Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(647,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.647");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 796 x^{12} - 2228 x^{11} + 5254 x^{10} - 10232 x^{9} + \cdots + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 647.6 | ||
Root | \(0.500000 - 3.05304i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.647 |
Dual form | 1134.2.k.c.971.6 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −0.360068 | − | 0.623656i | −0.161027 | − | 0.278907i | 0.774210 | − | 0.632929i | \(-0.218147\pi\) |
−0.935237 | + | 0.354021i | \(0.884814\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03982 | − | 2.43285i | 0.393015 | − | 0.919532i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.623656 | − | 0.360068i | −0.197217 | − | 0.113863i | ||||
\(11\) | −3.81944 | − | 2.20516i | −1.15161 | − | 0.664880i | −0.202328 | − | 0.979318i | \(-0.564851\pi\) |
−0.949278 | + | 0.314438i | \(0.898184\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.25451i | 0.347939i | 0.984751 | + | 0.173969i | \(0.0556594\pi\) | ||||
−0.984751 | + | 0.173969i | \(0.944341\pi\) | |||||||
\(14\) | −0.315916 | − | 2.62682i | −0.0844322 | − | 0.702048i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.25492 | − | 5.63769i | 0.789434 | − | 1.36734i | −0.136880 | − | 0.990588i | \(-0.543708\pi\) |
0.926314 | − | 0.376752i | \(-0.122959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.66633 | + | 2.69411i | −1.07053 | + | 0.618070i | −0.928326 | − | 0.371767i | \(-0.878752\pi\) |
−0.142203 | + | 0.989838i | \(0.545419\pi\) | |||||||
\(20\) | −0.720136 | −0.161027 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.41031 | −0.940282 | ||||||||
\(23\) | −5.95507 | + | 3.43816i | −1.24172 | + | 0.716906i | −0.969444 | − | 0.245313i | \(-0.921109\pi\) |
−0.272274 | + | 0.962220i | \(0.587776\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.24070 | − | 3.88101i | 0.448140 | − | 0.776202i | ||||
\(26\) | 0.627256 | + | 1.08644i | 0.123015 | + | 0.213068i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.58700 | − | 2.11694i | −0.299915 | − | 0.400063i | ||||
\(29\) | 0.0221465i | 0.00411251i | 0.999998 | + | 0.00205625i | \(0.000654527\pi\) | ||||
−0.999998 | + | 0.00205625i | \(0.999345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.21600 | + | 1.85676i | 0.577610 | + | 0.333483i | 0.760183 | − | 0.649709i | \(-0.225109\pi\) |
−0.182573 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.50984i | − | 1.11643i | ||||||
\(35\) | −1.89167 | + | 0.227503i | −0.319750 | + | 0.0384550i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.82735 | − | 3.16506i | −0.300414 | − | 0.520333i | 0.675815 | − | 0.737071i | \(-0.263792\pi\) |
−0.976230 | + | 0.216738i | \(0.930458\pi\) | |||||||
\(38\) | −2.69411 | + | 4.66633i | −0.437042 | + | 0.756978i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.623656 | + | 0.360068i | −0.0986087 | + | 0.0569317i | ||||
\(41\) | −1.96278 | −0.306534 | −0.153267 | − | 0.988185i | \(-0.548979\pi\) | ||||
−0.153267 | + | 0.988185i | \(0.548979\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.88445 | 1.50736 | 0.753682 | − | 0.657239i | \(-0.228276\pi\) | ||||
0.753682 | + | 0.657239i | \(0.228276\pi\) | |||||||
\(44\) | −3.81944 | + | 2.20516i | −0.575803 | + | 0.332440i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.43816 | + | 5.95507i | −0.506929 | + | 0.878027i | ||||
\(47\) | −4.11735 | − | 7.13145i | −0.600577 | − | 1.04023i | −0.992734 | − | 0.120331i | \(-0.961604\pi\) |
0.392157 | − | 0.919898i | \(-0.371729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.83755 | − | 5.05946i | −0.691079 | − | 0.722780i | ||||
\(50\) | − | 4.48140i | − | 0.633766i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.08644 | + | 0.627256i | 0.150662 | + | 0.0869847i | ||||
\(53\) | −2.95555 | − | 1.70638i | −0.405975 | − | 0.234390i | 0.283084 | − | 0.959095i | \(-0.408643\pi\) |
−0.689059 | + | 0.724705i | \(0.741976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.17602i | 0.428255i | ||||||||
\(56\) | −2.43285 | − | 1.03982i | −0.325104 | − | 0.138952i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.0110733 | + | 0.0191795i | 0.00145399 | + | 0.00251839i | ||||
\(59\) | 2.09076 | − | 3.62130i | 0.272193 | − | 0.471452i | −0.697230 | − | 0.716848i | \(-0.745584\pi\) |
0.969423 | + | 0.245395i | \(0.0789177\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.08448 | − | 4.09023i | 0.907075 | − | 0.523700i | 0.0275859 | − | 0.999619i | \(-0.491218\pi\) |
0.879489 | + | 0.475920i | \(0.157885\pi\) | |||||||
\(62\) | 3.71351 | 0.471616 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.782383 | − | 0.451709i | 0.0970427 | − | 0.0560276i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.60764 | + | 9.71272i | −0.685083 | + | 1.18660i | 0.288328 | + | 0.957532i | \(0.406901\pi\) |
−0.973411 | + | 0.229066i | \(0.926433\pi\) | |||||||
\(68\) | −3.25492 | − | 5.63769i | −0.394717 | − | 0.683670i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.52448 | + | 1.14286i | −0.182210 | + | 0.136598i | ||||
\(71\) | 2.47961i | 0.294275i | 0.989116 | + | 0.147138i | \(0.0470060\pi\) | ||||
−0.989116 | + | 0.147138i | \(0.952994\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.54555 | + | 4.93377i | 1.00018 | + | 0.577454i | 0.908302 | − | 0.418316i | \(-0.137379\pi\) |
0.0918788 | + | 0.995770i | \(0.470713\pi\) | |||||||
\(74\) | −3.16506 | − | 1.82735i | −0.367931 | − | 0.212425i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.38821i | 0.618070i | ||||||||
\(77\) | −9.33635 | + | 6.99918i | −1.06398 | + | 0.797631i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.23351 | − | 2.13650i | −0.138781 | − | 0.240375i | 0.788255 | − | 0.615349i | \(-0.210985\pi\) |
−0.927035 | + | 0.374974i | \(0.877652\pi\) | |||||||
\(80\) | −0.360068 | + | 0.623656i | −0.0402568 | + | 0.0697269i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.69981 | + | 0.981388i | −0.187713 | + | 0.108376i | ||||
\(83\) | 11.3925 | 1.25049 | 0.625244 | − | 0.780429i | \(-0.284999\pi\) | ||||
0.625244 | + | 0.780429i | \(0.284999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.68797 | −0.508482 | ||||||||
\(86\) | 8.56019 | − | 4.94223i | 0.923069 | − | 0.532934i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.20516 | + | 3.81944i | −0.235070 | + | 0.407154i | ||||
\(89\) | −7.50204 | − | 12.9939i | −0.795214 | − | 1.37735i | −0.922703 | − | 0.385512i | \(-0.874025\pi\) |
0.127489 | − | 0.991840i | \(-0.459308\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.05204 | + | 1.30447i | 0.319941 | + | 0.136745i | ||||
\(92\) | 6.87632i | 0.716906i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7.13145 | − | 4.11735i | −0.735553 | − | 0.424672i | ||||
\(95\) | 3.36039 | + | 1.94012i | 0.344769 | + | 0.199052i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.2660i | − | 1.04236i | −0.853448 | − | 0.521178i | \(-0.825493\pi\) | ||
0.853448 | − | 0.521178i | \(-0.174507\pi\) | |||||||
\(98\) | −6.71917 | − | 1.96284i | −0.678739 | − | 0.198277i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.24070 | − | 3.88101i | −0.224070 | − | 0.388101i | ||||
\(101\) | 2.27149 | − | 3.93433i | 0.226021 | − | 0.391481i | −0.730604 | − | 0.682802i | \(-0.760761\pi\) |
0.956625 | + | 0.291321i | \(0.0940947\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.3043 | − | 9.41328i | 1.60651 | − | 0.927518i | 0.616364 | − | 0.787461i | \(-0.288605\pi\) |
0.990144 | − | 0.140056i | \(-0.0447284\pi\) | |||||||
\(104\) | 1.25451 | 0.123015 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.41277 | −0.331477 | ||||||||
\(107\) | −0.881040 | + | 0.508669i | −0.0851734 | + | 0.0491749i | −0.541982 | − | 0.840390i | \(-0.682326\pi\) |
0.456808 | + | 0.889565i | \(0.348992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.26044 | + | 9.11136i | −0.503859 | + | 0.872710i | 0.496131 | + | 0.868248i | \(0.334754\pi\) |
−0.999990 | + | 0.00446195i | \(0.998580\pi\) | |||||||
\(110\) | 1.58801 | + | 2.75052i | 0.151411 | + | 0.262252i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.62682 | + | 0.315916i | −0.248211 | + | 0.0298513i | ||||
\(113\) | 5.50175i | 0.517562i | 0.965936 | + | 0.258781i | \(0.0833207\pi\) | ||||
−0.965936 | + | 0.258781i | \(0.916679\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.28846 | + | 2.47594i | 0.399901 | + | 0.230883i | ||||
