Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(151,450)]
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([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.e (of order \(3\), degree \(2\), 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: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.151 |
Dual form | 450.2.e.h.301.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.866025 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 1.73205i | − | 0.707107i | ||||||
\(7\) | 2.00000 | − | 3.46410i | 0.755929 | − | 1.30931i | −0.188982 | − | 0.981981i | \(-0.560519\pi\) |
0.944911 | − | 0.327327i | \(-0.106148\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | −1.50000 | − | 0.866025i | −0.433013 | − | 0.250000i | ||||
\(13\) | 2.00000 | + | 3.46410i | 0.554700 | + | 0.960769i | 0.997927 | + | 0.0643593i | \(0.0205004\pi\) |
−0.443227 | + | 0.896410i | \(0.646166\pi\) | |||||||
\(14\) | −2.00000 | − | 3.46410i | −0.534522 | − | 0.925820i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | −1.50000 | − | 2.59808i | −0.353553 | − | 0.612372i | ||||
\(19\) | −4.00000 | −0.917663 | −0.458831 | − | 0.888523i | \(-0.651732\pi\) | ||||
−0.458831 | + | 0.888523i | \(0.651732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 6.92820i | − | 1.51186i | ||||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | −1.50000 | + | 0.866025i | −0.306186 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.00000 | 0.784465 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | 3.00000 | − | 5.19615i | 0.557086 | − | 0.964901i | −0.440652 | − | 0.897678i | \(-0.645253\pi\) |
0.997738 | − | 0.0672232i | \(-0.0214140\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 6.92820i | −0.718421 | − | 1.24434i | −0.961625 | − | 0.274367i | \(-0.911532\pi\) |
0.243204 | − | 0.969975i | \(-0.421802\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 5.19615i | 0.904534i | ||||||||
\(34\) | −1.50000 | + | 2.59808i | −0.257248 | + | 0.445566i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.00000 | −0.500000 | ||||||||
\(37\) | 8.00000 | 1.31519 | 0.657596 | − | 0.753371i | \(-0.271573\pi\) | ||||
0.657596 | + | 0.753371i | \(0.271573\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | 6.00000 | + | 3.46410i | 0.960769 | + | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.00000 | + | 5.19615i | 0.468521 | + | 0.811503i | 0.999353 | − | 0.0359748i | \(-0.0114536\pi\) |
−0.530831 | + | 0.847477i | \(0.678120\pi\) | |||||||
\(42\) | −6.00000 | − | 3.46410i | −0.925820 | − | 0.534522i | ||||
\(43\) | 0.500000 | − | 0.866025i | 0.0762493 | − | 0.132068i | −0.825380 | − | 0.564578i | \(-0.809039\pi\) |
0.901629 | + | 0.432511i | \(0.142372\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | −6.00000 | + | 10.3923i | −0.875190 | + | 1.51587i | −0.0186297 | + | 0.999826i | \(0.505930\pi\) |
−0.856560 | + | 0.516047i | \(0.827403\pi\) | |||||||
\(48\) | 1.73205i | 0.250000i | ||||||||
\(49\) | −4.50000 | − | 7.79423i | −0.642857 | − | 1.11346i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.50000 | + | 2.59808i | −0.630126 | + | 0.363803i | ||||
\(52\) | 2.00000 | − | 3.46410i | 0.277350 | − | 0.480384i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 3.46410i | −0.267261 | + | 0.462910i | ||||
\(57\) | −6.00000 | + | 3.46410i | −0.794719 | + | 0.458831i | ||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.00000 | + | 6.92820i | −0.512148 | + | 0.887066i | 0.487753 | + | 0.872982i | \(0.337817\pi\) |
−0.999901 | + | 0.0140840i | \(0.995517\pi\) | |||||||
\(62\) | −8.00000 | −1.01600 | ||||||||
\(63\) | −6.00000 | − | 10.3923i | −0.755929 | − | 1.30931i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.50000 | + | 2.59808i | 0.553912 | + | 0.319801i | ||||
\(67\) | 2.00000 | + | 3.46410i | 0.244339 | + | 0.423207i | 0.961946 | − | 0.273241i | \(-0.0880957\pi\) |
−0.717607 | + | 0.696449i | \(0.754762\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | 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 | \(0.615871\pi\) | |||||||
\(72\) | −1.50000 | + | 2.59808i | −0.176777 | + | 0.306186i | ||||
\(73\) | 14.0000 | 1.63858 | 0.819288 | − | 0.573382i | \(-0.194369\pi\) | ||||
0.819288 | + | 0.573382i | \(0.194369\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | 6.00000 | + | 10.3923i | 0.683763 | + | 1.18431i | ||||
\(78\) | 6.00000 | − | 3.46410i | 0.679366 | − | 0.392232i | ||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 6.00000 | 0.662589 | ||||||||
\(83\) | 4.50000 | − | 7.79423i | 0.493939 | − | 0.855528i | −0.506036 | − | 0.862512i | \(-0.668890\pi\) |
0.999976 | + | 0.00698436i | \(0.00222321\pi\) | |||||||
\(84\) | −6.00000 | + | 3.46410i | −0.654654 | + | 0.377964i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.500000 | − | 0.866025i | −0.0539164 | − | 0.0933859i | ||||
\(87\) | − | 10.3923i | − | 1.11417i | ||||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −9.00000 | −0.953998 | −0.476999 | − | 0.878904i | \(-0.658275\pi\) | ||||
−0.476999 | + | 0.878904i | \(0.658275\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | 3.00000 | − | 5.19615i | 0.312772 | − | 0.541736i | ||||
\(93\) | −12.0000 | − | 6.92820i | −1.24434 | − | 0.718421i | ||||
\(94\) | 6.00000 | + | 10.3923i | 0.618853 | + | 1.07188i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | + | 0.866025i | 0.153093 | + | 0.0883883i | ||||
\(97\) | 3.50000 | − | 6.06218i | 0.355371 | − | 0.615521i | −0.631810 | − | 0.775123i | \(-0.717688\pi\) |
0.987181 | + | 0.159602i | \(0.0510211\pi\) | |||||||
\(98\) | −9.00000 | −0.909137 | ||||||||
\(99\) | 4.50000 | + | 7.79423i | 0.452267 | + | 0.783349i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 5.19615i | 0.514496i | ||||||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | −2.00000 | − | 3.46410i | −0.196116 | − | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | − | 6.92820i | 1.13899 | − | 0.657596i | ||||
\(112\) | 2.00000 | + | 3.46410i | 0.188982 | + | 0.327327i | ||||
\(113\) | −1.50000 | − | 2.59808i | −0.141108 | − | 0.244406i | 0.786806 | − | 0.617200i | \(-0.211733\pi\) |
−0.927914 | + | 0.372794i | \(0.878400\pi\) | |||||||
\(114\) | 6.92820i | 0.648886i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.00000 | −0.557086 | ||||||||
\(117\) | 12.0000 | 1.10940 | ||||||||
\(118\) | 9.00000 | 0.828517 | ||||||||
\(119\) | −6.00000 | + | 10.3923i | −0.550019 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 4.00000 | + | 6.92820i | 0.362143 | + | 0.627250i | ||||
\(123\) | 9.00000 | + | 5.19615i | 0.811503 | + | 0.468521i | ||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.0000 | −1.06904 | ||||||||
\(127\) | −16.0000 | −1.41977 | −0.709885 | − | 0.704317i | \(-0.751253\pi\) | ||||
−0.709885 | + | 0.704317i | \(0.751253\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | − | 1.73205i | − | 0.152499i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.00000 | − | 10.3923i | −0.524222 | − | 0.907980i | −0.999602 | − | 0.0281993i | \(-0.991023\pi\) |
0.475380 | − | 0.879781i | \(-0.342311\pi\) | |||||||
\(132\) | 4.50000 | − | 2.59808i | 0.391675 | − | 0.226134i | ||||
\(133\) | −8.00000 | + | 13.8564i | −0.693688 | + | 1.20150i | ||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −9.00000 | + | 15.5885i | −0.768922 | + | 1.33181i | 0.169226 | + | 0.985577i | \(0.445873\pi\) |
−0.938148 | + | 0.346235i | \(0.887460\pi\) | |||||||
\(138\) | 9.00000 | − | 5.19615i | 0.766131 | − | 0.442326i | ||||
\(139\) | −5.50000 | − | 9.52628i | −0.466504 | − | 0.808008i | 0.532764 | − | 0.846264i | \(-0.321153\pi\) |
