Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 233.1 | ||
Character | \(\chi\) | \(=\) | 363.233 |
Dual form | 363.2.f.i.215.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.739839 | + | 2.27699i | −0.523145 | + | 1.61008i | 0.244809 | + | 0.969571i | \(0.421275\pi\) |
−0.767954 | + | 0.640505i | \(0.778725\pi\) | |||||||
\(3\) | −1.29120 | − | 1.15447i | −0.745476 | − | 0.666532i | ||||
\(4\) | −3.01929 | − | 2.19364i | −1.50965 | − | 1.09682i | ||||
\(5\) | −1.17866 | + | 0.382969i | −0.527112 | + | 0.171269i | −0.560470 | − | 0.828175i | \(-0.689380\pi\) |
0.0333587 | + | 0.999443i | \(0.489380\pi\) | |||||||
\(6\) | 3.58400 | − | 2.08594i | 1.46316 | − | 0.851580i | ||||
\(7\) | 1.66251 | − | 2.28825i | 0.628369 | − | 0.864876i | −0.369560 | − | 0.929207i | \(-0.620491\pi\) |
0.997929 | + | 0.0643314i | \(0.0204915\pi\) | |||||||
\(8\) | 3.35485 | − | 2.43744i | 1.18612 | − | 0.861766i | ||||
\(9\) | 0.334407 | + | 2.98130i | 0.111469 | + | 0.993768i | ||||
\(10\) | − | 2.96713i | − | 0.938288i | ||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.36603 | + | 6.31812i | 0.394338 | + | 1.82388i | ||||
\(13\) | 3.18230 | + | 1.03399i | 0.882610 | + | 0.286778i | 0.715041 | − | 0.699083i | \(-0.246408\pi\) |
0.167570 | + | 0.985860i | \(0.446408\pi\) | |||||||
\(14\) | 3.98033 | + | 5.47845i | 1.06379 | + | 1.46418i | ||||
\(15\) | 1.96401 | + | 0.866232i | 0.507105 | + | 0.223660i | ||||
\(16\) | 0.761449 | + | 2.34350i | 0.190362 | + | 0.585875i | ||||
\(17\) | 1.28144 | + | 3.94386i | 0.310795 | + | 0.956528i | 0.977451 | + | 0.211162i | \(0.0677249\pi\) |
−0.666656 | + | 0.745365i | \(0.732275\pi\) | |||||||
\(18\) | −7.03581 | − | 1.44424i | −1.65836 | − | 0.340411i | ||||
\(19\) | 1.43977 | + | 1.98168i | 0.330307 | + | 0.454628i | 0.941579 | − | 0.336792i | \(-0.109342\pi\) |
−0.611272 | + | 0.791420i | \(0.709342\pi\) | |||||||
\(20\) | 4.39881 | + | 1.42926i | 0.983604 | + | 0.319592i | ||||
\(21\) | −4.78834 | + | 1.03528i | −1.04490 | + | 0.225916i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | −7.14574 | − | 0.725837i | −1.45862 | − | 0.148161i | ||||
\(25\) | −2.80252 | + | 2.03615i | −0.560503 | + | 0.407230i | ||||
\(26\) | −4.70878 | + | 6.48108i | −0.923467 | + | 1.27104i | ||||
\(27\) | 3.01003 | − | 4.23553i | 0.579281 | − | 0.815128i | ||||
\(28\) | −10.0392 | + | 3.26193i | −1.89723 | + | 0.616447i | ||||
\(29\) | 4.39285 | + | 3.19159i | 0.815731 | + | 0.592663i | 0.915486 | − | 0.402349i | \(-0.131806\pi\) |
−0.0997555 | + | 0.995012i | \(0.531806\pi\) | |||||||
\(30\) | −3.42545 | + | 3.83116i | −0.625400 | + | 0.699471i | ||||
\(31\) | 0.0606144 | − | 0.186552i | 0.0108867 | − | 0.0335057i | −0.945466 | − | 0.325722i | \(-0.894393\pi\) |
0.956352 | + | 0.292216i | \(0.0943927\pi\) | |||||||
\(32\) | 2.39417 | 0.423233 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.92820 | −1.70267 | ||||||||
\(35\) | −1.08320 | + | 3.33375i | −0.183094 | + | 0.563506i | ||||
\(36\) | 5.53025 | − | 9.73500i | 0.921708 | − | 1.62250i | ||||
\(37\) | 8.46564 | + | 6.15064i | 1.39174 | + | 1.01116i | 0.995672 | + | 0.0929395i | \(0.0296263\pi\) |
0.396070 | + | 0.918220i | \(0.370374\pi\) | |||||||
\(38\) | −5.57747 | + | 1.81223i | −0.904785 | + | 0.293982i | ||||
\(39\) | −2.91528 | − | 5.00895i | −0.466818 | − | 0.802074i | ||||
\(40\) | −3.02076 | + | 4.15771i | −0.477623 | + | 0.657392i | ||||
\(41\) | 5.81077 | − | 4.22177i | 0.907490 | − | 0.659330i | −0.0328886 | − | 0.999459i | \(-0.510471\pi\) |
0.940379 | + | 0.340129i | \(0.110471\pi\) | |||||||
\(42\) | 1.18529 | − | 11.6689i | 0.182894 | − | 1.80056i | ||||
\(43\) | 4.24264i | 0.646997i | 0.946229 | + | 0.323498i | \(0.104859\pi\) | ||||
−0.946229 | + | 0.323498i | \(0.895141\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.53590 | − | 3.38587i | −0.228958 | − | 0.504735i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.99016 | − | 2.73922i | −0.290295 | − | 0.399557i | 0.638815 | − | 0.769361i | \(-0.279425\pi\) |
−0.929110 | + | 0.369804i | \(0.879425\pi\) | |||||||
\(48\) | 1.72231 | − | 3.90500i | 0.248594 | − | 0.563638i | ||||
\(49\) | −0.309017 | − | 0.951057i | −0.0441453 | − | 0.135865i | ||||
\(50\) | −2.56288 | − | 7.88773i | −0.362446 | − | 1.11549i | ||||
\(51\) | 2.89847 | − | 6.57171i | 0.405867 | − | 0.920223i | ||||
\(52\) | −7.34008 | − | 10.1027i | −1.01789 | − | 1.40100i | ||||
\(53\) | −6.75612 | − | 2.19520i | −0.928025 | − | 0.301534i | −0.194270 | − | 0.980948i | \(-0.562234\pi\) |
−0.733755 | + | 0.679414i | \(0.762234\pi\) | |||||||
\(54\) | 7.41732 | + | 9.98743i | 1.00937 | + | 1.35912i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 11.7290i | − | 1.56735i | ||||||
\(57\) | 0.428745 | − | 4.22092i | 0.0567887 | − | 0.559075i | ||||
\(58\) | −10.5172 | + | 7.64121i | −1.38098 | + | 1.00334i | ||||
\(59\) | 7.42739 | − | 10.2229i | 0.966964 | − | 1.33091i | 0.0233981 | − | 0.999726i | \(-0.492551\pi\) |
0.943566 | − | 0.331185i | \(-0.107449\pi\) | |||||||
\(60\) | −4.02972 | − | 6.92375i | −0.520234 | − | 0.893852i | ||||
\(61\) | 4.29882 | − | 1.39677i | 0.550407 | − | 0.178838i | −0.0205933 | − | 0.999788i | \(-0.506556\pi\) |
0.571000 | + | 0.820950i | \(0.306556\pi\) | |||||||
\(62\) | 0.379932 | + | 0.276037i | 0.0482515 | + | 0.0350567i | ||||
\(63\) | 7.37791 | + | 4.19123i | 0.929529 | + | 0.528046i | ||||
\(64\) | −3.29420 | + | 10.1385i | −0.411775 | + | 1.26731i | ||||
\(65\) | −4.14682 | −0.514350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | 4.78240 | − | 14.7187i | 0.579951 | − | 1.78490i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.78952 | − | 4.93287i | −0.811503 | − | 0.589591i | ||||
\(71\) | 7.93478 | − | 2.57817i | 0.941685 | − | 0.305972i | 0.202353 | − | 0.979313i | \(-0.435141\pi\) |
0.739332 | + | 0.673341i | \(0.235141\pi\) | |||||||
\(72\) | 8.38864 | + | 9.18673i | 0.988611 | + | 1.08267i | ||||
\(73\) | −4.76479 | + | 6.55817i | −0.557676 | + | 0.767576i | −0.991029 | − | 0.133649i | \(-0.957331\pi\) |
0.433352 | + | 0.901225i | \(0.357331\pi\) | |||||||
\(74\) | −20.2682 | + | 14.7257i | −2.35613 | + | 1.71183i | ||||
\(75\) | 5.96928 | + | 0.606337i | 0.689274 | + | 0.0700138i | ||||
\(76\) | − | 9.14162i | − | 1.04862i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.5622 | − | 2.93225i | 1.53561 | − | 0.332012i | ||||
\(79\) | 6.98881 | + | 2.27080i | 0.786303 | + | 0.255485i | 0.674529 | − | 0.738249i | \(-0.264347\pi\) |
0.111774 | + | 0.993734i | \(0.464347\pi\) | |||||||
\(80\) | −1.79498 | − | 2.47057i | −0.200684 | − | 0.276218i | ||||
\(81\) | −8.77634 | + | 1.99394i | −0.975149 | + | 0.221549i | ||||
\(82\) | 5.31390 | + | 16.3545i | 0.586822 | + | 1.80605i | ||||
\(83\) | 4.58416 | + | 14.1086i | 0.503177 | + | 1.54862i | 0.803815 | + | 0.594880i | \(0.202800\pi\) |
−0.300638 | + | 0.953738i | \(0.597200\pi\) | |||||||
\(84\) | 16.7284 | + | 7.37811i | 1.82522 | + | 0.805018i | ||||
\(85\) | −3.02076 | − | 4.15771i | −0.327647 | − | 0.450967i | ||||
\(86\) | −9.66046 | − | 3.13887i | −1.04171 | − | 0.338473i | ||||
\(87\) | −1.98747 | − | 9.19239i | −0.213079 | − | 0.985527i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.58244i | 1.01574i | 0.861435 | + | 0.507868i | \(0.169566\pi\) | ||||
−0.861435 | + | 0.507868i | \(0.830434\pi\) | |||||||
\(90\) | 8.84591 | − | 0.992229i | 0.932441 | − | 0.104590i | ||||
\(91\) | 7.65662 | − | 5.56286i | 0.802632 | − | 0.583146i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.293634 | + | 0.170899i | −0.0304484 | + | 0.0177214i | ||||
\(94\) | 7.70959 | − | 2.50500i | 0.795184 | − | 0.258371i | ||||
\(95\) | −2.45592 | − | 1.78433i | −0.251972 | − | 0.183069i | ||||
\(96\) | −3.09136 | − | 2.76399i | −0.315510 | − | 0.282099i | ||||
\(97\) | 0.700835 | − | 2.15695i | 0.0711590 | − | 0.219005i | −0.909152 | − | 0.416464i | \(-0.863269\pi\) |
0.980311 | + | 0.197459i | \(0.0632691\pi\) | |||||||
\(98\) | 2.39417 | 0.241848 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.9282 | 1.29282 | ||||||||
\(101\) | 0.145121 | − | 0.446637i | 0.0144401 | − | 0.0444421i | −0.943577 | − | 0.331154i | \(-0.892562\pi\) |
0.958017 | + | 0.286712i | \(0.0925621\pi\) | |||||||
\(102\) | 12.8193 | + | 11.4618i | 1.26930 | + | 1.13489i | ||||
\(103\) | −10.3004 | − | 7.48371i | −1.01493 | − | 0.737392i | −0.0496950 | − | 0.998764i | \(-0.515825\pi\) |
−0.965238 | + | 0.261372i | \(0.915825\pi\) | |||||||
\(104\) | 13.1964 | − | 4.28778i | 1.29402 | − | 0.420451i | ||||
\(105\) | 5.24733 | − | 3.05402i | 0.512087 | − | 0.298042i | ||||
\(106\) | 9.99689 | − | 13.7595i | 0.970984 | − | 1.33644i | ||||
\(107\) | −2.83585 | + | 2.06037i | −0.274152 | + | 0.199183i | −0.716363 | − | 0.697728i | \(-0.754194\pi\) |
0.442210 | + | 0.896911i | \(0.354194\pi\) | |||||||
\(108\) | −18.3794 | + | 6.18536i | −1.76856 | + | 0.595187i | ||||
\(109\) | − | 10.6945i | − | 1.02435i | −0.858881 | − | 0.512175i | \(-0.828840\pi\) | ||
0.858881 | − | 0.512175i | \(-0.171160\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.83013 | − | 17.7150i | −0.363540 | − | 1.68144i | ||||
\(112\) | 6.62842 | + | 2.15370i | 0.626327 | + | 0.203506i | ||||
\(113\) | −7.62258 | − | 10.4916i | −0.717072 | − | 0.986965i | −0.999616 | − | 0.0277104i | \(-0.991178\pi\) |
0.282544 | − | 0.959254i | \(-0.408822\pi\) | |||||||
\(114\) | 9.29380 | + | 4.09905i | 0.870444 | + | 0.383911i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.26207 | − | 19.2727i | −0.581419 | − | 1.78942i | ||||
\(117\) | −2.01846 | + | 9.83317i | −0.186607 | + | 0.909077i | ||||
\(118\) | 17.7824 | + | 24.4754i | 1.63701 | + | 2.25315i | ||||
\(119\) | 11.1549 | + | 3.62446i | 1.02257 | + | 0.332253i | ||||
