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 | 147.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 338.147 |
Dual form | 338.2.e.a.23.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/338\mathbb{Z}\right)^\times\).
\(n\) | \(171\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 3.00000i | 1.34164i | 0.741620 | + | 0.670820i | \(0.234058\pi\) | ||||
−0.741620 | + | 0.670820i | \(0.765942\pi\) | |||||||
\(6\) | 0.866025 | − | 0.500000i | 0.353553 | − | 0.204124i | ||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | −0.654654 | − | 0.755929i | \(-0.727186\pi\) |
0.327327 | + | 0.944911i | \(0.393852\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 1.50000 | − | 2.59808i | 0.474342 | − | 0.821584i | ||||
\(11\) | −5.19615 | − | 3.00000i | −1.56670 | − | 0.904534i | −0.996550 | − | 0.0829925i | \(-0.973552\pi\) |
−0.570149 | − | 0.821541i | \(-0.693114\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −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 | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | − | 2.00000i | − | 0.471405i | ||||||
\(19\) | −1.73205 | + | 1.00000i | −0.397360 | + | 0.229416i | −0.685344 | − | 0.728219i | \(-0.740348\pi\) |
0.287984 | + | 0.957635i | \(0.407015\pi\) | |||||||
\(20\) | −2.59808 | + | 1.50000i | −0.580948 | + | 0.335410i | ||||
\(21\) | − | 1.00000i | − | 0.218218i | ||||||
\(22\) | 3.00000 | + | 5.19615i | 0.639602 | + | 1.10782i | ||||
\(23\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(24\) | 0.866025 | + | 0.500000i | 0.176777 | + | 0.102062i | ||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | −0.866025 | − | 0.500000i | −0.163663 | − | 0.0944911i | ||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | 1.50000 | + | 2.59808i | 0.273861 | + | 0.474342i | ||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 5.19615 | − | 3.00000i | 0.904534 | − | 0.522233i | ||||
\(34\) | 3.00000i | 0.514496i | ||||||||
\(35\) | −1.50000 | − | 2.59808i | −0.253546 | − | 0.439155i | ||||
\(36\) | −1.00000 | + | 1.73205i | −0.166667 | + | 0.288675i | ||||
\(37\) | 6.06218 | + | 3.50000i | 0.996616 | + | 0.575396i | 0.907245 | − | 0.420602i | \(-0.138181\pi\) |
0.0893706 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(38\) | 2.00000 | 0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(42\) | −0.500000 | + | 0.866025i | −0.0771517 | + | 0.133631i | ||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | − | 6.00000i | − | 0.904534i | ||||||
\(45\) | −5.19615 | + | 3.00000i | −0.774597 | + | 0.447214i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | ||||
\(49\) | −3.00000 | + | 5.19615i | −0.428571 | + | 0.742307i | ||||
\(50\) | 3.46410 | + | 2.00000i | 0.489898 | + | 0.282843i | ||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 4.33013 | + | 2.50000i | 0.589256 | + | 0.340207i | ||||
\(55\) | 9.00000 | − | 15.5885i | 1.21356 | − | 2.10195i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | − | 2.00000i | − | 0.264906i | ||||||
\(58\) | 5.19615 | − | 3.00000i | 0.682288 | − | 0.393919i | ||||
\(59\) | −5.19615 | + | 3.00000i | −0.676481 | + | 0.390567i | −0.798528 | − | 0.601958i | \(-0.794388\pi\) |
0.122047 | + | 0.992524i | \(0.461054\pi\) | |||||||
\(60\) | − | 3.00000i | − | 0.387298i | ||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 2.00000 | − | 3.46410i | 0.254000 | − | 0.439941i | ||||
\(63\) | −1.73205 | − | 1.00000i | −0.218218 | − | 0.125988i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | 12.1244 | + | 7.00000i | 1.48123 | + | 0.855186i | 0.999773 | − | 0.0212861i | \(-0.00677610\pi\) |
0.481452 | + | 0.876472i | \(0.340109\pi\) | |||||||
\(68\) | 1.50000 | − | 2.59808i | 0.181902 | − | 0.315063i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.00000i | 0.358569i | ||||||||
\(71\) | 2.59808 | − | 1.50000i | 0.308335 | − | 0.178017i | −0.337846 | − | 0.941201i | \(-0.609698\pi\) |
0.646181 | + | 0.763184i | \(0.276365\pi\) | |||||||
\(72\) | 1.73205 | − | 1.00000i | 0.204124 | − | 0.117851i | ||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | −3.50000 | − | 6.06218i | −0.406867 | − | 0.704714i | ||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | −1.73205 | − | 1.00000i | −0.198680 | − | 0.114708i | ||||
\(77\) | 6.00000 | 0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | 0.900070 | 0.450035 | − | 0.893011i | \(-0.351411\pi\) | ||||
0.450035 | + | 0.893011i | \(0.351411\pi\) | |||||||
\(80\) | −2.59808 | − | 1.50000i | −0.290474 | − | 0.167705i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0.866025 | − | 0.500000i | 0.0944911 | − | 0.0545545i | ||||
\(85\) | 7.79423 | − | 4.50000i | 0.845403 | − | 0.488094i | ||||
\(86\) | 1.00000i | 0.107833i | ||||||||
\(87\) | −3.00000 | − | 5.19615i | −0.321634 | − | 0.557086i | ||||
\(88\) | −3.00000 | + | 5.19615i | −0.319801 | + | 0.553912i | ||||
\(89\) | 5.19615 | + | 3.00000i | 0.550791 | + | 0.317999i | 0.749441 | − | 0.662071i | \(-0.230322\pi\) |
−0.198650 | + | 0.980071i | \(0.563656\pi\) | |||||||
\(90\) | 6.00000 | 0.632456 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.46410 | − | 2.00000i | −0.359211 | − | 0.207390i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 8.66025 | − | 5.00000i | 0.879316 | − | 0.507673i | 0.00888289 | − | 0.999961i | \(-0.497172\pi\) |
0.870433 | + | 0.492287i | \(0.163839\pi\) | |||||||
\(98\) | 5.19615 | − | 3.00000i | 0.524891 | − | 0.303046i | ||||
\(99\) | − | 12.0000i | − | 1.20605i | ||||||
\(100\) | −2.00000 | − | 3.46410i | −0.200000 | − | 0.346410i | ||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | −2.59808 | − | 1.50000i | −0.257248 | − | 0.148522i | ||||
\(103\) | 4.00000 | 0.394132 | 0.197066 | − | 0.980390i | \(-0.436859\pi\) | ||||
0.197066 | + | 0.980390i | \(0.436859\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.00000 | 0.292770 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | −2.50000 | − | 4.33013i | −0.240563 | − | 0.416667i | ||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | −15.5885 | + | 9.00000i | −1.48630 | + | 0.858116i | ||||
\(111\) | −6.06218 | + | 3.50000i | −0.575396 | + | 0.332205i | ||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | −1.00000 | + | 1.73205i | −0.0936586 | + | 0.162221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 2.59808 | + | 1.50000i | 0.238165 | + | 0.137505i | ||||
\(120\) | −1.50000 | + | 2.59808i | −0.136931 | + | 0.237171i | ||||
\(121\) | 12.5000 | + | 21.6506i | 1.13636 | + | 1.96824i | ||||
\(122\) | 8.00000i | 0.724286i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.46410 | + | 2.00000i | −0.311086 | + | 0.179605i | ||||
\(125\) | 3.00000i | 0.268328i | ||||||||
\(126\) | 1.00000 | + | 1.73205i | 0.0890871 | + | 0.154303i | ||||
\(127\) | 10.0000 | − | 17.3205i | 0.887357 | − | 1.53695i | 0.0443678 | − | 0.999015i | \(-0.485873\pi\) |
0.842989 | − | 0.537931i | \(-0.180794\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 1.00000 | 0.0880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.0000 | −1.83478 | −0.917389 | − | 0.397991i | \(-0.869707\pi\) | ||||
−0.917389 | + | 0.397991i | \(0.869707\pi\) | |||||||
\(132\) | 5.19615 | + | 3.00000i | 0.452267 | + | 0.261116i | ||||
\(133\) | 1.00000 | − | 1.73205i | 0.0867110 | − | 0.150188i | ||||
\(134\) | −7.00000 | − | 12.1244i | −0.604708 | − | 1.04738i | ||||
\(135\) | − | 15.0000i | − | 1.29099i | ||||||
\(136\) | −2.59808 | + | 1.50000i | −0.222783 | + | 0.128624i | ||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | + | 11.2583i | 0.551323 | + | 0.954919i | 0.998179 | + | 0.0603135i | \(0.0192101\pi\) |
−0.446857 | + | 0.894606i | \(0.647457\pi\) | |||||||
\(140\) | 1.50000 | − | 2.59808i | 0.126773 | − | 0.219578i | ||||
\(141\) | −2.59808 | − | 1.50000i | −0.218797 | − | 0.126323i | ||||