−0.999268 | + | 0.0382553i | \(0.987820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.7846i | 1.75038i | ||||||||
\(142\) | −3.00000 | + | 5.19615i | −0.251754 | + | 0.436051i | ||||
\(143\) | −12.0000 | −1.00349 | ||||||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.00000 | − | 12.1244i | 0.579324 | − | 1.00342i | ||||
\(147\) | −13.5000 | − | 7.79423i | −1.11346 | − | 0.642857i | ||||
\(148\) | −4.00000 | − | 6.92820i | −0.328798 | − | 0.569495i | ||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.00000 | − | 8.66025i | 0.406894 | − | 0.704761i | −0.587646 | − | 0.809118i | \(-0.699945\pi\) |
0.994540 | + | 0.104357i | \(0.0332784\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | −4.50000 | + | 7.79423i | −0.363803 | + | 0.630126i | ||||
\(154\) | 12.0000 | 0.966988 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | − | 6.92820i | − | 0.554700i | ||||||
\(157\) | 2.00000 | + | 3.46410i | 0.159617 | + | 0.276465i | 0.934731 | − | 0.355357i | \(-0.115641\pi\) |
−0.775113 | + | 0.631822i | \(0.782307\pi\) | |||||||
\(158\) | 4.00000 | + | 6.92820i | 0.318223 | + | 0.551178i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.0000 | 1.89146 | ||||||||
\(162\) | −9.00000 | −0.707107 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.50000 | − | 7.79423i | −0.349268 | − | 0.604949i | ||||
\(167\) | −9.00000 | − | 15.5885i | −0.696441 | − | 1.20627i | −0.969693 | − | 0.244328i | \(-0.921432\pi\) |
0.273252 | − | 0.961943i | \(-0.411901\pi\) | |||||||
\(168\) | 6.92820i | 0.534522i | ||||||||
\(169\) | −1.50000 | + | 2.59808i | −0.115385 | + | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | + | 10.3923i | −0.458831 | + | 0.794719i | ||||
\(172\) | −1.00000 | −0.0762493 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | −9.00000 | − | 5.19615i | −0.682288 | − | 0.393919i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 13.5000 | + | 7.79423i | 1.01472 | + | 0.585850i | ||||
\(178\) | −4.50000 | + | 7.79423i | −0.337289 | + | 0.584202i | ||||
\(179\) | −3.00000 | −0.224231 | −0.112115 | − | 0.993695i | \(-0.535763\pi\) | ||||
−0.112115 | + | 0.993695i | \(0.535763\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 8.00000 | − | 13.8564i | 0.592999 | − | 1.02711i | ||||
\(183\) | 13.8564i | 1.02430i | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −12.0000 | + | 6.92820i | −0.879883 | + | 0.508001i | ||||
\(187\) | 4.50000 | − | 7.79423i | 0.329073 | − | 0.569970i | ||||
\(188\) | 12.0000 | 0.875190 | ||||||||
\(189\) | −18.0000 | − | 10.3923i | −1.30931 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 1.50000 | − | 0.866025i | 0.108253 | − | 0.0625000i | ||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | −3.50000 | − | 6.06218i | −0.251285 | − | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.50000 | + | 7.79423i | −0.321429 | + | 0.556731i | ||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 9.00000 | 0.639602 | ||||||||
\(199\) | 2.00000 | 0.141776 | 0.0708881 | − | 0.997484i | \(-0.477417\pi\) | ||||
0.0708881 | + | 0.997484i | \(0.477417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00000 | + | 3.46410i | 0.423207 | + | 0.244339i | ||||
\(202\) | 6.00000 | + | 10.3923i | 0.422159 | + | 0.731200i | ||||
\(203\) | −12.0000 | − | 20.7846i | −0.842235 | − | 1.45879i | ||||
\(204\) | 4.50000 | + | 2.59808i | 0.315063 | + | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | 18.0000 | 1.25109 | ||||||||
\(208\) | −4.00000 | −0.277350 | ||||||||
\(209\) | 6.00000 | − | 10.3923i | 0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.5000 | − | 19.9186i | −0.791693 | − | 1.37125i | −0.924918 | − | 0.380166i | \(-0.875867\pi\) |
0.133226 | − | 0.991086i | \(-0.457467\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.00000 | + | 5.19615i | −0.616670 | + | 0.356034i | ||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −32.0000 | −2.17230 | ||||||||
\(218\) | 1.00000 | − | 1.73205i | 0.0677285 | − | 0.117309i | ||||
\(219\) | 21.0000 | − | 12.1244i | 1.41905 | − | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.00000 | − | 10.3923i | −0.403604 | − | 0.699062i | ||||
\(222\) | − | 13.8564i | − | 0.929981i | ||||||
\(223\) | −1.00000 | + | 1.73205i | −0.0669650 | + | 0.115987i | −0.897564 | − | 0.440884i | \(-0.854665\pi\) |
0.830599 | + | 0.556871i | \(0.187998\pi\) | |||||||
\(224\) | 4.00000 | 0.267261 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00000 | −0.199557 | ||||||||
\(227\) | 13.5000 | − | 23.3827i | 0.896026 | − | 1.55196i | 0.0634974 | − | 0.997982i | \(-0.479775\pi\) |
0.832529 | − | 0.553981i | \(-0.186892\pi\) | |||||||
\(228\) | 6.00000 | + | 3.46410i | 0.397360 | + | 0.229416i | ||||
\(229\) | −4.00000 | − | 6.92820i | −0.264327 | − | 0.457829i | 0.703060 | − | 0.711131i | \(-0.251817\pi\) |
−0.967387 | + | 0.253302i | \(0.918483\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | + | 10.3923i | 1.18431 | + | 0.683763i | ||||
\(232\) | −3.00000 | + | 5.19615i | −0.196960 | + | 0.341144i | ||||
\(233\) | 15.0000 | 0.982683 | 0.491341 | − | 0.870967i | \(-0.336507\pi\) | ||||
0.491341 | + | 0.870967i | \(0.336507\pi\) | |||||||
\(234\) | 6.00000 | − | 10.3923i | 0.392232 | − | 0.679366i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.50000 | − | 7.79423i | 0.292925 | − | 0.507361i | ||||
\(237\) | 13.8564i | 0.900070i | ||||||||
\(238\) | 6.00000 | + | 10.3923i | 0.388922 | + | 0.673633i | ||||
\(239\) | −9.00000 | − | 15.5885i | −0.582162 | − | 1.00833i | −0.995223 | − | 0.0976302i | \(-0.968874\pi\) |
0.413061 | − | 0.910703i | \(-0.364460\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.0000 | + | 22.5167i | −0.837404 | + | 1.45043i | 0.0546547 | + | 0.998505i | \(0.482594\pi\) |
−0.892058 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.866025 | − | 0.500000i | ||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | − | 5.19615i | 0.573819 | − | 0.331295i | ||||
\(247\) | −8.00000 | − | 13.8564i | −0.509028 | − | 0.881662i | ||||
\(248\) | 4.00000 | + | 6.92820i | 0.254000 | + | 0.439941i | ||||
\(249\) | − | 15.5885i | − | 0.987878i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −6.00000 | + | 10.3923i | −0.377964 | + | 0.654654i | ||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | −8.00000 | + | 13.8564i | −0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −1.50000 | − | 2.59808i | −0.0935674 | − | 0.162064i | 0.815442 | − | 0.578838i | \(-0.196494\pi\) |
−0.909010 | + | 0.416775i | \(0.863160\pi\) | |||||||
\(258\) | −1.50000 | − | 0.866025i | −0.0933859 | − | 0.0539164i | ||||
\(259\) | 16.0000 | − | 27.7128i | 0.994192 | − | 1.72199i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | − | 15.5885i | −0.557086 | − | 0.964901i | ||||
\(262\) | −12.0000 | −0.741362 | ||||||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | − | 5.19615i | − | 0.319801i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 13.8564i | 0.490511 | + | 0.849591i | ||||
\(267\) | −13.5000 | + | 7.79423i | −0.826187 | + | 0.476999i | ||||
\(268\) | 2.00000 | − | 3.46410i | 0.122169 | − | 0.211604i | ||||
\(269\) | −12.0000 | −0.731653 | −0.365826 | − | 0.930683i | \(-0.619214\pi\) | ||||
−0.365826 | + | 0.930683i | \(0.619214\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | −0.242983 | −0.121491 | − | 0.992592i | \(-0.538768\pi\) | ||||
−0.121491 | + | 0.992592i | \(0.538768\pi\) | |||||||
\(272\) | 1.50000 | − | 2.59808i | 0.0909509 | − | 0.157532i | ||||
\(273\) | 24.0000 | − | 13.8564i | 1.45255 | − | 0.838628i | ||||
