Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(377,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.m (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 755.2 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.755 |
Dual form | 1134.2.m.b.377.2 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.866025 | − | 1.50000i | −0.387298 | − | 0.670820i | 0.604787 | − | 0.796387i | \(-0.293258\pi\) |
−0.992085 | + | 0.125567i | \(0.959925\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.73205i | − | 0.547723i | ||||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | − | 1.73205i | 0.832050 | − | 0.480384i | −0.0225039 | − | 0.999747i | \(-0.507164\pi\) |
0.854554 | + | 0.519362i | \(0.173830\pi\) | |||||||
\(14\) | −2.59808 | − | 0.500000i | −0.694365 | − | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 6.92820 | 1.68034 | 0.840168 | − | 0.542326i | \(-0.182456\pi\) | ||||
0.840168 | + | 0.542326i | \(0.182456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.73205i | 0.397360i | 0.980064 | + | 0.198680i | \(0.0636654\pi\) | ||||
−0.980064 | + | 0.198680i | \(0.936335\pi\) | |||||||
\(20\) | 0.866025 | − | 1.50000i | 0.193649 | − | 0.335410i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | −2.59808 | + | 1.50000i | −0.541736 | + | 0.312772i | −0.745782 | − | 0.666190i | \(-0.767924\pi\) |
0.204046 | + | 0.978961i | \(0.434591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | − | 1.73205i | 0.200000 | − | 0.346410i | ||||
\(26\) | 3.46410 | 0.679366 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | 5.19615 | + | 3.00000i | 0.964901 | + | 0.557086i | 0.897678 | − | 0.440652i | \(-0.145253\pi\) |
0.0672232 | + | 0.997738i | \(0.478586\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.50000 | + | 2.59808i | −0.808224 | + | 0.466628i | −0.846339 | − | 0.532645i | \(-0.821198\pi\) |
0.0381148 | + | 0.999273i | \(0.487865\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.00000 | + | 3.46410i | 1.02899 | + | 0.594089i | ||||
\(35\) | 3.46410 | + | 3.00000i | 0.585540 | + | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | −0.866025 | + | 1.50000i | −0.140488 | + | 0.243332i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 0.866025i | 0.237171 | − | 0.136931i | ||||
\(41\) | 6.06218 | + | 10.5000i | 0.946753 | + | 1.63982i | 0.752202 | + | 0.658932i | \(0.228992\pi\) |
0.194551 | + | 0.980892i | \(0.437675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | − | 1.73205i | 0.152499 | − | 0.264135i | −0.779647 | − | 0.626219i | \(-0.784601\pi\) |
0.932145 | + | 0.362084i | \(0.117935\pi\) | |||||||
\(44\) | 3.00000i | 0.452267i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 1.73205 | − | 3.00000i | 0.252646 | − | 0.437595i | −0.711608 | − | 0.702577i | \(-0.752033\pi\) |
0.964253 | + | 0.264982i | \(0.0853660\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 1.73205 | − | 1.00000i | 0.244949 | − | 0.141421i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.00000 | + | 1.73205i | 0.416025 | + | 0.240192i | ||||
\(53\) | 12.0000i | 1.64833i | 0.566352 | + | 0.824163i | \(0.308354\pi\) | ||||
−0.566352 | + | 0.824163i | \(0.691646\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.19615i | − | 0.700649i | ||||||
\(56\) | −0.866025 | − | 2.50000i | −0.115728 | − | 0.334077i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | −1.73205 | − | 3.00000i | −0.225494 | − | 0.390567i | 0.730974 | − | 0.682406i | \(-0.239066\pi\) |
−0.956467 | + | 0.291839i | \(0.905733\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | − | 3.46410i | −0.768221 | − | 0.443533i | 0.0640184 | − | 0.997949i | \(-0.479608\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | −5.19615 | −0.659912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −5.19615 | − | 3.00000i | −0.644503 | − | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 3.46410 | + | 6.00000i | 0.420084 | + | 0.727607i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.50000 | + | 4.33013i | 0.179284 | + | 0.517549i | ||||
\(71\) | 3.00000i | 0.356034i | 0.984027 | + | 0.178017i | \(0.0569683\pi\) | ||||
−0.984027 | + | 0.178017i | \(0.943032\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.46410i | − | 0.405442i | −0.979236 | − | 0.202721i | \(-0.935021\pi\) | ||
0.979236 | − | 0.202721i | \(-0.0649785\pi\) | |||||||
\(74\) | 6.06218 | + | 3.50000i | 0.704714 | + | 0.406867i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50000 | + | 0.866025i | −0.172062 | + | 0.0993399i | ||||
\(77\) | −7.79423 | − | 1.50000i | −0.888235 | − | 0.170941i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 1.73205 | 0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.1244i | 1.33891i | ||||||||
\(83\) | 8.66025 | − | 15.0000i | 0.950586 | − | 1.64646i | 0.206427 | − | 0.978462i | \(-0.433816\pi\) |
0.744160 | − | 0.668002i | \(-0.232850\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.00000 | − | 10.3923i | −0.650791 | − | 1.12720i | ||||
\(86\) | 1.73205 | − | 1.00000i | 0.186772 | − | 0.107833i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.50000 | + | 2.59808i | −0.159901 | + | 0.276956i | ||||
\(89\) | −5.19615 | −0.550791 | −0.275396 | − | 0.961331i | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.00000 | + | 6.92820i | −0.628971 | + | 0.726273i | ||||
\(92\) | −2.59808 | − | 1.50000i | −0.270868 | − | 0.156386i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.00000 | − | 1.73205i | 0.309426 | − | 0.178647i | ||||
\(95\) | 2.59808 | − | 1.50000i | 0.266557 | − | 0.153897i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.0000 | − | 6.92820i | −1.21842 | − | 0.703452i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) |
−0.964579 | + | 0.263795i | \(0.915026\pi\) | |||||||
\(98\) | 6.92820 | − | 1.00000i | 0.699854 | − | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.5000 | + | 9.52628i | −1.62579 | + | 0.938652i | −0.640464 | + | 0.767988i | \(0.721258\pi\) |
−0.985329 | + | 0.170664i | \(0.945409\pi\) | |||||||
\(104\) | 1.73205 | + | 3.00000i | 0.169842 | + | 0.294174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | + | 10.3923i | −0.582772 | + | 1.00939i | ||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.0000 | 1.24517 | 0.622587 | − | 0.782551i | \(-0.286082\pi\) | ||||
0.622587 | + | 0.782551i | \(0.286082\pi\) | |||||||
\(110\) | 2.59808 | − | 4.50000i | 0.247717 | − | 0.429058i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 10.3923 | − | 6.00000i | 0.977626 | − | 0.564433i | 0.0760733 | − | 0.997102i | \(-0.475762\pi\) |
0.901553 | + | 0.432670i | \(0.142428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.50000 | + | 2.59808i | 0.419627 | + | 0.242272i | ||||
\(116\) | 6.00000i | 0.557086i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.46410i | − | 0.318896i | ||||||
\(119\) | −17.3205 | + | 6.00000i | −1.58777 | + | 0.550019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | −3.46410 | − | 6.00000i | −0.313625 | − | 0.543214i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.50000 | − | 2.59808i | −0.404112 | − | 0.233314i | ||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.0000 | −1.95218 | −0.976092 | − | 0.217357i | \(-0.930256\pi\) | ||||
−0.976092 | + | 0.217357i | \(0.930256\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | 5.19615 | + | 9.00000i | 0.453990 | + | 0.786334i | 0.998630 | − | 0.0523366i | \(-0.0166669\pi\) |
−0.544640 | + | 0.838670i | \(0.683334\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50000 | − | 4.33013i | −0.130066 | − | 0.375470i | ||||
\(134\) | − | 2.00000i | − | 0.172774i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820i | 0.594089i | ||||||||
