Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(15,128)]
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([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.15");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.h (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: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 79.2 | ||
Character | \(\chi\) | \(=\) | 128.79 |
Dual form | 128.3.h.a.47.2 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | −0.936461 | − | 2.26082i | −0.312154 | − | 0.753605i | −0.999625 | − | 0.0273938i | \(-0.991279\pi\) |
0.687471 | − | 0.726212i | \(-0.258721\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.18221 | + | 7.68254i | −0.636442 | + | 1.53651i | 0.194945 | + | 0.980814i | \(0.437547\pi\) |
−0.831387 | + | 0.555693i | \(0.812453\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.67370 | + | 3.67370i | −0.524814 | + | 0.524814i | −0.919021 | − | 0.394208i | \(-0.871019\pi\) |
0.394208 | + | 0.919021i | \(0.371019\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.12963 | − | 2.12963i | 0.236625 | − | 0.236625i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.10089 | + | 14.7288i | −0.554626 | + | 1.33899i | 0.359345 | + | 0.933205i | \(0.383000\pi\) |
−0.913971 | + | 0.405781i | \(0.867000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.82075 | + | 6.80990i | 0.216981 | + | 0.523839i | 0.994466 | − | 0.105063i | \(-0.0335046\pi\) |
−0.777484 | + | 0.628902i | \(0.783505\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 20.3488 | 1.35659 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.67152i | 0.215972i | 0.994152 | + | 0.107986i | \(0.0344401\pi\) | ||||
−0.994152 | + | 0.107986i | \(0.965560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.65751 | − | 0.686564i | 0.0872375 | − | 0.0361349i | −0.338638 | − | 0.940917i | \(-0.609966\pi\) |
0.425875 | + | 0.904782i | \(0.359966\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.7458 | + | 4.86528i | 0.559325 | + | 0.231680i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.31529 | + | 8.31529i | 0.361534 | + | 0.361534i | 0.864378 | − | 0.502843i | \(-0.167713\pi\) |
−0.502843 | + | 0.864378i | \(0.667713\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −31.2172 | − | 31.2172i | −1.24869 | − | 1.24869i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.1564 | − | 11.2485i | −1.00579 | − | 0.416612i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −38.8592 | + | 16.0960i | −1.33997 | + | 0.555035i | −0.933483 | − | 0.358621i | \(-0.883247\pi\) |
−0.406489 | + | 0.913656i | \(0.633247\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.11293i | 0.132675i | 0.997797 | + | 0.0663376i | \(0.0211314\pi\) | ||||
−0.997797 | + | 0.0663376i | \(0.978869\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 39.0124 | 1.18220 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −16.5328 | − | 39.9138i | −0.472367 | − | 1.14039i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 19.8759 | − | 47.9847i | 0.537186 | − | 1.29688i | −0.389493 | − | 0.921030i | \(-0.627350\pi\) |
0.926679 | − | 0.375853i | \(-0.122650\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12.7544 | − | 12.7544i | 0.327036 | − | 0.327036i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 21.1187 | − | 21.1187i | 0.515091 | − | 0.515091i | −0.400991 | − | 0.916082i | \(-0.631334\pi\) |
0.916082 | + | 0.400991i | \(0.131334\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.102495 | − | 0.247444i | 0.00238360 | − | 0.00575451i | −0.922683 | − | 0.385559i | \(-0.874009\pi\) |
0.925067 | + | 0.379804i | \(0.124009\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.58403 | + | 23.1379i | 0.212978 | + | 0.514175i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 39.3838 | 0.837952 | 0.418976 | − | 0.907997i | \(-0.362389\pi\) | ||||
0.418976 | + | 0.907997i | \(0.362389\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22.0079i | 0.449141i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.30063 | − | 3.43823i | 0.162757 | − | 0.0674163i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22.6154 | + | 9.36759i | 0.426705 | + | 0.176747i | 0.585692 | − | 0.810534i | \(-0.300823\pi\) |
−0.158987 | + | 0.987281i | \(0.550823\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −93.7406 | − | 93.7406i | −1.70437 | − | 1.70437i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.10439 | − | 3.10439i | −0.0544630 | − | 0.0544630i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 101.380 | + | 41.9931i | 1.71831 | + | 0.711747i | 0.999869 | + | 0.0161592i | \(0.00514387\pi\) |
0.718441 | + | 0.695588i | \(0.244856\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0475 | + | 5.81867i | −0.230287 | + | 0.0953880i | −0.494843 | − | 0.868982i | \(-0.664775\pi\) |
0.264556 | + | 0.964370i | \(0.414775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.6472i | 0.248369i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −61.2936 | −0.942978 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.67448 | − | 8.87098i | −0.0548430 | − | 0.132403i | 0.894083 | − | 0.447901i | \(-0.147828\pi\) |
−0.948926 | + | 0.315498i | \(0.897828\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.0124 | − | 26.5863i | 0.159600 | − | 0.385309i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −75.7712 | + | 75.7712i | −1.06720 | + | 1.06720i | −0.0696271 | + | 0.997573i | \(0.522181\pi\) |
−0.997573 | + | 0.0696271i | \(0.977819\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −29.0378 | + | 29.0378i | −0.397779 | + | 0.397779i | −0.877449 | − | 0.479670i | \(-0.840756\pi\) |
0.479670 | + | 0.877449i | \(0.340756\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −41.3427 | + | 99.8102i | −0.551237 | + | 1.33080i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −31.6965 | − | 76.5221i | −0.411643 | − | 0.993793i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.76556 | −0.0350072 | −0.0175036 | − | 0.999847i | \(-0.505572\pi\) | ||||
−0.0175036 | + | 0.999847i | \(0.505572\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 44.8236i | 0.553378i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 79.1972 | − | 32.8045i | 0.954183 | − | 0.395235i | 0.149381 | − | 0.988780i | \(-0.452272\pi\) |
0.804801 | + | 0.593544i | \(0.202272\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.2066 | − | 11.6835i | −0.331842 | − | 0.137453i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 72.7802 | + | 72.7802i | 0.836554 | + | 0.836554i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 72.4200 | + | 72.4200i | 0.813708 | + | 0.813708i | 0.985188 | − | 0.171480i | \(-0.0548548\pi\) |
−0.171480 | + | 0.985188i | \(0.554855\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −35.3801 | − | 14.6549i | −0.388792 | − | 0.161043i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.29858 | − | 3.85160i | 0.0999847 | − | 0.0414150i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.9187i | 0.157039i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 66.0511 | 0.680940 | 0.340470 | − | 0.940255i | \(-0.389414\pi\) | ||||
0.340470 | + | 0.940255i | \(0.389414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.3743 | + | 44.3596i | 0.185599 | + | 0.448077i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.51179 | + | 18.1351i | −0.0743742 | + | 0.179555i | −0.956694 | − | 0.291095i | \(-0.905981\pi\) |
0.882320 | + | 0.470650i | \(0.155981\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.589180 | + | 0.589180i | −0.00572020 | + | 0.00572020i | −0.709961 | − | 0.704241i | \(-0.751288\pi\) |
0.704241 | + | 0.709961i | \(0.251288\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −74.7554 | + | 74.7554i | −0.711956 | + | 0.711956i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 55.4567 | − | 133.884i | 0.518287 | − | 1.25126i | −0.420668 | − | 0.907215i | \(-0.638204\pi\) |
0.938955 | − | 0.344041i | \(-0.111796\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 29.4015 | + | 70.9815i | 0.269739 | + | 0.651207i | 0.999471 | − | 0.0325264i | \(-0.0103553\pi\) |
