Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8044,2,Mod(1,8044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8044, 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("8044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8044 = 2^{2} \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8044.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: | \(64.2316633859\) |
Analytic rank: | \(0\) |
Dimension: | \(87\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8044.1 |
$q$-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 | ||||||||
\(3\) | −2.93853 | −1.69656 | −0.848281 | − | 0.529546i | \(-0.822362\pi\) | ||||
−0.848281 | + | 0.529546i | \(0.822362\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.993611 | 0.444356 | 0.222178 | − | 0.975006i | \(-0.428683\pi\) | ||||
0.222178 | + | 0.975006i | \(0.428683\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0902794 | 0.0341224 | 0.0170612 | − | 0.999854i | \(-0.494569\pi\) | ||||
0.0170612 | + | 0.999854i | \(0.494569\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.63497 | 1.87832 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.94385 | −0.586093 | −0.293047 | − | 0.956098i | \(-0.594669\pi\) | ||||
−0.293047 | + | 0.956098i | \(0.594669\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.99845 | −1.38632 | −0.693160 | − | 0.720784i | \(-0.743782\pi\) | ||||
−0.693160 | + | 0.720784i | \(0.743782\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.91976 | −0.753878 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.90558 | 0.462171 | 0.231086 | − | 0.972933i | \(-0.425772\pi\) | ||||
0.231086 | + | 0.972933i | \(0.425772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.66802 | 0.382671 | 0.191335 | − | 0.981525i | \(-0.438718\pi\) | ||||
0.191335 | + | 0.981525i | \(0.438718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.265289 | −0.0578907 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.16543 | 0.868552 | 0.434276 | − | 0.900780i | \(-0.357004\pi\) | ||||
0.434276 | + | 0.900780i | \(0.357004\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.01274 | −0.802547 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.74293 | −1.49013 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.760921 | 0.141299 | 0.0706497 | − | 0.997501i | \(-0.477493\pi\) | ||||
0.0706497 | + | 0.997501i | \(0.477493\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.97918 | 1.25350 | 0.626748 | − | 0.779222i | \(-0.284385\pi\) | ||||
0.626748 | + | 0.779222i | \(0.284385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.71207 | 0.994343 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0897026 | 0.0151625 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.35287 | −0.715607 | −0.357804 | − | 0.933797i | \(-0.616474\pi\) | ||||
−0.357804 | + | 0.933797i | \(0.616474\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 14.6881 | 2.35198 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.51969 | −1.01821 | −0.509103 | − | 0.860706i | \(-0.670023\pi\) | ||||
−0.509103 | + | 0.860706i | \(0.670023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.15623 | −1.24381 | −0.621906 | − | 0.783092i | \(-0.713642\pi\) | ||||
−0.621906 | + | 0.783092i | \(0.713642\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.59897 | 0.834645 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.47089 | −0.506281 | −0.253141 | − | 0.967429i | \(-0.581464\pi\) | ||||
−0.253141 | + | 0.967429i | \(0.581464\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99185 | −0.998836 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.59961 | −0.784102 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.23286 | −0.581428 | −0.290714 | − | 0.956810i | \(-0.593893\pi\) | ||||
−0.290714 | + | 0.956810i | \(0.593893\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.93143 | −0.260434 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.90154 | −0.649224 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.46613 | 0.451252 | 0.225626 | − | 0.974214i | \(-0.427557\pi\) | ||||
0.225626 | + | 0.974214i | \(0.427557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.4967 | 1.85611 | 0.928056 | − | 0.372441i | \(-0.121479\pi\) | ||||
0.928056 | + | 0.372441i | \(0.121479\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.508721 | 0.0640928 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.96652 | −0.616020 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.30826 | 0.770676 | 0.385338 | − | 0.922775i | \(-0.374085\pi\) | ||||
0.385338 | + | 0.922775i | \(0.374085\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.2402 | −1.47355 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.76891 | 0.684643 | 0.342322 | − | 0.939583i | \(-0.388787\pi\) | ||||
0.342322 | + | 0.939583i | \(0.388787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.41521 | 0.984925 | 0.492463 | − | 0.870334i | \(-0.336097\pi\) | ||||
0.492463 | + | 0.870334i | \(0.336097\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.7916 | 1.36157 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.175490 | −0.0199989 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.49939 | 0.956256 | 0.478128 | − | 0.878290i | \(-0.341315\pi\) | ||||
0.478128 | + | 0.878290i | \(0.341315\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.84795 | 0.649773 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0182 | −1.20941 | −0.604703 | − | 0.796451i | \(-0.706708\pi\) | ||||
−0.604703 | + | 0.796451i | \(0.706708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.89341 | 0.205369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.23599 | −0.239723 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.89197 | 0.624548 | 0.312274 | − | 0.949992i | \(-0.398909\pi\) | ||||
0.312274 | + | 0.949992i | \(0.398909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.451257 | −0.0473046 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.5085 | −2.12664 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.65737 | 0.170042 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.1368 | −1.43538 | −0.717688 | − | 0.696365i | \(-0.754800\pi\) | ||||
−0.717688 | + | 0.696365i | \(0.754800\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.9535 | −1.10087 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.49073 | 0.645852 | 0.322926 | − | 0.946424i | \(-0.395334\pi\) | ||||
0.322926 | + | 0.946424i | \(0.395334\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.96176 | 0.685963 | 0.342981 | − | 0.939342i | \(-0.388563\pi\) | ||||
