Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (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: | \(14.3730723638\) |
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: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.g.901.1 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | −2.00000 | − | 2.00000i | −0.534522 | − | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.00000 | + | 4.00000i | −0.852803 | + | 0.852803i | ||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 4.00000i | − | 0.755929i | ||||||
\(29\) | − | 6.00000i | − | 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0000 | 1.79605 | 0.898027 | − | 0.439941i | \(-0.145001\pi\) | ||||
0.898027 | + | 0.439941i | \(0.145001\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.707107 | − | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.00000 | − | 6.00000i | −1.02899 | − | 1.02899i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 4.00000 | − | 4.00000i | 0.648886 | − | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | −8.00000 | −1.20605 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | − | 4.00000i | −0.589768 | − | 0.589768i | ||||
\(47\) | −4.00000 | −0.583460 | −0.291730 | − | 0.956501i | \(-0.594231\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000i | 1.37361i | 0.726844 | + | 0.686803i | \(0.240986\pi\) | ||||
−0.726844 | + | 0.686803i | \(0.759014\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.00000 | − | 4.00000i | 0.534522 | − | 0.534522i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.00000 | − | 6.00000i | 0.787839 | − | 0.787839i | ||||
\(59\) | 8.00000i | 1.04151i | 0.853706 | + | 0.520756i | \(0.174350\pi\) | ||||
−0.853706 | + | 0.520756i | \(0.825650\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000i | 1.02430i | 0.858898 | + | 0.512148i | \(0.171150\pi\) | ||||
−0.858898 | + | 0.512148i | \(0.828850\pi\) | |||||||
\(62\) | 10.0000 | + | 10.0000i | 1.27000 | + | 1.27000i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 12.0000i | − | 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | − | 12.0000i | − | 1.45521i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.0000 | −1.17041 | −0.585206 | − | 0.810885i | \(-0.698986\pi\) | ||||
−0.585206 | + | 0.810885i | \(0.698986\pi\) | |||||||
\(74\) | −4.00000 | + | 4.00000i | −0.464991 | + | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | − | 8.00000i | − | 0.911685i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.0000 | −1.57512 | −0.787562 | − | 0.616236i | \(-0.788657\pi\) | ||||
−0.787562 | + | 0.616236i | \(0.788657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.0000 | − | 10.0000i | −1.10432 | − | 1.10432i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | − | 4.00000i | 0.431331 | − | 0.431331i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.00000 | − | 8.00000i | −0.852803 | − | 0.852803i | ||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 8.00000i | − | 0.834058i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.00000 | − | 4.00000i | −0.412568 | − | 0.412568i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | −3.00000 | − | 3.00000i | −0.303046 | − | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000i | 1.39305i | 0.717532 | + | 0.696526i | \(0.245272\pi\) | ||||
−0.717532 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.00000 | 0.197066 | 0.0985329 | − | 0.995134i | \(-0.468585\pi\) | ||||
0.0985329 | + | 0.995134i | \(0.468585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0000 | + | 10.0000i | −0.971286 | + | 0.971286i | ||||
\(107\) | − | 4.00000i | − | 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.00000 | 0.755929 | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 12.0000 | 1.11417 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.00000 | + | 8.00000i | −0.736460 | + | 0.736460i | ||||
\(119\) | 12.0000 | 1.10004 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | −8.00000 | + | 8.00000i | −0.724286 | + | 0.724286i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20.0000i | 1.79605i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | 12.0000 | − | 12.0000i | 1.03664 | − | 1.03664i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000 | − | 12.0000i | 1.02899 | − | 1.02899i | ||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.00000 | + | 4.00000i | 0.335673 | + | 0.335673i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0000 | − | 10.0000i | −0.827606 | − | 0.827606i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.00000 | −0.657596 | ||||||||
\(149\) | − | 6.00000i | − | 0.491539i | −0.969328 | − | 0.245770i | \(-0.920959\pi\) | ||
0.969328 | − | 0.245770i | \(-0.0790407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.00000 | −0.162758 | −0.0813788 | − | 0.996683i | \(-0.525932\pi\) | ||||
−0.0813788 | + | 0.996683i | \(0.525932\pi\) | |||||||