\(142\) | −3.00000 | −0.251754 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.00000 | −0.166667 | ||||||||
\(145\) | −15.5885 | − | 9.00000i | −1.29455 | − | 0.747409i | ||||
\(146\) | 1.00000 | − | 1.73205i | 0.0827606 | − | 0.143346i | ||||
\(147\) | −3.00000 | − | 5.19615i | −0.247436 | − | 0.428571i | ||||
\(148\) | 7.00000i | 0.575396i | ||||||||
\(149\) | 5.19615 | − | 3.00000i | 0.425685 | − | 0.245770i | −0.271821 | − | 0.962348i | \(-0.587626\pi\) |
0.697507 | + | 0.716578i | \(0.254293\pi\) | |||||||
\(150\) | −3.46410 | + | 2.00000i | −0.282843 | + | 0.163299i | ||||
\(151\) | 17.0000i | 1.38344i | 0.722166 | + | 0.691720i | \(0.243147\pi\) | ||||
−0.722166 | + | 0.691720i | \(0.756853\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | 3.00000 | − | 5.19615i | 0.242536 | − | 0.420084i | ||||
\(154\) | −5.19615 | − | 3.00000i | −0.418718 | − | 0.241747i | ||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −6.92820 | − | 4.00000i | −0.551178 | − | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.50000 | + | 2.59808i | 0.118585 | + | 0.205396i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.866025 | − | 0.500000i | 0.0680414 | − | 0.0392837i | ||||
\(163\) | −13.8564 | + | 8.00000i | −1.08532 | + | 0.626608i | −0.932326 | − | 0.361619i | \(-0.882224\pi\) |
−0.152992 | + | 0.988227i | \(0.548891\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.00000 | + | 15.5885i | 0.700649 | + | 1.21356i | ||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −9.00000 | −0.690268 | ||||||||
\(171\) | −3.46410 | − | 2.00000i | −0.264906 | − | 0.152944i | ||||
\(172\) | 0.500000 | − | 0.866025i | 0.0381246 | − | 0.0660338i | ||||
\(173\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(174\) | 6.00000i | 0.454859i | ||||||||
\(175\) | 3.46410 | − | 2.00000i | 0.261861 | − | 0.151186i | ||||
\(176\) | 5.19615 | − | 3.00000i | 0.391675 | − | 0.226134i | ||||
\(177\) | − | 6.00000i | − | 0.450988i | ||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | 1.50000 | − | 2.59808i | 0.112115 | − | 0.194189i | −0.804508 | − | 0.593942i | \(-0.797571\pi\) |
0.916623 | + | 0.399753i | \(0.130904\pi\) | |||||||
\(180\) | −5.19615 | − | 3.00000i | −0.387298 | − | 0.223607i | ||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000 | 0.591377 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.5000 | + | 18.1865i | −0.771975 | + | 1.33710i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | 18.0000i | 1.31629i | ||||||||
\(188\) | −2.59808 | + | 1.50000i | −0.189484 | + | 0.109399i | ||||
\(189\) | 4.33013 | − | 2.50000i | 0.314970 | − | 0.181848i | ||||
\(190\) | 6.00000i | 0.435286i | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 3.46410 | + | 2.00000i | 0.249351 | + | 0.143963i | 0.619467 | − | 0.785022i | \(-0.287349\pi\) |
−0.370116 | + | 0.928986i | \(0.620682\pi\) | |||||||
\(194\) | −10.0000 | −0.717958 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 2.59808 | + | 1.50000i | 0.185105 | + | 0.106871i | 0.589689 | − | 0.807630i | \(-0.299250\pi\) |
−0.404584 | + | 0.914501i | \(0.632584\pi\) | |||||||
\(198\) | −6.00000 | + | 10.3923i | −0.426401 | + | 0.738549i | ||||
\(199\) | 1.00000 | + | 1.73205i | 0.0708881 | + | 0.122782i | 0.899291 | − | 0.437351i | \(-0.144083\pi\) |
−0.828403 | + | 0.560133i | \(0.810750\pi\) | |||||||
\(200\) | 4.00000i | 0.282843i | ||||||||
\(201\) | −12.1244 | + | 7.00000i | −0.855186 | + | 0.493742i | ||||
\(202\) | 10.3923 | − | 6.00000i | 0.731200 | − | 0.422159i | ||||
\(203\) | − | 6.00000i | − | 0.421117i | ||||||
\(204\) | 1.50000 | + | 2.59808i | 0.105021 | + | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.46410 | − | 2.00000i | −0.241355 | − | 0.139347i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | −2.59808 | − | 1.50000i | −0.179284 | − | 0.103510i | ||||
\(211\) | 6.50000 | − | 11.2583i | 0.447478 | − | 0.775055i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.00000i | 0.205557i | ||||||||
\(214\) | 10.3923 | − | 6.00000i | 0.710403 | − | 0.410152i | ||||
\(215\) | 2.59808 | − | 1.50000i | 0.177187 | − | 0.102299i | ||||
\(216\) | 5.00000i | 0.340207i | ||||||||
\(217\) | −2.00000 | − | 3.46410i | −0.135769 | − | 0.235159i | ||||
\(218\) | 3.50000 | − | 6.06218i | 0.237050 | − | 0.410582i | ||||
\(219\) | −1.73205 | − | 1.00000i | −0.117041 | − | 0.0675737i | ||||
\(220\) | 18.0000 | 1.21356 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.00000 | 0.469809 | ||||||||
\(223\) | −16.4545 | − | 9.50000i | −1.10187 | − | 0.636167i | −0.165161 | − | 0.986267i | \(-0.552814\pi\) |
−0.936713 | + | 0.350100i | \(0.886148\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | −4.00000 | − | 6.92820i | −0.266667 | − | 0.461880i | ||||
\(226\) | − | 6.00000i | − | 0.399114i | ||||||
\(227\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(228\) | 1.73205 | − | 1.00000i | 0.114708 | − | 0.0662266i | ||||
\(229\) | − | 13.0000i | − | 0.859064i | −0.903052 | − | 0.429532i | \(-0.858679\pi\) | ||
0.903052 | − | 0.429532i | \(-0.141321\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.00000 | + | 5.19615i | −0.197386 | + | 0.341882i | ||||
\(232\) | 5.19615 | + | 3.00000i | 0.341144 | + | 0.196960i | ||||
\(233\) | 27.0000 | 1.76883 | 0.884414 | − | 0.466702i | \(-0.154558\pi\) | ||||
0.884414 | + | 0.466702i | \(0.154558\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | −5.19615 | − | 3.00000i | −0.338241 | − | 0.195283i | ||||
\(237\) | −4.00000 | + | 6.92820i | −0.259828 | + | 0.450035i | ||||
\(238\) | −1.50000 | − | 2.59808i | −0.0972306 | − | 0.168408i | ||||
\(239\) | − | 15.0000i | − | 0.970269i | −0.874439 | − | 0.485135i | \(-0.838771\pi\) | ||
0.874439 | − | 0.485135i | \(-0.161229\pi\) | |||||||
\(240\) | 2.59808 | − | 1.50000i | 0.167705 | − | 0.0968246i | ||||
\(241\) | −8.66025 | + | 5.00000i | −0.557856 | + | 0.322078i | −0.752285 | − | 0.658838i | \(-0.771048\pi\) |
0.194429 | + | 0.980917i | \(0.437715\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | 4.00000 | − | 6.92820i | 0.256074 | − | 0.443533i | ||||
\(245\) | −15.5885 | − | 9.00000i | −0.995910 | − | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | 10.3923 | + | 6.00000i | 0.658586 | + | 0.380235i | ||||
\(250\) | 1.50000 | − | 2.59808i | 0.0948683 | − | 0.164317i | ||||
\(251\) | 12.0000 | + | 20.7846i | 0.757433 | + | 1.31191i | 0.944156 | + | 0.329500i | \(0.106880\pi\) |
−0.186722 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(252\) | − | 2.00000i | − | 0.125988i | ||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −17.3205 | + | 10.0000i | −1.08679 | + | 0.627456i | ||||
\(255\) | 9.00000i | 0.563602i | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.50000 | − | 7.79423i | 0.280702 | − | 0.486191i | −0.690856 | − | 0.722993i | \(-0.742766\pi\) |
0.971558 | + | 0.236802i | \(0.0760993\pi\) | |||||||
\(258\) | −0.866025 | − | 0.500000i | −0.0539164 | − | 0.0311286i | ||||
\(259\) | −7.00000 | −0.434959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.0000 | −0.742781 | ||||||||
\(262\) | 18.1865 | + | 10.5000i | 1.12357 | + | 0.648692i | ||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | −3.00000 | − | 5.19615i | −0.184637 | − | 0.319801i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.73205 | + | 1.00000i | −0.106199 | + | 0.0613139i | ||||
\(267\) | −5.19615 | + | 3.00000i | −0.317999 | + | 0.183597i | ||||
\(268\) | 14.0000i | 0.855186i | ||||||||
\(269\) | −12.0000 | − | 20.7846i | −0.731653 | − | 1.26726i | −0.956176 | − | 0.292791i | \(-0.905416\pi\) |
0.224523 | − | 0.974469i | \(-0.427917\pi\) | |||||||
\(270\) | −7.50000 | + | 12.9904i | −0.456435 | + | 0.790569i | ||||
\(271\) | −9.52628 | − | 5.50000i | −0.578680 | − | 0.334101i | 0.181928 | − | 0.983312i | \(-0.441766\pi\) |
−0.760609 | + | 0.649211i | \(0.775099\pi\) | |||||||
