Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(370,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([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("819.370");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fm (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 370.6 | ||
Character | \(\chi\) | \(=\) | 819.370 |
Dual form | 819.2.fm.f.622.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{12}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.281068 | + | 1.04896i | 0.198745 | + | 0.741726i | 0.991266 | + | 0.131881i | \(0.0421016\pi\) |
−0.792521 | + | 0.609845i | \(0.791232\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.710736 | − | 0.410344i | 0.355368 | − | 0.205172i | ||||
\(5\) | −1.02734 | − | 1.02734i | −0.459441 | − | 0.459441i | 0.439031 | − | 0.898472i | \(-0.355322\pi\) |
−0.898472 | + | 0.439031i | \(0.855322\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.22381 | − | 2.34570i | −0.462557 | − | 0.886590i | ||||
\(8\) | 2.16598 | + | 2.16598i | 0.765790 | + | 0.765790i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.788887 | − | 1.36639i | 0.249468 | − | 0.432091i | ||||
\(11\) | −0.972198 | + | 0.260500i | −0.293129 | + | 0.0785436i | −0.402387 | − | 0.915470i | \(-0.631819\pi\) |
0.109258 | + | 0.994013i | \(0.465153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.05530 | − | 1.91446i | 0.847387 | − | 0.530975i | ||||
\(14\) | 2.11656 | − | 1.94303i | 0.565676 | − | 0.519295i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.842549 | + | 1.45934i | −0.210637 | + | 0.364834i | ||||
\(17\) | −2.37035 | − | 4.10557i | −0.574895 | − | 0.995747i | −0.996053 | − | 0.0887595i | \(-0.971710\pi\) |
0.421159 | − | 0.906987i | \(-0.361624\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.391878 | + | 1.46251i | −0.0899030 | + | 0.335522i | −0.996197 | − | 0.0871243i | \(-0.972232\pi\) |
0.906294 | + | 0.422647i | \(0.138899\pi\) | |||||||
\(20\) | −1.15173 | − | 0.308606i | −0.257535 | − | 0.0690064i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.546507 | − | 0.946578i | −0.116516 | − | 0.201811i | ||||
\(23\) | 0.337046 | + | 0.194594i | 0.0702790 | + | 0.0405756i | 0.534728 | − | 0.845024i | \(-0.320414\pi\) |
−0.464449 | + | 0.885600i | \(0.653748\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 2.88914i | − | 0.577827i | ||||||
\(26\) | 2.86693 | + | 2.66679i | 0.562252 | + | 0.523000i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.83235 | − | 1.16499i | −0.346281 | − | 0.220162i | ||||
\(29\) | 4.30065 | − | 7.44895i | 0.798611 | − | 1.38324i | −0.121909 | − | 0.992541i | \(-0.538902\pi\) |
0.920521 | − | 0.390694i | \(-0.127765\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.92542 | − | 2.92542i | −0.525420 | − | 0.525420i | 0.393783 | − | 0.919203i | \(-0.371166\pi\) |
−0.919203 | + | 0.393783i | \(0.871166\pi\) | |||||||
\(32\) | 4.14997 | + | 1.11198i | 0.733618 | + | 0.196572i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.64034 | − | 3.64034i | 0.624313 | − | 0.624313i | ||||
\(35\) | −1.15256 | + | 3.66710i | −0.194818 | + | 0.619854i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.77690 | − | 2.61971i | 1.60731 | − | 0.430678i | 0.660072 | − | 0.751202i | \(-0.270526\pi\) |
0.947240 | + | 0.320524i | \(0.103859\pi\) | |||||||
\(38\) | −1.64425 | −0.266733 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 4.45041i | − | 0.703671i | ||||||
\(41\) | 8.64616 | − | 2.31673i | 1.35030 | − | 0.361813i | 0.490056 | − | 0.871691i | \(-0.336976\pi\) |
0.860247 | + | 0.509878i | \(0.170310\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.28885 | + | 4.78557i | −1.26404 | + | 0.729792i | −0.973853 | − | 0.227179i | \(-0.927050\pi\) |
−0.290184 | + | 0.956971i | \(0.593717\pi\) | |||||||
\(44\) | −0.584082 | + | 0.584082i | −0.0880537 | + | 0.0880537i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.109388 | + | 0.408241i | −0.0161284 | + | 0.0601919i | ||||
\(47\) | 4.78928 | − | 4.78928i | 0.698588 | − | 0.698588i | −0.265518 | − | 0.964106i | \(-0.585543\pi\) |
0.964106 | + | 0.265518i | \(0.0855430\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.00458 | + | 5.74137i | −0.572082 | + | 0.820196i | ||||
\(50\) | 3.03058 | − | 0.812042i | 0.428589 | − | 0.114840i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.38592 | − | 2.61440i | 0.192193 | − | 0.362552i | ||||
\(53\) | −12.7329 | −1.74900 | −0.874498 | − | 0.485029i | \(-0.838809\pi\) | ||||
−0.874498 | + | 0.485029i | \(0.838809\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.26640 | + | 0.731158i | 0.170762 | + | 0.0985893i | ||||
\(56\) | 2.42998 | − | 7.73148i | 0.324720 | − | 1.03316i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.02241 | + | 2.41755i | 1.18470 | + | 0.317440i | ||||
\(59\) | 0.889636 | + | 0.238377i | 0.115821 | + | 0.0310341i | 0.316264 | − | 0.948671i | \(-0.397572\pi\) |
−0.200443 | + | 0.979705i | \(0.564238\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.36449 | + | 4.82924i | −1.07096 | + | 0.618321i | −0.928445 | − | 0.371471i | \(-0.878854\pi\) |
−0.142519 | + | 0.989792i | \(0.545520\pi\) | |||||||
\(62\) | 2.24640 | − | 3.89088i | 0.285293 | − | 0.494142i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.03588i | 1.00449i | ||||||||
\(65\) | −5.10564 | − | 1.17203i | −0.633277 | − | 0.145373i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.71328 | + | 6.39405i | 0.209311 | + | 0.781158i | 0.988092 | + | 0.153863i | \(0.0491713\pi\) |
−0.778782 | + | 0.627295i | \(0.784162\pi\) | |||||||
\(68\) | −3.36939 | − | 1.94532i | −0.408598 | − | 0.235904i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.17059 | − | 0.178284i | −0.498481 | − | 0.0213090i | ||||
\(71\) | 2.56663 | + | 0.687727i | 0.304603 | + | 0.0816182i | 0.407883 | − | 0.913034i | \(-0.366267\pi\) |
−0.103280 | + | 0.994652i | \(0.532934\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.46596 | − | 2.46596i | 0.288619 | − | 0.288619i | −0.547915 | − | 0.836534i | \(-0.684578\pi\) |
0.836534 | + | 0.547915i | \(0.184578\pi\) | |||||||
\(74\) | 5.49594 | + | 9.51925i | 0.638890 | + | 1.10659i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.321609 | + | 1.20026i | 0.0368911 | + | 0.137680i | ||||
\(77\) | 1.80084 | + | 1.96168i | 0.205225 | + | 0.223554i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.06532 | 0.794911 | 0.397455 | − | 0.917622i | \(-0.369893\pi\) | ||||
0.397455 | + | 0.917622i | \(0.369893\pi\) | |||||||
\(80\) | 2.36483 | − | 0.633653i | 0.264396 | − | 0.0708446i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.86031 | + | 8.41830i | 0.536731 | + | 0.929646i | ||||
\(83\) | 2.43414 | + | 2.43414i | 0.267181 | + | 0.267181i | 0.827963 | − | 0.560782i | \(-0.189499\pi\) |
−0.560782 | + | 0.827963i | \(0.689499\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.78266 | + | 6.65299i | −0.193357 | + | 0.721618i | ||||
\(86\) | −7.34959 | − | 7.34959i | −0.792526 | − | 0.792526i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.67000 | − | 1.54152i | −0.284623 | − | 0.164327i | ||||
\(89\) | 2.79345 | + | 10.4253i | 0.296105 | + | 1.10508i | 0.940336 | + | 0.340248i | \(0.110511\pi\) |
−0.644231 | + | 0.764831i | \(0.722822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.22984 | − | 4.82387i | −0.862722 | − | 0.505679i | ||||
\(92\) | 0.319401 | 0.0332999 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.36986 | + | 3.67764i | 0.657001 | + | 0.379320i | ||||
\(95\) | 1.90509 | − | 1.09990i | 0.195458 | − | 0.112848i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.55710 | + | 13.2753i | −0.361169 | + | 1.34790i | 0.511372 | + | 0.859359i | \(0.329137\pi\) |
−0.872541 | + | 0.488541i | \(0.837529\pi\) | |||||||
\(98\) | −7.14802 | − | 2.58692i | −0.722059 | − | 0.261318i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.18554 | − | 2.05341i | −0.118554 | − | 0.205341i | ||||
\(101\) | 1.97748 | − | 3.42510i | 0.196767 | − | 0.340810i | −0.750711 | − | 0.660630i | \(-0.770289\pi\) |
0.947478 | + | 0.319820i | \(0.103622\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.7709 | 1.25835 | 0.629176 | − | 0.777263i | \(-0.283393\pi\) | ||||
0.629176 | + | 0.777263i | \(0.283393\pi\) | |||||||
\(104\) | 10.7644 | + | 2.47103i | 1.05554 | + | 0.242305i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.57880 | − | 13.3563i | −0.347604 | − | 1.29728i | ||||
\(107\) | −1.79997 | + | 3.11764i | −0.174010 | + | 0.301394i | −0.939818 | − | 0.341675i | \(-0.889006\pi\) |
0.765808 | + | 0.643069i | \(0.222339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.0623175 | + | 0.0623175i | −0.00596893 | + | 0.00596893i | −0.710085 | − | 0.704116i | \(-0.751343\pi\) |
0.704116 | + | 0.710085i | \(0.251343\pi\) | |||||||
\(110\) | −0.411010 | + | 1.53391i | −0.0391882 | + | 0.146252i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.45428 | + | 0.190411i | 0.420890 | + | 0.0179922i | ||||