\(152\) | 8.00000 | + | 8.00000i | 0.648886 | + | 0.648886i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.00000 | − | 8.00000i | 0.644658 | − | 0.644658i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0000i | 1.59617i | 0.602542 | + | 0.798087i | \(0.294154\pi\) | ||||
−0.602542 | + | 0.798087i | \(0.705846\pi\) | |||||||
\(158\) | −14.0000 | − | 14.0000i | −1.11378 | − | 1.11378i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.00000 | 0.630488 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.0000i | 1.56652i | 0.621694 | + | 0.783260i | \(0.286445\pi\) | ||||
−0.621694 | + | 0.783260i | \(0.713555\pi\) | |||||||
\(164\) | − | 20.0000i | − | 1.56174i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000 | 1.85718 | 0.928588 | − | 0.371113i | \(-0.121024\pi\) | ||||
0.928588 | + | 0.371113i | \(0.121024\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 10.0000i | 0.760286i | 0.924928 | + | 0.380143i | \(0.124125\pi\) | ||||
−0.924928 | + | 0.380143i | \(0.875875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 16.0000i | − | 1.20605i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.0000 | − | 14.0000i | −1.04934 | − | 1.04934i | ||||
\(179\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000i | 1.48659i | 0.668965 | + | 0.743294i | \(0.266738\pi\) | ||||
−0.668965 | + | 0.743294i | \(0.733262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.00000 | − | 8.00000i | 0.589768 | − | 0.589768i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 24.0000i | − | 1.75505i | ||||||
\(188\) | − | 8.00000i | − | 0.583460i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 10.0000 | + | 10.0000i | 0.717958 | + | 0.717958i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 6.00000i | − | 0.428571i | ||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.00000 | −0.425329 | −0.212664 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212664 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.0000 | + | 14.0000i | −0.985037 | + | 0.985037i | ||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.00000 | + | 2.00000i | 0.139347 | + | 0.139347i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | −20.0000 | −1.37361 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.00000 | − | 4.00000i | 0.273434 | − | 0.273434i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.0000 | −1.35769 | ||||||||
\(218\) | 4.00000 | − | 4.00000i | 0.270914 | − | 0.270914i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0000 | −0.669650 | −0.334825 | − | 0.942280i | \(-0.608677\pi\) | ||||
−0.334825 | + | 0.942280i | \(0.608677\pi\) | |||||||
\(224\) | 8.00000 | + | 8.00000i | 0.534522 | + | 0.534522i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | + | 6.00000i | 0.399114 | + | 0.399114i | ||||
\(227\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0000 | + | 12.0000i | 0.787839 | + | 0.787839i | ||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −16.0000 | −1.04151 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.0000 | + | 12.0000i | 0.777844 | + | 0.777844i | ||||
\(239\) | −16.0000 | −1.03495 | −0.517477 | − | 0.855697i | \(-0.673129\pi\) | ||||
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.0000 | −1.93247 | −0.966235 | − | 0.257663i | \(-0.917048\pi\) | ||||
−0.966235 | + | 0.257663i | \(0.917048\pi\) | |||||||
\(242\) | −5.00000 | − | 5.00000i | −0.321412 | − | 0.321412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.0000 | −1.02430 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −20.0000 | + | 20.0000i | −1.27000 | + | 1.27000i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.0000i | − | 1.00591i | ||||||
\(254\) | 6.00000 | + | 6.00000i | 0.376473 | + | 0.376473i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 8.00000i | − | 0.497096i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.00000 | + | 8.00000i | −0.490511 | + | 0.490511i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.0000 | 1.46603 | ||||||||
\(269\) | 10.0000i | 0.609711i | 0.952399 | + | 0.304855i | \(0.0986081\pi\) | ||||
−0.952399 | + | 0.304855i | \(0.901392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00000 | −0.121491 | −0.0607457 | − | 0.998153i | \(-0.519348\pi\) | ||||
−0.0607457 | + | 0.998153i | \(0.519348\pi\) | |||||||
\(272\) | 24.0000 | 1.45521 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | − | 2.00000i | −0.120824 | − | 0.120824i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 16.0000i | − | 0.961347i | −0.876900 | − | 0.480673i | \(-0.840392\pi\) | ||
0.876900 | − | 0.480673i | \(-0.159608\pi\) | |||||||
\(278\) | −4.00000 | + | 4.00000i | −0.239904 | + | 0.239904i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 8.00000i | 0.474713i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0000 | 1.18056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 20.0000i | − | 1.17041i | ||||||