\(116\) | 0.0191795 | + | 0.0110733i | 0.00178077 | + | 0.00102813i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.18151i | − | 0.384939i | ||||||
\(119\) | −10.3311 | − | 13.7809i | −0.947054 | − | 1.26329i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.22543 | + | 7.31866i | 0.384130 | + | 0.665333i | ||||
\(122\) | 4.09023 | − | 7.08448i | 0.370312 | − | 0.641399i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.21600 | − | 1.85676i | 0.288805 | − | 0.166742i | ||||
\(125\) | −6.82790 | −0.610706 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.28997 | 0.646880 | 0.323440 | − | 0.946249i | \(-0.395161\pi\) | ||||
0.323440 | + | 0.946249i | \(0.395161\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.451709 | − | 0.782383i | 0.0396175 | − | 0.0686196i | ||||
\(131\) | 3.82644 | + | 6.62759i | 0.334318 | + | 0.579055i | 0.983354 | − | 0.181703i | \(-0.0581609\pi\) |
−0.649036 | + | 0.760758i | \(0.724828\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.70222 | + | 14.1539i | 0.147602 | + | 1.22730i | ||||
\(134\) | 11.2153i | 0.968853i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.63769 | − | 3.25492i | −0.483428 | − | 0.279107i | ||||
\(137\) | −2.07631 | − | 1.19876i | −0.177391 | − | 0.102417i | 0.408675 | − | 0.912680i | \(-0.365991\pi\) |
−0.586066 | + | 0.810263i | \(0.699324\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.9971i | 1.10240i | 0.834372 | + | 0.551201i | \(0.185830\pi\) | ||||
−0.834372 | + | 0.551201i | \(0.814170\pi\) | |||||||
\(140\) | −0.748811 | + | 1.75198i | −0.0632861 | + | 0.148070i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.23980 | + | 2.14740i | 0.104042 | + | 0.180206i | ||||
\(143\) | 2.76639 | − | 4.79153i | 0.231337 | − | 0.400688i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0138118 | − | 0.00797426i | 0.00114701 | − | 0.000662226i | ||||
\(146\) | 9.86755 | 0.816644 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.65470 | −0.300414 | ||||||||
\(149\) | 3.79969 | − | 2.19375i | 0.311282 | − | 0.179719i | −0.336218 | − | 0.941784i | \(-0.609148\pi\) |
0.647500 | + | 0.762065i | \(0.275814\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.27064 | + | 14.3252i | −0.673056 | + | 1.16577i | 0.303978 | + | 0.952679i | \(0.401685\pi\) |
−0.977033 | + | 0.213087i | \(0.931648\pi\) | |||||||
\(152\) | 2.69411 | + | 4.66633i | 0.218521 | + | 0.378489i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.58593 | + | 10.7296i | −0.369545 | + | 0.864619i | ||||
\(155\) | − | 2.67423i | − | 0.214800i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.9547 | + | 11.5209i | 1.59256 | + | 0.919465i | 0.992866 | + | 0.119237i | \(0.0380448\pi\) |
0.599695 | + | 0.800229i | \(0.295289\pi\) | |||||||
\(158\) | −2.13650 | − | 1.23351i | −0.169971 | − | 0.0981327i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.720136i | 0.0569317i | ||||||||
\(161\) | 2.17234 | + | 18.0629i | 0.171205 | + | 1.42355i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.68095 | + | 4.64354i | 0.209988 | + | 0.363710i | 0.951711 | − | 0.306997i | \(-0.0993241\pi\) |
−0.741722 | + | 0.670707i | \(0.765991\pi\) | |||||||
\(164\) | −0.981388 | + | 1.69981i | −0.0766335 | + | 0.132733i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.86619 | − | 5.69625i | 0.765765 | − | 0.442115i | ||||
\(167\) | 11.3689 | 0.879755 | 0.439877 | − | 0.898058i | \(-0.355022\pi\) | ||||
0.439877 | + | 0.898058i | \(0.355022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4262 | 0.878939 | ||||||||
\(170\) | −4.05990 | + | 2.34398i | −0.311380 | + | 0.179775i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.94223 | − | 8.56019i | 0.376841 | − | 0.652708i | ||||
\(173\) | 11.9236 | + | 20.6523i | 0.906536 | + | 1.57017i | 0.818842 | + | 0.574019i | \(0.194617\pi\) |
0.0876944 | + | 0.996147i | \(0.472050\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.11200 | − | 9.48685i | −0.537617 | − | 0.717138i | ||||
\(176\) | 4.41031i | 0.332440i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.9939 | − | 7.50204i | −0.973935 | − | 0.562302i | ||||
\(179\) | 9.25956 | + | 5.34601i | 0.692092 | + | 0.399580i | 0.804395 | − | 0.594094i | \(-0.202489\pi\) |
−0.112303 | + | 0.993674i | \(0.535823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.7895i | − | 1.69393i | −0.531649 | − | 0.846964i | \(-0.678428\pi\) | ||
0.531649 | − | 0.846964i | \(-0.321572\pi\) | |||||||
\(182\) | 3.29538 | − | 0.396321i | 0.244270 | − | 0.0293772i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.43816 | + | 5.95507i | 0.253465 | + | 0.439014i | ||||
\(185\) | −1.31594 | + | 2.27928i | −0.0967499 | + | 0.167576i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −24.8640 | + | 14.3552i | −1.81823 | + | 1.04976i | ||||
\(188\) | −8.23469 | −0.600577 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.88024 | 0.281503 | ||||||||
\(191\) | −4.98861 | + | 2.88017i | −0.360963 | + | 0.208402i | −0.669503 | − | 0.742809i | \(-0.733493\pi\) |
0.308540 | + | 0.951211i | \(0.400160\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.7218 | − | 22.0349i | 0.915738 | − | 1.58610i | 0.109920 | − | 0.993940i | \(-0.464940\pi\) |
0.805818 | − | 0.592164i | \(-0.201726\pi\) | |||||||
\(194\) | −5.13301 | − | 8.89063i | −0.368529 | − | 0.638310i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.80039 | + | 1.65971i | −0.485742 | + | 0.118551i | ||||
\(197\) | − | 0.133910i | − | 0.00954067i | −0.999989 | − | 0.00477033i | \(-0.998482\pi\) | ||
0.999989 | − | 0.00477033i | \(-0.00151845\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.89988 | − | 2.25160i | −0.276455 | − | 0.159612i | 0.355362 | − | 0.934729i | \(-0.384358\pi\) |
−0.631818 | + | 0.775117i | \(0.717691\pi\) | |||||||
\(200\) | −3.88101 | − | 2.24070i | −0.274429 | − | 0.158442i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 4.54298i | − | 0.319643i | ||||||
\(203\) | 0.0538793 | + | 0.0230284i | 0.00378158 | + | 0.00161628i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.706733 | + | 1.22410i | 0.0493604 | + | 0.0854947i | ||||
\(206\) | 9.41328 | − | 16.3043i | 0.655854 | − | 1.13597i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.08644 | − | 0.627256i | 0.0753309 | − | 0.0434923i | ||||
\(209\) | 23.7637 | 1.64377 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −25.7693 | −1.77403 | −0.887016 | − | 0.461738i | \(-0.847226\pi\) | ||||
−0.887016 | + | 0.461738i | \(0.847226\pi\) | |||||||
\(212\) | −2.95555 | + | 1.70638i | −0.202988 | + | 0.117195i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.508669 | + | 0.881040i | −0.0347719 | + | 0.0602267i | ||||
\(215\) | −3.55907 | − | 6.16450i | −0.242727 | − | 0.420415i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.86127 | − | 5.89335i | 0.533658 | − | 0.400067i | ||||
\(218\) | 10.5209i | 0.712564i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.75052 | + | 1.58801i | 0.185440 | + | 0.107064i | ||||
\(221\) | 7.07254 | + | 4.08333i | 0.475751 | + | 0.274675i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.10783i | − | 0.0741861i | −0.999312 | − | 0.0370930i | \(-0.988190\pi\) | ||
0.999312 | − | 0.0370930i | \(-0.0118098\pi\) | |||||||
\(224\) | −2.11694 | + | 1.58700i | −0.141444 | + | 0.106036i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.75088 | + | 4.76466i | 0.182986 | + | 0.316940i | ||||
\(227\) | −2.19998 | + | 3.81048i | −0.146018 | + | 0.252911i | −0.929752 | − | 0.368186i | \(-0.879979\pi\) |
0.783734 | + | 0.621096i | \(0.213312\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.39374 | − | 1.95937i | 0.224264 | − | 0.129479i | −0.383659 | − | 0.923475i | \(-0.625336\pi\) |
0.607923 | + | 0.793996i | \(0.292003\pi\) | |||||||
\(230\) | 4.95189 | 0.326518 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.0221465 | 0.00145399 | ||||||||
\(233\) | 18.1850 | − | 10.4991i | 1.19134 | − | 0.687819i | 0.232727 | − | 0.972542i | \(-0.425235\pi\) |
0.958610 | + | 0.284723i | \(0.0919017\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.96505 | + | 5.13561i | −0.193418 | + | 0.335011i | ||||
\(236\) | −2.09076 | − | 3.62130i | −0.136097 | − | 0.235726i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −15.8375 | − | 6.76906i | −1.02659 | − | 0.438773i | ||||
\(239\) | 26.2305i | 1.69671i | 0.529429 | + | 0.848354i | \(0.322406\pi\) | ||||
−0.529429 | + | 0.848354i | \(0.677594\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.24909 | − | 2.45321i | −0.273708 | − | 0.158025i | 0.356864 | − | 0.934157i | \(-0.383846\pi\) |
−0.630572 | + | 0.776131i | \(0.717179\pi\) | |||||||
