Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [810,3,Mod(269,810)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("810.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 810 = 2 \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 810.j (of order \(6\), degree \(2\), 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: | \(22.0709014132\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.6 | ||
Character | \(\chi\) | \(=\) | 810.269 |
Dual form | 810.3.j.h.539.6 |
$q$-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 \(\left(\mathbb{Z}/810\mathbb{Z}\right)^\times\).
\(n\) | \(487\) | \(731\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 4.24042 | − | 2.64931i | 0.848084 | − | 0.529861i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.20611 | + | 4.73780i | 1.17230 | + | 0.676828i | 0.954221 | − | 0.299102i | \(-0.0966872\pi\) |
0.218080 | + | 0.975931i | \(0.430021\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.246293 | + | 7.06678i | 0.0246293 | + | 0.706678i | ||||
\(11\) | 17.6547 | + | 10.1930i | 1.60498 | + | 0.926633i | 0.990471 | + | 0.137720i | \(0.0439775\pi\) |
0.614505 | + | 0.788913i | \(0.289356\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.29129 | + | 3.05493i | −0.407023 | + | 0.234995i | −0.689510 | − | 0.724277i | \(-0.742174\pi\) |
0.282487 | + | 0.959271i | \(0.408841\pi\) | |||||||
\(14\) | −11.6052 | + | 6.70026i | −0.828942 | + | 0.478590i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −24.0002 | −1.41178 | −0.705888 | − | 0.708323i | \(-0.749452\pi\) | ||||
−0.705888 | + | 0.708323i | \(0.749452\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.0752 | 0.846062 | 0.423031 | − | 0.906115i | \(-0.360966\pi\) | ||||
0.423031 | + | 0.906115i | \(0.360966\pi\) | |||||||
\(20\) | −8.82915 | − | 4.69532i | −0.441458 | − | 0.234766i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −24.9676 | + | 14.4150i | −1.13489 | + | 0.655229i | ||||
\(23\) | 21.6389 | + | 37.4798i | 0.940824 | + | 1.62955i | 0.763905 | + | 0.645329i | \(0.223280\pi\) |
0.176919 | + | 0.984225i | \(0.443387\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.9624 | − | 22.4683i | 0.438494 | − | 0.898734i | ||||
\(26\) | − | 8.64064i | − | 0.332332i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 18.9512i | − | 0.676828i | ||||||
\(29\) | −16.9927 | − | 9.81073i | −0.585954 | − | 0.338301i | 0.177542 | − | 0.984113i | \(-0.443186\pi\) |
−0.763496 | + | 0.645812i | \(0.776519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15.2536 | − | 26.4200i | −0.492052 | − | 0.852260i | 0.507906 | − | 0.861413i | \(-0.330420\pi\) |
−0.999958 | + | 0.00915307i | \(0.997086\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 16.9707 | − | 29.3941i | 0.499138 | − | 0.864533i | ||||
\(35\) | 47.3492 | − | 1.65023i | 1.35284 | − | 0.0471493i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 44.8335i | − | 1.21172i | −0.795573 | − | 0.605858i | \(-0.792830\pi\) | ||
0.795573 | − | 0.605858i | \(-0.207170\pi\) | |||||||
\(38\) | −11.3669 | + | 19.6880i | −0.299128 | + | 0.518105i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.9937 | − | 7.49337i | 0.299843 | − | 0.187334i | ||||
\(41\) | −41.6479 | + | 24.0454i | −1.01580 | + | 0.586473i | −0.912885 | − | 0.408217i | \(-0.866151\pi\) |
−0.102917 | + | 0.994690i | \(0.532818\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 41.6597 | + | 24.0522i | 0.968830 | + | 0.559354i | 0.898879 | − | 0.438196i | \(-0.144382\pi\) |
0.0699506 | + | 0.997550i | \(0.477716\pi\) | |||||||
\(44\) | − | 40.7719i | − | 0.926633i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −61.2042 | −1.33053 | ||||||||
\(47\) | −34.0385 | + | 58.9564i | −0.724223 | + | 1.25439i | 0.235070 | + | 0.971979i | \(0.424468\pi\) |
−0.959293 | + | 0.282413i | \(0.908865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20.3935 | + | 35.3225i | 0.416193 | + | 0.720868i | ||||
\(50\) | 19.7664 | + | 29.3136i | 0.395329 | + | 0.586272i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.5826 | + | 6.10986i | 0.203511 | + | 0.117497i | ||||
\(53\) | 61.7484 | 1.16506 | 0.582532 | − | 0.812808i | \(-0.302062\pi\) | ||||
0.582532 | + | 0.812808i | \(0.302062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 101.868 | − | 3.55032i | 1.85214 | − | 0.0645512i | ||||
\(56\) | 23.2104 | + | 13.4005i | 0.414471 | + | 0.239295i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 24.0313 | − | 13.8745i | 0.414332 | − | 0.239215i | ||||
\(59\) | 43.6833 | − | 25.2206i | 0.740395 | − | 0.427467i | −0.0818182 | − | 0.996647i | \(-0.526073\pi\) |
0.822213 | + | 0.569180i | \(0.192739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24.4987 | − | 42.4330i | 0.401619 | − | 0.695624i | −0.592303 | − | 0.805715i | \(-0.701781\pi\) |
0.993921 | + | 0.110092i | \(0.0351144\pi\) | |||||||
\(62\) | 43.1438 | 0.695867 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | −14.3439 | + | 26.9724i | −0.220675 | + | 0.414961i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −47.7100 | + | 27.5454i | −0.712089 | + | 0.411125i | −0.811834 | − | 0.583888i | \(-0.801531\pi\) |
0.0997448 | + | 0.995013i | \(0.468197\pi\) | |||||||
\(68\) | 24.0002 | + | 41.5696i | 0.352944 | + | 0.611317i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −31.4599 | + | 59.1576i | −0.449427 | + | 0.845109i | ||||
\(71\) | 23.5982i | 0.332369i | 0.986095 | + | 0.166184i | \(0.0531447\pi\) | ||||
−0.986095 | + | 0.166184i | \(0.946855\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 40.4303i | − | 0.553840i | −0.960893 | − | 0.276920i | \(-0.910686\pi\) | ||
0.960893 | − | 0.276920i | \(-0.0893137\pi\) | |||||||
\(74\) | 54.9096 | + | 31.7021i | 0.742021 | + | 0.428406i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.0752 | − | 27.8430i | −0.211515 | − | 0.366355i | ||||
\(77\) | 96.5844 | + | 167.289i | 1.25434 | + | 2.17259i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.6169 | + | 28.7813i | −0.210340 | + | 0.364320i | −0.951821 | − | 0.306654i | \(-0.900791\pi\) |
0.741481 | + | 0.670974i | \(0.234124\pi\) | |||||||
\(80\) | 0.696621 | + | 19.9879i | 0.00870776 | + | 0.249848i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 68.0107i | − | 0.829399i | ||||||
\(83\) | −11.3572 | + | 19.6713i | −0.136834 | + | 0.237003i | −0.926296 | − | 0.376795i | \(-0.877026\pi\) |
0.789463 | + | 0.613799i | \(0.210359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −101.771 | + | 63.5839i | −1.19731 | + | 0.748046i | ||||
\(86\) | −58.9157 | + | 34.0150i | −0.685066 | + | 0.395523i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 49.9351 | + | 28.8301i | 0.567445 | + | 0.327614i | ||||
\(89\) | 79.5266i | 0.893557i | 0.894644 | + | 0.446779i | \(0.147429\pi\) | ||||
−0.894644 | + | 0.446779i | \(0.852571\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −57.8946 | −0.636204 | ||||||||
\(92\) | 43.2779 | − | 74.9595i | 0.470412 | − | 0.814777i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −48.1377 | − | 83.3770i | −0.512103 | − | 0.886989i | ||||
\(95\) | 68.1655 | − | 42.5880i | 0.717532 | − | 0.448295i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −103.825 | − | 59.9431i | −1.07036 | − | 0.617970i | −0.142077 | − | 0.989856i | \(-0.545378\pi\) |
−0.928279 | + | 0.371885i | \(0.878711\pi\) | |||||||
\(98\) | −57.6815 | −0.588586 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −49.8787 | + | 3.48099i | −0.498787 | + | 0.0348099i | ||||
\(101\) | −19.1196 | − | 11.0387i | −0.189303 | − | 0.109294i | 0.402353 | − | 0.915485i | \(-0.368192\pi\) |
−0.591656 | + | 0.806190i | \(0.701526\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.9238 | − | 9.19358i | 0.154600 | − | 0.0892581i | −0.420705 | − | 0.907198i | \(-0.638217\pi\) |
0.575304 | + | 0.817940i | \(0.304884\pi\) | |||||||
\(104\) | −14.9660 | + | 8.64064i | −0.143904 | + | 0.0830831i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −43.6627 | + | 75.6260i | −0.411912 | + | 0.713453i | ||||
\(107\) | 60.8601 | 0.568786 | 0.284393 | − | 0.958708i | \(-0.408208\pi\) | ||||
0.284393 | + | 0.958708i | \(0.408208\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80.4892 | 0.738433 | 0.369216 | − | 0.929343i | \(-0.379626\pi\) | ||||
0.369216 | + | 0.929343i | \(0.379626\pi\) | |||||||
\(110\) | −67.6832 | + | 127.273i | −0.615302 | + | 1.15702i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −32.8244 | + | 18.9512i | −0.293075 | + | 0.169207i | ||||
\(113\) | 11.3778 | + | 19.7069i | 0.100689 | + | 0.174398i | 0.911969 | − | 0.410260i | \(-0.134562\pi\) |
