Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(305,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.cn (of order \(12\), degree \(4\), not 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: | \(4.98266508613\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | 16.0.9349208943630483456.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 48 x^{14} - 196 x^{13} + 642 x^{12} - 1668 x^{11} + 3580 x^{10} - 6328 x^{9} + \cdots + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 353.4 | ||
Root | \(0.500000 + 2.00333i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.353 |
Dual form | 624.2.cn.d.449.4 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.45865 | + | 0.933998i | 0.842150 | + | 0.539244i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.02097 | − | 2.02097i | −0.903805 | − | 0.903805i | 0.0919576 | − | 0.995763i | \(-0.470688\pi\) |
−0.995763 | + | 0.0919576i | \(0.970688\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.46723 | + | 0.929042i | −1.31049 | + | 0.351145i | −0.845407 | − | 0.534122i | \(-0.820642\pi\) |
−0.465083 | + | 0.885267i | \(0.653975\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.25529 | + | 2.72474i | 0.418432 | + | 0.908248i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.05922 | − | 1.08766i | −1.22390 | − | 0.327943i | −0.411699 | − | 0.911320i | \(-0.635064\pi\) |
−0.812201 | + | 0.583377i | \(0.801731\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.60121 | − | 0.176977i | −0.998795 | − | 0.0490845i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.06030 | − | 4.83546i | −0.273768 | − | 1.24851i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.72704 | − | 2.99132i | 0.418869 | − | 0.725502i | −0.576957 | − | 0.816774i | \(-0.695760\pi\) |
0.995826 | + | 0.0912724i | \(0.0290934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.581191 | − | 2.16903i | −0.133334 | − | 0.497611i | 0.866665 | − | 0.498891i | \(-0.166259\pi\) |
−0.999999 | + | 0.00128023i | \(0.999592\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.92518 | − | 1.88324i | −1.29298 | − | 0.410958i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.51618 | − | 2.62611i | −0.316146 | − | 0.547581i | 0.663534 | − | 0.748146i | \(-0.269056\pi\) |
−0.979680 | + | 0.200565i | \(0.935722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.16864i | 0.633728i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.713876 | + | 5.14688i | −0.137386 | + | 0.990518i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.74432 | + | 1.00708i | −0.323911 | + | 0.187010i | −0.653135 | − | 0.757242i | \(-0.726546\pi\) |
0.329223 | + | 0.944252i | \(0.393213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.21829 | + | 1.21829i | −0.218812 | + | 0.218812i | −0.807998 | − | 0.589186i | \(-0.799449\pi\) |
0.589186 | + | 0.807998i | \(0.299449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.90508 | − | 5.37782i | −0.853865 | − | 0.936158i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.88473 | + | 5.12960i | 1.50179 | + | 0.867061i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.25335 | + | 4.67758i | −0.206050 | + | 0.768990i | 0.783077 | + | 0.621925i | \(0.213649\pi\) |
−0.989127 | + | 0.147065i | \(0.953017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.08759 | − | 3.62167i | −0.814666 | − | 0.579931i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.05521 | + | 7.67015i | −0.320970 | + | 1.19788i | 0.597332 | + | 0.801994i | \(0.296228\pi\) |
−0.918302 | + | 0.395881i | \(0.870439\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.68905 | + | 0.975173i | 0.257578 | + | 0.148712i | 0.623229 | − | 0.782039i | \(-0.285820\pi\) |
−0.365651 | + | 0.930752i | \(0.619154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.96971 | − | 8.04354i | 0.442699 | − | 1.19906i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.957390 | + | 0.957390i | −0.139650 | + | 0.139650i | −0.773476 | − | 0.633826i | \(-0.781484\pi\) |
0.633826 | + | 0.773476i | \(0.281484\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.09639 | − | 2.94240i | 0.728056 | − | 0.420343i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.31303 | − | 2.75023i | 0.743973 | − | 0.385109i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.22186i | − | 0.991999i | −0.868323 | − | 0.495999i | \(-0.834802\pi\) | ||
0.868323 | − | 0.495999i | \(-0.165198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00542 | + | 10.4017i | 0.809771 | + | 1.40256i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.17812 | − | 3.70668i | 0.156046 | − | 0.490962i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.66284 | − | 9.93785i | −0.346672 | − | 1.29380i | −0.890647 | − | 0.454696i | \(-0.849748\pi\) |
0.543975 | − | 0.839101i | \(-0.316919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.137104 | + | 0.237470i | −0.0175543 | + | 0.0304050i | −0.874669 | − | 0.484720i | \(-0.838921\pi\) |
0.857115 | + | 0.515125i | \(0.172255\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.88380 | − | 8.28110i | −0.867277 | − | 1.04332i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.92026 | + | 7.63559i | 0.858353 | + | 0.947079i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.10121 | − | 1.09891i | −0.501042 | − | 0.134254i | −0.000558430 | − | 1.00000i | \(-0.500178\pi\) |
−0.500484 | + | 0.865746i | \(0.666844\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.241204 | − | 5.24667i | 0.0290376 | − | 0.631625i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.6578 | − | 2.85575i | 1.26485 | − | 0.338915i | 0.436793 | − | 0.899562i | \(-0.356114\pi\) |
0.828055 | + | 0.560647i | \(0.189447\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0822 | + | 10.0822i | 1.18003 | + | 1.18003i | 0.979735 | + | 0.200296i | \(0.0641903\pi\) |
0.200296 | + | 0.979735i | \(0.435810\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.95950 | + | 4.62192i | −0.341734 | + | 0.533694i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 15.0847 | 1.71906 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.58051 | −0.177821 | −0.0889105 | − | 0.996040i | \(-0.528339\pi\) | ||||
−0.0889105 | + | 0.996040i | \(0.528339\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.84847 | + | 6.84072i | −0.649830 | + | 0.760080i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.58938 | − | 2.58938i | −0.284221 | − | 0.284221i | 0.550569 | − | 0.834790i | \(-0.314411\pi\) |
−0.834790 | + | 0.550569i | \(0.814411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.53567 | + | 2.55507i | −1.03429 | + | 0.277137i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.48495 | − | 0.160213i | −0.373626 | − | 0.0171766i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.50933 | − | 2.54802i | −1.00799 | − | 0.270089i | −0.283199 | − | 0.959061i | \(-0.591396\pi\) |
−0.724788 | + | 0.688972i | \(0.758062\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.6506 | − | 2.73205i | 1.32615 | − | 0.286397i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.91495 | + | 0.639175i | −0.302266 | + | 0.0662794i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.20898 | + | 5.55812i | −0.329235 | + | 0.570251i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.07638 | − | 7.74915i | −0.210824 | − | 0.786807i | −0.987595 | − | 0.157023i | \(-0.949810\pi\) |
0.776771 | − | 0.629784i | \(-0.216856\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.13191 | − | 12.4257i | −0.214265 | − | 1.24883i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.05342 | − | 1.82458i | −0.104820 | − | 0.181553i | 0.808845 | − | 0.588022i | \(-0.200093\pi\) |
−0.913665 | + | 0.406469i | \(0.866760\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2629i | 1.40537i | 0.711503 | + | 0.702683i | \(0.248015\pi\) | ||||
−0.711503 | + | 0.702683i | \(0.751985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.16864 | + | 15.7806i | 0.797178 | + | 1.54003i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.9906 | + | 6.92275i | −1.15917 | + | 0.669248i | −0.951105 | − | 0.308867i | \(-0.900050\pi\) |
−0.208066 | + | 0.978115i | \(0.566717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.84220 | − | 5.84220i | 0.559581 | − | 0.559581i | −0.369607 | − | 0.929188i | \(-0.620508\pi\) |