−0.729732 | + | 0.683733i | \(0.760355\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −127.098 | −1.14502 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 134.274i | 1.18826i | 0.804368 | + | 0.594131i | \(0.202504\pi\) | ||||
−0.804368 | + | 0.594131i | \(0.797496\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −90.3436 | + | 37.4215i | −0.785596 | + | 0.325405i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.5097 | + | 8.49541i | 0.175297 | + | 0.0726103i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −13.4880 | − | 13.4880i | −0.113345 | − | 0.113345i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −94.1580 | − | 94.1580i | −0.778166 | − | 0.778166i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −67.5224 | − | 27.9687i | −0.548963 | − | 0.227388i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 147.104 | − | 60.9325i | 1.17683 | − | 0.487460i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 95.5030i | − | 0.751992i | −0.926621 | − | 0.375996i | \(-0.877301\pi\) | ||
0.926621 | − | 0.375996i | \(-0.122699\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.655407 | −0.00508068 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 67.1188 | + | 162.039i | 0.512357 | + | 1.23694i | 0.942508 | + | 0.334183i | \(0.108460\pi\) |
−0.430151 | + | 0.902757i | \(0.641540\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.56697 | + | 8.61142i | −0.0268193 | + | 0.0647475i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 172.835 | − | 172.835i | 1.28026 | − | 1.28026i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 88.7244 | − | 88.7244i | 0.647624 | − | 0.647624i | −0.304794 | − | 0.952418i | \(-0.598588\pi\) |
0.952418 | + | 0.304794i | \(0.0985878\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 27.6838 | − | 66.8346i | 0.199164 | − | 0.480824i | −0.792469 | − | 0.609912i | \(-0.791205\pi\) |
0.991633 | + | 0.129087i | \(0.0412048\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −36.8813 | − | 89.0394i | −0.261570 | − | 0.631485i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −117.511 | −0.821756 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 349.758i | − | 2.41213i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 49.7558 | − | 20.6095i | 0.338475 | − | 0.140201i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −100.536 | − | 41.6433i | −0.674737 | − | 0.279485i | 0.0188878 | − | 0.999822i | \(-0.493987\pi\) |
−0.693625 | + | 0.720336i | \(0.743987\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 134.706 | + | 134.706i | 0.892096 | + | 0.892096i | 0.994720 | − | 0.102624i | \(-0.0327239\pi\) |
−0.102624 | + | 0.994720i | \(0.532724\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.81897 | + | 7.81897i | 0.0511044 | + | 0.0511044i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −31.5977 | − | 13.0882i | −0.203856 | − | 0.0844401i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −56.0501 | + | 23.2167i | −0.357007 | + | 0.147877i | −0.553976 | − | 0.832533i | \(-0.686890\pi\) |
0.196969 | + | 0.980410i | \(0.436890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 59.9015i | − | 0.376739i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −61.0957 | −0.379476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −85.7621 | − | 207.048i | −0.526148 | − | 1.27023i | −0.934029 | − | 0.357198i | \(-0.883732\pi\) |
0.407881 | − | 0.913035i | \(-0.366268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −124.146 | + | 299.715i | −0.752399 | + | 1.81645i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −72.6395 | + | 72.6395i | −0.434967 | + | 0.434967i | −0.890314 | − | 0.455347i | \(-0.849515\pi\) |
0.455347 | + | 0.890314i | \(0.349515\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 81.0829 | − | 81.0829i | 0.479781 | − | 0.479781i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.06776 | − | 4.99201i | 0.0120922 | − | 0.0291930i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.05480 | − | 9.78916i | −0.0234382 | − | 0.0565847i | 0.911727 | − | 0.410796i | \(-0.134749\pi\) |
−0.935165 | + | 0.354212i | \(0.884749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 229.365 | 1.31066 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 268.527i | − | 1.51710i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −214.146 | + | 88.7024i | −1.19635 | + | 0.495544i | −0.889817 | − | 0.456317i | \(-0.849168\pi\) |
−0.306531 | + | 0.951861i | \(0.599168\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −98.2125 | − | 40.6810i | −0.542611 | − | 0.224757i | 0.0945057 | − | 0.995524i | \(-0.469873\pi\) |
−0.637116 | + | 0.770768i | \(0.719873\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 26.3099 | + | 26.3099i | 0.143770 | + | 0.143770i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 305.395 | + | 305.395i | 1.65078 | + | 1.65078i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −54.0772 | − | 22.3995i | −0.289183 | − | 0.119783i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 141.088 | − | 58.4405i | 0.746497 | − | 0.309209i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 181.842i | 0.952052i | 0.879431 | + | 0.476026i | \(0.157923\pi\) | ||||
−0.879431 | + | 0.476026i | \(0.842077\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −221.267 | −1.14646 | −0.573230 | − | 0.819394i | \(-0.694310\pi\) | ||||
−0.573230 | + | 0.819394i | \(0.694310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 57.3990 | + | 138.574i | 0.294354 | + | 0.710633i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.4361 | + | 37.2660i | −0.0783556 | + | 0.189167i | −0.958203 | − | 0.286089i | \(-0.907645\pi\) |
0.879847 | + | 0.475256i | \(0.157645\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 135.618 | − | 135.618i | 0.681498 | − | 0.681498i | −0.278840 | − | 0.960338i | \(-0.589950\pi\) |
0.960338 | + | 0.278840i | \(0.0899498\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16.6146 | + | 16.6146i | −0.0826599 | + | 0.0826599i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 83.6250 | − | 201.889i | 0.411946 | − | 0.994526i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 95.0411 | + | 229.450i | 0.463615 | + | 1.11927i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.4170 | 0.171096 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 28.6019i | 0.136851i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −138.015 | + | 57.1678i | −0.654100 | + | 0.270937i | −0.684954 | − | 0.728587i | \(-0.740178\pi\) |
0.0308532 | + | 0.999524i | \(0.490178\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 242.262 | + | 100.348i | 1.13738 | + | 0.471118i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.57484 | + | 1.57484i | 0.00732483 | + | 0.00732483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1097 | − | 15.1097i | −0.0696298 | − | 0.0696298i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 92.8420 | + | 38.4564i | 0.423936 | + | 0.175600i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25.0027 | + | 10.3564i | −0.113134 | + | 0.0468618i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 30.6228i | − | 0.137322i | −0.997640 | − | 0.0686609i | \(-0.978127\pi\) | ||
0.997640 | − | 0.0686609i | \(-0.0218727\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −132.962 | −0.590944 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.41171 | − | 20.3077i | −0.0370560 | − | 0.0894611i | 0.904268 | − | 0.426965i | \(-0.140417\pi\) |
−0.941324 | + | 0.337504i | \(0.890417\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 76.6532 | − | 185.057i | 0.334730 | − | 0.808110i | −0.663474 | − | 0.748199i | \(-0.730919\pi\) |
0.998204 | − | 0.0599101i | \(-0.0190814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −143.320 | + | 143.320i | −0.620432 | + | 0.620432i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −127.558 | + | 127.558i | −0.547461 | + | 0.547461i | −0.925706 | − | 0.378245i | \(-0.876528\pi\) |
