Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2541,2,Mod(1,2541)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2541, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2541.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2541 = 3 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2541.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: | \(20.2899871536\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 231) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.35567\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.162147 | 0.114655 | 0.0573277 | − | 0.998355i | \(-0.481742\pi\) | ||||
0.0573277 | + | 0.998355i | \(0.481742\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.97371 | −0.986854 | ||||||||
\(5\) | −4.38705 | −1.96195 | −0.980975 | − | 0.194133i | \(-0.937811\pi\) | ||||
−0.980975 | + | 0.194133i | \(0.937811\pi\) | |||||||
\(6\) | −0.162147 | −0.0661963 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −0.644326 | −0.227804 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −0.711349 | −0.224948 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.97371 | 0.569761 | ||||||||
\(13\) | 1.67571 | 0.464757 | 0.232379 | − | 0.972625i | \(-0.425349\pi\) | ||||
0.232379 | + | 0.972625i | \(0.425349\pi\) | |||||||
\(14\) | −0.162147 | −0.0433357 | ||||||||
\(15\) | 4.38705 | 1.13273 | ||||||||
\(16\) | 3.84294 | 0.960735 | ||||||||
\(17\) | 6.18663 | 1.50048 | 0.750239 | − | 0.661167i | \(-0.229938\pi\) | ||||
0.750239 | + | 0.661167i | \(0.229938\pi\) | |||||||
\(18\) | 0.162147 | 0.0382185 | ||||||||
\(19\) | −3.47528 | −0.797284 | −0.398642 | − | 0.917107i | \(-0.630518\pi\) | ||||
−0.398642 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(20\) | 8.65877 | 1.93616 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.568595 | 0.118560 | 0.0592801 | − | 0.998241i | \(-0.481119\pi\) | ||||
0.0592801 | + | 0.998241i | \(0.481119\pi\) | |||||||
\(24\) | 0.644326 | 0.131522 | ||||||||
\(25\) | 14.2462 | 2.84925 | ||||||||
\(26\) | 0.271711 | 0.0532869 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.97371 | 0.372996 | ||||||||
\(29\) | −8.86742 | −1.64664 | −0.823320 | − | 0.567578i | \(-0.807880\pi\) | ||||
−0.823320 | + | 0.567578i | \(0.807880\pi\) | |||||||
\(30\) | 0.711349 | 0.129874 | ||||||||
\(31\) | 4.33447 | 0.778494 | 0.389247 | − | 0.921133i | \(-0.372735\pi\) | ||||
0.389247 | + | 0.921133i | \(0.372735\pi\) | |||||||
\(32\) | 1.91177 | 0.337957 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00314 | 0.172038 | ||||||||
\(35\) | 4.38705 | 0.741547 | ||||||||
\(36\) | −1.97371 | −0.328951 | ||||||||
\(37\) | 0.969445 | 0.159376 | 0.0796879 | − | 0.996820i | \(-0.474608\pi\) | ||||
0.0796879 | + | 0.996820i | \(0.474608\pi\) | |||||||
\(38\) | −0.563507 | −0.0914129 | ||||||||
\(39\) | −1.67571 | −0.268328 | ||||||||
\(40\) | 2.82669 | 0.446939 | ||||||||
\(41\) | 5.77725 | 0.902255 | 0.451128 | − | 0.892459i | \(-0.351022\pi\) | ||||
0.451128 | + | 0.892459i | \(0.351022\pi\) | |||||||
\(42\) | 0.162147 | 0.0250199 | ||||||||
\(43\) | −5.04388 | −0.769184 | −0.384592 | − | 0.923087i | \(-0.625658\pi\) | ||||
−0.384592 | + | 0.923087i | \(0.625658\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.38705 | −0.653983 | ||||||||
\(46\) | 0.0921961 | 0.0135936 | ||||||||
\(47\) | 4.67256 | 0.681563 | 0.340782 | − | 0.940143i | \(-0.389308\pi\) | ||||
0.340782 | + | 0.940143i | \(0.389308\pi\) | |||||||
\(48\) | −3.84294 | −0.554681 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 2.30999 | 0.326682 | ||||||||
\(51\) | −6.18663 | −0.866301 | ||||||||
\(52\) | −3.30735 | −0.458647 | ||||||||
\(53\) | −2.37882 | −0.326756 | −0.163378 | − | 0.986564i | \(-0.552239\pi\) | ||||
−0.163378 | + | 0.986564i | \(0.552239\pi\) | |||||||
\(54\) | −0.162147 | −0.0220654 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.644326 | 0.0861016 | ||||||||
\(57\) | 3.47528 | 0.460312 | ||||||||
\(58\) | −1.43783 | −0.188796 | ||||||||
\(59\) | −2.84901 | −0.370910 | −0.185455 | − | 0.982653i | \(-0.559376\pi\) | ||||
−0.185455 | + | 0.982653i | \(0.559376\pi\) | |||||||
\(60\) | −8.65877 | −1.11784 | ||||||||
\(61\) | 9.29883 | 1.19059 | 0.595296 | − | 0.803506i | \(-0.297035\pi\) | ||||
0.595296 | + | 0.803506i | \(0.297035\pi\) | |||||||
\(62\) | 0.702822 | 0.0892585 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | −7.37589 | −0.921987 | ||||||||
\(65\) | −7.35141 | −0.911830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.14275 | −0.872626 | −0.436313 | − | 0.899795i | \(-0.643716\pi\) | ||||
−0.436313 | + | 0.899795i | \(0.643716\pi\) | |||||||
\(68\) | −12.2106 | −1.48075 | ||||||||
\(69\) | −0.568595 | −0.0684508 | ||||||||
\(70\) | 0.711349 | 0.0850224 | ||||||||
\(71\) | −0.794487 | −0.0942882 | −0.0471441 | − | 0.998888i | \(-0.515012\pi\) | ||||
−0.0471441 | + | 0.998888i | \(0.515012\pi\) | |||||||
\(72\) | −0.644326 | −0.0759345 | ||||||||
\(73\) | 2.38705 | 0.279384 | 0.139692 | − | 0.990195i | \(-0.455389\pi\) | ||||
0.139692 | + | 0.990195i | \(0.455389\pi\) | |||||||
\(74\) | 0.157193 | 0.0182733 | ||||||||
\(75\) | −14.2462 | −1.64501 | ||||||||
\(76\) | 6.85919 | 0.786803 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.271711 | −0.0307652 | ||||||||
\(79\) | −0.670617 | −0.0754504 | −0.0377252 | − | 0.999288i | \(-0.512011\pi\) | ||||
−0.0377252 | + | 0.999288i | \(0.512011\pi\) | |||||||
\(80\) | −16.8592 | −1.88491 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.936765 | 0.103448 | ||||||||
\(83\) | −9.28503 | −1.01916 | −0.509582 | − | 0.860422i | \(-0.670200\pi\) | ||||
−0.509582 | + | 0.860422i | \(0.670200\pi\) | |||||||
\(84\) | −1.97371 | −0.215349 | ||||||||
\(85\) | −27.1411 | −2.94386 | ||||||||
\(86\) | −0.817850 | −0.0881911 | ||||||||
\(87\) | 8.86742 | 0.950688 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.2106 | −1.29432 | −0.647161 | − | 0.762354i | \(-0.724044\pi\) | ||||
−0.647161 | + | 0.762354i | \(0.724044\pi\) | |||||||
\(90\) | −0.711349 | −0.0749827 | ||||||||
\(91\) | −1.67571 | −0.175662 | ||||||||
\(92\) | −1.12224 | −0.117002 | ||||||||
\(93\) | −4.33447 | −0.449464 | ||||||||
\(94\) | 0.757643 | 0.0781449 | ||||||||
\(95\) | 15.2462 | 1.56423 | ||||||||
\(96\) | −1.91177 | −0.195120 | ||||||||
\(97\) | 15.0596 | 1.52907 | 0.764536 | − | 0.644581i | \(-0.222968\pi\) | ||||
0.764536 | + | 0.644581i | \(0.222968\pi\) | |||||||
\(98\) | 0.162147 | 0.0163793 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −28.1179 | −2.81179 | ||||||||
\(101\) | 5.76079 | 0.573220 | 0.286610 | − | 0.958047i | \(-0.407472\pi\) | ||||
0.286610 | + | 0.958047i | \(0.407472\pi\) | |||||||
\(102\) | −1.00314 | −0.0993261 | ||||||||
\(103\) | 7.71449 | 0.760132 | 0.380066 | − | 0.924959i | \(-0.375901\pi\) | ||||
0.380066 | + | 0.924959i | \(0.375901\pi\) | |||||||
\(104\) | −1.07970 | −0.105873 | ||||||||
\(105\) | −4.38705 | −0.428133 | ||||||||
\(106\) | −0.385719 | −0.0374644 | ||||||||
\(107\) | −16.4634 | −1.59158 | −0.795790 | − | 0.605573i | \(-0.792944\pi\) | ||||
−0.795790 | + | 0.605573i | \(0.792944\pi\) | |||||||
\(108\) | 1.97371 | 0.189920 | ||||||||
