Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(301,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, 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("600.301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.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: | \(4.79102412128\) |
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 | 301.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.301 |
Dual form | 600.2.k.a.301.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | + | 1.00000i | 0.408248 | + | 0.408248i | ||||
\(7\) | −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 | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.00000i | 1.20605i | 0.797724 | + | 0.603023i | \(0.206037\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(12\) | −2.00000 | −0.577350 | ||||||||
\(13\) | 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 | \(-0.240633\pi\) | ||||
0.727607 | + | 0.685994i | \(0.240633\pi\) | |||||||
\(18\) | 1.00000 | − | 1.00000i | 0.235702 | − | 0.235702i | ||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | −4.00000 | − | 4.00000i | −0.852803 | − | 0.852803i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 2.00000 | − | 2.00000i | 0.408248 | − | 0.408248i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 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 | ||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | −6.00000 | + | 6.00000i | −1.02899 | + | 1.02899i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00000i | 0.333333i | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | −4.00000 | − | 4.00000i | −0.648886 | − | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0000 | 1.56174 | 0.780869 | − | 0.624695i | \(-0.214777\pi\) | ||||
0.780869 | + | 0.624695i | \(0.214777\pi\) | |||||||
\(42\) | −2.00000 | − | 2.00000i | −0.308607 | − | 0.308607i | ||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 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 | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | 4.00000i | 0.577350i | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.00000i | − | 0.840168i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.0000i | 1.37361i | 0.726844 | + | 0.686803i | \(0.240986\pi\) | ||||
−0.726844 | + | 0.686803i | \(0.759014\pi\) | |||||||
\(54\) | −1.00000 | − | 1.00000i | −0.136083 | − | 0.136083i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.00000 | − | 4.00000i | −0.534522 | − | 0.534522i | ||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 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 | \(-0.828850\pi\) | ||
0.858898 | − | 0.512148i | \(-0.171150\pi\) | |||||||
\(62\) | −10.0000 | + | 10.0000i | −1.27000 | + | 1.27000i | ||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | + | 4.00000i | −0.492366 | + | 0.492366i | ||||
\(67\) | 12.0000i | 1.46603i | 0.680211 | + | 0.733017i | \(0.261888\pi\) | ||||
−0.680211 | + | 0.733017i | \(0.738112\pi\) | |||||||
\(68\) | − | 12.0000i | − | 1.45521i | ||||||
\(69\) | − | 4.00000i | − | 0.481543i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.00000 | −0.474713 | −0.237356 | − | 0.971423i | \(-0.576281\pi\) | ||||
−0.237356 | + | 0.971423i | \(0.576281\pi\) | |||||||
\(72\) | −2.00000 | − | 2.00000i | −0.235702 | − | 0.235702i | ||||
\(73\) | −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 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −10.0000 | + | 10.0000i | −1.10432 | + | 1.10432i | ||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 4.00000 | 0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 4.00000i | −0.431331 | − | 0.431331i | ||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | −8.00000 | + | 8.00000i | −0.852803 | + | 0.852803i | ||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 8.00000i | − | 0.834058i | ||||||
\(93\) | − | 10.0000i | − | 1.03695i | ||||||
\(94\) | −4.00000 | + | 4.00000i | −0.412568 | + | 0.412568i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.00000 | − | 4.00000i | −0.408248 | − | 0.408248i | ||||
\(97\) | 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 | ||||
\(99\) | − | 4.00000i | − | 0.402015i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.0000i | 1.39305i | 0.717532 | + | 0.696526i | \(0.245272\pi\) | ||||
−0.717532 | + | 0.696526i | \(0.754728\pi\) | |||||||
\(102\) | 6.00000 | + | 6.00000i | 0.594089 | + | 0.594089i | ||||
\(103\) | 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 | \(-0.0619344\pi\) | |||||||
\(108\) | 2.00000 | 0.192450 | ||||||||
\(109\) | 4.00000i | 0.383131i | 0.981480 | + | 0.191565i | \(0.0613564\pi\) | ||||
−0.981480 | + | 0.191565i | \(0.938644\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 8.00000 | 0.755929 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | −4.00000 | + | 4.00000i | −0.374634 | + | 0.374634i | ||||
\(115\) | 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 | ||||
\(123\) | − | 10.0000i | − | 0.901670i | ||||||
\(124\) | − | 20.0000i | − | 1.79605i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | + | 2.00000i | −0.178174 | + | 0.178174i | ||||
