Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [34,2,Mod(13,34)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(34, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("34.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 34 = 2 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 34.c (of order \(4\), 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: | \(0.271491366872\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 13.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 34.13 |
Dual form | 34.2.c.b.21.1 |
$q$-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 \(\left(\mathbb{Z}/34\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | − | 1.00000i | −0.447214 | − | 0.447214i | 0.447214 | − | 0.894427i | \(-0.352416\pi\) |
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | − | 3.00000i | − | 1.00000i | ||||||
\(10\) | 1.00000 | − | 1.00000i | 0.316228 | − | 0.316228i | ||||
\(11\) | −4.00000 | + | 4.00000i | −1.20605 | + | 1.20605i | −0.233748 | + | 0.972297i | \(0.575099\pi\) |
−0.972297 | + | 0.233748i | \(0.924901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | + | 4.00000i | −0.242536 | + | 0.970143i | ||||
\(18\) | 3.00000 | 0.707107 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 1.00000 | + | 1.00000i | 0.223607 | + | 0.223607i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | − | 4.00000i | −0.852803 | − | 0.852803i | ||||
\(23\) | 4.00000 | − | 4.00000i | 0.834058 | − | 0.834058i | −0.154011 | − | 0.988069i | \(-0.549219\pi\) |
0.988069 | + | 0.154011i | \(0.0492193\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | 4.00000i | 0.784465i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 3.00000i | −0.557086 | − | 0.557086i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | − | 4.00000i | −0.718421 | − | 0.718421i | 0.249861 | − | 0.968282i | \(-0.419615\pi\) |
−0.968282 | + | 0.249861i | \(0.919615\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.00000 | − | 1.00000i | −0.685994 | − | 0.171499i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.00000i | 0.500000i | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | −4.00000 | −0.648886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | + | 1.00000i | −0.158114 | + | 0.158114i | ||||
\(41\) | 1.00000 | − | 1.00000i | 0.156174 | − | 0.156174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) |
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | 4.00000 | − | 4.00000i | 0.603023 | − | 0.603023i | ||||
\(45\) | −3.00000 | + | 3.00000i | −0.447214 | + | 0.447214i | ||||
\(46\) | 4.00000 | + | 4.00000i | 0.589768 | + | 0.589768i | ||||
\(47\) | 8.00000 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 3.00000 | 0.424264 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.00000 | −0.554700 | ||||||||
\(53\) | − | 4.00000i | − | 0.549442i | −0.961524 | − | 0.274721i | \(-0.911414\pi\) | ||
0.961524 | − | 0.274721i | \(-0.0885855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000 | 1.07872 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.00000 | − | 3.00000i | 0.393919 | − | 0.393919i | ||||
\(59\) | 4.00000i | 0.520756i | 0.965507 | + | 0.260378i | \(0.0838471\pi\) | ||||
−0.965507 | + | 0.260378i | \(0.916153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | + | 9.00000i | −1.15233 | + | 1.15233i | −0.166248 | + | 0.986084i | \(0.553165\pi\) |
−0.986084 | + | 0.166248i | \(0.946835\pi\) | |||||||
\(62\) | 4.00000 | − | 4.00000i | 0.508001 | − | 0.508001i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | − | 4.00000i | −0.496139 | − | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | 1.00000 | − | 4.00000i | 0.121268 | − | 0.485071i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | − | 4.00000i | −0.474713 | − | 0.474713i | 0.428723 | − | 0.903436i | \(-0.358964\pi\) |
−0.903436 | + | 0.428723i | \(0.858964\pi\) | |||||||
\(72\) | −3.00000 | −0.353553 | ||||||||
\(73\) | 5.00000 | + | 5.00000i | 0.585206 | + | 0.585206i | 0.936329 | − | 0.351123i | \(-0.114200\pi\) |
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −3.00000 | + | 3.00000i | −0.348743 | + | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.00000i | − | 0.458831i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.00000 | − | 8.00000i | 0.900070 | − | 0.900070i | −0.0953714 | − | 0.995442i | \(-0.530404\pi\) |
0.995442 | + | 0.0953714i | \(0.0304039\pi\) | |||||||
\(80\) | −1.00000 | − | 1.00000i | −0.111803 | − | 0.111803i | ||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 1.00000 | + | 1.00000i | 0.110432 | + | 0.110432i | ||||
\(83\) | − | 4.00000i | − | 0.439057i | −0.975606 | − | 0.219529i | \(-0.929548\pi\) | ||
0.975606 | − | 0.219529i | \(-0.0704519\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00000 | − | 3.00000i | 0.542326 | − | 0.325396i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | + | 4.00000i | 0.426401 | + | 0.426401i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | −3.00000 | − | 3.00000i | −0.316228 | − | 0.316228i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.00000 | + | 4.00000i | −0.417029 | + | 0.417029i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000i | 0.825137i | ||||||||
\(95\) | 4.00000 | − | 4.00000i | 0.410391 | − | 0.410391i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.00000 | + | 3.00000i | 0.304604 | + | 0.304604i | 0.842812 | − | 0.538208i | \(-0.180899\pi\) |
−0.538208 | + | 0.842812i | \(0.680899\pi\) | |||||||
\(98\) | −7.00000 | −0.707107 | ||||||||
\(99\) | 12.0000 | + | 12.0000i | 1.20605 | + | 1.20605i | ||||
\(100\) | 3.00000i | 0.300000i | ||||||||
\(101\) | 12.0000 | 1.19404 | 0.597022 | − | 0.802225i | \(-0.296350\pi\) | ||||
0.597022 | + | 0.802225i | \(0.296350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0000 | −1.57653 | −0.788263 | − | 0.615338i | \(-0.789020\pi\) | ||||
−0.788263 | + | 0.615338i | \(0.789020\pi\) | |||||||
\(104\) | − | 4.00000i | − | 0.392232i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00000 | 0.388514 | ||||||||
\(107\) | 8.00000 | + | 8.00000i | 0.773389 | + | 0.773389i | 0.978697 | − | 0.205308i | \(-0.0658197\pi\) |
−0.205308 | + | 0.978697i | \(0.565820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00000 | − | 3.00000i | 0.287348 | − | 0.287348i | −0.548683 | − | 0.836031i | \(-0.684871\pi\) |
0.836031 | + | 0.548683i | \(0.184871\pi\) | |||||||
\(110\) | 8.00000i | 0.762770i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.00000 | + | 1.00000i | −0.0940721 | + | 0.0940721i | −0.752577 | − | 0.658505i | \(-0.771189\pi\) |
0.658505 | + | 0.752577i | \(0.271189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | −0.746004 | ||||||||
\(116\) | 3.00000 | + | 3.00000i | 0.278543 | + | 0.278543i | ||||
