Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,3,Mod(799,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.799");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.f (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: | \(33.1336001462\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 799.11 | ||
Character | \(\chi\) | \(=\) | 1216.799 |
Dual form | 1216.3.f.b.799.12 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −3.50746 | −1.16915 | −0.584577 | − | 0.811338i | \(-0.698739\pi\) | ||||
−0.584577 | + | 0.811338i | \(0.698739\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.252768i | − 0.0505536i | −0.999680 | − | 0.0252768i | \(-0.991953\pi\) | ||||
0.999680 | − | 0.0252768i | \(-0.00804671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.190530i | − 0.0272185i | −0.999907 | − | 0.0136093i | \(-0.995668\pi\) | ||||
0.999907 | − | 0.0136093i | \(-0.00433209\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.30228 | 0.366920 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.60842 | 0.509857 | 0.254928 | − | 0.966960i | \(-0.417948\pi\) | ||||
0.254928 | + | 0.966960i | \(0.417948\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 14.5700i | − 1.12077i | −0.828232 | − | 0.560386i | \(-0.810653\pi\) | ||||
0.828232 | − | 0.560386i | \(-0.189347\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.886574i | 0.0591049i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −18.9541 | −1.11495 | −0.557474 | − | 0.830195i | \(-0.688229\pi\) | ||||
−0.557474 | + | 0.830195i | \(0.688229\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.668275i | 0.0318226i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.0016i | 1.43485i | 0.696636 | + | 0.717425i | \(0.254679\pi\) | ||||
−0.696636 | + | 0.717425i | \(0.745321\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9361 | 0.997444 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 19.9845 | 0.740167 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 45.4090i | − 1.56583i | −0.622129 | − | 0.782914i | \(-0.713732\pi\) | ||||
0.622129 | − | 0.782914i | \(-0.286268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.68424i | 0.215621i | 0.994171 | + | 0.107810i | \(0.0343839\pi\) | ||||
−0.994171 | + | 0.107810i | \(0.965616\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −19.6713 | −0.596101 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.0481598 | −0.00137599 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.92687i | 0.106132i | 0.998591 | + | 0.0530658i | \(0.0168993\pi\) | ||||
−0.998591 | + | 0.0530658i | \(0.983101\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 51.1038i | 1.31035i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −19.6255 | −0.478671 | −0.239335 | − | 0.970937i | \(-0.576930\pi\) | ||||
−0.239335 | + | 0.970937i | \(0.576930\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.22162 | −0.0516657 | −0.0258328 | − | 0.999666i | \(-0.508224\pi\) | ||||
−0.0258328 | + | 0.999666i | \(0.508224\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 0.834712i | − 0.0185491i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.41053i | 0.115118i | 0.998342 | + | 0.0575588i | \(0.0183317\pi\) | ||||
−0.998342 | + | 0.0575588i | \(0.981668\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.9637 | 0.999259 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 66.4808 | 1.30354 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 61.2112i | − 1.15493i | −0.816416 | − | 0.577464i | \(-0.804042\pi\) | ||||
0.816416 | − | 0.577464i | \(-0.195958\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.41763i | − 0.0257751i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.2887 | −0.268222 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −25.8963 | −0.438920 | −0.219460 | − | 0.975622i | \(-0.570429\pi\) | ||||
−0.219460 | + | 0.975622i | \(0.570429\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32.9728i | 0.540538i | 0.962785 | + | 0.270269i | \(0.0871127\pi\) | ||||
−0.962785 | + | 0.270269i | \(0.912887\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 0.629183i | − 0.00998702i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.68284 | −0.0566590 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29.2118 | −0.435997 | −0.217999 | − | 0.975949i | \(-0.569953\pi\) | ||||
−0.217999 | + | 0.975949i | \(0.569953\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 115.752i | − 1.67756i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.5166i | 0.148121i | 0.997254 | + | 0.0740604i | \(0.0235958\pi\) | ||||
−0.997254 | + | 0.0740604i | \(0.976404\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −91.2827 | −1.25045 | −0.625224 | − | 0.780445i | \(-0.714993\pi\) | ||||
−0.625224 | + | 0.780445i | \(0.714993\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −87.4624 | −1.16617 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.06857i | − 0.0138775i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 22.7410i | 0.287861i | 0.989588 | + | 0.143931i | \(0.0459742\pi\) | ||||
−0.989588 | + | 0.143931i | \(0.954026\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −99.8155 | −1.23229 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −144.739 | −1.74384 | −0.871920 | − | 0.489649i | \(-0.837125\pi\) | ||||
−0.871920 | + | 0.489649i | \(0.837125\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.79099i | 0.0563646i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 159.270i | 1.83069i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −37.1587 | −0.417513 | −0.208757 | − | 0.977968i | \(-0.566942\pi\) | ||||
−0.208757 | + | 0.977968i | \(0.566942\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.77602 | −0.0305057 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 23.4447i | − 0.252094i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 1.10179i | − 0.0115978i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −117.690 | −1.21330 | −0.606651 | − | 0.794968i | \(-0.707487\pi\) | ||||
−0.606651 | + | 0.794968i | \(0.707487\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.5206 | 0.187077 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 71.9079i | 0.711959i | 0.934494 | + | 0.355980i | \(0.115853\pi\) | ||||
−0.934494 | + | 0.355980i | \(0.884147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 147.791i | 1.43486i | 0.696630 | + | 0.717431i | \(0.254682\pi\) | ||||
−0.696630 | + | 0.717431i | \(0.745318\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.168919 | 0.00160875 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −19.4286 | −0.181576 | −0.0907880 | − | 0.995870i | \(-0.528939\pi\) | ||||
