.952634i | \(-0.598362\pi\) | ||||
−0.304118 | + | 0.952634i | \(0.598362\pi\) | |||||||
\(270\) | −57.4784 | −3.49802 | ||||||||
\(271\) | 12.4706 | 0.757535 | 0.378768 | − | 0.925492i | \(-0.376348\pi\) | ||||
0.378768 | + | 0.925492i | \(0.376348\pi\) | |||||||
\(272\) | −42.0594 | −2.55023 | ||||||||
\(273\) | 67.4540 | 4.08250 | ||||||||
\(274\) | 0.559781 | 0.0338176 | ||||||||
\(275\) | −5.05482 | −0.304817 | ||||||||
\(276\) | 133.716 | 8.04874 | ||||||||
\(277\) | −30.0747 | −1.80702 | −0.903508 | − | 0.428572i | \(-0.859017\pi\) | ||||
−0.903508 | + | 0.428572i | \(0.859017\pi\) | |||||||
\(278\) | 1.46411 | 0.0878116 | ||||||||
\(279\) | −36.3601 | −2.17682 | ||||||||
\(280\) | 55.3604 | 3.30842 | ||||||||
\(281\) | 23.9708 | 1.42998 | 0.714988 | − | 0.699137i | \(-0.246432\pi\) | ||||
0.714988 | + | 0.699137i | \(0.246432\pi\) | |||||||
\(282\) | −74.7988 | −4.45420 | ||||||||
\(283\) | 1.38317 | 0.0822211 | 0.0411105 | − | 0.999155i | \(-0.486910\pi\) | ||||
0.0411105 | + | 0.999155i | \(0.486910\pi\) | |||||||
\(284\) | −5.03901 | −0.299010 | ||||||||
\(285\) | −19.1906 | −1.13676 | ||||||||
\(286\) | 28.9503 | 1.71187 | ||||||||
\(287\) | −20.1681 | −1.19049 | ||||||||
\(288\) | −99.4692 | −5.86128 | ||||||||
\(289\) | −3.17941 | −0.187024 | ||||||||
\(290\) | −5.81292 | −0.341346 | ||||||||
\(291\) | 34.3397 | 2.01303 | ||||||||
\(292\) | −80.5497 | −4.71381 | ||||||||
\(293\) | 22.7327 | 1.32806 | 0.664030 | − | 0.747706i | \(-0.268845\pi\) | ||||
0.664030 | + | 0.747706i | \(0.268845\pi\) | |||||||
\(294\) | −90.2384 | −5.26281 | ||||||||
\(295\) | −11.1540 | −0.649409 | ||||||||
\(296\) | 68.5833 | 3.98632 | ||||||||
\(297\) | 28.7496 | 1.66822 | ||||||||
\(298\) | 23.5410 | 1.36369 | ||||||||
\(299\) | −41.9076 | −2.42358 | ||||||||
\(300\) | −37.4577 | −2.16262 | ||||||||
\(301\) | −21.5871 | −1.24426 | ||||||||
\(302\) | 19.6465 | 1.13053 | ||||||||
\(303\) | 52.3748 | 3.00885 | ||||||||
\(304\) | −41.6995 | −2.39163 | ||||||||
\(305\) | 16.9047 | 0.967959 | ||||||||
\(306\) | 70.6298 | 4.03764 | ||||||||
\(307\) | −8.24446 | −0.470536 | −0.235268 | − | 0.971931i | \(-0.575597\pi\) | ||||
−0.235268 | + | 0.971931i | \(0.575597\pi\) | |||||||
\(308\) | −45.9135 | −2.61616 | ||||||||
\(309\) | −26.0760 | −1.48341 | ||||||||
\(310\) | 22.0041 | 1.24975 | ||||||||
\(311\) | −2.81256 | −0.159486 | −0.0797429 | − | 0.996815i | \(-0.525410\pi\) | ||||
−0.0797429 | + | 0.996815i | \(0.525410\pi\) | |||||||
\(312\) | 129.383 | 7.32484 | ||||||||
\(313\) | −25.0286 | −1.41470 | −0.707351 | − | 0.706862i | \(-0.750110\pi\) | ||||
−0.707351 | + | 0.706862i | \(0.750110\pi\) | |||||||
\(314\) | 7.97167 | 0.449867 | ||||||||
\(315\) | −49.1678 | −2.77029 | ||||||||
\(316\) | −17.9893 | −1.01197 | ||||||||
\(317\) | −14.0682 | −0.790152 | −0.395076 | − | 0.918649i | \(-0.629282\pi\) | ||||
−0.395076 | + | 0.918649i | \(0.629282\pi\) | |||||||
\(318\) | 13.7562 | 0.771412 | ||||||||
\(319\) | 2.90751 | 0.162789 | ||||||||
\(320\) | 23.2368 | 1.29898 | ||||||||
\(321\) | −48.6330 | −2.71443 | ||||||||
\(322\) | 92.8424 | 5.17390 | ||||||||
\(323\) | 13.7023 | 0.762417 | ||||||||
\(324\) | 104.791 | 5.82175 | ||||||||
\(325\) | 11.7395 | 0.651193 | ||||||||
\(326\) | −18.5347 | −1.02654 | ||||||||
\(327\) | 15.6940 | 0.867882 | ||||||||
\(328\) | −38.6842 | −2.13598 | ||||||||
\(329\) | −37.1785 | −2.04972 | ||||||||
\(330\) | −29.9427 | −1.64829 | ||||||||
\(331\) | 2.70772 | 0.148830 | 0.0744149 | − | 0.997227i | \(-0.476291\pi\) | ||||
0.0744149 | + | 0.997227i | \(0.476291\pi\) | |||||||
\(332\) | −25.3682 | −1.39226 | ||||||||
\(333\) | −60.9115 | −3.33793 | ||||||||
\(334\) | −42.4210 | −2.32118 | ||||||||
\(335\) | −20.0359 | −1.09468 | ||||||||
\(336\) | −151.596 | −8.27021 | ||||||||
\(337\) | 11.9779 | 0.652477 | 0.326238 | − | 0.945288i | \(-0.394219\pi\) | ||||
0.326238 | + | 0.945288i | \(0.394219\pi\) | |||||||
\(338\) | −32.7450 | −1.78109 | ||||||||
\(339\) | −3.18762 | −0.173128 | ||||||||
\(340\) | −30.5985 | −1.65944 | ||||||||
\(341\) | −11.0060 | −0.596011 | ||||||||
\(342\) | 70.0254 | 3.78654 | ||||||||
\(343\) | −15.4276 | −0.833012 | ||||||||
\(344\) | −41.4058 | −2.23245 | ||||||||
\(345\) | 43.3441 | 2.33357 | ||||||||
\(346\) | 42.9443 | 2.30870 | ||||||||
\(347\) | −15.8771 | −0.852329 | −0.426164 | − | 0.904646i | \(-0.640135\pi\) | ||||
−0.426164 | + | 0.904646i | \(0.640135\pi\) | |||||||
\(348\) | 21.5456 | 1.15496 | ||||||||
\(349\) | −4.20634 | −0.225160 | −0.112580 | − | 0.993643i | \(-0.535911\pi\) | ||||
−0.112580 | + | 0.993643i | \(0.535911\pi\) | |||||||
\(350\) | −26.0079 | −1.39018 | ||||||||
\(351\) | −66.7694 | −3.56389 | ||||||||
\(352\) | −30.1089 | −1.60481 | ||||||||
\(353\) | 3.21012 | 0.170858 | 0.0854288 | − | 0.996344i | \(-0.472774\pi\) | ||||
0.0854288 | + | 0.996344i | \(0.472774\pi\) | |||||||
\(354\) | 57.7510 | 3.06943 | ||||||||
\(355\) | −1.63340 | −0.0866918 | ||||||||
\(356\) | −87.9615 | −4.66195 | ||||||||
\(357\) | 49.8138 | 2.63642 | ||||||||
\(358\) | 59.8037 | 3.16072 | ||||||||
