Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.230149 | −0.162740 | −0.0813700 | − | 0.996684i | \(-0.525930\pi\) | ||||
−0.0813700 | + | 0.996684i | \(0.525930\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94703 | −0.973516 | ||||||||
\(5\) | 2.59479 | 1.16042 | 0.580212 | − | 0.814466i | \(-0.302970\pi\) | ||||
0.580212 | + | 0.814466i | \(0.302970\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.77655 | −1.80537 | −0.902683 | − | 0.430307i | \(-0.858405\pi\) | ||||
−0.902683 | + | 0.430307i | \(0.858405\pi\) | |||||||
\(8\) | 0.908406 | 0.321170 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.597188 | −0.188847 | ||||||||
\(11\) | −3.70131 | −1.11599 | −0.557994 | − | 0.829845i | \(-0.688429\pi\) | ||||
−0.557994 | + | 0.829845i | \(0.688429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.06512 | −0.850112 | −0.425056 | − | 0.905167i | \(-0.639746\pi\) | ||||
−0.425056 | + | 0.905167i | \(0.639746\pi\) | |||||||
\(14\) | 1.09932 | 0.293805 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.68499 | 0.921248 | ||||||||
\(17\) | 3.40309 | 0.825370 | 0.412685 | − | 0.910874i | \(-0.364591\pi\) | ||||
0.412685 | + | 0.910874i | \(0.364591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00538 | 1.14831 | 0.574157 | − | 0.818745i | \(-0.305330\pi\) | ||||
0.574157 | + | 0.818745i | \(0.305330\pi\) | |||||||
\(20\) | −5.05213 | −1.12969 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.851854 | 0.181616 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.73291 | 0.346582 | ||||||||
\(26\) | 0.705435 | 0.138347 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.30009 | 1.75755 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.71761 | 1.20652 | 0.603259 | − | 0.797545i | \(-0.293869\pi\) | ||||
0.603259 | + | 0.797545i | \(0.293869\pi\) | |||||||
\(32\) | −2.66491 | −0.471094 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.783218 | −0.134321 | ||||||||
\(35\) | −12.3941 | −2.09499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.21966 | 0.200511 | 0.100256 | − | 0.994962i | \(-0.468034\pi\) | ||||
0.100256 | + | 0.994962i | \(0.468034\pi\) | |||||||
\(38\) | −1.15198 | −0.186877 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.35712 | 0.372693 | ||||||||
\(41\) | −8.51699 | −1.33013 | −0.665065 | − | 0.746785i | \(-0.731596\pi\) | ||||
−0.665065 | + | 0.746785i | \(0.731596\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.34577 | 1.27272 | 0.636359 | − | 0.771393i | \(-0.280440\pi\) | ||||
0.636359 | + | 0.771393i | \(0.280440\pi\) | |||||||
\(44\) | 7.20657 | 1.08643 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.230149 | −0.0339336 | ||||||||
\(47\) | 3.13922 | 0.457903 | 0.228951 | − | 0.973438i | \(-0.426470\pi\) | ||||
0.228951 | + | 0.973438i | \(0.426470\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.8154 | 2.25934 | ||||||||
\(50\) | −0.398828 | −0.0564028 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.96789 | 0.827597 | ||||||||
\(53\) | 6.13173 | 0.842258 | 0.421129 | − | 0.907001i | \(-0.361634\pi\) | ||||
0.421129 | + | 0.907001i | \(0.361634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.60411 | −1.29502 | ||||||||
\(56\) | −4.33904 | −0.579829 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.230149 | −0.0302201 | ||||||||
\(59\) | −3.83602 | −0.499408 | −0.249704 | − | 0.968322i | \(-0.580333\pi\) | ||||
−0.249704 | + | 0.968322i | \(0.580333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.39205 | 0.434307 | 0.217154 | − | 0.976137i | \(-0.430323\pi\) | ||||
0.217154 | + | 0.976137i | \(0.430323\pi\) | |||||||
\(62\) | −1.54605 | −0.196349 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.75666 | −0.844583 | ||||||||
\(65\) | −7.95333 | −0.986490 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.42070 | 0.173566 | 0.0867830 | − | 0.996227i | \(-0.472341\pi\) | ||||
0.0867830 | + | 0.996227i | \(0.472341\pi\) | |||||||
\(68\) | −6.62592 | −0.803511 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.85250 | 0.340938 | ||||||||
\(71\) | −1.21273 | −0.143925 | −0.0719626 | − | 0.997407i | \(-0.522926\pi\) | ||||
−0.0719626 | + | 0.997407i | \(0.522926\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.66204 | −1.01382 | −0.506908 | − | 0.862000i | \(-0.669212\pi\) | ||||
−0.506908 | + | 0.862000i | \(0.669212\pi\) | |||||||
\(74\) | −0.280704 | −0.0326312 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −9.74564 | −1.11790 | ||||||||
\(77\) | 17.6795 | 2.01477 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2141 | −1.37419 | −0.687095 | − | 0.726567i | \(-0.741115\pi\) | ||||
−0.687095 | + | 0.726567i | \(0.741115\pi\) | |||||||
\(80\) | 9.56177 | 1.06904 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.96018 | 0.216465 | ||||||||
\(83\) | 14.6713 | 1.61038 | 0.805192 | − | 0.593014i | \(-0.202062\pi\) | ||||
0.805192 | + | 0.593014i | \(0.202062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.83029 | 0.957779 | ||||||||
\(86\) | −1.92077 | −0.207122 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.36229 | −0.358422 | ||||||||
\(89\) | −10.8906 | −1.15440 | −0.577198 | − | 0.816604i | \(-0.695854\pi\) | ||||
−0.577198 | + | 0.816604i | \(0.695854\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.6407 | 1.53476 | ||||||||
\(92\) | −1.94703 | −0.202992 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.722489 | −0.0745191 | ||||||||
\(95\) | 12.9879 | 1.33253 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.64503 | −0.167027 | −0.0835137 | − | 0.996507i | \(-0.526614\pi\) | ||||
−0.0835137 | + | 0.996507i | \(0.526614\pi\) | |||||||
\(98\) | −3.63990 | −0.367686 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.37403 | −0.337403 | ||||||||
\(101\) | −18.2082 | −1.81178 | −0.905890 | − | 0.423512i | \(-0.860797\pi\) | ||||
−0.905890 | + | 0.423512i | \(0.860797\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.91947 | −0.780329 | −0.390164 | − | 0.920745i | \(-0.627582\pi\) | ||||
−0.390164 | + | 0.920745i | \(0.627582\pi\) | |||||||
\(104\) | −2.78437 | −0.273030 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.41121 | −0.137069 | ||||||||
\(107\) | 10.1399 | 0.980259 | 0.490130 | − | 0.871650i | \(-0.336949\pi\) | ||||
0.490130 | + | 0.871650i | \(0.336949\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.2734 | −1.75027 | −0.875137 | − | 0.483874i | \(-0.839229\pi\) | ||||
−0.875137 | + | 0.483874i | \(0.839229\pi\) | |||||||
\(110\) | 2.21038 | 0.210751 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −17.6015 | −1.66319 | ||||||||
\(113\) | −8.88638 | −0.835961 | −0.417980 | − | 0.908456i | \(-0.637262\pi\) | ||||
