Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(349,600)]
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, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.349");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.d (of order \(2\), degree \(1\), not 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 | 349.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.349 |
Dual form | 600.2.d.d.349.1 |
$q$-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 | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | + | 1.00000i | 0.408248 | + | 0.408248i | ||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | −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 | \(0.793963\pi\) | |||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | −2.00000 | + | 2.00000i | −0.534522 | + | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | − | 6.00000i | − | 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 1.00000 | + | 1.00000i | 0.235702 | + | 0.235702i | ||||
\(19\) | − | 4.00000i | − | 0.917663i | −0.888523 | − | 0.458831i | \(-0.848268\pi\) | ||
0.888523 | − | 0.458831i | \(-0.151732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | −4.00000 | + | 4.00000i | −0.852803 | + | 0.852803i | ||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | −2.00000 | + | 2.00000i | −0.408248 | + | 0.408248i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −4.00000 | −0.755929 | ||||||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 4.00000i | 0.696311i | ||||||||
\(34\) | 6.00000 | − | 6.00000i | 1.02899 | − | 1.02899i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.00000i | 0.333333i | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 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 | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | −8.00000 | −1.20605 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | + | 4.00000i | −0.589768 | + | 0.589768i | ||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | −4.00000 | −0.577350 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 6.00000i | − | 0.840168i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.0000 | −1.37361 | −0.686803 | − | 0.726844i | \(-0.740986\pi\) | ||||
−0.686803 | + | 0.726844i | \(0.740986\pi\) | |||||||
\(54\) | 1.00000 | + | 1.00000i | 0.136083 | + | 0.136083i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.00000 | − | 4.00000i | −0.534522 | − | 0.534522i | ||||
\(57\) | − | 4.00000i | − | 0.529813i | ||||||
\(58\) | −6.00000 | + | 6.00000i | −0.787839 | + | 0.787839i | ||||
\(59\) | − | 8.00000i | − | 1.04151i | −0.853706 | − | 0.520756i | \(-0.825650\pi\) | ||
0.853706 | − | 0.520756i | \(-0.174350\pi\) | |||||||
\(60\) | 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 | ||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.00000 | + | 4.00000i | −0.492366 | + | 0.492366i | ||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 12.0000 | 1.45521 | ||||||||
\(69\) | 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 | ||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | −4.00000 | − | 4.00000i | −0.464991 | − | 0.464991i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00000 | 0.917663 | ||||||||
\(77\) | −8.00000 | −0.911685 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 10.0000 | + | 10.0000i | 1.10432 | + | 1.10432i | ||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −4.00000 | −0.436436 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.00000 | − | 4.00000i | −0.431331 | − | 0.431331i | ||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | −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 | ||||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | 10.0000 | 1.03695 | ||||||||
\(94\) | 4.00000 | − | 4.00000i | 0.412568 | − | 0.412568i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.00000 | − | 4.00000i | −0.408248 | − | 0.408248i | ||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 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 | ||||
\(103\) | 2.00000i | 0.197066i | 0.995134 | + | 0.0985329i | \(0.0314150\pi\) | ||||
−0.995134 | + | 0.0985329i | \(0.968585\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.0000 | − | 10.0000i | −0.971286 | − | 0.971286i | ||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 2.00000i | 0.192450i | ||||||||
\(109\) | − | 4.00000i | − | 0.383131i | −0.981480 | − | 0.191565i | \(-0.938644\pi\) | ||
0.981480 | − | 0.191565i | \(-0.0613564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | − | 8.00000i | − | 0.755929i | ||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 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 | ||||
\(123\) | 10.0000 | 0.901670 | ||||||||
\(124\) | 20.0000i | 1.79605i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | + | 2.00000i | −0.178174 | + | 0.178174i | ||||
\(127\) | − | 6.00000i | − | 0.532414i | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | −4.00000 | −0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | −8.00000 | −0.696311 | ||||||||