\(359\) | 5.27319 | 0.278308 | 0.139154 | − | 0.990271i | \(-0.455562\pi\) | ||||
0.139154 | + | 0.990271i | \(0.455562\pi\) | |||||||
\(360\) | −94.3081 | −4.97047 | ||||||||
\(361\) | −5.41494 | −0.284997 | ||||||||
\(362\) | −19.1412 | −1.00604 | ||||||||
\(363\) | −20.0871 | −1.05430 | ||||||||
\(364\) | 106.632 | 5.58902 | ||||||||
\(365\) | −26.1103 | −1.36667 | ||||||||
\(366\) | −87.5260 | −4.57506 | ||||||||
\(367\) | −33.5018 | −1.74878 | −0.874389 | − | 0.485225i | \(-0.838738\pi\) | ||||
−0.874389 | + | 0.485225i | \(0.838738\pi\) | |||||||
\(368\) | 94.1827 | 4.90961 | ||||||||
\(369\) | 34.3570 | 1.78855 | ||||||||
\(370\) | 36.8620 | 1.91636 | ||||||||
\(371\) | 6.83750 | 0.354985 | ||||||||
\(372\) | −81.5581 | −4.22859 | ||||||||
\(373\) | −30.8460 | −1.59714 | −0.798572 | − | 0.601899i | \(-0.794411\pi\) | ||||
−0.798572 | + | 0.601899i | \(0.794411\pi\) | |||||||
\(374\) | 21.3794 | 1.10550 | ||||||||
\(375\) | −38.1752 | −1.97136 | ||||||||
\(376\) | −71.3115 | −3.67761 | ||||||||
\(377\) | −6.75254 | −0.347774 | ||||||||
\(378\) | 147.922 | 7.60827 | ||||||||
\(379\) | −12.2344 | −0.628438 | −0.314219 | − | 0.949351i | \(-0.601743\pi\) | ||||
−0.314219 | + | 0.949351i | \(0.601743\pi\) | |||||||
\(380\) | −30.3367 | −1.55624 | ||||||||
\(381\) | 9.16608 | 0.469593 | ||||||||
\(382\) | 23.4738 | 1.20102 | ||||||||
\(383\) | −28.8684 | −1.47511 | −0.737554 | − | 0.675289i | \(-0.764019\pi\) | ||||
−0.737554 | + | 0.675289i | \(0.764019\pi\) | |||||||
\(384\) | −31.7556 | −1.62052 | ||||||||
\(385\) | −14.8829 | −0.758503 | ||||||||
\(386\) | 0.212645 | 0.0108233 | ||||||||
\(387\) | 36.7742 | 1.86934 | ||||||||
\(388\) | 54.2844 | 2.75587 | ||||||||
\(389\) | 13.4361 | 0.681238 | 0.340619 | − | 0.940201i | \(-0.389363\pi\) | ||||
0.340619 | + | 0.940201i | \(0.389363\pi\) | |||||||
\(390\) | 69.5402 | 3.52131 | ||||||||
\(391\) | −30.9481 | −1.56511 | ||||||||
\(392\) | −86.0313 | −4.34524 | ||||||||
\(393\) | 51.6719 | 2.60650 | ||||||||
\(394\) | 54.3955 | 2.74041 | ||||||||
\(395\) | −5.83123 | −0.293401 | ||||||||
\(396\) | 78.2149 | 3.93045 | ||||||||
\(397\) | 6.92657 | 0.347634 | 0.173817 | − | 0.984778i | \(-0.444390\pi\) | ||||
0.173817 | + | 0.984778i | \(0.444390\pi\) | |||||||
\(398\) | 11.3824 | 0.570549 | ||||||||
\(399\) | 49.3875 | 2.47247 | ||||||||
\(400\) | −26.3834 | −1.31917 | ||||||||
\(401\) | 3.98177 | 0.198840 | 0.0994201 | − | 0.995046i | \(-0.468301\pi\) | ||||
0.0994201 | + | 0.995046i | \(0.468301\pi\) | |||||||
\(402\) | 103.738 | 5.17399 | ||||||||
\(403\) | 25.5609 | 1.27328 | ||||||||
\(404\) | 82.7943 | 4.11917 | ||||||||
\(405\) | 33.9683 | 1.68790 | ||||||||
\(406\) | 14.9596 | 0.742435 | ||||||||
\(407\) | −18.4377 | −0.913922 | ||||||||
\(408\) | 95.5471 | 4.73029 | ||||||||
\(409\) | −31.1055 | −1.53807 | −0.769034 | − | 0.639207i | \(-0.779263\pi\) | ||||
−0.769034 | + | 0.639207i | \(0.779263\pi\) | |||||||
\(410\) | −20.7919 | −1.02684 | ||||||||
\(411\) | −0.672557 | −0.0331748 | ||||||||
\(412\) | −41.2210 | −2.03082 | ||||||||
\(413\) | 28.7049 | 1.41248 | ||||||||
\(414\) | −158.160 | −7.77312 | ||||||||
\(415\) | −8.22314 | −0.403658 | ||||||||
\(416\) | 69.9264 | 3.42842 | ||||||||
\(417\) | −1.75908 | −0.0861424 | ||||||||
\(418\) | 21.1964 | 1.03675 | ||||||||
\(419\) | 14.6888 | 0.717595 | 0.358797 | − | 0.933415i | \(-0.383187\pi\) | ||||
0.358797 | + | 0.933415i | \(0.383187\pi\) | |||||||
\(420\) | −110.287 | −5.38144 | ||||||||
\(421\) | 38.7452 | 1.88832 | 0.944162 | − | 0.329480i | \(-0.106874\pi\) | ||||
0.944162 | + | 0.329480i | \(0.106874\pi\) | |||||||
\(422\) | 51.7969 | 2.52144 | ||||||||
\(423\) | 63.3346 | 3.07943 | ||||||||
\(424\) | 13.1149 | 0.636916 | ||||||||
\(425\) | 8.66949 | 0.420532 | ||||||||
\(426\) | 8.45712 | 0.409749 | ||||||||
\(427\) | −43.5045 | −2.10533 | ||||||||
\(428\) | −76.8793 | −3.71610 | ||||||||
\(429\) | −34.7827 | −1.67933 | ||||||||
\(430\) | −22.2547 | −1.07322 | ||||||||
\(431\) | 9.91713 | 0.477691 | 0.238846 | − | 0.971058i | \(-0.423231\pi\) | ||||
0.238846 | + | 0.971058i | \(0.423231\pi\) | |||||||
\(432\) | 150.057 | 7.21962 | ||||||||
\(433\) | 18.2435 | 0.876727 | 0.438363 | − | 0.898798i | \(-0.355558\pi\) | ||||
0.438363 | + | 0.898798i | \(0.355558\pi\) | |||||||
\(434\) | −56.6279 | −2.71823 | ||||||||
\(435\) | 6.98401 | 0.334858 | ||||||||
\(436\) | 24.8092 | 1.18815 | ||||||||
\(437\) | −30.6833 | −1.46778 | ||||||||
\(438\) | 135.189 | 6.45958 | ||||||||
\(439\) | −18.5053 | −0.883209 | −0.441604 | − | 0.897210i | \(-0.645590\pi\) | ||||
−0.441604 | + | 0.897210i | \(0.645590\pi\) | |||||||
\(440\) | −28.5467 | −1.36091 | ||||||||
\(441\) | 76.4078 | 3.63847 | ||||||||
\(442\) | −49.6524 | −2.36173 | ||||||||
\(443\) | 5.94598 | 0.282502 | 0.141251 | − | 0.989974i | \(-0.454888\pi\) | ||||
0.141251 | + | 0.989974i | \(0.454888\pi\) | |||||||
\(444\) | −136.629 | −6.48411 | ||||||||
\(445\) | −28.5128 | −1.35164 | ||||||||
\(446\) | 20.4765 | 0.969589 | ||||||||
\(447\) | −28.2837 | −1.33777 | ||||||||
\(448\) | −59.8003 | −2.82530 | ||||||||