0.378245 | + | 0.925706i | \(0.376528\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −125.327 | + | 302.567i | −0.533308 | + | 1.28752i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.58984 | + | 6.25243i | 0.0109276 | + | 0.0263816i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −397.241 | −1.66210 | −0.831048 | − | 0.556200i | \(-0.812259\pi\) | ||||
−0.831048 | + | 0.556200i | \(0.812259\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 401.128i | 1.66443i | 0.554451 | + | 0.832216i | \(0.312928\pi\) | ||||
−0.554451 | + | 0.832216i | \(0.687072\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −143.069 | + | 59.2612i | −0.588763 | + | 0.243873i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −169.077 | − | 70.0338i | −0.690109 | − | 0.285852i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.35087 | + | 9.35087i | 0.0378578 | + | 0.0378578i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −148.330 | − | 148.330i | −0.595703 | − | 0.595703i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −220.193 | − | 91.2070i | −0.877264 | − | 0.363375i | −0.101829 | − | 0.994802i | \(-0.532469\pi\) |
−0.775435 | + | 0.631427i | \(0.782469\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −173.205 | + | 71.7440i | −0.684606 | + | 0.283573i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 74.7111i | 0.292985i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 436.624 | 1.69893 | 0.849463 | − | 0.527648i | \(-0.176926\pi\) | ||||
0.849463 | + | 0.527648i | \(0.176926\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 103.263 | + | 249.299i | 0.398699 | + | 0.962545i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −48.4771 | + | 117.034i | −0.185736 | + | 0.448407i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 324.662 | − | 324.662i | 1.23445 | − | 1.23445i | 0.272219 | − | 0.962235i | \(-0.412242\pi\) |
0.962235 | − | 0.272219i | \(-0.0877576\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −143.934 | + | 143.934i | −0.543146 | + | 0.543146i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 95.9098 | − | 231.547i | 0.359213 | − | 0.867217i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −98.7998 | − | 238.524i | −0.367286 | − | 0.886706i | −0.994193 | − | 0.107612i | \(-0.965680\pi\) |
0.626907 | − | 0.779094i | \(-0.284320\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 91.7678 | 0.338627 | 0.169313 | − | 0.985562i | \(-0.445845\pi\) | ||||
0.169313 | + | 0.985562i | \(0.445845\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 93.7117i | 0.343266i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 650.247 | − | 269.341i | 2.36453 | − | 0.979422i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 42.7749 | + | 17.7179i | 0.154422 | + | 0.0639636i | 0.458556 | − | 0.888666i | \(-0.348367\pi\) |
−0.304134 | + | 0.952629i | \(0.598367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.75902 | + | 8.75902i | 0.0313943 | + | 0.0313943i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −167.424 | − | 167.424i | −0.595813 | − | 0.595813i | 0.343382 | − | 0.939196i | \(-0.388427\pi\) |
−0.939196 | + | 0.343382i | \(0.888427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 494.380 | + | 204.779i | 1.74693 | + | 0.723601i | 0.998151 | + | 0.0607762i | \(0.0193576\pi\) |
0.748775 | + | 0.662824i | \(0.230642\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.7284 | − | 13.9708i | 0.118345 | − | 0.0490202i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 155.168i | 0.540653i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 275.520 | 0.953356 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −61.8543 | − | 149.329i | −0.212558 | − | 0.513160i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 146.767 | − | 354.328i | 0.500913 | − | 1.20931i | −0.448075 | − | 0.893996i | \(-0.647890\pi\) |
0.948987 | − | 0.315314i | \(-0.102110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −645.227 | + | 645.227i | −2.18721 | + | 2.18721i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 331.356 | − | 331.356i | 1.11568 | − | 1.11568i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −33.1709 | + | 80.0817i | −0.110940 | + | 0.267832i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.532500 | + | 1.28557i | 0.00176910 | + | 0.00427099i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 48.0346 | 0.158530 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 126.437i | − | 0.414547i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 53.4306 | − | 22.1317i | 0.174041 | − | 0.0720902i | −0.293962 | − | 0.955817i | \(-0.594974\pi\) |
0.468003 | + | 0.883727i | \(0.344974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.88377 | + | 0.780284i | 0.00609635 | + | 0.00252519i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −274.515 | − | 274.515i | −0.882685 | − | 0.882685i | 0.111122 | − | 0.993807i | \(-0.464556\pi\) |
−0.993807 | + | 0.111122i | \(0.964556\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −78.4013 | − | 78.4013i | −0.250483 | − | 0.250483i | 0.570685 | − | 0.821169i | \(-0.306678\pi\) |
−0.821169 | + | 0.570685i | \(0.806678\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −120.210 | − | 49.7928i | −0.381620 | − | 0.158072i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −136.520 | + | 56.5483i | −0.430661 | + | 0.178386i | −0.587475 | − | 0.809243i | \(-0.699878\pi\) |
0.156814 | + | 0.987628i | \(0.449878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 670.551i | − | 2.10204i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −354.621 | −1.10474 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.52073 | + | 6.08558i | 0.00780412 | + | 0.0188408i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 124.530 | − | 300.643i | 0.383170 | − | 0.925054i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 132.943 | − | 132.943i | 0.406553 | − | 0.406553i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −144.684 | + | 144.684i | −0.439769 | + | 0.439769i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −143.690 | + | 346.898i | −0.434109 | + | 1.04803i | 0.543841 | + | 0.839189i | \(0.316970\pi\) |
−0.977949 | + | 0.208843i | \(0.933030\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −59.8612 | − | 144.518i | −0.179763 | − | 0.433987i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 79.8446 | 0.238342 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 479.136i | 1.42177i | 0.703310 | + | 0.710884i | \(0.251705\pi\) | ||||
−0.703310 | + | 0.710884i | \(0.748295\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 303.568 | − | 125.742i | 0.895481 | − | 0.370920i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −60.5787 | − | 25.0925i | −0.177650 | − | 0.0735851i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −260.861 | − | 260.861i | −0.760529 | − | 0.760529i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 169.206 | + | 169.206i | 0.490453 | + | 0.490453i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −172.145 | − | 71.3048i | −0.496095 | − | 0.205489i | 0.120585 | − | 0.992703i | \(-0.461523\pi\) |
−0.616680 | + | 0.787214i | \(0.711523\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 388.120 | − | 160.765i | 1.11209 | − | 0.460644i | 0.250434 | − | 0.968134i | \(-0.419427\pi\) |
0.861658 | + | 0.507490i | \(0.169427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 216.662i | − | 0.617269i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −165.952 | −0.470120 | −0.235060 | − | 0.971981i | \(-0.575529\pi\) | ||||
−0.235060 | + | 0.971981i | \(0.575529\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −340.995 | − | 823.235i | −0.960550 | − | 2.31897i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −17.8630 | + | 43.1250i | −0.0500363 | + | 0.120798i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −100.971 | + | 100.971i | −0.281257 | + | 0.281257i | −0.833610 | − | 0.552353i | \(-0.813730\pi\) |
