Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,5,Mod(5,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.5");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.k (of order \(18\), degree \(6\), 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: | \(11.1639560131\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 5.10 | ||
Character | \(\chi\) | \(=\) | 108.5 |
Dual form | 108.5.k.a.65.10 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{18}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 6.98131 | − | 5.67991i | 0.775701 | − | 0.631101i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.75895 | − | 24.0650i | −0.350358 | − | 0.962600i | −0.982255 | − | 0.187548i | \(-0.939946\pi\) |
0.631898 | − | 0.775052i | \(-0.282276\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.632293 | − | 3.58591i | −0.0129039 | − | 0.0731819i | 0.977676 | − | 0.210119i | \(-0.0673852\pi\) |
−0.990580 | + | 0.136937i | \(0.956274\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 16.4774 | − | 79.3063i | 0.203424 | − | 0.979091i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −22.6368 | + | 62.1941i | −0.187081 | + | 0.514001i | −0.997406 | − | 0.0719797i | \(-0.977068\pi\) |
0.810325 | + | 0.585981i | \(0.199291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −236.237 | − | 198.227i | −1.39785 | − | 1.17294i | −0.962042 | − | 0.272901i | \(-0.912017\pi\) |
−0.435812 | − | 0.900038i | \(-0.643539\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −197.836 | − | 118.255i | −0.879271 | − | 0.525579i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 205.336 | + | 118.551i | 0.710505 | + | 0.410210i | 0.811248 | − | 0.584702i | \(-0.198789\pi\) |
−0.100743 | + | 0.994912i | \(0.532122\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 25.2661 | + | 43.7622i | 0.0699892 | + | 0.121225i | 0.898896 | − | 0.438161i | \(-0.144370\pi\) |
−0.828907 | + | 0.559386i | \(0.811037\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −24.7819 | − | 21.4430i | −0.0561947 | − | 0.0486236i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −330.376 | − | 58.2542i | −0.624530 | − | 0.110121i | −0.147577 | − | 0.989051i | \(-0.547147\pi\) |
−0.476952 | + | 0.878929i | \(0.658259\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.6276 | + | 19.8259i | −0.0378042 | + | 0.0317215i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −335.419 | − | 647.252i | −0.460108 | − | 0.887863i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −402.857 | − | 480.107i | −0.479022 | − | 0.570876i | 0.471368 | − | 0.881936i | \(-0.343760\pi\) |
−0.950390 | + | 0.311060i | \(0.899316\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 111.849 | − | 634.330i | 0.116389 | − | 0.660073i | −0.869665 | − | 0.493643i | \(-0.835665\pi\) |
0.986053 | − | 0.166430i | \(-0.0532239\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 195.222 | + | 562.771i | 0.179267 | + | 0.516778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −80.7568 | + | 46.6249i | −0.0659239 | + | 0.0380612i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 978.384 | − | 1694.61i | 0.714671 | − | 1.23785i | −0.248416 | − | 0.968654i | \(-0.579910\pi\) |
0.963086 | − | 0.269193i | \(-0.0867568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2775.15 | − | 42.0759i | −1.82456 | − | 0.0276633i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −724.003 | + | 862.834i | −0.430698 | + | 0.513286i | −0.937124 | − | 0.348998i | \(-0.886522\pi\) |
0.506426 | + | 0.862284i | \(0.330967\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 296.362 | + | 107.867i | 0.160282 | + | 0.0583380i | 0.420915 | − | 0.907100i | \(-0.361709\pi\) |
−0.260633 | + | 0.965438i | \(0.583931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2052.83 | + | 298.112i | −1.01374 | + | 0.147216i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3610.79 | − | 636.681i | 1.63458 | − | 0.288221i | 0.720411 | − | 0.693547i | \(-0.243953\pi\) |
0.914172 | + | 0.405326i | \(0.132842\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2243.74 | − | 816.656i | 0.934504 | − | 0.340131i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2106.87 | − | 338.649i | 0.810023 | − | 0.130200i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3927.39i | 1.39815i | 0.715051 | + | 0.699073i | \(0.246404\pi\) | ||||
−0.715051 | + | 0.699073i | \(0.753596\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1694.98 | 0.560323 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 424.955 | + | 162.008i | 0.130796 | + | 0.0498640i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 662.491 | + | 1820.18i | 0.190316 | + | 0.522890i | 0.997748 | − | 0.0670710i | \(-0.0213654\pi\) |
−0.807432 | + | 0.589961i | \(0.799143\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 633.851 | + | 3594.75i | 0.170344 | + | 0.966070i | 0.943382 | + | 0.331710i | \(0.107625\pi\) |
−0.773037 | + | 0.634361i | \(0.781263\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −294.804 | − | 8.94148i | −0.0742766 | − | 0.00225283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2701.14 | + | 7421.31i | −0.639322 | + | 1.75652i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1252.37 | − | 1050.86i | −0.278986 | − | 0.234097i | 0.492548 | − | 0.870285i | \(-0.336066\pi\) |
−0.771534 | + | 0.636188i | \(0.780510\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2637.34 | + | 1469.81i | −0.553946 | + | 0.308720i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6356.50 | + | 3669.93i | 1.26096 | + | 0.728016i | 0.973260 | − | 0.229705i | \(-0.0737761\pi\) |
0.287700 | + | 0.957721i | \(0.407109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −832.121 | − | 1441.28i | −0.156150 | − | 0.270459i | 0.777327 | − | 0.629096i | \(-0.216575\pi\) |
−0.933477 | + | 0.358637i | \(0.883242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −52.3423 | + | 272.614i | −0.00930530 | + | 0.0484646i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 237.336 | + | 41.8487i | 0.0400296 | + | 0.00705830i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8242.86 | − | 6916.58i | 1.32076 | − | 1.10825i | 0.334617 | − | 0.942354i | \(-0.391393\pi\) |
0.986143 | − | 0.165895i | \(-0.0530513\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6017.99 | − | 2613.52i | −0.917237 | − | 0.398341i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4039.89 | + | 4814.55i | 0.586426 | + | 0.698875i | 0.974915 | − | 0.222578i | \(-0.0714473\pi\) |
−0.388489 | + | 0.921453i | \(0.627003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1054.40 | − | 5979.79i | 0.145937 | − | 0.827652i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5539.43 | − | 1063.58i | −0.731858 | − | 0.140518i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4492.85 | − | 2593.95i | 0.567207 | − | 0.327477i | −0.188826 | − | 0.982011i | \(-0.560468\pi\) |
0.756033 | + | 0.654533i | \(0.227135\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −561.452 | + | 972.463i | −0.0678000 | + | 0.117433i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2822.08 | − | 5063.75i | −0.326289 | − | 0.585472i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 831.832 | − | 991.339i | 0.0921698 | − | 0.109844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3954.60 | − | 1439.36i | −0.420300 | − | 0.152977i | 0.123208 | − | 0.992381i | \(-0.460682\pi\) |
−0.543507 | + | 0.839404i | \(0.682904\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4559.39 | + | 2820.04i | 0.465197 | + | 0.287730i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −15898.8 | + | 2803.39i | −1.55856 | + | 0.274815i | −0.885451 | − | 0.464732i | \(-0.846151\pi\) |
−0.673104 | + | 0.739548i | \(0.735039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13317.2 | − | 4847.05i | 1.25527 | − | 0.456881i | 0.373091 | − | 0.927795i | \(-0.378298\pi\) |
0.882179 | + | 0.470914i | \(0.156076\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −298.963 | + | 784.194i | −0.0271168 | + | 0.0711287i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 5472.24i | − | 0.477967i | −0.971024 | − | 0.238984i | \(-0.923186\pi\) | ||
0.971024 | − | 0.238984i | \(-0.0768142\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8864.19 | −0.746081 | −0.373041 | − | 0.927815i | \(-0.621685\pi\) | ||||
