Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} + \cdots - 375 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.26764\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.26764 | −1.01412 | −0.507059 | − | 0.861911i | \(-0.669267\pi\) | ||||
−0.507059 | + | 0.861911i | \(0.669267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.397853 | −0.150374 | −0.0751872 | − | 0.997169i | \(-0.523955\pi\) | ||||
−0.0751872 | + | 0.997169i | \(0.523955\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.26764 | 0.717090 | ||||||||
\(11\) | 3.96969 | 1.19691 | 0.598453 | − | 0.801158i | \(-0.295782\pi\) | ||||
0.598453 | + | 0.801158i | \(0.295782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.823528 | 0.228406 | 0.114203 | − | 0.993457i | \(-0.463569\pi\) | ||||
0.114203 | + | 0.993457i | \(0.463569\pi\) | |||||||
\(14\) | 0.397853 | 0.106331 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.85300 | −1.66210 | −0.831049 | − | 0.556200i | \(-0.812259\pi\) | ||||
−0.831049 | + | 0.556200i | \(0.812259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.38692 | −1.92409 | −0.962045 | − | 0.272890i | \(-0.912020\pi\) | ||||
−0.962045 | + | 0.272890i | \(0.912020\pi\) | |||||||
\(20\) | −2.26764 | −0.507059 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.96969 | −0.846340 | ||||||||
\(23\) | 8.28167 | 1.72685 | 0.863424 | − | 0.504479i | \(-0.168315\pi\) | ||||
0.863424 | + | 0.504479i | \(0.168315\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.142177 | 0.0284355 | ||||||||
\(26\) | −0.823528 | −0.161507 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.397853 | −0.0751872 | ||||||||
\(29\) | 8.78572 | 1.63147 | 0.815734 | − | 0.578428i | \(-0.196333\pi\) | ||||
0.815734 | + | 0.578428i | \(0.196333\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00807 | 0.719871 | 0.359936 | − | 0.932977i | \(-0.382799\pi\) | ||||
0.359936 | + | 0.932977i | \(0.382799\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.85300 | 1.17528 | ||||||||
\(35\) | 0.902187 | 0.152497 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.694576 | 0.114188 | 0.0570938 | − | 0.998369i | \(-0.481817\pi\) | ||||
0.0570938 | + | 0.998369i | \(0.481817\pi\) | |||||||
\(38\) | 8.38692 | 1.36054 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.26764 | 0.358545 | ||||||||
\(41\) | 9.11675 | 1.42380 | 0.711899 | − | 0.702282i | \(-0.247836\pi\) | ||||
0.711899 | + | 0.702282i | \(0.247836\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.24158 | −1.25683 | −0.628414 | − | 0.777879i | \(-0.716296\pi\) | ||||
−0.628414 | + | 0.777879i | \(0.716296\pi\) | |||||||
\(44\) | 3.96969 | 0.598453 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.28167 | −1.22107 | ||||||||
\(47\) | 1.58117 | 0.230638 | 0.115319 | − | 0.993329i | \(-0.463211\pi\) | ||||
0.115319 | + | 0.993329i | \(0.463211\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.84171 | −0.977388 | ||||||||
\(50\) | −0.142177 | −0.0201069 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.823528 | 0.114203 | ||||||||
\(53\) | −7.80173 | −1.07165 | −0.535825 | − | 0.844329i | \(-0.679999\pi\) | ||||
−0.535825 | + | 0.844329i | \(0.679999\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.00181 | −1.21380 | ||||||||
\(56\) | 0.397853 | 0.0531654 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.78572 | −1.15362 | ||||||||
\(59\) | −10.9286 | −1.42278 | −0.711390 | − | 0.702797i | \(-0.751934\pi\) | ||||
−0.711390 | + | 0.702797i | \(0.751934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.40891 | −1.07665 | −0.538325 | − | 0.842737i | \(-0.680943\pi\) | ||||
−0.538325 | + | 0.842737i | \(0.680943\pi\) | |||||||
\(62\) | −4.00807 | −0.509026 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.86746 | −0.231630 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.4002 | −1.39276 | −0.696379 | − | 0.717674i | \(-0.745207\pi\) | ||||
−0.696379 | + | 0.717674i | \(0.745207\pi\) | |||||||
\(68\) | −6.85300 | −0.831049 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.902187 | −0.107832 | ||||||||
\(71\) | 14.7645 | 1.75223 | 0.876113 | − | 0.482105i | \(-0.160128\pi\) | ||||
0.876113 | + | 0.482105i | \(0.160128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.27672 | 0.734635 | 0.367317 | − | 0.930096i | \(-0.380276\pi\) | ||||
0.367317 | + | 0.930096i | \(0.380276\pi\) | |||||||
\(74\) | −0.694576 | −0.0807428 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −8.38692 | −0.962045 | ||||||||
\(77\) | −1.57935 | −0.179984 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.64978 | 1.08569 | 0.542843 | − | 0.839834i | \(-0.317348\pi\) | ||||
0.542843 | + | 0.839834i | \(0.317348\pi\) | |||||||
\(80\) | −2.26764 | −0.253530 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.11675 | −1.00678 | ||||||||
\(83\) | 8.76097 | 0.961641 | 0.480820 | − | 0.876819i | \(-0.340339\pi\) | ||||
0.480820 | + | 0.876819i | \(0.340339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15.5401 | 1.68556 | ||||||||
\(86\) | 8.24158 | 0.888712 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.96969 | −0.423170 | ||||||||
\(89\) | −9.24953 | −0.980448 | −0.490224 | − | 0.871596i | \(-0.663085\pi\) | ||||
−0.490224 | + | 0.871596i | \(0.663085\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.327643 | −0.0343464 | ||||||||
\(92\) | 8.28167 | 0.863424 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.58117 | −0.163086 | ||||||||
\(95\) | 19.0185 | 1.95125 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.05434 | −0.817794 | −0.408897 | − | 0.912580i | \(-0.634087\pi\) | ||||
−0.408897 | + | 0.912580i | \(0.634087\pi\) | |||||||
\(98\) | 6.84171 | 0.691117 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.142177 | 0.0142177 | ||||||||
\(101\) | −9.77230 | −0.972380 | −0.486190 | − | 0.873853i | \(-0.661614\pi\) | ||||
−0.486190 | + | 0.873853i | \(0.661614\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.13814 | 0.210678 | 0.105339 | − | 0.994436i | \(-0.466407\pi\) | ||||
0.105339 | + | 0.994436i | \(0.466407\pi\) | |||||||
\(104\) | −0.823528 | −0.0807536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.80173 | 0.757771 | ||||||||
\(107\) | −9.52464 | −0.920782 | −0.460391 | − | 0.887716i | \(-0.652291\pi\) | ||||
−0.460391 | + | 0.887716i | \(0.652291\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.2092 | 1.64834 | 0.824170 | − | 0.566343i | \(-0.191642\pi\) | ||||
0.824170 | + | 0.566343i | \(0.191642\pi\) | |||||||
\(110\) | 9.00181 | 0.858288 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.397853 | −0.0375936 | ||||||||
