Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [619,2,Mod(1,619)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(619, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("619.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 619 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 619.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: | \(4.94273988512\) |
Analytic rank: | \(1\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 619.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.32447 | −1.64365 | −0.821825 | − | 0.569740i | \(-0.807044\pi\) | ||||
−0.821825 | + | 0.569740i | \(0.807044\pi\) | |||||||
\(3\) | 0.941827 | 0.543764 | 0.271882 | − | 0.962331i | \(-0.412354\pi\) | ||||
0.271882 | + | 0.962331i | \(0.412354\pi\) | |||||||
\(4\) | 3.40317 | 1.70158 | ||||||||
\(5\) | −2.38281 | −1.06563 | −0.532814 | − | 0.846233i | \(-0.678865\pi\) | ||||
−0.532814 | + | 0.846233i | \(0.678865\pi\) | |||||||
\(6\) | −2.18925 | −0.893757 | ||||||||
\(7\) | 2.74500 | 1.03751 | 0.518757 | − | 0.854922i | \(-0.326395\pi\) | ||||
0.518757 | + | 0.854922i | \(0.326395\pi\) | |||||||
\(8\) | −3.26162 | −1.15316 | ||||||||
\(9\) | −2.11296 | −0.704321 | ||||||||
\(10\) | 5.53878 | 1.75152 | ||||||||
\(11\) | −1.86219 | −0.561471 | −0.280736 | − | 0.959785i | \(-0.590578\pi\) | ||||
−0.280736 | + | 0.959785i | \(0.590578\pi\) | |||||||
\(12\) | 3.20519 | 0.925260 | ||||||||
\(13\) | −0.255352 | −0.0708218 | −0.0354109 | − | 0.999373i | \(-0.511274\pi\) | ||||
−0.0354109 | + | 0.999373i | \(0.511274\pi\) | |||||||
\(14\) | −6.38068 | −1.70531 | ||||||||
\(15\) | −2.24420 | −0.579450 | ||||||||
\(16\) | 0.775212 | 0.193803 | ||||||||
\(17\) | −1.20093 | −0.291268 | −0.145634 | − | 0.989339i | \(-0.546522\pi\) | ||||
−0.145634 | + | 0.989339i | \(0.546522\pi\) | |||||||
\(18\) | 4.91152 | 1.15766 | ||||||||
\(19\) | 5.01739 | 1.15107 | 0.575534 | − | 0.817778i | \(-0.304794\pi\) | ||||
0.575534 | + | 0.817778i | \(0.304794\pi\) | |||||||
\(20\) | −8.10912 | −1.81325 | ||||||||
\(21\) | 2.58532 | 0.564162 | ||||||||
\(22\) | 4.32861 | 0.922862 | ||||||||
\(23\) | −7.51313 | −1.56660 | −0.783298 | − | 0.621646i | \(-0.786464\pi\) | ||||
−0.783298 | + | 0.621646i | \(0.786464\pi\) | |||||||
\(24\) | −3.07188 | −0.627045 | ||||||||
\(25\) | 0.677806 | 0.135561 | ||||||||
\(26\) | 0.593557 | 0.116406 | ||||||||
\(27\) | −4.81552 | −0.926748 | ||||||||
\(28\) | 9.34170 | 1.76542 | ||||||||
\(29\) | 3.96355 | 0.736013 | 0.368007 | − | 0.929823i | \(-0.380040\pi\) | ||||
0.368007 | + | 0.929823i | \(0.380040\pi\) | |||||||
\(30\) | 5.21658 | 0.952412 | ||||||||
\(31\) | −3.35980 | −0.603438 | −0.301719 | − | 0.953397i | \(-0.597560\pi\) | ||||
−0.301719 | + | 0.953397i | \(0.597560\pi\) | |||||||
\(32\) | 4.72129 | 0.834613 | ||||||||
\(33\) | −1.75386 | −0.305308 | ||||||||
\(34\) | 2.79152 | 0.478742 | ||||||||
\(35\) | −6.54083 | −1.10560 | ||||||||
\(36\) | −7.19076 | −1.19846 | ||||||||
\(37\) | −10.4323 | −1.71506 | −0.857532 | − | 0.514431i | \(-0.828003\pi\) | ||||
−0.857532 | + | 0.514431i | \(0.828003\pi\) | |||||||
\(38\) | −11.6628 | −1.89195 | ||||||||
\(39\) | −0.240497 | −0.0385103 | ||||||||
\(40\) | 7.77184 | 1.22884 | ||||||||
\(41\) | 2.91555 | 0.455333 | 0.227666 | − | 0.973739i | \(-0.426890\pi\) | ||||
0.227666 | + | 0.973739i | \(0.426890\pi\) | |||||||
\(42\) | −6.00950 | −0.927285 | ||||||||
\(43\) | 4.62423 | 0.705189 | 0.352594 | − | 0.935776i | \(-0.385300\pi\) | ||||
0.352594 | + | 0.935776i | \(0.385300\pi\) | |||||||
\(44\) | −6.33734 | −0.955390 | ||||||||
\(45\) | 5.03480 | 0.750543 | ||||||||
\(46\) | 17.4641 | 2.57493 | ||||||||
\(47\) | 2.71557 | 0.396107 | 0.198054 | − | 0.980191i | \(-0.436538\pi\) | ||||
0.198054 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(48\) | 0.730115 | 0.105383 | ||||||||
\(49\) | 0.535042 | 0.0764346 | ||||||||
\(50\) | −1.57554 | −0.222815 | ||||||||
\(51\) | −1.13107 | −0.158381 | ||||||||
\(52\) | −0.869004 | −0.120509 | ||||||||
\(53\) | 5.72390 | 0.786238 | 0.393119 | − | 0.919488i | \(-0.371396\pi\) | ||||
0.393119 | + | 0.919488i | \(0.371396\pi\) | |||||||
\(54\) | 11.1935 | 1.52325 | ||||||||
\(55\) | 4.43725 | 0.598319 | ||||||||
\(56\) | −8.95316 | −1.19642 | ||||||||
\(57\) | 4.72551 | 0.625910 | ||||||||
\(58\) | −9.21317 | −1.20975 | ||||||||
\(59\) | −11.3736 | −1.48071 | −0.740357 | − | 0.672214i | \(-0.765343\pi\) | ||||
−0.740357 | + | 0.672214i | \(0.765343\pi\) | |||||||
\(60\) | −7.63738 | −0.985982 | ||||||||
\(61\) | −14.0158 | −1.79454 | −0.897268 | − | 0.441486i | \(-0.854452\pi\) | ||||
−0.897268 | + | 0.441486i | \(0.854452\pi\) | |||||||
\(62\) | 7.80976 | 0.991840 | ||||||||
\(63\) | −5.80009 | −0.730742 | ||||||||
\(64\) | −12.5249 | −1.56561 | ||||||||
\(65\) | 0.608455 | 0.0754696 | ||||||||
\(66\) | 4.07680 | 0.501819 | ||||||||
\(67\) | −8.99998 | −1.09952 | −0.549762 | − | 0.835322i | \(-0.685281\pi\) | ||||
−0.549762 | + | 0.835322i | \(0.685281\pi\) | |||||||
\(68\) | −4.08695 | −0.495616 | ||||||||
\(69\) | −7.07607 | −0.851858 | ||||||||
\(70\) | 15.2040 | 1.81722 | ||||||||
\(71\) | −13.8636 | −1.64530 | −0.822651 | − | 0.568547i | \(-0.807506\pi\) | ||||
−0.822651 | + | 0.568547i | \(0.807506\pi\) | |||||||
\(72\) | 6.89168 | 0.812193 | ||||||||
\(73\) | −2.68365 | −0.314097 | −0.157049 | − | 0.987591i | \(-0.550198\pi\) | ||||
−0.157049 | + | 0.987591i | \(0.550198\pi\) | |||||||
\(74\) | 24.2496 | 2.81896 | ||||||||
\(75\) | 0.638376 | 0.0737133 | ||||||||
\(76\) | 17.0750 | 1.95864 | ||||||||
\(77\) | −5.11172 | −0.582534 | ||||||||
\(78\) | 0.559028 | 0.0632975 | ||||||||
\(79\) | −4.49955 | −0.506239 | −0.253120 | − | 0.967435i | \(-0.581457\pi\) | ||||
−0.253120 | + | 0.967435i | \(0.581457\pi\) | |||||||
\(80\) | −1.84719 | −0.206522 | ||||||||
\(81\) | 1.80350 | 0.200389 | ||||||||
\(82\) | −6.77712 | −0.748407 | ||||||||
\(83\) | −14.9897 | −1.64533 | −0.822667 | − | 0.568523i | \(-0.807515\pi\) | ||||
−0.822667 | + | 0.568523i | \(0.807515\pi\) | |||||||
\(84\) | 8.79827 | 0.959970 | ||||||||
\(85\) | 2.86159 | 0.310383 | ||||||||
\(86\) | −10.7489 | −1.15908 | ||||||||
\(87\) | 3.73298 | 0.400217 | ||||||||
\(88\) | 6.07376 | 0.647465 | ||||||||
\(89\) | −8.04823 | −0.853110 | −0.426555 | − | 0.904462i | \(-0.640273\pi\) | ||||
−0.426555 | + | 0.904462i | \(0.640273\pi\) | |||||||
\(90\) | −11.7032 | −1.23363 | ||||||||
\(91\) | −0.700941 | −0.0734786 | ||||||||
\(92\) | −25.5684 | −2.66569 | ||||||||
\(93\) | −3.16435 | −0.328128 | ||||||||
\(94\) | −6.31227 | −0.651061 | ||||||||
\(95\) | −11.9555 | −1.22661 | ||||||||
\(96\) | 4.44663 | 0.453833 | ||||||||
\(97\) | 9.92292 | 1.00752 | 0.503760 | − | 0.863844i | \(-0.331950\pi\) | ||||
0.503760 | + | 0.863844i | \(0.331950\pi\) | |||||||
\(98\) | −1.24369 | −0.125632 | ||||||||
\(99\) | 3.93474 | 0.395456 | ||||||||
\(100\) | 2.30669 | 0.230669 | ||||||||
\(101\) | 10.8706 | 1.08167 | 0.540833 | − | 0.841130i | \(-0.318109\pi\) | ||||
0.540833 | + | 0.841130i | \(0.318109\pi\) | |||||||
\(102\) | 2.62913 | 0.260322 | ||||||||
\(103\) | −4.36654 | −0.430248 | −0.215124 | − | 0.976587i | \(-0.569016\pi\) | ||||
−0.215124 | + | 0.976587i | \(0.569016\pi\) | |||||||
