Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,2,Mod(111,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.111");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.f (of order \(2\), degree \(1\), 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: | \(0.894324502638\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 111.2 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.111 |
Dual form | 112.2.f.a.111.1 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −2.00000 | −1.15470 | −0.577350 | − | 0.816497i | \(-0.695913\pi\) | ||||
−0.577350 | + | 0.816497i | \(0.695913\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.92820i | − | 1.78885i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.00000 | − | 3.46410i | −0.872872 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.46410i | − | 0.722315i | −0.932505 | − | 0.361158i | \(-0.882382\pi\) | ||
0.932505 | − | 0.361158i | \(-0.117618\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.92820i | − | 1.20605i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | + | 6.92820i | −1.01419 | + | 1.17108i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.92820i | 1.10940i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820i | 1.08200i | 0.841021 | + | 0.541002i | \(0.181955\pi\) | ||||
−0.841021 | + | 0.541002i | \(0.818045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.3923i | − | 1.58481i | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||
0.609994 | − | 0.792406i | \(-0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.46410i | 0.516398i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.0000 | −1.61808 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.00000 | −0.781133 | −0.390567 | − | 0.920575i | \(-0.627721\pi\) | ||||
−0.390567 | + | 0.920575i | \(0.627721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.46410i | − | 0.443533i | −0.975100 | − | 0.221766i | \(-0.928818\pi\) | ||
0.975100 | − | 0.221766i | \(-0.0711822\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000 | + | 1.73205i | 0.251976 | + | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.46410i | 0.423207i | 0.977356 | + | 0.211604i | \(0.0678686\pi\) | ||||
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.92820i | 0.834058i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.46410i | 0.411113i | 0.978645 | + | 0.205557i | \(0.0659005\pi\) | ||||
−0.978645 | + | 0.205557i | \(0.934100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 14.0000 | 1.61658 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | + | 6.92820i | −0.683763 | + | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.46410i | 0.389742i | 0.980829 | + | 0.194871i | \(0.0624288\pi\) | ||||
−0.980829 | + | 0.194871i | \(0.937571\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −12.0000 | −1.28654 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.92820i | 0.734388i | 0.930144 | + | 0.367194i | \(0.119682\pi\) | ||||
−0.930144 | + | 0.367194i | \(0.880318\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | − | 6.92820i | 0.628971 | − | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.0000 | −1.65912 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 6.92820i | − | 0.710819i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.8564i | − | 1.40690i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) | ||
0.710742 | − | 0.703452i | \(-0.248359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.46410i | 0.348155i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.3923i | − | 1.03407i | −0.855963 | − | 0.517036i | \(-0.827035\pi\) | ||
0.855963 | − | 0.517036i | \(-0.172965\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.0000 | − | 13.8564i | 1.17108 | − | 1.35225i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.3923i | − | 1.00466i | −0.864675 | − | 0.502331i | \(-0.832476\pi\) | ||
0.864675 | − | 0.502331i | \(-0.167524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.0000 | −1.69330 | −0.846649 | − | 0.532152i | \(-0.821383\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0000 | 1.11901 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 3.46410i | − | 0.320256i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 13.8564i | − | 1.24939i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3923i | 0.922168i | 0.887357 | + | 0.461084i | \(0.152539\pi\) | ||||
−0.887357 | + | 0.461084i | \(0.847461\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 20.7846i | 1.82998i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0000 | −1.57267 | −0.786334 | − | 0.617802i | \(-0.788023\pi\) | ||||
−0.786334 | + | 0.617802i | \(0.788023\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | − | 3.46410i | −0.346844 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.8564i | 1.19257i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | −0.512615 | −0.256307 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.00000 | 0.169638 | 0.0848189 | − | 0.996396i | \(-0.472969\pi\) | ||||
0.0848189 | + | 0.996396i | \(0.472969\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.0000 | 1.00349 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 20.7846i | 1.72607i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.00000 | − | 13.8564i | −0.164957 | − | 1.14286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.46410i | − | 0.281905i | −0.990016 | − | 0.140952i | \(-0.954984\pi\) | ||
0.990016 | − | 0.140952i | \(-0.0450164\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.7128i | 2.22595i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.3923i | 0.829396i | 0.909959 | + | 0.414698i | \(0.136113\pi\) | ||||