\(109\) | 9.74355 | 0.933263 | 0.466632 | − | 0.884452i | \(-0.345467\pi\) | ||||
0.466632 | + | 0.884452i | \(0.345467\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.969445 | −0.0920157 | ||||||||
\(112\) | −3.84294 | −0.363124 | ||||||||
\(113\) | −2.85725 | −0.268787 | −0.134394 | − | 0.990928i | \(-0.542909\pi\) | ||||
−0.134394 | + | 0.990928i | \(0.542909\pi\) | |||||||
\(114\) | 0.563507 | 0.0527773 | ||||||||
\(115\) | −2.49446 | −0.232609 | ||||||||
\(116\) | 17.5017 | 1.62499 | ||||||||
\(117\) | 1.67571 | 0.154919 | ||||||||
\(118\) | −0.461960 | −0.0425268 | ||||||||
\(119\) | −6.18663 | −0.567127 | ||||||||
\(120\) | −2.82669 | −0.258040 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1.50778 | 0.136508 | ||||||||
\(123\) | −5.77725 | −0.520917 | ||||||||
\(124\) | −8.55498 | −0.768260 | ||||||||
\(125\) | −40.5638 | −3.62813 | ||||||||
\(126\) | −0.162147 | −0.0144452 | ||||||||
\(127\) | −16.0514 | −1.42433 | −0.712165 | − | 0.702012i | \(-0.752285\pi\) | ||||
−0.712165 | + | 0.702012i | \(0.752285\pi\) | |||||||
\(128\) | −5.01953 | −0.443668 | ||||||||
\(129\) | 5.04388 | 0.444089 | ||||||||
\(130\) | −1.19201 | −0.104546 | ||||||||
\(131\) | 0.750136 | 0.0655397 | 0.0327699 | − | 0.999463i | \(-0.489567\pi\) | ||||
0.0327699 | + | 0.999463i | \(0.489567\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.47528 | 0.301345 | ||||||||
\(134\) | −1.15818 | −0.100051 | ||||||||
\(135\) | 4.38705 | 0.377578 | ||||||||
\(136\) | −3.98620 | −0.341814 | ||||||||
\(137\) | −13.0082 | −1.11137 | −0.555684 | − | 0.831393i | \(-0.687544\pi\) | ||||
−0.555684 | + | 0.831393i | \(0.687544\pi\) | |||||||
\(138\) | −0.0921961 | −0.00784826 | ||||||||
\(139\) | 3.90112 | 0.330889 | 0.165444 | − | 0.986219i | \(-0.447094\pi\) | ||||
0.165444 | + | 0.986219i | \(0.447094\pi\) | |||||||
\(140\) | −8.65877 | −0.731799 | ||||||||
\(141\) | −4.67256 | −0.393501 | ||||||||
\(142\) | −0.128824 | −0.0108107 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.84294 | 0.320245 | ||||||||
\(145\) | 38.9019 | 3.23062 | ||||||||
\(146\) | 0.387054 | 0.0320328 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −1.91340 | −0.157281 | ||||||||
\(149\) | 18.5434 | 1.51914 | 0.759568 | − | 0.650428i | \(-0.225410\pi\) | ||||
0.759568 | + | 0.650428i | \(0.225410\pi\) | |||||||
\(150\) | −2.30999 | −0.188610 | ||||||||
\(151\) | 20.7979 | 1.69251 | 0.846255 | − | 0.532779i | \(-0.178852\pi\) | ||||
0.846255 | + | 0.532779i | \(0.178852\pi\) | |||||||
\(152\) | 2.23921 | 0.181624 | ||||||||
\(153\) | 6.18663 | 0.500159 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.0156 | −1.52737 | ||||||||
\(156\) | 3.30735 | 0.264800 | ||||||||
\(157\) | 5.80975 | 0.463669 | 0.231834 | − | 0.972755i | \(-0.425527\pi\) | ||||
0.231834 | + | 0.972755i | \(0.425527\pi\) | |||||||
\(158\) | −0.108739 | −0.00865079 | ||||||||
\(159\) | 2.37882 | 0.188653 | ||||||||
\(160\) | −8.38705 | −0.663055 | ||||||||
\(161\) | −0.568595 | −0.0448116 | ||||||||
\(162\) | 0.162147 | 0.0127395 | ||||||||
\(163\) | −8.90307 | −0.697342 | −0.348671 | − | 0.937245i | \(-0.613367\pi\) | ||||
−0.348671 | + | 0.937245i | \(0.613367\pi\) | |||||||
\(164\) | −11.4026 | −0.890394 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.50554 | −0.116853 | ||||||||
\(167\) | −3.82355 | −0.295875 | −0.147937 | − | 0.988997i | \(-0.547263\pi\) | ||||
−0.147937 | + | 0.988997i | \(0.547263\pi\) | |||||||
\(168\) | −0.644326 | −0.0497108 | ||||||||
\(169\) | −10.1920 | −0.784001 | ||||||||
\(170\) | −4.40085 | −0.337530 | ||||||||
\(171\) | −3.47528 | −0.265761 | ||||||||
\(172\) | 9.95514 | 0.759072 | ||||||||
\(173\) | 1.75061 | 0.133096 | 0.0665482 | − | 0.997783i | \(-0.478801\pi\) | ||||
0.0665482 | + | 0.997783i | \(0.478801\pi\) | |||||||
\(174\) | 1.43783 | 0.109001 | ||||||||
\(175\) | −14.2462 | −1.07691 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.84901 | 0.214145 | ||||||||
\(178\) | −1.97991 | −0.148401 | ||||||||
\(179\) | −12.8541 | −0.960761 | −0.480380 | − | 0.877060i | \(-0.659501\pi\) | ||||
−0.480380 | + | 0.877060i | \(0.659501\pi\) | |||||||
\(180\) | 8.65877 | 0.645386 | ||||||||
\(181\) | −22.0831 | −1.64142 | −0.820712 | − | 0.571342i | \(-0.806423\pi\) | ||||
−0.820712 | + | 0.571342i | \(0.806423\pi\) | |||||||
\(182\) | −0.271711 | −0.0201406 | ||||||||
\(183\) | −9.29883 | −0.687389 | ||||||||
\(184\) | −0.366361 | −0.0270085 | ||||||||
\(185\) | −4.25301 | −0.312687 | ||||||||
\(186\) | −0.702822 | −0.0515334 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −9.22227 | −0.672603 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 2.47214 | 0.179348 | ||||||||
\(191\) | 14.7160 | 1.06481 | 0.532405 | − | 0.846490i | \(-0.321288\pi\) | ||||
0.532405 | + | 0.846490i | \(0.321288\pi\) | |||||||
\(192\) | 7.37589 | 0.532309 | ||||||||
\(193\) | 8.51287 | 0.612770 | 0.306385 | − | 0.951908i | \(-0.400881\pi\) | ||||
0.306385 | + | 0.951908i | \(0.400881\pi\) | |||||||
\(194\) | 2.44187 | 0.175316 | ||||||||
\(195\) | 7.35141 | 0.526445 | ||||||||
\(196\) | −1.97371 | −0.140979 | ||||||||
\(197\) | −4.72273 | −0.336480 | −0.168240 | − | 0.985746i | \(-0.553808\pi\) | ||||
−0.168240 | + | 0.985746i | \(0.553808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.7620 | 1.18822 | 0.594112 | − | 0.804382i | \(-0.297504\pi\) | ||||
0.594112 | + | 0.804382i | \(0.297504\pi\) | |||||||
\(200\) | −9.17922 | −0.649069 | ||||||||
\(201\) | 7.14275 | 0.503811 | ||||||||
\(202\) | 0.934096 | 0.0657227 | ||||||||
\(203\) | 8.86742 | 0.622371 | ||||||||
\(204\) | 12.2106 | 0.854913 | ||||||||
\(205\) | −25.3451 | −1.77018 | ||||||||
\(206\) | 1.25088 | 0.0871532 | ||||||||
\(207\) | 0.568595 | 0.0395201 | ||||||||
\(208\) | 6.43964 | 0.446509 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.711349 | −0.0490877 | ||||||||
\(211\) | −10.1454 | −0.698440 | −0.349220 | − | 0.937041i | \(-0.613553\pi\) | ||||
−0.349220 | + | 0.937041i | \(0.613553\pi\) | |||||||
\(212\) | 4.69510 | 0.322461 | ||||||||
\(213\) | 0.794487 | 0.0544373 | ||||||||
\(214\) | −2.66950 | −0.182483 | ||||||||
\(215\) | 22.1278 | 1.50910 | ||||||||
\(216\) | 0.644326 | 0.0438408 | ||||||||
\(217\) | −4.33447 | −0.294243 | ||||||||
\(218\) | 1.57989 | 0.107004 | ||||||||
\(219\) | −2.38705 | −0.161302 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3670 | 0.697358 | ||||||||
\(222\) | −0.157193 | −0.0105501 | ||||||||
\(223\) | −6.11172 | −0.409271 | −0.204636 | − | 0.978838i | \(-0.565601\pi\) | ||||
−0.204636 | + | 0.978838i | \(0.565601\pi\) | |||||||
\(224\) | −1.91177 | −0.127736 | ||||||||
\(225\) | 14.2462 | 0.949750 | ||||||||
\(226\) | −0.463295 | −0.0308179 | ||||||||
\(227\) | 14.2090 | 0.943081 | 0.471541 | − | 0.881844i | \(-0.343698\pi\) | ||||
0.471541 | + | 0.881844i | \(0.343698\pi\) | |||||||
\(228\) | −6.85919 | −0.454261 | ||||||||
\(229\) | −2.72781 | −0.180259 | −0.0901295 | − | 0.995930i | \(-0.528728\pi\) | ||||
−0.0901295 | + | 0.995930i | \(0.528728\pi\) | |||||||
\(230\) | −0.404469 | −0.0266699 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.71351 | 0.375110 | ||||||||
\(233\) | −17.7897 | −1.16544 | −0.582720 | − | 0.812673i | \(-0.698012\pi\) | ||||
