Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,4,Mod(17,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.t (of order \(6\), degree \(2\), 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: | \(14.8684813214\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + \cdots + 7375227456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{18} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.3 | ||
Root | \(-1.35249 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.17 |
Dual form | 252.4.t.a.89.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27106 | − | 7.39769i | −0.382015 | − | 0.661670i | 0.609335 | − | 0.792913i | \(-0.291436\pi\) |
−0.991350 | + | 0.131243i | \(0.958103\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.5787 | − | 13.5933i | −0.679184 | − | 0.733968i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.4679 | + | 15.8586i | 0.752900 | + | 0.434687i | 0.826741 | − | 0.562583i | \(-0.190192\pi\) |
−0.0738410 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 9.92568i | − | 0.211761i | −0.994379 | − | 0.105880i | \(-0.966234\pi\) | ||
0.994379 | − | 0.105880i | \(-0.0337660\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −63.7751 | + | 110.462i | −0.909866 | + | 1.57593i | −0.0956180 | + | 0.995418i | \(0.530483\pi\) |
−0.814248 | + | 0.580517i | \(0.802851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −100.923 | + | 58.2677i | −1.21859 | + | 0.703554i | −0.964616 | − | 0.263657i | \(-0.915071\pi\) |
−0.253974 | + | 0.967211i | \(0.581738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −55.8271 | + | 32.2318i | −0.506120 | + | 0.292208i | −0.731237 | − | 0.682123i | \(-0.761057\pi\) |
0.225118 | + | 0.974332i | \(0.427723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 26.0161 | − | 45.0612i | 0.208129 | − | 0.360489i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113.016i | 0.723671i | 0.932242 | + | 0.361836i | \(0.117850\pi\) | ||||
−0.932242 | + | 0.361836i | \(0.882150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.33498 | + | 3.65751i | 0.0367031 | + | 0.0211906i | 0.518239 | − | 0.855236i | \(-0.326588\pi\) |
−0.481536 | + | 0.876426i | \(0.659921\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −46.8346 | + | 151.111i | −0.226185 | + | 0.729783i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −184.736 | − | 319.972i | −0.820822 | − | 1.42171i | −0.905071 | − | 0.425261i | \(-0.860182\pi\) |
0.0842481 | − | 0.996445i | \(-0.473151\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −211.959 | −0.807376 | −0.403688 | − | 0.914897i | \(-0.632272\pi\) | ||||
−0.403688 | + | 0.914897i | \(0.632272\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −432.263 | −1.53301 | −0.766506 | − | 0.642237i | \(-0.778007\pi\) | ||||
−0.766506 | + | 0.642237i | \(0.778007\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 200.021 | + | 346.446i | 0.620766 | + | 1.07520i | 0.989343 | + | 0.145601i | \(0.0465117\pi\) |
−0.368577 | + | 0.929597i | \(0.620155\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.5540 | + | 341.971i | −0.0774170 | + | 0.996999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 121.869 | + | 70.3612i | 0.315849 | + | 0.182356i | 0.649541 | − | 0.760327i | \(-0.274961\pi\) |
−0.333692 | + | 0.942682i | \(0.608294\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 270.933i | − | 0.664228i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −259.447 | + | 449.375i | −0.572493 | + | 0.991587i | 0.423816 | + | 0.905748i | \(0.360690\pi\) |
−0.996309 | + | 0.0858389i | \(0.972643\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.5627 | − | 13.6039i | 0.0494573 | − | 0.0285542i | −0.475067 | − | 0.879949i | \(-0.657576\pi\) |
0.524525 | + | 0.851395i | \(0.324243\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −73.4271 | + | 42.3932i | −0.140116 | + | 0.0808958i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 68.3597 | − | 118.403i | 0.124649 | − | 0.215898i | −0.796947 | − | 0.604050i | \(-0.793553\pi\) |
0.921596 | + | 0.388151i | \(0.126886\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 604.779i | − | 1.01090i | −0.862855 | − | 0.505451i | \(-0.831326\pi\) | ||
0.862855 | − | 0.505451i | \(-0.168674\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41.9780 | − | 24.2360i | −0.0673035 | − | 0.0388577i | 0.465971 | − | 0.884800i | \(-0.345705\pi\) |
−0.533274 | + | 0.845942i | \(0.679039\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −129.940 | − | 572.860i | −0.192312 | − | 0.847837i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 415.618 | + | 719.872i | 0.591907 | + | 1.02521i | 0.993975 | + | 0.109604i | \(0.0349582\pi\) |
−0.402068 | + | 0.915610i | \(0.631708\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 37.2350 | 0.0492418 | 0.0246209 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246209 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1089.55 | 1.39033 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −235.356 | − | 407.649i | −0.280311 | − | 0.485513i | 0.691150 | − | 0.722711i | \(-0.257104\pi\) |
−0.971461 | + | 0.237198i | \(0.923771\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −134.922 | + | 124.852i | −0.155425 | + | 0.143825i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 862.093 | + | 497.730i | 0.931041 | + | 0.537537i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 522.691i | − | 0.547126i | −0.961854 | − | 0.273563i | \(-0.911798\pi\) | ||
0.961854 | − | 0.273563i | \(-0.0882022\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 527.361 | − | 913.417i | 0.519549 | − | 0.899885i | −0.480193 | − | 0.877163i | \(-0.659433\pi\) |
0.999742 | − | 0.0227221i | \(-0.00723329\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −643.991 | + | 371.808i | −0.616061 | + | 0.355683i | −0.775334 | − | 0.631552i | \(-0.782418\pi\) |
0.159273 | + | 0.987235i | \(0.449085\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 204.383 | − | 118.001i | 0.184659 | − | 0.106613i | −0.404821 | − | 0.914396i | \(-0.632666\pi\) |
