Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(49,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.j (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: | \(3.59326809096\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.49 |
Dual form | 450.2.j.d.349.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | −0.866025 | + | 1.50000i | −0.500000 | + | 0.866025i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.73205i | 0.707107i | ||||||||
\(7\) | 3.46410 | − | 2.00000i | 1.30931 | − | 0.755929i | 0.327327 | − | 0.944911i | \(-0.393852\pi\) |
0.981981 | + | 0.188982i | \(0.0605189\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.50000 | − | 2.59808i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0.866025 | + | 1.50000i | 0.250000 | + | 0.433013i | ||||
\(13\) | 3.46410 | + | 2.00000i | 0.960769 | + | 0.554700i | 0.896410 | − | 0.443227i | \(-0.146166\pi\) |
0.0643593 | + | 0.997927i | \(0.479500\pi\) | |||||||
\(14\) | 2.00000 | − | 3.46410i | 0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.00000i | 0.727607i | 0.931476 | + | 0.363803i | \(0.118522\pi\) | ||||
−0.931476 | + | 0.363803i | \(0.881478\pi\) | |||||||
\(18\) | −2.59808 | − | 1.50000i | −0.612372 | − | 0.353553i | ||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.92820i | 1.51186i | ||||||||
\(22\) | −2.59808 | − | 1.50000i | −0.553912 | − | 0.319801i | ||||
\(23\) | 5.19615 | + | 3.00000i | 1.08347 | + | 0.625543i | 0.931831 | − | 0.362892i | \(-0.118211\pi\) |
0.151642 | + | 0.988436i | \(0.451544\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | + | 6.92820i | −0.718421 | + | 1.24434i | 0.243204 | + | 0.969975i | \(0.421802\pi\) |
−0.961625 | + | 0.274367i | \(0.911532\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 5.19615 | 0.904534 | ||||||||
\(34\) | 1.50000 | + | 2.59808i | 0.257248 | + | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | − | 8.00000i | − | 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | 3.46410 | − | 2.00000i | 0.561951 | − | 0.324443i | ||||
\(39\) | −6.00000 | + | 3.46410i | −0.960769 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 3.46410 | + | 6.00000i | 0.534522 | + | 0.925820i | ||||
\(43\) | −0.866025 | + | 0.500000i | −0.132068 | + | 0.0762493i | −0.564578 | − | 0.825380i | \(-0.690961\pi\) |
0.432511 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −10.3923 | + | 6.00000i | −1.51587 | + | 0.875190i | −0.516047 | + | 0.856560i | \(0.672597\pi\) |
−0.999826 | + | 0.0186297i | \(0.994070\pi\) | |||||||
\(48\) | 1.73205 | 0.250000 | ||||||||
\(49\) | 4.50000 | − | 7.79423i | 0.642857 | − | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | − | 2.59808i | −0.630126 | − | 0.363803i | ||||
\(52\) | 3.46410 | − | 2.00000i | 0.480384 | − | 0.277350i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 4.50000 | − | 2.59808i | 0.612372 | − | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | − | 3.46410i | −0.267261 | − | 0.462910i | ||||
\(57\) | −3.46410 | + | 6.00000i | −0.458831 | + | 0.794719i | ||||
\(58\) | −5.19615 | − | 3.00000i | −0.682288 | − | 0.393919i | ||||
\(59\) | −4.50000 | + | 7.79423i | −0.585850 | + | 1.01472i | 0.408919 | + | 0.912571i | \(0.365906\pi\) |
−0.994769 | + | 0.102151i | \(0.967427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | − | 6.92820i | −0.512148 | − | 0.887066i | −0.999901 | − | 0.0140840i | \(-0.995517\pi\) |
0.487753 | − | 0.872982i | \(-0.337817\pi\) | |||||||
\(62\) | 8.00000i | 1.01600i | ||||||||
\(63\) | −10.3923 | − | 6.00000i | −1.30931 | − | 0.755929i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.50000 | − | 2.59808i | 0.553912 | − | 0.319801i | ||||
\(67\) | −3.46410 | − | 2.00000i | −0.423207 | − | 0.244339i | 0.273241 | − | 0.961946i | \(-0.411904\pi\) |
−0.696449 | + | 0.717607i | \(0.745238\pi\) | |||||||
\(68\) | 2.59808 | + | 1.50000i | 0.315063 | + | 0.181902i | ||||
\(69\) | −9.00000 | + | 5.19615i | −1.08347 | + | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.00000 | −0.712069 | −0.356034 | − | 0.934473i | \(-0.615871\pi\) | ||||
−0.356034 | + | 0.934473i | \(0.615871\pi\) | |||||||
\(72\) | −2.59808 | + | 1.50000i | −0.306186 | + | 0.176777i | ||||
\(73\) | 14.0000i | 1.63858i | 0.573382 | + | 0.819288i | \(0.305631\pi\) | ||||
−0.573382 | + | 0.819288i | \(0.694369\pi\) | |||||||
\(74\) | −4.00000 | − | 6.92820i | −0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | −10.3923 | − | 6.00000i | −1.18431 | − | 0.683763i | ||||
\(78\) | −3.46410 | + | 6.00000i | −0.392232 | + | 0.679366i | ||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | − | 6.00000i | − | 0.662589i | ||||||
\(83\) | −7.79423 | + | 4.50000i | −0.855528 | + | 0.493939i | −0.862512 | − | 0.506036i | \(-0.831110\pi\) |
0.00698436 | + | 0.999976i | \(0.497777\pi\) | |||||||
\(84\) | 6.00000 | + | 3.46410i | 0.654654 | + | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.500000 | + | 0.866025i | −0.0539164 | + | 0.0933859i | ||||
\(87\) | 10.3923 | 1.11417 | ||||||||
\(88\) | −2.59808 | + | 1.50000i | −0.276956 | + | 0.159901i | ||||
\(89\) | 9.00000 | 0.953998 | 0.476999 | − | 0.878904i | \(-0.341725\pi\) | ||||
0.476999 | + | 0.878904i | \(0.341725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 5.19615 | − | 3.00000i | 0.541736 | − | 0.312772i | ||||
\(93\) | −6.92820 | − | 12.0000i | −0.718421 | − | 1.24434i | ||||
\(94\) | −6.00000 | + | 10.3923i | −0.618853 | + | 1.07188i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | − | 0.866025i | 0.153093 | − | 0.0883883i | ||||
\(97\) | 6.06218 | − | 3.50000i | 0.615521 | − | 0.355371i | −0.159602 | − | 0.987181i | \(-0.551021\pi\) |
0.775123 | + | 0.631810i | \(0.217688\pi\) | |||||||
\(98\) | − | 9.00000i | − | 0.909137i | ||||||
\(99\) | −4.50000 | + | 7.79423i | −0.452267 | + | 0.783349i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | −5.19615 | −0.514496 | ||||||||
\(103\) | −6.92820 | − | 4.00000i | −0.682656 | − | 0.394132i | 0.118199 | − | 0.992990i | \(-0.462288\pi\) |
−0.800855 | + | 0.598858i | \(0.795621\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 12.0000i | − | 1.16008i | −0.814587 | − | 0.580042i | \(-0.803036\pi\) | ||
0.814587 | − | 0.580042i | \(-0.196964\pi\) | |||||||
\(108\) | 2.59808 | − | 4.50000i | 0.250000 | − | 0.433013i | ||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | + | 6.92820i | 1.13899 | + | 0.657596i | ||||
\(112\) | −3.46410 | − | 2.00000i | −0.327327 | − | 0.188982i | ||||
\(113\) | −2.59808 | − | 1.50000i | −0.244406 | − | 0.141108i | 0.372794 | − | 0.927914i | \(-0.378400\pi\) |
−0.617200 | + | 0.786806i | \(0.711733\pi\) | |||||||
\(114\) | 6.92820i | 0.648886i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | − | 12.0000i | − | 1.10940i | ||||||
\(118\) | 9.00000i | 0.828517i | ||||||||
\(119\) | 6.00000 | + | 10.3923i | 0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | −6.92820 | − | 4.00000i | −0.627250 | − | 0.362143i | ||||
\(123\) | 5.19615 | + | 9.00000i | 0.468521 | + | 0.811503i | ||||
\(124\) | 4.00000 | + | 6.92820i | 0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.0000 | −1.06904 | ||||||||
\(127\) | 16.0000i | 1.41977i | 0.704317 | + | 0.709885i | \(0.251253\pi\) | ||||
−0.704317 | + | 0.709885i | \(0.748747\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | − | 1.73205i | − | 0.152499i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | + | 10.3923i | −0.524222 | + | 0.907980i | 0.475380 | + | 0.879781i | \(0.342311\pi\) |
−0.999602 | + | 0.0281993i | \(0.991023\pi\) | |||||||
\(132\) | 2.59808 | − | 4.50000i | 0.226134 | − | 0.391675i | ||||
\(133\) | 13.8564 | − | 8.00000i | 1.20150 | − | 0.693688i | ||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −15.5885 | + | 9.00000i | −1.33181 | + | 0.768922i | −0.985577 | − | 0.169226i | \(-0.945873\pi\) |
−0.346235 | + | 0.938148i | \(0.612540\pi\) | |||||||