−0.582720 | + | 0.812673i | \(0.698012\pi\) | |||||||
\(234\) | 0.271711 | 0.0177623 | ||||||||
\(235\) | −20.4988 | −1.33719 | ||||||||
\(236\) | 5.62312 | 0.366034 | ||||||||
\(237\) | 0.670617 | 0.0435613 | ||||||||
\(238\) | −1.00314 | −0.0650242 | ||||||||
\(239\) | 12.7058 | 0.821869 | 0.410934 | − | 0.911665i | \(-0.365202\pi\) | ||||
0.410934 | + | 0.911665i | \(0.365202\pi\) | |||||||
\(240\) | 16.8592 | 1.08826 | ||||||||
\(241\) | −18.6604 | −1.20202 | −0.601012 | − | 0.799240i | \(-0.705235\pi\) | ||||
−0.601012 | + | 0.799240i | \(0.705235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −18.3532 | −1.17494 | ||||||||
\(245\) | −4.38705 | −0.280279 | ||||||||
\(246\) | −0.936765 | −0.0597260 | ||||||||
\(247\) | −5.82355 | −0.370543 | ||||||||
\(248\) | −2.79281 | −0.177344 | ||||||||
\(249\) | 9.28503 | 0.588415 | ||||||||
\(250\) | −6.57730 | −0.415985 | ||||||||
\(251\) | 18.8493 | 1.18976 | 0.594878 | − | 0.803816i | \(-0.297200\pi\) | ||||
0.594878 | + | 0.803816i | \(0.297200\pi\) | |||||||
\(252\) | 1.97371 | 0.124332 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −2.60269 | −0.163307 | ||||||||
\(255\) | 27.1411 | 1.69964 | ||||||||
\(256\) | 13.9379 | 0.871118 | ||||||||
\(257\) | −10.3345 | −0.644647 | −0.322323 | − | 0.946630i | \(-0.604464\pi\) | ||||
−0.322323 | + | 0.946630i | \(0.604464\pi\) | |||||||
\(258\) | 0.817850 | 0.0509171 | ||||||||
\(259\) | −0.969445 | −0.0602384 | ||||||||
\(260\) | 14.5095 | 0.899844 | ||||||||
\(261\) | −8.86742 | −0.548880 | ||||||||
\(262\) | 0.121632 | 0.00751448 | ||||||||
\(263\) | −4.14979 | −0.255887 | −0.127943 | − | 0.991781i | \(-0.540838\pi\) | ||||
−0.127943 | + | 0.991781i | \(0.540838\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.4360 | 0.641079 | ||||||||
\(266\) | 0.563507 | 0.0345508 | ||||||||
\(267\) | 12.2106 | 0.747277 | ||||||||
\(268\) | 14.0977 | 0.861155 | ||||||||
\(269\) | −5.06228 | −0.308653 | −0.154326 | − | 0.988020i | \(-0.549321\pi\) | ||||
−0.154326 | + | 0.988020i | \(0.549321\pi\) | |||||||
\(270\) | 0.711349 | 0.0432913 | ||||||||
\(271\) | −26.3160 | −1.59859 | −0.799293 | − | 0.600942i | \(-0.794792\pi\) | ||||
−0.799293 | + | 0.600942i | \(0.794792\pi\) | |||||||
\(272\) | 23.7749 | 1.44156 | ||||||||
\(273\) | 1.67571 | 0.101418 | ||||||||
\(274\) | −2.10925 | −0.127424 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.12224 | 0.0675510 | ||||||||
\(277\) | 25.8187 | 1.55130 | 0.775648 | − | 0.631165i | \(-0.217423\pi\) | ||||
0.775648 | + | 0.631165i | \(0.217423\pi\) | |||||||
\(278\) | 0.632556 | 0.0379382 | ||||||||
\(279\) | 4.33447 | 0.259498 | ||||||||
\(280\) | −2.82669 | −0.168927 | ||||||||
\(281\) | −5.43844 | −0.324430 | −0.162215 | − | 0.986755i | \(-0.551864\pi\) | ||||
−0.162215 | + | 0.986755i | \(0.551864\pi\) | |||||||
\(282\) | −0.757643 | −0.0451170 | ||||||||
\(283\) | 25.3839 | 1.50892 | 0.754458 | − | 0.656348i | \(-0.227900\pi\) | ||||
0.754458 | + | 0.656348i | \(0.227900\pi\) | |||||||
\(284\) | 1.56809 | 0.0930487 | ||||||||
\(285\) | −15.2462 | −0.903110 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.77725 | −0.341020 | ||||||||
\(288\) | 1.91177 | 0.112652 | ||||||||
\(289\) | 21.2744 | 1.25143 | ||||||||
\(290\) | 6.30783 | 0.370408 | ||||||||
\(291\) | −15.0596 | −0.882810 | ||||||||
\(292\) | −4.71135 | −0.275711 | ||||||||
\(293\) | 6.75402 | 0.394574 | 0.197287 | − | 0.980346i | \(-0.436787\pi\) | ||||
0.197287 | + | 0.980346i | \(0.436787\pi\) | |||||||
\(294\) | −0.162147 | −0.00945662 | ||||||||
\(295\) | 12.4988 | 0.727707 | ||||||||
\(296\) | −0.624638 | −0.0363064 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00676 | 0.174177 | ||||||||
\(299\) | 0.952798 | 0.0551017 | ||||||||
\(300\) | 28.1179 | 1.62339 | ||||||||
\(301\) | 5.04388 | 0.290724 | ||||||||
\(302\) | 3.37232 | 0.194055 | ||||||||
\(303\) | −5.76079 | −0.330949 | ||||||||
\(304\) | −13.3553 | −0.765979 | ||||||||
\(305\) | −40.7945 | −2.33588 | ||||||||
\(306\) | 1.00314 | 0.0573460 | ||||||||
\(307\) | −17.6396 | −1.00674 | −0.503372 | − | 0.864070i | \(-0.667908\pi\) | ||||
−0.503372 | + | 0.864070i | \(0.667908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.71449 | −0.438862 | ||||||||
\(310\) | −3.08332 | −0.175121 | ||||||||
\(311\) | −12.2414 | −0.694149 | −0.347074 | − | 0.937838i | \(-0.612825\pi\) | ||||
−0.347074 | + | 0.937838i | \(0.612825\pi\) | |||||||
\(312\) | 1.07970 | 0.0611260 | ||||||||
\(313\) | 3.15951 | 0.178586 | 0.0892931 | − | 0.996005i | \(-0.471539\pi\) | ||||
0.0892931 | + | 0.996005i | \(0.471539\pi\) | |||||||
\(314\) | 0.942035 | 0.0531621 | ||||||||
\(315\) | 4.38705 | 0.247182 | ||||||||
\(316\) | 1.32360 | 0.0744585 | ||||||||
\(317\) | 8.43364 | 0.473681 | 0.236840 | − | 0.971549i | \(-0.423888\pi\) | ||||
0.236840 | + | 0.971549i | \(0.423888\pi\) | |||||||
\(318\) | 0.385719 | 0.0216301 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 32.3584 | 1.80889 | ||||||||
\(321\) | 16.4634 | 0.918899 | ||||||||
\(322\) | −0.0921961 | −0.00513789 | ||||||||
\(323\) | −21.5003 | −1.19631 | ||||||||
\(324\) | −1.97371 | −0.109650 | ||||||||
\(325\) | 23.8725 | 1.32421 | ||||||||
\(326\) | −1.44361 | −0.0799540 | ||||||||
\(327\) | −9.74355 | −0.538820 | ||||||||
\(328\) | −3.72243 | −0.205537 | ||||||||
\(329\) | −4.67256 | −0.257607 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.13284 | 0.337092 | 0.168546 | − | 0.985694i | \(-0.446093\pi\) | ||||
0.168546 | + | 0.985694i | \(0.446093\pi\) | |||||||
\(332\) | 18.3259 | 1.00577 | ||||||||
\(333\) | 0.969445 | 0.0531253 | ||||||||
\(334\) | −0.619977 | −0.0339237 | ||||||||
\(335\) | 31.3356 | 1.71205 | ||||||||
\(336\) | 3.84294 | 0.209650 | ||||||||
\(337\) | −29.8792 | −1.62763 | −0.813813 | − | 0.581127i | \(-0.802612\pi\) | ||||
−0.813813 | + | 0.581127i | \(0.802612\pi\) | |||||||
\(338\) | −1.65261 | −0.0898899 | ||||||||
\(339\) | 2.85725 | 0.155184 | ||||||||
\(340\) | 53.5686 | 2.90516 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −0.563507 | −0.0304710 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 3.24990 | 0.175223 | ||||||||
\(345\) | 2.49446 | 0.134297 | ||||||||
\(346\) | 0.283857 | 0.0152602 | ||||||||
\(347\) | −29.1716 | −1.56602 | −0.783008 | − | 0.622012i | \(-0.786315\pi\) | ||||
−0.783008 | + | 0.622012i | \(0.786315\pi\) | |||||||
\(348\) | −17.5017 | −0.938190 | ||||||||
\(349\) | 13.3924 | 0.716881 | 0.358440 | − | 0.933553i | \(-0.383309\pi\) | ||||
0.358440 | + | 0.933553i | \(0.383309\pi\) | |||||||
\(350\) | −2.30999 | −0.123474 | ||||||||
\(351\) | −1.67571 | −0.0894425 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.3175 | −1.13462 | −0.567309 | − | 0.823505i | \(-0.692015\pi\) | ||||
−0.567309 | + | 0.823505i | \(0.692015\pi\) | |||||||
\(354\) | 0.461960 | 0.0245529 | ||||||||
\(355\) | 3.48546 | 0.184989 | ||||||||
\(356\) | 24.1002 | 1.27731 | ||||||||
\(357\) | 6.18663 | 0.327431 | ||||||||
\(358\) | −2.08426 | −0.110156 | ||||||||
\(359\) | −20.6234 | −1.08846 | −0.544231 | − | 0.838935i | \(-0.683179\pi\) | ||||
−0.544231 | + | 0.838935i | \(0.683179\pi\) | |||||||
\(360\) | 2.82669 | 0.148980 | ||||||||
