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 | 377.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.377 |
Dual form | 1134.2.m.c.755.2 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | \(-0.706742\pi\) |
0.992085 | + | 0.125567i | \(0.0400750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 1.73205i | − | 0.547723i | ||||||
\(11\) | 2.59808 | − | 1.50000i | 0.783349 | − | 0.452267i | −0.0542666 | − | 0.998526i | \(-0.517282\pi\) |
0.837616 | + | 0.546259i | \(0.183949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | − | 1.73205i | −0.832050 | − | 0.480384i | 0.0225039 | − | 0.999747i | \(-0.492836\pi\) |
−0.854554 | + | 0.519362i | \(0.826170\pi\) | |||||||
\(14\) | −0.866025 | − | 2.50000i | −0.231455 | − | 0.668153i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −6.92820 | −1.68034 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(18\) | 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 | 0.204046 | − | 0.978961i | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | 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 | 0.0672232 | − | 0.997738i | \(-0.478586\pi\) |
0.897678 | + | 0.440652i | \(0.145253\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 2.59808i | 0.808224 | + | 0.466628i | 0.846339 | − | 0.532645i | \(-0.178802\pi\) |
−0.0381148 | + | 0.999273i | \(0.512135\pi\) | |||||||
\(32\) | −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 | −0.194551 | + | 0.980892i | \(0.562325\pi\) |
−0.752202 | + | 0.658932i | \(0.771008\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | + | 1.73205i | 0.152499 | + | 0.264135i | 0.932145 | − | 0.362084i | \(-0.117935\pi\) |
−0.779647 | + | 0.626219i | \(0.784601\pi\) | |||||||
\(44\) | − | 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 | \(-0.247967\pi\) |
−0.964253 | + | 0.264982i | \(0.914634\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | 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 | \(-0.691646\pi\) | ||
0.566352 | − | 0.824163i | \(-0.308354\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.19615i | − | 0.700649i | ||||||
\(56\) | −2.59808 | − | 0.500000i | −0.347183 | − | 0.0668153i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | − | 5.19615i | 0.393919 | − | 0.682288i | ||||
\(59\) | 1.73205 | − | 3.00000i | 0.225494 | − | 0.390567i | −0.730974 | − | 0.682406i | \(-0.760934\pi\) |
0.956467 | + | 0.291839i | \(0.0942671\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.00000 | − | 3.46410i | 0.768221 | − | 0.443533i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.832240 | + | 0.554416i | \(0.187058\pi\) | |||||||
\(62\) | 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 | −0.920623 | − | 0.390453i | \(-0.872318\pi\) |
0.798454 | + | 0.602056i | \(0.205652\pi\) | |||||||
\(68\) | −3.46410 | + | 6.00000i | −0.420084 | + | 0.727607i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.50000 | − | 0.866025i | −0.537853 | − | 0.103510i | ||||
\(71\) | − | 3.00000i | − | 0.356034i | −0.984027 | − | 0.178017i | \(-0.943032\pi\) | ||
0.984027 | − | 0.178017i | \(-0.0569683\pi\) | |||||||
\(72\) | 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 | ||||
\(77\) | −2.59808 | − | 7.50000i | −0.296078 | − | 0.854704i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | + | 8.66025i | 0.562544 | + | 0.974355i | 0.997274 | + | 0.0737937i | \(0.0235106\pi\) |
−0.434730 | + | 0.900561i | \(0.643156\pi\) | |||||||
\(80\) | −1.73205 | −0.193649 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 12.1244i | 1.33891i | ||||||||
\(83\) | −8.66025 | − | 15.0000i | −0.950586 | − | 1.64646i | −0.744160 | − | 0.668002i | \(-0.767150\pi\) |
−0.206427 | − | 0.978462i | \(-0.566184\pi\) | |||||||
\(84\) | 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 | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 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 | \(-0.418307\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | −6.92820 | + | 1.00000i | −0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.5000 | + | 9.52628i | 1.62579 | + | 0.938652i | 0.985329 | + | 0.170664i | \(0.0545913\pi\) |
