Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, 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("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.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: | \(6.97549476762\) |
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 | 159.6 | ||
Character | \(\chi\) | \(=\) | 256.159 |
Dual form | 256.3.h.a.95.6 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{5}{8}\right)\) | \(-1\) |
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 | \(0.00872079\pi\) |
−0.687471 | + | 0.726212i | \(0.741279\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.18221 | − | 7.68254i | 0.636442 | − | 1.53651i | −0.194945 | − | 0.980814i | \(-0.562453\pi\) |
0.831387 | − | 0.555693i | \(-0.187547\pi\) | |||||||
\(6\) | 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 | \(-0.617000\pi\) |
0.913971 | − | 0.405781i | \(-0.133000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82075 | − | 6.80990i | −0.216981 | − | 0.523839i | 0.777484 | − | 0.628902i | \(-0.216495\pi\) |
−0.994466 | + | 0.105063i | \(0.966495\pi\) | |||||||
\(14\) | 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 | −0.425875 | − | 0.904782i | \(-0.640034\pi\) |
0.338638 | + | 0.940917i | \(0.390034\pi\) | |||||||
\(20\) | 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 | 0.406489 | − | 0.913656i | \(-0.366753\pi\) |
0.933483 | + | 0.358621i | \(0.116753\pi\) | |||||||
\(30\) | 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 | \(0.372650\pi\) |
−0.926679 | + | 0.375853i | \(0.877350\pi\) | |||||||
\(38\) | 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 | −0.925067 | − | 0.379804i | \(-0.875991\pi\) |
0.922683 | + | 0.385559i | \(0.125991\pi\) | |||||||
\(44\) | 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 | 0.158987 | − | 0.987281i | \(-0.449177\pi\) |
−0.585692 | + | 0.810534i | \(0.699177\pi\) | |||||||
\(54\) | 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 | \(-0.994856\pi\) |
−0.718441 | − | 0.695588i | \(-0.755144\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.0475 | − | 5.81867i | 0.230287 | − | 0.0953880i | −0.264556 | − | 0.964370i | \(-0.585225\pi\) |
0.494843 | + | 0.868982i | \(0.335225\pi\) | |||||||
\(62\) | 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 | 0.948926 | − | 0.315498i | \(-0.102172\pi\) |
−0.894083 | + | 0.447901i | \(0.852172\pi\) | |||||||
\(68\) | 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 | −0.804801 | − | 0.593544i | \(-0.797728\pi\) |
−0.149381 | + | 0.988780i | \(0.547728\pi\) | |||||||
\(84\) | 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 | −0.882320 | − | 0.470650i | \(-0.844019\pi\) |
0.956694 | + | 0.291095i | \(0.0940195\pi\) | |||||||
\(102\) | 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 | \(0.361796\pi\) |
−0.938955 | + | 0.344041i | \(0.888204\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −29.4015 | − | 70.9815i | −0.269739 | − | 0.651207i | 0.729732 | − | 0.683733i | \(-0.239645\pi\) |
−0.999471 | + | 0.0325264i | \(0.989645\pi\) | |||||||
\(110\) | 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 | \(-0.891540\pi\) |
0.430151 | − | 0.902757i | \(-0.358460\pi\) | |||||||
\(132\) | 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 | −0.991633 | − | 0.129087i | \(-0.958795\pi\) |
0.792469 | + | 0.609912i | \(0.208795\pi\) | |||||||
\(140\) | 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 | 0.693625 | − | 0.720336i | \(-0.256013\pi\) |
−0.0188878 | + | 0.999822i | \(0.506013\pi\) | |||||||
\(150\) | 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 | −0.196969 | − | 0.980410i | \(-0.563110\pi\) |
0.553976 | + | 0.832533i | \(0.313110\pi\) | |||||||
\(158\) | 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 | \(0.116268\pi\) |
−0.407881 | + | 0.913035i | \(0.633732\pi\) | |||||||