\(113\) | −0.853149 | −0.0802575 | −0.0401288 | − | 0.999195i | \(-0.512777\pi\) | ||||
−0.0401288 | + | 0.999195i | \(0.512777\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −18.7798 | −1.75123 | ||||||||
\(116\) | 8.78572 | 0.815734 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.9286 | 1.00606 | ||||||||
\(119\) | 2.72649 | 0.249937 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.75840 | 0.432582 | ||||||||
\(122\) | 8.40891 | 0.761307 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00807 | 0.359936 | ||||||||
\(125\) | 11.0158 | 0.985281 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3267 | 0.916349 | 0.458175 | − | 0.888862i | \(-0.348503\pi\) | ||||
0.458175 | + | 0.888862i | \(0.348503\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.86746 | 0.163787 | ||||||||
\(131\) | 7.41831 | 0.648141 | 0.324070 | − | 0.946033i | \(-0.394949\pi\) | ||||
0.324070 | + | 0.946033i | \(0.394949\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.33676 | 0.289334 | ||||||||
\(134\) | 11.4002 | 0.984829 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.85300 | 0.587640 | ||||||||
\(137\) | 15.1282 | 1.29249 | 0.646245 | − | 0.763130i | \(-0.276338\pi\) | ||||
0.646245 | + | 0.763130i | \(0.276338\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.7814 | −1.16892 | −0.584460 | − | 0.811423i | \(-0.698694\pi\) | ||||
−0.584460 | + | 0.811423i | \(0.698694\pi\) | |||||||
\(140\) | 0.902187 | 0.0762487 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.7645 | −1.23901 | ||||||||
\(143\) | 3.26915 | 0.273380 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −19.9228 | −1.65450 | ||||||||
\(146\) | −6.27672 | −0.519465 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.694576 | 0.0570938 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9871 | 1.38239 | 0.691197 | − | 0.722666i | \(-0.257084\pi\) | ||||
0.691197 | + | 0.722666i | \(0.257084\pi\) | |||||||
\(152\) | 8.38692 | 0.680269 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.57935 | 0.127268 | ||||||||
\(155\) | −9.08885 | −0.730034 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.17392 | 0.0936891 | 0.0468445 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468445 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(158\) | −9.64978 | −0.767695 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.26764 | 0.179272 | ||||||||
\(161\) | −3.29489 | −0.259674 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.5592 | 1.37534 | 0.687670 | − | 0.726023i | \(-0.258633\pi\) | ||||
0.687670 | + | 0.726023i | \(0.258633\pi\) | |||||||
\(164\) | 9.11675 | 0.711899 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.76097 | −0.679983 | ||||||||
\(167\) | 4.50119 | 0.348312 | 0.174156 | − | 0.984718i | \(-0.444280\pi\) | ||||
0.174156 | + | 0.984718i | \(0.444280\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.3218 | −0.947831 | ||||||||
\(170\) | −15.5401 | −1.19187 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −8.24158 | −0.628414 | ||||||||
\(173\) | −6.31389 | −0.480036 | −0.240018 | − | 0.970768i | \(-0.577153\pi\) | ||||
−0.240018 | + | 0.970768i | \(0.577153\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.0565658 | −0.00427597 | ||||||||
\(176\) | 3.96969 | 0.299226 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.24953 | 0.693282 | ||||||||
\(179\) | 7.46421 | 0.557901 | 0.278951 | − | 0.960305i | \(-0.410013\pi\) | ||||
0.278951 | + | 0.960305i | \(0.410013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.8449 | 1.17774 | 0.588872 | − | 0.808226i | \(-0.299572\pi\) | ||||
0.588872 | + | 0.808226i | \(0.299572\pi\) | |||||||
\(182\) | 0.327643 | 0.0242865 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.28167 | −0.610533 | ||||||||
\(185\) | −1.57505 | −0.115800 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −27.2043 | −1.98937 | ||||||||
\(188\) | 1.58117 | 0.115319 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −19.0185 | −1.37975 | ||||||||
\(191\) | −16.6457 | −1.20444 | −0.602221 | − | 0.798330i | \(-0.705717\pi\) | ||||
−0.602221 | + | 0.798330i | \(0.705717\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.73110 | −0.700460 | −0.350230 | − | 0.936664i | \(-0.613897\pi\) | ||||
−0.350230 | + | 0.936664i | \(0.613897\pi\) | |||||||
\(194\) | 8.05434 | 0.578268 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.84171 | −0.488694 | ||||||||
\(197\) | 2.03744 | 0.145161 | 0.0725806 | − | 0.997363i | \(-0.476877\pi\) | ||||
0.0725806 | + | 0.997363i | \(0.476877\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.4304 | −1.44827 | −0.724137 | − | 0.689656i | \(-0.757762\pi\) | ||||
−0.724137 | + | 0.689656i | \(0.757762\pi\) | |||||||
\(200\) | −0.142177 | −0.0100535 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.77230 | 0.687577 | ||||||||
\(203\) | −3.49543 | −0.245331 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.6735 | −1.44390 | ||||||||
\(206\) | −2.13814 | −0.148972 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.823528 | 0.0571014 | ||||||||
\(209\) | −33.2934 | −2.30295 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9296 | 1.02780 | 0.513898 | − | 0.857851i | \(-0.328201\pi\) | ||||
0.513898 | + | 0.857851i | \(0.328201\pi\) | |||||||
\(212\) | −7.80173 | −0.535825 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.52464 | 0.651091 | ||||||||
\(215\) | 18.6889 | 1.27457 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.59463 | −0.108250 | ||||||||
\(218\) | −17.2092 | −1.16555 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.00181 | −0.606902 | ||||||||
\(221\) | −5.64364 | −0.379632 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.1349 | −1.08047 | −0.540235 | − | 0.841514i | \(-0.681665\pi\) | ||||
−0.540235 | + | 0.841514i | \(0.681665\pi\) | |||||||
\(224\) | 0.397853 | 0.0265827 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.853149 | 0.0567506 | ||||||||
\(227\) | −19.4983 | −1.29415 | −0.647074 | − | 0.762427i | \(-0.724008\pi\) | ||||
−0.647074 | + | 0.762427i | \(0.724008\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.0086 | −0.727467 | −0.363734 | − | 0.931503i | \(-0.618498\pi\) | ||||
−0.363734 | + | 0.931503i | \(0.618498\pi\) | |||||||
\(230\) | 18.7798 | 1.23830 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.78572 | −0.576811 | ||||||||
\(233\) | −28.0188 | −1.83558 | −0.917788 | − | 0.397071i | \(-0.870027\pi\) | ||||
−0.917788 | + | 0.397071i | \(0.870027\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.58553 | −0.233894 | ||||||||
\(236\) | −10.9286 | −0.711390 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.72649 | −0.176732 | ||||||||