−0.0907880 | + | 0.995870i | \(0.528939\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 156.427i | 1.43511i | 0.696500 | + | 0.717557i | \(0.254740\pi\) | ||||
−0.696500 | + | 0.717557i | \(0.745260\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 13.7733i | − 0.124084i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.58861 | −0.0671558 | −0.0335779 | − | 0.999436i | \(-0.510690\pi\) | ||||
−0.0335779 | + | 0.999436i | \(0.510690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.34174 | 0.0725368 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 48.1144i | − 0.411234i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.61132i | 0.0303472i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −89.5456 | −0.740046 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 68.8357 | 0.559640 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 12.6223i | − 0.100978i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 150.835i | − 1.18767i | −0.804585 | − | 0.593837i | \(-0.797612\pi\) | ||||
0.804585 | − | 0.593837i | \(-0.202388\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.79226 | 0.0604051 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −55.7865 | −0.425851 | −0.212926 | − | 0.977068i | \(-0.568299\pi\) | ||||
−0.212926 | + | 0.977068i | \(0.568299\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.830499i | − 0.00624435i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 5.05145i | − 0.0374181i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −131.228 | −0.957866 | −0.478933 | − | 0.877851i | \(-0.658976\pi\) | ||||
−0.478933 | + | 0.877851i | \(0.658976\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −213.144 | −1.53341 | −0.766706 | − | 0.641998i | \(-0.778106\pi\) | ||||
−0.766706 | + | 0.641998i | \(0.778106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 18.9772i | − 0.134590i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 81.7149i | − 0.571433i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.4780 | −0.0791583 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −171.738 | −1.16829 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 108.251i | − 0.726514i | −0.931689 | − | 0.363257i | \(-0.881665\pi\) | ||||
0.931689 | − | 0.363257i | \(-0.118335\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 99.9886i | − 0.662176i | −0.943600 | − | 0.331088i | \(-0.892584\pi\) | ||||
0.943600 | − | 0.331088i | \(-0.107416\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −62.5918 | −0.409097 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.68956 | 0.0109004 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.7332i | − 0.0683646i | −0.999416 | − | 0.0341823i | \(-0.989117\pi\) | ||||
0.999416 | − | 0.0341823i | \(-0.0108827\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 214.696i | 1.35029i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.28777 | 0.0390545 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 28.7669 | 0.176484 | 0.0882419 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882419 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.97228i | 0.0301350i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 294.712i | 1.76474i | 0.470554 | + | 0.882371i | \(0.344054\pi\) | ||||
−0.470554 | + | 0.882371i | \(0.655946\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −43.2857 | −0.256128 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.3943 | 0.0841773 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 179.476i | 1.03743i | 0.854947 | + | 0.518716i | \(0.173590\pi\) | ||||
−0.854947 | + | 0.518716i | \(0.826410\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 4.75107i | − 0.0271489i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 90.8301 | 0.513164 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −187.374 | −1.04678 | −0.523391 | − | 0.852093i | \(-0.675333\pi\) | ||||
−0.523391 | + | 0.852093i | \(0.675333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 76.7083i | − 0.423803i | −0.977291 | − | 0.211901i | \(-0.932034\pi\) | ||||
0.977291 | − | 0.211901i | \(-0.0679655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 115.651i | − 0.631972i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.992587 | 0.00536534 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −106.303 | −0.568463 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 3.80764i | − 0.0201463i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 109.452i | − 0.573046i | −0.958073 | − | 0.286523i | \(-0.907500\pi\) | ||||
0.958073 | − | 0.286523i | \(-0.0924995\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −254.694 | −1.31966 | −0.659830 | − | 0.751415i | \(-0.729372\pi\) | ||||
−0.659830 | + | 0.751415i | \(0.729372\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12.9174 | 0.0662431 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 96.8634i | − 0.491693i | −0.969309 | − | 0.245846i | \(-0.920934\pi\) | ||||
0.969309 | − | 0.245846i | \(-0.0790659\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 123.397i | 0.620087i | 0.950722 | + | 0.310044i | \(0.100344\pi\) | ||||
−0.950722 | + | 0.310044i | \(0.899656\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 102.459 | 0.509748 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.65176 | −0.0426195 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.96070i | 0.0241985i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 108.980i | 0.526476i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.4466 | 0.116969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 47.1948 | 0.223672 | 0.111836 | − | 0.993727i | \(-0.464327\pi\) | ||||
0.111836 | + | 0.993727i | \(0.464327\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 36.8865i | − 0.173176i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.561555i | 0.00261189i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.27355 | 0.00586887 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 320.171 | 1.46197 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 276.162i | 1.24960i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 208.654i | − 0.935666i | −0.883817 | − | 0.467833i | \(-0.845035\pi\) | ||||
0.883817 | − | 0.467833i | \(-0.154965\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 82.3461 | 0.365983 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 252.772 | 1.11353 | 0.556766 | − | 0.830669i | \(-0.312042\pi\) | ||||
0.556766 | + | 0.830669i | \(0.312042\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 272.172i | − 1.18853i | −0.804271 | − | 0.594263i | \(-0.797444\pi\) | ||||