−0.909959 | + | 0.414698i | \(0.863887\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | −0.951662 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000 | − | 6.92820i | 0.472866 | − | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3205i | 1.35665i | 0.734763 | + | 0.678323i | \(0.237293\pi\) | ||||
−0.734763 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 24.0000 | 1.86840 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.0000 | 0.928588 | 0.464294 | − | 0.885681i | \(-0.346308\pi\) | ||||
0.464294 | + | 0.885681i | \(0.346308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | −0.152944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 3.46410i | − | 0.263371i | −0.991292 | − | 0.131685i | \(-0.957961\pi\) | ||
0.991292 | − | 0.131685i | \(-0.0420389\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.0000 | − | 12.1244i | −1.05830 | − | 0.916515i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 10.3923i | − | 0.776757i | −0.921500 | − | 0.388379i | \(-0.873035\pi\) | ||
0.921500 | − | 0.388379i | \(-0.126965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3205i | 1.28742i | 0.765268 | + | 0.643712i | \(0.222606\pi\) | ||||
−0.765268 | + | 0.643712i | \(0.777394\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.92820i | 0.512148i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 6.92820i | − | 0.509372i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | + | 6.92820i | 0.581914 | + | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.2487i | − | 1.75458i | −0.479965 | − | 0.877288i | \(-0.659351\pi\) | ||
0.479965 | − | 0.877288i | \(-0.340649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00000 | −0.143963 | −0.0719816 | − | 0.997406i | \(-0.522932\pi\) | ||||
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −24.0000 | −1.71868 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.0000 | −1.41776 | −0.708881 | − | 0.705328i | \(-0.750800\pi\) | ||||
−0.708881 | + | 0.705328i | \(0.750800\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.0000 | + | 10.3923i | 0.842235 | + | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.0000 | −1.67623 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 3.46410i | − | 0.240772i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 6.92820i | − | 0.479234i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 6.92820i | − | 0.474713i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 36.0000 | 2.45518 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | + | 13.8564i | 1.08615 | + | 0.940634i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 13.8564i | 0.936329i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.00000 | −0.466667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 10.3923i | − | 0.686743i | −0.939200 | − | 0.343371i | \(-0.888431\pi\) | ||
0.939200 | − | 0.343371i | \(-0.111569\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.0000 | − | 13.8564i | 0.789542 | − | 0.911685i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 6.92820i | − | 0.450035i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.3923i | 0.672222i | 0.941822 | + | 0.336111i | \(0.109112\pi\) | ||||
−0.941822 | + | 0.336111i | \(0.890888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 27.7128i | − | 1.78514i | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||
0.450910 | − | 0.892570i | \(-0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.0000 | 0.641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −24.0000 | + | 3.46410i | −1.53330 | + | 0.221313i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820i | 0.440831i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −30.0000 | −1.89358 | −0.946792 | − | 0.321847i | \(-0.895696\pi\) | ||||
−0.946792 | + | 0.321847i | \(0.895696\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.0000 | 0.754434 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 27.7128i | − | 1.72868i | −0.502910 | − | 0.864339i | \(-0.667737\pi\) | ||
0.502910 | − | 0.864339i | \(-0.332263\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | − | 3.46410i | −0.248548 | − | 0.215249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 24.2487i | − | 1.49524i | −0.664127 | − | 0.747620i | \(-0.731197\pi\) | ||
0.664127 | − | 0.747620i | \(-0.268803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.7846i | 1.27679i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 13.8564i | − | 0.847998i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.46410i | − | 0.211210i | −0.994408 | − | 0.105605i | \(-0.966322\pi\) | ||
0.994408 | − | 0.105605i | \(-0.0336779\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −12.0000 | + | 13.8564i | −0.726273 | + | 0.838628i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 24.2487i | − | 1.46225i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000 | 0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.0000 | −0.832214 | −0.416107 | − | 0.909316i | \(-0.636606\pi\) | ||||
−0.416107 | + | 0.909316i | \(0.636606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.8564i | 0.820783i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0000 | + | 13.8564i | −0.708338 | + | 0.817918i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 27.7128i | 1.62455i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10.3923i | − | 0.607125i | −0.952812 | − | 0.303562i | \(-0.901824\pi\) | ||
0.952812 | − | 0.303562i | \(-0.0981761\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 20.7846i | − | 1.21013i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.8564i | 0.804030i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.0000 | − | 20.7846i | 1.03750 | − | 1.19800i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.7846i | 1.19404i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.0000 | 0.687118 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000 | 1.25561 | 0.627803 | − | 0.778372i | \(-0.283954\pi\) | ||||