−0.373041 | + | 0.927815i | \(0.621685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2794.83 | − | 17387.7i | −0.226835 | − | 1.41123i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1907.44 | − | 5240.66i | −0.149381 | − | 0.410421i | 0.842322 | − | 0.538975i | \(-0.181188\pi\) |
−0.991702 | + | 0.128555i | \(0.958966\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1491.86 | + | 8460.75i | 0.112806 | + | 0.639754i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −19613.2 | + | 15468.9i | −1.43277 | + | 1.13002i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 295.280 | − | 811.275i | 0.0208516 | − | 0.0572894i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7859.97 | + | 6595.30i | 0.536847 | + | 0.450468i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −153.678 | + | 10136.0i | −0.0101578 | + | 0.669970i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13177.5 | − | 7608.01i | −0.843357 | − | 0.486912i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12709.1 | − | 22012.8i | −0.787967 | − | 1.36480i | −0.927211 | − | 0.374540i | \(-0.877800\pi\) |
0.139244 | − | 0.990258i | \(-0.455533\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2681.67 | − | 930.255i | 0.161148 | − | 0.0559014i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6066.88 | − | 1069.75i | −0.353527 | − | 0.0623364i | −0.00593554 | − | 0.999982i | \(-0.501889\pi\) |
−0.347592 | + | 0.937646i | \(0.613000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 140.952 | − | 118.272i | 0.00796832 | − | 0.00668622i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12638.2 | + | 13741.1i | −0.693454 | + | 0.753970i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13079.1 | + | 15587.0i | 0.696845 | + | 0.830467i | 0.992165 | − | 0.124931i | \(-0.0398709\pi\) |
−0.295321 | + | 0.955398i | \(0.595426\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1564.03 | − | 8870.06i | 0.0809498 | − | 0.459089i | −0.917207 | − | 0.398410i | \(-0.869562\pi\) |
0.998157 | − | 0.0606794i | \(-0.0193267\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21591.8 | − | 24953.8i | 1.08605 | − | 1.25516i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17676.2 | − | 10205.4i | 0.864404 | − | 0.499064i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8025.16 | + | 13900.0i | −0.381696 | + | 0.661117i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11025.7 | − | 18445.6i | 0.510238 | − | 0.853606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9361.36 | − | 11156.4i | 0.421664 | − | 0.502519i | −0.512834 | − | 0.858488i | \(-0.671404\pi\) |
0.934498 | + | 0.355968i | \(0.115849\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4398.99 | − | 1601.10i | −0.192930 | − | 0.0702207i | 0.243748 | − | 0.969839i | \(-0.421623\pi\) |
−0.436678 | + | 0.899618i | \(0.643845\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 12785.2 | − | 14331.0i | 0.546167 | − | 0.612202i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16244.8 | + | 2864.40i | −0.676164 | + | 0.119226i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4131.63 | + | 1503.79i | −0.167619 | + | 0.0610082i | −0.424466 | − | 0.905444i | \(-0.639538\pi\) |
0.256848 | + | 0.966452i | \(0.417316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 22307.2 | + | 27418.3i | 0.882370 | + | 1.08454i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1221.53i | 0.0471252i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −48545.4 | −1.82714 | −0.913572 | − | 0.406677i | \(-0.866688\pi\) | ||||
−0.913572 | + | 0.406677i | \(0.866688\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11833.2 | − | 9627.31i | 0.434643 | − | 0.353620i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14935.4 | − | 41034.8i | −0.535532 | − | 1.47136i | −0.852399 | − | 0.522891i | \(-0.824853\pi\) |
0.316868 | − | 0.948470i | \(-0.397369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11554.7 | + | 65530.0i | 0.404562 | + | 2.29439i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3886.94 | − | 1282.68i | 0.132928 | − | 0.0438657i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7728.43 | + | 21233.7i | −0.258225 | + | 0.709469i | 0.741051 | + | 0.671448i | \(0.234327\pi\) |
−0.999277 | + | 0.0380204i | \(0.987895\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 86.0336 | + | 72.1907i | 0.00280926 | + | 0.00235725i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14963.5 | + | 8944.35i | 0.477625 | + | 0.285497i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 47920.0 | + | 27666.6i | 1.49558 | + | 0.863476i | 0.999987 | − | 0.00507689i | \(-0.00161603\pi\) |
0.495597 | + | 0.868553i | \(0.334949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20301.3 | + | 35162.8i | 0.619678 | + | 1.07331i | 0.989544 | + | 0.144229i | \(0.0460702\pi\) |
−0.369866 | + | 0.929085i | \(0.620596\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24842.9 | + | 21495.8i | 0.741824 | + | 0.641877i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −49350.4 | − | 8701.82i | −1.44194 | − | 0.254253i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12021.3 | + | 10087.1i | −0.343770 | + | 0.288458i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2108.90 | + | 1612.04i | −0.0590382 | + | 0.0451285i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10391.8 | − | 12384.5i | −0.284856 | − | 0.339478i | 0.604575 | − | 0.796549i | \(-0.293343\pi\) |
−0.889430 | + | 0.457071i | \(0.848899\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5546.95 | − | 31458.3i | 0.148915 | − | 0.844542i | −0.815224 | − | 0.579146i | \(-0.803386\pi\) |
0.964140 | − | 0.265396i | \(-0.0855027\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 23294.9 | + | 67152.7i | 0.612620 | + | 1.76601i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 50661.7 | − | 29249.5i | 1.30541 | − | 0.753679i | 0.324083 | − | 0.946028i | \(-0.394944\pi\) |
0.981326 | + | 0.192350i | \(0.0616108\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8677.79 | + | 15030.4i | −0.219131 | + | 0.379545i | −0.954542 | − | 0.298075i | \(-0.903655\pi\) |
0.735412 | + | 0.677620i | \(0.236989\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14712.0 | − | 223.057i | −0.364148 | − | 0.00552109i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1466.90 | + | 1748.18i | −0.0355965 | + | 0.0424223i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 27105.6 | + | 9865.63i | 0.644988 | + | 0.234756i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −10063.7 | + | 25241.0i | −0.234863 | + | 0.589070i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3293.69 | + | 580.767i | −0.0754033 | + | 0.0132956i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6345.41 | − | 2309.54i | 0.142526 | − | 0.0518753i | −0.269772 | − | 0.962924i | \(-0.586948\pi\) |
0.412298 | + | 0.911049i | \(0.364726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 65221.5 | − | 10483.4i | 1.43758 | − | 0.231070i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8076.75i | − | 0.174727i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2345.37 | −0.0498072 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13995.6 | − | 5335.62i | −0.291812 | − | 0.111249i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −25008.1 | − | 68709.2i | −0.512031 | − | 1.40679i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14045.2 | + | 79654.1i | 0.282434 | + | 1.60176i | 0.714310 | + | 0.699830i | \(0.246741\pi\) |
−0.431876 | + | 0.901933i | \(0.642148\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1183.00 | + | 2200.50i | 0.0233679 | + | 0.0434666i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4625.90 | + | 12709.6i | −0.0897728 | + | 0.246649i | −0.976451 | − | 0.215738i | \(-0.930784\pi\) |
0.886679 | + | 0.462386i | \(0.153007\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14498.7 | − | 12165.9i | −0.276477 | − | 0.231992i | 0.493996 | − | 0.869464i | \(-0.335536\pi\) |
−0.770473 | + | 0.637472i | \(0.779980\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1894.61 | − | 1055.89i | 0.0355055 | − | 0.0197876i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −46376.2 | − | 26775.3i | −0.854247 | − | 0.493200i | 0.00783474 | − | 0.999969i | \(-0.497506\pi\) |
