Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [306,2,Mod(13,306)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(306, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("306.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 306 = 2 \cdot 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 306.n (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.44342230185\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 157.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 306.157 |
Dual form | 306.2.n.c.115.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/306\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0.732051 | + | 2.73205i | 0.327383 | + | 1.22181i | 0.911894 | + | 0.410425i | \(0.134620\pi\) |
−0.584511 | + | 0.811386i | \(0.698714\pi\) | |||||||
\(6\) | 0.866025 | − | 1.50000i | 0.353553 | − | 0.612372i | ||||
\(7\) | −0.267949 | + | 1.00000i | −0.101275 | + | 0.377964i | −0.997896 | − | 0.0648349i | \(-0.979348\pi\) |
0.896621 | + | 0.442799i | \(0.146015\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 2.00000 | + | 2.00000i | 0.632456 | + | 0.632456i | ||||
\(11\) | 0.598076 | − | 2.23205i | 0.180327 | − | 0.672989i | −0.815256 | − | 0.579101i | \(-0.803404\pi\) |
0.995583 | − | 0.0938879i | \(-0.0299295\pi\) | |||||||
\(12\) | − | 1.73205i | − | 0.500000i | ||||||
\(13\) | −1.73205 | + | 3.00000i | −0.480384 | + | 0.832050i | −0.999747 | − | 0.0225039i | \(-0.992836\pi\) |
0.519362 | + | 0.854554i | \(0.326170\pi\) | |||||||
\(14\) | 0.267949 | + | 1.00000i | 0.0716124 | + | 0.267261i | ||||
\(15\) | 3.46410 | + | 3.46410i | 0.894427 | + | 0.894427i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.86603 | − | 2.96410i | −0.695113 | − | 0.718900i | ||||
\(18\) | − | 3.00000i | − | 0.707107i | ||||||
\(19\) | 1.00000i | 0.229416i | 0.993399 | + | 0.114708i | \(0.0365932\pi\) | ||||
−0.993399 | + | 0.114708i | \(0.963407\pi\) | |||||||
\(20\) | 2.73205 | + | 0.732051i | 0.610905 | + | 0.163692i | ||||
\(21\) | 0.464102 | + | 1.73205i | 0.101275 | + | 0.377964i | ||||
\(22\) | −0.598076 | − | 2.23205i | −0.127510 | − | 0.475875i | ||||
\(23\) | −1.73205 | + | 0.464102i | −0.361158 | + | 0.0967719i | −0.434835 | − | 0.900510i | \(-0.643193\pi\) |
0.0736772 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(24\) | −0.866025 | − | 1.50000i | −0.176777 | − | 0.306186i | ||||
\(25\) | −2.59808 | + | 1.50000i | −0.519615 | + | 0.300000i | ||||
\(26\) | 3.46410i | 0.679366i | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0.732051 | + | 0.732051i | 0.138345 | + | 0.138345i | ||||
\(29\) | −8.46410 | − | 2.26795i | −1.57174 | − | 0.421148i | −0.635386 | − | 0.772194i | \(-0.719159\pi\) |
−0.936358 | + | 0.351047i | \(0.885826\pi\) | |||||||
\(30\) | 4.73205 | + | 1.26795i | 0.863950 | + | 0.231495i | ||||
\(31\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −1.03590 | − | 3.86603i | −0.180327 | − | 0.672989i | ||||
\(34\) | −3.96410 | − | 1.13397i | −0.679838 | − | 0.194475i | ||||
\(35\) | −2.92820 | −0.494957 | ||||||||
\(36\) | −1.50000 | − | 2.59808i | −0.250000 | − | 0.433013i | ||||
\(37\) | 3.46410 | − | 3.46410i | 0.569495 | − | 0.569495i | −0.362492 | − | 0.931987i | \(-0.618074\pi\) |
0.931987 | + | 0.362492i | \(0.118074\pi\) | |||||||
\(38\) | 0.500000 | + | 0.866025i | 0.0811107 | + | 0.140488i | ||||
\(39\) | 6.00000i | 0.960769i | ||||||||
\(40\) | 2.73205 | − | 0.732051i | 0.431975 | − | 0.115747i | ||||
\(41\) | −9.96410 | + | 2.66987i | −1.55613 | + | 0.416964i | −0.931436 | − | 0.363905i | \(-0.881443\pi\) |
−0.624695 | + | 0.780869i | \(0.714777\pi\) | |||||||
\(42\) | 1.26795 | + | 1.26795i | 0.195649 | + | 0.195649i | ||||
\(43\) | 4.50000 | − | 2.59808i | 0.686244 | − | 0.396203i | −0.115960 | − | 0.993254i | \(-0.536994\pi\) |
0.802203 | + | 0.597051i | \(0.203661\pi\) | |||||||
\(44\) | −1.63397 | − | 1.63397i | −0.246331 | − | 0.246331i | ||||
\(45\) | 8.19615 | + | 2.19615i | 1.22181 | + | 0.327383i | ||||
\(46\) | −1.26795 | + | 1.26795i | −0.186949 | + | 0.186949i | ||||
\(47\) | 5.00000 | + | 8.66025i | 0.729325 | + | 1.26323i | 0.957169 | + | 0.289530i | \(0.0934991\pi\) |
−0.227844 | + | 0.973698i | \(0.573168\pi\) | |||||||
\(48\) | −1.50000 | − | 0.866025i | −0.216506 | − | 0.125000i | ||||
\(49\) | 5.13397 | + | 2.96410i | 0.733425 | + | 0.423443i | ||||
\(50\) | −1.50000 | + | 2.59808i | −0.212132 | + | 0.367423i | ||||
\(51\) | −6.86603 | − | 1.96410i | −0.961436 | − | 0.275029i | ||||
\(52\) | 1.73205 | + | 3.00000i | 0.240192 | + | 0.416025i | ||||
\(53\) | 2.53590i | 0.348332i | 0.984716 | + | 0.174166i | \(0.0557230\pi\) | ||||
−0.984716 | + | 0.174166i | \(0.944277\pi\) | |||||||
\(54\) | −2.59808 | − | 4.50000i | −0.353553 | − | 0.612372i | ||||
\(55\) | 6.53590 | 0.881300 | ||||||||
\(56\) | 1.00000 | + | 0.267949i | 0.133631 | + | 0.0358062i | ||||
\(57\) | 0.866025 | + | 1.50000i | 0.114708 | + | 0.198680i | ||||
\(58\) | −8.46410 | + | 2.26795i | −1.11139 | + | 0.297796i | ||||
\(59\) | −1.50000 | − | 0.866025i | −0.195283 | − | 0.112747i | 0.399170 | − | 0.916877i | \(-0.369298\pi\) |
−0.594454 | + | 0.804130i | \(0.702632\pi\) | |||||||
\(60\) | 4.73205 | − | 1.26795i | 0.610905 | − | 0.163692i | ||||
\(61\) | −2.73205 | + | 10.1962i | −0.349803 | + | 1.30548i | 0.537096 | + | 0.843521i | \(0.319521\pi\) |
−0.886899 | + | 0.461963i | \(0.847145\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.19615 | + | 2.19615i | 0.276689 | + | 0.276689i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −9.46410 | − | 2.53590i | −1.17388 | − | 0.314539i | ||||
\(66\) | −2.83013 | − | 2.83013i | −0.348365 | − | 0.348365i | ||||
\(67\) | 2.33013 | − | 4.03590i | 0.284670 | − | 0.493063i | −0.687859 | − | 0.725844i | \(-0.741449\pi\) |
0.972529 | + | 0.232781i | \(0.0747825\pi\) | |||||||
\(68\) | −4.00000 | + | 1.00000i | −0.485071 | + | 0.121268i | ||||
\(69\) | −2.19615 | + | 2.19615i | −0.264386 | + | 0.264386i | ||||
\(70\) | −2.53590 | + | 1.46410i | −0.303098 | + | 0.174994i | ||||
\(71\) | 5.46410 | − | 5.46410i | 0.648470 | − | 0.648470i | −0.304153 | − | 0.952623i | \(-0.598374\pi\) |
0.952623 | + | 0.304153i | \(0.0983736\pi\) | |||||||
\(72\) | −2.59808 | − | 1.50000i | −0.306186 | − | 0.176777i | ||||
\(73\) | 3.90192 | − | 3.90192i | 0.456686 | − | 0.456686i | −0.440880 | − | 0.897566i | \(-0.645334\pi\) |
0.897566 | + | 0.440880i | \(0.145334\pi\) | |||||||
\(74\) | 1.26795 | − | 4.73205i | 0.147396 | − | 0.550090i | ||||
\(75\) | −2.59808 | + | 4.50000i | −0.300000 | + | 0.519615i | ||||
\(76\) | 0.866025 | + | 0.500000i | 0.0993399 | + | 0.0573539i | ||||
\(77\) | 2.07180 | + | 1.19615i | 0.236103 | + | 0.136314i | ||||
\(78\) | 3.00000 | + | 5.19615i | 0.339683 | + | 0.588348i | ||||
\(79\) | −3.26795 | + | 12.1962i | −0.367673 | + | 1.37217i | 0.496088 | + | 0.868272i | \(0.334769\pi\) |
−0.863761 | + | 0.503902i | \(0.831897\pi\) | |||||||
\(80\) | 2.00000 | − | 2.00000i | 0.223607 | − | 0.223607i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | −7.29423 | + | 7.29423i | −0.805513 | + | 0.805513i | ||||
\(83\) | −3.92820 | + | 2.26795i | −0.431176 | + | 0.248940i | −0.699848 | − | 0.714292i | \(-0.746749\pi\) |
0.268671 | + | 0.963232i | \(0.413415\pi\) | |||||||
\(84\) | 1.73205 | + | 0.464102i | 0.188982 | + | 0.0506376i | ||||
\(85\) | 6.00000 | − | 10.0000i | 0.650791 | − | 1.08465i | ||||
\(86\) | 2.59808 | − | 4.50000i | 0.280158 | − | 0.485247i | ||||
\(87\) | −14.6603 | + | 3.92820i | −1.57174 | + | 0.421148i | ||||
\(88\) | −2.23205 | − | 0.598076i | −0.237937 | − | 0.0637551i | ||||
\(89\) | 6.92820 | 0.734388 | 0.367194 | − | 0.930144i | \(-0.380318\pi\) | ||||
0.367194 | + | 0.930144i | \(0.380318\pi\) | |||||||
\(90\) | 8.19615 | − | 2.19615i | 0.863950 | − | 0.231495i | ||||
\(91\) | −2.53590 | − | 2.53590i | −0.265834 | − | 0.265834i | ||||
\(92\) | −0.464102 | + | 1.73205i | −0.0483859 | + | 0.180579i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.66025 | + | 5.00000i | 0.893237 | + | 0.515711i | ||||
\(95\) | −2.73205 | + | 0.732051i | −0.280302 | + | 0.0751068i | ||||
\(96\) | −1.73205 | −0.176777 | ||||||||
\(97\) | 2.50000 | + | 0.669873i | 0.253837 | + | 0.0680153i | 0.383493 | − | 0.923544i | \(-0.374721\pi\) |
−0.129657 | + | 0.991559i | \(0.541388\pi\) | |||||||
\(98\) | 5.92820 | 0.598839 | ||||||||
\(99\) | −4.90192 | − | 4.90192i | −0.492662 | − | 0.492662i | ||||
\(100\) | 3.00000i | 0.300000i | ||||||||
\(101\) | −8.73205 | − | 15.1244i | −0.868872 | − | 1.50493i | −0.863151 | − | 0.504946i | \(-0.831512\pi\) |
−0.00572059 | − | 0.999984i | \(-0.501821\pi\) | |||||||
\(102\) | −6.92820 | + | 1.73205i | −0.685994 | + | 0.171499i | ||||
\(103\) | −3.73205 | + | 6.46410i | −0.367730 | + | 0.636927i | −0.989210 | − | 0.146503i | \(-0.953198\pi\) |
0.621480 | + | 0.783430i | \(0.286532\pi\) | |||||||
\(104\) | 3.00000 | + | 1.73205i | 0.294174 | + | 0.169842i | ||||
\(105\) | −4.39230 | + | 2.53590i | −0.428645 | + | 0.247478i | ||||
\(106\) | 1.26795 | + | 2.19615i | 0.123154 | + | 0.213309i | ||||
\(107\) | 13.2942 | − | 13.2942i | 1.28520 | − | 1.28520i | 0.347534 | − | 0.937667i | \(-0.387019\pi\) |
0.937667 | − | 0.347534i | \(-0.112981\pi\) | |||||||
\(108\) | −4.50000 | − | 2.59808i | −0.433013 | − | 0.250000i | ||||
\(109\) | −4.92820 | − | 4.92820i | −0.472036 | − | 0.472036i | 0.430537 | − | 0.902573i | \(-0.358324\pi\) |
−0.902573 | + | 0.430537i | \(0.858324\pi\) | |||||||
\(110\) | 5.66025 | − | 3.26795i | 0.539684 | − | 0.311587i | ||||
\(111\) | 2.19615 | − | 8.19615i | 0.208450 | − | 0.777944i | ||||
\(112\) | 1.00000 | − | 0.267949i | 0.0944911 | − | 0.0253188i | ||||
\(113\) | −6.09808 | + | 1.63397i | −0.573659 | + | 0.153711i | −0.533974 | − | 0.845501i | \(-0.679302\pi\) |
−0.0396847 | + | 0.999212i | \(0.512635\pi\) | |||||||
\(114\) | 1.50000 | + | 0.866025i | 0.140488 | + | 0.0811107i | ||||
\(115\) | −2.53590 | − | 4.39230i | −0.236474 | − | 0.409585i | ||||