\(242\) | 7.31866 | + | 4.22543i | 0.470461 | + | 0.271621i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 8.18045i | − | 0.523700i | ||||||
\(245\) | −1.41351 | + | 4.83872i | −0.0903061 | + | 0.309134i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.37979 | − | 5.85396i | −0.215051 | − | 0.372479i | ||||
\(248\) | 1.85676 | − | 3.21600i | 0.117904 | − | 0.204216i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.91313 | + | 3.41395i | −0.373979 | + | 0.215917i | ||||
\(251\) | 28.3990 | 1.79253 | 0.896264 | − | 0.443521i | \(-0.146271\pi\) | ||||
0.896264 | + | 0.443521i | \(0.146271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.3267 | 1.90663 | ||||||||
\(254\) | 6.31330 | − | 3.64498i | 0.396132 | − | 0.228707i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −10.4625 | − | 18.1215i | −0.652630 | − | 1.13039i | −0.982482 | − | 0.186356i | \(-0.940332\pi\) |
0.329852 | − | 0.944032i | \(-0.393001\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.60025 | + | 1.15458i | −0.596530 | + | 0.0717421i | ||||
\(260\) | − | 0.903418i | − | 0.0560276i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.62759 | + | 3.82644i | 0.409454 | + | 0.236398i | ||||
\(263\) | −19.5793 | − | 11.3041i | −1.20731 | − | 0.697040i | −0.245138 | − | 0.969488i | \(-0.578833\pi\) |
−0.962171 | + | 0.272448i | \(0.912167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.45766i | 0.150973i | ||||||||
\(266\) | 8.55111 | + | 11.4065i | 0.524302 | + | 0.699378i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.60764 | + | 9.71272i | 0.342541 | + | 0.593299i | ||||
\(269\) | −10.0754 | + | 17.4511i | −0.614309 | + | 1.06401i | 0.376196 | + | 0.926540i | \(0.377232\pi\) |
−0.990505 | + | 0.137474i | \(0.956102\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.753738 | + | 0.435171i | −0.0457863 | + | 0.0264347i | −0.522718 | − | 0.852505i | \(-0.675082\pi\) |
0.476932 | + | 0.878940i | \(0.341749\pi\) | |||||||
\(272\) | −6.50984 | −0.394717 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.39751 | −0.144839 | ||||||||
\(275\) | −17.1165 | + | 9.88220i | −1.03216 | + | 0.595919i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.63594 | + | 14.9579i | −0.518884 | + | 0.898733i | 0.480876 | + | 0.876789i | \(0.340319\pi\) |
−0.999759 | + | 0.0219439i | \(0.993014\pi\) | |||||||
\(278\) | 6.49857 | + | 11.2559i | 0.389758 | + | 0.675081i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.227503 | + | 1.89167i | 0.0135959 | + | 0.113049i | ||||
\(281\) | 30.3053i | 1.80786i | 0.427678 | + | 0.903931i | \(0.359332\pi\) | ||||
−0.427678 | + | 0.903931i | \(0.640668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.02502 | + | 2.90119i | 0.298706 | + | 0.172458i | 0.641862 | − | 0.766821i | \(-0.278162\pi\) |
−0.343155 | + | 0.939279i | \(0.611496\pi\) | |||||||
\(284\) | 2.14740 | + | 1.23980i | 0.127425 | + | 0.0735688i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 5.53279i | − | 0.327161i | ||||||
\(287\) | −2.04093 | + | 4.77515i | −0.120473 | + | 0.281868i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.6890 | − | 21.9780i | −0.746412 | − | 1.29282i | ||||
\(290\) | 0.00797426 | − | 0.0138118i | 0.000468265 | − | 0.000811058i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.54555 | − | 4.93377i | 0.500090 | − | 0.288727i | ||||
\(293\) | 17.2563 | 1.00813 | 0.504063 | − | 0.863667i | \(-0.331838\pi\) | ||||
0.504063 | + | 0.863667i | \(0.331838\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.01126 | −0.175322 | ||||||||
\(296\) | −3.16506 | + | 1.82735i | −0.183966 | + | 0.106213i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.19375 | − | 3.79969i | 0.127081 | − | 0.220110i | ||||
\(299\) | −4.31321 | − | 7.47070i | −0.249439 | − | 0.432042i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2780 | − | 24.0474i | 0.592417 | − | 1.38607i | ||||
\(302\) | 16.5413i | 0.951844i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.66633 | + | 2.69411i | 0.267632 | + | 0.154518i | ||||
\(305\) | −5.10179 | − | 2.94552i | −0.292128 | − | 0.168660i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.5843i | − | 0.775300i | −0.921807 | − | 0.387650i | \(-0.873287\pi\) | ||
0.921807 | − | 0.387650i | \(-0.126713\pi\) | |||||||
\(308\) | 1.39329 | + | 11.5851i | 0.0793901 | + | 0.660123i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.33712 | − | 2.31595i | −0.0759431 | − | 0.131537i | ||||
\(311\) | 9.38959 | − | 16.2632i | 0.532435 | − | 0.922204i | −0.466848 | − | 0.884337i | \(-0.654611\pi\) |
0.999283 | − | 0.0378663i | \(-0.0120561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.7766 | + | 6.22185i | −0.609127 | + | 0.351680i | −0.772624 | − | 0.634864i | \(-0.781056\pi\) |
0.163497 | + | 0.986544i | \(0.447723\pi\) | |||||||
\(314\) | 23.0417 | 1.30032 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2.46702 | −0.138781 | ||||||||
\(317\) | 24.2326 | − | 13.9907i | 1.36104 | − | 0.785795i | 0.371275 | − | 0.928523i | \(-0.378921\pi\) |
0.989762 | + | 0.142728i | \(0.0455873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0488366 | − | 0.0845875i | 0.00273432 | − | 0.00473599i | ||||
\(320\) | 0.360068 | + | 0.623656i | 0.0201284 | + | 0.0348634i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.9127 | + | 14.5567i | 0.608144 | + | 0.811216i | ||||
\(323\) | 35.0764i | 1.95170i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.86877 | + | 2.81099i | 0.270071 | + | 0.155925i | ||||
\(326\) | 4.64354 | + | 2.68095i | 0.257182 | + | 0.148484i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.96278i | 0.108376i | ||||||||
\(329\) | −21.6311 | + | 2.60147i | −1.19256 | + | 0.143424i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9738 | − | 22.4713i | −0.713106 | − | 1.23514i | −0.963685 | − | 0.267040i | \(-0.913954\pi\) |
0.250579 | − | 0.968096i | \(-0.419379\pi\) | |||||||
\(332\) | 5.69625 | − | 9.86619i | 0.312622 | − | 0.541478i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.84579 | − | 5.68447i | 0.538738 | − | 0.311040i | ||||
\(335\) | 8.07653 | 0.441268 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.98199 | −0.162439 | −0.0812197 | − | 0.996696i | \(-0.525882\pi\) | ||||
−0.0812197 | + | 0.996696i | \(0.525882\pi\) | |||||||
\(338\) | 9.89538 | − | 5.71310i | 0.538238 | − | 0.310752i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.34398 | + | 4.05990i | −0.127120 | + | 0.220179i | ||||
\(341\) | −8.18888 | − | 14.1835i | −0.443452 | − | 0.768082i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3391 | + | 6.50813i | −0.936223 | + | 0.351406i | ||||
\(344\) | − | 9.88445i | − | 0.532934i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.6523 | + | 11.9236i | 1.11028 | + | 0.641018i | ||||
\(347\) | −0.960504 | − | 0.554547i | −0.0515625 | − | 0.0297696i | 0.473997 | − | 0.880526i | \(-0.342811\pi\) |
−0.525560 | + | 0.850757i | \(0.676144\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 20.5877i | − | 1.10203i | −0.834494 | − | 0.551017i | \(-0.814240\pi\) | ||
0.834494 | − | 0.551017i | \(-0.185760\pi\) | |||||||
\(350\) | −10.9026 | − | 4.65985i | −0.582768 | − | 0.249080i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.20516 | + | 3.81944i | 0.117535 | + | 0.203577i | ||||
\(353\) | −12.4002 | + | 21.4777i | −0.659994 | + | 1.14314i | 0.320623 | + | 0.947207i | \(0.396108\pi\) |
−0.980617 | + | 0.195936i | \(0.937225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.54642 | − | 0.892827i | 0.0820756 | − | 0.0473864i | ||||
\(356\) | −15.0041 | −0.795214 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.6920 | 0.565091 | ||||||||
\(359\) | 16.5875 | − | 9.57681i | 0.875456 | − | 0.505445i | 0.00629854 | − | 0.999980i | \(-0.497995\pi\) |
0.869157 | + | 0.494535i | \(0.164662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.01641 | − | 8.68868i | 0.264022 | − | 0.457299i | ||||
\(362\) | −11.3947 | − | 19.7363i | −0.598894 | − | 1.03732i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.65572 | − | 1.99091i | 0.139198 | − | 0.104352i | ||||
\(365\) | − | 7.10597i | − | 0.371944i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.5233 | + | 8.38501i | 0.758108 | + | 0.437694i | 0.828616 | − | 0.559817i | \(-0.189129\pi\) |
−0.0705081 | + | 0.997511i | \(0.522462\pi\) | |||||||
\(368\) | 5.95507 | + | 3.43816i | 0.310430 | + | 0.179227i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.63188i | 0.136825i | ||||||||
