Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + \cdots + 7375227456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{18} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.7 | ||
Root | \(-8.00527 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.17 |
Dual form | 1008.4.bt.b.593.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.36813 | + | 7.56582i | 0.390697 | + | 0.676707i | 0.992542 | − | 0.121906i | \(-0.0389006\pi\) |
−0.601844 | + | 0.798613i | \(0.705567\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.4904 | − | 11.5338i | −0.782406 | − | 0.622769i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7.60916 | + | 4.39315i | 0.208568 | + | 0.120417i | 0.600646 | − | 0.799515i | \(-0.294910\pi\) |
−0.392078 | + | 0.919932i | \(0.628244\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.8322i | 0.252435i | 0.992003 | + | 0.126217i | \(0.0402837\pi\) | ||||
−0.992003 | + | 0.126217i | \(0.959716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.2920 | + | 38.6108i | −0.318035 | + | 0.550853i | −0.980078 | − | 0.198613i | \(-0.936356\pi\) |
0.662043 | + | 0.749466i | \(0.269690\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.0856 | + | 5.82291i | −0.121778 | + | 0.0703088i | −0.559652 | − | 0.828728i | \(-0.689065\pi\) |
0.437873 | + | 0.899037i | \(0.355732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 123.521 | − | 71.3151i | 1.11982 | − | 0.646531i | 0.178469 | − | 0.983946i | \(-0.442886\pi\) |
0.941356 | + | 0.337414i | \(0.109552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.3389 | − | 42.1563i | 0.194711 | − | 0.337250i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 234.018i | 1.49848i | 0.662298 | + | 0.749241i | \(0.269581\pi\) | ||||
−0.662298 | + | 0.749241i | \(0.730419\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −252.809 | − | 145.960i | −1.46471 | − | 0.845649i | −0.465484 | − | 0.885056i | \(-0.654120\pi\) |
−0.999223 | + | 0.0394074i | \(0.987453\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 23.9672 | − | 160.013i | 0.115748 | − | 0.772774i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.4515 | + | 76.9923i | 0.197508 | + | 0.342093i | 0.947720 | − | 0.319104i | \(-0.103382\pi\) |
−0.750212 | + | 0.661197i | \(0.770049\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −145.961 | −0.555984 | −0.277992 | − | 0.960583i | \(-0.589669\pi\) | ||||
−0.277992 | + | 0.960583i | \(0.589669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −144.633 | −0.512938 | −0.256469 | − | 0.966552i | \(-0.582559\pi\) | ||||
−0.256469 | + | 0.966552i | \(0.582559\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −120.183 | − | 208.164i | −0.372991 | − | 0.646039i | 0.617033 | − | 0.786937i | \(-0.288334\pi\) |
−0.990024 | + | 0.140898i | \(0.955001\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 76.9412 | + | 334.259i | 0.224318 | + | 0.974516i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −263.538 | − | 152.154i | −0.683015 | − | 0.394339i | 0.117975 | − | 0.993017i | \(-0.462360\pi\) |
−0.800990 | + | 0.598678i | \(0.795693\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 76.7594i | 0.188186i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.54196 | − | 6.13486i | 0.00781566 | − | 0.0135371i | −0.862091 | − | 0.506753i | \(-0.830846\pi\) |
0.869907 | + | 0.493216i | \(0.164179\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −149.810 | + | 86.4927i | −0.314445 | + | 0.181545i | −0.648914 | − | 0.760862i | \(-0.724777\pi\) |
0.334469 | + | 0.942407i | \(0.391443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −89.5199 | + | 51.6844i | −0.170824 | + | 0.0986255i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −243.280 | + | 421.373i | −0.443603 | + | 0.768342i | −0.997954 | − | 0.0639408i | \(-0.979633\pi\) |
0.554351 | + | 0.832283i | \(0.312966\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 653.710i | − | 1.09269i | −0.837560 | − | 0.546345i | \(-0.816019\pi\) | ||
0.837560 | − | 0.546345i | \(-0.183981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −99.0378 | − | 57.1795i | −0.158788 | − | 0.0916761i | 0.418501 | − | 0.908217i | \(-0.362556\pi\) |
−0.577288 | + | 0.816540i | \(0.695889\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −59.5896 | − | 151.421i | −0.0881931 | − | 0.224104i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 147.307 | + | 255.144i | 0.209789 | + | 0.363366i | 0.951648 | − | 0.307190i | \(-0.0993888\pi\) |
−0.741859 | + | 0.670556i | \(0.766055\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −877.193 | −1.16005 | −0.580027 | − | 0.814597i | \(-0.696958\pi\) | ||||
−0.580027 | + | 0.814597i | \(0.696958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −389.496 | −0.497021 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −710.379 | − | 1230.41i | −0.846068 | − | 1.46543i | −0.884691 | − | 0.466179i | \(-0.845630\pi\) |
0.0386225 | − | 0.999254i | \(-0.487703\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 136.470 | − | 171.452i | 0.157208 | − | 0.197506i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −88.1102 | − | 50.8704i | −0.0951570 | − | 0.0549389i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 738.981i | − | 0.773527i | −0.922179 | − | 0.386764i | \(-0.873593\pi\) | ||
0.922179 | − | 0.386764i | \(-0.126407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 831.442 | − | 1440.10i | 0.819125 | − | 1.41877i | −0.0872031 | − | 0.996191i | \(-0.527793\pi\) |
0.906328 | − | 0.422575i | \(-0.138874\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 394.807 | − | 227.942i | 0.377684 | − | 0.218056i | −0.299126 | − | 0.954214i | \(-0.596695\pi\) |
0.676810 | + | 0.736158i | \(0.263362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1279.07 | + | 738.474i | −1.15563 | + | 0.667205i | −0.950254 | − | 0.311477i | \(-0.899176\pi\) |
−0.205380 | + | 0.978682i | \(0.565843\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −784.202 | + | 1358.28i | −0.689110 | + | 1.19357i | 0.283016 | + | 0.959115i | \(0.408665\pi\) |
