Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [338,2,Mod(23,338)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(338, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("338.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 338 = 2 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 338.e (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: | \(2.69894358832\) |
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 26) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 23.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.23 |
Dual form | 338.2.e.c.147.2 |
$q$-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 \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).
\(n\) | \(171\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | 0.973494 | − | 0.228714i | \(-0.0734519\pi\) |
−0.684819 | + | 0.728714i | \(0.740119\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | − | 3.00000i | − | 1.34164i | −0.741620 | − | 0.670820i | \(-0.765942\pi\) | ||
0.741620 | − | 0.670820i | \(-0.234058\pi\) | |||||||
\(6\) | 0.866025 | + | 0.500000i | 0.353553 | + | 0.204124i | ||||
\(7\) | −2.59808 | − | 1.50000i | −0.981981 | − | 0.566947i | −0.0791130 | − | 0.996866i | \(-0.525209\pi\) |
−0.902867 | + | 0.429919i | \(0.858542\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | −1.50000 | − | 2.59808i | −0.474342 | − | 0.821584i | ||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 2.59808 | − | 1.50000i | 0.670820 | − | 0.387298i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | − | 2.00000i | − | 0.471405i | ||||||
\(19\) | 5.19615 | + | 3.00000i | 1.19208 | + | 0.688247i | 0.958778 | − | 0.284157i | \(-0.0917138\pi\) |
0.233301 | + | 0.972404i | \(0.425047\pi\) | |||||||
\(20\) | −2.59808 | − | 1.50000i | −0.580948 | − | 0.335410i | ||||
\(21\) | − | 3.00000i | − | 0.654654i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | −2.59808 | + | 1.50000i | −0.490990 | + | 0.283473i | ||||
\(29\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.00000i | 0.514496i | ||||||||
\(35\) | −4.50000 | + | 7.79423i | −0.760639 | + | 1.31747i | ||||
\(36\) | −1.00000 | − | 1.73205i | −0.166667 | − | 0.288675i | ||||
\(37\) | 2.59808 | − | 1.50000i | 0.427121 | − | 0.246598i | −0.270998 | − | 0.962580i | \(-0.587354\pi\) |
0.698119 | + | 0.715981i | \(0.254020\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(42\) | −1.50000 | − | 2.59808i | −0.231455 | − | 0.400892i | ||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.19615 | − | 3.00000i | −0.774597 | − | 0.447214i | ||||
\(46\) | 5.19615 | + | 3.00000i | 0.766131 | + | 0.442326i | ||||
\(47\) | 3.00000i | 0.437595i | 0.975770 | + | 0.218797i | \(0.0702134\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 1.00000 | + | 1.73205i | 0.142857 | + | 0.247436i | ||||
\(50\) | −3.46410 | + | 2.00000i | −0.489898 | + | 0.282843i | ||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 4.33013 | − | 2.50000i | 0.589256 | − | 0.340207i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.50000 | + | 2.59808i | −0.200446 | + | 0.347183i | ||||
\(57\) | 6.00000i | 0.794719i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.19615 | + | 3.00000i | 0.676481 | + | 0.390567i | 0.798528 | − | 0.601958i | \(-0.205612\pi\) |
−0.122047 | + | 0.992524i | \(0.538946\pi\) | |||||||
\(60\) | − | 3.00000i | − | 0.387298i | ||||||
\(61\) | 4.00000 | − | 6.92820i | 0.512148 | − | 0.887066i | −0.487753 | − | 0.872982i | \(-0.662183\pi\) |
0.999901 | − | 0.0140840i | \(-0.00448323\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.19615 | + | 3.00000i | −0.654654 | + | 0.377964i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.3923 | + | 6.00000i | −1.26962 | + | 0.733017i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | −3.00000 | + | 5.19615i | −0.361158 | + | 0.625543i | ||||
\(70\) | 9.00000i | 1.07571i | ||||||||
\(71\) | −12.9904 | − | 7.50000i | −1.54167 | − | 0.890086i | −0.998733 | − | 0.0503155i | \(-0.983977\pi\) |
−0.542941 | − | 0.839771i | \(-0.682689\pi\) | |||||||
\(72\) | −1.73205 | − | 1.00000i | −0.204124 | − | 0.117851i | ||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 1.50000 | − | 2.59808i | 0.174371 | − | 0.302020i | ||||
\(75\) | −2.00000 | − | 3.46410i | −0.230940 | − | 0.400000i | ||||
\(76\) | 5.19615 | − | 3.00000i | 0.596040 | − | 0.344124i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | −2.59808 | + | 1.50000i | −0.290474 | + | 0.167705i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | −2.59808 | − | 1.50000i | −0.283473 | − | 0.163663i | ||||
\(85\) | 7.79423 | + | 4.50000i | 0.845403 | + | 0.488094i | ||||
\(86\) | − | 1.00000i | − | 0.107833i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.19615 | + | 3.00000i | −0.550791 | + | 0.317999i | −0.749441 | − | 0.662071i | \(-0.769678\pi\) |
0.198650 | + | 0.980071i | \(0.436344\pi\) | |||||||
\(90\) | −6.00000 | −0.632456 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.00000 | 0.625543 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | 9.00000 | − | 15.5885i | 0.923381 | − | 1.59934i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | 10.3923 | + | 6.00000i | 1.05518 | + | 0.609208i | 0.924095 | − | 0.382164i | \(-0.124821\pi\) |
0.131084 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(98\) | 1.73205 | + | 1.00000i | 0.174964 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | −2.59808 | + | 1.50000i | −0.257248 | + | 0.148522i | ||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.00000 | −0.878310 | ||||||||
\(106\) | −5.19615 | + | 3.00000i | −0.504695 | + | 0.291386i | ||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 2.50000 | − | 4.33013i | 0.240563 | − | 0.416667i | ||||
\(109\) | 9.00000i | 0.862044i | 0.902342 | + | 0.431022i | \(0.141847\pi\) | ||||
−0.902342 | + | 0.431022i | \(0.858153\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.59808 | + | 1.50000i | 0.246598 | + | 0.142374i | ||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | 3.00000 | + | 5.19615i | 0.280976 | + | 0.486664i | ||||
\(115\) | 15.5885 | − | 9.00000i | 1.45363 | − | 0.839254i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 7.79423 | − | 4.50000i | 0.714496 | − | 0.412514i | ||||
\(120\) | −1.50000 | − | 2.59808i | −0.136931 | − | 0.237171i | ||||
\(121\) | −5.50000 | + | 9.52628i | −0.500000 | + | 0.866025i | ||||
\(122\) | − | 8.00000i | − | 0.724286i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3.00000i | − | 0.268328i | ||||||
\(126\) | −3.00000 | + | 5.19615i | −0.267261 | + | 0.462910i | ||||
\(127\) | 1.00000 | + | 1.73205i | 0.0887357 | + | 0.153695i | 0.906977 | − | 0.421180i | \(-0.138384\pi\) |
−0.818241 | + | 0.574875i | \(0.805051\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | −0.262111 | −0.131056 | − | 0.991375i | \(-0.541837\pi\) | ||||
−0.131056 | + | 0.991375i | \(0.541837\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.00000 | − | 15.5885i | −0.780399 | − | 1.35169i | ||||
\(134\) | −6.00000 | + | 10.3923i | −0.518321 | + | 0.897758i | ||||
\(135\) | − | 15.0000i | − | 1.29099i | ||||||
\(136\) | 2.59808 | + | 1.50000i | 0.222783 | + | 0.128624i | ||||
\(137\) | −15.5885 | − | 9.00000i | −1.33181 | − | 0.768922i | −0.346235 | − | 0.938148i | \(-0.612540\pi\) |
−0.985577 | + | 0.169226i | \(0.945873\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | −2.50000 | + | 4.33013i | −0.212047 | + | 0.367277i | −0.952355 | − | 0.304991i | \(-0.901346\pi\) |
0.740308 | + | 0.672268i | \(0.234680\pi\) | |||||||
