Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.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: | \(48.2615829817\) |
Analytic rank: | \(1\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.33939 | −1.35065 | −0.675325 | − | 0.737520i | \(-0.735997\pi\) | ||||
−0.675325 | + | 0.737520i | \(0.735997\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09632 | 0.937502 | 0.468751 | − | 0.883330i | \(-0.344704\pi\) | ||||
0.468751 | + | 0.883330i | \(0.344704\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.25063 | 0.472693 | 0.236346 | − | 0.971669i | \(-0.424050\pi\) | ||||
0.236346 | + | 0.971669i | \(0.424050\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.47276 | 0.824255 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.62252 | 0.489208 | 0.244604 | − | 0.969623i | \(-0.421342\pi\) | ||||
0.244604 | + | 0.969623i | \(0.421342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.29185 | −0.635644 | −0.317822 | − | 0.948150i | \(-0.602952\pi\) | ||||
−0.317822 | + | 0.948150i | \(0.602952\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.90411 | −1.26624 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.81594 | 0.682965 | 0.341483 | − | 0.939888i | \(-0.389071\pi\) | ||||
0.341483 | + | 0.939888i | \(0.389071\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.10341 | −0.482556 | −0.241278 | − | 0.970456i | \(-0.577567\pi\) | ||||
−0.241278 | + | 0.970456i | \(0.577567\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.92571 | −0.638442 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.36031 | −0.909187 | −0.454593 | − | 0.890699i | \(-0.650215\pi\) | ||||
−0.454593 | + | 0.890699i | \(0.650215\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.605452 | −0.121090 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.23341 | 0.237370 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.61572 | 0.300031 | 0.150016 | − | 0.988684i | \(-0.452068\pi\) | ||||
0.150016 | + | 0.988684i | \(0.452068\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.58233 | 0.284194 | 0.142097 | − | 0.989853i | \(-0.454615\pi\) | ||||
0.142097 | + | 0.989853i | \(0.454615\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.79571 | −0.660749 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.62171 | 0.443150 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.61455 | 0.429829 | 0.214914 | − | 0.976633i | \(-0.431053\pi\) | ||||
0.214914 | + | 0.976633i | \(0.431053\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.36154 | 0.858533 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.86557 | 0.291352 | 0.145676 | − | 0.989332i | \(-0.453464\pi\) | ||||
0.145676 | + | 0.989332i | \(0.453464\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.96037 | −1.51894 | −0.759471 | − | 0.650541i | \(-0.774542\pi\) | ||||
−0.759471 | + | 0.650541i | \(0.774542\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.18370 | 0.772741 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.873354 | −0.127392 | −0.0636959 | − | 0.997969i | \(-0.520289\pi\) | ||||
−0.0636959 | + | 0.997969i | \(0.520289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.43593 | −0.776562 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.58759 | −0.922447 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.32199 | −0.593671 | −0.296836 | − | 0.954929i | \(-0.595931\pi\) | ||||
−0.296836 | + | 0.954929i | \(0.595931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.40132 | 0.458633 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.92071 | 0.651764 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.88548 | −1.28698 | −0.643490 | − | 0.765454i | \(-0.722514\pi\) | ||||
−0.643490 | + | 0.765454i | \(0.722514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.72317 | −0.860814 | −0.430407 | − | 0.902635i | \(-0.641630\pi\) | ||||
−0.430407 | + | 0.902635i | \(0.641630\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.09251 | 0.389619 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.80444 | −0.595918 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.19005 | −1.12274 | −0.561372 | − | 0.827564i | \(-0.689726\pi\) | ||||
−0.561372 | + | 0.827564i | \(0.689726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.2005 | 1.22799 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.51180 | −0.772809 | −0.386404 | − | 0.922329i | \(-0.626283\pi\) | ||||
−0.386404 | + | 0.922329i | \(0.626283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2610 | 1.20096 | 0.600481 | − | 0.799639i | \(-0.294976\pi\) | ||||
0.600481 | + | 0.799639i | \(0.294976\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.41639 | 0.163551 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.02917 | 0.231245 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.8872 | 1.22491 | 0.612455 | − | 0.790506i | \(-0.290182\pi\) | ||||
0.612455 | + | 0.790506i | \(0.290182\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.3037 | −1.14486 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.56323 | −0.281351 | −0.140676 | − | 0.990056i | \(-0.544928\pi\) | ||||
−0.140676 | + | 0.990056i | \(0.544928\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.90310 | 0.640281 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.77980 | −0.405237 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.69018 | −0.921158 | −0.460579 | − | 0.887619i | \(-0.652358\pi\) | ||||
−0.460579 | + | 0.887619i | \(0.652358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.86625 | −0.300465 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.70169 | −0.383847 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.40942 | −0.452397 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.9626 | 1.41769 | 0.708845 | − | 0.705365i | \(-0.249217\pi\) | ||||
0.708845 | + | 0.705365i | \(0.249217\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.01211 | 0.403232 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.943829 | 0.0939145 | 0.0469572 | − | 0.998897i | \(-0.485048\pi\) | ||||
0.0469572 | + | 0.998897i | \(0.485048\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9923 | −1.08310 | −0.541550 | − | 0.840668i | \(-0.682162\pi\) | ||||
−0.541550 | + | 0.840668i | \(0.682162\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.13322 | −0.598541 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.67435 | 0.161866 | 0.0809328 | − | 0.996720i | \(-0.474210\pi\) | ||||
