Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(181,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.181");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.b (of order \(2\), degree \(1\), 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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 181.4 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.181 |
Dual form | 1170.2.b.f.181.1 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.12311i | 1.18042i | 0.807249 | + | 0.590211i | \(0.200956\pi\) | ||||
−0.807249 | + | 0.590211i | \(0.799044\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | − | 5.12311i | − | 1.54467i | −0.635213 | − | 0.772337i | \(-0.719088\pi\) | ||
0.635213 | − | 0.772337i | \(-0.280912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56155 | − | 0.561553i | 0.987797 | − | 0.155747i | ||||
\(14\) | −3.12311 | −0.834685 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.12311 | 1.09225 | ||||||||
\(23\) | 5.12311 | 1.06824 | 0.534121 | − | 0.845408i | \(-0.320643\pi\) | ||||
0.534121 | + | 0.845408i | \(0.320643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0.561553 | + | 3.56155i | 0.110130 | + | 0.698478i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 3.12311i | − | 0.590211i | ||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.12311i | 0.560926i | 0.959865 | + | 0.280463i | \(0.0904881\pi\) | ||||
−0.959865 | + | 0.280463i | \(0.909512\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.00000i | − | 0.342997i | ||||||
\(35\) | 3.12311 | 0.527901 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.12311i | − | 0.842233i | −0.907006 | − | 0.421117i | \(-0.861638\pi\) | ||
0.907006 | − | 0.421117i | \(-0.138362\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | − | 0.876894i | − | 0.136948i | −0.997653 | − | 0.0684739i | \(-0.978187\pi\) | ||
0.997653 | − | 0.0684739i | \(-0.0218130\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.24621 | 0.952538 | 0.476269 | − | 0.879300i | \(-0.341989\pi\) | ||||
0.476269 | + | 0.879300i | \(0.341989\pi\) | |||||||
\(44\) | 5.12311i | 0.772337i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.12311i | 0.755361i | ||||||||
\(47\) | 6.24621i | 0.911104i | 0.890209 | + | 0.455552i | \(0.150558\pi\) | ||||
−0.890209 | + | 0.455552i | \(0.849442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.75379 | −0.393398 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.56155 | + | 0.561553i | −0.493899 | + | 0.0778734i | ||||
\(53\) | 13.3693 | 1.83642 | 0.918208 | − | 0.396098i | \(-0.129636\pi\) | ||||
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.12311 | −0.690799 | ||||||||
\(56\) | 3.12311 | 0.417343 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 1.12311i | 0.146216i | 0.997324 | + | 0.0731079i | \(0.0232918\pi\) | ||||
−0.997324 | + | 0.0731079i | \(0.976708\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | −3.12311 | −0.396635 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.561553 | − | 3.56155i | −0.0696521 | − | 0.441756i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.87689i | 0.595807i | 0.954596 | + | 0.297904i | \(0.0962874\pi\) | ||||
−0.954596 | + | 0.297904i | \(0.903713\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.12311i | 0.373283i | ||||||||
\(71\) | − | 10.2462i | − | 1.21600i | −0.793936 | − | 0.608001i | \(-0.791972\pi\) | ||
0.793936 | − | 0.608001i | \(-0.208028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13.1231i | − | 1.53594i | −0.640484 | − | 0.767972i | \(-0.721266\pi\) | ||
0.640484 | − | 0.767972i | \(-0.278734\pi\) | |||||||
\(74\) | 5.12311 | 0.595549 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000i | 0.688247i | ||||||||
\(77\) | 16.0000 | 1.82337 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.876894 | 0.0968368 | ||||||||
\(83\) | 6.24621i | 0.685611i | 0.939406 | + | 0.342805i | \(0.111377\pi\) | ||||
−0.939406 | + | 0.342805i | \(0.888623\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.00000i | 0.216930i | ||||||||
\(86\) | 6.24621i | 0.673546i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.12311 | −0.546125 | ||||||||
\(89\) | − | 3.12311i | − | 0.331049i | −0.986206 | − | 0.165524i | \(-0.947068\pi\) | ||
0.986206 | − | 0.165524i | \(-0.0529316\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.75379 | + | 11.1231i | 0.183847 | + | 1.16602i | ||||
\(92\) | −5.12311 | −0.534121 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.24621 | −0.644247 | ||||||||
\(95\) | −6.00000 | −0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.1231i | − | 1.33245i | −0.745751 | − | 0.666225i | \(-0.767909\pi\) | ||
0.745751 | − | 0.666225i | \(-0.232091\pi\) | |||||||
\(98\) | − | 2.75379i | − | 0.278175i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 12.2462 | 1.21854 | 0.609272 | − | 0.792961i | \(-0.291462\pi\) | ||||
0.609272 | + | 0.792961i | \(0.291462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.1231 | −1.29306 | −0.646529 | − | 0.762889i | \(-0.723780\pi\) | ||||
−0.646529 | + | 0.762889i | \(0.723780\pi\) | |||||||
\(104\) | −0.561553 | − | 3.56155i | −0.0550648 | − | 0.349239i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.3693i | 1.29854i | ||||||||
\(107\) | 8.00000 | 0.773389 | 0.386695 | − | 0.922208i | \(-0.373617\pi\) | ||||
0.386695 | + | 0.922208i | \(0.373617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.87689i | 0.275557i | 0.990463 | + | 0.137778i | \(0.0439961\pi\) | ||||
−0.990463 | + | 0.137778i | \(0.956004\pi\) | |||||||
\(110\) | − | 5.12311i | − | 0.488469i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.12311i | 0.295106i | ||||||||
\(113\) | −12.2462 | −1.15203 | −0.576013 | − | 0.817440i | \(-0.695392\pi\) | ||||
−0.576013 | + | 0.817440i | \(0.695392\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 5.12311i | − | 0.477732i | ||||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.12311 | −0.103390 | ||||||||
\(119\) | − | 6.24621i | − | 0.572589i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −15.2462 | −1.38602 | ||||||||
\(122\) | 10.0000i | 0.905357i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 3.12311i | − | 0.280463i | ||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1231 | −1.16449 | −0.582244 | − | 0.813014i | \(-0.697825\pi\) | ||||
−0.582244 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.56155 | − | 0.561553i | 0.312369 | − | 0.0492514i | ||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.7386 | 1.62485 | ||||||||
\(134\) | −4.87689 | −0.421300 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000i | 0.171499i | ||||||||
\(137\) | 10.4924i | 0.896428i | 0.893926 | + | 0.448214i | \(0.147940\pi\) | ||||