0.929188 | + | 0.369607i | \(0.120508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.19705 | + | 5.65231i | −0.588198 | + | 0.536493i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.5920 | − | 9.00205i | −1.46677 | − | 0.846841i | −0.467463 | − | 0.884012i | \(-0.654832\pi\) |
−0.999309 | + | 0.0371710i | \(0.988165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.24312 | + | 8.37145i | −0.209172 | + | 0.780641i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.03836 | − | 10.0345i | −0.373346 | − | 0.927692i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.20898 | + | 11.9761i | −0.294167 | + | 1.09785i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.76795 | + | 3.33013i | 0.524359 | + | 0.302739i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.1617 | + | 9.26846i | −0.916252 | + | 0.835709i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.70112 | + | 3.70112i | −0.331039 | + | 0.331039i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.9209 | − | 10.3466i | 1.59022 | − | 0.918114i | 0.596952 | − | 0.802277i | \(-0.296378\pi\) |
0.993268 | − | 0.115837i | \(-0.0369549\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.55291 | + | 3.00000i | 0.136726 | + | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.68295i | 0.409151i | 0.978851 | + | 0.204576i | \(0.0655814\pi\) | ||||
−0.978851 | + | 0.204576i | \(0.934419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.03025 | + | 6.98059i | 0.349467 | + | 0.605294i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.8444 | − | 8.95897i | 1.01940 | − | 0.771065i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.41832 | + | 5.29326i | 0.121176 | + | 0.452234i | 0.999675 | − | 0.0255107i | \(-0.00812118\pi\) |
−0.878499 | + | 0.477744i | \(0.841455\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.34662 | − | 12.7247i | 0.623132 | − | 1.07930i | −0.365767 | − | 0.930706i | \(-0.619193\pi\) |
0.988899 | − | 0.148590i | \(-0.0474734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.29069 | + | 0.502292i | −0.192911 | + | 0.0423006i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.4256 | + | 4.63529i | 1.20633 | + | 0.387622i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.56049 | + | 1.48993i | 0.461774 | + | 0.123732i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 10.1820 | + | 0.468097i | 0.839800 | + | 0.0386080i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.98255 | − | 2.67482i | 0.817803 | − | 0.219130i | 0.174417 | − | 0.984672i | \(-0.444196\pi\) |
0.643386 | + | 0.765542i | \(0.277529\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.48932 | + | 6.48932i | 0.528094 | + | 0.528094i | 0.920004 | − | 0.391910i | \(-0.128186\pi\) |
−0.391910 | + | 0.920004i | \(0.628186\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.3185 | + | 0.950753i | 0.834204 | + | 0.0768638i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.92427 | 0.395527 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1431 | −1.12874 | −0.564372 | − | 0.825520i | \(-0.690882\pi\) | ||||
−0.564372 | + | 0.825520i | \(0.690882\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.74520 | − | 10.5341i | 0.534929 | − | 0.835411i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.69672 | + | 7.69672i | 0.606587 | + | 0.606587i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07638 | + | 0.288415i | −0.0843084 | + | 0.0225904i | −0.300727 | − | 0.953710i | \(-0.597229\pi\) |
0.216418 | + | 0.976301i | \(0.430563\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.955381 | + | 20.7814i | −0.0743763 | + | 1.61783i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.39478 | + | 1.44553i | 0.417461 | + | 0.111858i | 0.461434 | − | 0.887174i | \(-0.347335\pi\) |
−0.0439735 | + | 0.999033i | \(0.514002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9374 | + | 1.27466i | 0.995181 | + | 0.0980507i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.18050 | − | 4.30638i | 0.396163 | − | 0.329317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.74765 | + | 15.1514i | −0.665072 | + | 1.15194i | 0.314194 | + | 0.949359i | \(0.398266\pi\) |
−0.979266 | + | 0.202579i | \(0.935068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.94380 | − | 10.9864i | −0.222530 | − | 0.830494i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.39779 | − | 16.9829i | 0.405723 | − | 1.27651i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.60754 | − | 7.98049i | −0.344384 | − | 0.596490i | 0.640858 | − | 0.767660i | \(-0.278579\pi\) |
−0.985242 | + | 0.171169i | \(0.945245\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.8110i | − | 1.02656i | −0.858220 | − | 0.513282i | \(-0.828429\pi\) | ||
0.858220 | − | 0.513282i | \(-0.171571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.421783 | + | 0.218331i | −0.0311791 | + | 0.0161395i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 11.9862 | − | 6.92026i | 0.881246 | − | 0.508788i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.2640 | + | 10.2640i | −0.750577 | + | 0.750577i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.30649 | − | 18.5086i | −0.167773 | − | 1.34631i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.6614 | − | 11.3515i | −1.42265 | − | 0.821366i | −0.426123 | − | 0.904665i | \(-0.640121\pi\) |
−0.996525 | + | 0.0832996i | \(0.973454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.18821 | + | 19.3627i | −0.373456 | + | 1.39376i | 0.482133 | + | 0.876098i | \(0.339862\pi\) |
−0.855588 | + | 0.517657i | \(0.826804\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.96258 | + | 17.6011i | 0.212155 | + | 1.26044i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.82369 | − | 18.0023i | 0.343674 | − | 1.28261i | −0.550480 | − | 0.834849i | \(-0.685555\pi\) |
0.894154 | − | 0.447760i | \(-0.147778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.90611 | + | 2.25519i | 0.276897 | + | 0.159866i | 0.632018 | − | 0.774954i | \(-0.282227\pi\) |
−0.355121 | + | 0.934820i | \(0.615560\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.95582 | − | 5.43345i | −0.349557 | − | 0.383246i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.11233 | − | 5.11233i | 0.358815 | − | 0.358815i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6547 | − | 11.3476i | 1.37274 | − | 0.792552i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.25221 | − | 7.42775i | 0.365054 | − | 0.516264i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.43672i | 0.652752i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.28841 | − | 7.42775i | −0.295227 | − | 0.511348i | 0.679811 | − | 0.733387i | \(-0.262062\pi\) |
−0.975038 | + | 0.222040i | \(0.928728\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 18.2132 | + | 5.78884i | 1.24795 | + | 0.396645i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.44272 | − | 5.38431i | −0.0983928 | − | 0.367207i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.09226 | − | 5.35596i | 0.209916 | − | 0.363586i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.28960 | + | 24.1231i | 0.357438 | + | 1.63009i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.74882 | + | 10.4667i | −0.453975 | + | 0.704067i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.3575 | − | 5.45476i | −1.36324 | − | 0.365278i | −0.498232 | − | 0.867043i | \(-0.666017\pi\) |
−0.865004 | + | 0.501765i | \(0.832684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.63374 | + | 3.97758i | −0.575582 | + | 0.265172i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.85544 | − | 1.30101i | 0.322267 | − | 0.0863512i | −0.0940589 | − | 0.995567i | \(-0.529984\pi\) |
0.416326 | + | 0.909215i | \(0.363318\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.92484 | − | 9.92484i | −0.655852 | − | 0.655852i | 0.298544 | − | 0.954396i | \(-0.403499\pi\) |
−0.954396 | + | 0.298544i | \(0.903499\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 22.0033 | + | 14.0891i | 1.44771 | + | 0.926995i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7944 | −1.23126 | −0.615630 | − | 0.788035i | \(-0.711098\pi\) | ||||
−0.615630 | + | 0.788035i | \(0.711098\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.86971 | 0.252432 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.30540 | − | 1.47619i | −0.149752 | − | 0.0958889i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.82142 | + | 6.82142i | 0.441241 | + | 0.441241i | 0.892429 | − | 0.451188i | \(-0.149000\pi\) |