\(113\) | 1.09268 | + | 1.89259i | 0.102791 | + | 0.178039i | 0.912834 | − | 0.408332i | \(-0.133889\pi\) |
−0.810042 | + | 0.586371i | \(0.800556\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.146347 | − | 0.546176i | −0.0136470 | − | 0.0509312i | ||||
\(116\) | − | 7.05898i | − | 0.655410i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.00019i | 0.0920751i | ||||||||
\(119\) | −6.72955 | + | 10.5846i | −0.616897 | + | 0.970285i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.64897 | + | 4.99349i | −0.786270 | + | 0.453953i | ||||
\(122\) | −7.41666 | − | 7.41666i | −0.671473 | − | 0.671473i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.27962 | − | 0.878773i | −0.294519 | − | 0.0789161i | ||||
\(125\) | −8.10484 | + | 8.10484i | −0.724919 | + | 0.724919i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.3666 | − | 7.13987i | −1.09736 | − | 0.633561i | −0.161834 | − | 0.986818i | \(-0.551741\pi\) |
−0.935526 | + | 0.353257i | \(0.885074\pi\) | |||||||
\(128\) | −0.129367 | + | 0.0346639i | −0.0114346 | + | 0.00306389i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.205617 | − | 5.68503i | −0.0180338 | − | 0.498610i | ||||
\(131\) | 17.8888i | 1.56295i | 0.623934 | + | 0.781477i | \(0.285533\pi\) | ||||
−0.623934 | + | 0.781477i | \(0.714467\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.91018 | − | 0.870606i | 0.339056 | − | 0.0754912i | ||||
\(134\) | −6.22555 | + | 3.59432i | −0.537805 | + | 0.310502i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.75845 | − | 14.0267i | 0.322284 | − | 1.20278i | ||||
\(137\) | 0.654988 | − | 2.44445i | 0.0559594 | − | 0.208843i | −0.932285 | − | 0.361724i | \(-0.882188\pi\) |
0.988245 | + | 0.152881i | \(0.0488550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.86338 | − | 5.11727i | 0.751782 | − | 0.434041i | −0.0745556 | − | 0.997217i | \(-0.523754\pi\) |
0.826337 | + | 0.563176i | \(0.190421\pi\) | |||||||
\(140\) | 0.685607 | + | 3.07929i | 0.0579444 | + | 0.260247i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.88559i | 0.242153i | ||||||||
\(143\) | −2.47164 | + | 2.65714i | −0.206689 | + | 0.222201i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0709 | + | 3.23438i | −1.00243 | + | 0.268601i | ||||
\(146\) | 3.27979 | + | 1.89359i | 0.271437 | + | 0.156714i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.87381 | − | 5.87381i | 0.482825 | − | 0.482825i | ||||
\(149\) | −8.14575 | − | 2.18265i | −0.667326 | − | 0.178809i | −0.0907761 | − | 0.995871i | \(-0.528935\pi\) |
−0.576550 | + | 0.817062i | \(0.695601\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.453678 | − | 0.453678i | −0.0369198 | − | 0.0369198i | 0.688406 | − | 0.725326i | \(-0.258311\pi\) |
−0.725326 | + | 0.688406i | \(0.758311\pi\) | |||||||
\(152\) | −4.01656 | + | 2.31896i | −0.325786 | + | 0.188093i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.55156 | + | 2.44037i | −0.125028 | + | 0.196651i | ||||
\(155\) | 6.01081i | 0.482800i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 8.10530i | − | 0.646874i | −0.946250 | − | 0.323437i | \(-0.895162\pi\) | ||
0.946250 | − | 0.323437i | \(-0.104838\pi\) | |||||||
\(158\) | 1.98583 | + | 7.41123i | 0.157984 | + | 0.589606i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.12105 | − | 5.40583i | −0.246741 | − | 0.427368i | ||||
\(161\) | 0.0439771 | − | 1.02875i | 0.00346588 | − | 0.0810771i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.55525 | − | 13.2684i | 0.278469 | − | 1.03926i | −0.675012 | − | 0.737807i | \(-0.735862\pi\) |
0.953481 | − | 0.301453i | \(-0.0974717\pi\) | |||||||
\(164\) | 5.19448 | − | 5.19448i | 0.405621 | − | 0.405621i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.86915 | + | 3.23746i | −0.145074 | + | 0.251276i | ||||
\(167\) | 5.75214 | + | 21.4673i | 0.445114 | + | 1.66119i | 0.715636 | + | 0.698473i | \(0.246137\pi\) |
−0.270523 | + | 0.962714i | \(0.587196\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.66969 | − | 11.6985i | 0.436130 | − | 0.899884i | ||||
\(170\) | −7.47975 | −0.573671 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.92745 | + | 6.80255i | −0.299466 | + | 0.518690i | ||||
\(173\) | −6.33728 | − | 10.9765i | −0.481815 | − | 0.834527i | 0.517967 | − | 0.855400i | \(-0.326689\pi\) |
−0.999782 | + | 0.0208728i | \(0.993355\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.77703 | + | 3.53575i | −0.512295 | + | 0.267278i | ||||
\(176\) | 0.438968 | − | 1.63825i | 0.0330884 | − | 0.123488i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.1505 | + | 5.86042i | −0.760816 | + | 0.439257i | ||||
\(179\) | −9.48849 | − | 5.47818i | −0.709203 | − | 0.409459i | 0.101563 | − | 0.994829i | \(-0.467616\pi\) |
−0.810766 | + | 0.585370i | \(0.800949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.38394 | 0.325856 | 0.162928 | − | 0.986638i | \(-0.447906\pi\) | ||||
0.162928 | + | 0.986638i | \(0.447906\pi\) | |||||||
\(182\) | 2.74689 | − | 9.98860i | 0.203613 | − | 0.740404i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.308549 | + | 1.15152i | 0.0227466 | + | 0.0848913i | ||||
\(185\) | −12.7356 | − | 7.35288i | −0.936338 | − | 0.540595i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.37395 | + | 3.37395i | 0.246728 | + | 0.246728i | ||||
\(188\) | 1.43866 | − | 5.36916i | 0.104925 | − | 0.391586i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.68921 | + | 1.68921i | 0.122548 | + | 0.122548i | ||||
\(191\) | 4.92507 | + | 8.53047i | 0.356366 | + | 0.617243i | 0.987351 | − | 0.158552i | \(-0.0506824\pi\) |
−0.630985 | + | 0.775795i | \(0.717349\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.2874 | − | 3.29240i | 0.884465 | − | 0.236992i | 0.212133 | − | 0.977241i | \(-0.431959\pi\) |
0.672333 | + | 0.740249i | \(0.265292\pi\) | |||||||
\(194\) | −14.9250 | −1.07155 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.490261 | + | 5.72385i | −0.0350187 | + | 0.408847i | ||||
\(197\) | 0.404048 | + | 1.50793i | 0.0287873 | + | 0.107436i | 0.978825 | − | 0.204701i | \(-0.0656221\pi\) |
−0.950037 | + | 0.312136i | \(0.898955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.84499 | + | 10.1238i | 0.414340 | + | 0.717659i | 0.995359 | − | 0.0962317i | \(-0.0306790\pi\) |
−0.581019 | + | 0.813890i | \(0.697346\pi\) | |||||||
\(200\) | 6.25781 | − | 6.25781i | 0.442494 | − | 0.442494i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.14860 | + | 1.11161i | 0.291894 | + | 0.0782128i | ||||
\(203\) | −22.7362 | − | 0.971923i | −1.59577 | − | 0.0682156i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.2626 | − | 6.50249i | −0.786617 | − | 0.454153i | ||||
\(206\) | 3.58948 | + | 13.3961i | 0.250091 | + | 0.933351i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.219604 | + | 6.07174i | 0.0152268 | + | 0.420999i | ||||
\(209\) | − | 1.52393i | − | 0.105413i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.0809 | + | 19.1926i | −0.762838 | + | 1.32127i | 0.178544 | + | 0.983932i | \(0.442861\pi\) |
−0.941382 | + | 0.337343i | \(0.890472\pi\) | |||||||
\(212\) | −9.04972 | + | 5.22486i | −0.621537 | + | 0.358845i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.77619 | − | 1.01183i | −0.258135 | − | 0.0691670i | ||||
\(215\) | 13.4319 | + | 3.59907i | 0.916048 | + | 0.245454i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.28198 | + | 10.4423i | −0.222795 | + | 0.708869i | ||||
\(218\) | −0.0828838 | − | 0.0478530i | −0.00561360 | − | 0.00324101i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.20010 | 0.0809110 | ||||||||
\(221\) | −15.1021 | − | 8.00580i | −1.01588 | − | 0.538528i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2842 | + | 3.55949i | −0.889575 | + | 0.238361i | −0.674534 | − | 0.738244i | \(-0.735655\pi\) |
−0.215041 | + | 0.976605i | \(0.568989\pi\) | |||||||
\(224\) | −2.47041 | − | 11.0954i | −0.165061 | − | 0.741344i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.67813 | + | 1.67813i | −0.111627 | + | 0.111627i | ||||
\(227\) | 1.04021 | − | 3.88213i | 0.0690413 | − | 0.257666i | −0.922775 | − | 0.385339i | \(-0.874084\pi\) |
0.991816 | + | 0.127674i | \(0.0407510\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.36272 | − | 1.36272i | 0.0900509 | − | 0.0900509i | −0.660646 | − | 0.750697i | \(-0.729718\pi\) |
0.750697 | + | 0.660646i | \(0.229718\pi\) | |||||||
\(230\) | 0.531783 | − | 0.307025i | 0.0350647 | − | 0.0202446i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 25.4494 | − | 6.81915i | 1.67084 | − | 0.447699i | ||||
\(233\) | − | 1.13013i | − | 0.0740376i | −0.999315 | − | 0.0370188i | \(-0.988214\pi\) | ||
0.999315 | − | 0.0370188i | \(-0.0117861\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.84046 | −0.641921 | ||||||||
\(236\) | 0.730113 | − | 0.195633i | 0.0475263 | − | 0.0127346i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.9942 | − | 4.08405i | −0.842290 | − | 0.264729i | ||||