\(361\) | −6.92242 | −0.364338 | ||||||||
\(362\) | −3.58072 | −0.188198 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.30735 | 0.173352 | ||||||||
\(365\) | −10.4721 | −0.548137 | ||||||||
\(366\) | −1.50778 | −0.0788129 | ||||||||
\(367\) | 32.8546 | 1.71499 | 0.857497 | − | 0.514489i | \(-0.172018\pi\) | ||||
0.857497 | + | 0.514489i | \(0.172018\pi\) | |||||||
\(368\) | 2.18508 | 0.113905 | ||||||||
\(369\) | 5.77725 | 0.300752 | ||||||||
\(370\) | −0.689613 | −0.0358513 | ||||||||
\(371\) | 2.37882 | 0.123502 | ||||||||
\(372\) | 8.55498 | 0.443555 | ||||||||
\(373\) | 26.0979 | 1.35130 | 0.675650 | − | 0.737223i | \(-0.263863\pi\) | ||||
0.675650 | + | 0.737223i | \(0.263863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 40.5638 | 2.09470 | ||||||||
\(376\) | −3.01065 | −0.155262 | ||||||||
\(377\) | −14.8592 | −0.765287 | ||||||||
\(378\) | 0.162147 | 0.00833995 | ||||||||
\(379\) | −11.6733 | −0.599616 | −0.299808 | − | 0.953999i | \(-0.596923\pi\) | ||||
−0.299808 | + | 0.953999i | \(0.596923\pi\) | |||||||
\(380\) | −30.0916 | −1.54367 | ||||||||
\(381\) | 16.0514 | 0.822337 | ||||||||
\(382\) | 2.38615 | 0.122086 | ||||||||
\(383\) | −15.3701 | −0.785376 | −0.392688 | − | 0.919672i | \(-0.628455\pi\) | ||||
−0.392688 | + | 0.919672i | \(0.628455\pi\) | |||||||
\(384\) | 5.01953 | 0.256152 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.38034 | 0.0702573 | ||||||||
\(387\) | −5.04388 | −0.256395 | ||||||||
\(388\) | −29.7233 | −1.50897 | ||||||||
\(389\) | −9.64424 | −0.488983 | −0.244491 | − | 0.969651i | \(-0.578621\pi\) | ||||
−0.244491 | + | 0.969651i | \(0.578621\pi\) | |||||||
\(390\) | 1.19201 | 0.0603598 | ||||||||
\(391\) | 3.51769 | 0.177897 | ||||||||
\(392\) | −0.644326 | −0.0325434 | ||||||||
\(393\) | −0.750136 | −0.0378394 | ||||||||
\(394\) | −0.765777 | −0.0385793 | ||||||||
\(395\) | 2.94203 | 0.148030 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.2855 | 1.01810 | 0.509050 | − | 0.860737i | \(-0.329997\pi\) | ||||
0.509050 | + | 0.860737i | \(0.329997\pi\) | |||||||
\(398\) | 2.71791 | 0.136236 | ||||||||
\(399\) | −3.47528 | −0.173982 | ||||||||
\(400\) | 54.7475 | 2.73737 | ||||||||
\(401\) | −8.15655 | −0.407319 | −0.203659 | − | 0.979042i | \(-0.565283\pi\) | ||||
−0.203659 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(402\) | 1.15818 | 0.0577646 | ||||||||
\(403\) | 7.26330 | 0.361811 | ||||||||
\(404\) | −11.3701 | −0.565684 | ||||||||
\(405\) | −4.38705 | −0.217994 | ||||||||
\(406\) | 1.43783 | 0.0713582 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.98620 | 0.197347 | ||||||||
\(409\) | −9.67209 | −0.478254 | −0.239127 | − | 0.970988i | \(-0.576861\pi\) | ||||
−0.239127 | + | 0.970988i | \(0.576861\pi\) | |||||||
\(410\) | −4.10964 | −0.202961 | ||||||||
\(411\) | 13.0082 | 0.641649 | ||||||||
\(412\) | −15.2262 | −0.750139 | ||||||||
\(413\) | 2.84901 | 0.140191 | ||||||||
\(414\) | 0.0921961 | 0.00453119 | ||||||||
\(415\) | 40.7339 | 1.99955 | ||||||||
\(416\) | 3.20357 | 0.157068 | ||||||||
\(417\) | −3.90112 | −0.191039 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.9357 | −0.925072 | −0.462536 | − | 0.886601i | \(-0.653060\pi\) | ||||
−0.462536 | + | 0.886601i | \(0.653060\pi\) | |||||||
\(420\) | 8.65877 | 0.422504 | ||||||||
\(421\) | −13.0950 | −0.638210 | −0.319105 | − | 0.947719i | \(-0.603382\pi\) | ||||
−0.319105 | + | 0.947719i | \(0.603382\pi\) | |||||||
\(422\) | −1.64505 | −0.0800799 | ||||||||
\(423\) | 4.67256 | 0.227188 | ||||||||
\(424\) | 1.53274 | 0.0744362 | ||||||||
\(425\) | 88.1362 | 4.27524 | ||||||||
\(426\) | 0.128824 | 0.00624153 | ||||||||
\(427\) | −9.29883 | −0.450002 | ||||||||
\(428\) | 32.4940 | 1.57066 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.58795 | 0.173027 | ||||||||
\(431\) | −16.3034 | −0.785309 | −0.392655 | − | 0.919686i | \(-0.628443\pi\) | ||||
−0.392655 | + | 0.919686i | \(0.628443\pi\) | |||||||
\(432\) | −3.84294 | −0.184894 | ||||||||
\(433\) | 11.6842 | 0.561508 | 0.280754 | − | 0.959780i | \(-0.409415\pi\) | ||||
0.280754 | + | 0.959780i | \(0.409415\pi\) | |||||||
\(434\) | −0.702822 | −0.0337366 | ||||||||
\(435\) | −38.9019 | −1.86520 | ||||||||
\(436\) | −19.2309 | −0.920995 | ||||||||
\(437\) | −1.97603 | −0.0945262 | ||||||||
\(438\) | −0.387054 | −0.0184942 | ||||||||
\(439\) | 11.7172 | 0.559230 | 0.279615 | − | 0.960112i | \(-0.409793\pi\) | ||||
0.279615 | + | 0.960112i | \(0.409793\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 1.68098 | 0.0799558 | ||||||||
\(443\) | −12.5671 | −0.597081 | −0.298540 | − | 0.954397i | \(-0.596500\pi\) | ||||
−0.298540 | + | 0.954397i | \(0.596500\pi\) | |||||||
\(444\) | 1.91340 | 0.0908060 | ||||||||
\(445\) | 53.5686 | 2.53939 | ||||||||
\(446\) | −0.990999 | −0.0469252 | ||||||||
\(447\) | −18.5434 | −0.877074 | ||||||||
\(448\) | 7.37589 | 0.348478 | ||||||||
\(449\) | −15.9360 | −0.752068 | −0.376034 | − | 0.926606i | \(-0.622712\pi\) | ||||
−0.376034 | + | 0.926606i | \(0.622712\pi\) | |||||||
\(450\) | 2.30999 | 0.108894 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 5.63937 | 0.265254 | ||||||||
\(453\) | −20.7979 | −0.977171 | ||||||||
\(454\) | 2.30394 | 0.108129 | ||||||||
\(455\) | 7.35141 | 0.344639 | ||||||||
\(456\) | −2.23921 | −0.104861 | ||||||||
\(457\) | −23.7945 | −1.11306 | −0.556530 | − | 0.830828i | \(-0.687867\pi\) | ||||
−0.556530 | + | 0.830828i | \(0.687867\pi\) | |||||||
\(458\) | −0.442307 | −0.0206677 | ||||||||
\(459\) | −6.18663 | −0.288767 | ||||||||
\(460\) | 4.92333 | 0.229552 | ||||||||
\(461\) | −22.6035 | −1.05275 | −0.526375 | − | 0.850252i | \(-0.676449\pi\) | ||||
−0.526375 | + | 0.850252i | \(0.676449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.03759 | 0.141169 | 0.0705843 | − | 0.997506i | \(-0.477514\pi\) | ||||
0.0705843 | + | 0.997506i | \(0.477514\pi\) | |||||||
\(464\) | −34.0770 | −1.58198 | ||||||||
\(465\) | 19.0156 | 0.881825 | ||||||||
\(466\) | −2.88454 | −0.133624 | ||||||||
\(467\) | −23.0051 | −1.06455 | −0.532274 | − | 0.846572i | \(-0.678662\pi\) | ||||
−0.532274 | + | 0.846572i | \(0.678662\pi\) | |||||||
\(468\) | −3.30735 | −0.152882 | ||||||||
\(469\) | 7.14275 | 0.329822 | ||||||||
\(470\) | −3.32382 | −0.153316 | ||||||||
\(471\) | −5.80975 | −0.267699 | ||||||||
\(472\) | 1.83569 | 0.0844946 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.108739 | 0.00499454 | ||||||||
\(475\) | −49.5097 | −2.27166 | ||||||||
\(476\) | 12.2106 | 0.559672 | ||||||||
\(477\) | −2.37882 | −0.108919 | ||||||||
\(478\) | 2.06021 | 0.0942317 | ||||||||
\(479\) | 8.17283 | 0.373426 | 0.186713 | − | 0.982414i | \(-0.440217\pi\) | ||||
0.186713 | + | 0.982414i | \(0.440217\pi\) | |||||||
\(480\) | 8.38705 | 0.382815 | ||||||||
\(481\) | 1.62450 | 0.0740710 | ||||||||
\(482\) | −3.02573 | −0.137818 | ||||||||
\(483\) | 0.568595 | 0.0258720 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −66.0673 | −2.99996 | ||||||||
\(486\) | −0.162147 | −0.00735515 | ||||||||
\(487\) | −0.999232 | −0.0452795 | −0.0226398 | − | 0.999744i | \(-0.507207\pi\) | ||||
−0.0226398 | + | 0.999744i | \(0.507207\pi\) | |||||||
\(488\) | −5.99147 | −0.271221 | ||||||||