\(138\) | −5.19615 | + | 9.00000i | −0.442326 | + | 0.766131i | ||||
\(139\) | 5.50000 | − | 9.52628i | 0.466504 | − | 0.808008i | −0.532764 | − | 0.846264i | \(-0.678847\pi\) |
0.999268 | + | 0.0382553i | \(0.0121800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 20.7846i | − | 1.75038i | ||||||
\(142\) | −5.19615 | + | 3.00000i | −0.436051 | + | 0.251754i | ||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.00000 | + | 12.1244i | 0.579324 | + | 1.00342i | ||||
\(147\) | 7.79423 | + | 13.5000i | 0.642857 | + | 1.11346i | ||||
\(148\) | −6.92820 | − | 4.00000i | −0.569495 | − | 0.328798i | ||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | + | 8.66025i | 0.406894 | + | 0.704761i | 0.994540 | − | 0.104357i | \(-0.0332784\pi\) |
−0.587646 | + | 0.809118i | \(0.699945\pi\) | |||||||
\(152\) | − | 4.00000i | − | 0.324443i | ||||||
\(153\) | 7.79423 | − | 4.50000i | 0.630126 | − | 0.363803i | ||||
\(154\) | −12.0000 | −0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.92820i | 0.554700i | ||||||||
\(157\) | −3.46410 | − | 2.00000i | −0.276465 | − | 0.159617i | 0.355357 | − | 0.934731i | \(-0.384359\pi\) |
−0.631822 | + | 0.775113i | \(0.717693\pi\) | |||||||
\(158\) | 6.92820 | + | 4.00000i | 0.551178 | + | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | 9.00000i | 0.707107i | ||||||||
\(163\) | 11.0000i | 0.861586i | 0.902451 | + | 0.430793i | \(0.141766\pi\) | ||||
−0.902451 | + | 0.430793i | \(0.858234\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | + | 7.79423i | −0.349268 | + | 0.604949i | ||||
\(167\) | 15.5885 | + | 9.00000i | 1.20627 | + | 0.696441i | 0.961943 | − | 0.273252i | \(-0.0880992\pi\) |
0.244328 | + | 0.969693i | \(0.421432\pi\) | |||||||
\(168\) | 6.92820 | 0.534522 | ||||||||
\(169\) | 1.50000 | + | 2.59808i | 0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | − | 10.3923i | −0.458831 | − | 0.794719i | ||||
\(172\) | 1.00000i | 0.0762493i | ||||||||
\(173\) | −5.19615 | + | 3.00000i | −0.395056 | + | 0.228086i | −0.684349 | − | 0.729155i | \(-0.739913\pi\) |
0.289292 | + | 0.957241i | \(0.406580\pi\) | |||||||
\(174\) | 9.00000 | − | 5.19615i | 0.682288 | − | 0.393919i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | + | 2.59808i | −0.113067 | + | 0.195837i | ||||
\(177\) | −7.79423 | − | 13.5000i | −0.585850 | − | 1.01472i | ||||
\(178\) | 7.79423 | − | 4.50000i | 0.584202 | − | 0.337289i | ||||
\(179\) | 3.00000 | 0.224231 | 0.112115 | − | 0.993695i | \(-0.464237\pi\) | ||||
0.112115 | + | 0.993695i | \(0.464237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 13.8564 | − | 8.00000i | 1.02711 | − | 0.592999i | ||||
\(183\) | 13.8564 | 1.02430 | ||||||||
\(184\) | 3.00000 | − | 5.19615i | 0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.0000 | − | 6.92820i | −0.879883 | − | 0.508001i | ||||
\(187\) | 7.79423 | − | 4.50000i | 0.569970 | − | 0.329073i | ||||
\(188\) | 12.0000i | 0.875190i | ||||||||
\(189\) | 18.0000 | − | 10.3923i | 1.30931 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | 0.866025 | − | 1.50000i | 0.0625000 | − | 0.108253i | ||||
\(193\) | −4.33013 | − | 2.50000i | −0.311689 | − | 0.179954i | 0.335993 | − | 0.941865i | \(-0.390928\pi\) |
−0.647682 | + | 0.761911i | \(0.724262\pi\) | |||||||
\(194\) | 3.50000 | − | 6.06218i | 0.251285 | − | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | − | 7.79423i | −0.321429 | − | 0.556731i | ||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 9.00000i | 0.639602i | ||||||||
\(199\) | −2.00000 | −0.141776 | −0.0708881 | − | 0.997484i | \(-0.522583\pi\) | ||||
−0.0708881 | + | 0.997484i | \(0.522583\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | − | 3.46410i | 0.423207 | − | 0.244339i | ||||
\(202\) | −10.3923 | − | 6.00000i | −0.731200 | − | 0.422159i | ||||
\(203\) | −20.7846 | − | 12.0000i | −1.45879 | − | 0.842235i | ||||
\(204\) | −4.50000 | + | 2.59808i | −0.315063 | + | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | − | 18.0000i | − | 1.25109i | ||||||
\(208\) | − | 4.00000i | − | 0.277350i | ||||||
\(209\) | −6.00000 | − | 10.3923i | −0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5000 | + | 19.9186i | −0.791693 | + | 1.37125i | 0.133226 | + | 0.991086i | \(0.457467\pi\) |
−0.924918 | + | 0.380166i | \(0.875867\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.19615 | − | 9.00000i | 0.356034 | − | 0.616670i | ||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 5.19615i | − | 0.353553i | ||||||
\(217\) | 32.0000i | 2.17230i | ||||||||
\(218\) | −1.73205 | + | 1.00000i | −0.117309 | + | 0.0677285i | ||||
\(219\) | −21.0000 | − | 12.1244i | −1.41905 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | + | 10.3923i | −0.403604 | + | 0.699062i | ||||
\(222\) | 13.8564 | 0.929981 | ||||||||
\(223\) | 1.73205 | − | 1.00000i | 0.115987 | − | 0.0669650i | −0.440884 | − | 0.897564i | \(-0.645335\pi\) |
0.556871 | + | 0.830599i | \(0.312002\pi\) | |||||||
\(224\) | −4.00000 | −0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00000 | −0.199557 | ||||||||
\(227\) | 23.3827 | − | 13.5000i | 1.55196 | − | 0.896026i | 0.553981 | − | 0.832529i | \(-0.313108\pi\) |
0.997982 | − | 0.0634974i | \(-0.0202255\pi\) | |||||||
\(228\) | 3.46410 | + | 6.00000i | 0.229416 | + | 0.397360i | ||||
\(229\) | 4.00000 | − | 6.92820i | 0.264327 | − | 0.457829i | −0.703060 | − | 0.711131i | \(-0.748183\pi\) |
0.967387 | + | 0.253302i | \(0.0815167\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | − | 10.3923i | 1.18431 | − | 0.683763i | ||||
\(232\) | −5.19615 | + | 3.00000i | −0.341144 | + | 0.196960i | ||||
\(233\) | 15.0000i | 0.982683i | 0.870967 | + | 0.491341i | \(0.163493\pi\) | ||||
−0.870967 | + | 0.491341i | \(0.836507\pi\) | |||||||
\(234\) | −6.00000 | − | 10.3923i | −0.392232 | − | 0.679366i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.50000 | + | 7.79423i | 0.292925 | + | 0.507361i | ||||
\(237\) | −13.8564 | −0.900070 | ||||||||
\(238\) | 10.3923 | + | 6.00000i | 0.673633 | + | 0.388922i | ||||
\(239\) | 9.00000 | − | 15.5885i | 0.582162 | − | 1.00833i | −0.413061 | − | 0.910703i | \(-0.635540\pi\) |
0.995223 | − | 0.0976302i | \(-0.0311262\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | − | 22.5167i | −0.837404 | − | 1.45043i | −0.892058 | − | 0.451920i | \(-0.850739\pi\) |
0.0546547 | − | 0.998505i | \(-0.482594\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | −7.79423 | − | 13.5000i | −0.500000 | − | 0.866025i | ||||
\(244\) | −8.00000 | −0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | + | 5.19615i | 0.573819 | + | 0.331295i | ||||
\(247\) | 13.8564 | + | 8.00000i | 0.881662 | + | 0.509028i | ||||
\(248\) | 6.92820 | + | 4.00000i | 0.439941 | + | 0.254000i | ||||
\(249\) | − | 15.5885i | − | 0.987878i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −10.3923 | + | 6.00000i | −0.654654 | + | 0.377964i | ||||
\(253\) | − | 18.0000i | − | 1.13165i | ||||||
\(254\) | 8.00000 | + | 13.8564i | 0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 2.59808 | + | 1.50000i | 0.162064 | + | 0.0935674i | 0.578838 | − | 0.815442i | \(-0.303506\pi\) |
−0.416775 | + | 0.909010i | \(0.636840\pi\) | |||||||
\(258\) | −0.866025 | − | 1.50000i | −0.0539164 | − | 0.0933859i | ||||
\(259\) | −16.0000 | − | 27.7128i | −0.994192 | − | 1.72199i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | + | 15.5885i | −0.557086 | + | 0.964901i | ||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | 20.7846 | − | 12.0000i | 1.28163 | − | 0.739952i | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | − | 5.19615i | − | 0.319801i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | − | 13.8564i | 0.490511 | − | 0.849591i | ||||
\(267\) | −7.79423 | + | 13.5000i | −0.476999 | + | 0.826187i | ||||
\(268\) | −3.46410 | + | 2.00000i | −0.211604 | + | 0.122169i | ||||
\(269\) | 12.0000 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | 2.59808 | − | 1.50000i | 0.157532 | − | 0.0909509i | ||||
