Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1932,2,Mod(1609,1932)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1932, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1932.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1932.k (of order \(2\), degree \(1\), 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: | \(15.4270976705\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.23 | ||
Character | \(\chi\) | \(=\) | 1932.1609 |
Dual form | 1932.2.k.a.1609.21 |
$q$-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 \(\left(\mathbb{Z}/1932\mathbb{Z}\right)^\times\).
\(n\) | \(829\) | \(925\) | \(967\) | \(1289\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.248143 | −0.110973 | −0.0554865 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554865 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.652227 | − | 2.56410i | −0.246519 | − | 0.969138i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.05549i | 1.22278i | 0.791331 | + | 0.611388i | \(0.209388\pi\) | ||||
−0.791331 | + | 0.611388i | \(0.790612\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.46658i | − | 1.51616i | −0.652163 | − | 0.758079i | \(-0.726138\pi\) | ||
0.652163 | − | 0.758079i | \(-0.273862\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.248143i | − | 0.0640702i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.349644 | 0.0848011 | 0.0424005 | − | 0.999101i | \(-0.486499\pi\) | ||||
0.0424005 | + | 0.999101i | \(0.486499\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.87946 | 0.890008 | 0.445004 | − | 0.895528i | \(-0.353202\pi\) | ||||
0.445004 | + | 0.895528i | \(0.353202\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.56410 | − | 0.652227i | 0.559532 | − | 0.142328i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.300350 | + | 4.78642i | 0.0626272 | + | 0.998037i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93843 | −0.987685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.50660 | −0.651158 | −0.325579 | − | 0.945515i | \(-0.605559\pi\) | ||||
−0.325579 | + | 0.945515i | \(0.605559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 7.87222i | − | 1.41389i | −0.707267 | − | 0.706947i | \(-0.750072\pi\) | ||
0.707267 | − | 0.706947i | \(-0.249928\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.05549 | −0.705970 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.161846 | + | 0.636263i | 0.0273569 | + | 0.107548i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.76156i | 0.618396i | 0.950998 | + | 0.309198i | \(0.100061\pi\) | ||||
−0.950998 | + | 0.309198i | \(0.899939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.46658 | 0.875354 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.40062i | − | 0.843435i | −0.906727 | − | 0.421718i | \(-0.861427\pi\) | ||
0.906727 | − | 0.421718i | \(-0.138573\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 11.4582i | − | 1.74737i | −0.486495 | − | 0.873683i | \(-0.661725\pi\) | ||
0.486495 | − | 0.873683i | \(-0.338275\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.248143 | 0.0369910 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.86784i | − | 0.272452i | −0.990678 | − | 0.136226i | \(-0.956503\pi\) | ||
0.990678 | − | 0.136226i | \(-0.0434973\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.14920 | + | 3.34475i | −0.878457 | + | 0.477821i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.349644i | 0.0489599i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.71322i | − | 1.33421i | −0.744962 | − | 0.667107i | \(-0.767532\pi\) | ||
0.744962 | − | 0.667107i | \(-0.232468\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.00634i | − | 0.135695i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.87946i | 0.513847i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 12.5854i | − | 1.63848i | −0.573453 | − | 0.819239i | \(-0.694396\pi\) | ||
0.573453 | − | 0.819239i | \(-0.305604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.03300 | 0.516372 | 0.258186 | − | 0.966095i | \(-0.416875\pi\) | ||||
0.258186 | + | 0.966095i | \(0.416875\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.652227 | + | 2.56410i | 0.0821729 | + | 0.323046i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.35649i | 0.168252i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 4.70293i | − | 0.574554i | −0.957848 | − | 0.287277i | \(-0.907250\pi\) | ||
0.957848 | − | 0.287277i | \(-0.0927500\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.78642 | + | 0.300350i | −0.576217 | + | 0.0361578i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.9003 | 1.64966 | 0.824829 | − | 0.565382i | \(-0.191271\pi\) | ||||
0.824829 | + | 0.565382i | \(0.191271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.64759i | − | 1.12917i | −0.825377 | − | 0.564583i | \(-0.809037\pi\) | ||
0.825377 | − | 0.564583i | \(-0.190963\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 4.93843i | − | 0.570240i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.3987 | − | 2.64510i | 1.18504 | − | 0.301437i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.98013i | 0.785326i | 0.919682 | + | 0.392663i | \(0.128446\pi\) | ||||
−0.919682 | + | 0.392663i | \(0.871554\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2060 | −1.33978 | −0.669890 | − | 0.742461i | \(-0.733659\pi\) | ||||
−0.669890 | + | 0.742461i | \(0.733659\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0867616 | −0.00941062 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.50660i | − | 0.375947i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.84062 | 0.725104 | 0.362552 | − | 0.931964i | \(-0.381906\pi\) | ||||
0.362552 | + | 0.931964i | \(0.381906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.0169 | + | 3.56545i | −1.46937 | + | 0.373761i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.87222 | 0.816312 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.962660 | −0.0987668 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.02306 | 0.103876 | 0.0519379 | − | 0.998650i | \(-0.483460\pi\) | ||||
0.0519379 | + | 0.998650i | \(0.483460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.05549i | − | 0.407592i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.90088i | 0.985174i | 0.870263 | + | 0.492587i | \(0.163949\pi\) | ||||
−0.870263 | + | 0.492587i | \(0.836051\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.54945 | 0.645337 | 0.322668 | − | 0.946512i | \(-0.395420\pi\) | ||||
0.322668 | + | 0.946512i | \(0.395420\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.636263 | + | 0.161846i | −0.0620929 | + | 0.0157945i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5.20163i | − | 0.502860i | −0.967875 | − | 0.251430i | \(-0.919099\pi\) | ||
0.967875 | − | 0.251430i | \(-0.0809009\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.98642i | 0.669177i | 0.942364 | + | 0.334589i | \(0.108597\pi\) | ||||
