Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(139,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.bi (of order \(6\), 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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 223.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.223 |
Dual form | 252.2.bi.a.139.1 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | − | 1.36603i | −0.258819 | − | 0.965926i | ||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | −1.73205 | + | 1.00000i | −0.866025 | + | 0.500000i | ||||
\(5\) | −1.50000 | + | 0.866025i | −0.670820 | + | 0.387298i | −0.796387 | − | 0.604787i | \(-0.793258\pi\) |
0.125567 | + | 0.992085i | \(0.459925\pi\) | |||||||
\(6\) | 0.633975 | + | 2.36603i | 0.258819 | + | 0.965926i | ||||
\(7\) | 2.59808 | + | 0.500000i | 0.981981 | + | 0.188982i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 3.00000 | 1.00000 | ||||||||
\(10\) | 1.73205 | + | 1.73205i | 0.547723 | + | 0.547723i | ||||
\(11\) | −0.866025 | − | 0.500000i | −0.261116 | − | 0.150756i | 0.363727 | − | 0.931505i | \(-0.381504\pi\) |
−0.624844 | + | 0.780750i | \(0.714837\pi\) | |||||||
\(12\) | 3.00000 | − | 1.73205i | 0.866025 | − | 0.500000i | ||||
\(13\) | 1.50000 | − | 0.866025i | 0.416025 | − | 0.240192i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | −0.267949 | − | 3.73205i | −0.0716124 | − | 0.997433i | ||||
\(15\) | 2.59808 | − | 1.50000i | 0.670820 | − | 0.387298i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | 3.46410i | 0.840168i | 0.907485 | + | 0.420084i | \(0.137999\pi\) | ||||
−0.907485 | + | 0.420084i | \(0.862001\pi\) | |||||||
\(18\) | −1.09808 | − | 4.09808i | −0.258819 | − | 0.965926i | ||||
\(19\) | 6.92820 | 1.58944 | 0.794719 | − | 0.606977i | \(-0.207618\pi\) | ||||
0.794719 | + | 0.606977i | \(0.207618\pi\) | |||||||
\(20\) | 1.73205 | − | 3.00000i | 0.387298 | − | 0.670820i | ||||
\(21\) | −4.50000 | − | 0.866025i | −0.981981 | − | 0.188982i | ||||
\(22\) | −0.366025 | + | 1.36603i | −0.0780369 | + | 0.291238i | ||||
\(23\) | 4.33013 | − | 2.50000i | 0.902894 | − | 0.521286i | 0.0247559 | − | 0.999694i | \(-0.492119\pi\) |
0.878138 | + | 0.478407i | \(0.158786\pi\) | |||||||
\(24\) | −3.46410 | − | 3.46410i | −0.707107 | − | 0.707107i | ||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | −1.73205 | − | 1.73205i | −0.339683 | − | 0.339683i | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −5.00000 | + | 1.73205i | −0.944911 | + | 0.327327i | ||||
\(29\) | −2.50000 | + | 4.33013i | −0.464238 | + | 0.804084i | −0.999167 | − | 0.0408130i | \(-0.987005\pi\) |
0.534928 | + | 0.844897i | \(0.320339\pi\) | |||||||
\(30\) | −3.00000 | − | 3.00000i | −0.547723 | − | 0.547723i | ||||
\(31\) | 4.33013 | + | 7.50000i | 0.777714 | + | 1.34704i | 0.933257 | + | 0.359211i | \(0.116954\pi\) |
−0.155543 | + | 0.987829i | \(0.549713\pi\) | |||||||
\(32\) | −5.46410 | − | 1.46410i | −0.965926 | − | 0.258819i | ||||
\(33\) | 1.50000 | + | 0.866025i | 0.261116 | + | 0.150756i | ||||
\(34\) | 4.73205 | − | 1.26795i | 0.811540 | − | 0.217451i | ||||
\(35\) | −4.33013 | + | 1.50000i | −0.731925 | + | 0.253546i | ||||
\(36\) | −5.19615 | + | 3.00000i | −0.866025 | + | 0.500000i | ||||
\(37\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(38\) | −2.53590 | − | 9.46410i | −0.411377 | − | 1.53528i | ||||
\(39\) | −2.59808 | + | 1.50000i | −0.416025 | + | 0.240192i | ||||
\(40\) | −4.73205 | − | 1.26795i | −0.748203 | − | 0.200480i | ||||
\(41\) | 7.50000 | − | 4.33013i | 1.17130 | − | 0.676252i | 0.217317 | − | 0.976101i | \(-0.430270\pi\) |
0.953987 | + | 0.299849i | \(0.0969363\pi\) | |||||||
\(42\) | 0.464102 | + | 6.46410i | 0.0716124 | + | 0.997433i | ||||
\(43\) | 0.866025 | + | 0.500000i | 0.132068 | + | 0.0762493i | 0.564578 | − | 0.825380i | \(-0.309039\pi\) |
−0.432511 | + | 0.901629i | \(0.642372\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | −4.50000 | + | 2.59808i | −0.670820 | + | 0.387298i | ||||
\(46\) | −5.00000 | − | 5.00000i | −0.737210 | − | 0.737210i | ||||
\(47\) | −2.59808 | + | 4.50000i | −0.378968 | + | 0.656392i | −0.990912 | − | 0.134509i | \(-0.957054\pi\) |
0.611944 | + | 0.790901i | \(0.290388\pi\) | |||||||
\(48\) | −3.46410 | + | 6.00000i | −0.500000 | + | 0.866025i | ||||
\(49\) | 6.50000 | + | 2.59808i | 0.928571 | + | 0.371154i | ||||
\(50\) | 2.73205 | + | 0.732051i | 0.386370 | + | 0.103528i | ||||
\(51\) | − | 6.00000i | − | 0.840168i | ||||||
\(52\) | −1.73205 | + | 3.00000i | −0.240192 | + | 0.416025i | ||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 1.90192 | + | 7.09808i | 0.258819 | + | 0.965926i | ||||
\(55\) | 1.73205 | 0.233550 | ||||||||
\(56\) | 4.19615 | + | 6.19615i | 0.560734 | + | 0.827996i | ||||
\(57\) | −12.0000 | −1.58944 | ||||||||
\(58\) | 6.83013 | + | 1.83013i | 0.896840 | + | 0.240307i | ||||
\(59\) | −4.33013 | − | 7.50000i | −0.563735 | − | 0.976417i | −0.997166 | − | 0.0752304i | \(-0.976031\pi\) |
0.433432 | − | 0.901186i | \(-0.357303\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | −4.50000 | − | 2.59808i | −0.576166 | − | 0.332650i | 0.183442 | − | 0.983030i | \(-0.441276\pi\) |
−0.759608 | + | 0.650381i | \(0.774609\pi\) | |||||||
\(62\) | 8.66025 | − | 8.66025i | 1.09985 | − | 1.09985i | ||||
\(63\) | 7.79423 | + | 1.50000i | 0.981981 | + | 0.188982i | ||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −1.50000 | + | 2.59808i | −0.186052 | + | 0.322252i | ||||
\(66\) | 0.633975 | − | 2.36603i | 0.0780369 | − | 0.291238i | ||||
\(67\) | −12.9904 | + | 7.50000i | −1.58703 | + | 0.916271i | −0.593234 | + | 0.805030i | \(0.702149\pi\) |
−0.993793 | + | 0.111241i | \(0.964517\pi\) | |||||||
\(68\) | −3.46410 | − | 6.00000i | −0.420084 | − | 0.727607i | ||||
\(69\) | −7.50000 | + | 4.33013i | −0.902894 | + | 0.521286i | ||||
\(70\) | 3.63397 | + | 5.36603i | 0.434343 | + | 0.641363i | ||||
\(71\) | − | 4.00000i | − | 0.474713i | −0.971423 | − | 0.237356i | \(-0.923719\pi\) | ||
0.971423 | − | 0.237356i | \(-0.0762809\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.707107 | + | 0.707107i | ||||
\(73\) | − | 10.3923i | − | 1.21633i | −0.793812 | − | 0.608164i | \(-0.791906\pi\) | ||
0.793812 | − | 0.608164i | \(-0.208094\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205 | − | 3.00000i | 0.200000 | − | 0.346410i | ||||
\(76\) | −12.0000 | + | 6.92820i | −1.37649 | + | 0.794719i | ||||
\(77\) | −2.00000 | − | 1.73205i | −0.227921 | − | 0.197386i | ||||
\(78\) | 3.00000 | + | 3.00000i | 0.339683 | + | 0.339683i | ||||
\(79\) | 2.59808 | + | 1.50000i | 0.292306 | + | 0.168763i | 0.638982 | − | 0.769222i | \(-0.279356\pi\) |
−0.346675 | + | 0.937985i | \(0.612689\pi\) | |||||||
\(80\) | 6.92820i | 0.774597i | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | −8.66025 | − | 8.66025i | −0.956365 | − | 0.956365i | ||||
\(83\) | 0.866025 | − | 1.50000i | 0.0950586 | − | 0.164646i | −0.814574 | − | 0.580059i | \(-0.803029\pi\) |
0.909633 | + | 0.415413i | \(0.136363\pi\) | |||||||
\(84\) | 8.66025 | − | 3.00000i | 0.944911 | − | 0.327327i | ||||
\(85\) | −3.00000 | − | 5.19615i | −0.325396 | − | 0.563602i | ||||
\(86\) | 0.366025 | − | 1.36603i | 0.0394695 | − | 0.147302i | ||||
\(87\) | 4.33013 | − | 7.50000i | 0.464238 | − | 0.804084i | ||||
\(88\) | −0.732051 | − | 2.73205i | −0.0780369 | − | 0.291238i | ||||
\(89\) | 17.3205i | 1.83597i | 0.396615 | + | 0.917985i | \(0.370185\pi\) | ||||
−0.396615 | + | 0.917985i | \(0.629815\pi\) | |||||||
\(90\) | 5.19615 | + | 5.19615i | 0.547723 | + | 0.547723i | ||||
\(91\) | 4.33013 | − | 1.50000i | 0.453921 | − | 0.157243i | ||||
\(92\) | −5.00000 | + | 8.66025i | −0.521286 | + | 0.902894i | ||||
\(93\) | −7.50000 | − | 12.9904i | −0.777714 | − | 1.34704i | ||||
\(94\) | 7.09808 | + | 1.90192i | 0.732111 | + | 0.196168i | ||||
\(95\) | −10.3923 | + | 6.00000i | −1.06623 | + | 0.615587i | ||||
\(96\) | 9.46410 | + | 2.53590i | 0.965926 | + | 0.258819i | ||||
\(97\) | −4.50000 | − | 2.59808i | −0.456906 | − | 0.263795i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | 1.16987 | − | 9.83013i | 0.118175 | − | 0.992993i | ||||
\(99\) | −2.59808 | − | 1.50000i | −0.261116 | − | 0.150756i | ||||
\(100\) | − | 4.00000i | − | 0.400000i | ||||||
\(101\) | 10.5000 | + | 6.06218i | 1.04479 | + | 0.603209i | 0.921186 | − | 0.389123i | \(-0.127222\pi\) |
0.123603 | + | 0.992332i | \(0.460555\pi\) | |||||||
\(102\) | −8.19615 | + | 2.19615i | −0.811540 | + | 0.217451i | ||||
\(103\) | −4.33013 | − | 7.50000i | −0.426660 | − | 0.738997i | 0.569914 | − | 0.821705i | \(-0.306977\pi\) |
−0.996574 | + | 0.0827075i | \(0.973643\pi\) | |||||||
\(104\) | 4.73205 | + | 1.26795i | 0.464016 | + | 0.124333i | ||||
\(105\) | 7.50000 | − | 2.59808i | 0.731925 | − | 0.253546i | ||||
\(106\) | −1.46410 | − | 5.46410i | −0.142206 | − | 0.530720i | ||||
\(107\) | − | 2.00000i | − | 0.193347i | −0.995316 | − | 0.0966736i | \(-0.969180\pi\) | ||
0.995316 | − | 0.0966736i | \(-0.0308203\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.866025 | − | 0.500000i | ||||
\(109\) | 12.0000 | 1.14939 | 0.574696 | − | 0.818367i | \(-0.305120\pi\) | ||||
0.574696 | + | 0.818367i | \(0.305120\pi\) | |||||||
\(110\) | −0.633975 | − | 2.36603i | −0.0604471 | − | 0.225592i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 6.92820 | − | 8.00000i | 0.654654 | − | 0.755929i | ||||
\(113\) | −9.50000 | − | 16.4545i | −0.893685 | − | 1.54791i | −0.835424 | − | 0.549606i | \(-0.814778\pi\) |
−0.0582609 | − | 0.998301i | \(-0.518556\pi\) | |||||||
\(114\) | 4.39230 | + | 16.3923i | 0.411377 | + | 1.53528i | ||||
\(115\) | −4.33013 | + | 7.50000i | −0.403786 | + | 0.699379i | ||||
\(116\) | − | 10.0000i | − | 0.928477i | ||||||
\(117\) | 4.50000 | − | 2.59808i | 0.416025 | − | 0.240192i | ||||
\(118\) | −8.66025 | + | 8.66025i | −0.797241 | + | 0.797241i | ||||