0.552353 | + | 0.833610i | \(0.313730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −252.990 | + | 252.990i | −0.700802 | + | 0.700802i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −124.699 | + | 301.049i | −0.343523 | + | 0.829337i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −130.680 | − | 315.489i | −0.358027 | − | 0.864353i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 651.959 | 1.77645 | 0.888227 | − | 0.459405i | \(-0.151937\pi\) | ||||
0.888227 | + | 0.459405i | \(0.151937\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 89.9501i | − | 0.243767i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −117.496 | + | 48.6683i | −0.316700 | + | 0.131181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 605.919 | + | 250.980i | 1.62445 | + | 0.672868i | 0.994593 | − | 0.103845i | \(-0.0331146\pi\) |
0.629854 | + | 0.776713i | \(0.283115\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −275.515 | − | 275.515i | −0.734705 | − | 0.734705i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −219.224 | − | 219.224i | −0.581497 | − | 0.581497i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 431.591 | + | 178.771i | 1.13876 | + | 0.471691i | 0.870750 | − | 0.491725i | \(-0.163634\pi\) |
0.268011 | + | 0.963416i | \(0.413634\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −215.915 | + | 89.4348i | −0.566705 | + | 0.234737i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 583.987i | 1.52477i | 0.647124 | + | 0.762385i | \(0.275972\pi\) | ||||
−0.647124 | + | 0.762385i | \(0.724028\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 688.749 | 1.78896 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.308688 | − | 0.745239i | −0.000797644 | − | 0.00192568i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −57.9070 | + | 139.800i | −0.148861 | + | 0.359383i | −0.980667 | − | 0.195684i | \(-0.937307\pi\) |
0.831806 | + | 0.555067i | \(0.187307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.5297 | + | 30.5297i | −0.0780812 | + | 0.0780812i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 303.487 | − | 303.487i | 0.772231 | − | 0.772231i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.80061 | − | 21.2466i | 0.0222800 | − | 0.0537888i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 216.482 | + | 522.634i | 0.545295 | + | 1.31646i | 0.920944 | + | 0.389696i | \(0.127420\pi\) |
−0.375649 | + | 0.926762i | \(0.622580\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 22.8092 | 0.0571658 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 271.900i | 0.678055i | 0.940776 | + | 0.339028i | \(0.110098\pi\) | ||||
−0.940776 | + | 0.339028i | \(0.889902\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.0087 | + | 11.6016i | −0.0695004 | + | 0.0287880i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −344.359 | − | 142.638i | −0.850269 | − | 0.352193i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 585.498 | + | 585.498i | 1.43857 | + | 1.43857i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −181.723 | − | 181.723i | −0.444310 | − | 0.444310i | 0.449147 | − | 0.893458i | \(-0.351728\pi\) |
−0.893458 | + | 0.449147i | \(0.851728\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −283.677 | − | 117.503i | −0.690211 | − | 0.285895i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −526.710 | + | 218.171i | −1.27533 | + | 0.528258i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 712.826i | 1.71765i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −177.026 | −0.424522 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 84.5458 | + | 204.112i | 0.201780 | + | 0.487140i | 0.992084 | − | 0.125575i | \(-0.0400775\pi\) |
−0.790304 | + | 0.612715i | \(0.790077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1417 | − | 31.7269i | 0.0312155 | − | 0.0753608i | −0.907503 | − | 0.420045i | \(-0.862014\pi\) |
0.938719 | + | 0.344685i | \(0.112014\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 83.8728 | − | 83.8728i | 0.198281 | − | 0.198281i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 114.615 | − | 114.615i | 0.269682 | − | 0.269682i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 30.2302 | − | 72.9823i | 0.0707968 | − | 0.170919i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 110.045 | + | 265.671i | 0.256514 | + | 0.619280i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −18.4839 | −0.0428861 | −0.0214431 | − | 0.999770i | \(-0.506826\pi\) | ||||
−0.0214431 | + | 0.999770i | \(0.506826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 370.297i | − | 0.855190i | −0.903970 | − | 0.427595i | \(-0.859361\pi\) | ||
0.903970 | − | 0.427595i | \(-0.140639\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −790.739 | + | 327.535i | −1.81779 | + | 0.752954i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.4917 | + | 8.07372i | 0.0446034 | + | 0.0184753i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.47108 | + | 1.47108i | 0.00335099 | + | 0.00335099i | 0.708780 | − | 0.705429i | \(-0.249246\pi\) |
−0.705429 | + | 0.708780i | \(0.749246\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 46.8687 | + | 46.8687i | 0.106278 | + | 0.106278i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.4970 | − | 6.41908i | −0.0349820 | − | 0.0144900i | 0.365124 | − | 0.930959i | \(-0.381027\pi\) |
−0.400106 | + | 0.916469i | \(0.631027\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −786.825 | + | 325.914i | −1.76815 | + | 0.732390i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 266.290i | 0.595728i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −349.645 | −0.778719 | −0.389359 | − | 0.921086i | \(-0.627304\pi\) | ||||
−0.389359 | + | 0.921086i | \(0.627304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 182.211 | + | 439.897i | 0.404016 | + | 0.975382i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 178.399 | − | 430.694i | 0.393817 | − | 0.950759i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 225.174 | − | 225.174i | 0.494888 | − | 0.494888i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 167.442 | − | 167.442i | 0.366393 | − | 0.366393i | −0.499767 | − | 0.866160i | \(-0.666581\pi\) |
0.866160 | + | 0.499767i | \(0.166581\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 41.2992 | − | 99.7051i | 0.0899764 | − | 0.217222i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 299.864 | + | 723.935i | 0.650463 | + | 1.57036i | 0.812107 | + | 0.583508i | \(0.198320\pi\) |
−0.161644 | + | 0.986849i | \(0.551680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 70.4485 | 0.152157 | 0.0760783 | − | 0.997102i | \(-0.475760\pi\) | ||||
0.0760783 | + | 0.997102i | \(0.475760\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 83.6933i | 0.179986i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 89.8391 | − | 37.2126i | 0.192375 | − | 0.0796843i | −0.284416 | − | 0.958701i | \(-0.591800\pi\) |
0.476791 | + | 0.879017i | \(0.341800\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.0882 | + | 19.0904i | 0.0982691 | + | 0.0407044i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 104.977 | + | 104.977i | 0.222882 | + | 0.222882i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.01925 | + | 3.01925i | 0.00638320 | + | 0.00638320i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −73.1756 | − | 30.3103i | −0.154054 | − | 0.0638112i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 68.1118 | − | 28.2128i | 0.142792 | − | 0.0591464i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 900.546i | − | 1.88005i | −0.341101 | − | 0.940027i | \(-0.610800\pi\) | ||
0.341101 | − | 0.940027i | \(-0.389200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 382.836 | 0.795917 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 57.2137 | + | 138.126i | 0.118455 | + | 0.285976i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −210.189 | + | 507.440i | −0.433379 | + | 1.04627i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 175.466 | − | 175.466i | 0.360301 | − | 0.360301i | −0.503623 | − | 0.863924i | \(-0.668000\pi\) |
0.863924 | + | 0.503623i | \(0.168000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −387.785 | + | 387.785i | −0.793015 | + | 0.793015i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 111.990 | − | 270.368i | 0.228086 | − | 0.550648i | −0.767858 | − | 0.640620i | \(-0.778678\pi\) |