−0.893926 | + | 0.448214i | \(0.852060\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4924 | −1.39887 | −0.699435 | − | 0.714697i | \(-0.746565\pi\) | ||||
−0.699435 | + | 0.714697i | \(0.746565\pi\) | |||||||
\(140\) | −3.12311 | −0.263951 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.2462 | 0.859843 | ||||||||
\(143\) | −2.87689 | − | 18.2462i | −0.240578 | − | 1.52582i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000i | 0.166091i | ||||||||
\(146\) | 13.1231 | 1.08608 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.12311i | 0.421117i | ||||||||
\(149\) | 14.0000i | 1.14692i | 0.819232 | + | 0.573462i | \(0.194400\pi\) | ||||
−0.819232 | + | 0.573462i | \(0.805600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.3693i | 1.08798i | 0.839092 | + | 0.543990i | \(0.183087\pi\) | ||||
−0.839092 | + | 0.543990i | \(0.816913\pi\) | |||||||
\(152\) | −6.00000 | −0.486664 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 16.0000i | 1.28932i | ||||||||
\(155\) | 3.12311 | 0.250854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.3693 | 1.70546 | 0.852729 | − | 0.522354i | \(-0.174946\pi\) | ||||
0.852729 | + | 0.522354i | \(0.174946\pi\) | |||||||
\(158\) | 8.00000i | 0.636446i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 16.0000i | 1.26098i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 7.12311i | − | 0.557925i | −0.960302 | − | 0.278962i | \(-0.910010\pi\) | ||
0.960302 | − | 0.278962i | \(-0.0899905\pi\) | |||||||
\(164\) | 0.876894i | 0.0684739i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.24621 | −0.484800 | ||||||||
\(167\) | 22.2462i | 1.72146i | 0.509059 | + | 0.860732i | \(0.329994\pi\) | ||||
−0.509059 | + | 0.860732i | \(0.670006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.3693 | − | 4.00000i | 0.951486 | − | 0.307692i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.24621 | −0.476269 | ||||||||
\(173\) | −23.1231 | −1.75802 | −0.879009 | − | 0.476806i | \(-0.841794\pi\) | ||||
−0.879009 | + | 0.476806i | \(0.841794\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.12311i | − | 0.236085i | ||||||
\(176\) | − | 5.12311i | − | 0.386169i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.12311 | 0.234087 | ||||||||
\(179\) | −16.4924 | −1.23270 | −0.616351 | − | 0.787472i | \(-0.711390\pi\) | ||||
−0.616351 | + | 0.787472i | \(0.711390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.2462 | −1.50489 | −0.752445 | − | 0.658656i | \(-0.771125\pi\) | ||||
−0.752445 | + | 0.658656i | \(0.771125\pi\) | |||||||
\(182\) | −11.1231 | + | 1.75379i | −0.824499 | + | 0.129999i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5.12311i | − | 0.377680i | ||||||
\(185\) | −5.12311 | −0.376658 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.2462i | 0.749277i | ||||||||
\(188\) | − | 6.24621i | − | 0.455552i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 6.00000i | − | 0.435286i | ||||||
\(191\) | −16.4924 | −1.19335 | −0.596675 | − | 0.802483i | \(-0.703512\pi\) | ||||
−0.596675 | + | 0.802483i | \(0.703512\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 25.1231i | − | 1.80840i | −0.427109 | − | 0.904200i | \(-0.640468\pi\) | ||
0.427109 | − | 0.904200i | \(-0.359532\pi\) | |||||||
\(194\) | 13.1231 | 0.942184 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.75379 | 0.196699 | ||||||||
\(197\) | − | 16.2462i | − | 1.15749i | −0.815507 | − | 0.578747i | \(-0.803542\pi\) | ||
0.815507 | − | 0.578747i | \(-0.196458\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2462 | 1.29344 | 0.646720 | − | 0.762728i | \(-0.276140\pi\) | ||||
0.646720 | + | 0.762728i | \(0.276140\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.2462i | 0.861640i | ||||||||
\(203\) | − | 6.24621i | − | 0.438398i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.876894 | −0.0612450 | ||||||||
\(206\) | − | 13.1231i | − | 0.914330i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.56155 | − | 0.561553i | 0.246949 | − | 0.0389367i | ||||
\(209\) | −30.7386 | −2.12624 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | −13.3693 | −0.918208 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.00000i | 0.546869i | ||||||||
\(215\) | − | 6.24621i | − | 0.425988i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.75379 | −0.662130 | ||||||||
\(218\) | −2.87689 | −0.194848 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.12311 | 0.345400 | ||||||||
\(221\) | −7.12311 | + | 1.12311i | −0.479152 | + | 0.0755483i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.36932i | 0.627416i | 0.949520 | + | 0.313708i | \(0.101571\pi\) | ||||
−0.949520 | + | 0.313708i | \(0.898429\pi\) | |||||||
\(224\) | −3.12311 | −0.208671 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 12.2462i | − | 0.814606i | ||||||
\(227\) | − | 8.00000i | − | 0.530979i | −0.964114 | − | 0.265489i | \(-0.914466\pi\) | ||
0.964114 | − | 0.265489i | \(-0.0855335\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 5.12311i | − | 0.338544i | −0.985569 | − | 0.169272i | \(-0.945858\pi\) | ||
0.985569 | − | 0.169272i | \(-0.0541417\pi\) | |||||||
\(230\) | 5.12311 | 0.337808 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | 7.75379 | 0.507968 | 0.253984 | − | 0.967208i | \(-0.418259\pi\) | ||||
0.253984 | + | 0.967208i | \(0.418259\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.24621 | 0.407458 | ||||||||
\(236\) | − | 1.12311i | − | 0.0731079i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.24621 | 0.404882 | ||||||||
\(239\) | − | 4.49242i | − | 0.290591i | −0.989388 | − | 0.145295i | \(-0.953587\pi\) | ||
0.989388 | − | 0.145295i | \(-0.0464132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 14.2462i | − | 0.917679i | −0.888519 | − | 0.458840i | \(-0.848265\pi\) | ||
0.888519 | − | 0.458840i | \(-0.151735\pi\) | |||||||
\(242\) | − | 15.2462i | − | 0.980064i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.0000 | −0.640184 | ||||||||
\(245\) | 2.75379i | 0.175933i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.36932 | − | 21.3693i | −0.214384 | − | 1.35970i | ||||
\(248\) | 3.12311 | 0.198317 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −26.2462 | −1.65665 | −0.828323 | − | 0.560251i | \(-0.810705\pi\) | ||||
−0.828323 | + | 0.560251i | \(0.810705\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 26.2462i | − | 1.65009i | ||||||
\(254\) | − | 13.1231i | − | 0.823417i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.2462 | 0.763898 | 0.381949 | − | 0.924183i | \(-0.375253\pi\) | ||||
0.381949 | + | 0.924183i | \(0.375253\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | 0.994192 | ||||||||
