Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(289,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.12960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{6} + 8x^{4} - 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 576) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1441.2 | ||
Root | \(-0.535233 + 0.309017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1441 |
Dual form | 1728.2.r.d.289.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.35410 | − | 1.93649i | −1.50000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.93649 | + | 3.35410i | 0.731925 | + | 1.26773i | 0.956059 | + | 0.293173i | \(0.0947112\pi\) |
−0.224134 | + | 0.974558i | \(0.571955\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | − | 1.50000i | 0.783349 | − | 0.452267i | −0.0542666 | − | 0.998526i | \(-0.517282\pi\) |
0.837616 | + | 0.546259i | \(0.183949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.35410 | − | 1.93649i | −0.930261 | − | 0.537086i | −0.0433666 | − | 0.999059i | \(-0.513808\pi\) |
−0.886894 | + | 0.461973i | \(0.847142\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.93649 | + | 3.35410i | −0.403786 | + | 0.699379i | −0.994179 | − | 0.107737i | \(-0.965639\pi\) |
0.590393 | + | 0.807116i | \(0.298973\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | + | 8.66025i | 1.00000 | + | 1.73205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.35410 | − | 1.93649i | 0.622841 | − | 0.359597i | −0.155133 | − | 0.987894i | \(-0.549581\pi\) |
0.777974 | + | 0.628296i | \(0.216247\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.93649 | − | 3.35410i | 0.347804 | − | 0.602414i | −0.638055 | − | 0.769991i | \(-0.720261\pi\) |
0.985859 | + | 0.167576i | \(0.0535941\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 15.0000i | − | 2.53546i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.74597i | 1.27343i | 0.771100 | + | 0.636715i | \(0.219707\pi\) | ||||
−0.771100 | + | 0.636715i | \(0.780293\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50000 | − | 7.79423i | 0.702782 | − | 1.21725i | −0.264704 | − | 0.964330i | \(-0.585274\pi\) |
0.967486 | − | 0.252924i | \(-0.0813924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.06218 | − | 3.50000i | 0.924473 | − | 0.533745i | 0.0394140 | − | 0.999223i | \(-0.487451\pi\) |
0.885059 | + | 0.465478i | \(0.154118\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.93649 | − | 3.35410i | −0.282466 | − | 0.489246i | 0.689525 | − | 0.724262i | \(-0.257819\pi\) |
−0.971992 | + | 0.235016i | \(0.924486\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.00000 | + | 6.92820i | −0.571429 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.74597i | 1.06399i | 0.846747 | + | 0.531995i | \(0.178558\pi\) | ||||
−0.846747 | + | 0.531995i | \(0.821442\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −11.6190 | −1.56670 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.59808 | + | 1.50000i | 0.338241 | + | 0.195283i | 0.659494 | − | 0.751710i | \(-0.270771\pi\) |
−0.321253 | + | 0.946993i | \(0.604104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0623 | − | 5.80948i | 1.28835 | − | 0.743827i | 0.309987 | − | 0.950741i | \(-0.399675\pi\) |
0.978359 | + | 0.206914i | \(0.0663419\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.50000 | + | 12.9904i | 0.930261 | + | 1.61126i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.52628 | + | 5.50000i | 1.16382 | + | 0.671932i | 0.952217 | − | 0.305424i | \(-0.0987981\pi\) |
0.211604 | + | 0.977356i | \(0.432131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.74597 | 0.919277 | 0.459639 | − | 0.888106i | \(-0.347979\pi\) | ||||
0.459639 | + | 0.888106i | \(0.347979\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.00000 | 0.936329 | 0.468165 | − | 0.883641i | \(-0.344915\pi\) | ||||
0.468165 | + | 0.883641i | \(0.344915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.0623 | + | 5.80948i | 1.14671 | + | 0.662051i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.93649 | − | 3.35410i | −0.217872 | − | 0.377366i | 0.736285 | − | 0.676672i | \(-0.236578\pi\) |
−0.954157 | + | 0.299306i | \(0.903245\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.59808 | + | 1.50000i | −0.285176 | + | 0.164646i | −0.635764 | − | 0.771883i | \(-0.719315\pi\) |
0.350588 | + | 0.936530i | \(0.385982\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 15.0000i | − | 1.57243i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.87298 | − | 6.70820i | 0.397360 | − | 0.688247i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.500000 | − | 0.866025i | −0.0507673 | − | 0.0879316i | 0.839525 | − | 0.543321i | \(-0.182833\pi\) |
−0.890292 | + | 0.455389i | \(0.849500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.35410 | + | 1.93649i | −0.333746 | + | 0.192688i | −0.657503 | − | 0.753452i | \(-0.728387\pi\) |
0.323757 | + | 0.946140i | \(0.395054\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.80948 | − | 10.0623i | 0.572425 | − | 0.991468i | −0.423892 | − | 0.905713i | \(-0.639336\pi\) |
0.996316 | − | 0.0857555i | \(-0.0273304\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 6.00000i | − | 0.580042i | −0.957020 | − | 0.290021i | \(-0.906338\pi\) | ||
0.957020 | − | 0.290021i | \(-0.0936623\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.74597i | − | 0.741929i | −0.928647 | − | 0.370965i | \(-0.879027\pi\) | ||
0.928647 | − | 0.370965i | \(-0.120973\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.50000 | − | 2.59808i | 0.141108 | − | 0.244406i | −0.786806 | − | 0.617200i | \(-0.788267\pi\) |