\(371\) | −7.22462 | + | 5.41608i | −0.375083 | + | 0.281189i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.2507 | − | 22.9509i | −0.686094 | − | 1.18835i | −0.973092 | − | 0.230419i | \(-0.925990\pi\) |
0.286997 | − | 0.957931i | \(-0.407343\pi\) | |||||||
\(374\) | −14.3552 | + | 24.8640i | −0.742291 | + | 1.28568i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.13145 | + | 4.11735i | −0.367777 | + | 0.212336i | ||||
\(377\) | −0.0277831 | −0.00143090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.7747 | −0.861657 | −0.430829 | − | 0.902434i | \(-0.641779\pi\) | ||||
−0.430829 | + | 0.902434i | \(0.641779\pi\) | |||||||
\(380\) | 3.36039 | − | 1.94012i | 0.172384 | − | 0.0995262i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.88017 | + | 4.98861i | −0.147363 | + | 0.255239i | ||||
\(383\) | 8.36992 | + | 14.4971i | 0.427683 | + | 0.740769i | 0.996667 | − | 0.0815798i | \(-0.0259966\pi\) |
−0.568984 | + | 0.822349i | \(0.692663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.72680 | + | 3.30249i | 0.393794 | + | 0.168311i | ||||
\(386\) | − | 25.4437i | − | 1.29505i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.89063 | − | 5.13301i | −0.451353 | − | 0.260589i | ||||
\(389\) | 7.82510 | + | 4.51783i | 0.396749 | + | 0.229063i | 0.685080 | − | 0.728468i | \(-0.259767\pi\) |
−0.288332 | + | 0.957531i | \(0.593101\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.7638i | 2.26380i | ||||||||
\(392\) | −5.05946 | + | 4.83755i | −0.255541 | + | 0.244333i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.0669548 | − | 0.115969i | −0.00337314 | − | 0.00584244i | ||||
\(395\) | −0.888294 | + | 1.53857i | −0.0446949 | + | 0.0774139i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.4999 | + | 7.79420i | −0.677543 | + | 0.391180i | −0.798929 | − | 0.601426i | \(-0.794600\pi\) |
0.121386 | + | 0.992605i | \(0.461266\pi\) | |||||||
\(398\) | −4.50320 | −0.225725 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.48140 | −0.224070 | ||||||||
\(401\) | 10.7706 | − | 6.21840i | 0.537857 | − | 0.310532i | −0.206353 | − | 0.978478i | \(-0.566160\pi\) |
0.744210 | + | 0.667946i | \(0.232826\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.32932 | + | 4.03450i | −0.116032 | + | 0.200973i | ||||
\(404\) | −2.27149 | − | 3.93433i | −0.113011 | − | 0.195740i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0581750 | − | 0.00699646i | 0.00288718 | − | 0.000347228i | ||||
\(407\) | 16.1184i | 0.798958i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.18775 | + | 0.685749i | 0.0587306 | + | 0.0339081i | 0.529078 | − | 0.848573i | \(-0.322538\pi\) |
−0.470347 | + | 0.882481i | \(0.655871\pi\) | |||||||
\(410\) | 1.22410 | + | 0.706733i | 0.0604539 | + | 0.0349030i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 18.8266i | − | 0.927518i | ||||||
\(413\) | −6.63607 | − | 8.85200i | −0.326540 | − | 0.435578i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.10207 | − | 7.10500i | −0.201363 | − | 0.348771i | ||||
\(416\) | 0.627256 | − | 1.08644i | 0.0307537 | − | 0.0532670i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.5800 | − | 11.8819i | 1.00660 | − | 0.581160i | ||||
\(419\) | 15.2548 | 0.745248 | 0.372624 | − | 0.927983i | \(-0.378458\pi\) | ||||
0.372624 | + | 0.927983i | \(0.378458\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.37509 | 0.456914 | 0.228457 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228457 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(422\) | −22.3169 | + | 12.8847i | −1.08637 | + | 0.627215i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.70638 | + | 2.95555i | −0.0828694 | + | 0.143534i | ||||
\(425\) | −14.5866 | − | 25.2648i | −0.707555 | − | 1.22552i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.58434 | − | 21.4886i | −0.125065 | − | 1.03991i | ||||
\(428\) | 1.01734i | 0.0491749i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.16450 | − | 3.55907i | −0.297278 | − | 0.171634i | ||||
\(431\) | 6.44133 | + | 3.71890i | 0.310268 | + | 0.179133i | 0.647046 | − | 0.762451i | \(-0.276004\pi\) |
−0.336779 | + | 0.941584i | \(0.609337\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.40343i | 0.307729i | 0.988092 | + | 0.153865i | \(0.0491720\pi\) | ||||
−0.988092 | + | 0.153865i | \(0.950828\pi\) | |||||||
\(434\) | 3.86138 | − | 9.03443i | 0.185352 | − | 0.433666i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.26044 | + | 9.11136i | 0.251930 | + | 0.436355i | ||||
\(437\) | 18.5255 | − | 32.0872i | 0.886197 | − | 1.53494i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7661 | + | 10.2573i | −0.847930 | + | 0.489553i | −0.859952 | − | 0.510375i | \(-0.829507\pi\) |
0.0120217 | + | 0.999928i | \(0.496173\pi\) | |||||||
\(440\) | 3.17602 | 0.151411 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.16667 | 0.388449 | ||||||||
\(443\) | −22.4927 | + | 12.9861i | −1.06866 | + | 0.616990i | −0.927815 | − | 0.373041i | \(-0.878315\pi\) |
−0.140844 | + | 0.990032i | \(0.544982\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.40249 | + | 9.35738i | −0.256102 | + | 0.443582i | ||||
\(446\) | −0.553917 | − | 0.959412i | −0.0262287 | − | 0.0454295i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.03982 | + | 2.43285i | −0.0491269 | + | 0.114942i | ||||
\(449\) | 2.44022i | 0.115161i | 0.998341 | + | 0.0575805i | \(0.0183386\pi\) | ||||
−0.998341 | + | 0.0575805i | \(0.981661\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.49671 | + | 4.32823i | 0.353006 | + | 0.203808i | ||||
\(452\) | 4.76466 | + | 2.75088i | 0.224111 | + | 0.129390i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.39997i | 0.206501i | ||||||||
\(455\) | −0.285405 | − | 2.37312i | −0.0133800 | − | 0.111254i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.6605 | − | 23.6607i | −0.639011 | − | 1.10680i | −0.985650 | − | 0.168801i | \(-0.946011\pi\) |
0.346639 | − | 0.937998i | \(-0.387323\pi\) | |||||||
\(458\) | 1.95937 | − | 3.39374i | 0.0915555 | − | 0.158579i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.28846 | − | 2.47594i | 0.199950 | − | 0.115441i | ||||
\(461\) | 12.7947 | 0.595910 | 0.297955 | − | 0.954580i | \(-0.403696\pi\) | ||||
0.297955 | + | 0.954580i | \(0.403696\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.4026 | −1.27350 | −0.636752 | − | 0.771068i | \(-0.719723\pi\) | ||||
−0.636752 | + | 0.771068i | \(0.719723\pi\) | |||||||
\(464\) | 0.0191795 | − | 0.0110733i | 0.000890384 | − | 0.000514064i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.4991 | − | 18.1850i | 0.486361 | − | 0.842403i | ||||
\(467\) | −12.8190 | − | 22.2031i | −0.593191 | − | 1.02744i | −0.993799 | − | 0.111187i | \(-0.964535\pi\) |
0.400609 | − | 0.916249i | \(-0.368799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 17.7987 | + | 23.7421i | 0.821867 | + | 1.09631i | ||||
\(470\) | 5.93010i | 0.273535i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.62130 | − | 2.09076i | −0.166684 | − | 0.0962348i | ||||
\(473\) | −37.7531 | − | 21.7968i | −1.73589 | − | 1.00222i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.1468i | 1.10793i | ||||||||
\(476\) | −17.1002 | + | 2.05657i | −0.783786 | + | 0.0942625i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.1152 | + | 22.7163i | 0.599877 | + | 1.03902i | ||||
\(479\) | 17.8762 | − | 30.9625i | 0.816784 | − | 1.41471i | −0.0912565 | − | 0.995827i | \(-0.529088\pi\) |
0.908040 | − | 0.418883i | \(-0.137578\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.97061 | − | 2.29243i | 0.181044 | − | 0.104526i | ||||
\(482\) | −4.90643 | −0.223482 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.45086 | 0.384130 | ||||||||
\(485\) | −6.40246 | + | 3.69646i | −0.290721 | + | 0.167848i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.94736 | + | 8.56907i | −0.224186 | + | 0.388302i | −0.956075 | − | 0.293122i | \(-0.905306\pi\) |
0.731889 | + | 0.681424i | \(0.238639\pi\) | |||||||
\(488\) | −4.09023 | − | 7.08448i | −0.185156 | − | 0.320699i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.19522 | + | 4.89721i | 0.0539945 | + | 0.221233i | ||||
\(491\) | − | 38.7331i | − | 1.74800i | −0.485924 | − | 0.874001i | \(-0.661517\pi\) | ||
0.485924 | − | 0.874001i | \(-0.338483\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.124855 | + | 0.0720852i | 0.00562320 | + | 0.00324655i | ||||
\(494\) | −5.85396 | − | 3.37979i | −0.263382 | − | 0.152064i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.71351i | − | 0.166742i | ||||||