\(119\) | −1.73205 | + | 9.00000i | −0.158777 | + | 0.825029i | ||||
\(120\) | 8.19615 | + | 2.19615i | 0.748203 | + | 0.200480i | ||||
\(121\) | −5.00000 | − | 8.66025i | −0.454545 | − | 0.787296i | ||||
\(122\) | −1.90192 | + | 7.09808i | −0.172192 | + | 0.642630i | ||||
\(123\) | −12.9904 | + | 7.50000i | −1.17130 | + | 0.676252i | ||||
\(124\) | −15.0000 | − | 8.66025i | −1.34704 | − | 0.777714i | ||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | −0.803848 | − | 11.1962i | −0.0716124 | − | 0.997433i | ||||
\(127\) | − | 18.0000i | − | 1.59724i | −0.601834 | − | 0.798621i | \(-0.705563\pi\) | ||
0.601834 | − | 0.798621i | \(-0.294437\pi\) | |||||||
\(128\) | 10.9282 | − | 2.92820i | 0.965926 | − | 0.258819i | ||||
\(129\) | −1.50000 | − | 0.866025i | −0.132068 | − | 0.0762493i | ||||
\(130\) | 4.09808 | + | 1.09808i | 0.359425 | + | 0.0963077i | ||||
\(131\) | 6.06218 | + | 10.5000i | 0.529655 | + | 0.917389i | 0.999402 | + | 0.0345880i | \(0.0110119\pi\) |
−0.469747 | + | 0.882801i | \(0.655655\pi\) | |||||||
\(132\) | −3.46410 | −0.301511 | ||||||||
\(133\) | 18.0000 | + | 3.46410i | 1.56080 | + | 0.300376i | ||||
\(134\) | 15.0000 | + | 15.0000i | 1.29580 | + | 1.29580i | ||||
\(135\) | 7.79423 | − | 4.50000i | 0.670820 | − | 0.387298i | ||||
\(136\) | −6.92820 | + | 6.92820i | −0.594089 | + | 0.594089i | ||||
\(137\) | −2.50000 | + | 4.33013i | −0.213589 | + | 0.369948i | −0.952835 | − | 0.303488i | \(-0.901849\pi\) |
0.739246 | + | 0.673436i | \(0.235182\pi\) | |||||||
\(138\) | 8.66025 | + | 8.66025i | 0.737210 | + | 0.737210i | ||||
\(139\) | −4.33013 | − | 7.50000i | −0.367277 | − | 0.636142i | 0.621862 | − | 0.783127i | \(-0.286376\pi\) |
−0.989139 | + | 0.146985i | \(0.953043\pi\) | |||||||
\(140\) | 6.00000 | − | 6.92820i | 0.507093 | − | 0.585540i | ||||
\(141\) | 4.50000 | − | 7.79423i | 0.378968 | − | 0.656392i | ||||
\(142\) | −5.46410 | + | 1.46410i | −0.458537 | + | 0.122865i | ||||
\(143\) | −1.73205 | −0.144841 | ||||||||
\(144\) | 6.00000 | − | 10.3923i | 0.500000 | − | 0.866025i | ||||
\(145\) | − | 8.66025i | − | 0.719195i | ||||||
\(146\) | −14.1962 | + | 3.80385i | −1.17488 | + | 0.314809i | ||||
\(147\) | −11.2583 | − | 4.50000i | −0.928571 | − | 0.371154i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.50000 | + | 6.06218i | 0.286731 | + | 0.496633i | 0.973028 | − | 0.230689i | \(-0.0740980\pi\) |
−0.686296 | + | 0.727322i | \(0.740765\pi\) | |||||||
\(150\) | −4.73205 | − | 1.26795i | −0.386370 | − | 0.103528i | ||||
\(151\) | 9.52628 | + | 5.50000i | 0.775238 | + | 0.447584i | 0.834740 | − | 0.550645i | \(-0.185618\pi\) |
−0.0595022 | + | 0.998228i | \(0.518951\pi\) | |||||||
\(152\) | 13.8564 | + | 13.8564i | 1.12390 | + | 1.12390i | ||||
\(153\) | 10.3923i | 0.840168i | ||||||||
\(154\) | −1.63397 | + | 3.36603i | −0.131669 | + | 0.271242i | ||||
\(155\) | −12.9904 | − | 7.50000i | −1.04341 | − | 0.602414i | ||||
\(156\) | 3.00000 | − | 5.19615i | 0.240192 | − | 0.416025i | ||||
\(157\) | 4.50000 | − | 2.59808i | 0.359139 | − | 0.207349i | −0.309564 | − | 0.950879i | \(-0.600183\pi\) |
0.668703 | + | 0.743530i | \(0.266850\pi\) | |||||||
\(158\) | 1.09808 | − | 4.09808i | 0.0873583 | − | 0.326025i | ||||
\(159\) | −6.92820 | −0.549442 | ||||||||
\(160\) | 9.46410 | − | 2.53590i | 0.748203 | − | 0.200480i | ||||
\(161\) | 12.5000 | − | 4.33013i | 0.985138 | − | 0.341262i | ||||
\(162\) | −3.29423 | − | 12.2942i | −0.258819 | − | 0.965926i | ||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | −8.66025 | + | 15.0000i | −0.676252 | + | 1.17130i | ||||
\(165\) | −3.00000 | −0.233550 | ||||||||
\(166\) | −2.36603 | − | 0.633975i | −0.183639 | − | 0.0492060i | ||||
\(167\) | 6.06218 | + | 10.5000i | 0.469105 | + | 0.812514i | 0.999376 | − | 0.0353139i | \(-0.0112431\pi\) |
−0.530271 | + | 0.847828i | \(0.677910\pi\) | |||||||
\(168\) | −7.26795 | − | 10.7321i | −0.560734 | − | 0.827996i | ||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | −6.00000 | + | 6.00000i | −0.460179 | + | 0.460179i | ||||
\(171\) | 20.7846 | 1.58944 | ||||||||
\(172\) | −2.00000 | −0.152499 | ||||||||
\(173\) | −7.50000 | − | 4.33013i | −0.570214 | − | 0.329213i | 0.187021 | − | 0.982356i | \(-0.440117\pi\) |
−0.757235 | + | 0.653143i | \(0.773450\pi\) | |||||||
\(174\) | −11.8301 | − | 3.16987i | −0.896840 | − | 0.240307i | ||||
\(175\) | −3.46410 | + | 4.00000i | −0.261861 | + | 0.302372i | ||||
\(176\) | −3.46410 | + | 2.00000i | −0.261116 | + | 0.150756i | ||||
\(177\) | 7.50000 | + | 12.9904i | 0.563735 | + | 0.976417i | ||||
\(178\) | 23.6603 | − | 6.33975i | 1.77341 | − | 0.475184i | ||||
\(179\) | 2.00000i | 0.149487i | 0.997203 | + | 0.0747435i | \(0.0238138\pi\) | ||||
−0.997203 | + | 0.0747435i | \(0.976186\pi\) | |||||||
\(180\) | 5.19615 | − | 9.00000i | 0.387298 | − | 0.670820i | ||||
\(181\) | 17.3205i | 1.28742i | 0.765268 | + | 0.643712i | \(0.222606\pi\) | ||||
−0.765268 | + | 0.643712i | \(0.777394\pi\) | |||||||
\(182\) | −3.63397 | − | 5.36603i | −0.269368 | − | 0.397756i | ||||
\(183\) | 7.79423 | + | 4.50000i | 0.576166 | + | 0.332650i | ||||
\(184\) | 13.6603 | + | 3.66025i | 1.00705 | + | 0.269838i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −15.0000 | + | 15.0000i | −1.09985 | + | 1.09985i | ||||
\(187\) | 1.73205 | − | 3.00000i | 0.126660 | − | 0.219382i | ||||
\(188\) | − | 10.3923i | − | 0.757937i | ||||||
\(189\) | −13.5000 | − | 2.59808i | −0.981981 | − | 0.188982i | ||||
\(190\) | 12.0000 | + | 12.0000i | 0.870572 | + | 0.870572i | ||||
\(191\) | 4.33013 | + | 2.50000i | 0.313317 | + | 0.180894i | 0.648410 | − | 0.761291i | \(-0.275434\pi\) |
−0.335093 | + | 0.942185i | \(0.608768\pi\) | |||||||
\(192\) | − | 13.8564i | − | 1.00000i | ||||||
\(193\) | −4.50000 | − | 7.79423i | −0.323917 | − | 0.561041i | 0.657376 | − | 0.753563i | \(-0.271667\pi\) |
−0.981293 | + | 0.192522i | \(0.938333\pi\) | |||||||
\(194\) | −1.90192 | + | 7.09808i | −0.136550 | + | 0.509612i | ||||
\(195\) | 2.59808 | − | 4.50000i | 0.186052 | − | 0.322252i | ||||
\(196\) | −13.8564 | + | 2.00000i | −0.989743 | + | 0.142857i | ||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | −1.09808 | + | 4.09808i | −0.0780369 | + | 0.291238i | ||||
\(199\) | −17.3205 | −1.22782 | −0.613909 | − | 0.789377i | \(-0.710404\pi\) | ||||
−0.613909 | + | 0.789377i | \(0.710404\pi\) | |||||||
\(200\) | −5.46410 | + | 1.46410i | −0.386370 | + | 0.103528i | ||||
\(201\) | 22.5000 | − | 12.9904i | 1.58703 | − | 0.916271i | ||||
\(202\) | 4.43782 | − | 16.5622i | 0.312244 | − | 1.16531i | ||||
\(203\) | −8.66025 | + | 10.0000i | −0.607831 | + | 0.701862i | ||||
\(204\) | 6.00000 | + | 10.3923i | 0.420084 | + | 0.727607i | ||||
\(205\) | −7.50000 | + | 12.9904i | −0.523823 | + | 0.907288i | ||||
\(206\) | −8.66025 | + | 8.66025i | −0.603388 | + | 0.603388i | ||||
\(207\) | 12.9904 | − | 7.50000i | 0.902894 | − | 0.521286i | ||||
\(208\) | − | 6.92820i | − | 0.480384i | ||||||
\(209\) | −6.00000 | − | 3.46410i | −0.415029 | − | 0.239617i | ||||
\(210\) | −6.29423 | − | 9.29423i | −0.434343 | − | 0.641363i | ||||
\(211\) | 0.866025 | − | 0.500000i | 0.0596196 | − | 0.0344214i | −0.469894 | − | 0.882723i | \(-0.655708\pi\) |
0.529514 | + | 0.848301i | \(0.322374\pi\) | |||||||
\(212\) | −6.92820 | + | 4.00000i | −0.475831 | + | 0.274721i | ||||
\(213\) | 6.92820i | 0.474713i | ||||||||
\(214\) | −2.73205 | + | 0.732051i | −0.186759 | + | 0.0500420i | ||||
\(215\) | −1.73205 | −0.118125 | ||||||||
\(216\) | −10.3923 | − | 10.3923i | −0.707107 | − | 0.707107i | ||||
\(217\) | 7.50000 | + | 21.6506i | 0.509133 | + | 1.46974i | ||||
\(218\) | −4.39230 | − | 16.3923i | −0.297484 | − | 1.11023i | ||||
\(219\) | 18.0000i | 1.21633i | ||||||||
\(220\) | −3.00000 | + | 1.73205i | −0.202260 | + | 0.116775i | ||||
\(221\) | 3.00000 | + | 5.19615i | 0.201802 | + | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.866025 | − | 1.50000i | 0.0579934 | − | 0.100447i | −0.835571 | − | 0.549382i | \(-0.814863\pi\) |
0.893565 | + | 0.448935i | \(0.148196\pi\) | |||||||
\(224\) | −13.4641 | − | 6.53590i | −0.899608 | − | 0.436698i | ||||
\(225\) | −3.00000 | + | 5.19615i | −0.200000 | + | 0.346410i | ||||
\(226\) | −19.0000 | + | 19.0000i | −1.26386 | + | 1.26386i | ||||
\(227\) | 2.59808 | − | 4.50000i | 0.172440 | − | 0.298675i | −0.766832 | − | 0.641848i | \(-0.778168\pi\) |
0.939272 | + | 0.343172i | \(0.111501\pi\) | |||||||
\(228\) | 20.7846 | − | 12.0000i | 1.37649 | − | 0.794719i | ||||
\(229\) | −1.50000 | + | 0.866025i | −0.0991228 | + | 0.0572286i | −0.548742 | − | 0.835992i | \(-0.684893\pi\) |
0.449619 | + | 0.893220i | \(0.351560\pi\) | |||||||
\(230\) | 11.8301 | + | 3.16987i | 0.780055 | + | 0.209015i | ||||
\(231\) | 3.46410 | + | 3.00000i | 0.227921 | + | 0.197386i | ||||
\(232\) | −13.6603 | + | 3.66025i | −0.896840 | + | 0.240307i | ||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | −5.19615 | − | 5.19615i | −0.339683 | − | 0.339683i | ||||
\(235\) | − | 9.00000i | − | 0.587095i | ||||||
\(236\) | 15.0000 | + | 8.66025i | 0.976417 | + | 0.563735i | ||||
\(237\) | −4.50000 | − | 2.59808i | −0.292306 | − | 0.168763i | ||||
\(238\) | 12.9282 | − | 0.928203i | 0.838011 | − | 0.0601665i | ||||
\(239\) | 21.6506 | − | 12.5000i | 1.40046 | − | 0.808558i | 0.406023 | − | 0.913863i | \(-0.366915\pi\) |
0.994440 | + | 0.105305i | \(0.0335819\pi\) | |||||||
\(240\) | − | 12.0000i | − | 0.774597i | ||||||
\(241\) | −25.5000 | − | 14.7224i | −1.64260 | − | 0.948355i | −0.979905 | − | 0.199465i | \(-0.936079\pi\) |
−0.662695 | − | 0.748890i | \(-0.730587\pi\) | |||||||
\(242\) | −10.0000 | + | 10.0000i | −0.642824 | + | 0.642824i | ||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 10.3923 | 0.665299 | ||||||||
\(245\) | −12.0000 | + | 1.73205i | −0.766652 | + | 0.110657i | ||||
