Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,4,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(19.8246417619\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.12 | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.4.h.b.239.11 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.13969 | + | 5.06963i | −0.219333 | + | 0.975650i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 14.6453i | 1.30991i | 0.755667 | + | 0.654956i | \(0.227313\pi\) | ||||
−0.755667 | + | 0.654956i | \(0.772687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −24.4022 | − | 11.5556i | −0.903786 | − | 0.427985i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.9027 | −0.381075 | −0.190537 | − | 0.981680i | \(-0.561023\pi\) | ||||
−0.190537 | + | 0.981680i | \(0.561023\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −45.4743 | −0.970176 | −0.485088 | − | 0.874465i | \(-0.661213\pi\) | ||||
−0.485088 | + | 0.874465i | \(0.661213\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −74.2459 | − | 16.6910i | −1.27801 | − | 0.287307i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 120.873i | 1.72447i | 0.506506 | + | 0.862236i | \(0.330937\pi\) | ||||
−0.506506 | + | 0.862236i | \(0.669063\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 34.9253i | − | 0.421706i | −0.977518 | − | 0.210853i | \(-0.932376\pi\) | ||
0.977518 | − | 0.210853i | \(-0.0676242\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −35.4874 | − | 7.97783i | −0.368761 | − | 0.0829002i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 151.440 | 1.37293 | 0.686465 | − | 0.727163i | \(-0.259162\pi\) | ||||
0.686465 | + | 0.727163i | \(0.259162\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −89.4834 | −0.715867 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 86.3935 | − | 110.540i | 0.615794 | − | 0.787907i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 224.601i | − | 1.43819i | −0.694913 | − | 0.719093i | \(-0.744557\pi\) | ||
0.694913 | − | 0.719093i | \(-0.255443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 44.2927i | − | 0.256620i | −0.991734 | − | 0.128310i | \(-0.959045\pi\) | ||
0.991734 | − | 0.128310i | \(-0.0409552\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 15.8448 | − | 70.4815i | 0.0835824 | − | 0.371795i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −102.517 | −0.495100 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −224.904 | −0.999299 | −0.499649 | − | 0.866228i | \(-0.666538\pi\) | ||||
−0.499649 | + | 0.866228i | \(0.666538\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 51.8266 | − | 230.538i | 0.212792 | − | 0.946553i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 459.995i | 1.75217i | 0.482153 | + | 0.876087i | \(0.339855\pi\) | ||||
−0.482153 | + | 0.876087i | \(0.660145\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 497.722i | − | 1.76516i | −0.470161 | − | 0.882581i | \(-0.655804\pi\) | ||
0.470161 | − | 0.882581i | \(-0.344196\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 169.235 | − | 357.377i | 0.560623 | − | 1.18388i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −134.391 | −0.417085 | −0.208543 | − | 0.978013i | \(-0.566872\pi\) | ||||
−0.208543 | + | 0.978013i | \(0.566872\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −612.781 | − | 137.758i | −1.68248 | − | 0.378234i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 282.447i | 0.732020i | 0.930611 | + | 0.366010i | \(0.119276\pi\) | ||||
−0.930611 | + | 0.366010i | \(0.880724\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 203.608i | − | 0.499174i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 177.058 | + | 39.8040i | 0.411438 | + | 0.0924942i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −48.3707 | −0.106734 | −0.0533672 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533672 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −343.594 | −0.721192 | −0.360596 | − | 0.932722i | \(-0.617427\pi\) | ||||
−0.360596 | + | 0.932722i | \(0.617427\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 80.8892 | − | 170.816i | 0.161763 | − | 0.341599i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 665.982i | − | 1.27084i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 678.793i | − | 1.23773i | −0.785498 | − | 0.618864i | \(-0.787593\pi\) | ||
0.785498 | − | 0.618864i | \(-0.212407\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −172.594 | + | 767.743i | −0.301129 | + | 1.33950i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −820.561 | −1.37159 | −0.685794 | − | 0.727796i | \(-0.740545\pi\) | ||||
−0.685794 | + | 0.727796i | \(0.740545\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 370.525 | 0.594064 | 0.297032 | − | 0.954868i | \(-0.404003\pi\) | ||||
0.297032 | + | 0.954868i | \(0.404003\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 101.983 | − | 453.647i | 0.157014 | − | 0.698436i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 97.3188i | − | 0.144033i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 986.876i | 1.40547i | 0.711451 | + | 0.702736i | \(0.248038\pi\) | ||||
−0.711451 | + | 0.702736i | \(0.751962\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 461.936 | + | 563.965i | 0.633657 | + | 0.773614i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 484.889 | 0.641247 | 0.320624 | − | 0.947207i | \(-0.396108\pi\) | ||||
0.320624 | + | 0.947207i | \(0.396108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1770.22 | −2.25891 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1138.64 | + | 255.976i | 1.40317 | + | 0.315442i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 980.557i | − | 1.16785i | −0.811807 | − | 0.583926i | \(-0.801516\pi\) | ||
0.811807 | − | 0.583926i | \(-0.198484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 318.320i | − | 0.366692i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 224.548 | + | 50.4800i | 0.250371 | + | 0.0562852i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 511.490 | 0.552398 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −488.599 | −0.511440 | −0.255720 | − | 0.966751i | \(-0.582313\pi\) | ||||
−0.255720 | + | 0.966751i | \(0.582313\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 339.256 | + | 160.654i | 0.344410 | + | 0.163094i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 171.807i | 0.169262i | 0.996412 | + | 0.0846309i | \(0.0269711\pi\) | ||||
−0.996412 | + | 0.0846309i | \(0.973029\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1178.61i | 1.12750i | 0.825946 | + | 0.563749i | \(0.190642\pi\) | ||||
−0.825946 | + | 0.563749i | \(0.809358\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 116.837 | − | 519.722i | 0.108592 | − | 0.483044i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 401.039 | 0.362336 | 0.181168 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181168 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −866.058 | −0.761039 | −0.380520 | − | 0.924773i | \(-0.624255\pi\) | ||||
−0.380520 | + | 0.924773i | \(0.624255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 256.321 | − | 1140.18i | 0.219180 | − | 0.974966i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 419.806i | 0.349487i | 0.984614 | + | 0.174744i | \(0.0559096\pi\) | ||||