\(273\) | −13.8564 | + | 24.0000i | −0.838628 | + | 1.45255i | ||||
\(274\) | −9.00000 | + | 15.5885i | −0.543710 | + | 0.941733i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 10.3923i | 0.625543i | ||||||||
\(277\) | −1.73205 | + | 1.00000i | −0.104069 | + | 0.0600842i | −0.551131 | − | 0.834419i | \(-0.685804\pi\) |
0.447062 | + | 0.894503i | \(0.352470\pi\) | |||||||
\(278\) | − | 11.0000i | − | 0.659736i | ||||||
\(279\) | 24.0000 | 1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | + | 15.5885i | 0.536895 | + | 0.929929i | 0.999069 | + | 0.0431402i | \(0.0137362\pi\) |
−0.462174 | + | 0.886789i | \(0.652930\pi\) | |||||||
\(282\) | −10.3923 | − | 18.0000i | −0.618853 | − | 1.07188i | ||||
\(283\) | 0.866025 | + | 0.500000i | 0.0514799 | + | 0.0297219i | 0.525519 | − | 0.850782i | \(-0.323871\pi\) |
−0.474039 | + | 0.880504i | \(0.657204\pi\) | |||||||
\(284\) | −3.00000 | + | 5.19615i | −0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | − | 10.3923i | −0.354787 | − | 0.614510i | ||||
\(287\) | − | 24.0000i | − | 1.41668i | ||||||
\(288\) | 3.00000i | 0.176777i | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.1244i | 0.710742i | ||||||||
\(292\) | 12.1244 | + | 7.00000i | 0.709524 | + | 0.409644i | ||||
\(293\) | 10.3923 | + | 6.00000i | 0.607125 | + | 0.350524i | 0.771839 | − | 0.635818i | \(-0.219337\pi\) |
−0.164714 | + | 0.986341i | \(0.552670\pi\) | |||||||
\(294\) | 13.5000 | + | 7.79423i | 0.787336 | + | 0.454569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | −7.79423 | − | 13.5000i | −0.452267 | − | 0.783349i | ||||
\(298\) | 6.00000i | 0.347571i | ||||||||
\(299\) | 12.0000 | + | 20.7846i | 0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | + | 3.46410i | −0.115278 | + | 0.199667i | ||||
\(302\) | 8.66025 | + | 5.00000i | 0.498342 | + | 0.287718i | ||||
\(303\) | 20.7846 | 1.19404 | ||||||||
\(304\) | −2.00000 | − | 3.46410i | −0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.50000 | − | 7.79423i | 0.257248 | − | 0.445566i | ||||
\(307\) | 1.00000i | 0.0570730i | 0.999593 | + | 0.0285365i | \(0.00908469\pi\) | ||||
−0.999593 | + | 0.0285365i | \(0.990915\pi\) | |||||||
\(308\) | −10.3923 | + | 6.00000i | −0.592157 | + | 0.341882i | ||||
\(309\) | 12.0000 | − | 6.92820i | 0.682656 | − | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | + | 5.19615i | −0.170114 | + | 0.294647i | −0.938460 | − | 0.345389i | \(-0.887747\pi\) |
0.768345 | + | 0.640036i | \(0.221080\pi\) | |||||||
\(312\) | 3.46410 | + | 6.00000i | 0.196116 | + | 0.339683i | ||||
\(313\) | 14.7224 | − | 8.50000i | 0.832161 | − | 0.480448i | −0.0224310 | − | 0.999748i | \(-0.507141\pi\) |
0.854592 | + | 0.519300i | \(0.173807\pi\) | |||||||
\(314\) | −4.00000 | −0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 15.5885 | − | 9.00000i | 0.875535 | − | 0.505490i | 0.00635137 | − | 0.999980i | \(-0.497978\pi\) |
0.869184 | + | 0.494489i | \(0.164645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | + | 15.5885i | −0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | + | 10.3923i | 1.00466 | + | 0.580042i | ||||
\(322\) | 20.7846 | − | 12.0000i | 1.15828 | − | 0.668734i | ||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 4.50000 | + | 7.79423i | 0.250000 | + | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.50000 | + | 9.52628i | 0.304617 | + | 0.527612i | ||||
\(327\) | 1.73205 | − | 3.00000i | 0.0957826 | − | 0.165900i | ||||
\(328\) | −5.19615 | − | 3.00000i | −0.286910 | − | 0.165647i | ||||
\(329\) | −24.0000 | + | 41.5692i | −1.32316 | + | 2.29179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | − | 14.7224i | −0.467202 | − | 0.809218i | 0.532096 | − | 0.846684i | \(-0.321405\pi\) |
−0.999298 | + | 0.0374662i | \(0.988071\pi\) | |||||||
\(332\) | 9.00000i | 0.493939i | ||||||||
\(333\) | −20.7846 | + | 12.0000i | −1.13899 | + | 0.657596i | ||||
\(334\) | 18.0000 | 0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.00000 | − | 3.46410i | 0.327327 | − | 0.188982i | ||||
\(337\) | −11.2583 | − | 6.50000i | −0.613280 | − | 0.354078i | 0.160968 | − | 0.986960i | \(-0.448538\pi\) |
−0.774248 | + | 0.632882i | \(0.781872\pi\) | |||||||
\(338\) | 2.59808 | + | 1.50000i | 0.141317 | + | 0.0815892i | ||||
\(339\) | 4.50000 | − | 2.59808i | 0.244406 | − | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | −10.3923 | − | 6.00000i | −0.561951 | − | 0.324443i | ||||
\(343\) | − | 8.00000i | − | 0.431959i | ||||||
\(344\) | 0.500000 | + | 0.866025i | 0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | 23.3827 | + | 13.5000i | 1.25525 | + | 0.724718i | 0.972147 | − | 0.234372i | \(-0.0753034\pi\) |
0.283101 | + | 0.959090i | \(0.408637\pi\) | |||||||
\(348\) | 5.19615 | − | 9.00000i | 0.278543 | − | 0.482451i | ||||
\(349\) | 7.00000 | + | 12.1244i | 0.374701 | + | 0.649002i | 0.990282 | − | 0.139072i | \(-0.0444119\pi\) |
−0.615581 | + | 0.788074i | \(0.711079\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | + | 10.3923i | 0.960769 | + | 0.554700i | ||||
\(352\) | 3.00000i | 0.159901i | ||||||||
\(353\) | −7.79423 | + | 4.50000i | −0.414845 | + | 0.239511i | −0.692869 | − | 0.721063i | \(-0.743654\pi\) |
0.278024 | + | 0.960574i | \(0.410320\pi\) | |||||||
\(354\) | −13.5000 | − | 7.79423i | −0.717517 | − | 0.414259i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.50000 | − | 7.79423i | 0.238500 | − | 0.413093i | ||||
\(357\) | −20.7846 | −1.10004 | ||||||||
\(358\) | 2.59808 | − | 1.50000i | 0.137313 | − | 0.0792775i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 1.73205 | − | 1.00000i | 0.0910346 | − | 0.0525588i | ||||
\(363\) | 1.73205 | + | 3.00000i | 0.0909091 | + | 0.157459i | ||||
\(364\) | 8.00000 | − | 13.8564i | 0.419314 | − | 0.726273i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.0000 | − | 6.92820i | 0.627250 | − | 0.362143i | ||||
\(367\) | −22.5167 | + | 13.0000i | −1.17536 | + | 0.678594i | −0.954937 | − | 0.296810i | \(-0.904077\pi\) |
−0.220423 | + | 0.975404i | \(0.570744\pi\) | |||||||
\(368\) | − | 6.00000i | − | 0.312772i | ||||||
\(369\) | −18.0000 | −0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −13.8564 | −0.718421 | ||||||||
\(373\) | −6.92820 | − | 4.00000i | −0.358729 | − | 0.207112i | 0.309794 | − | 0.950804i | \(-0.399740\pi\) |
−0.668523 | + | 0.743691i | \(0.733073\pi\) | |||||||
\(374\) | 4.50000 | − | 7.79423i | 0.232689 | − | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | + | 10.3923i | 0.309426 | + | 0.535942i | ||||
\(377\) | − | 24.0000i | − | 1.23606i | ||||||
\(378\) | 10.3923 | − | 18.0000i | 0.534522 | − | 0.925820i | ||||
\(379\) | −29.0000 | −1.48963 | −0.744815 | − | 0.667271i | \(-0.767462\pi\) | ||||
−0.744815 | + | 0.667271i | \(0.767462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0000 | − | 13.8564i | −1.22956 | − | 0.709885i | ||||
\(382\) | −5.19615 | − | 3.00000i | −0.265858 | − | 0.153493i | ||||
\(383\) | −15.5885 | − | 9.00000i | −0.796533 | − | 0.459879i | 0.0457244 | − | 0.998954i | \(-0.485440\pi\) |
−0.842257 | + | 0.539076i | \(0.818774\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | 2.59808 | + | 1.50000i | 0.132068 | + | 0.0762493i | ||||
\(388\) | − | 7.00000i | − | 0.355371i | ||||||
\(389\) | −3.00000 | − | 5.19615i | −0.152106 | − | 0.263455i | 0.779895 | − | 0.625910i | \(-0.215272\pi\) |
−0.932002 | + | 0.362454i | \(0.881939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | + | 15.5885i | −0.455150 | + | 0.788342i | ||||
\(392\) | −7.79423 | − | 4.50000i | −0.393668 | − | 0.227284i | ||||
\(393\) | −10.3923 | − | 18.0000i | −0.524222 | − | 0.907980i | ||||
\(394\) | 9.00000 | + | 15.5885i | 0.453413 | + | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.50000 | + | 7.79423i | 0.226134 | + | 0.391675i | ||||
\(397\) | − | 14.0000i | − | 0.702640i | −0.936255 | − | 0.351320i | \(-0.885733\pi\) | ||
