Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,4,Mod(17,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.88806112018\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{-7}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 8) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 17.1 | ||
Root | \(0.500000 + 1.32288i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 32.17 |
Dual form | 32.4.b.a.17.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 5.29150i | − 1.01835i | −0.860663 | − | 0.509175i | \(-0.829951\pi\) | ||||
0.860663 | − | 0.509175i | \(-0.170049\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 10.5830i | − 0.946573i | −0.880909 | − | 0.473286i | \(-0.843068\pi\) | ||||
0.880909 | − | 0.473286i | \(-0.156932\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000 | 0.431959 | 0.215980 | − | 0.976398i | \(-0.430705\pi\) | ||||
0.215980 | + | 0.976398i | \(0.430705\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.0370370 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 15.8745i | 0.435122i | 0.976047 | + | 0.217561i | \(0.0698101\pi\) | ||||
−0.976047 | + | 0.217561i | \(0.930190\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 52.9150i | 1.12892i | 0.825460 | + | 0.564461i | \(0.190916\pi\) | ||||
−0.825460 | + | 0.564461i | \(0.809084\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −56.0000 | −0.963943 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −14.0000 | −0.199735 | −0.0998676 | − | 0.995001i | \(-0.531842\pi\) | ||||
−0.0998676 | + | 0.995001i | \(0.531842\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 37.0405i | 0.447246i | 0.974676 | + | 0.223623i | \(0.0717885\pi\) | ||||
−0.974676 | + | 0.223623i | \(0.928212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 42.3320i | − 0.439886i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 152.000 | 1.37801 | 0.689004 | − | 0.724757i | \(-0.258048\pi\) | ||||
0.689004 | + | 0.724757i | \(0.258048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.0000 | 0.104000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 137.579i | − 0.980633i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 158.745i | − 1.01649i | −0.861212 | − | 0.508245i | \(-0.830294\pi\) | ||||
0.861212 | − | 0.508245i | \(-0.169706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −224.000 | −1.29779 | −0.648897 | − | 0.760877i | \(-0.724769\pi\) | ||||
−0.648897 | + | 0.760877i | \(0.724769\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 84.0000 | 0.443107 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 84.6640i | − 0.408881i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 243.409i | 1.08152i | 0.841177 | + | 0.540760i | \(0.181863\pi\) | ||||
−0.841177 | + | 0.540760i | \(0.818137\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 280.000 | 1.14964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70.0000 | −0.266638 | −0.133319 | − | 0.991073i | \(-0.542564\pi\) | ||||
−0.133319 | + | 0.991073i | \(0.542564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 439.195i | 1.55759i | 0.627276 | + | 0.778797i | \(0.284170\pi\) | ||||
−0.627276 | + | 0.778797i | \(0.715830\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.5830i | 0.0350583i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −336.000 | −1.04278 | −0.521390 | − | 0.853319i | \(-0.674586\pi\) | ||||
−0.521390 | + | 0.853319i | \(0.674586\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 74.0810i | 0.203400i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 31.7490i | 0.0822842i | 0.999153 | + | 0.0411421i | \(0.0130996\pi\) | ||||
−0.999153 | + | 0.0411421i | \(0.986900\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 168.000 | 0.411875 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 196.000 | 0.455453 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 534.442i | − 1.17929i | −0.807661 | − | 0.589647i | \(-0.799267\pi\) | ||||
0.807661 | − | 0.589647i | \(-0.200733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 95.2470i | 0.199920i | 0.994991 | + | 0.0999601i | \(0.0318715\pi\) | ||||
−0.994991 | + | 0.0999601i | \(0.968128\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.00000 | −0.0159985 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 560.000 | 1.06861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 174.620i | − 0.318406i | −0.987246 | − | 0.159203i | \(-0.949108\pi\) | ||||
0.987246 | − | 0.159203i | \(-0.0508924\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 804.308i | − 1.40329i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 72.0000 | 0.120350 | 0.0601748 | − | 0.998188i | \(-0.480834\pi\) | ||||
0.0601748 | + | 0.998188i | \(0.480834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −294.000 | −0.471371 | −0.235686 | − | 0.971829i | \(-0.575734\pi\) | ||||
−0.235686 | + | 0.971829i | \(0.575734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 68.7895i | − 0.105908i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 126.996i | 0.187955i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 464.000 | 0.660811 | 0.330406 | − | 0.943839i | \(-0.392814\pi\) | ||||
0.330406 | + | 0.943839i | \(0.392814\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −755.000 | −1.03567 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 545.025i | 0.720774i | 0.932803 | + | 0.360387i | \(0.117355\pi\) | ||||
−0.932803 | + | 0.360387i | \(0.882645\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 148.162i | 0.189064i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −840.000 | −1.03514 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 266.000 | 0.316808 | 0.158404 | − | 0.987374i | \(-0.449365\pi\) | ||||
0.158404 | + | 0.987374i | \(0.449365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 423.320i | 0.487649i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1185.30i | 1.32161i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 392.000 | 0.423351 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 994.000 | 1.04047 | 0.520234 | − | 0.854024i | \(-0.325845\pi\) | ||||
0.520234 | + | 0.854024i | \(0.325845\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 15.8745i | − 0.0161156i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 751.393i | 0.740262i | 0.928980 | + | 0.370131i | \(0.120687\pi\) | ||||
−0.928980 | + | 0.370131i | \(0.879313\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1176.00 | −1.12500 | −0.562499 | − | 0.826798i | \(-0.690160\pi\) | ||||
−0.562499 | + | 0.826798i | \(0.690160\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −448.000 | −0.416384 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 269.867i | 0.243822i | 0.992541 | + | 0.121911i | \(0.0389023\pi\) | ||||
−0.992541 | + | 0.121911i | \(0.961098\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 1894.36i | − 1.66465i | −0.554290 | − | 0.832324i | \(-0.687010\pi\) | ||||