\(137\) | 15.5885 | + | 9.00000i | 1.33181 | + | 0.768922i | 0.985577 | − | 0.169226i | \(-0.0541268\pi\) |
0.346235 | + | 0.938148i | \(0.387460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | + | 1.73205i | −0.254457 | + | 0.146911i | −0.621803 | − | 0.783174i | \(-0.713600\pi\) |
0.367347 | + | 0.930084i | \(0.380266\pi\) | |||||||
\(140\) | −0.866025 | + | 4.50000i | −0.0731925 | + | 0.380319i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.50000 | + | 2.59808i | −0.125877 | + | 0.218026i | ||||
\(143\) | 10.3923 | 0.869048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.3923i | − | 0.863034i | ||||||
\(146\) | 1.73205 | − | 3.00000i | 0.143346 | − | 0.248282i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.50000 | + | 6.06218i | 0.287698 | + | 0.498308i | ||||
\(149\) | −10.3923 | + | 6.00000i | −0.851371 | + | 0.491539i | −0.861113 | − | 0.508413i | \(-0.830232\pi\) |
0.00974235 | + | 0.999953i | \(0.496899\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | −1.73205 | −0.140488 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.00000 | − | 5.19615i | −0.483494 | − | 0.418718i | ||||
\(155\) | 7.79423 | + | 4.50000i | 0.626048 | + | 0.361449i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | + | 5.19615i | −0.718278 | + | 0.414698i | −0.814119 | − | 0.580699i | \(-0.802779\pi\) |
0.0958404 | + | 0.995397i | \(0.469446\pi\) | |||||||
\(158\) | 8.66025 | − | 5.00000i | 0.688973 | − | 0.397779i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.50000 | + | 0.866025i | 0.118585 | + | 0.0684653i | ||||
\(161\) | 5.19615 | − | 6.00000i | 0.409514 | − | 0.472866i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −6.06218 | + | 10.5000i | −0.473377 | + | 0.819912i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0000 | − | 8.66025i | 1.16423 | − | 0.672166i | ||||
\(167\) | −3.46410 | − | 6.00000i | −0.268060 | − | 0.464294i | 0.700301 | − | 0.713848i | \(-0.253049\pi\) |
−0.968361 | + | 0.249554i | \(0.919716\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | − | 12.0000i | − | 0.920358i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −2.59808 | + | 4.50000i | −0.197528 | + | 0.342129i | −0.947726 | − | 0.319084i | \(-0.896625\pi\) |
0.750198 | + | 0.661213i | \(0.229958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | + | 5.19615i | −0.0755929 | + | 0.392792i | ||||
\(176\) | −2.59808 | + | 1.50000i | −0.195837 | + | 0.113067i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.50000 | − | 2.59808i | −0.337289 | − | 0.194734i | ||||
\(179\) | − | 12.0000i | − | 0.896922i | −0.893802 | − | 0.448461i | \(-0.851972\pi\) | ||
0.893802 | − | 0.448461i | \(-0.148028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | −8.66025 | + | 3.00000i | −0.641941 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50000 | − | 2.59808i | −0.110581 | − | 0.191533i | ||||
\(185\) | −6.06218 | − | 10.5000i | −0.445700 | − | 0.771975i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | + | 10.3923i | 1.31629 | + | 0.759961i | ||||
\(188\) | 3.46410 | 0.252646 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.00000 | 0.217643 | ||||||||
\(191\) | −18.1865 | − | 10.5000i | −1.31593 | − | 0.759753i | −0.332860 | − | 0.942976i | \(-0.608014\pi\) |
−0.983071 | + | 0.183223i | \(0.941347\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | + | 12.1244i | 0.503871 | + | 0.872730i | 0.999990 | + | 0.00447566i | \(0.00142465\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | −6.92820 | − | 12.0000i | −0.497416 | − | 0.861550i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.50000 | + | 2.59808i | 0.464286 | + | 0.185577i | ||||
\(197\) | − | 12.0000i | − | 0.854965i | −0.904024 | − | 0.427482i | \(-0.859401\pi\) | ||
0.904024 | − | 0.427482i | \(-0.140599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.73205i | − | 0.122782i | −0.998114 | − | 0.0613909i | \(-0.980446\pi\) | ||
0.998114 | − | 0.0613909i | \(-0.0195536\pi\) | |||||||
\(200\) | 1.73205 | + | 1.00000i | 0.122474 | + | 0.0707107i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.5885 | − | 3.00000i | −1.09410 | − | 0.210559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.5000 | − | 18.1865i | 0.733352 | − | 1.27020i | ||||
\(206\) | −19.0526 | −1.32745 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.46410i | 0.240192i | ||||||||
\(209\) | −2.59808 | + | 4.50000i | −0.179713 | + | 0.311272i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | − | 13.8564i | −0.550743 | − | 0.953914i | −0.998221 | − | 0.0596196i | \(-0.981011\pi\) |
0.447478 | − | 0.894295i | \(-0.352322\pi\) | |||||||
\(212\) | −10.3923 | + | 6.00000i | −0.713746 | + | 0.412082i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46410 | −0.236250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.00000 | − | 10.3923i | 0.610960 | − | 0.705476i | ||||
\(218\) | 11.2583 | + | 6.50000i | 0.762510 | + | 0.440236i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.50000 | − | 2.59808i | 0.303390 | − | 0.175162i | ||||
\(221\) | 20.7846 | − | 12.0000i | 1.39812 | − | 0.807207i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5000 | + | 7.79423i | 0.904027 | + | 0.521940i | 0.878504 | − | 0.477734i | \(-0.158542\pi\) |
0.0255224 | + | 0.999674i | \(0.491875\pi\) | |||||||
\(224\) | 1.73205 | − | 2.00000i | 0.115728 | − | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | −10.3923 | + | 18.0000i | −0.689761 | + | 1.19470i | 0.282153 | + | 0.959369i | \(0.408951\pi\) |
−0.971915 | + | 0.235333i | \(0.924382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 2.59808 | + | 4.50000i | 0.171312 | + | 0.296721i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | + | 5.19615i | −0.196960 | + | 0.341144i | ||||
\(233\) | − | 24.0000i | − | 1.57229i | −0.618041 | − | 0.786146i | \(-0.712073\pi\) | ||
0.618041 | − | 0.786146i | \(-0.287927\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | 1.73205 | − | 3.00000i | 0.112747 | − | 0.195283i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −18.0000 | − | 3.46410i | −1.16677 | − | 0.224544i | ||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0000 | − | 8.66025i | −0.966235 | − | 0.557856i | −0.0681486 | − | 0.997675i | \(-0.521709\pi\) |
−0.898086 | + | 0.439819i | \(0.855043\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | −11.2583 | − | 4.50000i | −0.719268 | − | 0.287494i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00000 | + | 5.19615i | 0.190885 | + | 0.330623i | ||||
\(248\) | −2.59808 | − | 4.50000i | −0.164978 | − | 0.285750i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −10.5000 | − | 6.06218i | −0.664078 | − | 0.383406i | ||||
\(251\) | −13.8564 | −0.874609 | −0.437304 | − | 0.899314i | \(-0.644067\pi\) | ||||
−0.437304 | + | 0.899314i | \(0.644067\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.00000 | −0.565825 | ||||||||
\(254\) | −19.0526 | − | 11.0000i | −1.19546 | − | 0.690201i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2.59808 | − | 4.50000i | −0.162064 | − | 0.280702i | 0.773545 | − | 0.633741i | \(-0.218482\pi\) |
−0.935609 | + | 0.353039i | \(0.885148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.5000 | + | 6.06218i | −1.08740 | + | 0.376685i | ||||
\(260\) | − | 6.00000i | − | 0.372104i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3923i | 0.642039i | ||||||||
\(263\) | 23.3827 | + | 13.5000i | 1.44184 | + | 0.832446i | 0.997972 | − | 0.0636476i | \(-0.0202734\pi\) |
0.443866 | + | 0.896093i | \(0.353607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000 | − | 10.3923i | 1.10573 | − | 0.638394i | ||||