−0.942364 | + | 0.334589i | \(0.891403\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.76156 | −0.357031 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.89960i | 0.554987i | 0.960727 | + | 0.277494i | \(0.0895038\pi\) | ||||
−0.960727 | + | 0.277494i | \(0.910496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0745296 | − | 1.18772i | −0.00694992 | − | 0.110755i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.46658i | 0.505386i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.228047 | − | 0.896521i | −0.0209051 | − | 0.0821839i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.44697 | −0.495179 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.40062 | 0.486958 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.46615 | 0.220579 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.08378 | −0.806055 | −0.403028 | − | 0.915188i | \(-0.632042\pi\) | ||||
−0.403028 | + | 0.915188i | \(0.632042\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.4582 | 1.00884 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 16.8087i | − | 1.46858i | −0.678835 | − | 0.734291i | \(-0.737515\pi\) | ||
0.678835 | − | 0.734291i | \(-0.262485\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.53029 | − | 9.94731i | −0.219404 | − | 0.862541i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.248143i | 0.0213567i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 14.9328i | − | 1.27579i | −0.770122 | − | 0.637897i | \(-0.779805\pi\) | ||
0.770122 | − | 0.637897i | \(-0.220195\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.0692691i | 0.00587533i | 0.999996 | + | 0.00293766i | \(0.000935089\pi\) | ||||
−0.999996 | + | 0.00293766i | \(0.999065\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.86784 | 0.157300 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 22.1697 | 1.85392 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.870137 | 0.0722609 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.34475 | − | 6.14920i | −0.275870 | − | 0.507177i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.35388i | 0.438607i | 0.975657 | + | 0.219303i | \(0.0703785\pi\) | ||||
−0.975657 | + | 0.219303i | \(0.929622\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.79280 | 0.634169 | 0.317085 | − | 0.948397i | \(-0.397296\pi\) | ||||
0.317085 | + | 0.948397i | \(0.397296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.349644 | −0.0282670 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.95344i | 0.156904i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.35019 | −0.666418 | −0.333209 | − | 0.942853i | \(-0.608131\pi\) | ||||
−0.333209 | + | 0.942853i | \(0.608131\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.71322 | 0.770309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0769 | − | 3.89196i | 0.951797 | − | 0.306729i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.50912 | −0.274856 | −0.137428 | − | 0.990512i | \(-0.543884\pi\) | ||||
−0.137428 | + | 0.990512i | \(0.543884\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00634 | 0.0783435 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.07693i | − | 0.547629i | −0.961782 | − | 0.273815i | \(-0.911715\pi\) | ||
0.961782 | − | 0.273815i | \(-0.0882855\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16.8835 | −1.29873 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.87946 | −0.296669 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.8180i | 0.822477i | 0.911528 | + | 0.411238i | \(0.134904\pi\) | ||||
−0.911528 | + | 0.411238i | \(0.865096\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.22098 | + | 12.6626i | 0.243483 | + | 0.957203i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.5854 | 0.945975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.95147 | 0.743808 | 0.371904 | − | 0.928271i | \(-0.378705\pi\) | ||||
0.371904 | + | 0.928271i | \(0.378705\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.14027 | 0.456402 | 0.228201 | − | 0.973614i | \(-0.426716\pi\) | ||||
0.228201 | + | 0.973614i | \(0.426716\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.03300i | 0.298128i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 0.933404i | − | 0.0686252i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41798i | 0.103693i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.56410 | + | 0.652227i | −0.186511 | + | 0.0474426i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 0.686980i | − | 0.0497081i | −0.999691 | − | 0.0248541i | \(-0.992088\pi\) | ||
0.999691 | − | 0.0248541i | \(-0.00791211\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.09247 | −0.150619 | −0.0753096 | − | 0.997160i | \(-0.523995\pi\) | ||||
−0.0753096 | + | 0.997160i | \(0.523995\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.35649 | −0.0971405 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.87120 | 0.703294 | 0.351647 | − | 0.936133i | \(-0.385622\pi\) | ||||
0.351647 | + | 0.936133i | \(0.385622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7198 | 1.04346 | 0.521731 | − | 0.853110i | \(-0.325286\pi\) | ||||
0.521731 | + | 0.853110i | \(0.325286\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.70293 | 0.331719 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.28710 | + | 8.99126i | 0.160523 | + | 0.631062i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.34013i | 0.0935985i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.300350 | − | 4.78642i | −0.0208757 | − | 0.332679i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 15.7331i | 1.08828i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.39018 | −0.371075 | −0.185538 | − | 0.982637i | \(-0.559403\pi\) | ||||
−0.185538 | + | 0.982637i | \(0.559403\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.9003i | 0.952431i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.84328i | 0.193910i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.1852 | + | 5.13448i | −1.37026 | + | 0.348551i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.64759 | 0.651924 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.91136i | − | 0.128572i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 20.0807i | − | 1.34470i | −0.740233 | − | 0.672351i | \(-0.765285\pi\) | ||
0.740233 | − | 0.672351i | \(-0.234715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.93843 | 0.329228 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5820 | −1.03421 | −0.517107 | − | 0.855921i | \(-0.672991\pi\) | ||||
−0.517107 | + | 0.855921i | \(0.672991\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.89135 | 0.521475 | 0.260738 | − | 0.965410i | \(-0.416034\pi\) | ||||
0.260738 | + | 0.965410i | \(0.416034\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.64510 | + | 10.3987i | 0.174035 | + | 0.684182i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.5621 | −1.01951 | −0.509753 | − | 0.860321i | \(-0.670263\pi\) | ||||