\(239\) | 23.4730 | 1.51834 | 0.759172 | − | 0.650890i | \(-0.225604\pi\) | ||||
0.759172 | + | 0.650890i | \(0.225604\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.6148 | 1.07025 | 0.535126 | − | 0.844772i | \(-0.320264\pi\) | ||||
0.535126 | + | 0.844772i | \(0.320264\pi\) | |||||||
\(242\) | −4.75840 | −0.305882 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.40891 | −0.538325 | ||||||||
\(245\) | 15.5145 | 0.991186 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.90686 | −0.439473 | ||||||||
\(248\) | −4.00807 | −0.254513 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.0158 | −0.696699 | ||||||||
\(251\) | 21.7503 | 1.37287 | 0.686434 | − | 0.727193i | \(-0.259175\pi\) | ||||
0.686434 | + | 0.727193i | \(0.259175\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.8756 | 2.06687 | ||||||||
\(254\) | −10.3267 | −0.647957 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 25.0548 | 1.56288 | 0.781438 | − | 0.623983i | \(-0.214486\pi\) | ||||
0.781438 | + | 0.623983i | \(0.214486\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.276339 | −0.0171709 | ||||||||
\(260\) | −1.86746 | −0.115815 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.41831 | −0.458305 | ||||||||
\(263\) | −1.10598 | −0.0681979 | −0.0340989 | − | 0.999418i | \(-0.510856\pi\) | ||||
−0.0340989 | + | 0.999418i | \(0.510856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.6915 | 1.08678 | ||||||||
\(266\) | −3.33676 | −0.204590 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −11.4002 | −0.696379 | ||||||||
\(269\) | −14.9971 | −0.914389 | −0.457195 | − | 0.889367i | \(-0.651146\pi\) | ||||
−0.457195 | + | 0.889367i | \(0.651146\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.6135 | 1.55591 | 0.777955 | − | 0.628320i | \(-0.216257\pi\) | ||||
0.777955 | + | 0.628320i | \(0.216257\pi\) | |||||||
\(272\) | −6.85300 | −0.415524 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.1282 | −0.913929 | ||||||||
\(275\) | 0.564399 | 0.0340346 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.2735 | −1.03786 | −0.518932 | − | 0.854815i | \(-0.673670\pi\) | ||||
−0.518932 | + | 0.854815i | \(0.673670\pi\) | |||||||
\(278\) | 13.7814 | 0.826551 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.902187 | −0.0539160 | ||||||||
\(281\) | 3.74260 | 0.223265 | 0.111632 | − | 0.993750i | \(-0.464392\pi\) | ||||
0.111632 | + | 0.993750i | \(0.464392\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.91599 | −0.470557 | −0.235278 | − | 0.971928i | \(-0.575600\pi\) | ||||
−0.235278 | + | 0.971928i | \(0.575600\pi\) | |||||||
\(284\) | 14.7645 | 0.876113 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.26915 | −0.193309 | ||||||||
\(287\) | −3.62713 | −0.214103 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 29.9636 | 1.76257 | ||||||||
\(290\) | 19.9228 | 1.16991 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.27672 | 0.367317 | ||||||||
\(293\) | −26.0968 | −1.52459 | −0.762295 | − | 0.647230i | \(-0.775927\pi\) | ||||
−0.762295 | + | 0.647230i | \(0.775927\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.7821 | 1.44287 | ||||||||
\(296\) | −0.694576 | −0.0403714 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 6.82019 | 0.394422 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.27894 | 0.188995 | ||||||||
\(302\) | −16.9871 | −0.977500 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.38692 | −0.481023 | ||||||||
\(305\) | 19.0684 | 1.09185 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.74645 | 0.499186 | 0.249593 | − | 0.968351i | \(-0.419703\pi\) | ||||
0.249593 | + | 0.968351i | \(0.419703\pi\) | |||||||
\(308\) | −1.57935 | −0.0899920 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.08885 | 0.516212 | ||||||||
\(311\) | 11.6816 | 0.662403 | 0.331201 | − | 0.943560i | \(-0.392546\pi\) | ||||
0.331201 | + | 0.943560i | \(0.392546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.9981 | 1.35645 | 0.678226 | − | 0.734854i | \(-0.262749\pi\) | ||||
0.678226 | + | 0.734854i | \(0.262749\pi\) | |||||||
\(314\) | −1.17392 | −0.0662482 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.64978 | 0.542843 | ||||||||
\(317\) | 30.2788 | 1.70063 | 0.850314 | − | 0.526276i | \(-0.176412\pi\) | ||||
0.850314 | + | 0.526276i | \(0.176412\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.8765 | 1.95271 | ||||||||
\(320\) | −2.26764 | −0.126765 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.29489 | 0.183617 | ||||||||
\(323\) | 57.4755 | 3.19803 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.117087 | 0.00649482 | ||||||||
\(326\) | −17.5592 | −0.972513 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.11675 | −0.503388 | ||||||||
\(329\) | −0.629075 | −0.0346820 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.27876 | 0.235182 | 0.117591 | − | 0.993062i | \(-0.462483\pi\) | ||||
0.117591 | + | 0.993062i | \(0.462483\pi\) | |||||||
\(332\) | 8.76097 | 0.480820 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.50119 | −0.246294 | ||||||||
\(335\) | 25.8516 | 1.41242 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.8901 | −1.24690 | −0.623450 | − | 0.781863i | \(-0.714270\pi\) | ||||
−0.623450 | + | 0.781863i | \(0.714270\pi\) | |||||||
\(338\) | 12.3218 | 0.670218 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.5401 | 0.842781 | ||||||||
\(341\) | 15.9108 | 0.861618 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.50697 | 0.297349 | ||||||||
\(344\) | 8.24158 | 0.444356 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.31389 | 0.339437 | ||||||||
\(347\) | 17.5781 | 0.943645 | 0.471822 | − | 0.881694i | \(-0.343596\pi\) | ||||
0.471822 | + | 0.881694i | \(0.343596\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.75698 | −0.361693 | −0.180846 | − | 0.983511i | \(-0.557884\pi\) | ||||
−0.180846 | + | 0.983511i | \(0.557884\pi\) | |||||||
\(350\) | 0.0565658 | 0.00302357 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.96969 | −0.211585 | ||||||||
\(353\) | 3.34841 | 0.178218 | 0.0891090 | − | 0.996022i | \(-0.471598\pi\) | ||||
0.0891090 | + | 0.996022i | \(0.471598\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.4806 | −1.77696 | ||||||||
\(356\) | −9.24953 | −0.490224 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.46421 | −0.394496 | ||||||||
\(359\) | 19.7588 | 1.04283 | 0.521415 | − | 0.853304i | \(-0.325405\pi\) | ||||
0.521415 | + | 0.853304i | \(0.325405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 51.3403 | 2.70212 | ||||||||
\(362\) | −15.8449 | −0.832791 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.327643 | −0.0171732 | ||||||||