\(127\) | 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 | ||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | − | 8.00000i | − | 0.696311i | ||||||
\(133\) | − | 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 | \(-0.472772\pi\) | ||||
0.0854358 | + | 0.996344i | \(0.472772\pi\) | |||||||
\(138\) | 4.00000 | + | 4.00000i | 0.340503 | + | 0.340503i | ||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 4.00000i | − | 0.336861i | ||||||
\(142\) | 4.00000 | − | 4.00000i | 0.335673 | − | 0.335673i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 4.00000 | 0.333333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | − | 10.0000i | 0.827606 | − | 0.827606i | ||||
\(147\) | 3.00000i | 0.247436i | ||||||||
\(148\) | −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 | ||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 8.00000 | + | 8.00000i | 0.644658 | + | 0.644658i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.0000i | − | 1.59617i | −0.602542 | − | 0.798087i | \(-0.705846\pi\) | ||
0.602542 | − | 0.798087i | \(-0.294154\pi\) | |||||||
\(158\) | 14.0000 | − | 14.0000i | 1.11378 | − | 1.11378i | ||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.00000 | −0.630488 | ||||||||
\(162\) | −1.00000 | + | 1.00000i | −0.0785674 | + | 0.0785674i | ||||
\(163\) | − | 20.0000i | − | 1.56652i | −0.621694 | − | 0.783260i | \(-0.713555\pi\) | ||
0.621694 | − | 0.783260i | \(-0.286445\pi\) | |||||||
\(164\) | − | 20.0000i | − | 1.56174i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.0000 | −1.85718 | −0.928588 | − | 0.371113i | \(-0.878976\pi\) | ||||
−0.928588 | + | 0.371113i | \(0.878976\pi\) | |||||||
\(168\) | −4.00000 | + | 4.00000i | −0.308607 | + | 0.308607i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.00000i | − | 0.305888i | ||||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 10.0000i | 0.760286i | 0.924928 | + | 0.380143i | \(0.124125\pi\) | ||||
−0.924928 | + | 0.380143i | \(0.875875\pi\) | |||||||
\(174\) | 6.00000 | − | 6.00000i | 0.454859 | − | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 16.0000i | − | 1.20605i | ||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | −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 | \(-0.733262\pi\) | ||
0.668965 | − | 0.743294i | \(-0.266738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.00000 | −0.591377 | ||||||||
\(184\) | 8.00000 | + | 8.00000i | 0.589768 | + | 0.589768i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.0000 | + | 10.0000i | 0.733236 | + | 0.733236i | ||||
\(187\) | 24.0000i | 1.75505i | ||||||||
\(188\) | − | 8.00000i | − | 0.583460i | ||||||
\(189\) | − | 2.00000i | − | 0.145479i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | 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 | \(0.884060\pi\) | |||||||
\(198\) | 4.00000 | + | 4.00000i | 0.284268 | + | 0.284268i | ||||
\(199\) | −6.00000 | −0.425329 | −0.212664 | − | 0.977125i | \(-0.568214\pi\) | ||||
−0.212664 | + | 0.977125i | \(0.568214\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | −14.0000 | − | 14.0000i | −0.985037 | − | 0.985037i | ||||
\(203\) | 12.0000i | 0.842235i | ||||||||
\(204\) | −12.0000 | −0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | + | 2.00000i | −0.139347 | + | 0.139347i | ||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000i | 0.826114i | 0.910705 | + | 0.413057i | \(0.135539\pi\) | ||||
−0.910705 | + | 0.413057i | \(0.864461\pi\) | |||||||
\(212\) | 20.0000 | 1.37361 | ||||||||
\(213\) | 4.00000i | 0.274075i | ||||||||
\(214\) | 4.00000 | + | 4.00000i | 0.273434 | + | 0.273434i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.00000 | + | 2.00000i | −0.136083 | + | 0.136083i | ||||
\(217\) | −20.0000 | −1.35769 | ||||||||
\(218\) | −4.00000 | − | 4.00000i | −0.270914 | − | 0.270914i | ||||
\(219\) | 10.0000i | 0.675737i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.00000 | − | 4.00000i | 0.268462 | − | 0.268462i | ||||
\(223\) | −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 | \(\pi\) | |||||||||
\(228\) | − | 8.00000i | − | 0.529813i | ||||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | 12.0000 | − | 12.0000i | 0.787839 | − | 0.787839i | ||||
\(233\) | 6.00000 | 0.393073 | 0.196537 | − | 0.980497i | \(-0.437031\pi\) | ||||
0.196537 | + | 0.980497i | \(0.437031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.0000 | 1.04151 | ||||||||
\(237\) | 14.0000i | 0.909398i | ||||||||
\(238\) | 12.0000 | − | 12.0000i | 0.777844 | − | 0.777844i | ||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 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 | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −16.0000 | −1.02430 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.0000 | + | 10.0000i | 0.637577 | + | 0.637577i | ||||
\(247\) | 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 | \(0.876365\pi\) | |||||||
\(252\) | − | 4.00000i | − | 0.251976i | ||||||
\(253\) | 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 | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | −4.00000 | + | 4.00000i | −0.249029 | + | 0.249029i | ||||