−0.509753 | + | 0.860321i | \(0.670263\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.463491i | 0.0302348i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.98013 | −0.453408 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.6315 | 0.881748 | 0.440874 | − | 0.897569i | \(-0.354669\pi\) | ||||
0.440874 | + | 0.897569i | \(0.354669\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.6041 | −1.77814 | −0.889069 | − | 0.457773i | \(-0.848647\pi\) | ||||
−0.889069 | + | 0.457773i | \(0.848647\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.52588 | − | 0.829976i | 0.0974849 | − | 0.0530252i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.2074i | − | 1.34939i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 12.2060i | − | 0.773522i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.8899 | −1.25544 | −0.627721 | − | 0.778439i | \(-0.716012\pi\) | ||||
−0.627721 | + | 0.778439i | \(0.716012\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.4113 | + | 1.21806i | −1.22037 | + | 0.0765790i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.0867616i | − | 0.00543322i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.75374i | 0.358909i | 0.983766 | + | 0.179454i | \(0.0574332\pi\) | ||||
−0.983766 | + | 0.179454i | \(0.942567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.64500 | − | 2.45339i | 0.599311 | − | 0.152446i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.50660 | 0.217053 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.0037i | 0.678516i | 0.940693 | + | 0.339258i | \(0.110176\pi\) | ||||
−0.940693 | + | 0.339258i | \(0.889824\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.41027i | 0.148062i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.84062i | 0.418639i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3564i | 1.11921i | 0.828759 | + | 0.559606i | \(0.189048\pi\) | ||||
−0.828759 | + | 0.559606i | \(0.810952\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 29.9547i | − | 1.81962i | −0.415027 | − | 0.909809i | \(-0.636228\pi\) | ||
0.415027 | − | 0.909809i | \(-0.363772\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.56545 | − | 14.0169i | −0.215791 | − | 0.848339i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 20.0277i | − | 1.20772i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.6594 | −1.12113 | −0.560567 | − | 0.828109i | \(-0.689417\pi\) | ||||
−0.560567 | + | 0.828109i | \(0.689417\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.87222i | 0.471298i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.0173097i | 0.00103261i | 1.00000 | 0.000516305i | \(0.000164345\pi\) | |||||
−1.00000 | 0.000516305i | \(0.999836\pi\) | ||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.120744 | 0.00717752 | 0.00358876 | − | 0.999994i | \(-0.498858\pi\) | ||||
0.00358876 | + | 0.999994i | \(0.498858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 0.962660i | − | 0.0570230i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.8477 | + | 3.52243i | −0.817405 | + | 0.207923i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8777 | −0.992809 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.02306i | 0.0599727i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.5499 | −1.66790 | −0.833950 | − | 0.551839i | \(-0.813926\pi\) | ||||
−0.833950 | + | 0.551839i | \(0.813926\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.12297i | 0.181827i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.05549 | 0.235323 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 26.1653 | − | 1.64189i | 1.51318 | − | 0.0949527i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −29.3801 | + | 7.47338i | −1.69344 | + | 0.430759i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.90088 | −0.568790 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00076 | −0.0573033 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.73639i | 0.555685i | 0.960627 | + | 0.277843i | \(0.0896194\pi\) | ||||
−0.960627 | + | 0.277843i | \(0.910381\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.54945i | 0.372585i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.8161i | 1.40719i | 0.710601 | + | 0.703596i | \(0.248423\pi\) | ||||
−0.710601 | + | 0.703596i | \(0.751577\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.1571 | 1.36544 | 0.682719 | − | 0.730681i | \(-0.260797\pi\) | ||||
0.682719 | + | 0.730681i | \(0.260797\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.161846 | − | 0.636263i | −0.00911897 | − | 0.0358494i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.882476 | 0.0495648 | 0.0247824 | − | 0.999693i | \(-0.492111\pi\) | ||||
0.0247824 | + | 0.999693i | \(0.492111\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 14.2210i | − | 0.796220i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.20163 | 0.290327 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.35643 | 0.0754736 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 26.9963i | 1.49749i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.98642 | −0.386350 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.78932 | + | 1.21825i | −0.264044 | + | 0.0671645i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.48030 | 0.246259 | 0.123130 | − | 0.992391i | \(-0.460707\pi\) | ||||
0.123130 | + | 0.992391i | \(0.460707\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.76156i | − | 0.206132i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.16700i | 0.0637599i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 7.99001i | − | 0.435243i | −0.976033 | − | 0.217622i | \(-0.930170\pi\) | ||
0.976033 | − | 0.217622i | \(-0.0698299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.89960 | −0.320422 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 31.9257 | 1.72887 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.5869 | + | 13.5856i | 0.679631 | + | 0.733554i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.18772 | − | 0.0745296i | 0.0639445 | − | 0.00401254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.18595 | −0.439445 | −0.219723 | − | 0.975562i | \(-0.570515\pi\) | ||||
−0.219723 | + | 0.975562i | \(0.570515\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.3084i | 1.24767i | 0.781557 | + | 0.623834i | \(0.214426\pi\) | ||||
−0.781557 | + | 0.623834i | \(0.785574\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.46658 | −0.291785 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 20.6822i | − | 1.10080i | −0.834901 | − | 0.550400i | \(-0.814475\pi\) | ||
0.834901 | − | 0.550400i | \(-0.185525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.44925 | −0.183067 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.896521 | − | 0.228047i | 0.0474489 | − | 0.0120695i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.3509i | 0.915748i | 0.889017 | + | 0.457874i | \(0.151389\pi\) | ||||
−0.889017 | + | 0.457874i | \(0.848611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.94982 | −0.207885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.44697i | − | 0.285892i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.39398i | 0.125307i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2971 | 0.798501 | 0.399250 | − | 0.916842i | \(-0.369270\pi\) | ||||
