Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2001,2,Mod(1,2001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2001, 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("2001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2001 = 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2001.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: | \(15.9780654445\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.05971\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.05971 | −0.749325 | −0.374663 | − | 0.927161i | \(-0.622241\pi\) | ||||
−0.374663 | + | 0.927161i | \(0.622241\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.877023 | −0.438512 | ||||||||
\(5\) | −1.30384 | −0.583095 | −0.291548 | − | 0.956556i | \(-0.594170\pi\) | ||||
−0.291548 | + | 0.956556i | \(0.594170\pi\) | |||||||
\(6\) | 1.05971 | 0.432623 | ||||||||
\(7\) | 0.720797 | 0.272436 | 0.136218 | − | 0.990679i | \(-0.456505\pi\) | ||||
0.136218 | + | 0.990679i | \(0.456505\pi\) | |||||||
\(8\) | 3.04880 | 1.07791 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.38169 | 0.436928 | ||||||||
\(11\) | 4.26781 | 1.28679 | 0.643396 | − | 0.765534i | \(-0.277525\pi\) | ||||
0.643396 | + | 0.765534i | \(0.277525\pi\) | |||||||
\(12\) | 0.877023 | 0.253175 | ||||||||
\(13\) | 6.49237 | 1.80066 | 0.900330 | − | 0.435208i | \(-0.143325\pi\) | ||||
0.900330 | + | 0.435208i | \(0.143325\pi\) | |||||||
\(14\) | −0.763833 | −0.204143 | ||||||||
\(15\) | 1.30384 | 0.336650 | ||||||||
\(16\) | −1.47678 | −0.369196 | ||||||||
\(17\) | 1.60761 | 0.389902 | 0.194951 | − | 0.980813i | \(-0.437545\pi\) | ||||
0.194951 | + | 0.980813i | \(0.437545\pi\) | |||||||
\(18\) | −1.05971 | −0.249775 | ||||||||
\(19\) | 0.0676063 | 0.0155100 | 0.00775498 | − | 0.999970i | \(-0.497531\pi\) | ||||
0.00775498 | + | 0.999970i | \(0.497531\pi\) | |||||||
\(20\) | 1.14350 | 0.255694 | ||||||||
\(21\) | −0.720797 | −0.157291 | ||||||||
\(22\) | −4.52262 | −0.964226 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | −3.04880 | −0.622333 | ||||||||
\(25\) | −3.30000 | −0.660000 | ||||||||
\(26\) | −6.88000 | −1.34928 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.632156 | −0.119466 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | −1.38169 | −0.252260 | ||||||||
\(31\) | −3.80124 | −0.682723 | −0.341362 | − | 0.939932i | \(-0.610888\pi\) | ||||
−0.341362 | + | 0.939932i | \(0.610888\pi\) | |||||||
\(32\) | −4.53264 | −0.801265 | ||||||||
\(33\) | −4.26781 | −0.742930 | ||||||||
\(34\) | −1.70359 | −0.292163 | ||||||||
\(35\) | −0.939804 | −0.158856 | ||||||||
\(36\) | −0.877023 | −0.146171 | ||||||||
\(37\) | −3.80081 | −0.624849 | −0.312425 | − | 0.949943i | \(-0.601141\pi\) | ||||
−0.312425 | + | 0.949943i | \(0.601141\pi\) | |||||||
\(38\) | −0.0716428 | −0.0116220 | ||||||||
\(39\) | −6.49237 | −1.03961 | ||||||||
\(40\) | −3.97515 | −0.628526 | ||||||||
\(41\) | −0.467762 | −0.0730521 | −0.0365261 | − | 0.999333i | \(-0.511629\pi\) | ||||
−0.0365261 | + | 0.999333i | \(0.511629\pi\) | |||||||
\(42\) | 0.763833 | 0.117862 | ||||||||
\(43\) | 0.971410 | 0.148139 | 0.0740693 | − | 0.997253i | \(-0.476401\pi\) | ||||
0.0740693 | + | 0.997253i | \(0.476401\pi\) | |||||||
\(44\) | −3.74296 | −0.564273 | ||||||||
\(45\) | −1.30384 | −0.194365 | ||||||||
\(46\) | −1.05971 | −0.156245 | ||||||||
\(47\) | 7.97915 | 1.16388 | 0.581939 | − | 0.813232i | \(-0.302294\pi\) | ||||
0.581939 | + | 0.813232i | \(0.302294\pi\) | |||||||
\(48\) | 1.47678 | 0.213155 | ||||||||
\(49\) | −6.48045 | −0.925779 | ||||||||
\(50\) | 3.49703 | 0.494555 | ||||||||
\(51\) | −1.60761 | −0.225110 | ||||||||
\(52\) | −5.69396 | −0.789610 | ||||||||
\(53\) | 13.3791 | 1.83776 | 0.918881 | − | 0.394535i | \(-0.129094\pi\) | ||||
0.918881 | + | 0.394535i | \(0.129094\pi\) | |||||||
\(54\) | 1.05971 | 0.144208 | ||||||||
\(55\) | −5.56454 | −0.750322 | ||||||||
\(56\) | 2.19756 | 0.293662 | ||||||||
\(57\) | −0.0676063 | −0.00895468 | ||||||||
\(58\) | 1.05971 | 0.139146 | ||||||||
\(59\) | −4.90374 | −0.638413 | −0.319206 | − | 0.947685i | \(-0.603416\pi\) | ||||
−0.319206 | + | 0.947685i | \(0.603416\pi\) | |||||||
\(60\) | −1.14350 | −0.147625 | ||||||||
\(61\) | 7.29114 | 0.933534 | 0.466767 | − | 0.884380i | \(-0.345419\pi\) | ||||
0.466767 | + | 0.884380i | \(0.345419\pi\) | |||||||
\(62\) | 4.02820 | 0.511582 | ||||||||
\(63\) | 0.720797 | 0.0908119 | ||||||||
\(64\) | 7.75683 | 0.969604 | ||||||||
\(65\) | −8.46502 | −1.04996 | ||||||||
\(66\) | 4.52262 | 0.556696 | ||||||||
\(67\) | 13.6988 | 1.67358 | 0.836788 | − | 0.547526i | \(-0.184430\pi\) | ||||
0.836788 | + | 0.547526i | \(0.184430\pi\) | |||||||
\(68\) | −1.40991 | −0.170977 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0.995916 | 0.119035 | ||||||||
\(71\) | −0.843676 | −0.100126 | −0.0500630 | − | 0.998746i | \(-0.515942\pi\) | ||||
−0.0500630 | + | 0.998746i | \(0.515942\pi\) | |||||||
\(72\) | 3.04880 | 0.359304 | ||||||||
\(73\) | −3.56146 | −0.416837 | −0.208419 | − | 0.978040i | \(-0.566832\pi\) | ||||
−0.208419 | + | 0.978040i | \(0.566832\pi\) | |||||||
\(74\) | 4.02774 | 0.468215 | ||||||||
\(75\) | 3.30000 | 0.381051 | ||||||||
\(76\) | −0.0592923 | −0.00680130 | ||||||||
\(77\) | 3.07622 | 0.350568 | ||||||||
\(78\) | 6.88000 | 0.779007 | ||||||||
\(79\) | 3.50616 | 0.394474 | 0.197237 | − | 0.980356i | \(-0.436803\pi\) | ||||
0.197237 | + | 0.980356i | \(0.436803\pi\) | |||||||
\(80\) | 1.92549 | 0.215276 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.495690 | 0.0547398 | ||||||||
\(83\) | −8.90808 | −0.977789 | −0.488894 | − | 0.872343i | \(-0.662600\pi\) | ||||
−0.488894 | + | 0.872343i | \(0.662600\pi\) | |||||||
\(84\) | 0.632156 | 0.0689738 | ||||||||
\(85\) | −2.09606 | −0.227350 | ||||||||
\(86\) | −1.02941 | −0.111004 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 13.0117 | 1.38705 | ||||||||
\(89\) | 15.1294 | 1.60371 | 0.801856 | − | 0.597517i | \(-0.203846\pi\) | ||||
0.801856 | + | 0.597517i | \(0.203846\pi\) | |||||||
\(90\) | 1.38169 | 0.145643 | ||||||||
\(91\) | 4.67968 | 0.490564 | ||||||||
\(92\) | −0.877023 | −0.0914360 | ||||||||
\(93\) | 3.80124 | 0.394170 | ||||||||
\(94\) | −8.45555 | −0.872124 | ||||||||
\(95\) | −0.0881479 | −0.00904378 | ||||||||
\(96\) | 4.53264 | 0.462611 | ||||||||
\(97\) | 0.847630 | 0.0860637 | 0.0430319 | − | 0.999074i | \(-0.486298\pi\) | ||||
0.0430319 | + | 0.999074i | \(0.486298\pi\) | |||||||
\(98\) | 6.86737 | 0.693709 | ||||||||
\(99\) | 4.26781 | 0.428931 | ||||||||
\(100\) | 2.89418 | 0.289418 | ||||||||
\(101\) | −4.21499 | −0.419407 | −0.209704 | − | 0.977765i | \(-0.567250\pi\) | ||||
−0.209704 | + | 0.977765i | \(0.567250\pi\) | |||||||
\(102\) | 1.70359 | 0.168681 | ||||||||
\(103\) | −3.25548 | −0.320772 | −0.160386 | − | 0.987054i | \(-0.551274\pi\) | ||||
−0.160386 | + | 0.987054i | \(0.551274\pi\) | |||||||
\(104\) | 19.7939 | 1.94095 | ||||||||
\(105\) | 0.939804 | 0.0917155 | ||||||||
\(106\) | −14.1779 | −1.37708 | ||||||||
\(107\) | 9.91828 | 0.958836 | 0.479418 | − | 0.877587i | \(-0.340848\pi\) | ||||
0.479418 | + | 0.877587i | \(0.340848\pi\) | |||||||
\(108\) | 0.877023 | 0.0843916 | ||||||||
\(109\) | −14.9445 | −1.43142 | −0.715711 | − | 0.698396i | \(-0.753897\pi\) | ||||
