Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4334,2,Mod(1,4334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4334, 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("4334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4334 = 2 \cdot 11 \cdot 197 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4334.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: | \(34.6071642360\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4334.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.18604 | 1.26211 | 0.631056 | − | 0.775737i | \(-0.282622\pi\) | ||||
0.631056 | + | 0.775737i | \(0.282622\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.389300 | 0.174100 | 0.0870502 | − | 0.996204i | \(-0.472256\pi\) | ||||
0.0870502 | + | 0.996204i | \(0.472256\pi\) | |||||||
\(6\) | 2.18604 | 0.892448 | ||||||||
\(7\) | 4.93283 | 1.86443 | 0.932216 | − | 0.361901i | \(-0.117872\pi\) | ||||
0.932216 | + | 0.361901i | \(0.117872\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.77878 | 0.592927 | ||||||||
\(10\) | 0.389300 | 0.123108 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 2.18604 | 0.631056 | ||||||||
\(13\) | 0.775260 | 0.215019 | 0.107509 | − | 0.994204i | \(-0.465712\pi\) | ||||
0.107509 | + | 0.994204i | \(0.465712\pi\) | |||||||
\(14\) | 4.93283 | 1.31835 | ||||||||
\(15\) | 0.851027 | 0.219734 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.68472 | −1.37875 | −0.689374 | − | 0.724406i | \(-0.742114\pi\) | ||||
−0.689374 | + | 0.724406i | \(0.742114\pi\) | |||||||
\(18\) | 1.77878 | 0.419263 | ||||||||
\(19\) | −1.12311 | −0.257660 | −0.128830 | − | 0.991667i | \(-0.541122\pi\) | ||||
−0.128830 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | 0.389300 | 0.0870502 | ||||||||
\(21\) | 10.7834 | 2.35312 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 7.98354 | 1.66468 | 0.832342 | − | 0.554263i | \(-0.187000\pi\) | ||||
0.832342 | + | 0.554263i | \(0.187000\pi\) | |||||||
\(24\) | 2.18604 | 0.446224 | ||||||||
\(25\) | −4.84845 | −0.969689 | ||||||||
\(26\) | 0.775260 | 0.152041 | ||||||||
\(27\) | −2.66964 | −0.513772 | ||||||||
\(28\) | 4.93283 | 0.932216 | ||||||||
\(29\) | −9.93968 | −1.84575 | −0.922876 | − | 0.385097i | \(-0.874168\pi\) | ||||
−0.922876 | + | 0.385097i | \(0.874168\pi\) | |||||||
\(30\) | 0.851027 | 0.155376 | ||||||||
\(31\) | 3.43616 | 0.617152 | 0.308576 | − | 0.951200i | \(-0.400148\pi\) | ||||
0.308576 | + | 0.951200i | \(0.400148\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.18604 | 0.380541 | ||||||||
\(34\) | −5.68472 | −0.974922 | ||||||||
\(35\) | 1.92035 | 0.324598 | ||||||||
\(36\) | 1.77878 | 0.296464 | ||||||||
\(37\) | 6.94346 | 1.14150 | 0.570749 | − | 0.821125i | \(-0.306653\pi\) | ||||
0.570749 | + | 0.821125i | \(0.306653\pi\) | |||||||
\(38\) | −1.12311 | −0.182193 | ||||||||
\(39\) | 1.69475 | 0.271378 | ||||||||
\(40\) | 0.389300 | 0.0615538 | ||||||||
\(41\) | 5.59521 | 0.873824 | 0.436912 | − | 0.899504i | \(-0.356072\pi\) | ||||
0.436912 | + | 0.899504i | \(0.356072\pi\) | |||||||
\(42\) | 10.7834 | 1.66391 | ||||||||
\(43\) | 7.79970 | 1.18944 | 0.594721 | − | 0.803932i | \(-0.297262\pi\) | ||||
0.594721 | + | 0.803932i | \(0.297262\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 0.692480 | 0.103229 | ||||||||
\(46\) | 7.98354 | 1.17711 | ||||||||
\(47\) | 2.14271 | 0.312547 | 0.156274 | − | 0.987714i | \(-0.450052\pi\) | ||||
0.156274 | + | 0.987714i | \(0.450052\pi\) | |||||||
\(48\) | 2.18604 | 0.315528 | ||||||||
\(49\) | 17.3328 | 2.47611 | ||||||||
\(50\) | −4.84845 | −0.685674 | ||||||||
\(51\) | −12.4270 | −1.74013 | ||||||||
\(52\) | 0.775260 | 0.107509 | ||||||||
\(53\) | −6.84216 | −0.939844 | −0.469922 | − | 0.882708i | \(-0.655718\pi\) | ||||
−0.469922 | + | 0.882708i | \(0.655718\pi\) | |||||||
\(54\) | −2.66964 | −0.363291 | ||||||||
\(55\) | 0.389300 | 0.0524932 | ||||||||
\(56\) | 4.93283 | 0.659177 | ||||||||
\(57\) | −2.45517 | −0.325195 | ||||||||
\(58\) | −9.93968 | −1.30514 | ||||||||
\(59\) | −2.55627 | −0.332798 | −0.166399 | − | 0.986059i | \(-0.553214\pi\) | ||||
−0.166399 | + | 0.986059i | \(0.553214\pi\) | |||||||
\(60\) | 0.851027 | 0.109867 | ||||||||
\(61\) | 0.705682 | 0.0903533 | 0.0451767 | − | 0.998979i | \(-0.485615\pi\) | ||||
0.0451767 | + | 0.998979i | \(0.485615\pi\) | |||||||
\(62\) | 3.43616 | 0.436392 | ||||||||
\(63\) | 8.77442 | 1.10547 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.301809 | 0.0374348 | ||||||||
\(66\) | 2.18604 | 0.269083 | ||||||||
\(67\) | 3.66172 | 0.447350 | 0.223675 | − | 0.974664i | \(-0.428195\pi\) | ||||
0.223675 | + | 0.974664i | \(0.428195\pi\) | |||||||
\(68\) | −5.68472 | −0.689374 | ||||||||
\(69\) | 17.4524 | 2.10102 | ||||||||
\(70\) | 1.92035 | 0.229526 | ||||||||
\(71\) | −5.92511 | −0.703182 | −0.351591 | − | 0.936154i | \(-0.614359\pi\) | ||||
−0.351591 | + | 0.936154i | \(0.614359\pi\) | |||||||
\(72\) | 1.77878 | 0.209631 | ||||||||
\(73\) | 6.54769 | 0.766349 | 0.383175 | − | 0.923676i | \(-0.374831\pi\) | ||||
0.383175 | + | 0.923676i | \(0.374831\pi\) | |||||||
\(74\) | 6.94346 | 0.807161 | ||||||||
\(75\) | −10.5989 | −1.22386 | ||||||||
\(76\) | −1.12311 | −0.128830 | ||||||||
\(77\) | 4.93283 | 0.562148 | ||||||||
\(78\) | 1.69475 | 0.191893 | ||||||||
\(79\) | −16.3774 | −1.84260 | −0.921302 | − | 0.388847i | \(-0.872874\pi\) | ||||
−0.921302 | + | 0.388847i | \(0.872874\pi\) | |||||||
\(80\) | 0.389300 | 0.0435251 | ||||||||
\(81\) | −11.1723 | −1.24136 | ||||||||
\(82\) | 5.59521 | 0.617887 | ||||||||
\(83\) | −12.4454 | −1.36605 | −0.683027 | − | 0.730393i | \(-0.739337\pi\) | ||||
−0.683027 | + | 0.730393i | \(0.739337\pi\) | |||||||
\(84\) | 10.7834 | 1.17656 | ||||||||
\(85\) | −2.21306 | −0.240041 | ||||||||
\(86\) | 7.79970 | 0.841063 | ||||||||
\(87\) | −21.7286 | −2.32955 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 13.1347 | 1.39228 | 0.696138 | − | 0.717908i | \(-0.254900\pi\) | ||||
0.696138 | + | 0.717908i | \(0.254900\pi\) | |||||||
\(90\) | 0.692480 | 0.0729938 | ||||||||
\(91\) | 3.82422 | 0.400888 | ||||||||
\(92\) | 7.98354 | 0.832342 | ||||||||
\(93\) | 7.51158 | 0.778915 | ||||||||
\(94\) | 2.14271 | 0.221004 | ||||||||
\(95\) | −0.437228 | −0.0448586 | ||||||||
\(96\) | 2.18604 | 0.223112 | ||||||||
\(97\) | 1.45637 | 0.147872 | 0.0739358 | − | 0.997263i | \(-0.476444\pi\) | ||||
0.0739358 | + | 0.997263i | \(0.476444\pi\) | |||||||
\(98\) | 17.3328 | 1.75087 | ||||||||
\(99\) | 1.77878 | 0.178774 | ||||||||
\(100\) | −4.84845 | −0.484845 | ||||||||
\(101\) | −19.0906 | −1.89958 | −0.949792 | − | 0.312882i | \(-0.898706\pi\) | ||||
−0.949792 | + | 0.312882i | \(0.898706\pi\) | |||||||
\(102\) | −12.4270 | −1.23046 | ||||||||
\(103\) | −18.8529 | −1.85764 | −0.928818 | − | 0.370536i | \(-0.879174\pi\) | ||||
−0.928818 | + | 0.370536i | \(0.879174\pi\) | |||||||
\(104\) | 0.775260 | 0.0760205 | ||||||||
\(105\) | 4.19797 | 0.409680 | ||||||||
\(106\) | −6.84216 | −0.664570 | ||||||||
\(107\) | 4.43808 | 0.429046 | 0.214523 | − | 0.976719i | \(-0.431180\pi\) | ||||
0.214523 | + | 0.976719i | \(0.431180\pi\) | |||||||
\(108\) | −2.66964 | −0.256886 | ||||||||
