Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 17.8 | ||
Character | \(\chi\) | \(=\) | 128.17 |
Dual form | 128.4.g.a.113.8 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 1.20185 | − | 2.90153i | 0.231297 | − | 0.558400i | −0.765033 | − | 0.643991i | \(-0.777278\pi\) |
0.996330 | + | 0.0855902i | \(0.0272776\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.98512 | + | 1.65069i | −0.356440 | + | 0.147642i | −0.553716 | − | 0.832706i | \(-0.686791\pi\) |
0.197276 | + | 0.980348i | \(0.436791\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −22.4050 | + | 22.4050i | −1.20976 | + | 1.20976i | −0.238651 | + | 0.971105i | \(0.576705\pi\) |
−0.971105 | + | 0.238651i | \(0.923295\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 12.1174 | + | 12.1174i | 0.448794 | + | 0.448794i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.5161 | + | 39.8735i | 0.452709 | + | 1.09294i | 0.971288 | + | 0.237907i | \(0.0764614\pi\) |
−0.518578 | + | 0.855030i | \(0.673539\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.9201 | + | 7.42277i | 0.382320 | + | 0.158362i | 0.565562 | − | 0.824706i | \(-0.308659\pi\) |
−0.183242 | + | 0.983068i | \(0.558659\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.5469i | 0.233185i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 45.9852i | − | 0.656062i | −0.944667 | − | 0.328031i | \(-0.893615\pi\) | ||
0.944667 | − | 0.328031i | \(-0.106385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.0023 | + | 10.3563i | 0.301890 | + | 0.125047i | 0.528486 | − | 0.848942i | \(-0.322760\pi\) |
−0.226596 | + | 0.973989i | \(0.572760\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38.0813 | + | 91.9364i | 0.395715 | + | 0.955341i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 40.3415 | + | 40.3415i | 0.365729 | + | 0.365729i | 0.865917 | − | 0.500188i | \(-0.166736\pi\) |
−0.500188 | + | 0.865917i | \(0.666736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −75.2319 | + | 75.2319i | −0.601856 | + | 0.601856i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 128.064 | − | 53.0458i | 0.912812 | − | 0.378099i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −88.6955 | + | 214.130i | −0.567943 | + | 1.37113i | 0.335344 | + | 0.942096i | \(0.391148\pi\) |
−0.903286 | + | 0.429039i | \(0.858852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −260.478 | −1.50913 | −0.754567 | − | 0.656223i | \(-0.772153\pi\) | ||||
−0.754567 | + | 0.656223i | \(0.772153\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 135.544 | 0.715007 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 52.3029 | − | 126.270i | 0.252594 | − | 0.609817i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 70.4470 | − | 29.1801i | 0.313011 | − | 0.129654i | −0.220647 | − | 0.975354i | \(-0.570817\pi\) |
0.533658 | + | 0.845700i | \(0.320817\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 43.0748 | − | 43.0748i | 0.176859 | − | 0.176859i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −251.246 | − | 251.246i | −0.957026 | − | 0.957026i | 0.0420884 | − | 0.999114i | \(-0.486599\pi\) |
−0.999114 | + | 0.0420884i | \(0.986599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 95.7143 | + | 231.075i | 0.339449 | + | 0.819501i | 0.997769 | + | 0.0667635i | \(0.0212673\pi\) |
−0.658320 | + | 0.752738i | \(0.728733\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −68.2916 | − | 28.2873i | −0.226229 | − | 0.0937072i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 15.5684i | − | 0.0483167i | −0.999708 | − | 0.0241584i | \(-0.992309\pi\) | ||
0.999708 | − | 0.0241584i | \(-0.00769059\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 660.968i | − | 1.92702i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −133.428 | − | 55.2676i | −0.366345 | − | 0.151745i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 171.815 | + | 414.797i | 0.445294 | + | 1.07503i | 0.974065 | + | 0.226270i | \(0.0726531\pi\) |
−0.528771 | + | 0.848765i | \(0.677347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −131.638 | − | 131.638i | −0.322728 | − | 0.322728i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 60.0981 | − | 60.0981i | 0.139652 | − | 0.139652i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −53.3294 | + | 22.0897i | −0.117676 | + | 0.0487431i | −0.440745 | − | 0.897633i | \(-0.645286\pi\) |
0.323069 | + | 0.946376i | \(0.395286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 297.690 | − | 718.686i | 0.624840 | − | 1.50850i | −0.221118 | − | 0.975247i | \(-0.570971\pi\) |
0.845958 | − | 0.533250i | \(-0.179029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −542.983 | −1.08586 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −83.6667 | −0.159655 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 377.382 | − | 911.080i | 0.688127 | − | 1.66128i | −0.0603949 | − | 0.998175i | \(-0.519236\pi\) |
0.748522 | − | 0.663110i | \(-0.230764\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 165.537 | − | 68.5675i | 0.288815 | − | 0.119631i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 359.297 | − | 359.297i | 0.600574 | − | 0.600574i | −0.339891 | − | 0.940465i | \(-0.610390\pi\) |
0.940465 | + | 0.339891i | \(0.110390\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 605.446 | + | 605.446i | 0.970714 | + | 0.970714i | 0.999583 | − | 0.0288694i | \(-0.00919069\pi\) |
−0.0288694 | + | 0.999583i | \(0.509191\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 127.870 | + | 308.706i | 0.196869 | + | 0.475284i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1263.41 | − | 523.321i | −1.86986 | − | 0.774520i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 380.220i | 0.541494i | 0.962650 | + | 0.270747i | \(0.0872707\pi\) | ||||
−0.962650 | + | 0.270747i | \(0.912729\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 27.3544i | 0.0375232i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −235.183 | − | 97.4158i | −0.311020 | − | 0.128829i | 0.221713 | − | 0.975112i | \(-0.428835\pi\) |
−0.532733 | + | 0.846283i | \(0.678835\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 75.9074 | + | 183.257i | 0.0968625 | + | 0.233847i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 514.706 | + | 514.706i | 0.634279 | + | 0.634279i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −949.793 | + | 949.793i | −1.13121 | + | 1.13121i | −0.141237 | + | 0.989976i | \(0.545108\pi\) |
−0.989976 | + | 0.141237i | \(0.954892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −567.808 | + | 235.194i | −0.654093 | + | 0.270934i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −313.056 | + | 755.785i | −0.349058 | + | 0.842701i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −116.732 | −0.126068 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 663.589 | 0.694611 | 0.347305 | − | 0.937752i | \(-0.387097\pi\) | ||||
0.347305 | + | 0.937752i | \(0.387097\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −283.031 | + | 683.298i | −0.287331 | + | 0.693677i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 937.978 | − | 388.523i | 0.924082 | − | 0.382767i | 0.130651 | − | 0.991428i | \(-0.458293\pi\) |
0.793430 | + | 0.608661i | \(0.208293\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 954.756 | − | 954.756i | 0.913348 | − | 0.913348i | −0.0831859 | − | 0.996534i | \(-0.526510\pi\) |
0.996534 | + | 0.0831859i | \(0.0265095\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −303.517 | − | 303.517i | −0.282098 | − | 0.282098i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 172.355 | + | 416.102i | 0.155721 | + | 0.375945i | 0.982416 | − | 0.186706i | \(-0.0597813\pi\) |
−0.826694 | + | 0.562651i | \(0.809781\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 253.241 | + | 104.896i | 0.222533 | + | 0.0921761i | 0.491164 | − | 0.871067i | \(-0.336571\pi\) |
−0.268632 | + | 0.963243i | \(0.586571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 239.475i | − | 0.204774i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1164.80i | 0.969690i | 0.874600 | + | 0.484845i | \(0.161124\pi\) | ||||