\(260\) | 0.561553 | + | 3.56155i | 0.0348260 | + | 0.220878i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 4.00000i | − | 0.247121i | ||||||
\(263\) | 27.3693 | 1.68766 | 0.843832 | − | 0.536607i | \(-0.180294\pi\) | ||||
0.843832 | + | 0.536607i | \(0.180294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 13.3693i | − | 0.821271i | ||||||
\(266\) | 18.7386i | 1.14894i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.87689i | − | 0.297904i | ||||||
\(269\) | 16.2462 | 0.990549 | 0.495274 | − | 0.868737i | \(-0.335067\pi\) | ||||
0.495274 | + | 0.868737i | \(0.335067\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.1231i | 1.40463i | 0.711867 | + | 0.702314i | \(0.247850\pi\) | ||||
−0.711867 | + | 0.702314i | \(0.752150\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.4924 | −0.633870 | ||||||||
\(275\) | 5.12311i | 0.308935i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −29.8617 | −1.79422 | −0.897109 | − | 0.441809i | \(-0.854337\pi\) | ||||
−0.897109 | + | 0.441809i | \(0.854337\pi\) | |||||||
\(278\) | − | 16.4924i | − | 0.989150i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 3.12311i | − | 0.186641i | ||||||
\(281\) | 3.12311i | 0.186309i | 0.995652 | + | 0.0931544i | \(0.0296950\pi\) | ||||
−0.995652 | + | 0.0931544i | \(0.970305\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 10.2462i | 0.608001i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.2462 | − | 2.87689i | 1.07892 | − | 0.170114i | ||||
\(287\) | 2.73863 | 0.161656 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −2.00000 | −0.117444 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.1231i | 0.767972i | ||||||||
\(293\) | − | 28.7386i | − | 1.67893i | −0.543415 | − | 0.839464i | \(-0.682869\pi\) | ||
0.543415 | − | 0.839464i | \(-0.317131\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.12311 | 0.0653897 | ||||||||
\(296\) | −5.12311 | −0.297774 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −14.0000 | −0.810998 | ||||||||
\(299\) | 18.2462 | − | 2.87689i | 1.05521 | − | 0.166375i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 19.5076i | 1.12440i | ||||||||
\(302\) | −13.3693 | −0.769318 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.00000i | − | 0.344124i | ||||||
\(305\) | − | 10.0000i | − | 0.572598i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.1231i | 1.77629i | 0.459564 | + | 0.888145i | \(0.348006\pi\) | ||||
−0.459564 | + | 0.888145i | \(0.651994\pi\) | |||||||
\(308\) | −16.0000 | −0.911685 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.12311i | 0.177380i | ||||||||
\(311\) | −8.49242 | −0.481561 | −0.240781 | − | 0.970580i | \(-0.577403\pi\) | ||||
−0.240781 | + | 0.970580i | \(0.577403\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.2462 | 0.918290 | 0.459145 | − | 0.888361i | \(-0.348156\pi\) | ||||
0.459145 | + | 0.888361i | \(0.348156\pi\) | |||||||
\(314\) | 21.3693i | 1.20594i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.2462i | 0.573678i | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −16.0000 | −0.891645 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.56155 | + | 0.561553i | −0.197559 | + | 0.0311493i | ||||
\(326\) | 7.12311 | 0.394512 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.876894 | −0.0484184 | ||||||||
\(329\) | −19.5076 | −1.07549 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.75379i | − | 0.426187i | −0.977032 | − | 0.213093i | \(-0.931646\pi\) | ||
0.977032 | − | 0.213093i | \(-0.0683539\pi\) | |||||||
\(332\) | − | 6.24621i | − | 0.342805i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.2462 | −1.21726 | ||||||||
\(335\) | 4.87689 | 0.266453 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.00000 | 0.326841 | 0.163420 | − | 0.986557i | \(-0.447747\pi\) | ||||
0.163420 | + | 0.986557i | \(0.447747\pi\) | |||||||
\(338\) | 4.00000 | + | 12.3693i | 0.217571 | + | 0.672802i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 2.00000i | − | 0.108465i | ||||||
\(341\) | 16.0000 | 0.866449 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2614i | 0.716046i | ||||||||
\(344\) | − | 6.24621i | − | 0.336773i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 23.1231i | − | 1.24311i | ||||||
\(347\) | 14.2462 | 0.764777 | 0.382388 | − | 0.924002i | \(-0.375102\pi\) | ||||
0.382388 | + | 0.924002i | \(0.375102\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.3693i | 1.03682i | 0.855133 | + | 0.518408i | \(0.173475\pi\) | ||||
−0.855133 | + | 0.518408i | \(0.826525\pi\) | |||||||
\(350\) | 3.12311 | 0.166937 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.12311 | 0.273062 | ||||||||
\(353\) | 12.2462i | 0.651800i | 0.945404 | + | 0.325900i | \(0.105667\pi\) | ||||
−0.945404 | + | 0.325900i | \(0.894333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.2462 | −0.543812 | ||||||||
\(356\) | 3.12311i | 0.165524i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 16.4924i | − | 0.871652i | ||||||
\(359\) | − | 17.7538i | − | 0.937009i | −0.883461 | − | 0.468505i | \(-0.844793\pi\) | ||
0.883461 | − | 0.468505i | \(-0.155207\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | − | 20.2462i | − | 1.06412i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.75379 | − | 11.1231i | −0.0919235 | − | 0.583009i | ||||
\(365\) | −13.1231 | −0.686895 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.63068 | 0.450518 | 0.225259 | − | 0.974299i | \(-0.427677\pi\) | ||||
0.225259 | + | 0.974299i | \(0.427677\pi\) | |||||||
\(368\) | 5.12311 | 0.267060 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 5.12311i | − | 0.266338i | ||||||
\(371\) | 41.7538i | 2.16775i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.12311 | 0.368820 | 0.184410 | − | 0.982849i | \(-0.440963\pi\) | ||||
0.184410 | + | 0.982849i | \(0.440963\pi\) | |||||||
\(374\) | −10.2462 | −0.529819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.24621 | 0.322124 | ||||||||
\(377\) | −7.12311 | + | 1.12311i | −0.366859 | + | 0.0578429i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.00000i | − | 0.308199i | −0.988055 | − | 0.154100i | \(-0.950752\pi\) | ||
0.988055 | − | 0.154100i | \(-0.0492477\pi\) | |||||||
\(380\) | 6.00000 | 0.307794 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 16.4924i | − | 0.843826i | ||||||
\(383\) | − | 1.75379i | − | 0.0896144i | −0.998996 | − | 0.0448072i | \(-0.985733\pi\) | ||
0.998996 | − | 0.0448072i | \(-0.0142674\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 16.0000i | − | 0.815436i | ||||||
\(386\) | 25.1231 | 1.27873 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.1231i | 0.666225i | ||||||||