0.399250 | + | 0.916842i | \(0.369270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.40062i | 0.281145i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.9057 | + | 6.33523i | −1.29304 | + | 0.328909i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 19.8672i | − | 1.02869i | −0.857584 | − | 0.514343i | \(-0.828036\pi\) | ||
0.857584 | − | 0.514343i | \(-0.171964\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.46615i | 0.127351i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 19.1691i | 0.987258i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.96163i | 0.152129i | 0.997103 | + | 0.0760644i | \(0.0242355\pi\) | ||||
−0.997103 | + | 0.0760644i | \(0.975765\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 9.08378i | − | 0.465376i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.82827 | 0.348908 | 0.174454 | − | 0.984665i | \(-0.444184\pi\) | ||||
0.174454 | + | 0.984665i | \(0.444184\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.58036 | + | 0.656363i | −0.131507 | + | 0.0334513i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.4582i | 0.582456i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.7609i | 0.697706i | 0.937177 | + | 0.348853i | \(0.113429\pi\) | ||||
−0.937177 | + | 0.348853i | \(0.886571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.105015 | + | 1.67354i | 0.00531085 | + | 0.0846346i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.8087 | 0.847887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.73207i | − | 0.0871499i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.0290i | 1.30636i | 0.757203 | + | 0.653180i | \(0.226565\pi\) | ||||
−0.757203 | + | 0.653180i | \(0.773435\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.94731 | − | 2.53029i | 0.497988 | − | 0.126673i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 33.8292i | 1.68935i | 0.535279 | + | 0.844675i | \(0.320207\pi\) | ||||
−0.535279 | + | 0.844675i | \(0.679793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.0342 | −2.14368 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.248143 | −0.0123303 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.2549 | −0.756160 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.2940i | 1.20126i | 0.799527 | + | 0.600630i | \(0.205083\pi\) | ||||
−0.799527 | + | 0.600630i | \(0.794917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.9328 | 0.736580 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.2702 | + | 8.20853i | −1.58791 | + | 0.403915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.02883 | 0.148679 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0692691 | −0.00339212 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5498 | 1.05277 | 0.526387 | − | 0.850245i | \(-0.323546\pi\) | ||||
0.526387 | + | 0.850245i | \(0.323546\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 37.1329i | − | 1.80975i | −0.425682 | − | 0.904873i | \(-0.639966\pi\) | ||
0.425682 | − | 0.904873i | \(-0.360034\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.86784i | 0.0908173i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.72669 | −0.0837567 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.63043 | − | 10.3410i | −0.127295 | − | 0.500436i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 22.1697i | 1.07036i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 35.6918i | − | 1.71921i | −0.510958 | − | 0.859606i | \(-0.670709\pi\) | ||
0.510958 | − | 0.859606i | \(-0.329291\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.2866 | −0.830743 | −0.415372 | − | 0.909652i | \(-0.636348\pi\) | ||||
−0.415372 | + | 0.909652i | \(0.636348\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.870137i | 0.0417199i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.16519 | + | 18.5687i | 0.0557387 | + | 0.888261i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.6110i | 1.36553i | 0.730638 | + | 0.682765i | \(0.239223\pi\) | ||||
−0.730638 | + | 0.682765i | \(0.760777\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.14920 | − | 3.34475i | 0.292819 | − | 0.159274i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0921 | 1.00212 | 0.501058 | − | 0.865414i | \(-0.332944\pi\) | ||||
0.501058 | + | 0.865414i | \(0.332944\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.69745 | −0.0804669 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.35388 | −0.253230 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.5513 | 1.11146 | 0.555728 | − | 0.831364i | \(-0.312440\pi\) | ||||
0.555728 | + | 0.831364i | \(0.312440\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.9021 | 1.03133 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.79280i | 0.366138i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.47818 | − | 0.884742i | 0.163060 | − | 0.0414774i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.9541i | 1.26086i | 0.776247 | + | 0.630429i | \(0.217121\pi\) | ||||
−0.776247 | + | 0.630429i | \(0.782879\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 0.349644i | − | 0.0163200i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 18.4634i | − | 0.859924i | −0.902847 | − | 0.429962i | \(-0.858527\pi\) | ||
0.902847 | − | 0.429962i | \(-0.141473\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.3889 | 1.64466 | 0.822331 | − | 0.569009i | \(-0.192673\pi\) | ||||
0.822331 | + | 0.569009i | \(0.192673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.95344 | −0.0905885 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.9569 | 0.692123 | 0.346062 | − | 0.938212i | \(-0.387519\pi\) | ||||
0.346062 | + | 0.938212i | \(0.387519\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.0588 | + | 3.06738i | −0.556822 | + | 0.141638i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 8.35019i | − | 0.384757i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 46.4688 | 2.13664 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.1584 | −0.879048 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.71322i | 0.444738i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.1485 | 0.555078 | 0.277539 | − | 0.960714i | \(-0.410481\pi\) | ||||
0.277539 | + | 0.960714i | \(0.410481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.5629 | 0.937586 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.89196 | + | 12.0769i | 0.177090 | + | 0.549520i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.253865 | −0.0115274 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.1745 | 0.868879 | 0.434440 | − | 0.900701i | \(-0.356946\pi\) | ||||
0.434440 | + | 0.900701i | \(0.356946\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.50912i | − | 0.158688i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.0026 | −0.586800 | −0.293400 | − | 0.955990i | \(-0.594787\pi\) | ||||