\(489\) | 8.90307 | 0.402611 | ||||||||
\(490\) | −0.711349 | −0.0321355 | ||||||||
\(491\) | 24.2957 | 1.09645 | 0.548224 | − | 0.836331i | \(-0.315304\pi\) | ||||
0.548224 | + | 0.836331i | \(0.315304\pi\) | |||||||
\(492\) | 11.4026 | 0.514069 | ||||||||
\(493\) | −54.8595 | −2.47075 | ||||||||
\(494\) | −0.944272 | −0.0424848 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.6571 | 0.747927 | ||||||||
\(497\) | 0.794487 | 0.0356376 | ||||||||
\(498\) | 1.50554 | 0.0674650 | ||||||||
\(499\) | −41.0807 | −1.83902 | −0.919512 | − | 0.393061i | \(-0.871416\pi\) | ||||
−0.919512 | + | 0.393061i | \(0.871416\pi\) | |||||||
\(500\) | 80.0611 | 3.58044 | ||||||||
\(501\) | 3.82355 | 0.170823 | ||||||||
\(502\) | 3.05636 | 0.136412 | ||||||||
\(503\) | −10.3270 | −0.460457 | −0.230228 | − | 0.973137i | \(-0.573947\pi\) | ||||
−0.230228 | + | 0.973137i | \(0.573947\pi\) | |||||||
\(504\) | 0.644326 | 0.0287005 | ||||||||
\(505\) | −25.2729 | −1.12463 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1920 | 0.452643 | ||||||||
\(508\) | 31.6807 | 1.40561 | ||||||||
\(509\) | −40.6105 | −1.80003 | −0.900014 | − | 0.435860i | \(-0.856444\pi\) | ||||
−0.900014 | + | 0.435860i | \(0.856444\pi\) | |||||||
\(510\) | 4.40085 | 0.194873 | ||||||||
\(511\) | −2.38705 | −0.105597 | ||||||||
\(512\) | 12.2990 | 0.543546 | ||||||||
\(513\) | 3.47528 | 0.153437 | ||||||||
\(514\) | −1.67571 | −0.0739122 | ||||||||
\(515\) | −33.8439 | −1.49134 | ||||||||
\(516\) | −9.95514 | −0.438251 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −0.157193 | −0.00690666 | ||||||||
\(519\) | −1.75061 | −0.0768433 | ||||||||
\(520\) | 4.73670 | 0.207718 | ||||||||
\(521\) | −22.2145 | −0.973234 | −0.486617 | − | 0.873615i | \(-0.661769\pi\) | ||||
−0.486617 | + | 0.873615i | \(0.661769\pi\) | |||||||
\(522\) | −1.43783 | −0.0629320 | ||||||||
\(523\) | −22.6653 | −0.991085 | −0.495543 | − | 0.868584i | \(-0.665031\pi\) | ||||
−0.495543 | + | 0.868584i | \(0.665031\pi\) | |||||||
\(524\) | −1.48055 | −0.0646781 | ||||||||
\(525\) | 14.2462 | 0.621757 | ||||||||
\(526\) | −0.672876 | −0.0293388 | ||||||||
\(527\) | 26.8158 | 1.16811 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.6767 | −0.985943 | ||||||||
\(530\) | 1.69217 | 0.0735032 | ||||||||
\(531\) | −2.84901 | −0.123637 | ||||||||
\(532\) | −6.85919 | −0.297384 | ||||||||
\(533\) | 9.68098 | 0.419330 | ||||||||
\(534\) | 1.97991 | 0.0856793 | ||||||||
\(535\) | 72.2260 | 3.12260 | ||||||||
\(536\) | 4.60226 | 0.198787 | ||||||||
\(537\) | 12.8541 | 0.554695 | ||||||||
\(538\) | −0.820835 | −0.0353887 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −8.65877 | −0.372614 | ||||||||
\(541\) | −6.26662 | −0.269423 | −0.134712 | − | 0.990885i | \(-0.543011\pi\) | ||||
−0.134712 | + | 0.990885i | \(0.543011\pi\) | |||||||
\(542\) | −4.26707 | −0.183286 | ||||||||
\(543\) | 22.0831 | 0.947677 | ||||||||
\(544\) | 11.8274 | 0.507097 | ||||||||
\(545\) | −42.7455 | −1.83102 | ||||||||
\(546\) | 0.271711 | 0.0116282 | ||||||||
\(547\) | 34.0916 | 1.45765 | 0.728827 | − | 0.684698i | \(-0.240066\pi\) | ||||
0.728827 | + | 0.684698i | \(0.240066\pi\) | |||||||
\(548\) | 25.6745 | 1.09676 | ||||||||
\(549\) | 9.29883 | 0.396864 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.8168 | 1.31284 | ||||||||
\(552\) | 0.366361 | 0.0155933 | ||||||||
\(553\) | 0.670617 | 0.0285176 | ||||||||
\(554\) | 4.18643 | 0.177865 | ||||||||
\(555\) | 4.25301 | 0.180530 | ||||||||
\(556\) | −7.69968 | −0.326539 | ||||||||
\(557\) | −26.3992 | −1.11857 | −0.559284 | − | 0.828976i | \(-0.688924\pi\) | ||||
−0.559284 | + | 0.828976i | \(0.688924\pi\) | |||||||
\(558\) | 0.702822 | 0.0297528 | ||||||||
\(559\) | −8.45205 | −0.357484 | ||||||||
\(560\) | 16.8592 | 0.712431 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.881827 | −0.0371976 | ||||||||
\(563\) | −6.85125 | −0.288746 | −0.144373 | − | 0.989523i | \(-0.546116\pi\) | ||||
−0.144373 | + | 0.989523i | \(0.546116\pi\) | |||||||
\(564\) | 9.22227 | 0.388328 | ||||||||
\(565\) | 12.5349 | 0.527347 | ||||||||
\(566\) | 4.11593 | 0.173005 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0.511908 | 0.0214792 | ||||||||
\(569\) | 18.4008 | 0.771404 | 0.385702 | − | 0.922623i | \(-0.373959\pi\) | ||||
0.385702 | + | 0.922623i | \(0.373959\pi\) | |||||||
\(570\) | −2.47214 | −0.103546 | ||||||||
\(571\) | 0.336889 | 0.0140984 | 0.00704918 | − | 0.999975i | \(-0.497756\pi\) | ||||
0.00704918 | + | 0.999975i | \(0.497756\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −14.7160 | −0.614768 | ||||||||
\(574\) | −0.936765 | −0.0390998 | ||||||||
\(575\) | 8.10035 | 0.337808 | ||||||||
\(576\) | −7.37589 | −0.307329 | ||||||||
\(577\) | −25.8347 | −1.07551 | −0.537757 | − | 0.843100i | \(-0.680728\pi\) | ||||
−0.537757 | + | 0.843100i | \(0.680728\pi\) | |||||||
\(578\) | 3.44958 | 0.143484 | ||||||||
\(579\) | −8.51287 | −0.353783 | ||||||||
\(580\) | −76.7809 | −3.18815 | ||||||||
\(581\) | 9.28503 | 0.385208 | ||||||||
\(582\) | −2.44187 | −0.101219 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.53804 | −0.0636446 | ||||||||
\(585\) | −7.35141 | −0.303943 | ||||||||
\(586\) | 1.09515 | 0.0452401 | ||||||||
\(587\) | −3.73415 | −0.154125 | −0.0770623 | − | 0.997026i | \(-0.524554\pi\) | ||||
−0.0770623 | + | 0.997026i | \(0.524554\pi\) | |||||||
\(588\) | 1.97371 | 0.0813944 | ||||||||
\(589\) | −15.0635 | −0.620681 | ||||||||
\(590\) | 2.02664 | 0.0834355 | ||||||||
\(591\) | 4.72273 | 0.194267 | ||||||||
\(592\) | 3.72552 | 0.153118 | ||||||||
\(593\) | 17.5647 | 0.721295 | 0.360648 | − | 0.932702i | \(-0.382556\pi\) | ||||
0.360648 | + | 0.932702i | \(0.382556\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.1411 | 1.11268 | ||||||||
\(596\) | −36.5993 | −1.49917 | ||||||||
\(597\) | −16.7620 | −0.686021 | ||||||||
\(598\) | 0.154494 | 0.00631771 | ||||||||
\(599\) | 11.3088 | 0.462066 | 0.231033 | − | 0.972946i | \(-0.425789\pi\) | ||||
0.231033 | + | 0.972946i | \(0.425789\pi\) | |||||||
\(600\) | 9.17922 | 0.374740 | ||||||||
\(601\) | −28.9821 | −1.18220 | −0.591102 | − | 0.806596i | \(-0.701307\pi\) | ||||
−0.591102 | + | 0.806596i | \(0.701307\pi\) | |||||||
\(602\) | 0.817850 | 0.0333331 | ||||||||
\(603\) | −7.14275 | −0.290875 | ||||||||
\(604\) | −41.0490 | −1.67026 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.934096 | −0.0379450 | ||||||||
\(607\) | 7.34347 | 0.298062 | 0.149031 | − | 0.988832i | \(-0.452385\pi\) | ||||
0.149031 | + | 0.988832i | \(0.452385\pi\) | |||||||
\(608\) | −6.64395 | −0.269448 | ||||||||
\(609\) | −8.86742 | −0.359326 | ||||||||
\(610\) | −6.61471 | −0.267822 | ||||||||
\(611\) | 7.82984 | 0.316761 | ||||||||
\(612\) | −12.2106 | −0.493584 | ||||||||
\(613\) | 18.9535 | 0.765526 | 0.382763 | − | 0.923847i | \(-0.374973\pi\) | ||||
0.382763 | + | 0.923847i | \(0.374973\pi\) | |||||||
\(614\) | −2.86021 | −0.115429 | ||||||||
\(615\) | 25.3451 | 1.02201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.2571 | 1.01681 | 0.508407 | − | 0.861117i | \(-0.330234\pi\) | ||||
0.508407 | + | 0.861117i | \(0.330234\pi\) | |||||||
\(618\) | −1.25088 | −0.0503179 | ||||||||
