Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(33\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −2.60209 | −1.50232 | −0.751158 | − | 0.660122i | \(-0.770504\pi\) | ||||
−0.751158 | + | 0.660122i | \(0.770504\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.12945 | 0.505105 | 0.252553 | − | 0.967583i | \(-0.418730\pi\) | ||||
0.252553 | + | 0.967583i | \(0.418730\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.15113 | 0.435087 | 0.217544 | − | 0.976051i | \(-0.430196\pi\) | ||||
0.217544 | + | 0.976051i | \(0.430196\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.77086 | 1.25695 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.62351 | −1.39404 | −0.697020 | − | 0.717052i | \(-0.745491\pi\) | ||||
−0.697020 | + | 0.717052i | \(0.745491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.29696 | 1.74646 | 0.873231 | − | 0.487307i | \(-0.162021\pi\) | ||||
0.873231 | + | 0.487307i | \(0.162021\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.93893 | −0.758828 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.65086 | −1.12800 | −0.564000 | − | 0.825775i | \(-0.690738\pi\) | ||||
−0.564000 | + | 0.825775i | \(0.690738\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.55120 | −1.04412 | −0.522058 | − | 0.852910i | \(-0.674836\pi\) | ||||
−0.522058 | + | 0.852910i | \(0.674836\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.99535 | −0.653638 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.09579 | −1.68809 | −0.844044 | − | 0.536274i | \(-0.819831\pi\) | ||||
−0.844044 | + | 0.536274i | \(0.819831\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.72434 | −0.744869 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.00585 | −0.386025 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.35654 | −0.808989 | −0.404494 | − | 0.914541i | \(-0.632552\pi\) | ||||
−0.404494 | + | 0.914541i | \(0.632552\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.23462 | 0.580955 | 0.290477 | − | 0.956882i | \(-0.406186\pi\) | ||||
0.290477 | + | 0.956882i | \(0.406186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.0308 | 2.09429 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.30015 | 0.219765 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.34814 | −0.221632 | −0.110816 | − | 0.993841i | \(-0.535346\pi\) | ||||
−0.110816 | + | 0.993841i | \(0.535346\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.3852 | −2.62374 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.554523 | −0.0866019 | −0.0433010 | − | 0.999062i | \(-0.513787\pi\) | ||||
−0.0433010 | + | 0.999062i | \(0.513787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.45396 | −0.374225 | −0.187113 | − | 0.982338i | \(-0.559913\pi\) | ||||
−0.187113 | + | 0.982338i | \(0.559913\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.25900 | 0.634894 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.98010 | 0.726423 | 0.363211 | − | 0.931707i | \(-0.381680\pi\) | ||||
0.363211 | + | 0.931707i | \(0.381680\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.67489 | −0.810699 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 12.1019 | 1.69461 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5645 | 1.58851 | 0.794253 | − | 0.607587i | \(-0.207862\pi\) | ||||
0.794253 | + | 0.607587i | \(0.207862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.22202 | −0.704137 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 11.8426 | 1.56859 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.43649 | 1.09834 | 0.549169 | − | 0.835712i | \(-0.314944\pi\) | ||||
0.549169 | + | 0.835712i | \(0.314944\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.328087 | −0.0420073 | −0.0210036 | − | 0.999779i | \(-0.506686\pi\) | ||||
−0.0210036 | + | 0.999779i | \(0.506686\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.34076 | 0.546884 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.11209 | 0.882147 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.55790 | −0.312498 | −0.156249 | − | 0.987718i | \(-0.549940\pi\) | ||||
−0.156249 | + | 0.987718i | \(0.549940\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.0659 | 2.53604 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.67099 | 1.14774 | 0.573868 | − | 0.818948i | \(-0.305442\pi\) | ||||
0.573868 | + | 0.818948i | \(0.305442\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.53114 | −0.179206 | −0.0896031 | − | 0.995978i | \(-0.528560\pi\) | ||||
−0.0896031 | + | 0.995978i | \(0.528560\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.69107 | 1.11903 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.32227 | −0.606529 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.1977 | 1.37235 | 0.686176 | − | 0.727436i | \(-0.259288\pi\) | ||||
0.686176 | + | 0.727436i | \(0.259288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.09319 | −0.677021 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.49665 | −0.493571 | −0.246786 | − | 0.969070i | \(-0.579374\pi\) | ||||
−0.246786 | + | 0.969070i | \(0.579374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.25291 | −0.569758 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.3361 | 1.21536 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.9749 | 1.48133 | 0.740667 | − | 0.671872i | \(-0.234510\pi\) | ||||
0.740667 | + | 0.671872i | \(0.234510\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.24863 | 0.759863 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.41677 | −0.872778 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.14035 | −0.527389 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5290 | 1.47519 | 0.737596 | − | 0.675242i | \(-0.235961\pi\) | ||||
0.737596 | + | 0.675242i | \(0.235961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.4346 | −1.75224 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.3268 | −1.22657 | −0.613283 | − | 0.789863i | \(-0.710151\pi\) | ||||
−0.613283 | + | 0.789863i | \(0.710151\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.2957 | −1.11300 | −0.556501 | − | 0.830847i | \(-0.687856\pi\) | ||||
−0.556501 | + | 0.830847i | \(0.687856\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.38309 | −0.330156 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −18.0989 | −1.74969 | −0.874845 | − | 0.484402i | \(-0.839037\pi\) | ||||
−0.874845 | + | 0.484402i | \(0.839037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.42098 | −0.710801 | −0.355400 | − | 0.934714i | \(-0.615655\pi\) | ||||
