Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [92,2,Mod(91,92)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(92, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("92.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 92 = 2^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 92.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: | \(0.734623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.8869743.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 3x^{3} + 8 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 91.2 | ||
Root | \(1.33454 - 0.467979i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 92.91 |
Dual form | 92.2.b.b.91.1 |
$q$-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 \(\left(\mathbb{Z}/92\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33454 | + | 0.467979i | −0.943662 | + | 0.330911i | ||||
\(3\) | 3.43410i | 1.98268i | 0.131319 | + | 0.991340i | \(0.458079\pi\) | ||||
−0.131319 | + | 0.991340i | \(0.541921\pi\) | |||||||
\(4\) | 1.56199 | − | 1.24907i | 0.780996 | − | 0.624536i | ||||
\(5\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(6\) | −1.60709 | − | 4.58295i | −0.656091 | − | 1.87098i | ||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | −1.50000 | + | 2.39792i | −0.530330 | + | 0.847791i | ||||
\(9\) | −8.79306 | −2.93102 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 4.28944 | + | 5.36404i | 1.23826 | + | 1.54846i | ||||
\(13\) | 4.88325 | 1.35437 | 0.677185 | − | 0.735812i | \(-0.263199\pi\) | ||||
0.677185 | + | 0.735812i | \(0.263199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.879635 | − | 3.90208i | 0.219909 | − | 0.975520i | ||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 11.7347 | − | 4.11497i | 2.76589 | − | 0.969907i | ||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.79583i | 1.00000i | ||||||||
\(24\) | −8.23469 | − | 5.15115i | −1.68090 | − | 1.05147i | ||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −6.51690 | + | 2.28526i | −1.27807 | + | 0.448176i | ||||
\(27\) | − | 19.8940i | − | 3.82860i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.70287 | 1.24469 | 0.622346 | − | 0.782742i | \(-0.286180\pi\) | ||||
0.622346 | + | 0.782742i | \(0.286180\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.309728i | − | 0.0556288i | −0.999613 | − | 0.0278144i | \(-0.991145\pi\) | ||
0.999613 | − | 0.0278144i | \(-0.00885474\pi\) | |||||||
\(32\) | 0.652183 | + | 5.61913i | 0.115291 | + | 0.993332i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −13.7347 | + | 10.9832i | −2.28911 | + | 1.83053i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 16.7696i | 2.68528i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.97345 | −0.620548 | −0.310274 | − | 0.950647i | \(-0.600421\pi\) | ||||
−0.310274 | + | 0.950647i | \(0.600421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.24435 | − | 6.40023i | −0.330911 | − | 0.943662i | ||||
\(47\) | − | 6.55848i | − | 0.956652i | −0.878182 | − | 0.478326i | \(-0.841244\pi\) | ||
0.878182 | − | 0.478326i | \(-0.158756\pi\) | |||||||
\(48\) | 13.4001 | + | 3.02076i | 1.93415 | + | 0.436009i | ||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | −6.67270 | + | 2.33989i | −0.943662 | + | 0.330911i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.62760 | − | 6.09954i | 1.05776 | − | 0.845854i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 9.30996 | + | 26.5493i | 1.26692 | + | 3.61290i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.94525 | + | 3.13680i | −1.17457 | + | 0.411882i | ||||
\(59\) | − | 9.59166i | − | 1.24873i | −0.781133 | − | 0.624364i | \(-0.785358\pi\) | ||
0.781133 | − | 0.624364i | \(-0.214642\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0.144946 | + | 0.413344i | 0.0184082 | + | 0.0524948i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.50000 | − | 7.19375i | −0.437500 | − | 0.899218i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −16.4694 | −1.98268 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.0461i | − | 1.66697i | −0.552542 | − | 0.833485i | \(-0.686342\pi\) | ||
0.552542 | − | 0.833485i | \(-0.313658\pi\) | |||||||
\(72\) | 13.1896 | − | 21.0850i | 1.55441 | − | 2.48489i | ||||
\(73\) | −7.61268 | −0.890997 | −0.445498 | − | 0.895283i | \(-0.646973\pi\) | ||||
−0.445498 | + | 0.895283i | \(0.646973\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.1705i | 1.98268i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −7.84782 | − | 22.3797i | −0.888590 | − | 2.53400i | ||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 41.9388 | 4.65986 | ||||||||
