Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6005,2,Mod(1,6005)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6005, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6005.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6005 = 5 \cdot 1201 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6005.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: | \(47.9501664138\) |
Analytic rank: | \(1\) |
Dimension: | \(83\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6005.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64292 | −1.86882 | −0.934412 | − | 0.356195i | \(-0.884074\pi\) | ||||
−0.934412 | + | 0.356195i | \(0.884074\pi\) | |||||||
\(3\) | 0.725582 | 0.418915 | 0.209457 | − | 0.977818i | \(-0.432830\pi\) | ||||
0.209457 | + | 0.977818i | \(0.432830\pi\) | |||||||
\(4\) | 4.98500 | 2.49250 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.91765 | −0.782878 | ||||||||
\(7\) | −1.58856 | −0.600418 | −0.300209 | − | 0.953873i | \(-0.597056\pi\) | ||||
−0.300209 | + | 0.953873i | \(0.597056\pi\) | |||||||
\(8\) | −7.88911 | −2.78922 | ||||||||
\(9\) | −2.47353 | −0.824510 | ||||||||
\(10\) | 2.64292 | 0.835763 | ||||||||
\(11\) | −2.20527 | −0.664913 | −0.332456 | − | 0.943119i | \(-0.607877\pi\) | ||||
−0.332456 | + | 0.943119i | \(0.607877\pi\) | |||||||
\(12\) | 3.61703 | 1.04415 | ||||||||
\(13\) | −1.50571 | −0.417608 | −0.208804 | − | 0.977957i | \(-0.566957\pi\) | ||||
−0.208804 | + | 0.977957i | \(0.566957\pi\) | |||||||
\(14\) | 4.19842 | 1.12207 | ||||||||
\(15\) | −0.725582 | −0.187344 | ||||||||
\(16\) | 10.8802 | 2.72006 | ||||||||
\(17\) | −0.196046 | −0.0475480 | −0.0237740 | − | 0.999717i | \(-0.507568\pi\) | ||||
−0.0237740 | + | 0.999717i | \(0.507568\pi\) | |||||||
\(18\) | 6.53733 | 1.54086 | ||||||||
\(19\) | 0.106463 | 0.0244244 | 0.0122122 | − | 0.999925i | \(-0.496113\pi\) | ||||
0.0122122 | + | 0.999925i | \(0.496113\pi\) | |||||||
\(20\) | −4.98500 | −1.11468 | ||||||||
\(21\) | −1.15263 | −0.251524 | ||||||||
\(22\) | 5.82833 | 1.24260 | ||||||||
\(23\) | 6.89598 | 1.43791 | 0.718955 | − | 0.695056i | \(-0.244621\pi\) | ||||
0.718955 | + | 0.695056i | \(0.244621\pi\) | |||||||
\(24\) | −5.72419 | −1.16845 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.97946 | 0.780436 | ||||||||
\(27\) | −3.97149 | −0.764314 | ||||||||
\(28\) | −7.91896 | −1.49654 | ||||||||
\(29\) | 2.34916 | 0.436228 | 0.218114 | − | 0.975923i | \(-0.430010\pi\) | ||||
0.218114 | + | 0.975923i | \(0.430010\pi\) | |||||||
\(30\) | 1.91765 | 0.350114 | ||||||||
\(31\) | −3.29794 | −0.592327 | −0.296164 | − | 0.955137i | \(-0.595707\pi\) | ||||
−0.296164 | + | 0.955137i | \(0.595707\pi\) | |||||||
\(32\) | −12.9773 | −2.29409 | ||||||||
\(33\) | −1.60010 | −0.278542 | ||||||||
\(34\) | 0.518132 | 0.0888589 | ||||||||
\(35\) | 1.58856 | 0.268515 | ||||||||
\(36\) | −12.3306 | −2.05509 | ||||||||
\(37\) | 2.70790 | 0.445177 | 0.222588 | − | 0.974913i | \(-0.428549\pi\) | ||||
0.222588 | + | 0.974913i | \(0.428549\pi\) | |||||||
\(38\) | −0.281374 | −0.0456449 | ||||||||
\(39\) | −1.09251 | −0.174942 | ||||||||
\(40\) | 7.88911 | 1.24738 | ||||||||
\(41\) | 6.80561 | 1.06286 | 0.531429 | − | 0.847103i | \(-0.321655\pi\) | ||||
0.531429 | + | 0.847103i | \(0.321655\pi\) | |||||||
\(42\) | 3.04630 | 0.470054 | ||||||||
\(43\) | −0.922325 | −0.140653 | −0.0703266 | − | 0.997524i | \(-0.522404\pi\) | ||||
−0.0703266 | + | 0.997524i | \(0.522404\pi\) | |||||||
\(44\) | −10.9933 | −1.65730 | ||||||||
\(45\) | 2.47353 | 0.368732 | ||||||||
\(46\) | −18.2255 | −2.68720 | ||||||||
\(47\) | 4.83852 | 0.705770 | 0.352885 | − | 0.935667i | \(-0.385201\pi\) | ||||
0.352885 | + | 0.935667i | \(0.385201\pi\) | |||||||
\(48\) | 7.89450 | 1.13947 | ||||||||
\(49\) | −4.47649 | −0.639498 | ||||||||
\(50\) | −2.64292 | −0.373765 | ||||||||
\(51\) | −0.142247 | −0.0199186 | ||||||||
\(52\) | −7.50596 | −1.04089 | ||||||||
\(53\) | 10.8808 | 1.49460 | 0.747299 | − | 0.664488i | \(-0.231350\pi\) | ||||
0.747299 | + | 0.664488i | \(0.231350\pi\) | |||||||
\(54\) | 10.4963 | 1.42837 | ||||||||
\(55\) | 2.20527 | 0.297358 | ||||||||
\(56\) | 12.5323 | 1.67470 | ||||||||
\(57\) | 0.0772479 | 0.0102317 | ||||||||
\(58\) | −6.20863 | −0.815233 | ||||||||
\(59\) | −1.06512 | −0.138667 | −0.0693336 | − | 0.997594i | \(-0.522087\pi\) | ||||
−0.0693336 | + | 0.997594i | \(0.522087\pi\) | |||||||
\(60\) | −3.61703 | −0.466956 | ||||||||
\(61\) | −4.43798 | −0.568225 | −0.284112 | − | 0.958791i | \(-0.591699\pi\) | ||||
−0.284112 | + | 0.958791i | \(0.591699\pi\) | |||||||
\(62\) | 8.71617 | 1.10696 | ||||||||
\(63\) | 3.92934 | 0.495051 | ||||||||
\(64\) | 12.5375 | 1.56719 | ||||||||
\(65\) | 1.50571 | 0.186760 | ||||||||
\(66\) | 4.22893 | 0.520545 | ||||||||
\(67\) | 4.61448 | 0.563748 | 0.281874 | − | 0.959451i | \(-0.409044\pi\) | ||||
0.281874 | + | 0.959451i | \(0.409044\pi\) | |||||||
\(68\) | −0.977288 | −0.118514 | ||||||||
\(69\) | 5.00360 | 0.602362 | ||||||||
\(70\) | −4.19842 | −0.501807 | ||||||||
\(71\) | −4.52381 | −0.536877 | −0.268439 | − | 0.963297i | \(-0.586508\pi\) | ||||
−0.268439 | + | 0.963297i | \(0.586508\pi\) | |||||||
\(72\) | 19.5140 | 2.29974 | ||||||||
\(73\) | 8.64022 | 1.01126 | 0.505630 | − | 0.862750i | \(-0.331260\pi\) | ||||
0.505630 | + | 0.862750i | \(0.331260\pi\) | |||||||
\(74\) | −7.15676 | −0.831956 | ||||||||
\(75\) | 0.725582 | 0.0837830 | ||||||||
\(76\) | 0.530720 | 0.0608778 | ||||||||
\(77\) | 3.50319 | 0.399225 | ||||||||
\(78\) | 2.88742 | 0.326936 | ||||||||
\(79\) | −10.2342 | −1.15143 | −0.575717 | − | 0.817649i | \(-0.695277\pi\) | ||||
−0.575717 | + | 0.817649i | \(0.695277\pi\) | |||||||
\(80\) | −10.8802 | −1.21645 | ||||||||
\(81\) | 4.53895 | 0.504328 | ||||||||
\(82\) | −17.9867 | −1.98629 | ||||||||
\(83\) | 16.8943 | 1.85439 | 0.927195 | − | 0.374580i | \(-0.122213\pi\) | ||||
0.927195 | + | 0.374580i | \(0.122213\pi\) | |||||||
\(84\) | −5.74585 | −0.626923 | ||||||||
\(85\) | 0.196046 | 0.0212641 | ||||||||
\(86\) | 2.43763 | 0.262856 | ||||||||
\(87\) | 1.70451 | 0.182742 | ||||||||
\(88\) | 17.3976 | 1.85459 | ||||||||
\(89\) | −2.90154 | −0.307563 | −0.153782 | − | 0.988105i | \(-0.549145\pi\) | ||||
−0.153782 | + | 0.988105i | \(0.549145\pi\) | |||||||
\(90\) | −6.53733 | −0.689096 | ||||||||
\(91\) | 2.39190 | 0.250740 | ||||||||
\(92\) | 34.3765 | 3.58399 | ||||||||
\(93\) | −2.39292 | −0.248135 | ||||||||
\(94\) | −12.7878 | −1.31896 | ||||||||
\(95\) | −0.106463 | −0.0109229 | ||||||||
\(96\) | −9.41612 | −0.961029 | ||||||||
\(97\) | 5.85530 | 0.594516 | 0.297258 | − | 0.954797i | \(-0.403928\pi\) | ||||
0.297258 | + | 0.954797i | \(0.403928\pi\) | |||||||
\(98\) | 11.8310 | 1.19511 | ||||||||
\(99\) | 5.45479 | 0.548227 | ||||||||
\(100\) | 4.98500 | 0.498500 | ||||||||
\(101\) | 5.86367 | 0.583457 | 0.291729 | − | 0.956501i | \(-0.405770\pi\) | ||||
0.291729 | + | 0.956501i | \(0.405770\pi\) | |||||||
\(102\) | 0.375947 | 0.0372243 | ||||||||
\(103\) | −6.26730 | −0.617536 | −0.308768 | − | 0.951137i | \(-0.599917\pi\) | ||||
−0.308768 | + | 0.951137i | \(0.599917\pi\) | |||||||
\(104\) | 11.8787 | 1.16480 | ||||||||
\(105\) | 1.15263 | 0.112485 | ||||||||
\(106\) | −28.7571 | −2.79314 | ||||||||