0.627803 | + | 0.778372i | \(0.283954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.92820i | − | 0.391605i | −0.980643 | − | 0.195803i | \(-0.937269\pi\) | ||
0.980643 | − | 0.195803i | \(-0.0627312\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.00000 | + | 6.92820i | −0.338062 | + | 0.390360i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 20.7846i | 1.16371i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.7846i | 1.16008i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 24.2487i | 1.34508i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −28.0000 | −1.54840 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.46410i | 0.190404i | 0.995458 | + | 0.0952021i | \(0.0303497\pi\) | ||||
−0.995458 | + | 0.0952021i | \(0.969650\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.00000 | −0.109599 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 36.0000 | 1.95525 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.7128i | 1.50073i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.0000 | −1.29212 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.3205i | 0.929814i | 0.885360 | + | 0.464907i | \(0.153912\pi\) | ||||
−0.885360 | + | 0.464907i | \(0.846088\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.46410i | − | 0.185429i | −0.995693 | − | 0.0927146i | \(-0.970446\pi\) | ||
0.995693 | − | 0.0927146i | \(-0.0295544\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 13.8564i | − | 0.739600i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.7128i | 1.47500i | 0.675345 | + | 0.737502i | \(0.263995\pi\) | ||||
−0.675345 | + | 0.737502i | \(0.736005\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −12.0000 | −0.636894 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 31.1769i | − | 1.64545i | −0.568436 | − | 0.822727i | \(-0.692451\pi\) | ||
0.568436 | − | 0.822727i | \(-0.307549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.00000 | 0.104973 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 24.0000 | 1.25622 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.92820i | 0.360668i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | + | 10.3923i | 0.623009 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000 | 0.724893 | 0.362446 | − | 0.932005i | \(-0.381942\pi\) | ||||
0.362446 | + | 0.932005i | \(0.381942\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.8564i | 0.715542i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 20.7846i | − | 1.07046i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.2487i | − | 1.24557i | −0.782392 | − | 0.622786i | \(-0.786001\pi\) | ||
0.782392 | − | 0.622786i | \(-0.213999\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 20.7846i | − | 1.06483i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −24.0000 | − | 20.7846i | −1.22315 | − | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 10.3923i | − | 0.528271i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 36.0000 | 1.81596 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.0000 | −0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.3923i | 0.521575i | 0.965396 | + | 0.260787i | \(0.0839822\pi\) | ||||
−0.965396 | + | 0.260787i | \(0.916018\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.00000 | + | 6.92820i | 0.400501 | + | 0.346844i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 27.7128i | − | 1.38047i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 38.1051i | − | 1.89346i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 6.92820i | − | 0.343418i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.92820i | − | 0.342578i | −0.985221 | − | 0.171289i | \(-0.945207\pi\) | ||
0.985221 | − | 0.171289i | \(-0.0547931\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.0000 | − | 10.3923i | −0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.7846i | 1.02028i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.0000 | −1.26716 | −0.633581 | − | 0.773676i | \(-0.718416\pi\) | ||||
−0.633581 | + | 0.773676i | \(0.718416\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00000 | − | 6.92820i | 0.290360 | − | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −24.0000 | −1.15873 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38.1051i | 1.83546i | 0.397206 | + | 0.917729i | \(0.369980\pi\) | ||||
−0.397206 | + | 0.917729i | \(0.630020\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 41.5692i | − | 1.99309i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.92820i | 0.331421i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.0000 | 1.33637 | 0.668184 | − | 0.743996i | \(-0.267072\pi\) | ||||
0.668184 | + | 0.743996i | \(0.267072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.46410i | 0.164584i | 0.996608 | + | 0.0822922i | \(0.0262241\pi\) | ||||
−0.996608 | + | 0.0822922i | \(0.973776\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −24.0000 | −1.13771 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.0000 | −1.13012 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.92820i | 0.325515i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 24.0000 | + | 20.7846i | 1.12514 | + | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.0000 | −1.59045 | −0.795226 | − | 0.606313i | \(-0.792648\pi\) | ||||
−0.795226 | + | 0.606313i | \(0.792648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.1051i | 1.77473i | 0.461065 | + | 0.887366i | \(0.347467\pi\) | ||||
−0.461065 | + | 0.887366i | \(0.652533\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 24.2487i | − | 1.12693i | −0.826139 | − | 0.563467i | \(-0.809467\pi\) | ||