\(82\) | 5.30272 | − | 1.85949i | 0.585588 | − | 0.205346i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 23.0183i | 2.46783i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.99034 | + | 7.49105i | 0.624536 | + | 0.780996i | ||||
\(93\) | 1.06364 | 0.110294 | ||||||||
\(94\) | 3.06923 | + | 8.75255i | 0.316567 | + | 0.902756i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −19.2967 | + | 2.23966i | −1.96946 | + | 0.228585i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 9.34178 | − | 3.27585i | 0.943662 | − | 0.330911i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.80996 | − | 6.24536i | 0.780996 | − | 0.624536i | ||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | −7.32488 | + | 11.7096i | −0.718264 | + | 1.14822i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −24.8490 | − | 31.0742i | −2.39110 | − | 2.99012i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.4698 | − | 8.37237i | 0.972099 | − | 0.777355i | ||||
\(117\) | −42.9388 | −3.96969 | ||||||||
\(118\) | 4.48870 | + | 12.8005i | 0.413218 | + | 1.17838i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 13.6452i | − | 1.23035i | ||||||
\(124\) | −0.386873 | − | 0.483792i | −0.0347422 | − | 0.0434458i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.9143i | 1.85585i | 0.372769 | + | 0.927924i | \(0.378408\pi\) | ||||
−0.372769 | + | 0.927924i | \(0.621592\pi\) | |||||||
\(128\) | 8.03741 | + | 7.96241i | 0.710413 | + | 0.703785i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.81465i | − | 0.245917i | −0.992412 | − | 0.122958i | \(-0.960762\pi\) | ||
0.992412 | − | 0.122958i | \(-0.0392382\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(138\) | 21.9790 | − | 7.70732i | 1.87098 | − | 0.656091i | ||||
\(139\) | 10.9218i | 0.926372i | 0.886261 | + | 0.463186i | \(0.153294\pi\) | ||||
−0.886261 | + | 0.463186i | \(0.846706\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.5225 | 1.89674 | ||||||||
\(142\) | 6.57330 | + | 18.7451i | 0.551619 | + | 1.57306i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.73469 | + | 34.3112i | −0.644557 | + | 2.85927i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.1594 | − | 3.56257i | 0.840800 | − | 0.294841i | ||||
\(147\) | − | 24.0387i | − | 1.98268i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(150\) | −8.03544 | − | 22.9147i | −0.656091 | − | 1.87098i | ||||
\(151\) | − | 20.2949i | − | 1.65157i | −0.563982 | − | 0.825787i | \(-0.690731\pi\) | ||
0.563982 | − | 0.825787i | \(-0.309269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 20.9464 | + | 26.1940i | 1.67706 | + | 2.09720i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −55.9689 | + | 19.6265i | −4.39733 | + | 1.54200i | ||||
\(163\) | 9.68285i | 0.758420i | 0.925311 | + | 0.379210i | \(0.123804\pi\) | ||||
−0.925311 | + | 0.379210i | \(0.876196\pi\) | |||||||
\(164\) | −6.20649 | + | 4.96312i | −0.484645 | + | 0.387555i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.59166i | 0.742225i | 0.928588 | + | 0.371113i | \(0.121024\pi\) | ||||
−0.928588 | + | 0.371113i | \(0.878976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.8462 | 0.834321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0000 | −1.36851 | −0.684257 | − | 0.729241i | \(-0.739873\pi\) | ||||
−0.684257 | + | 0.729241i | \(0.739873\pi\) | |||||||
\(174\) | −10.7721 | − | 30.7189i | −0.816631 | − | 2.32879i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 32.9388 | 2.47583 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 17.7900i | − | 1.32968i | −0.746984 | − | 0.664842i | \(-0.768499\pi\) | ||
0.746984 | − | 0.664842i | \(-0.231501\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −11.5000 | − | 7.19375i | −0.847791 | − | 0.530330i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.41947 | + | 0.497760i | −0.104080 | + | 0.0364975i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.19201 | − | 10.2443i | −0.597464 | − | 0.747141i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | 24.7041 | − | 12.0194i | 1.78286 | − | 0.867423i | ||||
\(193\) | −27.1457 | −1.95399 | −0.976995 | − | 0.213262i | \(-0.931591\pi\) | ||||
−0.976995 | + | 0.213262i | \(0.931591\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −10.9339 | + | 8.74351i | −0.780996 | + | 0.624536i | ||||
\(197\) | 28.0555 | 1.99887 | 0.999436 | − | 0.0335834i | \(-0.0106919\pi\) | ||||
0.999436 | + | 0.0335834i | \(0.0106919\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | −7.50000 | + | 11.9896i | −0.530330 | + | 0.847791i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.00724 | + | 2.80787i | −0.563387 | + | 0.197561i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 42.1700i | − | 2.93102i | ||||||