0.554290 | − | 0.832324i | \(-0.312990\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1288.00 | 1.10137 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1710.00 | −1.42357 | −0.711784 | − | 0.702398i | \(-0.752113\pi\) | ||||
−0.711784 | + | 0.702398i | \(0.752113\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 1608.62i | − 1.30439i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 52.9150i | − 0.0418119i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −112.000 | −0.0862775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1079.00 | 0.810669 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 370.405i | 0.271531i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1460.45i | − 1.04502i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1664.00 | 1.16265 | 0.581323 | − | 0.813673i | \(-0.302535\pi\) | ||||
0.581323 | + | 0.813673i | \(0.302535\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2324.00 | 1.58618 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 672.021i | 0.448204i | 0.974566 | + | 0.224102i | \(0.0719449\pi\) | ||||
−0.974566 | + | 0.224102i | \(0.928055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 296.324i | 0.193192i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1456.00 | −0.928241 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1062.00 | −0.662283 | −0.331142 | − | 0.943581i | \(-0.607434\pi\) | ||||
−0.331142 | + | 0.943581i | \(0.607434\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2693.37i | − 1.64352i | −0.569835 | − | 0.821759i | \(-0.692993\pi\) | ||||
0.569835 | − | 0.821759i | \(-0.307007\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1777.94i | 1.06191i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −840.000 | −0.491219 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1680.00 | −0.962182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1476.33i | 0.828337i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 793.725i | 0.436406i | 0.975903 | + | 0.218203i | \(0.0700195\pi\) | ||||
−0.975903 | + | 0.218203i | \(0.929980\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −744.000 | −0.400966 | −0.200483 | − | 0.979697i | \(-0.564251\pi\) | ||||
−0.200483 | + | 0.979697i | \(0.564251\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.0000 | 0.00739760 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2370.59i | 1.22846i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 179.911i | 0.0914552i | 0.998954 | + | 0.0457276i | \(0.0145606\pi\) | ||||
−0.998954 | + | 0.0457276i | \(0.985439\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 168.000 | 0.0837941 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1216.00 | 0.595244 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1772.65i | 0.851809i | 0.904768 | + | 0.425905i | \(0.140044\pi\) | ||||
−0.904768 | + | 0.425905i | \(0.859956\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 888.972i | − 0.419433i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1960.00 | 0.908200 | 0.454100 | − | 0.890951i | \(-0.349961\pi\) | ||||
0.454100 | + | 0.890951i | \(0.349961\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −603.000 | −0.274465 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 37.0405i | − 0.0165647i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2000.19i | 0.879026i | 0.898236 | + | 0.439513i | \(0.144849\pi\) | ||||
−0.898236 | + | 0.439513i | \(0.855151\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 104.000 | 0.0449238 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2828.00 | −1.20094 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 3264.86i | − 1.36328i | −0.731688 | − | 0.681639i | \(-0.761267\pi\) | ||||
0.731688 | − | 0.681639i | \(-0.238733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 2338.84i | − 0.960469i | −0.877140 | − | 0.480235i | \(-0.840552\pi\) | ||||
0.877140 | − | 0.480235i | \(-0.159448\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 504.000 | 0.203589 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2576.00 | 1.02374 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 222.243i | − 0.0869092i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1100.63i | − 0.423594i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3904.00 | −1.47897 | −0.739486 | − | 0.673172i | \(-0.764931\pi\) | ||||
−0.739486 | + | 0.673172i | \(0.764931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3330.00 | 1.24196 | 0.620981 | − | 0.783826i | \(-0.286734\pi\) | ||||
0.620981 | + | 0.783826i | \(0.286734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 2963.24i | − 1.08822i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1195.88i | − 0.432502i | −0.976338 | − | 0.216251i | \(-0.930617\pi\) | ||||
0.976338 | − | 0.216251i | \(-0.0693829\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1736.00 | 0.618401 | 0.309200 | − | 0.950997i | \(-0.399939\pi\) | ||||
0.309200 | + | 0.950997i | \(0.399939\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −924.000 | −0.324248 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 1269.96i | − 0.439083i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 740.810i | 0.252392i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −152.000 | −0.0510373 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −588.000 | −0.194607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2915.62i | 0.951277i | 0.879641 | + | 0.475638i | \(0.157783\pi\) | ||||
−0.879641 | + | 0.475638i | \(0.842217\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 380.988i | − 0.122558i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4648.00 | 1.47438 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1792.00 | −0.560594 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1555.70i | 0.480021i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 740.810i | − 0.225486i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1568.00 | −0.470857 | −0.235428 | − | 0.971892i | \(-0.575649\pi\) | ||||
−0.235428 | + | 0.971892i | \(0.575649\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | −0.00385185 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1264.67i | 0.369775i | 0.982760 | + | 0.184888i | \(0.0591922\pi\) | ||||
−0.982760 | + | 0.184888i | \(0.940808\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5153.92i | 1.48725i | 0.668595 | + | 0.743626i | \(0.266896\pi\) | ||||
−0.668595 | + | 0.743626i | \(0.733104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 672.000 | 0.191404 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −838.000 | −0.235619 | −0.117809 | − | 0.993036i | \(-0.537587\pi\) | ||||
−0.117809 | + | 0.993036i | \(0.537587\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3555.89i | 0.987067i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 2455.26i | − 0.672937i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6288.00 | −1.70183 | −0.850914 | − | 0.525305i | \(-0.823951\pi\) | ||||