\(120\) | 8.70035 | − | 1.88108i | 0.794230 | − | 0.171719i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 10.8217i | 0.979755i | ||||||||
\(123\) | −12.3768 | − | 1.25719i | −1.11598 | − | 0.113357i | ||||
\(124\) | −0.592242 | + | 0.430289i | −0.0531849 | + | 0.0386411i | ||||
\(125\) | 6.16568 | − | 8.48633i | 0.551475 | − | 0.759040i | ||||
\(126\) | −15.0019 | + | 13.6986i | −1.33647 | + | 1.22037i | ||||
\(127\) | −13.7138 | + | 4.45588i | −1.21690 | + | 0.395396i | −0.845953 | − | 0.533257i | \(-0.820968\pi\) |
−0.370949 | + | 0.928653i | \(0.620968\pi\) | |||||||
\(128\) | −16.7743 | − | 12.1872i | −1.48265 | − | 1.07721i | ||||
\(129\) | 4.89799 | − | 5.47811i | 0.431244 | − | 0.482320i | ||||
\(130\) | 3.06798 | − | 9.44228i | 0.269080 | − | 0.828143i | ||||
\(131\) | 13.5516 | 1.18401 | 0.592005 | − | 0.805934i | \(-0.298337\pi\) | ||||
0.592005 | + | 0.805934i | \(0.298337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | 0.600751 | ||||||||
\(134\) | −1.47968 | + | 4.55398i | −0.127825 | + | 0.393404i | ||||
\(135\) | −1.92572 | + | 6.14499i | −0.165740 | + | 0.528876i | ||||
\(136\) | 13.9120 | + | 10.1076i | 1.19294 | + | 0.866723i | ||||
\(137\) | −16.9636 | + | 5.51181i | −1.44930 | + | 0.470905i | −0.924783 | − | 0.380496i | \(-0.875753\pi\) |
−0.524515 | + | 0.851401i | \(0.675753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.04260 | + | 4.18778i | −0.258070 | + | 0.355203i | −0.918317 | − | 0.395846i | \(-0.870452\pi\) |
0.660247 | + | 0.751048i | \(0.270452\pi\) | |||||||
\(140\) | 10.5836 | − | 7.68940i | 0.894473 | − | 0.649873i | ||||
\(141\) | −0.592644 | + | 5.83447i | −0.0499096 | + | 0.491351i | ||||
\(142\) | 19.9749i | 1.67625i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.73205 | + | 3.05379i | −0.561004 | + | 0.254483i | ||||
\(145\) | −6.39994 | − | 2.07947i | −0.531486 | − | 0.172690i | ||||
\(146\) | −11.4077 | − | 15.7014i | −0.944109 | − | 1.29946i | ||||
\(147\) | −0.698961 | + | 1.58476i | −0.0576493 | + | 0.130709i | ||||
\(148\) | −12.0679 | − | 37.1412i | −0.991976 | − | 3.05299i | ||||
\(149\) | −2.90624 | − | 8.94448i | −0.238088 | − | 0.732761i | −0.996697 | − | 0.0812137i | \(-0.974120\pi\) |
0.758608 | − | 0.651547i | \(-0.225880\pi\) | |||||||
\(150\) | −5.79694 | + | 13.1434i | −0.473318 | + | 1.07316i | ||||
\(151\) | −9.69263 | − | 13.3408i | −0.788775 | − | 1.08566i | −0.994260 | − | 0.106995i | \(-0.965877\pi\) |
0.205484 | − | 0.978660i | \(-0.434123\pi\) | |||||||
\(152\) | 9.66046 | + | 3.13887i | 0.783566 | + | 0.254596i | ||||
\(153\) | −11.3293 | + | 5.13922i | −0.915922 | + | 0.415481i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.243094i | 0.0195258i | ||||||||
\(156\) | −2.18578 | + | 21.5186i | −0.175002 | + | 1.72287i | ||||
\(157\) | 9.27465 | − | 6.73843i | 0.740198 | − | 0.537785i | −0.152575 | − | 0.988292i | \(-0.548757\pi\) |
0.892773 | + | 0.450507i | \(0.148757\pi\) | |||||||
\(158\) | −10.3412 | + | 14.2334i | −0.822701 | + | 1.13235i | ||||
\(159\) | 6.18924 | + | 10.6342i | 0.490838 | + | 0.843345i | ||||
\(160\) | −2.82191 | + | 0.916893i | −0.223091 | + | 0.0724868i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.95290 | − | 21.4589i | 0.153434 | − | 1.68597i | ||||
\(163\) | 3.82943 | − | 11.7858i | 0.299944 | − | 0.923134i | −0.681571 | − | 0.731752i | \(-0.738703\pi\) |
0.981516 | − | 0.191382i | \(-0.0612969\pi\) | |||||||
\(164\) | −26.8055 | −2.09316 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35.5167 | −2.75663 | ||||||||
\(167\) | −1.62480 | + | 5.00062i | −0.125731 | + | 0.386960i | −0.994034 | − | 0.109075i | \(-0.965211\pi\) |
0.868303 | + | 0.496035i | \(0.165211\pi\) | |||||||
\(168\) | −13.5407 | + | 15.1445i | −1.04469 | + | 1.16842i | ||||
\(169\) | −1.45934 | − | 1.06028i | −0.112257 | − | 0.0815596i | ||||
\(170\) | 11.7019 | − | 3.80219i | 0.897499 | − | 0.291615i | ||||
\(171\) | −5.42652 | + | 4.95509i | −0.414976 | + | 0.378925i | ||||
\(172\) | 9.30685 | − | 12.8098i | 0.709640 | − | 0.976736i | ||||
\(173\) | −9.16562 | + | 6.65922i | −0.696850 | + | 0.506291i | −0.878905 | − | 0.476998i | \(-0.841725\pi\) |
0.182055 | + | 0.983288i | \(0.441725\pi\) | |||||||
\(174\) | 22.4014 | + | 2.27545i | 1.69825 | + | 0.172501i | ||||
\(175\) | 9.79796i | 0.740656i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.3923 | + | 4.62518i | −1.60794 | + | 0.347650i | ||||
\(178\) | −21.8191 | − | 7.08946i | −1.63541 | − | 0.531378i | ||||
\(179\) | 13.3979 | + | 18.4406i | 1.00140 | + | 1.37832i | 0.924460 | + | 0.381280i | \(0.124517\pi\) |
0.0769449 | + | 0.997035i | \(0.475483\pi\) | |||||||
\(180\) | −2.79006 | + | 13.5921i | −0.207959 | + | 1.01310i | ||||
\(181\) | 3.97285 | + | 12.2272i | 0.295299 | + | 0.908838i | 0.983121 | + | 0.182958i | \(0.0585673\pi\) |
−0.687821 | + | 0.725880i | \(0.741433\pi\) | |||||||
\(182\) | 7.00191 | + | 21.5497i | 0.519016 | + | 1.59737i | ||||
\(183\) | −7.16317 | − | 3.15933i | −0.529517 | − | 0.233545i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −12.3336 | − | 4.00743i | −0.906784 | − | 0.294632i | ||||
\(186\) | −0.171894 | − | 0.795040i | −0.0126039 | − | 0.0582951i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 12.6362i | 0.921592i | ||||||||
\(189\) | −4.68773 | − | 13.9293i | −0.340982 | − | 1.01321i | ||||
\(190\) | 5.87989 | − | 4.27199i | 0.426572 | − | 0.309923i | ||||
\(191\) | −1.45690 | + | 2.00525i | −0.105418 | + | 0.145095i | −0.858466 | − | 0.512870i | \(-0.828582\pi\) |
0.753049 | + | 0.657965i | \(0.228582\pi\) | |||||||
\(192\) | 15.9581 | − | 9.28781i | 1.15167 | − | 0.670290i | ||||
\(193\) | −2.72534 | + | 0.885517i | −0.196174 | + | 0.0637409i | −0.405456 | − | 0.914114i | \(-0.632887\pi\) |
0.209282 | + | 0.977855i | \(0.432887\pi\) | |||||||
\(194\) | 4.39285 | + | 3.19159i | 0.315388 | + | 0.229143i | ||||
\(195\) | 5.35439 | + | 4.78738i | 0.383436 | + | 0.342831i | ||||
\(196\) | −1.15327 | + | 3.54939i | −0.0823762 | + | 0.253528i | ||||
\(197\) | −10.6878 | −0.761476 | −0.380738 | − | 0.924683i | \(-0.624330\pi\) | ||||
−0.380738 | + | 0.924683i | \(0.624330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.66025 | 0.543021 | 0.271511 | − | 0.962435i | \(-0.412477\pi\) | ||||
0.271511 | + | 0.962435i | \(0.412477\pi\) | |||||||
\(200\) | −4.43904 | + | 13.6619i | −0.313887 | + | 0.966046i | ||||
\(201\) | −2.58240 | − | 2.30894i | −0.182149 | − | 0.162860i | ||||
\(202\) | 0.909623 | + | 0.660880i | 0.0640008 | + | 0.0464993i | ||||
\(203\) | 14.6063 | − | 4.74587i | 1.02516 | − | 0.333095i | ||||
\(204\) | −23.1673 | + | 13.4837i | −1.62204 | + | 0.944048i | ||||
\(205\) | −5.23210 | + | 7.20137i | −0.365426 | + | 0.502966i | ||||
\(206\) | 24.6610 | − | 17.9173i | 1.71821 | − | 1.24836i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.24504i | 0.571691i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.07180 | + | 14.2076i | 0.211974 | + | 0.980419i | ||||
\(211\) | −1.80195 | − | 0.585490i | −0.124052 | − | 0.0403068i | 0.246333 | − | 0.969185i | \(-0.420774\pi\) |
−0.370385 | + | 0.928878i | \(0.620774\pi\) | |||||||
\(212\) | 15.5832 | + | 21.4485i | 1.07026 | + | 1.47309i | ||||
\(213\) | −13.2218 | − | 5.83152i | −0.905944 | − | 0.399569i | ||||
\(214\) | −2.59336 | − | 7.98156i | −0.177279 | − | 0.545608i | ||||
\(215\) | −1.62480 | − | 5.00062i | −0.110810 | − | 0.341039i | ||||
\(216\) | −0.225646 | − | 21.5464i | −0.0153532 | − | 1.46604i | ||||
\(217\) | −0.326105 | − | 0.448845i | −0.0221374 | − | 0.0304696i | ||||
\(218\) | 24.3514 | + | 7.91224i | 1.64928 | + | 0.535884i | ||||
\(219\) | 13.7235 | − | 2.96713i | 0.927349 | − | 0.200500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8755i | 0.933370i | ||||||||
\(222\) | 43.1707 | + | 4.38511i | 2.89742 | + | 0.294309i | ||||
\(223\) | −10.4591 | + | 7.59901i | −0.700396 | + | 0.508867i | −0.880061 | − | 0.474861i | \(-0.842498\pi\) |
0.179665 | + | 0.983728i | \(0.442498\pi\) | |||||||
\(224\) | 3.98033 | − | 5.47845i | 0.265947 | − | 0.366044i | ||||
\(225\) | −7.00756 | − | 7.67425i | −0.467170 | − | 0.511617i | ||||
\(226\) | 29.5287 | − | 9.59446i | 1.96422 | − | 0.638214i | ||||
\(227\) | −4.25378 | − | 3.09055i | −0.282333 | − | 0.205127i | 0.437601 | − | 0.899169i | \(-0.355828\pi\) |
−0.719935 | + | 0.694042i | \(0.755828\pi\) | |||||||
\(228\) | −10.5537 | + | 11.8037i | −0.698936 | + | 0.781718i | ||||
\(229\) | 1.71069 | − | 5.26495i | 0.113045 | − | 0.347918i | −0.878489 | − | 0.477763i | \(-0.841448\pi\) |
0.991534 | + | 0.129845i | \(0.0414479\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.5167 | 1.47829 | ||||||||
\(233\) | 1.67792 | − | 5.16410i | 0.109924 | − | 0.338311i | −0.880931 | − | 0.473246i | \(-0.843082\pi\) |
0.990855 | + | 0.134934i | \(0.0430823\pi\) | |||||||
\(234\) | −20.8967 | − | 11.8710i | −1.36606 | − | 0.776030i | ||||
\(235\) | 3.39476 | + | 2.46644i | 0.221450 | + | 0.160893i | ||||
\(236\) | −44.8509 | + | 14.5729i | −2.91955 | + | 0.948618i | ||||
\(237\) | −6.40240 | − | 11.0004i | −0.415881 | − | 0.714554i | ||||
\(238\) | −16.5057 | + | 22.7182i | −1.06991 | + | 1.47260i | ||||
\(239\) | 8.12763 | − | 5.90507i | 0.525733 | − | 0.381967i | −0.293026 | − | 0.956104i | \(-0.594662\pi\) |
0.818759 | + | 0.574137i | \(0.194662\pi\) | |||||||
\(240\) | −0.534520 | + | 5.26225i | −0.0345031 | + | 0.339677i | ||||
\(241\) | − | 3.76217i | − | 0.242343i | −0.992632 | − | 0.121171i | \(-0.961335\pi\) | ||
0.992632 | − | 0.121171i | \(-0.0386650\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6340 | + | 7.55743i | 0.874620 | + | 0.484809i | ||||
\(244\) | −16.0434 | − | 5.21282i | −1.02707 | − | 0.333716i | ||||
\(245\) | 0.728450 | + | 1.00263i | 0.0465390 | + | 0.0640554i | ||||
\(246\) | 12.0194 | − | 27.2517i | 0.766331 | − | 1.73751i | ||||
