Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(19,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([10, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.x (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: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 19.7 | ||
Character | \(\chi\) | \(=\) | 637.19 |
Dual form | 637.2.x.b.570.8 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.26733 | + | 0.607529i | 1.60324 | + | 0.429588i | 0.946020 | − | 0.324108i | \(-0.105064\pi\) |
0.657223 | + | 0.753696i | \(0.271731\pi\) | |||||||
\(3\) | − | 2.76026i | − | 1.59364i | −0.604219 | − | 0.796818i | \(-0.706515\pi\) | ||
0.604219 | − | 0.796818i | \(-0.293485\pi\) | |||||||
\(4\) | 3.03963 | + | 1.75493i | 1.51982 | + | 0.877467i | ||||
\(5\) | 1.53921 | − | 0.412430i | 0.688355 | − | 0.184444i | 0.102346 | − | 0.994749i | \(-0.467365\pi\) |
0.586009 | + | 0.810305i | \(0.300698\pi\) | |||||||
\(6\) | 1.67694 | − | 6.25841i | 0.684607 | − | 2.55499i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.50608 | + | 2.50608i | 0.886032 | + | 0.886032i | ||||
\(9\) | −4.61904 | −1.53968 | ||||||||
\(10\) | 3.74046 | 1.18284 | ||||||||
\(11\) | 2.22138 | + | 2.22138i | 0.669770 | + | 0.669770i | 0.957663 | − | 0.287892i | \(-0.0929546\pi\) |
−0.287892 | + | 0.957663i | \(0.592955\pi\) | |||||||
\(12\) | 4.84407 | − | 8.39018i | 1.39836 | − | 2.42204i | ||||
\(13\) | 1.04831 | + | 3.44979i | 0.290748 | + | 0.956800i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.13841 | − | 4.24862i | −0.293937 | − | 1.09699i | ||||
\(16\) | 0.649718 | + | 1.12534i | 0.162430 | + | 0.281336i | ||||
\(17\) | −0.320795 | + | 0.555633i | −0.0778042 | + | 0.134761i | −0.902302 | − | 0.431104i | \(-0.858124\pi\) |
0.824498 | + | 0.565865i | \(0.191458\pi\) | |||||||
\(18\) | −10.4729 | − | 2.80620i | −2.46848 | − | 0.661427i | ||||
\(19\) | −5.57436 | − | 5.57436i | −1.27885 | − | 1.27885i | −0.941314 | − | 0.337532i | \(-0.890408\pi\) |
−0.337532 | − | 0.941314i | \(-0.609592\pi\) | |||||||
\(20\) | 5.40242 | + | 1.44757i | 1.20802 | + | 0.323687i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.68704 | + | 6.38614i | 0.786080 | + | 1.36153i | ||||
\(23\) | 0.126569 | − | 0.0730744i | 0.0263914 | − | 0.0152371i | −0.486746 | − | 0.873543i | \(-0.661816\pi\) |
0.513138 | + | 0.858306i | \(0.328483\pi\) | |||||||
\(24\) | 6.91743 | − | 6.91743i | 1.41201 | − | 1.41201i | ||||
\(25\) | −2.13106 | + | 1.23037i | −0.426212 | + | 0.246074i | ||||
\(26\) | 0.281008 | + | 8.45868i | 0.0551103 | + | 1.65888i | ||||
\(27\) | 4.46896i | 0.860051i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.49412 | − | 2.58790i | 0.277452 | − | 0.480561i | −0.693299 | − | 0.720650i | \(-0.743843\pi\) |
0.970751 | + | 0.240089i | \(0.0771768\pi\) | |||||||
\(30\) | − | 10.3246i | − | 1.88501i | ||||||
\(31\) | −1.73252 | + | 6.46586i | −0.311170 | + | 1.16130i | 0.616333 | + | 0.787486i | \(0.288618\pi\) |
−0.927503 | + | 0.373817i | \(0.878049\pi\) | |||||||
\(32\) | −1.04513 | − | 3.90048i | −0.184755 | − | 0.689514i | ||||
\(33\) | 6.13158 | − | 6.13158i | 1.06737 | − | 1.06737i | ||||
\(34\) | −1.06491 | + | 1.06491i | −0.182631 | + | 0.182631i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −14.0402 | − | 8.10610i | −2.34003 | − | 1.35102i | ||||
\(37\) | −1.00675 | + | 3.75725i | −0.165509 | + | 0.617688i | 0.832466 | + | 0.554077i | \(0.186929\pi\) |
−0.997975 | + | 0.0636115i | \(0.979738\pi\) | |||||||
\(38\) | −9.25232 | − | 16.0255i | −1.50092 | − | 2.59968i | ||||
\(39\) | 9.52232 | − | 2.89360i | 1.52479 | − | 0.463347i | ||||
\(40\) | 4.89096 | + | 2.82380i | 0.773328 | + | 0.446481i | ||||
\(41\) | −5.60356 | + | 1.50147i | −0.875129 | + | 0.234490i | −0.668305 | − | 0.743888i | \(-0.732980\pi\) |
−0.206825 | + | 0.978378i | \(0.566313\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.42713 | − | 1.40130i | 0.370133 | − | 0.213697i | −0.303383 | − | 0.952869i | \(-0.598116\pi\) |
0.673517 | + | 0.739172i | \(0.264783\pi\) | |||||||
\(44\) | 2.85380 | + | 10.6505i | 0.430227 | + | 1.60563i | ||||
\(45\) | −7.10966 | + | 1.90503i | −1.05985 | + | 0.283985i | ||||
\(46\) | 0.331367 | − | 0.0887896i | 0.0488574 | − | 0.0130913i | ||||
\(47\) | 0.816005 | + | 3.04537i | 0.119027 | + | 0.444213i | 0.999557 | − | 0.0297773i | \(-0.00947981\pi\) |
−0.880530 | + | 0.473990i | \(0.842813\pi\) | |||||||
\(48\) | 3.10624 | − | 1.79339i | 0.448348 | − | 0.258854i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.57930 | + | 1.49497i | −0.789032 | + | 0.211420i | ||||
\(51\) | 1.53369 | + | 0.885477i | 0.214760 | + | 0.123992i | ||||
\(52\) | −2.86768 | + | 12.3258i | −0.397676 | + | 1.70928i | ||||
\(53\) | 3.66059 | + | 6.34033i | 0.502821 | + | 0.870912i | 0.999995 | + | 0.00326078i | \(0.00103794\pi\) |
−0.497173 | + | 0.867651i | \(0.665629\pi\) | |||||||
\(54\) | −2.71502 | + | 10.1326i | −0.369467 | + | 1.37887i | ||||
\(55\) | 4.33533 | + | 2.50300i | 0.584575 | + | 0.337505i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.3867 | + | 15.3867i | −2.03802 | + | 2.03802i | ||||
\(58\) | 4.95989 | − | 4.95989i | 0.651266 | − | 0.651266i | ||||
\(59\) | −1.07349 | − | 4.00631i | −0.139756 | − | 0.521578i | −0.999933 | − | 0.0115814i | \(-0.996313\pi\) |
0.860177 | − | 0.509996i | \(-0.170353\pi\) | |||||||
\(60\) | 3.99568 | − | 14.9121i | 0.515840 | − | 1.92514i | ||||
\(61\) | 4.50671i | 0.577025i | 0.957476 | + | 0.288512i | \(0.0931607\pi\) | ||||
−0.957476 | + | 0.288512i | \(0.906839\pi\) | |||||||
\(62\) | −7.85639 | + | 13.6077i | −0.997763 | + | 1.72818i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 12.0775i | − | 1.50969i | ||||||
\(65\) | 3.03636 | + | 4.87760i | 0.376614 | + | 0.604991i | ||||
\(66\) | 17.6274 | − | 10.1772i | 2.16978 | − | 1.25273i | ||||
\(67\) | −1.00126 | + | 1.00126i | −0.122323 | + | 0.122323i | −0.765618 | − | 0.643295i | \(-0.777567\pi\) |
0.643295 | + | 0.765618i | \(0.277567\pi\) | |||||||
\(68\) | −1.95020 | + | 1.12595i | −0.236496 | + | 0.136541i | ||||
\(69\) | −0.201704 | − | 0.349362i | −0.0242823 | − | 0.0420582i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.8300 | + | 3.70574i | 1.64132 | + | 0.439791i | 0.957165 | − | 0.289544i | \(-0.0935038\pi\) |
0.684157 | + | 0.729335i | \(0.260170\pi\) | |||||||
\(72\) | −11.5757 | − | 11.5757i | −1.36420 | − | 1.36420i | ||||
\(73\) | 6.81760 | + | 1.82677i | 0.797940 | + | 0.213807i | 0.634679 | − | 0.772776i | \(-0.281132\pi\) |
0.163261 | + | 0.986583i | \(0.447799\pi\) | |||||||
\(74\) | −4.56527 | + | 7.90729i | −0.530702 | + | 0.919203i | ||||
\(75\) | 3.39614 | + | 5.88228i | 0.392152 | + | 0.679227i | ||||
\(76\) | −7.16138 | − | 26.7267i | −0.821467 | − | 3.06576i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 23.3482 | − | 0.775656i | 2.64366 | − | 0.0878258i | ||||
\(79\) | 0.316458 | − | 0.548121i | 0.0356043 | − | 0.0616685i | −0.847674 | − | 0.530517i | \(-0.821998\pi\) |
0.883278 | + | 0.468849i | \(0.155331\pi\) | |||||||
\(80\) | 1.46418 | + | 1.46418i | 0.163700 | + | 0.163700i | ||||
\(81\) | −1.52162 | −0.169069 | ||||||||
\(82\) | −13.6173 | −1.50378 | ||||||||
\(83\) | −1.07813 | − | 1.07813i | −0.118340 | − | 0.118340i | 0.645457 | − | 0.763797i | \(-0.276667\pi\) |
−0.763797 | + | 0.645457i | \(0.776667\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.264611 | + | 0.987541i | −0.0287011 | + | 0.107114i | ||||
\(86\) | 6.35443 | − | 1.70266i | 0.685215 | − | 0.183603i | ||||
\(87\) | −7.14327 | − | 4.12417i | −0.765839 | − | 0.442158i | ||||
\(88\) | 11.1339i | 1.18688i | ||||||||
\(89\) | 13.1203 | + | 3.51557i | 1.39075 | + | 0.372649i | 0.875013 | − | 0.484099i | \(-0.160853\pi\) |
0.515734 | + | 0.856749i | \(0.327519\pi\) | |||||||
\(90\) | −17.2773 | −1.82119 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.512963 | 0.0534801 | ||||||||
\(93\) | 17.8475 | + | 4.78221i | 1.85069 | + | 0.495892i | ||||
\(94\) | 7.40060i | 0.763314i | ||||||||
\(95\) | −10.8791 | − | 6.28107i | −1.11618 | − | 0.644425i | ||||
\(96\) | −10.7663 | + | 2.88483i | −1.09884 | + | 0.294432i | ||||
\(97\) | −0.0487160 | + | 0.181811i | −0.00494637 | + | 0.0184601i | −0.968355 | − | 0.249577i | \(-0.919708\pi\) |
0.963409 | + | 0.268037i | \(0.0863750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.2606 | − | 10.2606i | −1.03123 | − | 1.03123i | ||||
\(100\) | −8.63686 | −0.863686 | ||||||||
\(101\) | −1.19381 | −0.118788 | −0.0593942 | − | 0.998235i | \(-0.518917\pi\) | ||||
−0.0593942 | + | 0.998235i | \(0.518917\pi\) | |||||||
\(102\) | 2.93943 | + | 2.93943i | 0.291047 | + | 0.291047i | ||||
\(103\) | 2.39792 | − | 4.15331i | 0.236274 | − | 0.409238i | −0.723368 | − | 0.690462i | \(-0.757407\pi\) |
0.959642 | + | 0.281224i | \(0.0907404\pi\) | |||||||
\(104\) | −6.01830 | + | 11.2726i | −0.590143 | + | 1.10537i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.44783 | + | 16.5995i | 0.432012 | + | 1.61229i | ||||
\(107\) | −7.64819 | − | 13.2471i | −0.739378 | − | 1.28064i | −0.952776 | − | 0.303675i | \(-0.901786\pi\) |
0.213397 | − | 0.976966i | \(-0.431547\pi\) | |||||||
\(108\) | −7.84273 | + | 13.5840i | −0.754667 | + | 1.30712i | ||||
\(109\) | −12.4638 | − | 3.33967i | −1.19382 | − | 0.319883i | −0.393424 | − | 0.919357i | \(-0.628710\pi\) |
−0.800394 | + | 0.599475i | \(0.795376\pi\) | |||||||
\(110\) | 8.30896 | + | 8.30896i | 0.792228 | + | 0.792228i | ||||
\(111\) | 10.3710 | + | 2.77890i | 0.984370 | + | 0.263761i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.770731 | − | 1.33494i | −0.0725042 | − | 0.125581i | 0.827494 | − | 0.561475i | \(-0.189766\pi\) |
−0.899998 | + | 0.435894i | \(0.856432\pi\) | |||||||