−0.972126 | + | 0.234458i | \(0.924668\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1077.27i | − | 0.896820i | −0.893828 | − | 0.448410i | \(-0.851990\pi\) | ||
0.893828 | − | 0.448410i | \(-0.148010\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1079.11 | + | 623.026i | 0.875025 | + | 0.505196i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 768.349 | − | 302.373i | 0.591886 | − | 0.232928i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −626.900 | − | 1085.82i | −0.471000 | − | 0.815795i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1517.29 | 1.08569 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1518.00 | −1.06063 | −0.530317 | − | 0.847799i | \(-0.677927\pi\) | ||||
−0.530317 | + | 0.847799i | \(0.677927\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 201.672 | + | 349.306i | 0.134505 | + | 0.232969i | 0.925408 | − | 0.378972i | \(-0.123722\pi\) |
−0.790903 | + | 0.611941i | \(0.790389\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 213.304 | + | 31.9493i | 0.139066 | + | 0.0208298i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −467.650 | − | 269.998i | −0.291636 | − | 0.168376i | 0.347044 | − | 0.937849i | \(-0.387186\pi\) |
−0.638679 | + | 0.769473i | \(0.720519\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2042.22i | 1.24618i | 0.782151 | + | 0.623089i | \(0.214123\pi\) | ||||
−0.782151 | + | 0.623089i | \(0.785877\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −51.9805 | + | 90.0328i | −0.0303974 | + | 0.0526498i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1770.53 | + | 1022.22i | −1.01403 | + | 0.585452i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 180.517 | − | 104.222i | 0.0992521 | − | 0.0573032i | −0.449552 | − | 0.893254i | \(-0.648416\pi\) |
0.548804 | + | 0.835951i | \(0.315083\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −230.045 | + | 398.449i | −0.123979 | + | 0.214737i | −0.921333 | − | 0.388774i | \(-0.872899\pi\) |
0.797355 | + | 0.603511i | \(0.206232\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 2550.28i | − | 1.32157i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2330.15 | − | 1345.31i | −1.18450 | − | 0.683869i | −0.227446 | − | 0.973791i | \(-0.573037\pi\) |
−0.957050 | + | 0.289921i | \(0.906371\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2612.40 | − | 391.293i | −1.27880 | − | 0.191542i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1137.44 | − | 1970.10i | −0.546571 | − | 0.946689i | −0.998506 | − | 0.0546381i | \(-0.982599\pi\) |
0.451935 | − | 0.892051i | \(-0.350734\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3214.68 | −1.48958 | −0.744789 | − | 0.667300i | \(-0.767450\pi\) | ||||
−0.744789 | + | 0.667300i | \(0.767450\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2057.00 | 0.936277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1782.11 | − | 3086.71i | −0.783187 | − | 1.35652i | −0.930076 | − | 0.367367i | \(-0.880259\pi\) |
0.146889 | − | 0.989153i | \(-0.453074\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −838.903 | + | 330.138i | −0.362372 | + | 0.142606i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −302.852 | − | 174.852i | −0.126459 | − | 0.0730113i | 0.435436 | − | 0.900220i | \(-0.356594\pi\) |
−0.561895 | + | 0.827208i | \(0.689928\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1664.25i | 0.683439i | 0.939802 | + | 0.341720i | \(0.111009\pi\) | ||||
−0.939802 | + | 0.341720i | \(0.888991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −388.340 | + | 672.624i | −0.154331 | + | 0.267310i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −339.246 | + | 195.864i | −0.132664 | + | 0.0765935i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −213.721 | + | 123.392i | −0.0809650 | + | 0.0467452i | −0.539936 | − | 0.841706i | \(-0.681552\pi\) |
0.458971 | + | 0.888451i | \(0.348218\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1274.22 | + | 2207.01i | −0.475235 | + | 0.823130i | −0.999598 | − | 0.0283643i | \(-0.990970\pi\) |
0.524363 | + | 0.851495i | \(0.324303\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4579.00i | 1.65604i | 0.560697 | + | 0.828021i | \(0.310533\pi\) | ||||
−0.560697 | + | 0.828021i | \(0.689467\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2151.47 | − | 1242.15i | −0.766402 | − | 0.442482i | 0.0651876 | − | 0.997873i | \(-0.479235\pi\) |
−0.831590 | + | 0.555391i | \(0.812569\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2699.12 | − | 3391.00i | 0.933207 | − | 1.17242i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −637.578 | − | 1104.32i | −0.217221 | − | 0.376238i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −102.324 | −0.0338655 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5736.87 | −1.87177 | −0.935883 | − | 0.352311i | \(-0.885396\pi\) | ||||
−0.935883 | + | 0.352311i | \(0.885396\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −631.775 | − | 1094.27i | −0.200403 | − | 0.347109i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1979.83 | + | 5030.87i | 0.619352 | + | 1.57381i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −456.849 | − | 263.762i | −0.139054 | − | 0.0802830i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5391.46i | 1.61901i | 0.587115 | + | 0.809504i | \(0.300264\pi\) | ||||
−0.587115 | + | 0.809504i | \(0.699736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 747.447 | − | 1294.62i | 0.218545 | − | 0.378532i | −0.735818 | − | 0.677179i | \(-0.763202\pi\) |
0.954364 | + | 0.298647i | \(0.0965355\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 693.480 | − | 400.381i | 0.200115 | − | 0.115537i | −0.396594 | − | 0.917994i | \(-0.629808\pi\) |
0.596709 | + | 0.802457i | \(0.296475\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2273.75 | + | 1312.75i | −0.639305 | + | 0.369103i | −0.784347 | − | 0.620323i | \(-0.787002\pi\) |
0.145042 | + | 0.989426i | \(0.453668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1049.95 | − | 1818.57i | 0.291453 | − | 0.504811i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6283.85i | − | 1.70070i | −0.526214 | − | 0.850352i | \(-0.676389\pi\) | ||