−0.850914 | + | 0.525305i | \(0.823951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2926.00 | −0.782076 | −0.391038 | − | 0.920375i | \(-0.627884\pi\) | ||||
−0.391038 | + | 0.920375i | \(0.627884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 280.450i | 0.0740364i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2952.66i | 0.769953i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1960.00 | −0.504906 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2884.00 | 0.734000 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 5444.96i | − 1.36925i | −0.728894 | − | 0.684627i | \(-0.759965\pi\) | ||||
0.728894 | − | 0.684627i | \(-0.240035\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2412.93i | 0.599602i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 784.000 | 0.192533 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2562.00 | 0.621841 | 0.310921 | − | 0.950436i | \(-0.399363\pi\) | ||||
0.310921 | + | 0.950436i | \(0.399363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1947.27i | 0.467172i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 158.745i | 0.0376478i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5896.00 | 1.38237 | 0.691184 | − | 0.722679i | \(-0.257089\pi\) | ||||
0.691184 | + | 0.722679i | \(0.257089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 336.000 | 0.0778880 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 1407.54i | − 0.322622i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 5365.58i | − 1.21615i | −0.793878 | − | 0.608077i | \(-0.791941\pi\) | ||||
0.793878 | − | 0.608077i | \(-0.208059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1680.00 | 0.376578 | 0.188289 | − | 0.982114i | \(-0.439706\pi\) | ||||
0.188289 | + | 0.982114i | \(0.439706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2240.00 | 0.496597 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 206.369i | 0.0452527i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1576.87i | − 0.342039i | −0.985268 | − | 0.171019i | \(-0.945294\pi\) | ||||
0.985268 | − | 0.171019i | \(-0.0547061\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 224.000 | 0.0480664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2742.00 | −0.582114 | −0.291057 | − | 0.956706i | \(-0.594007\pi\) | ||||
−0.291057 | + | 0.956706i | \(0.594007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2989.70i | − 0.627983i | −0.949426 | − | 0.313991i | \(-0.898334\pi\) | ||||
0.949426 | − | 0.313991i | \(-0.101666\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 2074.27i | − 0.431120i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −560.000 | −0.115177 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4717.00 | −0.960106 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 5259.75i | − 1.05956i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9238.96i | − 1.84214i | −0.389401 | − | 0.921068i | \(-0.627318\pi\) | ||||
0.389401 | − | 0.921068i | \(-0.372682\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5656.00 | −1.11629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2184.00 | 0.426695 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8043.08i | 1.55566i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3513.56i | 0.672818i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3976.00 | 0.753846 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1008.00 | 0.189239 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2587.54i | − 0.481039i | −0.970644 | − | 0.240520i | \(-0.922682\pi\) | ||||
0.970644 | − | 0.240520i | \(-0.0773178\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6222.81i | 1.14564i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2744.00 | 0.500315 | 0.250157 | − | 0.968205i | \(-0.419518\pi\) | ||||
0.250157 | + | 0.968205i | \(0.419518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2282.00 | 0.412097 | 0.206048 | − | 0.978542i | \(-0.433940\pi\) | ||||
0.206048 | + | 0.978542i | \(0.433940\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 84.6640i | 0.0151437i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9577.62i | 1.69695i | 0.529237 | + | 0.848474i | \(0.322478\pi\) | ||||
−0.529237 | + | 0.848474i | \(0.677522\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2520.00 | 0.442298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1428.00 | 0.248297 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 518.567i | − 0.0893308i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 687.895i | 0.117408i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10024.0 | −1.69519 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2688.00 | −0.450438 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4249.08i | 0.705590i | 0.935701 | + | 0.352795i | \(0.114769\pi\) | ||||
−0.935701 | + | 0.352795i | \(0.885231\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 243.409i | − 0.0400563i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1848.00 | −0.301394 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6130.00 | 0.990868 | 0.495434 | − | 0.868646i | \(-0.335009\pi\) | ||||
0.495434 | + | 0.868646i | \(0.335009\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9048.47i | 1.44969i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3555.89i | − 0.564699i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8512.00 | −1.32832 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 2481.71i | − 0.383935i | −0.981401 | − | 0.191967i | \(-0.938513\pi\) | ||||
0.981401 | − | 0.191967i | \(-0.0614868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 328.073i | − 0.0503191i | −0.999683 | − | 0.0251595i | \(-0.991991\pi\) | ||||
0.999683 | − | 0.0251595i | \(-0.00800937\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7280.00 | 1.10706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10206.0 | −1.53884 | −0.769420 | − | 0.638743i | \(-0.779455\pi\) | ||||
−0.769420 | + | 0.638743i | \(0.779455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 761.976i | − 0.113920i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 592.648i | 0.0878607i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3176.00 | 0.466916 | 0.233458 | − | 0.972367i | \(-0.424996\pi\) | ||||
0.233458 | + | 0.972367i | \(0.424996\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5487.00 | 0.799971 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 5709.53i | − 0.825545i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3111.40i | 0.446187i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11760.0 | 1.67266 | 0.836331 | − | 0.548225i | \(-0.184696\pi\) | ||||
0.836331 | + | 0.548225i | \(0.184696\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 70.0000 | 0.00987549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 253.992i | 0.0355434i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 10974.6i | − 1.52344i | −0.647908 | − | 0.761719i | \(-0.724356\pi\) | ||||