−0.715711 | + | 0.698396i | \(0.753897\pi\) | |||||||
\(110\) | 5.89677 | 0.562235 | ||||||||
\(111\) | 3.80081 | 0.360757 | ||||||||
\(112\) | −1.06446 | −0.100582 | ||||||||
\(113\) | 9.05430 | 0.851757 | 0.425879 | − | 0.904780i | \(-0.359965\pi\) | ||||
0.425879 | + | 0.904780i | \(0.359965\pi\) | |||||||
\(114\) | 0.0716428 | 0.00670997 | ||||||||
\(115\) | −1.30384 | −0.121584 | ||||||||
\(116\) | 0.877023 | 0.0814296 | ||||||||
\(117\) | 6.49237 | 0.600220 | ||||||||
\(118\) | 5.19653 | 0.478379 | ||||||||
\(119\) | 1.15876 | 0.106223 | ||||||||
\(120\) | 3.97515 | 0.362880 | ||||||||
\(121\) | 7.21416 | 0.655833 | ||||||||
\(122\) | −7.72646 | −0.699521 | ||||||||
\(123\) | 0.467762 | 0.0421767 | ||||||||
\(124\) | 3.33378 | 0.299382 | ||||||||
\(125\) | 10.8219 | 0.967938 | ||||||||
\(126\) | −0.763833 | −0.0680476 | ||||||||
\(127\) | −16.8234 | −1.49284 | −0.746420 | − | 0.665476i | \(-0.768229\pi\) | ||||
−0.746420 | + | 0.665476i | \(0.768229\pi\) | |||||||
\(128\) | 0.845320 | 0.0747164 | ||||||||
\(129\) | −0.971410 | −0.0855279 | ||||||||
\(130\) | 8.97043 | 0.786759 | ||||||||
\(131\) | 20.0112 | 1.74838 | 0.874192 | − | 0.485581i | \(-0.161392\pi\) | ||||
0.874192 | + | 0.485581i | \(0.161392\pi\) | |||||||
\(132\) | 3.74296 | 0.325783 | ||||||||
\(133\) | 0.0487304 | 0.00422547 | ||||||||
\(134\) | −14.5167 | −1.25405 | ||||||||
\(135\) | 1.30384 | 0.112217 | ||||||||
\(136\) | 4.90127 | 0.420280 | ||||||||
\(137\) | −17.5827 | −1.50219 | −0.751097 | − | 0.660192i | \(-0.770475\pi\) | ||||
−0.751097 | + | 0.660192i | \(0.770475\pi\) | |||||||
\(138\) | 1.05971 | 0.0902082 | ||||||||
\(139\) | −11.2785 | −0.956634 | −0.478317 | − | 0.878187i | \(-0.658753\pi\) | ||||
−0.478317 | + | 0.878187i | \(0.658753\pi\) | |||||||
\(140\) | 0.824230 | 0.0696602 | ||||||||
\(141\) | −7.97915 | −0.671966 | ||||||||
\(142\) | 0.894049 | 0.0750269 | ||||||||
\(143\) | 27.7082 | 2.31707 | ||||||||
\(144\) | −1.47678 | −0.123065 | ||||||||
\(145\) | 1.30384 | 0.108278 | ||||||||
\(146\) | 3.77410 | 0.312347 | ||||||||
\(147\) | 6.48045 | 0.534499 | ||||||||
\(148\) | 3.33340 | 0.274004 | ||||||||
\(149\) | 8.68520 | 0.711519 | 0.355760 | − | 0.934578i | \(-0.384222\pi\) | ||||
0.355760 | + | 0.934578i | \(0.384222\pi\) | |||||||
\(150\) | −3.49703 | −0.285531 | ||||||||
\(151\) | −3.77830 | −0.307474 | −0.153737 | − | 0.988112i | \(-0.549131\pi\) | ||||
−0.153737 | + | 0.988112i | \(0.549131\pi\) | |||||||
\(152\) | 0.206118 | 0.0167184 | ||||||||
\(153\) | 1.60761 | 0.129967 | ||||||||
\(154\) | −3.25989 | −0.262689 | ||||||||
\(155\) | 4.95621 | 0.398093 | ||||||||
\(156\) | 5.69396 | 0.455882 | ||||||||
\(157\) | −22.4357 | −1.79056 | −0.895280 | − | 0.445503i | \(-0.853025\pi\) | ||||
−0.895280 | + | 0.445503i | \(0.853025\pi\) | |||||||
\(158\) | −3.71550 | −0.295589 | ||||||||
\(159\) | −13.3791 | −1.06103 | ||||||||
\(160\) | 5.90984 | 0.467214 | ||||||||
\(161\) | 0.720797 | 0.0568068 | ||||||||
\(162\) | −1.05971 | −0.0832584 | ||||||||
\(163\) | 9.58430 | 0.750701 | 0.375350 | − | 0.926883i | \(-0.377522\pi\) | ||||
0.375350 | + | 0.926883i | \(0.377522\pi\) | |||||||
\(164\) | 0.410238 | 0.0320342 | ||||||||
\(165\) | 5.56454 | 0.433199 | ||||||||
\(166\) | 9.43994 | 0.732682 | ||||||||
\(167\) | −22.7911 | −1.76363 | −0.881816 | − | 0.471594i | \(-0.843679\pi\) | ||||
−0.881816 | + | 0.471594i | \(0.843679\pi\) | |||||||
\(168\) | −2.19756 | −0.169546 | ||||||||
\(169\) | 29.1509 | 2.24238 | ||||||||
\(170\) | 2.22121 | 0.170359 | ||||||||
\(171\) | 0.0676063 | 0.00516999 | ||||||||
\(172\) | −0.851949 | −0.0649605 | ||||||||
\(173\) | 3.11958 | 0.237177 | 0.118589 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118589 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(174\) | −1.05971 | −0.0803361 | ||||||||
\(175\) | −2.37863 | −0.179808 | ||||||||
\(176\) | −6.30262 | −0.475078 | ||||||||
\(177\) | 4.90374 | 0.368588 | ||||||||
\(178\) | −16.0327 | −1.20170 | ||||||||
\(179\) | −4.43515 | −0.331499 | −0.165749 | − | 0.986168i | \(-0.553004\pi\) | ||||
−0.165749 | + | 0.986168i | \(0.553004\pi\) | |||||||
\(180\) | 1.14350 | 0.0852313 | ||||||||
\(181\) | 7.57878 | 0.563326 | 0.281663 | − | 0.959513i | \(-0.409114\pi\) | ||||
0.281663 | + | 0.959513i | \(0.409114\pi\) | |||||||
\(182\) | −4.95909 | −0.367592 | ||||||||
\(183\) | −7.29114 | −0.538976 | ||||||||
\(184\) | 3.04880 | 0.224760 | ||||||||
\(185\) | 4.95565 | 0.364347 | ||||||||
\(186\) | −4.02820 | −0.295362 | ||||||||
\(187\) | 6.86095 | 0.501722 | ||||||||
\(188\) | −6.99790 | −0.510374 | ||||||||
\(189\) | −0.720797 | −0.0524303 | ||||||||
\(190\) | 0.0934108 | 0.00677673 | ||||||||
\(191\) | 23.8728 | 1.72738 | 0.863688 | − | 0.504026i | \(-0.168149\pi\) | ||||
0.863688 | + | 0.504026i | \(0.168149\pi\) | |||||||
\(192\) | −7.75683 | −0.559801 | ||||||||
\(193\) | −23.7901 | −1.71245 | −0.856224 | − | 0.516605i | \(-0.827196\pi\) | ||||
−0.856224 | + | 0.516605i | \(0.827196\pi\) | |||||||
\(194\) | −0.898238 | −0.0644897 | ||||||||
\(195\) | 8.46502 | 0.606192 | ||||||||
\(196\) | 5.68351 | 0.405965 | ||||||||
\(197\) | 10.2899 | 0.733125 | 0.366562 | − | 0.930393i | \(-0.380535\pi\) | ||||
0.366562 | + | 0.930393i | \(0.380535\pi\) | |||||||
\(198\) | −4.52262 | −0.321409 | ||||||||
\(199\) | 6.69895 | 0.474876 | 0.237438 | − | 0.971403i | \(-0.423692\pi\) | ||||
0.237438 | + | 0.971403i | \(0.423692\pi\) | |||||||
\(200\) | −10.0610 | −0.711423 | ||||||||
\(201\) | −13.6988 | −0.966240 | ||||||||
\(202\) | 4.46665 | 0.314273 | ||||||||
\(203\) | −0.720797 | −0.0505900 | ||||||||
\(204\) | 1.40991 | 0.0987133 | ||||||||
\(205\) | 0.609887 | 0.0425964 | ||||||||
\(206\) | 3.44986 | 0.240363 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −9.58783 | −0.664796 | ||||||||
\(209\) | 0.288531 | 0.0199581 | ||||||||
\(210\) | −0.995916 | −0.0687247 | ||||||||
\(211\) | 19.4730 | 1.34058 | 0.670288 | − | 0.742101i | \(-0.266170\pi\) | ||||
0.670288 | + | 0.742101i | \(0.266170\pi\) | |||||||
\(212\) | −11.7338 | −0.805880 | ||||||||
\(213\) | 0.843676 | 0.0578077 | ||||||||
\(214\) | −10.5105 | −0.718480 | ||||||||
\(215\) | −1.26656 | −0.0863789 | ||||||||
\(216\) | −3.04880 | −0.207444 | ||||||||
\(217\) | −2.73992 | −0.185998 | ||||||||
\(218\) | 15.8368 | 1.07260 | ||||||||
\(219\) | 3.56146 | 0.240661 | ||||||||
\(220\) | 4.88023 | 0.329025 | ||||||||
\(221\) | 10.4372 | 0.702081 | ||||||||
\(222\) | −4.02774 | −0.270324 | ||||||||
\(223\) | 5.45268 | 0.365138 | 0.182569 | − | 0.983193i | \(-0.441559\pi\) | ||||
0.182569 | + | 0.983193i | \(0.441559\pi\) | |||||||
\(224\) | −3.26711 | −0.218293 | ||||||||
\(225\) | −3.30000 | −0.220000 | ||||||||
\(226\) | −9.59490 | −0.638243 | ||||||||
\(227\) | 12.7976 | 0.849407 | 0.424704 | − | 0.905332i | \(-0.360378\pi\) | ||||
0.424704 | + | 0.905332i | \(0.360378\pi\) | |||||||
\(228\) | 0.0592923 | 0.00392673 | ||||||||
\(229\) | −17.9481 | −1.18604 | −0.593021 | − | 0.805187i | \(-0.702065\pi\) | ||||
−0.593021 | + | 0.805187i | \(0.702065\pi\) | |||||||
\(230\) | 1.38169 | 0.0911058 | ||||||||
\(231\) | −3.07622 | −0.202400 | ||||||||
\(232\) | −3.04880 | −0.200163 | ||||||||