−0.984614 | + | 0.174744i | \(0.944090\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2217.87i | 1.79842i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1109.67 | + | 525.483i | 0.876832 | + | 0.415221i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −846.112 | −0.651789 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1137.72 | −0.854782 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2332.00 | − | 524.251i | −1.70951 | − | 0.384310i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 520.150i | 0.372189i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 204.993i | 0.143230i | 0.997432 | + | 0.0716151i | \(0.0228153\pi\) | ||||
−0.997432 | + | 0.0716151i | \(0.977185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2523.27 | + | 567.249i | 1.72218 | + | 0.387159i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 44.9236 | 0.0299618 | 0.0149809 | − | 0.999888i | \(-0.495231\pi\) | ||||
0.0149809 | + | 0.999888i | \(0.495231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 244.477 | 0.159390 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1618.89 | + | 1265.25i | 1.03209 | + | 0.806636i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 729.133i | − | 0.454701i | −0.973813 | − | 0.227350i | \(-0.926994\pi\) | ||
0.973813 | − | 0.227350i | \(-0.0730063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1890.32i | 1.15349i | 0.816926 | + | 0.576743i | \(0.195677\pi\) | ||||
−0.816926 | + | 0.576743i | \(0.804323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 153.165 | − | 681.314i | 0.0914807 | − | 0.406929i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 632.215 | 0.369709 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3289.34 | 1.88390 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 55.8448 | − | 248.412i | 0.0313333 | − | 0.139379i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 734.918i | 0.404073i | 0.979378 | + | 0.202036i | \(0.0647559\pi\) | ||||
−0.979378 | + | 0.202036i | \(0.935244\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 990.698i | 0.533920i | 0.963708 | + | 0.266960i | \(0.0860191\pi\) | ||||
−0.963708 | + | 0.266960i | \(0.913981\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1396.76 | − | 2949.57i | 0.738049 | − | 1.55855i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 648.678 | 0.336149 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1520.81 | 0.773080 | 0.386540 | − | 0.922273i | \(-0.373670\pi\) | ||||
0.386540 | + | 0.922273i | \(0.373670\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1431.90 | − | 321.902i | −0.714195 | − | 0.160556i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1060.08i | 0.518919i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3135.82i | 1.50685i | 0.657535 | + | 0.753424i | \(0.271599\pi\) | ||||
−0.657535 | + | 0.753424i | \(0.728401\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1032.22 | + | 232.050i | 0.487019 | + | 0.109485i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4075.35 | −1.88839 | −0.944193 | − | 0.329394i | \(-0.893156\pi\) | ||||
−0.944193 | + | 0.329394i | \(0.893156\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −129.091 | −0.0587578 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −403.583 | + | 852.255i | −0.180484 | + | 0.381132i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 721.361i | − | 0.317018i | −0.987358 | − | 0.158509i | \(-0.949331\pi\) | ||
0.987358 | − | 0.158509i | \(-0.0506687\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 626.384i | − | 0.270572i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 55.1276 | − | 245.222i | 0.0234104 | − | 0.104135i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4087.07 | 1.70660 | 0.853301 | − | 0.521418i | \(-0.174597\pi\) | ||||
0.853301 | + | 0.521418i | \(0.174597\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3549.84 | −1.45778 | −0.728889 | − | 0.684632i | \(-0.759963\pi\) | ||||
−0.728889 | + | 0.684632i | \(0.759963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 391.591 | − | 1741.89i | 0.158182 | − | 0.703631i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3293.78i | − | 1.30899i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1680.46i | − | 0.657152i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 773.782 | + | 604.755i | 0.297801 | + | 0.232748i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1269.54 | 0.480945 | 0.240473 | − | 0.970656i | \(-0.422698\pi\) | ||||
0.240473 | + | 0.970656i | \(0.422698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1979.22 | 0.738172 | 0.369086 | − | 0.929395i | \(-0.379671\pi\) | ||||
0.369086 | + | 0.929395i | \(0.379671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3376.28 | + | 759.013i | 1.23990 | + | 0.278739i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4655.85i | 1.68384i | 0.539606 | + | 0.841918i | \(0.318573\pi\) | ||||
−0.539606 | + | 0.841918i | \(0.681427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 166.378i | 0.0592676i | 0.999561 | + | 0.0296338i | \(0.00943411\pi\) | ||||
−0.999561 | + | 0.0296338i | \(0.990566\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3441.23 | + | 773.613i | 1.20759 | + | 0.271475i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1572.21 | 0.543584 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6736.74 | −2.29519 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3695.47 | − | 1749.98i | −1.24083 | − | 0.587594i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 485.556i | 0.160701i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1923.89i | 0.627707i | 0.949471 | + | 0.313853i | \(0.101620\pi\) | ||||
−0.949471 | + | 0.313853i | \(0.898380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 935.185 | − | 4159.94i | 0.300835 | − | 1.33819i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7289.27 | 2.31220 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 310.049 | 0.0969931 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −422.283 | + | 1878.42i | −0.130298 | + | 0.579598i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 5496.62i | − | 1.67304i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3286.15i | 0.986803i | 0.869802 | + | 0.493402i | \(0.164247\pi\) | ||||
−0.869802 | + | 0.493402i | \(0.835753\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2183.59 | + | 1034.03i | 0.646990 | + | 0.306380i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4610.89 | −1.34817 | −0.674087 | − | 0.738652i | \(-0.735463\pi\) | ||||
−0.674087 | + | 0.738652i | \(0.735463\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5100.93 | −1.47196 | −0.735980 | − | 0.677003i | \(-0.763278\pi\) | ||||
−0.735980 | + | 0.677003i | \(0.763278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 493.370 | + | 110.913i | 0.140525 | + | 0.0315912i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6943.92i | 1.95241i | 0.216853 | + | 0.976204i | \(0.430421\pi\) | ||||
−0.216853 | + | 0.976204i | \(0.569579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1968.20i | − | 0.546345i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5003.09 | − | 1124.73i | −1.37125 | − | 0.308267i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3416.16 | −0.924572 | −0.462286 | − | 0.886731i | \(-0.652971\pi\) | ||||