0.927914 | + | 0.372794i | \(0.121600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.9904 | − | 7.50000i | 1.21136 | − | 0.699379i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 19.3649i | − | 1.73205i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 15.4919 | 1.37469 | 0.687343 | − | 0.726333i | \(-0.258777\pi\) | ||||
0.687343 | + | 0.726333i | \(0.258777\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | + | 1.50000i | 0.226995 | + | 0.131056i | 0.609185 | − | 0.793028i | \(-0.291497\pi\) |
−0.382190 | + | 0.924084i | \(0.624830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.70820 | + | 3.87298i | −0.581675 | + | 0.335830i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5000 | + | 18.1865i | 0.897076 | + | 1.55378i | 0.831215 | + | 0.555952i | \(0.187646\pi\) |
0.0658609 | + | 0.997829i | \(0.479021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.866025 | + | 0.500000i | 0.0734553 | + | 0.0424094i | 0.536278 | − | 0.844042i | \(-0.319830\pi\) |
−0.462822 | + | 0.886451i | \(0.653163\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.6190 | −0.971625 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.0000 | −1.24568 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.0623 | − | 5.80948i | −0.824336 | − | 0.475931i | 0.0275733 | − | 0.999620i | \(-0.491222\pi\) |
−0.851909 | + | 0.523689i | \(0.824555\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.80948 | + | 10.0623i | 0.472768 | + | 0.818859i | 0.999514 | − | 0.0311639i | \(-0.00992140\pi\) |
−0.526746 | + | 0.850023i | \(0.676588\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.9904 | + | 7.50000i | −1.04341 | + | 0.602414i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.35410 | + | 1.93649i | 0.267686 | + | 0.154549i | 0.627836 | − | 0.778346i | \(-0.283941\pi\) |
−0.360149 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.0000 | −1.18217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000i | 0.156652i | 0.996928 | + | 0.0783260i | \(0.0249575\pi\) | ||||
−0.996928 | + | 0.0783260i | \(0.975042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.93649 | − | 3.35410i | 0.149850 | − | 0.259548i | −0.781322 | − | 0.624128i | \(-0.785454\pi\) |
0.931172 | + | 0.364580i | \(0.118788\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | + | 1.73205i | 0.0769231 | + | 0.133235i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.7705 | + | 9.68246i | −1.27504 | + | 0.736144i | −0.975932 | − | 0.218076i | \(-0.930022\pi\) |
−0.299106 | + | 0.954220i | \(0.596689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.3649 | + | 33.5410i | −1.46385 | + | 2.53546i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 18.0000i | − | 1.34538i | −0.739923 | − | 0.672692i | \(-0.765138\pi\) | ||
0.739923 | − | 0.672692i | \(-0.234862\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.74597i | − | 0.575753i | −0.957668 | − | 0.287877i | \(-0.907051\pi\) | ||
0.957668 | − | 0.287877i | \(-0.0929493\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.0000 | − | 25.9808i | 1.10282 | − | 1.91014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5554 | + | 23.4787i | 0.980837 | + | 1.69886i | 0.659145 | + | 0.752016i | \(0.270918\pi\) |
0.321692 | + | 0.946844i | \(0.395748\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | + | 4.33013i | −0.179954 | + | 0.311689i | −0.941865 | − | 0.335993i | \(-0.890928\pi\) |
0.761911 | + | 0.647682i | \(0.224262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.74597 | 0.549097 | 0.274549 | − | 0.961573i | \(-0.411472\pi\) | ||||
0.274549 | + | 0.961573i | \(0.411472\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.9904 | + | 7.50000i | 0.911746 | + | 0.526397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.1869 | + | 17.4284i | −2.10835 | + | 1.21725i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.00000 | + | 5.19615i | 0.207514 | + | 0.359425i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.866025 | − | 0.500000i | −0.0596196 | − | 0.0344214i | 0.469894 | − | 0.882723i | \(-0.344292\pi\) |
−0.529514 | + | 0.848301i | \(0.677626\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −27.1109 | −1.84895 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.0000 | 1.01827 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.5554 | − | 23.4787i | −0.907740 | − | 1.57225i | −0.817197 | − | 0.576358i | \(-0.804473\pi\) |
−0.0905425 | − | 0.995893i | \(-0.528860\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.1865 | + | 10.5000i | −1.20708 | + | 0.696909i | −0.962121 | − | 0.272623i | \(-0.912109\pi\) |
−0.244962 | + | 0.969533i | \(0.578775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.35410 | + | 1.93649i | 0.221645 | + | 0.127967i | 0.606712 | − | 0.794922i | \(-0.292488\pi\) |
−0.385067 | + | 0.922889i | \(0.625822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.0000i | 0.978492i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.68246 | + | 16.7705i | −0.626306 | + | 1.08479i | 0.361981 | + | 0.932186i | \(0.382101\pi\) |
−0.988287 | + | 0.152608i | \(0.951233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | − | 9.52628i | −0.354286 | − | 0.613642i | 0.632709 | − | 0.774389i | \(-0.281943\pi\) |
−0.986996 | + | 0.160748i | \(0.948609\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.8328 | − | 15.4919i | 1.71429 | − | 0.989743i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.87298 | − | 6.70820i | 0.246432 | − | 0.426833i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.00000i | 0.378717i | 0.981908 | + | 0.189358i | \(0.0606408\pi\) | ||||