\(239\) | −3.62833 | + | 3.62833i | −0.234697 | + | 0.234697i | −0.814650 | − | 0.579953i | \(-0.803071\pi\) |
0.579953 | + | 0.814650i | \(0.303071\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.46780 | − | 2.53689i | −0.609875 | − | 0.163415i | −0.0593540 | − | 0.998237i | \(-0.518904\pi\) |
−0.550521 | + | 0.834822i | \(0.685571\pi\) | |||||||
\(242\) | −7.66890 | − | 7.66890i | −0.492976 | − | 0.492976i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.96330 | + | 6.86463i | −0.253724 | + | 0.439463i | ||||
\(245\) | 10.0124 | − | 1.78428i | 0.639671 | − | 0.113994i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.60261 | + | 5.21863i | 0.101972 | + | 0.332054i | ||||
\(248\) | − | 12.6728i | − | 0.804723i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.7797 | − | 6.22363i | −0.681765 | − | 0.393617i | ||||
\(251\) | 14.1820 | + | 24.5639i | 0.895158 | + | 1.55046i | 0.833610 | + | 0.552354i | \(0.186270\pi\) |
0.0615480 | + | 0.998104i | \(0.480396\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.378367 | − | 0.101383i | −0.0237878 | − | 0.00637391i | ||||
\(254\) | 4.01357 | − | 14.9789i | 0.251834 | − | 0.939857i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.96316 | + | 13.7926i | 0.497698 | + | 0.862037i | ||||
\(257\) | 3.32083 | − | 5.75185i | 0.207148 | − | 0.358790i | −0.743667 | − | 0.668550i | \(-0.766915\pi\) |
0.950815 | + | 0.309760i | \(0.100249\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.1101 | − | 19.7276i | −1.12531 | − | 1.22581i | ||||
\(260\) | −4.10970 | + | 1.26206i | −0.254873 | + | 0.0782698i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.7646 | + | 5.02797i | −1.15928 | + | 0.310629i | ||||
\(263\) | 6.24723 | − | 10.8205i | 0.385221 | − | 0.667222i | −0.606579 | − | 0.795023i | \(-0.707459\pi\) |
0.991800 | + | 0.127801i | \(0.0407920\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.0810 | + | 13.0810i | 0.803561 | + | 0.803561i | ||||
\(266\) | 2.01226 | + | 3.85692i | 0.123379 | + | 0.236483i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.84145 | + | 3.84145i | 0.234654 | + | 0.234654i | ||||
\(269\) | −7.27737 | + | 4.20159i | −0.443709 | + | 0.256176i | −0.705170 | − | 0.709038i | \(-0.749129\pi\) |
0.261460 | + | 0.965214i | \(0.415796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0939748 | + | 0.350719i | 0.00570857 | + | 0.0213047i | 0.968721 | − | 0.248151i | \(-0.0798229\pi\) |
−0.963013 | + | 0.269456i | \(0.913156\pi\) | |||||||
\(272\) | 7.98855 | 0.484377 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.74822 | 0.166026 | ||||||||
\(275\) | 0.752619 | + | 2.80881i | 0.0453846 | + | 0.169378i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.5251 | − | 7.80875i | 0.812647 | − | 0.469182i | −0.0352270 | − | 0.999379i | \(-0.511215\pi\) |
0.847874 | + | 0.530197i | \(0.177882\pi\) | |||||||
\(278\) | 7.85901 | + | 7.85901i | 0.471352 | + | 0.471352i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.4393 | + | 5.44645i | −0.623867 | + | 0.325488i | ||||
\(281\) | 0.848694 | + | 0.848694i | 0.0506289 | + | 0.0506289i | 0.731968 | − | 0.681339i | \(-0.238602\pi\) |
−0.681339 | + | 0.731968i | \(0.738602\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9723 | − | 20.7366i | 0.711678 | − | 1.23266i | −0.252549 | − | 0.967584i | \(-0.581269\pi\) |
0.964227 | − | 0.265078i | \(-0.0853976\pi\) | |||||||
\(284\) | 2.10640 | − | 0.564409i | 0.124992 | − | 0.0334915i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.48193 | − | 1.84581i | −0.205891 | − | 0.109145i | ||||
\(287\) | −16.0156 | − | 17.4460i | −0.945371 | − | 1.02981i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.73713 | + | 4.74084i | −0.161007 | + | 0.278873i | ||||
\(290\) | −6.78546 | − | 11.7528i | −0.398456 | − | 0.690146i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.740755 | − | 2.76454i | 0.0433494 | − | 0.161782i | ||||
\(293\) | 18.6502 | + | 4.99730i | 1.08956 | + | 0.291946i | 0.758505 | − | 0.651667i | \(-0.225930\pi\) |
0.331051 | + | 0.943613i | \(0.392597\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.669066 | − | 1.15886i | −0.0389545 | − | 0.0674712i | ||||
\(296\) | 26.8508 | + | 15.5023i | 1.56067 | + | 0.901055i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 9.15803i | − | 0.530510i | ||||||
\(299\) | 1.40232 | − | 0.0507193i | 0.0810982 | − | 0.00293317i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.3695 | + | 13.5865i | 1.23172 | + | 0.783112i | ||||
\(302\) | 0.348375 | − | 0.603403i | 0.0200467 | − | 0.0347220i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.80412 | − | 1.80412i | −0.103473 | − | 0.103473i | ||||
\(305\) | 13.5545 | + | 3.63191i | 0.776127 | + | 0.207963i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1942 | − | 17.1942i | 0.981322 | − | 0.981322i | −0.0185063 | − | 0.999829i | \(-0.505891\pi\) |
0.999829 | + | 0.0185063i | \(0.00589106\pi\) | |||||||
\(308\) | 2.08488 | + | 0.655273i | 0.118797 | + | 0.0373377i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.30509 | + | 1.68944i | −0.358105 | + | 0.0959539i | ||||
\(311\) | −14.0638 | −0.797487 | −0.398744 | − | 0.917062i | \(-0.630554\pi\) | ||||
−0.398744 | + | 0.917062i | \(0.630554\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 18.8063i | − | 1.06300i | −0.847060 | − | 0.531498i | \(-0.821629\pi\) | ||
0.847060 | − | 0.531498i | \(-0.178371\pi\) | |||||||
\(314\) | 8.50213 | − | 2.27814i | 0.479803 | − | 0.128563i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.02158 | − | 2.89921i | 0.282486 | − | 0.163093i | ||||
\(317\) | 1.67207 | − | 1.67207i | 0.0939128 | − | 0.0939128i | −0.658590 | − | 0.752502i | \(-0.728847\pi\) |
0.752502 | + | 0.658590i | \(0.228847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.24064 | + | 8.36218i | −0.125452 | + | 0.468192i | ||||
\(320\) | 8.25560 | − | 8.25560i | 0.461502 | − | 0.461502i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.09148 | − | 0.243019i | 0.0608258 | − | 0.0135429i | ||||
\(323\) | 6.93332 | − | 1.85778i | 0.385780 | − | 0.103369i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.53113 | − | 8.82717i | −0.306812 | − | 0.489643i | ||||
\(326\) | 14.9172 | 0.826190 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 23.7454 | + | 13.7094i | 1.31112 | + | 0.756976i | ||||
\(329\) | −17.0954 | − | 5.37302i | −0.942497 | − | 0.296224i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.2290 | − | 8.90368i | −1.82643 | − | 0.489391i | −0.828886 | − | 0.559418i | \(-0.811025\pi\) |
−0.997545 | + | 0.0700274i | \(0.977691\pi\) | |||||||
\(332\) | 2.72886 | + | 0.731196i | 0.149766 | + | 0.0401296i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.9015 | + | 12.0675i | −1.14368 | + | 0.660304i | ||||
\(335\) | 4.80875 | − | 8.32901i | 0.262730 | − | 0.455062i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.43766i | − | 0.187261i | −0.995607 | − | 0.0936305i | \(-0.970153\pi\) | ||
0.995607 | − | 0.0936305i | \(-0.0298472\pi\) | |||||||
\(338\) | 13.8648 | + | 2.65921i | 0.754145 | + | 0.144642i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.46301 | + | 5.46002i | 0.0793428 | + | 0.296111i | ||||
\(341\) | 3.60616 | + | 2.08201i | 0.195284 | + | 0.112747i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3684 | + | 2.36717i | 0.991798 | + | 0.127815i | ||||
\(344\) | −28.3189 | − | 7.58803i | −1.52685 | − | 0.409119i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.73268 | − | 9.73268i | 0.523232 | − | 0.523232i | ||||
\(347\) | 9.46705 | + | 16.3974i | 0.508218 | + | 0.880259i | 0.999955 | + | 0.00951518i | \(0.00302882\pi\) |
−0.491737 | + | 0.870744i | \(0.663638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.44404 | + | 31.5136i | 0.451999 | + | 1.68688i | 0.696764 | + | 0.717300i | \(0.254623\pi\) |
−0.244765 | + | 0.969582i | \(0.578711\pi\) | |||||||
\(350\) | −5.61366 | − | 6.11504i | −0.300063 | − | 0.326863i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.32426 | −0.230484 | ||||||||
\(353\) | −31.7685 | + | 8.51233i | −1.69086 | + | 0.453066i | −0.970613 | − | 0.240647i | \(-0.922640\pi\) |
−0.720251 | + | 0.693713i | \(0.755974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.93028 | − | 3.34334i | −0.102449 | − | 0.177446i | ||||
\(356\) | 6.26336 | + | 6.26336i | 0.331957 | + | 0.331957i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.07948 | − | 11.4928i | 0.162756 | − | 0.607412i | ||||
\(359\) | 1.45164 | + | 1.45164i | 0.0766146 | + | 0.0766146i | 0.744376 | − | 0.667761i | \(-0.232747\pi\) |
−0.667761 | + | 0.744376i | \(0.732747\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.4691 | + | 8.35375i | 0.761533 | + | 0.439671i | ||||
\(362\) | 1.23218 | + | 4.59857i | 0.0647622 | + | 0.241696i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.82869 | − | 0.0514311i | −0.410335 | − | 0.00269572i | ||||