−0.355400 | + | 0.934714i | \(0.615655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50797 | 0.332962 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.9717 | −1.50249 | −0.751246 | − | 0.660022i | \(-0.770547\pi\) | ||||
−0.751246 | + | 0.660022i | \(0.770547\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.14378 | −0.852662 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.7449 | 2.19522 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.35376 | −0.490778 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.3768 | 0.943347 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.44292 | 0.130103 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.85371 | −0.881342 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6115 | −1.20783 | −0.603914 | − | 0.797050i | \(-0.706393\pi\) | ||||
−0.603914 | + | 0.797050i | \(0.706393\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.38542 | 0.562205 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.1024 | 1.40688 | 0.703438 | − | 0.710757i | \(-0.251647\pi\) | ||||
0.703438 | + | 0.710757i | \(0.251647\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.23903 | −0.454282 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.26550 | −0.194983 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.35245 | 0.371854 | 0.185927 | − | 0.982564i | \(-0.440471\pi\) | ||||
0.185927 | + | 0.982564i | \(0.440471\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.7434 | 1.25052 | 0.625260 | − | 0.780416i | \(-0.284993\pi\) | ||||
0.625260 | + | 0.780416i | \(0.284993\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9587 | −1.09132 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29.1140 | −2.43464 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.92049 | −0.408624 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14.7666 | 1.21793 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.64454 | 0.626265 | 0.313133 | − | 0.949709i | \(-0.398622\pi\) | ||||
0.313133 | + | 0.949709i | \(0.398622\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.45004 | −0.769033 | −0.384517 | − | 0.923118i | \(-0.625632\pi\) | ||||
−0.384517 | + | 0.923118i | \(0.625632\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −17.5377 | −1.41784 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.65334 | 0.293443 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.8117 | 1.50133 | 0.750667 | − | 0.660681i | \(-0.229732\pi\) | ||||
0.750667 | + | 0.660681i | \(0.229732\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −30.0919 | −2.38644 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.31932 | −0.734465 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 23.3994 | 1.83278 | 0.916390 | − | 0.400287i | \(-0.131090\pi\) | ||||
0.916390 | + | 0.400287i | \(0.131090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.5881 | 1.05784 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5886 | −0.819374 | −0.409687 | − | 0.912226i | \(-0.634362\pi\) | ||||
−0.409687 | + | 0.912226i | \(0.634362\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.6517 | 2.05013 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.1619 | −1.31241 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 24.8869 | 1.89212 | 0.946058 | − | 0.323998i | \(-0.105027\pi\) | ||||
0.946058 | + | 0.323998i | \(0.105027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.28721 | −0.324083 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.9525 | −1.65005 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8944 | −0.889028 | −0.444514 | − | 0.895772i | \(-0.646624\pi\) | ||||
−0.444514 | + | 0.895772i | \(0.646624\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.52664 | 0.633781 | 0.316890 | − | 0.948462i | \(-0.397361\pi\) | ||||
0.316890 | + | 0.948462i | \(0.397361\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.853712 | 0.0631082 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.52265 | −0.111948 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.5033 | 1.57248 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.30900 | −0.167955 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.12540 | −0.226146 | −0.113073 | − | 0.993587i | \(-0.536069\pi\) | ||||
−0.113073 | + | 0.993587i | \(0.536069\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.18560 | −0.589212 | −0.294606 | − | 0.955619i | \(-0.595188\pi\) | ||||
−0.294606 | + | 0.955619i | \(0.595188\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −18.5063 | −1.32526 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.7451 | 0.836802 | 0.418401 | − | 0.908262i | \(-0.362591\pi\) | ||||
0.418401 | + | 0.908262i | \(0.362591\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.24878 | 0.230300 | 0.115150 | − | 0.993348i | \(-0.463265\pi\) | ||||
0.115150 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.65589 | 0.469470 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.01495 | −0.351981 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.626306 | −0.0437431 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −30.5281 | −2.12185 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0425 | 1.45554 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.14046 | 0.560412 | 0.280206 | − | 0.959940i | \(-0.409597\pi\) | ||||
0.280206 | + | 0.959940i | \(0.409597\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −25.1648 | −1.72426 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.77162 | −0.189023 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.72348 | 0.252766 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.98416 | 0.269224 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −29.2863 | −1.97001 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.323283 | 0.0216486 | 0.0108243 | − | 0.999941i | \(-0.496554\pi\) | ||||
0.0108243 | + | 0.999941i | \(0.496554\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.0440 | −0.936265 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.7413 | 0.978412 | 0.489206 | − | 0.872168i | \(-0.337287\pi\) | ||||
0.489206 | + | 0.872168i | \(0.337287\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.49931 | −0.297323 | −0.148661 | − | 0.988888i | \(-0.547496\pi\) | ||||
−0.148661 | + | 0.988888i | \(0.547496\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.8490 | 0.911198 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.11271 | −0.203921 | −0.101960 | − | 0.994788i | \(-0.532511\pi\) | ||||