\(208\) | 4.29548 | − | 19.0549i | 0.297838 | − | 1.32122i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 28.7750i | 1.98095i | 0.137686 | + | 0.990476i | \(0.456034\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 48.2359 | 3.30507 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 47.7041 | + | 29.8410i | 3.24585 | + | 2.03042i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 26.1427i | − | 1.76656i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 28.7750i | − | 1.92692i | −0.267860 | − | 0.963458i | \(-0.586316\pi\) | ||
0.267860 | − | 0.963458i | \(-0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −43.9653 | −2.93102 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.0543 | + | 16.0729i | −0.660098 | + | 1.05524i | ||||
\(233\) | −9.43229 | −0.617930 | −0.308965 | − | 0.951073i | \(-0.599983\pi\) | ||||
−0.308965 | + | 0.951073i | \(0.599983\pi\) | |||||||
\(234\) | 57.3035 | − | 20.0944i | 3.74604 | − | 1.31361i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.9807 | − | 14.9821i | −0.779876 | − | 0.975251i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.1631i | 1.75703i | 0.477711 | + | 0.878517i | \(0.341467\pi\) | ||||
−0.477711 | + | 0.878517i | \(0.658533\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(242\) | 14.6799 | − | 5.14777i | 0.943662 | − | 0.330911i | ||||
\(243\) | 84.3401i | 5.41042i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.38568 | + | 18.2101i | 0.407136 | + | 1.16103i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0.742702 | + | 0.464592i | 0.0471616 | + | 0.0295016i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −9.78747 | − | 27.9110i | −0.614121 | − | 1.75129i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.4525 | − | 6.86482i | −0.903280 | − | 0.429051i | ||||
\(257\) | −25.3261 | −1.57980 | −0.789899 | − | 0.613237i | \(-0.789867\pi\) | ||||
−0.789899 | + | 0.613237i | \(0.789867\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −58.9388 | −3.64822 | ||||||||
\(262\) | 1.31720 | + | 3.75626i | 0.0813766 | + | 0.232062i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.24402 | 0.0758493 | 0.0379247 | − | 0.999281i | \(-0.487925\pi\) | ||||
0.0379247 | + | 0.999281i | \(0.487925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 28.7750i | − | 1.74796i | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||
0.485965 | − | 0.873978i | \(-0.338468\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −25.7250 | + | 20.5714i | −1.54846 | + | 1.23826i | ||||
\(277\) | 29.8751 | 1.79502 | 0.897511 | − | 0.440992i | \(-0.145373\pi\) | ||||
0.897511 | + | 0.440992i | \(0.145373\pi\) | |||||||
\(278\) | −5.11115 | − | 14.5755i | −0.306547 | − | 0.874182i | ||||
\(279\) | 2.72346i | 0.163049i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | −30.0571 | + | 10.5400i | −1.78988 | + | 0.627651i | ||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | −17.5446 | − | 21.9400i | −1.04108 | − | 1.30190i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −5.73469 | − | 49.4094i | −0.337920 | − | 2.91148i | ||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.8909 | + | 9.50879i | −0.695865 | + | 0.556460i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 11.2496 | + | 32.0806i | 0.656091 | + | 1.87098i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.4193i | 1.35437i | ||||||||
\(300\) | 21.4472 | + | 26.8202i | 1.23826 | + | 1.54846i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.49758 | + | 27.0843i | 0.546524 | + | 1.55853i | ||||
\(303\) | 20.6046i | 1.18370i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.7750i | 1.64228i | 0.570730 | + | 0.821138i | \(0.306660\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 34.6508i | 1.96486i | 0.186621 | + | 0.982432i | \(0.440246\pi\) | ||||
−0.186621 | + | 0.982432i | \(0.559754\pi\) | |||||||
\(312\) | −40.2121 | − | 25.1544i | −2.27656 | − | 1.42409i | ||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 65.5080 | − | 52.3846i | 3.63933 | − | 2.91025i | ||||
\(325\) | 24.4163 | 1.35437 | ||||||||
\(326\) | −4.53137 | − | 12.9221i | −0.250969 | − | 0.715692i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.96017 | − | 9.52799i | 0.329095 | − | 0.526095i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 31.5264i | − | 1.73285i | −0.499310 | − | 0.866423i | \(-0.666413\pi\) | ||