\(365\) | −14.2333 | −0.745006 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.61191 | 0.292939 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(368\) | 8.28167 | 0.431712 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.57505 | 0.0818827 | ||||||||
\(371\) | 3.10394 | 0.161149 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.40480 | 0.331628 | 0.165814 | − | 0.986157i | \(-0.446975\pi\) | ||||
0.165814 | + | 0.986157i | \(0.446975\pi\) | |||||||
\(374\) | 27.2043 | 1.40670 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.58117 | −0.0815428 | ||||||||
\(377\) | 7.23529 | 0.372636 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.1296 | −0.879891 | −0.439945 | − | 0.898025i | \(-0.645002\pi\) | ||||
−0.439945 | + | 0.898025i | \(0.645002\pi\) | |||||||
\(380\) | 19.0185 | 0.975627 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.6457 | 0.851669 | ||||||||
\(383\) | 22.0618 | 1.12730 | 0.563652 | − | 0.826012i | \(-0.309396\pi\) | ||||
0.563652 | + | 0.826012i | \(0.309396\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.58140 | 0.182525 | ||||||||
\(386\) | 9.73110 | 0.495300 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.05434 | −0.408897 | ||||||||
\(389\) | −15.0190 | −0.761494 | −0.380747 | − | 0.924679i | \(-0.624333\pi\) | ||||
−0.380747 | + | 0.924679i | \(0.624333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −56.7543 | −2.87019 | ||||||||
\(392\) | 6.84171 | 0.345559 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.03744 | −0.102645 | ||||||||
\(395\) | −21.8822 | −1.10101 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.26395 | −0.464944 | −0.232472 | − | 0.972603i | \(-0.574681\pi\) | ||||
−0.232472 | + | 0.972603i | \(0.574681\pi\) | |||||||
\(398\) | 20.4304 | 1.02408 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.142177 | 0.00710887 | ||||||||
\(401\) | −12.8908 | −0.643733 | −0.321867 | − | 0.946785i | \(-0.604310\pi\) | ||||
−0.321867 | + | 0.946785i | \(0.604310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.30076 | 0.164423 | ||||||||
\(404\) | −9.77230 | −0.486190 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.49543 | 0.173475 | ||||||||
\(407\) | 2.75725 | 0.136672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.86517 | −0.487801 | −0.243901 | − | 0.969800i | \(-0.578427\pi\) | ||||
−0.243901 | + | 0.969800i | \(0.578427\pi\) | |||||||
\(410\) | 20.6735 | 1.02099 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.13814 | 0.105339 | ||||||||
\(413\) | 4.34797 | 0.213950 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −19.8667 | −0.975218 | ||||||||
\(416\) | −0.823528 | −0.0403768 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 33.2934 | 1.62843 | ||||||||
\(419\) | 16.8632 | 0.823823 | 0.411912 | − | 0.911224i | \(-0.364861\pi\) | ||||
0.411912 | + | 0.911224i | \(0.364861\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.7035 | 0.814078 | 0.407039 | − | 0.913411i | \(-0.366561\pi\) | ||||
0.407039 | + | 0.913411i | \(0.366561\pi\) | |||||||
\(422\) | −14.9296 | −0.726762 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.80173 | 0.378885 | ||||||||
\(425\) | −0.974342 | −0.0472625 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.34551 | 0.161901 | ||||||||
\(428\) | −9.52464 | −0.460391 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −18.6889 | −0.901259 | ||||||||
\(431\) | −3.42714 | −0.165079 | −0.0825397 | − | 0.996588i | \(-0.526303\pi\) | ||||
−0.0825397 | + | 0.996588i | \(0.526303\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.04647 | 0.434746 | 0.217373 | − | 0.976089i | \(-0.430251\pi\) | ||||
0.217373 | + | 0.976089i | \(0.430251\pi\) | |||||||
\(434\) | 1.59463 | 0.0765445 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.2092 | 0.824170 | ||||||||
\(437\) | −69.4577 | −3.32261 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.9907 | 0.763193 | 0.381597 | − | 0.924329i | \(-0.375374\pi\) | ||||
0.381597 | + | 0.924329i | \(0.375374\pi\) | |||||||
\(440\) | 9.00181 | 0.429144 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.64364 | 0.268441 | ||||||||
\(443\) | −2.78120 | −0.132139 | −0.0660693 | − | 0.997815i | \(-0.521046\pi\) | ||||
−0.0660693 | + | 0.997815i | \(0.521046\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.9746 | 0.994290 | ||||||||
\(446\) | 16.1349 | 0.764008 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.397853 | −0.0187968 | ||||||||
\(449\) | −22.6866 | −1.07065 | −0.535324 | − | 0.844647i | \(-0.679810\pi\) | ||||
−0.535324 | + | 0.844647i | \(0.679810\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.1906 | 1.70415 | ||||||||
\(452\) | −0.853149 | −0.0401288 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.4983 | 0.915101 | ||||||||
\(455\) | 0.742976 | 0.0348313 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.54589 | 0.306204 | 0.153102 | − | 0.988210i | \(-0.451074\pi\) | ||||
0.153102 | + | 0.988210i | \(0.451074\pi\) | |||||||
\(458\) | 11.0086 | 0.514397 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −18.7798 | −0.875614 | ||||||||
\(461\) | 8.49455 | 0.395631 | 0.197815 | − | 0.980239i | \(-0.436615\pi\) | ||||
0.197815 | + | 0.980239i | \(0.436615\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4676 | 1.36947 | 0.684737 | − | 0.728790i | \(-0.259917\pi\) | ||||
0.684737 | + | 0.728790i | \(0.259917\pi\) | |||||||
\(464\) | 8.78572 | 0.407867 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.0188 | 1.29795 | ||||||||
\(467\) | 26.8493 | 1.24244 | 0.621218 | − | 0.783638i | \(-0.286638\pi\) | ||||
0.621218 | + | 0.783638i | \(0.286638\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.53562 | 0.209435 | ||||||||
\(470\) | 3.58553 | 0.165388 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.9286 | 0.503029 | ||||||||
\(473\) | −32.7165 | −1.50430 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.19243 | −0.0547124 | ||||||||
\(476\) | 2.72649 | 0.124968 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −23.4730 | −1.07363 | ||||||||
\(479\) | 17.1551 | 0.783837 | 0.391919 | − | 0.920000i | \(-0.371811\pi\) | ||||
0.391919 | + | 0.920000i | \(0.371811\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.572003 | 0.0260811 | ||||||||
\(482\) | −16.6148 | −0.756782 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.75840 | 0.216291 | ||||||||
\(485\) | 18.2643 | 0.829340 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0684 | 0.637501 | 0.318750 | − | 0.947839i | \(-0.396737\pi\) | ||||
0.318750 | + | 0.947839i | \(0.396737\pi\) | |||||||