−0.101960 | + | 0.994788i | \(0.532511\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.62478 | 0.366920 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −31.7396 | −2.06171 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.8753 | −1.54436 | −0.772181 | − | 0.635403i | \(-0.780834\pi\) | ||||
−0.772181 | + | 0.635403i | \(0.780834\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.35938 | −0.474059 | −0.237030 | − | 0.971502i | \(-0.576174\pi\) | ||||
−0.237030 | + | 0.971502i | \(0.576174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.8726 | 1.40313 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.40951 | −0.409488 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −28.6587 | −1.82351 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.7007 | 0.741500 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.5069 | 1.73622 | 0.868109 | − | 0.496374i | \(-0.165335\pi\) | ||||
0.868109 | + | 0.496374i | \(0.165335\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.4309 | 2.35326 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 13.6685 | 0.855957 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.1452 | −0.695219 | −0.347609 | − | 0.937639i | \(-0.613006\pi\) | ||||
−0.347609 | + | 0.937639i | \(0.613006\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.55188 | −0.0964294 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.4279 | −1.01686 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.56516 | −0.466488 | −0.233244 | − | 0.972418i | \(-0.574934\pi\) | ||||
−0.233244 | + | 0.972418i | \(0.574934\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0615 | 0.802363 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −36.3638 | −2.22543 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.6010 | −0.707326 | −0.353663 | − | 0.935373i | \(-0.615064\pi\) | ||||
−0.353663 | + | 0.935373i | \(0.615064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4477 | 0.634650 | 0.317325 | − | 0.948317i | \(-0.397215\pi\) | ||||
0.317325 | + | 0.948317i | \(0.397215\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.8616 | −1.14155 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.2195 | 1.03838 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.67812 | 0.220997 | 0.110499 | − | 0.993876i | \(-0.464755\pi\) | ||||
0.110499 | + | 0.993876i | \(0.464755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 12.1973 | 0.730233 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.8358 | −1.95882 | −0.979409 | − | 0.201887i | \(-0.935293\pi\) | ||||
−0.979409 | + | 0.201887i | \(0.935293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 29.9506 | 1.78038 | 0.890190 | − | 0.455590i | \(-0.150572\pi\) | ||||
0.890190 | + | 0.455590i | \(0.150572\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.3756 | 0.792305 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.638329 | −0.0376794 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.63050 | 0.272382 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −37.8056 | −2.21620 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2661 | 0.658174 | 0.329087 | − | 0.944300i | \(-0.393259\pi\) | ||||
0.329087 | + | 0.944300i | \(0.393259\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.52859 | 0.554776 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.27405 | 0.538135 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −50.9788 | −2.94818 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.82483 | −0.162821 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.0755 | 1.84269 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.370558 | −0.0212181 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.2757 | 0.871833 | 0.435916 | − | 0.899987i | \(-0.356424\pi\) | ||||
0.435916 | + | 0.899987i | \(0.356424\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29.3925 | 1.67208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.451128 | −0.0255811 | −0.0127906 | − | 0.999918i | \(-0.504071\pi\) | ||||
−0.0127906 | + | 0.999918i | \(0.504071\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6107 | 0.769321 | 0.384660 | − | 0.923058i | \(-0.374319\pi\) | ||||
0.384660 | + | 0.923058i | \(0.374319\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.90267 | 0.276234 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.1587 | −1.63772 | −0.818858 | − | 0.573996i | \(-0.805393\pi\) | ||||
−0.818858 | + | 0.573996i | \(0.805393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.1425 | 1.12776 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 47.0950 | 2.62859 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.1670 | 1.17776 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.4520 | −1.30088 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.3100 | 1.06785 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.73276 | 0.316057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.87857 | 0.488010 | 0.244005 | − | 0.969774i | \(-0.421539\pi\) | ||||
0.244005 | + | 0.969774i | \(0.421539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.08364 | −0.278582 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.88902 | −0.157844 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.2390 | 1.37486 | 0.687428 | − | 0.726253i | \(-0.258740\pi\) | ||||
0.687428 | + | 0.726253i | \(0.258740\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 41.5598 | 2.25722 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.9553 | −0.809874 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.5905 | −0.787812 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.7929 | 1.28097 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.3324 | −1.25255 | −0.626275 | − | 0.779603i | \(-0.715421\pi\) | ||||
−0.626275 | + | 0.779603i | \(0.715421\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.0473 | 1.34075 | 0.670376 | − | 0.742022i | \(-0.266133\pi\) | ||||
0.670376 | + | 0.742022i | \(0.266133\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.6307 | −0.674179 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.4167 | −1.45924 | −0.729621 | − | 0.683851i | \(-0.760304\pi\) | ||||
−0.729621 | + | 0.683851i | \(0.760304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.9229 | 0.579727 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.9309 | 0.737304 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.4902 | 1.55643 | 0.778216 | − | 0.627997i | \(-0.216125\pi\) | ||||
