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 | 289.3 | ||
Root | \(1.40126 + 0.809017i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.289 |
Dual form | 1728.2.r.d.1441.3 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.93649 | + | 3.35410i | −0.731925 | + | 1.26773i | 0.224134 | + | 0.974558i | \(0.428045\pi\) |
−0.956059 | + | 0.293173i | \(0.905289\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35410 | − | 1.93649i | 0.930261 | − | 0.537086i | 0.0433666 | − | 0.999059i | \(-0.486192\pi\) |
0.886894 | + | 0.461973i | \(0.152858\pi\) | |||||||
\(14\) | 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 | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.93649 | + | 3.35410i | 0.403786 | + | 0.699379i | 0.994179 | − | 0.107737i | \(-0.0343606\pi\) |
−0.590393 | + | 0.807116i | \(0.701027\pi\) | |||||||
\(24\) | 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 | \(-0.450419\pi\) |
−0.777974 | + | 0.628296i | \(0.783753\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.93649 | − | 3.35410i | −0.347804 | − | 0.602414i | 0.638055 | − | 0.769991i | \(-0.279739\pi\) |
−0.985859 | + | 0.167576i | \(0.946406\pi\) | |||||||
\(32\) | 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 | 0.967486 | + | 0.252924i | \(0.0813924\pi\) |
−0.264704 | + | 0.964330i | \(0.585274\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.06218 | + | 3.50000i | 0.924473 | + | 0.533745i | 0.885059 | − | 0.465478i | \(-0.154118\pi\) |
0.0394140 | + | 0.999223i | \(0.487451\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.93649 | − | 3.35410i | 0.282466 | − | 0.489246i | −0.689525 | − | 0.724262i | \(-0.742181\pi\) |
0.971992 | + | 0.235016i | \(0.0755141\pi\) | |||||||
\(48\) | 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 | −0.321253 | − | 0.946993i | \(-0.604104\pi\) |
0.659494 | + | 0.751710i | \(0.270771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.0623 | − | 5.80948i | −1.28835 | − | 0.743827i | −0.309987 | − | 0.950741i | \(-0.600325\pi\) |
−0.978359 | + | 0.206914i | \(0.933658\pi\) | |||||||
\(62\) | 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 | 0.211604 | − | 0.977356i | \(-0.432131\pi\) |
0.952217 | + | 0.305424i | \(0.0987981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.74597 | −0.919277 | −0.459639 | − | 0.888106i | \(-0.652021\pi\) | ||||
−0.459639 | + | 0.888106i | \(0.652021\pi\) | |||||||
\(72\) | 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 | \(-0.763422\pi\) |
0.954157 | + | 0.299306i | \(0.0967550\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.59808 | − | 1.50000i | −0.285176 | − | 0.164646i | 0.350588 | − | 0.936530i | \(-0.385982\pi\) |
−0.635764 | + | 0.771883i | \(0.719315\pi\) | |||||||
\(84\) | 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 | −0.890292 | − | 0.455389i | \(-0.849500\pi\) |
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.35410 | + | 1.93649i | 0.333746 | + | 0.192688i | 0.657503 | − | 0.753452i | \(-0.271613\pi\) |
−0.323757 | + | 0.946140i | \(0.604946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.80948 | − | 10.0623i | −0.572425 | − | 0.991468i | −0.996316 | − | 0.0857555i | \(-0.972670\pi\) |
0.423892 | − | 0.905713i | \(-0.360664\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.00000i | 0.580042i | 0.957020 | + | 0.290021i | \(0.0936623\pi\) | ||||
−0.957020 | + | 0.290021i | \(0.906338\pi\) | |||||||
\(108\) | 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 | 0.927914 | − | 0.372794i | \(-0.121600\pi\) |