\(233\) | 24.8070 | 1.62516 | 0.812579 | − | 0.582851i | \(-0.198063\pi\) | ||||
0.812579 | + | 0.582851i | \(0.198063\pi\) | |||||||
\(234\) | −6.88000 | −0.449760 | ||||||||
\(235\) | −10.4035 | −0.678652 | ||||||||
\(236\) | 4.30070 | 0.279952 | ||||||||
\(237\) | −3.50616 | −0.227750 | ||||||||
\(238\) | −1.22794 | −0.0795957 | ||||||||
\(239\) | 6.47432 | 0.418789 | 0.209394 | − | 0.977831i | \(-0.432851\pi\) | ||||
0.209394 | + | 0.977831i | \(0.432851\pi\) | |||||||
\(240\) | −1.92549 | −0.124290 | ||||||||
\(241\) | −1.06870 | −0.0688413 | −0.0344207 | − | 0.999407i | \(-0.510959\pi\) | ||||
−0.0344207 | + | 0.999407i | \(0.510959\pi\) | |||||||
\(242\) | −7.64489 | −0.491432 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −6.39450 | −0.409366 | ||||||||
\(245\) | 8.44948 | 0.539817 | ||||||||
\(246\) | −0.495690 | −0.0316040 | ||||||||
\(247\) | 0.438925 | 0.0279282 | ||||||||
\(248\) | −11.5892 | −0.735916 | ||||||||
\(249\) | 8.90808 | 0.564526 | ||||||||
\(250\) | −11.4680 | −0.725300 | ||||||||
\(251\) | −10.6611 | −0.672920 | −0.336460 | − | 0.941698i | \(-0.609230\pi\) | ||||
−0.336460 | + | 0.941698i | \(0.609230\pi\) | |||||||
\(252\) | −0.632156 | −0.0398221 | ||||||||
\(253\) | 4.26781 | 0.268315 | ||||||||
\(254\) | 17.8279 | 1.11862 | ||||||||
\(255\) | 2.09606 | 0.131261 | ||||||||
\(256\) | −16.4095 | −1.02559 | ||||||||
\(257\) | 26.4765 | 1.65156 | 0.825781 | − | 0.563991i | \(-0.190735\pi\) | ||||
0.825781 | + | 0.563991i | \(0.190735\pi\) | |||||||
\(258\) | 1.02941 | 0.0640882 | ||||||||
\(259\) | −2.73961 | −0.170231 | ||||||||
\(260\) | 7.42402 | 0.460418 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −21.2059 | −1.31011 | ||||||||
\(263\) | 3.04107 | 0.187520 | 0.0937602 | − | 0.995595i | \(-0.470111\pi\) | ||||
0.0937602 | + | 0.995595i | \(0.470111\pi\) | |||||||
\(264\) | −13.0117 | −0.800814 | ||||||||
\(265\) | −17.4442 | −1.07159 | ||||||||
\(266\) | −0.0516399 | −0.00316625 | ||||||||
\(267\) | −15.1294 | −0.925904 | ||||||||
\(268\) | −12.0142 | −0.733883 | ||||||||
\(269\) | −30.1319 | −1.83718 | −0.918589 | − | 0.395215i | \(-0.870670\pi\) | ||||
−0.918589 | + | 0.395215i | \(0.870670\pi\) | |||||||
\(270\) | −1.38169 | −0.0840868 | ||||||||
\(271\) | 18.0654 | 1.09740 | 0.548699 | − | 0.836020i | \(-0.315123\pi\) | ||||
0.548699 | + | 0.836020i | \(0.315123\pi\) | |||||||
\(272\) | −2.37409 | −0.143950 | ||||||||
\(273\) | −4.67968 | −0.283227 | ||||||||
\(274\) | 18.6325 | 1.12563 | ||||||||
\(275\) | −14.0838 | −0.849283 | ||||||||
\(276\) | 0.877023 | 0.0527906 | ||||||||
\(277\) | 15.0741 | 0.905712 | 0.452856 | − | 0.891584i | \(-0.350405\pi\) | ||||
0.452856 | + | 0.891584i | \(0.350405\pi\) | |||||||
\(278\) | 11.9519 | 0.716830 | ||||||||
\(279\) | −3.80124 | −0.227574 | ||||||||
\(280\) | −2.86527 | −0.171233 | ||||||||
\(281\) | 17.4085 | 1.03850 | 0.519252 | − | 0.854621i | \(-0.326211\pi\) | ||||
0.519252 | + | 0.854621i | \(0.326211\pi\) | |||||||
\(282\) | 8.45555 | 0.503521 | ||||||||
\(283\) | 27.6295 | 1.64240 | 0.821202 | − | 0.570638i | \(-0.193304\pi\) | ||||
0.821202 | + | 0.570638i | \(0.193304\pi\) | |||||||
\(284\) | 0.739924 | 0.0439064 | ||||||||
\(285\) | 0.0881479 | 0.00522143 | ||||||||
\(286\) | −29.3625 | −1.73624 | ||||||||
\(287\) | −0.337161 | −0.0199020 | ||||||||
\(288\) | −4.53264 | −0.267088 | ||||||||
\(289\) | −14.4156 | −0.847977 | ||||||||
\(290\) | −1.38169 | −0.0811355 | ||||||||
\(291\) | −0.847630 | −0.0496889 | ||||||||
\(292\) | 3.12348 | 0.182788 | ||||||||
\(293\) | 9.65321 | 0.563946 | 0.281973 | − | 0.959422i | \(-0.409011\pi\) | ||||
0.281973 | + | 0.959422i | \(0.409011\pi\) | |||||||
\(294\) | −6.86737 | −0.400513 | ||||||||
\(295\) | 6.39370 | 0.372256 | ||||||||
\(296\) | −11.5879 | −0.673533 | ||||||||
\(297\) | −4.26781 | −0.247643 | ||||||||
\(298\) | −9.20376 | −0.533159 | ||||||||
\(299\) | 6.49237 | 0.375464 | ||||||||
\(300\) | −2.89418 | −0.167095 | ||||||||
\(301\) | 0.700189 | 0.0403582 | ||||||||
\(302\) | 4.00389 | 0.230398 | ||||||||
\(303\) | 4.21499 | 0.242145 | ||||||||
\(304\) | −0.0998399 | −0.00572621 | ||||||||
\(305\) | −9.50648 | −0.544339 | ||||||||
\(306\) | −1.70359 | −0.0973878 | ||||||||
\(307\) | 23.4872 | 1.34048 | 0.670242 | − | 0.742143i | \(-0.266190\pi\) | ||||
0.670242 | + | 0.742143i | \(0.266190\pi\) | |||||||
\(308\) | −2.69792 | −0.153728 | ||||||||
\(309\) | 3.25548 | 0.185198 | ||||||||
\(310\) | −5.25213 | −0.298301 | ||||||||
\(311\) | 10.2227 | 0.579679 | 0.289839 | − | 0.957075i | \(-0.406398\pi\) | ||||
0.289839 | + | 0.957075i | \(0.406398\pi\) | |||||||
\(312\) | −19.7939 | −1.12061 | ||||||||
\(313\) | 4.95500 | 0.280073 | 0.140036 | − | 0.990146i | \(-0.455278\pi\) | ||||
0.140036 | + | 0.990146i | \(0.455278\pi\) | |||||||
\(314\) | 23.7752 | 1.34171 | ||||||||
\(315\) | −0.939804 | −0.0529520 | ||||||||
\(316\) | −3.07498 | −0.172981 | ||||||||
\(317\) | 6.20695 | 0.348617 | 0.174309 | − | 0.984691i | \(-0.444231\pi\) | ||||
0.174309 | + | 0.984691i | \(0.444231\pi\) | |||||||
\(318\) | 14.1779 | 0.795058 | ||||||||
\(319\) | −4.26781 | −0.238951 | ||||||||
\(320\) | −10.1137 | −0.565372 | ||||||||
\(321\) | −9.91828 | −0.553584 | ||||||||
\(322\) | −0.763833 | −0.0425667 | ||||||||
\(323\) | 0.108684 | 0.00604736 | ||||||||
\(324\) | −0.877023 | −0.0487235 | ||||||||
\(325\) | −21.4248 | −1.18844 | ||||||||
\(326\) | −10.1565 | −0.562519 | ||||||||
\(327\) | 14.9445 | 0.826432 | ||||||||
\(328\) | −1.42611 | −0.0787439 | ||||||||
\(329\) | 5.75135 | 0.317082 | ||||||||
\(330\) | −5.89677 | −0.324607 | ||||||||
\(331\) | 4.70041 | 0.258358 | 0.129179 | − | 0.991621i | \(-0.458766\pi\) | ||||
0.129179 | + | 0.991621i | \(0.458766\pi\) | |||||||
\(332\) | 7.81259 | 0.428772 | ||||||||
\(333\) | −3.80081 | −0.208283 | ||||||||
\(334\) | 24.1519 | 1.32153 | ||||||||
\(335\) | −17.8611 | −0.975855 | ||||||||
\(336\) | 1.06446 | 0.0580711 | ||||||||
\(337\) | −9.18682 | −0.500438 | −0.250219 | − | 0.968189i | \(-0.580503\pi\) | ||||
−0.250219 | + | 0.968189i | \(0.580503\pi\) | |||||||
\(338\) | −30.8914 | −1.68027 | ||||||||
\(339\) | −9.05430 | −0.491762 | ||||||||
\(340\) | 1.83830 | 0.0996956 | ||||||||
\(341\) | −16.2230 | −0.878523 | ||||||||
\(342\) | −0.0716428 | −0.00387400 | ||||||||
\(343\) | −9.71667 | −0.524651 | ||||||||
\(344\) | 2.96163 | 0.159681 | ||||||||
\(345\) | 1.30384 | 0.0701964 | ||||||||
\(346\) | −3.30584 | −0.177723 | ||||||||
\(347\) | −19.5451 | −1.04923 | −0.524617 | − | 0.851339i | \(-0.675791\pi\) | ||||
−0.524617 | + | 0.851339i | \(0.675791\pi\) | |||||||
\(348\) | −0.877023 | −0.0470134 | ||||||||
\(349\) | 35.7643 | 1.91442 | 0.957209 | − | 0.289398i | \(-0.0934551\pi\) | ||||
0.957209 | + | 0.289398i | \(0.0934551\pi\) | |||||||
\(350\) | 2.52065 | 0.134734 | ||||||||
\(351\) | −6.49237 | −0.346537 | ||||||||
\(352\) | −19.3444 | −1.03106 | ||||||||
\(353\) | 17.5958 | 0.936532 | 0.468266 | − | 0.883588i | \(-0.344879\pi\) | ||||
0.468266 | + | 0.883588i | \(0.344879\pi\) | |||||||
\(354\) | −5.19653 | −0.276192 | ||||||||
\(355\) | 1.10002 | 0.0583830 | ||||||||
\(356\) | −13.2688 | −0.703246 | ||||||||
\(357\) | −1.15876 | −0.0613280 | ||||||||
\(358\) | 4.69995 | 0.248400 | ||||||||