\(389\) | 0.246211 | 0.0124834 | 0.00624170 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624170 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2462 | −0.518173 | ||||||||
\(392\) | 2.75379i | 0.139087i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.2462 | 0.818472 | ||||||||
\(395\) | − | 8.00000i | − | 0.402524i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 15.3693i | − | 0.771364i | −0.922632 | − | 0.385682i | \(-0.873966\pi\) | ||
0.922632 | − | 0.385682i | \(-0.126034\pi\) | |||||||
\(398\) | 18.2462i | 0.914600i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 1.36932i | 0.0683804i | 0.999415 | + | 0.0341902i | \(0.0108852\pi\) | ||||
−0.999415 | + | 0.0341902i | \(0.989115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.75379 | + | 11.1231i | 0.0873624 | + | 0.554081i | ||||
\(404\) | −12.2462 | −0.609272 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.24621 | 0.309994 | ||||||||
\(407\) | −26.2462 | −1.30098 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.49242i | 0.419923i | 0.977710 | + | 0.209962i | \(0.0673339\pi\) | ||||
−0.977710 | + | 0.209962i | \(0.932666\pi\) | |||||||
\(410\) | − | 0.876894i | − | 0.0433067i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.1231 | 0.646529 | ||||||||
\(413\) | −3.50758 | −0.172597 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.24621 | 0.306614 | ||||||||
\(416\) | 0.561553 | + | 3.56155i | 0.0275324 | + | 0.174619i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 30.7386i | − | 1.50348i | ||||||
\(419\) | 28.0000 | 1.36789 | 0.683945 | − | 0.729534i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729534i | \(0.260263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 0.630683i | − | 0.0307376i | −0.999882 | − | 0.0153688i | \(-0.995108\pi\) | ||
0.999882 | − | 0.0153688i | \(-0.00489224\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 13.3693i | − | 0.649271i | ||||||
\(425\) | 2.00000 | 0.0970143 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.2311i | 1.51138i | ||||||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.24621 | 0.301219 | ||||||||
\(431\) | 32.4924i | 1.56510i | 0.622585 | + | 0.782552i | \(0.286083\pi\) | ||||
−0.622585 | + | 0.782552i | \(0.713917\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.0000 | −0.865025 | −0.432512 | − | 0.901628i | \(-0.642373\pi\) | ||||
−0.432512 | + | 0.901628i | \(0.642373\pi\) | |||||||
\(434\) | − | 9.75379i | − | 0.468197i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 2.87689i | − | 0.137778i | ||||||
\(437\) | − | 30.7386i | − | 1.47043i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −36.4924 | −1.74169 | −0.870844 | − | 0.491559i | \(-0.836427\pi\) | ||||
−0.870844 | + | 0.491559i | \(0.836427\pi\) | |||||||
\(440\) | 5.12311i | 0.244234i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.12311 | − | 7.12311i | −0.0534207 | − | 0.338812i | ||||
\(443\) | 3.50758 | 0.166650 | 0.0833250 | − | 0.996522i | \(-0.473446\pi\) | ||||
0.0833250 | + | 0.996522i | \(0.473446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.12311 | −0.148049 | ||||||||
\(446\) | −9.36932 | −0.443650 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 3.12311i | − | 0.147553i | ||||||
\(449\) | 28.8769i | 1.36278i | 0.731918 | + | 0.681392i | \(0.238625\pi\) | ||||
−0.731918 | + | 0.681392i | \(0.761375\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.49242 | −0.211540 | ||||||||
\(452\) | 12.2462 | 0.576013 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.00000 | 0.375459 | ||||||||
\(455\) | 11.1231 | − | 1.75379i | 0.521459 | − | 0.0822189i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 31.3693i | 1.46739i | 0.679476 | + | 0.733697i | \(0.262207\pi\) | ||||
−0.679476 | + | 0.733697i | \(0.737793\pi\) | |||||||
\(458\) | 5.12311 | 0.239387 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.12311i | 0.238866i | ||||||||
\(461\) | − | 18.4924i | − | 0.861278i | −0.902524 | − | 0.430639i | \(-0.858288\pi\) | ||
0.902524 | − | 0.430639i | \(-0.141712\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.8617i | − | 1.01600i | −0.861357 | − | 0.508001i | \(-0.830385\pi\) | ||
0.861357 | − | 0.508001i | \(-0.169615\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.75379i | 0.359187i | ||||||||
\(467\) | 22.2462 | 1.02943 | 0.514716 | − | 0.857361i | \(-0.327897\pi\) | ||||
0.514716 | + | 0.857361i | \(0.327897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.2311 | −0.703305 | ||||||||
\(470\) | 6.24621i | 0.288116i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.12311 | 0.0516951 | ||||||||
\(473\) | − | 32.0000i | − | 1.47136i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000i | 0.275299i | ||||||||
\(476\) | 6.24621i | 0.286295i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.49242 | 0.205479 | ||||||||
\(479\) | 12.4924i | 0.570793i | 0.958409 | + | 0.285397i | \(0.0921253\pi\) | ||||
−0.958409 | + | 0.285397i | \(0.907875\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.87689 | − | 18.2462i | −0.131175 | − | 0.831956i | ||||
\(482\) | 14.2462 | 0.648897 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 15.2462 | 0.693010 | ||||||||
\(485\) | −13.1231 | −0.595890 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3693i | 0.787079i | 0.919308 | + | 0.393539i | \(0.128750\pi\) | ||||
−0.919308 | + | 0.393539i | \(0.871250\pi\) | |||||||
\(488\) | − | 10.0000i | − | 0.452679i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.75379 | −0.124403 | ||||||||
\(491\) | −38.7386 | −1.74825 | −0.874125 | − | 0.485701i | \(-0.838564\pi\) | ||||
−0.874125 | + | 0.485701i | \(0.838564\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.00000 | 0.180151 | ||||||||
\(494\) | 21.3693 | − | 3.36932i | 0.961451 | − | 0.151593i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.12311i | 0.140232i | ||||||||
\(497\) | 32.0000 | 1.43540 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 34.4924i | 1.54409i | 0.635566 | + | 0.772046i | \(0.280767\pi\) | ||||
−0.635566 | + | 0.772046i | \(0.719233\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 26.2462i | − | 1.17143i | ||||||
\(503\) | −35.3693 | −1.57704 | −0.788520 | − | 0.615009i | \(-0.789152\pi\) | ||||
−0.788520 | + | 0.615009i | \(0.789152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.2462i | − | 0.544949i | ||||||
\(506\) | 26.2462 | 1.16679 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.1231 | 0.582244 | ||||||||
\(509\) | − | 32.2462i | − | 1.42929i | −0.699488 | − | 0.714644i | \(-0.746589\pi\) | ||
0.699488 | − | 0.714644i | \(-0.253411\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.9848 | 1.81306 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 12.2462i | 0.540157i | ||||||||