0.342981 | + | 0.939342i | \(0.388563\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.263594 | −0.0257241 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 16.2160 | 1.56766 | 0.783830 | − | 0.620976i | \(-0.213263\pi\) | ||||
0.783830 | + | 0.620976i | \(0.213263\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.74889 | −0.359079 | −0.179539 | − | 0.983751i | \(-0.557461\pi\) | ||||
−0.179539 | + | 0.983751i | \(0.557461\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.7910 | 1.21407 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −19.8492 | −1.86726 | −0.933629 | − | 0.358242i | \(-0.883376\pi\) | ||||
−0.933629 | + | 0.358242i | \(0.883376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.13882 | 0.385947 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −28.1661 | −2.60396 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.172035 | 0.0157704 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.22144 | −0.656495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.1583 | 1.72745 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.95516 | −0.800974 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.24961 | 0.377092 | 0.188546 | − | 0.982064i | \(-0.439623\pi\) | ||||
0.188546 | + | 0.982064i | \(0.439623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 23.9673 | 2.11021 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.5332 | −1.61925 | −0.809625 | − | 0.586948i | \(-0.800329\pi\) | ||||
−0.809625 | + | 0.586948i | \(0.800329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.150588 | 0.0130576 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.69347 | −0.662148 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.82769 | −0.412457 | −0.206229 | − | 0.978504i | \(-0.566119\pi\) | ||||
−0.206229 | + | 0.978504i | \(0.566119\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.8345 | −1.68234 | −0.841168 | − | 0.540774i | \(-0.818132\pi\) | ||||
−0.841168 | + | 0.540774i | \(0.818132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.1993 | 0.858937 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.71624 | 0.812513 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.756059 | 0.0627873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 20.5458 | 1.69459 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.8187 | 1.95131 | 0.975653 | − | 0.219319i | \(-0.0703837\pi\) | ||||
0.975653 | + | 0.219319i | \(0.0703837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.6928 | 1.35844 | 0.679220 | − | 0.733935i | \(-0.262318\pi\) | ||||
0.679220 | + | 0.733935i | \(0.262318\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.7379 | 0.868107 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.93459 | 0.556999 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.607785 | −0.0485066 | −0.0242533 | − | 0.999706i | \(-0.507721\pi\) | ||||
−0.0242533 | + | 0.999706i | \(0.507721\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 12.4384 | 0.986429 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.376052 | 0.0296371 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.13567 | −0.715561 | −0.357780 | − | 0.933806i | \(-0.616466\pi\) | ||||
−0.357780 | + | 0.933806i | \(0.616466\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.67557 | 0.441843 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.0373 | −0.776712 | −0.388356 | − | 0.921509i | \(-0.626957\pi\) | ||||
−0.388356 | + | 0.921509i | \(0.626957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.9845 | 0.921884 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.39925 | 0.718779 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.8825 | 1.13149 | 0.565746 | − | 0.824579i | \(-0.308588\pi\) | ||||
0.565746 | + | 0.824579i | \(0.308588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.362267 | −0.0273848 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1853 | −0.765577 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.0439 | −1.27392 | −0.636962 | − | 0.770895i | \(-0.719809\pi\) | ||||
−0.636962 | + | 0.770895i | \(0.719809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.6336 | −1.53368 | −0.766840 | − | 0.641838i | \(-0.778172\pi\) | ||||
−0.766840 | + | 0.641838i | \(0.778172\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −42.5990 | −3.14901 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.32506 | −0.317985 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.70417 | −0.270875 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.699027 | −0.0508467 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.6628 | 1.27803 | 0.639017 | − | 0.769193i | \(-0.279341\pi\) | ||||
0.639017 | + | 0.769193i | \(0.279341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.46575 | 0.105507 | 0.0527534 | − | 0.998608i | \(-0.483200\pi\) | ||||
0.0527534 | + | 0.998608i | \(0.483200\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.5943 | 1.04512 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.1739 | −0.724857 | −0.362429 | − | 0.932012i | \(-0.618052\pi\) | ||||
−0.362429 | + | 0.932012i | \(0.618052\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.9364 | 1.20059 | 0.600296 | − | 0.799778i | \(-0.295049\pi\) | ||||
0.600296 | + | 0.799778i | \(0.295049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −18.5370 | −1.30750 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0686954 | 0.00482147 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.47804 | −0.452446 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 23.4721 | 1.63142 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.24239 | −0.224281 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.3590 | 1.19504 | 0.597522 | − | 0.801853i | \(-0.296152\pi\) | ||||
0.597522 | + | 0.801853i | \(0.296152\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.9521 | −1.16154 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.10412 | −0.552696 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.630075 | 0.0427723 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −24.7283 | −1.67099 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.52495 | −0.640717 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.3974 | 1.63377 | 0.816885 | − | 0.576800i | \(-0.195699\pi\) | ||||
0.816885 | + | 0.576800i | \(0.195699\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −22.6116 | −1.50744 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.6528 | −1.03891 | −0.519457 | − | 0.854497i | \(-0.673866\pi\) | ||||