\(247\) | 2.53275 | + | 7.79500i | 0.161155 | + | 0.495984i | ||||
\(248\) | −0.251357 | − | 0.773599i | −0.0159612 | − | 0.0491236i | ||||
\(249\) | 10.3688 | − | 23.5093i | 0.657098 | − | 1.48984i | ||||
\(250\) | 14.7617 | + | 20.3177i | 0.933611 | + | 1.28500i | ||||
\(251\) | −8.16598 | − | 2.65329i | −0.515432 | − | 0.167474i | 0.0397393 | − | 0.999210i | \(-0.487347\pi\) |
−0.555171 | + | 0.831736i | \(0.687347\pi\) | |||||||
\(252\) | −13.0820 | − | 28.8391i | −0.824088 | − | 1.81669i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 34.5228i | − | 2.16615i | ||||||
\(255\) | −0.899540 | + | 8.85581i | −0.0563314 | + | 0.554573i | ||||
\(256\) | 22.9118 | − | 16.6464i | 1.43199 | − | 1.04040i | ||||
\(257\) | −13.5931 | + | 18.7093i | −0.847912 | + | 1.16705i | 0.136407 | + | 0.990653i | \(0.456445\pi\) |
−0.984319 | + | 0.176398i | \(0.943555\pi\) | |||||||
\(258\) | 8.84988 | + | 15.2056i | 0.550969 | + | 0.946660i | ||||
\(259\) | 28.1484 | − | 9.14596i | 1.74905 | − | 0.568302i | ||||
\(260\) | 12.5205 | + | 9.09666i | 0.776487 | + | 0.564151i | ||||
\(261\) | −8.04610 | + | 14.1637i | −0.498041 | + | 0.876711i | ||||
\(262\) | −10.0260 | + | 30.8569i | −0.619409 | + | 1.90635i | ||||
\(263\) | 23.4721 | 1.44735 | 0.723675 | − | 0.690141i | \(-0.242451\pi\) | ||||
0.723675 | + | 0.690141i | \(0.242451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.80385 | 0.540816 | ||||||||
\(266\) | −5.12576 | + | 15.7755i | −0.314280 | + | 0.967255i | ||||
\(267\) | 11.0626 | − | 12.3729i | 0.677021 | − | 0.757207i | ||||
\(268\) | −6.03859 | − | 4.38729i | −0.368865 | − | 0.267996i | ||||
\(269\) | −15.5537 | + | 5.05372i | −0.948328 | + | 0.308131i | −0.742036 | − | 0.670360i | \(-0.766140\pi\) |
−0.206292 | + | 0.978490i | \(0.566140\pi\) | |||||||
\(270\) | −12.5674 | − | 8.93115i | −0.764825 | − | 0.543533i | ||||
\(271\) | 5.37331 | − | 7.39573i | 0.326405 | − | 0.449258i | −0.614004 | − | 0.789303i | \(-0.710442\pi\) |
0.940409 | + | 0.340045i | \(0.110442\pi\) | |||||||
\(272\) | −8.26669 | + | 6.00611i | −0.501242 | + | 0.364174i | ||||
\(273\) | −16.3084 | − | 1.65654i | −0.987029 | − | 0.100259i | ||||
\(274\) | − | 42.7038i | − | 2.57983i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.96886 | + | 1.93940i | 0.358634 | + | 0.116527i | 0.482792 | − | 0.875735i | \(-0.339623\pi\) |
−0.124158 | + | 0.992262i | \(0.539623\pi\) | |||||||
\(278\) | −7.28450 | − | 10.0263i | −0.436895 | − | 0.601335i | ||||
\(279\) | 0.576438 | + | 0.118326i | 0.0345105 | + | 0.00708397i | ||||
\(280\) | 4.49184 | + | 13.8245i | 0.268439 | + | 0.826170i | ||||
\(281\) | −0.251357 | − | 0.773599i | −0.0149947 | − | 0.0461490i | 0.943279 | − | 0.332001i | \(-0.107724\pi\) |
−0.958274 | + | 0.285852i | \(0.907724\pi\) | |||||||
\(282\) | −12.8466 | − | 5.66602i | −0.765003 | − | 0.337406i | ||||
\(283\) | −3.99322 | − | 5.49619i | −0.237372 | − | 0.326715i | 0.673667 | − | 0.739035i | \(-0.264718\pi\) |
−0.911039 | + | 0.412321i | \(0.864718\pi\) | |||||||
\(284\) | −29.6130 | − | 9.62185i | −1.75721 | − | 0.570952i | ||||
\(285\) | 1.11114 | + | 5.13922i | 0.0658181 | + | 0.304421i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 20.3152i | − | 1.19917i | ||||||
\(288\) | 0.800628 | + | 7.13775i | 0.0471774 | + | 0.420596i | ||||
\(289\) | −0.158691 | + | 0.115296i | −0.00933474 | + | 0.00678209i | ||||
\(290\) | 9.46985 | − | 13.0341i | 0.556089 | − | 0.765391i | ||||
\(291\) | −3.39505 | + | 1.97596i | −0.199021 | + | 0.115833i | ||||
\(292\) | 28.7726 | − | 9.34878i | 1.68379 | − | 0.547096i | ||||
\(293\) | 26.3198 | + | 19.1225i | 1.53762 | + | 1.11715i | 0.951806 | + | 0.306701i | \(0.0992251\pi\) |
0.585814 | + | 0.810446i | \(0.300775\pi\) | |||||||
\(294\) | −3.09136 | − | 2.76399i | −0.180292 | − | 0.161199i | ||||
\(295\) | −4.83928 | + | 14.8938i | −0.281754 | + | 0.867150i | ||||
\(296\) | 43.3928 | 2.52215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.5167 | 1.30436 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −16.6929 | − | 14.9252i | −0.963767 | − | 0.861707i | ||||
\(301\) | 9.70820 | + | 7.05342i | 0.559572 | + | 0.406553i | ||||
\(302\) | 37.5478 | − | 12.2000i | 2.16063 | − | 0.702032i | ||||
\(303\) | −0.703009 | + | 0.409161i | −0.0403868 | + | 0.0235057i | ||||
\(304\) | −3.54775 | + | 4.88306i | −0.203477 | + | 0.280063i | ||||
\(305\) | −4.53191 | + | 3.29263i | −0.259496 | + | 0.188535i | ||||
\(306\) | −3.32006 | − | 29.5990i | −0.189795 | − | 1.69206i | ||||
\(307\) | 31.1870i | 1.77994i | 0.456021 | + | 0.889969i | \(0.349274\pi\) | ||||
−0.456021 | + | 0.889969i | \(0.650726\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.66025 | + | 21.5545i | 0.265113 | + | 1.22619i | ||||
\(310\) | −0.553524 | − | 0.179851i | −0.0314380 | − | 0.0102148i | ||||
\(311\) | 0.390375 | + | 0.537306i | 0.0221362 | + | 0.0304678i | 0.819942 | − | 0.572447i | \(-0.194006\pi\) |
−0.797805 | + | 0.602915i | \(0.794006\pi\) | |||||||
\(312\) | −21.9894 | − | 9.69846i | −1.24490 | − | 0.549067i | ||||
\(313\) | −2.28435 | − | 7.03050i | −0.129119 | − | 0.397387i | 0.865510 | − | 0.500892i | \(-0.166994\pi\) |
−0.994629 | + | 0.103504i | \(0.966994\pi\) | |||||||
\(314\) | 8.48159 | + | 26.1037i | 0.478644 | + | 1.47311i | ||||
\(315\) | −10.3011 | − | 2.11452i | −0.580404 | − | 0.119140i | ||||
\(316\) | −16.1199 | − | 22.1872i | −0.906817 | − | 1.24813i | ||||
\(317\) | 23.4039 | + | 7.60439i | 1.31449 | + | 0.427105i | 0.880601 | − | 0.473859i | \(-0.157139\pi\) |
0.433893 | + | 0.900964i | \(0.357139\pi\) | |||||||
\(318\) | −28.7930 | + | 6.22526i | −1.61463 | + | 0.349095i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 13.2114i | − | 0.738540i | ||||||
\(321\) | 6.04029 | + | 0.613550i | 0.337136 | + | 0.0342450i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.97049 | + | 8.21767i | −0.332207 | + | 0.457244i | ||||
\(324\) | 30.8723 | + | 13.2319i | 1.71513 | + | 0.735105i | ||||
\(325\) | −11.0238 | + | 3.58185i | −0.611490 | + | 0.198685i | ||||
\(326\) | 24.0030 | + | 17.4392i | 1.32940 | + | 0.965866i | ||||
\(327\) | −12.3465 | + | 13.8088i | −0.682763 | + | 0.763629i | ||||
\(328\) | 9.20395 | − | 28.3268i | 0.508203 | − | 1.56409i | ||||
\(329\) | −9.57668 | −0.527979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.392305 | −0.0215630 | −0.0107815 | − | 0.999942i | \(-0.503432\pi\) | ||||
−0.0107815 | + | 0.999942i | \(0.503432\pi\) | |||||||
\(332\) | 17.1083 | − | 52.6540i | 0.938940 | − | 2.88976i | ||||
\(333\) | −15.5060 | + | 27.2955i | −0.849722 | + | 1.49578i | ||||
\(334\) | −10.1843 | − | 7.39931i | −0.557259 | − | 0.404872i | ||||
\(335\) | −2.35731 | + | 0.765938i | −0.128794 | + | 0.0418477i | ||||
\(336\) | −6.07225 | − | 10.4332i | −0.331268 | − | 0.569176i | ||||
\(337\) | 5.00937 | − | 6.89480i | 0.272878 | − | 0.375584i | −0.650481 | − | 0.759523i | \(-0.725433\pi\) |
0.923359 | + | 0.383939i | \(0.125433\pi\) | |||||||
\(338\) | 3.49392 | − | 2.53848i | 0.190044 | − | 0.138075i | ||||
\(339\) | −2.26990 | + | 22.3468i | −0.123284 | + | 1.21371i | ||||
\(340\) | 19.1798i | 1.04017i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.26795 | − | 16.0221i | −0.393006 | − | 0.866376i | ||||
\(343\) | 16.1400 | + | 5.24419i | 0.871476 | + | 0.283160i | ||||
\(344\) | 10.3412 | + | 14.2334i | 0.557560 | + | 0.767415i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.38189 | − | 25.7968i | −0.450613 | − | 1.38684i | ||||
\(347\) | 0.396479 | + | 1.22024i | 0.0212841 | + | 0.0655057i | 0.961134 | − | 0.276081i | \(-0.0890358\pi\) |
−0.939850 | + | 0.341587i | \(0.889036\pi\) | |||||||
\(348\) | −14.1641 | + | 32.1143i | −0.759275 | + | 1.72151i | ||||
\(349\) | 11.9418 | + | 16.4365i | 0.639231 | + | 0.879826i | 0.998574 | − | 0.0533798i | \(-0.0169994\pi\) |
−0.359344 | + | 0.933205i | \(0.616999\pi\) | |||||||
\(350\) | −22.3099 | − | 7.24891i | −1.19251 | − | 0.387471i | ||||
\(351\) | 13.9583 | − | 10.3664i | 0.745040 | − | 0.553316i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.58244i | − | 0.510022i | −0.966938 | − | 0.255011i | \(-0.917921\pi\) | ||
0.966938 | − | 0.255011i | \(-0.0820790\pi\) | |||||||
\(354\) | 5.29537 | − | 52.1320i | 0.281446 | − | 2.77078i | ||||
\(355\) | −8.36503 | + | 6.07755i | −0.443970 | + | 0.322563i | ||||
\(356\) | 21.0205 | − | 28.9322i | 1.11408 | − | 1.53340i | ||||
\(357\) | −10.2190 | − | 17.5579i | −0.540844 | − | 0.929264i | ||||
\(358\) | −51.9014 | + | 16.8638i | −2.74307 | + | 0.891278i | ||||
\(359\) | −27.8768 | − | 20.2537i | −1.47128 | − | 1.06895i | −0.980240 | − | 0.197813i | \(-0.936616\pi\) |
−0.491042 | − | 0.871136i | \(-0.663384\pi\) | |||||||
\(360\) | −13.4056 | − | 7.61542i | −0.706535 | − | 0.401368i | ||||
\(361\) | 4.01722 | − | 12.3637i | 0.211433 | − | 0.650723i | ||||
\(362\) | −30.7804 | −1.61778 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −35.3205 | −1.85130 | ||||||||
\(365\) | 3.10448 | − | 9.55460i | 0.162496 | − | 0.500111i | ||||
\(366\) | 12.4934 | − | 13.9731i | 0.653039 | − | 0.730384i | ||||
\(367\) | 19.3002 | + | 14.0224i | 1.00746 | + | 0.731966i | 0.963676 | − | 0.267075i | \(-0.0860572\pi\) |
0.0437885 | + | 0.999041i | \(0.486057\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.5296 | + | 15.9119i | 0.756378 | + | 0.828340i | ||||
\(370\) | 18.2497 | − | 25.1186i | 0.948759 | − | 1.30586i | ||||
\(371\) | −16.2553 | + | 11.8101i | −0.843931 | + | 0.613152i | ||||
\(372\) | 1.26146 | + | 0.128134i | 0.0654036 | + | 0.00664345i | ||||
\(373\) | − | 9.62209i | − | 0.498213i | −0.968476 | − | 0.249107i | \(-0.919863\pi\) | ||
0.968476 | − | 0.249107i | \(-0.0801369\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.7583 | + | 3.83949i | −0.917036 | + | 0.198270i | ||||