−0.981908 | + | 0.189358i | \(0.939359\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.6190i | 0.730477i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.5000 | + | 18.1865i | −0.654972 | + | 1.13444i | 0.326929 | + | 0.945049i | \(0.393986\pi\) |
−0.981901 | + | 0.189396i | \(0.939347\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −25.9808 | + | 15.0000i | −1.61437 | + | 0.932055i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.80948 | − | 10.0623i | −0.358228 | − | 0.620468i | 0.629437 | − | 0.777051i | \(-0.283285\pi\) |
−0.987665 | + | 0.156583i | \(0.949952\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.0000 | − | 25.9808i | 0.921443 | − | 1.59599i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.2379i | 1.41684i | 0.705791 | + | 0.708420i | \(0.250592\pi\) | ||||
−0.705791 | + | 0.708420i | \(0.749408\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 25.9808 | + | 15.0000i | 1.56670 | + | 0.904534i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.7705 | − | 9.68246i | 1.00764 | − | 0.581763i | 0.0971418 | − | 0.995271i | \(-0.469030\pi\) |
0.910500 | + | 0.413508i | \(0.135697\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5000 | − | 23.3827i | −0.805342 | − | 1.39489i | −0.916060 | − | 0.401042i | \(-0.868648\pi\) |
0.110717 | − | 0.993852i | \(-0.464685\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9186 | − | 11.5000i | −1.18404 | − | 0.683604i | −0.227092 | − | 0.973873i | \(-0.572922\pi\) |
−0.956945 | + | 0.290269i | \(0.906255\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 34.8569 | 2.05753 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.4787 | + | 13.5554i | 1.37164 | + | 0.791917i | 0.991135 | − | 0.132861i | \(-0.0424164\pi\) |
0.380506 | + | 0.924778i | \(0.375750\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.80948 | − | 10.0623i | −0.338241 | − | 0.585850i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.9904 | − | 7.50000i | 0.751253 | − | 0.433736i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.4787 | + | 13.5554i | 1.35329 | + | 0.781323i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −45.0000 | −2.57669 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000i | 0.570730i | 0.958419 | + | 0.285365i | \(0.0921148\pi\) | ||||
−0.958419 | + | 0.285365i | \(0.907885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.5554 | − | 23.4787i | 0.768659 | − | 1.33136i | −0.169632 | − | 0.985507i | \(-0.554258\pi\) |
0.938290 | − | 0.345848i | \(-0.112409\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | + | 14.7224i | 0.480448 | + | 0.832161i | 0.999748 | − | 0.0224310i | \(-0.00714060\pi\) |
−0.519300 | + | 0.854592i | \(0.673807\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.0623 | + | 5.80948i | −0.565155 | + | 0.326293i | −0.755212 | − | 0.655480i | \(-0.772466\pi\) |
0.190057 | + | 0.981773i | \(0.439133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.80948 | − | 10.0623i | 0.325268 | − | 0.563381i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 38.7298i | − | 2.14834i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.50000 | − | 12.9904i | 0.413488 | − | 0.716183i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.4545 | + | 9.50000i | −0.904420 | + | 0.522167i | −0.878632 | − | 0.477500i | \(-0.841543\pi\) |
−0.0257885 | + | 0.999667i | \(0.508210\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.3014 | − | 36.8951i | −1.16382 | − | 2.01580i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.50000 | − | 4.33013i | 0.136184 | − | 0.235877i | −0.789865 | − | 0.613280i | \(-0.789850\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 11.6190i | − | 0.629201i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.87298 | −0.209121 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.9904 | − | 7.50000i | −0.697360 | − | 0.402621i | 0.109003 | − | 0.994041i | \(-0.465234\pi\) |
−0.806363 | + | 0.591420i | \(0.798567\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.7705 | − | 9.68246i | 0.897705 | − | 0.518290i | 0.0212500 | − | 0.999774i | \(-0.493235\pi\) |
0.876455 | + | 0.481484i | \(0.159902\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | − | 2.59808i | −0.0798369 | − | 0.138282i | 0.823343 | − | 0.567545i | \(-0.192107\pi\) |
−0.903179 | + | 0.429263i | \(0.858773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.9808 | − | 15.0000i | −1.37892 | − | 0.796117i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 30.9839 | 1.63527 | 0.817633 | − | 0.575740i | \(-0.195286\pi\) | ||||
0.817633 | + | 0.575740i | \(0.195286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −26.8328 | − | 15.4919i | −1.40449 | − | 0.810885i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.80948 | + | 10.0623i | 0.303252 | + | 0.525248i | 0.976871 | − | 0.213831i | \(-0.0685942\pi\) |
−0.673619 | + | 0.739079i | \(0.735261\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.9808 | + | 15.0000i | −1.34885 | + | 0.778761i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.35410 | − | 1.93649i | −0.173669 | − | 0.100268i | 0.410646 | − | 0.911795i | \(-0.365303\pi\) |
−0.584315 | + | 0.811527i | \(0.698637\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.0000 | −0.772539 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000i | 0.821865i | 0.911666 | + | 0.410932i | \(0.134797\pi\) | ||||
−0.911666 | + | 0.410932i | \(0.865203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.93649 | − | 3.35410i | 0.0989501 | − | 0.171387i | −0.812300 | − | 0.583240i | \(-0.801785\pi\) |