0.589480 | + | 0.807783i | \(0.299333\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116.269 | − | 201.385i | 0.102171 | − | 0.176965i | −0.810408 | − | 0.585866i | \(-0.800755\pi\) |
0.912579 | + | 0.408901i | \(0.134088\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2266.43i | − | 1.88680i | −0.331661 | − | 0.943398i | \(-0.607609\pi\) | ||
0.331661 | − | 0.943398i | \(-0.392391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 476.882 | + | 275.328i | 0.386691 | + | 0.223256i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2303.74 | − | 522.549i | 1.77465 | − | 0.402538i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −162.508 | − | 281.472i | −0.122095 | − | 0.211474i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1512.23 | −1.08206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1675.71 | 1.17083 | 0.585414 | − | 0.810735i | \(-0.300932\pi\) | ||||
0.585414 | + | 0.810735i | \(0.300932\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 593.103 | + | 1027.28i | 0.395570 | + | 0.685147i | 0.993174 | − | 0.116645i | \(-0.0372138\pi\) |
−0.597604 | + | 0.801791i | \(0.703881\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2061.52 | + | 638.938i | 1.34403 | + | 0.416564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2743.44 | − | 1583.92i | −1.71086 | − | 0.987764i | −0.933406 | − | 0.358821i | \(-0.883179\pi\) |
−0.777451 | − | 0.628943i | \(-0.783488\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 607.821i | 0.370897i | 0.982654 | + | 0.185448i | \(0.0593738\pi\) | ||||
−0.982654 | + | 0.185448i | \(0.940626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 157.408 | − | 272.638i | 0.0920496 | − | 0.159435i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 836.055 | − | 482.696i | 0.478832 | − | 0.276454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1117.57 | − | 645.230i | 0.614463 | − | 0.354760i | −0.160247 | − | 0.987077i | \(-0.551229\pi\) |
0.774710 | + | 0.632317i | \(0.217896\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1452.49 | + | 2515.79i | −0.782796 | + | 1.35584i | 0.147510 | + | 0.989060i | \(0.452874\pi\) |
−0.930307 | + | 0.366782i | \(0.880459\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 62.4857i | − | 0.0323805i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1022.35 | − | 590.254i | −0.519697 | − | 0.300047i | 0.217114 | − | 0.976146i | \(-0.430336\pi\) |
−0.736811 | + | 0.676099i | \(0.763669\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1140.37 | + | 353.440i | 0.558220 | + | 0.173012i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −803.791 | − | 1392.21i | −0.386244 | − | 0.668994i | 0.605697 | − | 0.795695i | \(-0.292894\pi\) |
−0.991941 | + | 0.126701i | \(0.959561\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2621.57 | −1.21475 | −0.607374 | − | 0.794416i | \(-0.707777\pi\) | ||||
−0.607374 | + | 0.794416i | \(0.707777\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2098.48 | 0.955157 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1321.78 | + | 2289.40i | 0.580887 | + | 1.00613i | 0.995375 | + | 0.0960706i | \(0.0306275\pi\) |
−0.414488 | + | 0.910055i | \(0.636039\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −939.777 | + | 213.166i | −0.405945 | + | 0.0920791i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3594.15 | + | 2075.08i | 1.50078 | + | 0.866475i | 1.00000 | 0.000899820i | \(0.000286422\pi\) | |
0.500779 | + | 0.865575i | \(0.333047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4040.50i | − | 1.65927i | −0.558304 | − | 0.829636i | \(-0.688548\pi\) | ||
0.558304 | − | 0.829636i | \(-0.311452\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1578.04 | + | 2733.24i | −0.627133 | + | 1.08623i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3503.54 | + | 2022.77i | −1.37008 | + | 0.791014i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3227.37 | + | 1863.32i | −1.22264 | + | 0.705892i | −0.965480 | − | 0.260477i | \(-0.916120\pi\) |
−0.257161 | + | 0.966369i | \(0.582787\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −668.472 | + | 1157.83i | −0.249314 | + | 0.431825i | −0.963336 | − | 0.268299i | \(-0.913539\pi\) |
0.714022 | + | 0.700124i | \(0.246872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3451.92i | − | 1.24842i | −0.781256 | − | 0.624210i | \(-0.785421\pi\) | ||
0.781256 | − | 0.624210i | \(-0.214579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4621.37 | − | 2668.15i | −1.64623 | − | 0.950453i | −0.978551 | − | 0.206006i | \(-0.933953\pi\) |
−0.667682 | − | 0.744447i | \(-0.732713\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1536.25 | − | 1421.59i | 0.531151 | − | 0.491506i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 905.289 | + | 1568.01i | 0.308430 | + | 0.534216i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3696.18 | −1.22330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1800.90 | 0.587578 | 0.293789 | − | 0.955870i | \(-0.405084\pi\) | ||||
0.293789 | + | 0.955870i | \(0.405084\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1846.22 | + | 3197.75i | 0.585634 | + | 1.01435i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.9682 | − | 132.120i | −0.00937501 | − | 0.0413312i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1096.41 | + | 633.011i | 0.333721 | + | 0.192674i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2815.72i | − | 0.845535i | −0.906238 | − | 0.422768i | \(-0.861059\pi\) | ||
0.906238 | − | 0.422768i | \(-0.138941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1976.56 | + | 3423.50i | −0.577925 | + | 1.00100i | 0.417792 | + | 0.908543i | \(0.362804\pi\) |
−0.995717 | + | 0.0924528i | \(0.970529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2132.66 | + | 1231.29i | −0.615416 | + | 0.355311i | −0.775082 | − | 0.631860i | \(-0.782292\pi\) |
0.159666 | + | 0.987171i | \(0.448958\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4505.33 | + | 2601.16i | −1.26676 | + | 0.731362i | −0.974373 | − | 0.224939i | \(-0.927782\pi\) |