\(272\) | 3.00000 | 0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.7846 | + | 12.0000i | 1.25336 | + | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.0000 | − | 24.2487i | −0.841178 | − | 1.45696i | −0.888899 | − | 0.458103i | \(-0.848529\pi\) |
0.0477206 | − | 0.998861i | \(-0.484804\pi\) | |||||||
\(278\) | − | 13.0000i | − | 0.779688i | ||||||
\(279\) | −6.92820 | + | 4.00000i | −0.414781 | + | 0.239474i | ||||
\(280\) | −2.59808 | + | 1.50000i | −0.155265 | + | 0.0896421i | ||||
\(281\) | − | 6.00000i | − | 0.357930i | −0.983855 | − | 0.178965i | \(-0.942725\pi\) | ||
0.983855 | − | 0.178965i | \(-0.0572749\pi\) | |||||||
\(282\) | 1.50000 | + | 2.59808i | 0.0893237 | + | 0.154713i | ||||
\(283\) | −2.00000 | + | 3.46410i | −0.118888 | + | 0.205919i | −0.919327 | − | 0.393494i | \(-0.871266\pi\) |
0.800439 | + | 0.599414i | \(0.204600\pi\) | |||||||
\(284\) | 2.59808 | + | 1.50000i | 0.154167 | + | 0.0890086i | ||||
\(285\) | 6.00000 | 0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.73205 | + | 1.00000i | 0.102062 | + | 0.0589256i | ||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 9.00000 | + | 15.5885i | 0.528498 | + | 0.915386i | ||||
\(291\) | 10.0000i | 0.586210i | ||||||||
\(292\) | −1.73205 | + | 1.00000i | −0.101361 | + | 0.0585206i | ||||
\(293\) | 18.1865 | − | 10.5000i | 1.06247 | − | 0.613417i | 0.136355 | − | 0.990660i | \(-0.456461\pi\) |
0.926114 | + | 0.377244i | \(0.123128\pi\) | |||||||
\(294\) | 6.00000i | 0.349927i | ||||||||
\(295\) | −9.00000 | − | 15.5885i | −0.524000 | − | 0.907595i | ||||
\(296\) | 3.50000 | − | 6.06218i | 0.203433 | − | 0.352357i | ||||
\(297\) | 25.9808 | + | 15.0000i | 1.50756 | + | 0.870388i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 0.866025 | + | 0.500000i | 0.0499169 | + | 0.0288195i | ||||
\(302\) | 8.50000 | − | 14.7224i | 0.489120 | − | 0.847181i | ||||
\(303\) | −6.00000 | − | 10.3923i | −0.344691 | − | 0.597022i | ||||
\(304\) | − | 2.00000i | − | 0.114708i | ||||||
\(305\) | 20.7846 | − | 12.0000i | 1.19012 | − | 0.687118i | ||||
\(306\) | −5.19615 | + | 3.00000i | −0.297044 | + | 0.171499i | ||||
\(307\) | 2.00000i | 0.114146i | 0.998370 | + | 0.0570730i | \(0.0181768\pi\) | ||||
−0.998370 | + | 0.0570730i | \(0.981823\pi\) | |||||||
\(308\) | 3.00000 | + | 5.19615i | 0.170941 | + | 0.296078i | ||||
\(309\) | −2.00000 | + | 3.46410i | −0.113776 | + | 0.197066i | ||||
\(310\) | 10.3923 | + | 6.00000i | 0.590243 | + | 0.340777i | ||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.00000 | −0.0565233 | −0.0282617 | − | 0.999601i | \(-0.508997\pi\) | ||||
−0.0282617 | + | 0.999601i | \(0.508997\pi\) | |||||||
\(314\) | −12.1244 | − | 7.00000i | −0.684217 | − | 0.395033i | ||||
\(315\) | 3.00000 | − | 5.19615i | 0.169031 | − | 0.292770i | ||||
\(316\) | 4.00000 | + | 6.92820i | 0.225018 | + | 0.389742i | ||||
\(317\) | 6.00000i | 0.336994i | 0.985702 | + | 0.168497i | \(0.0538913\pi\) | ||||
−0.985702 | + | 0.168497i | \(0.946109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.1769 | − | 18.0000i | 1.74557 | − | 1.00781i | ||||
\(320\) | − | 3.00000i | − | 0.167705i | ||||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.19615 | + | 3.00000i | 0.289122 | + | 0.166924i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 16.0000 | 0.886158 | ||||||||
\(327\) | −6.06218 | − | 3.50000i | −0.335239 | − | 0.193550i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.50000 | − | 2.59808i | −0.0826977 | − | 0.143237i | ||||
\(330\) | − | 18.0000i | − | 0.990867i | ||||||
\(331\) | −6.92820 | + | 4.00000i | −0.380808 | + | 0.219860i | −0.678170 | − | 0.734905i | \(-0.737227\pi\) |
0.297361 | + | 0.954765i | \(0.403893\pi\) | |||||||
\(332\) | 10.3923 | − | 6.00000i | 0.570352 | − | 0.329293i | ||||
\(333\) | 14.0000i | 0.767195i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.0000 | + | 36.3731i | −1.14735 | + | 1.98727i | ||||
\(336\) | 0.866025 | + | 0.500000i | 0.0472456 | + | 0.0272772i | ||||
\(337\) | −23.0000 | −1.25289 | −0.626445 | − | 0.779466i | \(-0.715491\pi\) | ||||
−0.626445 | + | 0.779466i | \(0.715491\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 7.79423 | + | 4.50000i | 0.422701 | + | 0.244047i | ||||
\(341\) | 12.0000 | − | 20.7846i | 0.649836 | − | 1.12555i | ||||
\(342\) | 2.00000 | + | 3.46410i | 0.108148 | + | 0.187317i | ||||
\(343\) | − | 13.0000i | − | 0.701934i | ||||||
\(344\) | −0.866025 | + | 0.500000i | −0.0466930 | + | 0.0269582i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.50000 | − | 2.59808i | −0.0805242 | − | 0.139472i | 0.822951 | − | 0.568112i | \(-0.192326\pi\) |
−0.903475 | + | 0.428640i | \(0.858993\pi\) | |||||||
\(348\) | 3.00000 | − | 5.19615i | 0.160817 | − | 0.278543i | ||||
\(349\) | 16.4545 | + | 9.50000i | 0.880788 | + | 0.508523i | 0.870918 | − | 0.491428i | \(-0.163525\pi\) |
0.00987003 | + | 0.999951i | \(0.496858\pi\) | |||||||
\(350\) | −4.00000 | −0.213809 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.00000 | −0.319801 | ||||||||
\(353\) | 20.7846 | + | 12.0000i | 1.10625 | + | 0.638696i | 0.937856 | − | 0.347024i | \(-0.112808\pi\) |
0.168397 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(354\) | −3.00000 | + | 5.19615i | −0.159448 | + | 0.276172i | ||||
\(355\) | 4.50000 | + | 7.79423i | 0.238835 | + | 0.413675i | ||||
\(356\) | 6.00000i | 0.317999i | ||||||||
\(357\) | −2.59808 | + | 1.50000i | −0.137505 | + | 0.0793884i | ||||
\(358\) | −2.59808 | + | 1.50000i | −0.137313 | + | 0.0792775i | ||||
\(359\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(360\) | 3.00000 | + | 5.19615i | 0.158114 | + | 0.273861i | ||||
\(361\) | −7.50000 | + | 12.9904i | −0.394737 | + | 0.683704i | ||||
\(362\) | 17.3205 | + | 10.0000i | 0.910346 | + | 0.525588i | ||||
\(363\) | −25.0000 | −1.31216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | −6.92820 | − | 4.00000i | −0.362143 | − | 0.209083i | ||||
\(367\) | −13.0000 | + | 22.5167i | −0.678594 | + | 1.17536i | 0.296810 | + | 0.954937i | \(0.404077\pi\) |
−0.975404 | + | 0.220423i | \(0.929256\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 18.1865 | − | 10.5000i | 0.945473 | − | 0.545869i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 4.00000i | − | 0.207390i | ||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 9.00000 | − | 15.5885i | 0.465379 | − | 0.806060i | ||||
\(375\) | −2.59808 | − | 1.50000i | −0.134164 | − | 0.0774597i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −5.00000 | −0.257172 | ||||||||
\(379\) | 17.3205 | + | 10.0000i | 0.889695 | + | 0.513665i | 0.873843 | − | 0.486209i | \(-0.161621\pi\) |
0.0158521 | + | 0.999874i | \(0.494954\pi\) | |||||||
\(380\) | 3.00000 | − | 5.19615i | 0.153897 | − | 0.266557i | ||||
\(381\) | 10.0000 | + | 17.3205i | 0.512316 | + | 0.887357i | ||||
\(382\) | − | 18.0000i | − | 0.920960i | ||||||
\(383\) | −18.1865 | + | 10.5000i | −0.929288 | + | 0.536525i | −0.886586 | − | 0.462563i | \(-0.846930\pi\) |
−0.0427020 | + | 0.999088i | \(0.513597\pi\) | |||||||
\(384\) | −0.866025 | + | 0.500000i | −0.0441942 | + | 0.0255155i | ||||
\(385\) | 18.0000i | 0.917365i | ||||||||
\(386\) | −2.00000 | − | 3.46410i | −0.101797 | − | 0.176318i | ||||
\(387\) | 1.00000 | − | 1.73205i | 0.0508329 | − | 0.0880451i | ||||
\(388\) | 8.66025 | + | 5.00000i | 0.439658 | + | 0.253837i | ||||
\(389\) | 6.00000 | 0.304212 | 0.152106 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152106 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.19615 | + | 3.00000i | 0.262445 | + | 0.151523i | ||||
\(393\) | 10.5000 | − | 18.1865i | 0.529655 | − | 0.917389i | ||||
\(394\) | −1.50000 | − | 2.59808i | −0.0755689 | − | 0.130889i | ||||
\(395\) | 24.0000i | 1.20757i | ||||||||
\(396\) | 10.3923 | − | 6.00000i | 0.522233 | − | 0.301511i | ||||
\(397\) | −29.4449 | + | 17.0000i | −1.47780 | + | 0.853206i | −0.999685 | − | 0.0250943i | \(-0.992011\pi\) |