\(104\) | 0.832860 | 0.0816687 | ||||||||
\(105\) | −6.16033 | −0.601187 | ||||||||
\(106\) | −13.3050 | −1.29230 | ||||||||
\(107\) | 6.90907 | 0.667925 | 0.333963 | − | 0.942586i | \(-0.391614\pi\) | ||||
0.333963 | + | 0.942586i | \(0.391614\pi\) | |||||||
\(108\) | −16.3880 | −1.57694 | ||||||||
\(109\) | 3.38023 | 0.323767 | 0.161884 | − | 0.986810i | \(-0.448243\pi\) | ||||
0.161884 | + | 0.986810i | \(0.448243\pi\) | |||||||
\(110\) | −10.3143 | −0.983427 | ||||||||
\(111\) | −9.82544 | −0.932590 | ||||||||
\(112\) | 2.12796 | 0.201073 | ||||||||
\(113\) | 9.39928 | 0.884210 | 0.442105 | − | 0.896963i | \(-0.354232\pi\) | ||||
0.442105 | + | 0.896963i | \(0.354232\pi\) | |||||||
\(114\) | −10.9843 | −1.02878 | ||||||||
\(115\) | 17.9024 | 1.66941 | ||||||||
\(116\) | 13.4886 | 1.25239 | ||||||||
\(117\) | 0.539548 | 0.0498812 | ||||||||
\(118\) | 26.4376 | 2.43377 | ||||||||
\(119\) | −3.29655 | −0.302194 | ||||||||
\(120\) | 7.31973 | 0.668197 | ||||||||
\(121\) | −7.53225 | −0.684750 | ||||||||
\(122\) | 32.5793 | 2.94959 | ||||||||
\(123\) | 2.74594 | 0.247593 | ||||||||
\(124\) | −11.4340 | −1.02680 | ||||||||
\(125\) | 10.2990 | 0.921169 | ||||||||
\(126\) | 13.4821 | 1.20108 | ||||||||
\(127\) | 11.1964 | 0.993521 | 0.496760 | − | 0.867888i | \(-0.334523\pi\) | ||||
0.496760 | + | 0.867888i | \(0.334523\pi\) | |||||||
\(128\) | 19.6712 | 1.73871 | ||||||||
\(129\) | 4.35522 | 0.383456 | ||||||||
\(130\) | −1.41434 | −0.124046 | ||||||||
\(131\) | −5.31260 | −0.464164 | −0.232082 | − | 0.972696i | \(-0.574554\pi\) | ||||
−0.232082 | + | 0.972696i | \(0.574554\pi\) | |||||||
\(132\) | −5.96868 | −0.519507 | ||||||||
\(133\) | 13.7728 | 1.19425 | ||||||||
\(134\) | 20.9202 | 1.80723 | ||||||||
\(135\) | 11.4745 | 0.987568 | ||||||||
\(136\) | 3.91697 | 0.335877 | ||||||||
\(137\) | 5.99870 | 0.512503 | 0.256252 | − | 0.966610i | \(-0.417512\pi\) | ||||
0.256252 | + | 0.966610i | \(0.417512\pi\) | |||||||
\(138\) | 16.4481 | 1.40016 | ||||||||
\(139\) | −7.88334 | −0.668656 | −0.334328 | − | 0.942457i | \(-0.608509\pi\) | ||||
−0.334328 | + | 0.942457i | \(0.608509\pi\) | |||||||
\(140\) | −22.2596 | −1.88128 | ||||||||
\(141\) | 2.55760 | 0.215389 | ||||||||
\(142\) | 32.2254 | 2.70430 | ||||||||
\(143\) | 0.475513 | 0.0397644 | ||||||||
\(144\) | −1.63799 | −0.136499 | ||||||||
\(145\) | −9.44441 | −0.784316 | ||||||||
\(146\) | 6.23806 | 0.516266 | ||||||||
\(147\) | 0.503917 | 0.0415624 | ||||||||
\(148\) | −35.5029 | −2.91832 | ||||||||
\(149\) | −3.21065 | −0.263027 | −0.131513 | − | 0.991314i | \(-0.541984\pi\) | ||||
−0.131513 | + | 0.991314i | \(0.541984\pi\) | |||||||
\(150\) | −1.48389 | −0.121159 | ||||||||
\(151\) | 8.92072 | 0.725958 | 0.362979 | − | 0.931797i | \(-0.381760\pi\) | ||||
0.362979 | + | 0.931797i | \(0.381760\pi\) | |||||||
\(152\) | −16.3648 | −1.32736 | ||||||||
\(153\) | 2.53751 | 0.205146 | ||||||||
\(154\) | 11.8820 | 0.957482 | ||||||||
\(155\) | 8.00578 | 0.643040 | ||||||||
\(156\) | −0.818451 | −0.0655285 | ||||||||
\(157\) | 9.68416 | 0.772880 | 0.386440 | − | 0.922315i | \(-0.373705\pi\) | ||||
0.386440 | + | 0.922315i | \(0.373705\pi\) | |||||||
\(158\) | 10.4591 | 0.832079 | ||||||||
\(159\) | 5.39092 | 0.427528 | ||||||||
\(160\) | −11.2499 | −0.889386 | ||||||||
\(161\) | −20.6236 | −1.62536 | ||||||||
\(162\) | −4.19218 | −0.329369 | ||||||||
\(163\) | 11.3711 | 0.890654 | 0.445327 | − | 0.895368i | \(-0.353088\pi\) | ||||
0.445327 | + | 0.895368i | \(0.353088\pi\) | |||||||
\(164\) | 9.92211 | 0.774787 | ||||||||
\(165\) | 4.17912 | 0.325344 | ||||||||
\(166\) | 34.8431 | 2.70435 | ||||||||
\(167\) | 3.06492 | 0.237171 | 0.118585 | − | 0.992944i | \(-0.462164\pi\) | ||||
0.118585 | + | 0.992944i | \(0.462164\pi\) | |||||||
\(168\) | −8.43233 | −0.650568 | ||||||||
\(169\) | −12.9348 | −0.994984 | ||||||||
\(170\) | −6.65167 | −0.510160 | ||||||||
\(171\) | −10.6016 | −0.810722 | ||||||||
\(172\) | 15.7370 | 1.19994 | ||||||||
\(173\) | −7.41249 | −0.563561 | −0.281780 | − | 0.959479i | \(-0.590925\pi\) | ||||
−0.281780 | + | 0.959479i | \(0.590925\pi\) | |||||||
\(174\) | −8.67721 | −0.657817 | ||||||||
\(175\) | 1.86058 | 0.140647 | ||||||||
\(176\) | −1.44359 | −0.108815 | ||||||||
\(177\) | −10.7119 | −0.805159 | ||||||||
\(178\) | 18.7079 | 1.40221 | ||||||||
\(179\) | 3.84060 | 0.287060 | 0.143530 | − | 0.989646i | \(-0.454155\pi\) | ||||
0.143530 | + | 0.989646i | \(0.454155\pi\) | |||||||
\(180\) | 17.1343 | 1.27711 | ||||||||
\(181\) | 11.4730 | 0.852779 | 0.426389 | − | 0.904540i | \(-0.359785\pi\) | ||||
0.426389 | + | 0.904540i | \(0.359785\pi\) | |||||||
\(182\) | 1.62932 | 0.120773 | ||||||||
\(183\) | −13.2004 | −0.975804 | ||||||||
\(184\) | 24.5050 | 1.80653 | ||||||||
\(185\) | 24.8583 | 1.82762 | ||||||||
\(186\) | 7.35544 | 0.539327 | ||||||||
\(187\) | 2.23635 | 0.163538 | ||||||||
\(188\) | 9.24155 | 0.674009 | ||||||||
\(189\) | −13.2186 | −0.961514 | ||||||||
\(190\) | 27.7903 | 2.01612 | ||||||||
\(191\) | 8.76977 | 0.634558 | 0.317279 | − | 0.948332i | \(-0.397231\pi\) | ||||
0.317279 | + | 0.948332i | \(0.397231\pi\) | |||||||
\(192\) | −11.7963 | −0.851325 | ||||||||
\(193\) | 14.3062 | 1.02979 | 0.514893 | − | 0.857255i | \(-0.327832\pi\) | ||||
0.514893 | + | 0.857255i | \(0.327832\pi\) | |||||||
\(194\) | −23.0656 | −1.65601 | ||||||||
\(195\) | 0.573060 | 0.0410376 | ||||||||
\(196\) | 1.82084 | 0.130060 | ||||||||
\(197\) | −14.7770 | −1.05282 | −0.526408 | − | 0.850232i | \(-0.676462\pi\) | ||||
−0.526408 | + | 0.850232i | \(0.676462\pi\) | |||||||
\(198\) | −9.14618 | −0.649991 | ||||||||
\(199\) | −9.48815 | −0.672597 | −0.336299 | − | 0.941755i | \(-0.609175\pi\) | ||||
−0.336299 | + | 0.941755i | \(0.609175\pi\) | |||||||
\(200\) | −2.21075 | −0.156323 | ||||||||
\(201\) | −8.47643 | −0.597881 | ||||||||
\(202\) | −25.2684 | −1.77788 | ||||||||
\(203\) | 10.8800 | 0.763624 | ||||||||
\(204\) | −3.84920 | −0.269498 | ||||||||
\(205\) | −6.94722 | −0.485215 | ||||||||
\(206\) | 10.1499 | 0.707177 | ||||||||
\(207\) | 15.8750 | 1.10339 | ||||||||
\(208\) | −0.197952 | −0.0137255 | ||||||||
\(209\) | −9.34334 | −0.646292 | ||||||||
\(210\) | 14.3195 | 0.988140 | ||||||||
\(211\) | 20.0056 | 1.37724 | 0.688621 | − | 0.725121i | \(-0.258216\pi\) | ||||
0.688621 | + | 0.725121i | \(0.258216\pi\) | |||||||
\(212\) | 19.4794 | 1.33785 | ||||||||
\(213\) | −13.0571 | −0.894656 | ||||||||
\(214\) | −16.0599 | −1.09783 | ||||||||
\(215\) | −11.0187 | −0.751468 | ||||||||
\(216\) | 15.7064 | 1.06869 | ||||||||
\(217\) | −9.22266 | −0.626075 | ||||||||
\(218\) | −7.85725 | −0.532160 | ||||||||
\(219\) | −2.52753 | −0.170795 | ||||||||
\(220\) | 15.1007 | 1.01809 | ||||||||
\(221\) | 0.306659 | 0.0206281 | ||||||||
\(222\) | 22.8390 | 1.53285 | ||||||||
\(223\) | 3.46929 | 0.232321 | 0.116160 | − | 0.993230i | \(-0.462941\pi\) | ||||
0.116160 | + | 0.993230i | \(0.462941\pi\) | |||||||
\(224\) | 12.9599 | 0.865923 | ||||||||
\(225\) | −1.43218 | −0.0954785 | ||||||||
\(226\) | −21.8484 | −1.45333 | ||||||||
\(227\) | 14.5883 | 0.968262 | 0.484131 | − | 0.874996i | \(-0.339136\pi\) | ||||
0.484131 | + | 0.874996i | \(0.339136\pi\) | |||||||
\(228\) | 16.0817 | 1.06504 | ||||||||