\(259\) | 8.00000i | 0.497096i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000i | 0.371391i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 8.00000 | + | 8.00000i | 0.492366 | + | 0.492366i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 8.00000i | 0.490511 | + | 0.490511i | ||||
\(267\) | − | 14.0000i | − | 0.856786i | ||||||
\(268\) | 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 | ||||||||
\(276\) | −8.00000 | −0.481543 | ||||||||
\(277\) | 16.0000i | 0.961347i | 0.876900 | + | 0.480673i | \(0.159608\pi\) | ||||
−0.876900 | + | 0.480673i | \(0.840392\pi\) | |||||||
\(278\) | 4.00000 | + | 4.00000i | 0.239904 | + | 0.239904i | ||||
\(279\) | −10.0000 | −0.598684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 4.00000 | + | 4.00000i | 0.238197 | + | 0.238197i | ||||
\(283\) | 4.00000i | 0.237775i | 0.992908 | + | 0.118888i | \(0.0379328\pi\) | ||||
−0.992908 | + | 0.118888i | \(0.962067\pi\) | |||||||
\(284\) | 8.00000i | 0.474713i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0000 | −1.18056 | ||||||||
\(288\) | −4.00000 | + | 4.00000i | −0.235702 | + | 0.235702i | ||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.0000i | − | 0.586210i | ||||||
\(292\) | 20.0000i | 1.17041i | ||||||||
\(293\) | 2.00000i | 0.116841i | 0.998292 | + | 0.0584206i | \(0.0186065\pi\) | ||||
−0.998292 | + | 0.0584206i | \(0.981394\pi\) | |||||||
\(294\) | −3.00000 | − | 3.00000i | −0.174964 | − | 0.174964i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.00000 | − | 8.00000i | 0.464991 | − | 0.464991i | ||||
\(297\) | −4.00000 | −0.232104 | ||||||||
\(298\) | 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 | ||||
\(303\) | 14.0000 | 0.804279 | ||||||||
\(304\) | − | 16.0000i | − | 0.917663i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | − | 6.00000i | 0.342997 | − | 0.342997i | ||||
\(307\) | − | 28.0000i | − | 1.59804i | −0.601302 | − | 0.799022i | \(-0.705351\pi\) | ||
0.601302 | − | 0.799022i | \(-0.294649\pi\) | |||||||
\(308\) | −16.0000 | −0.911685 | ||||||||
\(309\) | − | 2.00000i | − | 0.113776i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 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 | \(-0.168688\pi\) | |||||||
\(318\) | −10.0000 | + | 10.0000i | −0.560772 | + | 0.560772i | ||||
\(319\) | 24.0000 | 1.34374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 8.00000 | − | 8.00000i | 0.445823 | − | 0.445823i | ||||
\(323\) | 24.0000i | 1.33540i | ||||||||
\(324\) | − | 2.00000i | − | 0.111111i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.0000 | + | 20.0000i | 1.10770 | + | 1.10770i | ||||
\(327\) | 4.00000 | 0.221201 | ||||||||
\(328\) | 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 | \(0.0350627\pi\) | ||||
−0.993939 | + | 0.109930i | \(0.964937\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | 24.0000 | − | 24.0000i | 1.31322 | − | 1.31322i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 8.00000i | − | 0.436436i | ||||||
\(337\) | −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 | ||||
\(339\) | 6.00000i | 0.325875i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 40.0000i | 2.16612i | ||||||||
\(342\) | 4.00000 | + | 4.00000i | 0.216295 | + | 0.216295i | ||||
\(343\) | 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 | \(-0.141297\pi\) | |||||||
\(348\) | 12.0000i | 0.643268i | ||||||||
\(349\) | 8.00000i | 0.428230i | 0.976808 | + | 0.214115i | \(0.0686868\pi\) | ||||
−0.976808 | + | 0.214115i | \(0.931313\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.0000 | + | 16.0000i | 0.852803 | + | 0.852803i | ||||
\(353\) | 18.0000 | 0.958043 | 0.479022 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479022 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(354\) | −8.00000 | + | 8.00000i | −0.425195 | + | 0.425195i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 28.0000i | − | 1.48400i | ||||||
\(357\) | 12.0000i | 0.635107i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 20.0000 | + | 20.0000i | 1.05118 | + | 1.05118i | ||||
\(363\) | 5.00000i | 0.262432i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.00000 | − | 8.00000i | 0.418167 | − | 0.418167i | ||||
\(367\) | 18.0000 | 0.939592 | 0.469796 | − | 0.882775i | \(-0.344327\pi\) | ||||
0.469796 | + | 0.882775i | \(0.344327\pi\) | |||||||
\(368\) | −16.0000 | −0.834058 | ||||||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20.0000i | − | 1.03835i | ||||||
\(372\) | −20.0000 | −1.03695 | ||||||||
\(373\) | − | 20.0000i | − | 1.03556i | −0.855514 | − | 0.517780i | \(-0.826758\pi\) | ||
0.855514 | − | 0.517780i | \(-0.173242\pi\) | |||||||
\(374\) | −24.0000 | − | 24.0000i | −1.24101 | − | 1.24101i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.00000 | + | 8.00000i | 0.412568 | + | 0.412568i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.00000 | + | 2.00000i | 0.102869 | + | 0.102869i | ||||
\(379\) | − | 36.0000i | − | 1.84920i | −0.380945 | − | 0.924598i | \(-0.624401\pi\) | ||
0.380945 | − | 0.924598i | \(-0.375599\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 6.00000i | − | 0.307389i | ||||||