\(619\) | −15.5725 | −0.625912 | −0.312956 | − | 0.949768i | \(-0.601319\pi\) | ||||
−0.312956 | + | 0.949768i | \(0.601319\pi\) | |||||||
\(620\) | 37.5312 | 1.50729 | ||||||||
\(621\) | −0.568595 | −0.0228169 | ||||||||
\(622\) | −1.98492 | −0.0795879 | ||||||||
\(623\) | 12.2106 | 0.489207 | ||||||||
\(624\) | −6.43964 | −0.257792 | ||||||||
\(625\) | 106.724 | 4.26897 | ||||||||
\(626\) | 0.512306 | 0.0204759 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.4668 | −0.457573 | ||||||||
\(629\) | 5.99760 | 0.239140 | ||||||||
\(630\) | 0.711349 | 0.0283408 | ||||||||
\(631\) | −36.0169 | −1.43381 | −0.716905 | − | 0.697170i | \(-0.754442\pi\) | ||||
−0.716905 | + | 0.697170i | \(0.754442\pi\) | |||||||
\(632\) | 0.432096 | 0.0171879 | ||||||||
\(633\) | 10.1454 | 0.403244 | ||||||||
\(634\) | 1.36749 | 0.0543100 | ||||||||
\(635\) | 70.4183 | 2.79446 | ||||||||
\(636\) | −4.69510 | −0.186173 | ||||||||
\(637\) | 1.67571 | 0.0663939 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.794487 | −0.0314294 | ||||||||
\(640\) | 22.0209 | 0.870454 | ||||||||
\(641\) | −26.7410 | −1.05620 | −0.528102 | − | 0.849181i | \(-0.677096\pi\) | ||||
−0.528102 | + | 0.849181i | \(0.677096\pi\) | |||||||
\(642\) | 2.66950 | 0.105357 | ||||||||
\(643\) | 7.31364 | 0.288422 | 0.144211 | − | 0.989547i | \(-0.453936\pi\) | ||||
0.144211 | + | 0.989547i | \(0.453936\pi\) | |||||||
\(644\) | 1.12224 | 0.0442225 | ||||||||
\(645\) | −22.1278 | −0.871280 | ||||||||
\(646\) | −3.48621 | −0.137163 | ||||||||
\(647\) | −35.0221 | −1.37686 | −0.688431 | − | 0.725302i | \(-0.741700\pi\) | ||||
−0.688431 | + | 0.725302i | \(0.741700\pi\) | |||||||
\(648\) | −0.644326 | −0.0253115 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 3.87086 | 0.151828 | ||||||||
\(651\) | 4.33447 | 0.169881 | ||||||||
\(652\) | 17.5721 | 0.688175 | ||||||||
\(653\) | −4.05138 | −0.158543 | −0.0792714 | − | 0.996853i | \(-0.525259\pi\) | ||||
−0.0792714 | + | 0.996853i | \(0.525259\pi\) | |||||||
\(654\) | −1.57989 | −0.0617786 | ||||||||
\(655\) | −3.29089 | −0.128586 | ||||||||
\(656\) | 22.2016 | 0.866828 | ||||||||
\(657\) | 2.38705 | 0.0931279 | ||||||||
\(658\) | −0.757643 | −0.0295360 | ||||||||
\(659\) | 28.6360 | 1.11550 | 0.557750 | − | 0.830009i | \(-0.311665\pi\) | ||||
0.557750 | + | 0.830009i | \(0.311665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.2741 | 1.76096 | 0.880479 | − | 0.474085i | \(-0.157221\pi\) | ||||
0.880479 | + | 0.474085i | \(0.157221\pi\) | |||||||
\(662\) | 0.994424 | 0.0386494 | ||||||||
\(663\) | −10.3670 | −0.402620 | ||||||||
\(664\) | 5.98258 | 0.232169 | ||||||||
\(665\) | −15.2462 | −0.591224 | ||||||||
\(666\) | 0.157193 | 0.00609110 | ||||||||
\(667\) | −5.04197 | −0.195226 | ||||||||
\(668\) | 7.54657 | 0.291985 | ||||||||
\(669\) | 6.11172 | 0.236293 | ||||||||
\(670\) | 5.08099 | 0.196296 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.91177 | 0.0737483 | ||||||||
\(673\) | 0.0509075 | 0.00196234 | 0.000981170 | − | 1.00000i | \(-0.499688\pi\) | ||||
0.000981170 | 1.00000i | \(0.499688\pi\) | ||||||||
\(674\) | −4.84484 | −0.186616 | ||||||||
\(675\) | −14.2462 | −0.548338 | ||||||||
\(676\) | 20.1161 | 0.773694 | ||||||||
\(677\) | 39.1437 | 1.50442 | 0.752208 | − | 0.658925i | \(-0.228989\pi\) | ||||
0.752208 | + | 0.658925i | \(0.228989\pi\) | |||||||
\(678\) | 0.463295 | 0.0177927 | ||||||||
\(679\) | −15.0596 | −0.577935 | ||||||||
\(680\) | 17.4877 | 0.670622 | ||||||||
\(681\) | −14.2090 | −0.544488 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.4140 | 0.589800 | 0.294900 | − | 0.955528i | \(-0.404714\pi\) | ||||
0.294900 | + | 0.955528i | \(0.404714\pi\) | |||||||
\(684\) | 6.85919 | 0.262268 | ||||||||
\(685\) | 57.0678 | 2.18045 | ||||||||
\(686\) | −0.162147 | −0.00619081 | ||||||||
\(687\) | 2.72781 | 0.104073 | ||||||||
\(688\) | −19.3833 | −0.738982 | ||||||||
\(689\) | −3.98620 | −0.151862 | ||||||||
\(690\) | 0.404469 | 0.0153979 | ||||||||
\(691\) | −38.2746 | −1.45603 | −0.728017 | − | 0.685559i | \(-0.759558\pi\) | ||||
−0.728017 | + | 0.685559i | \(0.759558\pi\) | |||||||
\(692\) | −3.45520 | −0.131347 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.73010 | −0.179552 | ||||||||
\(695\) | −17.1144 | −0.649188 | ||||||||
\(696\) | −5.71351 | −0.216570 | ||||||||
\(697\) | 35.7417 | 1.35381 | ||||||||
\(698\) | 2.17155 | 0.0821942 | ||||||||
\(699\) | 17.7897 | 0.672867 | ||||||||
\(700\) | 28.1179 | 1.06276 | ||||||||
\(701\) | −1.38873 | −0.0524516 | −0.0262258 | − | 0.999656i | \(-0.508349\pi\) | ||||
−0.0262258 | + | 0.999656i | \(0.508349\pi\) | |||||||
\(702\) | −0.271711 | −0.0102551 | ||||||||
\(703\) | −3.36909 | −0.127068 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 20.4988 | 0.772029 | ||||||||
\(706\) | −3.45658 | −0.130090 | ||||||||
\(707\) | −5.76079 | −0.216657 | ||||||||
\(708\) | −5.62312 | −0.211330 | ||||||||
\(709\) | −12.8361 | −0.482071 | −0.241036 | − | 0.970516i | \(-0.577487\pi\) | ||||
−0.241036 | + | 0.970516i | \(0.577487\pi\) | |||||||
\(710\) | 0.565157 | 0.0212100 | ||||||||
\(711\) | −0.670617 | −0.0251501 | ||||||||
\(712\) | 7.86760 | 0.294851 | ||||||||
\(713\) | 2.46456 | 0.0922985 | ||||||||
\(714\) | 1.00314 | 0.0375417 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 25.3702 | 0.948131 | ||||||||
\(717\) | −12.7058 | −0.474506 | ||||||||
\(718\) | −3.34403 | −0.124798 | ||||||||
\(719\) | −21.5055 | −0.802021 | −0.401011 | − | 0.916073i | \(-0.631341\pi\) | ||||
−0.401011 | + | 0.916073i | \(0.631341\pi\) | |||||||
\(720\) | −16.8592 | −0.628305 | ||||||||
\(721\) | −7.71449 | −0.287303 | ||||||||
\(722\) | −1.12245 | −0.0417733 | ||||||||
\(723\) | 18.6604 | 0.693988 | ||||||||
\(724\) | 43.5856 | 1.61985 | ||||||||
\(725\) | −126.327 | −4.69168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.35770 | −0.198706 | −0.0993531 | − | 0.995052i | \(-0.531677\pi\) | ||||
−0.0993531 | + | 0.995052i | \(0.531677\pi\) | |||||||
\(728\) | 1.07970 | 0.0400164 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.69803 | −0.0628468 | ||||||||
\(731\) | −31.2046 | −1.15414 | ||||||||
\(732\) | 18.3532 | 0.678353 | ||||||||
\(733\) | 41.4506 | 1.53101 | 0.765506 | − | 0.643429i | \(-0.222489\pi\) | ||||
0.765506 | + | 0.643429i | \(0.222489\pi\) | |||||||
\(734\) | 5.32727 | 0.196633 | ||||||||
\(735\) | 4.38705 | 0.161819 | ||||||||
\(736\) | 1.08703 | 0.0400683 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.936765 | 0.0344828 | ||||||||
\(739\) | 42.6086 | 1.56738 | 0.783691 | − | 0.621151i | \(-0.213335\pi\) | ||||
0.783691 | + | 0.621151i | \(0.213335\pi\) | |||||||
\(740\) | 8.39420 | 0.308577 | ||||||||
\(741\) | 5.82355 | 0.213933 | ||||||||
\(742\) | 0.385719 | 0.0141602 | ||||||||
\(743\) | −30.4479 | −1.11702 | −0.558512 | − | 0.829496i | \(-0.688628\pi\) | ||||
−0.558512 | + | 0.829496i | \(0.688628\pi\) | |||||||
\(744\) | 2.79281 | 0.102389 | ||||||||
\(745\) | −81.3510 | −2.98047 | ||||||||
\(746\) | 4.23171 | 0.154934 | ||||||||
\(747\) | −9.28503 | −0.339722 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.4634 | 0.601561 | ||||||||
\(750\) | 6.57730 | 0.240169 | ||||||||