\(140\) | 4.50000 | + | 7.79423i | 0.380319 | + | 0.658733i | ||||
\(141\) | −2.59808 | + | 1.50000i | −0.218797 | + | 0.126323i | ||||
\(142\) | −15.0000 | −1.25877 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.00000 | + | 5.19615i | 0.248282 | + | 0.430037i | ||||
\(147\) | −1.00000 | + | 1.73205i | −0.0824786 | + | 0.142857i | ||||
\(148\) | − | 3.00000i | − | 0.246598i | ||||||
\(149\) | 5.19615 | + | 3.00000i | 0.425685 | + | 0.245770i | 0.697507 | − | 0.716578i | \(-0.254293\pi\) |
−0.271821 | + | 0.962348i | \(0.587626\pi\) | |||||||
\(150\) | −3.46410 | − | 2.00000i | −0.282843 | − | 0.163299i | ||||
\(151\) | − | 15.0000i | − | 1.22068i | −0.792139 | − | 0.610341i | \(-0.791032\pi\) | ||
0.792139 | − | 0.610341i | \(-0.208968\pi\) | |||||||
\(152\) | 3.00000 | − | 5.19615i | 0.243332 | − | 0.421464i | ||||
\(153\) | 3.00000 | + | 5.19615i | 0.242536 | + | 0.420084i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | 8.66025 | − | 5.00000i | 0.688973 | − | 0.397779i | ||||
\(159\) | −3.00000 | − | 5.19615i | −0.237915 | − | 0.412082i | ||||
\(160\) | −1.50000 | + | 2.59808i | −0.118585 | + | 0.205396i | ||||
\(161\) | − | 18.0000i | − | 1.41860i | ||||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | −5.19615 | − | 3.00000i | −0.406994 | − | 0.234978i | 0.282503 | − | 0.959266i | \(-0.408835\pi\) |
−0.689497 | + | 0.724288i | \(0.742169\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | −10.3923 | + | 6.00000i | −0.804181 | + | 0.464294i | −0.844931 | − | 0.534875i | \(-0.820359\pi\) |
0.0407502 | + | 0.999169i | \(0.487025\pi\) | |||||||
\(168\) | −3.00000 | −0.231455 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 10.3923 | − | 6.00000i | 0.794719 | − | 0.458831i | ||||
\(172\) | −0.500000 | − | 0.866025i | −0.0381246 | − | 0.0660338i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.3923 | + | 6.00000i | 0.785584 | + | 0.453557i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | −3.00000 | + | 5.19615i | −0.224860 | + | 0.389468i | ||||
\(179\) | −7.50000 | − | 12.9904i | −0.560576 | − | 0.970947i | −0.997446 | − | 0.0714220i | \(-0.977246\pi\) |
0.436870 | − | 0.899525i | \(-0.356087\pi\) | |||||||
\(180\) | −5.19615 | + | 3.00000i | −0.387298 | + | 0.223607i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 5.19615 | − | 3.00000i | 0.383065 | − | 0.221163i | ||||
\(185\) | −4.50000 | − | 7.79423i | −0.330847 | − | 0.573043i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.59808 | + | 1.50000i | 0.189484 | + | 0.109399i | ||||
\(189\) | −12.9904 | − | 7.50000i | −0.944911 | − | 0.545545i | ||||
\(190\) | − | 18.0000i | − | 1.30586i | ||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 5.19615 | − | 3.00000i | 0.374027 | − | 0.215945i | −0.301189 | − | 0.953564i | \(-0.597384\pi\) |
0.675216 | + | 0.737620i | \(0.264050\pi\) | |||||||
\(194\) | 12.0000 | 0.861550 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 2.59808 | − | 1.50000i | 0.185105 | − | 0.106871i | −0.404584 | − | 0.914501i | \(-0.632584\pi\) |
0.589689 | + | 0.807630i | \(0.299250\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | − | 17.3205i | 0.708881 | − | 1.22782i | −0.256391 | − | 0.966573i | \(-0.582534\pi\) |
0.965272 | − | 0.261245i | \(-0.0841331\pi\) | |||||||
\(200\) | 4.00000i | 0.282843i | ||||||||
\(201\) | −10.3923 | − | 6.00000i | −0.733017 | − | 0.423207i | ||||
\(202\) | −10.3923 | − | 6.00000i | −0.731200 | − | 0.422159i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −1.50000 | + | 2.59808i | −0.105021 | + | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 12.1244 | − | 7.00000i | 0.844744 | − | 0.487713i | ||||
\(207\) | 12.0000 | 0.834058 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −7.79423 | + | 4.50000i | −0.537853 | + | 0.310530i | ||||
\(211\) | 11.5000 | + | 19.9186i | 0.791693 | + | 1.37125i | 0.924918 | + | 0.380166i | \(0.124133\pi\) |
−0.133226 | + | 0.991086i | \(0.542533\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | − | 15.0000i | − | 1.02778i | ||||||
\(214\) | 10.3923 | + | 6.00000i | 0.710403 | + | 0.410152i | ||||
\(215\) | −2.59808 | − | 1.50000i | −0.177187 | − | 0.102299i | ||||
\(216\) | − | 5.00000i | − | 0.340207i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.50000 | + | 7.79423i | 0.304778 | + | 0.527892i | ||||
\(219\) | −5.19615 | + | 3.00000i | −0.351123 | + | 0.202721i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.00000 | 0.201347 | ||||||||
\(223\) | −7.79423 | + | 4.50000i | −0.521940 | + | 0.301342i | −0.737728 | − | 0.675098i | \(-0.764101\pi\) |
0.215788 | + | 0.976440i | \(0.430768\pi\) | |||||||
\(224\) | 1.50000 | + | 2.59808i | 0.100223 | + | 0.173591i | ||||
\(225\) | −4.00000 | + | 6.92820i | −0.266667 | + | 0.461880i | ||||
\(226\) | − | 6.00000i | − | 0.399114i | ||||||
\(227\) | 10.3923 | + | 6.00000i | 0.689761 | + | 0.398234i | 0.803523 | − | 0.595274i | \(-0.202957\pi\) |
−0.113761 | + | 0.993508i | \(0.536290\pi\) | |||||||
\(228\) | 5.19615 | + | 3.00000i | 0.344124 | + | 0.198680i | ||||
\(229\) | 9.00000i | 0.594737i | 0.954763 | + | 0.297368i | \(0.0961089\pi\) | ||||
−0.954763 | + | 0.297368i | \(0.903891\pi\) | |||||||
\(230\) | 9.00000 | − | 15.5885i | 0.593442 | − | 1.02787i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −21.0000 | −1.37576 | −0.687878 | − | 0.725826i | \(-0.741458\pi\) | ||||
−0.687878 | + | 0.725826i | \(0.741458\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | 5.19615 | − | 3.00000i | 0.338241 | − | 0.195283i | ||||
\(237\) | 5.00000 | + | 8.66025i | 0.324785 | + | 0.562544i | ||||
\(238\) | 4.50000 | − | 7.79423i | 0.291692 | − | 0.505225i | ||||
\(239\) | 9.00000i | 0.582162i | 0.956698 | + | 0.291081i | \(0.0940149\pi\) | ||||
−0.956698 | + | 0.291081i | \(0.905985\pi\) | |||||||
\(240\) | −2.59808 | − | 1.50000i | −0.167705 | − | 0.0968246i | ||||
\(241\) | 25.9808 | + | 15.0000i | 1.67357 | + | 0.966235i | 0.965615 | + | 0.259975i | \(0.0837143\pi\) |
0.707953 | + | 0.706260i | \(0.249619\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | 8.00000 | − | 13.8564i | 0.513200 | − | 0.888889i | ||||
\(244\) | −4.00000 | − | 6.92820i | −0.256074 | − | 0.443533i | ||||
\(245\) | 5.19615 | − | 3.00000i | 0.331970 | − | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.19615 | + | 3.00000i | −0.329293 | + | 0.190117i | ||||
\(250\) | −1.50000 | − | 2.59808i | −0.0948683 | − | 0.164317i | ||||
\(251\) | −6.00000 | + | 10.3923i | −0.378717 | + | 0.655956i | −0.990876 | − | 0.134778i | \(-0.956968\pi\) |
0.612159 | + | 0.790735i | \(0.290301\pi\) | |||||||
\(252\) | 6.00000i | 0.377964i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.73205 | + | 1.00000i | 0.108679 | + | 0.0627456i | ||||
\(255\) | 9.00000i | 0.563602i | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1.50000 | − | 2.59808i | −0.0935674 | − | 0.162064i | 0.815442 | − | 0.578838i | \(-0.196494\pi\) |
−0.909010 | + | 0.416775i | \(0.863160\pi\) | |||||||
\(258\) | 0.866025 | − | 0.500000i | 0.0539164 | − | 0.0311286i | ||||
\(259\) | −9.00000 | −0.559233 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.59808 | + | 1.50000i | −0.160510 | + | 0.0926703i | ||||
\(263\) | −12.0000 | − | 20.7846i | −0.739952 | − | 1.28163i | −0.952517 | − | 0.304487i | \(-0.901515\pi\) |
0.212565 | − | 0.977147i | \(-0.431818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0000i | 1.10573i | ||||||||
\(266\) | −15.5885 | − | 9.00000i | −0.955790 | − | 0.551825i | ||||
\(267\) | −5.19615 | − | 3.00000i | −0.317999 | − | 0.183597i | ||||