\(246\) | 15.0000 | + | 15.0000i | 0.956365 | + | 0.956365i | ||||
\(247\) | 10.3923 | − | 6.00000i | 0.661247 | − | 0.381771i | ||||
\(248\) | −6.33975 | + | 23.6603i | −0.402574 | + | 1.50243i | ||||
\(249\) | −1.50000 | + | 2.59808i | −0.0950586 | + | 0.164646i | ||||
\(250\) | −16.5622 | + | 4.43782i | −1.04748 | + | 0.280673i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −15.0000 | + | 5.19615i | −0.944911 | + | 0.327327i | ||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | −24.5885 | + | 6.58846i | −1.54282 | + | 0.413397i | ||||
\(255\) | 5.19615 | + | 9.00000i | 0.325396 | + | 0.563602i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −25.5000 | + | 14.7224i | −1.59065 | + | 0.918360i | −0.597450 | + | 0.801906i | \(0.703819\pi\) |
−0.993196 | + | 0.116454i | \(0.962847\pi\) | |||||||
\(258\) | −0.633975 | + | 2.36603i | −0.0394695 | + | 0.147302i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | −7.50000 | + | 12.9904i | −0.464238 | + | 0.804084i | ||||
\(262\) | 12.1244 | − | 12.1244i | 0.749045 | − | 0.749045i | ||||
\(263\) | 16.4545 | + | 9.50000i | 1.01463 | + | 0.585795i | 0.912543 | − | 0.408981i | \(-0.134116\pi\) |
0.102084 | + | 0.994776i | \(0.467449\pi\) | |||||||
\(264\) | 1.26795 | + | 4.73205i | 0.0780369 | + | 0.291238i | ||||
\(265\) | −6.00000 | + | 3.46410i | −0.368577 | + | 0.212798i | ||||
\(266\) | −1.85641 | − | 25.8564i | −0.113824 | − | 1.58536i | ||||
\(267\) | − | 30.0000i | − | 1.83597i | ||||||
\(268\) | 15.0000 | − | 25.9808i | 0.916271 | − | 1.58703i | ||||
\(269\) | − | 10.3923i | − | 0.633630i | −0.948487 | − | 0.316815i | \(-0.897387\pi\) | ||
0.948487 | − | 0.316815i | \(-0.102613\pi\) | |||||||
\(270\) | −9.00000 | − | 9.00000i | −0.547723 | − | 0.547723i | ||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 12.0000 | + | 6.92820i | 0.727607 | + | 0.420084i | ||||
\(273\) | −7.50000 | + | 2.59808i | −0.453921 | + | 0.157243i | ||||
\(274\) | 6.83013 | + | 1.83013i | 0.412623 | + | 0.110562i | ||||
\(275\) | 1.73205 | − | 1.00000i | 0.104447 | − | 0.0603023i | ||||
\(276\) | 8.66025 | − | 15.0000i | 0.521286 | − | 0.902894i | ||||
\(277\) | −11.5000 | + | 19.9186i | −0.690968 | + | 1.19679i | 0.280553 | + | 0.959839i | \(0.409482\pi\) |
−0.971521 | + | 0.236953i | \(0.923851\pi\) | |||||||
\(278\) | −8.66025 | + | 8.66025i | −0.519408 | + | 0.519408i | ||||
\(279\) | 12.9904 | + | 22.5000i | 0.777714 | + | 1.34704i | ||||
\(280\) | −11.6603 | − | 5.66025i | −0.696833 | − | 0.338265i | ||||
\(281\) | −0.500000 | + | 0.866025i | −0.0298275 | + | 0.0516627i | −0.880554 | − | 0.473946i | \(-0.842829\pi\) |
0.850726 | + | 0.525609i | \(0.176162\pi\) | |||||||
\(282\) | −12.2942 | − | 3.29423i | −0.732111 | − | 0.196168i | ||||
\(283\) | −7.79423 | − | 13.5000i | −0.463319 | − | 0.802492i | 0.535805 | − | 0.844342i | \(-0.320008\pi\) |
−0.999124 | + | 0.0418500i | \(0.986675\pi\) | |||||||
\(284\) | 4.00000 | + | 6.92820i | 0.237356 | + | 0.411113i | ||||
\(285\) | 18.0000 | − | 10.3923i | 1.06623 | − | 0.615587i | ||||
\(286\) | 0.633975 | + | 2.36603i | 0.0374877 | + | 0.139906i | ||||
\(287\) | 21.6506 | − | 7.50000i | 1.27800 | − | 0.442711i | ||||
\(288\) | −16.3923 | − | 4.39230i | −0.965926 | − | 0.258819i | ||||
\(289\) | 5.00000 | 0.294118 | ||||||||
\(290\) | −11.8301 | + | 3.16987i | −0.694689 | + | 0.186141i | ||||
\(291\) | 7.79423 | + | 4.50000i | 0.456906 | + | 0.263795i | ||||
\(292\) | 10.3923 | + | 18.0000i | 0.608164 | + | 1.05337i | ||||
\(293\) | 22.5000 | − | 12.9904i | 1.31446 | − | 0.758906i | 0.331632 | − | 0.943409i | \(-0.392401\pi\) |
0.982832 | + | 0.184503i | \(0.0590674\pi\) | |||||||
\(294\) | −2.02628 | + | 17.0263i | −0.118175 | + | 0.992993i | ||||
\(295\) | 12.9904 | + | 7.50000i | 0.756329 | + | 0.436667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.50000 | + | 2.59808i | 0.261116 | + | 0.150756i | ||||
\(298\) | 7.00000 | − | 7.00000i | 0.405499 | − | 0.405499i | ||||
\(299\) | 4.33013 | − | 7.50000i | 0.250418 | − | 0.433736i | ||||
\(300\) | 6.92820i | 0.400000i | ||||||||
\(301\) | 2.00000 | + | 1.73205i | 0.115278 | + | 0.0998337i | ||||
\(302\) | 4.02628 | − | 15.0263i | 0.231686 | − | 0.864665i | ||||
\(303\) | −18.1865 | − | 10.5000i | −1.04479 | − | 0.603209i | ||||
\(304\) | 13.8564 | − | 24.0000i | 0.794719 | − | 1.37649i | ||||
\(305\) | 9.00000 | 0.515339 | ||||||||
\(306\) | 14.1962 | − | 3.80385i | 0.811540 | − | 0.217451i | ||||
\(307\) | −13.8564 | −0.790827 | −0.395413 | − | 0.918503i | \(-0.629399\pi\) | ||||
−0.395413 | + | 0.918503i | \(0.629399\pi\) | |||||||
\(308\) | 5.19615 | + | 1.00000i | 0.296078 | + | 0.0569803i | ||||
\(309\) | 7.50000 | + | 12.9904i | 0.426660 | + | 0.738997i | ||||
\(310\) | −5.49038 | + | 20.4904i | −0.311833 | + | 1.16378i | ||||
\(311\) | −12.9904 | − | 22.5000i | −0.736617 | − | 1.27586i | −0.954010 | − | 0.299774i | \(-0.903089\pi\) |
0.217393 | − | 0.976084i | \(-0.430245\pi\) | |||||||
\(312\) | −8.19615 | − | 2.19615i | −0.464016 | − | 0.124333i | ||||
\(313\) | −7.50000 | − | 4.33013i | −0.423925 | − | 0.244753i | 0.272830 | − | 0.962062i | \(-0.412040\pi\) |
−0.696755 | + | 0.717309i | \(0.745374\pi\) | |||||||
\(314\) | −5.19615 | − | 5.19615i | −0.293236 | − | 0.293236i | ||||
\(315\) | −12.9904 | + | 4.50000i | −0.731925 | + | 0.253546i | ||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | 11.5000 | − | 19.9186i | 0.645904 | − | 1.11874i | −0.338188 | − | 0.941079i | \(-0.609814\pi\) |
0.984092 | − | 0.177660i | \(-0.0568529\pi\) | |||||||
\(318\) | 2.53590 | + | 9.46410i | 0.142206 | + | 0.530720i | ||||
\(319\) | 4.33013 | − | 2.50000i | 0.242441 | − | 0.139973i | ||||
\(320\) | −6.92820 | − | 12.0000i | −0.387298 | − | 0.670820i | ||||
\(321\) | 3.46410i | 0.193347i | ||||||||
\(322\) | −10.4904 | − | 15.4904i | −0.584606 | − | 0.863245i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | −15.5885 | + | 9.00000i | −0.866025 | + | 0.500000i | ||||
\(325\) | 3.46410i | 0.192154i | ||||||||
\(326\) | 8.19615 | − | 2.19615i | 0.453943 | − | 0.121634i | ||||
\(327\) | −20.7846 | −1.14939 | ||||||||
\(328\) | 23.6603 | + | 6.33975i | 1.30642 | + | 0.350054i | ||||
\(329\) | −9.00000 | + | 10.3923i | −0.496186 | + | 0.572946i | ||||
\(330\) | 1.09808 | + | 4.09808i | 0.0604471 | + | 0.225592i | ||||
\(331\) | −25.1147 | − | 14.5000i | −1.38043 | − | 0.796992i | −0.388221 | − | 0.921567i | \(-0.626910\pi\) |
−0.992210 | + | 0.124574i | \(0.960243\pi\) | |||||||
\(332\) | 3.46410i | 0.190117i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1244 | − | 12.1244i | 0.663415 | − | 0.663415i | ||||
\(335\) | 12.9904 | − | 22.5000i | 0.709740 | − | 1.22931i | ||||
\(336\) | −12.0000 | + | 13.8564i | −0.654654 | + | 0.755929i | ||||
\(337\) | −7.50000 | − | 12.9904i | −0.408551 | − | 0.707631i | 0.586177 | − | 0.810183i | \(-0.300632\pi\) |
−0.994728 | + | 0.102552i | \(0.967299\pi\) | |||||||
\(338\) | 13.6603 | + | 3.66025i | 0.743020 | + | 0.199092i | ||||
\(339\) | 16.4545 | + | 28.5000i | 0.893685 | + | 1.54791i | ||||
\(340\) | 10.3923 | + | 6.00000i | 0.563602 | + | 0.325396i | ||||
\(341\) | − | 8.66025i | − | 0.468979i | ||||||
\(342\) | −7.60770 | − | 28.3923i | −0.411377 | − | 1.53528i | ||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 0.732051 | + | 2.73205i | 0.0394695 | + | 0.147302i | ||||
\(345\) | 7.50000 | − | 12.9904i | 0.403786 | − | 0.699379i | ||||
\(346\) | −3.16987 | + | 11.8301i | −0.170413 | + | 0.635992i | ||||
\(347\) | 4.33013 | − | 2.50000i | 0.232453 | − | 0.134207i | −0.379250 | − | 0.925294i | \(-0.623818\pi\) |
0.611703 | + | 0.791087i | \(0.290485\pi\) | |||||||
\(348\) | 17.3205i | 0.928477i | ||||||||
\(349\) | 22.5000 | + | 12.9904i | 1.20440 | + | 0.695359i | 0.961530 | − | 0.274700i | \(-0.0885786\pi\) |
0.242867 | + | 0.970059i | \(0.421912\pi\) | |||||||
\(350\) | 6.73205 | + | 3.26795i | 0.359843 | + | 0.174679i | ||||
\(351\) | −7.79423 | + | 4.50000i | −0.416025 | + | 0.240192i | ||||
\(352\) | 4.00000 | + | 4.00000i | 0.213201 | + | 0.213201i | ||||
\(353\) | 7.50000 | + | 4.33013i | 0.399185 | + | 0.230469i | 0.686132 | − | 0.727477i | \(-0.259307\pi\) |
−0.286947 | + | 0.957946i | \(0.592641\pi\) | |||||||
\(354\) | 15.0000 | − | 15.0000i | 0.797241 | − | 0.797241i | ||||
\(355\) | 3.46410 | + | 6.00000i | 0.183855 | + | 0.318447i | ||||
\(356\) | −17.3205 | − | 30.0000i | −0.917985 | − | 1.59000i | ||||
\(357\) | 3.00000 | − | 15.5885i | 0.158777 | − | 0.825029i | ||||
\(358\) | 2.73205 | − | 0.732051i | 0.144393 | − | 0.0386901i | ||||
\(359\) | 10.0000i | 0.527780i | 0.964553 | + | 0.263890i | \(0.0850056\pi\) | ||||
−0.964553 | + | 0.263890i | \(0.914994\pi\) | |||||||
\(360\) | −14.1962 | − | 3.80385i | −0.748203 | − | 0.200480i | ||||
\(361\) | 29.0000 | 1.52632 | ||||||||
\(362\) | 23.6603 | − | 6.33975i | 1.24356 | − | 0.333210i | ||||
\(363\) | 8.66025 | + | 15.0000i | 0.454545 | + | 0.787296i | ||||
\(364\) | −6.00000 | + | 6.92820i | −0.314485 | + | 0.363137i | ||||
\(365\) | 9.00000 | + | 15.5885i | 0.471082 | + | 0.815937i | ||||
\(366\) | 3.29423 | − | 12.2942i | 0.172192 | − | 0.642630i | ||||
\(367\) | −11.2583 | + | 19.5000i | −0.587680 | + | 1.01789i | 0.406855 | + | 0.913493i | \(0.366625\pi\) |
−0.994535 | + | 0.104399i | \(0.966708\pi\) | |||||||
\(368\) | − | 20.0000i | − | 1.04257i | ||||||
\(369\) | 22.5000 | − | 12.9904i | 1.17130 | − | 0.676252i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.3923 | + | 2.00000i | 0.539542 | + | 0.103835i | ||||
\(372\) | 25.9808 | + | 15.0000i | 1.34704 | + | 0.777714i | ||||
\(373\) | −0.500000 | − | 0.866025i | −0.0258890 | − | 0.0448411i | 0.852791 | − | 0.522253i | \(-0.174908\pi\) |
−0.878680 | + | 0.477412i | \(0.841575\pi\) | |||||||
\(374\) | −4.73205 | − | 1.26795i | −0.244689 | − | 0.0655641i | ||||