−0.417980 | + | 0.908456i | \(0.637262\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.59479 | 0.241965 | ||||||||
\(116\) | −1.94703 | −0.180777 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.882858 | 0.0812737 | ||||||||
\(119\) | −16.2550 | −1.49009 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.69971 | 0.245428 | ||||||||
\(122\) | −0.780677 | −0.0706791 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.0794 | −1.17456 | ||||||||
\(125\) | −8.47739 | −0.758241 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.25291 | 0.821063 | 0.410532 | − | 0.911846i | \(-0.365343\pi\) | ||||
0.410532 | + | 0.911846i | \(0.365343\pi\) | |||||||
\(128\) | 6.88486 | 0.608541 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.83045 | 0.160541 | ||||||||
\(131\) | 3.01107 | 0.263078 | 0.131539 | − | 0.991311i | \(-0.458008\pi\) | ||||
0.131539 | + | 0.991311i | \(0.458008\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −23.9085 | −2.07313 | ||||||||
\(134\) | −0.326972 | −0.0282461 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.09139 | 0.265084 | ||||||||
\(137\) | −14.1358 | −1.20770 | −0.603850 | − | 0.797098i | \(-0.706367\pi\) | ||||
−0.603850 | + | 0.797098i | \(0.706367\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.05151 | 0.598101 | 0.299051 | − | 0.954237i | \(-0.403330\pi\) | ||||
0.299051 | + | 0.954237i | \(0.403330\pi\) | |||||||
\(140\) | 24.1317 | 2.03950 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.279110 | 0.0234224 | ||||||||
\(143\) | 11.3450 | 0.948714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.59479 | 0.215485 | ||||||||
\(146\) | 1.99356 | 0.164988 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.37472 | −0.195201 | ||||||||
\(149\) | −8.33724 | −0.683013 | −0.341507 | − | 0.939879i | \(-0.610937\pi\) | ||||
−0.341507 | + | 0.939879i | \(0.610937\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0416 | −0.817170 | −0.408585 | − | 0.912720i | \(-0.633978\pi\) | ||||
−0.408585 | + | 0.912720i | \(0.633978\pi\) | |||||||
\(152\) | 4.54692 | 0.368804 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.06892 | −0.327883 | ||||||||
\(155\) | 17.4308 | 1.40007 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.30825 | −0.264027 | −0.132014 | − | 0.991248i | \(-0.542144\pi\) | ||||
−0.132014 | + | 0.991248i | \(0.542144\pi\) | |||||||
\(158\) | 2.81106 | 0.223636 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.91487 | −0.546668 | ||||||||
\(161\) | −4.77655 | −0.376445 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.69369 | −0.132660 | −0.0663301 | − | 0.997798i | \(-0.521129\pi\) | ||||
−0.0663301 | + | 0.997798i | \(0.521129\pi\) | |||||||
\(164\) | 16.5828 | 1.29490 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.37659 | −0.262074 | ||||||||
\(167\) | −4.53024 | −0.350561 | −0.175280 | − | 0.984519i | \(-0.556083\pi\) | ||||
−0.175280 | + | 0.984519i | \(0.556083\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.60503 | −0.277310 | ||||||||
\(170\) | −2.03228 | −0.155869 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.2495 | −1.23901 | ||||||||
\(173\) | −21.7611 | −1.65447 | −0.827234 | − | 0.561858i | \(-0.810087\pi\) | ||||
−0.827234 | + | 0.561858i | \(0.810087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.27734 | −0.625708 | ||||||||
\(176\) | −13.6393 | −1.02810 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.50645 | 0.187866 | ||||||||
\(179\) | 20.8274 | 1.55671 | 0.778357 | − | 0.627822i | \(-0.216053\pi\) | ||||
0.778357 | + | 0.627822i | \(0.216053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.54612 | −0.486569 | −0.243285 | − | 0.969955i | \(-0.578225\pi\) | ||||
−0.243285 | + | 0.969955i | \(0.578225\pi\) | |||||||
\(182\) | −3.36954 | −0.249767 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.908406 | 0.0669686 | ||||||||
\(185\) | 3.16476 | 0.232678 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.5959 | −0.921103 | ||||||||
\(188\) | −6.11216 | −0.445775 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.98915 | −0.216856 | ||||||||
\(191\) | −21.0972 | −1.52654 | −0.763271 | − | 0.646078i | \(-0.776408\pi\) | ||||
−0.763271 | + | 0.646078i | \(0.776408\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.55042 | 0.399528 | 0.199764 | − | 0.979844i | \(-0.435982\pi\) | ||||
0.199764 | + | 0.979844i | \(0.435982\pi\) | |||||||
\(194\) | 0.378602 | 0.0271820 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.7931 | −2.19951 | ||||||||
\(197\) | 20.1657 | 1.43674 | 0.718372 | − | 0.695659i | \(-0.244888\pi\) | ||||
0.718372 | + | 0.695659i | \(0.244888\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.4093 | −1.65944 | −0.829719 | − | 0.558181i | \(-0.811500\pi\) | ||||
−0.829719 | + | 0.558181i | \(0.811500\pi\) | |||||||
\(200\) | 1.57419 | 0.111312 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.19060 | 0.294849 | ||||||||
\(203\) | −4.77655 | −0.335248 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −22.0998 | −1.54351 | ||||||||
\(206\) | 1.82266 | 0.126991 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −11.2950 | −0.783164 | ||||||||
\(209\) | −18.5265 | −1.28150 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.1869 | 1.80278 | 0.901391 | − | 0.433007i | \(-0.142547\pi\) | ||||
0.901391 | + | 0.433007i | \(0.142547\pi\) | |||||||
\(212\) | −11.9387 | −0.819952 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.33369 | −0.159527 | ||||||||
\(215\) | 21.6555 | 1.47689 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −32.0870 | −2.17821 | ||||||||
\(218\) | 4.20561 | 0.284840 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18.6995 | 1.26072 | ||||||||
\(221\) | −10.4309 | −0.701657 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.4965 | −0.970755 | −0.485378 | − | 0.874305i | \(-0.661318\pi\) | ||||
−0.485378 | + | 0.874305i | \(0.661318\pi\) | |||||||
\(224\) | 12.7291 | 0.850497 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.04519 | 0.136044 | ||||||||
\(227\) | −13.7819 | −0.914738 | −0.457369 | − | 0.889277i | \(-0.651208\pi\) | ||||
−0.457369 | + | 0.889277i | \(0.651208\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.3057 | 1.80441 | 0.902207 | − | 0.431303i | \(-0.141946\pi\) | ||||
0.902207 | + | 0.431303i | \(0.141946\pi\) | |||||||
\(230\) | −0.597188 | −0.0393774 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.908406 | 0.0596398 | ||||||||
\(233\) | −8.33427 | −0.545996 | −0.272998 | − | 0.962015i | \(-0.588015\pi\) | ||||
−0.272998 | + | 0.962015i | \(0.588015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.14561 | 0.531361 | ||||||||