−0.862081 | + | 0.506770i | \(0.830839\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −46948.5 | − | 81317.1i | −0.850131 | − | 1.47247i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18260.4 | − | 95105.5i | 0.325098 | − | 1.69320i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −41032.0 | − | 7235.05i | −0.718335 | − | 0.126662i | −0.197480 | − | 0.980307i | \(-0.563276\pi\) |
−0.520855 | + | 0.853645i | \(0.674387\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −71951.4 | + | 60374.4i | −1.23881 | + | 1.03949i | −0.241196 | + | 0.970477i | \(0.577540\pi\) |
−0.997616 | + | 0.0690098i | \(0.978016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −56858.0 | + | 15935.9i | −0.962895 | + | 0.269875i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −39305.6 | − | 46842.6i | −0.654821 | − | 0.780386i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2706.03 | − | 15346.7i | 0.0443546 | − | 0.251548i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 55549.9 | + | 10665.7i | 0.895952 | + | 0.172024i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 53554.3 | − | 30919.6i | 0.850054 | − | 0.490779i | −0.0106150 | − | 0.999944i | \(-0.503379\pi\) |
0.860669 | + | 0.509165i | \(0.170046\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11101.7 | − | 19228.8i | 0.173440 | − | 0.300407i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −26603.6 | − | 47735.6i | −0.409128 | − | 0.734112i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6611.38 | − | 7879.13i | 0.100098 | − | 0.119292i | −0.713670 | − | 0.700482i | \(-0.752968\pi\) |
0.813768 | + | 0.581190i | \(0.197413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6695.35 | − | 2436.91i | −0.0998099 | − | 0.0363278i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −44713.5 | + | 24038.3i | −0.656384 | + | 0.352876i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 64659.5 | − | 11401.2i | 0.934805 | − | 0.164831i | 0.314558 | − | 0.949238i | \(-0.398144\pi\) |
0.620247 | + | 0.784407i | \(0.287032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 94512.7 | − | 34399.8i | 1.34586 | − | 0.489851i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16632.6 | − | 43628.1i | 0.233312 | − | 0.611989i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 78857.5i | 1.08978i | 0.838508 | + | 0.544890i | \(0.183428\pi\) | ||||
−0.838508 | + | 0.544890i | \(0.816572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −85836.1 | −1.16878 | −0.584388 | − | 0.811474i | \(-0.698666\pi\) | ||||
−0.584388 | + | 0.811474i | \(0.698666\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1603.83 | + | 9978.06i | 0.0215195 | + | 0.133882i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −698.202 | − | 1918.29i | −0.00923242 | − | 0.0253659i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12768.2 | − | 72412.3i | −0.166407 | − | 0.943741i | −0.947602 | − | 0.319454i | \(-0.896501\pi\) |
0.781195 | − | 0.624287i | \(-0.214611\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −48463.4 | − | 19322.4i | −0.622595 | − | 0.248230i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −50983.9 | + | 140077.i | −0.645685 | + | 1.77401i | −0.0126027 | + | 0.999921i | \(0.504012\pi\) |
−0.633082 | + | 0.774084i | \(0.718211\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −43283.8 | − | 36319.5i | −0.540447 | − | 0.453489i | 0.331244 | − | 0.943545i | \(-0.392532\pi\) |
−0.871691 | + | 0.490056i | \(0.836976\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 176.566 | − | 11645.6i | 0.00217379 | − | 0.143374i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3551.83 | + | 2050.65i | 0.0431209 | + | 0.0248959i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13651.9 | − | 23645.9i | −0.163455 | − | 0.283113i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35783.7 | + | 12413.2i | −0.422570 | + | 0.146587i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8976.28 | − | 1582.76i | −0.104559 | − | 0.0184366i | 0.121124 | − | 0.992637i | \(-0.461350\pi\) |
−0.225683 | + | 0.974201i | \(0.572461\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 37999.9 | − | 31885.7i | 0.436655 | − | 0.366397i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 47848.1 | − | 6209.38i | 0.542440 | − | 0.0703939i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 66499.6 | + | 79251.2i | 0.743835 | + | 0.886469i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 199.414 | − | 1130.93i | 0.00220101 | − | 0.0124825i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −95071.6 | + | 109875.i | −1.03554 | + | 1.19678i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 80955.7 | − | 46739.8i | 0.870258 | − | 0.502444i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −55967.7 | + | 96939.0i | −0.593829 | + | 1.02854i | 0.399882 | + | 0.916566i | \(0.369051\pi\) |
−0.993711 | + | 0.111975i | \(0.964282\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 65440.4 | − | 109479.i | 0.685376 | − | 1.14660i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15433.3 | − | 18392.6i | 0.159565 | − | 0.190162i | −0.680338 | − | 0.732898i | \(-0.738167\pi\) |
0.839903 | + | 0.542736i | \(0.182612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 166946. | + | 60763.3i | 1.70407 | + | 0.620230i | 0.996278 | − | 0.0861930i | \(-0.0274702\pi\) |
0.707790 | + | 0.706423i | \(0.249692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2367.00 | + | 7172.78i | 0.0238548 | + | 0.0722880i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −168850. | + | 29772.9i | −1.68029 | + | 0.296280i | −0.930743 | − | 0.365674i | \(-0.880838\pi\) |
−0.749544 | + | 0.661954i | \(0.769727\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 38979.2 | − | 14187.3i | 0.383047 | − | 0.139418i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31081.8 | − | 38203.4i | −0.301645 | − | 0.370760i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11981.3i | 0.114841i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9511.75 | 0.0900521 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −61883.7 | + | 50347.8i | −0.578736 | + | 0.470852i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4566.16 | − | 12545.4i | −0.0421851 | − | 0.115903i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −21564.0 | − | 122296.i | −0.196822 | − | 1.11623i | −0.909800 | − | 0.415047i | \(-0.863765\pi\) |
0.712978 | − | 0.701186i | \(-0.247346\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −118272. | − | 105515.i | −1.06658 | − | 0.951535i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14319.6 | + | 39342.7i | −0.127597 | + | 0.350570i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 144069. | + | 120888.i | 1.26856 | + | 1.06445i | 0.994715 | + | 0.102674i | \(0.0327400\pi\) |
0.273845 | + | 0.961774i | \(0.411704\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −43082.9 | − | 25752.6i | −0.374892 | − | 0.224089i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 36919.7 | + | 21315.6i | 0.317504 | + | 0.183311i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8718.45 | − | 15100.8i | −0.0741056 | − | 0.128355i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 58471.4 | + | 50593.5i | 0.491253 | + | 0.425066i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 126703. | + | 22341.2i | 1.05227 | + | 0.185544i | 0.672925 | − | 0.739710i | \(-0.265037\pi\) |
0.379347 | + | 0.925254i | \(0.376149\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36525.7 | − | 30648.7i | 0.299881 | − | 0.251630i | −0.480414 | − | 0.877042i | \(-0.659514\pi\) |
0.780295 | + | 0.625412i | \(0.215069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −49064.1 | + | 219394.i | −0.398244 | + | 1.78078i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 94657.4 | + | 112808.i | 0.759635 | + | 0.905298i | 0.997825 | − | 0.0659209i | \(-0.0209985\pi\) |
−0.238190 | + | 0.971219i | \(0.576554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32640.6 | − | 185114.i | 0.259001 | − | 1.46887i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2546.52 | − | 7340.92i | −0.0199807 | − | 0.0575989i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 65225.6 | − | 37658.0i | 0.506092 | − | 0.292192i | −0.225134 | − | 0.974328i | \(-0.572282\pi\) |