\(375\) | 21.0000i | 1.08444i | ||||||||
\(376\) | −14.1962 | + | 3.80385i | −0.732111 | + | 0.196168i | ||||
\(377\) | 8.66025i | 0.446026i | ||||||||
\(378\) | 1.39230 | + | 19.3923i | 0.0716124 | + | 0.997433i | ||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 12.0000 | − | 20.7846i | 0.615587 | − | 1.06623i | ||||
\(381\) | 31.1769i | 1.59724i | ||||||||
\(382\) | 1.83013 | − | 6.83013i | 0.0936374 | − | 0.349460i | ||||
\(383\) | −0.866025 | − | 1.50000i | −0.0442518 | − | 0.0766464i | 0.843051 | − | 0.537833i | \(-0.180757\pi\) |
−0.887303 | + | 0.461187i | \(0.847424\pi\) | |||||||
\(384\) | −18.9282 | + | 5.07180i | −0.965926 | + | 0.258819i | ||||
\(385\) | 4.50000 | + | 0.866025i | 0.229341 | + | 0.0441367i | ||||
\(386\) | −9.00000 | + | 9.00000i | −0.458088 | + | 0.458088i | ||||
\(387\) | 2.59808 | + | 1.50000i | 0.132068 | + | 0.0762493i | ||||
\(388\) | 10.3923 | 0.527589 | ||||||||
\(389\) | 8.50000 | − | 14.7224i | 0.430967 | − | 0.746457i | −0.565990 | − | 0.824412i | \(-0.691506\pi\) |
0.996957 | + | 0.0779554i | \(0.0248392\pi\) | |||||||
\(390\) | −7.09808 | − | 1.90192i | −0.359425 | − | 0.0963077i | ||||
\(391\) | 8.66025 | + | 15.0000i | 0.437968 | + | 0.758583i | ||||
\(392\) | 7.80385 | + | 18.1962i | 0.394154 | + | 0.919044i | ||||
\(393\) | −10.5000 | − | 18.1865i | −0.529655 | − | 0.917389i | ||||
\(394\) | −0.732051 | − | 2.73205i | −0.0368802 | − | 0.137639i | ||||
\(395\) | −5.19615 | −0.261447 | ||||||||
\(396\) | 6.00000 | 0.301511 | ||||||||
\(397\) | 17.3205i | 0.869291i | 0.900602 | + | 0.434646i | \(0.143126\pi\) | ||||
−0.900602 | + | 0.434646i | \(0.856874\pi\) | |||||||
\(398\) | 6.33975 | + | 23.6603i | 0.317783 | + | 1.18598i | ||||
\(399\) | −31.1769 | − | 6.00000i | −1.56080 | − | 0.300376i | ||||
\(400\) | 4.00000 | + | 6.92820i | 0.200000 | + | 0.346410i | ||||
\(401\) | −2.50000 | − | 4.33013i | −0.124844 | − | 0.216236i | 0.796828 | − | 0.604206i | \(-0.206510\pi\) |
−0.921672 | + | 0.387970i | \(0.873176\pi\) | |||||||
\(402\) | −25.9808 | − | 25.9808i | −1.29580 | − | 1.29580i | ||||
\(403\) | 12.9904 | + | 7.50000i | 0.647097 | + | 0.373602i | ||||
\(404\) | −24.2487 | −1.20642 | ||||||||
\(405\) | −13.5000 | + | 7.79423i | −0.670820 | + | 0.387298i | ||||
\(406\) | 16.8301 | + | 8.16987i | 0.835265 | + | 0.405464i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 12.0000 | − | 12.0000i | 0.594089 | − | 0.594089i | ||||
\(409\) | −13.5000 | + | 7.79423i | −0.667532 | + | 0.385400i | −0.795141 | − | 0.606425i | \(-0.792603\pi\) |
0.127609 | + | 0.991825i | \(0.459270\pi\) | |||||||
\(410\) | 20.4904 | + | 5.49038i | 1.01195 | + | 0.271151i | ||||
\(411\) | 4.33013 | − | 7.50000i | 0.213589 | − | 0.369948i | ||||
\(412\) | 15.0000 | + | 8.66025i | 0.738997 | + | 0.426660i | ||||
\(413\) | −7.50000 | − | 21.6506i | −0.369051 | − | 1.06536i | ||||
\(414\) | −15.0000 | − | 15.0000i | −0.737210 | − | 0.737210i | ||||
\(415\) | 3.00000i | 0.147264i | ||||||||
\(416\) | −9.46410 | + | 2.53590i | −0.464016 | + | 0.124333i | ||||
\(417\) | 7.50000 | + | 12.9904i | 0.367277 | + | 0.636142i | ||||
\(418\) | −2.53590 | + | 9.46410i | −0.124035 | + | 0.462904i | ||||
\(419\) | −12.9904 | − | 22.5000i | −0.634622 | − | 1.09920i | −0.986595 | − | 0.163187i | \(-0.947823\pi\) |
0.351974 | − | 0.936010i | \(-0.385511\pi\) | |||||||
\(420\) | −10.3923 | + | 12.0000i | −0.507093 | + | 0.585540i | ||||
\(421\) | 5.50000 | − | 9.52628i | 0.268054 | − | 0.464282i | −0.700306 | − | 0.713843i | \(-0.746953\pi\) |
0.968359 | + | 0.249561i | \(0.0802862\pi\) | |||||||
\(422\) | −1.00000 | − | 1.00000i | −0.0486792 | − | 0.0486792i | ||||
\(423\) | −7.79423 | + | 13.5000i | −0.378968 | + | 0.656392i | ||||
\(424\) | 8.00000 | + | 8.00000i | 0.388514 | + | 0.388514i | ||||
\(425\) | −6.00000 | − | 3.46410i | −0.291043 | − | 0.168034i | ||||
\(426\) | 9.46410 | − | 2.53590i | 0.458537 | − | 0.122865i | ||||
\(427\) | −10.3923 | − | 9.00000i | −0.502919 | − | 0.435541i | ||||
\(428\) | 2.00000 | + | 3.46410i | 0.0966736 | + | 0.167444i | ||||
\(429\) | 3.00000 | 0.144841 | ||||||||
\(430\) | 0.633975 | + | 2.36603i | 0.0305730 | + | 0.114100i | ||||
\(431\) | − | 26.0000i | − | 1.25238i | −0.779672 | − | 0.626188i | \(-0.784614\pi\) | ||
0.779672 | − | 0.626188i | \(-0.215386\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.500000 | + | 0.866025i | ||||
\(433\) | − | 17.3205i | − | 0.832370i | −0.909280 | − | 0.416185i | \(-0.863367\pi\) | ||
0.909280 | − | 0.416185i | \(-0.136633\pi\) | |||||||
\(434\) | 26.8301 | − | 18.1699i | 1.28789 | − | 0.872182i | ||||
\(435\) | 15.0000i | 0.719195i | ||||||||
\(436\) | −20.7846 | + | 12.0000i | −0.995402 | + | 0.574696i | ||||
\(437\) | 30.0000 | − | 17.3205i | 1.43509 | − | 0.828552i | ||||
\(438\) | 24.5885 | − | 6.58846i | 1.17488 | − | 0.314809i | ||||
\(439\) | 9.52628 | − | 16.5000i | 0.454665 | − | 0.787502i | −0.544004 | − | 0.839082i | \(-0.683092\pi\) |
0.998669 | + | 0.0515804i | \(0.0164258\pi\) | |||||||
\(440\) | 3.46410 | + | 3.46410i | 0.165145 | + | 0.165145i | ||||
\(441\) | 19.5000 | + | 7.79423i | 0.928571 | + | 0.371154i | ||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | −30.3109 | − | 17.5000i | −1.44011 | − | 0.831450i | −0.442257 | − | 0.896888i | \(-0.645822\pi\) |
−0.997857 | + | 0.0654382i | \(0.979155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −15.0000 | − | 25.9808i | −0.711068 | − | 1.23161i | ||||
\(446\) | −2.36603 | − | 0.633975i | −0.112035 | − | 0.0300196i | ||||
\(447\) | −6.06218 | − | 10.5000i | −0.286731 | − | 0.496633i | ||||
\(448\) | −4.00000 | + | 20.7846i | −0.188982 | + | 0.981981i | ||||
\(449\) | −20.0000 | −0.943858 | −0.471929 | − | 0.881636i | \(-0.656442\pi\) | ||||
−0.471929 | + | 0.881636i | \(0.656442\pi\) | |||||||
\(450\) | 8.19615 | + | 2.19615i | 0.386370 | + | 0.103528i | ||||
\(451\) | −8.66025 | −0.407795 | ||||||||
\(452\) | 32.9090 | + | 19.0000i | 1.54791 | + | 0.893685i | ||||
\(453\) | −16.5000 | − | 9.52628i | −0.775238 | − | 0.447584i | ||||
\(454\) | −7.09808 | − | 1.90192i | −0.333129 | − | 0.0892617i | ||||
\(455\) | −5.19615 | + | 6.00000i | −0.243599 | + | 0.281284i | ||||
\(456\) | −24.0000 | − | 24.0000i | −1.12390 | − | 1.12390i | ||||
\(457\) | 7.50000 | − | 12.9904i | 0.350835 | − | 0.607664i | −0.635561 | − | 0.772051i | \(-0.719231\pi\) |
0.986396 | + | 0.164386i | \(0.0525644\pi\) | |||||||
\(458\) | 1.73205 | + | 1.73205i | 0.0809334 | + | 0.0809334i | ||||
\(459\) | − | 18.0000i | − | 0.840168i | ||||||
\(460\) | − | 17.3205i | − | 0.807573i | ||||||
\(461\) | −10.5000 | − | 6.06218i | −0.489034 | − | 0.282344i | 0.235140 | − | 0.971962i | \(-0.424445\pi\) |
−0.724174 | + | 0.689618i | \(0.757779\pi\) | |||||||
\(462\) | 2.83013 | − | 5.83013i | 0.131669 | − | 0.271242i | ||||
\(463\) | −33.7750 | + | 19.5000i | −1.56966 | + | 0.906242i | −0.573449 | + | 0.819242i | \(0.694395\pi\) |
−0.996208 | + | 0.0870004i | \(0.972272\pi\) | |||||||
\(464\) | 10.0000 | + | 17.3205i | 0.464238 | + | 0.804084i | ||||
\(465\) | 22.5000 | + | 12.9904i | 1.04341 | + | 0.602414i | ||||
\(466\) | 5.12436 | + | 19.1244i | 0.237381 | + | 0.885919i | ||||
\(467\) | 20.7846 | 0.961797 | 0.480899 | − | 0.876776i | \(-0.340311\pi\) | ||||
0.480899 | + | 0.876776i | \(0.340311\pi\) | |||||||
\(468\) | −5.19615 | + | 9.00000i | −0.240192 | + | 0.416025i | ||||
\(469\) | −37.5000 | + | 12.9904i | −1.73159 | + | 0.599840i | ||||
\(470\) | −12.2942 | + | 3.29423i | −0.567090 | + | 0.151951i | ||||
\(471\) | −7.79423 | + | 4.50000i | −0.359139 | + | 0.207349i | ||||
\(472\) | 6.33975 | − | 23.6603i | 0.291810 | − | 1.08905i | ||||
\(473\) | −0.500000 | − | 0.866025i | −0.0229900 | − | 0.0398199i | ||||
\(474\) | −1.90192 | + | 7.09808i | −0.0873583 | + | 0.326025i | ||||
\(475\) | −6.92820 | + | 12.0000i | −0.317888 | + | 0.550598i | ||||
\(476\) | −6.00000 | − | 17.3205i | −0.275010 | − | 0.793884i | ||||
\(477\) | 12.0000 | 0.549442 | ||||||||
\(478\) | −25.0000 | − | 25.0000i | −1.14347 | − | 1.14347i | ||||
\(479\) | 16.4545 | − | 28.5000i | 0.751825 | − | 1.30220i | −0.195113 | − | 0.980781i | \(-0.562507\pi\) |
0.946938 | − | 0.321417i | \(-0.104159\pi\) | |||||||
\(480\) | −16.3923 | + | 4.39230i | −0.748203 | + | 0.200480i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.7776 | + | 40.2224i | −0.490905 | + | 1.83208i | ||||
\(483\) | −21.6506 | + | 7.50000i | −0.985138 | + | 0.341262i | ||||
\(484\) | 17.3205 | + | 10.0000i | 0.787296 | + | 0.454545i | ||||
\(485\) | 9.00000 | 0.408669 | ||||||||
\(486\) | 5.70577 | + | 21.2942i | 0.258819 | + | 0.965926i | ||||
\(487\) | − | 10.0000i | − | 0.453143i | −0.973995 | − | 0.226572i | \(-0.927248\pi\) | ||
0.973995 | − | 0.226572i | \(-0.0727517\pi\) | |||||||
\(488\) | −3.80385 | − | 14.1962i | −0.172192 | − | 0.642630i | ||||
\(489\) | − | 10.3923i | − | 0.469956i | ||||||
\(490\) | 6.75833 | + | 15.7583i | 0.305310 | + | 0.711889i | ||||
\(491\) | 16.4545 | − | 9.50000i | 0.742580 | − | 0.428729i | −0.0804264 | − | 0.996761i | \(-0.525628\pi\) |
0.823007 | + | 0.568032i | \(0.192295\pi\) | |||||||
\(492\) | 15.0000 | − | 25.9808i | 0.676252 | − | 1.17130i | ||||
\(493\) | −15.0000 | − | 8.66025i | −0.675566 | − | 0.390038i | ||||
\(494\) | −12.0000 | − | 12.0000i | −0.539906 | − | 0.539906i | ||||
\(495\) | 5.19615 | 0.233550 | ||||||||
\(496\) | 34.6410 | 1.55543 | ||||||||
\(497\) | 2.00000 | − | 10.3923i | 0.0897123 | − | 0.466159i | ||||
\(498\) | 4.09808 | + | 1.09808i | 0.183639 | + | 0.0492060i | ||||
\(499\) | 6.06218 | − | 3.50000i | 0.271380 | − | 0.156682i | −0.358134 | − | 0.933670i | \(-0.616587\pi\) |
0.629515 | + | 0.776989i | \(0.283254\pi\) | |||||||
\(500\) | 12.1244 | + | 21.0000i | 0.542218 | + | 0.939149i | ||||