\(266\) | 0.866025 | − | 4.50000i | 0.0530994 | − | 0.275913i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.00000 | − | 1.73205i | 0.0610847 | − | 0.105802i | ||||
\(269\) | −1.73205 | −0.105605 | −0.0528025 | − | 0.998605i | \(-0.516815\pi\) | ||||
−0.0528025 | + | 0.998605i | \(0.516815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.3205i | − | 1.05215i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||
0.850439 | − | 0.526073i | \(-0.176336\pi\) | |||||||
\(272\) | −3.46410 | + | 6.00000i | −0.210042 | + | 0.363803i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.00000 | + | 15.5885i | 0.543710 | + | 0.941733i | ||||
\(275\) | 5.19615 | − | 3.00000i | 0.313340 | − | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.50000 | + | 9.52628i | −0.330463 | + | 0.572379i | −0.982603 | − | 0.185720i | \(-0.940538\pi\) |
0.652140 | + | 0.758099i | \(0.273872\pi\) | |||||||
\(278\) | −3.46410 | −0.207763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | + | 3.46410i | −0.179284 | + | 0.207020i | ||||
\(281\) | −25.9808 | − | 15.0000i | −1.54988 | − | 0.894825i | −0.998150 | − | 0.0608039i | \(-0.980634\pi\) |
−0.551733 | − | 0.834021i | \(-0.686033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 27.0000 | − | 15.5885i | 1.60498 | − | 0.926638i | 0.614514 | − | 0.788906i | \(-0.289352\pi\) |
0.990470 | − | 0.137732i | \(-0.0439811\pi\) | |||||||
\(284\) | −2.59808 | + | 1.50000i | −0.154167 | + | 0.0890086i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.00000 | + | 5.19615i | 0.532181 | + | 0.307255i | ||||
\(287\) | −24.2487 | − | 21.0000i | −1.43136 | − | 1.23959i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.0000 | 1.82353 | ||||||||
\(290\) | 5.19615 | − | 9.00000i | 0.305129 | − | 0.528498i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.00000 | − | 1.73205i | 0.175562 | − | 0.101361i | ||||
\(293\) | 3.46410 | + | 6.00000i | 0.202375 | + | 0.350524i | 0.949293 | − | 0.314392i | \(-0.101801\pi\) |
−0.746918 | + | 0.664916i | \(0.768467\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.00000 | + | 5.19615i | −0.174667 | + | 0.302532i | ||||
\(296\) | 7.00000i | 0.406867i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −12.0000 | −0.695141 | ||||||||
\(299\) | −5.19615 | + | 9.00000i | −0.300501 | + | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | + | 5.19615i | −0.0576390 | + | 0.299501i | ||||
\(302\) | 6.92820 | − | 4.00000i | 0.398673 | − | 0.230174i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.50000 | − | 0.866025i | −0.0860309 | − | 0.0496700i | ||||
\(305\) | 12.0000i | 0.687118i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.5885i | 0.889680i | 0.895610 | + | 0.444840i | \(0.146740\pi\) | ||||
−0.895610 | + | 0.444840i | \(0.853260\pi\) | |||||||
\(308\) | −2.59808 | − | 7.50000i | −0.148039 | − | 0.427352i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.50000 | + | 7.79423i | 0.255583 | + | 0.442682i | ||||
\(311\) | 12.1244 | + | 21.0000i | 0.687509 | + | 1.19080i | 0.972641 | + | 0.232313i | \(0.0746292\pi\) |
−0.285132 | + | 0.958488i | \(0.592037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0000 | + | 8.66025i | 0.847850 | + | 0.489506i | 0.859925 | − | 0.510421i | \(-0.170510\pi\) |
−0.0120748 | + | 0.999927i | \(0.503844\pi\) | |||||||
\(314\) | −10.3923 | −0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0.866025 | + | 1.50000i | 0.0484123 | + | 0.0838525i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.50000 | − | 2.59808i | 0.417959 | − | 0.144785i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 6.92820i | − | 0.384308i | ||||||
\(326\) | 1.73205 | + | 1.00000i | 0.0959294 | + | 0.0553849i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.5000 | + | 6.06218i | −0.579766 | + | 0.334728i | ||||
\(329\) | −1.73205 | + | 9.00000i | −0.0954911 | + | 0.496186i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | + | 24.2487i | −0.769510 | + | 1.33283i | 0.168320 | + | 0.985732i | \(0.446166\pi\) |
−0.937829 | + | 0.347097i | \(0.887167\pi\) | |||||||
\(332\) | 17.3205 | 0.950586 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 6.92820i | − | 0.379094i | ||||||
\(335\) | −1.73205 | + | 3.00000i | −0.0946320 | + | 0.163908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.50000 | + | 4.33013i | 0.136184 | + | 0.235877i | 0.926049 | − | 0.377403i | \(-0.123183\pi\) |
−0.789865 | + | 0.613280i | \(0.789850\pi\) | |||||||
\(338\) | −0.866025 | + | 0.500000i | −0.0471056 | + | 0.0271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.00000 | − | 10.3923i | 0.325396 | − | 0.563602i | ||||
\(341\) | −15.5885 | −0.844162 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 1.73205 | + | 1.00000i | 0.0933859 | + | 0.0539164i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.50000 | + | 2.59808i | −0.241921 | + | 0.139673i | ||||
\(347\) | 23.3827 | − | 13.5000i | 1.25525 | − | 0.724718i | 0.283101 | − | 0.959090i | \(-0.408637\pi\) |
0.972147 | + | 0.234372i | \(0.0753034\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | − | 13.8564i | −1.28469 | − | 0.741716i | −0.306988 | − | 0.951713i | \(-0.599321\pi\) |
−0.977702 | + | 0.209997i | \(0.932655\pi\) | |||||||
\(350\) | −3.46410 | + | 4.00000i | −0.185164 | + | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 9.52628 | − | 16.5000i | 0.507033 | − | 0.878206i | −0.492934 | − | 0.870067i | \(-0.664076\pi\) |
0.999967 | − | 0.00813978i | \(-0.00259100\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.50000 | − | 2.59808i | 0.238835 | − | 0.137892i | ||||
\(356\) | −2.59808 | − | 4.50000i | −0.137698 | − | 0.238500i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | − | 10.3923i | 0.317110 | − | 0.549250i | ||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.0000 | 0.842105 | ||||||||
\(362\) | −6.92820 | + | 12.0000i | −0.364138 | + | 0.630706i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.00000 | − | 1.73205i | −0.471728 | − | 0.0907841i | ||||
\(365\) | −5.19615 | + | 3.00000i | −0.271979 | + | 0.157027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.50000 | + | 0.866025i | 0.0782994 | + | 0.0452062i | 0.538639 | − | 0.842537i | \(-0.318939\pi\) |
−0.460339 | + | 0.887743i | \(0.652272\pi\) | |||||||
\(368\) | − | 3.00000i | − | 0.156386i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12.1244i | − | 0.630315i | ||||||
\(371\) | −10.3923 | − | 30.0000i | −0.539542 | − | 1.55752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50000 | − | 4.33013i | −0.129445 | − | 0.224205i | 0.794017 | − | 0.607896i | \(-0.207986\pi\) |
−0.923462 | + | 0.383691i | \(0.874653\pi\) | |||||||
\(374\) | 10.3923 | + | 18.0000i | 0.537373 | + | 0.930758i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.00000 | + | 1.73205i | 0.154713 | + | 0.0893237i | ||||
\(377\) | 20.7846 | 1.07046 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.00000 | −0.102733 | −0.0513665 | − | 0.998680i | \(-0.516358\pi\) | ||||
−0.0513665 | + | 0.998680i | \(0.516358\pi\) | |||||||
\(380\) | 2.59808 | + | 1.50000i | 0.133278 | + | 0.0769484i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5000 | − | 18.1865i | −0.537227 | − | 0.930504i | ||||
\(383\) | −6.92820 | − | 12.0000i | −0.354015 | − | 0.613171i | 0.632934 | − | 0.774206i | \(-0.281850\pi\) |
−0.986949 | + | 0.161034i | \(0.948517\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.50000 | + | 12.9904i | 0.229341 | + | 0.662051i | ||||
\(386\) | 14.0000i | 0.712581i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 13.8564i | − | 0.703452i | ||||||
\(389\) | 20.7846 | + | 12.0000i | 1.05382 | + | 0.608424i | 0.923717 | − | 0.383076i | \(-0.125135\pi\) |