\(382\) | 8.00000 | − | 8.00000i | 0.409316 | − | 0.409316i | ||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | −8.00000 | + | 8.00000i | −0.408248 | + | 0.408248i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | + | 14.0000i | −0.712581 | + | 0.712581i | ||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | − | 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 | ||||||||
\(396\) | −8.00000 | −0.402015 | ||||||||
\(397\) | − | 20.0000i | − | 1.00377i | −0.864934 | − | 0.501886i | \(-0.832640\pi\) | ||
0.864934 | − | 0.501886i | \(-0.167360\pi\) | |||||||
\(398\) | 6.00000 | − | 6.00000i | 0.300753 | − | 0.300753i | ||||
\(399\) | −8.00000 | −0.400501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.0000 | 1.49813 | 0.749064 | − | 0.662497i | \(-0.230503\pi\) | ||||
0.749064 | + | 0.662497i | \(0.230503\pi\) | |||||||
\(402\) | −12.0000 | + | 12.0000i | −0.598506 | + | 0.598506i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 28.0000 | 1.39305 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0000 | − | 12.0000i | −0.595550 | − | 0.595550i | ||||
\(407\) | 16.0000 | 0.793091 | ||||||||
\(408\) | 12.0000 | − | 12.0000i | 0.594089 | − | 0.594089i | ||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.00000i | − | 0.0986527i | ||||||
\(412\) | − | 4.00000i | − | 0.197066i | ||||||
\(413\) | − | 16.0000i | − | 0.787309i | ||||||
\(414\) | 4.00000 | − | 4.00000i | 0.196589 | − | 0.196589i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 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 | \(0.162044\pi\) | ||||
−0.873195 | + | 0.487370i | \(0.837956\pi\) | |||||||
\(422\) | −12.0000 | − | 12.0000i | −0.584151 | − | 0.584151i | ||||
\(423\) | −4.00000 | −0.194487 | ||||||||
\(424\) | −20.0000 | + | 20.0000i | −0.971286 | + | 0.971286i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.00000 | − | 4.00000i | −0.193801 | − | 0.193801i | ||||
\(427\) | 16.0000i | 0.774294i | ||||||||
\(428\) | −8.00000 | −0.386695 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0000 | −1.73406 | −0.867029 | − | 0.498257i | \(-0.833974\pi\) | ||||
−0.867029 | + | 0.498257i | \(0.833974\pi\) | |||||||
\(432\) | − | 4.00000i | − | 0.192450i | ||||||
\(433\) | −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 | ||||||||
\(438\) | −10.0000 | − | 10.0000i | −0.477818 | − | 0.477818i | ||||
\(439\) | 2.00000 | 0.0954548 | 0.0477274 | − | 0.998860i | \(-0.484802\pi\) | ||||
0.0477274 | + | 0.998860i | \(0.484802\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.0000i | − | 0.760183i | −0.924949 | − | 0.380091i | \(-0.875893\pi\) | ||
0.924949 | − | 0.380091i | \(-0.124107\pi\) | |||||||
\(444\) | 8.00000i | 0.379663i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.0000 | − | 10.0000i | 0.473514 | − | 0.473514i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | − | 16.0000i | − | 0.755929i | ||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0000i | 1.88353i | ||||||||
\(452\) | 12.0000i | 0.564433i | ||||||||
\(453\) | 2.00000i | 0.0939682i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.00000 | + | 8.00000i | 0.374634 | + | 0.374634i | ||||
\(457\) | −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 | ||||
\(459\) | 6.00000i | 0.280056i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 34.0000i | − | 1.58354i | −0.610821 | − | 0.791769i | \(-0.709160\pi\) | ||
0.610821 | − | 0.791769i | \(-0.290840\pi\) | |||||||
\(462\) | 8.00000 | − | 8.00000i | 0.372194 | − | 0.372194i | ||||
\(463\) | 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 | ||||||||
\(471\) | −20.0000 | −0.921551 | ||||||||
\(472\) | −16.0000 | + | 16.0000i | −0.736460 | + | 0.736460i | ||||
\(473\) | −16.0000 | −0.735681 | ||||||||
\(474\) | −14.0000 | − | 14.0000i | −0.643041 | − | 0.643041i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.0000i | 1.10004i | ||||||||
\(477\) | − | 10.0000i | − | 0.457869i | ||||||
\(478\) | −16.0000 | + | 16.0000i | −0.731823 | + | 0.731823i | ||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 30.0000 | − | 30.0000i | 1.36646 | − | 1.36646i | ||||
\(483\) | 8.00000i | 0.364013i | ||||||||
\(484\) | 10.0000i | 0.454545i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | + | 1.00000i | 0.0453609 | + | 0.0453609i | ||||
\(487\) | 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 | ||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.0000i | − | 1.80517i | −0.430507 | − | 0.902587i | \(-0.641665\pi\) | ||
0.430507 | − | 0.902587i | \(-0.358335\pi\) | |||||||
\(492\) | −20.0000 | −0.901670 | ||||||||
\(493\) | − | 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 | \(-0.852257\pi\) | ||
0.894203 | − | 0.447661i | \(-0.147743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000i | 1.07224i | ||||||||
\(502\) | −12.0000 | − | 12.0000i | −0.535586 | − | 0.535586i | ||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 4.00000 | + | 4.00000i | 0.178174 | + | 0.178174i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −16.0000 | − | 16.0000i | −0.711287 | − | 0.711287i | ||||
\(507\) | − | 13.0000i | − | 0.577350i | ||||||
\(508\) | − | 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 | ||||
\(513\) | −4.00000 | −0.176604 | ||||||||