0.778216 | + | 0.627997i | \(0.216125\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.71342 | 0.0901798 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −27.0014 | −1.41720 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.72934 | −0.0905180 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.98251 | 0.155686 | 0.0778430 | − | 0.996966i | \(-0.475197\pi\) | ||||
0.0778430 | + | 0.996966i | \(0.475197\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.09103 | −0.108855 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.3123 | 0.691139 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.2692 | −1.04950 | −0.524749 | − | 0.851257i | \(-0.675841\pi\) | ||||
−0.524749 | + | 0.851257i | \(0.675841\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 25.6402 | 1.32405 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.4329 | −1.41287 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 31.7494 | 1.63086 | 0.815430 | − | 0.578856i | \(-0.196501\pi\) | ||||
0.815430 | + | 0.578856i | \(0.196501\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.4184 | 1.81454 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.7728 | 0.959244 | 0.479622 | − | 0.877475i | \(-0.340774\pi\) | ||||
0.479622 | + | 0.877475i | \(0.340774\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.01123 | −0.306361 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.25354 | −0.470384 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.83208 | 0.244996 | 0.122498 | − | 0.992469i | \(-0.460909\pi\) | ||||
0.122498 | + | 0.992469i | \(0.460909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.6524 | 1.90416 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −41.8999 | −2.11357 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 13.7767 | 0.693182 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4136 | −0.572833 | −0.286416 | − | 0.958105i | \(-0.592464\pi\) | ||||
−0.286416 | + | 0.958105i | \(0.592464\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 13.6324 | 0.682475 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6191 | 0.879856 | 0.439928 | − | 0.898033i | \(-0.355004\pi\) | ||||
0.439928 | + | 0.898033i | \(0.355004\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.3683 | 1.01462 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −6.88195 | −0.341967 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.23312 | 0.308964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.1583 | −0.996766 | −0.498383 | − | 0.866957i | \(-0.666073\pi\) | ||||
−0.498383 | + | 0.866957i | \(0.666073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.3254 | −0.558643 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.71151 | 0.477872 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.07874 | −0.249305 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −38.3637 | −1.87868 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.1359 | −1.17912 | −0.589558 | − | 0.807726i | \(-0.700698\pi\) | ||||
−0.589558 | + | 0.807726i | \(0.700698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.4653 | 0.607521 | 0.303761 | − | 0.952748i | \(-0.401758\pi\) | ||||
0.303761 | + | 0.952748i | \(0.401758\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 18.7793 | 0.913080 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.3214 | 0.840211 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.377672 | −0.0182768 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 75.7572 | 3.65759 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.5636 | −1.32769 | −0.663846 | − | 0.747869i | \(-0.731077\pi\) | ||||
−0.663846 | + | 0.747869i | \(0.731077\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.3610 | 1.55517 | 0.777585 | − | 0.628777i | \(-0.216444\pi\) | ||||
0.777585 | + | 0.628777i | \(0.216444\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.8035 | 0.613883 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 36.8455 | 1.76256 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.07883 | −0.433309 | −0.216655 | − | 0.976248i | \(-0.569515\pi\) | ||||
−0.216655 | + | 0.976248i | \(0.569515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.3992 | −1.01901 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.5951 | 1.26357 | 0.631785 | − | 0.775144i | \(-0.282323\pi\) | ||||
0.631785 | + | 0.775144i | \(0.282323\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.7839 | 0.748229 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.8918 | −0.940849 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.1248 | 1.18571 | 0.592856 | − | 0.805309i | \(-0.298000\pi\) | ||||
0.592856 | + | 0.805309i | \(0.298000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.56384 | 0.120727 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 24.5898 | 1.15533 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.18696 | 0.383811 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.1200 | −0.707286 | −0.353643 | − | 0.935381i | \(-0.615057\pi\) | ||||
−0.353643 | + | 0.935381i | \(0.615057\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.32891 | 0.435436 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.88979 | 0.320890 | 0.160445 | − | 0.987045i | \(-0.448707\pi\) | ||||
0.160445 | + | 0.987045i | \(0.448707\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.67494 | 0.263737 | 0.131869 | − | 0.991267i | \(-0.457902\pi\) | ||||
0.131869 | + | 0.991267i | \(0.457902\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.50631 | −0.440845 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.1968 | 1.58244 | 0.791220 | − | 0.611532i | \(-0.209447\pi\) | ||||
0.791220 | + | 0.611532i | \(0.209447\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.94449 | −0.135964 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −48.9496 | −2.25548 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.3459 | 0.521685 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 16.9502 | 0.777730 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 43.6081 | 1.99668 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.1549 | 0.601062 | 0.300531 | − | 0.953772i | \(-0.402836\pi\) | ||||