0.0809328 | + | 0.996720i | \(0.474210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9052 | 1.81079 | 0.905393 | − | 0.424575i | \(-0.139577\pi\) | ||||
0.905393 | + | 0.424575i | \(0.139577\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.11645 | −0.580548 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.5153 | −1.64770 | −0.823850 | − | 0.566808i | \(-0.808178\pi\) | ||||
−0.823850 | + | 0.566808i | \(0.808178\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.14059 | −0.852364 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.66720 | −0.523933 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.52169 | 0.322833 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.36743 | −0.760676 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.36429 | −0.393515 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7508 | −1.05102 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.8379 | 1.31665 | 0.658325 | − | 0.752734i | \(-0.271265\pi\) | ||||
0.658325 | + | 0.752734i | \(0.271265\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.3012 | 2.05156 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.59201 | 0.401206 | 0.200603 | − | 0.979673i | \(-0.435710\pi\) | ||||
0.200603 | + | 0.979673i | \(0.435710\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.63059 | −0.228101 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.58562 | 0.222535 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.2387 | 1.81454 | 0.907271 | − | 0.420547i | \(-0.138162\pi\) | ||||
0.907271 | + | 0.420547i | \(0.138162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6904 | −0.906744 | −0.453372 | − | 0.891321i | \(-0.649779\pi\) | ||||
−0.453372 | + | 0.891321i | \(0.649779\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.04312 | 0.172062 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.71857 | −0.310962 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.38706 | 0.281280 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 12.7168 | 1.04886 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.40860 | 0.525013 | 0.262507 | − | 0.964930i | \(-0.415451\pi\) | ||||
0.262507 | + | 0.964930i | \(0.415451\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.70122 | 0.382579 | 0.191290 | − | 0.981534i | \(-0.438733\pi\) | ||||
0.191290 | + | 0.981534i | \(0.438733\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.96315 | 0.562938 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.31706 | 0.266433 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.5259 | 1.47853 | 0.739263 | − | 0.673417i | \(-0.235174\pi\) | ||||
0.739263 | + | 0.673417i | \(0.235174\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.1108 | 0.801842 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.45312 | −0.429766 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.55440 | 0.591706 | 0.295853 | − | 0.955233i | \(-0.404396\pi\) | ||||
0.295853 | + | 0.955233i | \(0.404396\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.95702 | −0.619453 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.7889 | −1.53131 | −0.765656 | − | 0.643250i | \(-0.777586\pi\) | ||||
−0.765656 | + | 0.643250i | \(0.777586\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.74743 | −0.595956 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.20125 | −0.397749 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.22823 | 0.321466 | 0.160733 | − | 0.986998i | \(-0.448614\pi\) | ||||
0.160733 | + | 0.986998i | \(0.448614\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.757195 | −0.0572386 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 23.1260 | 1.73826 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.6397 | −1.16897 | −0.584484 | − | 0.811405i | \(-0.698703\pi\) | ||||
−0.584484 | + | 0.811405i | \(0.698703\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.49282 | 0.185290 | 0.0926449 | − | 0.995699i | \(-0.470468\pi\) | ||||
0.0926449 | + | 0.995699i | \(0.470468\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 15.7282 | 1.16266 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.48092 | 0.402965 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.56891 | 0.334112 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.54254 | 0.112203 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.21349 | −0.0878051 | −0.0439025 | − | 0.999036i | \(-0.513979\pi\) | ||||
−0.0439025 | + | 0.999036i | \(0.513979\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4818 | 0.898458 | 0.449229 | − | 0.893417i | \(-0.351699\pi\) | ||||
0.449229 | + | 0.893417i | \(0.351699\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.2395 | 0.804876 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.03381 | 0.429891 | 0.214945 | − | 0.976626i | \(-0.431043\pi\) | ||||
0.214945 | + | 0.976626i | \(0.431043\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.7229 | −1.11457 | −0.557283 | − | 0.830323i | \(-0.688156\pi\) | ||||
−0.557283 | + | 0.830323i | \(0.688156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.4991 | 1.51643 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.02066 | 0.141823 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.91082 | 0.273143 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10.7820 | −0.749402 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.41283 | −0.236070 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7874 | −0.742634 | −0.371317 | − | 0.928506i | \(-0.621094\pi\) | ||||
−0.371317 | + | 0.928506i | \(0.621094\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.2337 | 1.04379 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.8801 | −1.42401 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.97890 | 0.134337 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.0046 | −1.62208 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.45370 | −0.434123 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5370 | −1.37526 | −0.687629 | − | 0.726062i | \(-0.741349\pi\) | ||||
−0.687629 | + | 0.726062i | \(0.741349\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.49714 | −0.0998094 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.5179 | 1.02996 | 0.514981 | − | 0.857202i | \(-0.327799\pi\) | ||||
0.514981 | + | 0.857202i | \(0.327799\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7606 | −1.57014 | −0.785072 | − | 0.619404i | \(-0.787374\pi\) | ||||