\(133\) | 8.00000 | 0.693688 | ||||||||
\(134\) | 12.0000 | + | 12.0000i | 1.03664 | + | 1.03664i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.0000 | + | 12.0000i | 1.02899 | + | 1.02899i | ||||
\(137\) | − | 2.00000i | − | 0.170872i | −0.996344 | − | 0.0854358i | \(-0.972772\pi\) | ||
0.996344 | − | 0.0854358i | \(-0.0272282\pi\) | |||||||
\(138\) | −4.00000 | + | 4.00000i | −0.340503 | + | 0.340503i | ||||
\(139\) | 4.00000i | 0.339276i | 0.985506 | + | 0.169638i | \(0.0542598\pi\) | ||||
−0.985506 | + | 0.169638i | \(0.945740\pi\) | |||||||
\(140\) | 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 | ||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | − | 8.00000i | − | 0.657596i | ||||||
\(149\) | 6.00000i | 0.491539i | 0.969328 | + | 0.245770i | \(0.0790407\pi\) | ||||
−0.969328 | + | 0.245770i | \(0.920959\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | −8.00000 | − | 8.00000i | −0.644658 | − | 0.644658i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0000 | −1.59617 | −0.798087 | − | 0.602542i | \(-0.794154\pi\) | ||||
−0.798087 | + | 0.602542i | \(0.794154\pi\) | |||||||
\(158\) | 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 | ||||
\(163\) | 20.0000 | 1.56652 | 0.783260 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783260 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(164\) | 20.0000i | 1.56174i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.0000i | 1.85718i | 0.371113 | + | 0.928588i | \(0.378976\pi\) | ||||
−0.371113 | + | 0.928588i | \(0.621024\pi\) | |||||||
\(168\) | −4.00000 | − | 4.00000i | −0.308607 | − | 0.308607i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 4.00000i | − | 0.305888i | ||||||
\(172\) | − | 8.00000i | − | 0.609994i | ||||||
\(173\) | −10.0000 | −0.760286 | −0.380143 | − | 0.924928i | \(-0.624125\pi\) | ||||
−0.380143 | + | 0.924928i | \(0.624125\pi\) | |||||||
\(174\) | −6.00000 | + | 6.00000i | −0.454859 | + | 0.454859i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 16.0000i | − | 1.20605i | ||||||
\(177\) | − | 8.00000i | − | 0.601317i | ||||||
\(178\) | −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 | ||||||||
\(183\) | − | 8.00000i | − | 0.591377i | ||||||
\(184\) | −8.00000 | − | 8.00000i | −0.589768 | − | 0.589768i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.0000 | + | 10.0000i | 0.733236 | + | 0.733236i | ||||
\(187\) | 24.0000 | 1.75505 | ||||||||
\(188\) | 8.00000 | 0.583460 | ||||||||
\(189\) | 2.00000i | 0.145479i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | − | 8.00000i | − | 0.577350i | ||||||
\(193\) | 14.0000i | 1.00774i | 0.863779 | + | 0.503871i | \(0.168091\pi\) | ||||
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | 10.0000 | − | 10.0000i | 0.717958 | − | 0.717958i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00000i | 0.428571i | ||||||||
\(197\) | 10.0000 | 0.712470 | 0.356235 | − | 0.934396i | \(-0.384060\pi\) | ||||
0.356235 | + | 0.934396i | \(0.384060\pi\) | |||||||
\(198\) | −4.00000 | + | 4.00000i | −0.284268 | + | 0.284268i | ||||
\(199\) | 6.00000 | 0.425329 | 0.212664 | − | 0.977125i | \(-0.431786\pi\) | ||||
0.212664 | + | 0.977125i | \(0.431786\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.0000 | 0.846415 | ||||||||
\(202\) | −14.0000 | + | 14.0000i | −0.985037 | + | 0.985037i | ||||
\(203\) | −12.0000 | −0.842235 | ||||||||
\(204\) | 12.0000 | 0.840168 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | + | 2.00000i | −0.139347 | + | 0.139347i | ||||
\(207\) | 4.00000i | 0.278019i | ||||||||
\(208\) | 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 | \(0.864461\pi\) | |||||||
\(212\) | − | 20.0000i | − | 1.37361i | ||||||
\(213\) | −4.00000 | −0.274075 | ||||||||
\(214\) | −4.00000 | − | 4.00000i | −0.273434 | − | 0.273434i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.00000 | + | 2.00000i | −0.136083 | + | 0.136083i | ||||
\(217\) | 20.0000i | 1.35769i | ||||||||
\(218\) | 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 | ||||
\(223\) | − | 10.0000i | − | 0.669650i | −0.942280 | − | 0.334825i | \(-0.891323\pi\) | ||
0.942280 | − | 0.334825i | \(-0.108677\pi\) | |||||||
\(224\) | 8.00000 | − | 8.00000i | 0.534522 | − | 0.534522i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | − | 6.00000i | 0.399114 | − | 0.399114i | ||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 8.00000 | 0.529813 | ||||||||
\(229\) | 4.00000i | 0.264327i | 0.991228 | + | 0.132164i | \(0.0421925\pi\) | ||||
−0.991228 | + | 0.132164i | \(0.957808\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.00000 | −0.526361 | ||||||||
\(232\) | −12.0000 | − | 12.0000i | −0.787839 | − | 0.787839i | ||||
\(233\) | 6.00000i | 0.393073i | 0.980497 | + | 0.196537i | \(0.0629694\pi\) | ||||
−0.980497 | + | 0.196537i | \(0.937031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.0000 | 1.04151 | ||||||||
\(237\) | 14.0000 | 0.909398 | ||||||||
\(238\) | 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 | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 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 | \(0.876365\pi\) | |||||||