\(751\) | 9.06635 | 0.330836 | 0.165418 | − | 0.986224i | \(-0.447103\pi\) | ||||
0.165418 | + | 0.986224i | \(0.447103\pi\) | |||||||
\(752\) | 17.9564 | 0.654802 | ||||||||
\(753\) | −18.8493 | −0.686906 | ||||||||
\(754\) | −2.40938 | −0.0877443 | ||||||||
\(755\) | −91.2415 | −3.32062 | ||||||||
\(756\) | −1.97371 | −0.0717831 | ||||||||
\(757\) | 7.83076 | 0.284614 | 0.142307 | − | 0.989823i | \(-0.454548\pi\) | ||||
0.142307 | + | 0.989823i | \(0.454548\pi\) | |||||||
\(758\) | −1.89279 | −0.0687493 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.82355 | −0.356338 | ||||||||
\(761\) | 26.4983 | 0.960564 | 0.480282 | − | 0.877114i | \(-0.340534\pi\) | ||||
0.480282 | + | 0.877114i | \(0.340534\pi\) | |||||||
\(762\) | 2.60269 | 0.0942854 | ||||||||
\(763\) | −9.74355 | −0.352740 | ||||||||
\(764\) | −29.0450 | −1.05081 | ||||||||
\(765\) | −27.1411 | −0.981288 | ||||||||
\(766\) | −2.49222 | −0.0900476 | ||||||||
\(767\) | −4.77411 | −0.172383 | ||||||||
\(768\) | −13.9379 | −0.502940 | ||||||||
\(769\) | −26.3995 | −0.951989 | −0.475995 | − | 0.879448i | \(-0.657912\pi\) | ||||
−0.475995 | + | 0.879448i | \(0.657912\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3345 | 0.372187 | ||||||||
\(772\) | −16.8019 | −0.604714 | ||||||||
\(773\) | 34.1566 | 1.22853 | 0.614264 | − | 0.789100i | \(-0.289453\pi\) | ||||
0.614264 | + | 0.789100i | \(0.289453\pi\) | |||||||
\(774\) | −0.817850 | −0.0293970 | ||||||||
\(775\) | 61.7499 | 2.21812 | ||||||||
\(776\) | −9.70330 | −0.348328 | ||||||||
\(777\) | 0.969445 | 0.0347787 | ||||||||
\(778\) | −1.56379 | −0.0560645 | ||||||||
\(779\) | −20.0776 | −0.719354 | ||||||||
\(780\) | −14.5095 | −0.519525 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0.570383 | 0.0203969 | ||||||||
\(783\) | 8.86742 | 0.316896 | ||||||||
\(784\) | 3.84294 | 0.137248 | ||||||||
\(785\) | −25.4877 | −0.909695 | ||||||||
\(786\) | −0.121632 | −0.00433849 | ||||||||
\(787\) | 11.7503 | 0.418853 | 0.209426 | − | 0.977824i | \(-0.432840\pi\) | ||||
0.209426 | + | 0.977824i | \(0.432840\pi\) | |||||||
\(788\) | 9.32128 | 0.332057 | ||||||||
\(789\) | 4.14979 | 0.147736 | ||||||||
\(790\) | 0.477043 | 0.0169724 | ||||||||
\(791\) | 2.85725 | 0.101592 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.5821 | 0.553337 | ||||||||
\(794\) | 3.28924 | 0.116731 | ||||||||
\(795\) | −10.4360 | −0.370127 | ||||||||
\(796\) | −33.0832 | −1.17260 | ||||||||
\(797\) | 15.3027 | 0.542050 | 0.271025 | − | 0.962572i | \(-0.412637\pi\) | ||||
0.271025 | + | 0.962572i | \(0.412637\pi\) | |||||||
\(798\) | −0.563507 | −0.0199479 | ||||||||
\(799\) | 28.9074 | 1.02267 | ||||||||
\(800\) | 27.2356 | 0.962924 | ||||||||
\(801\) | −12.2106 | −0.431440 | ||||||||
\(802\) | −1.32256 | −0.0467013 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −14.0977 | −0.497188 | ||||||||
\(805\) | 2.49446 | 0.0879181 | ||||||||
\(806\) | 1.17772 | 0.0414835 | ||||||||
\(807\) | 5.06228 | 0.178201 | ||||||||
\(808\) | −3.71182 | −0.130581 | ||||||||
\(809\) | 18.2311 | 0.640973 | 0.320486 | − | 0.947253i | \(-0.396154\pi\) | ||||
0.320486 | + | 0.947253i | \(0.396154\pi\) | |||||||
\(810\) | −0.711349 | −0.0249942 | ||||||||
\(811\) | 6.23292 | 0.218868 | 0.109434 | − | 0.993994i | \(-0.465096\pi\) | ||||
0.109434 | + | 0.993994i | \(0.465096\pi\) | |||||||
\(812\) | −17.5017 | −0.614189 | ||||||||
\(813\) | 26.3160 | 0.922944 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.0582 | 1.36815 | ||||||||
\(816\) | −23.7749 | −0.832286 | ||||||||
\(817\) | 17.5289 | 0.613258 | ||||||||
\(818\) | −1.56830 | −0.0548344 | ||||||||
\(819\) | −1.67571 | −0.0585539 | ||||||||
\(820\) | 50.0239 | 1.74691 | ||||||||
\(821\) | −29.6399 | −1.03444 | −0.517219 | − | 0.855853i | \(-0.673033\pi\) | ||||
−0.517219 | + | 0.855853i | \(0.673033\pi\) | |||||||
\(822\) | 2.10925 | 0.0735685 | ||||||||
\(823\) | −19.7302 | −0.687753 | −0.343876 | − | 0.939015i | \(-0.611740\pi\) | ||||
−0.343876 | + | 0.939015i | \(0.611740\pi\) | |||||||
\(824\) | −4.97065 | −0.173161 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.461960 | 0.0160736 | ||||||||
\(827\) | 41.1710 | 1.43166 | 0.715828 | − | 0.698276i | \(-0.246049\pi\) | ||||
0.715828 | + | 0.698276i | \(0.246049\pi\) | |||||||
\(828\) | −1.12224 | −0.0390006 | ||||||||
\(829\) | 22.7961 | 0.791742 | 0.395871 | − | 0.918306i | \(-0.370443\pi\) | ||||
0.395871 | + | 0.918306i | \(0.370443\pi\) | |||||||
\(830\) | 6.60489 | 0.229259 | ||||||||
\(831\) | −25.8187 | −0.895642 | ||||||||
\(832\) | −12.3598 | −0.428500 | ||||||||
\(833\) | 6.18663 | 0.214354 | ||||||||
\(834\) | −0.632556 | −0.0219036 | ||||||||
\(835\) | 16.7741 | 0.580492 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.33447 | −0.149821 | ||||||||
\(838\) | −3.07038 | −0.106064 | ||||||||
\(839\) | −47.2725 | −1.63203 | −0.816013 | − | 0.578033i | \(-0.803820\pi\) | ||||
−0.816013 | + | 0.578033i | \(0.803820\pi\) | |||||||
\(840\) | 2.82669 | 0.0975301 | ||||||||
\(841\) | 49.6312 | 1.71142 | ||||||||
\(842\) | −2.12331 | −0.0731742 | ||||||||
\(843\) | 5.43844 | 0.187310 | ||||||||
\(844\) | 20.0241 | 0.689258 | ||||||||
\(845\) | 44.7129 | 1.53817 | ||||||||
\(846\) | 0.757643 | 0.0260483 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.14167 | −0.313926 | ||||||||
\(849\) | −25.3839 | −0.871174 | ||||||||
\(850\) | 14.2910 | 0.490179 | ||||||||
\(851\) | 0.551222 | 0.0188956 | ||||||||
\(852\) | −1.56809 | −0.0537217 | ||||||||
\(853\) | 10.8549 | 0.371664 | 0.185832 | − | 0.982582i | \(-0.440502\pi\) | ||||
0.185832 | + | 0.982582i | \(0.440502\pi\) | |||||||
\(854\) | −1.50778 | −0.0515951 | ||||||||
\(855\) | 15.2462 | 0.521411 | ||||||||
\(856\) | 10.6078 | 0.362567 | ||||||||
\(857\) | 28.5431 | 0.975014 | 0.487507 | − | 0.873119i | \(-0.337906\pi\) | ||||
0.487507 | + | 0.873119i | \(0.337906\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.8034 | −1.25572 | −0.627858 | − | 0.778328i | \(-0.716068\pi\) | ||||
−0.627858 | + | 0.778328i | \(0.716068\pi\) | |||||||
\(860\) | −43.6737 | −1.48926 | ||||||||
\(861\) | 5.77725 | 0.196888 | ||||||||
\(862\) | −2.64356 | −0.0900399 | ||||||||
\(863\) | −45.1551 | −1.53710 | −0.768549 | − | 0.639790i | \(-0.779021\pi\) | ||||
−0.768549 | + | 0.639790i | \(0.779021\pi\) | |||||||
\(864\) | −1.91177 | −0.0650399 | ||||||||
\(865\) | −7.68003 | −0.261129 | ||||||||
\(866\) | 1.89457 | 0.0643800 | ||||||||
\(867\) | −21.2744 | −0.722516 | ||||||||
\(868\) | 8.55498 | 0.290375 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.30783 | −0.213855 | ||||||||
\(871\) | −11.9692 | −0.405559 | ||||||||
\(872\) | −6.27802 | −0.212601 | ||||||||
\(873\) | 15.0596 | 0.509691 | ||||||||
\(874\) | −0.320407 | −0.0108379 | ||||||||
\(875\) | 40.5638 | 1.37131 | ||||||||
\(876\) | 4.71135 | 0.159182 | ||||||||
\(877\) | 34.8517 | 1.17686 | 0.588428 | − | 0.808549i | \(-0.299747\pi\) | ||||
0.588428 | + | 0.808549i | \(0.299747\pi\) | |||||||
\(878\) | 1.89991 | 0.0641187 | ||||||||
\(879\) | −6.75402 | −0.227808 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −35.3563 | −1.19118 | −0.595592 | − | 0.803287i | \(-0.703083\pi\) | ||||