\(117\) | − | 12.0000i | − | 1.10940i | ||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 21.0000i | − | 1.90909i | ||||||
\(122\) | −9.00000 | − | 9.00000i | −0.814822 | − | 0.814822i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.00000 | + | 4.00000i | 0.359211 | + | 0.359211i | ||||
\(125\) | −8.00000 | + | 8.00000i | −0.715542 | + | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.00000 | − | 4.00000i | 0.350823 | − | 0.350823i | ||||
\(131\) | −4.00000 | − | 4.00000i | −0.349482 | − | 0.349482i | 0.510435 | − | 0.859916i | \(-0.329484\pi\) |
−0.859916 | + | 0.510435i | \(0.829484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 12.0000i | − | 1.03664i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | + | 1.00000i | 0.342997 | + | 0.0857493i | ||||
\(137\) | 8.00000 | 0.683486 | 0.341743 | − | 0.939793i | \(-0.388983\pi\) | ||||
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | − | 8.00000i | −0.678551 | − | 0.678551i | 0.281121 | − | 0.959672i | \(-0.409294\pi\) |
−0.959672 | + | 0.281121i | \(0.909294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.00000 | − | 4.00000i | 0.335673 | − | 0.335673i | ||||
\(143\) | −16.0000 | + | 16.0000i | −1.33799 | + | 1.33799i | ||||
\(144\) | − | 3.00000i | − | 0.250000i | ||||||
\(145\) | 6.00000i | 0.498273i | ||||||||
\(146\) | −5.00000 | + | 5.00000i | −0.413803 | + | 0.413803i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.00000 | − | 3.00000i | −0.246598 | − | 0.246598i | ||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 12.0000 | + | 3.00000i | 0.970143 | + | 0.242536i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000i | 0.642575i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 8.00000 | + | 8.00000i | 0.636446 | + | 0.636446i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | − | 1.00000i | 0.0790569 | − | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 9.00000i | − | 0.707107i | ||||||
\(163\) | 4.00000 | − | 4.00000i | 0.313304 | − | 0.313304i | −0.532884 | − | 0.846188i | \(-0.678892\pi\) |
0.846188 | + | 0.532884i | \(0.178892\pi\) | |||||||
\(164\) | −1.00000 | + | 1.00000i | −0.0780869 | + | 0.0780869i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 8.00000 | + | 8.00000i | 0.619059 | + | 0.619059i | 0.945290 | − | 0.326231i | \(-0.105779\pi\) |
−0.326231 | + | 0.945290i | \(0.605779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 3.00000 | + | 5.00000i | 0.230089 | + | 0.383482i | ||||
\(171\) | 12.0000 | 0.917663 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | 5.00000 | + | 5.00000i | 0.380143 | + | 0.380143i | 0.871154 | − | 0.491011i | \(-0.163372\pi\) |
−0.491011 | + | 0.871154i | \(0.663372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | + | 4.00000i | −0.301511 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000i | 0.298974i | 0.988764 | + | 0.149487i | \(0.0477622\pi\) | ||||
−0.988764 | + | 0.149487i | \(0.952238\pi\) | |||||||
\(180\) | 3.00000 | − | 3.00000i | 0.223607 | − | 0.223607i | ||||
\(181\) | 11.0000 | − | 11.0000i | 0.817624 | − | 0.817624i | −0.168140 | − | 0.985763i | \(-0.553776\pi\) |
0.985763 | + | 0.168140i | \(0.0537759\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | − | 4.00000i | −0.294884 | − | 0.294884i | ||||
\(185\) | − | 6.00000i | − | 0.441129i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.0000 | − | 20.0000i | −0.877527 | − | 1.46254i | ||||
\(188\) | −8.00000 | −0.583460 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | + | 4.00000i | 0.290191 | + | 0.290191i | ||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.0000 | + | 11.0000i | −0.791797 | + | 0.791797i | −0.981786 | − | 0.189989i | \(-0.939155\pi\) |
0.189989 | + | 0.981786i | \(0.439155\pi\) | |||||||
\(194\) | −3.00000 | + | 3.00000i | −0.215387 | + | 0.215387i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 7.00000i | − | 0.500000i | ||||||
\(197\) | 5.00000 | − | 5.00000i | 0.356235 | − | 0.356235i | −0.506188 | − | 0.862423i | \(-0.668946\pi\) |
0.862423 | + | 0.506188i | \(0.168946\pi\) | |||||||
\(198\) | −12.0000 | + | 12.0000i | −0.852803 | + | 0.852803i | ||||
\(199\) | 12.0000 | + | 12.0000i | 0.850657 | + | 0.850657i | 0.990214 | − | 0.139557i | \(-0.0445677\pi\) |
−0.139557 | + | 0.990214i | \(0.544568\pi\) | |||||||
\(200\) | −3.00000 | −0.212132 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.0000i | 0.844317i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | − | 16.0000i | − | 1.11477i | ||||||
\(207\) | −12.0000 | − | 12.0000i | −0.834058 | − | 0.834058i | ||||
\(208\) | 4.00000 | 0.277350 | ||||||||
\(209\) | −16.0000 | − | 16.0000i | −1.10674 | − | 1.10674i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | − | 16.0000i | 1.10149 | − | 1.10149i | 0.107254 | − | 0.994232i | \(-0.465794\pi\) |
0.994232 | − | 0.107254i | \(-0.0342057\pi\) | |||||||
\(212\) | 4.00000i | 0.274721i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | + | 8.00000i | −0.546869 | + | 0.546869i | ||||
\(215\) | −4.00000 | + | 4.00000i | −0.272798 | + | 0.272798i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.00000 | + | 3.00000i | 0.203186 | + | 0.203186i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.00000 | −0.539360 | ||||||||
\(221\) | −4.00000 | + | 16.0000i | −0.269069 | + | 1.07628i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000i | 1.07144i | 0.844396 | + | 0.535720i | \(0.179960\pi\) | ||||
−0.844396 | + | 0.535720i | \(0.820040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −9.00000 | −0.600000 | ||||||||
\(226\) | −1.00000 | − | 1.00000i | −0.0665190 | − | 0.0665190i | ||||
\(227\) | 20.0000 | − | 20.0000i | 1.32745 | − | 1.32745i | 0.419856 | − | 0.907591i | \(-0.362081\pi\) |
0.907591 | − | 0.419856i | \(-0.137919\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | − | 8.00000i | − | 0.527504i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | + | 3.00000i | −0.196960 | + | 0.196960i | ||||
\(233\) | −5.00000 | − | 5.00000i | −0.327561 | − | 0.327561i | 0.524097 | − | 0.851658i | \(-0.324403\pi\) |
−0.851658 | + | 0.524097i | \(0.824403\pi\) | |||||||
\(234\) | 12.0000 | 0.784465 | ||||||||
\(235\) | −8.00000 | − | 8.00000i | −0.521862 | − | 0.521862i | ||||
\(236\) | − | 4.00000i | − | 0.260378i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.0000 | + | 21.0000i | 1.35273 | + | 1.35273i | 0.882595 | + | 0.470134i | \(0.155794\pi\) |
0.470134 | + | 0.882595i | \(0.344206\pi\) | |||||||
\(242\) | 21.0000 | 1.34993 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.00000 | − | 9.00000i | 0.576166 | − | 0.576166i | ||||
\(245\) | 7.00000 | − | 7.00000i | 0.447214 | − | 0.447214i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000i | 1.01806i | ||||||||