−0.811280 | + | 0.584658i | \(0.801229\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 191.054 | + | 101.602i | 1.66134 | + | 0.883494i | ||||
\(116\) | 39.2429i | 0.338301i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 71.3345i | 0.604530i | ||||||||
\(119\) | −196.948 | − | 113.708i | −1.65503 | − | 0.955530i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 147.293 | + | 255.119i | 1.21730 | + | 2.10842i | ||||
\(122\) | 34.6464 | + | 60.0094i | 0.283987 | + | 0.491880i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −30.5072 | + | 52.8401i | −0.246026 | + | 0.426130i | ||||
\(125\) | −13.0405 | − | 124.318i | −0.104324 | − | 0.994543i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 73.3562i | 0.577608i | 0.957388 | + | 0.288804i | \(0.0932576\pi\) | ||||
−0.957388 | + | 0.288804i | \(0.906742\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −22.8917 | − | 36.6400i | −0.176090 | − | 0.281846i | ||||
\(131\) | 78.8523 | − | 45.5254i | 0.601926 | − | 0.347522i | −0.167873 | − | 0.985809i | \(-0.553690\pi\) |
0.769799 | + | 0.638286i | \(0.220356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 131.915 | + | 76.1609i | 0.991839 | + | 0.572639i | ||||
\(134\) | − | 77.9101i | − | 0.581419i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −67.8828 | −0.499138 | ||||||||
\(137\) | 13.9419 | − | 24.1480i | 0.101765 | − | 0.176263i | −0.810647 | − | 0.585536i | \(-0.800884\pi\) |
0.912412 | + | 0.409273i | \(0.134218\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.3690 | − | 30.0839i | −0.124957 | − | 0.216431i | 0.796759 | − | 0.604297i | \(-0.206546\pi\) |
−0.921716 | + | 0.387866i | \(0.873212\pi\) | |||||||
\(140\) | −50.2075 | − | 80.3611i | −0.358625 | − | 0.574008i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −28.9017 | − | 16.6864i | −0.203533 | − | 0.117510i | ||||
\(143\) | −124.555 | −0.871015 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −98.0477 | + | 3.41718i | −0.676191 | + | 0.0235668i | ||||
\(146\) | 49.5168 | + | 28.5886i | 0.339156 | + | 0.195812i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −77.6539 | + | 44.8335i | −0.524688 | + | 0.302929i | ||||
\(149\) | −0.274589 | + | 0.158534i | −0.00184288 | + | 0.00106399i | −0.500921 | − | 0.865493i | \(-0.667005\pi\) |
0.499078 | + | 0.866557i | \(0.333672\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 52.6638 | − | 91.2164i | 0.348767 | − | 0.604082i | −0.637264 | − | 0.770646i | \(-0.719934\pi\) |
0.986031 | + | 0.166564i | \(0.0532671\pi\) | |||||||
\(152\) | 45.4674 | 0.299128 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −273.182 | −1.77391 | ||||||||
\(155\) | −134.677 | − | 71.6206i | −0.868881 | − | 0.462069i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −39.4927 | + | 22.8011i | −0.251546 | + | 0.145230i | −0.620472 | − | 0.784229i | \(-0.713059\pi\) |
0.368926 | + | 0.929459i | \(0.379726\pi\) | |||||||
\(158\) | −23.4998 | − | 40.7029i | −0.148733 | − | 0.257613i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −24.9726 | − | 13.2804i | −0.156079 | − | 0.0830023i | ||||
\(161\) | 410.084i | 2.54711i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 152.794i | − | 0.937384i | −0.883362 | − | 0.468692i | \(-0.844725\pi\) | ||
0.883362 | − | 0.468692i | \(-0.155275\pi\) | |||||||
\(164\) | 83.2957 | + | 48.0908i | 0.507901 | + | 0.293237i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.0615 | − | 27.8194i | −0.0967561 | − | 0.167587i | ||||
\(167\) | 6.86420 | + | 11.8891i | 0.0411030 | + | 0.0711925i | 0.885845 | − | 0.463981i | \(-0.153579\pi\) |
−0.844742 | + | 0.535174i | \(0.820246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −65.8348 | + | 114.029i | −0.389555 | + | 0.674729i | ||||
\(170\) | −5.91107 | − | 169.604i | −0.0347710 | − | 0.997671i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 96.2089i | − | 0.559354i | ||||||
\(173\) | 5.21536 | − | 9.03326i | 0.0301466 | − | 0.0522154i | −0.850558 | − | 0.525880i | \(-0.823736\pi\) |
0.880705 | + | 0.473665i | \(0.157069\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 196.409 | − | 132.440i | 1.12234 | − | 0.756802i | ||||
\(176\) | −70.6189 | + | 40.7719i | −0.401244 | + | 0.231658i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −97.3998 | − | 56.2338i | −0.547190 | − | 0.315920i | ||||
\(179\) | − | 62.4650i | − | 0.348967i | −0.984660 | − | 0.174483i | \(-0.944174\pi\) | ||
0.984660 | − | 0.174483i | \(-0.0558255\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 343.029 | 1.89519 | 0.947594 | − | 0.319477i | \(-0.103507\pi\) | ||||
0.947594 | + | 0.319477i | \(0.103507\pi\) | |||||||
\(182\) | 40.9376 | − | 70.9061i | 0.224932 | − | 0.389594i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 61.2042 | + | 106.009i | 0.332631 | + | 0.576135i | ||||
\(185\) | −118.778 | − | 190.113i | −0.642041 | − | 1.02764i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −423.717 | − | 244.633i | −2.26587 | − | 1.30820i | ||||
\(188\) | 136.154 | 0.724223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.95920 | + | 113.600i | 0.0208379 | + | 0.597893i | ||||
\(191\) | 10.9445 | + | 6.31882i | 0.0573012 | + | 0.0330829i | 0.528377 | − | 0.849010i | \(-0.322801\pi\) |
−0.471076 | + | 0.882093i | \(0.656134\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 145.600 | − | 84.0622i | 0.754405 | − | 0.435556i | −0.0728786 | − | 0.997341i | \(-0.523219\pi\) |
0.827283 | + | 0.561785i | \(0.189885\pi\) | |||||||
\(194\) | 146.830 | − | 84.7724i | 0.756856 | − | 0.436971i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 40.7869 | − | 70.6451i | 0.208097 | − | 0.360434i | ||||
\(197\) | −372.044 | −1.88855 | −0.944275 | − | 0.329157i | \(-0.893235\pi\) | ||||
−0.944275 | + | 0.329157i | \(0.893235\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 231.821 | 1.16493 | 0.582466 | − | 0.812855i | \(-0.302088\pi\) | ||||
0.582466 | + | 0.812855i | \(0.302088\pi\) | |||||||
\(200\) | 31.0062 | − | 63.5501i | 0.155031 | − | 0.317750i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 27.0392 | − | 15.6111i | 0.133858 | − | 0.0772827i | ||||
\(203\) | −92.9625 | − | 161.016i | −0.457943 | − | 0.793181i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −112.901 | + | 212.301i | −0.550736 | + | 1.03561i | ||||
\(206\) | 26.0034i | 0.126230i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 24.4394i | − | 0.117497i | ||||||
\(209\) | 283.803 | + | 163.854i | 1.35791 | + | 0.783989i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4506 | − | 18.1010i | −0.0495289 | − | 0.0857866i | 0.840198 | − | 0.542280i | \(-0.182439\pi\) |
−0.889727 | + | 0.456493i | \(0.849105\pi\) | |||||||
\(212\) | −61.7484 | − | 106.951i | −0.291266 | − | 0.504487i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −43.0346 | + | 74.5381i | −0.201096 | + | 0.348309i | ||||
\(215\) | 240.376 | − | 8.37765i | 1.11803 | − | 0.0389658i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 289.074i | − | 1.33214i | ||||||
\(218\) | −56.9144 | + | 98.5787i | −0.261075 | + | 0.452196i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −108.017 | − | 172.890i | −0.490987 | − | 0.785863i | ||||
\(221\) | 126.992 | − | 73.3189i | 0.574625 | − | 0.331760i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.6598 | + | 7.88652i | 0.0612549 | + | 0.0353655i | 0.530315 | − | 0.847801i | \(-0.322074\pi\) |
−0.469060 | + | 0.883166i | \(0.655407\pi\) | |||||||
\(224\) | − | 53.6021i | − | 0.239295i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −32.1813 | −0.142395 | ||||||||
\(227\) | 170.673 | − | 295.614i | 0.751863 | − | 1.30227i | −0.195056 | − | 0.980792i | \(-0.562489\pi\) |
0.946919 | − | 0.321473i | \(-0.104178\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −60.2263 | − | 104.315i | −0.262997 | − | 0.455524i | 0.704040 | − | 0.710160i | \(-0.251378\pi\) |
−0.967037 | + | 0.254636i | \(0.918044\pi\) | |||||||
\(230\) | −259.532 | + | 162.149i | −1.12840 | + | 0.704994i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −48.0626 | − | 27.7489i | −0.207166 | − | 0.119607i | ||||
\(233\) | 307.400 | 1.31931 | 0.659657 | − | 0.751567i | \(-0.270702\pi\) | ||||
0.659657 | + | 0.751567i | \(0.270702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.8560 | + | 340.178i | 0.0504509 | + | 1.44757i | ||||
\(236\) | −87.3666 | − | 50.4411i | −0.370197 | − | 0.213734i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 278.527 | − | 160.808i | 1.17028 | − | 0.675662i | ||||
\(239\) | −103.129 | + | 59.5417i | −0.431503 | + | 0.249128i | −0.699987 | − | 0.714156i | \(-0.746811\pi\) |