0.936255 | − | 0.351320i | \(-0.114267\pi\) | |||||||
\(398\) | −1.73205 | + | 1.00000i | −0.0868199 | + | 0.0501255i | ||||
\(399\) | 27.7128i | 1.38738i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | − | 12.9904i | 0.374532 | − | 0.648709i | −0.615725 | − | 0.787961i | \(-0.711137\pi\) |
0.990257 | + | 0.139253i | \(0.0444700\pi\) | |||||||
\(402\) | 3.46410 | − | 6.00000i | 0.172774 | − | 0.299253i | ||||
\(403\) | −27.7128 | + | 16.0000i | −1.38047 | + | 0.797017i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.0000 | −1.19110 | ||||||||
\(407\) | −20.7846 | + | 12.0000i | −1.03025 | + | 0.594818i | ||||
\(408\) | −2.59808 | + | 4.50000i | −0.128624 | + | 0.222783i | ||||
\(409\) | −11.0000 | + | 19.0526i | −0.543915 | + | 0.942088i | 0.454759 | + | 0.890614i | \(0.349725\pi\) |
−0.998674 | + | 0.0514740i | \(0.983608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 31.1769i | − | 1.53784i | ||||||
\(412\) | −6.92820 | + | 4.00000i | −0.341328 | + | 0.197066i | ||||
\(413\) | 36.0000i | 1.77144i | ||||||||
\(414\) | −9.00000 | − | 15.5885i | −0.442326 | − | 0.766131i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | − | 3.46410i | −0.0980581 | − | 0.169842i | ||||
\(417\) | 9.52628 | + | 16.5000i | 0.466504 | + | 0.808008i | ||||
\(418\) | −10.3923 | − | 6.00000i | −0.508304 | − | 0.293470i | ||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | − | 27.7128i | −0.779792 | − | 1.35064i | −0.932061 | − | 0.362301i | \(-0.881991\pi\) |
0.152269 | − | 0.988339i | \(-0.451342\pi\) | |||||||
\(422\) | 23.0000i | 1.11962i | ||||||||
\(423\) | 31.1769 | + | 18.0000i | 1.51587 | + | 0.875190i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 10.3923i | − | 0.503509i | ||||||
\(427\) | −27.7128 | − | 16.0000i | −1.34112 | − | 0.774294i | ||||
\(428\) | −10.3923 | − | 6.00000i | −0.502331 | − | 0.290021i | ||||
\(429\) | 18.0000 | + | 10.3923i | 0.869048 | + | 0.501745i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | −2.59808 | − | 4.50000i | −0.125000 | − | 0.216506i | ||||
\(433\) | − | 7.00000i | − | 0.336399i | −0.985753 | − | 0.168199i | \(-0.946205\pi\) | ||
0.985753 | − | 0.168199i | \(-0.0537952\pi\) | |||||||
\(434\) | 16.0000 | + | 27.7128i | 0.768025 | + | 1.33026i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | 20.7846 | + | 12.0000i | 0.994263 | + | 0.574038i | ||||
\(438\) | −24.2487 | −1.15865 | ||||||||
\(439\) | 7.00000 | + | 12.1244i | 0.334092 | + | 0.578664i | 0.983310 | − | 0.181938i | \(-0.0582371\pi\) |
−0.649218 | + | 0.760602i | \(0.724904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.0000 | −1.28571 | ||||||||
\(442\) | 12.0000i | 0.570782i | ||||||||
\(443\) | 7.79423 | − | 4.50000i | 0.370315 | − | 0.213801i | −0.303281 | − | 0.952901i | \(-0.598082\pi\) |
0.673596 | + | 0.739100i | \(0.264749\pi\) | |||||||
\(444\) | 12.0000 | − | 6.92820i | 0.569495 | − | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.00000 | − | 1.73205i | 0.0473514 | − | 0.0820150i | ||||
\(447\) | −5.19615 | − | 9.00000i | −0.245770 | − | 0.425685i | ||||
\(448\) | −3.46410 | + | 2.00000i | −0.163663 | + | 0.0944911i | ||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | −2.59808 | + | 1.50000i | −0.122203 | + | 0.0705541i | ||||
\(453\) | −17.3205 | −0.813788 | ||||||||
\(454\) | 13.5000 | − | 23.3827i | 0.633586 | − | 1.09740i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | + | 3.46410i | 0.280976 | + | 0.162221i | ||||
\(457\) | 8.66025 | − | 5.00000i | 0.405110 | − | 0.233890i | −0.283577 | − | 0.958950i | \(-0.591521\pi\) |
0.688686 | + | 0.725059i | \(0.258188\pi\) | |||||||
\(458\) | − | 8.00000i | − | 0.373815i | ||||||
\(459\) | 15.5885i | 0.727607i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | + | 5.19615i | 0.139724 | + | 0.242009i | 0.927392 | − | 0.374091i | \(-0.122045\pi\) |
−0.787668 | + | 0.616100i | \(0.788712\pi\) | |||||||
\(462\) | 10.3923 | − | 18.0000i | 0.483494 | − | 0.837436i | ||||
\(463\) | −12.1244 | − | 7.00000i | −0.563467 | − | 0.325318i | 0.191069 | − | 0.981577i | \(-0.438805\pi\) |
−0.754536 | + | 0.656259i | \(0.772138\pi\) | |||||||
\(464\) | −3.00000 | + | 5.19615i | −0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.50000 | + | 12.9904i | 0.347431 | + | 0.601768i | ||||
\(467\) | − | 9.00000i | − | 0.416470i | −0.978079 | − | 0.208235i | \(-0.933228\pi\) | ||
0.978079 | − | 0.208235i | \(-0.0667719\pi\) | |||||||
\(468\) | −10.3923 | − | 6.00000i | −0.480384 | − | 0.277350i | ||||
\(469\) | −16.0000 | −0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | − | 3.46410i | 0.276465 | − | 0.159617i | ||||
\(472\) | 7.79423 | + | 4.50000i | 0.358758 | + | 0.207129i | ||||
\(473\) | 2.59808 | + | 1.50000i | 0.119460 | + | 0.0689701i | ||||
\(474\) | −12.0000 | + | 6.92820i | −0.551178 | + | 0.318223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 18.0000i | − | 0.823301i | ||||||
\(479\) | −6.00000 | − | 10.3923i | −0.274147 | − | 0.474837i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
−0.969920 | + | 0.243426i | \(0.921729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | − | 27.7128i | 0.729537 | − | 1.26360i | ||||
\(482\) | −22.5167 | − | 13.0000i | −1.02561 | − | 0.592134i | ||||
\(483\) | −20.7846 | + | 36.0000i | −0.945732 | + | 1.63806i | ||||
\(484\) | −1.00000 | − | 1.73205i | −0.0454545 | − | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | − | 7.79423i | −0.612372 | − | 0.353553i | ||||
\(487\) | − | 2.00000i | − | 0.0906287i | −0.998973 | − | 0.0453143i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453143i | \(-0.0144289\pi\) | |||||||
\(488\) | −6.92820 | + | 4.00000i | −0.313625 | + | 0.181071i | ||||
\(489\) | −16.5000 | − | 9.52628i | −0.746156 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50000 | − | 12.9904i | 0.338470 | − | 0.586248i | −0.645675 | − | 0.763612i | \(-0.723424\pi\) |
0.984145 | + | 0.177365i | \(0.0567572\pi\) | |||||||
\(492\) | 10.3923 | 0.468521 | ||||||||
\(493\) | 15.5885 | − | 9.00000i | 0.702069 | − | 0.405340i | ||||
\(494\) | 16.0000 | 0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −20.7846 | + | 12.0000i | −0.932317 | + | 0.538274i | ||||
\(498\) | −7.79423 | − | 13.5000i | −0.349268 | − | 0.604949i | ||||
\(499\) | 5.50000 | − | 9.52628i | 0.246214 | − | 0.426455i | −0.716258 | − | 0.697835i | \(-0.754147\pi\) |
0.962472 | + | 0.271380i | \(0.0874801\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.0000 | + | 15.5885i | −1.20627 | + | 0.696441i | ||||
\(502\) | −10.3923 | + | 6.00000i | −0.463831 | + | 0.267793i | ||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | −6.00000 | + | 10.3923i | −0.267261 | + | 0.462910i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | − | 15.5885i | −0.400099 | − | 0.692991i | ||||
\(507\) | −5.19615 | −0.230769 | ||||||||
\(508\) | 13.8564 | + | 8.00000i | 0.614779 | + | 0.354943i | ||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0000 | + | 48.4974i | 1.23865 | + | 2.14540i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 20.7846 | 0.917663 | ||||||||
\(514\) | 3.00000 | 0.132324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.50000 | − | 0.866025i | −0.0660338 | − | 0.0381246i | ||||
\(517\) | 31.1769 | + | 18.0000i | 1.37116 | + | 0.791639i | ||||
\(518\) | −27.7128 | − | 16.0000i | −1.21763 | − | 0.703000i | ||||
\(519\) | − | 10.3923i | − | 0.456172i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 18.0000i | 0.787839i | ||||||||
\(523\) | 29.0000i | 1.26808i | 0.773300 | + | 0.634041i | \(0.218605\pi\) | ||||
−0.773300 | + | 0.634041i | \(0.781395\pi\) | |||||||
\(524\) | 6.00000 | + | 10.3923i | 0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | − | 20.7846i | 0.523225 | − | 0.906252i | ||||
\(527\) | −20.7846 | − | 12.0000i | −0.905392 | − | 0.522728i | ||||