\(497\) | 6.03252 | + | 2.57835i | 0.270596 | + | 0.115655i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.72202 | + | 9.91083i | 0.256153 | + | 0.443670i | 0.965208 | − | 0.261483i | \(-0.0842116\pi\) |
−0.709055 | + | 0.705153i | \(0.750878\pi\) | |||||||
\(500\) | −3.41395 | + | 5.91313i | −0.152676 | + | 0.264443i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.5942 | − | 14.1995i | 1.09769 | − | 0.633754i | ||||
\(503\) | −23.3446 | −1.04088 | −0.520442 | − | 0.853897i | \(-0.674233\pi\) | ||||
−0.520442 | + | 0.853897i | \(0.674233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.27156 | −0.145582 | ||||||||
\(506\) | 26.2637 | − | 15.1634i | 1.16757 | − | 0.674094i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.64498 | − | 6.31330i | 0.161720 | − | 0.280107i | ||||
\(509\) | −10.0656 | − | 17.4341i | −0.446149 | − | 0.772753i | 0.551983 | − | 0.833856i | \(-0.313871\pi\) |
−0.998131 | + | 0.0611031i | \(0.980538\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.8890 | − | 15.6598i | 0.924074 | − | 0.692750i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.1215 | − | 10.4625i | −0.799305 | − | 0.461479i | ||||
\(515\) | −11.7413 | − | 6.77884i | −0.517383 | − | 0.298711i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.3176i | 1.59724i | ||||||||
\(518\) | −7.73677 | + | 5.80002i | −0.339934 | + | 0.254838i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.451709 | − | 0.782383i | −0.0198088 | − | 0.0343098i | ||||
\(521\) | −2.27906 | + | 3.94745i | −0.0998474 | + | 0.172941i | −0.911621 | − | 0.411031i | \(-0.865169\pi\) |
0.811774 | + | 0.583972i | \(0.198502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.2504 | + | 14.0009i | −1.06039 | + | 0.612219i | −0.925541 | − | 0.378647i | \(-0.876389\pi\) |
−0.134853 | + | 0.990866i | \(0.543056\pi\) | |||||||
\(524\) | 7.65288 | 0.334318 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −22.6082 | −0.985764 | ||||||||
\(527\) | 20.9356 | − | 12.0872i | 0.911970 | − | 0.526526i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.1419 | − | 21.0304i | 0.527909 | − | 0.914366i | ||||
\(530\) | 1.22883 | + | 2.12839i | 0.0533769 | + | 0.0924515i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 13.1087 | + | 5.60277i | 0.568335 | + | 0.242911i | ||||
\(533\) | − | 2.46232i | − | 0.106655i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.634469 | + | 0.366311i | 0.0274305 | + | 0.0158370i | ||||
\(536\) | 9.71272 | + | 5.60764i | 0.419526 | + | 0.242213i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.1508i | 0.868764i | ||||||||
\(539\) | 7.31985 | + | 29.9919i | 0.315288 | + | 1.29184i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.70552 | + | 8.15020i | 0.202306 | + | 0.350405i | 0.949271 | − | 0.314459i | \(-0.101823\pi\) |
−0.746965 | + | 0.664863i | \(0.768490\pi\) | |||||||
\(542\) | −0.435171 | + | 0.753738i | −0.0186922 | + | 0.0323758i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.63769 | + | 3.25492i | −0.241714 | + | 0.139554i | ||||
\(545\) | 7.57647 | 0.324540 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.4285 | 0.916216 | 0.458108 | − | 0.888896i | \(-0.348527\pi\) | ||||
0.458108 | + | 0.888896i | \(0.348527\pi\) | |||||||
\(548\) | −2.07631 | + | 1.19876i | −0.0886954 | + | 0.0512083i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.88220 | + | 17.1165i | −0.421378 | + | 0.729849i | ||||
\(551\) | −0.0596651 | − | 0.103343i | −0.00254182 | − | 0.00440256i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.48042 | + | 0.779371i | −0.275575 | + | 0.0331422i | ||||
\(554\) | 17.2719i | 0.733812i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.2559 | + | 6.49857i | 0.477354 | + | 0.275601i | ||||
\(557\) | −27.3775 | − | 15.8064i | −1.16002 | − | 0.669740i | −0.208714 | − | 0.977977i | \(-0.566928\pi\) |
−0.951310 | + | 0.308237i | \(0.900261\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.4002i | 0.524471i | ||||||||
\(560\) | 1.14286 | + | 1.52448i | 0.0482946 | + | 0.0644211i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.1526 | + | 26.2452i | 0.639176 | + | 1.10709i | ||||
\(563\) | −5.37125 | + | 9.30328i | −0.226371 | + | 0.392087i | −0.956730 | − | 0.290977i | \(-0.906020\pi\) |
0.730359 | + | 0.683064i | \(0.239353\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.43120 | − | 1.98101i | 0.144352 | − | 0.0833415i | ||||
\(566\) | 5.80239 | 0.243893 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.47961 | 0.104042 | ||||||||
\(569\) | −26.0909 | + | 15.0636i | −1.09379 | + | 0.631499i | −0.934582 | − | 0.355747i | \(-0.884227\pi\) |
−0.159205 | + | 0.987245i | \(0.550893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.77343 | − | 8.26783i | 0.199762 | − | 0.345998i | −0.748689 | − | 0.662921i | \(-0.769316\pi\) |
0.948451 | + | 0.316923i | \(0.102650\pi\) | |||||||
\(572\) | −2.76639 | − | 4.79153i | −0.115669 | − | 0.200344i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.620073 | + | 5.15587i | 0.0258814 | + | 0.215202i | ||||
\(575\) | 30.8156i | 1.28510i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.3763 | − | 18.6925i | −1.34784 | − | 0.778178i | −0.359900 | − | 0.932991i | \(-0.617189\pi\) |
−0.987944 | + | 0.154813i | \(0.950523\pi\) | |||||||
\(578\) | −21.9780 | − | 12.6890i | −0.914164 | − | 0.527793i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 0.0159485i | − | 0.000662226i | ||||||
\(581\) | 11.8461 | − | 27.7163i | 0.491461 | − | 1.14986i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.52569 | + | 13.0349i | 0.311682 | + | 0.539850i | ||||
\(584\) | 4.93377 | − | 8.54555i | 0.204161 | − | 0.353617i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.9444 | − | 8.62817i | 0.617348 | − | 0.356426i | ||||
\(587\) | −21.7523 | −0.897813 | −0.448906 | − | 0.893579i | \(-0.648186\pi\) | ||||
−0.448906 | + | 0.893579i | \(0.648186\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0092 | −0.824464 | ||||||||
\(590\) | −2.60782 | + | 1.50563i | −0.107362 | + | 0.0619857i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.82735 | + | 3.16506i | −0.0751036 | + | 0.130083i | ||||
\(593\) | −15.0439 | − | 26.0569i | −0.617780 | − | 1.07003i | −0.989890 | − | 0.141838i | \(-0.954699\pi\) |
0.372110 | − | 0.928189i | \(-0.378635\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.87464 | + | 11.4051i | −0.199841 | + | 0.467565i | ||||
\(596\) | − | 4.38750i | − | 0.179719i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.47070 | − | 4.31321i | −0.305500 | − | 0.176380i | ||||
\(599\) | 9.96294 | + | 5.75211i | 0.407075 | + | 0.235025i | 0.689532 | − | 0.724255i | \(-0.257816\pi\) |
−0.282457 | + | 0.959280i | \(0.591150\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 36.9294i | − | 1.50638i | −0.657801 | − | 0.753191i | \(-0.728513\pi\) | ||
0.657801 | − | 0.753191i | \(-0.271487\pi\) | |||||||
\(602\) | −3.12266 | − | 25.9647i | −0.127270 | − | 1.05824i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.27064 | + | 14.3252i | 0.336528 | + | 0.582883i | ||||
\(605\) | 3.04288 | − | 5.27043i | 0.123711 | − | 0.214274i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.4941 | + | 12.9870i | −0.913008 | + | 0.527125i | −0.881398 | − | 0.472375i | \(-0.843397\pi\) |
−0.0316101 | + | 0.999500i | \(0.510063\pi\) | |||||||
\(608\) | 5.38821 | 0.218521 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −5.89104 | −0.238521 | ||||||||
\(611\) | 8.94648 | − | 5.16526i | 0.361936 | − | 0.208964i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.92902 | + | 5.07322i | −0.118302 | + | 0.204905i | −0.919095 | − | 0.394036i | \(-0.871078\pi\) |
0.800793 | + | 0.598941i | \(0.204412\pi\) | |||||||
\(614\) | −6.79217 | − | 11.7644i | −0.274110 | − | 0.474772i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.99918 | + | 9.33635i | 0.282005 | + | 0.376172i | ||||
\(617\) | 42.9297i | 1.72828i | 0.503248 | + | 0.864142i | \(0.332138\pi\) | ||||
−0.503248 | + | 0.864142i | \(0.667862\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.5874 | − | 14.1955i | −0.988251 | − | 0.570567i | −0.0835001 | − | 0.996508i | \(-0.526610\pi\) |
−0.904751 | + | 0.425941i | \(0.859943\pi\) | |||||||
\(620\) | −2.31595 | − | 1.33712i | −0.0930109 | − | 0.0536999i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 18.7792i | − | 0.752976i | ||||||
\(623\) | −39.4130 | + | 4.74003i | −1.57905 | + | 0.189905i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.74500 | − | 15.1468i | −0.349800 | − | 0.605872i | ||||