0.268484 | + | 0.963284i | \(0.413477\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 157.300 | − | 272.452i | 0.652697 | − | 1.13050i | −0.329769 | − | 0.944062i | \(-0.606971\pi\) |
0.982466 | − | 0.186443i | \(-0.0596958\pi\) | |||||||
\(242\) | −416.608 | −1.72152 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −97.9949 | −0.401619 | ||||||||
\(245\) | 180.057 | + | 95.7539i | 0.734927 | + | 0.390832i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −85.0584 | + | 49.1085i | −0.344366 | + | 0.198820i | ||||
\(248\) | −43.1438 | − | 74.7272i | −0.173967 | − | 0.301319i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 161.479 | + | 71.9347i | 0.645915 | + | 0.287739i | ||||
\(251\) | 148.193i | 0.590411i | 0.955434 | + | 0.295206i | \(0.0953882\pi\) | ||||
−0.955434 | + | 0.295206i | \(0.904612\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 882.260i | 3.48719i | ||||||||
\(254\) | −89.8427 | − | 51.8707i | −0.353711 | − | 0.204215i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −147.158 | − | 254.885i | −0.572598 | − | 0.991770i | −0.996298 | − | 0.0859668i | \(-0.972602\pi\) |
0.423700 | − | 0.905803i | \(-0.360731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 212.412 | − | 367.908i | 0.820123 | − | 1.42050i | ||||
\(260\) | 61.0615 | − | 2.12813i | 0.234852 | − | 0.00818511i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 128.765i | 0.491471i | ||||||||
\(263\) | 34.7322 | − | 60.1580i | 0.132062 | − | 0.228738i | −0.792409 | − | 0.609990i | \(-0.791174\pi\) |
0.924471 | + | 0.381252i | \(0.124507\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 261.839 | − | 163.590i | 0.988072 | − | 0.617322i | ||||
\(266\) | −186.555 | + | 107.708i | −0.701336 | + | 0.404917i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 95.4200 | + | 55.0907i | 0.356045 | + | 0.205562i | ||||
\(269\) | − | 262.460i | − | 0.975687i | −0.872931 | − | 0.487844i | \(-0.837784\pi\) | ||
0.872931 | − | 0.487844i | \(-0.162216\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −375.110 | −1.38417 | −0.692084 | − | 0.721817i | \(-0.743307\pi\) | ||||
−0.692084 | + | 0.721817i | \(0.743307\pi\) | |||||||
\(272\) | 48.0004 | − | 83.1391i | 0.176472 | − | 0.305659i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 19.7168 | + | 34.1504i | 0.0719590 | + | 0.124637i | ||||
\(275\) | 422.557 | − | 284.934i | 1.53657 | − | 1.03612i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −126.760 | − | 73.1851i | −0.457619 | − | 0.264206i | 0.253424 | − | 0.967355i | \(-0.418443\pi\) |
−0.711042 | + | 0.703149i | \(0.751777\pi\) | |||||||
\(278\) | 49.1268 | 0.176715 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 133.924 | − | 4.66754i | 0.478300 | − | 0.0166698i | ||||
\(281\) | −68.5625 | − | 39.5846i | −0.243995 | − | 0.140870i | 0.373017 | − | 0.927825i | \(-0.378323\pi\) |
−0.617011 | + | 0.786954i | \(0.711657\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −187.343 | + | 108.163i | −0.661991 | + | 0.382201i | −0.793035 | − | 0.609176i | \(-0.791500\pi\) |
0.131044 | + | 0.991377i | \(0.458167\pi\) | |||||||
\(284\) | 40.8732 | − | 23.5982i | 0.143920 | − | 0.0830921i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 88.0738 | − | 152.548i | 0.307950 | − | 0.533386i | ||||
\(287\) | −455.689 | −1.58777 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 287.010 | 0.993113 | ||||||||
\(290\) | 65.1451 | − | 122.500i | 0.224638 | − | 0.422413i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −70.0274 | + | 40.4303i | −0.239820 | + | 0.138460i | ||||
\(293\) | −208.166 | − | 360.554i | −0.710464 | − | 1.23056i | −0.964683 | − | 0.263413i | \(-0.915152\pi\) |
0.254220 | − | 0.967147i | \(-0.418181\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 118.419 | − | 222.676i | 0.401419 | − | 0.754834i | ||||
\(296\) | − | 126.808i | − | 0.428406i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 0.448403i | − | 0.00150471i | ||||||
\(299\) | −228.996 | − | 132.211i | −0.765873 | − | 0.442177i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 227.909 | + | 394.750i | 0.757174 | + | 1.31146i | ||||
\(302\) | 74.4779 | + | 129.000i | 0.246616 | + | 0.427151i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −32.1503 | + | 55.6860i | −0.105758 | + | 0.183178i | ||||
\(305\) | −8.53317 | − | 244.839i | −0.0279776 | − | 0.802750i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 331.571i | − | 1.08004i | −0.841653 | − | 0.540018i | \(-0.818417\pi\) | ||
0.841653 | − | 0.540018i | \(-0.181583\pi\) | |||||||
\(308\) | 193.169 | − | 334.578i | 0.627172 | − | 1.08629i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 182.948 | − | 114.301i | 0.590154 | − | 0.368713i | ||||
\(311\) | −340.840 | + | 196.784i | −1.09595 | + | 0.632745i | −0.935154 | − | 0.354243i | \(-0.884739\pi\) |
−0.160794 | + | 0.986988i | \(0.551405\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −220.083 | − | 127.065i | −0.703141 | − | 0.405959i | 0.105375 | − | 0.994433i | \(-0.466396\pi\) |
−0.808516 | + | 0.588474i | \(0.799729\pi\) | |||||||
\(314\) | − | 64.4914i | − | 0.205387i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 66.4675 | 0.210340 | ||||||||
\(317\) | 215.992 | − | 374.108i | 0.681361 | − | 1.18015i | −0.293204 | − | 0.956050i | \(-0.594722\pi\) |
0.974566 | − | 0.224103i | \(-0.0719451\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −200.001 | − | 346.412i | −0.626962 | − | 1.08593i | ||||
\(320\) | 33.9234 | − | 21.1944i | 0.106011 | − | 0.0662326i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −502.248 | − | 289.973i | −1.55978 | − | 0.900538i | ||||
\(323\) | −385.807 | −1.19445 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6342 | + | 152.376i | 0.0327206 | + | 0.468849i | ||||
\(326\) | 187.133 | + | 108.041i | 0.574028 | + | 0.331415i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −117.798 | + | 68.0107i | −0.359140 | + | 0.207350i | ||||
\(329\) | −558.647 | + | 322.535i | −1.69802 | + | 0.980350i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −95.8658 | + | 166.044i | −0.289625 | + | 0.501645i | −0.973720 | − | 0.227748i | \(-0.926864\pi\) |
0.684095 | + | 0.729393i | \(0.260197\pi\) | |||||||
\(332\) | 45.4288 | 0.136834 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.4149 | −0.0581284 | ||||||||
\(335\) | −129.334 | + | 243.202i | −0.386073 | + | 0.725977i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −220.065 | + | 127.055i | −0.653013 | + | 0.377017i | −0.789610 | − | 0.613609i | \(-0.789717\pi\) |
0.136597 | + | 0.990627i | \(0.456384\pi\) | |||||||
\(338\) | −93.1045 | − | 161.262i | −0.275457 | − | 0.477106i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 211.901 | + | 112.689i | 0.623240 | + | 0.331437i | ||||
\(341\) | − | 621.919i | − | 1.82381i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 77.8236i | − | 0.226891i | ||||||
\(344\) | 117.831 | + | 68.0300i | 0.342533 | + | 0.197762i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.37563 | + | 12.7750i | 0.0213168 | + | 0.0369219i | ||||
\(347\) | 160.397 | + | 277.817i | 0.462241 | + | 0.800624i | 0.999072 | − | 0.0430652i | \(-0.0137123\pi\) |
−0.536832 | + | 0.843689i | \(0.680379\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −152.262 | + | 263.726i | −0.436281 | + | 0.755661i | −0.997399 | − | 0.0720745i | \(-0.977038\pi\) |
0.561118 | + | 0.827736i | \(0.310371\pi\) | |||||||
\(350\) | 23.3235 | + | 334.200i | 0.0666387 | + | 0.954857i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 115.320i | − | 0.327614i | ||||||
\(353\) | −107.879 | + | 186.852i | −0.305607 | + | 0.529326i | −0.977396 | − | 0.211416i | \(-0.932193\pi\) |
0.671790 | + | 0.740742i | \(0.265526\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 62.5188 | + | 100.066i | 0.176109 | + | 0.281877i | ||||
\(356\) | 137.744 | − | 79.5266i | 0.386922 | − | 0.223389i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 76.5037 | + | 44.1695i | 0.213698 | + | 0.123378i | ||||
\(359\) | 638.110i | 1.77746i | 0.458427 | + | 0.888732i | \(0.348413\pi\) | ||||
−0.458427 | + | 0.888732i | \(0.651587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −102.589 | −0.284180 | ||||||||
\(362\) | −242.558 | + | 420.123i | −0.670050 | + | 1.16056i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 57.8946 | + | 100.276i | 0.159051 | + | 0.275484i | ||||
\(365\) | −107.112 | − | 171.442i | −0.293458 | − | 0.469703i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −320.949 | − | 185.300i | −0.874519 | − | 0.504904i | −0.00567194 | − | 0.999984i | \(-0.501805\pi\) |
−0.868847 | + | 0.495080i | \(0.835139\pi\) | |||||||