−0.595592 | + | 0.803287i | \(0.703083\pi\) | |||||||
\(882\) | 0.162147 | 0.00545978 | ||||||||
\(883\) | −24.8870 | −0.837516 | −0.418758 | − | 0.908098i | \(-0.637534\pi\) | ||||
−0.418758 | + | 0.908098i | \(0.637534\pi\) | |||||||
\(884\) | −20.4614 | −0.688190 | ||||||||
\(885\) | −12.4988 | −0.420142 | ||||||||
\(886\) | −2.03772 | −0.0684586 | ||||||||
\(887\) | −49.5708 | −1.66442 | −0.832212 | − | 0.554457i | \(-0.812926\pi\) | ||||
−0.832212 | + | 0.554457i | \(0.812926\pi\) | |||||||
\(888\) | 0.624638 | 0.0209615 | ||||||||
\(889\) | 16.0514 | 0.538346 | ||||||||
\(890\) | 8.68599 | 0.291155 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 12.0628 | 0.403891 | ||||||||
\(893\) | −16.2385 | −0.543399 | ||||||||
\(894\) | −3.00676 | −0.100561 | ||||||||
\(895\) | 56.3916 | 1.88496 | ||||||||
\(896\) | 5.01953 | 0.167691 | ||||||||
\(897\) | −0.952798 | −0.0318130 | ||||||||
\(898\) | −2.58398 | −0.0862287 | ||||||||
\(899\) | −38.4356 | −1.28190 | ||||||||
\(900\) | −28.1179 | −0.937264 | ||||||||
\(901\) | −14.7169 | −0.490291 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.04388 | −0.167850 | ||||||||
\(904\) | 1.84100 | 0.0612307 | ||||||||
\(905\) | 96.8798 | 3.22039 | ||||||||
\(906\) | −3.37232 | −0.112038 | ||||||||
\(907\) | −1.42826 | −0.0474246 | −0.0237123 | − | 0.999719i | \(-0.507549\pi\) | ||||
−0.0237123 | + | 0.999719i | \(0.507549\pi\) | |||||||
\(908\) | −28.0443 | −0.930684 | ||||||||
\(909\) | 5.76079 | 0.191073 | ||||||||
\(910\) | 1.19201 | 0.0395148 | ||||||||
\(911\) | 54.1725 | 1.79482 | 0.897408 | − | 0.441202i | \(-0.145448\pi\) | ||||
0.897408 | + | 0.441202i | \(0.145448\pi\) | |||||||
\(912\) | 13.3553 | 0.442238 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −3.85821 | −0.127618 | ||||||||
\(915\) | 40.7945 | 1.34862 | ||||||||
\(916\) | 5.38391 | 0.177889 | ||||||||
\(917\) | −0.750136 | −0.0247717 | ||||||||
\(918\) | −1.00314 | −0.0331087 | ||||||||
\(919\) | −22.9009 | −0.755432 | −0.377716 | − | 0.925921i | \(-0.623290\pi\) | ||||
−0.377716 | + | 0.925921i | \(0.623290\pi\) | |||||||
\(920\) | 1.60724 | 0.0529892 | ||||||||
\(921\) | 17.6396 | 0.581244 | ||||||||
\(922\) | −3.66510 | −0.120704 | ||||||||
\(923\) | −1.33133 | −0.0438211 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 13.8110 | 0.454101 | ||||||||
\(926\) | 0.492536 | 0.0161857 | ||||||||
\(927\) | 7.71449 | 0.253377 | ||||||||
\(928\) | −16.9525 | −0.556493 | ||||||||
\(929\) | −14.5306 | −0.476733 | −0.238366 | − | 0.971175i | \(-0.576612\pi\) | ||||
−0.238366 | + | 0.971175i | \(0.576612\pi\) | |||||||
\(930\) | 3.08332 | 0.101106 | ||||||||
\(931\) | −3.47528 | −0.113898 | ||||||||
\(932\) | 35.1116 | 1.15012 | ||||||||
\(933\) | 12.2414 | 0.400767 | ||||||||
\(934\) | −3.73021 | −0.122056 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.07970 | −0.0352911 | ||||||||
\(937\) | 30.6351 | 1.00080 | 0.500402 | − | 0.865793i | \(-0.333186\pi\) | ||||
0.500402 | + | 0.865793i | \(0.333186\pi\) | |||||||
\(938\) | 1.15818 | 0.0378158 | ||||||||
\(939\) | −3.15951 | −0.103107 | ||||||||
\(940\) | 40.4586 | 1.31961 | ||||||||
\(941\) | 21.0533 | 0.686319 | 0.343159 | − | 0.939277i | \(-0.388503\pi\) | ||||
0.343159 | + | 0.939277i | \(0.388503\pi\) | |||||||
\(942\) | −0.942035 | −0.0306932 | ||||||||
\(943\) | 3.28492 | 0.106972 | ||||||||
\(944\) | −10.9486 | −0.356346 | ||||||||
\(945\) | −4.38705 | −0.142711 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.729464 | 0.0237044 | 0.0118522 | − | 0.999930i | \(-0.496227\pi\) | ||||
0.0118522 | + | 0.999930i | \(0.496227\pi\) | |||||||
\(948\) | −1.32360 | −0.0429886 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | −8.02786 | −0.260458 | ||||||||
\(951\) | −8.43364 | −0.273480 | ||||||||
\(952\) | 3.98620 | 0.129194 | ||||||||
\(953\) | 39.0151 | 1.26382 | 0.631911 | − | 0.775041i | \(-0.282271\pi\) | ||||
0.631911 | + | 0.775041i | \(0.282271\pi\) | |||||||
\(954\) | −0.385719 | −0.0124881 | ||||||||
\(955\) | −64.5597 | −2.08910 | ||||||||
\(956\) | −25.0775 | −0.811065 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.32520 | 0.0428153 | ||||||||
\(959\) | 13.0082 | 0.420058 | ||||||||
\(960\) | −32.3584 | −1.04436 | ||||||||
\(961\) | −12.2124 | −0.393947 | ||||||||
\(962\) | 0.263409 | 0.00849264 | ||||||||
\(963\) | −16.4634 | −0.530527 | ||||||||
\(964\) | 36.8302 | 1.18622 | ||||||||
\(965\) | −37.3464 | −1.20222 | ||||||||
\(966\) | 0.0921961 | 0.00296636 | ||||||||
\(967\) | 2.46386 | 0.0792324 | 0.0396162 | − | 0.999215i | \(-0.487386\pi\) | ||||
0.0396162 | + | 0.999215i | \(0.487386\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.5003 | 0.690688 | ||||||||
\(970\) | −10.7126 | −0.343962 | ||||||||
\(971\) | 34.6794 | 1.11291 | 0.556457 | − | 0.830876i | \(-0.312160\pi\) | ||||
0.556457 | + | 0.830876i | \(0.312160\pi\) | |||||||
\(972\) | 1.97371 | 0.0633067 | ||||||||
\(973\) | −3.90112 | −0.125064 | ||||||||
\(974\) | −0.162023 | −0.00519154 | ||||||||
\(975\) | −23.8725 | −0.764532 | ||||||||
\(976\) | 35.7348 | 1.14384 | ||||||||
\(977\) | −25.1338 | −0.804100 | −0.402050 | − | 0.915618i | \(-0.631702\pi\) | ||||
−0.402050 | + | 0.915618i | \(0.631702\pi\) | |||||||
\(978\) | 1.44361 | 0.0461615 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 8.65877 | 0.276594 | ||||||||
\(981\) | 9.74355 | 0.311088 | ||||||||
\(982\) | 3.93948 | 0.125714 | ||||||||
\(983\) | 30.3900 | 0.969290 | 0.484645 | − | 0.874711i | \(-0.338949\pi\) | ||||
0.484645 | + | 0.874711i | \(0.338949\pi\) | |||||||
\(984\) | 3.72243 | 0.118667 | ||||||||
\(985\) | 20.7189 | 0.660158 | ||||||||
\(986\) | −8.89531 | −0.283284 | ||||||||
\(987\) | 4.67256 | 0.148729 | ||||||||
\(988\) | 11.4940 | 0.365672 | ||||||||
\(989\) | −2.86792 | −0.0911947 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.09793 | −0.257239 | −0.128620 | − | 0.991694i | \(-0.541055\pi\) | ||||
−0.128620 | + | 0.991694i | \(0.541055\pi\) | |||||||
\(992\) | 8.28653 | 0.263097 | ||||||||
\(993\) | −6.13284 | −0.194620 | ||||||||
\(994\) | 0.128824 | 0.00408604 | ||||||||
\(995\) | −73.5356 | −2.33124 | ||||||||
\(996\) | −18.3259 | −0.580680 | ||||||||
\(997\) | −45.8866 | −1.45324 | −0.726621 | − | 0.687038i | \(-0.758910\pi\) | ||||
−0.726621 | + | 0.687038i | \(0.758910\pi\) | |||||||
\(998\) | −6.66112 | −0.210854 | ||||||||
\(999\) | −0.969445 | −0.0306719 |
(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 | 2541.2.a.bn.1.2 | 4 | ||
3.2 | odd | 2 | 7623.2.a.ci.1.3 | 4 | |||
11.3 | even | 5 | 231.2.j.f.64.1 | ✓ | 8 | ||
11.4 | even | 5 | 231.2.j.f.148.1 | yes | 8 | ||
11.10 | odd | 2 | 2541.2.a.bm.1.3 | 4 | |||
33.14 | odd | 10 | 693.2.m.f.64.2 | 8 | |||
33.26 | odd | 10 | 693.2.m.f.379.2 | 8 | |||
33.32 | even | 2 | 7623.2.a.cl.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
231.2.j.f.64.1 | ✓ | 8 | 11.3 | even | 5 | ||
231.2.j.f.148.1 | yes | 8 | 11.4 | even | 5 | ||
693.2.m.f.64.2 | 8 | 33.14 | odd | 10 | |||
693.2.m.f.379.2 | 8 | 33.26 | odd | 10 | |||
2541.2.a.bm.1.3 | 4 | 11.10 | odd | 2 | |||
2541.2.a.bn.1.2 | 4 | 1.1 | even | 1 | trivial | ||
7623.2.a.ci.1.3 | 4 | 3.2 | odd | 2 | |||
7623.2.a.cl.1.2 | 4 | 33.32 | even | 2 |