\(293\) | 2.00000i | 0.116841i | 0.998292 | + | 0.0584206i | \(0.0186065\pi\) | ||||
−0.998292 | + | 0.0584206i | \(0.981394\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | − | 8.00000i | −0.464991 | − | 0.464991i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | − | 6.00000i | 0.347571 | − | 0.347571i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.00000i | 0.461112i | ||||||||
\(302\) | −2.00000 | − | 2.00000i | −0.115087 | − | 0.115087i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.0000i | 0.917663i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.0000i | 1.59804i | 0.601302 | + | 0.799022i | \(0.294649\pi\) | ||||
−0.601302 | + | 0.799022i | \(0.705351\pi\) | |||||||
\(308\) | 16.0000 | 0.911685 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.00000 | −0.339140 | −0.169570 | − | 0.985518i | \(-0.554238\pi\) | ||||
−0.169570 | + | 0.985518i | \(0.554238\pi\) | |||||||
\(314\) | −20.0000 | + | 20.0000i | −1.12867 | + | 1.12867i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 28.0000i | − | 1.57512i | ||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.00000 | + | 8.00000i | 0.445823 | + | 0.445823i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −20.0000 | + | 20.0000i | −1.10770 | + | 1.10770i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 20.0000 | − | 20.0000i | 1.10432 | − | 1.10432i | ||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.00000i | − | 0.219860i | −0.993939 | − | 0.109930i | \(-0.964937\pi\) | ||
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 24.0000 | + | 24.0000i | 1.31322 | + | 1.31322i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −30.0000 | −1.63420 | −0.817102 | − | 0.576493i | \(-0.804421\pi\) | ||||
−0.817102 | + | 0.576493i | \(0.804421\pi\) | |||||||
\(338\) | 13.0000 | + | 13.0000i | 0.707107 | + | 0.707107i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0000i | 2.16612i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 8.00000 | + | 8.00000i | 0.431331 | + | 0.431331i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | + | 10.0000i | −0.537603 | + | 0.537603i | ||||
\(347\) | − | 16.0000i | − | 0.858925i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.00000i | − | 0.428230i | −0.976808 | − | 0.214115i | \(-0.931313\pi\) | ||
0.976808 | − | 0.214115i | \(-0.0686868\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | − | 16.0000i | 0.852803 | − | 0.852803i | ||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 28.0000i | − | 1.48400i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | −20.0000 | + | 20.0000i | −1.05118 | + | 1.05118i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | 16.0000 | 0.834058 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20.0000i | − | 1.03835i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.0000i | 1.03556i | 0.855514 | + | 0.517780i | \(0.173242\pi\) | ||||
−0.855514 | + | 0.517780i | \(0.826758\pi\) | |||||||
\(374\) | 24.0000 | − | 24.0000i | 1.24101 | − | 1.24101i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00000 | − | 8.00000i | 0.412568 | − | 0.412568i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.0000i | 1.84920i | 0.380945 | + | 0.924598i | \(0.375599\pi\) | ||||
−0.380945 | + | 0.924598i | \(0.624401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.00000 | + | 8.00000i | 0.409316 | + | 0.409316i | ||||
\(383\) | 24.0000 | 1.22634 | 0.613171 | − | 0.789950i | \(-0.289894\pi\) | ||||
0.613171 | + | 0.789950i | \(0.289894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0000 | + | 14.0000i | 0.712581 | + | 0.712581i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 20.0000i | 1.01535i | ||||||||
\(389\) | 10.0000i | 0.507020i | 0.967333 | + | 0.253510i | \(0.0815851\pi\) | ||||
−0.967333 | + | 0.253510i | \(0.918415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | 6.00000 | − | 6.00000i | 0.303046 | − | 0.303046i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.0000 | + | 10.0000i | −0.503793 | + | 0.503793i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0000i | 1.00377i | 0.864934 | + | 0.501886i | \(0.167360\pi\) | ||||
−0.864934 | + | 0.501886i | \(0.832640\pi\) | |||||||
\(398\) | −6.00000 | − | 6.00000i | −0.300753 | − | 0.300753i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −30.0000 | −1.49813 | −0.749064 | − | 0.662497i | \(-0.769497\pi\) | ||||
−0.749064 | + | 0.662497i | \(0.769497\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −28.0000 | −1.39305 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | + | 12.0000i | −0.595550 | + | 0.595550i | ||||
\(407\) | −16.0000 | −0.793091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.00000i | 0.197066i | ||||||||
\(413\) | − | 16.0000i | − | 0.787309i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 16.0000 | + | 16.0000i | 0.782586 | + | 0.782586i | ||||