\(107\) | 10.4352 | 1.00881 | 0.504403 | − | 0.863468i | \(-0.331713\pi\) | ||||
0.504403 | + | 0.863468i | \(0.331713\pi\) | |||||||
\(108\) | −19.7979 | −1.90505 | ||||||||
\(109\) | 11.7361 | 1.12411 | 0.562055 | − | 0.827100i | \(-0.310011\pi\) | ||||
0.562055 | + | 0.827100i | \(0.310011\pi\) | |||||||
\(110\) | −5.82833 | −0.555710 | ||||||||
\(111\) | 1.96480 | 0.186491 | ||||||||
\(112\) | −17.2839 | −1.63317 | ||||||||
\(113\) | −3.92494 | −0.369227 | −0.184614 | − | 0.982811i | \(-0.559103\pi\) | ||||
−0.184614 | + | 0.982811i | \(0.559103\pi\) | |||||||
\(114\) | −0.204160 | −0.0191213 | ||||||||
\(115\) | −6.89598 | −0.643053 | ||||||||
\(116\) | 11.7106 | 1.08730 | ||||||||
\(117\) | 3.72442 | 0.344322 | ||||||||
\(118\) | 2.81503 | 0.259144 | ||||||||
\(119\) | 0.311429 | 0.0285487 | ||||||||
\(120\) | 5.72419 | 0.522545 | ||||||||
\(121\) | −6.13680 | −0.557891 | ||||||||
\(122\) | 11.7292 | 1.06191 | ||||||||
\(123\) | 4.93803 | 0.445247 | ||||||||
\(124\) | −16.4402 | −1.47638 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −10.3849 | −0.925162 | ||||||||
\(127\) | −16.5053 | −1.46461 | −0.732304 | − | 0.680978i | \(-0.761555\pi\) | ||||
−0.732304 | + | 0.680978i | \(0.761555\pi\) | |||||||
\(128\) | −7.18095 | −0.634712 | ||||||||
\(129\) | −0.669222 | −0.0589217 | ||||||||
\(130\) | −3.97946 | −0.349022 | ||||||||
\(131\) | 15.1146 | 1.32057 | 0.660285 | − | 0.751015i | \(-0.270435\pi\) | ||||
0.660285 | + | 0.751015i | \(0.270435\pi\) | |||||||
\(132\) | −7.97650 | −0.694266 | ||||||||
\(133\) | −0.169123 | −0.0146648 | ||||||||
\(134\) | −12.1957 | −1.05355 | ||||||||
\(135\) | 3.97149 | 0.341812 | ||||||||
\(136\) | 1.54662 | 0.132622 | ||||||||
\(137\) | −20.7872 | −1.77597 | −0.887986 | − | 0.459870i | \(-0.847896\pi\) | ||||
−0.887986 | + | 0.459870i | \(0.847896\pi\) | |||||||
\(138\) | −13.2241 | −1.12571 | ||||||||
\(139\) | −19.2498 | −1.63275 | −0.816373 | − | 0.577525i | \(-0.804019\pi\) | ||||
−0.816373 | + | 0.577525i | \(0.804019\pi\) | |||||||
\(140\) | 7.91896 | 0.669274 | ||||||||
\(141\) | 3.51074 | 0.295658 | ||||||||
\(142\) | 11.9560 | 1.00333 | ||||||||
\(143\) | 3.32049 | 0.277673 | ||||||||
\(144\) | −26.9126 | −2.24272 | ||||||||
\(145\) | −2.34916 | −0.195087 | ||||||||
\(146\) | −22.8354 | −1.88987 | ||||||||
\(147\) | −3.24806 | −0.267895 | ||||||||
\(148\) | 13.4989 | 1.10960 | ||||||||
\(149\) | 0.437062 | 0.0358056 | 0.0179028 | − | 0.999840i | \(-0.494301\pi\) | ||||
0.0179028 | + | 0.999840i | \(0.494301\pi\) | |||||||
\(150\) | −1.91765 | −0.156576 | ||||||||
\(151\) | 10.1252 | 0.823976 | 0.411988 | − | 0.911189i | \(-0.364835\pi\) | ||||
0.411988 | + | 0.911189i | \(0.364835\pi\) | |||||||
\(152\) | −0.839902 | −0.0681250 | ||||||||
\(153\) | 0.484925 | 0.0392039 | ||||||||
\(154\) | −9.25863 | −0.746082 | ||||||||
\(155\) | 3.29794 | 0.264897 | ||||||||
\(156\) | −5.44619 | −0.436044 | ||||||||
\(157\) | −9.04644 | −0.721984 | −0.360992 | − | 0.932569i | \(-0.617562\pi\) | ||||
−0.360992 | + | 0.932569i | \(0.617562\pi\) | |||||||
\(158\) | 27.0480 | 2.15183 | ||||||||
\(159\) | 7.89494 | 0.626109 | ||||||||
\(160\) | 12.9773 | 1.02595 | ||||||||
\(161\) | −10.9546 | −0.863347 | ||||||||
\(162\) | −11.9961 | −0.942500 | ||||||||
\(163\) | −7.83580 | −0.613747 | −0.306874 | − | 0.951750i | \(-0.599283\pi\) | ||||
−0.306874 | + | 0.951750i | \(0.599283\pi\) | |||||||
\(164\) | 33.9260 | 2.64917 | ||||||||
\(165\) | 1.60010 | 0.124568 | ||||||||
\(166\) | −44.6502 | −3.46553 | ||||||||
\(167\) | −23.6721 | −1.83180 | −0.915902 | − | 0.401403i | \(-0.868523\pi\) | ||||
−0.915902 | + | 0.401403i | \(0.868523\pi\) | |||||||
\(168\) | 9.09320 | 0.701556 | ||||||||
\(169\) | −10.7328 | −0.825603 | ||||||||
\(170\) | −0.518132 | −0.0397389 | ||||||||
\(171\) | −0.263341 | −0.0201382 | ||||||||
\(172\) | −4.59779 | −0.350578 | ||||||||
\(173\) | −22.8064 | −1.73394 | −0.866968 | − | 0.498363i | \(-0.833935\pi\) | ||||
−0.866968 | + | 0.498363i | \(0.833935\pi\) | |||||||
\(174\) | −4.50487 | −0.341513 | ||||||||
\(175\) | −1.58856 | −0.120084 | ||||||||
\(176\) | −23.9938 | −1.80860 | ||||||||
\(177\) | −0.772833 | −0.0580897 | ||||||||
\(178\) | 7.66853 | 0.574781 | ||||||||
\(179\) | −18.8078 | −1.40576 | −0.702881 | − | 0.711308i | \(-0.748103\pi\) | ||||
−0.702881 | + | 0.711308i | \(0.748103\pi\) | |||||||
\(180\) | 12.3306 | 0.919066 | ||||||||
\(181\) | −4.20617 | −0.312642 | −0.156321 | − | 0.987706i | \(-0.549963\pi\) | ||||
−0.156321 | + | 0.987706i | \(0.549963\pi\) | |||||||
\(182\) | −6.32160 | −0.468588 | ||||||||
\(183\) | −3.22011 | −0.238038 | ||||||||
\(184\) | −54.4031 | −4.01065 | ||||||||
\(185\) | −2.70790 | −0.199089 | ||||||||
\(186\) | 6.32429 | 0.463720 | ||||||||
\(187\) | 0.432333 | 0.0316153 | ||||||||
\(188\) | 24.1200 | 1.75913 | ||||||||
\(189\) | 6.30894 | 0.458908 | ||||||||
\(190\) | 0.281374 | 0.0204130 | ||||||||
\(191\) | 5.80324 | 0.419908 | 0.209954 | − | 0.977711i | \(-0.432669\pi\) | ||||
0.209954 | + | 0.977711i | \(0.432669\pi\) | |||||||
\(192\) | 9.09700 | 0.656519 | ||||||||
\(193\) | 19.4678 | 1.40132 | 0.700661 | − | 0.713494i | \(-0.252889\pi\) | ||||
0.700661 | + | 0.713494i | \(0.252889\pi\) | |||||||
\(194\) | −15.4751 | −1.11104 | ||||||||
\(195\) | 1.09251 | 0.0782366 | ||||||||
\(196\) | −22.3153 | −1.59395 | ||||||||
\(197\) | 8.73362 | 0.622244 | 0.311122 | − | 0.950370i | \(-0.399295\pi\) | ||||
0.311122 | + | 0.950370i | \(0.399295\pi\) | |||||||
\(198\) | −14.4166 | −1.02454 | ||||||||
\(199\) | −4.34045 | −0.307686 | −0.153843 | − | 0.988095i | \(-0.549165\pi\) | ||||
−0.153843 | + | 0.988095i | \(0.549165\pi\) | |||||||
\(200\) | −7.88911 | −0.557844 | ||||||||
\(201\) | 3.34818 | 0.236163 | ||||||||
\(202\) | −15.4972 | −1.09038 | ||||||||
\(203\) | −3.73177 | −0.261919 | ||||||||
\(204\) | −0.709102 | −0.0496471 | ||||||||
\(205\) | −6.80561 | −0.475325 | ||||||||
\(206\) | 16.5640 | 1.15407 | ||||||||
\(207\) | −17.0574 | −1.18557 | ||||||||
\(208\) | −16.3825 | −1.13592 | ||||||||
\(209\) | −0.234780 | −0.0162401 | ||||||||
\(210\) | −3.04630 | −0.210214 | ||||||||
\(211\) | −13.5782 | −0.934762 | −0.467381 | − | 0.884056i | \(-0.654802\pi\) | ||||
−0.467381 | + | 0.884056i | \(0.654802\pi\) | |||||||
\(212\) | 54.2410 | 3.72529 | ||||||||
\(213\) | −3.28239 | −0.224906 | ||||||||
\(214\) | −27.5793 | −1.88528 | ||||||||
\(215\) | 0.922325 | 0.0629020 | ||||||||
\(216\) | 31.3315 | 2.13184 | ||||||||
\(217\) | 5.23896 | 0.355644 | ||||||||
\(218\) | −31.0174 | −2.10076 | ||||||||
\(219\) | 6.26918 | 0.423632 | ||||||||
\(220\) | 10.9933 | 0.741165 | ||||||||
\(221\) | 0.295188 | 0.0198565 | ||||||||
\(222\) | −5.19281 | −0.348519 | ||||||||
\(223\) | 0.381218 | 0.0255282 | 0.0127641 | − | 0.999919i | \(-0.495937\pi\) | ||||
0.0127641 | + | 0.999919i | \(0.495937\pi\) | |||||||
\(224\) | 20.6152 | 1.37741 | ||||||||
\(225\) | −2.47353 | −0.164902 | ||||||||
\(226\) | 10.3733 | 0.690021 | ||||||||
\(227\) | 5.43424 | 0.360683 | 0.180342 | − | 0.983604i | \(-0.442280\pi\) | ||||
0.180342 | + | 0.983604i | \(0.442280\pi\) | |||||||
\(228\) | 0.385081 | 0.0255026 | ||||||||
\(229\) | 23.9439 | 1.58226 | 0.791130 | − | 0.611648i | \(-0.209493\pi\) | ||||
