Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1567,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1567");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1567.3 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1567 |
Dual form | 1764.2.b.a.1567.2 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.707107 | + | 0.707107i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 2.00000i | − | 1.00000i | ||||||
\(5\) | − | 1.73205i | − | 0.774597i | −0.921954 | − | 0.387298i | \(-0.873408\pi\) | ||
0.921954 | − | 0.387298i | \(-0.126592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | + | 1.73205i | 0.547723 | + | 0.547723i | ||||
\(11\) | 1.00000i | 0.301511i | 0.988571 | + | 0.150756i | \(0.0481707\pi\) | ||||
−0.988571 | + | 0.150756i | \(0.951829\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.73205i | 0.420084i | 0.977692 | + | 0.210042i | \(0.0673601\pi\) | ||||
−0.977692 | + | 0.210042i | \(0.932640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.19615 | −1.19208 | −0.596040 | − | 0.802955i | \(-0.703260\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | −3.46410 | −0.774597 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.00000i | −0.213201 | − | 0.213201i | ||||
\(23\) | − | 1.00000i | − | 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | 0.400000 | ||||||||
\(26\) | −3.46410 | − | 3.46410i | −0.679366 | − | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.73205 | −0.311086 | −0.155543 | − | 0.987829i | \(-0.549713\pi\) | ||||
−0.155543 | + | 0.987829i | \(0.549713\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.707107 | − | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.73205 | − | 1.73205i | −0.297044 | − | 0.297044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | 0.493197 | 0.246598 | − | 0.969118i | \(-0.420687\pi\) | ||||
0.246598 | + | 0.969118i | \(0.420687\pi\) | |||||||
\(38\) | 5.19615 | − | 5.19615i | 0.842927 | − | 0.842927i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.46410 | − | 3.46410i | 0.547723 | − | 0.547723i | ||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 2.00000 | 0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | + | 1.00000i | 0.147442 | + | 0.147442i | ||||
\(47\) | −8.66025 | −1.26323 | −0.631614 | − | 0.775283i | \(-0.717607\pi\) | ||||
−0.631614 | + | 0.775283i | \(0.717607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.00000 | + | 2.00000i | −0.282843 | + | 0.282843i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.92820 | 0.960769 | ||||||||
\(53\) | 1.00000 | 0.137361 | 0.0686803 | − | 0.997639i | \(-0.478121\pi\) | ||||
0.0686803 | + | 0.997639i | \(0.478121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.73205 | 0.233550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.00000 | − | 4.00000i | 0.525226 | − | 0.525226i | ||||
\(59\) | 5.19615 | 0.676481 | 0.338241 | − | 0.941060i | \(-0.390168\pi\) | ||||
0.338241 | + | 0.941060i | \(0.390168\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.19615i | 0.665299i | 0.943051 | + | 0.332650i | \(0.107943\pi\) | ||||
−0.943051 | + | 0.332650i | \(0.892057\pi\) | |||||||
\(62\) | 1.73205 | − | 1.73205i | 0.219971 | − | 0.219971i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 6.00000 | 0.744208 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.00000i | − | 0.366508i | −0.983066 | − | 0.183254i | \(-0.941337\pi\) | ||
0.983066 | − | 0.183254i | \(-0.0586631\pi\) | |||||||
\(68\) | 3.46410 | 0.420084 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0000i | 1.66149i | 0.556650 | + | 0.830747i | \(0.312086\pi\) | ||||
−0.556650 | + | 0.830747i | \(0.687914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.66025i | 1.01361i | 0.862062 | + | 0.506803i | \(0.169173\pi\) | ||||
−0.862062 | + | 0.506803i | \(0.830827\pi\) | |||||||
\(74\) | −3.00000 | + | 3.00000i | −0.348743 | + | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3923i | 1.19208i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.00000i | 1.01258i | 0.862364 | + | 0.506290i | \(0.168983\pi\) | ||||
−0.862364 | + | 0.506290i | \(0.831017\pi\) | |||||||
\(80\) | 6.92820i | 0.774597i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.46410 | − | 3.46410i | −0.382546 | − | 0.382546i | ||||
\(83\) | −13.8564 | −1.52094 | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | 0.325396 | ||||||||
\(86\) | −2.00000 | − | 2.00000i | −0.215666 | − | 0.215666i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 2.00000i | −0.213201 | + | 0.213201i | ||||
\(89\) | 15.5885i | 1.65237i | 0.563397 | + | 0.826187i | \(0.309494\pi\) | ||||
−0.563397 | + | 0.826187i | \(0.690506\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.00000 | −0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.66025 | − | 8.66025i | 0.893237 | − | 0.893237i | ||||
\(95\) | 9.00000i | 0.923381i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 17.3205i | − | 1.75863i | −0.476240 | − | 0.879316i | \(-0.658000\pi\) | ||
0.476240 | − | 0.879316i | \(-0.342000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | − | 4.00000i | − | 0.400000i | ||||||
\(101\) | 8.66025i | 0.861727i | 0.902417 | + | 0.430864i | \(0.141791\pi\) | ||||
−0.902417 | + | 0.430864i | \(0.858209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.66025 | −0.853320 | −0.426660 | − | 0.904412i | \(-0.640310\pi\) | ||||
−0.426660 | + | 0.904412i | \(0.640310\pi\) | |||||||