0.130105 | + | 0.991500i | \(0.458469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | + | 10.3923i | −0.910299 | + | 0.525561i | ||||
\(392\) | 4.33013 | + | 5.50000i | 0.218704 | + | 0.277792i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.00000 | − | 10.3923i | 0.302276 | − | 0.523557i | ||||
\(395\) | −17.3205 | −0.871489 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 20.7846i | − | 1.04315i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) | ||
0.853206 | − | 0.521575i | \(-0.174655\pi\) | |||||||
\(398\) | 0.866025 | − | 1.50000i | 0.0434099 | − | 0.0751882i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | + | 1.73205i | 0.0500000 | + | 0.0866025i | ||||
\(401\) | −15.5885 | + | 9.00000i | −0.778450 | + | 0.449439i | −0.835881 | − | 0.548911i | \(-0.815043\pi\) |
0.0574304 | + | 0.998350i | \(0.481709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | + | 15.5885i | −0.448322 | + | 0.776516i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | − | 10.3923i | −0.595550 | − | 0.515761i | ||||
\(407\) | 18.1865 | + | 10.5000i | 0.901473 | + | 0.520466i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | + | 1.73205i | −0.148340 | + | 0.0856444i | −0.572333 | − | 0.820021i | \(-0.693962\pi\) |
0.423993 | + | 0.905666i | \(0.360628\pi\) | |||||||
\(410\) | 18.1865 | − | 10.5000i | 0.898169 | − | 0.518558i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −16.5000 | − | 9.52628i | −0.812897 | − | 0.469326i | ||||
\(413\) | 6.92820 | + | 6.00000i | 0.340915 | + | 0.295241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −30.0000 | −1.47264 | ||||||||
\(416\) | −1.73205 | + | 3.00000i | −0.0849208 | + | 0.147087i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.50000 | + | 2.59808i | −0.220102 | + | 0.127076i | ||||
\(419\) | −3.46410 | − | 6.00000i | −0.169232 | − | 0.293119i | 0.768918 | − | 0.639348i | \(-0.220796\pi\) |
−0.938150 | + | 0.346228i | \(0.887462\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.50000 | − | 11.2583i | 0.316791 | − | 0.548697i | −0.663026 | − | 0.748596i | \(-0.730728\pi\) |
0.979817 | + | 0.199899i | \(0.0640614\pi\) | |||||||
\(422\) | − | 16.0000i | − | 0.778868i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | 6.92820 | − | 12.0000i | 0.336067 | − | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | + | 3.46410i | 0.871081 | + | 0.167640i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | − | 1.73205i | −0.144673 | − | 0.0835269i | ||||
\(431\) | 21.0000i | 1.01153i | 0.862670 | + | 0.505767i | \(0.168791\pi\) | ||||
−0.862670 | + | 0.505767i | \(0.831209\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3923i | 0.499422i | 0.968320 | + | 0.249711i | \(0.0803357\pi\) | ||||
−0.968320 | + | 0.249711i | \(0.919664\pi\) | |||||||
\(434\) | 12.9904 | − | 4.50000i | 0.623558 | − | 0.216007i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.50000 | + | 11.2583i | 0.311294 | + | 0.539176i | ||||
\(437\) | −2.59808 | − | 4.50000i | −0.124283 | − | 0.215264i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.00000 | + | 5.19615i | 0.429547 | + | 0.247999i | 0.699153 | − | 0.714972i | \(-0.253560\pi\) |
−0.269607 | + | 0.962970i | \(0.586894\pi\) | |||||||
\(440\) | 5.19615 | 0.247717 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.0000 | 1.14156 | ||||||||
\(443\) | −7.79423 | − | 4.50000i | −0.370315 | − | 0.213801i | 0.303281 | − | 0.952901i | \(-0.401918\pi\) |
−0.673596 | + | 0.739100i | \(0.735251\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | + | 7.79423i | 0.213320 | + | 0.369482i | ||||
\(446\) | 7.79423 | + | 13.5000i | 0.369067 | + | 0.639244i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | 12.0000i | 0.566315i | 0.959073 | + | 0.283158i | \(0.0913819\pi\) | ||||
−0.959073 | + | 0.283158i | \(0.908618\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.3731i | 1.71274i | ||||||||
\(452\) | 10.3923 | + | 6.00000i | 0.488813 | + | 0.282216i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −18.0000 | + | 10.3923i | −0.844782 | + | 0.487735i | ||||
\(455\) | 15.5885 | + | 3.00000i | 0.730798 | + | 0.140642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | − | 14.7224i | 0.397613 | − | 0.688686i | −0.595818 | − | 0.803120i | \(-0.703172\pi\) |
0.993431 | + | 0.114433i | \(0.0365053\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.19615i | 0.242272i | ||||||||
\(461\) | −9.52628 | + | 16.5000i | −0.443683 | + | 0.768482i | −0.997959 | − | 0.0638511i | \(-0.979662\pi\) |
0.554276 | + | 0.832333i | \(0.312995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | − | 27.7128i | −0.743583 | − | 1.28792i | −0.950854 | − | 0.309640i | \(-0.899791\pi\) |
0.207271 | − | 0.978284i | \(-0.433542\pi\) | |||||||
\(464\) | −5.19615 | + | 3.00000i | −0.241225 | + | 0.139272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | − | 20.7846i | 0.555889 | − | 0.962828i | ||||
\(467\) | 31.1769 | 1.44270 | 0.721348 | − | 0.692573i | \(-0.243523\pi\) | ||||
0.721348 | + | 0.692573i | \(0.243523\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | + | 3.46410i | 0.184703 | + | 0.159957i | ||||
\(470\) | −5.19615 | − | 3.00000i | −0.239681 | − | 0.138380i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.00000 | − | 1.73205i | 0.138086 | − | 0.0797241i | ||||
\(473\) | 5.19615 | − | 3.00000i | 0.238919 | − | 0.137940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.00000 | + | 1.73205i | 0.137649 | + | 0.0794719i | ||||
\(476\) | −13.8564 | − | 12.0000i | −0.635107 | − | 0.550019i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.8564 | − | 24.0000i | 0.633115 | − | 1.09659i | −0.353796 | − | 0.935323i | \(-0.615109\pi\) |
0.986911 | − | 0.161265i | \(-0.0515575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.0000 | − | 12.1244i | 0.957518 | − | 0.552823i | ||||
\(482\) | −8.66025 | − | 15.0000i | −0.394464 | − | 0.683231i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 24.0000i | 1.08978i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0000 | 0.453143 | 0.226572 | − | 0.973995i | \(-0.427248\pi\) | ||||
0.226572 | + | 0.973995i | \(0.427248\pi\) | |||||||
\(488\) | 3.46410 | − | 6.00000i | 0.156813 | − | 0.271607i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −7.50000 | − | 9.52628i | −0.338815 | − | 0.430353i | ||||
\(491\) | −7.79423 | + | 4.50000i | −0.351749 | + | 0.203082i | −0.665455 | − | 0.746438i | \(-0.731763\pi\) |
0.313707 | + | 0.949520i | \(0.398429\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0000 | + | 20.7846i | 1.62136 | + | 0.936092i | ||||
\(494\) | 6.00000i | 0.269953i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.19615i | − | 0.233314i | ||||||
\(497\) | −2.59808 | − | 7.50000i | −0.116540 | − | 0.336421i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.00000 | − | 8.66025i | −0.223831 | − | 0.387686i | 0.732137 | − | 0.681157i | \(-0.238523\pi\) |
−0.955968 | + | 0.293471i | \(0.905190\pi\) | |||||||
\(500\) | −6.06218 | − | 10.5000i | −0.271109 | − | 0.469574i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | − | 6.92820i | −0.535586 | − | 0.309221i | ||||
\(503\) | 24.2487 | 1.08120 | 0.540598 | − | 0.841281i | \(-0.318198\pi\) | ||||
0.540598 | + | 0.841281i | \(0.318198\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.79423 | − | 4.50000i | −0.346496 | − | 0.200049i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −11.0000 | − | 19.0526i | −0.488046 | − | 0.845321i | ||||
\(509\) | −6.92820 | − | 12.0000i | −0.307087 | − | 0.531891i | 0.670637 | − | 0.741786i | \(-0.266021\pi\) |
−0.977724 | + | 0.209895i | \(0.932688\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | + | 8.66025i | 0.132712 | + | 0.383107i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 5.19615i | − | 0.229192i | ||||||