\(236\) | 7.46886 | 0.486181 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.74108 | 0.242498 | ||||||||
\(239\) | 21.1215 | 1.36624 | 0.683119 | − | 0.730307i | \(-0.260623\pi\) | ||||
0.683119 | + | 0.730307i | \(0.260623\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.71214 | −0.432367 | −0.216184 | − | 0.976353i | \(-0.569361\pi\) | ||||
−0.216184 | + | 0.976353i | \(0.569361\pi\) | |||||||
\(242\) | −0.621336 | −0.0399410 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.60442 | −0.422805 | ||||||||
\(245\) | 41.0376 | 2.62180 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.3421 | −0.976195 | ||||||||
\(248\) | 6.10231 | 0.387497 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.95106 | 0.123396 | ||||||||
\(251\) | 23.6023 | 1.48976 | 0.744882 | − | 0.667197i | \(-0.232506\pi\) | ||||
0.744882 | + | 0.667197i | \(0.232506\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.70131 | −0.232699 | ||||||||
\(254\) | −2.12955 | −0.133620 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.9288 | 0.745549 | ||||||||
\(257\) | −11.8463 | −0.738955 | −0.369477 | − | 0.929240i | \(-0.620463\pi\) | ||||
−0.369477 | + | 0.929240i | \(0.620463\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.82578 | −0.361996 | ||||||||
\(260\) | 15.4854 | 0.960363 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.692995 | −0.0428134 | ||||||||
\(263\) | 3.24225 | 0.199926 | 0.0999630 | − | 0.994991i | \(-0.468128\pi\) | ||||
0.0999630 | + | 0.994991i | \(0.468128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9105 | 0.977376 | ||||||||
\(266\) | 5.50251 | 0.337381 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.76614 | −0.168969 | ||||||||
\(269\) | 3.56842 | 0.217570 | 0.108785 | − | 0.994065i | \(-0.465304\pi\) | ||||
0.108785 | + | 0.994065i | \(0.465304\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.17978 | 0.375395 | 0.187697 | − | 0.982227i | \(-0.439898\pi\) | ||||
0.187697 | + | 0.982227i | \(0.439898\pi\) | |||||||
\(272\) | 12.5404 | 0.760371 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.25333 | 0.196541 | ||||||||
\(275\) | −6.41405 | −0.386782 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.3224 | 1.22106 | 0.610529 | − | 0.791994i | \(-0.290957\pi\) | ||||
0.610529 | + | 0.791994i | \(0.290957\pi\) | |||||||
\(278\) | −1.62290 | −0.0973350 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −11.2589 | −0.672847 | ||||||||
\(281\) | 2.07151 | 0.123576 | 0.0617880 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617880 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.58757 | −0.332147 | −0.166073 | − | 0.986113i | \(-0.553109\pi\) | ||||
−0.166073 | + | 0.986113i | \(0.553109\pi\) | |||||||
\(284\) | 2.36123 | 0.140113 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.61104 | −0.154394 | ||||||||
\(287\) | 40.6818 | 2.40137 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.41898 | −0.318764 | ||||||||
\(290\) | −0.597188 | −0.0350681 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 16.8653 | 0.986965 | ||||||||
\(293\) | 17.7965 | 1.03969 | 0.519843 | − | 0.854262i | \(-0.325991\pi\) | ||||
0.519843 | + | 0.854262i | \(0.325991\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.95366 | −0.579525 | ||||||||
\(296\) | 1.10795 | 0.0643982 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.91881 | 0.111154 | ||||||||
\(299\) | −3.06512 | −0.177261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −39.8640 | −2.29772 | ||||||||
\(302\) | 2.31105 | 0.132986 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.4448 | 1.05788 | ||||||||
\(305\) | 8.80163 | 0.503980 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.7399 | −0.784180 | −0.392090 | − | 0.919927i | \(-0.628248\pi\) | ||||
−0.392090 | + | 0.919927i | \(0.628248\pi\) | |||||||
\(308\) | −34.4225 | −1.96141 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.01167 | −0.227848 | ||||||||
\(311\) | 5.10837 | 0.289669 | 0.144835 | − | 0.989456i | \(-0.453735\pi\) | ||||
0.144835 | + | 0.989456i | \(0.453735\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −31.5536 | −1.78351 | −0.891756 | − | 0.452516i | \(-0.850527\pi\) | ||||
−0.891756 | + | 0.452516i | \(0.850527\pi\) | |||||||
\(314\) | 0.761391 | 0.0429678 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.7812 | 1.33780 | ||||||||
\(317\) | 6.59462 | 0.370391 | 0.185195 | − | 0.982702i | \(-0.440708\pi\) | ||||
0.185195 | + | 0.982702i | \(0.440708\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.70131 | −0.207234 | ||||||||
\(320\) | −17.5321 | −0.980073 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.09932 | 0.0612626 | ||||||||
\(323\) | 17.0338 | 0.947784 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.31159 | −0.294634 | ||||||||
\(326\) | 0.389802 | 0.0215891 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.73688 | −0.427198 | ||||||||
\(329\) | −14.9946 | −0.826681 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.9553 | −0.931947 | −0.465974 | − | 0.884799i | \(-0.654296\pi\) | ||||
−0.465974 | + | 0.884799i | \(0.654296\pi\) | |||||||
\(332\) | −28.5655 | −1.56773 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.04263 | 0.0570502 | ||||||||
\(335\) | 3.68641 | 0.201410 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.3791 | 1.49143 | 0.745717 | − | 0.666263i | \(-0.232107\pi\) | ||||
0.745717 | + | 0.666263i | \(0.232107\pi\) | |||||||
\(338\) | 0.829694 | 0.0451294 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −17.1928 | −0.932413 | ||||||||
\(341\) | −24.8640 | −1.34646 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −42.1072 | −2.27358 | ||||||||
\(344\) | 7.58135 | 0.408759 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.00830 | 0.269248 | ||||||||
\(347\) | −2.62438 | −0.140884 | −0.0704421 | − | 0.997516i | \(-0.522441\pi\) | ||||
−0.0704421 | + | 0.997516i | \(0.522441\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.65979 | 0.356490 | 0.178245 | − | 0.983986i | \(-0.442958\pi\) | ||||
0.178245 | + | 0.983986i | \(0.442958\pi\) | |||||||
\(350\) | 1.90502 | 0.101828 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.86366 | 0.525735 | ||||||||
\(353\) | −3.89509 | −0.207315 | −0.103657 | − | 0.994613i | \(-0.533055\pi\) | ||||
−0.103657 | + | 0.994613i | \(0.533055\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.14679 | −0.167014 | ||||||||
\(356\) | 21.2042 | 1.12382 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.79341 | −0.253340 | ||||||||
\(359\) | 13.3307 | 0.703565 | 0.351783 | − | 0.936082i | \(-0.385576\pi\) | ||||