\(114\) | −44.2345 | + | 25.5388i | −4.14294 | + | 2.39193i | ||||
\(115\) | 0.164677 | − | 0.164677i | 0.0153562 | − | 0.0153562i | ||||
\(116\) | 9.08318 | − | 5.24418i | 0.843352 | − | 0.486910i | ||||
\(117\) | −4.84217 | − | 15.9347i | −0.447658 | − | 1.47316i | ||||
\(118\) | − | 9.73580i | − | 0.896253i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 7.79441 | − | 13.5003i | 0.711529 | − | 1.23240i | ||||
\(121\) | − | 1.13097i | − | 0.102815i | ||||||
\(122\) | −2.73796 | + | 10.2182i | −0.247883 | + | 0.925111i | ||||
\(123\) | 4.14445 | + | 15.4673i | 0.373692 | + | 1.39464i | ||||
\(124\) | −16.6134 | + | 16.6134i | −1.49193 | + | 1.49193i | ||||
\(125\) | −8.40660 | + | 8.40660i | −0.751910 | + | 0.751910i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.81842 | + | 1.62722i | 0.250095 | + | 0.144392i | 0.619808 | − | 0.784754i | \(-0.287211\pi\) |
−0.369713 | + | 0.929146i | \(0.620544\pi\) | |||||||
\(128\) | 5.24716 | − | 19.5827i | 0.463788 | − | 1.73088i | ||||
\(129\) | −3.86796 | − | 6.69950i | −0.340555 | − | 0.589858i | ||||
\(130\) | 3.92114 | + | 12.9038i | 0.343907 | + | 1.13174i | ||||
\(131\) | −14.2615 | − | 8.23390i | −1.24604 | − | 0.719400i | −0.275720 | − | 0.961238i | \(-0.588916\pi\) |
−0.970317 | + | 0.241838i | \(0.922250\pi\) | |||||||
\(132\) | 29.3983 | − | 7.87724i | 2.55879 | − | 0.685626i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.87848 | + | 1.66189i | −0.248663 | + | 0.143565i | ||||
\(135\) | 1.84313 | + | 6.87866i | 0.158632 | + | 0.592021i | ||||
\(136\) | −2.19640 | + | 0.588523i | −0.188339 | + | 0.0504654i | ||||
\(137\) | 0.365056 | − | 0.0978163i | 0.0311888 | − | 0.00835701i | −0.243191 | − | 0.969978i | \(-0.578194\pi\) |
0.274380 | + | 0.961621i | \(0.411527\pi\) | |||||||
\(138\) | −0.245082 | − | 0.914659i | −0.0208628 | − | 0.0778610i | ||||
\(139\) | 8.52132 | − | 4.91978i | 0.722769 | − | 0.417291i | −0.0930022 | − | 0.995666i | \(-0.529646\pi\) |
0.815771 | + | 0.578375i | \(0.196313\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.40602 | − | 2.25239i | 0.707914 | − | 0.189685i | ||||
\(142\) | 29.1058 | + | 16.8043i | 2.44251 | + | 1.41018i | ||||
\(143\) | −5.33460 | + | 9.99197i | −0.446102 | + | 0.835570i | ||||
\(144\) | −3.00107 | − | 5.19801i | −0.250089 | − | 0.433167i | ||||
\(145\) | 1.23244 | − | 4.59954i | 0.102349 | − | 0.381971i | ||||
\(146\) | 14.3479 | + | 8.28378i | 1.18744 | + | 0.685570i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.65388 | + | 9.65388i | −0.793544 | + | 0.793544i | ||||
\(149\) | 3.92698 | − | 3.92698i | 0.321711 | − | 0.321711i | −0.527712 | − | 0.849423i | \(-0.676950\pi\) |
0.849423 | + | 0.527712i | \(0.176950\pi\) | |||||||
\(150\) | 4.12650 | + | 15.4003i | 0.336927 | + | 1.25743i | ||||
\(151\) | 1.22809 | − | 4.58330i | 0.0999406 | − | 0.372983i | −0.897782 | − | 0.440441i | \(-0.854822\pi\) |
0.997722 | + | 0.0674576i | \(0.0214887\pi\) | |||||||
\(152\) | − | 27.9396i | − | 2.26620i | ||||||
\(153\) | 1.48176 | − | 2.56649i | 0.119793 | − | 0.207488i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6669i | 0.856782i | ||||||||
\(156\) | 34.0224 | + | 7.91556i | 2.72398 | + | 0.633752i | ||||
\(157\) | −10.9293 | + | 6.31006i | −0.872257 | + | 0.503598i | −0.868098 | − | 0.496394i | \(-0.834657\pi\) |
−0.00415919 | + | 0.999991i | \(0.501324\pi\) | |||||||
\(158\) | 1.05051 | − | 1.05051i | 0.0835744 | − | 0.0835744i | ||||
\(159\) | 17.5010 | − | 10.1042i | 1.38792 | − | 0.801314i | ||||
\(160\) | −3.21735 | − | 5.57262i | −0.254354 | − | 0.440554i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.45001 | − | 0.924428i | −0.271058 | − | 0.0726299i | ||||
\(163\) | −9.23004 | − | 9.23004i | −0.722952 | − | 0.722952i | 0.246253 | − | 0.969206i | \(-0.420801\pi\) |
−0.969206 | + | 0.246253i | \(0.920801\pi\) | |||||||
\(164\) | −19.6678 | − | 5.26996i | −1.53579 | − | 0.411515i | ||||
\(165\) | 6.90893 | − | 11.9666i | 0.537860 | − | 0.931601i | ||||
\(166\) | −1.78948 | − | 3.09948i | −0.138891 | − | 0.240566i | ||||
\(167\) | 4.79697 | + | 17.9025i | 0.371201 | + | 1.38534i | 0.858817 | + | 0.512282i | \(0.171200\pi\) |
−0.487616 | + | 0.873058i | \(0.662133\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8021 | + | 7.23288i | −0.830931 | + | 0.556375i | ||||
\(170\) | −1.19992 | + | 2.07832i | −0.0920296 | + | 0.159400i | ||||
\(171\) | 25.7482 | + | 25.7482i | 1.96901 | + | 1.96901i | ||||
\(172\) | 9.83677 | 0.750047 | ||||||||
\(173\) | −5.59369 | −0.425280 | −0.212640 | − | 0.977131i | \(-0.568206\pi\) | ||||
−0.212640 | + | 0.977131i | \(0.568206\pi\) | |||||||
\(174\) | −13.6906 | − | 13.6906i | −1.03788 | − | 1.03788i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.05655 | + | 3.94308i | −0.0796402 | + | 0.297221i | ||||
\(177\) | −11.0585 | + | 2.96311i | −0.831205 | + | 0.222721i | ||||
\(178\) | 27.6122 | + | 15.9419i | 2.06962 | + | 1.19490i | ||||
\(179\) | − | 9.49080i | − | 0.709376i | −0.934985 | − | 0.354688i | \(-0.884587\pi\) | ||
0.934985 | − | 0.354688i | \(-0.115413\pi\) | |||||||
\(180\) | −24.9540 | − | 6.68640i | −1.85996 | − | 0.498375i | ||||
\(181\) | −6.91516 | −0.514000 | −0.257000 | − | 0.966411i | \(-0.582734\pi\) | ||||
−0.257000 | + | 0.966411i | \(0.582734\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.4397 | 0.919568 | ||||||||
\(184\) | 0.500321 | + | 0.134060i | 0.0368841 | + | 0.00988307i | ||||
\(185\) | 6.19841i | 0.455716i | ||||||||
\(186\) | 37.5607 | + | 21.6857i | 2.75408 | + | 1.59007i | ||||
\(187\) | −1.94688 | + | 0.521664i | −0.142370 | + | 0.0381479i | ||||
\(188\) | −2.86407 | + | 10.6889i | −0.208884 | + | 0.779565i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.8506 | − | 20.8506i | −1.51266 | − | 1.51266i | ||||
\(191\) | −2.50503 | −0.181257 | −0.0906287 | − | 0.995885i | \(-0.528888\pi\) | ||||
−0.0906287 | + | 0.995885i | \(0.528888\pi\) | |||||||
\(192\) | −33.3370 | −2.40589 | ||||||||
\(193\) | −15.9501 | − | 15.9501i | −1.14811 | − | 1.14811i | −0.986924 | − | 0.161187i | \(-0.948468\pi\) |
−0.161187 | − | 0.986924i | \(-0.551532\pi\) | |||||||
\(194\) | −0.220911 | + | 0.382628i | −0.0158605 | + | 0.0274711i | ||||
\(195\) | 13.4634 | − | 8.38114i | 0.964136 | − | 0.600186i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.63560 | − | 17.3003i | −0.330273 | − | 1.23259i | −0.908904 | − | 0.417005i | \(-0.863080\pi\) |
0.578631 | − | 0.815589i | \(-0.303587\pi\) | |||||||
\(198\) | −17.0306 | − | 29.4978i | −1.21031 | − | 2.09632i | ||||
\(199\) | 8.20617 | − | 14.2135i | 0.581720 | − | 1.00757i | −0.413556 | − | 0.910479i | \(-0.635713\pi\) |
0.995276 | − | 0.0970896i | \(-0.0309533\pi\) | |||||||
\(200\) | −8.42400 | − | 2.25720i | −0.595667 | − | 0.159608i | ||||
\(201\) | 2.76374 | + | 2.76374i | 0.194939 | + | 0.194939i | ||||
\(202\) | −2.70675 | − | 0.725273i | −0.190447 | − | 0.0510300i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3.10791 | + | 5.38306i | 0.217597 | + | 0.376889i | ||||
\(205\) | −8.00580 | + | 4.62215i | −0.559150 | + | 0.322825i | ||||
\(206\) | 7.96012 | − | 7.96012i | 0.554608 | − | 0.554608i | ||||
\(207\) | −0.584624 | + | 0.337533i | −0.0406342 | + | 0.0234602i | ||||
\(208\) | −3.20110 | + | 3.42110i | −0.221956 | + | 0.237210i | ||||
\(209\) | − | 24.7655i | − | 1.71307i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.93176 | − | 8.54207i | 0.339517 | − | 0.588060i | −0.644825 | − | 0.764330i | \(-0.723070\pi\) |
0.984342 | + | 0.176270i | \(0.0564032\pi\) | |||||||
\(212\) | 25.6964i | 1.76484i | ||||||||
\(213\) | 10.2288 | − | 38.1744i | 0.700867 | − | 2.61567i | ||||
\(214\) | −9.29299 | − | 34.6819i | −0.635256 | − | 2.37081i | ||||
\(215\) | 3.15792 | − | 3.15792i | 0.215368 | − | 0.215368i | ||||
\(216\) | −11.1996 | + | 11.1996i | −0.762033 | + | 0.762033i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −26.2306 | − | 15.1443i | −1.77656 | − | 1.02570i | ||||
\(219\) | 5.04236 | − | 18.8184i | 0.340731 | − | 1.27163i | ||||
\(220\) | 8.78520 | + | 15.2164i | 0.592298 | + | 1.02589i | ||||
\(221\) | −2.25311 | − | 0.524201i | −0.151561 | − | 0.0352616i | ||||
\(222\) | 21.8262 | + | 12.6013i | 1.46488 | + | 0.845747i | ||||
\(223\) | 8.41926 | − | 2.25594i | 0.563796 | − | 0.151069i | 0.0343461 | − | 0.999410i | \(-0.489065\pi\) |
0.529450 | + | 0.848341i | \(0.322398\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 9.84344 | − | 5.68312i | 0.656230 | − | 0.378874i | ||||
\(226\) | −0.936482 | − | 3.49500i | −0.0622939 | − | 0.232484i | ||||
\(227\) | 16.3175 | − | 4.37226i | 1.08303 | − | 0.290197i | 0.327194 | − | 0.944957i | \(-0.393897\pi\) |
0.755837 | + | 0.654760i | \(0.227230\pi\) | |||||||
\(228\) | −73.7725 | + | 19.7673i | −4.88570 | + | 1.30912i | ||||
\(229\) | −0.632892 | − | 2.36198i | −0.0418227 | − | 0.156084i | 0.941857 | − | 0.336015i | \(-0.109079\pi\) |
−0.983679 | + | 0.179931i | \(0.942413\pi\) | |||||||
\(230\) | 0.473424 | − | 0.273331i | 0.0312166 | − | 0.0180229i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.2299 | − | 2.74108i | 0.671624 | − | 0.179961i | ||||
\(233\) | −4.65474 | − | 2.68741i | −0.304942 | − | 0.176058i | 0.339719 | − | 0.940527i | \(-0.389668\pi\) |
−0.644661 | + | 0.764469i | \(0.723001\pi\) | |||||||
\(234\) | −1.29799 | − | 39.0710i | −0.0848521 | − | 2.55415i | ||||
\(235\) | 2.51200 | + | 4.35092i | 0.163865 | + | 0.283823i | ||||
\(236\) | 3.76780 | − | 14.0616i | 0.245263 | − | 0.915334i | ||||
\(237\) | −1.51296 | − | 0.873507i | −0.0982772 | − | 0.0567404i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.9572 | + | 11.9572i | −0.773448 | + | 0.773448i | −0.978708 | − | 0.205260i | \(-0.934196\pi\) |
0.205260 | + | 0.978708i | \(0.434196\pi\) | |||||||