\(359\) | 5.45515 | 0.287912 | 0.143956 | − | 0.989584i | \(-0.454018\pi\) | ||||
0.143956 | + | 0.989584i | \(0.454018\pi\) | |||||||
\(360\) | −3.97515 | −0.209509 | ||||||||
\(361\) | −18.9954 | −0.999759 | ||||||||
\(362\) | −8.03128 | −0.422115 | ||||||||
\(363\) | −7.21416 | −0.378645 | ||||||||
\(364\) | −4.10419 | −0.215118 | ||||||||
\(365\) | 4.64358 | 0.243056 | ||||||||
\(366\) | 7.72646 | 0.403869 | ||||||||
\(367\) | 7.87986 | 0.411326 | 0.205663 | − | 0.978623i | \(-0.434065\pi\) | ||||
0.205663 | + | 0.978623i | \(0.434065\pi\) | |||||||
\(368\) | −1.47678 | −0.0769827 | ||||||||
\(369\) | −0.467762 | −0.0243507 | ||||||||
\(370\) | −5.25153 | −0.273014 | ||||||||
\(371\) | 9.64362 | 0.500672 | ||||||||
\(372\) | −3.33378 | −0.172848 | ||||||||
\(373\) | −12.3211 | −0.637961 | −0.318980 | − | 0.947761i | \(-0.603340\pi\) | ||||
−0.318980 | + | 0.947761i | \(0.603340\pi\) | |||||||
\(374\) | −7.27059 | −0.375953 | ||||||||
\(375\) | −10.8219 | −0.558839 | ||||||||
\(376\) | 24.3268 | 1.25456 | ||||||||
\(377\) | −6.49237 | −0.334374 | ||||||||
\(378\) | 0.763833 | 0.0392873 | ||||||||
\(379\) | 21.0221 | 1.07983 | 0.539916 | − | 0.841719i | \(-0.318456\pi\) | ||||
0.539916 | + | 0.841719i | \(0.318456\pi\) | |||||||
\(380\) | 0.0773078 | 0.00396580 | ||||||||
\(381\) | 16.8234 | 0.861891 | ||||||||
\(382\) | −25.2982 | −1.29437 | ||||||||
\(383\) | −26.7325 | −1.36597 | −0.682983 | − | 0.730434i | \(-0.739318\pi\) | ||||
−0.682983 | + | 0.730434i | \(0.739318\pi\) | |||||||
\(384\) | −0.845320 | −0.0431375 | ||||||||
\(385\) | −4.01090 | −0.204414 | ||||||||
\(386\) | 25.2105 | 1.28318 | ||||||||
\(387\) | 0.971410 | 0.0493795 | ||||||||
\(388\) | −0.743391 | −0.0377400 | ||||||||
\(389\) | 18.2034 | 0.922949 | 0.461474 | − | 0.887154i | \(-0.347321\pi\) | ||||
0.461474 | + | 0.887154i | \(0.347321\pi\) | |||||||
\(390\) | −8.97043 | −0.454235 | ||||||||
\(391\) | 1.60761 | 0.0813002 | ||||||||
\(392\) | −19.7576 | −0.997909 | ||||||||
\(393\) | −20.0112 | −1.00943 | ||||||||
\(394\) | −10.9043 | −0.549349 | ||||||||
\(395\) | −4.57147 | −0.230016 | ||||||||
\(396\) | −3.74296 | −0.188091 | ||||||||
\(397\) | −14.9475 | −0.750193 | −0.375096 | − | 0.926986i | \(-0.622390\pi\) | ||||
−0.375096 | + | 0.926986i | \(0.622390\pi\) | |||||||
\(398\) | −7.09892 | −0.355837 | ||||||||
\(399\) | −0.0487304 | −0.00243957 | ||||||||
\(400\) | 4.87339 | 0.243669 | ||||||||
\(401\) | 5.93728 | 0.296494 | 0.148247 | − | 0.988950i | \(-0.452637\pi\) | ||||
0.148247 | + | 0.988950i | \(0.452637\pi\) | |||||||
\(402\) | 14.5167 | 0.724028 | ||||||||
\(403\) | −24.6791 | −1.22935 | ||||||||
\(404\) | 3.69665 | 0.183915 | ||||||||
\(405\) | −1.30384 | −0.0647884 | ||||||||
\(406\) | 0.763833 | 0.0379084 | ||||||||
\(407\) | −16.2211 | −0.804051 | ||||||||
\(408\) | −4.90127 | −0.242649 | ||||||||
\(409\) | 28.1625 | 1.39255 | 0.696274 | − | 0.717776i | \(-0.254840\pi\) | ||||
0.696274 | + | 0.717776i | \(0.254840\pi\) | |||||||
\(410\) | −0.646301 | −0.0319185 | ||||||||
\(411\) | 17.5827 | 0.867292 | ||||||||
\(412\) | 2.85514 | 0.140662 | ||||||||
\(413\) | −3.53460 | −0.173926 | ||||||||
\(414\) | −1.05971 | −0.0520817 | ||||||||
\(415\) | 11.6147 | 0.570144 | ||||||||
\(416\) | −29.4276 | −1.44281 | ||||||||
\(417\) | 11.2785 | 0.552313 | ||||||||
\(418\) | −0.305758 | −0.0149551 | ||||||||
\(419\) | −15.7587 | −0.769862 | −0.384931 | − | 0.922945i | \(-0.625775\pi\) | ||||
−0.384931 | + | 0.922945i | \(0.625775\pi\) | |||||||
\(420\) | −0.824230 | −0.0402183 | ||||||||
\(421\) | −37.5081 | −1.82803 | −0.914017 | − | 0.405676i | \(-0.867036\pi\) | ||||
−0.914017 | + | 0.405676i | \(0.867036\pi\) | |||||||
\(422\) | −20.6357 | −1.00453 | ||||||||
\(423\) | 7.97915 | 0.387959 | ||||||||
\(424\) | 40.7902 | 1.98095 | ||||||||
\(425\) | −5.30510 | −0.257335 | ||||||||
\(426\) | −0.894049 | −0.0433168 | ||||||||
\(427\) | 5.25543 | 0.254328 | ||||||||
\(428\) | −8.69856 | −0.420461 | ||||||||
\(429\) | −27.7082 | −1.33776 | ||||||||
\(430\) | 1.34218 | 0.0647259 | ||||||||
\(431\) | 10.7335 | 0.517013 | 0.258507 | − | 0.966009i | \(-0.416770\pi\) | ||||
0.258507 | + | 0.966009i | \(0.416770\pi\) | |||||||
\(432\) | 1.47678 | 0.0710518 | ||||||||
\(433\) | 29.9000 | 1.43690 | 0.718452 | − | 0.695576i | \(-0.244851\pi\) | ||||
0.718452 | + | 0.695576i | \(0.244851\pi\) | |||||||
\(434\) | 2.90351 | 0.139373 | ||||||||
\(435\) | −1.30384 | −0.0625144 | ||||||||
\(436\) | 13.1067 | 0.627696 | ||||||||
\(437\) | 0.0676063 | 0.00323405 | ||||||||
\(438\) | −3.77410 | −0.180333 | ||||||||
\(439\) | 27.6423 | 1.31930 | 0.659648 | − | 0.751575i | \(-0.270705\pi\) | ||||
0.659648 | + | 0.751575i | \(0.270705\pi\) | |||||||
\(440\) | −16.9652 | −0.808782 | ||||||||
\(441\) | −6.48045 | −0.308593 | ||||||||
\(442\) | −11.0603 | −0.526087 | ||||||||
\(443\) | 16.5336 | 0.785534 | 0.392767 | − | 0.919638i | \(-0.371518\pi\) | ||||
0.392767 | + | 0.919638i | \(0.371518\pi\) | |||||||
\(444\) | −3.33340 | −0.158196 | ||||||||
\(445\) | −19.7263 | −0.935117 | ||||||||
\(446\) | −5.77823 | −0.273607 | ||||||||
\(447\) | −8.68520 | −0.410796 | ||||||||
\(448\) | 5.59110 | 0.264155 | ||||||||
\(449\) | 15.6126 | 0.736805 | 0.368403 | − | 0.929666i | \(-0.379905\pi\) | ||||
0.368403 | + | 0.929666i | \(0.379905\pi\) | |||||||
\(450\) | 3.49703 | 0.164852 | ||||||||
\(451\) | −1.99632 | −0.0940029 | ||||||||
\(452\) | −7.94084 | −0.373506 | ||||||||
\(453\) | 3.77830 | 0.177520 | ||||||||
\(454\) | −13.5617 | −0.636482 | ||||||||
\(455\) | −6.10156 | −0.286045 | ||||||||
\(456\) | −0.206118 | −0.00965237 | ||||||||
\(457\) | −39.1168 | −1.82981 | −0.914903 | − | 0.403674i | \(-0.867733\pi\) | ||||
−0.914903 | + | 0.403674i | \(0.867733\pi\) | |||||||
\(458\) | 19.0197 | 0.888731 | ||||||||
\(459\) | −1.60761 | −0.0750366 | ||||||||
\(460\) | 1.14350 | 0.0533159 | ||||||||
\(461\) | 27.3047 | 1.27171 | 0.635854 | − | 0.771810i | \(-0.280648\pi\) | ||||
0.635854 | + | 0.771810i | \(0.280648\pi\) | |||||||
\(462\) | 3.25989 | 0.151664 | ||||||||
\(463\) | 25.1953 | 1.17093 | 0.585463 | − | 0.810699i | \(-0.300913\pi\) | ||||
0.585463 | + | 0.810699i | \(0.300913\pi\) | |||||||
\(464\) | 1.47678 | 0.0685580 | ||||||||
\(465\) | −4.95621 | −0.229839 | ||||||||
\(466\) | −26.2881 | −1.21777 | ||||||||
\(467\) | 10.5362 | 0.487556 | 0.243778 | − | 0.969831i | \(-0.421613\pi\) | ||||
0.243778 | + | 0.969831i | \(0.421613\pi\) | |||||||
\(468\) | −5.69396 | −0.263203 | ||||||||
\(469\) | 9.87407 | 0.455942 | ||||||||
\(470\) | 11.0247 | 0.508531 | ||||||||
\(471\) | 22.4357 | 1.03378 | ||||||||
\(472\) | −14.9505 | −0.688154 | ||||||||
\(473\) | 4.14579 | 0.190624 | ||||||||
\(474\) | 3.71550 | 0.170658 | ||||||||
\(475\) | −0.223101 | −0.0102366 | ||||||||
\(476\) | −1.01626 | −0.0465801 | ||||||||
\(477\) | 13.3791 | 0.612587 | ||||||||
\(478\) | −6.86087 | −0.313809 | ||||||||
\(479\) | 22.6259 | 1.03380 | 0.516902 | − | 0.856045i | \(-0.327085\pi\) | ||||
0.516902 | + | 0.856045i | \(0.327085\pi\) | |||||||
\(480\) | −5.90984 | −0.269746 | ||||||||
\(481\) | −24.6763 | −1.12514 | ||||||||
\(482\) | 1.13251 | 0.0515845 | ||||||||
\(483\) | −0.720797 | −0.0327974 | ||||||||
\(484\) | −6.32699 | −0.287590 | ||||||||