\(419\) | − | 4.00000i | − | 0.195413i | −0.995215 | − | 0.0977064i | \(-0.968849\pi\) | ||
0.995215 | − | 0.0977064i | \(-0.0311506\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 20.0000i | − | 0.974740i | −0.873195 | − | 0.487370i | \(-0.837956\pi\) | ||
0.873195 | − | 0.487370i | \(-0.162044\pi\) | |||||||
\(422\) | 12.0000 | − | 12.0000i | 0.584151 | − | 0.584151i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.0000 | − | 20.0000i | −0.971286 | − | 0.971286i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 16.0000i | − | 0.774294i | ||||||
\(428\) | 8.00000 | 0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 36.0000 | 1.73406 | 0.867029 | − | 0.498257i | \(-0.166026\pi\) | ||||
0.867029 | + | 0.498257i | \(0.166026\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | −20.0000 | − | 20.0000i | −0.960031 | − | 0.960031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 16.0000i | 0.765384i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00000 | 0.0954548 | 0.0477274 | − | 0.998860i | \(-0.484802\pi\) | ||||
0.0477274 | + | 0.998860i | \(0.484802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.0000i | − | 0.760183i | −0.924949 | − | 0.380091i | \(-0.875893\pi\) | ||
0.924949 | − | 0.380091i | \(-0.124107\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.0000 | − | 10.0000i | −0.473514 | − | 0.473514i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.0000i | 0.755929i | ||||||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 40.0000i | − | 1.88353i | ||||||
\(452\) | 12.0000i | 0.564433i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.0000 | −0.842004 | −0.421002 | − | 0.907060i | \(-0.638322\pi\) | ||||
−0.421002 | + | 0.907060i | \(0.638322\pi\) | |||||||
\(458\) | −4.00000 | + | 4.00000i | −0.186908 | + | 0.186908i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 34.0000i | − | 1.58354i | −0.610821 | − | 0.791769i | \(-0.709160\pi\) | ||
0.610821 | − | 0.791769i | \(-0.290840\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.0000 | 1.02243 | 0.511213 | − | 0.859454i | \(-0.329196\pi\) | ||||
0.511213 | + | 0.859454i | \(0.329196\pi\) | |||||||
\(464\) | 24.0000i | 1.11417i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | − | 6.00000i | −0.277945 | − | 0.277945i | ||||
\(467\) | 8.00000i | 0.370196i | 0.982720 | + | 0.185098i | \(0.0592602\pi\) | ||||
−0.982720 | + | 0.185098i | \(0.940740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.0000 | − | 16.0000i | −0.736460 | − | 0.736460i | ||||
\(473\) | 16.0000 | 0.735681 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.0000i | 1.10004i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −16.0000 | − | 16.0000i | −0.731823 | − | 0.731823i | ||||
\(479\) | −4.00000 | −0.182765 | −0.0913823 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913823 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −30.0000 | − | 30.0000i | −1.36646 | − | 1.36646i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 10.0000i | − | 0.454545i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.0000 | 1.35943 | 0.679715 | − | 0.733476i | \(-0.262104\pi\) | ||||
0.679715 | + | 0.733476i | \(0.262104\pi\) | |||||||
\(488\) | −16.0000 | − | 16.0000i | −0.724286 | − | 0.724286i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.0000i | − | 1.80517i | −0.430507 | − | 0.902587i | \(-0.641665\pi\) | ||
0.430507 | − | 0.902587i | \(-0.358335\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 36.0000i | 1.62136i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −40.0000 | −1.79605 | ||||||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | + | 12.0000i | −0.535586 | + | 0.535586i | ||||
\(503\) | −12.0000 | −0.535054 | −0.267527 | − | 0.963550i | \(-0.586206\pi\) | ||||
−0.267527 | + | 0.963550i | \(0.586206\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.0000 | − | 16.0000i | 0.711287 | − | 0.711287i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.0000i | 0.532414i | ||||||||
\(509\) | 18.0000i | 0.797836i | 0.916987 | + | 0.398918i | \(0.130614\pi\) | ||||
−0.916987 | + | 0.398918i | \(0.869386\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | 0.884748 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.00000 | − | 2.00000i | −0.0882162 | − | 0.0882162i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 16.0000i | − | 0.703679i | ||||||
\(518\) | 8.00000 | − | 8.00000i | 0.351500 | − | 0.351500i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.0000i | − | 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −60.0000 | −2.61364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.0000 | −0.693688 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 24.0000 | + | 24.0000i | 1.03664 | + | 1.03664i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.0000 | + | 10.0000i | −0.431131 | + | 0.431131i | ||||