\(514\) | −2.00000 | + | 2.00000i | −0.0882162 | + | 0.0882162i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 8.00000i | − | 0.352180i | ||||||
\(517\) | 16.0000i | 0.703679i | ||||||||
\(518\) | −8.00000 | − | 8.00000i | −0.351500 | − | 0.351500i | ||||
\(519\) | 10.0000 | 0.438951 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.00000 | −0.262865 | −0.131432 | − | 0.991325i | \(-0.541958\pi\) | ||||
−0.131432 | + | 0.991325i | \(0.541958\pi\) | |||||||
\(522\) | −6.00000 | − | 6.00000i | −0.262613 | − | 0.262613i | ||||
\(523\) | 20.0000i | 0.874539i | 0.899331 | + | 0.437269i | \(0.144054\pi\) | ||||
−0.899331 | + | 0.437269i | \(0.855946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 60.0000 | 2.61364 | ||||||||
\(528\) | −16.0000 | −0.696311 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.00000i | − | 0.347170i | ||||||
\(532\) | −16.0000 | −0.693688 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 14.0000 | + | 14.0000i | 0.605839 | + | 0.605839i | ||||
\(535\) | 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 | \(-0.605227\pi\) | ||
0.324593 | − | 0.945854i | \(-0.394773\pi\) | |||||||
\(542\) | 2.00000 | − | 2.00000i | 0.0859074 | − | 0.0859074i | ||||
\(543\) | −20.0000 | −0.858282 | ||||||||
\(544\) | 24.0000 | − | 24.0000i | 1.02899 | − | 1.02899i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000i | 0.171028i | 0.996337 | + | 0.0855138i | \(0.0272532\pi\) | ||||
−0.996337 | + | 0.0855138i | \(0.972747\pi\) | |||||||
\(548\) | − | 4.00000i | − | 0.170872i | ||||||
\(549\) | 8.00000i | 0.341432i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | 8.00000 | − | 8.00000i | 0.340503 | − | 0.340503i | ||||
\(553\) | 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 | \(0.650845\pi\) | |||||||
\(558\) | 10.0000 | − | 10.0000i | 0.423334 | − | 0.423334i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 10.0000 | − | 10.0000i | 0.421825 | − | 0.421825i | ||||
\(563\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | − | 4.00000i | −0.168133 | − | 0.168133i | ||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | −8.00000 | − | 8.00000i | −0.335673 | − | 0.335673i | ||||
\(569\) | 2.00000 | 0.0838444 | 0.0419222 | − | 0.999121i | \(-0.486652\pi\) | ||||
0.0419222 | + | 0.999121i | \(0.486652\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 20.0000i | − | 0.836974i | −0.908223 | − | 0.418487i | \(-0.862561\pi\) | ||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000i | 0.334205i | ||||||||
\(574\) | 20.0000 | − | 20.0000i | 0.834784 | − | 0.834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 8.00000i | − | 0.333333i | ||||||
\(577\) | 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 | ||||
\(579\) | − | 14.0000i | − | 0.581820i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.0000 | + | 10.0000i | 0.414513 | + | 0.414513i | ||||
\(583\) | −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 | \(-0.0796572\pi\) | |||||||
\(588\) | 6.00000 | 0.247436 | ||||||||
\(589\) | 40.0000i | 1.64817i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 16.0000i | 0.657596i | ||||||||
\(593\) | −22.0000 | −0.903432 | −0.451716 | − | 0.892162i | \(-0.649188\pi\) | ||||
−0.451716 | + | 0.892162i | \(0.649188\pi\) | |||||||
\(594\) | 4.00000 | − | 4.00000i | 0.164122 | − | 0.164122i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.0000 | −0.491539 | ||||||||
\(597\) | 6.00000i | 0.245564i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 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 | ||||
\(603\) | − | 12.0000i | − | 0.488678i | ||||||
\(604\) | 4.00000i | 0.162758i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0000 | + | 14.0000i | −0.568711 | + | 0.568711i | ||||
\(607\) | −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 | ||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12.0000i | 0.485071i | ||||||||
\(613\) | 20.0000i | 0.807792i | 0.914805 | + | 0.403896i | \(0.132344\pi\) | ||||
−0.914805 | + | 0.403896i | \(0.867656\pi\) | |||||||
\(614\) | 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 | \(-0.461462\pi\) | ||||
0.120775 | + | 0.992680i | \(0.461462\pi\) | |||||||
\(618\) | 2.00000 | + | 2.00000i | 0.0804518 | + | 0.0804518i | ||||
\(619\) | 20.0000i | 0.803868i | 0.915669 | + | 0.401934i | \(0.131662\pi\) | ||||
−0.915669 | + | 0.401934i | \(0.868338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000i | 0.160514i | ||||||||
\(622\) | −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 | ||||
\(627\) | 16.0000i | 0.638978i | ||||||||
\(628\) | −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 | ||||
\(633\) | 12.0000 | 0.476957 | ||||||||
\(634\) | 18.0000 | + | 18.0000i | 0.714871 | + | 0.714871i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 20.0000i | − | 0.793052i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −24.0000 | + | 24.0000i | −0.950169 | + | 0.950169i | ||||
\(639\) | 4.00000 | 0.158238 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.0000 | 0.552967 | 0.276483 | − | 0.961019i | \(-0.410831\pi\) | ||||
0.276483 | + | 0.961019i | \(0.410831\pi\) | |||||||
\(642\) | 4.00000 | − | 4.00000i | 0.157867 | − | 0.157867i | ||||