−0.874600 | + | 0.484845i | \(0.838876\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −227.357 | − | 94.1743i | −0.184358 | − | 0.0763635i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 127.201 | + | 307.091i | 0.100511 | + | 0.242655i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1030.30 | + | 1030.30i | 0.793675 | + | 0.793675i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −375.954 | + | 375.954i | −0.282459 | + | 0.282459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1030.96 | + | 427.038i | −0.755760 | + | 0.313046i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 381.960 | − | 922.133i | 0.273308 | − | 0.659825i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 624.520 | 0.436356 | 0.218178 | − | 0.975909i | \(-0.429989\pi\) | ||||
0.218178 | + | 0.975909i | \(0.429989\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 785.506 | 0.536123 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −370.999 | + | 895.672i | −0.247438 | + | 0.597368i | −0.997985 | − | 0.0634490i | \(-0.979790\pi\) |
0.750547 | + | 0.660817i | \(0.229790\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −792.208 | + | 328.143i | −0.516490 | + | 0.213937i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −422.788 | + | 422.788i | −0.269539 | + | 0.269539i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1408.41 | + | 1408.41i | 0.878308 | + | 0.878308i | 0.993360 | − | 0.115051i | \(-0.0367032\pi\) |
−0.115051 | + | 0.993360i | \(0.536703\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 127.491 | + | 307.790i | 0.0777958 | + | 0.187816i | 0.957992 | − | 0.286794i | \(-0.0925894\pi\) |
−0.880197 | + | 0.474609i | \(0.842589\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −45.1722 | − | 18.7110i | −0.0269801 | − | 0.0111755i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 837.134i | 0.489543i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 999.742i | − | 0.572580i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1917.82 | − | 794.387i | −1.07605 | − | 0.445714i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −765.994 | − | 1849.27i | −0.421159 | − | 1.01677i | −0.982006 | − | 0.188849i | \(-0.939524\pi\) |
0.560847 | − | 0.827919i | \(-0.310476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −773.796 | − | 773.796i | −0.417024 | − | 0.417024i | 0.467153 | − | 0.884177i | \(-0.345280\pi\) |
−0.884177 | + | 0.467153i | \(0.845280\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 557.223 | − | 557.223i | 0.294437 | − | 0.294437i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1038.04 | − | 429.968i | 0.537916 | − | 0.222812i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 640.806 | − | 1547.04i | 0.325745 | − | 0.786417i | −0.673154 | − | 0.739502i | \(-0.735061\pi\) |
0.998899 | − | 0.0469150i | \(-0.0149390\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1410.04 | 0.703295 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1807.70 | −0.884887 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 636.715 | − | 1537.17i | 0.305959 | − | 0.738651i | −0.693869 | − | 0.720102i | \(-0.744095\pi\) |
0.999828 | − | 0.0185496i | \(-0.00590487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −540.160 | + | 223.742i | −0.254857 | + | 0.105565i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1241.93 | + | 1241.93i | −0.575469 | + | 0.575469i | −0.933651 | − | 0.358183i | \(-0.883396\pi\) |
0.358183 | + | 0.933651i | \(0.383396\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1287.48 | − | 1287.48i | −0.586017 | − | 0.586017i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 177.472 | + | 428.455i | 0.0793661 | + | 0.191607i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1247.56 | + | 516.757i | 0.548268 | + | 0.227100i | 0.639583 | − | 0.768722i | \(-0.279107\pi\) |
−0.0913149 | + | 0.995822i | \(0.529107\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3371.14i | − | 1.45620i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 181.286i | 0.0769845i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 985.168 | + | 408.070i | 0.411368 | + | 0.170394i | 0.578763 | − | 0.815496i | \(-0.303536\pi\) |
−0.167395 | + | 0.985890i | \(0.553536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −120.962 | − | 292.028i | −0.0496742 | − | 0.119924i | 0.897095 | − | 0.441839i | \(-0.145674\pi\) |
−0.946769 | + | 0.321914i | \(0.895674\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1727.51 | − | 1727.51i | −0.697822 | − | 0.697822i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −232.573 | + | 232.573i | −0.0924274 | + | 0.0924274i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1833.59 | − | 759.499i | 0.717035 | − | 0.297006i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1680.78 | + | 4057.76i | −0.646872 | + | 1.56169i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −584.594 | −0.221465 | −0.110732 | − | 0.993850i | \(-0.535320\pi\) | ||||
−0.110732 | + | 0.993850i | \(0.535320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 660.360 | 0.246289 | 0.123145 | − | 0.992389i | \(-0.460702\pi\) | ||||
0.123145 | + | 0.992389i | \(0.460702\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −100.555 | + | 242.762i | −0.0369277 | + | 0.0891514i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −827.877 | + | 342.918i | −0.299410 | + | 0.124020i | −0.527331 | − | 0.849660i | \(-0.676807\pi\) |
0.227921 | + | 0.973680i | \(0.426807\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 153.764 | − | 153.764i | 0.0547742 | − | 0.0547742i | −0.679189 | − | 0.733963i | \(-0.737668\pi\) |
0.733963 | + | 0.679189i | \(0.237668\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2189.97 | − | 2189.97i | −0.768500 | − | 0.768500i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2810.36 | − | 6784.80i | −0.971667 | − | 2.34581i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1415.98 | + | 586.516i | 0.482420 | + | 0.199825i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 977.671i | 0.328274i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1167.97i | 0.386557i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5199.68 | + | 2153.78i | 1.69650 | + | 0.702712i | 0.999891 | − | 0.0147412i | \(-0.00469245\pi\) |
0.696606 | + | 0.717454i | \(0.254692\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −610.690 | − | 1474.34i | −0.196450 | − | 0.474272i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −762.866 | − | 762.866i | −0.241986 | − | 0.241986i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5836.00 | − | 5836.00i | 1.82568 | − | 1.82568i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2484.38 | − | 1029.06i | 0.766570 | − | 0.317524i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 341.338 | − | 824.062i | 0.103895 | − | 0.250825i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −998.982 | −0.299986 | −0.149993 | − | 0.988687i | \(-0.547925\pi\) | ||||
−0.149993 | + | 0.988687i | \(0.547925\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1823.24 | −0.540218 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1393.39 | + | 3363.95i | −0.407413 | + | 0.983583i | 0.578402 | + | 0.815752i | \(0.303676\pi\) |
−0.985816 | + | 0.167831i | \(0.946324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 941.495 | − | 389.980i | 0.271684 | − | 0.112535i | −0.242682 | − | 0.970106i | \(-0.578027\pi\) |
0.514366 | + | 0.857571i | \(0.328027\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3036.87 | + | 3036.87i | −0.864984 | + | 0.864984i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 540.109 | + | 540.109i | 0.151861 | + | 0.151861i | 0.778949 | − | 0.627088i | \(-0.215753\pi\) |
−0.627088 | + | 0.778949i | \(0.715753\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.6986 | + | 62.0420i | 0.00713359 | + | 0.0172220i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1103.22 | + | 456.969i | 0.302371 | + | 0.125246i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2875.66i | 0.778287i | 0.921177 | + | 0.389144i | \(0.127229\pi\) | ||||
