Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [720,2,Mod(179,720)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(720, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("720.179");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 720 = 2^{4} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 720.u (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.74922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 179.18 | ||
Character | \(\chi\) | \(=\) | 720.179 |
Dual form | 720.2.u.a.539.18 |
$q$-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 \(\left(\mathbb{Z}/720\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(271\) | \(577\) | \(641\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.612434 | − | 1.27473i | −0.433056 | − | 0.901367i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.24985 | + | 1.56137i | −0.624925 | + | 0.780685i | ||||
\(5\) | 2.22047 | + | 0.263678i | 0.993023 | + | 0.117921i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.95946i | − | 1.11857i | −0.828976 | − | 0.559284i | \(-0.811076\pi\) | ||
0.828976 | − | 0.559284i | \(-0.188924\pi\) | |||||||
\(8\) | 2.75577 | + | 0.636981i | 0.974311 | + | 0.225207i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.02377 | − | 2.99197i | −0.323745 | − | 0.946144i | ||||
\(11\) | −1.04021 | + | 1.04021i | −0.313636 | + | 0.313636i | −0.846317 | − | 0.532680i | \(-0.821185\pi\) |
0.532680 | + | 0.846317i | \(0.321185\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.00780247 | + | 0.00780247i | −0.00216402 | + | 0.00216402i | −0.708188 | − | 0.706024i | \(-0.750487\pi\) |
0.706024 | + | 0.708188i | \(0.250487\pi\) | |||||||
\(14\) | −3.77249 | + | 1.81247i | −1.00824 | + | 0.484403i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.875749 | − | 3.90296i | −0.218937 | − | 0.975739i | ||||
\(17\) | −2.00003 | −0.485079 | −0.242539 | − | 0.970142i | \(-0.577980\pi\) | ||||
−0.242539 | + | 0.970142i | \(0.577980\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.10608 | − | 5.10608i | 1.17141 | − | 1.17141i | 0.189542 | − | 0.981873i | \(-0.439300\pi\) |
0.981873 | − | 0.189542i | \(-0.0607003\pi\) | |||||||
\(20\) | −3.18695 | + | 3.13741i | −0.712624 | + | 0.701546i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.96305 | + | 0.688925i | 0.418524 | + | 0.146879i | ||||
\(23\) | 6.49393 | 1.35408 | 0.677039 | − | 0.735947i | \(-0.263263\pi\) | ||||
0.677039 | + | 0.735947i | \(0.263263\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.86095 | + | 1.17098i | 0.972189 | + | 0.234196i | ||||
\(26\) | 0.0147245 | + | 0.00516751i | 0.00288771 | + | 0.00101343i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.62080 | + | 3.69888i | 0.873250 | + | 0.699022i | ||||
\(29\) | −5.45997 | + | 5.45997i | −1.01389 | + | 1.01389i | −0.0139895 | + | 0.999902i | \(0.504453\pi\) |
−0.999902 | + | 0.0139895i | \(0.995547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.99178i | − | 0.896550i | −0.893896 | − | 0.448275i | \(-0.852039\pi\) | ||
0.893896 | − | 0.448275i | \(-0.147961\pi\) | |||||||
\(32\) | −4.43886 | + | 3.50664i | −0.784687 | + | 0.619892i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.22489 | + | 2.54949i | 0.210066 | + | 0.437234i | ||||
\(35\) | 0.780345 | − | 6.57137i | 0.131902 | − | 1.11076i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.74547 | − | 3.74547i | −0.615752 | − | 0.615752i | 0.328687 | − | 0.944439i | \(-0.393394\pi\) |
−0.944439 | + | 0.328687i | \(0.893394\pi\) | |||||||
\(38\) | −9.63598 | − | 3.38171i | −1.56316 | − | 0.548586i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.95113 | + | 2.14103i | 0.940957 | + | 0.338527i | ||||
\(41\) | 10.4245 | 1.62803 | 0.814017 | − | 0.580841i | \(-0.197276\pi\) | ||||
0.814017 | + | 0.580841i | \(0.197276\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.52161 | − | 3.52161i | 0.537040 | − | 0.537040i | −0.385618 | − | 0.922658i | \(-0.626012\pi\) |
0.922658 | + | 0.385618i | \(0.126012\pi\) | |||||||
\(44\) | −0.324047 | − | 2.92427i | −0.0488519 | − | 0.440850i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.97710 | − | 8.27798i | −0.586391 | − | 1.22052i | ||||
\(47\) | − | 10.6419i | − | 1.55228i | −0.630563 | − | 0.776138i | \(-0.717176\pi\) | ||
0.630563 | − | 0.776138i | \(-0.282824\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.75838 | −0.251197 | ||||||||
\(50\) | −1.48433 | − | 6.91352i | −0.209916 | − | 0.977719i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.00243062 | − | 0.0219345i | −0.000337066 | − | 0.00304176i | ||||
\(53\) | 2.98006 | − | 2.98006i | 0.409342 | − | 0.409342i | −0.472167 | − | 0.881509i | \(-0.656528\pi\) |
0.881509 | + | 0.472167i | \(0.156528\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.58404 | + | 2.03548i | −0.348432 | + | 0.274464i | ||||
\(56\) | 1.88512 | − | 8.15557i | 0.251909 | − | 1.08983i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.3038 | + | 3.61610i | 1.35296 | + | 0.474817i | ||||
\(59\) | −5.47867 | + | 5.47867i | −0.713262 | + | 0.713262i | −0.967216 | − | 0.253954i | \(-0.918269\pi\) |
0.253954 | + | 0.967216i | \(0.418269\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.67845 | − | 4.67845i | −0.599014 | − | 0.599014i | 0.341037 | − | 0.940050i | \(-0.389222\pi\) |
−0.940050 | + | 0.341037i | \(0.889222\pi\) | |||||||
\(62\) | −6.36315 | + | 3.05713i | −0.808120 | + | 0.388256i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.18851 | + | 3.51074i | 0.898564 | + | 0.438843i | ||||
\(65\) | −0.0193825 | + | 0.0152678i | −0.00240410 | + | 0.00189374i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.29404 | + | 2.29404i | 0.280261 | + | 0.280261i | 0.833213 | − | 0.552952i | \(-0.186499\pi\) |
−0.552952 | + | 0.833213i | \(0.686499\pi\) | |||||||
\(68\) | 2.49974 | − | 3.12279i | 0.303138 | − | 0.378693i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.85461 | + | 3.02980i | −1.05833 | + | 0.362131i | ||||
\(71\) | − | 0.212315i | − | 0.0251971i | −0.999921 | − | 0.0125986i | \(-0.995990\pi\) | ||
0.999921 | − | 0.0125986i | \(-0.00401036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.4980 | −1.93094 | −0.965472 | − | 0.260505i | \(-0.916111\pi\) | ||||
−0.965472 | + | 0.260505i | \(0.916111\pi\) | |||||||
\(74\) | −2.48059 | + | 7.06830i | −0.288363 | + | 0.821673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.59064 | + | 14.3543i | 0.182459 | + | 1.64655i | ||||
\(77\) | 3.07847 | + | 3.07847i | 0.350824 | + | 0.350824i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.54833i | − | 0.511727i | −0.966713 | − | 0.255863i | \(-0.917640\pi\) | ||
0.966713 | − | 0.255863i | \(-0.0823597\pi\) | |||||||
\(80\) | −0.915447 | − | 8.89730i | −0.102350 | − | 0.994748i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.38432 | − | 13.2884i | −0.705030 | − | 1.46746i | ||||
\(83\) | −4.68359 | + | 4.68359i | −0.514090 | + | 0.514090i | −0.915777 | − | 0.401687i | \(-0.868424\pi\) |
0.401687 | + | 0.915777i | \(0.368424\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.44100 | − | 0.527365i | −0.481694 | − | 0.0572008i | ||||
\(86\) | −6.64583 | − | 2.33233i | −0.716639 | − | 0.251502i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.52918 | + | 2.20399i | −0.376212 | + | 0.234946i | ||||
\(89\) | −0.123094 | −0.0130479 | −0.00652395 | − | 0.999979i | \(-0.502077\pi\) | ||||
−0.00652395 | + | 0.999979i | \(0.502077\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0230911 | + | 0.0230911i | 0.00242060 | + | 0.00242060i | ||||
\(92\) | −8.11644 | + | 10.1394i | −0.846197 | + | 1.05711i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −13.5655 | + | 6.51744i | −1.39917 | + | 0.672223i | ||||
\(95\) | 12.6842 | − | 9.99152i | 1.30138 | − | 1.02511i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.29464i | − | 0.842193i | −0.907016 | − | 0.421096i | \(-0.861645\pi\) | ||
0.907016 | − | 0.421096i | \(-0.138355\pi\) | |||||||
\(98\) | 1.07689 | + | 2.24145i | 0.108782 | + | 0.226420i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.90379 | + | 6.12619i | −0.790379 | + | 0.612619i | ||||
\(101\) | 7.95152 | + | 7.95152i | 0.791205 | + | 0.791205i | 0.981690 | − | 0.190485i | \(-0.0610060\pi\) |
−0.190485 | + | 0.981690i | \(0.561006\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.14632i | 0.605615i | 0.953052 | + | 0.302808i | \(0.0979240\pi\) | ||||
−0.953052 | + | 0.302808i | \(0.902076\pi\) | |||||||
\(104\) | −0.0264718 | + | 0.0165318i | −0.00259578 | + | 0.00162107i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.62384 | − | 1.97367i | −0.546236 | − | 0.191699i | ||||
\(107\) | 5.83941 | + | 5.83941i | 0.564517 | + | 0.564517i | 0.930587 | − | 0.366070i | \(-0.119297\pi\) |
−0.366070 | + | 0.930587i | \(0.619297\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.9696 | + | 10.9696i | 1.05070 | + | 1.05070i | 0.998644 | + | 0.0520513i | \(0.0165759\pi\) |