\(116\) | −6.19615 | + | 6.19615i | −0.575298 | + | 0.575298i | ||||
\(117\) | 5.19615 | + | 9.00000i | 0.480384 | + | 0.832050i | ||||
\(118\) | −1.73205 | −0.159448 | ||||||||
\(119\) | 3.73205 | − | 2.07180i | 0.342117 | − | 0.189921i | ||||
\(120\) | 3.46410 | − | 3.46410i | 0.316228 | − | 0.316228i | ||||
\(121\) | 4.90192 | + | 2.83013i | 0.445629 | + | 0.257284i | ||||
\(122\) | 2.73205 | + | 10.1962i | 0.247348 | + | 0.923116i | ||||
\(123\) | −12.6340 | + | 12.6340i | −1.13917 | + | 1.13917i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.00000 | + | 4.00000i | 0.357771 | + | 0.357771i | ||||
\(126\) | 3.00000 | + | 0.803848i | 0.267261 | + | 0.0716124i | ||||
\(127\) | 2.00000i | 0.177471i | 0.996055 | + | 0.0887357i | \(0.0282826\pi\) | ||||
−0.996055 | + | 0.0887357i | \(0.971717\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 4.50000 | − | 7.79423i | 0.396203 | − | 0.686244i | ||||
\(130\) | −9.46410 | + | 2.53590i | −0.830057 | + | 0.222413i | ||||
\(131\) | 4.63397 | + | 17.2942i | 0.404872 | + | 1.51100i | 0.804291 | + | 0.594235i | \(0.202545\pi\) |
−0.399419 | + | 0.916768i | \(0.630788\pi\) | |||||||
\(132\) | −3.86603 | − | 1.03590i | −0.336494 | − | 0.0901634i | ||||
\(133\) | −1.00000 | − | 0.267949i | −0.0867110 | − | 0.0232341i | ||||
\(134\) | − | 4.66025i | − | 0.402585i | ||||||
\(135\) | 14.1962 | − | 3.80385i | 1.22181 | − | 0.327383i | ||||
\(136\) | −2.96410 | + | 2.86603i | −0.254170 | + | 0.245760i | ||||
\(137\) | −10.9641 | − | 18.9904i | −0.936726 | − | 1.62246i | −0.771526 | − | 0.636198i | \(-0.780506\pi\) |
−0.165200 | − | 0.986260i | \(-0.552827\pi\) | |||||||
\(138\) | −0.803848 | + | 3.00000i | −0.0684280 | + | 0.255377i | ||||
\(139\) | 5.69615 | + | 21.2583i | 0.483141 | + | 1.80311i | 0.588288 | + | 0.808651i | \(0.299802\pi\) |
−0.105147 | + | 0.994457i | \(0.533531\pi\) | |||||||
\(140\) | −1.46410 | + | 2.53590i | −0.123739 | + | 0.214323i | ||||
\(141\) | 15.0000 | + | 8.66025i | 1.26323 | + | 0.729325i | ||||
\(142\) | 2.00000 | − | 7.46410i | 0.167836 | − | 0.626373i | ||||
\(143\) | 5.66025 | + | 5.66025i | 0.473334 | + | 0.473334i | ||||
\(144\) | −3.00000 | −0.250000 | ||||||||
\(145\) | − | 24.7846i | − | 2.05825i | ||||||
\(146\) | 1.42820 | − | 5.33013i | 0.118199 | − | 0.441124i | ||||
\(147\) | 10.2679 | 0.846886 | ||||||||
\(148\) | −1.26795 | − | 4.73205i | −0.104225 | − | 0.388972i | ||||
\(149\) | 5.73205 | − | 9.92820i | 0.469588 | − | 0.813350i | −0.529808 | − | 0.848118i | \(-0.677736\pi\) |
0.999395 | + | 0.0347678i | \(0.0110692\pi\) | |||||||
\(150\) | 5.19615i | 0.424264i | ||||||||
\(151\) | 18.1244 | − | 10.4641i | 1.47494 | − | 0.851557i | 0.475338 | − | 0.879803i | \(-0.342326\pi\) |
0.999601 | + | 0.0282467i | \(0.00899239\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | −12.0000 | + | 3.00000i | −0.970143 | + | 0.242536i | ||||
\(154\) | 2.39230 | 0.192777 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.19615 | + | 3.00000i | 0.416025 | + | 0.240192i | ||||
\(157\) | 10.1962 | − | 17.6603i | 0.813742 | − | 1.40944i | −0.0964865 | − | 0.995334i | \(-0.530760\pi\) |
0.910228 | − | 0.414107i | \(-0.135906\pi\) | |||||||
\(158\) | 3.26795 | + | 12.1962i | 0.259984 | + | 0.970274i | ||||
\(159\) | 2.19615 | + | 3.80385i | 0.174166 | + | 0.301665i | ||||
\(160\) | 0.732051 | − | 2.73205i | 0.0578737 | − | 0.215988i | ||||
\(161\) | − | 1.85641i | − | 0.146305i | ||||||
\(162\) | −7.79423 | − | 4.50000i | −0.612372 | − | 0.353553i | ||||
\(163\) | −4.26795 | − | 4.26795i | −0.334292 | − | 0.334292i | 0.519922 | − | 0.854214i | \(-0.325961\pi\) |
−0.854214 | + | 0.519922i | \(0.825961\pi\) | |||||||
\(164\) | −2.66987 | + | 9.96410i | −0.208482 | + | 0.778066i | ||||
\(165\) | 9.80385 | − | 5.66025i | 0.763228 | − | 0.440650i | ||||
\(166\) | −2.26795 | + | 3.92820i | −0.176027 | + | 0.304888i | ||||
\(167\) | −6.19615 | − | 23.1244i | −0.479473 | − | 1.78942i | −0.603756 | − | 0.797170i | \(-0.706330\pi\) |
0.124283 | − | 0.992247i | \(-0.460337\pi\) | |||||||
\(168\) | 1.73205 | − | 0.464102i | 0.133631 | − | 0.0358062i | ||||
\(169\) | 0.500000 | + | 0.866025i | 0.0384615 | + | 0.0666173i | ||||
\(170\) | 0.196152 | − | 11.6603i | 0.0150442 | − | 0.894301i | ||||
\(171\) | 2.59808 | + | 1.50000i | 0.198680 | + | 0.114708i | ||||
\(172\) | − | 5.19615i | − | 0.396203i | ||||||
\(173\) | 3.73205 | + | 1.00000i | 0.283743 | + | 0.0760286i | 0.397883 | − | 0.917436i | \(-0.369745\pi\) |
−0.114141 | + | 0.993465i | \(0.536412\pi\) | |||||||
\(174\) | −10.7321 | + | 10.7321i | −0.813595 | + | 0.813595i | ||||
\(175\) | −0.803848 | − | 3.00000i | −0.0607652 | − | 0.226779i | ||||
\(176\) | −2.23205 | + | 0.598076i | −0.168247 | + | 0.0450817i | ||||
\(177\) | −3.00000 | −0.225494 | ||||||||
\(178\) | 6.00000 | − | 3.46410i | 0.449719 | − | 0.259645i | ||||
\(179\) | 9.07180i | 0.678058i | 0.940776 | + | 0.339029i | \(0.110098\pi\) | ||||
−0.940776 | + | 0.339029i | \(0.889902\pi\) | |||||||
\(180\) | 6.00000 | − | 6.00000i | 0.447214 | − | 0.447214i | ||||
\(181\) | −11.2679 | − | 11.2679i | −0.837540 | − | 0.837540i | 0.150995 | − | 0.988535i | \(-0.451752\pi\) |
−0.988535 | + | 0.150995i | \(0.951752\pi\) | |||||||
\(182\) | −3.46410 | − | 0.928203i | −0.256776 | − | 0.0688030i | ||||
\(183\) | 4.73205 | + | 17.6603i | 0.349803 | + | 1.30548i | ||||
\(184\) | 0.464102 | + | 1.73205i | 0.0342140 | + | 0.127688i | ||||
\(185\) | 12.0000 | + | 6.92820i | 0.882258 | + | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.33013 | + | 4.62436i | −0.609159 | + | 0.338166i | ||||
\(188\) | 10.0000 | 0.729325 | ||||||||
\(189\) | 5.19615 | + | 1.39230i | 0.377964 | + | 0.101275i | ||||
\(190\) | −2.00000 | + | 2.00000i | −0.145095 | + | 0.145095i | ||||
\(191\) | 3.92820 | + | 6.80385i | 0.284235 | + | 0.492309i | 0.972423 | − | 0.233223i | \(-0.0749271\pi\) |
−0.688189 | + | 0.725532i | \(0.741594\pi\) | |||||||
\(192\) | −1.50000 | + | 0.866025i | −0.108253 | + | 0.0625000i | ||||
\(193\) | −5.59808 | + | 1.50000i | −0.402958 | + | 0.107972i | −0.454605 | − | 0.890693i | \(-0.650220\pi\) |
0.0516469 | + | 0.998665i | \(0.483553\pi\) | |||||||
\(194\) | 2.50000 | − | 0.669873i | 0.179490 | − | 0.0480941i | ||||
\(195\) | −16.3923 | + | 4.39230i | −1.17388 | + | 0.314539i | ||||
\(196\) | 5.13397 | − | 2.96410i | 0.366712 | − | 0.211722i | ||||
\(197\) | 9.46410 | + | 9.46410i | 0.674289 | + | 0.674289i | 0.958702 | − | 0.284413i | \(-0.0917986\pi\) |
−0.284413 | + | 0.958702i | \(0.591799\pi\) | |||||||
\(198\) | −6.69615 | − | 1.79423i | −0.475875 | − | 0.127510i | ||||
\(199\) | −3.66025 | + | 3.66025i | −0.259469 | + | 0.259469i | −0.824838 | − | 0.565369i | \(-0.808734\pi\) |
0.565369 | + | 0.824838i | \(0.308734\pi\) | |||||||
\(200\) | 1.50000 | + | 2.59808i | 0.106066 | + | 0.183712i | ||||
\(201\) | − | 8.07180i | − | 0.569341i | ||||||
\(202\) | −15.1244 | − | 8.73205i | −1.06415 | − | 0.614385i | ||||
\(203\) | 4.53590 | − | 7.85641i | 0.318358 | − | 0.551412i | ||||
\(204\) | −5.13397 | + | 4.96410i | −0.359450 | + | 0.347557i | ||||
\(205\) | −14.5885 | − | 25.2679i | −1.01890 | − | 1.76479i | ||||
\(206\) | 7.46410i | 0.520049i | ||||||||
\(207\) | −1.39230 | + | 5.19615i | −0.0967719 | + | 0.361158i | ||||
\(208\) | 3.46410 | 0.240192 | ||||||||
\(209\) | 2.23205 | + | 0.598076i | 0.154394 | + | 0.0413698i | ||||
\(210\) | −2.53590 | + | 4.39230i | −0.174994 | + | 0.303098i | ||||
\(211\) | 15.2942 | − | 4.09808i | 1.05290 | − | 0.282123i | 0.309449 | − | 0.950916i | \(-0.399855\pi\) |
0.743449 | + | 0.668793i | \(0.233189\pi\) | |||||||
\(212\) | 2.19615 | + | 1.26795i | 0.150832 | + | 0.0870831i | ||||
\(213\) | 3.46410 | − | 12.9282i | 0.237356 | − | 0.885826i | ||||
\(214\) | 4.86603 | − | 18.1603i | 0.332635 | − | 1.24141i | ||||
\(215\) | 10.3923 | + | 10.3923i | 0.708749 | + | 0.708749i | ||||
\(216\) | −5.19615 | −0.353553 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −6.73205 | − | 1.80385i | −0.455952 | − | 0.122172i | ||||
\(219\) | 2.47372 | − | 9.23205i | 0.167159 | − | 0.623844i | ||||
\(220\) | 3.26795 | − | 5.66025i | 0.220325 | − | 0.381614i | ||||
\(221\) | 13.8564 | − | 3.46410i | 0.932083 | − | 0.233021i | ||||
\(222\) | −2.19615 | − | 8.19615i | −0.147396 | − | 0.550090i | ||||
\(223\) | −2.07180 | + | 1.19615i | −0.138738 | + | 0.0801003i | −0.567762 | − | 0.823193i | \(-0.692191\pi\) |
0.429025 | + | 0.903293i | \(0.358857\pi\) | |||||||
\(224\) | 0.732051 | − | 0.732051i | 0.0489122 | − | 0.0489122i | ||||
\(225\) | 9.00000i | 0.600000i | ||||||||
\(226\) | −4.46410 | + | 4.46410i | −0.296948 | + | 0.296948i | ||||
\(227\) | 1.69615 | − | 6.33013i | 0.112578 | − | 0.420145i | −0.886517 | − | 0.462697i | \(-0.846882\pi\) |
0.999094 | + | 0.0425513i | \(0.0135486\pi\) | |||||||
\(228\) | 1.73205 | 0.114708 | ||||||||
\(229\) | −11.5359 | − | 6.66025i | −0.762314 | − | 0.440122i | 0.0678122 | − | 0.997698i | \(-0.478398\pi\) |
−0.830126 | + | 0.557576i | \(0.811731\pi\) | |||||||
\(230\) | −4.39230 | − | 2.53590i | −0.289620 | − | 0.167212i | ||||
\(231\) | 4.14359 | 0.272628 | ||||||||
\(232\) | −2.26795 | + | 8.46410i | −0.148898 | + | 0.555695i | ||||
\(233\) | −9.75833 | + | 9.75833i | −0.639289 | + | 0.639289i | −0.950380 | − | 0.311091i | \(-0.899306\pi\) |
0.311091 | + | 0.950380i | \(0.399306\pi\) | |||||||
\(234\) | 9.00000 | + | 5.19615i | 0.588348 | + | 0.339683i | ||||
\(235\) | −20.0000 | + | 20.0000i | −1.30466 | + | 1.30466i | ||||
\(236\) | −1.50000 | + | 0.866025i | −0.0976417 | + | 0.0563735i | ||||
\(237\) | 5.66025 | + | 21.1244i | 0.367673 | + | 1.37217i | ||||
\(238\) | 2.19615 | − | 3.66025i | 0.142355 | − | 0.237259i | ||||
\(239\) | −8.46410 | + | 14.6603i | −0.547497 | + | 0.948293i | 0.450948 | + | 0.892550i | \(0.351086\pi\) |
−0.998445 | + | 0.0557428i | \(0.982247\pi\) | |||||||
\(240\) | 1.26795 | − | 4.73205i | 0.0818458 | − | 0.305453i | ||||
\(241\) | 11.5981 | + | 3.10770i | 0.747098 | + | 0.200184i | 0.612230 | − | 0.790679i | \(-0.290272\pi\) |