0.911250 | + | 0.411853i | \(0.135118\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −22.5000 | − | 38.9711i | −1.14671 | − | 1.98615i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.35410 | + | 1.93649i | −0.170060 | + | 0.0981840i | −0.582614 | − | 0.812749i | \(-0.697970\pi\) |
0.412554 | + | 0.910933i | \(0.364637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.0000i | 0.754732i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.74597i | 0.388759i | 0.980926 | + | 0.194379i | \(0.0622693\pi\) | ||||
−0.980926 | + | 0.194379i | \(0.937731\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | + | 2.59808i | −0.0749064 | + | 0.129742i | −0.901046 | − | 0.433724i | \(-0.857199\pi\) |
0.826139 | + | 0.563466i | \(0.190532\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.9904 | + | 7.50000i | −0.647097 | + | 0.373602i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.6190 | + | 20.1246i | 0.575930 | + | 0.997540i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5000 | + | 19.9186i | −0.568638 | + | 0.984911i | 0.428063 | + | 0.903749i | \(0.359196\pi\) |
−0.996701 | + | 0.0811615i | \(0.974137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.6190i | 0.571731i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.6190 | 0.570352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.5788 | + | 16.5000i | 1.39617 | + | 0.806078i | 0.993989 | − | 0.109483i | \(-0.0349196\pi\) |
0.402179 | + | 0.915561i | \(0.368253\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.35410 | + | 1.93649i | −0.163469 | + | 0.0943788i | −0.579503 | − | 0.814970i | \(-0.696753\pi\) |
0.416034 | + | 0.909349i | \(0.363420\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 38.9711 | + | 22.5000i | 1.88595 | + | 1.08885i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.4919 | −0.746220 | −0.373110 | − | 0.927787i | \(-0.621709\pi\) | ||||
−0.373110 | + | 0.927787i | \(0.621709\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −20.0000 | −0.961139 | −0.480569 | − | 0.876957i | \(-0.659570\pi\) | ||||
−0.480569 | + | 0.876957i | \(0.659570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.70820 | − | 3.87298i | −0.320897 | − | 0.185270i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.80948 | + | 10.0623i | 0.277271 | + | 0.480248i | 0.970706 | − | 0.240272i | \(-0.0772366\pi\) |
−0.693434 | + | 0.720520i | \(0.743903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.9904 | + | 7.50000i | −0.617192 | + | 0.356336i | −0.775775 | − | 0.631010i | \(-0.782641\pi\) |
0.158583 | + | 0.987346i | \(0.449307\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.2492 | − | 23.2379i | −1.90800 | − | 1.10158i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12.0000 | −0.566315 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 27.0000i | − | 1.27138i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −29.0474 | + | 50.3115i | −1.36176 | + | 2.35864i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5000 | − | 25.1147i | −0.678281 | − | 1.17482i | −0.975498 | − | 0.220008i | \(-0.929392\pi\) |
0.297217 | − | 0.954810i | \(-0.403942\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.1869 | − | 17.4284i | 1.40594 | − | 0.811723i | 0.410951 | − | 0.911657i | \(-0.365197\pi\) |
0.994994 | + | 0.0999348i | \(0.0318634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.68246 | − | 16.7705i | 0.449982 | − | 0.779392i | −0.548402 | − | 0.836215i | \(-0.684764\pi\) |
0.998384 | + | 0.0568230i | \(0.0180971\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000i | 0.277647i | 0.990317 | + | 0.138823i | \(0.0443321\pi\) | ||||
−0.990317 | + | 0.138823i | \(0.955668\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 42.6028i | 1.96722i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.5000 | − | 18.1865i | 0.482791 | − | 0.836218i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −17.3205 | + | 10.0000i | −0.794719 | + | 0.458831i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.80948 | − | 10.0623i | −0.265442 | − | 0.459758i | 0.702238 | − | 0.711943i | \(-0.252184\pi\) |
−0.967679 | + | 0.252184i | \(0.918851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.0000 | − | 25.9808i | 0.683941 | − | 1.18462i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.87298i | 0.175863i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.9839 | −1.40401 | −0.702007 | − | 0.712171i | \(-0.747712\pi\) | ||||
−0.702007 | + | 0.712171i | \(0.747712\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1865 | − | 10.5000i | −0.820747 | − | 0.473858i | 0.0299272 | − | 0.999552i | \(-0.490472\pi\) |
−0.850674 | + | 0.525694i | \(0.823806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.0000 | + | 25.9808i | 0.672842 | + | 1.16540i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.06218 | − | 3.50000i | −0.271380 | − | 0.156682i | 0.358134 | − | 0.933670i | \(-0.383413\pi\) |
−0.629515 | + | 0.776989i | \(0.716746\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.74597 | −0.345376 | −0.172688 | − | 0.984977i | \(-0.555245\pi\) | ||||
−0.172688 | + | 0.984977i | \(0.555245\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0000 | 0.667491 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.35410 | + | 1.93649i | 0.148668 | + | 0.0858335i | 0.572489 | − | 0.819913i | \(-0.305978\pi\) |