\(240\) | 4.04151 | − | 4.04151i | 0.260878 | − | 0.260878i | ||||
\(241\) | 3.48047 | + | 12.9893i | 0.224197 | + | 0.836713i | 0.982725 | + | 0.185073i | \(0.0592521\pi\) |
−0.758528 | + | 0.651640i | \(0.774081\pi\) | |||||||
\(242\) | 0.687097 | − | 2.56428i | 0.0441682 | − | 0.164838i | ||||
\(243\) | 17.6069i | 1.12949i | ||||||||
\(244\) | −7.90898 | + | 13.6987i | −0.506320 | + | 0.876972i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 37.5873i | 2.39648i | ||||||||
\(247\) | 13.3867 | − | 25.0740i | 0.851778 | − | 1.59542i | ||||
\(248\) | −20.5458 | + | 11.8621i | −1.30466 | + | 0.753245i | ||||
\(249\) | −2.97593 | + | 2.97593i | −0.188592 | + | 0.188592i | ||||
\(250\) | −24.1678 | + | 13.9533i | −1.52850 | + | 0.882483i | ||||
\(251\) | −6.40248 | − | 11.0894i | −0.404121 | − | 0.699958i | 0.590098 | − | 0.807332i | \(-0.299089\pi\) |
−0.994219 | + | 0.107374i | \(0.965756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.443482 | + | 0.118831i | 0.0278815 | + | 0.00747082i | ||||
\(254\) | 5.40171 | + | 5.40171i | 0.338933 | + | 0.338933i | ||||
\(255\) | 2.72587 | + | 0.730395i | 0.170701 | + | 0.0457391i | ||||
\(256\) | 11.7166 | − | 20.2937i | 0.732286 | − | 1.26836i | ||||
\(257\) | −5.19036 | − | 8.98997i | −0.323766 | − | 0.560779i | 0.657496 | − | 0.753458i | \(-0.271616\pi\) |
−0.981262 | + | 0.192679i | \(0.938282\pi\) | |||||||
\(258\) | −4.69979 | − | 17.5399i | −0.292596 | − | 1.09198i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.669566 | + | 20.1547i | 0.0415247 | + | 1.24994i | ||||
\(261\) | −6.90141 | + | 11.9536i | −0.427187 | + | 0.739909i | ||||
\(262\) | −27.3333 | − | 27.3333i | −1.68865 | − | 1.68865i | ||||
\(263\) | −4.37954 | −0.270054 | −0.135027 | − | 0.990842i | \(-0.543112\pi\) | ||||
−0.135027 | + | 0.990842i | \(0.543112\pi\) | |||||||
\(264\) | 30.7324 | 1.89145 | ||||||||
\(265\) | 8.24936 | + | 8.24936i | 0.506754 | + | 0.506754i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.70388 | − | 36.2154i | 0.593868 | − | 2.21635i | ||||
\(268\) | −4.80061 | + | 1.28632i | −0.293244 | + | 0.0785744i | ||||
\(269\) | −10.1192 | − | 5.84233i | −0.616980 | − | 0.356213i | 0.158713 | − | 0.987325i | \(-0.449266\pi\) |
−0.775692 | + | 0.631112i | \(0.782599\pi\) | |||||||
\(270\) | 16.7159i | 1.01730i | ||||||||
\(271\) | 29.6470 | + | 7.94389i | 1.80093 | + | 0.482557i | 0.994122 | − | 0.108262i | \(-0.0345287\pi\) |
0.806804 | + | 0.590819i | \(0.201195\pi\) | |||||||
\(272\) | −0.833705 | −0.0505508 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.887127 | 0.0535933 | ||||||||
\(275\) | −7.46700 | − | 2.00078i | −0.450277 | − | 0.120651i | ||||
\(276\) | − | 1.41591i | − | 0.0852278i | ||||||
\(277\) | 16.5109 | + | 9.53260i | 0.992047 | + | 0.572758i | 0.905885 | − | 0.423523i | \(-0.139207\pi\) |
0.0861613 | + | 0.996281i | \(0.472540\pi\) | |||||||
\(278\) | 22.3095 | − | 5.97782i | 1.33804 | − | 0.358526i | ||||
\(279\) | 8.00258 | − | 29.8660i | 0.479102 | − | 1.78803i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.8671 | + | 11.8671i | 0.707931 | + | 0.707931i | 0.966100 | − | 0.258169i | \(-0.0831190\pi\) |
−0.258169 | + | 0.966100i | \(0.583119\pi\) | |||||||
\(282\) | 20.4276 | 1.21645 | ||||||||
\(283\) | 8.43728 | 0.501544 | 0.250772 | − | 0.968046i | \(-0.419315\pi\) | ||||
0.250772 | + | 0.968046i | \(0.419315\pi\) | |||||||
\(284\) | 35.5349 | + | 35.5349i | 2.10861 | + | 2.10861i | ||||
\(285\) | −17.3374 | + | 30.0292i | −1.02698 | + | 1.77878i | ||||
\(286\) | −18.1657 | + | 19.4141i | −1.07416 | + | 1.14798i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.82750 | + | 18.0165i | 0.284463 | + | 1.06163i | ||||
\(289\) | 8.29418 | + | 14.3659i | 0.487893 | + | 0.845055i | ||||
\(290\) | 5.58870 | − | 9.67992i | 0.328180 | − | 0.568424i | ||||
\(291\) | 0.501845 | + | 0.134469i | 0.0294187 | + | 0.00788271i | ||||
\(292\) | 17.5172 | + | 17.5172i | 1.02511 | + | 1.02511i | ||||
\(293\) | 8.00676 | + | 2.14541i | 0.467760 | + | 0.125336i | 0.484998 | − | 0.874516i | \(-0.338820\pi\) |
−0.0172376 | + | 0.999851i | \(0.505487\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.30465 | − | 5.72382i | −0.192404 | − | 0.333253i | ||||
\(296\) | −11.9390 | + | 6.89296i | −0.693938 | + | 0.400645i | ||||
\(297\) | −9.92724 | + | 9.92724i | −0.576037 | + | 0.576037i | ||||
\(298\) | 11.2895 | − | 6.51800i | 0.653984 | − | 0.377578i | ||||
\(299\) | 0.384774 | + | 0.360031i | 0.0222520 | + | 0.0208211i | ||||
\(300\) | 23.8400i | 1.37640i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.56897 | − | 9.64574i | 0.320458 | − | 0.555050i | ||||
\(303\) | 3.29522i | 0.189306i | ||||||||
\(304\) | 2.65131 | − | 9.89484i | 0.152063 | − | 0.567508i | ||||
\(305\) | 1.85870 | + | 6.93677i | 0.106429 | + | 0.397198i | ||||
\(306\) | 4.91886 | − | 4.91886i | 0.281192 | − | 0.281192i | ||||
\(307\) | 17.3438 | − | 17.3438i | 0.989863 | − | 0.989863i | −0.0100865 | − | 0.999949i | \(-0.503211\pi\) |
0.999949 | + | 0.0100865i | \(0.00321069\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.4642 | − | 6.61887i | −0.652177 | − | 0.376535i | ||||
\(310\) | −6.48042 | + | 24.1853i | −0.368063 | + | 1.37363i | ||||
\(311\) | 11.8560 | + | 20.5353i | 0.672294 | + | 1.16445i | 0.977252 | + | 0.212082i | \(0.0680243\pi\) |
−0.304958 | + | 0.952366i | \(0.598642\pi\) | |||||||
\(312\) | 31.1153 | + | 16.6121i | 1.76155 | + | 0.940474i | ||||
\(313\) | −12.1862 | − | 7.03573i | −0.688808 | − | 0.397683i | 0.114358 | − | 0.993440i | \(-0.463519\pi\) |
−0.803165 | + | 0.595756i | \(0.796852\pi\) | |||||||
\(314\) | −28.6140 | + | 7.66709i | −1.61478 | + | 0.432679i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.92383 | − | 1.11073i | 0.108224 | − | 0.0624832i | ||||
\(317\) | 4.33262 | + | 16.1695i | 0.243344 | + | 0.908172i | 0.974209 | + | 0.225649i | \(0.0724504\pi\) |
−0.730865 | + | 0.682522i | \(0.760883\pi\) | |||||||
\(318\) | 45.8190 | − | 12.2772i | 2.56940 | − | 0.688470i | ||||
\(319\) | 9.06771 | − | 2.42969i | 0.507694 | − | 0.136036i | ||||
\(320\) | −4.98112 | − | 18.5898i | −0.278453 | − | 1.03920i | ||||
\(321\) | −36.5653 | + | 21.1110i | −2.04088 | + | 1.17830i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.88553 | − | 1.30907i | 0.271838 | − | 0.0728388i | ||||
\(324\) | −4.62517 | − | 2.67034i | −0.256954 | − | 0.148352i | ||||
\(325\) | −6.47852 | − | 6.06191i | −0.359364 | − | 0.336254i | ||||
\(326\) | −15.3200 | − | 26.5350i | −0.848497 | − | 1.46964i | ||||
\(327\) | −9.21836 | + | 34.4034i | −0.509777 | + | 1.90251i | ||||
\(328\) | −17.8058 | − | 10.2802i | −0.983159 | − | 0.567627i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 22.9349 | − | 22.9349i | 1.26252 | − | 1.26252i | ||||
\(331\) | −6.84348 | + | 6.84348i | −0.376152 | + | 0.376152i | −0.869712 | − | 0.493560i | \(-0.835695\pi\) |
0.493560 | + | 0.869712i | \(0.335695\pi\) | |||||||
\(332\) | −1.38508 | − | 5.16918i | −0.0760160 | − | 0.283696i | ||||
\(333\) | 4.65022 | − | 17.3549i | 0.254831 | − | 0.951041i | ||||
\(334\) | 43.5052i | 2.38050i | ||||||||
\(335\) | −1.12820 | + | 1.95410i | −0.0616401 | + | 0.106764i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.0838i | 1.09403i | 0.837122 | + | 0.547016i | \(0.184236\pi\) | ||||
−0.837122 | + | 0.547016i | \(0.815764\pi\) | |||||||
\(338\) | −28.8861 | + | 9.83671i | −1.57120 | + | 0.535047i | ||||
\(339\) | −3.68479 | + | 2.12742i | −0.200131 | + | 0.115545i | ||||
\(340\) | −2.53739 | + | 2.53739i | −0.137609 | + | 0.137609i | ||||
\(341\) | −18.2117 | + | 10.5145i | −0.986218 | + | 0.569393i | ||||
\(342\) | 42.7368 | + | 74.0223i | 2.31094 | + | 4.00267i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 9.59434 | + | 2.57080i | 0.517292 | + | 0.138608i | ||||
\(345\) | −0.454552 | − | 0.454552i | −0.0244723 | − | 0.0244723i | ||||
\(346\) | −12.6827 | − | 3.39833i | −0.681827 | − | 0.182695i | ||||
\(347\) | 11.1008 | − | 19.2271i | 0.595920 | − | 1.03216i | −0.397496 | − | 0.917604i | \(-0.630121\pi\) |
0.993416 | − | 0.114560i | \(-0.0365458\pi\) | |||||||
\(348\) | −14.4753 | − | 25.0719i | −0.775957 | − | 1.34400i | ||||
\(349\) | 1.38593 | + | 5.17235i | 0.0741869 | + | 0.276869i | 0.993048 | − | 0.117713i | \(-0.0375561\pi\) |
−0.918861 | + | 0.394582i | \(0.870889\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.4170 | + | 4.68484i | −0.822897 | + | 0.250058i | ||||
\(352\) | 6.34281 | − | 10.9861i | 0.338073 | − | 0.585560i | ||||
\(353\) | −18.4554 | − | 18.4554i | −0.982281 | − | 0.982281i | 0.0175643 | − | 0.999846i | \(-0.494409\pi\) |
−0.999846 | + | 0.0175643i | \(0.994409\pi\) | |||||||
\(354\) | −26.8733 | −1.42830 | ||||||||
\(355\) | 22.8157 | 1.21093 | ||||||||
\(356\) | 33.7113 | + | 33.7113i | 1.78669 | + | 1.78669i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.76594 | − | 21.5188i | 0.304739 | − | 1.13730i | ||||
\(359\) | 21.8723 | − | 5.86066i | 1.15437 | − | 0.309314i | 0.369658 | − | 0.929168i | \(-0.379475\pi\) |
0.784717 | + | 0.619854i | \(0.212808\pi\) | |||||||
\(360\) | −22.5915 | − | 13.0432i | −1.19068 | − | 0.687438i | ||||
\(361\) | 43.1470i | 2.27089i | ||||||||
\(362\) | −15.6789 | − | 4.20116i | −0.824066 | − | 0.220808i | ||||
\(363\) | −3.12177 | −0.163850 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.2471 | 0.588702 | ||||||||
\(366\) | 28.2049 | + | 7.55747i | 1.47429 | + | 0.395035i | ||||
\(367\) | 14.1961i | 0.741032i | 0.928826 | + | 0.370516i | \(0.120819\pi\) | ||||
−0.928826 | + | 0.370516i | \(0.879181\pi\) | |||||||
\(368\) | 0.164468 | + | 0.0949555i | 0.00857347 | + | 0.00494990i | ||||
\(369\) | 25.8831 | − | 6.93534i | 1.34742 | − | 0.361040i | ||||