−0.292384 | + | 0.956301i | \(0.594448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1708.60 | − | 2959.38i | 0.474284 | − | 0.821485i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1510.80i | 0.408894i | 0.978878 | + | 0.204447i | \(0.0655396\pi\) | ||||
−0.978878 | + | 0.204447i | \(0.934460\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1360.97 | − | 785.759i | −0.363768 | − | 0.210022i | 0.306964 | − | 0.951721i | \(-0.400687\pi\) |
−0.670732 | + | 0.741699i | \(0.734020\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2643.21 | − | 1264.14i | 0.689259 | − | 0.329644i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 578.346 | + | 1001.73i | 0.148985 | + | 0.258050i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3863.31 | −0.971514 | −0.485757 | − | 0.874094i | \(-0.661456\pi\) | ||||
−0.485757 | + | 0.874094i | \(0.661456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2044.61 | −0.508077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2911.09 | + | 5042.16i | 0.706572 | + | 1.22382i | 0.966121 | + | 0.258089i | \(0.0830929\pi\) |
−0.259549 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2025.74 | + | 6536.00i | −0.485997 | + | 1.56806i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 935.656 | + | 540.201i | 0.219373 | + | 0.126655i | 0.605660 | − | 0.795724i | \(-0.292909\pi\) |
−0.386287 | + | 0.922379i | \(0.626243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1202.07i | − | 0.278651i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1142.76 | + | 1979.32i | −0.259016 | + | 0.448630i | −0.965979 | − | 0.258622i | \(-0.916732\pi\) |
0.706962 | + | 0.707251i | \(0.250065\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1966.85 | + | 1135.56i | −0.440877 | + | 0.254540i | −0.703969 | − | 0.710230i | \(-0.748591\pi\) |
0.263093 | + | 0.964771i | \(0.415257\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1429.22 | − | 825.159i | 0.313400 | − | 0.180942i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −824.549 | + | 1428.16i | −0.178853 | + | 0.309783i | −0.941488 | − | 0.337046i | \(-0.890572\pi\) |
0.762635 | + | 0.646829i | \(0.223905\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7573.33i | − | 1.60778i | −0.594776 | − | 0.803892i | \(-0.702759\pi\) | ||
0.594776 | − | 0.803892i | \(-0.297241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4526.00 | + | 2613.09i | 0.950682 | + | 0.548877i | 0.893293 | − | 0.449475i | \(-0.148389\pi\) |
0.0573894 | + | 0.998352i | \(0.481722\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2666.16 | + | 2881.21i | 0.548357 | + | 0.592588i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5678.02 | − | 9834.62i | −1.15571 | − | 2.00175i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4924.11 | −0.981808 | −0.490904 | − | 0.871214i | \(-0.663333\pi\) | ||||
−0.490904 | + | 0.871214i | \(0.663333\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4432.45 | 0.874805 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 319.922 | + | 554.122i | 0.0618782 | + | 0.107176i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5437.30 | + | 5875.87i | 1.04120 | + | 1.12518i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −201.275 | − | 116.206i | −0.0377869 | − | 0.0218163i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10064.5i | − | 1.87105i | −0.353256 | − | 0.935527i | \(-0.614925\pi\) | ||
0.353256 | − | 0.935527i | \(-0.385075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1150.12 | − | 1992.06i | 0.209701 | − | 0.363214i | −0.741919 | − | 0.670490i | \(-0.766084\pi\) |
0.951620 | + | 0.307276i | \(0.0994175\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 898.271 | − | 518.617i | 0.162215 | − | 0.0936548i | −0.416695 | − | 0.909046i | \(-0.636812\pi\) |
0.578910 | + | 0.815392i | \(0.303478\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7214.93 | − | 4165.54i | 1.27833 | − | 0.738044i | 0.301789 | − | 0.953375i | \(-0.402416\pi\) |
0.976541 | + | 0.215330i | \(0.0690828\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1792.27 | + | 3104.31i | −0.314570 | + | 0.544852i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 14864.1i | − | 2.56056i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −447.263 | − | 258.227i | −0.0763375 | − | 0.0440735i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2193.34 | − | 7076.77i | 0.367546 | − | 1.18588i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1397.99 | + | 2421.39i | 0.232146 | + | 0.402089i | 0.958440 | − | 0.285296i | \(-0.0920918\pi\) |
−0.726293 | + | 0.687385i | \(0.758759\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1167.87 | −0.190471 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4675.27 | 0.755721 | 0.377861 | − | 0.925863i | \(-0.376660\pi\) | ||||
0.377861 | + | 0.925863i | \(0.376660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 116.006 | + | 200.928i | 0.0184225 | + | 0.0319087i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4982.51 | − | 3940.58i | 0.784345 | − | 0.620324i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2303.50 | + | 1329.93i | 0.356364 | + | 0.205747i | 0.667485 | − | 0.744623i | \(-0.267371\pi\) |
−0.311120 | + | 0.950370i | \(0.600704\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12826.3i | 1.96727i | 0.180181 | + | 0.983633i | \(0.442332\pi\) | ||||
−0.180181 | + | 0.983633i | \(0.557668\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4113.76 | + | 7125.25i | −0.620265 | + | 1.07433i | 0.369171 | + | 0.929361i | \(0.379642\pi\) |
−0.989436 | + | 0.144969i | \(0.953692\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4473.97 | + | 2583.05i | −0.668883 | + | 0.386180i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.38244 | − | 4.26226i | 0.00108532 | − | 0.000626611i | −0.499457 | − | 0.866339i | \(-0.666467\pi\) |
0.500543 | + | 0.865712i | \(0.333134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3360.74 | − | 5820.98i | 0.489976 | − | 0.848663i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 414.054i | 0.0593769i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6325.97 | + | 3652.30i | 0.899763 | + | 0.519478i | 0.877123 | − | 0.480265i | \(-0.159460\pi\) |