−0.478110 | + | 0.878300i | \(0.658678\pi\) | |||||||
\(398\) | − | 2.00000i | − | 0.100251i | ||||||
\(399\) | 1.00000 | + | 1.73205i | 0.0500626 | + | 0.0867110i | ||||
\(400\) | 2.00000 | − | 3.46410i | 0.100000 | − | 0.173205i | ||||
\(401\) | −31.1769 | − | 18.0000i | −1.55690 | − | 0.898877i | −0.997551 | − | 0.0699455i | \(-0.977717\pi\) |
−0.559350 | − | 0.828932i | \(-0.688949\pi\) | |||||||
\(402\) | 14.0000 | 0.698257 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | −2.59808 | − | 1.50000i | −0.129099 | − | 0.0745356i | ||||
\(406\) | −3.00000 | + | 5.19615i | −0.148888 | + | 0.257881i | ||||
\(407\) | −21.0000 | − | 36.3731i | −1.04093 | − | 1.80295i | ||||
\(408\) | − | 3.00000i | − | 0.148522i | ||||||
\(409\) | −27.7128 | + | 16.0000i | −1.37031 | + | 0.791149i | −0.990967 | − | 0.134107i | \(-0.957183\pi\) |
−0.379344 | + | 0.925256i | \(0.623850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.00000 | + | 3.46410i | 0.0985329 | + | 0.170664i | ||||
\(413\) | 3.00000 | − | 5.19615i | 0.147620 | − | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 36.0000 | 1.76717 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.0000 | −0.636613 | ||||||||
\(418\) | −10.3923 | − | 6.00000i | −0.508304 | − | 0.293470i | ||||
\(419\) | −4.50000 | + | 7.79423i | −0.219839 | + | 0.380773i | −0.954759 | − | 0.297382i | \(-0.903887\pi\) |
0.734919 | + | 0.678155i | \(0.237220\pi\) | |||||||
\(420\) | 1.50000 | + | 2.59808i | 0.0731925 | + | 0.126773i | ||||
\(421\) | − | 17.0000i | − | 0.828529i | −0.910156 | − | 0.414265i | \(-0.864039\pi\) | ||
0.910156 | − | 0.414265i | \(-0.135961\pi\) | |||||||
\(422\) | −11.2583 | + | 6.50000i | −0.548047 | + | 0.316415i | ||||
\(423\) | −5.19615 | + | 3.00000i | −0.252646 | + | 0.145865i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 1.50000 | − | 2.59808i | 0.0726752 | − | 0.125877i | ||||
\(427\) | 6.92820 | + | 4.00000i | 0.335279 | + | 0.193574i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.00000 | −0.144673 | ||||||||
\(431\) | −28.5788 | − | 16.5000i | −1.37659 | − | 0.794777i | −0.384846 | − | 0.922981i | \(-0.625746\pi\) |
−0.991748 | + | 0.128204i | \(0.959079\pi\) | |||||||
\(432\) | 2.50000 | − | 4.33013i | 0.120281 | − | 0.208333i | ||||
\(433\) | −12.5000 | − | 21.6506i | −0.600712 | − | 1.04046i | −0.992713 | − | 0.120499i | \(-0.961551\pi\) |
0.392002 | − | 0.919964i | \(-0.371783\pi\) | |||||||
\(434\) | 4.00000i | 0.192006i | ||||||||
\(435\) | 15.5885 | − | 9.00000i | 0.747409 | − | 0.431517i | ||||
\(436\) | −6.06218 | + | 3.50000i | −0.290326 | + | 0.167620i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 1.00000 | + | 1.73205i | 0.0477818 | + | 0.0827606i | ||||
\(439\) | 13.0000 | − | 22.5167i | 0.620456 | − | 1.07466i | −0.368945 | − | 0.929451i | \(-0.620281\pi\) |
0.989401 | − | 0.145210i | \(-0.0463858\pi\) | |||||||
\(440\) | −15.5885 | − | 9.00000i | −0.743151 | − | 0.429058i | ||||
\(441\) | −12.0000 | −0.571429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.0000 | 0.997740 | 0.498870 | − | 0.866677i | \(-0.333748\pi\) | ||||
0.498870 | + | 0.866677i | \(0.333748\pi\) | |||||||
\(444\) | −6.06218 | − | 3.50000i | −0.287698 | − | 0.166103i | ||||
\(445\) | −9.00000 | + | 15.5885i | −0.426641 | + | 0.738964i | ||||
\(446\) | 9.50000 | + | 16.4545i | 0.449838 | + | 0.779142i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 0.866025 | − | 0.500000i | 0.0409159 | − | 0.0236228i | ||||
\(449\) | 5.19615 | − | 3.00000i | 0.245222 | − | 0.141579i | −0.372353 | − | 0.928091i | \(-0.621449\pi\) |
0.617574 | + | 0.786513i | \(0.288115\pi\) | |||||||
\(450\) | 8.00000i | 0.377124i | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −14.7224 | − | 8.50000i | −0.691720 | − | 0.399365i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | −8.66025 | − | 5.00000i | −0.405110 | − | 0.233890i | 0.283577 | − | 0.958950i | \(-0.408479\pi\) |
−0.688686 | + | 0.725059i | \(0.741812\pi\) | |||||||
\(458\) | −6.50000 | + | 11.2583i | −0.303725 | + | 0.526067i | ||||
\(459\) | 7.50000 | + | 12.9904i | 0.350070 | + | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.79423 | + | 4.50000i | −0.363013 | + | 0.209586i | −0.670402 | − | 0.741998i | \(-0.733878\pi\) |
0.307388 | + | 0.951584i | \(0.400545\pi\) | |||||||
\(462\) | 5.19615 | − | 3.00000i | 0.241747 | − | 0.139573i | ||||
\(463\) | − | 40.0000i | − | 1.85896i | −0.368875 | − | 0.929479i | \(-0.620257\pi\) | ||
0.368875 | − | 0.929479i | \(-0.379743\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 6.00000 | − | 10.3923i | 0.278243 | − | 0.481932i | ||||
\(466\) | −23.3827 | − | 13.5000i | −1.08318 | − | 0.625375i | ||||
\(467\) | −36.0000 | −1.66588 | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||||
−0.832941 | + | 0.553362i | \(0.813345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | −0.646460 | ||||||||
\(470\) | 7.79423 | + | 4.50000i | 0.359521 | + | 0.207570i | ||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | 6.00000i | 0.275880i | ||||||||
\(474\) | 6.92820 | − | 4.00000i | 0.318223 | − | 0.183726i | ||||
\(475\) | 6.92820 | − | 4.00000i | 0.317888 | − | 0.183533i | ||||
\(476\) | 3.00000i | 0.137505i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.50000 | + | 12.9904i | −0.343042 | + | 0.594166i | ||||
\(479\) | 18.1865 | + | 10.5000i | 0.830964 | + | 0.479757i | 0.854183 | − | 0.519973i | \(-0.174058\pi\) |
−0.0232187 | + | 0.999730i | \(0.507391\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 10.0000 | 0.455488 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | + | 21.6506i | −0.568182 | + | 0.984120i | ||||
\(485\) | 15.0000 | + | 25.9808i | 0.681115 | + | 1.17973i | ||||
\(486\) | 16.0000i | 0.725775i | ||||||||
\(487\) | 13.8564 | − | 8.00000i | 0.627894 | − | 0.362515i | −0.152042 | − | 0.988374i | \(-0.548585\pi\) |
0.779936 | + | 0.625859i | \(0.215252\pi\) | |||||||
\(488\) | −6.92820 | + | 4.00000i | −0.313625 | + | 0.181071i | ||||
\(489\) | − | 16.0000i | − | 0.723545i | ||||||
\(490\) | 9.00000 | + | 15.5885i | 0.406579 | + | 0.704215i | ||||
\(491\) | −4.50000 | + | 7.79423i | −0.203082 | + | 0.351749i | −0.949520 | − | 0.313707i | \(-0.898429\pi\) |
0.746438 | + | 0.665455i | \(0.231763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.0000 | 0.810679 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 36.0000 | 1.61808 | ||||||||
\(496\) | −3.46410 | − | 2.00000i | −0.155543 | − | 0.0898027i | ||||
\(497\) | −1.50000 | + | 2.59808i | −0.0672842 | + | 0.116540i | ||||
\(498\) | −6.00000 | − | 10.3923i | −0.268866 | − | 0.465690i | ||||
\(499\) | 40.0000i | 1.79065i | 0.445418 | + | 0.895323i | \(0.353055\pi\) | ||||
−0.445418 | + | 0.895323i | \(0.646945\pi\) | |||||||
\(500\) | −2.59808 | + | 1.50000i | −0.116190 | + | 0.0670820i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 24.0000i | − | 1.07117i | ||||||
\(503\) | 15.0000 | + | 25.9808i | 0.668817 | + | 1.15842i | 0.978235 | + | 0.207499i | \(0.0665323\pi\) |
−0.309418 | + | 0.950926i | \(0.600134\pi\) | |||||||
\(504\) | −1.00000 | + | 1.73205i | −0.0445435 | + | 0.0771517i | ||||
\(505\) | −31.1769 | − | 18.0000i | −1.38735 | − | 0.800989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.0000 | 0.887357 | ||||||||
\(509\) | −15.5885 | − | 9.00000i | −0.690946 | − | 0.398918i | 0.113020 | − | 0.993593i | \(-0.463948\pi\) |
−0.803966 | + | 0.594675i | \(0.797281\pi\) | |||||||
\(510\) | 4.50000 | − | 7.79423i | 0.199263 | − | 0.345134i | ||||
\(511\) | −1.00000 | − | 1.73205i | −0.0442374 | − | 0.0766214i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 8.66025 | − | 5.00000i | 0.382360 | − | 0.220755i | ||||
\(514\) | −7.79423 | + | 4.50000i | −0.343789 | + | 0.198486i | ||||
\(515\) | 12.0000i | 0.528783i | ||||||||