\(109\) | 3.10342 | 0.297254 | 0.148627 | − | 0.988893i | \(-0.452515\pi\) | ||||
0.148627 | + | 0.988893i | \(0.452515\pi\) | |||||||
\(110\) | 0.389300 | 0.0371183 | ||||||||
\(111\) | 15.1787 | 1.44070 | ||||||||
\(112\) | 4.93283 | 0.466108 | ||||||||
\(113\) | −1.47551 | −0.138804 | −0.0694022 | − | 0.997589i | \(-0.522109\pi\) | ||||
−0.0694022 | + | 0.997589i | \(0.522109\pi\) | |||||||
\(114\) | −2.45517 | −0.229948 | ||||||||
\(115\) | 3.10799 | 0.289822 | ||||||||
\(116\) | −9.93968 | −0.922876 | ||||||||
\(117\) | 1.37902 | 0.127490 | ||||||||
\(118\) | −2.55627 | −0.235323 | ||||||||
\(119\) | −28.0417 | −2.57058 | ||||||||
\(120\) | 0.851027 | 0.0776878 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0.705682 | 0.0638894 | ||||||||
\(123\) | 12.2314 | 1.10286 | ||||||||
\(124\) | 3.43616 | 0.308576 | ||||||||
\(125\) | −3.83400 | −0.342924 | ||||||||
\(126\) | 8.77442 | 0.781687 | ||||||||
\(127\) | 15.6271 | 1.38668 | 0.693341 | − | 0.720610i | \(-0.256138\pi\) | ||||
0.693341 | + | 0.720610i | \(0.256138\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 17.0505 | 1.50121 | ||||||||
\(130\) | 0.301809 | 0.0264704 | ||||||||
\(131\) | −12.0105 | −1.04937 | −0.524683 | − | 0.851298i | \(-0.675816\pi\) | ||||
−0.524683 | + | 0.851298i | \(0.675816\pi\) | |||||||
\(132\) | 2.18604 | 0.190271 | ||||||||
\(133\) | −5.54012 | −0.480389 | ||||||||
\(134\) | 3.66172 | 0.316324 | ||||||||
\(135\) | −1.03929 | −0.0894479 | ||||||||
\(136\) | −5.68472 | −0.487461 | ||||||||
\(137\) | −21.2914 | −1.81904 | −0.909522 | − | 0.415655i | \(-0.863552\pi\) | ||||
−0.909522 | + | 0.415655i | \(0.863552\pi\) | |||||||
\(138\) | 17.4524 | 1.48564 | ||||||||
\(139\) | −6.41890 | −0.544444 | −0.272222 | − | 0.962234i | \(-0.587759\pi\) | ||||
−0.272222 | + | 0.962234i | \(0.587759\pi\) | |||||||
\(140\) | 1.92035 | 0.162299 | ||||||||
\(141\) | 4.68406 | 0.394469 | ||||||||
\(142\) | −5.92511 | −0.497224 | ||||||||
\(143\) | 0.775260 | 0.0648305 | ||||||||
\(144\) | 1.77878 | 0.148232 | ||||||||
\(145\) | −3.86952 | −0.321346 | ||||||||
\(146\) | 6.54769 | 0.541891 | ||||||||
\(147\) | 37.8902 | 3.12513 | ||||||||
\(148\) | 6.94346 | 0.570749 | ||||||||
\(149\) | 12.3096 | 1.00844 | 0.504220 | − | 0.863575i | \(-0.331780\pi\) | ||||
0.504220 | + | 0.863575i | \(0.331780\pi\) | |||||||
\(150\) | −10.5989 | −0.865397 | ||||||||
\(151\) | −12.2838 | −0.999641 | −0.499820 | − | 0.866129i | \(-0.666601\pi\) | ||||
−0.499820 | + | 0.866129i | \(0.666601\pi\) | |||||||
\(152\) | −1.12311 | −0.0910964 | ||||||||
\(153\) | −10.1119 | −0.817497 | ||||||||
\(154\) | 4.93283 | 0.397498 | ||||||||
\(155\) | 1.33770 | 0.107446 | ||||||||
\(156\) | 1.69475 | 0.135689 | ||||||||
\(157\) | 14.1766 | 1.13142 | 0.565709 | − | 0.824605i | \(-0.308603\pi\) | ||||
0.565709 | + | 0.824605i | \(0.308603\pi\) | |||||||
\(158\) | −16.3774 | −1.30292 | ||||||||
\(159\) | −14.9573 | −1.18619 | ||||||||
\(160\) | 0.389300 | 0.0307769 | ||||||||
\(161\) | 39.3814 | 3.10369 | ||||||||
\(162\) | −11.1723 | −0.877777 | ||||||||
\(163\) | −1.04017 | −0.0814722 | −0.0407361 | − | 0.999170i | \(-0.512970\pi\) | ||||
−0.0407361 | + | 0.999170i | \(0.512970\pi\) | |||||||
\(164\) | 5.59521 | 0.436912 | ||||||||
\(165\) | 0.851027 | 0.0662524 | ||||||||
\(166\) | −12.4454 | −0.965947 | ||||||||
\(167\) | 11.9099 | 0.921614 | 0.460807 | − | 0.887500i | \(-0.347560\pi\) | ||||
0.460807 | + | 0.887500i | \(0.347560\pi\) | |||||||
\(168\) | 10.7834 | 0.831955 | ||||||||
\(169\) | −12.3990 | −0.953767 | ||||||||
\(170\) | −2.21306 | −0.169734 | ||||||||
\(171\) | −1.99777 | −0.152773 | ||||||||
\(172\) | 7.79970 | 0.594721 | ||||||||
\(173\) | −4.62647 | −0.351744 | −0.175872 | − | 0.984413i | \(-0.556275\pi\) | ||||
−0.175872 | + | 0.984413i | \(0.556275\pi\) | |||||||
\(174\) | −21.7286 | −1.64724 | ||||||||
\(175\) | −23.9165 | −1.80792 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −5.58811 | −0.420028 | ||||||||
\(178\) | 13.1347 | 0.984488 | ||||||||
\(179\) | 21.5158 | 1.60817 | 0.804085 | − | 0.594515i | \(-0.202656\pi\) | ||||
0.804085 | + | 0.594515i | \(0.202656\pi\) | |||||||
\(180\) | 0.692480 | 0.0516144 | ||||||||
\(181\) | 11.5012 | 0.854877 | 0.427439 | − | 0.904044i | \(-0.359416\pi\) | ||||
0.427439 | + | 0.904044i | \(0.359416\pi\) | |||||||
\(182\) | 3.82422 | 0.283470 | ||||||||
\(183\) | 1.54265 | 0.114036 | ||||||||
\(184\) | 7.98354 | 0.588554 | ||||||||
\(185\) | 2.70309 | 0.198735 | ||||||||
\(186\) | 7.51158 | 0.550776 | ||||||||
\(187\) | −5.68472 | −0.415708 | ||||||||
\(188\) | 2.14271 | 0.156274 | ||||||||
\(189\) | −13.1689 | −0.957893 | ||||||||
\(190\) | −0.437228 | −0.0317199 | ||||||||
\(191\) | −14.2034 | −1.02772 | −0.513862 | − | 0.857873i | \(-0.671786\pi\) | ||||
−0.513862 | + | 0.857873i | \(0.671786\pi\) | |||||||
\(192\) | 2.18604 | 0.157764 | ||||||||
\(193\) | −8.33214 | −0.599760 | −0.299880 | − | 0.953977i | \(-0.596947\pi\) | ||||
−0.299880 | + | 0.953977i | \(0.596947\pi\) | |||||||
\(194\) | 1.45637 | 0.104561 | ||||||||
\(195\) | 0.659767 | 0.0472469 | ||||||||
\(196\) | 17.3328 | 1.23805 | ||||||||
\(197\) | 1.00000 | 0.0712470 | ||||||||
\(198\) | 1.77878 | 0.126412 | ||||||||
\(199\) | −4.67312 | −0.331269 | −0.165635 | − | 0.986187i | \(-0.552967\pi\) | ||||
−0.165635 | + | 0.986187i | \(0.552967\pi\) | |||||||
\(200\) | −4.84845 | −0.342837 | ||||||||
\(201\) | 8.00467 | 0.564606 | ||||||||
\(202\) | −19.0906 | −1.34321 | ||||||||
\(203\) | −49.0307 | −3.44128 | ||||||||
\(204\) | −12.4270 | −0.870067 | ||||||||
\(205\) | 2.17822 | 0.152133 | ||||||||
\(206\) | −18.8529 | −1.31355 | ||||||||
\(207\) | 14.2010 | 0.987036 | ||||||||
\(208\) | 0.775260 | 0.0537546 | ||||||||
\(209\) | −1.12311 | −0.0776873 | ||||||||
\(210\) | 4.19797 | 0.289687 | ||||||||
\(211\) | 9.76819 | 0.672470 | 0.336235 | − | 0.941778i | \(-0.390846\pi\) | ||||
0.336235 | + | 0.941778i | \(0.390846\pi\) | |||||||
\(212\) | −6.84216 | −0.469922 | ||||||||
\(213\) | −12.9525 | −0.887494 | ||||||||
\(214\) | 4.43808 | 0.303381 | ||||||||
\(215\) | 3.03642 | 0.207082 | ||||||||
\(216\) | −2.66964 | −0.181646 | ||||||||
\(217\) | 16.9500 | 1.15064 | ||||||||
\(218\) | 3.10342 | 0.210190 | ||||||||
\(219\) | 14.3135 | 0.967219 | ||||||||
\(220\) | 0.389300 | 0.0262466 | ||||||||
\(221\) | −4.40714 | −0.296456 | ||||||||
\(222\) | 15.1787 | 1.01873 | ||||||||
\(223\) | −4.69464 | −0.314376 | −0.157188 | − | 0.987569i | \(-0.550243\pi\) | ||||
−0.157188 | + | 0.987569i | \(0.550243\pi\) | |||||||
\(224\) | 4.93283 | 0.329588 | ||||||||
\(225\) | −8.62432 | −0.574955 | ||||||||
\(226\) | −1.47551 | −0.0981496 | ||||||||
\(227\) | 27.9405 | 1.85448 | 0.927239 | − | 0.374471i | \(-0.122176\pi\) | ||||
0.927239 | + | 0.374471i | \(0.122176\pi\) | |||||||
\(228\) | −2.45517 | −0.162598 | ||||||||
\(229\) | −6.53180 | −0.431633 | −0.215817 | − | 0.976434i | \(-0.569241\pi\) | ||||
−0.215817 | + | 0.976434i | \(0.569241\pi\) | |||||||
\(230\) | 3.10799 | 0.204935 | ||||||||
\(231\) | 10.7834 | 0.709493 | ||||||||
\(232\) | −9.93968 | −0.652572 | ||||||||
\(233\) | 4.47438 | 0.293126 | 0.146563 | − | 0.989201i | \(-0.453179\pi\) | ||||