\(229\) | −22.7498 | −1.50335 | −0.751674 | − | 0.659535i | \(-0.770753\pi\) | ||||
−0.751674 | + | 0.659535i | \(0.770753\pi\) | |||||||
\(230\) | −41.6136 | −2.74392 | ||||||||
\(231\) | −4.81435 | −0.316761 | ||||||||
\(232\) | −12.9276 | −0.848739 | ||||||||
\(233\) | 16.0603 | 1.05214 | 0.526071 | − | 0.850440i | \(-0.323665\pi\) | ||||
0.526071 | + | 0.850440i | \(0.323665\pi\) | |||||||
\(234\) | −1.25416 | −0.0819873 | ||||||||
\(235\) | −6.47071 | −0.422102 | ||||||||
\(236\) | −38.7062 | −2.51956 | ||||||||
\(237\) | −4.23780 | −0.275275 | ||||||||
\(238\) | 7.66273 | 0.496701 | ||||||||
\(239\) | −6.39830 | −0.413871 | −0.206936 | − | 0.978355i | \(-0.566349\pi\) | ||||
−0.206936 | + | 0.978355i | \(0.566349\pi\) | |||||||
\(240\) | −1.73973 | −0.112299 | ||||||||
\(241\) | 5.36580 | 0.345641 | 0.172821 | − | 0.984953i | \(-0.444712\pi\) | ||||
0.172821 | + | 0.984953i | \(0.444712\pi\) | |||||||
\(242\) | 17.5085 | 1.12549 | ||||||||
\(243\) | 16.1452 | 1.03571 | ||||||||
\(244\) | −47.6980 | −3.05355 | ||||||||
\(245\) | −1.27491 | −0.0814508 | ||||||||
\(246\) | −6.38287 | −0.406957 | ||||||||
\(247\) | −1.28120 | −0.0815207 | ||||||||
\(248\) | 10.9584 | 0.695859 | ||||||||
\(249\) | −14.1177 | −0.894673 | ||||||||
\(250\) | −23.9397 | −1.51408 | ||||||||
\(251\) | 7.22722 | 0.456178 | 0.228089 | − | 0.973640i | \(-0.426752\pi\) | ||||
0.228089 | + | 0.973640i | \(0.426752\pi\) | |||||||
\(252\) | −19.7387 | −1.24342 | ||||||||
\(253\) | 13.9909 | 0.879599 | ||||||||
\(254\) | −26.0257 | −1.63300 | ||||||||
\(255\) | 2.69512 | 0.168775 | ||||||||
\(256\) | −20.6754 | −1.29221 | ||||||||
\(257\) | 26.2044 | 1.63458 | 0.817292 | − | 0.576224i | \(-0.195474\pi\) | ||||
0.817292 | + | 0.576224i | \(0.195474\pi\) | |||||||
\(258\) | −10.1236 | −0.630267 | ||||||||
\(259\) | −28.6368 | −1.77940 | ||||||||
\(260\) | 2.07068 | 0.128418 | ||||||||
\(261\) | −8.37484 | −0.518390 | ||||||||
\(262\) | 12.3490 | 0.762922 | ||||||||
\(263\) | 24.7575 | 1.52661 | 0.763305 | − | 0.646038i | \(-0.223575\pi\) | ||||
0.763305 | + | 0.646038i | \(0.223575\pi\) | |||||||
\(264\) | 5.72043 | 0.352068 | ||||||||
\(265\) | −13.6390 | −0.837837 | ||||||||
\(266\) | −32.0144 | −1.96293 | ||||||||
\(267\) | −7.58003 | −0.463891 | ||||||||
\(268\) | −30.6284 | −1.87093 | ||||||||
\(269\) | −28.0824 | −1.71221 | −0.856107 | − | 0.516799i | \(-0.827123\pi\) | ||||
−0.856107 | + | 0.516799i | \(0.827123\pi\) | |||||||
\(270\) | −26.6722 | −1.62322 | ||||||||
\(271\) | 10.7255 | 0.651527 | 0.325763 | − | 0.945451i | \(-0.394379\pi\) | ||||
0.325763 | + | 0.945451i | \(0.394379\pi\) | |||||||
\(272\) | −0.930973 | −0.0564485 | ||||||||
\(273\) | −0.660165 | −0.0399550 | ||||||||
\(274\) | −13.9438 | −0.842375 | ||||||||
\(275\) | −1.26220 | −0.0761137 | ||||||||
\(276\) | −24.0810 | −1.44951 | ||||||||
\(277\) | −4.80306 | −0.288588 | −0.144294 | − | 0.989535i | \(-0.546091\pi\) | ||||
−0.144294 | + | 0.989535i | \(0.546091\pi\) | |||||||
\(278\) | 18.3246 | 1.09904 | ||||||||
\(279\) | 7.09913 | 0.425014 | ||||||||
\(280\) | 21.3337 | 1.27493 | ||||||||
\(281\) | −0.246932 | −0.0147307 | −0.00736536 | − | 0.999973i | \(-0.502344\pi\) | ||||
−0.00736536 | + | 0.999973i | \(0.502344\pi\) | |||||||
\(282\) | −5.94507 | −0.354024 | ||||||||
\(283\) | −23.7812 | −1.41364 | −0.706822 | − | 0.707391i | \(-0.749872\pi\) | ||||
−0.706822 | + | 0.707391i | \(0.749872\pi\) | |||||||
\(284\) | −47.1800 | −2.79962 | ||||||||
\(285\) | −11.2600 | −0.666986 | ||||||||
\(286\) | −1.10532 | −0.0653587 | ||||||||
\(287\) | 8.00320 | 0.472414 | ||||||||
\(288\) | −9.97590 | −0.587835 | ||||||||
\(289\) | −15.5578 | −0.915163 | ||||||||
\(290\) | 21.9533 | 1.28914 | ||||||||
\(291\) | 9.34568 | 0.547853 | ||||||||
\(292\) | −9.13290 | −0.534462 | ||||||||
\(293\) | −21.0999 | −1.23267 | −0.616334 | − | 0.787485i | \(-0.711383\pi\) | ||||
−0.616334 | + | 0.787485i | \(0.711383\pi\) | |||||||
\(294\) | −1.17134 | −0.0683140 | ||||||||
\(295\) | 27.1011 | 1.57789 | ||||||||
\(296\) | 34.0263 | 1.97774 | ||||||||
\(297\) | 8.96742 | 0.520342 | ||||||||
\(298\) | 7.46306 | 0.432324 | ||||||||
\(299\) | 1.91849 | 0.110949 | ||||||||
\(300\) | 2.17250 | 0.125429 | ||||||||
\(301\) | 12.6935 | 0.731643 | ||||||||
\(302\) | −20.7360 | −1.19322 | ||||||||
\(303\) | 10.2382 | 0.588171 | ||||||||
\(304\) | 3.88954 | 0.223081 | ||||||||
\(305\) | 33.3970 | 1.91231 | ||||||||
\(306\) | −5.89838 | −0.337188 | ||||||||
\(307\) | −15.7384 | −0.898238 | −0.449119 | − | 0.893472i | \(-0.648262\pi\) | ||||
−0.449119 | + | 0.893472i | \(0.648262\pi\) | |||||||
\(308\) | −17.3960 | −0.991230 | ||||||||
\(309\) | −4.11252 | −0.233953 | ||||||||
\(310\) | −18.6092 | −1.05693 | ||||||||
\(311\) | −15.2313 | −0.863685 | −0.431843 | − | 0.901949i | \(-0.642136\pi\) | ||||
−0.431843 | + | 0.901949i | \(0.642136\pi\) | |||||||
\(312\) | 0.784410 | 0.0444085 | ||||||||
\(313\) | −3.63478 | −0.205450 | −0.102725 | − | 0.994710i | \(-0.532756\pi\) | ||||
−0.102725 | + | 0.994710i | \(0.532756\pi\) | |||||||
\(314\) | −22.5106 | −1.27034 | ||||||||
\(315\) | 13.8205 | 0.778699 | ||||||||
\(316\) | −15.3127 | −0.861408 | ||||||||
\(317\) | −22.2278 | −1.24844 | −0.624218 | − | 0.781250i | \(-0.714582\pi\) | ||||
−0.624218 | + | 0.781250i | \(0.714582\pi\) | |||||||
\(318\) | −12.5310 | −0.702706 | ||||||||
\(319\) | −7.38089 | −0.413250 | ||||||||
\(320\) | 29.8446 | 1.66836 | ||||||||
\(321\) | 6.50715 | 0.363194 | ||||||||
\(322\) | 47.9389 | 2.67153 | ||||||||
\(323\) | −6.02552 | −0.335269 | ||||||||
\(324\) | 6.13760 | 0.340978 | ||||||||
\(325\) | −0.173079 | −0.00960068 | ||||||||
\(326\) | −26.4318 | −1.46392 | ||||||||
\(327\) | 3.18359 | 0.176053 | ||||||||
\(328\) | −9.50943 | −0.525070 | ||||||||
\(329\) | 7.45426 | 0.410966 | ||||||||
\(330\) | −9.71425 | −0.534752 | ||||||||
\(331\) | 25.5276 | 1.40312 | 0.701561 | − | 0.712610i | \(-0.252487\pi\) | ||||
0.701561 | + | 0.712610i | \(0.252487\pi\) | |||||||
\(332\) | −51.0125 | −2.79967 | ||||||||
\(333\) | 22.0431 | 1.20796 | ||||||||
\(334\) | −7.12432 | −0.389826 | ||||||||
\(335\) | 21.4453 | 1.17168 | ||||||||
\(336\) | 2.00417 | 0.109336 | ||||||||
\(337\) | 14.0309 | 0.764312 | 0.382156 | − | 0.924098i | \(-0.375182\pi\) | ||||
0.382156 | + | 0.924098i | \(0.375182\pi\) | |||||||
\(338\) | 30.0666 | 1.63541 | ||||||||
\(339\) | 8.85249 | 0.480801 | ||||||||
\(340\) | 9.73846 | 0.528142 | ||||||||
\(341\) | 6.25658 | 0.338813 | ||||||||
\(342\) | 24.6430 | 1.33254 | ||||||||
\(343\) | −17.7463 | −0.958212 | ||||||||
\(344\) | −15.0825 | −0.813193 | ||||||||
\(345\) | 16.8610 | 0.907763 | ||||||||
\(346\) | 17.2301 | 0.926297 | ||||||||
\(347\) | 12.9272 | 0.693969 | 0.346984 | − | 0.937871i | \(-0.387206\pi\) | ||||
0.346984 | + | 0.937871i | \(0.387206\pi\) | |||||||
\(348\) | 12.7040 | 0.681003 | ||||||||
\(349\) | 7.14951 | 0.382705 | 0.191352 | − | 0.981521i | \(-0.438713\pi\) | ||||
0.191352 | + | 0.981521i | \(0.438713\pi\) | |||||||
\(350\) | −4.32486 | −0.231174 | ||||||||
\(351\) | 1.22965 | 0.0656339 | ||||||||
\(352\) | −8.79193 | −0.468611 | ||||||||
\(353\) | −1.51745 | −0.0807657 | −0.0403828 | − | 0.999184i | \(-0.512858\pi\) | ||||
−0.0403828 | + | 0.999184i | \(0.512858\pi\) | |||||||