0.499310 | − | 0.866423i | \(-0.333587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.48870 | − | 12.8005i | −0.245610 | − | 0.700410i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | −14.4746 | + | 5.07578i | −0.787317 | + | 0.276086i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 24.0217 | − | 8.42362i | 1.29142 | − | 0.452857i | ||||
\(347\) | − | 9.59166i | − | 0.514907i | −0.966291 | − | 0.257454i | \(-0.917117\pi\) | ||
0.966291 | − | 0.257454i | \(-0.0828835\pi\) | |||||||
\(348\) | 28.7516 | + | 35.9545i | 1.54125 | + | 1.92736i | ||||
\(349\) | 10.3421 | 0.553600 | 0.276800 | − | 0.960928i | \(-0.410726\pi\) | ||||
0.276800 | + | 0.960928i | \(0.410726\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 97.1473i | − | 5.18534i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.7849 | −1.63852 | −0.819258 | − | 0.573425i | \(-0.805614\pi\) | ||||
−0.819258 | + | 0.573425i | \(0.805614\pi\) | |||||||
\(354\) | −43.9581 | + | 15.4146i | −2.33635 | + | 0.819279i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.32533 | + | 23.7414i | 0.440007 | + | 1.25477i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 37.7751i | − | 1.98268i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(368\) | 18.7137 | + | 4.21858i | 0.975520 | + | 0.219909i | ||||
\(369\) | 34.9388 | 1.81884 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.66139 | − | 1.32856i | 0.0861392 | − | 0.0688827i | ||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.7267 | + | 9.83772i | 0.811041 | + | 0.507341i | ||||
\(377\) | 32.7318 | 1.68577 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −71.8220 | −3.67955 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | −27.3437 | + | 27.6013i | −1.39538 | + | 1.40852i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 36.2270 | − | 12.7036i | 1.84391 | − | 0.646597i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 10.5000 | − | 16.7854i | 0.530330 | − | 0.847791i | ||||
\(393\) | 9.66579 | 0.487574 | ||||||||
\(394\) | −37.4412 | + | 13.1294i | −1.88626 | + | 0.661449i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39.6416 | −1.98956 | −0.994778 | − | 0.102061i | \(-0.967456\pi\) | ||||
−0.994778 | + | 0.102061i | \(0.967456\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.39818 | − | 19.5104i | 0.219909 | − | 0.975520i | ||||
\(401\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1.51248i | − | 0.0753420i | ||||||
\(404\) | 9.37195 | − | 7.49444i | 0.466272 | − | 0.372862i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.9122 | 1.82519 | 0.912595 | − | 0.408864i | \(-0.134075\pi\) | ||||
0.912595 | + | 0.408864i | \(0.134075\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 19.7347 | + | 56.2776i | 0.969907 | + | 2.76589i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.18478 | + | 27.4397i | 0.156147 | + | 1.34534i | ||||
\(417\) | −37.5065 | −1.83670 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | −13.4661 | − | 38.4014i | −0.655519 | − | 1.86935i | ||||
\(423\) | 57.6691i | 2.80397i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −64.3727 | + | 22.5734i | −3.11887 | + | 1.09368i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −77.6279 | − | 17.4994i | −3.73487 | − | 0.841942i | ||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.2342 | + | 34.8885i | 0.584575 | + | 1.66704i | ||||
\(439\) | − | 41.5190i | − | 1.98159i | −0.135364 | − | 0.990796i | \(-0.543220\pi\) | ||
0.135364 | − | 0.990796i | \(-0.456780\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 61.5514 | 2.93102 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.3946i | 1.82418i | 0.409988 | + | 0.912091i | \(0.365533\pi\) | ||||
−0.409988 | + | 0.912091i | \(0.634467\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.4661 | + | 38.4014i | 0.637638 | + | 1.81836i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 58.6734 | − | 20.5748i | 2.76589 | − | 0.969907i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 69.6947 | 3.27454 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.0024 | −1.67680 | −0.838399 | − | 0.545056i | \(-0.816508\pi\) | ||||
−0.838399 | + | 0.545056i | \(0.816508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 28.7750i | − | 1.33729i | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||
0.743583 | − | 0.668644i | \(-0.233125\pi\) | |||||||
\(464\) | 5.89608 | − | 26.1551i | 0.273719 | − | 1.21422i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.5878 | − | 4.41411i | 0.583117 | − | 0.204480i | ||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | −67.0700 | + | 53.6336i | −3.10031 | + | 2.47922i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 23.0000 | + | 14.3875i | 1.05866 | + | 0.662238i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.7118 | − | 36.2502i | −0.581422 | − | 1.65805i | ||||