\(268\) | 12.0000i | 0.733017i | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | −7.50000 | − | 12.9904i | −0.456435 | − | 0.790569i | ||||
\(271\) | 12.9904 | − | 7.50000i | 0.789109 | − | 0.455593i | −0.0505395 | − | 0.998722i | \(-0.516094\pi\) |
0.839649 | + | 0.543130i | \(0.182761\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.0000 | −1.08742 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | −4.00000 | + | 6.92820i | −0.240337 | + | 0.416275i | −0.960810 | − | 0.277207i | \(-0.910591\pi\) |
0.720473 | + | 0.693482i | \(0.243925\pi\) | |||||||
\(278\) | 5.00000i | 0.299880i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.79423 | + | 4.50000i | 0.465794 | + | 0.268926i | ||||
\(281\) | − | 30.0000i | − | 1.78965i | −0.446417 | − | 0.894825i | \(-0.647300\pi\) | ||
0.446417 | − | 0.894825i | \(-0.352700\pi\) | |||||||
\(282\) | −1.50000 | + | 2.59808i | −0.0893237 | + | 0.154713i | ||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | −12.9904 | + | 7.50000i | −0.770837 | + | 0.445043i | ||||
\(285\) | 18.0000 | 1.06623 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.73205 | + | 1.00000i | −0.102062 | + | 0.0589256i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.0000i | 0.703452i | ||||||||
\(292\) | 5.19615 | + | 3.00000i | 0.304082 | + | 0.175562i | ||||
\(293\) | 7.79423 | + | 4.50000i | 0.455344 | + | 0.262893i | 0.710084 | − | 0.704117i | \(-0.248657\pi\) |
−0.254741 | + | 0.967009i | \(0.581990\pi\) | |||||||
\(294\) | 2.00000i | 0.116642i | ||||||||
\(295\) | 9.00000 | − | 15.5885i | 0.524000 | − | 0.907595i | ||||
\(296\) | −1.50000 | − | 2.59808i | −0.0871857 | − | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | −0.230940 | ||||||||
\(301\) | −2.59808 | + | 1.50000i | −0.149751 | + | 0.0864586i | ||||
\(302\) | −7.50000 | − | 12.9904i | −0.431577 | − | 0.747512i | ||||
\(303\) | 6.00000 | − | 10.3923i | 0.344691 | − | 0.597022i | ||||
\(304\) | − | 6.00000i | − | 0.344124i | ||||||
\(305\) | −20.7846 | − | 12.0000i | −1.19012 | − | 0.687118i | ||||
\(306\) | 5.19615 | + | 3.00000i | 0.297044 | + | 0.171499i | ||||
\(307\) | 18.0000i | 1.02731i | 0.857996 | + | 0.513657i | \(0.171710\pi\) | ||||
−0.857996 | + | 0.513657i | \(0.828290\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 7.00000 | + | 12.1244i | 0.398216 | + | 0.689730i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.0000 | 1.07394 | 0.536972 | − | 0.843600i | \(-0.319568\pi\) | ||||
0.536972 | + | 0.843600i | \(0.319568\pi\) | |||||||
\(314\) | −19.0526 | + | 11.0000i | −1.07520 | + | 0.620766i | ||||
\(315\) | 9.00000 | + | 15.5885i | 0.507093 | + | 0.878310i | ||||
\(316\) | 5.00000 | − | 8.66025i | 0.281272 | − | 0.487177i | ||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | −5.19615 | − | 3.00000i | −0.291386 | − | 0.168232i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.00000i | 0.167705i | ||||||||
\(321\) | −6.00000 | + | 10.3923i | −0.334887 | + | 0.580042i | ||||
\(322\) | −9.00000 | − | 15.5885i | −0.501550 | − | 0.868711i | ||||
\(323\) | −15.5885 | + | 9.00000i | −0.867365 | + | 0.500773i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | −0.332309 | ||||||||
\(327\) | −7.79423 | + | 4.50000i | −0.431022 | + | 0.248851i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | − | 7.79423i | 0.248093 | − | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.9808 | − | 15.0000i | −1.42803 | − | 0.824475i | −0.431066 | − | 0.902320i | \(-0.641863\pi\) |
−0.996965 | + | 0.0778456i | \(0.975196\pi\) | |||||||
\(332\) | 5.19615 | + | 3.00000i | 0.285176 | + | 0.164646i | ||||
\(333\) | − | 6.00000i | − | 0.328798i | ||||||
\(334\) | −6.00000 | + | 10.3923i | −0.328305 | + | 0.568642i | ||||
\(335\) | 18.0000 | + | 31.1769i | 0.983445 | + | 1.70338i | ||||
\(336\) | −2.59808 | + | 1.50000i | −0.141737 | + | 0.0818317i | ||||
\(337\) | 13.0000 | 0.708155 | 0.354078 | − | 0.935216i | \(-0.384795\pi\) | ||||
0.354078 | + | 0.935216i | \(0.384795\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 7.79423 | − | 4.50000i | 0.422701 | − | 0.244047i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 6.00000 | − | 10.3923i | 0.324443 | − | 0.561951i | ||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | −0.866025 | − | 0.500000i | −0.0466930 | − | 0.0269582i | ||||
\(345\) | 15.5885 | + | 9.00000i | 0.839254 | + | 0.484544i | ||||
\(346\) | − | 6.00000i | − | 0.322562i | ||||||
\(347\) | −16.5000 | + | 28.5788i | −0.885766 | + | 1.53419i | −0.0409337 | + | 0.999162i | \(0.513033\pi\) |
−0.844833 | + | 0.535031i | \(0.820300\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1865 | + | 10.5000i | −0.973503 | + | 0.562052i | −0.900302 | − | 0.435265i | \(-0.856655\pi\) |
−0.0732005 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(350\) | 12.0000 | 0.641427 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.19615 | − | 3.00000i | 0.276563 | − | 0.159674i | −0.355303 | − | 0.934751i | \(-0.615622\pi\) |
0.631867 | + | 0.775077i | \(0.282289\pi\) | |||||||
\(354\) | 3.00000 | + | 5.19615i | 0.159448 | + | 0.276172i | ||||
\(355\) | −22.5000 | + | 38.9711i | −1.19418 | + | 2.06837i | ||||
\(356\) | 6.00000i | 0.317999i | ||||||||
\(357\) | 7.79423 | + | 4.50000i | 0.412514 | + | 0.238165i | ||||
\(358\) | −12.9904 | − | 7.50000i | −0.686563 | − | 0.396387i | ||||
\(359\) | 24.0000i | 1.26667i | 0.773877 | + | 0.633336i | \(0.218315\pi\) | ||||
−0.773877 | + | 0.633336i | \(0.781685\pi\) | |||||||
\(360\) | −3.00000 | + | 5.19615i | −0.158114 | + | 0.273861i | ||||
\(361\) | 8.50000 | + | 14.7224i | 0.447368 | + | 0.774865i | ||||
\(362\) | 1.73205 | − | 1.00000i | 0.0910346 | − | 0.0525588i | ||||
\(363\) | −11.0000 | −0.577350 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.0000 | 0.942163 | ||||||||
\(366\) | 6.92820 | − | 4.00000i | 0.362143 | − | 0.209083i | ||||
\(367\) | −4.00000 | − | 6.92820i | −0.208798 | − | 0.361649i | 0.742538 | − | 0.669804i | \(-0.233622\pi\) |
−0.951336 | + | 0.308155i | \(0.900289\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.79423 | − | 4.50000i | −0.405203 | − | 0.233944i | ||||
\(371\) | 15.5885 | + | 9.00000i | 0.809312 | + | 0.467257i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.00000 | + | 3.46410i | −0.103556 | + | 0.179364i | −0.913147 | − | 0.407630i | \(-0.866355\pi\) |
0.809591 | + | 0.586994i | \(0.199689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.59808 | − | 1.50000i | 0.134164 | − | 0.0774597i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −15.0000 | −0.771517 | ||||||||
\(379\) | −5.19615 | + | 3.00000i | −0.266908 | + | 0.154100i | −0.627482 | − | 0.778631i | \(-0.715914\pi\) |
0.360573 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(380\) | −9.00000 | − | 15.5885i | −0.461690 | − | 0.799671i | ||||
\(381\) | −1.00000 | + | 1.73205i | −0.0512316 | + | 0.0887357i | ||||
\(382\) | 12.0000i | 0.613973i | ||||||||
\(383\) | 7.79423 | + | 4.50000i | 0.398266 | + | 0.229939i | 0.685736 | − | 0.727851i | \(-0.259481\pi\) |
−0.287469 | + | 0.957790i | \(0.592814\pi\) | |||||||
\(384\) | −0.866025 | − | 0.500000i | −0.0441942 | − | 0.0255155i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.00000 | − | 5.19615i | 0.152696 | − | 0.264477i | ||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 10.3923 | − | 6.00000i | 0.527589 | − | 0.304604i | ||||
\(389\) | −30.0000 | −1.52106 | −0.760530 | − | 0.649303i | \(-0.775061\pi\) | ||||