\(274\) | 9.00000 | + | 15.5885i | 0.543710 | + | 0.941733i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 10.3923i | − | 0.625543i | ||||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | −11.0000 | −0.659736 | ||||||||
\(279\) | −24.0000 | −1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | − | 15.5885i | 0.536895 | − | 0.929929i | −0.462174 | − | 0.886789i | \(-0.652930\pi\) |
0.999069 | − | 0.0431402i | \(-0.0137362\pi\) | |||||||
\(282\) | 18.0000 | + | 10.3923i | 1.07188 | + | 0.618853i | ||||
\(283\) | 0.500000 | + | 0.866025i | 0.0297219 | + | 0.0514799i | 0.880504 | − | 0.474039i | \(-0.157204\pi\) |
−0.850782 | + | 0.525519i | \(0.823871\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.00000 | + | 10.3923i | −0.354787 | + | 0.614510i | ||||
\(287\) | 24.0000 | 1.41668 | ||||||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 12.1244i | − | 0.710742i | ||||||
\(292\) | −7.00000 | − | 12.1244i | −0.409644 | − | 0.709524i | ||||
\(293\) | 6.00000 | + | 10.3923i | 0.350524 | + | 0.607125i | 0.986341 | − | 0.164714i | \(-0.0526703\pi\) |
−0.635818 | + | 0.771839i | \(0.719337\pi\) | |||||||
\(294\) | −13.5000 | + | 7.79423i | −0.787336 | + | 0.454569i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.00000 | − | 3.46410i | −0.115278 | − | 0.199667i | ||||
\(302\) | −5.00000 | − | 8.66025i | −0.287718 | − | 0.498342i | ||||
\(303\) | 20.7846i | 1.19404i | ||||||||
\(304\) | 2.00000 | − | 3.46410i | 0.114708 | − | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.50000 | + | 7.79423i | 0.257248 | + | 0.445566i | ||||
\(307\) | −1.00000 | −0.0570730 | −0.0285365 | − | 0.999593i | \(-0.509085\pi\) | ||||
−0.0285365 | + | 0.999593i | \(0.509085\pi\) | |||||||
\(308\) | 6.00000 | − | 10.3923i | 0.341882 | − | 0.592157i | ||||
\(309\) | −12.0000 | − | 6.92820i | −0.682656 | − | 0.394132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.00000 | − | 5.19615i | −0.170114 | − | 0.294647i | 0.768345 | − | 0.640036i | \(-0.221080\pi\) |
−0.938460 | + | 0.345389i | \(0.887747\pi\) | |||||||
\(312\) | −6.00000 | − | 3.46410i | −0.339683 | − | 0.196116i | ||||
\(313\) | −8.50000 | + | 14.7224i | −0.480448 | + | 0.832161i | −0.999748 | − | 0.0224310i | \(-0.992859\pi\) |
0.519300 | + | 0.854592i | \(0.326193\pi\) | |||||||
\(314\) | 4.00000 | 0.225733 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | 0.450035 | ||||||||
\(317\) | 9.00000 | − | 15.5885i | 0.505490 | − | 0.875535i | −0.494489 | − | 0.869184i | \(-0.664645\pi\) |
0.999980 | − | 0.00635137i | \(-0.00202172\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0000 | − | 10.3923i | 1.00466 | − | 0.580042i | ||||
\(322\) | 12.0000 | − | 20.7846i | 0.668734 | − | 1.15828i | ||||
\(323\) | 12.0000 | 0.667698 | ||||||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.50000 | − | 9.52628i | 0.304617 | − | 0.527612i | ||||
\(327\) | 3.00000 | − | 1.73205i | 0.165900 | − | 0.0957826i | ||||
\(328\) | −3.00000 | − | 5.19615i | −0.165647 | − | 0.286910i | ||||
\(329\) | 24.0000 | + | 41.5692i | 1.32316 | + | 2.29179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | −9.00000 | −0.493939 | ||||||||
\(333\) | 12.0000 | − | 20.7846i | 0.657596 | − | 1.13899i | ||||
\(334\) | −18.0000 | −0.984916 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.00000 | + | 3.46410i | 0.327327 | + | 0.188982i | ||||
\(337\) | 6.50000 | + | 11.2583i | 0.354078 | + | 0.613280i | 0.986960 | − | 0.160968i | \(-0.0514616\pi\) |
−0.632882 | + | 0.774248i | \(0.718128\pi\) | |||||||
\(338\) | 1.50000 | + | 2.59808i | 0.0815892 | + | 0.141317i | ||||
\(339\) | −4.50000 | − | 2.59808i | −0.244406 | − | 0.141108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 6.00000 | + | 10.3923i | 0.324443 | + | 0.561951i | ||||
\(343\) | −8.00000 | −0.431959 | ||||||||
\(344\) | −0.500000 | + | 0.866025i | −0.0269582 | + | 0.0466930i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | −9.00000 | + | 5.19615i | −0.482451 | + | 0.278543i | ||||
\(349\) | −7.00000 | + | 12.1244i | −0.374701 | + | 0.649002i | −0.990282 | − | 0.139072i | \(-0.955588\pi\) |
0.615581 | + | 0.788074i | \(0.288921\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000 | − | 10.3923i | 0.960769 | − | 0.554700i | ||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | 4.50000 | − | 7.79423i | 0.239511 | − | 0.414845i | −0.721063 | − | 0.692869i | \(-0.756346\pi\) |
0.960574 | + | 0.278024i | \(0.0896796\pi\) | |||||||
\(354\) | 13.5000 | − | 7.79423i | 0.717517 | − | 0.414259i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.50000 | + | 7.79423i | 0.238500 | + | 0.413093i | ||||
\(357\) | 20.7846i | 1.10004i | ||||||||
\(358\) | −1.50000 | + | 2.59808i | −0.0792775 | + | 0.137313i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 1.00000 | − | 1.73205i | 0.0525588 | − | 0.0910346i | ||||
\(363\) | 3.00000 | + | 1.73205i | 0.157459 | + | 0.0909091i | ||||
\(364\) | −8.00000 | − | 13.8564i | −0.419314 | − | 0.726273i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.0000 | + | 6.92820i | 0.627250 | + | 0.362143i | ||||
\(367\) | −13.0000 | + | 22.5167i | −0.678594 | + | 1.17536i | 0.296810 | + | 0.954937i | \(0.404077\pi\) |
−0.975404 | + | 0.220423i | \(0.929256\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 13.8564i | 0.718421i | ||||||||
\(373\) | −4.00000 | − | 6.92820i | −0.207112 | − | 0.358729i | 0.743691 | − | 0.668523i | \(-0.233073\pi\) |
−0.950804 | + | 0.309794i | \(0.899740\pi\) | |||||||
\(374\) | −4.50000 | − | 7.79423i | −0.232689 | − | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | − | 10.3923i | 0.309426 | − | 0.535942i | ||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | −18.0000 | + | 10.3923i | −0.925820 | + | 0.534522i | ||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −24.0000 | + | 13.8564i | −1.22956 | + | 0.709885i | ||||
\(382\) | 3.00000 | + | 5.19615i | 0.153493 | + | 0.265858i | ||||
\(383\) | −9.00000 | − | 15.5885i | −0.459879 | − | 0.796533i | 0.539076 | − | 0.842257i | \(-0.318774\pi\) |
−0.998954 | + | 0.0457244i | \(0.985440\pi\) | |||||||
\(384\) | − | 1.73205i | − | 0.0883883i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | −0.254493 | ||||||||
\(387\) | −1.50000 | − | 2.59808i | −0.0762493 | − | 0.132068i | ||||
\(388\) | −7.00000 | −0.355371 | ||||||||
\(389\) | 3.00000 | − | 5.19615i | 0.152106 | − | 0.263455i | −0.779895 | − | 0.625910i | \(-0.784728\pi\) |
0.932002 | + | 0.362454i | \(0.118061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.00000 | − | 15.5885i | −0.455150 | − | 0.788342i | ||||
\(392\) | 4.50000 | + | 7.79423i | 0.227284 | + | 0.393668i | ||||
\(393\) | −18.0000 | − | 10.3923i | −0.907980 | − | 0.524222i | ||||
\(394\) | −9.00000 | + | 15.5885i | −0.453413 | + | 0.785335i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.50000 | − | 7.79423i | 0.226134 | − | 0.391675i | ||||
\(397\) | 14.0000 | 0.702640 | 0.351320 | − | 0.936255i | \(-0.385733\pi\) | ||||
0.351320 | + | 0.936255i | \(0.385733\pi\) | |||||||
\(398\) | 1.00000 | − | 1.73205i | 0.0501255 | − | 0.0868199i | ||||
\(399\) | 27.7128i | 1.38738i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.50000 | + | 12.9904i | 0.374532 | + | 0.648709i | 0.990257 | − | 0.139253i | \(-0.0444700\pi\) |
−0.615725 | + | 0.787961i | \(0.711137\pi\) | |||||||
\(402\) | 6.00000 | − | 3.46410i | 0.299253 | − | 0.172774i | ||||
\(403\) | 16.0000 | − | 27.7128i | 0.797017 | − | 1.38047i | ||||
\(404\) | 12.0000 | 0.597022 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −24.0000 | −1.19110 | ||||||||
\(407\) | −12.0000 | + | 20.7846i | −0.594818 | + | 1.03025i | ||||
\(408\) | 4.50000 | − | 2.59808i | 0.222783 | − | 0.128624i | ||||