0.0520513 | + | 0.998644i | \(0.483424\pi\) | |||||||
\(110\) | 4.17723 | + | 2.04735i | 0.398283 | + | 0.195207i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −11.5506 | + | 2.59174i | −1.09143 | + | 0.244896i | ||||
\(113\) | −9.95287 | −0.936288 | −0.468144 | − | 0.883652i | \(-0.655077\pi\) | ||||
−0.468144 | + | 0.883652i | \(0.655077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4196 | + | 1.71231i | 1.34463 | + | 0.159674i | ||||
\(116\) | −1.70089 | − | 15.3492i | −0.157923 | − | 1.42514i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.3391 | + | 3.62848i | 0.951794 | + | 0.334029i | ||||
\(119\) | 5.91900i | 0.542594i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.83591i | 0.803264i | ||||||||
\(122\) | −3.09850 | + | 8.82897i | −0.280525 | + | 0.799337i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.79401 | + | 6.23897i | 0.699923 | + | 0.560276i | ||||
\(125\) | 10.4848 | + | 3.88185i | 0.937790 | + | 0.347203i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.542244 | −0.0481164 | −0.0240582 | − | 0.999711i | \(-0.507659\pi\) | ||||
−0.0240582 | + | 0.999711i | \(0.507659\pi\) | |||||||
\(128\) | 0.0727470 | − | 11.3135i | 0.00642998 | − | 0.999979i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.0313327 | + | 0.0153568i | 0.00274806 | + | 0.00134688i | ||||
\(131\) | −5.55272 | − | 5.55272i | −0.485143 | − | 0.485143i | 0.421626 | − | 0.906770i | \(-0.361459\pi\) |
−0.906770 | + | 0.421626i | \(0.861459\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −15.1112 | − | 15.1112i | −1.31031 | − | 1.31031i | ||||
\(134\) | 1.51932 | − | 4.32922i | 0.131250 | − | 0.373987i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.51162 | − | 1.27398i | −0.472617 | − | 0.109243i | ||||
\(137\) | 5.80371i | 0.495844i | 0.968780 | + | 0.247922i | \(0.0797477\pi\) | ||||
−0.968780 | + | 0.247922i | \(0.920252\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.27873 | + | 6.27873i | 0.532555 | + | 0.532555i | 0.921332 | − | 0.388777i | \(-0.127102\pi\) |
−0.388777 | + | 0.921332i | \(0.627102\pi\) | |||||||
\(140\) | 9.28503 | + | 9.43164i | 0.784728 | + | 0.797119i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.270643 | + | 0.130029i | −0.0227119 | + | 0.0109118i | ||||
\(143\) | − | 0.0162325i | − | 0.00135743i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −13.5634 | + | 10.6840i | −1.12638 | + | 0.887259i | ||||
\(146\) | 10.1039 | + | 21.0304i | 0.836207 | + | 1.74049i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.5293 | − | 1.16679i | 0.865506 | − | 0.0959092i | ||||
\(149\) | 12.6568 | + | 12.6568i | 1.03689 | + | 1.03689i | 0.999293 | + | 0.0375933i | \(0.0119691\pi\) |
0.0375933 | + | 0.999293i | \(0.488031\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.1332 | 1.39428 | 0.697140 | − | 0.716935i | \(-0.254456\pi\) | ||||
0.697140 | + | 0.716935i | \(0.254456\pi\) | |||||||
\(152\) | 17.3236 | − | 10.8187i | 1.40513 | − | 0.877512i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.03884 | − | 5.80956i | 0.164295 | − | 0.468147i | ||||
\(155\) | 1.31622 | − | 11.0841i | 0.105722 | − | 0.890294i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.80235 | − | 4.80235i | 0.383269 | − | 0.383269i | −0.489009 | − | 0.872279i | \(-0.662642\pi\) |
0.872279 | + | 0.489009i | \(0.162642\pi\) | |||||||
\(158\) | −5.79787 | + | 2.78555i | −0.461254 | + | 0.221606i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −10.7810 | + | 6.61595i | −0.852310 | + | 0.523037i | ||||
\(161\) | − | 19.2185i | − | 1.51463i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.778039 | + | 0.778039i | 0.0609407 | + | 0.0609407i | 0.736920 | − | 0.675980i | \(-0.236279\pi\) |
−0.675980 | + | 0.736920i | \(0.736279\pi\) | |||||||
\(164\) | −13.0291 | + | 16.2765i | −1.01740 | + | 1.27098i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.83867 | + | 3.10190i | 0.686014 | + | 0.240754i | ||||
\(167\) | −5.26638 | −0.407525 | −0.203763 | − | 0.979020i | \(-0.565317\pi\) | ||||
−0.203763 | + | 0.979020i | \(0.565317\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9999i | 0.999991i | ||||||||
\(170\) | 2.04757 | + | 5.98403i | 0.157042 | + | 0.458954i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.09705 | + | 9.90001i | 0.0836492 | + | 0.754869i | ||||
\(173\) | 8.51881 | + | 8.51881i | 0.647673 | + | 0.647673i | 0.952430 | − | 0.304757i | \(-0.0985752\pi\) |
−0.304757 | + | 0.952430i | \(0.598575\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.46546 | − | 14.3858i | 0.261964 | − | 1.08746i | ||||
\(176\) | 4.97088 | + | 3.14894i | 0.374694 | + | 0.237361i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.0753866 | + | 0.156911i | 0.00565047 | + | 0.0117609i | ||||
\(179\) | −10.2479 | − | 10.2479i | −0.765966 | − | 0.765966i | 0.211428 | − | 0.977394i | \(-0.432189\pi\) |
−0.977394 | + | 0.211428i | \(0.932189\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.590728 | + | 0.590728i | −0.0439085 | + | 0.0439085i | −0.728720 | − | 0.684812i | \(-0.759884\pi\) |
0.684812 | + | 0.728720i | \(0.259884\pi\) | |||||||
\(182\) | 0.0152930 | − | 0.0435765i | 0.00113359 | − | 0.00323011i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.8958 | + | 4.13651i | 1.31929 | + | 0.304947i | ||||
\(185\) | −7.32909 | − | 9.30429i | −0.538846 | − | 0.684065i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.08046 | − | 2.08046i | 0.152138 | − | 0.152138i | ||||
\(188\) | 16.6159 | + | 13.3007i | 1.21184 | + | 0.970057i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −20.5047 | − | 10.0498i | −1.48757 | − | 0.729088i | ||||
\(191\) | −15.2046 | −1.10017 | −0.550083 | − | 0.835110i | \(-0.685404\pi\) | ||||
−0.550083 | + | 0.835110i | \(0.685404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.4277i | 0.894566i | 0.894392 | + | 0.447283i | \(0.147608\pi\) | ||||
−0.894392 | + | 0.447283i | \(0.852392\pi\) | |||||||
\(194\) | −10.5734 | + | 5.07991i | −0.759125 | + | 0.364717i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.19771 | − | 2.74547i | 0.156979 | − | 0.196105i | ||||
\(197\) | 7.54210 | − | 7.54210i | 0.537352 | − | 0.537352i | −0.385398 | − | 0.922750i | \(-0.625936\pi\) |
0.922750 | + | 0.385398i | \(0.125936\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0231 | 0.710517 | 0.355258 | − | 0.934768i | \(-0.384393\pi\) | ||||
0.355258 | + | 0.934768i | \(0.384393\pi\) | |||||||
\(200\) | 12.6498 | + | 6.32327i | 0.894472 | + | 0.447123i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.26622 | − | 15.0058i | 0.370530 | − | 1.05580i | ||||
\(203\) | 16.1585 | + | 16.1585i | 1.13411 | + | 1.13411i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.1473 | + | 2.74872i | 1.61668 | + | 0.191979i | ||||
\(206\) | 7.83488 | − | 3.76421i | 0.545882 | − | 0.262265i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.0372857 | + | 0.0236197i | 0.00258530 | + | 0.00163773i | ||||
\(209\) | 10.6228i | 0.734796i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.9950 | + | 15.9950i | −1.10114 | + | 1.10114i | −0.106867 | + | 0.994273i | \(0.534082\pi\) |
−0.994273 | + | 0.106867i | \(0.965918\pi\) | |||||||
\(212\) | 0.928345 | + | 8.37759i | 0.0637590 | + | 0.575375i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.86739 | − | 11.0199i | 0.264370 | − | 0.753305i | ||||
\(215\) | 8.74819 | − | 6.89104i | 0.596621 | − | 0.469965i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.7729 | −1.00285 | ||||||||
\(218\) | 7.26507 | − | 20.7014i | 0.492052 | − | 1.40207i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0515320 | − | 6.57869i | 0.00347428 | − | 0.443535i | ||||
\(221\) | 0.0156052 | − | 0.0156052i | 0.00104972 | − | 0.00104972i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −26.9611 | −1.80545 | −0.902724 | − | 0.430221i | \(-0.858436\pi\) | ||||
−0.902724 | + | 0.430221i | \(0.858436\pi\) | |||||||
\(224\) | 10.3777 | + | 13.1366i | 0.693392 | + | 0.877726i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.09547 | + | 12.6872i | 0.405465 | + | 0.843939i | ||||
\(227\) | −4.80422 | + | 4.80422i | −0.318867 | + | 0.318867i | −0.848332 | − | 0.529465i | \(-0.822393\pi\) |
0.529465 | + | 0.848332i | \(0.322393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.77289 | + | 3.77289i | −0.249320 | + | 0.249320i | −0.820691 | − | 0.571372i | \(-0.806412\pi\) |
0.571372 | + | 0.820691i | \(0.306412\pi\) | |||||||
\(230\) | −6.64829 | − | 19.4296i | −0.438376 | − | 1.28115i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −18.5243 | + | 11.5685i | −1.21618 | + | 0.759511i | ||||
\(233\) | 12.2685i | 0.803737i | 0.915697 | + | 0.401868i | \(0.131639\pi\) | ||||
−0.915697 | + | 0.401868i | \(0.868361\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.80603 | − | 23.6299i | 0.183045 | − | 1.54145i | ||||