\(539\) | − | 12.0000i | − | 0.516877i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 44.0000i | 1.89171i | 0.324593 | + | 0.945854i | \(0.394773\pi\) | ||||
−0.324593 | + | 0.945854i | \(0.605227\pi\) | |||||||
\(542\) | −2.00000 | − | 2.00000i | −0.0859074 | − | 0.0859074i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.0000 | + | 24.0000i | 1.02899 | + | 1.02899i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.00000i | − | 0.171028i | −0.996337 | − | 0.0855138i | \(-0.972747\pi\) | ||
0.996337 | − | 0.0855138i | \(-0.0272532\pi\) | |||||||
\(548\) | − | 4.00000i | − | 0.170872i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.0000 | −1.02243 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | 1.19068 | ||||||||
\(554\) | 16.0000 | − | 16.0000i | 0.679775 | − | 0.679775i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | 42.0000i | 1.77960i | 0.456354 | + | 0.889799i | \(0.349155\pi\) | ||||
−0.456354 | + | 0.889799i | \(0.650845\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.0000 | + | 10.0000i | 0.421825 | + | 0.421825i | ||||
\(563\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 4.00000 | − | 4.00000i | 0.168133 | − | 0.168133i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.00000 | + | 8.00000i | −0.335673 | + | 0.335673i | ||||
\(569\) | −2.00000 | −0.0838444 | −0.0419222 | − | 0.999121i | \(-0.513348\pi\) | ||||
−0.0419222 | + | 0.999121i | \(0.513348\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000i | 0.836974i | 0.908223 | + | 0.418487i | \(0.137439\pi\) | ||||
−0.908223 | + | 0.418487i | \(0.862561\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 20.0000 | + | 20.0000i | 0.834784 | + | 0.834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 19.0000 | + | 19.0000i | 0.790296 | + | 0.790296i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −40.0000 | −1.65663 | ||||||||
\(584\) | 20.0000 | − | 20.0000i | 0.827606 | − | 0.827606i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.00000 | + | 2.00000i | −0.0826192 | + | 0.0826192i | ||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 40.0000i | − | 1.64817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 16.0000i | − | 0.657596i | ||||||
\(593\) | 22.0000 | 0.903432 | 0.451716 | − | 0.892162i | \(-0.350812\pi\) | ||||
0.451716 | + | 0.892162i | \(0.350812\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.0000 | −0.490307 | −0.245153 | − | 0.969484i | \(-0.578838\pi\) | ||||
−0.245153 | + | 0.969484i | \(0.578838\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −14.0000 | −0.571072 | −0.285536 | − | 0.958368i | \(-0.592172\pi\) | ||||
−0.285536 | + | 0.958368i | \(0.592172\pi\) | |||||||
\(602\) | −8.00000 | + | 8.00000i | −0.326056 | + | 0.326056i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 4.00000i | − | 0.162758i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.00000 | −0.0811775 | −0.0405887 | − | 0.999176i | \(-0.512923\pi\) | ||||
−0.0405887 | + | 0.999176i | \(0.512923\pi\) | |||||||
\(608\) | −16.0000 | + | 16.0000i | −0.648886 | + | 0.648886i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 20.0000i | − | 0.807792i | −0.914805 | − | 0.403896i | \(-0.867656\pi\) | ||
0.914805 | − | 0.403896i | \(-0.132344\pi\) | |||||||
\(614\) | −28.0000 | + | 28.0000i | −1.12999 | + | 1.12999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.0000 | + | 16.0000i | 0.644658 | + | 0.644658i | ||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 20.0000i | − | 0.803868i | −0.915669 | − | 0.401934i | \(-0.868338\pi\) | ||
0.915669 | − | 0.401934i | \(-0.131662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.00000 | − | 8.00000i | −0.320771 | − | 0.320771i | ||||
\(623\) | 28.0000 | 1.12180 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.00000 | − | 6.00000i | −0.239808 | − | 0.239808i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.0000 | −1.59617 | ||||||||
\(629\) | − | 24.0000i | − | 0.956943i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | 28.0000 | − | 28.0000i | 1.11378 | − | 1.11378i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.0000 | − | 18.0000i | 0.714871 | − | 0.714871i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 24.0000 | + | 24.0000i | 0.950169 | + | 0.950169i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.0000 | −0.552967 | −0.276483 | − | 0.961019i | \(-0.589169\pi\) | ||||
−0.276483 | + | 0.961019i | \(0.589169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.0000i | − | 0.473234i | −0.971603 | − | 0.236617i | \(-0.923961\pi\) | ||
0.971603 | − | 0.236617i | \(-0.0760386\pi\) | |||||||
\(644\) | 16.0000i | 0.630488i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0000 | + | 24.0000i | −0.944267 | + | 0.944267i | ||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −40.0000 | −1.56652 | ||||||||