−0.462286 | + | 0.886731i | \(0.652971\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3724.80 | 0.995584 | 0.497792 | − | 0.867296i | \(-0.334144\pi\) | ||||
0.497792 | + | 0.867296i | \(0.334144\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3385.55 | + | 1699.10i | −0.893759 | + | 0.448548i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 717.617i | − | 0.187130i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1588.20i | 0.409129i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −552.624 | + | 2458.21i | −0.140647 | + | 0.625633i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4455.29 | −1.12038 | −0.560189 | − | 0.828365i | \(-0.689272\pi\) | ||||
−0.560189 | + | 0.828365i | \(0.689272\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2105.42 | −0.523188 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2017.50 | − | 8974.34i | 0.495453 | − | 2.20390i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1067.17i | 0.259020i | 0.991578 | + | 0.129510i | \(0.0413405\pi\) | ||||
−0.991578 | + | 0.129510i | \(0.958660\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1574.33i | − | 0.377699i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2595.40 | + | 5480.77i | −0.615523 | + | 1.29981i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2881.25 | −0.675533 | −0.337767 | − | 0.941230i | \(-0.609671\pi\) | ||||
−0.337767 | + | 0.941230i | \(0.609671\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4136.51 | −0.958881 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4971.05 | + | 1117.53i | 1.13941 | + | 0.256149i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5561.17i | 1.26049i | 0.776398 | + | 0.630243i | \(0.217045\pi\) | ||||
−0.776398 | + | 0.630243i | \(0.782955\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 5418.65i | − | 1.21461i | −0.794468 | − | 0.607306i | \(-0.792250\pi\) | ||
0.794468 | − | 0.607306i | \(-0.207750\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1613.76 | + | 362.786i | 0.357763 | + | 0.0804278i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1244.06 | 0.272799 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3291.26 | 0.713908 | 0.356954 | − | 0.934122i | \(-0.383815\pi\) | ||||
0.356954 | + | 0.934122i | \(0.383815\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −511.829 | + | 1080.84i | −0.109829 | + | 0.231929i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6394.15i | − | 1.35745i | −0.734393 | − | 0.678724i | \(-0.762533\pi\) | ||
0.734393 | − | 0.678724i | \(-0.237467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9183.66i | − | 1.92902i | −0.264050 | − | 0.964509i | \(-0.585058\pi\) | ||
0.264050 | − | 0.964509i | \(-0.414942\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −582.940 | + | 2593.06i | −0.121159 | + | 0.538947i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3219.96 | −0.662260 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9697.30 | −1.97381 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 556.851 | − | 2477.01i | 0.112176 | − | 0.498987i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3914.97i | − | 0.780598i | −0.920688 | − | 0.390299i | \(-0.872372\pi\) | ||
0.920688 | − | 0.390299i | \(-0.127628\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 708.402i | − | 0.139813i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1201.10 | + | 1536.81i | −0.234663 | + | 0.300251i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6886.61 | −1.33198 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3484.06 | 0.667168 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −870.998 | − | 195.807i | −0.165140 | − | 0.0371248i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5032.02i | − | 0.944698i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1579.23i | − | 0.293588i | −0.989167 | − | 0.146794i | \(-0.953104\pi\) | ||
0.989167 | − | 0.146794i | \(-0.0468955\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5975.14 | − | 1343.26i | −1.10004 | − | 0.247298i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −515.431 | −0.0939788 | −0.0469894 | − | 0.998895i | \(-0.514963\pi\) | ||||
−0.0469894 | + | 0.998895i | \(0.514963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10135.1 | 1.83026 | 0.915129 | − | 0.403161i | \(-0.132089\pi\) | ||||
0.915129 | + | 0.403161i | \(0.132089\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2501.64 | + | 1184.64i | 0.447464 | + | 0.211895i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7471.40i | − | 1.32377i | −0.749604 | − | 0.661886i | \(-0.769756\pi\) | ||
0.749604 | − | 0.661886i | \(-0.230244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3122.56i | 0.548056i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −457.060 | + | 2033.12i | −0.0794723 | + | 0.353513i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4221.53 | 0.727221 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4069.19 | 0.694517 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 987.037 | − | 4390.59i | 0.166921 | − | 0.742508i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 940.740i | − | 0.157643i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 6725.92i | − | 1.11689i | −0.829542 | − | 0.558444i | \(-0.811399\pi\) | ||
0.829542 | − | 0.558444i | \(-0.188601\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5488.16 | + | 2598.90i | 0.903152 | + | 0.427685i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9941.09 | 1.62131 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −75.0546 | −0.0121320 | −0.00606600 | − | 0.999982i | \(-0.501931\pi\) | ||||
−0.00606600 | + | 0.999982i | \(0.501931\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2128.26 | − | 478.449i | −0.340977 | − | 0.0766542i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 615.788i | 0.0977912i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 343.000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11243.8 | − | 2527.69i | −1.75462 | − | 0.394453i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4435.86 | 0.686252 | 0.343126 | − | 0.939289i | \(-0.388514\pi\) | ||||
0.343126 | + | 0.939289i | \(0.388514\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2611.13 | 0.400489 | 0.200245 | − | 0.979746i | \(-0.435826\pi\) | ||||
0.200245 | + | 0.979746i | \(0.435826\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3928.68 | + | 5026.74i | −0.597429 | + | 0.764409i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 916.862i | 0.138243i | 0.997608 | + | 0.0691213i | \(0.0220196\pi\) | ||||
−0.997608 | + | 0.0691213i | \(0.977980\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 12017.3i | − | 1.79666i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 964.305 | − | 4289.47i | 0.142959 | − | 0.635918i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3916.49 | 0.575778 | 0.287889 | − | 0.957664i | \(-0.407047\pi\) | ||||