\(104\) | −6.92820 | + | 6.92820i | −0.679366 | + | 0.679366i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00000 | + | 1.00000i | −0.0971286 | + | 0.0971286i | ||||
\(107\) | 13.0000i | 1.25676i | 0.777908 | + | 0.628379i | \(0.216281\pi\) | ||||
−0.777908 | + | 0.628379i | \(0.783719\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.00000 | 0.862044 | 0.431022 | − | 0.902342i | \(-0.358153\pi\) | ||||
0.431022 | + | 0.902342i | \(0.358153\pi\) | |||||||
\(110\) | −1.73205 | + | 1.73205i | −0.165145 | + | 0.165145i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0000 | 1.50515 | 0.752577 | − | 0.658505i | \(-0.228811\pi\) | ||||
0.752577 | + | 0.658505i | \(0.228811\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.73205 | −0.161515 | ||||||||
\(116\) | 8.00000i | 0.742781i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.19615 | + | 5.19615i | −0.478345 | + | 0.478345i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0000 | 0.909091 | ||||||||
\(122\) | −5.19615 | − | 5.19615i | −0.470438 | − | 0.470438i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.46410i | 0.311086i | ||||||||
\(125\) | − | 12.1244i | − | 1.08444i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000i | 0.532414i | 0.963916 | + | 0.266207i | \(0.0857705\pi\) | ||||
−0.963916 | + | 0.266207i | \(0.914230\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.00000 | + | 6.00000i | −0.526235 | + | 0.526235i | ||||
\(131\) | −5.19615 | −0.453990 | −0.226995 | − | 0.973896i | \(-0.572890\pi\) | ||||
−0.226995 | + | 0.973896i | \(0.572890\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.00000 | + | 3.00000i | 0.259161 | + | 0.259161i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | + | 3.46410i | −0.297044 | + | 0.297044i | ||||
\(137\) | −1.00000 | −0.0854358 | −0.0427179 | − | 0.999087i | \(-0.513602\pi\) | ||||
−0.0427179 | + | 0.999087i | \(0.513602\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.0000 | − | 14.0000i | −1.17485 | − | 1.17485i | ||||
\(143\) | −3.46410 | −0.289683 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.92820i | 0.575356i | ||||||||
\(146\) | −8.66025 | − | 8.66025i | −0.716728 | − | 0.716728i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 6.00000i | − | 0.493197i | ||||||
\(149\) | −1.00000 | −0.0819232 | −0.0409616 | − | 0.999161i | \(-0.513042\pi\) | ||||
−0.0409616 | + | 0.999161i | \(0.513042\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.00000i | 0.569652i | 0.958579 | + | 0.284826i | \(0.0919358\pi\) | ||||
−0.958579 | + | 0.284826i | \(0.908064\pi\) | |||||||
\(152\) | −10.3923 | − | 10.3923i | −0.842927 | − | 0.842927i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.00000i | 0.240966i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.73205i | 0.138233i | 0.997609 | + | 0.0691164i | \(0.0220180\pi\) | ||||
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | −9.00000 | − | 9.00000i | −0.716002 | − | 0.716002i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −6.92820 | − | 6.92820i | −0.547723 | − | 0.547723i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.0000i | 1.64485i | 0.568876 | + | 0.822423i | \(0.307379\pi\) | ||||
−0.568876 | + | 0.822423i | \(0.692621\pi\) | |||||||
\(164\) | 6.92820 | 0.541002 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.8564 | − | 13.8564i | 1.07547 | − | 1.07547i | ||||
\(167\) | 17.3205 | 1.34030 | 0.670151 | − | 0.742225i | \(-0.266230\pi\) | ||||
0.670151 | + | 0.742225i | \(0.266230\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −3.00000 | + | 3.00000i | −0.230089 | + | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | 0.304997 | ||||||||
\(173\) | − | 12.1244i | − | 0.921798i | −0.887453 | − | 0.460899i | \(-0.847527\pi\) | ||
0.887453 | − | 0.460899i | \(-0.152473\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.00000i | − | 0.301511i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −15.5885 | − | 15.5885i | −1.16840 | − | 1.16840i | ||||
\(179\) | − | 19.0000i | − | 1.42013i | −0.704138 | − | 0.710063i | \(-0.748666\pi\) | ||
0.704138 | − | 0.710063i | \(-0.251334\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | − | 2.00000i | 0.147442 | − | 0.147442i | ||||
\(185\) | − | 5.19615i | − | 0.382029i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73205 | −0.126660 | ||||||||
\(188\) | 17.3205i | 1.26323i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.00000 | − | 9.00000i | −0.652929 | − | 0.652929i | ||||
\(191\) | 1.00000i | 0.0723575i | 0.999345 | + | 0.0361787i | \(0.0115186\pi\) | ||||
−0.999345 | + | 0.0361787i | \(0.988481\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.0000 | −1.07972 | −0.539862 | − | 0.841754i | \(-0.681524\pi\) | ||||
−0.539862 | + | 0.841754i | \(0.681524\pi\) | |||||||
\(194\) | 17.3205 | + | 17.3205i | 1.24354 | + | 1.24354i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0000 | −1.13995 | −0.569976 | − | 0.821661i | \(-0.693048\pi\) | ||||
−0.569976 | + | 0.821661i | \(0.693048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22.5167 | −1.59616 | −0.798082 | − | 0.602549i | \(-0.794152\pi\) | ||||
−0.798082 | + | 0.602549i | \(0.794152\pi\) | |||||||
\(200\) | 4.00000 | + | 4.00000i | 0.282843 | + | 0.282843i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.66025 | − | 8.66025i | −0.609333 | − | 0.609333i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | 8.66025 | − | 8.66025i | 0.603388 | − | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 13.8564i | − | 0.960769i | ||||||