\(409\) | 11.0000 | + | 19.0526i | 0.543915 | + | 0.942088i | 0.998674 | + | 0.0514740i | \(0.0163919\pi\) |
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.1769i | 1.53784i | ||||||||
\(412\) | −4.00000 | + | 6.92820i | −0.197066 | + | 0.341328i | ||||
\(413\) | 36.0000 | 1.77144 | ||||||||
\(414\) | 9.00000 | − | 15.5885i | 0.442326 | − | 0.766131i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.00000 | + | 3.46410i | −0.0980581 | + | 0.169842i | ||||
\(417\) | −16.5000 | − | 9.52628i | −0.808008 | − | 0.466504i | ||||
\(418\) | −6.00000 | − | 10.3923i | −0.293470 | − | 0.508304i | ||||
\(419\) | −4.50000 | − | 7.79423i | −0.219839 | − | 0.380773i | 0.734919 | − | 0.678155i | \(-0.237220\pi\) |
−0.954759 | + | 0.297382i | \(0.903887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | + | 27.7128i | −0.779792 | + | 1.35064i | 0.152269 | + | 0.988339i | \(0.451342\pi\) |
−0.932061 | + | 0.362301i | \(0.881991\pi\) | |||||||
\(422\) | −23.0000 | −1.11962 | ||||||||
\(423\) | 18.0000 | + | 31.1769i | 0.875190 | + | 1.51587i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.3923i | 0.503509i | ||||||||
\(427\) | 16.0000 | + | 27.7128i | 0.774294 | + | 1.34112i | ||||
\(428\) | −6.00000 | − | 10.3923i | −0.290021 | − | 0.502331i | ||||
\(429\) | −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 | \(0.453841\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | −7.00000 | −0.336399 | −0.168199 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168199 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(434\) | −16.0000 | + | 27.7128i | −0.768025 | + | 1.33026i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −12.0000 | − | 20.7846i | −0.574038 | − | 0.994263i | ||||
\(438\) | − | 24.2487i | − | 1.15865i | ||||||
\(439\) | −7.00000 | + | 12.1244i | −0.334092 | + | 0.578664i | −0.983310 | − | 0.181938i | \(-0.941763\pi\) |
0.649218 | + | 0.760602i | \(0.275096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −27.0000 | −1.28571 | ||||||||
\(442\) | −12.0000 | −0.570782 | ||||||||
\(443\) | −4.50000 | + | 7.79423i | −0.213801 | + | 0.370315i | −0.952901 | − | 0.303281i | \(-0.901918\pi\) |
0.739100 | + | 0.673596i | \(0.235251\pi\) | |||||||
\(444\) | −12.0000 | − | 6.92820i | −0.569495 | − | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.00000 | + | 1.73205i | 0.0473514 | + | 0.0820150i | ||||
\(447\) | 9.00000 | + | 5.19615i | 0.425685 | + | 0.245770i | ||||
\(448\) | 2.00000 | − | 3.46410i | 0.0944911 | − | 0.163663i | ||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18.0000 | −0.847587 | ||||||||
\(452\) | −1.50000 | + | 2.59808i | −0.0705541 | + | 0.122203i | ||||
\(453\) | − | 17.3205i | − | 0.813788i | ||||||
\(454\) | −13.5000 | − | 23.3827i | −0.633586 | − | 1.09740i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.00000 | − | 3.46410i | 0.280976 | − | 0.162221i | ||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | −8.00000 | −0.373815 | ||||||||
\(459\) | 15.5885i | 0.727607i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.00000 | − | 5.19615i | 0.139724 | − | 0.242009i | −0.787668 | − | 0.616100i | \(-0.788712\pi\) |
0.927392 | + | 0.374091i | \(0.122045\pi\) | |||||||
\(462\) | 18.0000 | − | 10.3923i | 0.837436 | − | 0.483494i | ||||
\(463\) | −7.00000 | − | 12.1244i | −0.325318 | − | 0.563467i | 0.656259 | − | 0.754536i | \(-0.272138\pi\) |
−0.981577 | + | 0.191069i | \(0.938805\pi\) | |||||||
\(464\) | 3.00000 | + | 5.19615i | 0.139272 | + | 0.241225i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7.50000 | − | 12.9904i | 0.347431 | − | 0.601768i | ||||
\(467\) | 9.00000 | 0.416470 | 0.208235 | − | 0.978079i | \(-0.433228\pi\) | ||||
0.208235 | + | 0.978079i | \(0.433228\pi\) | |||||||
\(468\) | −6.00000 | − | 10.3923i | −0.277350 | − | 0.480384i | ||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.00000 | + | 3.46410i | 0.276465 | + | 0.159617i | ||||
\(472\) | −4.50000 | − | 7.79423i | −0.207129 | − | 0.358758i | ||||
\(473\) | 1.50000 | + | 2.59808i | 0.0689701 | + | 0.119460i | ||||
\(474\) | 12.0000 | + | 6.92820i | 0.551178 | + | 0.318223i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | 0.550019 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.0000 | −0.823301 | ||||||||
\(479\) | 6.00000 | − | 10.3923i | 0.274147 | − | 0.474837i | −0.695773 | − | 0.718262i | \(-0.744938\pi\) |
0.969920 | + | 0.243426i | \(0.0782712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.0000 | + | 27.7128i | 0.729537 | + | 1.26360i | ||||
\(482\) | 13.0000 | + | 22.5167i | 0.592134 | + | 1.02561i | ||||
\(483\) | 36.0000 | − | 20.7846i | 1.63806 | − | 0.945732i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | 4.00000 | − | 6.92820i | 0.181071 | − | 0.313625i | ||||
\(489\) | 16.5000 | − | 9.52628i | 0.746156 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.50000 | + | 12.9904i | 0.338470 | + | 0.586248i | 0.984145 | − | 0.177365i | \(-0.0567572\pi\) |
−0.645675 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(492\) | − | 10.3923i | − | 0.468521i | ||||||
\(493\) | −9.00000 | + | 15.5885i | −0.405340 | + | 0.702069i | ||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.00000 | 0.359211 | ||||||||
\(497\) | −12.0000 | + | 20.7846i | −0.538274 | + | 0.932317i | ||||
\(498\) | −13.5000 | − | 7.79423i | −0.604949 | − | 0.349268i | ||||
\(499\) | −5.50000 | − | 9.52628i | −0.246214 | − | 0.426455i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
−0.962472 | + | 0.271380i | \(0.912520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.0000 | − | 15.5885i | −1.20627 | − | 0.696441i | ||||
\(502\) | −6.00000 | + | 10.3923i | −0.267793 | + | 0.463831i | ||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 6.00000 | + | 10.3923i | 0.267261 | + | 0.462910i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.00000 | + | 15.5885i | −0.400099 | + | 0.692991i | ||||
\(507\) | 5.19615i | 0.230769i | ||||||||
\(508\) | 8.00000 | + | 13.8564i | 0.354943 | + | 0.614779i | ||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0000 | − | 48.4974i | 1.23865 | − | 2.14540i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 20.7846i | 0.917663i | ||||||||
\(514\) | −3.00000 | −0.132324 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.50000 | + | 0.866025i | −0.0660338 | + | 0.0381246i | ||||
\(517\) | −18.0000 | − | 31.1769i | −0.791639 | − | 1.37116i | ||||
\(518\) | −16.0000 | − | 27.7128i | −0.703000 | − | 1.21763i | ||||
\(519\) | − | 10.3923i | − | 0.456172i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | −18.0000 | −0.787839 | ||||||||
\(523\) | 29.0000 | 1.26808 | 0.634041 | − | 0.773300i | \(-0.281395\pi\) | ||||
0.634041 | + | 0.773300i | \(0.281395\pi\) | |||||||
\(524\) | −6.00000 | + | 10.3923i | −0.262111 | + | 0.453990i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 12.0000 | + | 20.7846i | 0.523225 | + | 0.906252i | ||||
\(527\) | 12.0000 | + | 20.7846i | 0.522728 | + | 0.905392i | ||||
\(528\) | −4.50000 | − | 2.59808i | −0.195837 | − | 0.113067i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.0000 | 1.17170 | ||||||||
\(532\) | 16.0000 | 0.693688 | ||||||||
\(533\) | −12.0000 | + | 20.7846i | −0.519778 | + | 0.900281i | ||||
\(534\) | 15.5885i | 0.674579i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | − | 3.46410i | −0.0863868 | − | 0.149626i | ||||
\(537\) | −4.50000 | + | 2.59808i | −0.194189 | + | 0.112115i | ||||
\(538\) | −6.00000 | + | 10.3923i | −0.258678 | + | 0.448044i | ||||
\(539\) | 27.0000 | 1.16297 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.00000 | 0.343947 | 0.171973 | − | 0.985102i | \(-0.444986\pi\) | ||||