\(252\) | −4.00000 | −0.251976 | ||||||||
\(253\) | −16.0000 | −1.00591 | ||||||||
\(254\) | 6.00000 | − | 6.00000i | 0.376473 | − | 0.376473i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | − | 2.00000i | − | 0.124757i | −0.998053 | − | 0.0623783i | \(-0.980131\pi\) | ||
0.998053 | − | 0.0623783i | \(-0.0198685\pi\) | |||||||
\(258\) | −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 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(264\) | −8.00000 | − | 8.00000i | −0.492366 | − | 0.492366i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.00000 | + | 8.00000i | 0.490511 | + | 0.490511i | ||||
\(267\) | −14.0000 | −0.856786 | ||||||||
\(268\) | 24.0000i | 1.46603i | ||||||||
\(269\) | − | 10.0000i | − | 0.609711i | −0.952399 | − | 0.304855i | \(-0.901392\pi\) | ||
0.952399 | − | 0.304855i | \(-0.0986081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.00000 | −0.121491 | −0.0607457 | − | 0.998153i | \(-0.519348\pi\) | ||||
−0.0607457 | + | 0.998153i | \(0.519348\pi\) | |||||||
\(272\) | 24.0000i | 1.45521i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | − | 2.00000i | 0.120824 | − | 0.120824i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.00000 | −0.481543 | ||||||||
\(277\) | 16.0000 | 0.961347 | 0.480673 | − | 0.876900i | \(-0.340392\pi\) | ||||
0.480673 | + | 0.876900i | \(0.340392\pi\) | |||||||
\(278\) | −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 | ||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | − | 8.00000i | − | 0.474713i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.0000i | 1.18056i | ||||||||
\(288\) | −4.00000 | − | 4.00000i | −0.235702 | − | 0.235702i | ||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 10.0000i | − | 0.586210i | ||||||
\(292\) | 20.0000 | 1.17041 | ||||||||
\(293\) | −2.00000 | −0.116841 | −0.0584206 | − | 0.998292i | \(-0.518606\pi\) | ||||
−0.0584206 | + | 0.998292i | \(0.518606\pi\) | |||||||
\(294\) | 3.00000 | + | 3.00000i | 0.174964 | + | 0.174964i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.00000 | − | 8.00000i | 0.464991 | − | 0.464991i | ||||
\(297\) | 4.00000i | 0.232104i | ||||||||
\(298\) | −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 | ||||
\(303\) | 14.0000i | 0.804279i | ||||||||
\(304\) | 16.0000i | 0.917663i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.00000 | − | 6.00000i | 0.342997 | − | 0.342997i | ||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | − | 16.0000i | − | 0.911685i | ||||||
\(309\) | 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 | ||||||||
\(313\) | − | 6.00000i | − | 0.339140i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) | ||
0.985518 | − | 0.169570i | \(-0.0542379\pi\) | |||||||
\(314\) | −20.0000 | − | 20.0000i | −1.12867 | − | 1.12867i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.0000i | 1.57512i | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | −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 | ||||
\(323\) | −24.0000 | −1.33540 | ||||||||
\(324\) | 2.00000i | 0.111111i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.0000 | + | 20.0000i | 1.10770 | + | 1.10770i | ||||
\(327\) | − | 4.00000i | − | 0.221201i | ||||||
\(328\) | −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 | ||||||||
\(333\) | −4.00000 | −0.219199 | ||||||||
\(334\) | −24.0000 | + | 24.0000i | −1.31322 | + | 1.31322i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 8.00000i | − | 0.436436i | ||||||
\(337\) | 30.0000i | 1.63420i | 0.576493 | + | 0.817102i | \(0.304421\pi\) | ||||
−0.576493 | + | 0.817102i | \(0.695579\pi\) | |||||||
\(338\) | −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 | ||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 8.00000 | − | 8.00000i | 0.431331 | − | 0.431331i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −10.0000 | − | 10.0000i | −0.537603 | − | 0.537603i | ||||
\(347\) | −16.0000 | −0.858925 | −0.429463 | − | 0.903085i | \(-0.641297\pi\) | ||||
−0.429463 | + | 0.903085i | \(0.641297\pi\) | |||||||
\(348\) | −12.0000 | −0.643268 | ||||||||
\(349\) | − | 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 | ||||
\(353\) | 18.0000i | 0.958043i | 0.877803 | + | 0.479022i | \(0.159008\pi\) | ||||
−0.877803 | + | 0.479022i | \(0.840992\pi\) | |||||||
\(354\) | 8.00000 | − | 8.00000i | 0.425195 | − | 0.425195i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 28.0000i | − | 1.48400i | ||||||
\(357\) | 12.0000 | 0.635107 | ||||||||
\(358\) | 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 | ||||
\(363\) | −5.00000 | −0.262432 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.00000 | − | 8.00000i | 0.418167 | − | 0.418167i | ||||
\(367\) | − | 18.0000i | − | 0.939592i | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||
0.882775 | − | 0.469796i | \(-0.155673\pi\) | |||||||
\(368\) | − | 16.0000i | − | 0.834058i | ||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 20.0000i | − | 1.03835i | ||||||