\(376\) | −13.3534 | − | 4.33878i | −0.688649 | − | 0.223756i | ||||
\(377\) | 10.6793 | + | 14.6987i | 0.550010 | + | 0.757024i | ||||
\(378\) | 35.1850 | − | 0.368478i | 1.80972 | − | 0.0189525i | ||||
\(379\) | −9.45235 | − | 29.0914i | −0.485535 | − | 1.49432i | −0.831205 | − | 0.555966i | \(-0.812348\pi\) |
0.345670 | − | 0.938356i | \(-0.387652\pi\) | |||||||
\(380\) | 3.50096 | + | 10.7748i | 0.179595 | + | 0.552738i | ||||
\(381\) | 22.8515 | + | 10.0787i | 1.17072 | + | 0.516347i | ||||
\(382\) | −3.48807 | − | 4.80091i | −0.178465 | − | 0.245636i | ||||
\(383\) | 9.02881 | + | 2.93364i | 0.461351 | + | 0.149902i | 0.530465 | − | 0.847707i | \(-0.322017\pi\) |
−0.0691142 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(384\) | 7.58922 | + | 35.1015i | 0.387286 | + | 1.79127i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6.86071i | − | 0.349201i | ||||||
\(387\) | −12.6486 | + | 1.41877i | −0.642964 | + | 0.0721201i | ||||
\(388\) | −6.84760 | + | 4.97507i | −0.347634 | + | 0.252571i | ||||
\(389\) | −11.2125 | + | 15.4327i | −0.568498 | + | 0.782470i | −0.992376 | − | 0.123249i | \(-0.960669\pi\) |
0.423878 | + | 0.905719i | \(0.360669\pi\) | |||||||
\(390\) | −14.8622 | + | 8.65001i | −0.752577 | + | 0.438010i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −3.35485 | − | 2.43744i | −0.169446 | − | 0.123109i | ||||
\(393\) | −17.4979 | − | 15.6449i | −0.882651 | − | 0.789181i | ||||
\(394\) | 7.90727 | − | 24.3361i | 0.398362 | − | 1.22603i | ||||
\(395\) | −9.10706 | −0.458226 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1962 | −1.06380 | −0.531902 | − | 0.846806i | \(-0.678523\pi\) | ||||
−0.531902 | + | 0.846806i | \(0.678523\pi\) | |||||||
\(398\) | −5.66736 | + | 17.4423i | −0.284079 | + | 0.874305i | ||||
\(399\) | −8.94571 | − | 7.99839i | −0.447846 | − | 0.400420i | ||||
\(400\) | −6.90569 | − | 5.01728i | −0.345284 | − | 0.250864i | ||||
\(401\) | −1.17866 | + | 0.382969i | −0.0588593 | + | 0.0191246i | −0.338299 | − | 0.941039i | \(-0.609851\pi\) |
0.279439 | + | 0.960163i | \(0.409851\pi\) | |||||||
\(402\) | 7.16799 | − | 4.17187i | 0.357507 | − | 0.208074i | ||||
\(403\) | 0.385786 | − | 0.530989i | 0.0192174 | − | 0.0264505i | ||||
\(404\) | −1.41793 | + | 1.03018i | −0.0705445 | + | 0.0512536i | ||||
\(405\) | 9.58069 | − | 5.71124i | 0.476068 | − | 0.283794i | ||||
\(406\) | 36.7696i | 1.82484i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.29423 | − | 29.1120i | −0.311611 | − | 1.44126i | ||||
\(409\) | 31.5945 | + | 10.2657i | 1.56225 | + | 0.507605i | 0.957407 | − | 0.288742i | \(-0.0932370\pi\) |
0.604840 | + | 0.796347i | \(0.293237\pi\) | |||||||
\(410\) | −12.5265 | − | 17.2413i | −0.618642 | − | 0.851487i | ||||
\(411\) | 28.2666 | + | 12.4671i | 1.39429 | + | 0.614955i | ||||
\(412\) | 14.6835 | + | 45.1910i | 0.723402 | + | 2.22640i | ||||
\(413\) | −11.0445 | − | 33.9914i | −0.543463 | − | 1.67261i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8063 | − | 14.8736i | −0.530460 | − | 0.730116i | ||||
\(416\) | 7.61896 | + | 2.47555i | 0.373550 | + | 0.121374i | ||||
\(417\) | 8.76327 | − | 1.89469i | 0.429139 | − | 0.0927832i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.0648i | − | 0.540553i | −0.962783 | − | 0.270277i | \(-0.912885\pi\) | ||
0.962783 | − | 0.270277i | \(-0.0871151\pi\) | |||||||
\(420\) | −22.5427 | − | 2.28980i | −1.09997 | − | 0.111731i | ||||
\(421\) | 15.5300 | − | 11.2832i | 0.756887 | − | 0.549910i | −0.141067 | − | 0.990000i | \(-0.545053\pi\) |
0.897954 | + | 0.440090i | \(0.145053\pi\) | |||||||
\(422\) | 2.66631 | − | 3.66987i | 0.129794 | − | 0.178646i | ||||
\(423\) | 7.50094 | − | 6.84930i | 0.364708 | − | 0.333024i | ||||
\(424\) | −28.0165 | + | 9.10310i | −1.36060 | + | 0.442086i | ||||
\(425\) | −11.6215 | − | 8.44355i | −0.563728 | − | 0.409572i | ||||
\(426\) | 23.0603 | − | 25.7916i | 1.11728 | − | 1.24961i | ||||
\(427\) | 3.95066 | − | 12.1589i | 0.191186 | − | 0.588410i | ||||
\(428\) | 13.0820 | 0.632342 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5885 | 0.607069 | ||||||||
\(431\) | −6.46031 | + | 19.8828i | −0.311182 | + | 0.957721i | 0.666115 | + | 0.745849i | \(0.267956\pi\) |
−0.977297 | + | 0.211872i | \(0.932044\pi\) | |||||||
\(432\) | 12.2179 | + | 3.82887i | 0.587836 | + | 0.184217i | ||||
\(433\) | −10.5597 | − | 7.67210i | −0.507469 | − | 0.368698i | 0.304394 | − | 0.952546i | \(-0.401546\pi\) |
−0.811863 | + | 0.583849i | \(0.801546\pi\) | |||||||
\(434\) | 1.26328 | − | 0.410465i | 0.0606394 | − | 0.0197029i | ||||
\(435\) | 5.86294 | + | 10.0735i | 0.281106 | + | 0.482989i | ||||
\(436\) | −23.4600 | + | 32.2899i | −1.12353 | + | 1.54641i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.39706 | + | 33.4435i | −0.162318 | + | 1.59799i | ||||
\(439\) | − | 8.38375i | − | 0.400134i | −0.979782 | − | 0.200067i | \(-0.935884\pi\) | ||
0.979782 | − | 0.200067i | \(-0.0641160\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.73205 | − | 1.23931i | 0.130098 | − | 0.0590149i | ||||
\(442\) | −31.5945 | − | 10.2657i | −1.50280 | − | 0.488288i | ||||
\(443\) | −14.9977 | − | 20.6425i | −0.712561 | − | 0.980756i | −0.999738 | − | 0.0228783i | \(-0.992717\pi\) |
0.287178 | − | 0.957877i | \(-0.407283\pi\) | |||||||
\(444\) | −27.2962 | + | 61.8888i | −1.29542 | + | 2.93711i | ||||
\(445\) | −3.66978 | − | 11.2944i | −0.173964 | − | 0.535406i | ||||
\(446\) | −9.56479 | − | 29.4374i | −0.452906 | − | 1.39390i | ||||
\(447\) | −6.57358 | + | 14.9043i | −0.310920 | + | 0.704949i | ||||
\(448\) | 17.7228 | + | 24.3933i | 0.837321 | + | 1.15247i | ||||
\(449\) | −38.3260 | − | 12.4529i | −1.80872 | − | 0.587687i | −0.808716 | − | 0.588199i | \(-0.799837\pi\) |
−1.00000 | 0.000512011i | \(0.999837\pi\) | ||||||||
\(450\) | 22.6587 | − | 10.2784i | 1.06814 | − | 0.484530i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 48.3984i | 2.27647i | ||||||||
\(453\) | −2.88633 | + | 28.4155i | −0.135612 | + | 1.33507i | ||||
\(454\) | 10.1843 | − | 7.39931i | 0.477972 | − | 0.347267i | ||||
\(455\) | −6.89413 | + | 9.48895i | −0.323202 | + | 0.444849i | ||||
\(456\) | −8.84988 | − | 15.2056i | −0.414433 | − | 0.712068i | ||||
\(457\) | −17.5203 | + | 5.69269i | −0.819565 | + | 0.266293i | −0.688644 | − | 0.725100i | \(-0.741794\pi\) |
−0.130922 | + | 0.991393i | \(0.541794\pi\) | |||||||
\(458\) | 10.7226 | + | 7.79044i | 0.501035 | + | 0.364023i | ||||
\(459\) | 20.5615 | + | 6.44359i | 0.959730 | + | 0.300761i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.86379 | 0.133380 | 0.0666901 | − | 0.997774i | \(-0.478756\pi\) | ||||
0.0666901 | + | 0.997774i | \(0.478756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.26795 | −0.0589266 | −0.0294633 | − | 0.999566i | \(-0.509380\pi\) | ||||
−0.0294633 | + | 0.999566i | \(0.509380\pi\) | |||||||
\(464\) | −4.13456 | + | 12.7249i | −0.191942 | + | 0.590737i | ||||
\(465\) | 0.280645 | − | 0.313884i | 0.0130146 | − | 0.0145560i | ||||
\(466\) | 10.5172 | + | 7.64121i | 0.487201 | + | 0.353972i | ||||
\(467\) | 18.4581 | − | 5.99739i | 0.854138 | − | 0.277526i | 0.150960 | − | 0.988540i | \(-0.451764\pi\) |
0.703178 | + | 0.711014i | \(0.251764\pi\) | |||||||
\(468\) | 27.6648 | − | 25.2614i | 1.27881 | − | 1.16771i | ||||
\(469\) | 3.32502 | − | 4.57649i | 0.153535 | − | 0.211323i | ||||
\(470\) | −8.12763 | + | 5.90507i | −0.374900 | + | 0.272381i | ||||
\(471\) | −19.7548 | − | 2.00661i | −0.910251 | − | 0.0924599i | ||||
\(472\) | − | 52.4002i | − | 2.41192i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 29.7846 | − | 6.43966i | 1.36805 | − | 0.295784i | ||||
\(475\) | −8.06998 | − | 2.62210i | −0.370276 | − | 0.120310i | ||||
\(476\) | −25.7292 | − | 35.4133i | −1.17930 | − | 1.62316i | ||||
\(477\) | 4.28525 | − | 20.8761i | 0.196208 | − | 0.955853i | ||||
\(478\) | 7.43265 | + | 22.8753i | 0.339961 | + | 1.04629i | ||||
\(479\) | −2.02128 | − | 6.22086i | −0.0923546 | − | 0.284238i | 0.894201 | − | 0.447666i | \(-0.147745\pi\) |
−0.986555 | + | 0.163428i | \(0.947745\pi\) | |||||||
\(480\) | 4.70218 | + | 2.07391i | 0.214624 | + | 0.0946604i | ||||
\(481\) | 20.5805 | + | 28.3266i | 0.938388 | + | 1.29158i | ||||
\(482\) | 8.56642 | + | 2.78340i | 0.390190 | + | 0.126780i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.81070i | 0.127627i | ||||||||
\(486\) | −27.2951 | + | 25.4532i | −1.23813 | + | 1.15458i | ||||
\(487\) | −26.8407 | + | 19.5009i | −1.21627 | + | 0.883670i | −0.995785 | − | 0.0917207i | \(-0.970763\pi\) |
−0.220483 | + | 0.975391i | \(0.570763\pi\) | |||||||
\(488\) | 11.0173 | − | 15.1641i | 0.498732 | − | 0.686445i | ||||
\(489\) | −18.5509 | + | 10.7969i | −0.838900 | + | 0.488251i | ||||
\(490\) | −2.82191 | + | 0.916893i | −0.127481 | + | 0.0414210i | ||||
\(491\) | −16.9133 | − | 12.2882i | −0.763288 | − | 0.554561i | 0.136629 | − | 0.990622i | \(-0.456373\pi\) |
−0.899917 | + | 0.436061i | \(0.856373\pi\) | |||||||
\(492\) | 34.6113 | + | 30.9461i | 1.56040 | + | 1.39516i | ||||
\(493\) | −6.95803 | + | 21.4146i | −0.313374 | + | 0.964466i | ||||
\(494\) | −19.6230 | −0.882880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.483340 | 0.0217026 | ||||||||
\(497\) | 7.29216 | − | 22.4430i | 0.327098 | − | 1.00670i | ||||
\(498\) | 45.8592 | + | 41.0028i | 2.05500 | + | 1.83738i | ||||
\(499\) | −20.8758 | − | 15.1671i | −0.934527 | − | 0.678974i | 0.0125700 | − | 0.999921i | \(-0.495999\pi\) |
−0.947097 | + | 0.320947i | \(0.895999\pi\) | |||||||
\(500\) | −37.2320 | + | 12.0974i | −1.66506 | + | 0.541012i | ||||
\(501\) | 7.87100 | − | 4.58103i | 0.351650 | − | 0.204665i | ||||
\(502\) | 12.0830 | − | 16.6309i | 0.539292 | − | 0.742271i | ||||
\(503\) | −2.83585 | + | 2.06037i | −0.126444 | + | 0.0918673i | −0.649210 | − | 0.760609i | \(-0.724900\pi\) |