0.287889 | + | 0.957664i | \(0.407047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5639.22 | 0.822164 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1296.64 | − | 5767.79i | 0.187482 | − | 0.833968i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5426.43i | 0.778171i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9856.78i | − | 1.40196i | −0.713180 | − | 0.700980i | \(-0.752746\pi\) | ||
0.713180 | − | 0.700980i | \(-0.247254\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5315.52 | − | 11224.9i | 0.749905 | − | 1.58359i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1977.13 | −0.276678 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11058.4 | −1.53508 | −0.767538 | − | 0.641003i | \(-0.778519\pi\) | ||||
−0.767538 | + | 0.641003i | \(0.778519\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2636.97 | − | 592.809i | −0.363126 | − | 0.0816335i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10213.6i | 1.39529i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3764.44i | 0.510202i | 0.966914 | + | 0.255101i | \(0.0821087\pi\) | ||||
−0.966914 | + | 0.255101i | \(0.917891\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1039.24 | − | 233.629i | −0.139742 | − | 0.0314152i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10258.1 | −1.36858 | −0.684290 | − | 0.729210i | \(-0.739888\pi\) | ||||
−0.684290 | + | 0.729210i | \(0.739888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1425.26 | 0.188670 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5751.48 | + | 12145.5i | −0.755463 | + | 1.59533i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11610.0i | 1.51324i | 0.653857 | + | 0.756618i | \(0.273150\pi\) | ||||
−0.653857 | + | 0.756618i | \(0.726850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18305.0i | 2.36758i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −51.1989 | + | 227.746i | −0.00657162 | + | 0.0292322i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14453.1 | −1.84104 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7004.43 | 0.885497 | 0.442749 | − | 0.896646i | \(-0.354003\pi\) | ||||
0.442749 | + | 0.896646i | \(0.354003\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −278.628 | + | 1239.41i | −0.0349595 | + | 0.155509i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2223.31i | 0.276875i | 0.990371 | + | 0.138438i | \(0.0442080\pi\) | ||||
−0.990371 | + | 0.138438i | \(0.955792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2014.18i | 0.248966i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8259.40 | + | 6765.17i | −1.01337 | + | 0.830035i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3126.78 | 0.380807 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2310.73 | −0.279359 | −0.139680 | − | 0.990197i | \(-0.544607\pi\) | ||||
−0.139680 | + | 0.990197i | \(0.544607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3696.43 | + | 830.985i | 0.443629 | + | 0.0997311i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 338.595i | − | 0.0403418i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7101.33i | 0.839977i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9583.20 | − | 2154.37i | −1.12540 | − | 0.252998i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9808.83 | 1.14366 | 0.571829 | − | 0.820373i | \(-0.306234\pi\) | ||||
0.571829 | + | 0.820373i | \(0.306234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2381.84 | −0.275733 | −0.137867 | − | 0.990451i | \(-0.544024\pi\) | ||||
−0.137867 | + | 0.990451i | \(0.544024\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3279.45 | + | 1552.97i | 0.376956 | + | 0.178506i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 10816.1i | − | 1.23449i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 2405.16i | − | 0.272585i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −720.529 | + | 3205.09i | −0.0810896 | + | 0.360707i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8717.18 | 0.974227 | 0.487114 | − | 0.873339i | \(-0.338050\pi\) | ||||
0.487114 | + | 0.873339i | \(0.338050\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14091.6 | 1.56397 | 0.781983 | − | 0.623300i | \(-0.214209\pi\) | ||||
0.781983 | + | 0.623300i | \(0.214209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3748.83 | + | 16675.7i | −0.413201 | + | 1.83802i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 5289.08i | − | 0.578973i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6819.29i | 0.741383i | 0.928756 | + | 0.370691i | \(0.120879\pi\) | ||||
−0.928756 | + | 0.370691i | \(0.879121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1195.71 | + | 566.224i | 0.129112 | + | 0.0611407i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9565.27 | −1.02587 | −0.512934 | − | 0.858428i | \(-0.671442\pi\) | ||||
−0.512934 | + | 0.858428i | \(0.671442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14360.5 | 1.52978 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3725.76 | − | 837.578i | −0.394233 | − | 0.0886266i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 752.859i | − | 0.0791306i | −0.999217 | − | 0.0395653i | \(-0.987403\pi\) | ||
0.999217 | − | 0.0395653i | \(-0.0125973\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 6395.17i | − | 0.667709i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5022.47 | − | 1129.09i | −0.520919 | − | 0.117106i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4661.87 | 0.480334 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14222.2 | −1.45577 | −0.727884 | − | 0.685700i | \(-0.759496\pi\) | ||||
−0.727884 | + | 0.685700i | \(0.759496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 13361.3 | + | 10442.7i | 1.35872 | + | 1.06192i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12808.3i | 1.29401i | 0.762484 | + | 0.647007i | \(0.223980\pi\) | ||||
−0.762484 | + | 0.647007i | \(0.776020\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1416.85i | 0.142217i | 0.997469 | + | 0.0711086i | \(0.0226537\pi\) | ||||
−0.997469 | + | 0.0711086i | \(0.977346\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −739.292 | + | 3288.56i | −0.0737287 | + | 0.327964i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12720.2 | 1.26043 | 0.630215 | − | 0.776421i | \(-0.282967\pi\) | ||||
0.630215 | + | 0.776421i | \(0.282967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4751.55 | 0.467817 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1733.25 | + | 7709.92i | −0.169562 | + | 0.754256i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6919.68i | 0.672658i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3125.24i | 0.301886i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3263.84 | − | 6892.33i | 0.313294 | − | 0.661589i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16314.1 | 1.55618 | 0.778092 | − | 0.628150i | \(-0.216188\pi\) | ||||
0.778092 | + | 0.628150i | \(0.216188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10227.4 | 0.969496 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5374.20 | − | 1208.16i | −0.506283 | − | 0.113816i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 7155.65i | − | 0.669941i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4903.33i | − | 0.456244i | −0.973632 | − | 0.228122i | \(-0.926741\pi\) | ||