−0.785072 | + | 0.619404i | \(0.787374\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.74702 | −0.312331 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.15292 | 0.272067 | 0.136033 | − | 0.990704i | \(-0.456565\pi\) | ||||
0.136033 | + | 0.990704i | \(0.456565\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.83083 | −0.119430 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.4695 | −1.65442 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.2605 | −0.922436 | −0.461218 | − | 0.887287i | \(-0.652587\pi\) | ||||
−0.461218 | + | 0.887287i | \(0.652587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.3800 | −1.31279 | −0.656397 | − | 0.754416i | \(-0.727920\pi\) | ||||
−0.656397 | + | 0.754416i | \(0.727920\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 20.4043 | 1.30893 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −11.3954 | −0.728028 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.82070 | 0.306734 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.99641 | 0.380007 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.9361 | −1.57395 | −0.786975 | − | 0.616985i | \(-0.788354\pi\) | ||||
−0.786975 | + | 0.616985i | \(0.788354\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.07468 | −0.444781 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.8097 | −0.864796 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.7037 | 1.29146 | 0.645731 | − | 0.763565i | \(-0.276553\pi\) | ||||
0.645731 | + | 0.763565i | \(0.276553\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.26982 | 0.203177 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.99529 | 0.247302 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.5536 | 1.08240 | 0.541200 | − | 0.840894i | \(-0.317970\pi\) | ||||
0.541200 | + | 0.840894i | \(0.317970\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.06027 | −0.556568 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.3298 | 1.24416 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −13.5851 | −0.828299 | −0.414149 | − | 0.910209i | \(-0.635921\pi\) | ||||
−0.414149 | + | 0.910209i | \(0.635921\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.2551 | 1.71638 | 0.858189 | − | 0.513334i | \(-0.171590\pi\) | ||||
0.858189 | + | 0.513334i | \(0.171590\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.70529 | 0.405822 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.982357 | −0.0592384 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.648466 | 0.0389625 | 0.0194813 | − | 0.999810i | \(-0.493799\pi\) | ||||
0.0194813 | + | 0.999810i | \(0.493799\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.91272 | 0.234249 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4489 | 1.45850 | 0.729250 | − | 0.684248i | \(-0.239869\pi\) | ||||
0.729250 | + | 0.684248i | \(0.239869\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.47153 | −0.325249 | −0.162624 | − | 0.986688i | \(-0.551996\pi\) | ||||
−0.162624 | + | 0.986688i | \(0.551996\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.3154 | 0.611030 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.33313 | 0.137720 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.07049 | −0.533558 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −32.6641 | −1.91480 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.1161 | −1.52572 | −0.762860 | − | 0.646564i | \(-0.776205\pi\) | ||||
−0.762860 | + | 0.646564i | \(0.776205\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.7231 | −1.20655 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.00123 | 0.116123 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.99316 | 0.577919 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.4567 | −0.717993 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.20799 | −0.126846 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.0939 | −0.807015 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −32.5909 | −1.86006 | −0.930031 | − | 0.367481i | \(-0.880220\pi\) | ||||
−0.930031 | + | 0.367481i | \(0.880220\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.7152 | 1.46289 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.0139 | −1.30500 | −0.652501 | − | 0.757788i | \(-0.726280\pi\) | ||||
−0.652501 | + | 0.757788i | \(0.726280\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −26.5159 | −1.49877 | −0.749383 | − | 0.662137i | \(-0.769650\pi\) | ||||
−0.749383 | + | 0.662137i | \(0.769650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.48288 | 0.365269 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.7282 | −1.38888 | −0.694438 | − | 0.719553i | \(-0.744347\pi\) | ||||
−0.694438 | + | 0.719553i | \(0.744347\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.62153 | 0.146778 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.91697 | −0.218624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.92308 | −0.329569 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.38760 | 0.0769704 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −44.2266 | −2.44574 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.09224 | −0.0602172 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 31.5628 | 1.73485 | 0.867423 | − | 0.497571i | \(-0.165775\pi\) | ||||
0.867423 | + | 0.497571i | \(0.165775\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.46516 | 0.354288 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.2653 | −1.05257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1570 | −0.607760 | −0.303880 | − | 0.952710i | \(-0.598282\pi\) | ||||
−0.303880 | + | 0.952710i | \(0.598282\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 40.9752 | 2.22547 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.56736 | 0.139030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5527 | −0.839768 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 21.3834 | 1.15125 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −32.8636 | −1.76421 | −0.882106 | − | 0.471051i | \(-0.843875\pi\) | ||||
−0.882106 | + | 0.471051i | \(0.843875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9749 | 1.28335 | 0.641673 | − | 0.766978i | \(-0.278241\pi\) | ||||
0.641673 | + | 0.766978i | \(0.278241\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.82679 | −0.150883 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3419 | 1.18914 | 0.594571 | − | 0.804043i | \(-0.297322\pi\) | ||||