\(365\) | −5.06677 | −0.265207 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.400843 | + | 0.231427i | 0.0209238 | + | 0.0120804i | 0.510425 | − | 0.859922i | \(-0.329488\pi\) |
−0.489502 | + | 0.872002i | \(0.662821\pi\) | |||||||
\(368\) | −0.567956 | + | 0.327909i | −0.0296067 | + | 0.0170935i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.13331 | − | 15.4257i | 0.214881 | − | 0.801946i | ||||
\(371\) | 15.5826 | + | 29.8675i | 0.809010 | + | 1.55064i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.17460 | + | 8.96266i | 0.267930 | + | 0.464069i | 0.968327 | − | 0.249685i | \(-0.0803269\pi\) |
−0.700397 | + | 0.713754i | \(0.746994\pi\) | |||||||
\(374\) | −2.59083 | + | 4.48744i | −0.133968 | + | 0.232040i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.7470 | 1.06994 | ||||||||
\(377\) | −1.12093 | − | 30.9922i | −0.0577309 | − | 1.59618i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.99214 | + | 14.8989i | 0.205062 | + | 0.765303i | 0.989431 | + | 0.145007i | \(0.0463206\pi\) |
−0.784368 | + | 0.620295i | \(0.787013\pi\) | |||||||
\(380\) | 0.902677 | − | 1.56348i | 0.0463064 | − | 0.0802050i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.56383 | + | 7.56383i | −0.386999 | + | 0.386999i | ||||
\(383\) | 8.40301 | − | 31.3605i | 0.429374 | − | 1.60245i | −0.324808 | − | 0.945780i | \(-0.605300\pi\) |
0.754182 | − | 0.656665i | \(-0.228034\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.165238 | − | 3.86539i | 0.00842128 | − | 0.196999i | ||||
\(386\) | 6.90717 | + | 11.9636i | 0.351566 | + | 0.608930i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.91927 | + | 10.8948i | 0.148203 | + | 0.553102i | ||||
\(389\) | 37.3829i | 1.89539i | 0.319179 | + | 0.947694i | \(0.396593\pi\) | ||||
−0.319179 | + | 0.947694i | \(0.603407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.84502i | − | 0.0933068i | ||||||
\(392\) | −21.1095 | + | 3.76186i | −1.06619 | + | 0.190003i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.46819 | + | 0.847660i | −0.0739664 | + | 0.0427045i | ||||
\(395\) | −7.25850 | − | 7.25850i | −0.365215 | − | 0.365215i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.9889 | + | 9.37524i | 1.75604 | + | 0.470530i | 0.985899 | − | 0.167343i | \(-0.0535187\pi\) |
0.770142 | + | 0.637873i | \(0.220185\pi\) | |||||||
\(398\) | −8.97663 | + | 8.97663i | −0.449958 | + | 0.449958i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.21622 | + | 2.43424i | 0.210811 | + | 0.121712i | ||||
\(401\) | 33.6403 | − | 9.01390i | 1.67992 | − | 0.450133i | 0.712161 | − | 0.702016i | \(-0.247716\pi\) |
0.967758 | + | 0.251883i | \(0.0810498\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.5386 | − | 3.33743i | −0.724220 | − | 0.166249i | ||||
\(404\) | − | 3.24579i | − | 0.161484i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.37089 | − | 24.1225i | −0.266553 | − | 1.19718i | ||||
\(407\) | −8.82265 | + | 5.09376i | −0.437323 | + | 0.252488i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.97572 | + | 11.1055i | −0.147140 | + | 0.549134i | 0.852511 | + | 0.522709i | \(0.175079\pi\) |
−0.999651 | + | 0.0264241i | \(0.991588\pi\) | |||||||
\(410\) | 3.65528 | − | 13.6417i | 0.180521 | − | 0.673715i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.07672 | − | 5.24044i | 0.447178 | − | 0.258178i | ||||
\(413\) | −0.529585 | − | 2.37854i | −0.0260592 | − | 0.117040i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 5.00138i | − | 0.245508i | ||||||
\(416\) | 14.8082 | − | 4.54751i | 0.726034 | − | 0.222960i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.59854 | − | 0.428328i | 0.0781872 | − | 0.0209502i | ||||
\(419\) | 25.3323 | + | 14.6256i | 1.23756 | + | 0.714507i | 0.968595 | − | 0.248642i | \(-0.0799844\pi\) |
0.268967 | + | 0.963149i | \(0.413318\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.84750 | + | 8.84750i | −0.431201 | + | 0.431201i | −0.889037 | − | 0.457836i | \(-0.848625\pi\) |
0.457836 | + | 0.889037i | \(0.348625\pi\) | |||||||
\(422\) | −23.2467 | − | 6.22894i | −1.13163 | − | 0.303220i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −27.5792 | − | 27.5792i | −1.33936 | − | 1.33936i | ||||
\(425\) | −11.8615 | + | 6.84826i | −0.575369 | + | 0.332190i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.5645 | + | 13.7105i | 1.04358 | + | 0.663497i | ||||
\(428\) | 2.95443i | 0.142808i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.1011i | 0.728239i | ||||||||
\(431\) | 3.91058 | + | 14.5945i | 0.188366 | + | 0.702992i | 0.993885 | + | 0.110422i | \(0.0352201\pi\) |
−0.805519 | + | 0.592570i | \(0.798113\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6099 | − | 28.7692i | −0.798222 | − | 1.38256i | −0.920773 | − | 0.390100i | \(-0.872441\pi\) |
0.122550 | − | 0.992462i | \(-0.460893\pi\) | |||||||
\(434\) | −11.8760 | − | 0.507674i | −0.570066 | − | 0.0243691i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.0187197 | + | 0.0698628i | −0.000896511 | + | 0.00334582i | ||||
\(437\) | −0.416676 | + | 0.416676i | −0.0199323 | + | 0.0199323i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.12262 | − | 5.40854i | 0.149035 | − | 0.258135i | −0.781836 | − | 0.623484i | \(-0.785717\pi\) |
0.930871 | + | 0.365348i | \(0.119050\pi\) | |||||||
\(440\) | 1.15933 | + | 4.32668i | 0.0552689 | + | 0.206266i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.15304 | − | 18.0916i | 0.197540 | − | 0.860530i | ||||
\(443\) | 17.0915 | 0.812043 | 0.406022 | − | 0.913863i | \(-0.366916\pi\) | ||||
0.406022 | + | 0.913863i | \(0.366916\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.84051 | − | 13.5802i | 0.371676 | − | 0.643762i | ||||
\(446\) | −7.46751 | − | 12.9341i | −0.353597 | − | 0.612448i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18.8497 | − | 9.83440i | 0.890566 | − | 0.464632i | ||||
\(449\) | 9.60577 | − | 35.8492i | 0.453324 | − | 1.69183i | −0.239644 | − | 0.970861i | \(-0.577031\pi\) |
0.692968 | − | 0.720968i | \(-0.256303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.80227 | + | 4.50464i | −0.367395 | + | 0.212115i | ||||
\(452\) | 1.55322 | + | 0.896753i | 0.0730574 | + | 0.0421797i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.36456 | 0.204839 | ||||||||
\(455\) | 3.49911 | + | 13.4106i | 0.164041 | + | 0.628700i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.07001 | + | 7.72540i | 0.0968312 | + | 0.361379i | 0.997291 | − | 0.0735609i | \(-0.0234363\pi\) |
−0.900460 | + | 0.434940i | \(0.856770\pi\) | |||||||
\(458\) | 1.81245 | + | 1.04642i | 0.0846902 | + | 0.0488959i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.328134 | − | 0.328134i | −0.0152993 | − | 0.0152993i | ||||
\(461\) | 2.87961 | − | 10.7469i | 0.134117 | − | 0.500531i | −0.865883 | − | 0.500247i | \(-0.833243\pi\) |
1.00000 | 0.000284720i | \(-9.06291e-5\pi\) | ||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.2312 | + | 24.2312i | 1.12612 | + | 1.12612i | 0.990803 | + | 0.135316i | \(0.0432049\pi\) |
0.135316 | + | 0.990803i | \(0.456795\pi\) | |||||||
\(464\) | 7.24702 | + | 12.5522i | 0.336435 | + | 0.582722i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.18546 | − | 0.317644i | 0.0549156 | − | 0.0147146i | ||||
\(467\) | 10.5574 | 0.488538 | 0.244269 | − | 0.969707i | \(-0.421452\pi\) | ||||
0.244269 | + | 0.969707i | \(0.421452\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9018 | − | 11.8439i | 0.595748 | − | 0.546902i | ||||
\(470\) | −2.76583 | − | 10.3222i | −0.127578 | − | 0.476129i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.41061 | + | 2.44325i | 0.0649287 | + | 0.112460i | ||||
\(473\) | 6.81176 | − | 6.81176i | 0.313205 | − | 0.313205i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.22539 | + | 1.13219i | 0.193874 | + | 0.0519484i | ||||
\(476\) | −0.439630 | + | 10.2843i | −0.0201504 | + | 0.471378i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.82578 | − | 2.78616i | −0.220726 | − | 0.127436i | ||||
\(479\) | 2.28082 | + | 8.51215i | 0.104214 | + | 0.388930i | 0.998255 | − | 0.0590545i | \(-0.0188086\pi\) |
−0.894041 | + | 0.447985i | \(0.852142\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.8560 | − | 26.7215i | 1.13334 | − | 1.21839i | ||||
\(482\) | − | 10.6444i | − | 0.484838i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.09809 | + | 7.09810i | −0.186277 | + | 0.322641i | ||||
\(485\) | 17.2926 | − | 9.98389i | 0.785217 | − | 0.453345i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.8298 | + | 5.31338i | 0.898574 | + | 0.240772i | 0.678404 | − | 0.734689i | \(-0.262672\pi\) |
0.220170 | + | 0.975461i | \(0.429339\pi\) | |||||||
\(488\) | −28.5774 | − | 7.65728i | −1.29364 | − | 0.346629i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.68581 | + | 10.0011i | 0.211683 | + | 0.451804i | ||||