0.731226 | + | 0.682136i | \(0.238949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 63883.7 | − | 110650.i | 0.490203 | − | 0.849057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 92333.6 | + | 1399.93i | 0.700723 | + | 0.0106241i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27395.8 | + | 32649.1i | −0.205636 | + | 0.245067i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 107072. | + | 38970.8i | 0.794954 | + | 0.289339i | 0.707394 | − | 0.706820i | \(-0.249871\pi\) |
0.0875599 | + | 0.996159i | \(0.472093\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 56498.5 | + | 71635.3i | 0.414939 | + | 0.526107i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14083.3 | − | 2483.26i | 0.102319 | − | 0.0180416i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 51753.2 | − | 18836.6i | 0.371980 | − | 0.135390i | −0.149264 | − | 0.988797i | \(-0.547690\pi\) |
0.521244 | + | 0.853408i | \(0.325468\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −135209. | + | 21732.8i | −0.961484 | + | 0.154545i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 193276.i | 1.35986i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 129313. | 0.900249 | 0.450125 | − | 0.892966i | \(-0.351380\pi\) | ||||
0.450125 | + | 0.892966i | \(0.351380\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −213757. | − | 81491.8i | −1.47255 | − | 0.561389i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 83657.1 | + | 229846.i | 0.570303 | + | 1.56689i | 0.804028 | + | 0.594591i | \(0.202686\pi\) |
−0.233726 | + | 0.972303i | \(0.575092\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1071.72 | − | 6078.03i | −0.00723037 | − | 0.0410055i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13437.8 | − | 21726.0i | 0.0897234 | − | 0.145063i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 43560.0 | − | 119680.i | 0.287865 | − | 0.790903i | −0.708500 | − | 0.705711i | \(-0.750628\pi\) |
0.996365 | − | 0.0851915i | \(-0.0271502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −60932.0 | − | 51128.0i | −0.398558 | − | 0.334430i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −48430.9 | + | 26991.0i | −0.313572 | + | 0.174757i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −238646. | − | 137783.i | −1.52954 | − | 0.883080i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 48666.8 | + | 84293.3i | 0.308782 | + | 0.534825i | 0.978096 | − | 0.208154i | \(-0.0667454\pi\) |
−0.669314 | + | 0.742979i | \(0.733412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 312.251 | − | 1626.29i | 0.00196136 | − | 0.0102153i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20496.9 | − | 3614.15i | −0.127467 | − | 0.0224759i | 0.109551 | − | 0.993981i | \(-0.465059\pi\) |
−0.237018 | + | 0.971505i | \(0.576170\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −152164. | + | 127681.i | −0.936919 | + | 0.786168i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10183.0 | + | 167715.i | −0.0620821 | + | 1.02249i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 83247.4 | + | 99210.3i | 0.502553 | + | 0.598919i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −50897.1 | + | 288652.i | −0.304261 | + | 1.72555i | 0.322702 | + | 0.946501i | \(0.395409\pi\) |
−0.626963 | + | 0.779049i | \(0.715702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 179842. | + | 34530.0i | 1.06465 | + | 0.204415i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6108.11 | − | 3526.52i | 0.0358102 | − | 0.0206750i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 80477.0 | − | 139390.i | 0.467278 | − | 0.809350i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −39462.1 | − | 70808.2i | −0.226939 | − | 0.407203i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39138.7 | + | 46643.7i | −0.222935 | + | 0.265684i | −0.865906 | − | 0.500207i | \(-0.833257\pi\) |
0.642971 | + | 0.765891i | \(0.277702\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −210167. | − | 76494.4i | −1.18577 | − | 0.431584i | −0.327533 | − | 0.944840i | \(-0.606217\pi\) |
−0.858236 | + | 0.513256i | \(0.828439\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9003.53 | − | 296850.i | 0.0503190 | − | 1.65904i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7201.98 | + | 1269.90i | −0.0398725 | + | 0.00703060i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12489.7 | − | 4545.87i | 0.0685007 | − | 0.0249322i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 65437.5 | − | 171646.i | 0.355559 | − | 0.932650i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 244624.i | 1.31687i | 0.752635 | + | 0.658437i | \(0.228782\pi\) | ||||
−0.752635 | + | 0.658437i | \(0.771218\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −119238. | −0.635971 | −0.317986 | − | 0.948096i | \(-0.603006\pi\) | ||||
−0.317986 | + | 0.948096i | \(0.603006\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 22924.5 | + | 142622.i | 0.121149 | + | 0.753718i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5797.98 | − | 15929.8i | −0.0303609 | − | 0.0834158i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16161.5 | − | 91656.5i | −0.0838597 | − | 0.475592i | −0.997597 | − | 0.0692860i | \(-0.977928\pi\) |
0.913737 | − | 0.406306i | \(-0.133183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27795.0 | − | 191399.i | −0.142919 | − | 0.984155i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 94532.4 | − | 259726.i | 0.481696 | − | 1.32345i | −0.426342 | − | 0.904562i | \(-0.640198\pi\) |
0.908038 | − | 0.418887i | \(-0.137580\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −101776. | − | 85400.2i | −0.513955 | − | 0.431259i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1987.06 | − | 131058.i | 0.00994477 | − | 0.655917i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −84746.9 | − | 48928.6i | −0.420369 | − | 0.242700i | 0.274866 | − | 0.961483i | \(-0.411366\pi\) |
−0.695235 | + | 0.718782i | \(0.744700\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37274.0 | − | 64560.5i | −0.183254 | − | 0.317405i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39804.8 | + | 13808.1i | −0.193972 | + | 0.0672878i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28320.1 | + | 4993.59i | 0.136795 | + | 0.0241207i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 132440. | − | 111130.i | 0.634141 | − | 0.532107i | −0.268072 | − | 0.963399i | \(-0.586387\pi\) |
0.902212 | + | 0.431292i | \(0.141942\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7858.62 | − | 172668.i | 0.0373010 | − | 0.819572i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −207164. | − | 246888.i | −0.974793 | − | 1.16171i | −0.986826 | − | 0.161785i | \(-0.948275\pi\) |
0.0120331 | − | 0.999928i | \(-0.496170\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 42566.1 | − | 241404.i | 0.198564 | − | 1.12611i | −0.708686 | − | 0.705524i | \(-0.750712\pi\) |
0.907250 | − | 0.420591i | \(-0.138177\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −97140.7 | + | 112266.i | −0.449257 | + | 0.519211i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 199445. | − | 115149.i | 0.914510 | − | 0.527992i | 0.0326303 | − | 0.999467i | \(-0.489612\pi\) |
0.881879 | + | 0.471475i | \(0.156278\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2976.43 | + | 5155.33i | −0.0135316 | + | 0.0234375i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20302.8 | + | 33965.7i | −0.0915197 | + | 0.153108i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13417.4 | + | 15990.2i | −0.0599715 | + | 0.0714713i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1464.60 | − | 533.072i | −0.00649131 | − | 0.00236264i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 311467. | + | 64713.0i | 1.36891 | + | 0.284416i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 133421. | − | 23525.7i | 0.581505 | − | 0.102535i | 0.124845 | − | 0.992176i | \(-0.460157\pi\) |
0.456660 | + | 0.889641i | \(0.349046\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −567048. | + | 206389.i | −2.45092 | + | 0.892063i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6938.19 | + | 8527.90i | 0.0297408 | + | 0.0365551i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 107775.i | 0.458177i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 253009. | 1.06679 | 0.533393 | − | 0.845868i | \(-0.320917\pi\) | ||||