0.134867 | + | 0.990864i | \(0.456939\pi\) | |||||||
\(242\) | 5.66025 | 0.363855 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 7.46410 | + | 7.46410i | 0.477840 | + | 0.477840i | ||||
\(245\) | −4.33975 | + | 16.1962i | −0.277256 | + | 1.03473i | ||||
\(246\) | −4.62436 | + | 17.2583i | −0.294838 | + | 1.10035i | ||||
\(247\) | −3.00000 | − | 1.73205i | −0.190885 | − | 0.110208i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.92820 | + | 6.80385i | −0.248940 | + | 0.431176i | ||||
\(250\) | 5.46410 | + | 1.46410i | 0.345580 | + | 0.0925979i | ||||
\(251\) | −6.80385 | −0.429455 | −0.214728 | − | 0.976674i | \(-0.568886\pi\) | ||||
−0.214728 | + | 0.976674i | \(0.568886\pi\) | |||||||
\(252\) | 3.00000 | − | 0.803848i | 0.188982 | − | 0.0506376i | ||||
\(253\) | 4.14359i | 0.260505i | ||||||||
\(254\) | 1.00000 | + | 1.73205i | 0.0627456 | + | 0.108679i | ||||
\(255\) | 0.339746 | − | 20.1962i | 0.0212757 | − | 1.26473i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 10.0359 | + | 5.79423i | 0.626022 | + | 0.361434i | 0.779210 | − | 0.626763i | \(-0.215621\pi\) |
−0.153188 | + | 0.988197i | \(0.548954\pi\) | |||||||
\(258\) | − | 9.00000i | − | 0.560316i | ||||||
\(259\) | 2.53590 | + | 4.39230i | 0.157573 | + | 0.272925i | ||||
\(260\) | −6.92820 | + | 6.92820i | −0.429669 | + | 0.429669i | ||||
\(261\) | −18.5885 | + | 18.5885i | −1.15060 | + | 1.15060i | ||||
\(262\) | 12.6603 | + | 12.6603i | 0.782153 | + | 0.782153i | ||||
\(263\) | 26.6603 | − | 15.3923i | 1.64394 | − | 0.949130i | 0.664529 | − | 0.747263i | \(-0.268632\pi\) |
0.979413 | − | 0.201868i | \(-0.0647011\pi\) | |||||||
\(264\) | −3.86603 | + | 1.03590i | −0.237937 | + | 0.0637551i | ||||
\(265\) | −6.92820 | + | 1.85641i | −0.425596 | + | 0.114038i | ||||
\(266\) | −1.00000 | + | 0.267949i | −0.0613139 | + | 0.0164290i | ||||
\(267\) | 10.3923 | − | 6.00000i | 0.635999 | − | 0.367194i | ||||
\(268\) | −2.33013 | − | 4.03590i | −0.142335 | − | 0.246532i | ||||
\(269\) | 1.46410 | − | 1.46410i | 0.0892679 | − | 0.0892679i | −0.661063 | − | 0.750331i | \(-0.729894\pi\) |
0.750331 | + | 0.661063i | \(0.229894\pi\) | |||||||
\(270\) | 10.3923 | − | 10.3923i | 0.632456 | − | 0.632456i | ||||
\(271\) | 17.4641 | 1.06087 | 0.530434 | − | 0.847726i | \(-0.322029\pi\) | ||||
0.530434 | + | 0.847726i | \(0.322029\pi\) | |||||||
\(272\) | −1.13397 | + | 3.96410i | −0.0687573 | + | 0.240359i | ||||
\(273\) | −6.00000 | − | 1.60770i | −0.363137 | − | 0.0973021i | ||||
\(274\) | −18.9904 | − | 10.9641i | −1.14725 | − | 0.662366i | ||||
\(275\) | 1.79423 | + | 6.69615i | 0.108196 | + | 0.403793i | ||||
\(276\) | 0.803848 | + | 3.00000i | 0.0483859 | + | 0.180579i | ||||
\(277\) | −28.3205 | − | 7.58846i | −1.70161 | − | 0.455946i | −0.728269 | − | 0.685291i | \(-0.759675\pi\) |
−0.973345 | + | 0.229345i | \(0.926342\pi\) | |||||||
\(278\) | 15.5622 | + | 15.5622i | 0.933357 | + | 0.933357i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.92820i | 0.174994i | ||||||||
\(281\) | −4.26795 | + | 2.46410i | −0.254605 | + | 0.146996i | −0.621871 | − | 0.783120i | \(-0.713627\pi\) |
0.367266 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(282\) | 17.3205 | 1.03142 | ||||||||
\(283\) | −28.7583 | + | 7.70577i | −1.70951 | + | 0.458061i | −0.975303 | − | 0.220870i | \(-0.929110\pi\) |
−0.734202 | + | 0.678931i | \(0.762444\pi\) | |||||||
\(284\) | −2.00000 | − | 7.46410i | −0.118678 | − | 0.442913i | ||||
\(285\) | −3.46410 | + | 3.46410i | −0.205196 | + | 0.205196i | ||||
\(286\) | 7.73205 | + | 2.07180i | 0.457206 | + | 0.122508i | ||||
\(287\) | − | 10.6795i | − | 0.630390i | ||||||
\(288\) | −2.59808 | + | 1.50000i | −0.153093 | + | 0.0883883i | ||||
\(289\) | −0.571797 | + | 16.9904i | −0.0336351 | + | 0.999434i | ||||
\(290\) | −12.3923 | − | 21.4641i | −0.727701 | − | 1.26042i | ||||
\(291\) | 4.33013 | − | 1.16025i | 0.253837 | − | 0.0680153i | ||||
\(292\) | −1.42820 | − | 5.33013i | −0.0835793 | − | 0.311922i | ||||
\(293\) | −7.73205 | + | 13.3923i | −0.451711 | + | 0.782387i | −0.998492 | − | 0.0548887i | \(-0.982520\pi\) |
0.546781 | + | 0.837276i | \(0.315853\pi\) | |||||||
\(294\) | 8.89230 | − | 5.13397i | 0.518610 | − | 0.299419i | ||||
\(295\) | 1.26795 | − | 4.73205i | 0.0738229 | − | 0.275511i | ||||
\(296\) | −3.46410 | − | 3.46410i | −0.201347 | − | 0.201347i | ||||
\(297\) | −11.5981 | − | 3.10770i | −0.672989 | − | 0.180327i | ||||
\(298\) | − | 11.4641i | − | 0.664098i | ||||||
\(299\) | 1.60770 | − | 6.00000i | 0.0929754 | − | 0.346989i | ||||
\(300\) | 2.59808 | + | 4.50000i | 0.150000 | + | 0.259808i | ||||
\(301\) | 1.39230 | + | 5.19615i | 0.0802511 | + | 0.299501i | ||||
\(302\) | 10.4641 | − | 18.1244i | 0.602141 | − | 1.04294i | ||||
\(303\) | −26.1962 | − | 15.1244i | −1.50493 | − | 0.868872i | ||||
\(304\) | 0.866025 | − | 0.500000i | 0.0496700 | − | 0.0286770i | ||||
\(305\) | −29.8564 | −1.70957 | ||||||||
\(306\) | −8.89230 | + | 8.59808i | −0.508339 | + | 0.491519i | ||||
\(307\) | 6.07180 | 0.346536 | 0.173268 | − | 0.984875i | \(-0.444567\pi\) | ||||
0.173268 | + | 0.984875i | \(0.444567\pi\) | |||||||
\(308\) | 2.07180 | − | 1.19615i | 0.118052 | − | 0.0681571i | ||||
\(309\) | 12.9282i | 0.735460i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.60770 | − | 17.1962i | −0.261278 | − | 0.975104i | −0.964489 | − | 0.264123i | \(-0.914918\pi\) |
0.703211 | − | 0.710982i | \(-0.251749\pi\) | |||||||
\(312\) | 6.00000 | 0.339683 | ||||||||
\(313\) | −2.52628 | + | 9.42820i | −0.142794 | + | 0.532914i | 0.857050 | + | 0.515233i | \(0.172295\pi\) |
−0.999844 | + | 0.0176802i | \(0.994372\pi\) | |||||||
\(314\) | − | 20.3923i | − | 1.15080i | ||||||
\(315\) | −4.39230 | + | 7.60770i | −0.247478 | + | 0.428645i | ||||
\(316\) | 8.92820 | + | 8.92820i | 0.502251 | + | 0.502251i | ||||
\(317\) | −6.66025 | + | 24.8564i | −0.374077 | + | 1.39607i | 0.480611 | + | 0.876934i | \(0.340415\pi\) |
−0.854689 | + | 0.519141i | \(0.826252\pi\) | |||||||
\(318\) | 3.80385 | + | 2.19615i | 0.213309 | + | 0.123154i | ||||
\(319\) | −10.1244 | + | 17.5359i | −0.566855 | + | 0.981822i | ||||
\(320\) | −0.732051 | − | 2.73205i | −0.0409229 | − | 0.152726i | ||||
\(321\) | 8.42820 | − | 31.4545i | 0.470416 | − | 1.75562i | ||||
\(322\) | −0.928203 | − | 1.60770i | −0.0517267 | − | 0.0895933i | ||||
\(323\) | 2.96410 | − | 2.86603i | 0.164927 | − | 0.159470i | ||||
\(324\) | −9.00000 | −0.500000 | ||||||||
\(325\) | − | 10.3923i | − | 0.576461i | ||||||
\(326\) | −5.83013 | − | 1.56218i | −0.322901 | − | 0.0865210i | ||||
\(327\) | −11.6603 | − | 3.12436i | −0.644814 | − | 0.172777i | ||||
\(328\) | 2.66987 | + | 9.96410i | 0.147419 | + | 0.550175i | ||||
\(329\) | −10.0000 | + | 2.67949i | −0.551318 | + | 0.147725i | ||||
\(330\) | 5.66025 | − | 9.80385i | 0.311587 | − | 0.539684i | ||||
\(331\) | 3.00000 | − | 1.73205i | 0.164895 | − | 0.0952021i | −0.415282 | − | 0.909693i | \(-0.636317\pi\) |
0.580176 | + | 0.814491i | \(0.302984\pi\) | |||||||
\(332\) | 4.53590i | 0.248940i | ||||||||
\(333\) | −3.80385 | − | 14.1962i | −0.208450 | − | 0.777944i | ||||
\(334\) | −16.9282 | − | 16.9282i | −0.926270 | − | 0.926270i | ||||
\(335\) | 12.7321 | + | 3.41154i | 0.695626 | + | 0.186392i | ||||
\(336\) | 1.26795 | − | 1.26795i | 0.0691723 | − | 0.0691723i | ||||
\(337\) | −0.964102 | − | 3.59808i | −0.0525180 | − | 0.196000i | 0.934683 | − | 0.355483i | \(-0.115684\pi\) |
−0.987201 | + | 0.159484i | \(0.949017\pi\) | |||||||
\(338\) | 0.866025 | + | 0.500000i | 0.0471056 | + | 0.0271964i | ||||
\(339\) | −7.73205 | + | 7.73205i | −0.419947 | + | 0.419947i | ||||
\(340\) | −5.66025 | − | 10.1962i | −0.306970 | − | 0.552964i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | −9.46410 | + | 9.46410i | −0.511013 | + | 0.511013i | ||||
\(344\) | −2.59808 | − | 4.50000i | −0.140079 | − | 0.242624i | ||||
\(345\) | −7.60770 | − | 4.39230i | −0.409585 | − | 0.236474i | ||||
\(346\) | 3.73205 | − | 1.00000i | 0.200636 | − | 0.0537603i | ||||
\(347\) | −9.79423 | + | 2.62436i | −0.525782 | + | 0.140883i | −0.511940 | − | 0.859021i | \(-0.671073\pi\) |
−0.0138421 | + | 0.999904i | \(0.504406\pi\) | |||||||
\(348\) | −3.92820 | + | 14.6603i | −0.210574 | + | 0.785872i | ||||
\(349\) | −17.0718 | + | 9.85641i | −0.913832 | + | 0.527601i | −0.881662 | − | 0.471881i | \(-0.843575\pi\) |
−0.0321701 | + | 0.999482i | \(0.510242\pi\) | |||||||
\(350\) | −2.19615 | − | 2.19615i | −0.117389 | − | 0.117389i | ||||
\(351\) | 15.5885 | + | 9.00000i | 0.832050 | + | 0.480384i | ||||
\(352\) | −1.63397 | + | 1.63397i | −0.0870911 | + | 0.0870911i | ||||
\(353\) | 10.8660 | + | 18.8205i | 0.578340 | + | 1.00171i | 0.995670 | + | 0.0929594i | \(0.0296327\pi\) |
−0.417330 | + | 0.908755i | \(0.637034\pi\) | |||||||
\(354\) | −2.59808 | + | 1.50000i | −0.138086 | + | 0.0797241i | ||||
\(355\) | 18.9282 | + | 10.9282i | 1.00460 | + | 0.580009i | ||||
\(356\) | 3.46410 | − | 6.00000i | 0.183597 | − | 0.317999i | ||||
\(357\) | 3.80385 | − | 6.33975i | 0.201321 | − | 0.335535i | ||||
\(358\) | 4.53590 | + | 7.85641i | 0.239730 | + | 0.415224i | ||||
\(359\) | 18.3923i | 0.970709i | 0.874318 | + | 0.485354i | \(0.161309\pi\) | ||||
−0.874318 | + | 0.485354i | \(0.838691\pi\) | |||||||
\(360\) | 2.19615 | − | 8.19615i | 0.115747 | − | 0.431975i | ||||
\(361\) | 18.0000 | 0.947368 | ||||||||
\(362\) | −15.3923 | − | 4.12436i | −0.809002 | − | 0.216771i | ||||
\(363\) | 9.80385 | 0.514569 | ||||||||
\(364\) | −3.46410 | + | 0.928203i | −0.181568 | + | 0.0486511i | ||||
\(365\) | 13.5167 | + | 7.80385i | 0.707494 | + | 0.408472i | ||||
\(366\) | 12.9282 | + | 12.9282i | 0.675768 | + | 0.675768i | ||||
\(367\) | 2.19615 | − | 8.19615i | 0.114638 | − | 0.427836i | −0.884621 | − | 0.466310i | \(-0.845583\pi\) |
0.999260 | + | 0.0384744i | \(0.0122498\pi\) | |||||||
\(368\) | 1.26795 | + | 1.26795i | 0.0660964 | + | 0.0660964i | ||||
\(369\) | −8.00962 | + | 29.8923i | −0.416964 | + | 1.55613i | ||||