0.594571 | + | 0.804043i | \(0.297322\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.6508 | −0.724509 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.23862 | −0.436034 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.7579 | 1.09556 | 0.547781 | − | 0.836622i | \(-0.315473\pi\) | ||||
0.547781 | + | 0.836622i | \(0.315473\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.5757 | −0.767140 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 19.5747 | 1.02741 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.5104 | 1.12590 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.1741 | −0.687680 | −0.343840 | − | 0.939028i | \(-0.611728\pi\) | ||||
−0.343840 | + | 0.939028i | \(0.611728\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.61311 | 0.240149 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.40520 | −0.280624 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.6258 | 0.757297 | 0.378648 | − | 0.925541i | \(-0.376389\pi\) | ||||
0.378648 | + | 0.925541i | \(0.376389\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.4898 | 1.41957 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.70298 | −0.190713 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.5163 | −1.41342 | −0.706710 | − | 0.707504i | \(-0.749821\pi\) | ||||
−0.706710 | + | 0.707504i | \(0.749821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.7117 | −1.77833 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.3191 | −1.08936 | −0.544678 | − | 0.838645i | \(-0.683348\pi\) | ||||
−0.544678 | + | 0.838645i | \(0.683348\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.25378 | 0.216793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −24.6297 | −1.25200 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.39267 | 0.374823 | 0.187412 | − | 0.982281i | \(-0.439990\pi\) | ||||
0.187412 | + | 0.982281i | \(0.439990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.2784 | −0.620943 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.7425 | −0.541888 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 22.8231 | 1.14835 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.6897 | −0.887819 | −0.443910 | − | 0.896072i | \(-0.646409\pi\) | ||||
−0.443910 | + | 0.896072i | \(0.646409\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.15398 | 0.308084 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.31176 | −0.365132 | −0.182566 | − | 0.983194i | \(-0.558440\pi\) | ||||
−0.182566 | + | 0.983194i | \(0.558440\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.62645 | −0.180646 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.5999 | −1.07331 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.24215 | 0.210276 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.69476 | 0.331034 | 0.165517 | − | 0.986207i | \(-0.447071\pi\) | ||||
0.165517 | + | 0.986207i | \(0.447071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −49.6856 | −2.45081 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.3631 | −0.608346 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.37335 | −0.263768 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.0090 | 1.22469 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.8104 | 0.528122 | 0.264061 | − | 0.964506i | \(-0.414938\pi\) | ||||
0.264061 | + | 0.964506i | \(0.414938\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.8037 | −1.50128 | −0.750641 | − | 0.660710i | \(-0.770255\pi\) | ||||
−0.750641 | + | 0.660710i | \(0.770255\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.15960 | −0.105003 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.70492 | −0.0827006 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.40819 | −0.406901 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.69920 | 0.420001 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.7273 | −1.52825 | −0.764124 | − | 0.645069i | \(-0.776828\pi\) | ||||
−0.764124 | + | 0.645069i | \(0.776828\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3277 | 1.26523 | 0.632614 | − | 0.774467i | \(-0.281982\pi\) | ||||
0.632614 | + | 0.774467i | \(0.281982\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.92367 | −0.379911 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.17152 | 0.438734 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.6301 | 1.46189 | 0.730947 | − | 0.682434i | \(-0.239078\pi\) | ||||
0.730947 | + | 0.682434i | \(0.239078\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.4418 | −0.640085 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.55685 | −0.454060 | −0.227030 | − | 0.973888i | \(-0.572902\pi\) | ||||
−0.227030 | + | 0.973888i | \(0.572902\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.2174 | −0.863587 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.9922 | −0.709109 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.4566 | −0.965407 | −0.482703 | − | 0.875784i | \(-0.660345\pi\) | ||||
−0.482703 | + | 0.875784i | \(0.660345\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.02692 | 0.142532 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.9980 | −0.516731 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.00857 | −0.281686 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5119 | −0.678837 | −0.339418 | − | 0.940636i | \(-0.610230\pi\) | ||||
−0.339418 | + | 0.940636i | \(0.610230\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.47321 | 0.162115 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.5993 | 0.586808 | 0.293404 | − | 0.955989i | \(-0.405212\pi\) | ||||
0.293404 | + | 0.955989i | \(0.405212\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.8428 | 1.20102 | 0.600508 | − | 0.799619i | \(-0.294965\pi\) | ||||
0.600508 | + | 0.799619i | \(0.294965\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.75991 | −0.359857 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.9066 | 0.550970 | 0.275485 | − | 0.961305i | \(-0.411162\pi\) | ||||
0.275485 | + | 0.961305i | \(0.411162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.4933 | −0.530712 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −43.3393 | −1.99697 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.1609 | −0.743078 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.27352 | 0.0584329 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.6873 | −0.489336 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.56415 | −0.345615 | −0.172807 | − | 0.984956i | \(-0.555284\pi\) | ||||