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | −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 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | 10.3923 | + | 6.00000i | 0.977626 | + | 0.564433i | 0.901553 | − | 0.432670i | \(-0.142428\pi\) |
0.0760733 | + | 0.997102i | \(0.475762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.50000 | + | 2.59808i | −0.419627 | + | 0.242272i | ||||
\(116\) | − | 6.00000i | − | 0.557086i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 3.46410i | − | 0.318896i | ||||||
\(119\) | −3.46410 | + | 18.0000i | −0.317554 | + | 1.65006i | ||||
\(120\) | 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 | \(-0.983333\pi\) |
0.544640 | + | 0.838670i | \(0.316666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50000 | + | 0.866025i | 0.390199 | + | 0.0750939i | ||||
\(134\) | 2.00000i | 0.172774i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.92820i | 0.594089i | ||||||||
\(137\) | 15.5885 | − | 9.00000i | 1.33181 | − | 0.768922i | 0.346235 | − | 0.938148i | \(-0.387460\pi\) |
0.985577 | + | 0.169226i | \(0.0541268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00000 | + | 1.73205i | 0.254457 | + | 0.146911i | 0.621803 | − | 0.783174i | \(-0.286400\pi\) |
−0.367347 | + | 0.930084i | \(0.619734\pi\) | |||||||
\(140\) | −4.33013 | + | 1.50000i | −0.365963 | + | 0.126773i | ||||
\(141\) | 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 | 0.00974235 | − | 0.999953i | \(-0.496899\pi\) |
−0.861113 | + | 0.508413i | \(0.830232\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 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 | \(-0.197221\pi\) |
−0.0958404 | + | 0.995397i | \(0.530554\pi\) | |||||||
\(158\) | 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 | \(-0.746951\pi\) |
0.968361 | + | 0.249554i | \(0.0802840\pi\) | |||||||
\(168\) | 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 | \(-0.103375\pi\) |
−0.750198 | + | 0.661213i | \(0.770042\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.00000 | − | 1.73205i | 0.377964 | − | 0.130931i | ||||
\(176\) | −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 | \(0.148028\pi\) | ||||
−0.893802 | + | 0.448461i | \(0.851972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.8564i | 1.02994i | 0.857209 | + | 0.514969i | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | −1.73205 | + | 9.00000i | −0.128388 | + | 0.667124i | ||||
\(183\) | 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 | −0.983071 | − | 0.183223i | \(-0.941347\pi\) |
−0.332860 | + | 0.942976i | \(0.608014\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | − | 12.1244i | 0.503871 | − | 0.872730i | −0.496119 | − | 0.868255i | \(-0.665242\pi\) |
0.999990 | − | 0.00447566i | \(-0.00142465\pi\) | |||||||
\(194\) | 6.92820 | − | 12.0000i | 0.497416 | − | 0.861550i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.50000 | + | 4.33013i | −0.392857 | + | 0.309295i | ||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −5.19615 | − | 15.0000i | −0.364698 | − | 1.05279i | ||||
\(204\) | 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 | 0.447478 | + | 0.894295i | \(0.352322\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | −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 | \(-0.841458\pi\) |
−0.0255224 | + | 0.999674i | \(0.508125\pi\) | |||||||
\(224\) | −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 | 0.971915 | + | 0.235333i | \(0.0756180\pi\) |
−0.282153 | + | 0.959369i | \(0.591049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(230\) | −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 | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.00000 | −0.391397 | ||||||||
\(236\) | −1.73205 | − | 3.00000i | −0.112747 | − | 0.195283i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | + | 17.3205i | 0.388922 | + | 1.12272i | ||||
\(239\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0000 | − | 8.66025i | 0.966235 | − | 0.557856i | 0.0681486 | − | 0.997675i | \(-0.478291\pi\) |
0.898086 | + | 0.439819i | \(0.144957\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.92820i | − | 0.443533i | ||||||