0.826139 | − | 0.563467i | \(-0.190533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 55.4256i | − | 2.57030i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 30.0000 | 1.38823 | 0.694117 | − | 0.719862i | \(-0.255795\pi\) | ||||
0.694117 | + | 0.719862i | \(0.255795\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | + | 6.92820i | −0.277054 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 20.7846i | − | 0.957704i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.0000 | 1.65528 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.0000 | 0.642364 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.00000 | 0.274721 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820i | 0.315899i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0000 | + | 13.8564i | −0.546019 | + | 0.630488i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 48.0000 | 2.17957 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.2487i | 1.09881i | 0.835555 | + | 0.549407i | \(0.185146\pi\) | ||||
−0.835555 | + | 0.549407i | \(0.814854\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 34.6410i | − | 1.56652i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.3205i | 0.781664i | 0.920462 | + | 0.390832i | \(0.127813\pi\) | ||||
−0.920462 | + | 0.390832i | \(0.872187\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.0000 | −0.539360 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | + | 6.92820i | −0.269137 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 10.3923i | − | 0.465223i | −0.972570 | − | 0.232612i | \(-0.925273\pi\) | ||
0.972570 | − | 0.232612i | \(-0.0747271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −24.0000 | −1.07224 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 36.0000 | 1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.00000 | −0.0888231 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 31.1769i | − | 1.38189i | −0.722906 | − | 0.690946i | \(-0.757194\pi\) | ||
0.722906 | − | 0.690946i | \(-0.242806\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | − | 13.8564i | 0.530849 | − | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.00000 | −0.353209 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 13.8564i | − | 0.610586i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.92820i | 0.304114i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.6410i | 1.51765i | 0.651294 | + | 0.758825i | \(0.274226\pi\) | ||||
−0.651294 | + | 0.758825i | \(0.725774\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.00000 | 0.0874539 | 0.0437269 | − | 0.999044i | \(-0.486077\pi\) | ||||
0.0437269 | + | 0.999044i | \(0.486077\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 28.0000 | + | 24.2487i | 1.22202 | + | 1.05830i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | 0.478261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | 1.03956 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.0000 | 1.55642 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.7846i | 0.896922i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0000 | + | 3.46410i | −1.03375 | + | 0.149209i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 34.6410i | − | 1.48659i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 48.4974i | 2.07740i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.3205i | 0.740571i | 0.928918 | + | 0.370286i | \(0.120740\pi\) | ||||
−0.928918 | + | 0.370286i | \(0.879260\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 3.46410i | − | 0.147844i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0000 | −0.511217 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | + | 6.92820i | −0.255146 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8564i | 0.588172i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.0000 | −0.762684 | −0.381342 | − | 0.924434i | \(-0.624538\pi\) | ||||
−0.381342 | + | 0.924434i | \(0.624538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.0000 | −1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0000 | −0.758610 | −0.379305 | − | 0.925272i | \(-0.623837\pi\) | ||||
−0.379305 | + | 0.925272i | \(0.623837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 62.3538i | − | 2.62325i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −22.0000 | − | 19.0526i | −0.923913 | − | 0.800132i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.0000 | −0.754599 | −0.377300 | − | 0.926091i | \(-0.623147\pi\) | ||||
−0.377300 | + | 0.926091i | \(0.623147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.0333i | 1.88459i | 0.334790 | + | 0.942293i | \(0.391335\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 48.4974i | 2.02601i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.2487i | 1.01124i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.7128i | 1.15370i | 0.816850 | + | 0.576850i | \(0.195718\pi\) | ||||
−0.816850 | + | 0.576850i | \(0.804282\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000 | 0.166234 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | + | 10.3923i | 0.497844 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7846i | 0.860811i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.0000 | 0.496139 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.0000 | 0.742940 | 0.371470 | − | 0.928445i | \(-0.378854\pi\) | ||||
0.371470 | + | 0.928445i | \(0.378854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 36.0000 | 1.48084 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.8564i | 0.569014i | 0.958674 | + | 0.284507i | \(0.0918300\pi\) | ||||
−0.958674 | + | 0.284507i | \(0.908170\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 40.0000 | 1.63709 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 24.2487i | − | 0.990775i | −0.868672 | − | 0.495388i | \(-0.835026\pi\) | ||