−0.172807 | + | 0.984956i | \(0.555284\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.99214 | −0.273218 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7570 | 0.580463 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.2701 | 1.32909 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.7371 | −1.48346 | −0.741729 | − | 0.670700i | \(-0.765994\pi\) | ||||
−0.741729 | + | 0.670700i | \(0.765994\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6727 | −0.799188 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.8368 | 0.940349 | 0.470175 | − | 0.882573i | \(-0.344191\pi\) | ||||
0.470175 | + | 0.882573i | \(0.344191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.54976 | 0.204911 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.41065 | 0.378031 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.14384 | −0.365301 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.136028 | −0.00608946 | −0.00304473 | − | 0.999995i | \(-0.500969\pi\) | ||||
−0.00304473 | + | 0.999995i | \(0.500969\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 46.2941 | 2.06827 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.33516 | −0.237883 | −0.118942 | − | 0.992901i | \(-0.537950\pi\) | ||||
−0.118942 | + | 0.992901i | \(0.537950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.97857 | 0.0880450 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.1243 | 0.804928 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.5868 | 0.868169 | 0.434085 | − | 0.900872i | \(-0.357072\pi\) | ||||
0.434085 | + | 0.900872i | \(0.357072\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8327 | 0.567686 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.59437 | −0.114544 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −23.0433 | −1.01541 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.41703 | −0.0623211 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.89149 | −0.434188 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.41975 | −0.193633 | −0.0968164 | − | 0.995302i | \(-0.530866\pi\) | ||||
−0.0968164 | + | 0.995302i | \(0.530866\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.5492 | −1.59818 | −0.799091 | − | 0.601209i | \(-0.794686\pi\) | ||||
−0.799091 | + | 0.601209i | \(0.794686\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.77138 | 0.0773092 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.45573 | 0.194095 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.98774 | −0.173380 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −24.4445 | −1.06080 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.27559 | −0.185197 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.50997 | 0.151749 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 36.5875 | 1.57887 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.81990 | −0.379900 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.1501 | −1.46823 | −0.734114 | − | 0.679026i | \(-0.762402\pi\) | ||||
−0.734114 | + | 0.679026i | \(0.762402\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.83169 | −0.250262 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.6312 | 1.69761 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.5083 | 1.64650 | 0.823248 | − | 0.567681i | \(-0.192159\pi\) | ||||
0.823248 | + | 0.567681i | \(0.192159\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.6248 | −0.709530 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.39852 | −0.144782 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.6159 | 0.579006 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.8220 | −0.544265 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.6617 | 1.25681 | 0.628403 | − | 0.777888i | \(-0.283709\pi\) | ||||
0.628403 | + | 0.777888i | \(0.283709\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.8277 | 0.965507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.6885 | −0.451268 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.7633 | −1.71797 | −0.858984 | − | 0.512002i | \(-0.828904\pi\) | ||||
−0.858984 | + | 0.512002i | \(0.828904\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −36.7176 | −1.54472 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.8861 | −0.541166 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.6807 | −1.28620 | −0.643100 | − | 0.765782i | \(-0.722352\pi\) | ||||
−0.643100 | + | 0.765782i | \(0.722352\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8969 | 0.665263 | 0.332631 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332631 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.83883 | 0.118594 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.63996 | 0.110094 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3106 | 1.22022 | 0.610109 | − | 0.792317i | \(-0.291126\pi\) | ||||
0.610109 | + | 0.792317i | \(0.291126\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −29.1998 | −1.21350 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.20565 | −0.132993 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.01251 | −0.290429 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.8803 | −0.491188 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.2565 | −0.505880 | −0.252940 | − | 0.967482i | \(-0.581398\pi\) | ||||
−0.252940 | + | 0.967482i | \(0.581398\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.32829 | −0.137140 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.1154 | −0.580632 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.7824 | 0.853429 | 0.426715 | − | 0.904386i | \(-0.359671\pi\) | ||||
0.426715 | + | 0.904386i | \(0.359671\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.38258 | 0.302656 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 36.7820 | 1.50539 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.3717 | −1.24095 | −0.620476 | − | 0.784225i | \(-0.713061\pi\) | ||||
−0.620476 | + | 0.784225i | \(0.713061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.4762 | 1.36552 | 0.682762 | − | 0.730641i | \(-0.260779\pi\) | ||||
0.682762 | + | 0.730641i | \(0.260779\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.7248 | −0.925427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −17.5408 | −0.713135 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 44.4310 | 1.80340 | 0.901699 | − | 0.432365i | \(-0.142321\pi\) | ||||
0.901699 | + | 0.432365i | \(0.142321\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.72712 | −0.191553 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.00160 | 0.0809759 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.0681 | −0.891321 | −0.445660 | − | 0.895202i | \(-0.647031\pi\) | ||||