−0.451188 | + | 0.892429i | \(0.649000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.18821 | − | 2.19402i | 0.527449 | − | 0.141330i | 0.0147390 | − | 0.999891i | \(-0.495308\pi\) |
0.512710 | + | 0.858562i | \(0.328642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9201 | + | 4.51572i | −0.957122 | + | 0.289684i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16.2462 | − | 4.35315i | −1.03793 | − | 0.278112i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.70912 | + | 7.91400i | 0.108749 | + | 0.503555i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.35851 | − | 6.19546i | −0.0860921 | − | 0.392621i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.51988 | + | 6.09661i | −0.222173 | + | 0.384814i | −0.955467 | − | 0.295096i | \(-0.904648\pi\) |
0.733295 | + | 0.679911i | \(0.237982\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.29820 | + | 12.3090i | 0.207356 | + | 0.773862i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −16.2956 | − | 5.17935i | −1.02047 | − | 0.324343i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.815993 | + | 1.41334i | 0.0509003 | + | 0.0881618i | 0.890353 | − | 0.455271i | \(-0.150458\pi\) |
−0.839453 | + | 0.543433i | \(0.817124\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 17.3827i | − | 1.08011i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.93367 | − | 3.48863i | −0.305387 | − | 0.215941i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.15209 | + | 5.28396i | −0.564342 | + | 0.325823i | −0.754886 | − | 0.655856i | \(-0.772308\pi\) |
0.190544 | + | 0.981679i | \(0.438975\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.5952 | + | 14.5952i | −0.896574 | + | 0.896574i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4909 | − | 12.5983i | −0.703231 | − | 0.771006i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.46392 | + | 4.30930i | 0.455083 | + | 0.262742i | 0.709975 | − | 0.704227i | \(-0.248706\pi\) |
−0.254891 | + | 0.966970i | \(0.582040\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.13290 | + | 19.1563i | −0.311802 | + | 1.16366i | 0.615129 | + | 0.788427i | \(0.289104\pi\) |
−0.926930 | + | 0.375233i | \(0.877563\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 21.0045 | + | 7.83057i | 1.27125 | + | 0.473928i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.44642 | − | 12.8622i | 0.207827 | − | 0.775620i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.4255 | − | 7.75123i | −0.806661 | − | 0.465726i | 0.0391339 | − | 0.999234i | \(-0.487540\pi\) |
−0.845795 | + | 0.533508i | \(0.820873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.84886 | − | 1.79022i | −0.290294 | − | 0.107178i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9452 | − | 11.9452i | 0.712591 | − | 0.712591i | −0.254486 | − | 0.967077i | \(-0.581906\pi\) |
0.967077 | + | 0.254486i | \(0.0819061\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.36808 | − | 0.789860i | 0.0813237 | − | 0.0469523i | −0.458787 | − | 0.888546i | \(-0.651716\pi\) |
0.540110 | + | 0.841594i | \(0.318382\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.87205 | + | 5.11015i | −0.584770 | + | 0.302699i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 28.5035i | − | 1.68251i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.53467 | + | 4.39017i | 0.149098 | + | 0.258245i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.20899 | − | 13.2426i | 0.246735 | − | 0.776295i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.01073 | + | 3.77209i | 0.0590474 | + | 0.220368i | 0.989145 | − | 0.146946i | \(-0.0469442\pi\) |
−0.930097 | + | 0.367314i | \(0.880278\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.7026 | + | 25.4656i | −0.856017 | + | 1.48266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.49585 | − | 20.1158i | 0.492979 | − | 1.16724i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.99533 | + | 9.72548i | 0.288887 | + | 0.562439i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.76230 | − | 1.81195i | −0.389772 | − | 0.104439i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.167586 | − | 3.64532i | 0.00962754 | − | 0.209418i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.757003 | − | 0.202838i | 0.0433459 | − | 0.0116145i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.7994 | − | 21.7994i | −1.24416 | − | 1.24416i | −0.958260 | − | 0.285899i | \(-0.907708\pi\) |
−0.285899 | − | 0.958260i | \(-0.592292\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.3215 | + | 20.8045i | −0.757835 | + | 1.18353i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.9295 | −1.18681 | −0.593403 | − | 0.804906i | \(-0.702216\pi\) | ||||
−0.593403 | + | 0.804906i | \(0.702216\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.6685 | −1.84653 | −0.923267 | − | 0.384159i | \(-0.874491\pi\) | ||||
−0.923267 | + | 0.384159i | \(0.874491\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.82390 | + | 30.6478i | −0.159109 | + | 1.72681i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.21085 | − | 5.21085i | −0.292671 | − | 0.292671i | 0.545464 | − | 0.838134i | \(-0.316354\pi\) |
−0.838134 | + | 0.545464i | \(0.816354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.17593 | − | 2.19073i | 0.457764 | − | 0.122657i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −23.9558 | − | 1.10132i | −1.33708 | − | 0.0614695i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.49202 | − | 2.00748i | −0.416867 | − | 0.111699i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.560775 | − | 11.4109i | 0.0311062 | − | 0.632964i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.9783 | − | 3.06510i | 0.773002 | − | 0.169500i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.43004 | − | 4.20895i | 0.133972 | − | 0.232047i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.72013 | − | 17.6158i | −0.259442 | − | 0.968251i | −0.965565 | − | 0.260162i | \(-0.916224\pi\) |
0.706123 | − | 0.708089i | \(-0.250443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.3186 | + | 2.45667i | −0.784652 | + | 0.134625i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.06754 | + | 10.5093i | 0.331505 | + | 0.574184i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.92484i | 0.268273i | 0.990963 | + | 0.134136i | \(0.0428260\pi\) | ||||
−0.990963 | + | 0.134136i | \(0.957174\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.3353 | − | 27.6937i | −0.778587 | − | 1.50412i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.27042 | − | 3.62023i | 0.339562 | − | 0.196046i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.83057 | − | 2.83057i | 0.152836 | − | 0.152836i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.0908 | + | 10.1159i | −0.597110 | + | 0.544622i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.9403 | + | 7.47108i | 0.694671 | + | 0.401069i | 0.805360 | − | 0.592787i | \(-0.201972\pi\) |
−0.110688 | + | 0.993855i | \(0.535306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.08448 | + | 30.1717i | −0.432752 | + | 1.61505i | 0.313636 | + | 0.949543i | \(0.398453\pi\) |
−0.746388 | + | 0.665511i | \(0.768214\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.48169 | − | 18.4086i | 0.185839 | − | 0.982580i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.67762 | − | 9.99302i | 0.142515 | − | 0.531875i | −0.857338 | − | 0.514754i | \(-0.827883\pi\) |
0.999853 | − | 0.0171211i | \(-0.00545007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −27.3105 | − | 15.7677i | −1.44949 | − | 0.836864i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.8664 | + | 14.4717i | −0.839740 | + | 0.765923i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.08944 | + | 9.08944i | −0.479722 | + | 0.479722i | −0.905043 | − | 0.425321i | \(-0.860161\pi\) |
0.425321 | + | 0.905043i | \(0.360161\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0876 | − | 6.97875i | 0.636187 | − | 0.367303i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.30306 | + | 10.2447i | 0.278339 | + | 0.537709i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 40.7516i | − | 2.13304i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.823475 | + | 1.42630i | 0.0429850 | + | 0.0744522i | 0.886717 | − | 0.462312i | \(-0.152980\pi\) |