\(164\) | 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 | 0.935165 | − | 0.354212i | \(-0.115251\pi\) |
−0.911727 | + | 0.410796i | \(0.865251\pi\) | |||||||
\(174\) | 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 | 0.306531 | − | 0.951861i | \(-0.400832\pi\) |
0.889817 | + | 0.456317i | \(0.150832\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 98.2125 | + | 40.6810i | 0.542611 | + | 0.224757i | 0.637116 | − | 0.770768i | \(-0.280127\pi\) |
−0.0945057 | + | 0.995524i | \(0.530127\pi\) | |||||||
\(182\) | 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 | −0.879847 | − | 0.475256i | \(-0.842355\pi\) |
0.958203 | + | 0.286089i | \(0.0923553\pi\) | |||||||
\(198\) | 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 | −0.0308532 | − | 0.999524i | \(-0.509822\pi\) |
0.684954 | + | 0.728587i | \(0.259822\pi\) | |||||||
\(212\) | 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 | 0.941324 | − | 0.337504i | \(-0.109583\pi\) |
−0.904268 | + | 0.426965i | \(0.859583\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −76.6532 | + | 185.057i | −0.334730 | + | 0.808110i | 0.663474 | + | 0.748199i | \(0.269081\pi\) |
−0.998204 | + | 0.0599101i | \(0.980919\pi\) | |||||||
\(230\) | 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 | 0.775435 | − | 0.631427i | \(-0.217531\pi\) |
0.101829 | + | 0.994802i | \(0.467531\pi\) | |||||||
\(252\) | 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 | \(0.0343205\pi\) |
−0.626907 | + | 0.779094i | \(0.715680\pi\) | |||||||
\(270\) | 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 | 0.304134 | − | 0.952629i | \(-0.401633\pi\) |
−0.458556 | + | 0.888666i | \(0.651633\pi\) | |||||||
\(278\) | 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 | \(-0.980642\pi\) |
−0.748775 | − | 0.662824i | \(-0.769358\pi\) | |||||||
\(284\) | 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 | \(0.352110\pi\) |
−0.948987 | + | 0.315314i | \(0.897890\pi\) | |||||||
\(294\) | 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 | −0.468003 | − | 0.883727i | \(-0.655026\pi\) |
0.293962 | + | 0.955817i | \(0.405026\pi\) | |||||||
\(308\) | 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 | −0.156814 | − | 0.987628i | \(-0.550122\pi\) |
0.587475 | + | 0.809243i | \(0.300122\pi\) | |||||||
\(318\) | 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 | \(-0.683030\pi\) |
0.977949 | − | 0.208843i | \(-0.0669696\pi\) | |||||||
\(332\) | 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 | 0.616680 | − | 0.787214i | \(-0.288477\pi\) |
−0.120585 | + | 0.992703i | \(0.538477\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −388.120 | + | 160.765i | −1.11209 | + | 0.460644i | −0.861658 | − | 0.507490i | \(-0.830573\pi\) |
−0.250434 | + | 0.968134i | \(0.580573\pi\) | |||||||
\(350\) | 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 | −0.629854 | − | 0.776713i | \(-0.716885\pi\) |
−0.994593 | + | 0.103845i | \(0.966885\pi\) | |||||||
\(374\) | 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 | −0.268011 | − | 0.963416i | \(-0.586366\pi\) |
−0.870750 | + | 0.491725i | \(0.836366\pi\) | |||||||
\(380\) | 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 | −0.831806 | − | 0.555067i | \(-0.812693\pi\) |
0.980667 | + | 0.195684i | \(0.0626927\pi\) | |||||||
\(390\) | 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 | \(-0.872580\pi\) |
0.375649 | − | 0.926762i | \(-0.377420\pi\) | |||||||
\(398\) | 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 | 0.790304 | − | 0.612715i | \(-0.209923\pi\) |
−0.992084 | + | 0.125575i | \(0.959923\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1417 | + | 31.7269i | −0.0312155 | + | 0.0753608i | −0.938719 | − | 0.344685i | \(-0.887986\pi\) |
0.907503 | + | 0.420045i | \(0.137986\pi\) | |||||||