0.791130 | + | 0.611648i | \(0.209493\pi\) | |||||||
\(230\) | 18.2255 | 1.20175 | ||||||||
\(231\) | 2.54185 | 0.167241 | ||||||||
\(232\) | −18.5328 | −1.21674 | ||||||||
\(233\) | 4.56100 | 0.298801 | 0.149401 | − | 0.988777i | \(-0.452266\pi\) | ||||
0.149401 | + | 0.988777i | \(0.452266\pi\) | |||||||
\(234\) | −9.84332 | −0.643478 | ||||||||
\(235\) | −4.83852 | −0.315630 | ||||||||
\(236\) | −5.30964 | −0.345628 | ||||||||
\(237\) | −7.42573 | −0.482353 | ||||||||
\(238\) | −0.823082 | −0.0533525 | ||||||||
\(239\) | 10.4438 | 0.675555 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(240\) | −7.89450 | −0.509588 | ||||||||
\(241\) | −10.3329 | −0.665601 | −0.332800 | − | 0.942997i | \(-0.607994\pi\) | ||||
−0.332800 | + | 0.942997i | \(0.607994\pi\) | |||||||
\(242\) | 16.2190 | 1.04260 | ||||||||
\(243\) | 15.2079 | 0.975585 | ||||||||
\(244\) | −22.1233 | −1.41630 | ||||||||
\(245\) | 4.47649 | 0.285992 | ||||||||
\(246\) | −13.0508 | −0.832088 | ||||||||
\(247\) | −0.160303 | −0.0101998 | ||||||||
\(248\) | 26.0178 | 1.65213 | ||||||||
\(249\) | 12.2582 | 0.776831 | ||||||||
\(250\) | 2.64292 | 0.167153 | ||||||||
\(251\) | −8.65525 | −0.546315 | −0.273157 | − | 0.961969i | \(-0.588068\pi\) | ||||
−0.273157 | + | 0.961969i | \(0.588068\pi\) | |||||||
\(252\) | 19.5878 | 1.23391 | ||||||||
\(253\) | −15.2075 | −0.956085 | ||||||||
\(254\) | 43.6221 | 2.73709 | ||||||||
\(255\) | 0.142247 | 0.00890786 | ||||||||
\(256\) | −6.09641 | −0.381026 | ||||||||
\(257\) | −3.72216 | −0.232182 | −0.116091 | − | 0.993239i | \(-0.537036\pi\) | ||||
−0.116091 | + | 0.993239i | \(0.537036\pi\) | |||||||
\(258\) | 1.76870 | 0.110114 | ||||||||
\(259\) | −4.30166 | −0.267292 | ||||||||
\(260\) | 7.50596 | 0.465500 | ||||||||
\(261\) | −5.81072 | −0.359674 | ||||||||
\(262\) | −39.9466 | −2.46791 | ||||||||
\(263\) | −8.98303 | −0.553917 | −0.276959 | − | 0.960882i | \(-0.589327\pi\) | ||||
−0.276959 | + | 0.960882i | \(0.589327\pi\) | |||||||
\(264\) | 12.6234 | 0.776914 | ||||||||
\(265\) | −10.8808 | −0.668404 | ||||||||
\(266\) | 0.446978 | 0.0274060 | ||||||||
\(267\) | −2.10531 | −0.128843 | ||||||||
\(268\) | 23.0032 | 1.40514 | ||||||||
\(269\) | −20.1493 | −1.22852 | −0.614262 | − | 0.789102i | \(-0.710546\pi\) | ||||
−0.614262 | + | 0.789102i | \(0.710546\pi\) | |||||||
\(270\) | −10.4963 | −0.638786 | ||||||||
\(271\) | −2.56521 | −0.155825 | −0.0779127 | − | 0.996960i | \(-0.524826\pi\) | ||||
−0.0779127 | + | 0.996960i | \(0.524826\pi\) | |||||||
\(272\) | −2.13302 | −0.129334 | ||||||||
\(273\) | 1.73552 | 0.105038 | ||||||||
\(274\) | 54.9389 | 3.31898 | ||||||||
\(275\) | −2.20527 | −0.132983 | ||||||||
\(276\) | 24.9429 | 1.50139 | ||||||||
\(277\) | −29.1691 | −1.75260 | −0.876301 | − | 0.481764i | \(-0.839996\pi\) | ||||
−0.876301 | + | 0.481764i | \(0.839996\pi\) | |||||||
\(278\) | 50.8756 | 3.05131 | ||||||||
\(279\) | 8.15755 | 0.488380 | ||||||||
\(280\) | −12.5323 | −0.748948 | ||||||||
\(281\) | −2.16718 | −0.129283 | −0.0646416 | − | 0.997909i | \(-0.520590\pi\) | ||||
−0.0646416 | + | 0.997909i | \(0.520590\pi\) | |||||||
\(282\) | −9.27859 | −0.552532 | ||||||||
\(283\) | 22.9618 | 1.36494 | 0.682468 | − | 0.730915i | \(-0.260907\pi\) | ||||
0.682468 | + | 0.730915i | \(0.260907\pi\) | |||||||
\(284\) | −22.5512 | −1.33817 | ||||||||
\(285\) | −0.0772479 | −0.00457577 | ||||||||
\(286\) | −8.77577 | −0.518922 | ||||||||
\(287\) | −10.8111 | −0.638159 | ||||||||
\(288\) | 32.0999 | 1.89150 | ||||||||
\(289\) | −16.9616 | −0.997739 | ||||||||
\(290\) | 6.20863 | 0.364583 | ||||||||
\(291\) | 4.24850 | 0.249051 | ||||||||
\(292\) | 43.0715 | 2.52057 | ||||||||
\(293\) | −5.64281 | −0.329657 | −0.164828 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164828 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(294\) | 8.58434 | 0.500649 | ||||||||
\(295\) | 1.06512 | 0.0620138 | ||||||||
\(296\) | −21.3629 | −1.24170 | ||||||||
\(297\) | 8.75820 | 0.508202 | ||||||||
\(298\) | −1.15512 | −0.0669143 | ||||||||
\(299\) | −10.3833 | −0.600484 | ||||||||
\(300\) | 3.61703 | 0.208829 | ||||||||
\(301\) | 1.46516 | 0.0844507 | ||||||||
\(302\) | −26.7600 | −1.53987 | ||||||||
\(303\) | 4.25457 | 0.244419 | ||||||||
\(304\) | 1.15835 | 0.0664358 | ||||||||
\(305\) | 4.43798 | 0.254118 | ||||||||
\(306\) | −1.28162 | −0.0732651 | ||||||||
\(307\) | −6.50334 | −0.371165 | −0.185582 | − | 0.982629i | \(-0.559417\pi\) | ||||
−0.185582 | + | 0.982629i | \(0.559417\pi\) | |||||||
\(308\) | 17.4634 | 0.995070 | ||||||||
\(309\) | −4.54744 | −0.258695 | ||||||||
\(310\) | −8.71617 | −0.495045 | ||||||||
\(311\) | −27.1012 | −1.53677 | −0.768383 | − | 0.639990i | \(-0.778939\pi\) | ||||
−0.768383 | + | 0.639990i | \(0.778939\pi\) | |||||||
\(312\) | 8.61896 | 0.487953 | ||||||||
\(313\) | 17.5031 | 0.989332 | 0.494666 | − | 0.869083i | \(-0.335290\pi\) | ||||
0.494666 | + | 0.869083i | \(0.335290\pi\) | |||||||
\(314\) | 23.9090 | 1.34926 | ||||||||
\(315\) | −3.92934 | −0.221393 | ||||||||
\(316\) | −51.0174 | −2.86995 | ||||||||
\(317\) | 22.1024 | 1.24139 | 0.620697 | − | 0.784050i | \(-0.286850\pi\) | ||||
0.620697 | + | 0.784050i | \(0.286850\pi\) | |||||||
\(318\) | −20.8656 | −1.17009 | ||||||||
\(319\) | −5.18052 | −0.290053 | ||||||||
\(320\) | −12.5375 | −0.700869 | ||||||||
\(321\) | 7.57157 | 0.422604 | ||||||||
\(322\) | 28.9522 | 1.61344 | ||||||||
\(323\) | −0.0208717 | −0.00116133 | ||||||||
\(324\) | 22.6267 | 1.25704 | ||||||||
\(325\) | −1.50571 | −0.0835217 | ||||||||
\(326\) | 20.7094 | 1.14699 | ||||||||
\(327\) | 8.51547 | 0.470906 | ||||||||
\(328\) | −53.6902 | −2.96455 | ||||||||
\(329\) | −7.68626 | −0.423757 | ||||||||
\(330\) | −4.22893 | −0.232795 | ||||||||
\(331\) | −12.8352 | −0.705485 | −0.352743 | − | 0.935720i | \(-0.614751\pi\) | ||||
−0.352743 | + | 0.935720i | \(0.614751\pi\) | |||||||
\(332\) | 84.2181 | 4.62207 | ||||||||
\(333\) | −6.69808 | −0.367053 | ||||||||
\(334\) | 62.5634 | 3.42332 | ||||||||
\(335\) | −4.61448 | −0.252116 | ||||||||
\(336\) | −12.5409 | −0.684160 | ||||||||
\(337\) | −4.86167 | −0.264832 | −0.132416 | − | 0.991194i | \(-0.542273\pi\) | ||||
−0.132416 | + | 0.991194i | \(0.542273\pi\) | |||||||
\(338\) | 28.3660 | 1.54291 | ||||||||
\(339\) | −2.84786 | −0.154675 | ||||||||
\(340\) | 0.977288 | 0.0530009 | ||||||||
\(341\) | 7.27283 | 0.393846 | ||||||||
\(342\) | 0.695987 | 0.0376347 | ||||||||
\(343\) | 18.2310 | 0.984384 | ||||||||
\(344\) | 7.27632 | 0.392313 | ||||||||
\(345\) | −5.00360 | −0.269385 | ||||||||
\(346\) | 60.2753 | 3.24042 | ||||||||
\(347\) | 28.4873 | 1.52928 | 0.764638 | − | 0.644460i | \(-0.222918\pi\) | ||||
0.764638 | + | 0.644460i | \(0.222918\pi\) | |||||||
\(348\) | 8.49697 | 0.455485 | ||||||||
\(349\) | 2.95588 | 0.158224 | 0.0791122 | − | 0.996866i | \(-0.474791\pi\) | ||||
0.0791122 | + | 0.996866i | \(0.474791\pi\) | |||||||
\(350\) | 4.19842 | 0.224415 | ||||||||
\(351\) | 5.97991 | 0.319184 | ||||||||
\(352\) | 28.6185 | 1.52537 | ||||||||
\(353\) | −18.4537 | −0.982193 | −0.491096 | − | 0.871105i | \(-0.663404\pi\) | ||||
−0.491096 | + | 0.871105i | \(0.663404\pi\) | |||||||
\(354\) | 2.04253 | 0.108559 | ||||||||