−0.423821 | + | 0.905746i | \(0.639311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.4919 | + | 26.8328i | 0.685323 | + | 1.18701i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.9711 | + | 22.5000i | −1.71727 | + | 0.991468i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.0623 | − | 5.80948i | −0.442540 | − | 0.255500i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.0000 | 0.788594 | 0.394297 | − | 0.918983i | \(-0.370988\pi\) | ||||
0.394297 | + | 0.918983i | \(0.370988\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.00000i | − | 0.349816i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) | ||
0.984585 | − | 0.174908i | \(-0.0559627\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.00000 | + | 6.92820i | 0.173913 | + | 0.301226i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.1869 | + | 17.4284i | −1.30754 | + | 0.754909i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.6190 | + | 20.1246i | −0.502331 | + | 0.870063i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.0000i | 1.03375i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.9839i | 1.33210i | 0.745907 | + | 0.666050i | \(0.232016\pi\) | ||||
−0.745907 | + | 0.666050i | \(0.767984\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.0000 | + | 25.9808i | −0.642529 | + | 1.11289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.5070 | − | 20.5000i | 1.51817 | − | 0.876517i | 0.518400 | − | 0.855138i | \(-0.326528\pi\) |
0.999771 | − | 0.0213785i | \(-0.00680549\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.87298 | + | 6.70820i | 0.164995 | + | 0.285779i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | − | 12.9904i | 0.318932 | − | 0.552407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 23.2379i | − | 0.984621i | −0.870420 | − | 0.492311i | \(-0.836152\pi\) | ||
0.870420 | − | 0.492311i | \(-0.163848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.1109 | −1.14667 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.5788 | + | 16.5000i | 1.20445 | + | 0.695392i | 0.961542 | − | 0.274656i | \(-0.0885641\pi\) |
0.242912 | + | 0.970048i | \(0.421897\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0623 | + | 5.80948i | −0.423324 | + | 0.244406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.50000 | − | 7.79423i | −0.188650 | − | 0.326751i | 0.756151 | − | 0.654398i | \(-0.227078\pi\) |
−0.944800 | + | 0.327647i | \(0.893744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.5070 | − | 20.5000i | −1.48592 | − | 0.857898i | −0.486052 | − | 0.873930i | \(-0.661563\pi\) |
−0.999871 | + | 0.0160316i | \(0.994897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −38.7298 | −1.61515 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.0000 | −1.83174 | −0.915872 | − | 0.401470i | \(-0.868499\pi\) | ||||
−0.915872 | + | 0.401470i | \(0.868499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0623 | − | 5.80948i | −0.417455 | − | 0.241018i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11.6190 | + | 20.1246i | 0.481208 | + | 0.833476i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 38.9711 | − | 22.5000i | 1.60851 | − | 0.928674i | 0.618808 | − | 0.785543i | \(-0.287616\pi\) |
0.989704 | − | 0.143132i | \(-0.0457173\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.70820 | + | 3.87298i | 0.276407 | + | 0.159583i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.0000 | 0.492781 | 0.246390 | − | 0.969171i | \(-0.420755\pi\) | ||||
0.246390 | + | 0.969171i | \(0.420755\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.68246 | − | 16.7705i | 0.395615 | − | 0.685224i | −0.597565 | − | 0.801821i | \(-0.703865\pi\) |
0.993179 | + | 0.116596i | \(0.0371983\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50000 | − | 14.7224i | −0.346722 | − | 0.600541i | 0.638943 | − | 0.769254i | \(-0.279372\pi\) |
−0.985665 | + | 0.168714i | \(0.946039\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.70820 | − | 3.87298i | 0.272727 | − | 0.157459i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5554 | − | 23.4787i | 0.550198 | − | 0.952972i | −0.448061 | − | 0.894003i | \(-0.647885\pi\) |
0.998260 | − | 0.0589688i | \(-0.0187813\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.0000i | 0.606835i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2379i | 0.938570i | 0.883047 | + | 0.469285i | \(0.155488\pi\) | ||||
−0.883047 | + | 0.469285i | \(0.844512\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −19.5000 | + | 33.7750i | −0.785040 | + | 1.35973i | 0.143934 | + | 0.989587i | \(0.454025\pi\) |
−0.928975 | + | 0.370143i | \(0.879309\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.7224 | − | 8.50000i | 0.591744 | − | 0.341644i | −0.174042 | − | 0.984738i | \(-0.555683\pi\) |
0.765787 | + | 0.643094i | \(0.222350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 23.2379 | + | 40.2492i | 0.931007 | + | 1.61255i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.4919 | 0.616724 | 0.308362 | − | 0.951269i | \(-0.400219\pi\) | ||||
0.308362 | + | 0.951269i | \(0.400219\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.9615 | − | 30.0000i | −2.06203 | − | 1.19051i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.8328 | − | 15.4919i | 1.06315 | − | 0.613813i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5000 | − | 18.1865i | −0.414725 | − | 0.718325i | 0.580674 | − | 0.814136i | \(-0.302789\pi\) |
−0.995400 | + | 0.0958109i | \(0.969456\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.06218 | + | 3.50000i | 0.239069 | + | 0.138027i | 0.614749 | − | 0.788723i | \(-0.289257\pi\) |
−0.375680 | + | 0.926750i | \(0.622591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −15.4919 | −0.609051 | −0.304525 | − | 0.952504i | \(-0.598498\pi\) | ||||