\(449\) | 31.8811 | 1.50456 | 0.752280 | − | 0.658843i | \(-0.228954\pi\) | ||||
0.752280 | + | 0.658843i | \(0.228954\pi\) | |||||||
\(450\) | 44.3052 | 2.08857 | ||||||||
\(451\) | 10.3997 | 0.489703 | ||||||||
\(452\) | −5.03901 | −0.237015 | ||||||||
\(453\) | −23.6045 | −1.10904 | ||||||||
\(454\) | 61.0310 | 2.86433 | ||||||||
\(455\) | 34.5647 | 1.62042 | ||||||||
\(456\) | 94.7294 | 4.43611 | ||||||||
\(457\) | 19.6807 | 0.920622 | 0.460311 | − | 0.887758i | \(-0.347738\pi\) | ||||
0.460311 | + | 0.887758i | \(0.347738\pi\) | |||||||
\(458\) | −26.4413 | −1.23552 | ||||||||
\(459\) | −49.3083 | −2.30151 | ||||||||
\(460\) | 68.5186 | 3.19469 | ||||||||
\(461\) | 16.7739 | 0.781240 | 0.390620 | − | 0.920552i | \(-0.372261\pi\) | ||||
0.390620 | + | 0.920552i | \(0.372261\pi\) | |||||||
\(462\) | 77.0580 | 3.58506 | ||||||||
\(463\) | 12.7776 | 0.593828 | 0.296914 | − | 0.954904i | \(-0.404043\pi\) | ||||
0.296914 | + | 0.954904i | \(0.404043\pi\) | |||||||
\(464\) | 15.1756 | 0.704510 | ||||||||
\(465\) | −26.4371 | −1.22599 | ||||||||
\(466\) | −63.8970 | −2.95997 | ||||||||
\(467\) | 6.77405 | 0.313466 | 0.156733 | − | 0.987641i | \(-0.449904\pi\) | ||||
0.156733 | + | 0.987641i | \(0.449904\pi\) | |||||||
\(468\) | −181.650 | −8.39678 | ||||||||
\(469\) | 51.5627 | 2.38094 | ||||||||
\(470\) | −38.3283 | −1.76795 | ||||||||
\(471\) | −9.57767 | −0.441316 | ||||||||
\(472\) | 55.0585 | 2.53427 | ||||||||
\(473\) | 11.1314 | 0.511822 | ||||||||
\(474\) | 30.1919 | 1.38676 | ||||||||
\(475\) | 8.59529 | 0.394379 | ||||||||
\(476\) | 78.7459 | 3.60931 | ||||||||
\(477\) | −11.6479 | −0.533319 | ||||||||
\(478\) | 28.6101 | 1.30859 | ||||||||
\(479\) | 41.0926 | 1.87757 | 0.938784 | − | 0.344507i | \(-0.111954\pi\) | ||||
0.938784 | + | 0.344507i | \(0.111954\pi\) | |||||||
\(480\) | −72.3233 | −3.30109 | ||||||||
\(481\) | 42.8205 | 1.95245 | ||||||||
\(482\) | 4.43462 | 0.201991 | ||||||||
\(483\) | −111.547 | −5.07556 | ||||||||
\(484\) | −31.7537 | −1.44335 | ||||||||
\(485\) | 17.5963 | 0.799009 | ||||||||
\(486\) | −70.3064 | −3.18916 | ||||||||
\(487\) | −31.4162 | −1.42360 | −0.711802 | − | 0.702380i | \(-0.752121\pi\) | ||||
−0.711802 | + | 0.702380i | \(0.752121\pi\) | |||||||
\(488\) | −83.4454 | −3.77739 | ||||||||
\(489\) | 22.2687 | 1.00703 | ||||||||
\(490\) | −46.2399 | −2.08891 | ||||||||
\(491\) | 22.1114 | 0.997873 | 0.498937 | − | 0.866638i | \(-0.333724\pi\) | ||||
0.498937 | + | 0.866638i | \(0.333724\pi\) | |||||||
\(492\) | 77.0650 | 3.47436 | ||||||||
\(493\) | −4.98666 | −0.224588 | ||||||||
\(494\) | −49.2275 | −2.21485 | ||||||||
\(495\) | 25.3534 | 1.13955 | ||||||||
\(496\) | −57.4455 | −2.57938 | ||||||||
\(497\) | 4.20358 | 0.188556 | ||||||||
\(498\) | 42.5763 | 1.90789 | ||||||||
\(499\) | −3.33469 | −0.149281 | −0.0746405 | − | 0.997211i | \(-0.523781\pi\) | ||||
−0.0746405 | + | 0.997211i | \(0.523781\pi\) | |||||||
\(500\) | −60.3476 | −2.69883 | ||||||||
\(501\) | 50.9673 | 2.27705 | ||||||||
\(502\) | 76.6634 | 3.42165 | ||||||||
\(503\) | 15.4875 | 0.690555 | 0.345278 | − | 0.938501i | \(-0.387785\pi\) | ||||
0.345278 | + | 0.938501i | \(0.387785\pi\) | |||||||
\(504\) | 242.704 | 10.8109 | ||||||||
\(505\) | 26.8378 | 1.19427 | ||||||||
\(506\) | −47.8743 | −2.12827 | ||||||||
\(507\) | 39.3420 | 1.74724 | ||||||||
\(508\) | 14.4898 | 0.642881 | ||||||||
\(509\) | −6.08134 | −0.269551 | −0.134775 | − | 0.990876i | \(-0.543031\pi\) | ||||
−0.134775 | + | 0.990876i | \(0.543031\pi\) | |||||||
\(510\) | 51.3544 | 2.27401 | ||||||||
\(511\) | 67.1952 | 2.97254 | ||||||||
\(512\) | 25.2871 | 1.11754 | ||||||||
\(513\) | −48.8863 | −2.15838 | ||||||||
\(514\) | 0.518686 | 0.0228783 | ||||||||
\(515\) | −13.3618 | −0.588793 | ||||||||
\(516\) | 82.4870 | 3.63129 | ||||||||
\(517\) | 19.1711 | 0.843145 | ||||||||
\(518\) | −94.8650 | −4.16813 | ||||||||
\(519\) | −51.5960 | −2.26481 | ||||||||
\(520\) | 66.2981 | 2.90737 | ||||||||
\(521\) | −13.4697 | −0.590120 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(522\) | −25.4842 | −1.11541 | ||||||||
\(523\) | −27.6027 | −1.20698 | −0.603491 | − | 0.797370i | \(-0.706224\pi\) | ||||
−0.603491 | + | 0.797370i | \(0.706224\pi\) | |||||||
\(524\) | 81.6832 | 3.56835 | ||||||||
\(525\) | 31.2476 | 1.36376 | ||||||||
\(526\) | −16.2806 | −0.709869 | ||||||||
\(527\) | 18.8764 | 0.822268 | ||||||||
\(528\) | 78.1704 | 3.40193 | ||||||||
\(529\) | 46.3014 | 2.01310 | ||||||||
\(530\) | 7.04897 | 0.306188 | ||||||||
\(531\) | −48.8997 | −2.12207 | ||||||||
\(532\) | 78.0720 | 3.38485 | ||||||||
\(533\) | −24.1528 | −1.04617 | ||||||||
\(534\) | 147.628 | 6.38850 | ||||||||
\(535\) | −24.9205 | −1.07741 | ||||||||
\(536\) | 98.9017 | 4.27190 | ||||||||
\(537\) | −71.8520 | −3.10064 | ||||||||
\(538\) | 26.4670 | 1.14107 | ||||||||
\(539\) | 23.1283 | 0.996208 | ||||||||
\(540\) | 109.168 | 4.69782 | ||||||||
\(541\) | 29.9625 | 1.28819 | 0.644095 | − | 0.764946i | \(-0.277234\pi\) | ||||
0.644095 | + | 0.764946i | \(0.277234\pi\) | |||||||
\(542\) | −33.0859 | −1.42116 | ||||||||