0.171973 | + | 0.985102i | \(0.444986\pi\) | |||||||
\(542\) | −2.00000 | + | 3.46410i | −0.0859074 | + | 0.148796i | ||||
\(543\) | 3.00000 | − | 1.73205i | 0.128742 | − | 0.0743294i | ||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 27.7128i | − | 1.18600i | ||||||
\(547\) | −10.0000 | + | 17.3205i | −0.427569 | + | 0.740571i | −0.996657 | − | 0.0817056i | \(-0.973963\pi\) |
0.569087 | + | 0.822277i | \(0.307297\pi\) | |||||||
\(548\) | 18.0000 | 0.768922 | ||||||||
\(549\) | 12.0000 | + | 20.7846i | 0.512148 | + | 0.887066i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | −9.00000 | − | 5.19615i | −0.383065 | − | 0.221163i | ||||
\(553\) | 16.0000 | + | 27.7128i | 0.680389 | + | 1.17847i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.50000 | + | 9.52628i | −0.233252 | + | 0.404004i | ||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | −12.0000 | + | 20.7846i | −0.508001 | + | 0.879883i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 15.5885i | − | 0.658145i | ||||||
\(562\) | −9.00000 | − | 15.5885i | −0.379642 | − | 0.657559i | ||||
\(563\) | 1.50000 | + | 2.59808i | 0.0632175 | + | 0.109496i | 0.895902 | − | 0.444252i | \(-0.146530\pi\) |
−0.832684 | + | 0.553748i | \(0.813197\pi\) | |||||||
\(564\) | 18.0000 | − | 10.3923i | 0.757937 | − | 0.437595i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.00000 | 0.0420331 | ||||||||
\(567\) | −36.0000 | −1.51186 | ||||||||
\(568\) | 6.00000 | 0.251754 | ||||||||
\(569\) | 13.5000 | − | 23.3827i | 0.565949 | − | 0.980253i | −0.431011 | − | 0.902347i | \(-0.641843\pi\) |
0.996961 | − | 0.0779066i | \(-0.0248236\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.5000 | + | 21.6506i | 0.523109 | + | 0.906051i | 0.999638 | + | 0.0268925i | \(0.00856117\pi\) |
−0.476530 | + | 0.879158i | \(0.658105\pi\) | |||||||
\(572\) | 6.00000 | + | 10.3923i | 0.250873 | + | 0.434524i | ||||
\(573\) | 10.3923i | 0.434145i | ||||||||
\(574\) | 12.0000 | − | 20.7846i | 0.500870 | − | 0.867533i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.50000 | − | 2.59808i | 0.0625000 | − | 0.108253i | ||||
\(577\) | 38.0000 | 1.58196 | 0.790980 | − | 0.611842i | \(-0.209571\pi\) | ||||
0.790980 | + | 0.611842i | \(0.209571\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | −7.50000 | − | 4.33013i | −0.311689 | − | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.0000 | − | 31.1769i | −0.746766 | − | 1.29344i | ||||
\(582\) | −10.5000 | − | 6.06218i | −0.435239 | − | 0.251285i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −14.0000 | −0.579324 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | 0.495715 | ||||||||
\(587\) | 1.50000 | − | 2.59808i | 0.0619116 | − | 0.107234i | −0.833408 | − | 0.552658i | \(-0.813614\pi\) |
0.895320 | + | 0.445424i | \(0.146947\pi\) | |||||||
\(588\) | 15.5885i | 0.642857i | ||||||||
\(589\) | 16.0000 | + | 27.7128i | 0.659269 | + | 1.14189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27.0000 | + | 15.5885i | −1.11063 | + | 0.641223i | ||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | −45.0000 | −1.84793 | −0.923964 | − | 0.382479i | \(-0.875070\pi\) | ||||
−0.923964 | + | 0.382479i | \(0.875070\pi\) | |||||||
\(594\) | 13.5000 | − | 7.79423i | 0.553912 | − | 0.319801i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | − | 5.19615i | 0.122885 | − | 0.212843i | ||||
\(597\) | 3.00000 | − | 1.73205i | 0.122782 | − | 0.0708881i | ||||
\(598\) | 12.0000 | + | 20.7846i | 0.490716 | + | 0.849946i | ||||
\(599\) | −9.00000 | − | 15.5885i | −0.367730 | − | 0.636927i | 0.621480 | − | 0.783430i | \(-0.286532\pi\) |
−0.989210 | + | 0.146503i | \(0.953198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5000 | − | 32.0429i | 0.754631 | − | 1.30706i | −0.190927 | − | 0.981604i | \(-0.561149\pi\) |
0.945558 | − | 0.325455i | \(-0.105517\pi\) | |||||||
\(602\) | −4.00000 | −0.163028 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | + | 10.3923i | 0.731200 | + | 0.422159i | ||||
\(607\) | 8.00000 | + | 13.8564i | 0.324710 | + | 0.562414i | 0.981454 | − | 0.191700i | \(-0.0614000\pi\) |
−0.656744 | + | 0.754114i | \(0.728067\pi\) | |||||||
\(608\) | −2.00000 | − | 3.46410i | −0.0811107 | − | 0.140488i | ||||
\(609\) | −36.0000 | − | 20.7846i | −1.45879 | − | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 9.00000 | 0.363803 | ||||||||
\(613\) | 14.0000 | 0.565455 | 0.282727 | − | 0.959200i | \(-0.408761\pi\) | ||||
0.282727 | + | 0.959200i | \(0.408761\pi\) | |||||||
\(614\) | −0.500000 | + | 0.866025i | −0.0201784 | + | 0.0349499i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | − | 10.3923i | −0.241747 | − | 0.418718i | ||||
\(617\) | −13.5000 | − | 23.3827i | −0.543490 | − | 0.941351i | −0.998700 | − | 0.0509678i | \(-0.983769\pi\) |
0.455211 | − | 0.890384i | \(-0.349564\pi\) | |||||||
\(618\) | −12.0000 | + | 6.92820i | −0.482711 | + | 0.278693i | ||||
\(619\) | −17.5000 | + | 30.3109i | −0.703384 | + | 1.21830i | 0.263887 | + | 0.964554i | \(0.414995\pi\) |
−0.967271 | + | 0.253744i | \(0.918338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.0000 | − | 15.5885i | 1.08347 | − | 0.625543i | ||||
\(622\) | −6.00000 | −0.240578 | ||||||||
\(623\) | −18.0000 | + | 31.1769i | −0.721155 | + | 1.24908i | ||||
\(624\) | −6.00000 | + | 3.46410i | −0.240192 | + | 0.138675i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.50000 | + | 14.7224i | 0.339728 | + | 0.588427i | ||||
\(627\) | − | 20.7846i | − | 0.830057i | ||||||
\(628\) | 2.00000 | − | 3.46410i | 0.0798087 | − | 0.138233i | ||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.0000 | 1.51276 | 0.756378 | − | 0.654135i | \(-0.226967\pi\) | ||||
0.756378 | + | 0.654135i | \(0.226967\pi\) | |||||||
\(632\) | 4.00000 | − | 6.92820i | 0.159111 | − | 0.275589i | ||||
\(633\) | −34.5000 | − | 19.9186i | −1.37125 | − | 0.791693i | ||||
\(634\) | −9.00000 | − | 15.5885i | −0.357436 | − | 0.619097i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0000 | − | 31.1769i | 0.713186 | − | 1.23527i | ||||
\(638\) | 18.0000 | 0.712627 | ||||||||
\(639\) | −9.00000 | + | 15.5885i | −0.356034 | + | 0.616670i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.5000 | − | 23.3827i | 0.533218 | − | 0.923561i | −0.466029 | − | 0.884769i | \(-0.654316\pi\) |
0.999247 | − | 0.0387913i | \(-0.0123508\pi\) | |||||||
\(642\) | − | 20.7846i | − | 0.820303i | ||||||
\(643\) | −11.5000 | − | 19.9186i | −0.453516 | − | 0.785512i | 0.545086 | − | 0.838380i | \(-0.316497\pi\) |
−0.998602 | + | 0.0528680i | \(0.983164\pi\) | |||||||
\(644\) | −12.0000 | − | 20.7846i | −0.472866 | − | 0.819028i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | − | 10.3923i | 0.236067 | − | 0.408880i | ||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 4.50000 | + | 7.79423i | 0.176777 | + | 0.306186i | ||||
\(649\) | −27.0000 | −1.05984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.0000 | + | 27.7128i | −1.88127 | + | 1.08615i | ||||
\(652\) | −5.50000 | − | 9.52628i | −0.215397 | − | 0.373078i | ||||
\(653\) | 12.0000 | + | 20.7846i | 0.469596 | + | 0.813365i | 0.999396 | − | 0.0347583i | \(-0.0110661\pi\) |
−0.529799 | + | 0.848123i | \(0.677733\pi\) | |||||||
\(654\) | − | 3.46410i | − | 0.135457i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.00000 | −0.234261 | ||||||||
\(657\) | 21.0000 | − | 36.3731i | 0.819288 | − | 1.41905i | ||||
\(658\) | 48.0000 | 1.87123 | ||||||||
\(659\) | 22.5000 | − | 38.9711i | 0.876476 | − | 1.51810i | 0.0212930 | − | 0.999773i | \(-0.493222\pi\) |