−0.293400 | + | 0.955990i | \(0.594787\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.22606 | −0.0552189 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.00634i | 0.0452316i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −9.06614 | − | 35.6417i | −0.406672 | − | 1.59875i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −37.0374 | −1.65802 | −0.829011 | − | 0.559232i | \(-0.811096\pi\) | ||||
−0.829011 | + | 0.559232i | \(0.811096\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.07693 | 0.316174 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.8200 | −0.616206 | −0.308103 | − | 0.951353i | \(-0.599694\pi\) | ||||
−0.308103 | + | 0.951353i | \(0.599694\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 2.45683i | − | 0.109328i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 16.8835i | − | 0.749823i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 33.4182i | 1.48123i | 0.671927 | + | 0.740617i | \(0.265467\pi\) | ||||
−0.671927 | + | 0.740617i | \(0.734533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.7374 | + | 6.29242i | −1.09432 | + | 0.278360i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 3.87946i | − | 0.171282i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.62520 | −0.0716149 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.57499 | 0.333148 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.8180 | −0.474857 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.6964 | 1.47627 | 0.738133 | − | 0.674655i | \(-0.235708\pi\) | ||||
0.738133 | + | 0.674655i | \(0.235708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.03787 | −0.132837 | −0.0664185 | − | 0.997792i | \(-0.521157\pi\) | ||||
−0.0664185 | + | 0.997792i | \(0.521157\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.6626 | + | 3.22098i | −0.552641 | + | 0.140575i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 2.75247i | − | 0.119900i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8196 | + | 2.87520i | −0.992156 | + | 0.125009i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.5854i | 0.546159i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −29.5229 | −1.27878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.29075i | 0.0558039i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.95147i | 0.429438i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.5646 | − | 24.9380i | −0.584268 | − | 1.07416i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9327 | −1.02895 | −0.514474 | − | 0.857506i | \(-0.672013\pi\) | ||||
−0.514474 | + | 0.857506i | \(0.672013\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.14027i | 0.263504i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.73363i | − | 0.0742605i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.70243 | −0.414846 | −0.207423 | − | 0.978251i | \(-0.566508\pi\) | ||||
−0.207423 | + | 0.978251i | \(0.566508\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.03300 | −0.172124 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6037 | −0.579536 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.8977 | − | 4.55263i | 0.761090 | − | 0.193598i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.933404 | 0.0396208 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 12.9311i | − | 0.547907i | −0.961743 | − | 0.273953i | \(-0.911669\pi\) | ||
0.961743 | − | 0.273953i | \(-0.0883314\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.6375 | −2.64928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.41798 | −0.0598670 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.3780 | −1.19599 | −0.597996 | − | 0.801499i | \(-0.704036\pi\) | ||||
−0.597996 | + | 0.801499i | \(0.704036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.46394i | − | 0.0615886i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.652227 | − | 2.56410i | −0.0273910 | − | 0.107682i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.41585i | − | 0.143200i | −0.997433 | − | 0.0716000i | \(-0.977190\pi\) | ||
0.997433 | − | 0.0716000i | \(-0.0228105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.5325i | 1.82178i | 0.412651 | + | 0.910889i | \(0.364603\pi\) | ||||
−0.412651 | + | 0.910889i | \(0.635397\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.686980 | 0.0286990 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.48325 | − | 23.6374i | −0.0618560 | − | 0.985746i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 39.0578i | − | 1.62600i | −0.582267 | − | 0.812998i | \(-0.697834\pi\) | ||
0.582267 | − | 0.812998i | \(-0.302166\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 2.09247i | − | 0.0869600i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.96107 | + | 31.2973i | 0.330281 | + | 1.29843i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.3919 | 1.63144 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 1.35649i | − | 0.0560841i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.8977i | 0.449798i | 0.974382 | + | 0.224899i | \(0.0722052\pi\) | ||||
−0.974382 | + | 0.224899i | \(0.927795\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 30.5399i | − | 1.25838i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.87120i | 0.406047i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.7874i | 1.42855i | 0.699866 | + | 0.714275i | \(0.253243\pi\) | ||||
−0.699866 | + | 0.714275i | \(0.746757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.0565883 | + | 0.222465i | 0.00231989 | + | 0.00912019i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.7198i | 0.602443i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.1144 | −0.740134 | −0.370067 | − | 0.929005i | \(-0.620665\pi\) | ||||
−0.370067 | + | 0.929005i | \(0.620665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.729850i | 0.0297712i | 0.999889 | + | 0.0148856i | \(0.00473841\pi\) | ||||
−0.999889 | + | 0.0148856i | \(0.995262\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.70293i | 0.191518i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.35163 | 0.0549515 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 20.2777i | − | 0.823047i | −0.911399 | − | 0.411523i | \(-0.864997\pi\) | ||
0.911399 | − | 0.411523i | \(-0.135003\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.99126 | + | 2.28710i | −0.364344 | + | 0.0926779i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.2107 | −0.413080 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.7029i | 1.19969i | 0.800117 | + | 0.599844i | \(0.204771\pi\) | ||||
−0.800117 | + | 0.599844i | \(0.795229\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.34013 | −0.0540391 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.0102i | 1.28868i | 0.764739 | + | 0.644340i | \(0.222868\pi\) | ||||
−0.764739 | + | 0.644340i | \(0.777132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.0226 | 1.89000 | 0.944999 | − | 0.327073i | \(-0.106062\pi\) | ||||