\(209\) | − | 5.19615i | − | 0.359425i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000i | 0.688428i | 0.938891 | + | 0.344214i | \(0.111855\pi\) | ||||
−0.938891 | + | 0.344214i | \(0.888145\pi\) | |||||||
\(212\) | − | 2.00000i | − | 0.137361i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −13.0000 | − | 13.0000i | −0.888662 | − | 0.888662i | ||||
\(215\) | 3.46410 | 0.236250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −9.00000 | + | 9.00000i | −0.609557 | + | 0.609557i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 3.46410i | − | 0.233550i | ||||||
\(221\) | −6.00000 | −0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.0000 | + | 16.0000i | −1.06430 | + | 1.06430i | ||||
\(227\) | −19.0526 | −1.26456 | −0.632281 | − | 0.774739i | \(-0.717881\pi\) | ||||
−0.632281 | + | 0.774739i | \(0.717881\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5885i | 1.03011i | 0.857156 | + | 0.515057i | \(0.172229\pi\) | ||||
−0.857156 | + | 0.515057i | \(0.827771\pi\) | |||||||
\(230\) | 1.73205 | − | 1.73205i | 0.114208 | − | 0.114208i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.00000 | − | 8.00000i | −0.525226 | − | 0.525226i | ||||
\(233\) | 7.00000 | 0.458585 | 0.229293 | − | 0.973358i | \(-0.426359\pi\) | ||||
0.229293 | + | 0.973358i | \(0.426359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.0000i | 0.978492i | ||||||||
\(236\) | − | 10.3923i | − | 0.676481i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.0000i | − | 1.29369i | −0.762620 | − | 0.646846i | \(-0.776088\pi\) | ||
0.762620 | − | 0.646846i | \(-0.223912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.19615i | − | 0.334714i | −0.985896 | − | 0.167357i | \(-0.946477\pi\) | ||
0.985896 | − | 0.167357i | \(-0.0535232\pi\) | |||||||
\(242\) | −10.0000 | + | 10.0000i | −0.642824 | + | 0.642824i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.3923 | 0.665299 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.0000i | − | 1.14531i | ||||||
\(248\) | −3.46410 | − | 3.46410i | −0.219971 | − | 0.219971i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.1244 | + | 12.1244i | 0.766812 | + | 0.766812i | ||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | −6.00000 | − | 6.00000i | −0.376473 | − | 0.376473i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 5.19615i | 0.324127i | 0.986780 | + | 0.162064i | \(0.0518150\pi\) | ||||
−0.986780 | + | 0.162064i | \(0.948185\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 12.0000i | − | 0.744208i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.19615 | − | 5.19615i | 0.321019 | − | 0.321019i | ||||
\(263\) | 23.0000i | 1.41824i | 0.705087 | + | 0.709120i | \(0.250908\pi\) | ||||
−0.705087 | + | 0.709120i | \(0.749092\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.73205i | − | 0.106399i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.00000 | −0.366508 | ||||||||
\(269\) | − | 22.5167i | − | 1.37287i | −0.727194 | − | 0.686433i | \(-0.759176\pi\) | ||
0.727194 | − | 0.686433i | \(-0.240824\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.5885 | −0.946931 | −0.473466 | − | 0.880812i | \(-0.656997\pi\) | ||||
−0.473466 | + | 0.880812i | \(0.656997\pi\) | |||||||
\(272\) | − | 6.92820i | − | 0.420084i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.00000 | − | 1.00000i | 0.0604122 | − | 0.0604122i | ||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.0000 | −0.781094 | −0.390547 | − | 0.920583i | \(-0.627714\pi\) | ||||
−0.390547 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(278\) | 6.92820 | − | 6.92820i | 0.415526 | − | 0.415526i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.00000 | 0.238620 | 0.119310 | − | 0.992857i | \(-0.461932\pi\) | ||||
0.119310 | + | 0.992857i | \(0.461932\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1244 | 0.720718 | 0.360359 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360359 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(284\) | 28.0000 | 1.66149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.46410 | − | 3.46410i | 0.204837 | − | 0.204837i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0000 | 0.823529 | ||||||||
\(290\) | −6.92820 | − | 6.92820i | −0.406838 | − | 0.406838i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 17.3205 | 1.01361 | ||||||||
\(293\) | 20.7846i | 1.21425i | 0.794606 | + | 0.607125i | \(0.207677\pi\) | ||||
−0.794606 | + | 0.607125i | \(0.792323\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.00000i | − | 0.524000i | ||||||
\(296\) | 6.00000 | + | 6.00000i | 0.348743 | + | 0.348743i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.00000 | − | 1.00000i | 0.0579284 | − | 0.0579284i | ||||
\(299\) | 3.46410 | 0.200334 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.00000 | − | 7.00000i | −0.402805 | − | 0.402805i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.7846 | 1.19208 | ||||||||
\(305\) | 9.00000 | 0.515339 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7846 | 1.18624 | 0.593120 | − | 0.805114i | \(-0.297896\pi\) | ||||
0.593120 | + | 0.805114i | \(0.297896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.00000 | − | 3.00000i | −0.170389 | − | 0.170389i | ||||
\(311\) | −8.66025 | −0.491078 | −0.245539 | − | 0.969387i | \(-0.578965\pi\) | ||||
−0.245539 | + | 0.969387i | \(0.578965\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.73205i | − | 0.0979013i | −0.998801 | − | 0.0489506i | \(-0.984412\pi\) | ||