0.855183 | − | 0.518327i | \(-0.173445\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | 8.50000 | + | 14.7224i | 0.330362 | + | 0.572204i | ||||
\(663\) | −18.0000 | − | 10.3923i | −0.699062 | − | 0.403604i | ||||
\(664\) | −4.50000 | + | 7.79423i | −0.174634 | + | 0.302475i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −12.0000 | − | 20.7846i | −0.464991 | − | 0.805387i | ||||
\(667\) | 36.0000 | 1.39393 | ||||||||
\(668\) | −9.00000 | + | 15.5885i | −0.348220 | + | 0.603136i | ||||
\(669\) | 3.46410i | 0.133930i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0000 | − | 20.7846i | −0.463255 | − | 0.802381i | ||||
\(672\) | 6.00000 | − | 3.46410i | 0.231455 | − | 0.133631i | ||||
\(673\) | 23.0000 | − | 39.8372i | 0.886585 | − | 1.53561i | 0.0426985 | − | 0.999088i | \(-0.486405\pi\) |
0.843886 | − | 0.536522i | \(-0.180262\pi\) | |||||||
\(674\) | 13.0000 | 0.500741 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | −9.00000 | + | 15.5885i | −0.345898 | + | 0.599113i | −0.985517 | − | 0.169580i | \(-0.945759\pi\) |
0.639618 | + | 0.768693i | \(0.279092\pi\) | |||||||
\(678\) | −4.50000 | + | 2.59808i | −0.172821 | + | 0.0997785i | ||||
\(679\) | −14.0000 | − | 24.2487i | −0.537271 | − | 0.930580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 46.7654i | − | 1.79205i | ||||||
\(682\) | 12.0000 | − | 20.7846i | 0.459504 | − | 0.795884i | ||||
\(683\) | 36.0000 | 1.37750 | 0.688751 | − | 0.724998i | \(-0.258159\pi\) | ||||
0.688751 | + | 0.724998i | \(0.258159\pi\) | |||||||
\(684\) | 12.0000 | 0.458831 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.00000 | + | 6.92820i | −0.152721 | + | 0.264520i | ||||
\(687\) | −12.0000 | − | 6.92820i | −0.457829 | − | 0.264327i | ||||
\(688\) | 0.500000 | + | 0.866025i | 0.0190623 | + | 0.0330169i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.50000 | − | 16.4545i | 0.361397 | − | 0.625958i | −0.626794 | − | 0.779185i | \(-0.715633\pi\) |
0.988191 | + | 0.153227i | \(0.0489666\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 36.0000 | 1.36753 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 10.3923i | 0.393919i | ||||||||
\(697\) | −9.00000 | − | 15.5885i | −0.340899 | − | 0.590455i | ||||
\(698\) | 7.00000 | + | 12.1244i | 0.264954 | + | 0.458914i | ||||
\(699\) | 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 | \(0.138769\pi\) | |||||||
\(702\) | − | 20.7846i | − | 0.784465i | ||||||
\(703\) | −32.0000 | −1.20690 | ||||||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.50000 | − | 7.79423i | −0.169360 | − | 0.293340i | ||||
\(707\) | 24.0000 | + | 41.5692i | 0.902613 | + | 1.56337i | ||||
\(708\) | − | 15.5885i | − | 0.585850i | ||||||
\(709\) | 26.0000 | − | 45.0333i | 0.976450 | − | 1.69126i | 0.301388 | − | 0.953502i | \(-0.402550\pi\) |
0.675063 | − | 0.737760i | \(-0.264116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | + | 20.7846i | 0.450035 | + | 0.779484i | ||||
\(712\) | 9.00000 | 0.337289 | ||||||||
\(713\) | 24.0000 | − | 41.5692i | 0.898807 | − | 1.55678i | ||||
\(714\) | 18.0000 | + | 10.3923i | 0.673633 | + | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.50000 | + | 2.59808i | 0.0560576 | + | 0.0970947i | ||||
\(717\) | −27.0000 | − | 15.5885i | −1.00833 | − | 0.582162i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.0000 | −1.19174 | ||||||||
\(722\) | −1.50000 | + | 2.59808i | −0.0558242 | + | 0.0966904i | ||||
\(723\) | 45.0333i | 1.67481i | ||||||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.00000 | − | 1.73205i | 0.111340 | − | 0.0642824i | ||||
\(727\) | −7.00000 | + | 12.1244i | −0.259616 | + | 0.449667i | −0.966139 | − | 0.258022i | \(-0.916929\pi\) |
0.706523 | + | 0.707690i | \(0.250263\pi\) | |||||||
\(728\) | −16.0000 | −0.592999 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 12.0000 | − | 6.92820i | 0.443533 | − | 0.256074i | ||||
\(733\) | 2.00000 | + | 3.46410i | 0.0738717 | + | 0.127950i | 0.900595 | − | 0.434659i | \(-0.143131\pi\) |
−0.826723 | + | 0.562609i | \(0.809798\pi\) | |||||||
\(734\) | 13.0000 | + | 22.5167i | 0.479839 | + | 0.831105i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | + | 5.19615i | −0.110581 | + | 0.191533i | ||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 9.00000 | − | 15.5885i | 0.331295 | − | 0.573819i | ||||
\(739\) | −25.0000 | −0.919640 | −0.459820 | − | 0.888012i | \(-0.652086\pi\) | ||||
−0.459820 | + | 0.888012i | \(0.652086\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −24.0000 | − | 13.8564i | −0.881662 | − | 0.509028i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(744\) | 12.0000 | + | 6.92820i | 0.439941 | + | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −8.00000 | −0.292901 | ||||||||
\(747\) | −13.5000 | − | 23.3827i | −0.493939 | − | 0.855528i | ||||
\(748\) | −9.00000 | −0.329073 | ||||||||
\(749\) | 24.0000 | − | 41.5692i | 0.876941 | − | 1.51891i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0000 | + | 29.4449i | 0.620339 | + | 1.07446i | 0.989423 | + | 0.145062i | \(0.0463382\pi\) |
−0.369084 | + | 0.929396i | \(0.620328\pi\) | |||||||
\(752\) | −6.00000 | − | 10.3923i | −0.218797 | − | 0.378968i | ||||
\(753\) | −18.0000 | + | 10.3923i | −0.655956 | + | 0.378717i | ||||
\(754\) | 12.0000 | − | 20.7846i | 0.437014 | − | 0.756931i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.7846i | 0.755929i | ||||||||
\(757\) | 20.0000 | 0.726912 | 0.363456 | − | 0.931611i | \(-0.381597\pi\) | ||||
0.363456 | + | 0.931611i | \(0.381597\pi\) | |||||||
\(758\) | 14.5000 | − | 25.1147i | 0.526664 | − | 0.912208i | ||||
\(759\) | −27.0000 | + | 15.5885i | −0.980038 | + | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.5000 | + | 33.7750i | 0.706874 | + | 1.22434i | 0.966011 | + | 0.258502i | \(0.0832288\pi\) |
−0.259136 | + | 0.965841i | \(0.583438\pi\) | |||||||
\(762\) | 27.7128i | 1.00393i | ||||||||
\(763\) | 4.00000 | − | 6.92820i | 0.144810 | − | 0.250818i | ||||
\(764\) | 6.00000 | 0.217072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0000 | −0.650366 | ||||||||
\(767\) | −18.0000 | + | 31.1769i | −0.649942 | + | 1.12573i | ||||
\(768\) | −1.50000 | − | 0.866025i | −0.0541266 | − | 0.0312500i | ||||
\(769\) | −2.50000 | − | 4.33013i | −0.0901523 | − | 0.156148i | 0.817423 | − | 0.576038i | \(-0.195402\pi\) |
−0.907575 | + | 0.419890i | \(0.862069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.50000 | − | 2.59808i | −0.162064 | − | 0.0935674i | ||||
\(772\) | −2.50000 | + | 4.33013i | −0.0899770 | + | 0.155845i | ||||
\(773\) | −42.0000 | −1.51064 | −0.755318 | − | 0.655359i | \(-0.772517\pi\) | ||||
−0.755318 | + | 0.655359i | \(0.772517\pi\) | |||||||
\(774\) | −3.00000 | −0.107833 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.50000 | + | 6.06218i | −0.125643 | + | 0.217620i | ||||
\(777\) | − | 55.4256i | − | 1.98838i | ||||||
\(778\) | −3.00000 | − | 5.19615i | −0.107555 | − | 0.186291i | ||||
\(779\) | −12.0000 | − | 20.7846i | −0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | − | 15.5885i | 0.322045 | − | 0.557799i | ||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | −27.0000 | − | 15.5885i | −0.964901 | − | 0.557086i | ||||
\(784\) | 9.00000 | 0.321429 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −18.0000 | + | 10.3923i | −0.642039 | + | 0.370681i | ||||
\(787\) | 2.00000 | + | 3.46410i | 0.0712923 | + | 0.123482i | 0.899468 | − | 0.436987i | \(-0.143954\pi\) |
−0.828176 | + | 0.560469i | \(0.810621\pi\) | |||||||
\(788\) | 9.00000 | + | 15.5885i | 0.320612 | + | 0.555316i | ||||
\(789\) | 41.5692i | 1.47990i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | −4.50000 | − | 7.79423i | −0.159901 | − | 0.276956i | ||||