\(370\) | 13.8564 | 0.720360 | ||||||||
\(371\) | −2.53590 | − | 0.679492i | −0.131657 | − | 0.0352775i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.19615 | − | 2.07180i | 0.0619344 | − | 0.107274i | −0.833396 | − | 0.552677i | \(-0.813606\pi\) |
0.895330 | + | 0.445403i | \(0.146940\pi\) | |||||||
\(374\) | −4.90192 | + | 8.16987i | −0.253472 | + | 0.422454i | ||||
\(375\) | 9.46410 | + | 2.53590i | 0.488724 | + | 0.130953i | ||||
\(376\) | 8.66025 | − | 5.00000i | 0.446619 | − | 0.257855i | ||||
\(377\) | 21.4641 | − | 21.4641i | 1.10546 | − | 1.10546i | ||||
\(378\) | 5.19615 | − | 1.39230i | 0.267261 | − | 0.0716124i | ||||
\(379\) | −3.16987 | + | 3.16987i | −0.162825 | + | 0.162825i | −0.783817 | − | 0.620992i | \(-0.786730\pi\) |
0.620992 | + | 0.783817i | \(0.286730\pi\) | |||||||
\(380\) | −0.732051 | + | 2.73205i | −0.0375534 | + | 0.140151i | ||||
\(381\) | 1.73205 | + | 3.00000i | 0.0887357 | + | 0.153695i | ||||
\(382\) | 6.80385 | + | 3.92820i | 0.348115 | + | 0.200984i | ||||
\(383\) | 1.26795 | + | 0.732051i | 0.0647892 | + | 0.0374060i | 0.532045 | − | 0.846716i | \(-0.321424\pi\) |
−0.467255 | + | 0.884122i | \(0.654757\pi\) | |||||||
\(384\) | −0.866025 | + | 1.50000i | −0.0441942 | + | 0.0765466i | ||||
\(385\) | −1.75129 | + | 6.53590i | −0.0892539 | + | 0.333100i | ||||
\(386\) | −4.09808 | + | 4.09808i | −0.208587 | + | 0.208587i | ||||
\(387\) | − | 15.5885i | − | 0.792406i | ||||||
\(388\) | 1.83013 | − | 1.83013i | 0.0929106 | − | 0.0929106i | ||||
\(389\) | −9.58846 | + | 5.53590i | −0.486154 | + | 0.280681i | −0.722978 | − | 0.690872i | \(-0.757227\pi\) |
0.236823 | + | 0.971553i | \(0.423894\pi\) | |||||||
\(390\) | −12.0000 | + | 12.0000i | −0.607644 | + | 0.607644i | ||||
\(391\) | 6.33975 | + | 3.80385i | 0.320615 | + | 0.192369i | ||||
\(392\) | 2.96410 | − | 5.13397i | 0.149710 | − | 0.259305i | ||||
\(393\) | 21.9282 | + | 21.9282i | 1.10613 | + | 1.10613i | ||||
\(394\) | 12.9282 | + | 3.46410i | 0.651313 | + | 0.174519i | ||||
\(395\) | −35.7128 | −1.79691 | ||||||||
\(396\) | −6.69615 | + | 1.79423i | −0.336494 | + | 0.0901634i | ||||
\(397\) | 5.07180 | + | 5.07180i | 0.254546 | + | 0.254546i | 0.822832 | − | 0.568285i | \(-0.192393\pi\) |
−0.568285 | + | 0.822832i | \(0.692393\pi\) | |||||||
\(398\) | −1.33975 | + | 5.00000i | −0.0671554 | + | 0.250627i | ||||
\(399\) | −1.73205 | + | 0.464102i | −0.0867110 | + | 0.0232341i | ||||
\(400\) | 2.59808 | + | 1.50000i | 0.129904 | + | 0.0750000i | ||||
\(401\) | −19.3564 | + | 5.18653i | −0.966613 | + | 0.259003i | −0.707397 | − | 0.706816i | \(-0.750131\pi\) |
−0.259216 | + | 0.965819i | \(0.583464\pi\) | |||||||
\(402\) | −4.03590 | − | 6.99038i | −0.201292 | − | 0.348649i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −17.4641 | −0.868872 | ||||||||
\(405\) | 18.0000 | − | 18.0000i | 0.894427 | − | 0.894427i | ||||
\(406\) | − | 9.07180i | − | 0.450226i | ||||||
\(407\) | −5.66025 | − | 9.80385i | −0.280568 | − | 0.485959i | ||||
\(408\) | −1.96410 | + | 6.86603i | −0.0972375 | + | 0.339919i | ||||
\(409\) | 15.5263 | − | 26.8923i | 0.767725 | − | 1.32974i | −0.171069 | − | 0.985259i | \(-0.554722\pi\) |
0.938794 | − | 0.344480i | \(-0.111945\pi\) | |||||||
\(410\) | −25.2679 | − | 14.5885i | −1.24790 | − | 0.720473i | ||||
\(411\) | −32.8923 | − | 18.9904i | −1.62246 | − | 0.936726i | ||||
\(412\) | 3.73205 | + | 6.46410i | 0.183865 | + | 0.318463i | ||||
\(413\) | 1.26795 | − | 1.26795i | 0.0623917 | − | 0.0623917i | ||||
\(414\) | 1.39230 | + | 5.19615i | 0.0684280 | + | 0.255377i | ||||
\(415\) | −9.07180 | − | 9.07180i | −0.445317 | − | 0.445317i | ||||
\(416\) | 3.00000 | − | 1.73205i | 0.147087 | − | 0.0849208i | ||||
\(417\) | 26.9545 | + | 26.9545i | 1.31997 | + | 1.31997i | ||||
\(418\) | 2.23205 | − | 0.598076i | 0.109173 | − | 0.0292529i | ||||
\(419\) | 7.63397 | − | 2.04552i | 0.372944 | − | 0.0999301i | −0.0674783 | − | 0.997721i | \(-0.521495\pi\) |
0.440422 | + | 0.897791i | \(0.354829\pi\) | |||||||
\(420\) | 5.07180i | 0.247478i | ||||||||
\(421\) | 8.39230 | + | 14.5359i | 0.409016 | + | 0.708436i | 0.994780 | − | 0.102045i | \(-0.0325387\pi\) |
−0.585764 | + | 0.810482i | \(0.699205\pi\) | |||||||
\(422\) | 11.1962 | − | 11.1962i | 0.545020 | − | 0.545020i | ||||
\(423\) | 30.0000 | 1.45865 | ||||||||
\(424\) | 2.53590 | 0.123154 | ||||||||
\(425\) | 11.8923 | + | 3.40192i | 0.576862 | + | 0.165018i | ||||
\(426\) | −3.46410 | − | 12.9282i | −0.167836 | − | 0.626373i | ||||
\(427\) | −9.46410 | − | 5.46410i | −0.458000 | − | 0.264426i | ||||
\(428\) | −4.86603 | − | 18.1603i | −0.235208 | − | 0.877809i | ||||
\(429\) | 13.3923 | + | 3.58846i | 0.646587 | + | 0.173252i | ||||
\(430\) | 14.1962 | + | 3.80385i | 0.684599 | + | 0.183438i | ||||
\(431\) | −20.5885 | − | 20.5885i | −0.991711 | − | 0.991711i | 0.00825484 | − | 0.999966i | \(-0.497372\pi\) |
−0.999966 | + | 0.00825484i | \(0.997372\pi\) | |||||||
\(432\) | −4.50000 | + | 2.59808i | −0.216506 | + | 0.125000i | ||||
\(433\) | − | 4.07180i | − | 0.195678i | −0.995202 | − | 0.0978390i | \(-0.968807\pi\) | ||
0.995202 | − | 0.0978390i | \(-0.0311930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.4641 | − | 37.1769i | −1.02912 | − | 1.78250i | ||||
\(436\) | −6.73205 | + | 1.80385i | −0.322407 | + | 0.0863886i | ||||
\(437\) | −0.464102 | − | 1.73205i | −0.0222010 | − | 0.0828552i | ||||
\(438\) | −2.47372 | − | 9.23205i | −0.118199 | − | 0.441124i | ||||
\(439\) | 6.73205 | + | 1.80385i | 0.321303 | + | 0.0860929i | 0.415866 | − | 0.909426i | \(-0.363479\pi\) |
−0.0945626 | + | 0.995519i | \(0.530145\pi\) | |||||||
\(440\) | − | 6.53590i | − | 0.311587i | ||||||
\(441\) | 15.4019 | − | 8.89230i | 0.733425 | − | 0.423443i | ||||
\(442\) | 10.2679 | − | 9.92820i | 0.488397 | − | 0.472236i | ||||
\(443\) | 6.06218 | + | 10.5000i | 0.288023 | + | 0.498870i | 0.973338 | − | 0.229377i | \(-0.0736688\pi\) |
−0.685315 | + | 0.728247i | \(0.740335\pi\) | |||||||
\(444\) | −6.00000 | − | 6.00000i | −0.284747 | − | 0.284747i | ||||
\(445\) | 5.07180 | + | 18.9282i | 0.240426 | + | 0.897283i | ||||
\(446\) | −1.19615 | + | 2.07180i | −0.0566395 | + | 0.0981024i | ||||
\(447\) | − | 19.8564i | − | 0.939176i | ||||||
\(448\) | 0.267949 | − | 1.00000i | 0.0126594 | − | 0.0472456i | ||||
\(449\) | −8.36603 | − | 8.36603i | −0.394817 | − | 0.394817i | 0.481583 | − | 0.876400i | \(-0.340062\pi\) |
−0.876400 | + | 0.481583i | \(0.840062\pi\) | |||||||
\(450\) | 4.50000 | + | 7.79423i | 0.212132 | + | 0.367423i | ||||
\(451\) | 23.8372i | 1.12245i | ||||||||
\(452\) | −1.63397 | + | 6.09808i | −0.0768557 | + | 0.286829i | ||||
\(453\) | 18.1244 | − | 31.3923i | 0.851557 | − | 1.47494i | ||||
\(454\) | −1.69615 | − | 6.33013i | −0.0796044 | − | 0.297088i | ||||
\(455\) | 5.07180 | − | 8.78461i | 0.237769 | − | 0.411829i | ||||
\(456\) | 1.50000 | − | 0.866025i | 0.0702439 | − | 0.0405554i | ||||
\(457\) | 23.1340 | − | 13.3564i | 1.08216 | − | 0.624786i | 0.150683 | − | 0.988582i | \(-0.451853\pi\) |
0.931479 | + | 0.363796i | \(0.118519\pi\) | |||||||
\(458\) | −13.3205 | −0.622426 | ||||||||
\(459\) | −15.4019 | + | 14.8923i | −0.718900 | + | 0.695113i | ||||
\(460\) | −5.07180 | −0.236474 | ||||||||
\(461\) | 15.5885 | − | 9.00000i | 0.726027 | − | 0.419172i | −0.0909401 | − | 0.995856i | \(-0.528987\pi\) |
0.816967 | + | 0.576685i | \(0.195654\pi\) | |||||||
\(462\) | 3.58846 | − | 2.07180i | 0.166950 | − | 0.0963887i | ||||
\(463\) | 13.8564 | − | 24.0000i | 0.643962 | − | 1.11537i | −0.340578 | − | 0.940216i | \(-0.610623\pi\) |
0.984540 | − | 0.175158i | \(-0.0560438\pi\) | |||||||
\(464\) | 2.26795 | + | 8.46410i | 0.105287 | + | 0.392936i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.57180 | + | 13.3301i | −0.165460 | + | 0.617506i | ||||
\(467\) | − | 36.8564i | − | 1.70551i | −0.522310 | − | 0.852756i | \(-0.674930\pi\) | ||
0.522310 | − | 0.852756i | \(-0.325070\pi\) | |||||||
\(468\) | 10.3923 | 0.480384 | ||||||||
\(469\) | 3.41154 | + | 3.41154i | 0.157530 | + | 0.157530i | ||||
\(470\) | −7.32051 | + | 27.3205i | −0.337670 | + | 1.26020i | ||||
\(471\) | − | 35.3205i | − | 1.62748i | ||||||
\(472\) | −0.866025 | + | 1.50000i | −0.0398621 | + | 0.0690431i | ||||
\(473\) | −3.10770 | − | 11.5981i | −0.142892 | − | 0.533280i | ||||
\(474\) | 15.4641 | + | 15.4641i | 0.710290 | + | 0.710290i | ||||
\(475\) | −1.50000 | − | 2.59808i | −0.0688247 | − | 0.119208i | ||||
\(476\) | 0.0717968 | − | 4.26795i | 0.00329080 | − | 0.195621i | ||||
\(477\) | 6.58846 | + | 3.80385i | 0.301665 | + | 0.174166i | ||||
\(478\) | 16.9282i | 0.774278i | ||||||||
\(479\) | 29.5885 | + | 7.92820i | 1.35193 | + | 0.362249i | 0.860847 | − | 0.508863i | \(-0.169934\pi\) |
0.491084 | + | 0.871112i | \(0.336601\pi\) | |||||||
\(480\) | −1.26795 | − | 4.73205i | −0.0578737 | − | 0.215988i | ||||
\(481\) | 4.39230 | + | 16.3923i | 0.200272 | + | 0.747425i | ||||
\(482\) | 11.5981 | − | 3.10770i | 0.528278 | − | 0.141552i | ||||
\(483\) | −1.60770 | − | 2.78461i | −0.0731527 | − | 0.126704i | ||||
\(484\) | 4.90192 | − | 2.83013i | 0.222815 | − | 0.128642i | ||||
\(485\) | 7.32051i | 0.332407i | ||||||||
\(486\) | −15.5885 | −0.707107 | ||||||||
\(487\) | 12.5885 | + | 12.5885i | 0.570437 | + | 0.570437i | 0.932251 | − | 0.361813i | \(-0.117842\pi\) |
−0.361813 | + | 0.932251i | \(0.617842\pi\) | |||||||
\(488\) | 10.1962 | + | 2.73205i | 0.461558 | + | 0.123674i | ||||
\(489\) | −10.0981 | − | 2.70577i | −0.456651 | − | 0.122359i | ||||
\(490\) | 4.33975 | + | 16.1962i | 0.196050 | + | 0.731668i | ||||
\(491\) | 10.3301 | + | 5.96410i | 0.466192 | + | 0.269156i | 0.714644 | − | 0.699488i | \(-0.246589\pi\) |
−0.248452 | + | 0.968644i | \(0.579922\pi\) | |||||||
\(492\) | 4.62436 | + | 17.2583i | 0.208482 | + | 0.778066i | ||||
\(493\) | 17.5359 | + | 31.5885i | 0.789777 | + | 1.42267i | ||||
\(494\) | −3.46410 | −0.155857 | ||||||||