\(515\) | 28.5788 | + | 16.5000i | 1.25933 | + | 0.727077i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.00000 | − | 5.19615i | 0.395820 | − | 0.228527i | ||||
\(518\) | −18.1865 | − | 3.50000i | −0.799070 | − | 0.153781i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | −22.5167 | −0.986473 | −0.493236 | − | 0.869895i | \(-0.664186\pi\) | ||||
−0.493236 | + | 0.869895i | \(0.664186\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 39.8372i | 1.74196i | 0.491320 | + | 0.870979i | \(0.336514\pi\) | ||||
−0.491320 | + | 0.870979i | \(0.663486\pi\) | |||||||
\(524\) | −5.19615 | + | 9.00000i | −0.226995 | + | 0.393167i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 13.5000 | + | 23.3827i | 0.588628 | + | 1.01953i | ||||
\(527\) | −31.1769 | + | 18.0000i | −1.35809 | + | 0.784092i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 20.7846 | 0.902826 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.00000 | − | 3.46410i | 0.130066 | − | 0.150188i | ||||
\(533\) | 36.3731 | + | 21.0000i | 1.57549 | + | 0.909611i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.73205 | − | 1.00000i | 0.0748132 | − | 0.0431934i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.50000 | − | 0.866025i | −0.0646696 | − | 0.0373370i | ||||
\(539\) | 20.7846 | − | 3.00000i | 0.895257 | − | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −25.0000 | −1.07483 | −0.537417 | − | 0.843317i | \(-0.680600\pi\) | ||||
−0.537417 | + | 0.843317i | \(0.680600\pi\) | |||||||
\(542\) | 8.66025 | − | 15.0000i | 0.371990 | − | 0.644305i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.00000 | + | 3.46410i | −0.257248 | + | 0.148522i | ||||
\(545\) | −11.2583 | − | 19.5000i | −0.482254 | − | 0.835288i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | + | 6.92820i | −0.171028 | + | 0.296229i | −0.938779 | − | 0.344519i | \(-0.888042\pi\) |
0.767752 | + | 0.640747i | \(0.221375\pi\) | |||||||
\(548\) | 18.0000i | 0.768922i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | −5.19615 | + | 9.00000i | −0.221364 | + | 0.383413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.00000 | + | 25.9808i | −0.212622 | + | 1.10481i | ||||
\(554\) | −9.52628 | + | 5.50000i | −0.404733 | + | 0.233673i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00000 | − | 1.73205i | −0.127228 | − | 0.0734553i | ||||
\(557\) | − | 12.0000i | − | 0.508456i | −0.967144 | − | 0.254228i | \(-0.918179\pi\) | ||
0.967144 | − | 0.254228i | \(-0.0818214\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.92820i | − | 0.293032i | ||||||
\(560\) | −4.33013 | + | 1.50000i | −0.182981 | + | 0.0633866i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0000 | − | 25.9808i | −0.632737 | − | 1.09593i | ||||
\(563\) | −5.19615 | − | 9.00000i | −0.218992 | − | 0.379305i | 0.735508 | − | 0.677516i | \(-0.236943\pi\) |
−0.954500 | + | 0.298211i | \(0.903610\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | − | 10.3923i | −0.757266 | − | 0.437208i | ||||
\(566\) | 31.1769 | 1.31046 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | − | 27.7128i | −0.669579 | − | 1.15975i | −0.978022 | − | 0.208502i | \(-0.933141\pi\) |
0.308443 | − | 0.951243i | \(-0.400192\pi\) | |||||||
\(572\) | 5.19615 | + | 9.00000i | 0.217262 | + | 0.376309i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.5000 | − | 30.3109i | −0.438262 | − | 1.26515i | ||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 34.6410i | − | 1.44212i | −0.692870 | − | 0.721062i | \(-0.743654\pi\) | ||
0.692870 | − | 0.721062i | \(-0.256346\pi\) | |||||||
\(578\) | 26.8468 | + | 15.5000i | 1.11668 | + | 0.644715i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | − | 5.19615i | 0.373705 | − | 0.215758i | ||||
\(581\) | −8.66025 | + | 45.0000i | −0.359288 | + | 1.86691i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 31.1769i | −0.745484 | + | 1.29122i | ||||
\(584\) | 3.46410 | 0.143346 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.92820i | 0.286201i | ||||||||
\(587\) | −20.7846 | + | 36.0000i | −0.857873 | + | 1.48588i | 0.0160815 | + | 0.999871i | \(0.494881\pi\) |
−0.873954 | + | 0.486008i | \(0.838452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.50000 | − | 7.79423i | −0.185419 | − | 0.321156i | ||||
\(590\) | −5.19615 | + | 3.00000i | −0.213922 | + | 0.123508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.50000 | + | 6.06218i | −0.143849 | + | 0.249154i | ||||
\(593\) | 19.0526 | 0.782395 | 0.391197 | − | 0.920307i | \(-0.372061\pi\) | ||||
0.391197 | + | 0.920307i | \(0.372061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24.0000 | + | 20.7846i | 0.983904 | + | 0.852086i | ||||
\(596\) | −10.3923 | − | 6.00000i | −0.425685 | − | 0.245770i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.00000 | + | 5.19615i | −0.368037 | + | 0.212486i | ||||
\(599\) | 7.79423 | − | 4.50000i | 0.318464 | − | 0.183865i | −0.332244 | − | 0.943193i | \(-0.607806\pi\) |
0.650708 | + | 0.759328i | \(0.274472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.00000 | + | 5.19615i | 0.367118 | + | 0.211955i | 0.672198 | − | 0.740371i | \(-0.265350\pi\) |
−0.305081 | + | 0.952326i | \(0.598683\pi\) | |||||||
\(602\) | −3.46410 | + | 4.00000i | −0.141186 | + | 0.163028i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | −1.73205 | + | 3.00000i | −0.0704179 | + | 0.121967i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.0000 | + | 8.66025i | −0.608831 | + | 0.351509i | −0.772508 | − | 0.635005i | \(-0.780998\pi\) |
0.163677 | + | 0.986514i | \(0.447665\pi\) | |||||||
\(608\) | −0.866025 | − | 1.50000i | −0.0351220 | − | 0.0608330i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.00000 | + | 10.3923i | −0.242933 | + | 0.420772i | ||||
\(611\) | − | 12.0000i | − | 0.485468i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | −0.767403 | −0.383701 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383701 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(614\) | −7.79423 | + | 13.5000i | −0.314549 | + | 0.544816i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.50000 | − | 7.79423i | 0.0604367 | − | 0.314038i | ||||
\(617\) | −15.5885 | + | 9.00000i | −0.627568 | + | 0.362326i | −0.779809 | − | 0.626017i | \(-0.784684\pi\) |
0.152242 | + | 0.988343i | \(0.451351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.5000 | − | 9.52628i | −0.663191 | − | 0.382893i | 0.130301 | − | 0.991475i | \(-0.458406\pi\) |
−0.793492 | + | 0.608581i | \(0.791739\pi\) | |||||||
\(620\) | 9.00000i | 0.361449i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2487i | 0.972285i | ||||||||
\(623\) | 12.9904 | − | 4.50000i | 0.520449 | − | 0.180289i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 8.66025 | + | 15.0000i | 0.346133 | + | 0.599521i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.00000 | − | 5.19615i | −0.359139 | − | 0.207349i | ||||
\(629\) | 48.4974 | 1.93372 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.0000 | −1.35352 | −0.676759 | − | 0.736204i | \(-0.736616\pi\) | ||||
−0.676759 | + | 0.736204i | \(0.736616\pi\) | |||||||
\(632\) | 8.66025 | + | 5.00000i | 0.344486 | + | 0.198889i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | 19.0526 | + | 33.0000i | 0.756078 | + | 1.30957i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.00000 | − | 22.5167i | 0.356593 | − | 0.892143i | ||||
\(638\) | 18.0000i | 0.712627i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.73205i | 0.0684653i | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.50000 | + | 2.59808i | −0.177463 | + | 0.102458i | −0.586100 | − | 0.810239i | \(-0.699337\pi\) |