\(626\) | −6.22185 | + | 10.7766i | −0.248675 | + | 0.430718i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 19.9547 | − | 11.5209i | 0.796280 | − | 0.459733i | ||||
\(629\) | −23.7915 | −0.948630 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.6791 | −0.504749 | −0.252374 | − | 0.967630i | \(-0.581211\pi\) | ||||
−0.252374 | + | 0.967630i | \(0.581211\pi\) | |||||||
\(632\) | −2.13650 | + | 1.23351i | −0.0849854 | + | 0.0490663i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.9907 | − | 24.2326i | 0.555641 | − | 0.962399i | ||||
\(635\) | −2.62488 | − | 4.54643i | −0.104165 | − | 0.180420i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.34714 | − | 6.06876i | 0.251483 | − | 0.240453i | ||||
\(638\) | − | 0.0976732i | − | 0.00386692i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.623656 | + | 0.360068i | 0.0246522 | + | 0.0142329i | ||||
\(641\) | 30.5826 | + | 17.6569i | 1.20794 | + | 0.697406i | 0.962309 | − | 0.271957i | \(-0.0876710\pi\) |
0.245633 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.07091i | 0.357722i | 0.983874 | + | 0.178861i | \(0.0572412\pi\) | ||||
−0.983874 | + | 0.178861i | \(0.942759\pi\) | |||||||
\(644\) | 16.7291 | + | 7.15014i | 0.659218 | + | 0.281755i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.5382 | + | 30.3770i | 0.690031 | + | 1.19517i | ||||
\(647\) | −12.5913 | + | 21.8088i | −0.495017 | + | 0.857394i | −0.999983 | − | 0.00574473i | \(-0.998171\pi\) |
0.504967 | + | 0.863139i | \(0.331505\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.9710 | + | 9.22089i | −0.626918 | + | 0.361952i | ||||
\(650\) | 5.62197 | 0.220512 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.36190 | 0.209988 | ||||||||
\(653\) | −30.9107 | + | 17.8463i | −1.20963 | + | 0.698380i | −0.962679 | − | 0.270648i | \(-0.912762\pi\) |
−0.246952 | + | 0.969028i | \(0.579429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.75556 | − | 4.77276i | 0.107669 | − | 0.186487i | ||||
\(656\) | 0.981388 | + | 1.69981i | 0.0383168 | + | 0.0663666i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −17.4323 | + | 13.0685i | −0.679583 | + | 0.509462i | ||||
\(659\) | − | 8.24284i | − | 0.321096i | −0.987028 | − | 0.160548i | \(-0.948674\pi\) | ||
0.987028 | − | 0.160548i | \(-0.0513261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.2734 | + | 12.8596i | 0.866336 | + | 0.500179i | 0.866129 | − | 0.499821i | \(-0.166601\pi\) |
0.000207182 | 1.00000i | \(0.499934\pi\) | ||||||||
\(662\) | −22.4713 | − | 12.9738i | −0.873373 | − | 0.504242i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 11.3925i | − | 0.442115i | ||||||
\(665\) | 8.21423 | − | 6.15796i | 0.318534 | − | 0.238795i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.0761434 | − | 0.131884i | −0.00294828 | − | 0.00510658i | ||||
\(668\) | 5.68447 | − | 9.84579i | 0.219939 | − | 0.380945i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.99448 | − | 4.03826i | 0.270220 | − | 0.156012i | ||||
\(671\) | −36.0784 | −1.39279 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 40.0224 | 1.54275 | 0.771374 | − | 0.636382i | \(-0.219570\pi\) | ||||
0.771374 | + | 0.636382i | \(0.219570\pi\) | |||||||
\(674\) | −2.58248 | + | 1.49100i | −0.0994735 | + | 0.0574310i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.71310 | − | 9.89538i | 0.219735 | − | 0.380592i | ||||
\(677\) | 24.5616 | + | 42.5420i | 0.943979 | + | 1.63502i | 0.757782 | + | 0.652508i | \(0.226283\pi\) |
0.186197 | + | 0.982512i | \(0.440384\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.9757 | − | 10.6748i | −0.958480 | − | 0.409661i | ||||
\(680\) | 4.68797i | 0.179775i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −14.1835 | − | 8.18888i | −0.543116 | − | 0.313568i | ||||
\(683\) | −36.2000 | − | 20.9001i | −1.38516 | − | 0.799720i | −0.392391 | − | 0.919798i | \(-0.628352\pi\) |
−0.992764 | + | 0.120079i | \(0.961685\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.72653i | 0.0659675i | ||||||||
\(686\) | −11.7620 | + | 14.3058i | −0.449077 | + | 0.546196i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.94223 | − | 8.56019i | −0.188421 | − | 0.326354i | ||||
\(689\) | 2.14068 | − | 3.70776i | 0.0815534 | − | 0.141255i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8071 | − | 8.54891i | 0.563290 | − | 0.325216i | −0.191175 | − | 0.981556i | \(-0.561230\pi\) |
0.754465 | + | 0.656340i | \(0.227896\pi\) | |||||||
\(692\) | 23.8472 | 0.906536 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.10909 | −0.0421006 | ||||||||
\(695\) | 8.10574 | − | 4.67985i | 0.307468 | − | 0.177517i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.38868 | + | 11.0655i | −0.241989 | + | 0.419136i | ||||
\(698\) | −10.2939 | − | 17.8295i | −0.389628 | − | 0.674856i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.7719 | + | 1.41575i | −0.444934 | + | 0.0535103i | ||||
\(701\) | 0.310638i | 0.0117326i | 0.999983 | + | 0.00586632i | \(0.00186732\pi\) | ||||
−0.999983 | + | 0.00586632i | \(0.998133\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.0540 | + | 9.84615i | 0.643205 | + | 0.371355i | ||||
\(704\) | 3.81944 | + | 2.20516i | 0.143951 | + | 0.0831100i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 24.8003i | 0.933373i | ||||||||
\(707\) | −7.20972 | − | 9.61719i | −0.271149 | − | 0.361692i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.44666 | + | 12.8980i | 0.279665 | + | 0.484394i | 0.971302 | − | 0.237852i | \(-0.0764432\pi\) |
−0.691636 | + | 0.722246i | \(0.743110\pi\) | |||||||
\(710\) | 0.892827 | − | 1.54642i | 0.0335072 | − | 0.0580362i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −12.9939 | + | 7.50204i | −0.486967 | + | 0.281151i | ||||
\(713\) | −25.5353 | −0.956305 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.98436 | −0.149007 | ||||||||
\(716\) | 9.25956 | − | 5.34601i | 0.346046 | − | 0.199790i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.57681 | − | 16.5875i | 0.357403 | − | 0.619041i | ||||
\(719\) | 3.97677 | + | 6.88798i | 0.148309 | + | 0.256878i | 0.930602 | − | 0.366031i | \(-0.119284\pi\) |
−0.782294 | + | 0.622910i | \(0.785950\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.94762 | − | 49.4540i | −0.221501 | − | 1.84176i | ||||
\(722\) | − | 10.0328i | − | 0.373383i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.7363 | − | 11.3947i | −0.733493 | − | 0.423482i | ||||
\(725\) | 0.0859510 | + | 0.0496238i | 0.00319214 | + | 0.00184298i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.3509i | − | 1.34818i | −0.738649 | − | 0.674091i | \(-0.764536\pi\) | ||
0.738649 | − | 0.674091i | \(-0.235464\pi\) | |||||||
\(728\) | 1.30447 | − | 3.05204i | 0.0483467 | − | 0.113116i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.55299 | − | 6.15395i | −0.131502 | − | 0.227768i | ||||
\(731\) | 32.1731 | − | 55.7254i | 1.18997 | − | 2.06108i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.31396 | − | 5.37741i | 0.344019 | − | 0.198619i | −0.318029 | − | 0.948081i | \(-0.603021\pi\) |
0.662048 | + | 0.749462i | \(0.269688\pi\) | |||||||
\(734\) | 16.7700 | 0.618992 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.87632 | 0.253465 | ||||||||
\(737\) | 42.8362 | − | 24.7315i | 1.57789 | − | 0.910995i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.32601 | − | 2.29671i | 0.0487779 | − | 0.0844858i | −0.840606 | − | 0.541648i | \(-0.817801\pi\) |
0.889383 | + | 0.457162i | \(0.151134\pi\) | |||||||
\(740\) | 1.31594 | + | 2.27928i | 0.0483749 | + | 0.0837878i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.54866 | + | 8.30277i | −0.130276 | + | 0.304804i | ||||
\(743\) | − | 31.1629i | − | 1.14325i | −0.820513 | − | 0.571627i | \(-0.806312\pi\) | ||
0.820513 | − | 0.571627i | \(-0.193688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.73629 | − | 1.57980i | −0.100250 | − | 0.0578793i | ||||
\(746\) | −22.9509 | − | 13.2507i | −0.840291 | − | 0.485142i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 28.7104i | 1.04976i | ||||||||
\(749\) | 0.321394 | + | 2.67237i | 0.0117435 | + | 0.0976461i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6273 | + | 23.6031i | 0.497267 | + | 0.861291i | 0.999995 | − | 0.00315345i | \(-0.00100378\pi\) |
−0.502728 | + | 0.864444i | \(0.667670\pi\) | |||||||
\(752\) | −4.11735 | + | 7.13145i | −0.150144 | + | 0.260057i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0240609 | + | 0.0138915i | −0.000876245 | + | 0.000505900i | ||||
\(755\) | 11.9120 | 0.433521 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.1863 | 0.660993 | 0.330496 | − | 0.943807i | \(-0.392784\pi\) | ||||