−0.760530 | + | 0.649303i | \(0.775061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 1.73205 | − | 1.00000i | 0.0874818 | − | 0.0505076i | ||||
\(393\) | −1.50000 | − | 2.59808i | −0.0756650 | − | 0.131056i | ||||
\(394\) | 1.50000 | − | 2.59808i | 0.0755689 | − | 0.130889i | ||||
\(395\) | − | 30.0000i | − | 1.50946i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −15.5885 | − | 9.00000i | −0.782362 | − | 0.451697i | 0.0549046 | − | 0.998492i | \(-0.482515\pi\) |
−0.837267 | + | 0.546795i | \(0.815848\pi\) | |||||||
\(398\) | − | 20.0000i | − | 1.00251i | ||||||
\(399\) | 9.00000 | − | 15.5885i | 0.450564 | − | 0.780399i | ||||
\(400\) | 2.00000 | + | 3.46410i | 0.100000 | + | 0.173205i | ||||
\(401\) | 25.9808 | − | 15.0000i | 1.29742 | − | 0.749064i | 0.317460 | − | 0.948272i | \(-0.397170\pi\) |
0.979957 | + | 0.199207i | \(0.0638367\pi\) | |||||||
\(402\) | −12.0000 | −0.598506 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | −2.59808 | + | 1.50000i | −0.129099 | + | 0.0745356i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 3.00000i | 0.148522i | ||||||||
\(409\) | 5.19615 | + | 3.00000i | 0.256933 | + | 0.148340i | 0.622935 | − | 0.782274i | \(-0.285940\pi\) |
−0.366002 | + | 0.930614i | \(0.619274\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 18.0000i | − | 0.887875i | ||||||
\(412\) | 7.00000 | − | 12.1244i | 0.344865 | − | 0.597324i | ||||
\(413\) | −9.00000 | − | 15.5885i | −0.442861 | − | 0.767058i | ||||
\(414\) | 10.3923 | − | 6.00000i | 0.510754 | − | 0.294884i | ||||
\(415\) | 18.0000 | 0.883585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.00000 | −0.244851 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.50000 | − | 12.9904i | −0.366399 | − | 0.634622i | 0.622601 | − | 0.782540i | \(-0.286076\pi\) |
−0.989000 | + | 0.147918i | \(0.952743\pi\) | |||||||
\(420\) | −4.50000 | + | 7.79423i | −0.219578 | + | 0.380319i | ||||
\(421\) | − | 15.0000i | − | 0.731055i | −0.930800 | − | 0.365528i | \(-0.880889\pi\) | ||
0.930800 | − | 0.365528i | \(-0.119111\pi\) | |||||||
\(422\) | 19.9186 | + | 11.5000i | 0.969622 | + | 0.559811i | ||||
\(423\) | 5.19615 | + | 3.00000i | 0.252646 | + | 0.145865i | ||||
\(424\) | 6.00000i | 0.291386i | ||||||||
\(425\) | 6.00000 | − | 10.3923i | 0.291043 | − | 0.504101i | ||||
\(426\) | −7.50000 | − | 12.9904i | −0.363376 | − | 0.629386i | ||||
\(427\) | −20.7846 | + | 12.0000i | −1.00584 | + | 0.580721i | ||||
\(428\) | 12.0000 | 0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | −0.144673 | ||||||||
\(431\) | −12.9904 | + | 7.50000i | −0.625725 | + | 0.361262i | −0.779094 | − | 0.626907i | \(-0.784321\pi\) |
0.153370 | + | 0.988169i | \(0.450987\pi\) | |||||||
\(432\) | −2.50000 | − | 4.33013i | −0.120281 | − | 0.208333i | ||||
\(433\) | 5.50000 | − | 9.52628i | 0.264313 | − | 0.457804i | −0.703070 | − | 0.711120i | \(-0.748188\pi\) |
0.967383 | + | 0.253317i | \(0.0815214\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.79423 | + | 4.50000i | 0.373276 | + | 0.215511i | ||||
\(437\) | 36.0000i | 1.72211i | ||||||||
\(438\) | −3.00000 | + | 5.19615i | −0.143346 | + | 0.248282i | ||||
\(439\) | 5.00000 | + | 8.66025i | 0.238637 | + | 0.413331i | 0.960323 | − | 0.278889i | \(-0.0899661\pi\) |
−0.721686 | + | 0.692220i | \(0.756633\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.00000 | 0.190476 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.0000 | −0.997740 | −0.498870 | − | 0.866677i | \(-0.666252\pi\) | ||||
−0.498870 | + | 0.866677i | \(0.666252\pi\) | |||||||
\(444\) | 2.59808 | − | 1.50000i | 0.123299 | − | 0.0711868i | ||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | −4.50000 | + | 7.79423i | −0.213081 | + | 0.369067i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 2.59808 | + | 1.50000i | 0.122748 | + | 0.0708683i | ||||
\(449\) | −20.7846 | − | 12.0000i | −0.980886 | − | 0.566315i | −0.0783487 | − | 0.996926i | \(-0.524965\pi\) |
−0.902538 | + | 0.430611i | \(0.858298\pi\) | |||||||
\(450\) | 8.00000i | 0.377124i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.00000 | − | 5.19615i | −0.141108 | − | 0.244406i | ||||
\(453\) | 12.9904 | − | 7.50000i | 0.610341 | − | 0.352381i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | 0.280976 | ||||||||
\(457\) | 15.5885 | − | 9.00000i | 0.729197 | − | 0.421002i | −0.0889312 | − | 0.996038i | \(-0.528345\pi\) |
0.818128 | + | 0.575036i | \(0.195012\pi\) | |||||||
\(458\) | 4.50000 | + | 7.79423i | 0.210271 | + | 0.364200i | ||||
\(459\) | −7.50000 | + | 12.9904i | −0.350070 | + | 0.606339i | ||||
\(460\) | − | 18.0000i | − | 0.839254i | ||||||
\(461\) | 12.9904 | + | 7.50000i | 0.605022 | + | 0.349310i | 0.771015 | − | 0.636817i | \(-0.219749\pi\) |
−0.165992 | + | 0.986127i | \(0.553083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.0000i | − | 1.11537i | −0.830051 | − | 0.557687i | \(-0.811689\pi\) | ||
0.830051 | − | 0.557687i | \(-0.188311\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.1865 | + | 10.5000i | −0.842475 | + | 0.486403i | ||||
\(467\) | −12.0000 | −0.555294 | −0.277647 | − | 0.960683i | \(-0.589555\pi\) | ||||
−0.277647 | + | 0.960683i | \(0.589555\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 36.0000 | 1.66233 | ||||||||
\(470\) | 7.79423 | − | 4.50000i | 0.359521 | − | 0.207570i | ||||
\(471\) | −11.0000 | − | 19.0526i | −0.506853 | − | 0.877896i | ||||
\(472\) | 3.00000 | − | 5.19615i | 0.138086 | − | 0.239172i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 8.66025 | + | 5.00000i | 0.397779 | + | 0.229658i | ||||
\(475\) | −20.7846 | − | 12.0000i | −0.953663 | − | 0.550598i | ||||
\(476\) | − | 9.00000i | − | 0.412514i | ||||||
\(477\) | −6.00000 | + | 10.3923i | −0.274721 | + | 0.475831i | ||||
\(478\) | 4.50000 | + | 7.79423i | 0.205825 | + | 0.356500i | ||||
\(479\) | 33.7750 | − | 19.5000i | 1.54322 | − | 0.890978i | 0.544586 | − | 0.838705i | \(-0.316687\pi\) |
0.998633 | − | 0.0522726i | \(-0.0166465\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 30.0000 | 1.36646 | ||||||||
\(483\) | 15.5885 | − | 9.00000i | 0.709299 | − | 0.409514i | ||||
\(484\) | 5.50000 | + | 9.52628i | 0.250000 | + | 0.433013i | ||||
\(485\) | 18.0000 | − | 31.1769i | 0.817338 | − | 1.41567i | ||||
\(486\) | − | 16.0000i | − | 0.725775i | ||||||
\(487\) | 10.3923 | + | 6.00000i | 0.470920 | + | 0.271886i | 0.716625 | − | 0.697459i | \(-0.245686\pi\) |
−0.245705 | + | 0.969345i | \(0.579019\pi\) | |||||||
\(488\) | −6.92820 | − | 4.00000i | −0.313625 | − | 0.181071i | ||||
\(489\) | − | 6.00000i | − | 0.271329i | ||||||
\(490\) | 3.00000 | − | 5.19615i | 0.135526 | − | 0.234738i | ||||
\(491\) | −13.5000 | − | 23.3827i | −0.609246 | − | 1.05525i | −0.991365 | − | 0.131132i | \(-0.958139\pi\) |
0.382118 | − | 0.924113i | \(-0.375195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.5000 | + | 38.9711i | 1.00926 | + | 1.74809i | ||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | − | 36.0000i | − | 1.61158i | −0.592200 | − | 0.805791i | \(-0.701741\pi\) | ||
0.592200 | − | 0.805791i | \(-0.298259\pi\) | |||||||
\(500\) | −2.59808 | − | 1.50000i | −0.116190 | − | 0.0670820i | ||||
\(501\) | −10.3923 | − | 6.00000i | −0.464294 | − | 0.268060i | ||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 3.00000 | − | 5.19615i | 0.133763 | − | 0.231685i | −0.791361 | − | 0.611349i | \(-0.790627\pi\) |
0.925124 | + | 0.379664i | \(0.123960\pi\) | |||||||
\(504\) | 3.00000 | + | 5.19615i | 0.133631 | + | 0.231455i | ||||