−0.921177 | + | 0.389144i | \(0.872771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 179.902i | − | 0.0480851i | −0.999711 | − | 0.0240425i | \(-0.992346\pi\) | ||
0.999711 | − | 0.0240425i | \(-0.00765371\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3537.10 | + | 1465.11i | 0.933765 | + | 0.386778i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1091.05 | + | 2634.04i | 0.284510 | + | 0.686867i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 371.172 | + | 371.172i | 0.0956158 | + | 0.0956158i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −565.311 | + | 565.311i | −0.143876 | + | 0.143876i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5834.77 | + | 2416.84i | −1.46728 | + | 0.607767i | −0.966237 | − | 0.257655i | \(-0.917050\pi\) |
−0.501043 | + | 0.865422i | \(0.667050\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −942.270 | + | 2274.84i | −0.234150 | + | 0.565288i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 622.955 | 0.152984 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5382.92 | −1.30653 | −0.653263 | − | 0.757131i | \(-0.726600\pi\) | ||||
−0.653263 | + | 0.757131i | \(0.726600\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −924.585 | + | 2232.15i | −0.221818 | + | 0.535516i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3669.47 | + | 1519.94i | −0.870247 | + | 0.360468i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1725.28 | + | 1725.28i | −0.404508 | + | 0.404508i | −0.879818 | − | 0.475311i | \(-0.842336\pi\) |
0.475311 | + | 0.879818i | \(0.342336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1369.40 | − | 1369.40i | −0.317441 | − | 0.317441i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1614.34 | + | 3897.37i | 0.370023 | + | 0.893315i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7959.26 | + | 3296.83i | 1.80403 | + | 0.747255i | 0.984776 | + | 0.173826i | \(0.0556130\pi\) |
0.819256 | + | 0.573428i | \(0.194387\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1049.81i | 0.235320i | 0.993054 | + | 0.117660i | \(0.0375393\pi\) | ||||
−0.993054 | + | 0.117660i | \(0.962461\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1930.18i | 0.427912i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4242.30 | − | 1757.22i | −0.930256 | − | 0.385325i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1433.09 | + | 3459.78i | 0.310852 | + | 0.750463i | 0.999674 | + | 0.0255326i | \(0.00812818\pi\) |
−0.688822 | + | 0.724931i | \(0.741872\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3156.32 | − | 3156.32i | −0.677291 | − | 0.677291i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1634.94 | − | 1634.94i | 0.347089 | − | 0.347089i | −0.511935 | − | 0.859024i | \(-0.671071\pi\) |
0.859024 | + | 0.511935i | \(0.171071\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4367.76 | − | 1809.19i | 0.917443 | − | 0.380017i | 0.126542 | − | 0.991961i | \(-0.459612\pi\) |
0.790901 | + | 0.611944i | \(0.209612\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −140.295 | + | 338.702i | −0.0291591 | + | 0.0703963i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11258.3 | 2.31553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2798.36 | 0.569582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 797.537 | − | 1925.43i | 0.160661 | − | 0.387871i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −440.173 | + | 182.326i | −0.0877651 | + | 0.0363535i | −0.426134 | − | 0.904660i | \(-0.640125\pi\) |
0.338369 | + | 0.941014i | \(0.390125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 176.061 | − | 176.061i | 0.0347480 | − | 0.0347480i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4230.25 | + | 4230.25i | 0.826477 | + | 0.826477i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 423.480 | + | 1022.37i | 0.0819079 | + | 0.197743i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7321.71 | − | 3032.75i | −1.40205 | − | 0.580747i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3188.52i | − | 0.604540i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3355.44i | 0.629942i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.2214 | − | 8.37598i | −0.00375927 | − | 0.00155714i | 0.380803 | − | 0.924656i | \(-0.375648\pi\) |
−0.384562 | + | 0.923099i | \(0.625648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1622.78 | − | 3917.73i | −0.298759 | − | 0.721269i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 390.934 | + | 390.934i | 0.0712791 | + | 0.0712791i | 0.741848 | − | 0.670568i | \(-0.233950\pi\) |
−0.670568 | + | 0.741848i | \(0.733950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3353.24 | + | 3353.24i | −0.605548 | + | 0.605548i | −0.941779 | − | 0.336231i | \(-0.890848\pi\) |
0.336231 | + | 0.941779i | \(0.390848\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2163.85 | − | 896.296i | 0.387045 | − | 0.160319i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1362.73 | − | 3289.92i | 0.241447 | − | 0.582904i | −0.755980 | − | 0.654594i | \(-0.772839\pi\) |
0.997427 | + | 0.0716906i | \(0.0228394\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10003.0 | −1.75568 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1414.48 | 0.245946 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 476.236 | − | 1149.73i | 0.0820386 | − | 0.198059i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1906.60 | + | 789.738i | −0.325412 | + | 0.134790i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 608.717 | − | 608.717i | 0.102942 | − | 0.102942i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 348.810 | + | 348.810i | 0.0584514 | + | 0.0584514i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3035.45 | − | 7328.23i | −0.504059 | − | 1.21691i | −0.947255 | − | 0.320481i | \(-0.896155\pi\) |
0.443196 | − | 0.896425i | \(-0.353845\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1207.23 | + | 500.049i | 0.198665 | + | 0.0822899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4253.70i | 0.693745i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2973.12i | 0.480582i | 0.970701 | + | 0.240291i | \(0.0772429\pi\) | ||||
−0.970701 | + | 0.240291i | \(0.922757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3379.70 | + | 1399.92i | 0.541475 | + | 0.224286i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4302.09 | − | 10386.2i | −0.683200 | − | 1.64939i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7124.07 | + | 7124.07i | 1.12147 | + | 1.12147i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −546.500 | + | 546.500i | −0.0852828 | + | 0.0852828i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1239.20 | + | 513.294i | −0.191711 | + | 0.0794094i | −0.476474 | − | 0.879189i | \(-0.658085\pi\) |
0.284762 | + | 0.958598i | \(0.408085\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 618.263 | − | 1492.62i | 0.0948276 | − | 0.228934i | −0.869347 | − | 0.494202i | \(-0.835460\pi\) |
0.964175 | + | 0.265268i | \(0.0854604\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2688.67 | 0.408862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2669.91 | 0.402563 | 0.201282 | − | 0.979533i | \(-0.435489\pi\) | ||||
0.201282 | + | 0.979533i | \(0.435489\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −838.754 | + | 2024.93i | −0.125398 | + | 0.302739i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4227.72 | − | 1751.18i | 0.626763 | − | 0.259614i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6834.40 | − | 6834.40i | 1.00475 | − | 1.00475i | 0.00476246 | − | 0.999989i | \(-0.498484\pi\) |
0.999989 | − | 0.00476246i | \(-0.00151595\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4332.19 | − | 4332.19i | −0.631606 | − | 0.631606i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 639.000 | + | 1542.68i | 0.0923934 | + | 0.223057i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3412.18 | − | 1413.37i | −0.489320 | − | 0.202683i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 12688.1i | − | 1.80467i | −0.431034 | − | 0.902336i | \(-0.641851\pi\) | ||