0.330496 | + | 0.943807i | \(0.392784\pi\) | |||||||
\(758\) | −14.5273 | + | 8.38734i | −0.527655 | + | 0.304642i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.94012 | − | 3.36039i | 0.0703756 | − | 0.121894i | ||||
\(761\) | −4.08064 | − | 7.06787i | −0.147923 | − | 0.256210i | 0.782537 | − | 0.622605i | \(-0.213925\pi\) |
−0.930460 | + | 0.366394i | \(0.880592\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6967 | + | 22.2721i | 0.604460 | + | 0.806303i | ||||
\(764\) | 5.76035i | 0.208402i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.4971 | + | 8.36992i | 0.523803 | + | 0.302418i | ||||
\(767\) | 4.54295 | + | 2.62288i | 0.164037 | + | 0.0947066i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.7465i | − | 1.79391i | −0.442127 | − | 0.896953i | \(-0.645776\pi\) | ||
0.442127 | − | 0.896953i | \(-0.354224\pi\) | |||||||
\(770\) | 8.34285 | − | 1.00336i | 0.300656 | − | 0.0361585i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −12.7218 | − | 22.0349i | −0.457869 | − | 0.793052i | ||||
\(773\) | −9.09567 | + | 15.7542i | −0.327148 | + | 0.566638i | −0.981945 | − | 0.189168i | \(-0.939421\pi\) |
0.654796 | + | 0.755805i | \(0.272754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.4122 | − | 8.32087i | 0.517701 | − | 0.298895i | ||||
\(776\) | −10.2660 | −0.368529 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 9.03565 | 0.323944 | ||||||||
\(779\) | 9.15896 | − | 5.28793i | 0.328154 | − | 0.189460i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.46792 | − | 9.47072i | 0.195658 | − | 0.338889i | ||||
\(782\) | 22.3819 | + | 38.7666i | 0.800374 | + | 1.38629i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.96284 | + | 6.71917i | −0.0701015 | + | 0.239970i | ||||
\(785\) | − | 16.5932i | − | 0.592236i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.42794 | + | 0.824423i | 0.0509006 | + | 0.0293875i | 0.525234 | − | 0.850958i | \(-0.323978\pi\) |
−0.474334 | + | 0.880345i | \(0.657311\pi\) | |||||||
\(788\) | −0.115969 | − | 0.0669548i | −0.00413123 | − | 0.00238517i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.77659i | 0.0632082i | ||||||||
\(791\) | 13.3850 | + | 5.72083i | 0.475914 | + | 0.203409i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.13123 | + | 8.88756i | 0.182215 | + | 0.315606i | ||||
\(794\) | −7.79420 | + | 13.4999i | −0.276606 | + | 0.479095i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.89988 | + | 2.25160i | −0.138228 | + | 0.0798058i | ||||
\(797\) | 36.4437 | 1.29090 | 0.645451 | − | 0.763802i | \(-0.276670\pi\) | ||||
0.645451 | + | 0.763802i | \(0.276670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53.6065 | −1.89646 | ||||||||
\(800\) | −3.88101 | + | 2.24070i | −0.137214 | + | 0.0792208i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.21840 | − | 10.7706i | 0.219579 | − | 0.380322i | ||||
\(803\) | −21.7595 | − | 37.6885i | −0.767876 | − | 1.33000i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.4828 | − | 7.85866i | 0.369471 | − | 0.276981i | ||||
\(806\) | 4.65864i | 0.164094i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.93433 | − | 2.27149i | −0.138409 | − | 0.0799107i | ||||
\(809\) | 13.6983 | + | 7.90874i | 0.481608 | + | 0.278057i | 0.721086 | − | 0.692845i | \(-0.243643\pi\) |
−0.239478 | + | 0.970902i | \(0.576976\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.4667i | 0.683567i | 0.939779 | + | 0.341783i | \(0.111031\pi\) | ||||
−0.939779 | + | 0.341783i | \(0.888969\pi\) | |||||||
\(812\) | 0.0468828 | − | 0.0351466i | 0.00164526 | − | 0.00123340i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.05919 | + | 13.9589i | 0.282474 | + | 0.489260i | ||||
\(815\) | 1.93065 | − | 3.34398i | 0.0676276 | − | 0.117135i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −46.1241 | + | 26.6298i | −1.61368 | + | 0.931657i | ||||
\(818\) | 1.37150 | 0.0479533 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.41347 | 0.0493604 | ||||||||
\(821\) | −18.4672 | + | 10.6620i | −0.644508 | + | 0.372107i | −0.786349 | − | 0.617783i | \(-0.788031\pi\) |
0.141841 | + | 0.989889i | \(0.454698\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.97099 | − | 12.0741i | 0.242993 | − | 0.420877i | −0.718572 | − | 0.695452i | \(-0.755204\pi\) |
0.961566 | + | 0.274575i | \(0.0885373\pi\) | |||||||
\(824\) | −9.41328 | − | 16.3043i | −0.327927 | − | 0.567986i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.1730 | − | 4.34802i | −0.353964 | − | 0.151287i | ||||
\(827\) | − | 27.2974i | − | 0.949224i | −0.880195 | − | 0.474612i | \(-0.842588\pi\) | ||
0.880195 | − | 0.474612i | \(-0.157412\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.1694 | − | 19.1504i | −1.15202 | − | 0.665119i | −0.202642 | − | 0.979253i | \(-0.564953\pi\) |
−0.949379 | + | 0.314134i | \(0.898286\pi\) | |||||||
\(830\) | −7.10500 | − | 4.10207i | −0.246618 | − | 0.142385i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.25451i | − | 0.0434923i | ||||||
\(833\) | −44.2695 | + | 10.8045i | −1.53385 | + | 0.374352i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.09359 | − | 7.09031i | −0.141665 | − | 0.245370i | ||||
\(836\) | 11.8819 | − | 20.5800i | 0.410942 | − | 0.711773i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 13.2111 | − | 7.62742i | 0.456369 | − | 0.263485i | ||||
\(839\) | 5.81634 | 0.200803 | 0.100401 | − | 0.994947i | \(-0.467987\pi\) | ||||
0.100401 | + | 0.994947i | \(0.467987\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9995 | 0.999983 | ||||||||
\(842\) | 8.11907 | − | 4.68755i | 0.279802 | − | 0.161544i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.8847 | + | 22.3169i | −0.443508 | + | 0.768179i | ||||
\(845\) | −4.11421 | − | 7.12602i | −0.141533 | − | 0.245143i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.1989 | − | 2.66977i | 0.762764 | − | 0.0917343i | ||||
\(848\) | 3.41277i | 0.117195i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −25.2648 | − | 14.5866i | −0.866574 | − | 0.500317i | ||||
\(851\) | 21.7640 | + | 12.5654i | 0.746060 | + | 0.430738i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.7422i | 1.77162i | 0.464047 | + | 0.885810i | \(0.346397\pi\) | ||||
−0.464047 | + | 0.885810i | \(0.653603\pi\) | |||||||
\(854\) | −12.9824 | − | 17.3175i | −0.444249 | − | 0.592593i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.508669 | + | 0.881040i | 0.0173859 | + | 0.0301133i | ||||
\(857\) | −0.717546 | + | 1.24283i | −0.0245109 | + | 0.0424542i | −0.878021 | − | 0.478623i | \(-0.841136\pi\) |
0.853510 | + | 0.521077i | \(0.174470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.35458 | + | 1.35942i | −0.0803372 | + | 0.0463827i | −0.539630 | − | 0.841902i | \(-0.681436\pi\) |
0.459293 | + | 0.888285i | \(0.348103\pi\) | |||||||
\(860\) | −7.11815 | −0.242727 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.43780 | 0.253333 | ||||||||
\(863\) | 29.2938 | − | 16.9128i | 0.997171 | − | 0.575717i | 0.0897610 | − | 0.995963i | \(-0.471390\pi\) |
0.907410 | + | 0.420246i | \(0.138056\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.58663 | − | 14.8725i | 0.291954 | − | 0.505679i | ||||
\(866\) | 3.20172 | + | 5.54553i | 0.108799 | + | 0.188445i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.17316 | − | 9.75474i | −0.0398196 | − | 0.331097i | ||||
\(869\) | 10.8803i | 0.369090i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.1847 | − | 7.03485i | −0.412863 | − | 0.238367i | ||||
\(872\) | 9.11136 | + | 5.26044i | 0.308549 | + | 0.178141i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 37.0511i | − | 1.25327i | ||||||
\(875\) | −7.09978 | + | 16.6113i | −0.240016 | + | 0.561564i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.10648 | − | 1.91648i | −0.0373632 | − | 0.0647150i | 0.846739 | − | 0.532008i | \(-0.178563\pi\) |
−0.884102 | + | 0.467293i | \(0.845229\pi\) | |||||||
\(878\) | −10.2573 | + | 17.7661i | −0.346166 | + | 0.599577i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.75052 | − | 1.58801i | 0.0927199 | − | 0.0535319i | ||||
\(881\) | 48.6451 | 1.63890 | 0.819448 | − | 0.573153i | \(-0.194280\pi\) | ||||
0.819448 | + | 0.573153i | \(0.194280\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.22677 | 0.0412841 | 0.0206420 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206420 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(884\) | 7.07254 | − | 4.08333i | 0.237875 | − | 0.137337i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.9861 | + | 22.4927i | −0.436278 | + | 0.755656i | ||||