\(368\) | −173.112 | −0.470412 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 316.828 | − | 11.0422i | 0.856292 | − | 0.0298437i | ||||
\(371\) | 506.714 | + | 292.551i | 1.36581 | + | 0.788548i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 445.709 | − | 257.330i | 1.19493 | − | 0.689894i | 0.235510 | − | 0.971872i | \(-0.424324\pi\) |
0.959421 | + | 0.281978i | \(0.0909906\pi\) | |||||||
\(374\) | 599.227 | − | 345.964i | 1.60221 | − | 0.925036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −96.2754 | + | 166.754i | −0.256052 | + | 0.443494i | ||||
\(377\) | 119.884 | 0.317996 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −159.583 | −0.421063 | −0.210532 | − | 0.977587i | \(-0.567519\pi\) | ||||
−0.210532 | + | 0.977587i | \(0.567519\pi\) | |||||||
\(380\) | −141.930 | − | 75.4781i | −0.373500 | − | 0.198627i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −15.4779 | + | 8.93617i | −0.0405181 | + | 0.0233931i | ||||
\(383\) | −224.022 | − | 388.017i | −0.584913 | − | 1.01310i | −0.994886 | − | 0.101001i | \(-0.967795\pi\) |
0.409973 | − | 0.912098i | \(-0.365538\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 852.759 | + | 453.495i | 2.21496 | + | 1.17791i | ||||
\(386\) | 237.764i | 0.615969i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 239.772i | 0.617970i | ||||||||
\(389\) | −483.961 | − | 279.415i | −1.24412 | − | 0.718291i | −0.274187 | − | 0.961676i | \(-0.588409\pi\) |
−0.969930 | + | 0.243385i | \(0.921742\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −519.339 | − | 899.522i | −1.32823 | − | 2.30057i | ||||
\(392\) | 57.6815 | + | 99.9072i | 0.147147 | + | 0.254865i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 263.075 | − | 455.659i | 0.667703 | − | 1.15650i | ||||
\(395\) | 5.78784 | + | 166.068i | 0.0146527 | + | 0.420425i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 266.143i | − | 0.670385i | −0.942150 | − | 0.335192i | \(-0.891199\pi\) | ||
0.942150 | − | 0.335192i | \(-0.108801\pi\) | |||||||
\(398\) | −163.922 | + | 283.922i | −0.411865 | + | 0.713372i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 55.9079 | + | 82.9114i | 0.139770 | + | 0.207279i | ||||
\(401\) | 15.0865 | − | 8.71018i | 0.0376222 | − | 0.0217212i | −0.481071 | − | 0.876682i | \(-0.659752\pi\) |
0.518693 | + | 0.854961i | \(0.326419\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 161.423 | + | 93.1975i | 0.400553 | + | 0.231259i | ||||
\(404\) | 44.1549i | 0.109294i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 262.938 | 0.647630 | ||||||||
\(407\) | 456.986 | − | 791.523i | 1.12282 | − | 1.94477i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 222.882 | + | 386.042i | 0.544943 | + | 0.943869i | 0.998610 | + | 0.0526980i | \(0.0167821\pi\) |
−0.453667 | + | 0.891171i | \(0.649885\pi\) | |||||||
\(410\) | −180.181 | − | 288.394i | −0.439466 | − | 0.703400i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31.8475 | − | 18.3872i | −0.0772998 | − | 0.0446290i | ||||
\(413\) | 477.960 | 1.15729 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.95583 | + | 113.503i | 0.00953213 | + | 0.273502i | ||||
\(416\) | 29.9321 | + | 17.2813i | 0.0719521 | + | 0.0415416i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −401.358 | + | 231.724i | −0.960186 | + | 0.554364i | ||||
\(419\) | 309.570 | − | 178.730i | 0.738830 | − | 0.426563i | −0.0828141 | − | 0.996565i | \(-0.526391\pi\) |
0.821644 | + | 0.570002i | \(0.193057\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −287.514 | + | 497.988i | −0.682930 | + | 1.18287i | 0.291152 | + | 0.956677i | \(0.405961\pi\) |
−0.974083 | + | 0.226193i | \(0.927372\pi\) | |||||||
\(422\) | 29.5588 | 0.0700445 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 174.651 | 0.411912 | ||||||||
\(425\) | −263.099 | + | 539.245i | −0.619056 | + | 1.26881i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 402.078 | − | 232.140i | 0.941636 | − | 0.543654i | ||||
\(428\) | −60.8601 | − | 105.413i | −0.142196 | − | 0.246292i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −159.711 | + | 300.324i | −0.371422 | + | 0.698427i | ||||
\(431\) | 181.318i | 0.420691i | 0.977627 | + | 0.210346i | \(0.0674589\pi\) | ||||
−0.977627 | + | 0.210346i | \(0.932541\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 705.627i | − | 1.62962i | −0.579726 | − | 0.814811i | \(-0.696840\pi\) | ||
0.579726 | − | 0.814811i | \(-0.303160\pi\) | |||||||
\(434\) | 354.042 | + | 204.406i | 0.815766 | + | 0.470983i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −80.4892 | − | 139.411i | −0.184608 | − | 0.319751i | ||||
\(437\) | 347.850 | + | 602.493i | 0.795995 | + | 1.37870i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −142.777 | + | 247.296i | −0.325231 | + | 0.563317i | −0.981559 | − | 0.191159i | \(-0.938776\pi\) |
0.656328 | + | 0.754476i | \(0.272109\pi\) | |||||||
\(440\) | 288.126 | − | 10.0418i | 0.654831 | − | 0.0228223i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 207.377i | 0.469179i | ||||||||
\(443\) | −353.052 | + | 611.504i | −0.796957 | + | 1.38037i | 0.124632 | + | 0.992203i | \(0.460225\pi\) |
−0.921589 | + | 0.388167i | \(0.873108\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 210.690 | + | 337.226i | 0.473461 | + | 0.757812i | ||||
\(446\) | −19.3179 | + | 11.1532i | −0.0433138 | + | 0.0250072i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 65.6489 | + | 37.9024i | 0.146538 | + | 0.0846035i | ||||
\(449\) | − | 505.807i | − | 1.12652i | −0.826280 | − | 0.563260i | \(-0.809547\pi\) | ||
0.826280 | − | 0.563260i | \(-0.190453\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −980.376 | −2.17378 | ||||||||
\(452\) | 22.7556 | − | 39.4139i | 0.0503443 | − | 0.0871989i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 241.368 | + | 418.062i | 0.531648 | + | 0.920841i | ||||
\(455\) | −245.497 | + | 153.380i | −0.539555 | + | 0.337100i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −615.467 | − | 355.340i | −1.34676 | − | 0.777550i | −0.358967 | − | 0.933350i | \(-0.616871\pi\) |
−0.987788 | + | 0.155801i | \(0.950204\pi\) | |||||||
\(458\) | 170.346 | 0.371934 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.0741 | − | 432.516i | −0.0327699 | − | 0.940253i | ||||
\(461\) | 119.178 | + | 68.8073i | 0.258520 | + | 0.149257i | 0.623659 | − | 0.781696i | \(-0.285645\pi\) |
−0.365139 | + | 0.930953i | \(0.618979\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −298.053 | + | 172.081i | −0.643743 | + | 0.371665i | −0.786055 | − | 0.618157i | \(-0.787880\pi\) |
0.142312 | + | 0.989822i | \(0.454546\pi\) | |||||||
\(464\) | 67.9707 | − | 39.2429i | 0.146489 | − | 0.0845752i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −217.365 | + | 376.487i | −0.466448 | + | 0.807912i | ||||
\(467\) | 322.715 | 0.691038 | 0.345519 | − | 0.938412i | \(-0.387703\pi\) | ||||
0.345519 | + | 0.938412i | \(0.387703\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −522.018 | −1.11304 | ||||||||
\(470\) | −425.015 | − | 226.022i | −0.904288 | − | 0.480898i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 123.555 | − | 71.3345i | 0.261769 | − | 0.151132i | ||||
\(473\) | 490.327 | + | 849.272i | 1.03663 | + | 1.79550i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 176.222 | − | 361.183i | 0.370993 | − | 0.760384i | ||||
\(476\) | 454.832i | 0.955530i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 168.409i | − | 0.352321i | ||||||
\(479\) | −73.7251 | − | 42.5652i | −0.153915 | − | 0.0888626i | 0.421065 | − | 0.907031i | \(-0.361657\pi\) |
−0.574979 | + | 0.818168i | \(0.694990\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 136.963 | + | 237.227i | 0.284747 | + | 0.493196i | ||||
\(482\) | 222.456 | + | 385.305i | 0.461526 | + | 0.799387i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 294.586 | − | 510.238i | 0.608649 | − | 1.05421i | ||||
\(485\) | −599.067 | + | 20.8788i | −1.23519 | + | 0.0430491i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 437.344i | − | 0.898037i | −0.893522 | − | 0.449018i | \(-0.851774\pi\) | ||
0.893522 | − | 0.449018i | \(-0.148226\pi\) | |||||||
\(488\) | 69.2929 | − | 120.019i | 0.141994 | − | 0.245940i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −244.594 | + | 152.816i | −0.499171 | + | 0.311869i | ||||
\(491\) | 588.443 | − | 339.738i | 1.19846 | − | 0.691930i | 0.238247 | − | 0.971205i | \(-0.423427\pi\) |
0.960211 | + | 0.279275i | \(0.0900940\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 407.828 | + | 235.459i | 0.827237 | + | 0.477605i | ||||
\(494\) | − | 138.900i | − | 0.281174i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 122.029 | 0.246026 | ||||||||