0.431034 | − | 0.902336i | \(-0.358149\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 6088.92i | − | 0.859015i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13143.0 | − | 5444.03i | −1.83923 | − | 0.761832i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 921.648 | + | 2225.05i | 0.127939 | + | 0.308871i | 0.974850 | − | 0.222863i | \(-0.0715404\pi\) |
−0.846911 | + | 0.531735i | \(0.821540\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2216.54 | − | 2216.54i | −0.305231 | − | 0.305231i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3178.87 | + | 3178.87i | −0.434271 | + | 0.434271i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13206.6 | + | 5470.36i | −1.78992 | + | 0.741407i | −0.799955 | + | 0.600060i | \(0.795143\pi\) |
−0.989960 | + | 0.141348i | \(0.954857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 750.582 | − | 1812.06i | 0.100928 | − | 0.243661i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1489.39 | −0.198706 | −0.0993529 | − | 0.995052i | \(-0.531677\pi\) | ||||
−0.0993529 | + | 0.995052i | \(0.531677\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5898.68 | 0.780843 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1640.22 | + | 3959.85i | −0.215445 | + | 0.520130i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11998.3 | − | 4969.86i | 1.56385 | − | 0.647768i | 0.578097 | − | 0.815968i | \(-0.303795\pi\) |
0.985753 | + | 0.168200i | \(0.0537954\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1855.11 | − | 1855.11i | 0.239941 | − | 0.239941i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2152.93 | + | 2152.93i | 0.276339 | + | 0.276339i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −627.625 | − | 1515.22i | −0.0799475 | − | 0.193010i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8675.83 | − | 3593.64i | −1.09679 | − | 0.454307i | −0.240423 | − | 0.970668i | \(-0.577286\pi\) |
−0.856371 | + | 0.516361i | \(0.827286\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2693.00i | 0.337891i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3772.26i | − | 0.469769i | −0.972023 | − | 0.234885i | \(-0.924529\pi\) | ||
0.972023 | − | 0.234885i | \(-0.0754713\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4667.80 | − | 1933.47i | −0.576972 | − | 0.238990i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −45.1537 | − | 109.011i | −0.00554001 | − | 0.0133748i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2327.03 | + | 2327.03i | 0.283406 | + | 0.283406i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9020.80 | + | 9020.80i | −1.09059 | + | 1.09059i | −0.0951210 | + | 0.995466i | \(0.530324\pi\) |
−0.995466 | + | 0.0951210i | \(0.969676\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5779.24 | − | 2393.84i | 0.693598 | − | 0.287298i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 699.924 | − | 1689.77i | 0.0833922 | − | 0.201327i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1098.03 | 0.129880 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1046.29 | 0.122870 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3925.38 | − | 9476.72i | 0.457679 | − | 1.10494i | −0.511655 | − | 0.859191i | \(-0.670968\pi\) |
0.969335 | − | 0.245745i | \(-0.0790325\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4298.89 | + | 1780.66i | −0.497660 | + | 0.206138i | −0.617372 | − | 0.786671i | \(-0.711803\pi\) |
0.119712 | + | 0.992809i | \(0.461803\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 188.649 | − | 188.649i | 0.0216843 | − | 0.0216843i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3459.56 | + | 3459.56i | 0.394855 | + | 0.394855i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9432.43 | + | 22771.9i | 1.06901 | + | 2.58082i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2428.97 | + | 1006.11i | 0.273361 | + | 0.113230i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2281.76i | 0.255008i | 0.991838 | + | 0.127504i | \(0.0406966\pi\) | ||||
−0.991838 | + | 0.127504i | \(0.959303\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8491.53i | − | 0.942441i | −0.882016 | − | 0.471220i | \(-0.843814\pi\) | ||
0.882016 | − | 0.471220i | \(-0.156186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2900.78 | − | 1201.54i | −0.319729 | − | 0.132436i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 590.840 | + | 1426.41i | 0.0646767 | + | 0.156143i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3417.05 | + | 3417.05i | 0.371496 | + | 0.371496i | 0.868022 | − | 0.496526i | \(-0.165391\pi\) |
−0.496526 | + | 0.868022i | \(0.665391\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8009.24 | − | 8009.24i | 0.864835 | − | 0.864835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 984.558 | − | 407.817i | 0.105593 | − | 0.0437381i | −0.329261 | − | 0.944239i | \(-0.606800\pi\) |
0.434855 | + | 0.900501i | \(0.356800\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2217.23 | − | 5352.86i | 0.236195 | − | 0.570224i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6286.34 | −0.665176 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6407.14 | −0.673434 | −0.336717 | − | 0.941606i | \(-0.609317\pi\) | ||||
−0.336717 | + | 0.941606i | \(0.609317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5868.44 | − | 14167.7i | 0.612714 | − | 1.47922i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3175.18 | + | 1315.20i | −0.329323 | + | 0.136410i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1874.55 | − | 1874.55i | 0.193144 | − | 0.193144i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6405.90 | + | 6405.90i | 0.655701 | + | 0.655701i | 0.954360 | − | 0.298659i | \(-0.0965393\pi\) |
−0.298659 | + | 0.954360i | \(0.596539\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2439.32 | − | 5889.05i | −0.248057 | − | 0.598861i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11209.2 | − | 4642.99i | −1.13246 | − | 0.469080i | −0.263843 | − | 0.964566i | \(-0.584990\pi\) |
−0.868616 | + | 0.495486i | \(0.834990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10213.2i | 1.02515i | 0.858642 | + | 0.512576i | \(0.171309\pi\) | ||||
−0.858642 | + | 0.512576i | \(0.828691\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 3528.65i | − | 0.351908i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8301.10 | + | 3438.43i | 0.822546 | + | 0.340710i | 0.753948 | − | 0.656935i | \(-0.228147\pi\) |
0.0685986 | + | 0.997644i | \(0.478147\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11957.5 | + | 28868.0i | 1.17728 | + | 2.84222i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3718.64 | − | 3718.64i | −0.363792 | − | 0.363792i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7632.93 | + | 7632.93i | −0.741992 | + | 0.741992i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2660.09 | + | 1101.85i | −0.256954 | + | 0.106434i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2944.33 | + | 7108.24i | −0.282624 | + | 0.682314i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1983.62 | 0.189215 | 0.0946075 | − | 0.995515i | \(-0.469840\pi\) | ||||
0.0946075 | + | 0.995515i | \(0.469840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1479.02 | 0.140203 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2172.59 | + | 5245.10i | −0.204672 | + | 0.494121i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2644.48 | + | 1095.38i | −0.247587 | + | 0.102554i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2241.43 | − | 2241.43i | 0.208561 | − | 0.208561i | −0.595095 | − | 0.803655i | \(-0.702886\pi\) |
0.803655 | + | 0.595095i | \(0.202886\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3694.90 | − | 3694.90i | −0.341696 | − | 0.341696i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1553.51 | + | 3750.50i | 0.142788 | + | 0.344720i | 0.979053 | − | 0.203605i | \(-0.0652657\pi\) |