0.408637 | + | 0.912697i | \(0.366004\pi\) | |||||||
\(644\) | 7.79423 | + | 1.50000i | 0.307136 | + | 0.0591083i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | + | 10.3923i | −0.236067 | + | 0.408880i | ||||
\(647\) | 10.3923 | 0.408564 | 0.204282 | − | 0.978912i | \(-0.434514\pi\) | ||||
0.204282 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.3923i | − | 0.407934i | ||||||
\(650\) | 3.46410 | − | 6.00000i | 0.135873 | − | 0.235339i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.00000 | + | 1.73205i | 0.0391630 | + | 0.0678323i | ||||
\(653\) | 15.5885 | − | 9.00000i | 0.610023 | − | 0.352197i | −0.162951 | − | 0.986634i | \(-0.552101\pi\) |
0.772975 | + | 0.634437i | \(0.218768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | − | 15.5885i | 0.351659 | − | 0.609091i | ||||
\(656\) | −12.1244 | −0.473377 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.00000 | + | 6.92820i | −0.233904 | + | 0.270089i | ||||
\(659\) | −18.1865 | − | 10.5000i | −0.708447 | − | 0.409022i | 0.102039 | − | 0.994780i | \(-0.467463\pi\) |
−0.810486 | + | 0.585758i | \(0.800797\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0000 | + | 19.0526i | −1.28355 | + | 0.741059i | −0.977496 | − | 0.210955i | \(-0.932343\pi\) |
−0.306055 | + | 0.952014i | \(0.599009\pi\) | |||||||
\(662\) | −24.2487 | + | 14.0000i | −0.942453 | + | 0.544125i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15.0000 | + | 8.66025i | 0.582113 | + | 0.336083i | ||||
\(665\) | −5.19615 | + | 6.00000i | −0.201498 | + | 0.232670i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | −0.696963 | ||||||||
\(668\) | 3.46410 | − | 6.00000i | 0.134030 | − | 0.232147i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.00000 | + | 1.73205i | −0.115900 | + | 0.0669150i | ||||
\(671\) | −10.3923 | − | 18.0000i | −0.401190 | − | 0.694882i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.00000 | − | 12.1244i | 0.269830 | − | 0.467360i | −0.698988 | − | 0.715134i | \(-0.746366\pi\) |
0.968818 | + | 0.247774i | \(0.0796991\pi\) | |||||||
\(674\) | 5.00000i | 0.192593i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.00000 | −0.0384615 | ||||||||
\(677\) | 12.9904 | − | 22.5000i | 0.499261 | − | 0.864745i | −0.500739 | − | 0.865598i | \(-0.666938\pi\) |
1.00000 | 0.000853228i | \(0.000271591\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.0000 | + | 6.92820i | 1.38155 | + | 0.265880i | ||||
\(680\) | 10.3923 | − | 6.00000i | 0.398527 | − | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −13.5000 | − | 7.79423i | −0.516942 | − | 0.298456i | ||||
\(683\) | 33.0000i | 1.26271i | 0.775494 | + | 0.631355i | \(0.217501\pi\) | ||||
−0.775494 | + | 0.631355i | \(0.782499\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31.1769i | − | 1.19121i | ||||||
\(686\) | −16.4545 | + | 8.50000i | −0.628235 | + | 0.324532i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.00000 | + | 1.73205i | 0.0381246 | + | 0.0660338i | ||||
\(689\) | 20.7846 | + | 36.0000i | 0.791831 | + | 1.37149i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | − | 5.19615i | −0.342376 | − | 0.197671i | 0.318946 | − | 0.947773i | \(-0.396671\pi\) |
−0.661322 | + | 0.750102i | \(0.730004\pi\) | |||||||
\(692\) | −5.19615 | −0.197528 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.0000 | 1.02491 | ||||||||
\(695\) | 5.19615 | + | 3.00000i | 0.197101 | + | 0.113796i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.0000 | + | 72.7461i | 1.59086 | + | 2.75546i | ||||
\(698\) | −13.8564 | − | 24.0000i | −0.524473 | − | 0.908413i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.00000 | + | 1.73205i | −0.188982 | + | 0.0654654i | ||||
\(701\) | 6.00000i | 0.226617i | 0.993560 | + | 0.113308i | \(0.0361448\pi\) | ||||
−0.993560 | + | 0.113308i | \(0.963855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.1244i | 0.457279i | ||||||||
\(704\) | −2.59808 | − | 1.50000i | −0.0979187 | − | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.5000 | − | 9.52628i | 0.620986 | − | 0.358526i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.500000 | + | 0.866025i | −0.0187779 | + | 0.0325243i | −0.875262 | − | 0.483650i | \(-0.839311\pi\) |
0.856484 | + | 0.516174i | \(0.172644\pi\) | |||||||
\(710\) | 5.19615 | 0.195008 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 5.19615i | − | 0.194734i | ||||||
\(713\) | 7.79423 | − | 13.5000i | 0.291896 | − | 0.505579i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.00000 | − | 15.5885i | −0.336581 | − | 0.582975i | ||||
\(716\) | 10.3923 | − | 6.00000i | 0.388379 | − | 0.224231i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.46410 | 0.129189 | 0.0645946 | − | 0.997912i | \(-0.479425\pi\) | ||||
0.0645946 | + | 0.997912i | \(0.479425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 33.0000 | − | 38.1051i | 1.22898 | − | 1.41911i | ||||
\(722\) | 13.8564 | + | 8.00000i | 0.515682 | + | 0.297729i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.0000 | + | 6.92820i | −0.445976 | + | 0.257485i | ||||
\(725\) | 10.3923 | − | 6.00000i | 0.385961 | − | 0.222834i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.0000 | + | 25.9808i | 1.66896 | + | 0.963573i | 0.968201 | + | 0.250172i | \(0.0804873\pi\) |
0.700756 | + | 0.713401i | \(0.252846\pi\) | |||||||
\(728\) | −6.92820 | − | 6.00000i | −0.256776 | − | 0.222375i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 6.92820 | − | 12.0000i | 0.256249 | − | 0.443836i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.00000 | + | 5.19615i | −0.332423 | + | 0.191924i | −0.656916 | − | 0.753964i | \(-0.728139\pi\) |
0.324494 | + | 0.945888i | \(0.394806\pi\) | |||||||
\(734\) | 0.866025 | + | 1.50000i | 0.0319656 | + | 0.0553660i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.50000 | − | 2.59808i | 0.0552907 | − | 0.0957664i | ||||
\(737\) | − | 6.00000i | − | 0.221013i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | 6.06218 | − | 10.5000i | 0.222850 | − | 0.385988i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | − | 31.1769i | 0.220267 | − | 1.14454i | ||||
\(743\) | 23.3827 | − | 13.5000i | 0.857828 | − | 0.495267i | −0.00545664 | − | 0.999985i | \(-0.501737\pi\) |
0.863284 | + | 0.504718i | \(0.168404\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.0000 | + | 10.3923i | 0.659469 | + | 0.380745i | ||||
\(746\) | − | 5.00000i | − | 0.183063i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.7846i | 0.759961i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | + | 1.73205i | 0.0364905 | + | 0.0632034i | 0.883694 | − | 0.468065i | \(-0.155049\pi\) |
−0.847203 | + | 0.531269i | \(0.821715\pi\) | |||||||
\(752\) | 1.73205 | + | 3.00000i | 0.0631614 | + | 0.109399i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.0000 | + | 10.3923i | 0.655521 | + | 0.378465i | ||||
\(755\) | −13.8564 | −0.504286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | −1.73205 | − | 1.00000i | −0.0629109 | − | 0.0363216i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.50000 | + | 2.59808i | 0.0544107 | + | 0.0942421i | ||||
\(761\) | −6.92820 | − | 12.0000i | −0.251147 | − | 0.435000i | 0.712695 | − | 0.701474i | \(-0.247474\pi\) |
−0.963842 | + | 0.266475i | \(0.914141\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −32.5000 | + | 11.2583i | −1.17658 | + | 0.407579i | ||||
\(764\) | − | 21.0000i | − | 0.759753i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 13.8564i | − | 0.500652i | ||||||
\(767\) | −10.3923 | − | 6.00000i | −0.375244 | − | 0.216647i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.0000 | − | 19.0526i | 1.19001 | − | 0.687053i | 0.231701 | − | 0.972787i | \(-0.425571\pi\) |