\(491\) | 2.72329 | + | 1.57229i | 0.122900 | + | 0.0709565i | 0.560190 | − | 0.828364i | \(-0.310728\pi\) |
−0.437290 | + | 0.899321i | \(0.644062\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −40.7762 | −1.83647 | ||||||||
\(494\) | −5.02369 | + | 3.14786i | −0.226026 | + | 0.141629i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.73398 | − | 1.80436i | 0.302364 | − | 0.0810183i | ||||
\(497\) | −1.52787 | − | 6.86219i | −0.0685345 | − | 0.307811i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.7019 | + | 10.7019i | −0.479082 | + | 0.479082i | −0.904838 | − | 0.425756i | \(-0.860008\pi\) |
0.425756 | + | 0.904838i | \(0.360008\pi\) | |||||||
\(500\) | −2.43463 | + | 9.08617i | −0.108880 | + | 0.406346i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.7804 | + | 21.7804i | −0.972107 | + | 0.972107i | ||||
\(503\) | −22.4889 | + | 12.9840i | −1.00273 | + | 0.578926i | −0.909055 | − | 0.416677i | \(-0.863195\pi\) |
−0.0936745 | + | 0.995603i | \(0.529861\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.55031 | + | 1.48720i | −0.246985 | + | 0.0661795i | ||||
\(506\) | − | 0.425387i | − | 0.0189108i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.7192 | −0.519955 | ||||||||
\(509\) | 31.8249 | − | 8.52745i | 1.41061 | − | 0.377973i | 0.528469 | − | 0.848952i | \(-0.322766\pi\) |
0.882144 | + | 0.470980i | \(0.156100\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.80225 | − | 2.76652i | −0.389389 | − | 0.122384i | ||||
\(512\) | −12.4191 | + | 12.4191i | −0.548851 | + | 0.548851i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.96683 | + | 1.86676i | 0.307294 | + | 0.0823391i | ||||
\(515\) | −13.1201 | − | 13.1201i | −0.578139 | − | 0.578139i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.40852 | + | 5.90373i | −0.149907 | + | 0.259646i | ||||
\(518\) | 15.6033 | − | 24.5416i | 0.685568 | − | 1.07829i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.52012 | − | 13.5973i | −0.373632 | − | 0.596282i | ||||
\(521\) | − | 26.4544i | − | 1.15899i | −0.814976 | − | 0.579495i | \(-0.803250\pi\) | ||
0.814976 | − | 0.579495i | \(-0.196750\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.23888 | − | 5.33407i | −0.403988 | − | 0.233243i | 0.284215 | − | 0.958761i | \(-0.408267\pi\) |
−0.688203 | + | 0.725518i | \(0.741600\pi\) | |||||||
\(524\) | 7.34057 | + | 12.7142i | 0.320674 | + | 0.555424i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.1062 | + | 3.51179i | 0.571456 | + | 0.153121i | ||||
\(527\) | −5.07623 | + | 18.9448i | −0.221124 | + | 0.825247i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4243 | − | 19.7874i | −0.496707 | − | 0.860322i | ||||
\(530\) | −10.0448 | + | 17.3981i | −0.436318 | + | 0.755726i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.42186 | − | 2.22329i | 0.105001 | − | 0.0963919i | ||||
\(533\) | 21.9813 | − | 23.6310i | 0.952116 | − | 1.02357i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.05207 | − | 1.35370i | 0.218420 | − | 0.0585255i | ||||
\(536\) | −10.1385 | + | 17.5603i | −0.437915 | + | 0.758490i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.45273 | − | 6.45273i | −0.278197 | − | 0.278197i | ||||
\(539\) | 2.39762 | − | 6.62494i | 0.103273 | − | 0.285357i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.42225 | + | 3.42225i | 0.147134 | + | 0.147134i | 0.776836 | − | 0.629702i | \(-0.216823\pi\) |
−0.629702 | + | 0.776836i | \(0.716823\pi\) | |||||||
\(542\) | −0.341476 | + | 0.197151i | −0.0146677 | + | 0.00846838i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.27157 | − | 19.6738i | −0.226017 | − | 0.843506i | ||||
\(545\) | 0.128043 | 0.00548475 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.6406 | −0.839770 | −0.419885 | − | 0.907577i | \(-0.637930\pi\) | ||||
−0.419885 | + | 0.907577i | \(0.637930\pi\) | |||||||
\(548\) | −0.537540 | − | 2.00613i | −0.0229626 | − | 0.0856975i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.73479 | + | 1.57893i | −0.116612 | + | 0.0673259i | ||||
\(551\) | 9.20882 | + | 9.20882i | 0.392309 | + | 0.392309i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.64661 | − | 16.5731i | −0.367691 | − | 0.704759i | ||||
\(554\) | 11.9925 | + | 11.9925i | 0.509514 | + | 0.509514i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.19968 | − | 7.27406i | 0.178106 | − | 0.308489i | ||||
\(557\) | 34.1973 | − | 9.16315i | 1.44899 | − | 0.388255i | 0.553316 | − | 0.832971i | \(-0.313362\pi\) |
0.895672 | + | 0.444716i | \(0.146695\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.1631 | + | 30.4900i | −0.683627 | + | 1.28959i | ||||
\(560\) | −4.38045 | − | 4.77169i | −0.185108 | − | 0.201641i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.651705 | + | 1.12879i | −0.0274905 | + | 0.0476149i | ||||
\(563\) | −15.9428 | − | 27.6137i | −0.671908 | − | 1.16378i | −0.977362 | − | 0.211572i | \(-0.932142\pi\) |
0.305455 | − | 0.952207i | \(-0.401192\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.821772 | − | 3.06689i | 0.0345722 | − | 0.129025i | ||||
\(566\) | 25.1168 | + | 6.73003i | 1.05574 | + | 0.282884i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.06967 | + | 7.04888i | 0.170760 | + | 0.295764i | ||||
\(569\) | −23.6253 | − | 13.6401i | −0.990426 | − | 0.571823i | −0.0850245 | − | 0.996379i | \(-0.527097\pi\) |
−0.905402 | + | 0.424556i | \(0.860430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0144i | 1.38161i | 0.723042 | + | 0.690804i | \(0.242743\pi\) | ||||
−0.723042 | + | 0.690804i | \(0.757257\pi\) | |||||||
\(572\) | −0.666344 | + | 2.90275i | −0.0278612 | + | 0.121370i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 13.7987 | − | 21.7032i | 0.575946 | − | 0.905874i | ||||
\(575\) | 0.562208 | − | 0.973772i | 0.0234457 | − | 0.0406091i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.3031 | − | 18.3031i | −0.761967 | − | 0.761967i | 0.214711 | − | 0.976678i | \(-0.431119\pi\) |
−0.976678 | + | 0.214711i | \(0.931119\pi\) | |||||||
\(578\) | −5.74226 | − | 1.53863i | −0.238847 | − | 0.0639988i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.25199 | + | 7.25199i | −0.301123 | + | 0.301123i | ||||
\(581\) | 2.73082 | − | 8.68866i | 0.113294 | − | 0.360467i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.3789 | − | 3.31691i | 0.512681 | − | 0.137373i | ||||
\(584\) | 10.6824 | 0.442042 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.9678i | 0.866174i | ||||||||
\(587\) | −30.3048 | + | 8.12014i | −1.25081 | + | 0.335154i | −0.822650 | − | 0.568548i | \(-0.807505\pi\) |
−0.428162 | + | 0.903702i | \(0.640839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.42485 | − | 3.13204i | 0.223527 | − | 0.129053i | ||||
\(590\) | 1.02754 | − | 1.02754i | 0.0423031 | − | 0.0423031i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.41447 | + | 16.4750i | −0.181434 | + | 0.677120i | ||||
\(593\) | 14.5568 | − | 14.5568i | 0.597777 | − | 0.597777i | −0.341943 | − | 0.939721i | \(-0.611085\pi\) |
0.939721 | + | 0.341943i | \(0.111085\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.7875 | − | 3.96041i | 0.729217 | − | 0.162361i | ||||
\(596\) | −6.68512 | + | 1.79127i | −0.273833 | + | 0.0733733i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.447349 | + | 1.45672i | 0.0182934 | + | 0.0595696i | ||||
\(599\) | −17.9695 | −0.734214 | −0.367107 | − | 0.930179i | \(-0.619652\pi\) | ||||
−0.367107 | + | 0.930179i | \(0.619652\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −15.4598 | − | 8.92570i | −0.630617 | − | 0.364087i | 0.150374 | − | 0.988629i | \(-0.451952\pi\) |
−0.780991 | + | 0.624542i | \(0.785286\pi\) | |||||||
\(602\) | −8.24539 | + | 26.2344i | −0.336057 | + | 1.06923i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.508609 | − | 0.136281i | −0.0206950 | − | 0.00554521i | ||||
\(605\) | 14.0155 | + | 3.75543i | 0.569810 | + | 0.152680i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.2125 | − | 12.8244i | 0.901578 | − | 0.520526i | 0.0238664 | − | 0.999715i | \(-0.492402\pi\) |
0.877712 | + | 0.479189i | \(0.159069\pi\) | |||||||
\(608\) | −3.25256 | + | 5.63361i | −0.131909 | + | 0.228473i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.2389i | 0.617005i | ||||||||
\(611\) | 5.46380 | − | 23.8015i | 0.221042 | − | 0.962907i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.916231 | + | 3.41942i | 0.0370062 | + | 0.138109i | 0.981957 | − | 0.189102i | \(-0.0605578\pi\) |
−0.944951 | + | 0.327211i | \(0.893891\pi\) | |||||||
\(614\) | 22.8687 | + | 13.2032i | 0.922905 | + | 0.532839i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.348376 | + | 8.14954i | −0.0140365 | + | 0.328354i | ||||
\(617\) | 5.87829 | + | 1.57508i | 0.236651 | + | 0.0634105i | 0.375195 | − | 0.926946i | \(-0.377576\pi\) |
−0.138544 | + | 0.990356i | \(0.544242\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −34.1674 | + | 34.1674i | −1.37331 | + | 1.37331i | −0.517810 | + | 0.855496i | \(0.673253\pi\) |