−0.519457 | + | 0.854497i | \(0.673866\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.34199 | −0.220845 | −0.110422 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110422 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.515682 | 0.0339294 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.2902 | −0.870668 | −0.435334 | − | 0.900269i | \(-0.643370\pi\) | ||||
−0.435334 | + | 0.900269i | \(0.643370\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.44871 | −0.224969 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −24.9757 | −1.62235 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.3709 | 0.735520 | 0.367760 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367760 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.69200 | −0.302238 | −0.151119 | − | 0.988516i | \(-0.548288\pi\) | ||||
−0.151119 | + | 0.988516i | \(0.548288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.04441 | 0.387749 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.94718 | −0.443839 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.33753 | −0.530504 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 32.3774 | 2.05183 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −29.8428 | −1.88366 | −0.941830 | − | 0.336089i | \(-0.890896\pi\) | ||||
−0.941830 | + | 0.336089i | \(0.890896\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.09698 | −0.509053 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.56383 | −0.348421 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.498670 | −0.0311062 | −0.0155531 | − | 0.999879i | \(-0.504951\pi\) | ||||
−0.0155531 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.392974 | −0.0244182 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.28776 | 0.265406 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.3452 | 0.761240 | 0.380620 | − | 0.924732i | \(-0.375711\pi\) | ||||
0.380620 | + | 0.924732i | \(0.375711\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.20582 | −0.258361 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.3137 | −1.05958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −17.1416 | −1.04514 | −0.522572 | − | 0.852595i | \(-0.675027\pi\) | ||||
−0.522572 | + | 0.852595i | \(0.675027\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.2255 | 1.22861 | 0.614305 | − | 0.789069i | \(-0.289436\pi\) | ||||
0.614305 | + | 0.789069i | \(0.289436\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.32603 | 0.0802551 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.80016 | 0.470367 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6987 | 1.18358 | 0.591791 | − | 0.806092i | \(-0.298421\pi\) | ||||
0.591791 | + | 0.806092i | \(0.298421\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 39.3274 | 2.35447 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.58456 | −0.213837 | −0.106918 | − | 0.994268i | \(-0.534098\pi\) | ||||
−0.106918 | + | 0.994268i | \(0.534098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.12723 | 0.126451 | 0.0632253 | − | 0.997999i | \(-0.479861\pi\) | ||||
0.0632253 | + | 0.997999i | \(0.479861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.87022 | −0.288487 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.588594 | −0.0347436 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3688 | −0.786398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.5415 | 2.43520 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.56755 | −0.383681 | −0.191840 | − | 0.981426i | \(-0.561446\pi\) | ||||
−0.191840 | + | 0.981426i | \(0.561446\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.44399 | 0.200517 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.0511 | 0.873354 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −20.8207 | −1.20409 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.736339 | −0.0424419 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.0732 | −1.09573 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.4041 | 0.824775 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.76112 | 0.385877 | 0.192939 | − | 0.981211i | \(-0.438198\pi\) | ||||
0.192939 | + | 0.981211i | \(0.438198\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.4574 | −1.16378 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.5368 | 0.937713 | 0.468857 | − | 0.883274i | \(-0.344666\pi\) | ||||
0.468857 | + | 0.883274i | \(0.344666\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.1580 | 1.70463 | 0.852314 | − | 0.523030i | \(-0.175199\pi\) | ||||
0.852314 | + | 0.523030i | \(0.175199\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.505471 | 0.0284801 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.8341 | −1.00166 | −0.500830 | − | 0.865546i | \(-0.666972\pi\) | ||||
−0.500830 | + | 0.865546i | \(0.666972\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.47912 | −0.0828146 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −47.6512 | −2.65963 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.17855 | 0.176859 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.0575 | 1.11259 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.0162 | 0.609200 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.313350 | −0.0172755 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.38602 | −0.351008 | −0.175504 | − | 0.984479i | \(-0.556155\pi\) | ||||
−0.175504 | + | 0.984479i | \(0.556155\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −24.5283 | −1.34414 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.26796 | 0.342455 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.60743 | 0.305456 | 0.152728 | − | 0.988268i | \(-0.451194\pi\) | ||||
0.152728 | + | 0.988268i | \(0.451194\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 58.3275 | 3.16792 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5665 | −0.734666 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.26318 | −0.0682050 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.1620 | −0.654783 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.48735 | 0.240894 | 0.120447 | − | 0.992720i | \(-0.461567\pi\) | ||||
0.120447 | + | 0.992720i | \(0.461567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.57911 | 0.352172 | 0.176086 | − | 0.984375i | \(-0.443656\pi\) | ||||
0.176086 | + | 0.984375i | \(0.443656\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 38.7027 | 2.06580 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.6755 | 1.52624 | 0.763120 | − | 0.646257i | \(-0.223666\pi\) | ||||