\(488\) | 8.40891 | 0.380654 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.5145 | −0.700875 | ||||||||
\(491\) | −6.74375 | −0.304341 | −0.152171 | − | 0.988354i | \(-0.548626\pi\) | ||||
−0.152171 | + | 0.988354i | \(0.548626\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −60.2086 | −2.71166 | ||||||||
\(494\) | 6.90686 | 0.310754 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00807 | 0.179968 | ||||||||
\(497\) | −5.87412 | −0.263490 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.81728 | 0.215651 | 0.107825 | − | 0.994170i | \(-0.465611\pi\) | ||||
0.107825 | + | 0.994170i | \(0.465611\pi\) | |||||||
\(500\) | 11.0158 | 0.492641 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.7503 | −0.970764 | ||||||||
\(503\) | 36.1200 | 1.61051 | 0.805255 | − | 0.592929i | \(-0.202028\pi\) | ||||
0.805255 | + | 0.592929i | \(0.202028\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.1600 | 0.986108 | ||||||||
\(506\) | −32.8756 | −1.46150 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.3267 | 0.458175 | ||||||||
\(509\) | 27.1181 | 1.20199 | 0.600994 | − | 0.799254i | \(-0.294772\pi\) | ||||
0.600994 | + | 0.799254i | \(0.294772\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.49721 | −0.110470 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.0548 | −1.10512 | ||||||||
\(515\) | −4.84853 | −0.213652 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.27676 | 0.276052 | ||||||||
\(518\) | 0.276339 | 0.0121417 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.86746 | 0.0818937 | ||||||||
\(521\) | 3.14188 | 0.137648 | 0.0688240 | − | 0.997629i | \(-0.478075\pi\) | ||||
0.0688240 | + | 0.997629i | \(0.478075\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.3922 | −1.19778 | −0.598888 | − | 0.800833i | \(-0.704390\pi\) | ||||
−0.598888 | + | 0.800833i | \(0.704390\pi\) | |||||||
\(524\) | 7.41831 | 0.324070 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.10598 | 0.0482232 | ||||||||
\(527\) | −27.4673 | −1.19650 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 45.5861 | 1.98200 | ||||||||
\(530\) | −17.6915 | −0.768469 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.33676 | 0.144667 | ||||||||
\(533\) | 7.50790 | 0.325203 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.5984 | 0.933781 | ||||||||
\(536\) | 11.4002 | 0.492415 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.9971 | 0.646571 | ||||||||
\(539\) | −27.1594 | −1.16984 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.0959 | 0.563036 | 0.281518 | − | 0.959556i | \(-0.409162\pi\) | ||||
0.281518 | + | 0.959556i | \(0.409162\pi\) | |||||||
\(542\) | −25.6135 | −1.10019 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.85300 | 0.293820 | ||||||||
\(545\) | −39.0241 | −1.67161 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.4468 | −0.446674 | −0.223337 | − | 0.974741i | \(-0.571695\pi\) | ||||
−0.223337 | + | 0.974741i | \(0.571695\pi\) | |||||||
\(548\) | 15.1282 | 0.646245 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.564399 | −0.0240661 | ||||||||
\(551\) | −73.6851 | −3.13909 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.83920 | −0.163259 | ||||||||
\(554\) | 17.2735 | 0.733881 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.7814 | −0.584460 | ||||||||
\(557\) | 23.7259 | 1.00530 | 0.502650 | − | 0.864490i | \(-0.332358\pi\) | ||||
0.502650 | + | 0.864490i | \(0.332358\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.78717 | −0.287067 | ||||||||
\(560\) | 0.902187 | 0.0381244 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.74260 | −0.157872 | ||||||||
\(563\) | 15.4966 | 0.653106 | 0.326553 | − | 0.945179i | \(-0.394113\pi\) | ||||
0.326553 | + | 0.945179i | \(0.394113\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.93463 | 0.0813906 | ||||||||
\(566\) | 7.91599 | 0.332734 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7645 | −0.619506 | ||||||||
\(569\) | 9.61882 | 0.403242 | 0.201621 | − | 0.979464i | \(-0.435379\pi\) | ||||
0.201621 | + | 0.979464i | \(0.435379\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.8896 | 1.46008 | 0.730042 | − | 0.683402i | \(-0.239500\pi\) | ||||
0.730042 | + | 0.683402i | \(0.239500\pi\) | |||||||
\(572\) | 3.26915 | 0.136690 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.62713 | 0.151393 | ||||||||
\(575\) | 1.17747 | 0.0491037 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.66430 | 0.235808 | 0.117904 | − | 0.993025i | \(-0.462382\pi\) | ||||
0.117904 | + | 0.993025i | \(0.462382\pi\) | |||||||
\(578\) | −29.9636 | −1.24632 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.9228 | −0.827250 | ||||||||
\(581\) | −3.48558 | −0.144606 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.9704 | −1.28266 | ||||||||
\(584\) | −6.27672 | −0.259733 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.0968 | 1.07805 | ||||||||
\(587\) | 13.8612 | 0.572112 | 0.286056 | − | 0.958213i | \(-0.407656\pi\) | ||||
0.286056 | + | 0.958213i | \(0.407656\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.6154 | −1.38510 | ||||||||
\(590\) | −24.7821 | −1.02026 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.694576 | 0.0285469 | ||||||||
\(593\) | 42.2000 | 1.73295 | 0.866474 | − | 0.499222i | \(-0.166381\pi\) | ||||
0.866474 | + | 0.499222i | \(0.166381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.18269 | −0.253466 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.82019 | −0.278898 | ||||||||
\(599\) | −40.0156 | −1.63499 | −0.817497 | − | 0.575933i | \(-0.804639\pi\) | ||||
−0.817497 | + | 0.575933i | \(0.804639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4610 | 0.508296 | 0.254148 | − | 0.967165i | \(-0.418205\pi\) | ||||
0.254148 | + | 0.967165i | \(0.418205\pi\) | |||||||
\(602\) | −3.27894 | −0.133640 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.9871 | 0.691197 | ||||||||
\(605\) | −10.7903 | −0.438689 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2278 | 1.14573 | 0.572865 | − | 0.819650i | \(-0.305832\pi\) | ||||
0.572865 | + | 0.819650i | \(0.305832\pi\) | |||||||
\(608\) | 8.38692 | 0.340134 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.0684 | −0.772055 | ||||||||
\(611\) | 1.30214 | 0.0526790 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.70098 | 0.391819 | 0.195909 | − | 0.980622i | \(-0.437234\pi\) | ||||
0.195909 | + | 0.980622i | \(0.437234\pi\) | |||||||
\(614\) | −8.74645 | −0.352978 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.57935 | 0.0636339 | ||||||||
\(617\) | −20.3190 | −0.818012 | −0.409006 | − | 0.912532i | \(-0.634124\pi\) | ||||