0.0226398 | + | 0.999744i | \(0.492793\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −576.514 | − | 2541.65i | −0.0806768 | − | 0.355676i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4253.40 | + | 7367.10i | 0.590436 | + | 1.02266i | 0.994174 | + | 0.107790i | \(0.0343774\pi\) |
−0.403738 | + | 0.914875i | \(0.632289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1121.76 | 0.153245 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7735.02 | 1.04834 | 0.524171 | − | 0.851613i | \(-0.324375\pi\) | ||||
0.524171 | + | 0.851613i | \(0.324375\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3963.43 | − | 6864.86i | −0.528777 | − | 0.915869i | −0.999437 | − | 0.0335545i | \(-0.989317\pi\) |
0.470659 | − | 0.882315i | \(-0.344016\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3682.86 | + | 3407.97i | −0.487522 | + | 0.451133i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9283.67 | + | 5359.93i | 1.21003 | + | 0.698609i | 0.962765 | − | 0.270339i | \(-0.0871359\pi\) |
0.247262 | + | 0.968949i | \(0.420469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8222.34i | − | 1.06348i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3550.26 | − | 6149.23i | 0.452235 | − | 0.783295i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4886.86 | + | 2821.43i | −0.617795 | + | 0.356684i | −0.776010 | − | 0.630721i | \(-0.782759\pi\) |
0.158215 | + | 0.987405i | \(0.449426\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 159.937 | − | 92.3395i | 0.0199174 | − | 0.0114993i | −0.490008 | − | 0.871718i | \(-0.663006\pi\) |
0.509926 | + | 0.860218i | \(0.329673\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.3032 | − | 62.8790i | 0.00448733 | − | 0.00777228i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 11718.6i | − | 1.42720i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2321.40 | − | 1340.26i | −0.280651 | − | 0.162034i | 0.353067 | − | 0.935598i | \(-0.385139\pi\) |
−0.633718 | + | 0.773564i | \(0.718472\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9371.97 | − | 2125.81i | 1.11662 | − | 0.253279i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −159.033 | − | 275.453i | −0.0188111 | − | 0.0325818i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12735.7 | −1.48492 | −0.742460 | − | 0.669890i | \(-0.766341\pi\) | ||||
−0.742460 | + | 0.669890i | \(0.766341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3317.68 | 0.384070 | 0.192035 | − | 0.981388i | \(-0.438491\pi\) | ||||
0.192035 | + | 0.981388i | \(0.438491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3318.36 | + | 5747.56i | 0.378739 | + | 0.655994i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −481.309 | − | 149.175i | −0.0545485 | − | 0.0169065i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7748.89 | − | 4473.82i | −0.866011 | − | 0.499992i | 9.69024e−6 | − | 1.00000i | \(-0.499997\pi\) |
−0.866021 | + | 0.500008i | \(0.833330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 11833.0i | − | 1.31330i | −0.754194 | − | 0.656651i | \(-0.771972\pi\) | ||
0.754194 | − | 0.656651i | \(-0.228028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3756.14 | − | 6505.83i | 0.411169 | − | 0.712165i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7376.74 | − | 4258.96i | 0.801988 | − | 0.463028i | −0.0421781 | − | 0.999110i | \(-0.513430\pi\) |
0.844166 | + | 0.536082i | \(0.180096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7190.84 | + | 4151.64i | −0.771213 | + | 0.445260i | −0.833307 | − | 0.552810i | \(-0.813555\pi\) |
0.0620942 | + | 0.998070i | \(0.480222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2010.44 | + | 3482.19i | −0.214166 | + | 0.370947i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14235.2i | 1.49622i | 0.663575 | + | 0.748110i | \(0.269039\pi\) | ||||
−0.663575 | + | 0.748110i | \(0.730961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5822.08 | − | 3361.38i | −0.607873 | − | 0.350956i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1499.88 | + | 464.865i | 0.154539 | + | 0.0478972i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3046.98 | + | 5277.52i | 0.311885 | + | 0.540201i | 0.978770 | − | 0.204959i | \(-0.0657062\pi\) |
−0.666885 | + | 0.745160i | \(0.732373\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13335.2 | 1.34725 | 0.673625 | − | 0.739073i | \(-0.264736\pi\) | ||||
0.673625 | + | 0.739073i | \(0.264736\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6596.99 | −0.662178 | −0.331089 | − | 0.943600i | \(-0.607416\pi\) | ||||
−0.331089 | + | 0.943600i | \(0.607416\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2176.35 | + | 3769.54i | 0.215652 | + | 0.373519i | 0.953474 | − | 0.301475i | \(-0.0974791\pi\) |
−0.737822 | + | 0.674995i | \(0.764146\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2469.35 | + | 560.114i | −0.243122 | + | 0.0551464i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11873.4 | − | 6855.10i | −1.15420 | − | 0.666380i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6063.59i | 0.585719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 159.875 | − | 276.912i | 0.0152503 | − | 0.0264143i | −0.858300 | − | 0.513149i | \(-0.828479\pi\) |
0.873550 | + | 0.486735i | \(0.161812\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3175.94 | + | 1833.63i | −0.301061 | + | 0.173818i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3866.71 | + | 2232.45i | −0.362017 | + | 0.209011i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2919.49 | + | 5056.70i | −0.271652 | + | 0.470515i | −0.969285 | − | 0.245940i | \(-0.920903\pi\) |
0.697633 | + | 0.716455i | \(0.254237\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12442.2i | 1.14360i | 0.820392 | + | 0.571801i | \(0.193755\pi\) | ||||