−0.843732 | + | 0.536764i | \(0.819647\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23.4791 | + | 4.02837i | −1.22227 | + | 0.209709i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.70941 | + | 25.0398i | 0.348335 | + | 1.30000i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.97578 | − | 17.2786i | 0.516526 | − | 0.894650i | −0.483290 | − | 0.875461i | \(-0.660558\pi\) |
0.999816 | − | 0.0191892i | \(-0.00610849\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.85547 | + | 1.94179i | −0.457295 | + | 0.100273i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.45987 | − | 3.31800i | 0.332700 | − | 0.170886i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.8923 | + | 3.18653i | 0.610865 | + | 0.163681i | 0.550972 | − | 0.834524i | \(-0.314257\pi\) |
0.0598936 | + | 0.998205i | \(0.480924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 35.8039 | + | 1.64601i | 1.83429 | + | 0.0843275i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.3800 | − | 7.33645i | 1.39905 | − | 0.374875i | 0.521048 | − | 0.853527i | \(-0.325541\pi\) |
0.878005 | + | 0.478652i | \(0.158875\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −30.4858 | − | 30.4858i | −1.55370 | − | 1.55370i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.536843 | + | 5.82636i | −0.0272892 | + | 0.296170i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.9504 | −0.808717 | −0.404359 | − | 0.914601i | \(-0.632505\pi\) | ||||
−0.404359 | + | 0.914601i | \(0.632505\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.4740 | −0.529695 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.37387 | + | 6.83077i | −0.220632 | + | 0.344567i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.19416 | + | 3.19416i | 0.160716 | + | 0.160716i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.2594 | + | 3.28489i | −0.615281 | + | 0.164864i | −0.552981 | − | 0.833194i | \(-0.686510\pi\) |
−0.0622992 | + | 0.998058i | \(0.519843\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.641158 | + | 13.9465i | −0.0320980 | + | 0.698196i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8603 | + | 4.24976i | 0.792027 | + | 0.212223i | 0.632080 | − | 0.774903i | \(-0.282201\pi\) |
0.159946 | + | 0.987126i | \(0.448868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.60294 | − | 4.17172i | 0.229289 | − | 0.207808i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 25.6445 | − | 2.00530i | 1.27428 | − | 0.0996443i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1753 | − | 17.6241i | 0.504370 | − | 0.873594i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.82005 | − | 32.9169i | −0.436123 | − | 1.62763i | −0.738364 | − | 0.674403i | \(-0.764401\pi\) |
0.302240 | − | 0.953232i | \(-0.402266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.87506 | + | 9.04570i | −0.141816 | + | 0.446192i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.4653 | + | 31.9829i | 0.908620 | + | 1.57378i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4661i | 0.513761i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.6010 | − | 11.6991i | 1.10677 | − | 0.572909i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.4943 | − | 16.4512i | 1.39204 | − | 0.803693i | 0.398496 | − | 0.917170i | \(-0.369532\pi\) |
0.993541 | + | 0.113477i | \(0.0361989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.0945 | − | 17.0945i | 0.833137 | − | 0.833137i | −0.154808 | − | 0.987945i | \(-0.549476\pi\) |
0.987945 | + | 0.154808i | \(0.0494759\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.81045 | − | 1.40684i | −0.185270 | − | 0.0684027i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.47842 | + | 5.47237i | 0.459771 | + | 0.265449i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.254750 | − | 0.950740i | 0.0123282 | − | 0.0460095i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 16.7125 | + | 20.2347i | 0.806885 | + | 0.976941i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −0.454427 | + | 1.69594i | −0.0218890 | + | 0.0816908i | −0.976006 | − | 0.217742i | \(-0.930131\pi\) |
0.954117 | + | 0.299433i | \(0.0967975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.87140 | − | 5.12190i | −0.426332 | − | 0.246143i | 0.271451 | − | 0.962452i | \(-0.412497\pi\) |
−0.697783 | + | 0.716309i | \(0.745830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.71920 | + | 7.36677i | 0.322161 | + | 0.353210i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.81492 | + | 4.81492i | −0.230329 | + | 0.230329i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.67848 | − | 2.70112i | 0.223292 | − | 0.128917i | −0.384182 | − | 0.923257i | \(-0.625516\pi\) |
0.607473 | + | 0.794340i | \(0.292183\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.4148 | + | 10.1928i | 0.686418 | + | 0.485371i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.5731i | 0.644876i | 0.946591 | + | 0.322438i | \(0.104502\pi\) | ||||
−0.946591 | + | 0.322438i | \(0.895498\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0686 | + | 24.3675i | 0.666916 | + | 1.15513i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.0593 | + | 5.42208i | 0.806877 | + | 0.256455i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.525222 | + | 1.96016i | 0.0247868 | + | 0.0925055i | 0.977211 | − | 0.212269i | \(-0.0680854\pi\) |
−0.952424 | + | 0.304775i | \(0.901419\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.6851 | − | 28.8994i | 0.785670 | − | 1.36082i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.40461 | + | 15.5266i | 0.159962 | + | 0.729505i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −31.0879 | − | 20.0451i | −1.45742 | − | 0.939731i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.9328 | − | 7.75251i | −1.35342 | − | 0.362647i | −0.492022 | − | 0.870583i | \(-0.663742\pi\) |
−0.861395 | + | 0.507936i | \(0.830409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.1631 | + | 11.0243i | 0.661076 | + | 0.514570i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5621 | − | 4.16985i | 0.724798 | − | 0.194209i | 0.122487 | − | 0.992470i | \(-0.460913\pi\) |
0.602312 | + | 0.798261i | \(0.294246\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.07041 | + | 4.07041i | 0.189168 | + | 0.189168i | 0.795336 | − | 0.606168i | \(-0.207294\pi\) |
−0.606168 | + | 0.795336i | \(0.707294\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.18277 | + | 4.59926i | 0.333093 | + | 0.213286i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −36.8536 | −1.70538 | −0.852690 | − | 0.522417i | \(-0.825030\pi\) | ||||
−0.852690 | + | 0.522417i | \(0.825030\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.2408 | 0.703753 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.6298 | − | 13.2097i | −0.950572 | − | 0.608669i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.79555 | − | 5.79555i | −0.266480 | − | 0.266480i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.87289 | − | 1.84159i | 0.315350 | − | 0.0844977i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 19.6777 | − | 9.06556i | 0.900981 | − | 0.415084i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.5305 | − | 3.89342i | −0.663913 | − | 0.177895i | −0.0889019 | − | 0.996040i | \(-0.528336\pi\) |
−0.575011 | + | 0.818145i | \(0.695002\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.34141 | − | 16.6231i | 0.243547 | − | 0.757949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.03807 | + | 18.4155i | 0.183738 | + | 0.837935i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.4645 | + | 19.8571i | −0.520576 | + | 0.901664i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.33018 | − | 16.1605i | −0.196219 | − | 0.732301i | −0.991948 | − | 0.126647i | \(-0.959578\pi\) |
0.795728 | − | 0.605654i | \(-0.207088\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.83943 | − | 0.584640i | −0.0831820 | − | 0.0264383i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6333 | + | 21.8815i | 0.570132 | + | 0.987498i | 0.996552 | + | 0.0829727i | \(0.0264414\pi\) |
