Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8047,2,Mod(1,8047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8047, 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("8047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8047 = 13 \cdot 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8047.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: | \(64.2556185065\) |
Analytic rank: | \(1\) |
Dimension: | \(142\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 8047.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.50524 | −1.77147 | −0.885735 | − | 0.464190i | \(-0.846345\pi\) | ||||
−0.885735 | + | 0.464190i | \(0.846345\pi\) | |||||||
\(3\) | −0.199696 | −0.115295 | −0.0576473 | − | 0.998337i | \(-0.518360\pi\) | ||||
−0.0576473 | + | 0.998337i | \(0.518360\pi\) | |||||||
\(4\) | 4.27622 | 2.13811 | ||||||||
\(5\) | −1.81098 | −0.809895 | −0.404947 | − | 0.914340i | \(-0.632710\pi\) | ||||
−0.404947 | + | 0.914340i | \(0.632710\pi\) | |||||||
\(6\) | 0.500286 | 0.204241 | ||||||||
\(7\) | −1.67033 | −0.631326 | −0.315663 | − | 0.948871i | \(-0.602227\pi\) | ||||
−0.315663 | + | 0.948871i | \(0.602227\pi\) | |||||||
\(8\) | −5.70247 | −2.01613 | ||||||||
\(9\) | −2.96012 | −0.986707 | ||||||||
\(10\) | 4.53694 | 1.43471 | ||||||||
\(11\) | −2.18034 | −0.657397 | −0.328699 | − | 0.944435i | \(-0.606610\pi\) | ||||
−0.328699 | + | 0.944435i | \(0.606610\pi\) | |||||||
\(12\) | −0.853944 | −0.246512 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 4.18458 | 1.11837 | ||||||||
\(15\) | 0.361646 | 0.0933765 | ||||||||
\(16\) | 5.73360 | 1.43340 | ||||||||
\(17\) | −5.47406 | −1.32765 | −0.663827 | − | 0.747886i | \(-0.731069\pi\) | ||||
−0.663827 | + | 0.747886i | \(0.731069\pi\) | |||||||
\(18\) | 7.41581 | 1.74792 | ||||||||
\(19\) | −5.01728 | −1.15104 | −0.575521 | − | 0.817787i | \(-0.695201\pi\) | ||||
−0.575521 | + | 0.817787i | \(0.695201\pi\) | |||||||
\(20\) | −7.74415 | −1.73164 | ||||||||
\(21\) | 0.333558 | 0.0727884 | ||||||||
\(22\) | 5.46227 | 1.16456 | ||||||||
\(23\) | −7.67508 | −1.60036 | −0.800182 | − | 0.599757i | \(-0.795264\pi\) | ||||
−0.800182 | + | 0.599757i | \(0.795264\pi\) | |||||||
\(24\) | 1.13876 | 0.232448 | ||||||||
\(25\) | −1.72035 | −0.344070 | ||||||||
\(26\) | −2.50524 | −0.491318 | ||||||||
\(27\) | 1.19021 | 0.229057 | ||||||||
\(28\) | −7.14270 | −1.34984 | ||||||||
\(29\) | 6.13521 | 1.13928 | 0.569640 | − | 0.821895i | \(-0.307083\pi\) | ||||
0.569640 | + | 0.821895i | \(0.307083\pi\) | |||||||
\(30\) | −0.906008 | −0.165414 | ||||||||
\(31\) | 6.78991 | 1.21950 | 0.609752 | − | 0.792592i | \(-0.291269\pi\) | ||||
0.609752 | + | 0.792592i | \(0.291269\pi\) | |||||||
\(32\) | −2.95911 | −0.523101 | ||||||||
\(33\) | 0.435405 | 0.0757943 | ||||||||
\(34\) | 13.7138 | 2.35190 | ||||||||
\(35\) | 3.02494 | 0.511307 | ||||||||
\(36\) | −12.6581 | −2.10969 | ||||||||
\(37\) | 2.77921 | 0.456899 | 0.228450 | − | 0.973556i | \(-0.426634\pi\) | ||||
0.228450 | + | 0.973556i | \(0.426634\pi\) | |||||||
\(38\) | 12.5695 | 2.03904 | ||||||||
\(39\) | −0.199696 | −0.0319770 | ||||||||
\(40\) | 10.3271 | 1.63285 | ||||||||
\(41\) | 9.42791 | 1.47239 | 0.736196 | − | 0.676768i | \(-0.236620\pi\) | ||||
0.736196 | + | 0.676768i | \(0.236620\pi\) | |||||||
\(42\) | −0.835643 | −0.128943 | ||||||||
\(43\) | 9.65573 | 1.47249 | 0.736243 | − | 0.676718i | \(-0.236598\pi\) | ||||
0.736243 | + | 0.676718i | \(0.236598\pi\) | |||||||
\(44\) | −9.32361 | −1.40559 | ||||||||
\(45\) | 5.36072 | 0.799129 | ||||||||
\(46\) | 19.2279 | 2.83500 | ||||||||
\(47\) | −10.9626 | −1.59906 | −0.799532 | − | 0.600623i | \(-0.794919\pi\) | ||||
−0.799532 | + | 0.600623i | \(0.794919\pi\) | |||||||
\(48\) | −1.14498 | −0.165263 | ||||||||
\(49\) | −4.21000 | −0.601428 | ||||||||
\(50\) | 4.30989 | 0.609510 | ||||||||
\(51\) | 1.09315 | 0.153071 | ||||||||
\(52\) | 4.27622 | 0.593005 | ||||||||
\(53\) | 5.00152 | 0.687012 | 0.343506 | − | 0.939151i | \(-0.388385\pi\) | ||||
0.343506 | + | 0.939151i | \(0.388385\pi\) | |||||||
\(54\) | −2.98177 | −0.405767 | ||||||||
\(55\) | 3.94855 | 0.532423 | ||||||||
\(56\) | 9.52500 | 1.27283 | ||||||||
\(57\) | 1.00193 | 0.132709 | ||||||||
\(58\) | −15.3702 | −2.01820 | ||||||||
\(59\) | 9.88717 | 1.28720 | 0.643600 | − | 0.765362i | \(-0.277440\pi\) | ||||
0.643600 | + | 0.765362i | \(0.277440\pi\) | |||||||
\(60\) | 1.54648 | 0.199649 | ||||||||
\(61\) | 4.28862 | 0.549102 | 0.274551 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274551 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(62\) | −17.0103 | −2.16032 | ||||||||
\(63\) | 4.94438 | 0.622933 | ||||||||
\(64\) | −4.05394 | −0.506743 | ||||||||
\(65\) | −1.81098 | −0.224624 | ||||||||
\(66\) | −1.09079 | −0.134267 | ||||||||
\(67\) | 8.87803 | 1.08462 | 0.542312 | − | 0.840177i | \(-0.317549\pi\) | ||||
0.542312 | + | 0.840177i | \(0.317549\pi\) | |||||||
\(68\) | −23.4083 | −2.83867 | ||||||||
\(69\) | 1.53268 | 0.184513 | ||||||||
\(70\) | −7.57818 | −0.905766 | ||||||||
\(71\) | 10.8445 | 1.28701 | 0.643504 | − | 0.765442i | \(-0.277480\pi\) | ||||
0.643504 | + | 0.765442i | \(0.277480\pi\) | |||||||
\(72\) | 16.8800 | 1.98933 | ||||||||
\(73\) | 13.1005 | 1.53330 | 0.766651 | − | 0.642064i | \(-0.221921\pi\) | ||||
0.766651 | + | 0.642064i | \(0.221921\pi\) | |||||||
\(74\) | −6.96258 | −0.809384 | ||||||||
\(75\) | 0.343547 | 0.0396694 | ||||||||
\(76\) | −21.4550 | −2.46105 | ||||||||
\(77\) | 3.64189 | 0.415032 | ||||||||
\(78\) | 0.500286 | 0.0566463 | ||||||||
\(79\) | 1.61729 | 0.181960 | 0.0909798 | − | 0.995853i | \(-0.471000\pi\) | ||||
0.0909798 | + | 0.995853i | \(0.471000\pi\) | |||||||
\(80\) | −10.3834 | −1.16090 | ||||||||
\(81\) | 8.64268 | 0.960298 | ||||||||
\(82\) | −23.6192 | −2.60830 | ||||||||
\(83\) | −7.95866 | −0.873576 | −0.436788 | − | 0.899564i | \(-0.643884\pi\) | ||||
−0.436788 | + | 0.899564i | \(0.643884\pi\) | |||||||
\(84\) | 1.42637 | 0.155630 | ||||||||
\(85\) | 9.91342 | 1.07526 | ||||||||
\(86\) | −24.1899 | −2.60846 | ||||||||
\(87\) | −1.22518 | −0.131353 | ||||||||
\(88\) | 12.4333 | 1.32540 | ||||||||
\(89\) | −6.16302 | −0.653279 | −0.326639 | − | 0.945149i | \(-0.605916\pi\) | ||||
−0.326639 | + | 0.945149i | \(0.605916\pi\) | |||||||
\(90\) | −13.4299 | −1.41563 | ||||||||
\(91\) | −1.67033 | −0.175098 | ||||||||
\(92\) | −32.8203 | −3.42175 | ||||||||
\(93\) | −1.35592 | −0.140602 | ||||||||
\(94\) | 27.4640 | 2.83270 | ||||||||
\(95\) | 9.08619 | 0.932223 | ||||||||
\(96\) | 0.590922 | 0.0603107 | ||||||||
\(97\) | −2.74166 | −0.278373 | −0.139187 | − | 0.990266i | \(-0.544449\pi\) | ||||
−0.139187 | + | 0.990266i | \(0.544449\pi\) | |||||||
\(98\) | 10.5470 | 1.06541 | ||||||||
\(99\) | 6.45407 | 0.648658 | ||||||||
\(100\) | −7.35659 | −0.735659 | ||||||||
\(101\) | 5.41761 | 0.539073 | 0.269536 | − | 0.962990i | \(-0.413130\pi\) | ||||
0.269536 | + | 0.962990i | \(0.413130\pi\) | |||||||
\(102\) | −2.73860 | −0.271162 | ||||||||
\(103\) | −3.68710 | −0.363300 | −0.181650 | − | 0.983363i | \(-0.558144\pi\) | ||||
−0.181650 | + | 0.983363i | \(0.558144\pi\) | |||||||
\(104\) | −5.70247 | −0.559173 | ||||||||
\(105\) | −0.604068 | −0.0589510 | ||||||||