\(372\) | 20.0000i | 1.03695i | ||||||||
\(373\) | 20.0000 | 1.03556 | 0.517780 | − | 0.855514i | \(-0.326758\pi\) | ||||
0.517780 | + | 0.855514i | \(0.326758\pi\) | |||||||
\(374\) | 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 | \(0.375599\pi\) | ||||
−0.380945 | + | 0.924598i | \(0.624401\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 6.00000i | − | 0.307389i | ||||||
\(382\) | −8.00000 | − | 8.00000i | −0.409316 | − | 0.409316i | ||||
\(383\) | − | 24.0000i | − | 1.22634i | −0.789950 | − | 0.613171i | \(-0.789894\pi\) | ||
0.789950 | − | 0.613171i | \(-0.210106\pi\) | |||||||
\(384\) | 8.00000 | − | 8.00000i | 0.408248 | − | 0.408248i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | + | 14.0000i | −0.712581 | + | 0.712581i | ||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | 20.0000 | 1.01535 | ||||||||
\(389\) | − | 10.0000i | − | 0.507020i | −0.967333 | − | 0.253510i | \(-0.918415\pi\) | ||
0.967333 | − | 0.253510i | \(-0.0815851\pi\) | |||||||
\(390\) | 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 | ||||||||
\(397\) | −20.0000 | −1.00377 | −0.501886 | − | 0.864934i | \(-0.667360\pi\) | ||||
−0.501886 | + | 0.864934i | \(0.667360\pi\) | |||||||
\(398\) | 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 | ||||
\(407\) | − | 16.0000i | − | 0.793091i | ||||||
\(408\) | 12.0000 | + | 12.0000i | 0.594089 | + | 0.594089i | ||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.00000i | − | 0.0986527i | ||||||
\(412\) | −4.00000 | −0.197066 | ||||||||
\(413\) | 16.0000 | 0.787309 | ||||||||
\(414\) | −4.00000 | + | 4.00000i | −0.196589 | + | 0.196589i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000i | 0.195881i | ||||||||
\(418\) | 16.0000 | + | 16.0000i | 0.782586 | + | 0.782586i | ||||
\(419\) | 4.00000i | 0.195413i | 0.995215 | + | 0.0977064i | \(0.0311506\pi\) | ||||
−0.995215 | + | 0.0977064i | \(0.968849\pi\) | |||||||
\(420\) | 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 | ||||
\(423\) | − | 4.00000i | − | 0.194487i | ||||||
\(424\) | 20.0000 | − | 20.0000i | 0.971286 | − | 0.971286i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.00000 | − | 4.00000i | −0.193801 | − | 0.193801i | ||||
\(427\) | 16.0000 | 0.774294 | ||||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −36.0000 | −1.73406 | −0.867029 | − | 0.498257i | \(-0.833974\pi\) | ||||
−0.867029 | + | 0.498257i | \(0.833974\pi\) | |||||||
\(432\) | −4.00000 | −0.192450 | ||||||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | −20.0000 | + | 20.0000i | −0.960031 | + | 0.960031i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.00000 | 0.383131 | ||||||||
\(437\) | 16.0000 | 0.765384 | ||||||||
\(438\) | 10.0000 | − | 10.0000i | 0.477818 | − | 0.477818i | ||||
\(439\) | −2.00000 | −0.0954548 | −0.0477274 | − | 0.998860i | \(-0.515198\pi\) | ||||
−0.0477274 | + | 0.998860i | \(0.515198\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | 0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.0000 | 0.760183 | 0.380091 | − | 0.924949i | \(-0.375893\pi\) | ||||
0.380091 | + | 0.924949i | \(0.375893\pi\) | |||||||
\(444\) | − | 8.00000i | − | 0.379663i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.0000 | − | 10.0000i | 0.473514 | − | 0.473514i | ||||
\(447\) | 6.00000i | 0.283790i | ||||||||
\(448\) | 16.0000 | 0.755929 | ||||||||
\(449\) | 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 | ||||||||
\(452\) | 12.0000 | 0.564433 | ||||||||
\(453\) | −2.00000 | −0.0939682 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.00000 | + | 8.00000i | 0.374634 | + | 0.374634i | ||||
\(457\) | 18.0000i | 0.842004i | 0.907060 | + | 0.421002i | \(0.138322\pi\) | ||||
−0.907060 | + | 0.421002i | \(0.861678\pi\) | |||||||
\(458\) | −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 | ||||
\(463\) | 22.0000i | 1.02243i | 0.859454 | + | 0.511213i | \(0.170804\pi\) | ||||
−0.859454 | + | 0.511213i | \(0.829196\pi\) | |||||||
\(464\) | − | 24.0000i | − | 1.11417i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | + | 6.00000i | −0.277945 | + | 0.277945i | ||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0000i | 1.10822i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.0000 | −0.921551 | ||||||||
\(472\) | 16.0000 | + | 16.0000i | 0.736460 | + | 0.736460i | ||||
\(473\) | − | 16.0000i | − | 0.735681i | ||||||
\(474\) | 14.0000 | + | 14.0000i | 0.643041 | + | 0.643041i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 24.0000i | 1.10004i | ||||||||
\(477\) | −10.0000 | −0.457869 | ||||||||
\(478\) | −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 | ||||
\(483\) | −8.00000 | −0.364013 | ||||||||
\(484\) | − | 10.0000i | − | 0.454545i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | + | 1.00000i | 0.0453609 | + | 0.0453609i | ||||
\(487\) | − | 30.0000i | − | 1.35943i | −0.733476 | − | 0.679715i | \(-0.762104\pi\) | ||
0.733476 | − | 0.679715i | \(-0.237896\pi\) | |||||||
\(488\) | 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 | \(-0.358335\pi\) | |||||||