−0.820392 | + | 0.571801i | \(0.806245\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12483.9 | − | 7207.58i | −1.14046 | − | 0.658444i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8220.92 | + | 7607.31i | −0.741969 | + | 0.686589i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8348.40 | − | 14459.9i | −0.748949 | − | 1.29722i | −0.948327 | − | 0.317295i | \(-0.897225\pi\) |
0.199378 | − | 0.979923i | \(-0.436108\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4435.36 | −0.393167 | −0.196583 | − | 0.980487i | \(-0.562985\pi\) | ||||
−0.196583 | + | 0.980487i | \(0.562985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9009.57 | −0.793902 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11207.4 | + | 19411.8i | 0.975951 | + | 1.69040i | 0.676761 | + | 0.736203i | \(0.263383\pi\) |
0.299190 | + | 0.954193i | \(0.403283\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 198.581 | + | 875.476i | 0.0171912 | + | 0.0757901i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5501.05 | + | 3176.03i | 0.470689 | + | 0.271753i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12688.2i | 1.07936i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9561.15 | + | 16560.4i | −0.803996 | + | 1.39256i | 0.112971 | + | 0.993598i | \(0.463963\pi\) |
−0.916967 | + | 0.398963i | \(0.869370\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18873.4 | − | 10896.5i | 1.57796 | − | 0.911037i | 0.582819 | − | 0.812602i | \(-0.301950\pi\) |
0.995143 | − | 0.0984349i | \(-0.0313836\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −808.028 | + | 466.515i | −0.0667899 | + | 0.0385612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4005.72 | + | 6938.12i | −0.329229 | + | 0.570241i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2103.84i | 0.170970i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1745.87 | − | 1007.98i | −0.141085 | − | 0.0814554i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6152.57 | + | 8972.12i | −0.491670 | + | 0.716988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 101.107 | + | 175.122i | 0.00803498 | + | 0.0139170i | 0.870015 | − | 0.493025i | \(-0.164109\pi\) |
−0.861980 | + | 0.506942i | \(0.830776\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1986.38 | −0.156123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1510.85 | 0.118097 | 0.0590486 | − | 0.998255i | \(-0.481193\pi\) | ||||
0.0590486 | + | 0.998255i | \(0.481193\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6585.16 | − | 11405.8i | −0.509142 | − | 0.881859i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4557.49 | − | 14704.6i | 0.350459 | − | 1.13075i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3266.16 | − | 1885.72i | −0.248459 | − | 0.143448i | 0.370599 | − | 0.928793i | \(-0.379152\pi\) |
−0.619058 | + | 0.785345i | \(0.712486\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4290.51i | 0.324632i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3916.56 | − | 6783.67i | 0.293185 | − | 0.507811i | −0.681376 | − | 0.731933i | \(-0.738618\pi\) |
0.974561 | + | 0.224122i | \(0.0719515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16766.4 | + | 9680.07i | −1.24844 | + | 0.720785i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4941.75 | + | 2853.12i | −0.364093 | + | 0.210209i | −0.670875 | − | 0.741571i | \(-0.734081\pi\) |
0.306782 | + | 0.951780i | \(0.400748\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3568.83 | + | 6181.40i | −0.261560 | + | 0.453036i | −0.966657 | − | 0.256076i | \(-0.917570\pi\) |
0.705096 | + | 0.709111i | \(0.250904\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3354.18i | 0.243268i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6579.24 | − | 3798.52i | −0.474692 | − | 0.274064i | 0.243510 | − | 0.969898i | \(-0.421701\pi\) |
−0.718202 | + | 0.695835i | \(0.755035\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −468.367 | − | 506.145i | −0.0334443 | − | 0.0361419i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2231.66 | + | 3865.36i | 0.158535 | + | 0.274591i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8212.13 | −0.577429 | −0.288714 | − | 0.957415i | \(-0.593228\pi\) | ||||
−0.288714 | + | 0.957415i | \(0.593228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −852.457 | −0.0596348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9490.08 | − | 16437.3i | −0.657186 | − | 1.13828i | −0.981341 | − | 0.192275i | \(-0.938413\pi\) |
0.324155 | − | 0.946004i | \(-0.394920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13705.1 | − | 14810.5i | −0.944291 | − | 1.02046i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17794.3 | + | 10273.5i | 1.21378 | + | 0.700776i | 0.963580 | − | 0.267419i | \(-0.0861707\pi\) |
0.250199 | + | 0.968195i | \(0.419504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 15444.1i | − | 1.04821i | −0.851652 | − | 0.524107i | \(-0.824399\pi\) | ||
0.851652 | − | 0.524107i | \(-0.175601\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1388.16 | + | 2404.37i | −0.0932840 | + | 0.161573i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1320.67 | − | 762.488i | 0.0883102 | − | 0.0509859i | −0.455195 | − | 0.890392i | \(-0.650430\pi\) |
0.543505 | + | 0.839406i | \(0.317097\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3438.71 | − | 1985.34i | 0.227685 | − | 0.131454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8883.48 | − | 15386.6i | 0.585319 | − | 1.01380i | −0.409517 | − | 0.912302i | \(-0.634303\pi\) |
0.994836 | − | 0.101499i | \(-0.0323639\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21575.8i | 1.40779i | 0.710302 | + | 0.703897i | \(0.248558\pi\) | ||||
−0.710302 | + | 0.703897i | \(0.751442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7448.71 | + | 4300.51i | 0.483665 | + | 0.279244i | 0.721943 | − | 0.691953i | \(-0.243249\pi\) |
−0.238277 | + | 0.971197i | \(0.576583\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2580.81 | + | 8326.94i | −0.165968 | + | 0.535493i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3206.82 | + | 5554.37i | 0.205236 | + | 0.355480i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 47126.2 | 2.98736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5922.32 | −0.373635 | −0.186817 | − | 0.982395i | \(-0.559817\pi\) | ||||