0.998801 | − | 0.0489506i | \(-0.0155877\pi\) | |||||||
\(314\) | −1.73205 | − | 1.73205i | −0.0977453 | − | 0.0977453i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 18.0000 | 1.01258 | ||||||||
\(317\) | −11.0000 | −0.617822 | −0.308911 | − | 0.951091i | \(-0.599964\pi\) | ||||
−0.308911 | + | 0.951091i | \(0.599964\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 4.00000i | − | 0.223957i | ||||||
\(320\) | 13.8564 | 0.774597 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.00000i | − | 0.500773i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.92820i | 0.384308i | ||||||||
\(326\) | −21.0000 | − | 21.0000i | −1.16308 | − | 1.16308i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.92820 | + | 6.92820i | −0.382546 | + | 0.382546i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.00000i | − | 0.384755i | −0.981321 | − | 0.192377i | \(-0.938380\pi\) | ||
0.981321 | − | 0.192377i | \(-0.0616198\pi\) | |||||||
\(332\) | 27.7128i | 1.52094i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −17.3205 | + | 17.3205i | −0.947736 | + | 0.947736i | ||||
\(335\) | −5.19615 | −0.283896 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −1.00000 | + | 1.00000i | −0.0543928 | + | 0.0543928i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 6.00000i | − | 0.325396i | ||||||
\(341\) | − | 1.73205i | − | 0.0937958i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −4.00000 | + | 4.00000i | −0.215666 | + | 0.215666i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.1244 | + | 12.1244i | 0.651809 | + | 0.651809i | ||||
\(347\) | − | 13.0000i | − | 0.697877i | −0.937146 | − | 0.348938i | \(-0.886542\pi\) | ||
0.937146 | − | 0.348938i | \(-0.113458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.00000 | + | 4.00000i | 0.213201 | + | 0.213201i | ||||
\(353\) | 29.4449i | 1.56719i | 0.621271 | + | 0.783596i | \(0.286617\pi\) | ||||
−0.621271 | + | 0.783596i | \(0.713383\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.2487 | 1.28699 | ||||||||
\(356\) | 31.1769 | 1.65237 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0000 | + | 19.0000i | 1.00418 | + | 1.00418i | ||||
\(359\) | − | 23.0000i | − | 1.21389i | −0.794742 | − | 0.606947i | \(-0.792394\pi\) | ||
0.794742 | − | 0.606947i | \(-0.207606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.00000 | 0.421053 | ||||||||
\(362\) | −6.92820 | − | 6.92820i | −0.364138 | − | 0.364138i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.73205 | 0.0904123 | 0.0452062 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452062 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.19615 | + | 5.19615i | 0.270135 | + | 0.270135i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.0000 | −1.50156 | −0.750782 | − | 0.660551i | \(-0.770323\pi\) | ||||
−0.750782 | + | 0.660551i | \(0.770323\pi\) | |||||||
\(374\) | 1.73205 | − | 1.73205i | 0.0895622 | − | 0.0895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −17.3205 | − | 17.3205i | −0.893237 | − | 0.893237i | ||||
\(377\) | − | 13.8564i | − | 0.713641i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 18.0000 | 0.923381 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.00000 | − | 1.00000i | −0.0511645 | − | 0.0511645i | ||||
\(383\) | 5.19615 | 0.265511 | 0.132755 | − | 0.991149i | \(-0.457617\pi\) | ||||
0.132755 | + | 0.991149i | \(0.457617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.0000 | − | 15.0000i | 0.763480 | − | 0.763480i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −34.6410 | −1.75863 | ||||||||
\(389\) | 19.0000 | 0.963338 | 0.481669 | − | 0.876353i | \(-0.340031\pi\) | ||||
0.481669 | + | 0.876353i | \(0.340031\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.73205 | 0.0875936 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.0000 | − | 16.0000i | 0.806068 | − | 0.806068i | ||||
\(395\) | 15.5885 | 0.784340 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 19.0526i | − | 0.956221i | −0.878300 | − | 0.478110i | \(-0.841322\pi\) | ||
0.878300 | − | 0.478110i | \(-0.158678\pi\) | |||||||
\(398\) | 22.5167 | − | 22.5167i | 1.12866 | − | 1.12866i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | −0.400000 | ||||||||
\(401\) | 23.0000 | 1.14857 | 0.574283 | − | 0.818657i | \(-0.305281\pi\) | ||||
0.574283 | + | 0.818657i | \(0.305281\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.00000i | − | 0.298881i | ||||||
\(404\) | 17.3205 | 0.861727 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.9808i | 1.28467i | 0.766426 | + | 0.642333i | \(0.222033\pi\) | ||||
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | −6.00000 | + | 6.00000i | −0.296319 | + | 0.296319i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.3205i | 0.853320i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000i | 1.17811i | ||||||||
\(416\) | 13.8564 | + | 13.8564i | 0.679366 | + | 0.679366i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.19615 | + | 5.19615i | 0.254152 | + | 0.254152i | ||||
\(419\) | 20.7846 | 1.01539 | 0.507697 | − | 0.861536i | \(-0.330497\pi\) | ||||
0.507697 | + | 0.861536i | \(0.330497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | −10.0000 | − | 10.0000i | −0.486792 | − | 0.486792i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.00000 | + | 2.00000i | 0.0971286 | + | 0.0971286i | ||||