0.526214 | − | 0.850352i | \(-0.323611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −811.225 | − | 468.361i | −0.216828 | − | 0.125186i | 0.387653 | − | 0.921806i | \(-0.373286\pi\) |
−0.604481 | + | 0.796620i | \(0.706619\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2192.85 | + | 2042.21i | −0.571822 | + | 0.532539i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −68.8976 | − | 119.334i | −0.0177484 | − | 0.0307411i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2831.45 | −0.712031 | −0.356015 | − | 0.934480i | \(-0.615865\pi\) | ||||
−0.356015 | + | 0.934480i | \(0.615865\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1253.19 | 0.311413 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2844.65 | − | 4927.08i | −0.690445 | − | 1.19589i | −0.971692 | − | 0.236251i | \(-0.924081\pi\) |
0.281247 | − | 0.959636i | \(-0.409252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 243.898 | − | 1628.34i | 0.0585138 | − | 0.390657i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3479.60 | + | 2008.95i | 0.815823 | + | 0.471016i | 0.848974 | − | 0.528435i | \(-0.177221\pi\) |
−0.0331509 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2658.51i | − | 0.616268i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1908.81 | − | 3306.16i | 0.432648 | − | 0.749368i | −0.564453 | − | 0.825465i | \(-0.690913\pi\) |
0.997100 | + | 0.0760977i | \(0.0242461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6193.16 | − | 3575.62i | 1.38822 | − | 0.801489i | 0.395105 | − | 0.918636i | \(-0.370708\pi\) |
0.993115 | + | 0.117147i | \(0.0373747\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 370.398 | − | 213.849i | 0.0812212 | − | 0.0468931i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2741.91 | − | 4749.12i | 0.594748 | − | 1.03013i | −0.398834 | − | 0.917023i | \(-0.630585\pi\) |
0.993582 | − | 0.113111i | \(-0.0360815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5525.72i | 1.17308i | 0.809919 | + | 0.586542i | \(0.199511\pi\) | ||||
−0.809919 | + | 0.586542i | \(0.800489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −217.828 | − | 125.763i | −0.0457545 | − | 0.0264164i | 0.476948 | − | 0.878931i | \(-0.341743\pi\) |
−0.522703 | + | 0.852515i | \(0.675076\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2115.03 | + | 1683.49i | 0.435005 | + | 0.346249i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1462.64 | + | 2533.36i | 0.297707 | + | 0.515645i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9296.44 | 1.85360 | 0.926798 | − | 0.375560i | \(-0.122550\pi\) | ||||
0.926798 | + | 0.375560i | \(0.122550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 61.8869 | 0.0122142 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 843.811 | + | 1461.52i | 0.163207 | + | 0.282683i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2095.78 | + | 1668.17i | 0.401326 | + | 0.319442i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1308.78 | − | 755.622i | −0.245706 | − | 0.141858i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1498.96i | − | 0.278666i | −0.990246 | − | 0.139333i | \(-0.955504\pi\) | ||
0.990246 | − | 0.139333i | \(-0.0444958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3129.10 | + | 5419.77i | −0.570531 | + | 0.988189i | 0.425980 | + | 0.904733i | \(0.359929\pi\) |
−0.996511 | + | 0.0834566i | \(0.973404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1843.53 | + | 1064.36i | −0.332915 | + | 0.192208i | −0.657134 | − | 0.753773i | \(-0.728232\pi\) |
0.324220 | + | 0.945982i | \(0.394898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4547.45 | − | 2625.47i | 0.805710 | − | 0.465177i | −0.0397541 | − | 0.999209i | \(-0.512657\pi\) |
0.845464 | + | 0.534033i | \(0.179324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1028.07 | + | 1780.68i | −0.180442 | + | 0.312535i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 519.216i | − | 0.0894427i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 498.799 | + | 287.982i | 0.0851336 | + | 0.0491519i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −659.426 | + | 4402.55i | −0.110503 | + | 0.737752i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4401.99 | + | 7624.47i | 0.730983 | + | 1.26610i | 0.956464 | + | 0.291852i | \(0.0942714\pi\) |
−0.225481 | + | 0.974248i | \(0.572395\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4250.71 | −0.693257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1428.63 | −0.230927 | −0.115463 | − | 0.993312i | \(-0.536835\pi\) | ||||
−0.115463 | + | 0.993312i | \(0.536835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1282.45 | − | 2221.26i | −0.203661 | − | 0.352751i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2740.38 | − | 5730.96i | 0.431390 | − | 0.902166i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7896.72 | + | 4559.17i | 1.22167 | + | 0.705329i | 0.965273 | − | 0.261244i | \(-0.0841327\pi\) |
0.256393 | + | 0.966573i | \(0.417466\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 11899.1i | − | 1.82506i | −0.409011 | − | 0.912530i | \(-0.634126\pi\) | ||
0.409011 | − | 0.912530i | \(-0.365874\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4578.82 | − | 7930.75i | 0.690385 | − | 1.19578i | −0.281327 | − | 0.959612i | \(-0.590774\pi\) |
0.971712 | − | 0.236170i | \(-0.0758923\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4945.85 | − | 2855.49i | 0.739432 | − | 0.426911i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6729.83 | + | 3885.47i | −0.989379 | + | 0.571218i | −0.905089 | − | 0.425223i | \(-0.860196\pi\) |
−0.0842902 | + | 0.996441i | \(0.526862\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3361.69 | + | 5822.61i | −0.490113 | + | 0.848901i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 999.070i | − | 0.143270i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5456.63 | + | 3150.39i | 0.776114 | + | 0.448090i | 0.835051 | − | 0.550172i | \(-0.185438\pi\) |