0.973632 | − | 0.228122i | \(-0.0732586\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15897.4 | − | 3573.86i | −1.47016 | − | 0.330502i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1213.14 | 0.111503 | 0.0557517 | − | 0.998445i | \(-0.482244\pi\) | ||||
0.0557517 | + | 0.998445i | \(0.482244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27148.3 | 2.48011 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2352.82 | + | 4968.50i | −0.213639 | + | 0.451146i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5743.93i | − | 0.518411i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8093.93i | 0.726121i | 0.931766 | + | 0.363060i | \(0.118268\pi\) | ||||
−0.931766 | + | 0.363060i | \(0.881732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4644.64 | − | 20660.5i | 0.414186 | − | 1.84240i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3991.77 | −0.353846 | −0.176923 | − | 0.984225i | \(-0.556614\pi\) | ||||
−0.176923 | + | 0.984225i | \(0.556614\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2516.16 | −0.221718 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 147.123 | − | 654.442i | 0.0128875 | − | 0.0573270i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7309.19i | 0.636491i | 0.948008 | + | 0.318246i | \(0.103094\pi\) | ||||
−0.948008 | + | 0.318246i | \(0.896906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2593.67i | 0.224535i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3860.66 | − | 3017.32i | −0.332265 | − | 0.259684i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −17261.1 | −1.47692 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1868.40 | 0.158941 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3657.03 | + | 822.128i | 0.309299 | + | 0.0695326i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1657.13i | 0.139348i | 0.997570 | + | 0.0696739i | \(0.0221959\pi\) | ||||
−0.997570 | + | 0.0696739i | \(0.977804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5621.88i | − | 0.470034i | −0.971991 | − | 0.235017i | \(-0.924485\pi\) | ||
0.971991 | − | 0.235017i | \(-0.0755145\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3175.53 | + | 713.883i | 0.263984 | + | 0.0593455i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5353.80 | 0.442533 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10767.0 | 0.884936 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1180.35 | + | 558.953i | 0.0964651 | + | 0.0456808i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 20917.9i | − | 1.69992i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5873.32i | 0.474628i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4657.99 | + | 20719.9i | −0.374315 | + | 1.66505i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 681.232 | 0.0544392 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16776.8 | 1.33326 | 0.666629 | − | 0.745390i | \(-0.267737\pi\) | ||||
0.666629 | + | 0.745390i | \(0.267737\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4045.72 | − | 17996.4i | 0.319739 | − | 1.42228i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 12683.6i | − | 0.996894i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 19586.5i | − | 1.53100i | −0.643437 | − | 0.765499i | \(-0.722492\pi\) | ||
0.643437 | − | 0.765499i | \(-0.277508\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8384.46 | + | 3970.44i | 0.651803 | + | 0.308660i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7844.27 | −0.606492 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6908.13 | −0.531218 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16698.2 | + | 3753.89i | 1.27712 | + | 0.287106i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 13365.8i | − | 1.01674i | −0.861138 | − | 0.508372i | \(-0.830248\pi\) | ||
0.861138 | − | 0.508372i | \(-0.169752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22633.6i | 1.71252i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8519.31 | + | 1915.20i | 0.641151 | + | 0.144135i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10979.2 | 0.821877 | 0.410939 | − | 0.911663i | \(-0.365201\pi\) | ||||
0.410939 | + | 0.911663i | \(0.365201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6148.17 | −0.457797 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3947.75 | + | 3233.55i | −0.292399 | + | 0.239500i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24903.3i | 1.83480i | 0.397969 | + | 0.917399i | \(0.369715\pi\) | ||||
−0.397969 | + | 0.917399i | \(0.630285\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3896.72i | 0.285591i | 0.989752 | + | 0.142796i | \(0.0456091\pi\) | ||||
−0.989752 | + | 0.142796i | \(0.954391\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1446.88 | + | 6436.09i | −0.105487 | + | 0.469234i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13551.3 | −0.982835 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11824.8 | 0.853161 | 0.426581 | − | 0.904450i | \(-0.359718\pi\) | ||||
0.426581 | + | 0.904450i | \(0.359718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2255.69 | + | 10033.9i | −0.161906 | + | 0.720198i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3394.23i | 0.242369i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3926.77i | − | 0.278954i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7695.82 | + | 16251.4i | −0.543903 | + | 1.14857i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5957.49 | −0.418896 | −0.209448 | − | 0.977820i | \(-0.567167\pi\) | ||||
−0.209448 | + | 0.977820i | \(0.567167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1546.94 | −0.108218 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23603.4 | − | 5306.22i | −1.64283 | − | 0.369321i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 11547.6i | − | 0.799671i | −0.916587 | − | 0.399836i | \(-0.869067\pi\) | ||
0.916587 | − | 0.399836i | \(-0.130933\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 12391.5i | − | 0.853786i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −843.476 | − | 189.620i | −0.0578244 | − | 0.0129994i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −27338.0 | −1.86477 | −0.932386 | − | 0.361464i | \(-0.882277\pi\) | ||||
−0.932386 | + | 0.361464i | \(0.882277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15844.1 | −1.07536 | −0.537682 | − | 0.843148i | \(-0.680700\pi\) | ||||
−0.537682 | + | 0.843148i | \(0.680700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7843.86 | + | 16564.1i | −0.529729 | + | 1.11864i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 16662.1i | − | 1.11969i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 575.804i | 0.0385027i | 0.999815 | + | 0.0192514i | \(0.00612828\pi\) | ||||
−0.999815 | + | 0.0192514i | \(0.993872\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1791.83 | + | 7970.51i | −0.119226 | + | 0.530347i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6111.35 | 0.404646 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9646.06 | 0.635564 | 0.317782 | − | 0.948164i | \(-0.397062\pi\) | ||||
0.317782 | + | 0.948164i | \(0.397062\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7677.79 | − | 34152.8i | 0.503412 | − | 2.23930i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18960.4i | 1.23714i | 0.785728 | + | 0.618572i | \(0.212288\pi\) | ||||