\(370\) | −3.76571 | + | 14.0538i | −0.195770 | + | 0.730624i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 45.8573 | + | 45.8573i | 2.37759 | + | 2.37759i | ||||
\(373\) | 3.50642 | 0.181556 | 0.0907778 | − | 0.995871i | \(-0.471065\pi\) | ||||
0.0907778 | + | 0.995871i | \(0.471065\pi\) | |||||||
\(374\) | −4.73114 | −0.244641 | ||||||||
\(375\) | 23.2044 | + | 23.2044i | 1.19827 | + | 1.19827i | ||||
\(376\) | −5.58697 | + | 9.67691i | −0.288126 | + | 0.499048i | ||||
\(377\) | 10.4940 | + | 2.44150i | 0.540469 | + | 0.125744i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.94797 | + | 25.9302i | 0.356893 | + | 1.33194i | 0.878085 | + | 0.478504i | \(0.158821\pi\) |
−0.521192 | + | 0.853439i | \(0.674513\pi\) | |||||||
\(380\) | −22.0457 | − | 38.1843i | −1.13092 | − | 1.95882i | ||||
\(381\) | 4.49154 | − | 7.77958i | 0.230109 | − | 0.398560i | ||||
\(382\) | −5.67972 | − | 1.52188i | −0.290600 | − | 0.0778660i | ||||
\(383\) | −24.1497 | − | 24.1497i | −1.23399 | − | 1.23399i | −0.962417 | − | 0.271576i | \(-0.912455\pi\) |
−0.271576 | − | 0.962417i | \(-0.587545\pi\) | |||||||
\(384\) | −54.0533 | − | 14.4835i | −2.75839 | − | 0.739110i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.4739 | − | 45.8542i | −1.34749 | − | 2.33392i | ||||
\(387\) | −11.2110 | + | 6.47267i | −0.569887 | + | 0.329024i | ||||
\(388\) | −0.467145 | + | 0.467145i | −0.0237157 | + | 0.0237157i | ||||
\(389\) | −23.7849 | + | 13.7322i | −1.20594 | + | 0.696251i | −0.961870 | − | 0.273506i | \(-0.911817\pi\) |
−0.244072 | + | 0.969757i | \(0.578483\pi\) | |||||||
\(390\) | 35.6178 | − | 10.8234i | 1.80358 | − | 0.548063i | ||||
\(391\) | 0.0937676i | 0.00474203i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.7277 | + | 39.3656i | −1.14646 | + | 1.98573i | ||||
\(394\) | − | 42.0417i | − | 2.11803i | ||||||
\(395\) | 0.261034 | − | 0.974190i | 0.0131340 | − | 0.0490168i | ||||
\(396\) | −13.1818 | − | 49.1952i | −0.662412 | − | 2.47215i | ||||
\(397\) | 26.2097 | − | 26.2097i | 1.31543 | − | 1.31543i | 0.398076 | − | 0.917352i | \(-0.369678\pi\) |
0.917352 | − | 0.398076i | \(-0.130322\pi\) | |||||||
\(398\) | 27.2412 | − | 27.2412i | 1.36548 | − | 1.36548i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.76918 | − | 1.59879i | −0.138459 | − | 0.0799393i | ||||
\(401\) | 4.49729 | − | 16.7841i | 0.224584 | − | 0.838158i | −0.757987 | − | 0.652269i | \(-0.773817\pi\) |
0.982571 | − | 0.185888i | \(-0.0595163\pi\) | |||||||
\(402\) | 4.58725 | + | 7.94535i | 0.228791 | + | 0.396278i | ||||
\(403\) | −24.1221 | + | 0.801366i | −1.20161 | + | 0.0399189i | ||||
\(404\) | −3.62874 | − | 2.09505i | −0.180537 | − | 0.104233i | ||||
\(405\) | −2.34209 | + | 0.627561i | −0.116379 | + | 0.0311838i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.5826 | + | 6.10989i | −0.524562 | + | 0.302856i | ||||
\(408\) | 1.62448 | + | 6.06263i | 0.0804235 | + | 0.300145i | ||||
\(409\) | 10.8988 | − | 2.92033i | 0.538913 | − | 0.144401i | 0.0209119 | − | 0.999781i | \(-0.493343\pi\) |
0.518001 | + | 0.855380i | \(0.326676\pi\) | |||||||
\(410\) | −20.9599 | + | 5.61618i | −1.03513 | + | 0.277363i | ||||
\(411\) | −0.269999 | − | 1.00765i | −0.0133180 | − | 0.0497036i | ||||
\(412\) | 14.5776 | − | 8.41637i | 0.718186 | − | 0.414645i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.53060 | + | 0.410122i | −0.0752247 | + | 0.0201564i | ||||
\(415\) | −2.10413 | − | 1.21482i | −0.103287 | − | 0.0596330i | ||||
\(416\) | 12.3602 | − | 7.69439i | 0.606010 | − | 0.377248i | ||||
\(417\) | −13.5799 | − | 23.5211i | −0.665010 | − | 1.15183i | ||||
\(418\) | 15.0458 | − | 56.1515i | 0.735912 | − | 2.74646i | ||||
\(419\) | −16.1248 | − | 9.30964i | −0.787747 | − | 0.454806i | 0.0514220 | − | 0.998677i | \(-0.483625\pi\) |
−0.839169 | + | 0.543871i | \(0.816958\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.9024 | − | 18.9024i | 0.921247 | − | 0.921247i | −0.0758709 | − | 0.997118i | \(-0.524174\pi\) |
0.997118 | + | 0.0758709i | \(0.0241737\pi\) | |||||||
\(422\) | 16.3715 | − | 16.3715i | 0.796951 | − | 0.796951i | ||||
\(423\) | −3.76916 | − | 14.0667i | −0.183263 | − | 0.683945i | ||||
\(424\) | −6.71564 | + | 25.0631i | −0.326140 | + | 1.21717i | ||||
\(425\) | − | 1.57878i | − | 0.0765823i | ||||||
\(426\) | 46.3841 | − | 80.3397i | 2.24732 | − | 3.89247i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 53.6883i | − | 2.59512i | ||||||
\(429\) | 27.5804 | + | 14.7249i | 1.33160 | + | 0.710924i | ||||
\(430\) | 9.07856 | − | 5.24151i | 0.437807 | − | 0.252768i | ||||
\(431\) | −20.8750 | + | 20.8750i | −1.00552 | + | 1.00552i | −0.00553055 | + | 0.999985i | \(0.501760\pi\) |
−0.999985 | + | 0.00553055i | \(0.998240\pi\) | |||||||
\(432\) | −5.02912 | + | 2.90356i | −0.241964 | + | 0.139698i | ||||
\(433\) | −17.9660 | − | 31.1180i | −0.863390 | − | 1.49543i | −0.868637 | − | 0.495449i | \(-0.835004\pi\) |
0.00524758 | − | 0.999986i | \(-0.498330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6959 | − | 3.40186i | −0.608723 | − | 0.163107i | ||||
\(436\) | −32.0246 | − | 32.0246i | −1.53370 | − | 1.53370i | ||||
\(437\) | −1.11288 | − | 0.298196i | −0.0532363 | − | 0.0142646i | ||||
\(438\) | 22.8654 | − | 39.6040i | 1.09255 | − | 1.89235i | ||||
\(439\) | 4.87991 | + | 8.45226i | 0.232906 | + | 0.403404i | 0.958662 | − | 0.284548i | \(-0.0918434\pi\) |
−0.725756 | + | 0.687952i | \(0.758510\pi\) | |||||||
\(440\) | 4.59195 | + | 17.1374i | 0.218912 | + | 0.816992i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.79007 | − | 2.55737i | −0.227840 | − | 0.121641i | ||||
\(443\) | −19.3899 | + | 33.5843i | −0.921241 | + | 1.59564i | −0.123744 | + | 0.992314i | \(0.539490\pi\) |
−0.797497 | + | 0.603323i | \(0.793843\pi\) | |||||||
\(444\) | 26.6472 | + | 26.6472i | 1.26462 | + | 1.26462i | ||||
\(445\) | 21.6448 | 1.02606 | ||||||||
\(446\) | 20.4598 | 0.968799 | ||||||||
\(447\) | −10.8395 | − | 10.8395i | −0.512690 | − | 0.512690i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.42216 | + | 9.03963i | −0.114309 | + | 0.426606i | −0.999234 | − | 0.0391263i | \(-0.987543\pi\) |
0.884925 | + | 0.465733i | \(0.154209\pi\) | |||||||
\(450\) | 25.7710 | − | 6.90531i | 1.21486 | − | 0.325520i | ||||
\(451\) | −15.7830 | − | 9.11229i | −0.743190 | − | 0.429081i | ||||
\(452\) | − | 5.41033i | − | 0.254480i | ||||||
\(453\) | −12.6511 | − | 3.38985i | −0.594400 | − | 0.159269i | ||||
\(454\) | 39.6534 | 1.86103 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −77.1204 | −3.61150 | ||||||||
\(457\) | −18.5661 | − | 4.97477i | −0.868485 | − | 0.232710i | −0.203053 | − | 0.979168i | \(-0.565086\pi\) |
−0.665433 | + | 0.746458i | \(0.731753\pi\) | |||||||
\(458\) | − | 5.73989i | − | 0.268208i | ||||||
\(459\) | −2.48310 | − | 1.43362i | −0.115901 | − | 0.0669156i | ||||
\(460\) | 0.789557 | − | 0.211561i | 0.0368133 | − | 0.00986409i | ||||
\(461\) | −3.50466 | + | 13.0796i | −0.163228 | + | 0.609175i | 0.835031 | + | 0.550202i | \(0.185449\pi\) |
−0.998260 | + | 0.0589733i | \(0.981217\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.6336 | − | 14.6336i | −0.680081 | − | 0.680081i | 0.279937 | − | 0.960018i | \(-0.409686\pi\) |
−0.960018 | + | 0.279937i | \(0.909686\pi\) | |||||||
\(464\) | 3.88304 | 0.180266 | ||||||||
\(465\) | 29.4433 | 1.36540 | ||||||||
\(466\) | −8.92114 | − | 8.92114i | −0.413264 | − | 0.413264i | ||||
\(467\) | −15.4866 | + | 26.8236i | −0.716634 | + | 1.24125i | 0.245692 | + | 0.969348i | \(0.420985\pi\) |
−0.962326 | + | 0.271899i | \(0.912348\pi\) | |||||||
\(468\) | 13.2459 | − | 56.9334i | 0.612294 | − | 2.63175i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.05223 | + | 11.3911i | 0.140789 | + | 0.525431i | ||||
\(471\) | 17.4174 | + | 30.1678i | 0.802552 | + | 1.39006i | ||||
\(472\) | 7.34989 | − | 12.7304i | 0.338306 | − | 0.585963i | ||||
\(473\) | 8.50439 | + | 2.27874i | 0.391032 | + | 0.104777i | ||||
\(474\) | −2.89969 | − | 2.89969i | −0.133187 | − | 0.133187i | ||||
\(475\) | 18.7378 | + | 5.02078i | 0.859750 | + | 0.230369i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −16.9084 | − | 29.2862i | −0.774183 | − | 1.34092i | ||||
\(478\) | −34.3753 | + | 19.8466i | −1.57229 | + | 0.907761i | ||||
\(479\) | 5.19377 | − | 5.19377i | 0.237310 | − | 0.237310i | −0.578426 | − | 0.815735i | \(-0.696333\pi\) |
0.815735 | + | 0.578426i | \(0.196333\pi\) | |||||||
\(480\) | −15.3819 | + | 8.88072i | −0.702083 | + | 0.405348i | ||||
\(481\) | −14.0171 | + | 0.465666i | −0.639125 | + | 0.0212326i | ||||
\(482\) | 31.5654i | 1.43777i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.98478 | − | 3.43773i | 0.0902171 | − | 0.156261i | ||||
\(485\) | 0.299937i | 0.0136194i | ||||||||
\(486\) | −10.6967 | + | 39.9207i | −0.485213 | + | 1.81084i | ||||
\(487\) | −2.55251 | − | 9.52611i | −0.115665 | − | 0.431669i | 0.883670 | − | 0.468110i | \(-0.155065\pi\) |
−0.999336 | + | 0.0364405i | \(0.988398\pi\) | |||||||
\(488\) | −11.2942 | + | 11.2942i | −0.511263 | + | 0.511263i | ||||
\(489\) | −25.4773 | + | 25.4773i | −1.15212 | + | 1.15212i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.1372 | + | 19.1318i | 1.49546 | + | 0.863404i | 0.999986 | − | 0.00521946i | \(-0.00166141\pi\) |
0.495473 | + | 0.868623i | \(0.334995\pi\) | |||||||
\(492\) | −14.5465 | + | 54.2881i | −0.655805 | + | 2.44750i | ||||
\(493\) | 0.958615 | + | 1.66037i | 0.0431738 | + | 0.0747793i | ||||
\(494\) | 45.5853 | − | 48.7182i | 2.05098 | − | 2.19193i | ||||
\(495\) | −20.0250 | − | 11.5615i | −0.900058 | − | 0.519649i | ||||
\(496\) | −8.40197 | + | 2.25130i | −0.377260 | + | 0.101086i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −8.55536 | + | 4.93944i | −0.383375 | + | 0.221342i | ||||