\(497\) | −111.803 | + | 193.649i | −0.224956 | + | 0.389636i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −150.280 | − | 260.293i | −0.301162 | − | 0.521629i | 0.675237 | − | 0.737601i | \(-0.264041\pi\) |
−0.976400 | + | 0.215972i | \(0.930708\pi\) | |||||||
\(500\) | −202.284 | + | 146.905i | −0.404569 | + | 0.293810i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −181.499 | − | 104.788i | −0.361552 | − | 0.208742i | ||||
\(503\) | 371.067 | 0.737707 | 0.368853 | − | 0.929488i | \(-0.379750\pi\) | ||||
0.368853 | + | 0.929488i | \(0.379750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −110.320 | + | 3.84490i | −0.218456 | + | 0.00761367i | ||||
\(506\) | −1080.54 | − | 623.852i | −2.13546 | − | 1.23291i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 127.057 | − | 73.3562i | 0.250112 | − | 0.144402i | ||||
\(509\) | −503.727 | + | 290.827i | −0.989640 | + | 0.571369i | −0.905167 | − | 0.425057i | \(-0.860254\pi\) |
−0.0844732 | + | 0.996426i | \(0.526921\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 191.551 | − | 331.776i | 0.374855 | − | 0.649267i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 416.225 | 0.809777 | ||||||||
\(515\) | 43.1668 | − | 81.1716i | 0.0838191 | − | 0.157615i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1201.88 | + | 693.907i | −2.32472 | + | 1.34218i | ||||
\(518\) | 300.396 | + | 520.301i | 0.579915 | + | 1.00444i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −40.5706 | + | 76.2896i | −0.0780204 | + | 0.146711i | ||||
\(521\) | − | 1006.68i | − | 1.93222i | −0.258138 | − | 0.966108i | \(-0.583109\pi\) | ||
0.258138 | − | 0.966108i | \(-0.416891\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 674.227i | 1.28915i | 0.764540 | + | 0.644576i | \(0.222966\pi\) | ||||
−0.764540 | + | 0.644576i | \(0.777034\pi\) | |||||||
\(524\) | −157.705 | − | 91.0508i | −0.300963 | − | 0.173761i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.1188 | + | 85.0763i | 0.0933817 | + | 0.161742i | ||||
\(527\) | 366.090 | + | 634.086i | 0.694668 | + | 1.20320i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −671.988 | + | 1163.92i | −1.27030 | + | 2.20022i | ||||
\(530\) | 15.2082 | + | 436.362i | 0.0286947 | + | 0.823325i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 304.644i | − | 0.572639i | ||||||
\(533\) | 146.914 | − | 254.463i | 0.275636 | − | 0.477416i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 258.072 | − | 161.237i | 0.482378 | − | 0.301378i | ||||
\(536\) | −134.944 | + | 77.9101i | −0.251762 | + | 0.145355i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 321.446 | + | 185.587i | 0.597484 | + | 0.344958i | ||||
\(539\) | 831.480i | 1.54263i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 178.075 | 0.329159 | 0.164579 | − | 0.986364i | \(-0.447373\pi\) | ||||
0.164579 | + | 0.986364i | \(0.447373\pi\) | |||||||
\(542\) | 265.243 | − | 459.414i | 0.489378 | − | 0.847627i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 67.8828 | + | 117.576i | 0.124785 | + | 0.216133i | ||||
\(545\) | 341.308 | − | 213.240i | 0.626253 | − | 0.391267i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 178.531 | + | 103.075i | 0.326381 | + | 0.188436i | 0.654233 | − | 0.756293i | \(-0.272991\pi\) |
−0.327852 | + | 0.944729i | \(0.606325\pi\) | |||||||
\(548\) | −55.7674 | −0.101765 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 50.1786 | + | 719.003i | 0.0912338 | + | 1.30728i | ||||
\(551\) | −273.160 | − | 157.709i | −0.495754 | − | 0.286223i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −272.720 | + | 157.455i | −0.493164 | + | 0.284729i | ||||
\(554\) | 179.266 | − | 103.499i | 0.323585 | − | 0.186822i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −34.7379 | + | 60.1679i | −0.0624783 | + | 0.108216i | ||||
\(557\) | 37.8724 | 0.0679935 | 0.0339968 | − | 0.999422i | \(-0.489176\pi\) | ||||
0.0339968 | + | 0.999422i | \(0.489176\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −293.911 | −0.525781 | ||||||||
\(560\) | −88.9819 | + | 167.323i | −0.158896 | + | 0.298791i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 96.9621 | − | 55.9811i | 0.172530 | − | 0.0996105i | ||||
\(563\) | 158.628 | + | 274.751i | 0.281754 | + | 0.488012i | 0.971817 | − | 0.235737i | \(-0.0757505\pi\) |
−0.690063 | + | 0.723749i | \(0.742417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 100.456 | + | 53.4225i | 0.177799 | + | 0.0945531i | ||||
\(566\) | − | 305.931i | − | 0.540513i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 66.7457i | 0.117510i | ||||||||
\(569\) | 349.661 | + | 201.877i | 0.614518 | + | 0.354792i | 0.774732 | − | 0.632290i | \(-0.217885\pi\) |
−0.160214 | + | 0.987082i | \(0.551218\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −142.037 | − | 246.015i | −0.248751 | − | 0.430849i | 0.714429 | − | 0.699708i | \(-0.246687\pi\) |
−0.963180 | + | 0.268859i | \(0.913353\pi\) | |||||||
\(572\) | 124.555 | + | 215.736i | 0.217754 | + | 0.377161i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 322.221 | − | 558.103i | 0.561361 | − | 0.972305i | ||||
\(575\) | 1079.32 | − | 75.3250i | 1.87708 | − | 0.131000i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 105.236i | 0.182386i | 0.995833 | + | 0.0911928i | \(0.0290679\pi\) | ||||
−0.995833 | + | 0.0911928i | \(0.970932\pi\) | |||||||
\(578\) | −202.946 | + | 351.514i | −0.351118 | + | 0.608155i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 103.966 | + | 166.407i | 0.179253 | + | 0.286908i | ||||
\(581\) | −186.397 | + | 107.616i | −0.320821 | + | 0.185226i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1090.15 | + | 629.399i | 1.86990 | + | 1.07959i | ||||
\(584\) | − | 114.354i | − | 0.195812i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 588.782 | 1.00475 | ||||||||
\(587\) | −438.787 | + | 760.001i | −0.747508 | + | 1.29472i | 0.201507 | + | 0.979487i | \(0.435416\pi\) |
−0.949014 | + | 0.315234i | \(0.897917\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −245.205 | − | 424.707i | −0.416307 | − | 0.721064i | ||||
\(590\) | 188.987 | + | 302.488i | 0.320317 | + | 0.512692i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 155.308 | + | 89.6669i | 0.262344 | + | 0.151464i | ||||
\(593\) | 47.7971 | 0.0806022 | 0.0403011 | − | 0.999188i | \(-0.487168\pi\) | ||||
0.0403011 | + | 0.999188i | \(0.487168\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1136.39 | + | 39.6057i | −1.90990 | + | 0.0665643i | ||||
\(596\) | 0.549179 | + | 0.317069i | 0.000921441 | + | 0.000531994i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 323.849 | − | 186.974i | 0.541554 | − | 0.312666i | ||||
\(599\) | −985.107 | + | 568.752i | −1.64459 | + | 0.949502i | −0.665412 | + | 0.746476i | \(0.731744\pi\) |
−0.979173 | + | 0.203026i | \(0.934922\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −95.3631 | + | 165.174i | −0.158674 | + | 0.274832i | −0.934391 | − | 0.356250i | \(-0.884055\pi\) |
0.775717 | + | 0.631081i | \(0.217389\pi\) | |||||||
\(602\) | −644.625 | −1.07081 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −210.655 | −0.348767 | ||||||||
\(605\) | 1300.47 | + | 691.588i | 2.14954 | + | 1.14312i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −856.430 | + | 494.460i | −1.41092 | + | 0.814597i | −0.995475 | − | 0.0950207i | \(-0.969708\pi\) |
−0.415447 | + | 0.909617i | \(0.636375\pi\) | |||||||
\(608\) | −45.4674 | − | 78.7519i | −0.0747820 | − | 0.129526i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 305.899 | + | 162.676i | 0.501473 | + | 0.266682i | ||||
\(611\) | − | 415.941i | − | 0.680754i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 131.155i | − | 0.213956i | −0.994261 | − | 0.106978i | \(-0.965882\pi\) | ||
0.994261 | − | 0.106978i | \(-0.0341175\pi\) | |||||||
\(614\) | 406.090 | + | 234.456i | 0.661384 | + | 0.381850i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 273.182 | + | 473.165i | 0.443477 | + | 0.768125i | ||||
\(617\) | −216.658 | − | 375.263i | −0.351148 | − | 0.608207i | 0.635303 | − | 0.772263i | \(-0.280875\pi\) |
−0.986451 | + | 0.164057i | \(0.947542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −289.947 | + | 502.202i | −0.468411 | + | 0.811312i | −0.999348 | − | 0.0360992i | \(-0.988507\pi\) |
0.530937 | + | 0.847411i | \(0.321840\pi\) | |||||||
\(620\) | 10.6260 | + | 304.887i | 0.0171387 | + | 0.491754i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 556.589i | − | 0.894837i | ||||||
\(623\) | −376.781 | + | 652.604i | −0.604785 | + | 1.04752i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −384.653 | − | 492.612i | −0.615446 | − | 0.788179i | ||||