\(236\) | −1.70671 | − | 15.4018i | −0.111097 | − | 1.00257i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.54510 | − | 3.62499i | 0.489076 | − | 0.234974i | ||||
\(239\) | 12.4166 | 0.803164 | 0.401582 | − | 0.915823i | \(-0.368460\pi\) | ||||
0.401582 | + | 0.915823i | \(0.368460\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6958 | −1.07547 | −0.537735 | − | 0.843114i | \(-0.680720\pi\) | ||||
−0.537735 | + | 0.843114i | \(0.680720\pi\) | |||||||
\(242\) | 11.2634 | − | 5.41141i | 0.724036 | − | 0.347858i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.1521 | − | 1.45743i | 0.841979 | − | 0.0933021i | ||||
\(245\) | −3.90442 | − | 0.463646i | −0.249444 | − | 0.0296212i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0796800i | 0.00506992i | ||||||||
\(248\) | 3.17967 | − | 13.7562i | 0.201909 | − | 0.873518i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.47296 | − | 15.7426i | −0.0931583 | − | 0.995651i | ||||
\(251\) | −18.3923 | + | 18.3923i | −1.16091 | + | 1.16091i | −0.176634 | + | 0.984277i | \(0.556521\pi\) |
−0.984277 | + | 0.176634i | \(0.943479\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.75507 | + | 6.75507i | −0.424688 | + | 0.424688i | ||||
\(254\) | 0.332089 | + | 0.691212i | 0.0208371 | + | 0.0433705i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −14.4661 | + | 6.83602i | −0.904133 | + | 0.427251i | ||||
\(257\) | −29.8867 | −1.86428 | −0.932142 | − | 0.362094i | \(-0.882062\pi\) | ||||
−0.932142 | + | 0.362094i | \(0.882062\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.0846 | + | 11.0846i | −0.688761 | + | 0.688761i | ||||
\(260\) | 0.000386533 | − | 0.0493456i | 2.39717e−5 | − | 0.00306029i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.67752 | + | 10.4789i | −0.227198 | + | 0.647386i | ||||
\(263\) | −17.6640 | −1.08921 | −0.544605 | − | 0.838693i | \(-0.683320\pi\) | ||||
−0.544605 | + | 0.838693i | \(0.683320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.40289 | − | 5.83134i | 0.454756 | − | 0.358216i | ||||
\(266\) | −10.0080 | + | 28.5173i | −0.613632 | + | 1.74851i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.44905 | + | 0.714637i | −0.393938 | + | 0.0436534i | ||||
\(269\) | −0.0280978 | + | 0.0280978i | −0.00171315 | + | 0.00171315i | −0.707963 | − | 0.706250i | \(-0.750386\pi\) |
0.706250 | + | 0.707963i | \(0.250386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.7422i | − | 0.834779i | −0.908728 | − | 0.417390i | \(-0.862945\pi\) | ||
0.908728 | − | 0.417390i | \(-0.137055\pi\) | |||||||
\(272\) | 1.75152 | + | 7.80603i | 0.106202 | + | 0.473310i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.39813 | − | 3.55439i | 0.446938 | − | 0.214728i | ||||
\(275\) | −6.27449 | + | 3.83836i | −0.378366 | + | 0.231462i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 23.0188 | + | 23.0188i | 1.38306 | + | 1.38306i | 0.839126 | + | 0.543937i | \(0.183067\pi\) |
0.543937 | + | 0.839126i | \(0.316933\pi\) | |||||||
\(278\) | 4.15835 | − | 11.8490i | 0.249401 | − | 0.710654i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.33629 | − | 17.6121i | 0.378666 | − | 1.05253i | ||||
\(281\) | 19.3294 | 1.15309 | 0.576547 | − | 0.817064i | \(-0.304400\pi\) | ||||
0.576547 | + | 0.817064i | \(0.304400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.78511 | + | 2.78511i | −0.165557 | + | 0.165557i | −0.785023 | − | 0.619466i | \(-0.787349\pi\) |
0.619466 | + | 0.785023i | \(0.287349\pi\) | |||||||
\(284\) | 0.331502 | + | 0.265362i | 0.0196710 | + | 0.0157463i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0206920 | + | 0.00994132i | −0.00122354 | + | 0.000587842i | ||||
\(287\) | − | 30.8509i | − | 1.82107i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.9999 | −0.764699 | ||||||||
\(290\) | 21.9258 | + | 10.7463i | 1.28753 | + | 0.631046i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 20.6200 | − | 25.7595i | 1.20670 | − | 1.50746i | ||||
\(293\) | −17.8866 | + | 17.8866i | −1.04495 | + | 1.04495i | −0.0460045 | + | 0.998941i | \(0.514649\pi\) |
−0.998941 | + | 0.0460045i | \(0.985351\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.6098 | + | 10.7206i | −0.792394 | + | 0.624178i | ||||
\(296\) | −7.93585 | − | 12.7074i | −0.461262 | − | 0.738605i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.38250 | − | 23.8854i | 0.485585 | − | 1.38365i | ||||
\(299\) | −0.0506687 | + | 0.0506687i | −0.00293025 | + | 0.00293025i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.4220 | − | 10.4220i | −0.600716 | − | 0.600716i | ||||
\(302\) | −10.4929 | − | 21.8401i | −0.603801 | − | 1.25676i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24.4004 | − | 15.4572i | −1.39946 | − | 0.886529i | ||||
\(305\) | −9.15473 | − | 11.6219i | −0.524198 | − | 0.665470i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.4113 | + | 23.4113i | 1.33615 | + | 1.33615i | 0.899754 | + | 0.436397i | \(0.143746\pi\) |
0.436397 | + | 0.899754i | \(0.356254\pi\) | |||||||
\(308\) | −8.65425 | + | 0.959002i | −0.493121 | + | 0.0546442i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.9353 | + | 5.11044i | −0.848265 | + | 0.290253i | ||||
\(311\) | − | 24.0385i | − | 1.36310i | −0.731772 | − | 0.681549i | \(-0.761307\pi\) | ||
0.731772 | − | 0.681549i | \(-0.238693\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.7757 | 1.00474 | 0.502371 | − | 0.864652i | \(-0.332461\pi\) | ||||
0.502371 | + | 0.864652i | \(0.332461\pi\) | |||||||
\(314\) | −9.06280 | − | 3.18056i | −0.511444 | − | 0.179489i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.10162 | + | 5.68473i | 0.399497 | + | 0.319791i | ||||
\(317\) | 4.69302 | + | 4.69302i | 0.263586 | + | 0.263586i | 0.826509 | − | 0.562923i | \(-0.190323\pi\) |
−0.562923 | + | 0.826509i | \(0.690323\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 11.3591i | − | 0.635987i | ||||||
\(320\) | 15.0361 | + | 9.69094i | 0.840546 | + | 0.541740i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −24.4983 | + | 11.7700i | −1.36524 | + | 0.655919i | ||||
\(323\) | −10.2123 | + | 10.2123i | −0.568228 | + | 0.568228i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.0470639 | + | 0.0287909i | −0.00261064 | + | 0.00159703i | ||||
\(326\) | 0.515289 | − | 1.46828i | 0.0285392 | − | 0.0813207i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 28.7275 | + | 6.64021i | 1.58621 | + | 0.366644i | ||||
\(329\) | −31.4942 | −1.73633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.1568 | + | 20.1568i | 1.10792 | + | 1.10792i | 0.993424 | + | 0.114494i | \(0.0365247\pi\) |
0.114494 | + | 0.993424i | \(0.463475\pi\) | |||||||
\(332\) | −1.45903 | − | 13.1666i | −0.0800745 | − | 0.722610i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.22531 | + | 6.71320i | 0.176481 | + | 0.367330i | ||||
\(335\) | 4.48895 | + | 5.69873i | 0.245258 | + | 0.311355i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.5791i | 1.22996i | 0.788542 | + | 0.614980i | \(0.210836\pi\) | ||||
−0.788542 | + | 0.614980i | \(0.789164\pi\) | |||||||
\(338\) | 16.5713 | − | 7.96156i | 0.901359 | − | 0.433052i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.37400 | − | 6.27492i | 0.345679 | − | 0.340305i | ||||
\(341\) | 5.19252 | + | 5.19252i | 0.281191 | + | 0.281191i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 15.5124i | − | 0.837588i | ||||||
\(344\) | 11.9479 | − | 7.46154i | 0.644189 | − | 0.402299i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.64194 | − | 16.0764i | 0.303313 | − | 0.864270i | ||||
\(347\) | 8.61782 | + | 8.61782i | 0.462629 | + | 0.462629i | 0.899516 | − | 0.436887i | \(-0.143919\pi\) |
−0.436887 | + | 0.899516i | \(0.643919\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4945 | + | 11.4945i | 0.615284 | + | 0.615284i | 0.944318 | − | 0.329034i | \(-0.106723\pi\) |
−0.329034 | + | 0.944318i | \(0.606723\pi\) | |||||||
\(350\) | −20.4603 | + | 4.39281i | −1.09365 | + | 0.234806i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.969707 | − | 8.26502i | 0.0516855 | − | 0.440527i | ||||
\(353\) | −17.2352 | −0.917336 | −0.458668 | − | 0.888608i | \(-0.651673\pi\) | ||||
−0.458668 | + | 0.888608i | \(0.651673\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0559829 | − | 0.471438i | 0.00297126 | − | 0.0250213i | ||||
\(356\) | 0.153849 | − | 0.192195i | 0.00815396 | − | 0.0101863i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.78711 | + | 19.3395i | −0.358710 | + | 1.02212i | ||||
\(359\) | 2.27145i | 0.119882i | 0.998202 | + | 0.0599412i | \(0.0190913\pi\) | ||||
−0.998202 | + | 0.0599412i | \(0.980909\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 33.1441i | − | 1.74442i | ||||||
\(362\) | 1.11480 | + | 0.391234i | 0.0585925 | + | 0.0205628i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0649140 | + | 0.00719331i | −0.00340242 | + | 0.000377032i | ||||
\(365\) | −36.6333 | − | 4.35017i | −1.91747 | − | 0.227698i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.1335 | 1.62516 | 0.812579 | − | 0.582852i | \(-0.198063\pi\) | ||||