0.647908 | − | 0.761719i | \(-0.275644\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7728.00 | −1.06419 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8400.00 | 1.14754 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 3074.36i | − 0.416674i | −0.978057 | − | 0.208337i | \(-0.933195\pi\) | ||||
0.978057 | − | 0.208337i | \(-0.0668051\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 8805.06i | − 1.18398i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2688.00 | −0.358617 | −0.179309 | − | 0.983793i | \(-0.557386\pi\) | ||||
−0.179309 | + | 0.983793i | \(0.557386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1344.00 | 0.177913 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 439.195i | − 0.0576887i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10487.8i | 1.36697i | 0.729966 | + | 0.683484i | \(0.239536\pi\) | ||||
−0.729966 | + | 0.683484i | \(0.760464\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2128.00 | −0.275237 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3556.00 | 0.456429 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4910.51i | − 0.625506i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 5704.24i | − 0.721127i | −0.932735 | − | 0.360564i | \(-0.882584\pi\) | ||||
0.932735 | − | 0.360564i | \(-0.117416\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1568.00 | 0.196737 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12402.0 | 1.54445 | 0.772227 | − | 0.635346i | \(-0.219143\pi\) | ||||
0.772227 | + | 0.635346i | \(0.219143\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 11853.0i | − 1.46511i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7990.17i | 0.980333i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3864.00 | −0.470593 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12278.0 | −1.48437 | −0.742186 | − | 0.670194i | \(-0.766211\pi\) | ||||
−0.742186 | + | 0.670194i | \(0.766211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5619.58i | 0.674436i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 4275.53i | − 0.509407i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5768.00 | 0.682265 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14252.0 | −1.67368 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8207.12i | 0.956907i | 0.878113 | + | 0.478454i | \(0.158802\pi\) | ||||
−0.878113 | + | 0.478454i | \(0.841198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 1449.87i | − 0.167844i | −0.996472 | − | 0.0839221i | \(-0.973255\pi\) | ||||
0.996472 | − | 0.0839221i | \(-0.0267447\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 336.000 | 0.0386215 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −182.000 | −0.0207725 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 761.976i | 0.0863574i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4444.86i | 0.500233i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7632.00 | −0.852948 | −0.426474 | − | 0.904500i | \(-0.640244\pi\) | ||||
−0.426474 | + | 0.904500i | \(0.640244\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3794.00 | 0.421081 | 0.210540 | − | 0.977585i | \(-0.432478\pi\) | ||||
0.210540 | + | 0.977585i | \(0.432478\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8889.72i | 0.979838i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5630.16i | 0.616309i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1848.00 | 0.200912 | 0.100456 | − | 0.994942i | \(-0.467970\pi\) | ||||
0.100456 | + | 0.994942i | \(0.467970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 279.000 | 0.0301263 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12334.5i | 1.32287i | 0.750004 | + | 0.661433i | \(0.230051\pi\) | ||||
−0.750004 | + | 0.661433i | \(0.769949\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2815.08i | − 0.299882i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4200.00 | 0.444414 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3582.00 | −0.376492 | −0.188246 | − | 0.982122i | \(-0.560280\pi\) | ||||
−0.188246 | + | 0.982122i | \(0.560280\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 1111.22i | − 0.116020i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3936.88i | 0.408324i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4480.00 | 0.461595 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2714.00 | 0.277802 | 0.138901 | − | 0.990306i | \(-0.455643\pi\) | ||||
0.138901 | + | 0.990306i | \(0.455643\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1926.11i | 0.195867i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8349.99i | 0.843596i | 0.906690 | + | 0.421798i | \(0.138601\pi\) | ||||
−0.906690 | + | 0.421798i | \(0.861399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2224.00 | −0.223236 | −0.111618 | − | 0.993751i | \(-0.535603\pi\) | ||||
−0.111618 | + | 0.993751i | \(0.535603\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12544.0 | 1.25100 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 10292.0i | − 1.01982i | −0.860228 | − | 0.509910i | \(-0.829679\pi\) | ||||
0.860228 | − | 0.509910i | \(-0.170321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 1396.96i | − 0.137538i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 952.000 | 0.0931334 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6972.00 | −0.677744 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 481.527i | 0.0465136i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 31.7490i | − 0.00304756i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17696.0 | −1.68800 | −0.843999 | − | 0.536345i | \(-0.819805\pi\) | ||||
−0.843999 | + | 0.536345i | \(0.819805\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12880.0 | −1.22095 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6434.47i | − 0.606166i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 10519.5i | − 0.984879i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1304.00 | −0.121334 | −0.0606672 | − | 0.998158i | \(-0.519323\pi\) | ||||
−0.0606672 | + | 0.998158i | \(0.519323\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9380.00 | 0.867440 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 16662.9i | − 1.53154i | −0.643112 | − | 0.765772i | \(-0.722357\pi\) | ||||
0.643112 | − | 0.765772i | \(-0.277643\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2222.43i | 0.203029i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −168.000 | −0.0152546 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 576.000 | 0.0519862 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 3095.53i | − 0.277705i | −0.990313 | − | 0.138853i | \(-0.955659\pi\) | ||||
0.990313 | − | 0.138853i | \(-0.0443414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 10371.3i | − 0.924865i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19320.0 | 1.71260 | 0.856298 | − | 0.516481i | \(-0.172758\pi\) | ||||