\(248\) | −4.00000 | + | 4.00000i | −0.254000 | + | 0.254000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.00000 | − | 8.00000i | −0.505964 | − | 0.505964i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.0000i | 2.01182i | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0000i | 1.12281i | 0.827541 | + | 0.561405i | \(0.189739\pi\) | ||||
−0.827541 | + | 0.561405i | \(0.810261\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | + | 4.00000i | 0.248069 | + | 0.248069i | ||||
\(261\) | −9.00000 | + | 9.00000i | −0.557086 | + | 0.557086i | ||||
\(262\) | 4.00000 | − | 4.00000i | 0.247121 | − | 0.247121i | ||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | + | 4.00000i | −0.245718 | + | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.0000 | 0.733017 | ||||||||
\(269\) | −13.0000 | − | 13.0000i | −0.792624 | − | 0.792624i | 0.189296 | − | 0.981920i | \(-0.439379\pi\) |
−0.981920 | + | 0.189296i | \(0.939379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −1.00000 | + | 4.00000i | −0.0606339 | + | 0.242536i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000i | 0.483298i | ||||||||
\(275\) | 12.0000 | + | 12.0000i | 0.723627 | + | 0.723627i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.00000 | − | 7.00000i | −0.420589 | − | 0.420589i | 0.464817 | − | 0.885407i | \(-0.346120\pi\) |
−0.885407 | + | 0.464817i | \(0.846120\pi\) | |||||||
\(278\) | 8.00000 | − | 8.00000i | 0.479808 | − | 0.479808i | ||||
\(279\) | −12.0000 | + | 12.0000i | −0.718421 | + | 0.718421i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.00000 | − | 4.00000i | 0.237775 | − | 0.237775i | −0.578153 | − | 0.815928i | \(-0.696226\pi\) |
0.815928 | + | 0.578153i | \(0.196226\pi\) | |||||||
\(284\) | 4.00000 | + | 4.00000i | 0.237356 | + | 0.237356i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −16.0000 | − | 16.0000i | −0.946100 | − | 0.946100i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.00000 | 0.176777 | ||||||||
\(289\) | −15.0000 | − | 8.00000i | −0.882353 | − | 0.470588i | ||||
\(290\) | −6.00000 | −0.352332 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.00000 | − | 5.00000i | −0.292603 | − | 0.292603i | ||||
\(293\) | −6.00000 | −0.350524 | −0.175262 | − | 0.984522i | \(-0.556077\pi\) | ||||
−0.175262 | + | 0.984522i | \(0.556077\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.00000 | − | 4.00000i | 0.232889 | − | 0.232889i | ||||
\(296\) | 3.00000 | − | 3.00000i | 0.174371 | − | 0.174371i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 10.0000i | − | 0.579284i | ||||||
\(299\) | 16.0000 | − | 16.0000i | 0.925304 | − | 0.925304i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000i | 0.229416i | ||||||||
\(305\) | 18.0000 | 1.03068 | ||||||||
\(306\) | −3.00000 | + | 12.0000i | −0.171499 | + | 0.685994i | ||||
\(307\) | −12.0000 | −0.684876 | −0.342438 | − | 0.939540i | \(-0.611253\pi\) | ||||
−0.342438 | + | 0.939540i | \(0.611253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.00000 | −0.454369 | ||||||||
\(311\) | −24.0000 | − | 24.0000i | −1.36092 | − | 1.36092i | −0.872753 | − | 0.488162i | \(-0.837667\pi\) |
−0.488162 | − | 0.872753i | \(-0.662333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.00000 | − | 9.00000i | 0.508710 | − | 0.508710i | −0.405420 | − | 0.914130i | \(-0.632875\pi\) |
0.914130 | + | 0.405420i | \(0.132875\pi\) | |||||||
\(314\) | − | 2.00000i | − | 0.112867i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | + | 8.00000i | −0.450035 | + | 0.450035i | ||||
\(317\) | −15.0000 | + | 15.0000i | −0.842484 | + | 0.842484i | −0.989181 | − | 0.146697i | \(-0.953136\pi\) |
0.146697 | + | 0.989181i | \(0.453136\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 1.00000 | + | 1.00000i | 0.0559017 | + | 0.0559017i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −16.0000 | − | 4.00000i | −0.890264 | − | 0.222566i | ||||
\(324\) | 9.00000 | 0.500000 | ||||||||
\(325\) | − | 12.0000i | − | 0.665640i | ||||||
\(326\) | 4.00000 | + | 4.00000i | 0.221540 | + | 0.221540i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.00000 | − | 1.00000i | −0.0552158 | − | 0.0552158i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000i | 1.09930i | 0.835395 | + | 0.549650i | \(0.185239\pi\) | ||||
−0.835395 | + | 0.549650i | \(0.814761\pi\) | |||||||
\(332\) | 4.00000i | 0.219529i | ||||||||
\(333\) | 9.00000 | − | 9.00000i | 0.493197 | − | 0.493197i | ||||
\(334\) | −8.00000 | + | 8.00000i | −0.437741 | + | 0.437741i | ||||
\(335\) | 12.0000 | + | 12.0000i | 0.655630 | + | 0.655630i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.00000 | − | 7.00000i | −0.381314 | − | 0.381314i | 0.490261 | − | 0.871576i | \(-0.336901\pi\) |
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | 3.00000i | 0.163178i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.00000 | + | 3.00000i | −0.271163 | + | 0.162698i | ||||
\(341\) | 32.0000 | 1.73290 | ||||||||
\(342\) | 12.0000i | 0.648886i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.00000 | + | 5.00000i | −0.268802 | + | 0.268802i | ||||
\(347\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | − | 4.00000i | −0.213201 | − | 0.213201i | ||||
\(353\) | 14.0000 | 0.745145 | 0.372572 | − | 0.928003i | \(-0.378476\pi\) | ||||
0.372572 | + | 0.928003i | \(0.378476\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000i | 0.424596i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.00000 | −0.211407 | ||||||||
\(359\) | 24.0000i | 1.26667i | 0.773877 | + | 0.633336i | \(0.218315\pi\) | ||||
−0.773877 | + | 0.633336i | \(0.781685\pi\) | |||||||
\(360\) | 3.00000 | + | 3.00000i | 0.158114 | + | 0.158114i | ||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 11.0000 | + | 11.0000i | 0.578147 | + | 0.578147i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.0000i | − | 0.523424i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(368\) | 4.00000 | − | 4.00000i | 0.208514 | − | 0.208514i | ||||
\(369\) | −3.00000 | − | 3.00000i | −0.156174 | − | 0.156174i | ||||
\(370\) | 6.00000 | 0.311925 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.00000 | 0.207112 | 0.103556 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103556 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(374\) | 20.0000 | − | 12.0000i | 1.03418 | − | 0.620505i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.00000i | − | 0.412568i | ||||||
\(377\) | −12.0000 | − | 12.0000i | −0.618031 | − | 0.618031i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | + | 12.0000i | 0.616399 | + | 0.616399i | 0.944606 | − | 0.328207i | \(-0.106444\pi\) |
−0.328207 | + | 0.944606i | \(0.606444\pi\) | |||||||
\(380\) | −4.00000 | + | 4.00000i | −0.205196 | + | 0.205196i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 8.00000i | − | 0.409316i | ||||||
\(383\) | − | 24.0000i | − | 1.22634i | −0.789950 | − | 0.613171i | \(-0.789894\pi\) | ||