0.300531 | + | 0.953772i | \(0.402836\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.48916 | −0.387072 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 24.2497 | 1.10340 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.4097 | 0.745127 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.0148 | 1.08822 | 0.544108 | − | 0.839015i | \(-0.316868\pi\) | ||||
0.544108 | + | 0.839015i | \(0.316868\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −60.8872 | −2.75341 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.55445 | 0.340928 | 0.170464 | − | 0.985364i | \(-0.445473\pi\) | ||||
0.170464 | + | 0.985364i | \(0.445473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 20.2616 | 0.912539 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −19.6915 | −0.885067 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.1326 | 0.499365 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.71408 | 0.390096 | 0.195048 | − | 0.980794i | \(-0.437514\pi\) | ||||
0.195048 | + | 0.980794i | \(0.437514\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.5526 | 1.23096 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000 | 0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.9225 | −0.619545 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −69.3500 | −3.07994 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.3551 | −0.458982 | −0.229491 | − | 0.973311i | \(-0.573706\pi\) | ||||
−0.229491 | + | 0.973311i | \(0.573706\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.76254 | −0.0779703 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.12901 | 0.403056 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.7580 | −0.562183 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −23.0255 | −1.01266 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −64.7579 | −2.84256 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.38974 | 0.0608855 | 0.0304428 | − | 0.999537i | \(-0.490308\pi\) | ||||
0.0304428 | + | 0.999537i | \(0.490308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.05713 | 0.0462252 | 0.0231126 | − | 0.999733i | \(-0.492642\pi\) | ||||
0.0231126 | + | 0.999733i | \(0.492642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.1557 | 0.486875 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.0438 | −0.655317 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.5417 | 1.84964 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.8128 | 1.38056 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.49181 | −0.151247 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.4418 | −0.883778 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.9502 | 1.33560 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.2379 | 1.13015 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.96612 | 0.256503 | 0.128252 | − | 0.991742i | \(-0.459063\pi\) | ||||
0.128252 | + | 0.991742i | \(0.459063\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −22.1871 | −0.952139 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.38162 | −0.359029 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.9973 | −0.983292 | −0.491646 | − | 0.870795i | \(-0.663605\pi\) | ||||
−0.491646 | + | 0.870795i | \(0.663605\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.23717 | −0.0528012 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 19.8275 | 0.844679 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.0412 | 0.597092 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.96208 | 0.168181 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.09009 | 0.173303 | 0.0866514 | − | 0.996239i | \(-0.472383\pi\) | ||||
0.0866514 | + | 0.996239i | \(0.472383\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.4525 | −0.653570 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −55.9534 | −2.36236 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −44.2568 | −1.86520 | −0.932600 | − | 0.360911i | \(-0.882466\pi\) | ||||
−0.932600 | + | 0.360911i | \(0.882466\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0392 | −0.758917 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.01407 | −0.294563 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.59686 | −0.318477 | −0.159239 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159239 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0736 | 0.505265 | 0.252632 | − | 0.967562i | \(-0.418704\pi\) | ||||
0.252632 | + | 0.967562i | \(0.418704\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.13257 | 0.339743 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 30.1515 | 1.25740 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.2700 | −0.469174 | −0.234587 | − | 0.972095i | \(-0.575374\pi\) | ||||
−0.234587 | + | 0.972095i | \(0.575374\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21.2997 | 0.885183 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.17624 | −0.214747 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −53.4686 | −2.21444 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.8187 | 1.10882 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.1680 | 1.24517 | 0.622583 | − | 0.782553i | \(-0.286083\pi\) | ||||
0.622583 | + | 0.782553i | \(0.286083\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.7214 | −0.606585 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.5617 | −1.25714 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.24886 | 0.256610 | 0.128305 | − | 0.991735i | \(-0.459046\pi\) | ||||
0.128305 | + | 0.991735i | \(0.459046\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.04680 | −0.247895 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.45360 | −0.345983 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6174 | 0.556390 | 0.278195 | − | 0.960525i | \(-0.410264\pi\) | ||||
0.278195 | + | 0.960525i | \(0.410264\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.7493 | 1.53982 | 0.769912 | − | 0.638150i | \(-0.220300\pi\) | ||||
0.769912 | + | 0.638150i | \(0.220300\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.64550 | −0.392795 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11.7201 | 0.476489 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.9252 | 0.727562 | 0.363781 | − | 0.931485i | \(-0.381486\pi\) | ||||
0.363781 | + | 0.931485i | \(0.381486\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13.0493 | 0.528786 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 31.3595 | 1.26867 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.0328 | −0.526391 | −0.263195 | − | 0.964743i | \(-0.584776\pi\) | ||||