\(355\) | 4.52381 | 0.240099 | ||||||||
\(356\) | −14.4642 | −0.766601 | ||||||||
\(357\) | 0.225967 | 0.0119595 | ||||||||
\(358\) | 49.7075 | 2.62712 | ||||||||
\(359\) | −7.90800 | −0.417368 | −0.208684 | − | 0.977983i | \(-0.566918\pi\) | ||||
−0.208684 | + | 0.977983i | \(0.566918\pi\) | |||||||
\(360\) | −19.5140 | −1.02848 | ||||||||
\(361\) | −18.9887 | −0.999403 | ||||||||
\(362\) | 11.1165 | 0.584273 | ||||||||
\(363\) | −4.45275 | −0.233709 | ||||||||
\(364\) | 11.9236 | 0.624968 | ||||||||
\(365\) | −8.64022 | −0.452250 | ||||||||
\(366\) | 8.51049 | 0.444851 | ||||||||
\(367\) | −8.17603 | −0.426785 | −0.213393 | − | 0.976967i | \(-0.568451\pi\) | ||||
−0.213393 | + | 0.976967i | \(0.568451\pi\) | |||||||
\(368\) | 75.0299 | 3.91120 | ||||||||
\(369\) | −16.8339 | −0.876338 | ||||||||
\(370\) | 7.15676 | 0.372062 | ||||||||
\(371\) | −17.2848 | −0.897383 | ||||||||
\(372\) | −11.9287 | −0.618476 | ||||||||
\(373\) | 18.9560 | 0.981507 | 0.490753 | − | 0.871299i | \(-0.336722\pi\) | ||||
0.490753 | + | 0.871299i | \(0.336722\pi\) | |||||||
\(374\) | −1.14262 | −0.0590834 | ||||||||
\(375\) | −0.725582 | −0.0374689 | ||||||||
\(376\) | −38.1716 | −1.96855 | ||||||||
\(377\) | −3.53715 | −0.182172 | ||||||||
\(378\) | −16.6740 | −0.857618 | ||||||||
\(379\) | 4.90940 | 0.252179 | 0.126089 | − | 0.992019i | \(-0.459757\pi\) | ||||
0.126089 | + | 0.992019i | \(0.459757\pi\) | |||||||
\(380\) | −0.530720 | −0.0272254 | ||||||||
\(381\) | −11.9759 | −0.613546 | ||||||||
\(382\) | −15.3375 | −0.784734 | ||||||||
\(383\) | 6.72804 | 0.343787 | 0.171893 | − | 0.985116i | \(-0.445012\pi\) | ||||
0.171893 | + | 0.985116i | \(0.445012\pi\) | |||||||
\(384\) | −5.21037 | −0.265890 | ||||||||
\(385\) | −3.50319 | −0.178539 | ||||||||
\(386\) | −51.4517 | −2.61882 | ||||||||
\(387\) | 2.28140 | 0.115970 | ||||||||
\(388\) | 29.1887 | 1.48183 | ||||||||
\(389\) | 11.7736 | 0.596947 | 0.298473 | − | 0.954418i | \(-0.403523\pi\) | ||||
0.298473 | + | 0.954418i | \(0.403523\pi\) | |||||||
\(390\) | −2.88742 | −0.146210 | ||||||||
\(391\) | −1.35193 | −0.0683698 | ||||||||
\(392\) | 35.3155 | 1.78370 | ||||||||
\(393\) | 10.9669 | 0.553206 | ||||||||
\(394\) | −23.0822 | −1.16286 | ||||||||
\(395\) | 10.2342 | 0.514937 | ||||||||
\(396\) | 27.1922 | 1.36646 | ||||||||
\(397\) | −20.2666 | −1.01715 | −0.508575 | − | 0.861018i | \(-0.669827\pi\) | ||||
−0.508575 | + | 0.861018i | \(0.669827\pi\) | |||||||
\(398\) | 11.4714 | 0.575012 | ||||||||
\(399\) | −0.122713 | −0.00614332 | ||||||||
\(400\) | 10.8802 | 0.544012 | ||||||||
\(401\) | −24.1730 | −1.20714 | −0.603571 | − | 0.797310i | \(-0.706256\pi\) | ||||
−0.603571 | + | 0.797310i | \(0.706256\pi\) | |||||||
\(402\) | −8.84896 | −0.441346 | ||||||||
\(403\) | 4.96573 | 0.247361 | ||||||||
\(404\) | 29.2304 | 1.45427 | ||||||||
\(405\) | −4.53895 | −0.225542 | ||||||||
\(406\) | 9.86275 | 0.489480 | ||||||||
\(407\) | −5.97165 | −0.296004 | ||||||||
\(408\) | 1.12220 | 0.0555573 | ||||||||
\(409\) | 1.31937 | 0.0652387 | 0.0326194 | − | 0.999468i | \(-0.489615\pi\) | ||||
0.0326194 | + | 0.999468i | \(0.489615\pi\) | |||||||
\(410\) | 17.9867 | 0.888298 | ||||||||
\(411\) | −15.0828 | −0.743981 | ||||||||
\(412\) | −31.2425 | −1.53921 | ||||||||
\(413\) | 1.69201 | 0.0832582 | ||||||||
\(414\) | 45.0813 | 2.21563 | ||||||||
\(415\) | −16.8943 | −0.829308 | ||||||||
\(416\) | 19.5401 | 0.958032 | ||||||||
\(417\) | −13.9673 | −0.683982 | ||||||||
\(418\) | 0.620504 | 0.0303499 | ||||||||
\(419\) | 5.46987 | 0.267221 | 0.133610 | − | 0.991034i | \(-0.457343\pi\) | ||||
0.133610 | + | 0.991034i | \(0.457343\pi\) | |||||||
\(420\) | 5.74585 | 0.280369 | ||||||||
\(421\) | 19.3563 | 0.943367 | 0.471683 | − | 0.881768i | \(-0.343647\pi\) | ||||
0.471683 | + | 0.881768i | \(0.343647\pi\) | |||||||
\(422\) | 35.8860 | 1.74690 | ||||||||
\(423\) | −11.9682 | −0.581915 | ||||||||
\(424\) | −85.8401 | −4.16876 | ||||||||
\(425\) | −0.196046 | −0.00950961 | ||||||||
\(426\) | 8.67508 | 0.420309 | ||||||||
\(427\) | 7.04998 | 0.341172 | ||||||||
\(428\) | 52.0194 | 2.51445 | ||||||||
\(429\) | 2.40929 | 0.116321 | ||||||||
\(430\) | −2.43763 | −0.117553 | ||||||||
\(431\) | 25.5736 | 1.23184 | 0.615919 | − | 0.787810i | \(-0.288785\pi\) | ||||
0.615919 | + | 0.787810i | \(0.288785\pi\) | |||||||
\(432\) | −43.2108 | −2.07898 | ||||||||
\(433\) | −2.95021 | −0.141778 | −0.0708891 | − | 0.997484i | \(-0.522584\pi\) | ||||
−0.0708891 | + | 0.997484i | \(0.522584\pi\) | |||||||
\(434\) | −13.8461 | −0.664635 | ||||||||
\(435\) | −1.70451 | −0.0817248 | ||||||||
\(436\) | 58.5043 | 2.80185 | ||||||||
\(437\) | 0.734170 | 0.0351201 | ||||||||
\(438\) | −16.5689 | −0.791693 | ||||||||
\(439\) | 21.2335 | 1.01342 | 0.506710 | − | 0.862117i | \(-0.330862\pi\) | ||||
0.506710 | + | 0.862117i | \(0.330862\pi\) | |||||||
\(440\) | −17.3976 | −0.829397 | ||||||||
\(441\) | 11.0727 | 0.527273 | ||||||||
\(442\) | −0.780156 | −0.0371082 | ||||||||
\(443\) | −3.61334 | −0.171675 | −0.0858376 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858376 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(444\) | 9.79455 | 0.464829 | ||||||||
\(445\) | 2.90154 | 0.137546 | ||||||||
\(446\) | −1.00753 | −0.0477077 | ||||||||
\(447\) | 0.317124 | 0.0149995 | ||||||||
\(448\) | −19.9166 | −0.940969 | ||||||||
\(449\) | −14.8918 | −0.702789 | −0.351395 | − | 0.936227i | \(-0.614292\pi\) | ||||
−0.351395 | + | 0.936227i | \(0.614292\pi\) | |||||||
\(450\) | 6.53733 | 0.308173 | ||||||||
\(451\) | −15.0082 | −0.706708 | ||||||||
\(452\) | −19.5658 | −0.920299 | ||||||||
\(453\) | 7.34665 | 0.345176 | ||||||||
\(454\) | −14.3622 | −0.674054 | ||||||||
\(455\) | −2.39190 | −0.112134 | ||||||||
\(456\) | −0.609417 | −0.0285386 | ||||||||
\(457\) | 15.7572 | 0.737089 | 0.368545 | − | 0.929610i | \(-0.379856\pi\) | ||||
0.368545 | + | 0.929610i | \(0.379856\pi\) | |||||||
\(458\) | −63.2818 | −2.95696 | ||||||||
\(459\) | 0.778594 | 0.0363417 | ||||||||
\(460\) | −34.3765 | −1.60281 | ||||||||
\(461\) | −21.8079 | −1.01570 | −0.507848 | − | 0.861447i | \(-0.669559\pi\) | ||||
−0.507848 | + | 0.861447i | \(0.669559\pi\) | |||||||
\(462\) | −6.71789 | −0.312545 | ||||||||
\(463\) | 31.8937 | 1.48223 | 0.741113 | − | 0.671381i | \(-0.234298\pi\) | ||||
0.741113 | + | 0.671381i | \(0.234298\pi\) | |||||||
\(464\) | 25.5594 | 1.18657 | ||||||||
\(465\) | 2.39292 | 0.110969 | ||||||||
\(466\) | −12.0543 | −0.558407 | ||||||||
\(467\) | 25.3220 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(468\) | 18.5662 | 0.858224 | ||||||||
\(469\) | −7.33036 | −0.338485 | ||||||||
\(470\) | 12.7878 | 0.589857 | ||||||||
\(471\) | −6.56393 | −0.302450 | ||||||||
\(472\) | 8.40286 | 0.386773 | ||||||||
\(473\) | 2.03397 | 0.0935221 | ||||||||
\(474\) | 19.6256 | 0.901432 | ||||||||
\(475\) | 0.106463 | 0.00488488 | ||||||||
\(476\) | 1.55248 | 0.0711576 | ||||||||
\(477\) | −26.9141 | −1.23231 | ||||||||
\(478\) | −27.6022 | −1.26249 | ||||||||
\(479\) | −6.57375 | −0.300362 | −0.150181 | − | 0.988658i | \(-0.547986\pi\) | ||||
−0.150181 | + | 0.988658i | \(0.547986\pi\) | |||||||
\(480\) | 9.41612 | 0.429785 | ||||||||
\(481\) | −4.07731 | −0.185909 | ||||||||
\(482\) | 27.3090 | 1.24389 | ||||||||