−0.304525 | + | 0.952504i | \(0.598498\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | 0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.0623 | + | 5.80948i | 0.393768 | + | 0.227342i | 0.683792 | − | 0.729677i | \(-0.260330\pi\) |
−0.290023 | + | 0.957020i | \(0.593663\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.80948 | − | 10.0623i | −0.226995 | − | 0.393167i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.3827 | − | 13.5000i | 0.910860 | − | 0.525885i | 0.0301523 | − | 0.999545i | \(-0.490401\pi\) |
0.880708 | + | 0.473660i | \(0.157067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0623 | − | 5.80948i | −0.391378 | − | 0.225962i | 0.291379 | − | 0.956608i | \(-0.405886\pi\) |
−0.682757 | + | 0.730645i | \(0.739219\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 30.0000 | 1.16335 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0000i | 0.580802i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.4284 | − | 30.1869i | 0.672817 | − | 1.16535i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.5000 | + | 30.3109i | 0.674575 | + | 1.16840i | 0.976593 | + | 0.215096i | \(0.0690066\pi\) |
−0.302017 | + | 0.953302i | \(0.597660\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −16.7705 | + | 9.68246i | −0.644543 | + | 0.372127i | −0.786362 | − | 0.617765i | \(-0.788038\pi\) |
0.141819 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.93649 | − | 3.35410i | 0.0743157 | − | 0.128719i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 18.0000i | − | 0.688751i | −0.938832 | − | 0.344375i | \(-0.888091\pi\) | ||
0.938832 | − | 0.344375i | \(-0.111909\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 81.3327i | − | 3.10756i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 15.0000 | − | 25.9808i | 0.571454 | − | 0.989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.866025 | + | 0.500000i | −0.0329452 | + | 0.0190209i | −0.516382 | − | 0.856358i | \(-0.672722\pi\) |
0.483437 | + | 0.875379i | \(0.339388\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.93649 | − | 3.35410i | −0.0734553 | − | 0.127228i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.2379i | 0.877683i | 0.898564 | + | 0.438842i | \(0.144611\pi\) | ||||
−0.898564 | + | 0.438842i | \(0.855389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.4919 | −0.584289 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.9904 | − | 7.50000i | −0.488554 | − | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.35410 | − | 1.93649i | 0.125966 | − | 0.0727265i | −0.435693 | − | 0.900095i | \(-0.643497\pi\) |
0.561659 | + | 0.827369i | \(0.310163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.50000 | + | 12.9904i | 0.280877 | + | 0.486494i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 38.9711 | + | 22.5000i | 1.45744 | + | 0.841452i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 46.4758 | 1.73325 | 0.866627 | − | 0.498956i | \(-0.166283\pi\) | ||||
0.866627 | + | 0.498956i | \(0.166283\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 45.0000 | 1.67589 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.5410 | + | 19.3649i | 1.24568 | + | 0.719195i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17.4284 | − | 30.1869i | −0.646385 | − | 1.11957i | −0.983980 | − | 0.178279i | \(-0.942947\pi\) |
0.337595 | − | 0.941291i | \(-0.390386\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.35410 | − | 1.93649i | −0.123887 | − | 0.0715260i | 0.436776 | − | 0.899570i | \(-0.356120\pi\) |
−0.560663 | + | 0.828044i | \(0.689454\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 33.0000 | 1.21557 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 32.0000i | − | 1.17714i | −0.808447 | − | 0.588570i | \(-0.799691\pi\) | ||
0.808447 | − | 0.588570i | \(-0.200309\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.1744 | − | 43.6033i | 0.923559 | − | 1.59965i | 0.129696 | − | 0.991554i | \(-0.458600\pi\) |
0.793863 | − | 0.608097i | \(-0.208067\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.5000 | + | 38.9711i | 0.824336 | + | 1.42779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.1246 | − | 11.6190i | 0.735337 | − | 0.424547i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.5554 | − | 23.4787i | 0.494645 | − | 0.856750i | −0.505336 | − | 0.862923i | \(-0.668631\pi\) |
0.999981 | + | 0.00617232i | \(0.00196472\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 45.0000i | − | 1.63772i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.5000 | − | 18.1865i | 0.380625 | − | 0.659261i | −0.610527 | − | 0.791995i | \(-0.709042\pi\) |
0.991152 | + | 0.132734i | \(0.0423756\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.9808 | − | 15.0000i | 0.940567 | − | 0.543036i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.80948 | − | 10.0623i | −0.209768 | − | 0.363329i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.5000 | + | 19.9186i | −0.414701 | + | 0.718283i | −0.995397 | − | 0.0958377i | \(-0.969447\pi\) |
0.580696 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 38.7298i | − | 1.39302i | −0.717549 | − | 0.696508i | \(-0.754736\pi\) | ||
0.717549 | − | 0.696508i | \(-0.245264\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 38.7298 | 1.39122 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.5885 | + | 9.00000i | 0.558514 | + | 0.322458i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20.1246 | − | 11.6190i | 0.720115 | − | 0.415759i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.50000 | − | 12.9904i | −0.267686 | − | 0.463647i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.6506 | + | 12.5000i | 0.771762 | + | 0.445577i | 0.833503 | − | 0.552515i | \(-0.186332\pi\) |