\(354\) | 24.8996 | 1.32340 | ||||||||
\(355\) | 33.0343 | 1.75328 | ||||||||
\(356\) | −27.3895 | −1.45164 | ||||||||
\(357\) | −3.10478 | −0.164322 | ||||||||
\(358\) | −8.92736 | −0.471826 | ||||||||
\(359\) | −4.78861 | −0.252733 | −0.126367 | − | 0.991984i | \(-0.540332\pi\) | ||||
−0.126367 | + | 0.991984i | \(0.540332\pi\) | |||||||
\(360\) | −16.4216 | −0.865495 | ||||||||
\(361\) | 6.17422 | 0.324959 | ||||||||
\(362\) | −26.6686 | −1.40167 | ||||||||
\(363\) | −7.09407 | −0.372342 | ||||||||
\(364\) | −2.38542 | −0.125030 | ||||||||
\(365\) | 6.39463 | 0.334710 | ||||||||
\(366\) | 30.6840 | 1.60388 | ||||||||
\(367\) | 20.7387 | 1.08255 | 0.541276 | − | 0.840845i | \(-0.317941\pi\) | ||||
0.541276 | + | 0.840845i | \(0.317941\pi\) | |||||||
\(368\) | −5.82427 | −0.303611 | ||||||||
\(369\) | −6.16045 | −0.320700 | ||||||||
\(370\) | −57.7824 | −3.00396 | ||||||||
\(371\) | 15.7121 | 0.815733 | ||||||||
\(372\) | −10.7688 | −0.558337 | ||||||||
\(373\) | 9.32736 | 0.482952 | 0.241476 | − | 0.970407i | \(-0.422368\pi\) | ||||
0.241476 | + | 0.970407i | \(0.422368\pi\) | |||||||
\(374\) | −5.19834 | −0.268800 | ||||||||
\(375\) | 9.69986 | 0.500899 | ||||||||
\(376\) | −8.85717 | −0.456774 | ||||||||
\(377\) | −1.01210 | −0.0521258 | ||||||||
\(378\) | 30.7263 | 1.58039 | ||||||||
\(379\) | −30.8221 | −1.58322 | −0.791612 | − | 0.611025i | \(-0.790758\pi\) | ||||
−0.791612 | + | 0.611025i | \(0.790758\pi\) | |||||||
\(380\) | −40.6866 | −2.08718 | ||||||||
\(381\) | 10.5451 | 0.540241 | ||||||||
\(382\) | −20.3851 | −1.04299 | ||||||||
\(383\) | 17.4382 | 0.891051 | 0.445526 | − | 0.895269i | \(-0.353017\pi\) | ||||
0.445526 | + | 0.895269i | \(0.353017\pi\) | |||||||
\(384\) | 18.5269 | 0.945447 | ||||||||
\(385\) | 12.1803 | 0.620764 | ||||||||
\(386\) | −33.2544 | −1.69261 | ||||||||
\(387\) | −9.77082 | −0.496679 | ||||||||
\(388\) | 33.7694 | 1.71438 | ||||||||
\(389\) | −9.43027 | −0.478134 | −0.239067 | − | 0.971003i | \(-0.576841\pi\) | ||||
−0.239067 | + | 0.971003i | \(0.576841\pi\) | |||||||
\(390\) | −1.33206 | −0.0674515 | ||||||||
\(391\) | 9.02272 | 0.456299 | ||||||||
\(392\) | −1.74511 | −0.0881412 | ||||||||
\(393\) | −5.00355 | −0.252395 | ||||||||
\(394\) | 34.3487 | 1.73046 | ||||||||
\(395\) | 10.7216 | 0.539462 | ||||||||
\(396\) | 13.3906 | 0.672901 | ||||||||
\(397\) | −0.691864 | −0.0347236 | −0.0173618 | − | 0.999849i | \(-0.505527\pi\) | ||||
−0.0173618 | + | 0.999849i | \(0.505527\pi\) | |||||||
\(398\) | 22.0549 | 1.10551 | ||||||||
\(399\) | 12.9716 | 0.649390 | ||||||||
\(400\) | 0.525443 | 0.0262722 | ||||||||
\(401\) | 4.81354 | 0.240377 | 0.120188 | − | 0.992751i | \(-0.461650\pi\) | ||||
0.120188 | + | 0.992751i | \(0.461650\pi\) | |||||||
\(402\) | 19.7032 | 0.982707 | ||||||||
\(403\) | 0.857930 | 0.0427365 | ||||||||
\(404\) | 36.9945 | 1.84055 | ||||||||
\(405\) | −4.29740 | −0.213540 | ||||||||
\(406\) | −25.2902 | −1.25513 | ||||||||
\(407\) | 19.4270 | 0.962959 | ||||||||
\(408\) | 3.68911 | 0.182638 | ||||||||
\(409\) | −16.2943 | −0.805702 | −0.402851 | − | 0.915266i | \(-0.631981\pi\) | ||||
−0.402851 | + | 0.915266i | \(0.631981\pi\) | |||||||
\(410\) | 16.1486 | 0.797523 | ||||||||
\(411\) | 5.64973 | 0.278681 | ||||||||
\(412\) | −14.8601 | −0.732103 | ||||||||
\(413\) | −31.2205 | −1.53626 | ||||||||
\(414\) | −36.9009 | −1.81358 | ||||||||
\(415\) | 35.7177 | 1.75331 | ||||||||
\(416\) | −1.20559 | −0.0591088 | ||||||||
\(417\) | −7.42474 | −0.363591 | ||||||||
\(418\) | 21.7183 | 1.06228 | ||||||||
\(419\) | −29.1615 | −1.42463 | −0.712316 | − | 0.701859i | \(-0.752353\pi\) | ||||
−0.712316 | + | 0.701859i | \(0.752353\pi\) | |||||||
\(420\) | −20.9646 | −1.02297 | ||||||||
\(421\) | −30.0713 | −1.46559 | −0.732793 | − | 0.680452i | \(-0.761784\pi\) | ||||
−0.732793 | + | 0.680452i | \(0.761784\pi\) | |||||||
\(422\) | −46.5024 | −2.26370 | ||||||||
\(423\) | −5.73790 | −0.278986 | ||||||||
\(424\) | −18.6692 | −0.906657 | ||||||||
\(425\) | −0.813995 | −0.0394846 | ||||||||
\(426\) | 30.3508 | 1.47050 | ||||||||
\(427\) | −38.4734 | −1.86186 | ||||||||
\(428\) | 23.5127 | 1.13653 | ||||||||
\(429\) | 0.447851 | 0.0216224 | ||||||||
\(430\) | 25.6126 | 1.23515 | ||||||||
\(431\) | 15.5036 | 0.746780 | 0.373390 | − | 0.927674i | \(-0.378195\pi\) | ||||
0.373390 | + | 0.927674i | \(0.378195\pi\) | |||||||
\(432\) | −3.73305 | −0.179607 | ||||||||
\(433\) | 19.2412 | 0.924671 | 0.462336 | − | 0.886705i | \(-0.347012\pi\) | ||||
0.462336 | + | 0.886705i | \(0.347012\pi\) | |||||||
\(434\) | 21.4378 | 1.02905 | ||||||||
\(435\) | −8.89500 | −0.426483 | ||||||||
\(436\) | 11.5035 | 0.550917 | ||||||||
\(437\) | −37.6963 | −1.80326 | ||||||||
\(438\) | 5.87517 | 0.280727 | ||||||||
\(439\) | 36.9340 | 1.76276 | 0.881381 | − | 0.472406i | \(-0.156614\pi\) | ||||
0.881381 | + | 0.472406i | \(0.156614\pi\) | |||||||
\(440\) | −14.4726 | −0.689956 | ||||||||
\(441\) | −1.13052 | −0.0538345 | ||||||||
\(442\) | −0.712819 | −0.0339053 | ||||||||
\(443\) | −25.4167 | −1.20758 | −0.603792 | − | 0.797142i | \(-0.706344\pi\) | ||||
−0.603792 | + | 0.797142i | \(0.706344\pi\) | |||||||
\(444\) | −33.4376 | −1.58688 | ||||||||
\(445\) | 19.1774 | 0.909097 | ||||||||
\(446\) | −8.06427 | −0.381854 | ||||||||
\(447\) | −3.02387 | −0.143024 | ||||||||
\(448\) | −34.3809 | −1.62435 | ||||||||
\(449\) | 7.86170 | 0.371017 | 0.185508 | − | 0.982643i | \(-0.440607\pi\) | ||||
0.185508 | + | 0.982643i | \(0.440607\pi\) | |||||||
\(450\) | 3.32906 | 0.156933 | ||||||||
\(451\) | −5.42931 | −0.255656 | ||||||||
\(452\) | 31.9873 | 1.50456 | ||||||||
\(453\) | 8.40177 | 0.394750 | ||||||||
\(454\) | −33.9102 | −1.59148 | ||||||||
\(455\) | 1.67021 | 0.0783007 | ||||||||
\(456\) | −15.4128 | −0.721772 | ||||||||
\(457\) | −11.1115 | −0.519772 | −0.259886 | − | 0.965639i | \(-0.583685\pi\) | ||||
−0.259886 | + | 0.965639i | \(0.583685\pi\) | |||||||
\(458\) | 52.8812 | 2.47098 | ||||||||
\(459\) | 5.78309 | 0.269932 | ||||||||
\(460\) | 60.9248 | 2.84064 | ||||||||
\(461\) | 31.5317 | 1.46858 | 0.734288 | − | 0.678838i | \(-0.237516\pi\) | ||||
0.734288 | + | 0.678838i | \(0.237516\pi\) | |||||||
\(462\) | 11.1908 | 0.520644 | ||||||||
\(463\) | −0.0936264 | −0.00435119 | −0.00217559 | − | 0.999998i | \(-0.500693\pi\) | ||||
−0.00217559 | + | 0.999998i | \(0.500693\pi\) | |||||||
\(464\) | 3.07259 | 0.142642 | ||||||||
\(465\) | 7.54006 | 0.349662 | ||||||||
\(466\) | −37.3316 | −1.72935 | ||||||||
\(467\) | 4.38408 | 0.202871 | 0.101435 | − | 0.994842i | \(-0.467656\pi\) | ||||
0.101435 | + | 0.994842i | \(0.467656\pi\) | |||||||
\(468\) | 1.83617 | 0.0848771 | ||||||||
\(469\) | −24.7050 | −1.14077 | ||||||||
\(470\) | 15.0410 | 0.693788 | ||||||||
\(471\) | 9.12080 | 0.420264 | ||||||||
\(472\) | 37.0963 | 1.70750 | ||||||||
\(473\) | −8.61119 | −0.395943 | ||||||||
\(474\) | 9.85064 | 0.452455 | ||||||||
\(475\) | 3.40082 | 0.156040 | ||||||||
\(476\) | −11.2187 | −0.514208 | ||||||||
\(477\) | −12.0944 | −0.553764 | ||||||||
\(478\) | 14.8727 | 0.680259 | ||||||||
\(479\) | 3.94009 | 0.180028 | 0.0900138 | − | 0.995941i | \(-0.471309\pi\) | ||||
0.0900138 | + | 0.995941i | \(0.471309\pi\) | |||||||