−0.186817 | + | 0.982395i | \(0.559817\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7157.05 | − | 12396.4i | −0.447274 | − | 0.774701i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3394.29 | + | 263.567i | 0.211125 | + | 0.0163939i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19398.9 | − | 11199.9i | −1.19533 | − | 0.690127i | −0.235823 | − | 0.971796i | \(-0.575779\pi\) |
−0.959512 | + | 0.281669i | \(0.909112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19715.7i | 1.20919i | 0.796533 | + | 0.604595i | \(0.206665\pi\) | ||||
−0.796533 | + | 0.604595i | \(0.793335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3763.68 | − | 6518.89i | 0.228695 | − | 0.396111i | −0.728727 | − | 0.684805i | \(-0.759887\pi\) |
0.957422 | + | 0.288693i | \(0.0932208\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14252.9 | + | 8228.94i | −0.862060 | + | 0.497711i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14524.4 | − | 8385.65i | 0.870417 | − | 0.502536i | 0.00293044 | − | 0.999996i | \(-0.499067\pi\) |
0.867487 | + | 0.497460i | \(0.165734\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5066.36 | − | 8775.19i | 0.302227 | − | 0.523473i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20834.0i | 1.23153i | 0.787930 | + | 0.615765i | \(0.211153\pi\) | ||||
−0.787930 | + | 0.615765i | \(0.788847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22838.3 | + | 13185.7i | 1.34388 | + | 0.775892i | 0.987375 | − | 0.158400i | \(-0.0506334\pi\) |
0.356509 | + | 0.934292i | \(0.383967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4078.21 | − | 17979.4i | −0.237814 | − | 1.04844i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3642.69 | − | 6309.33i | −0.211463 | − | 0.366264i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 862.959 | 0.0496485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18150.5 | −1.03960 | −0.519800 | − | 0.854288i | \(-0.673993\pi\) | ||||
−0.519800 | + | 0.854288i | \(0.673993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11357.7 | − | 19672.2i | −0.644776 | − | 1.11679i | −0.984353 | − | 0.176207i | \(-0.943617\pi\) |
0.339577 | − | 0.940578i | \(-0.389716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7105.08 | + | 6574.76i | −0.401573 | + | 0.371600i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11788.2 | − | 6805.92i | −0.660414 | − | 0.381290i | 0.132021 | − | 0.991247i | \(-0.457854\pi\) |
−0.792435 | + | 0.609957i | \(0.791187\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 27060.1i | 1.50936i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 698.383 | − | 1209.63i | 0.0386158 | − | 0.0668845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24565.6 | − | 14182.9i | 1.35241 | − | 0.780817i | 0.363827 | − | 0.931467i | \(-0.381470\pi\) |
0.988587 | + | 0.150650i | \(0.0481367\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4496.47 | − | 2596.04i | 0.245411 | − | 0.141688i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13517.7 | − | 23413.3i | 0.734604 | − | 1.27237i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9203.01i | − | 0.495853i | −0.968779 | − | 0.247927i | \(-0.920251\pi\) | ||
0.968779 | − | 0.247927i | \(-0.0797492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37288.1 | + | 21528.3i | 2.00049 | + | 1.15499i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19049.8 | + | 4321.00i | −1.01336 | + | 0.229856i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10975.7 | + | 19010.4i | 0.581383 | + | 1.00698i | 0.995316 | + | 0.0966770i | \(0.0308214\pi\) |
−0.413933 | + | 0.910307i | \(0.635845\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −471.552 | −0.0247682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2689.19 | −0.140657 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5090.07 | + | 8816.26i | 0.264016 | + | 0.457289i | 0.967305 | − | 0.253615i | \(-0.0816195\pi\) |
−0.703289 | + | 0.710904i | \(0.748286\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13154.6 | + | 4077.09i | 0.679479 | + | 0.210594i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5092.62 | + | 2940.22i | 0.260876 | + | 0.150617i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19192.2i | − | 0.979093i | −0.871977 | − | 0.489546i | \(-0.837162\pi\) | ||
0.871977 | − | 0.489546i | \(-0.162838\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27567.6 | − | 47748.5i | 1.39484 | − | 2.41593i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30916.5 | − | 17849.6i | 1.55788 | − | 0.899442i | 0.560419 | − | 0.828209i | \(-0.310640\pi\) |
0.997460 | − | 0.0712328i | \(-0.0226933\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3755.40 | − | 2168.18i | 0.187696 | − | 0.108366i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13871.9 | + | 24026.9i | −0.690511 | + | 1.19600i | 0.281160 | + | 0.959661i | \(0.409281\pi\) |
−0.971671 | + | 0.236339i | \(0.924052\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 25212.0i | − | 1.24487i | −0.782671 | − | 0.622435i | \(-0.786143\pi\) | ||
0.782671 | − | 0.622435i | \(-0.213857\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9546.43 | − | 5511.63i | −0.469469 | − | 0.271048i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4174.89 | − | 1293.94i | −0.203668 | − | 0.0631238i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6479.18 | − | 11222.3i | −0.314818 | − | 0.545282i | 0.664580 | − | 0.747217i | \(-0.268610\pi\) |
−0.979399 | + | 0.201935i | \(0.935277\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24814.7 | 1.19616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1671.41 | −0.0802488 | −0.0401244 | − | 0.999195i | \(-0.512775\pi\) | ||||
−0.0401244 | + | 0.999195i | \(0.512775\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13983.9 | − | 24220.9i | −0.666120 | − | 1.15375i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) |