\(479\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.1819 | + | 13.7398i | −0.780996 | + | 0.624536i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −39.4694 | − | 112.555i | −1.79037 | − | 5.10561i | ||||
\(487\) | 40.8995i | 1.85333i | 0.375884 | + | 0.926667i | \(0.377339\pi\) | ||||
−0.375884 | + | 0.926667i | \(0.622661\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −33.2519 | −1.50370 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.67301i | 0.210890i | 0.994425 | + | 0.105445i | \(0.0336267\pi\) | ||||
−0.994425 | + | 0.105445i | \(0.966373\pi\) | |||||||
\(492\) | −17.0439 | − | 21.3137i | −0.768397 | − | 0.960897i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.20858 | − | 0.272448i | −0.0542670 | − | 0.0122333i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 11.5412i | − | 0.516656i | −0.966057 | − | 0.258328i | \(-0.916828\pi\) | ||
0.966057 | − | 0.258328i | \(-0.0831715\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −32.9388 | −1.47160 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.2469i | 1.65419i | ||||||||
\(508\) | 26.1235 | + | 32.6680i | 1.15904 | + | 1.44941i | ||||
\(509\) | −41.4612 | −1.83774 | −0.918869 | − | 0.394564i | \(-0.870896\pi\) | ||||
−0.918869 | + | 0.394564i | \(0.870896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.5000 | + | 2.39792i | 0.994369 | + | 0.105974i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33.7987 | − | 11.8521i | 1.49079 | − | 0.522772i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 61.8139i | − | 2.71333i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 78.6561 | − | 27.5821i | 3.44268 | − | 1.20724i | ||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | −3.51570 | − | 4.39645i | −0.153584 | − | 0.192060i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 84.3401i | 3.66005i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.4033 | −0.840452 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 61.0926 | 2.63634 | ||||||||
\(538\) | −1.66020 | + | 0.582176i | −0.0715761 | + | 0.0250994i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.575595 | −0.0247468 | −0.0123734 | − | 0.999923i | \(-0.503939\pi\) | ||||
−0.0123734 | + | 0.999923i | \(0.503939\pi\) | |||||||
\(542\) | 13.4661 | + | 38.4014i | 0.578418 | + | 1.64948i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 9.06340i | − | 0.387523i | −0.981049 | − | 0.193761i | \(-0.937931\pi\) | ||
0.981049 | − | 0.193761i | \(-0.0620688\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 24.7041 | − | 39.4922i | 1.05147 | − | 1.68090i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −39.8695 | + | 13.9809i | −1.69389 | + | 0.593993i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.6421 | + | 17.0597i | 0.578553 | + | 0.723493i | ||||
\(557\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(558\) | −1.27452 | − | 3.63456i | −0.0539548 | − | 0.153863i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 35.1799 | − | 28.1322i | 1.48134 | − | 1.18458i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 33.6815 | + | 21.0692i | 1.41324 | + | 0.884044i | ||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 23.9792i | 1.00000i | ||||||||
\(576\) | 30.7757 | + | 63.2551i | 1.28232 | + | 2.63563i | ||||
\(577\) | −32.6045 | −1.35734 | −0.678672 | − | 0.734441i | \(-0.737444\pi\) | ||||
−0.678672 | + | 0.734441i | \(0.737444\pi\) | |||||||
\(578\) | −22.6872 | + | 7.95564i | −0.943662 | + | 0.330911i | ||||
\(579\) | − | 93.2211i | − | 3.87414i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.4190 | − | 18.2546i | 0.472522 | − | 0.755379i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 25.2776i | − | 1.04332i | −0.853154 | − | 0.521660i | \(-0.825313\pi\) | ||
0.853154 | − | 0.521660i | \(-0.174687\pi\) | |||||||
\(588\) | −30.0261 | − | 37.5483i | −1.23826 | − | 1.54846i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 96.3455i | 3.96312i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.9597 | − | 31.2539i | −0.448176 | − | 1.27807i | ||||
\(599\) | 9.59166i | 0.391905i | 0.980613 | + | 0.195952i | \(0.0627798\pi\) | ||||
−0.980613 | + | 0.195952i | \(0.937220\pi\) | |||||||
\(600\) | −41.1734 | − | 25.7558i | −1.68090 | − | 1.05147i | ||||
\(601\) | 42.3711 | 1.72835 | 0.864176 | − | 0.503190i | \(-0.167841\pi\) | ||||