\(501\) | −10.5000 | − | 18.1865i | −0.469105 | − | 0.812514i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.3205 | −0.772283 | −0.386142 | − | 0.922440i | \(-0.626192\pi\) | ||||
−0.386142 | + | 0.922440i | \(0.626192\pi\) | |||||||
\(504\) | 12.5885 | + | 18.5885i | 0.560734 | + | 0.827996i | ||||
\(505\) | −21.0000 | −0.934488 | ||||||||
\(506\) | 1.83013 | + | 6.83013i | 0.0813591 | + | 0.303636i | ||||
\(507\) | 8.66025 | − | 15.0000i | 0.384615 | − | 0.666173i | ||||
\(508\) | 18.0000 | + | 31.1769i | 0.798621 | + | 1.38325i | ||||
\(509\) | −22.5000 | + | 12.9904i | −0.997295 | + | 0.575789i | −0.907447 | − | 0.420167i | \(-0.861972\pi\) |
−0.0898481 | + | 0.995955i | \(0.528638\pi\) | |||||||
\(510\) | 10.3923 | − | 10.3923i | 0.460179 | − | 0.460179i | ||||
\(511\) | 5.19615 | − | 27.0000i | 0.229864 | − | 1.19441i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | −36.0000 | −1.58944 | ||||||||
\(514\) | 29.4449 | + | 29.4449i | 1.29876 | + | 1.29876i | ||||
\(515\) | 12.9904 | + | 7.50000i | 0.572425 | + | 0.330489i | ||||
\(516\) | 3.46410 | 0.152499 | ||||||||
\(517\) | 4.50000 | − | 2.59808i | 0.197910 | − | 0.114263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.9904 | + | 7.50000i | 0.570214 | + | 0.329213i | ||||
\(520\) | −8.19615 | + | 2.19615i | −0.359425 | + | 0.0963077i | ||||
\(521\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(522\) | 20.4904 | + | 5.49038i | 0.896840 | + | 0.240307i | ||||
\(523\) | 24.2487 | 1.06032 | 0.530161 | − | 0.847897i | \(-0.322131\pi\) | ||||
0.530161 | + | 0.847897i | \(0.322131\pi\) | |||||||
\(524\) | −21.0000 | − | 12.1244i | −0.917389 | − | 0.529655i | ||||
\(525\) | 6.00000 | − | 6.92820i | 0.261861 | − | 0.302372i | ||||
\(526\) | 6.95448 | − | 25.9545i | 0.303230 | − | 1.13167i | ||||
\(527\) | −25.9808 | + | 15.0000i | −1.13174 | + | 0.653410i | ||||
\(528\) | 6.00000 | − | 3.46410i | 0.261116 | − | 0.150756i | ||||
\(529\) | 1.00000 | − | 1.73205i | 0.0434783 | − | 0.0753066i | ||||
\(530\) | 6.92820 | + | 6.92820i | 0.300942 | + | 0.300942i | ||||
\(531\) | −12.9904 | − | 22.5000i | −0.563735 | − | 0.976417i | ||||
\(532\) | −34.6410 | + | 12.0000i | −1.50188 | + | 0.520266i | ||||
\(533\) | 7.50000 | − | 12.9904i | 0.324861 | − | 0.562676i | ||||
\(534\) | −40.9808 | + | 10.9808i | −1.77341 | + | 0.475184i | ||||
\(535\) | 1.73205 | + | 3.00000i | 0.0748831 | + | 0.129701i | ||||
\(536\) | −40.9808 | − | 10.9808i | −1.77010 | − | 0.474297i | ||||
\(537\) | − | 3.46410i | − | 0.149487i | ||||||
\(538\) | −14.1962 | + | 3.80385i | −0.612040 | + | 0.163996i | ||||
\(539\) | −4.33013 | − | 5.50000i | −0.186512 | − | 0.236902i | ||||
\(540\) | −9.00000 | + | 15.5885i | −0.387298 | + | 0.670820i | ||||
\(541\) | 26.0000 | 1.11783 | 0.558914 | − | 0.829226i | \(-0.311218\pi\) | ||||
0.558914 | + | 0.829226i | \(0.311218\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 30.0000i | − | 1.28742i | ||||||
\(544\) | 5.07180 | − | 18.9282i | 0.217451 | − | 0.811540i | ||||
\(545\) | −18.0000 | + | 10.3923i | −0.771035 | + | 0.445157i | ||||
\(546\) | 6.29423 | + | 9.29423i | 0.269368 | + | 0.397756i | ||||
\(547\) | 23.3827 | + | 13.5000i | 0.999771 | + | 0.577218i | 0.908181 | − | 0.418578i | \(-0.137471\pi\) |
0.0915908 | + | 0.995797i | \(0.470805\pi\) | |||||||
\(548\) | − | 10.0000i | − | 0.427179i | ||||||
\(549\) | −13.5000 | − | 7.79423i | −0.576166 | − | 0.332650i | ||||
\(550\) | −2.00000 | − | 2.00000i | −0.0852803 | − | 0.0852803i | ||||
\(551\) | −17.3205 | + | 30.0000i | −0.737878 | + | 1.27804i | ||||
\(552\) | −23.6603 | − | 6.33975i | −1.00705 | − | 0.269838i | ||||
\(553\) | 6.00000 | + | 5.19615i | 0.255146 | + | 0.220963i | ||||
\(554\) | 31.4186 | + | 8.41858i | 1.33485 | + | 0.357671i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.0000 | + | 8.66025i | 0.636142 | + | 0.367277i | ||||
\(557\) | −40.0000 | −1.69485 | −0.847427 | − | 0.530912i | \(-0.821850\pi\) | ||||
−0.847427 | + | 0.530912i | \(0.821850\pi\) | |||||||
\(558\) | 25.9808 | − | 25.9808i | 1.09985 | − | 1.09985i | ||||
\(559\) | 1.73205 | 0.0732579 | ||||||||
\(560\) | −3.46410 | + | 18.0000i | −0.146385 | + | 0.760639i | ||||
\(561\) | −3.00000 | + | 5.19615i | −0.126660 | + | 0.219382i | ||||
\(562\) | 1.36603 | + | 0.366025i | 0.0576223 | + | 0.0154398i | ||||
\(563\) | 0.866025 | + | 1.50000i | 0.0364986 | + | 0.0632175i | 0.883698 | − | 0.468058i | \(-0.155046\pi\) |
−0.847199 | + | 0.531276i | \(0.821713\pi\) | |||||||
\(564\) | 18.0000i | 0.757937i | ||||||||
\(565\) | 28.5000 | + | 16.4545i | 1.19900 | + | 0.692245i | ||||
\(566\) | −15.5885 | + | 15.5885i | −0.655232 | + | 0.655232i | ||||
\(567\) | 23.3827 | + | 4.50000i | 0.981981 | + | 0.188982i | ||||
\(568\) | 8.00000 | − | 8.00000i | 0.335673 | − | 0.335673i | ||||
\(569\) | −3.50000 | + | 6.06218i | −0.146728 | + | 0.254140i | −0.930016 | − | 0.367519i | \(-0.880207\pi\) |
0.783289 | + | 0.621658i | \(0.213541\pi\) | |||||||
\(570\) | −20.7846 | − | 20.7846i | −0.870572 | − | 0.870572i | ||||
\(571\) | 7.79423 | − | 4.50000i | 0.326178 | − | 0.188319i | −0.327965 | − | 0.944690i | \(-0.606363\pi\) |
0.654143 | + | 0.756371i | \(0.273029\pi\) | |||||||
\(572\) | 3.00000 | − | 1.73205i | 0.125436 | − | 0.0724207i | ||||
\(573\) | −7.50000 | − | 4.33013i | −0.313317 | − | 0.180894i | ||||
\(574\) | −18.1699 | − | 26.8301i | −0.758396 | − | 1.11987i | ||||
\(575\) | 10.0000i | 0.417029i | ||||||||
\(576\) | 24.0000i | 1.00000i | ||||||||
\(577\) | − | 38.1051i | − | 1.58634i | −0.609002 | − | 0.793168i | \(-0.708430\pi\) | ||
0.609002 | − | 0.793168i | \(-0.291570\pi\) | |||||||
\(578\) | −1.83013 | − | 6.83013i | −0.0761232 | − | 0.284096i | ||||
\(579\) | 7.79423 | + | 13.5000i | 0.323917 | + | 0.561041i | ||||
\(580\) | 8.66025 | + | 15.0000i | 0.359597 | + | 0.622841i | ||||
\(581\) | 3.00000 | − | 3.46410i | 0.124461 | − | 0.143715i | ||||
\(582\) | 3.29423 | − | 12.2942i | 0.136550 | − | 0.509612i | ||||
\(583\) | −3.46410 | − | 2.00000i | −0.143468 | − | 0.0828315i | ||||
\(584\) | 20.7846 | − | 20.7846i | 0.860073 | − | 0.860073i | ||||
\(585\) | −4.50000 | + | 7.79423i | −0.186052 | + | 0.322252i | ||||
\(586\) | −25.9808 | − | 25.9808i | −1.07326 | − | 1.07326i | ||||
\(587\) | −12.9904 | + | 22.5000i | −0.536170 | + | 0.928674i | 0.462935 | + | 0.886392i | \(0.346796\pi\) |
−0.999106 | + | 0.0422823i | \(0.986537\pi\) | |||||||
\(588\) | 24.0000 | − | 3.46410i | 0.989743 | − | 0.142857i | ||||
\(589\) | 30.0000 | + | 51.9615i | 1.23613 | + | 2.14104i | ||||
\(590\) | 5.49038 | − | 20.4904i | 0.226035 | − | 0.843576i | ||||
\(591\) | −3.46410 | −0.142494 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 31.1769i | 1.28028i | 0.768257 | + | 0.640141i | \(0.221124\pi\) | ||||
−0.768257 | + | 0.640141i | \(0.778876\pi\) | |||||||
\(594\) | 1.90192 | − | 7.09808i | 0.0780369 | − | 0.291238i | ||||
\(595\) | −5.19615 | − | 15.0000i | −0.213021 | − | 0.614940i | ||||
\(596\) | −12.1244 | − | 7.00000i | −0.496633 | − | 0.286731i | ||||
\(597\) | 30.0000 | 1.22782 | ||||||||
\(598\) | −11.8301 | − | 3.16987i | −0.483770 | − | 0.129626i | ||||
\(599\) | −14.7224 | + | 8.50000i | −0.601542 | + | 0.347301i | −0.769648 | − | 0.638468i | \(-0.779568\pi\) |
0.168106 | + | 0.985769i | \(0.446235\pi\) | |||||||
\(600\) | 9.46410 | − | 2.53590i | 0.386370 | − | 0.103528i | ||||
\(601\) | −4.50000 | − | 2.59808i | −0.183559 | − | 0.105978i | 0.405405 | − | 0.914137i | \(-0.367131\pi\) |
−0.588964 | + | 0.808160i | \(0.700464\pi\) | |||||||
\(602\) | 1.63397 | − | 3.36603i | 0.0665958 | − | 0.137189i | ||||
\(603\) | −38.9711 | + | 22.5000i | −1.58703 | + | 0.916271i | ||||
\(604\) | −22.0000 | −0.895167 | ||||||||
\(605\) | 15.0000 | + | 8.66025i | 0.609837 | + | 0.352089i | ||||
\(606\) | −7.68653 | + | 28.6865i | −0.312244 | + | 1.16531i | ||||
\(607\) | −4.33013 | − | 7.50000i | −0.175754 | − | 0.304416i | 0.764668 | − | 0.644425i | \(-0.222903\pi\) |
−0.940422 | + | 0.340009i | \(0.889570\pi\) | |||||||
\(608\) | −37.8564 | − | 10.1436i | −1.53528 | − | 0.411377i | ||||
\(609\) | 15.0000 | − | 17.3205i | 0.607831 | − | 0.701862i | ||||
\(610\) | −3.29423 | − | 12.2942i | −0.133379 | − | 0.497779i | ||||
\(611\) | 9.00000i | 0.364101i | ||||||||
\(612\) | −10.3923 | − | 18.0000i | −0.420084 | − | 0.727607i | ||||
\(613\) | −40.0000 | −1.61558 | −0.807792 | − | 0.589467i | \(-0.799338\pi\) | ||||
−0.807792 | + | 0.589467i | \(0.799338\pi\) | |||||||
\(614\) | 5.07180 | + | 18.9282i | 0.204681 | + | 0.763880i | ||||
\(615\) | 12.9904 | − | 22.5000i | 0.523823 | − | 0.907288i | ||||
\(616\) | −0.535898 | − | 7.46410i | −0.0215920 | − | 0.300737i | ||||
\(617\) | 17.5000 | + | 30.3109i | 0.704523 | + | 1.22027i | 0.966863 | + | 0.255295i | \(0.0821725\pi\) |
−0.262340 | + | 0.964976i | \(0.584494\pi\) | |||||||
\(618\) | 15.0000 | − | 15.0000i | 0.603388 | − | 0.603388i | ||||
\(619\) | −4.33013 | + | 7.50000i | −0.174042 | + | 0.301450i | −0.939829 | − | 0.341644i | \(-0.889016\pi\) |
0.765787 | + | 0.643094i | \(0.222350\pi\) | |||||||
\(620\) | 30.0000 | 1.20483 | ||||||||
\(621\) | −22.5000 | + | 12.9904i | −0.902894 | + | 0.521286i | ||||
\(622\) | −25.9808 | + | 25.9808i | −1.04173 | + | 1.04173i | ||||
\(623\) | −8.66025 | + | 45.0000i | −0.346966 | + | 1.80289i | ||||
\(624\) | 12.0000i | 0.480384i | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | −3.16987 | + | 11.8301i | −0.126694 | + | 0.472827i | ||||
\(627\) | 10.3923 | + | 6.00000i | 0.415029 | + | 0.239617i | ||||
\(628\) | −5.19615 | + | 9.00000i | −0.207349 | + | 0.359139i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 10.9019 | + | 16.0981i | 0.434343 | + | 0.641363i | ||||
\(631\) | 6.00000i | 0.238856i | 0.992843 | + | 0.119428i | \(0.0381061\pi\) | ||||
−0.992843 | + | 0.119428i | \(0.961894\pi\) | |||||||
\(632\) | 2.19615 | + | 8.19615i | 0.0873583 | + | 0.326025i | ||||