\(495\) | 9.80385 | − | 16.9808i | 0.440650 | − | 0.763228i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000 | + | 6.92820i | 0.179425 | + | 0.310772i | ||||
\(498\) | 7.85641i | 0.352054i | ||||||||
\(499\) | −29.2583 | + | 7.83975i | −1.30978 | + | 0.350955i | −0.845141 | − | 0.534544i | \(-0.820484\pi\) |
−0.464642 | + | 0.885499i | \(0.653817\pi\) | |||||||
\(500\) | 5.46410 | − | 1.46410i | 0.244362 | − | 0.0654766i | ||||
\(501\) | −29.3205 | − | 29.3205i | −1.30994 | − | 1.30994i | ||||
\(502\) | −5.89230 | + | 3.40192i | −0.262986 | + | 0.151835i | ||||
\(503\) | 16.3923 | + | 16.3923i | 0.730897 | + | 0.730897i | 0.970797 | − | 0.239901i | \(-0.0771149\pi\) |
−0.239901 | + | 0.970797i | \(0.577115\pi\) | |||||||
\(504\) | 2.19615 | − | 2.19615i | 0.0978244 | − | 0.0978244i | ||||
\(505\) | 34.9282 | − | 34.9282i | 1.55428 | − | 1.55428i | ||||
\(506\) | 2.07180 | + | 3.58846i | 0.0921026 | + | 0.159526i | ||||
\(507\) | 1.50000 | + | 0.866025i | 0.0666173 | + | 0.0384615i | ||||
\(508\) | 1.73205 | + | 1.00000i | 0.0768473 | + | 0.0443678i | ||||
\(509\) | −5.85641 | + | 10.1436i | −0.259581 | + | 0.449607i | −0.966130 | − | 0.258057i | \(-0.916918\pi\) |
0.706549 | + | 0.707664i | \(0.250251\pi\) | |||||||
\(510\) | −9.80385 | − | 17.6603i | −0.434122 | − | 0.782009i | ||||
\(511\) | 2.85641 | + | 4.94744i | 0.126360 | + | 0.218862i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 5.19615 | 0.229416 | ||||||||
\(514\) | 11.5885 | 0.511145 | ||||||||
\(515\) | −20.3923 | − | 5.46410i | −0.898592 | − | 0.240777i | ||||
\(516\) | −4.50000 | − | 7.79423i | −0.198101 | − | 0.343122i | ||||
\(517\) | 22.3205 | − | 5.98076i | 0.981655 | − | 0.263034i | ||||
\(518\) | 4.39230 | + | 2.53590i | 0.192987 | + | 0.111421i | ||||
\(519\) | 6.46410 | − | 1.73205i | 0.283743 | − | 0.0760286i | ||||
\(520\) | −2.53590 | + | 9.46410i | −0.111207 | + | 0.415028i | ||||
\(521\) | 25.7583 | + | 25.7583i | 1.12849 | + | 1.12849i | 0.990422 | + | 0.138071i | \(0.0440901\pi\) |
0.138071 | + | 0.990422i | \(0.455910\pi\) | |||||||
\(522\) | −6.80385 | + | 25.3923i | −0.297796 | + | 1.11139i | ||||
\(523\) | −43.1769 | −1.88799 | −0.943997 | − | 0.329953i | \(-0.892967\pi\) | ||||
−0.943997 | + | 0.329953i | \(0.892967\pi\) | |||||||
\(524\) | 17.2942 | + | 4.63397i | 0.755502 | + | 0.202436i | ||||
\(525\) | −3.80385 | − | 3.80385i | −0.166014 | − | 0.166014i | ||||
\(526\) | 15.3923 | − | 26.6603i | 0.671136 | − | 1.16244i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.83013 | + | 2.83013i | −0.123165 | + | 0.123165i | ||||
\(529\) | −17.1340 | + | 9.89230i | −0.744955 | + | 0.430100i | ||||
\(530\) | −5.07180 | + | 5.07180i | −0.220305 | + | 0.220305i | ||||
\(531\) | −4.50000 | + | 2.59808i | −0.195283 | + | 0.112747i | ||||
\(532\) | −0.732051 | + | 0.732051i | −0.0317384 | + | 0.0317384i | ||||
\(533\) | 9.24871 | − | 34.5167i | 0.400606 | − | 1.49508i | ||||
\(534\) | 6.00000 | − | 10.3923i | 0.259645 | − | 0.449719i | ||||
\(535\) | 46.0526 | + | 26.5885i | 1.99103 | + | 1.14952i | ||||
\(536\) | −4.03590 | − | 2.33013i | −0.174324 | − | 0.100646i | ||||
\(537\) | 7.85641 | + | 13.6077i | 0.339029 | + | 0.587215i | ||||
\(538\) | 0.535898 | − | 2.00000i | 0.0231042 | − | 0.0862261i | ||||
\(539\) | 9.68653 | − | 9.68653i | 0.417229 | − | 0.417229i | ||||
\(540\) | 3.80385 | − | 14.1962i | 0.163692 | − | 0.610905i | ||||
\(541\) | −18.9282 | + | 18.9282i | −0.813787 | + | 0.813787i | −0.985199 | − | 0.171412i | \(-0.945167\pi\) |
0.171412 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(542\) | 15.1244 | − | 8.73205i | 0.649647 | − | 0.375074i | ||||
\(543\) | −26.6603 | − | 7.14359i | −1.14410 | − | 0.306561i | ||||
\(544\) | 1.00000 | + | 4.00000i | 0.0428746 | + | 0.171499i | ||||
\(545\) | 9.85641 | − | 17.0718i | 0.422202 | − | 0.731275i | ||||
\(546\) | −6.00000 | + | 1.60770i | −0.256776 | + | 0.0688030i | ||||
\(547\) | −31.5526 | − | 8.45448i | −1.34909 | − | 0.361488i | −0.489291 | − | 0.872120i | \(-0.662744\pi\) |
−0.859799 | + | 0.510633i | \(0.829411\pi\) | |||||||
\(548\) | −21.9282 | −0.936726 | ||||||||
\(549\) | 22.3923 | + | 22.3923i | 0.955680 | + | 0.955680i | ||||
\(550\) | 4.90192 | + | 4.90192i | 0.209019 | + | 0.209019i | ||||
\(551\) | 2.26795 | − | 8.46410i | 0.0966179 | − | 0.360583i | ||||
\(552\) | 2.19615 | + | 2.19615i | 0.0934745 | + | 0.0934745i | ||||
\(553\) | −11.3205 | − | 6.53590i | −0.481397 | − | 0.277935i | ||||
\(554\) | −28.3205 | + | 7.58846i | −1.20322 | + | 0.322403i | ||||
\(555\) | 24.0000 | 1.01874 | ||||||||
\(556\) | 21.2583 | + | 5.69615i | 0.901554 | + | 0.241571i | ||||
\(557\) | −38.7846 | −1.64336 | −0.821678 | − | 0.569952i | \(-0.806962\pi\) | ||||
−0.821678 | + | 0.569952i | \(0.806962\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 18.0000i | 0.761319i | ||||||||
\(560\) | 1.46410 | + | 2.53590i | 0.0618696 | + | 0.107161i | ||||
\(561\) | −8.49038 | + | 14.1506i | −0.358464 | + | 0.597440i | ||||
\(562\) | −2.46410 | + | 4.26795i | −0.103942 | + | 0.180033i | ||||
\(563\) | −8.89230 | − | 5.13397i | −0.374766 | − | 0.216371i | 0.300773 | − | 0.953696i | \(-0.402755\pi\) |
−0.675539 | + | 0.737325i | \(0.736089\pi\) | |||||||
\(564\) | 15.0000 | − | 8.66025i | 0.631614 | − | 0.364662i | ||||
\(565\) | −8.92820 | − | 15.4641i | −0.375612 | − | 0.650580i | ||||
\(566\) | −21.0526 | + | 21.0526i | −0.884905 | + | 0.884905i | ||||
\(567\) | 9.00000 | − | 2.41154i | 0.377964 | − | 0.101275i | ||||
\(568\) | −5.46410 | − | 5.46410i | −0.229269 | − | 0.229269i | ||||
\(569\) | −15.8205 | + | 9.13397i | −0.663230 | + | 0.382916i | −0.793507 | − | 0.608562i | \(-0.791747\pi\) |
0.130276 | + | 0.991478i | \(0.458414\pi\) | |||||||
\(570\) | −1.26795 | + | 4.73205i | −0.0531085 | + | 0.198204i | ||||
\(571\) | 14.1603 | − | 3.79423i | 0.592588 | − | 0.158784i | 0.0499524 | − | 0.998752i | \(-0.484093\pi\) |
0.542636 | + | 0.839968i | \(0.317426\pi\) | |||||||
\(572\) | 7.73205 | − | 2.07180i | 0.323293 | − | 0.0866262i | ||||
\(573\) | 11.7846 | + | 6.80385i | 0.492309 | + | 0.284235i | ||||
\(574\) | −5.33975 | − | 9.24871i | −0.222877 | − | 0.386034i | ||||
\(575\) | 3.80385 | − | 3.80385i | 0.158631 | − | 0.158631i | ||||
\(576\) | −1.50000 | + | 2.59808i | −0.0625000 | + | 0.108253i | ||||
\(577\) | 5.14359 | 0.214131 | 0.107065 | − | 0.994252i | \(-0.465855\pi\) | ||||
0.107065 | + | 0.994252i | \(0.465855\pi\) | |||||||
\(578\) | 8.00000 | + | 15.0000i | 0.332756 | + | 0.623918i | ||||
\(579\) | −7.09808 | + | 7.09808i | −0.294986 | + | 0.294986i | ||||
\(580\) | −21.4641 | − | 12.3923i | −0.891248 | − | 0.514562i | ||||
\(581\) | −1.21539 | − | 4.53590i | −0.0504229 | − | 0.188181i | ||||
\(582\) | 3.16987 | − | 3.16987i | 0.131395 | − | 0.131395i | ||||
\(583\) | 5.66025 | + | 1.51666i | 0.234424 | + | 0.0628137i | ||||
\(584\) | −3.90192 | − | 3.90192i | −0.161463 | − | 0.161463i | ||||
\(585\) | −20.7846 | + | 20.7846i | −0.859338 | + | 0.859338i | ||||
\(586\) | 15.4641i | 0.638816i | ||||||||
\(587\) | 8.47372 | − | 4.89230i | 0.349748 | − | 0.201927i | −0.314826 | − | 0.949149i | \(-0.601946\pi\) |
0.664574 | + | 0.747222i | \(0.268613\pi\) | |||||||
\(588\) | 5.13397 | − | 8.89230i | 0.211722 | − | 0.366712i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −1.26795 | − | 4.73205i | −0.0522006 | − | 0.194815i | ||||
\(591\) | 22.3923 | + | 6.00000i | 0.921096 | + | 0.246807i | ||||
\(592\) | −4.73205 | − | 1.26795i | −0.194486 | − | 0.0521124i | ||||
\(593\) | 6.92820i | 0.284507i | 0.989830 | + | 0.142254i | \(0.0454349\pi\) | ||||
−0.989830 | + | 0.142254i | \(0.954565\pi\) | |||||||
\(594\) | −11.5981 | + | 3.10770i | −0.475875 | + | 0.127510i | ||||
\(595\) | 8.39230 | + | 8.67949i | 0.344051 | + | 0.355824i | ||||
\(596\) | −5.73205 | − | 9.92820i | −0.234794 | − | 0.406675i | ||||
\(597\) | −2.32051 | + | 8.66025i | −0.0949721 | + | 0.354441i | ||||
\(598\) | −1.60770 | − | 6.00000i | −0.0657435 | − | 0.245358i | ||||
\(599\) | 4.73205 | − | 8.19615i | 0.193346 | − | 0.334886i | −0.753011 | − | 0.658008i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104733\pi\) | |||||||
\(600\) | 4.50000 | + | 2.59808i | 0.183712 | + | 0.106066i | ||||
\(601\) | −10.1340 | + | 37.8205i | −0.413373 | + | 1.54273i | 0.374698 | + | 0.927147i | \(0.377746\pi\) |
−0.788071 | + | 0.615584i | \(0.788920\pi\) | |||||||
\(602\) | 3.80385 | + | 3.80385i | 0.155033 | + | 0.155033i | ||||
\(603\) | −6.99038 | − | 12.1077i | −0.284670 | − | 0.493063i | ||||
\(604\) | − | 20.9282i | − | 0.851557i | ||||||
\(605\) | −4.14359 | + | 15.4641i | −0.168461 | + | 0.628705i | ||||
\(606\) | −30.2487 | −1.22877 | ||||||||
\(607\) | −12.5885 | − | 46.9808i | −0.510950 | − | 1.90689i | −0.410249 | − | 0.911974i | \(-0.634558\pi\) |
−0.100701 | − | 0.994917i | \(-0.532108\pi\) | |||||||
\(608\) | 0.500000 | − | 0.866025i | 0.0202777 | − | 0.0351220i | ||||
\(609\) | − | 15.7128i | − | 0.636715i | ||||||
\(610\) | −25.8564 | + | 14.9282i | −1.04690 | + | 0.604425i | ||||
\(611\) | −34.6410 | −1.40143 | ||||||||
\(612\) | −3.40192 | + | 11.8923i | −0.137515 | + | 0.480718i | ||||
\(613\) | −25.8564 | −1.04433 | −0.522165 | − | 0.852844i | \(-0.674876\pi\) | ||||
−0.522165 | + | 0.852844i | \(0.674876\pi\) | |||||||
\(614\) | 5.25833 | − | 3.03590i | 0.212209 | − | 0.122519i | ||||
\(615\) | −43.7654 | − | 25.2679i | −1.76479 | − | 1.01890i | ||||
\(616\) | 1.19615 | − | 2.07180i | 0.0481944 | − | 0.0834751i | ||||
\(617\) | −0.428203 | − | 1.59808i | −0.0172388 | − | 0.0643361i | 0.956771 | − | 0.290844i | \(-0.0939359\pi\) |
−0.974009 | + | 0.226507i | \(0.927269\pi\) | |||||||
\(618\) | 6.46410 | + | 11.1962i | 0.260024 | + | 0.450375i | ||||
\(619\) | −5.38269 | + | 20.0885i | −0.216348 | + | 0.807423i | 0.769339 | + | 0.638841i | \(0.220586\pi\) |
−0.985688 | + | 0.168583i | \(0.946081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.41154 | + | 9.00000i | 0.0967719 | + | 0.361158i | ||||
\(622\) | −12.5885 | − | 12.5885i | −0.504751 | − | 0.504751i | ||||