0.812579 | + | 0.582852i | \(0.198063\pi\) | |||||||
\(368\) | −5.68705 | − | 25.3455i | −0.296458 | − | 1.32123i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.37184 | + | 15.0408i | −0.383244 | + | 0.781936i | ||||
\(371\) | −8.81934 | − | 8.81934i | −0.457877 | − | 0.457877i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3199 | − | 20.3199i | −1.05212 | − | 1.05212i | −0.998565 | − | 0.0535601i | \(-0.982943\pi\) |
−0.0535601 | − | 0.998565i | \(-0.517057\pi\) | |||||||
\(374\) | −3.92616 | − | 1.37787i | −0.203017 | − | 0.0712480i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.77867 | − | 29.3265i | 0.349583 | − | 1.51240i | ||||
\(377\) | − | 0.0852026i | − | 0.00438816i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.61527 | − | 9.61527i | −0.493903 | − | 0.493903i | 0.415630 | − | 0.909534i | \(-0.363561\pi\) |
−0.909534 | + | 0.415630i | \(0.863561\pi\) | |||||||
\(380\) | −0.252954 | + | 32.2927i | −0.0129763 | + | 1.65658i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.31180 | + | 19.3817i | 0.476433 | + | 0.991653i | ||||
\(383\) | 1.17749i | 0.0601668i | 0.999547 | + | 0.0300834i | \(0.00957728\pi\) | ||||
−0.999547 | + | 0.0300834i | \(0.990423\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.02391 | + | 7.64736i | 0.307007 | + | 0.389746i | ||||
\(386\) | 15.8419 | − | 7.61115i | 0.806333 | − | 0.387397i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.9510 | + | 10.3671i | 0.657487 | + | 0.526307i | ||||
\(389\) | −23.7967 | − | 23.7967i | −1.20654 | − | 1.20654i | −0.972139 | − | 0.234403i | \(-0.924686\pi\) |
−0.234403 | − | 0.972139i | \(-0.575314\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.9881 | −0.656834 | ||||||||
\(392\) | −4.84568 | − | 1.12005i | −0.244744 | − | 0.0565712i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.2331 | − | 4.99507i | −0.717055 | − | 0.251648i | ||||
\(395\) | 1.19930 | − | 10.0994i | 0.0603431 | − | 0.508156i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.88396 | − | 5.88396i | 0.295308 | − | 0.295308i | −0.543865 | − | 0.839173i | \(-0.683040\pi\) |
0.839173 | + | 0.543865i | \(0.183040\pi\) | |||||||
\(398\) | −6.13847 | − | 12.7767i | −0.307693 | − | 0.640436i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.313307 | − | 19.9975i | 0.0156654 | − | 0.999877i | ||||
\(401\) | − | 15.4433i | − | 0.771202i | −0.922666 | − | 0.385601i | \(-0.873994\pi\) | ||
0.922666 | − | 0.385601i | \(-0.126006\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0389482 | + | 0.0389482i | 0.00194015 | + | 0.00194015i | ||||
\(404\) | −22.3535 | + | 2.47705i | −1.11213 | + | 0.123238i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 10.7017 | − | 30.4938i | 0.531115 | − | 1.51338i | ||||
\(407\) | 7.79218 | 0.386244 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.72546i | − | 0.431446i | −0.976455 | − | 0.215723i | \(-0.930789\pi\) | ||
0.976455 | − | 0.215723i | \(-0.0692109\pi\) | |||||||
\(410\) | −10.6723 | − | 31.1898i | −0.527068 | − | 1.54036i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.59668 | − | 7.68198i | −0.472795 | − | 0.378464i | ||||
\(413\) | 16.2139 | + | 16.2139i | 0.797833 | + | 0.797833i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −11.6347 | + | 9.16479i | −0.571125 | + | 0.449882i | ||||
\(416\) | 0.00727361 | − | 0.0619945i | 0.000356618 | − | 0.00303953i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.5412 | − | 6.50578i | 0.662321 | − | 0.318208i | ||||
\(419\) | 4.83085 | + | 4.83085i | 0.236003 | + | 0.236003i | 0.815193 | − | 0.579190i | \(-0.196631\pi\) |
−0.579190 | + | 0.815193i | \(0.696631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.2440 | − | 20.2440i | 0.986633 | − | 0.986633i | −0.0132784 | − | 0.999912i | \(-0.504227\pi\) |
0.999912 | + | 0.0132784i | \(0.00422678\pi\) | |||||||
\(422\) | 30.1851 | + | 10.5934i | 1.46939 | + | 0.515676i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.1106 | − | 6.31410i | 0.491013 | − | 0.306640i | ||||
\(425\) | −9.72204 | − | 2.34199i | −0.471588 | − | 0.113603i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8456 | + | 13.8456i | −0.670038 | + | 0.670038i | ||||
\(428\) | −16.4159 | + | 1.81909i | −0.793491 | + | 0.0879290i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.1419 | − | 6.93123i | −0.681982 | − | 0.334254i | ||||
\(431\) | −6.63538 | −0.319615 | −0.159808 | − | 0.987148i | \(-0.551087\pi\) | ||||
−0.159808 | + | 0.987148i | \(0.551087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.17952i | 0.104741i | 0.998628 | + | 0.0523706i | \(0.0166777\pi\) | ||||
−0.998628 | + | 0.0523706i | \(0.983322\pi\) | |||||||
\(434\) | 9.04745 | + | 18.8314i | 0.434291 | + | 0.903938i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.8379 | + | 3.41724i | −1.47687 | + | 0.163656i | ||||
\(437\) | 33.1585 | − | 33.1585i | 1.58619 | − | 1.58619i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −18.1795 | −0.867661 | −0.433830 | − | 0.900995i | \(-0.642838\pi\) | ||||
−0.433830 | + | 0.900995i | \(0.642838\pi\) | |||||||
\(440\) | −8.41758 | + | 3.96332i | −0.401293 | + | 0.188944i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0294495 | − | 0.0103352i | −0.00140077 | − | 0.000491595i | ||||
\(443\) | −20.1844 | − | 20.1844i | −0.958989 | − | 0.958989i | 0.0402025 | − | 0.999192i | \(-0.487200\pi\) |
−0.999192 | + | 0.0402025i | \(0.987200\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.273325 | − | 0.0324571i | −0.0129569 | − | 0.00153862i | ||||
\(446\) | 16.5119 | + | 34.3680i | 0.781860 | + | 1.62737i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.3899 | − | 21.2741i | 0.490876 | − | 1.00511i | ||||
\(449\) | − | 31.3405i | − | 1.47905i | −0.673129 | − | 0.739525i | \(-0.735050\pi\) | ||
0.673129 | − | 0.739525i | \(-0.264950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.8437 | + | 10.8437i | −0.510611 | + | 0.510611i | ||||
\(452\) | 12.4396 | − | 15.5401i | 0.585110 | − | 0.730945i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.06633 | + | 3.18180i | 0.425504 | + | 0.149329i | ||||
\(455\) | 0.0451843 | + | 0.0573616i | 0.00211827 | + | 0.00268915i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.6212 | 0.730727 | 0.365364 | − | 0.930865i | \(-0.380945\pi\) | ||||
0.365364 | + | 0.930865i | \(0.380945\pi\) | |||||||
\(458\) | 7.12005 | + | 2.49876i | 0.332698 | + | 0.116759i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −20.6958 | + | 20.3741i | −0.964948 | + | 0.949948i | ||||
\(461\) | 9.98698 | − | 9.98698i | 0.465140 | − | 0.465140i | −0.435196 | − | 0.900336i | \(-0.643321\pi\) |
0.900336 | + | 0.435196i | \(0.143321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.8119 | −1.29253 | −0.646264 | − | 0.763114i | \(-0.723670\pi\) | ||||
−0.646264 | + | 0.763114i | \(0.723670\pi\) | |||||||
\(464\) | 26.0916 | + | 16.5285i | 1.21127 | + | 0.767315i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 15.6390 | − | 7.51365i | 0.724462 | − | 0.348063i | ||||
\(467\) | −10.4295 | + | 10.4295i | −0.482620 | + | 0.482620i | −0.905967 | − | 0.423348i | \(-0.860855\pi\) |
0.423348 | + | 0.905967i | \(0.360855\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.78911 | − | 6.78911i | 0.313492 | − | 0.313492i | ||||
\(470\) | −31.8402 | + | 10.8948i | −1.46868 | + | 0.502542i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.5878 | + | 11.6081i | −0.855571 | + | 0.534308i | ||||
\(473\) | 7.32645i | 0.336871i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 30.7995 | − | 18.8413i | 1.41318 | − | 0.864497i | ||||
\(476\) | −9.24175 | − | 7.39786i | −0.423595 | − | 0.339081i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.60435 | − | 15.8278i | −0.347815 | − | 0.723946i | ||||
\(479\) | 23.5450 | 1.07580 | 0.537900 | − | 0.843009i | \(-0.319218\pi\) | ||||
0.537900 | + | 0.843009i | \(0.319218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0584478 | 0.00266499 | ||||||||
\(482\) | 10.2251 | + | 21.2825i | 0.465739 | + | 0.969393i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.7961 | − | 11.0436i | −0.627096 | − | 0.501980i | ||||
\(485\) | 2.18712 | − | 18.4180i | 0.0993119 | − | 0.836317i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.4005i | − | 0.697865i | −0.937148 | − | 0.348932i | \(-0.886544\pi\) | ||
0.937148 | − | 0.348932i | \(-0.113456\pi\) | |||||||
\(488\) | −9.91263 | − | 15.8728i | −0.448724 | − | 0.718527i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.80017 | + | 5.26101i | 0.0813236 | + | 0.237668i | ||||
\(491\) | −11.9089 | + | 11.9089i | −0.537443 | + | 0.537443i | −0.922777 | − | 0.385334i | \(-0.874086\pi\) |
0.385334 | + | 0.922777i | \(0.374086\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.9201 | − | 10.9201i | 0.491817 | − | 0.491817i | ||||