\(516\) | 0.500000 | + | 0.866025i | 0.0220113 | + | 0.0381246i | ||||
\(517\) | 9.00000 | − | 15.5885i | 0.395820 | − | 0.685580i | ||||
\(518\) | 6.06218 | + | 3.50000i | 0.266357 | + | 0.153781i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | −0.394297 | −0.197149 | − | 0.980374i | \(-0.563168\pi\) | ||||
−0.197149 | + | 0.980374i | \(0.563168\pi\) | |||||||
\(522\) | 10.3923 | + | 6.00000i | 0.454859 | + | 0.262613i | ||||
\(523\) | −10.0000 | + | 17.3205i | −0.437269 | + | 0.757373i | −0.997478 | − | 0.0709788i | \(-0.977388\pi\) |
0.560208 | + | 0.828352i | \(0.310721\pi\) | |||||||
\(524\) | −10.5000 | − | 18.1865i | −0.458695 | − | 0.794482i | ||||
\(525\) | 4.00000i | 0.174574i | ||||||||
\(526\) | −10.3923 | + | 6.00000i | −0.453126 | + | 0.261612i | ||||
\(527\) | 10.3923 | − | 6.00000i | 0.452696 | − | 0.261364i | ||||
\(528\) | 6.00000i | 0.261116i | ||||||||
\(529\) | 11.5000 | + | 19.9186i | 0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.3923 | − | 6.00000i | −0.450988 | − | 0.260378i | ||||
\(532\) | 2.00000 | 0.0867110 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.00000 | 0.259645 | ||||||||
\(535\) | −31.1769 | − | 18.0000i | −1.34790 | − | 0.778208i | ||||
\(536\) | 7.00000 | − | 12.1244i | 0.302354 | − | 0.523692i | ||||
\(537\) | 1.50000 | + | 2.59808i | 0.0647298 | + | 0.112115i | ||||
\(538\) | 24.0000i | 1.03471i | ||||||||
\(539\) | 31.1769 | − | 18.0000i | 1.34288 | − | 0.775315i | ||||
\(540\) | 12.9904 | − | 7.50000i | 0.559017 | − | 0.322749i | ||||
\(541\) | 11.0000i | 0.472927i | 0.971640 | + | 0.236463i | \(0.0759884\pi\) | ||||
−0.971640 | + | 0.236463i | \(0.924012\pi\) | |||||||
\(542\) | 5.50000 | + | 9.52628i | 0.236245 | + | 0.409189i | ||||
\(543\) | 10.0000 | − | 17.3205i | 0.429141 | − | 0.743294i | ||||
\(544\) | −2.59808 | − | 1.50000i | −0.111392 | − | 0.0643120i | ||||
\(545\) | −21.0000 | −0.899541 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.0000 | 0.726868 | 0.363434 | − | 0.931620i | \(-0.381604\pi\) | ||||
0.363434 | + | 0.931620i | \(0.381604\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00000 | − | 13.8564i | 0.341432 | − | 0.591377i | ||||
\(550\) | −12.0000 | − | 20.7846i | −0.511682 | − | 0.886259i | ||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.92820 | + | 4.00000i | −0.294617 | + | 0.170097i | ||||
\(554\) | 28.0000i | 1.18961i | ||||||||
\(555\) | −10.5000 | − | 18.1865i | −0.445700 | − | 0.771975i | ||||
\(556\) | −6.50000 | + | 11.2583i | −0.275661 | + | 0.477460i | ||||
\(557\) | −2.59808 | − | 1.50000i | −0.110084 | − | 0.0635570i | 0.443947 | − | 0.896053i | \(-0.353578\pi\) |
−0.554031 | + | 0.832496i | \(0.686911\pi\) | |||||||
\(558\) | 8.00000 | 0.338667 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | −15.5885 | − | 9.00000i | −0.658145 | − | 0.379980i | ||||
\(562\) | −3.00000 | + | 5.19615i | −0.126547 | + | 0.219186i | ||||
\(563\) | 19.5000 | + | 33.7750i | 0.821827 | + | 1.42345i | 0.904320 | + | 0.426855i | \(0.140378\pi\) |
−0.0824933 | + | 0.996592i | \(0.526288\pi\) | |||||||
\(564\) | − | 3.00000i | − | 0.126323i | ||||||
\(565\) | −15.5885 | + | 9.00000i | −0.655811 | + | 0.378633i | ||||
\(566\) | 3.46410 | − | 2.00000i | 0.145607 | − | 0.0840663i | ||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | −1.50000 | − | 2.59808i | −0.0629386 | − | 0.109013i | ||||
\(569\) | 7.50000 | − | 12.9904i | 0.314416 | − | 0.544585i | −0.664897 | − | 0.746935i | \(-0.731525\pi\) |
0.979313 | + | 0.202350i | \(0.0648579\pi\) | |||||||
\(570\) | −5.19615 | − | 3.00000i | −0.217643 | − | 0.125656i | ||||
\(571\) | −5.00000 | −0.209243 | −0.104622 | − | 0.994512i | \(-0.533363\pi\) | ||||
−0.104622 | + | 0.994512i | \(0.533363\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0000 | −0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.00000 | − | 1.73205i | −0.0416667 | − | 0.0721688i | ||||
\(577\) | − | 38.0000i | − | 1.58196i | −0.611842 | − | 0.790980i | \(-0.709571\pi\) | ||
0.611842 | − | 0.790980i | \(-0.290429\pi\) | |||||||
\(578\) | −6.92820 | + | 4.00000i | −0.288175 | + | 0.166378i | ||||
\(579\) | −3.46410 | + | 2.00000i | −0.143963 | + | 0.0831172i | ||||
\(580\) | − | 18.0000i | − | 0.747409i | ||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | 5.00000 | − | 8.66025i | 0.207257 | − | 0.358979i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 2.00000 | 0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.0000 | −0.867502 | ||||||||
\(587\) | 20.7846 | + | 12.0000i | 0.857873 | + | 0.495293i | 0.863299 | − | 0.504692i | \(-0.168394\pi\) |
−0.00542667 | + | 0.999985i | \(0.501727\pi\) | |||||||
\(588\) | 3.00000 | − | 5.19615i | 0.123718 | − | 0.214286i | ||||
\(589\) | −4.00000 | − | 6.92820i | −0.164817 | − | 0.285472i | ||||
\(590\) | 18.0000i | 0.741048i | ||||||||
\(591\) | −2.59808 | + | 1.50000i | −0.106871 | + | 0.0617018i | ||||
\(592\) | −6.06218 | + | 3.50000i | −0.249154 | + | 0.143849i | ||||
\(593\) | 18.0000i | 0.739171i | 0.929197 | + | 0.369586i | \(0.120500\pi\) | ||||
−0.929197 | + | 0.369586i | \(0.879500\pi\) | |||||||
\(594\) | −15.0000 | − | 25.9808i | −0.615457 | − | 1.06600i | ||||
\(595\) | −4.50000 | + | 7.79423i | −0.184482 | + | 0.319532i | ||||
\(596\) | 5.19615 | + | 3.00000i | 0.212843 | + | 0.122885i | ||||
\(597\) | −2.00000 | −0.0818546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.00000 | 0.245153 | 0.122577 | − | 0.992459i | \(-0.460884\pi\) | ||||
0.122577 | + | 0.992459i | \(0.460884\pi\) | |||||||
\(600\) | −3.46410 | − | 2.00000i | −0.141421 | − | 0.0816497i | ||||
\(601\) | 9.50000 | − | 16.4545i | 0.387513 | − | 0.671192i | −0.604601 | − | 0.796528i | \(-0.706668\pi\) |
0.992114 | + | 0.125336i | \(0.0400009\pi\) | |||||||
\(602\) | −0.500000 | − | 0.866025i | −0.0203785 | − | 0.0352966i | ||||
\(603\) | 28.0000i | 1.14025i | ||||||||
\(604\) | −14.7224 | + | 8.50000i | −0.599047 | + | 0.345860i | ||||
\(605\) | −64.9519 | + | 37.5000i | −2.64067 | + | 1.52459i | ||||
\(606\) | 12.0000i | 0.487467i | ||||||||
\(607\) | −7.00000 | − | 12.1244i | −0.284121 | − | 0.492112i | 0.688274 | − | 0.725450i | \(-0.258368\pi\) |
−0.972396 | + | 0.233338i | \(0.925035\pi\) | |||||||
\(608\) | −1.00000 | + | 1.73205i | −0.0405554 | + | 0.0702439i | ||||
\(609\) | 5.19615 | + | 3.00000i | 0.210559 | + | 0.121566i | ||||
\(610\) | −24.0000 | −0.971732 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.00000 | 0.242536 | ||||||||
\(613\) | 32.9090 | + | 19.0000i | 1.32918 | + | 0.767403i | 0.985173 | − | 0.171564i | \(-0.0548821\pi\) |
0.344008 | + | 0.938967i | \(0.388215\pi\) | |||||||
\(614\) | 1.00000 | − | 1.73205i | 0.0403567 | − | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 6.00000i | − | 0.241747i | ||||||
\(617\) | 20.7846 | − | 12.0000i | 0.836757 | − | 0.483102i | −0.0194037 | − | 0.999812i | \(-0.506177\pi\) |
0.856161 | + | 0.516710i | \(0.172843\pi\) | |||||||
\(618\) | 3.46410 | − | 2.00000i | 0.139347 | − | 0.0804518i | ||||
\(619\) | − | 28.0000i | − | 1.12542i | −0.826656 | − | 0.562708i | \(-0.809760\pi\) | ||
0.826656 | − | 0.562708i | \(-0.190240\pi\) | |||||||
\(620\) | −6.00000 | − | 10.3923i | −0.240966 | − | 0.417365i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −25.9808 | − | 15.0000i | −1.04173 | − | 0.601445i | ||||
\(623\) | −6.00000 | −0.240385 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0.866025 | + | 0.500000i | 0.0346133 | + | 0.0199840i | ||||
\(627\) | −6.00000 | + | 10.3923i | −0.239617 | + | 0.415029i | ||||
\(628\) | 7.00000 | + | 12.1244i | 0.279330 | + | 0.483814i | ||||
\(629\) | − | 21.0000i | − | 0.837325i | ||||||
\(630\) | −5.19615 | + | 3.00000i | −0.207020 | + | 0.119523i | ||||
\(631\) | 25.1147 | − | 14.5000i | 0.999802 | − | 0.577236i | 0.0916122 | − | 0.995795i | \(-0.470798\pi\) |