−0.445660 | + | 0.895202i | \(0.647031\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.14895 | −0.368921 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.50264 | −0.221528 | −0.110764 | − | 0.993847i | \(-0.535330\pi\) | ||||
−0.110764 | + | 0.993847i | \(0.535330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.2191 | −0.410742 | −0.205371 | − | 0.978684i | \(-0.565840\pi\) | ||||
−0.205371 | + | 0.978684i | \(0.565840\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.37805 | −0.215814 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.8682 | −0.435425 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6062 | −0.864247 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.98395 | 0.318848 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.36240 | 0.293558 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.94835 | 0.0775628 | 0.0387814 | − | 0.999248i | \(-0.487652\pi\) | ||||
0.0387814 | + | 0.999248i | \(0.487652\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.2359 | 1.00304 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.1049 | 1.23436 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 12.4583 | 0.493617 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −16.1022 | −0.636991 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.8027 | 1.45362 | 0.726810 | − | 0.686839i | \(-0.241002\pi\) | ||||
0.726810 | + | 0.686839i | \(0.241002\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −35.6800 | −1.40708 | −0.703540 | − | 0.710656i | \(-0.748398\pi\) | ||||
−0.703540 | + | 0.710656i | \(0.748398\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 48.8468 | 1.92334 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.3499 | −1.31112 | −0.655560 | − | 0.755143i | \(-0.727567\pi\) | ||||
−0.655560 | + | 0.755143i | \(0.727567\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −16.0394 | −0.629601 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.62943 | −0.181442 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.1440 | −1.21876 | −0.609379 | − | 0.792879i | \(-0.708581\pi\) | ||||
−0.609379 | + | 0.792879i | \(0.708581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.62631 | 0.376131 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.3731 | 0.989899 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.4428 | 0.523659 | 0.261829 | − | 0.965114i | \(-0.415674\pi\) | ||||
0.261829 | + | 0.965114i | \(0.415674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.8663 | −1.35614 | −0.678071 | − | 0.734996i | \(-0.737184\pi\) | ||||
−0.678071 | + | 0.734996i | \(0.737184\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.0978 | 0.586348 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.51455 | −0.213845 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.04503 | −0.272784 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 48.0441 | 1.85749 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.9085 | −0.421117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.97888 | 0.269016 | 0.134508 | − | 0.990913i | \(-0.457055\pi\) | ||||
0.134508 | + | 0.990913i | \(0.457055\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.746771 | −0.0287432 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.63867 | 0.139846 | 0.0699228 | − | 0.997552i | \(-0.477725\pi\) | ||||
0.0699228 | + | 0.997552i | \(0.477725\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4620 | 0.670132 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.3026 | −1.39112 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.6467 | 0.407385 | 0.203693 | − | 0.979035i | \(-0.434706\pi\) | ||||
0.203693 | + | 0.979035i | \(0.434706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.5230 | 1.70114 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 55.5854 | 2.12072 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.90535 | 0.377364 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.93492 | 0.0736079 | 0.0368039 | − | 0.999323i | \(-0.488282\pi\) | ||||
0.0368039 | + | 0.999323i | \(0.488282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.01765 | 0.190605 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.4104 | −0.850074 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.25332 | 0.198984 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.71531 | −0.367467 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.1282 | −0.533615 | −0.266807 | − | 0.963750i | \(-0.585969\pi\) | ||||
−0.266807 | + | 0.963750i | \(0.585969\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.49947 | −0.207416 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.28303 | 0.161308 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.18038 | 0.0443927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −25.0245 | −0.939814 | −0.469907 | − | 0.882716i | \(-0.655713\pi\) | ||||
−0.469907 | + | 0.882716i | \(0.655713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.9216 | 1.00964 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.89943 | −0.258386 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.79530 | −0.291528 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33.3610 | 1.24589 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.05269 | −0.225727 | −0.112864 | − | 0.993610i | \(-0.536002\pi\) | ||||
−0.112864 | + | 0.993610i | \(0.536002\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.7472 | −0.511974 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.6769 | 1.77312 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.978240 | −0.0363309 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.89602 | 0.107407 | 0.0537036 | − | 0.998557i | \(-0.482897\pi\) | ||||
0.0537036 | + | 0.998557i | \(0.482897\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −16.8224 | −0.623052 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.0478 | −1.03738 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 33.5724 | 1.24003 | 0.620013 | − | 0.784591i | \(-0.287127\pi\) | ||||
0.620013 | + | 0.784591i | \(0.287127\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.6584 | 0.983311 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.9110 | −0.549255 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −45.9758 | −1.69125 | −0.845623 | − | 0.533780i | \(-0.820771\pi\) | ||||