−0.836265 | + | 0.548325i | \(0.815266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9846.81 | + | 4078.68i | 0.899550 | + | 0.372606i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 3190.22i | − | 0.289677i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 16100.1i | 1.45310i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8740.71 | + | 3620.52i | 0.784144 | + | 0.324803i | 0.738587 | − | 0.674159i | \(-0.235494\pi\) |
0.0455575 | + | 0.998962i | \(0.485494\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2110.88 | + | 5096.11i | 0.188238 | + | 0.454446i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3856.31 | + | 3856.31i | 0.341838 | + | 0.341838i | 0.857058 | − | 0.515220i | \(-0.172290\pi\) |
−0.515220 | + | 0.857058i | \(0.672290\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3096.62 | + | 3096.62i | −0.272867 | + | 0.272867i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5283.03 | + | 2188.30i | −0.462776 | + | 0.191688i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −776.546 | + | 1874.75i | −0.0676224 | + | 0.163255i | −0.954078 | − | 0.299559i | \(-0.903160\pi\) |
0.886455 | + | 0.462814i | \(0.153160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27130.0 | −2.34865 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3751.24 | 0.322849 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2228.81 | + | 5380.82i | −0.190705 | + | 0.460403i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 620.767 | − | 257.130i | 0.0528071 | − | 0.0218734i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2998.78 | − | 2998.78i | 0.253626 | − | 0.253626i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4528.26 | − | 4528.26i | −0.380780 | − | 0.380780i | 0.490603 | − | 0.871383i | \(-0.336777\pi\) |
−0.871383 | + | 0.490603i | \(0.836777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1376.98 | + | 3324.33i | 0.115127 | + | 0.277940i | 0.970931 | − | 0.239359i | \(-0.0769373\pi\) |
−0.855804 | + | 0.517300i | \(0.826937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9781.48 | − | 4051.62i | −0.813141 | − | 0.336814i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11978.1i | 0.990086i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 8912.13i | − | 0.732484i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −913.887 | − | 378.544i | −0.0746880 | − | 0.0309368i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2637.43 | − | 6367.31i | −0.214333 | − | 0.517446i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1373.71 | − | 1373.71i | −0.111011 | − | 0.111011i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2368.06 | − | 2368.06i | 0.190296 | − | 0.190296i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26355.1 | − | 10916.6i | 2.10611 | − | 0.872380i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3507.90 | + | 8468.82i | −0.278773 | + | 0.673018i | −0.999802 | − | 0.0198866i | \(-0.993669\pi\) |
0.721029 | + | 0.692905i | \(0.243669\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −992.708 | −0.0784552 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1182.35 | −0.0929287 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2578.26 | − | 6224.46i | 0.201532 | − | 0.486542i | −0.790510 | − | 0.612450i | \(-0.790184\pi\) |
0.992042 | + | 0.125907i | \(0.0401842\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12315.9 | − | 5101.40i | 0.957429 | − | 0.396580i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4435.17 | + | 4435.17i | −0.342912 | + | 0.342912i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8518.82 | − | 8518.82i | −0.655076 | − | 0.655076i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 395.299 | + | 954.335i | 0.0302333 | + | 0.0729897i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8187.07 | + | 3391.19i | 0.622796 | + | 0.257970i | 0.671689 | − | 0.740834i | \(-0.265569\pi\) |
−0.0488930 | + | 0.998804i | \(0.515569\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4851.36i | 0.367067i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 6233.04i | − | 0.469089i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5205.06 | + | 2156.00i | 0.389639 | + | 0.161394i | 0.568898 | − | 0.822408i | \(-0.307370\pi\) |
−0.179259 | + | 0.983802i | \(0.557370\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1922.72 | − | 4641.86i | −0.143167 | − | 0.345636i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −612.876 | − | 612.876i | −0.0453939 | − | 0.0453939i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13921.3 | − | 13921.3i | 1.02568 | − | 1.02568i | 0.0260140 | − | 0.999662i | \(-0.491719\pi\) |
0.999662 | − | 0.0260140i | \(-0.00828146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −18276.2 | + | 7570.27i | −1.33947 | + | 0.554826i | −0.933341 | − | 0.358990i | \(-0.883121\pi\) |
−0.406128 | + | 0.913816i | \(0.633121\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −702.597 | + | 1696.22i | −0.0512241 | + | 0.123666i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6069.93 | −0.440232 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24309.7 | 1.75394 | 0.876972 | − | 0.480542i | \(-0.159560\pi\) | ||||
0.876972 | + | 0.480542i | \(0.159560\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 793.657 | − | 1916.06i | 0.0569659 | − | 0.137528i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7451.87 | − | 3086.66i | 0.532109 | − | 0.220407i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13701.7 | + | 13701.7i | −0.973356 | + | 0.973356i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1013.83 | − | 1013.83i | −0.0716522 | − | 0.0716522i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6035.14 | − | 14570.1i | −0.424356 | − | 1.02449i | −0.981048 | − | 0.193767i | \(-0.937929\pi\) |
0.556691 | − | 0.830719i | \(-0.312071\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6512.53 | − | 2697.58i | −0.455593 | − | 0.188713i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2814.25i | 0.195876i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 14290.4i | − | 0.989608i | −0.869005 | − | 0.494804i | \(-0.835240\pi\) | ||
0.869005 | − | 0.494804i | \(-0.164760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5806.57 | − | 2405.16i | −0.400078 | − | 0.165718i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −261.350 | − | 630.954i | −0.0179168 | − | 0.0432550i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2752.47 | − | 2752.47i | −0.187751 | − | 0.187751i | 0.606972 | − | 0.794723i | \(-0.292384\pi\) |
−0.794723 | + | 0.606972i | \(0.792384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10680.0 | + | 10680.0i | −0.724871 | + | 0.724871i | −0.969593 | − | 0.244722i | \(-0.921303\pi\) |
0.244722 | + | 0.969593i | \(0.421303\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15612.9 | − | 6467.06i | 1.05440 | − | 0.436748i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 877.637 | − | 2118.80i | 0.0589769 | − | 0.142383i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13933.7 | 0.931719 | 0.465859 | − | 0.884859i | \(-0.345745\pi\) | ||||
0.465859 | + | 0.884859i | \(0.345745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23064.0 | −1.53464 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 115.561 | − | 278.988i | 0.00765153 | − | 0.0184724i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −20129.3 | + | 8337.81i | −1.32629 | + | 0.549366i | −0.929594 | − | 0.368586i | \(-0.879842\pi\) |
−0.396692 | + | 0.917952i | \(0.629842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3403.59 | − | 3403.59i | 0.223164 | − | 0.223164i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4886.46 | + | 4886.46i | 0.318836 | + | 0.318836i | 0.848320 | − | 0.529484i | \(-0.177615\pi\) |
−0.529484 | + | 0.848320i | \(0.677615\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7135.77 | + | 17227.3i | 0.463345 | + | 1.11861i | 0.967015 | + | 0.254718i | \(0.0819827\pi\) |