\(633\) | −1.50000 | + | 0.866025i | −0.0596196 | + | 0.0344214i | ||||
\(634\) | −31.4186 | − | 8.41858i | −1.24779 | − | 0.334345i | ||||
\(635\) | 15.5885 | + | 27.0000i | 0.618609 | + | 1.07146i | ||||
\(636\) | 12.0000 | − | 6.92820i | 0.475831 | − | 0.274721i | ||||
\(637\) | 12.0000 | − | 1.73205i | 0.475457 | − | 0.0686264i | ||||
\(638\) | −5.00000 | − | 5.00000i | −0.197952 | − | 0.197952i | ||||
\(639\) | − | 12.0000i | − | 0.474713i | ||||||
\(640\) | −13.8564 | + | 13.8564i | −0.547723 | + | 0.547723i | ||||
\(641\) | 2.50000 | − | 4.33013i | 0.0987441 | − | 0.171030i | −0.812421 | − | 0.583071i | \(-0.801851\pi\) |
0.911165 | + | 0.412042i | \(0.135184\pi\) | |||||||
\(642\) | 4.73205 | − | 1.26795i | 0.186759 | − | 0.0500420i | ||||
\(643\) | 0.866025 | + | 1.50000i | 0.0341527 | + | 0.0591542i | 0.882597 | − | 0.470131i | \(-0.155793\pi\) |
−0.848444 | + | 0.529285i | \(0.822460\pi\) | |||||||
\(644\) | −17.3205 | + | 20.0000i | −0.682524 | + | 0.788110i | ||||
\(645\) | 3.00000 | 0.118125 | ||||||||
\(646\) | 32.7846 | − | 8.78461i | 1.28989 | − | 0.345626i | ||||
\(647\) | 34.6410 | 1.36188 | 0.680939 | − | 0.732340i | \(-0.261572\pi\) | ||||
0.680939 | + | 0.732340i | \(0.261572\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.707107 | + | 0.707107i | ||||
\(649\) | 8.66025i | 0.339945i | ||||||||
\(650\) | 4.73205 | − | 1.26795i | 0.185606 | − | 0.0497331i | ||||
\(651\) | −12.9904 | − | 37.5000i | −0.509133 | − | 1.46974i | ||||
\(652\) | −6.00000 | − | 10.3923i | −0.234978 | − | 0.406994i | ||||
\(653\) | 0.500000 | + | 0.866025i | 0.0195665 | + | 0.0338902i | 0.875643 | − | 0.482959i | \(-0.160438\pi\) |
−0.856076 | + | 0.516849i | \(0.827105\pi\) | |||||||
\(654\) | 7.60770 | + | 28.3923i | 0.297484 | + | 1.11023i | ||||
\(655\) | −18.1865 | − | 10.5000i | −0.710607 | − | 0.410269i | ||||
\(656\) | − | 34.6410i | − | 1.35250i | ||||||
\(657\) | − | 31.1769i | − | 1.21633i | ||||||
\(658\) | 17.4904 | + | 8.49038i | 0.681846 | + | 0.330990i | ||||
\(659\) | −14.7224 | − | 8.50000i | −0.573505 | − | 0.331113i | 0.185043 | − | 0.982730i | \(-0.440757\pi\) |
−0.758548 | + | 0.651617i | \(0.774091\pi\) | |||||||
\(660\) | 5.19615 | − | 3.00000i | 0.202260 | − | 0.116775i | ||||
\(661\) | −7.50000 | + | 4.33013i | −0.291716 | + | 0.168422i | −0.638716 | − | 0.769443i | \(-0.720534\pi\) |
0.346999 | + | 0.937865i | \(0.387201\pi\) | |||||||
\(662\) | −10.6147 | + | 39.6147i | −0.412553 | + | 1.53967i | ||||
\(663\) | −5.19615 | − | 9.00000i | −0.201802 | − | 0.349531i | ||||
\(664\) | 4.73205 | − | 1.26795i | 0.183639 | − | 0.0492060i | ||||
\(665\) | −30.0000 | + | 10.3923i | −1.16335 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.0000i | 0.968004i | ||||||||
\(668\) | −21.0000 | − | 12.1244i | −0.812514 | − | 0.469105i | ||||
\(669\) | −1.50000 | + | 2.59808i | −0.0579934 | + | 0.100447i | ||||
\(670\) | −35.4904 | − | 9.50962i | −1.37111 | − | 0.367389i | ||||
\(671\) | 2.59808 | + | 4.50000i | 0.100298 | + | 0.173721i | ||||
\(672\) | 23.3205 | + | 11.3205i | 0.899608 | + | 0.436698i | ||||
\(673\) | 19.5000 | − | 33.7750i | 0.751670 | − | 1.30193i | −0.195343 | − | 0.980735i | \(-0.562582\pi\) |
0.947013 | − | 0.321195i | \(-0.104085\pi\) | |||||||
\(674\) | −15.0000 | + | 15.0000i | −0.577778 | + | 0.577778i | ||||
\(675\) | 5.19615 | − | 9.00000i | 0.200000 | − | 0.346410i | ||||
\(676\) | − | 20.0000i | − | 0.769231i | ||||||
\(677\) | 4.50000 | + | 2.59808i | 0.172949 | + | 0.0998522i | 0.583976 | − | 0.811771i | \(-0.301496\pi\) |
−0.411027 | + | 0.911623i | \(0.634830\pi\) | |||||||
\(678\) | 32.9090 | − | 32.9090i | 1.26386 | − | 1.26386i | ||||
\(679\) | −10.3923 | − | 9.00000i | −0.398820 | − | 0.345388i | ||||
\(680\) | 4.39230 | − | 16.3923i | 0.168437 | − | 0.628616i | ||||
\(681\) | −4.50000 | + | 7.79423i | −0.172440 | + | 0.298675i | ||||
\(682\) | −11.8301 | + | 3.16987i | −0.452999 | + | 0.121381i | ||||
\(683\) | − | 14.0000i | − | 0.535695i | −0.963461 | − | 0.267848i | \(-0.913688\pi\) | ||
0.963461 | − | 0.267848i | \(-0.0863124\pi\) | |||||||
\(684\) | −36.0000 | + | 20.7846i | −1.37649 | + | 0.794719i | ||||
\(685\) | − | 8.66025i | − | 0.330891i | ||||||
\(686\) | 7.95448 | − | 24.9545i | 0.303704 | − | 0.952767i | ||||
\(687\) | 2.59808 | − | 1.50000i | 0.0991228 | − | 0.0572286i | ||||
\(688\) | 3.46410 | − | 2.00000i | 0.132068 | − | 0.0762493i | ||||
\(689\) | 6.00000 | − | 3.46410i | 0.228582 | − | 0.131972i | ||||
\(690\) | −20.4904 | − | 5.49038i | −0.780055 | − | 0.209015i | ||||
\(691\) | 4.33013 | − | 7.50000i | 0.164726 | − | 0.285313i | −0.771832 | − | 0.635826i | \(-0.780659\pi\) |
0.936558 | + | 0.350513i | \(0.113993\pi\) | |||||||
\(692\) | 17.3205 | 0.658427 | ||||||||
\(693\) | −6.00000 | − | 5.19615i | −0.227921 | − | 0.197386i | ||||
\(694\) | −5.00000 | − | 5.00000i | −0.189797 | − | 0.189797i | ||||
\(695\) | 12.9904 | + | 7.50000i | 0.492753 | + | 0.284491i | ||||
\(696\) | 23.6603 | − | 6.33975i | 0.896840 | − | 0.240307i | ||||
\(697\) | 15.0000 | + | 25.9808i | 0.568166 | + | 0.984092i | ||||
\(698\) | 9.50962 | − | 35.4904i | 0.359944 | − | 1.34333i | ||||
\(699\) | 24.2487 | 0.917170 | ||||||||
\(700\) | 2.00000 | − | 10.3923i | 0.0755929 | − | 0.392792i | ||||
\(701\) | 44.0000 | 1.66186 | 0.830929 | − | 0.556379i | \(-0.187810\pi\) | ||||
0.830929 | + | 0.556379i | \(0.187810\pi\) | |||||||
\(702\) | 9.00000 | + | 9.00000i | 0.339683 | + | 0.339683i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 4.00000 | − | 6.92820i | 0.150756 | − | 0.261116i | ||||
\(705\) | 15.5885i | 0.587095i | ||||||||
\(706\) | 3.16987 | − | 11.8301i | 0.119300 | − | 0.445233i | ||||
\(707\) | 24.2487 | + | 21.0000i | 0.911967 | + | 0.789786i | ||||
\(708\) | −25.9808 | − | 15.0000i | −0.976417 | − | 0.563735i | ||||
\(709\) | −7.50000 | + | 12.9904i | −0.281668 | + | 0.487864i | −0.971796 | − | 0.235824i | \(-0.924221\pi\) |
0.690127 | + | 0.723688i | \(0.257554\pi\) | |||||||
\(710\) | 6.92820 | − | 6.92820i | 0.260011 | − | 0.260011i | ||||
\(711\) | 7.79423 | + | 4.50000i | 0.292306 | + | 0.168763i | ||||
\(712\) | −34.6410 | + | 34.6410i | −1.29823 | + | 1.29823i | ||||
\(713\) | 37.5000 | + | 21.6506i | 1.40439 | + | 0.810823i | ||||
\(714\) | −22.3923 | + | 1.60770i | −0.838011 | + | 0.0601665i | ||||
\(715\) | 2.59808 | − | 1.50000i | 0.0971625 | − | 0.0560968i | ||||
\(716\) | −2.00000 | − | 3.46410i | −0.0747435 | − | 0.129460i | ||||
\(717\) | −37.5000 | + | 21.6506i | −1.40046 | + | 0.808558i | ||||
\(718\) | 13.6603 | − | 3.66025i | 0.509796 | − | 0.136599i | ||||
\(719\) | −34.6410 | −1.29189 | −0.645946 | − | 0.763383i | \(-0.723537\pi\) | ||||
−0.645946 | + | 0.763383i | \(0.723537\pi\) | |||||||
\(720\) | 20.7846i | 0.774597i | ||||||||
\(721\) | −7.50000 | − | 21.6506i | −0.279315 | − | 0.806312i | ||||
\(722\) | −10.6147 | − | 39.6147i | −0.395040 | − | 1.47431i | ||||
\(723\) | 44.1673 | + | 25.5000i | 1.64260 | + | 0.948355i | ||||
\(724\) | −17.3205 | − | 30.0000i | −0.643712 | − | 1.11494i | ||||
\(725\) | −5.00000 | − | 8.66025i | −0.185695 | − | 0.321634i | ||||
\(726\) | 17.3205 | − | 17.3205i | 0.642824 | − | 0.642824i | ||||
\(727\) | −14.7224 | + | 25.5000i | −0.546025 | + | 0.945743i | 0.452517 | + | 0.891756i | \(0.350526\pi\) |
−0.998542 | + | 0.0539868i | \(0.982807\pi\) | |||||||
\(728\) | 11.6603 | + | 5.66025i | 0.432158 | + | 0.209783i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 18.0000 | − | 18.0000i | 0.666210 | − | 0.666210i | ||||
\(731\) | −1.73205 | + | 3.00000i | −0.0640622 | + | 0.110959i | ||||
\(732\) | −18.0000 | −0.665299 | ||||||||
\(733\) | 19.5000 | − | 11.2583i | 0.720249 | − | 0.415836i | −0.0945954 | − | 0.995516i | \(-0.530156\pi\) |
0.814844 | + | 0.579680i | \(0.196822\pi\) | |||||||
\(734\) | 30.7583 | + | 8.24167i | 1.13531 | + | 0.304206i | ||||
\(735\) | 20.7846 | − | 3.00000i | 0.766652 | − | 0.110657i | ||||
\(736\) | −27.3205 | + | 7.32051i | −1.00705 | + | 0.269838i | ||||
\(737\) | 15.0000 | 0.552532 | ||||||||
\(738\) | −25.9808 | − | 25.9808i | −0.956365 | − | 0.956365i | ||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.0000 | + | 10.3923i | −0.661247 | + | 0.381771i | ||||
\(742\) | −1.07180 | − | 14.9282i | −0.0393469 | − | 0.548032i | ||||
\(743\) | −25.1147 | + | 14.5000i | −0.921370 | + | 0.531953i | −0.884072 | − | 0.467351i | \(-0.845209\pi\) |
−0.0372984 | + | 0.999304i | \(0.511875\pi\) | |||||||
\(744\) | 10.9808 | − | 40.9808i | 0.402574 | − | 1.50243i | ||||
\(745\) | −10.5000 | − | 6.06218i | −0.384690 | − | 0.222101i | ||||
\(746\) | −1.00000 | + | 1.00000i | −0.0366126 | + | 0.0366126i | ||||
\(747\) | 2.59808 | − | 4.50000i | 0.0950586 | − | 0.164646i | ||||
\(748\) | 6.92820i | 0.253320i | ||||||||
\(749\) | 1.00000 | − | 5.19615i | 0.0365392 | − | 0.189863i | ||||
\(750\) | 28.6865 | − | 7.68653i | 1.04748 | − | 0.280673i | ||||
\(751\) | 30.3109 | − | 17.5000i | 1.10606 | − | 0.638584i | 0.168254 | − | 0.985744i | \(-0.446187\pi\) |
0.937806 | + | 0.347160i | \(0.112854\pi\) | |||||||
\(752\) | 10.3923 | + | 18.0000i | 0.378968 | + | 0.656392i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.8301 | − | 3.16987i | 0.430828 | − | 0.115440i | ||||
\(755\) | −19.0526 | −0.693394 | ||||||||
\(756\) | 25.9808 | − | 9.00000i | 0.944911 | − | 0.327327i | ||||
\(757\) | 30.0000 | 1.09037 | 0.545184 | − | 0.838316i | \(-0.316460\pi\) | ||||
0.545184 | + | 0.838316i | \(0.316460\pi\) | |||||||
\(758\) | −10.9282 | + | 2.92820i | −0.396930 | + | 0.106357i | ||||
\(759\) | 8.66025 | 0.314347 | ||||||||
\(760\) | −32.7846 | − | 8.78461i | −1.18922 | − | 0.318651i | ||||
\(761\) | 19.5000 | − | 11.2583i | 0.706874 | − | 0.408114i | −0.103028 | − | 0.994678i | \(-0.532853\pi\) |
0.809903 | + | 0.586564i | \(0.199520\pi\) | |||||||