\(528\) | −2.59808 | − | 4.50000i | −0.113067 | − | 0.195837i | ||||
\(529\) | 6.50000 | + | 11.2583i | 0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0000 | 1.17170 | ||||||||
\(532\) | − | 16.0000i | − | 0.693688i | ||||||
\(533\) | 20.7846 | − | 12.0000i | 0.900281 | − | 0.519778i | ||||
\(534\) | 15.5885i | 0.674579i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | + | 3.46410i | −0.0863868 | + | 0.149626i | ||||
\(537\) | −2.59808 | + | 4.50000i | −0.112115 | + | 0.194189i | ||||
\(538\) | 10.3923 | − | 6.00000i | 0.448044 | − | 0.258678i | ||||
\(539\) | −27.0000 | −1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | −3.46410 | + | 2.00000i | −0.148796 | + | 0.0859074i | ||||
\(543\) | −1.73205 | + | 3.00000i | −0.0743294 | + | 0.128742i | ||||
\(544\) | 1.50000 | − | 2.59808i | 0.0643120 | − | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 27.7128i | 1.18600i | ||||||||
\(547\) | −17.3205 | + | 10.0000i | −0.740571 | + | 0.427569i | −0.822277 | − | 0.569087i | \(-0.807297\pi\) |
0.0817056 | + | 0.996657i | \(0.473963\pi\) | |||||||
\(548\) | 18.0000i | 0.768922i | ||||||||
\(549\) | −12.0000 | + | 20.7846i | −0.512148 | + | 0.887066i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | − | 20.7846i | −0.511217 | − | 0.885454i | ||||
\(552\) | 5.19615 | + | 9.00000i | 0.221163 | + | 0.383065i | ||||
\(553\) | 27.7128 | + | 16.0000i | 1.17847 | + | 0.680389i | ||||
\(554\) | −1.00000 | + | 1.73205i | −0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.50000 | − | 9.52628i | −0.233252 | − | 0.404004i | ||||
\(557\) | 6.00000i | 0.254228i | 0.991888 | + | 0.127114i | \(0.0405714\pi\) | ||||
−0.991888 | + | 0.127114i | \(0.959429\pi\) | |||||||
\(558\) | 20.7846 | − | 12.0000i | 0.879883 | − | 0.508001i | ||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5885i | 0.658145i | ||||||||
\(562\) | 15.5885 | + | 9.00000i | 0.657559 | + | 0.379642i | ||||
\(563\) | 2.59808 | + | 1.50000i | 0.109496 | + | 0.0632175i | 0.553748 | − | 0.832684i | \(-0.313197\pi\) |
−0.444252 | + | 0.895902i | \(0.646530\pi\) | |||||||
\(564\) | −18.0000 | − | 10.3923i | −0.757937 | − | 0.437595i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.00000 | 0.0420331 | ||||||||
\(567\) | 36.0000i | 1.51186i | ||||||||
\(568\) | 6.00000i | 0.251754i | ||||||||
\(569\) | −13.5000 | − | 23.3827i | −0.565949 | − | 0.980253i | −0.996961 | − | 0.0779066i | \(-0.975176\pi\) |
0.431011 | − | 0.902347i | \(-0.358157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5000 | − | 21.6506i | 0.523109 | − | 0.906051i | −0.476530 | − | 0.879158i | \(-0.658105\pi\) |
0.999638 | − | 0.0268925i | \(-0.00856117\pi\) | |||||||
\(572\) | −10.3923 | − | 6.00000i | −0.434524 | − | 0.250873i | ||||
\(573\) | 10.3923 | 0.434145 | ||||||||
\(574\) | −12.0000 | − | 20.7846i | −0.500870 | − | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | − | 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 | ||||
\(579\) | 7.50000 | − | 4.33013i | 0.311689 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | + | 31.1769i | −0.746766 | + | 1.29344i | ||||
\(582\) | 6.06218 | + | 10.5000i | 0.251285 | + | 0.435239i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.0000 | 0.579324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 2.59808 | − | 1.50000i | 0.107234 | − | 0.0619116i | −0.445424 | − | 0.895320i | \(-0.646947\pi\) |
0.552658 | + | 0.833408i | \(0.313614\pi\) | |||||||
\(588\) | 15.5885 | 0.642857 | ||||||||
\(589\) | −16.0000 | + | 27.7128i | −0.659269 | + | 1.14189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | − | 15.5885i | −1.11063 | − | 0.641223i | ||||
\(592\) | −6.92820 | + | 4.00000i | −0.284747 | + | 0.164399i | ||||
\(593\) | − | 45.0000i | − | 1.84793i | −0.382479 | − | 0.923964i | \(-0.624930\pi\) | ||
0.382479 | − | 0.923964i | \(-0.375070\pi\) | |||||||
\(594\) | −13.5000 | − | 7.79423i | −0.553912 | − | 0.319801i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | + | 5.19615i | 0.122885 | + | 0.212843i | ||||
\(597\) | 1.73205 | − | 3.00000i | 0.0708881 | − | 0.122782i | ||||
\(598\) | 20.7846 | + | 12.0000i | 0.849946 | + | 0.490716i | ||||
\(599\) | 9.00000 | − | 15.5885i | 0.367730 | − | 0.636927i | −0.621480 | − | 0.783430i | \(-0.713468\pi\) |
0.989210 | + | 0.146503i | \(0.0468017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5000 | + | 32.0429i | 0.754631 | + | 1.30706i | 0.945558 | + | 0.325455i | \(0.105517\pi\) |
−0.190927 | + | 0.981604i | \(0.561149\pi\) | |||||||
\(602\) | 4.00000i | 0.163028i | ||||||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | − | 10.3923i | 0.731200 | − | 0.422159i | ||||
\(607\) | −13.8564 | − | 8.00000i | −0.562414 | − | 0.324710i | 0.191700 | − | 0.981454i | \(-0.438600\pi\) |
−0.754114 | + | 0.656744i | \(0.771933\pi\) | |||||||
\(608\) | −3.46410 | − | 2.00000i | −0.140488 | − | 0.0811107i | ||||
\(609\) | 36.0000 | − | 20.7846i | 1.45879 | − | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | − | 9.00000i | − | 0.363803i | ||||||
\(613\) | 14.0000i | 0.565455i | 0.959200 | + | 0.282727i | \(0.0912392\pi\) | ||||
−0.959200 | + | 0.282727i | \(0.908761\pi\) | |||||||
\(614\) | 0.500000 | + | 0.866025i | 0.0201784 | + | 0.0349499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | + | 10.3923i | −0.241747 | + | 0.418718i | ||||
\(617\) | 23.3827 | + | 13.5000i | 0.941351 | + | 0.543490i | 0.890384 | − | 0.455211i | \(-0.150436\pi\) |
0.0509678 | + | 0.998700i | \(0.483769\pi\) | |||||||
\(618\) | 6.92820 | − | 12.0000i | 0.278693 | − | 0.482711i | ||||
\(619\) | 17.5000 | + | 30.3109i | 0.703384 | + | 1.21830i | 0.967271 | + | 0.253744i | \(0.0816620\pi\) |
−0.263887 | + | 0.964554i | \(0.585005\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.0000 | + | 15.5885i | 1.08347 | + | 0.625543i | ||||
\(622\) | 6.00000i | 0.240578i | ||||||||
\(623\) | 31.1769 | − | 18.0000i | 1.24908 | − | 0.721155i | ||||
\(624\) | 6.00000 | + | 3.46410i | 0.240192 | + | 0.138675i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.50000 | − | 14.7224i | 0.339728 | − | 0.588427i | ||||
\(627\) | 20.7846 | 0.830057 | ||||||||
\(628\) | −3.46410 | + | 2.00000i | −0.138233 | + | 0.0798087i | ||||
\(629\) | 24.0000 | 0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | 6.92820 | − | 4.00000i | 0.275589 | − | 0.159111i | ||||
\(633\) | −19.9186 | − | 34.5000i | −0.791693 | − | 1.37125i | ||||
\(634\) | 9.00000 | − | 15.5885i | 0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.1769 | − | 18.0000i | 1.23527 | − | 0.713186i | ||||
\(638\) | 18.0000i | 0.712627i | ||||||||
\(639\) | 9.00000 | + | 15.5885i | 0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5000 | + | 23.3827i | 0.533218 | + | 0.923561i | 0.999247 | + | 0.0387913i | \(0.0123508\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(642\) | 20.7846 | 0.820303 | ||||||||
\(643\) | −19.9186 | − | 11.5000i | −0.785512 | − | 0.453516i | 0.0528680 | − | 0.998602i | \(-0.483164\pi\) |
−0.838380 | + | 0.545086i | \(0.816497\pi\) | |||||||
\(644\) | 12.0000 | − | 20.7846i | 0.472866 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | − | 12.0000i | − | 0.471769i | −0.971781 | − | 0.235884i | \(-0.924201\pi\) | ||
0.971781 | − | 0.235884i | \(-0.0757987\pi\) | |||||||
\(648\) | 7.79423 | + | 4.50000i | 0.306186 | + | 0.176777i | ||||
\(649\) | 27.0000 | 1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.0000 | − | 27.7128i | −1.88127 | − | 1.08615i | ||||
\(652\) | 9.52628 | + | 5.50000i | 0.373078 | + | 0.215397i | ||||
\(653\) | 20.7846 | + | 12.0000i | 0.813365 | + | 0.469596i | 0.848123 | − | 0.529799i | \(-0.177733\pi\) |
−0.0347583 | + | 0.999396i | \(0.511066\pi\) | |||||||
\(654\) | − | 3.46410i | − | 0.135457i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 36.3731 | − | 21.0000i | 1.41905 | − | 0.819288i | ||||
\(658\) | 48.0000i | 1.87123i | ||||||||