−0.0589371 | + | 0.998262i | \(0.518771\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2063.85 | + | 5244.37i | 0.288813 | + | 0.733893i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5051.76 | − | 8749.90i | −0.701260 | − | 1.21462i | −0.968024 | − | 0.250857i | \(-0.919288\pi\) |
0.266764 | − | 0.963762i | \(-0.414046\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2768.93 | −0.378269 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1122.50 | −0.152134 | −0.0760671 | − | 0.997103i | \(-0.524236\pi\) | ||||
−0.0760671 | + | 0.997103i | \(0.524236\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5313.98 | + | 9204.08i | 0.708960 | + | 1.22795i | 0.965243 | + | 0.261353i | \(0.0841686\pi\) |
−0.256283 | + | 0.966602i | \(0.582498\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 885.330 | − | 1112.27i | 0.117196 | − | 0.147238i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11571.8 | + | 6680.96i | 1.50826 | + | 0.870792i | 0.999954 | + | 0.00961230i | \(0.00305974\pi\) |
0.508301 | + | 0.861179i | \(0.330274\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6359.01i | 0.822478i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1286.91 | + | 2229.00i | −0.163928 | + | 0.283932i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2304.31 | + | 1330.40i | −0.291310 | + | 0.168188i | −0.638533 | − | 0.769595i | \(-0.720458\pi\) |
0.347222 | + | 0.937783i | \(0.387125\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5288.60 | + | 3053.37i | −0.658603 | + | 0.380245i | −0.791745 | − | 0.610852i | \(-0.790827\pi\) |
0.133141 | + | 0.991097i | \(0.457494\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1727.02 | − | 2991.28i | 0.213471 | − | 0.369743i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 781.129i | 0.0951330i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1998.03 | − | 1153.56i | −0.241556 | − | 0.139462i | 0.374336 | − | 0.927293i | \(-0.377871\pi\) |
−0.615892 | + | 0.787831i | \(0.711204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −122.083 | + | 48.0439i | −0.0145455 | + | 0.00572418i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3831.69 | − | 6636.69i | −0.453230 | − | 0.785017i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11116.9 | −1.29617 | −0.648083 | − | 0.761570i | \(-0.724429\pi\) | ||||
−0.648083 | + | 0.761570i | \(0.724429\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4188.14 | 0.484840 | 0.242420 | − | 0.970171i | \(-0.422059\pi\) | ||||
0.242420 | + | 0.970171i | \(0.422059\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1085.12 | + | 1879.49i | 0.123850 | + | 0.214515i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3168.39 | + | 474.571i | 0.359085 | + | 0.0537847i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4253.15 | + | 2455.56i | 0.475329 | + | 0.274432i | 0.718468 | − | 0.695560i | \(-0.244844\pi\) |
−0.243139 | + | 0.969992i | \(0.578177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14412.6i | 1.59960i | 0.600268 | + | 0.799799i | \(0.295061\pi\) | ||||
−0.600268 | + | 0.799799i | \(0.704939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −830.522 | + | 1438.51i | −0.0909137 | + | 0.157467i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7721.97 | + | 4458.28i | −0.839520 | + | 0.484697i | −0.857101 | − | 0.515148i | \(-0.827737\pi\) |
0.0175809 | + | 0.999845i | \(0.494404\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1022.14 | + | 590.133i | −0.109624 | + | 0.0632913i | −0.553809 | − | 0.832643i | \(-0.686826\pi\) |
0.444186 | + | 0.895935i | \(0.353493\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6206.05 | − | 10749.2i | 0.661113 | − | 1.14508i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 12536.1i | 1.31763i | 0.752307 | + | 0.658813i | \(0.228941\pi\) | ||||
−0.752307 | + | 0.658813i | \(0.771059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1110.64 | − | 641.230i | −0.115960 | − | 0.0669498i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1893.30 | + | 283.583i | 0.195075 | + | 0.0292189i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5051.92 | + | 8750.18i | 0.517109 | + | 0.895659i | 0.999803 | + | 0.0198696i | \(0.00632509\pi\) |
−0.482694 | + | 0.875789i | \(0.660342\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 418.675 | 0.0422985 | 0.0211493 | − | 0.999776i | \(-0.493267\pi\) | ||||
0.0211493 | + | 0.999776i | \(0.493267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2178.42 | 0.218661 | 0.109330 | − | 0.994005i | \(-0.465129\pi\) | ||||
0.109330 | + | 0.994005i | \(0.465129\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1929.85 | + | 3342.59i | 0.191226 | + | 0.331213i | 0.945657 | − | 0.325166i | \(-0.105420\pi\) |
−0.754431 | + | 0.656380i | \(0.772087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8385.26 | − | 3299.90i | 0.825577 | − | 0.324894i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1100.54 | − | 635.394i | −0.106982 | − | 0.0617663i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 566.894i | 0.0547597i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8106.86 | − | 14041.5i | 0.773302 | − | 1.33940i | −0.162442 | − | 0.986718i | \(-0.551937\pi\) |
0.935744 | − | 0.352680i | \(-0.114730\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −910.985 | + | 525.957i | −0.0863562 | + | 0.0498578i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5591.00 | − | 3227.96i | 0.523452 | − | 0.302215i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9902.83 | − | 17152.2i | 0.921437 | − | 1.59598i | 0.124244 | − | 0.992252i | \(-0.460349\pi\) |
0.797193 | − | 0.603725i | \(-0.206317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11104.5i | 1.02065i | 0.859983 | + | 0.510323i | \(0.170474\pi\) | ||||
−0.859983 | + | 0.510323i | \(0.829526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9035.61 | − | 5216.71i | −0.825443 | − | 0.476570i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7539.78 | + | 9472.49i | −0.680494 | + | 0.854928i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 435.024 | + | 753.483i | 0.0390267 | + | 0.0675963i | 0.884879 | − | 0.465821i | \(-0.154241\pi\) |