−0.786806 | + | 0.617200i | \(0.788267\pi\) | |||||||
\(114\) | 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 | \(-0.741223\pi\) | ||||
−0.687343 | + | 0.726333i | \(0.741223\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | − | 1.50000i | 0.226995 | − | 0.131056i | −0.382190 | − | 0.924084i | \(-0.624830\pi\) |
0.609185 | + | 0.793028i | \(0.291497\pi\) | |||||||
\(132\) | 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 | 0.0658609 | − | 0.997829i | \(-0.479021\pi\) |
0.831215 | − | 0.555952i | \(-0.187646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.866025 | − | 0.500000i | 0.0734553 | − | 0.0424094i | −0.462822 | − | 0.886451i | \(-0.653163\pi\) |
0.536278 | + | 0.844042i | \(0.319830\pi\) | |||||||
\(140\) | 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 | \(-0.508778\pi\) |
0.851909 | + | 0.523689i | \(0.175445\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.80948 | + | 10.0623i | −0.472768 | + | 0.818859i | −0.999514 | − | 0.0311639i | \(-0.990079\pi\) |
0.526746 | + | 0.850023i | \(0.323412\pi\) | |||||||
\(152\) | 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 | \(-0.716059\pi\) |
0.360149 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(158\) | 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 | \(-0.975042\pi\) | ||
0.996928 | − | 0.0783260i | \(-0.0249575\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.93649 | − | 3.35410i | −0.149850 | − | 0.259548i | 0.781322 | − | 0.624128i | \(-0.214546\pi\) |
−0.931172 | + | 0.364580i | \(0.881212\pi\) | |||||||
\(168\) | 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 | \(-0.0699781\pi\) |
0.299106 | + | 0.954220i | \(0.403311\pi\) | |||||||
\(174\) | 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 | \(0.234862\pi\) | ||||
−0.739923 | + | 0.672692i | \(0.765138\pi\) | |||||||
\(180\) | 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 | −0.321692 | + | 0.946844i | \(0.604252\pi\) |
−0.659145 | + | 0.752016i | \(0.729082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 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 | \(-0.588528\pi\) | ||||
−0.274549 | + | 0.961573i | \(0.588528\pi\) | |||||||
\(200\) | 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 | −0.529514 | − | 0.848301i | \(-0.677626\pi\) |
0.469894 | + | 0.882723i | \(0.344292\pi\) | |||||||
\(212\) | 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 | 0.0905425 | − | 0.995893i | \(-0.471140\pi\) |
0.817197 | − | 0.576358i | \(-0.195527\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −18.1865 | − | 10.5000i | −1.20708 | − | 0.696909i | −0.244962 | − | 0.969533i | \(-0.578775\pi\) |
−0.962121 | + | 0.272623i | \(0.912109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.35410 | + | 1.93649i | −0.221645 | + | 0.127967i | −0.606712 | − | 0.794922i | \(-0.707512\pi\) |
0.385067 | + | 0.922889i | \(0.374178\pi\) | |||||||
\(230\) | 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 | 0.988287 | + | 0.152608i | \(0.0487673\pi\) |
−0.361981 | + | 0.932186i | \(0.617899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | + | 9.52628i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948609\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(242\) | 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 | \(-0.939359\pi\) | ||
0.981908 | − | 0.189358i | \(-0.0606408\pi\) | |||||||
\(252\) | 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 | −0.981901 | − | 0.189396i | \(-0.939347\pi\) |
0.326929 | − | 0.945049i | \(-0.393986\pi\) | |||||||