0.533393 | + | 0.845868i | \(0.320917\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −338910. | + | 275733.i | −1.41732 | + | 1.15311i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −86121.8 | − | 236618.i | −0.357232 | − | 0.981487i | −0.979986 | − | 0.199069i | \(-0.936208\pi\) |
0.622754 | − | 0.782418i | \(-0.286014\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25804.1 | − | 146342.i | −0.106168 | − | 0.602110i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 27928.7 | − | 134422.i | 0.113983 | − | 0.548607i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9140.86 | − | 25114.3i | 0.0370062 | − | 0.101674i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 49665.0 | + | 41673.9i | 0.199457 | + | 0.167364i | 0.737046 | − | 0.675843i | \(-0.236220\pi\) |
−0.537589 | + | 0.843207i | \(0.680665\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −337343. | − | 201645.i | −1.34399 | − | 0.803362i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −420415. | − | 242727.i | −1.66166 | − | 0.959360i | −0.971923 | − | 0.235300i | \(-0.924393\pi\) |
−0.689737 | − | 0.724060i | \(-0.742274\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 206721. | + | 358051.i | 0.810589 | + | 1.40398i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 452871. | + | 391855.i | 1.76181 | + | 1.52444i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −287186. | − | 50638.7i | −1.10848 | − | 0.195455i | −0.410703 | − | 0.911769i | \(-0.634717\pi\) |
−0.697778 | + | 0.716314i | \(0.745828\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4642.14 | + | 3895.22i | −0.0177777 | + | 0.0149173i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 19850.4 | − | 31032.2i | 0.0754284 | − | 0.117917i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −233289. | − | 278023.i | −0.879587 | − | 1.04825i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42139.1 | + | 238983.i | −0.157654 | + | 0.894098i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 66650.8 | + | 192136.i | 0.247440 | + | 0.713302i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41930.4 | + | 24208.5i | −0.154473 | + | 0.0891853i | −0.575244 | − | 0.817982i | \(-0.695093\pi\) |
0.420771 | + | 0.907167i | \(0.361760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −155771. | + | 269804.i | −0.569488 | + | 0.986382i | 0.427129 | + | 0.904191i | \(0.359525\pi\) |
−0.996617 | + | 0.0821910i | \(0.973808\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1010.66 | + | 15.3233i | 0.00366681 | + | 5.55948e-5i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 98167.0 | − | 116991.i | 0.353463 | − | 0.421241i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −157210. | − | 57219.7i | −0.561782 | − | 0.204472i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 155268. | − | 22548.0i | 0.550672 | − | 0.0799686i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 342073. | − | 60316.7i | 1.20411 | − | 0.212316i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −131690. | + | 47931.1i | −0.460091 | + | 0.167460i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 491688. | − | 79031.8i | 1.70507 | − | 0.274065i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 158034.i | 0.543968i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 333475. | 1.13938 | 0.569690 | − | 0.821860i | \(-0.307063\pi\) | ||||
0.569690 | + | 0.821860i | \(0.307063\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 341451. | + | 130173.i | 1.15805 | + | 0.441492i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 77641.0 | + | 213317.i | 0.261395 | + | 0.718178i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 58942.6 | + | 334280.i | 0.196995 | + | 1.11721i | 0.909549 | + | 0.415596i | \(0.136427\pi\) |
−0.712554 | + | 0.701617i | \(0.752462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 295530. | + | 8963.51i | 0.980522 | + | 0.0297395i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10831.9 | − | 29760.3i | 0.0356780 | − | 0.0980245i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30014.2 | − | 25184.9i | −0.0981468 | − | 0.0823549i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −393956. | + | 219556.i | −1.27897 | + | 0.712786i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −211847. | − | 122310.i | −0.682828 | − | 0.394231i | 0.118092 | − | 0.993003i | \(-0.462322\pi\) |
−0.800920 | + | 0.598772i | \(0.795656\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48629.6 | − | 84229.0i | −0.155624 | − | 0.269549i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26630.8 | + | 138701.i | −0.0846173 | + | 0.440711i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 465712. | + | 82117.5i | 1.46927 | + | 0.259071i | 0.850280 | − | 0.526331i | \(-0.176433\pi\) |
0.618986 | + | 0.785402i | \(0.287544\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −109409. | + | 91805.3i | −0.342734 | + | 0.287588i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5566.71 | + | 23232.5i | −0.0173154 | + | 0.0722653i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −190547. | − | 227085.i | −0.588542 | − | 0.701397i | 0.386783 | − | 0.922171i | \(-0.373586\pi\) |
−0.975325 | + | 0.220774i | \(0.929142\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −96134.7 | + | 545207.i | −0.294855 | + | 1.67220i | 0.372938 | + | 0.927856i | \(0.378350\pi\) |
−0.667792 | + | 0.744347i | \(0.732761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −142891. | − | 27435.4i | −0.435208 | − | 0.0835607i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8960.94 | − | 5173.60i | 0.0271030 | − | 0.0156479i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 127612. | − | 221030.i | 0.383300 | − | 0.663895i | −0.608232 | − | 0.793760i | \(-0.708121\pi\) |
0.991532 | + | 0.129864i | \(0.0414542\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −139955. | − | 251127.i | −0.417477 | − | 0.749092i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14710.2 | − | 17530.9i | 0.0435778 | − | 0.0519340i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −244261. | − | 88903.6i | −0.718648 | − | 0.261567i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 544049. | + | 336501.i | 1.58974 | + | 0.983273i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 390885. | − | 68923.6i | 1.13442 | − | 0.200029i | 0.425255 | − | 0.905073i | \(-0.360184\pi\) |
0.709163 | + | 0.705045i | \(0.249073\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30585.6 | − | 11132.3i | 0.0881631 | − | 0.0320887i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 187550. | − | 491953.i | 0.536961 | − | 1.40847i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 141628.i | 0.402754i | 0.979514 | + | 0.201377i | \(0.0645416\pi\) | ||||
−0.979514 | + | 0.201377i | \(0.935458\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −22109.7 | −0.0624523 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24788.8 | + | 154221.i | 0.0695515 | + | 0.432707i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 205094. | + | 563492.i | 0.571611 | + | 1.57049i | 0.801959 | + | 0.597379i | \(0.203791\pi\) |
−0.230348 | + | 0.973108i | \(0.573987\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −67002.3 | − | 379989.i | −0.185499 | − | 1.05202i | −0.925313 | − | 0.379204i | \(-0.876198\pi\) |
0.739814 | − | 0.672811i | \(-0.234913\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −103976. | + | 82005.3i | −0.285955 | + | 0.225532i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 89870.9 | − | 246918.i | 0.245532 | − | 0.674594i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 109301. | + | 91714.6i | 0.296652 | + | 0.248921i | 0.778949 | − | 0.627087i | \(-0.215753\pi\) |
−0.482297 | + | 0.876008i | \(0.660197\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −311.366 | + | 20536.4i | −0.000839529 | + | 0.0553720i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −979212. | − | 565348.i | −2.62297 | − | 1.51438i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 67410.6 | + | 116759.i | 0.179394 | + | 0.310719i | 0.941673 | − | 0.336529i | \(-0.109253\pi\) |
−0.762279 | + | 0.647248i | \(0.775920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 245268. | − | 85082.2i | 0.648472 | − | 0.224951i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 550083. | + | 96994.6i | 1.44497 | + | 0.254787i | 0.840487 | − | 0.541832i | \(-0.182269\pi\) |