\(653\) | − | 30.0000i | − | 1.17399i | −0.809590 | − | 0.586995i | \(-0.800311\pi\) | ||
0.809590 | − | 0.586995i | \(-0.199689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 40.0000 | 1.56174 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.00000 | + | 8.00000i | 0.311872 | + | 0.311872i | ||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 32.0000i | − | 1.24466i | −0.782757 | − | 0.622328i | \(-0.786187\pi\) | ||
0.782757 | − | 0.622328i | \(-0.213813\pi\) | |||||||
\(662\) | 4.00000 | − | 4.00000i | 0.155464 | − | 0.155464i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.0000i | 0.929284i | ||||||||
\(668\) | 48.0000i | 1.85718i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32.0000 | −1.23535 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | −30.0000 | − | 30.0000i | −1.15556 | − | 1.15556i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.0000i | 1.00000i | ||||||||
\(677\) | 38.0000i | 1.46046i | 0.683202 | + | 0.730229i | \(0.260587\pi\) | ||||
−0.683202 | + | 0.730229i | \(0.739413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.0000 | −0.767530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −40.0000 | + | 40.0000i | −1.53168 | + | 1.53168i | ||||
\(683\) | − | 48.0000i | − | 1.83667i | −0.395805 | − | 0.918334i | \(-0.629534\pi\) | ||
0.395805 | − | 0.918334i | \(-0.370466\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0000 | + | 20.0000i | 0.763604 | + | 0.763604i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.0000i | 0.609994i | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.0000i | − | 0.456502i | −0.973602 | − | 0.228251i | \(-0.926699\pi\) | ||
0.973602 | − | 0.228251i | \(-0.0733006\pi\) | |||||||
\(692\) | −20.0000 | −0.760286 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0000 | − | 16.0000i | 0.607352 | − | 0.607352i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 60.0000 | 2.27266 | ||||||||
\(698\) | 8.00000 | − | 8.00000i | 0.302804 | − | 0.302804i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 22.0000i | − | 0.830929i | −0.909610 | − | 0.415464i | \(-0.863619\pi\) | ||
0.909610 | − | 0.415464i | \(-0.136381\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | 0.603451 | ||||||||
\(704\) | 32.0000 | 1.20605 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | − | 18.0000i | −0.677439 | − | 0.677439i | ||||
\(707\) | − | 28.0000i | − | 1.05305i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 44.0000i | − | 1.65245i | −0.563337 | − | 0.826227i | \(-0.690483\pi\) | ||
0.563337 | − | 0.826227i | \(-0.309517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 28.0000 | − | 28.0000i | 1.04934 | − | 1.04934i | ||||
\(713\) | −40.0000 | −1.49801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12.0000 | − | 12.0000i | −0.447836 | − | 0.447836i | ||||
\(719\) | 36.0000 | 1.34257 | 0.671287 | − | 0.741198i | \(-0.265742\pi\) | ||||
0.671287 | + | 0.741198i | \(0.265742\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | 3.00000 | + | 3.00000i | 0.111648 | + | 0.111648i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −40.0000 | −1.48659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000i | 0.887672i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 24.0000i | − | 0.886460i | −0.896408 | − | 0.443230i | \(-0.853832\pi\) | ||
0.896408 | − | 0.443230i | \(-0.146168\pi\) | |||||||
\(734\) | 18.0000 | + | 18.0000i | 0.664392 | + | 0.664392i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | + | 16.0000i | 0.589768 | + | 0.589768i | ||||
\(737\) | 48.0000 | 1.76810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.0000i | − | 0.441427i | −0.975339 | − | 0.220714i | \(-0.929161\pi\) | ||
0.975339 | − | 0.220714i | \(-0.0708386\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.0000 | − | 20.0000i | 0.734223 | − | 0.734223i | ||||
\(743\) | −48.0000 | −1.76095 | −0.880475 | − | 0.474093i | \(-0.842776\pi\) | ||||
−0.880475 | + | 0.474093i | \(0.842776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.0000 | + | 20.0000i | −0.732252 | + | 0.732252i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 48.0000 | 1.75505 | ||||||||
\(749\) | 8.00000i | 0.292314i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0000 | 0.948753 | 0.474377 | − | 0.880322i | \(-0.342673\pi\) | ||||
0.474377 | + | 0.880322i | \(0.342673\pi\) | |||||||
\(752\) | 16.0000 | 0.583460 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.00000i | − | 0.290765i | −0.989376 | − | 0.145382i | \(-0.953559\pi\) | ||
0.989376 | − | 0.145382i | \(-0.0464413\pi\) | |||||||
\(758\) | −36.0000 | + | 36.0000i | −1.30758 | + | 1.30758i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.0000 | −0.362500 | −0.181250 | − | 0.983437i | \(-0.558014\pi\) | ||||
−0.181250 | + | 0.983437i | \(0.558014\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000i | 0.289619i | ||||||||