\(643\) | 12.0000i | 0.473234i | 0.971603 | + | 0.236617i | \(0.0760386\pi\) | ||||
−0.971603 | + | 0.236617i | \(0.923961\pi\) | |||||||
\(644\) | 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 | \(-0.575799\pi\) | ||||
−0.235884 | + | 0.971781i | \(0.575799\pi\) | |||||||
\(648\) | 2.00000 | + | 2.00000i | 0.0785674 | + | 0.0785674i | ||||
\(649\) | −32.0000 | −1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.0000i | 0.783862i | ||||||||
\(652\) | −40.0000 | −1.56652 | ||||||||
\(653\) | − | 30.0000i | − | 1.17399i | −0.809590 | − | 0.586995i | \(-0.800311\pi\) | ||
0.809590 | − | 0.586995i | \(-0.199689\pi\) | |||||||
\(654\) | −4.00000 | + | 4.00000i | −0.156412 | + | 0.156412i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −40.0000 | −1.56174 | ||||||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | 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 | \(0.213813\pi\) | ||||
−0.782757 | + | 0.622328i | \(0.786187\pi\) | |||||||
\(662\) | −4.00000 | − | 4.00000i | −0.155464 | − | 0.155464i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −4.00000 | − | 4.00000i | −0.154997 | − | 0.154997i | ||||
\(667\) | − | 24.0000i | − | 0.929284i | ||||||
\(668\) | 48.0000i | 1.85718i | ||||||||
\(669\) | 10.0000i | 0.386622i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0000 | 1.23535 | ||||||||
\(672\) | 8.00000 | + | 8.00000i | 0.308607 | + | 0.308607i | ||||
\(673\) | 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 | \(0.739413\pi\) | |||||||
\(678\) | −6.00000 | − | 6.00000i | −0.230429 | − | 0.230429i | ||||
\(679\) | −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 | \(-0.370466\pi\) | |||||||
\(684\) | −8.00000 | −0.305888 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.0000 | + | 20.0000i | −0.763604 | + | 0.763604i | ||||
\(687\) | −4.00000 | −0.152610 | ||||||||
\(688\) | − | 16.0000i | − | 0.609994i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000i | 0.456502i | 0.973602 | + | 0.228251i | \(0.0733006\pi\) | ||||
−0.973602 | + | 0.228251i | \(0.926699\pi\) | |||||||
\(692\) | 20.0000 | 0.760286 | ||||||||
\(693\) | 8.00000i | 0.303895i | ||||||||
\(694\) | 16.0000 | + | 16.0000i | 0.607352 | + | 0.607352i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0000 | − | 12.0000i | −0.454859 | − | 0.454859i | ||||
\(697\) | 60.0000 | 2.27266 | ||||||||
\(698\) | −8.00000 | − | 8.00000i | −0.302804 | − | 0.302804i | ||||
\(699\) | − | 6.00000i | − | 0.226941i | ||||||
\(700\) | 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 | ||||||
\(708\) | − | 16.0000i | − | 0.601317i | ||||||
\(709\) | 44.0000i | 1.65245i | 0.563337 | + | 0.826227i | \(0.309517\pi\) | ||||
−0.563337 | + | 0.826227i | \(0.690483\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | 28.0000 | + | 28.0000i | 1.04934 | + | 1.04934i | ||||
\(713\) | 40.0000 | 1.49801 | ||||||||
\(714\) | −12.0000 | − | 12.0000i | −0.449089 | − | 0.449089i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 16.0000i | − | 0.597531i | ||||||
\(718\) | −12.0000 | + | 12.0000i | −0.447836 | + | 0.447836i | ||||
\(719\) | −36.0000 | −1.34257 | −0.671287 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671287 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.00000 | −0.148968 | ||||||||
\(722\) | −3.00000 | + | 3.00000i | −0.111648 | + | 0.111648i | ||||
\(723\) | 30.0000i | 1.11571i | ||||||||
\(724\) | −40.0000 | −1.48659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.00000 | − | 5.00000i | −0.185567 | − | 0.185567i | ||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000i | 0.887672i | ||||||||
\(732\) | 16.0000i | 0.591377i | ||||||||
\(733\) | 24.0000i | 0.886460i | 0.896408 | + | 0.443230i | \(0.146168\pi\) | ||||
−0.896408 | + | 0.443230i | \(0.853832\pi\) | |||||||
\(734\) | −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 | ||||||||
\(738\) | 10.0000 | − | 10.0000i | 0.368105 | − | 0.368105i | ||||
\(739\) | 12.0000i | 0.441427i | 0.975339 | + | 0.220714i | \(0.0708386\pi\) | ||||
−0.975339 | + | 0.220714i | \(0.929161\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.0000 | + | 20.0000i | 0.734223 | + | 0.734223i | ||||
\(743\) | 48.0000 | 1.76095 | 0.880475 | − | 0.474093i | \(-0.157224\pi\) | ||||
0.880475 | + | 0.474093i | \(0.157224\pi\) | |||||||
\(744\) | 20.0000 | − | 20.0000i | 0.733236 | − | 0.733236i | ||||
\(745\) | 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 | ||||||||
\(753\) | 12.0000 | 0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | 8.00000i | 0.290765i | 0.989376 | + | 0.145382i | \(0.0464413\pi\) | ||||
−0.989376 | + | 0.145382i | \(0.953559\pi\) | |||||||
\(758\) | 36.0000 | + | 36.0000i | 1.30758 | + | 1.30758i | ||||
\(759\) | 16.0000 | 0.580763 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.0000 | 0.362500 | 0.181250 | − | 0.983437i | \(-0.441986\pi\) | ||||
0.181250 | + | 0.983437i | \(0.441986\pi\) | |||||||
\(762\) | 6.00000 | + | 6.00000i | 0.217357 | + | 0.217357i | ||||
\(763\) | − | 8.00000i | − | 0.289619i | ||||||
\(764\) | 16.0000i | 0.578860i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | − | 24.0000i | 0.867155 | − | 0.867155i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 16.0000i | − | 0.577350i | ||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.00000i | − | 0.0720282i | ||||||