\(245\) | −9.52628 | + | 7.50000i | −0.608612 | + | 0.479157i | ||||
\(246\) | 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 | \(-0.355933\pi\) | ||||
0.437304 | + | 0.899314i | \(0.355933\pi\) | |||||||
\(252\) | 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 | \(-0.781518\pi\) |
0.935609 | + | 0.353039i | \(0.114852\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.50000 | − | 18.1865i | 0.217479 | − | 1.13006i | ||||
\(260\) | 6.00000i | 0.372104i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.3923i | 0.642039i | ||||||||
\(263\) | 23.3827 | − | 13.5000i | 1.44184 | − | 0.832446i | 0.443866 | − | 0.896093i | \(-0.353607\pi\) |
0.997972 | + | 0.0636476i | \(0.0202734\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0000 | − | 10.3923i | −1.10573 | − | 0.638394i | ||||
\(266\) | 4.33013 | − | 1.50000i | 0.265497 | − | 0.0919709i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.00000 | + | 1.73205i | 0.0610847 | + | 0.105802i | ||||
\(269\) | 1.73205 | 0.105605 | 0.0528025 | − | 0.998605i | \(-0.483185\pi\) | ||||
0.0528025 | + | 0.998605i | \(0.483185\pi\) | |||||||
\(270\) | 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 | 0.652140 | − | 0.758099i | \(-0.273872\pi\) |
−0.982603 | + | 0.185720i | \(0.940538\pi\) | |||||||
\(278\) | 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 | −0.551733 | + | 0.834021i | \(0.686033\pi\) |
−0.998150 | + | 0.0608039i | \(0.980634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −27.0000 | − | 15.5885i | −1.60498 | − | 0.926638i | −0.990470 | − | 0.137732i | \(-0.956019\pi\) |
−0.614514 | − | 0.788906i | \(-0.710648\pi\) | |||||||
\(284\) | −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 | \(-0.898199\pi\) |
0.746918 | + | 0.664916i | \(0.231533\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 5.00000 | − | 1.73205i | 0.288195 | − | 0.0998337i | ||||
\(302\) | 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 | \(0.853260\pi\) | |||||||
\(308\) | −7.79423 | − | 1.50000i | −0.444117 | − | 0.0854704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.50000 | − | 7.79423i | 0.255583 | − | 0.442682i | ||||
\(311\) | −12.1244 | + | 21.0000i | −0.687509 | + | 1.19080i | 0.285132 | + | 0.958488i | \(0.407963\pi\) |
−0.972641 | + | 0.232313i | \(0.925371\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.0000 | + | 8.66025i | −0.847850 | + | 0.489506i | −0.859925 | − | 0.510421i | \(-0.829490\pi\) |
0.0120748 | + | 0.999927i | \(0.496156\pi\) | |||||||
\(314\) | 10.3923 | 0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.0000 | 0.562544 | ||||||||
\(317\) | −15.5885 | + | 9.00000i | −0.875535 | + | 0.505490i | −0.869184 | − | 0.494489i | \(-0.835355\pi\) |
−0.00635137 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | −0.866025 | + | 1.50000i | −0.0484123 | + | 0.0838525i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.50000 | + | 7.79423i | −0.0835917 | + | 0.434355i | ||||
\(323\) | − | 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 | ||||
\(329\) | −8.66025 | + | 3.00000i | −0.477455 | + | 0.165395i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.0000 | − | 24.2487i | −0.769510 | − | 1.33283i | −0.937829 | − | 0.347097i | \(-0.887167\pi\) |
0.168320 | − | 0.985732i | \(-0.446166\pi\) | |||||||
\(332\) | −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 | −0.789865 | − | 0.613280i | \(-0.789850\pi\) |
0.926049 | + | 0.377403i | \(0.123183\pi\) | |||||||
\(338\) | −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 | 0.972147 | − | 0.234372i | \(-0.0753034\pi\) |
0.283101 | + | 0.959090i | \(0.408637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.0000 | − | 13.8564i | 1.28469 | − | 0.741716i | 0.306988 | − | 0.951713i | \(-0.400679\pi\) |
0.977702 | + | 0.209997i | \(0.0673454\pi\) | |||||||
\(350\) | 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 | −0.999967 | − | 0.00813978i | \(-0.997409\pi\) |
0.492934 | − | 0.870067i | \(-0.335924\pi\) | |||||||
\(354\) | 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 | ||||||||
\(364\) | 3.00000 | + | 8.66025i | 0.157243 | + | 0.453921i | ||||