\(106\) | −12.5300 | −1.21702 | ||||||||
\(107\) | −7.66909 | −0.741398 | −0.370699 | − | 0.928753i | \(-0.620882\pi\) | ||||
−0.370699 | + | 0.928753i | \(0.620882\pi\) | |||||||
\(108\) | 5.08961 | 0.489748 | ||||||||
\(109\) | −8.41150 | −0.805676 | −0.402838 | − | 0.915271i | \(-0.631976\pi\) | ||||
−0.402838 | + | 0.915271i | \(0.631976\pi\) | |||||||
\(110\) | −9.89206 | −0.943171 | ||||||||
\(111\) | −0.554997 | −0.0526780 | ||||||||
\(112\) | −9.57701 | −0.904942 | ||||||||
\(113\) | 5.77055 | 0.542848 | 0.271424 | − | 0.962460i | \(-0.412505\pi\) | ||||
0.271424 | + | 0.962460i | \(0.412505\pi\) | |||||||
\(114\) | −2.51007 | −0.235090 | ||||||||
\(115\) | 13.8994 | 1.29613 | ||||||||
\(116\) | 26.2355 | 2.43590 | ||||||||
\(117\) | −2.96012 | −0.273663 | ||||||||
\(118\) | −24.7697 | −2.28024 | ||||||||
\(119\) | 9.14349 | 0.838182 | ||||||||
\(120\) | −2.06227 | −0.188259 | ||||||||
\(121\) | −6.24612 | −0.567829 | ||||||||
\(122\) | −10.7440 | −0.972718 | ||||||||
\(123\) | −1.88272 | −0.169759 | ||||||||
\(124\) | 29.0351 | 2.60743 | ||||||||
\(125\) | 12.1704 | 1.08856 | ||||||||
\(126\) | −12.3869 | −1.10351 | ||||||||
\(127\) | 17.1758 | 1.52411 | 0.762055 | − | 0.647513i | \(-0.224191\pi\) | ||||
0.762055 | + | 0.647513i | \(0.224191\pi\) | |||||||
\(128\) | 16.0743 | 1.42078 | ||||||||
\(129\) | −1.92821 | −0.169770 | ||||||||
\(130\) | 4.53694 | 0.397916 | ||||||||
\(131\) | −15.2987 | −1.33665 | −0.668326 | − | 0.743869i | \(-0.732989\pi\) | ||||
−0.668326 | + | 0.743869i | \(0.732989\pi\) | |||||||
\(132\) | 1.86189 | 0.162057 | ||||||||
\(133\) | 8.38051 | 0.726682 | ||||||||
\(134\) | −22.2416 | −1.92138 | ||||||||
\(135\) | −2.15545 | −0.185512 | ||||||||
\(136\) | 31.2157 | 2.67672 | ||||||||
\(137\) | −5.98203 | −0.511079 | −0.255540 | − | 0.966799i | \(-0.582253\pi\) | ||||
−0.255540 | + | 0.966799i | \(0.582253\pi\) | |||||||
\(138\) | −3.83973 | −0.326860 | ||||||||
\(139\) | 8.03303 | 0.681353 | 0.340676 | − | 0.940181i | \(-0.389344\pi\) | ||||
0.340676 | + | 0.940181i | \(0.389344\pi\) | |||||||
\(140\) | 12.9353 | 1.09323 | ||||||||
\(141\) | 2.18920 | 0.184363 | ||||||||
\(142\) | −27.1681 | −2.27990 | ||||||||
\(143\) | −2.18034 | −0.182329 | ||||||||
\(144\) | −16.9722 | −1.41435 | ||||||||
\(145\) | −11.1107 | −0.922697 | ||||||||
\(146\) | −32.8200 | −2.71620 | ||||||||
\(147\) | 0.840720 | 0.0693414 | ||||||||
\(148\) | 11.8845 | 0.976900 | ||||||||
\(149\) | −6.08884 | −0.498817 | −0.249408 | − | 0.968398i | \(-0.580236\pi\) | ||||
−0.249408 | + | 0.968398i | \(0.580236\pi\) | |||||||
\(150\) | −0.860668 | −0.0702732 | ||||||||
\(151\) | 20.2753 | 1.64998 | 0.824989 | − | 0.565149i | \(-0.191181\pi\) | ||||
0.824989 | + | 0.565149i | \(0.191181\pi\) | |||||||
\(152\) | 28.6109 | 2.32065 | ||||||||
\(153\) | 16.2039 | 1.31001 | ||||||||
\(154\) | −9.12380 | −0.735216 | ||||||||
\(155\) | −12.2964 | −0.987670 | ||||||||
\(156\) | −0.853944 | −0.0683702 | ||||||||
\(157\) | −1.45238 | −0.115913 | −0.0579564 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579564 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(158\) | −4.05170 | −0.322336 | ||||||||
\(159\) | −0.998784 | −0.0792087 | ||||||||
\(160\) | 5.35888 | 0.423657 | ||||||||
\(161\) | 12.8199 | 1.01035 | ||||||||
\(162\) | −21.6520 | −1.70114 | ||||||||
\(163\) | 19.2277 | 1.50603 | 0.753014 | − | 0.658005i | \(-0.228599\pi\) | ||||
0.753014 | + | 0.658005i | \(0.228599\pi\) | |||||||
\(164\) | 40.3158 | 3.14813 | ||||||||
\(165\) | −0.788510 | −0.0613854 | ||||||||
\(166\) | 19.9383 | 1.54752 | ||||||||
\(167\) | −10.4563 | −0.809131 | −0.404566 | − | 0.914509i | \(-0.632577\pi\) | ||||
−0.404566 | + | 0.914509i | \(0.632577\pi\) | |||||||
\(168\) | −1.90211 | −0.146751 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −24.8355 | −1.90479 | ||||||||
\(171\) | 14.8517 | 1.13574 | ||||||||
\(172\) | 41.2900 | 3.14833 | ||||||||
\(173\) | −16.8874 | −1.28393 | −0.641964 | − | 0.766735i | \(-0.721880\pi\) | ||||
−0.641964 | + | 0.766735i | \(0.721880\pi\) | |||||||
\(174\) | 3.06936 | 0.232687 | ||||||||
\(175\) | 2.87355 | 0.217220 | ||||||||
\(176\) | −12.5012 | −0.942314 | ||||||||
\(177\) | −1.97443 | −0.148407 | ||||||||
\(178\) | 15.4398 | 1.15726 | ||||||||
\(179\) | −5.00340 | −0.373972 | −0.186986 | − | 0.982363i | \(-0.559872\pi\) | ||||
−0.186986 | + | 0.982363i | \(0.559872\pi\) | |||||||
\(180\) | 22.9236 | 1.70863 | ||||||||
\(181\) | −24.3098 | −1.80693 | −0.903467 | − | 0.428658i | \(-0.858987\pi\) | ||||
−0.903467 | + | 0.428658i | \(0.858987\pi\) | |||||||
\(182\) | 4.18458 | 0.310181 | ||||||||
\(183\) | −0.856421 | −0.0633085 | ||||||||
\(184\) | 43.7669 | 3.22654 | ||||||||
\(185\) | −5.03309 | −0.370040 | ||||||||
\(186\) | 3.39690 | 0.249073 | ||||||||
\(187\) | 11.9353 | 0.872797 | ||||||||
\(188\) | −46.8786 | −3.41897 | ||||||||
\(189\) | −1.98805 | −0.144609 | ||||||||
\(190\) | −22.7631 | −1.65141 | ||||||||
\(191\) | 17.1577 | 1.24149 | 0.620745 | − | 0.784013i | \(-0.286830\pi\) | ||||
0.620745 | + | 0.784013i | \(0.286830\pi\) | |||||||
\(192\) | 0.809556 | 0.0584247 | ||||||||
\(193\) | −17.4734 | −1.25776 | −0.628880 | − | 0.777502i | \(-0.716486\pi\) | ||||
−0.628880 | + | 0.777502i | \(0.716486\pi\) | |||||||
\(194\) | 6.86851 | 0.493130 | ||||||||
\(195\) | 0.361646 | 0.0258980 | ||||||||
\(196\) | −18.0029 | −1.28592 | ||||||||
\(197\) | −19.8044 | −1.41100 | −0.705502 | − | 0.708708i | \(-0.749278\pi\) | ||||
−0.705502 | + | 0.708708i | \(0.749278\pi\) | |||||||
\(198\) | −16.1690 | −1.14908 | ||||||||
\(199\) | 5.54259 | 0.392904 | 0.196452 | − | 0.980513i | \(-0.437058\pi\) | ||||
0.196452 | + | 0.980513i | \(0.437058\pi\) | |||||||
\(200\) | 9.81024 | 0.693689 | ||||||||
\(201\) | −1.77291 | −0.125051 | ||||||||
\(202\) | −13.5724 | −0.954952 | ||||||||
\(203\) | −10.2478 | −0.719256 | ||||||||
\(204\) | 4.67454 | 0.327283 | ||||||||
\(205\) | −17.0738 | −1.19248 | ||||||||
\(206\) | 9.23705 | 0.643576 | ||||||||
\(207\) | 22.7192 | 1.57909 | ||||||||
\(208\) | 5.73360 | 0.397554 | ||||||||
\(209\) | 10.9394 | 0.756692 | ||||||||
\(210\) | 1.51333 | 0.104430 | ||||||||
\(211\) | −8.92280 | −0.614271 | −0.307135 | − | 0.951666i | \(-0.599370\pi\) | ||||
−0.307135 | + | 0.951666i | \(0.599370\pi\) | |||||||
\(212\) | 21.3876 | 1.46891 | ||||||||
\(213\) | −2.16561 | −0.148385 | ||||||||
\(214\) | 19.2129 | 1.31337 | ||||||||
\(215\) | −17.4863 | −1.19256 | ||||||||
\(216\) | −6.78715 | −0.461807 | ||||||||
\(217\) | −11.3414 | −0.769904 | ||||||||
\(218\) | 21.0728 | 1.42723 | ||||||||
\(219\) | −2.61613 | −0.176781 | ||||||||
\(220\) | 16.8849 | 1.13838 | ||||||||
\(221\) | −5.47406 | −0.368225 | ||||||||
\(222\) | 1.39040 | 0.0933175 | ||||||||
\(223\) | 8.38021 | 0.561181 | 0.280590 | − | 0.959828i | \(-0.409470\pi\) | ||||
0.280590 | + | 0.959828i | \(0.409470\pi\) | |||||||
\(224\) | 4.94268 | 0.330247 | ||||||||
\(225\) | 5.09245 | 0.339496 | ||||||||
\(226\) | −14.4566 | −0.961639 | ||||||||
\(227\) | −13.3752 | −0.887741 | −0.443871 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443871 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(228\) | 4.28447 | 0.283746 | ||||||||