0.789950 | − | 0.613171i | \(-0.210106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −11.0000 | − | 11.0000i | −0.559885 | − | 0.559885i | ||||
\(387\) | −12.0000 | −0.609994 | ||||||||
\(388\) | −3.00000 | − | 3.00000i | −0.152302 | − | 0.152302i | ||||
\(389\) | − | 6.00000i | − | 0.304212i | −0.988364 | − | 0.152106i | \(-0.951394\pi\) | ||
0.988364 | − | 0.152106i | \(-0.0486055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | + | 20.0000i | 0.606866 | + | 1.01144i | ||||
\(392\) | 7.00000 | 0.353553 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.00000 | + | 5.00000i | 0.251896 | + | 0.251896i | ||||
\(395\) | −16.0000 | −0.805047 | ||||||||
\(396\) | −12.0000 | − | 12.0000i | −0.603023 | − | 0.603023i | ||||
\(397\) | 15.0000 | − | 15.0000i | 0.752828 | − | 0.752828i | −0.222178 | − | 0.975006i | \(-0.571317\pi\) |
0.975006 | + | 0.222178i | \(0.0713165\pi\) | |||||||
\(398\) | −12.0000 | + | 12.0000i | −0.601506 | + | 0.601506i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 3.00000i | − | 0.150000i | ||||||
\(401\) | −19.0000 | + | 19.0000i | −0.948815 | + | 0.948815i | −0.998752 | − | 0.0499376i | \(-0.984098\pi\) |
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.0000 | − | 16.0000i | −0.797017 | − | 0.797017i | ||||
\(404\) | −12.0000 | −0.597022 | ||||||||
\(405\) | 9.00000 | + | 9.00000i | 0.447214 | + | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0000 | −1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | − | 2.00000i | − | 0.0987730i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 12.0000 | − | 12.0000i | 0.589768 | − | 0.589768i | ||||
\(415\) | −4.00000 | + | 4.00000i | −0.196352 | + | 0.196352i | ||||
\(416\) | 4.00000i | 0.196116i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.0000 | − | 16.0000i | 0.782586 | − | 0.782586i | ||||
\(419\) | −12.0000 | + | 12.0000i | −0.586238 | + | 0.586238i | −0.936611 | − | 0.350372i | \(-0.886055\pi\) |
0.350372 | + | 0.936611i | \(0.386055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.0000 | −1.36464 | −0.682318 | − | 0.731055i | \(-0.739028\pi\) | ||||
−0.682318 | + | 0.731055i | \(0.739028\pi\) | |||||||
\(422\) | 16.0000 | + | 16.0000i | 0.778868 | + | 0.778868i | ||||
\(423\) | − | 24.0000i | − | 1.16692i | ||||||
\(424\) | −4.00000 | −0.194257 | ||||||||
\(425\) | 12.0000 | + | 3.00000i | 0.582086 | + | 0.145521i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −8.00000 | − | 8.00000i | −0.386695 | − | 0.386695i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.00000 | − | 4.00000i | −0.192897 | − | 0.192897i | ||||
\(431\) | −24.0000 | + | 24.0000i | −1.15604 | + | 1.15604i | −0.170720 | + | 0.985320i | \(0.554609\pi\) |
−0.985320 | + | 0.170720i | \(0.945391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.00000 | + | 3.00000i | −0.143674 | + | 0.143674i | ||||
\(437\) | 16.0000 | + | 16.0000i | 0.765384 | + | 0.765384i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 12.0000 | + | 12.0000i | 0.572729 | + | 0.572729i | 0.932890 | − | 0.360161i | \(-0.117278\pi\) |
−0.360161 | + | 0.932890i | \(0.617278\pi\) | |||||||
\(440\) | − | 8.00000i | − | 0.381385i | ||||||
\(441\) | 21.0000 | 1.00000 | ||||||||
\(442\) | −16.0000 | − | 4.00000i | −0.761042 | − | 0.190261i | ||||
\(443\) | 4.00000 | 0.190046 | 0.0950229 | − | 0.995475i | \(-0.469708\pi\) | ||||
0.0950229 | + | 0.995475i | \(0.469708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −16.0000 | −0.757622 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.00000 | − | 3.00000i | 0.141579 | − | 0.141579i | −0.632765 | − | 0.774344i | \(-0.718080\pi\) |
0.774344 | + | 0.632765i | \(0.218080\pi\) | |||||||
\(450\) | − | 9.00000i | − | 0.424264i | ||||||
\(451\) | 8.00000i | 0.376705i | ||||||||
\(452\) | 1.00000 | − | 1.00000i | 0.0470360 | − | 0.0470360i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.0000 | + | 20.0000i | 0.938647 | + | 0.938647i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.0000i | − | 1.02912i | −0.857455 | − | 0.514558i | \(-0.827956\pi\) | ||
0.857455 | − | 0.514558i | \(-0.172044\pi\) | |||||||
\(458\) | 6.00000 | 0.280362 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.00000 | 0.373002 | ||||||||
\(461\) | − | 20.0000i | − | 0.931493i | −0.884918 | − | 0.465746i | \(-0.845786\pi\) | ||
0.884918 | − | 0.465746i | \(-0.154214\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.0000 | 1.11537 | 0.557687 | − | 0.830051i | \(-0.311689\pi\) | ||||
0.557687 | + | 0.830051i | \(0.311689\pi\) | |||||||
\(464\) | −3.00000 | − | 3.00000i | −0.139272 | − | 0.139272i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.00000 | − | 5.00000i | 0.231621 | − | 0.231621i | ||||
\(467\) | 28.0000i | 1.29569i | 0.761774 | + | 0.647843i | \(0.224329\pi\) | ||||
−0.761774 | + | 0.647843i | \(0.775671\pi\) | |||||||
\(468\) | 12.0000i | 0.554700i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 8.00000 | − | 8.00000i | 0.369012 | − | 0.369012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.00000 | 0.184115 | ||||||||
\(473\) | 16.0000 | + | 16.0000i | 0.735681 | + | 0.735681i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.0000 | 0.550598 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.0000 | −0.549442 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.00000 | − | 8.00000i | −0.365529 | − | 0.365529i | 0.500314 | − | 0.865844i | \(-0.333218\pi\) |
−0.865844 | + | 0.500314i | \(0.833218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.0000 | + | 12.0000i | 0.547153 | + | 0.547153i | ||||
\(482\) | −21.0000 | + | 21.0000i | −0.956524 | + | 0.956524i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.0000i | 0.954545i | ||||||||
\(485\) | − | 6.00000i | − | 0.272446i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | − | 20.0000i | 0.906287 | − | 0.906287i | −0.0896838 | − | 0.995970i | \(-0.528586\pi\) |
0.995970 | + | 0.0896838i | \(0.0285856\pi\) | |||||||
\(488\) | 9.00000 | + | 9.00000i | 0.407411 | + | 0.407411i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 7.00000 | + | 7.00000i | 0.316228 | + | 0.316228i | ||||
\(491\) | 20.0000i | 0.902587i | 0.892375 | + | 0.451294i | \(0.149037\pi\) | ||||
−0.892375 | + | 0.451294i | \(0.850963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0000 | − | 9.00000i | 0.675566 | − | 0.405340i | ||||
\(494\) | −16.0000 | −0.719874 | ||||||||
\(495\) | − | 24.0000i | − | 1.07872i | ||||||
\(496\) | −4.00000 | − | 4.00000i | −0.179605 | − | 0.179605i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.00000 | − | 8.00000i | 0.358129 | − | 0.358129i | −0.504994 | − | 0.863123i | \(-0.668505\pi\) |
0.863123 | + | 0.504994i | \(0.168505\pi\) | |||||||