0.958309 | + | 0.285734i | \(0.0922374\pi\) | |||||||
\(770\) | −2.59808 | + | 13.5000i | −0.0936282 | + | 0.486506i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | + | 12.1244i | −0.251936 | + | 0.436365i | ||||
\(773\) | −19.0526 | −0.685273 | −0.342636 | − | 0.939468i | \(-0.611320\pi\) | ||||
−0.342636 | + | 0.939468i | \(0.611320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.3923i | 0.373303i | ||||||||
\(776\) | 6.92820 | − | 12.0000i | 0.248708 | − | 0.430775i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.0000 | + | 20.7846i | 0.430221 | + | 0.745164i | ||||
\(779\) | −18.1865 | + | 10.5000i | −0.651600 | + | 0.376202i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | −20.7846 | −0.743256 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 15.5885 | + | 9.00000i | 0.556376 | + | 0.321224i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0000 | + | 8.66025i | −0.534692 | + | 0.308705i | −0.742925 | − | 0.669375i | \(-0.766562\pi\) |
0.208233 | + | 0.978079i | \(0.433229\pi\) | |||||||
\(788\) | 10.3923 | − | 6.00000i | 0.370211 | − | 0.213741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.0000 | − | 8.66025i | −0.533676 | − | 0.308118i | ||||
\(791\) | −20.7846 | + | 24.0000i | −0.739016 | + | 0.853342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 10.3923 | − | 18.0000i | 0.368809 | − | 0.638796i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.50000 | − | 0.866025i | 0.0531661 | − | 0.0306955i | ||||
\(797\) | −7.79423 | − | 13.5000i | −0.276086 | − | 0.478195i | 0.694323 | − | 0.719664i | \(-0.255704\pi\) |
−0.970408 | + | 0.241469i | \(0.922371\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | − | 20.7846i | 0.424529 | − | 0.735307i | ||||
\(800\) | 2.00000i | 0.0707107i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18.0000 | −0.635602 | ||||||||
\(803\) | 5.19615 | − | 9.00000i | 0.183368 | − | 0.317603i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.5000 | − | 2.59808i | −0.475812 | − | 0.0915702i | ||||
\(806\) | −15.5885 | + | 9.00000i | −0.549080 | + | 0.317011i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000i | 0.210949i | 0.994422 | + | 0.105474i | \(0.0336361\pi\) | ||||
−0.994422 | + | 0.105474i | \(0.966364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.3731i | − | 1.27723i | −0.769526 | − | 0.638616i | \(-0.779507\pi\) | ||
0.769526 | − | 0.638616i | \(-0.220493\pi\) | |||||||
\(812\) | −5.19615 | − | 15.0000i | −0.182349 | − | 0.526397i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.5000 | + | 18.1865i | 0.368025 | + | 0.637438i | ||||
\(815\) | −1.73205 | − | 3.00000i | −0.0606711 | − | 0.105085i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.00000 | + | 1.73205i | 0.104957 | + | 0.0605968i | ||||
\(818\) | −3.46410 | −0.121119 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21.0000 | 0.733352 | ||||||||
\(821\) | −25.9808 | − | 15.0000i | −0.906735 | − | 0.523504i | −0.0273557 | − | 0.999626i | \(-0.508709\pi\) |
−0.879379 | + | 0.476122i | \(0.842042\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | + | 3.46410i | 0.0697156 | + | 0.120751i | 0.898776 | − | 0.438408i | \(-0.144457\pi\) |
−0.829060 | + | 0.559159i | \(0.811124\pi\) | |||||||
\(824\) | −9.52628 | − | 16.5000i | −0.331864 | − | 0.574805i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.00000 | + | 8.66025i | 0.104383 | + | 0.301329i | ||||
\(827\) | 3.00000i | 0.104320i | 0.998639 | + | 0.0521601i | \(0.0166106\pi\) | ||||
−0.998639 | + | 0.0521601i | \(0.983389\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 38.1051i | − | 1.32345i | −0.749749 | − | 0.661723i | \(-0.769826\pi\) | ||
0.749749 | − | 0.661723i | \(-0.230174\pi\) | |||||||
\(830\) | −25.9808 | − | 15.0000i | −0.901805 | − | 0.520658i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | + | 1.73205i | −0.104006 | + | 0.0600481i | ||||
\(833\) | 38.1051 | − | 30.0000i | 1.32026 | − | 1.03944i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.00000 | + | 10.3923i | −0.207639 | + | 0.359641i | ||||
\(836\) | −5.19615 | −0.179713 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 6.92820i | − | 0.239331i | ||||||
\(839\) | 12.1244 | − | 21.0000i | 0.418579 | − | 0.725001i | −0.577218 | − | 0.816590i | \(-0.695862\pi\) |
0.995797 | + | 0.0915899i | \(0.0291949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.50000 | + | 6.06218i | 0.120690 | + | 0.209041i | ||||
\(842\) | 11.2583 | − | 6.50000i | 0.387988 | − | 0.224005i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | − | 13.8564i | 0.275371 | − | 0.476957i | ||||
\(845\) | 1.73205 | 0.0595844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.00000 | + | 3.46410i | 0.137442 | + | 0.119028i | ||||
\(848\) | −10.3923 | − | 6.00000i | −0.356873 | − | 0.206041i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.0000 | − | 6.92820i | 0.411597 | − | 0.237635i | ||||
\(851\) | −18.1865 | + | 10.5000i | −0.623426 | + | 0.359935i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.0000 | − | 6.92820i | −0.410872 | − | 0.237217i | 0.280292 | − | 0.959915i | \(-0.409569\pi\) |
−0.691164 | + | 0.722698i | \(0.742902\pi\) | |||||||
\(854\) | 13.8564 | + | 12.0000i | 0.474156 | + | 0.410632i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.6506 | + | 37.5000i | −0.739572 | + | 1.28098i | 0.213117 | + | 0.977027i | \(0.431639\pi\) |
−0.952688 | + | 0.303949i | \(0.901695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5000 | − | 14.7224i | 0.870049 | − | 0.502323i | 0.00268433 | − | 0.999996i | \(-0.499146\pi\) |
0.867364 | + | 0.497674i | \(0.165812\pi\) | |||||||
\(860\) | −1.73205 | − | 3.00000i | −0.0590624 | − | 0.102299i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.5000 | + | 18.1865i | −0.357631 | + | 0.619436i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | 0.306009 | ||||||||
\(866\) | −5.19615 | + | 9.00000i | −0.176572 | + | 0.305832i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.5000 | + | 2.59808i | 0.458220 | + | 0.0881845i | ||||
\(869\) | 25.9808 | − | 15.0000i | 0.881337 | − | 0.508840i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.00000 | − | 3.46410i | −0.203302 | − | 0.117377i | ||||
\(872\) | 13.0000i | 0.440236i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 5.19615i | − | 0.175762i | ||||||
\(875\) | 30.3109 | − | 10.5000i | 1.02470 | − | 0.354965i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.0000 | − | 43.3013i | −0.844190 | − | 1.46218i | −0.886323 | − | 0.463068i | \(-0.846749\pi\) |
0.0421327 | − | 0.999112i | \(-0.486585\pi\) | |||||||
\(878\) | 5.19615 | + | 9.00000i | 0.175362 | + | 0.303735i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.50000 | + | 2.59808i | 0.151695 | + | 0.0875811i | ||||
\(881\) | −25.9808 | −0.875314 | −0.437657 | − | 0.899142i | \(-0.644192\pi\) | ||||
−0.437657 | + | 0.899142i | \(0.644192\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.0000 | 0.538443 | 0.269221 | − | 0.963078i | \(-0.413234\pi\) | ||||
0.269221 | + | 0.963078i | \(0.413234\pi\) | |||||||
\(884\) | 20.7846 | + | 12.0000i | 0.699062 | + | 0.403604i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | − | 7.79423i | −0.151180 | − | 0.261852i | ||||
\(887\) | 12.1244 | + | 21.0000i | 0.407096 | + | 0.705111i | 0.994563 | − | 0.104137i | \(-0.0332081\pi\) |
−0.587467 | + | 0.809248i | \(0.699875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 55.0000 | − | 19.0526i | 1.84464 | − | 0.639002i | ||||
\(890\) | 9.00000i | 0.301681i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 15.5885i | 0.521940i | ||||||||