\(229\) | 1.90637 | 0.125976 | 0.0629882 | − | 0.998014i | \(-0.479937\pi\) | ||||
0.0629882 | + | 0.998014i | \(0.479937\pi\) | |||||||
\(230\) | −34.8213 | −2.29605 | ||||||||
\(231\) | −0.727271 | −0.0478509 | ||||||||
\(232\) | −34.9858 | −2.29693 | ||||||||
\(233\) | −26.1365 | −1.71226 | −0.856129 | − | 0.516763i | \(-0.827137\pi\) | ||||
−0.856129 | + | 0.516763i | \(0.827137\pi\) | |||||||
\(234\) | 7.41581 | 0.484787 | ||||||||
\(235\) | 19.8531 | 1.29507 | ||||||||
\(236\) | 42.2797 | 2.75217 | ||||||||
\(237\) | −0.322967 | −0.0209790 | ||||||||
\(238\) | −22.9066 | −1.48482 | ||||||||
\(239\) | −17.2966 | −1.11883 | −0.559413 | − | 0.828889i | \(-0.688973\pi\) | ||||
−0.559413 | + | 0.828889i | \(0.688973\pi\) | |||||||
\(240\) | 2.07353 | 0.133846 | ||||||||
\(241\) | 24.0170 | 1.54707 | 0.773536 | − | 0.633753i | \(-0.218486\pi\) | ||||
0.773536 | + | 0.633753i | \(0.218486\pi\) | |||||||
\(242\) | 15.6480 | 1.00589 | ||||||||
\(243\) | −5.29655 | −0.339774 | ||||||||
\(244\) | 18.3391 | 1.17404 | ||||||||
\(245\) | 7.62422 | 0.487094 | ||||||||
\(246\) | 4.71665 | 0.300723 | ||||||||
\(247\) | −5.01728 | −0.319242 | ||||||||
\(248\) | −38.7192 | −2.45867 | ||||||||
\(249\) | 1.58931 | 0.100719 | ||||||||
\(250\) | −30.4898 | −1.92834 | ||||||||
\(251\) | −4.70182 | −0.296776 | −0.148388 | − | 0.988929i | \(-0.547408\pi\) | ||||
−0.148388 | + | 0.988929i | \(0.547408\pi\) | |||||||
\(252\) | 21.1432 | 1.33190 | ||||||||
\(253\) | 16.7343 | 1.05207 | ||||||||
\(254\) | −43.0296 | −2.69992 | ||||||||
\(255\) | −1.97967 | −0.123972 | ||||||||
\(256\) | −32.1621 | −2.01013 | ||||||||
\(257\) | 25.4987 | 1.59057 | 0.795284 | − | 0.606238i | \(-0.207322\pi\) | ||||
0.795284 | + | 0.606238i | \(0.207322\pi\) | |||||||
\(258\) | 4.83063 | 0.300742 | ||||||||
\(259\) | −4.64220 | −0.288452 | ||||||||
\(260\) | −7.74415 | −0.480272 | ||||||||
\(261\) | −18.1610 | −1.12413 | ||||||||
\(262\) | 38.3268 | 2.36784 | ||||||||
\(263\) | −8.65026 | −0.533398 | −0.266699 | − | 0.963780i | \(-0.585933\pi\) | ||||
−0.266699 | + | 0.963780i | \(0.585933\pi\) | |||||||
\(264\) | −2.48288 | −0.152811 | ||||||||
\(265\) | −9.05765 | −0.556407 | ||||||||
\(266\) | −20.9952 | −1.28730 | ||||||||
\(267\) | 1.23073 | 0.0753195 | ||||||||
\(268\) | 37.9644 | 2.31904 | ||||||||
\(269\) | −17.3019 | −1.05492 | −0.527458 | − | 0.849581i | \(-0.676855\pi\) | ||||
−0.527458 | + | 0.849581i | \(0.676855\pi\) | |||||||
\(270\) | 5.39992 | 0.328629 | ||||||||
\(271\) | −9.79266 | −0.594862 | −0.297431 | − | 0.954743i | \(-0.596130\pi\) | ||||
−0.297431 | + | 0.954743i | \(0.596130\pi\) | |||||||
\(272\) | −31.3861 | −1.90306 | ||||||||
\(273\) | 0.333558 | 0.0201879 | ||||||||
\(274\) | 14.9864 | 0.905362 | ||||||||
\(275\) | 3.75095 | 0.226191 | ||||||||
\(276\) | 6.55408 | 0.394509 | ||||||||
\(277\) | −25.6167 | −1.53916 | −0.769578 | − | 0.638552i | \(-0.779534\pi\) | ||||
−0.769578 | + | 0.638552i | \(0.779534\pi\) | |||||||
\(278\) | −20.1247 | −1.20700 | ||||||||
\(279\) | −20.0990 | −1.20329 | ||||||||
\(280\) | −17.2496 | −1.03086 | ||||||||
\(281\) | −11.7051 | −0.698266 | −0.349133 | − | 0.937073i | \(-0.613524\pi\) | ||||
−0.349133 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(282\) | −5.48446 | −0.326595 | ||||||||
\(283\) | −9.34959 | −0.555775 | −0.277888 | − | 0.960614i | \(-0.589634\pi\) | ||||
−0.277888 | + | 0.960614i | \(0.589634\pi\) | |||||||
\(284\) | 46.3736 | 2.75177 | ||||||||
\(285\) | −1.81448 | −0.107480 | ||||||||
\(286\) | 5.46227 | 0.322991 | ||||||||
\(287\) | −15.7477 | −0.929559 | ||||||||
\(288\) | 8.75931 | 0.516147 | ||||||||
\(289\) | 12.9653 | 0.762667 | ||||||||
\(290\) | 27.8350 | 1.63453 | ||||||||
\(291\) | 0.547499 | 0.0320949 | ||||||||
\(292\) | 56.0208 | 3.27837 | ||||||||
\(293\) | 28.0922 | 1.64116 | 0.820582 | − | 0.571529i | \(-0.193650\pi\) | ||||
0.820582 | + | 0.571529i | \(0.193650\pi\) | |||||||
\(294\) | −2.10620 | −0.122836 | ||||||||
\(295\) | −17.9055 | −1.04250 | ||||||||
\(296\) | −15.8483 | −0.921167 | ||||||||
\(297\) | −2.59507 | −0.150581 | ||||||||
\(298\) | 15.2540 | 0.883640 | ||||||||
\(299\) | −7.67508 | −0.443861 | ||||||||
\(300\) | 1.46908 | 0.0848175 | ||||||||
\(301\) | −16.1283 | −0.929618 | ||||||||
\(302\) | −50.7944 | −2.92289 | ||||||||
\(303\) | −1.08188 | −0.0621522 | ||||||||
\(304\) | −28.7671 | −1.64990 | ||||||||
\(305\) | −7.76661 | −0.444715 | ||||||||
\(306\) | −40.5946 | −2.32064 | ||||||||
\(307\) | −8.69391 | −0.496187 | −0.248094 | − | 0.968736i | \(-0.579804\pi\) | ||||
−0.248094 | + | 0.968736i | \(0.579804\pi\) | |||||||
\(308\) | 15.5735 | 0.887383 | ||||||||
\(309\) | 0.736298 | 0.0418866 | ||||||||
\(310\) | 30.8054 | 1.74963 | ||||||||
\(311\) | −1.47728 | −0.0837688 | −0.0418844 | − | 0.999122i | \(-0.513336\pi\) | ||||
−0.0418844 | + | 0.999122i | \(0.513336\pi\) | |||||||
\(312\) | 1.13876 | 0.0644696 | ||||||||
\(313\) | −0.326946 | −0.0184801 | −0.00924005 | − | 0.999957i | \(-0.502941\pi\) | ||||
−0.00924005 | + | 0.999957i | \(0.502941\pi\) | |||||||
\(314\) | 3.63856 | 0.205336 | ||||||||
\(315\) | −8.95418 | −0.504511 | ||||||||
\(316\) | 6.91590 | 0.389050 | ||||||||
\(317\) | 31.5000 | 1.76922 | 0.884609 | − | 0.466334i | \(-0.154426\pi\) | ||||
0.884609 | + | 0.466334i | \(0.154426\pi\) | |||||||
\(318\) | 2.50219 | 0.140316 | ||||||||
\(319\) | −13.3768 | −0.748959 | ||||||||
\(320\) | 7.34161 | 0.410408 | ||||||||
\(321\) | 1.53149 | 0.0854792 | ||||||||
\(322\) | −32.1169 | −1.78981 | ||||||||
\(323\) | 27.4649 | 1.52819 | ||||||||
\(324\) | 36.9580 | 2.05322 | ||||||||
\(325\) | −1.72035 | −0.0954279 | ||||||||
\(326\) | −48.1699 | −2.66788 | ||||||||
\(327\) | 1.67974 | 0.0928900 | ||||||||
\(328\) | −53.7623 | −2.96853 | ||||||||
\(329\) | 18.3112 | 1.00953 | ||||||||
\(330\) | 1.97541 | 0.108743 | ||||||||
\(331\) | 21.4205 | 1.17738 | 0.588689 | − | 0.808360i | \(-0.299644\pi\) | ||||
0.588689 | + | 0.808360i | \(0.299644\pi\) | |||||||
\(332\) | −34.0330 | −1.86780 | ||||||||
\(333\) | −8.22680 | −0.450826 | ||||||||
\(334\) | 26.1955 | 1.43335 | ||||||||
\(335\) | −16.0779 | −0.878432 | ||||||||
\(336\) | 1.91249 | 0.104335 | ||||||||
\(337\) | 8.42630 | 0.459010 | 0.229505 | − | 0.973308i | \(-0.426289\pi\) | ||||
0.229505 | + | 0.973308i | \(0.426289\pi\) | |||||||
\(338\) | −2.50524 | −0.136267 | ||||||||
\(339\) | −1.15236 | −0.0625874 | ||||||||
\(340\) | 42.3919 | 2.29903 | ||||||||
\(341\) | −14.8043 | −0.801699 | ||||||||
\(342\) | −37.2072 | −2.01193 | ||||||||
\(343\) | 18.7244 | 1.01102 | ||||||||
\(344\) | −55.0615 | −2.96872 | ||||||||
\(345\) | −2.77566 | −0.149436 | ||||||||
\(346\) | 42.3071 | 2.27444 | ||||||||
\(347\) | −4.41119 | −0.236805 | −0.118403 | − | 0.992966i | \(-0.537777\pi\) | ||||
−0.118403 | + | 0.992966i | \(0.537777\pi\) | |||||||
\(348\) | −5.23912 | −0.280846 | ||||||||
\(349\) | 2.18734 | 0.117085 | 0.0585427 | − | 0.998285i | \(-0.481355\pi\) | ||||
0.0585427 | + | 0.998285i | \(0.481355\pi\) | |||||||
\(350\) | −7.19894 | −0.384799 | ||||||||
\(351\) | 1.19021 | 0.0635289 | ||||||||
\(352\) | 6.45186 | 0.343885 | ||||||||
\(353\) | −2.53760 | −0.135063 | −0.0675315 | − | 0.997717i | \(-0.521512\pi\) | ||||