\(485\) | −1.10517 | −0.0501834 | ||||||||
\(486\) | 1.05971 | 0.0480692 | ||||||||
\(487\) | −1.33179 | −0.0603490 | −0.0301745 | − | 0.999545i | \(-0.509606\pi\) | ||||
−0.0301745 | + | 0.999545i | \(0.509606\pi\) | |||||||
\(488\) | 22.2292 | 1.00627 | ||||||||
\(489\) | −9.58430 | −0.433417 | ||||||||
\(490\) | −8.95396 | −0.404499 | ||||||||
\(491\) | −37.5483 | −1.69453 | −0.847265 | − | 0.531170i | \(-0.821753\pi\) | ||||
−0.847265 | + | 0.531170i | \(0.821753\pi\) | |||||||
\(492\) | −0.410238 | −0.0184950 | ||||||||
\(493\) | −1.60761 | −0.0724030 | ||||||||
\(494\) | −0.465132 | −0.0209273 | ||||||||
\(495\) | −5.56454 | −0.250107 | ||||||||
\(496\) | 5.61361 | 0.252059 | ||||||||
\(497\) | −0.608119 | −0.0272779 | ||||||||
\(498\) | −9.43994 | −0.423014 | ||||||||
\(499\) | −34.2219 | −1.53198 | −0.765992 | − | 0.642850i | \(-0.777752\pi\) | ||||
−0.765992 | + | 0.642850i | \(0.777752\pi\) | |||||||
\(500\) | −9.49104 | −0.424452 | ||||||||
\(501\) | 22.7911 | 1.01823 | ||||||||
\(502\) | 11.2976 | 0.504236 | ||||||||
\(503\) | 28.4032 | 1.26643 | 0.633217 | − | 0.773974i | \(-0.281734\pi\) | ||||
0.633217 | + | 0.773974i | \(0.281734\pi\) | |||||||
\(504\) | 2.19756 | 0.0978873 | ||||||||
\(505\) | 5.49568 | 0.244554 | ||||||||
\(506\) | −4.52262 | −0.201055 | ||||||||
\(507\) | −29.1509 | −1.29464 | ||||||||
\(508\) | 14.7546 | 0.654627 | ||||||||
\(509\) | −6.08138 | −0.269553 | −0.134776 | − | 0.990876i | \(-0.543032\pi\) | ||||
−0.134776 | + | 0.990876i | \(0.543032\pi\) | |||||||
\(510\) | −2.22121 | −0.0983568 | ||||||||
\(511\) | −2.56709 | −0.113561 | ||||||||
\(512\) | 15.6986 | 0.693785 | ||||||||
\(513\) | −0.0676063 | −0.00298489 | ||||||||
\(514\) | −28.0573 | −1.23756 | ||||||||
\(515\) | 4.24463 | 0.187041 | ||||||||
\(516\) | 0.851949 | 0.0375050 | ||||||||
\(517\) | 34.0535 | 1.49767 | ||||||||
\(518\) | 2.90318 | 0.127559 | ||||||||
\(519\) | −3.11958 | −0.136934 | ||||||||
\(520\) | −25.8081 | −1.13176 | ||||||||
\(521\) | −38.6489 | −1.69324 | −0.846619 | − | 0.532200i | \(-0.821366\pi\) | ||||
−0.846619 | + | 0.532200i | \(0.821366\pi\) | |||||||
\(522\) | 1.05971 | 0.0463821 | ||||||||
\(523\) | 2.97908 | 0.130266 | 0.0651331 | − | 0.997877i | \(-0.479253\pi\) | ||||
0.0651331 | + | 0.997877i | \(0.479253\pi\) | |||||||
\(524\) | −17.5503 | −0.766686 | ||||||||
\(525\) | 2.37863 | 0.103812 | ||||||||
\(526\) | −3.22264 | −0.140514 | ||||||||
\(527\) | −6.11090 | −0.266195 | ||||||||
\(528\) | 6.30262 | 0.274287 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 18.4857 | 0.802970 | ||||||||
\(531\) | −4.90374 | −0.212804 | ||||||||
\(532\) | −0.0427377 | −0.00185292 | ||||||||
\(533\) | −3.03688 | −0.131542 | ||||||||
\(534\) | 16.0327 | 0.693803 | ||||||||
\(535\) | −12.9319 | −0.559093 | ||||||||
\(536\) | 41.7649 | 1.80397 | ||||||||
\(537\) | 4.43515 | 0.191391 | ||||||||
\(538\) | 31.9310 | 1.37664 | ||||||||
\(539\) | −27.6573 | −1.19128 | ||||||||
\(540\) | −1.14350 | −0.0492083 | ||||||||
\(541\) | 26.1703 | 1.12515 | 0.562574 | − | 0.826747i | \(-0.309811\pi\) | ||||
0.562574 | + | 0.826747i | \(0.309811\pi\) | |||||||
\(542\) | −19.1441 | −0.822308 | ||||||||
\(543\) | −7.57878 | −0.325237 | ||||||||
\(544\) | −7.28670 | −0.312415 | ||||||||
\(545\) | 19.4852 | 0.834656 | ||||||||
\(546\) | 4.95909 | 0.212229 | ||||||||
\(547\) | 11.0205 | 0.471204 | 0.235602 | − | 0.971850i | \(-0.424294\pi\) | ||||
0.235602 | + | 0.971850i | \(0.424294\pi\) | |||||||
\(548\) | 15.4205 | 0.658729 | ||||||||
\(549\) | 7.29114 | 0.311178 | ||||||||
\(550\) | 14.9246 | 0.636389 | ||||||||
\(551\) | −0.0676063 | −0.00288013 | ||||||||
\(552\) | −3.04880 | −0.129765 | ||||||||
\(553\) | 2.52723 | 0.107469 | ||||||||
\(554\) | −15.9741 | −0.678673 | ||||||||
\(555\) | −4.95565 | −0.210356 | ||||||||
\(556\) | 9.89155 | 0.419495 | ||||||||
\(557\) | −26.2157 | −1.11080 | −0.555398 | − | 0.831585i | \(-0.687434\pi\) | ||||
−0.555398 | + | 0.831585i | \(0.687434\pi\) | |||||||
\(558\) | 4.02820 | 0.170527 | ||||||||
\(559\) | 6.30675 | 0.266747 | ||||||||
\(560\) | 1.38789 | 0.0586489 | ||||||||
\(561\) | −6.86095 | −0.289670 | ||||||||
\(562\) | −18.4479 | −0.778177 | ||||||||
\(563\) | −39.8761 | −1.68058 | −0.840288 | − | 0.542140i | \(-0.817614\pi\) | ||||
−0.840288 | + | 0.542140i | \(0.817614\pi\) | |||||||
\(564\) | 6.99790 | 0.294665 | ||||||||
\(565\) | −11.8054 | −0.496656 | ||||||||
\(566\) | −29.2791 | −1.23069 | ||||||||
\(567\) | 0.720797 | 0.0302706 | ||||||||
\(568\) | −2.57220 | −0.107927 | ||||||||
\(569\) | −15.2160 | −0.637886 | −0.318943 | − | 0.947774i | \(-0.603328\pi\) | ||||
−0.318943 | + | 0.947774i | \(0.603328\pi\) | |||||||
\(570\) | −0.0934108 | −0.00391255 | ||||||||
\(571\) | −11.9807 | −0.501377 | −0.250688 | − | 0.968068i | \(-0.580657\pi\) | ||||
−0.250688 | + | 0.968068i | \(0.580657\pi\) | |||||||
\(572\) | −24.3007 | −1.01606 | ||||||||
\(573\) | −23.8728 | −0.997301 | ||||||||
\(574\) | 0.357292 | 0.0149131 | ||||||||
\(575\) | −3.30000 | −0.137620 | ||||||||
\(576\) | 7.75683 | 0.323201 | ||||||||
\(577\) | −21.5518 | −0.897212 | −0.448606 | − | 0.893730i | \(-0.648079\pi\) | ||||
−0.448606 | + | 0.893730i | \(0.648079\pi\) | |||||||
\(578\) | 15.2763 | 0.635410 | ||||||||
\(579\) | 23.7901 | 0.988682 | ||||||||
\(580\) | −1.14350 | −0.0474812 | ||||||||
\(581\) | −6.42092 | −0.266384 | ||||||||
\(582\) | 0.898238 | 0.0372332 | ||||||||
\(583\) | 57.0994 | 2.36482 | ||||||||
\(584\) | −10.8582 | −0.449314 | ||||||||
\(585\) | −8.46502 | −0.349985 | ||||||||
\(586\) | −10.2296 | −0.422579 | ||||||||
\(587\) | −21.9895 | −0.907604 | −0.453802 | − | 0.891102i | \(-0.649933\pi\) | ||||
−0.453802 | + | 0.891102i | \(0.649933\pi\) | |||||||
\(588\) | −5.68351 | −0.234384 | ||||||||
\(589\) | −0.256988 | −0.0105890 | ||||||||
\(590\) | −6.77544 | −0.278940 | ||||||||
\(591\) | −10.2899 | −0.423270 | ||||||||
\(592\) | 5.61297 | 0.230692 | ||||||||
\(593\) | −18.0058 | −0.739411 | −0.369706 | − | 0.929149i | \(-0.620541\pi\) | ||||
−0.369706 | + | 0.929149i | \(0.620541\pi\) | |||||||
\(594\) | 4.52262 | 0.185565 | ||||||||
\(595\) | −1.51084 | −0.0619382 | ||||||||
\(596\) | −7.61712 | −0.312009 | ||||||||
\(597\) | −6.69895 | −0.274170 | ||||||||
\(598\) | −6.88000 | −0.281344 | ||||||||
\(599\) | 42.1452 | 1.72201 | 0.861004 | − | 0.508599i | \(-0.169836\pi\) | ||||
0.861004 | + | 0.508599i | \(0.169836\pi\) | |||||||
\(600\) | 10.0610 | 0.410740 | ||||||||
\(601\) | −1.18690 | −0.0484145 | −0.0242073 | − | 0.999707i | \(-0.507706\pi\) | ||||
−0.0242073 | + | 0.999707i | \(0.507706\pi\) | |||||||
\(602\) | −0.741995 | −0.0302414 | ||||||||
\(603\) | 13.6988 | 0.557859 | ||||||||
\(604\) | 3.31366 | 0.134831 | ||||||||
\(605\) | −9.40612 | −0.382413 | ||||||||
\(606\) | −4.46665 | −0.181445 | ||||||||
\(607\) | −21.2693 | −0.863296 | −0.431648 | − | 0.902042i | \(-0.642068\pi\) | ||||
−0.431648 | + | 0.902042i | \(0.642068\pi\) | |||||||
\(608\) | −0.306435 | −0.0124276 | ||||||||
\(609\) | 0.720797 | 0.0292082 | ||||||||
\(610\) | 10.0741 | 0.407887 | ||||||||
\(611\) | 51.8036 | 2.09575 | ||||||||
\(612\) | −1.40991 | −0.0569922 | ||||||||
\(613\) | 3.41464 | 0.137916 | 0.0689580 | − | 0.997620i | \(-0.478033\pi\) | ||||