−0.409006 | + | 0.912532i | \(0.634124\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.6405 | 0.628645 | 0.314323 | − | 0.949316i | \(-0.398223\pi\) | ||||
0.314323 | + | 0.949316i | \(0.398223\pi\) | |||||||
\(620\) | −9.08885 | −0.365017 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.6816 | −0.468389 | ||||||||
\(623\) | 3.67996 | 0.147434 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.6907 | −1.02763 | ||||||||
\(626\) | −23.9981 | −0.959156 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.17392 | 0.0468445 | ||||||||
\(629\) | −4.75993 | −0.189791 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.45340 | 0.177287 | 0.0886436 | − | 0.996063i | \(-0.471747\pi\) | ||||
0.0886436 | + | 0.996063i | \(0.471747\pi\) | |||||||
\(632\) | −9.64978 | −0.383848 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −30.2788 | −1.20253 | ||||||||
\(635\) | −23.4173 | −0.929287 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.63434 | −0.223241 | ||||||||
\(638\) | −34.8765 | −1.38078 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.26764 | 0.0896362 | ||||||||
\(641\) | 42.1227 | 1.66375 | 0.831874 | − | 0.554964i | \(-0.187268\pi\) | ||||
0.831874 | + | 0.554964i | \(0.187268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.4065 | 0.410392 | 0.205196 | − | 0.978721i | \(-0.434217\pi\) | ||||
0.205196 | + | 0.978721i | \(0.434217\pi\) | |||||||
\(644\) | −3.29489 | −0.129837 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −57.4755 | −2.26135 | ||||||||
\(647\) | −32.4987 | −1.27765 | −0.638827 | − | 0.769350i | \(-0.720580\pi\) | ||||
−0.638827 | + | 0.769350i | \(0.720580\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −43.3830 | −1.70293 | ||||||||
\(650\) | −0.117087 | −0.00459253 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 17.5592 | 0.687670 | ||||||||
\(653\) | 42.1198 | 1.64827 | 0.824137 | − | 0.566391i | \(-0.191661\pi\) | ||||
0.824137 | + | 0.566391i | \(0.191661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.8220 | −0.657291 | ||||||||
\(656\) | 9.11675 | 0.355949 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.629075 | 0.0245239 | ||||||||
\(659\) | 38.1964 | 1.48792 | 0.743960 | − | 0.668224i | \(-0.232945\pi\) | ||||
0.743960 | + | 0.668224i | \(0.232945\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.9691 | 1.36014 | 0.680070 | − | 0.733147i | \(-0.261949\pi\) | ||||
0.680070 | + | 0.733147i | \(0.261949\pi\) | |||||||
\(662\) | −4.27876 | −0.166299 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.76097 | −0.339991 | ||||||||
\(665\) | −7.56657 | −0.293419 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 72.7605 | 2.81730 | ||||||||
\(668\) | 4.50119 | 0.174156 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −25.8516 | −0.998733 | ||||||||
\(671\) | −33.3807 | −1.28865 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.28107 | 0.357759 | 0.178880 | − | 0.983871i | \(-0.442753\pi\) | ||||
0.178880 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(674\) | 22.8901 | 0.881692 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3218 | −0.473915 | ||||||||
\(677\) | 43.5582 | 1.67408 | 0.837039 | − | 0.547143i | \(-0.184285\pi\) | ||||
0.837039 | + | 0.547143i | \(0.184285\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.20445 | 0.122975 | ||||||||
\(680\) | −15.5401 | −0.595936 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −15.9108 | −0.609256 | ||||||||
\(683\) | 10.2891 | 0.393702 | 0.196851 | − | 0.980433i | \(-0.436929\pi\) | ||||
0.196851 | + | 0.980433i | \(0.436929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −34.3053 | −1.31074 | ||||||||
\(686\) | −5.50697 | −0.210257 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −8.24158 | −0.314207 | ||||||||
\(689\) | −6.42494 | −0.244771 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.7310 | −0.750603 | −0.375302 | − | 0.926903i | \(-0.622461\pi\) | ||||
−0.375302 | + | 0.926903i | \(0.622461\pi\) | |||||||
\(692\) | −6.31389 | −0.240018 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.5781 | −0.667257 | ||||||||
\(695\) | 31.2511 | 1.18542 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −62.4771 | −2.36649 | ||||||||
\(698\) | 6.75698 | 0.255755 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.0565658 | −0.00213798 | ||||||||
\(701\) | 44.6961 | 1.68815 | 0.844073 | − | 0.536228i | \(-0.180151\pi\) | ||||
0.844073 | + | 0.536228i | \(0.180151\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.82535 | −0.219707 | ||||||||
\(704\) | 3.96969 | 0.149613 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.34841 | −0.126019 | ||||||||
\(707\) | 3.88794 | 0.146221 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.66685 | 0.250379 | 0.125189 | − | 0.992133i | \(-0.460046\pi\) | ||||
0.125189 | + | 0.992133i | \(0.460046\pi\) | |||||||
\(710\) | 33.4806 | 1.25650 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.24953 | 0.346641 | ||||||||
\(713\) | 33.1935 | 1.24311 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.41324 | −0.277239 | ||||||||
\(716\) | 7.46421 | 0.278951 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.7588 | −0.737391 | ||||||||
\(719\) | 21.3307 | 0.795502 | 0.397751 | − | 0.917493i | \(-0.369791\pi\) | ||||
0.397751 | + | 0.917493i | \(0.369791\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.850668 | −0.0316805 | ||||||||
\(722\) | −51.3403 | −1.91069 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15.8449 | 0.588872 | ||||||||
\(725\) | 1.24913 | 0.0463916 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.2804 | −1.04886 | −0.524430 | − | 0.851453i | \(-0.675722\pi\) | ||||
−0.524430 | + | 0.851453i | \(0.675722\pi\) | |||||||
\(728\) | 0.327643 | 0.0121433 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.2333 | 0.526799 | ||||||||
\(731\) | 56.4795 | 2.08897 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.79861 | 0.251112 | 0.125556 | − | 0.992087i | \(-0.459928\pi\) | ||||
0.125556 | + | 0.992087i | \(0.459928\pi\) | |||||||
\(734\) | −5.61191 | −0.207139 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.28167 | −0.305266 | ||||||||
\(737\) | −45.2553 | −1.66700 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18.8897 | −0.694870 | −0.347435 | − | 0.937704i | \(-0.612947\pi\) | ||||
−0.347435 | + | 0.937704i | \(0.612947\pi\) | |||||||
\(740\) | −1.57505 | −0.0578998 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.10394 | −0.113949 | ||||||||
\(743\) | −19.5087 | −0.715704 | −0.357852 | − | 0.933778i | \(-0.616491\pi\) | ||||
−0.357852 | + | 0.933778i | \(0.616491\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.26764 | −0.0830798 | ||||||||