\(623\) | −1.85641 | + | 6.92820i | −0.0743754 | + | 0.277573i | ||||
\(624\) | 5.19615 | − | 3.00000i | 0.208013 | − | 0.120096i | ||||
\(625\) | −15.5000 | + | 26.8468i | −0.620000 | + | 1.07387i | ||||
\(626\) | 2.52628 | + | 9.42820i | 0.100970 | + | 0.376827i | ||||
\(627\) | 3.86603 | − | 1.03590i | 0.154394 | − | 0.0413698i | ||||
\(628\) | −10.1962 | − | 17.6603i | −0.406871 | − | 0.704721i | ||||
\(629\) | −20.1962 | − | 0.339746i | −0.805273 | − | 0.0135466i | ||||
\(630\) | 8.78461i | 0.349987i | ||||||||
\(631\) | − | 21.4641i | − | 0.854472i | −0.904140 | − | 0.427236i | \(-0.859487\pi\) | ||
0.904140 | − | 0.427236i | \(-0.140513\pi\) | |||||||
\(632\) | 12.1962 | + | 3.26795i | 0.485137 | + | 0.129992i | ||||
\(633\) | 19.3923 | − | 19.3923i | 0.770775 | − | 0.770775i | ||||
\(634\) | 6.66025 | + | 24.8564i | 0.264512 | + | 0.987174i | ||||
\(635\) | −5.46410 | + | 1.46410i | −0.216836 | + | 0.0581011i | ||||
\(636\) | 4.39230 | 0.174166 | ||||||||
\(637\) | −17.7846 | + | 10.2679i | −0.704652 | + | 0.406831i | ||||
\(638\) | 20.2487i | 0.801654i | ||||||||
\(639\) | −6.00000 | − | 22.3923i | −0.237356 | − | 0.885826i | ||||
\(640\) | −2.00000 | − | 2.00000i | −0.0790569 | − | 0.0790569i | ||||
\(641\) | −44.9186 | − | 12.0359i | −1.77418 | − | 0.475389i | −0.784675 | − | 0.619907i | \(-0.787170\pi\) |
−0.989502 | + | 0.144518i | \(0.953837\pi\) | |||||||
\(642\) | −8.42820 | − | 31.4545i | −0.332635 | − | 1.24141i | ||||
\(643\) | −6.16025 | − | 22.9904i | −0.242937 | − | 0.906652i | −0.974409 | − | 0.224781i | \(-0.927833\pi\) |
0.731473 | − | 0.681871i | \(-0.238833\pi\) | |||||||
\(644\) | −1.60770 | − | 0.928203i | −0.0633521 | − | 0.0365763i | ||||
\(645\) | 24.5885 | + | 6.58846i | 0.968170 | + | 0.259420i | ||||
\(646\) | 1.13397 | − | 3.96410i | 0.0446156 | − | 0.155965i | ||||
\(647\) | 15.4641 | 0.607957 | 0.303978 | − | 0.952679i | \(-0.401685\pi\) | ||||
0.303978 | + | 0.952679i | \(0.401685\pi\) | |||||||
\(648\) | −7.79423 | + | 4.50000i | −0.306186 | + | 0.176777i | ||||
\(649\) | −2.83013 | + | 2.83013i | −0.111092 | + | 0.111092i | ||||
\(650\) | −5.19615 | − | 9.00000i | −0.203810 | − | 0.353009i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.83013 | + | 1.56218i | −0.228325 | + | 0.0611796i | ||||
\(653\) | −23.3923 | + | 6.26795i | −0.915412 | + | 0.245284i | −0.685623 | − | 0.727957i | \(-0.740470\pi\) |
−0.229789 | + | 0.973241i | \(0.573803\pi\) | |||||||
\(654\) | −11.6603 | + | 3.12436i | −0.455952 | + | 0.122172i | ||||
\(655\) | −43.8564 | + | 25.3205i | −1.71361 | + | 0.989354i | ||||
\(656\) | 7.29423 | + | 7.29423i | 0.284792 | + | 0.284792i | ||||
\(657\) | −4.28461 | − | 15.9904i | −0.167159 | − | 0.623844i | ||||
\(658\) | −7.32051 | + | 7.32051i | −0.285383 | + | 0.285383i | ||||
\(659\) | 16.9282 | + | 29.3205i | 0.659429 | + | 1.14216i | 0.980764 | + | 0.195199i | \(0.0625353\pi\) |
−0.321334 | + | 0.946966i | \(0.604131\pi\) | |||||||
\(660\) | − | 11.3205i | − | 0.440650i | ||||||
\(661\) | −30.2487 | − | 17.4641i | −1.17654 | − | 0.679275i | −0.221327 | − | 0.975200i | \(-0.571039\pi\) |
−0.955211 | + | 0.295925i | \(0.904372\pi\) | |||||||
\(662\) | 1.73205 | − | 3.00000i | 0.0673181 | − | 0.116598i | ||||
\(663\) | 17.7846 | − | 17.1962i | 0.690697 | − | 0.667843i | ||||
\(664\) | 2.26795 | + | 3.92820i | 0.0880135 | + | 0.152444i | ||||
\(665\) | − | 2.92820i | − | 0.113551i | ||||||
\(666\) | −10.3923 | − | 10.3923i | −0.402694 | − | 0.402694i | ||||
\(667\) | 15.7128 | 0.608403 | ||||||||
\(668\) | −23.1244 | − | 6.19615i | −0.894708 | − | 0.239736i | ||||
\(669\) | −2.07180 | + | 3.58846i | −0.0801003 | + | 0.138738i | ||||
\(670\) | 12.7321 | − | 3.41154i | 0.491882 | − | 0.131799i | ||||
\(671\) | 21.1244 | + | 12.1962i | 0.815497 | + | 0.470827i | ||||
\(672\) | 0.464102 | − | 1.73205i | 0.0179031 | − | 0.0668153i | ||||
\(673\) | 6.75833 | − | 25.2224i | 0.260514 | − | 0.972253i | −0.704424 | − | 0.709779i | \(-0.748795\pi\) |
0.964939 | − | 0.262474i | \(-0.0845385\pi\) | |||||||
\(674\) | −2.63397 | − | 2.63397i | −0.101457 | − | 0.101457i | ||||
\(675\) | 7.79423 | + | 13.5000i | 0.300000 | + | 0.519615i | ||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 40.0526 | + | 10.7321i | 1.53934 | + | 0.412466i | 0.926054 | − | 0.377391i | \(-0.123179\pi\) |
0.613291 | + | 0.789857i | \(0.289845\pi\) | |||||||
\(678\) | −2.83013 | + | 10.5622i | −0.108690 | + | 0.405638i | ||||
\(679\) | −1.33975 | + | 2.32051i | −0.0514147 | + | 0.0890529i | ||||
\(680\) | −10.0000 | − | 6.00000i | −0.383482 | − | 0.230089i | ||||
\(681\) | −2.93782 | − | 10.9641i | −0.112578 | − | 0.420145i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.8827 | − | 14.8827i | 0.569470 | − | 0.569470i | −0.362510 | − | 0.931980i | \(-0.618080\pi\) |
0.931980 | + | 0.362510i | \(0.118080\pi\) | |||||||
\(684\) | 2.59808 | − | 1.50000i | 0.0993399 | − | 0.0573539i | ||||
\(685\) | 43.8564 | − | 43.8564i | 1.67567 | − | 1.67567i | ||||
\(686\) | −3.46410 | + | 12.9282i | −0.132260 | + | 0.493601i | ||||
\(687\) | −23.0718 | −0.880244 | ||||||||
\(688\) | −4.50000 | − | 2.59808i | −0.171561 | − | 0.0990507i | ||||
\(689\) | −7.60770 | − | 4.39230i | −0.289830 | − | 0.167333i | ||||
\(690\) | −8.78461 | −0.334424 | ||||||||
\(691\) | 12.2417 | − | 45.6865i | 0.465695 | − | 1.73800i | −0.188880 | − | 0.982000i | \(-0.560486\pi\) |
0.654575 | − | 0.755997i | \(-0.272848\pi\) | |||||||
\(692\) | 2.73205 | − | 2.73205i | 0.103857 | − | 0.103857i | ||||
\(693\) | 6.21539 | − | 3.58846i | 0.236103 | − | 0.136314i | ||||
\(694\) | −7.16987 | + | 7.16987i | −0.272165 | + | 0.272165i | ||||
\(695\) | −53.9090 | + | 31.1244i | −2.04488 | + | 1.18061i | ||||
\(696\) | 3.92820 | + | 14.6603i | 0.148898 | + | 0.555695i | ||||
\(697\) | 36.4711 | + | 21.8827i | 1.38144 | + | 0.828866i | ||||
\(698\) | −9.85641 | + | 17.0718i | −0.373070 | + | 0.646177i | ||||
\(699\) | −6.18653 | + | 23.0885i | −0.233996 | + | 0.873286i | ||||
\(700\) | −3.00000 | − | 0.803848i | −0.113389 | − | 0.0303826i | ||||
\(701\) | −38.7846 | −1.46487 | −0.732437 | − | 0.680835i | \(-0.761617\pi\) | ||||
−0.732437 | + | 0.680835i | \(0.761617\pi\) | |||||||
\(702\) | 18.0000 | 0.679366 | ||||||||
\(703\) | 3.46410 | + | 3.46410i | 0.130651 | + | 0.130651i | ||||
\(704\) | −0.598076 | + | 2.23205i | −0.0225408 | + | 0.0841236i | ||||
\(705\) | −12.6795 | + | 47.3205i | −0.477537 | + | 1.78219i | ||||
\(706\) | 18.8205 | + | 10.8660i | 0.708319 | + | 0.408948i | ||||
\(707\) | 17.4641 | − | 4.67949i | 0.656805 | − | 0.175990i | ||||
\(708\) | −1.50000 | + | 2.59808i | −0.0563735 | + | 0.0976417i | ||||
\(709\) | −16.9282 | − | 4.53590i | −0.635752 | − | 0.170349i | −0.0734735 | − | 0.997297i | \(-0.523408\pi\) |
−0.562279 | + | 0.826948i | \(0.690075\pi\) | |||||||
\(710\) | 21.8564 | 0.820256 | ||||||||
\(711\) | 26.7846 | + | 26.7846i | 1.00450 | + | 1.00450i | ||||
\(712\) | − | 6.92820i | − | 0.259645i | ||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0.124356 | − | 7.39230i | 0.00465389 | − | 0.276650i | ||||
\(715\) | −11.3205 | + | 19.6077i | −0.423363 | + | 0.733286i | ||||
\(716\) | 7.85641 | + | 4.53590i | 0.293608 | + | 0.169514i | ||||
\(717\) | 29.3205i | 1.09499i | ||||||||
\(718\) | 9.19615 | + | 15.9282i | 0.343197 | + | 0.594435i | ||||
\(719\) | −3.85641 | + | 3.85641i | −0.143820 | + | 0.143820i | −0.775351 | − | 0.631531i | \(-0.782427\pi\) |
0.631531 | + | 0.775351i | \(0.282427\pi\) | |||||||
\(720\) | −2.19615 | − | 8.19615i | −0.0818458 | − | 0.305453i | ||||
\(721\) | −5.46410 | − | 5.46410i | −0.203494 | − | 0.203494i | ||||
\(722\) | 15.5885 | − | 9.00000i | 0.580142 | − | 0.334945i | ||||
\(723\) | 20.0885 | − | 5.38269i | 0.747098 | − | 0.200184i | ||||
\(724\) | −15.3923 | + | 4.12436i | −0.572051 | + | 0.153280i | ||||
\(725\) | 25.3923 | − | 6.80385i | 0.943047 | − | 0.252689i | ||||
\(726\) | 8.49038 | − | 4.90192i | 0.315108 | − | 0.181927i | ||||
\(727\) | 3.53590 | + | 6.12436i | 0.131139 | + | 0.227140i | 0.924116 | − | 0.382112i | \(-0.124803\pi\) |
−0.792977 | + | 0.609252i | \(0.791470\pi\) | |||||||
\(728\) | −2.53590 | + | 2.53590i | −0.0939866 | + | 0.0939866i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 15.6077 | 0.577667 | ||||||||
\(731\) | −20.5981 | − | 5.89230i | −0.761847 | − | 0.217935i | ||||
\(732\) | 17.6603 | + | 4.73205i | 0.652742 | + | 0.174902i | ||||
\(733\) | −10.8564 | − | 6.26795i | −0.400991 | − | 0.231512i | 0.285921 | − | 0.958253i | \(-0.407701\pi\) |
−0.686911 | + | 0.726741i | \(0.741034\pi\) | |||||||
\(734\) | −2.19615 | − | 8.19615i | −0.0810615 | − | 0.302526i | ||||
\(735\) | 7.51666 | + | 28.0526i | 0.277256 | + | 1.03473i | ||||
\(736\) | 1.73205 | + | 0.464102i | 0.0638442 | + | 0.0171070i | ||||
\(737\) | −7.61474 | − | 7.61474i | −0.280492 | − | 0.280492i | ||||
\(738\) | 8.00962 | + | 29.8923i | 0.294838 | + | 1.10035i | ||||
\(739\) | 0.215390i | 0.00792326i | 0.999992 | + | 0.00396163i | \(0.00126103\pi\) | ||||
−0.999992 | + | 0.00396163i | \(0.998739\pi\) | |||||||
\(740\) | 12.0000 | − | 6.92820i | 0.441129 | − | 0.254686i | ||||
\(741\) | −6.00000 | −0.220416 | ||||||||
\(742\) | −2.53590 | + | 0.679492i | −0.0930958 | + | 0.0249449i | ||||
\(743\) | −4.85641 | − | 18.1244i | −0.178164 | − | 0.664918i | −0.995991 | − | 0.0894536i | \(-0.971488\pi\) |
0.817827 | − | 0.575465i | \(-0.195179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.3205 | + | 8.39230i | 1.14749 | + | 0.307470i | ||||
\(746\) | − | 2.39230i | − | 0.0875885i | ||||||
\(747\) | 13.6077i | 0.497880i | ||||||||
\(748\) | −0.160254 | + | 9.52628i | −0.00585947 | + | 0.348315i | ||||
\(749\) | 9.73205 | + | 16.8564i | 0.355601 | + | 0.615920i | ||||
\(750\) | 9.46410 | − | 2.53590i | 0.345580 | − | 0.0925979i | ||||
\(751\) | 4.73205 | + | 17.6603i | 0.172675 | + | 0.644432i | 0.996936 | + | 0.0782218i | \(0.0249242\pi\) |
−0.824261 | + | 0.566210i | \(0.808409\pi\) | |||||||