−0.845623 | + | 0.533780i | \(0.820771\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.2775 | −0.414290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.2913 | 0.707730 | 0.353865 | − | 0.935297i | \(-0.384867\pi\) | ||||
0.353865 | + | 0.935297i | \(0.384867\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.4345 | 0.492201 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.33828 | −0.231905 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.09399 | 0.0765127 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.4782 | −0.382356 | −0.191178 | − | 0.981555i | \(-0.561231\pi\) | ||||
−0.191178 | + | 0.981555i | \(0.561231\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58.3353 | 2.12585 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.85524 | 0.358669 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.99185 | −0.290469 | −0.145234 | − | 0.989397i | \(-0.546394\pi\) | ||||
−0.145234 | + | 0.989397i | \(0.546394\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.5505 | 0.600744 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.2015 | −1.16730 | −0.583651 | − | 0.812005i | \(-0.698376\pi\) | ||||
−0.583651 | + | 0.812005i | \(0.698376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.6433 | 0.855945 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.5970 | 0.527755 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 22.6560 | 0.818062 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 53.4278 | 1.92665 | 0.963327 | − | 0.268330i | \(-0.0864716\pi\) | ||||
0.963327 | + | 0.268330i | \(0.0864716\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −48.4341 | −1.74431 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 23.3664 | 0.840431 | 0.420215 | − | 0.907424i | \(-0.361955\pi\) | ||||
0.420215 | + | 0.907424i | \(0.361955\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.958023 | −0.0344132 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.64940 | −0.274421 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.92406 | −0.140594 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.5655 | −0.378064 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.99284 | 0.0712184 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.8361 | 1.38612 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.2603 | −0.472680 | −0.236340 | − | 0.971670i | \(-0.575948\pi\) | ||||
−0.236340 | + | 0.971670i | \(0.575948\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −41.0648 | −1.46194 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.9051 | −0.778856 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.4085 | 0.547172 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 21.1955 | 0.751728 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.1666 | 1.63531 | 0.817653 | − | 0.575712i | \(-0.195275\pi\) | ||||
0.817653 | + | 0.575712i | \(0.195275\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.45931 | −0.0870042 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −21.4888 | −0.759269 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.6487 | 0.587520 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4315 | −0.402906 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 31.7809 | 1.11874 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.37430 | 0.294425 | 0.147212 | − | 0.989105i | \(-0.452970\pi\) | ||||
0.147212 | + | 0.989105i | \(0.452970\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.15993 | −0.0407306 | −0.0203653 | − | 0.999793i | \(-0.506483\pi\) | ||||
−0.0203653 | + | 0.999793i | \(0.506483\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −66.0999 | −2.31822 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.8364 | 0.554726 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.9508 | 0.732975 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.08756 | −0.247659 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.9098 | 0.625055 | 0.312527 | − | 0.949909i | \(-0.398824\pi\) | ||||
0.312527 | + | 0.949909i | \(0.398824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.8323 | −1.14446 | −0.572232 | − | 0.820092i | \(-0.693922\pi\) | ||||
−0.572232 | + | 0.820092i | \(0.693922\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.29812 | 0.0800103 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.3422 | 1.05510 | 0.527552 | − | 0.849523i | \(-0.323110\pi\) | ||||
0.527552 | + | 0.849523i | \(0.323110\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5415 | 0.366121 | 0.183061 | − | 0.983102i | \(-0.441400\pi\) | ||||
0.183061 | + | 0.983102i | \(0.441400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.51702 | −0.0526247 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −15.3072 | −0.530365 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −41.4838 | −1.43561 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.95166 | 0.0674592 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.1469 | 0.937215 | 0.468608 | − | 0.883406i | \(-0.344756\pi\) | ||||
0.468608 | + | 0.883406i | \(0.344756\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3895 | −0.909981 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −57.1956 | −1.96992 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −16.2411 | −0.558710 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.4645 | −0.359566 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.8001 | 0.439297 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.4002 | −0.390794 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.6156 | 1.32217 | 0.661086 | − | 0.750310i | \(-0.270096\pi\) | ||||
0.661086 | + | 0.750310i | \(0.270096\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10.9035 | −0.372891 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.7952 | −0.812830 | −0.406415 | − | 0.913689i | \(-0.633221\pi\) | ||||
−0.406415 | + | 0.913689i | \(0.633221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.0722 | −1.36724 | −0.683622 | − | 0.729836i | \(-0.739596\pi\) | ||||
−0.683622 | + | 0.729836i | \(0.739596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.45811 | −0.186012 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.1693 | −1.84394 | −0.921972 | − | 0.387257i | \(-0.873423\pi\) | ||||