0.804271 | − | 0.594263i | \(-0.202556\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.74797i | 0.0162250i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −231.151 | −0.992065 | −0.496032 | − | 0.868304i | \(-0.665210\pi\) | ||||
−0.496032 | + | 0.868304i | \(0.665210\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.36761 | 0.00581961 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 79.7633i | − 0.336554i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 129.434i | − 0.541564i | −0.962641 | − | 0.270782i | \(-0.912718\pi\) | ||||
0.962641 | − | 0.270782i | \(-0.0872822\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 255.763 | 1.06126 | 0.530629 | − | 0.847604i | \(-0.321956\pi\) | ||||
0.530629 | + | 0.847604i | \(0.321956\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 170.238 | 0.700569 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 12.3765i | − 0.0505161i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 63.5093i | − 0.257123i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 507.665 | 2.03882 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −176.045 | −0.701375 | −0.350688 | − | 0.936493i | \(-0.614052\pi\) | ||||
−0.350688 | + | 0.936493i | \(0.614052\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 185.087i | 0.731568i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 16.8042i | − 0.0658989i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −309.494 | −1.20426 | −0.602128 | − | 0.798400i | \(-0.705680\pi\) | ||||
−0.602128 | + | 0.798400i | \(0.705680\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.748185 | 0.00288874 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 149.954i | − 0.574535i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 296.602i | 1.12777i | 0.825855 | + | 0.563883i | \(0.190693\pi\) | ||||
−0.825855 | + | 0.563883i | \(0.809307\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.4722 | −0.0583858 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 130.333 | 0.488137 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 171.921i | − 0.639113i | −0.947567 | − | 0.319557i | \(-0.896466\pi\) | ||||
0.947567 | − | 0.319557i | \(-0.103534\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 295.403i | 1.09005i | 0.838420 | + | 0.545024i | \(0.183479\pi\) | ||||
−0.838420 | + | 0.545024i | \(0.816521\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.73678 | 0.0356659 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 139.852 | 0.508554 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.5342i | 0.0596901i | 0.999555 | + | 0.0298451i | \(0.00950139\pi\) | ||||
−0.999555 | + | 0.0298451i | \(0.990499\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.0733i | 0.0791156i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 238.073 | 0.847235 | 0.423618 | − | 0.905841i | \(-0.360760\pi\) | ||||
0.423618 | + | 0.905841i | \(0.360760\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −35.7247 | −0.126236 | −0.0631179 | − | 0.998006i | \(-0.520104\pi\) | ||||
−0.0631179 | + | 0.998006i | \(0.520104\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.86449i | 0.0135596i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.73924i | 0.0130287i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 70.2579 | 0.243107 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 412.794 | 1.41854 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 65.8283i | 0.224670i | 0.993670 | + | 0.112335i | \(0.0358330\pi\) | ||||
−0.993670 | + | 0.112335i | \(0.964167\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.54574i | 0.0221890i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 112.082 | 0.377379 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 480.834 | 1.60814 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.423285i | 0.00140626i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 252.214i | − 0.832390i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.33448 | 0.0273262 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −93.8652 | −0.305750 | −0.152875 | − | 0.988246i | \(-0.548853\pi\) | ||||
−0.152875 | + | 0.988246i | \(0.548853\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 518.370i | − 1.67757i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 205.284i | 0.660078i | 0.943967 | + | 0.330039i | \(0.107062\pi\) | ||||
−0.943967 | + | 0.330039i | \(0.892938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 605.663 | 1.93503 | 0.967513 | − | 0.252821i | \(-0.0813584\pi\) | ||||
0.967513 | + | 0.252821i | \(0.0813584\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.159037 | −0.000504880 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 341.870i | 1.07845i | 0.842160 | + | 0.539227i | \(0.181284\pi\) | ||||
−0.842160 | + | 0.539227i | \(0.818716\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 254.673i | − 0.798349i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 68.1452 | 0.212290 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −82.6190 | −0.255786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 363.320i | − 1.11791i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 548.663i | − 1.67787i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.03087 | 0.00313333 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −108.076 | −0.326513 | −0.163256 | − | 0.986584i | \(-0.552200\pi\) | ||||
−0.163256 | + | 0.986584i | \(0.552200\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 12.9676i | 0.0389419i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.38381i | 0.0220412i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 507.918 | 1.50718 | 0.753588 | − | 0.657347i | \(-0.228322\pi\) | ||||
0.753588 | + | 0.657347i | \(0.228322\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 26.6167 | 0.0785155 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 37.4881i | 0.109936i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 18.6650i | − 0.0544168i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −29.2583 | −0.0848067 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −461.716 | −1.33059 | −0.665297 | − | 0.746579i | \(-0.731695\pi\) | ||||
−0.665297 | + | 0.746579i | \(0.731695\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 289.712i | 0.830121i | 0.909794 | + | 0.415060i | \(0.136240\pi\) | ||||
−0.909794 | + | 0.415060i | \(0.863760\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 291.175i | − 0.829558i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.1345 | −0.0485398 | −0.0242699 | − | 0.999705i | \(-0.507726\pi\) | ||||
−0.0242699 | + | 0.999705i | \(0.507726\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.65825 | 0.00748804 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 12.6666i | − 0.0354805i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 455.304i | − 1.26826i | −0.773228 | − | 0.634128i | \(-0.781359\pi\) | ||||