\(483\) | −7.94849 | −0.361669 | ||||||||
\(484\) | −30.5920 | −1.39054 | ||||||||
\(485\) | −5.85530 | −0.265875 | ||||||||
\(486\) | −40.1931 | −1.82320 | ||||||||
\(487\) | −27.1114 | −1.22853 | −0.614267 | − | 0.789098i | \(-0.710548\pi\) | ||||
−0.614267 | + | 0.789098i | \(0.710548\pi\) | |||||||
\(488\) | 35.0117 | 1.58490 | ||||||||
\(489\) | −5.68551 | −0.257108 | ||||||||
\(490\) | −11.8310 | −0.534469 | ||||||||
\(491\) | −6.01516 | −0.271460 | −0.135730 | − | 0.990746i | \(-0.543338\pi\) | ||||
−0.135730 | + | 0.990746i | \(0.543338\pi\) | |||||||
\(492\) | 24.6161 | 1.10978 | ||||||||
\(493\) | −0.460542 | −0.0207418 | ||||||||
\(494\) | 0.423667 | 0.0190617 | ||||||||
\(495\) | −5.45479 | −0.245175 | ||||||||
\(496\) | −35.8824 | −1.61117 | ||||||||
\(497\) | 7.18632 | 0.322351 | ||||||||
\(498\) | −32.3973 | −1.45176 | ||||||||
\(499\) | −2.72643 | −0.122052 | −0.0610259 | − | 0.998136i | \(-0.519437\pi\) | ||||
−0.0610259 | + | 0.998136i | \(0.519437\pi\) | |||||||
\(500\) | −4.98500 | −0.222936 | ||||||||
\(501\) | −17.1761 | −0.767369 | ||||||||
\(502\) | 22.8751 | 1.02097 | ||||||||
\(503\) | 19.6780 | 0.877400 | 0.438700 | − | 0.898633i | \(-0.355439\pi\) | ||||
0.438700 | + | 0.898633i | \(0.355439\pi\) | |||||||
\(504\) | −30.9990 | −1.38081 | ||||||||
\(505\) | −5.86367 | −0.260930 | ||||||||
\(506\) | 40.1920 | 1.78675 | ||||||||
\(507\) | −7.78755 | −0.345857 | ||||||||
\(508\) | −82.2789 | −3.65054 | ||||||||
\(509\) | 39.7918 | 1.76374 | 0.881870 | − | 0.471492i | \(-0.156285\pi\) | ||||
0.881870 | + | 0.471492i | \(0.156285\pi\) | |||||||
\(510\) | −0.375947 | −0.0166472 | ||||||||
\(511\) | −13.7255 | −0.607179 | ||||||||
\(512\) | 30.4742 | 1.34678 | ||||||||
\(513\) | −0.422819 | −0.0186679 | ||||||||
\(514\) | 9.83736 | 0.433908 | ||||||||
\(515\) | 6.26730 | 0.276170 | ||||||||
\(516\) | −3.33607 | −0.146862 | ||||||||
\(517\) | −10.6702 | −0.469276 | ||||||||
\(518\) | 11.3689 | 0.499521 | ||||||||
\(519\) | −16.5479 | −0.726372 | ||||||||
\(520\) | −11.8787 | −0.520915 | ||||||||
\(521\) | −25.1736 | −1.10287 | −0.551437 | − | 0.834216i | \(-0.685920\pi\) | ||||
−0.551437 | + | 0.834216i | \(0.685920\pi\) | |||||||
\(522\) | 15.3572 | 0.672168 | ||||||||
\(523\) | −30.9819 | −1.35475 | −0.677373 | − | 0.735640i | \(-0.736881\pi\) | ||||
−0.677373 | + | 0.735640i | \(0.736881\pi\) | |||||||
\(524\) | 75.3464 | 3.29152 | ||||||||
\(525\) | −1.15263 | −0.0503048 | ||||||||
\(526\) | 23.7414 | 1.03517 | ||||||||
\(527\) | 0.646546 | 0.0281640 | ||||||||
\(528\) | −17.4095 | −0.757650 | ||||||||
\(529\) | 24.5545 | 1.06759 | ||||||||
\(530\) | 28.7571 | 1.24913 | ||||||||
\(531\) | 2.63461 | 0.114332 | ||||||||
\(532\) | −0.843079 | −0.0365521 | ||||||||
\(533\) | −10.2473 | −0.443858 | ||||||||
\(534\) | 5.56415 | 0.240784 | ||||||||
\(535\) | −10.4352 | −0.451152 | ||||||||
\(536\) | −36.4041 | −1.57242 | ||||||||
\(537\) | −13.6466 | −0.588894 | ||||||||
\(538\) | 53.2529 | 2.29589 | ||||||||
\(539\) | 9.87185 | 0.425211 | ||||||||
\(540\) | 19.7979 | 0.851966 | ||||||||
\(541\) | −5.90962 | −0.254074 | −0.127037 | − | 0.991898i | \(-0.540547\pi\) | ||||
−0.127037 | + | 0.991898i | \(0.540547\pi\) | |||||||
\(542\) | 6.77963 | 0.291210 | ||||||||
\(543\) | −3.05192 | −0.130970 | ||||||||
\(544\) | 2.54415 | 0.109080 | ||||||||
\(545\) | −11.7361 | −0.502717 | ||||||||
\(546\) | −4.58683 | −0.196298 | ||||||||
\(547\) | 29.0896 | 1.24378 | 0.621891 | − | 0.783104i | \(-0.286365\pi\) | ||||
0.621891 | + | 0.783104i | \(0.286365\pi\) | |||||||
\(548\) | −103.624 | −4.42661 | ||||||||
\(549\) | 10.9775 | 0.468507 | ||||||||
\(550\) | 5.82833 | 0.248521 | ||||||||
\(551\) | 0.250099 | 0.0106546 | ||||||||
\(552\) | −39.4739 | −1.68012 | ||||||||
\(553\) | 16.2576 | 0.691342 | ||||||||
\(554\) | 77.0915 | 3.27530 | ||||||||
\(555\) | −1.96480 | −0.0834013 | ||||||||
\(556\) | −95.9603 | −4.06962 | ||||||||
\(557\) | −41.8074 | −1.77144 | −0.885718 | − | 0.464224i | \(-0.846333\pi\) | ||||
−0.885718 | + | 0.464224i | \(0.846333\pi\) | |||||||
\(558\) | −21.5597 | −0.912696 | ||||||||
\(559\) | 1.38875 | 0.0587379 | ||||||||
\(560\) | 17.2839 | 0.730377 | ||||||||
\(561\) | 0.313693 | 0.0132441 | ||||||||
\(562\) | 5.72768 | 0.241608 | ||||||||
\(563\) | −4.68519 | −0.197457 | −0.0987286 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987286 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(564\) | 17.5010 | 0.736927 | ||||||||
\(565\) | 3.92494 | 0.165123 | ||||||||
\(566\) | −60.6861 | −2.55083 | ||||||||
\(567\) | −7.21038 | −0.302807 | ||||||||
\(568\) | 35.6888 | 1.49747 | ||||||||
\(569\) | 26.2582 | 1.10080 | 0.550401 | − | 0.834900i | \(-0.314475\pi\) | ||||
0.550401 | + | 0.834900i | \(0.314475\pi\) | |||||||
\(570\) | 0.204160 | 0.00855131 | ||||||||
\(571\) | −33.9283 | −1.41986 | −0.709928 | − | 0.704274i | \(-0.751272\pi\) | ||||
−0.709928 | + | 0.704274i | \(0.751272\pi\) | |||||||
\(572\) | 16.5526 | 0.692101 | ||||||||
\(573\) | 4.21073 | 0.175906 | ||||||||
\(574\) | 28.5728 | 1.19261 | ||||||||
\(575\) | 6.89598 | 0.287582 | ||||||||
\(576\) | −31.0120 | −1.29217 | ||||||||
\(577\) | −8.47874 | −0.352974 | −0.176487 | − | 0.984303i | \(-0.556473\pi\) | ||||
−0.176487 | + | 0.984303i | \(0.556473\pi\) | |||||||
\(578\) | 44.8280 | 1.86460 | ||||||||
\(579\) | 14.1255 | 0.587034 | ||||||||
\(580\) | −11.7106 | −0.486254 | ||||||||
\(581\) | −26.8375 | −1.11341 | ||||||||
\(582\) | −11.2284 | −0.465433 | ||||||||
\(583\) | −23.9951 | −0.993777 | ||||||||
\(584\) | −68.1636 | −2.82063 | ||||||||
\(585\) | −3.72442 | −0.153986 | ||||||||
\(586\) | 14.9135 | 0.616070 | ||||||||
\(587\) | 5.70816 | 0.235601 | 0.117801 | − | 0.993037i | \(-0.462416\pi\) | ||||
0.117801 | + | 0.993037i | \(0.462416\pi\) | |||||||
\(588\) | −16.1916 | −0.667729 | ||||||||
\(589\) | −0.351110 | −0.0144672 | ||||||||
\(590\) | −2.81503 | −0.115893 | ||||||||
\(591\) | 6.33695 | 0.260667 | ||||||||
\(592\) | 29.4626 | 1.21091 | ||||||||
\(593\) | 1.98524 | 0.0815239 | 0.0407620 | − | 0.999169i | \(-0.487021\pi\) | ||||
0.0407620 | + | 0.999169i | \(0.487021\pi\) | |||||||
\(594\) | −23.1472 | −0.949740 | ||||||||
\(595\) | −0.311429 | −0.0127674 | ||||||||
\(596\) | 2.17876 | 0.0892454 | ||||||||
\(597\) | −3.14935 | −0.128894 | ||||||||
\(598\) | 27.4423 | 1.12220 | ||||||||
\(599\) | −18.5941 | −0.759733 | −0.379867 | − | 0.925041i | \(-0.624030\pi\) | ||||
−0.379867 | + | 0.925041i | \(0.624030\pi\) | |||||||
\(600\) | −5.72419 | −0.233689 | ||||||||
\(601\) | 18.5747 | 0.757678 | 0.378839 | − | 0.925463i | \(-0.376323\pi\) | ||||
0.378839 | + | 0.925463i | \(0.376323\pi\) | |||||||
\(602\) | −3.87231 | −0.157823 | ||||||||
\(603\) | −11.4141 | −0.464816 | ||||||||
\(604\) | 50.4741 | 2.05376 | ||||||||
\(605\) | 6.13680 | 0.249496 | ||||||||
\(606\) | −11.2445 | −0.456775 | ||||||||
\(607\) | −0.730606 | −0.0296544 | −0.0148272 | − | 0.999890i | \(-0.504720\pi\) | ||||
−0.0148272 | + | 0.999890i | \(0.504720\pi\) | |||||||
\(608\) | −1.38161 | −0.0560318 | ||||||||
\(609\) | −2.70770 | −0.109722 | ||||||||
\(610\) | −11.7292 | −0.474901 | ||||||||
\(611\) | −7.28540 | −0.294736 | ||||||||
\(612\) | 2.41735 | 0.0977157 | ||||||||