\(425\) | 3.46410i | 0.168034i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 26.0000 | 1.25676 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.46410 | + | 3.46410i | −0.167054 | + | 0.167054i | ||||
\(431\) | − | 23.0000i | − | 1.10787i | −0.832560 | − | 0.553936i | \(-0.813125\pi\) | ||
0.832560 | − | 0.553936i | \(-0.186875\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.3923i | − | 0.499422i | −0.968320 | − | 0.249711i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249711i | \(-0.0803357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 18.0000i | − | 0.862044i | ||||||
\(437\) | 5.19615i | 0.248566i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5167 | 1.07466 | 0.537331 | − | 0.843372i | \(-0.319433\pi\) | ||||
0.537331 | + | 0.843372i | \(0.319433\pi\) | |||||||
\(440\) | 3.46410 | + | 3.46410i | 0.165145 | + | 0.165145i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 6.00000 | − | 6.00000i | 0.285391 | − | 0.285391i | ||||
\(443\) | 17.0000i | 0.807694i | 0.914826 | + | 0.403847i | \(0.132327\pi\) | ||||
−0.914826 | + | 0.403847i | \(0.867673\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 27.0000 | 1.27992 | ||||||||
\(446\) | −6.92820 | + | 6.92820i | −0.328060 | + | 0.328060i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.00000 | −0.377543 | −0.188772 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188772 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.46410 | −0.163118 | ||||||||
\(452\) | − | 32.0000i | − | 1.50515i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 19.0526 | − | 19.0526i | 0.894181 | − | 0.894181i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0000 | 0.701670 | 0.350835 | − | 0.936437i | \(-0.385898\pi\) | ||||
0.350835 | + | 0.936437i | \(0.385898\pi\) | |||||||
\(458\) | −15.5885 | − | 15.5885i | −0.728401 | − | 0.728401i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.46410i | 0.161515i | ||||||||
\(461\) | 17.3205i | 0.806696i | 0.915047 | + | 0.403348i | \(0.132154\pi\) | ||||
−0.915047 | + | 0.403348i | \(0.867846\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 30.0000i | − | 1.39422i | −0.716965 | − | 0.697109i | \(-0.754469\pi\) | ||
0.716965 | − | 0.697109i | \(-0.245531\pi\) | |||||||
\(464\) | 16.0000 | 0.742781 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.00000 | + | 7.00000i | −0.324269 | + | 0.324269i | ||||
\(467\) | 8.66025 | 0.400749 | 0.200374 | − | 0.979719i | \(-0.435784\pi\) | ||||
0.200374 | + | 0.979719i | \(0.435784\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −15.0000 | − | 15.0000i | −0.691898 | − | 0.691898i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.3923 | + | 10.3923i | 0.478345 | + | 0.478345i | ||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.3923 | −0.476832 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.0000 | + | 20.0000i | 0.914779 | + | 0.914779i | ||||
\(479\) | 12.1244 | 0.553976 | 0.276988 | − | 0.960873i | \(-0.410664\pi\) | ||||
0.276988 | + | 0.960873i | \(0.410664\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.3923i | 0.473848i | ||||||||
\(482\) | 5.19615 | + | 5.19615i | 0.236678 | + | 0.236678i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 20.0000i | − | 0.909091i | ||||||
\(485\) | −30.0000 | −1.36223 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 31.0000i | − | 1.40474i | −0.711810 | − | 0.702372i | \(-0.752124\pi\) | ||
0.711810 | − | 0.702372i | \(-0.247876\pi\) | |||||||
\(488\) | −10.3923 | + | 10.3923i | −0.470438 | + | 0.470438i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.0000i | − | 1.44414i | −0.691820 | − | 0.722070i | \(-0.743191\pi\) | ||
0.691820 | − | 0.722070i | \(-0.256809\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.92820i | − | 0.312031i | ||||||
\(494\) | 18.0000 | + | 18.0000i | 0.809858 | + | 0.809858i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 35.0000i | − | 1.56682i | −0.621508 | − | 0.783408i | \(-0.713480\pi\) | ||
0.621508 | − | 0.783408i | \(-0.286520\pi\) | |||||||
\(500\) | −24.2487 | −1.08444 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.46410 | + | 3.46410i | −0.154610 | + | 0.154610i | ||||
\(503\) | 6.92820 | 0.308913 | 0.154457 | − | 0.988000i | \(-0.450637\pi\) | ||||
0.154457 | + | 0.988000i | \(0.450637\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0000 | 0.667491 | ||||||||
\(506\) | −1.00000 | + | 1.00000i | −0.0444554 | + | 0.0444554i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 12.0000 | 0.532414 | ||||||||
\(509\) | 12.1244i | 0.537403i | 0.963224 | + | 0.268701i | \(0.0865945\pi\) | ||||
−0.963224 | + | 0.268701i | \(0.913406\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.19615 | − | 5.19615i | −0.229192 | − | 0.229192i | ||||
\(515\) | 15.0000i | 0.660979i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.66025i | − | 0.380878i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.0000 | + | 12.0000i | 0.526235 | + | 0.526235i | ||||
\(521\) | − | 1.73205i | − | 0.0758825i | −0.999280 | − | 0.0379413i | \(-0.987920\pi\) | ||
0.999280 | − | 0.0379413i | \(-0.0120800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.9808 | −1.13606 | −0.568030 | − | 0.823008i | \(-0.692294\pi\) | ||||
−0.568030 | + | 0.823008i | \(0.692294\pi\) | |||||||
\(524\) | 10.3923i | 0.453990i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.0000 | − | 23.0000i | −1.00285 | − | 1.00285i | ||||