\(500\) | 8.00000 | − | 8.00000i | 0.357771 | − | 0.357771i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | 4.00000 | − | 4.00000i | 0.178351 | − | 0.178351i | −0.612286 | − | 0.790637i | \(-0.709750\pi\) |
0.790637 | + | 0.612286i | \(0.209750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0000 | − | 12.0000i | −0.533993 | − | 0.533993i | ||||
\(506\) | −32.0000 | −1.42257 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | −30.0000 | −1.32973 | −0.664863 | − | 0.746965i | \(-0.731510\pi\) | ||||
−0.664863 | + | 0.746965i | \(0.731510\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −18.0000 | −0.793946 | ||||||||
\(515\) | 16.0000 | + | 16.0000i | 0.705044 | + | 0.705044i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −32.0000 | + | 32.0000i | −1.40736 | + | 1.40736i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.00000 | + | 4.00000i | −0.175412 | + | 0.175412i | ||||
\(521\) | 1.00000 | − | 1.00000i | 0.0438108 | − | 0.0438108i | −0.684862 | − | 0.728673i | \(-0.740138\pi\) |
0.728673 | + | 0.684862i | \(0.240138\pi\) | |||||||
\(522\) | −9.00000 | − | 9.00000i | −0.393919 | − | 0.393919i | ||||
\(523\) | −36.0000 | −1.57417 | −0.787085 | − | 0.616844i | \(-0.788411\pi\) | ||||
−0.787085 | + | 0.616844i | \(0.788411\pi\) | |||||||
\(524\) | 4.00000 | + | 4.00000i | 0.174741 | + | 0.174741i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 20.0000 | − | 12.0000i | 0.871214 | − | 0.522728i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 9.00000i | − | 0.391304i | ||||||
\(530\) | −4.00000 | − | 4.00000i | −0.173749 | − | 0.173749i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.00000 | − | 4.00000i | 0.173259 | − | 0.173259i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 16.0000i | − | 0.691740i | ||||||
\(536\) | 12.0000i | 0.518321i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.0000 | − | 13.0000i | 0.560470 | − | 0.560470i | ||||
\(539\) | −28.0000 | − | 28.0000i | −1.20605 | − | 1.20605i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | − | 9.00000i | −0.386940 | − | 0.386940i | 0.486654 | − | 0.873595i | \(-0.338217\pi\) |
−0.873595 | + | 0.486654i | \(0.838217\pi\) | |||||||
\(542\) | − | 8.00000i | − | 0.343629i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | − | 1.00000i | −0.171499 | − | 0.0428746i | ||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | − | 12.0000i | −0.513083 | − | 0.513083i | 0.402387 | − | 0.915470i | \(-0.368181\pi\) |
−0.915470 | + | 0.402387i | \(0.868181\pi\) | |||||||
\(548\) | −8.00000 | −0.341743 | ||||||||
\(549\) | 27.0000 | + | 27.0000i | 1.15233 | + | 1.15233i | ||||
\(550\) | −12.0000 | + | 12.0000i | −0.511682 | + | 0.511682i | ||||
\(551\) | 12.0000 | − | 12.0000i | 0.511217 | − | 0.511217i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.00000 | − | 7.00000i | 0.297402 | − | 0.297402i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.00000 | + | 8.00000i | 0.339276 | + | 0.339276i | ||||
\(557\) | 28.0000 | 1.18640 | 0.593199 | − | 0.805056i | \(-0.297865\pi\) | ||||
0.593199 | + | 0.805056i | \(0.297865\pi\) | |||||||
\(558\) | −12.0000 | − | 12.0000i | −0.508001 | − | 0.508001i | ||||
\(559\) | − | 16.0000i | − | 0.676728i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 4.00000i | − | 0.168580i | −0.996441 | − | 0.0842900i | \(-0.973138\pi\) | ||
0.996441 | − | 0.0842900i | \(-0.0268622\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.00000 | 0.0841406 | ||||||||
\(566\) | 4.00000 | + | 4.00000i | 0.168133 | + | 0.168133i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | + | 4.00000i | −0.167836 | + | 0.167836i | ||||
\(569\) | 24.0000i | 1.00613i | 0.864248 | + | 0.503066i | \(0.167795\pi\) | ||||
−0.864248 | + | 0.503066i | \(0.832205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.0000 | + | 24.0000i | −1.00437 | + | 1.00437i | −0.00437833 | + | 0.999990i | \(0.501394\pi\) |
−0.999990 | + | 0.00437833i | \(0.998606\pi\) | |||||||
\(572\) | 16.0000 | − | 16.0000i | 0.668994 | − | 0.668994i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | − | 12.0000i | −0.500435 | − | 0.500435i | ||||
\(576\) | 3.00000i | 0.125000i | ||||||||
\(577\) | −32.0000 | −1.33218 | −0.666089 | − | 0.745873i | \(-0.732033\pi\) | ||||
−0.666089 | + | 0.745873i | \(0.732033\pi\) | |||||||
\(578\) | 8.00000 | − | 15.0000i | 0.332756 | − | 0.623918i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 6.00000i | − | 0.249136i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.0000 | + | 16.0000i | 0.662652 | + | 0.662652i | ||||
\(584\) | 5.00000 | − | 5.00000i | 0.206901 | − | 0.206901i | ||||
\(585\) | −12.0000 | + | 12.0000i | −0.496139 | + | 0.496139i | ||||
\(586\) | − | 6.00000i | − | 0.247858i | ||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | − | 16.0000i | 0.659269 | − | 0.659269i | ||||
\(590\) | 4.00000 | + | 4.00000i | 0.164677 | + | 0.164677i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.00000 | + | 3.00000i | 0.123299 | + | 0.123299i | ||||
\(593\) | 16.0000i | 0.657041i | 0.944497 | + | 0.328521i | \(0.106550\pi\) | ||||
−0.944497 | + | 0.328521i | \(0.893450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 16.0000 | + | 16.0000i | 0.654289 | + | 0.654289i | ||||
\(599\) | 40.0000 | 1.63436 | 0.817178 | − | 0.576386i | \(-0.195537\pi\) | ||||
0.817178 | + | 0.576386i | \(0.195537\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.0000 | + | 19.0000i | −0.775026 | + | 0.775026i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) |
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 36.0000i | 1.46603i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.0000 | + | 21.0000i | −0.853771 | + | 0.853771i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0000 | + | 28.0000i | 1.13648 | + | 1.13648i | 0.989076 | + | 0.147409i | \(0.0470935\pi\) |
0.147409 | + | 0.989076i | \(0.452907\pi\) | |||||||
\(608\) | −4.00000 | −0.162221 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0000i | 0.728799i | ||||||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | −12.0000 | − | 3.00000i | −0.485071 | − | 0.121268i | ||||
\(613\) | −26.0000 | −1.05013 | −0.525065 | − | 0.851062i | \(-0.675959\pi\) | ||||
−0.525065 | + | 0.851062i | \(0.675959\pi\) | |||||||
\(614\) | − | 12.0000i | − | 0.484281i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.00000 | + | 3.00000i | 0.120775 | + | 0.120775i | 0.764911 | − | 0.644136i | \(-0.222783\pi\) |
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.00000 | − | 8.00000i | 0.321547 | − | 0.321547i | −0.527813 | − | 0.849360i | \(-0.676988\pi\) |
0.849360 | + | 0.527813i | \(0.176988\pi\) | |||||||
\(620\) | − | 8.00000i | − | 0.321288i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.0000 | − | 24.0000i | 0.962312 | − | 0.962312i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 9.00000 | + | 9.00000i | 0.359712 | + | 0.359712i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.00000 | 0.0798087 | ||||||||