\(492\) | 20.0000i | 0.901670i | ||||||||
\(493\) | 36.0000 | 1.62136 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −40.0000 | −1.79605 | ||||||||
\(497\) | − | 8.00000i | − | 0.358849i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.0000i | 1.07224i | ||||||||
\(502\) | −12.0000 | + | 12.0000i | −0.535586 | + | 0.535586i | ||||
\(503\) | 12.0000i | 0.535054i | 0.963550 | + | 0.267527i | \(0.0862064\pi\) | ||||
−0.963550 | + | 0.267527i | \(0.913794\pi\) | |||||||
\(504\) | −4.00000 | − | 4.00000i | −0.178174 | − | 0.178174i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −16.0000 | − | 16.0000i | −0.711287 | − | 0.711287i | ||||
\(507\) | −13.0000 | −0.577350 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | − | 18.0000i | − | 0.797836i | −0.916987 | − | 0.398918i | \(-0.869386\pi\) | ||
0.916987 | − | 0.398918i | \(-0.130614\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | 0.884748 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | − | 4.00000i | − | 0.176604i | ||||||
\(514\) | 2.00000 | − | 2.00000i | 0.0882162 | − | 0.0882162i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 8.00000i | − | 0.352180i | ||||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 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 | ||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 60.0000i | − | 2.61364i | ||||||
\(528\) | − | 16.0000i | − | 0.696311i | ||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 8.00000i | − | 0.347170i | ||||||
\(532\) | 16.0000i | 0.693688i | ||||||||
\(533\) | 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 | ||||
\(543\) | − | 20.0000i | − | 0.858282i | ||||||
\(544\) | −24.0000 | + | 24.0000i | −1.02899 | + | 1.02899i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.00000 | 0.171028 | 0.0855138 | − | 0.996337i | \(-0.472747\pi\) | ||||
0.0855138 | + | 0.996337i | \(0.472747\pi\) | |||||||
\(548\) | 4.00000 | 0.170872 | ||||||||
\(549\) | − | 8.00000i | − | 0.341432i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.0000 | 1.02243 | ||||||||
\(552\) | −8.00000 | − | 8.00000i | −0.340503 | − | 0.340503i | ||||
\(553\) | 28.0000i | 1.19068i | ||||||||
\(554\) | 16.0000 | + | 16.0000i | 0.679775 | + | 0.679775i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | 42.0000 | 1.77960 | 0.889799 | − | 0.456354i | \(-0.150845\pi\) | ||||
0.889799 | + | 0.456354i | \(0.150845\pi\) | |||||||
\(558\) | 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 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 8.00000 | 0.336861 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | − | 4.00000i | −0.168133 | − | 0.168133i | ||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | 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 | \(-0.862561\pi\) | ||
0.908223 | − | 0.418487i | \(-0.137439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | −0.334205 | ||||||||
\(574\) | −20.0000 | + | 20.0000i | −0.834784 | + | 0.834784i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 8.00000i | − | 0.333333i | ||||||
\(577\) | − | 2.00000i | − | 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | −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 | ||||
\(583\) | − | 40.0000i | − | 1.65663i | ||||||
\(584\) | 20.0000 | + | 20.0000i | 0.827606 | + | 0.827606i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.00000 | − | 2.00000i | −0.0826192 | − | 0.0826192i | ||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 6.00000i | 0.247436i | ||||||||
\(589\) | − | 40.0000i | − | 1.64817i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | 0.411345 | ||||||||
\(592\) | 16.0000 | 0.657596 | ||||||||
\(593\) | − | 22.0000i | − | 0.903432i | −0.892162 | − | 0.451716i | \(-0.850812\pi\) | ||
0.892162 | − | 0.451716i | \(-0.149188\pi\) | |||||||
\(594\) | −4.00000 | + | 4.00000i | −0.164122 | + | 0.164122i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.0000 | −0.491539 | ||||||||
\(597\) | 6.00000 | 0.245564 | ||||||||
\(598\) | 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 | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | − | 4.00000i | − | 0.162758i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −14.0000 | + | 14.0000i | −0.568711 | + | 0.568711i | ||||
\(607\) | 2.00000i | 0.0811775i | 0.999176 | + | 0.0405887i | \(0.0129233\pi\) | ||||
−0.999176 | + | 0.0405887i | \(0.987077\pi\) | |||||||
\(608\) | −16.0000 | + | 16.0000i | −0.648886 | + | 0.648886i | ||||
\(609\) | −12.0000 | −0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 12.0000 | 0.485071 | ||||||||
\(613\) | −20.0000 | −0.807792 | −0.403896 | − | 0.914805i | \(-0.632344\pi\) | ||||
−0.403896 | + | 0.914805i | \(0.632344\pi\) | |||||||
\(614\) | −28.0000 | − | 28.0000i | −1.12999 | − | 1.12999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.0000 | − | 16.0000i | 0.644658 | − | 0.644658i | ||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | −2.00000 | + | 2.00000i | −0.0804518 | + | 0.0804518i | ||||
\(619\) | − | 20.0000i | − | 0.803868i | −0.915669 | − | 0.401934i | \(-0.868338\pi\) | ||