\(258\) | 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 | \(-0.716715\pi\) |
0.987665 | + | 0.156583i | \(0.0500479\pi\) | |||||||
\(264\) | 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 | \(-0.530970\pi\) |
−0.910500 | + | 0.413508i | \(0.864303\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.5000 | + | 23.3827i | −0.805342 | + | 1.39489i | 0.110717 | + | 0.993852i | \(0.464685\pi\) |
−0.916060 | + | 0.401042i | \(0.868648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9186 | + | 11.5000i | −1.18404 | + | 0.683604i | −0.956945 | − | 0.290269i | \(-0.906255\pi\) |
−0.227092 | + | 0.973873i | \(0.572922\pi\) | |||||||
\(284\) | 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 | \(-0.957584\pi\) |
−0.380506 | + | 0.924778i | \(0.624250\pi\) | |||||||
\(294\) | 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 | \(-0.907885\pi\) | ||
0.958419 | − | 0.285365i | \(-0.0921148\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5554 | − | 23.4787i | −0.768659 | − | 1.33136i | −0.938290 | − | 0.345848i | \(-0.887591\pi\) |
0.169632 | − | 0.985507i | \(-0.445742\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.50000 | − | 14.7224i | 0.480448 | − | 0.832161i | −0.519300 | − | 0.854592i | \(-0.673807\pi\) |
0.999748 | + | 0.0224310i | \(0.00714060\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0623 | + | 5.80948i | 0.565155 | + | 0.326293i | 0.755212 | − | 0.655480i | \(-0.227534\pi\) |
−0.190057 | + | 0.981773i | \(0.560867\pi\) | |||||||
\(318\) | 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 | −0.0257885 | − | 0.999667i | \(-0.508210\pi\) |
−0.878632 | + | 0.477500i | \(0.841543\pi\) | |||||||
\(332\) | 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 | 0.926049 | − | 0.377403i | \(-0.123183\pi\) |
−0.789865 | + | 0.613280i | \(0.789850\pi\) | |||||||
\(338\) | 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 | −0.806363 | − | 0.591420i | \(-0.798567\pi\) |
0.109003 | + | 0.994041i | \(0.465234\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.7705 | − | 9.68246i | −0.897705 | − | 0.518290i | −0.0212500 | − | 0.999774i | \(-0.506765\pi\) |
−0.876455 | + | 0.481484i | \(0.840098\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.50000 | + | 2.59808i | −0.0798369 | + | 0.138282i | −0.903179 | − | 0.429263i | \(-0.858773\pi\) |
0.823343 | + | 0.567545i | \(0.192107\pi\) | |||||||
\(354\) | 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 | \(-0.804714\pi\) | ||||
−0.817633 | + | 0.575740i | \(0.804714\pi\) | |||||||
\(360\) | 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 | \(-0.931406\pi\) |
0.673619 | + | 0.739079i | \(0.264739\pi\) | |||||||
\(368\) | 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 | \(-0.634697\pi\) |
0.584315 | + | 0.811527i | \(0.301363\pi\) | |||||||
\(374\) | 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 | \(-0.865203\pi\) | ||
0.911666 | − | 0.410932i | \(-0.134797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.93649 | − | 3.35410i | −0.0989501 | − | 0.171387i | 0.812300 | − | 0.583240i | \(-0.198215\pi\) |
−0.911250 | + | 0.411853i | \(0.864882\pi\) | |||||||
\(384\) | 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 | \(-0.302030\pi\) |
−0.412554 | + | 0.910933i | \(0.635363\pi\) | |||||||
\(390\) | 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 | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 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 | −0.996701 | − | 0.0811615i | \(-0.974137\pi\) |