\(746\) | −6.40480 | −0.234496 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −27.2043 | −0.994686 | ||||||||
\(749\) | 3.78941 | 0.138462 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.1392 | 0.479458 | 0.239729 | − | 0.970840i | \(-0.422941\pi\) | ||||
0.239729 | + | 0.970840i | \(0.422941\pi\) | |||||||
\(752\) | 1.58117 | 0.0576594 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.23529 | −0.263494 | ||||||||
\(755\) | −38.5207 | −1.40191 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.5014 | −0.817827 | −0.408913 | − | 0.912573i | \(-0.634092\pi\) | ||||
−0.408913 | + | 0.912573i | \(0.634092\pi\) | |||||||
\(758\) | 17.1296 | 0.622177 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −19.0185 | −0.689873 | ||||||||
\(761\) | −4.15691 | −0.150688 | −0.0753440 | − | 0.997158i | \(-0.524005\pi\) | ||||
−0.0753440 | + | 0.997158i | \(0.524005\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.84672 | −0.247868 | ||||||||
\(764\) | −16.6457 | −0.602221 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −22.0618 | −0.797125 | ||||||||
\(767\) | −8.99999 | −0.324971 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −17.5274 | −0.632055 | −0.316028 | − | 0.948750i | \(-0.602349\pi\) | ||||
−0.316028 | + | 0.948750i | \(0.602349\pi\) | |||||||
\(770\) | −3.58140 | −0.129065 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.73110 | −0.350230 | ||||||||
\(773\) | 5.94560 | 0.213849 | 0.106924 | − | 0.994267i | \(-0.465900\pi\) | ||||
0.106924 | + | 0.994267i | \(0.465900\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.569857 | 0.0204699 | ||||||||
\(776\) | 8.05434 | 0.289134 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.0190 | 0.538458 | ||||||||
\(779\) | −76.4614 | −2.73951 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58.6105 | 2.09725 | ||||||||
\(782\) | 56.7543 | 2.02953 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.84171 | −0.244347 | ||||||||
\(785\) | −2.66203 | −0.0950118 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.7311 | −1.13109 | −0.565545 | − | 0.824717i | \(-0.691334\pi\) | ||||
−0.565545 | + | 0.824717i | \(0.691334\pi\) | |||||||
\(788\) | 2.03744 | 0.0725806 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 21.8822 | 0.778534 | ||||||||
\(791\) | 0.339428 | 0.0120687 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.92498 | −0.245913 | ||||||||
\(794\) | 9.26395 | 0.328765 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.4304 | −0.724137 | ||||||||
\(797\) | 21.1583 | 0.749466 | 0.374733 | − | 0.927133i | \(-0.377734\pi\) | ||||
0.374733 | + | 0.927133i | \(0.377734\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8358 | −0.383342 | ||||||||
\(800\) | −0.142177 | −0.00502673 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 12.8908 | 0.455188 | ||||||||
\(803\) | 24.9166 | 0.879288 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.47162 | 0.263340 | ||||||||
\(806\) | −3.30076 | −0.116264 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.77230 | 0.343788 | ||||||||
\(809\) | 18.8833 | 0.663900 | 0.331950 | − | 0.943297i | \(-0.392293\pi\) | ||||
0.331950 | + | 0.943297i | \(0.392293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.7651 | −0.764275 | −0.382137 | − | 0.924105i | \(-0.624812\pi\) | ||||
−0.382137 | + | 0.924105i | \(0.624812\pi\) | |||||||
\(812\) | −3.49543 | −0.122665 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.75725 | −0.0966415 | ||||||||
\(815\) | −39.8178 | −1.39476 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 69.1214 | 2.41825 | ||||||||
\(818\) | 9.86517 | 0.344928 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −20.6735 | −0.721949 | ||||||||
\(821\) | 12.5288 | 0.437259 | 0.218630 | − | 0.975808i | \(-0.429841\pi\) | ||||
0.218630 | + | 0.975808i | \(0.429841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.12788 | 0.0741733 | 0.0370867 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370867 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(824\) | −2.13814 | −0.0744858 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.34797 | −0.151285 | ||||||||
\(827\) | −14.0345 | −0.488026 | −0.244013 | − | 0.969772i | \(-0.578464\pi\) | ||||
−0.244013 | + | 0.969772i | \(0.578464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.43826 | −0.154147 | −0.0770735 | − | 0.997025i | \(-0.524558\pi\) | ||||
−0.0770735 | + | 0.997025i | \(0.524558\pi\) | |||||||
\(830\) | 19.8667 | 0.689583 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.823528 | 0.0285507 | ||||||||
\(833\) | 46.8863 | 1.62451 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −10.2071 | −0.353230 | ||||||||
\(836\) | −33.2934 | −1.15148 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −16.8632 | −0.582531 | ||||||||
\(839\) | 6.15626 | 0.212538 | 0.106269 | − | 0.994337i | \(-0.466110\pi\) | ||||
0.106269 | + | 0.994337i | \(0.466110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.1889 | 1.66169 | ||||||||
\(842\) | −16.7035 | −0.575640 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 14.9296 | 0.513898 | ||||||||
\(845\) | 27.9414 | 0.961212 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.89315 | −0.0650493 | ||||||||
\(848\) | −7.80173 | −0.267912 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.974342 | 0.0334197 | ||||||||
\(851\) | 5.75225 | 0.197185 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.14473 | 0.313110 | 0.156555 | − | 0.987669i | \(-0.449961\pi\) | ||||
0.156555 | + | 0.987669i | \(0.449961\pi\) | |||||||
\(854\) | −3.34551 | −0.114481 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.52464 | 0.325546 | ||||||||
\(857\) | 25.6375 | 0.875762 | 0.437881 | − | 0.899033i | \(-0.355729\pi\) | ||||
0.437881 | + | 0.899033i | \(0.355729\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.45085 | −0.185981 | −0.0929903 | − | 0.995667i | \(-0.529643\pi\) | ||||
−0.0929903 | + | 0.995667i | \(0.529643\pi\) | |||||||
\(860\) | 18.6889 | 0.637286 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.42714 | 0.116729 | ||||||||
\(863\) | −15.4896 | −0.527272 | −0.263636 | − | 0.964622i | \(-0.584922\pi\) | ||||
−0.263636 | + | 0.964622i | \(0.584922\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.3176 | 0.486814 | ||||||||
\(866\) | −9.04647 | −0.307412 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.59463 | −0.0541251 | ||||||||
\(869\) | 38.3066 | 1.29946 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.38840 | −0.318114 | ||||||||
\(872\) | −17.2092 | −0.582776 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 69.4577 | 2.34944 | ||||||||