−0.0617409 | + | 0.998092i | \(0.519665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.6190 | 0.413122 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45.0000 | −1.59800 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.7705 | + | 9.68246i | 0.594042 | + | 0.342970i | 0.766694 | − | 0.642013i | \(-0.221900\pi\) |
−0.172652 | + | 0.984983i | \(0.555234\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.7846 | − | 12.0000i | 0.733473 | − | 0.423471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 50.3115 | + | 29.0474i | 1.77325 | + | 1.02379i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0000 | 0.421898 | 0.210949 | − | 0.977497i | \(-0.432345\pi\) | ||||
0.210949 | + | 0.977497i | \(0.432345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.0000i | 1.19390i | 0.802278 | + | 0.596951i | \(0.203621\pi\) | ||||
−0.802278 | + | 0.596951i | \(0.796379\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.87298 | − | 6.70820i | 0.135665 | − | 0.234978i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.00000 | + | 12.1244i | 0.244899 | + | 0.424178i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.8951 | + | 21.3014i | −1.28765 | + | 0.743424i | −0.978234 | − | 0.207503i | \(-0.933466\pi\) |
−0.309414 | + | 0.950927i | \(0.600133\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.93649 | − | 3.35410i | 0.0675019 | − | 0.116917i | −0.830299 | − | 0.557318i | \(-0.811830\pi\) |
0.897801 | + | 0.440401i | \(0.145164\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 6.00000i | − | 0.208640i | −0.994544 | − | 0.104320i | \(-0.966733\pi\) | ||
0.994544 | − | 0.104320i | \(-0.0332667\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.74597i | 0.269029i | 0.990912 | + | 0.134514i | \(0.0429474\pi\) | ||||
−0.990912 | + | 0.134514i | \(0.957053\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.9904 | + | 7.50000i | −0.449551 | + | 0.259548i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −25.1744 | − | 43.6033i | −0.869117 | − | 1.50535i | −0.862901 | − | 0.505373i | \(-0.831355\pi\) |
−0.00621569 | − | 0.999981i | \(-0.501979\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | + | 12.1244i | −0.241379 | + | 0.418081i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 7.74597i | − | 0.266469i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.74597 | −0.266155 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.9808 | − | 15.0000i | −0.890609 | − | 0.514193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.0623 | − | 5.80948i | 0.344527 | − | 0.198913i | −0.317745 | − | 0.948176i | \(-0.602926\pi\) |
0.662272 | + | 0.749263i | \(0.269592\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5000 | + | 18.1865i | 0.358673 | + | 0.621240i | 0.987739 | − | 0.156112i | \(-0.0498959\pi\) |
−0.629066 | + | 0.777352i | \(0.716563\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2583 | − | 6.50000i | −0.384129 | − | 0.221777i | 0.295484 | − | 0.955348i | \(-0.404519\pi\) |
−0.679613 | + | 0.733571i | \(0.737852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.4919 | −0.527352 | −0.263676 | − | 0.964611i | \(-0.584935\pi\) | ||||
−0.263676 | + | 0.964611i | \(0.584935\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 75.0000 | 2.55008 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.0623 | − | 5.80948i | −0.341340 | − | 0.197073i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.3014 | − | 36.8951i | −0.721771 | − | 1.25014i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 64.9519 | − | 37.5000i | 2.19578 | − | 1.26773i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.4787 | + | 13.5554i | 0.792820 | + | 0.457735i | 0.840954 | − | 0.541106i | \(-0.181994\pi\) |
−0.0481345 | + | 0.998841i | \(0.515328\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.0000 | 0.404290 | 0.202145 | − | 0.979356i | \(-0.435209\pi\) | ||||
0.202145 | + | 0.979356i | \(0.435209\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.0000i | 1.68263i | 0.540542 | + | 0.841317i | \(0.318219\pi\) | ||||
−0.540542 | + | 0.841317i | \(0.681781\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.4284 | + | 30.1869i | −0.585189 | + | 1.01358i | 0.409663 | + | 0.912237i | \(0.365646\pi\) |
−0.994852 | + | 0.101340i | \(0.967687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.0000 | + | 51.9615i | 1.00617 | + | 1.74273i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.70820 | − | 3.87298i | 0.224481 | − | 0.129604i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.8569 | + | 60.3738i | −1.16514 | + | 2.01807i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 15.0000i | − | 0.500278i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.0000 | + | 25.9808i | −0.498617 | + | 0.863630i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4545 | − | 9.50000i | 0.546362 | − | 0.315442i | −0.201291 | − | 0.979531i | \(-0.564514\pi\) |
0.747653 | + | 0.664089i | \(0.231180\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.68246 | + | 16.7705i | 0.320794 | + | 0.555632i | 0.980652 | − | 0.195759i | \(-0.0627169\pi\) |
−0.659858 | + | 0.751390i | \(0.729384\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.50000 | + | 7.79423i | −0.148928 | + | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.6190i | 0.383692i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.4758 | 1.53310 | 0.766548 | − | 0.642188i | \(-0.221973\pi\) | ||||