−0.0675315 | + | 0.997717i | \(0.521512\pi\) | |||||||
\(354\) | 4.94642 | 0.262899 | ||||||||
\(355\) | −19.6392 | −1.04234 | ||||||||
\(356\) | −26.3544 | −1.39678 | ||||||||
\(357\) | −1.82592 | −0.0966379 | ||||||||
\(358\) | 12.5347 | 0.662480 | ||||||||
\(359\) | 13.5734 | 0.716378 | 0.358189 | − | 0.933649i | \(-0.383394\pi\) | ||||
0.358189 | + | 0.933649i | \(0.383394\pi\) | |||||||
\(360\) | −30.5693 | −1.61115 | ||||||||
\(361\) | 6.17306 | 0.324898 | ||||||||
\(362\) | 60.9019 | 3.20093 | ||||||||
\(363\) | 1.24733 | 0.0654676 | ||||||||
\(364\) | −7.14270 | −0.374379 | ||||||||
\(365\) | −23.7248 | −1.24181 | ||||||||
\(366\) | 2.14554 | 0.112149 | ||||||||
\(367\) | −29.6207 | −1.54619 | −0.773094 | − | 0.634291i | \(-0.781292\pi\) | ||||
−0.773094 | + | 0.634291i | \(0.781292\pi\) | |||||||
\(368\) | −44.0058 | −2.29396 | ||||||||
\(369\) | −27.9078 | −1.45282 | ||||||||
\(370\) | 12.6091 | 0.655516 | ||||||||
\(371\) | −8.35419 | −0.433728 | ||||||||
\(372\) | −5.79820 | −0.300623 | ||||||||
\(373\) | −23.3609 | −1.20958 | −0.604792 | − | 0.796383i | \(-0.706744\pi\) | ||||
−0.604792 | + | 0.796383i | \(0.706744\pi\) | |||||||
\(374\) | −29.9008 | −1.54613 | ||||||||
\(375\) | −2.43039 | −0.125505 | ||||||||
\(376\) | 62.5141 | 3.22392 | ||||||||
\(377\) | 6.13521 | 0.315979 | ||||||||
\(378\) | 4.98053 | 0.256171 | ||||||||
\(379\) | 2.29228 | 0.117747 | 0.0588733 | − | 0.998265i | \(-0.481249\pi\) | ||||
0.0588733 | + | 0.998265i | \(0.481249\pi\) | |||||||
\(380\) | 38.8545 | 1.99319 | ||||||||
\(381\) | −3.42995 | −0.175722 | ||||||||
\(382\) | −42.9842 | −2.19926 | ||||||||
\(383\) | 5.12776 | 0.262016 | 0.131008 | − | 0.991381i | \(-0.458179\pi\) | ||||
0.131008 | + | 0.991381i | \(0.458179\pi\) | |||||||
\(384\) | −3.20997 | −0.163808 | ||||||||
\(385\) | −6.59539 | −0.336132 | ||||||||
\(386\) | 43.7750 | 2.22809 | ||||||||
\(387\) | −28.5821 | −1.45291 | ||||||||
\(388\) | −11.7239 | −0.595193 | ||||||||
\(389\) | 6.32423 | 0.320651 | 0.160326 | − | 0.987064i | \(-0.448746\pi\) | ||||
0.160326 | + | 0.987064i | \(0.448746\pi\) | |||||||
\(390\) | −0.906008 | −0.0458775 | ||||||||
\(391\) | 42.0138 | 2.12473 | ||||||||
\(392\) | 24.0074 | 1.21256 | ||||||||
\(393\) | 3.05509 | 0.154109 | ||||||||
\(394\) | 49.6147 | 2.49955 | ||||||||
\(395\) | −2.92889 | −0.147368 | ||||||||
\(396\) | 27.5990 | 1.38690 | ||||||||
\(397\) | −8.25134 | −0.414123 | −0.207061 | − | 0.978328i | \(-0.566390\pi\) | ||||
−0.207061 | + | 0.978328i | \(0.566390\pi\) | |||||||
\(398\) | −13.8855 | −0.696017 | ||||||||
\(399\) | −1.67355 | −0.0837825 | ||||||||
\(400\) | −9.86381 | −0.493190 | ||||||||
\(401\) | 17.6036 | 0.879082 | 0.439541 | − | 0.898222i | \(-0.355141\pi\) | ||||
0.439541 | + | 0.898222i | \(0.355141\pi\) | |||||||
\(402\) | 4.44156 | 0.221525 | ||||||||
\(403\) | 6.78991 | 0.338230 | ||||||||
\(404\) | 23.1669 | 1.15260 | ||||||||
\(405\) | −15.6517 | −0.777741 | ||||||||
\(406\) | 25.6732 | 1.27414 | ||||||||
\(407\) | −6.05962 | −0.300364 | ||||||||
\(408\) | −6.23364 | −0.308611 | ||||||||
\(409\) | 29.1750 | 1.44261 | 0.721304 | − | 0.692618i | \(-0.243543\pi\) | ||||
0.721304 | + | 0.692618i | \(0.243543\pi\) | |||||||
\(410\) | 42.7738 | 2.11245 | ||||||||
\(411\) | 1.19459 | 0.0589246 | ||||||||
\(412\) | −15.7668 | −0.776776 | ||||||||
\(413\) | −16.5148 | −0.812642 | ||||||||
\(414\) | −56.9169 | −2.79731 | ||||||||
\(415\) | 14.4130 | 0.707505 | ||||||||
\(416\) | −2.95911 | −0.145082 | ||||||||
\(417\) | −1.60416 | −0.0785563 | ||||||||
\(418\) | −27.4057 | −1.34046 | ||||||||
\(419\) | 13.6855 | 0.668579 | 0.334289 | − | 0.942470i | \(-0.391504\pi\) | ||||
0.334289 | + | 0.942470i | \(0.391504\pi\) | |||||||
\(420\) | −2.58312 | −0.126044 | ||||||||
\(421\) | 17.8598 | 0.870432 | 0.435216 | − | 0.900326i | \(-0.356672\pi\) | ||||
0.435216 | + | 0.900326i | \(0.356672\pi\) | |||||||
\(422\) | 22.3537 | 1.08816 | ||||||||
\(423\) | 32.4507 | 1.57781 | ||||||||
\(424\) | −28.5210 | −1.38510 | ||||||||
\(425\) | 9.41730 | 0.456806 | ||||||||
\(426\) | 5.42537 | 0.262860 | ||||||||
\(427\) | −7.16342 | −0.346662 | ||||||||
\(428\) | −32.7947 | −1.58519 | ||||||||
\(429\) | 0.435405 | 0.0210216 | ||||||||
\(430\) | 43.8074 | 2.11258 | ||||||||
\(431\) | 7.48144 | 0.360368 | 0.180184 | − | 0.983633i | \(-0.442331\pi\) | ||||
0.180184 | + | 0.983633i | \(0.442331\pi\) | |||||||
\(432\) | 6.82421 | 0.328330 | ||||||||
\(433\) | 15.7749 | 0.758095 | 0.379048 | − | 0.925377i | \(-0.376252\pi\) | ||||
0.379048 | + | 0.925377i | \(0.376252\pi\) | |||||||
\(434\) | 28.4129 | 1.36386 | ||||||||
\(435\) | 2.21877 | 0.106382 | ||||||||
\(436\) | −35.9694 | −1.72262 | ||||||||
\(437\) | 38.5080 | 1.84209 | ||||||||
\(438\) | 6.55402 | 0.313163 | ||||||||
\(439\) | −19.0397 | −0.908716 | −0.454358 | − | 0.890819i | \(-0.650131\pi\) | ||||
−0.454358 | + | 0.890819i | \(0.650131\pi\) | |||||||
\(440\) | −22.5165 | −1.07343 | ||||||||
\(441\) | 12.4621 | 0.593433 | ||||||||
\(442\) | 13.7138 | 0.652300 | ||||||||
\(443\) | 10.6043 | 0.503826 | 0.251913 | − | 0.967750i | \(-0.418940\pi\) | ||||
0.251913 | + | 0.967750i | \(0.418940\pi\) | |||||||
\(444\) | −2.37329 | −0.112631 | ||||||||
\(445\) | 11.1611 | 0.529087 | ||||||||
\(446\) | −20.9944 | −0.994115 | ||||||||
\(447\) | 1.21592 | 0.0575109 | ||||||||
\(448\) | 6.77142 | 0.319920 | ||||||||
\(449\) | 31.2631 | 1.47540 | 0.737699 | − | 0.675130i | \(-0.235912\pi\) | ||||
0.737699 | + | 0.675130i | \(0.235912\pi\) | |||||||
\(450\) | −12.7578 | −0.601408 | ||||||||
\(451\) | −20.5560 | −0.967946 | ||||||||
\(452\) | 24.6761 | 1.16067 | ||||||||
\(453\) | −4.04889 | −0.190234 | ||||||||
\(454\) | 33.5080 | 1.57261 | ||||||||
\(455\) | 3.02494 | 0.141811 | ||||||||
\(456\) | −5.71348 | −0.267558 | ||||||||
\(457\) | 39.2077 | 1.83406 | 0.917030 | − | 0.398819i | \(-0.130580\pi\) | ||||
0.917030 | + | 0.398819i | \(0.130580\pi\) | |||||||
\(458\) | −4.77591 | −0.223164 | ||||||||
\(459\) | −6.51530 | −0.304108 | ||||||||
\(460\) | 59.4369 | 2.77126 | ||||||||
\(461\) | 8.61472 | 0.401227 | 0.200614 | − | 0.979670i | \(-0.435706\pi\) | ||||
0.200614 | + | 0.979670i | \(0.435706\pi\) | |||||||
\(462\) | 1.82199 | 0.0847665 | ||||||||
\(463\) | −11.9212 | −0.554023 | −0.277012 | − | 0.960867i | \(-0.589344\pi\) | ||||
−0.277012 | + | 0.960867i | \(0.589344\pi\) | |||||||
\(464\) | 35.1768 | 1.63304 | ||||||||
\(465\) | 2.45554 | 0.113873 | ||||||||
\(466\) | 65.4781 | 3.03321 | ||||||||
\(467\) | 22.9991 | 1.06427 | 0.532135 | − | 0.846660i | \(-0.321390\pi\) | ||||
0.532135 | + | 0.846660i | \(0.321390\pi\) | |||||||
\(468\) | −12.6581 | −0.585122 | ||||||||
\(469\) | −14.8292 | −0.684751 | ||||||||
\(470\) | −49.7368 | −2.29419 | ||||||||
\(471\) | 0.290035 | 0.0133641 | ||||||||
\(472\) | −56.3813 | −2.59516 | ||||||||
\(473\) | −21.0528 | −0.968008 | ||||||||
\(474\) | 0.809109 | 0.0371636 | ||||||||
\(475\) | 8.63148 | 0.396039 | ||||||||
\(476\) | 39.0996 | 1.79213 | ||||||||
\(477\) | −14.8051 | −0.677879 | ||||||||
\(478\) | 43.3322 | 1.98197 | ||||||||
\(479\) | −24.7332 | −1.13009 | −0.565044 | − | 0.825061i | \(-0.691141\pi\) | ||||