\(505\) | −31.1769 | + | 18.0000i | −1.38735 | + | 0.800989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | −5.19615 | + | 3.00000i | −0.230315 | + | 0.132973i | −0.610718 | − | 0.791849i | \(-0.709119\pi\) |
0.380402 | + | 0.924821i | \(0.375786\pi\) | |||||||
\(510\) | 4.50000 | + | 7.79423i | 0.199263 | + | 0.345134i | ||||
\(511\) | 9.00000 | − | 15.5885i | 0.398137 | − | 0.689593i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 25.9808 | + | 15.0000i | 1.14708 | + | 0.662266i | ||||
\(514\) | −2.59808 | − | 1.50000i | −0.114596 | − | 0.0661622i | ||||
\(515\) | − | 42.0000i | − | 1.85074i | ||||||
\(516\) | 0.500000 | − | 0.866025i | 0.0220113 | − | 0.0381246i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −7.79423 | + | 4.50000i | −0.342459 | + | 0.197719i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0000 | 1.18289 | 0.591446 | − | 0.806345i | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.00000 | + | 13.8564i | 0.349816 | + | 0.605898i | 0.986216 | − | 0.165460i | \(-0.0529109\pi\) |
−0.636401 | + | 0.771358i | \(0.719578\pi\) | |||||||
\(524\) | −1.50000 | + | 2.59808i | −0.0655278 | + | 0.113497i | ||||
\(525\) | 12.0000i | 0.523723i | ||||||||
\(526\) | −20.7846 | − | 12.0000i | −0.906252 | − | 0.523225i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 9.00000 | + | 15.5885i | 0.390935 | + | 0.677119i | ||||
\(531\) | 10.3923 | − | 6.00000i | 0.450988 | − | 0.260378i | ||||
\(532\) | −18.0000 | −0.780399 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −6.00000 | −0.259645 | ||||||||
\(535\) | 31.1769 | − | 18.0000i | 1.34790 | − | 0.778208i | ||||
\(536\) | 6.00000 | + | 10.3923i | 0.259161 | + | 0.448879i | ||||
\(537\) | 7.50000 | − | 12.9904i | 0.323649 | − | 0.560576i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.9904 | − | 7.50000i | −0.559017 | − | 0.322749i | ||||
\(541\) | − | 15.0000i | − | 0.644900i | −0.946586 | − | 0.322450i | \(-0.895494\pi\) | ||
0.946586 | − | 0.322450i | \(-0.104506\pi\) | |||||||
\(542\) | 7.50000 | − | 12.9904i | 0.322153 | − | 0.557985i | ||||
\(543\) | 1.00000 | + | 1.73205i | 0.0429141 | + | 0.0743294i | ||||
\(544\) | 2.59808 | − | 1.50000i | 0.111392 | − | 0.0643120i | ||||
\(545\) | 27.0000 | 1.15655 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.0000 | −1.58201 | −0.791003 | − | 0.611812i | \(-0.790441\pi\) | ||||
−0.791003 | + | 0.611812i | \(0.790441\pi\) | |||||||
\(548\) | −15.5885 | + | 9.00000i | −0.665906 | + | 0.384461i | ||||
\(549\) | −8.00000 | − | 13.8564i | −0.341432 | − | 0.591377i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 5.19615 | + | 3.00000i | 0.221163 | + | 0.127688i | ||||
\(553\) | −25.9808 | − | 15.0000i | −1.10481 | − | 0.637865i | ||||
\(554\) | 8.00000i | 0.339887i | ||||||||
\(555\) | 4.50000 | − | 7.79423i | 0.191014 | − | 0.330847i | ||||
\(556\) | 2.50000 | + | 4.33013i | 0.106024 | + | 0.183638i | ||||
\(557\) | −23.3827 | + | 13.5000i | −0.990756 | + | 0.572013i | −0.905500 | − | 0.424346i | \(-0.860504\pi\) |
−0.0852559 | + | 0.996359i | \(0.527171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 9.00000 | 0.380319 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0000 | − | 25.9808i | −0.632737 | − | 1.09593i | ||||
\(563\) | −19.5000 | + | 33.7750i | −0.821827 | + | 1.42345i | 0.0824933 | + | 0.996592i | \(0.473712\pi\) |
−0.904320 | + | 0.426855i | \(0.859622\pi\) | |||||||
\(564\) | 3.00000i | 0.126323i | ||||||||
\(565\) | −15.5885 | − | 9.00000i | −0.655811 | − | 0.378633i | ||||
\(566\) | −3.46410 | − | 2.00000i | −0.145607 | − | 0.0840663i | ||||
\(567\) | 3.00000i | 0.125988i | ||||||||
\(568\) | −7.50000 | + | 12.9904i | −0.314693 | + | 0.545064i | ||||
\(569\) | −22.5000 | − | 38.9711i | −0.943249 | − | 1.63376i | −0.759220 | − | 0.650835i | \(-0.774419\pi\) |
−0.184030 | − | 0.982921i | \(-0.558914\pi\) | |||||||
\(570\) | 15.5885 | − | 9.00000i | 0.652929 | − | 0.376969i | ||||
\(571\) | −23.0000 | −0.962520 | −0.481260 | − | 0.876578i | \(-0.659821\pi\) | ||||
−0.481260 | + | 0.876578i | \(0.659821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | − | 20.7846i | −0.500435 | − | 0.866778i | ||||
\(576\) | −1.00000 | + | 1.73205i | −0.0416667 | + | 0.0721688i | ||||
\(577\) | − | 42.0000i | − | 1.74848i | −0.485491 | − | 0.874241i | \(-0.661359\pi\) | ||
0.485491 | − | 0.874241i | \(-0.338641\pi\) | |||||||
\(578\) | 6.92820 | + | 4.00000i | 0.288175 | + | 0.166378i | ||||
\(579\) | 5.19615 | + | 3.00000i | 0.215945 | + | 0.124676i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.00000 | − | 15.5885i | 0.373383 | − | 0.646718i | ||||
\(582\) | 6.00000 | + | 10.3923i | 0.248708 | + | 0.430775i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | 0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.00000 | 0.371787 | ||||||||
\(587\) | 15.5885 | − | 9.00000i | 0.643404 | − | 0.371470i | −0.142520 | − | 0.989792i | \(-0.545521\pi\) |
0.785925 | + | 0.618322i | \(0.212187\pi\) | |||||||
\(588\) | 1.00000 | + | 1.73205i | 0.0412393 | + | 0.0714286i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | − | 18.0000i | − | 0.741048i | ||||||
\(591\) | 2.59808 | + | 1.50000i | 0.106871 | + | 0.0617018i | ||||
\(592\) | −2.59808 | − | 1.50000i | −0.106780 | − | 0.0616496i | ||||
\(593\) | 36.0000i | 1.47834i | 0.673517 | + | 0.739171i | \(0.264783\pi\) | ||||
−0.673517 | + | 0.739171i | \(0.735217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.5000 | − | 23.3827i | −0.553446 | − | 0.958597i | ||||
\(596\) | 5.19615 | − | 3.00000i | 0.212843 | − | 0.122885i | ||||
\(597\) | 20.0000 | 0.818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | −3.46410 | + | 2.00000i | −0.141421 | + | 0.0816497i | ||||
\(601\) | −18.5000 | − | 32.0429i | −0.754631 | − | 1.30706i | −0.945558 | − | 0.325455i | \(-0.894483\pi\) |
0.190927 | − | 0.981604i | \(-0.438851\pi\) | |||||||
\(602\) | −1.50000 | + | 2.59808i | −0.0611354 | + | 0.105890i | ||||
\(603\) | 24.0000i | 0.977356i | ||||||||
\(604\) | −12.9904 | − | 7.50000i | −0.528571 | − | 0.305171i | ||||
\(605\) | 28.5788 | + | 16.5000i | 1.16190 | + | 0.670820i | ||||
\(606\) | − | 12.0000i | − | 0.487467i | ||||||
\(607\) | 11.0000 | − | 19.0526i | 0.446476 | − | 0.773320i | −0.551678 | − | 0.834058i | \(-0.686012\pi\) |
0.998154 | + | 0.0607380i | \(0.0193454\pi\) | |||||||
\(608\) | −3.00000 | − | 5.19615i | −0.121666 | − | 0.210732i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0000 | −0.971732 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.00000 | 0.242536 | ||||||||
\(613\) | 5.19615 | − | 3.00000i | 0.209871 | − | 0.121169i | −0.391381 | − | 0.920229i | \(-0.628002\pi\) |
0.601251 | + | 0.799060i | \(0.294669\pi\) | |||||||
\(614\) | 9.00000 | + | 15.5885i | 0.363210 | + | 0.629099i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.3923 | + | 6.00000i | 0.418378 | + | 0.241551i | 0.694383 | − | 0.719605i | \(-0.255677\pi\) |
−0.276005 | + | 0.961156i | \(0.589011\pi\) | |||||||
\(618\) | 12.1244 | + | 7.00000i | 0.487713 | + | 0.281581i | ||||
\(619\) | 24.0000i | 0.964641i | 0.875995 | + | 0.482321i | \(0.160206\pi\) | ||||
−0.875995 | + | 0.482321i | \(0.839794\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.0000 | + | 25.9808i | 0.601929 | + | 1.04257i | ||||
\(622\) | −15.5885 | + | 9.00000i | −0.625040 | + | 0.360867i | ||||
\(623\) | 18.0000 | 0.721155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 16.4545 | − | 9.50000i | 0.657653 | − | 0.379696i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.0000 | + | 19.0526i | −0.438948 | + | 0.760280i | ||||