0.428063 | − | 0.903749i | \(-0.359196\pi\) | |||||||
\(410\) | 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 | 0.402179 | − | 0.915561i | \(-0.368253\pi\) |
0.993989 | + | 0.109483i | \(0.0349196\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.35410 | + | 1.93649i | 0.163469 | + | 0.0943788i | 0.579503 | − | 0.814970i | \(-0.303247\pi\) |
−0.416034 | + | 0.909349i | \(0.636580\pi\) | |||||||
\(422\) | 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 | \(-0.378291\pi\) | ||||
0.373110 | + | 0.927787i | \(0.378291\pi\) | |||||||
\(432\) | 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 | \(-0.922763\pi\) |
0.693434 | + | 0.720520i | \(0.256097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.9904 | − | 7.50000i | −0.617192 | − | 0.356336i | 0.158583 | − | 0.987346i | \(-0.449307\pi\) |
−0.775775 | + | 0.631010i | \(0.782641\pi\) | |||||||
\(444\) | 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 | 0.297217 | + | 0.954810i | \(0.403942\pi\) |
−0.975498 | + | 0.220008i | \(0.929392\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.1869 | − | 17.4284i | −1.40594 | − | 0.811723i | −0.410951 | − | 0.911657i | \(-0.634803\pi\) |
−0.994994 | + | 0.0999348i | \(0.968137\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.68246 | − | 16.7705i | −0.449982 | − | 0.779392i | 0.548402 | − | 0.836215i | \(-0.315236\pi\) |
−0.998384 | + | 0.0568230i | \(0.981903\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 6.00000i | − | 0.277647i | −0.990317 | − | 0.138823i | \(-0.955668\pi\) | ||
0.990317 | − | 0.138823i | \(-0.0443321\pi\) | |||||||
\(468\) | 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 | \(-0.747816\pi\) |
0.967679 | + | 0.252184i | \(0.0811489\pi\) | |||||||
\(480\) | 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 | \(-0.252288\pi\) | ||||
0.702007 | + | 0.712171i | \(0.252288\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.1865 | + | 10.5000i | −0.820747 | + | 0.473858i | −0.850674 | − | 0.525694i | \(-0.823806\pi\) |
0.0299272 | + | 0.999552i | \(0.490472\pi\) | |||||||
\(492\) | 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 | −0.629515 | − | 0.776989i | \(-0.716746\pi\) |
0.358134 | + | 0.933670i | \(0.383413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.74597 | 0.345376 | 0.172688 | − | 0.984977i | \(-0.444755\pi\) | ||||
0.172688 | + | 0.984977i | \(0.444755\pi\) | |||||||
\(504\) | 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 | \(-0.694022\pi\) |
0.423821 | + | 0.905746i | \(0.360689\pi\) | |||||||
\(510\) | 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 | \(0.0559627\pi\) | ||||
−0.984585 | + | 0.174908i | \(0.944037\pi\) | |||||||
\(524\) | 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 | 0.999771 | + | 0.0213785i | \(0.00680549\pi\) |
0.518400 | + | 0.855138i | \(0.326528\pi\) | |||||||
\(548\) | 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 | 0.242912 | − | 0.970048i | \(-0.421897\pi\) |
0.961542 | + | 0.274656i | \(0.0885641\pi\) | |||||||
\(564\) | 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 | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.5070 | + | 20.5000i | −1.48592 | + | 0.857898i | −0.999871 | − | 0.0160316i | \(-0.994897\pi\) |
−0.486052 | + | 0.873930i | \(0.661563\pi\) | |||||||
\(572\) | 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 | 0.989704 | + | 0.143132i | \(0.0457173\pi\) |
0.618808 | + | 0.785543i | \(0.287616\pi\) | |||||||
\(588\) | 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 | \(-0.296135\pi\) |