0.868672 | − | 0.495388i | \(-0.164974\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.7846i | − | 0.847822i | −0.905704 | − | 0.423911i | \(-0.860657\pi\) | ||
0.905704 | − | 0.423911i | \(-0.139343\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.46410i | 0.141069i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.46410i | − | 0.140836i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0000 | 0.649420 | 0.324710 | − | 0.945814i | \(-0.394733\pi\) | ||||
0.324710 | + | 0.945814i | \(0.394733\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −24.0000 | − | 20.7846i | −0.972529 | − | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.0000 | 1.53481 | 0.767403 | − | 0.641165i | \(-0.221549\pi\) | ||||
0.767403 | + | 0.641165i | \(0.221549\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 48.0000 | 1.93555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.0000 | −0.724653 | −0.362326 | − | 0.932051i | \(-0.618017\pi\) | ||||
−0.362326 | + | 0.932051i | \(0.618017\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.0000 | 1.04503 | 0.522514 | − | 0.852631i | \(-0.324994\pi\) | ||||
0.522514 | + | 0.852631i | \(0.324994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 13.8564i | − | 0.556038i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0000 | + | 13.8564i | −0.480770 | + | 0.555145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.8564i | 0.553372i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.46410i | 0.137904i | 0.997620 | + | 0.0689519i | \(0.0219655\pi\) | ||||
−0.997620 | + | 0.0689519i | \(0.978035\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 6.92820i | − | 0.275371i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36.0000 | −1.42862 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | − | 3.46410i | 0.950915 | − | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.46410i | 0.137038i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.0000 | 1.18493 | 0.592464 | − | 0.805597i | \(-0.298155\pi\) | ||||
0.592464 | + | 0.805597i | \(0.298155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −26.0000 | −1.02534 | −0.512670 | − | 0.858586i | \(-0.671344\pi\) | ||||
−0.512670 | + | 0.858586i | \(0.671344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −72.0000 | −2.83500 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 20.7846i | − | 0.815867i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −32.0000 | − | 27.7128i | −1.25418 | − | 1.08615i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 62.3538i | − | 2.43637i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.92820i | − | 0.270295i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.46410i | 0.134942i | 0.997721 | + | 0.0674711i | \(0.0214931\pi\) | ||||
−0.997721 | + | 0.0674711i | \(0.978507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.46410i | 0.134738i | 0.997728 | + | 0.0673690i | \(0.0214605\pi\) | ||||
−0.997728 | + | 0.0673690i | \(0.978540\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12.0000 | − | 13.8564i | 0.465340 | − | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 20.7846i | − | 0.804783i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.0000 | −1.23719 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0000 | −0.539660 | −0.269830 | − | 0.962908i | \(-0.586968\pi\) | ||||
−0.269830 | + | 0.962908i | \(0.586968\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −28.0000 | −1.07772 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.46410i | 0.133136i | 0.997782 | + | 0.0665681i | \(0.0212050\pi\) | ||||
−0.997782 | + | 0.0665681i | \(0.978795\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | − | 27.7128i | 0.921035 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 38.1051i | − | 1.45805i | −0.684486 | − | 0.729026i | \(-0.739973\pi\) | ||
0.684486 | − | 0.729026i | \(-0.260027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 20.7846i | − | 0.794139i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.7846i | 0.792982i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 20.7846i | − | 0.791831i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.0000 | −0.380418 | −0.190209 | − | 0.981744i | \(-0.560917\pi\) | ||||
−0.190209 | + | 0.981744i | \(0.560917\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.00000 | + | 6.92820i | −0.227921 | + | 0.263181i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.92820i | 0.262802i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000 | 0.453882 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.0000 | − | 20.7846i | 0.676960 | − | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.46410i | 0.129914i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 27.7128i | − | 1.03785i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.5692i | 1.55460i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 20.7846i | − | 0.776215i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 48.0000 | 1.79010 | 0.895049 | − | 0.445968i | \(-0.147140\pi\) | ||||
0.895049 | + | 0.445968i | \(0.147140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | − | 6.92820i | −0.297936 | − | 0.258020i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 55.4256i | 2.06130i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −42.0000 | −1.55984 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.0000 | −1.03846 | −0.519231 | − | 0.854634i | \(-0.673782\pi\) | ||||
−0.519231 | + | 0.854634i | \(0.673782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.9615i | 1.91924i | 0.281295 | + | 0.959621i | \(0.409236\pi\) | ||||
−0.281295 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 48.0000 | − | 6.92820i | 1.77051 | − | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.0000 | −0.442026 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 10.3923i | − | 0.382287i | −0.981562 | − | 0.191144i | \(-0.938780\pi\) | ||