0.763120 | + | 0.646257i | \(0.223666\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.73205 | 0.304226 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.505529 | −0.0267554 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.2823 | 0.859349 | 0.429674 | − | 0.902984i | \(-0.358628\pi\) | ||||
0.429674 | + | 0.902984i | \(0.358628\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2177 | −0.853563 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.2204 | 1.11378 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.36144 | 0.437658 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.0374 | −1.09814 | −0.549071 | − | 0.835776i | \(-0.685018\pi\) | ||||
−0.549071 | + | 0.835776i | \(0.685018\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −36.7383 | −1.91252 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.382140 | −0.0198397 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.21288 | −0.373469 | −0.186734 | − | 0.982410i | \(-0.559790\pi\) | ||||
−0.186734 | + | 0.982410i | \(0.559790\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 26.3150 | 1.35890 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.80342 | −0.195886 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.4066 | 0.688653 | 0.344326 | − | 0.938850i | \(-0.388107\pi\) | ||||
0.344326 | + | 0.938850i | \(0.388107\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.4876 | −0.639760 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.1806 | 0.980083 | 0.490041 | − | 0.871699i | \(-0.336982\pi\) | ||||
0.490041 | + | 0.871699i | \(0.336982\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.174368 | −0.00888664 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −45.9601 | −2.33628 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.2519 | 1.68594 | 0.842970 | − | 0.537961i | \(-0.180805\pi\) | ||||
0.842970 | + | 0.537961i | \(0.180805\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.93757 | 0.401420 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 54.4603 | 2.74716 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.44509 | 0.424919 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.5765 | 1.48440 | 0.742202 | − | 0.670176i | \(-0.233781\pi\) | ||||
0.742202 | + | 0.670176i | \(0.233781\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.442508 | −0.0221531 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 36.9351 | 1.84445 | 0.922225 | − | 0.386653i | \(-0.126369\pi\) | ||||
0.922225 | + | 0.386653i | \(0.126369\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −34.8851 | −1.73775 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 5.81059 | 0.288731 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.46133 | 0.419413 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.1196 | −1.34098 | −0.670489 | − | 0.741920i | \(-0.733915\pi\) | ||||
−0.670489 | + | 0.741920i | \(0.733915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.1863 | 0.699759 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.312920 | 0.0153978 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.9478 | −0.537408 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 58.2842 | 2.85419 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.77960 | 0.380059 | 0.190029 | − | 0.981778i | \(-0.439142\pi\) | ||||
0.190029 | + | 0.981778i | \(0.439142\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3117 | 0.941197 | 0.470598 | − | 0.882347i | \(-0.344038\pi\) | ||||
0.470598 | + | 0.882347i | \(0.344038\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −19.5583 | −0.950959 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.64659 | −0.370914 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.30875 | 0.0633350 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.5515 | −1.37848 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.444289 | −0.0214006 | −0.0107003 | − | 0.999943i | \(-0.503406\pi\) | ||||
−0.0107003 | + | 0.999943i | \(0.503406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.2096 | 1.93235 | 0.966176 | − | 0.257883i | \(-0.0830250\pi\) | ||||
0.966176 | + | 0.257883i | \(0.0830250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.22170 | −0.106523 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.94803 | 0.332369 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.12968 | 0.292554 | 0.146277 | − | 0.989244i | \(-0.453271\pi\) | ||||
0.146277 | + | 0.989244i | \(0.453271\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −39.3988 | −1.87614 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.1176 | 1.14586 | 0.572931 | − | 0.819604i | \(-0.305806\pi\) | ||||
0.572931 | + | 0.819604i | \(0.305806\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.85433 | 0.277522 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −69.9921 | −3.31051 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.5748 | 0.735018 | 0.367509 | − | 0.930020i | \(-0.380211\pi\) | ||||
0.367509 | + | 0.930020i | \(0.380211\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.6733 | 0.596763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −49.0523 | −2.30468 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.448374 | −0.0210201 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.0953 | −0.799687 | −0.399843 | − | 0.916583i | \(-0.630935\pi\) | ||||
−0.399843 | + | 0.916583i | \(0.630935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.7548 | −0.688694 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.72235 | −0.313091 | −0.156545 | − | 0.987671i | \(-0.550036\pi\) | ||||
−0.156545 | + | 0.987671i | \(0.550036\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.254221 | −0.0118147 | −0.00590733 | − | 0.999983i | \(-0.501880\pi\) | ||||
−0.00590733 | + | 0.999983i | \(0.501880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.3775 | −0.944984 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.98714 | −0.138228 | −0.0691142 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691142 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.569506 | 0.0262973 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.78600 | 0.0822944 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.8545 | 0.728990 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.69334 | −0.307111 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −23.8520 | −1.09211 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.77202 | 0.400804 | 0.200402 | − | 0.979714i | \(-0.435775\pi\) | ||||