0.995944 | + | 0.0899713i | \(0.0286775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −59.0968 | − | 142.672i | −0.119872 | − | 0.289396i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −399.265 | −0.806596 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 556.721i | − | 1.12016i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −96.4128 | + | 39.9355i | −0.193212 | + | 0.0800310i | −0.477192 | − | 0.878799i | \(-0.658345\pi\) |
0.283980 | + | 0.958830i | \(0.408345\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 232.249 | + | 96.2005i | 0.463570 | + | 0.192017i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −491.151 | − | 491.151i | −0.976442 | − | 0.976442i | 0.0232864 | − | 0.999729i | \(-0.492587\pi\) |
−0.999729 | + | 0.0232864i | \(0.992587\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −115.419 | − | 115.419i | −0.228553 | − | 0.228553i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −259.245 | − | 107.383i | −0.511331 | − | 0.211800i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 891.336 | − | 369.204i | 1.75115 | − | 0.725351i | 0.753457 | − | 0.657498i | \(-0.228385\pi\) |
0.997695 | − | 0.0678534i | \(-0.0216150\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 213.352i | − | 0.417519i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −52.7348 | −0.102797 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.65150 | − | 6.40130i | −0.00514855 | − | 0.0124297i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −240.276 | + | 580.077i | −0.464750 | + | 1.12201i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.3343 | + | 18.3343i | −0.0353263 | + | 0.0353263i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 285.723 | − | 285.723i | 0.548413 | − | 0.548413i | −0.377569 | − | 0.925982i | \(-0.623240\pi\) |
0.925982 | + | 0.377569i | \(0.123240\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −260.696 | + | 629.375i | −0.498462 | + | 1.20339i | 0.451849 | + | 0.892094i | \(0.350764\pi\) |
−0.950312 | + | 0.311300i | \(0.899236\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −214.792 | − | 518.553i | −0.409127 | − | 0.987720i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.1007 | −0.0286541 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 390.712i | − | 0.738586i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 305.332 | − | 126.473i | 0.575013 | − | 0.238178i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 203.387 | + | 84.2457i | 0.381589 | + | 0.158059i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 852.096 | + | 852.096i | 1.59270 | + | 1.59270i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 401.079 | + | 401.079i | 0.746889 | + | 0.746889i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −324.151 | − | 134.268i | −0.601393 | − | 0.249105i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 355.077 | − | 147.078i | 0.656335 | − | 0.271863i | −0.0295603 | − | 0.999563i | \(-0.509411\pi\) |
0.685895 | + | 0.727700i | \(0.259411\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 260.137i | 0.479073i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −638.880 | −1.17226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −404.897 | − | 977.508i | −0.740214 | − | 1.78704i | −0.605010 | − | 0.796218i | \(-0.706831\pi\) |
−0.135204 | − | 0.990818i | \(-0.543169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.5244 | + | 42.3076i | −0.0319205 | + | 0.0770630i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −53.3586 | + | 53.3586i | −0.0968396 | + | 0.0968396i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.1598 | − | 10.1598i | 0.0183722 | − | 0.0183722i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 404.451 | − | 976.431i | 0.728741 | − | 1.75934i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −296.952 | − | 716.907i | −0.533128 | − | 1.28709i | −0.929441 | − | 0.368970i | \(-0.879711\pi\) |
0.396313 | − | 0.918115i | \(-0.370289\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.97418 | 0.00353163 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 143.235i | 0.255321i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 44.6869 | − | 18.5099i | 0.0793728 | − | 0.0328773i | −0.342644 | − | 0.939465i | \(-0.611322\pi\) |
0.422017 | + | 0.906588i | \(0.361322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1031.56 | − | 427.287i | −1.82577 | − | 0.756260i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −164.668 | − | 164.668i | −0.290420 | − | 0.290420i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 487.094 | + | 487.094i | 0.856053 | + | 0.856053i | 0.990870 | − | 0.134818i | \(-0.0430449\pi\) |
−0.134818 | + | 0.990870i | \(0.543045\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 252.561 | + | 104.614i | 0.442313 | + | 0.183212i | 0.592714 | − | 0.805413i | \(-0.298056\pi\) |
−0.150401 | + | 0.988625i | \(0.548056\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 411.111 | − | 170.288i | 0.717472 | − | 0.297187i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 519.161i | − | 0.902889i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 460.004 | 0.797234 | 0.398617 | − | 0.917118i | \(-0.369490\pi\) | ||||
0.398617 | + | 0.917118i | \(0.369490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 207.208 | + | 500.244i | 0.357872 | + | 0.863979i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −170.432 | + | 411.460i | −0.293343 | + | 0.708193i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −275.947 | + | 275.947i | −0.473323 | + | 0.473323i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −130.533 | + | 130.533i | −0.223133 | + | 0.223133i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −68.3015 | + | 164.895i | −0.116357 | + | 0.280911i | −0.971319 | − | 0.237780i | \(-0.923580\pi\) |
0.854962 | + | 0.518690i | \(0.173580\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.82379 | + | 6.81723i | 0.00479421 | + | 0.0115742i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 98.7067 | 0.167016 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 167.545i | − | 0.282538i | −0.989971 | − | 0.141269i | \(-0.954882\pi\) | ||
0.989971 | − | 0.141269i | \(-0.0451182\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 146.544 | − | 60.7006i | 0.246293 | − | 0.102018i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −433.609 | − | 179.607i | −0.726313 | − | 0.300848i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 316.998 | + | 316.998i | 0.529213 | + | 0.529213i | 0.920338 | − | 0.391125i | \(-0.127914\pi\) |
−0.391125 | + | 0.920338i | \(0.627914\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −224.198 | − | 224.198i | −0.373042 | − | 0.373042i | 0.495542 | − | 0.868584i | \(-0.334970\pi\) |
−0.868584 | + | 0.495542i | \(0.834970\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.7172 | − | 11.0666i | −0.0443071 | − | 0.0183526i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1023.00 | − | 423.742i | 1.69091 | − | 0.700400i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 89.2468i | − | 0.147029i | −0.997294 | − | 0.0735146i | \(-0.976578\pi\) | ||
0.997294 | − | 0.0735146i | \(-0.0234216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −534.745 | −0.878070 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 111.092 | + | 268.200i | 0.181820 | + | 0.438952i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 202.134 | − | 487.995i | 0.329746 | − | 0.796076i | −0.668865 | − | 0.743384i | \(-0.733220\pi\) |
0.998611 | − | 0.0526926i | \(-0.0167803\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 429.741 | − | 429.741i | 0.698766 | − | 0.698766i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 380.984 | − | 380.984i | 0.617479 | − | 0.617479i | −0.327405 | − | 0.944884i | \(-0.606174\pi\) |
0.944884 | + | 0.327405i | \(0.106174\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 371.320 | − | 896.447i | 0.599871 | − | 1.44822i | −0.273841 | − | 0.961775i | \(-0.588294\pi\) |