−0.426419 | + | 0.904526i | \(0.640225\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.95708i | 0.313331i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −20.8034 | + | 29.4204i | −0.935043 | + | 1.32235i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −34.3000 | + | 19.8031i | −1.53856 | + | 0.888290i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.37946 | + | 1.37946i | −0.0617533 | + | 0.0617533i | −0.737309 | − | 0.675556i | \(-0.763904\pi\) |
0.675556 | + | 0.737309i | \(0.263904\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.51896 | + | 7.14723i | 0.291245 | + | 0.319315i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.77777 | − | 5.64520i | −0.435969 | − | 0.251707i | 0.265917 | − | 0.963996i | \(-0.414325\pi\) |
−0.701886 | + | 0.712289i | \(0.747659\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.55849 | + | 5.81637i | −0.0693520 | + | 0.258825i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 17.6805 | + | 13.9427i | 0.785218 | + | 0.619219i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.73260 | + | 36.3226i | −0.431390 | + | 1.60997i | 0.318171 | + | 0.948033i | \(0.396931\pi\) |
−0.749561 | + | 0.661936i | \(0.769735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44.3241 | − | 25.5905i | −1.96078 | − | 1.13206i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.5787 | − | 1.44290i | 0.511210 | − | 0.0637056i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 28.8249 | − | 28.8249i | 1.27018 | − | 1.27018i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.92757 | − | 2.84493i | 0.216714 | − | 0.125120i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.9111 | + | 13.9302i | −1.18127 | + | 0.611468i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.2111i | 0.797843i | 0.916985 | + | 0.398922i | \(0.130615\pi\) | ||||
−0.916985 | + | 0.398922i | \(0.869385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16.9049 | + | 29.2801i | 0.739199 | + | 1.28033i | 0.952857 | + | 0.303421i | \(0.0981289\pi\) |
−0.213658 | + | 0.976909i | \(0.568538\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.96732 | − | 18.7748i | 0.260435 | − | 0.819398i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.54027 | + | 5.74835i | 0.0670951 | + | 0.250402i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.90238 | − | 11.9553i | 0.300103 | − | 0.519794i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 23.7354 | − | 19.7305i | 1.03003 | − | 0.856230i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.75867 | − | 27.2580i | 0.379380 | − | 1.18068i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 38.2233 | + | 10.2419i | 1.65254 | + | 0.442795i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.732997 | − | 15.9441i | 0.0316312 | − | 0.688041i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.8877 | + | 6.40069i | −1.02892 | + | 0.275697i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.97355 | − | 4.97355i | −0.213829 | − | 0.213829i | 0.592063 | − | 0.805892i | \(-0.298314\pi\) |
−0.805892 | + | 0.592063i | \(0.798314\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.8995 | − | 20.1454i | 0.553569 | − | 0.864521i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.6138 | −1.01150 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.15870 | 0.0922995 | 0.0461497 | − | 0.998935i | \(-0.485305\pi\) | ||||
0.0461497 | + | 0.998935i | \(0.485305\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.819152 | − | 0.0754770i | −0.0349606 | − | 0.00322128i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.19818 | + | 3.19818i | 0.136247 | + | 0.136247i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.47999 | − | 1.46836i | 0.233033 | − | 0.0624409i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 23.9472 | + | 1.10092i | 1.01650 | + | 0.0467315i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.17782 | + | 0.583545i | 0.0922772 | + | 0.0247256i | 0.304662 | − | 0.952460i | \(-0.401456\pi\) |
−0.212385 | + | 0.977186i | \(0.568123\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.91003 | − | 3.81072i | −0.249968 | − | 0.161176i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.5581 | + | 5.38497i | −1.03684 | + | 0.227354i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.1490 | + | 31.4349i | −0.764888 | + | 1.32482i | 0.175418 | + | 0.984494i | \(0.443872\pi\) |
−0.940306 | + | 0.340330i | \(0.889461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.3181 | + | 49.7038i | 0.560297 | + | 2.09106i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.9227 | − | 29.1518i | 0.584698 | − | 1.22426i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.5376 | − | 33.8400i | −0.819057 | − | 1.41865i | −0.906378 | − | 0.422468i | \(-0.861164\pi\) |
0.0873209 | − | 0.996180i | \(-0.472169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 31.9061i | 1.33523i | 0.744508 | + | 0.667614i | \(0.232684\pi\) | ||||
−0.744508 | + | 0.667614i | \(0.767316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0767 | − | 34.9215i | −0.755165 | − | 1.45887i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.32119 | − | 4.80424i | 0.347018 | − | 0.200351i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.31011 | − | 9.31011i | 0.387585 | − | 0.387585i | −0.486240 | − | 0.873825i | \(-0.661632\pi\) |
0.873825 | + | 0.486240i | \(0.161632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.6525 | + | 23.3975i | −1.06608 | + | 0.972366i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.3836 | + | 6.57233i | 0.472271 | + | 0.272666i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.85495 | + | 29.3151i | −0.325319 | + | 1.21411i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −12.1181 | + | 28.4409i | −0.501021 | + | 1.17589i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.58008 | − | 28.2892i | 0.312863 | − | 1.16762i | −0.613099 | − | 0.790006i | \(-0.710077\pi\) |
0.925962 | − | 0.377615i | \(-0.123256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.35059 | + | 1.93446i | 0.138058 | + | 0.0797081i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.8501 | − | 21.7536i | 0.981064 | − | 0.894824i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.7368 | − | 12.7368i | 0.523037 | − | 0.523037i | −0.395450 | − | 0.918487i | \(-0.629411\pi\) |
0.918487 | + | 0.395450i | \(0.129411\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.6886 | − | 17.7181i | 1.25811 | − | 0.726370i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.59128 | + | 6.93783i | 0.146981 | + | 0.283946i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.6579i | 0.639764i | 0.947457 | + | 0.319882i | \(0.103643\pi\) | ||||
−0.947457 | + | 0.319882i | \(0.896357\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.99832 | − | 6.92529i | −0.163095 | − | 0.282488i | 0.772882 | − | 0.634549i | \(-0.218814\pi\) |
−0.935977 | + | 0.352061i | \(0.885481\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.15396 | − | 12.5542i | −0.0877160 | − | 0.511247i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.92677 | − | 18.3869i | −0.200302 | − | 0.747535i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.24581 | − | 3.88985i | 0.0911545 | − | 0.157884i | −0.816843 | − | 0.576860i | \(-0.804278\pi\) |
0.907997 | + | 0.418976i | \(0.137611\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.2320 | − | 2.68217i | 0.495665 | − | 0.108687i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.61719 | − | 3.27832i | 0.146336 | − | 0.132627i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.5112 | + | 8.17546i | 1.23234 | + | 0.330204i | 0.815489 | − | 0.578773i | \(-0.196468\pi\) |
0.416848 | + | 0.908976i | \(0.363135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 39.2678 | + | 1.80525i | 1.58343 | + | 0.0727948i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.23513 | − | 1.40275i | 0.210758 | − | 0.0564725i | −0.151895 | − | 0.988397i | \(-0.548538\pi\) |
0.362653 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.22455 | − | 7.22455i | −0.290379 | − | 0.290379i | 0.546851 | − | 0.837230i | \(-0.315826\pi\) |
−0.837230 | + | 0.546851i | \(0.815826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.5986 | − | 5.92890i | 0.585823 | − | 0.237919i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 35.3382 | 1.41580 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 30.8029 | 1.23212 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.81388 | + | 13.7648i | −0.351992 | + | 0.549715i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 11.8276 | + | 11.8276i | 0.471596 | + | 0.471596i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 20.2844 | − | 5.43520i | 0.807511 | − | 0.216372i | 0.168632 | − | 0.985679i | \(-0.446065\pi\) |