0.312861 | − | 0.949799i | \(-0.398713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4199.99 | + | 952.669i | −0.199279 | + | 0.0452017i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4460.35 | + | 2575.19i | 0.209979 | + | 0.121231i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22787.5i | 1.06858i | 0.845301 | + | 0.534290i | \(0.179421\pi\) | ||||
−0.845301 | + | 0.534290i | \(0.820579\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −754.803 | + | 1307.36i | −0.0351208 | + | 0.0608310i | −0.883052 | − | 0.469276i | \(-0.844515\pi\) |
0.847931 | + | 0.530107i | \(0.177848\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 329.623 | − | 190.308i | 0.0152779 | − | 0.00882072i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21391.4 | − | 12350.4i | 0.983861 | − | 0.568032i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9590.96 | − | 16612.0i | 0.439426 | − | 0.761108i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10084.0i | 0.458490i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4781.43 | − | 2760.56i | −0.216569 | − | 0.125036i | 0.387792 | − | 0.921747i | \(-0.373238\pi\) |
−0.604360 | + | 0.796711i | \(0.706571\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30808.2 | + | 28508.7i | −1.38485 | + | 1.28148i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −135.028 | − | 233.876i | −0.00604665 | − | 0.0104731i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 32608.8 | 1.44926 | 0.724631 | − | 0.689137i | \(-0.242010\pi\) | ||||
0.724631 | + | 0.689137i | \(0.242010\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −51025.3 | −2.25926 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −768.700 | − | 1331.43i | −0.0337819 | − | 0.0585119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2255.93 | − | 9945.64i | −0.0987717 | − | 0.435451i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8150.32 | − | 4705.59i | −0.354203 | − | 0.204499i | 0.312332 | − | 0.949973i | \(-0.398890\pi\) |
−0.666535 | + | 0.745474i | \(0.732223\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26945.2i | 1.16668i | 0.812230 | + | 0.583338i | \(0.198254\pi\) | ||||
−0.812230 | + | 0.583338i | \(0.801746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6866.08 | + | 11892.4i | −0.295102 | + | 0.511132i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43625.1 | − | 25187.0i | 1.86812 | − | 1.07856i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8629.02 | − | 4981.97i | 0.366815 | − | 0.211781i | −0.305251 | − | 0.952272i | \(-0.598740\pi\) |
0.672066 | + | 0.740491i | \(0.265407\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.5282 | + | 66.7327i | −0.00163184 | + | 0.00282644i | −0.866840 | − | 0.498586i | \(-0.833853\pi\) |
0.865208 | + | 0.501413i | \(0.167186\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17261.3i | 0.725797i | 0.931829 | + | 0.362898i | \(0.118213\pi\) | ||||
−0.931829 | + | 0.362898i | \(0.881787\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1435.89 | − | 829.014i | −0.0601576 | − | 0.0347320i | 0.469620 | − | 0.882869i | \(-0.344391\pi\) |
−0.529777 | + | 0.848137i | \(0.677724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −36081.2 | − | 24742.4i | −1.50077 | − | 1.02914i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11196.9 | + | 19393.6i | 0.464053 | + | 0.803763i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31632.6 | 1.30164 | 0.650821 | − | 0.759231i | \(-0.274425\pi\) | ||||
0.650821 | + | 0.759231i | \(0.274425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11616.5 | 0.476300 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −8962.74 | − | 15523.9i | −0.364885 | − | 0.631999i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1781.99 | + | 5749.56i | −0.0722904 | + | 0.233243i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20626.6 | + | 11908.8i | 0.830869 | + | 0.479702i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7848.64i | 0.315044i | 0.987516 | + | 0.157522i | \(0.0503505\pi\) | ||||
−0.987516 | + | 0.157522i | \(0.949650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4290.84 | + | 7431.96i | −0.171030 | + | 0.296232i | −0.938780 | − | 0.344517i | \(-0.888043\pi\) |
0.767750 | + | 0.640749i | \(0.221376\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35896.5 | + | 20724.8i | −1.42581 | + | 0.823192i | −0.996787 | − | 0.0801010i | \(-0.974476\pi\) |
−0.429024 | + | 0.903293i | \(0.641142\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5665.14 | + | 3270.77i | −0.223457 | + | 0.129013i | −0.607550 | − | 0.794281i | \(-0.707848\pi\) |
0.384093 | + | 0.923294i | \(0.374514\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11290.8 | − | 19556.3i | 0.443815 | − | 0.768711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26364.5i | 1.02918i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1175.23 | − | 678.517i | −0.0457187 | − | 0.0263957i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19021.8 | + | 20556.2i | 0.734921 | + | 0.794200i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7853.26 | − | 13602.3i | −0.302378 | − | 0.523735i | 0.674296 | − | 0.738461i | \(-0.264447\pi\) |
−0.976674 | + | 0.214727i | \(0.931114\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15432.4 | −0.590161 | −0.295080 | − | 0.955472i | \(-0.595346\pi\) | ||||
−0.295080 | + | 0.955472i | \(0.595346\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17372.6 | 0.662101 | 0.331050 | − | 0.943613i | \(-0.392597\pi\) | ||||
0.331050 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15942.5 | − | 27613.3i | −0.603493 | − | 1.04528i | −0.992288 | − | 0.123956i | \(-0.960442\pi\) |
0.388795 | − | 0.921324i | \(-0.372891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21078.2 | − | 22778.4i | −0.795208 | − | 0.859349i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40373.2 | − | 23309.5i | −1.51292 | − | 0.873485i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 35451.2i | − | 1.32403i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −413.355 | + | 715.952i | −0.0153350 | + | 0.0265610i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15544.4 | + | 8974.58i | −0.574762 | + | 0.331839i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29890.4 | + | 17257.2i | −1.09789 | + | 0.633867i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4017.29 | + | 6958.16i | −0.147070 | + | 0.254732i | −0.930143 | − | 0.367197i | \(-0.880317\pi\) |