0.864176 | + | 0.503190i | \(0.167841\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.3498 | − | 31.7004i | −1.03147 | − | 1.28987i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.64252 | − | 27.4977i | −0.391701 | − | 1.11702i | ||||
\(607\) | − | 28.7750i | − | 1.16794i | −0.811775 | − | 0.583970i | \(-0.801498\pi\) | ||
0.811775 | − | 0.583970i | \(-0.198502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 32.0267i | − | 1.29566i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | −13.4661 | − | 38.4014i | −0.543447 | − | 1.54975i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 95.4081 | 3.82860 | ||||||||
\(622\) | −16.2158 | − | 46.2428i | −0.650195 | − | 1.85417i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 65.4363 | + | 14.7511i | 2.61955 | + | 0.590518i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −98.8163 | −3.92759 | ||||||||
\(634\) | −40.0362 | + | 14.0394i | −1.59004 | + | 0.557574i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.1828 | −1.35437 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 123.509i | 4.88592i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 47.7677i | − | 1.87794i | −0.343996 | − | 0.938971i | \(-0.611781\pi\) | ||
0.343996 | − | 0.938971i | \(-0.388219\pi\) | |||||||
\(648\) | −62.9081 | + | 100.566i | −2.47126 | + | 3.95059i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −32.5845 | + | 11.4263i | −1.27807 | + | 0.448176i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.0946 | + | 15.1245i | 0.473661 | + | 0.592322i | ||||
\(653\) | 12.1617 | 0.475925 | 0.237962 | − | 0.971274i | \(-0.423520\pi\) | ||||
0.237962 | + | 0.971274i | \(0.423520\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.49518 | + | 15.5047i | −0.136464 | + | 0.605357i | ||||
\(657\) | 66.9388 | 2.61153 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 14.7537 | + | 42.0732i | 0.573418 | + | 1.63522i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.1458i | 1.24469i | ||||||||
\(668\) | 11.9807 | + | 14.9821i | 0.463547 | + | 0.579675i | ||||
\(669\) | 98.8163 | 3.82046 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.6868 | −0.835966 | −0.417983 | − | 0.908455i | \(-0.637263\pi\) | ||||
−0.417983 | + | 0.908455i | \(0.637263\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 99.4699i | − | 3.82860i | ||||||
\(676\) | 16.9416 | − | 13.5477i | 0.651601 | − | 0.521064i | ||||
\(677\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 44.0239i | − | 1.68453i | −0.539066 | − | 0.842263i | \(-0.681223\pi\) | ||
0.539066 | − | 0.842263i | \(-0.318777\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.7750i | 1.09465i | 0.836919 | + | 0.547326i | \(0.184354\pi\) | ||||
−0.836919 | + | 0.547326i | \(0.815646\pi\) | |||||||
\(692\) | −28.1158 | + | 22.4833i | −1.06880 | + | 0.854687i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.48870 | + | 12.8005i | 0.170389 | + | 0.485899i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −55.1961 | − | 34.5275i | −2.09220 | − | 1.30876i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −13.8019 | + | 4.83989i | −0.522411 | + | 0.183192i | ||||
\(699\) | − | 32.3915i | − | 1.22516i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 45.4629 | + | 129.647i | 1.71589 | + | 4.89321i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 41.0837 | − | 14.4067i | 1.54621 | − | 0.542203i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 51.4501 | − | 41.1429i | 1.93361 | − | 1.54624i | ||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.48540 | 0.0556288 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −22.2210 | − | 27.7878i | −0.830436 | − | 1.03848i | ||||
\(717\) | −93.2809 | −3.48364 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 47.9583i | 1.78854i | 0.447524 | + | 0.894272i | \(0.352306\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 25.3563 | − | 8.89160i | 0.943662 | − | 0.330911i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 33.5144 | 1.24469 | ||||||||
\(726\) | 17.6780 | + | 50.4124i | 0.656091 | + | 1.87098i | ||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −163.816 | −6.06727 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −26.9484 | + | 3.12776i | −0.993332 | + | 0.115291i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −46.6272 | + | 16.3506i | −1.71637 | + | 0.601874i | ||||
\(739\) | 52.1310i | 1.91767i | 0.283964 | + | 0.958835i | \(0.408350\pi\) | ||||
−0.283964 | + | 0.958835i | \(0.591650\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(744\) | −1.59546 | + | 2.55051i | −0.0584923 | + | 0.0935064i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | −25.5917 | − | 5.76907i | −0.933234 | − | 0.210376i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −43.6819 | + | 15.3178i | −1.59080 | + | 0.557841i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.2730 | 1.20614 | 0.603072 | − | 0.797687i | \(-0.293943\pi\) | ||||