0.522765 | + | 0.852477i | \(0.324900\pi\) | |||||||
\(504\) | 34.9677 | − | 3.92226i | 1.55758 | − | 0.174711i | ||||
\(505\) | 0.582009i | 0.0258991i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.660254 | + | 3.05379i | 0.0293229 | + | 0.135624i | ||||
\(508\) | 51.1806 | + | 16.6296i | 2.27077 | + | 0.737818i | ||||
\(509\) | 6.89413 | + | 9.48895i | 0.305577 | + | 0.420590i | 0.933995 | − | 0.357285i | \(-0.116297\pi\) |
−0.628419 | + | 0.777875i | \(0.716297\pi\) | |||||||
\(510\) | −19.4991 | − | 8.60012i | −0.863435 | − | 0.380820i | ||||
\(511\) | 7.08520 | + | 21.8060i | 0.313431 | + | 0.964641i | ||||
\(512\) | 8.13823 | + | 25.0469i | 0.359662 | + | 1.10693i | ||||
\(513\) | 12.7272 | − | 0.133287i | 0.561921 | − | 0.00588475i | ||||
\(514\) | −32.5441 | − | 44.7931i | −1.43546 | − | 1.97574i | ||||
\(515\) | 15.0067 | + | 4.87598i | 0.661275 | + | 0.214861i | ||||
\(516\) | −26.8055 | + | 5.79555i | −1.18005 | + | 0.255135i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 70.8601i | 3.11342i | ||||||||
\(519\) | 19.5225 | + | 1.98302i | 0.856944 | + | 0.0870451i | ||||
\(520\) | −13.9120 | + | 10.1076i | −0.610081 | + | 0.443250i | ||||
\(521\) | −1.45690 | + | 2.00525i | −0.0638280 | + | 0.0878517i | −0.839738 | − | 0.542992i | \(-0.817291\pi\) |
0.775910 | + | 0.630844i | \(0.217291\pi\) | |||||||
\(522\) | −26.2978 | − | 28.7998i | −1.15102 | − | 1.26053i | ||||
\(523\) | 34.3198 | − | 11.1512i | 1.50070 | − | 0.487607i | 0.560479 | − | 0.828169i | \(-0.310617\pi\) |
0.940222 | + | 0.340561i | \(0.110617\pi\) | |||||||
\(524\) | −40.9163 | − | 29.7274i | −1.78744 | − | 1.29865i | ||||
\(525\) | 11.3114 | − | 12.6511i | 0.493671 | − | 0.552141i | ||||
\(526\) | −17.3656 | + | 53.4457i | −0.757175 | + | 2.33034i | ||||
\(527\) | 0.813410 | 0.0354327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | −6.51343 | + | 20.0463i | −0.282925 | + | 0.870755i | ||||
\(531\) | 32.9614 | + | 18.7247i | 1.43040 | + | 0.812582i | ||||
\(532\) | −20.9183 | − | 15.1980i | −0.906922 | − | 0.658917i | ||||
\(533\) | 22.8569 | − | 7.42665i | 0.990041 | − | 0.321684i | ||||
\(534\) | 19.9883 | + | 34.3434i | 0.864980 | + | 1.48618i | ||||
\(535\) | 2.55344 | − | 3.51451i | 0.110395 | − | 0.151946i | ||||
\(536\) | 6.70970 | − | 4.87488i | 0.289815 | − | 0.210563i | ||||
\(537\) | 3.98971 | − | 39.2780i | 0.172169 | − | 1.69497i | ||||
\(538\) | − | 39.1547i | − | 1.68808i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.2942 | − | 14.3292i | 0.830291 | − | 0.616629i | ||||
\(541\) | −5.01960 | − | 1.63097i | −0.215809 | − | 0.0701207i | 0.199117 | − | 0.979976i | \(-0.436193\pi\) |
−0.414926 | + | 0.909855i | \(0.636193\pi\) | |||||||
\(542\) | 12.8646 | + | 17.7066i | 0.552583 | + | 0.760565i | ||||
\(543\) | 8.98612 | − | 20.3743i | 0.385632 | − | 0.874344i | ||||
\(544\) | 3.06798 | + | 9.44228i | 0.131539 | + | 0.404835i | ||||
\(545\) | 4.09568 | + | 12.6052i | 0.175439 | + | 0.539947i | ||||
\(546\) | 15.8375 | − | 35.9085i | 0.677783 | − | 1.53674i | ||||
\(547\) | −12.4091 | − | 17.0797i | −0.530576 | − | 0.730275i | 0.456642 | − | 0.889650i | \(-0.349052\pi\) |
−0.987218 | + | 0.159375i | \(0.949052\pi\) | |||||||
\(548\) | 63.3090 | + | 20.5703i | 2.70443 | + | 0.878721i | ||||
\(549\) | 5.60175 | + | 12.3490i | 0.239077 | + | 0.527042i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.3004i | 0.566615i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.8151 | − | 12.2169i | 0.715051 | − | 0.519515i | ||||
\(554\) | −8.83199 | + | 12.1562i | −0.375235 | + | 0.516467i | ||||
\(555\) | 11.2987 | + | 19.4131i | 0.479604 | + | 0.824042i | ||||
\(556\) | 18.3730 | − | 5.96975i | 0.779189 | − | 0.253174i | ||||
\(557\) | 8.40576 | + | 6.10714i | 0.356163 | + | 0.258768i | 0.751450 | − | 0.659790i | \(-0.229355\pi\) |
−0.395287 | + | 0.918558i | \(0.629355\pi\) | |||||||
\(558\) | −0.695898 | + | 1.22500i | −0.0294597 | + | 0.0518585i | ||||
\(559\) | −4.38685 | + | 13.5013i | −0.185544 | + | 0.571046i | ||||
\(560\) | −8.63744 | −0.364998 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.94744 | 0.0821478 | ||||||||
\(563\) | 10.9382 | − | 33.6644i | 0.460992 | − | 1.41879i | −0.402963 | − | 0.915216i | \(-0.632020\pi\) |
0.863954 | − | 0.503570i | \(-0.167980\pi\) | |||||||
\(564\) | 14.5881 | − | 16.3159i | 0.614271 | − | 0.687025i | ||||
\(565\) | 13.0024 | + | 9.44677i | 0.547013 | + | 0.397428i | ||||
\(566\) | 15.4691 | − | 5.02622i | 0.650216 | − | 0.211268i | ||||
\(567\) | −10.0281 | + | 23.3974i | −0.421141 | + | 0.982597i | ||||
\(568\) | 20.3359 | − | 27.9899i | 0.853275 | − | 1.17443i | ||||
\(569\) | 25.4209 | − | 18.4694i | 1.06570 | − | 0.774276i | 0.0905647 | − | 0.995891i | \(-0.471133\pi\) |
0.975134 | + | 0.221615i | \(0.0711328\pi\) | |||||||
\(570\) | −12.5240 | − | 1.27214i | −0.524573 | − | 0.0532842i | ||||
\(571\) | − | 27.3233i | − | 1.14345i | −0.820447 | − | 0.571723i | \(-0.806275\pi\) | ||
0.820447 | − | 0.571723i | \(-0.193725\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.19615 | − | 0.907241i | 0.175297 | − | 0.0379005i | ||||
\(574\) | 46.2575 | + | 15.0300i | 1.93075 | + | 0.627340i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −31.3276 | − | 6.43062i | −1.30532 | − | 0.267943i | ||||
\(577\) | 1.48447 | + | 4.56873i | 0.0617993 | + | 0.190199i | 0.977190 | − | 0.212369i | \(-0.0681178\pi\) |
−0.915390 | + | 0.402568i | \(0.868118\pi\) | |||||||
\(578\) | −0.145121 | − | 0.446637i | −0.00603625 | − | 0.0185777i | ||||
\(579\) | 4.54127 | + | 2.00294i | 0.188729 | + | 0.0832392i | ||||
\(580\) | 14.7617 | + | 20.3177i | 0.612945 | + | 0.843647i | ||||
\(581\) | 39.9051 | + | 12.9660i | 1.65554 | + | 0.537918i | ||||
\(582\) | −1.98747 | − | 9.19239i | −0.0823831 | − | 0.381037i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 33.6156i | 1.39102i | ||||||||
\(585\) | −1.38673 | − | 12.3629i | −0.0573341 | − | 0.511145i | ||||
\(586\) | −63.0141 | + | 45.7824i | −2.60309 | + | 1.89125i | ||||
\(587\) | −3.83744 | + | 5.28178i | −0.158388 | + | 0.218002i | −0.880834 | − | 0.473425i | \(-0.843018\pi\) |
0.722446 | + | 0.691427i | \(0.243018\pi\) | |||||||
\(588\) | 5.58676 | − | 3.25157i | 0.230394 | − | 0.134093i | ||||
\(589\) | 0.456957 | − | 0.148474i | 0.0188286 | − | 0.00611778i | ||||
\(590\) | −30.3327 | − | 22.0380i | −1.24878 | − | 0.907291i | ||||
\(591\) | 13.8001 | + | 12.3387i | 0.567662 | + | 0.507548i | ||||
\(592\) | −7.96788 | + | 24.5226i | −0.327478 | + | 1.00787i | ||||
\(593\) | −26.3359 | −1.08148 | −0.540742 | − | 0.841188i | \(-0.681857\pi\) | ||||
−0.540742 | + | 0.841188i | \(0.681857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.5359 | −0.595914 | ||||||||
\(596\) | −10.8462 | + | 33.3813i | −0.444279 | + | 1.36735i | ||||
\(597\) | −9.89094 | − | 8.84352i | −0.404809 | − | 0.361941i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.58851 | + | 0.841058i | −0.105764 | + | 0.0343647i | −0.361421 | − | 0.932403i | \(-0.617708\pi\) |
0.255657 | + | 0.966768i | \(0.417708\pi\) | |||||||
\(600\) | 21.5040 | − | 12.5156i | 0.877896 | − | 0.510948i | ||||
\(601\) | −24.4106 | + | 33.5983i | −0.995730 | + | 1.37050i | −0.0678213 | + | 0.997697i | \(0.521605\pi\) |
−0.927909 | + | 0.372807i | \(0.878395\pi\) | |||||||
\(602\) | −23.2431 | + | 16.8871i | −0.947318 | + | 0.688267i | ||||
\(603\) | 0.668814 | + | 5.96261i | 0.0272362 | + | 0.242816i | ||||
\(604\) | 61.5419i | 2.50410i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.411543 | − | 1.90346i | −0.0167178 | − | 0.0773228i | ||||
\(607\) | −42.2226 | − | 13.7189i | −1.71376 | − | 0.556835i | −0.722808 | − | 0.691049i | \(-0.757149\pi\) |
−0.990952 | + | 0.134214i | \(0.957149\pi\) | |||||||
\(608\) | 3.44706 | + | 4.74448i | 0.139797 | + | 0.192414i | ||||
\(609\) | −24.3386 | − | 10.7346i | −0.986251 | − | 0.434988i | ||||
\(610\) | −4.14439 | − | 12.7551i | −0.167802 | − | 0.516440i | ||||
\(611\) | −3.50096 | − | 10.7748i | −0.141634 | − | 0.435903i | ||||
\(612\) | 45.4802 | + | 9.33574i | 1.83843 | + | 0.377375i | ||||
\(613\) | −9.06227 | − | 12.4731i | −0.366021 | − | 0.503785i | 0.585793 | − | 0.810461i | \(-0.300783\pi\) |
−0.951814 | + | 0.306676i | \(0.900783\pi\) | |||||||
\(614\) | −71.0126 | − | 23.0734i | −2.86583 | − | 0.931166i | ||||
\(615\) | 15.0695 | − | 3.25813i | 0.607659 | − | 0.131381i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 13.6325i | − | 0.548822i | −0.961613 | − | 0.274411i | \(-0.911517\pi\) | ||
0.961613 | − | 0.274411i | \(-0.0884828\pi\) | |||||||
\(618\) | −52.5273 | − | 5.33552i | −2.11296 | − | 0.214626i | ||||
\(619\) | 0.116170 | − | 0.0844022i | 0.00466925 | − | 0.00339241i | −0.585448 | − | 0.810710i | \(-0.699081\pi\) |
0.590117 | + | 0.807317i | \(0.299081\pi\) | |||||||
\(620\) | 0.533263 | − | 0.733973i | 0.0214163 | − | 0.0294771i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.51226 | + | 0.491361i | −0.0606359 | + | 0.0197018i | ||||
\(623\) | 21.9270 | + | 15.9309i | 0.878485 | + | 0.638257i | ||||
\(624\) | 9.51864 | − | 10.6460i | 0.381051 | − | 0.426182i | ||||
\(625\) | 1.33511 | − | 4.10905i | 0.0534044 | − | 0.164362i | ||||
\(626\) | 17.6984 | 0.707372 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −42.7846 | −1.70729 | ||||||||
\(629\) | −13.4091 | + | 41.2690i | −0.534656 | + | 1.64550i | ||||
\(630\) | 12.4359 | − | 21.8912i | 0.495459 | − | 0.872166i | ||||
\(631\) | −22.1028 | − | 16.0586i | −0.879897 | − | 0.639282i | 0.0533274 | − | 0.998577i | \(-0.483017\pi\) |
−0.933224 | + | 0.359295i | \(0.883017\pi\) | |||||||
\(632\) | 28.9814 | − | 9.41662i | 1.15282 | − | 0.374573i | ||||
\(633\) | 1.65076 | + | 2.83629i | 0.0656117 | + | 0.112732i | ||||