\(365\) | −5.19615 | − | 3.00000i | −0.271979 | − | 0.157027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 0.866025i | −0.0782994 | + | 0.0452062i | −0.538639 | − | 0.842537i | \(-0.681061\pi\) |
0.460339 | + | 0.887743i | \(0.347728\pi\) | |||||||
\(368\) | 3.00000i | 0.156386i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 12.1244i | − | 0.630315i | ||||||
\(371\) | −31.1769 | − | 6.00000i | −1.61862 | − | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50000 | + | 4.33013i | −0.129445 | + | 0.224205i | −0.923462 | − | 0.383691i | \(-0.874653\pi\) |
0.794017 | + | 0.607896i | \(0.207986\pi\) | |||||||
\(374\) | −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 | \(-0.718150\pi\) |
0.986949 | + | 0.161034i | \(0.0514830\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.5000 | − | 2.59808i | −0.688024 | − | 0.132410i | ||||
\(386\) | − | 14.0000i | − | 0.712581i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 13.8564i | − | 0.703452i | ||||||
\(389\) | 20.7846 | − | 12.0000i | 1.05382 | − | 0.608424i | 0.130105 | − | 0.991500i | \(-0.458469\pi\) |
0.923717 | + | 0.383076i | \(0.125135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | + | 10.3923i | 0.910299 | + | 0.525561i | ||||
\(392\) | −2.59808 | + | 6.50000i | −0.131223 | + | 0.328300i | ||||
\(393\) | 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 | 0.0574304 | − | 0.998350i | \(-0.481709\pi\) |
−0.835881 | + | 0.548911i | \(0.815043\pi\) | |||||||
\(402\) | 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 | \(-0.306038\pi\) |
−0.423993 | + | 0.905666i | \(0.639372\pi\) | |||||||
\(410\) | 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 | \(-0.779204\pi\) |
0.938150 | + | 0.346228i | \(0.112538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.50000 | + | 11.2583i | 0.316791 | + | 0.548697i | 0.979817 | − | 0.199899i | \(-0.0640614\pi\) |
−0.663026 | + | 0.748596i | \(0.730728\pi\) | |||||||
\(422\) | 16.0000i | 0.778868i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.0000 | −0.582772 | ||||||||
\(425\) | −6.92820 | − | 12.0000i | −0.336067 | − | 0.582086i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.00000 | − | 17.3205i | −0.290360 | − | 0.838198i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.00000 | − | 1.73205i | 0.144673 | − | 0.0835269i | ||||
\(431\) | − | 21.0000i | − | 1.01153i | −0.862670 | − | 0.505767i | \(-0.831209\pi\) | ||
0.862670 | − | 0.505767i | \(-0.168791\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3923i | 0.499422i | 0.968320 | + | 0.249711i | \(0.0803357\pi\) | ||||
−0.968320 | + | 0.249711i | \(0.919664\pi\) | |||||||
\(434\) | 2.59808 | − | 13.5000i | 0.124712 | − | 0.648021i | ||||
\(435\) | 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 | \(-0.746440\pi\) |
0.269607 | + | 0.962970i | \(0.413106\pi\) | |||||||
\(440\) | −5.19615 | −0.247717 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.0000 | 1.14156 | ||||||||
\(443\) | −7.79423 | + | 4.50000i | −0.370315 | + | 0.213801i | −0.673596 | − | 0.739100i | \(-0.735251\pi\) |
0.303281 | + | 0.952901i | \(0.401918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.50000 | − | 7.79423i | 0.213320 | − | 0.369482i | ||||
\(446\) | −7.79423 | + | 13.5000i | −0.369067 | + | 0.639244i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.500000 | + | 2.59808i | −0.0236228 | + | 0.122748i | ||||
\(449\) | − | 12.0000i | − | 0.566315i | −0.959073 | − | 0.283158i | \(-0.908618\pi\) | ||
0.959073 | − | 0.283158i | \(-0.0913819\pi\) | |||||||
\(450\) | 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 | ||||
\(455\) | 5.19615 | + | 15.0000i | 0.243599 | + | 0.703211i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | + | 14.7224i | 0.397613 | + | 0.688686i | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.19615i | 0.242272i | ||||||||
\(461\) | 9.52628 | + | 16.5000i | 0.443683 | + | 0.768482i | 0.997959 | − | 0.0638511i | \(-0.0203383\pi\) |
−0.554276 | + | 0.832333i | \(0.687005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | + | 27.7128i | −0.743583 | + | 1.28792i | 0.207271 | + | 0.978284i | \(0.433542\pi\) |
−0.950854 | + | 0.309640i | \(0.899791\pi\) | |||||||