\(875\) | −4.38266 | −0.148161 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.33464 | −0.0788353 | −0.0394177 | − | 0.999223i | \(-0.512550\pi\) | ||||
−0.0394177 | + | 0.999223i | \(0.512550\pi\) | |||||||
\(878\) | −15.9907 | −0.539659 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.00181 | −0.303451 | ||||||||
\(881\) | 57.6543 | 1.94242 | 0.971211 | − | 0.238220i | \(-0.0765640\pi\) | ||||
0.971211 | + | 0.238220i | \(0.0765640\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.7235 | 0.865663 | 0.432832 | − | 0.901475i | \(-0.357514\pi\) | ||||
0.432832 | + | 0.901475i | \(0.357514\pi\) | |||||||
\(884\) | −5.64364 | −0.189816 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.78120 | 0.0934361 | ||||||||
\(887\) | 46.8090 | 1.57169 | 0.785846 | − | 0.618422i | \(-0.212228\pi\) | ||||
0.785846 | + | 0.618422i | \(0.212228\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.10853 | −0.137796 | ||||||||
\(890\) | −20.9746 | −0.703069 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.1349 | −0.540235 | ||||||||
\(893\) | −13.2612 | −0.443768 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9261 | −0.565778 | ||||||||
\(896\) | 0.397853 | 0.0132913 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.6866 | 0.757062 | ||||||||
\(899\) | 35.2138 | 1.17445 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 53.4653 | 1.78119 | ||||||||
\(902\) | −36.1906 | −1.20502 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.853149 | 0.0283753 | ||||||||
\(905\) | −35.9305 | −1.19437 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.4229 | −1.14299 | −0.571497 | − | 0.820604i | \(-0.693637\pi\) | ||||
−0.571497 | + | 0.820604i | \(0.693637\pi\) | |||||||
\(908\) | −19.4983 | −0.647074 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.742976 | −0.0246294 | ||||||||
\(911\) | −6.77761 | −0.224552 | −0.112276 | − | 0.993677i | \(-0.535814\pi\) | ||||
−0.112276 | + | 0.993677i | \(0.535814\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.7783 | 1.15099 | ||||||||
\(914\) | −6.54589 | −0.216519 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.0086 | −0.363734 | ||||||||
\(917\) | −2.95140 | −0.0974638 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.3820 | 1.20013 | 0.600066 | − | 0.799950i | \(-0.295141\pi\) | ||||
0.600066 | + | 0.799950i | \(0.295141\pi\) | |||||||
\(920\) | 18.7798 | 0.619152 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.49455 | −0.279753 | ||||||||
\(923\) | 12.1590 | 0.400218 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0987530 | 0.00324698 | ||||||||
\(926\) | −29.4676 | −0.968365 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −8.78572 | −0.288405 | ||||||||
\(929\) | −49.3214 | −1.61818 | −0.809091 | − | 0.587683i | \(-0.800040\pi\) | ||||
−0.809091 | + | 0.587683i | \(0.800040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 57.3809 | 1.88058 | ||||||||
\(932\) | −28.0188 | −0.917788 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.8493 | −0.878535 | ||||||||
\(935\) | 61.6894 | 2.01746 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.8573 | 0.746717 | 0.373358 | − | 0.927687i | \(-0.378206\pi\) | ||||
0.373358 | + | 0.927687i | \(0.378206\pi\) | |||||||
\(938\) | −4.53562 | −0.148093 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.58553 | −0.116947 | ||||||||
\(941\) | −33.8585 | −1.10375 | −0.551877 | − | 0.833925i | \(-0.686088\pi\) | ||||
−0.551877 | + | 0.833925i | \(0.686088\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 75.5019 | 2.45868 | ||||||||
\(944\) | −10.9286 | −0.355695 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.7165 | 1.06370 | ||||||||
\(947\) | 0.515622 | 0.0167555 | 0.00837774 | − | 0.999965i | \(-0.497333\pi\) | ||||
0.00837774 | + | 0.999965i | \(0.497333\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.16906 | 0.167795 | ||||||||
\(950\) | 1.19243 | 0.0386875 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.72649 | −0.0883661 | ||||||||
\(953\) | 5.49709 | 0.178068 | 0.0890341 | − | 0.996029i | \(-0.471622\pi\) | ||||
0.0890341 | + | 0.996029i | \(0.471622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.7464 | 1.22145 | ||||||||
\(956\) | 23.4730 | 0.759172 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.1551 | −0.554257 | ||||||||
\(959\) | −6.01881 | −0.194357 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.9353 | −0.481785 | ||||||||
\(962\) | −0.572003 | −0.0184421 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.6148 | 0.535126 | ||||||||
\(965\) | 22.0666 | 0.710349 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.6176 | 0.341440 | 0.170720 | − | 0.985320i | \(-0.445391\pi\) | ||||
0.170720 | + | 0.985320i | \(0.445391\pi\) | |||||||
\(968\) | −4.75840 | −0.152941 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.2643 | −0.586432 | ||||||||
\(971\) | −51.8122 | −1.66273 | −0.831366 | − | 0.555725i | \(-0.812441\pi\) | ||||
−0.831366 | + | 0.555725i | \(0.812441\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.48296 | 0.175776 | ||||||||
\(974\) | −14.0684 | −0.450781 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.40891 | −0.269163 | ||||||||
\(977\) | −33.6732 | −1.07730 | −0.538651 | − | 0.842529i | \(-0.681066\pi\) | ||||
−0.538651 | + | 0.842529i | \(0.681066\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −36.7177 | −1.17350 | ||||||||
\(980\) | 15.5145 | 0.495593 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.74375 | 0.215202 | ||||||||
\(983\) | −51.2822 | −1.63565 | −0.817823 | − | 0.575469i | \(-0.804819\pi\) | ||||
−0.817823 | + | 0.575469i | \(0.804819\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.62016 | −0.147211 | ||||||||
\(986\) | 60.2086 | 1.91743 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.90686 | −0.219737 | ||||||||
\(989\) | −68.2540 | −2.17035 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.69020 | 0.212521 | 0.106261 | − | 0.994338i | \(-0.466112\pi\) | ||||
0.106261 | + | 0.994338i | \(0.466112\pi\) | |||||||
\(992\) | −4.00807 | −0.127256 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.87412 | 0.186316 | ||||||||
\(995\) | 46.3288 | 1.46872 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.3841 | 0.328869 | 0.164435 | − | 0.986388i | \(-0.447420\pi\) | ||||
0.164435 | + | 0.986388i | \(0.447420\pi\) | |||||||
\(998\) | −4.81728 | −0.152488 | ||||||||
\(999\) | 0 | 0 |
(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 | 8046.2.a.l.1.2 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.m.1.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.m.1.11 | yes | 12 | 3.2 | odd | 2 |