0.944999 | + | 0.327073i | \(0.106062\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.78642 | − | 0.300350i | 0.192072 | − | 0.0120526i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.46164 | − | 17.5400i | −0.178752 | − | 0.702726i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0802 | 0.963207 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −15.7331 | −0.628319 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.31521i | 0.0524407i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 34.8593i | − | 1.38772i | −0.720108 | − | 0.693862i | \(-0.755908\pi\) | ||
0.720108 | − | 0.693862i | \(-0.244092\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 5.39018i | − | 0.214240i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.25408 | 0.0894503 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.2844 | + | 33.6151i | 0.724452 | + | 1.33188i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.9003 | −0.549886 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7753i | 0.939066i | 0.882915 | + | 0.469533i | \(0.155578\pi\) | ||||
−0.882915 | + | 0.469533i | \(0.844422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.3414 | −0.999367 | −0.499684 | − | 0.866208i | \(-0.666550\pi\) | ||||
−0.499684 | + | 0.866208i | \(0.666550\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.84328 | −0.111954 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 47.5590i | − | 1.86974i | −0.354994 | − | 0.934868i | \(-0.615517\pi\) | ||
0.354994 | − | 0.934868i | \(-0.384483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.0399 | 2.00349 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.13448 | − | 20.1852i | −0.201236 | − | 0.791119i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.23220 | 0.322151 | 0.161075 | − | 0.986942i | \(-0.448504\pi\) | ||||
0.161075 | + | 0.986942i | \(0.448504\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.17096i | 0.162973i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 9.64759i | 0.376388i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 41.6169i | 1.62117i | 0.585624 | + | 0.810583i | \(0.300849\pi\) | ||||
−0.585624 | + | 0.810583i | \(0.699151\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.58613 | 0.178380 | 0.0891898 | − | 0.996015i | \(-0.471572\pi\) | ||||
0.0891898 | + | 0.996015i | \(0.471572\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.91136 | 0.0742309 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.627873 | + | 2.46835i | 0.0243479 | + | 0.0957187i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.05320 | − | 16.7840i | −0.0407802 | − | 0.649880i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.0807 | 0.776364 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.3558i | 0.631407i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.5644 | 0.754151 | 0.377076 | − | 0.926182i | \(-0.376930\pi\) | ||||
0.377076 | + | 0.926182i | \(0.376930\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.93843i | 0.190080i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.22886 | 0.316261 | 0.158130 | − | 0.987418i | \(-0.449453\pi\) | ||||
0.158130 | + | 0.987418i | \(0.449453\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.667266 | − | 2.62322i | −0.0256073 | − | 0.100670i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.5820i | − | 0.597104i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 45.1557 | 1.72783 | 0.863917 | − | 0.503634i | \(-0.168004\pi\) | ||||
0.863917 | + | 0.503634i | \(0.168004\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.70546i | 0.141578i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.89135i | 0.301074i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −53.0981 | −2.02288 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.1471i | − | 0.690349i | −0.938539 | − | 0.345174i | \(-0.887820\pi\) | ||
0.938539 | − | 0.345174i | \(-0.112180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.3987 | + | 2.64510i | −0.395013 | + | 0.100479i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.0171886i | − | 0.000652002i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1.88829i | − | 0.0715242i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 15.5621i | − | 0.588612i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 23.7085i | − | 0.895458i | −0.894169 | − | 0.447729i | \(-0.852233\pi\) | ||
0.894169 | − | 0.447729i | \(-0.147767\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.5928i | 0.550378i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.463491 | −0.0174561 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.3868 | − | 6.45762i | 0.954769 | − | 0.242864i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 25.0512i | − | 0.940819i | −0.882448 | − | 0.470409i | \(-0.844106\pi\) | ||
0.882448 | − | 0.470409i | \(-0.155894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 6.98013i | − | 0.261775i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.6797 | − | 2.36442i | 1.41112 | − | 0.0885482i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.50124 | −0.205735 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.6315i | 0.509078i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 11.1554i | − | 0.416028i | −0.978126 | − | 0.208014i | \(-0.933300\pi\) | ||
0.978126 | − | 0.208014i | \(-0.0667000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.27173 | − | 16.7934i | −0.159088 | − | 0.625420i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 27.6041i | − | 1.02661i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 17.3171 | 0.643139 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.8412 | −0.884221 | −0.442110 | − | 0.896961i | \(-0.645770\pi\) | ||||
−0.442110 | + | 0.896961i | \(0.645770\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.00630i | − | 0.148179i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.7749 | 0.804273 | 0.402137 | − | 0.915580i | \(-0.368268\pi\) | ||||
0.402137 | + | 0.915580i | \(0.368268\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.829976 | + | 1.52588i | 0.0306141 | + | 0.0562829i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.0727 | 0.702550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 37.8156 | 1.39107 | 0.695534 | − | 0.718493i | \(-0.255168\pi\) | ||||
0.695534 | + | 0.718493i | \(0.255168\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 21.2074 | 0.779072 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 32.1362i | 1.17896i | 0.807782 | + | 0.589482i | \(0.200668\pi\) | ||||
−0.807782 | + | 0.589482i | \(0.799332\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1.32853i | − | 0.0486735i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.2060 | 0.446593 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.3375 | + | 3.39264i | −0.487341 | + | 0.123965i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 53.2188i | 1.94198i | 0.239116 | + | 0.970991i | \(0.423143\pi\) | ||||