\(613\) | −24.6791 | −0.996781 | −0.498390 | − | 0.866953i | \(-0.666075\pi\) | ||||
−0.498390 | + | 0.866953i | \(0.666075\pi\) | |||||||
\(614\) | 17.1878 | 0.693642 | ||||||||
\(615\) | −4.93803 | −0.199120 | ||||||||
\(616\) | −27.6370 | −1.11353 | ||||||||
\(617\) | 44.7941 | 1.80334 | 0.901672 | − | 0.432421i | \(-0.142341\pi\) | ||||
0.901672 | + | 0.432421i | \(0.142341\pi\) | |||||||
\(618\) | 12.0185 | 0.483455 | ||||||||
\(619\) | 0.750312 | 0.0301576 | 0.0150788 | − | 0.999886i | \(-0.495200\pi\) | ||||
0.0150788 | + | 0.999886i | \(0.495200\pi\) | |||||||
\(620\) | 16.4402 | 0.660256 | ||||||||
\(621\) | −27.3873 | −1.09902 | ||||||||
\(622\) | 71.6261 | 2.87195 | ||||||||
\(623\) | 4.60927 | 0.184666 | ||||||||
\(624\) | −11.8868 | −0.475854 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −46.2591 | −1.84889 | ||||||||
\(627\) | −0.170352 | −0.00680321 | ||||||||
\(628\) | −45.0965 | −1.79955 | ||||||||
\(629\) | −0.530872 | −0.0211673 | ||||||||
\(630\) | 10.3849 | 0.413745 | ||||||||
\(631\) | −4.85918 | −0.193441 | −0.0967205 | − | 0.995312i | \(-0.530835\pi\) | ||||
−0.0967205 | + | 0.995312i | \(0.530835\pi\) | |||||||
\(632\) | 80.7385 | 3.21160 | ||||||||
\(633\) | −9.85209 | −0.391585 | ||||||||
\(634\) | −58.4148 | −2.31995 | ||||||||
\(635\) | 16.5053 | 0.654993 | ||||||||
\(636\) | 39.3563 | 1.56058 | ||||||||
\(637\) | 6.74029 | 0.267060 | ||||||||
\(638\) | 13.6917 | 0.542059 | ||||||||
\(639\) | 11.1898 | 0.442661 | ||||||||
\(640\) | 7.18095 | 0.283852 | ||||||||
\(641\) | −0.703440 | −0.0277842 | −0.0138921 | − | 0.999904i | \(-0.504422\pi\) | ||||
−0.0138921 | + | 0.999904i | \(0.504422\pi\) | |||||||
\(642\) | −20.0110 | −0.789772 | ||||||||
\(643\) | −39.2347 | −1.54726 | −0.773632 | − | 0.633635i | \(-0.781562\pi\) | ||||
−0.773632 | + | 0.633635i | \(0.781562\pi\) | |||||||
\(644\) | −54.6089 | −2.15189 | ||||||||
\(645\) | 0.669222 | 0.0263506 | ||||||||
\(646\) | 0.0551621 | 0.00217032 | ||||||||
\(647\) | −26.5099 | −1.04221 | −0.521107 | − | 0.853492i | \(-0.674481\pi\) | ||||
−0.521107 | + | 0.853492i | \(0.674481\pi\) | |||||||
\(648\) | −35.8083 | −1.40668 | ||||||||
\(649\) | 2.34888 | 0.0922015 | ||||||||
\(650\) | 3.97946 | 0.156087 | ||||||||
\(651\) | 3.80129 | 0.148984 | ||||||||
\(652\) | −39.0615 | −1.52977 | ||||||||
\(653\) | 18.6994 | 0.731763 | 0.365881 | − | 0.930661i | \(-0.380768\pi\) | ||||
0.365881 | + | 0.930661i | \(0.380768\pi\) | |||||||
\(654\) | −22.5057 | −0.880041 | ||||||||
\(655\) | −15.1146 | −0.590577 | ||||||||
\(656\) | 74.0467 | 2.89104 | ||||||||
\(657\) | −21.3718 | −0.833795 | ||||||||
\(658\) | 20.3141 | 0.791927 | ||||||||
\(659\) | −37.8549 | −1.47462 | −0.737308 | − | 0.675557i | \(-0.763903\pi\) | ||||
−0.737308 | + | 0.675557i | \(0.763903\pi\) | |||||||
\(660\) | 7.97650 | 0.310485 | ||||||||
\(661\) | −22.6193 | −0.879790 | −0.439895 | − | 0.898049i | \(-0.644984\pi\) | ||||
−0.439895 | + | 0.898049i | \(0.644984\pi\) | |||||||
\(662\) | 33.9223 | 1.31843 | ||||||||
\(663\) | 0.214183 | 0.00831817 | ||||||||
\(664\) | −133.281 | −5.17230 | ||||||||
\(665\) | 0.169123 | 0.00655831 | ||||||||
\(666\) | 17.7025 | 0.685957 | ||||||||
\(667\) | 16.1997 | 0.627257 | ||||||||
\(668\) | −118.006 | −4.56577 | ||||||||
\(669\) | 0.276605 | 0.0106942 | ||||||||
\(670\) | 12.1957 | 0.471160 | ||||||||
\(671\) | 9.78692 | 0.377820 | ||||||||
\(672\) | 14.9580 | 0.577019 | ||||||||
\(673\) | 0.472818 | 0.0182258 | 0.00911289 | − | 0.999958i | \(-0.497099\pi\) | ||||
0.00911289 | + | 0.999958i | \(0.497099\pi\) | |||||||
\(674\) | 12.8490 | 0.494924 | ||||||||
\(675\) | −3.97149 | −0.152863 | ||||||||
\(676\) | −53.5032 | −2.05782 | ||||||||
\(677\) | −45.2312 | −1.73838 | −0.869189 | − | 0.494480i | \(-0.835359\pi\) | ||||
−0.869189 | + | 0.494480i | \(0.835359\pi\) | |||||||
\(678\) | 7.52666 | 0.289060 | ||||||||
\(679\) | −9.30147 | −0.356958 | ||||||||
\(680\) | −1.54662 | −0.0593104 | ||||||||
\(681\) | 3.94299 | 0.151096 | ||||||||
\(682\) | −19.2215 | −0.736028 | ||||||||
\(683\) | −12.8065 | −0.490028 | −0.245014 | − | 0.969520i | \(-0.578793\pi\) | ||||
−0.245014 | + | 0.969520i | \(0.578793\pi\) | |||||||
\(684\) | −1.31275 | −0.0501944 | ||||||||
\(685\) | 20.7872 | 0.794239 | ||||||||
\(686\) | −48.1831 | −1.83964 | ||||||||
\(687\) | 17.3733 | 0.662832 | ||||||||
\(688\) | −10.0351 | −0.382585 | ||||||||
\(689\) | −16.3834 | −0.624157 | ||||||||
\(690\) | 13.2241 | 0.503432 | ||||||||
\(691\) | −3.26394 | −0.124166 | −0.0620830 | − | 0.998071i | \(-0.519774\pi\) | ||||
−0.0620830 | + | 0.998071i | \(0.519774\pi\) | |||||||
\(692\) | −113.690 | −4.32184 | ||||||||
\(693\) | −8.66525 | −0.329166 | ||||||||
\(694\) | −75.2894 | −2.85795 | ||||||||
\(695\) | 19.2498 | 0.730186 | ||||||||
\(696\) | −13.4470 | −0.509708 | ||||||||
\(697\) | −1.33421 | −0.0505368 | ||||||||
\(698\) | −7.81213 | −0.295694 | ||||||||
\(699\) | 3.30938 | 0.125172 | ||||||||
\(700\) | −7.91896 | −0.299308 | ||||||||
\(701\) | −5.12310 | −0.193497 | −0.0967485 | − | 0.995309i | \(-0.530844\pi\) | ||||
−0.0967485 | + | 0.995309i | \(0.530844\pi\) | |||||||
\(702\) | −15.8044 | −0.596499 | ||||||||
\(703\) | 0.288293 | 0.0108732 | ||||||||
\(704\) | −27.6486 | −1.04205 | ||||||||
\(705\) | −3.51074 | −0.132222 | ||||||||
\(706\) | 48.7716 | 1.83554 | ||||||||
\(707\) | −9.31477 | −0.350318 | ||||||||
\(708\) | −3.85257 | −0.144789 | ||||||||
\(709\) | 21.6961 | 0.814815 | 0.407407 | − | 0.913247i | \(-0.366433\pi\) | ||||
0.407407 | + | 0.913247i | \(0.366433\pi\) | |||||||
\(710\) | −11.9560 | −0.448702 | ||||||||
\(711\) | 25.3145 | 0.949369 | ||||||||
\(712\) | 22.8906 | 0.857861 | ||||||||
\(713\) | −22.7425 | −0.851714 | ||||||||
\(714\) | −0.597213 | −0.0223501 | ||||||||
\(715\) | −3.32049 | −0.124179 | ||||||||
\(716\) | −93.7570 | −3.50386 | ||||||||
\(717\) | 7.57785 | 0.283000 | ||||||||
\(718\) | 20.9002 | 0.779987 | ||||||||
\(719\) | −23.8369 | −0.888967 | −0.444483 | − | 0.895787i | \(-0.646613\pi\) | ||||
−0.444483 | + | 0.895787i | \(0.646613\pi\) | |||||||
\(720\) | 26.9126 | 1.00297 | ||||||||
\(721\) | 9.95596 | 0.370779 | ||||||||
\(722\) | 50.1854 | 1.86771 | ||||||||
\(723\) | −7.49737 | −0.278830 | ||||||||
\(724\) | −20.9678 | −0.779260 | ||||||||
\(725\) | 2.34916 | 0.0872455 | ||||||||
\(726\) | 11.7682 | 0.436760 | ||||||||
\(727\) | 31.0562 | 1.15181 | 0.575905 | − | 0.817517i | \(-0.304650\pi\) | ||||
0.575905 | + | 0.817517i | \(0.304650\pi\) | |||||||
\(728\) | −18.8700 | −0.699368 | ||||||||
\(729\) | −2.58231 | −0.0956410 | ||||||||
\(730\) | 22.8354 | 0.845175 | ||||||||
\(731\) | 0.180818 | 0.00668778 | ||||||||
\(732\) | −16.0523 | −0.593309 | ||||||||
\(733\) | −30.2746 | −1.11822 | −0.559109 | − | 0.829094i | \(-0.688857\pi\) | ||||
−0.559109 | + | 0.829094i | \(0.688857\pi\) | |||||||
\(734\) | 21.6086 | 0.797586 | ||||||||
\(735\) | 3.24806 | 0.119806 | ||||||||
\(736\) | −89.4914 | −3.29870 | ||||||||
\(737\) | −10.1762 | −0.374844 | ||||||||
\(738\) | 44.4906 | 1.63772 | ||||||||
\(739\) | −15.6635 | −0.576192 | −0.288096 | − | 0.957602i | \(-0.593022\pi\) | ||||
−0.288096 | + | 0.957602i | \(0.593022\pi\) | |||||||
\(740\) | −13.4989 | −0.496229 | ||||||||