\(422\) | 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 | 0.400106 | − | 0.916469i | \(-0.368973\pi\) |
−0.365124 | + | 0.930959i | \(0.618973\pi\) | |||||||
\(444\) | 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 | \(-0.801680\pi\) |
0.161644 | − | 0.986849i | \(-0.448320\pi\) | |||||||
\(462\) | 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 | −0.476791 | − | 0.879017i | \(-0.658200\pi\) |
0.284416 | + | 0.958701i | \(0.408200\pi\) | |||||||
\(468\) | 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 | −0.995944 | − | 0.0899713i | \(-0.971322\pi\) |
0.767858 | + | 0.640620i | \(0.221322\pi\) | |||||||
\(492\) | 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 | −0.283980 | − | 0.958830i | \(-0.591655\pi\) |
0.477192 | + | 0.878799i | \(0.341655\pi\) | |||||||
\(500\) | 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 | \(0.771615\pi\) |
−0.997695 | + | 0.0678534i | \(0.978385\pi\) | |||||||
\(510\) | 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 | \(-0.649236\pi\) |
0.950312 | − | 0.311300i | \(-0.100764\pi\) | |||||||
\(524\) | 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 | −0.685895 | − | 0.727700i | \(-0.740589\pi\) |
0.0295603 | + | 0.999563i | \(0.490589\pi\) | |||||||
\(542\) | 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 | \(0.293169\pi\) |
0.135204 | + | 0.990818i | \(0.456831\pi\) | |||||||
\(548\) | 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 | \(0.120289\pi\) |
−0.396313 | + | 0.918115i | \(0.629711\pi\) | |||||||
\(558\) | 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 | −0.422017 | − | 0.906588i | \(-0.638678\pi\) |
0.342644 | + | 0.939465i | \(0.388678\pi\) | |||||||
\(564\) | 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 | 0.150401 | − | 0.988625i | \(-0.451944\pi\) |
−0.592714 | + | 0.805413i | \(0.701944\pi\) | |||||||
\(572\) | 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 | −0.854962 | − | 0.518690i | \(-0.826420\pi\) |
0.971319 | + | 0.237780i | \(0.0764197\pi\) | |||||||
\(588\) | 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 | \(0.266780\pi\) |
−0.998611 | + | 0.0526926i | \(0.983220\pi\) | |||||||
\(614\) | 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 | \(0.411706\pi\) |
−0.873712 | + | 0.486443i | \(0.838294\pi\) | |||||||
\(620\) | 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 | \(-0.900265\pi\) |
0.454732 | − | 0.890629i | \(-0.349735\pi\) | |||||||
\(644\) | 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 | \(0.0721282\pi\) |
−0.530170 | + | 0.847892i | \(0.677872\pi\) | |||||||
\(654\) | 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 | 0.337209 | − | 0.941430i | \(-0.390517\pi\) |
0.904134 | + | 0.427248i | \(0.140517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.2123 | + | 14.5854i | 0.0532712 | + | 0.0220657i | 0.409160 | − | 0.912463i | \(-0.365822\pi\) |
−0.355889 | + | 0.934528i | \(0.615822\pi\) | |||||||
\(662\) | 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 | \(-0.740333\pi\) |
0.999539 | − | 0.0303647i | \(-0.00966689\pi\) | |||||||
\(678\) | 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 | \(-0.630281\pi\) |
0.930102 | − | 0.367302i | \(-0.119719\pi\) | |||||||
\(684\) | 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 | −0.817168 | − | 0.576399i | \(-0.804457\pi\) |
−0.170249 | + | 0.985401i | \(0.554457\pi\) | |||||||
\(692\) | 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 | 0.0591703 | − | 0.998248i | \(-0.481154\pi\) |
0.747708 | + | 0.664028i | \(0.231154\pi\) | |||||||
\(702\) | 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 | \(0.433838\pi\) |
−0.837806 | + | 0.545968i | \(0.816162\pi\) | |||||||
\(710\) | 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 | 0.0903463 | − | 0.995910i | \(-0.471203\pi\) |
0.768099 | + | 0.640331i | \(0.221203\pi\) | |||||||