\(527\) | − | 3.00000i | − | 0.130682i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 1.73205 | + | 1.73205i | 0.0752355 | + | 0.0752355i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.5167 | 0.973480 | ||||||||
\(536\) | 6.00000 | − | 6.00000i | 0.259161 | − | 0.259161i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.5167 | + | 22.5167i | 0.970762 | + | 0.970762i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.0000 | −0.816874 | −0.408437 | − | 0.912787i | \(-0.633926\pi\) | ||||
−0.408437 | + | 0.912787i | \(0.633926\pi\) | |||||||
\(542\) | 15.5885 | − | 15.5885i | 0.669582 | − | 0.669582i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.92820 | + | 6.92820i | 0.297044 | + | 0.297044i | ||||
\(545\) | − | 15.5885i | − | 0.667736i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 2.00000i | 0.0854358i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.00000 | − | 2.00000i | −0.0852803 | − | 0.0852803i | ||||
\(551\) | 20.7846 | 0.885454 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0000 | − | 13.0000i | 0.552317 | − | 0.552317i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.8564i | 0.587643i | ||||||||
\(557\) | −37.0000 | −1.56774 | −0.783870 | − | 0.620925i | \(-0.786757\pi\) | ||||
−0.783870 | + | 0.620925i | \(0.786757\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.92820 | −0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.00000 | + | 4.00000i | −0.168730 | + | 0.168730i | ||||
\(563\) | −22.5167 | −0.948964 | −0.474482 | − | 0.880265i | \(-0.657365\pi\) | ||||
−0.474482 | + | 0.880265i | \(0.657365\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 27.7128i | − | 1.16589i | ||||||
\(566\) | −12.1244 | + | 12.1244i | −0.509625 | + | 0.509625i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −28.0000 | + | 28.0000i | −1.17485 | + | 1.17485i | ||||
\(569\) | 13.0000 | 0.544988 | 0.272494 | − | 0.962157i | \(-0.412151\pi\) | ||||
0.272494 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 21.0000i | − | 0.878823i | −0.898286 | − | 0.439411i | \(-0.855187\pi\) | ||
0.898286 | − | 0.439411i | \(-0.144813\pi\) | |||||||
\(572\) | 6.92820i | 0.289683i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.00000i | − | 0.0834058i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 32.9090i | − | 1.37002i | −0.728535 | − | 0.685009i | \(-0.759798\pi\) | ||
0.728535 | − | 0.685009i | \(-0.240202\pi\) | |||||||
\(578\) | −14.0000 | + | 14.0000i | −0.582323 | + | 0.582323i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.8564 | 0.575356 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00000i | 0.0414158i | ||||||||
\(584\) | −17.3205 | + | 17.3205i | −0.716728 | + | 0.716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.7846 | − | 20.7846i | −0.858604 | − | 0.858604i | ||||
\(587\) | −6.92820 | −0.285958 | −0.142979 | − | 0.989726i | \(-0.545668\pi\) | ||||
−0.142979 | + | 0.989726i | \(0.545668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.00000 | 0.370839 | ||||||||
\(590\) | 9.00000 | + | 9.00000i | 0.370524 | + | 0.370524i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | −0.493197 | ||||||||
\(593\) | − | 15.5885i | − | 0.640141i | −0.947394 | − | 0.320071i | \(-0.896293\pi\) | ||
0.947394 | − | 0.320071i | \(-0.103707\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.00000i | 0.0819232i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.46410 | + | 3.46410i | −0.141658 | + | 0.141658i | ||||
\(599\) | − | 17.0000i | − | 0.694601i | −0.937754 | − | 0.347301i | \(-0.887098\pi\) | ||
0.937754 | − | 0.347301i | \(-0.112902\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.1051i | 1.55434i | 0.629291 | + | 0.777170i | \(0.283346\pi\) | ||||
−0.629291 | + | 0.777170i | \(0.716654\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.0000 | 0.569652 | ||||||||
\(605\) | − | 17.3205i | − | 0.704179i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.5885 | 0.632716 | 0.316358 | − | 0.948640i | \(-0.397540\pi\) | ||||
0.316358 | + | 0.948640i | \(0.397540\pi\) | |||||||
\(608\) | −20.7846 | + | 20.7846i | −0.842927 | + | 0.842927i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.00000 | + | 9.00000i | −0.364399 | + | 0.364399i | ||||
\(611\) | − | 30.0000i | − | 1.21367i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.0000 | −1.25208 | −0.626039 | − | 0.779792i | \(-0.715325\pi\) | ||||
−0.626039 | + | 0.779792i | \(0.715325\pi\) | |||||||
\(614\) | −20.7846 | + | 20.7846i | −0.838799 | + | 0.838799i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −20.0000 | −0.805170 | −0.402585 | − | 0.915383i | \(-0.631888\pi\) | ||||
−0.402585 | + | 0.915383i | \(0.631888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.5885 | 0.626553 | 0.313276 | − | 0.949662i | \(-0.398573\pi\) | ||||
0.313276 | + | 0.949662i | \(0.398573\pi\) | |||||||
\(620\) | 6.00000 | 0.240966 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.66025 | − | 8.66025i | 0.347245 | − | 0.347245i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | 1.73205 | + | 1.73205i | 0.0692267 | + | 0.0692267i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.46410 | 0.138233 | ||||||||
\(629\) | 5.19615i | 0.207184i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.0000i | 1.19428i | 0.802137 | + | 0.597141i | \(0.203697\pi\) | ||||
−0.802137 | + | 0.597141i | \(0.796303\pi\) | |||||||
\(632\) | −18.0000 | + | 18.0000i | −0.716002 | + | 0.716002i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 11.0000 | − | 11.0000i | 0.436866 | − | 0.436866i | ||||