\(659\) | −22.5000 | − | 38.9711i | −0.876476 | − | 1.51810i | −0.855183 | − | 0.518327i | \(-0.826555\pi\) |
−0.0212930 | − | 0.999773i | \(-0.506778\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | − | 8.66025i | 0.194477 | − | 0.336845i | −0.752252 | − | 0.658876i | \(-0.771032\pi\) |
0.946729 | + | 0.322031i | \(0.104366\pi\) | |||||||
\(662\) | −14.7224 | − | 8.50000i | −0.572204 | − | 0.330362i | ||||
\(663\) | −10.3923 | − | 18.0000i | −0.403604 | − | 0.699062i | ||||
\(664\) | 4.50000 | + | 7.79423i | 0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.0000 | + | 20.7846i | −0.464991 | + | 0.805387i | ||||
\(667\) | − | 36.0000i | − | 1.39393i | ||||||
\(668\) | 15.5885 | − | 9.00000i | 0.603136 | − | 0.348220i | ||||
\(669\) | 3.46410i | 0.133930i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | + | 20.7846i | −0.463255 | + | 0.802381i | ||||
\(672\) | 3.46410 | − | 6.00000i | 0.133631 | − | 0.231455i | ||||
\(673\) | −39.8372 | + | 23.0000i | −1.53561 | + | 0.886585i | −0.536522 | + | 0.843886i | \(0.680262\pi\) |
−0.999088 | + | 0.0426985i | \(0.986405\pi\) | |||||||
\(674\) | −13.0000 | −0.500741 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −15.5885 | + | 9.00000i | −0.599113 | + | 0.345898i | −0.768693 | − | 0.639618i | \(-0.779092\pi\) |
0.169580 | + | 0.985517i | \(0.445759\pi\) | |||||||
\(678\) | 2.59808 | − | 4.50000i | 0.0997785 | − | 0.172821i | ||||
\(679\) | 14.0000 | − | 24.2487i | 0.537271 | − | 0.930580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 46.7654i | 1.79205i | ||||||||
\(682\) | 20.7846 | − | 12.0000i | 0.795884 | − | 0.459504i | ||||
\(683\) | 36.0000i | 1.37750i | 0.724998 | + | 0.688751i | \(0.241841\pi\) | ||||
−0.724998 | + | 0.688751i | \(0.758159\pi\) | |||||||
\(684\) | −12.0000 | −0.458831 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.00000 | − | 6.92820i | −0.152721 | − | 0.264520i | ||||
\(687\) | 6.92820 | + | 12.0000i | 0.264327 | + | 0.457829i | ||||
\(688\) | 0.866025 | + | 0.500000i | 0.0330169 | + | 0.0190623i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.50000 | + | 16.4545i | 0.361397 | + | 0.625958i | 0.988191 | − | 0.153227i | \(-0.0489666\pi\) |
−0.626794 | + | 0.779185i | \(0.715633\pi\) | |||||||
\(692\) | 6.00000i | 0.228086i | ||||||||
\(693\) | 36.0000i | 1.36753i | ||||||||
\(694\) | 27.0000 | 1.02491 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 10.3923i | − | 0.393919i | ||||||
\(697\) | 15.5885 | + | 9.00000i | 0.590455 | + | 0.340899i | ||||
\(698\) | 12.1244 | + | 7.00000i | 0.458914 | + | 0.264954i | ||||
\(699\) | −22.5000 | − | 12.9904i | −0.851028 | − | 0.491341i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.0000 | 1.81293 | 0.906467 | − | 0.422276i | \(-0.138769\pi\) | ||||
0.906467 | + | 0.422276i | \(0.138769\pi\) | |||||||
\(702\) | 20.7846 | 0.784465 | ||||||||
\(703\) | − | 32.0000i | − | 1.20690i | ||||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.50000 | + | 7.79423i | −0.169360 | + | 0.293340i | ||||
\(707\) | −41.5692 | − | 24.0000i | −1.56337 | − | 0.902613i | ||||
\(708\) | −15.5885 | −0.585850 | ||||||||
\(709\) | −26.0000 | − | 45.0333i | −0.976450 | − | 1.69126i | −0.675063 | − | 0.737760i | \(-0.735884\pi\) |
−0.301388 | − | 0.953502i | \(-0.597450\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | − | 20.7846i | 0.450035 | − | 0.779484i | ||||
\(712\) | − | 9.00000i | − | 0.337289i | ||||||
\(713\) | −41.5692 | + | 24.0000i | −1.55678 | + | 0.898807i | ||||
\(714\) | −18.0000 | + | 10.3923i | −0.673633 | + | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.50000 | − | 2.59808i | 0.0560576 | − | 0.0970947i | ||||
\(717\) | 15.5885 | + | 27.0000i | 0.582162 | + | 1.00833i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.0000 | 0.895049 | 0.447524 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447524 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | −1.19174 | ||||||||
\(722\) | −2.59808 | + | 1.50000i | −0.0966904 | + | 0.0558242i | ||||
\(723\) | 45.0333 | 1.67481 | ||||||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.00000 | + | 1.73205i | 0.111340 | + | 0.0642824i | ||||
\(727\) | −12.1244 | + | 7.00000i | −0.449667 | + | 0.259616i | −0.707690 | − | 0.706523i | \(-0.750263\pi\) |
0.258022 | + | 0.966139i | \(0.416929\pi\) | |||||||
\(728\) | − | 16.0000i | − | 0.592999i | ||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50000 | − | 2.59808i | −0.0554795 | − | 0.0960933i | ||||
\(732\) | 6.92820 | − | 12.0000i | 0.256074 | − | 0.443533i | ||||
\(733\) | 3.46410 | + | 2.00000i | 0.127950 | + | 0.0738717i | 0.562609 | − | 0.826723i | \(-0.309798\pi\) |
−0.434659 | + | 0.900595i | \(0.643131\pi\) | |||||||
\(734\) | −13.0000 | + | 22.5167i | −0.479839 | + | 0.831105i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | − | 5.19615i | −0.110581 | − | 0.191533i | ||||
\(737\) | 12.0000i | 0.442026i | ||||||||
\(738\) | −15.5885 | + | 9.00000i | −0.573819 | + | 0.331295i | ||||
\(739\) | 25.0000 | 0.919640 | 0.459820 | − | 0.888012i | \(-0.347914\pi\) | ||||
0.459820 | + | 0.888012i | \(0.347914\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | + | 13.8564i | −0.881662 | + | 0.509028i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(744\) | −12.0000 | + | 6.92820i | −0.439941 | + | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.00000 | −0.292901 | ||||||||
\(747\) | 23.3827 | + | 13.5000i | 0.855528 | + | 0.493939i | ||||
\(748\) | − | 9.00000i | − | 0.329073i | ||||||
\(749\) | −24.0000 | − | 41.5692i | −0.876941 | − | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0000 | − | 29.4449i | 0.620339 | − | 1.07446i | −0.369084 | − | 0.929396i | \(-0.620328\pi\) |
0.989423 | − | 0.145062i | \(-0.0463382\pi\) | |||||||
\(752\) | 10.3923 | + | 6.00000i | 0.378968 | + | 0.218797i | ||||
\(753\) | 10.3923 | − | 18.0000i | 0.378717 | − | 0.655956i | ||||
\(754\) | −12.0000 | − | 20.7846i | −0.437014 | − | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 20.7846i | − | 0.755929i | ||||||
\(757\) | − | 20.0000i | − | 0.726912i | −0.931611 | − | 0.363456i | \(-0.881597\pi\) | ||
0.931611 | − | 0.363456i | \(-0.118403\pi\) | |||||||
\(758\) | −25.1147 | + | 14.5000i | −0.912208 | + | 0.526664i | ||||
\(759\) | 27.0000 | + | 15.5885i | 0.980038 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5000 | − | 33.7750i | 0.706874 | − | 1.22434i | −0.259136 | − | 0.965841i | \(-0.583438\pi\) |
0.966011 | − | 0.258502i | \(-0.0832288\pi\) | |||||||
\(762\) | −27.7128 | −1.00393 | ||||||||
\(763\) | −6.92820 | + | 4.00000i | −0.250818 | + | 0.144810i | ||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0000 | −0.650366 | ||||||||
\(767\) | −31.1769 | + | 18.0000i | −1.12573 | + | 0.649942i | ||||
\(768\) | −0.866025 | − | 1.50000i | −0.0312500 | − | 0.0541266i | ||||
\(769\) | 2.50000 | − | 4.33013i | 0.0901523 | − | 0.156148i | −0.817423 | − | 0.576038i | \(-0.804598\pi\) |
0.907575 | + | 0.419890i | \(0.137931\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50000 | + | 2.59808i | −0.162064 | + | 0.0935674i | ||||
\(772\) | −4.33013 | + | 2.50000i | −0.155845 | + | 0.0899770i | ||||
\(773\) | − | 42.0000i | − | 1.51064i | −0.655359 | − | 0.755318i | \(-0.727483\pi\) | ||
0.655359 | − | 0.755318i | \(-0.272517\pi\) | |||||||
\(774\) | 3.00000 | 0.107833 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.50000 | − | 6.06218i | −0.125643 | − | 0.217620i | ||||
\(777\) | 55.4256 | 1.98838 | ||||||||
\(778\) | −5.19615 | − | 3.00000i | −0.186291 | − | 0.107555i | ||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | + | 15.5885i | 0.322045 | + | 0.557799i | ||||
\(782\) | 18.0000i | 0.643679i | ||||||||
\(783\) | −15.5885 | − | 27.0000i | −0.557086 | − | 0.964901i | ||||
\(784\) | −9.00000 | −0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.0000 | − | 10.3923i | −0.642039 | − | 0.370681i | ||||