−0.565044 | + | 0.825061i | \(0.691141\pi\) | |||||||
\(480\) | −1.07015 | −0.0488453 | ||||||||
\(481\) | 2.77921 | 0.126721 | ||||||||
\(482\) | −60.1683 | −2.74059 | ||||||||
\(483\) | −2.56009 | −0.116488 | ||||||||
\(484\) | −26.7098 | −1.21408 | ||||||||
\(485\) | 4.96509 | 0.225453 | ||||||||
\(486\) | 13.2691 | 0.601899 | ||||||||
\(487\) | 15.8497 | 0.718217 | 0.359109 | − | 0.933296i | \(-0.383081\pi\) | ||||
0.359109 | + | 0.933296i | \(0.383081\pi\) | |||||||
\(488\) | −24.4557 | −1.10706 | ||||||||
\(489\) | −3.83969 | −0.173637 | ||||||||
\(490\) | −19.1005 | −0.862872 | ||||||||
\(491\) | −0.602420 | −0.0271868 | −0.0135934 | − | 0.999908i | \(-0.504327\pi\) | ||||
−0.0135934 | + | 0.999908i | \(0.504327\pi\) | |||||||
\(492\) | −8.05090 | −0.362963 | ||||||||
\(493\) | −33.5845 | −1.51257 | ||||||||
\(494\) | 12.5695 | 0.565527 | ||||||||
\(495\) | −11.6882 | −0.525345 | ||||||||
\(496\) | 38.9307 | 1.74804 | ||||||||
\(497\) | −18.1139 | −0.812522 | ||||||||
\(498\) | −3.98161 | −0.178420 | ||||||||
\(499\) | −22.1344 | −0.990870 | −0.495435 | − | 0.868645i | \(-0.664991\pi\) | ||||
−0.495435 | + | 0.868645i | \(0.664991\pi\) | |||||||
\(500\) | 52.0434 | 2.32745 | ||||||||
\(501\) | 2.08808 | 0.0932885 | ||||||||
\(502\) | 11.7792 | 0.525730 | ||||||||
\(503\) | 34.3426 | 1.53126 | 0.765630 | − | 0.643281i | \(-0.222427\pi\) | ||||
0.765630 | + | 0.643281i | \(0.222427\pi\) | |||||||
\(504\) | −28.1952 | −1.25591 | ||||||||
\(505\) | −9.81119 | −0.436592 | ||||||||
\(506\) | −41.9233 | −1.86372 | ||||||||
\(507\) | −0.199696 | −0.00886881 | ||||||||
\(508\) | 73.4476 | 3.25871 | ||||||||
\(509\) | −37.0427 | −1.64189 | −0.820945 | − | 0.571007i | \(-0.806553\pi\) | ||||
−0.820945 | + | 0.571007i | \(0.806553\pi\) | |||||||
\(510\) | 4.95954 | 0.219612 | ||||||||
\(511\) | −21.8822 | −0.968013 | ||||||||
\(512\) | 48.4250 | 2.14010 | ||||||||
\(513\) | −5.97163 | −0.263654 | ||||||||
\(514\) | −63.8804 | −2.81764 | ||||||||
\(515\) | 6.67726 | 0.294235 | ||||||||
\(516\) | −8.24545 | −0.362986 | ||||||||
\(517\) | 23.9023 | 1.05122 | ||||||||
\(518\) | 11.6298 | 0.510984 | ||||||||
\(519\) | 3.37235 | 0.148030 | ||||||||
\(520\) | 10.3271 | 0.452871 | ||||||||
\(521\) | 40.2968 | 1.76544 | 0.882718 | − | 0.469904i | \(-0.155711\pi\) | ||||
0.882718 | + | 0.469904i | \(0.155711\pi\) | |||||||
\(522\) | 45.4975 | 1.99137 | ||||||||
\(523\) | −26.1770 | −1.14464 | −0.572320 | − | 0.820030i | \(-0.693956\pi\) | ||||
−0.572320 | + | 0.820030i | \(0.693956\pi\) | |||||||
\(524\) | −65.4205 | −2.85791 | ||||||||
\(525\) | −0.573837 | −0.0250443 | ||||||||
\(526\) | 21.6710 | 0.944898 | ||||||||
\(527\) | −37.1684 | −1.61908 | ||||||||
\(528\) | 2.49644 | 0.108644 | ||||||||
\(529\) | 35.9068 | 1.56116 | ||||||||
\(530\) | 22.6916 | 0.985659 | ||||||||
\(531\) | −29.2672 | −1.27009 | ||||||||
\(532\) | 35.8369 | 1.55373 | ||||||||
\(533\) | 9.42791 | 0.408368 | ||||||||
\(534\) | −3.08327 | −0.133426 | ||||||||
\(535\) | 13.8886 | 0.600455 | ||||||||
\(536\) | −50.6267 | −2.18674 | ||||||||
\(537\) | 0.999159 | 0.0431169 | ||||||||
\(538\) | 43.3454 | 1.86875 | ||||||||
\(539\) | 9.17922 | 0.395377 | ||||||||
\(540\) | −9.21718 | −0.396644 | ||||||||
\(541\) | 15.7254 | 0.676086 | 0.338043 | − | 0.941131i | \(-0.390235\pi\) | ||||
0.338043 | + | 0.941131i | \(0.390235\pi\) | |||||||
\(542\) | 24.5329 | 1.05378 | ||||||||
\(543\) | 4.85457 | 0.208330 | ||||||||
\(544\) | 16.1983 | 0.694497 | ||||||||
\(545\) | 15.2331 | 0.652513 | ||||||||
\(546\) | −0.835643 | −0.0357622 | ||||||||
\(547\) | 18.5417 | 0.792788 | 0.396394 | − | 0.918081i | \(-0.370261\pi\) | ||||
0.396394 | + | 0.918081i | \(0.370261\pi\) | |||||||
\(548\) | −25.5805 | −1.09274 | ||||||||
\(549\) | −12.6948 | −0.541803 | ||||||||
\(550\) | −9.39702 | −0.400690 | ||||||||
\(551\) | −30.7820 | −1.31136 | ||||||||
\(552\) | −8.74007 | −0.372002 | ||||||||
\(553\) | −2.70141 | −0.114876 | ||||||||
\(554\) | 64.1759 | 2.72657 | ||||||||
\(555\) | 1.00509 | 0.0426636 | ||||||||
\(556\) | 34.3510 | 1.45681 | ||||||||
\(557\) | −18.3607 | −0.777969 | −0.388985 | − | 0.921244i | \(-0.627174\pi\) | ||||
−0.388985 | + | 0.921244i | \(0.627174\pi\) | |||||||
\(558\) | 50.3527 | 2.13160 | ||||||||
\(559\) | 9.65573 | 0.408394 | ||||||||
\(560\) | 17.3438 | 0.732908 | ||||||||
\(561\) | −2.38343 | −0.100629 | ||||||||
\(562\) | 29.3240 | 1.23696 | ||||||||
\(563\) | −8.23909 | −0.347236 | −0.173618 | − | 0.984813i | \(-0.555546\pi\) | ||||
−0.173618 | + | 0.984813i | \(0.555546\pi\) | |||||||
\(564\) | 9.36148 | 0.394189 | ||||||||
\(565\) | −10.4504 | −0.439650 | ||||||||
\(566\) | 23.4230 | 0.984540 | ||||||||
\(567\) | −14.4361 | −0.606261 | ||||||||
\(568\) | −61.8406 | −2.59477 | ||||||||
\(569\) | −20.3979 | −0.855125 | −0.427563 | − | 0.903986i | \(-0.640628\pi\) | ||||
−0.427563 | + | 0.903986i | \(0.640628\pi\) | |||||||
\(570\) | 4.54569 | 0.190398 | ||||||||
\(571\) | 36.7042 | 1.53602 | 0.768011 | − | 0.640437i | \(-0.221247\pi\) | ||||
0.768011 | + | 0.640437i | \(0.221247\pi\) | |||||||
\(572\) | −9.32361 | −0.389840 | ||||||||
\(573\) | −3.42633 | −0.143137 | ||||||||
\(574\) | 39.4518 | 1.64669 | ||||||||
\(575\) | 13.2038 | 0.550637 | ||||||||
\(576\) | 12.0002 | 0.500007 | ||||||||
\(577\) | −37.8458 | −1.57554 | −0.787770 | − | 0.615970i | \(-0.788764\pi\) | ||||
−0.787770 | + | 0.615970i | \(0.788764\pi\) | |||||||
\(578\) | −32.4813 | −1.35104 | ||||||||
\(579\) | 3.48936 | 0.145013 | ||||||||
\(580\) | −47.5119 | −1.97283 | ||||||||
\(581\) | 13.2936 | 0.551511 | ||||||||
\(582\) | −1.37161 | −0.0568553 | ||||||||
\(583\) | −10.9050 | −0.451640 | ||||||||
\(584\) | −74.7054 | −3.09133 | ||||||||
\(585\) | 5.36072 | 0.221639 | ||||||||
\(586\) | −70.3776 | −2.90727 | ||||||||
\(587\) | 5.02106 | 0.207241 | 0.103621 | − | 0.994617i | \(-0.466957\pi\) | ||||
0.103621 | + | 0.994617i | \(0.466957\pi\) | |||||||
\(588\) | 3.59510 | 0.148259 | ||||||||
\(589\) | −34.0669 | −1.40370 | ||||||||
\(590\) | 44.8575 | 1.84675 | ||||||||
\(591\) | 3.95486 | 0.162681 | ||||||||
\(592\) | 15.9349 | 0.654920 | ||||||||
\(593\) | −15.2200 | −0.625012 | −0.312506 | − | 0.949916i | \(-0.601168\pi\) | ||||
−0.312506 | + | 0.949916i | \(0.601168\pi\) | |||||||
\(594\) | 6.50126 | 0.266750 | ||||||||
\(595\) | −16.5587 | −0.678840 | ||||||||
\(596\) | −26.0372 | −1.06652 | ||||||||
\(597\) | −1.10683 | −0.0452997 | ||||||||
\(598\) | 19.2279 | 0.786287 | ||||||||
\(599\) | 28.8366 | 1.17823 | 0.589115 | − | 0.808049i | \(-0.299476\pi\) | ||||
0.589115 | + | 0.808049i | \(0.299476\pi\) | |||||||
\(600\) | −1.95907 | −0.0799786 | ||||||||
\(601\) | 17.2014 | 0.701658 | 0.350829 | − | 0.936439i | \(-0.385900\pi\) | ||||
0.350829 | + | 0.936439i | \(0.385900\pi\) | |||||||
\(602\) | 40.4051 | 1.64679 | ||||||||
\(603\) | −26.2801 | −1.07021 | ||||||||
\(604\) | 86.7015 | 3.52783 | ||||||||
\(605\) | 11.3116 | 0.459882 | ||||||||
\(606\) | 2.71036 | 0.110101 | ||||||||
\(607\) | 17.8409 | 0.724140 | 0.362070 | − | 0.932151i | \(-0.382070\pi\) | ||||
0.362070 | + | 0.932151i | \(0.382070\pi\) | |||||||
\(608\) | 14.8467 | 0.602111 | ||||||||
\(609\) | 2.04645 | 0.0829263 | ||||||||