0.200402 | + | 0.979714i | \(0.435775\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.7576 | 0.992061 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.10504 | −0.0502811 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.0465 | −0.637819 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.52387 | −0.340939 | −0.170469 | − | 0.985363i | \(-0.554528\pi\) | ||||
−0.170469 | + | 0.985363i | \(0.554528\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26.8455 | 1.21399 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.5017 | 0.564194 | 0.282097 | − | 0.959386i | \(-0.408970\pi\) | ||||
0.282097 | + | 0.959386i | \(0.408970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.45000 | 0.0653045 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.8836 | −0.489180 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.520813 | 0.0233617 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 38.3059 | 1.71481 | 0.857405 | − | 0.514642i | \(-0.172075\pi\) | ||||
0.857405 | + | 0.514642i | \(0.172075\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.4950 | 1.31774 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.1748 | 1.07790 | 0.538950 | − | 0.842338i | \(-0.318821\pi\) | ||||
0.538950 | + | 0.842338i | \(0.318821\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.44926 | 0.286988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −35.2168 | −1.56403 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7740 | 1.14241 | 0.571205 | − | 0.820807i | \(-0.306476\pi\) | ||||
0.571205 | + | 0.820807i | \(0.306476\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.759719 | 0.0336080 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.9154 | −0.570228 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.91729 | 0.304812 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.74689 | 0.296728 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.7326 | −1.91965 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 44.0797 | 1.93117 | 0.965583 | − | 0.260096i | \(-0.0837541\pi\) | ||||
0.965583 | + | 0.260096i | \(0.0837541\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2946 | 1.14978 | 0.574891 | − | 0.818230i | \(-0.305045\pi\) | ||||
0.574891 | + | 0.818230i | \(0.305045\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.06453 | 0.0464601 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.2994 | 0.579330 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.64919 | −0.245617 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.5315 | 0.847597 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 32.5884 | 1.41156 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.1124 | 0.696600 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 50.0842 | 2.16129 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.5911 | 0.585411 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.6723 | −1.14673 | −0.573367 | − | 0.819299i | \(-0.694363\pi\) | ||||
−0.573367 | + | 0.819299i | \(0.694363\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60.6324 | 2.60198 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.72494 | −0.159559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.8020 | 1.14597 | 0.572986 | − | 0.819565i | \(-0.305785\pi\) | ||||
0.572986 | + | 0.819565i | \(0.305785\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 81.6884 | 3.48638 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.26923 | 0.0540711 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.767320 | 0.0326298 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.7093 | 0.539481 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.8469 | −1.77311 | −0.886555 | − | 0.462624i | \(-0.846908\pi\) | ||||
−0.886555 | + | 0.462624i | \(0.846908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.7685 | 1.72432 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.8848 | 0.459557 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.8189 | 1.21457 | 0.607286 | − | 0.794483i | \(-0.292258\pi\) | ||||
0.607286 | + | 0.794483i | \(0.292258\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −19.7224 | −0.829728 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.527950 | 0.0221718 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.3798 | 0.644757 | 0.322378 | − | 0.946611i | \(-0.395518\pi\) | ||||
0.322378 | + | 0.946611i | \(0.395518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.1127 | −0.799842 | −0.399921 | − | 0.916550i | \(-0.630962\pi\) | ||||
−0.399921 | + | 0.916550i | \(0.630962\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −51.9026 | −2.16826 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.7148 | −0.697054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.0005 | 0.416325 | 0.208163 | − | 0.978094i | \(-0.433252\pi\) | ||||
0.208163 | + | 0.978094i | \(0.433252\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.30714 | −0.178999 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.994718 | −0.0412678 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.22806 | 0.340771 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.9862 | −1.15708 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.85018 | 0.117640 | 0.0588198 | − | 0.998269i | \(-0.481266\pi\) | ||||
0.0588198 | + | 0.998269i | \(0.481266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.6414 | 0.479676 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.8962 | 1.22977 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.6777 | 1.34191 | 0.670956 | − | 0.741497i | \(-0.265884\pi\) | ||||
0.670956 | + | 0.741497i | \(0.265884\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.170936 | 0.00700767 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −49.7683 | −2.03688 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.9216 | 1.75373 | 0.876864 | − | 0.480739i | \(-0.159632\pi\) | ||||
0.876864 | + | 0.480739i | \(0.159632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.6295 | −1.61652 | −0.808260 | − | 0.588826i | \(-0.799590\pi\) | ||||
−0.808260 | + | 0.588826i | \(0.799590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.5468 | 1.44758 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.17531 | −0.291718 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.6352 | 1.40580 | 0.702899 | − | 0.711289i | \(-0.251888\pi\) | ||||