−0.993179 | + | 0.116596i | \(0.962802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.50000 | + | 14.7224i | −0.346722 | + | 0.600541i | −0.985665 | − | 0.168714i | \(-0.946039\pi\) |
0.638943 | + | 0.769254i | \(0.279372\pi\) | |||||||
\(602\) | 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 | −0.998260 | − | 0.0589688i | \(-0.981219\pi\) |
0.448061 | − | 0.894003i | \(-0.352115\pi\) | |||||||
\(608\) | 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 | −0.928975 | − | 0.370143i | \(-0.879309\pi\) |
0.143934 | − | 0.989587i | \(-0.454025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.7224 | + | 8.50000i | 0.591744 | + | 0.341644i | 0.765787 | − | 0.643094i | \(-0.222350\pi\) |
−0.174042 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(620\) | 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 | \(-0.599781\pi\) | ||||
−0.308362 | + | 0.951269i | \(0.599781\pi\) | |||||||
\(632\) | 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 | −0.995400 | − | 0.0958109i | \(-0.969456\pi\) |
0.580674 | + | 0.814136i | \(0.302789\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.06218 | − | 3.50000i | 0.239069 | − | 0.138027i | −0.375680 | − | 0.926750i | \(-0.622591\pi\) |
0.614749 | + | 0.788723i | \(0.289257\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.4919 | 0.609051 | 0.304525 | − | 0.952504i | \(-0.401502\pi\) | ||||
0.304525 | + | 0.952504i | \(0.401502\pi\) | |||||||
\(648\) | 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 | \(-0.739670\pi\) |
0.290023 | + | 0.957020i | \(0.406337\pi\) | |||||||
\(654\) | 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 | 0.880708 | − | 0.473660i | \(-0.157067\pi\) |
0.0301523 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0623 | − | 5.80948i | 0.391378 | − | 0.225962i | −0.291379 | − | 0.956608i | \(-0.594114\pi\) |
0.682757 | + | 0.730645i | \(0.260781\pi\) | |||||||
\(662\) | 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 | −0.302017 | − | 0.953302i | \(-0.597660\pi\) |
0.976593 | − | 0.215096i | \(-0.0690066\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.7705 | + | 9.68246i | 0.644543 | + | 0.372127i | 0.786362 | − | 0.617765i | \(-0.211962\pi\) |
−0.141819 | + | 0.989893i | \(0.545295\pi\) | |||||||
\(678\) | 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 | \(0.111909\pi\) | ||||
−0.938832 | + | 0.344375i | \(0.888091\pi\) | |||||||
\(684\) | 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 | 0.483437 | − | 0.875379i | \(-0.339388\pi\) |
−0.516382 | + | 0.856358i | \(0.672722\pi\) | |||||||
\(692\) | 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 | \(-0.356503\pi\) |
−0.561659 | + | 0.827369i | \(0.689837\pi\) | |||||||
\(710\) | 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 | \(-0.833717\pi\) | ||||
−0.866627 | + | 0.498956i | \(0.833717\pi\) | |||||||
\(720\) | 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 | −0.337595 | − | 0.941291i | \(-0.609614\pi\) |
0.983980 | − | 0.178279i | \(-0.0570531\pi\) | |||||||
\(728\) | 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 | \(-0.643880\pi\) |
0.560663 | + | 0.828044i | \(0.310546\pi\) | |||||||
\(734\) | 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 | \(0.200309\pi\) | ||||
−0.808447 | + | 0.588570i | \(0.799691\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −25.1744 | − | 43.6033i | −0.923559 | − | 1.59965i | −0.793863 | − | 0.608097i | \(-0.791933\pi\) |
−0.129696 | − | 0.991554i | \(-0.541400\pi\) | |||||||