\(629\) | −15.0000 | + | 9.00000i | −0.598089 | + | 0.358854i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 40.0000i | − | 1.59237i | −0.605050 | − | 0.796187i | \(-0.706847\pi\) | ||
0.605050 | − | 0.796187i | \(-0.293153\pi\) | |||||||
\(632\) | −8.00000 | − | 8.00000i | −0.318223 | − | 0.318223i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −15.0000 | − | 15.0000i | −0.595726 | − | 0.595726i | ||||
\(635\) | 8.00000 | − | 8.00000i | 0.317470 | − | 0.317470i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0000i | 1.10940i | ||||||||
\(638\) | 24.0000i | 0.950169i | ||||||||
\(639\) | −12.0000 | + | 12.0000i | −0.474713 | + | 0.474713i | ||||
\(640\) | −1.00000 | + | 1.00000i | −0.0395285 | + | 0.0395285i | ||||
\(641\) | 11.0000 | + | 11.0000i | 0.434474 | + | 0.434474i | 0.890147 | − | 0.455673i | \(-0.150601\pi\) |
−0.455673 | + | 0.890147i | \(0.650601\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.00000 | − | 16.0000i | 0.157378 | − | 0.629512i | ||||
\(647\) | −32.0000 | −1.25805 | −0.629025 | − | 0.777385i | \(-0.716546\pi\) | ||||
−0.629025 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(648\) | 9.00000i | 0.353553i | ||||||||
\(649\) | −16.0000 | − | 16.0000i | −0.628055 | − | 0.628055i | ||||
\(650\) | 12.0000 | 0.470679 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | + | 4.00000i | −0.156652 | + | 0.156652i | ||||
\(653\) | 29.0000 | − | 29.0000i | 1.13486 | − | 1.13486i | 0.145499 | − | 0.989358i | \(-0.453521\pi\) |
0.989358 | − | 0.145499i | \(-0.0464789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.00000i | 0.312586i | ||||||||
\(656\) | 1.00000 | − | 1.00000i | 0.0390434 | − | 0.0390434i | ||||
\(657\) | 15.0000 | − | 15.0000i | 0.585206 | − | 0.585206i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 20.0000i | − | 0.777910i | −0.921257 | − | 0.388955i | \(-0.872836\pi\) | ||
0.921257 | − | 0.388955i | \(-0.127164\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 9.00000 | + | 9.00000i | 0.348743 | + | 0.348743i | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | −8.00000 | − | 8.00000i | −0.309529 | − | 0.309529i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −12.0000 | + | 12.0000i | −0.463600 | + | 0.463600i | ||||
\(671\) | − | 72.0000i | − | 2.77953i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.0000 | − | 19.0000i | 0.732396 | − | 0.732396i | −0.238698 | − | 0.971094i | \(-0.576721\pi\) |
0.971094 | + | 0.238698i | \(0.0767205\pi\) | |||||||
\(674\) | 7.00000 | − | 7.00000i | 0.269630 | − | 0.269630i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.00000 | −0.115385 | ||||||||
\(677\) | 13.0000 | + | 13.0000i | 0.499631 | + | 0.499631i | 0.911323 | − | 0.411692i | \(-0.135062\pi\) |
−0.411692 | + | 0.911323i | \(0.635062\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00000 | − | 5.00000i | −0.115045 | − | 0.191741i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 32.0000i | 1.22534i | ||||||||
\(683\) | 20.0000 | + | 20.0000i | 0.765279 | + | 0.765279i | 0.977271 | − | 0.211993i | \(-0.0679953\pi\) |
−0.211993 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(684\) | −12.0000 | −0.458831 | ||||||||
\(685\) | −8.00000 | − | 8.00000i | −0.305664 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | − | 16.0000i | − | 0.609551i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0000 | + | 24.0000i | −0.913003 | + | 0.913003i | −0.996507 | − | 0.0835044i | \(-0.973389\pi\) |
0.0835044 | + | 0.996507i | \(0.473389\pi\) | |||||||
\(692\) | −5.00000 | − | 5.00000i | −0.190071 | − | 0.190071i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000i | 0.606915i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | + | 5.00000i | 0.113633 | + | 0.189389i | ||||
\(698\) | −4.00000 | −0.151402 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.0000 | + | 12.0000i | −0.452589 | + | 0.452589i | ||||
\(704\) | 4.00000 | − | 4.00000i | 0.150756 | − | 0.150756i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.0000i | 0.526897i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.0000 | − | 23.0000i | −0.863783 | − | 0.863783i | 0.127992 | − | 0.991775i | \(-0.459147\pi\) |
−0.991775 | + | 0.127992i | \(0.959147\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | −24.0000 | − | 24.0000i | −0.900070 | − | 0.900070i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.0000 | −1.19841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0000 | 1.19673 | ||||||||
\(716\) | − | 4.00000i | − | 0.149487i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.0000 | −0.895672 | ||||||||
\(719\) | −8.00000 | − | 8.00000i | −0.298350 | − | 0.298350i | 0.542018 | − | 0.840367i | \(-0.317661\pi\) |
−0.840367 | + | 0.542018i | \(0.817661\pi\) | |||||||
\(720\) | −3.00000 | + | 3.00000i | −0.111803 | + | 0.111803i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.00000i | 0.111648i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.0000 | + | 11.0000i | −0.408812 | + | 0.408812i | ||||
\(725\) | −9.00000 | + | 9.00000i | −0.334252 | + | 0.334252i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.0000 | 1.78022 | 0.890111 | − | 0.455744i | \(-0.150627\pi\) | ||||
0.890111 | + | 0.455744i | \(0.150627\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000i | 1.00000i | ||||||||
\(730\) | 10.0000 | 0.370117 | ||||||||
\(731\) | 16.0000 | + | 4.00000i | 0.591781 | + | 0.147945i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.0000i | 1.32969i | 0.746981 | + | 0.664845i | \(0.231502\pi\) | ||||
−0.746981 | + | 0.664845i | \(0.768498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.00000 | + | 4.00000i | 0.147442 | + | 0.147442i | ||||
\(737\) | 48.0000 | − | 48.0000i | 1.76810 | − | 1.76810i | ||||
\(738\) | 3.00000 | − | 3.00000i | 0.110432 | − | 0.110432i | ||||
\(739\) | 4.00000i | 0.147142i | 0.997290 | + | 0.0735712i | \(0.0234396\pi\) | ||||
−0.997290 | + | 0.0735712i | \(0.976560\pi\) | |||||||
\(740\) | 6.00000i | 0.220564i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10.0000 | + | 10.0000i | 0.366372 | + | 0.366372i | ||||
\(746\) | 4.00000i | 0.146450i | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 12.0000 | + | 20.0000i | 0.438763 | + | 0.731272i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.0000 | + | 16.0000i | 0.583848 | + | 0.583848i | 0.935959 | − | 0.352110i | \(-0.114536\pi\) |
−0.352110 | + | 0.935959i | \(0.614536\pi\) | |||||||
\(752\) | 8.00000 | 0.291730 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.0000 | − | 12.0000i | 0.437014 | − | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.0000i | − | 0.799604i | −0.916602 | − | 0.399802i | \(-0.869079\pi\) | ||