0.702899 | + | 0.711289i | \(0.251888\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.201864 | −0.00817993 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3491 | 0.701868 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.0502 | −0.971378 | −0.485689 | − | 0.874132i | \(-0.661431\pi\) | ||||
−0.485689 | + | 0.874132i | \(0.661431\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 19.0359 | 0.767603 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.0804 | 0.808405 | 0.404202 | − | 0.914670i | \(-0.367549\pi\) | ||||
0.404202 | + | 0.914670i | \(0.367549\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.0284 | 1.24714 | 0.623569 | − | 0.781768i | \(-0.285682\pi\) | ||||
0.623569 | + | 0.781768i | \(0.285682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.2527 | −1.29425 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.531923 | 0.0213111 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.1657 | 0.446630 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.52786 | 0.380506 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.29475 | −0.330733 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.5762 | 0.460839 | 0.230420 | − | 0.973091i | \(-0.425990\pi\) | ||||
0.230420 | + | 0.973091i | \(0.425990\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −51.0100 | −2.02747 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.22246 | 0.167563 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 34.9484 | 1.38471 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.5076 | 1.28598 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.85742 | −0.310350 | −0.155175 | − | 0.987887i | \(-0.549594\pi\) | ||||
−0.155175 | + | 0.987887i | \(0.549594\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.3808 | −1.35585 | −0.677923 | − | 0.735133i | \(-0.737120\pi\) | ||||
−0.677923 | + | 0.735133i | \(0.737120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.8142 | 0.937684 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.8578 | −1.48834 | −0.744172 | − | 0.667988i | \(-0.767156\pi\) | ||||
−0.744172 | + | 0.667988i | \(0.767156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.73765 | −0.264476 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.85150 | −0.0725659 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 30.4658 | 1.19222 | 0.596110 | − | 0.802903i | \(-0.296712\pi\) | ||||
0.596110 | + | 0.802903i | \(0.296712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.4148 | −0.719524 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 47.4194 | 1.85001 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.4945 | −1.42162 | −0.710812 | − | 0.703382i | \(-0.751672\pi\) | ||||
−0.710812 | + | 0.703382i | \(0.751672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.7959 | 1.62567 | 0.812836 | − | 0.582492i | \(-0.197922\pi\) | ||||
0.812836 | + | 0.582492i | \(0.197922\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27.9894 | 1.08702 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.149626 | 0.00580224 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.16956 | 0.122726 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −71.6925 | −2.77179 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −28.1794 | −1.08785 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.81464 | 0.108497 | 0.0542483 | − | 0.998527i | \(-0.482724\pi\) | ||||
0.0542483 | + | 0.998527i | \(0.482724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.0704 | 1.19590 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1290 | 0.427722 | 0.213861 | − | 0.976864i | \(-0.431396\pi\) | ||||
0.213861 | + | 0.976864i | \(0.431396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.27626 | −0.0489785 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 45.9963 | 1.76258 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7571 | 0.832513 | 0.416257 | − | 0.909247i | \(-0.363342\pi\) | ||||
0.416257 | + | 0.909247i | \(0.363342\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.79684 | −0.183278 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.82054 | 0.374677 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 21.1578 | 0.806046 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.958497 | 0.0364629 | 0.0182315 | − | 0.999834i | \(-0.494196\pi\) | ||||
0.0182315 | + | 0.999834i | \(0.494196\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.988878 | −0.0375644 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.7077 | −0.747557 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.4238 | −0.470585 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 39.0536 | 1.47714 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.0162 | 1.62470 | 0.812350 | − | 0.583170i | \(-0.198188\pi\) | ||||
0.812350 | + | 0.583170i | \(0.198188\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.26068 | −0.273842 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.1342 | 0.381674 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.585979 | 0.0220380 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.2585 | −1.32416 | −0.662080 | − | 0.749434i | \(-0.730326\pi\) | ||||
−0.662080 | + | 0.749434i | \(0.730326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47.8938 | 1.79616 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.0713 | 1.08873 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.65417 | 0.361045 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −33.4136 | −1.24786 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.0227 | −1.15695 | −0.578476 | − | 0.815699i | \(-0.696353\pi\) | ||||
−0.578476 | + | 0.815699i | \(0.696353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.628504 | 0.0234067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.7876 | 0.512765 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.05337 | −0.113399 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −25.9640 | −0.962953 | −0.481477 | − | 0.876459i | \(-0.659899\pi\) | ||||
−0.481477 | + | 0.876459i | \(0.659899\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.3055 | −1.30761 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.5423 | −0.574855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.5111 | 1.45937 | 0.729687 | − | 0.683781i | \(-0.239666\pi\) | ||||
0.729687 | + | 0.683781i | \(0.239666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20.4145 | 0.753000 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.2623 | −0.451688 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.53098 | −0.0563178 | −0.0281589 | − | 0.999603i | \(-0.508964\pi\) | ||||