0.0689580 | + | 0.997620i | \(0.478033\pi\) | |||||||
\(614\) | −24.8895 | −1.00446 | ||||||||
\(615\) | −0.609887 | −0.0245930 | ||||||||
\(616\) | 9.37878 | 0.377882 | ||||||||
\(617\) | −3.56041 | −0.143337 | −0.0716684 | − | 0.997429i | \(-0.522832\pi\) | ||||
−0.0716684 | + | 0.997429i | \(0.522832\pi\) | |||||||
\(618\) | −3.44986 | −0.138774 | ||||||||
\(619\) | −19.6807 | −0.791033 | −0.395516 | − | 0.918459i | \(-0.629434\pi\) | ||||
−0.395516 | + | 0.918459i | \(0.629434\pi\) | |||||||
\(620\) | −4.34671 | −0.174568 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −10.8331 | −0.434368 | ||||||||
\(623\) | 10.9052 | 0.436908 | ||||||||
\(624\) | 9.58783 | 0.383820 | ||||||||
\(625\) | 2.39000 | 0.0956000 | ||||||||
\(626\) | −5.25084 | −0.209866 | ||||||||
\(627\) | −0.288531 | −0.0115228 | ||||||||
\(628\) | 19.6766 | 0.785182 | ||||||||
\(629\) | −6.11021 | −0.243630 | ||||||||
\(630\) | 0.995916 | 0.0396783 | ||||||||
\(631\) | −39.8399 | −1.58600 | −0.793000 | − | 0.609221i | \(-0.791482\pi\) | ||||
−0.793000 | + | 0.609221i | \(0.791482\pi\) | |||||||
\(632\) | 10.6896 | 0.425208 | ||||||||
\(633\) | −19.4730 | −0.773982 | ||||||||
\(634\) | −6.57755 | −0.261228 | ||||||||
\(635\) | 21.9351 | 0.870467 | ||||||||
\(636\) | 11.7338 | 0.465275 | ||||||||
\(637\) | −42.0735 | −1.66701 | ||||||||
\(638\) | 4.52262 | 0.179052 | ||||||||
\(639\) | −0.843676 | −0.0333753 | ||||||||
\(640\) | −1.10216 | −0.0435668 | ||||||||
\(641\) | 5.19938 | 0.205363 | 0.102682 | − | 0.994714i | \(-0.467258\pi\) | ||||
0.102682 | + | 0.994714i | \(0.467258\pi\) | |||||||
\(642\) | 10.5105 | 0.414815 | ||||||||
\(643\) | −9.54077 | −0.376251 | −0.188126 | − | 0.982145i | \(-0.560241\pi\) | ||||
−0.188126 | + | 0.982145i | \(0.560241\pi\) | |||||||
\(644\) | −0.632156 | −0.0249104 | ||||||||
\(645\) | 1.26656 | 0.0498709 | ||||||||
\(646\) | −0.115173 | −0.00453144 | ||||||||
\(647\) | −38.0573 | −1.49619 | −0.748093 | − | 0.663594i | \(-0.769030\pi\) | ||||
−0.748093 | + | 0.663594i | \(0.769030\pi\) | |||||||
\(648\) | 3.04880 | 0.119768 | ||||||||
\(649\) | −20.9282 | −0.821505 | ||||||||
\(650\) | 22.7040 | 0.890525 | ||||||||
\(651\) | 2.73992 | 0.107386 | ||||||||
\(652\) | −8.40566 | −0.329191 | ||||||||
\(653\) | −7.10248 | −0.277942 | −0.138971 | − | 0.990296i | \(-0.544379\pi\) | ||||
−0.138971 | + | 0.990296i | \(0.544379\pi\) | |||||||
\(654\) | −15.8368 | −0.619267 | ||||||||
\(655\) | −26.0914 | −1.01947 | ||||||||
\(656\) | 0.690783 | 0.0269706 | ||||||||
\(657\) | −3.56146 | −0.138946 | ||||||||
\(658\) | −6.09474 | −0.237598 | ||||||||
\(659\) | 17.2293 | 0.671157 | 0.335579 | − | 0.942012i | \(-0.391068\pi\) | ||||
0.335579 | + | 0.942012i | \(0.391068\pi\) | |||||||
\(660\) | −4.88023 | −0.189963 | ||||||||
\(661\) | 6.28912 | 0.244618 | 0.122309 | − | 0.992492i | \(-0.460970\pi\) | ||||
0.122309 | + | 0.992492i | \(0.460970\pi\) | |||||||
\(662\) | −4.98105 | −0.193594 | ||||||||
\(663\) | −10.4372 | −0.405346 | ||||||||
\(664\) | −27.1589 | −1.05397 | ||||||||
\(665\) | −0.0635367 | −0.00246385 | ||||||||
\(666\) | 4.02774 | 0.156072 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | 19.9884 | 0.773373 | ||||||||
\(669\) | −5.45268 | −0.210813 | ||||||||
\(670\) | 18.9275 | 0.731233 | ||||||||
\(671\) | 31.1172 | 1.20126 | ||||||||
\(672\) | 3.26711 | 0.126032 | ||||||||
\(673\) | −33.1852 | −1.27920 | −0.639598 | − | 0.768709i | \(-0.720899\pi\) | ||||
−0.639598 | + | 0.768709i | \(0.720899\pi\) | |||||||
\(674\) | 9.73533 | 0.374991 | ||||||||
\(675\) | 3.30000 | 0.127017 | ||||||||
\(676\) | −25.5660 | −0.983308 | ||||||||
\(677\) | −27.3019 | −1.04930 | −0.524649 | − | 0.851318i | \(-0.675804\pi\) | ||||
−0.524649 | + | 0.851318i | \(0.675804\pi\) | |||||||
\(678\) | 9.59490 | 0.368490 | ||||||||
\(679\) | 0.610969 | 0.0234468 | ||||||||
\(680\) | −6.39047 | −0.245063 | ||||||||
\(681\) | −12.7976 | −0.490405 | ||||||||
\(682\) | 17.1916 | 0.658299 | ||||||||
\(683\) | −5.32782 | −0.203863 | −0.101932 | − | 0.994791i | \(-0.532502\pi\) | ||||
−0.101932 | + | 0.994791i | \(0.532502\pi\) | |||||||
\(684\) | −0.0592923 | −0.00226710 | ||||||||
\(685\) | 22.9251 | 0.875922 | ||||||||
\(686\) | 10.2968 | 0.393134 | ||||||||
\(687\) | 17.9481 | 0.684762 | ||||||||
\(688\) | −1.43456 | −0.0546922 | ||||||||
\(689\) | 86.8621 | 3.30918 | ||||||||
\(690\) | −1.38169 | −0.0525999 | ||||||||
\(691\) | −2.75150 | −0.104672 | −0.0523360 | − | 0.998630i | \(-0.516667\pi\) | ||||
−0.0523360 | + | 0.998630i | \(0.516667\pi\) | |||||||
\(692\) | −2.73594 | −0.104005 | ||||||||
\(693\) | 3.07622 | 0.116856 | ||||||||
\(694\) | 20.7120 | 0.786217 | ||||||||
\(695\) | 14.7054 | 0.557808 | ||||||||
\(696\) | 3.04880 | 0.115564 | ||||||||
\(697\) | −0.751977 | −0.0284832 | ||||||||
\(698\) | −37.8996 | −1.43452 | ||||||||
\(699\) | −24.8070 | −0.938285 | ||||||||
\(700\) | 2.08611 | 0.0788477 | ||||||||
\(701\) | −37.4534 | −1.41460 | −0.707298 | − | 0.706916i | \(-0.750086\pi\) | ||||
−0.707298 | + | 0.706916i | \(0.750086\pi\) | |||||||
\(702\) | 6.88000 | 0.259669 | ||||||||
\(703\) | −0.256959 | −0.00969139 | ||||||||
\(704\) | 33.1047 | 1.24768 | ||||||||
\(705\) | 10.4035 | 0.391820 | ||||||||
\(706\) | −18.6464 | −0.701767 | ||||||||
\(707\) | −3.03815 | −0.114262 | ||||||||
\(708\) | −4.30070 | −0.161630 | ||||||||
\(709\) | 29.7909 | 1.11882 | 0.559411 | − | 0.828891i | \(-0.311028\pi\) | ||||
0.559411 | + | 0.828891i | \(0.311028\pi\) | |||||||
\(710\) | −1.16570 | −0.0437478 | ||||||||
\(711\) | 3.50616 | 0.131491 | ||||||||
\(712\) | 46.1265 | 1.72866 | ||||||||
\(713\) | −3.80124 | −0.142358 | ||||||||
\(714\) | 1.22794 | 0.0459546 | ||||||||
\(715\) | −36.1270 | −1.35107 | ||||||||
\(716\) | 3.88973 | 0.145366 | ||||||||
\(717\) | −6.47432 | −0.241788 | ||||||||
\(718\) | −5.78086 | −0.215740 | ||||||||
\(719\) | −2.28034 | −0.0850422 | −0.0425211 | − | 0.999096i | \(-0.513539\pi\) | ||||
−0.0425211 | + | 0.999096i | \(0.513539\pi\) | |||||||
\(720\) | 1.92549 | 0.0717588 | ||||||||
\(721\) | −2.34654 | −0.0873898 | ||||||||
\(722\) | 20.1296 | 0.749145 | ||||||||
\(723\) | 1.06870 | 0.0397455 | ||||||||
\(724\) | −6.64677 | −0.247025 | ||||||||
\(725\) | 3.30000 | 0.122559 | ||||||||
\(726\) | 7.64489 | 0.283729 | ||||||||
\(727\) | 17.1529 | 0.636164 | 0.318082 | − | 0.948063i | \(-0.396961\pi\) | ||||
0.318082 | + | 0.948063i | \(0.396961\pi\) | |||||||
\(728\) | 14.2674 | 0.528785 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.92082 | −0.182128 | ||||||||
\(731\) | 1.56164 | 0.0577595 | ||||||||
\(732\) | 6.39450 | 0.236347 | ||||||||
\(733\) | 7.35753 | 0.271757 | 0.135878 | − | 0.990726i | \(-0.456614\pi\) | ||||
0.135878 | + | 0.990726i | \(0.456614\pi\) | |||||||
\(734\) | −8.35034 | −0.308217 | ||||||||
\(735\) | −8.44948 | −0.311664 | ||||||||
\(736\) | −4.53264 | −0.167075 | ||||||||
\(737\) | 58.4639 | 2.15354 | ||||||||
\(738\) | 0.495690 | 0.0182466 | ||||||||
\(739\) | 24.1145 | 0.887067 | 0.443534 | − | 0.896258i | \(-0.353725\pi\) | ||||
0.443534 | + | 0.896258i | \(0.353725\pi\) | |||||||
\(740\) | −4.34622 | −0.159770 | ||||||||
\(741\) | −0.438925 | −0.0161243 | ||||||||
\(742\) | −10.2194 | −0.375166 | ||||||||