0.915669 | − | 0.401934i | \(-0.131662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000i | 0.160514i | ||||||||
\(622\) | 8.00000 | + | 8.00000i | 0.320771 | + | 0.320771i | ||||
\(623\) | − | 28.0000i | − | 1.12180i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.00000 | − | 6.00000i | 0.239808 | − | 0.239808i | ||||
\(627\) | 16.0000 | 0.638978 | ||||||||
\(628\) | − | 40.0000i | − | 1.59617i | ||||||
\(629\) | 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 | ||||
\(633\) | 12.0000i | 0.476957i | ||||||||
\(634\) | −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 | ||||
\(643\) | −12.0000 | −0.473234 | −0.236617 | − | 0.971603i | \(-0.576039\pi\) | ||||
−0.236617 | + | 0.971603i | \(0.576039\pi\) | |||||||
\(644\) | − | 16.0000i | − | 0.630488i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.0000 | − | 24.0000i | −0.944267 | − | 0.944267i | ||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | −2.00000 | + | 2.00000i | −0.0785674 | + | 0.0785674i | ||||
\(649\) | 32.0000 | 1.25611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.0000i | 0.783862i | ||||||||
\(652\) | 40.0000i | 1.56652i | ||||||||
\(653\) | 30.0000 | 1.17399 | 0.586995 | − | 0.809590i | \(-0.300311\pi\) | ||||
0.586995 | + | 0.809590i | \(0.300311\pi\) | |||||||
\(654\) | 4.00000 | − | 4.00000i | 0.156412 | − | 0.156412i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −40.0000 | −1.56174 | ||||||||
\(657\) | − | 10.0000i | − | 0.390137i | ||||||
\(658\) | 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 | ||||
\(667\) | −24.0000 | −0.929284 | ||||||||
\(668\) | −48.0000 | −1.85718 | ||||||||
\(669\) | − | 10.0000i | − | 0.386622i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0000 | 1.23535 | ||||||||
\(672\) | 8.00000 | − | 8.00000i | 0.308607 | − | 0.308607i | ||||
\(673\) | 2.00000i | 0.0770943i | 0.999257 | + | 0.0385472i | \(0.0122730\pi\) | ||||
−0.999257 | + | 0.0385472i | \(0.987727\pi\) | |||||||
\(674\) | −30.0000 | + | 30.0000i | −1.15556 | + | 1.15556i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 26.0000i | − | 1.00000i | ||||||
\(677\) | 38.0000 | 1.46046 | 0.730229 | − | 0.683202i | \(-0.239413\pi\) | ||||
0.730229 | + | 0.683202i | \(0.239413\pi\) | |||||||
\(678\) | 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 | ||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 8.00000 | 0.305888 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −20.0000 | + | 20.0000i | −0.763604 | + | 0.763604i | ||||
\(687\) | 4.00000i | 0.152610i | ||||||||
\(688\) | 16.0000 | 0.609994 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.0000i | 0.456502i | 0.973602 | + | 0.228251i | \(0.0733006\pi\) | ||||
−0.973602 | + | 0.228251i | \(0.926699\pi\) | |||||||
\(692\) | − | 20.0000i | − | 0.760286i | ||||||
\(693\) | −8.00000 | −0.303895 | ||||||||
\(694\) | −16.0000 | − | 16.0000i | −0.607352 | − | 0.607352i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12.0000 | − | 12.0000i | −0.454859 | − | 0.454859i | ||||
\(697\) | − | 60.0000i | − | 2.27266i | ||||||
\(698\) | 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 | ||||||||
\(703\) | 16.0000i | 0.603451i | ||||||||
\(704\) | 32.0000 | 1.20605 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0000 | + | 18.0000i | −0.677439 | + | 0.677439i | ||||
\(707\) | −28.0000 | −1.05305 | ||||||||
\(708\) | 16.0000 | 0.601317 | ||||||||
\(709\) | − | 44.0000i | − | 1.65245i | −0.563337 | − | 0.826227i | \(-0.690483\pi\) | ||
0.563337 | − | 0.826227i | \(-0.309517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | 0.525041 | ||||||||
\(712\) | 28.0000 | − | 28.0000i | 1.04934 | − | 1.04934i | ||||
\(713\) | 40.0000i | 1.49801i | ||||||||
\(714\) | 12.0000 | + | 12.0000i | 0.449089 | + | 0.449089i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.0000 | −0.597531 | ||||||||
\(718\) | −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 | ||||
\(723\) | −30.0000 | −1.11571 | ||||||||
\(724\) | 40.0000 | 1.48659 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −5.00000 | − | 5.00000i | −0.185567 | − | 0.185567i | ||||
\(727\) | − | 14.0000i | − | 0.519231i | −0.965712 | − | 0.259616i | \(-0.916404\pi\) | ||
0.965712 | − | 0.259616i | \(-0.0835959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0000i | 0.887672i | ||||||||
\(732\) | 16.0000 | 0.591377 | ||||||||
\(733\) | −24.0000 | −0.886460 | −0.443230 | − | 0.896408i | \(-0.646168\pi\) | ||||
−0.443230 | + | 0.896408i | \(0.646168\pi\) | |||||||
\(734\) | 18.0000 | − | 18.0000i | 0.664392 | − | 0.664392i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.0000 | − | 16.0000i | 0.589768 | − | 0.589768i | ||||
\(737\) | 48.0000i | 1.76810i | ||||||||
\(738\) | 10.0000 | + | 10.0000i | 0.368105 | + | 0.368105i | ||||
\(739\) | − | 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 | ||||
\(743\) | 48.0000i | 1.76095i | 0.474093 | + | 0.880475i | \(0.342776\pi\) | ||||
−0.474093 | + | 0.880475i | \(0.657224\pi\) | |||||||