−0.0281589 | + | 0.999603i | \(0.508964\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.5001 | 0.900033 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.06503 | −0.332564 | −0.166282 | − | 0.986078i | \(-0.553176\pi\) | ||||
−0.166282 | + | 0.986078i | \(0.553176\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.6666 | 0.867076 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −62.0873 | −2.27166 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.46397 | 0.0534923 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.20210 | 0.153337 | 0.0766684 | − | 0.997057i | \(-0.475572\pi\) | ||||
0.0766684 | + | 0.997057i | \(0.475572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 87.6940 | 3.19575 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.5861 | 0.603632 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.9627 | −1.08901 | −0.544507 | − | 0.838756i | \(-0.683283\pi\) | ||||
−0.544507 | + | 0.838756i | \(0.683283\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.7932 | 0.863639 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.5367 | 1.25195 | 0.625977 | − | 0.779841i | \(-0.284700\pi\) | ||||
0.625977 | + | 0.779841i | \(0.284700\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.338448 | −0.0122526 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.6693 | 0.385749 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.3253 | −0.625580 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 51.8849 | 1.87102 | 0.935510 | − | 0.353302i | \(-0.114941\pi\) | ||||
0.935510 | + | 0.353302i | \(0.114941\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.46536 | 0.0527735 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2464 | 0.440473 | 0.220237 | − | 0.975447i | \(-0.429317\pi\) | ||||
0.220237 | + | 0.975447i | \(0.429317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0056 | −1.00599 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.15477 | 0.0414270 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −10.8750 | −0.389637 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.2139 | −0.401265 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.89176 | −0.210554 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.603902 | −0.0215542 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.6784 | −0.630166 | −0.315083 | − | 0.949064i | \(-0.602032\pi\) | ||||
−0.315083 | + | 0.949064i | \(0.602032\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −36.2769 | −1.29149 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.79197 | −0.0637153 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −72.4610 | −2.57317 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.3589 | 0.438326 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.4972 | −0.442672 | −0.221336 | − | 0.975198i | \(-0.571042\pi\) | ||||
−0.221336 | + | 0.975198i | \(0.571042\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.61406 | −0.233989 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 33.2011 | 1.17310 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16.3579 | −0.577258 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.373650 | 0.0131694 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 50.3712 | 1.77315 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32.5348 | 1.14386 | 0.571932 | − | 0.820301i | \(-0.306194\pi\) | ||||
0.571932 | + | 0.820301i | \(0.306194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −45.4673 | −1.59657 | −0.798287 | − | 0.602277i | \(-0.794260\pi\) | ||||
−0.798287 | + | 0.602277i | \(0.794260\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −59.4332 | −2.08441 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.07730 | −0.317964 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −13.6048 | −0.475971 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.54282 | −0.0888532 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.0616 | 0.455852 | 0.227926 | − | 0.973678i | \(-0.426806\pi\) | ||||
0.227926 | + | 0.973678i | \(0.426806\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −29.9980 | −1.04566 | −0.522832 | − | 0.852436i | \(-0.675125\pi\) | ||||
−0.522832 | + | 0.852436i | \(0.675125\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.9210 | −0.798008 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.9927 | −1.21682 | −0.608408 | − | 0.793625i | \(-0.708191\pi\) | ||||
−0.608408 | + | 0.793625i | \(0.708191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −55.1169 | −1.91429 | −0.957145 | − | 0.289609i | \(-0.906475\pi\) | ||||
−0.957145 | + | 0.289609i | \(0.906475\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −57.8853 | −2.00802 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.3235 | −0.461633 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.97321 | −0.345137 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −54.0393 | −1.86787 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.53512 | 0.260141 | 0.130071 | − | 0.991505i | \(-0.458480\pi\) | ||||
0.130071 | + | 0.991505i | \(0.458480\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4210 | −0.980034 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.5333 | 0.362787 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.9079 | 0.409645 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.651947 | −0.0224012 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.25092 | −0.214531 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.1316 | −0.621542 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.3575 | −0.388872 | −0.194436 | − | 0.980915i | \(-0.562288\pi\) | ||||
−0.194436 | + | 0.980915i | \(0.562288\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.33920 | 0.319394 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.3738 | −1.00339 | −0.501694 | − | 0.865045i | \(-0.667290\pi\) | ||||
−0.501694 | + | 0.865045i | \(0.667290\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 54.9469 | 1.87477 | 0.937383 | − | 0.348301i | \(-0.113241\pi\) | ||||
0.937383 | + | 0.348301i | \(0.113241\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.72960 | 0.0589447 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.27307 | −0.315659 | −0.157830 | − | 0.987466i | \(-0.550450\pi\) | ||||