−0.855496 | + | 0.517810i | \(0.826747\pi\) | |||||||
\(620\) | 2.46650 | + | 4.27210i | 0.0990569 | + | 0.171572i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3.95289 | − | 14.7524i | −0.158496 | − | 0.591517i | ||||
\(623\) | 21.0359 | − | 19.3112i | 0.842786 | − | 0.773685i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.20722 | 0.0882889 | ||||||||
\(626\) | 19.7270 | − | 5.28584i | 0.788451 | − | 0.211265i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.32596 | − | 5.76073i | −0.132720 | − | 0.229878i | ||||
\(629\) | −33.9301 | − | 33.9301i | −1.35288 | − | 1.35288i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.80135 | − | 10.4548i | 0.111520 | − | 0.416199i | −0.887483 | − | 0.460841i | \(-0.847548\pi\) |
0.999003 | + | 0.0446417i | \(0.0142146\pi\) | |||||||
\(632\) | 15.3033 | + | 15.3033i | 0.608734 | + | 0.608734i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.22390 | + | 1.28397i | 0.0883222 | + | 0.0509928i | ||||
\(635\) | 5.36966 | + | 20.0398i | 0.213088 | + | 0.795257i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.24355 | + | 25.2082i | −0.0492714 | + | 0.998785i | ||||
\(638\) | −9.40135 | −0.372203 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.168516 | + | 0.0972930i | 0.00666120 | + | 0.00384584i | ||||
\(641\) | −26.3470 | + | 15.2114i | −1.04064 | + | 0.600815i | −0.920015 | − | 0.391883i | \(-0.871824\pi\) |
−0.120627 | + | 0.992698i | \(0.538490\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.55469 | + | 20.7304i | −0.219056 | + | 0.817527i | 0.765644 | + | 0.643265i | \(0.222421\pi\) |
−0.984699 | + | 0.174262i | \(0.944246\pi\) | |||||||
\(644\) | −0.390886 | − | 0.749218i | −0.0154031 | − | 0.0295233i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.89746 | + | 6.75060i | 0.153344 | + | 0.265599i | ||||
\(647\) | −3.76958 | + | 6.52911i | −0.148198 | + | 0.256686i | −0.930561 | − | 0.366136i | \(-0.880681\pi\) |
0.782364 | + | 0.622822i | \(0.214014\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.927000 | −0.0363879 | ||||||||
\(650\) | 7.70471 | − | 8.28296i | 0.302204 | − | 0.324884i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.91775 | − | 10.8892i | −0.114268 | − | 0.426454i | ||||
\(653\) | 11.4217 | − | 19.7830i | 0.446966 | − | 0.774167i | −0.551221 | − | 0.834359i | \(-0.685838\pi\) |
0.998187 | + | 0.0601918i | \(0.0191712\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.3779 | − | 18.3779i | 0.718086 | − | 0.718086i | ||||
\(656\) | −3.90392 | + | 14.5696i | −0.152422 | + | 0.568848i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.831126 | − | 19.4425i | 0.0324007 | − | 0.757947i | ||||
\(659\) | −13.0916 | − | 22.6753i | −0.509975 | − | 0.883303i | −0.999933 | − | 0.0115568i | \(-0.996321\pi\) |
0.489958 | − | 0.871746i | \(-0.337012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.50623 | + | 16.8175i | 0.175272 | + | 0.654124i | 0.996505 | + | 0.0835312i | \(0.0266198\pi\) |
−0.821233 | + | 0.570593i | \(0.806713\pi\) | |||||||
\(662\) | − | 37.3584i | − | 1.45197i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.5446i | 0.409209i | ||||||||
\(665\) | −4.91151 | − | 3.12269i | −0.190460 | − | 0.121093i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.89904 | − | 1.67376i | 0.112251 | − | 0.0648083i | ||||
\(668\) | 12.8972 | + | 12.8972i | 0.499008 | + | 0.499008i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0884 | + | 2.70317i | 0.389748 | + | 0.104433i | ||||
\(671\) | 6.87393 | − | 6.87393i | 0.265365 | − | 0.265365i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.2813 | + | 7.66796i | 0.511957 | + | 0.295578i | 0.733638 | − | 0.679541i | \(-0.237821\pi\) |
−0.221681 | + | 0.975119i | \(0.571154\pi\) | |||||||
\(674\) | 3.60596 | − | 0.966213i | 0.138896 | − | 0.0372172i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.770743 | − | 10.6411i | −0.0296440 | − | 0.409271i | ||||
\(677\) | 4.31369i | 0.165789i | 0.996558 | + | 0.0828943i | \(0.0264164\pi\) | ||||
−0.996558 | + | 0.0828943i | \(0.973584\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 35.4930 | − | 7.90254i | 1.36210 | − | 0.303272i | ||||
\(680\) | −18.2714 | + | 10.5490i | −0.700678 | + | 0.404537i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.17037 | + | 4.36789i | −0.0448159 | + | 0.167255i | ||||
\(683\) | 2.11067 | − | 7.87714i | 0.0807627 | − | 0.301410i | −0.913715 | − | 0.406355i | \(-0.866800\pi\) |
0.994478 | + | 0.104944i | \(0.0334664\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.18418 | + | 1.83839i | −0.121661 | + | 0.0702412i | ||||
\(686\) | 2.67969 | + | 19.9330i | 0.102311 | + | 0.761045i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 16.1283i | − | 0.614886i | ||||||
\(689\) | −38.9028 | + | 24.3766i | −1.48208 | + | 0.928674i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.79665 | − | 2.35706i | 0.334640 | − | 0.0896666i | −0.0875862 | − | 0.996157i | \(-0.527915\pi\) |
0.422227 | + | 0.906490i | \(0.361249\pi\) | |||||||
\(692\) | −9.00827 | − | 5.20093i | −0.342443 | − | 0.197710i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.5393 | + | 14.5393i | −0.551905 | + | 0.551905i | ||||
\(695\) | −14.3629 | − | 3.84853i | −0.544816 | − | 0.145983i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.0059 | − | 30.0059i | −1.13656 | − | 1.13656i | ||||
\(698\) | −30.6831 | + | 17.7149i | −1.16137 | + | 0.670518i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.36581 | + | 5.29390i | −0.127216 | + | 0.200091i | ||||
\(701\) | 42.0549i | 1.58839i | 0.607663 | + | 0.794195i | \(0.292107\pi\) | ||||
−0.607663 | + | 0.794195i | \(0.707893\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.3254i | 0.578009i | ||||||||
\(704\) | −2.09335 | − | 7.81247i | −0.0788959 | − | 0.294444i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.8582 | − | 30.9312i | −0.672101 | − | 1.16411i | ||||
\(707\) | −10.4543 | − | 0.446900i | −0.393175 | − | 0.0168074i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.70279 | − | 17.5510i | 0.176617 | − | 0.659143i | −0.819654 | − | 0.572859i | \(-0.805834\pi\) |
0.996271 | − | 0.0862837i | \(-0.0274991\pi\) | |||||||
\(710\) | 2.96449 | − | 2.96449i | 0.111255 | − | 0.111255i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.5304 | + | 28.6315i | −0.619504 | + | 1.07301i | ||||
\(713\) | −0.416733 | − | 1.55527i | −0.0156068 | − | 0.0582453i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.26901 | − | 0.190570i | 0.197050 | − | 0.00712693i | ||||
\(716\) | −8.99175 | −0.336038 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.11470 | + | 1.93072i | −0.0416003 | + | 0.0720538i | ||||
\(719\) | −22.3307 | − | 38.6778i | −0.832793 | − | 1.44244i | −0.895815 | − | 0.444427i | \(-0.853407\pi\) |
0.0630222 | − | 0.998012i | \(-0.479926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.6291 | − | 29.9566i | −0.582059 | − | 1.11564i | ||||
\(722\) | −4.69594 | + | 17.5255i | −0.174765 | + | 0.652231i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.11583 | − | 1.79892i | 0.115799 | − | 0.0668565i | ||||
\(725\) | −21.5210 | − | 12.4252i | −0.799271 | − | 0.461459i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.6855 | −0.804272 | −0.402136 | − | 0.915580i | \(-0.631732\pi\) | ||||
−0.402136 | + | 0.915580i | \(0.631732\pi\) | |||||||
\(728\) | −7.37728 | − | 28.2741i | −0.273420 | − | 1.04791i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.42410 | − | 5.31483i | −0.0527085 | − | 0.196711i | ||||
\(731\) | 39.2949 | + | 22.6869i | 1.45338 | + | 0.839107i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.4440 | − | 36.4440i | −1.34609 | − | 1.34609i | −0.889865 | − | 0.456223i | \(-0.849202\pi\) |
−0.456223 | − | 0.889865i | \(-0.650798\pi\) | |||||||
\(734\) | −0.130093 | + | 0.485514i | −0.00480183 | + | 0.0179207i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.18235 | + | 1.18235i | 0.0435819 | + | 0.0435819i | ||||
\(737\) | −3.33130 | − | 5.76998i | −0.122710 | − | 0.212540i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.28312 | + | 1.68356i | −0.231128 | + | 0.0619307i | −0.372524 | − | 0.928022i | \(-0.621508\pi\) |
0.141396 | + | 0.989953i | \(0.454841\pi\) | |||||||
\(740\) | −12.0688 | −0.443659 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.9500 | + | 24.7403i | −0.989364 | + | 0.908246i | ||||
\(743\) | −6.75798 | − | 25.2211i | −0.247926 | − | 0.925273i | −0.971890 | − | 0.235435i | \(-0.924348\pi\) |
0.723964 | − | 0.689838i | \(-0.242318\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.12615 | + | 10.6108i | 0.224445 | + | 0.388750i | ||||
\(746\) | −7.94705 | + | 7.94705i | −0.290962 | + | 0.290962i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.78247 | + | 1.01351i | 0.138301 | + | 0.0370576i | ||||