\(629\) | 9.00000i | 0.358854i | ||||||||
\(630\) | 15.5885 | + | 9.00000i | 0.621059 | + | 0.358569i | ||||
\(631\) | 12.9904 | + | 7.50000i | 0.517139 | + | 0.298570i | 0.735763 | − | 0.677239i | \(-0.236824\pi\) |
−0.218624 | + | 0.975809i | \(0.570157\pi\) | |||||||
\(632\) | − | 10.0000i | − | 0.397779i | ||||||
\(633\) | −11.5000 | + | 19.9186i | −0.457084 | + | 0.791693i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | 5.19615 | − | 3.00000i | 0.206203 | − | 0.119051i | ||||
\(636\) | −6.00000 | −0.237915 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −25.9808 | + | 15.0000i | −1.02778 | + | 0.593391i | ||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | −31.1769 | − | 18.0000i | −1.22950 | − | 0.709851i | −0.262573 | − | 0.964912i | \(-0.584571\pi\) |
−0.966925 | + | 0.255062i | \(0.917904\pi\) | |||||||
\(644\) | −15.5885 | − | 9.00000i | −0.614271 | − | 0.354650i | ||||
\(645\) | − | 3.00000i | − | 0.118125i | ||||||
\(646\) | −9.00000 | + | 15.5885i | −0.354100 | + | 0.613320i | ||||
\(647\) | 21.0000 | + | 36.3731i | 0.825595 | + | 1.42997i | 0.901464 | + | 0.432855i | \(0.142494\pi\) |
−0.0758684 | + | 0.997118i | \(0.524173\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −5.19615 | + | 3.00000i | −0.203497 | + | 0.117489i | ||||
\(653\) | 18.0000 | + | 31.1769i | 0.704394 | + | 1.22005i | 0.966910 | + | 0.255119i | \(0.0821147\pi\) |
−0.262515 | + | 0.964928i | \(0.584552\pi\) | |||||||
\(654\) | −4.50000 | + | 7.79423i | −0.175964 | + | 0.304778i | ||||
\(655\) | 9.00000i | 0.351659i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.3923 | + | 6.00000i | 0.405442 | + | 0.234082i | ||||
\(658\) | − | 9.00000i | − | 0.350857i | ||||||
\(659\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.9808 | − | 15.0000i | 1.01053 | − | 0.583432i | 0.0991864 | − | 0.995069i | \(-0.468376\pi\) |
0.911348 | + | 0.411636i | \(0.135043\pi\) | |||||||
\(662\) | −30.0000 | −1.16598 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | −46.7654 | + | 27.0000i | −1.81348 | + | 1.04702i | ||||
\(666\) | −3.00000 | − | 5.19615i | −0.116248 | − | 0.201347i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 12.0000i | 0.464294i | ||||||||
\(669\) | −7.79423 | − | 4.50000i | −0.301342 | − | 0.173980i | ||||
\(670\) | 31.1769 | + | 18.0000i | 1.20447 | + | 0.695401i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.50000 | + | 2.59808i | −0.0578638 | + | 0.100223i | ||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | 11.2583 | − | 6.50000i | 0.433655 | − | 0.250371i | ||||
\(675\) | −20.0000 | −0.769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 5.19615 | − | 3.00000i | 0.199557 | − | 0.115214i | ||||
\(679\) | −18.0000 | − | 31.1769i | −0.690777 | − | 1.19646i | ||||
\(680\) | 4.50000 | − | 7.79423i | 0.172567 | − | 0.298895i | ||||
\(681\) | 12.0000i | 0.459841i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.19615 | − | 3.00000i | −0.198825 | − | 0.114792i | 0.397282 | − | 0.917697i | \(-0.369953\pi\) |
−0.596107 | + | 0.802905i | \(0.703287\pi\) | |||||||
\(684\) | − | 12.0000i | − | 0.458831i | ||||||
\(685\) | −27.0000 | + | 46.7654i | −1.03162 | + | 1.78681i | ||||
\(686\) | 7.50000 | + | 12.9904i | 0.286351 | + | 0.495975i | ||||
\(687\) | −7.79423 | + | 4.50000i | −0.297368 | + | 0.171686i | ||||
\(688\) | −1.00000 | −0.0381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.0000 | 0.685248 | ||||||||
\(691\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(692\) | −3.00000 | − | 5.19615i | −0.114043 | − | 0.197528i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.0000i | 1.25266i | ||||||||
\(695\) | 12.9904 | + | 7.50000i | 0.492753 | + | 0.284491i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −10.5000 | + | 18.1865i | −0.397431 | + | 0.688370i | ||||
\(699\) | −10.5000 | − | 18.1865i | −0.397146 | − | 0.687878i | ||||
\(700\) | 10.3923 | − | 6.00000i | 0.392792 | − | 0.226779i | ||||
\(701\) | 42.0000 | 1.58632 | 0.793159 | − | 0.609015i | \(-0.208435\pi\) | ||||
0.793159 | + | 0.609015i | \(0.208435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.50000 | + | 7.79423i | 0.169480 | + | 0.293548i | ||||
\(706\) | 3.00000 | − | 5.19615i | 0.112906 | − | 0.195560i | ||||
\(707\) | 36.0000i | 1.35392i | ||||||||
\(708\) | 5.19615 | + | 3.00000i | 0.195283 | + | 0.112747i | ||||
\(709\) | 5.19615 | + | 3.00000i | 0.195146 | + | 0.112667i | 0.594389 | − | 0.804178i | \(-0.297394\pi\) |
−0.399244 | + | 0.916845i | \(0.630727\pi\) | |||||||
\(710\) | 45.0000i | 1.68882i | ||||||||
\(711\) | 10.0000 | − | 17.3205i | 0.375029 | − | 0.649570i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 9.00000 | 0.336817 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.0000 | −0.560576 | ||||||||
\(717\) | −7.79423 | + | 4.50000i | −0.291081 | + | 0.168056i | ||||
\(718\) | 12.0000 | + | 20.7846i | 0.447836 | + | 0.775675i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 6.00000i | 0.223607i | ||||||||
\(721\) | −36.3731 | − | 21.0000i | −1.35460 | − | 0.782081i | ||||
\(722\) | 14.7224 | + | 8.50000i | 0.547912 | + | 0.316337i | ||||
\(723\) | 30.0000i | 1.11571i | ||||||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.52628 | + | 5.50000i | −0.353553 | + | 0.204124i | ||||
\(727\) | 28.0000 | 1.03846 | 0.519231 | − | 0.854634i | \(-0.326218\pi\) | ||||
0.519231 | + | 0.854634i | \(0.326218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 15.5885 | − | 9.00000i | 0.576955 | − | 0.333105i | ||||
\(731\) | 1.50000 | + | 2.59808i | 0.0554795 | + | 0.0960933i | ||||
\(732\) | 4.00000 | − | 6.92820i | 0.147844 | − | 0.256074i | ||||
\(733\) | − | 9.00000i | − | 0.332423i | −0.986090 | − | 0.166211i | \(-0.946847\pi\) | ||
0.986090 | − | 0.166211i | \(-0.0531534\pi\) | |||||||
\(734\) | −6.92820 | − | 4.00000i | −0.255725 | − | 0.147643i | ||||
\(735\) | 5.19615 | + | 3.00000i | 0.191663 | + | 0.110657i | ||||
\(736\) | − | 6.00000i | − | 0.221163i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.1769 | + | 18.0000i | −1.14686 | + | 0.662141i | −0.948120 | − | 0.317911i | \(-0.897019\pi\) |
−0.198741 | + | 0.980052i | \(0.563685\pi\) | |||||||
\(740\) | −9.00000 | −0.330847 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.0000 | 0.660801 | ||||||||
\(743\) | −33.7750 | + | 19.5000i | −1.23908 | + | 0.715386i | −0.968907 | − | 0.247425i | \(-0.920416\pi\) |
−0.270177 | + | 0.962811i | \(0.587082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | − | 15.5885i | 0.329734 | − | 0.571117i | ||||
\(746\) | 4.00000i | 0.146450i | ||||||||
\(747\) | 10.3923 | + | 6.00000i | 0.380235 | + | 0.219529i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 36.0000i | − | 1.31541i | ||||||
\(750\) | 1.50000 | − | 2.59808i | 0.0547723 | − | 0.0948683i | ||||
\(751\) | −16.0000 | − | 27.7128i | −0.583848 | − | 1.01125i | −0.995018 | − | 0.0996961i | \(-0.968213\pi\) |
0.411170 | − | 0.911559i | \(-0.365120\pi\) | |||||||
\(752\) | 2.59808 | − | 1.50000i | 0.0947421 | − | 0.0546994i | ||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.0000 | −1.63772 | ||||||||
\(756\) | −12.9904 | + | 7.50000i | −0.472456 | + | 0.272772i | ||||
\(757\) | 1.00000 | + | 1.73205i | 0.0363456 | + | 0.0629525i | 0.883626 | − | 0.468193i | \(-0.155095\pi\) |
−0.847280 | + | 0.531146i | \(0.821762\pi\) | |||||||
\(758\) | −3.00000 | + | 5.19615i | −0.108965 | + | 0.188733i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −15.5885 | − | 9.00000i | −0.565453 | − | 0.326464i | ||||