0.603072 | + | 0.797687i | \(0.293943\pi\) | |||||||
\(762\) | 95.8493 | − | 33.6112i | 3.47225 | − | 1.21760i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 46.8385i | − | 1.69124i | ||||||
\(768\) | 23.5745 | − | 49.6313i | 0.850671 | − | 1.79092i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 86.9724i | − | 3.13223i | ||||||
\(772\) | −42.4013 | + | 33.9069i | −1.52606 | + | 1.22034i | ||||
\(773\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.54864i | − | 0.0556288i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 133.347i | − | 4.76542i | ||||||
\(784\) | −6.15745 | + | 27.3146i | −0.219909 | + | 0.975520i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −12.8994 | + | 4.52338i | −0.460105 | + | 0.161344i | ||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 43.8225 | − | 35.0434i | 1.56111 | − | 1.24837i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 52.9033 | − | 18.5514i | 1.87747 | − | 0.658366i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 3.26092 | + | 28.0957i | 0.115291 | + | 0.993332i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.707809 | + | 2.01846i | 0.0249315 | + | 0.0710974i | ||||
\(807\) | 4.27210i | 0.150385i | ||||||||
\(808\) | −9.00000 | + | 14.3875i | −0.316619 | + | 0.506150i | ||||
\(809\) | 42.0000 | 1.47664 | 0.738321 | − | 0.674450i | \(-0.235619\pi\) | ||||
0.738321 | + | 0.674450i | \(0.235619\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.6680i | 1.04178i | 0.853622 | + | 0.520892i | \(0.174401\pi\) | ||||
−0.853622 | + | 0.520892i | \(0.825599\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 98.8163 | 3.46564 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −49.2608 | + | 17.2741i | −1.72236 | + | 0.603976i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 54.0000 | 1.88461 | 0.942306 | − | 0.334751i | \(-0.108652\pi\) | ||||
0.942306 | + | 0.334751i | \(0.108652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.1533i | 0.772214i | 0.922454 | + | 0.386107i | \(0.126180\pi\) | ||||
−0.922454 | + | 0.386107i | \(0.873820\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(828\) | −52.6734 | − | 65.8693i | −1.83053 | − | 2.28911i | ||||
\(829\) | −2.00000 | −0.0694629 | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347314 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 102.594i | 3.55895i | ||||||||
\(832\) | −17.0914 | − | 35.1289i | −0.592537 | − | 1.21788i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 50.0539 | − | 17.5522i | 1.73322 | − | 0.607784i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.16172 | −0.212980 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.9285 | 0.549258 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 35.9420 | + | 44.9463i | 1.23718 | + | 1.54712i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −26.9879 | − | 76.9617i | −0.927864 | − | 2.64600i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 75.3440 | − | 60.2501i | 2.58124 | − | 2.06414i | ||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.1907 | 1.50952 | 0.754762 | − | 0.655998i | \(-0.227752\pi\) | ||||
0.754762 | + | 0.655998i | \(0.227752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.8921i | 1.73642i | 0.496201 | + | 0.868208i | \(0.334728\pi\) | ||||
−0.496201 | + | 0.868208i | \(0.665272\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.1878i | 0.414877i | 0.978248 | + | 0.207438i | \(0.0665126\pi\) | ||||
−0.978248 | + | 0.207438i | \(0.933487\pi\) | |||||||
\(864\) | 111.787 | − | 12.9745i | 3.80307 | − | 0.441402i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 58.3797i | 1.98268i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −32.6542 | − | 40.8347i | −1.10328 | − | 1.37968i | ||||
\(877\) | 14.0000 | 0.472746 | 0.236373 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236373 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(878\) | 19.4300 | + | 55.4087i | 0.655731 | + | 1.86995i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | −82.1428 | + | 28.8048i | −2.76589 | + | 0.969907i | ||||
\(883\) | 28.7750i | 0.968355i | 0.874970 | + | 0.484178i | \(0.160881\pi\) | ||||
−0.874970 | + | 0.484178i | \(0.839119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.9679 | − | 51.2391i | −0.603642 | − | 1.72141i | ||||
\(887\) | − | 29.0215i | − | 0.974445i | −0.873278 | − | 0.487223i | \(-0.838010\pi\) | ||