\(480\) | −10.5955 | −0.483616 | ||||||||
\(481\) | 2.66391 | 0.121464 | ||||||||
\(482\) | −12.4726 | −0.568113 | ||||||||
\(483\) | −19.4238 | −0.883815 | ||||||||
\(484\) | −25.6335 | −1.16516 | ||||||||
\(485\) | −23.6445 | −1.07364 | ||||||||
\(486\) | −37.5290 | −1.70235 | ||||||||
\(487\) | −21.8295 | −0.989189 | −0.494594 | − | 0.869124i | \(-0.664683\pi\) | ||||
−0.494594 | + | 0.869124i | \(0.664683\pi\) | |||||||
\(488\) | 45.7142 | 2.06938 | ||||||||
\(489\) | 10.7096 | 0.484305 | ||||||||
\(490\) | 2.96348 | 0.133877 | ||||||||
\(491\) | 30.7528 | 1.38785 | 0.693927 | − | 0.720045i | \(-0.255879\pi\) | ||||
0.693927 | + | 0.720045i | \(0.255879\pi\) | |||||||
\(492\) | 9.34491 | 0.421301 | ||||||||
\(493\) | −4.75994 | −0.214377 | ||||||||
\(494\) | 2.97811 | 0.133991 | ||||||||
\(495\) | −9.37575 | −0.421409 | ||||||||
\(496\) | −2.60456 | −0.116948 | ||||||||
\(497\) | −38.0555 | −1.70702 | ||||||||
\(498\) | 32.8162 | 1.47053 | ||||||||
\(499\) | 8.68664 | 0.388867 | 0.194434 | − | 0.980916i | \(-0.437713\pi\) | ||||
0.194434 | + | 0.980916i | \(0.437713\pi\) | |||||||
\(500\) | 35.0492 | 1.56745 | ||||||||
\(501\) | 2.88663 | 0.128965 | ||||||||
\(502\) | −16.7995 | −0.749797 | ||||||||
\(503\) | −20.7993 | −0.927393 | −0.463697 | − | 0.885994i | \(-0.653477\pi\) | ||||
−0.463697 | + | 0.885994i | \(0.653477\pi\) | |||||||
\(504\) | 18.9177 | 0.842661 | ||||||||
\(505\) | −25.9027 | −1.15265 | ||||||||
\(506\) | −32.5214 | −1.44575 | ||||||||
\(507\) | −12.1823 | −0.541037 | ||||||||
\(508\) | 38.1033 | 1.69056 | ||||||||
\(509\) | −31.4884 | −1.39570 | −0.697849 | − | 0.716245i | \(-0.745859\pi\) | ||||
−0.697849 | + | 0.716245i | \(0.745859\pi\) | |||||||
\(510\) | −6.26473 | −0.277407 | ||||||||
\(511\) | −7.36662 | −0.325880 | ||||||||
\(512\) | 8.71689 | 0.385236 | ||||||||
\(513\) | −24.1614 | −1.06675 | ||||||||
\(514\) | −60.9113 | −2.68668 | ||||||||
\(515\) | 10.4047 | 0.458484 | ||||||||
\(516\) | 14.8216 | 0.652483 | ||||||||
\(517\) | −5.05691 | −0.222403 | ||||||||
\(518\) | 66.5653 | 2.92471 | ||||||||
\(519\) | −6.98128 | −0.306444 | ||||||||
\(520\) | −1.98455 | −0.0870283 | ||||||||
\(521\) | 3.10018 | 0.135821 | 0.0679107 | − | 0.997691i | \(-0.478367\pi\) | ||||
0.0679107 | + | 0.997691i | \(0.478367\pi\) | |||||||
\(522\) | 19.4671 | 0.852051 | ||||||||
\(523\) | 21.3138 | 0.931989 | 0.465994 | − | 0.884788i | \(-0.345697\pi\) | ||||
0.465994 | + | 0.884788i | \(0.345697\pi\) | |||||||
\(524\) | −18.0797 | −0.789813 | ||||||||
\(525\) | 1.75234 | 0.0764785 | ||||||||
\(526\) | −57.5480 | −2.50921 | ||||||||
\(527\) | 4.03487 | 0.175762 | ||||||||
\(528\) | −1.35961 | −0.0591696 | ||||||||
\(529\) | 33.4471 | 1.45422 | ||||||||
\(530\) | 31.7035 | 1.37711 | ||||||||
\(531\) | 24.0319 | 1.04290 | ||||||||
\(532\) | 46.8710 | 2.03212 | ||||||||
\(533\) | −0.744491 | −0.0322475 | ||||||||
\(534\) | 17.6196 | 0.762473 | ||||||||
\(535\) | −16.4630 | −0.711759 | ||||||||
\(536\) | 29.3545 | 1.26792 | ||||||||
\(537\) | 3.61718 | 0.156093 | ||||||||
\(538\) | 65.2767 | 2.81428 | ||||||||
\(539\) | −0.996350 | −0.0429158 | ||||||||
\(540\) | 39.0497 | 1.68043 | ||||||||
\(541\) | −17.5862 | −0.756088 | −0.378044 | − | 0.925788i | \(-0.623403\pi\) | ||||
−0.378044 | + | 0.925788i | \(0.623403\pi\) | |||||||
\(542\) | −24.9311 | −1.07088 | ||||||||
\(543\) | 10.8055 | 0.463710 | ||||||||
\(544\) | −5.66992 | −0.243096 | ||||||||
\(545\) | −8.05446 | −0.345015 | ||||||||
\(546\) | 1.53453 | 0.0656720 | ||||||||
\(547\) | 29.5940 | 1.26535 | 0.632675 | − | 0.774418i | \(-0.281957\pi\) | ||||
0.632675 | + | 0.774418i | \(0.281957\pi\) | |||||||
\(548\) | 20.4146 | 0.872067 | ||||||||
\(549\) | 29.6148 | 1.26393 | ||||||||
\(550\) | 2.93395 | 0.125104 | ||||||||
\(551\) | 19.8867 | 0.847202 | ||||||||
\(552\) | 23.0795 | 0.982327 | ||||||||
\(553\) | −12.3513 | −0.525230 | ||||||||
\(554\) | 11.1646 | 0.474337 | ||||||||
\(555\) | 23.4122 | 0.993793 | ||||||||
\(556\) | −26.8283 | −1.13777 | ||||||||
\(557\) | −33.7370 | −1.42948 | −0.714741 | − | 0.699389i | \(-0.753455\pi\) | ||||
−0.714741 | + | 0.699389i | \(0.753455\pi\) | |||||||
\(558\) | −16.5017 | −0.698574 | ||||||||
\(559\) | −1.18080 | −0.0499427 | ||||||||
\(560\) | −5.07053 | −0.214269 | ||||||||
\(561\) | 2.10626 | 0.0889263 | ||||||||
\(562\) | 0.573986 | 0.0242121 | ||||||||
\(563\) | 44.0966 | 1.85845 | 0.929225 | − | 0.369514i | \(-0.120476\pi\) | ||||
0.929225 | + | 0.369514i | \(0.120476\pi\) | |||||||
\(564\) | 8.70394 | 0.366502 | ||||||||
\(565\) | −22.3967 | −0.942238 | ||||||||
\(566\) | 55.2787 | 2.32354 | ||||||||
\(567\) | 4.95061 | 0.207906 | ||||||||
\(568\) | 45.2177 | 1.89729 | ||||||||
\(569\) | 1.02357 | 0.0429105 | 0.0214552 | − | 0.999770i | \(-0.493170\pi\) | ||||
0.0214552 | + | 0.999770i | \(0.493170\pi\) | |||||||
\(570\) | 26.1736 | 1.09629 | ||||||||
\(571\) | 11.8651 | 0.496538 | 0.248269 | − | 0.968691i | \(-0.420138\pi\) | ||||
0.248269 | + | 0.968691i | \(0.420138\pi\) | |||||||
\(572\) | 1.61825 | 0.0676624 | ||||||||
\(573\) | 8.25960 | 0.345050 | ||||||||
\(574\) | −18.6032 | −0.776483 | ||||||||
\(575\) | −5.09244 | −0.212370 | ||||||||
\(576\) | 26.4647 | 1.10269 | ||||||||
\(577\) | 29.0611 | 1.20983 | 0.604915 | − | 0.796290i | \(-0.293207\pi\) | ||||
0.604915 | + | 0.796290i | \(0.293207\pi\) | |||||||
\(578\) | 36.1636 | 1.50421 | ||||||||
\(579\) | 13.4740 | 0.559960 | ||||||||
\(580\) | −32.1409 | −1.33458 | ||||||||
\(581\) | −41.1468 | −1.70706 | ||||||||
\(582\) | −21.7238 | −0.900479 | ||||||||
\(583\) | −10.6590 | −0.441450 | ||||||||
\(584\) | 8.75304 | 0.362203 | ||||||||
\(585\) | −1.28564 | −0.0531548 | ||||||||
\(586\) | 49.0461 | 2.02607 | ||||||||
\(587\) | 5.95025 | 0.245593 | 0.122797 | − | 0.992432i | \(-0.460814\pi\) | ||||
0.122797 | + | 0.992432i | \(0.460814\pi\) | |||||||
\(588\) | 1.71491 | 0.0707219 | ||||||||
\(589\) | −16.8574 | −0.694598 | ||||||||
\(590\) | −62.9958 | −2.59350 | ||||||||
\(591\) | −13.9173 | −0.572483 | ||||||||
\(592\) | −8.08726 | −0.332384 | ||||||||
\(593\) | 35.6093 | 1.46230 | 0.731149 | − | 0.682217i | \(-0.238984\pi\) | ||||
0.731149 | + | 0.682217i | \(0.238984\pi\) | |||||||
\(594\) | −20.8445 | −0.855261 | ||||||||
\(595\) | 7.85506 | 0.322026 | ||||||||
\(596\) | −10.9264 | −0.447562 | ||||||||
\(597\) | −8.93620 | −0.365734 | ||||||||
\(598\) | −4.45947 | −0.182361 | ||||||||
\(599\) | −26.9522 | −1.10124 | −0.550619 | − | 0.834757i | \(-0.685608\pi\) | ||||
−0.550619 | + | 0.834757i | \(0.685608\pi\) | |||||||
\(600\) | −2.08214 | −0.0850030 | ||||||||
\(601\) | −27.4005 | −1.11769 | −0.558844 | − | 0.829273i | \(-0.688755\pi\) | ||||
−0.558844 | + | 0.829273i | \(0.688755\pi\) | |||||||
\(602\) | −29.5057 | −1.20256 | ||||||||
\(603\) | 19.0166 | 0.774417 | ||||||||
\(604\) | 30.3587 | 1.23528 | ||||||||
\(605\) | 17.9480 | 0.729688 | ||||||||
\(606\) | −23.7985 | −0.966747 | ||||||||
\(607\) | −48.4251 | −1.96551 | −0.982756 | − | 0.184906i | \(-0.940802\pi\) | ||||
−0.982756 | + | 0.184906i | \(0.940802\pi\) | |||||||
\(608\) | 23.6885 | 0.960697 | ||||||||
\(609\) | 10.2470 | 0.415231 | ||||||||
\(610\) | −77.6304 | −3.14316 | ||||||||
\(611\) | −0.693426 | −0.0280530 | ||||||||