\(793\) | −32.0000 | −1.13635 | ||||||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.00000 | − | 1.73205i | −0.0354441 | − | 0.0613909i | ||||
\(797\) | −6.00000 | − | 10.3923i | −0.212531 | − | 0.368114i | 0.739975 | − | 0.672634i | \(-0.234837\pi\) |
−0.952506 | + | 0.304520i | \(0.901504\pi\) | |||||||
\(798\) | 24.0000 | + | 13.8564i | 0.849591 | + | 0.490511i | ||||
\(799\) | 18.0000 | − | 31.1769i | 0.636794 | − | 1.10296i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.5000 | + | 23.3827i | −0.476999 | + | 0.826187i | ||||
\(802\) | 15.0000 | 0.529668 | ||||||||
\(803\) | −21.0000 | + | 36.3731i | −0.741074 | + | 1.28358i | ||||
\(804\) | − | 6.92820i | − | 0.244339i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16.0000 | − | 27.7128i | −0.563576 | − | 0.976142i | ||||
\(807\) | −18.0000 | + | 10.3923i | −0.633630 | + | 0.365826i | ||||
\(808\) | 6.00000 | − | 10.3923i | 0.211079 | − | 0.365600i | ||||
\(809\) | 45.0000 | 1.58212 | 0.791058 | − | 0.611741i | \(-0.209531\pi\) | ||||
0.791058 | + | 0.611741i | \(0.209531\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.00000 | 0.175574 | 0.0877869 | − | 0.996139i | \(-0.472021\pi\) | ||||
0.0877869 | + | 0.996139i | \(0.472021\pi\) | |||||||
\(812\) | −12.0000 | + | 20.7846i | −0.421117 | + | 0.729397i | ||||
\(813\) | −6.00000 | + | 3.46410i | −0.210429 | + | 0.121491i | ||||
\(814\) | 12.0000 | + | 20.7846i | 0.420600 | + | 0.728500i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 5.19615i | − | 0.181902i | ||||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 24.0000 | − | 41.5692i | 0.838628 | − | 1.45255i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −12.0000 | + | 20.7846i | −0.418803 | + | 0.725388i | −0.995819 | − | 0.0913446i | \(-0.970884\pi\) |
0.577016 | + | 0.816733i | \(0.304217\pi\) | |||||||
\(822\) | 27.0000 | + | 15.5885i | 0.941733 | + | 0.543710i | ||||
\(823\) | 20.0000 | + | 34.6410i | 0.697156 | + | 1.20751i | 0.969448 | + | 0.245295i | \(0.0788849\pi\) |
−0.272292 | + | 0.962215i | \(0.587782\pi\) | |||||||
\(824\) | 4.00000 | + | 6.92820i | 0.139347 | + | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0000 | − | 31.1769i | 0.626300 | − | 1.08478i | ||||
\(827\) | 15.0000 | 0.521601 | 0.260801 | − | 0.965393i | \(-0.416014\pi\) | ||||
0.260801 | + | 0.965393i | \(0.416014\pi\) | |||||||
\(828\) | −9.00000 | − | 15.5885i | −0.312772 | − | 0.541736i | ||||
\(829\) | 20.0000 | 0.694629 | 0.347314 | − | 0.937749i | \(-0.387094\pi\) | ||||
0.347314 | + | 0.937749i | \(0.387094\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.46410i | 0.120168i | ||||||||
\(832\) | 2.00000 | + | 3.46410i | 0.0693375 | + | 0.120096i | ||||
\(833\) | 13.5000 | + | 23.3827i | 0.467747 | + | 0.810162i | ||||
\(834\) | −16.5000 | + | 9.52628i | −0.571348 | + | 0.329868i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | −36.0000 | + | 20.7846i | −1.24434 | + | 0.718421i | ||||
\(838\) | −9.00000 | −0.310900 | ||||||||
\(839\) | −24.0000 | + | 41.5692i | −0.828572 | + | 1.43513i | 0.0705865 | + | 0.997506i | \(0.477513\pi\) |
−0.899158 | + | 0.437623i | \(0.855820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | 16.0000 | + | 27.7128i | 0.551396 | + | 0.955047i | ||||
\(843\) | − | 31.1769i | − | 1.07379i | ||||||
\(844\) | −11.5000 | + | 19.9186i | −0.395846 | + | 0.685626i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 36.0000 | 1.23771 | ||||||||
\(847\) | 8.00000 | 0.274883 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.50000 | + | 0.866025i | 0.0514799 | + | 0.0297219i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 24.0000 | + | 41.5692i | 0.822709 | + | 1.42497i | ||||
\(852\) | 9.00000 | + | 5.19615i | 0.308335 | + | 0.178017i | ||||
\(853\) | 23.0000 | − | 39.8372i | 0.787505 | − | 1.36400i | −0.139986 | − | 0.990153i | \(-0.544706\pi\) |
0.927491 | − | 0.373845i | \(-0.121961\pi\) | |||||||
\(854\) | 32.0000 | 1.09502 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 13.5000 | − | 23.3827i | 0.461151 | − | 0.798737i | −0.537867 | − | 0.843029i | \(-0.680770\pi\) |
0.999019 | + | 0.0442921i | \(0.0141032\pi\) | |||||||
\(858\) | 20.7846i | 0.709575i | ||||||||
\(859\) | 8.00000 | + | 13.8564i | 0.272956 | + | 0.472774i | 0.969618 | − | 0.244626i | \(-0.0786652\pi\) |
−0.696661 | + | 0.717400i | \(0.745332\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.0000 | − | 20.7846i | 1.22688 | − | 0.708338i | ||||
\(862\) | 3.00000 | − | 5.19615i | 0.102180 | − | 0.176982i | ||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 4.50000 | − | 2.59808i | 0.153093 | − | 0.0883883i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.50000 | + | 6.06218i | −0.118935 | + | 0.206001i | ||||
\(867\) | −12.0000 | + | 6.92820i | −0.407541 | + | 0.235294i | ||||
\(868\) | 16.0000 | + | 27.7128i | 0.543075 | + | 0.940634i | ||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.00000 | + | 13.8564i | −0.271070 | + | 0.469506i | ||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | −10.5000 | − | 18.1865i | −0.355371 | − | 0.615521i | ||||
\(874\) | −24.0000 | −0.811812 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −21.0000 | − | 12.1244i | −0.709524 | − | 0.409644i | ||||
\(877\) | 8.00000 | + | 13.8564i | 0.270141 | + | 0.467898i | 0.968898 | − | 0.247462i | \(-0.0795964\pi\) |
−0.698757 | + | 0.715359i | \(0.746263\pi\) | |||||||
\(878\) | 7.00000 | + | 12.1244i | 0.236239 | + | 0.409177i | ||||
\(879\) | 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 | \(0.331359\pi\) | |||||||
\(882\) | −13.5000 | + | 23.3827i | −0.454569 | + | 0.787336i | ||||
\(883\) | −13.0000 | −0.437485 | −0.218742 | − | 0.975783i | \(-0.570195\pi\) | ||||
−0.218742 | + | 0.975783i | \(0.570195\pi\) | |||||||
\(884\) | −6.00000 | + | 10.3923i | −0.201802 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.50000 | + | 7.79423i | 0.151180 | + | 0.261852i | ||||
\(887\) | −15.0000 | − | 25.9808i | −0.503651 | − | 0.872349i | −0.999991 | − | 0.00422062i | \(-0.998657\pi\) |
0.496340 | − | 0.868128i | \(-0.334677\pi\) | |||||||
\(888\) | −12.0000 | + | 6.92820i | −0.402694 | + | 0.232495i | ||||
\(889\) | −32.0000 | + | 55.4256i | −1.07325 | + | 1.85892i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.0000 | 0.904534 | ||||||||
\(892\) | 2.00000 | 0.0669650 | ||||||||
\(893\) | 24.0000 | − | 41.5692i | 0.803129 | − | 1.39106i | ||||
\(894\) | 9.00000 | − | 5.19615i | 0.301005 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | − | 3.46410i | −0.0668153 | − | 0.115728i | ||||
\(897\) | 41.5692i | 1.38796i | ||||||||
\(898\) | 9.00000 | − | 15.5885i | 0.300334 | − | 0.520194i | ||||
\(899\) | −48.0000 | −1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −9.00000 | + | 15.5885i | −0.299667 | + | 0.519039i | ||||
\(903\) | −6.00000 | − | 3.46410i | −0.199667 | − | 0.115278i | ||||
\(904\) | 1.50000 | + | 2.59808i | 0.0498893 | + | 0.0864107i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.0000 | − | 8.66025i | −0.498342 | − | 0.287718i | ||||
\(907\) | −8.50000 | + | 14.7224i | −0.282238 | + | 0.488850i | −0.971936 | − | 0.235247i | \(-0.924410\pi\) |
0.689698 | + | 0.724097i | \(0.257743\pi\) | |||||||
\(908\) | −27.0000 | −0.896026 | ||||||||
\(909\) | 18.0000 | + | 31.1769i | 0.597022 | + | 1.03407i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.00000 | − | 15.5885i | 0.298183 | − | 0.516469i | −0.677537 | − | 0.735489i | \(-0.736953\pi\) |
0.975720 | + | 0.219020i | \(0.0702860\pi\) | |||||||
\(912\) | − | 6.92820i | − | 0.229416i | ||||||
\(913\) | 13.5000 | + | 23.3827i | 0.446785 | + | 0.773854i | ||||