0.773228 | − | 0.634128i | \(-0.218641\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 314.078 | 0.865228 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 23.0734i | 0.0632147i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 186.157i | − 0.507240i | −0.967304 | − | 0.253620i | \(-0.918379\pi\) | ||||
0.967304 | − | 0.253620i | \(-0.0816213\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −64.8089 | −0.175634 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.6625 | −0.0314354 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 387.069i | 1.03772i | 0.854860 | + | 0.518859i | \(0.173643\pi\) | ||||
−0.854860 | + | 0.518859i | \(0.826357\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 44.2721i | 0.118059i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −661.611 | −1.75494 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 561.796 | 1.48231 | 0.741156 | − | 0.671333i | \(-0.234278\pi\) | ||||
0.741156 | + | 0.671333i | \(0.234278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 529.047i | 1.38857i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 466.656i | 1.21842i | 0.793008 | + | 0.609211i | \(0.208514\pi\) | ||||
−0.793008 | + | 0.609211i | \(0.791486\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.270100 | −0.000701560 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.33643 | −0.0189572 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 213.259i | − 0.548224i | −0.961698 | − | 0.274112i | \(-0.911616\pi\) | ||||
0.961698 | − | 0.274112i | \(-0.0883839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 625.515i | − 1.59978i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 195.669 | 0.497885 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.74820 | 0.0145524 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 727.022i | 1.83129i | 0.401988 | + | 0.915645i | \(0.368319\pi\) | ||||
−0.401988 | + | 0.915645i | \(0.631681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.91294i | 0.00730061i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 217.429 | 0.542216 | 0.271108 | − | 0.962549i | \(-0.412610\pi\) | ||||
0.271108 | + | 0.962549i | \(0.412610\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 97.3895 | 0.241661 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.2302i | 0.0622967i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.0236i | 0.0541119i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 504.230 | 1.23284 | 0.616418 | − | 0.787419i | \(-0.288583\pi\) | ||||
0.616418 | + | 0.787419i | \(0.288583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 460.276 | 1.11989 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.93400i | 0.0119467i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.5853i | 0.0881574i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 747.595 | 1.79279 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −453.677 | −1.08276 | −0.541381 | − | 0.840778i | \(-0.682098\pi\) | ||||
−0.541381 | + | 0.840778i | \(0.682098\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 7.49122i | − 0.0177939i | −0.999960 | − | 0.00889693i | \(-0.997168\pi\) | ||||
0.999960 | − | 0.00889693i | \(-0.00283202\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.8671i | 0.0422390i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −472.641 | −1.11210 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.28230 | 0.0147126 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 286.612i | 0.668093i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 576.583i | − 1.33778i | −0.743362 | − | 0.668890i | \(-0.766770\pi\) | ||||
0.743362 | − | 0.668890i | \(-0.233230\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −272.573 | −0.629498 | −0.314749 | − | 0.949175i | \(-0.601920\pi\) | ||||
−0.314749 | + | 0.949175i | \(0.601920\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 40.2585 | 0.0925482 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 143.850i | 0.329177i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 447.790i | − 1.02002i | −0.860168 | − | 0.510011i | \(-0.829641\pi\) | ||||
0.860168 | − | 0.510011i | \(-0.170359\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 161.692 | 0.366649 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −134.192 | −0.302916 | −0.151458 | − | 0.988464i | \(-0.548397\pi\) | ||||
−0.151458 | + | 0.988464i | \(0.548397\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.39253i | 0.0211068i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 379.685i | 0.849407i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 279.068 | 0.621533 | 0.310767 | − | 0.950486i | \(-0.399414\pi\) | ||||
0.310767 | + | 0.950486i | \(0.399414\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −110.068 | −0.244053 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 350.706i | 0.774186i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.701689i | 0.00154217i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −158.492 | −0.346809 | −0.173405 | − | 0.984851i | \(-0.555477\pi\) | ||||
−0.173405 | + | 0.984851i | \(0.555477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −378.789 | −0.825247 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.3312i | 0.0614559i | 0.999528 | + | 0.0307279i | \(0.00978255\pi\) | ||||
−0.999528 | + | 0.0307279i | \(0.990217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 161.928i | 0.349737i | 0.984592 | + | 0.174869i | \(0.0559501\pi\) | ||||
−0.984592 | + | 0.174869i | \(0.944050\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.92607 | −0.0127442 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −329.554 | −0.705683 | −0.352842 | − | 0.935683i | \(-0.614785\pi\) | ||||
−0.352842 | + | 0.935683i | \(0.614785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.56571i | 0.0118672i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 37.6464i | 0.0799287i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.4598 | −0.0263421 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 108.694 | 0.228829 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 202.137i | − 0.423767i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 387.409i | 0.808786i | 0.914585 | + | 0.404393i | \(0.132517\pi\) | ||||
−0.914585 | + | 0.404393i | \(0.867483\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.2146 | 0.118949 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −22.0541 | −0.0456607 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.7483i | 0.0613368i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 682.598i | − 1.40164i | −0.713339 | − | 0.700819i | \(-0.752818\pi\) | ||||