\(734\) | 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 | 0.957018 | − | 0.290028i | \(-0.0936646\pi\) |
−0.881795 | + | 0.471633i | \(0.843665\pi\) | |||||||
\(740\) | 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 | 0.789183 | − | 0.614158i | \(-0.210504\pi\) |
0.123761 | + | 0.992312i | \(0.460504\pi\) | |||||||
\(758\) | 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 | \(-0.693965\pi\) |
0.984545 | − | 0.175131i | \(-0.0560350\pi\) | |||||||
\(774\) | 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 | 0.0210600 | − | 0.999778i | \(-0.493296\pi\) |
0.721842 | + | 0.692058i | \(0.243296\pi\) | |||||||
\(788\) | 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 | 0.0658733 | − | 0.997828i | \(-0.479017\pi\) |
0.752150 | + | 0.658991i | \(0.229017\pi\) | |||||||
\(798\) | 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 | \(-0.631275\pi\) |
0.931243 | − | 0.364398i | \(-0.118725\pi\) | |||||||
\(812\) | 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 | 0.363787 | − | 0.931482i | \(-0.381483\pi\) |
−0.401421 | + | 0.915894i | \(0.631483\pi\) | |||||||
\(822\) | 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 | 0.727507 | − | 0.686100i | \(-0.240679\pi\) |
0.0292791 | + | 0.999571i | \(0.490679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1209.84 | + | 501.131i | −1.45939 | + | 0.604500i | −0.964412 | − | 0.264403i | \(-0.914825\pi\) |
−0.494981 | + | 0.868904i | \(0.664825\pi\) | |||||||
\(830\) | 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 | 0.132719 | − | 0.991154i | \(-0.457629\pi\) |
−0.607005 | + | 0.794698i | \(0.707629\pi\) | |||||||
\(854\) | 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 | −0.285653 | − | 0.958333i | \(-0.592211\pi\) |
−0.879631 | + | 0.475657i | \(0.842211\pi\) | |||||||
\(860\) | 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 | 0.999966 | − | 0.00820433i | \(-0.00261155\pi\) |
−0.712884 | + | 0.701282i | \(0.752612\pi\) | |||||||
\(878\) | 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 | −0.988252 | − | 0.152832i | \(-0.951161\pi\) |
−0.590731 | + | 0.806869i | \(0.701161\pi\) | |||||||
\(884\) | 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 | −0.884045 | − | 0.467402i | \(-0.845190\pi\) |
0.955617 | + | 0.294611i | \(0.0951900\pi\) | |||||||
\(908\) | 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 | \(-0.873955\pi\) |
0.379648 | − | 0.925131i | \(-0.376045\pi\) | |||||||
\(942\) | 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 | −0.688521 | − | 0.725216i | \(-0.741740\pi\) |
0.0259471 | + | 0.999663i | \(0.491740\pi\) | |||||||
\(948\) | 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 | \(0.305663\pi\) |
−0.984749 | + | 0.173980i | \(0.944337\pi\) | |||||||
\(972\) | 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 | −0.890341 | − | 0.455293i | \(-0.849534\pi\) |
0.951508 | + | 0.307625i | \(0.0995344\pi\) | |||||||
\(998\) | 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 | 256.3.h.a.159.6 | 28 | ||
4.3 | odd | 2 | 256.3.h.b.159.2 | 28 | |||
8.3 | odd | 2 | 32.3.h.a.11.3 | yes | 28 | ||
8.5 | even | 2 | 128.3.h.a.79.2 | 28 | |||
24.11 | even | 2 | 288.3.u.a.235.5 | 28 | |||
32.3 | odd | 8 | inner | 256.3.h.a.95.6 | 28 | ||
32.13 | even | 8 | 32.3.h.a.3.3 | ✓ | 28 | ||
32.19 | odd | 8 | 128.3.h.a.47.2 | 28 | |||
32.29 | even | 8 | 256.3.h.b.95.2 | 28 | |||
96.77 | 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 | 32.13 | even | 8 | ||
32.3.h.a.11.3 | yes | 28 | 8.3 | odd | 2 | ||
128.3.h.a.47.2 | 28 | 32.19 | odd | 8 | |||
128.3.h.a.79.2 | 28 | 8.5 | even | 2 | |||
256.3.h.a.95.6 | 28 | 32.3 | odd | 8 | inner | ||
256.3.h.a.159.6 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.b.95.2 | 28 | 32.29 | even | 8 | |||
256.3.h.b.159.2 | 28 | 4.3 | odd | 2 | |||
288.3.u.a.163.5 | 28 | 96.77 | odd | 8 | |||
288.3.u.a.235.5 | 28 | 24.11 | even | 2 |