0.873712 | − | 0.486443i | \(-0.161706\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −132.278 | − | 319.348i | −0.213008 | − | 0.514248i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −532.098 | −0.854090 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 220.337i | 0.352539i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 64.6636 | − | 26.7845i | 0.103132 | − | 0.0427186i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 176.177 | + | 72.9747i | 0.280090 | + | 0.116017i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −384.726 | − | 384.726i | −0.609708 | − | 0.609708i | 0.333162 | − | 0.942870i | \(-0.391885\pi\) |
−0.942870 | + | 0.333162i | \(0.891885\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 258.492 | + | 258.492i | 0.408360 | + | 0.408360i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 733.706 | + | 303.911i | 1.15544 | + | 0.478600i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −149.872 | + | 62.0789i | −0.235277 | + | 0.0974551i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 322.729i | 0.505053i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −407.931 | −0.636398 | −0.318199 | − | 0.948024i | \(-0.603078\pi\) | ||||
−0.318199 | + | 0.948024i | \(0.603078\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 319.302 | + | 770.863i | 0.496582 | + | 1.19885i | 0.951313 | + | 0.308226i | \(0.0997352\pi\) |
−0.454732 | + | 0.890629i | \(0.650265\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.08564 | − | 5.03519i | 0.00323356 | − | 0.00780650i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.6565 | − | 48.6565i | 0.0752033 | − | 0.0752033i | −0.668505 | − | 0.743708i | \(-0.733065\pi\) |
0.743708 | + | 0.668505i | \(0.233065\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1237.02 | + | 1237.02i | −1.90604 | + | 1.90604i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.0106 | + | 48.3098i | −0.0307382 | + | 0.0742085i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −290.106 | − | 700.378i | −0.444267 | − | 1.07255i | −0.974436 | − | 0.224663i | \(-0.927872\pi\) |
0.530170 | − | 0.847892i | \(-0.322128\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1458.46 | −2.22665 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 123.680i | 0.188249i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −818.045 | + | 338.845i | −1.24134 | + | 0.514181i | −0.904134 | − | 0.427248i | \(-0.859483\pi\) |
−0.337209 | + | 0.941430i | \(0.609483\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.2123 | − | 14.5854i | −0.0532712 | − | 0.0220657i | 0.355889 | − | 0.934528i | \(-0.384178\pi\) |
−0.409160 | + | 0.912463i | \(0.634178\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46.8281 | + | 46.8281i | 0.0706306 | + | 0.0706306i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −54.8067 | − | 54.8067i | −0.0824161 | − | 0.0824161i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −456.969 | − | 189.283i | −0.685110 | − | 0.283782i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −69.2325 | + | 28.6770i | −0.103487 | + | 0.0428655i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 242.402i | − | 0.361256i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 114.199 | 0.169687 | 0.0848434 | − | 0.996394i | \(-0.472961\pi\) | ||||
0.0848434 | + | 0.996394i | \(0.472961\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 496.599 | + | 1198.90i | 0.735702 | + | 1.77614i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −212.733 | + | 513.583i | −0.314229 | + | 0.758617i | 0.685310 | + | 0.728252i | \(0.259667\pi\) |
−0.999539 | + | 0.0303647i | \(0.990333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −242.652 | + | 242.652i | −0.357366 | + | 0.357366i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −38.0347 | + | 38.0347i | −0.0558512 | + | 0.0558512i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −363.453 | + | 877.454i | −0.532142 | + | 1.28471i | 0.397959 | + | 0.917403i | \(0.369719\pi\) |
−0.930102 | + | 0.367302i | \(0.880281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 399.289 | + | 963.969i | 0.582904 | + | 1.40725i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −490.163 | −0.713483 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 180.432i | 0.261875i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 682.306 | − | 282.620i | 0.987418 | − | 0.409002i | 0.170249 | − | 0.985401i | \(-0.445543\pi\) |
0.817168 | + | 0.576399i | \(0.195543\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −230.465 | − | 95.4619i | −0.332562 | − | 0.137752i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 425.364 | + | 425.364i | 0.612034 | + | 0.612034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 77.5377 | + | 77.5377i | 0.111245 | + | 0.111245i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 407.840 | + | 168.933i | 0.583462 | + | 0.241678i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −565.621 | + | 234.288i | −0.806878 | + | 0.334220i | −0.747708 | − | 0.664028i | \(-0.768846\pi\) |
−0.0591703 | + | 0.998248i | \(0.518846\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 93.1812i | − | 0.132548i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 801.413 | 1.13676 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −39.0267 | − | 94.2188i | −0.0552004 | − | 0.133266i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 447.695 | − | 1080.83i | 0.631446 | − | 1.52444i | −0.206360 | − | 0.978476i | \(-0.566162\pi\) |
0.837806 | − | 0.545968i | \(-0.183838\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.88963 | + | 5.88963i | −0.00828358 | + | 0.00828358i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.2002 | + | 34.2002i | −0.0479666 | + | 0.0479666i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 373.945 | − | 902.783i | 0.523000 | − | 1.26263i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 372.001 | + | 898.089i | 0.518829 | + | 1.25257i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −122.001 | −0.169681 | −0.0848406 | − | 0.996395i | \(-0.527038\pi\) | ||||
−0.0848406 | + | 0.996395i | \(0.527038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.32894i | − | 0.00600408i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 906.877 | − | 375.641i | 1.25433 | − | 0.519559i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1715.55 | + | 710.604i | 2.36628 | + | 0.980144i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −438.189 | − | 438.189i | −0.602736 | − | 0.602736i | 0.338301 | − | 0.941038i | \(-0.390148\pi\) |
−0.941038 | + | 0.338301i | \(0.890148\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 553.213 | + | 553.213i | 0.758866 | + | 0.758866i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.908495 | + | 0.376311i | 0.00124281 | + | 0.000514789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −629.241 | + | 260.640i | −0.858446 | + | 0.355580i | −0.768099 | − | 0.640331i | \(-0.778797\pi\) |
−0.0903463 | + | 0.995910i | \(0.528797\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 447.835i | 0.609299i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 153.077 | 0.207703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −55.5902 | − | 134.207i | −0.0752235 | − | 0.181606i | 0.881795 | − | 0.471633i | \(-0.156335\pi\) |
−0.957018 | + | 0.290028i | \(0.906335\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.3839 | − | 29.8973i | 0.0167124 | − | 0.0403473i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 180.295 | − | 180.295i | 0.242658 | − | 0.242658i | −0.575291 | − | 0.817949i | \(-0.695111\pi\) |
0.817949 | + | 0.575291i | \(0.195111\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 639.853 | − | 639.853i | 0.858863 | − | 0.858863i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 98.7991 | − | 238.522i | 0.132261 | − | 0.319307i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 288.119 | + | 695.581i | 0.384672 | + | 0.928680i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 264.213 | 0.351815 | 0.175908 | − | 0.984407i | \(-0.443714\pi\) | ||||