\(610\) | 19.4572 | 0.787800 | ||||||||
\(611\) | −10.9626 | −0.443501 | ||||||||
\(612\) | 69.2913 | 2.80094 | ||||||||
\(613\) | 23.8354 | 0.962702 | 0.481351 | − | 0.876528i | \(-0.340146\pi\) | ||||
0.481351 | + | 0.876528i | \(0.340146\pi\) | |||||||
\(614\) | 21.7803 | 0.878981 | ||||||||
\(615\) | 3.40956 | 0.137487 | ||||||||
\(616\) | −20.7677 | −0.836756 | ||||||||
\(617\) | −26.0279 | −1.04784 | −0.523921 | − | 0.851767i | \(-0.675531\pi\) | ||||
−0.523921 | + | 0.851767i | \(0.675531\pi\) | |||||||
\(618\) | −1.84460 | −0.0742008 | ||||||||
\(619\) | 1.00000 | 0.0401934 | ||||||||
\(620\) | −52.5821 | −2.11175 | ||||||||
\(621\) | −9.13497 | −0.366574 | ||||||||
\(622\) | 3.70094 | 0.148394 | ||||||||
\(623\) | 10.2943 | 0.412432 | ||||||||
\(624\) | −1.14498 | −0.0458358 | ||||||||
\(625\) | −13.4386 | −0.537546 | ||||||||
\(626\) | 0.819079 | 0.0327370 | ||||||||
\(627\) | −2.18455 | −0.0872425 | ||||||||
\(628\) | −6.21071 | −0.247834 | ||||||||
\(629\) | −15.2136 | −0.606604 | ||||||||
\(630\) | 22.4323 | 0.893726 | ||||||||
\(631\) | 0.213627 | 0.00850434 | 0.00425217 | − | 0.999991i | \(-0.498646\pi\) | ||||
0.00425217 | + | 0.999991i | \(0.498646\pi\) | |||||||
\(632\) | −9.22256 | −0.366854 | ||||||||
\(633\) | 1.78185 | 0.0708221 | ||||||||
\(634\) | −78.9151 | −3.13412 | ||||||||
\(635\) | −31.1051 | −1.23437 | ||||||||
\(636\) | −4.27102 | −0.169357 | ||||||||
\(637\) | −4.21000 | −0.166806 | ||||||||
\(638\) | 33.5122 | 1.32676 | ||||||||
\(639\) | −32.1011 | −1.26990 | ||||||||
\(640\) | −29.1102 | −1.15068 | ||||||||
\(641\) | 23.5677 | 0.930870 | 0.465435 | − | 0.885082i | \(-0.345898\pi\) | ||||
0.465435 | + | 0.885082i | \(0.345898\pi\) | |||||||
\(642\) | −3.83674 | −0.151424 | ||||||||
\(643\) | 11.3833 | 0.448913 | 0.224456 | − | 0.974484i | \(-0.427939\pi\) | ||||
0.224456 | + | 0.974484i | \(0.427939\pi\) | |||||||
\(644\) | 54.8207 | 2.16024 | ||||||||
\(645\) | 3.49195 | 0.137496 | ||||||||
\(646\) | −68.8061 | −2.70714 | ||||||||
\(647\) | −40.4963 | −1.59207 | −0.796036 | − | 0.605249i | \(-0.793074\pi\) | ||||
−0.796036 | + | 0.605249i | \(0.793074\pi\) | |||||||
\(648\) | −49.2846 | −1.93608 | ||||||||
\(649\) | −21.5574 | −0.846202 | ||||||||
\(650\) | 4.30989 | 0.169048 | ||||||||
\(651\) | 2.26483 | 0.0887658 | ||||||||
\(652\) | 82.2217 | 3.22005 | ||||||||
\(653\) | −32.9583 | −1.28976 | −0.644879 | − | 0.764284i | \(-0.723092\pi\) | ||||
−0.644879 | + | 0.764284i | \(0.723092\pi\) | |||||||
\(654\) | −4.20816 | −0.164552 | ||||||||
\(655\) | 27.7056 | 1.08255 | ||||||||
\(656\) | 54.0559 | 2.11053 | ||||||||
\(657\) | −38.7792 | −1.51292 | ||||||||
\(658\) | −45.8740 | −1.78835 | ||||||||
\(659\) | 1.01809 | 0.0396592 | 0.0198296 | − | 0.999803i | \(-0.493688\pi\) | ||||
0.0198296 | + | 0.999803i | \(0.493688\pi\) | |||||||
\(660\) | −3.37184 | −0.131249 | ||||||||
\(661\) | −41.5968 | −1.61793 | −0.808963 | − | 0.587859i | \(-0.799971\pi\) | ||||
−0.808963 | + | 0.587859i | \(0.799971\pi\) | |||||||
\(662\) | −53.6635 | −2.08569 | ||||||||
\(663\) | 1.09315 | 0.0424544 | ||||||||
\(664\) | 45.3840 | 1.76124 | ||||||||
\(665\) | −15.1769 | −0.588536 | ||||||||
\(666\) | 20.6101 | 0.798625 | ||||||||
\(667\) | −47.0882 | −1.82326 | ||||||||
\(668\) | −44.7133 | −1.73001 | ||||||||
\(669\) | −1.67350 | −0.0647011 | ||||||||
\(670\) | 40.2791 | 1.55612 | ||||||||
\(671\) | −9.35066 | −0.360978 | ||||||||
\(672\) | −0.987034 | −0.0380757 | ||||||||
\(673\) | −40.3372 | −1.55488 | −0.777442 | − | 0.628954i | \(-0.783483\pi\) | ||||
−0.777442 | + | 0.628954i | \(0.783483\pi\) | |||||||
\(674\) | −21.1099 | −0.813122 | ||||||||
\(675\) | −2.04758 | −0.0788115 | ||||||||
\(676\) | 4.27622 | 0.164470 | ||||||||
\(677\) | −14.3476 | −0.551421 | −0.275711 | − | 0.961241i | \(-0.588913\pi\) | ||||
−0.275711 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(678\) | 2.88693 | 0.110872 | ||||||||
\(679\) | 4.57948 | 0.175744 | ||||||||
\(680\) | −56.5309 | −2.16786 | ||||||||
\(681\) | 2.67097 | 0.102352 | ||||||||
\(682\) | 37.0883 | 1.42019 | ||||||||
\(683\) | −26.7994 | −1.02545 | −0.512725 | − | 0.858553i | \(-0.671364\pi\) | ||||
−0.512725 | + | 0.858553i | \(0.671364\pi\) | |||||||
\(684\) | 63.5093 | 2.42834 | ||||||||
\(685\) | 10.8333 | 0.413920 | ||||||||
\(686\) | −46.9091 | −1.79100 | ||||||||
\(687\) | −0.380694 | −0.0145244 | ||||||||
\(688\) | 55.3621 | 2.11066 | ||||||||
\(689\) | 5.00152 | 0.190543 | ||||||||
\(690\) | 6.95368 | 0.264722 | ||||||||
\(691\) | 51.1814 | 1.94703 | 0.973515 | − | 0.228622i | \(-0.0734218\pi\) | ||||
0.973515 | + | 0.228622i | \(0.0734218\pi\) | |||||||
\(692\) | −72.2144 | −2.74518 | ||||||||
\(693\) | −10.7804 | −0.409515 | ||||||||
\(694\) | 11.0511 | 0.419493 | ||||||||
\(695\) | −14.5477 | −0.551824 | ||||||||
\(696\) | 6.98653 | 0.264824 | ||||||||
\(697\) | −51.6089 | −1.95483 | ||||||||
\(698\) | −5.47980 | −0.207413 | ||||||||
\(699\) | 5.21935 | 0.197414 | ||||||||
\(700\) | 12.2879 | 0.464441 | ||||||||
\(701\) | −13.1856 | −0.498012 | −0.249006 | − | 0.968502i | \(-0.580104\pi\) | ||||
−0.249006 | + | 0.968502i | \(0.580104\pi\) | |||||||
\(702\) | −2.98177 | −0.112540 | ||||||||
\(703\) | −13.9441 | −0.525910 | ||||||||
\(704\) | 8.83897 | 0.333131 | ||||||||
\(705\) | −3.96459 | −0.149315 | ||||||||
\(706\) | 6.35730 | 0.239260 | ||||||||
\(707\) | −9.04920 | −0.340330 | ||||||||
\(708\) | −8.44309 | −0.317311 | ||||||||
\(709\) | 42.3122 | 1.58907 | 0.794533 | − | 0.607221i | \(-0.207716\pi\) | ||||
0.794533 | + | 0.607221i | \(0.207716\pi\) | |||||||
\(710\) | 49.2009 | 1.84648 | ||||||||
\(711\) | −4.78738 | −0.179541 | ||||||||
\(712\) | 35.1444 | 1.31709 | ||||||||
\(713\) | −52.1131 | −1.95165 | ||||||||
\(714\) | 4.57436 | 0.171191 | ||||||||
\(715\) | 3.94855 | 0.147667 | ||||||||
\(716\) | −21.3956 | −0.799592 | ||||||||
\(717\) | 3.45407 | 0.128995 | ||||||||
\(718\) | −34.0047 | −1.26904 | ||||||||
\(719\) | −26.5241 | −0.989182 | −0.494591 | − | 0.869126i | \(-0.664682\pi\) | ||||
−0.494591 | + | 0.869126i | \(0.664682\pi\) | |||||||
\(720\) | 30.7362 | 1.14547 | ||||||||
\(721\) | 6.15867 | 0.229361 | ||||||||
\(722\) | −15.4650 | −0.575548 | ||||||||
\(723\) | −4.79610 | −0.178369 | ||||||||
\(724\) | −103.954 | −3.86342 | ||||||||
\(725\) | −10.5547 | −0.391992 | ||||||||
\(726\) | −3.12485 | −0.115974 | ||||||||
\(727\) | 24.4085 | 0.905262 | 0.452631 | − | 0.891698i | \(-0.350486\pi\) | ||||
0.452631 | + | 0.891698i | \(0.350486\pi\) | |||||||
\(728\) | 9.52500 | 0.353020 | ||||||||
\(729\) | −24.8704 | −0.921124 | ||||||||
\(730\) | 59.4363 | 2.19984 | ||||||||
\(731\) | −52.8561 | −1.95495 | ||||||||
\(732\) | −3.66224 | −0.135360 | ||||||||
\(733\) | 16.4822 | 0.608782 | 0.304391 | − | 0.952547i | \(-0.401547\pi\) | ||||
0.304391 | + | 0.952547i | \(0.401547\pi\) | |||||||
\(734\) | 74.2070 | 2.73903 | ||||||||
\(735\) | −1.52253 | −0.0561592 | ||||||||
\(736\) | 22.7114 | 0.837152 | ||||||||
\(737\) | −19.3571 | −0.713029 | ||||||||
\(738\) | 69.9156 | 2.57363 | ||||||||
\(739\) | 3.85289 | 0.141731 | 0.0708654 | − | 0.997486i | \(-0.477424\pi\) | ||||
0.0708654 | + | 0.997486i | \(0.477424\pi\) | |||||||