0.873278 | − | 0.487223i | \(-0.161990\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −35.9420 | − | 44.9463i | −1.20343 | − | 1.50491i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −80.4242 | −2.68528 | ||||||||
\(898\) | −24.0217 | + | 8.42362i | −0.801615 | + | 0.281100i | ||||
\(899\) | − | 2.07607i | − | 0.0692407i | ||||||
\(900\) | −68.6734 | + | 54.9159i | −2.28911 | + | 1.83053i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −93.0104 | + | 32.6157i | −3.09006 | + | 1.08358i | ||||
\(907\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −52.7584 | −1.74988 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −98.8163 | −3.25611 | ||||||||
\(922\) | 48.0466 | − | 16.8484i | 1.58233 | − | 0.554871i | ||||
\(923\) | − | 68.5909i | − | 2.25770i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.4661 | + | 38.4014i | 0.442523 | + | 1.26195i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.37150 | + | 37.6643i | 0.143502 | + | 1.23639i | ||||
\(929\) | 60.0845 | 1.97131 | 0.985653 | − | 0.168782i | \(-0.0539833\pi\) | ||||
0.985653 | + | 0.168782i | \(0.0539833\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −14.7332 | + | 11.7816i | −0.482601 | + | 0.385920i | ||||
\(933\) | −118.994 | −3.89570 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 64.4081 | − | 102.964i | 2.10525 | − | 3.36547i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 19.0560i | − | 0.620548i | ||||||
\(944\) | −37.4275 | − | 8.43717i | −1.21816 | − | 0.274606i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 36.5362i | − | 1.18727i | −0.804735 | − | 0.593634i | \(-0.797693\pi\) | ||
0.804735 | − | 0.593634i | \(-0.202307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.1746 | −1.20674 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 103.023i | 3.34075i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 33.9287 | + | 42.4285i | 1.09733 | + | 1.37224i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9041 | 0.996905 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 62.1236i | 1.99776i | 0.0473194 | + | 0.998880i | \(0.484932\pi\) | ||||
−0.0473194 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(968\) | 16.5000 | − | 26.3771i | 0.530330 | − | 0.847791i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(972\) | 105.347 | + | 131.739i | 3.37900 | + | 4.22551i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19.1401 | − | 54.5820i | −0.613288 | − | 1.74892i | ||||
\(975\) | 83.8480i | 2.68528i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(978\) | 44.3760 | − | 15.5612i | 1.41899 | − | 0.497592i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.18687 | − | 6.23632i | −0.0697859 | − | 0.199009i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 32.7201 | + | 20.4678i | 1.04308 | + | 0.652491i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 28.7750i | − | 0.914068i | −0.889449 | − | 0.457034i | \(-0.848912\pi\) | ||
0.889449 | − | 0.457034i | \(-0.151088\pi\) | |||||||
\(992\) | 1.74040 | − | 0.201999i | 0.0552578 | − | 0.00641349i | ||||
\(993\) | 108.265 | 3.43568 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.0000 | −0.823428 | −0.411714 | − | 0.911313i | \(-0.635070\pi\) | ||||
−0.411714 | + | 0.911313i | \(0.635070\pi\) | |||||||
\(998\) | 5.40105 | + | 15.4022i | 0.170967 | + | 0.487549i | ||||
\(999\) | 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 | 92.2.b.b.91.2 | yes | 6 | |
3.2 | odd | 2 | 828.2.e.b.91.5 | 6 | |||
4.3 | odd | 2 | inner | 92.2.b.b.91.1 | ✓ | 6 | |
8.3 | odd | 2 | 1472.2.c.c.1471.6 | 6 | |||
8.5 | even | 2 | 1472.2.c.c.1471.1 | 6 | |||
12.11 | even | 2 | 828.2.e.b.91.6 | 6 | |||
23.22 | odd | 2 | CM | 92.2.b.b.91.2 | yes | 6 | |
69.68 | even | 2 | 828.2.e.b.91.5 | 6 | |||
92.91 | even | 2 | inner | 92.2.b.b.91.1 | ✓ | 6 | |
184.45 | odd | 2 | 1472.2.c.c.1471.1 | 6 | |||
184.91 | even | 2 | 1472.2.c.c.1471.6 | 6 | |||
276.275 | odd | 2 | 828.2.e.b.91.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
92.2.b.b.91.1 | ✓ | 6 | 4.3 | odd | 2 | inner | |
92.2.b.b.91.1 | ✓ | 6 | 92.91 | even | 2 | inner | |
92.2.b.b.91.2 | yes | 6 | 1.1 | even | 1 | trivial | |
92.2.b.b.91.2 | yes | 6 | 23.22 | odd | 2 | CM | |
828.2.e.b.91.5 | 6 | 3.2 | odd | 2 | |||
828.2.e.b.91.5 | 6 | 69.68 | even | 2 | |||
828.2.e.b.91.6 | 6 | 12.11 | even | 2 | |||
828.2.e.b.91.6 | 6 | 276.275 | odd | 2 | |||
1472.2.c.c.1471.1 | 6 | 8.5 | even | 2 | |||
1472.2.c.c.1471.1 | 6 | 184.45 | odd | 2 | |||
1472.2.c.c.1471.6 | 6 | 8.3 | odd | 2 | |||
1472.2.c.c.1471.6 | 6 | 184.91 | even | 2 |