0.351783 | + | 0.936082i | \(0.385576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.05387 | 0.318625 | ||||||||
\(362\) | 1.50658 | 0.0791843 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −28.5059 | −1.49412 | ||||||||
\(365\) | −22.4761 | −1.17646 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.83274 | −0.0956684 | −0.0478342 | − | 0.998855i | \(-0.515232\pi\) | ||||
−0.0478342 | + | 0.998855i | \(0.515232\pi\) | |||||||
\(368\) | 3.68499 | 0.192094 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.728368 | −0.0378660 | ||||||||
\(371\) | −29.2885 | −1.52058 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −37.0251 | −1.91709 | −0.958544 | − | 0.284945i | \(-0.908025\pi\) | ||||
−0.958544 | + | 0.284945i | \(0.908025\pi\) | |||||||
\(374\) | 2.89893 | 0.149900 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.85169 | 0.147065 | ||||||||
\(377\) | −3.06512 | −0.157862 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.53785 | 0.438560 | 0.219280 | − | 0.975662i | \(-0.429629\pi\) | ||||
0.219280 | + | 0.975662i | \(0.429629\pi\) | |||||||
\(380\) | −25.2878 | −1.29724 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 4.85551 | 0.248430 | ||||||||
\(383\) | −18.2560 | −0.932841 | −0.466420 | − | 0.884563i | \(-0.654457\pi\) | ||||
−0.466420 | + | 0.884563i | \(0.654457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.8745 | 2.33798 | ||||||||
\(386\) | −1.27743 | −0.0650192 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.20292 | 0.162604 | ||||||||
\(389\) | −19.6829 | −0.997965 | −0.498983 | − | 0.866612i | \(-0.666293\pi\) | ||||
−0.498983 | + | 0.866612i | \(0.666293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.40309 | 0.172102 | ||||||||
\(392\) | 14.3668 | 0.725633 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.64111 | −0.233816 | ||||||||
\(395\) | −31.6929 | −1.59464 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.39049 | −0.0697869 | −0.0348934 | − | 0.999391i | \(-0.511109\pi\) | ||||
−0.0348934 | + | 0.999391i | \(0.511109\pi\) | |||||||
\(398\) | 5.38762 | 0.270057 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.38577 | 0.319289 | ||||||||
\(401\) | 5.28138 | 0.263739 | 0.131870 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131870 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.5903 | −1.02568 | ||||||||
\(404\) | 35.4519 | 1.76380 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.09932 | 0.0545583 | ||||||||
\(407\) | −4.51435 | −0.223768 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.95248 | 0.195438 | 0.0977188 | − | 0.995214i | \(-0.468845\pi\) | ||||
0.0977188 | + | 0.995214i | \(0.468845\pi\) | |||||||
\(410\) | 5.08624 | 0.251192 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 15.4195 | 0.759662 | ||||||||
\(413\) | 18.3230 | 0.901614 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.0689 | 1.86873 | ||||||||
\(416\) | 8.16827 | 0.400483 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.26386 | 0.208552 | ||||||||
\(419\) | −6.29691 | −0.307624 | −0.153812 | − | 0.988100i | \(-0.549155\pi\) | ||||
−0.153812 | + | 0.988100i | \(0.549155\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.87154 | 0.237424 | 0.118712 | − | 0.992929i | \(-0.462123\pi\) | ||||
0.118712 | + | 0.992929i | \(0.462123\pi\) | |||||||
\(422\) | −6.02690 | −0.293385 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.57010 | 0.270508 | ||||||||
\(425\) | 5.89725 | 0.286059 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.2023 | −0.784083 | ||||||||
\(428\) | −19.7427 | −0.954298 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.98399 | −0.240349 | ||||||||
\(431\) | −24.0540 | −1.15864 | −0.579321 | − | 0.815100i | \(-0.696682\pi\) | ||||
−0.579321 | + | 0.815100i | \(0.696682\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.1836 | −0.969961 | −0.484980 | − | 0.874525i | \(-0.661173\pi\) | ||||
−0.484980 | + | 0.874525i | \(0.661173\pi\) | |||||||
\(434\) | 7.38479 | 0.354481 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 35.5789 | 1.70392 | ||||||||
\(437\) | 5.00538 | 0.239440 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.4320 | −1.26153 | −0.630766 | − | 0.775973i | \(-0.717259\pi\) | ||||
−0.630766 | + | 0.775973i | \(0.717259\pi\) | |||||||
\(440\) | −8.72443 | −0.415921 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.40066 | 0.114188 | ||||||||
\(443\) | −31.8533 | −1.51339 | −0.756697 | − | 0.653765i | \(-0.773188\pi\) | ||||
−0.756697 | + | 0.653765i | \(0.773188\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.2586 | −1.33959 | ||||||||
\(446\) | 3.33635 | 0.157981 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 32.2735 | 1.52478 | ||||||||
\(449\) | 29.9464 | 1.41326 | 0.706629 | − | 0.707584i | \(-0.250215\pi\) | ||||
0.706629 | + | 0.707584i | \(0.250215\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.5240 | 1.48441 | ||||||||
\(452\) | 17.3021 | 0.813821 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.17190 | 0.148864 | ||||||||
\(455\) | 37.9895 | 1.78097 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.3812 | −1.09373 | −0.546864 | − | 0.837221i | \(-0.684179\pi\) | ||||
−0.546864 | + | 0.837221i | \(0.684179\pi\) | |||||||
\(458\) | −6.28439 | −0.293650 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.05213 | −0.235557 | ||||||||
\(461\) | 3.01774 | 0.140550 | 0.0702751 | − | 0.997528i | \(-0.477612\pi\) | ||||
0.0702751 | + | 0.997528i | \(0.477612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.43464 | −0.113147 | −0.0565736 | − | 0.998398i | \(-0.518018\pi\) | ||||
−0.0565736 | + | 0.998398i | \(0.518018\pi\) | |||||||
\(464\) | 3.68499 | 0.171072 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.91812 | 0.0888554 | ||||||||
\(467\) | 6.71105 | 0.310551 | 0.155275 | − | 0.987871i | \(-0.450374\pi\) | ||||
0.155275 | + | 0.987871i | \(0.450374\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.78603 | −0.313350 | ||||||||
\(470\) | −1.87470 | −0.0864737 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.48467 | −0.160395 | ||||||||
\(473\) | −30.8903 | −1.42034 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.67389 | 0.397985 | ||||||||
\(476\) | 31.6490 | 1.45063 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.86110 | −0.222342 | ||||||||
\(479\) | 33.6174 | 1.53602 | 0.768008 | − | 0.640440i | \(-0.221248\pi\) | ||||
0.768008 | + | 0.640440i | \(0.221248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.73842 | −0.170457 | ||||||||
\(482\) | 1.54479 | 0.0703634 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.25642 | −0.238928 | ||||||||
\(485\) | −4.26850 | −0.193822 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.3802 | −1.01414 | −0.507072 | − | 0.861904i | \(-0.669272\pi\) | ||||