0.146563 | + | 0.989201i | \(0.453179\pi\) | |||||||
\(234\) | 1.37902 | 0.0901493 | ||||||||
\(235\) | 0.834159 | 0.0544146 | ||||||||
\(236\) | −2.55627 | −0.166399 | ||||||||
\(237\) | −35.8018 | −2.32557 | ||||||||
\(238\) | −28.0417 | −1.81768 | ||||||||
\(239\) | −22.0632 | −1.42715 | −0.713573 | − | 0.700580i | \(-0.752924\pi\) | ||||
−0.713573 | + | 0.700580i | \(0.752924\pi\) | |||||||
\(240\) | 0.851027 | 0.0549336 | ||||||||
\(241\) | −9.29260 | −0.598589 | −0.299294 | − | 0.954161i | \(-0.596751\pi\) | ||||
−0.299294 | + | 0.954161i | \(0.596751\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | −16.4142 | −1.05297 | ||||||||
\(244\) | 0.705682 | 0.0451767 | ||||||||
\(245\) | 6.74765 | 0.431092 | ||||||||
\(246\) | 12.2314 | 0.779843 | ||||||||
\(247\) | −0.870705 | −0.0554016 | ||||||||
\(248\) | 3.43616 | 0.218196 | ||||||||
\(249\) | −27.2061 | −1.72411 | ||||||||
\(250\) | −3.83400 | −0.242484 | ||||||||
\(251\) | 20.3196 | 1.28256 | 0.641281 | − | 0.767306i | \(-0.278403\pi\) | ||||
0.641281 | + | 0.767306i | \(0.278403\pi\) | |||||||
\(252\) | 8.77442 | 0.552736 | ||||||||
\(253\) | 7.98354 | 0.501921 | ||||||||
\(254\) | 15.6271 | 0.980532 | ||||||||
\(255\) | −4.83785 | −0.302958 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.26798 | 0.0790942 | 0.0395471 | − | 0.999218i | \(-0.487408\pi\) | ||||
0.0395471 | + | 0.999218i | \(0.487408\pi\) | |||||||
\(258\) | 17.0505 | 1.06152 | ||||||||
\(259\) | 34.2509 | 2.12825 | ||||||||
\(260\) | 0.301809 | 0.0187174 | ||||||||
\(261\) | −17.6805 | −1.09440 | ||||||||
\(262\) | −12.0105 | −0.742014 | ||||||||
\(263\) | 9.41962 | 0.580838 | 0.290419 | − | 0.956900i | \(-0.406205\pi\) | ||||
0.290419 | + | 0.956900i | \(0.406205\pi\) | |||||||
\(264\) | 2.18604 | 0.134542 | ||||||||
\(265\) | −2.66366 | −0.163627 | ||||||||
\(266\) | −5.54012 | −0.339686 | ||||||||
\(267\) | 28.7130 | 1.75721 | ||||||||
\(268\) | 3.66172 | 0.223675 | ||||||||
\(269\) | −4.91837 | −0.299878 | −0.149939 | − | 0.988695i | \(-0.547908\pi\) | ||||
−0.149939 | + | 0.988695i | \(0.547908\pi\) | |||||||
\(270\) | −1.03929 | −0.0632492 | ||||||||
\(271\) | −26.7158 | −1.62287 | −0.811436 | − | 0.584442i | \(-0.801314\pi\) | ||||
−0.811436 | + | 0.584442i | \(0.801314\pi\) | |||||||
\(272\) | −5.68472 | −0.344687 | ||||||||
\(273\) | 8.35992 | 0.505965 | ||||||||
\(274\) | −21.2914 | −1.28626 | ||||||||
\(275\) | −4.84845 | −0.292372 | ||||||||
\(276\) | 17.4524 | 1.05051 | ||||||||
\(277\) | 25.6570 | 1.54158 | 0.770789 | − | 0.637091i | \(-0.219862\pi\) | ||||
0.770789 | + | 0.637091i | \(0.219862\pi\) | |||||||
\(278\) | −6.41890 | −0.384980 | ||||||||
\(279\) | 6.11217 | 0.365926 | ||||||||
\(280\) | 1.92035 | 0.114763 | ||||||||
\(281\) | 0.483127 | 0.0288210 | 0.0144105 | − | 0.999896i | \(-0.495413\pi\) | ||||
0.0144105 | + | 0.999896i | \(0.495413\pi\) | |||||||
\(282\) | 4.68406 | 0.278932 | ||||||||
\(283\) | −9.30471 | −0.553107 | −0.276554 | − | 0.960998i | \(-0.589192\pi\) | ||||
−0.276554 | + | 0.960998i | \(0.589192\pi\) | |||||||
\(284\) | −5.92511 | −0.351591 | ||||||||
\(285\) | −0.955799 | −0.0566166 | ||||||||
\(286\) | 0.775260 | 0.0458421 | ||||||||
\(287\) | 27.6002 | 1.62919 | ||||||||
\(288\) | 1.77878 | 0.104816 | ||||||||
\(289\) | 15.3161 | 0.900945 | ||||||||
\(290\) | −3.86952 | −0.227226 | ||||||||
\(291\) | 3.18368 | 0.186631 | ||||||||
\(292\) | 6.54769 | 0.383175 | ||||||||
\(293\) | 4.60308 | 0.268915 | 0.134457 | − | 0.990919i | \(-0.457071\pi\) | ||||
0.134457 | + | 0.990919i | \(0.457071\pi\) | |||||||
\(294\) | 37.8902 | 2.20980 | ||||||||
\(295\) | −0.995156 | −0.0579402 | ||||||||
\(296\) | 6.94346 | 0.403581 | ||||||||
\(297\) | −2.66964 | −0.154908 | ||||||||
\(298\) | 12.3096 | 0.713075 | ||||||||
\(299\) | 6.18932 | 0.357938 | ||||||||
\(300\) | −10.5989 | −0.611928 | ||||||||
\(301\) | 38.4745 | 2.21764 | ||||||||
\(302\) | −12.2838 | −0.706853 | ||||||||
\(303\) | −41.7328 | −2.39749 | ||||||||
\(304\) | −1.12311 | −0.0644149 | ||||||||
\(305\) | 0.274722 | 0.0157305 | ||||||||
\(306\) | −10.1119 | −0.578058 | ||||||||
\(307\) | 4.14367 | 0.236492 | 0.118246 | − | 0.992984i | \(-0.462273\pi\) | ||||
0.118246 | + | 0.992984i | \(0.462273\pi\) | |||||||
\(308\) | 4.93283 | 0.281074 | ||||||||
\(309\) | −41.2133 | −2.34454 | ||||||||
\(310\) | 1.33770 | 0.0759761 | ||||||||
\(311\) | 32.5675 | 1.84673 | 0.923367 | − | 0.383919i | \(-0.125426\pi\) | ||||
0.923367 | + | 0.383919i | \(0.125426\pi\) | |||||||
\(312\) | 1.69475 | 0.0959464 | ||||||||
\(313\) | 11.0509 | 0.624635 | 0.312318 | − | 0.949978i | \(-0.398895\pi\) | ||||
0.312318 | + | 0.949978i | \(0.398895\pi\) | |||||||
\(314\) | 14.1766 | 0.800033 | ||||||||
\(315\) | 3.41588 | 0.192463 | ||||||||
\(316\) | −16.3774 | −0.921302 | ||||||||
\(317\) | 7.53342 | 0.423119 | 0.211559 | − | 0.977365i | \(-0.432146\pi\) | ||||
0.211559 | + | 0.977365i | \(0.432146\pi\) | |||||||
\(318\) | −14.9573 | −0.838762 | ||||||||
\(319\) | −9.93968 | −0.556515 | ||||||||
\(320\) | 0.389300 | 0.0217625 | ||||||||
\(321\) | 9.70184 | 0.541504 | ||||||||
\(322\) | 39.3814 | 2.19464 | ||||||||
\(323\) | 6.38458 | 0.355248 | ||||||||
\(324\) | −11.1723 | −0.620682 | ||||||||
\(325\) | −3.75881 | −0.208501 | ||||||||
\(326\) | −1.04017 | −0.0576095 | ||||||||
\(327\) | 6.78421 | 0.375168 | ||||||||
\(328\) | 5.59521 | 0.308944 | ||||||||
\(329\) | 10.5696 | 0.582723 | ||||||||
\(330\) | 0.851027 | 0.0468475 | ||||||||
\(331\) | 11.5271 | 0.633584 | 0.316792 | − | 0.948495i | \(-0.397394\pi\) | ||||
0.316792 | + | 0.948495i | \(0.397394\pi\) | |||||||
\(332\) | −12.4454 | −0.683027 | ||||||||
\(333\) | 12.3509 | 0.676825 | ||||||||
\(334\) | 11.9099 | 0.651679 | ||||||||
\(335\) | 1.42551 | 0.0778838 | ||||||||
\(336\) | 10.7834 | 0.588281 | ||||||||
\(337\) | 16.1314 | 0.878732 | 0.439366 | − | 0.898308i | \(-0.355203\pi\) | ||||
0.439366 | + | 0.898308i | \(0.355203\pi\) | |||||||
\(338\) | −12.3990 | −0.674415 | ||||||||
\(339\) | −3.22553 | −0.175187 | ||||||||
\(340\) | −2.21306 | −0.120020 | ||||||||
\(341\) | 3.43616 | 0.186078 | ||||||||
\(342\) | −1.99777 | −0.108027 | ||||||||
\(343\) | 50.9697 | 2.75211 | ||||||||
\(344\) | 7.79970 | 0.420531 | ||||||||
\(345\) | 6.79421 | 0.365788 | ||||||||
\(346\) | −4.62647 | −0.248721 | ||||||||
\(347\) | −0.902306 | −0.0484383 | −0.0242192 | − | 0.999707i | \(-0.507710\pi\) | ||||
−0.0242192 | + | 0.999707i | \(0.507710\pi\) | |||||||
\(348\) | −21.7286 | −1.16477 | ||||||||
\(349\) | 20.8256 | 1.11477 | 0.557385 | − | 0.830254i | \(-0.311805\pi\) | ||||
0.557385 | + | 0.830254i | \(0.311805\pi\) | |||||||
\(350\) | −23.9165 | −1.27839 | ||||||||
\(351\) | −2.06966 | −0.110470 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −19.4315 | −1.03424 | −0.517118 | − | 0.855914i | \(-0.672995\pi\) | ||||
−0.517118 | + | 0.855914i | \(0.672995\pi\) | |||||||
\(354\) | −5.58811 | −0.297005 | ||||||||
\(355\) | −2.30665 | −0.122424 | ||||||||
\(356\) | 13.1347 | 0.696138 | ||||||||
\(357\) | −61.3004 | −3.24436 | ||||||||
\(358\) | 21.5158 | 1.13715 | ||||||||
\(359\) | −13.6692 | −0.721433 | −0.360717 | − | 0.932675i | \(-0.617468\pi\) | ||||