\(543\) | 22.9974 | 0.986914 | ||||||||
\(544\) | 51.6396 | 2.21403 | ||||||||
\(545\) | 8.04193 | 0.344479 | ||||||||
\(546\) | −178.963 | −7.65891 | ||||||||
\(547\) | 14.3899 | 0.615268 | 0.307634 | − | 0.951505i | \(-0.400463\pi\) | ||||
0.307634 | + | 0.951505i | \(0.400463\pi\) | |||||||
\(548\) | −1.06318 | −0.0454169 | ||||||||
\(549\) | 74.1112 | 3.16299 | ||||||||
\(550\) | 13.4110 | 0.571847 | ||||||||
\(551\) | −4.94398 | −0.210621 | ||||||||
\(552\) | −213.956 | −9.10659 | ||||||||
\(553\) | 15.0068 | 0.638154 | ||||||||
\(554\) | 79.7917 | 3.39002 | ||||||||
\(555\) | −44.2883 | −1.87994 | ||||||||
\(556\) | −2.78076 | −0.117931 | ||||||||
\(557\) | −28.3468 | −1.20109 | −0.600546 | − | 0.799591i | \(-0.705050\pi\) | ||||
−0.600546 | + | 0.799591i | \(0.705050\pi\) | |||||||
\(558\) | 96.4673 | 4.08379 | ||||||||
\(559\) | −25.8521 | −1.09343 | ||||||||
\(560\) | −77.6805 | −3.28260 | ||||||||
\(561\) | −25.6865 | −1.08449 | ||||||||
\(562\) | −63.5971 | −2.68268 | ||||||||
\(563\) | −32.8296 | −1.38360 | −0.691802 | − | 0.722087i | \(-0.743183\pi\) | ||||
−0.691802 | + | 0.722087i | \(0.743183\pi\) | |||||||
\(564\) | 142.064 | 5.98197 | ||||||||
\(565\) | −1.63340 | −0.0687176 | ||||||||
\(566\) | −3.66971 | −0.154249 | ||||||||
\(567\) | −87.4179 | −3.67121 | ||||||||
\(568\) | 8.06283 | 0.338309 | ||||||||
\(569\) | −20.0665 | −0.841231 | −0.420616 | − | 0.907239i | \(-0.638186\pi\) | ||||
−0.420616 | + | 0.907239i | \(0.638186\pi\) | |||||||
\(570\) | 50.9149 | 2.13259 | ||||||||
\(571\) | 22.3214 | 0.934123 | 0.467061 | − | 0.884225i | \(-0.345313\pi\) | ||||
0.467061 | + | 0.884225i | \(0.345313\pi\) | |||||||
\(572\) | −54.9847 | −2.29903 | ||||||||
\(573\) | −28.2029 | −1.17819 | ||||||||
\(574\) | 53.5083 | 2.23339 | ||||||||
\(575\) | −19.4134 | −0.809594 | ||||||||
\(576\) | 101.872 | 4.24465 | ||||||||
\(577\) | 9.36579 | 0.389903 | 0.194952 | − | 0.980813i | \(-0.437545\pi\) | ||||
0.194952 | + | 0.980813i | \(0.437545\pi\) | |||||||
\(578\) | 8.43533 | 0.350863 | ||||||||
\(579\) | −0.255485 | −0.0106176 | ||||||||
\(580\) | 11.0404 | 0.458426 | ||||||||
\(581\) | 21.1624 | 0.877964 | ||||||||
\(582\) | −91.1071 | −3.77651 | ||||||||
\(583\) | −3.52576 | −0.146022 | ||||||||
\(584\) | 128.886 | 5.33335 | ||||||||
\(585\) | −58.8820 | −2.43447 | ||||||||
\(586\) | −60.3125 | −2.49149 | ||||||||
\(587\) | −30.0310 | −1.23951 | −0.619756 | − | 0.784795i | \(-0.712768\pi\) | ||||
−0.619756 | + | 0.784795i | \(0.712768\pi\) | |||||||
\(588\) | 171.388 | 7.06792 | ||||||||
\(589\) | 18.7148 | 0.771132 | ||||||||
\(590\) | 29.5927 | 1.21831 | ||||||||
\(591\) | −65.3543 | −2.68832 | ||||||||
\(592\) | −96.2345 | −3.95521 | ||||||||
\(593\) | −18.8196 | −0.772827 | −0.386414 | − | 0.922326i | \(-0.626286\pi\) | ||||
−0.386414 | + | 0.922326i | \(0.626286\pi\) | |||||||
\(594\) | −76.2760 | −3.12964 | ||||||||
\(595\) | 25.5256 | 1.04645 | ||||||||
\(596\) | −44.7110 | −1.83144 | ||||||||
\(597\) | −13.6756 | −0.559704 | ||||||||
\(598\) | 111.186 | 4.54671 | ||||||||
\(599\) | 22.0322 | 0.900210 | 0.450105 | − | 0.892976i | \(-0.351387\pi\) | ||||
0.450105 | + | 0.892976i | \(0.351387\pi\) | |||||||
\(600\) | 59.9355 | 2.44686 | ||||||||
\(601\) | 15.5878 | 0.635841 | 0.317920 | − | 0.948117i | \(-0.397016\pi\) | ||||
0.317920 | + | 0.948117i | \(0.397016\pi\) | |||||||
\(602\) | 57.2729 | 2.33427 | ||||||||
\(603\) | −87.8385 | −3.57706 | ||||||||
\(604\) | −37.3141 | −1.51829 | ||||||||
\(605\) | −10.2930 | −0.418470 | ||||||||
\(606\) | −138.956 | −5.64471 | ||||||||
\(607\) | 24.3938 | 0.990113 | 0.495056 | − | 0.868861i | \(-0.335147\pi\) | ||||
0.495056 | + | 0.868861i | \(0.335147\pi\) | |||||||
\(608\) | 51.1977 | 2.07634 | ||||||||
\(609\) | −17.9735 | −0.728322 | ||||||||
\(610\) | −44.8500 | −1.81592 | ||||||||
\(611\) | −44.5239 | −1.80125 | ||||||||
\(612\) | −134.146 | −5.42253 | ||||||||
\(613\) | 32.7273 | 1.32184 | 0.660922 | − | 0.750454i | \(-0.270165\pi\) | ||||
0.660922 | + | 0.750454i | \(0.270165\pi\) | |||||||
\(614\) | 21.8735 | 0.882742 | ||||||||
\(615\) | 24.9807 | 1.00732 | ||||||||
\(616\) | 73.4654 | 2.96001 | ||||||||
\(617\) | −31.3596 | −1.26249 | −0.631244 | − | 0.775584i | \(-0.717456\pi\) | ||||
−0.631244 | + | 0.775584i | \(0.717456\pi\) | |||||||
\(618\) | 69.1825 | 2.78293 | ||||||||
\(619\) | 6.53679 | 0.262736 | 0.131368 | − | 0.991334i | \(-0.458063\pi\) | ||||
0.131368 | + | 0.991334i | \(0.458063\pi\) | |||||||
\(620\) | −41.7920 | −1.67841 | ||||||||
\(621\) | 110.415 | 4.43079 | ||||||||
\(622\) | 7.46205 | 0.299201 | ||||||||
\(623\) | 73.3782 | 2.93984 | ||||||||
\(624\) | −181.547 | −7.26768 | ||||||||
\(625\) | −7.90170 | −0.316068 | ||||||||
\(626\) | 66.4038 | 2.65403 | ||||||||
\(627\) | −25.4667 | −1.01704 | ||||||||
\(628\) | −15.1404 | −0.604169 | ||||||||
\(629\) | 31.6223 | 1.26086 | ||||||||
\(630\) | 130.448 | 5.19716 | ||||||||
\(631\) | −2.05051 | −0.0816297 | −0.0408148 | − | 0.999167i | \(-0.512995\pi\) | ||||
−0.0408148 | + | 0.999167i | \(0.512995\pi\) | |||||||