\(752\) | 5.00000 | − | 8.66025i | 0.182331 | − | 0.315807i | ||||
\(753\) | −10.2058 | + | 5.89230i | −0.371919 | + | 0.214728i | ||||
\(754\) | 7.85641 | − | 29.3205i | 0.286113 | − | 1.06779i | ||||
\(755\) | 41.8564 | + | 41.8564i | 1.52331 | + | 1.52331i | ||||
\(756\) | 3.80385 | − | 3.80385i | 0.138345 | − | 0.138345i | ||||
\(757\) | − | 35.8564i | − | 1.30322i | −0.758553 | − | 0.651612i | \(-0.774093\pi\) | ||
0.758553 | − | 0.651612i | \(-0.225907\pi\) | |||||||
\(758\) | −1.16025 | + | 4.33013i | −0.0421423 | + | 0.157277i | ||||
\(759\) | 3.58846 | + | 6.21539i | 0.130253 | + | 0.225604i | ||||
\(760\) | 0.732051 | + | 2.73205i | 0.0265543 | + | 0.0991019i | ||||
\(761\) | 1.92820 | − | 3.33975i | 0.0698973 | − | 0.121066i | −0.828959 | − | 0.559310i | \(-0.811066\pi\) |
0.898856 | + | 0.438244i | \(0.144400\pi\) | |||||||
\(762\) | 3.00000 | + | 1.73205i | 0.108679 | + | 0.0627456i | ||||
\(763\) | 6.24871 | − | 3.60770i | 0.226219 | − | 0.130607i | ||||
\(764\) | 7.85641 | 0.284235 | ||||||||
\(765\) | −16.9808 | − | 30.5885i | −0.613941 | − | 1.10593i | ||||
\(766\) | 1.46410 | 0.0529001 | ||||||||
\(767\) | 5.19615 | − | 3.00000i | 0.187622 | − | 0.108324i | ||||
\(768\) | 1.73205i | 0.0625000i | ||||||||
\(769\) | 1.53590 | − | 2.66025i | 0.0553859 | − | 0.0959312i | −0.837003 | − | 0.547198i | \(-0.815694\pi\) |
0.892389 | + | 0.451267i | \(0.149028\pi\) | |||||||
\(770\) | 1.75129 | + | 6.53590i | 0.0631121 | + | 0.235537i | ||||
\(771\) | 20.0718 | 0.722868 | ||||||||
\(772\) | −1.50000 | + | 5.59808i | −0.0539862 | + | 0.201479i | ||||
\(773\) | 23.1769i | 0.833616i | 0.908995 | + | 0.416808i | \(0.136851\pi\) | ||||
−0.908995 | + | 0.416808i | \(0.863149\pi\) | |||||||
\(774\) | −7.79423 | − | 13.5000i | −0.280158 | − | 0.485247i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.669873 | − | 2.50000i | 0.0240470 | − | 0.0897448i | ||||
\(777\) | 7.60770 | + | 4.39230i | 0.272925 | + | 0.157573i | ||||
\(778\) | −5.53590 | + | 9.58846i | −0.198472 | + | 0.343763i | ||||
\(779\) | −2.66987 | − | 9.96410i | −0.0956581 | − | 0.357001i | ||||
\(780\) | −4.39230 | + | 16.3923i | −0.157270 | + | 0.586939i | ||||
\(781\) | −8.92820 | − | 15.4641i | −0.319476 | − | 0.553349i | ||||
\(782\) | 7.39230 | + | 0.124356i | 0.264348 | + | 0.00444695i | ||||
\(783\) | −11.7846 | + | 43.9808i | −0.421148 | + | 1.57174i | ||||
\(784\) | − | 5.92820i | − | 0.211722i | ||||||
\(785\) | 55.7128 | + | 14.9282i | 1.98848 | + | 0.532810i | ||||
\(786\) | 29.9545 | + | 8.02628i | 1.06844 | + | 0.286288i | ||||
\(787\) | −11.0263 | − | 41.1506i | −0.393044 | − | 1.46686i | −0.825086 | − | 0.565008i | \(-0.808873\pi\) |
0.432041 | − | 0.901854i | \(-0.357794\pi\) | |||||||
\(788\) | 12.9282 | − | 3.46410i | 0.460548 | − | 0.123404i | ||||
\(789\) | 26.6603 | − | 46.1769i | 0.949130 | − | 1.64394i | ||||
\(790\) | −30.9282 | + | 17.8564i | −1.10038 | + | 0.635302i | ||||
\(791\) | − | 6.53590i | − | 0.232390i | ||||||
\(792\) | −4.90192 | + | 4.90192i | −0.174182 | + | 0.174182i | ||||
\(793\) | −25.8564 | − | 25.8564i | −0.918188 | − | 0.918188i | ||||
\(794\) | 6.92820 | + | 1.85641i | 0.245873 | + | 0.0658814i | ||||
\(795\) | −8.78461 | + | 8.78461i | −0.311558 | + | 0.311558i | ||||
\(796\) | 1.33975 | + | 5.00000i | 0.0474860 | + | 0.177220i | ||||
\(797\) | 19.1769 | + | 11.0718i | 0.679281 | + | 0.392183i | 0.799584 | − | 0.600554i | \(-0.205053\pi\) |
−0.120303 | + | 0.992737i | \(0.538387\pi\) | |||||||
\(798\) | −1.26795 | + | 1.26795i | −0.0448849 | + | 0.0448849i | ||||
\(799\) | 11.3397 | − | 39.6410i | 0.401171 | − | 1.40240i | ||||
\(800\) | 3.00000 | 0.106066 | ||||||||
\(801\) | 10.3923 | − | 18.0000i | 0.367194 | − | 0.635999i | ||||
\(802\) | −14.1699 | + | 14.1699i | −0.500356 | + | 0.500356i | ||||
\(803\) | −6.37564 | − | 11.0429i | −0.224992 | − | 0.389697i | ||||
\(804\) | −6.99038 | − | 4.03590i | −0.246532 | − | 0.142335i | ||||
\(805\) | 5.07180 | − | 1.35898i | 0.178757 | − | 0.0478979i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.928203 | − | 3.46410i | 0.0326743 | − | 0.121942i | ||||
\(808\) | −15.1244 | + | 8.73205i | −0.532073 | + | 0.307192i | ||||
\(809\) | 22.1506 | + | 22.1506i | 0.778775 | + | 0.778775i | 0.979622 | − | 0.200848i | \(-0.0643696\pi\) |
−0.200848 | + | 0.979622i | \(0.564370\pi\) | |||||||
\(810\) | 6.58846 | − | 24.5885i | 0.231495 | − | 0.863950i | ||||
\(811\) | −13.9737 | + | 13.9737i | −0.490684 | + | 0.490684i | −0.908522 | − | 0.417838i | \(-0.862788\pi\) |
0.417838 | + | 0.908522i | \(0.362788\pi\) | |||||||
\(812\) | −4.53590 | − | 7.85641i | −0.159179 | − | 0.275706i | ||||
\(813\) | 26.1962 | − | 15.1244i | 0.918739 | − | 0.530434i | ||||
\(814\) | −9.80385 | − | 5.66025i | −0.343625 | − | 0.198392i | ||||
\(815\) | 8.53590 | − | 14.7846i | 0.298999 | − | 0.517882i | ||||
\(816\) | 1.73205 | + | 6.92820i | 0.0606339 | + | 0.242536i | ||||
\(817\) | 2.59808 | + | 4.50000i | 0.0908952 | + | 0.157435i | ||||
\(818\) | − | 31.0526i | − | 1.08573i | ||||||
\(819\) | −10.3923 | + | 2.78461i | −0.363137 | + | 0.0973021i | ||||
\(820\) | −29.1769 | −1.01890 | ||||||||
\(821\) | −29.0526 | − | 7.78461i | −1.01394 | − | 0.271685i | −0.286666 | − | 0.958031i | \(-0.592547\pi\) |
−0.727275 | + | 0.686346i | \(0.759214\pi\) | |||||||
\(822\) | −37.9808 | −1.32473 | ||||||||
\(823\) | 6.92820 | − | 1.85641i | 0.241502 | − | 0.0647103i | −0.136038 | − | 0.990704i | \(-0.543437\pi\) |
0.377540 | + | 0.925993i | \(0.376770\pi\) | |||||||
\(824\) | 6.46410 | + | 3.73205i | 0.225188 | + | 0.130012i | ||||
\(825\) | 8.49038 | + | 8.49038i | 0.295597 | + | 0.295597i | ||||
\(826\) | 0.464102 | − | 1.73205i | 0.0161482 | − | 0.0602658i | ||||
\(827\) | −13.3397 | − | 13.3397i | −0.463868 | − | 0.463868i | 0.436053 | − | 0.899921i | \(-0.356376\pi\) |
−0.899921 | + | 0.436053i | \(0.856376\pi\) | |||||||
\(828\) | 3.80385 | + | 3.80385i | 0.132193 | + | 0.132193i | ||||
\(829\) | −22.0000 | −0.764092 | −0.382046 | − | 0.924143i | \(-0.624780\pi\) | ||||
−0.382046 | + | 0.924143i | \(0.624780\pi\) | |||||||
\(830\) | −12.3923 | − | 3.32051i | −0.430143 | − | 0.115257i | ||||
\(831\) | −49.0526 | + | 13.1436i | −1.70161 | + | 0.455946i | ||||
\(832\) | 1.73205 | − | 3.00000i | 0.0600481 | − | 0.104006i | ||||
\(833\) | −5.92820 | − | 23.7128i | −0.205400 | − | 0.821600i | ||||
\(834\) | 36.8205 | + | 9.86603i | 1.27499 | + | 0.341633i | ||||
\(835\) | 58.6410 | − | 33.8564i | 2.02936 | − | 1.17165i | ||||
\(836\) | 1.63397 | − | 1.63397i | 0.0565122 | − | 0.0565122i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.58846 | − | 5.58846i | 0.193050 | − | 0.193050i | ||||
\(839\) | 5.85641 | − | 21.8564i | 0.202186 | − | 0.754567i | −0.788103 | − | 0.615543i | \(-0.788937\pi\) |
0.990289 | − | 0.139024i | \(-0.0443965\pi\) | |||||||
\(840\) | 2.53590 | + | 4.39230i | 0.0874968 | + | 0.151549i | ||||
\(841\) | 41.3827 | + | 23.8923i | 1.42699 | + | 0.823873i | ||||
\(842\) | 14.5359 | + | 8.39230i | 0.500940 | + | 0.289218i | ||||
\(843\) | −4.26795 | + | 7.39230i | −0.146996 | + | 0.254605i | ||||
\(844\) | 4.09808 | − | 15.2942i | 0.141062 | − | 0.526449i | ||||
\(845\) | −2.00000 | + | 2.00000i | −0.0688021 | + | 0.0688021i | ||||
\(846\) | 25.9808 | − | 15.0000i | 0.893237 | − | 0.515711i | ||||
\(847\) | −4.14359 | + | 4.14359i | −0.142376 | + | 0.142376i | ||||
\(848\) | 2.19615 | − | 1.26795i | 0.0754162 | − | 0.0435416i | ||||
\(849\) | −36.4641 | + | 36.4641i | −1.25144 | + | 1.25144i | ||||
\(850\) | 12.0000 | − | 3.00000i | 0.411597 | − | 0.102899i | ||||
\(851\) | −4.39230 | + | 7.60770i | −0.150566 | + | 0.260788i | ||||
\(852\) | −9.46410 | − | 9.46410i | −0.324235 | − | 0.324235i | ||||
\(853\) | −2.46410 | − | 0.660254i | −0.0843692 | − | 0.0226067i | 0.216387 | − | 0.976308i | \(-0.430573\pi\) |
−0.300757 | + | 0.953701i | \(0.597239\pi\) | |||||||
\(854\) | −10.9282 | −0.373955 | ||||||||
\(855\) | −2.19615 | + | 8.19615i | −0.0751068 | + | 0.280302i | ||||
\(856\) | −13.2942 | − | 13.2942i | −0.454387 | − | 0.454387i | ||||
\(857\) | 6.50962 | − | 24.2942i | 0.222364 | − | 0.829875i | −0.761079 | − | 0.648659i | \(-0.775330\pi\) |
0.983443 | − | 0.181216i | \(-0.0580033\pi\) | |||||||
\(858\) | 13.3923 | − | 3.58846i | 0.457206 | − | 0.122508i | ||||
\(859\) | −29.8923 | − | 17.2583i | −1.01991 | − | 0.588847i | −0.105834 | − | 0.994384i | \(-0.533751\pi\) |
−0.914079 | + | 0.405537i | \(0.867084\pi\) | |||||||
\(860\) | 14.1962 | − | 3.80385i | 0.484085 | − | 0.129710i | ||||
\(861\) | −9.24871 | − | 16.0192i | −0.315195 | − | 0.545934i | ||||
\(862\) | −28.1244 | − | 7.53590i | −0.957919 | − | 0.256674i | ||||
\(863\) | 33.8564 | 1.15249 | 0.576243 | − | 0.817279i | \(-0.304518\pi\) | ||||
0.576243 | + | 0.817279i | \(0.304518\pi\) | |||||||
\(864\) | −2.59808 | + | 4.50000i | −0.0883883 | + | 0.153093i | ||||
\(865\) | 10.9282i | 0.371570i | ||||||||
\(866\) | −2.03590 | − | 3.52628i | −0.0691826 | − | 0.119828i | ||||
\(867\) | 13.8564 | + | 25.9808i | 0.470588 | + | 0.882353i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.2679 | + | 14.5885i | 0.857156 | + | 0.494880i | ||||
\(870\) | −37.1769 | − | 21.4641i | −1.26042 | − | 0.727701i | ||||
\(871\) | 8.07180 | + | 13.9808i | 0.273502 | + | 0.473720i | ||||
\(872\) | −4.92820 | + | 4.92820i | −0.166890 | + | 0.166890i | ||||
\(873\) | 5.49038 | − | 5.49038i | 0.185821 | − | 0.185821i | ||||
\(874\) | −1.26795 | − | 1.26795i | −0.0428890 | − | 0.0428890i | ||||
\(875\) | −5.07180 | + | 2.92820i | −0.171458 | + | 0.0989913i | ||||
\(876\) | −6.75833 | − | 6.75833i | −0.228343 | − | 0.228343i | ||||
\(877\) | −9.26795 | + | 2.48334i | −0.312956 | + | 0.0838564i | −0.411879 | − | 0.911239i | \(-0.635127\pi\) |
0.0989221 | + | 0.995095i | \(0.468461\pi\) | |||||||
\(878\) | 6.73205 | − | 1.80385i | 0.227196 | − | 0.0608769i | ||||
\(879\) | 26.7846i | 0.903422i | ||||||||
\(880\) | −3.26795 | − | 5.66025i | −0.110163 | − | 0.190807i | ||||