\(464\) | −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 | \(-0.756477\pi\) | ||||
−0.721348 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(468\) | 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 | −0.986911 | − | 0.161265i | \(-0.948443\pi\) |
0.353796 | − | 0.935323i | \(-0.384891\pi\) | |||||||
\(480\) | 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 | ||||||||
\(490\) | −4.50000 | + | 11.2583i | −0.203289 | + | 0.508600i | ||||
\(491\) | −7.79423 | − | 4.50000i | −0.351749 | − | 0.203082i | 0.313707 | − | 0.949520i | \(-0.398429\pi\) |
−0.665455 | + | 0.746438i | \(0.731763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −36.0000 | + | 20.7846i | −1.62136 | + | 0.936092i | ||||
\(494\) | − | 6.00000i | − | 0.269953i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.19615i | − | 0.233314i | ||||||
\(497\) | −7.79423 | − | 1.50000i | −0.349619 | − | 0.0672842i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.00000 | + | 8.66025i | −0.223831 | + | 0.387686i | −0.955968 | − | 0.293471i | \(-0.905190\pi\) |
0.732137 | + | 0.681157i | \(0.238523\pi\) | |||||||
\(500\) | 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 | \(-0.681802\pi\) | ||||
−0.540598 | + | 0.841281i | \(0.681802\pi\) | |||||||
\(504\) | 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 | \(-0.733979\pi\) |
0.977724 | + | 0.209895i | \(0.0673123\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.00000 | − | 1.73205i | −0.398137 | − | 0.0766214i | ||||
\(512\) | 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 | ||||
\(518\) | −6.06218 | − | 17.5000i | −0.266357 | − | 0.768906i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | + | 5.19615i | 0.131559 | + | 0.227866i | ||||
\(521\) | 22.5167 | 0.986473 | 0.493236 | − | 0.869895i | \(-0.335814\pi\) | ||||
0.493236 | + | 0.869895i | \(0.335814\pi\) | |||||||
\(522\) | 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 | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | − | 18.0000i | − | 0.768922i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.00000 | 0.255841 | ||||||||
\(551\) | 5.19615 | + | 9.00000i | 0.221364 | + | 0.383413i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.0000 | − | 8.66025i | 1.06311 | − | 0.368271i | ||||
\(554\) | −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 | \(0.0818214\pi\) | ||||
−0.967144 | + | 0.254228i | \(0.918179\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.92820i | − | 0.293032i | ||||||
\(560\) | −0.866025 | + | 4.50000i | −0.0365963 | + | 0.190160i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0000 | + | 25.9808i | −0.632737 | + | 1.09593i | ||||
\(563\) | 5.19615 | − | 9.00000i | 0.218992 | − | 0.379305i | −0.735508 | − | 0.677516i | \(-0.763057\pi\) |
0.954500 | + | 0.298211i | \(0.0963899\pi\) | |||||||
\(564\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | + | 27.7128i | −0.669579 | + | 1.15975i | 0.308443 | + | 0.951243i | \(0.400192\pi\) |
−0.978022 | + | 0.208502i | \(0.933141\pi\) | |||||||
\(572\) | −5.19615 | + | 9.00000i | −0.217262 | + | 0.376309i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 31.5000 | + | 6.06218i | 1.31478 | + | 0.253030i | ||||
\(575\) | − | 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 | ||||
\(581\) | −43.3013 | + | 15.0000i | −1.79644 | + | 0.622305i | ||||
\(582\) | 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 | 0.873954 | + | 0.486008i | \(0.161548\pi\) |
−0.0160815 | + | 0.999871i | \(0.505119\pi\) | |||||||
\(588\) | 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 | \(-0.627939\pi\) | ||||
−0.391197 | + | 0.920307i | \(0.627939\pi\) | |||||||
\(594\) | 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 | 0.650708 | − | 0.759328i | \(-0.274472\pi\) |
−0.332244 | + | 0.943193i | \(0.607806\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.00000 | + | 5.19615i | −0.367118 | + | 0.211955i | −0.672198 | − | 0.740371i | \(-0.734650\pi\) |
0.305081 | + | 0.952326i | \(0.401317\pi\) | |||||||
\(602\) | 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 | \(-0.219002\pi\) |
−0.163677 | + | 0.986514i | \(0.552335\pi\) | |||||||