0.908190 | + | 0.418559i | \(0.137465\pi\) | |||||||
\(632\) | − | 8.00000i | − | 0.318223i | ||||||
\(633\) | 6.50000 | + | 11.2583i | 0.258352 | + | 0.447478i | ||||
\(634\) | 3.00000 | − | 5.19615i | 0.119145 | − | 0.206366i | ||||
\(635\) | 51.9615 | + | 30.0000i | 2.06203 | + | 1.19051i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −36.0000 | −1.42525 | ||||||||
\(639\) | 5.19615 | + | 3.00000i | 0.205557 | + | 0.118678i | ||||
\(640\) | −1.50000 | + | 2.59808i | −0.0592927 | + | 0.102698i | ||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | 12.0000i | 0.473602i | ||||||||
\(643\) | −12.1244 | + | 7.00000i | −0.478138 | + | 0.276053i | −0.719640 | − | 0.694347i | \(-0.755693\pi\) |
0.241502 | + | 0.970400i | \(0.422360\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00000i | 0.118125i | ||||||||
\(646\) | −3.00000 | − | 5.19615i | −0.118033 | − | 0.204440i | ||||
\(647\) | −3.00000 | + | 5.19615i | −0.117942 | + | 0.204282i | −0.918952 | − | 0.394369i | \(-0.870963\pi\) |
0.801010 | + | 0.598651i | \(0.204296\pi\) | |||||||
\(648\) | 0.866025 | + | 0.500000i | 0.0340207 | + | 0.0196419i | ||||
\(649\) | 36.0000 | 1.41312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.00000 | 0.156772 | ||||||||
\(652\) | −13.8564 | − | 8.00000i | −0.542659 | − | 0.313304i | ||||
\(653\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(654\) | 3.50000 | + | 6.06218i | 0.136861 | + | 0.237050i | ||||
\(655\) | − | 63.0000i | − | 2.46161i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.46410 | + | 2.00000i | −0.135147 | + | 0.0780274i | ||||
\(658\) | 3.00000i | 0.116952i | ||||||||
\(659\) | 18.0000 | + | 31.1769i | 0.701180 | + | 1.21448i | 0.968052 | + | 0.250748i | \(0.0806766\pi\) |
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(660\) | −9.00000 | + | 15.5885i | −0.350325 | + | 0.606780i | ||||
\(661\) | 19.0526 | + | 11.0000i | 0.741059 | + | 0.427850i | 0.822454 | − | 0.568831i | \(-0.192604\pi\) |
−0.0813955 | + | 0.996682i | \(0.525938\pi\) | |||||||
\(662\) | 8.00000 | 0.310929 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 5.19615 | + | 3.00000i | 0.201498 | + | 0.116335i | ||||
\(666\) | 7.00000 | − | 12.1244i | 0.271244 | − | 0.469809i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.4545 | − | 9.50000i | 0.636167 | − | 0.367291i | ||||
\(670\) | 36.3731 | − | 21.0000i | 1.40521 | − | 0.811301i | ||||
\(671\) | 48.0000i | 1.85302i | ||||||||
\(672\) | −0.500000 | − | 0.866025i | −0.0192879 | − | 0.0334077i | ||||
\(673\) | −9.50000 | + | 16.4545i | −0.366198 | + | 0.634274i | −0.988968 | − | 0.148132i | \(-0.952674\pi\) |
0.622770 | + | 0.782405i | \(0.286007\pi\) | |||||||
\(674\) | 19.9186 | + | 11.5000i | 0.767235 | + | 0.442963i | ||||
\(675\) | 20.0000 | 0.769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 48.0000 | 1.84479 | 0.922395 | − | 0.386248i | \(-0.126229\pi\) | ||||
0.922395 | + | 0.386248i | \(0.126229\pi\) | |||||||
\(678\) | 5.19615 | + | 3.00000i | 0.199557 | + | 0.115214i | ||||
\(679\) | −5.00000 | + | 8.66025i | −0.191882 | + | 0.332350i | ||||
\(680\) | −4.50000 | − | 7.79423i | −0.172567 | − | 0.298895i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.7846 | + | 12.0000i | −0.795884 | + | 0.459504i | ||||
\(683\) | 20.7846 | − | 12.0000i | 0.795301 | − | 0.459167i | −0.0465244 | − | 0.998917i | \(-0.514815\pi\) |
0.841825 | + | 0.539750i | \(0.181481\pi\) | |||||||
\(684\) | − | 4.00000i | − | 0.152944i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.50000 | + | 11.2583i | −0.248171 | + | 0.429845i | ||||
\(687\) | 11.2583 | + | 6.50000i | 0.429532 | + | 0.247990i | ||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.92820 | + | 4.00000i | 0.263561 | + | 0.152167i | 0.625958 | − | 0.779857i | \(-0.284708\pi\) |
−0.362397 | + | 0.932024i | \(0.618041\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.00000 | + | 10.3923i | 0.227921 | + | 0.394771i | ||||
\(694\) | 3.00000i | 0.113878i | ||||||||
\(695\) | −33.7750 | + | 19.5000i | −1.28116 | + | 0.739677i | ||||
\(696\) | −5.19615 | + | 3.00000i | −0.196960 | + | 0.113715i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −9.50000 | − | 16.4545i | −0.359580 | − | 0.622811i | ||||
\(699\) | −13.5000 | + | 23.3827i | −0.510617 | + | 0.884414i | ||||
\(700\) | 3.46410 | + | 2.00000i | 0.130931 | + | 0.0755929i | ||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.0000 | −0.528020 | ||||||||
\(704\) | 5.19615 | + | 3.00000i | 0.195837 | + | 0.113067i | ||||
\(705\) | 4.50000 | − | 7.79423i | 0.169480 | − | 0.293548i | ||||
\(706\) | −12.0000 | − | 20.7846i | −0.451626 | − | 0.782239i | ||||
\(707\) | − | 12.0000i | − | 0.451306i | ||||||
\(708\) | 5.19615 | − | 3.00000i | 0.195283 | − | 0.112747i | ||||
\(709\) | 22.5167 | − | 13.0000i | 0.845631 | − | 0.488225i | −0.0135434 | − | 0.999908i | \(-0.504311\pi\) |
0.859174 | + | 0.511683i | \(0.170978\pi\) | |||||||
\(710\) | − | 9.00000i | − | 0.337764i | ||||||
\(711\) | 8.00000 | + | 13.8564i | 0.300023 | + | 0.519656i | ||||
\(712\) | 3.00000 | − | 5.19615i | 0.112430 | − | 0.194734i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 3.00000 | 0.112272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.00000 | 0.112115 | ||||||||
\(717\) | 12.9904 | + | 7.50000i | 0.485135 | + | 0.280093i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | − | 6.00000i | − | 0.223607i | ||||||
\(721\) | −3.46410 | + | 2.00000i | −0.129010 | + | 0.0744839i | ||||
\(722\) | 12.9904 | − | 7.50000i | 0.483452 | − | 0.279121i | ||||
\(723\) | − | 10.0000i | − | 0.371904i | ||||||
\(724\) | −10.0000 | − | 17.3205i | −0.371647 | − | 0.643712i | ||||
\(725\) | 12.0000 | − | 20.7846i | 0.445669 | − | 0.771921i | ||||
\(726\) | 21.6506 | + | 12.5000i | 0.803530 | + | 0.463919i | ||||
\(727\) | 10.0000 | 0.370879 | 0.185440 | − | 0.982656i | \(-0.440629\pi\) | ||||
0.185440 | + | 0.982656i | \(0.440629\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 5.19615 | + | 3.00000i | 0.192318 | + | 0.111035i | ||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 4.00000 | + | 6.92820i | 0.147844 | + | 0.256074i | ||||
\(733\) | − | 23.0000i | − | 0.849524i | −0.905305 | − | 0.424762i | \(-0.860358\pi\) | ||
0.905305 | − | 0.424762i | \(-0.139642\pi\) | |||||||
\(734\) | 22.5167 | − | 13.0000i | 0.831105 | − | 0.479839i | ||||
\(735\) | 15.5885 | − | 9.00000i | 0.574989 | − | 0.331970i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −42.0000 | − | 72.7461i | −1.54709 | − | 2.67964i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.3205 | − | 10.0000i | −0.637145 | − | 0.367856i | 0.146369 | − | 0.989230i | \(-0.453241\pi\) |
−0.783514 | + | 0.621374i | \(0.786575\pi\) | |||||||
\(740\) | −21.0000 | −0.771975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.79423 | − | 4.50000i | −0.285943 | − | 0.165089i | 0.350168 | − | 0.936687i | \(-0.386124\pi\) |
−0.636111 | + | 0.771598i | \(0.719458\pi\) | |||||||
\(744\) | −2.00000 | + | 3.46410i | −0.0733236 | + | 0.127000i | ||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | − | 4.00000i | − | 0.146450i | ||||||
\(747\) | 20.7846 | − | 12.0000i | 0.760469 | − | 0.439057i | ||||
\(748\) | −15.5885 | + | 9.00000i | −0.569970 | + | 0.329073i | ||||
\(749\) | − | 12.0000i | − | 0.438470i | ||||||
\(750\) | 1.50000 | + | 2.59808i | 0.0547723 | + | 0.0948683i | ||||
\(751\) | −20.0000 | + | 34.6410i | −0.729810 | + | 1.26407i | 0.227153 | + | 0.973859i | \(0.427058\pi\) |
−0.956963 | + | 0.290209i | \(0.906275\pi\) | |||||||
\(752\) | −2.59808 | − | 1.50000i | −0.0947421 | − | 0.0546994i | ||||
\(753\) | −24.0000 | −0.874609 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −51.0000 | −1.85608 | ||||||||
\(756\) | 4.33013 | + | 2.50000i | 0.157485 | + | 0.0909241i | ||||
\(757\) | 8.00000 | − | 13.8564i | 0.290765 | − | 0.503620i | −0.683226 | − | 0.730207i | \(-0.739424\pi\) |