\(635\) | 10.3923 | 0.412406 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 4.00000 | + | 4.00000i | 0.158362 | + | 0.158362i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −13.8564 | + | 13.8564i | −0.547723 | + | 0.547723i | ||||
\(641\) | 13.0000 | 0.513469 | 0.256735 | − | 0.966482i | \(-0.417353\pi\) | ||||
0.256735 | + | 0.966482i | \(0.417353\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.8564 | −0.546443 | −0.273222 | − | 0.961951i | \(-0.588089\pi\) | ||||
−0.273222 | + | 0.961951i | \(0.588089\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | + | 9.00000i | 0.354100 | + | 0.354100i | ||||
\(647\) | 32.9090 | 1.29378 | 0.646892 | − | 0.762581i | \(-0.276068\pi\) | ||||
0.646892 | + | 0.762581i | \(0.276068\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.19615i | 0.203967i | ||||||||
\(650\) | −6.92820 | − | 6.92820i | −0.271746 | − | 0.271746i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 42.0000 | 1.64485 | ||||||||
\(653\) | −31.0000 | −1.21312 | −0.606562 | − | 0.795036i | \(-0.707452\pi\) | ||||
−0.606562 | + | 0.795036i | \(0.707452\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000i | 0.351659i | ||||||||
\(656\) | − | 13.8564i | − | 0.541002i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.0000i | 1.48027i | 0.672458 | + | 0.740135i | \(0.265238\pi\) | ||||
−0.672458 | + | 0.740135i | \(0.734762\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 39.8372i | − | 1.54949i | −0.632276 | − | 0.774743i | \(-0.717879\pi\) | ||
0.632276 | − | 0.774743i | \(-0.282121\pi\) | |||||||
\(662\) | 7.00000 | + | 7.00000i | 0.272063 | + | 0.272063i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −27.7128 | − | 27.7128i | −1.07547 | − | 1.07547i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000i | 0.154881i | ||||||||
\(668\) | − | 34.6410i | − | 1.34030i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.19615 | − | 5.19615i | 0.200745 | − | 0.200745i | ||||
\(671\) | −5.19615 | −0.200595 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 2.00000i | − | 0.0769231i | ||||||
\(677\) | − | 43.3013i | − | 1.66420i | −0.554623 | − | 0.832102i | \(-0.687138\pi\) | ||
0.554623 | − | 0.832102i | \(-0.312862\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.00000 | + | 6.00000i | 0.230089 | + | 0.230089i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.73205 | + | 1.73205i | 0.0663237 | + | 0.0663237i | ||||
\(683\) | 25.0000i | 0.956598i | 0.878197 | + | 0.478299i | \(0.158747\pi\) | ||||
−0.878197 | + | 0.478299i | \(0.841253\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.73205i | 0.0661783i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8.00000i | − | 0.304997i | ||||||
\(689\) | 3.46410i | 0.131972i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1244 | 0.461232 | 0.230616 | − | 0.973045i | \(-0.425926\pi\) | ||||
0.230616 | + | 0.973045i | \(0.425926\pi\) | |||||||
\(692\) | −24.2487 | −0.921798 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.0000 | + | 13.0000i | 0.493473 | + | 0.493473i | ||||
\(695\) | 12.0000i | 0.455186i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | −10.3923 | − | 10.3923i | −0.393355 | − | 0.393355i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.5885 | −0.587930 | ||||||||
\(704\) | −8.00000 | −0.301511 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −29.4449 | − | 29.4449i | −1.10817 | − | 1.10817i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.00000 | −0.338002 | −0.169001 | − | 0.985616i | \(-0.554054\pi\) | ||||
−0.169001 | + | 0.985616i | \(0.554054\pi\) | |||||||
\(710\) | −24.2487 | + | 24.2487i | −0.910038 | + | 0.910038i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −31.1769 | + | 31.1769i | −1.16840 | + | 1.16840i | ||||
\(713\) | 1.73205i | 0.0648658i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000i | 0.224387i | ||||||||
\(716\) | −38.0000 | −1.42013 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 23.0000 | + | 23.0000i | 0.858352 | + | 0.858352i | ||||
\(719\) | −25.9808 | −0.968919 | −0.484459 | − | 0.874814i | \(-0.660984\pi\) | ||||
−0.484459 | + | 0.874814i | \(0.660984\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −8.00000 | + | 8.00000i | −0.297729 | + | 0.297729i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.8564 | 0.514969 | ||||||||
\(725\) | −8.00000 | −0.297113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.0000 | + | 15.0000i | −0.555175 | + | 0.555175i | ||||
\(731\) | −3.46410 | −0.128124 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 43.3013i | − | 1.59937i | −0.600420 | − | 0.799684i | \(-0.705000\pi\) | ||
0.600420 | − | 0.799684i | \(-0.295000\pi\) | |||||||
\(734\) | −1.73205 | + | 1.73205i | −0.0639312 | + | 0.0639312i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | − | 4.00000i | −0.147442 | − | 0.147442i | ||||
\(737\) | 3.00000 | 0.110506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 51.0000i | 1.87607i | 0.346547 | + | 0.938033i | \(0.387354\pi\) | ||||
−0.346547 | + | 0.938033i | \(0.612646\pi\) | |||||||
\(740\) | −10.3923 | −0.382029 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.0000i | 1.24734i | 0.781688 | + | 0.623670i | \(0.214359\pi\) | ||||
−0.781688 | + | 0.623670i | \(0.785641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.73205i | 0.0634574i | ||||||||