−0.360717 | + | 0.932675i | \(0.617468\pi\) | |||||||
\(360\) | 0.692480 | 0.0364969 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 11.5012 | 0.604489 | ||||||||
\(363\) | 2.18604 | 0.114737 | ||||||||
\(364\) | 3.82422 | 0.200444 | ||||||||
\(365\) | 2.54902 | 0.133422 | ||||||||
\(366\) | 1.54265 | 0.0806356 | ||||||||
\(367\) | 13.1334 | 0.685556 | 0.342778 | − | 0.939416i | \(-0.388632\pi\) | ||||
0.342778 | + | 0.939416i | \(0.388632\pi\) | |||||||
\(368\) | 7.98354 | 0.416171 | ||||||||
\(369\) | 9.95265 | 0.518114 | ||||||||
\(370\) | 2.70309 | 0.140527 | ||||||||
\(371\) | −33.7512 | −1.75228 | ||||||||
\(372\) | 7.51158 | 0.389457 | ||||||||
\(373\) | −18.4840 | −0.957063 | −0.478532 | − | 0.878070i | \(-0.658831\pi\) | ||||
−0.478532 | + | 0.878070i | \(0.658831\pi\) | |||||||
\(374\) | −5.68472 | −0.293950 | ||||||||
\(375\) | −8.38129 | −0.432808 | ||||||||
\(376\) | 2.14271 | 0.110502 | ||||||||
\(377\) | −7.70584 | −0.396871 | ||||||||
\(378\) | −13.1689 | −0.677333 | ||||||||
\(379\) | −22.5634 | −1.15901 | −0.579503 | − | 0.814970i | \(-0.696753\pi\) | ||||
−0.579503 | + | 0.814970i | \(0.696753\pi\) | |||||||
\(380\) | −0.437228 | −0.0224293 | ||||||||
\(381\) | 34.1615 | 1.75015 | ||||||||
\(382\) | −14.2034 | −0.726710 | ||||||||
\(383\) | −33.1128 | −1.69198 | −0.845992 | − | 0.533196i | \(-0.820991\pi\) | ||||
−0.845992 | + | 0.533196i | \(0.820991\pi\) | |||||||
\(384\) | 2.18604 | 0.111556 | ||||||||
\(385\) | 1.92035 | 0.0978701 | ||||||||
\(386\) | −8.33214 | −0.424095 | ||||||||
\(387\) | 13.8740 | 0.705253 | ||||||||
\(388\) | 1.45637 | 0.0739358 | ||||||||
\(389\) | −23.0986 | −1.17115 | −0.585574 | − | 0.810619i | \(-0.699131\pi\) | ||||
−0.585574 | + | 0.810619i | \(0.699131\pi\) | |||||||
\(390\) | 0.659767 | 0.0334086 | ||||||||
\(391\) | −45.3842 | −2.29518 | ||||||||
\(392\) | 17.3328 | 0.875437 | ||||||||
\(393\) | −26.2556 | −1.32442 | ||||||||
\(394\) | 1.00000 | 0.0503793 | ||||||||
\(395\) | −6.37574 | −0.320798 | ||||||||
\(396\) | 1.77878 | 0.0893871 | ||||||||
\(397\) | −1.24697 | −0.0625834 | −0.0312917 | − | 0.999510i | \(-0.509962\pi\) | ||||
−0.0312917 | + | 0.999510i | \(0.509962\pi\) | |||||||
\(398\) | −4.67312 | −0.234243 | ||||||||
\(399\) | −12.1109 | −0.606305 | ||||||||
\(400\) | −4.84845 | −0.242422 | ||||||||
\(401\) | 1.76907 | 0.0883431 | 0.0441715 | − | 0.999024i | \(-0.485935\pi\) | ||||
0.0441715 | + | 0.999024i | \(0.485935\pi\) | |||||||
\(402\) | 8.00467 | 0.399237 | ||||||||
\(403\) | 2.66392 | 0.132699 | ||||||||
\(404\) | −19.0906 | −0.949792 | ||||||||
\(405\) | −4.34937 | −0.216122 | ||||||||
\(406\) | −49.0307 | −2.43335 | ||||||||
\(407\) | 6.94346 | 0.344175 | ||||||||
\(408\) | −12.4270 | −0.615230 | ||||||||
\(409\) | 19.8592 | 0.981973 | 0.490986 | − | 0.871167i | \(-0.336636\pi\) | ||||
0.490986 | + | 0.871167i | \(0.336636\pi\) | |||||||
\(410\) | 2.17822 | 0.107574 | ||||||||
\(411\) | −46.5438 | −2.29584 | ||||||||
\(412\) | −18.8529 | −0.928818 | ||||||||
\(413\) | −12.6096 | −0.620479 | ||||||||
\(414\) | 14.2010 | 0.697940 | ||||||||
\(415\) | −4.84498 | −0.237831 | ||||||||
\(416\) | 0.775260 | 0.0380103 | ||||||||
\(417\) | −14.0320 | −0.687150 | ||||||||
\(418\) | −1.12311 | −0.0549332 | ||||||||
\(419\) | −32.6124 | −1.59322 | −0.796609 | − | 0.604495i | \(-0.793375\pi\) | ||||
−0.796609 | + | 0.604495i | \(0.793375\pi\) | |||||||
\(420\) | 4.19797 | 0.204840 | ||||||||
\(421\) | 16.3556 | 0.797124 | 0.398562 | − | 0.917141i | \(-0.369509\pi\) | ||||
0.398562 | + | 0.917141i | \(0.369509\pi\) | |||||||
\(422\) | 9.76819 | 0.475508 | ||||||||
\(423\) | 3.81142 | 0.185318 | ||||||||
\(424\) | −6.84216 | −0.332285 | ||||||||
\(425\) | 27.5621 | 1.33696 | ||||||||
\(426\) | −12.9525 | −0.627553 | ||||||||
\(427\) | 3.48101 | 0.168458 | ||||||||
\(428\) | 4.43808 | 0.214523 | ||||||||
\(429\) | 1.69475 | 0.0818234 | ||||||||
\(430\) | 3.03642 | 0.146429 | ||||||||
\(431\) | −27.6455 | −1.33164 | −0.665819 | − | 0.746113i | \(-0.731918\pi\) | ||||
−0.665819 | + | 0.746113i | \(0.731918\pi\) | |||||||
\(432\) | −2.66964 | −0.128443 | ||||||||
\(433\) | 28.8663 | 1.38723 | 0.693614 | − | 0.720347i | \(-0.256018\pi\) | ||||
0.693614 | + | 0.720347i | \(0.256018\pi\) | |||||||
\(434\) | 16.9500 | 0.813624 | ||||||||
\(435\) | −8.45894 | −0.405575 | ||||||||
\(436\) | 3.10342 | 0.148627 | ||||||||
\(437\) | −8.96641 | −0.428922 | ||||||||
\(438\) | 14.3135 | 0.683927 | ||||||||
\(439\) | −30.2827 | −1.44531 | −0.722657 | − | 0.691207i | \(-0.757079\pi\) | ||||
−0.722657 | + | 0.691207i | \(0.757079\pi\) | |||||||
\(440\) | 0.389300 | 0.0185592 | ||||||||
\(441\) | 30.8312 | 1.46815 | ||||||||
\(442\) | −4.40714 | −0.209626 | ||||||||
\(443\) | −17.5265 | −0.832711 | −0.416356 | − | 0.909202i | \(-0.636693\pi\) | ||||
−0.416356 | + | 0.909202i | \(0.636693\pi\) | |||||||
\(444\) | 15.1787 | 0.720349 | ||||||||
\(445\) | 5.11334 | 0.242396 | ||||||||
\(446\) | −4.69464 | −0.222298 | ||||||||
\(447\) | 26.9093 | 1.27276 | ||||||||
\(448\) | 4.93283 | 0.233054 | ||||||||
\(449\) | −0.319442 | −0.0150754 | −0.00753770 | − | 0.999972i | \(-0.502399\pi\) | ||||
−0.00753770 | + | 0.999972i | \(0.502399\pi\) | |||||||
\(450\) | −8.62432 | −0.406554 | ||||||||
\(451\) | 5.59521 | 0.263468 | ||||||||
\(452\) | −1.47551 | −0.0694022 | ||||||||
\(453\) | −26.8529 | −1.26166 | ||||||||
\(454\) | 27.9405 | 1.31131 | ||||||||
\(455\) | 1.48877 | 0.0697947 | ||||||||
\(456\) | −2.45517 | −0.114974 | ||||||||
\(457\) | −13.8474 | −0.647755 | −0.323878 | − | 0.946099i | \(-0.604987\pi\) | ||||
−0.323878 | + | 0.946099i | \(0.604987\pi\) | |||||||
\(458\) | −6.53180 | −0.305211 | ||||||||
\(459\) | 15.1761 | 0.708362 | ||||||||
\(460\) | 3.10799 | 0.144911 | ||||||||
\(461\) | −20.5144 | −0.955451 | −0.477726 | − | 0.878509i | \(-0.658539\pi\) | ||||
−0.477726 | + | 0.878509i | \(0.658539\pi\) | |||||||
\(462\) | 10.7834 | 0.501688 | ||||||||
\(463\) | −19.8953 | −0.924613 | −0.462306 | − | 0.886720i | \(-0.652978\pi\) | ||||
−0.462306 | + | 0.886720i | \(0.652978\pi\) | |||||||
\(464\) | −9.93968 | −0.461438 | ||||||||
\(465\) | 2.92426 | 0.135609 | ||||||||
\(466\) | 4.47438 | 0.207271 | ||||||||
\(467\) | 21.9574 | 1.01607 | 0.508034 | − | 0.861337i | \(-0.330372\pi\) | ||||
0.508034 | + | 0.861337i | \(0.330372\pi\) | |||||||
\(468\) | 1.37902 | 0.0637452 | ||||||||
\(469\) | 18.0626 | 0.834054 | ||||||||
\(470\) | 0.834159 | 0.0384769 | ||||||||
\(471\) | 30.9907 | 1.42798 | ||||||||
\(472\) | −2.55627 | −0.117662 | ||||||||
\(473\) | 7.79970 | 0.358630 | ||||||||
\(474\) | −35.8018 | −1.64443 | ||||||||
\(475\) | 5.44535 | 0.249850 | ||||||||
\(476\) | −28.0417 | −1.28529 | ||||||||
\(477\) | −12.1707 | −0.557259 | ||||||||
\(478\) | −22.0632 | −1.00915 | ||||||||
\(479\) | −7.94047 | −0.362809 | −0.181405 | − | 0.983409i | \(-0.558064\pi\) | ||||
−0.181405 | + | 0.983409i | \(0.558064\pi\) | |||||||
\(480\) | 0.851027 | 0.0388439 | ||||||||
\(481\) | 5.38299 | 0.245443 | ||||||||
\(482\) | −9.29260 | −0.423266 | ||||||||
\(483\) | 86.0894 | 3.91720 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.566964 | 0.0257445 | ||||||||