\(626\) | 311.245 | − | 179.697i | 0.497196 | − | 0.287056i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 78.9855 | + | 45.6023i | 0.125773 | + | 0.0726151i | ||||
\(629\) | 1076.01i | 1.71067i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1026.45 | 1.62671 | 0.813354 | − | 0.581768i | \(-0.197639\pi\) | ||||
0.813354 | + | 0.581768i | \(0.197639\pi\) | |||||||
\(632\) | −46.9997 | + | 81.4058i | −0.0743665 | + | 0.128807i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 305.458 | + | 529.069i | 0.481795 | + | 0.834494i | ||||
\(635\) | 194.343 | + | 311.061i | 0.306052 | + | 0.489860i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −215.816 | − | 124.601i | −0.338800 | − | 0.195606i | ||||
\(638\) | 565.688 | 0.886658 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.97034 | + | 56.5342i | 0.00307866 | + | 0.0883347i | ||||
\(641\) | 282.653 | + | 163.190i | 0.440957 | + | 0.254586i | 0.704003 | − | 0.710197i | \(-0.251394\pi\) |
−0.263047 | + | 0.964783i | \(0.584727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 483.731 | − | 279.282i | 0.752303 | − | 0.434342i | −0.0742223 | − | 0.997242i | \(-0.523647\pi\) |
0.826525 | + | 0.562899i | \(0.190314\pi\) | |||||||
\(644\) | 710.286 | − | 410.084i | 1.10293 | − | 0.636776i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 272.807 | − | 472.516i | 0.422302 | − | 0.731448i | ||||
\(647\) | −404.040 | −0.624483 | −0.312241 | − | 0.950003i | \(-0.601080\pi\) | ||||
−0.312241 | + | 0.950003i | \(0.601080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1028.29 | 1.58442 | ||||||||
\(650\) | −194.141 | − | 94.7218i | −0.298679 | − | 0.145726i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −264.646 | + | 152.794i | −0.405899 | + | 0.234346i | ||||
\(653\) | 357.001 | + | 618.344i | 0.546709 | + | 0.946928i | 0.998497 | + | 0.0548026i | \(0.0174530\pi\) |
−0.451788 | + | 0.892125i | \(0.649214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 213.756 | − | 401.951i | 0.326346 | − | 0.613666i | ||||
\(656\) | − | 192.363i | − | 0.293237i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 912.267i | − | 1.38642i | ||||||
\(659\) | −110.583 | − | 63.8450i | −0.167804 | − | 0.0968817i | 0.413746 | − | 0.910392i | \(-0.364220\pi\) |
−0.581550 | + | 0.813511i | \(0.697554\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 202.346 | + | 350.474i | 0.306121 | + | 0.530217i | 0.977510 | − | 0.210888i | \(-0.0676354\pi\) |
−0.671389 | + | 0.741105i | \(0.734302\pi\) | |||||||
\(662\) | −135.575 | − | 234.822i | −0.204796 | − | 0.354716i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −32.1230 | + | 55.6387i | −0.0483781 | + | 0.0837933i | ||||
\(665\) | 761.147 | − | 26.5277i | 1.14458 | − | 0.0398912i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 849.175i | − | 1.27313i | ||||||
\(668\) | 13.7284 | − | 23.7783i | 0.0205515 | − | 0.0355962i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −206.408 | − | 330.372i | −0.308071 | − | 0.493092i | ||||
\(671\) | 865.037 | − | 499.430i | 1.28918 | − | 0.744306i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1073.07 | − | 619.539i | −1.59446 | − | 0.920562i | −0.992528 | − | 0.122016i | \(-0.961064\pi\) |
−0.601933 | − | 0.798547i | \(-0.705603\pi\) | |||||||
\(674\) | − | 359.365i | − | 0.533183i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 263.339 | 0.389555 | ||||||||
\(677\) | −339.544 | + | 588.107i | −0.501541 | + | 0.868695i | 0.498457 | + | 0.866914i | \(0.333900\pi\) |
−0.999998 | + | 0.00178078i | \(0.999433\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −567.997 | − | 983.799i | −0.836520 | − | 1.44889i | ||||
\(680\) | −287.852 | + | 179.842i | −0.423311 | + | 0.264474i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 761.692 | + | 439.763i | 1.11685 | + | 0.644814i | ||||
\(683\) | −439.600 | −0.643632 | −0.321816 | − | 0.946802i | \(-0.604293\pi\) | ||||
−0.321816 | + | 0.946802i | \(0.604293\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85610 | − | 139.334i | −0.00708919 | − | 0.203407i | ||||
\(686\) | 95.3141 | + | 55.0296i | 0.138942 | + | 0.0802181i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −166.639 | + | 96.2089i | −0.242207 | + | 0.139839i | ||||
\(689\) | −326.729 | + | 188.637i | −0.474207 | + | 0.273784i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 162.345 | − | 281.189i | 0.234941 | − | 0.406931i | −0.724314 | − | 0.689470i | \(-0.757843\pi\) |
0.959256 | + | 0.282539i | \(0.0911768\pi\) | |||||||
\(692\) | −20.8614 | −0.0301466 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −453.673 | −0.653707 | ||||||||
\(695\) | −153.353 | − | 81.5528i | −0.220652 | − | 0.117342i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 999.557 | − | 577.095i | 1.43409 | − | 0.827969i | ||||
\(698\) | −215.331 | − | 372.965i | −0.308497 | − | 0.534333i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −425.802 | − | 207.750i | −0.608289 | − | 0.296785i | ||||
\(701\) | − | 319.512i | − | 0.455795i | −0.973685 | − | 0.227898i | \(-0.926815\pi\) | ||
0.973685 | − | 0.227898i | \(-0.0731851\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 720.706i | − | 1.02519i | ||||||
\(704\) | 141.238 | + | 81.5437i | 0.200622 | + | 0.115829i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −152.564 | − | 264.249i | −0.216096 | − | 0.374290i | ||||
\(707\) | −104.598 | − | 181.170i | −0.147947 | − | 0.256252i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 553.311 | − | 958.363i | 0.780411 | − | 1.35171i | −0.151292 | − | 0.988489i | \(-0.548343\pi\) |
0.931703 | − | 0.363222i | \(-0.118323\pi\) | |||||||
\(710\) | −166.763 | + | 5.81206i | −0.234877 | + | 0.00818600i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 224.935i | 0.315920i | ||||||||
\(713\) | 660.145 | − | 1143.40i | 0.925869 | − | 1.60365i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −528.166 | + | 329.985i | −0.738694 | + | 0.461517i | ||||
\(716\) | −108.193 | + | 62.4650i | −0.151107 | + | 0.0872417i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −781.522 | − | 451.212i | −1.08847 | − | 0.628429i | ||||
\(719\) | − | 992.085i | − | 1.37981i | −0.723899 | − | 0.689906i | \(-0.757652\pi\) | ||
0.723899 | − | 0.689906i | \(-0.242348\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 174.229 | 0.241650 | ||||||||
\(722\) | 72.5413 | − | 125.645i | 0.100473 | − | 0.174024i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −343.029 | − | 594.144i | −0.473797 | − | 0.820641i | ||||
\(725\) | −406.711 | + | 274.249i | −0.560980 | + | 0.378274i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.01986 | + | 3.47557i | 0.00828041 | + | 0.00478070i | 0.504134 | − | 0.863625i | \(-0.331812\pi\) |
−0.495854 | + | 0.868406i | \(0.665145\pi\) | |||||||
\(728\) | −163.751 | −0.224932 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 285.712 | − | 9.95769i | 0.391386 | − | 0.0136407i | ||||
\(731\) | −999.841 | − | 577.258i | −1.36777 | − | 0.789683i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −216.107 | + | 124.770i | −0.294826 | + | 0.170218i | −0.640116 | − | 0.768278i | \(-0.721114\pi\) |
0.345290 | + | 0.938496i | \(0.387780\pi\) | |||||||
\(734\) | 453.890 | − | 262.053i | 0.618379 | − | 0.357021i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 122.408 | − | 212.018i | 0.166316 | − | 0.288067i | ||||
\(737\) | −1123.08 | −1.52385 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −961.297 | −1.30081 | −0.650404 | − | 0.759588i | \(-0.725400\pi\) | ||||
−0.650404 | + | 0.759588i | \(0.725400\pi\) | |||||||
\(740\) | −210.508 | + | 395.842i | −0.284470 | + | 0.534921i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −716.602 | + | 413.730i | −0.965770 | + | 0.557588i | ||||
\(743\) | −398.376 | − | 690.008i | −0.536172 | − | 0.928678i | −0.999106 | − | 0.0422847i | \(-0.986536\pi\) |
0.462933 | − | 0.886393i | \(-0.346797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.744369 | + | 1.39972i | −0.000999153 | + | 0.00187882i | ||||
\(746\) | 727.840i | 0.975657i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 978.533i | 1.30820i | ||||||||
\(749\) | 499.424 | + | 288.343i | 0.666788 | + | 0.384970i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −153.068 | − | 265.122i | −0.203820 | − | 0.353026i | 0.745936 | − | 0.666017i | \(-0.232002\pi\) |
−0.949756 | + | 0.312991i | \(0.898669\pi\) | |||||||
\(752\) | −136.154 | − | 235.826i | −0.181056 | − | 0.313598i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −84.7710 | + | 146.828i | −0.112428 | + | 0.194732i | ||||