\(893\) | 5.19615 | + | 3.00000i | 0.173883 | + | 0.100391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0000 | + | 10.3923i | −0.601674 | + | 0.347376i | ||||
\(896\) | 2.59808 | + | 0.500000i | 0.0867956 | + | 0.0167038i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.00000 | + | 10.3923i | −0.200223 | + | 0.346796i | ||||
\(899\) | −31.1769 | −1.03981 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.1384i | 2.76974i | ||||||||
\(902\) | −18.1865 | + | 31.5000i | −0.605545 | + | 1.04884i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | + | 10.3923i | 0.199557 | + | 0.345643i | ||||
\(905\) | 20.7846 | − | 12.0000i | 0.690904 | − | 0.398893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.00000 | − | 6.92820i | 0.132818 | − | 0.230047i | −0.791944 | − | 0.610594i | \(-0.790931\pi\) |
0.924762 | + | 0.380547i | \(0.124264\pi\) | |||||||
\(908\) | −20.7846 | −0.689761 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | + | 10.3923i | 0.397796 | + | 0.344502i | ||||
\(911\) | −10.3923 | − | 6.00000i | −0.344312 | − | 0.198789i | 0.317865 | − | 0.948136i | \(-0.397034\pi\) |
−0.662177 | + | 0.749347i | \(0.730367\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.0000 | − | 25.9808i | 1.48928 | − | 0.859838i | ||||
\(914\) | 14.7224 | − | 8.50000i | 0.486975 | − | 0.281155i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −20.7846 | − | 18.0000i | −0.686368 | − | 0.594412i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.00000 | 0.131948 | 0.0659739 | − | 0.997821i | \(-0.478985\pi\) | ||||
0.0659739 | + | 0.997821i | \(0.478985\pi\) | |||||||
\(920\) | −2.59808 | + | 4.50000i | −0.0856560 | + | 0.148361i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.5000 | + | 9.52628i | −0.543399 | + | 0.313731i | ||||
\(923\) | 5.19615 | + | 9.00000i | 0.171033 | + | 0.296239i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.00000 | − | 12.1244i | 0.230159 | − | 0.398646i | ||||
\(926\) | − | 32.0000i | − | 1.05159i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | −13.8564 | + | 24.0000i | −0.454614 | + | 0.787414i | −0.998666 | − | 0.0516371i | \(-0.983556\pi\) |
0.544052 | + | 0.839052i | \(0.316889\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.50000 | + | 9.52628i | 0.245803 | + | 0.312211i | ||||
\(932\) | 20.7846 | − | 12.0000i | 0.680823 | − | 0.393073i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.0000 | + | 15.5885i | 0.883467 | + | 0.510070i | ||||
\(935\) | − | 36.0000i | − | 1.17733i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.92820i | 0.226335i | 0.993576 | + | 0.113167i | \(0.0360996\pi\) | ||||
−0.993576 | + | 0.113167i | \(0.963900\pi\) | |||||||
\(938\) | 1.73205 | + | 5.00000i | 0.0565535 | + | 0.163256i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.00000 | − | 5.19615i | −0.0978492 | − | 0.169480i | ||||
\(941\) | 6.06218 | + | 10.5000i | 0.197621 | + | 0.342290i | 0.947757 | − | 0.318994i | \(-0.103345\pi\) |
−0.750135 | + | 0.661284i | \(0.770012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.5000 | − | 18.1865i | −1.02578 | − | 0.592235i | ||||
\(944\) | 3.46410 | 0.112747 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.00000 | 0.195077 | ||||||||
\(947\) | −12.9904 | − | 7.50000i | −0.422131 | − | 0.243717i | 0.273858 | − | 0.961770i | \(-0.411700\pi\) |
−0.695988 | + | 0.718053i | \(0.745034\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | − | 10.3923i | −0.194768 | − | 0.337348i | ||||
\(950\) | 1.73205 | + | 3.00000i | 0.0561951 | + | 0.0973329i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.00000 | − | 17.3205i | −0.194461 | − | 0.561361i | ||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.3731i | 1.17700i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 24.0000 | − | 13.8564i | 0.775405 | − | 0.447680i | ||||
\(959\) | −46.7654 | − | 9.00000i | −1.51013 | − | 0.290625i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | + | 3.46410i | −0.0645161 | + | 0.111745i | ||||
\(962\) | 24.2487 | 0.781810 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 17.3205i | − | 0.557856i | ||||||
\(965\) | 12.1244 | − | 21.0000i | 0.390297 | − | 0.676014i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | + | 13.8564i | 0.257263 | + | 0.445592i | 0.965508 | − | 0.260375i | \(-0.0838461\pi\) |
−0.708245 | + | 0.705967i | \(0.750513\pi\) | |||||||
\(968\) | 1.73205 | − | 1.00000i | 0.0556702 | − | 0.0321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.0000 | + | 20.7846i | −0.385297 | + | 0.667354i | ||||
\(971\) | 3.46410 | 0.111168 | 0.0555842 | − | 0.998454i | \(-0.482298\pi\) | ||||
0.0555842 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | − | 6.92820i | 0.192351 | − | 0.222108i | ||||
\(974\) | 8.66025 | + | 5.00000i | 0.277492 | + | 0.160210i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.00000 | − | 3.46410i | 0.192055 | − | 0.110883i | ||||
\(977\) | −41.5692 | + | 24.0000i | −1.32992 | + | 0.767828i | −0.985287 | − | 0.170910i | \(-0.945329\pi\) |
−0.344631 | + | 0.938738i | \(0.611996\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5000 | − | 7.79423i | −0.431462 | − | 0.249105i | ||||
\(980\) | −1.73205 | − | 12.0000i | −0.0553283 | − | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.00000 | −0.287202 | ||||||||
\(983\) | −1.73205 | + | 3.00000i | −0.0552438 | + | 0.0956851i | −0.892325 | − | 0.451394i | \(-0.850927\pi\) |
0.837081 | + | 0.547079i | \(0.184260\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0000 | + | 10.3923i | −0.573528 | + | 0.331126i | ||||
\(986\) | 20.7846 | + | 36.0000i | 0.661917 | + | 1.14647i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.00000 | + | 5.19615i | −0.0954427 | + | 0.165312i | ||||
\(989\) | 6.00000i | 0.190789i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | 2.59808 | − | 4.50000i | 0.0824890 | − | 0.142875i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.50000 | − | 7.79423i | 0.0475771 | − | 0.247218i | ||||
\(995\) | −2.59808 | + | 1.50000i | −0.0823646 | + | 0.0475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | − | 10.0000i | − | 0.316544i | ||||||
\(999\) | 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 | 1134.2.m.b.755.2 | 4 | ||
3.2 | odd | 2 | inner | 1134.2.m.b.755.1 | 4 | ||
7.6 | odd | 2 | 1134.2.m.c.755.2 | 4 | |||
9.2 | odd | 6 | 378.2.d.b.377.3 | yes | 4 | ||
9.4 | even | 3 | 1134.2.m.c.377.1 | 4 | |||
9.5 | odd | 6 | 1134.2.m.c.377.2 | 4 | |||
9.7 | even | 3 | 378.2.d.b.377.2 | yes | 4 | ||
21.20 | even | 2 | 1134.2.m.c.755.1 | 4 | |||
36.7 | odd | 6 | 3024.2.k.e.1889.3 | 4 | |||
36.11 | even | 6 | 3024.2.k.e.1889.1 | 4 | |||
63.13 | odd | 6 | inner | 1134.2.m.b.377.1 | 4 | ||
63.20 | even | 6 | 378.2.d.b.377.4 | yes | 4 | ||
63.34 | odd | 6 | 378.2.d.b.377.1 | ✓ | 4 | ||
63.41 | even | 6 | inner | 1134.2.m.b.377.2 | 4 | ||
252.83 | odd | 6 | 3024.2.k.e.1889.4 | 4 | |||
252.223 | even | 6 | 3024.2.k.e.1889.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.d.b.377.1 | ✓ | 4 | 63.34 | odd | 6 | ||
378.2.d.b.377.2 | yes | 4 | 9.7 | even | 3 | ||
378.2.d.b.377.3 | yes | 4 | 9.2 | odd | 6 | ||
378.2.d.b.377.4 | yes | 4 | 63.20 | even | 6 | ||
1134.2.m.b.377.1 | 4 | 63.13 | odd | 6 | inner | ||
1134.2.m.b.377.2 | 4 | 63.41 | even | 6 | inner | ||
1134.2.m.b.755.1 | 4 | 3.2 | odd | 2 | inner | ||
1134.2.m.b.755.2 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.m.c.377.1 | 4 | 9.4 | even | 3 | |||
1134.2.m.c.377.2 | 4 | 9.5 | odd | 6 | |||
1134.2.m.c.755.1 | 4 | 21.20 | even | 2 | |||
1134.2.m.c.755.2 | 4 | 7.6 | odd | 2 | |||
3024.2.k.e.1889.1 | 4 | 36.11 | even | 6 | |||
3024.2.k.e.1889.2 | 4 | 252.223 | even | 6 | |||
3024.2.k.e.1889.3 | 4 | 36.7 | odd | 6 | |||
3024.2.k.e.1889.4 | 4 | 252.83 | odd | 6 |