\(632\) | 28.7843 | 1.14498 | ||||||||
\(633\) | −62.2322 | −2.47351 | ||||||||
\(634\) | 37.3247 | 1.48235 | ||||||||
\(635\) | 4.69688 | 0.186390 | ||||||||
\(636\) | −26.1270 | −1.03600 | ||||||||
\(637\) | −53.7143 | −2.12824 | ||||||||
\(638\) | −7.71396 | −0.305399 | ||||||||
\(639\) | −7.16092 | −0.283282 | ||||||||
\(640\) | −16.2722 | −0.643216 | ||||||||
\(641\) | 26.0642 | 1.02947 | 0.514736 | − | 0.857349i | \(-0.327890\pi\) | ||||
0.514736 | + | 0.857349i | \(0.327890\pi\) | |||||||
\(642\) | 129.029 | 5.09236 | ||||||||
\(643\) | 8.02091 | 0.316314 | 0.158157 | − | 0.987414i | \(-0.449445\pi\) | ||||
0.158157 | + | 0.987414i | \(0.449445\pi\) | |||||||
\(644\) | −176.334 | −6.94853 | ||||||||
\(645\) | 26.7382 | 1.05282 | ||||||||
\(646\) | −36.3538 | −1.43032 | ||||||||
\(647\) | −33.5034 | −1.31716 | −0.658578 | − | 0.752512i | \(-0.728842\pi\) | ||||
−0.658578 | + | 0.752512i | \(0.728842\pi\) | |||||||
\(648\) | −167.675 | −6.58690 | ||||||||
\(649\) | −14.8017 | −0.581019 | ||||||||
\(650\) | −31.1464 | −1.22166 | ||||||||
\(651\) | 68.0365 | 2.66656 | ||||||||
\(652\) | 35.2025 | 1.37864 | ||||||||
\(653\) | 27.2781 | 1.06747 | 0.533736 | − | 0.845651i | \(-0.320787\pi\) | ||||
0.533736 | + | 0.845651i | \(0.320787\pi\) | |||||||
\(654\) | −41.6381 | −1.62818 | ||||||||
\(655\) | 26.4777 | 1.03457 | ||||||||
\(656\) | 54.2808 | 2.11931 | ||||||||
\(657\) | −114.469 | −4.46586 | ||||||||
\(658\) | 98.6387 | 3.84534 | ||||||||
\(659\) | 32.9389 | 1.28312 | 0.641559 | − | 0.767073i | \(-0.278288\pi\) | ||||
0.641559 | + | 0.767073i | \(0.278288\pi\) | |||||||
\(660\) | 56.8695 | 2.21364 | ||||||||
\(661\) | 3.84905 | 0.149711 | 0.0748554 | − | 0.997194i | \(-0.476150\pi\) | ||||
0.0748554 | + | 0.997194i | \(0.476150\pi\) | |||||||
\(662\) | −7.18389 | −0.279210 | ||||||||
\(663\) | 59.6556 | 2.31683 | ||||||||
\(664\) | 40.5913 | 1.57525 | ||||||||
\(665\) | 25.3071 | 0.981368 | ||||||||
\(666\) | 161.605 | 6.26207 | ||||||||
\(667\) | 11.1665 | 0.432369 | ||||||||
\(668\) | 80.5695 | 3.11733 | ||||||||
\(669\) | −24.6017 | −0.951158 | ||||||||
\(670\) | 53.1574 | 2.05365 | ||||||||
\(671\) | 22.4332 | 0.866022 | ||||||||
\(672\) | 186.125 | 7.17995 | ||||||||
\(673\) | −10.9814 | −0.423300 | −0.211650 | − | 0.977346i | \(-0.567884\pi\) | ||||
−0.211650 | + | 0.977346i | \(0.567884\pi\) | |||||||
\(674\) | −31.7787 | −1.22407 | ||||||||
\(675\) | −30.9305 | −1.19051 | ||||||||
\(676\) | 62.1920 | 2.39200 | ||||||||
\(677\) | 37.6395 | 1.44660 | 0.723301 | − | 0.690533i | \(-0.242624\pi\) | ||||
0.723301 | + | 0.690533i | \(0.242624\pi\) | |||||||
\(678\) | 8.45712 | 0.324794 | ||||||||
\(679\) | −45.2845 | −1.73786 | ||||||||
\(680\) | 48.9602 | 1.87754 | ||||||||
\(681\) | −73.3266 | −2.80988 | ||||||||
\(682\) | 29.2003 | 1.11814 | ||||||||
\(683\) | −3.96056 | −0.151547 | −0.0757733 | − | 0.997125i | \(-0.524143\pi\) | ||||
−0.0757733 | + | 0.997125i | \(0.524143\pi\) | |||||||
\(684\) | −132.998 | −5.08530 | ||||||||
\(685\) | −0.344631 | −0.0131677 | ||||||||
\(686\) | 40.9312 | 1.56276 | ||||||||
\(687\) | 31.7682 | 1.21203 | ||||||||
\(688\) | 58.0997 | 2.21503 | ||||||||
\(689\) | 8.18840 | 0.311953 | ||||||||
\(690\) | −114.997 | −4.37785 | ||||||||
\(691\) | 23.8477 | 0.907208 | 0.453604 | − | 0.891203i | \(-0.350138\pi\) | ||||
0.453604 | + | 0.891203i | \(0.350138\pi\) | |||||||
\(692\) | −81.5633 | −3.10057 | ||||||||
\(693\) | −65.2476 | −2.47855 | ||||||||
\(694\) | 42.1238 | 1.59900 | ||||||||
\(695\) | −0.901386 | −0.0341915 | ||||||||
\(696\) | −34.4747 | −1.30676 | ||||||||
\(697\) | −17.8365 | −0.675605 | ||||||||
\(698\) | 11.1599 | 0.422408 | ||||||||
\(699\) | 76.7699 | 2.90370 | ||||||||
\(700\) | 49.3963 | 1.86701 | ||||||||
\(701\) | −38.7044 | −1.46185 | −0.730923 | − | 0.682460i | \(-0.760910\pi\) | ||||
−0.730923 | + | 0.682460i | \(0.760910\pi\) | |||||||
\(702\) | 177.147 | 6.68598 | ||||||||
\(703\) | 31.3517 | 1.18245 | ||||||||
\(704\) | 30.8361 | 1.16218 | ||||||||
\(705\) | 46.0501 | 1.73435 | ||||||||
\(706\) | −8.51682 | −0.320535 | ||||||||
\(707\) | −69.0677 | −2.59756 | ||||||||
\(708\) | −109.685 | −4.12223 | ||||||||
\(709\) | −6.74522 | −0.253322 | −0.126661 | − | 0.991946i | \(-0.540426\pi\) | ||||
−0.126661 | + | 0.991946i | \(0.540426\pi\) | |||||||
\(710\) | 4.33359 | 0.162637 | ||||||||
\(711\) | −25.5645 | −0.958743 | ||||||||
\(712\) | 140.746 | 5.27467 | ||||||||
\(713\) | −42.2694 | −1.58300 | ||||||||
\(714\) | −132.162 | −4.94602 | ||||||||
\(715\) | −17.8234 | −0.666556 | ||||||||
\(716\) | −113.584 | −4.24483 | ||||||||
\(717\) | −34.3740 | −1.28372 | ||||||||
\(718\) | −13.9904 | −0.522116 | ||||||||
\(719\) | 37.0830 | 1.38296 | 0.691482 | − | 0.722394i | \(-0.256958\pi\) | ||||
0.691482 | + | 0.722394i | \(0.256958\pi\) | |||||||
\(720\) | 132.331 | 4.93168 | ||||||||
\(721\) | 34.3869 | 1.28064 | ||||||||
\(722\) | 14.3665 | 0.534664 | ||||||||
\(723\) | −5.32804 | −0.198152 | ||||||||
\(724\) | 36.3545 | 1.35110 | ||||||||
\(725\) | −3.12807 | −0.116173 | ||||||||