0.766548 | + | 0.642188i | \(0.221973\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25.9808 | − | 15.0000i | −0.855167 | − | 0.493731i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −67.0820 | + | 38.7298i | −2.20564 | + | 1.27343i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5000 | − | 33.7750i | −0.639774 | − | 1.10812i | −0.985482 | − | 0.169779i | \(-0.945695\pi\) |
0.345708 | − | 0.938342i | \(-0.387639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8564 | − | 8.00000i | −0.454125 | − | 0.262189i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00000 | 0.130674 | 0.0653372 | − | 0.997863i | \(-0.479188\pi\) | ||||
0.0653372 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.35410 | − | 1.93649i | −0.109341 | − | 0.0631278i | 0.444332 | − | 0.895862i | \(-0.353441\pi\) |
−0.553673 | + | 0.832734i | \(0.686774\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.4284 | + | 30.1869i | 0.567548 | + | 0.983021i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.1673 | − | 25.5000i | 1.43524 | − | 0.828639i | 0.437730 | − | 0.899106i | \(-0.355783\pi\) |
0.997514 | + | 0.0704677i | \(0.0224492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.8328 | − | 15.4919i | −0.871030 | − | 0.502889i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 105.000i | − | 3.39772i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −40.6663 | + | 70.4361i | −1.31318 | + | 2.27450i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.00000 | + | 13.8564i | 0.258065 | + | 0.446981i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.7705 | − | 9.68246i | 0.539862 | − | 0.311689i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.0474 | + | 50.3115i | −0.934101 | + | 1.61791i | −0.157871 | + | 0.987460i | \(0.550463\pi\) |
−0.776230 | + | 0.630450i | \(0.782870\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.0000i | 0.770197i | 0.922876 | + | 0.385098i | \(0.125832\pi\) | ||||
−0.922876 | + | 0.385098i | \(0.874168\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.87298i | 0.124162i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.50000 | + | 7.79423i | −0.143968 | + | 0.249359i | −0.928987 | − | 0.370111i | \(-0.879319\pi\) |
0.785020 | + | 0.619471i | \(0.212653\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 31.1769 | − | 18.0000i | 0.996419 | − | 0.575282i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.4284 | + | 30.1869i | 0.555880 | + | 0.962813i | 0.997834 | + | 0.0657754i | \(0.0209521\pi\) |
−0.441954 | + | 0.897038i | \(0.645715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.1109i | 0.862076i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.4758 | −1.47635 | −0.738176 | − | 0.674608i | \(-0.764313\pi\) | ||||
−0.738176 | + | 0.674608i | \(0.764313\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.9808 | − | 15.0000i | −0.823646 | − | 0.475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.3115 | + | 29.0474i | −1.59338 | + | 0.919940i | −0.600661 | + | 0.799504i | \(0.705096\pi\) |
−0.992721 | + | 0.120436i | \(0.961571\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1728.2.r.d.1441.2 | 8 | ||
3.2 | odd | 2 | 576.2.r.d.481.2 | yes | 8 | ||
4.3 | odd | 2 | inner | 1728.2.r.d.1441.1 | 8 | ||
8.3 | odd | 2 | inner | 1728.2.r.d.1441.3 | 8 | ||
8.5 | even | 2 | inner | 1728.2.r.d.1441.4 | 8 | ||
9.2 | odd | 6 | 576.2.r.d.97.3 | yes | 8 | ||
9.4 | even | 3 | 5184.2.d.g.2593.3 | 4 | |||
9.5 | odd | 6 | 5184.2.d.h.2593.1 | 4 | |||
9.7 | even | 3 | inner | 1728.2.r.d.289.4 | 8 | ||
12.11 | even | 2 | 576.2.r.d.481.4 | yes | 8 | ||
24.5 | odd | 2 | 576.2.r.d.481.3 | yes | 8 | ||
24.11 | even | 2 | 576.2.r.d.481.1 | yes | 8 | ||
36.7 | odd | 6 | inner | 1728.2.r.d.289.3 | 8 | ||
36.11 | even | 6 | 576.2.r.d.97.1 | ✓ | 8 | ||
36.23 | even | 6 | 5184.2.d.h.2593.2 | 4 | |||
36.31 | odd | 6 | 5184.2.d.g.2593.4 | 4 | |||
72.5 | odd | 6 | 5184.2.d.h.2593.3 | 4 | |||
72.11 | even | 6 | 576.2.r.d.97.4 | yes | 8 | ||
72.13 | even | 6 | 5184.2.d.g.2593.1 | 4 | |||
72.29 | odd | 6 | 576.2.r.d.97.2 | yes | 8 | ||
72.43 | odd | 6 | inner | 1728.2.r.d.289.1 | 8 | ||
72.59 | even | 6 | 5184.2.d.h.2593.4 | 4 | |||
72.61 | even | 6 | inner | 1728.2.r.d.289.2 | 8 | ||
72.67 | odd | 6 | 5184.2.d.g.2593.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.d.97.1 | ✓ | 8 | 36.11 | even | 6 | ||
576.2.r.d.97.2 | yes | 8 | 72.29 | odd | 6 | ||
576.2.r.d.97.3 | yes | 8 | 9.2 | odd | 6 | ||
576.2.r.d.97.4 | yes | 8 | 72.11 | even | 6 | ||
576.2.r.d.481.1 | yes | 8 | 24.11 | even | 2 | ||
576.2.r.d.481.2 | yes | 8 | 3.2 | odd | 2 | ||
576.2.r.d.481.3 | yes | 8 | 24.5 | odd | 2 | ||
576.2.r.d.481.4 | yes | 8 | 12.11 | even | 2 | ||
1728.2.r.d.289.1 | 8 | 72.43 | odd | 6 | inner | ||
1728.2.r.d.289.2 | 8 | 72.61 | even | 6 | inner | ||
1728.2.r.d.289.3 | 8 | 36.7 | odd | 6 | inner | ||
1728.2.r.d.289.4 | 8 | 9.7 | even | 3 | inner | ||
1728.2.r.d.1441.1 | 8 | 4.3 | odd | 2 | inner | ||
1728.2.r.d.1441.2 | 8 | 1.1 | even | 1 | trivial | ||
1728.2.r.d.1441.3 | 8 | 8.3 | odd | 2 | inner | ||
1728.2.r.d.1441.4 | 8 | 8.5 | even | 2 | inner | ||
5184.2.d.g.2593.1 | 4 | 72.13 | even | 6 | |||
5184.2.d.g.2593.2 | 4 | 72.67 | odd | 6 | |||
5184.2.d.g.2593.3 | 4 | 9.4 | even | 3 | |||
5184.2.d.g.2593.4 | 4 | 36.31 | odd | 6 | |||
5184.2.d.h.2593.1 | 4 | 9.5 | odd | 6 | |||
5184.2.d.h.2593.2 | 4 | 36.23 | even | 6 | |||
5184.2.d.h.2593.3 | 4 | 72.5 | odd | 6 | |||
5184.2.d.h.2593.4 | 4 | 72.59 | even | 6 |