0.604481 | + | 0.796619i | \(0.293380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 206114. | − | 172950.i | 0.537931 | − | 0.451377i | −0.332899 | − | 0.942963i | \(-0.608027\pi\) |
0.870830 | + | 0.491585i | \(0.163582\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 73109.3 | + | 233376.i | 0.189579 | + | 0.605164i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12142.5 | − | 14470.8i | −0.0312846 | − | 0.0372835i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −71013.6 | + | 402738.i | −0.181795 | + | 1.03101i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −19695.6 | + | 22762.4i | −0.0500995 | + | 0.0579005i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 401795. | − | 231976.i | 1.01555 | − | 0.586330i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −263153. | + | 455795.i | −0.660922 | + | 1.14475i | 0.319451 | + | 0.947603i | \(0.396501\pi\) |
−0.980374 | + | 0.197148i | \(0.936832\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31181.3 | − | 52165.0i | 0.0778192 | − | 0.130188i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −418421. | + | 498654.i | −1.03769 | + | 1.23666i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −691939. | − | 251845.i | −1.70525 | − | 0.620661i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 395787. | − | 443640.i | 0.969303 | − | 1.08650i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −505241. | + | 89087.6i | −1.22965 | + | 0.216821i | −0.750476 | − | 0.660898i | \(-0.770176\pi\) |
−0.479176 | + | 0.877719i | \(0.659065\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20896.4 | + | 7605.67i | −0.0505417 | + | 0.0183957i | −0.367167 | − | 0.930155i | \(-0.619672\pi\) |
0.316626 | + | 0.948551i | \(0.397450\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −45875.2 | − | 56386.3i | −0.110270 | − | 0.135536i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 341326.i | 0.815381i | 0.913120 | + | 0.407690i | \(0.133666\pi\) | ||||
−0.913120 | + | 0.407690i | \(0.866334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −128201. | −0.304370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16373.8 | + | 13321.5i | −0.0386355 | + | 0.0314334i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25633.4 | − | 70427.1i | −0.0601145 | − | 0.165163i | 0.906000 | − | 0.423278i | \(-0.139121\pi\) |
−0.966114 | + | 0.258115i | \(0.916899\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 27395.8 | + | 155369.i | 0.0638560 | + | 0.362145i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −128013. | + | 42244.1i | −0.296568 | + | 0.0978667i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 97130.3 | − | 266863.i | 0.223658 | − | 0.614495i | −0.776215 | − | 0.630469i | \(-0.782863\pi\) |
0.999872 | + | 0.0159741i | \(0.00508493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 118548. | + | 99473.7i | 0.271326 | + | 0.227670i | 0.768291 | − | 0.640101i | \(-0.221108\pi\) |
−0.496964 | + | 0.867771i | \(0.665552\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −564851. | − | 337636.i | −1.28501 | − | 0.768108i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4080.82 | − | 2356.06i | −0.00922792 | − | 0.00532774i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 105126. | + | 182084.i | 0.236298 | + | 0.409279i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 550481. | + | 476314.i | 1.22996 | + | 1.06424i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −237920. | − | 41951.8i | −0.528429 | − | 0.0931763i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 606326. | − | 508768.i | 1.33868 | − | 1.12328i | 0.356715 | − | 0.934213i | \(-0.383897\pi\) |
0.981963 | − | 0.189071i | \(-0.0605478\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20757.5 | + | 8643.03i | 0.0455583 | + | 0.0189696i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 319117. | + | 380309.i | 0.696262 | + | 0.829773i | 0.992098 | − | 0.125466i | \(-0.0400426\pi\) |
−0.295836 | + | 0.955239i | \(0.595598\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2660.94 | + | 15090.9i | −0.00577159 | + | 0.0327323i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39894.3 | + | 115004.i | 0.0860233 | + | 0.247981i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 54865.2 | − | 31676.5i | 0.117613 | − | 0.0679040i | −0.440039 | − | 0.897978i | \(-0.645036\pi\) |
0.557653 | + | 0.830074i | \(0.311702\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 260543. | − | 451274.i | 0.555263 | − | 0.961744i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −170321. | − | 2582.35i | −0.360874 | − | 0.00547144i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 778514. | − | 927796.i | 1.63994 | − | 1.95440i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 205774. | + | 74895.6i | 0.430958 | + | 0.156856i | 0.548385 | − | 0.836226i | \(-0.315243\pi\) |
−0.117428 | + | 0.993081i | \(0.537465\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7229.53 | − | 18132.7i | 0.0150537 | − | 0.0377568i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −227157. | + | 40054.0i | −0.470281 | + | 0.0829232i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −250953. | + | 91339.6i | −0.516568 | + | 0.188015i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −475848. | + | 76485.7i | −0.973899 | + | 0.156540i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 484481.i | 0.985919i | 0.870052 | + | 0.492959i | \(0.164085\pi\) | ||||
−0.870052 | + | 0.492959i | \(0.835915\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 98879.8 | 0.200077 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −789636. | − | 301037.i | −1.58872 | − | 0.605678i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20105.4 | + | 55239.2i | 0.0402230 | + | 0.110512i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −68351.0 | − | 387638.i | −0.135973 | − | 0.771140i | −0.974177 | − | 0.225784i | \(-0.927506\pi\) |
0.838205 | − | 0.545356i | \(-0.183606\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −412708. | − | 767678.i | −0.816402 | − | 1.51859i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −73904.8 | + | 203052.i | −0.145376 | + | 0.399418i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −400417. | − | 335990.i | −0.783249 | − | 0.657224i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −327552. | + | 182548.i | −0.637150 | + | 0.355090i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −643290. | − | 371404.i | −1.24437 | − | 0.718437i | −0.274389 | − | 0.961619i | \(-0.588475\pi\) |
−0.969981 | + | 0.243182i | \(0.921809\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25801.4 | − | 44689.4i | −0.0496333 | − | 0.0859674i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −159394. | + | 830170.i | −0.304927 | + | 1.58815i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 19037.1 | + | 3356.76i | 0.0362181 | + | 0.00638622i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 511540. | − | 429233.i | 0.967856 | − | 0.812128i | −0.0143568 | − | 0.999897i | \(-0.504570\pi\) |
0.982213 | + | 0.187769i | \(0.0601256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −306429. | + | 434201.i | −0.576600 | + | 0.817026i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 48066.0 | + | 57282.9i | 0.0899505 | + | 0.107199i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 90190.3 | − | 511495.i | 0.167862 | − | 0.951991i | −0.778203 | − | 0.628013i | \(-0.783868\pi\) |
0.946065 | − | 0.323978i | \(-0.105020\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −540467. | − | 103771.i | −1.00045 | − | 0.192088i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 93707.0 | − | 54101.8i | 0.172519 | − | 0.0996039i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −18612.0 | + | 32237.0i | −0.0340804 | + | 0.0590290i | −0.882563 | − | 0.470195i | \(-0.844184\pi\) |
0.848482 | + | 0.529224i | \(0.177517\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −68276.0 | − | 122510.i | −0.124346 | − | 0.223118i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −533099. | + | 635323.i | −0.965674 | + | 1.15085i | 0.0228434 | + | 0.999739i | \(0.492728\pi\) |