\(486\) | −16.4142 | −0.744562 | ||||||||
\(487\) | 13.9288 | 0.631172 | 0.315586 | − | 0.948897i | \(-0.397799\pi\) | ||||
0.315586 | + | 0.948897i | \(0.397799\pi\) | |||||||
\(488\) | 0.705682 | 0.0319447 | ||||||||
\(489\) | −2.27385 | −0.102827 | ||||||||
\(490\) | 6.74765 | 0.304828 | ||||||||
\(491\) | −9.36573 | −0.422670 | −0.211335 | − | 0.977414i | \(-0.567781\pi\) | ||||
−0.211335 | + | 0.977414i | \(0.567781\pi\) | |||||||
\(492\) | 12.2314 | 0.551432 | ||||||||
\(493\) | 56.5043 | 2.54483 | ||||||||
\(494\) | −0.870705 | −0.0391748 | ||||||||
\(495\) | 0.692480 | 0.0311247 | ||||||||
\(496\) | 3.43616 | 0.154288 | ||||||||
\(497\) | −29.2275 | −1.31103 | ||||||||
\(498\) | −27.2061 | −1.21913 | ||||||||
\(499\) | −2.10961 | −0.0944391 | −0.0472195 | − | 0.998885i | \(-0.515036\pi\) | ||||
−0.0472195 | + | 0.998885i | \(0.515036\pi\) | |||||||
\(500\) | −3.83400 | −0.171462 | ||||||||
\(501\) | 26.0355 | 1.16318 | ||||||||
\(502\) | 20.3196 | 0.906909 | ||||||||
\(503\) | 12.7055 | 0.566508 | 0.283254 | − | 0.959045i | \(-0.408586\pi\) | ||||
0.283254 | + | 0.959045i | \(0.408586\pi\) | |||||||
\(504\) | 8.77442 | 0.390844 | ||||||||
\(505\) | −7.43197 | −0.330718 | ||||||||
\(506\) | 7.98354 | 0.354912 | ||||||||
\(507\) | −27.1047 | −1.20376 | ||||||||
\(508\) | 15.6271 | 0.693341 | ||||||||
\(509\) | 20.5922 | 0.912731 | 0.456366 | − | 0.889792i | \(-0.349151\pi\) | ||||
0.456366 | + | 0.889792i | \(0.349151\pi\) | |||||||
\(510\) | −4.83785 | −0.214224 | ||||||||
\(511\) | 32.2986 | 1.42881 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.99830 | 0.132378 | ||||||||
\(514\) | 1.26798 | 0.0559281 | ||||||||
\(515\) | −7.33946 | −0.323415 | ||||||||
\(516\) | 17.0505 | 0.750605 | ||||||||
\(517\) | 2.14271 | 0.0942365 | ||||||||
\(518\) | 34.2509 | 1.50490 | ||||||||
\(519\) | −10.1137 | −0.443941 | ||||||||
\(520\) | 0.301809 | 0.0132352 | ||||||||
\(521\) | −7.09017 | −0.310626 | −0.155313 | − | 0.987865i | \(-0.549639\pi\) | ||||
−0.155313 | + | 0.987865i | \(0.549639\pi\) | |||||||
\(522\) | −17.6805 | −0.773855 | ||||||||
\(523\) | −8.26602 | −0.361448 | −0.180724 | − | 0.983534i | \(-0.557844\pi\) | ||||
−0.180724 | + | 0.983534i | \(0.557844\pi\) | |||||||
\(524\) | −12.0105 | −0.524683 | ||||||||
\(525\) | −52.2826 | −2.28180 | ||||||||
\(526\) | 9.41962 | 0.410715 | ||||||||
\(527\) | −19.5336 | −0.850897 | ||||||||
\(528\) | 2.18604 | 0.0951353 | ||||||||
\(529\) | 40.7369 | 1.77117 | ||||||||
\(530\) | −2.66366 | −0.115702 | ||||||||
\(531\) | −4.54704 | −0.197325 | ||||||||
\(532\) | −5.54012 | −0.240195 | ||||||||
\(533\) | 4.33774 | 0.187888 | ||||||||
\(534\) | 28.7130 | 1.24253 | ||||||||
\(535\) | 1.72775 | 0.0746970 | ||||||||
\(536\) | 3.66172 | 0.158162 | ||||||||
\(537\) | 47.0345 | 2.02969 | ||||||||
\(538\) | −4.91837 | −0.212046 | ||||||||
\(539\) | 17.3328 | 0.746575 | ||||||||
\(540\) | −1.03929 | −0.0447239 | ||||||||
\(541\) | −1.71185 | −0.0735982 | −0.0367991 | − | 0.999323i | \(-0.511716\pi\) | ||||
−0.0367991 | + | 0.999323i | \(0.511716\pi\) | |||||||
\(542\) | −26.7158 | −1.14754 | ||||||||
\(543\) | 25.1421 | 1.07895 | ||||||||
\(544\) | −5.68472 | −0.243730 | ||||||||
\(545\) | 1.20816 | 0.0517520 | ||||||||
\(546\) | 8.35992 | 0.357771 | ||||||||
\(547\) | −28.6175 | −1.22360 | −0.611799 | − | 0.791013i | \(-0.709554\pi\) | ||||
−0.611799 | + | 0.791013i | \(0.709554\pi\) | |||||||
\(548\) | −21.2914 | −0.909522 | ||||||||
\(549\) | 1.25525 | 0.0535729 | ||||||||
\(550\) | −4.84845 | −0.206738 | ||||||||
\(551\) | 11.1634 | 0.475576 | ||||||||
\(552\) | 17.4524 | 0.742822 | ||||||||
\(553\) | −80.7870 | −3.43541 | ||||||||
\(554\) | 25.6570 | 1.09006 | ||||||||
\(555\) | 5.90907 | 0.250826 | ||||||||
\(556\) | −6.41890 | −0.272222 | ||||||||
\(557\) | 14.9097 | 0.631744 | 0.315872 | − | 0.948802i | \(-0.397703\pi\) | ||||
0.315872 | + | 0.948802i | \(0.397703\pi\) | |||||||
\(558\) | 6.11217 | 0.258749 | ||||||||
\(559\) | 6.04680 | 0.255752 | ||||||||
\(560\) | 1.92035 | 0.0811496 | ||||||||
\(561\) | −12.4270 | −0.524670 | ||||||||
\(562\) | 0.483127 | 0.0203795 | ||||||||
\(563\) | −25.6860 | −1.08254 | −0.541268 | − | 0.840850i | \(-0.682056\pi\) | ||||
−0.541268 | + | 0.840850i | \(0.682056\pi\) | |||||||
\(564\) | 4.68406 | 0.197235 | ||||||||
\(565\) | −0.574417 | −0.0241659 | ||||||||
\(566\) | −9.30471 | −0.391106 | ||||||||
\(567\) | −55.1109 | −2.31444 | ||||||||
\(568\) | −5.92511 | −0.248612 | ||||||||
\(569\) | −30.8376 | −1.29278 | −0.646389 | − | 0.763008i | \(-0.723722\pi\) | ||||
−0.646389 | + | 0.763008i | \(0.723722\pi\) | |||||||
\(570\) | −0.955799 | −0.0400340 | ||||||||
\(571\) | −23.7625 | −0.994429 | −0.497214 | − | 0.867628i | \(-0.665644\pi\) | ||||
−0.497214 | + | 0.867628i | \(0.665644\pi\) | |||||||
\(572\) | 0.775260 | 0.0324153 | ||||||||
\(573\) | −31.0493 | −1.29710 | ||||||||
\(574\) | 27.6002 | 1.15201 | ||||||||
\(575\) | −38.7078 | −1.61423 | ||||||||
\(576\) | 1.77878 | 0.0741159 | ||||||||
\(577\) | 36.5603 | 1.52202 | 0.761012 | − | 0.648738i | \(-0.224703\pi\) | ||||
0.761012 | + | 0.648738i | \(0.224703\pi\) | |||||||
\(578\) | 15.3161 | 0.637065 | ||||||||
\(579\) | −18.2144 | −0.756965 | ||||||||
\(580\) | −3.86952 | −0.160673 | ||||||||
\(581\) | −61.3907 | −2.54692 | ||||||||
\(582\) | 3.18368 | 0.131968 | ||||||||
\(583\) | −6.84216 | −0.283373 | ||||||||
\(584\) | 6.54769 | 0.270945 | ||||||||
\(585\) | 0.536852 | 0.0221961 | ||||||||
\(586\) | 4.60308 | 0.190151 | ||||||||
\(587\) | −19.7982 | −0.817159 | −0.408580 | − | 0.912723i | \(-0.633976\pi\) | ||||
−0.408580 | + | 0.912723i | \(0.633976\pi\) | |||||||
\(588\) | 37.8902 | 1.56256 | ||||||||
\(589\) | −3.85919 | −0.159015 | ||||||||
\(590\) | −0.995156 | −0.0409699 | ||||||||
\(591\) | 2.18604 | 0.0899218 | ||||||||
\(592\) | 6.94346 | 0.285375 | ||||||||
\(593\) | 3.89133 | 0.159798 | 0.0798988 | − | 0.996803i | \(-0.474540\pi\) | ||||
0.0798988 | + | 0.996803i | \(0.474540\pi\) | |||||||
\(594\) | −2.66964 | −0.109537 | ||||||||
\(595\) | −10.9167 | −0.447539 | ||||||||
\(596\) | 12.3096 | 0.504220 | ||||||||
\(597\) | −10.2156 | −0.418099 | ||||||||
\(598\) | 6.18932 | 0.253100 | ||||||||
\(599\) | 47.0370 | 1.92188 | 0.960939 | − | 0.276761i | \(-0.0892609\pi\) | ||||
0.960939 | + | 0.276761i | \(0.0892609\pi\) | |||||||
\(600\) | −10.5989 | −0.432699 | ||||||||
\(601\) | 33.3486 | 1.36032 | 0.680158 | − | 0.733065i | \(-0.261911\pi\) | ||||
0.680158 | + | 0.733065i | \(0.261911\pi\) | |||||||
\(602\) | 38.4745 | 1.56811 | ||||||||
\(603\) | 6.51340 | 0.265246 | ||||||||
\(604\) | −12.2838 | −0.499820 | ||||||||
\(605\) | 0.389300 | 0.0158273 | ||||||||
\(606\) | −41.7328 | −1.69528 | ||||||||
\(607\) | −25.9755 | −1.05431 | −0.527157 | − | 0.849768i | \(-0.676742\pi\) | ||||
−0.527157 | + | 0.849768i | \(0.676742\pi\) | |||||||
\(608\) | −1.12311 | −0.0455482 | ||||||||
\(609\) | −107.183 | −4.34328 | ||||||||
\(610\) | 0.274722 | 0.0111232 | ||||||||
\(611\) | 1.66116 | 0.0672034 | ||||||||
\(612\) | −10.1119 | −0.408748 | ||||||||
\(613\) | −24.4618 | −0.988005 | −0.494002 | − | 0.869461i | \(-0.664467\pi\) | ||||