0.638879 | + | 0.769307i | \(0.279398\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.682229 | − | 14.8398i | 0.0271162 | − | 0.589830i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −57.1277 | − | 15.3073i | −2.26705 | − | 0.607453i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18.8739 | + | 9.69426i | −0.747811 | + | 0.384100i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 21.1599 | + | 25.4550i | 0.837072 | + | 1.00698i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.3437 | − | 36.9683i | 0.843024 | − | 1.46016i | −0.0443019 | − | 0.999018i | \(-0.514106\pi\) |
0.887326 | − | 0.461143i | \(-0.152560\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.813185 | + | 3.03485i | 0.0320689 | + | 0.119683i | 0.980105 | − | 0.198481i | \(-0.0636007\pi\) |
−0.948036 | + | 0.318163i | \(0.896934\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.92452 | − | 9.20130i | 0.115153 | − | 0.362301i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.2351 | + | 31.5841i | 0.716895 | + | 1.24170i | 0.962224 | + | 0.272258i | \(0.0877705\pi\) |
−0.245329 | + | 0.969440i | \(0.578896\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 43.2361i | 1.69717i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.51297 | − | 4.92427i | 0.372843 | − | 0.192998i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.3421 | + | 22.7142i | −1.53957 | + | 0.888874i | −0.540711 | + | 0.841208i | \(0.681845\pi\) |
−0.998863 | + | 0.0476658i | \(0.984822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.46410 | − | 9.46410i | 0.369793 | − | 0.369793i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.8153 | + | 40.1275i | −0.577999 | + | 1.56552i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11.4858 | + | 6.63132i | 0.447422 | + | 0.258319i | 0.706741 | − | 0.707472i | \(-0.250165\pi\) |
−0.259319 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.40763 | − | 8.98541i | 0.0936460 | − | 0.349492i | −0.903165 | − | 0.429294i | \(-0.858762\pi\) |
0.996811 | + | 0.0798025i | \(0.0254290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.6200 | + | 8.96385i | −0.761979 | + | 0.348127i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.96256 | − | 22.2526i | 0.231218 | − | 0.862918i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.28941 | + | 3.05384i | 0.204807 | + | 0.118245i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.5996 | − | 26.9704i | −0.951075 | − | 1.04274i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.814821 | − | 0.814821i | 0.0314558 | − | 0.0314558i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.9273 | + | 13.2371i | −0.883782 | + | 0.510252i | −0.871904 | − | 0.489678i | \(-0.837114\pi\) |
−0.0118785 | + | 0.999929i | \(0.503781\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.3086 | − | 2.26202i | −0.627719 | − | 0.0870650i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0789i | 1.57879i | 0.613885 | + | 0.789396i | \(0.289606\pi\) | ||||
−0.613885 | + | 0.789396i | \(0.710394\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.3986 | + | 24.9390i | 0.552566 | + | 0.957073i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.29751 | + | 2.63726i | 0.317961 | + | 0.101060i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.54160 | + | 5.75334i | 0.0589878 | + | 0.220145i | 0.989128 | − | 0.147060i | \(-0.0469812\pi\) |
−0.930140 | + | 0.367206i | \(0.880315\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.83113 | − | 13.5639i | 0.299212 | − | 0.518250i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.20704 | − | 23.7466i | −0.198661 | − | 0.905989i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.27810 | + | 26.0074i | −0.0486917 | + | 0.990803i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.6429 | − | 7.40689i | −1.05159 | − | 0.281771i | −0.308679 | − | 0.951166i | \(-0.599887\pi\) |
−0.742907 | + | 0.669395i | \(0.766553\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.9358 | + | 41.1020i | 0.719311 | + | 1.56134i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −40.5636 | + | 10.8690i | −1.53866 | + | 0.412284i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.3944 | + | 19.3944i | 0.734617 | + | 0.734617i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.4143 | − | 17.5539i | −1.03691 | − | 0.663950i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.672924 | 0.0254160 | 0.0127080 | − | 0.999919i | \(-0.495955\pi\) | ||||
0.0127080 | + | 0.999919i | \(0.495955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.8743 | 0.410131 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.64454 | + | 3.61430i | 0.212586 | + | 0.136123i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.34758 | + | 5.34758i | 0.201116 | + | 0.201116i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.5534 | − | 7.91881i | 1.10990 | − | 0.297397i | 0.343111 | − | 0.939295i | \(-0.388519\pi\) |
0.766790 | + | 0.641898i | \(0.221853\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.98400 | − | 4.30648i | −0.0744060 | − | 0.161506i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.04653 | + | 1.35221i | 0.188994 | + | 0.0506408i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −19.7859 | − | 38.5214i | −0.739950 | − | 1.44062i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.57884 | + | 16.3212i | 0.133654 | + | 0.609528i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5566 | − | 20.0165i | 0.430987 | − | 0.746491i | −0.565972 | − | 0.824425i | \(-0.691499\pi\) |
0.996959 | + | 0.0779336i | \(0.0248322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.2508 | − | 49.4528i | −0.493487 | − | 1.84172i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 13.9929 | + | 4.44747i | 0.520402 | + | 0.165403i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.19108 | − | 5.52711i | −0.118514 | − | 0.205272i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 11.5379i | − | 0.427917i | −0.976843 | − | 0.213959i | \(-0.931364\pi\) | ||
0.976843 | − | 0.213959i | \(-0.0686357\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9808 | − | 7.34847i | −0.962250 | − | 0.272166i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.83411 | − | 3.36832i | 0.215782 | − | 0.124582i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.910162 | + | 0.910162i | −0.0336176 | + | 0.0336176i | −0.723716 | − | 0.690098i | \(-0.757567\pi\) |
0.690098 | + | 0.723716i | \(0.257567\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −19.6316 | − | 21.5236i | −0.724121 | − | 0.793909i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 15.4524 | + | 8.92147i | 0.569198 | + | 0.328626i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.23160 | − | 12.0605i | 0.118876 | − | 0.443652i | −0.880671 | − | 0.473728i | \(-0.842908\pi\) |
0.999548 | + | 0.0300754i | \(0.00957473\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.89866 | + | 13.1400i | −0.179957 | + | 0.482711i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.8573 | + | 44.2519i | −0.435001 | + | 1.62345i | 0.306063 | + | 0.952011i | \(0.400988\pi\) |
−0.741064 | + | 0.671435i | \(0.765678\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.5802 | − | 14.7687i | −0.937185 | − | 0.541084i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.80496 | − | 10.3058i | 0.139216 | − | 0.377070i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 35.1425 | − | 35.1425i | 1.28408 | − | 1.28408i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8766 | + | 8.01168i | −0.506366 | + | 0.292350i | −0.731338 | − | 0.682015i | \(-0.761104\pi\) |
0.224973 | + | 0.974365i | \(0.427771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.8285 | + | 5.60523i | −0.394611 | + | 0.204266i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 26.2295i | − | 0.954588i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.6277 | + | 27.0680i | 0.567998 | + | 0.983802i | 0.996764 | + | 0.0803861i | \(0.0256153\pi\) |