0.175908 | + | 0.984407i | \(0.443714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 583.228i | 0.774539i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1463.55 | + | 606.223i | −1.93848 | + | 0.802945i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −691.098 | − | 286.262i | −0.912944 | − | 0.378154i | −0.123761 | − | 0.992312i | \(-0.539496\pi\) |
−0.789183 | + | 0.614158i | \(0.789496\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 324.400 | + | 324.400i | 0.427404 | + | 0.427404i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 287.342 | + | 287.342i | 0.377585 | + | 0.377585i | 0.870230 | − | 0.492645i | \(-0.163970\pi\) |
−0.492645 | + | 0.870230i | \(0.663970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −368.777 | − | 152.752i | −0.483325 | − | 0.200200i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −84.9511 | + | 35.1879i | −0.111047 | + | 0.0459973i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 808.842i | 1.05455i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1240.31 | −1.61289 | −0.806446 | − | 0.591308i | \(-0.798612\pi\) | ||||
−0.806446 | + | 0.591308i | \(0.798612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −408.881 | − | 987.127i | −0.530326 | − | 1.28032i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −318.633 | + | 769.248i | −0.412203 | + | 0.995146i | 0.572342 | + | 0.820015i | \(0.306035\pi\) |
−0.984545 | + | 0.175131i | \(0.943965\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 128.394 | − | 128.394i | 0.165670 | − | 0.165670i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 466.918 | − | 466.918i | 0.600924 | − | 0.600924i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.5052 | − | 49.5039i | 0.0263224 | − | 0.0635480i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −653.751 | − | 1578.29i | −0.837069 | − | 2.02086i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1236.33 | 1.57897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 504.487i | − | 0.642659i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −584.664 | + | 242.176i | −0.742902 | + | 0.307720i | −0.721842 | − | 0.692058i | \(-0.756704\pi\) |
−0.0210600 | + | 0.999778i | \(0.506704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1038.03 | − | 429.967i | −1.31563 | − | 0.544952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −493.280 | − | 493.280i | −0.623616 | − | 0.623616i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −79.2491 | − | 79.2491i | −0.0999358 | − | 0.0999358i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 460.196 | + | 190.619i | 0.578863 | + | 0.239773i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −651.965 | + | 270.053i | −0.818024 | + | 0.338837i | −0.752150 | − | 0.658991i | \(-0.770983\pi\) |
−0.0658733 | + | 0.997828i | \(0.520983\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 144.598i | 0.180974i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 308.455 | 0.385088 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −250.537 | − | 604.850i | −0.312002 | − | 0.753238i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 194.419 | − | 469.370i | 0.241515 | − | 0.583068i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −446.737 | + | 446.737i | −0.553577 | + | 0.553577i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −734.385 | + | 734.385i | −0.907769 | + | 0.907769i | −0.996092 | − | 0.0883227i | \(-0.971849\pi\) |
0.0883227 | + | 0.996092i | \(0.471849\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −430.173 | + | 1038.53i | −0.530423 | + | 1.28055i | 0.400820 | + | 0.916157i | \(0.368725\pi\) |
−0.931243 | + | 0.364398i | \(0.881275\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −85.9370 | − | 207.470i | −0.105704 | − | 0.255191i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1863.57 | 2.28658 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 0.480510i | − | 0.000588140i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −106.556 | + | 44.1370i | −0.130105 | + | 0.0538913i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.8969 | + | 12.7979i | 0.0376333 | + | 0.0155882i | 0.401421 | − | 0.915894i | \(-0.368517\pi\) |
−0.363787 | + | 0.931482i | \(0.618517\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −581.324 | − | 581.324i | −0.706348 | − | 0.706348i | 0.259417 | − | 0.965765i | \(-0.416470\pi\) |
−0.965765 | + | 0.259417i | \(0.916470\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1217.86 | − | 1217.86i | −1.47620 | − | 1.47620i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −625.862 | − | 259.241i | −0.756786 | − | 0.313471i | −0.0292791 | − | 0.999571i | \(-0.509321\pi\) |
−0.727507 | + | 0.686100i | \(0.759321\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1209.84 | − | 501.131i | 1.45939 | − | 0.604500i | 0.494981 | − | 0.868904i | \(-0.335175\pi\) |
0.964412 | + | 0.264403i | \(0.0851750\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 113.298i | − | 0.136340i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −80.8024 | −0.0970017 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −326.901 | − | 789.210i | −0.391499 | − | 0.945162i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 46.2644 | − | 111.692i | 0.0552741 | − | 0.133444i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 92.2651 | − | 92.2651i | 0.109970 | − | 0.109970i | −0.649981 | − | 0.759951i | \(-0.725223\pi\) |
0.759951 | + | 0.649981i | \(0.225223\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 656.279 | − | 656.279i | 0.780355 | − | 0.780355i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −221.728 | + | 535.300i | −0.263023 | + | 0.634994i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 364.900 | + | 880.946i | 0.431834 | + | 1.04254i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 691.816 | 0.816784 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 1309.47i | − | 1.54237i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 564.280 | − | 233.733i | 0.663079 | − | 0.274656i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 404.566 | + | 167.577i | 0.474286 | + | 0.196456i | 0.607005 | − | 0.794698i | \(-0.292371\pi\) |
−0.132719 | + | 0.991154i | \(0.542371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.7713 | + | 31.7713i | 0.0371594 | + | 0.0371594i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −870.817 | − | 870.817i | −1.01612 | − | 1.01612i | −0.999868 | − | 0.0162551i | \(-0.994826\pi\) |
−0.0162551 | − | 0.999868i | \(-0.505174\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1000.98 | + | 414.619i | 1.16528 | + | 0.482677i | 0.879631 | − | 0.475657i | \(-0.157789\pi\) |
0.285653 | + | 0.958333i | \(0.407789\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 350.805 | − | 145.308i | 0.407439 | − | 0.168767i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 130.559i | − | 0.151285i | −0.997135 | − | 0.0756423i | \(-0.975899\pi\) | ||
0.997135 | − | 0.0756423i | \(-0.0241007\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 88.1088 | 0.101860 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −258.014 | − | 622.900i | −0.297594 | − | 0.718455i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 16.8724 | − | 40.7336i | 0.0194159 | − | 0.0468741i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.0457 | − | 50.0457i | 0.0574577 | − | 0.0574577i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 140.664 | − | 140.664i | 0.161128 | − | 0.161128i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −316.568 | + | 764.264i | −0.361792 | + | 0.873444i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −251.771 | − | 607.829i | −0.287082 | − | 0.693077i | 0.712884 | − | 0.701282i | \(-0.247388\pi\) |
−0.999966 | + | 0.00820433i | \(0.997388\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −938.512 | −1.06770 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 349.331i | − | 0.396516i | −0.980150 | − | 0.198258i | \(-0.936472\pi\) | ||