0.856298 | + | 0.516481i | \(0.172758\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7952.00 | 0.700712 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3190.78i | 0.279502i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 4476.61i | − 0.389828i | −0.980820 | − | 0.194914i | \(-0.937557\pi\) | ||||
0.980820 | − | 0.194914i | \(-0.0624427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2352.00 | −0.203613 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5096.00 | 0.438585 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12445.6i | 1.06489i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5333.83i | − 0.453737i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10584.0 | 0.895156 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2982.00 | −0.250756 | −0.125378 | − | 0.992109i | \(-0.540014\pi\) | ||||
−0.125378 | + | 0.992109i | \(0.540014\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 2016.06i | − 0.168559i | −0.996442 | − | 0.0842794i | \(-0.973141\pi\) | ||||
0.996442 | − | 0.0842794i | \(-0.0268588\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 550.316i | − 0.0457481i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3136.00 | 0.259215 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10937.0 | 0.898907 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 534.442i | 0.0436776i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3704.05i | − 0.301014i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2856.00 | 0.230796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17276.0 | −1.38830 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4428.99i | − 0.353933i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15419.4i | 1.22539i | 0.790321 | + | 0.612693i | \(0.209914\pi\) | ||||
−0.790321 | + | 0.612693i | \(0.790086\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −12376.0 | −0.978094 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20048.0 | −1.57571 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12609.7i | 0.985649i | 0.870129 | + | 0.492824i | \(0.164035\pi\) | ||||
−0.870129 | + | 0.492824i | \(0.835965\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 95.2470i | − 0.00740445i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5880.00 | 0.454621 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3712.00 | 0.285444 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 13630.9i | − 1.04252i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 7143.53i | − 0.543413i | −0.962380 | − | 0.271706i | \(-0.912412\pi\) | ||||
0.962380 | − | 0.271706i | \(-0.0875880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23240.0 | −1.75840 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1176.00 | −0.0885040 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7572.14i | 0.566834i | 0.958997 | + | 0.283417i | \(0.0914681\pi\) | ||||
−0.958997 | + | 0.283417i | \(0.908532\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18096.9i | 1.34751i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6040.00 | −0.447365 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15594.0 | 1.14892 | 0.574459 | − | 0.818533i | \(-0.305212\pi\) | ||||
0.574459 | + | 0.818533i | \(0.305212\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16737.0i | 1.22666i | 0.789827 | + | 0.613330i | \(0.210170\pi\) | ||||
−0.789827 | + | 0.613330i | \(0.789830\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 20658.0i | 1.50611i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1976.00 | 0.143313 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6594.00 | 0.475757 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 17620.7i | − 1.26475i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4360.20i | 0.311345i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −504.000 | −0.0358037 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −560.000 | −0.0395780 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23213.8i | 1.63226i | 0.577868 | + | 0.816130i | \(0.303885\pi\) | ||||
−0.577868 | + | 0.816130i | \(0.696115\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 8297.08i | − 0.580433i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6328.00 | −0.440438 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14322.0 | 0.991794 | 0.495897 | − | 0.868381i | \(-0.334839\pi\) | ||||
0.495897 | + | 0.868381i | \(0.334839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1185.30i | 0.0816679i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 9186.05i | − 0.629749i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 16088.0 | 1.09739 | 0.548696 | − | 0.836022i | \(-0.315124\pi\) | ||||
0.548696 | + | 0.836022i | \(0.315124\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −21238.0 | −1.44146 | −0.720729 | − | 0.693217i | \(-0.756193\pi\) | ||||
−0.720729 | + | 0.693217i | \(0.756193\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 174.620i | 0.0117928i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 11419.1i | − 0.767357i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13664.0 | 0.913681 | 0.456841 | − | 0.889549i | \(-0.348981\pi\) | ||||
0.456841 | + | 0.889549i | \(0.348981\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6720.00 | −0.447140 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 17779.4i | − 1.17722i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20393.5i | 1.34369i | 0.740690 | + | 0.671846i | \(0.234499\pi\) | ||||
−0.740690 | + | 0.671846i | \(0.765501\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3920.00 | 0.257024 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3782.00 | −0.246771 | −0.123385 | − | 0.992359i | \(-0.539375\pi\) | ||||
−0.123385 | + | 0.992359i | \(0.539375\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 5825.94i | − 0.378295i | −0.981949 | − | 0.189147i | \(-0.939428\pi\) | ||||
0.981949 | − | 0.189147i | \(-0.0605724\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 20912.0i | − 1.35132i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2128.00 | 0.136848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13831.0 | −0.885184 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3111.40i | 0.198178i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 3407.73i | − 0.216017i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2056.00 | −0.129712 | −0.0648558 | − | 0.997895i | \(-0.520659\pi\) | ||||
−0.0648558 | + | 0.997895i | \(0.520659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15428.0 | 0.968733 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 17610.1i | − 1.10053i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 14763.3i | − 0.918278i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −72.0000 | −0.00445740 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11842.0 | 0.729689 | 0.364845 | − | 0.931068i | \(-0.381122\pi\) | ||||