−0.785728 | + | 0.618572i | \(0.787712\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26238.0i | 1.70370i | 0.523783 | + | 0.851852i | \(0.324520\pi\) | ||||
−0.523783 | + | 0.851852i | \(0.675480\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13083.4 | − | 16740.2i | 0.845442 | − | 1.08174i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6863.90 | 0.441406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18803.1 | −1.20340 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2461.59 | − | 553.383i | −0.156788 | − | 0.0352472i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 27184.9i | − | 1.72326i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 31385.8i | − | 1.98011i | −0.140680 | − | 0.990055i | \(-0.544929\pi\) | ||
0.140680 | − | 0.990055i | \(-0.455071\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9753.41 | − | 2192.64i | −0.612422 | − | 0.137677i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3002.18 | −0.187619 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2228.24 | 0.138597 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 20023.5 | + | 9482.08i | 1.23962 | + | 0.587019i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6203.66i | 0.382262i | 0.981565 | + | 0.191131i | \(0.0612155\pi\) | ||||
−0.981565 | + | 0.191131i | \(0.938785\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1900.46i | − | 0.116558i | −0.998300 | − | 0.0582791i | \(-0.981439\pi\) | ||
0.998300 | − | 0.0582791i | \(-0.0185613\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8307.51 | + | 36953.9i | −0.507144 | + | 2.25590i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5220.82 | −0.317236 | −0.158618 | − | 0.987340i | \(-0.550704\pi\) | ||||
−0.158618 | + | 0.987340i | \(0.550704\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 672.484 | 0.0406738 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −353.360 | + | 1571.83i | −0.0212738 | + | 0.0946313i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5266.00i | 0.315581i | 0.987473 | + | 0.157790i | \(0.0504370\pi\) | ||||
−0.987473 | + | 0.157790i | \(0.949563\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 657.917i | 0.0392473i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9041.63 | − | 4281.64i | −0.536906 | − | 0.254251i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19994.5 | 1.18191 | 0.590954 | − | 0.806706i | \(-0.298752\pi\) | ||||
0.590954 | + | 0.806706i | \(0.298752\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16431.9 | −0.966911 | −0.483456 | − | 0.875369i | \(-0.660619\pi\) | ||||
−0.483456 | + | 0.875369i | \(0.660619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 27865.8 | + | 6264.44i | 1.63230 | + | 0.366954i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3580.43i | 0.208787i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34013.6i | − | 1.97453i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16659.6 | − | 3745.20i | −0.962775 | − | 0.216439i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4776.88 | 0.274828 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8167.51 | −0.467807 | −0.233904 | − | 0.972260i | \(-0.575150\pi\) | ||||
−0.233904 | + | 0.972260i | \(0.575150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −7730.78 | + | 9891.52i | −0.440827 | + | 0.564037i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 34191.6i | 1.94105i | 0.241000 | + | 0.970525i | \(0.422524\pi\) | ||||
−0.241000 | + | 0.970525i | \(0.577476\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3420.19i | − | 0.193306i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5254.99 | − | 23375.5i | 0.295700 | − | 1.31535i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.6262 | 0.00126760 | 0.000633799 | − | 1.00000i | \(-0.499798\pi\) | ||||
0.000633799 | 1.00000i | \(0.499798\pi\) | ||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10678.3 | 0.595618 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5813.47 | − | 25859.8i | 0.322850 | − | 1.43612i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 12844.1i | − | 0.710188i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 27943.6i | − | 1.53839i | −0.639016 | − | 0.769193i | \(-0.720658\pi\) | ||
0.639016 | − | 0.769193i | \(-0.279342\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1124.58 | + | 2374.80i | −0.0616438 | + | 0.130175i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −27684.2 | −1.51096 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55601.0 | −3.02158 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35203.1 | − | 7913.91i | −1.90487 | − | 0.428228i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4454.40i | 0.240001i | 0.992774 | + | 0.120000i | \(0.0382896\pi\) | ||||
−0.992774 | + | 0.120000i | \(0.961710\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7854.86i | 0.421410i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9978.02 | + | 2243.13i | 0.533041 | + | 0.119832i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1202.65 | −0.0639750 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1733.18 | 0.0918067 | 0.0459034 | − | 0.998946i | \(-0.485383\pi\) | ||||
0.0459034 | + | 0.998946i | \(0.485383\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11403.9 | − | 24082.0i | 0.601521 | − | 1.27025i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 6707.68i | − | 0.352321i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9258.94i | 0.484287i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3893.36 | − | 17318.6i | 0.202789 | − | 0.902059i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5157.90 | −0.267534 | −0.133767 | − | 0.991013i | \(-0.542707\pi\) | ||||
−0.133767 | + | 0.991013i | \(0.542707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8250.30 | −0.426154 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4245.12 | + | 18883.4i | −0.218365 | + | 0.971341i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20098.1i | 1.02955i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6924.59i | − | 0.353259i | −0.984277 | − | 0.176629i | \(-0.943481\pi\) | ||
0.984277 | − | 0.176629i | \(-0.0565194\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4755.32 | − | 19099.9i | −0.241595 | − | 0.970377i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 60161.2 | 3.04397 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17794.3 | −0.896655 | −0.448327 | − | 0.893869i | \(-0.647980\pi\) | ||||
−0.448327 | + | 0.893869i | \(0.647980\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3638.05 | + | 817.861i | 0.182574 | + | 0.0410439i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9437.05i | 0.471667i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 619.992i | 0.0308617i | 0.999881 | + | 0.0154308i | \(0.00491198\pi\) | ||||
−0.999881 | + | 0.0154308i | \(0.995088\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8051.60 | − | 1810.06i | −0.399167 | − | 0.0897357i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9464.45 | 0.467318 | 0.233659 | − | 0.972319i | \(-0.424930\pi\) | ||||