\(515\) | 13.1231i | 0.578273i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.0000 | 1.40736 | ||||||||
\(518\) | 16.0000i | 0.703000i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.56155 | + | 0.561553i | −0.156184 | + | 0.0246257i | ||||
\(521\) | −0.246211 | −0.0107867 | −0.00539336 | − | 0.999985i | \(-0.501717\pi\) | ||||
−0.00539336 | + | 0.999985i | \(0.501717\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.7386 | −1.16920 | −0.584599 | − | 0.811322i | \(-0.698748\pi\) | ||||
−0.584599 | + | 0.811322i | \(0.698748\pi\) | |||||||
\(524\) | 4.00000 | 0.174741 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.3693i | 1.19336i | ||||||||
\(527\) | − | 6.24621i | − | 0.272089i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 13.3693 | 0.580726 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −18.7386 | −0.812423 | ||||||||
\(533\) | −0.492423 | − | 3.12311i | −0.0213292 | − | 0.135277i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 8.00000i | − | 0.345870i | ||||||
\(536\) | 4.87689 | 0.210650 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.2462i | 0.700424i | ||||||||
\(539\) | 14.1080i | 0.607672i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.8769i | 0.467634i | 0.972281 | + | 0.233817i | \(0.0751217\pi\) | ||||
−0.972281 | + | 0.233817i | \(0.924878\pi\) | |||||||
\(542\) | −23.1231 | −0.993222 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.00000i | − | 0.0857493i | ||||||
\(545\) | 2.87689 | 0.123233 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.9848 | 0.897247 | 0.448624 | − | 0.893721i | \(-0.351914\pi\) | ||||
0.448624 | + | 0.893721i | \(0.351914\pi\) | |||||||
\(548\) | − | 10.4924i | − | 0.448214i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.12311 | −0.218450 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.9848i | 1.06246i | ||||||||
\(554\) | − | 29.8617i | − | 1.26870i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.4924 | 0.699435 | ||||||||
\(557\) | − | 11.7538i | − | 0.498024i | −0.968500 | − | 0.249012i | \(-0.919894\pi\) | ||
0.968500 | − | 0.249012i | \(-0.0801059\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.2462 | − | 3.50758i | 0.940914 | − | 0.148355i | ||||
\(560\) | 3.12311 | 0.131975 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.12311 | −0.131740 | ||||||||
\(563\) | 32.9848 | 1.39015 | 0.695073 | − | 0.718939i | \(-0.255372\pi\) | ||||
0.695073 | + | 0.718939i | \(0.255372\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12.2462i | 0.515202i | ||||||||
\(566\) | − | 4.00000i | − | 0.168133i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.2462 | −0.429921 | ||||||||
\(569\) | 12.7386 | 0.534031 | 0.267016 | − | 0.963692i | \(-0.413962\pi\) | ||||
0.267016 | + | 0.963692i | \(0.413962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.49242 | −0.355397 | −0.177698 | − | 0.984085i | \(-0.556865\pi\) | ||||
−0.177698 | + | 0.984085i | \(0.556865\pi\) | |||||||
\(572\) | 2.87689 | + | 18.2462i | 0.120289 | + | 0.762912i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.73863i | 0.114308i | ||||||||
\(575\) | −5.12311 | −0.213648 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.3693i | 1.13940i | 0.821853 | + | 0.569700i | \(0.192941\pi\) | ||||
−0.821853 | + | 0.569700i | \(0.807059\pi\) | |||||||
\(578\) | − | 13.0000i | − | 0.540729i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.00000i | − | 0.0830455i | ||||||
\(581\) | −19.5076 | −0.809311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 68.4924i | − | 2.83667i | ||||||
\(584\) | −13.1231 | −0.543038 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.7386 | 1.18718 | ||||||||
\(587\) | 16.4924i | 0.680715i | 0.940296 | + | 0.340358i | \(0.110548\pi\) | ||||
−0.940296 | + | 0.340358i | \(0.889452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.7386 | 0.772112 | ||||||||
\(590\) | 1.12311i | 0.0462375i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 5.12311i | − | 0.210558i | ||||||
\(593\) | 5.50758i | 0.226169i | 0.993585 | + | 0.113085i | \(0.0360731\pi\) | ||||
−0.993585 | + | 0.113085i | \(0.963927\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.24621 | −0.256070 | ||||||||
\(596\) | − | 14.0000i | − | 0.573462i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.87689 | + | 18.2462i | 0.117645 | + | 0.746143i | ||||
\(599\) | 36.4924 | 1.49104 | 0.745520 | − | 0.666483i | \(-0.232201\pi\) | ||||
0.745520 | + | 0.666483i | \(0.232201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.0000 | 1.55005 | 0.775026 | − | 0.631929i | \(-0.217737\pi\) | ||||
0.775026 | + | 0.631929i | \(0.217737\pi\) | |||||||
\(602\) | −19.5076 | −0.795070 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 13.3693i | − | 0.543990i | ||||||
\(605\) | 15.2462i | 0.619847i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.3693 | 0.623821 | 0.311911 | − | 0.950111i | \(-0.399031\pi\) | ||||
0.311911 | + | 0.950111i | \(0.399031\pi\) | |||||||
\(608\) | 6.00000 | 0.243332 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 10.0000 | 0.404888 | ||||||||
\(611\) | 3.50758 | + | 22.2462i | 0.141901 | + | 0.899985i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3693i | 1.59011i | 0.606536 | + | 0.795056i | \(0.292559\pi\) | ||||
−0.606536 | + | 0.795056i | \(0.707441\pi\) | |||||||
\(614\) | −31.1231 | −1.25603 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 16.0000i | − | 0.644658i | ||||||
\(617\) | 40.7386i | 1.64008i | 0.572309 | + | 0.820038i | \(0.306048\pi\) | ||||
−0.572309 | + | 0.820038i | \(0.693952\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.9848i | 1.56693i | 0.621434 | + | 0.783467i | \(0.286550\pi\) | ||||
−0.621434 | + | 0.783467i | \(0.713450\pi\) | |||||||
\(620\) | −3.12311 | −0.125427 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 8.49242i | − | 0.340515i | ||||||
\(623\) | 9.75379 | 0.390777 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.2462i | 0.649329i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −21.3693 | −0.852729 | ||||||||
\(629\) | 10.2462i | 0.408543i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.6155i | − | 1.41783i | −0.705293 | − | 0.708916i | \(-0.749185\pi\) | ||
0.705293 | − | 0.708916i | \(-0.250815\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.00000 | 0.238290 | ||||||||
\(635\) | 13.1231i | 0.520775i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.80776 | + | 1.54640i | −0.388598 | + | 0.0612705i | ||||
\(638\) | −10.2462 | −0.405651 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 2.00000 | 0.0789953 | 0.0394976 | − | 0.999220i | \(-0.487424\pi\) | ||||
0.0394976 | + | 0.999220i | \(0.487424\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.3693i | 0.684979i | 0.939522 | + | 0.342489i | \(0.111270\pi\) | ||||