\(887\) | 15.4263 | + | 26.7192i | 0.517966 | + | 0.897143i | 0.999782 | + | 0.0208707i | \(0.00664385\pi\) |
−0.481816 | + | 0.876272i | \(0.660023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.58025 | − | 17.7354i | 0.254234 | − | 0.594827i | ||||
\(890\) | 10.8050i | 0.362184i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.959412 | − | 0.553917i | −0.0321235 | − | 0.0185465i | ||||
\(893\) | 38.4258 | + | 22.1851i | 1.28587 | + | 0.742397i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.69971i | − | 0.257373i | ||||||
\(896\) | 0.315916 | + | 2.62682i | 0.0105540 | + | 0.0877560i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.22011 | + | 2.11329i | 0.0407156 | + | 0.0705215i | ||||
\(899\) | −0.0411207 | + | 0.0712232i | −0.00137145 | + | 0.00237543i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.2401 | + | 11.1083i | −0.640981 | + | 0.370071i | ||||
\(902\) | 8.65646 | 0.288229 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.50175 | 0.182986 | ||||||||
\(905\) | −14.2128 | + | 8.20576i | −0.472449 | + | 0.272769i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.23138 | − | 14.2572i | 0.273318 | − | 0.473401i | −0.696391 | − | 0.717662i | \(-0.745212\pi\) |
0.969709 | + | 0.244261i | \(0.0785454\pi\) | |||||||
\(908\) | 2.19998 | + | 3.81048i | 0.0730090 | + | 0.126455i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.43373 | − | 1.91248i | −0.0475276 | − | 0.0633981i | ||||
\(911\) | 13.8920i | 0.460264i | 0.973159 | + | 0.230132i | \(0.0739158\pi\) | ||||
−0.973159 | + | 0.230132i | \(0.926084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −43.5130 | − | 25.1222i | −1.44007 | − | 0.831425i | ||||
\(914\) | −23.6607 | − | 13.6605i | −0.782625 | − | 0.451849i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 3.91875i | − | 0.129479i | ||||||
\(917\) | 20.1028 | − | 2.41767i | 0.663852 | − | 0.0798385i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.8502 | − | 30.9174i | −0.588822 | − | 1.01987i | −0.994387 | − | 0.105804i | \(-0.966258\pi\) |
0.405565 | − | 0.914066i | \(-0.367075\pi\) | |||||||
\(920\) | 2.47594 | − | 4.28846i | 0.0816294 | − | 0.141386i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.0806 | − | 6.39736i | 0.364919 | − | 0.210686i | ||||
\(923\) | −3.11070 | −0.102390 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.3782 | −0.538512 | ||||||||
\(926\) | −23.7313 | + | 13.7013i | −0.779859 | + | 0.450252i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.0110733 | − | 0.0191795i | 0.000363498 | − | 0.000629597i | ||||
\(929\) | 2.66526 | + | 4.61636i | 0.0874443 | + | 0.151458i | 0.906430 | − | 0.422356i | \(-0.138797\pi\) |
−0.818986 | + | 0.573814i | \(0.805463\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.2043 | + | 10.5762i | 1.18655 | + | 0.346621i | ||||
\(932\) | − | 20.9982i | − | 0.687819i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −22.2031 | − | 12.8190i | −0.726507 | − | 0.419449i | ||||
\(935\) | 17.9054 | + | 10.3377i | 0.585570 | + | 0.338079i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 0.645033i | − | 0.0210723i | −0.999944 | − | 0.0105362i | \(-0.996646\pi\) | ||
0.999944 | − | 0.0105362i | \(-0.00335383\pi\) | |||||||
\(938\) | 27.2851 | + | 11.6619i | 0.890892 | + | 0.380774i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.96505 | + | 5.13561i | 0.0967092 | + | 0.167505i | ||||
\(941\) | −5.14487 | + | 8.91117i | −0.167718 | + | 0.290496i | −0.937617 | − | 0.347670i | \(-0.886973\pi\) |
0.769899 | + | 0.638165i | \(0.220306\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6885 | − | 6.74834i | 0.380629 | − | 0.219756i | ||||
\(944\) | −4.18151 | −0.136097 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −43.5935 | −1.41735 | ||||||||
\(947\) | −4.26637 | + | 2.46319i | −0.138638 | + | 0.0800429i | −0.567715 | − | 0.823225i | \(-0.692172\pi\) |
0.429077 | + | 0.903268i | \(0.358839\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.18947 | + | 10.7205i | −0.200919 | + | 0.348002i | ||||
\(950\) | 12.0734 | + | 20.9117i | 0.391712 | + | 0.678465i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −13.7809 | + | 10.3311i | −0.446642 | + | 0.334834i | ||||
\(953\) | − | 6.13857i | − | 0.198848i | −0.995045 | − | 0.0994239i | \(-0.968300\pi\) | ||
0.995045 | − | 0.0994239i | \(-0.0317000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.59248 | + | 2.07412i | 0.116250 | + | 0.0671168i | ||||
\(956\) | 22.7163 | + | 13.1152i | 0.734696 | + | 0.424177i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 35.7524i | − | 1.15511i | ||||||
\(959\) | −5.07538 | + | 3.80486i | −0.163893 | + | 0.122865i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.60492 | − | 14.9042i | −0.277578 | − | 0.480779i | ||||
\(962\) | 2.29243 | − | 3.97061i | 0.0739109 | − | 0.128017i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.24909 | + | 2.45321i | −0.136854 | + | 0.0790127i | ||||
\(965\) | −18.3229 | −0.589835 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7940 | 0.475744 | 0.237872 | − | 0.971296i | \(-0.423550\pi\) | ||||
0.237872 | + | 0.971296i | \(0.423550\pi\) | |||||||
\(968\) | 7.31866 | − | 4.22543i | 0.235231 | − | 0.135811i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.69646 | + | 6.40246i | −0.118686 | + | 0.205571i | ||||
\(971\) | −3.00256 | − | 5.20059i | −0.0963569 | − | 0.166895i | 0.813817 | − | 0.581121i | \(-0.197386\pi\) |
−0.910174 | + | 0.414226i | \(0.864052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.6201 | + | 13.5147i | 1.01369 | + | 0.433261i | ||||
\(974\) | 9.89471i | 0.317047i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.08448 | − | 4.09023i | −0.226769 | − | 0.130925i | ||||
\(977\) | 7.64962 | + | 4.41651i | 0.244733 | + | 0.141297i | 0.617350 | − | 0.786688i | \(-0.288206\pi\) |
−0.372617 | + | 0.927985i | \(0.621540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 66.1727i | 2.11489i | ||||||||
\(980\) | 3.48369 | + | 3.64350i | 0.111283 | + | 0.116387i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −19.3666 | − | 33.5439i | −0.618012 | − | 1.07043i | ||||
\(983\) | −21.0094 | + | 36.3893i | −0.670094 | + | 1.16064i | 0.307783 | + | 0.951457i | \(0.400413\pi\) |
−0.977877 | + | 0.209181i | \(0.932920\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.0835136 | + | 0.0482166i | −0.00266096 | + | 0.00153631i | ||||
\(986\) | 0.144170 | 0.00459132 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.75957 | −0.215051 | ||||||||
\(989\) | −58.8626 | + | 33.9843i | −1.87172 | + | 1.08064i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.95731 | − | 13.7825i | 0.252772 | − | 0.437815i | −0.711516 | − | 0.702670i | \(-0.751991\pi\) |
0.964288 | + | 0.264856i | \(0.0853243\pi\) | |||||||
\(992\) | −1.85676 | − | 3.21600i | −0.0589521 | − | 0.102108i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.51349 | − | 0.783349i | 0.206595 | − | 0.0248463i | ||||
\(995\) | 3.24291i | 0.102807i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.7367 | + | 14.2817i | 0.783419 | + | 0.452307i | 0.837641 | − | 0.546222i | \(-0.183934\pi\) |
−0.0542215 | + | 0.998529i | \(0.517268\pi\) | |||||||
\(998\) | 9.91083 | + | 5.72202i | 0.313722 | + | 0.181127i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1134.2.k.c.647.6 | ✓ | 16 | |
3.2 | odd | 2 | 1134.2.k.d.647.3 | yes | 16 | ||
7.5 | odd | 6 | 1134.2.k.d.971.3 | yes | 16 | ||
9.2 | odd | 6 | 1134.2.t.g.1025.6 | 16 | |||
9.4 | even | 3 | 1134.2.l.h.269.6 | 16 | |||
9.5 | odd | 6 | 1134.2.l.g.269.3 | 16 | |||
9.7 | even | 3 | 1134.2.t.h.1025.3 | 16 | |||
21.5 | even | 6 | inner | 1134.2.k.c.971.6 | yes | 16 | |
63.5 | even | 6 | 1134.2.t.h.593.3 | 16 | |||
63.40 | odd | 6 | 1134.2.t.g.593.6 | 16 | |||
63.47 | even | 6 | 1134.2.l.h.215.2 | 16 | |||
63.61 | odd | 6 | 1134.2.l.g.215.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1134.2.k.c.647.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1134.2.k.c.971.6 | yes | 16 | 21.5 | even | 6 | inner | |
1134.2.k.d.647.3 | yes | 16 | 3.2 | odd | 2 | ||
1134.2.k.d.971.3 | yes | 16 | 7.5 | odd | 6 | ||
1134.2.l.g.215.7 | 16 | 63.61 | odd | 6 | |||
1134.2.l.g.269.3 | 16 | 9.5 | odd | 6 | |||
1134.2.l.h.215.2 | 16 | 63.47 | even | 6 | |||
1134.2.l.h.269.6 | 16 | 9.4 | even | 3 | |||
1134.2.t.g.593.6 | 16 | 63.40 | odd | 6 | |||
1134.2.t.g.1025.6 | 16 | 9.2 | odd | 6 | |||
1134.2.t.h.593.3 | 16 | 63.5 | even | 6 | |||
1134.2.t.h.1025.3 | 16 | 9.7 | even | 3 |