−0.921972 | + | 0.387257i | \(0.873423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.86371 | 0.301375 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.2195 | 0.720650 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.6647 | 0.599235 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.0622 | 0.713665 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 34.5263 | 1.16854 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −14.6959 | −0.496812 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.8631 | −0.974636 | −0.487318 | − | 0.873224i | \(-0.662025\pi\) | ||||
−0.487318 | + | 0.873224i | \(0.662025\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 61.0959 | 2.06071 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0933 | 0.575887 | 0.287943 | − | 0.957647i | \(-0.407028\pi\) | ||||
0.287943 | + | 0.957647i | \(0.407028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.46810 | −0.150363 | −0.0751817 | − | 0.997170i | \(-0.523954\pi\) | ||||
−0.0751817 | + | 0.997170i | \(0.523954\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 48.4795 | 1.62962 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.1368 | 1.41481 | 0.707407 | − | 0.706807i | \(-0.249865\pi\) | ||||
0.707407 | + | 0.706807i | \(0.249865\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.5567 | 0.622371 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.7180 | −0.560074 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.83703 | 0.0614737 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.7858 | −1.09591 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −23.3779 | −0.780567 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.55659 | 0.0852672 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.1705 | −0.405457 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.1412 | 0.969757 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.22574 | 0.173710 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.0919 | −1.59686 | −0.798432 | − | 0.602084i | \(-0.794337\pi\) | ||||
−0.798432 | + | 0.602084i | \(0.794337\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.33387 | 0.0774095 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 36.4297 | 1.20697 | 0.603484 | − | 0.797375i | \(-0.293779\pi\) | ||||
0.603484 | + | 0.797375i | \(0.293779\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.15890 | −0.137639 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 32.9712 | 1.08999 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.74289 | 0.189647 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6771 | 0.418180 | 0.209090 | − | 0.977896i | \(-0.432950\pi\) | ||||
0.209090 | + | 0.977896i | \(0.432950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 76.2430 | 2.51229 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.9241 | 0.491231 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.58298 | −0.0520481 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −27.1813 | −0.892751 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.4959 | −1.75514 | −0.877572 | − | 0.479445i | \(-0.840838\pi\) | ||||
−0.877572 | + | 0.479445i | \(0.840838\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.4340 | 0.374735 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 53.8387 | 1.76260 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.57789 | 0.313231 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.4650 | −0.341875 | −0.170938 | − | 0.985282i | \(-0.554680\pi\) | ||||
−0.170938 | + | 0.985282i | \(0.554680\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.0311 | 2.02431 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.13648 | −0.102246 | −0.0511232 | − | 0.998692i | \(-0.516280\pi\) | ||||
−0.0511232 | + | 0.998692i | \(0.516280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.13444 | −0.264894 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.23365 | 0.105191 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.84338 | −0.157389 | −0.0786943 | − | 0.996899i | \(-0.525075\pi\) | ||||
−0.0786943 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.5167 | −0.763385 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 57.8491 | 1.87589 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.5101 | 0.858748 | 0.429374 | − | 0.903127i | \(-0.358734\pi\) | ||||
0.429374 | + | 0.903127i | \(0.358734\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.54386 | −0.0823174 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.13280 | −0.198245 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 26.5617 | 0.857721 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.4962 | −0.919234 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.14028 | 0.133419 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.1658 | 0.842306 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.0463 | 0.355225 | 0.177612 | − | 0.984101i | \(-0.443163\pi\) | ||||
0.177612 | + | 0.984101i | \(0.443163\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.8564 | 0.445133 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.3228 | 1.16565 | 0.582827 | − | 0.812596i | \(-0.301946\pi\) | ||||
0.582827 | + | 0.812596i | \(0.301946\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.3697 | −0.428611 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.24615 | −0.103960 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 12.0389 | 0.385157 | 0.192579 | − | 0.981282i | \(-0.438315\pi\) | ||||
0.192579 | + | 0.981282i | \(0.438315\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1000 | −0.450638 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 46.7480 | 1.49255 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.2927 | 1.47651 | 0.738254 | − | 0.674523i | \(-0.235651\pi\) | ||||
0.738254 | + | 0.674523i | \(0.235651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.6488 | 0.403023 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.55518 | 0.0813323 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 43.4303 | 1.38100 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.4998 | 0.905325 | 0.452663 | − | 0.891682i | \(-0.350474\pi\) | ||||
0.452663 | + | 0.891682i | \(0.350474\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −73.8378 | −2.34317 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.9601 | −1.04491 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.9609 | −0.505488 | −0.252744 | − | 0.967533i | \(-0.581333\pi\) | ||||
−0.252744 | + | 0.967533i | \(0.581333\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.22481 | 0.102028 |
(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 | 6044.2.a.a.1.13 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.a.1.13 | ✓ | 63 | 1.1 | even | 1 | trivial |