−0.503670 | + | 0.863896i | \(0.668017\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7306.23 | + | 3026.34i | 0.472124 | + | 0.195560i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 42560.2i | − | 2.73698i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 8993.94i | − | 0.575612i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3388.91 | + | 1403.73i | 0.215853 | + | 0.0894094i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1341.85 | − | 3239.52i | −0.0850608 | − | 0.205355i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9484.77 | − | 9484.77i | −0.598388 | − | 0.598388i | 0.341496 | − | 0.939883i | \(-0.389067\pi\) |
−0.939883 | + | 0.341496i | \(0.889067\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12498.5 | − | 12498.5i | 0.784790 | − | 0.784790i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2488.79 | + | 1030.89i | −0.155535 | + | 0.0644245i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4906.21 | − | 11844.6i | 0.305167 | − | 0.736737i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8707.53 | 0.539068 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26621.4 | −1.64038 | −0.820189 | − | 0.572092i | \(-0.806132\pi\) | ||||
−0.820189 | + | 0.572092i | \(0.806132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3206.34 | − | 7740.79i | 0.196650 | − | 0.474754i | −0.794539 | − | 0.607213i | \(-0.792287\pi\) |
0.991188 | + | 0.132459i | \(0.0422873\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3130.33 | + | 1296.63i | −0.191096 | + | 0.0791545i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11415.8 | − | 11415.8i | 0.693664 | − | 0.693664i | −0.269373 | − | 0.963036i | \(-0.586816\pi\) |
0.963036 | + | 0.269373i | \(0.0868163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1761.59 | − | 1761.59i | −0.106546 | − | 0.106546i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9919.33 | − | 23947.4i | −0.597188 | − | 1.44174i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24638.3 | + | 10205.5i | 1.47652 | + | 0.611596i | 0.968336 | − | 0.249650i | \(-0.0803156\pi\) |
0.508188 | + | 0.861246i | \(0.330316\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4181.76i | − | 0.249458i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14672.9i | 0.871301i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13287.3 | − | 5503.77i | −0.785430 | − | 0.325336i | −0.0463255 | − | 0.998926i | \(-0.514751\pi\) |
−0.739105 | + | 0.673591i | \(0.764751\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1075.25 | − | 2595.89i | −0.0632716 | − | 0.152751i | 0.889081 | − | 0.457749i | \(-0.151344\pi\) |
−0.952353 | + | 0.304998i | \(0.901344\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1980.81 | − | 1980.81i | −0.116030 | − | 0.116030i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2615.38 | − | 2615.38i | 0.152511 | − | 0.152511i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12216.4 | + | 5060.20i | −0.709177 | + | 0.293751i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1200.63 | + | 2898.58i | −0.0693858 | + | 0.167512i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 33573.2 | 1.93156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2416.06 | 0.138384 | 0.0691920 | − | 0.997603i | \(-0.477958\pi\) | ||||
0.0691920 | + | 0.997603i | \(0.477958\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5643.76 | + | 13625.2i | −0.321820 | + | 0.776942i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10314.0 | + | 4272.22i | −0.585526 | + | 0.242533i | −0.655724 | − | 0.755000i | \(-0.727637\pi\) |
0.0701988 | + | 0.997533i | \(0.477637\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14867.7 | + | 14867.7i | −0.840310 | + | 0.840310i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8085.96 | + | 8085.96i | 0.455000 | + | 0.455000i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −3410.41 | − | 8233.45i | −0.191062 | − | 0.461265i | 0.799098 | − | 0.601200i | \(-0.205311\pi\) |
−0.990161 | + | 0.139935i | \(0.955311\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7937.51 | − | 3287.83i | −0.442740 | − | 0.183389i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3200.48i | − | 0.177738i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8708.57i | 0.481524i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3706.50 | + | 1535.28i | 0.204055 | + | 0.0845224i | 0.482370 | − | 0.875967i | \(-0.339776\pi\) |
−0.278315 | + | 0.960490i | \(0.589776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8967.98 | − | 21650.6i | −0.491580 | − | 1.18678i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1016.13 | − | 1016.13i | −0.0554591 | − | 0.0554591i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11553.6 | + | 11553.6i | −0.627868 | + | 0.627868i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2216.27 | − | 918.011i | 0.119924 | − | 0.0496743i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6159.04 | + | 14869.2i | −0.331846 | + | 0.801146i | 0.666600 | + | 0.745415i | \(0.267749\pi\) |
−0.998446 | + | 0.0557306i | \(0.982251\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2063.53 | 0.110708 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 210.903 | 0.0112668 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12310.5 | + | 29720.2i | −0.654859 | + | 1.58097i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1554.84 | + | 644.034i | −0.0823598 | + | 0.0341145i | −0.423483 | − | 0.905904i | \(-0.639193\pi\) |
0.341123 | + | 0.940019i | \(0.389193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4607.29 | + | 4607.29i | −0.243020 | + | 0.243020i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10508.0 | − | 10508.0i | −0.551935 | − | 0.551935i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1381.85 | − | 3336.08i | −0.0722773 | − | 0.174493i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8343.81 | + | 3456.12i | 0.434596 | + | 0.180016i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33535.5i | 1.73945i | 0.493540 | + | 0.869723i | \(0.335703\pi\) | ||||
−0.493540 | + | 0.869723i | \(0.664297\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 42782.6i | 2.20986i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −521.991 | − | 216.216i | −0.0268507 | − | 0.0111219i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9436.67 | − | 22782.1i | −0.483406 | − | 1.16704i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15842.6 | + | 15842.6i | 0.808210 | + | 0.808210i | 0.984363 | − | 0.176153i | \(-0.0563654\pi\) |
−0.176153 | + | 0.984363i | \(0.556365\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7979.90 | − | 7979.90i | 0.405421 | − | 0.405421i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10626.0 | − | 4401.44i | 0.537644 | − | 0.222699i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10693.1 | − | 25815.3i | 0.538823 | − | 1.30083i | −0.386722 | − | 0.922196i | \(-0.626393\pi\) |
0.925545 | − | 0.378638i | \(-0.123607\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8954.03 | 0.449353 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 42560.8 | 2.12720 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2894.05 | − | 6986.86i | 0.144059 | − | 0.347789i | −0.835337 | − | 0.549738i | \(-0.814728\pi\) |
0.979396 | + | 0.201949i | \(0.0647276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1523.06 | − | 630.873i | 0.0755075 | − | 0.0312762i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15149.2 | + | 15149.2i | −0.748009 | + | 0.748009i | −0.974105 | − | 0.226096i | \(-0.927404\pi\) |
0.226096 | + | 0.974105i | \(0.427404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6105.16 | + | 6105.16i | 0.300236 | + | 0.300236i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1669.38 | − | 4030.24i | −0.0817664 | − | 0.197401i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13184.4 | − | 5461.15i | −0.643187 | − | 0.266417i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 23633.7i | − | 1.14834i | −0.818735 | − | 0.574171i | \(-0.805324\pi\) | ||