0.364845 | + | 0.931068i | \(0.381122\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16250.2i | 0.996649i | 0.866991 | + | 0.498325i | \(0.166051\pi\) | ||||
−0.866991 | + | 0.498325i | \(0.833949\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 24594.9i | − 1.50143i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19320.0 | −1.17395 | −0.586976 | − | 0.809604i | \(-0.699682\pi\) | ||||
−0.586976 | + | 0.809604i | \(0.699682\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8484.00 | 0.513137 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9482.37i | 0.570881i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 2317.68i | − 0.138894i | −0.997586 | − | 0.0694470i | \(-0.977877\pi\) | ||||
0.997586 | − | 0.0694470i | \(-0.0221235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7112.00 | 0.424258 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 294.000 | 0.0174582 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 27732.8i | − 1.63932i | −0.572847 | − | 0.819662i | \(-0.694161\pi\) | ||||
0.572847 | − | 0.819662i | \(-0.305839\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22467.7i | 1.32208i | 0.750352 | + | 0.661039i | \(0.229884\pi\) | ||||
−0.750352 | + | 0.661039i | \(0.770116\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3920.00 | −0.229623 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3136.00 | 0.182870 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 24129.3i | − 1.40073i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8297.08i | 0.479497i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1512.00 | −0.0869897 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10078.0 | −0.577234 | −0.288617 | − | 0.957445i | \(-0.593195\pi\) | ||||
−0.288617 | + | 0.957445i | \(0.593195\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 1788.53i | − 0.101986i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16160.2i | 0.917413i | 0.888588 | + | 0.458707i | \(0.151687\pi\) | ||||
−0.888588 | + | 0.458707i | \(0.848313\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7952.00 | 0.449440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6692.00 | 0.376561 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16356.0i | 0.916320i | 0.888870 | + | 0.458160i | \(0.151491\pi\) | ||||
−0.888870 | + | 0.458160i | \(0.848509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11239.2i | 0.626899i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27272.0 | 1.51454 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1680.00 | −0.0928925 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29246.1i | 1.61009i | 0.593211 | + | 0.805047i | \(0.297860\pi\) | ||||
−0.593211 | + | 0.805047i | \(0.702140\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 126.996i | − 0.00696130i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28504.0 | −1.55571 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 980.000 | 0.0532570 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4434.28i | 0.239943i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2465.84i | 0.132858i | 0.997791 | + | 0.0664290i | \(0.0211606\pi\) | ||||
−0.997791 | + | 0.0664290i | \(0.978839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9016.00 | −0.483705 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18816.0 | 1.00518 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6011.15i | 0.319763i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 31674.9i | − 1.67782i | −0.544267 | − | 0.838912i | \(-0.683192\pi\) | ||||
0.544267 | − | 0.838912i | \(-0.316808\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −464.000 | −0.0244745 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34048.0 | −1.78837 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8889.72i | 0.464975i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 33273.0i | 1.73306i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9296.00 | 0.482173 | 0.241086 | − | 0.970504i | \(-0.422496\pi\) | ||||
0.241086 | + | 0.970504i | \(0.422496\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9408.00 | −0.485953 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15482.9i | 0.796427i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 2063.69i | − 0.105715i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21672.0 | −1.10560 | −0.552799 | − | 0.833315i | \(-0.686440\pi\) | ||||
−0.552799 | + | 0.833315i | \(0.686440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18901.0 | −0.960270 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 6148.73i | − 0.311106i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 9471.79i | − 0.477283i | −0.971108 | − | 0.238642i | \(-0.923298\pi\) | ||||
0.971108 | − | 0.238642i | \(-0.0767021\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15624.0 | 0.784082 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2772.00 | 0.138545 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 6863.08i | − 0.341627i | −0.985303 | − | 0.170814i | \(-0.945360\pi\) | ||||
0.985303 | − | 0.170814i | \(-0.0546396\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10371.3i | 0.514171i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17432.0 | −0.860724 | −0.430362 | − | 0.902656i | \(-0.641614\pi\) | ||||
−0.430362 | + | 0.902656i | \(0.641614\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8400.00 | 0.413090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 545.025i | − 0.0266953i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2158.93i | 0.105321i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11632.0 | 0.565190 | 0.282595 | − | 0.959239i | \(-0.408805\pi\) | ||||
0.282595 | + | 0.959239i | \(0.408805\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28812.0 | −1.39438 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7873.76i | 0.379543i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16731.7i | − 0.803336i | −0.915785 | − | 0.401668i | \(-0.868431\pi\) | ||||
0.915785 | − | 0.401668i | \(-0.131569\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12768.0 | 0.610605 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 39466.0 | 1.87995 | 0.939975 | − | 0.341244i | \(-0.110848\pi\) | ||||
0.939975 | + | 0.341244i | \(0.110848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 15154.9i | − 0.719060i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 148.162i | − 0.00700237i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 28280.0 | 1.33133 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35266.0 | 1.65374 | 0.826869 | − | 0.562395i | \(-0.190120\pi\) | ||||
0.826869 | + | 0.562395i | \(0.190120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 13556.8i | − 0.633252i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16244.9i | 0.755872i | 0.925832 | + | 0.377936i | \(0.123366\pi\) | ||||