−0.494002 | + | 0.869461i | \(0.664467\pi\) | |||||||
\(614\) | 4.14367 | 0.167225 | ||||||||
\(615\) | 4.76167 | 0.192009 | ||||||||
\(616\) | 4.93283 | 0.198749 | ||||||||
\(617\) | −25.8086 | −1.03902 | −0.519508 | − | 0.854465i | \(-0.673885\pi\) | ||||
−0.519508 | + | 0.854465i | \(0.673885\pi\) | |||||||
\(618\) | −41.2133 | −1.65784 | ||||||||
\(619\) | 42.1127 | 1.69265 | 0.846326 | − | 0.532666i | \(-0.178810\pi\) | ||||
0.846326 | + | 0.532666i | \(0.178810\pi\) | |||||||
\(620\) | 1.33770 | 0.0537232 | ||||||||
\(621\) | −21.3131 | −0.855267 | ||||||||
\(622\) | 32.5675 | 1.30584 | ||||||||
\(623\) | 64.7912 | 2.59580 | ||||||||
\(624\) | 1.69475 | 0.0678444 | ||||||||
\(625\) | 22.7496 | 0.909986 | ||||||||
\(626\) | 11.0509 | 0.441684 | ||||||||
\(627\) | −2.45517 | −0.0980501 | ||||||||
\(628\) | 14.1766 | 0.565709 | ||||||||
\(629\) | −39.4717 | −1.57384 | ||||||||
\(630\) | 3.41588 | 0.136092 | ||||||||
\(631\) | 15.3047 | 0.609270 | 0.304635 | − | 0.952469i | \(-0.401466\pi\) | ||||
0.304635 | + | 0.952469i | \(0.401466\pi\) | |||||||
\(632\) | −16.3774 | −0.651459 | ||||||||
\(633\) | 21.3537 | 0.848732 | ||||||||
\(634\) | 7.53342 | 0.299190 | ||||||||
\(635\) | 6.08364 | 0.241422 | ||||||||
\(636\) | −14.9573 | −0.593094 | ||||||||
\(637\) | 13.4374 | 0.532409 | ||||||||
\(638\) | −9.93968 | −0.393516 | ||||||||
\(639\) | −10.5395 | −0.416935 | ||||||||
\(640\) | 0.389300 | 0.0153884 | ||||||||
\(641\) | 15.4150 | 0.608855 | 0.304428 | − | 0.952535i | \(-0.401535\pi\) | ||||
0.304428 | + | 0.952535i | \(0.401535\pi\) | |||||||
\(642\) | 9.70184 | 0.382901 | ||||||||
\(643\) | 42.3479 | 1.67004 | 0.835020 | − | 0.550220i | \(-0.185456\pi\) | ||||
0.835020 | + | 0.550220i | \(0.185456\pi\) | |||||||
\(644\) | 39.3814 | 1.55184 | ||||||||
\(645\) | 6.63775 | 0.261361 | ||||||||
\(646\) | 6.38458 | 0.251198 | ||||||||
\(647\) | −22.5470 | −0.886414 | −0.443207 | − | 0.896419i | \(-0.646159\pi\) | ||||
−0.443207 | + | 0.896419i | \(0.646159\pi\) | |||||||
\(648\) | −11.1723 | −0.438889 | ||||||||
\(649\) | −2.55627 | −0.100342 | ||||||||
\(650\) | −3.75881 | −0.147433 | ||||||||
\(651\) | 37.0533 | 1.45223 | ||||||||
\(652\) | −1.04017 | −0.0407361 | ||||||||
\(653\) | −23.1557 | −0.906154 | −0.453077 | − | 0.891471i | \(-0.649674\pi\) | ||||
−0.453077 | + | 0.891471i | \(0.649674\pi\) | |||||||
\(654\) | 6.78421 | 0.265284 | ||||||||
\(655\) | −4.67571 | −0.182695 | ||||||||
\(656\) | 5.59521 | 0.218456 | ||||||||
\(657\) | 11.6469 | 0.454389 | ||||||||
\(658\) | 10.5696 | 0.412047 | ||||||||
\(659\) | 43.3685 | 1.68940 | 0.844699 | − | 0.535242i | \(-0.179780\pi\) | ||||
0.844699 | + | 0.535242i | \(0.179780\pi\) | |||||||
\(660\) | 0.851027 | 0.0331262 | ||||||||
\(661\) | 27.2414 | 1.05957 | 0.529784 | − | 0.848132i | \(-0.322273\pi\) | ||||
0.529784 | + | 0.848132i | \(0.322273\pi\) | |||||||
\(662\) | 11.5271 | 0.448012 | ||||||||
\(663\) | −9.63420 | −0.374161 | ||||||||
\(664\) | −12.4454 | −0.482973 | ||||||||
\(665\) | −2.15677 | −0.0836359 | ||||||||
\(666\) | 12.3509 | 0.478588 | ||||||||
\(667\) | −79.3538 | −3.07259 | ||||||||
\(668\) | 11.9099 | 0.460807 | ||||||||
\(669\) | −10.2627 | −0.396778 | ||||||||
\(670\) | 1.42551 | 0.0550722 | ||||||||
\(671\) | 0.705682 | 0.0272425 | ||||||||
\(672\) | 10.7834 | 0.415977 | ||||||||
\(673\) | −49.4379 | −1.90569 | −0.952845 | − | 0.303458i | \(-0.901859\pi\) | ||||
−0.952845 | + | 0.303458i | \(0.901859\pi\) | |||||||
\(674\) | 16.1314 | 0.621357 | ||||||||
\(675\) | 12.9436 | 0.498199 | ||||||||
\(676\) | −12.3990 | −0.476884 | ||||||||
\(677\) | 24.6273 | 0.946504 | 0.473252 | − | 0.880927i | \(-0.343080\pi\) | ||||
0.473252 | + | 0.880927i | \(0.343080\pi\) | |||||||
\(678\) | −3.22553 | −0.123876 | ||||||||
\(679\) | 7.18400 | 0.275697 | ||||||||
\(680\) | −2.21306 | −0.0848671 | ||||||||
\(681\) | 61.0792 | 2.34056 | ||||||||
\(682\) | 3.43616 | 0.131577 | ||||||||
\(683\) | 18.4662 | 0.706588 | 0.353294 | − | 0.935512i | \(-0.385062\pi\) | ||||
0.353294 | + | 0.935512i | \(0.385062\pi\) | |||||||
\(684\) | −1.99777 | −0.0763867 | ||||||||
\(685\) | −8.28874 | −0.316696 | ||||||||
\(686\) | 50.9697 | 1.94603 | ||||||||
\(687\) | −14.2788 | −0.544770 | ||||||||
\(688\) | 7.79970 | 0.297361 | ||||||||
\(689\) | −5.30446 | −0.202084 | ||||||||
\(690\) | 6.79421 | 0.258651 | ||||||||
\(691\) | −48.7834 | −1.85581 | −0.927904 | − | 0.372818i | \(-0.878392\pi\) | ||||
−0.927904 | + | 0.372818i | \(0.878392\pi\) | |||||||
\(692\) | −4.62647 | −0.175872 | ||||||||
\(693\) | 8.77442 | 0.333313 | ||||||||
\(694\) | −0.902306 | −0.0342511 | ||||||||
\(695\) | −2.49888 | −0.0947880 | ||||||||
\(696\) | −21.7286 | −0.823619 | ||||||||
\(697\) | −31.8072 | −1.20478 | ||||||||
\(698\) | 20.8256 | 0.788261 | ||||||||
\(699\) | 9.78117 | 0.369958 | ||||||||
\(700\) | −23.9165 | −0.903960 | ||||||||
\(701\) | 23.4917 | 0.887268 | 0.443634 | − | 0.896208i | \(-0.353689\pi\) | ||||
0.443634 | + | 0.896208i | \(0.353689\pi\) | |||||||
\(702\) | −2.06966 | −0.0781144 | ||||||||
\(703\) | −7.79829 | −0.294118 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 1.82351 | 0.0686773 | ||||||||
\(706\) | −19.4315 | −0.731315 | ||||||||
\(707\) | −94.1705 | −3.54165 | ||||||||
\(708\) | −5.58811 | −0.210014 | ||||||||
\(709\) | −42.2792 | −1.58783 | −0.793915 | − | 0.608029i | \(-0.791961\pi\) | ||||
−0.793915 | + | 0.608029i | \(0.791961\pi\) | |||||||
\(710\) | −2.30665 | −0.0865670 | ||||||||
\(711\) | −29.1319 | −1.09253 | ||||||||
\(712\) | 13.1347 | 0.492244 | ||||||||
\(713\) | 27.4327 | 1.02736 | ||||||||
\(714\) | −61.3004 | −2.29411 | ||||||||
\(715\) | 0.301809 | 0.0112870 | ||||||||
\(716\) | 21.5158 | 0.804085 | ||||||||
\(717\) | −48.2310 | −1.80122 | ||||||||
\(718\) | −13.6692 | −0.510130 | ||||||||
\(719\) | −11.8908 | −0.443454 | −0.221727 | − | 0.975109i | \(-0.571169\pi\) | ||||
−0.221727 | + | 0.975109i | \(0.571169\pi\) | |||||||
\(720\) | 0.692480 | 0.0258072 | ||||||||
\(721\) | −92.9983 | −3.46344 | ||||||||
\(722\) | −17.7386 | −0.660163 | ||||||||
\(723\) | −20.3140 | −0.755486 | ||||||||
\(724\) | 11.5012 | 0.427439 | ||||||||
\(725\) | 48.1920 | 1.78981 | ||||||||
\(726\) | 2.18604 | 0.0811316 | ||||||||
\(727\) | 24.3114 | 0.901660 | 0.450830 | − | 0.892610i | \(-0.351128\pi\) | ||||
0.450830 | + | 0.892610i | \(0.351128\pi\) | |||||||
\(728\) | 3.82422 | 0.141735 | ||||||||
\(729\) | −2.36523 | −0.0876010 | ||||||||
\(730\) | 2.54902 | 0.0943434 | ||||||||
\(731\) | −44.3391 | −1.63994 | ||||||||
\(732\) | 1.54265 | 0.0570180 | ||||||||
\(733\) | 23.7766 | 0.878210 | 0.439105 | − | 0.898436i | \(-0.355296\pi\) | ||||
0.439105 | + | 0.898436i | \(0.355296\pi\) | |||||||
\(734\) | 13.1334 | 0.484762 | ||||||||
\(735\) | 14.7507 | 0.544086 | ||||||||
\(736\) | 7.98354 | 0.294277 | ||||||||
\(737\) | 3.66172 | 0.134881 | ||||||||
\(738\) | 9.95265 | 0.366362 | ||||||||
\(739\) | 5.71016 | 0.210052 | 0.105026 | − | 0.994469i | \(-0.466507\pi\) | ||||
0.105026 | + | 0.994469i | \(0.466507\pi\) | |||||||
\(740\) | 2.70309 | 0.0993676 | ||||||||
\(741\) | −1.90340 | −0.0699230 | ||||||||
\(742\) | −33.7512 | −1.23905 | ||||||||