0.980150 | − | 0.198258i | \(-0.0635284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1394.24 | − | 577.514i | 1.57898 | − | 0.654036i | 0.590731 | − | 0.806869i | \(-0.298839\pi\) |
0.988252 | + | 0.152832i | \(0.0488395\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2062.97 | + | 854.510i | 2.33104 | + | 0.965548i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 980.070 | + | 980.070i | 1.10493 | + | 1.10493i | 0.993807 | + | 0.111120i | \(0.0354439\pi\) |
0.111120 | + | 0.993807i | \(0.464556\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 350.849 | + | 350.849i | 0.394656 | + | 0.394656i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −660.200 | − | 273.464i | −0.740965 | − | 0.306918i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 65.2790 | − | 27.0395i | 0.0731008 | − | 0.0302793i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1927.46i | − | 2.15358i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 212.113 | 0.236470 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −66.2018 | − | 159.825i | −0.0736393 | − | 0.177781i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.3933 | + | 83.0327i | −0.0381723 | + | 0.0921561i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.40777 | − | 2.40777i | 0.00266641 | − | 0.00266641i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 625.066 | − | 625.066i | 0.690681 | − | 0.690681i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −64.9162 | + | 156.722i | −0.0715725 | + | 0.172791i | −0.955617 | − | 0.294611i | \(-0.904810\pi\) |
0.884045 | + | 0.467402i | \(0.154810\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 22.6236 | + | 54.6183i | 0.0248885 | + | 0.0600861i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 989.468 | 1.08613 | 0.543067 | − | 0.839689i | \(-0.317263\pi\) | ||||
0.543067 | + | 0.839689i | \(0.317263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1366.62i | 1.49684i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −285.850 | + | 118.403i | −0.312405 | + | 0.129402i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −841.857 | − | 348.708i | −0.918055 | − | 0.380271i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −594.043 | − | 594.043i | −0.646402 | − | 0.646402i | 0.305720 | − | 0.952122i | \(-0.401103\pi\) |
−0.952122 | + | 0.305720i | \(0.901103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −100.071 | − | 100.071i | −0.108655 | − | 0.108655i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −729.727 | − | 302.263i | −0.790603 | − | 0.327478i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2118.42 | + | 877.478i | −2.29018 | + | 0.948625i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.50947i | 0.00270709i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1637.29 | 1.76242 | 0.881209 | − | 0.472726i | \(-0.156730\pi\) | ||||
0.881209 | + | 0.472726i | \(0.156730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.1098 | + | 36.4784i | 0.0162297 | + | 0.0391819i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −363.556 | + | 877.701i | −0.389663 | + | 0.940730i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 344.170 | − | 344.170i | 0.368096 | − | 0.368096i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −407.126 | + | 407.126i | −0.434500 | + | 0.434500i | −0.890156 | − | 0.455656i | \(-0.849405\pi\) |
0.455656 | + | 0.890156i | \(0.349405\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −103.831 | + | 250.671i | −0.110576 | + | 0.266955i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 510.935 | + | 1233.51i | 0.542970 | + | 1.31085i | 0.922618 | + | 0.385715i | \(0.126045\pi\) |
−0.379648 | + | 0.925131i | \(0.623955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 351.217 | 0.372446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1269.88i | 1.34379i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 627.458 | − | 259.902i | 0.662574 | − | 0.274447i | −0.0259471 | − | 0.999663i | \(-0.508260\pi\) |
0.688521 | + | 0.725216i | \(0.258260\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −279.654 | − | 115.836i | −0.294682 | − | 0.122061i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 255.691 | + | 255.691i | 0.268865 | + | 0.268865i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1189.93 | − | 1189.93i | −1.24862 | − | 1.24862i | −0.956330 | − | 0.292290i | \(-0.905583\pi\) |
−0.292290 | − | 0.956330i | \(-0.594417\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1397.01 | − | 578.660i | −1.46284 | − | 0.605926i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1515.99 | + | 627.945i | −1.58411 | + | 0.656159i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 651.893i | 0.679764i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 944.084 | 0.982397 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −167.022 | − | 403.226i | −0.173439 | − | 0.418719i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 704.118 | − | 1699.89i | 0.729656 | − | 1.76155i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −633.832 | + | 633.832i | −0.655462 | + | 0.655462i | −0.954303 | − | 0.298841i | \(-0.903400\pi\) |
0.298841 | + | 0.954303i | \(0.403400\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.3978 | − | 11.3978i | 0.0117625 | − | 0.0117625i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 399.517 | − | 964.518i | 0.411449 | − | 0.993325i | −0.573301 | − | 0.819345i | \(-0.694337\pi\) |
0.984749 | − | 0.173980i | \(-0.0556627\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 143.828 | + | 347.232i | 0.147819 | + | 0.356867i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −796.316 | −0.816734 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 122.057i | 0.124931i | 0.998047 | + | 0.0624653i | \(0.0198963\pi\) | ||||
−0.998047 | + | 0.0624653i | \(0.980104\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1508.49 | + | 624.837i | −1.54085 | + | 0.638240i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 213.779 | + | 88.5500i | 0.217919 | + | 0.0902650i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1257.94 | − | 1257.94i | −1.27970 | − | 1.27970i | −0.940835 | − | 0.338864i | \(-0.889957\pi\) |
−0.338864 | − | 0.940835i | \(-0.610043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −237.176 | − | 237.176i | −0.240788 | − | 0.240788i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 462.595 | + | 191.613i | 0.468688 | + | 0.194137i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.90984 | − | 1.20530i | 0.00294220 | − | 0.00121870i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1409.81i | 1.42261i | 0.702884 | + | 0.711304i | \(0.251895\pi\) | ||||
−0.702884 | + | 0.711304i | \(0.748105\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 918.834 | 0.925311 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 610.326 | + | 1473.46i | 0.613393 | + | 1.48086i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −60.9825 | + | 147.225i | −0.0611660 | + | 0.147668i | −0.951508 | − | 0.307625i | \(-0.900466\pi\) |
0.890341 | + | 0.455293i | \(0.150466\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1079.51 | + | 1079.51i | −1.08059 | + | 1.08059i |
(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 | 128.3.h.a.79.2 | 28 | ||
4.3 | odd | 2 | 32.3.h.a.11.3 | yes | 28 | ||
8.3 | odd | 2 | 256.3.h.b.159.2 | 28 | |||
8.5 | even | 2 | 256.3.h.a.159.6 | 28 | |||
12.11 | even | 2 | 288.3.u.a.235.5 | 28 | |||
32.3 | odd | 8 | inner | 128.3.h.a.47.2 | 28 | ||
32.13 | even | 8 | 256.3.h.b.95.2 | 28 | |||
32.19 | odd | 8 | 256.3.h.a.95.6 | 28 | |||
32.29 | even | 8 | 32.3.h.a.3.3 | ✓ | 28 | ||
96.29 | odd | 8 | 288.3.u.a.163.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.3.3 | ✓ | 28 | 32.29 | even | 8 | ||
32.3.h.a.11.3 | yes | 28 | 4.3 | odd | 2 | ||
128.3.h.a.47.2 | 28 | 32.3 | odd | 8 | inner | ||
128.3.h.a.79.2 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.a.95.6 | 28 | 32.19 | odd | 8 | |||
256.3.h.a.159.6 | 28 | 8.5 | even | 2 | |||
256.3.h.b.95.2 | 28 | 32.13 | even | 8 | |||
256.3.h.b.159.2 | 28 | 8.3 | odd | 2 | |||
288.3.u.a.163.5 | 28 | 96.29 | odd | 8 | |||
288.3.u.a.235.5 | 28 | 12.11 | even | 2 |