0.713339 | − | 0.700819i | \(-0.247182\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −100.899 | −0.206337 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −923.123 | −1.88009 | −0.940044 | − | 0.341054i | \(-0.889216\pi\) | ||||
−0.940044 | + | 0.341054i | \(0.889216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 860.687i | 1.74582i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 4.68142i | − 0.00945741i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.00372 | 0.00403163 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 711.486 | 1.42582 | 0.712912 | − | 0.701254i | \(-0.247376\pi\) | ||||
0.712912 | + | 0.701254i | \(0.247376\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1033.69i | − 2.06326i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 762.691i | − 1.51628i | −0.652090 | − | 0.758142i | \(-0.726108\pi\) | ||||
0.652090 | − | 0.758142i | \(-0.273892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1760 | 0.0359921 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 151.823 | 0.299453 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 526.156i | − 1.03371i | −0.856074 | − | 0.516853i | \(-0.827104\pi\) | ||||
0.856074 | − | 0.516853i | \(-0.172896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.3921i | 0.0340353i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 87.1105 | 0.169806 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 37.3568 | 0.0725374 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 30.3445i | 0.0586935i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 629.504i | − 1.21292i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −902.077 | −1.73143 | −0.865717 | − | 0.500534i | \(-0.833137\pi\) | ||||
−0.865717 | + | 0.500534i | \(0.833137\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −493.138 | −0.942902 | −0.471451 | − | 0.881892i | \(-0.656270\pi\) | ||||
−0.471451 | + | 0.881892i | \(0.656270\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.6642i | 0.0317413i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 126.694i | − 0.240406i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −560.103 | −1.05880 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −85.5168 | −0.161049 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 285.944i | 0.536480i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.91094i | 0.00917932i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 657.206 | 1.22385 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 274.609 | 0.509479 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 689.780i | 1.27501i | 0.770447 | + | 0.637504i | \(0.220033\pi\) | ||||
−0.770447 | + | 0.637504i | \(0.779967\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 269.051i | 0.495490i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.5398 | 0.0725502 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.71102 | 0.0159251 | 0.00796254 | − | 0.999968i | \(-0.497465\pi\) | ||||
0.00796254 | + | 0.999968i | \(0.497465\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 108.886i | 0.198335i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 197.933i | − 0.359226i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.33284 | 0.00783515 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.48146 | −0.00627290 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 271.055i | 0.486633i | 0.969947 | + | 0.243317i | \(0.0782354\pi\) | ||||
−0.969947 | + | 0.243317i | \(0.921765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.3691i | 0.0579054i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 372.852 | 0.664621 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −194.488 | −0.345450 | −0.172725 | − | 0.984970i | \(-0.555257\pi\) | ||||
−0.172725 | + | 0.984970i | \(0.555257\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.91816i | 0.00339497i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.0178i | 0.0335411i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1046.92 | 1.83992 | 0.919961 | − | 0.392010i | \(-0.128220\pi\) | ||||
0.919961 | + | 0.392010i | \(0.128220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −374.483 | −0.655838 | −0.327919 | − | 0.944706i | \(-0.606347\pi\) | ||||
−0.327919 | + | 0.944706i | \(0.606347\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 383.898i | 0.669979i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 822.930i | 1.43118i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −972.710 | −1.68581 | −0.842903 | − | 0.538066i | \(-0.819155\pi\) | ||||
−0.842903 | + | 0.538066i | \(0.819155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 893.331 | 1.54289 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.5770i | 0.0474647i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 343.298i | − 0.588848i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.1618 | −0.0207894 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −154.819 | −0.263746 | −0.131873 | − | 0.991267i | \(-0.542099\pi\) | ||||
−0.131873 | + | 0.991267i | \(0.542099\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 29.1359i | 0.0494668i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 339.745i | 0.574864i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 417.721 | 0.704420 | 0.352210 | − | 0.935921i | \(-0.385430\pi\) | ||||
0.352210 | + | 0.935921i | \(0.385430\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.912825 | 0.00153416 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 432.811i | − 0.724977i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 759.367i | 1.26772i | 0.773446 | + | 0.633862i | \(0.218531\pi\) | ||||
−0.773446 | + | 0.633862i | \(0.781469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 362.886 | 0.603803 | 0.301902 | − | 0.953339i | \(-0.402379\pi\) | ||||
0.301902 | + | 0.953339i | \(0.402379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −96.4657 | −0.159976 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.6343i | 0.0374120i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 1076.91i | − 1.77415i | −0.461624 | − | 0.887076i | \(-0.652733\pi\) | ||||
0.461624 | − | 0.887076i | \(-0.347267\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.3457 | 0.0498288 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 78.8315 | 0.129021 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 468.337i | − 0.764009i | −0.924161 | − | 0.382004i | \(-0.875234\pi\) | ||||
0.924161 | − | 0.382004i | \(-0.124766\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 17.3995i | − 0.0282918i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −99.9309 | −0.161962 | −0.0809812 | − | 0.996716i | \(-0.525805\pi\) | ||||