\(744\) | 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 | \(-0.331369\pi\) |
−0.999981 | + | 0.00617232i | \(0.998035\pi\) | |||||||
\(752\) | 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 | 0.991152 | − | 0.132734i | \(-0.0423756\pi\) |
−0.610527 | + | 0.791995i | \(0.709042\pi\) | |||||||
\(762\) | 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 | 0.580696 | − | 0.814120i | \(-0.302780\pi\) |
−0.995397 | + | 0.0958377i | \(0.969447\pi\) | |||||||
\(770\) | 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 | −0.0617409 | − | 0.998092i | \(-0.519665\pi\) |
0.833503 | + | 0.552515i | \(0.186332\pi\) | |||||||
\(788\) | 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 | \(-0.778100\pi\) |
0.172652 | + | 0.984983i | \(0.444766\pi\) | |||||||
\(798\) | 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 | \(-0.796379\pi\) | ||
0.802278 | − | 0.596951i | \(-0.203621\pi\) | |||||||
\(812\) | 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 | \(-0.0665337\pi\) |
0.309414 | + | 0.950927i | \(0.399867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.93649 | − | 3.35410i | −0.0675019 | − | 0.116917i | 0.830299 | − | 0.557318i | \(-0.188170\pi\) |
−0.897801 | + | 0.440401i | \(0.854836\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.00000i | 0.208640i | 0.994544 | + | 0.104320i | \(0.0332667\pi\) | ||||
−0.994544 | + | 0.104320i | \(0.966733\pi\) | |||||||
\(828\) | 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 | 0.00621569 | − | 0.999981i | \(-0.498021\pi\) |
0.862901 | − | 0.505373i | \(-0.168645\pi\) | |||||||
\(840\) | 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 | \(-0.397074\pi\) |
−0.662272 | + | 0.749263i | \(0.730408\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5000 | − | 18.1865i | 0.358673 | − | 0.621240i | −0.629066 | − | 0.777352i | \(-0.716563\pi\) |
0.987739 | + | 0.156112i | \(0.0498959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.2583 | + | 6.50000i | −0.384129 | + | 0.221777i | −0.679613 | − | 0.733571i | \(-0.737852\pi\) |
0.295484 | + | 0.955348i | \(0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.4919 | 0.527352 | 0.263676 | − | 0.964611i | \(-0.415065\pi\) | ||||
0.263676 | + | 0.964611i | \(0.415065\pi\) | |||||||
\(864\) | 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 | \(-0.818006\pi\) |
0.0481345 | + | 0.998841i | \(0.484672\pi\) | |||||||
\(878\) | 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 | \(-0.681781\pi\) | ||
0.540542 | − | 0.841317i | \(-0.318219\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 17.4284 | + | 30.1869i | 0.585189 | + | 1.01358i | 0.994852 | + | 0.101340i | \(0.0323131\pi\) |
−0.409663 | + | 0.912237i | \(0.634354\pi\) | |||||||
\(888\) | 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 | 0.747653 | − | 0.664089i | \(-0.231180\pi\) |
−0.201291 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.68246 | + | 16.7705i | −0.320794 | + | 0.555632i | −0.980652 | − | 0.195759i | \(-0.937283\pi\) |
0.659858 | + | 0.751390i | \(0.270616\pi\) | |||||||
\(912\) | 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 | \(-0.778027\pi\) | ||||
−0.766548 | + | 0.642188i | \(0.778027\pi\) | |||||||
\(920\) | 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 | 0.345708 | + | 0.938342i | \(0.387639\pi\) |
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(930\) | 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 | \(-0.646559\pi\) |
0.553673 | + | 0.832734i | \(0.313226\pi\) | |||||||