\(608\) | 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 | ||||||||
\(616\) | −7.50000 | + | 2.59808i | −0.302184 | + | 0.104679i | ||||
\(617\) | −15.5885 | − | 9.00000i | −0.627568 | − | 0.362326i | 0.152242 | − | 0.988343i | \(-0.451351\pi\) |
−0.779809 | + | 0.626017i | \(0.784684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5000 | − | 9.52628i | 0.663191 | − | 0.382893i | −0.130301 | − | 0.991475i | \(-0.541594\pi\) |
0.793492 | + | 0.608581i | \(0.208261\pi\) | |||||||
\(620\) | − | 9.00000i | − | 0.361449i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.2487i | 0.972285i | ||||||||
\(623\) | 2.59808 | − | 13.5000i | 0.104090 | − | 0.540866i | ||||
\(624\) | 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 | ||||||||
\(637\) | 15.0000 | + | 19.0526i | 0.594322 | + | 0.754890i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.73205i | 0.0684653i | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.50000 | + | 2.59808i | 0.177463 | + | 0.102458i | 0.586100 | − | 0.810239i | \(-0.300663\pi\) |
−0.408637 | + | 0.912697i | \(0.633996\pi\) | |||||||
\(644\) | 2.59808 | + | 7.50000i | 0.102379 | + | 0.295541i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | − | 10.3923i | −0.236067 | − | 0.408880i | ||||
\(647\) | −10.3923 | −0.408564 | −0.204282 | − | 0.978912i | \(-0.565486\pi\) | ||||
−0.204282 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(648\) | 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 | 0.772975 | − | 0.634437i | \(-0.218768\pi\) |
−0.162951 | + | 0.986634i | \(0.552101\pi\) | |||||||
\(654\) | 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 | −0.810486 | − | 0.585758i | \(-0.800797\pi\) |
0.102039 | + | 0.994780i | \(0.467463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 33.0000 | + | 19.0526i | 1.28355 | + | 0.741059i | 0.977496 | − | 0.210955i | \(-0.0676574\pi\) |
0.306055 | + | 0.952014i | \(0.400991\pi\) | |||||||
\(662\) | −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 | 0.968818 | − | 0.247774i | \(-0.0796991\pi\) |
−0.698988 | + | 0.715134i | \(0.746366\pi\) | |||||||
\(674\) | − | 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 | \(-0.333062\pi\) |
−1.00000 | 0.000853228i | \(0.999728\pi\) | ||||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0000 | − | 34.6410i | −0.460518 | − | 1.32940i | ||||
\(680\) | 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 | \(-0.782499\pi\) | ||
0.775494 | − | 0.631355i | \(-0.217501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 31.1769i | − | 1.19121i | ||||||
\(686\) | −0.866025 | + | 18.5000i | −0.0330650 | + | 0.706333i | ||||
\(687\) | 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 | \(-0.603329\pi\) |
0.661322 | + | 0.750102i | \(0.269996\pi\) | |||||||
\(692\) | 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 | ||||||||
\(700\) | 1.00000 | − | 5.19615i | 0.0377964 | − | 0.196396i | ||||
\(701\) | − | 6.00000i | − | 0.226617i | −0.993560 | − | 0.113308i | \(-0.963855\pi\) | ||
0.993560 | − | 0.113308i | \(-0.0361448\pi\) | |||||||
\(702\) | 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 | 0.856484 | − | 0.516174i | \(-0.172644\pi\) |
−0.875262 | + | 0.483650i | \(0.839311\pi\) | |||||||
\(710\) | −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 | \(-0.520575\pi\) | ||||
−0.0645946 | + | 0.997912i | \(0.520575\pi\) | |||||||
\(720\) | 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 | −0.700756 | + | 0.713401i | \(0.747154\pi\) |
−0.968201 | + | 0.250172i | \(0.919513\pi\) | |||||||
\(728\) | 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 | \(-0.271861\pi\) |
−0.324494 | + | 0.945888i | \(0.605194\pi\) | |||||||
\(734\) | −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 | ||||||||
\(742\) | −30.0000 | + | 10.3923i | −1.10133 | + | 0.381514i | ||||
\(743\) | 23.3827 | + | 13.5000i | 0.857828 | + | 0.495267i | 0.863284 | − | 0.504718i | \(-0.168404\pi\) |
−0.00545664 | + | 0.999985i | \(0.501737\pi\) | |||||||
\(744\) | 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 | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | −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 | \(-0.752526\pi\) |