\(744\) | −20.0000 | + | 20.0000i | −0.733236 | + | 0.733236i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 20.0000 | + | 20.0000i | 0.732252 | + | 0.732252i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 48.0000i | 1.75505i | ||||||||
\(749\) | − | 8.00000i | − | 0.292314i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 26.0000 | 0.948753 | 0.474377 | − | 0.880322i | \(-0.342673\pi\) | ||||
0.474377 | + | 0.880322i | \(0.342673\pi\) | |||||||
\(752\) | 16.0000i | 0.583460i | ||||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.00000 | −0.145479 | ||||||||
\(757\) | 8.00000 | 0.290765 | 0.145382 | − | 0.989376i | \(-0.453559\pi\) | ||||
0.145382 | + | 0.989376i | \(0.453559\pi\) | |||||||
\(758\) | −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 | ||||
\(763\) | 8.00000 | 0.289619 | ||||||||
\(764\) | − | 16.0000i | − | 0.578860i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.0000 | − | 24.0000i | 0.867155 | − | 0.867155i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 16.0000 | 0.577350 | ||||||||
\(769\) | 6.00000 | 0.216366 | 0.108183 | − | 0.994131i | \(-0.465497\pi\) | ||||
0.108183 | + | 0.994131i | \(0.465497\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 2.00000i | − | 0.0720282i | ||||||
\(772\) | −28.0000 | −1.00774 | ||||||||
\(773\) | 6.00000 | 0.215805 | 0.107903 | − | 0.994161i | \(-0.465587\pi\) | ||||
0.107903 | + | 0.994161i | \(0.465587\pi\) | |||||||
\(774\) | −4.00000 | − | 4.00000i | −0.143777 | − | 0.143777i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 20.0000 | + | 20.0000i | 0.717958 | + | 0.717958i | ||||
\(777\) | − | 8.00000i | − | 0.286998i | ||||||
\(778\) | 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 | ||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | 20.0000i | 0.712470i | ||||||||
\(789\) | 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 | ||||||||
\(797\) | −30.0000 | −1.06265 | −0.531327 | − | 0.847167i | \(-0.678307\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | 40.0000 | 1.41157 | ||||||||
\(804\) | 24.0000i | 0.846415i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 10.0000i | − | 0.352017i | ||||||
\(808\) | −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 | \(-0.977627\pi\) | ||
0.997531 | − | 0.0702295i | \(-0.0223732\pi\) | |||||||
\(812\) | − | 24.0000i | − | 0.842235i | ||||||
\(813\) | −2.00000 | −0.0701431 | ||||||||
\(814\) | 16.0000 | − | 16.0000i | 0.560800 | − | 0.560800i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 24.0000i | 0.840168i | ||||||||
\(817\) | 16.0000i | 0.559769i | ||||||||
\(818\) | 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 | ||||
\(823\) | − | 42.0000i | − | 1.46403i | −0.681290 | − | 0.732014i | \(-0.738581\pi\) | ||
0.681290 | − | 0.732014i | \(-0.261419\pi\) | |||||||
\(824\) | −4.00000 | − | 4.00000i | −0.139347 | − | 0.139347i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0000 | + | 16.0000i | 0.556711 | + | 0.556711i | ||||
\(827\) | 4.00000 | 0.139094 | 0.0695468 | − | 0.997579i | \(-0.477845\pi\) | ||||
0.0695468 | + | 0.997579i | \(0.477845\pi\) | |||||||
\(828\) | −8.00000 | −0.278019 | ||||||||
\(829\) | 44.0000i | 1.52818i | 0.645108 | + | 0.764092i | \(0.276812\pi\) | ||||
−0.645108 | + | 0.764092i | \(0.723188\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.0000 | 0.555034 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 18.0000i | − | 0.623663i | ||||||
\(834\) | −4.00000 | + | 4.00000i | −0.138509 | + | 0.138509i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 32.0000i | 1.10674i | ||||||||
\(837\) | 10.0000 | 0.345651 | ||||||||
\(838\) | −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 | ||||
\(843\) | −10.0000 | −0.344418 | ||||||||
\(844\) | −24.0000 | −0.826114 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | − | 4.00000i | 0.137523 | − | 0.137523i | ||||
\(847\) | − | 10.0000i | − | 0.343604i | ||||||
\(848\) | 40.0000 | 1.37361 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 16.0000i | − | 0.548473i | ||||||
\(852\) | − | 8.00000i | − | 0.274075i | ||||||
\(853\) | −44.0000 | −1.50653 | −0.753266 | − | 0.657716i | \(-0.771523\pi\) | ||||
−0.753266 | + | 0.657716i | \(0.771523\pi\) | |||||||
\(854\) | 16.0000 | + | 16.0000i | 0.547509 | + | 0.547509i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | − | 8.00000i | 0.273434 | − | 0.273434i | ||||
\(857\) | 6.00000i | 0.204956i | 0.994735 | + | 0.102478i | \(0.0326771\pi\) | ||||
−0.994735 | + | 0.102478i | \(0.967323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.0000i | 1.50126i | 0.660722 | + | 0.750630i | \(0.270250\pi\) | ||||
−0.660722 | + | 0.750630i | \(0.729750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.0000i | 0.681598i | ||||||||
\(862\) | −36.0000 | − | 36.0000i | −1.22616 | − | 1.22616i | ||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | −4.00000 | − | 4.00000i | −0.136083 | − | 0.136083i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 14.0000 | − | 14.0000i | 0.475739 | − | 0.475739i | ||||