\(762\) | 42.5885 | − | 11.4115i | 1.54282 | − | 0.413397i | ||||
\(763\) | 31.1769 | + | 6.00000i | 1.12868 | + | 0.217215i | ||||
\(764\) | −10.0000 | −0.361787 | ||||||||
\(765\) | −9.00000 | − | 15.5885i | −0.325396 | − | 0.563602i | ||||
\(766\) | −1.73205 | + | 1.73205i | −0.0625815 | + | 0.0625815i | ||||
\(767\) | −12.9904 | − | 7.50000i | −0.469055 | − | 0.270809i | ||||
\(768\) | 13.8564 | + | 24.0000i | 0.500000 | + | 0.866025i | ||||
\(769\) | 22.5000 | − | 12.9904i | 0.811371 | − | 0.468445i | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) |
0.847432 | + | 0.530904i | \(0.178148\pi\) | |||||||
\(770\) | −0.464102 | − | 6.46410i | −0.0167251 | − | 0.232950i | ||||
\(771\) | 44.1673 | − | 25.5000i | 1.59065 | − | 0.918360i | ||||
\(772\) | 15.5885 | + | 9.00000i | 0.561041 | + | 0.323917i | ||||
\(773\) | − | 24.2487i | − | 0.872166i | −0.899907 | − | 0.436083i | \(-0.856365\pi\) | ||
0.899907 | − | 0.436083i | \(-0.143635\pi\) | |||||||
\(774\) | 1.09808 | − | 4.09808i | 0.0394695 | − | 0.147302i | ||||
\(775\) | −17.3205 | −0.622171 | ||||||||
\(776\) | −3.80385 | − | 14.1962i | −0.136550 | − | 0.509612i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −23.2224 | − | 6.22243i | −0.832565 | − | 0.223085i | ||||
\(779\) | 51.9615 | − | 30.0000i | 1.86171 | − | 1.07486i | ||||
\(780\) | 10.3923i | 0.372104i | ||||||||
\(781\) | −2.00000 | + | 3.46410i | −0.0715656 | + | 0.123955i | ||||
\(782\) | 17.3205 | − | 17.3205i | 0.619380 | − | 0.619380i | ||||
\(783\) | 12.9904 | − | 22.5000i | 0.464238 | − | 0.804084i | ||||
\(784\) | 22.0000 | − | 17.3205i | 0.785714 | − | 0.618590i | ||||
\(785\) | −4.50000 | + | 7.79423i | −0.160612 | + | 0.278188i | ||||
\(786\) | −21.0000 | + | 21.0000i | −0.749045 | + | 0.749045i | ||||
\(787\) | 6.06218 | + | 10.5000i | 0.216093 | + | 0.374285i | 0.953610 | − | 0.301044i | \(-0.0973351\pi\) |
−0.737517 | + | 0.675329i | \(0.764002\pi\) | |||||||
\(788\) | −3.46410 | + | 2.00000i | −0.123404 | + | 0.0712470i | ||||
\(789\) | −28.5000 | − | 16.4545i | −1.01463 | − | 0.585795i | ||||
\(790\) | 1.90192 | + | 7.09808i | 0.0676674 | + | 0.252538i | ||||
\(791\) | −16.4545 | − | 47.5000i | −0.585054 | − | 1.68891i | ||||
\(792\) | −2.19615 | − | 8.19615i | −0.0780369 | − | 0.291238i | ||||
\(793\) | −9.00000 | −0.319599 | ||||||||
\(794\) | 23.6603 | − | 6.33975i | 0.839671 | − | 0.224989i | ||||
\(795\) | 10.3923 | − | 6.00000i | 0.368577 | − | 0.212798i | ||||
\(796\) | 30.0000 | − | 17.3205i | 1.06332 | − | 0.613909i | ||||
\(797\) | −4.50000 | + | 2.59808i | −0.159398 | + | 0.0920286i | −0.577577 | − | 0.816336i | \(-0.696002\pi\) |
0.418179 | + | 0.908365i | \(0.362668\pi\) | |||||||
\(798\) | 3.21539 | + | 44.7846i | 0.113824 | + | 1.58536i | ||||
\(799\) | −15.5885 | − | 9.00000i | −0.551480 | − | 0.318397i | ||||
\(800\) | 8.00000 | − | 8.00000i | 0.282843 | − | 0.282843i | ||||
\(801\) | 51.9615i | 1.83597i | ||||||||
\(802\) | −5.00000 | + | 5.00000i | −0.176556 | + | 0.176556i | ||||
\(803\) | −5.19615 | + | 9.00000i | −0.183368 | + | 0.317603i | ||||
\(804\) | −25.9808 | + | 45.0000i | −0.916271 | + | 1.58703i | ||||
\(805\) | −15.0000 | + | 17.3205i | −0.528681 | + | 0.610468i | ||||
\(806\) | 5.49038 | − | 20.4904i | 0.193390 | − | 0.721743i | ||||
\(807\) | 18.0000i | 0.633630i | ||||||||
\(808\) | 8.87564 | + | 33.1244i | 0.312244 | + | 1.16531i | ||||
\(809\) | 8.00000 | 0.281265 | 0.140633 | − | 0.990062i | \(-0.455086\pi\) | ||||
0.140633 | + | 0.990062i | \(0.455086\pi\) | |||||||
\(810\) | 15.5885 | + | 15.5885i | 0.547723 | + | 0.547723i | ||||
\(811\) | 20.7846 | 0.729846 | 0.364923 | − | 0.931038i | \(-0.381095\pi\) | ||||
0.364923 | + | 0.931038i | \(0.381095\pi\) | |||||||
\(812\) | 5.00000 | − | 25.9808i | 0.175466 | − | 0.911746i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.19615 | − | 9.00000i | −0.182013 | − | 0.315256i | ||||
\(816\) | −20.7846 | − | 12.0000i | −0.727607 | − | 0.420084i | ||||
\(817\) | 6.00000 | + | 3.46410i | 0.209913 | + | 0.121194i | ||||
\(818\) | 15.5885 | + | 15.5885i | 0.545038 | + | 0.545038i | ||||
\(819\) | 12.9904 | − | 4.50000i | 0.453921 | − | 0.157243i | ||||
\(820\) | − | 30.0000i | − | 1.04765i | ||||||
\(821\) | −20.5000 | + | 35.5070i | −0.715455 | + | 1.23920i | 0.247329 | + | 0.968932i | \(0.420447\pi\) |
−0.962784 | + | 0.270273i | \(0.912886\pi\) | |||||||
\(822\) | −11.8301 | − | 3.16987i | −0.412623 | − | 0.110562i | ||||
\(823\) | 7.79423 | − | 4.50000i | 0.271690 | − | 0.156860i | −0.357966 | − | 0.933735i | \(-0.616529\pi\) |
0.629655 | + | 0.776875i | \(0.283196\pi\) | |||||||
\(824\) | 6.33975 | − | 23.6603i | 0.220856 | − | 0.824244i | ||||
\(825\) | −3.00000 | + | 1.73205i | −0.104447 | + | 0.0603023i | ||||
\(826\) | −26.8301 | + | 18.1699i | −0.933540 | + | 0.632211i | ||||
\(827\) | 50.0000i | 1.73867i | 0.494223 | + | 0.869335i | \(0.335453\pi\) | ||||
−0.494223 | + | 0.869335i | \(0.664547\pi\) | |||||||
\(828\) | −15.0000 | + | 25.9808i | −0.521286 | + | 0.902894i | ||||
\(829\) | − | 10.3923i | − | 0.360940i | −0.983581 | − | 0.180470i | \(-0.942238\pi\) | ||
0.983581 | − | 0.180470i | \(-0.0577618\pi\) | |||||||
\(830\) | 4.09808 | − | 1.09808i | 0.142246 | − | 0.0381148i | ||||
\(831\) | 19.9186 | − | 34.5000i | 0.690968 | − | 1.19679i | ||||
\(832\) | 6.92820 | + | 12.0000i | 0.240192 | + | 0.416025i | ||||
\(833\) | −9.00000 | + | 22.5167i | −0.311832 | + | 0.780156i | ||||
\(834\) | 15.0000 | − | 15.0000i | 0.519408 | − | 0.519408i | ||||
\(835\) | −18.1865 | − | 10.5000i | −0.629371 | − | 0.363367i | ||||
\(836\) | 13.8564 | 0.479234 | ||||||||
\(837\) | −22.5000 | − | 38.9711i | −0.777714 | − | 1.34704i | ||||
\(838\) | −25.9808 | + | 25.9808i | −0.897491 | + | 0.897491i | ||||
\(839\) | 0.866025 | − | 1.50000i | 0.0298985 | − | 0.0517858i | −0.850689 | − | 0.525669i | \(-0.823815\pi\) |
0.880587 | + | 0.473884i | \(0.157148\pi\) | |||||||
\(840\) | 20.1962 | + | 9.80385i | 0.696833 | + | 0.338265i | ||||
\(841\) | 2.00000 | + | 3.46410i | 0.0689655 | + | 0.119452i | ||||
\(842\) | −15.0263 | − | 4.02628i | −0.517840 | − | 0.138755i | ||||
\(843\) | 0.866025 | − | 1.50000i | 0.0298275 | − | 0.0516627i | ||||
\(844\) | −1.00000 | + | 1.73205i | −0.0344214 | + | 0.0596196i | ||||
\(845\) | − | 17.3205i | − | 0.595844i | ||||||
\(846\) | 21.2942 | + | 5.70577i | 0.732111 | + | 0.196168i | ||||
\(847\) | −8.66025 | − | 25.0000i | −0.297570 | − | 0.859010i | ||||
\(848\) | 8.00000 | − | 13.8564i | 0.274721 | − | 0.475831i | ||||
\(849\) | 13.5000 | + | 23.3827i | 0.463319 | + | 0.802492i | ||||
\(850\) | −2.53590 | + | 9.46410i | −0.0869806 | + | 0.324616i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −6.92820 | − | 12.0000i | −0.237356 | − | 0.411113i | ||||
\(853\) | −34.5000 | − | 19.9186i | −1.18126 | − | 0.681999i | −0.224952 | − | 0.974370i | \(-0.572223\pi\) |
−0.956305 | + | 0.292370i | \(0.905556\pi\) | |||||||
\(854\) | −8.49038 | + | 17.4904i | −0.290535 | + | 0.598509i | ||||
\(855\) | −31.1769 | + | 18.0000i | −1.06623 | + | 0.615587i | ||||
\(856\) | 4.00000 | − | 4.00000i | 0.136717 | − | 0.136717i | ||||
\(857\) | 25.5000 | + | 14.7224i | 0.871063 | + | 0.502909i | 0.867701 | − | 0.497086i | \(-0.165597\pi\) |
0.00336193 | + | 0.999994i | \(0.498930\pi\) | |||||||
\(858\) | −1.09808 | − | 4.09808i | −0.0374877 | − | 0.139906i | ||||
\(859\) | 18.1865 | + | 31.5000i | 0.620517 | + | 1.07477i | 0.989390 | + | 0.145286i | \(0.0464103\pi\) |
−0.368873 | + | 0.929480i | \(0.620256\pi\) | |||||||
\(860\) | 3.00000 | − | 1.73205i | 0.102299 | − | 0.0590624i | ||||
\(861\) | −37.5000 | + | 12.9904i | −1.27800 | + | 0.442711i | ||||
\(862\) | −35.5167 | + | 9.51666i | −1.20970 | + | 0.324139i | ||||
\(863\) | − | 10.0000i | − | 0.340404i | −0.985409 | − | 0.170202i | \(-0.945558\pi\) | ||
0.985409 | − | 0.170202i | \(-0.0544420\pi\) | |||||||
\(864\) | 28.3923 | + | 7.60770i | 0.965926 | + | 0.258819i | ||||
\(865\) | 15.0000 | 0.510015 | ||||||||
\(866\) | −23.6603 | + | 6.33975i | −0.804008 | + | 0.215433i | ||||
\(867\) | −8.66025 | −0.294118 | ||||||||
\(868\) | −34.6410 | − | 30.0000i | −1.17579 | − | 1.01827i | ||||
\(869\) | −1.50000 | − | 2.59808i | −0.0508840 | − | 0.0881337i | ||||
\(870\) | 20.4904 | − | 5.49038i | 0.694689 | − | 0.186141i | ||||
\(871\) | −12.9904 | + | 22.5000i | −0.440162 | + | 0.762383i | ||||
\(872\) | 24.0000 | + | 24.0000i | 0.812743 | + | 0.812743i | ||||
\(873\) | −13.5000 | − | 7.79423i | −0.456906 | − | 0.263795i | ||||
\(874\) | −34.6410 | − | 34.6410i | −1.17175 | − | 1.17175i | ||||
\(875\) | 6.06218 | − | 31.5000i | 0.204939 | − | 1.06489i | ||||
\(876\) | −18.0000 | − | 31.1769i | −0.608164 | − | 1.05337i | ||||
\(877\) | −12.5000 | − | 21.6506i | −0.422095 | − | 0.731090i | 0.574049 | − | 0.818821i | \(-0.305372\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | −26.0263 | − | 6.97372i | −0.878344 | − | 0.235352i | ||||
\(879\) | −38.9711 | + | 22.5000i | −1.31446 | + | 0.758906i | ||||
\(880\) | 3.46410 | − | 6.00000i | 0.116775 | − | 0.202260i | ||||
\(881\) | 31.1769i | 1.05038i | 0.850986 | + | 0.525188i | \(0.176005\pi\) | ||||
−0.850986 | + | 0.525188i | \(0.823995\pi\) | |||||||
\(882\) | 3.50962 | − | 29.4904i | 0.118175 | − | 0.992993i | ||||
\(883\) | 26.0000i | 0.874970i | 0.899226 | + | 0.437485i | \(0.144131\pi\) | ||||
−0.899226 | + | 0.437485i | \(0.855869\pi\) | |||||||
\(884\) | −10.3923 | − | 6.00000i | −0.349531 | − | 0.201802i | ||||
\(885\) | −22.5000 | − | 12.9904i | −0.756329 | − | 0.436667i | ||||
\(886\) | −12.8109 | + | 47.8109i | −0.430390 | + | 1.60624i | ||||
\(887\) | 4.33013 | + | 7.50000i | 0.145391 | + | 0.251825i | 0.929519 | − | 0.368774i | \(-0.120223\pi\) |
−0.784127 | + | 0.620600i | \(0.786889\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.00000 | − | 46.7654i | 0.301850 | − | 1.56846i | ||||