0.981562 | − | 0.191144i | \(-0.0612196\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 13.8564i | − | 0.509028i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.2487i | 0.889599i | 0.895630 | + | 0.444799i | \(0.146725\pi\) | ||||
−0.895630 | + | 0.444799i | \(0.853275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.7846i | 0.761489i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | 0.219529 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | − | 20.7846i | 0.657706 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 45.0333i | − | 1.64329i | −0.570000 | − | 0.821645i | \(-0.693057\pi\) | ||
0.570000 | − | 0.821645i | \(-0.306943\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 60.0000 | 2.18652 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.0000 | 0.436725 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.0000 | −0.363456 | −0.181728 | − | 0.983349i | \(-0.558169\pi\) | ||||
−0.181728 | + | 0.983349i | \(0.558169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.0000 | −0.871145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.7846i | 0.753442i | 0.926327 | + | 0.376721i | \(0.122948\pi\) | ||||
−0.926327 | + | 0.376721i | \(0.877052\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.0000 | + | 24.2487i | 1.01367 | + | 0.877862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20.7846i | 0.750489i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.8564i | − | 0.499675i | −0.968288 | − | 0.249837i | \(-0.919623\pi\) | ||
0.968288 | − | 0.249837i | \(-0.0803772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 55.4256i | 1.99611i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.46410i | 0.124595i | 0.998058 | + | 0.0622975i | \(0.0198428\pi\) | ||||
−0.998058 | + | 0.0622975i | \(0.980157\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −56.0000 | −2.01158 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.00000 | + | 6.92820i | 0.286998 | + | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 13.8564i | − | 0.496457i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.0000 | −0.429394 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −36.0000 | −1.28490 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34.0000 | −1.21197 | −0.605985 | − | 0.795476i | \(-0.707221\pi\) | ||||
−0.605985 | + | 0.795476i | \(0.707221\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.4974i | 1.72655i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −36.0000 | − | 31.1769i | −1.28001 | − | 1.10852i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.0000 | −0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 41.5692i | − | 1.47431i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 17.3205i | − | 0.613524i | −0.951786 | − | 0.306762i | \(-0.900754\pi\) | ||
0.951786 | − | 0.306762i | \(-0.0992455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.92820i | 0.244796i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 24.0000 | 0.846942 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 24.0000 | + | 20.7846i | 0.845889 | + | 0.732561i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.92820i | 0.243884i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 30.0000 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323177\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323177\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.0000 | −0.772524 | −0.386262 | − | 0.922389i | \(-0.626234\pi\) | ||||
−0.386262 | + | 0.922389i | \(0.626234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.0000 | −0.561144 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −60.0000 | −2.10171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.7846i | 0.727161i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 6.00000 | − | 6.92820i | 0.209657 | − | 0.242091i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.46410i | 0.120751i | 0.998176 | + | 0.0603755i | \(0.0192298\pi\) | ||||
−0.998176 | + | 0.0603755i | \(0.980770\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 48.4974i | 1.68846i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 24.2487i | − | 0.843210i | −0.906780 | − | 0.421605i | \(-0.861467\pi\) | ||
0.906780 | − | 0.421605i | \(-0.138533\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 3.46410i | − | 0.120313i | −0.998189 | − | 0.0601566i | \(-0.980840\pi\) | ||
0.998189 | − | 0.0601566i | \(-0.0191600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.00000 | 0.138758 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.5692i | 1.43856i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.0000 | 1.10608 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 12.0000 | 0.413302 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.46410i | 0.119169i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.00000 | − | 1.73205i | −0.0687208 | − | 0.0595140i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.0000 | 0.960958 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.92820i | 0.237496i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.46410i | 0.118609i | 0.998240 | + | 0.0593043i | \(0.0188882\pi\) | ||||
−0.998240 | + | 0.0593043i | \(0.981112\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.92820i | − | 0.236940i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34.6410i | − | 1.18331i | −0.806190 | − | 0.591657i | \(-0.798474\pi\) | ||
0.806190 | − | 0.591657i | \(-0.201526\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0000 | −0.477674 | −0.238837 | − | 0.971060i | \(-0.576766\pi\) | ||||