−0.939522 | + | 0.342489i | \(0.888730\pi\) | |||||||
\(644\) | − | 16.0000i | − | 0.630488i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | −29.6155 | −1.16431 | −0.582153 | − | 0.813079i | \(-0.697790\pi\) | ||||
−0.582153 | + | 0.813079i | \(0.697790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.75379 | 0.225856 | ||||||||
\(650\) | −0.561553 | − | 3.56155i | −0.0220259 | − | 0.139696i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.12311i | 0.278962i | ||||||||
\(653\) | 13.8617 | 0.542452 | 0.271226 | − | 0.962516i | \(-0.412571\pi\) | ||||
0.271226 | + | 0.962516i | \(0.412571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.00000i | 0.156293i | ||||||||
\(656\) | − | 0.876894i | − | 0.0342370i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 19.5076i | − | 0.760485i | ||||||
\(659\) | 21.7538 | 0.847407 | 0.423704 | − | 0.905801i | \(-0.360730\pi\) | ||||
0.423704 | + | 0.905801i | \(0.360730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.12311i | 0.354848i | 0.984135 | + | 0.177424i | \(0.0567763\pi\) | ||||
−0.984135 | + | 0.177424i | \(0.943224\pi\) | |||||||
\(662\) | 7.75379 | 0.301360 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.24621 | 0.242400 | ||||||||
\(665\) | − | 18.7386i | − | 0.726653i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −10.2462 | −0.396735 | ||||||||
\(668\) | − | 22.2462i | − | 0.860732i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.87689i | 0.188411i | ||||||||
\(671\) | − | 51.2311i | − | 1.97775i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.9848 | 1.04019 | 0.520095 | − | 0.854109i | \(-0.325897\pi\) | ||||
0.520095 | + | 0.854109i | \(0.325897\pi\) | |||||||
\(674\) | 6.00000i | 0.231111i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3693 | + | 4.00000i | −0.475743 | + | 0.153846i | ||||
\(677\) | −12.8769 | −0.494899 | −0.247450 | − | 0.968901i | \(-0.579592\pi\) | ||||
−0.247450 | + | 0.968901i | \(0.579592\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.9848 | 1.57285 | ||||||||
\(680\) | 2.00000 | 0.0766965 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.0000i | 0.612672i | ||||||||
\(683\) | 16.9848i | 0.649907i | 0.945730 | + | 0.324954i | \(0.105349\pi\) | ||||
−0.945730 | + | 0.324954i | \(0.894651\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.4924 | 0.400895 | ||||||||
\(686\) | −13.2614 | −0.506321 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.24621 | 0.238135 | ||||||||
\(689\) | 47.6155 | − | 7.50758i | 1.81401 | − | 0.286016i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.7386i | 1.09327i | 0.837371 | + | 0.546635i | \(0.184091\pi\) | ||||
−0.837371 | + | 0.546635i | \(0.815909\pi\) | |||||||
\(692\) | 23.1231 | 0.879009 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2462i | 0.540779i | ||||||||
\(695\) | 16.4924i | 0.625593i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.75379i | 0.0664295i | ||||||||
\(698\) | −19.3693 | −0.733139 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.12311i | 0.118042i | ||||||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.7386 | −1.15933 | ||||||||
\(704\) | 5.12311i | 0.193084i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −12.2462 | −0.460892 | ||||||||
\(707\) | 38.2462i | 1.43840i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.61553i | − | 0.0606724i | −0.999540 | − | 0.0303362i | \(-0.990342\pi\) | ||
0.999540 | − | 0.0303362i | \(-0.00965780\pi\) | |||||||
\(710\) | − | 10.2462i | − | 0.384533i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.12311 | −0.117043 | ||||||||
\(713\) | 16.0000i | 0.599205i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.2462 | + | 2.87689i | −0.682370 | + | 0.107590i | ||||
\(716\) | 16.4924 | 0.616351 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 17.7538 | 0.662566 | ||||||||
\(719\) | 20.0000 | 0.745874 | 0.372937 | − | 0.927857i | \(-0.378351\pi\) | ||||
0.372937 | + | 0.927857i | \(0.378351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 40.9848i | − | 1.52636i | ||||||
\(722\) | − | 17.0000i | − | 0.632674i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.2462 | 0.752445 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.8617 | 0.736631 | 0.368316 | − | 0.929701i | \(-0.379935\pi\) | ||||
0.368316 | + | 0.929701i | \(0.379935\pi\) | |||||||
\(728\) | 11.1231 | − | 1.75379i | 0.412250 | − | 0.0649997i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 13.1231i | − | 0.485708i | ||||||
\(731\) | −12.4924 | −0.462049 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.3693i | 1.30640i | 0.757187 | + | 0.653198i | \(0.226573\pi\) | ||||
−0.757187 | + | 0.653198i | \(0.773427\pi\) | |||||||
\(734\) | 8.63068i | 0.318564i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.12311i | 0.188840i | ||||||||
\(737\) | 24.9848 | 0.920329 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 37.2311i | − | 1.36957i | −0.728747 | − | 0.684783i | \(-0.759897\pi\) | ||
0.728747 | − | 0.684783i | \(-0.240103\pi\) | |||||||
\(740\) | 5.12311 | 0.188329 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −41.7538 | −1.53283 | ||||||||
\(743\) | 16.0000i | 0.586983i | 0.955962 | + | 0.293492i | \(0.0948173\pi\) | ||||
−0.955962 | + | 0.293492i | \(0.905183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0000 | 0.512920 | ||||||||
\(746\) | 7.12311i | 0.260795i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 10.2462i | − | 0.374639i | ||||||
\(749\) | 24.9848i | 0.912926i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.2462 | −0.957738 | −0.478869 | − | 0.877886i | \(-0.658953\pi\) | ||||
−0.478869 | + | 0.877886i | \(0.658953\pi\) | |||||||
\(752\) | 6.24621i | 0.227776i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.12311 | − | 7.12311i | −0.0409011 | − | 0.259408i | ||||
\(755\) | 13.3693 | 0.486559 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.12311 | −0.113511 | −0.0567556 | − | 0.998388i | \(-0.518076\pi\) | ||||
−0.0567556 | + | 0.998388i | \(0.518076\pi\) | |||||||
\(758\) | 6.00000 | 0.217930 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.00000i | 0.217643i | ||||||||
\(761\) | 3.12311i | 0.113212i | 0.998397 | + | 0.0566062i | \(0.0180280\pi\) | ||||
−0.998397 | + | 0.0566062i | \(0.981972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.98485 | −0.325273 | ||||||||
\(764\) | 16.4924 | 0.596675 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.75379 | 0.0633670 | ||||||||
\(767\) | 0.630683 | + | 4.00000i | 0.0227726 | + | 0.144432i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 32.9848i | − | 1.18946i | −0.803924 | − | 0.594732i | \(-0.797258\pi\) | ||