\(743\) | 3.82636 | 0.140376 | 0.0701878 | − | 0.997534i | \(-0.477640\pi\) | ||||
0.0701878 | + | 0.997534i | \(0.477640\pi\) | |||||||
\(744\) | 11.5892 | 0.424881 | ||||||||
\(745\) | −11.3241 | −0.414883 | ||||||||
\(746\) | 13.0567 | 0.478040 | ||||||||
\(747\) | −8.90808 | −0.325930 | ||||||||
\(748\) | −6.01721 | −0.220011 | ||||||||
\(749\) | 7.14906 | 0.261221 | ||||||||
\(750\) | 11.4680 | 0.418752 | ||||||||
\(751\) | 19.0615 | 0.695564 | 0.347782 | − | 0.937575i | \(-0.386935\pi\) | ||||
0.347782 | + | 0.937575i | \(0.386935\pi\) | |||||||
\(752\) | −11.7835 | −0.429699 | ||||||||
\(753\) | 10.6611 | 0.388511 | ||||||||
\(754\) | 6.88000 | 0.250555 | ||||||||
\(755\) | 4.92630 | 0.179286 | ||||||||
\(756\) | 0.632156 | 0.0229913 | ||||||||
\(757\) | 46.5969 | 1.69359 | 0.846797 | − | 0.531916i | \(-0.178528\pi\) | ||||
0.846797 | + | 0.531916i | \(0.178528\pi\) | |||||||
\(758\) | −22.2772 | −0.809146 | ||||||||
\(759\) | −4.26781 | −0.154912 | ||||||||
\(760\) | −0.268745 | −0.00974841 | ||||||||
\(761\) | −13.6355 | −0.494288 | −0.247144 | − | 0.968979i | \(-0.579492\pi\) | ||||
−0.247144 | + | 0.968979i | \(0.579492\pi\) | |||||||
\(762\) | −17.8279 | −0.645837 | ||||||||
\(763\) | −10.7719 | −0.389971 | ||||||||
\(764\) | −20.9370 | −0.757475 | ||||||||
\(765\) | −2.09606 | −0.0757833 | ||||||||
\(766\) | 28.3286 | 1.02355 | ||||||||
\(767\) | −31.8369 | −1.14956 | ||||||||
\(768\) | 16.4095 | 0.592125 | ||||||||
\(769\) | −7.50359 | −0.270586 | −0.135293 | − | 0.990806i | \(-0.543198\pi\) | ||||
−0.135293 | + | 0.990806i | \(0.543198\pi\) | |||||||
\(770\) | 4.25038 | 0.153173 | ||||||||
\(771\) | −26.4765 | −0.953529 | ||||||||
\(772\) | 20.8645 | 0.750929 | ||||||||
\(773\) | −54.1536 | −1.94777 | −0.973885 | − | 0.227043i | \(-0.927094\pi\) | ||||
−0.973885 | + | 0.227043i | \(0.927094\pi\) | |||||||
\(774\) | −1.02941 | −0.0370013 | ||||||||
\(775\) | 12.5441 | 0.450597 | ||||||||
\(776\) | 2.58425 | 0.0927692 | ||||||||
\(777\) | 2.73961 | 0.0982830 | ||||||||
\(778\) | −19.2902 | −0.691589 | ||||||||
\(779\) | −0.0316237 | −0.00113304 | ||||||||
\(780\) | −7.42402 | −0.265822 | ||||||||
\(781\) | −3.60065 | −0.128841 | ||||||||
\(782\) | −1.70359 | −0.0609203 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 9.57022 | 0.341794 | ||||||||
\(785\) | 29.2525 | 1.04407 | ||||||||
\(786\) | 21.2059 | 0.756391 | ||||||||
\(787\) | −29.3341 | −1.04565 | −0.522823 | − | 0.852441i | \(-0.675121\pi\) | ||||
−0.522823 | + | 0.852441i | \(0.675121\pi\) | |||||||
\(788\) | −9.02448 | −0.321484 | ||||||||
\(789\) | −3.04107 | −0.108265 | ||||||||
\(790\) | 4.84442 | 0.172357 | ||||||||
\(791\) | 6.52632 | 0.232049 | ||||||||
\(792\) | 13.0117 | 0.462350 | ||||||||
\(793\) | 47.3368 | 1.68098 | ||||||||
\(794\) | 15.8399 | 0.562139 | ||||||||
\(795\) | 17.4442 | 0.618683 | ||||||||
\(796\) | −5.87514 | −0.208239 | ||||||||
\(797\) | −26.7775 | −0.948507 | −0.474253 | − | 0.880388i | \(-0.657282\pi\) | ||||
−0.474253 | + | 0.880388i | \(0.657282\pi\) | |||||||
\(798\) | 0.0516399 | 0.00182803 | ||||||||
\(799\) | 12.8273 | 0.453798 | ||||||||
\(800\) | 14.9577 | 0.528835 | ||||||||
\(801\) | 15.1294 | 0.534571 | ||||||||
\(802\) | −6.29177 | −0.222170 | ||||||||
\(803\) | −15.1996 | −0.536383 | ||||||||
\(804\) | 12.0142 | 0.423708 | ||||||||
\(805\) | −0.939804 | −0.0331237 | ||||||||
\(806\) | 26.1526 | 0.921185 | ||||||||
\(807\) | 30.1319 | 1.06069 | ||||||||
\(808\) | −12.8507 | −0.452085 | ||||||||
\(809\) | 44.6884 | 1.57116 | 0.785579 | − | 0.618761i | \(-0.212365\pi\) | ||||
0.785579 | + | 0.618761i | \(0.212365\pi\) | |||||||
\(810\) | 1.38169 | 0.0485476 | ||||||||
\(811\) | 44.3620 | 1.55776 | 0.778880 | − | 0.627174i | \(-0.215788\pi\) | ||||
0.778880 | + | 0.627174i | \(0.215788\pi\) | |||||||
\(812\) | 0.632156 | 0.0221843 | ||||||||
\(813\) | −18.0654 | −0.633583 | ||||||||
\(814\) | 17.1896 | 0.602496 | ||||||||
\(815\) | −12.4964 | −0.437730 | ||||||||
\(816\) | 2.37409 | 0.0831097 | ||||||||
\(817\) | 0.0656735 | 0.00229762 | ||||||||
\(818\) | −29.8440 | −1.04347 | ||||||||
\(819\) | 4.67968 | 0.163521 | ||||||||
\(820\) | −0.534885 | −0.0186790 | ||||||||
\(821\) | −21.3612 | −0.745510 | −0.372755 | − | 0.927930i | \(-0.621587\pi\) | ||||
−0.372755 | + | 0.927930i | \(0.621587\pi\) | |||||||
\(822\) | −18.6325 | −0.649884 | ||||||||
\(823\) | 16.2985 | 0.568131 | 0.284065 | − | 0.958805i | \(-0.408317\pi\) | ||||
0.284065 | + | 0.958805i | \(0.408317\pi\) | |||||||
\(824\) | −9.92532 | −0.345765 | ||||||||
\(825\) | 14.0838 | 0.490334 | ||||||||
\(826\) | 3.74564 | 0.130327 | ||||||||
\(827\) | 5.01177 | 0.174276 | 0.0871381 | − | 0.996196i | \(-0.472228\pi\) | ||||
0.0871381 | + | 0.996196i | \(0.472228\pi\) | |||||||
\(828\) | −0.877023 | −0.0304787 | ||||||||
\(829\) | −19.5777 | −0.679962 | −0.339981 | − | 0.940432i | \(-0.610421\pi\) | ||||
−0.339981 | + | 0.940432i | \(0.610421\pi\) | |||||||
\(830\) | −12.3082 | −0.427223 | ||||||||
\(831\) | −15.0741 | −0.522913 | ||||||||
\(832\) | 50.3602 | 1.74593 | ||||||||
\(833\) | −10.4180 | −0.360963 | ||||||||
\(834\) | −11.9519 | −0.413862 | ||||||||
\(835\) | 29.7160 | 1.02837 | ||||||||
\(836\) | −0.253048 | −0.00875185 | ||||||||
\(837\) | 3.80124 | 0.131390 | ||||||||
\(838\) | 16.6996 | 0.576877 | ||||||||
\(839\) | 43.9097 | 1.51593 | 0.757965 | − | 0.652295i | \(-0.226194\pi\) | ||||
0.757965 | + | 0.652295i | \(0.226194\pi\) | |||||||
\(840\) | 2.86527 | 0.0988613 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 39.7476 | 1.36979 | ||||||||
\(843\) | −17.4085 | −0.599581 | ||||||||
\(844\) | −17.0783 | −0.587859 | ||||||||
\(845\) | −38.0081 | −1.30752 | ||||||||
\(846\) | −8.45555 | −0.290708 | ||||||||
\(847\) | 5.19995 | 0.178672 | ||||||||
\(848\) | −19.7580 | −0.678494 | ||||||||
\(849\) | −27.6295 | −0.948242 | ||||||||
\(850\) | 5.62185 | 0.192828 | ||||||||
\(851\) | −3.80081 | −0.130290 | ||||||||
\(852\) | −0.739924 | −0.0253494 | ||||||||
\(853\) | 26.4519 | 0.905696 | 0.452848 | − | 0.891588i | \(-0.350408\pi\) | ||||
0.452848 | + | 0.891588i | \(0.350408\pi\) | |||||||
\(854\) | −5.56921 | −0.190574 | ||||||||
\(855\) | −0.0881479 | −0.00301459 | ||||||||
\(856\) | 30.2388 | 1.03354 | ||||||||
\(857\) | −26.0097 | −0.888475 | −0.444238 | − | 0.895909i | \(-0.646525\pi\) | ||||
−0.444238 | + | 0.895909i | \(0.646525\pi\) | |||||||
\(858\) | 29.3625 | 1.00242 | ||||||||
\(859\) | 12.0451 | 0.410973 | 0.205486 | − | 0.978660i | \(-0.434122\pi\) | ||||
0.205486 | + | 0.978660i | \(0.434122\pi\) | |||||||
\(860\) | 1.11081 | 0.0378782 | ||||||||
\(861\) | 0.337161 | 0.0114904 | ||||||||
\(862\) | −11.3743 | −0.387411 | ||||||||
\(863\) | −26.1020 | −0.888523 | −0.444262 | − | 0.895897i | \(-0.646534\pi\) | ||||
−0.444262 | + | 0.895897i | \(0.646534\pi\) | |||||||
\(864\) | 4.53264 | 0.154204 | ||||||||
\(865\) | −4.06743 | −0.138297 | ||||||||
\(866\) | −31.6853 | −1.07671 | ||||||||
\(867\) | 14.4156 | 0.489579 | ||||||||
\(868\) | 2.40298 | 0.0815623 | ||||||||
\(869\) | 14.9636 | 0.507606 | ||||||||
\(870\) | 1.38169 | 0.0468436 | ||||||||
\(871\) | 88.9378 | 3.01354 | ||||||||
\(872\) | −45.5628 | −1.54295 | ||||||||
\(873\) | 0.847630 | 0.0286879 | ||||||||