−0.507072 | + | 0.861904i | \(0.669272\pi\) | |||||||
\(488\) | 3.08135 | 0.139486 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −9.44477 | −0.426671 | ||||||||
\(491\) | 13.3390 | 0.601983 | 0.300991 | − | 0.953627i | \(-0.402682\pi\) | ||||
0.300991 | + | 0.953627i | \(0.402682\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.40309 | 0.153267 | ||||||||
\(494\) | 3.53097 | 0.158866 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.7543 | 1.11150 | ||||||||
\(497\) | 5.79269 | 0.259837 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.5475 | −0.696001 | −0.348000 | − | 0.937494i | \(-0.613139\pi\) | ||||
−0.348000 | + | 0.937494i | \(0.613139\pi\) | |||||||
\(500\) | 16.5057 | 0.738160 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.43205 | −0.242444 | ||||||||
\(503\) | −25.5361 | −1.13860 | −0.569300 | − | 0.822130i | \(-0.692786\pi\) | ||||
−0.569300 | + | 0.822130i | \(0.692786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −47.2463 | −2.10243 | ||||||||
\(506\) | 0.851854 | 0.0378695 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.0157 | −0.799318 | ||||||||
\(509\) | 10.4831 | 0.464653 | 0.232327 | − | 0.972638i | \(-0.425366\pi\) | ||||
0.232327 | + | 0.972638i | \(0.425366\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 41.3747 | 1.83031 | ||||||||
\(512\) | −16.5151 | −0.729872 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.72643 | 0.120257 | ||||||||
\(515\) | −20.5493 | −0.905512 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6192 | −0.511013 | ||||||||
\(518\) | 1.34080 | 0.0589113 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.22486 | −0.316831 | ||||||||
\(521\) | −13.6878 | −0.599673 | −0.299836 | − | 0.953991i | \(-0.596932\pi\) | ||||
−0.299836 | + | 0.953991i | \(0.596932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.86730 | 0.300286 | 0.150143 | − | 0.988664i | \(-0.452027\pi\) | ||||
0.150143 | + | 0.988664i | \(0.452027\pi\) | |||||||
\(524\) | −5.86265 | −0.256111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.746202 | −0.0325360 | ||||||||
\(527\) | 22.8606 | 0.995824 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −3.66180 | −0.159058 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 46.5505 | 2.01822 | ||||||||
\(533\) | 26.1056 | 1.13076 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.3108 | 1.13752 | ||||||||
\(536\) | 1.29057 | 0.0557442 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.821268 | −0.0354074 | ||||||||
\(539\) | −58.5377 | −2.52140 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8009 | 0.550355 | 0.275178 | − | 0.961393i | \(-0.411263\pi\) | ||||
0.275178 | + | 0.961393i | \(0.411263\pi\) | |||||||
\(542\) | −1.42227 | −0.0610917 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.06893 | −0.388827 | ||||||||
\(545\) | −47.4156 | −2.03106 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.3728 | 1.59794 | 0.798972 | − | 0.601368i | \(-0.205377\pi\) | ||||
0.798972 | + | 0.601368i | \(0.205377\pi\) | |||||||
\(548\) | 27.5228 | 1.17571 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.47619 | 0.0629449 | ||||||||
\(551\) | 5.00538 | 0.213237 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 58.3411 | 2.48092 | ||||||||
\(554\) | −4.67719 | −0.198715 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.7295 | −0.582261 | ||||||||
\(557\) | −35.1787 | −1.49057 | −0.745286 | − | 0.666745i | \(-0.767687\pi\) | ||||
−0.745286 | + | 0.666745i | \(0.767687\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.5808 | −1.08195 | ||||||||
\(560\) | −45.6722 | −1.93000 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.476757 | −0.0201108 | ||||||||
\(563\) | −26.0407 | −1.09749 | −0.548743 | − | 0.835991i | \(-0.684894\pi\) | ||||
−0.548743 | + | 0.835991i | \(0.684894\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.0583 | −0.970068 | ||||||||
\(566\) | 1.28597 | 0.0540535 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.10166 | −0.0462244 | ||||||||
\(569\) | −17.4792 | −0.732767 | −0.366383 | − | 0.930464i | \(-0.619404\pi\) | ||||
−0.366383 | + | 0.930464i | \(0.619404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.05298 | 0.337007 | 0.168503 | − | 0.985701i | \(-0.446107\pi\) | ||||
0.168503 | + | 0.985701i | \(0.446107\pi\) | |||||||
\(572\) | −22.0890 | −0.923588 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.36288 | −0.390799 | ||||||||
\(575\) | 1.73291 | 0.0722674 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.1194 | −1.58693 | −0.793466 | − | 0.608614i | \(-0.791726\pi\) | ||||
−0.793466 | + | 0.608614i | \(0.791726\pi\) | |||||||
\(578\) | 1.24717 | 0.0518756 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.05213 | −0.209778 | ||||||||
\(581\) | −70.0782 | −2.90733 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6955 | −0.939950 | ||||||||
\(584\) | −7.86865 | −0.325607 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.09586 | −0.169198 | ||||||||
\(587\) | −31.8205 | −1.31337 | −0.656687 | − | 0.754163i | \(-0.728043\pi\) | ||||
−0.656687 | + | 0.754163i | \(0.728043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 33.6242 | 1.38546 | ||||||||
\(590\) | 2.29083 | 0.0943118 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.49445 | 0.184721 | ||||||||
\(593\) | 33.9571 | 1.39445 | 0.697226 | − | 0.716852i | \(-0.254418\pi\) | ||||
0.697226 | + | 0.716852i | \(0.254418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −42.1783 | −1.72914 | ||||||||
\(596\) | 16.2329 | 0.664924 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.705435 | 0.0288474 | ||||||||
\(599\) | 4.88042 | 0.199408 | 0.0997042 | − | 0.995017i | \(-0.468210\pi\) | ||||
0.0997042 | + | 0.995017i | \(0.468210\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.53581 | 0.144229 | 0.0721143 | − | 0.997396i | \(-0.477025\pi\) | ||||
0.0721143 | + | 0.997396i | \(0.477025\pi\) | |||||||
\(602\) | 9.17466 | 0.373931 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.5512 | 0.795528 | ||||||||
\(605\) | 7.00517 | 0.284800 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.9417 | −0.971764 | −0.485882 | − | 0.874024i | \(-0.661502\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661502\pi\) | |||||||
\(608\) | −13.3389 | −0.540964 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.02569 | −0.0820177 | ||||||||
\(611\) | −9.62210 | −0.389268 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.8422 | 1.00337 | 0.501684 | − | 0.865051i | \(-0.332714\pi\) | ||||
0.501684 | + | 0.865051i | \(0.332714\pi\) | |||||||