−0.239116 | + | 0.970991i | \(0.576857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 19.8899i | − | 0.724830i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.93373 | −0.0703756 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.976339i | 0.0354857i | 0.999843 | + | 0.0177428i | \(0.00564801\pi\) | ||||
−0.999843 | + | 0.0177428i | \(0.994352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.21806 | − | 19.4113i | −0.0442129 | − | 0.704584i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.1794i | − | 1.52900i | −0.644623 | − | 0.764500i | \(-0.722986\pi\) | ||
0.644623 | − | 0.764500i | \(-0.277014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.9139 | − | 4.55673i | 0.648525 | − | 0.164965i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0867616 | 0.00313687 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −68.7990 | −2.48419 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.3735 | −1.05924 | −0.529618 | − | 0.848236i | \(-0.677665\pi\) | ||||
−0.529618 | + | 0.848236i | \(0.677665\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.75374 | −0.207216 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.7233 | 0.781332 | 0.390666 | − | 0.920532i | \(-0.372245\pi\) | ||||
0.390666 | + | 0.920532i | \(0.372245\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.8764i | 1.39648i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.45339 | + | 9.64500i | 0.0880149 | + | 0.346013i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 20.9515i | − | 0.750664i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 56.3724i | 2.01716i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.50660i | 0.125316i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.07204 | 0.0739543 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8818 | 0.494834 | 0.247417 | − | 0.968909i | \(-0.420418\pi\) | ||||
0.247417 | + | 0.968909i | \(0.420418\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −11.0037 | −0.391741 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.1271 | − | 3.84788i | 0.537859 | − | 0.136815i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 22.0467i | − | 0.782902i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.41027 | −0.0854834 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.2781 | 0.541177 | 0.270588 | − | 0.962695i | \(-0.412782\pi\) | ||||
0.270588 | + | 0.962695i | \(0.412782\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.653077i | − | 0.0231042i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.84062 | −0.241701 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 39.1257 | 1.38072 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.99681 | + | 0.965762i | −0.105624 | + | 0.0340386i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.3564 | −0.646177 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.7917 | −0.801313 | −0.400656 | − | 0.916228i | \(-0.631218\pi\) | ||||
−0.400656 | + | 0.916228i | \(0.631218\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.2968i | − | 1.34478i | −0.740196 | − | 0.672391i | \(-0.765268\pi\) | ||
0.740196 | − | 0.672391i | \(-0.234732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 29.9547 | 1.05056 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.870764 | 0.0305015 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 44.4518i | − | 1.55517i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.0169 | − | 3.56545i | 0.489788 | − | 0.124587i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.3811 | −0.362304 | −0.181152 | − | 0.983455i | \(-0.557983\pi\) | ||||
−0.181152 | + | 0.983455i | \(0.557983\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.1306 | 1.39886 | 0.699432 | − | 0.714699i | \(-0.253436\pi\) | ||||
0.699432 | + | 0.714699i | \(0.253436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20.0277 | 0.697276 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.4365i | 0.606326i | 0.952939 | + | 0.303163i | \(0.0980426\pi\) | ||||
−0.952939 | + | 0.303163i | \(0.901957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.92638i | 0.101637i | 0.998708 | + | 0.0508187i | \(0.0161831\pi\) | ||||
−0.998708 | + | 0.0508187i | \(0.983817\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 18.6594i | − | 0.647287i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.15003 | + | 1.16947i | −0.0744941 | + | 0.0405198i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.75609i | 0.0607720i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.87222 | −0.272104 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −53.2071 | −1.83691 | −0.918456 | − | 0.395524i | \(-0.870563\pi\) | ||||
−0.918456 | + | 0.395524i | \(0.870563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.7038 | −0.575993 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.0173097 | −0.000596178 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.18953 | 0.144124 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.55267 | + | 13.9666i | 0.122071 | + | 0.479897i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.120744i | 0.00414394i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.0044 | + | 1.12978i | −0.617182 | + | 0.0387284i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.3053i | − | 1.14035i | −0.821522 | − | 0.570176i | \(-0.806875\pi\) | ||
0.821522 | − | 0.570176i | \(-0.193125\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.962660 | 0.0329223 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.3676i | − | 0.969018i | −0.874786 | − | 0.484509i | \(-0.838998\pi\) | ||
0.874786 | − | 0.484509i | \(-0.161002\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.7811i | 1.39143i | 0.718316 | + | 0.695717i | \(0.244913\pi\) | ||||
−0.718316 | + | 0.695717i | \(0.755087\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.52243 | − | 13.8477i | −0.120044 | − | 0.471929i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 37.0714 | 1.26193 | 0.630963 | − | 0.775813i | \(-0.282660\pi\) | ||||
0.630963 | + | 0.775813i | \(0.282660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 2.68441i | − | 0.0912726i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 16.8777i | − | 0.573198i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −28.3078 | −0.960278 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −25.7089 | −0.871114 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.02306 | −0.0346253 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.60849 | − | 6.32345i | −0.0543769 | − | 0.213772i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.932860 | −0.0315004 | −0.0157502 | − | 0.999876i | \(-0.505014\pi\) | ||||
−0.0157502 | + | 0.999876i | \(0.505014\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 28.5499i | − | 0.962963i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.0199 | −1.28092 | −0.640461 | − | 0.767991i | \(-0.721257\pi\) | ||||
−0.640461 | + | 0.767991i | \(0.721257\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.9372 | 0.670941 | 0.335470 | − | 0.942051i | \(-0.391105\pi\) | ||||