\(743\) | 25.5682 | 0.938006 | 0.469003 | − | 0.883197i | \(-0.344613\pi\) | ||||
0.469003 | + | 0.883197i | \(0.344613\pi\) | |||||||
\(744\) | 7.51158 | 0.275388 | ||||||||
\(745\) | 4.79212 | 0.175570 | ||||||||
\(746\) | −18.4840 | −0.676746 | ||||||||
\(747\) | −22.1376 | −0.809971 | ||||||||
\(748\) | −5.68472 | −0.207854 | ||||||||
\(749\) | 21.8923 | 0.799927 | ||||||||
\(750\) | −8.38129 | −0.306042 | ||||||||
\(751\) | −13.7750 | −0.502658 | −0.251329 | − | 0.967902i | \(-0.580868\pi\) | ||||
−0.251329 | + | 0.967902i | \(0.580868\pi\) | |||||||
\(752\) | 2.14271 | 0.0781368 | ||||||||
\(753\) | 44.4195 | 1.61874 | ||||||||
\(754\) | −7.70584 | −0.280630 | ||||||||
\(755\) | −4.78208 | −0.174038 | ||||||||
\(756\) | −13.1689 | −0.478946 | ||||||||
\(757\) | −7.81397 | −0.284003 | −0.142002 | − | 0.989866i | \(-0.545354\pi\) | ||||
−0.142002 | + | 0.989866i | \(0.545354\pi\) | |||||||
\(758\) | −22.5634 | −0.819541 | ||||||||
\(759\) | 17.4524 | 0.633480 | ||||||||
\(760\) | −0.437228 | −0.0158599 | ||||||||
\(761\) | 25.4522 | 0.922641 | 0.461321 | − | 0.887234i | \(-0.347376\pi\) | ||||
0.461321 | + | 0.887234i | \(0.347376\pi\) | |||||||
\(762\) | 34.1615 | 1.23754 | ||||||||
\(763\) | 15.3086 | 0.554210 | ||||||||
\(764\) | −14.2034 | −0.513862 | ||||||||
\(765\) | −3.93656 | −0.142327 | ||||||||
\(766\) | −33.1128 | −1.19641 | ||||||||
\(767\) | −1.98177 | −0.0715577 | ||||||||
\(768\) | 2.18604 | 0.0788820 | ||||||||
\(769\) | −2.16932 | −0.0782277 | −0.0391139 | − | 0.999235i | \(-0.512454\pi\) | ||||
−0.0391139 | + | 0.999235i | \(0.512454\pi\) | |||||||
\(770\) | 1.92035 | 0.0692046 | ||||||||
\(771\) | 2.77185 | 0.0998258 | ||||||||
\(772\) | −8.33214 | −0.299880 | ||||||||
\(773\) | 53.0166 | 1.90688 | 0.953438 | − | 0.301589i | \(-0.0975170\pi\) | ||||
0.953438 | + | 0.301589i | \(0.0975170\pi\) | |||||||
\(774\) | 13.8740 | 0.498689 | ||||||||
\(775\) | −16.6600 | −0.598445 | ||||||||
\(776\) | 1.45637 | 0.0522805 | ||||||||
\(777\) | 74.8739 | 2.68609 | ||||||||
\(778\) | −23.0986 | −0.828126 | ||||||||
\(779\) | −6.28404 | −0.225149 | ||||||||
\(780\) | 0.659767 | 0.0236235 | ||||||||
\(781\) | −5.92511 | −0.212017 | ||||||||
\(782\) | −45.3842 | −1.62294 | ||||||||
\(783\) | 26.5353 | 0.948296 | ||||||||
\(784\) | 17.3328 | 0.619027 | ||||||||
\(785\) | 5.51896 | 0.196980 | ||||||||
\(786\) | −26.2556 | −0.936505 | ||||||||
\(787\) | −17.3658 | −0.619024 | −0.309512 | − | 0.950896i | \(-0.600166\pi\) | ||||
−0.309512 | + | 0.950896i | \(0.600166\pi\) | |||||||
\(788\) | 1.00000 | 0.0356235 | ||||||||
\(789\) | 20.5917 | 0.733083 | ||||||||
\(790\) | −6.37574 | −0.226839 | ||||||||
\(791\) | −7.27844 | −0.258792 | ||||||||
\(792\) | 1.77878 | 0.0632062 | ||||||||
\(793\) | 0.547087 | 0.0194276 | ||||||||
\(794\) | −1.24697 | −0.0442531 | ||||||||
\(795\) | −5.82287 | −0.206516 | ||||||||
\(796\) | −4.67312 | −0.165635 | ||||||||
\(797\) | 5.17702 | 0.183380 | 0.0916898 | − | 0.995788i | \(-0.470773\pi\) | ||||
0.0916898 | + | 0.995788i | \(0.470773\pi\) | |||||||
\(798\) | −12.1109 | −0.428722 | ||||||||
\(799\) | −12.1807 | −0.430924 | ||||||||
\(800\) | −4.84845 | −0.171418 | ||||||||
\(801\) | 23.3638 | 0.825518 | ||||||||
\(802\) | 1.76907 | 0.0624680 | ||||||||
\(803\) | 6.54769 | 0.231063 | ||||||||
\(804\) | 8.00467 | 0.282303 | ||||||||
\(805\) | 15.3312 | 0.540354 | ||||||||
\(806\) | 2.66392 | 0.0938324 | ||||||||
\(807\) | −10.7518 | −0.378480 | ||||||||
\(808\) | −19.0906 | −0.671604 | ||||||||
\(809\) | −52.5823 | −1.84870 | −0.924348 | − | 0.381551i | \(-0.875390\pi\) | ||||
−0.924348 | + | 0.381551i | \(0.875390\pi\) | |||||||
\(810\) | −4.34937 | −0.152821 | ||||||||
\(811\) | −14.0755 | −0.494256 | −0.247128 | − | 0.968983i | \(-0.579487\pi\) | ||||
−0.247128 | + | 0.968983i | \(0.579487\pi\) | |||||||
\(812\) | −49.0307 | −1.72064 | ||||||||
\(813\) | −58.4019 | −2.04825 | ||||||||
\(814\) | 6.94346 | 0.243368 | ||||||||
\(815\) | −0.404937 | −0.0141843 | ||||||||
\(816\) | −12.4270 | −0.435034 | ||||||||
\(817\) | −8.75994 | −0.306471 | ||||||||
\(818\) | 19.8592 | 0.694360 | ||||||||
\(819\) | 6.80246 | 0.237697 | ||||||||
\(820\) | 2.17822 | 0.0760666 | ||||||||
\(821\) | −0.748229 | −0.0261134 | −0.0130567 | − | 0.999915i | \(-0.504156\pi\) | ||||
−0.0130567 | + | 0.999915i | \(0.504156\pi\) | |||||||
\(822\) | −46.5438 | −1.62340 | ||||||||
\(823\) | 18.1188 | 0.631581 | 0.315790 | − | 0.948829i | \(-0.397730\pi\) | ||||
0.315790 | + | 0.948829i | \(0.397730\pi\) | |||||||
\(824\) | −18.8529 | −0.656773 | ||||||||
\(825\) | −10.5989 | −0.369007 | ||||||||
\(826\) | −12.6096 | −0.438745 | ||||||||
\(827\) | 39.5905 | 1.37670 | 0.688348 | − | 0.725380i | \(-0.258336\pi\) | ||||
0.688348 | + | 0.725380i | \(0.258336\pi\) | |||||||
\(828\) | 14.2010 | 0.493518 | ||||||||
\(829\) | −33.1881 | −1.15267 | −0.576334 | − | 0.817214i | \(-0.695517\pi\) | ||||
−0.576334 | + | 0.817214i | \(0.695517\pi\) | |||||||
\(830\) | −4.84498 | −0.168172 | ||||||||
\(831\) | 56.0872 | 1.94564 | ||||||||
\(832\) | 0.775260 | 0.0268773 | ||||||||
\(833\) | −98.5320 | −3.41393 | ||||||||
\(834\) | −14.0320 | −0.485888 | ||||||||
\(835\) | 4.63652 | 0.160453 | ||||||||
\(836\) | −1.12311 | −0.0388437 | ||||||||
\(837\) | −9.17329 | −0.317075 | ||||||||
\(838\) | −32.6124 | −1.12658 | ||||||||
\(839\) | −1.85772 | −0.0641356 | −0.0320678 | − | 0.999486i | \(-0.510209\pi\) | ||||
−0.0320678 | + | 0.999486i | \(0.510209\pi\) | |||||||
\(840\) | 4.19797 | 0.144844 | ||||||||
\(841\) | 69.7973 | 2.40680 | ||||||||
\(842\) | 16.3556 | 0.563652 | ||||||||
\(843\) | 1.05614 | 0.0363753 | ||||||||
\(844\) | 9.76819 | 0.336235 | ||||||||
\(845\) | −4.82692 | −0.166051 | ||||||||
\(846\) | 3.81142 | 0.131039 | ||||||||
\(847\) | 4.93283 | 0.169494 | ||||||||
\(848\) | −6.84216 | −0.234961 | ||||||||
\(849\) | −20.3405 | −0.698084 | ||||||||
\(850\) | 27.5621 | 0.945371 | ||||||||
\(851\) | 55.4334 | 1.90023 | ||||||||
\(852\) | −12.9525 | −0.443747 | ||||||||
\(853\) | 33.5899 | 1.15010 | 0.575048 | − | 0.818120i | \(-0.304983\pi\) | ||||
0.575048 | + | 0.818120i | \(0.304983\pi\) | |||||||
\(854\) | 3.48101 | 0.119118 | ||||||||
\(855\) | −0.777733 | −0.0265979 | ||||||||
\(856\) | 4.43808 | 0.151691 | ||||||||
\(857\) | −30.9089 | −1.05583 | −0.527914 | − | 0.849298i | \(-0.677026\pi\) | ||||
−0.527914 | + | 0.849298i | \(0.677026\pi\) | |||||||
\(858\) | 1.69475 | 0.0578579 | ||||||||
\(859\) | 1.76822 | 0.0603308 | 0.0301654 | − | 0.999545i | \(-0.490397\pi\) | ||||
0.0301654 | + | 0.999545i | \(0.490397\pi\) | |||||||
\(860\) | 3.03642 | 0.103541 | ||||||||
\(861\) | 60.3351 | 2.05622 | ||||||||
\(862\) | −27.6455 | −0.941610 | ||||||||
\(863\) | −9.88514 | −0.336494 | −0.168247 | − | 0.985745i | \(-0.553811\pi\) | ||||
−0.168247 | + | 0.985745i | \(0.553811\pi\) | |||||||
\(864\) | −2.66964 | −0.0908229 | ||||||||
\(865\) | −1.80109 | −0.0612388 | ||||||||
\(866\) | 28.8663 | 0.980918 | ||||||||
\(867\) | 33.4816 | 1.13709 | ||||||||
\(868\) | 16.9500 | 0.575319 | ||||||||
\(869\) | −16.3774 | −0.555566 | ||||||||
\(870\) | −8.45894 | −0.286785 | ||||||||
\(871\) | 2.83879 | 0.0961886 | ||||||||