\(787\) | −3.46410 | − | 2.00000i | −0.123482 | − | 0.0712923i | 0.436987 | − | 0.899468i | \(-0.356046\pi\) |
−0.560469 | + | 0.828176i | \(0.689379\pi\) | |||||||
\(788\) | 15.5885 | + | 9.00000i | 0.555316 | + | 0.320612i | ||||
\(789\) | 41.5692i | 1.47990i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 7.79423 | + | 4.50000i | 0.276956 | + | 0.159901i | ||||
\(793\) | − | 32.0000i | − | 1.13635i | ||||||
\(794\) | −7.00000 | − | 12.1244i | −0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.00000 | + | 1.73205i | −0.0354441 | + | 0.0613909i | ||||
\(797\) | 10.3923 | + | 6.00000i | 0.368114 | + | 0.212531i | 0.672634 | − | 0.739975i | \(-0.265163\pi\) |
−0.304520 | + | 0.952506i | \(0.598496\pi\) | |||||||
\(798\) | 13.8564 | + | 24.0000i | 0.490511 | + | 0.849591i | ||||
\(799\) | −18.0000 | − | 31.1769i | −0.636794 | − | 1.10296i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.5000 | − | 23.3827i | −0.476999 | − | 0.826187i | ||||
\(802\) | − | 15.0000i | − | 0.529668i | ||||||
\(803\) | 36.3731 | − | 21.0000i | 1.28358 | − | 0.741074i | ||||
\(804\) | − | 6.92820i | − | 0.244339i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.0000 | + | 27.7128i | −0.563576 | + | 0.976142i | ||||
\(807\) | −10.3923 | + | 18.0000i | −0.365826 | + | 0.633630i | ||||
\(808\) | −10.3923 | + | 6.00000i | −0.365600 | + | 0.211079i | ||||
\(809\) | −45.0000 | −1.58212 | −0.791058 | − | 0.611741i | \(-0.790469\pi\) | ||||
−0.791058 | + | 0.611741i | \(0.790469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.00000 | 0.175574 | 0.0877869 | − | 0.996139i | \(-0.472021\pi\) | ||||
0.0877869 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(812\) | −20.7846 | + | 12.0000i | −0.729397 | + | 0.421117i | ||||
\(813\) | 3.46410 | − | 6.00000i | 0.121491 | − | 0.210429i | ||||
\(814\) | −12.0000 | + | 20.7846i | −0.420600 | + | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 5.19615i | 0.181902i | ||||||||
\(817\) | −3.46410 | + | 2.00000i | −0.121194 | + | 0.0699711i | ||||
\(818\) | 22.0000i | 0.769212i | ||||||||
\(819\) | −24.0000 | − | 41.5692i | −0.838628 | − | 1.45255i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0000 | − | 20.7846i | −0.418803 | − | 0.725388i | 0.577016 | − | 0.816733i | \(-0.304217\pi\) |
−0.995819 | + | 0.0913446i | \(0.970884\pi\) | |||||||
\(822\) | −15.5885 | − | 27.0000i | −0.543710 | − | 0.941733i | ||||
\(823\) | 34.6410 | + | 20.0000i | 1.20751 | + | 0.697156i | 0.962215 | − | 0.272292i | \(-0.0877817\pi\) |
0.245295 | + | 0.969448i | \(0.421115\pi\) | |||||||
\(824\) | −4.00000 | + | 6.92820i | −0.139347 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0000 | + | 31.1769i | 0.626300 | + | 1.08478i | ||||
\(827\) | − | 15.0000i | − | 0.521601i | −0.965393 | − | 0.260801i | \(-0.916014\pi\) | ||
0.965393 | − | 0.260801i | \(-0.0839865\pi\) | |||||||
\(828\) | −15.5885 | − | 9.00000i | −0.541736 | − | 0.312772i | ||||
\(829\) | −20.0000 | −0.694629 | −0.347314 | − | 0.937749i | \(-0.612906\pi\) | ||||
−0.347314 | + | 0.937749i | \(0.612906\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 3.46410i | − | 0.120168i | ||||||
\(832\) | −3.46410 | − | 2.00000i | −0.120096 | − | 0.0693375i | ||||
\(833\) | 23.3827 | + | 13.5000i | 0.810162 | + | 0.467747i | ||||
\(834\) | 16.5000 | + | 9.52628i | 0.571348 | + | 0.329868i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | −20.7846 | + | 36.0000i | −0.718421 | + | 1.24434i | ||||
\(838\) | − | 9.00000i | − | 0.310900i | ||||||
\(839\) | 24.0000 | + | 41.5692i | 0.828572 | + | 1.43513i | 0.899158 | + | 0.437623i | \(0.144180\pi\) |
−0.0705865 | + | 0.997506i | \(0.522487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −27.7128 | − | 16.0000i | −0.955047 | − | 0.551396i | ||||
\(843\) | −31.1769 | −1.07379 | ||||||||
\(844\) | 11.5000 | + | 19.9186i | 0.395846 | + | 0.685626i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 36.0000 | 1.23771 | ||||||||
\(847\) | − | 8.00000i | − | 0.274883i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.50000 | + | 0.866025i | −0.0514799 | + | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | − | 41.5692i | 0.822709 | − | 1.42497i | ||||
\(852\) | −5.19615 | − | 9.00000i | −0.178017 | − | 0.308335i | ||||
\(853\) | −39.8372 | + | 23.0000i | −1.36400 | + | 0.787505i | −0.990153 | − | 0.139986i | \(-0.955294\pi\) |
−0.373845 | + | 0.927491i | \(0.621961\pi\) | |||||||
\(854\) | −32.0000 | −1.09502 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 23.3827 | − | 13.5000i | 0.798737 | − | 0.461151i | −0.0442921 | − | 0.999019i | \(-0.514103\pi\) |
0.843029 | + | 0.537867i | \(0.180770\pi\) | |||||||
\(858\) | 20.7846 | 0.709575 | ||||||||
\(859\) | −8.00000 | + | 13.8564i | −0.272956 | + | 0.472774i | −0.969618 | − | 0.244626i | \(-0.921335\pi\) |
0.696661 | + | 0.717400i | \(0.254668\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.0000 | + | 20.7846i | 1.22688 | + | 0.708338i | ||||
\(862\) | 5.19615 | − | 3.00000i | 0.176982 | − | 0.102180i | ||||
\(863\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(864\) | −4.50000 | − | 2.59808i | −0.153093 | − | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.50000 | − | 6.06218i | −0.118935 | − | 0.206001i | ||||
\(867\) | −6.92820 | + | 12.0000i | −0.235294 | + | 0.407541i | ||||
\(868\) | 27.7128 | + | 16.0000i | 0.940634 | + | 0.543075i | ||||
\(869\) | 12.0000 | − | 20.7846i | 0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | − | 13.8564i | −0.271070 | − | 0.469506i | ||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | −18.1865 | − | 10.5000i | −0.615521 | − | 0.355371i | ||||
\(874\) | 24.0000 | 0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.0000 | + | 12.1244i | −0.709524 | + | 0.409644i | ||||
\(877\) | −13.8564 | − | 8.00000i | −0.467898 | − | 0.270141i | 0.247462 | − | 0.968898i | \(-0.420404\pi\) |
−0.715359 | + | 0.698757i | \(0.753737\pi\) | |||||||
\(878\) | 12.1244 | + | 7.00000i | 0.409177 | + | 0.236239i | ||||
\(879\) | −18.0000 | + | 10.3923i | −0.607125 | + | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | −23.3827 | + | 13.5000i | −0.787336 | + | 0.454569i | ||||
\(883\) | − | 13.0000i | − | 0.437485i | −0.975783 | − | 0.218742i | \(-0.929805\pi\) | ||
0.975783 | − | 0.218742i | \(-0.0701954\pi\) | |||||||
\(884\) | 6.00000 | + | 10.3923i | 0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.50000 | − | 7.79423i | 0.151180 | − | 0.261852i | ||||
\(887\) | 25.9808 | + | 15.0000i | 0.872349 | + | 0.503651i | 0.868128 | − | 0.496340i | \(-0.165323\pi\) |
0.00422062 | + | 0.999991i | \(0.498657\pi\) | |||||||
\(888\) | 6.92820 | − | 12.0000i | 0.232495 | − | 0.402694i | ||||
\(889\) | 32.0000 | + | 55.4256i | 1.07325 | + | 1.85892i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | 0.904534 | ||||||||
\(892\) | − | 2.00000i | − | 0.0669650i | ||||||
\(893\) | −41.5692 | + | 24.0000i | −1.39106 | + | 0.803129i | ||||
\(894\) | −9.00000 | − | 5.19615i | −0.301005 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | + | 3.46410i | −0.0668153 | + | 0.115728i | ||||
\(897\) | −41.5692 | −1.38796 | ||||||||
\(898\) | −15.5885 | + | 9.00000i | −0.520194 | + | 0.300334i | ||||
\(899\) | 48.0000 | 1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −15.5885 | + | 9.00000i | −0.519039 | + | 0.299667i | ||||
\(903\) | −3.46410 | − | 6.00000i | −0.115278 | − | 0.199667i | ||||
\(904\) | −1.50000 | + | 2.59808i | −0.0498893 | + | 0.0864107i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.0000 | + | 8.66025i | −0.498342 | + | 0.287718i | ||||
\(907\) | −14.7224 | + | 8.50000i | −0.488850 | + | 0.282238i | −0.724097 | − | 0.689698i | \(-0.757743\pi\) |
0.235247 | + | 0.971936i | \(0.424410\pi\) | |||||||
\(908\) | − | 27.0000i | − | 0.896026i | ||||||
\(909\) | −18.0000 | + | 31.1769i | −0.597022 | + | 1.03407i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.00000 | + | 15.5885i | 0.298183 | + | 0.516469i | 0.975720 | − | 0.219020i | \(-0.0702860\pi\) |