\(942\) | 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 | 0.997514 | − | 0.0704677i | \(-0.0224492\pi\) |
0.437730 | + | 0.899106i | \(0.355783\pi\) | |||||||
\(948\) | 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 | 0.776230 | + | 0.630450i | \(0.217130\pi\) |
0.157871 | + | 0.987460i | \(0.449537\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 24.0000i | − | 0.770197i | −0.922876 | − | 0.385098i | \(-0.874168\pi\) | ||
0.922876 | − | 0.385098i | \(-0.125832\pi\) | |||||||
\(972\) | 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 | 0.785020 | − | 0.619471i | \(-0.212653\pi\) |
−0.928987 | + | 0.370111i | \(0.879319\pi\) | |||||||
\(978\) | 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 | 0.441954 | + | 0.897038i | \(0.354285\pi\) |
−0.997834 | + | 0.0657754i | \(0.979048\pi\) | |||||||
\(984\) | 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 | \(-0.235687\pi\) | ||||
0.738176 | + | 0.674608i | \(0.235687\pi\) | |||||||
\(992\) | 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 | 0.992721 | + | 0.120436i | \(0.0384292\pi\) |
0.600661 | + | 0.799504i | \(0.294904\pi\) | |||||||
\(998\) | 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.289.3 | 8 | ||
3.2 | odd | 2 | 576.2.r.d.97.1 | ✓ | 8 | ||
4.3 | odd | 2 | inner | 1728.2.r.d.289.4 | 8 | ||
8.3 | odd | 2 | inner | 1728.2.r.d.289.2 | 8 | ||
8.5 | even | 2 | inner | 1728.2.r.d.289.1 | 8 | ||
9.2 | odd | 6 | 5184.2.d.h.2593.2 | 4 | |||
9.4 | even | 3 | inner | 1728.2.r.d.1441.1 | 8 | ||
9.5 | odd | 6 | 576.2.r.d.481.4 | yes | 8 | ||
9.7 | even | 3 | 5184.2.d.g.2593.4 | 4 | |||
12.11 | even | 2 | 576.2.r.d.97.3 | yes | 8 | ||
24.5 | odd | 2 | 576.2.r.d.97.4 | yes | 8 | ||
24.11 | even | 2 | 576.2.r.d.97.2 | yes | 8 | ||
36.7 | odd | 6 | 5184.2.d.g.2593.3 | 4 | |||
36.11 | even | 6 | 5184.2.d.h.2593.1 | 4 | |||
36.23 | even | 6 | 576.2.r.d.481.2 | yes | 8 | ||
36.31 | odd | 6 | inner | 1728.2.r.d.1441.2 | 8 | ||
72.5 | odd | 6 | 576.2.r.d.481.1 | yes | 8 | ||
72.11 | even | 6 | 5184.2.d.h.2593.3 | 4 | |||
72.13 | even | 6 | inner | 1728.2.r.d.1441.3 | 8 | ||
72.29 | odd | 6 | 5184.2.d.h.2593.4 | 4 | |||
72.43 | odd | 6 | 5184.2.d.g.2593.1 | 4 | |||
72.59 | even | 6 | 576.2.r.d.481.3 | yes | 8 | ||
72.61 | even | 6 | 5184.2.d.g.2593.2 | 4 | |||
72.67 | odd | 6 | inner | 1728.2.r.d.1441.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
576.2.r.d.97.1 | ✓ | 8 | 3.2 | odd | 2 | ||
576.2.r.d.97.2 | yes | 8 | 24.11 | even | 2 | ||
576.2.r.d.97.3 | yes | 8 | 12.11 | even | 2 | ||
576.2.r.d.97.4 | yes | 8 | 24.5 | odd | 2 | ||
576.2.r.d.481.1 | yes | 8 | 72.5 | odd | 6 | ||
576.2.r.d.481.2 | yes | 8 | 36.23 | even | 6 | ||
576.2.r.d.481.3 | yes | 8 | 72.59 | even | 6 | ||
576.2.r.d.481.4 | yes | 8 | 9.5 | odd | 6 | ||
1728.2.r.d.289.1 | 8 | 8.5 | even | 2 | inner | ||
1728.2.r.d.289.2 | 8 | 8.3 | odd | 2 | inner | ||
1728.2.r.d.289.3 | 8 | 1.1 | even | 1 | trivial | ||
1728.2.r.d.289.4 | 8 | 4.3 | odd | 2 | inner | ||
1728.2.r.d.1441.1 | 8 | 9.4 | even | 3 | inner | ||
1728.2.r.d.1441.2 | 8 | 36.31 | odd | 6 | inner | ||
1728.2.r.d.1441.3 | 8 | 72.13 | even | 6 | inner | ||
1728.2.r.d.1441.4 | 8 | 72.67 | odd | 6 | inner | ||
5184.2.d.g.2593.1 | 4 | 72.43 | odd | 6 | |||
5184.2.d.g.2593.2 | 4 | 72.61 | even | 6 | |||
5184.2.d.g.2593.3 | 4 | 36.7 | odd | 6 | |||
5184.2.d.g.2593.4 | 4 | 9.7 | even | 3 | |||
5184.2.d.h.2593.1 | 4 | 36.11 | even | 6 | |||
5184.2.d.h.2593.2 | 4 | 9.2 | odd | 6 | |||
5184.2.d.h.2593.3 | 4 | 72.11 | even | 6 | |||
5184.2.d.h.2593.4 | 4 | 72.29 | odd | 6 |