\(612\) | 8.63558 | 0.349073 | ||||||||
\(613\) | −45.8551 | −1.85207 | −0.926035 | − | 0.377438i | \(-0.876805\pi\) | ||||
−0.926035 | + | 0.377438i | \(0.876805\pi\) | |||||||
\(614\) | 36.5835 | 1.47639 | ||||||||
\(615\) | −6.54308 | −0.263842 | ||||||||
\(616\) | 16.6725 | 0.671754 | ||||||||
\(617\) | −42.3649 | −1.70555 | −0.852774 | − | 0.522280i | \(-0.825082\pi\) | ||||
−0.852774 | + | 0.522280i | \(0.825082\pi\) | |||||||
\(618\) | 9.55944 | 0.384537 | ||||||||
\(619\) | −1.00000 | −0.0401934 | ||||||||
\(620\) | 27.2450 | 1.09419 | ||||||||
\(621\) | 36.1797 | 1.45184 | ||||||||
\(622\) | 35.4046 | 1.41960 | ||||||||
\(623\) | −22.0924 | −0.885114 | ||||||||
\(624\) | −0.186436 | −0.00746342 | ||||||||
\(625\) | −27.9296 | −1.11718 | ||||||||
\(626\) | 8.44895 | 0.337688 | ||||||||
\(627\) | −8.79980 | −0.351430 | ||||||||
\(628\) | 32.9568 | 1.31512 | ||||||||
\(629\) | 12.5285 | 0.499542 | ||||||||
\(630\) | −32.1254 | −1.27991 | ||||||||
\(631\) | −20.4064 | −0.812365 | −0.406182 | − | 0.913792i | \(-0.633140\pi\) | ||||
−0.406182 | + | 0.913792i | \(0.633140\pi\) | |||||||
\(632\) | 14.6758 | 0.583773 | ||||||||
\(633\) | 18.8418 | 0.748895 | ||||||||
\(634\) | 51.6678 | 2.05199 | ||||||||
\(635\) | −26.6790 | −1.05872 | ||||||||
\(636\) | 18.3462 | 0.727475 | ||||||||
\(637\) | −0.136624 | −0.00541324 | ||||||||
\(638\) | 17.1567 | 0.679239 | ||||||||
\(639\) | 29.2932 | 1.15882 | ||||||||
\(640\) | −46.8729 | −1.85281 | ||||||||
\(641\) | 21.3992 | 0.845218 | 0.422609 | − | 0.906312i | \(-0.361114\pi\) | ||||
0.422609 | + | 0.906312i | \(0.361114\pi\) | |||||||
\(642\) | −15.1257 | −0.596963 | ||||||||
\(643\) | −47.4855 | −1.87265 | −0.936323 | − | 0.351141i | \(-0.885794\pi\) | ||||
−0.936323 | + | 0.351141i | \(0.885794\pi\) | |||||||
\(644\) | −70.1854 | −2.76569 | ||||||||
\(645\) | −10.3777 | −0.408621 | ||||||||
\(646\) | 14.0062 | 0.551065 | ||||||||
\(647\) | 10.9819 | 0.431745 | 0.215872 | − | 0.976422i | \(-0.430740\pi\) | ||||
0.215872 | + | 0.976422i | \(0.430740\pi\) | |||||||
\(648\) | −5.88233 | −0.231080 | ||||||||
\(649\) | 21.1798 | 0.831378 | ||||||||
\(650\) | 0.402317 | 0.0157802 | ||||||||
\(651\) | −8.68615 | −0.340437 | ||||||||
\(652\) | 38.6978 | 1.51552 | ||||||||
\(653\) | −14.9284 | −0.584193 | −0.292097 | − | 0.956389i | \(-0.594353\pi\) | ||||
−0.292097 | + | 0.956389i | \(0.594353\pi\) | |||||||
\(654\) | −7.40017 | −0.289369 | ||||||||
\(655\) | 12.6589 | 0.494625 | ||||||||
\(656\) | 2.26017 | 0.0882448 | ||||||||
\(657\) | 5.67045 | 0.221225 | ||||||||
\(658\) | −17.3272 | −0.675485 | ||||||||
\(659\) | 4.65349 | 0.181274 | 0.0906371 | − | 0.995884i | \(-0.471110\pi\) | ||||
0.0906371 | + | 0.995884i | \(0.471110\pi\) | |||||||
\(660\) | 14.2223 | 0.553601 | ||||||||
\(661\) | 49.1804 | 1.91290 | 0.956448 | − | 0.291904i | \(-0.0942889\pi\) | ||||
0.956448 | + | 0.291904i | \(0.0942889\pi\) | |||||||
\(662\) | −59.3381 | −2.30624 | ||||||||
\(663\) | 0.288819 | 0.0112168 | ||||||||
\(664\) | 48.8908 | 1.89733 | ||||||||
\(665\) | −32.8179 | −1.27262 | ||||||||
\(666\) | −51.2386 | −1.98545 | ||||||||
\(667\) | −29.7787 | −1.15304 | ||||||||
\(668\) | 10.4304 | 0.403566 | ||||||||
\(669\) | 3.26747 | 0.126328 | ||||||||
\(670\) | −49.8490 | −1.92583 | ||||||||
\(671\) | 26.1000 | 1.00758 | ||||||||
\(672\) | 12.2060 | 0.470857 | ||||||||
\(673\) | 23.7019 | 0.913642 | 0.456821 | − | 0.889559i | \(-0.348988\pi\) | ||||
0.456821 | + | 0.889559i | \(0.348988\pi\) | |||||||
\(674\) | −32.6144 | −1.25626 | ||||||||
\(675\) | −3.26399 | −0.125631 | ||||||||
\(676\) | −44.0193 | −1.69305 | ||||||||
\(677\) | 19.9839 | 0.768042 | 0.384021 | − | 0.923324i | \(-0.374539\pi\) | ||||
0.384021 | + | 0.923324i | \(0.374539\pi\) | |||||||
\(678\) | −20.5774 | −0.790269 | ||||||||
\(679\) | 27.2385 | 1.04532 | ||||||||
\(680\) | −9.33341 | −0.357920 | ||||||||
\(681\) | 13.7397 | 0.526506 | ||||||||
\(682\) | −14.5432 | −0.556890 | ||||||||
\(683\) | −38.9144 | −1.48902 | −0.744508 | − | 0.667613i | \(-0.767316\pi\) | ||||
−0.744508 | + | 0.667613i | \(0.767316\pi\) | |||||||
\(684\) | −36.0789 | −1.37951 | ||||||||
\(685\) | −14.2938 | −0.546137 | ||||||||
\(686\) | 41.2508 | 1.57496 | ||||||||
\(687\) | −21.4263 | −0.817466 | ||||||||
\(688\) | 3.58476 | 0.136668 | ||||||||
\(689\) | −1.46161 | −0.0556828 | ||||||||
\(690\) | −39.1928 | −1.49204 | ||||||||
\(691\) | −14.8343 | −0.564323 | −0.282161 | − | 0.959367i | \(-0.591051\pi\) | ||||
−0.282161 | + | 0.959367i | \(0.591051\pi\) | |||||||
\(692\) | −25.2259 | −0.958946 | ||||||||
\(693\) | 10.8009 | 0.410291 | ||||||||
\(694\) | −30.0489 | −1.14064 | ||||||||
\(695\) | 18.7845 | 0.712538 | ||||||||
\(696\) | −12.1756 | −0.461514 | ||||||||
\(697\) | −3.50136 | −0.132624 | ||||||||
\(698\) | −16.6188 | −0.629032 | ||||||||
\(699\) | 15.1260 | 0.572117 | ||||||||
\(700\) | 6.33186 | 0.239322 | ||||||||
\(701\) | −44.4851 | −1.68018 | −0.840090 | − | 0.542447i | \(-0.817498\pi\) | ||||
−0.840090 | + | 0.542447i | \(0.817498\pi\) | |||||||
\(702\) | −2.85829 | −0.107879 | ||||||||
\(703\) | −52.3431 | −1.97416 | ||||||||
\(704\) | 23.3238 | 0.879048 | ||||||||
\(705\) | −6.09428 | −0.229524 | ||||||||
\(706\) | 3.52727 | 0.132750 | ||||||||
\(707\) | 29.8399 | 1.12224 | ||||||||
\(708\) | −36.4545 | −1.37004 | ||||||||
\(709\) | −20.6230 | −0.774513 | −0.387256 | − | 0.921972i | \(-0.626577\pi\) | ||||
−0.387256 | + | 0.921972i | \(0.626577\pi\) | |||||||
\(710\) | −76.7873 | −2.88177 | ||||||||
\(711\) | 9.50738 | 0.356555 | ||||||||
\(712\) | 26.2503 | 0.983770 | ||||||||
\(713\) | 25.2426 | 0.945343 | ||||||||
\(714\) | 7.21697 | 0.270088 | ||||||||
\(715\) | −1.13306 | −0.0423740 | ||||||||
\(716\) | 13.0702 | 0.488456 | ||||||||
\(717\) | −6.02609 | −0.225048 | ||||||||
\(718\) | 11.1310 | 0.415405 | ||||||||
\(719\) | 40.4151 | 1.50723 | 0.753615 | − | 0.657316i | \(-0.228309\pi\) | ||||
0.753615 | + | 0.657316i | \(0.228309\pi\) | |||||||
\(720\) | 3.90304 | 0.145458 | ||||||||
\(721\) | −11.9862 | −0.446388 | ||||||||
\(722\) | −14.3518 | −0.534119 | ||||||||
\(723\) | 5.05365 | 0.187947 | ||||||||
\(724\) | 39.0444 | 1.45107 | ||||||||
\(725\) | 2.68652 | 0.0997748 | ||||||||
\(726\) | 16.4900 | 0.612000 | ||||||||
\(727\) | 47.9355 | 1.77783 | 0.888914 | − | 0.458074i | \(-0.151461\pi\) | ||||
0.888914 | + | 0.458074i | \(0.151461\pi\) | |||||||
\(728\) | 2.28620 | 0.0847323 | ||||||||
\(729\) | 9.79545 | 0.362794 | ||||||||
\(730\) | −14.8641 | −0.550147 | ||||||||
\(731\) | −5.55336 | −0.205399 | ||||||||
\(732\) | −44.9233 | −1.66041 | ||||||||
\(733\) | −21.6201 | −0.798555 | −0.399278 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399278 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(734\) | −48.2066 | −1.77934 | ||||||||
\(735\) | −1.20074 | −0.0442900 | ||||||||
\(736\) | −35.4716 | −1.30750 | ||||||||
\(737\) | 16.7597 | 0.617351 | ||||||||
\(738\) | 14.3198 | 0.527119 | ||||||||
\(739\) | 25.2860 | 0.930161 | 0.465081 | − | 0.885268i | \(-0.346025\pi\) | ||||
0.465081 | + | 0.885268i | \(0.346025\pi\) | |||||||
\(740\) | 84.5969 | 3.10985 | ||||||||
\(741\) | −1.20667 | −0.0443280 | ||||||||
\(742\) | −36.5224 | −1.34078 | ||||||||