−0.845852 | + | 0.533417i | \(0.820908\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12435.5 | 1.10233 | 0.551166 | − | 0.834396i | \(-0.314183\pi\) | ||||
0.551166 | + | 0.834396i | \(0.314183\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14527.4 | 1.28012 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9850.04 | + | 17060.8i | 0.857751 | + | 1.48567i | 0.874069 | + | 0.485802i | \(0.161472\pi\) |
−0.0163174 | + | 0.999867i | \(0.505194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 775.595 | + | 1970.84i | 0.0671434 | + | 0.170616i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3449.13 | + | 1991.36i | 0.295120 | + | 0.170388i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2111.94i | − | 0.179657i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4813.26 | + | 8336.82i | −0.404747 | + | 0.701042i | −0.994292 | − | 0.106694i | \(-0.965974\pi\) |
0.589545 | + | 0.807735i | \(0.299307\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1451.42 | + | 837.977i | −0.121350 | + | 0.0700615i | −0.559446 | − | 0.828867i | \(-0.688986\pi\) |
0.438096 | + | 0.898928i | \(0.355653\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11271.2 | − | 6507.45i | 0.931656 | − | 0.537892i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4088.17 | − | 7080.92i | 0.336005 | − | 0.581978i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1727.04i | − | 0.140350i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11174.3 | − | 6451.50i | −0.903006 | − | 0.521351i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −882.992 | + | 2881.44i | −0.0705624 | + | 0.230265i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4323.06 | + | 7487.76i | 0.343554 | + | 0.595054i | 0.985090 | − | 0.172040i | \(-0.0550357\pi\) |
−0.641536 | + | 0.767093i | \(0.721702\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13702.0 | −1.07693 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −183.297 | −0.0143276 | −0.00716382 | − | 0.999974i | \(-0.502280\pi\) | ||||
−0.00716382 | + | 0.999974i | \(0.502280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1362.66 | − | 2360.20i | −0.105356 | − | 0.182483i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 808.250 | − | 5396.14i | 0.0621524 | − | 0.414950i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18922.7 | + | 10925.0i | 1.43946 | + | 0.831072i | 0.997812 | − | 0.0661167i | \(-0.0210610\pi\) |
0.441647 | + | 0.897189i | \(0.354394\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1711.32i | − | 0.129483i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7624.11 | − | 13205.3i | 0.570724 | − | 0.988523i | −0.425767 | − | 0.904833i | \(-0.639996\pi\) |
0.996492 | − | 0.0836908i | \(-0.0266708\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8150.40 | − | 4705.64i | 0.606885 | − | 0.350385i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10861.9 | + | 6271.10i | −0.800269 | + | 0.462035i | −0.843565 | − | 0.537027i | \(-0.819547\pi\) |
0.0432965 | + | 0.999062i | \(0.486214\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5721.40 | − | 9909.76i | 0.419323 | − | 0.726288i | −0.576549 | − | 0.817063i | \(-0.695601\pi\) |
0.995871 | + | 0.0907745i | \(0.0289343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 6942.93i | − | 0.503548i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9599.35 | + | 5542.18i | 0.692593 | + | 0.399869i | 0.804583 | − | 0.593841i | \(-0.202389\pi\) |
−0.111990 | + | 0.993709i | \(0.535722\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12710.8 | + | 10117.4i | 0.907633 | + | 0.722445i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1336.87 | − | 2315.53i | −0.0949700 | − | 0.164493i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1493.49 | 0.105014 | 0.0525068 | − | 0.998621i | \(-0.483279\pi\) | ||||
0.0525068 | + | 0.998621i | \(0.483279\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3399.64 | 0.237826 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2832.72 | − | 4906.42i | −0.196165 | − | 0.339768i | 0.751117 | − | 0.660170i | \(-0.229516\pi\) |
−0.947282 | + | 0.320401i | \(0.896182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5643.95 | + | 4492.39i | 0.388873 | + | 0.309529i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4487.18 | − | 2590.68i | −0.306079 | − | 0.176715i | 0.339091 | − | 0.940753i | \(-0.389880\pi\) |
−0.645171 | + | 0.764039i | \(0.723214\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13911.4i | 0.944186i | 0.881549 | + | 0.472093i | \(0.156501\pi\) | ||||
−0.881549 | + | 0.472093i | \(0.843499\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5476.76 | − | 9486.03i | 0.368036 | − | 0.637458i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6537.98 | + | 3774.70i | −0.437180 | + | 0.252406i | −0.702401 | − | 0.711782i | \(-0.747889\pi\) |
0.265221 | + | 0.964188i | \(0.414555\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2463.03 | − | 1422.03i | 0.163083 | − | 0.0941557i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6443.77 | − | 11160.9i | 0.424570 | − | 0.735377i | −0.571810 | − | 0.820386i | \(-0.693759\pi\) |
0.996380 | + | 0.0850093i | \(0.0270920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22388.7i | − | 1.46084i | −0.683000 | − | 0.730419i | \(-0.739325\pi\) | ||
0.683000 | − | 0.730419i | \(-0.260675\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4791.17 | − | 2766.18i | −0.311104 | − | 0.179616i | 0.336316 | − | 0.941749i | \(-0.390819\pi\) |
−0.647420 | + | 0.762133i | \(0.724152\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3897.73 | + | 26022.5i | −0.250657 | + | 1.67347i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3585.37 | + | 6210.04i | 0.229463 | + | 0.397442i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −3963.65 | −0.251257 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24188.4 | 1.52603 | 0.763015 | − | 0.646381i | \(-0.223718\pi\) | ||||