−0.925832 | + | 0.377936i | \(0.876634\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2912.00 | −0.134970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10304.0 | 0.475745 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2592.84i | − 0.119253i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1142.96i | 0.0523668i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21840.0 | −0.996805 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1904.00 | 0.0865690 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34844.5i | − 1.57824i | −0.614240 | − | 0.789119i | \(-0.710537\pi\) | ||||
0.614240 | − | 0.789119i | \(-0.289463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 31198.7i | − 1.40774i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13680.0 | −0.614924 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5040.00 | −0.225694 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 1777.94i | − 0.0793172i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2550.50i | 0.113354i | 0.998393 | + | 0.0566772i | \(0.0180506\pi\) | ||||
−0.998393 | + | 0.0566772i | \(0.981949\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4704.00 | 0.208280 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −266.000 | −0.0117336 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 4667.11i | − 0.205104i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 12868.9i | − 0.563441i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28392.0 | −1.23847 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24390.0 | −1.05996 | −0.529979 | − | 0.848010i | \(-0.677800\pi\) | ||||
−0.529979 | + | 0.848010i | \(0.677800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9582.91i | 0.414922i | 0.978243 | + | 0.207461i | \(0.0665200\pi\) | ||||
−0.978243 | + | 0.207461i | \(0.933480\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 8889.72i | − 0.383489i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18760.0 | 0.806300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16268.0 | −0.696628 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 423.320i | − 0.0180611i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 8773.31i | − 0.372948i | −0.982460 | − | 0.186474i | \(-0.940294\pi\) | ||||
0.982460 | − | 0.186474i | \(-0.0597061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 21688.0 | 0.918586 | 0.459293 | − | 0.888285i | \(-0.348103\pi\) | ||||
0.459293 | + | 0.888285i | \(0.348103\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1092.00 | 0.0460831 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19446.3i | 0.817670i | 0.912608 | + | 0.408835i | \(0.134065\pi\) | ||||
−0.912608 | + | 0.408835i | \(0.865935\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 19546.8i | − 0.818925i | −0.912327 | − | 0.409462i | \(-0.865716\pi\) | ||||
0.912327 | − | 0.409462i | \(-0.134284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8344.00 | −0.348315 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3906.00 | 0.162467 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 20742.7i | − 0.859677i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30817.7i | 1.27266i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18760.0 | 0.771951 | 0.385976 | − | 0.922509i | \(-0.373865\pi\) | ||||
0.385976 | + | 0.922509i | \(0.373865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −811.000 | −0.0332527 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 14509.3i | 0.592796i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6381.55i | 0.259801i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8632.00 | 0.350176 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15820.0 | −0.639506 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36998.2i | 1.49034i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28732.9i | 1.15333i | 0.816979 | + | 0.576667i | \(0.195647\pi\) | ||||
−0.816979 | + | 0.576667i | \(0.804353\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −392.000 | −0.0156797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8778.00 | 0.349884 | 0.174942 | − | 0.984579i | \(-0.444026\pi\) | ||||
0.174942 | + | 0.984579i | \(0.444026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5646.03i | 0.224261i | 0.993693 | + | 0.112130i | \(0.0357675\pi\) | ||||
−0.993693 | + | 0.112130i | \(0.964233\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2963.24i | 0.117290i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9312.00 | 0.367305 | 0.183652 | − | 0.982991i | \(-0.441208\pi\) | ||||
0.183652 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21168.0 | 0.832062 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24960.0i | 0.977724i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7365.77i | 0.287534i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9240.00 | 0.359455 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −994.000 | −0.0385359 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 11683.6i | − 0.451405i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 137.579i | 0.00529728i | 0.999996 | + | 0.00264864i | \(0.000843089\pi\) | ||||
−0.999996 | + | 0.00264864i | \(0.999157\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −48888.0 | −1.87594 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31150.0 | −1.19123 | −0.595613 | − | 0.803272i | \(-0.703091\pi\) | ||||
−0.595613 | + | 0.803272i | \(0.703091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 12577.9i | − 0.479366i | −0.970851 | − | 0.239683i | \(-0.922957\pi\) | ||||
0.970851 | − | 0.239683i | \(-0.0770435\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 29928.7i | 1.13677i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −37128.0 | −1.40545 | −0.702726 | − | 0.711460i | \(-0.748034\pi\) | ||||
−0.702726 | + | 0.711460i | \(0.748034\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13312.0 | 0.502216 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 11985.3i | − 0.450641i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 12445.6i | − 0.466379i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34552.0 | −1.29044 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 42560.0 | 1.58421 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35558.9i | 1.31919i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 444.486i | − 0.0164351i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 18592.0 | 0.685164 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24752.0 | −0.909154 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 35204.4i | − 1.28880i | −0.764688 | − | 0.644400i | \(-0.777107\pi\) | ||||