0.973991 | + | 0.226587i | \(0.0727569\pi\) | |||||||
\(758\) | −10.0000 | − | 17.3205i | −0.363216 | − | 0.629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.19615 | + | 3.00000i | −0.188484 | + | 0.108821i | ||||
\(761\) | −5.19615 | + | 3.00000i | −0.188360 | + | 0.108750i | −0.591215 | − | 0.806514i | \(-0.701351\pi\) |
0.402854 | + | 0.915264i | \(0.368018\pi\) | |||||||
\(762\) | − | 20.0000i | − | 0.724524i | ||||||
\(763\) | −3.50000 | − | 6.06218i | −0.126709 | − | 0.219466i | ||||
\(764\) | −9.00000 | + | 15.5885i | −0.325609 | + | 0.563971i | ||||
\(765\) | 15.5885 | + | 9.00000i | 0.563602 | + | 0.325396i | ||||
\(766\) | 21.0000 | 0.758761 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 27.7128 | + | 16.0000i | 0.999350 | + | 0.576975i | 0.908056 | − | 0.418849i | \(-0.137566\pi\) |
0.0912938 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(770\) | 9.00000 | − | 15.5885i | 0.324337 | − | 0.561769i | ||||
\(771\) | 4.50000 | + | 7.79423i | 0.162064 | + | 0.280702i | ||||
\(772\) | 4.00000i | 0.143963i | ||||||||
\(773\) | 33.7750 | − | 19.5000i | 1.21480 | − | 0.701366i | 0.251000 | − | 0.967987i | \(-0.419240\pi\) |
0.963802 | + | 0.266621i | \(0.0859071\pi\) | |||||||
\(774\) | −1.73205 | + | 1.00000i | −0.0622573 | + | 0.0359443i | ||||
\(775\) | − | 16.0000i | − | 0.574737i | ||||||
\(776\) | −5.00000 | − | 8.66025i | −0.179490 | − | 0.310885i | ||||
\(777\) | 3.50000 | − | 6.06218i | 0.125562 | − | 0.217479i | ||||
\(778\) | −5.19615 | − | 3.00000i | −0.186291 | − | 0.107555i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.0000 | − | 25.9808i | 0.536056 | − | 0.928477i | ||||
\(784\) | −3.00000 | − | 5.19615i | −0.107143 | − | 0.185577i | ||||
\(785\) | 42.0000i | 1.49904i | ||||||||
\(786\) | −18.1865 | + | 10.5000i | −0.648692 | + | 0.374523i | ||||
\(787\) | −34.6410 | + | 20.0000i | −1.23482 | + | 0.712923i | −0.968031 | − | 0.250832i | \(-0.919296\pi\) |
−0.266788 | + | 0.963755i | \(0.585962\pi\) | |||||||
\(788\) | 3.00000i | 0.106871i | ||||||||
\(789\) | 6.00000 | + | 10.3923i | 0.213606 | + | 0.369976i | ||||
\(790\) | 12.0000 | − | 20.7846i | 0.426941 | − | 0.739483i | ||||
\(791\) | −5.19615 | − | 3.00000i | −0.184754 | − | 0.106668i | ||||
\(792\) | −12.0000 | −0.426401 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 34.0000 | 1.20661 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.00000 | + | 1.73205i | −0.0354441 | + | 0.0613909i | ||||
\(797\) | −21.0000 | − | 36.3731i | −0.743858 | − | 1.28840i | −0.950726 | − | 0.310031i | \(-0.899660\pi\) |
0.206868 | − | 0.978369i | \(-0.433673\pi\) | |||||||
\(798\) | − | 2.00000i | − | 0.0707992i | ||||||
\(799\) | 7.79423 | − | 4.50000i | 0.275740 | − | 0.159199i | ||||
\(800\) | −3.46410 | + | 2.00000i | −0.122474 | + | 0.0707107i | ||||
\(801\) | 12.0000i | 0.423999i | ||||||||
\(802\) | 18.0000 | + | 31.1769i | 0.635602 | + | 1.10090i | ||||
\(803\) | 6.00000 | − | 10.3923i | 0.211735 | − | 0.366736i | ||||
\(804\) | −12.1244 | − | 7.00000i | −0.427593 | − | 0.246871i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0000 | 0.844840 | ||||||||
\(808\) | 10.3923 | + | 6.00000i | 0.365600 | + | 0.211079i | ||||
\(809\) | 16.5000 | − | 28.5788i | 0.580109 | − | 1.00478i | −0.415357 | − | 0.909659i | \(-0.636343\pi\) |
0.995466 | − | 0.0951198i | \(-0.0303234\pi\) | |||||||
\(810\) | 1.50000 | + | 2.59808i | 0.0527046 | + | 0.0912871i | ||||
\(811\) | − | 20.0000i | − | 0.702295i | −0.936320 | − | 0.351147i | \(-0.885792\pi\) | ||
0.936320 | − | 0.351147i | \(-0.114208\pi\) | |||||||
\(812\) | 5.19615 | − | 3.00000i | 0.182349 | − | 0.105279i | ||||
\(813\) | 9.52628 | − | 5.50000i | 0.334101 | − | 0.192893i | ||||
\(814\) | 42.0000i | 1.47210i | ||||||||
\(815\) | −24.0000 | − | 41.5692i | −0.840683 | − | 1.45611i | ||||
\(816\) | −1.50000 | + | 2.59808i | −0.0525105 | + | 0.0909509i | ||||
\(817\) | 1.73205 | + | 1.00000i | 0.0605968 | + | 0.0349856i | ||||
\(818\) | 32.0000 | 1.11885 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.59808 | − | 1.50000i | −0.0906735 | − | 0.0523504i | 0.453978 | − | 0.891013i | \(-0.350005\pi\) |
−0.544651 | + | 0.838663i | \(0.683338\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.00000 | + | 12.1244i | 0.244005 | + | 0.422628i | 0.961851 | − | 0.273573i | \(-0.0882054\pi\) |
−0.717847 | + | 0.696201i | \(0.754872\pi\) | |||||||
\(824\) | − | 4.00000i | − | 0.139347i | ||||||
\(825\) | −20.7846 | + | 12.0000i | −0.723627 | + | 0.417786i | ||||
\(826\) | −5.19615 | + | 3.00000i | −0.180797 | + | 0.104383i | ||||
\(827\) | 18.0000i | 0.625921i | 0.949766 | + | 0.312961i | \(0.101321\pi\) | ||||
−0.949766 | + | 0.312961i | \(0.898679\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.0000 | − | 32.9090i | 0.659897 | − | 1.14298i | −0.320745 | − | 0.947166i | \(-0.603933\pi\) |
0.980642 | − | 0.195810i | \(-0.0627335\pi\) | |||||||
\(830\) | −31.1769 | − | 18.0000i | −1.08217 | − | 0.624789i | ||||
\(831\) | 28.0000 | 0.971309 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 11.2583 | + | 6.50000i | 0.389844 | + | 0.225077i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.00000 | + | 10.3923i | 0.207514 | + | 0.359425i | ||||
\(837\) | − | 20.0000i | − | 0.691301i | ||||||
\(838\) | 7.79423 | − | 4.50000i | 0.269247 | − | 0.155450i | ||||
\(839\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(840\) | − | 3.00000i | − | 0.103510i | ||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −8.50000 | + | 14.7224i | −0.292929 | + | 0.507369i | ||||
\(843\) | 5.19615 | + | 3.00000i | 0.178965 | + | 0.103325i | ||||
\(844\) | 13.0000 | 0.447478 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | −21.6506 | − | 12.5000i | −0.743925 | − | 0.429505i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.00000 | − | 3.46410i | −0.0686398 | − | 0.118888i | ||||
\(850\) | − | 12.0000i | − | 0.411597i | ||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −2.59808 | + | 1.50000i | −0.0890086 | + | 0.0513892i | ||||
\(853\) | − | 37.0000i | − | 1.26686i | −0.773802 | − | 0.633428i | \(-0.781647\pi\) | ||
0.773802 | − | 0.633428i | \(-0.218353\pi\) | |||||||
\(854\) | −4.00000 | − | 6.92820i | −0.136877 | − | 0.237078i | ||||
\(855\) | 6.00000 | − | 10.3923i | 0.205196 | − | 0.355409i | ||||
\(856\) | 10.3923 | + | 6.00000i | 0.355202 | + | 0.205076i | ||||
\(857\) | 42.0000 | 1.43469 | 0.717346 | − | 0.696717i | \(-0.245357\pi\) | ||||
0.717346 | + | 0.696717i | \(0.245357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.00000 | −0.136478 | −0.0682391 | − | 0.997669i | \(-0.521738\pi\) | ||||
−0.0682391 | + | 0.997669i | \(0.521738\pi\) | |||||||
\(860\) | 2.59808 | + | 1.50000i | 0.0885937 | + | 0.0511496i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.5000 | + | 28.5788i | 0.561992 | + | 0.973399i | ||||
\(863\) | 45.0000i | 1.53182i | 0.642949 | + | 0.765909i | \(0.277711\pi\) | ||||
−0.642949 | + | 0.765909i | \(0.722289\pi\) | |||||||
\(864\) | −4.33013 | + | 2.50000i | −0.147314 | + | 0.0850517i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 25.0000i | 0.849535i | ||||||||
\(867\) | 4.00000 | + | 6.92820i | 0.135847 | + | 0.235294i | ||||
\(868\) | 2.00000 | − | 3.46410i | 0.0678844 | − | 0.117579i | ||||
\(869\) | −41.5692 | − | 24.0000i | −1.41014 | − | 0.814144i | ||||
\(870\) | −18.0000 | −0.610257 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7.00000 | 0.237050 | ||||||||
\(873\) | 17.3205 | + | 10.0000i | 0.586210 | + | 0.338449i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | − | 2.59808i | −0.0507093 | − | 0.0878310i | ||||
\(876\) | − | 2.00000i | − | 0.0675737i | ||||||
\(877\) | 11.2583 | − | 6.50000i | 0.380167 | − | 0.219489i | −0.297724 | − | 0.954652i | \(-0.596228\pi\) |
0.677891 | + | 0.735163i | \(0.262894\pi\) | |||||||