\(726\) | 53.2932 | 1.97790 | ||||||||
\(727\) | −16.6745 | −0.618422 | −0.309211 | − | 0.950993i | \(-0.600065\pi\) | ||||
−0.309211 | + | 0.950993i | \(0.600065\pi\) | |||||||
\(728\) | −170.619 | −6.32358 | ||||||||
\(729\) | 22.0825 | 0.817869 | ||||||||
\(730\) | 69.2734 | 2.56393 | ||||||||
\(731\) | −19.0914 | −0.706120 | ||||||||
\(732\) | 166.236 | 6.14428 | ||||||||
\(733\) | 28.5766 | 1.05550 | 0.527751 | − | 0.849399i | \(-0.323035\pi\) | ||||
0.527751 | + | 0.849399i | \(0.323035\pi\) | |||||||
\(734\) | 88.8840 | 3.28077 | ||||||||
\(735\) | 55.5556 | 2.04920 | ||||||||
\(736\) | −115.635 | −4.26237 | ||||||||
\(737\) | −26.5884 | −0.979395 | ||||||||
\(738\) | −91.1529 | −3.35538 | ||||||||
\(739\) | 6.37684 | 0.234576 | 0.117288 | − | 0.993098i | \(-0.462580\pi\) | ||||
0.117288 | + | 0.993098i | \(0.462580\pi\) | |||||||
\(740\) | −70.0113 | −2.57366 | ||||||||
\(741\) | 59.1451 | 2.17275 | ||||||||
\(742\) | −18.1407 | −0.665964 | ||||||||
\(743\) | 34.9524 | 1.28228 | 0.641139 | − | 0.767425i | \(-0.278462\pi\) | ||||
0.641139 | + | 0.767425i | \(0.278462\pi\) | |||||||
\(744\) | 130.500 | 4.78435 | ||||||||
\(745\) | −14.4931 | −0.530987 | ||||||||
\(746\) | 81.8378 | 2.99630 | ||||||||
\(747\) | −36.0507 | −1.31903 | ||||||||
\(748\) | −40.6054 | −1.48468 | ||||||||
\(749\) | 64.1334 | 2.34338 | ||||||||
\(750\) | 101.283 | 3.69834 | ||||||||
\(751\) | −47.6699 | −1.73950 | −0.869750 | − | 0.493493i | \(-0.835720\pi\) | ||||
−0.869750 | + | 0.493493i | \(0.835720\pi\) | |||||||
\(752\) | 100.063 | 3.64891 | ||||||||
\(753\) | −92.1083 | −3.35661 | ||||||||
\(754\) | 17.9153 | 0.652435 | ||||||||
\(755\) | −12.0954 | −0.440197 | ||||||||
\(756\) | −280.945 | −10.2179 | ||||||||
\(757\) | 15.9954 | 0.581363 | 0.290681 | − | 0.956820i | \(-0.406118\pi\) | ||||
0.290681 | + | 0.956820i | \(0.406118\pi\) | |||||||
\(758\) | 32.4592 | 1.17897 | ||||||||
\(759\) | 57.5193 | 2.08782 | ||||||||
\(760\) | 48.5412 | 1.76077 | ||||||||
\(761\) | −3.36358 | −0.121930 | −0.0609648 | − | 0.998140i | \(-0.519418\pi\) | ||||
−0.0609648 | + | 0.998140i | \(0.519418\pi\) | |||||||
\(762\) | −24.3187 | −0.880972 | ||||||||
\(763\) | −20.6961 | −0.749248 | ||||||||
\(764\) | −44.5833 | −1.61297 | ||||||||
\(765\) | −43.4835 | −1.57215 | ||||||||
\(766\) | 76.5912 | 2.76735 | ||||||||
\(767\) | 34.3762 | 1.24125 | ||||||||
\(768\) | −6.44311 | −0.232496 | ||||||||
\(769\) | 28.0621 | 1.01195 | 0.505973 | − | 0.862549i | \(-0.331133\pi\) | ||||
0.505973 | + | 0.862549i | \(0.331133\pi\) | |||||||
\(770\) | 39.4860 | 1.42298 | ||||||||
\(771\) | −0.623183 | −0.0224434 | ||||||||
\(772\) | −0.403872 | −0.0145357 | ||||||||
\(773\) | 46.3326 | 1.66647 | 0.833233 | − | 0.552922i | \(-0.186487\pi\) | ||||
0.833233 | + | 0.552922i | \(0.186487\pi\) | |||||||
\(774\) | −97.5661 | −3.50694 | ||||||||
\(775\) | 11.8409 | 0.425338 | ||||||||
\(776\) | −86.8595 | −3.11808 | ||||||||
\(777\) | 113.977 | 4.08890 | ||||||||
\(778\) | −35.6475 | −1.27803 | ||||||||
\(779\) | −17.6838 | −0.633589 | ||||||||
\(780\) | −132.076 | −4.72910 | ||||||||
\(781\) | −2.16758 | −0.0775622 | ||||||||
\(782\) | 82.1089 | 2.93621 | ||||||||
\(783\) | 17.7911 | 0.635801 | ||||||||
\(784\) | 120.717 | 4.31133 | ||||||||
\(785\) | −4.90779 | −0.175166 | ||||||||
\(786\) | −137.091 | −4.88989 | ||||||||
\(787\) | 44.1689 | 1.57445 | 0.787226 | − | 0.616665i | \(-0.211517\pi\) | ||||
0.787226 | + | 0.616665i | \(0.211517\pi\) | |||||||
\(788\) | −103.312 | −3.68035 | ||||||||
\(789\) | 19.5606 | 0.696375 | ||||||||
\(790\) | 15.4709 | 0.550431 | ||||||||
\(791\) | 4.20358 | 0.149462 | ||||||||
\(792\) | −125.150 | −4.44703 | ||||||||
\(793\) | −52.0998 | −1.85012 | ||||||||
\(794\) | −18.3770 | −0.652174 | ||||||||
\(795\) | −8.46908 | −0.300367 | ||||||||
\(796\) | −21.6184 | −0.766245 | ||||||||
\(797\) | −27.5301 | −0.975167 | −0.487584 | − | 0.873076i | \(-0.662122\pi\) | ||||
−0.487584 | + | 0.873076i | \(0.662122\pi\) | |||||||
\(798\) | −131.031 | −4.63843 | ||||||||
\(799\) | −32.8803 | −1.16322 | ||||||||
\(800\) | 32.3929 | 1.14526 | ||||||||
\(801\) | −125.002 | −4.41672 | ||||||||
\(802\) | −10.5641 | −0.373031 | ||||||||
\(803\) | −34.6493 | −1.22275 | ||||||||
\(804\) | −197.028 | −6.94864 | ||||||||
\(805\) | −57.1588 | −2.01458 | ||||||||
\(806\) | −67.8161 | −2.38872 | ||||||||
\(807\) | −31.7991 | −1.11938 | ||||||||
\(808\) | −132.478 | −4.66055 | ||||||||
\(809\) | 17.9031 | 0.629439 | 0.314720 | − | 0.949185i | \(-0.398090\pi\) | ||||
0.314720 | + | 0.949185i | \(0.398090\pi\) | |||||||
\(810\) | −90.1216 | −3.16655 | ||||||||
\(811\) | −31.9472 | −1.12182 | −0.560909 | − | 0.827877i | \(-0.689548\pi\) | ||||
−0.560909 | + | 0.827877i | \(0.689548\pi\) | |||||||
\(812\) | −28.4126 | −0.997086 | ||||||||
\(813\) | 39.7515 | 1.39415 | ||||||||
\(814\) | 48.9172 | 1.71455 | ||||||||
\(815\) | 11.4109 | 0.399708 | ||||||||
\(816\) | −134.070 | −4.69337 | ||||||||
\(817\) | −18.9280 | −0.662207 | ||||||||
\(818\) | 82.5264 | 2.88547 | ||||||||
\(819\) | 151.534 | 5.29503 | ||||||||