−0.988517 | + | 0.151107i | \(0.951716\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −350475. | − | 127563.i | −0.631458 | − | 0.229832i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 448391. | − | 241058.i | 0.803555 | − | 0.431996i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19623.0 | + | 3460.06i | −0.0349785 | + | 0.00616766i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 410674. | − | 149473.i | 0.728144 | − | 0.265023i | 0.0487651 | − | 0.998810i | \(-0.484471\pi\) |
0.679379 | + | 0.733787i | \(0.262249\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 198259. | − | 520042.i | 0.349657 | − | 0.917167i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 119886.i | 0.210317i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 515657. | 0.899848 | 0.449924 | − | 0.893067i | \(-0.351451\pi\) | ||||
0.449924 | + | 0.893067i | \(0.351451\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31712.9 | − | 197299.i | −0.0550494 | − | 0.342484i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −194402. | − | 534114.i | −0.335684 | − | 0.922284i | −0.986603 | − | 0.163137i | \(-0.947839\pi\) |
0.650920 | − | 0.759147i | \(-0.274383\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5604.77 | + | 31786.2i | 0.00962739 | + | 0.0545996i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −456862. | − | 182152.i | −0.780660 | − | 0.311250i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 204303. | − | 561318.i | 0.347283 | − | 0.954153i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −61792.2 | − | 51849.8i | −0.104491 | − | 0.0876788i | 0.589045 | − | 0.808100i | \(-0.299504\pi\) |
−0.693537 | + | 0.720421i | \(0.743948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1403.34 | − | 92558.7i | 0.00236077 | − | 0.155707i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 418443. | + | 241588.i | 0.700288 | + | 0.404312i | 0.807455 | − | 0.589930i | \(-0.200844\pi\) |
−0.107167 | + | 0.994241i | \(0.534178\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9933.44 | + | 17205.2i | 0.0165385 | + | 0.0286455i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −60583.7 | + | 21016.1i | −0.100349 | + | 0.0348106i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −56052.2 | − | 9883.51i | −0.0923672 | − | 0.0162868i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −372139. | + | 312262.i | −0.610103 | + | 0.511937i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −175624. | + | 421787.i | −0.286458 | + | 0.687970i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 72377.5 | + | 86256.2i | 0.117453 | + | 0.139975i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13069.5 | − | 74120.9i | 0.0211013 | − | 0.119672i | −0.972438 | − | 0.233163i | \(-0.925092\pi\) |
0.993539 | + | 0.113492i | \(0.0362035\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 386650. | − | 446855.i | 0.621104 | − | 0.717816i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17586.5 | + | 10153.6i | −0.0281077 | + | 0.0162280i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 562835. | − | 974860.i | 0.895025 | − | 1.55023i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 464435. | − | 776979.i | 0.734836 | − | 1.22935i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −226447. | + | 269869.i | −0.356493 | + | 0.424851i | −0.914249 | − | 0.405154i | \(-0.867218\pi\) |
0.557756 | + | 0.830005i | \(0.311663\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 816905. | + | 297329.i | 1.27961 | + | 0.465740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −131686. | − | 399053.i | −0.205246 | − | 0.621964i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 108475. | − | 19127.1i | 0.168229 | − | 0.0296633i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29396.2 | − | 10699.3i | 0.0453628 | − | 0.0165107i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 447903. | + | 550529.i | 0.687760 | + | 0.845343i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.15808e6i | 1.76947i | 0.466094 | + | 0.884735i | \(0.345661\pi\) | ||||
−0.466094 | + | 0.884735i | \(0.654339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −351292. | −0.534105 | −0.267053 | − | 0.963682i | \(-0.586050\pi\) | ||||
−0.267053 | + | 0.963682i | \(0.586050\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −599249. | + | 487541.i | −0.906621 | + | 0.737616i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 425206. | + | 1.16825e6i | 0.640154 | + | 1.75881i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2767.42 | + | 15694.8i | 0.00414601 | + | 0.0235132i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 67871.3 | + | 60550.3i | 0.101185 | + | 0.0902711i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −134780. | + | 370305.i | −0.199958 | + | 0.549380i | −0.998627 | − | 0.0523911i | \(-0.983316\pi\) |
0.798669 | + | 0.601771i | \(0.205538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 287702. | + | 241410.i | 0.424759 | + | 0.356415i | 0.829970 | − | 0.557808i | \(-0.188357\pi\) |
−0.405211 | + | 0.914223i | \(0.632802\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −15770.1 | − | 9426.48i | −0.0231700 | − | 0.0138497i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 170424. | + | 98394.3i | 0.249184 | + | 0.143866i | 0.619390 | − | 0.785083i | \(-0.287380\pi\) |
−0.370207 | + | 0.928949i | \(0.620713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −61104.9 | − | 105837.i | −0.0889134 | − | 0.154003i | 0.818139 | − | 0.575021i | \(-0.195006\pi\) |
−0.907052 | + | 0.421018i | \(0.861673\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −500434. | − | 433010.i | −0.724678 | − | 0.627041i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 557536. | + | 98308.7i | 0.803495 | + | 0.141678i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −856684. | + | 718843.i | −1.22870 | + | 1.03101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −448088. | + | 140372.i | −0.639605 | + | 0.200368i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 495313. | + | 590291.i | 0.703648 | + | 0.838576i | 0.992934 | − | 0.118667i | \(-0.0378622\pi\) |
−0.289286 | + | 0.957243i | \(0.593418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 54609.7 | − | 309707.i | 0.0772107 | − | 0.437884i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 439691. | + | 1.26751e6i | 0.618717 | + | 1.78359i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.47577e6 | − | 852038.i | 2.06684 | − | 1.19329i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18680.4 | − | 32355.3i | 0.0260386 | − | 0.0451003i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −508469. | − | 7709.22i | −0.705422 | − | 0.0106954i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −421953. | + | 502864.i | −0.582646 | + | 0.694371i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −222039. | − | 80815.4i | −0.305162 | − | 0.111070i | 0.184900 | − | 0.982757i | \(-0.440804\pi\) |
−0.490062 | + | 0.871687i | \(0.663026\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −64913.1 | − | 82304.2i | −0.0887974 | − | 0.112587i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 230266. | − | 40602.2i | 0.313523 | − | 0.0552825i | −0.0146727 | − | 0.999892i | \(-0.504671\pi\) |
0.328195 | + | 0.944610i | \(0.393560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 243605. | − | 88665.0i | 0.330141 | − | 0.120162i | −0.171631 | − | 0.985161i | \(-0.554904\pi\) |
0.501772 | + | 0.865000i | \(0.332681\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36443.9 | − | 5857.83i | 0.0491607 | − | 0.00790188i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.16509e6i | 1.56437i | 0.623049 | + | 0.782183i | \(0.285894\pi\) | ||||
−0.623049 | + | 0.782183i | \(0.714106\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 578682. | 0.773406 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −229615. | − | 87537.3i | −0.305465 | − | 0.116454i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 243579. | + | 669227.i | 0.322552 | + | 0.886204i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 87547.3 | + | 496505.i | 0.115400 | + | 0.654467i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −179311. | + | 289908.i | −0.235277 | + | 0.380392i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18949.6 | + | 52063.7i | −0.0247505 | + | 0.0680015i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 246319. | + | 206686.i | 0.320257 | + | 0.268727i | 0.788716 | − | 0.614758i | \(-0.210746\pi\) |