\(740\) | −21.5226 | −0.791187 | ||||||||
\(741\) | 1.00193 | 0.0368068 | ||||||||
\(742\) | 20.9292 | 0.768336 | ||||||||
\(743\) | 28.3467 | 1.03994 | 0.519970 | − | 0.854184i | \(-0.325943\pi\) | ||||
0.519970 | + | 0.854184i | \(0.325943\pi\) | |||||||
\(744\) | 7.73208 | 0.283472 | ||||||||
\(745\) | 11.0268 | 0.403989 | ||||||||
\(746\) | 58.5247 | 2.14274 | ||||||||
\(747\) | 23.5586 | 0.861964 | ||||||||
\(748\) | 51.0380 | 1.86613 | ||||||||
\(749\) | 12.8099 | 0.468064 | ||||||||
\(750\) | 6.08869 | 0.222328 | ||||||||
\(751\) | 47.2765 | 1.72515 | 0.862573 | − | 0.505933i | \(-0.168852\pi\) | ||||
0.862573 | + | 0.505933i | \(0.168852\pi\) | |||||||
\(752\) | −62.8554 | −2.29210 | ||||||||
\(753\) | 0.938934 | 0.0342167 | ||||||||
\(754\) | −15.3702 | −0.559748 | ||||||||
\(755\) | −36.7181 | −1.33631 | ||||||||
\(756\) | −8.50133 | −0.309190 | ||||||||
\(757\) | −25.9581 | −0.943464 | −0.471732 | − | 0.881742i | \(-0.656371\pi\) | ||||
−0.471732 | + | 0.881742i | \(0.656371\pi\) | |||||||
\(758\) | −5.74271 | −0.208585 | ||||||||
\(759\) | −3.34177 | −0.121298 | ||||||||
\(760\) | −51.8137 | −1.87948 | ||||||||
\(761\) | 29.6907 | 1.07629 | 0.538143 | − | 0.842853i | \(-0.319126\pi\) | ||||
0.538143 | + | 0.842853i | \(0.319126\pi\) | |||||||
\(762\) | 8.59284 | 0.311286 | ||||||||
\(763\) | 14.0500 | 0.508644 | ||||||||
\(764\) | 73.3702 | 2.65444 | ||||||||
\(765\) | −29.3449 | −1.06097 | ||||||||
\(766\) | −12.8463 | −0.464154 | ||||||||
\(767\) | 9.88717 | 0.357005 | ||||||||
\(768\) | 6.42264 | 0.231757 | ||||||||
\(769\) | −12.3306 | −0.444652 | −0.222326 | − | 0.974972i | \(-0.571365\pi\) | ||||
−0.222326 | + | 0.974972i | \(0.571365\pi\) | |||||||
\(770\) | 16.5230 | 0.595448 | ||||||||
\(771\) | −5.09200 | −0.183384 | ||||||||
\(772\) | −74.7199 | −2.68923 | ||||||||
\(773\) | −35.0532 | −1.26078 | −0.630388 | − | 0.776280i | \(-0.717104\pi\) | ||||
−0.630388 | + | 0.776280i | \(0.717104\pi\) | |||||||
\(774\) | 71.6051 | 2.57379 | ||||||||
\(775\) | −11.6810 | −0.419595 | ||||||||
\(776\) | 15.6342 | 0.561236 | ||||||||
\(777\) | 0.927029 | 0.0332570 | ||||||||
\(778\) | −15.8437 | −0.568024 | ||||||||
\(779\) | −47.3024 | −1.69479 | ||||||||
\(780\) | 1.54648 | 0.0553727 | ||||||||
\(781\) | −23.6448 | −0.846076 | ||||||||
\(782\) | −105.255 | −3.76390 | ||||||||
\(783\) | 7.30220 | 0.260959 | ||||||||
\(784\) | −24.1384 | −0.862087 | ||||||||
\(785\) | 2.63024 | 0.0938772 | ||||||||
\(786\) | −7.65372 | −0.272999 | ||||||||
\(787\) | −23.3001 | −0.830558 | −0.415279 | − | 0.909694i | \(-0.636316\pi\) | ||||
−0.415279 | + | 0.909694i | \(0.636316\pi\) | |||||||
\(788\) | −84.6878 | −3.01688 | ||||||||
\(789\) | 1.72742 | 0.0614979 | ||||||||
\(790\) | 7.33756 | 0.261059 | ||||||||
\(791\) | −9.63872 | −0.342714 | ||||||||
\(792\) | −36.8041 | −1.30778 | ||||||||
\(793\) | 4.28862 | 0.152294 | ||||||||
\(794\) | 20.6716 | 0.733606 | ||||||||
\(795\) | 1.80878 | 0.0641507 | ||||||||
\(796\) | 23.7013 | 0.840071 | ||||||||
\(797\) | 38.2905 | 1.35632 | 0.678159 | − | 0.734915i | \(-0.262778\pi\) | ||||
0.678159 | + | 0.734915i | \(0.262778\pi\) | |||||||
\(798\) | 4.19265 | 0.148418 | ||||||||
\(799\) | 60.0101 | 2.12301 | ||||||||
\(800\) | 5.09070 | 0.179983 | ||||||||
\(801\) | 18.2433 | 0.644595 | ||||||||
\(802\) | −44.1012 | −1.55727 | ||||||||
\(803\) | −28.5636 | −1.00799 | ||||||||
\(804\) | −7.58134 | −0.267373 | ||||||||
\(805\) | −23.2166 | −0.818278 | ||||||||
\(806\) | −17.0103 | −0.599164 | ||||||||
\(807\) | 3.45512 | 0.121626 | ||||||||
\(808\) | −30.8938 | −1.08684 | ||||||||
\(809\) | −12.9823 | −0.456434 | −0.228217 | − | 0.973610i | \(-0.573290\pi\) | ||||
−0.228217 | + | 0.973610i | \(0.573290\pi\) | |||||||
\(810\) | 39.2113 | 1.37774 | ||||||||
\(811\) | 0.891683 | 0.0313112 | 0.0156556 | − | 0.999877i | \(-0.495016\pi\) | ||||
0.0156556 | + | 0.999877i | \(0.495016\pi\) | |||||||
\(812\) | −43.8219 | −1.53785 | ||||||||
\(813\) | 1.95556 | 0.0685843 | ||||||||
\(814\) | 15.1808 | 0.532086 | ||||||||
\(815\) | −34.8209 | −1.21972 | ||||||||
\(816\) | 6.26768 | 0.219413 | ||||||||
\(817\) | −48.4455 | −1.69489 | ||||||||
\(818\) | −73.0902 | −2.55554 | ||||||||
\(819\) | 4.94438 | 0.172771 | ||||||||
\(820\) | −73.0111 | −2.54966 | ||||||||
\(821\) | 7.76982 | 0.271169 | 0.135584 | − | 0.990766i | \(-0.456709\pi\) | ||||
0.135584 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(822\) | −2.99273 | −0.104383 | ||||||||
\(823\) | −30.8395 | −1.07500 | −0.537500 | − | 0.843264i | \(-0.680631\pi\) | ||||
−0.537500 | + | 0.843264i | \(0.680631\pi\) | |||||||
\(824\) | 21.0255 | 0.732459 | ||||||||
\(825\) | −0.749050 | −0.0260786 | ||||||||
\(826\) | 41.3736 | 1.43957 | ||||||||
\(827\) | 26.2937 | 0.914322 | 0.457161 | − | 0.889384i | \(-0.348866\pi\) | ||||
0.457161 | + | 0.889384i | \(0.348866\pi\) | |||||||
\(828\) | 97.1521 | 3.37627 | ||||||||
\(829\) | −44.8084 | −1.55626 | −0.778129 | − | 0.628104i | \(-0.783831\pi\) | ||||
−0.778129 | + | 0.628104i | \(0.783831\pi\) | |||||||
\(830\) | −36.1079 | −1.25332 | ||||||||
\(831\) | 5.11555 | 0.177456 | ||||||||
\(832\) | −4.05394 | −0.140545 | ||||||||
\(833\) | 23.0458 | 0.798489 | ||||||||
\(834\) | 4.01881 | 0.139160 | ||||||||
\(835\) | 18.9361 | 0.655311 | ||||||||
\(836\) | 46.7791 | 1.61789 | ||||||||
\(837\) | 8.08144 | 0.279335 | ||||||||
\(838\) | −34.2854 | −1.18437 | ||||||||
\(839\) | 34.8353 | 1.20265 | 0.601323 | − | 0.799006i | \(-0.294640\pi\) | ||||
0.601323 | + | 0.799006i | \(0.294640\pi\) | |||||||
\(840\) | 3.44468 | 0.118853 | ||||||||
\(841\) | 8.64076 | 0.297957 | ||||||||
\(842\) | −44.7430 | −1.54195 | ||||||||
\(843\) | 2.33746 | 0.0805063 | ||||||||
\(844\) | −38.1558 | −1.31338 | ||||||||
\(845\) | −1.81098 | −0.0622996 | ||||||||
\(846\) | −81.2968 | −2.79504 | ||||||||
\(847\) | 10.4331 | 0.358485 | ||||||||
\(848\) | 28.6767 | 0.984763 | ||||||||
\(849\) | 1.86708 | 0.0640779 | ||||||||
\(850\) | −23.5926 | −0.809219 | ||||||||
\(851\) | −21.3306 | −0.731205 | ||||||||
\(852\) | −9.26062 | −0.317264 | ||||||||
\(853\) | 7.73941 | 0.264992 | 0.132496 | − | 0.991184i | \(-0.457701\pi\) | ||||
0.132496 | + | 0.991184i | \(0.457701\pi\) | |||||||
\(854\) | 17.9461 | 0.614102 | ||||||||
\(855\) | −26.8962 | −0.919831 | ||||||||
\(856\) | 43.7327 | 1.49475 | ||||||||
\(857\) | 37.5440 | 1.28248 | 0.641240 | − | 0.767340i | \(-0.278420\pi\) | ||||
0.641240 | + | 0.767340i | \(0.278420\pi\) | |||||||
\(858\) | −1.09079 | −0.0372391 | ||||||||
\(859\) | −12.7009 | −0.433350 | −0.216675 | − | 0.976244i | \(-0.569521\pi\) | ||||
−0.216675 | + | 0.976244i | \(0.569521\pi\) | |||||||
\(860\) | −74.7754 | −2.54982 | ||||||||
\(861\) | 3.14476 | 0.107173 | ||||||||
\(862\) | −18.7428 | −0.638382 | ||||||||
\(863\) | 20.4656 | 0.696657 | 0.348329 | − | 0.937372i | \(-0.386749\pi\) | ||||
0.348329 | + | 0.937372i | \(0.386749\pi\) | |||||||
\(864\) | −3.52197 | −0.119820 | ||||||||
\(865\) | 30.5828 | 1.03985 | ||||||||
\(866\) | −39.5200 | −1.34294 | ||||||||
\(867\) | −2.58913 | −0.0879314 | ||||||||
\(868\) | −48.4983 | −1.64614 | ||||||||
\(869\) | −3.52625 | −0.119620 | ||||||||
\(870\) | −5.55855 | −0.188452 | ||||||||