\(614\) | 3.16223 | 0.127617 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.0602 | 0.647082 | ||||||||
\(617\) | −14.1565 | −0.569919 | −0.284960 | − | 0.958539i | \(-0.591980\pi\) | ||||
−0.284960 | + | 0.958539i | \(0.591980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.7115 | 0.631500 | 0.315750 | − | 0.948842i | \(-0.397744\pi\) | ||||
0.315750 | + | 0.948842i | \(0.397744\pi\) | |||||||
\(620\) | −33.9382 | −1.36299 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.17569 | −0.0471408 | ||||||||
\(623\) | 52.0192 | 2.08411 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.6616 | −1.22646 | ||||||||
\(626\) | 7.26203 | 0.290249 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.44127 | 0.257035 | ||||||||
\(629\) | 4.15062 | 0.165496 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8165 | 1.06755 | 0.533774 | − | 0.845627i | \(-0.320773\pi\) | ||||
0.533774 | + | 0.845627i | \(0.320773\pi\) | |||||||
\(632\) | −11.0953 | −0.441349 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.51775 | −0.0602774 | ||||||||
\(635\) | 24.0093 | 0.952781 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −48.4761 | −1.92069 | ||||||||
\(638\) | 0.851854 | 0.0337252 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 17.8647 | 0.706166 | ||||||||
\(641\) | −9.40758 | −0.371577 | −0.185789 | − | 0.982590i | \(-0.559484\pi\) | ||||
−0.185789 | + | 0.982590i | \(0.559484\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.8530 | −0.664616 | −0.332308 | − | 0.943171i | \(-0.607827\pi\) | ||||
−0.332308 | + | 0.943171i | \(0.607827\pi\) | |||||||
\(644\) | 9.30009 | 0.366475 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.92031 | −0.154242 | ||||||||
\(647\) | 7.52867 | 0.295983 | 0.147991 | − | 0.988989i | \(-0.452719\pi\) | ||||
0.147991 | + | 0.988989i | \(0.452719\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.1983 | 0.557333 | ||||||||
\(650\) | 1.22246 | 0.0479487 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.29767 | 0.129147 | ||||||||
\(653\) | −8.35597 | −0.326995 | −0.163497 | − | 0.986544i | \(-0.552277\pi\) | ||||
−0.163497 | + | 0.986544i | \(0.552277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.81308 | 0.305282 | ||||||||
\(656\) | −31.3851 | −1.22538 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.45100 | 0.134534 | ||||||||
\(659\) | −47.0599 | −1.83319 | −0.916596 | − | 0.399815i | \(-0.869074\pi\) | ||||
−0.916596 | + | 0.399815i | \(0.869074\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4971 | −0.758350 | −0.379175 | − | 0.925325i | \(-0.623792\pi\) | ||||
−0.379175 | + | 0.925325i | \(0.623792\pi\) | |||||||
\(662\) | 3.90225 | 0.151665 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.3275 | 0.517207 | ||||||||
\(665\) | −62.0373 | −2.40570 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 8.82052 | 0.341276 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.848423 | −0.0327775 | ||||||||
\(671\) | −12.5550 | −0.484681 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.3526 | −0.977271 | −0.488636 | − | 0.872488i | \(-0.662505\pi\) | ||||
−0.488636 | + | 0.872488i | \(0.662505\pi\) | |||||||
\(674\) | −6.30127 | −0.242716 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.01910 | 0.269965 | ||||||||
\(677\) | 10.0166 | 0.384969 | 0.192485 | − | 0.981300i | \(-0.438345\pi\) | ||||
0.192485 | + | 0.981300i | \(0.438345\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.85756 | 0.301545 | ||||||||
\(680\) | 8.02148 | 0.307610 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.72242 | 0.219123 | ||||||||
\(683\) | −22.0140 | −0.842342 | −0.421171 | − | 0.906981i | \(-0.638381\pi\) | ||||
−0.421171 | + | 0.906981i | \(0.638381\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −36.6793 | −1.40144 | ||||||||
\(686\) | 9.69094 | 0.370002 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 30.7541 | 1.17249 | ||||||||
\(689\) | −18.7945 | −0.716014 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.6597 | −0.900059 | −0.450029 | − | 0.893014i | \(-0.648586\pi\) | ||||
−0.450029 | + | 0.893014i | \(0.648586\pi\) | |||||||
\(692\) | 42.3696 | 1.61065 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.603999 | 0.0229275 | ||||||||
\(695\) | 18.2972 | 0.694051 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.9841 | −1.09785 | ||||||||
\(698\) | −1.53275 | −0.0580153 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 16.1162 | 0.609136 | ||||||||
\(701\) | 44.6815 | 1.68760 | 0.843799 | − | 0.536659i | \(-0.180314\pi\) | ||||
0.843799 | + | 0.536659i | \(0.180314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.10488 | 0.230250 | ||||||||
\(704\) | 25.0085 | 0.942544 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.896452 | 0.0337384 | ||||||||
\(707\) | 86.9722 | 3.27093 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.8352 | −0.594705 | −0.297353 | − | 0.954768i | \(-0.596104\pi\) | ||||
−0.297353 | + | 0.954768i | \(0.596104\pi\) | |||||||
\(710\) | 0.724230 | 0.0271799 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.89304 | −0.370757 | ||||||||
\(713\) | 6.71761 | 0.251576 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 29.4378 | 1.10091 | ||||||||
\(716\) | −40.5516 | −1.51549 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.06804 | −0.114498 | ||||||||
\(719\) | −52.1881 | −1.94629 | −0.973144 | − | 0.230196i | \(-0.926063\pi\) | ||||
−0.973144 | + | 0.230196i | \(0.926063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.8277 | 1.40878 | ||||||||
\(722\) | −1.39329 | −0.0518530 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.7455 | 0.473683 | ||||||||
\(725\) | 1.73291 | 0.0643587 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0872 | −0.522467 | −0.261233 | − | 0.965276i | \(-0.584129\pi\) | ||||
−0.261233 | + | 0.965276i | \(0.584129\pi\) | |||||||
\(728\) | 13.2997 | 0.492920 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.17287 | 0.191456 | ||||||||
\(731\) | 28.4014 | 1.05046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.7271 | −1.20880 | −0.604401 | − | 0.796680i | \(-0.706588\pi\) | ||||
−0.604401 | + | 0.796680i | \(0.706588\pi\) | |||||||
\(734\) | 0.421804 | 0.0155691 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.66491 | −0.0982299 | ||||||||
\(737\) | −5.25845 | −0.193697 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.7120 | 1.01940 | 0.509701 | − | 0.860351i | \(-0.329756\pi\) | ||||
0.509701 | + | 0.860351i | \(0.329756\pi\) | |||||||
\(740\) | −6.16189 | −0.226516 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.74073 | 0.247460 | ||||||||
\(743\) | 21.1573 | 0.776186 | 0.388093 | − | 0.921620i | \(-0.373134\pi\) | ||||