0.763015 | + | 0.646381i | \(0.223718\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6630.81 | − | 11484.9i | −0.414387 | − | 0.717739i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3955.00 | + | 910.380i | −0.246002 | + | 0.0566257i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7955.44 | − | 4593.08i | −0.490205 | − | 0.283020i | 0.234455 | − | 0.972127i | \(-0.424670\pi\) |
−0.724659 | + | 0.689107i | \(0.758003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21051.2i | − | 1.29110i | −0.763718 | − | 0.645550i | \(-0.776628\pi\) | ||
0.763718 | − | 0.645550i | \(-0.223372\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1834.16 | + | 3176.85i | −0.111450 | + | 0.193037i | −0.916355 | − | 0.400367i | \(-0.868883\pi\) |
0.804905 | + | 0.593403i | \(0.202216\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 53.9027 | − | 31.1207i | 0.00326019 | − | 0.00188227i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6653.57 | − | 3841.44i | 0.398736 | − | 0.230210i | −0.287203 | − | 0.957870i | \(-0.592725\pi\) |
0.685938 | + | 0.727660i | \(0.259392\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1761.85 | + | 3051.62i | −0.105101 | + | 0.182041i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 529.107i | − | 0.0312763i | −0.999878 | − | 0.0156382i | \(-0.995022\pi\) | ||
0.999878 | − | 0.0156382i | \(-0.00497798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11918.0 | − | 6880.84i | −0.701294 | − | 0.404892i | 0.106535 | − | 0.994309i | \(-0.466024\pi\) |
−0.807829 | + | 0.589417i | \(0.799358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 690.017 | + | 1753.38i | 0.0402372 | + | 0.102245i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16689.0 | + | 28906.1i | 0.968815 | + | 1.67804i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1519.90 | −0.0874443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31045.7 | −1.77819 | −0.889095 | − | 0.457722i | \(-0.848666\pi\) | ||||
−0.889095 | + | 0.457722i | \(0.848666\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2924.24 | + | 5064.94i | 0.166009 | + | 0.287535i | 0.937013 | − | 0.349295i | \(-0.113579\pi\) |
−0.771004 | + | 0.636830i | \(0.780245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8523.29 | + | 10708.1i | −0.481729 | + | 0.605213i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11813.9 | + | 6820.78i | 0.661856 | + | 0.382123i | 0.792984 | − | 0.609242i | \(-0.208526\pi\) |
−0.131127 | + | 0.991366i | \(0.541860\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 4717.54i | − | 0.263136i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1800.31 | − | 3118.23i | 0.0995447 | − | 0.172417i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12034.8 | + | 6948.27i | −0.662552 | + | 0.382525i | −0.793249 | − | 0.608898i | \(-0.791612\pi\) |
0.130696 | + | 0.991422i | \(0.458279\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15451.1 | + | 8920.68i | −0.843298 | + | 0.486879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3253.76 | − | 5635.69i | 0.176822 | − | 0.306265i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 30902.8i | − | 1.66503i | −0.554005 | − | 0.832513i | \(-0.686901\pi\) | ||
0.554005 | − | 0.832513i | \(-0.313099\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −896.638 | − | 517.674i | −0.0481044 | − | 0.0277731i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −28657.8 | + | 11277.9i | −1.52445 | + | 0.599926i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2160.65 | + | 3742.35i | 0.114450 | + | 0.198233i | 0.917560 | − | 0.397598i | \(-0.130156\pi\) |
−0.803110 | + | 0.595831i | \(0.796823\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41636.5 | −2.18695 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −908.229 | −0.0475047 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16131.0 | − | 27939.7i | −0.836696 | − | 1.44920i | −0.892642 | − | 0.450767i | \(-0.851151\pi\) |
0.0559456 | − | 0.998434i | \(-0.482183\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8349.93 | − | 1250.68i | −0.431301 | − | 0.0646014i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9865.30 | + | 5695.74i | 0.505363 | + | 0.291771i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12056.4i | 0.615056i | 0.951539 | + | 0.307528i | \(0.0995017\pi\) | ||||
−0.951539 | + | 0.307528i | \(0.900498\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3224.15 | − | 5584.40i | 0.163132 | − | 0.282553i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22122.9 | + | 12772.7i | −1.11477 | + | 0.643615i | −0.940061 | − | 0.341005i | \(-0.889233\pi\) |
−0.174712 | + | 0.984620i | \(0.555899\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3702.31 | + | 2137.53i | −0.185043 | + | 0.106834i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12402.9 | + | 21482.4i | −0.617384 | + | 1.06934i | 0.372577 | + | 0.928001i | \(0.378474\pi\) |
−0.989961 | + | 0.141340i | \(0.954859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23318.4i | 1.15137i | 0.817671 | + | 0.575686i | \(0.195265\pi\) | ||||
−0.817671 | + | 0.575686i | \(0.804735\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1577.05 | + | 910.508i | 0.0775550 | + | 0.0447764i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27051.7 | + | 4051.88i | 1.31969 | + | 0.197667i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −155.921 | − | 270.063i | −0.00757607 | − | 0.0131221i | 0.862213 | − | 0.506547i | \(-0.169078\pi\) |
−0.869789 | + | 0.493425i | \(0.835745\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4019.46 | −0.193752 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26444.1 | −1.26965 | −0.634825 | − | 0.772656i | \(-0.718928\pi\) | ||||
−0.634825 | + | 0.772656i | \(0.718928\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10265.6 | − | 17780.5i | −0.488997 | − | 0.846968i | 0.510922 | − | 0.859627i | \(-0.329304\pi\) |