\(494\) | 0.101570 | − | 0.0487987i | 0.00456986 | − | 0.00219556i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.4827 | + | 4.37154i | −0.874798 | + | 0.196288i | ||||
\(497\) | −0.628336 | −0.0281847 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.4502 | − | 16.4502i | 0.736411 | − | 0.736411i | −0.235471 | − | 0.971881i | \(-0.575663\pi\) |
0.971881 | + | 0.235471i | \(0.0756631\pi\) | |||||||
\(500\) | −19.1654 | + | 11.5189i | −0.857105 | + | 0.515143i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 34.7092 | + | 12.1811i | 1.54915 | + | 0.543667i | ||||
\(503\) | 11.4298 | 0.509632 | 0.254816 | − | 0.966990i | \(-0.417985\pi\) | ||||
0.254816 | + | 0.966990i | \(0.417985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.5594 | + | 19.7527i | 0.692386 | + | 0.878985i | ||||
\(506\) | 12.7479 | + | 4.47383i | 0.566713 | + | 0.198886i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.677724 | − | 0.846643i | 0.0300691 | − | 0.0375637i | ||||
\(509\) | −26.8748 | + | 26.8748i | −1.19120 | + | 1.19120i | −0.214473 | + | 0.976730i | \(0.568803\pi\) |
−0.976730 | + | 0.214473i | \(0.931197\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.8251i | 2.15990i | ||||||||
\(512\) | 17.5736 | + | 14.2537i | 0.776650 | + | 0.629932i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.3036 | + | 38.0974i | 0.807339 | + | 1.68040i | ||||
\(515\) | −1.62065 | + | 13.6477i | −0.0714145 | + | 0.601390i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.0698 | + | 11.0698i | 0.486850 | + | 0.486850i | ||||
\(518\) | 20.9183 | + | 7.34121i | 0.919098 | + | 0.322554i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.0631389 | + | 0.0297282i | −0.00276882 | + | 0.00130367i | ||||
\(521\) | 18.0720 | 0.791749 | 0.395874 | − | 0.918305i | \(-0.370442\pi\) | ||||
0.395874 | + | 0.918305i | \(0.370442\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2127 | + | 10.2127i | −0.446571 | + | 0.446571i | −0.894213 | − | 0.447642i | \(-0.852264\pi\) |
0.447642 | + | 0.894213i | \(0.352264\pi\) | |||||||
\(524\) | 15.6099 | − | 1.72978i | 0.681922 | − | 0.0755657i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.8180 | + | 22.5168i | 0.471689 | + | 0.981778i | ||||
\(527\) | 9.98371i | 0.434897i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.1711 | 0.833526 | ||||||||
\(530\) | −11.9671 | − | 5.86535i | −0.519819 | − | 0.254774i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 42.4809 | − | 4.70743i | 1.84178 | − | 0.204093i | ||||
\(533\) | −0.0813369 | + | 0.0813369i | −0.00352309 | + | 0.00352309i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.4265 | + | 14.5059i | 0.494010 | + | 0.627147i | ||||
\(536\) | 4.86058 | + | 7.78310i | 0.209945 | + | 0.336179i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.0530249 | + | 0.0186089i | 0.00228607 | + | 0.000802287i | ||||
\(539\) | 1.82909 | − | 1.82909i | 0.0787844 | − | 0.0787844i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.93323 | − | 4.93323i | −0.212096 | − | 0.212096i | 0.593061 | − | 0.805157i | \(-0.297919\pi\) |
−0.805157 | + | 0.593061i | \(0.797919\pi\) | |||||||
\(542\) | −17.5175 | + | 8.41618i | −0.752442 | + | 0.361506i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.87785 | − | 7.01339i | 0.380635 | − | 0.300697i | ||||
\(545\) | 21.4652 | + | 27.2500i | 0.919466 | + | 1.16726i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.5794 | − | 25.5794i | −1.09370 | − | 1.09370i | −0.995130 | − | 0.0985674i | \(-0.968574\pi\) |
−0.0985674 | − | 0.995130i | \(-0.531426\pi\) | |||||||
\(548\) | −9.06173 | − | 7.25377i | −0.387098 | − | 0.309865i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.73556 | + | 5.64752i | 0.372486 | + | 0.240811i | ||||
\(551\) | 55.7581i | 2.37538i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4606 | −0.572402 | ||||||||
\(554\) | 15.2451 | − | 43.4401i | 0.647704 | − | 1.84559i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −17.6509 | + | 1.95595i | −0.748565 | + | 0.0829506i | ||||
\(557\) | −4.34156 | − | 4.34156i | −0.183958 | − | 0.183958i | 0.609120 | − | 0.793078i | \(-0.291523\pi\) |
−0.793078 | + | 0.609120i | \(0.791523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0549545i | 0.00232433i | ||||||||
\(560\) | −26.3312 | + | 2.70922i | −1.11269 | + | 0.114486i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.8380 | − | 24.6396i | −0.499354 | − | 1.03936i | ||||
\(563\) | −16.4606 | + | 16.4606i | −0.693731 | + | 0.693731i | −0.963051 | − | 0.269320i | \(-0.913201\pi\) |
0.269320 | + | 0.963051i | \(0.413201\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.1000 | − | 2.62436i | −0.929755 | − | 0.110408i | ||||
\(566\) | 5.25594 | + | 1.84455i | 0.220924 | + | 0.0775324i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.135240 | − | 0.585090i | 0.00567457 | − | 0.0245499i | ||||
\(569\) | 27.5819 | 1.15629 | 0.578146 | − | 0.815933i | \(-0.303776\pi\) | ||||
0.578146 | + | 0.815933i | \(0.303776\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.33390 | + | 4.33390i | 0.181368 | + | 0.181368i | 0.791952 | − | 0.610584i | \(-0.209065\pi\) |
−0.610584 | + | 0.791952i | \(0.709065\pi\) | |||||||
\(572\) | 0.0253449 | + | 0.0202882i | 0.00105972 | + | 0.000848291i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −39.3264 | + | 18.8941i | −1.64145 | + | 0.788625i | ||||
\(575\) | 31.5666 | + | 7.60425i | 1.31642 | + | 0.317119i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.4805i | − | 1.35218i | −0.736819 | − | 0.676090i | \(-0.763673\pi\) | ||
0.736819 | − | 0.676090i | \(-0.236327\pi\) | |||||||
\(578\) | 7.96156 | + | 16.5713i | 0.331157 | + | 0.689274i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.270486 | − | 34.5308i | 0.0112313 | − | 1.43382i | ||||
\(581\) | 13.8609 | + | 13.8609i | 0.575046 | + | 0.575046i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.19979i | 0.256769i | ||||||||
\(584\) | −45.4647 | − | 10.5089i | −1.88134 | − | 0.434862i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 33.7548 | + | 11.8461i | 1.39440 | + | 0.489360i | ||||
\(587\) | 30.2712 | + | 30.2712i | 1.24942 | + | 1.24942i | 0.955975 | + | 0.293450i | \(0.0948033\pi\) |
0.293450 | + | 0.955975i | \(0.405197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.4884 | − | 25.4884i | −1.05023 | − | 1.05023i | ||||
\(590\) | 22.0009 | + | 10.7831i | 0.905764 | + | 0.443934i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −11.3383 | + | 17.8985i | −0.466002 | + | 0.735624i | ||||
\(593\) | 38.4245 | 1.57790 | 0.788952 | − | 0.614455i | \(-0.210624\pi\) | ||||
0.788952 | + | 0.614455i | \(0.210624\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.56071 | + | 13.1429i | −0.0639830 | + | 0.538808i | ||||
\(596\) | −35.5811 | + | 3.94284i | −1.45746 | + | 0.161505i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0956199 | + | 0.0335575i | 0.00391019 | + | 0.00137227i | ||||
\(599\) | − | 20.1491i | − | 0.823269i | −0.911349 | − | 0.411635i | \(-0.864958\pi\) | ||
0.911349 | − | 0.411635i | \(-0.135042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.75831i | − | 0.153305i | −0.997058 | − | 0.0766524i | \(-0.975577\pi\) | ||
0.997058 | − | 0.0766524i | \(-0.0244232\pi\) | |||||||
\(602\) | −6.90243 | + | 19.6681i | −0.281322 | + | 0.801610i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −21.4139 | + | 26.7513i | −0.871321 | + | 1.08849i | ||||
\(605\) | −2.32984 | + | 19.6198i | −0.0947214 | + | 0.797660i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.55683 | 0.0631899 | 0.0315949 | − | 0.999501i | \(-0.489941\pi\) | ||||
0.0315949 | + | 0.999501i | \(0.489941\pi\) | |||||||
\(608\) | −4.75998 | + | 40.5703i | −0.193043 | + | 1.64534i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.20812 | + | 18.7874i | −0.372826 | + | 0.760681i | ||||
\(611\) | 0.0830329 | + | 0.0830329i | 0.00335915 | + | 0.00335915i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.5306 | + | 19.5306i | 0.788832 | + | 0.788832i | 0.981303 | − | 0.192471i | \(-0.0616501\pi\) |
−0.192471 | + | 0.981303i | \(0.561650\pi\) | |||||||
\(614\) | 15.5051 | − | 44.1808i | 0.625734 | − | 1.78299i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.52262 | + | 10.4445i | 0.262804 | + | 0.420819i | ||||
\(617\) | − | 4.07636i | − | 0.164108i | −0.996628 | − | 0.0820540i | \(-0.973852\pi\) | ||
0.996628 | − | 0.0820540i | \(-0.0261480\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.05003 | + | 5.05003i | 0.202978 | + | 0.202978i | 0.801275 | − | 0.598297i | \(-0.204156\pi\) |
−0.598297 | + | 0.801275i | \(0.704156\pi\) | |||||||
\(620\) | 15.6613 | + | 15.9085i | 0.628971 | + | 0.638903i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.6425 | + | 14.7220i | −1.22865 | + | 0.590298i | ||||
\(623\) | 0.364290i | 0.0145950i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.2576 | + | 11.3841i | 0.890305 | + | 0.455365i | ||||