\(820\) | 39.4896 | 1.37904 | ||||||||
\(821\) | −0.620164 | −0.0216439 | −0.0108219 | − | 0.999941i | \(-0.503445\pi\) | ||||
−0.0108219 | + | 0.999941i | \(0.503445\pi\) | |||||||
\(822\) | 1.78437 | 0.0622370 | ||||||||
\(823\) | −19.4882 | −0.679316 | −0.339658 | − | 0.940549i | \(-0.610311\pi\) | ||||
−0.339658 | + | 0.940549i | \(0.610311\pi\) | |||||||
\(824\) | 65.9571 | 2.29772 | ||||||||
\(825\) | −16.1128 | −0.560977 | ||||||||
\(826\) | −76.1574 | −2.64986 | ||||||||
\(827\) | −10.1962 | −0.354556 | −0.177278 | − | 0.984161i | \(-0.556729\pi\) | ||||
−0.177278 | + | 0.984161i | \(0.556729\pi\) | |||||||
\(828\) | 300.390 | 10.4393 | ||||||||
\(829\) | −9.48036 | −0.329266 | −0.164633 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164633 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(830\) | 21.8169 | 0.757276 | ||||||||
\(831\) | −95.8668 | −3.32558 | ||||||||
\(832\) | −71.6152 | −2.48281 | ||||||||
\(833\) | −39.6673 | −1.37439 | ||||||||
\(834\) | 4.66703 | 0.161606 | ||||||||
\(835\) | 26.1167 | 0.903804 | ||||||||
\(836\) | −40.2579 | −1.39235 | ||||||||
\(837\) | −67.3460 | −2.32782 | ||||||||
\(838\) | −38.9710 | −1.34623 | ||||||||
\(839\) | 42.1445 | 1.45499 | 0.727495 | − | 0.686113i | \(-0.240684\pi\) | ||||
0.727495 | + | 0.686113i | \(0.240684\pi\) | |||||||
\(840\) | 176.468 | 6.08873 | ||||||||
\(841\) | −27.2007 | −0.937957 | ||||||||
\(842\) | −102.795 | −3.54256 | ||||||||
\(843\) | 76.4097 | 2.63169 | ||||||||
\(844\) | −98.3770 | −3.38627 | ||||||||
\(845\) | 20.1596 | 0.693511 | ||||||||
\(846\) | −168.034 | −5.77712 | ||||||||
\(847\) | 26.4892 | 0.910181 | ||||||||
\(848\) | −18.4025 | −0.631946 | ||||||||
\(849\) | 4.40903 | 0.151317 | ||||||||
\(850\) | −23.0011 | −0.788932 | ||||||||
\(851\) | −70.8111 | −2.42737 | ||||||||
\(852\) | −16.0624 | −0.550290 | ||||||||
\(853\) | 19.5852 | 0.670585 | 0.335293 | − | 0.942114i | \(-0.391165\pi\) | ||||
0.335293 | + | 0.942114i | \(0.391165\pi\) | |||||||
\(854\) | 115.422 | 3.94967 | ||||||||
\(855\) | −43.1114 | −1.47438 | ||||||||
\(856\) | 123.013 | 4.20451 | ||||||||
\(857\) | −47.5609 | −1.62465 | −0.812325 | − | 0.583205i | \(-0.801798\pi\) | ||||
−0.812325 | + | 0.583205i | \(0.801798\pi\) | |||||||
\(858\) | 92.2825 | 3.15047 | ||||||||
\(859\) | 1.90388 | 0.0649595 | 0.0324797 | − | 0.999472i | \(-0.489660\pi\) | ||||
0.0324797 | + | 0.999472i | \(0.489660\pi\) | |||||||
\(860\) | 42.2680 | 1.44133 | ||||||||
\(861\) | −64.2883 | −2.19094 | ||||||||
\(862\) | −26.3113 | −0.896165 | ||||||||
\(863\) | 7.87449 | 0.268051 | 0.134025 | − | 0.990978i | \(-0.457210\pi\) | ||||
0.134025 | + | 0.990978i | \(0.457210\pi\) | |||||||
\(864\) | −184.237 | −6.26786 | ||||||||
\(865\) | −26.4388 | −0.898946 | ||||||||
\(866\) | −48.4021 | −1.64477 | ||||||||
\(867\) | −10.1347 | −0.344194 | ||||||||
\(868\) | 107.552 | 3.65057 | ||||||||
\(869\) | −7.73827 | −0.262503 | ||||||||
\(870\) | −18.5294 | −0.628204 | ||||||||
\(871\) | 61.7501 | 2.09232 | ||||||||
\(872\) | −39.6968 | −1.34430 | ||||||||
\(873\) | 77.1434 | 2.61091 | ||||||||
\(874\) | 81.4062 | 2.75361 | ||||||||
\(875\) | 50.3425 | 1.70189 | ||||||||
\(876\) | −256.762 | −8.67518 | ||||||||
\(877\) | 40.7578 | 1.37629 | 0.688147 | − | 0.725571i | \(-0.258424\pi\) | ||||
0.688147 | + | 0.725571i | \(0.258424\pi\) | |||||||
\(878\) | 49.0966 | 1.65693 | ||||||||
\(879\) | 72.4633 | 2.44413 | ||||||||
\(880\) | 40.0561 | 1.35029 | ||||||||
\(881\) | −13.5227 | −0.455590 | −0.227795 | − | 0.973709i | \(-0.573152\pi\) | ||||
−0.227795 | + | 0.973709i | \(0.573152\pi\) | |||||||
\(882\) | −202.719 | −6.82589 | ||||||||
\(883\) | −12.7088 | −0.427686 | −0.213843 | − | 0.976868i | \(-0.568598\pi\) | ||||
−0.213843 | + | 0.976868i | \(0.568598\pi\) | |||||||
\(884\) | 94.3039 | 3.17178 | ||||||||
\(885\) | −35.5546 | −1.19515 | ||||||||
\(886\) | −15.7754 | −0.529983 | ||||||||
\(887\) | −11.7992 | −0.396179 | −0.198090 | − | 0.980184i | \(-0.563474\pi\) | ||||
−0.198090 | + | 0.980184i | \(0.563474\pi\) | |||||||
\(888\) | 218.617 | 7.33632 | ||||||||
\(889\) | −12.0875 | −0.405402 | ||||||||
\(890\) | 75.6476 | 2.53571 | ||||||||
\(891\) | 45.0772 | 1.51014 | ||||||||
\(892\) | −38.8906 | −1.30215 | ||||||||
\(893\) | −32.5989 | −1.09088 | ||||||||
\(894\) | 75.0398 | 2.50971 | ||||||||
\(895\) | −36.8184 | −1.23070 | ||||||||
\(896\) | 41.8768 | 1.39901 | ||||||||
\(897\) | −133.585 | −4.46029 | ||||||||
\(898\) | −84.5840 | −2.82261 | ||||||||
\(899\) | −6.81085 | −0.227155 | ||||||||
\(900\) | −84.1480 | −2.80493 | ||||||||
\(901\) | 6.04701 | 0.201455 | ||||||||
\(902\) | −27.5916 | −0.918700 | ||||||||
\(903\) | −68.8114 | −2.28990 | ||||||||
\(904\) | 8.06283 | 0.268166 | ||||||||
\(905\) | 11.7843 | 0.391724 | ||||||||
\(906\) | 62.6254 | 2.08059 | ||||||||
\(907\) | 40.2844 | 1.33762 | 0.668811 | − | 0.743433i | \(-0.266804\pi\) | ||||
0.668811 | + | 0.743433i | \(0.266804\pi\) | |||||||
\(908\) | −115.915 | −3.84678 | ||||||||
\(909\) | 117.659 | 3.90250 | ||||||||
\(910\) | −91.7042 | −3.03996 | ||||||||