0.764688 | − | 0.644400i | \(-0.222893\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 751.393i | − 0.0274171i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10512.0 | 0.382303 | 0.191152 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191152 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8652.00 | −0.313625 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 5333.83i | − 0.192712i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5376.17i | 0.193606i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46104.0 | 1.65488 | 0.827438 | − | 0.561557i | \(-0.189798\pi\) | ||||
0.827438 | + | 0.561557i | \(0.189798\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13692.0 | −0.489866 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3809.88i | 0.135865i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3164.32i | 0.112478i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1176.00 | 0.0416666 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5726.00 | −0.202222 | −0.101111 | − | 0.994875i | \(-0.532240\pi\) | ||||
−0.101111 | + | 0.994875i | \(0.532240\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 10334.3i | − 0.363795i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 14519.9i | − 0.509496i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2352.00 | −0.0822659 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1274.00 | 0.0444181 | 0.0222091 | − | 0.999753i | \(-0.492930\pi\) | ||||
0.0222091 | + | 0.999753i | \(0.492930\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 12075.2i | − 0.419659i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 26446.9i | − 0.916201i | −0.888900 | − | 0.458101i | \(-0.848530\pi\) | ||||
0.888900 | − | 0.458101i | \(-0.151470\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10640.0 | −0.367430 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11648.0 | −0.400962 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 23922.9i | − 0.820897i | −0.911884 | − | 0.410448i | \(-0.865372\pi\) | ||||
0.911884 | − | 0.410448i | \(-0.134628\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 15557.0i | − 0.532141i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50680.0 | 1.72809 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38250.0 | 1.30015 | 0.650073 | − | 0.759872i | \(-0.274738\pi\) | ||||
0.650073 | + | 0.759872i | \(0.274738\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41316.1i | 1.39995i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 13334.6i | − 0.450414i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8496.00 | −0.286079 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20385.0 | 0.684267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 269.867i | − 0.00903046i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 35241.4i | − 1.17561i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4664.00 | −0.155103 | −0.0775513 | − | 0.996988i | \(-0.524710\pi\) | ||||
−0.0775513 | + | 0.996988i | \(0.524710\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2744.00 | −0.0909701 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 30971.2i | − 1.02360i | −0.859106 | − | 0.511798i | \(-0.828980\pi\) | ||||
0.859106 | − | 0.511798i | \(-0.171020\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 21547.0i | − 0.709933i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3640.00 | 0.119562 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4814.00 | −0.157639 | −0.0788196 | − | 0.996889i | \(-0.525115\pi\) | ||||
−0.0788196 | + | 0.996889i | \(0.525115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4222.62i | 0.137850i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1894.36i | 0.0616536i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12376.0 | 0.401560 | 0.200780 | − | 0.979636i | \(-0.435652\pi\) | ||||
0.200780 | + | 0.979636i | \(0.435652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12656.0 | −0.409395 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14223.6i | 0.458704i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 66757.6i | 2.14638i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45344.0 | −1.45348 | −0.726740 | − | 0.686912i | \(-0.758966\pi\) | ||||
−0.726740 | + | 0.686912i | \(0.758966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22484.0 | 0.718538 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 18372.1i | − 0.585361i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 26002.4i | − 0.825984i | −0.910735 | − | 0.412992i | \(-0.864484\pi\) | ||||
0.910735 | − | 0.412992i | \(-0.135516\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33488.0 | 1.06057 |
(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 | 32.4.b.a.17.1 | 2 | ||
3.2 | odd | 2 | 288.4.d.a.145.2 | 2 | |||
4.3 | odd | 2 | 8.4.b.a.5.1 | ✓ | 2 | ||
5.2 | odd | 4 | 800.4.f.a.49.2 | 4 | |||
5.3 | odd | 4 | 800.4.f.a.49.3 | 4 | |||
5.4 | even | 2 | 800.4.d.a.401.2 | 2 | |||
8.3 | odd | 2 | 8.4.b.a.5.2 | yes | 2 | ||
8.5 | even | 2 | inner | 32.4.b.a.17.2 | 2 | ||
12.11 | even | 2 | 72.4.d.b.37.2 | 2 | |||
16.3 | odd | 4 | 256.4.a.l.1.1 | 2 | |||
16.5 | even | 4 | 256.4.a.j.1.1 | 2 | |||
16.11 | odd | 4 | 256.4.a.l.1.2 | 2 | |||
16.13 | even | 4 | 256.4.a.j.1.2 | 2 | |||
20.3 | even | 4 | 200.4.f.a.149.2 | 4 | |||
20.7 | even | 4 | 200.4.f.a.149.3 | 4 | |||
20.19 | odd | 2 | 200.4.d.a.101.2 | 2 | |||
24.5 | odd | 2 | 288.4.d.a.145.1 | 2 | |||
24.11 | even | 2 | 72.4.d.b.37.1 | 2 | |||
40.3 | even | 4 | 200.4.f.a.149.4 | 4 | |||
40.13 | odd | 4 | 800.4.f.a.49.1 | 4 | |||
40.19 | odd | 2 | 200.4.d.a.101.1 | 2 | |||
40.27 | even | 4 | 200.4.f.a.149.1 | 4 | |||
40.29 | even | 2 | 800.4.d.a.401.1 | 2 | |||
40.37 | odd | 4 | 800.4.f.a.49.4 | 4 | |||
48.5 | odd | 4 | 2304.4.a.v.1.1 | 2 | |||
48.11 | even | 4 | 2304.4.a.bn.1.1 | 2 | |||
48.29 | odd | 4 | 2304.4.a.v.1.2 | 2 | |||
48.35 | even | 4 | 2304.4.a.bn.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.4.b.a.5.1 | ✓ | 2 | 4.3 | odd | 2 | ||
8.4.b.a.5.2 | yes | 2 | 8.3 | odd | 2 | ||
32.4.b.a.17.1 | 2 | 1.1 | even | 1 | trivial | ||
32.4.b.a.17.2 | 2 | 8.5 | even | 2 | inner | ||
72.4.d.b.37.1 | 2 | 24.11 | even | 2 | |||
72.4.d.b.37.2 | 2 | 12.11 | even | 2 | |||
200.4.d.a.101.1 | 2 | 40.19 | odd | 2 | |||
200.4.d.a.101.2 | 2 | 20.19 | odd | 2 | |||
200.4.f.a.149.1 | 4 | 40.27 | even | 4 | |||
200.4.f.a.149.2 | 4 | 20.3 | even | 4 | |||
200.4.f.a.149.3 | 4 | 20.7 | even | 4 | |||
200.4.f.a.149.4 | 4 | 40.3 | even | 4 | |||
256.4.a.j.1.1 | 2 | 16.5 | even | 4 | |||
256.4.a.j.1.2 | 2 | 16.13 | even | 4 | |||
256.4.a.l.1.1 | 2 | 16.3 | odd | 4 | |||
256.4.a.l.1.2 | 2 | 16.11 | odd | 4 | |||
288.4.d.a.145.1 | 2 | 24.5 | odd | 2 | |||
288.4.d.a.145.2 | 2 | 3.2 | odd | 2 | |||
800.4.d.a.401.1 | 2 | 40.29 | even | 2 | |||
800.4.d.a.401.2 | 2 | 5.4 | even | 2 | |||
800.4.f.a.49.1 | 4 | 40.13 | odd | 4 | |||
800.4.f.a.49.2 | 4 | 5.2 | odd | 4 | |||
800.4.f.a.49.3 | 4 | 5.3 | odd | 4 | |||
800.4.f.a.49.4 | 4 | 40.37 | odd | 4 | |||
2304.4.a.v.1.1 | 2 | 48.5 | odd | 4 | |||
2304.4.a.v.1.2 | 2 | 48.29 | odd | 4 | |||
2304.4.a.bn.1.1 | 2 | 48.11 | even | 4 | |||
2304.4.a.bn.1.2 | 2 | 48.35 | even | 4 |