−0.263195 | + | 0.964743i | \(0.584776\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.62970 | 0.0657159 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.1504 | −1.37484 | −0.687421 | − | 0.726259i | \(-0.741257\pi\) | ||||
−0.687421 | + | 0.726259i | \(0.741257\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.0115 | −1.04549 | −0.522746 | − | 0.852489i | \(-0.675092\pi\) | ||||
−0.522746 | + | 0.852489i | \(0.675092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 16.2389 | 0.651645 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16.0869 | 0.644509 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.49246 | 0.299698 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −54.7544 | −2.18668 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.27000 | 0.250001 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.9082 | −1.07120 | −0.535599 | − | 0.844472i | \(-0.679914\pi\) | ||||
−0.535599 | + | 0.844472i | \(0.679914\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.1822 | −0.841916 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −15.3735 | −0.610080 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −35.7346 | −1.41585 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 36.4680 | 1.44265 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.9550 | 0.669684 | 0.334842 | − | 0.942274i | \(-0.391317\pi\) | ||||
0.334842 | + | 0.942274i | \(0.391317\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.26548 | 0.365395 | 0.182697 | − | 0.983169i | \(-0.441517\pi\) | ||||
0.182697 | + | 0.983169i | \(0.441517\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.21201 | 0.283973 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.2625 | 1.42563 | 0.712814 | − | 0.701353i | \(-0.247421\pi\) | ||||
0.712814 | + | 0.701353i | \(0.247421\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.0062 | −1.53113 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.68881 | −0.379734 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.2455 | 1.02706 | 0.513532 | − | 0.858070i | \(-0.328337\pi\) | ||||
0.513532 | + | 0.858070i | \(0.328337\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1869 | 0.710620 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.77371 | −0.225254 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.87094 | 0.150790 | 0.0753952 | − | 0.997154i | \(-0.475978\pi\) | ||||
0.0753952 | + | 0.997154i | \(0.475978\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.8920 | 1.70720 | 0.853601 | − | 0.520928i | \(-0.174414\pi\) | ||||
0.853601 | + | 0.520928i | \(0.174414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 76.2054 | 2.95957 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.91722 | −0.229460 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 35.2696 | 1.36564 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.841211 | −0.0325231 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.51691 | 0.0585598 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.8052 | 0.493603 | 0.246802 | − | 0.969066i | \(-0.420620\pi\) | ||||
0.246802 | + | 0.969066i | \(0.420620\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.47046 | 0.287538 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.9187 | −0.765538 | −0.382769 | − | 0.923844i | \(-0.625030\pi\) | ||||
−0.382769 | + | 0.923844i | \(0.625030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.7248 | 0.641837 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.3581 | −1.46988 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.48171 | 0.133224 | 0.0666120 | − | 0.997779i | \(-0.478781\pi\) | ||||
0.0666120 | + | 0.997779i | \(0.478781\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.91587 | 0.187826 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.7076 | 0.446672 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 72.8212 | 2.77427 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.8255 | 1.36287 | 0.681434 | − | 0.731880i | \(-0.261357\pi\) | ||||
0.681434 | + | 0.731880i | \(0.261357\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.0695 | −0.762378 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.6519 | 0.631644 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.57901 | 0.0976869 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.09956 | 0.306353 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.4520 | −0.621382 | −0.310691 | − | 0.950511i | \(-0.600560\pi\) | ||||
−0.310691 | + | 0.950511i | \(0.600560\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.13564 | 0.231410 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.6362 | −0.551230 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −14.1898 | −0.533663 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 53.0877 | 1.99375 | 0.996874 | − | 0.0790033i | \(-0.0251738\pi\) | ||||
0.996874 | + | 0.0790033i | \(0.0251738\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 45.9959 | 1.72498 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.1868 | −0.980703 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −32.8828 | −1.22975 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 62.1255 | 2.32012 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.1024 | −0.451343 | −0.225672 | − | 0.974203i | \(-0.572458\pi\) | ||||
−0.225672 | + | 0.974203i | \(0.572458\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0029 | −0.484253 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 19.1498 | 0.712187 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.2252 | 0.602590 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30.8602 | 1.14454 | 0.572271 | − | 0.820064i | \(-0.306062\pi\) | ||||
0.572271 | + | 0.820064i | \(0.306062\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.6347 | −1.43092 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.4130 | 0.422126 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.5216 | −1.49670 | −0.748351 | − | 0.663303i | \(-0.769154\pi\) | ||||
−0.748351 | + | 0.663303i | \(0.769154\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 16.6781 | 0.615181 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 11.8265 | 0.435634 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.6325 | 0.758979 | 0.379489 | − | 0.925196i | \(-0.376100\pi\) | ||||
0.379489 | + | 0.925196i | \(0.376100\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 74.5725 | 2.73949 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −49.2312 | −1.80612 | −0.903059 | − | 0.429517i | \(-0.858684\pi\) | ||||