0.233659 | + | 0.972319i | \(0.424930\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10763.1 | −0.529299 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11832.4 | − | 5603.19i | −0.579550 | − | 0.274444i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2807.27i | 0.136950i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19159.6i | 0.930953i | 0.885060 | + | 0.465476i | \(0.154117\pi\) | ||||
−0.885060 | + | 0.465476i | \(0.845883\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5077.64 | − | 22586.6i | 0.245736 | − | 1.09310i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14509.0 | −0.699387 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14913.4 | −0.716031 | −0.358016 | − | 0.933716i | \(-0.616547\pi\) | ||||
−0.358016 | + | 0.933716i | \(0.616547\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2399.53 | − | 10673.7i | 0.114753 | − | 0.510449i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 12228.8i | − | 0.582515i | −0.956645 | − | 0.291258i | \(-0.905926\pi\) | ||
0.956645 | − | 0.291258i | \(-0.0940737\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 6062.40i | − | 0.287646i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 43197.2 | + | 20455.9i | 2.04157 | + | 0.966778i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2199.62 | 0.103551 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16296.5 | 0.764197 | 0.382099 | − | 0.924122i | \(-0.375202\pi\) | ||||
0.382099 | + | 0.924122i | \(0.375202\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5410.15 | − | 1216.24i | −0.252713 | − | 0.0568118i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19766.2i | 0.919714i | 0.887993 | + | 0.459857i | \(0.152099\pi\) | ||||
−0.887993 | + | 0.459857i | \(0.847901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3963.46i | 0.183706i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7981.27 | + | 1794.25i | 0.368502 | + | 0.0828421i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 16065.5 | 0.738903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11408.0 | 0.522677 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24827.5 | − | 19404.1i | −1.13316 | − | 0.885627i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 22272.6i | 1.01267i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16693.4i | 0.756108i | 0.925784 | + | 0.378054i | \(0.123407\pi\) | ||||
−0.925784 | + | 0.378054i | \(0.876593\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3283.73 | − | 14606.8i | 0.148167 | − | 0.659084i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2938.64 | −0.132094 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15624.7 | 0.699684 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4714.33 | − | 20970.5i | 0.210315 | − | 0.935532i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 6666.68i | − | 0.296293i | −0.988965 | − | 0.148147i | \(-0.952669\pi\) | ||
0.988965 | − | 0.148147i | \(-0.0473308\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 16244.3i | − | 0.719252i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11330.9 | + | 23927.8i | −0.499823 | + | 1.05549i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5151.29 | −0.226383 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15525.1 | −0.679737 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −28193.1 | − | 6338.01i | −1.22979 | − | 0.276467i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9909.58i | − | 0.430658i | −0.976542 | − | 0.215329i | \(-0.930918\pi\) | ||
0.976542 | − | 0.215329i | \(-0.0690824\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6564.87i | 0.284246i | 0.989849 | + | 0.142123i | \(0.0453929\pi\) | ||||
−0.989849 | + | 0.142123i | \(0.954607\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27470.5 | + | 6175.58i | 1.18504 | + | 0.266405i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45924.8 | −1.97384 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17383.1 | −0.744380 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3678.38 | + | 7767.71i | −0.156939 | + | 0.331411i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 11978.5i | − | 0.509199i | −0.967047 | − | 0.254599i | \(-0.918056\pi\) | ||
0.967047 | − | 0.254599i | \(-0.0819436\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18871.4i | 0.799290i | 0.916670 | + | 0.399645i | \(0.130867\pi\) | ||||
−0.916670 | + | 0.399645i | \(0.869133\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1417.84 | + | 6306.92i | −0.0598339 | + | 0.266156i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39287.6 | −1.65195 | −0.825976 | − | 0.563705i | \(-0.809376\pi\) | ||||
−0.825976 | + | 0.563705i | \(0.809376\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 112.278 | 0.00470397 | 0.00235198 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235198 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3751.01 | + | 16685.4i | −0.156584 | + | 0.696524i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 5922.78i | − | 0.246353i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 59684.6i | − | 2.47362i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4896.13 | − | 3826.60i | −0.202192 | − | 0.158025i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11797.5 | 0.485454 | 0.242727 | − | 0.970095i | \(-0.421958\pi\) | ||||
0.242727 | + | 0.970095i | \(0.421958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26056.8 | −1.06838 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32416.0 | + | 7287.35i | 1.32439 | + | 0.297734i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1890.57i | − | 0.0769675i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7964.01i | − | 0.323077i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 46557.7 | + | 10466.5i | 1.88205 | + | 0.423098i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34059.5 | −1.37197 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26383.7 | 1.05904 | 0.529520 | − | 0.848297i | \(-0.322372\pi\) | ||||
0.529520 | + | 0.848297i | \(0.322372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12481.5 | − | 5910.58i | −0.499249 | − | 0.236418i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2222.10i | − | 0.0885712i | −0.999019 | − | 0.0442856i | \(-0.985899\pi\) | ||
0.999019 | − | 0.0442856i | \(-0.0141012\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6113.29i | 0.242820i | 0.992602 | + | 0.121410i | \(0.0387416\pi\) | ||||
−0.992602 | + | 0.121410i | \(0.961258\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3669.76 | − | 16324.0i | 0.145256 | − | 0.646133i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23982.7 | 0.945978 | 0.472989 | − | 0.881068i | \(-0.343175\pi\) | ||||
0.472989 | + | 0.881068i | \(0.343175\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10564.5 | 0.415265 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11051.9 | − | 49161.7i | 0.432921 | − | 1.92574i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 13720.2i | − | 0.535589i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30867.6i | 1.20081i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11922.9 | + | 5646.05i | 0.462232 | + | 0.218889i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3641.05 | −0.140674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4314.94 | 0.166140 | 0.0830702 | − | 0.996544i | \(-0.473527\pi\) | ||||