0.963842 | + | 0.266475i | \(0.0858589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.50000 | − | 33.7750i | 0.235316 | − | 1.22274i | ||||
\(764\) | 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 | \(-0.574429\pi\) |
−0.958309 | + | 0.285734i | \(0.907763\pi\) | |||||||
\(770\) | −12.9904 | + | 4.50000i | −0.468141 | + | 0.162169i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.00000 | − | 12.1244i | −0.251936 | − | 0.436365i | ||||
\(773\) | 19.0526 | 0.685273 | 0.342636 | − | 0.939468i | \(-0.388680\pi\) | ||||
0.342636 | + | 0.939468i | \(0.388680\pi\) | |||||||
\(774\) | 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 | \(-0.233438\pi\) |
−0.208233 | + | 0.978079i | \(0.566771\pi\) | |||||||
\(788\) | 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 | \(-0.744296\pi\) |
0.970408 | + | 0.241469i | \(0.0776293\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 4.50000 | + | 12.9904i | 0.158604 | + | 0.457851i | ||||
\(806\) | −15.5885 | − | 9.00000i | −0.549080 | − | 0.317011i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.00000i | − | 0.210949i | −0.994422 | − | 0.105474i | \(-0.966364\pi\) | ||
0.994422 | − | 0.105474i | \(-0.0336361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.3731i | − | 1.27723i | −0.769526 | − | 0.638616i | \(-0.779507\pi\) | ||
0.769526 | − | 0.638616i | \(-0.220493\pi\) | |||||||
\(812\) | −15.5885 | − | 3.00000i | −0.547048 | − | 0.105279i | ||||
\(813\) | 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 | −0.879379 | − | 0.476122i | \(-0.842042\pi\) |
−0.0273557 | + | 0.999626i | \(0.508709\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000 | − | 3.46410i | 0.0697156 | − | 0.120751i | −0.829060 | − | 0.559159i | \(-0.811124\pi\) |
0.898776 | + | 0.438408i | \(0.144457\pi\) | |||||||
\(824\) | 9.52628 | − | 16.5000i | 0.331864 | − | 0.574805i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.00000 | − | 1.73205i | −0.313150 | − | 0.0602658i | ||||
\(827\) | − | 3.00000i | − | 0.104320i | −0.998639 | − | 0.0521601i | \(-0.983389\pi\) | ||
0.998639 | − | 0.0521601i | \(-0.0166106\pi\) | |||||||
\(828\) | 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 | ||||
\(833\) | 45.0333 | + | 18.0000i | 1.56031 | + | 0.623663i | ||||
\(834\) | 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 | \(-0.304138\pi\) |
−0.995797 | + | 0.0915899i | \(0.970805\pi\) | |||||||
\(840\) | 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 | \(-0.590431\pi\) |
0.691164 | + | 0.722698i | \(0.257098\pi\) | |||||||
\(854\) | −13.8564 | − | 12.0000i | −0.474156 | − | 0.410632i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.6506 | + | 37.5000i | 0.739572 | + | 1.28098i | 0.952688 | + | 0.303949i | \(0.0983052\pi\) |
−0.213117 | + | 0.977027i | \(0.568361\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.5000 | − | 14.7224i | −0.870049 | − | 0.502323i | −0.00268433 | − | 0.999996i | \(-0.500854\pi\) |
−0.867364 | + | 0.497674i | \(0.834188\pi\) | |||||||
\(860\) | 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 | ||||||||
\(868\) | −4.50000 | − | 12.9904i | −0.152740 | − | 0.440922i | ||||
\(869\) | 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 | ||||||
\(875\) | 6.06218 | − | 31.5000i | 0.204939 | − | 1.06489i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.0000 | + | 43.3013i | −0.844190 | + | 1.46218i | 0.0421327 | + | 0.999112i | \(0.486585\pi\) |
−0.886323 | + | 0.463068i | \(0.846749\pi\) | |||||||
\(878\) | −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 | \(-0.355808\pi\) | ||||
0.437657 | + | 0.899142i | \(0.355808\pi\) | |||||||
\(882\) | 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 | \(-0.966792\pi\) |
0.587467 | + | 0.809248i | \(0.300125\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.0000 | + | 57.1577i | −0.368928 | + | 1.91701i | ||||
\(890\) | − | 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 | ||||
\(896\) | 0.866025 | + | 2.50000i | 0.0289319 | + | 0.0835191i | ||||
\(897\) | 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 | 0.924762 | − | 0.380547i | \(-0.124264\pi\) |