0.335470 | + | 0.942051i | \(0.391105\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.12297 | −0.104978 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.8042i | 0.530654i | 0.964159 | + | 0.265327i | \(0.0854799\pi\) | ||||
−0.964159 | + | 0.265327i | \(0.914520\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.92469 | + | 23.2917i | 0.198708 | + | 0.781179i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.05549i | 0.135864i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 7.24619i | − | 0.242485i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.46939 | −0.0825425 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.64189 | + | 26.1653i | 0.0548210 | + | 0.873635i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 27.6047i | 0.920668i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 3.39617i | − | 0.113143i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.47338 | − | 29.3801i | −0.248699 | − | 0.977708i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.52366 | −0.0506483 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 20.0631i | − | 0.666185i | −0.942894 | − | 0.333093i | \(-0.891908\pi\) | ||
0.942894 | − | 0.333093i | \(-0.108092\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 9.90088i | − | 0.328391i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 24.2258i | − | 0.802637i | −0.915939 | − | 0.401318i | \(-0.868552\pi\) | ||
0.915939 | − | 0.401318i | \(-0.131448\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 49.5011i | − | 1.63825i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1.00076i | − | 0.0330841i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −43.0991 | + | 10.9631i | −1.42326 | + | 0.362033i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 28.8911i | − | 0.953030i | −0.879166 | − | 0.476515i | \(-0.841900\pi\) | ||
0.879166 | − | 0.476515i | \(-0.158100\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.73639 | −0.320825 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 75.9870i | − | 2.50114i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 18.5762i | − | 0.610781i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.54945 | −0.215112 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 40.6003i | − | 1.33205i | −0.745929 | − | 0.666026i | \(-0.767994\pi\) | ||
0.745929 | − | 0.666026i | \(-0.232006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −23.8556 | + | 12.9758i | −0.781834 | + | 0.425265i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.8161 | −0.812442 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 0.351861i | − | 0.0115071i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.1559 | −1.08316 | −0.541579 | − | 0.840650i | \(-0.682173\pi\) | ||||
−0.541579 | + | 0.840650i | \(0.682173\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.1571i | 0.788336i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.1569 | 0.657095 | 0.328548 | − | 0.944487i | \(-0.393441\pi\) | ||||
0.328548 | + | 0.944487i | \(0.393441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.8496 | − | 1.62207i | 0.841780 | − | 0.0528220i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.636263 | − | 0.161846i | 0.0206976 | − | 0.00526484i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.5374 | −0.439907 | −0.219954 | − | 0.975510i | \(-0.570591\pi\) | ||||
−0.219954 | + | 0.975510i | \(0.570591\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −52.7394 | −1.71199 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.882476i | 0.0286163i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.0790i | 0.941962i | 0.882143 | + | 0.470981i | \(0.156100\pi\) | ||||
−0.882143 | + | 0.470981i | \(0.843900\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.170469i | 0.00551626i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.2210 | 0.459698 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −38.2891 | + | 9.73956i | −1.23642 | + | 0.314507i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9719 | −0.999094 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.20163i | 0.167620i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.519231 | 0.0167146 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.24367 | 0.265099 | 0.132549 | − | 0.991176i | \(-0.457684\pi\) | ||||
0.132549 | + | 0.991176i | \(0.457684\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.35643i | 0.0435747i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 44.4456 | 1.42633 | 0.713163 | − | 0.700998i | \(-0.247262\pi\) | ||||
0.713163 | + | 0.700998i | \(0.247262\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.177613 | − | 0.0451792i | 0.00569400 | − | 0.00144838i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −26.9963 | −0.864574 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 27.6030i | − | 0.883098i | −0.897237 | − | 0.441549i | \(-0.854429\pi\) | ||
0.897237 | − | 0.441549i | \(-0.145571\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.7420i | 0.886639i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 6.98642i | − | 0.223059i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.9436 | 1.84811 | 0.924057 | − | 0.382255i | \(-0.124852\pi\) | ||||
0.924057 | + | 0.382255i | \(0.124852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.44947 | −0.0780465 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.21825 | − | 4.78932i | −0.0387775 | − | 0.152446i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.8440 | − | 3.44148i | 1.74394 | − | 0.109433i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 59.2749 | 1.88293 | 0.941464 | − | 0.337113i | \(-0.109450\pi\) | ||||
0.941464 | + | 0.337113i | \(0.109450\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.48030i | 0.142178i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.65263 | −0.115796 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.648259i | 0.0205306i | 0.999947 | + | 0.0102653i | \(0.00326760\pi\) | ||||
−0.999947 | + | 0.0102653i | \(0.996732\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.76156 | 0.119010 |
(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 | 1932.2.k.a.1609.23 | yes | 32 | |
3.2 | odd | 2 | 5796.2.k.d.5473.17 | 32 | |||
7.6 | odd | 2 | inner | 1932.2.k.a.1609.22 | yes | 32 | |
21.20 | even | 2 | 5796.2.k.d.5473.15 | 32 | |||
23.22 | odd | 2 | inner | 1932.2.k.a.1609.24 | yes | 32 | |
69.68 | even | 2 | 5796.2.k.d.5473.16 | 32 | |||
161.160 | even | 2 | inner | 1932.2.k.a.1609.21 | ✓ | 32 | |
483.482 | odd | 2 | 5796.2.k.d.5473.18 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1932.2.k.a.1609.21 | ✓ | 32 | 161.160 | even | 2 | inner | |
1932.2.k.a.1609.22 | yes | 32 | 7.6 | odd | 2 | inner | |
1932.2.k.a.1609.23 | yes | 32 | 1.1 | even | 1 | trivial | |
1932.2.k.a.1609.24 | yes | 32 | 23.22 | odd | 2 | inner | |
5796.2.k.d.5473.15 | 32 | 21.20 | even | 2 | |||
5796.2.k.d.5473.16 | 32 | 69.68 | even | 2 | |||
5796.2.k.d.5473.17 | 32 | 3.2 | odd | 2 | |||
5796.2.k.d.5473.18 | 32 | 483.482 | odd | 2 |