\(499\) | 0.000375951 | 0.00140307i | 1.68299e−5 | 6.28100e-5i | 0.965934 | − | 0.258788i | \(-0.0833230\pi\) | ||
−0.965917 | + | 0.258850i | \(0.916656\pi\) | |||||||
\(500\) | −40.3060 | + | 10.8000i | −1.80254 | + | 0.482989i | ||||
\(501\) | 49.4157 | − | 13.2409i | 2.20773 | − | 0.591559i | ||||
\(502\) | −7.77938 | − | 29.0331i | −0.347211 | − | 1.29581i | ||||
\(503\) | 21.6205 | − | 12.4826i | 0.964012 | − | 0.556573i | 0.0666068 | − | 0.997779i | \(-0.478783\pi\) |
0.897406 | + | 0.441206i | \(0.145449\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.83752 | + | 0.492362i | −0.0817686 | + | 0.0219098i | ||||
\(506\) | 0.933326 | + | 0.538856i | 0.0414914 | + | 0.0239551i | ||||
\(507\) | 19.9646 | + | 29.8166i | 0.886660 | + | 1.32420i | ||||
\(508\) | 5.71132 | + | 9.89229i | 0.253399 | + | 0.438900i | ||||
\(509\) | 0.678383 | − | 2.53176i | 0.0300688 | − | 0.112218i | −0.949260 | − | 0.314491i | \(-0.898166\pi\) |
0.979329 | + | 0.202273i | \(0.0648328\pi\) | |||||||
\(510\) | 5.73671 | + | 3.31209i | 0.254026 | + | 0.146662i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 10.2233 | − | 10.2233i | 0.451811 | − | 0.451811i | ||||
\(513\) | 24.9116 | − | 24.9116i | 1.09987 | − | 1.09987i | ||||
\(514\) | −6.30659 | − | 23.5365i | −0.278172 | − | 1.03815i | ||||
\(515\) | 1.97795 | − | 7.38179i | 0.0871587 | − | 0.325281i | ||||
\(516\) | − | 27.1521i | − | 1.19530i | ||||||
\(517\) | −4.95226 | + | 8.57757i | −0.217800 | + | 0.377241i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.4400i | 0.677742i | ||||||||
\(520\) | −4.61428 | + | 19.8330i | −0.202350 | + | 0.869734i | ||||
\(521\) | −25.8598 | + | 14.9302i | −1.13294 | + | 0.654102i | −0.944672 | − | 0.328016i | \(-0.893620\pi\) |
−0.188266 | + | 0.982118i | \(0.560287\pi\) | |||||||
\(522\) | −22.9099 | + | 22.9099i | −1.00274 | + | 1.00274i | ||||
\(523\) | 13.9268 | − | 8.04062i | 0.608975 | − | 0.351592i | −0.163589 | − | 0.986529i | \(-0.552307\pi\) |
0.772564 | + | 0.634937i | \(0.218974\pi\) | |||||||
\(524\) | −28.8999 | − | 50.0561i | −1.26250 | − | 2.18671i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.92985 | − | 2.66069i | −0.432962 | − | 0.116012i | ||||
\(527\) | −3.03686 | − | 3.03686i | −0.132288 | − | 0.132288i | ||||
\(528\) | 10.8839 | + | 2.91634i | 0.473663 | + | 0.126918i | ||||
\(529\) | −11.4893 | + | 19.9001i | −0.499536 | + | 0.865221i | ||||
\(530\) | 13.6923 | + | 23.7157i | 0.594755 | + | 1.03015i | ||||
\(531\) | 4.95848 | + | 18.5053i | 0.215180 | + | 0.803062i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −11.0540 | − | 17.7571i | −0.478802 | − | 0.769146i | ||||
\(534\) | 44.0038 | − | 76.2168i | 1.90423 | − | 3.29822i | ||||
\(535\) | −17.2356 | − | 17.2356i | −0.745162 | − | 0.745162i | ||||
\(536\) | −5.01847 | −0.216765 | ||||||||
\(537\) | −26.1971 | −1.13049 | ||||||||
\(538\) | −19.3942 | − | 19.3942i | −0.836143 | − | 0.836143i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.46915 | + | 24.1432i | −0.278388 | + | 1.03896i | ||||
\(541\) | −17.0022 | + | 4.55572i | −0.730980 | + | 0.195866i | −0.605066 | − | 0.796176i | \(-0.706853\pi\) |
−0.125915 | + | 0.992041i | \(0.540187\pi\) | |||||||
\(542\) | 62.3933 | + | 36.0228i | 2.68002 | + | 1.54731i | ||||
\(543\) | 19.0876i | 0.819129i | ||||||||
\(544\) | 2.50251 | + | 0.670546i | 0.107294 | + | 0.0287494i | ||||
\(545\) | −20.5618 | −0.880771 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.8734 | −0.678698 | −0.339349 | − | 0.940661i | \(-0.610207\pi\) | ||||
−0.339349 | + | 0.940661i | \(0.610207\pi\) | |||||||
\(548\) | 1.28130 | + | 0.343322i | 0.0547343 | + | 0.0146660i | ||||
\(549\) | − | 20.8166i | − | 0.888433i | ||||||
\(550\) | −15.7146 | − | 9.07284i | −0.670073 | − | 0.386867i | ||||
\(551\) | −22.7547 | + | 6.09709i | −0.969381 | + | 0.259745i | ||||
\(552\) | 0.370042 | − | 1.38101i | 0.0157500 | − | 0.0587799i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 31.6444 | + | 31.6444i | 1.34444 | + | 1.34444i | ||||
\(555\) | 17.1092 | 0.726246 | ||||||||
\(556\) | 34.5356 | 1.46464 | ||||||||
\(557\) | 1.79108 | + | 1.79108i | 0.0758906 | + | 0.0758906i | 0.744033 | − | 0.668143i | \(-0.232910\pi\) |
−0.668143 | + | 0.744033i | \(0.732910\pi\) | |||||||
\(558\) | 36.2889 | − | 62.8543i | 1.53623 | − | 2.66083i | ||||
\(559\) | 7.37857 | + | 6.90409i | 0.312080 | + | 0.292012i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.43993 | + | 5.37389i | 0.0607938 | + | 0.226886i | ||||
\(562\) | 19.6970 | + | 34.1162i | 0.830867 | + | 1.43910i | ||||
\(563\) | −10.1159 | + | 17.5213i | −0.426336 | + | 0.738436i | −0.996544 | − | 0.0830642i | \(-0.973529\pi\) |
0.570208 | + | 0.821500i | \(0.306863\pi\) | |||||||
\(564\) | 29.5040 | + | 7.90558i | 1.24234 | + | 0.332885i | ||||
\(565\) | −1.73689 | − | 1.73689i | −0.0730714 | − | 0.0730714i | ||||
\(566\) | 19.1301 | + | 5.12589i | 0.804098 | + | 0.215457i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 25.3722 | + | 43.9460i | 1.06459 | + | 1.84393i | ||||
\(569\) | 12.8801 | − | 7.43632i | 0.539961 | − | 0.311747i | −0.205102 | − | 0.978741i | \(-0.565753\pi\) |
0.745063 | + | 0.666994i | \(0.232419\pi\) | |||||||
\(570\) | −57.5532 | + | 57.5532i | −2.41064 | + | 2.41064i | ||||
\(571\) | 31.9767 | − | 18.4617i | 1.33818 | − | 0.772600i | 0.351645 | − | 0.936133i | \(-0.385622\pi\) |
0.986538 | + | 0.163533i | \(0.0522891\pi\) | |||||||
\(572\) | −33.7505 | + | 21.0101i | −1.41118 | + | 0.878475i | ||||
\(573\) | 6.91453i | 0.288859i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.179817 | + | 0.311452i | −0.00749888 | + | 0.0129884i | ||||
\(576\) | 55.7864i | 2.32443i | ||||||||
\(577\) | 5.31122 | − | 19.8217i | 0.221109 | − | 0.825189i | −0.762817 | − | 0.646614i | \(-0.776184\pi\) |
0.983926 | − | 0.178575i | \(-0.0571488\pi\) | |||||||
\(578\) | 10.0779 | + | 37.6113i | 0.419186 | + | 1.56442i | ||||
\(579\) | −44.0263 | + | 44.0263i | −1.82967 | + | 1.82967i | ||||
\(580\) | 11.8181 | − | 11.8181i | 0.490718 | − | 0.490718i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.05615 | + | 0.609771i | 0.0437790 | + | 0.0252758i | ||||
\(583\) | −5.95271 | + | 22.2158i | −0.246536 | + | 0.920086i | ||||
\(584\) | 12.5074 | + | 21.6635i | 0.517560 | + | 0.896441i | ||||
\(585\) | −14.0251 | − | 22.5298i | −0.579865 | − | 0.931492i | ||||
\(586\) | 16.8506 | + | 9.72867i | 0.696090 | + | 0.401888i | ||||
\(587\) | −19.8321 | + | 5.31399i | −0.818557 | + | 0.219332i | −0.643715 | − | 0.765265i | \(-0.722608\pi\) |
−0.174842 | + | 0.984597i | \(0.555941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.7007 | − | 26.3853i | 1.88307 | − | 1.08719i | ||||
\(590\) | −4.01534 | − | 14.9854i | −0.165309 | − | 0.616941i | ||||
\(591\) | −47.7533 | + | 12.7955i | −1.96431 | + | 0.526335i | ||||
\(592\) | −4.88231 | + | 1.30821i | −0.200662 | + | 0.0537671i | ||||
\(593\) | 10.7660 | + | 40.1793i | 0.442107 | + | 1.64997i | 0.723464 | + | 0.690362i | \(0.242549\pi\) |
−0.281357 | + | 0.959603i | \(0.590784\pi\) | |||||||
\(594\) | −28.5394 | + | 16.4772i | −1.17099 | + | 0.676069i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 18.8282 | − | 5.04500i | 0.771233 | − | 0.206651i | ||||
\(597\) | −39.2330 | − | 22.6512i | −1.60570 | − | 0.927050i | ||||
\(598\) | 0.653680 | + | 1.05007i | 0.0267310 | + | 0.0429405i | ||||
\(599\) | 2.16999 | + | 3.75853i | 0.0886634 | + | 0.153569i | 0.906946 | − | 0.421246i | \(-0.138407\pi\) |
−0.818283 | + | 0.574816i | \(0.805074\pi\) | |||||||
\(600\) | −6.23047 | + | 23.2524i | −0.254358 | + | 0.949277i | ||||
\(601\) | 5.72067 | + | 3.30283i | 0.233351 | + | 0.134725i | 0.612117 | − | 0.790767i | \(-0.290318\pi\) |
−0.378766 | + | 0.925492i | \(0.623652\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.62485 | − | 4.62485i | 0.188339 | − | 0.188339i | ||||
\(604\) | 11.7763 | − | 11.7763i | 0.479172 | − | 0.479172i | ||||
\(605\) | −0.466446 | − | 1.74080i | −0.0189637 | − | 0.0707735i | ||||
\(606\) | −2.00194 | + | 7.47135i | −0.0813233 | + | 0.303503i | ||||
\(607\) | − | 46.0468i | − | 1.86898i | −0.355985 | − | 0.934492i | \(-0.615854\pi\) | ||
0.355985 | − | 0.934492i | \(-0.384146\pi\) | |||||||
\(608\) | −15.9168 | + | 27.5686i | −0.645510 | + | 1.11806i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.8571i | 0.682526i | ||||||||
\(611\) | −9.65047 | + | 6.00753i | −0.390416 | + | 0.243039i | ||||
\(612\) | 9.00804 | − | 5.20079i | 0.364128 | − | 0.210230i | ||||
\(613\) | 20.2929 | − | 20.2929i | 0.819624 | − | 0.819624i | −0.166429 | − | 0.986053i | \(-0.553224\pi\) |
0.986053 | + | 0.166429i | \(0.0532237\pi\) | |||||||
\(614\) | 49.8609 | − | 28.7872i | 2.01222 | − | 1.16176i | ||||
\(615\) | 12.7583 | + | 22.0981i | 0.514466 | + | 0.891081i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.0947548 | + | 0.0253895i | 0.00381469 | + | 0.00102214i | 0.260726 | − | 0.965413i | \(-0.416038\pi\) |
−0.256911 | + | 0.966435i | \(0.582705\pi\) | |||||||
\(618\) | −21.9720 | − | 21.9720i | −0.883844 | − | 0.883844i | ||||
\(619\) | 40.8542 | + | 10.9468i | 1.64207 | + | 0.439991i | 0.957376 | − | 0.288843i | \(-0.0932706\pi\) |
0.684691 | + | 0.728834i | \(0.259937\pi\) | |||||||
\(620\) | −18.7196 | + | 32.4233i | −0.751798 | + | 1.30215i | ||||
\(621\) | 0.326566 | + | 0.565629i | 0.0131047 | + | 0.0226979i | ||||
\(622\) | 14.4058 | + | 53.7630i | 0.577619 | + | 2.15570i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 9.44312 | + | 8.83587i | 0.378027 | + | 0.353718i | ||||
\(625\) | −3.32054 | + | 5.75135i | −0.132822 | + | 0.230054i | ||||
\(626\) | −23.3558 | − | 23.3558i | −0.933486 | − | 0.933486i | ||||