−0.791944 | + | 0.610594i | \(0.790931\pi\) | |||||||
\(908\) | 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 | −0.662177 | − | 0.749347i | \(-0.730367\pi\) |
0.317865 | + | 0.948136i | \(0.397034\pi\) | |||||||
\(912\) | 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 | \(-0.0164439\pi\) |
−0.544052 | + | 0.839052i | \(0.683111\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.50000 | − | 11.2583i | 0.147482 | − | 0.368977i | ||||
\(932\) | 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 | \(0.963900\pi\) | |||||||
\(938\) | 5.19615 | + | 1.00000i | 0.169660 | + | 0.0326512i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.00000 | + | 5.19615i | −0.0978492 | + | 0.169480i | ||||
\(941\) | −6.06218 | + | 10.5000i | −0.197621 | + | 0.342290i | −0.947757 | − | 0.318994i | \(-0.896655\pi\) |
0.750135 | + | 0.661284i | \(0.229988\pi\) | |||||||
\(942\) | 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 | −0.695988 | − | 0.718053i | \(-0.745034\pi\) |
0.273858 | + | 0.961770i | \(0.411700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | + | 10.3923i | −0.194768 | + | 0.337348i | ||||
\(950\) | −1.73205 | + | 3.00000i | −0.0561951 | + | 0.0973329i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 18.0000 | + | 3.46410i | 0.583383 | + | 0.112272i | ||||
\(953\) | 18.0000i | 0.583077i | 0.956559 | + | 0.291539i | \(0.0941672\pi\) | ||||
−0.956559 | + | 0.291539i | \(0.905833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 36.3731i | 1.17700i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.0000 | − | 13.8564i | −0.775405 | − | 0.447680i | ||||
\(959\) | −15.5885 | − | 45.0000i | −0.503378 | − | 1.45313i | ||||
\(960\) | 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 | −0.708245 | − | 0.705967i | \(-0.750513\pi\) |
0.965508 | + | 0.260375i | \(0.0838461\pi\) | |||||||
\(968\) | 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 | \(-0.517702\pi\) | ||||
−0.0555842 | + | 0.998454i | \(0.517702\pi\) | |||||||
\(972\) | 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 | −0.344631 | − | 0.938738i | \(-0.611996\pi\) |
−0.985287 | + | 0.170910i | \(0.945329\pi\) | |||||||
\(978\) | 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 | \(-0.149073\pi\) |
−0.837081 | + | 0.547079i | \(0.815740\pi\) | |||||||
\(984\) | 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 | ||||||||
\(994\) | −7.50000 | + | 2.59808i | −0.237886 | + | 0.0824060i | ||||
\(995\) | −2.59808 | − | 1.50000i | −0.0823646 | − | 0.0475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(998\) | 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.c.377.2 | 4 | ||
3.2 | odd | 2 | inner | 1134.2.m.c.377.1 | 4 | ||
7.6 | odd | 2 | 1134.2.m.b.377.2 | 4 | |||
9.2 | odd | 6 | 1134.2.m.b.755.2 | 4 | |||
9.4 | even | 3 | 378.2.d.b.377.3 | yes | 4 | ||
9.5 | odd | 6 | 378.2.d.b.377.2 | yes | 4 | ||
9.7 | even | 3 | 1134.2.m.b.755.1 | 4 | |||
21.20 | even | 2 | 1134.2.m.b.377.1 | 4 | |||
36.23 | even | 6 | 3024.2.k.e.1889.3 | 4 | |||
36.31 | odd | 6 | 3024.2.k.e.1889.1 | 4 | |||
63.13 | odd | 6 | 378.2.d.b.377.4 | yes | 4 | ||
63.20 | even | 6 | inner | 1134.2.m.c.755.2 | 4 | ||
63.34 | odd | 6 | inner | 1134.2.m.c.755.1 | 4 | ||
63.41 | even | 6 | 378.2.d.b.377.1 | ✓ | 4 | ||
252.139 | even | 6 | 3024.2.k.e.1889.4 | 4 | |||
252.167 | odd | 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 | 63.41 | even | 6 | ||
378.2.d.b.377.2 | yes | 4 | 9.5 | odd | 6 | ||
378.2.d.b.377.3 | yes | 4 | 9.4 | even | 3 | ||
378.2.d.b.377.4 | yes | 4 | 63.13 | odd | 6 | ||
1134.2.m.b.377.1 | 4 | 21.20 | even | 2 | |||
1134.2.m.b.377.2 | 4 | 7.6 | odd | 2 | |||
1134.2.m.b.755.1 | 4 | 9.7 | even | 3 | |||
1134.2.m.b.755.2 | 4 | 9.2 | odd | 6 | |||
1134.2.m.c.377.1 | 4 | 3.2 | odd | 2 | inner | ||
1134.2.m.c.377.2 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.m.c.755.1 | 4 | 63.34 | odd | 6 | inner | ||
1134.2.m.c.755.2 | 4 | 63.20 | even | 6 | inner | ||
3024.2.k.e.1889.1 | 4 | 36.31 | odd | 6 | |||
3024.2.k.e.1889.2 | 4 | 252.167 | odd | 6 | |||
3024.2.k.e.1889.3 | 4 | 36.23 | even | 6 | |||
3024.2.k.e.1889.4 | 4 | 252.139 | even | 6 |