−0.999920 | + | 0.0126584i | \(0.995971\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27029.5 | − | 10637.1i | 1.28248 | − | 0.504703i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 72.5886 | + | 41.9090i | 0.00341724 | + | 0.00197294i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19950.3i | 0.935533i | 0.883852 | + | 0.467767i | \(0.154941\pi\) | ||||
−0.883852 | + | 0.467767i | \(0.845059\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19809.6 | − | 34311.3i | 0.921737 | − | 1.59650i | 0.125011 | − | 0.992155i | \(-0.460103\pi\) |
0.796726 | − | 0.604340i | \(-0.206563\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12306.2 | + | 7105.00i | −0.570390 | + | 0.329315i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1472.10 | − | 849.920i | 0.0677068 | − | 0.0390906i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2871.84 | − | 4974.18i | 0.131578 | − | 0.227900i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 23506.0i | − | 1.06874i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28877.8 | − | 16672.6i | −1.30798 | − | 0.755163i | −0.326222 | − | 0.945293i | \(-0.605776\pi\) |
−0.981759 | + | 0.190130i | \(0.939109\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12425.0 | + | 15610.0i | −0.558512 | + | 0.701678i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1023.39 | − | 1772.57i | −0.0458283 | − | 0.0793769i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15138.0 | −0.672793 | −0.336397 | − | 0.941720i | \(-0.609208\pi\) | ||||
−0.336397 | + | 0.941720i | \(0.609208\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10716.5 | 0.474496 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −502.396 | − | 870.176i | −0.0220787 | − | 0.0382414i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8450.86 | − | 21474.2i | −0.370005 | − | 0.940206i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16961.8 | + | 9792.91i | 0.737139 | + | 0.425588i | 0.821028 | − | 0.570888i | \(-0.193401\pi\) |
−0.0838890 | + | 0.996475i | \(0.526734\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11787.4i | 0.510371i | 0.966892 | + | 0.255186i | \(0.0821365\pi\) | ||||
−0.966892 | + | 0.255186i | \(0.917863\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9936.96 | − | 17211.3i | 0.427088 | − | 0.739737i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1458.71 | − | 842.185i | 0.0624648 | − | 0.0360640i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −798.937 | + | 461.266i | −0.0339623 | + | 0.0196082i | −0.516885 | − | 0.856055i | \(-0.672909\pi\) |
0.482923 | + | 0.875663i | \(0.339575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11788.0 | − | 20417.4i | 0.499275 | − | 0.864770i | −0.500725 | − | 0.865607i | \(-0.666933\pi\) |
1.00000 | 0.000836881i | \(0.000266387\pi\) | ||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9010.27i | 0.378861i | 0.981894 | + | 0.189430i | \(0.0606641\pi\) | ||||
−0.981894 | + | 0.189430i | \(0.939336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1211.73 | − | 699.593i | −0.0507661 | − | 0.0293098i | 0.474402 | − | 0.880308i | \(-0.342664\pi\) |
−0.525168 | + | 0.850998i | \(0.675998\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14621.2 | − | 4480.53i | −0.608156 | − | 0.186364i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14042.1 | − | 24321.7i | −0.581974 | − | 1.00801i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10339.8 | −0.425472 | −0.212736 | − | 0.977110i | \(-0.568237\pi\) | ||||
−0.212736 | + | 0.977110i | \(0.568237\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −30375.2 | −1.24545 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8985.24 | + | 15562.9i | 0.365801 | + | 0.633585i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3439.70 | + | 22964.5i | −0.139539 | + | 0.931607i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10981.4 | + | 6340.12i | 0.442348 | + | 0.255390i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39316.9i | 1.57818i | 0.614280 | + | 0.789088i | \(0.289447\pi\) | ||||
−0.614280 | + | 0.789088i | \(0.710553\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −179.865 | + | 311.534i | −0.00716926 | + | 0.0124175i | −0.869588 | − | 0.493778i | \(-0.835615\pi\) |
0.862419 | + | 0.506196i | \(0.168949\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32209.0 | + | 18595.9i | −1.27934 | + | 0.738630i | −0.976728 | − | 0.214482i | \(-0.931194\pi\) |
−0.302617 | + | 0.953112i | \(0.597860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11006.3 | − | 6354.50i | 0.434136 | − | 0.250649i | −0.266971 | − | 0.963705i | \(-0.586023\pi\) |
0.701107 | + | 0.713056i | \(0.252689\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 15569.0 | − | 26966.2i | 0.611978 | − | 1.05998i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2588.57i | 0.101049i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4985.75 | − | 2878.53i | −0.193956 | − | 0.111981i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21986.1 | − | 17500.2i | −0.849448 | − | 0.676132i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7481.41 | − | 12958.2i | −0.288061 | − | 0.498936i | 0.685286 | − | 0.728274i | \(-0.259677\pi\) |
−0.973347 | + | 0.229338i | \(0.926344\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48954.8 | −1.87211 | −0.936056 | − | 0.351851i | \(-0.885552\pi\) | ||||
−0.936056 | + | 0.351851i | \(0.885552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4761.13 | −0.181455 | −0.0907276 | − | 0.995876i | \(-0.528919\pi\) | ||||
−0.0907276 | + | 0.995876i | \(0.528919\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −19477.6 | − | 33736.1i | −0.737308 | − | 1.27706i | −0.953703 | − | 0.300749i | \(-0.902763\pi\) |
0.216395 | − | 0.976306i | \(-0.430570\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 21996.3 | + | 17508.3i | 0.829847 | + | 0.660530i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2424.24 | + | 1399.64i | 0.0908444 | + | 0.0524491i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3055.10i | − | 0.114101i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34157.1 | − | 59161.8i | 1.26719 | − | 2.19484i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11749.6 | − | 6783.62i | 0.434445 | − | 0.250827i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12591.4 | + | 7269.64i | −0.462488 | + | 0.267018i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7610.74 | − | 13182.2i | 0.278622 | − | 0.482588i | −0.692420 | − | 0.721494i | \(-0.743456\pi\) |