0.388093 | + | 0.921620i | \(0.373134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.6334 | −0.792585 | ||||||||
\(746\) | 8.52130 | 0.311987 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.5246 | 0.896708 | ||||||||
\(749\) | −48.4336 | −1.76973 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.3387 | 1.07058 | 0.535291 | − | 0.844668i | \(-0.320202\pi\) | ||||
0.535291 | + | 0.844668i | \(0.320202\pi\) | |||||||
\(752\) | 11.5680 | 0.421842 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.705435 | 0.0256904 | ||||||||
\(755\) | −26.0557 | −0.948263 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.3555 | −1.39405 | −0.697027 | − | 0.717045i | \(-0.745494\pi\) | ||||
−0.697027 | + | 0.717045i | \(0.745494\pi\) | |||||||
\(758\) | −1.96498 | −0.0713712 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 11.7983 | 0.427969 | ||||||||
\(761\) | 5.41281 | 0.196214 | 0.0981071 | − | 0.995176i | \(-0.468721\pi\) | ||||
0.0981071 | + | 0.995176i | \(0.468721\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 87.2838 | 3.15989 | ||||||||
\(764\) | 41.0770 | 1.48611 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.20161 | 0.151810 | ||||||||
\(767\) | 11.7579 | 0.424553 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.7821 | −0.569119 | −0.284559 | − | 0.958658i | \(-0.591847\pi\) | ||||
−0.284559 | + | 0.958658i | \(0.591847\pi\) | |||||||
\(770\) | −10.5580 | −0.380483 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.8068 | −0.388947 | ||||||||
\(773\) | 35.5162 | 1.27743 | 0.638715 | − | 0.769443i | \(-0.279466\pi\) | ||||
0.638715 | + | 0.769443i | \(0.279466\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.6410 | 0.418158 | ||||||||
\(776\) | −1.49435 | −0.0536442 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.53001 | 0.162409 | ||||||||
\(779\) | −42.6308 | −1.52741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.48871 | 0.160619 | ||||||||
\(782\) | −0.783218 | −0.0280078 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 58.2797 | 2.08142 | ||||||||
\(785\) | −8.58420 | −0.306383 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 45.4908 | 1.62157 | 0.810785 | − | 0.585344i | \(-0.199040\pi\) | ||||
0.810785 | + | 0.585344i | \(0.199040\pi\) | |||||||
\(788\) | −39.2632 | −1.39869 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.29409 | 0.259512 | ||||||||
\(791\) | 42.4462 | 1.50921 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.3970 | −0.369210 | ||||||||
\(794\) | 0.320021 | 0.0113571 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.5786 | 1.61549 | ||||||||
\(797\) | −30.5490 | −1.08210 | −0.541051 | − | 0.840990i | \(-0.681973\pi\) | ||||
−0.541051 | + | 0.840990i | \(0.681973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.6831 | 0.377939 | ||||||||
\(800\) | −4.61806 | −0.163273 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.21550 | −0.0429210 | ||||||||
\(803\) | 32.0609 | 1.13141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.3941 | −0.436835 | ||||||||
\(806\) | 4.73884 | 0.166918 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.5404 | −0.581890 | ||||||||
\(809\) | −25.5128 | −0.896981 | −0.448491 | − | 0.893788i | \(-0.648038\pi\) | ||||
−0.448491 | + | 0.893788i | \(0.648038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.4381 | 1.77112 | 0.885560 | − | 0.464524i | \(-0.153775\pi\) | ||||
0.885560 | + | 0.464524i | \(0.153775\pi\) | |||||||
\(812\) | 9.30009 | 0.326369 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.03897 | 0.0364160 | ||||||||
\(815\) | −4.39477 | −0.153942 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.7738 | 1.46148 | ||||||||
\(818\) | −0.909660 | −0.0318055 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 43.0289 | 1.50264 | ||||||||
\(821\) | −2.96844 | −0.103599 | −0.0517996 | − | 0.998657i | \(-0.516496\pi\) | ||||
−0.0517996 | + | 0.998657i | \(0.516496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.1118 | 0.631336 | 0.315668 | − | 0.948870i | \(-0.397771\pi\) | ||||
0.315668 | + | 0.948870i | \(0.397771\pi\) | |||||||
\(824\) | −7.19410 | −0.250618 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.21701 | −0.146729 | ||||||||
\(827\) | 40.2128 | 1.39834 | 0.699168 | − | 0.714957i | \(-0.253554\pi\) | ||||
0.699168 | + | 0.714957i | \(0.253554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −40.4489 | −1.40485 | −0.702424 | − | 0.711759i | \(-0.747899\pi\) | ||||
−0.702424 | + | 0.711759i | \(0.747899\pi\) | |||||||
\(830\) | −8.76152 | −0.304117 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.7100 | 0.717990 | ||||||||
\(833\) | 53.8212 | 1.86480 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.7550 | −0.406799 | ||||||||
\(836\) | 36.0717 | 1.24756 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.44923 | 0.0500627 | ||||||||
\(839\) | 33.9645 | 1.17259 | 0.586293 | − | 0.810099i | \(-0.300587\pi\) | ||||
0.586293 | + | 0.810099i | \(0.300587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −1.12118 | −0.0386384 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −50.9867 | −1.75504 | ||||||||
\(845\) | −9.35427 | −0.321797 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.8953 | −0.443087 | ||||||||
\(848\) | 22.5954 | 0.775929 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.35725 | −0.0465532 | ||||||||
\(851\) | 1.21966 | 0.0418095 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.1443 | 0.723967 | 0.361983 | − | 0.932185i | \(-0.382100\pi\) | ||||
0.361983 | + | 0.932185i | \(0.382100\pi\) | |||||||
\(854\) | 3.72894 | 0.127602 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.21113 | 0.314830 | ||||||||
\(857\) | 20.8537 | 0.712350 | 0.356175 | − | 0.934419i | \(-0.384081\pi\) | ||||
0.356175 | + | 0.934419i | \(0.384081\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.2514 | −1.33924 | −0.669621 | − | 0.742703i | \(-0.733543\pi\) | ||||
−0.669621 | + | 0.742703i | \(0.733543\pi\) | |||||||
\(860\) | −42.1639 | −1.43778 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.53601 | 0.188557 | ||||||||
\(863\) | −57.0716 | −1.94274 | −0.971371 | − | 0.237569i | \(-0.923649\pi\) | ||||
−0.971371 | + | 0.237569i | \(0.923649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −56.4654 | −1.91988 | ||||||||
\(866\) | 4.64523 | 0.157851 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 62.4743 | 2.12052 | ||||||||
\(869\) | 45.2081 | 1.53358 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.35461 | −0.147550 | ||||||||
\(872\) | −16.5997 | −0.562136 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.15198 | −0.0389665 | ||||||||