\(743\) | −10.4850 | −0.384659 | −0.192329 | − | 0.981330i | \(-0.561604\pi\) | ||||
−0.192329 | + | 0.981330i | \(0.561604\pi\) | |||||||
\(744\) | 10.3209 | 0.378383 | ||||||||
\(745\) | 7.65038 | 0.280288 | ||||||||
\(746\) | −21.6812 | −0.793804 | ||||||||
\(747\) | 31.6727 | 1.15884 | ||||||||
\(748\) | 7.61068 | 0.278274 | ||||||||
\(749\) | 18.9654 | 0.692981 | ||||||||
\(750\) | −22.5471 | −0.823302 | ||||||||
\(751\) | −37.4832 | −1.36778 | −0.683890 | − | 0.729585i | \(-0.739713\pi\) | ||||
−0.683890 | + | 0.729585i | \(0.739713\pi\) | |||||||
\(752\) | 2.10514 | 0.0767667 | ||||||||
\(753\) | 6.80679 | 0.248053 | ||||||||
\(754\) | 2.35260 | 0.0856765 | ||||||||
\(755\) | −21.2564 | −0.773600 | ||||||||
\(756\) | −44.9852 | −1.63610 | ||||||||
\(757\) | 18.8295 | 0.684370 | 0.342185 | − | 0.939633i | \(-0.388833\pi\) | ||||
0.342185 | + | 0.939633i | \(0.388833\pi\) | |||||||
\(758\) | 71.6450 | 2.60226 | ||||||||
\(759\) | 13.1770 | 0.478294 | ||||||||
\(760\) | 38.9944 | 1.41447 | ||||||||
\(761\) | 31.2878 | 1.13418 | 0.567091 | − | 0.823655i | \(-0.308069\pi\) | ||||
0.567091 | + | 0.823655i | \(0.308069\pi\) | |||||||
\(762\) | −24.5117 | −0.887966 | ||||||||
\(763\) | 9.27874 | 0.335913 | ||||||||
\(764\) | 29.8450 | 1.07975 | ||||||||
\(765\) | −6.04642 | −0.218609 | ||||||||
\(766\) | −40.5346 | −1.46458 | ||||||||
\(767\) | 2.90426 | 0.104867 | ||||||||
\(768\) | −19.4726 | −0.702658 | ||||||||
\(769\) | 44.2952 | 1.59733 | 0.798664 | − | 0.601778i | \(-0.205541\pi\) | ||||
0.798664 | + | 0.601778i | \(0.205541\pi\) | |||||||
\(770\) | −28.3127 | −1.02032 | ||||||||
\(771\) | 24.6800 | 0.888828 | ||||||||
\(772\) | 48.6865 | 1.75227 | ||||||||
\(773\) | −13.4312 | −0.483086 | −0.241543 | − | 0.970390i | \(-0.577653\pi\) | ||||
−0.241543 | + | 0.970390i | \(0.577653\pi\) | |||||||
\(774\) | 22.7120 | 0.816366 | ||||||||
\(775\) | −2.27729 | −0.0818027 | ||||||||
\(776\) | −32.3648 | −1.16183 | ||||||||
\(777\) | −26.9709 | −0.967575 | ||||||||
\(778\) | 21.9204 | 0.785884 | ||||||||
\(779\) | 14.6285 | 0.524119 | ||||||||
\(780\) | 1.95022 | 0.0698290 | ||||||||
\(781\) | 25.8166 | 0.923790 | ||||||||
\(782\) | −20.9731 | −0.749995 | ||||||||
\(783\) | −19.0866 | −0.682099 | ||||||||
\(784\) | 0.414771 | 0.0148133 | ||||||||
\(785\) | −23.0756 | −0.823602 | ||||||||
\(786\) | 11.6306 | 0.414850 | ||||||||
\(787\) | 0.114645 | 0.00408666 | 0.00204333 | − | 0.999998i | \(-0.499350\pi\) | ||||
0.00204333 | + | 0.999998i | \(0.499350\pi\) | |||||||
\(788\) | −50.2885 | −1.79145 | ||||||||
\(789\) | 23.3172 | 0.830115 | ||||||||
\(790\) | −24.9220 | −0.886686 | ||||||||
\(791\) | 25.8011 | 0.917380 | ||||||||
\(792\) | −12.8336 | −0.456023 | ||||||||
\(793\) | 3.57895 | 0.127092 | ||||||||
\(794\) | 1.60822 | 0.0570735 | ||||||||
\(795\) | −12.8456 | −0.455586 | ||||||||
\(796\) | −32.2898 | −1.14448 | ||||||||
\(797\) | 32.5605 | 1.15335 | 0.576676 | − | 0.816973i | \(-0.304350\pi\) | ||||
0.576676 | + | 0.816973i | \(0.304350\pi\) | |||||||
\(798\) | −30.1520 | −1.06737 | ||||||||
\(799\) | −3.26120 | −0.115373 | ||||||||
\(800\) | 3.20011 | 0.113141 | ||||||||
\(801\) | 17.0056 | 0.600863 | ||||||||
\(802\) | −11.1889 | −0.395095 | ||||||||
\(803\) | 4.99746 | 0.176357 | ||||||||
\(804\) | −28.8467 | −1.01734 | ||||||||
\(805\) | 49.1421 | 1.73203 | ||||||||
\(806\) | −1.99423 | −0.0702439 | ||||||||
\(807\) | −26.4487 | −0.931040 | ||||||||
\(808\) | −35.4558 | −1.24733 | ||||||||
\(809\) | 15.3849 | 0.540905 | 0.270453 | − | 0.962733i | \(-0.412827\pi\) | ||||
0.270453 | + | 0.962733i | \(0.412827\pi\) | |||||||
\(810\) | 9.98918 | 0.350984 | ||||||||
\(811\) | −25.5460 | −0.897040 | −0.448520 | − | 0.893773i | \(-0.648049\pi\) | ||||
−0.448520 | + | 0.893773i | \(0.648049\pi\) | |||||||
\(812\) | 37.0263 | 1.29937 | ||||||||
\(813\) | 10.1015 | 0.354277 | ||||||||
\(814\) | −45.1574 | −1.58277 | ||||||||
\(815\) | −27.0952 | −0.949105 | ||||||||
\(816\) | −0.876815 | −0.0306947 | ||||||||
\(817\) | 23.2016 | 0.811720 | ||||||||
\(818\) | 37.8757 | 1.32429 | ||||||||
\(819\) | 1.48106 | 0.0517525 | ||||||||
\(820\) | −23.6425 | −0.825634 | ||||||||
\(821\) | −7.11236 | −0.248223 | −0.124111 | − | 0.992268i | \(-0.539608\pi\) | ||||
−0.124111 | + | 0.992268i | \(0.539608\pi\) | |||||||
\(822\) | −13.1326 | −0.458053 | ||||||||
\(823\) | 18.9835 | 0.661725 | 0.330862 | − | 0.943679i | \(-0.392660\pi\) | ||||
0.330862 | + | 0.943679i | \(0.392660\pi\) | |||||||
\(824\) | 14.2420 | 0.496143 | ||||||||
\(825\) | −1.18878 | −0.0413879 | ||||||||
\(826\) | 72.5712 | 2.52507 | ||||||||
\(827\) | −36.8002 | −1.27967 | −0.639833 | − | 0.768514i | \(-0.720997\pi\) | ||||
−0.639833 | + | 0.768514i | \(0.720997\pi\) | |||||||
\(828\) | 54.0251 | 1.87750 | ||||||||
\(829\) | −40.1162 | −1.39329 | −0.696646 | − | 0.717415i | \(-0.745325\pi\) | ||||
−0.696646 | + | 0.717415i | \(0.745325\pi\) | |||||||
\(830\) | −83.0248 | −2.88183 | ||||||||
\(831\) | −4.52365 | −0.156924 | ||||||||
\(832\) | 3.19826 | 0.110880 | ||||||||
\(833\) | −0.642547 | −0.0222629 | ||||||||
\(834\) | 17.2586 | 0.597616 | ||||||||
\(835\) | −7.30314 | −0.252736 | ||||||||
\(836\) | −31.7969 | −1.09972 | ||||||||
\(837\) | 16.1792 | 0.559235 | ||||||||
\(838\) | 67.7850 | 2.34159 | ||||||||
\(839\) | −13.6474 | −0.471161 | −0.235581 | − | 0.971855i | \(-0.575699\pi\) | ||||
−0.235581 | + | 0.971855i | \(0.575699\pi\) | |||||||
\(840\) | 20.0927 | 0.693263 | ||||||||
\(841\) | −13.2902 | −0.458284 | ||||||||
\(842\) | 69.8999 | 2.40891 | ||||||||
\(843\) | −0.232567 | −0.00801003 | ||||||||
\(844\) | 68.0824 | 2.34349 | ||||||||
\(845\) | 30.8212 | 1.06028 | ||||||||
\(846\) | 13.3376 | 0.458556 | ||||||||
\(847\) | −20.6760 | −0.710437 | ||||||||
\(848\) | 4.43724 | 0.152375 | ||||||||
\(849\) | −22.3977 | −0.768689 | ||||||||
\(850\) | 1.89211 | 0.0648988 | ||||||||
\(851\) | 78.3794 | 2.68681 | ||||||||
\(852\) | −44.4354 | −1.52233 | ||||||||
\(853\) | −21.9685 | −0.752188 | −0.376094 | − | 0.926581i | \(-0.622733\pi\) | ||||
−0.376094 | + | 0.926581i | \(0.622733\pi\) | |||||||
\(854\) | 89.4302 | 3.06024 | ||||||||
\(855\) | 25.2616 | 0.863927 | ||||||||
\(856\) | −22.5348 | −0.770223 | ||||||||
\(857\) | −32.3888 | −1.10638 | −0.553190 | − | 0.833055i | \(-0.686590\pi\) | ||||
−0.553190 | + | 0.833055i | \(0.686590\pi\) | |||||||
\(858\) | −1.04102 | −0.0355397 | ||||||||
\(859\) | −53.0965 | −1.81163 | −0.905815 | − | 0.423673i | \(-0.860741\pi\) | ||||
−0.905815 | + | 0.423673i | \(0.860741\pi\) | |||||||
\(860\) | −37.4984 | −1.27869 | ||||||||
\(861\) | 7.53763 | 0.256882 | ||||||||
\(862\) | −36.0376 | −1.22744 | ||||||||
\(863\) | −43.8757 | −1.49354 | −0.746772 | − | 0.665080i | \(-0.768398\pi\) | ||||
−0.746772 | + | 0.665080i | \(0.768398\pi\) | |||||||
\(864\) | −22.7355 | −0.773476 | ||||||||
\(865\) | 17.6626 | 0.600546 | ||||||||
\(866\) | −44.7255 | −1.51984 | ||||||||
\(867\) | −14.6527 | −0.497633 | ||||||||
\(868\) | −31.3862 | −1.06532 | ||||||||
\(869\) | 8.37902 | 0.284239 | ||||||||
\(870\) | 20.6762 | 0.700988 | ||||||||
\(871\) | 2.29816 | 0.0778702 | ||||||||
\(872\) | −11.0250 | −0.373355 | ||||||||
\(873\) | −20.9668 | −0.709618 | ||||||||