\(634\) | −34.6302 | + | 47.6644i | −1.37534 | + | 1.89300i | ||||
\(635\) | 14.4574 | − | 10.5039i | 0.573724 | − | 0.416835i | ||||
\(636\) | 4.64048 | − | 45.6847i | 0.184007 | − | 1.81151i | ||||
\(637\) | − | 3.34607i | − | 0.132576i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3397 | + | 22.7938i | 0.409034 | + | 0.901710i | ||||
\(640\) | 24.4384 | + | 7.94053i | 0.966014 | + | 0.313877i | ||||
\(641\) | −27.7717 | − | 38.2245i | −1.09692 | − | 1.50978i | −0.839410 | − | 0.543499i | \(-0.817099\pi\) |
−0.257506 | − | 0.966277i | \(-0.582901\pi\) | |||||||
\(642\) | −5.86589 | + | 13.2998i | −0.231508 | + | 0.524900i | ||||
\(643\) | −1.17545 | − | 3.61767i | −0.0463554 | − | 0.142667i | 0.925200 | − | 0.379480i | \(-0.123897\pi\) |
−0.971555 | + | 0.236813i | \(0.923897\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.67511 | + | 8.33259i | −0.144707 | + | 0.328095i | ||||
\(646\) | −14.2944 | − | 19.6745i | −0.562404 | − | 0.774083i | ||||
\(647\) | −15.8696 | − | 5.15633i | −0.623897 | − | 0.202716i | −0.0200272 | − | 0.999799i | \(-0.506375\pi\) |
−0.603870 | + | 0.797083i | \(0.706375\pi\) | |||||||
\(648\) | −24.5832 | + | 28.0812i | −0.965720 | + | 1.10313i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 27.7511i | − | 1.08849i | ||||||
\(651\) | −0.0971096 | + | 0.956027i | −0.00380603 | + | 0.0374697i | ||||
\(652\) | −37.4160 | + | 27.1843i | −1.46532 | + | 1.06462i | ||||
\(653\) | 22.8154 | − | 31.4028i | 0.892837 | − | 1.22888i | −0.0798602 | − | 0.996806i | \(-0.525447\pi\) |
0.972697 | − | 0.232079i | \(-0.0745526\pi\) | |||||||
\(654\) | −22.3081 | − | 38.3292i | −0.872316 | − | 1.49879i | ||||
\(655\) | −15.9727 | + | 5.18985i | −0.624105 | + | 0.202784i | ||||
\(656\) | 14.3183 | + | 10.4029i | 0.559037 | + | 0.406164i | ||||
\(657\) | −21.1453 | − | 12.0122i | −0.824956 | − | 0.468640i | ||||
\(658\) | 7.08520 | − | 21.8060i | 0.276210 | − | 0.850087i | ||||
\(659\) | −13.5516 | −0.527896 | −0.263948 | − | 0.964537i | \(-0.585025\pi\) | ||||
−0.263948 | + | 0.964537i | \(0.585025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.19615 | 0.124316 | 0.0621580 | − | 0.998066i | \(-0.480202\pi\) | ||||
0.0621580 | + | 0.998066i | \(0.480202\pi\) | |||||||
\(662\) | 0.290243 | − | 0.893275i | 0.0112806 | − | 0.0347181i | ||||
\(663\) | 16.0189 | − | 17.9161i | 0.622121 | − | 0.695805i | ||||
\(664\) | 49.7680 | + | 36.1586i | 1.93137 | + | 1.40323i | ||||
\(665\) | −8.16598 | + | 2.65329i | −0.316663 | + | 0.102890i | ||||
\(666\) | −50.6796 | − | 55.5012i | −1.96379 | − | 2.15063i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 15.8753 | − | 11.5341i | 0.614235 | − | 0.446268i | ||||
\(669\) | 22.2777 | + | 2.26288i | 0.861305 | + | 0.0874881i | ||||
\(670\) | − | 5.93426i | − | 0.229260i | ||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4641 | + | 2.47863i | −0.442237 | + | 0.0956151i | ||||
\(673\) | −34.6095 | − | 11.2453i | −1.33410 | − | 0.433475i | −0.446785 | − | 0.894641i | \(-0.647431\pi\) |
−0.887314 | + | 0.461166i | \(0.847431\pi\) | |||||||
\(674\) | 11.9933 | + | 16.5073i | 0.461964 | + | 0.635839i | ||||
\(675\) | 0.188496 | + | 17.9990i | 0.00725521 | + | 0.692782i | ||||
\(676\) | 2.08032 | + | 6.40256i | 0.0800122 | + | 0.246252i | ||||
\(677\) | −3.55408 | − | 10.9383i | −0.136594 | − | 0.420394i | 0.859240 | − | 0.511572i | \(-0.170937\pi\) |
−0.995835 | + | 0.0911783i | \(0.970937\pi\) | |||||||
\(678\) | −49.2040 | − | 21.7016i | −1.88967 | − | 0.833444i | ||||
\(679\) | −3.77048 | − | 5.18962i | −0.144698 | − | 0.199160i | ||||
\(680\) | −20.2684 | − | 6.58559i | −0.777257 | − | 0.252546i | ||||
\(681\) | 1.92455 | + | 8.90138i | 0.0737488 | + | 0.341102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 41.2946i | − | 1.58009i | −0.613047 | − | 0.790046i | \(-0.710056\pi\) | ||
0.613047 | − | 0.790046i | \(-0.289944\pi\) | |||||||
\(684\) | 27.2539 | − | 3.05702i | 1.04208 | − | 0.116888i | ||||
\(685\) | 17.8834 | − | 12.9931i | 0.683290 | − | 0.496439i | ||||
\(686\) | −23.8820 | + | 32.8707i | −0.911817 | + | 1.25501i | ||||
\(687\) | −8.28706 | + | 4.82319i | −0.316171 | + | 0.184016i | ||||
\(688\) | −9.94263 | + | 3.23056i | −0.379059 | + | 0.123164i | ||||
\(689\) | −19.2302 | − | 13.9715i | −0.732611 | − | 0.532273i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.799877 | − | 2.46177i | 0.0304288 | − | 0.0936501i | −0.934689 | − | 0.355467i | \(-0.884322\pi\) |
0.965117 | + | 0.261817i | \(0.0843217\pi\) | |||||||
\(692\) | 42.2817 | 1.60731 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.07180 | −0.116604 | ||||||||
\(695\) | 1.98239 | − | 6.10118i | 0.0751965 | − | 0.231431i | ||||
\(696\) | −29.0736 | − | 25.9948i | −1.10203 | − | 0.985329i | ||||
\(697\) | 24.0963 | + | 17.5070i | 0.912711 | + | 0.663123i | ||||
\(698\) | −46.2608 | + | 15.0310i | −1.75100 | + | 0.568933i | ||||
\(699\) | −8.12832 | + | 4.73080i | −0.307441 | + | 0.178935i | ||||
\(700\) | 21.4932 | − | 29.5829i | 0.812368 | − | 1.11813i | ||||
\(701\) | −16.1162 | + | 11.7091i | −0.608700 | + | 0.442247i | −0.848956 | − | 0.528463i | \(-0.822769\pi\) |
0.240256 | + | 0.970710i | \(0.422769\pi\) | |||||||
\(702\) | 13.2772 | + | 39.4524i | 0.501116 | + | 1.48904i | ||||
\(703\) | 25.6317i | 0.966718i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.53590 | − | 7.10381i | −0.0578453 | − | 0.267545i | ||||
\(706\) | 21.8191 | + | 7.08946i | 0.821174 | + | 0.266815i | ||||
\(707\) | −0.780751 | − | 1.07461i | −0.0293632 | − | 0.0404149i | ||||
\(708\) | 74.7356 | + | 32.9623i | 2.80874 | + | 1.23880i | ||||
\(709\) | 12.1507 | + | 37.3960i | 0.456329 | + | 1.40444i | 0.869567 | + | 0.493814i | \(0.164398\pi\) |
−0.413238 | + | 0.910623i | \(0.635602\pi\) | |||||||
\(710\) | −7.64975 | − | 23.5435i | −0.287090 | − | 0.883572i | ||||
\(711\) | −4.43284 | + | 21.5951i | −0.166245 | + | 0.809881i | ||||
\(712\) | 23.3566 | + | 32.1476i | 0.875327 | + | 1.20478i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 47.5396 | − | 10.2784i | 1.77913 | − | 0.384661i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 85.0677i | − | 3.17913i | ||||||
\(717\) | −17.3116 | − | 1.75845i | −0.646515 | − | 0.0656705i | ||||
\(718\) | 66.7418 | − | 48.4908i | 2.49078 | − | 1.80966i | ||||
\(719\) | 21.0728 | − | 29.0042i | 0.785881 | − | 1.08167i | −0.208727 | − | 0.977974i | \(-0.566932\pi\) |
0.994609 | − | 0.103699i | \(-0.0330678\pi\) | |||||||
\(720\) | 6.76527 | − | 6.17754i | 0.252127 | − | 0.230223i | ||||
\(721\) | −34.2491 | + | 11.1282i | −1.27550 | + | 0.414437i | ||||
\(722\) | 25.1800 | + | 18.2944i | 0.937103 | + | 0.680845i | ||||
\(723\) | −4.34330 | + | 4.85772i | −0.161529 | + | 0.180661i | ||||
\(724\) | 14.8269 | − | 45.6324i | 0.551036 | − | 1.69592i | ||||
\(725\) | −18.8096 | −0.698570 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9282 | −1.07289 | −0.536444 | − | 0.843936i | \(-0.680233\pi\) | ||||
−0.536444 | + | 0.843936i | \(0.680233\pi\) | |||||||
\(728\) | 12.1277 | − | 37.3251i | 0.449481 | − | 1.38336i | ||||
\(729\) | −8.87941 | − | 25.4982i | −0.328867 | − | 0.944376i | ||||
\(730\) | 19.4589 | + | 14.1377i | 0.720207 | + | 0.523261i | ||||
\(731\) | −16.7324 | + | 5.43669i | −0.618870 | + | 0.201083i | ||||
\(732\) | 14.6972 | + | 25.2524i | 0.543226 | + | 0.933355i | ||||
\(733\) | 16.8697 | − | 23.2191i | 0.623095 | − | 0.857617i | −0.374479 | − | 0.927236i | \(-0.622178\pi\) |
0.997574 | + | 0.0696189i | \(0.0221783\pi\) | |||||||
\(734\) | −46.2081 | + | 33.5721i | −1.70557 | + | 1.23917i | ||||
\(735\) | 0.216923 | − | 2.13557i | 0.00800131 | − | 0.0787715i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −46.9808 | + | 21.3114i | −1.72939 | + | 0.784484i | ||||
\(739\) | −21.4234 | − | 6.96088i | −0.788072 | − | 0.256060i | −0.112789 | − | 0.993619i | \(-0.535978\pi\) |
−0.675283 | + | 0.737559i | \(0.735978\pi\) | |||||||
\(740\) | 28.4478 | + | 39.1551i | 1.04576 | + | 1.43937i | ||||
\(741\) | 5.72879 | − | 12.9889i | 0.210452 | − | 0.477159i | ||||
\(742\) | −14.8653 | − | 45.7507i | −0.545722 | − | 1.67956i | ||||
\(743\) | 8.77184 | + | 26.9969i | 0.321807 | + | 0.990421i | 0.972861 | + | 0.231390i | \(0.0743273\pi\) |
−0.651054 | + | 0.759032i | \(0.725673\pi\) | |||||||
\(744\) | −0.568541 | + | 1.28906i | −0.0208437 | + | 0.0472591i | ||||
\(745\) | 6.85092 | + | 9.42948i | 0.250998 | + | 0.345470i | ||||
\(746\) | 21.9094 | + | 7.11880i | 0.802161 | + | 0.260638i | ||||
\(747\) | −40.5290 | + | 18.3848i | −1.48288 | + | 0.672664i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.91451i | 0.362268i | ||||||||
\(750\) | 4.39583 | − | 43.2762i | 0.160513 | − | 1.58022i | ||||
\(751\) | −3.94448 | + | 2.86583i | −0.143936 | + | 0.104576i | −0.657423 | − | 0.753522i | \(-0.728353\pi\) |
0.513487 | + | 0.858097i | \(0.328353\pi\) | |||||||
\(752\) | 4.90396 | − | 6.74973i | 0.178829 | − | 0.246137i | ||||
\(753\) | 7.48079 | + | 12.8533i | 0.272615 | + | 0.468400i | ||||
\(754\) | −41.3699 | + | 13.4419i | −1.50660 | + | 0.489525i | ||||
\(755\) | 16.5334 | + | 12.0122i | 0.601712 | + | 0.437169i | ||||
\(756\) | −16.4023 | + | 52.3398i | −0.596546 | + | 1.90358i | ||||
\(757\) | −2.05813 | + | 6.33428i | −0.0748041 | + | 0.230223i | −0.981467 | − | 0.191634i | \(-0.938621\pi\) |
0.906662 | + | 0.421857i | \(0.138621\pi\) | |||||||
\(758\) | 73.2340 | 2.65998 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.5885 | −0.456631 | ||||||||
\(761\) | 8.93119 | − | 27.4874i | 0.323755 | − | 0.996417i | −0.648244 | − | 0.761433i | \(-0.724496\pi\) |
0.971999 | − | 0.234984i | \(-0.0755037\pi\) | |||||||
\(762\) | −39.8555 | + | 44.5760i | −1.44381 | + | 1.61482i | ||||
\(763\) | −24.4717 | − | 17.7797i | −0.885936 | − | 0.643670i | ||||