\(627\) | −68.3592 | −2.73001 | ||||||||
\(628\) | −44.2950 | −1.76756 | ||||||||
\(629\) | −1.76469 | − | 1.76469i | −0.0703629 | − | 0.0703629i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.02584 | − | 7.56053i | 0.0806473 | − | 0.300980i | −0.913807 | − | 0.406148i | \(-0.866872\pi\) |
0.994454 | + | 0.105169i | \(0.0335383\pi\) | |||||||
\(632\) | 2.16670 | − | 0.580566i | 0.0861868 | − | 0.0230937i | ||||
\(633\) | −23.5783 | − | 13.6130i | −0.937154 | − | 0.541066i | ||||
\(634\) | 39.2938i | 1.56056i | ||||||||
\(635\) | 5.00926 | + | 1.34223i | 0.198786 | + | 0.0532646i | ||||
\(636\) | 70.9288 | 2.81251 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.0356 | 0.872397 | ||||||||
\(639\) | −63.8813 | − | 17.1170i | −2.52711 | − | 0.677136i | ||||
\(640\) | − | 32.3059i | − | 1.27700i | ||||||
\(641\) | 28.9275 | + | 16.7013i | 1.14257 | + | 0.659661i | 0.947065 | − | 0.321042i | \(-0.104033\pi\) |
0.195502 | + | 0.980703i | \(0.437366\pi\) | |||||||
\(642\) | −95.7311 | + | 25.6511i | −3.77820 | + | 1.01237i | ||||
\(643\) | −4.94009 | + | 18.4367i | −0.194818 | + | 0.727071i | 0.797496 | + | 0.603324i | \(0.206158\pi\) |
−0.992314 | + | 0.123746i | \(0.960509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.71667 | − | 8.71667i | −0.343219 | − | 0.343219i | ||||
\(646\) | 11.8724 | 0.467113 | ||||||||
\(647\) | −32.9045 | −1.29361 | −0.646804 | − | 0.762656i | \(-0.723895\pi\) | ||||
−0.646804 | + | 0.762656i | \(0.723895\pi\) | |||||||
\(648\) | −3.81330 | − | 3.81330i | −0.149800 | − | 0.149800i | ||||
\(649\) | 6.51491 | − | 11.2842i | 0.255733 | − | 0.442942i | ||||
\(650\) | −11.0061 | − | 17.6802i | −0.431696 | − | 0.693475i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −11.8578 | − | 44.2541i | −0.464389 | − | 1.73312i | ||||
\(653\) | −13.9982 | − | 24.2457i | −0.547793 | − | 0.948806i | −0.998425 | − | 0.0560961i | \(-0.982135\pi\) |
0.450632 | − | 0.892710i | \(-0.351199\pi\) | |||||||
\(654\) | −41.8021 | + | 72.4034i | −1.63459 | + | 2.83120i | ||||
\(655\) | −25.3474 | − | 6.79182i | −0.990405 | − | 0.265378i | ||||
\(656\) | −5.33041 | − | 5.33041i | −0.208117 | − | 0.208117i | ||||
\(657\) | −31.4907 | − | 8.43792i | −1.22857 | − | 0.329195i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.35203 | − | 9.27000i | −0.208486 | − | 0.361108i | 0.742752 | − | 0.669567i | \(-0.233520\pi\) |
−0.951238 | + | 0.308459i | \(0.900187\pi\) | |||||||
\(660\) | 42.0013 | − | 24.2494i | 1.63490 | − | 0.943908i | ||||
\(661\) | 16.9884 | − | 16.9884i | 0.660772 | − | 0.660772i | −0.294790 | − | 0.955562i | \(-0.595250\pi\) |
0.955562 | + | 0.294790i | \(0.0952498\pi\) | |||||||
\(662\) | −19.6740 | + | 11.3588i | −0.764653 | + | 0.441473i | ||||
\(663\) | −1.44693 | + | 6.21917i | −0.0561942 | + | 0.241532i | ||||
\(664\) | − | 5.40377i | − | 0.209707i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 21.0872 | − | 36.5240i | 0.817111 | − | 1.41528i | ||||
\(667\) | − | 0.436729i | − | 0.0169102i | ||||||
\(668\) | −16.8367 | + | 62.8356i | −0.651433 | + | 2.43118i | ||||
\(669\) | −6.22697 | − | 23.2394i | −0.240748 | − | 0.898486i | ||||
\(670\) | −3.74517 | + | 3.74517i | −0.144688 | + | 0.144688i | ||||
\(671\) | −10.0111 | + | 10.0111i | −0.386474 | + | 0.386474i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.79792 | + | 2.77008i | 0.184946 | + | 0.106779i | 0.589615 | − | 0.807685i | \(-0.299280\pi\) |
−0.404668 | + | 0.914464i | \(0.632613\pi\) | |||||||
\(674\) | −12.2015 | + | 45.5365i | −0.469983 | + | 1.75400i | ||||
\(675\) | −5.49846 | − | 9.52362i | −0.211636 | − | 0.366564i | ||||
\(676\) | −45.5277 | + | 3.02832i | −1.75106 | + | 0.116474i | ||||
\(677\) | 38.1640 | + | 22.0340i | 1.46676 | + | 0.846835i | 0.999309 | − | 0.0371822i | \(-0.0118382\pi\) |
0.467454 | + | 0.884018i | \(0.345172\pi\) | |||||||
\(678\) | −9.64710 | + | 2.58493i | −0.370495 | + | 0.0992738i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.13799 | + | 1.81172i | −0.120336 | + | 0.0694763i | ||||
\(681\) | −12.0686 | − | 45.0406i | −0.462469 | − | 1.72596i | ||||
\(682\) | −47.6798 | + | 12.7758i | −1.82575 | + | 0.489209i | ||||
\(683\) | −4.97587 | + | 1.33328i | −0.190396 | + | 0.0510166i | −0.352757 | − | 0.935715i | \(-0.614756\pi\) |
0.162361 | + | 0.986731i | \(0.448089\pi\) | |||||||
\(684\) | 33.0787 | + | 123.451i | 1.26480 | + | 4.72028i | ||||
\(685\) | 0.521554 | − | 0.301120i | 0.0199276 | − | 0.0115052i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.51969 | + | 1.74695i | −0.248742 | + | 0.0666501i | ||||
\(688\) | 3.15390 | + | 1.82090i | 0.120241 | + | 0.0694213i | ||||
\(689\) | −18.0354 | + | 19.2749i | −0.687094 | + | 0.734315i | ||||
\(690\) | −0.754466 | − | 1.30677i | −0.0287220 | − | 0.0497480i | ||||
\(691\) | −0.790947 | + | 2.95186i | −0.0300891 | + | 0.112294i | −0.979337 | − | 0.202234i | \(-0.935180\pi\) |
0.949248 | + | 0.314528i | \(0.101846\pi\) | |||||||
\(692\) | −17.0028 | − | 9.81655i | −0.646348 | − | 0.373169i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.8501 | − | 36.8501i | 1.39881 | − | 1.39881i | ||||
\(695\) | 11.0870 | − | 11.0870i | 0.420555 | − | 0.420555i | ||||
\(696\) | −7.56611 | − | 28.2371i | −0.286793 | − | 1.07032i | ||||
\(697\) | 0.963328 | − | 3.59519i | 0.0364886 | − | 0.136177i | ||||
\(698\) | 12.5694i | 0.475759i | ||||||||
\(699\) | −7.41796 | + | 12.8483i | −0.280573 | + | 0.485967i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 11.0158i | − | 0.416061i | −0.978122 | − | 0.208031i | \(-0.933295\pi\) | ||
0.978122 | − | 0.208031i | \(-0.0667054\pi\) | |||||||
\(702\) | −37.8015 | + | 1.25581i | −1.42673 | + | 0.0473977i | ||||
\(703\) | 26.5563 | − | 15.3323i | 1.00159 | − | 0.578267i | ||||
\(704\) | 26.8287 | − | 26.8287i | 1.01114 | − | 1.01114i | ||||
\(705\) | 12.0097 | − | 6.93378i | 0.452310 | − | 0.261141i | ||||
\(706\) | −30.6322 | − | 53.0566i | −1.15286 | − | 1.99681i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −38.8138 | − | 10.4001i | −1.45871 | − | 0.390860i | ||||
\(709\) | 19.9197 | + | 19.9197i | 0.748101 | + | 0.748101i | 0.974122 | − | 0.226021i | \(-0.0725719\pi\) |
−0.226021 | + | 0.974122i | \(0.572572\pi\) | |||||||
\(710\) | 51.7306 | + | 13.8612i | 1.94141 | + | 0.520200i | ||||
\(711\) | −1.46173 | + | 2.53179i | −0.0548192 | + | 0.0949496i | ||||
\(712\) | 24.0702 | + | 41.6907i | 0.902067 | + | 1.56243i | ||||
\(713\) | 0.253206 | + | 0.944977i | 0.00948263 | + | 0.0353897i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.09008 | + | 17.5799i | −0.152960 | + | 0.657450i | ||||
\(716\) | 16.6557 | − | 28.8486i | 0.622454 | − | 1.07812i | ||||
\(717\) | 33.0050 | + | 33.0050i | 1.23260 | + | 1.23260i | ||||
\(718\) | 53.1522 | 1.98362 | ||||||||
\(719\) | −42.1118 | −1.57050 | −0.785252 | − | 0.619176i | \(-0.787467\pi\) | ||||
−0.785252 | + | 0.619176i | \(0.787467\pi\) | |||||||
\(720\) | −6.76309 | − | 6.76309i | −0.252045 | − | 0.252045i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −26.2130 | + | 97.8284i | −0.975548 | + | 3.64079i | ||||
\(723\) | 35.8538 | − | 9.60699i | 1.33342 | − | 0.357288i | ||||
\(724\) | −21.0195 | − | 12.1356i | −0.781185 | − | 0.451018i | ||||
\(725\) | 7.35329i | 0.273094i | ||||||||
\(726\) | −7.07808 | − | 1.89657i | −0.262692 | − | 0.0703881i | ||||
\(727\) | 10.0901 | 0.374223 | 0.187111 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187111 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44.0349 | 1.63092 | ||||||||
\(730\) | 25.5009 | + | 6.83295i | 0.943832 | + | 0.252899i | ||||
\(731\) | 1.79812i | 0.0665060i | ||||||||
\(732\) | 37.8121 | + | 21.8308i | 1.39758 | + | 0.806891i | ||||
\(733\) | 25.6687 | − | 6.87790i | 0.948093 | − | 0.254041i | 0.248540 | − | 0.968622i | \(-0.420049\pi\) |
0.699553 | + | 0.714581i | \(0.253382\pi\) | |||||||
\(734\) | −8.62455 | + | 32.1873i | −0.318338 | + | 1.18805i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.417306 | − | 0.417306i | −0.0153821 | − | 0.0153821i | ||||
\(737\) | −4.44835 | −0.163857 | ||||||||
\(738\) | 62.8988 | 2.31534 | ||||||||
\(739\) | 17.7896 | + | 17.7896i | 0.654402 | + | 0.654402i | 0.954050 | − | 0.299648i | \(-0.0968692\pi\) |
−0.299648 | + | 0.954050i | \(0.596869\pi\) | |||||||
\(740\) | −10.8778 | + | 18.8409i | −0.399876 | + | 0.692605i | ||||
\(741\) | −69.2108 | − | 36.9509i | −2.54252 | − | 1.35742i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.81817 | − | 10.5175i | −0.103388 | − | 0.385851i | 0.894769 | − | 0.446530i | \(-0.147340\pi\) |
−0.998157 | + | 0.0606785i | \(0.980674\pi\) | |||||||
\(744\) | 32.7425 | + | 56.7117i | 1.20040 | + | 2.07915i | ||||
\(745\) | 4.42484 | − | 7.66405i | 0.162114 | − | 0.280789i | ||||
\(746\) | 7.95021 | + | 2.13025i | 0.291078 | + | 0.0779941i | ||||
\(747\) | 4.97993 | + | 4.97993i | 0.182206 | + | 0.182206i | ||||
\(748\) | −6.83328 | − | 1.83097i | −0.249850 | − | 0.0669470i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 38.5147 | + | 66.7094i | 1.40636 | + | 2.43588i | ||||
\(751\) | 27.9154 | − | 16.1170i | 1.01865 | − | 0.588117i | 0.104936 | − | 0.994479i | \(-0.466536\pi\) |
0.913712 | + | 0.406362i | \(0.133203\pi\) | |||||||
\(752\) | −2.89692 | + | 2.89692i | −0.105640 | + | 0.105640i | ||||
\(753\) | −30.6097 | + | 17.6725i | −1.11548 | + | 0.644022i | ||||
\(754\) | 22.3101 | + | 11.9111i | 0.812485 | + | 0.433777i | ||||
\(755\) | − | 7.56115i | − | 0.275179i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.9609 | + | 29.3771i | −0.616453 | + | 1.06773i | 0.373675 | + | 0.927560i | \(0.378098\pi\) |
−0.990128 | + | 0.140168i | \(0.955236\pi\) | |||||||
\(758\) | 63.0133i | 2.28875i | ||||||||