\(772\) | − | 28.0000i | − | 1.00774i | ||||||
\(773\) | − | 6.00000i | − | 0.215805i | −0.994161 | − | 0.107903i | \(-0.965587\pi\) | ||
0.994161 | − | 0.107903i | \(-0.0344134\pi\) | |||||||
\(774\) | 4.00000 | + | 4.00000i | 0.143777 | + | 0.143777i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.0000 | + | 20.0000i | 0.717958 | + | 0.717958i | ||||
\(777\) | 8.00000 | 0.286998 | ||||||||
\(778\) | −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 | ||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 12.0000 | 0.428571 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 28.0000i | − | 0.998092i | −0.866575 | − | 0.499046i | \(-0.833684\pi\) | ||
0.866575 | − | 0.499046i | \(-0.166316\pi\) | |||||||
\(788\) | 20.0000 | 0.712470 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 8.00000 | − | 8.00000i | 0.284268 | − | 0.284268i | ||||
\(793\) | 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 | \(-0.178307\pi\) | |||||||
\(798\) | 8.00000 | − | 8.00000i | 0.283197 | − | 0.283197i | ||||
\(799\) | 24.0000 | 0.849059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | −30.0000 | + | 30.0000i | −1.05934 | + | 1.05934i | ||||
\(803\) | − | 40.0000i | − | 1.41157i | ||||||
\(804\) | − | 24.0000i | − | 0.846415i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.0000 | 0.352017 | ||||||||
\(808\) | −28.0000 | + | 28.0000i | −0.985037 | + | 0.985037i | ||||
\(809\) | 10.0000 | 0.351581 | 0.175791 | − | 0.984428i | \(-0.443752\pi\) | ||||
0.175791 | + | 0.984428i | \(0.443752\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 4.00000i | − | 0.140459i | −0.997531 | − | 0.0702295i | \(-0.977627\pi\) | ||
0.997531 | − | 0.0702295i | \(-0.0223732\pi\) | |||||||
\(812\) | 24.0000 | 0.842235 | ||||||||
\(813\) | 2.00000i | 0.0701431i | ||||||||
\(814\) | −16.0000 | + | 16.0000i | −0.560800 | + | 0.560800i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 24.0000i | 0.840168i | ||||||||
\(817\) | −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 | \(-0.0558313\pi\) | |||||||
\(822\) | 2.00000 | + | 2.00000i | 0.0697580 | + | 0.0697580i | ||||
\(823\) | −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 | \(0.977845\pi\) | |||||||
\(828\) | 8.00000i | 0.278019i | ||||||||
\(829\) | − | 44.0000i | − | 1.52818i | −0.645108 | − | 0.764092i | \(-0.723188\pi\) | ||
0.645108 | − | 0.764092i | \(-0.276812\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.0000 | 0.555034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0000 | −0.623663 | ||||||||
\(834\) | 4.00000 | − | 4.00000i | 0.138509 | − | 0.138509i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.0000i | 1.10674i | ||||||||
\(837\) | 10.0000i | 0.345651i | ||||||||
\(838\) | 4.00000 | + | 4.00000i | 0.138178 | + | 0.138178i | ||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | −20.0000 | − | 20.0000i | −0.689246 | − | 0.689246i | ||||
\(843\) | 10.0000i | 0.344418i | ||||||||
\(844\) | 24.0000 | 0.826114 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | − | 4.00000i | 0.137523 | − | 0.137523i | ||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | − | 40.0000i | − | 1.37361i | ||||||
\(849\) | 4.00000 | 0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.0000i | − | 0.548473i | ||||||
\(852\) | 8.00000 | 0.274075 | ||||||||
\(853\) | 44.0000i | 1.50653i | 0.657716 | + | 0.753266i | \(0.271523\pi\) | ||||
−0.657716 | + | 0.753266i | \(0.728477\pi\) | |||||||
\(854\) | −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 | \(-0.532677\pi\) | ||||
−0.102478 | + | 0.994735i | \(0.532677\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 44.0000i | − | 1.50126i | −0.660722 | − | 0.750630i | \(-0.729750\pi\) | ||
0.660722 | − | 0.750630i | \(-0.270250\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000i | 0.681598i | ||||||||
\(862\) | 36.0000 | − | 36.0000i | 1.22616 | − | 1.22616i | ||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 4.00000 | + | 4.00000i | 0.136083 | + | 0.136083i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.0000 | − | 14.0000i | 0.475739 | − | 0.475739i | ||||
\(867\) | − | 19.0000i | − | 0.645274i | ||||||
\(868\) | 40.0000i | 1.35769i | ||||||||
\(869\) | − | 56.0000i | − | 1.89967i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.00000 | + | 8.00000i | −0.270914 | + | 0.270914i | ||||
\(873\) | −10.0000 | −0.338449 | ||||||||
\(874\) | −16.0000 | − | 16.0000i | −0.541208 | − | 0.541208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0000 | 0.675737 | ||||||||
\(877\) | − | 44.0000i | − | 1.48577i | −0.669417 | − | 0.742887i | \(-0.733456\pi\) | ||
0.669417 | − | 0.742887i | \(-0.266544\pi\) | |||||||
\(878\) | −2.00000 | + | 2.00000i | −0.0674967 | + | 0.0674967i | ||||
\(879\) | 2.00000 | 0.0674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | −3.00000 | + | 3.00000i | −0.101015 | + | 0.101015i | ||||
\(883\) | 28.0000i | 0.942275i | 0.882060 | + | 0.471138i | \(0.156156\pi\) | ||||