−0.428765 | + | 0.903416i | \(0.641051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.68572 | + | 21.0350i | −0.242676 | + | 0.763523i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.45283 | − | 16.6182i | −0.161415 | − | 0.602409i | −0.998470 | − | 0.0552906i | \(-0.982391\pi\) |
0.837055 | − | 0.547118i | \(-0.184275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.8286 | + | 25.6839i | −0.536832 | + | 0.929820i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −18.9320 | − | 22.7749i | −0.684488 | − | 0.823428i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.83066 | + | 36.2595i | 0.282749 | + | 1.30925i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.224553 | + | 0.0601687i | 0.00809758 | + | 0.00216974i | 0.262866 | − | 0.964832i | \(-0.415332\pi\) |
−0.254768 | + | 0.967002i | \(0.581999\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.129813 | + | 2.82370i | −0.00467512 | + | 0.101693i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −42.7466 | + | 11.4539i | −1.53749 | + | 0.411968i | −0.925453 | − | 0.378863i | \(-0.876315\pi\) |
−0.612034 | + | 0.790831i | \(0.709648\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.86034 | − | 3.86034i | −0.138667 | − | 0.138667i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.2354 | − | 25.3552i | 0.582441 | − | 0.909612i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 17.8313 | 0.638872 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −46.3684 | −1.65919 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.93810 | − | 9.69672i | −0.140736 | − | 0.346533i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.5828 | + | 28.5828i | 1.02017 | + | 1.02017i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.4083 | + | 5.46839i | −0.727478 | + | 0.194927i | −0.603506 | − | 0.797358i | \(-0.706230\pi\) |
−0.123972 | + | 0.992286i | \(0.539563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2849 | − | 0.840607i | −0.650959 | − | 0.0299264i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 62.4244 | + | 16.7266i | 2.21955 | + | 0.594728i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.535765 | − | 0.830916i | 0.0190256 | − | 0.0295067i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −34.9210 | + | 7.65732i | −1.23852 | + | 0.271577i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.0370 | − | 20.8487i | 0.426373 | − | 0.738501i | −0.570174 | − | 0.821524i | \(-0.693124\pi\) |
0.996548 | + | 0.0830233i | \(0.0264576\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.21041 | + | 4.51731i | 0.0428212 | + | 0.159811i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.99431 | − | 29.1090i | −0.176465 | − | 1.02852i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.9598 | − | 51.8918i | −1.05726 | − | 1.83122i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 31.1097i | − | 1.09647i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.86234 | + | 13.2570i | 0.241566 | + | 0.466669i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 22.2703 | − | 12.8578i | 0.782982 | − | 0.452055i | −0.0545042 | − | 0.998514i | \(-0.517358\pi\) |
0.837486 | + | 0.546459i | \(0.184025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.99463 | + | 5.99463i | −0.210500 | + | 0.210500i | −0.804480 | − | 0.593980i | \(-0.797556\pi\) |
0.593980 | + | 0.804480i | \(0.297556\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.3790 | + | 23.1481i | −0.890080 | + | 0.811838i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.75821 | + | 1.59245i | 0.0966157 | + | 0.0557811i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.13352 | − | 4.23037i | 0.0396570 | − | 0.148002i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 23.3244 | + | 31.0402i | 0.815021 | + | 1.08463i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13.7528 | + | 51.3262i | −0.479977 | + | 1.79130i | 0.121710 | + | 0.992566i | \(0.461162\pi\) |
−0.601687 | + | 0.798732i | \(0.705504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.92634 | + | 5.73097i | 0.346010 | + | 0.199769i | 0.662927 | − | 0.748684i | \(-0.269314\pi\) |
−0.316916 | + | 0.948454i | \(0.602647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.0404 | − | 15.5424i | 0.593269 | − | 0.541118i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.57665 | + | 4.57665i | −0.159146 | + | 0.159146i | −0.782188 | − | 0.623042i | \(-0.785896\pi\) |
0.623042 | + | 0.782188i | \(0.285896\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.2625 | − | 24.9776i | 1.50257 | − | 0.867509i | 0.502574 | − | 0.864534i | \(-0.332387\pi\) |
0.999996 | − | 0.00297446i | \(-0.000946803\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.3434 | − | 23.8457i | −0.428189 | − | 0.827198i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 20.3266i | − | 0.704275i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.98133 | − | 13.8241i | −0.276205 | − | 0.478401i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.40071 | − | 7.14013i | −0.186676 | − | 0.246799i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.00183 | − | 11.2030i | −0.103635 | − | 0.386770i | 0.894552 | − | 0.446964i | \(-0.147495\pi\) |
−0.998187 | + | 0.0601939i | \(0.980828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.4716 | + | 21.6014i | −0.430054 | + | 0.744876i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.5806 | − | 6.26702i | 0.984369 | − | 0.215848i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.5700 | − | 28.7221i | −0.810832 | − | 0.988069i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.0926 | − | 6.18765i | −0.793472 | − | 0.212610i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.73327 | + | 0.125656i | 0.0938055 | + | 0.00431250i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.1841 | − | 3.80063i | 0.486226 | − | 0.130284i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.56247 | − | 1.56247i | −0.0534978 | − | 0.0534978i | 0.679852 | − | 0.733350i | \(-0.262044\pi\) |
−0.733350 | + | 0.679852i | \(0.762044\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.1727 | − | 1.76658i | −0.655692 | − | 0.0604157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.5804 | 0.737174 | 0.368587 | − | 0.929593i | \(-0.379842\pi\) | ||||
0.368587 | + | 0.929593i | \(0.379842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.5544 | −0.360110 | −0.180055 | − | 0.983657i | \(-0.557628\pi\) | ||||
−0.180055 | + | 0.983657i | \(0.557628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.6223 | − | 41.5766i | 0.907284 | − | 1.41693i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.4177 | − | 21.4177i | −0.729066 | − | 0.729066i | 0.241368 | − | 0.970434i | \(-0.422404\pi\) |
−0.970434 | + | 0.241368i | \(0.922404\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 48.2992 | − | 12.9417i | 1.64222 | − | 0.440032i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.403231 | + | 8.77108i | −0.0136944 | + | 0.297881i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.41562 | + | 1.71906i | 0.217635 | + | 0.0583152i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.5748 | + | 4.68323i | 0.493848 | + | 0.158685i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 18.5080 | − | 15.3851i | 0.626400 | − | 0.520706i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.39415 | − | 16.2711i | 0.317580 | − | 0.550065i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.1109 | + | 37.7342i | 0.341420 | + | 1.27419i | 0.896740 | + | 0.442558i | \(0.145929\pi\) |
−0.555320 | + | 0.831637i | \(0.687404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.04883 | + | 6.44617i | −0.0691054 | + | 0.217424i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.39708 | + | 5.88391i | 0.114450 | + | 0.198234i | 0.917560 | − | 0.397598i | \(-0.130156\pi\) |
−0.803110 | + | 0.595831i | \(0.796823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.6560i | 1.36818i | 0.729397 | + | 0.684091i | \(0.239801\pi\) | ||||
−0.729397 | + | 0.684091i | \(0.760199\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −45.2307 | + | 23.4131i | −1.52041 | + | 0.787023i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.04299 | + | 5.22097i | −0.303634 | + | 0.175303i | −0.644074 | − | 0.764963i | \(-0.722757\pi\) |