\(749\) | 9.51586 | + | 0.406783i | 0.347702 | + | 0.0148635i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.8018 | + | 18.3608i | 1.16046 | + | 0.669993i | 0.951415 | − | 0.307912i | \(-0.0996303\pi\) |
0.209048 | + | 0.977905i | \(0.432964\pi\) | |||||||
\(752\) | 2.95397 | + | 11.0244i | 0.107720 | + | 0.402017i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 32.1945 | − | 9.88671i | 1.17245 | − | 0.360053i | ||||
\(755\) | 0.932165i | 0.0339250i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.3385 | − | 43.8875i | 0.920943 | − | 1.59512i | 0.122984 | − | 0.992409i | \(-0.460754\pi\) |
0.797959 | − | 0.602711i | \(-0.205913\pi\) | |||||||
\(758\) | −14.5062 | + | 8.37517i | −0.526890 | + | 0.304200i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.50876 | + | 1.74402i | 0.236097 | + | 0.0632621i | ||||
\(761\) | −25.8358 | − | 6.92269i | −0.936548 | − | 0.250947i | −0.241903 | − | 0.970300i | \(-0.577772\pi\) |
−0.694645 | + | 0.719353i | \(0.744438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.222443 | + | 0.0699131i | 0.00805296 | + | 0.00253102i | ||||
\(764\) | 7.00085 | + | 4.04194i | 0.253282 | + | 0.146232i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.2576 | 1.27391 | ||||||||
\(767\) | 3.17447 | − | 0.974858i | 0.114623 | − | 0.0352001i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.6180 | + | 6.06047i | −0.815626 | + | 0.218546i | −0.642433 | − | 0.766342i | \(-0.722075\pi\) |
−0.173193 | + | 0.984888i | \(0.555408\pi\) | |||||||
\(770\) | 4.10108 | − | 0.913110i | 0.147793 | − | 0.0329062i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.38208 | − | 7.38208i | 0.265687 | − | 0.265687i | ||||
\(773\) | −3.07578 | + | 11.4790i | −0.110628 | + | 0.412869i | −0.998923 | − | 0.0464045i | \(-0.985224\pi\) |
0.888295 | + | 0.459274i | \(0.151890\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.45192 | + | 8.45192i | −0.303602 | + | 0.303602i | ||||
\(776\) | −36.4586 | + | 21.0494i | −1.30879 | + | 0.755628i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −39.2131 | + | 10.5071i | −1.40586 | + | 0.376699i | ||||
\(779\) | 13.5530i | 0.485585i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.67443 | −0.0956986 | ||||||||
\(782\) | 1.93535 | − | 0.518576i | 0.0692080 | − | 0.0185442i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.00455 | − | 10.6814i | −0.178734 | − | 0.381479i | ||||
\(785\) | −8.32692 | + | 8.32692i | −0.297201 | + | 0.297201i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.37868 | + | 0.369415i | 0.0491445 | + | 0.0131682i | 0.283308 | − | 0.959029i | \(-0.408568\pi\) |
−0.234163 | + | 0.972197i | \(0.575235\pi\) | |||||||
\(788\) | 0.905941 | + | 0.905941i | 0.0322728 | + | 0.0322728i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.57374 | − | 9.65400i | 0.198305 | − | 0.343474i | ||||
\(791\) | 3.10219 | − | 4.87927i | 0.110301 | − | 0.173487i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3106 | + | 30.7683i | −0.579208 | + | 1.09261i | ||||
\(794\) | 39.3369i | 1.39602i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.30849 | + | 4.79691i | 0.294487 | + | 0.170022i | ||||
\(797\) | 15.8960 | + | 27.5327i | 0.563065 | + | 0.975258i | 0.997227 | + | 0.0744227i | \(0.0237114\pi\) |
−0.434161 | + | 0.900835i | \(0.642955\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.0150 | − | 8.31044i | −1.09723 | − | 0.294002i | ||||
\(800\) | 3.21266 | − | 11.9898i | 0.113585 | − | 0.423904i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.9104 | + | 32.7538i | 0.667750 | + | 1.15658i | ||||
\(803\) | −1.75502 | + | 3.03978i | −0.0619333 | + | 0.107272i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.10206 | + | 1.01170i | −0.0388426 | + | 0.0356578i | ||||
\(806\) | −0.585506 | − | 16.1884i | −0.0206236 | − | 0.570213i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.7019 | − | 3.13551i | 0.411671 | − | 0.110307i | ||||
\(809\) | −7.21908 | + | 12.5038i | −0.253809 | + | 0.439611i | −0.964571 | − | 0.263822i | \(-0.915017\pi\) |
0.710762 | + | 0.703432i | \(0.248350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.5212 | + | 16.5212i | 0.580138 | + | 0.580138i | 0.934941 | − | 0.354803i | \(-0.115452\pi\) |
−0.354803 | + | 0.934941i | \(0.615452\pi\) | |||||||
\(812\) | −16.5582 | + | 8.63886i | −0.581080 | + | 0.303164i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.82291 | − | 7.82291i | −0.274193 | − | 0.274193i | ||||
\(815\) | −17.2836 | + | 9.97871i | −0.605419 | + | 0.349539i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.75072 | − | 13.9979i | −0.131221 | − | 0.489723i | ||||
\(818\) | −12.4856 | −0.436550 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −10.6730 | −0.372718 | ||||||||
\(821\) | 7.38477 | + | 27.5603i | 0.257730 | + | 0.961862i | 0.966551 | + | 0.256474i | \(0.0825607\pi\) |
−0.708821 | + | 0.705388i | \(0.750773\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.0527072 | − | 0.0304305i | 0.00183726 | − | 0.00106074i | −0.499081 | − | 0.866555i | \(-0.666329\pi\) |
0.500918 | + | 0.865495i | \(0.332996\pi\) | |||||||
\(824\) | 27.6614 | + | 27.6614i | 0.963632 | + | 0.963632i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.34614 | − | 1.22404i | 0.0816328 | − | 0.0425900i | ||||
\(827\) | 37.2665 | + | 37.2665i | 1.29588 | + | 1.29588i | 0.931087 | + | 0.364798i | \(0.118862\pi\) |
0.364798 | + | 0.931087i | \(0.381138\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.17299 | − | 3.76373i | 0.0754711 | − | 0.130720i | −0.825820 | − | 0.563934i | \(-0.809287\pi\) |
0.901291 | + | 0.433214i | \(0.142621\pi\) | |||||||
\(830\) | 5.24624 | − | 1.40573i | 0.182100 | − | 0.0487935i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 15.3844 | + | 24.5520i | 0.533357 | + | 0.851188i | ||||
\(833\) | 33.0638 | + | 2.83200i | 1.14559 | + | 0.0981228i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.1448 | − | 27.9636i | 0.558714 | − | 0.967722i | ||||
\(836\) | −0.625336 | − | 1.08311i | −0.0216277 | − | 0.0374603i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.22156 | + | 30.6833i | −0.284009 | + | 1.05994i | ||||
\(839\) | −46.4621 | − | 12.4495i | −1.60405 | − | 0.429804i | −0.657788 | − | 0.753203i | \(-0.728508\pi\) |
−0.946263 | + | 0.323399i | \(0.895174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4912 | − | 38.9560i | −0.775560 | − | 1.34331i | ||||
\(842\) | −11.7674 | − | 6.79392i | −0.405532 | − | 0.234134i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.1879i | 0.626052i | ||||||||
\(845\) | −17.8431 | + | 6.19363i | −0.613820 | + | 0.213067i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.2979 | + | 14.1768i | 0.766165 | + | 0.487120i | ||||
\(848\) | 10.7281 | − | 18.5816i | 0.368404 | − | 0.638094i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.5174 | − | 10.5174i | −0.360745 | − | 0.360745i | ||||
\(851\) | 3.80505 | + | 1.01956i | 0.130435 | + | 0.0349500i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.74166 | − | 3.74166i | 0.128112 | − | 0.128112i | −0.640143 | − | 0.768255i | \(-0.721125\pi\) |
0.768255 | + | 0.640143i | \(0.221125\pi\) | |||||||
\(854\) | −8.32064 | + | 26.4738i | −0.284727 | + | 0.905915i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.6514 | + | 2.85405i | −0.364059 | + | 0.0975493i | ||||
\(857\) | −10.1411 | −0.346413 | −0.173207 | − | 0.984885i | \(-0.555413\pi\) | ||||
−0.173207 | + | 0.984885i | \(0.555413\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 32.3015i | − | 1.10211i | −0.834468 | − | 0.551056i | \(-0.814225\pi\) | ||
0.834468 | − | 0.551056i | \(-0.185775\pi\) | |||||||
\(860\) | 11.0234 | − | 2.95371i | 0.375894 | − | 0.100721i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −14.2099 | + | 8.20407i | −0.483990 | + | 0.279432i | ||||
\(863\) | −30.9883 | + | 30.9883i | −1.05486 | + | 1.05486i | −0.0564495 | + | 0.998405i | \(0.517978\pi\) |
−0.998405 | + | 0.0564495i | \(0.982022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.76606 | + | 17.7872i | −0.162051 | + | 0.604782i | ||||
\(866\) | 25.5092 | − | 25.5092i | 0.866839 | − | 0.866839i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.95230 | + | 8.76845i | 0.0662655 | + | 0.297621i | ||||
\(869\) | −6.86889 | + | 1.84051i | −0.233011 | + | 0.0624352i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.4757 | + | 16.2557i | 0.592143 | + | 0.550804i | ||||
\(872\) | −0.269957 | −0.00914189 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.554190 | − | 0.319962i | −0.0187458 | − | 0.0108229i | ||||
\(875\) | 28.9303 | + | 9.09271i | 0.978022 | + | 0.307390i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0303 | − | 4.56327i | −0.575074 | − | 0.154091i | −0.0404512 | − | 0.999182i | \(-0.512880\pi\) |
−0.534623 | + | 0.845091i | \(0.679546\pi\) | |||||||
\(878\) | 6.55100 | + | 1.75533i | 0.221086 | + | 0.0592397i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.13401 | + | 1.23207i | −0.0719376 | + | 0.0415332i | ||||