\(626\) | −10.8864 | − | 22.6592i | −0.435110 | − | 0.905642i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.49603 | + | 13.5005i | 0.0596979 | + | 0.538727i | ||||
\(629\) | 7.49105 | + | 7.49105i | 0.298688 | + | 0.298688i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.782254 | −0.0311411 | −0.0155705 | − | 0.999879i | \(-0.504956\pi\) | ||||
−0.0155705 | + | 0.999879i | \(0.504956\pi\) | |||||||
\(632\) | 2.89720 | − | 12.5341i | 0.115244 | − | 0.498581i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.10815 | − | 8.85648i | 0.123440 | − | 0.351736i | ||||
\(635\) | −1.20404 | − | 0.142978i | −0.0477807 | − | 0.00567391i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.0137197 | − | 0.0137197i | 0.000543593 | − | 0.000543593i | ||||
\(638\) | −14.4797 | + | 6.95668i | −0.573257 | + | 0.275418i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.14465 | − | 25.1020i | 0.124303 | − | 0.992244i | ||||
\(641\) | 2.92420i | 0.115499i | 0.998331 | + | 0.0577495i | \(0.0183925\pi\) | ||||
−0.998331 | + | 0.0577495i | \(0.981608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.2222 | − | 30.2222i | −1.19185 | − | 1.19185i | −0.976548 | − | 0.215301i | \(-0.930927\pi\) |
−0.215301 | − | 0.976548i | \(-0.569073\pi\) | |||||||
\(644\) | 30.0072 | + | 24.0202i | 1.18245 | + | 0.946530i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.2723 | + | 6.76353i | 0.758257 | + | 0.266108i | ||||
\(647\) | −48.8394 | −1.92007 | −0.960037 | − | 0.279871i | \(-0.909708\pi\) | ||||
−0.960037 | + | 0.279871i | \(0.909708\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 11.3980i | − | 0.447410i | ||||||
\(650\) | 0.0655240 | + | 0.0423611i | 0.00257006 | + | 0.00166154i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.18724 | + | 0.242374i | −0.0856588 | + | 0.00949210i | ||||
\(653\) | 4.18933 | + | 4.18933i | 0.163941 | + | 0.163941i | 0.784310 | − | 0.620369i | \(-0.213017\pi\) |
−0.620369 | + | 0.784310i | \(0.713017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.8655 | − | 13.7938i | −0.424550 | − | 0.538967i | ||||
\(656\) | −9.12925 | − | 40.6864i | −0.356437 | − | 1.58854i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 19.2881 | + | 40.1464i | 0.751928 | + | 1.56507i | ||||
\(659\) | 13.0512 | + | 13.0512i | 0.508402 | + | 0.508402i | 0.914036 | − | 0.405634i | \(-0.132949\pi\) |
−0.405634 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.41832 | − | 8.41832i | 0.327435 | − | 0.327435i | −0.524175 | − | 0.851610i | \(-0.675626\pi\) |
0.851610 | + | 0.524175i | \(0.175626\pi\) | |||||||
\(662\) | 13.3497 | − | 38.0391i | 0.518850 | − | 1.47843i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.8902 | + | 9.92352i | −0.616660 | + | 0.385107i | ||||
\(665\) | −29.5694 | − | 37.5384i | −1.14665 | − | 1.45568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.4567 | + | 35.4567i | −1.37289 | + | 1.37289i | ||||
\(668\) | 6.58219 | − | 8.22277i | 0.254673 | − | 0.318149i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.51513 | − | 9.21227i | 0.174435 | − | 0.355901i | ||||
\(671\) | 9.73317 | 0.375745 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.96622i | 0.345622i | 0.984955 | + | 0.172811i | \(0.0552850\pi\) | ||||
−0.984955 | + | 0.172811i | \(0.944715\pi\) | |||||||
\(674\) | 28.7821 | − | 13.8282i | 1.10865 | − | 0.532642i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.2976 | − | 16.2479i | −0.780677 | − | 0.624919i | ||||
\(677\) | 16.5376 | − | 16.5376i | 0.635590 | − | 0.635590i | −0.313874 | − | 0.949464i | \(-0.601627\pi\) |
0.949464 | + | 0.313874i | \(0.101627\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −24.5476 | −0.942051 | ||||||||
\(680\) | −11.9024 | − | 4.28213i | −0.456438 | − | 0.164212i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.43896 | − | 9.79910i | 0.131685 | − | 0.375227i | ||||
\(683\) | 3.42707 | + | 3.42707i | 0.131133 | + | 0.131133i | 0.769627 | − | 0.638494i | \(-0.220442\pi\) |
−0.638494 | + | 0.769627i | \(0.720442\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.53031 | + | 12.8869i | −0.0584702 | + | 0.492385i | ||||
\(686\) | −19.7740 | + | 9.50029i | −0.754974 | + | 0.362723i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16.8287 | − | 10.6606i | −0.641589 | − | 0.406433i | ||||
\(689\) | 0.0465036i | 0.00177165i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.7477 | − | 18.7477i | 0.713195 | − | 0.713195i | −0.254008 | − | 0.967202i | \(-0.581749\pi\) |
0.967202 | + | 0.254008i | \(0.0817489\pi\) | |||||||
\(692\) | −23.9483 | + | 2.65377i | −0.910376 | + | 0.100881i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.70751 | − | 16.2632i | 0.216654 | − | 0.617343i | ||||
\(695\) | 12.2862 | + | 15.5973i | 0.466040 | + | 0.591639i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −20.8493 | −0.789725 | ||||||||
\(698\) | 7.61269 | − | 21.6919i | 0.288145 | − | 0.821050i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.1302 | + | 23.3909i | 0.685256 | + | 0.884093i | ||||
\(701\) | 28.2156 | − | 28.2156i | 1.06569 | − | 1.06569i | 0.0680026 | − | 0.997685i | \(-0.478337\pi\) |
0.997685 | − | 0.0680026i | \(-0.0216626\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.2493 | −1.44260 | ||||||||
\(704\) | −11.1295 | + | 3.82567i | −0.419459 | + | 0.144185i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.5554 | + | 21.9701i | 0.397258 | + | 0.826857i | ||||
\(707\) | 23.5322 | − | 23.5322i | 0.885018 | − | 0.885018i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.7577 | − | 10.7577i | 0.404013 | − | 0.404013i | −0.475631 | − | 0.879645i | \(-0.657780\pi\) |
0.879645 | + | 0.475631i | \(0.157780\pi\) | |||||||
\(710\) | −0.635240 | + | 0.217362i | −0.0238401 | + | 0.00815744i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −0.339217 | − | 0.0784082i | −0.0127127 | − | 0.00293847i | ||||
\(713\) | − | 32.4162i | − | 1.21400i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.00428015 | − | 0.0360437i | 0.000160069 | − | 0.00134796i | ||||
\(716\) | 28.8092 | − | 3.19242i | 1.07665 | − | 0.119307i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.89547 | − | 1.39111i | 0.108058 | − | 0.0519158i | ||||
\(719\) | −1.68057 | −0.0626748 | −0.0313374 | − | 0.999509i | \(-0.509977\pi\) | ||||
−0.0313374 | + | 0.999509i | \(0.509977\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.1898 | 0.677422 | ||||||||
\(722\) | −42.2496 | + | 20.2985i | −1.57237 | + | 0.755433i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.184023 | − | 1.66067i | −0.00683916 | − | 0.0617182i | ||||
\(725\) | −32.9342 | + | 20.1471i | −1.22314 | + | 0.748246i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.3069i | − | 1.23528i | −0.786460 | − | 0.617641i | \(-0.788088\pi\) | ||
0.786460 | − | 0.617641i | \(-0.211912\pi\) | |||||||
\(728\) | 0.0489250 | + | 0.0783422i | 0.00181328 | + | 0.00290355i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 16.8902 | + | 49.3615i | 0.625133 | + | 1.82695i | ||||
\(731\) | −7.04332 | + | 7.04332i | −0.260507 | + | 0.260507i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.28476 | + | 9.28476i | −0.342941 | + | 0.342941i | −0.857472 | − | 0.514531i | \(-0.827966\pi\) |
0.514531 | + | 0.857472i | \(0.327966\pi\) | |||||||
\(734\) | −19.0672 | − | 39.6867i | −0.703784 | − | 1.46486i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.8256 | + | 22.7719i | −1.06253 | + | 0.839382i | ||||
\(737\) | −4.77258 | −0.175800 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.0117 | + | 24.0117i | −0.883286 | + | 0.883286i | −0.993867 | − | 0.110581i | \(-0.964729\pi\) |
0.110581 | + | 0.993867i | \(0.464729\pi\) | |||||||
\(740\) | 23.6877 | + | 0.185550i | 0.870777 | + | 0.00682094i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.84098 | + | 16.6435i | −0.214429 | + | 0.611002i | ||||
\(743\) | 25.5380 | 0.936897 | 0.468448 | − | 0.883491i | \(-0.344813\pi\) | ||||
0.468448 | + | 0.883491i | \(0.344813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.7667 | + | 31.4414i | 0.907382 | + | 1.15192i | ||||
\(746\) | −13.4577 | + | 38.3469i | −0.492722 | + | 1.40398i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.648103 | + | 5.84863i | 0.0236970 | + | 0.213847i | ||||
\(749\) | 17.2815 | − | 17.2815i | 0.631451 | − | 0.631451i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.6627i | 1.41082i | 0.708799 | + | 0.705411i | \(0.249238\pi\) | ||||
−0.708799 | + | 0.705411i | \(0.750762\pi\) | |||||||
\(752\) | −41.5348 | + | 9.31961i | −1.51462 | + | 0.339851i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.108610 | + | 0.0521809i | −0.00395534 | + | 0.00190032i | ||||
\(755\) | 38.0437 | + | 4.51766i | 1.38455 | + | 0.164414i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.0622 | + | 28.0622i | 1.01994 | + | 1.01994i | 0.999797 | + | 0.0201412i | \(0.00641158\pi\) |
0.0201412 | + | 0.999797i | \(0.493588\pi\) | |||||||