\(764\) | 16.0000i | 0.578860i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | + | 24.0000i | 0.867155 | + | 0.867155i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.0000i | 1.00774i | ||||||||
\(773\) | − | 6.00000i | − | 0.215805i | −0.994161 | − | 0.107903i | \(-0.965587\pi\) | ||
0.994161 | − | 0.107903i | \(-0.0344134\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −20.0000 | + | 20.0000i | −0.717958 | + | 0.717958i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.0000 | + | 10.0000i | −0.358517 | + | 0.358517i | ||||
\(779\) | 40.0000i | 1.43315i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000i | 0.572525i | ||||||||
\(782\) | 24.0000 | + | 24.0000i | 0.858238 | + | 0.858238i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000i | 0.998092i | 0.866575 | + | 0.499046i | \(0.166316\pi\) | ||||
−0.866575 | + | 0.499046i | \(0.833684\pi\) | |||||||
\(788\) | −20.0000 | −0.712470 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −20.0000 | + | 20.0000i | −0.709773 | + | 0.709773i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 12.0000i | − | 0.425329i | ||||||
\(797\) | − | 30.0000i | − | 1.06265i | −0.847167 | − | 0.531327i | \(-0.821693\pi\) | ||
0.847167 | − | 0.531327i | \(-0.178307\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −30.0000 | − | 30.0000i | −1.05934 | − | 1.05934i | ||||
\(803\) | − | 40.0000i | − | 1.41157i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.0000 | − | 28.0000i | −0.985037 | − | 0.985037i | ||||
\(809\) | −10.0000 | −0.351581 | −0.175791 | − | 0.984428i | \(-0.556248\pi\) | ||||
−0.175791 | + | 0.984428i | \(0.556248\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000i | 0.140459i | 0.997531 | + | 0.0702295i | \(0.0223732\pi\) | ||||
−0.997531 | + | 0.0702295i | \(0.977627\pi\) | |||||||
\(812\) | −24.0000 | −0.842235 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.0000 | − | 16.0000i | −0.560800 | − | 0.560800i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.0000 | −0.559769 | ||||||||
\(818\) | −6.00000 | − | 6.00000i | −0.209785 | − | 0.209785i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 10.0000i | − | 0.349002i | −0.984657 | − | 0.174501i | \(-0.944169\pi\) | ||
0.984657 | − | 0.174501i | \(-0.0558313\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.0000 | −1.46403 | −0.732014 | − | 0.681290i | \(-0.761419\pi\) | ||||
−0.732014 | + | 0.681290i | \(0.761419\pi\) | |||||||
\(824\) | −4.00000 | + | 4.00000i | −0.139347 | + | 0.139347i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0000 | − | 16.0000i | 0.556711 | − | 0.556711i | ||||
\(827\) | 4.00000i | 0.139094i | 0.997579 | + | 0.0695468i | \(0.0221553\pi\) | ||||
−0.997579 | + | 0.0695468i | \(0.977845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0000i | 1.52818i | 0.645108 | + | 0.764092i | \(0.276812\pi\) | ||||
−0.645108 | + | 0.764092i | \(0.723188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000 | 0.623663 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.0000i | 1.10674i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.00000 | − | 4.00000i | 0.138178 | − | 0.138178i | ||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 20.0000 | − | 20.0000i | 0.689246 | − | 0.689246i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 24.0000 | 0.826114 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | − | 40.0000i | − | 1.37361i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.0000i | − | 0.548473i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.0000i | − | 1.50653i | −0.657716 | − | 0.753266i | \(-0.728477\pi\) | ||
0.657716 | − | 0.753266i | \(-0.271523\pi\) | |||||||
\(854\) | 16.0000 | − | 16.0000i | 0.547509 | − | 0.547509i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | + | 8.00000i | 0.273434 | + | 0.273434i | ||||
\(857\) | 6.00000 | 0.204956 | 0.102478 | − | 0.994735i | \(-0.467323\pi\) | ||||
0.102478 | + | 0.994735i | \(0.467323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 36.0000 | + | 36.0000i | 1.22616 | + | 1.22616i | ||||
\(863\) | 24.0000 | 0.816970 | 0.408485 | − | 0.912765i | \(-0.366057\pi\) | ||||
0.408485 | + | 0.912765i | \(0.366057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.0000 | − | 14.0000i | −0.475739 | − | 0.475739i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 40.0000i | − | 1.35769i | ||||||
\(869\) | − | 56.0000i | − | 1.89967i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.00000 | + | 8.00000i | 0.270914 | + | 0.270914i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −16.0000 | + | 16.0000i | −0.541208 | + | 0.541208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.0000i | 1.48577i | 0.669417 | + | 0.742887i | \(0.266544\pi\) | ||||
−0.669417 | + | 0.742887i | \(0.733456\pi\) | |||||||