−0.903059 | + | 0.429517i | \(0.858684\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.63413 | 0.316330 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.9562 | −0.620396 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −20.8343 | −0.761268 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.0160 | 0.766883 | 0.383442 | − | 0.923565i | \(-0.374739\pi\) | ||||
0.383442 | + | 0.923565i | \(0.374739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −71.5753 | −2.60835 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.6733 | −0.388443 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.41383 | −0.124078 | −0.0620389 | − | 0.998074i | \(-0.519760\pi\) | ||||
−0.0620389 | + | 0.998074i | \(0.519760\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −97.3985 | −3.53534 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.6666 | 1.61916 | 0.809582 | − | 0.587007i | \(-0.199694\pi\) | ||||
0.809582 | + | 0.587007i | \(0.199694\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.54253 | −0.309260 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19.8080 | −0.716160 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 53.1242 | 1.91820 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32.5210 | 1.17274 | 0.586369 | − | 0.810044i | \(-0.300557\pi\) | ||||
0.586369 | + | 0.810044i | \(0.300557\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 29.0008 | 1.04444 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.27718 | −0.333677 | −0.166838 | − | 0.985984i | \(-0.553356\pi\) | ||||
−0.166838 | + | 0.985984i | \(0.553356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.0468 | −0.432735 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.03814 | 0.144867 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.52374 | 0.0904225 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44.7139 | −1.59999 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.73855 | 0.312290 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 21.2468 | 0.758332 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.5268 | 0.838640 | 0.419320 | − | 0.907839i | \(-0.362269\pi\) | ||||
0.419320 | + | 0.907839i | \(0.362269\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 19.6852 | 0.700812 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.3856 | −0.653715 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.06595 | −0.0733641 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.9872 | −1.20540 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.8975 | 1.51951 | 0.759754 | − | 0.650210i | \(-0.225319\pi\) | ||||
0.759754 | + | 0.650210i | \(0.225319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.1618 | −0.819404 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 52.6973 | 1.86197 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.07923 | 0.249821 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.5257 | −0.370982 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 30.1869 | 1.06263 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.29970 | −0.0808533 | −0.0404266 | − | 0.999183i | \(-0.512872\pi\) | ||||
−0.0404266 | + | 0.999183i | \(0.512872\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.5348 | −0.615732 | −0.307866 | − | 0.951430i | \(-0.599615\pi\) | ||||
−0.307866 | + | 0.951430i | \(0.599615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −27.1857 | −0.953444 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 26.4284 | 0.925747 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1685 | 0.390735 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.3336 | 0.955112 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.91753 | 0.206523 | 0.103262 | − | 0.994654i | \(-0.467072\pi\) | ||||
0.103262 | + | 0.994654i | \(0.467072\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.4796 | 0.609300 | 0.304650 | − | 0.952464i | \(-0.401460\pi\) | ||||
0.304650 | + | 0.952464i | \(0.401460\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −44.8067 | −1.55997 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.1717 | 1.46645 | 0.733226 | − | 0.679985i | \(-0.238014\pi\) | ||||
0.733226 | + | 0.679985i | \(0.238014\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.7023 | −1.58731 | −0.793653 | − | 0.608371i | \(-0.791823\pi\) | ||||
−0.793653 | + | 0.608371i | \(0.791823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.57080 | −0.332007 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.3931 | 0.914468 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.9593 | −0.413870 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.48815 | −0.224263 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −47.6299 | −1.64437 | −0.822184 | − | 0.569222i | \(-0.807245\pi\) | ||||
−0.822184 | + | 0.569222i | \(0.807245\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0206 | −0.345537 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 85.4415 | 2.94276 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 30.1017 | 1.03553 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.9451 | 0.410438 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −77.9341 | −2.67469 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9142 | 0.374135 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.0088 | −0.513890 | −0.256945 | − | 0.966426i | \(-0.582716\pi\) | ||||
−0.256945 | + | 0.966426i | \(0.582716\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.3835 | −0.662903 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.2556 | 1.30679 | 0.653393 | − | 0.757019i | \(-0.273345\pi\) | ||||
0.653393 | + | 0.757019i | \(0.273345\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0573 | 0.889062 | 0.444531 | − | 0.895763i | \(-0.353370\pi\) | ||||
0.444531 | + | 0.895763i | \(0.353370\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.66099 | 0.0566064 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.3364 | 0.998624 | 0.499312 | − | 0.866422i | \(-0.333586\pi\) | ||||
0.499312 | + | 0.866422i | \(0.333586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.1085 | 0.955717 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.0490 | −0.409205 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −56.3963 | −1.91311 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.1070 | −0.545765 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 54.7867 | 1.85425 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.3429 | −0.383461 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.9083 | 0.706022 | 0.353011 | − | 0.935619i | \(-0.385158\pi\) | ||||