−0.882060 | + | 0.471138i | \(0.843844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0000 | + | 16.0000i | 0.537531 | + | 0.537531i | ||||
\(887\) | −16.0000 | −0.537227 | −0.268614 | − | 0.963248i | \(-0.586566\pi\) | ||||
−0.268614 | + | 0.963248i | \(0.586566\pi\) | |||||||
\(888\) | −8.00000 | − | 8.00000i | −0.268462 | − | 0.268462i | ||||
\(889\) | −12.0000 | −0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.00000i | 0.134005i | ||||||||
\(892\) | 20.0000i | 0.669650i | ||||||||
\(893\) | 16.0000i | 0.535420i | ||||||||
\(894\) | 6.00000 | − | 6.00000i | 0.200670 | − | 0.200670i | ||||
\(895\) | 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 | ||||
\(903\) | −8.00000 | −0.266223 | ||||||||
\(904\) | −12.0000 | − | 12.0000i | −0.399114 | − | 0.399114i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.00000 | − | 2.00000i | −0.0664455 | − | 0.0664455i | ||||
\(907\) | 52.0000i | 1.72663i | 0.504664 | + | 0.863316i | \(0.331616\pi\) | ||||
−0.504664 | + | 0.863316i | \(0.668384\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 14.0000i | − | 0.464351i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −48.0000 | −1.59031 | −0.795155 | − | 0.606406i | \(-0.792611\pi\) | ||||
−0.795155 | + | 0.606406i | \(0.792611\pi\) | |||||||
\(912\) | −16.0000 | −0.529813 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.0000 | − | 18.0000i | 0.595387 | − | 0.595387i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.00000 | −0.264327 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −6.00000 | − | 6.00000i | −0.198030 | − | 0.198030i | ||||
\(919\) | −26.0000 | −0.857661 | −0.428830 | − | 0.903385i | \(-0.641074\pi\) | ||||
−0.428830 | + | 0.903385i | \(0.641074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0000 | −0.922631 | ||||||||
\(922\) | 34.0000 | + | 34.0000i | 1.11973 | + | 1.11973i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 16.0000i | 0.526361i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −22.0000 | + | 22.0000i | −0.722965 | + | 0.722965i | ||||
\(927\) | −2.00000 | −0.0656886 | ||||||||
\(928\) | −24.0000 | − | 24.0000i | −0.787839 | − | 0.787839i | ||||
\(929\) | 46.0000 | 1.50921 | 0.754606 | − | 0.656179i | \(-0.227828\pi\) | ||||
0.754606 | + | 0.656179i | \(0.227828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 12.0000i | − | 0.393284i | ||||||
\(932\) | − | 12.0000i | − | 0.393073i | ||||||
\(933\) | − | 8.00000i | − | 0.261908i | ||||||
\(934\) | −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 | ||||
\(939\) | 6.00000i | 0.195803i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 26.0000i | − | 0.847576i | −0.905761 | − | 0.423788i | \(-0.860700\pi\) | ||
0.905761 | − | 0.423788i | \(-0.139300\pi\) | |||||||
\(942\) | 20.0000 | − | 20.0000i | 0.651635 | − | 0.651635i | ||||
\(943\) | 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 | \(0.801125\pi\) | |||||||
\(948\) | 28.0000 | 0.909398 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | −24.0000 | − | 24.0000i | −0.777844 | − | 0.777844i | ||||
\(953\) | 26.0000 | 0.842223 | 0.421111 | − | 0.907009i | \(-0.361640\pi\) | ||||
0.421111 | + | 0.907009i | \(0.361640\pi\) | |||||||
\(954\) | 10.0000 | + | 10.0000i | 0.323762 | + | 0.323762i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 32.0000i | − | 1.03495i | ||||||
\(957\) | − | 24.0000i | − | 0.775810i | ||||||
\(958\) | −4.00000 | + | 4.00000i | −0.129234 | + | 0.129234i | ||||
\(959\) | −4.00000 | −0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | 60.0000i | 1.93247i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.00000 | − | 8.00000i | −0.257396 | − | 0.257396i | ||||
\(967\) | −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 | ||||
\(969\) | 24.0000 | 0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.0000i | 0.385098i | 0.981287 | + | 0.192549i | \(0.0616755\pi\) | ||||
−0.981287 | + | 0.192549i | \(0.938325\pi\) | |||||||
\(972\) | −2.00000 | −0.0641500 | ||||||||
\(973\) | 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 | \(-0.385529\pi\) | ||||
0.351921 | + | 0.936030i | \(0.385529\pi\) | |||||||
\(978\) | 20.0000 | − | 20.0000i | 0.639529 | − | 0.639529i | ||||
\(979\) | 56.0000i | 1.78977i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 4.00000i | − | 0.127710i | ||||||
\(982\) | 40.0000 | + | 40.0000i | 1.27645 | + | 1.27645i | ||||
\(983\) | 32.0000 | 1.02064 | 0.510321 | − | 0.859984i | \(-0.329527\pi\) | ||||
0.510321 | + | 0.859984i | \(0.329527\pi\) | |||||||
\(984\) | 20.0000 | − | 20.0000i | 0.637577 | − | 0.637577i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.0000 | + | 36.0000i | 1.14647 | + | 1.14647i | ||||
\(987\) | 8.00000i | 0.254643i | ||||||||
\(988\) | 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 | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | −8.00000 | + | 8.00000i | −0.253745 | + | 0.253745i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0000i | 0.886769i | 0.896332 | + | 0.443384i | \(0.146222\pi\) | ||||
−0.896332 | + | 0.443384i | \(0.853778\pi\) | |||||||
\(998\) | 20.0000 | + | 20.0000i | 0.633089 | + | 0.633089i | ||||
\(999\) | 4.00000 | 0.126554 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))