−0.238837 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.0000 | − | 27.7128i | 0.817918 | − | 0.944450i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.1769i | 1.06127i | 0.847599 | + | 0.530637i | \(0.178047\pi\) | ||||
−0.847599 | + | 0.530637i | \(0.821953\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −34.0000 | −1.15470 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.0000 | −0.407072 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 13.8564i | − | 0.468968i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | − | 13.8564i | 0.405674 | − | 0.468432i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0000 | 1.28317 | 0.641584 | − | 0.767052i | \(-0.278277\pi\) | ||||
0.641584 | + | 0.767052i | \(0.278277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.7846i | 0.701047i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.8564i | − | 0.466834i | −0.972377 | − | 0.233417i | \(-0.925009\pi\) | ||
0.972377 | − | 0.233417i | \(-0.0749907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.46410i | 0.116576i | 0.998300 | + | 0.0582882i | \(0.0185642\pi\) | ||||
−0.998300 | + | 0.0582882i | \(0.981436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 41.5692i | 1.39733i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.0000 | −0.402921 | −0.201460 | − | 0.979497i | \(-0.564569\pi\) | ||||
−0.201460 | + | 0.979497i | \(0.564569\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.0000 | + | 20.7846i | −0.603701 | + | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 38.1051i | − | 1.27657i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 36.0000 | 1.20335 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 24.0000 | 0.801337 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000 | 1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.0000 | + | 41.5692i | −1.19800 | + | 1.38334i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −60.0000 | −1.99447 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 24.2487i | − | 0.805165i | −0.915384 | − | 0.402583i | \(-0.868113\pi\) | ||
0.915384 | − | 0.402583i | \(-0.131887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 10.3923i | − | 0.344691i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3923i | 0.344312i | 0.985070 | + | 0.172156i | \(0.0550734\pi\) | ||||
−0.985070 | + | 0.172156i | \(0.944927\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.7846i | 0.687870i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −24.0000 | −0.793416 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.0000 | − | 31.1769i | −1.18882 | − | 1.02955i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1769i | 1.02843i | 0.857661 | + | 0.514216i | \(0.171917\pi\) | ||||
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.0000 | −1.44985 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 12.0000 | 0.394985 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | 0.460317 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.00000 | −0.131377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 41.5692i | − | 1.36384i | −0.731426 | − | 0.681921i | \(-0.761145\pi\) | ||
0.731426 | − | 0.681921i | \(-0.238855\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.00000 | − | 13.8564i | −0.0655474 | − | 0.454125i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0000 | −0.785725 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 48.4974i | 1.58434i | 0.610299 | + | 0.792171i | \(0.291049\pi\) | ||||
−0.610299 | + | 0.792171i | \(0.708951\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.8564i | 0.452187i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.2487i | 0.790485i | 0.918577 | + | 0.395243i | \(0.129340\pi\) | ||||
−0.918577 | + | 0.395243i | \(0.870660\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | 0.781548 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −24.0000 | + | 27.7128i | −0.780720 | + | 0.901498i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 24.2487i | − | 0.787977i | −0.919115 | − | 0.393989i | \(-0.871095\pi\) | ||
0.919115 | − | 0.393989i | \(-0.128905\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0000 | −0.779073 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 84.0000 | 2.71818 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 41.5692i | − | 1.34374i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.0000 | − | 10.3923i | −0.387500 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 10.3923i | − | 0.334887i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 6.92820i | − | 0.223027i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2487i | 0.779786i | 0.920860 | + | 0.389893i | \(0.127488\pi\) | ||||
−0.920860 | + | 0.389893i | \(0.872512\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | 0.577647 | 0.288824 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288824 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000 | + | 3.46410i | 0.128234 | + | 0.111054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 48.4974i | − | 1.55316i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0000 | −0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 62.3538i | − | 1.98676i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.0000 | −1.14473 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.46410i | 0.110041i | 0.998485 | + | 0.0550204i | \(0.0175224\pi\) | ||||
−0.998485 | + | 0.0550204i | \(0.982478\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 6.92820i | − | 0.219860i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 69.2820i | − | 2.19639i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 51.9615i | − | 1.64564i | −0.568304 | − | 0.822819i | \(-0.692400\pi\) | ||
0.568304 | − | 0.822819i | \(-0.307600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.00000 | −0.253109 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))