\(878\) | 2.00000 | + | 2.00000i | 0.0674967 | + | 0.0674967i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.00000 | 0.202145 | 0.101073 | − | 0.994879i | \(-0.467773\pi\) | ||||
0.101073 | + | 0.994879i | \(0.467773\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.0000i | − | 0.942275i | −0.882060 | − | 0.471138i | \(-0.843844\pi\) | ||
0.882060 | − | 0.471138i | \(-0.156156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0000 | − | 16.0000i | 0.537531 | − | 0.537531i | ||||
\(887\) | 16.0000 | 0.537227 | 0.268614 | − | 0.963248i | \(-0.413434\pi\) | ||||
0.268614 | + | 0.963248i | \(0.413434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 20.0000i | − | 0.669650i | ||||||
\(893\) | 16.0000i | 0.535420i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.0000 | + | 16.0000i | −0.534522 | + | 0.534522i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | + | 18.0000i | 0.600668 | + | 0.600668i | ||||
\(899\) | − | 60.0000i | − | 2.00111i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 60.0000i | − | 1.99889i | ||||||
\(902\) | 40.0000 | − | 40.0000i | 1.33185 | − | 1.33185i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.0000 | + | 12.0000i | −0.399114 | + | 0.399114i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52.0000i | − | 1.72663i | −0.504664 | − | 0.863316i | \(-0.668384\pi\) | ||
0.504664 | − | 0.863316i | \(-0.331616\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −18.0000 | − | 18.0000i | −0.595387 | − | 0.595387i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.00000 | −0.264327 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 34.0000 | − | 34.0000i | 1.11973 | − | 1.11973i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 22.0000 | + | 22.0000i | 0.722965 | + | 0.722965i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −24.0000 | + | 24.0000i | −0.787839 | + | 0.787839i | ||||
\(929\) | −46.0000 | −1.50921 | −0.754606 | − | 0.656179i | \(-0.772172\pi\) | ||||
−0.754606 | + | 0.656179i | \(0.772172\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.0000i | 0.393284i | ||||||||
\(932\) | − | 12.0000i | − | 0.393073i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.00000 | + | 8.00000i | −0.261768 | + | 0.261768i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.0000 | −0.718709 | −0.359354 | − | 0.933201i | \(-0.617003\pi\) | ||||
−0.359354 | + | 0.933201i | \(0.617003\pi\) | |||||||
\(938\) | −24.0000 | + | 24.0000i | −0.783628 | + | 0.783628i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.0000i | − | 0.847576i | −0.905761 | − | 0.423788i | \(-0.860700\pi\) | ||
0.905761 | − | 0.423788i | \(-0.139300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0000 | 1.30258 | ||||||||
\(944\) | − | 32.0000i | − | 1.04151i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | + | 16.0000i | 0.520205 | + | 0.520205i | ||||
\(947\) | 36.0000i | 1.16984i | 0.811090 | + | 0.584921i | \(0.198875\pi\) | ||||
−0.811090 | + | 0.584921i | \(0.801125\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −24.0000 | + | 24.0000i | −0.777844 | + | 0.777844i | ||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 32.0000i | − | 1.03495i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.00000 | − | 4.00000i | −0.129234 | − | 0.129234i | ||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 60.0000i | − | 1.93247i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0000 | −1.47926 | −0.739630 | − | 0.673014i | \(-0.765000\pi\) | ||||
−0.739630 | + | 0.673014i | \(0.765000\pi\) | |||||||
\(968\) | 10.0000 | − | 10.0000i | 0.321412 | − | 0.321412i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.00000i | − | 0.256468i | ||||||
\(974\) | 30.0000 | + | 30.0000i | 0.961262 | + | 0.961262i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 32.0000i | − | 1.02430i | ||||||
\(977\) | −22.0000 | −0.703842 | −0.351921 | − | 0.936030i | \(-0.614471\pi\) | ||||
−0.351921 | + | 0.936030i | \(0.614471\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 56.0000i | − | 1.78977i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40.0000 | − | 40.0000i | 1.27645 | − | 1.27645i | ||||
\(983\) | −32.0000 | −1.02064 | −0.510321 | − | 0.859984i | \(-0.670473\pi\) | ||||
−0.510321 | + | 0.859984i | \(0.670473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −36.0000 | + | 36.0000i | −1.14647 | + | 1.14647i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.0000i | 0.508770i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | −40.0000 | − | 40.0000i | −1.27000 | − | 1.27000i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.00000 | − | 8.00000i | −0.253745 | − | 0.253745i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 28.0000i | − | 0.886769i | −0.896332 | − | 0.443384i | \(-0.853778\pi\) | ||
0.896332 | − | 0.443384i | \(-0.146222\pi\) | |||||||
\(998\) | −20.0000 | + | 20.0000i | −0.633089 | + | 0.633089i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))