\(871\) | 8.87803 | 0.300821 | ||||||||
\(872\) | 47.9663 | 1.62434 | ||||||||
\(873\) | 8.11565 | 0.274673 | ||||||||
\(874\) | −96.4716 | −3.26320 | ||||||||
\(875\) | −20.3286 | −0.687233 | ||||||||
\(876\) | −11.1871 | −0.377978 | ||||||||
\(877\) | −18.1890 | −0.614198 | −0.307099 | − | 0.951678i | \(-0.599358\pi\) | ||||
−0.307099 | + | 0.951678i | \(0.599358\pi\) | |||||||
\(878\) | 47.6990 | 1.60976 | ||||||||
\(879\) | −5.60990 | −0.189217 | ||||||||
\(880\) | 22.6394 | 0.763175 | ||||||||
\(881\) | −43.5593 | −1.46755 | −0.733775 | − | 0.679392i | \(-0.762243\pi\) | ||||
−0.733775 | + | 0.679392i | \(0.762243\pi\) | |||||||
\(882\) | −31.2205 | −1.05125 | ||||||||
\(883\) | −25.1561 | −0.846569 | −0.423285 | − | 0.905997i | \(-0.639123\pi\) | ||||
−0.423285 | + | 0.905997i | \(0.639123\pi\) | |||||||
\(884\) | −23.4083 | −0.787306 | ||||||||
\(885\) | 3.57565 | 0.120194 | ||||||||
\(886\) | −26.5663 | −0.892513 | ||||||||
\(887\) | −34.8592 | −1.17046 | −0.585229 | − | 0.810868i | \(-0.698995\pi\) | ||||
−0.585229 | + | 0.810868i | \(0.698995\pi\) | |||||||
\(888\) | 3.16485 | 0.106206 | ||||||||
\(889\) | −28.6893 | −0.962209 | ||||||||
\(890\) | −27.9612 | −0.937262 | ||||||||
\(891\) | −18.8440 | −0.631297 | ||||||||
\(892\) | 35.8356 | 1.19987 | ||||||||
\(893\) | 55.0026 | 1.84059 | ||||||||
\(894\) | −3.04616 | −0.101879 | ||||||||
\(895\) | 9.06106 | 0.302878 | ||||||||
\(896\) | −26.8494 | −0.896975 | ||||||||
\(897\) | 1.53268 | 0.0511748 | ||||||||
\(898\) | −78.3216 | −2.61362 | ||||||||
\(899\) | 41.6575 | 1.38936 | ||||||||
\(900\) | 21.7764 | 0.725880 | ||||||||
\(901\) | −27.3786 | −0.912114 | ||||||||
\(902\) | 51.4978 | 1.71469 | ||||||||
\(903\) | 3.22075 | 0.107180 | ||||||||
\(904\) | −32.9064 | −1.09445 | ||||||||
\(905\) | 44.0246 | 1.46343 | ||||||||
\(906\) | 10.1434 | 0.336993 | ||||||||
\(907\) | −32.8978 | −1.09235 | −0.546177 | − | 0.837670i | \(-0.683917\pi\) | ||||
−0.546177 | + | 0.837670i | \(0.683917\pi\) | |||||||
\(908\) | −57.1951 | −1.89809 | ||||||||
\(909\) | −16.0368 | −0.531907 | ||||||||
\(910\) | −7.57818 | −0.251214 | ||||||||
\(911\) | −2.27484 | −0.0753687 | −0.0376843 | − | 0.999290i | \(-0.511998\pi\) | ||||
−0.0376843 | + | 0.999290i | \(0.511998\pi\) | |||||||
\(912\) | 5.74467 | 0.190225 | ||||||||
\(913\) | 17.3526 | 0.574287 | ||||||||
\(914\) | −98.2246 | −3.24898 | ||||||||
\(915\) | 1.55096 | 0.0512732 | ||||||||
\(916\) | 8.15205 | 0.269351 | ||||||||
\(917\) | 25.5538 | 0.843862 | ||||||||
\(918\) | 16.3224 | 0.538719 | ||||||||
\(919\) | 30.4370 | 1.00402 | 0.502012 | − | 0.864861i | \(-0.332593\pi\) | ||||
0.502012 | + | 0.864861i | \(0.332593\pi\) | |||||||
\(920\) | −79.2609 | −2.61316 | ||||||||
\(921\) | 1.73614 | 0.0572077 | ||||||||
\(922\) | −21.5819 | −0.710762 | ||||||||
\(923\) | 10.8445 | 0.356952 | ||||||||
\(924\) | −3.10997 | −0.102310 | ||||||||
\(925\) | −4.78121 | −0.157205 | ||||||||
\(926\) | 29.8653 | 0.981436 | ||||||||
\(927\) | 10.9143 | 0.358471 | ||||||||
\(928\) | −18.1547 | −0.595958 | ||||||||
\(929\) | 12.7484 | 0.418263 | 0.209131 | − | 0.977888i | \(-0.432936\pi\) | ||||
0.209131 | + | 0.977888i | \(0.432936\pi\) | |||||||
\(930\) | −6.15172 | −0.201723 | ||||||||
\(931\) | 21.1227 | 0.692269 | ||||||||
\(932\) | −111.765 | −3.66099 | ||||||||
\(933\) | 0.295007 | 0.00965809 | ||||||||
\(934\) | −57.6181 | −1.88532 | ||||||||
\(935\) | −21.6146 | −0.706874 | ||||||||
\(936\) | 16.8800 | 0.551740 | ||||||||
\(937\) | −1.91330 | −0.0625047 | −0.0312524 | − | 0.999512i | \(-0.509950\pi\) | ||||
−0.0312524 | + | 0.999512i | \(0.509950\pi\) | |||||||
\(938\) | 37.1508 | 1.21302 | ||||||||
\(939\) | 0.0652899 | 0.00213066 | ||||||||
\(940\) | 84.8963 | 2.76901 | ||||||||
\(941\) | −6.83999 | −0.222977 | −0.111489 | − | 0.993766i | \(-0.535562\pi\) | ||||
−0.111489 | + | 0.993766i | \(0.535562\pi\) | |||||||
\(942\) | −0.726607 | −0.0236741 | ||||||||
\(943\) | −72.3599 | −2.35636 | ||||||||
\(944\) | 56.6891 | 1.84507 | ||||||||
\(945\) | 3.60032 | 0.117118 | ||||||||
\(946\) | 52.7422 | 1.71480 | ||||||||
\(947\) | 1.43457 | 0.0466173 | 0.0233086 | − | 0.999728i | \(-0.492580\pi\) | ||||
0.0233086 | + | 0.999728i | \(0.492580\pi\) | |||||||
\(948\) | −1.38108 | −0.0448553 | ||||||||
\(949\) | 13.1005 | 0.425262 | ||||||||
\(950\) | −21.6239 | −0.701572 | ||||||||
\(951\) | −6.29043 | −0.203981 | ||||||||
\(952\) | −52.1405 | −1.68988 | ||||||||
\(953\) | 52.6773 | 1.70638 | 0.853192 | − | 0.521597i | \(-0.174664\pi\) | ||||
0.853192 | + | 0.521597i | \(0.174664\pi\) | |||||||
\(954\) | 37.0903 | 1.20084 | ||||||||
\(955\) | −31.0723 | −1.00548 | ||||||||
\(956\) | −73.9641 | −2.39217 | ||||||||
\(957\) | 2.67130 | 0.0863509 | ||||||||
\(958\) | 61.9625 | 2.00192 | ||||||||
\(959\) | 9.99196 | 0.322657 | ||||||||
\(960\) | −1.46609 | −0.0473179 | ||||||||
\(961\) | 15.1029 | 0.487190 | ||||||||
\(962\) | −6.96258 | −0.224483 | ||||||||
\(963\) | 22.7014 | 0.731543 | ||||||||
\(964\) | 102.702 | 3.30781 | ||||||||
\(965\) | 31.6439 | 1.01865 | ||||||||
\(966\) | 6.41362 | 0.206355 | ||||||||
\(967\) | −8.06123 | −0.259232 | −0.129616 | − | 0.991564i | \(-0.541374\pi\) | ||||
−0.129616 | + | 0.991564i | \(0.541374\pi\) | |||||||
\(968\) | 35.6183 | 1.14482 | ||||||||
\(969\) | −5.48463 | −0.176192 | ||||||||
\(970\) | −12.4387 | −0.399384 | ||||||||
\(971\) | 13.2340 | 0.424701 | 0.212350 | − | 0.977194i | \(-0.431888\pi\) | ||||
0.212350 | + | 0.977194i | \(0.431888\pi\) | |||||||
\(972\) | −22.6492 | −0.726473 | ||||||||
\(973\) | −13.4178 | −0.430155 | ||||||||
\(974\) | −39.7072 | −1.27230 | ||||||||
\(975\) | 0.343547 | 0.0110023 | ||||||||
\(976\) | 24.5893 | 0.787083 | ||||||||
\(977\) | −30.5092 | −0.976075 | −0.488037 | − | 0.872823i | \(-0.662287\pi\) | ||||
−0.488037 | + | 0.872823i | \(0.662287\pi\) | |||||||
\(978\) | 9.61934 | 0.307592 | ||||||||
\(979\) | 13.4375 | 0.429464 | ||||||||
\(980\) | 32.6028 | 1.04146 | ||||||||
\(981\) | 24.8991 | 0.794966 | ||||||||
\(982\) | 1.50920 | 0.0481607 | ||||||||
\(983\) | −19.2281 | −0.613282 | −0.306641 | − | 0.951825i | \(-0.599205\pi\) | ||||
−0.306641 | + | 0.951825i | \(0.599205\pi\) | |||||||
\(984\) | 10.7361 | 0.342255 | ||||||||
\(985\) | 35.8653 | 1.14276 | ||||||||
\(986\) | 84.1372 | 2.67947 | ||||||||
\(987\) | −3.65668 | −0.116393 | ||||||||
\(988\) | −21.4550 | −0.682573 | ||||||||
\(989\) | −74.1085 | −2.35651 | ||||||||
\(990\) | 29.2817 | 0.930634 | ||||||||
\(991\) | 22.4644 | 0.713607 | 0.356803 | − | 0.934180i | \(-0.383867\pi\) | ||||
0.356803 | + | 0.934180i | \(0.383867\pi\) | |||||||
\(992\) | −20.0921 | −0.637924 | ||||||||
\(993\) | −4.27759 | −0.135745 | ||||||||
\(994\) | 45.3797 | 1.43936 | ||||||||
\(995\) | −10.0375 | −0.318211 | ||||||||
\(996\) | 6.79625 | 0.215347 | ||||||||
\(997\) | 44.8710 | 1.42108 | 0.710540 | − | 0.703657i | \(-0.248451\pi\) | ||||
0.710540 | + | 0.703657i | \(0.248451\pi\) | |||||||
\(998\) | 55.4518 | 1.75530 | ||||||||
\(999\) | 3.30785 | 0.104656 |
(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 | 8047.2.a.b.1.13 | ✓ | 142 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8047.2.a.b.1.13 | ✓ | 142 | 1.1 | even | 1 | trivial |