\(911\) | 0.493027 | 0.0163347 | 0.00816736 | − | 0.999967i | \(-0.497400\pi\) | ||||
0.00816736 | + | 0.999967i | \(0.497400\pi\) | |||||||
\(912\) | −132.922 | −4.40149 | ||||||||
\(913\) | −10.9124 | −0.361148 | ||||||||
\(914\) | −52.2150 | −1.72712 | ||||||||
\(915\) | 53.8857 | 1.78141 | ||||||||
\(916\) | 50.2194 | 1.65930 | ||||||||
\(917\) | −68.1408 | −2.25021 | ||||||||
\(918\) | 130.820 | 4.31772 | ||||||||
\(919\) | 12.7766 | 0.421462 | 0.210731 | − | 0.977544i | \(-0.432416\pi\) | ||||
0.210731 | + | 0.977544i | \(0.432416\pi\) | |||||||
\(920\) | −109.635 | −3.61457 | ||||||||
\(921\) | −26.2802 | −0.865962 | ||||||||
\(922\) | −44.5031 | −1.46563 | ||||||||
\(923\) | 5.03410 | 0.165699 | ||||||||
\(924\) | −146.355 | −4.81472 | ||||||||
\(925\) | 19.8363 | 0.652213 | ||||||||
\(926\) | −33.9005 | −1.11404 | ||||||||
\(927\) | −58.5791 | −1.92399 | ||||||||
\(928\) | −18.6323 | −0.611634 | ||||||||
\(929\) | −23.3053 | −0.764623 | −0.382311 | − | 0.924034i | \(-0.624872\pi\) | ||||
−0.382311 | + | 0.924034i | \(0.624872\pi\) | |||||||
\(930\) | 70.1407 | 2.30000 | ||||||||
\(931\) | −39.3278 | −1.28892 | ||||||||
\(932\) | 121.358 | 3.97522 | ||||||||
\(933\) | −8.96539 | −0.293514 | ||||||||
\(934\) | −17.9723 | −0.588072 | ||||||||
\(935\) | −13.1623 | −0.430453 | ||||||||
\(936\) | 290.655 | 9.50036 | ||||||||
\(937\) | 19.0057 | 0.620889 | 0.310444 | − | 0.950592i | \(-0.399522\pi\) | ||||
0.310444 | + | 0.950592i | \(0.399522\pi\) | |||||||
\(938\) | −136.802 | −4.46673 | ||||||||
\(939\) | −79.7818 | −2.60358 | ||||||||
\(940\) | 72.7963 | 2.37435 | ||||||||
\(941\) | 26.0101 | 0.847905 | 0.423953 | − | 0.905684i | \(-0.360642\pi\) | ||||
0.423953 | + | 0.905684i | \(0.360642\pi\) | |||||||
\(942\) | 25.4106 | 0.827924 | ||||||||
\(943\) | 39.9408 | 1.30065 | ||||||||
\(944\) | −77.2569 | −2.51450 | ||||||||
\(945\) | −91.0685 | −2.96246 | ||||||||
\(946\) | −29.5329 | −0.960196 | ||||||||
\(947\) | 36.9855 | 1.20187 | 0.600934 | − | 0.799299i | \(-0.294796\pi\) | ||||
0.600934 | + | 0.799299i | \(0.294796\pi\) | |||||||
\(948\) | −57.3429 | −1.86241 | ||||||||
\(949\) | 80.4712 | 2.61220 | ||||||||
\(950\) | −22.8043 | −0.739869 | ||||||||
\(951\) | −44.8442 | −1.45417 | ||||||||
\(952\) | −126.000 | −4.08368 | ||||||||
\(953\) | −61.1788 | −1.98178 | −0.990888 | − | 0.134686i | \(-0.956997\pi\) | ||||
−0.990888 | + | 0.134686i | \(0.956997\pi\) | |||||||
\(954\) | 30.9031 | 1.00053 | ||||||||
\(955\) | −14.4517 | −0.467647 | ||||||||
\(956\) | −54.3386 | −1.75744 | ||||||||
\(957\) | 9.26805 | 0.299593 | ||||||||
\(958\) | −109.023 | −3.52238 | ||||||||
\(959\) | 0.886915 | 0.0286400 | ||||||||
\(960\) | 74.0701 | 2.39060 | ||||||||
\(961\) | −5.21834 | −0.168333 | ||||||||
\(962\) | −113.608 | −3.66286 | ||||||||
\(963\) | −109.253 | −3.52063 | ||||||||
\(964\) | −8.42259 | −0.271273 | ||||||||
\(965\) | −0.130915 | −0.00421432 | ||||||||
\(966\) | 295.946 | 9.52192 | ||||||||
\(967\) | 27.2888 | 0.877550 | 0.438775 | − | 0.898597i | \(-0.355413\pi\) | ||||
0.438775 | + | 0.898597i | \(0.355413\pi\) | |||||||
\(968\) | 50.8086 | 1.63305 | ||||||||
\(969\) | 43.6778 | 1.40313 | ||||||||
\(970\) | −46.6851 | −1.49897 | ||||||||
\(971\) | 50.8894 | 1.63312 | 0.816560 | − | 0.577261i | \(-0.195878\pi\) | ||||
0.816560 | + | 0.577261i | \(0.195878\pi\) | |||||||
\(972\) | 133.532 | 4.28303 | ||||||||
\(973\) | 2.31973 | 0.0743673 | ||||||||
\(974\) | 83.3507 | 2.67073 | ||||||||
\(975\) | 37.4212 | 1.19844 | ||||||||
\(976\) | 117.089 | 3.74792 | ||||||||
\(977\) | −3.85414 | −0.123305 | −0.0616525 | − | 0.998098i | \(-0.519637\pi\) | ||||
−0.0616525 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(978\) | −59.0815 | −1.88922 | ||||||||
\(979\) | −37.8376 | −1.20929 | ||||||||
\(980\) | 87.8226 | 2.80539 | ||||||||
\(981\) | 35.2563 | 1.12565 | ||||||||
\(982\) | −58.6640 | −1.87204 | ||||||||
\(983\) | 0.663283 | 0.0211554 | 0.0105777 | − | 0.999944i | \(-0.496633\pi\) | ||||
0.0105777 | + | 0.999944i | \(0.496633\pi\) | |||||||
\(984\) | −123.310 | −3.93099 | ||||||||
\(985\) | −33.4888 | −1.06704 | ||||||||
\(986\) | 13.2302 | 0.421334 | ||||||||
\(987\) | −118.511 | −3.77224 | ||||||||
\(988\) | 93.4969 | 2.97453 | ||||||||
\(989\) | 42.7509 | 1.35940 | ||||||||
\(990\) | −67.2656 | −2.13784 | ||||||||
\(991\) | −18.4606 | −0.586419 | −0.293210 | − | 0.956048i | \(-0.594723\pi\) | ||||
−0.293210 | + | 0.956048i | \(0.594723\pi\) | |||||||
\(992\) | 70.5302 | 2.23934 | ||||||||
\(993\) | 8.63119 | 0.273903 | ||||||||
\(994\) | −11.1526 | −0.353738 | ||||||||
\(995\) | −7.00763 | −0.222157 | ||||||||
\(996\) | −80.8643 | −2.56228 | ||||||||
\(997\) | −11.3310 | −0.358858 | −0.179429 | − | 0.983771i | \(-0.557425\pi\) | ||||
−0.179429 | + | 0.983771i | \(0.557425\pi\) | |||||||
\(998\) | 8.84730 | 0.280056 | ||||||||
\(999\) | −112.820 | −3.56947 |
(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 | 8023.2.a.c.1.10 | ✓ | 158 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8023.2.a.c.1.10 | ✓ | 158 | 1.1 | even | 1 | trivial |