\(759\) | 0.328004 | − | 1.22413i | 0.0119058 | − | 0.0444330i | ||||
\(760\) | −11.5231 | − | 43.0048i | −0.417987 | − | 1.55995i | ||||
\(761\) | −6.85232 | + | 6.85232i | −0.248397 | + | 0.248397i | −0.820312 | − | 0.571916i | \(-0.806200\pi\) |
0.571916 | + | 0.820312i | \(0.306200\pi\) | |||||||
\(762\) | 14.9101 | − | 14.9101i | 0.540137 | − | 0.540137i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.61437 | − | 4.39616i | −0.275478 | − | 0.159047i | ||||
\(765\) | 1.22225 | − | 4.56149i | 0.0441904 | − | 0.164921i | ||||
\(766\) | −40.0837 | − | 69.4270i | −1.44828 | − | 2.50850i | ||||
\(767\) | 12.6956 | − | 7.90316i | 0.458411 | − | 0.285366i | ||||
\(768\) | −56.0159 | − | 32.3408i | −2.02130 | − | 1.16700i | ||||
\(769\) | −14.6001 | + | 3.91210i | −0.526495 | + | 0.141074i | −0.512269 | − | 0.858825i | \(-0.671195\pi\) |
−0.0142256 | + | 0.999899i | \(0.504528\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.8147 | + | 14.3268i | −0.893678 | + | 0.515965i | ||||
\(772\) | −20.4911 | − | 76.4737i | −0.737490 | − | 2.75235i | ||||
\(773\) | −37.7776 | + | 10.1225i | −1.35877 | + | 0.364081i | −0.863364 | − | 0.504582i | \(-0.831647\pi\) |
−0.495404 | + | 0.868663i | \(0.664980\pi\) | |||||||
\(774\) | −29.3513 | + | 7.86466i | −1.05501 | + | 0.282689i | ||||
\(775\) | −4.26328 | − | 15.9108i | −0.153142 | − | 0.571532i | ||||
\(776\) | −0.577718 | + | 0.333546i | −0.0207389 | + | 0.0119736i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −62.2709 | + | 16.6854i | −2.23252 | + | 0.598202i | ||||
\(779\) | 39.6060 | + | 22.8665i | 1.41903 | + | 0.819279i | ||||
\(780\) | 55.6323 | − | 1.84818i | 1.99195 | − | 0.0661753i | ||||
\(781\) | 22.4898 | + | 38.9535i | 0.804750 | + | 1.39387i | ||||
\(782\) | −0.0569665 | + | 0.212602i | −0.00203712 | + | 0.00760263i | ||||
\(783\) | 11.5652 | + | 6.67718i | 0.413307 | + | 0.238623i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −14.2201 | + | 14.2201i | −0.507537 | + | 0.507537i | ||||
\(786\) | −75.4469 | + | 75.4469i | −2.69110 | + | 2.69110i | ||||
\(787\) | −0.451508 | − | 1.68505i | −0.0160945 | − | 0.0600656i | 0.957412 | − | 0.288727i | \(-0.0932319\pi\) |
−0.973506 | + | 0.228661i | \(0.926565\pi\) | |||||||
\(788\) | 16.2703 | − | 60.7217i | 0.579607 | − | 2.16312i | ||||
\(789\) | 12.0887i | 0.430368i | ||||||||
\(790\) | 1.18370 | − | 2.05022i | 0.0421141 | − | 0.0729437i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | − | 51.4278i | − | 1.82741i | ||||||
\(793\) | −15.5472 | + | 4.72441i | −0.552097 | + | 0.167769i | ||||
\(794\) | 75.3492 | − | 43.5029i | 2.67404 | − | 1.54386i | ||||
\(795\) | 22.7704 | − | 22.7704i | 0.807582 | − | 0.807582i | ||||
\(796\) | 49.8875 | − | 28.8026i | 1.76822 | − | 1.02088i | ||||
\(797\) | 12.2921 | + | 21.2905i | 0.435407 | + | 0.754148i | 0.997329 | − | 0.0730430i | \(-0.0232710\pi\) |
−0.561921 | + | 0.827191i | \(0.689938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.95388 | − | 0.523540i | −0.0691233 | − | 0.0185215i | ||||
\(800\) | 7.02627 | + | 7.02627i | 0.248416 | + | 0.248416i | ||||
\(801\) | −60.6030 | − | 16.2385i | −2.14130 | − | 0.573760i | ||||
\(802\) | 20.3936 | − | 35.3228i | 0.720125 | − | 1.24729i | ||||
\(803\) | 11.0865 | + | 19.2024i | 0.391235 | + | 0.677638i | ||||
\(804\) | 3.55057 | + | 13.2509i | 0.125219 | + | 0.467324i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −55.1795 | − | 12.8379i | −1.94362 | − | 0.452195i | ||||
\(807\) | −16.1264 | + | 27.9317i | −0.567675 | + | 0.983241i | ||||
\(808\) | −2.99178 | − | 2.99178i | −0.105250 | − | 0.105250i | ||||
\(809\) | −2.82935 | −0.0994746 | −0.0497373 | − | 0.998762i | \(-0.515838\pi\) | ||||
−0.0497373 | + | 0.998762i | \(0.515838\pi\) | |||||||
\(810\) | −5.69155 | −0.199981 | ||||||||
\(811\) | 6.39483 | + | 6.39483i | 0.224553 | + | 0.224553i | 0.810412 | − | 0.585860i | \(-0.199243\pi\) |
−0.585860 | + | 0.810412i | \(0.699243\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 21.9272 | − | 81.8334i | 0.769020 | − | 2.87002i | ||||
\(814\) | −27.7063 | + | 7.42387i | −0.971104 | + | 0.260207i | ||||
\(815\) | −18.0137 | − | 10.4002i | −0.630993 | − | 0.364304i | ||||
\(816\) | 2.30124i | 0.0805596i | ||||||||
\(817\) | −21.3410 | − | 5.71832i | −0.746629 | − | 0.200059i | ||||
\(818\) | 26.4854 | 0.926041 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −32.4463 | −1.13307 | ||||||||
\(821\) | −36.0437 | − | 9.65789i | −1.25793 | − | 0.337063i | −0.432538 | − | 0.901616i | \(-0.642382\pi\) |
−0.825397 | + | 0.564553i | \(0.809049\pi\) | |||||||
\(822\) | − | 2.44870i | − | 0.0854082i | ||||||
\(823\) | −34.1966 | − | 19.7434i | −1.19202 | − | 0.688212i | −0.233254 | − | 0.972416i | \(-0.574937\pi\) |
−0.958764 | + | 0.284204i | \(0.908271\pi\) | |||||||
\(824\) | 16.4179 | − | 4.39916i | 0.571944 | − | 0.153252i | ||||
\(825\) | −5.52266 | + | 20.6109i | −0.192274 | + | 0.717578i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.4804 | − | 24.4804i | −0.851267 | − | 0.851267i | 0.139022 | − | 0.990289i | \(-0.455604\pi\) |
−0.990289 | + | 0.139022i | \(0.955604\pi\) | |||||||
\(828\) | −2.36939 | −0.0823421 | ||||||||
\(829\) | −13.4781 | −0.468112 | −0.234056 | − | 0.972223i | \(-0.575200\pi\) | ||||
−0.234056 | + | 0.972223i | \(0.575200\pi\) | |||||||
\(830\) | −4.03271 | − | 4.03271i | −0.139977 | − | 0.139977i | ||||
\(831\) | 26.3125 | − | 45.5745i | 0.912769 | − | 1.58096i | ||||
\(832\) | 41.6648 | − | 12.6609i | 1.44447 | − | 0.438938i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −16.5003 | − | 61.5801i | −0.571360 | − | 2.13234i | ||||
\(835\) | 14.7671 | + | 25.5773i | 0.511036 | + | 0.885141i | ||||
\(836\) | 43.4618 | − | 75.2781i | 1.50316 | − | 2.60355i | ||||
\(837\) | −28.8957 | − | 7.74257i | −0.998780 | − | 0.267622i | ||||
\(838\) | −30.9043 | − | 30.9043i | −1.06757 | − | 1.06757i | ||||
\(839\) | −48.1190 | − | 12.8935i | −1.66125 | − | 0.445132i | −0.698522 | − | 0.715589i | \(-0.746158\pi\) |
−0.962732 | + | 0.270457i | \(0.912825\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0352 | + | 17.3815i | 0.346041 | + | 0.599360i | ||||
\(842\) | 54.3417 | − | 31.3742i | 1.87274 | − | 1.08123i | ||||
\(843\) | 32.7562 | − | 32.7562i | 1.12819 | − | 1.12819i | ||||
\(844\) | 29.9815 | − | 17.3098i | 1.03201 | − | 0.595829i | ||||
\(845\) | −13.6436 | + | 15.5880i | −0.469356 | + | 0.536244i | ||||
\(846\) | − | 34.1836i | − | 1.17526i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.75671 | + | 8.23886i | −0.163346 | + | 0.282924i | ||||
\(849\) | − | 23.2891i | − | 0.799280i | ||||||
\(850\) | 0.959157 | − | 3.57962i | 0.0328988 | − | 0.122780i | ||||
\(851\) | 0.147136 | + | 0.549117i | 0.00504374 | + | 0.0188235i | ||||
\(852\) | 98.0855 | − | 98.0855i | 3.36035 | − | 3.36035i | ||||
\(853\) | 15.4604 | − | 15.4604i | 0.529355 | − | 0.529355i | −0.391025 | − | 0.920380i | \(-0.627879\pi\) |
0.920380 | + | 0.391025i | \(0.127879\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 50.2511 | + | 29.0125i | 1.71855 | + | 0.992207i | ||||
\(856\) | 14.0312 | − | 52.3651i | 0.479576 | − | 1.78980i | ||||
\(857\) | 12.5050 | + | 21.6594i | 0.427164 | + | 0.739869i | 0.996620 | − | 0.0821525i | \(-0.0261794\pi\) |
−0.569456 | + | 0.822022i | \(0.692846\pi\) | |||||||
\(858\) | 53.5881 | + | 50.1420i | 1.82947 | + | 1.71182i | ||||
\(859\) | 30.9754 | + | 17.8837i | 1.05687 | + | 0.610183i | 0.924564 | − | 0.381026i | \(-0.124429\pi\) |
0.132304 | + | 0.991209i | \(0.457762\pi\) | |||||||
\(860\) | 15.1409 | − | 4.05698i | 0.516299 | − | 0.138342i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −60.0127 | + | 34.6484i | −2.04404 | + | 1.18013i | ||||
\(863\) | 10.7130 | + | 39.9815i | 0.364675 | + | 1.36099i | 0.867861 | + | 0.496807i | \(0.165494\pi\) |
−0.503186 | + | 0.864178i | \(0.667839\pi\) | |||||||
\(864\) | 17.4311 | − | 4.67065i | 0.593018 | − | 0.158899i | ||||
\(865\) | −8.60985 | + | 2.30700i | −0.292744 | + | 0.0784405i | ||||
\(866\) | −21.8297 | − | 81.4695i | −0.741803 | − | 2.76845i | ||||
\(867\) | 39.6537 | − | 22.8941i | 1.34671 | − | 0.777524i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.92056 | − | 0.514612i | 0.0651504 | − | 0.0174570i | ||||
\(870\) | −26.7191 | − | 15.4263i | −0.905862 | − | 0.523000i | ||||
\(871\) | −4.50376 | − | 2.40451i | −0.152604 | − | 0.0814736i | ||||
\(872\) | −22.8658 | − | 39.6048i | −0.774335 | − | 1.34119i | ||||
\(873\) | 0.225021 | − | 0.839790i | 0.00761581 | − | 0.0284226i | ||||
\(874\) | −2.34210 | − | 1.35221i | −0.0792229 | − | 0.0457393i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 48.3519 | − | 48.3519i | 1.63366 | − | 1.63366i | ||||
\(877\) | 17.7428 | − | 17.7428i | 0.599133 | − | 0.599133i | −0.340949 | − | 0.940082i | \(-0.610748\pi\) |
0.940082 | + | 0.340949i | \(0.110748\pi\) | |||||||
\(878\) | 5.92937 | + | 22.1287i | 0.200107 | + | 0.746808i | ||||
\(879\) | 5.92188 | − | 22.1007i | 0.199740 | − | 0.745440i | ||||
\(880\) | 6.50498i | 0.219283i | ||||||||
\(881\) | 18.7477 | − | 32.4719i | 0.631624 | − | 1.09401i | −0.355595 | − | 0.934640i | \(-0.615722\pi\) |
0.987220 | − | 0.159365i | \(-0.0509448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.9652i | 0.671881i | 0.941883 | + | 0.335941i | \(0.109054\pi\) | ||||
−0.941883 | + | 0.335941i | \(0.890946\pi\) | |||||||
\(884\) | −5.92869 | − | 5.54744i | −0.199403 | − | 0.186581i | ||||
\(885\) | −15.7992 | + | 9.12168i | −0.531085 | + | 0.306622i | ||||
\(886\) | −64.3666 | + | 64.3666i | −2.16244 | + | 2.16244i | ||||
\(887\) | −44.5877 | + | 25.7427i | −1.49711 | + | 0.864355i | −0.999994 | − | 0.00333069i | \(-0.998940\pi\) |
−0.497113 | + | 0.867686i | \(0.665606\pi\) | |||||||