\(881\) | 4.32051 | − | 4.32051i | 0.145562 | − | 0.145562i | −0.630570 | − | 0.776132i | \(-0.717179\pi\) |
0.776132 | + | 0.630570i | \(0.217179\pi\) | |||||||
\(882\) | 8.89230 | − | 15.4019i | 0.299419 | − | 0.518610i | ||||
\(883\) | 48.3731 | 1.62788 | 0.813942 | − | 0.580947i | \(-0.197318\pi\) | ||||
0.813942 | + | 0.580947i | \(0.197318\pi\) | |||||||
\(884\) | 3.92820 | − | 13.7321i | 0.132120 | − | 0.461859i | ||||
\(885\) | −2.19615 | − | 8.19615i | −0.0738229 | − | 0.275511i | ||||
\(886\) | 10.5000 | + | 6.06218i | 0.352754 | + | 0.203663i | ||||
\(887\) | 5.71281 | + | 21.3205i | 0.191817 | + | 0.715873i | 0.993068 | + | 0.117543i | \(0.0375019\pi\) |
−0.801250 | + | 0.598329i | \(0.795831\pi\) | |||||||
\(888\) | −8.19615 | − | 2.19615i | −0.275045 | − | 0.0736980i | ||||
\(889\) | −2.00000 | − | 0.535898i | −0.0670778 | − | 0.0179735i | ||||
\(890\) | 13.8564 | + | 13.8564i | 0.464468 | + | 0.464468i | ||||
\(891\) | −20.0885 | + | 5.38269i | −0.672989 | + | 0.180327i | ||||
\(892\) | 2.39230i | 0.0801003i | ||||||||
\(893\) | −8.66025 | + | 5.00000i | −0.289804 | + | 0.167319i | ||||
\(894\) | −9.92820 | − | 17.1962i | −0.332049 | − | 0.575125i | ||||
\(895\) | −24.7846 | + | 6.64102i | −0.828458 | + | 0.221985i | ||||
\(896\) | −0.267949 | − | 1.00000i | −0.00895155 | − | 0.0334077i | ||||
\(897\) | −2.78461 | − | 10.3923i | −0.0929754 | − | 0.346989i | ||||
\(898\) | −11.4282 | − | 3.06218i | −0.381364 | − | 0.102186i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 7.79423 | + | 4.50000i | 0.259808 | + | 0.150000i | ||||
\(901\) | 7.51666 | − | 7.26795i | 0.250416 | − | 0.242130i | ||||
\(902\) | 11.9186 | + | 20.6436i | 0.396845 | + | 0.687356i | ||||
\(903\) | 6.58846 | + | 6.58846i | 0.219250 | + | 0.219250i | ||||
\(904\) | 1.63397 | + | 6.09808i | 0.0543452 | + | 0.202819i | ||||
\(905\) | 22.5359 | − | 39.0333i | 0.749119 | − | 1.29751i | ||||
\(906\) | − | 36.2487i | − | 1.20428i | ||||||
\(907\) | 9.91858 | − | 37.0167i | 0.329341 | − | 1.22912i | −0.580534 | − | 0.814236i | \(-0.697156\pi\) |
0.909875 | − | 0.414882i | \(-0.136177\pi\) | |||||||
\(908\) | −4.63397 | − | 4.63397i | −0.153784 | − | 0.153784i | ||||
\(909\) | −52.3923 | −1.73774 | ||||||||
\(910\) | − | 10.1436i | − | 0.336257i | ||||||
\(911\) | −9.66025 | + | 36.0526i | −0.320058 | + | 1.19447i | 0.599128 | + | 0.800653i | \(0.295514\pi\) |
−0.919187 | + | 0.393822i | \(0.871153\pi\) | |||||||
\(912\) | 0.866025 | − | 1.50000i | 0.0286770 | − | 0.0496700i | ||||
\(913\) | 2.71281 | + | 10.1244i | 0.0897810 | + | 0.335067i | ||||
\(914\) | 13.3564 | − | 23.1340i | 0.441791 | − | 0.765204i | ||||
\(915\) | −44.7846 | + | 25.8564i | −1.48053 | + | 0.854786i | ||||
\(916\) | −11.5359 | + | 6.66025i | −0.381157 | + | 0.220061i | ||||
\(917\) | −18.5359 | −0.612109 | ||||||||
\(918\) | −5.89230 | + | 20.5981i | −0.194475 | + | 0.679838i | ||||
\(919\) | 8.92820 | 0.294514 | 0.147257 | − | 0.989098i | \(-0.452956\pi\) | ||||
0.147257 | + | 0.989098i | \(0.452956\pi\) | |||||||
\(920\) | −4.39230 | + | 2.53590i | −0.144810 | + | 0.0836061i | ||||
\(921\) | 9.10770 | − | 5.25833i | 0.300109 | − | 0.173268i | ||||
\(922\) | 9.00000 | − | 15.5885i | 0.296399 | − | 0.513378i | ||||
\(923\) | 6.92820 | + | 25.8564i | 0.228045 | + | 0.851074i | ||||
\(924\) | 2.07180 | − | 3.58846i | 0.0681571 | − | 0.118052i | ||||
\(925\) | −3.80385 | + | 14.1962i | −0.125070 | + | 0.466767i | ||||
\(926\) | − | 27.7128i | − | 0.910700i | ||||||
\(927\) | 11.1962 | + | 19.3923i | 0.367730 | + | 0.636927i | ||||
\(928\) | 6.19615 | + | 6.19615i | 0.203399 | + | 0.203399i | ||||
\(929\) | 7.04552 | − | 26.2942i | 0.231156 | − | 0.862686i | −0.748688 | − | 0.662922i | \(-0.769316\pi\) |
0.979844 | − | 0.199763i | \(-0.0640174\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.96410 | + | 5.13397i | −0.0971445 | + | 0.168259i | ||||
\(932\) | 3.57180 | + | 13.3301i | 0.116998 | + | 0.436643i | ||||
\(933\) | −21.8038 | − | 21.8038i | −0.713826 | − | 0.713826i | ||||
\(934\) | −18.4282 | − | 31.9186i | −0.602989 | − | 1.04441i | ||||
\(935\) | −18.7321 | − | 19.3731i | −0.612604 | − | 0.633567i | ||||
\(936\) | 9.00000 | − | 5.19615i | 0.294174 | − | 0.169842i | ||||
\(937\) | 41.7128i | 1.36270i | 0.731959 | + | 0.681349i | \(0.238606\pi\) | ||||
−0.731959 | + | 0.681349i | \(0.761394\pi\) | |||||||
\(938\) | 4.66025 | + | 1.24871i | 0.152163 | + | 0.0407719i | ||||
\(939\) | 4.37564 | + | 16.3301i | 0.142794 | + | 0.532914i | ||||
\(940\) | 7.32051 | + | 27.3205i | 0.238769 | + | 0.891097i | ||||
\(941\) | −4.73205 | + | 1.26795i | −0.154260 | + | 0.0413340i | −0.335123 | − | 0.942174i | \(-0.608778\pi\) |
0.180862 | + | 0.983508i | \(0.442111\pi\) | |||||||
\(942\) | −17.6603 | − | 30.5885i | −0.575402 | − | 0.996626i | ||||
\(943\) | 16.0192 | − | 9.24871i | 0.521658 | − | 0.301179i | ||||
\(944\) | 1.73205i | 0.0563735i | ||||||||
\(945\) | 15.2154i | 0.494957i | ||||||||
\(946\) | −8.49038 | − | 8.49038i | −0.276046 | − | 0.276046i | ||||
\(947\) | 15.6962 | + | 4.20577i | 0.510056 | + | 0.136669i | 0.504663 | − | 0.863316i | \(-0.331617\pi\) |
0.00539312 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(948\) | 21.1244 | + | 5.66025i | 0.686087 | + | 0.183837i | ||||
\(949\) | 4.94744 | + | 18.4641i | 0.160601 | + | 0.599370i | ||||
\(950\) | −2.59808 | − | 1.50000i | −0.0842927 | − | 0.0486664i | ||||
\(951\) | 11.5359 | + | 43.0526i | 0.374077 | + | 1.39607i | ||||
\(952\) | −2.07180 | − | 3.73205i | −0.0671473 | − | 0.120956i | ||||
\(953\) | 4.66025 | 0.150960 | 0.0754802 | − | 0.997147i | \(-0.475951\pi\) | ||||
0.0754802 | + | 0.997147i | \(0.475951\pi\) | |||||||
\(954\) | 7.60770 | 0.246308 | ||||||||
\(955\) | −15.7128 | + | 15.7128i | −0.508455 | + | 0.508455i | ||||
\(956\) | 8.46410 | + | 14.6603i | 0.273749 | + | 0.474147i | ||||
\(957\) | 35.0718i | 1.13371i | ||||||||
\(958\) | 29.5885 | − | 7.92820i | 0.955960 | − | 0.256149i | ||||
\(959\) | 21.9282 | − | 5.87564i | 0.708099 | − | 0.189734i | ||||
\(960\) | −3.46410 | − | 3.46410i | −0.111803 | − | 0.111803i | ||||
\(961\) | 26.8468 | − | 15.5000i | 0.866025 | − | 0.500000i | ||||
\(962\) | 12.0000 | + | 12.0000i | 0.386896 | + | 0.386896i | ||||
\(963\) | −14.5981 | − | 54.4808i | −0.470416 | − | 1.75562i | ||||
\(964\) | 8.49038 | − | 8.49038i | 0.273457 | − | 0.273457i | ||||
\(965\) | −8.19615 | − | 14.1962i | −0.263843 | − | 0.456990i | ||||
\(966\) | −2.78461 | − | 1.60770i | −0.0895933 | − | 0.0517267i | ||||
\(967\) | −19.1436 | − | 11.0526i | −0.615616 | − | 0.355426i | 0.159544 | − | 0.987191i | \(-0.448998\pi\) |
−0.775160 | + | 0.631764i | \(0.782331\pi\) | |||||||
\(968\) | 2.83013 | − | 4.90192i | 0.0909637 | − | 0.157554i | ||||
\(969\) | 1.96410 | − | 6.86603i | 0.0630960 | − | 0.220569i | ||||
\(970\) | 3.66025 | + | 6.33975i | 0.117524 | + | 0.203557i | ||||
\(971\) | 22.3923i | 0.718603i | 0.933221 | + | 0.359302i | \(0.116985\pi\) | ||||
−0.933221 | + | 0.359302i | \(0.883015\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | −22.7846 | −0.730441 | ||||||||
\(974\) | 17.1962 | + | 4.60770i | 0.551000 | + | 0.147640i | ||||
\(975\) | −9.00000 | − | 15.5885i | −0.288231 | − | 0.499230i | ||||
\(976\) | 10.1962 | − | 2.73205i | 0.326371 | − | 0.0874508i | ||||
\(977\) | −38.4282 | − | 22.1865i | −1.22943 | − | 0.709810i | −0.262517 | − | 0.964927i | \(-0.584553\pi\) |
−0.966910 | + | 0.255117i | \(0.917886\pi\) | |||||||
\(978\) | −10.0981 | + | 2.70577i | −0.322901 | + | 0.0865210i | ||||
\(979\) | 4.14359 | − | 15.4641i | 0.132430 | − | 0.494235i | ||||
\(980\) | 11.8564 | + | 11.8564i | 0.378739 | + | 0.378739i | ||||
\(981\) | −20.1962 | + | 5.41154i | −0.644814 | + | 0.172777i | ||||
\(982\) | 11.9282 | 0.380644 | ||||||||
\(983\) | 25.6603 | + | 6.87564i | 0.818435 | + | 0.219299i | 0.643662 | − | 0.765310i | \(-0.277414\pi\) |
0.174773 | + | 0.984609i | \(0.444081\pi\) | |||||||
\(984\) | 12.6340 | + | 12.6340i | 0.402756 | + | 0.402756i | ||||
\(985\) | −18.9282 | + | 32.7846i | −0.603103 | + | 1.04460i | ||||
\(986\) | 30.9808 | + | 18.5885i | 0.986628 | + | 0.591977i | ||||
\(987\) | −12.6795 | + | 12.6795i | −0.403593 | + | 0.403593i | ||||
\(988\) | −3.00000 | + | 1.73205i | −0.0954427 | + | 0.0551039i | ||||
\(989\) | −6.58846 | + | 6.58846i | −0.209501 | + | 0.209501i | ||||
\(990\) | − | 19.6077i | − | 0.623173i | ||||||
\(991\) | 2.14359 | − | 2.14359i | 0.0680935 | − | 0.0680935i | −0.672240 | − | 0.740333i | \(-0.734668\pi\) |
0.740333 | + | 0.672240i | \(0.234668\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.00000 | − | 5.19615i | 0.0952021 | − | 0.164895i | ||||
\(994\) | 6.92820 | + | 4.00000i | 0.219749 | + | 0.126872i | ||||
\(995\) | −12.6795 | − | 7.32051i | −0.401967 | − | 0.232076i | ||||
\(996\) | 3.92820 | + | 6.80385i | 0.124470 | + | 0.215588i | ||||
\(997\) | 4.39230 | − | 16.3923i | 0.139106 | − | 0.519150i | −0.860842 | − | 0.508873i | \(-0.830062\pi\) |
0.999947 | − | 0.0102763i | \(-0.00327112\pi\) | |||||||
\(998\) | −21.4186 | + | 21.4186i | −0.677993 | + | 0.677993i | ||||
\(999\) | −18.0000 | − | 18.0000i | −0.569495 | − | 0.569495i |
(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 | 306.2.n.c.157.1 | yes | 4 | |
3.2 | odd | 2 | 918.2.o.b.361.1 | 4 | |||
9.2 | odd | 6 | 918.2.o.c.667.1 | 4 | |||
9.7 | even | 3 | 306.2.n.b.259.1 | yes | 4 | ||
17.13 | even | 4 | 306.2.n.b.13.1 | ✓ | 4 | ||
51.47 | odd | 4 | 918.2.o.c.523.1 | 4 | |||
153.47 | odd | 12 | 918.2.o.b.829.1 | 4 | |||
153.115 | even | 12 | inner | 306.2.n.c.115.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
306.2.n.b.13.1 | ✓ | 4 | 17.13 | even | 4 | ||
306.2.n.b.259.1 | yes | 4 | 9.7 | even | 3 | ||
306.2.n.c.115.1 | yes | 4 | 153.115 | even | 12 | inner | |
306.2.n.c.157.1 | yes | 4 | 1.1 | even | 1 | trivial | |
918.2.o.b.361.1 | 4 | 3.2 | odd | 2 | |||
918.2.o.b.829.1 | 4 | 153.47 | odd | 12 | |||
918.2.o.c.523.1 | 4 | 51.47 | odd | 4 | |||
918.2.o.c.667.1 | 4 | 9.2 | odd | 6 |