−0.0809812 | + | 0.996716i | \(0.525805\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 693.446 | 1.12027 | 0.560134 | − | 0.828402i | \(-0.310750\pi\) | ||||
0.560134 | + | 0.828402i | \(0.310750\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 659.520i | 1.06203i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.07983i | 0.0113641i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 620.212 | 0.992340 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −85.7453 | −0.136755 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 74.4303i | − 0.118331i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 735.284i | 1.16527i | 0.812735 | + | 0.582634i | \(0.197978\pi\) | ||||
−0.812735 | + | 0.582634i | \(0.802022\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −165.534 | −0.261507 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −38.1262 | −0.0600412 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 713.402i | − 1.11994i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 34.7287i | 0.0543486i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −927.322 | −1.44668 | −0.723340 | − | 0.690492i | \(-0.757394\pi\) | ||||
−0.723340 | + | 0.690492i | \(0.757394\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1230.08 | −1.91304 | −0.956519 | − | 0.291671i | \(-0.905789\pi\) | ||||
−0.956519 | + | 0.291671i | \(0.905789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.96963i | − 0.00305370i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 760.883i | 1.17602i | 0.808855 | + | 0.588009i | \(0.200088\pi\) | ||||
−0.808855 | + | 0.588009i | \(0.799912\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −145.237 | −0.223786 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.46691 | −0.00686161 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 598.576i | − 0.916655i | −0.888783 | − | 0.458328i | \(-0.848449\pi\) | ||||
0.888783 | − | 0.458328i | \(-0.151551\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.1010i | 0.0215283i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −301.442 | −0.458815 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 536.626 | 0.814304 | 0.407152 | − | 0.913360i | \(-0.366522\pi\) | ||||
0.407152 | + | 0.913360i | \(0.366522\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 104.138i | 0.157547i | 0.996893 | + | 0.0787733i | \(0.0251003\pi\) | ||||
−0.996893 | + | 0.0787733i | \(0.974900\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 968.627i | − 1.46098i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.209924 | −0.000315675 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1498.57 | 2.24673 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 731.844i | 1.09394i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 184.926i | 0.275597i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −115.118 | −0.171052 | −0.0855261 | − | 0.996336i | \(-0.527257\pi\) | ||||
−0.0855261 | + | 0.996336i | \(0.527257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 498.336 | 0.738276 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 938.327i | − 1.38601i | −0.720934 | − | 0.693004i | \(-0.756287\pi\) | ||||
0.720934 | − | 0.693004i | \(-0.243713\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22.4235i | 0.0330243i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −886.588 | −1.30189 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −732.196 | −1.07203 | −0.536015 | − | 0.844209i | \(-0.680071\pi\) | ||||
−0.536015 | + | 0.844209i | \(0.680071\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 33.1702i | 0.0484236i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 954.634i | 1.38957i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −891.849 | −1.29441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −565.948 | −0.819028 | −0.409514 | − | 0.912304i | \(-0.634302\pi\) | ||||
−0.409514 | + | 0.912304i | \(0.634302\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 3.52872i | − 0.00509195i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.8761i | 0.0775195i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 371.984 | 0.533692 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 810.753 | 1.15988 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 786.820i | − 1.12243i | −0.827672 | − | 0.561213i | \(-0.810335\pi\) | ||||
0.827672 | − | 0.561213i | \(-0.189665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.1168i | 0.0243483i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.79683 | −0.00680402 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.7006 | 0.0193785 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 529.321i | − 0.746574i | −0.927716 | − | 0.373287i | \(-0.878231\pi\) | ||||
0.927716 | − | 0.373287i | \(-0.121769\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 75.0973i | 0.105622i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −220.590 | −0.309383 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −20.6549 | −0.0288880 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 453.984i | 0.633171i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1027.92i | 1.42965i | 0.699301 | + | 0.714827i | \(0.253495\pi\) | ||||
−0.699301 | + | 0.714827i | \(0.746505\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.1585 | 0.0390548 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −897.080 | −1.24077 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 1132.32i | − 1.56183i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1195.70i | 1.64471i | 0.568975 | + | 0.822355i | \(0.307340\pi\) | ||||
−0.568975 | + | 0.822355i | \(0.692660\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 301.235 | 0.413217 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 42.1089 | 0.0576045 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1054.08i | − 1.43804i | −0.694988 | − | 0.719021i | \(-0.744590\pi\) | ||||
0.694988 | − | 0.719021i | \(-0.255410\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 43.4099i | 0.0590611i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −163.832 | −0.222296 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 127.708 | 0.172812 | 0.0864059 | − | 0.996260i | \(-0.472462\pi\) | ||||
0.0864059 | + | 0.996260i | \(0.472462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 222.756i | 0.300616i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 761.866i | 1.02539i | 0.858570 | + | 0.512696i | \(0.171353\pi\) | ||||