0.818735 | − | 0.574171i | \(-0.194676\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19834.5i | 0.959905i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4360.97 | + | 1806.37i | 0.210214 | + | 0.0870736i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8369.97 | − | 20206.9i | −0.401865 | − | 0.970188i | −0.987213 | − | 0.159406i | \(-0.949042\pi\) |
0.585348 | − | 0.810782i | \(-0.300958\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5468.05 | + | 5468.05i | 0.261499 | + | 0.261499i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4475.11 | − | 4475.11i | 0.213170 | − | 0.213170i | −0.592442 | − | 0.805613i | \(-0.701836\pi\) |
0.805613 | + | 0.592442i | \(0.201836\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8024.05 | + | 3323.67i | −0.380721 | + | 0.157700i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1300.80 | + | 3140.41i | −0.0614778 | + | 0.148420i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1119.64 | −0.0527089 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6556.87 | −0.307473 | −0.153736 | − | 0.988112i | \(-0.549131\pi\) | ||||
−0.153736 | + | 0.988112i | \(0.549131\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6469.48 | + | 15618.7i | −0.302195 | + | 0.729564i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16437.5 | − | 6808.62i | 0.764832 | − | 0.316804i | 0.0340547 | − | 0.999420i | \(-0.489158\pi\) |
0.730777 | + | 0.682616i | \(0.239158\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19596.2 | − | 19596.2i | 0.908281 | − | 0.908281i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5365.43 | + | 5365.43i | 0.247727 | + | 0.247727i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3679.74 | − | 8883.69i | −0.169243 | − | 0.408590i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20260.6 | + | 8392.23i | 0.928275 | + | 0.384504i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 32127.2i | 1.46633i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7222.93i | 0.328404i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20223.1 | + | 8376.67i | 0.915978 | + | 0.379410i | 0.790342 | − | 0.612666i | \(-0.209903\pi\) |
0.125636 | + | 0.992076i | \(0.459903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2932.43 | + | 7079.50i | 0.132316 | + | 0.319439i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26097.3 | − | 26097.3i | −1.17309 | − | 1.17309i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10669.3 | − | 10669.3i | 0.477777 | − | 0.477777i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5619.20 | + | 2327.55i | −0.250682 | + | 0.103836i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9378.36 | + | 22641.4i | −0.416811 | + | 1.00627i | 0.566454 | + | 0.824093i | \(0.308315\pi\) |
−0.983266 | + | 0.182178i | \(0.941685\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −715.917 | −0.0316988 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23018.1 | −1.01536 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14141.6 | + | 34140.9i | −0.621478 | + | 1.50038i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7203.90 | − | 2983.96i | 0.315409 | − | 0.130647i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 19131.7 | − | 19131.7i | 0.834534 | − | 0.834534i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19542.5 | + | 19542.5i | 0.849293 | + | 0.849293i | 0.990045 | − | 0.140752i | \(-0.0449520\pi\) |
−0.140752 | + | 0.990045i | \(0.544952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −718.754 | − | 1735.23i | −0.0311207 | − | 0.0751319i | 0.907555 | − | 0.419933i | \(-0.137946\pi\) |
−0.938676 | + | 0.344801i | \(0.887946\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3046.07 | + | 1261.72i | 0.131403 | + | 0.0544287i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7176.81i | 0.308457i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6768.63i | 0.289846i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9730.33 | − | 4030.43i | −0.415147 | − | 0.171959i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7505.22 | + | 18119.2i | 0.319043 | + | 0.770237i | 0.999305 | + | 0.0372687i | \(0.0118658\pi\) |
−0.680263 | + | 0.732969i | \(0.738134\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21223.2 | + | 21223.2i | 0.898901 | + | 0.898901i | 0.995339 | − | 0.0964384i | \(-0.0307451\pi\) |
−0.0964384 | + | 0.995339i | \(0.530745\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10197.3 | + | 10197.3i | −0.430331 | + | 0.430331i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38266.7 | + | 15850.6i | −1.60902 | + | 0.666479i | −0.992655 | − | 0.120979i | \(-0.961397\pi\) |
−0.616368 | + | 0.787458i | \(0.711397\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 204.285 | − | 493.187i | 0.00855862 | − | 0.0206623i | −0.919542 | − | 0.392991i | \(-0.871440\pi\) |
0.928101 | + | 0.372328i | \(0.121440\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11761.0 | 0.490958 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −30394.8 | −1.26424 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2899.19 | − | 6999.27i | 0.120157 | − | 0.290084i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −33357.8 | + | 13817.3i | −1.37756 | + | 0.570602i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29085.3 | + | 29085.3i | −1.19682 | + | 1.19682i | −0.221711 | + | 0.975112i | \(0.571164\pi\) |
−0.975112 | + | 0.221711i | \(0.928836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20739.1 | − | 20739.1i | −0.850345 | − | 0.850345i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2778.87 | − | 6708.78i | −0.113534 | − | 0.274096i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7255.99 | + | 3005.53i | 0.295401 | + | 0.122359i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 16846.5i | − | 0.683414i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 14847.6i | − | 0.600197i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4019.10 | + | 1664.77i | 0.161896 | + | 0.0670593i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12547.7 | + | 30292.7i | 0.503662 | + | 1.21595i | 0.947476 | + | 0.319828i | \(0.103625\pi\) |
−0.443814 | + | 0.896119i | \(0.646375\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1414.49 | − | 1414.49i | −0.0565785 | − | 0.0565785i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23194.0 | − | 23194.0i | 0.924495 | − | 0.924495i | −0.0728478 | − | 0.997343i | \(-0.523209\pi\) |
0.997343 | + | 0.0728478i | \(0.0232087\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31813.5 | − | 13177.6i | 1.26363 | − | 0.523415i | 0.352612 | − | 0.935770i | \(-0.385294\pi\) |
0.911023 | + | 0.412355i | \(0.135294\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 13530.9 | − | 32666.4i | 0.535576 | − | 1.29300i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11588.4 | 0.457096 | 0.228548 | − | 0.973533i | \(-0.426602\pi\) | ||||
0.228548 | + | 0.973533i | \(0.426602\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5824.69 | −0.228954 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3363.22 | − | 8119.53i | 0.131743 | − | 0.318055i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −15160.7 | + | 6279.76i | −0.591819 | + | 0.245140i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13525.5 | − | 13525.5i | 0.526169 | − | 0.526169i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8041.00 | + | 8041.00i | 0.311737 | + | 0.311737i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12102.6 | + | 29218.2i | 0.467591 | + | 1.12886i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33657.5 | − | 13941.4i | −1.29593 | − | 0.536794i | −0.375186 | − | 0.926950i | \(-0.622421\pi\) |
−0.920749 | + | 0.390156i | \(0.872421\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1496.31i | 0.0574165i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 12045.9i | − | 0.460656i | −0.973113 | − | 0.230328i | \(-0.926020\pi\) | ||