−0.468459 | + | 0.883485i | \(0.655191\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −71656.2 | + | 39934.7i | −0.0927418 | + | 0.0516860i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −427889. | − | 247042.i | −0.551288 | − | 0.318286i | 0.198353 | − | 0.980131i | \(-0.436441\pi\) |
−0.749641 | + | 0.661844i | \(0.769774\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −181880. | − | 315025.i | −0.233272 | − | 0.404039i | 0.725497 | − | 0.688225i | \(-0.241610\pi\) |
−0.958769 | + | 0.284186i | \(0.908277\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 84181.3 | − | 438440.i | 0.107480 | − | 0.559788i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.12707e6 | − | 198734.i | −1.43254 | − | 0.252595i | −0.597093 | − | 0.802172i | \(-0.703678\pi\) |
−0.835443 | + | 0.549578i | \(0.814789\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −70900.2 | + | 59492.3i | −0.0897106 | + | 0.0752761i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 298774. | − | 315122.i | 0.376346 | − | 0.396939i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 119093. | + | 141930.i | 0.149343 | + | 0.177980i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 246069. | − | 1.39553e6i | 0.307192 | − | 1.74218i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 914394. | + | 175565.i | 1.13644 | + | 0.218200i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −349605. | + | 201845.i | −0.432572 | + | 0.249746i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −465595. | + | 806434.i | −0.573533 | + | 0.993389i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5031.41 | − | 9028.03i | −0.00617041 | − | 0.0110718i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 668376. | − | 796540.i | 0.816063 | − | 0.972546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.30217e6 | + | 473949.i | 1.58289 | + | 0.576126i | 0.975831 | − | 0.218529i | \(-0.0701257\pi\) |
0.607062 | + | 0.794654i | \(0.292348\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −39643.8 | + | 1.30707e6i | −0.0479785 | + | 1.58187i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 313406. | − | 55262.0i | 0.377634 | − | 0.0665871i | 0.0183904 | − | 0.999831i | \(-0.494146\pi\) |
0.359244 | + | 0.933244i | \(0.383035\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −390887. | + | 142271.i | −0.468932 | + | 0.170677i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 299699. | − | 786126.i | 0.357967 | − | 0.938966i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22431.7i | 0.0266762i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −303248. | −0.359060 | −0.179530 | − | 0.983753i | \(-0.557458\pi\) | ||||
−0.179530 | + | 0.983753i | \(0.557458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 159876. | + | 994653.i | 0.188480 | + | 1.17261i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −774165. | − | 2.12700e6i | −0.908721 | − | 2.49669i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10480.3 | + | 59437.0i | 0.0122488 | + | 0.0694662i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −164970. | − | 1.13600e6i | −0.191976 | − | 1.32196i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −319502. | + | 877826.i | −0.370205 | + | 1.01713i | 0.605077 | + | 0.796167i | \(0.293142\pi\) |
−0.975282 | + | 0.220964i | \(0.929080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 92429.2 | + | 77557.3i | 0.106638 | + | 0.0894795i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3275.89 | − | 216064.i | 0.00376327 | − | 0.248210i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 348039. | + | 200941.i | 0.398112 | + | 0.229850i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56054.9 | − | 97089.9i | −0.0638461 | − | 0.110585i | 0.832335 | − | 0.554272i | \(-0.187003\pi\) |
−0.896182 | + | 0.443688i | \(0.853670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.51063e6 | − | 524029.i | 1.71328 | − | 0.594325i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −462012. | − | 81465.1i | −0.521764 | − | 0.0920010i | −0.0934373 | − | 0.995625i | \(-0.529785\pi\) |
−0.428326 | + | 0.903624i | \(0.640897\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 289457. | − | 242883.i | 0.325507 | − | 0.273133i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 57265.4 | + | 36631.1i | 0.0641252 | + | 0.0410191i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −928332. | − | 1.10634e6i | −1.03515 | − | 1.23364i | −0.971838 | − | 0.235650i | \(-0.924278\pi\) |
−0.0633116 | − | 0.997994i | \(-0.520166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −89121.2 | + | 505432.i | −0.0989575 | + | 0.561216i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.00969e6 | + | 1.16691e6i | −1.11642 | + | 1.29025i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45142e6 | − | 837978.i | 1.59811 | − | 0.922670i | 0.606261 | − | 0.795266i | \(-0.292669\pi\) |
0.991851 | − | 0.127405i | \(-0.0406647\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −207012. | + | 358554.i | −0.226980 | + | 0.393141i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 191544. | − | 320444.i | 0.209143 | − | 0.349887i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47623.9 | − | 56756.0i | 0.0517831 | − | 0.0617127i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 477962. | + | 173964.i | 0.517543 | + | 0.188370i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −433984. | − | 90168.1i | −0.467973 | − | 0.0972300i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −805630. | + | 142054.i | −0.865130 | + | 0.152546i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.24831e6 | − | 454348.i | 1.33497 | − | 0.485888i | 0.426742 | − | 0.904373i | \(-0.359661\pi\) |
0.908223 | + | 0.418486i | \(0.137439\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 68052.4 | + | 83644.8i | 0.0724763 | + | 0.0890823i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.47439e6i | − | 1.56378i | −0.623417 | − | 0.781889i | \(-0.714256\pi\) | ||
0.623417 | − | 0.781889i | \(-0.285744\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32796.2 | −0.0346416 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 66404.5 | − | 54025.8i | 0.0698535 | − | 0.0568319i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −464456. | − | 1.27608e6i | −0.486582 | − | 1.33687i | −0.903757 | − | 0.428046i | \(-0.859202\pi\) |
0.417175 | − | 0.908826i | \(-0.363020\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59624.5 | + | 338147.i | 0.0622099 | + | 0.352810i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −146058. | + | 702987.i | −0.151771 | + | 0.730481i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −625431. | + | 1.71836e6i | −0.647251 | + | 1.77831i | −0.0196048 | + | 0.999808i | \(0.506241\pi\) |
−0.627646 | + | 0.778499i | \(0.715981\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.14763e6 | − | 962978.i | −1.18285 | − | 0.992531i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −103135. | − | 61648.1i | −0.105869 | − | 0.0632828i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −91627.2 | − | 52901.0i | −0.0936767 | − | 0.0540843i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −506647. | − | 877538.i | −0.515891 | − | 0.893550i | −0.999830 | − | 0.0184477i | \(-0.994128\pi\) |
0.483939 | − | 0.875102i | \(-0.339206\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −845172. | − | 731302.i | −0.857130 | − | 0.741649i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 437714. | + | 77180.9i | 0.442125 | + | 0.0779585i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −663978. | + | 557144.i | −0.667980 | + | 0.560502i | −0.912467 | − | 0.409151i | \(-0.865825\pi\) |
0.244487 | + | 0.969653i | \(0.421380\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.42501e6 | − | 64856.2i | −1.42786 | − | 0.0649861i |
(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 | 108.5.k.a.5.10 | ✓ | 72 | |
3.2 | odd | 2 | 324.5.k.a.125.10 | 72 | |||
27.11 | odd | 18 | inner | 108.5.k.a.65.10 | yes | 72 | |
27.16 | even | 9 | 324.5.k.a.197.10 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.5.k.a.5.10 | ✓ | 72 | 1.1 | even | 1 | trivial | |
108.5.k.a.65.10 | yes | 72 | 27.11 | odd | 18 | inner | |
324.5.k.a.125.10 | 72 | 3.2 | odd | 2 | |||
324.5.k.a.197.10 | 72 | 27.16 | even | 9 |