\(874\) | 87.6240 | 2.96393 | ||||||||
\(875\) | 28.2708 | 0.955726 | ||||||||
\(876\) | −8.60161 | −0.290621 | ||||||||
\(877\) | −35.6541 | −1.20395 | −0.601977 | − | 0.798513i | \(-0.705620\pi\) | ||||
−0.601977 | + | 0.798513i | \(0.705620\pi\) | |||||||
\(878\) | −85.8520 | −2.89736 | ||||||||
\(879\) | −19.8724 | −0.670280 | ||||||||
\(880\) | 3.43981 | 0.115956 | ||||||||
\(881\) | 38.2274 | 1.28791 | 0.643956 | − | 0.765062i | \(-0.277292\pi\) | ||||
0.643956 | + | 0.765062i | \(0.277292\pi\) | |||||||
\(882\) | 2.62787 | 0.0884850 | ||||||||
\(883\) | 16.3896 | 0.551553 | 0.275777 | − | 0.961222i | \(-0.411065\pi\) | ||||
0.275777 | + | 0.961222i | \(0.411065\pi\) | |||||||
\(884\) | 1.04361 | 0.0351004 | ||||||||
\(885\) | 25.5246 | 0.857999 | ||||||||
\(886\) | 59.0804 | 1.98484 | ||||||||
\(887\) | −26.0909 | −0.876046 | −0.438023 | − | 0.898964i | \(-0.644321\pi\) | ||||
−0.438023 | + | 0.898964i | \(0.644321\pi\) | |||||||
\(888\) | 32.0469 | 1.07542 | ||||||||
\(889\) | 30.7342 | 1.03079 | ||||||||
\(890\) | −44.5774 | −1.49424 | ||||||||
\(891\) | −3.35845 | −0.112512 | ||||||||
\(892\) | 11.8066 | 0.395313 | ||||||||
\(893\) | 13.6251 | 0.455946 | ||||||||
\(894\) | 7.02891 | 0.235082 | ||||||||
\(895\) | −9.15143 | −0.305899 | ||||||||
\(896\) | 53.9976 | 1.80393 | ||||||||
\(897\) | 1.80688 | 0.0603301 | ||||||||
\(898\) | −18.2743 | −0.609821 | ||||||||
\(899\) | −13.3167 | −0.444138 | ||||||||
\(900\) | −4.87394 | −0.162465 | ||||||||
\(901\) | −6.87399 | −0.229006 | ||||||||
\(902\) | 12.6203 | 0.420209 | ||||||||
\(903\) | 11.9551 | 0.397841 | ||||||||
\(904\) | −30.6569 | −1.01963 | ||||||||
\(905\) | −27.3379 | −0.908744 | ||||||||
\(906\) | −19.5297 | −0.648830 | ||||||||
\(907\) | 30.1941 | 1.00258 | 0.501290 | − | 0.865280i | \(-0.332859\pi\) | ||||
0.501290 | + | 0.865280i | \(0.332859\pi\) | |||||||
\(908\) | 49.6466 | 1.64758 | ||||||||
\(909\) | −22.9692 | −0.761840 | ||||||||
\(910\) | −3.88236 | −0.128699 | ||||||||
\(911\) | −42.4012 | −1.40481 | −0.702406 | − | 0.711776i | \(-0.747891\pi\) | ||||
−0.702406 | + | 0.711776i | \(0.747891\pi\) | |||||||
\(912\) | 3.66327 | 0.121303 | ||||||||
\(913\) | 27.9137 | 0.923808 | ||||||||
\(914\) | 25.8283 | 0.854324 | ||||||||
\(915\) | 31.4542 | 1.03984 | ||||||||
\(916\) | −77.4213 | −2.55807 | ||||||||
\(917\) | −14.5831 | −0.481576 | ||||||||
\(918\) | −13.4426 | −0.443673 | ||||||||
\(919\) | −37.3392 | −1.23171 | −0.615853 | − | 0.787861i | \(-0.711188\pi\) | ||||
−0.615853 | + | 0.787861i | \(0.711188\pi\) | |||||||
\(920\) | −58.3908 | −1.92509 | ||||||||
\(921\) | −14.8228 | −0.488429 | ||||||||
\(922\) | −73.2945 | −2.41383 | ||||||||
\(923\) | 3.54008 | 0.116523 | ||||||||
\(924\) | −16.3840 | −0.538995 | ||||||||
\(925\) | −7.07109 | −0.232496 | ||||||||
\(926\) | 0.217632 | 0.00715183 | ||||||||
\(927\) | 9.22633 | 0.303033 | ||||||||
\(928\) | 18.7131 | 0.614286 | ||||||||
\(929\) | 17.3494 | 0.569214 | 0.284607 | − | 0.958644i | \(-0.408137\pi\) | ||||
0.284607 | + | 0.958644i | \(0.408137\pi\) | |||||||
\(930\) | −17.5266 | −0.574721 | ||||||||
\(931\) | 2.68452 | 0.0879815 | ||||||||
\(932\) | 54.6557 | 1.79031 | ||||||||
\(933\) | −14.3452 | −0.469641 | ||||||||
\(934\) | −10.1907 | −0.333449 | ||||||||
\(935\) | −5.32882 | −0.174271 | ||||||||
\(936\) | −1.75980 | −0.0575209 | ||||||||
\(937\) | 13.7236 | 0.448331 | 0.224165 | − | 0.974551i | \(-0.428034\pi\) | ||||
0.224165 | + | 0.974551i | \(0.428034\pi\) | |||||||
\(938\) | 57.4260 | 1.87503 | ||||||||
\(939\) | −3.42334 | −0.111716 | ||||||||
\(940\) | −22.0209 | −0.718242 | ||||||||
\(941\) | −39.8341 | −1.29855 | −0.649276 | − | 0.760552i | \(-0.724928\pi\) | ||||
−0.649276 | + | 0.760552i | \(0.724928\pi\) | |||||||
\(942\) | −21.2010 | −0.690767 | ||||||||
\(943\) | −21.9049 | −0.713322 | ||||||||
\(944\) | −8.81693 | −0.286967 | ||||||||
\(945\) | 31.4975 | 1.02462 | ||||||||
\(946\) | 20.0165 | 0.650792 | ||||||||
\(947\) | 45.4204 | 1.47596 | 0.737982 | − | 0.674820i | \(-0.235779\pi\) | ||||
0.737982 | + | 0.674820i | \(0.235779\pi\) | |||||||
\(948\) | −14.4219 | −0.468403 | ||||||||
\(949\) | 0.685273 | 0.0222449 | ||||||||
\(950\) | −7.90510 | −0.256475 | ||||||||
\(951\) | −20.9347 | −0.678855 | ||||||||
\(952\) | 10.7521 | 0.348477 | ||||||||
\(953\) | 44.3724 | 1.43736 | 0.718682 | − | 0.695339i | \(-0.244746\pi\) | ||||
0.718682 | + | 0.695339i | \(0.244746\pi\) | |||||||
\(954\) | 28.1131 | 0.910194 | ||||||||
\(955\) | −20.8967 | −0.676202 | ||||||||
\(956\) | −21.7745 | −0.704237 | ||||||||
\(957\) | −6.95152 | −0.224711 | ||||||||
\(958\) | −9.15864 | −0.295902 | ||||||||
\(959\) | 16.4664 | 0.531729 | ||||||||
\(960\) | 28.1084 | 0.907195 | ||||||||
\(961\) | −19.7118 | −0.635863 | ||||||||
\(962\) | −6.19218 | −0.199644 | ||||||||
\(963\) | −14.5986 | −0.470434 | ||||||||
\(964\) | 18.2607 | 0.588138 | ||||||||
\(965\) | −34.0891 | −1.09737 | ||||||||
\(966\) | 45.1501 | 1.45268 | ||||||||
\(967\) | 23.9029 | 0.768667 | 0.384333 | − | 0.923194i | \(-0.374431\pi\) | ||||
0.384333 | + | 0.923194i | \(0.374431\pi\) | |||||||
\(968\) | 24.5673 | 0.789625 | ||||||||
\(969\) | −5.67500 | −0.182307 | ||||||||
\(970\) | 54.9609 | 1.76469 | ||||||||
\(971\) | 13.9630 | 0.448095 | 0.224047 | − | 0.974578i | \(-0.428073\pi\) | ||||
0.224047 | + | 0.974578i | \(0.428073\pi\) | |||||||
\(972\) | 54.9447 | 1.76235 | ||||||||
\(973\) | −21.6398 | −0.693740 | ||||||||
\(974\) | 50.7420 | 1.62588 | ||||||||
\(975\) | −0.163010 | −0.00522050 | ||||||||
\(976\) | −10.8652 | −0.347787 | ||||||||
\(977\) | 12.3442 | 0.394925 | 0.197462 | − | 0.980310i | \(-0.436730\pi\) | ||||
0.197462 | + | 0.980310i | \(0.436730\pi\) | |||||||
\(978\) | −24.8942 | −0.796028 | ||||||||
\(979\) | 14.9873 | 0.478997 | ||||||||
\(980\) | −4.33872 | −0.138595 | ||||||||
\(981\) | −7.14230 | −0.228036 | ||||||||
\(982\) | −71.4840 | −2.28115 | ||||||||
\(983\) | 36.0663 | 1.15034 | 0.575168 | − | 0.818035i | \(-0.304937\pi\) | ||||
0.575168 | + | 0.818035i | \(0.304937\pi\) | |||||||
\(984\) | −8.95623 | −0.285514 | ||||||||
\(985\) | 35.2108 | 1.12191 | ||||||||
\(986\) | 11.0643 | 0.352360 | ||||||||
\(987\) | 7.02062 | 0.223469 | ||||||||
\(988\) | −4.36013 | −0.138714 | ||||||||
\(989\) | −34.7424 | −1.10475 | ||||||||
\(990\) | 21.7937 | 0.692648 | ||||||||
\(991\) | −31.2015 | −0.991147 | −0.495574 | − | 0.868566i | \(-0.665042\pi\) | ||||
−0.495574 | + | 0.868566i | \(0.665042\pi\) | |||||||
\(992\) | −15.8626 | −0.503637 | ||||||||
\(993\) | 24.0425 | 0.762967 | ||||||||
\(994\) | 88.4589 | 2.80575 | ||||||||
\(995\) | 22.6085 | 0.716738 | ||||||||
\(996\) | −48.0449 | −1.52236 | ||||||||
\(997\) | −26.0238 | −0.824181 | −0.412091 | − | 0.911143i | \(-0.635201\pi\) | ||||
−0.412091 | + | 0.911143i | \(0.635201\pi\) | |||||||
\(998\) | −20.1918 | −0.639162 | ||||||||
\(999\) | 50.2371 | 1.58943 |
(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 | 619.2.a.a.1.4 | ✓ | 21 | |
3.2 | odd | 2 | 5571.2.a.e.1.18 | 21 | |||
4.3 | odd | 2 | 9904.2.a.j.1.7 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
619.2.a.a.1.4 | ✓ | 21 | 1.1 | even | 1 | trivial | |
5571.2.a.e.1.18 | 21 | 3.2 | odd | 2 | |||
9904.2.a.j.1.7 | 21 | 4.3 | odd | 2 |