\(881\) | −2.42023 | + | 4.19196i | −0.0815396 | + | 0.141231i | −0.903911 | − | 0.427720i | \(-0.859317\pi\) |
0.822372 | + | 0.568950i | \(0.192650\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.3796i | 0.786785i | 0.919371 | + | 0.393393i | \(0.128699\pi\) | ||||
−0.919371 | + | 0.393393i | \(0.871301\pi\) | |||||||
\(884\) | −14.0187 | + | 0.507031i | −0.471500 | + | 0.0170533i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.80387 | + | 17.9283i | 0.161389 | + | 0.602313i | ||||
\(887\) | 43.5357 | + | 25.1353i | 1.46178 | + | 0.843962i | 0.999094 | − | 0.0425584i | \(-0.0135509\pi\) |
0.462690 | + | 0.886520i | \(0.346884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.61357 | + | 37.7462i | −0.0541174 | + | 1.26597i | ||||
\(890\) | 16.4487 | + | 4.40743i | 0.551363 | + | 0.147737i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.98094 | + | 7.98094i | −0.267222 | + | 0.267222i | ||||
\(893\) | 5.12755 | + | 8.88117i | 0.171587 | + | 0.297197i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.11996 | + | 15.3759i | 0.137715 | + | 0.513960i | ||||
\(896\) | 0.239632 | + | 0.261035i | 0.00800555 | + | 0.00872056i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.3042 | 1.34497 | ||||||||
\(899\) | −34.3725 | + | 9.21008i | −1.14639 | + | 0.307173i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 30.1814 | + | 52.2757i | 1.00549 | + | 1.74156i | ||||
\(902\) | −6.91815 | − | 6.91815i | −0.230349 | − | 0.230349i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.73257 | + | 6.46604i | −0.0576244 | + | 0.215057i | ||||
\(905\) | −4.50381 | − | 4.50381i | −0.149712 | − | 0.149712i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.7089 | − | 18.3071i | −1.05288 | − | 0.607878i | −0.129422 | − | 0.991590i | \(-0.541312\pi\) |
−0.923453 | + | 0.383712i | \(0.874646\pi\) | |||||||
\(908\) | −0.853689 | − | 3.18601i | −0.0283307 | − | 0.105732i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.0837 | + | 7.43971i | −0.433721 | + | 0.246624i | ||||
\(911\) | −40.8424 | −1.35317 | −0.676585 | − | 0.736365i | \(-0.736541\pi\) | ||||
−0.676585 | + | 0.736365i | \(0.736541\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.00056 | − | 1.73237i | −0.0993039 | − | 0.0573331i | ||||
\(914\) | −7.52181 | + | 4.34272i | −0.248799 | + | 0.143644i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.409350 | − | 1.52772i | 0.0135253 | − | 0.0504771i | ||||
\(917\) | 41.9617 | − | 21.8925i | 1.38570 | − | 0.722955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.1413 | + | 21.0293i | 0.400504 | + | 0.693693i | 0.993787 | − | 0.111301i | \(-0.0355018\pi\) |
−0.593283 | + | 0.804994i | \(0.702168\pi\) | |||||||
\(920\) | 0.866021 | − | 1.49999i | 0.0285519 | − | 0.0494533i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.0824 | 0.397912 | ||||||||
\(923\) | 9.15845 | − | 2.81250i | 0.301454 | − | 0.0925746i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.56871 | − | 28.2468i | −0.248858 | − | 0.928749i | ||||
\(926\) | −18.6069 | + | 32.2281i | −0.611461 | + | 1.05908i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.1307 | − | 26.1307i | 0.857781 | − | 0.857781i | ||||
\(929\) | −0.812091 | + | 3.03077i | −0.0266438 | + | 0.0994362i | −0.977967 | − | 0.208758i | \(-0.933058\pi\) |
0.951324 | + | 0.308194i | \(0.0997246\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.82750 | − | 8.10665i | −0.223762 | − | 0.265685i | ||||
\(932\) | −0.463744 | − | 0.803228i | −0.0151904 | − | 0.0263106i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.96734 | + | 11.0743i | 0.0970944 | + | 0.362361i | ||||
\(935\) | − | 6.93241i | − | 0.226714i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.6319i | − | 1.29472i | −0.762185 | − | 0.647359i | \(-0.775874\pi\) | ||
0.762185 | − | 0.647359i | \(-0.224126\pi\) | |||||||
\(938\) | 16.0501 | + | 10.2045i | 0.524053 | + | 0.333188i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.99397 | + | 4.03797i | −0.228118 | + | 0.131704i | ||||
\(941\) | −9.63423 | − | 9.63423i | −0.314067 | − | 0.314067i | 0.532416 | − | 0.846483i | \(-0.321284\pi\) |
−0.846483 | + | 0.532416i | \(0.821284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.36498 | + | 0.901643i | 0.109579 | + | 0.0293615i | ||||
\(944\) | −1.09743 | + | 1.09743i | −0.0357185 | + | 0.0357185i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.05982 | + | 5.23069i | 0.294560 | + | 0.170064i | ||||
\(947\) | −51.2831 | + | 13.7413i | −1.66648 | + | 0.446531i | −0.964157 | − | 0.265331i | \(-0.914519\pi\) |
−0.702319 | + | 0.711862i | \(0.747852\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.81326 | − | 12.2552i | 0.0913224 | − | 0.397821i | ||||
\(950\) | 4.75047i | 0.154126i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −37.5020 | + | 8.34986i | −1.21545 | + | 0.270621i | ||||
\(953\) | 28.0071 | − | 16.1699i | 0.907238 | − | 0.523794i | 0.0276968 | − | 0.999616i | \(-0.491183\pi\) |
0.879542 | + | 0.475822i | \(0.157849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.70398 | − | 13.8234i | 0.119858 | − | 0.447316i | ||||
\(956\) | −1.08992 | + | 4.06765i | −0.0352506 | + | 0.131557i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.28783 | + | 4.78498i | −0.267768 | + | 0.154596i | ||||
\(959\) | −6.53551 | + | 1.45514i | −0.211043 | + | 0.0469889i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 13.8839i | − | 0.447867i | ||||||
\(962\) | 35.0159 | + | 18.5624i | 1.12896 | + | 0.598475i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.77010 | + | 2.08199i | −0.250258 | + | 0.0670565i | ||||
\(965\) | −16.0058 | − | 9.24094i | −0.515244 | − | 0.297476i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.38328 | − | 5.38328i | 0.173115 | − | 0.173115i | −0.615232 | − | 0.788346i | \(-0.710938\pi\) |
0.788346 | + | 0.615232i | \(0.210938\pi\) | |||||||
\(968\) | −29.5493 | − | 7.91771i | −0.949750 | − | 0.254485i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 15.3331 | + | 15.3331i | 0.492316 | + | 0.492316i | ||||
\(971\) | 36.0969 | − | 20.8405i | 1.15840 | − | 0.668804i | 0.207483 | − | 0.978239i | \(-0.433473\pi\) |
0.950921 | + | 0.309434i | \(0.100140\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.8507 | − | 14.5282i | −0.732558 | − | 0.465753i | ||||
\(974\) | 22.2941i | 0.714348i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 16.2755i | − | 0.520966i | ||||||
\(977\) | 2.38909 | + | 8.91619i | 0.0764336 | + | 0.285254i | 0.993555 | − | 0.113355i | \(-0.0361597\pi\) |
−0.917121 | + | 0.398609i | \(0.869493\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.43157 | − | 9.40776i | −0.173594 | − | 0.300673i | ||||
\(980\) | 6.38402 | − | 5.37669i | 0.203930 | − | 0.171752i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.883840 | + | 3.29853i | −0.0282045 | + | 0.105260i | ||||
\(983\) | 23.8714 | − | 23.8714i | 0.761380 | − | 0.761380i | −0.215192 | − | 0.976572i | \(-0.569038\pi\) |
0.976572 | + | 0.215192i | \(0.0690378\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.13406 | − | 1.96426i | 0.0361343 | − | 0.0625864i | ||||
\(986\) | −11.4609 | − | 42.7726i | −0.364989 | − | 1.36216i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.28047 | + | 3.05145i | 0.104365 | + | 0.0970796i | ||||
\(989\) | −3.72497 | −0.118447 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.66281 | + | 4.61212i | −0.0845869 | + | 0.146509i | −0.905215 | − | 0.424954i | \(-0.860290\pi\) |
0.820628 | + | 0.571462i | \(0.193624\pi\) | |||||||
\(992\) | −8.88738 | − | 15.3934i | −0.282175 | − | 0.488741i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.76871 | − | 3.53141i | 0.214691 | − | 0.112010i | ||||
\(995\) | 4.39582 | − | 16.4054i | 0.139357 | − | 0.520087i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6452 | − | 16.5383i | 0.907203 | − | 0.523774i | 0.0276726 | − | 0.999617i | \(-0.491190\pi\) |
0.879530 | + | 0.475843i | \(0.157857\pi\) | |||||||
\(998\) | −14.2338 | − | 8.21788i | −0.450563 | − | 0.260132i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 819.2.fm.f.370.6 | 32 | ||
3.2 | odd | 2 | 273.2.by.c.97.3 | yes | 32 | ||
7.6 | odd | 2 | 819.2.fm.e.370.6 | 32 | |||
13.11 | odd | 12 | 819.2.fm.e.622.6 | 32 | |||
21.20 | even | 2 | 273.2.by.d.97.3 | yes | 32 | ||
39.11 | even | 12 | 273.2.by.d.76.3 | yes | 32 | ||
91.76 | even | 12 | inner | 819.2.fm.f.622.6 | 32 | ||
273.167 | odd | 12 | 273.2.by.c.76.3 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.by.c.76.3 | ✓ | 32 | 273.167 | odd | 12 | ||
273.2.by.c.97.3 | yes | 32 | 3.2 | odd | 2 | ||
273.2.by.d.76.3 | yes | 32 | 39.11 | even | 12 | ||
273.2.by.d.97.3 | yes | 32 | 21.20 | even | 2 | ||
819.2.fm.e.370.6 | 32 | 7.6 | odd | 2 | |||
819.2.fm.e.622.6 | 32 | 13.11 | odd | 12 | |||
819.2.fm.f.370.6 | 32 | 1.1 | even | 1 | trivial | ||
819.2.fm.f.622.6 | 32 | 91.76 | even | 12 | inner |