0.340440 | + | 0.940266i | \(0.389424\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.5233 | + | 52.5233i | −1.76158 | + | 1.76158i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.1806 | − | 21.4068i | 1.04459 | − | 0.717154i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.63304 | + | 1.52018i | 0.0881112 | + | 0.0508710i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.81664 | + | 25.4400i | −0.227855 | + | 0.850367i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.79716 | + | 18.8517i | −0.0600056 | + | 0.629438i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.898169 | − | 3.35201i | 0.0299556 | − | 0.111796i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.6029 | − | 12.4724i | −0.719697 | − | 0.415517i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.17144 | − | 8.95897i | −0.271928 | − | 0.298136i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.9116 | + | 27.9116i | −0.927814 | + | 0.927814i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.9759 | − | 19.6160i | 1.12815 | − | 0.651338i | 0.184681 | − | 0.982799i | \(-0.440875\pi\) |
0.943469 | + | 0.331461i | \(0.107542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.64917 | − | 5.16071i | 0.121035 | − | 0.171170i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.0923i | − | 1.06326i | −0.846975 | − | 0.531632i | \(-0.821579\pi\) | ||
0.846975 | − | 0.531632i | \(-0.178421\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.69447 | + | 13.3272i | 0.254650 | + | 0.441066i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.29365 | + | 0.411170i | 0.0427667 | + | 0.0135929i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.35066 | − | 16.2369i | −0.143671 | − | 0.536189i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.6421 | − | 28.8249i | 0.548972 | − | 0.950847i | −0.449374 | − | 0.893344i | \(-0.648353\pi\) |
0.998345 | − | 0.0575028i | \(-0.0183138\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.4370 | − | 52.1582i | −0.376862 | − | 1.71867i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −38.8863 | + | 8.39796i | −1.27996 | + | 0.276422i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.8216 | − | 3.97143i | −0.487330 | − | 0.130580i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −38.8628 | + | 17.9042i | −1.27642 | + | 0.588049i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2156 | − | 5.68470i | 0.696060 | − | 0.186509i | 0.106595 | − | 0.994303i | \(-0.466005\pi\) |
0.589465 | + | 0.807794i | \(0.299338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.34415 | − | 9.34415i | −0.306242 | − | 0.306242i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.5288 | − | 19.5481i | −0.999467 | − | 0.639978i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 41.4864 | 1.35675 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.9423 | 1.82755 | 0.913777 | − | 0.406216i | \(-0.133152\pi\) | ||||
0.913777 | + | 0.406216i | \(0.133152\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −47.6518 | − | 30.5123i | −1.55506 | − | 0.995732i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.1600 | − | 17.1600i | −0.559401 | − | 0.559401i | 0.369736 | − | 0.929137i | \(-0.379448\pi\) |
−0.929137 | + | 0.369736i | \(0.879448\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.2587 | − | 6.23215i | 0.757407 | − | 0.202947i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −32.7441 | + | 42.0668i | −1.06516 | + | 1.36843i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 46.0604 | + | 12.3419i | 1.49676 | + | 0.401056i | 0.912014 | − | 0.410159i | \(-0.134527\pi\) |
0.584748 | + | 0.811215i | \(0.301193\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −34.5237 | − | 38.0924i | −1.12069 | − | 1.23653i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.73386 | − | 12.4677i | −0.0886516 | − | 0.404293i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.5278 | + | 37.2872i | −0.697353 | + | 1.20785i | 0.272029 | + | 0.962289i | \(0.412305\pi\) |
−0.969381 | + | 0.245561i | \(0.921028\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.7940 | + | 62.6761i | 0.543441 | + | 2.02815i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.9719 | + | 4.44080i | 0.451648 | + | 0.143551i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.83532 | − | 17.0353i | −0.317599 | − | 0.550098i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.0315i | 0.904242i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −33.9144 | − | 23.9811i | −1.09288 | − | 0.772781i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49.6166 | − | 28.6461i | 1.59721 | − | 0.922152i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.96226 | − | 4.96226i | 0.159576 | − | 0.159576i | −0.622803 | − | 0.782379i | \(-0.714006\pi\) |
0.782379 | + | 0.622803i | \(0.214006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.05322 | − | 9.92573i | −0.290831 | − | 0.318861i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.5285 | − | 15.8936i | −0.883432 | − | 0.510050i | −0.0116437 | − | 0.999932i | \(-0.503706\pi\) |
−0.871789 | + | 0.489882i | \(0.837040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −13.6506 | + | 50.9448i | −0.437619 | + | 1.63322i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.4758 | − | 16.1207i | 0.367518 | − | 0.516277i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.80392 | + | 6.73232i | −0.0577125 | + | 0.215386i | −0.988760 | − | 0.149512i | \(-0.952230\pi\) |
0.931047 | + | 0.364898i | \(0.118896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.8290 | + | 20.6859i | 1.14510 | + | 0.661124i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.2522 | + | 8.58482i | 0.742385 | + | 0.274092i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.5636 | − | 10.5636i | 0.336926 | − | 0.336926i | −0.518283 | − | 0.855209i | \(-0.673429\pi\) |
0.855209 | + | 0.518283i | \(0.173429\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.1306 | + | 26.6335i | −1.46984 | + | 0.848614i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.47571 | − | 3.86971i | 0.237954 | − | 0.123174i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 5.91416i | − | 0.188059i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.1927 | + | 22.8505i | 0.419081 | + | 0.725870i | 0.995847 | − | 0.0910396i | \(-0.0290190\pi\) |
−0.576766 | + | 0.816909i | \(0.695686\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.56810 | − | 30.1038i | 0.303635 | − | 0.955315i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.33645 | − | 12.4518i | −0.105773 | − | 0.394749i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.6325 | + | 25.3443i | −0.463416 | + | 0.802660i | −0.999129 | − | 0.0417401i | \(-0.986710\pi\) |
0.535712 | + | 0.844401i | \(0.320043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −23.1802 | − | 9.79008i | −0.733390 | − | 0.309744i |
(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 | 624.2.cn.d.353.4 | 16 | ||
3.2 | odd | 2 | inner | 624.2.cn.d.353.3 | 16 | ||
4.3 | odd | 2 | 78.2.k.a.41.3 | yes | 16 | ||
12.11 | even | 2 | 78.2.k.a.41.1 | ✓ | 16 | ||
13.7 | odd | 12 | inner | 624.2.cn.d.449.3 | 16 | ||
39.20 | even | 12 | inner | 624.2.cn.d.449.4 | 16 | ||
52.3 | odd | 6 | 1014.2.g.c.239.8 | 16 | |||
52.7 | even | 12 | 78.2.k.a.59.1 | yes | 16 | ||
52.11 | even | 12 | 1014.2.g.c.437.4 | 16 | |||
52.15 | even | 12 | 1014.2.g.d.437.8 | 16 | |||
52.23 | odd | 6 | 1014.2.g.d.239.4 | 16 | |||
156.11 | odd | 12 | 1014.2.g.c.437.8 | 16 | |||
156.23 | even | 6 | 1014.2.g.d.239.8 | 16 | |||
156.59 | odd | 12 | 78.2.k.a.59.3 | yes | 16 | ||
156.107 | even | 6 | 1014.2.g.c.239.4 | 16 | |||
156.119 | odd | 12 | 1014.2.g.d.437.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
78.2.k.a.41.1 | ✓ | 16 | 12.11 | even | 2 | ||
78.2.k.a.41.3 | yes | 16 | 4.3 | odd | 2 | ||
78.2.k.a.59.1 | yes | 16 | 52.7 | even | 12 | ||
78.2.k.a.59.3 | yes | 16 | 156.59 | odd | 12 | ||
624.2.cn.d.353.3 | 16 | 3.2 | odd | 2 | inner | ||
624.2.cn.d.353.4 | 16 | 1.1 | even | 1 | trivial | ||
624.2.cn.d.449.3 | 16 | 13.7 | odd | 12 | inner | ||
624.2.cn.d.449.4 | 16 | 39.20 | even | 12 | inner | ||
1014.2.g.c.239.4 | 16 | 156.107 | even | 6 | |||
1014.2.g.c.239.8 | 16 | 52.3 | odd | 6 | |||
1014.2.g.c.437.4 | 16 | 52.11 | even | 12 | |||
1014.2.g.c.437.8 | 16 | 156.11 | odd | 12 | |||
1014.2.g.d.239.4 | 16 | 52.23 | odd | 6 | |||
1014.2.g.d.239.8 | 16 | 156.23 | even | 6 | |||
1014.2.g.d.437.4 | 16 | 156.119 | odd | 12 | |||
1014.2.g.d.437.8 | 16 | 52.15 | even | 12 |