\(878\) | −22.5167 | + | 13.0000i | −0.759900 | + | 0.438729i | ||||
\(879\) | 21.0000i | 0.708312i | ||||||||
\(880\) | 9.00000 | + | 15.5885i | 0.303390 | + | 0.525487i | ||||
\(881\) | 10.5000 | − | 18.1865i | 0.353754 | − | 0.612720i | −0.633150 | − | 0.774029i | \(-0.718238\pi\) |
0.986904 | + | 0.161309i | \(0.0515717\pi\) | |||||||
\(882\) | 10.3923 | + | 6.00000i | 0.349927 | + | 0.202031i | ||||
\(883\) | −29.0000 | −0.975928 | −0.487964 | − | 0.872864i | \(-0.662260\pi\) | ||||
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.0000 | 0.605063 | ||||||||
\(886\) | −18.1865 | − | 10.5000i | −0.610989 | − | 0.352754i | ||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 3.50000 | + | 6.06218i | 0.117452 | + | 0.203433i | ||||
\(889\) | 20.0000i | 0.670778i | ||||||||
\(890\) | 15.5885 | − | 9.00000i | 0.522526 | − | 0.301681i | ||||
\(891\) | 5.19615 | − | 3.00000i | 0.174078 | − | 0.100504i | ||||
\(892\) | − | 19.0000i | − | 0.636167i | ||||||
\(893\) | −3.00000 | − | 5.19615i | −0.100391 | − | 0.173883i | ||||
\(894\) | 3.00000 | − | 5.19615i | 0.100335 | − | 0.173785i | ||||
\(895\) | 7.79423 | + | 4.50000i | 0.260532 | + | 0.150418i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.00000 | −0.200223 | ||||||||
\(899\) | −20.7846 | − | 12.0000i | −0.693206 | − | 0.400222i | ||||
\(900\) | 4.00000 | − | 6.92820i | 0.133333 | − | 0.230940i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.866025 | + | 0.500000i | −0.0288195 | + | 0.0166390i | ||||
\(904\) | 5.19615 | − | 3.00000i | 0.172821 | − | 0.0997785i | ||||
\(905\) | − | 60.0000i | − | 1.99447i | ||||||
\(906\) | 8.50000 | + | 14.7224i | 0.282394 | + | 0.489120i | ||||
\(907\) | −18.5000 | + | 32.0429i | −0.614282 | + | 1.06397i | 0.376228 | + | 0.926527i | \(0.377221\pi\) |
−0.990510 | + | 0.137441i | \(0.956112\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.0000 | −0.796030 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 1.73205 | + | 1.00000i | 0.0573539 | + | 0.0331133i | ||||
\(913\) | −36.0000 | + | 62.3538i | −1.19143 | + | 2.06361i | ||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | 24.0000i | 0.793416i | ||||||||
\(916\) | 11.2583 | − | 6.50000i | 0.371986 | − | 0.214766i | ||||
\(917\) | 18.1865 | − | 10.5000i | 0.600572 | − | 0.346741i | ||||
\(918\) | − | 15.0000i | − | 0.495074i | ||||||
\(919\) | 8.00000 | + | 13.8564i | 0.263896 | + | 0.457081i | 0.967274 | − | 0.253735i | \(-0.0816592\pi\) |
−0.703378 | + | 0.710816i | \(0.748326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.73205 | − | 1.00000i | −0.0570730 | − | 0.0329511i | ||||
\(922\) | 9.00000 | 0.296399 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −6.00000 | −0.197386 | ||||||||
\(925\) | −24.2487 | − | 14.0000i | −0.797293 | − | 0.460317i | ||||
\(926\) | −20.0000 | + | 34.6410i | −0.657241 | + | 1.13837i | ||||
\(927\) | 4.00000 | + | 6.92820i | 0.131377 | + | 0.227552i | ||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | −31.1769 | + | 18.0000i | −1.02288 | + | 0.590561i | −0.914937 | − | 0.403596i | \(-0.867760\pi\) |
−0.107944 | + | 0.994157i | \(0.534427\pi\) | |||||||
\(930\) | −10.3923 | + | 6.00000i | −0.340777 | + | 0.196748i | ||||
\(931\) | − | 12.0000i | − | 0.393284i | ||||||
\(932\) | 13.5000 | + | 23.3827i | 0.442207 | + | 0.765925i | ||||
\(933\) | −15.0000 | + | 25.9808i | −0.491078 | + | 0.850572i | ||||
\(934\) | 31.1769 | + | 18.0000i | 1.02014 | + | 0.588978i | ||||
\(935\) | −54.0000 | −1.76599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 12.1244 | + | 7.00000i | 0.395874 | + | 0.228558i | ||||
\(939\) | 0.500000 | − | 0.866025i | 0.0163169 | − | 0.0282617i | ||||
\(940\) | −4.50000 | − | 7.79423i | −0.146774 | − | 0.254220i | ||||
\(941\) | 21.0000i | 0.684580i | 0.939594 | + | 0.342290i | \(0.111203\pi\) | ||||
−0.939594 | + | 0.342290i | \(0.888797\pi\) | |||||||
\(942\) | 12.1244 | − | 7.00000i | 0.395033 | − | 0.228072i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 6.00000i | − | 0.195283i | ||||||
\(945\) | 7.50000 | + | 12.9904i | 0.243975 | + | 0.422577i | ||||
\(946\) | 3.00000 | − | 5.19615i | 0.0975384 | − | 0.168941i | ||||
\(947\) | −5.19615 | − | 3.00000i | −0.168852 | − | 0.0974869i | 0.413192 | − | 0.910644i | \(-0.364414\pi\) |
−0.582045 | + | 0.813157i | \(0.697747\pi\) | |||||||
\(948\) | −8.00000 | −0.259828 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.00000 | −0.259554 | ||||||||
\(951\) | −5.19615 | − | 3.00000i | −0.168497 | − | 0.0972817i | ||||
\(952\) | 1.50000 | − | 2.59808i | 0.0486153 | − | 0.0842041i | ||||
\(953\) | 7.50000 | + | 12.9904i | 0.242949 | + | 0.420800i | 0.961553 | − | 0.274620i | \(-0.0885520\pi\) |
−0.718604 | + | 0.695419i | \(0.755219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.7654 | + | 27.0000i | −1.51329 | + | 0.873699i | ||||
\(956\) | 12.9904 | − | 7.50000i | 0.420139 | − | 0.242567i | ||||
\(957\) | 36.0000i | 1.16371i | ||||||||
\(958\) | −10.5000 | − | 18.1865i | −0.339240 | − | 0.587580i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.59808 | + | 1.50000i | 0.0838525 | + | 0.0484123i | ||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.0000 | −0.773389 | ||||||||
\(964\) | −8.66025 | − | 5.00000i | −0.278928 | − | 0.161039i | ||||
\(965\) | −6.00000 | + | 10.3923i | −0.193147 | + | 0.334540i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.0000i | 0.996893i | 0.866921 | + | 0.498446i | \(0.166096\pi\) | ||||
−0.866921 | + | 0.498446i | \(0.833904\pi\) | |||||||
\(968\) | 21.6506 | − | 12.5000i | 0.695878 | − | 0.401765i | ||||
\(969\) | −5.19615 | + | 3.00000i | −0.166924 | + | 0.0963739i | ||||
\(970\) | − | 30.0000i | − | 0.963242i | ||||||
\(971\) | 1.50000 | + | 2.59808i | 0.0481373 | + | 0.0833762i | 0.889090 | − | 0.457732i | \(-0.151338\pi\) |
−0.840953 | + | 0.541108i | \(0.818005\pi\) | |||||||
\(972\) | 8.00000 | − | 13.8564i | 0.256600 | − | 0.444444i | ||||
\(973\) | −11.2583 | − | 6.50000i | −0.360925 | − | 0.208380i | ||||
\(974\) | −16.0000 | −0.512673 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.00000 | 0.256074 | ||||||||
\(977\) | −46.7654 | − | 27.0000i | −1.49616 | − | 0.863807i | −0.496167 | − | 0.868227i | \(-0.665259\pi\) |
−0.999990 | + | 0.00442082i | \(0.998593\pi\) | |||||||
\(978\) | −8.00000 | + | 13.8564i | −0.255812 | + | 0.443079i | ||||
\(979\) | −18.0000 | − | 31.1769i | −0.575282 | − | 0.996419i | ||||
\(980\) | − | 18.0000i | − | 0.574989i | ||||||
\(981\) | −12.1244 | + | 7.00000i | −0.387101 | + | 0.223493i | ||||
\(982\) | 7.79423 | − | 4.50000i | 0.248724 | − | 0.143601i | ||||
\(983\) | 39.0000i | 1.24391i | 0.783054 | + | 0.621953i | \(0.213661\pi\) | ||||
−0.783054 | + | 0.621953i | \(0.786339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.50000 | + | 7.79423i | −0.143382 | + | 0.248345i | ||||
\(986\) | −15.5885 | − | 9.00000i | −0.496438 | − | 0.286618i | ||||
\(987\) | 3.00000 | 0.0954911 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −31.1769 | − | 18.0000i | −0.990867 | − | 0.572078i | ||||
\(991\) | −1.00000 | + | 1.73205i | −0.0317660 | + | 0.0550204i | −0.881471 | − | 0.472237i | \(-0.843446\pi\) |
0.849705 | + | 0.527258i | \(0.176780\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | − | 8.00000i | − | 0.253872i | ||||||
\(994\) | 2.59808 | − | 1.50000i | 0.0824060 | − | 0.0475771i | ||||
\(995\) | −5.19615 | + | 3.00000i | −0.164729 | + | 0.0951064i | ||||
\(996\) | 12.0000i | 0.380235i | ||||||||
\(997\) | 23.0000 | + | 39.8372i | 0.728417 | + | 1.26166i | 0.957552 | + | 0.288261i | \(0.0930771\pi\) |
−0.229135 | + | 0.973395i | \(0.573590\pi\) | |||||||
\(998\) | 20.0000 | − | 34.6410i | 0.633089 | − | 1.09654i | ||||
\(999\) | −30.3109 | − | 17.5000i | −0.958994 | − | 0.553675i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))