0.353011 | + | 0.935619i | \(0.385158\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.3155 | −0.988786 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.68502 | 0.124151 | 0.0620757 | − | 0.998071i | \(-0.480228\pi\) | ||||
0.0620757 | + | 0.998071i | \(0.480228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.00202305 | 6.80812e−5 0 | 3.40406e−5 | − | 1.00000i | \(-0.499989\pi\) | ||||
3.40406e−5 | 1.00000i | \(0.499989\pi\) | ||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.7942 | −0.833449 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.5580 | 0.656694 | 0.328347 | − | 0.944557i | \(-0.393508\pi\) | ||||
0.328347 | + | 0.944557i | \(0.393508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.6687 | −0.525510 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.1719 | 0.943795 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.6654 | −0.758470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.4341 | −0.449053 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 132.651 | 4.42910 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.0917 | −0.469986 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.7849 | −1.79183 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.35047 | 0.244608 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.63042 | 0.320126 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.64015 | 0.253687 | 0.126844 | − | 0.991923i | \(-0.459515\pi\) | ||||
0.126844 | + | 0.991923i | \(0.459515\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −46.4828 | −1.54174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.3768 | −1.20522 | −0.602608 | − | 0.798037i | \(-0.705872\pi\) | ||||
−0.602608 | + | 0.798037i | \(0.705872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7903 | 0.688058 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.964225 | 0.0318763 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.5360 | 0.612113 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −55.9427 | −1.84538 | −0.922690 | − | 0.385543i | \(-0.874014\pi\) | ||||
−0.922690 | + | 0.385543i | \(0.874014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −39.7488 | −1.30977 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 60.8978 | 2.00448 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.02093 | 0.165087 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −42.5946 | −1.39899 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.47640 | −0.114057 | −0.0570285 | − | 0.998373i | \(-0.518163\pi\) | ||||
−0.0570285 | + | 0.998373i | \(0.518163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 25.8276 | 0.846465 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.17387 | 0.0384309 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24.2869 | 0.794266 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.1396 | −1.83400 | −0.917001 | − | 0.398886i | \(-0.869397\pi\) | ||||
−0.917001 | + | 0.398886i | \(0.869397\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −35.4162 | −1.15576 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.7192 | 0.708024 | 0.354012 | − | 0.935241i | \(-0.384817\pi\) | ||||
0.354012 | + | 0.935241i | \(0.384817\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.48930 | 0.146192 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.60789 | −0.0848348 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.7946 | −1.09818 | −0.549088 | − | 0.835764i | \(-0.685025\pi\) | ||||
−0.549088 | + | 0.835764i | \(0.685025\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.64151 | −0.312977 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 75.8735 | 2.46037 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.0311 | 0.324938 | 0.162469 | − | 0.986714i | \(-0.448054\pi\) | ||||
0.162469 | + | 0.986714i | \(0.448054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.52998 | −0.114228 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −52.4125 | −1.69426 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.01024 | 0.161789 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5372 | −0.662491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −68.2486 | −2.19928 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.24522 | −0.297614 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.6091 | 1.69180 | 0.845898 | − | 0.533345i | \(-0.179065\pi\) | ||||
0.845898 | + | 0.533345i | \(0.179065\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −55.0784 | −1.76937 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −54.9841 | −1.76452 | −0.882262 | − | 0.470759i | \(-0.843980\pi\) | ||||
−0.882262 | + | 0.470759i | \(0.843980\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 16.9716 | 0.544085 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 61.0242 | 1.95434 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6271 | 0.787892 | 0.393946 | − | 0.919134i | \(-0.371110\pi\) | ||||
0.393946 | + | 0.919134i | \(0.371110\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −64.6129 | −2.06504 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.9835 | −0.893444 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 35.9409 | 1.14634 | 0.573169 | − | 0.819437i | \(-0.305714\pi\) | ||||
0.573169 | + | 0.819437i | \(0.305714\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2655 | 0.422673 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.9171 | −0.474818 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.8667 | 0.631726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.5366 | 0.970028 | 0.485014 | − | 0.874506i | \(-0.338815\pi\) | ||||
0.485014 | + | 0.874506i | \(0.338815\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.1028 | −0.733146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.66933 | 0.116326 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.1530 | −1.43001 | −0.715006 | − | 0.699119i | \(-0.753576\pi\) | ||||
−0.715006 | + | 0.699119i | \(0.753576\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.70416 | 0.0855557 |
(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 | 8048.2.a.y.1.5 | 33 | ||
4.3 | odd | 2 | 4024.2.a.f.1.29 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.f.1.29 | ✓ | 33 | 4.3 | odd | 2 | ||
8048.2.a.y.1.5 | 33 | 1.1 | even | 1 | trivial |