\(890\) | −30.0000 | + | 30.0000i | −1.00560 | + | 1.00560i | ||||
\(891\) | −7.79423 | − | 4.50000i | −0.261116 | − | 0.150756i | ||||
\(892\) | 3.46410i | 0.115987i | ||||||||
\(893\) | −18.0000 | + | 31.1769i | −0.602347 | + | 1.04330i | ||||
\(894\) | −12.1244 | + | 12.1244i | −0.405499 | + | 0.405499i | ||||
\(895\) | −1.73205 | − | 3.00000i | −0.0578961 | − | 0.100279i | ||||
\(896\) | 29.8564 | − | 2.14359i | 0.997433 | − | 0.0716124i | ||||
\(897\) | −7.50000 | + | 12.9904i | −0.250418 | + | 0.433736i | ||||
\(898\) | 7.32051 | + | 27.3205i | 0.244289 | + | 0.911697i | ||||
\(899\) | −43.3013 | −1.44418 | ||||||||
\(900\) | − | 12.0000i | − | 0.400000i | ||||||
\(901\) | 13.8564i | 0.461624i | ||||||||
\(902\) | 3.16987 | + | 11.8301i | 0.105545 | + | 0.393900i | ||||
\(903\) | −3.46410 | − | 3.00000i | −0.115278 | − | 0.0998337i | ||||
\(904\) | 13.9090 | − | 51.9090i | 0.462605 | − | 1.72647i | ||||
\(905\) | −15.0000 | − | 25.9808i | −0.498617 | − | 0.863630i | ||||
\(906\) | −6.97372 | + | 26.0263i | −0.231686 | + | 0.864665i | ||||
\(907\) | −19.9186 | − | 11.5000i | −0.661386 | − | 0.381851i | 0.131419 | − | 0.991327i | \(-0.458047\pi\) |
−0.792805 | + | 0.609476i | \(0.791380\pi\) | |||||||
\(908\) | 10.3923i | 0.344881i | ||||||||
\(909\) | 31.5000 | + | 18.1865i | 1.04479 | + | 0.603209i | ||||
\(910\) | 10.0981 | + | 4.90192i | 0.334748 | + | 0.162497i | ||||
\(911\) | −35.5070 | − | 20.5000i | −1.17640 | − | 0.679195i | −0.221222 | − | 0.975224i | \(-0.571004\pi\) |
−0.955179 | + | 0.296028i | \(0.904338\pi\) | |||||||
\(912\) | −24.0000 | + | 41.5692i | −0.794719 | + | 1.37649i | ||||
\(913\) | −1.50000 | + | 0.866025i | −0.0496428 | + | 0.0286613i | ||||
\(914\) | −20.4904 | − | 5.49038i | −0.677762 | − | 0.181606i | ||||
\(915\) | −15.5885 | −0.515339 | ||||||||
\(916\) | 1.73205 | − | 3.00000i | 0.0572286 | − | 0.0991228i | ||||
\(917\) | 10.5000 | + | 30.3109i | 0.346741 | + | 1.00095i | ||||
\(918\) | −24.5885 | + | 6.58846i | −0.811540 | + | 0.217451i | ||||
\(919\) | 50.0000i | 1.64935i | 0.565608 | + | 0.824674i | \(0.308641\pi\) | ||||
−0.565608 | + | 0.824674i | \(0.691359\pi\) | |||||||
\(920\) | −23.6603 | + | 6.33975i | −0.780055 | + | 0.209015i | ||||
\(921\) | 24.0000 | 0.790827 | ||||||||
\(922\) | −4.43782 | + | 16.5622i | −0.146152 | + | 0.545446i | ||||
\(923\) | −3.46410 | − | 6.00000i | −0.114022 | − | 0.197492i | ||||
\(924\) | −9.00000 | − | 1.73205i | −0.296078 | − | 0.0569803i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 39.0000 | + | 39.0000i | 1.28162 | + | 1.28162i | ||||
\(927\) | −12.9904 | − | 22.5000i | −0.426660 | − | 0.738997i | ||||
\(928\) | 20.0000 | − | 20.0000i | 0.656532 | − | 0.656532i | ||||
\(929\) | −22.5000 | − | 12.9904i | −0.738201 | − | 0.426201i | 0.0832138 | − | 0.996532i | \(-0.473482\pi\) |
−0.821415 | + | 0.570331i | \(0.806815\pi\) | |||||||
\(930\) | 9.50962 | − | 35.4904i | 0.311833 | − | 1.16378i | ||||
\(931\) | 45.0333 | + | 18.0000i | 1.47591 | + | 0.589926i | ||||
\(932\) | 24.2487 | − | 14.0000i | 0.794293 | − | 0.458585i | ||||
\(933\) | 22.5000 | + | 38.9711i | 0.736617 | + | 1.27586i | ||||
\(934\) | −7.60770 | − | 28.3923i | −0.248931 | − | 0.929025i | ||||
\(935\) | 6.00000i | 0.196221i | ||||||||
\(936\) | 14.1962 | + | 3.80385i | 0.464016 | + | 0.124333i | ||||
\(937\) | − | 38.1051i | − | 1.24484i | −0.782683 | − | 0.622420i | \(-0.786150\pi\) | ||
0.782683 | − | 0.622420i | \(-0.213850\pi\) | |||||||
\(938\) | 31.4711 | + | 46.4711i | 1.02757 | + | 1.51734i | ||||
\(939\) | 12.9904 | + | 7.50000i | 0.423925 | + | 0.244753i | ||||
\(940\) | 9.00000 | + | 15.5885i | 0.293548 | + | 0.508439i | ||||
\(941\) | 4.50000 | − | 2.59808i | 0.146696 | − | 0.0846949i | −0.424856 | − | 0.905261i | \(-0.639675\pi\) |
0.571551 | + | 0.820566i | \(0.306342\pi\) | |||||||
\(942\) | 9.00000 | + | 9.00000i | 0.293236 | + | 0.293236i | ||||
\(943\) | 21.6506 | − | 37.5000i | 0.705042 | − | 1.22117i | ||||
\(944\) | −34.6410 | −1.12747 | ||||||||
\(945\) | 22.5000 | − | 7.79423i | 0.731925 | − | 0.253546i | ||||
\(946\) | −1.00000 | + | 1.00000i | −0.0325128 | + | 0.0325128i | ||||
\(947\) | 30.3109 | + | 17.5000i | 0.984972 | + | 0.568674i | 0.903767 | − | 0.428024i | \(-0.140790\pi\) |
0.0812041 | + | 0.996697i | \(0.474123\pi\) | |||||||
\(948\) | 10.3923 | 0.337526 | ||||||||
\(949\) | −9.00000 | − | 15.5885i | −0.292152 | − | 0.506023i | ||||
\(950\) | 18.9282 | + | 5.07180i | 0.614112 | + | 0.164551i | ||||
\(951\) | −19.9186 | + | 34.5000i | −0.645904 | + | 1.11874i | ||||
\(952\) | −21.4641 | + | 14.5359i | −0.695656 | + | 0.471111i | ||||
\(953\) | −40.0000 | −1.29573 | −0.647864 | − | 0.761756i | \(-0.724337\pi\) | ||||
−0.647864 | + | 0.761756i | \(0.724337\pi\) | |||||||
\(954\) | −4.39230 | − | 16.3923i | −0.142206 | − | 0.530720i | ||||
\(955\) | −8.66025 | −0.280239 | ||||||||
\(956\) | −25.0000 | + | 43.3013i | −0.808558 | + | 1.40046i | ||||
\(957\) | −7.50000 | + | 4.33013i | −0.242441 | + | 0.139973i | ||||
\(958\) | −44.9545 | − | 12.0455i | −1.45241 | − | 0.389173i | ||||
\(959\) | −8.66025 | + | 10.0000i | −0.279654 | + | 0.322917i | ||||
\(960\) | 12.0000 | + | 20.7846i | 0.387298 | + | 0.670820i | ||||
\(961\) | −22.0000 | + | 38.1051i | −0.709677 | + | 1.22920i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 6.00000i | − | 0.193347i | ||||||
\(964\) | 58.8897 | 1.89671 | ||||||||
\(965\) | 13.5000 | + | 7.79423i | 0.434580 | + | 0.250905i | ||||
\(966\) | 18.1699 | + | 26.8301i | 0.584606 | + | 0.863245i | ||||
\(967\) | −12.9904 | + | 7.50000i | −0.417742 | + | 0.241184i | −0.694111 | − | 0.719868i | \(-0.744202\pi\) |
0.276368 | + | 0.961052i | \(0.410869\pi\) | |||||||
\(968\) | 7.32051 | − | 27.3205i | 0.235290 | − | 0.878114i | ||||
\(969\) | − | 41.5692i | − | 1.33540i | ||||||
\(970\) | −3.29423 | − | 12.2942i | −0.105771 | − | 0.394744i | ||||
\(971\) | 3.46410 | 0.111168 | 0.0555842 | − | 0.998454i | \(-0.482298\pi\) | ||||
0.0555842 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(972\) | 27.0000 | − | 15.5885i | 0.866025 | − | 0.500000i | ||||
\(973\) | −7.50000 | − | 21.6506i | −0.240439 | − | 0.694087i | ||||
\(974\) | −13.6603 | + | 3.66025i | −0.437703 | + | 0.117282i | ||||
\(975\) | − | 6.00000i | − | 0.192154i | ||||||
\(976\) | −18.0000 | + | 10.3923i | −0.576166 | + | 0.332650i | ||||
\(977\) | 2.50000 | + | 4.33013i | 0.0799821 | + | 0.138533i | 0.903242 | − | 0.429132i | \(-0.141180\pi\) |
−0.823260 | + | 0.567665i | \(0.807847\pi\) | |||||||
\(978\) | −14.1962 | + | 3.80385i | −0.453943 | + | 0.121634i | ||||
\(979\) | 8.66025 | − | 15.0000i | 0.276783 | − | 0.479402i | ||||
\(980\) | 19.0526 | − | 15.0000i | 0.608612 | − | 0.479157i | ||||
\(981\) | 36.0000 | 1.14939 | ||||||||
\(982\) | −19.0000 | − | 19.0000i | −0.606314 | − | 0.606314i | ||||
\(983\) | −0.866025 | + | 1.50000i | −0.0276219 | + | 0.0478426i | −0.879506 | − | 0.475888i | \(-0.842127\pi\) |
0.851884 | + | 0.523731i | \(0.175460\pi\) | |||||||
\(984\) | −40.9808 | − | 10.9808i | −1.30642 | − | 0.350054i | ||||
\(985\) | −3.00000 | + | 1.73205i | −0.0955879 | + | 0.0551877i | ||||
\(986\) | −6.33975 | + | 23.6603i | −0.201899 | + | 0.753496i | ||||
\(987\) | 15.5885 | − | 18.0000i | 0.496186 | − | 0.572946i | ||||
\(988\) | −12.0000 | + | 20.7846i | −0.381771 | + | 0.661247i | ||||
\(989\) | 5.00000 | 0.158991 | ||||||||
\(990\) | −1.90192 | − | 7.09808i | −0.0604471 | − | 0.225592i | ||||
\(991\) | 34.0000i | 1.08005i | 0.841650 | + | 0.540023i | \(0.181584\pi\) | ||||
−0.841650 | + | 0.540023i | \(0.818416\pi\) | |||||||
\(992\) | −12.6795 | − | 47.3205i | −0.402574 | − | 1.50243i | ||||
\(993\) | 43.5000 | + | 25.1147i | 1.38043 | + | 0.796992i | ||||
\(994\) | −14.9282 | + | 1.07180i | −0.473494 | + | 0.0339953i | ||||
\(995\) | 25.9808 | − | 15.0000i | 0.823646 | − | 0.475532i | ||||
\(996\) | − | 6.00000i | − | 0.190117i | ||||||
\(997\) | 22.5000 | + | 12.9904i | 0.712582 | + | 0.411409i | 0.812016 | − | 0.583635i | \(-0.198370\pi\) |
−0.0994342 | + | 0.995044i | \(0.531703\pi\) | |||||||
\(998\) | −7.00000 | − | 7.00000i | −0.221581 | − | 0.221581i | ||||
\(999\) | 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 | 252.2.bi.a.223.1 | yes | 4 | |
3.2 | odd | 2 | 756.2.bi.b.559.2 | 4 | |||
4.3 | odd | 2 | inner | 252.2.bi.a.223.2 | yes | 4 | |
7.6 | odd | 2 | 252.2.bi.b.223.1 | yes | 4 | ||
9.4 | even | 3 | 252.2.bi.b.139.2 | yes | 4 | ||
9.5 | odd | 6 | 756.2.bi.a.307.1 | 4 | |||
12.11 | even | 2 | 756.2.bi.b.559.1 | 4 | |||
21.20 | even | 2 | 756.2.bi.a.559.2 | 4 | |||
28.27 | even | 2 | 252.2.bi.b.223.2 | yes | 4 | ||
36.23 | even | 6 | 756.2.bi.a.307.2 | 4 | |||
36.31 | odd | 6 | 252.2.bi.b.139.1 | yes | 4 | ||
63.13 | odd | 6 | inner | 252.2.bi.a.139.2 | yes | 4 | |
63.41 | even | 6 | 756.2.bi.b.307.1 | 4 | |||
84.83 | odd | 2 | 756.2.bi.a.559.1 | 4 | |||
252.139 | even | 6 | inner | 252.2.bi.a.139.1 | ✓ | 4 | |
252.167 | odd | 6 | 756.2.bi.b.307.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.bi.a.139.1 | ✓ | 4 | 252.139 | even | 6 | inner | |
252.2.bi.a.139.2 | yes | 4 | 63.13 | odd | 6 | inner | |
252.2.bi.a.223.1 | yes | 4 | 1.1 | even | 1 | trivial | |
252.2.bi.a.223.2 | yes | 4 | 4.3 | odd | 2 | inner | |
252.2.bi.b.139.1 | yes | 4 | 36.31 | odd | 6 | ||
252.2.bi.b.139.2 | yes | 4 | 9.4 | even | 3 | ||
252.2.bi.b.223.1 | yes | 4 | 7.6 | odd | 2 | ||
252.2.bi.b.223.2 | yes | 4 | 28.27 | even | 2 | ||
756.2.bi.a.307.1 | 4 | 9.5 | odd | 6 | |||
756.2.bi.a.307.2 | 4 | 36.23 | even | 6 | |||
756.2.bi.a.559.1 | 4 | 84.83 | odd | 2 | |||
756.2.bi.a.559.2 | 4 | 21.20 | even | 2 | |||
756.2.bi.b.307.1 | 4 | 63.41 | even | 6 | |||
756.2.bi.b.307.2 | 4 | 252.167 | odd | 6 | |||
756.2.bi.b.559.1 | 4 | 12.11 | even | 2 | |||
756.2.bi.b.559.2 | 4 | 3.2 | odd | 2 |