\(741\) | −0.116313 | −0.00427286 | ||||||||
\(742\) | 45.6823 | 1.67705 | ||||||||
\(743\) | −13.5579 | −0.497390 | −0.248695 | − | 0.968582i | \(-0.580002\pi\) | ||||
−0.248695 | + | 0.968582i | \(0.580002\pi\) | |||||||
\(744\) | 18.8780 | 0.692102 | ||||||||
\(745\) | −0.437062 | −0.0160127 | ||||||||
\(746\) | −50.0992 | −1.83426 | ||||||||
\(747\) | −41.7886 | −1.52896 | ||||||||
\(748\) | 2.15518 | 0.0788012 | ||||||||
\(749\) | −16.5769 | −0.605705 | ||||||||
\(750\) | 1.91765 | 0.0700227 | ||||||||
\(751\) | −17.7221 | −0.646690 | −0.323345 | − | 0.946281i | \(-0.604807\pi\) | ||||
−0.323345 | + | 0.946281i | \(0.604807\pi\) | |||||||
\(752\) | 52.6442 | 1.91974 | ||||||||
\(753\) | −6.28009 | −0.228859 | ||||||||
\(754\) | 9.34838 | 0.340448 | ||||||||
\(755\) | −10.1252 | −0.368493 | ||||||||
\(756\) | 31.4501 | 1.14383 | ||||||||
\(757\) | −16.3245 | −0.593324 | −0.296662 | − | 0.954983i | \(-0.595873\pi\) | ||||
−0.296662 | + | 0.954983i | \(0.595873\pi\) | |||||||
\(758\) | −12.9751 | −0.471278 | ||||||||
\(759\) | −11.0343 | −0.400518 | ||||||||
\(760\) | 0.839902 | 0.0304664 | ||||||||
\(761\) | −6.27548 | −0.227486 | −0.113743 | − | 0.993510i | \(-0.536284\pi\) | ||||
−0.113743 | + | 0.993510i | \(0.536284\pi\) | |||||||
\(762\) | 31.6514 | 1.14661 | ||||||||
\(763\) | −18.6434 | −0.674936 | ||||||||
\(764\) | 28.9292 | 1.04662 | ||||||||
\(765\) | −0.484925 | −0.0175325 | ||||||||
\(766\) | −17.7816 | −0.642477 | ||||||||
\(767\) | 1.60376 | 0.0579086 | ||||||||
\(768\) | −4.42344 | −0.159617 | ||||||||
\(769\) | 17.8973 | 0.645392 | 0.322696 | − | 0.946503i | \(-0.395411\pi\) | ||||
0.322696 | + | 0.946503i | \(0.395411\pi\) | |||||||
\(770\) | 9.25863 | 0.333658 | ||||||||
\(771\) | −2.70073 | −0.0972645 | ||||||||
\(772\) | 97.0469 | 3.49280 | ||||||||
\(773\) | 14.7341 | 0.529950 | 0.264975 | − | 0.964255i | \(-0.414636\pi\) | ||||
0.264975 | + | 0.964255i | \(0.414636\pi\) | |||||||
\(774\) | −6.02954 | −0.216727 | ||||||||
\(775\) | −3.29794 | −0.118465 | ||||||||
\(776\) | −46.1931 | −1.65824 | ||||||||
\(777\) | −3.12120 | −0.111973 | ||||||||
\(778\) | −31.1167 | −1.11559 | ||||||||
\(779\) | 0.724549 | 0.0259597 | ||||||||
\(780\) | 5.44619 | 0.195005 | ||||||||
\(781\) | 9.97620 | 0.356976 | ||||||||
\(782\) | 3.57303 | 0.127771 | ||||||||
\(783\) | −9.32967 | −0.333415 | ||||||||
\(784\) | −48.7053 | −1.73947 | ||||||||
\(785\) | 9.04644 | 0.322881 | ||||||||
\(786\) | −28.9846 | −1.03384 | ||||||||
\(787\) | 18.2463 | 0.650409 | 0.325204 | − | 0.945644i | \(-0.394567\pi\) | ||||
0.325204 | + | 0.945644i | \(0.394567\pi\) | |||||||
\(788\) | 43.5371 | 1.55094 | ||||||||
\(789\) | −6.51792 | −0.232044 | ||||||||
\(790\) | −27.0480 | −0.962326 | ||||||||
\(791\) | 6.23499 | 0.221691 | ||||||||
\(792\) | −43.0335 | −1.52913 | ||||||||
\(793\) | 6.68230 | 0.237295 | ||||||||
\(794\) | 53.5628 | 1.90087 | ||||||||
\(795\) | −7.89494 | −0.280005 | ||||||||
\(796\) | −21.6372 | −0.766909 | ||||||||
\(797\) | −33.4749 | −1.18574 | −0.592871 | − | 0.805297i | \(-0.702006\pi\) | ||||
−0.592871 | + | 0.805297i | \(0.702006\pi\) | |||||||
\(798\) | 0.324319 | 0.0114808 | ||||||||
\(799\) | −0.948570 | −0.0335580 | ||||||||
\(800\) | −12.9773 | −0.458818 | ||||||||
\(801\) | 7.17706 | 0.253589 | ||||||||
\(802\) | 63.8871 | 2.25593 | ||||||||
\(803\) | −19.0540 | −0.672400 | ||||||||
\(804\) | 16.6907 | 0.588635 | ||||||||
\(805\) | 10.9546 | 0.386101 | ||||||||
\(806\) | −13.1240 | −0.462274 | ||||||||
\(807\) | −14.6200 | −0.514647 | ||||||||
\(808\) | −46.2591 | −1.62739 | ||||||||
\(809\) | 1.36726 | 0.0480702 | 0.0240351 | − | 0.999711i | \(-0.492349\pi\) | ||||
0.0240351 | + | 0.999711i | \(0.492349\pi\) | |||||||
\(810\) | 11.9961 | 0.421499 | ||||||||
\(811\) | 12.2338 | 0.429587 | 0.214794 | − | 0.976659i | \(-0.431092\pi\) | ||||
0.214794 | + | 0.976659i | \(0.431092\pi\) | |||||||
\(812\) | −18.6029 | −0.652833 | ||||||||
\(813\) | −1.86127 | −0.0652776 | ||||||||
\(814\) | 15.7826 | 0.553178 | ||||||||
\(815\) | 7.83580 | 0.274476 | ||||||||
\(816\) | −1.54768 | −0.0541797 | ||||||||
\(817\) | −0.0981938 | −0.00343537 | ||||||||
\(818\) | −3.48699 | −0.121920 | ||||||||
\(819\) | −5.91645 | −0.206737 | ||||||||
\(820\) | −33.9260 | −1.18475 | ||||||||
\(821\) | −17.0960 | −0.596654 | −0.298327 | − | 0.954464i | \(-0.596429\pi\) | ||||
−0.298327 | + | 0.954464i | \(0.596429\pi\) | |||||||
\(822\) | 39.8627 | 1.39037 | ||||||||
\(823\) | −34.6417 | −1.20753 | −0.603767 | − | 0.797161i | \(-0.706334\pi\) | ||||
−0.603767 | + | 0.797161i | \(0.706334\pi\) | |||||||
\(824\) | 49.4434 | 1.72244 | ||||||||
\(825\) | −1.60010 | −0.0557084 | ||||||||
\(826\) | −4.47183 | −0.155595 | ||||||||
\(827\) | 4.58823 | 0.159548 | 0.0797742 | − | 0.996813i | \(-0.474580\pi\) | ||||
0.0797742 | + | 0.996813i | \(0.474580\pi\) | |||||||
\(828\) | −85.0313 | −2.95504 | ||||||||
\(829\) | 19.9524 | 0.692974 | 0.346487 | − | 0.938055i | \(-0.387374\pi\) | ||||
0.346487 | + | 0.938055i | \(0.387374\pi\) | |||||||
\(830\) | 44.6502 | 1.54983 | ||||||||
\(831\) | −21.1646 | −0.734191 | ||||||||
\(832\) | −18.8779 | −0.654472 | ||||||||
\(833\) | 0.877596 | 0.0304069 | ||||||||
\(834\) | 36.9144 | 1.27824 | ||||||||
\(835\) | 23.6721 | 0.819207 | ||||||||
\(836\) | −1.17038 | −0.0404784 | ||||||||
\(837\) | 13.0977 | 0.452724 | ||||||||
\(838\) | −14.4564 | −0.499388 | ||||||||
\(839\) | −18.7009 | −0.645626 | −0.322813 | − | 0.946463i | \(-0.604629\pi\) | ||||
−0.322813 | + | 0.946463i | \(0.604629\pi\) | |||||||
\(840\) | −9.09320 | −0.313745 | ||||||||
\(841\) | −23.4815 | −0.809705 | ||||||||
\(842\) | −51.1570 | −1.76299 | ||||||||
\(843\) | −1.57247 | −0.0541587 | ||||||||
\(844\) | −67.6873 | −2.32989 | ||||||||
\(845\) | 10.7328 | 0.369221 | ||||||||
\(846\) | 31.6310 | 1.08750 | ||||||||
\(847\) | 9.74865 | 0.334968 | ||||||||
\(848\) | 118.386 | 4.06540 | ||||||||
\(849\) | 16.6606 | 0.571792 | ||||||||
\(850\) | 0.518132 | 0.0177718 | ||||||||
\(851\) | 18.6736 | 0.640124 | ||||||||
\(852\) | −16.3627 | −0.560578 | ||||||||
\(853\) | −19.0246 | −0.651391 | −0.325696 | − | 0.945475i | \(-0.605598\pi\) | ||||
−0.325696 | + | 0.945475i | \(0.605598\pi\) | |||||||
\(854\) | −18.6325 | −0.637591 | ||||||||
\(855\) | 0.263341 | 0.00900606 | ||||||||
\(856\) | −82.3242 | −2.81378 | ||||||||
\(857\) | 2.40859 | 0.0822757 | 0.0411379 | − | 0.999153i | \(-0.486902\pi\) | ||||
0.0411379 | + | 0.999153i | \(0.486902\pi\) | |||||||
\(858\) | −6.36754 | −0.217384 | ||||||||
\(859\) | −25.1119 | −0.856807 | −0.428403 | − | 0.903588i | \(-0.640924\pi\) | ||||
−0.428403 | + | 0.903588i | \(0.640924\pi\) | |||||||
\(860\) | 4.59779 | 0.156783 | ||||||||
\(861\) | −7.84433 | −0.267334 | ||||||||
\(862\) | −67.5889 | −2.30209 | ||||||||
\(863\) | −34.4222 | −1.17174 | −0.585872 | − | 0.810403i | \(-0.699248\pi\) | ||||
−0.585872 | + | 0.810403i | \(0.699248\pi\) | |||||||
\(864\) | 51.5394 | 1.75341 | ||||||||
\(865\) | 22.8064 | 0.775440 | ||||||||
\(866\) | 7.79717 | 0.264958 | ||||||||
\(867\) | −12.3070 | −0.417968 | ||||||||
\(868\) | 26.1162 | 0.886443 | ||||||||
\(869\) | 22.5691 | 0.765603 | ||||||||
\(870\) | 4.50487 | 0.152729 | ||||||||