\(875\) | 40.4927 | 1.36890 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.49604 | 0.0505176 | 0.0252588 | − | 0.999681i | \(-0.491959\pi\) | ||||
0.0252588 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(878\) | 6.08331 | 0.205302 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −35.3911 | −1.19303 | ||||||||
\(881\) | 34.7534 | 1.17087 | 0.585435 | − | 0.810719i | \(-0.300924\pi\) | ||||
0.585435 | + | 0.810719i | \(0.300924\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5140 | −0.724002 | −0.362001 | − | 0.932178i | \(-0.617906\pi\) | ||||
−0.362001 | + | 0.932178i | \(0.617906\pi\) | |||||||
\(884\) | 20.3093 | 0.683074 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.33100 | 0.246290 | ||||||||
\(887\) | 10.3028 | 0.345934 | 0.172967 | − | 0.984928i | \(-0.444665\pi\) | ||||
0.172967 | + | 0.984928i | \(0.444665\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −44.1970 | −1.48232 | ||||||||
\(890\) | 6.50370 | 0.218005 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 28.2251 | 0.945045 | ||||||||
\(893\) | 15.7130 | 0.525816 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 54.0427 | 1.80645 | ||||||||
\(896\) | −32.8859 | −1.09864 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.89214 | −0.229994 | ||||||||
\(899\) | 6.71761 | 0.224045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.8668 | 0.695175 | ||||||||
\(902\) | −7.25523 | −0.241573 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.07244 | −0.268485 | ||||||||
\(905\) | −16.9858 | −0.564626 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.4319 | −0.578818 | −0.289409 | − | 0.957206i | \(-0.593459\pi\) | ||||
−0.289409 | + | 0.957206i | \(0.593459\pi\) | |||||||
\(908\) | 26.8338 | 0.890511 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.74325 | −0.289836 | ||||||||
\(911\) | 33.5503 | 1.11157 | 0.555785 | − | 0.831326i | \(-0.312418\pi\) | ||||
0.555785 | + | 0.831326i | \(0.312418\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.3030 | −1.79717 | ||||||||
\(914\) | 5.38117 | 0.177993 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −53.1651 | −1.75663 | ||||||||
\(917\) | −14.3825 | −0.474953 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −24.8480 | −0.819661 | −0.409831 | − | 0.912162i | \(-0.634412\pi\) | ||||
−0.409831 | + | 0.912162i | \(0.634412\pi\) | |||||||
\(920\) | 2.35712 | 0.0777119 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.694531 | −0.0228732 | ||||||||
\(923\) | 3.71718 | 0.122352 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.11357 | 0.0694937 | ||||||||
\(926\) | 0.560330 | 0.0184136 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.66491 | −0.0874800 | ||||||||
\(929\) | 30.1456 | 0.989044 | 0.494522 | − | 0.869165i | \(-0.335343\pi\) | ||||
0.494522 | + | 0.869165i | \(0.335343\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 79.1622 | 2.59444 | ||||||||
\(932\) | 16.2271 | 0.531536 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.54454 | −0.0505390 | ||||||||
\(935\) | −32.6836 | −1.06887 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.8757 | −1.66204 | −0.831019 | − | 0.556244i | \(-0.812242\pi\) | ||||
−0.831019 | + | 0.556244i | \(0.812242\pi\) | |||||||
\(938\) | 1.56180 | 0.0509946 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −15.8598 | −0.517288 | ||||||||
\(941\) | 55.5956 | 1.81236 | 0.906182 | − | 0.422888i | \(-0.138984\pi\) | ||||
0.906182 | + | 0.422888i | \(0.138984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.51699 | −0.277351 | ||||||||
\(944\) | −14.1357 | −0.460079 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.10938 | 0.231146 | ||||||||
\(947\) | −54.0049 | −1.75492 | −0.877462 | − | 0.479647i | \(-0.840765\pi\) | ||||
−0.877462 | + | 0.479647i | \(0.840765\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.5502 | 0.861857 | ||||||||
\(950\) | −1.99629 | −0.0647682 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.7662 | −0.478574 | ||||||||
\(953\) | 51.8326 | 1.67902 | 0.839511 | − | 0.543342i | \(-0.182841\pi\) | ||||
0.839511 | + | 0.543342i | \(0.182841\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −54.7428 | −1.77144 | ||||||||
\(956\) | −41.1243 | −1.33005 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.73701 | −0.249971 | ||||||||
\(959\) | 67.5202 | 2.18034 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1263 | 0.455686 | ||||||||
\(962\) | 0.860393 | 0.0277402 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0688 | 0.420916 | ||||||||
\(965\) | 14.4022 | 0.463622 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −37.8809 | −1.21817 | −0.609083 | − | 0.793106i | \(-0.708462\pi\) | ||||
−0.609083 | + | 0.793106i | \(0.708462\pi\) | |||||||
\(968\) | 2.45243 | 0.0788241 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.982391 | 0.0315427 | ||||||||
\(971\) | −2.62752 | −0.0843210 | −0.0421605 | − | 0.999111i | \(-0.513424\pi\) | ||||
−0.0421605 | + | 0.999111i | \(0.513424\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.6819 | −1.07979 | ||||||||
\(974\) | 5.15078 | 0.165042 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.4997 | 0.400105 | ||||||||
\(977\) | −29.4200 | −0.941229 | −0.470615 | − | 0.882339i | \(-0.655968\pi\) | ||||
−0.470615 | + | 0.882339i | \(0.655968\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.3093 | 1.28829 | ||||||||
\(980\) | −79.9015 | −2.55236 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.06997 | −0.0979667 | ||||||||
\(983\) | 23.9487 | 0.763845 | 0.381923 | − | 0.924194i | \(-0.375262\pi\) | ||||
0.381923 | + | 0.924194i | \(0.375262\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.3256 | 1.66723 | ||||||||
\(986\) | −0.783218 | −0.0249427 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.8716 | 0.950341 | ||||||||
\(989\) | 8.34577 | 0.265380 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.962968 | 0.0305897 | 0.0152948 | − | 0.999883i | \(-0.495131\pi\) | ||||
0.0152948 | + | 0.999883i | \(0.495131\pi\) | |||||||
\(992\) | −17.9018 | −0.568383 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.33318 | −0.0422860 | ||||||||
\(995\) | −60.7420 | −1.92565 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.5602 | −1.60126 | −0.800629 | − | 0.599161i | \(-0.795501\pi\) | ||||
−0.800629 | + | 0.599161i | \(0.795501\pi\) | |||||||
\(998\) | 3.57824 | 0.113267 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6003.2.a.t.1.11 | ✓ | 22 | |
3.2 | odd | 2 | 6003.2.a.u.1.12 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.11 | ✓ | 22 | 1.1 | even | 1 | trivial | |
6003.2.a.u.1.12 | yes | 22 | 3.2 | odd | 2 |