\(764\) | 8.79762 | − | 2.85852i | 0.318287 | − | 0.103418i | ||||
\(765\) | 11.3852 | − | 10.3962i | 0.411634 | − | 0.375874i | ||||
\(766\) | −13.3597 | + | 18.3881i | −0.482707 | + | 0.664389i | ||||
\(767\) | 34.2066 | − | 24.8525i | 1.23513 | − | 0.897373i | ||||
\(768\) | −48.8014 | − | 4.95707i | −1.76097 | − | 0.178873i | ||||
\(769\) | − | 11.9329i | − | 0.430311i | −0.976580 | − | 0.215155i | \(-0.930974\pi\) | ||
0.976580 | − | 0.215155i | \(-0.0690258\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.1506 | − | 8.46467i | 1.40998 | − | 0.304848i | ||||
\(772\) | 10.1711 | + | 3.30479i | 0.366066 | + | 0.118942i | ||||
\(773\) | 18.1590 | + | 24.9937i | 0.653132 | + | 0.898959i | 0.999230 | − | 0.0392390i | \(-0.0124934\pi\) |
−0.346098 | + | 0.938199i | \(0.612493\pi\) | |||||||
\(774\) | 6.12741 | − | 29.8504i | 0.220245 | − | 1.07295i | ||||
\(775\) | 0.209975 | + | 0.646235i | 0.00754251 | + | 0.0232135i | ||||
\(776\) | −2.90624 | − | 8.94448i | −0.104328 | − | 0.321088i | ||||
\(777\) | −46.9040 | − | 20.6871i | −1.68267 | − | 0.742146i | ||||
\(778\) | −26.8447 | − | 36.9486i | −0.962429 | − | 1.32467i | ||||
\(779\) | 16.7324 | + | 5.43669i | 0.599500 | + | 0.194789i | ||||
\(780\) | −5.66467 | − | 26.2001i | −0.202828 | − | 0.938115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 26.7407 | − | 8.99924i | 0.955634 | − | 0.321607i | ||||
\(784\) | 1.99350 | − | 1.44836i | 0.0711964 | − | 0.0517272i | ||||
\(785\) | −8.35103 | + | 11.4942i | −0.298061 | + | 0.410246i | ||||
\(786\) | 48.5689 | − | 28.2678i | 1.73240 | − | 1.00828i | ||||
\(787\) | −43.3037 | + | 14.0702i | −1.54361 | + | 0.501550i | −0.952370 | − | 0.304945i | \(-0.901362\pi\) |
−0.591241 | + | 0.806495i | \(0.701362\pi\) | |||||||
\(788\) | 32.2697 | + | 23.4453i | 1.14956 | + | 0.835203i | ||||
\(789\) | −30.3072 | − | 27.0978i | −1.07897 | − | 0.964706i | ||||
\(790\) | 6.73776 | − | 20.7367i | 0.239719 | − | 0.737778i | ||||
\(791\) | −36.6799 | −1.30419 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1244 | 0.537082 | ||||||||
\(794\) | 15.6817 | − | 48.2635i | 0.556524 | − | 1.71281i | ||||
\(795\) | −11.3675 | − | 10.1638i | −0.403165 | − | 0.360471i | ||||
\(796\) | −23.1285 | − | 16.8039i | −0.819770 | − | 0.595598i | ||||
\(797\) | 14.6063 | − | 4.74587i | 0.517381 | − | 0.168107i | −0.0386754 | − | 0.999252i | \(-0.512314\pi\) |
0.556056 | + | 0.831145i | \(0.312314\pi\) | |||||||
\(798\) | 24.8307 | − | 14.4518i | 0.878995 | − | 0.511588i | ||||
\(799\) | 8.25286 | − | 11.3591i | 0.291965 | − | 0.401855i | ||||
\(800\) | −6.70970 | + | 4.87488i | −0.237224 | + | 0.172353i | ||||
\(801\) | −28.5682 | + | 3.20444i | −1.00941 | + | 0.113223i | ||||
\(802\) | − | 2.96713i | − | 0.104773i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.73205 | + | 12.6362i | 0.0963520 | + | 0.445646i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.923638 | + | 1.27128i | 0.0325338 | + | 0.0447789i | ||||
\(807\) | 25.9174 | + | 11.4309i | 0.912335 | + | 0.402388i | ||||
\(808\) | −0.601792 | − | 1.85213i | −0.0211710 | − | 0.0651576i | ||||
\(809\) | 16.0251 | + | 49.3202i | 0.563413 | + | 1.73401i | 0.672621 | + | 0.739987i | \(0.265168\pi\) |
−0.109208 | + | 0.994019i | \(0.534832\pi\) | |||||||
\(810\) | 5.91627 | + | 26.0405i | 0.207877 | + | 0.914971i | ||||
\(811\) | 15.2887 | + | 21.0431i | 0.536858 | + | 0.738922i | 0.988156 | − | 0.153452i | \(-0.0490389\pi\) |
−0.451298 | + | 0.892373i | \(0.649039\pi\) | |||||||
\(812\) | −54.5114 | − | 17.7118i | −1.91297 | − | 0.621563i | ||||
\(813\) | −15.4762 | + | 3.34607i | −0.542773 | + | 0.117352i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 15.3580i | 0.537966i | ||||||||
\(816\) | 17.6078 | + | 1.78854i | 0.616397 | + | 0.0626113i | ||||
\(817\) | −8.40755 | + | 6.10844i | −0.294143 | + | 0.213707i | ||||
\(818\) | −46.7497 | + | 64.3454i | −1.63456 | + | 2.24979i | ||||
\(819\) | 19.1450 | + | 20.9664i | 0.668981 | + | 0.732627i | ||||
\(820\) | 31.5945 | − | 10.2657i | 1.10333 | − | 0.358493i | ||||
\(821\) | 17.6732 | + | 12.8403i | 0.616798 | + | 0.448130i | 0.851802 | − | 0.523864i | \(-0.175510\pi\) |
−0.235003 | + | 0.971995i | \(0.575510\pi\) | |||||||
\(822\) | −49.3002 | + | 55.1393i | −1.71954 | + | 1.92320i | ||||
\(823\) | 10.1591 | − | 31.2666i | 0.354125 | − | 1.08989i | −0.602390 | − | 0.798202i | \(-0.705785\pi\) |
0.956515 | − | 0.291683i | \(-0.0942152\pi\) | |||||||
\(824\) | −52.7976 | −1.83929 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 85.5692 | 2.97733 | ||||||||
\(827\) | −5.81248 | + | 17.8890i | −0.202120 | + | 0.622060i | 0.797700 | + | 0.603055i | \(0.206050\pi\) |
−0.999819 | + | 0.0190055i | \(0.993950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.8474 | − | 11.5138i | −0.550403 | − | 0.399891i | 0.277531 | − | 0.960717i | \(-0.410484\pi\) |
−0.827934 | + | 0.560826i | \(0.810484\pi\) | |||||||
\(830\) | 41.8620 | − | 13.6018i | 1.45305 | − | 0.472125i | ||||
\(831\) | −5.46803 | − | 9.39501i | −0.189684 | − | 0.325909i | ||||
\(832\) | −20.9662 | + | 28.8576i | −0.726874 | + | 1.00046i | ||||
\(833\) | 3.35485 | − | 2.43744i | 0.116239 | − | 0.0844524i | ||||
\(834\) | −2.16923 | + | 21.3557i | −0.0751142 | + | 0.739486i | ||||
\(835\) | − | 6.51626i | − | 0.225505i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.607695 | − | 0.818262i | −0.0210050 | − | 0.0282833i | ||||
\(838\) | 25.1946 | + | 8.18621i | 0.870331 | + | 0.282788i | ||||
\(839\) | 11.0173 | + | 15.1641i | 0.380361 | + | 0.523522i | 0.955680 | − | 0.294407i | \(-0.0951222\pi\) |
−0.575319 | + | 0.817929i | \(0.695122\pi\) | |||||||
\(840\) | 10.1600 | − | 23.0359i | 0.350554 | − | 0.794813i | ||||
\(841\) | 0.149360 | + | 0.459683i | 0.00515035 | + | 0.0158511i | ||||
\(842\) | 14.2021 | + | 43.7095i | 0.489436 | + | 1.50633i | ||||
\(843\) | −0.568541 | + | 1.28906i | −0.0195816 | + | 0.0443975i | ||||
\(844\) | 4.15627 | + | 5.72061i | 0.143065 | + | 0.196912i | ||||
\(845\) | 2.12612 | + | 0.690818i | 0.0731407 | + | 0.0237649i | ||||
\(846\) | 10.0463 | + | 22.1469i | 0.345399 | + | 0.761428i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 17.5045i | − | 0.601107i | ||||||
\(849\) | −1.18913 | + | 11.7067i | −0.0408107 | + | 0.401774i | ||||
\(850\) | 27.8240 | − | 20.2153i | 0.954354 | − | 0.693379i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 27.1283 | + | 46.6110i | 0.929399 | + | 1.59687i | ||||
\(853\) | 40.4818 | − | 13.1533i | 1.38607 | − | 0.450362i | 0.481411 | − | 0.876495i | \(-0.340125\pi\) |
0.904660 | + | 0.426133i | \(0.140125\pi\) | |||||||
\(854\) | 24.7628 | + | 17.9912i | 0.847366 | + | 0.615648i | ||||
\(855\) | 4.49836 | − | 7.91854i | 0.153841 | − | 0.270808i | ||||
\(856\) | −4.49184 | + | 13.8245i | −0.153528 | + | 0.472510i | ||||
\(857\) | 56.3029 | 1.92327 | 0.961635 | − | 0.274332i | \(-0.0884568\pi\) | ||||
0.961635 | + | 0.274332i | \(0.0884568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.12436 | 0.0383625 | 0.0191813 | − | 0.999816i | \(-0.493894\pi\) | ||||
0.0191813 | + | 0.999816i | \(0.493894\pi\) | |||||||
\(860\) | −6.06384 | + | 18.6626i | −0.206775 | + | 0.636388i | ||||
\(861\) | −23.4533 | + | 26.2310i | −0.799285 | + | 0.893952i | ||||
\(862\) | −40.4934 | − | 29.4202i | −1.37921 | − | 1.00205i | ||||
\(863\) | −27.4869 | + | 8.93103i | −0.935665 | + | 0.304016i | −0.736877 | − | 0.676027i | \(-0.763700\pi\) |
−0.198787 | + | 0.980043i | \(0.563700\pi\) | |||||||
\(864\) | 7.20653 | − | 10.1406i | 0.245171 | − | 0.344989i | ||||
\(865\) | 8.25286 | − | 11.3591i | 0.280606 | − | 0.386220i | ||||
\(866\) | 25.2818 | − | 18.3683i | 0.859111 | − | 0.624181i | ||||
\(867\) | 0.338007 | + | 0.0343334i | 0.0114793 | + | 0.00116602i | ||||
\(868\) | 2.07055i | 0.0702791i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −27.2750 | + | 5.89706i | −0.924709 | + | 0.199929i | ||||
\(871\) | 6.36459 | + | 2.06798i | 0.215656 | + | 0.0700709i | ||||
\(872\) | −26.0673 | − | 35.8786i | −0.882750 | − | 1.21500i | ||||
\(873\) | 6.66488 | + | 1.36810i | 0.225572 | + | 0.0463033i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.16831 | − | 28.2172i | −0.309946 | − | 0.953914i | ||||
\(876\) | −47.9441 | − | 21.1459i | −1.61988 | − | 0.714453i | ||||
\(877\) | 16.9133 | + | 23.2792i | 0.571123 | + | 0.786084i | 0.992687 | − | 0.120715i | \(-0.0385187\pi\) |
−0.421564 | + | 0.906799i | \(0.638519\pi\) | |||||||
\(878\) | 19.0897 | + | 6.20262i | 0.644247 | + | 0.209328i | ||||
\(879\) | −11.9079 | − | 55.0764i | −0.401645 | − | 1.85768i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.6325i | − | 0.459289i | −0.973275 | − | 0.229644i | \(-0.926244\pi\) | ||
0.973275 | − | 0.229644i | \(-0.0737563\pi\) | |||||||
\(882\) | 0.800628 | + | 7.13775i | 0.0269585 | + | 0.240340i | ||||
\(883\) | 9.27465 | − | 6.73843i | 0.312117 | − | 0.226766i | −0.420687 | − | 0.907206i | \(-0.638211\pi\) |
0.732804 | + | 0.680439i | \(0.238211\pi\) | |||||||
\(884\) | 30.4380 | − | 41.8943i | 1.02374 | − | 1.40906i | ||||
\(885\) | 23.4429 | − | 13.6441i | 0.788024 | − | 0.458641i | ||||
\(886\) | 58.0987 | − | 18.8774i | 1.95186 | − | 0.634199i | ||||
\(887\) | 36.6625 | + | 26.6369i | 1.23101 | + | 0.894378i | 0.996965 | − | 0.0778484i | \(-0.0248050\pi\) |
0.234041 | + | 0.972227i | \(0.424805\pi\) | |||||||
\(888\) | −56.0289 | − | 50.0956i | −1.88021 | − | 1.68110i | ||||
\(889\) | −12.6031 | + | 38.7885i | −0.422696 | + | 1.30092i | ||||
\(890\) | 28.4323 | 0.953053 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48.2487 | 1.61549 | ||||||||
\(893\) | 2.56288 | − | 7.88773i | 0.0857635 | − | 0.263953i | ||||
\(894\) | −29.0736 | − | 25.9948i | −0.972365 | − | 0.869395i | ||||
\(895\) | −22.8537 | − | 16.6042i | −0.763915 | − | 0.555016i | ||||