\(871\) | −6.94806 | −0.235426 | ||||||||
\(872\) | −92.5870 | −3.13539 | ||||||||
\(873\) | −14.4833 | −0.490184 | ||||||||
\(874\) | −1.94035 | −0.0656333 | ||||||||
\(875\) | 1.58856 | 0.0537030 | ||||||||
\(876\) | 31.2519 | 1.05590 | ||||||||
\(877\) | −2.73222 | −0.0922607 | −0.0461303 | − | 0.998935i | \(-0.514689\pi\) | ||||
−0.0461303 | + | 0.998935i | \(0.514689\pi\) | |||||||
\(878\) | −56.1183 | −1.89390 | ||||||||
\(879\) | −4.09432 | −0.138098 | ||||||||
\(880\) | 23.9938 | 0.808832 | ||||||||
\(881\) | −29.0709 | −0.979423 | −0.489712 | − | 0.871884i | \(-0.662898\pi\) | ||||
−0.489712 | + | 0.871884i | \(0.662898\pi\) | |||||||
\(882\) | −29.2643 | −0.985380 | ||||||||
\(883\) | −23.8399 | −0.802276 | −0.401138 | − | 0.916018i | \(-0.631385\pi\) | ||||
−0.401138 | + | 0.916018i | \(0.631385\pi\) | |||||||
\(884\) | 1.47151 | 0.0494923 | ||||||||
\(885\) | 0.772833 | 0.0259785 | ||||||||
\(886\) | 9.54976 | 0.320830 | ||||||||
\(887\) | 8.48623 | 0.284940 | 0.142470 | − | 0.989799i | \(-0.454496\pi\) | ||||
0.142470 | + | 0.989799i | \(0.454496\pi\) | |||||||
\(888\) | −15.5006 | −0.520165 | ||||||||
\(889\) | 26.2196 | 0.879377 | ||||||||
\(890\) | −7.66853 | −0.257050 | ||||||||
\(891\) | −10.0096 | −0.335334 | ||||||||
\(892\) | 1.90037 | 0.0636291 | ||||||||
\(893\) | 0.515125 | 0.0172380 | ||||||||
\(894\) | −0.838133 | −0.0280314 | ||||||||
\(895\) | 18.8078 | 0.628676 | ||||||||
\(896\) | 11.4073 | 0.381093 | ||||||||
\(897\) | −7.53396 | −0.251551 | ||||||||
\(898\) | 39.3579 | 1.31339 | ||||||||
\(899\) | −7.74738 | −0.258390 | ||||||||
\(900\) | −12.3306 | −0.411019 | ||||||||
\(901\) | −2.13314 | −0.0710652 | ||||||||
\(902\) | 39.6654 | 1.32071 | ||||||||
\(903\) | 1.06310 | 0.0353776 | ||||||||
\(904\) | 30.9643 | 1.02986 | ||||||||
\(905\) | 4.20617 | 0.139818 | ||||||||
\(906\) | −19.4166 | −0.645072 | ||||||||
\(907\) | −52.7608 | −1.75189 | −0.875947 | − | 0.482407i | \(-0.839763\pi\) | ||||
−0.875947 | + | 0.482407i | \(0.839763\pi\) | |||||||
\(908\) | 27.0897 | 0.899004 | ||||||||
\(909\) | −14.5040 | −0.481066 | ||||||||
\(910\) | 6.32160 | 0.209559 | ||||||||
\(911\) | −5.96419 | −0.197603 | −0.0988013 | − | 0.995107i | \(-0.531501\pi\) | ||||
−0.0988013 | + | 0.995107i | \(0.531501\pi\) | |||||||
\(912\) | 0.840476 | 0.0278309 | ||||||||
\(913\) | −37.2564 | −1.23301 | ||||||||
\(914\) | −41.6449 | −1.37749 | ||||||||
\(915\) | 3.22011 | 0.106454 | ||||||||
\(916\) | 119.361 | 3.94378 | ||||||||
\(917\) | −24.0104 | −0.792894 | ||||||||
\(918\) | −2.05776 | −0.0679161 | ||||||||
\(919\) | 23.8602 | 0.787075 | 0.393538 | − | 0.919308i | \(-0.371251\pi\) | ||||
0.393538 | + | 0.919308i | \(0.371251\pi\) | |||||||
\(920\) | 54.4031 | 1.79362 | ||||||||
\(921\) | −4.71870 | −0.155486 | ||||||||
\(922\) | 57.6365 | 1.89816 | ||||||||
\(923\) | 6.81153 | 0.224204 | ||||||||
\(924\) | 12.6711 | 0.416849 | ||||||||
\(925\) | 2.70790 | 0.0890353 | ||||||||
\(926\) | −84.2923 | −2.77002 | ||||||||
\(927\) | 15.5024 | 0.509165 | ||||||||
\(928\) | −30.4858 | −1.00075 | ||||||||
\(929\) | 53.5677 | 1.75750 | 0.878750 | − | 0.477282i | \(-0.158378\pi\) | ||||
0.878750 | + | 0.477282i | \(0.158378\pi\) | |||||||
\(930\) | −6.32429 | −0.207382 | ||||||||
\(931\) | −0.476582 | −0.0156194 | ||||||||
\(932\) | 22.7366 | 0.744762 | ||||||||
\(933\) | −19.6641 | −0.643774 | ||||||||
\(934\) | −66.9239 | −2.18982 | ||||||||
\(935\) | −0.432333 | −0.0141388 | ||||||||
\(936\) | −29.3823 | −0.960391 | ||||||||
\(937\) | 36.9692 | 1.20773 | 0.603866 | − | 0.797086i | \(-0.293626\pi\) | ||||
0.603866 | + | 0.797086i | \(0.293626\pi\) | |||||||
\(938\) | 19.3735 | 0.632568 | ||||||||
\(939\) | 12.6999 | 0.414446 | ||||||||
\(940\) | −24.1200 | −0.786708 | ||||||||
\(941\) | 27.6823 | 0.902419 | 0.451209 | − | 0.892418i | \(-0.350993\pi\) | ||||
0.451209 | + | 0.892418i | \(0.350993\pi\) | |||||||
\(942\) | 17.3479 | 0.565226 | ||||||||
\(943\) | 46.9314 | 1.52830 | ||||||||
\(944\) | −11.5888 | −0.377183 | ||||||||
\(945\) | −6.30894 | −0.205230 | ||||||||
\(946\) | −5.37561 | −0.174776 | ||||||||
\(947\) | 16.2867 | 0.529248 | 0.264624 | − | 0.964352i | \(-0.414752\pi\) | ||||
0.264624 | + | 0.964352i | \(0.414752\pi\) | |||||||
\(948\) | −37.0173 | −1.20226 | ||||||||
\(949\) | −13.0096 | −0.422311 | ||||||||
\(950\) | −0.281374 | −0.00912897 | ||||||||
\(951\) | 16.0371 | 0.520038 | ||||||||
\(952\) | −2.45690 | −0.0796286 | ||||||||
\(953\) | 28.9689 | 0.938396 | 0.469198 | − | 0.883093i | \(-0.344543\pi\) | ||||
0.469198 | + | 0.883093i | \(0.344543\pi\) | |||||||
\(954\) | 71.1317 | 2.30297 | ||||||||
\(955\) | −5.80324 | −0.187789 | ||||||||
\(956\) | 52.0625 | 1.68382 | ||||||||
\(957\) | −3.75889 | −0.121508 | ||||||||
\(958\) | 17.3739 | 0.561324 | ||||||||
\(959\) | 33.0217 | 1.06633 | ||||||||
\(960\) | −9.09700 | −0.293604 | ||||||||
\(961\) | −20.1236 | −0.649148 | ||||||||
\(962\) | 10.7760 | 0.347432 | ||||||||
\(963\) | −25.8117 | −0.831771 | ||||||||
\(964\) | −51.5095 | −1.65901 | ||||||||
\(965\) | −19.4678 | −0.626690 | ||||||||
\(966\) | 21.0072 | 0.675895 | ||||||||
\(967\) | 41.0047 | 1.31862 | 0.659310 | − | 0.751871i | \(-0.270848\pi\) | ||||
0.659310 | + | 0.751871i | \(0.270848\pi\) | |||||||
\(968\) | 48.4139 | 1.55608 | ||||||||
\(969\) | −0.0151441 | −0.000486499 0 | ||||||||
\(970\) | 15.4751 | 0.496874 | ||||||||
\(971\) | −0.504941 | −0.0162043 | −0.00810216 | − | 0.999967i | \(-0.502579\pi\) | ||||
−0.00810216 | + | 0.999967i | \(0.502579\pi\) | |||||||
\(972\) | 75.8112 | 2.43165 | ||||||||
\(973\) | 30.5794 | 0.980330 | ||||||||
\(974\) | 71.6531 | 2.29591 | ||||||||
\(975\) | −1.09251 | −0.0349885 | ||||||||
\(976\) | −48.2863 | −1.54561 | ||||||||
\(977\) | −12.9340 | −0.413794 | −0.206897 | − | 0.978363i | \(-0.566337\pi\) | ||||
−0.206897 | + | 0.978363i | \(0.566337\pi\) | |||||||
\(978\) | 15.0263 | 0.480489 | ||||||||
\(979\) | 6.39868 | 0.204503 | ||||||||
\(980\) | 22.3153 | 0.712836 | ||||||||
\(981\) | −29.0295 | −0.926841 | ||||||||
\(982\) | 15.8976 | 0.507312 | ||||||||
\(983\) | −44.5059 | −1.41952 | −0.709759 | − | 0.704445i | \(-0.751196\pi\) | ||||
−0.709759 | + | 0.704445i | \(0.751196\pi\) | |||||||
\(984\) | −38.9566 | −1.24189 | ||||||||
\(985\) | −8.73362 | −0.278276 | ||||||||
\(986\) | 1.21717 | 0.0387627 | ||||||||
\(987\) | −5.57701 | −0.177518 | ||||||||
\(988\) | −0.799110 | −0.0254231 | ||||||||
\(989\) | −6.36033 | −0.202247 | ||||||||
\(990\) | 14.4166 | 0.458188 | ||||||||
\(991\) | 26.9874 | 0.857282 | 0.428641 | − | 0.903475i | \(-0.358992\pi\) | ||||
0.428641 | + | 0.903475i | \(0.358992\pi\) | |||||||
\(992\) | 42.7985 | 1.35885 | ||||||||
\(993\) | −9.31297 | −0.295538 | ||||||||
\(994\) | −18.9928 | −0.602416 | ||||||||
\(995\) | 4.34045 | 0.137602 | ||||||||
\(996\) | 61.1071 | 1.93625 | ||||||||
\(997\) | 10.9214 | 0.345883 | 0.172941 | − | 0.984932i | \(-0.444673\pi\) | ||||
0.172941 | + | 0.984932i | \(0.444673\pi\) | |||||||
\(998\) | 7.20572 | 0.228093 | ||||||||
\(999\) | −10.7544 | −0.340255 |
(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 | 6005.2.a.d.1.1 | ✓ | 83 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6005.2.a.d.1.1 | ✓ | 83 | 1.1 | even | 1 | trivial |