−0.858570 | + | 0.512696i | \(0.828647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −27.3623 | −0.0367279 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −477.968 | −0.639850 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.70173i | 0.00494223i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1067.78i | 1.42181i | 0.703289 | + | 0.710904i | \(0.251714\pi\) | ||||
−0.703289 | + | 0.710904i | \(0.748286\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 617.472 | 0.820015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −25.2739 | −0.0334754 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 728.624i | − 0.962515i | −0.876579 | − | 0.481257i | \(-0.840180\pi\) | ||||
0.876579 | − | 0.481257i | \(-0.159820\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 649.185i | − 0.855316i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −854.584 | −1.12297 | −0.561487 | − | 0.827485i | \(-0.689771\pi\) | ||||
−0.561487 | + | 0.827485i | \(0.689771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 29.8040 | 0.0390617 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.8212i | 0.0206813i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 377.309i | 0.491928i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1220.06 | 1.58656 | 0.793279 | − | 0.608859i | \(-0.208372\pi\) | ||||
0.793279 | + | 0.608859i | \(0.208372\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1085.54 | 1.40796 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 400.055i | − 0.517536i | −0.965940 | − | 0.258768i | \(-0.916684\pi\) | ||||
0.965940 | − | 0.258768i | \(-0.0833165\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 166.679i | 0.215070i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.62423 | −0.00337739 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −85.5455 | −0.109815 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 58.9814i | 0.0755204i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 907.478i | − 1.15898i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.71302 | −0.00345608 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −470.101 | −0.597333 | −0.298666 | − | 0.954358i | \(-0.596542\pi\) | ||||
−0.298666 | + | 0.954358i | \(0.596542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1040.32i | − 1.31853i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.44585i | 0.00182788i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 480.415 | 0.605820 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 54.2682 | 0.0682619 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 349.833i | 0.438938i | 0.975619 | + | 0.219469i | \(0.0704325\pi\) | ||||
−0.975619 | + | 0.219469i | \(0.929568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 102.552i | − 0.128350i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −122.709 | −0.153194 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −511.952 | −0.637550 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.58935i | − 0.00197434i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 603.008i | 0.747221i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 202.721 | 0.250582 | 0.125291 | − | 0.992120i | \(-0.460014\pi\) | ||||
0.125291 | + | 0.992120i | \(0.460014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1087.10 | −1.34045 | −0.670225 | − | 0.742158i | \(-0.733802\pi\) | ||||
−0.670225 | + | 0.742158i | \(0.733802\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1036.11i | − 1.27443i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 7.27134i | − 0.00892190i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.68383 | −0.0118529 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.16721 | −0.0111932 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 296.394i | − 0.361016i | −0.983574 | − | 0.180508i | \(-0.942226\pi\) | ||||
0.983574 | − | 0.180508i | \(-0.0577742\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 1308.89i | − 1.59038i | −0.606358 | − | 0.795192i | \(-0.707370\pi\) | ||||
0.606358 | − | 0.795192i | \(-0.292630\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −490.526 | −0.594578 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 746.411 | 0.902553 | 0.451276 | − | 0.892384i | \(-0.350969\pi\) | ||||
0.451276 | + | 0.892384i | \(0.350969\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 875.724i | 1.05636i | 0.849132 | + | 0.528181i | \(0.177126\pi\) | ||||
−0.849132 | + | 0.528181i | \(0.822874\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 57.9930i | − 0.0697870i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −928.063 | −1.11412 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 74.4938 | 0.0892141 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 133.581i | 0.159595i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1366.87i | 1.62917i | 0.580047 | + | 0.814583i | \(0.303034\pi\) | ||||
−0.580047 | + | 0.814583i | \(0.696966\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1220.98 | −1.45182 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −835.032 | −0.990548 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10.9412i | 0.0129482i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.0611i | 0.0201429i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 125.303 | 0.147589 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −129.593 | −0.152283 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1507.40i | 1.76718i | 0.468265 | + | 0.883588i | \(0.344879\pi\) | ||||
−0.468265 | + | 0.883588i | \(0.655121\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 3.63842i | − 0.00425547i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 236.639 | 0.276124 | 0.138062 | − | 0.990424i | \(-0.455913\pi\) | ||||
0.138062 | + | 0.990424i | \(0.455913\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 993.051 | 1.15605 | 0.578027 | − | 0.816018i | \(-0.303823\pi\) | ||||
0.578027 | + | 0.816018i | \(0.303823\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 13.1152i | − 0.0152326i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.9720i | 0.0463175i | 0.999732 | + | 0.0231588i | \(0.00737232\pi\) | ||||
−0.999732 | + | 0.0231588i | \(0.992628\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 45.3657 | 0.0524459 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −246.427 | −0.284229 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 127.541i | 0.146768i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 425.617i | 0.488653i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −388.647 | −0.445185 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.40491 | −0.00274847 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 738.081i | − 0.841597i | −0.907154 | − | 0.420799i | \(-0.861750\pi\) | ||||