0.803924 | − | 0.594732i | \(-0.202742\pi\) | |||||||
\(770\) | 16.0000 | 0.576600 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 25.1231i | 0.904200i | ||||||||
\(773\) | 16.2462i | 0.584336i | 0.956367 | + | 0.292168i | \(0.0943766\pi\) | ||||
−0.956367 | + | 0.292168i | \(0.905623\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.12311i | − | 0.112185i | ||||||
\(776\) | −13.1231 | −0.471092 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.246211i | 0.00882710i | ||||||||
\(779\) | −5.26137 | −0.188508 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −52.4924 | −1.87833 | ||||||||
\(782\) | − | 10.2462i | − | 0.366404i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.75379 | −0.0983496 | ||||||||
\(785\) | − | 21.3693i | − | 0.762704i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.3845i | − | 0.441459i | −0.975335 | − | 0.220729i | \(-0.929156\pi\) | ||
0.975335 | − | 0.220729i | \(-0.0708438\pi\) | |||||||
\(788\) | 16.2462i | 0.578747i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 8.00000 | 0.284627 | ||||||||
\(791\) | − | 38.2462i | − | 1.35988i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 35.6155 | − | 5.61553i | 1.26474 | − | 0.199413i | ||||
\(794\) | 15.3693 | 0.545437 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.2462 | −0.646720 | ||||||||
\(797\) | −25.8617 | −0.916070 | −0.458035 | − | 0.888934i | \(-0.651447\pi\) | ||||
−0.458035 | + | 0.888934i | \(0.651447\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.4924i | − | 0.441950i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.36932 | −0.0483523 | ||||||||
\(803\) | −67.2311 | −2.37253 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.0000 | 0.563926 | ||||||||
\(806\) | −11.1231 | + | 1.75379i | −0.391795 | + | 0.0617746i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.2462i | − | 0.430820i | ||||||
\(809\) | 13.5076 | 0.474901 | 0.237451 | − | 0.971400i | \(-0.423688\pi\) | ||||
0.237451 | + | 0.971400i | \(0.423688\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.7538i | − | 0.974567i | −0.873244 | − | 0.487284i | \(-0.837988\pi\) | ||
0.873244 | − | 0.487284i | \(-0.162012\pi\) | |||||||
\(812\) | 6.24621i | 0.219199i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 26.2462i | − | 0.919929i | ||||||
\(815\) | −7.12311 | −0.249512 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 37.4773i | − | 1.31116i | ||||||
\(818\) | −8.49242 | −0.296931 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.876894 | 0.0306225 | ||||||||
\(821\) | − | 44.2462i | − | 1.54420i | −0.635499 | − | 0.772102i | \(-0.719206\pi\) | ||
0.635499 | − | 0.772102i | \(-0.280794\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.8769 | −1.49459 | −0.747297 | − | 0.664490i | \(-0.768649\pi\) | ||||
−0.747297 | + | 0.664490i | \(0.768649\pi\) | |||||||
\(824\) | 13.1231i | 0.457165i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 3.50758i | − | 0.122044i | ||||||
\(827\) | − | 1.26137i | − | 0.0438620i | −0.999759 | − | 0.0219310i | \(-0.993019\pi\) | ||
0.999759 | − | 0.0219310i | \(-0.00698141\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.2462 | −0.842106 | −0.421053 | − | 0.907036i | \(-0.638339\pi\) | ||||
−0.421053 | + | 0.907036i | \(0.638339\pi\) | |||||||
\(830\) | 6.24621i | 0.216809i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.56155 | + | 0.561553i | −0.123475 | + | 0.0194683i | ||||
\(833\) | 5.50758 | 0.190826 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.2462 | 0.769862 | ||||||||
\(836\) | 30.7386 | 1.06312 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.0000i | 0.967244i | ||||||||
\(839\) | 46.7386i | 1.61360i | 0.590827 | + | 0.806798i | \(0.298802\pi\) | ||||
−0.590827 | + | 0.806798i | \(0.701198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0.630683 | 0.0217348 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | −4.00000 | − | 12.3693i | −0.137604 | − | 0.425517i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 47.6155i | − | 1.63609i | ||||||
\(848\) | 13.3693 | 0.459104 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.00000i | 0.0685994i | ||||||||
\(851\) | − | 26.2462i | − | 0.899709i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.8617i | 1.22788i | 0.789352 | + | 0.613941i | \(0.210417\pi\) | ||||
−0.789352 | + | 0.613941i | \(0.789583\pi\) | |||||||
\(854\) | −31.2311 | −1.06870 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 8.00000i | − | 0.273434i | ||||||
\(857\) | 30.4924 | 1.04160 | 0.520801 | − | 0.853678i | \(-0.325633\pi\) | ||||
0.520801 | + | 0.853678i | \(0.325633\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | 6.24621i | 0.212994i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.4924 | −1.10670 | ||||||||
\(863\) | 6.24621i | 0.212624i | 0.994333 | + | 0.106312i | \(0.0339042\pi\) | ||||
−0.994333 | + | 0.106312i | \(0.966096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.1231i | 0.786209i | ||||||||
\(866\) | − | 18.0000i | − | 0.611665i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.75379 | 0.331065 | ||||||||
\(869\) | − | 40.9848i | − | 1.39032i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.73863 | + | 17.3693i | 0.0927951 | + | 0.588537i | ||||
\(872\) | 2.87689 | 0.0974239 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30.7386 | 1.03975 | ||||||||
\(875\) | −3.12311 | −0.105580 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 18.8769i | − | 0.637427i | −0.947851 | − | 0.318714i | \(-0.896749\pi\) | ||
0.947851 | − | 0.318714i | \(-0.103251\pi\) | |||||||
\(878\) | − | 36.4924i | − | 1.23156i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −5.12311 | −0.172700 | ||||||||
\(881\) | −28.2462 | −0.951639 | −0.475820 | − | 0.879543i | \(-0.657848\pi\) | ||||
−0.475820 | + | 0.879543i | \(0.657848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.75379 | −0.328241 | −0.164121 | − | 0.986440i | \(-0.552479\pi\) | ||||
−0.164121 | + | 0.986440i | \(0.552479\pi\) | |||||||
\(884\) | 7.12311 | − | 1.12311i | 0.239576 | − | 0.0377741i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.50758i | 0.117839i | ||||||||
\(887\) | 18.8769 | 0.633824 | 0.316912 | − | 0.948455i | \(-0.397354\pi\) | ||||
0.316912 | + | 0.948455i | \(0.397354\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 40.9848i | − | 1.37459i | ||||||
\(890\) | − | 3.12311i | − | 0.104687i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 9.36932i | − | 0.313708i | ||||||
\(893\) | 37.4773 | 1.25413 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.4924i | 0.551281i | ||||||||
\(896\) | 3.12311 | 0.104336 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.8769 | −0.963634 | ||||||||