0.0830702 | + | 0.996544i | \(0.473527\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 19847.4 | + | 4461.85i | 0.761590 | + | 0.171211i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13908.4i | 0.531880i | 0.963990 | + | 0.265940i | \(0.0856823\pi\) | ||||
−0.963990 | + | 0.265940i | \(0.914318\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31012.0i | 1.18192i | 0.806700 | + | 0.590961i | \(0.201251\pi\) | ||||
−0.806700 | + | 0.590961i | \(0.798749\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3591.33 | + | 807.358i | 0.136408 | + | 0.0306656i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38618.3 | 1.46187 | 0.730934 | − | 0.682449i | \(-0.239085\pi\) | ||||
0.730934 | + | 0.682449i | \(0.239085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1434.95 | −0.0541359 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6422.16 | − | 7840.63i | −0.241471 | − | 0.294805i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4693.67i | 0.175887i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59856.1i | 2.23550i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7848.60 | − | 34912.6i | 0.292149 | − | 1.29955i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9948.20 | −0.369067 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34140.2 | −1.26235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3970.74 | + | 17662.9i | −0.146332 | + | 0.650923i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 51988.4i | − | 1.90956i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27884.1i | 1.02081i | 0.859933 | + | 0.510407i | \(0.170505\pi\) | ||||
−0.859933 | + | 0.510407i | \(0.829495\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1985.33 | − | 4192.47i | 0.0724416 | − | 0.152976i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39542.4 | 1.43809 | 0.719043 | − | 0.694965i | \(-0.244580\pi\) | ||||
0.719043 | + | 0.694965i | \(0.244580\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6741.27 | −0.244363 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 25510.5 | + | 5734.94i | 0.921694 | + | 0.207204i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 314.465i | 0.0113245i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 13478.3i | − | 0.483796i | −0.970302 | − | 0.241898i | \(-0.922230\pi\) | ||
0.970302 | − | 0.241898i | \(-0.0777699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8006.12 | + | 1799.84i | 0.286439 | + | 0.0643937i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 37314.4 | 1.33068 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20125.2 | 0.715365 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13619.6 | − | 28760.8i | 0.482553 | − | 1.01902i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21231.5i | 0.749819i | 0.927061 | + | 0.374910i | \(0.122326\pi\) | ||||
−0.927061 | + | 0.374910i | \(0.877674\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1711.34i | 0.0602437i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 587.431 | − | 2613.04i | 0.0206127 | − | 0.0916904i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24610.8 | 0.860811 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30386.4 | 1.05942 | 0.529712 | − | 0.848177i | \(-0.322300\pi\) | ||||
0.529712 | + | 0.848177i | \(0.322300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11550.9 | + | 51381.3i | −0.401437 | + | 1.78569i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28605.3i | 0.990973i | 0.868616 | + | 0.495487i | \(0.165010\pi\) | ||||
−0.868616 | + | 0.495487i | \(0.834990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 69661.5i | 2.40561i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8856.78 | + | 11332.2i | −0.304880 | + | 0.390093i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4517.34 | 0.155009 | 0.0775047 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775047 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16849.3 | −0.576347 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37877.2 | + | 8515.08i | 1.29154 | + | 0.290347i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 32311.2i | − | 1.09828i | −0.835729 | − | 0.549141i | \(-0.814955\pi\) | ||
0.835729 | − | 0.549141i | \(-0.185045\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18592.7i | 0.629996i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −15830.2 | − | 3558.75i | −0.534711 | − | 0.120207i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5103.93 | 0.171861 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27829.2 | 0.934146 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9786.24 | − | 4634.25i | −0.327474 | − | 0.155074i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28986.1i | 0.966940i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50510.3i | − | 1.67973i | −0.542793 | − | 0.839867i | \(-0.682633\pi\) | ||
0.542793 | − | 0.839867i | \(-0.317367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4811.24 | + | 21401.6i | −0.159504 | + | 0.709513i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46193.8 | −1.52671 | −0.763353 | − | 0.645982i | \(-0.776448\pi\) | ||||
−0.763353 | + | 0.645982i | \(0.776448\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13232.2 | −0.435977 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4637.62 | + | 20629.3i | −0.152331 | + | 0.677606i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34716.0i | 1.13681i | 0.822749 | + | 0.568405i | \(0.192439\pi\) | ||||
−0.822749 | + | 0.568405i | \(0.807561\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13632.4i | 0.445038i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21133.7 | + | 10007.8i | 0.687816 | + | 0.325714i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33172.7 | −1.07634 | −0.538171 | − | 0.842836i | \(-0.680885\pi\) | ||||
−0.538171 | + | 0.842836i | \(0.680885\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −68186.1 | −2.20567 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4769.20 | + | 1072.15i | 0.153805 | + | 0.0345765i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 75375.0i | − | 2.42344i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 46668.6i | 1.49594i | 0.663733 | + | 0.747969i | \(0.268971\pi\) | ||||
−0.663733 | + | 0.747969i | \(0.731029\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34097.9 | + | 7665.46i | 1.08969 | + | 0.244971i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2436.65 | −0.0776353 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47034.8 | −1.49409 | −0.747045 | − | 0.664774i | \(-0.768528\pi\) | ||||
−0.747045 | + | 0.664774i | \(0.768528\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −19430.3 | + | 24861.0i | −0.615362 | + | 0.787354i |
(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 | 336.4.h.b.239.12 | yes | 24 | |
3.2 | odd | 2 | inner | 336.4.h.b.239.14 | yes | 24 | |
4.3 | odd | 2 | inner | 336.4.h.b.239.13 | yes | 24 | |
12.11 | even | 2 | inner | 336.4.h.b.239.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.4.h.b.239.11 | ✓ | 24 | 12.11 | even | 2 | inner | |
336.4.h.b.239.12 | yes | 24 | 1.1 | even | 1 | trivial | |
336.4.h.b.239.13 | yes | 24 | 4.3 | odd | 2 | inner | |
336.4.h.b.239.14 | yes | 24 | 3.2 | odd | 2 | inner |