\(755\) | −18.3434 | − | 526.319i | −0.0242958 | − | 0.697111i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 411.616i | − | 0.543746i | −0.962333 | − | 0.271873i | \(-0.912357\pi\) | ||
0.962333 | − | 0.271873i | \(-0.0876431\pi\) | |||||||
\(758\) | 112.842 | − | 195.448i | 0.148868 | − | 0.257847i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 192.801 | − | 120.457i | 0.253686 | − | 0.158496i | ||||
\(761\) | −463.859 | + | 267.809i | −0.609539 | + | 0.351918i | −0.772785 | − | 0.634668i | \(-0.781137\pi\) |
0.163246 | + | 0.986585i | \(0.447804\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 660.503 | + | 381.341i | 0.865665 | + | 0.499792i | ||||
\(764\) | − | 25.2753i | − | 0.0330829i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 633.629 | 0.827192 | ||||||||
\(767\) | −154.094 | + | 266.899i | −0.200905 | + | 0.347977i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 540.916 | + | 936.894i | 0.703402 | + | 1.21833i | 0.967265 | + | 0.253768i | \(0.0816700\pi\) |
−0.263863 | + | 0.964560i | \(0.584997\pi\) | |||||||
\(770\) | −1158.41 | + | 723.743i | −1.50442 | + | 0.939926i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −291.200 | − | 168.124i | −0.377202 | − | 0.217778i | ||||
\(773\) | −166.623 | −0.215554 | −0.107777 | − | 0.994175i | \(-0.534373\pi\) | ||||
−0.107777 | + | 0.994175i | \(0.534373\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −760.830 | + | 53.0977i | −0.981717 | + | 0.0685132i | ||||
\(776\) | −293.660 | − | 169.545i | −0.378428 | − | 0.218485i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 684.425 | − | 395.153i | 0.879723 | − | 0.507908i | ||||
\(779\) | −669.497 | + | 386.534i | −0.859431 | + | 0.496193i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −240.535 | + | 416.619i | −0.307984 | + | 0.533444i | ||||
\(782\) | 1468.91 | 1.87841 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −163.148 | −0.208097 | ||||||||
\(785\) | −107.059 | + | 201.315i | −0.136380 | + | 0.256452i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 352.266 | − | 203.381i | 0.447607 | − | 0.258426i | −0.259212 | − | 0.965820i | \(-0.583463\pi\) |
0.706819 | + | 0.707395i | \(0.250130\pi\) | |||||||
\(788\) | 372.044 | + | 644.400i | 0.472138 | + | 0.817766i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −207.484 | − | 110.339i | −0.262637 | − | 0.139670i | ||||
\(791\) | 215.623i | 0.272596i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 299.368i | 0.377513i | ||||||||
\(794\) | 325.957 | + | 188.191i | 0.410525 | + | 0.237017i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −231.821 | − | 401.526i | −0.291233 | − | 0.504430i | ||||
\(797\) | 51.6178 | + | 89.4047i | 0.0647652 | + | 0.112177i | 0.896590 | − | 0.442862i | \(-0.146037\pi\) |
−0.831825 | + | 0.555039i | \(0.812704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 816.931 | − | 1414.97i | 1.02244 | − | 1.77092i | ||||
\(800\) | −141.078 | + | 9.84573i | −0.176348 | + | 0.0123072i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 24.6361i | 0.0307184i | ||||||||
\(803\) | 412.105 | − | 713.787i | 0.513207 | − | 0.888900i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1086.44 | + | 1738.93i | 1.34961 | + | 2.16016i | ||||
\(806\) | −228.286 | + | 131.801i | −0.283234 | + | 0.163525i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −54.0784 | − | 31.2222i | −0.0669288 | − | 0.0386413i | ||||
\(809\) | − | 833.545i | − | 1.03034i | −0.857088 | − | 0.515170i | \(-0.827729\pi\) | ||
0.857088 | − | 0.515170i | \(-0.172271\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 814.193 | 1.00394 | 0.501968 | − | 0.864886i | \(-0.332609\pi\) | ||||
0.501968 | + | 0.864886i | \(0.332609\pi\) | |||||||
\(812\) | −185.925 | + | 322.032i | −0.228972 | + | 0.396591i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 646.276 | + | 1119.38i | 0.793951 | + | 1.37516i | ||||
\(815\) | −404.797 | − | 647.909i | −0.496683 | − | 0.794981i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 669.687 | + | 386.644i | 0.819690 | + | 0.473248i | ||||
\(818\) | −630.405 | −0.770666 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 480.616 | − | 16.7505i | 0.586118 | − | 0.0204275i | ||||
\(821\) | 133.926 | + | 77.3220i | 0.163125 | + | 0.0941803i | 0.579340 | − | 0.815086i | \(-0.303310\pi\) |
−0.416215 | + | 0.909266i | \(0.636644\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 955.975 | − | 551.932i | 1.16157 | − | 0.670635i | 0.209893 | − | 0.977724i | \(-0.432688\pi\) |
0.951681 | + | 0.307090i | \(0.0993551\pi\) | |||||||
\(824\) | 45.0392 | − | 26.0034i | 0.0546592 | − | 0.0315575i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −337.969 | + | 585.379i | −0.409163 | + | 0.708691i | ||||
\(827\) | 423.629 | 0.512248 | 0.256124 | − | 0.966644i | \(-0.417554\pi\) | ||||
0.256124 | + | 0.966644i | \(0.417554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 325.734 | 0.392924 | 0.196462 | − | 0.980511i | \(-0.437055\pi\) | ||||
0.196462 | + | 0.980511i | \(0.437055\pi\) | |||||||
\(830\) | −141.810 | − | 75.4140i | −0.170855 | − | 0.0908602i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −42.3303 | + | 24.4394i | −0.0508778 | + | 0.0293743i | ||||
\(833\) | −489.447 | − | 847.748i | −0.587572 | − | 1.01770i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 60.6051 | + | 32.2296i | 0.0725809 | + | 0.0385983i | ||||
\(836\) | − | 655.415i | − | 0.783989i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 505.525i | 0.603252i | ||||||||
\(839\) | −1050.83 | − | 606.698i | −1.25248 | − | 0.723121i | −0.280880 | − | 0.959743i | \(-0.590626\pi\) |
−0.971602 | + | 0.236622i | \(0.923960\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −227.999 | − | 394.906i | −0.271105 | − | 0.469567i | ||||
\(842\) | −406.606 | − | 704.261i | −0.482904 | − | 0.836415i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.9012 | + | 36.2020i | −0.0247645 | + | 0.0428933i | ||||
\(845\) | 22.9310 | + | 657.949i | 0.0271372 | + | 0.778637i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2791.38i | 3.29561i | ||||||||
\(848\) | −123.497 | + | 213.903i | −0.145633 | + | 0.252244i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −474.399 | − | 703.533i | −0.558116 | − | 0.827685i | ||||
\(851\) | 1680.35 | − | 970.149i | 1.97456 | − | 1.14001i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.3535 | − | 17.5246i | −0.0355844 | − | 0.0205446i | 0.482102 | − | 0.876115i | \(-0.339873\pi\) |
−0.517687 | + | 0.855570i | \(0.673207\pi\) | |||||||
\(854\) | 656.591i | 0.768842i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 172.138 | 0.201096 | ||||||||
\(857\) | 548.707 | − | 950.388i | 0.640265 | − | 1.10897i | −0.345109 | − | 0.938563i | \(-0.612158\pi\) |
0.985374 | − | 0.170408i | \(-0.0545087\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −452.145 | − | 783.137i | −0.526362 | − | 0.911685i | −0.999528 | − | 0.0307121i | \(-0.990223\pi\) |
0.473167 | − | 0.880973i | \(-0.343111\pi\) | |||||||
\(860\) | −254.887 | − | 407.966i | −0.296380 | − | 0.474380i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −222.068 | − | 128.211i | −0.257620 | − | 0.148737i | ||||
\(863\) | 179.328 | 0.207796 | 0.103898 | − | 0.994588i | \(-0.466868\pi\) | ||||
0.103898 | + | 0.994588i | \(0.466868\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.81656 | − | 52.1219i | −0.00210007 | − | 0.0602566i | ||||
\(866\) | 864.213 | + | 498.953i | 0.997936 | + | 0.576159i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −500.691 | + | 289.074i | −0.576833 | + | 0.333035i | ||||
\(869\) | −586.733 | + | 338.751i | −0.675182 | + | 0.389817i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 168.298 | − | 291.501i | 0.193224 | − | 0.334674i | ||||
\(872\) | 227.658 | 0.261075 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −983.868 | −1.12571 | ||||||||
\(875\) | 481.981 | − | 1081.95i | 0.550836 | − | 1.23651i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1045.75 | − | 603.765i | 1.19242 | − | 0.688443i | 0.233564 | − | 0.972341i | \(-0.424961\pi\) |
0.958854 | + | 0.283898i | \(0.0916278\pi\) | |||||||
\(878\) | −201.917 | − | 349.730i | −0.229973 | − | 0.398326i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −191.437 | + | 359.981i | −0.217542 | + | 0.409069i | ||||
\(881\) | − | 407.569i | − | 0.462621i | −0.972880 | − | 0.231311i | \(-0.925699\pi\) | ||
0.972880 | − | 0.231311i | \(-0.0743013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 85.9086i | 0.0972918i | 0.998816 | + | 0.0486459i | \(0.0154906\pi\) | ||||
−0.998816 | + | 0.0486459i | \(0.984509\pi\) | |||||||