\(899\) | − | 6.24621i | − | 0.208323i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.7386 | −0.890793 | ||||||||
\(902\) | − | 4.49242i | − | 0.149581i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.2462i | 0.407303i | ||||||||
\(905\) | 20.2462i | 0.673007i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.7538 | 0.855141 | 0.427570 | − | 0.903982i | \(-0.359370\pi\) | ||||
0.427570 | + | 0.903982i | \(0.359370\pi\) | |||||||
\(908\) | 8.00000i | 0.265489i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.75379 | + | 11.1231i | 0.0581375 | + | 0.368727i | ||||
\(911\) | −4.00000 | −0.132526 | −0.0662630 | − | 0.997802i | \(-0.521108\pi\) | ||||
−0.0662630 | + | 0.997802i | \(0.521108\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 32.0000 | 1.05905 | ||||||||
\(914\) | −31.3693 | −1.03760 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.12311i | 0.169272i | ||||||||
\(917\) | − | 12.4924i | − | 0.412536i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.7538 | −0.717591 | −0.358796 | − | 0.933416i | \(-0.616813\pi\) | ||||
−0.358796 | + | 0.933416i | \(0.616813\pi\) | |||||||
\(920\) | −5.12311 | −0.168904 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.4924 | 0.609016 | ||||||||
\(923\) | −5.75379 | − | 36.4924i | −0.189388 | − | 1.20116i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.12311i | 0.168447i | ||||||||
\(926\) | 21.8617 | 0.718421 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | − | 28.1080i | − | 0.922192i | −0.887350 | − | 0.461096i | \(-0.847456\pi\) | ||
0.887350 | − | 0.461096i | \(-0.152544\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.5227i | 0.541511i | ||||||||
\(932\) | −7.75379 | −0.253984 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 22.2462i | 0.727918i | ||||||||
\(935\) | 10.2462 | 0.335087 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.2462 | −0.661415 | −0.330707 | − | 0.943733i | \(-0.607287\pi\) | ||||
−0.330707 | + | 0.943733i | \(0.607287\pi\) | |||||||
\(938\) | − | 15.2311i | − | 0.497312i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.24621 | −0.203729 | ||||||||
\(941\) | 14.0000i | 0.456387i | 0.973616 | + | 0.228193i | \(0.0732819\pi\) | ||||
−0.973616 | + | 0.228193i | \(0.926718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.49242i | − | 0.146293i | ||||||
\(944\) | 1.12311i | 0.0365540i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 32.0000 | 1.04041 | ||||||||
\(947\) | − | 8.49242i | − | 0.275967i | −0.990435 | − | 0.137983i | \(-0.955938\pi\) | ||
0.990435 | − | 0.137983i | \(-0.0440620\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.36932 | − | 46.7386i | −0.239218 | − | 1.51720i | ||||
\(950\) | −6.00000 | −0.194666 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.24621 | −0.202441 | ||||||||
\(953\) | −22.9848 | −0.744552 | −0.372276 | − | 0.928122i | \(-0.621423\pi\) | ||||
−0.372276 | + | 0.928122i | \(0.621423\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.4924i | 0.533682i | ||||||||
\(956\) | 4.49242i | 0.145295i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.4924 | −0.403612 | ||||||||
\(959\) | −32.7689 | −1.05816 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.2462 | 0.685362 | ||||||||
\(962\) | 18.2462 | − | 2.87689i | 0.588281 | − | 0.0927548i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.2462i | 0.458840i | ||||||||
\(965\) | −25.1231 | −0.808741 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.6155i | − | 1.53121i | −0.643310 | − | 0.765606i | \(-0.722439\pi\) | ||
0.643310 | − | 0.765606i | \(-0.277561\pi\) | |||||||
\(968\) | 15.2462i | 0.490032i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 13.1231i | − | 0.421358i | ||||||
\(971\) | −37.7538 | −1.21158 | −0.605788 | − | 0.795626i | \(-0.707142\pi\) | ||||
−0.605788 | + | 0.795626i | \(0.707142\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 51.5076i | − | 1.65126i | ||||||
\(974\) | −17.3693 | −0.556549 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | 4.73863i | 0.151602i | 0.997123 | + | 0.0758012i | \(0.0241514\pi\) | ||||
−0.997123 | + | 0.0758012i | \(0.975849\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0000 | −0.511362 | ||||||||
\(980\) | − | 2.75379i | − | 0.0879666i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 38.7386i | − | 1.23620i | ||||||
\(983\) | 60.4924i | 1.92941i | 0.263335 | + | 0.964704i | \(0.415177\pi\) | ||||
−0.263335 | + | 0.964704i | \(0.584823\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.2462 | −0.517647 | ||||||||
\(986\) | 4.00000i | 0.127386i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.36932 | + | 21.3693i | 0.107192 | + | 0.679849i | ||||
\(989\) | 32.0000 | 1.01754 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30.7386 | −0.976445 | −0.488222 | − | 0.872719i | \(-0.662355\pi\) | ||||
−0.488222 | + | 0.872719i | \(0.662355\pi\) | |||||||
\(992\) | −3.12311 | −0.0991587 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 32.0000i | 1.01498i | ||||||||
\(995\) | − | 18.2462i | − | 0.578444i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.3542 | 1.21469 | 0.607344 | − | 0.794439i | \(-0.292235\pi\) | ||||
0.607344 | + | 0.794439i | \(0.292235\pi\) | |||||||
\(998\) | −34.4924 | −1.09184 | ||||||||
\(999\) | 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 | 1170.2.b.f.181.4 | 4 | ||
3.2 | odd | 2 | 390.2.b.d.181.2 | ✓ | 4 | ||
12.11 | even | 2 | 3120.2.g.o.961.3 | 4 | |||
13.12 | even | 2 | inner | 1170.2.b.f.181.1 | 4 | ||
15.2 | even | 4 | 1950.2.f.o.649.1 | 4 | |||
15.8 | even | 4 | 1950.2.f.l.649.4 | 4 | |||
15.14 | odd | 2 | 1950.2.b.h.1351.3 | 4 | |||
39.5 | even | 4 | 5070.2.a.bd.1.1 | 2 | |||
39.8 | even | 4 | 5070.2.a.bh.1.2 | 2 | |||
39.38 | odd | 2 | 390.2.b.d.181.3 | yes | 4 | ||
156.155 | even | 2 | 3120.2.g.o.961.2 | 4 | |||
195.38 | even | 4 | 1950.2.f.o.649.3 | 4 | |||
195.77 | even | 4 | 1950.2.f.l.649.2 | 4 | |||
195.194 | odd | 2 | 1950.2.b.h.1351.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.b.d.181.2 | ✓ | 4 | 3.2 | odd | 2 | ||
390.2.b.d.181.3 | yes | 4 | 39.38 | odd | 2 | ||
1170.2.b.f.181.1 | 4 | 13.12 | even | 2 | inner | ||
1170.2.b.f.181.4 | 4 | 1.1 | even | 1 | trivial | ||
1950.2.b.h.1351.2 | 4 | 195.194 | odd | 2 | |||
1950.2.b.h.1351.3 | 4 | 15.14 | odd | 2 | |||
1950.2.f.l.649.2 | 4 | 195.77 | even | 4 | |||
1950.2.f.l.649.4 | 4 | 15.8 | even | 4 | |||
1950.2.f.o.649.1 | 4 | 15.2 | even | 4 | |||
1950.2.f.o.649.3 | 4 | 195.38 | even | 4 | |||
3120.2.g.o.961.2 | 4 | 156.155 | even | 2 | |||
3120.2.g.o.961.3 | 4 | 12.11 | even | 2 | |||
5070.2.a.bd.1.1 | 2 | 39.5 | even | 4 | |||
5070.2.a.bh.1.2 | 2 | 39.8 | even | 4 |