\(888\) | 19.0264 | + | 32.9546i | 0.638483 | + | 1.10588i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 49.0758 | + | 13.1498i | 1.64502 | + | 0.440783i | ||||
\(891\) | −3.38009 | − | 3.38009i | −0.113237 | − | 0.113237i | ||||
\(892\) | 29.5505 | + | 7.91803i | 0.989424 | + | 0.265115i | ||||
\(893\) | 12.4273 | − | 21.5247i | 0.415863 | − | 0.720297i | ||||
\(894\) | −17.9914 | − | 31.1620i | −0.601722 | − | 1.04221i | ||||
\(895\) | −3.91429 | − | 14.6083i | −0.130840 | − | 0.488303i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.993778 | − | 1.06208i | 0.0331813 | − | 0.0354617i | ||||
\(898\) | −10.9837 | + | 19.0243i | −0.366530 | + | 0.634848i | ||||
\(899\) | 14.1444 | + | 14.1444i | 0.471742 | + | 0.471742i | ||||
\(900\) | 39.8940 | 1.32980 | ||||||||
\(901\) | −4.69720 | −0.156486 | ||||||||
\(902\) | −30.2492 | − | 30.2492i | −1.00719 | − | 1.00719i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.41396 | − | 5.27699i | 0.0470277 | − | 0.175510i | ||||
\(905\) | −10.6439 | + | 2.85202i | −0.353814 | + | 0.0948042i | ||||
\(906\) | −26.6247 | − | 15.3718i | −0.884548 | − | 0.510694i | ||||
\(907\) | − | 28.9564i | − | 0.961483i | −0.876862 | − | 0.480742i | \(-0.840368\pi\) | ||
0.876862 | − | 0.480742i | \(-0.159632\pi\) | |||||||
\(908\) | 57.2723 | + | 15.3461i | 1.90065 | + | 0.509277i | ||||
\(909\) | 5.51424 | 0.182896 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.65299 | 0.121029 | 0.0605144 | − | 0.998167i | \(-0.480726\pi\) | ||||
0.0605144 | + | 0.998167i | \(0.480726\pi\) | |||||||
\(912\) | −27.3123 | − | 7.31832i | −0.904402 | − | 0.242334i | ||||
\(913\) | − | 4.78988i | − | 0.158522i | ||||||
\(914\) | −39.0731 | − | 22.5589i | −1.29242 | − | 0.746181i | ||||
\(915\) | 19.1473 | − | 5.13050i | 0.632990 | − | 0.169609i | ||||
\(916\) | 2.22137 | − | 8.29025i | 0.0733960 | − | 0.273918i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −4.75904 | − | 4.75904i | −0.157072 | − | 0.157072i | ||||
\(919\) | 42.7339 | 1.40966 | 0.704831 | − | 0.709375i | \(-0.251023\pi\) | ||||
0.704831 | + | 0.709375i | \(0.251023\pi\) | |||||||
\(920\) | 0.825389 | 0.0272123 | ||||||||
\(921\) | −47.8734 | − | 47.8734i | −1.57748 | − | 1.57748i | ||||
\(922\) | −15.8924 | + | 27.5265i | −0.523389 | + | 0.906536i | ||||
\(923\) | 1.71407 | + | 51.5954i | 0.0564192 | + | 1.69828i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.47735 | − | 9.24560i | −0.0814548 | − | 0.303994i | ||||
\(926\) | −24.2888 | − | 42.0695i | −0.798181 | − | 1.38249i | ||||
\(927\) | −11.0761 | + | 19.1843i | −0.363786 | + | 0.630095i | ||||
\(928\) | −11.6556 | − | 3.12311i | −0.382614 | − | 0.102521i | ||||
\(929\) | 11.9693 | + | 11.9693i | 0.392700 | + | 0.392700i | 0.875649 | − | 0.482949i | \(-0.160434\pi\) |
−0.482949 | + | 0.875649i | \(0.660434\pi\) | |||||||
\(930\) | 66.7576 | + | 17.8876i | 2.18907 | + | 0.586559i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.43247 | − | 16.3375i | −0.308971 | − | 0.535153i | ||||
\(933\) | 56.6826 | − | 32.7257i | 1.85571 | − | 1.07139i | ||||
\(934\) | −51.4093 | + | 51.4093i | −1.68216 | + | 1.68216i | ||||
\(935\) | −2.78150 | + | 1.60590i | −0.0909648 | + | 0.0525186i | ||||
\(936\) | 27.7988 | − | 52.0684i | 0.908631 | − | 1.70191i | ||||
\(937\) | 46.5686i | 1.52133i | 0.649145 | + | 0.760665i | \(0.275127\pi\) | ||||
−0.649145 | + | 0.760665i | \(0.724873\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.4205 | + | 33.6372i | −0.633763 | + | 1.09771i | ||||
\(940\) | 17.6336i | 0.575145i | ||||||||
\(941\) | −3.08022 | + | 11.4955i | −0.100412 | + | 0.374744i | −0.997784 | − | 0.0665310i | \(-0.978807\pi\) |
0.897372 | + | 0.441275i | \(0.145474\pi\) | |||||||
\(942\) | 21.1632 | + | 78.9820i | 0.689533 | + | 2.57337i | ||||
\(943\) | −0.599516 | + | 0.599516i | −0.0195229 | + | 0.0195229i | ||||
\(944\) | 3.81102 | − | 3.81102i | 0.124038 | − | 0.124038i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.8978 | + | 10.3333i | 0.581909 | + | 0.335965i | ||||
\(947\) | 11.1818 | − | 41.7309i | 0.363358 | − | 1.35607i | −0.506274 | − | 0.862373i | \(-0.668978\pi\) |
0.869633 | − | 0.493699i | \(-0.164356\pi\) | |||||||
\(948\) | −3.06589 | − | 5.31028i | −0.0995756 | − | 0.172470i | ||||
\(949\) | 0.844961 | + | 25.4343i | 0.0274286 | + | 0.825633i | ||||
\(950\) | 39.4345 | + | 22.7675i | 1.27942 | + | 0.738676i | ||||
\(951\) | 44.6321 | − | 11.9591i | 1.44730 | − | 0.387802i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −50.8066 | + | 29.3332i | −1.64579 | + | 0.950195i | −0.667066 | + | 0.744999i | \(0.732450\pi\) |
−0.978721 | + | 0.205196i | \(0.934217\pi\) | |||||||
\(954\) | −20.5447 | − | 76.6738i | −0.665159 | − | 2.48241i | ||||
\(955\) | −3.85576 | + | 1.03315i | −0.124770 | + | 0.0334319i | ||||
\(956\) | −57.3297 | + | 15.3614i | −1.85417 | + | 0.496825i | ||||
\(957\) | −6.70657 | − | 25.0292i | −0.216792 | − | 0.809080i | ||||
\(958\) | 14.9314 | − | 8.62062i | 0.482410 | − | 0.278520i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −51.3127 | + | 13.7492i | −1.65611 | + | 0.443753i | ||||
\(961\) | −11.9589 | − | 6.90448i | −0.385771 | − | 0.222725i | ||||
\(962\) | −32.0643 | − | 7.45998i | −1.03379 | − | 0.240519i | ||||
\(963\) | 35.3273 | + | 61.1886i | 1.13840 | + | 1.97178i | ||||
\(964\) | −12.2160 | + | 45.5907i | −0.393450 | + | 1.46838i | ||||
\(965\) | −31.1288 | − | 17.9722i | −1.00207 | − | 0.578546i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.53769 | + | 7.53769i | −0.242396 | + | 0.242396i | −0.817841 | − | 0.575445i | \(-0.804829\pi\) |
0.575445 | + | 0.817841i | \(0.304829\pi\) | |||||||
\(968\) | 2.83430 | − | 2.83430i | 0.0910978 | − | 0.0910978i | ||||
\(969\) | −3.61338 | − | 13.4853i | −0.116079 | − | 0.433211i | ||||
\(970\) | −0.182220 | + | 0.680055i | −0.00585074 | + | 0.0218353i | ||||
\(971\) | − | 31.5596i | − | 1.01280i | −0.862300 | − | 0.506398i | \(-0.830977\pi\) | ||
0.862300 | − | 0.506398i | \(-0.169023\pi\) | |||||||
\(972\) | −30.8990 | + | 53.5187i | −0.991086 | + | 1.71661i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 23.1495i | − | 0.741759i | ||||||
\(975\) | −16.7324 | + | 17.8824i | −0.535867 | + | 0.572695i | ||||
\(976\) | −5.07160 | + | 2.92809i | −0.162338 | + | 0.0937259i | ||||
\(977\) | −0.807539 | + | 0.807539i | −0.0258355 | + | 0.0258355i | −0.719907 | − | 0.694071i | \(-0.755815\pi\) |
0.694071 | + | 0.719907i | \(0.255815\pi\) | |||||||
\(978\) | −73.2436 | + | 42.2872i | −2.34207 | + | 1.35220i | ||||
\(979\) | 21.3357 | + | 36.9545i | 0.681891 | + | 1.18107i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 57.5708 | + | 15.4261i | 1.83810 | + | 0.492516i | ||||
\(982\) | 63.5097 | + | 63.5097i | 2.02668 | + | 2.02668i | ||||
\(983\) | 28.4968 | + | 7.63569i | 0.908907 | + | 0.243541i | 0.682837 | − | 0.730570i | \(-0.260746\pi\) |
0.226069 | + | 0.974111i | \(0.427412\pi\) | |||||||
\(984\) | −28.3759 | + | 49.1485i | −0.904591 | + | 1.56680i | ||||
\(985\) | −14.2703 | − | 24.7169i | −0.454690 | − | 0.787546i | ||||
\(986\) | 1.16477 | + | 4.34699i | 0.0370939 | + | 0.138436i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 84.6940 | − | 52.7230i | 2.69448 | − | 1.67734i | ||||
\(989\) | 0.204799 | − | 0.354722i | 0.00651222 | − | 0.0112795i | ||||
\(990\) | −38.3794 | − | 38.3794i | −1.21978 | − | 1.21978i | ||||
\(991\) | −45.6092 | −1.44882 | −0.724412 | − | 0.689367i | \(-0.757889\pi\) | ||||
−0.724412 | + | 0.689367i | \(0.757889\pi\) | |||||||
\(992\) | 27.0307 | 0.858225 | ||||||||
\(993\) | 18.8898 | + | 18.8898i | 0.599450 | + | 0.599450i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.76894 | − | 25.2620i | 0.214590 | − | 0.800860i | ||||
\(996\) | −14.2683 | + | 3.82317i | −0.452108 | + | 0.121142i | ||||
\(997\) | 22.5784 | + | 13.0357i | 0.715065 | + | 0.412843i | 0.812934 | − | 0.582356i | \(-0.197869\pi\) |
−0.0978683 | + | 0.995199i | \(0.531202\pi\) | |||||||
\(998\) | 0.00340962i | 0.000107930i | ||||||||
\(999\) | −16.7910 | − | 4.49913i | −0.531243 | − | 0.142346i |
(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 | 637.2.x.b.19.7 | 32 | ||
7.2 | even | 3 | 91.2.bc.a.6.2 | yes | 32 | ||
7.3 | odd | 6 | 637.2.bb.b.227.2 | 32 | |||
7.4 | even | 3 | 637.2.bb.b.227.1 | 32 | |||
7.5 | odd | 6 | 91.2.bc.a.6.1 | ✓ | 32 | ||
7.6 | odd | 2 | inner | 637.2.x.b.19.8 | 32 | ||
13.11 | odd | 12 | 637.2.bb.b.362.2 | 32 | |||
21.2 | odd | 6 | 819.2.fm.g.370.8 | 32 | |||
21.5 | even | 6 | 819.2.fm.g.370.7 | 32 | |||
91.11 | odd | 12 | inner | 637.2.x.b.570.7 | 32 | ||
91.24 | even | 12 | inner | 637.2.x.b.570.8 | 32 | ||
91.37 | odd | 12 | 91.2.bc.a.76.1 | yes | 32 | ||
91.76 | even | 12 | 637.2.bb.b.362.1 | 32 | |||
91.89 | even | 12 | 91.2.bc.a.76.2 | yes | 32 | ||
273.89 | odd | 12 | 819.2.fm.g.622.8 | 32 | |||
273.128 | even | 12 | 819.2.fm.g.622.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.bc.a.6.1 | ✓ | 32 | 7.5 | odd | 6 | ||
91.2.bc.a.6.2 | yes | 32 | 7.2 | even | 3 | ||
91.2.bc.a.76.1 | yes | 32 | 91.37 | odd | 12 | ||
91.2.bc.a.76.2 | yes | 32 | 91.89 | even | 12 | ||
637.2.x.b.19.7 | 32 | 1.1 | even | 1 | trivial | ||
637.2.x.b.19.8 | 32 | 7.6 | odd | 2 | inner | ||
637.2.x.b.570.7 | 32 | 91.11 | odd | 12 | inner | ||
637.2.x.b.570.8 | 32 | 91.24 | even | 12 | inner | ||
637.2.bb.b.227.1 | 32 | 7.4 | even | 3 | |||
637.2.bb.b.227.2 | 32 | 7.3 | odd | 6 | |||
637.2.bb.b.362.1 | 32 | 91.76 | even | 12 | |||
637.2.bb.b.362.2 | 32 | 13.11 | odd | 12 | |||
819.2.fm.g.370.7 | 32 | 21.5 | even | 6 | |||
819.2.fm.g.370.8 | 32 | 21.2 | odd | 6 | |||
819.2.fm.g.622.7 | 32 | 273.128 | even | 12 | |||
819.2.fm.g.622.8 | 32 | 273.89 | odd | 12 |