\(872\) | 3.10342 | 0.105095 | ||||||||
\(873\) | 2.59056 | 0.0876771 | ||||||||
\(874\) | −8.96641 | −0.303293 | ||||||||
\(875\) | −18.9125 | −0.639358 | ||||||||
\(876\) | 14.3135 | 0.483609 | ||||||||
\(877\) | 14.3047 | 0.483034 | 0.241517 | − | 0.970397i | \(-0.422355\pi\) | ||||
0.241517 | + | 0.970397i | \(0.422355\pi\) | |||||||
\(878\) | −30.2827 | −1.02199 | ||||||||
\(879\) | 10.0625 | 0.339401 | ||||||||
\(880\) | 0.389300 | 0.0131233 | ||||||||
\(881\) | 13.5867 | 0.457747 | 0.228873 | − | 0.973456i | \(-0.426496\pi\) | ||||
0.228873 | + | 0.973456i | \(0.426496\pi\) | |||||||
\(882\) | 30.8312 | 1.03814 | ||||||||
\(883\) | 28.2712 | 0.951401 | 0.475700 | − | 0.879607i | \(-0.342195\pi\) | ||||
0.475700 | + | 0.879607i | \(0.342195\pi\) | |||||||
\(884\) | −4.40714 | −0.148228 | ||||||||
\(885\) | −2.17545 | −0.0731270 | ||||||||
\(886\) | −17.5265 | −0.588816 | ||||||||
\(887\) | 28.8603 | 0.969034 | 0.484517 | − | 0.874782i | \(-0.338995\pi\) | ||||
0.484517 | + | 0.874782i | \(0.338995\pi\) | |||||||
\(888\) | 15.1787 | 0.509364 | ||||||||
\(889\) | 77.0858 | 2.58538 | ||||||||
\(890\) | 5.11334 | 0.171400 | ||||||||
\(891\) | −11.1723 | −0.374286 | ||||||||
\(892\) | −4.69464 | −0.157188 | ||||||||
\(893\) | −2.40651 | −0.0805308 | ||||||||
\(894\) | 26.9093 | 0.899980 | ||||||||
\(895\) | 8.37612 | 0.279983 | ||||||||
\(896\) | 4.93283 | 0.164794 | ||||||||
\(897\) | 13.5301 | 0.451758 | ||||||||
\(898\) | −0.319442 | −0.0106599 | ||||||||
\(899\) | −34.1543 | −1.13911 | ||||||||
\(900\) | −8.62432 | −0.287477 | ||||||||
\(901\) | 38.8958 | 1.29581 | ||||||||
\(902\) | 5.59521 | 0.186300 | ||||||||
\(903\) | 84.1070 | 2.79891 | ||||||||
\(904\) | −1.47551 | −0.0490748 | ||||||||
\(905\) | 4.47742 | 0.148834 | ||||||||
\(906\) | −26.8529 | −0.892127 | ||||||||
\(907\) | 39.5765 | 1.31412 | 0.657058 | − | 0.753840i | \(-0.271801\pi\) | ||||
0.657058 | + | 0.753840i | \(0.271801\pi\) | |||||||
\(908\) | 27.9405 | 0.927239 | ||||||||
\(909\) | −33.9580 | −1.12631 | ||||||||
\(910\) | 1.48877 | 0.0493523 | ||||||||
\(911\) | 34.5285 | 1.14398 | 0.571990 | − | 0.820260i | \(-0.306172\pi\) | ||||
0.571990 | + | 0.820260i | \(0.306172\pi\) | |||||||
\(912\) | −2.45517 | −0.0812988 | ||||||||
\(913\) | −12.4454 | −0.411881 | ||||||||
\(914\) | −13.8474 | −0.458032 | ||||||||
\(915\) | 0.600554 | 0.0198537 | ||||||||
\(916\) | −6.53180 | −0.215817 | ||||||||
\(917\) | −59.2459 | −1.95647 | ||||||||
\(918\) | 15.1761 | 0.500887 | ||||||||
\(919\) | 28.8019 | 0.950087 | 0.475044 | − | 0.879962i | \(-0.342432\pi\) | ||||
0.475044 | + | 0.879962i | \(0.342432\pi\) | |||||||
\(920\) | 3.10799 | 0.102468 | ||||||||
\(921\) | 9.05825 | 0.298479 | ||||||||
\(922\) | −20.5144 | −0.675606 | ||||||||
\(923\) | −4.59351 | −0.151197 | ||||||||
\(924\) | 10.7834 | 0.354747 | ||||||||
\(925\) | −33.6650 | −1.10690 | ||||||||
\(926\) | −19.8953 | −0.653800 | ||||||||
\(927\) | −33.5353 | −1.10144 | ||||||||
\(928\) | −9.93968 | −0.326286 | ||||||||
\(929\) | −36.9290 | −1.21160 | −0.605801 | − | 0.795616i | \(-0.707147\pi\) | ||||
−0.605801 | + | 0.795616i | \(0.707147\pi\) | |||||||
\(930\) | 2.92426 | 0.0958903 | ||||||||
\(931\) | −19.4666 | −0.637993 | ||||||||
\(932\) | 4.47438 | 0.146563 | ||||||||
\(933\) | 71.1939 | 2.33078 | ||||||||
\(934\) | 21.9574 | 0.718468 | ||||||||
\(935\) | −2.21306 | −0.0723749 | ||||||||
\(936\) | 1.37902 | 0.0450746 | ||||||||
\(937\) | 4.93365 | 0.161175 | 0.0805876 | − | 0.996748i | \(-0.474320\pi\) | ||||
0.0805876 | + | 0.996748i | \(0.474320\pi\) | |||||||
\(938\) | 18.0626 | 0.589765 | ||||||||
\(939\) | 24.1578 | 0.788360 | ||||||||
\(940\) | 0.834159 | 0.0272073 | ||||||||
\(941\) | 2.18510 | 0.0712323 | 0.0356162 | − | 0.999366i | \(-0.488661\pi\) | ||||
0.0356162 | + | 0.999366i | \(0.488661\pi\) | |||||||
\(942\) | 30.9907 | 1.00973 | ||||||||
\(943\) | 44.6695 | 1.45464 | ||||||||
\(944\) | −2.55627 | −0.0831994 | ||||||||
\(945\) | −5.12664 | −0.166770 | ||||||||
\(946\) | 7.79970 | 0.253590 | ||||||||
\(947\) | 22.0405 | 0.716219 | 0.358109 | − | 0.933680i | \(-0.383421\pi\) | ||||
0.358109 | + | 0.933680i | \(0.383421\pi\) | |||||||
\(948\) | −35.8018 | −1.16279 | ||||||||
\(949\) | 5.07616 | 0.164779 | ||||||||
\(950\) | 5.44535 | 0.176670 | ||||||||
\(951\) | 16.4684 | 0.534023 | ||||||||
\(952\) | −28.0417 | −0.908838 | ||||||||
\(953\) | −8.09447 | −0.262206 | −0.131103 | − | 0.991369i | \(-0.541852\pi\) | ||||
−0.131103 | + | 0.991369i | \(0.541852\pi\) | |||||||
\(954\) | −12.1707 | −0.394041 | ||||||||
\(955\) | −5.52939 | −0.178927 | ||||||||
\(956\) | −22.0632 | −0.713573 | ||||||||
\(957\) | −21.7286 | −0.702385 | ||||||||
\(958\) | −7.94047 | −0.256545 | ||||||||
\(959\) | −105.027 | −3.39149 | ||||||||
\(960\) | 0.851027 | 0.0274668 | ||||||||
\(961\) | −19.1928 | −0.619124 | ||||||||
\(962\) | 5.38299 | 0.173555 | ||||||||
\(963\) | 7.89438 | 0.254393 | ||||||||
\(964\) | −9.29260 | −0.299294 | ||||||||
\(965\) | −3.24370 | −0.104419 | ||||||||
\(966\) | 86.0894 | 2.76988 | ||||||||
\(967\) | −18.0109 | −0.579190 | −0.289595 | − | 0.957149i | \(-0.593521\pi\) | ||||
−0.289595 | + | 0.957149i | \(0.593521\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 13.9570 | 0.448362 | ||||||||
\(970\) | 0.566964 | 0.0182041 | ||||||||
\(971\) | 4.49226 | 0.144163 | 0.0720817 | − | 0.997399i | \(-0.477036\pi\) | ||||
0.0720817 | + | 0.997399i | \(0.477036\pi\) | |||||||
\(972\) | −16.4142 | −0.526485 | ||||||||
\(973\) | −31.6633 | −1.01508 | ||||||||
\(974\) | 13.9288 | 0.446306 | ||||||||
\(975\) | −8.21691 | −0.263152 | ||||||||
\(976\) | 0.705682 | 0.0225883 | ||||||||
\(977\) | −19.0488 | −0.609425 | −0.304712 | − | 0.952444i | \(-0.598560\pi\) | ||||
−0.304712 | + | 0.952444i | \(0.598560\pi\) | |||||||
\(978\) | −2.27385 | −0.0727097 | ||||||||
\(979\) | 13.1347 | 0.419787 | ||||||||
\(980\) | 6.74765 | 0.215546 | ||||||||
\(981\) | 5.52031 | 0.176250 | ||||||||
\(982\) | −9.36573 | −0.298873 | ||||||||
\(983\) | −58.8520 | −1.87709 | −0.938544 | − | 0.345159i | \(-0.887825\pi\) | ||||
−0.938544 | + | 0.345159i | \(0.887825\pi\) | |||||||
\(984\) | 12.2314 | 0.389921 | ||||||||
\(985\) | 0.389300 | 0.0124041 | ||||||||
\(986\) | 56.5043 | 1.79946 | ||||||||
\(987\) | 23.1057 | 0.735462 | ||||||||
\(988\) | −0.870705 | −0.0277008 | ||||||||
\(989\) | 62.2692 | 1.98005 | ||||||||
\(990\) | 0.692480 | 0.0220085 | ||||||||
\(991\) | 25.3312 | 0.804673 | 0.402337 | − | 0.915492i | \(-0.368198\pi\) | ||||
0.402337 | + | 0.915492i | \(0.368198\pi\) | |||||||
\(992\) | 3.43616 | 0.109098 | ||||||||
\(993\) | 25.1986 | 0.799655 | ||||||||
\(994\) | −29.2275 | −0.927042 | ||||||||
\(995\) | −1.81925 | −0.0576741 | ||||||||
\(996\) | −27.2061 | −0.862057 | ||||||||
\(997\) | 52.7205 | 1.66968 | 0.834838 | − | 0.550496i | \(-0.185561\pi\) | ||||
0.834838 | + | 0.550496i | \(0.185561\pi\) | |||||||
\(998\) | −2.10961 | −0.0667785 | ||||||||
\(999\) | −18.5365 | −0.586470 |
(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 | 4334.2.a.g.1.19 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4334.2.a.g.1.19 | ✓ | 26 | 1.1 | even | 1 | trivial |