−0.157830 | + | 0.987466i | \(0.550450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7874 | 0.502786 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.2845 | 1.33417 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.5216 | −0.560455 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.5315 | −1.06840 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −79.6605 | −2.69610 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.808466 | −0.0273311 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.6606 | 0.630123 | 0.315062 | − | 0.949071i | \(-0.397975\pi\) | ||||
0.315062 | + | 0.949071i | \(0.397975\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19.2990 | 0.650938 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.4878 | 1.06085 | 0.530425 | − | 0.847732i | \(-0.322032\pi\) | ||||
0.530425 | + | 0.847732i | \(0.322032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.9879 | 0.739951 | 0.369976 | − | 0.929041i | \(-0.379366\pi\) | ||||
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10.1203 | −0.340189 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.7514 | −0.394572 | −0.197286 | − | 0.980346i | \(-0.563213\pi\) | ||||
−0.197286 | + | 0.980346i | \(0.563213\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.383652 | 0.0128673 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.3676 | −0.380827 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.78952 | −0.193739 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −16.9351 | −0.566076 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 61.1823 | 2.04282 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.31060 | 0.177118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.06606 | −0.268720 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.16376 | 0.0720053 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.5017 | −0.681501 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.4075 | 1.50773 | 0.753865 | − | 0.657029i | \(-0.228187\pi\) | ||||
0.753865 | + | 0.657029i | \(0.228187\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.5750 | 1.21312 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.9445 | −0.826447 | −0.413224 | − | 0.910630i | \(-0.635597\pi\) | ||||
−0.413224 | + | 0.910630i | \(0.635597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 21.4178 | 0.708825 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −42.3268 | −1.39928 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.67316 | −0.0552527 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.9718 | −1.58244 | −0.791221 | − | 0.611530i | \(-0.790554\pi\) | ||||
−0.791221 | + | 0.611530i | \(0.790554\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −19.8677 | −0.654665 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −28.8356 | −0.949135 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.4669 | 0.574309 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 39.2293 | 1.28846 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −39.9180 | −1.30967 | −0.654833 | − | 0.755774i | \(-0.727261\pi\) | ||||
−0.654833 | + | 0.755774i | \(0.727261\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.6626 | −0.382225 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −48.5938 | −1.59089 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.68050 | −0.120365 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −37.3385 | −1.21980 | −0.609899 | − | 0.792480i | \(-0.708790\pi\) | ||||
−0.609899 | + | 0.792480i | \(0.708790\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −88.6201 | −2.89201 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.2129 | 0.463329 | 0.231664 | − | 0.972796i | \(-0.425583\pi\) | ||||
0.231664 | + | 0.972796i | \(0.425583\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −27.1573 | −0.884364 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.694561 | −0.0225941 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.0125 | −0.650318 | −0.325159 | − | 0.945659i | \(-0.605418\pi\) | ||||
−0.325159 | + | 0.945659i | \(0.605418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −42.0630 | −1.36542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.4059 | 1.69938 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.36568 | −0.303384 | −0.151692 | − | 0.988428i | \(-0.548472\pi\) | ||||
−0.151692 | + | 0.988428i | \(0.548472\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.5499 | 0.567903 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.34643 | 0.140500 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.435840 | −0.0140740 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.7089 | 0.571255 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 91.3766 | 2.94457 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.45638 | 0.0468826 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −13.5061 | −0.434328 | −0.217164 | − | 0.976135i | \(-0.569681\pi\) | ||||
−0.217164 | + | 0.976135i | \(0.569681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.34027 | −0.300053 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.8866 | −1.50466 | −0.752331 | − | 0.658785i | \(-0.771071\pi\) | ||||
−0.752331 | + | 0.658785i | \(0.771071\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.79064 | −0.0574053 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −58.9395 | −1.88757 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −12.1818 | −0.389731 | −0.194866 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194866 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.4531 | −0.366043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −21.1249 | −0.674466 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.3909 | −0.841740 | −0.420870 | − | 0.907121i | \(-0.638275\pi\) | ||||
−0.420870 | + | 0.907121i | \(0.638275\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.1089 | −0.322095 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.920788 | 0.0293090 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −33.9742 | −1.08032 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.7104 | 0.467291 | 0.233645 | − | 0.972322i | \(-0.424935\pi\) | ||||
0.233645 | + | 0.972322i | \(0.424935\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7655 | 0.595506 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.8282 | 0.533491 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.2442 | 0.767821 | 0.383911 | − | 0.923370i | \(-0.374577\pi\) | ||||
0.383911 | + | 0.923370i | \(0.374577\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.7040 | 1.06635 |
(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 | 8044.2.a.b.1.5 | ✓ | 87 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8044.2.a.b.1.5 | ✓ | 87 | 1.1 | even | 1 | trivial |