\(884\) | −253.984 | − | 146.638i | −0.287312 | − | 0.165880i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −499.291 | − | 864.797i | −0.563534 | − | 0.976069i | ||||
\(887\) | 199.282 | + | 345.167i | 0.224670 | + | 0.389140i | 0.956220 | − | 0.292647i | \(-0.0945362\pi\) |
−0.731550 | + | 0.681787i | \(0.761203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −347.547 | + | 601.969i | −0.390942 | + | 0.677131i | ||||
\(890\) | −561.997 | + | 19.5868i | −0.631457 | + | 0.0220077i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 31.5461i | − | 0.0353655i | ||||||
\(893\) | −547.175 | + | 947.734i | −0.612738 | + | 1.06129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −165.489 | − | 264.878i | −0.184904 | − | 0.295953i | ||||
\(896\) | −92.8415 | + | 53.6021i | −0.103618 | + | 0.0598237i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 619.485 | + | 357.660i | 0.689850 | + | 0.398285i | ||||
\(899\) | 598.596i | 0.665847i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1481.97 | −1.64481 | ||||||||
\(902\) | 693.231 | − | 1200.71i | 0.768548 | − | 1.33116i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.1813 | + | 55.7397i | 0.0355988 | + | 0.0616589i | ||||
\(905\) | 1454.59 | − | 908.789i | 1.60728 | − | 1.00419i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1034.37 | − | 597.195i | −1.14043 | − | 0.658429i | −0.193895 | − | 0.981022i | \(-0.562112\pi\) |
−0.946538 | + | 0.322593i | \(0.895446\pi\) | |||||||
\(908\) | −682.692 | −0.751863 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −14.2590 | − | 409.128i | −0.0156692 | − | 0.449591i | ||||
\(911\) | 1168.23 | + | 674.478i | 1.28236 | + | 0.740371i | 0.977279 | − | 0.211956i | \(-0.0679833\pi\) |
0.305080 | + | 0.952327i | \(0.401317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −401.017 | + | 231.527i | −0.439230 | + | 0.253590i | ||||
\(914\) | 870.402 | − | 502.527i | 0.952300 | − | 0.549811i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −120.453 | + | 208.630i | −0.131498 | + | 0.227762i | ||||
\(917\) | 862.761 | 0.940852 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1571.32 | 1.70982 | 0.854908 | − | 0.518780i | \(-0.173614\pi\) | ||||
0.854908 | + | 0.518780i | \(0.173614\pi\) | |||||||
\(920\) | 540.381 | + | 287.373i | 0.587371 | + | 0.312362i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −168.543 | + | 97.3082i | −0.182801 | + | 0.105540i | ||||
\(923\) | −72.0907 | − | 124.865i | −0.0781048 | − | 0.135282i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1007.33 | − | 491.481i | −1.08901 | − | 0.531330i | ||||
\(926\) | − | 486.718i | − | 0.525614i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 110.996i | 0.119607i | ||||||||
\(929\) | −217.900 | − | 125.805i | −0.234554 | − | 0.135420i | 0.378117 | − | 0.925758i | \(-0.376572\pi\) |
−0.612671 | + | 0.790338i | \(0.709905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 327.829 | + | 567.816i | 0.352125 | + | 0.609899i | ||||
\(932\) | −307.400 | − | 532.433i | −0.329829 | − | 0.571280i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −228.194 | + | 395.243i | −0.244319 | + | 0.423173i | ||||
\(935\) | −2444.85 | + | 85.2083i | −2.61481 | + | 0.0911319i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1592.01i | 1.69905i | 0.527546 | + | 0.849526i | \(0.323112\pi\) | ||||
−0.527546 | + | 0.849526i | \(0.676888\pi\) | |||||||
\(938\) | 369.122 | − | 639.339i | 0.393521 | − | 0.681598i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 577.350 | − | 360.714i | 0.614203 | − | 0.383738i | ||||
\(941\) | −883.684 | + | 510.195i | −0.939091 | + | 0.542184i | −0.889675 | − | 0.456594i | \(-0.849069\pi\) |
−0.0494154 | + | 0.998778i | \(0.515736\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1802.43 | − | 1040.63i | −1.91138 | − | 1.10354i | ||||
\(944\) | 201.764i | 0.213734i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1386.85 | −1.46602 | ||||||||
\(947\) | 337.033 | − | 583.758i | 0.355895 | − | 0.616429i | −0.631375 | − | 0.775477i | \(-0.717509\pi\) |
0.987271 | + | 0.159048i | \(0.0508426\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 123.512 | + | 213.929i | 0.130149 | + | 0.225425i | ||||
\(950\) | 317.749 | + | 471.221i | 0.334473 | + | 0.496022i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −557.054 | − | 321.615i | −0.585140 | − | 0.337831i | ||||
\(953\) | −836.522 | −0.877778 | −0.438889 | − | 0.898541i | \(-0.644628\pi\) | ||||
−0.438889 | + | 0.898541i | \(0.644628\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 63.1499 | − | 2.20091i | 0.0661256 | − | 0.00230462i | ||||
\(956\) | 206.258 | + | 119.083i | 0.215751 | + | 0.124564i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 104.263 | − | 60.1963i | 0.108834 | − | 0.0628353i | ||||
\(959\) | 228.817 | − | 132.107i | 0.238599 | − | 0.137755i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1541 | − | 26.2477i | 0.0157691 | − | 0.0273129i | ||||
\(962\) | −387.390 | −0.402692 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −629.200 | −0.652697 | ||||||||
\(965\) | 394.699 | − | 742.199i | 0.409015 | − | 0.769118i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 881.781 | − | 509.096i | 0.911873 | − | 0.526470i | 0.0308394 | − | 0.999524i | \(-0.490182\pi\) |
0.881033 | + | 0.473054i | \(0.156849\pi\) | |||||||
\(968\) | 416.608 | + | 721.586i | 0.430380 | + | 0.745440i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 398.033 | − | 748.468i | 0.410344 | − | 0.771617i | ||||
\(971\) | 997.549i | 1.02734i | 0.857987 | + | 0.513671i | \(0.171715\pi\) | ||||
−0.857987 | + | 0.513671i | \(0.828285\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 329.163i | − | 0.338297i | ||||||
\(974\) | 535.635 | + | 309.249i | 0.549933 | + | 0.317504i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 97.9949 | + | 169.732i | 0.100405 | + | 0.173906i | ||||
\(977\) | −552.008 | − | 956.105i | −0.565003 | − | 0.978613i | −0.997049 | − | 0.0767621i | \(-0.975542\pi\) |
0.432047 | − | 0.901851i | \(-0.357792\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −810.612 | + | 1404.02i | −0.828000 | + | 1.43414i | ||||
\(980\) | −14.2065 | − | 407.622i | −0.0144965 | − | 0.415941i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 960.923i | 0.978537i | ||||||||
\(983\) | 608.302 | − | 1053.61i | 0.618822 | − | 1.07183i | −0.370879 | − | 0.928681i | \(-0.620944\pi\) |
0.989701 | − | 0.143150i | \(-0.0457230\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1577.63 | + | 985.659i | −1.60165 | + | 1.00067i | ||||
\(986\) | −576.755 | + | 332.990i | −0.584945 | + | 0.337718i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 170.117 | + | 98.2170i | 0.172183 | + | 0.0994099i | ||||
\(989\) | 2081.86i | 2.10502i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 736.595 | 0.743285 | 0.371642 | − | 0.928376i | \(-0.378795\pi\) | ||||
0.371642 | + | 0.928376i | \(0.378795\pi\) | |||||||
\(992\) | −86.2875 | + | 149.454i | −0.0869834 | + | 0.150660i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −158.114 | − | 273.861i | −0.159068 | − | 0.275514i | ||||
\(995\) | 983.020 | − | 614.165i | 0.987960 | − | 0.617252i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 650.499 | + | 375.566i | 0.652456 | + | 0.376696i | 0.789397 | − | 0.613884i | \(-0.210394\pi\) |
−0.136941 | + | 0.990579i | \(0.543727\pi\) | |||||||
\(998\) | 425.056 | 0.425908 | ||||||||
\(999\) | 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 | 810.3.j.h.269.6 | 24 | ||
3.2 | odd | 2 | inner | 810.3.j.h.269.12 | 24 | ||
5.4 | even | 2 | 810.3.j.g.269.12 | 24 | |||
9.2 | odd | 6 | 810.3.b.c.809.7 | ✓ | 24 | ||
9.4 | even | 3 | 810.3.j.g.539.6 | 24 | |||
9.5 | odd | 6 | 810.3.j.g.539.12 | 24 | |||
9.7 | even | 3 | 810.3.b.c.809.18 | yes | 24 | ||
15.14 | odd | 2 | 810.3.j.g.269.6 | 24 | |||
45.4 | even | 6 | inner | 810.3.j.h.539.12 | 24 | ||
45.14 | odd | 6 | inner | 810.3.j.h.539.6 | 24 | ||
45.29 | odd | 6 | 810.3.b.c.809.17 | yes | 24 | ||
45.34 | even | 6 | 810.3.b.c.809.8 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
810.3.b.c.809.7 | ✓ | 24 | 9.2 | odd | 6 | ||
810.3.b.c.809.8 | yes | 24 | 45.34 | even | 6 | ||
810.3.b.c.809.17 | yes | 24 | 45.29 | odd | 6 | ||
810.3.b.c.809.18 | yes | 24 | 9.7 | even | 3 | ||
810.3.j.g.269.6 | 24 | 15.14 | odd | 2 | |||
810.3.j.g.269.12 | 24 | 5.4 | even | 2 | |||
810.3.j.g.539.6 | 24 | 9.4 | even | 3 | |||
810.3.j.g.539.12 | 24 | 9.5 | odd | 6 | |||
810.3.j.h.269.6 | 24 | 1.1 | even | 1 | trivial | ||
810.3.j.h.269.12 | 24 | 3.2 | odd | 2 | inner | ||
810.3.j.h.539.6 | 24 | 45.14 | odd | 6 | inner | ||
810.3.j.h.539.12 | 24 | 45.4 | even | 6 | inner |