0.973113 | − | 0.230328i | \(-0.0739799\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −875.893 | − | 362.807i | −0.0333818 | − | 0.0138272i | 0.365930 | − | 0.930642i | \(-0.380751\pi\) |
−0.399312 | + | 0.916815i | \(0.630751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −299.247 | − | 722.445i | −0.0113662 | − | 0.0274404i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −34149.9 | − | 34149.9i | −1.29272 | − | 1.29272i | −0.933098 | − | 0.359622i | \(-0.882906\pi\) |
−0.359622 | − | 0.933098i | \(-0.617094\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13992.4 | + | 13992.4i | −0.527884 | + | 0.527884i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1090.72 | + | 451.789i | −0.0410105 | + | 0.0169871i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 161.231 | − | 389.245i | 0.00604186 | − | 0.0145863i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4599.61 | −0.171785 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3475.40 | 0.129365 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23103.2 | − | 55776.0i | 0.857102 | − | 2.06923i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19074.6 | − | 7900.94i | 0.705289 | − | 0.292140i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17599.2 | + | 17599.2i | −0.648578 | + | 0.648578i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 964.096 | + | 964.096i | 0.0354118 | + | 0.0354118i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15871.7 | − | 38317.6i | −0.581048 | − | 1.40277i | −0.891864 | − | 0.452304i | \(-0.850602\pi\) |
0.310816 | − | 0.950470i | \(-0.399398\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16073.8 | + | 6657.98i | 0.586506 | + | 0.242939i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 19522.9i | − | 0.710015i | −0.934863 | − | 0.355008i | \(-0.884478\pi\) | ||
0.934863 | − | 0.355008i | \(-0.115522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10986.5i | − | 0.398247i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9735.93 | + | 4032.76i | 0.351760 | + | 0.145704i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11755.3 | − | 28379.8i | −0.423330 | − | 1.02201i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15534.4 | + | 15534.4i | 0.557597 | + | 0.557597i | 0.928623 | − | 0.371026i | \(-0.120994\pi\) |
−0.371026 | + | 0.928623i | \(0.620994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.6064 | + | 48.6064i | −0.00173902 | + | 0.00173902i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9105.64 | − | 3771.68i | 0.324719 | − | 0.134503i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3104.59 | + | 7495.14i | −0.110355 | + | 0.266420i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 23138.4 | 0.819811 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4318.29 | 0.152506 | 0.0762532 | − | 0.997088i | \(-0.475704\pi\) | ||||
0.0762532 | + | 0.997088i | \(0.475704\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6845.16 | − | 16525.7i | 0.240968 | − | 0.581748i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1604.15 | − | 664.462i | 0.0562889 | − | 0.0233156i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6053.39 | + | 6053.39i | −0.211729 | + | 0.211729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18383.8 | − | 18383.8i | −0.640953 | − | 0.640953i | 0.309837 | − | 0.950790i | \(-0.399726\pi\) |
−0.950790 | + | 0.309837i | \(0.899726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5699.44 | + | 13759.7i | 0.198077 | + | 0.478200i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1124.52 | − | 465.790i | −0.0389566 | − | 0.0161364i | 0.363120 | − | 0.931742i | \(-0.381711\pi\) |
−0.402077 | + | 0.915606i | \(0.631711\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 20271.3i | − | 0.700025i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 18945.1i | − | 0.652154i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9864.83 | + | 4086.15i | 0.338505 | + | 0.140213i | 0.545459 | − | 0.838137i | \(-0.316355\pi\) |
−0.206955 | + | 0.978351i | \(0.566355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6355.60 | + | 15343.8i | 0.217399 | + | 0.524847i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7908.02 | − | 7908.02i | −0.269648 | − | 0.269648i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2417.47 | − | 2417.47i | 0.0821717 | − | 0.0821717i | −0.664826 | − | 0.746998i | \(-0.731494\pi\) |
0.746998 | + | 0.664826i | \(0.231494\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2329.68 | − | 964.984i | 0.0789388 | − | 0.0326975i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12022.2 | + | 29024.1i | −0.406083 | + | 0.980371i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −63110.7 | −2.12508 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 38057.6 | 1.27749 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2953.59 | + | 7130.60i | −0.0988350 | + | 0.238609i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2631.62 | + | 1090.05i | −0.0877873 | + | 0.0363627i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 25629.3 | − | 25629.3i | 0.852309 | − | 0.852309i | −0.138108 | − | 0.990417i | \(-0.544102\pi\) |
0.990417 | + | 0.138108i | \(0.0441021\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2763.63 | − | 2763.63i | −0.0916207 | − | 0.0916207i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11851.2 | + | 28611.4i | 0.391683 | + | 0.945607i | 0.989573 | + | 0.144029i | \(0.0460059\pi\) |
−0.597890 | + | 0.801578i | \(0.703994\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9752.46 | − | 4039.60i | −0.321325 | − | 0.133097i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6481.20i | 0.212887i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 39097.2i | − | 1.28028i | −0.768259 | − | 0.640139i | \(-0.778877\pi\) | ||
0.768259 | − | 0.640139i | \(-0.221123\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53558.5 | − | 22184.7i | −1.74845 | − | 0.724234i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1797.56 | + | 4339.70i | 0.0585033 | + | 0.141239i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2866.32 | + | 2866.32i | 0.0930026 | + | 0.0930026i | 0.752077 | − | 0.659075i | \(-0.229052\pi\) |
−0.659075 | + | 0.752077i | \(0.729052\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2733.14 | − | 2733.14i | 0.0884112 | − | 0.0884112i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1431.30 | − | 592.865i | 0.0461589 | − | 0.0191197i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5460.64 | + | 13183.1i | −0.175569 | + | 0.423862i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −49476.9 | −1.58596 | −0.792979 | − | 0.609249i | \(-0.791471\pi\) | ||||
−0.792979 | + | 0.609249i | \(0.791471\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24911.3 | −0.796108 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −358.952 | + | 866.586i | −0.0114367 | + | 0.0276107i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45633.0 | − | 18901.8i | 1.44956 | − | 0.600427i | 0.487465 | − | 0.873143i | \(-0.337922\pi\) |
0.962095 | + | 0.272716i | \(0.0879218\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7473.84 | − | 7473.84i | 0.236699 | − | 0.236699i |
(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 | 128.4.g.a.17.8 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.13.9 | yes | 44 | ||
8.3 | odd | 2 | 256.4.g.b.33.8 | 44 | |||
8.5 | even | 2 | 256.4.g.a.33.4 | 44 | |||
32.5 | even | 8 | inner | 128.4.g.a.113.8 | 44 | ||
32.11 | odd | 8 | 256.4.g.b.225.8 | 44 | |||
32.21 | even | 8 | 256.4.g.a.225.4 | 44 | |||
32.27 | odd | 8 | 32.4.g.a.5.9 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.9 | ✓ | 44 | 32.27 | odd | 8 | ||
32.4.g.a.13.9 | yes | 44 | 4.3 | odd | 2 | ||
128.4.g.a.17.8 | 44 | 1.1 | even | 1 | trivial | ||
128.4.g.a.113.8 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.a.33.4 | 44 | 8.5 | even | 2 | |||
256.4.g.a.225.4 | 44 | 32.21 | even | 8 | |||
256.4.g.b.33.8 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.225.8 | 44 | 32.11 | odd | 8 |