\(761\) | 25.9808 | + | 15.0000i | 0.941802 | + | 0.543750i | 0.890525 | − | 0.454935i | \(-0.150337\pi\) |
0.0512772 | + | 0.998684i | \(0.483671\pi\) | |||||||
\(762\) | 2.00000i | 0.0724524i | ||||||||
\(763\) | 13.5000 | − | 23.3827i | 0.488733 | − | 0.846510i | ||||
\(764\) | 6.00000 | + | 10.3923i | 0.217072 | + | 0.375980i | ||||
\(765\) | 15.5885 | − | 9.00000i | 0.563602 | − | 0.325396i | ||||
\(766\) | 9.00000 | 0.325183 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 20.7846 | − | 12.0000i | 0.749512 | − | 0.432731i | −0.0760054 | − | 0.997107i | \(-0.524217\pi\) |
0.825518 | + | 0.564376i | \(0.190883\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.50000 | − | 2.59808i | 0.0540212 | − | 0.0935674i | ||||
\(772\) | − | 6.00000i | − | 0.215945i | ||||||
\(773\) | −18.1865 | − | 10.5000i | −0.654124 | − | 0.377659i | 0.135910 | − | 0.990721i | \(-0.456604\pi\) |
−0.790034 | + | 0.613062i | \(0.789937\pi\) | |||||||
\(774\) | −1.73205 | − | 1.00000i | −0.0622573 | − | 0.0359443i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.00000 | − | 10.3923i | 0.215387 | − | 0.373062i | ||||
\(777\) | −4.50000 | − | 7.79423i | −0.161437 | − | 0.279616i | ||||
\(778\) | −25.9808 | + | 15.0000i | −0.931455 | + | 0.537776i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −15.5885 | + | 9.00000i | −0.557442 | + | 0.321839i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | − | 1.73205i | 0.0357143 | − | 0.0618590i | ||||
\(785\) | 66.0000i | 2.35564i | ||||||||
\(786\) | −2.59808 | − | 1.50000i | −0.0926703 | − | 0.0535032i | ||||
\(787\) | 10.3923 | + | 6.00000i | 0.370446 | + | 0.213877i | 0.673653 | − | 0.739048i | \(-0.264724\pi\) |
−0.303207 | + | 0.952925i | \(0.598058\pi\) | |||||||
\(788\) | − | 3.00000i | − | 0.106871i | ||||||
\(789\) | 12.0000 | − | 20.7846i | 0.427211 | − | 0.739952i | ||||
\(790\) | −15.0000 | − | 25.9808i | −0.533676 | − | 0.924354i | ||||
\(791\) | −15.5885 | + | 9.00000i | −0.554262 | + | 0.320003i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −18.0000 | −0.638796 | ||||||||
\(795\) | −15.5885 | + | 9.00000i | −0.552866 | + | 0.319197i | ||||
\(796\) | −10.0000 | − | 17.3205i | −0.354441 | − | 0.613909i | ||||
\(797\) | −9.00000 | + | 15.5885i | −0.318796 | + | 0.552171i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749997i | \(0.269945\pi\) | |||||||
\(798\) | − | 18.0000i | − | 0.637193i | ||||||
\(799\) | −7.79423 | − | 4.50000i | −0.275740 | − | 0.159199i | ||||
\(800\) | 3.46410 | + | 2.00000i | 0.122474 | + | 0.0707107i | ||||
\(801\) | 12.0000i | 0.423999i | ||||||||
\(802\) | 15.0000 | − | 25.9808i | 0.529668 | − | 0.917413i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −10.3923 | + | 6.00000i | −0.366508 | + | 0.211604i | ||||
\(805\) | −54.0000 | −1.90325 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −10.3923 | + | 6.00000i | −0.365600 | + | 0.211079i | ||||
\(809\) | −7.50000 | − | 12.9904i | −0.263686 | − | 0.456717i | 0.703533 | − | 0.710663i | \(-0.251605\pi\) |
−0.967219 | + | 0.253946i | \(0.918272\pi\) | |||||||
\(810\) | −1.50000 | + | 2.59808i | −0.0527046 | + | 0.0912871i | ||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.9904 | + | 7.50000i | 0.455593 | + | 0.263036i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.00000 | + | 15.5885i | −0.315256 | + | 0.546040i | ||||
\(816\) | 1.50000 | + | 2.59808i | 0.0525105 | + | 0.0909509i | ||||
\(817\) | 5.19615 | − | 3.00000i | 0.181790 | − | 0.104957i | ||||
\(818\) | 6.00000 | 0.209785 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.9711 | − | 22.5000i | 1.36010 | − | 0.785255i | 0.370465 | − | 0.928846i | \(-0.379198\pi\) |
0.989637 | + | 0.143591i | \(0.0458650\pi\) | |||||||
\(822\) | −9.00000 | − | 15.5885i | −0.313911 | − | 0.543710i | ||||
\(823\) | −7.00000 | + | 12.1244i | −0.244005 | + | 0.422628i | −0.961851 | − | 0.273573i | \(-0.911795\pi\) |
0.717847 | + | 0.696201i | \(0.245128\pi\) | |||||||
\(824\) | − | 14.0000i | − | 0.487713i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.5885 | − | 9.00000i | −0.542392 | − | 0.313150i | ||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | 6.00000 | − | 10.3923i | 0.208514 | − | 0.361158i | ||||
\(829\) | 10.0000 | + | 17.3205i | 0.347314 | + | 0.601566i | 0.985771 | − | 0.168091i | \(-0.0537604\pi\) |
−0.638457 | + | 0.769657i | \(0.720427\pi\) | |||||||
\(830\) | 15.5885 | − | 9.00000i | 0.541083 | − | 0.312395i | ||||
\(831\) | −8.00000 | −0.277517 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | −4.33013 | + | 2.50000i | −0.149940 | + | 0.0865679i | ||||
\(835\) | 18.0000 | + | 31.1769i | 0.622916 | + | 1.07892i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.9904 | − | 7.50000i | −0.448745 | − | 0.259083i | ||||
\(839\) | −20.7846 | − | 12.0000i | −0.717564 | − | 0.414286i | 0.0962912 | − | 0.995353i | \(-0.469302\pi\) |
−0.813856 | + | 0.581067i | \(0.802635\pi\) | |||||||
\(840\) | 9.00000i | 0.310530i | ||||||||
\(841\) | 14.5000 | − | 25.1147i | 0.500000 | − | 0.866025i | ||||
\(842\) | −7.50000 | − | 12.9904i | −0.258467 | − | 0.447678i | ||||
\(843\) | 25.9808 | − | 15.0000i | 0.894825 | − | 0.516627i | ||||
\(844\) | 23.0000 | 0.791693 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 28.5788 | − | 16.5000i | 0.981981 | − | 0.566947i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 2.00000 | − | 3.46410i | 0.0686398 | − | 0.118888i | ||||
\(850\) | − | 12.0000i | − | 0.411597i | ||||||
\(851\) | 15.5885 | + | 9.00000i | 0.534365 | + | 0.308516i | ||||
\(852\) | −12.9904 | − | 7.50000i | −0.445043 | − | 0.256946i | ||||
\(853\) | − | 39.0000i | − | 1.33533i | −0.744460 | − | 0.667667i | \(-0.767293\pi\) | ||
0.744460 | − | 0.667667i | \(-0.232707\pi\) | |||||||
\(854\) | −12.0000 | + | 20.7846i | −0.410632 | + | 0.711235i | ||||
\(855\) | −18.0000 | − | 31.1769i | −0.615587 | − | 1.06623i | ||||
\(856\) | 10.3923 | − | 6.00000i | 0.355202 | − | 0.205076i | ||||
\(857\) | 18.0000 | 0.614868 | 0.307434 | − | 0.951569i | \(-0.400530\pi\) | ||||
0.307434 | + | 0.951569i | \(0.400530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.0000 | 1.36478 | 0.682391 | − | 0.730987i | \(-0.260940\pi\) | ||||
0.682391 | + | 0.730987i | \(0.260940\pi\) | |||||||
\(860\) | −2.59808 | + | 1.50000i | −0.0885937 | + | 0.0511496i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7.50000 | + | 12.9904i | −0.255451 | + | 0.442454i | ||||
\(863\) | − | 39.0000i | − | 1.32758i | −0.747921 | − | 0.663788i | \(-0.768948\pi\) | ||
0.747921 | − | 0.663788i | \(-0.231052\pi\) | |||||||
\(864\) | −4.33013 | − | 2.50000i | −0.147314 | − | 0.0850517i | ||||
\(865\) | −15.5885 | − | 9.00000i | −0.530023 | − | 0.306009i | ||||
\(866\) | − | 11.0000i | − | 0.373795i | ||||||
\(867\) | −4.00000 | + | 6.92820i | −0.135847 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 9.00000 | 0.304778 | ||||||||
\(873\) | 20.7846 | − | 12.0000i | 0.703452 | − | 0.406138i | ||||
\(874\) | 18.0000 | + | 31.1769i | 0.608859 | + | 1.05457i | ||||
\(875\) | −4.50000 | + | 7.79423i | −0.152128 | + | 0.263493i | ||||
\(876\) | 6.00000i | 0.202721i | ||||||||
\(877\) | −2.59808 | − | 1.50000i | −0.0877308 | − | 0.0506514i | 0.455493 | − | 0.890239i | \(-0.349463\pi\) |
−0.543224 | + | 0.839588i | \(0.682796\pi\) | |||||||
\(878\) | 8.66025 | + | 5.00000i | 0.292269 | + | 0.168742i | ||||
\(879\) | 9.00000i | 0.303562i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.5000 | + | 28.5788i | 0.555899 | + | 0.962846i | 0.997833 | + | 0.0657979i | \(0.0209593\pi\) |