\(874\) | −0.0716428 | −0.00242336 | ||||||||
\(875\) | 7.80038 | 0.263701 | ||||||||
\(876\) | −3.12348 | −0.105533 | ||||||||
\(877\) | −7.72870 | −0.260980 | −0.130490 | − | 0.991450i | \(-0.541655\pi\) | ||||
−0.130490 | + | 0.991450i | \(0.541655\pi\) | |||||||
\(878\) | −29.2927 | −0.988582 | ||||||||
\(879\) | −9.65321 | −0.325595 | ||||||||
\(880\) | 8.21762 | 0.277016 | ||||||||
\(881\) | −14.2550 | −0.480262 | −0.240131 | − | 0.970741i | \(-0.577190\pi\) | ||||
−0.240131 | + | 0.970741i | \(0.577190\pi\) | |||||||
\(882\) | 6.86737 | 0.231236 | ||||||||
\(883\) | 18.3998 | 0.619203 | 0.309601 | − | 0.950866i | \(-0.399804\pi\) | ||||
0.309601 | + | 0.950866i | \(0.399804\pi\) | |||||||
\(884\) | −9.15365 | −0.307871 | ||||||||
\(885\) | −6.39370 | −0.214922 | ||||||||
\(886\) | −17.5207 | −0.588621 | ||||||||
\(887\) | 0.871823 | 0.0292730 | 0.0146365 | − | 0.999893i | \(-0.495341\pi\) | ||||
0.0146365 | + | 0.999893i | \(0.495341\pi\) | |||||||
\(888\) | 11.5879 | 0.388865 | ||||||||
\(889\) | −12.1263 | −0.406703 | ||||||||
\(890\) | 20.9041 | 0.700707 | ||||||||
\(891\) | 4.26781 | 0.142977 | ||||||||
\(892\) | −4.78212 | −0.160117 | ||||||||
\(893\) | 0.539441 | 0.0180517 | ||||||||
\(894\) | 9.20376 | 0.307820 | ||||||||
\(895\) | 5.78273 | 0.193295 | ||||||||
\(896\) | 0.609304 | 0.0203554 | ||||||||
\(897\) | −6.49237 | −0.216774 | ||||||||
\(898\) | −16.5448 | −0.552107 | ||||||||
\(899\) | 3.80124 | 0.126779 | ||||||||
\(900\) | 2.89418 | 0.0964726 | ||||||||
\(901\) | 21.5083 | 0.716547 | ||||||||
\(902\) | 2.11551 | 0.0704387 | ||||||||
\(903\) | −0.700189 | −0.0233008 | ||||||||
\(904\) | 27.6048 | 0.918120 | ||||||||
\(905\) | −9.88152 | −0.328473 | ||||||||
\(906\) | −4.00389 | −0.133020 | ||||||||
\(907\) | 55.9890 | 1.85908 | 0.929542 | − | 0.368716i | \(-0.120202\pi\) | ||||
0.929542 | + | 0.368716i | \(0.120202\pi\) | |||||||
\(908\) | −11.2238 | −0.372475 | ||||||||
\(909\) | −4.21499 | −0.139802 | ||||||||
\(910\) | 6.46586 | 0.214341 | ||||||||
\(911\) | 53.4421 | 1.77061 | 0.885307 | − | 0.465007i | \(-0.153948\pi\) | ||||
0.885307 | + | 0.465007i | \(0.153948\pi\) | |||||||
\(912\) | 0.0998399 | 0.00330603 | ||||||||
\(913\) | −38.0179 | −1.25821 | ||||||||
\(914\) | 41.4523 | 1.37112 | ||||||||
\(915\) | 9.50648 | 0.314274 | ||||||||
\(916\) | 15.7409 | 0.520093 | ||||||||
\(917\) | 14.4240 | 0.476322 | ||||||||
\(918\) | 1.70359 | 0.0562269 | ||||||||
\(919\) | 42.9636 | 1.41724 | 0.708619 | − | 0.705591i | \(-0.249319\pi\) | ||||
0.708619 | + | 0.705591i | \(0.249319\pi\) | |||||||
\(920\) | −3.97515 | −0.131057 | ||||||||
\(921\) | −23.4872 | −0.773929 | ||||||||
\(922\) | −28.9350 | −0.952922 | ||||||||
\(923\) | −5.47746 | −0.180293 | ||||||||
\(924\) | 2.69792 | 0.0887550 | ||||||||
\(925\) | 12.5427 | 0.412400 | ||||||||
\(926\) | −26.6996 | −0.877404 | ||||||||
\(927\) | −3.25548 | −0.106924 | ||||||||
\(928\) | 4.53264 | 0.148791 | ||||||||
\(929\) | 12.0253 | 0.394537 | 0.197269 | − | 0.980349i | \(-0.436793\pi\) | ||||
0.197269 | + | 0.980349i | \(0.436793\pi\) | |||||||
\(930\) | 5.25213 | 0.172224 | ||||||||
\(931\) | −0.438120 | −0.0143588 | ||||||||
\(932\) | −21.7563 | −0.712651 | ||||||||
\(933\) | −10.2227 | −0.334678 | ||||||||
\(934\) | −11.1652 | −0.365338 | ||||||||
\(935\) | −8.94559 | −0.292552 | ||||||||
\(936\) | 19.7939 | 0.646985 | ||||||||
\(937\) | −30.0372 | −0.981274 | −0.490637 | − | 0.871364i | \(-0.663236\pi\) | ||||
−0.490637 | + | 0.871364i | \(0.663236\pi\) | |||||||
\(938\) | −10.4636 | −0.341649 | ||||||||
\(939\) | −4.95500 | −0.161700 | ||||||||
\(940\) | 9.12415 | 0.297597 | ||||||||
\(941\) | 19.6719 | 0.641286 | 0.320643 | − | 0.947200i | \(-0.396101\pi\) | ||||
0.320643 | + | 0.947200i | \(0.396101\pi\) | |||||||
\(942\) | −23.7752 | −0.774638 | ||||||||
\(943\) | −0.467762 | −0.0152324 | ||||||||
\(944\) | 7.24177 | 0.235699 | ||||||||
\(945\) | 0.939804 | 0.0305718 | ||||||||
\(946\) | −4.39332 | −0.142839 | ||||||||
\(947\) | −18.8653 | −0.613041 | −0.306520 | − | 0.951864i | \(-0.599165\pi\) | ||||
−0.306520 | + | 0.951864i | \(0.599165\pi\) | |||||||
\(948\) | 3.07498 | 0.0998708 | ||||||||
\(949\) | −23.1223 | −0.750582 | ||||||||
\(950\) | 0.236421 | 0.00767052 | ||||||||
\(951\) | −6.20695 | −0.201274 | ||||||||
\(952\) | 3.53282 | 0.114499 | ||||||||
\(953\) | −33.1756 | −1.07466 | −0.537331 | − | 0.843371i | \(-0.680568\pi\) | ||||
−0.537331 | + | 0.843371i | \(0.680568\pi\) | |||||||
\(954\) | −14.1779 | −0.459027 | ||||||||
\(955\) | −31.1263 | −1.00722 | ||||||||
\(956\) | −5.67813 | −0.183644 | ||||||||
\(957\) | 4.26781 | 0.137959 | ||||||||
\(958\) | −23.9768 | −0.774655 | ||||||||
\(959\) | −12.6736 | −0.409251 | ||||||||
\(960\) | 10.1137 | 0.326417 | ||||||||
\(961\) | −16.5506 | −0.533889 | ||||||||
\(962\) | 26.1496 | 0.843097 | ||||||||
\(963\) | 9.91828 | 0.319612 | ||||||||
\(964\) | 0.937279 | 0.0301877 | ||||||||
\(965\) | 31.0185 | 0.998520 | ||||||||
\(966\) | 0.763833 | 0.0245759 | ||||||||
\(967\) | −41.8683 | −1.34640 | −0.673198 | − | 0.739463i | \(-0.735080\pi\) | ||||
−0.673198 | + | 0.739463i | \(0.735080\pi\) | |||||||
\(968\) | 21.9945 | 0.706931 | ||||||||
\(969\) | −0.108684 | −0.00349145 | ||||||||
\(970\) | 1.17116 | 0.0376037 | ||||||||
\(971\) | 24.2057 | 0.776799 | 0.388400 | − | 0.921491i | \(-0.373028\pi\) | ||||
0.388400 | + | 0.921491i | \(0.373028\pi\) | |||||||
\(972\) | 0.877023 | 0.0281305 | ||||||||
\(973\) | −8.12954 | −0.260621 | ||||||||
\(974\) | 1.41130 | 0.0452210 | ||||||||
\(975\) | 21.4248 | 0.686144 | ||||||||
\(976\) | −10.7674 | −0.344657 | ||||||||
\(977\) | 11.7282 | 0.375218 | 0.187609 | − | 0.982244i | \(-0.439926\pi\) | ||||
0.187609 | + | 0.982244i | \(0.439926\pi\) | |||||||
\(978\) | 10.1565 | 0.324770 | ||||||||
\(979\) | 64.5693 | 2.06364 | ||||||||
\(980\) | −7.41039 | −0.236716 | ||||||||
\(981\) | −14.9445 | −0.477141 | ||||||||
\(982\) | 39.7902 | 1.26975 | ||||||||
\(983\) | −1.37537 | −0.0438675 | −0.0219338 | − | 0.999759i | \(-0.506982\pi\) | ||||
−0.0219338 | + | 0.999759i | \(0.506982\pi\) | |||||||
\(984\) | 1.42611 | 0.0454628 | ||||||||
\(985\) | −13.4164 | −0.427482 | ||||||||
\(986\) | 1.70359 | 0.0542534 | ||||||||
\(987\) | −5.75135 | −0.183067 | ||||||||
\(988\) | −0.384948 | −0.0122468 | ||||||||
\(989\) | 0.971410 | 0.0308890 | ||||||||
\(990\) | 5.89677 | 0.187412 | ||||||||
\(991\) | 60.9345 | 1.93565 | 0.967824 | − | 0.251629i | \(-0.0809662\pi\) | ||||
0.967824 | + | 0.251629i | \(0.0809662\pi\) | |||||||
\(992\) | 17.2297 | 0.547042 | ||||||||
\(993\) | −4.70041 | −0.149163 | ||||||||
\(994\) | 0.644428 | 0.0204400 | ||||||||
\(995\) | −8.73436 | −0.276898 | ||||||||
\(996\) | −7.81259 | −0.247551 | ||||||||
\(997\) | −9.78792 | −0.309986 | −0.154993 | − | 0.987916i | \(-0.549536\pi\) | ||||
−0.154993 | + | 0.987916i | \(0.549536\pi\) | |||||||
\(998\) | 36.2652 | 1.14795 | ||||||||
\(999\) | 3.80081 | 0.120252 |
(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 | 2001.2.a.l.1.4 | ✓ | 11 | |
3.2 | odd | 2 | 6003.2.a.m.1.8 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2001.2.a.l.1.4 | ✓ | 11 | 1.1 | even | 1 | trivial | |
6003.2.a.m.1.8 | 11 | 3.2 | odd | 2 |