0.783074 | + | 0.621929i | \(0.213651\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 51249.1i | 1.86384i | 0.362662 | + | 0.931921i | \(0.381868\pi\) | ||||
−0.362662 | + | 0.931921i | \(0.618132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1022.77 | + | 590.496i | 0.0370742 | + | 0.0214048i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 6503.71 | − | 20984.1i | 0.234211 | − | 0.755676i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18992.6 | + | 32896.2i | 0.681730 | + | 1.18079i | 0.974453 | + | 0.224593i | \(0.0721053\pi\) |
−0.292723 | + | 0.956197i | \(0.594561\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6002.84 | −0.214069 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19224.4 | −0.683347 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13009.3 | + | 22532.8i | 0.459443 | + | 0.795778i | 0.998932 | − | 0.0462144i | \(-0.0147158\pi\) |
−0.539489 | + | 0.841993i | \(0.681382\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17245.9 | − | 36059.8i | −0.607103 | − | 1.26940i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29927.7 | + | 17278.7i | 1.04678 | + | 0.604359i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 44218.3i | 1.54168i | 0.637031 | + | 0.770838i | \(0.280162\pi\) | ||||
−0.637031 | + | 0.770838i | \(0.719838\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3103.46 | + | 5375.35i | −0.107513 | + | 0.186218i | −0.914762 | − | 0.403993i | \(-0.867622\pi\) |
0.807249 | + | 0.590211i | \(0.200955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11833.0 | − | 6831.81i | 0.408629 | − | 0.235922i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34277.2 | + | 19790.0i | −1.17620 | + | 0.679079i | −0.955132 | − | 0.296180i | \(-0.904287\pi\) |
−0.221067 | + | 0.975259i | \(0.570954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −240.559 | + | 416.660i | −0.00822853 | + | 0.0142522i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23083.3i | 0.784619i | 0.919833 | + | 0.392310i | \(0.128324\pi\) | ||||
−0.919833 | + | 0.392310i | \(0.871676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27568.6 | + | 15916.7i | 0.934135 | + | 0.539323i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12978.1 | + | 57215.9i | 0.437001 | + | 1.92659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14868.7 | − | 25753.4i | −0.499102 | − | 0.864470i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11420.3 | 0.380967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34489.9 | −1.14697 | −0.573486 | − | 0.819215i | \(-0.694409\pi\) | ||||
−0.573486 | + | 0.819215i | \(0.694409\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2501.31 | − | 4332.39i | −0.0826681 | − | 0.143185i | 0.821727 | − | 0.569881i | \(-0.193011\pi\) |
−0.904395 | + | 0.426696i | \(0.859677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8262.27 | − | 7645.58i | 0.272226 | − | 0.251907i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −41676.7 | − | 24062.0i | −1.36474 | − | 0.787936i | −0.374493 | − | 0.927230i | \(-0.622183\pi\) |
−0.990251 | + | 0.139294i | \(0.955517\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14929.7i | − | 0.487391i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10394.8 | − | 18004.3i | 0.337276 | − | 0.584179i | −0.646643 | − | 0.762793i | \(-0.723828\pi\) |
0.983919 | + | 0.178613i | \(0.0571611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25536.2 | + | 14743.3i | −0.826042 | + | 0.476916i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24132.0 | − | 13932.6i | 0.775888 | − | 0.447959i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24701.8 | + | 42784.7i | −0.791803 | + | 1.37144i | 0.133046 | + | 0.991110i | \(0.457524\pi\) |
−0.924849 | + | 0.380334i | \(0.875809\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 45583.3i | 1.45235i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36971.1 | − | 21345.3i | −1.17441 | − | 0.678047i | −0.219696 | − | 0.975568i | \(-0.570507\pi\) |
−0.954715 | + | 0.297522i | \(0.903840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.4.t.a.17.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 252.4.t.a.17.6 | yes | 16 | |
4.3 | odd | 2 | 1008.4.bt.b.17.3 | 16 | |||
7.2 | even | 3 | 1764.4.t.b.1097.3 | 16 | |||
7.3 | odd | 6 | 1764.4.f.a.881.5 | 16 | |||
7.4 | even | 3 | 1764.4.f.a.881.11 | 16 | |||
7.5 | odd | 6 | inner | 252.4.t.a.89.6 | yes | 16 | |
7.6 | odd | 2 | 1764.4.t.b.521.6 | 16 | |||
12.11 | even | 2 | 1008.4.bt.b.17.6 | 16 | |||
21.2 | odd | 6 | 1764.4.t.b.1097.6 | 16 | |||
21.5 | even | 6 | inner | 252.4.t.a.89.3 | yes | 16 | |
21.11 | odd | 6 | 1764.4.f.a.881.6 | 16 | |||
21.17 | even | 6 | 1764.4.f.a.881.12 | 16 | |||
21.20 | even | 2 | 1764.4.t.b.521.3 | 16 | |||
28.19 | even | 6 | 1008.4.bt.b.593.6 | 16 | |||
84.47 | odd | 6 | 1008.4.bt.b.593.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.t.a.17.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
252.4.t.a.17.6 | yes | 16 | 3.2 | odd | 2 | inner | |
252.4.t.a.89.3 | yes | 16 | 21.5 | even | 6 | inner | |
252.4.t.a.89.6 | yes | 16 | 7.5 | odd | 6 | inner | |
1008.4.bt.b.17.3 | 16 | 4.3 | odd | 2 | |||
1008.4.bt.b.17.6 | 16 | 12.11 | even | 2 | |||
1008.4.bt.b.593.3 | 16 | 84.47 | odd | 6 | |||
1008.4.bt.b.593.6 | 16 | 28.19 | even | 6 | |||
1764.4.f.a.881.5 | 16 | 7.3 | odd | 6 | |||
1764.4.f.a.881.6 | 16 | 21.11 | odd | 6 | |||
1764.4.f.a.881.11 | 16 | 7.4 | even | 3 | |||
1764.4.f.a.881.12 | 16 | 21.17 | even | 6 | |||
1764.4.t.b.521.3 | 16 | 21.20 | even | 2 | |||
1764.4.t.b.521.6 | 16 | 7.6 | odd | 2 | |||
1764.4.t.b.1097.3 | 16 | 7.2 | even | 3 | |||
1764.4.t.b.1097.6 | 16 | 21.2 | odd | 6 |