0.971043 | + | 0.238906i | \(0.0767889\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 6441.70i | − | 0.234273i | −0.993116 | − | 0.117137i | \(-0.962628\pi\) | ||
0.993116 | − | 0.117137i | \(-0.0373716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6674.70 | − | 3853.64i | −0.241950 | − | 0.139690i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1106.54 | − | 7387.61i | 0.0398485 | − | 0.266042i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9334.12 | + | 16167.2i | 0.335042 | + | 0.580311i | 0.983493 | − | 0.180946i | \(-0.0579160\pi\) |
−0.648451 | + | 0.761257i | \(0.724583\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7734.79 | 0.275833 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4327.61 | 0.153828 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11274.5 | + | 19527.9i | 0.398173 | + | 0.689656i | 0.993501 | − | 0.113827i | \(-0.0363109\pi\) |
−0.595327 | + | 0.803483i | \(0.702978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2722.36 | − | 2923.17i | −0.0958342 | − | 0.102903i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2963.74 | − | 1711.12i | −0.103663 | − | 0.0598497i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22939.2i | 0.799779i | 0.916563 | + | 0.399889i | \(0.130951\pi\) | ||||
−0.916563 | + | 0.399889i | \(0.869049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1808.45 | + | 3132.32i | −0.0626501 | + | 0.108513i | −0.895649 | − | 0.444761i | \(-0.853289\pi\) |
0.832999 | + | 0.553274i | \(0.186622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18029.3 | + | 10409.2i | −0.622604 | + | 0.359461i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12567.3 | − | 7255.75i | 0.431239 | − | 0.248976i | −0.268635 | − | 0.963242i | \(-0.586573\pi\) |
0.699874 | + | 0.714266i | \(0.253239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 676.557 | − | 1171.83i | 0.0231422 | − | 0.0400835i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 31649.8i | − | 1.07580i | −0.843008 | − | 0.537901i | \(-0.819218\pi\) | ||
0.843008 | − | 0.537901i | \(-0.180782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1867.12 | − | 1077.98i | −0.0632656 | − | 0.0365264i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3662.31 | + | 9306.17i | 0.123318 | + | 0.313360i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27712.9 | + | 48000.2i | 0.930245 | + | 1.61123i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22263.8 | −0.742691 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −26409.0 | −0.878238 | −0.439119 | − | 0.898429i | \(-0.644709\pi\) | ||||
−0.439119 | + | 0.898429i | \(0.644709\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4525.04 | − | 7837.61i | −0.149553 | − | 0.259033i | 0.781510 | − | 0.623893i | \(-0.214450\pi\) |
−0.931062 | + | 0.364861i | \(0.881117\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23554.6 | − | 29592.5i | 0.776081 | − | 0.975018i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17401.7 | + | 10046.8i | 0.569834 | + | 0.328994i | 0.757083 | − | 0.653319i | \(-0.226624\pi\) |
−0.187249 | + | 0.982313i | \(0.559957\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 12483.2i | − | 0.407523i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12838.6 | − | 22237.2i | 0.416571 | − | 0.721522i | −0.579021 | − | 0.815313i | \(-0.696565\pi\) |
0.995592 | + | 0.0937907i | \(0.0298985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34643.9 | + | 20001.7i | −1.12066 | + | 0.647011i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17865.3 | + | 10314.5i | −0.574400 | + | 0.331630i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2851.55 | − | 4939.03i | 0.0914051 | − | 0.158318i | −0.816697 | − | 0.577066i | \(-0.804198\pi\) |
0.908103 | + | 0.418748i | \(0.137531\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 21703.6i | − | 0.691507i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8147.55 | − | 4703.99i | −0.258812 | − | 0.149425i | 0.364981 | − | 0.931015i | \(-0.381076\pi\) |
−0.623792 | + | 0.781590i | \(0.714409\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.4.bt.b.17.7 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.b.17.2 | 16 | ||
4.3 | odd | 2 | 252.4.t.a.17.7 | yes | 16 | ||
7.5 | odd | 6 | inner | 1008.4.bt.b.593.2 | 16 | ||
12.11 | even | 2 | 252.4.t.a.17.2 | ✓ | 16 | ||
21.5 | even | 6 | inner | 1008.4.bt.b.593.7 | 16 | ||
28.3 | even | 6 | 1764.4.f.a.881.14 | 16 | |||
28.11 | odd | 6 | 1764.4.f.a.881.4 | 16 | |||
28.19 | even | 6 | 252.4.t.a.89.2 | yes | 16 | ||
28.23 | odd | 6 | 1764.4.t.b.1097.7 | 16 | |||
28.27 | even | 2 | 1764.4.t.b.521.2 | 16 | |||
84.11 | even | 6 | 1764.4.f.a.881.13 | 16 | |||
84.23 | even | 6 | 1764.4.t.b.1097.2 | 16 | |||
84.47 | odd | 6 | 252.4.t.a.89.7 | yes | 16 | ||
84.59 | odd | 6 | 1764.4.f.a.881.3 | 16 | |||
84.83 | odd | 2 | 1764.4.t.b.521.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.t.a.17.2 | ✓ | 16 | 12.11 | even | 2 | ||
252.4.t.a.17.7 | yes | 16 | 4.3 | odd | 2 | ||
252.4.t.a.89.2 | yes | 16 | 28.19 | even | 6 | ||
252.4.t.a.89.7 | yes | 16 | 84.47 | odd | 6 | ||
1008.4.bt.b.17.2 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.b.17.7 | 16 | 1.1 | even | 1 | trivial | ||
1008.4.bt.b.593.2 | 16 | 7.5 | odd | 6 | inner | ||
1008.4.bt.b.593.7 | 16 | 21.5 | even | 6 | inner | ||
1764.4.f.a.881.3 | 16 | 84.59 | odd | 6 | |||
1764.4.f.a.881.4 | 16 | 28.11 | odd | 6 | |||
1764.4.f.a.881.13 | 16 | 84.11 | even | 6 | |||
1764.4.f.a.881.14 | 16 | 28.3 | even | 6 | |||
1764.4.t.b.521.2 | 16 | 28.27 | even | 2 | |||
1764.4.t.b.521.7 | 16 | 84.83 | odd | 2 | |||
1764.4.t.b.1097.2 | 16 | 84.23 | even | 6 | |||
1764.4.t.b.1097.7 | 16 | 28.23 | odd | 6 |