\(867\) | −19.0000 | −0.645274 | ||||||||
\(868\) | −40.0000 | −1.35769 | ||||||||
\(869\) | 56.0000i | 1.89967i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8.00000 | + | 8.00000i | 0.270914 | + | 0.270914i | ||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | 16.0000 | + | 16.0000i | 0.541208 | + | 0.541208i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 20.0000 | 0.675737 | ||||||||
\(877\) | −44.0000 | −1.48577 | −0.742887 | − | 0.669417i | \(-0.766544\pi\) | ||||
−0.742887 | + | 0.669417i | \(0.766544\pi\) | |||||||
\(878\) | −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 | ||||
\(883\) | −28.0000 | −0.942275 | −0.471138 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471138 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0000 | + | 16.0000i | 0.537531 | + | 0.537531i | ||||
\(887\) | 16.0000i | 0.537227i | 0.963248 | + | 0.268614i | \(0.0865655\pi\) | ||||
−0.963248 | + | 0.268614i | \(0.913434\pi\) | |||||||
\(888\) | 8.00000 | − | 8.00000i | 0.268462 | − | 0.268462i | ||||
\(889\) | 12.0000 | 0.402467 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.00000i | 0.134005i | ||||||||
\(892\) | 20.0000 | 0.669650 | ||||||||
\(893\) | −16.0000 | −0.535420 | ||||||||
\(894\) | −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 | ||||
\(903\) | − | 8.00000i | − | 0.266223i | ||||||
\(904\) | 12.0000 | + | 12.0000i | 0.399114 | + | 0.399114i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.00000 | − | 2.00000i | −0.0664455 | − | 0.0664455i | ||||
\(907\) | 52.0000 | 1.72663 | 0.863316 | − | 0.504664i | \(-0.168384\pi\) | ||||
0.863316 | + | 0.504664i | \(0.168384\pi\) | |||||||
\(908\) | 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 | \(0.792611\pi\) | |||||||
\(912\) | 16.0000i | 0.529813i | ||||||||
\(913\) | 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 | \(-0.358926\pi\) | ||||
0.428830 | + | 0.903385i | \(0.358926\pi\) | |||||||
\(920\) | 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 | ||||
\(927\) | 2.00000i | 0.0656886i | ||||||||
\(928\) | 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 | ||||||
\(932\) | −12.0000 | −0.393073 | ||||||||
\(933\) | 8.00000 | 0.261908 | ||||||||
\(934\) | 8.00000 | + | 8.00000i | 0.261768 | + | 0.261768i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.0000i | 0.718709i | 0.933201 | + | 0.359354i | \(0.117003\pi\) | ||||
−0.933201 | + | 0.359354i | \(0.882997\pi\) | |||||||
\(938\) | −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 | ||||
\(943\) | 40.0000i | 1.30258i | ||||||||
\(944\) | 32.0000i | 1.04151i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 16.0000 | − | 16.0000i | 0.520205 | − | 0.520205i | ||||
\(947\) | 36.0000 | 1.16984 | 0.584921 | − | 0.811090i | \(-0.301125\pi\) | ||||
0.584921 | + | 0.811090i | \(0.301125\pi\) | |||||||
\(948\) | 28.0000i | 0.909398i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | −24.0000 | + | 24.0000i | −0.777844 | + | 0.777844i | ||||
\(953\) | 26.0000i | 0.842223i | 0.907009 | + | 0.421111i | \(0.138360\pi\) | ||||
−0.907009 | + | 0.421111i | \(0.861640\pi\) | |||||||
\(954\) | −10.0000 | − | 10.0000i | −0.323762 | − | 0.323762i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 32.0000i | − | 1.03495i | ||||||
\(957\) | −24.0000 | −0.775810 | ||||||||
\(958\) | −4.00000 | − | 4.00000i | −0.129234 | − | 0.129234i | ||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 69.0000 | 2.22581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | − | 60.0000i | − | 1.93247i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −8.00000 | − | 8.00000i | −0.257396 | − | 0.257396i | ||||
\(967\) | 46.0000i | 1.47926i | 0.673014 | + | 0.739630i | \(0.265000\pi\) | ||||
−0.673014 | + | 0.739630i | \(0.735000\pi\) | |||||||
\(968\) | 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 | \(0.938325\pi\) | |||||||
\(972\) | 2.00000i | 0.0641500i | ||||||||
\(973\) | −8.00000 | −0.256468 | ||||||||
\(974\) | 30.0000 | − | 30.0000i | 0.961262 | − | 0.961262i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.0000i | 1.02430i | ||||||||
\(977\) | − | 22.0000i | − | 0.703842i | −0.936030 | − | 0.351921i | \(-0.885529\pi\) | ||
0.936030 | − | 0.351921i | \(-0.114471\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | 32.0000i | 1.02064i | 0.859984 | + | 0.510321i | \(0.170473\pi\) | ||||
−0.859984 | + | 0.510321i | \(0.829527\pi\) | |||||||
\(984\) | −20.0000 | + | 20.0000i | −0.637577 | + | 0.637577i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 36.0000 | + | 36.0000i | 1.14647 | + | 1.14647i | ||||
\(987\) | 8.00000 | 0.254643 | ||||||||
\(988\) | 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 | ||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | 8.00000 | − | 8.00000i | 0.253745 | − | 0.253745i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.0000 | 0.886769 | 0.443384 | − | 0.896332i | \(-0.353778\pi\) | ||||
0.443384 | + | 0.896332i | \(0.353778\pi\) | |||||||
\(998\) | −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 \(a_p\))