\(914\) | −5.00000 | − | 8.66025i | −0.165385 | − | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | + | 6.92820i | −0.132164 | + | 0.228914i | ||||
\(917\) | −48.0000 | −1.58510 | ||||||||
\(918\) | 13.5000 | + | 7.79423i | 0.445566 | + | 0.257248i | ||||
\(919\) | −46.0000 | −1.51740 | −0.758700 | − | 0.651440i | \(-0.774165\pi\) | ||||
−0.758700 | + | 0.651440i | \(0.774165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.50000 | + | 0.866025i | −0.0494267 | + | 0.0285365i | ||||
\(922\) | −3.00000 | − | 5.19615i | −0.0987997 | − | 0.171126i | ||||
\(923\) | −12.0000 | − | 20.7846i | −0.394985 | − | 0.684134i | ||||
\(924\) | − | 20.7846i | − | 0.683763i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −14.0000 | −0.460069 | ||||||||
\(927\) | −24.0000 | −0.788263 | ||||||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | −21.0000 | + | 36.3731i | −0.688988 | + | 1.19336i | 0.283178 | + | 0.959067i | \(0.408611\pi\) |
−0.972166 | + | 0.234294i | \(0.924722\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000 | + | 31.1769i | 0.589926 | + | 1.02178i | ||||
\(932\) | −7.50000 | − | 12.9904i | −0.245671 | − | 0.425514i | ||||
\(933\) | −9.00000 | − | 5.19615i | −0.294647 | − | 0.170114i | ||||
\(934\) | 4.50000 | − | 7.79423i | 0.147244 | − | 0.255035i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.0000 | −0.392232 | ||||||||
\(937\) | −37.0000 | −1.20874 | −0.604369 | − | 0.796705i | \(-0.706575\pi\) | ||||
−0.604369 | + | 0.796705i | \(0.706575\pi\) | |||||||
\(938\) | 8.00000 | − | 13.8564i | 0.261209 | − | 0.452428i | ||||
\(939\) | 29.4449i | 0.960897i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.0000 | − | 20.7846i | −0.391189 | − | 0.677559i | 0.601418 | − | 0.798935i | \(-0.294603\pi\) |
−0.992607 | + | 0.121376i | \(0.961269\pi\) | |||||||
\(942\) | 6.00000 | − | 3.46410i | 0.195491 | − | 0.112867i | ||||
\(943\) | −18.0000 | + | 31.1769i | −0.586161 | + | 1.01526i | ||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.00000 | 0.0975384 | ||||||||
\(947\) | 4.50000 | − | 7.79423i | 0.146230 | − | 0.253278i | −0.783601 | − | 0.621264i | \(-0.786619\pi\) |
0.929831 | + | 0.367986i | \(0.119953\pi\) | |||||||
\(948\) | 12.0000 | − | 6.92820i | 0.389742 | − | 0.225018i | ||||
\(949\) | 28.0000 | + | 48.4974i | 0.908918 | + | 1.57429i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 31.1769i | − | 1.01098i | ||||||
\(952\) | 6.00000 | − | 10.3923i | 0.194461 | − | 0.336817i | ||||
\(953\) | −27.0000 | −0.874616 | −0.437308 | − | 0.899312i | \(-0.644068\pi\) | ||||
−0.437308 | + | 0.899312i | \(0.644068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.00000 | + | 15.5885i | −0.291081 | + | 0.504167i | ||||
\(957\) | 27.0000 | + | 15.5885i | 0.872786 | + | 0.503903i | ||||
\(958\) | −6.00000 | − | 10.3923i | −0.193851 | − | 0.335760i | ||||
\(959\) | 36.0000 | + | 62.3538i | 1.16250 | + | 2.01351i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.5000 | + | 28.5788i | −0.532258 | + | 0.921898i | ||||
\(962\) | 32.0000 | 1.03172 | ||||||||
\(963\) | 18.0000 | − | 31.1769i | 0.580042 | − | 1.00466i | ||||
\(964\) | 26.0000 | 0.837404 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | − | 41.5692i | − | 1.33747i | ||||||
\(967\) | 14.0000 | + | 24.2487i | 0.450210 | + | 0.779786i | 0.998399 | − | 0.0565684i | \(-0.0180159\pi\) |
−0.548189 | + | 0.836354i | \(0.684683\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | 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 | \(0.642628\pi\) | |||||||
\(972\) | 15.5885i | 0.500000i | ||||||||
\(973\) | −44.0000 | −1.41058 | ||||||||
\(974\) | 1.00000 | − | 1.73205i | 0.0320421 | − | 0.0554985i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | − | 6.92820i | −0.128037 | − | 0.221766i | ||||
\(977\) | 27.0000 | + | 46.7654i | 0.863807 | + | 1.49616i | 0.868227 | + | 0.496167i | \(0.165259\pi\) |
−0.00442082 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(978\) | − | 19.0526i | − | 0.609234i | ||||||
\(979\) | 13.5000 | − | 23.3827i | 0.431462 | − | 0.747314i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | − | 5.19615i | 0.0957826 | − | 0.165900i | ||||
\(982\) | 15.0000 | 0.478669 | ||||||||
\(983\) | −27.0000 | + | 46.7654i | −0.861166 | + | 1.49158i | 0.00963785 | + | 0.999954i | \(0.496932\pi\) |
−0.870804 | + | 0.491630i | \(0.836401\pi\) | |||||||
\(984\) | −9.00000 | − | 5.19615i | −0.286910 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | + | 15.5885i | 0.286618 | + | 0.496438i | ||||
\(987\) | 72.0000 | + | 41.5692i | 2.29179 | + | 1.32316i | ||||
\(988\) | −8.00000 | + | 13.8564i | −0.254514 | + | 0.440831i | ||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.0000 | −0.508257 | −0.254128 | − | 0.967170i | \(-0.581789\pi\) | ||||
−0.254128 | + | 0.967170i | \(0.581789\pi\) | |||||||
\(992\) | 4.00000 | − | 6.92820i | 0.127000 | − | 0.219971i | ||||
\(993\) | 29.4449i | 0.934405i | ||||||||
\(994\) | 12.0000 | + | 20.7846i | 0.380617 | + | 0.659248i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −13.5000 | + | 7.79423i | −0.427764 | + | 0.246970i | ||||
\(997\) | 5.00000 | − | 8.66025i | 0.158352 | − | 0.274273i | −0.775923 | − | 0.630828i | \(-0.782715\pi\) |
0.934274 | + | 0.356555i | \(0.116049\pi\) | |||||||
\(998\) | −11.0000 | −0.348199 | ||||||||
\(999\) | − | 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.e.h.151.1 | yes | 2 | |
3.2 | odd | 2 | 1350.2.e.e.451.1 | 2 | |||
5.2 | odd | 4 | 450.2.j.d.349.2 | 4 | |||
5.3 | odd | 4 | 450.2.j.d.349.1 | 4 | |||
5.4 | even | 2 | 450.2.e.a.151.1 | ✓ | 2 | ||
9.2 | odd | 6 | 4050.2.a.t.1.1 | 1 | |||
9.4 | even | 3 | inner | 450.2.e.h.301.1 | yes | 2 | |
9.5 | odd | 6 | 1350.2.e.e.901.1 | 2 | |||
9.7 | even | 3 | 4050.2.a.b.1.1 | 1 | |||
15.2 | even | 4 | 1350.2.j.d.1099.1 | 4 | |||
15.8 | even | 4 | 1350.2.j.d.1099.2 | 4 | |||
15.14 | odd | 2 | 1350.2.e.f.451.1 | 2 | |||
45.2 | even | 12 | 4050.2.c.e.649.2 | 2 | |||
45.4 | even | 6 | 450.2.e.a.301.1 | yes | 2 | ||
45.7 | odd | 12 | 4050.2.c.q.649.1 | 2 | |||
45.13 | odd | 12 | 450.2.j.d.49.2 | 4 | |||
45.14 | odd | 6 | 1350.2.e.f.901.1 | 2 | |||
45.22 | odd | 12 | 450.2.j.d.49.1 | 4 | |||
45.23 | even | 12 | 1350.2.j.d.199.1 | 4 | |||
45.29 | odd | 6 | 4050.2.a.p.1.1 | 1 | |||
45.32 | even | 12 | 1350.2.j.d.199.2 | 4 | |||
45.34 | even | 6 | 4050.2.a.bj.1.1 | 1 | |||
45.38 | even | 12 | 4050.2.c.e.649.1 | 2 | |||
45.43 | odd | 12 | 4050.2.c.q.649.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.e.a.151.1 | ✓ | 2 | 5.4 | even | 2 | ||
450.2.e.a.301.1 | yes | 2 | 45.4 | even | 6 | ||
450.2.e.h.151.1 | yes | 2 | 1.1 | even | 1 | trivial | |
450.2.e.h.301.1 | yes | 2 | 9.4 | even | 3 | inner | |
450.2.j.d.49.1 | 4 | 45.22 | odd | 12 | |||
450.2.j.d.49.2 | 4 | 45.13 | odd | 12 | |||
450.2.j.d.349.1 | 4 | 5.3 | odd | 4 | |||
450.2.j.d.349.2 | 4 | 5.2 | odd | 4 | |||
1350.2.e.e.451.1 | 2 | 3.2 | odd | 2 | |||
1350.2.e.e.901.1 | 2 | 9.5 | odd | 6 | |||
1350.2.e.f.451.1 | 2 | 15.14 | odd | 2 | |||
1350.2.e.f.901.1 | 2 | 45.14 | odd | 6 | |||
1350.2.j.d.199.1 | 4 | 45.23 | even | 12 | |||
1350.2.j.d.199.2 | 4 | 45.32 | even | 12 | |||
1350.2.j.d.1099.1 | 4 | 15.2 | even | 4 | |||
1350.2.j.d.1099.2 | 4 | 15.8 | even | 4 | |||
4050.2.a.b.1.1 | 1 | 9.7 | even | 3 | |||
4050.2.a.p.1.1 | 1 | 45.29 | odd | 6 | |||
4050.2.a.t.1.1 | 1 | 9.2 | odd | 6 | |||
4050.2.a.bj.1.1 | 1 | 45.34 | even | 6 | |||
4050.2.c.e.649.1 | 2 | 45.38 | even | 12 | |||
4050.2.c.e.649.2 | 2 | 45.2 | even | 12 | |||
4050.2.c.q.649.1 | 2 | 45.7 | odd | 12 | |||
4050.2.c.q.649.2 | 2 | 45.43 | odd | 12 |