−0.441934 | + | 0.897048i | \(0.645707\pi\) | |||||||
\(882\) | 3.46410 | − | 2.00000i | 0.116642 | − | 0.0673435i | ||||
\(883\) | −11.0000 | −0.370179 | −0.185090 | − | 0.982722i | \(-0.559258\pi\) | ||||
−0.185090 | + | 0.982722i | \(0.559258\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.0000 | 0.605063 | ||||||||
\(886\) | −18.1865 | + | 10.5000i | −0.610989 | + | 0.352754i | ||||
\(887\) | 6.00000 | + | 10.3923i | 0.201460 | + | 0.348939i | 0.948999 | − | 0.315279i | \(-0.102098\pi\) |
−0.747539 | + | 0.664218i | \(0.768765\pi\) | |||||||
\(888\) | 1.50000 | − | 2.59808i | 0.0503367 | − | 0.0871857i | ||||
\(889\) | − | 6.00000i | − | 0.201234i | ||||||
\(890\) | 15.5885 | + | 9.00000i | 0.522526 | + | 0.301681i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.00000i | 0.301342i | ||||||||
\(893\) | −9.00000 | + | 15.5885i | −0.301174 | + | 0.521648i | ||||
\(894\) | 3.00000 | + | 5.19615i | 0.100335 | + | 0.173785i | ||||
\(895\) | −38.9711 | + | 22.5000i | −1.30266 | + | 0.752092i | ||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −24.0000 | −0.800890 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 4.00000 | + | 6.92820i | 0.133333 | + | 0.230940i | ||||
\(901\) | 9.00000 | − | 15.5885i | 0.299833 | − | 0.519327i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.59808 | − | 1.50000i | −0.0864586 | − | 0.0499169i | ||||
\(904\) | −5.19615 | − | 3.00000i | −0.172821 | − | 0.0997785i | ||||
\(905\) | − | 6.00000i | − | 0.199447i | ||||||
\(906\) | 7.50000 | − | 12.9904i | 0.249171 | − | 0.431577i | ||||
\(907\) | 8.50000 | + | 14.7224i | 0.282238 | + | 0.488850i | 0.971936 | − | 0.235247i | \(-0.0755899\pi\) |
−0.689698 | + | 0.724097i | \(0.742257\pi\) | |||||||
\(908\) | 10.3923 | − | 6.00000i | 0.344881 | − | 0.199117i | ||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 5.19615 | − | 3.00000i | 0.172062 | − | 0.0993399i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.00000 | − | 15.5885i | 0.297694 | − | 0.515620i | ||||
\(915\) | − | 24.0000i | − | 0.793416i | ||||||
\(916\) | 7.79423 | + | 4.50000i | 0.257529 | + | 0.148684i | ||||
\(917\) | 7.79423 | + | 4.50000i | 0.257388 | + | 0.148603i | ||||
\(918\) | 15.0000i | 0.495074i | ||||||||
\(919\) | 10.0000 | − | 17.3205i | 0.329870 | − | 0.571351i | −0.652616 | − | 0.757689i | \(-0.726329\pi\) |
0.982486 | + | 0.186338i | \(0.0596619\pi\) | |||||||
\(920\) | −9.00000 | − | 15.5885i | −0.296721 | − | 0.513936i | ||||
\(921\) | −15.5885 | + | 9.00000i | −0.513657 | + | 0.296560i | ||||
\(922\) | 15.0000 | 0.493999 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.3923 | + | 6.00000i | −0.341697 | + | 0.197279i | ||||
\(926\) | −12.0000 | − | 20.7846i | −0.394344 | − | 0.683025i | ||||
\(927\) | 14.0000 | − | 24.2487i | 0.459820 | − | 0.796432i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 31.1769 | + | 18.0000i | 1.02288 | + | 0.590561i | 0.914937 | − | 0.403596i | \(-0.132240\pi\) |
0.107944 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000i | 0.393284i | ||||||||
\(932\) | −10.5000 | + | 18.1865i | −0.343939 | + | 0.595720i | ||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | −10.3923 | + | 6.00000i | −0.340047 | + | 0.196326i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.00000 | −0.0653372 | −0.0326686 | − | 0.999466i | \(-0.510401\pi\) | ||||
−0.0326686 | + | 0.999466i | \(0.510401\pi\) | |||||||
\(938\) | 31.1769 | − | 18.0000i | 1.01796 | − | 0.587721i | ||||
\(939\) | 9.50000 | + | 16.4545i | 0.310021 | + | 0.536972i | ||||
\(940\) | 4.50000 | − | 7.79423i | 0.146774 | − | 0.254220i | ||||
\(941\) | − | 45.0000i | − | 1.46696i | −0.679712 | − | 0.733479i | \(-0.737895\pi\) | ||
0.679712 | − | 0.733479i | \(-0.262105\pi\) | |||||||
\(942\) | −19.0526 | − | 11.0000i | −0.620766 | − | 0.358399i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 6.00000i | − | 0.195283i | ||||||
\(945\) | −22.5000 | + | 38.9711i | −0.731925 | + | 1.26773i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.5692 | − | 24.0000i | 1.35082 | − | 0.779895i | 0.362454 | − | 0.932002i | \(-0.381939\pi\) |
0.988364 | + | 0.152106i | \(0.0486057\pi\) | |||||||
\(948\) | 10.0000 | 0.324785 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −24.0000 | −0.778663 | ||||||||
\(951\) | −15.5885 | + | 9.00000i | −0.505490 | + | 0.291845i | ||||
\(952\) | −4.50000 | − | 7.79423i | −0.145846 | − | 0.252612i | ||||
\(953\) | −4.50000 | + | 7.79423i | −0.145769 | + | 0.252480i | −0.929660 | − | 0.368419i | \(-0.879899\pi\) |
0.783890 | + | 0.620899i | \(0.213232\pi\) | |||||||
\(954\) | 12.0000i | 0.388514i | ||||||||
\(955\) | 31.1769 | + | 18.0000i | 1.00886 | + | 0.582466i | ||||
\(956\) | 7.79423 | + | 4.50000i | 0.252083 | + | 0.145540i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.5000 | − | 33.7750i | 0.630016 | − | 1.09122i | ||||
\(959\) | 27.0000 | + | 46.7654i | 0.871875 | + | 1.51013i | ||||
\(960\) | −2.59808 | + | 1.50000i | −0.0838525 | + | 0.0484123i | ||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.0000 | 0.773389 | ||||||||
\(964\) | 25.9808 | − | 15.0000i | 0.836784 | − | 0.483117i | ||||
\(965\) | −9.00000 | − | 15.5885i | −0.289720 | − | 0.501810i | ||||
\(966\) | 9.00000 | − | 15.5885i | 0.289570 | − | 0.501550i | ||||
\(967\) | 3.00000i | 0.0964735i | 0.998836 | + | 0.0482367i | \(0.0153602\pi\) | ||||
−0.998836 | + | 0.0482367i | \(0.984640\pi\) | |||||||
\(968\) | 9.52628 | + | 5.50000i | 0.306186 | + | 0.176777i | ||||
\(969\) | −15.5885 | − | 9.00000i | −0.500773 | − | 0.289122i | ||||
\(970\) | − | 36.0000i | − | 1.15589i | ||||||
\(971\) | −13.5000 | + | 23.3827i | −0.433236 | + | 0.750386i | −0.997150 | − | 0.0754473i | \(-0.975962\pi\) |
0.563914 | + | 0.825833i | \(0.309295\pi\) | |||||||
\(972\) | −8.00000 | − | 13.8564i | −0.256600 | − | 0.444444i | ||||
\(973\) | 12.9904 | − | 7.50000i | 0.416452 | − | 0.240439i | ||||
\(974\) | 12.0000 | 0.384505 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | −10.3923 | + | 6.00000i | −0.332479 | + | 0.191957i | −0.656941 | − | 0.753942i | \(-0.728150\pi\) |
0.324462 | + | 0.945899i | \(0.394817\pi\) | |||||||
\(978\) | −3.00000 | − | 5.19615i | −0.0959294 | − | 0.166155i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 6.00000i | − | 0.191663i | ||||||
\(981\) | 15.5885 | + | 9.00000i | 0.497701 | + | 0.287348i | ||||
\(982\) | −23.3827 | − | 13.5000i | −0.746171 | − | 0.430802i | ||||
\(983\) | − | 9.00000i | − | 0.287055i | −0.989646 | − | 0.143528i | \(-0.954155\pi\) | ||
0.989646 | − | 0.143528i | \(-0.0458446\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.50000 | − | 7.79423i | −0.143382 | − | 0.248345i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.00000 | 0.286473 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.00000 | − | 1.73205i | −0.0317660 | − | 0.0550204i | 0.849705 | − | 0.527258i | \(-0.176780\pi\) |
−0.881471 | + | 0.472237i | \(0.843446\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30.0000i | − | 0.952021i | ||||||
\(994\) | 38.9711 | + | 22.5000i | 1.23609 | + | 0.713657i | ||||
\(995\) | −51.9615 | − | 30.0000i | −1.64729 | − | 0.951064i | ||||
\(996\) | 6.00000i | 0.190117i | ||||||||
\(997\) | −4.00000 | + | 6.92820i | −0.126681 | + | 0.219418i | −0.922389 | − | 0.386263i | \(-0.873766\pi\) |
0.795708 | + | 0.605681i | \(0.207099\pi\) | |||||||
\(998\) | −18.0000 | − | 31.1769i | −0.569780 | − | 0.986888i | ||||
\(999\) | 12.9904 | − | 7.50000i | 0.410997 | − | 0.237289i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))