−0.677537 | + | 0.735489i | \(0.736953\pi\) | |||||||
\(912\) | 6.92820 | 0.229416 | ||||||||
\(913\) | 23.3827 | + | 13.5000i | 0.773854 | + | 0.446785i | ||||
\(914\) | 5.00000 | − | 8.66025i | 0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | − | 6.92820i | −0.132164 | − | 0.228914i | ||||
\(917\) | 48.0000i | 1.58510i | ||||||||
\(918\) | 7.79423 | + | 13.5000i | 0.257248 | + | 0.445566i | ||||
\(919\) | 46.0000 | 1.51740 | 0.758700 | − | 0.651440i | \(-0.225835\pi\) | ||||
0.758700 | + | 0.651440i | \(0.225835\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.50000 | − | 0.866025i | −0.0494267 | − | 0.0285365i | ||||
\(922\) | 5.19615 | + | 3.00000i | 0.171126 | + | 0.0987997i | ||||
\(923\) | −20.7846 | − | 12.0000i | −0.684134 | − | 0.394985i | ||||
\(924\) | − | 20.7846i | − | 0.683763i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.0000 | −0.460069 | ||||||||
\(927\) | 24.0000i | 0.788263i | ||||||||
\(928\) | 6.00000i | 0.196960i | ||||||||
\(929\) | 21.0000 | + | 36.3731i | 0.688988 | + | 1.19336i | 0.972166 | + | 0.234294i | \(0.0752779\pi\) |
−0.283178 | + | 0.959067i | \(0.591389\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | − | 31.1769i | 0.589926 | − | 1.02178i | ||||
\(932\) | 12.9904 | + | 7.50000i | 0.425514 | + | 0.245671i | ||||
\(933\) | −5.19615 | − | 9.00000i | −0.170114 | − | 0.294647i | ||||
\(934\) | −4.50000 | − | 7.79423i | −0.147244 | − | 0.255035i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0000 | −0.392232 | ||||||||
\(937\) | 37.0000i | 1.20874i | 0.796705 | + | 0.604369i | \(0.206575\pi\) | ||||
−0.796705 | + | 0.604369i | \(0.793425\pi\) | |||||||
\(938\) | −13.8564 | + | 8.00000i | −0.452428 | + | 0.261209i | ||||
\(939\) | 29.4449i | 0.960897i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | + | 20.7846i | −0.391189 | + | 0.677559i | −0.992607 | − | 0.121376i | \(-0.961269\pi\) |
0.601418 | + | 0.798935i | \(0.294603\pi\) | |||||||
\(942\) | 3.46410 | − | 6.00000i | 0.112867 | − | 0.195491i | ||||
\(943\) | 31.1769 | − | 18.0000i | 1.01526 | − | 0.586161i | ||||
\(944\) | 9.00000 | 0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | 7.79423 | − | 4.50000i | 0.253278 | − | 0.146230i | −0.367986 | − | 0.929831i | \(-0.619953\pi\) |
0.621264 | + | 0.783601i | \(0.286619\pi\) | |||||||
\(948\) | −6.92820 | + | 12.0000i | −0.225018 | + | 0.389742i | ||||
\(949\) | −28.0000 | + | 48.4974i | −0.908918 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 31.1769i | 1.01098i | ||||||||
\(952\) | 10.3923 | − | 6.00000i | 0.336817 | − | 0.194461i | ||||
\(953\) | − | 27.0000i | − | 0.874616i | −0.899312 | − | 0.437308i | \(-0.855932\pi\) | ||
0.899312 | − | 0.437308i | \(-0.144068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | − | 15.5885i | −0.291081 | − | 0.504167i | ||||
\(957\) | −15.5885 | − | 27.0000i | −0.503903 | − | 0.872786i | ||||
\(958\) | −10.3923 | − | 6.00000i | −0.335760 | − | 0.193851i | ||||
\(959\) | −36.0000 | + | 62.3538i | −1.16250 | + | 2.01351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | − | 28.5788i | −0.532258 | − | 0.921898i | ||||
\(962\) | − | 32.0000i | − | 1.03172i | ||||||
\(963\) | −31.1769 | + | 18.0000i | −1.00466 | + | 0.580042i | ||||
\(964\) | −26.0000 | −0.837404 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 41.5692i | 1.33747i | ||||||||
\(967\) | −24.2487 | − | 14.0000i | −0.779786 | − | 0.450210i | 0.0565684 | − | 0.998399i | \(-0.481984\pi\) |
−0.836354 | + | 0.548189i | \(0.815317\pi\) | |||||||
\(968\) | −1.73205 | − | 1.00000i | −0.0556702 | − | 0.0321412i | ||||
\(969\) | −18.0000 | − | 10.3923i | −0.578243 | − | 0.333849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.0000 | −0.866471 | −0.433236 | − | 0.901281i | \(-0.642628\pi\) | ||||
−0.433236 | + | 0.901281i | \(0.642628\pi\) | |||||||
\(972\) | −15.5885 | −0.500000 | ||||||||
\(973\) | − | 44.0000i | − | 1.41058i | ||||||
\(974\) | −1.00000 | − | 1.73205i | −0.0320421 | − | 0.0554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | + | 6.92820i | −0.128037 | + | 0.221766i | ||||
\(977\) | −46.7654 | − | 27.0000i | −1.49616 | − | 0.863807i | −0.496167 | − | 0.868227i | \(-0.665259\pi\) |
−0.999990 | + | 0.00442082i | \(0.998593\pi\) | |||||||
\(978\) | −19.0526 | −0.609234 | ||||||||
\(979\) | −13.5000 | − | 23.3827i | −0.431462 | − | 0.747314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | + | 5.19615i | 0.0957826 | + | 0.165900i | ||||
\(982\) | − | 15.0000i | − | 0.478669i | ||||||
\(983\) | 46.7654 | − | 27.0000i | 1.49158 | − | 0.861166i | 0.491630 | − | 0.870804i | \(-0.336401\pi\) |
0.999954 | + | 0.00963785i | \(0.00306787\pi\) | |||||||
\(984\) | 9.00000 | − | 5.19615i | 0.286910 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | − | 15.5885i | 0.286618 | − | 0.496438i | ||||
\(987\) | −41.5692 | − | 72.0000i | −1.32316 | − | 2.29179i | ||||
\(988\) | 13.8564 | − | 8.00000i | 0.440831 | − | 0.254514i | ||||
\(989\) | −6.00000 | −0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 6.92820 | − | 4.00000i | 0.219971 | − | 0.127000i | ||||
\(993\) | 29.4449 | 0.934405 | ||||||||
\(994\) | −12.0000 | + | 20.7846i | −0.380617 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.5000 | − | 7.79423i | −0.427764 | − | 0.246970i | ||||
\(997\) | 8.66025 | − | 5.00000i | 0.274273 | − | 0.158352i | −0.356555 | − | 0.934274i | \(-0.616049\pi\) |
0.630828 | + | 0.775923i | \(0.282715\pi\) | |||||||
\(998\) | − | 11.0000i | − | 0.348199i | ||||||
\(999\) | − | 41.5692i | − | 1.31519i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.j.d.49.2 | 4 | ||
3.2 | odd | 2 | 1350.2.j.d.199.1 | 4 | |||
5.2 | odd | 4 | 450.2.e.h.301.1 | yes | 2 | ||
5.3 | odd | 4 | 450.2.e.a.301.1 | yes | 2 | ||
5.4 | even | 2 | inner | 450.2.j.d.49.1 | 4 | ||
9.2 | odd | 6 | 1350.2.j.d.1099.2 | 4 | |||
9.4 | even | 3 | 4050.2.c.q.649.2 | 2 | |||
9.5 | odd | 6 | 4050.2.c.e.649.1 | 2 | |||
9.7 | even | 3 | inner | 450.2.j.d.349.1 | 4 | ||
15.2 | even | 4 | 1350.2.e.e.901.1 | 2 | |||
15.8 | even | 4 | 1350.2.e.f.901.1 | 2 | |||
15.14 | odd | 2 | 1350.2.j.d.199.2 | 4 | |||
45.2 | even | 12 | 1350.2.e.e.451.1 | 2 | |||
45.4 | even | 6 | 4050.2.c.q.649.1 | 2 | |||
45.7 | odd | 12 | 450.2.e.h.151.1 | yes | 2 | ||
45.13 | odd | 12 | 4050.2.a.bj.1.1 | 1 | |||
45.14 | odd | 6 | 4050.2.c.e.649.2 | 2 | |||
45.22 | odd | 12 | 4050.2.a.b.1.1 | 1 | |||
45.23 | even | 12 | 4050.2.a.p.1.1 | 1 | |||
45.29 | odd | 6 | 1350.2.j.d.1099.1 | 4 | |||
45.32 | even | 12 | 4050.2.a.t.1.1 | 1 | |||
45.34 | even | 6 | inner | 450.2.j.d.349.2 | 4 | ||
45.38 | even | 12 | 1350.2.e.f.451.1 | 2 | |||
45.43 | odd | 12 | 450.2.e.a.151.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.a.151.1 | ✓ | 2 | 45.43 | odd | 12 | ||
450.2.e.a.301.1 | yes | 2 | 5.3 | odd | 4 | ||
450.2.e.h.151.1 | yes | 2 | 45.7 | odd | 12 | ||
450.2.e.h.301.1 | yes | 2 | 5.2 | odd | 4 | ||
450.2.j.d.49.1 | 4 | 5.4 | even | 2 | inner | ||
450.2.j.d.49.2 | 4 | 1.1 | even | 1 | trivial | ||
450.2.j.d.349.1 | 4 | 9.7 | even | 3 | inner | ||
450.2.j.d.349.2 | 4 | 45.34 | even | 6 | inner | ||
1350.2.e.e.451.1 | 2 | 45.2 | even | 12 | |||
1350.2.e.e.901.1 | 2 | 15.2 | even | 4 | |||
1350.2.e.f.451.1 | 2 | 45.38 | even | 12 | |||
1350.2.e.f.901.1 | 2 | 15.8 | even | 4 | |||
1350.2.j.d.199.1 | 4 | 3.2 | odd | 2 | |||
1350.2.j.d.199.2 | 4 | 15.14 | odd | 2 | |||
1350.2.j.d.1099.1 | 4 | 45.29 | odd | 6 | |||
1350.2.j.d.1099.2 | 4 | 9.2 | odd | 6 | |||
4050.2.a.b.1.1 | 1 | 45.22 | odd | 12 | |||
4050.2.a.p.1.1 | 1 | 45.23 | even | 12 | |||
4050.2.a.t.1.1 | 1 | 45.32 | even | 12 | |||
4050.2.a.bj.1.1 | 1 | 45.13 | odd | 12 | |||
4050.2.c.e.649.1 | 2 | 9.5 | odd | 6 | |||
4050.2.c.e.649.2 | 2 | 45.14 | odd | 6 | |||
4050.2.c.q.649.1 | 2 | 45.4 | even | 6 | |||
4050.2.c.q.649.2 | 2 | 9.4 | even | 3 |