\(896\) | −55.7747 | + | 18.1223i | −1.86330 | + | 0.605423i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 56.7102 | − | 78.0548i | 1.89244 | − | 2.60472i | ||||
\(899\) | 0.861667 | − | 0.626038i | 0.0287382 | − | 0.0208795i | ||||
\(900\) | 4.32328 | + | 38.5429i | 0.144109 | + | 1.28476i | ||||
\(901\) | − | 29.4582i | − | 0.981397i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.39230 | − | 20.3152i | −0.146167 | − | 0.676048i | ||||
\(904\) | −51.1452 | − | 16.6181i | −1.70107 | − | 0.552710i | ||||
\(905\) | −9.36525 | − | 12.8902i | −0.311312 | − | 0.428484i | ||||
\(906\) | −62.5663 | − | 27.5950i | −2.07863 | − | 0.916783i | ||||
\(907\) | −8.17191 | − | 25.1506i | −0.271344 | − | 0.835111i | −0.990164 | − | 0.139914i | \(-0.955317\pi\) |
0.718820 | − | 0.695196i | \(-0.244683\pi\) | |||||||
\(908\) | 6.06384 | + | 18.6626i | 0.201235 | + | 0.619339i | ||||
\(909\) | 1.38009 | + | 0.283292i | 0.0457747 | + | 0.00939620i | ||||
\(910\) | −16.5057 | − | 22.7182i | −0.547159 | − | 0.753100i | ||||
\(911\) | −30.2446 | − | 9.82708i | −1.00205 | − | 0.325586i | −0.238365 | − | 0.971176i | \(-0.576612\pi\) |
−0.763684 | + | 0.645590i | \(0.776612\pi\) | |||||||
\(912\) | 10.2182 | − | 2.20925i | 0.338358 | − | 0.0731557i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 44.1053i | − | 1.45887i | ||||||
\(915\) | 9.65285 | + | 0.980500i | 0.319113 | + | 0.0324143i | ||||
\(916\) | −16.7145 | + | 12.1438i | −0.552263 | + | 0.401242i | ||||
\(917\) | 22.5297 | − | 31.0094i | 0.743995 | − | 1.02402i | ||||
\(918\) | −29.8842 | + | 42.0512i | −0.986326 | + | 1.38790i | ||||
\(919\) | 37.1064 | − | 12.0566i | 1.22403 | − | 0.397710i | 0.375480 | − | 0.926831i | \(-0.377478\pi\) |
0.848547 | + | 0.529120i | \(0.177478\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 36.0044 | − | 40.2688i | 1.18639 | − | 1.32690i | ||||
\(922\) | −2.11875 | + | 6.52083i | −0.0697772 | + | 0.214752i | ||||
\(923\) | 27.9166 | 0.918887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.2487 | −1.19185 | ||||||||
\(926\) | 0.938079 | − | 2.88711i | 0.0308272 | − | 0.0948763i | ||||
\(927\) | 18.8667 | − | 33.2114i | 0.619663 | − | 1.09080i | ||||
\(928\) | 10.5172 | + | 7.64121i | 0.345245 | + | 0.250835i | ||||
\(929\) | 30.3912 | − | 9.87471i | 0.997104 | − | 0.323979i | 0.235396 | − | 0.971900i | \(-0.424361\pi\) |
0.761708 | + | 0.647921i | \(0.224361\pi\) | |||||||
\(930\) | 0.507079 | + | 0.871249i | 0.0166278 | + | 0.0285694i | ||||
\(931\) | 1.43977 | − | 1.98168i | 0.0471867 | − | 0.0649469i | ||||
\(932\) | −16.3943 | + | 11.9112i | −0.537014 | + | 0.390163i | ||||
\(933\) | 0.116249 | − | 1.14445i | 0.00380581 | − | 0.0374675i | ||||
\(934\) | 46.4660i | 1.52041i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.1962 | + | 37.9087i | 0.562074 | + | 1.23908i | ||||
\(937\) | 27.1991 | + | 8.83753i | 0.888556 | + | 0.288709i | 0.717506 | − | 0.696553i | \(-0.245284\pi\) |
0.171051 | + | 0.985262i | \(0.445284\pi\) | |||||||
\(938\) | 7.96065 | + | 10.9569i | 0.259925 | + | 0.357755i | ||||
\(939\) | −5.16693 | + | 11.7150i | −0.168616 | + | 0.382305i | ||||
\(940\) | −4.83928 | − | 14.8938i | −0.157840 | − | 0.485782i | ||||
\(941\) | 0.633603 | + | 1.95003i | 0.0206549 | + | 0.0635692i | 0.960853 | − | 0.277060i | \(-0.0893600\pi\) |
−0.940198 | + | 0.340629i | \(0.889360\pi\) | |||||||
\(942\) | 19.1844 | − | 43.4968i | 0.625061 | − | 1.41720i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 29.6130 | + | 9.62185i | 0.963821 | + | 0.313165i | ||||
\(945\) | 10.8597 | + | 14.6226i | 0.353266 | + | 0.475674i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.2297i | 0.982334i | 0.871065 | + | 0.491167i | \(0.163429\pi\) | ||||
−0.871065 | + | 0.491167i | \(0.836571\pi\) | |||||||
\(948\) | −4.80030 | + | 47.2581i | −0.155906 | + | 1.53487i | ||||
\(949\) | −21.9441 | + | 15.9433i | −0.712334 | + | 0.517541i | ||||
\(950\) | 11.9410 | − | 16.4353i | 0.387417 | − | 0.533233i | ||||
\(951\) | −21.4401 | − | 36.8379i | −0.695244 | − | 1.19455i | ||||
\(952\) | 46.2575 | − | 15.0300i | 1.49922 | − | 0.487125i | ||||
\(953\) | −44.5493 | − | 32.3669i | −1.44309 | − | 1.04847i | −0.987385 | − | 0.158338i | \(-0.949386\pi\) |
−0.455707 | − | 0.890130i | \(-0.650614\pi\) | |||||||
\(954\) | 44.3644 | + | 25.2025i | 1.43635 | + | 0.815960i | ||||
\(955\) | 0.949237 | − | 2.92145i | 0.0307166 | − | 0.0945360i | ||||
\(956\) | −37.4933 | −1.21262 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.6603 | 0.505960 | ||||||||
\(959\) | −15.5897 | + | 47.9803i | −0.503419 | + | 1.54936i | ||||
\(960\) | −15.2521 | + | 17.0586i | −0.492261 | + | 0.550564i | ||||
\(961\) | 25.0484 | + | 18.1987i | 0.808013 | + | 0.587056i | ||||
\(962\) | −79.7256 | + | 25.9044i | −2.57046 | + | 0.835192i | ||||
\(963\) | −7.09091 | − | 7.76554i | −0.228502 | − | 0.250241i | ||||
\(964\) | −8.25286 | + | 11.3591i | −0.265807 | + | 0.365851i | ||||
\(965\) | 2.87312 | − | 2.08744i | 0.0924889 | − | 0.0671971i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.0518i | 1.44877i | 0.689397 | + | 0.724383i | \(0.257875\pi\) | ||||
−0.689397 | + | 0.724383i | \(0.742125\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.1962 | − | 3.71794i | 0.552420 | − | 0.119437i | ||||
\(970\) | −6.39994 | − | 2.07947i | −0.205490 | − | 0.0667676i | ||||
\(971\) | −4.37070 | − | 6.01575i | −0.140262 | − | 0.193055i | 0.733107 | − | 0.680114i | \(-0.238070\pi\) |
−0.873369 | + | 0.487059i | \(0.838070\pi\) | |||||||
\(972\) | −24.5866 | − | 52.7262i | −0.788617 | − | 1.69119i | ||||
\(973\) | 4.52432 | + | 13.9244i | 0.145043 | + | 0.446397i | ||||
\(974\) | −24.5456 | − | 75.5435i | −0.786491 | − | 2.42057i | ||||
\(975\) | 18.3691 | + | 8.10173i | 0.588282 | + | 0.259463i | ||||
\(976\) | 6.54666 | + | 9.01070i | 0.209553 | + | 0.288426i | ||||
\(977\) | −10.6079 | − | 3.44672i | −0.339377 | − | 0.110270i | 0.134370 | − | 0.990931i | \(-0.457099\pi\) |
−0.473747 | + | 0.880661i | \(0.657099\pi\) | |||||||
\(978\) | −10.8597 | − | 50.2281i | −0.347255 | − | 1.60612i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 4.62518i | − | 0.147746i | ||||||
\(981\) | 31.8837 | − | 3.57633i | 1.01797 | − | 0.114183i | ||||
\(982\) | 40.4934 | − | 29.4202i | 1.29220 | − | 0.938835i | ||||
\(983\) | 0.285775 | − | 0.393335i | 0.00911479 | − | 0.0125454i | −0.804435 | − | 0.594040i | \(-0.797532\pi\) |
0.813550 | + | 0.581495i | \(0.197532\pi\) | |||||||
\(984\) | −44.5866 | + | 25.9500i | −1.42137 | + | 0.827257i | ||||
\(985\) | 12.5973 | − | 4.09310i | 0.401383 | − | 0.130417i | ||||
\(986\) | −43.6131 | − | 31.6867i | −1.38892 | − | 1.00911i | ||||
\(987\) | 12.3654 | + | 11.0560i | 0.393596 | + | 0.351915i | ||||
\(988\) | 9.45235 | − | 29.0914i | 0.300719 | − | 0.925519i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8564 | 0.630760 | 0.315380 | − | 0.948966i | \(-0.397868\pi\) | ||||
0.315380 | + | 0.948966i | \(0.397868\pi\) | |||||||
\(992\) | 0.145121 | − | 0.446637i | 0.00460760 | − | 0.0141807i | ||||
\(993\) | 0.506545 | + | 0.452903i | 0.0160747 | + | 0.0143725i | ||||
\(994\) | 45.7074 | + | 33.2084i | 1.44975 | + | 1.05330i | ||||
\(995\) | −9.02881 | + | 2.93364i | −0.286233 | + | 0.0930026i | ||||
\(996\) | −82.8776 | + | 48.2359i | −2.62608 | + | 1.52841i | ||||
\(997\) | −35.5430 | + | 48.9208i | −1.12566 | + | 1.54934i | −0.329597 | + | 0.944122i | \(0.606913\pi\) |
−0.796062 | + | 0.605215i | \(0.793087\pi\) | |||||||
\(998\) | 49.9801 | − | 36.3127i | 1.58209 | − | 1.14946i | ||||
\(999\) | 51.5331 | − | 17.3428i | 1.63043 | − | 0.548702i |
(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 | 363.2.f.i.233.1 | 32 | ||
3.2 | odd | 2 | inner | 363.2.f.i.233.8 | 32 | ||
11.2 | odd | 10 | inner | 363.2.f.i.239.1 | 32 | ||
11.3 | even | 5 | inner | 363.2.f.i.161.8 | 32 | ||
11.4 | even | 5 | 363.2.d.e.362.2 | yes | 8 | ||
11.5 | even | 5 | inner | 363.2.f.i.215.2 | 32 | ||
11.6 | odd | 10 | inner | 363.2.f.i.215.8 | 32 | ||
11.7 | odd | 10 | 363.2.d.e.362.8 | yes | 8 | ||
11.8 | odd | 10 | inner | 363.2.f.i.161.2 | 32 | ||
11.9 | even | 5 | inner | 363.2.f.i.239.7 | 32 | ||
11.10 | odd | 2 | inner | 363.2.f.i.233.7 | 32 | ||
33.2 | even | 10 | inner | 363.2.f.i.239.8 | 32 | ||
33.5 | odd | 10 | inner | 363.2.f.i.215.7 | 32 | ||
33.8 | even | 10 | inner | 363.2.f.i.161.7 | 32 | ||
33.14 | odd | 10 | inner | 363.2.f.i.161.1 | 32 | ||
33.17 | even | 10 | inner | 363.2.f.i.215.1 | 32 | ||
33.20 | odd | 10 | inner | 363.2.f.i.239.2 | 32 | ||
33.26 | odd | 10 | 363.2.d.e.362.7 | yes | 8 | ||
33.29 | even | 10 | 363.2.d.e.362.1 | ✓ | 8 | ||
33.32 | even | 2 | inner | 363.2.f.i.233.2 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.e.362.1 | ✓ | 8 | 33.29 | even | 10 | ||
363.2.d.e.362.2 | yes | 8 | 11.4 | even | 5 | ||
363.2.d.e.362.7 | yes | 8 | 33.26 | odd | 10 | ||
363.2.d.e.362.8 | yes | 8 | 11.7 | odd | 10 | ||
363.2.f.i.161.1 | 32 | 33.14 | odd | 10 | inner | ||
363.2.f.i.161.2 | 32 | 11.8 | odd | 10 | inner | ||
363.2.f.i.161.7 | 32 | 33.8 | even | 10 | inner | ||
363.2.f.i.161.8 | 32 | 11.3 | even | 5 | inner | ||
363.2.f.i.215.1 | 32 | 33.17 | even | 10 | inner | ||
363.2.f.i.215.2 | 32 | 11.5 | even | 5 | inner | ||
363.2.f.i.215.7 | 32 | 33.5 | odd | 10 | inner | ||
363.2.f.i.215.8 | 32 | 11.6 | odd | 10 | inner | ||
363.2.f.i.233.1 | 32 | 1.1 | even | 1 | trivial | ||
363.2.f.i.233.2 | 32 | 33.32 | even | 2 | inner | ||
363.2.f.i.233.7 | 32 | 11.10 | odd | 2 | inner | ||
363.2.f.i.233.8 | 32 | 3.2 | odd | 2 | inner | ||
363.2.f.i.239.1 | 32 | 11.2 | odd | 10 | inner | ||
363.2.f.i.239.2 | 32 | 33.20 | odd | 10 | inner | ||
363.2.f.i.239.7 | 32 | 11.9 | even | 5 | inner | ||
363.2.f.i.239.8 | 32 | 33.2 | even | 10 | inner |