\(758\) | −6.36812 | + | 18.1455i | −0.231300 | + | 0.659076i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 41.3192 | − | 19.4547i | 1.49881 | − | 0.705695i | ||||
\(761\) | −12.1544 | −0.440597 | −0.220299 | − | 0.975432i | \(-0.570703\pi\) | ||||
−0.220299 | + | 0.975432i | \(0.570703\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.4640 | − | 32.4640i | 1.17528 | − | 1.17528i | ||||
\(764\) | 19.0035 | − | 23.7400i | 0.687521 | − | 0.858882i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.50097 | − | 0.721132i | 0.0542323 | − | 0.0260556i | ||||
\(767\) | − | 0.0854944i | − | 0.00308702i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.0426731 | −0.00153883 | −0.000769416 | − | 1.00000i | \(-0.500245\pi\) | ||||
−0.000769416 | 1.00000i | \(0.500245\pi\) | ||||||||
\(770\) | 6.05904 | − | 12.3623i | 0.218353 | − | 0.445507i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.4042 | − | 15.5328i | −0.698374 | − | 0.559037i | ||||
\(773\) | 4.96973 | − | 4.96973i | 0.178749 | − | 0.178749i | −0.612061 | − | 0.790810i | \(-0.709659\pi\) |
0.790810 | + | 0.612061i | \(0.209659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.84526 | − | 24.2648i | 0.209968 | − | 0.871616i | ||||
\(776\) | 5.28353 | − | 22.8581i | 0.189667 | − | 0.820558i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.7604 | + | 44.9082i | −0.565037 | + | 1.61004i | ||||
\(779\) | 53.2283 | − | 53.2283i | 1.90710 | − | 1.90710i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.220853 | + | 0.220853i | 0.00790274 | + | 0.00790274i | ||||
\(782\) | 7.95432 | + | 16.5562i | 0.284446 | + | 0.592049i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.53990 | + | 6.86286i | 0.0549963 | + | 0.245102i | ||||
\(785\) | 11.9297 | − | 9.39719i | 0.425791 | − | 0.335400i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.8577 | − | 16.8577i | −0.600911 | − | 0.600911i | 0.339643 | − | 0.940554i | \(-0.389694\pi\) |
−0.940554 | + | 0.339643i | \(0.889694\pi\) | |||||||
\(788\) | 2.34951 | + | 21.2025i | 0.0836978 | + | 0.755308i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.6085 | + | 4.65644i | −0.484167 | + | 0.165669i | ||||
\(791\) | 29.4551i | 1.04730i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0730069 | 0.00259255 | ||||||||
\(794\) | −11.1040 | − | 3.89690i | −0.394065 | − | 0.138296i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.5273 | + | 15.6497i | −0.444020 | + | 0.554689i | ||||
\(797\) | 0.0286009 | + | 0.0286009i | 0.00101310 | + | 0.00101310i | 0.707613 | − | 0.706600i | \(-0.249772\pi\) |
−0.706600 | + | 0.707613i | \(0.749772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.2841i | 0.752976i | ||||||||
\(800\) | −25.6833 | + | 11.8478i | −0.908040 | + | 0.418883i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.6860 | + | 9.45801i | −0.695136 | + | 0.333974i | ||||
\(803\) | 17.1615 | − | 17.1615i | 0.605614 | − | 0.605614i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.06750 | − | 42.6740i | 0.178606 | − | 1.50406i | ||||
\(806\) | 0.0257951 | − | 0.0735014i | 0.000908593 | − | 0.00258898i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.8476 | + | 26.9775i | 0.592695 | + | 0.949065i | ||||
\(809\) | −1.19014 | −0.0418431 | −0.0209216 | − | 0.999781i | \(-0.506660\pi\) | ||||
−0.0209216 | + | 0.999781i | \(0.506660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.9807 | + | 13.9807i | 0.490928 | + | 0.490928i | 0.908598 | − | 0.417671i | \(-0.137153\pi\) |
−0.417671 | + | 0.908598i | \(0.637153\pi\) | |||||||
\(812\) | −45.4252 | + | 5.03370i | −1.59411 | + | 0.176648i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.77219 | − | 9.93289i | −0.167265 | − | 0.348148i | ||||
\(815\) | 1.52246 | + | 1.93276i | 0.0533294 | + | 0.0677017i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 35.9632i | − | 1.25819i | ||||||
\(818\) | −11.1226 | + | 5.34377i | −0.388892 | + | 0.186840i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33.2224 | + | 32.7060i | −1.16018 | + | 1.14214i | ||||
\(821\) | −13.0285 | − | 13.0285i | −0.454699 | − | 0.454699i | 0.442212 | − | 0.896911i | \(-0.354194\pi\) |
−0.896911 | + | 0.442212i | \(0.854194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.1886i | 1.54032i | 0.637851 | + | 0.770160i | \(0.279823\pi\) | ||||
−0.637851 | + | 0.770160i | \(0.720177\pi\) | |||||||
\(824\) | −3.91509 | + | 16.9378i | −0.136389 | + | 0.590058i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.7383 | − | 30.5982i | 0.373634 | − | 1.06465i | ||||
\(827\) | −14.3077 | − | 14.3077i | −0.497528 | − | 0.497528i | 0.413139 | − | 0.910668i | \(-0.364432\pi\) |
−0.910668 | + | 0.413139i | \(0.864432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.86701 | − | 1.86701i | −0.0648439 | − | 0.0648439i | 0.673941 | − | 0.738785i | \(-0.264600\pi\) |
−0.738785 | + | 0.673941i | \(0.764600\pi\) | |||||||
\(830\) | 18.8081 | + | 9.21824i | 0.652838 | + | 0.319970i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −0.0834806 | + | 0.0286957i | −0.00289417 | + | 0.000994844i | ||||
\(833\) | 3.51681 | 0.121850 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6938 | − | 1.38863i | −0.404682 | − | 0.0480556i | ||||
\(836\) | −16.5862 | − | 13.2769i | −0.573644 | − | 0.459193i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.19943 | − | 9.11659i | 0.110523 | − | 0.314927i | ||||
\(839\) | − | 11.8696i | − | 0.409786i | −0.978784 | − | 0.204893i | \(-0.934315\pi\) | ||
0.978784 | − | 0.204893i | \(-0.0656846\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 30.6226i | − | 1.05595i | ||||||
\(842\) | −38.2037 | − | 13.4075i | −1.31659 | − | 0.462051i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.98275 | − | 44.9654i | −0.171513 | − | 1.54777i | ||||
\(845\) | −3.42779 | + | 28.8658i | −0.117919 | + | 0.993014i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.1495 | 0.898507 | ||||||||
\(848\) | −14.2408 | − | 9.02124i | −0.489031 | − | 0.309791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.96871 | + | 13.8273i | 0.101826 | + | 0.474271i | ||||
\(851\) | −24.3228 | − | 24.3228i | −0.833775 | − | 0.833775i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.7299 | − | 11.7299i | −0.401626 | − | 0.401626i | 0.477180 | − | 0.878806i | \(-0.341659\pi\) |
−0.878806 | + | 0.477180i | \(0.841659\pi\) | |||||||
\(854\) | 26.1289 | + | 9.16986i | 0.894114 | + | 0.313786i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.3725 | + | 19.8116i | 0.422882 | + | 0.677148i | ||||
\(857\) | 19.0655i | 0.651266i | 0.945496 | + | 0.325633i | \(0.105577\pi\) | ||||
−0.945496 | + | 0.325633i | \(0.894423\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.2411 | − | 22.2411i | −0.758858 | − | 0.758858i | 0.217256 | − | 0.976115i | \(-0.430289\pi\) |
−0.976115 | + | 0.217256i | \(0.930289\pi\) | |||||||
\(860\) | −0.174460 | + | 22.2719i | −0.00594903 | + | 0.759466i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.06373 | + | 8.45829i | 0.138411 | + | 0.288091i | ||||
\(863\) | 39.9598i | 1.36025i | 0.733097 | + | 0.680124i | \(0.238074\pi\) | ||||
−0.733097 | + | 0.680124i | \(0.761926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6695 | + | 21.1620i | 0.566781 | + | 0.719529i | ||||
\(866\) | 2.77829 | − | 1.33481i | 0.0944103 | − | 0.0453588i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 18.4640 | − | 23.0660i | 0.626708 | − | 0.782912i | ||||
\(869\) | 4.73123 | + | 4.73123i | 0.160496 | + | 0.160496i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.0357983 | −0.00121298 | ||||||||
\(872\) | 23.2422 | + | 37.2170i | 0.787081 | + | 1.26033i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −62.5754 | − | 21.9606i | −2.11664 | − | 0.742829i | ||||
\(875\) | 11.4882 | − | 31.0293i | 0.388370 | − | 1.04898i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.1486 | + | 24.1486i | −0.815442 | + | 0.815442i | −0.985444 | − | 0.170002i | \(-0.945623\pi\) |
0.170002 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(878\) | 11.1337 | + | 23.1739i | 0.375746 | + | 0.782081i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.2074 | + | 8.30284i | 0.344090 | + | 0.279889i | ||||
\(881\) | 31.7726i | 1.07045i | 0.844711 | + | 0.535223i | \(0.179772\pi\) | ||||
−0.844711 | + | 0.535223i | \(0.820228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.59278 | − | 1.59278i | −0.0536012 | − | 0.0536012i | 0.679798 | − | 0.733399i | \(-0.262067\pi\) |
−0.733399 | + | 0.679798i | \(0.762067\pi\) | |||||||
\(884\) | 0.00486131 | + | 0.0438696i | 0.000163504 | + | 0.00147549i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13.3680 | + | 38.0911i | −0.449105 | + | 1.27970i | ||||
\(887\) | 8.63569 | 0.289958 | 0.144979 | − | 0.989435i | \(-0.453689\pi\) | ||||
0.144979 | + | 0.989435i | \(0.453689\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.60475i | 0.0538215i | ||||||||