0.916602 | − | 0.399802i | \(-0.130921\pi\) | |||||||
\(758\) | −12.0000 | + | 12.0000i | −0.435860 | + | 0.435860i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | − | 4.00000i | −0.145095 | − | 0.145095i | ||||
\(761\) | −8.00000 | −0.290000 | −0.145000 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.145000 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.00000 | 0.289430 | ||||||||
\(765\) | −9.00000 | − | 15.0000i | −0.325396 | − | 0.542326i | ||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 16.0000i | 0.577727i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.0000 | 1.44244 | 0.721218 | − | 0.692708i | \(-0.243582\pi\) | ||||
0.721218 | + | 0.692708i | \(0.243582\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.0000 | − | 11.0000i | 0.395899 | − | 0.395899i | ||||
\(773\) | 6.00000i | 0.215805i | 0.994161 | + | 0.107903i | \(0.0344134\pi\) | ||||
−0.994161 | + | 0.107903i | \(0.965587\pi\) | |||||||
\(774\) | − | 12.0000i | − | 0.431331i | ||||||
\(775\) | −12.0000 | + | 12.0000i | −0.431053 | + | 0.431053i | ||||
\(776\) | 3.00000 | − | 3.00000i | 0.107694 | − | 0.107694i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | 4.00000 | + | 4.00000i | 0.143315 | + | 0.143315i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.0000 | 1.14505 | ||||||||
\(782\) | −20.0000 | + | 12.0000i | −0.715199 | + | 0.429119i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 7.00000i | 0.250000i | ||||||||
\(785\) | 2.00000 | + | 2.00000i | 0.0713831 | + | 0.0713831i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.0000 | − | 12.0000i | −0.427754 | − | 0.427754i | 0.460109 | − | 0.887863i | \(-0.347810\pi\) |
−0.887863 | + | 0.460109i | \(0.847810\pi\) | |||||||
\(788\) | −5.00000 | + | 5.00000i | −0.178118 | + | 0.178118i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 16.0000i | − | 0.569254i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 12.0000 | − | 12.0000i | 0.426401 | − | 0.426401i | ||||
\(793\) | −36.0000 | + | 36.0000i | −1.27840 | + | 1.27840i | ||||
\(794\) | 15.0000 | + | 15.0000i | 0.532330 | + | 0.532330i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0000 | − | 12.0000i | −0.425329 | − | 0.425329i | ||||
\(797\) | − | 12.0000i | − | 0.425062i | −0.977154 | − | 0.212531i | \(-0.931829\pi\) | ||
0.977154 | − | 0.212531i | \(-0.0681706\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | + | 32.0000i | −0.283020 | + | 1.13208i | ||||
\(800\) | 3.00000 | 0.106066 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −19.0000 | − | 19.0000i | −0.670913 | − | 0.670913i | ||||
\(803\) | −40.0000 | −1.41157 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16.0000 | − | 16.0000i | 0.563576 | − | 0.563576i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.0000i | − | 0.422159i | ||||||
\(809\) | 23.0000 | − | 23.0000i | 0.808637 | − | 0.808637i | −0.175791 | − | 0.984428i | \(-0.556248\pi\) |
0.984428 | + | 0.175791i | \(0.0562482\pi\) | |||||||
\(810\) | −9.00000 | + | 9.00000i | −0.316228 | + | 0.316228i | ||||
\(811\) | −4.00000 | − | 4.00000i | −0.140459 | − | 0.140459i | 0.633381 | − | 0.773840i | \(-0.281667\pi\) |
−0.773840 | + | 0.633381i | \(0.781667\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 24.0000i | − | 0.841200i | ||||||
\(815\) | −8.00000 | −0.280228 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | 0.559769 | ||||||||
\(818\) | − | 10.0000i | − | 0.349642i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.00000 | 0.0698430 | ||||||||
\(821\) | −19.0000 | − | 19.0000i | −0.663105 | − | 0.663105i | 0.293006 | − | 0.956111i | \(-0.405344\pi\) |
−0.956111 | + | 0.293006i | \(0.905344\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.0000 | + | 36.0000i | −1.25488 | + | 1.25488i | −0.301376 | + | 0.953506i | \(0.597446\pi\) |
−0.953506 | + | 0.301376i | \(0.902554\pi\) | |||||||
\(824\) | 16.0000i | 0.557386i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.0000 | + | 20.0000i | −0.695468 | + | 0.695468i | −0.963430 | − | 0.267961i | \(-0.913650\pi\) |
0.267961 | + | 0.963430i | \(0.413650\pi\) | |||||||
\(828\) | 12.0000 | + | 12.0000i | 0.417029 | + | 0.417029i | ||||
\(829\) | 30.0000 | 1.04194 | 0.520972 | − | 0.853574i | \(-0.325570\pi\) | ||||
0.520972 | + | 0.853574i | \(0.325570\pi\) | |||||||
\(830\) | −4.00000 | − | 4.00000i | −0.138842 | − | 0.138842i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.00000 | −0.138675 | ||||||||
\(833\) | −28.0000 | − | 7.00000i | −0.970143 | − | 0.242536i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 16.0000i | − | 0.553703i | ||||||
\(836\) | 16.0000 | + | 16.0000i | 0.553372 | + | 0.553372i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.0000 | − | 12.0000i | −0.414533 | − | 0.414533i | ||||
\(839\) | −32.0000 | + | 32.0000i | −1.10476 | + | 1.10476i | −0.110935 | + | 0.993828i | \(0.535385\pi\) |
−0.993828 | + | 0.110935i | \(0.964615\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | − | 28.0000i | − | 0.964944i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.0000 | + | 16.0000i | −0.550743 | + | 0.550743i | ||||
\(845\) | −3.00000 | − | 3.00000i | −0.103203 | − | 0.103203i | ||||
\(846\) | 24.0000 | 0.825137 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 4.00000i | − | 0.137361i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.00000 | + | 12.0000i | −0.102899 | + | 0.411597i | ||||
\(851\) | 24.0000 | 0.822709 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.0000 | − | 25.0000i | −0.855984 | − | 0.855984i | 0.134878 | − | 0.990862i | \(-0.456936\pi\) |
−0.990862 | + | 0.134878i | \(0.956936\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.0000 | − | 12.0000i | −0.410391 | − | 0.410391i | ||||
\(856\) | 8.00000 | − | 8.00000i | 0.273434 | − | 0.273434i | ||||
\(857\) | −15.0000 | + | 15.0000i | −0.512390 | + | 0.512390i | −0.915258 | − | 0.402868i | \(-0.868013\pi\) |
0.402868 | + | 0.915258i | \(0.368013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 36.0000i | − | 1.22830i | −0.789188 | − | 0.614152i | \(-0.789498\pi\) | ||
0.789188 | − | 0.614152i | \(-0.210502\pi\) | |||||||
\(860\) | 4.00000 | − | 4.00000i | 0.136399 | − | 0.136399i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −24.0000 | − | 24.0000i | −0.817443 | − | 0.817443i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 10.0000i | − | 0.340010i | ||||||
\(866\) | 14.0000 | 0.475739 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 64.0000i | 2.17105i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48.0000 | −1.62642 | ||||||||
\(872\) | −3.00000 | − | 3.00000i | −0.101593 | − | 0.101593i | ||||
\(873\) | 9.00000 | − | 9.00000i | 0.304604 | − | 0.304604i | ||||