0.907154 | − | 0.420799i | \(-0.138250\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 230.890i | − 0.262674i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −403.793 | −0.458335 | −0.229168 | − | 0.973387i | \(-0.573600\pi\) | ||||
−0.229168 | + | 0.973387i | \(0.573600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1279.75 | 1.44932 | 0.724661 | − | 0.689106i | \(-0.241997\pi\) | ||||
0.724661 | + | 0.689106i | \(0.241997\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 22.9589i | − 0.0259423i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1343.82i | 1.51502i | 0.652826 | + | 0.757508i | \(0.273583\pi\) | ||||
−0.652826 | + | 0.757508i | \(0.726417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.7384 | −0.0323267 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −559.808 | −0.628291 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.5839i | 0.0264098i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.3621i | 0.0529186i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1686.51 | −1.88016 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 303.525 | 0.337625 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1160.20i | 1.28768i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.48466i | − 0.00164414i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −19.3894 | −0.0214247 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −939.932 | −1.03631 | −0.518154 | − | 0.855287i | \(-0.673381\pi\) | ||||
−0.518154 | + | 0.855287i | \(0.673381\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 237.460i | 0.261232i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 809.909i | − 0.889033i | −0.895771 | − | 0.444516i | \(-0.853376\pi\) | ||||
0.895771 | − | 0.444516i | \(-0.146624\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −811.756 | −0.889109 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −29.2329 | −0.0319485 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.6290i | 0.0115910i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1333.20i | 1.45070i | 0.688379 | + | 0.725351i | \(0.258323\pi\) | ||||
−0.688379 | + | 0.725351i | \(0.741677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 329.229 | 0.357469 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 153.227 | 0.166010 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 97.9209i | 0.105860i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 488.047i | 0.526480i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −394.413 | −0.424556 | −0.212278 | − | 0.977209i | \(-0.568088\pi\) | ||||
−0.212278 | + | 0.977209i | \(0.568088\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 213.428 | 0.229246 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 720.027i | − 0.771733i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 26.8699i | 0.0287379i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −334.853 | −0.357368 | −0.178684 | − | 0.983907i | \(-0.557184\pi\) | ||||
−0.178684 | + | 0.983907i | \(0.557184\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2124.34 | −2.26234 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 1801.39i | − 1.91434i | −0.289530 | − | 0.957169i | \(-0.593499\pi\) | ||||
0.289530 | − | 0.957169i | \(-0.406501\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 647.672i | − 0.686821i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.962450 | −0.00101847 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1602.98 | −1.69269 | −0.846345 | − | 0.532636i | \(-0.821202\pi\) | ||||
−0.846345 | + | 0.532636i | \(0.821202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1329.99i | 1.40147i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1199.10i | − 1.26088i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1518.38 | −1.59327 | −0.796634 | − | 0.604462i | \(-0.793388\pi\) | ||||
−0.796634 | + | 0.604462i | \(0.793388\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.6659 | −0.0289696 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 893.256i | 0.933392i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 25.0028i | 0.0260717i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 916.321 | 0.953508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −64.1589 | −0.0666239 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 64.3786i | 0.0667136i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1080.13i | 1.11699i | 0.829508 | + | 0.558495i | \(0.188621\pi\) | ||||
−0.829508 | + | 0.558495i | \(0.811379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 289.783 | 0.299054 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −110.309 | −0.113604 | −0.0568018 | − | 0.998385i | \(-0.518090\pi\) | ||||
−0.0568018 | + | 0.998385i | \(0.518090\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.6103i | 0.0417372i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1274.33i | 1.30701i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1429.36 | −1.46301 | −0.731503 | − | 0.681839i | \(-0.761181\pi\) | ||||
−0.731503 | + | 0.681839i | \(0.761181\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −208.402 | −0.212872 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 516.568i | 0.526573i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 661.986i | − 0.673434i | −0.941606 | − | 0.336717i | \(-0.890683\pi\) | ||||
0.941606 | − | 0.336717i | \(-0.109317\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.4840 | −0.0248568 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.61572 | −0.00366334 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 73.3170i | − 0.0741325i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 668.232i | − 0.674301i | −0.941451 | − | 0.337150i | \(-0.890537\pi\) | ||||
0.941451 | − | 0.337150i | \(-0.109463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 379.072 | 0.381744 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31.1909 | 0.0313476 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1799.71i | − 1.80512i | −0.430560 | − | 0.902562i | \(-0.641684\pi\) | ||||
0.430560 | − | 0.902562i | \(-0.358316\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 78.4766i | 0.0785552i |
(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 | 1216.3.f.b.799.11 | ✓ | 48 | |
4.3 | odd | 2 | inner | 1216.3.f.b.799.37 | yes | 48 | |
8.3 | odd | 2 | inner | 1216.3.f.b.799.12 | yes | 48 | |
8.5 | even | 2 | inner | 1216.3.f.b.799.38 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.3.f.b.799.11 | ✓ | 48 | 1.1 | even | 1 | trivial | |
1216.3.f.b.799.12 | yes | 48 | 8.3 | odd | 2 | inner | |
1216.3.f.b.799.37 | yes | 48 | 4.3 | odd | 2 | inner | |
1216.3.f.b.799.38 | yes | 48 | 8.5 | even | 2 | inner |