\(890\) | 0.126020 | + | 0.368292i | 0.00422419 | + | 0.0123452i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.6973 | − | 42.0962i | 1.12827 | − | 1.40948i | ||||
\(893\) | −54.3382 | − | 54.3382i | −1.81836 | − | 1.81836i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −20.0530 | − | 25.4573i | −0.670298 | − | 0.850944i | ||||
\(896\) | −33.4817 | − | 0.215291i | −1.11855 | − | 0.00719238i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −39.9506 | + | 19.1940i | −1.33317 | + | 0.640512i | ||||
\(899\) | 27.2550 | + | 27.2550i | 0.909004 | + | 0.909004i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.96020 | + | 5.96020i | −0.198563 | + | 0.198563i | ||||
\(902\) | 20.4638 | + | 7.18171i | 0.681371 | + | 0.239125i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.4278 | − | 6.33979i | −0.912235 | − | 0.210858i | ||||
\(905\) | −1.46745 | + | 1.15593i | −0.0487798 | + | 0.0384244i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.8316 | + | 12.8316i | −0.426068 | + | 0.426068i | −0.887286 | − | 0.461219i | \(-0.847412\pi\) |
0.461219 | + | 0.887286i | \(0.347412\pi\) | |||||||
\(908\) | −1.49661 | − | 13.5057i | −0.0496667 | − | 0.448203i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0454478 | − | 0.0927278i | 0.00150658 | − | 0.00307390i | ||||
\(911\) | −52.5129 | −1.73983 | −0.869915 | − | 0.493202i | \(-0.835826\pi\) | ||||
−0.869915 | + | 0.493202i | \(0.835826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 9.74386i | − | 0.322475i | ||||||
\(914\) | −9.56693 | − | 19.9127i | −0.316446 | − | 0.658653i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.17533 | − | 10.6064i | −0.0388340 | − | 0.350446i | ||||
\(917\) | −16.4330 | + | 16.4330i | −0.542666 | + | 0.542666i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.7005 | 1.44155 | 0.720773 | − | 0.693172i | \(-0.243787\pi\) | ||||
0.720773 | + | 0.693172i | \(0.243787\pi\) | |||||||
\(920\) | 38.6462 | + | 13.9037i | 1.27413 | + | 0.458391i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.8470 | − | 6.61430i | −0.620694 | − | 0.217830i | ||||
\(923\) | 0.00165658 | + | 0.00165658i | 5.45270e−5 | + | 5.45270e-5i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8207 | − | 22.5924i | −0.454421 | − | 0.742833i | ||||
\(926\) | 17.0329 | + | 35.4525i | 0.559737 | + | 1.16504i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.08989 | − | 43.3822i | 0.167084 | − | 1.42409i | ||||
\(929\) | 11.4938i | 0.377099i | 0.982064 | + | 0.188550i | \(0.0603786\pi\) | ||||
−0.982064 | + | 0.188550i | \(0.939621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.97840 | + | 8.97840i | −0.294255 | + | 0.294255i | ||||
\(932\) | −19.1557 | − | 15.3338i | −0.627465 | − | 0.502275i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 19.6821 | + | 6.90737i | 0.644019 | + | 0.226016i | ||||
\(935\) | 5.16816 | − | 4.07102i | 0.169017 | − | 0.133137i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.9308 | −1.76184 | −0.880922 | − | 0.473261i | \(-0.843077\pi\) | ||||
−0.880922 | + | 0.473261i | \(0.843077\pi\) | |||||||
\(938\) | −12.8121 | − | 4.49637i | −0.418331 | − | 0.146812i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 33.3879 | + | 33.9151i | 1.08899 | + | 1.10619i | ||||
\(941\) | 6.98130 | − | 6.98130i | 0.227584 | − | 0.227584i | −0.584099 | − | 0.811683i | \(-0.698552\pi\) |
0.811683 | + | 0.584099i | \(0.198552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 67.6960 | 2.20448 | ||||||||
\(944\) | 26.1810 | + | 16.5851i | 0.852118 | + | 0.539798i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 9.33922 | − | 4.48697i | 0.303644 | − | 0.145884i | ||||
\(947\) | 5.16523 | − | 5.16523i | 0.167847 | − | 0.167847i | −0.618185 | − | 0.786032i | \(-0.712132\pi\) |
0.786032 | + | 0.618185i | \(0.212132\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.128725 | − | 0.128725i | 0.00417860 | − | 0.00417860i | ||||
\(950\) | −42.8801 | − | 27.7219i | −1.39121 | − | 0.899416i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.77029 | + | 16.3114i | −0.122196 | + | 0.528655i | ||||
\(953\) | 20.7891i | 0.673424i | 0.941608 | + | 0.336712i | \(0.109315\pi\) | ||||
−0.941608 | + | 0.336712i | \(0.890685\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −33.7613 | − | 4.00912i | −1.09249 | − | 0.129732i | ||||
\(956\) | −15.5189 | + | 19.3869i | −0.501917 | + | 0.627018i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.4198 | − | 30.0134i | −0.465881 | − | 0.969690i | ||||
\(959\) | 17.1758 | 0.554636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.08216 | 0.196199 | ||||||||
\(962\) | −0.0357954 | − | 0.0745050i | −0.00115409 | − | 0.00240214i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.8672 | − | 26.0683i | 0.672088 | − | 0.839603i | ||||
\(965\) | −3.27692 | + | 27.5953i | −0.105488 | + | 0.888325i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50.2701i | − | 1.61658i | −0.588786 | − | 0.808289i | \(-0.700394\pi\) | ||
0.588786 | − | 0.808289i | \(-0.299606\pi\) | |||||||
\(968\) | −5.62830 | + | 24.3497i | −0.180901 | + | 0.782629i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.8173 | + | 8.49181i | −0.796836 | + | 0.272656i | ||||
\(971\) | −19.7427 | + | 19.7427i | −0.633574 | + | 0.633574i | −0.948963 | − | 0.315388i | \(-0.897865\pi\) |
0.315388 | + | 0.948963i | \(0.397865\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.5816 | − | 18.5816i | 0.595700 | − | 0.595700i | ||||
\(974\) | −19.6315 | + | 9.43181i | −0.629032 | + | 0.302215i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −14.1626 | + | 22.3569i | −0.453334 | + | 0.715627i | ||||
\(977\) | −29.6872 | −0.949779 | −0.474889 | − | 0.880045i | \(-0.657512\pi\) | ||||
−0.474889 | + | 0.880045i | \(0.657512\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.128044 | − | 0.128044i | 0.00409229 | − | 0.00409229i | ||||
\(980\) | 5.60386 | − | 5.51675i | 0.179009 | − | 0.176226i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.4741 | + | 7.88719i | 0.717176 | + | 0.251690i | ||||
\(983\) | 0.250996 | 0.00800552 | 0.00400276 | − | 0.999992i | \(-0.498726\pi\) | ||||
0.00400276 | + | 0.999992i | \(0.498726\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 18.7357 | − | 14.7583i | 0.596968 | − | 0.470238i | ||||
\(986\) | −20.6080 | − | 7.23230i | −0.656292 | − | 0.230323i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.124410 | − | 0.0995881i | −0.00395801 | − | 0.00316832i | ||||
\(989\) | 22.8691 | − | 22.8691i | 0.727194 | − | 0.727194i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.2980i | 1.05775i | 0.848701 | + | 0.528873i | \(0.177385\pi\) | ||||
−0.848701 | + | 0.528873i | \(0.822615\pi\) | |||||||
\(992\) | 17.5044 | + | 22.1578i | 0.555764 | + | 0.703511i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.384814 | + | 0.800956i | 0.0122056 | + | 0.0254048i | ||||
\(995\) | 22.2559 | + | 2.64287i | 0.705559 | + | 0.0837845i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 14.4987 | + | 14.4987i | 0.459180 | + | 0.459180i | 0.898386 | − | 0.439207i | \(-0.144740\pi\) |
−0.439207 | + | 0.898386i | \(0.644740\pi\) | |||||||
\(998\) | −31.0441 | − | 10.8948i | −0.982684 | − | 0.344869i | ||||
\(999\) | 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 | 720.2.u.a.179.18 | yes | 96 | |
3.2 | odd | 2 | inner | 720.2.u.a.179.31 | yes | 96 | |
4.3 | odd | 2 | 2880.2.u.a.2159.47 | 96 | |||
5.4 | even | 2 | inner | 720.2.u.a.179.32 | yes | 96 | |
12.11 | even | 2 | 2880.2.u.a.2159.2 | 96 | |||
15.14 | odd | 2 | inner | 720.2.u.a.179.17 | ✓ | 96 | |
16.5 | even | 4 | 2880.2.u.a.719.23 | 96 | |||
16.11 | odd | 4 | inner | 720.2.u.a.539.17 | yes | 96 | |
20.19 | odd | 2 | 2880.2.u.a.2159.26 | 96 | |||
48.5 | odd | 4 | 2880.2.u.a.719.26 | 96 | |||
48.11 | even | 4 | inner | 720.2.u.a.539.32 | yes | 96 | |
60.59 | even | 2 | 2880.2.u.a.2159.23 | 96 | |||
80.59 | odd | 4 | inner | 720.2.u.a.539.31 | yes | 96 | |
80.69 | even | 4 | 2880.2.u.a.719.2 | 96 | |||
240.59 | even | 4 | inner | 720.2.u.a.539.18 | yes | 96 | |
240.149 | odd | 4 | 2880.2.u.a.719.47 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
720.2.u.a.179.17 | ✓ | 96 | 15.14 | odd | 2 | inner | |
720.2.u.a.179.18 | yes | 96 | 1.1 | even | 1 | trivial | |
720.2.u.a.179.31 | yes | 96 | 3.2 | odd | 2 | inner | |
720.2.u.a.179.32 | yes | 96 | 5.4 | even | 2 | inner | |
720.2.u.a.539.17 | yes | 96 | 16.11 | odd | 4 | inner | |
720.2.u.a.539.18 | yes | 96 | 240.59 | even | 4 | inner | |
720.2.u.a.539.31 | yes | 96 | 80.59 | odd | 4 | inner | |
720.2.u.a.539.32 | yes | 96 | 48.11 | even | 4 | inner | |
2880.2.u.a.719.2 | 96 | 80.69 | even | 4 | |||
2880.2.u.a.719.23 | 96 | 16.5 | even | 4 | |||
2880.2.u.a.719.26 | 96 | 48.5 | odd | 4 | |||
2880.2.u.a.719.47 | 96 | 240.149 | odd | 4 | |||
2880.2.u.a.2159.2 | 96 | 12.11 | even | 2 | |||
2880.2.u.a.2159.23 | 96 | 60.59 | even | 2 | |||
2880.2.u.a.2159.26 | 96 | 20.19 | odd | 2 | |||
2880.2.u.a.2159.47 | 96 | 4.3 | odd | 2 |