\(874\) | −16.0000 | + | 16.0000i | −0.541208 | + | 0.541208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.0000 | − | 35.0000i | 1.18187 | − | 1.18187i | 0.202606 | − | 0.979260i | \(-0.435059\pi\) |
0.979260 | − | 0.202606i | \(-0.0649409\pi\) | |||||||
\(878\) | −12.0000 | + | 12.0000i | −0.404980 | + | 0.404980i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.00000 | 0.269680 | ||||||||
\(881\) | −39.0000 | − | 39.0000i | −1.31394 | − | 1.31394i | −0.918483 | − | 0.395460i | \(-0.870585\pi\) |
−0.395460 | − | 0.918483i | \(-0.629415\pi\) | |||||||
\(882\) | 21.0000i | 0.707107i | ||||||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 4.00000 | − | 16.0000i | 0.134535 | − | 0.538138i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.00000i | 0.134383i | ||||||||
\(887\) | 28.0000 | + | 28.0000i | 0.940148 | + | 0.940148i | 0.998307 | − | 0.0581593i | \(-0.0185231\pi\) |
−0.0581593 | + | 0.998307i | \(0.518523\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.0000 | − | 36.0000i | 1.20605 | − | 1.20605i | ||||
\(892\) | − | 16.0000i | − | 0.535720i | ||||||
\(893\) | 32.0000i | 1.07084i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.00000 | − | 4.00000i | 0.133705 | − | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.00000 | + | 3.00000i | 0.100111 | + | 0.100111i | ||||
\(899\) | 24.0000i | 0.800445i | ||||||||
\(900\) | 9.00000 | 0.300000 | ||||||||
\(901\) | 16.0000 | + | 4.00000i | 0.533037 | + | 0.133259i | ||||
\(902\) | −8.00000 | −0.266371 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.00000 | + | 1.00000i | 0.0332595 | + | 0.0332595i | ||||
\(905\) | −22.0000 | −0.731305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | − | 20.0000i | 0.664089 | − | 0.664089i | −0.292252 | − | 0.956341i | \(-0.594405\pi\) |
0.956341 | + | 0.292252i | \(0.0944047\pi\) | |||||||
\(908\) | −20.0000 | + | 20.0000i | −0.663723 | + | 0.663723i | ||||
\(909\) | − | 36.0000i | − | 1.19404i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.00000 | + | 4.00000i | −0.132526 | + | 0.132526i | −0.770258 | − | 0.637732i | \(-0.779873\pi\) |
0.637732 | + | 0.770258i | \(0.279873\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.0000 | + | 16.0000i | 0.529523 | + | 0.529523i | ||||
\(914\) | 22.0000 | 0.727695 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 6.00000i | 0.198246i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 8.00000i | 0.263752i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.0000 | 0.658665 | ||||||||
\(923\) | −16.0000 | − | 16.0000i | −0.526646 | − | 0.526646i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | − | 9.00000i | 0.295918 | − | 0.295918i | ||||
\(926\) | 24.0000i | 0.788689i | ||||||||
\(927\) | 48.0000i | 1.57653i | ||||||||
\(928\) | 3.00000 | − | 3.00000i | 0.0984798 | − | 0.0984798i | ||||
\(929\) | 13.0000 | − | 13.0000i | 0.426516 | − | 0.426516i | −0.460924 | − | 0.887440i | \(-0.652482\pi\) |
0.887440 | + | 0.460924i | \(0.152482\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | 5.00000 | + | 5.00000i | 0.163780 | + | 0.163780i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −28.0000 | −0.916188 | ||||||||
\(935\) | −8.00000 | + | 32.0000i | −0.261628 | + | 1.04651i | ||||
\(936\) | −12.0000 | −0.392232 | ||||||||
\(937\) | 48.0000i | 1.56809i | 0.620703 | + | 0.784046i | \(0.286847\pi\) | ||||
−0.620703 | + | 0.784046i | \(0.713153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.00000 | + | 8.00000i | 0.260931 | + | 0.260931i | ||||
\(941\) | 1.00000 | − | 1.00000i | 0.0325991 | − | 0.0325991i | −0.690619 | − | 0.723218i | \(-0.742662\pi\) |
0.723218 | + | 0.690619i | \(0.242662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.00000i | − | 0.260516i | ||||||
\(944\) | 4.00000i | 0.130189i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.0000 | + | 16.0000i | −0.520205 | + | 0.520205i | ||||
\(947\) | −12.0000 | − | 12.0000i | −0.389948 | − | 0.389948i | 0.484721 | − | 0.874669i | \(-0.338921\pi\) |
−0.874669 | + | 0.484721i | \(0.838921\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.0000 | + | 20.0000i | 0.649227 | + | 0.649227i | ||||
\(950\) | 12.0000i | 0.389331i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | − | 12.0000i | − | 0.388514i | ||||||
\(955\) | 8.00000 | + | 8.00000i | 0.258874 | + | 0.258874i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00000 | − | 8.00000i | 0.258468 | − | 0.258468i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000i | 0.0322581i | ||||||||
\(962\) | −12.0000 | + | 12.0000i | −0.386896 | + | 0.386896i | ||||
\(963\) | 24.0000 | − | 24.0000i | 0.773389 | − | 0.773389i | ||||
\(964\) | −21.0000 | − | 21.0000i | −0.676364 | − | 0.676364i | ||||
\(965\) | 22.0000 | 0.708205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 32.0000i | − | 1.02905i | −0.857475 | − | 0.514525i | \(-0.827968\pi\) | ||
0.857475 | − | 0.514525i | \(-0.172032\pi\) | |||||||
\(968\) | −21.0000 | −0.674966 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.00000 | 0.192648 | ||||||||
\(971\) | − | 20.0000i | − | 0.641831i | −0.947108 | − | 0.320915i | \(-0.896010\pi\) | ||
0.947108 | − | 0.320915i | \(-0.103990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 20.0000 | + | 20.0000i | 0.640841 | + | 0.640841i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.00000 | + | 9.00000i | −0.288083 | + | 0.288083i | ||||
\(977\) | 8.00000i | 0.255943i | 0.991778 | + | 0.127971i | \(0.0408466\pi\) | ||||
−0.991778 | + | 0.127971i | \(0.959153\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −7.00000 | + | 7.00000i | −0.223607 | + | 0.223607i | ||||
\(981\) | −9.00000 | − | 9.00000i | −0.287348 | − | 0.287348i | ||||
\(982\) | −20.0000 | −0.638226 | ||||||||
\(983\) | −20.0000 | − | 20.0000i | −0.637901 | − | 0.637901i | 0.312136 | − | 0.950037i | \(-0.398955\pi\) |
−0.950037 | + | 0.312136i | \(0.898955\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −10.0000 | −0.318626 | ||||||||
\(986\) | 9.00000 | + | 15.0000i | 0.286618 | + | 0.477697i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 16.0000i | − | 0.509028i | ||||||
\(989\) | −16.0000 | − | 16.0000i | −0.508770 | − | 0.508770i | ||||
\(990\) | 24.0000 | 0.762770 | ||||||||
\(991\) | −24.0000 | − | 24.0000i | −0.762385 | − | 0.762385i | 0.214368 | − | 0.976753i | \(-0.431231\pi\) |
−0.976753 | + | 0.214368i | \(0.931231\pi\) | |||||||
\(992\) | 4.00000 | − | 4.00000i | 0.127000 | − | 0.127000i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 24.0000i | − | 0.760851i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.0000 | + | 35.0000i | −1.10846 | + | 1.10846i | −0.115108 | + | 0.993353i | \(0.536721\pi\) |
−0.993353 | + | 0.115108i | \(0.963279\pi\) | |||||||
\(998\) | 8.00000 | + | 8.00000i | 0.253236 | + | 0.253236i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))