\(746\) | 29.0000 | − | 29.0000i | 1.06177 | − | 1.06177i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.46410i | 0.126660i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 25.0000i | − | 0.912263i | −0.889912 | − | 0.456131i | \(-0.849235\pi\) | ||
0.889912 | − | 0.456131i | \(-0.150765\pi\) | |||||||
\(752\) | 34.6410 | 1.26323 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13.8564 | + | 13.8564i | 0.504621 | + | 0.504621i | ||||
\(755\) | 12.1244 | 0.441250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0000 | −1.74459 | −0.872295 | − | 0.488980i | \(-0.837369\pi\) | ||||
−0.872295 | + | 0.488980i | \(0.837369\pi\) | |||||||
\(758\) | 8.00000 | + | 8.00000i | 0.290573 | + | 0.290573i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −18.0000 | + | 18.0000i | −0.652929 | + | 0.652929i | ||||
\(761\) | 19.0526i | 0.690655i | 0.938482 | + | 0.345327i | \(0.112232\pi\) | ||||
−0.938482 | + | 0.345327i | \(0.887768\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.00000 | 0.0723575 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.19615 | + | 5.19615i | −0.187745 | + | 0.187745i | ||||
\(767\) | 18.0000i | 0.649942i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.46410i | − | 0.124919i | −0.998048 | − | 0.0624593i | \(-0.980106\pi\) | ||
0.998048 | − | 0.0624593i | \(-0.0198944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 30.0000i | 1.07972i | ||||||||
\(773\) | − | 25.9808i | − | 0.934463i | −0.884135 | − | 0.467232i | \(-0.845251\pi\) | ||
0.884135 | − | 0.467232i | \(-0.154749\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.46410 | −0.124434 | ||||||||
\(776\) | 34.6410 | − | 34.6410i | 1.24354 | − | 1.24354i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −19.0000 | + | 19.0000i | −0.681183 | + | 0.681183i | ||||
\(779\) | − | 18.0000i | − | 0.644917i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | −0.500959 | ||||||||
\(782\) | −1.73205 | + | 1.73205i | −0.0619380 | + | 0.0619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.00000 | 0.107075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.19615 | −0.185223 | −0.0926114 | − | 0.995702i | \(-0.529521\pi\) | ||||
−0.0926114 | + | 0.995702i | \(0.529521\pi\) | |||||||
\(788\) | 32.0000i | 1.13995i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.5885 | + | 15.5885i | −0.554612 | + | 0.554612i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.0000 | −0.639199 | ||||||||
\(794\) | 19.0526 | + | 19.0526i | 0.676150 | + | 0.676150i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 45.0333i | 1.59616i | ||||||||
\(797\) | 10.3923i | 0.368114i | 0.982916 | + | 0.184057i | \(0.0589232\pi\) | ||||
−0.982916 | + | 0.184057i | \(0.941077\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 15.0000i | − | 0.530662i | ||||||
\(800\) | 8.00000 | − | 8.00000i | 0.282843 | − | 0.282843i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −23.0000 | + | 23.0000i | −0.812158 | + | 0.812158i | ||||
\(803\) | −8.66025 | −0.305614 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.00000 | + | 6.00000i | 0.211341 | + | 0.211341i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −17.3205 | + | 17.3205i | −0.609333 | + | 0.609333i | ||||
\(809\) | −43.0000 | −1.51180 | −0.755900 | − | 0.654687i | \(-0.772800\pi\) | ||||
−0.755900 | + | 0.654687i | \(0.772800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8564 | 0.486564 | 0.243282 | − | 0.969956i | \(-0.421776\pi\) | ||||
0.243282 | + | 0.969956i | \(0.421776\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.00000 | − | 3.00000i | −0.105150 | − | 0.105150i | ||||
\(815\) | 36.3731 | 1.27409 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10.3923i | − | 0.363581i | ||||||
\(818\) | −25.9808 | − | 25.9808i | −0.908396 | − | 0.908396i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 12.0000i | − | 0.419058i | ||||||
\(821\) | 11.0000 | 0.383903 | 0.191951 | − | 0.981404i | \(-0.438518\pi\) | ||||
0.191951 | + | 0.981404i | \(0.438518\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.00000i | 0.313720i | 0.987621 | + | 0.156860i | \(0.0501372\pi\) | ||||
−0.987621 | + | 0.156860i | \(0.949863\pi\) | |||||||
\(824\) | −17.3205 | − | 17.3205i | −0.603388 | − | 0.603388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.0000i | − | 0.765015i | −0.923952 | − | 0.382507i | \(-0.875061\pi\) | ||
0.923952 | − | 0.382507i | \(-0.124939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 8.66025i | − | 0.300783i | −0.988627 | − | 0.150392i | \(-0.951947\pi\) | ||
0.988627 | − | 0.150392i | \(-0.0480534\pi\) | |||||||
\(830\) | −24.0000 | − | 24.0000i | −0.833052 | − | 0.833052i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −27.7128 | −0.960769 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 30.0000i | − | 1.03819i | ||||||
\(836\) | −10.3923 | −0.359425 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.7846 | + | 20.7846i | −0.717992 | + | 0.717992i | ||||
\(839\) | −48.4974 | −1.67432 | −0.837158 | − | 0.546960i | \(-0.815785\pi\) | ||||
−0.837158 | + | 0.546960i | \(0.815785\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 20.0000 | − | 20.0000i | 0.689246 | − | 0.689246i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | − | 1.73205i | − | 0.0595844i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.46410 | − | 3.46410i | −0.118818 | − | 0.118818i | ||||
\(851\) | − | 3.00000i | − | 0.102839i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.2487i | − | 0.830260i | −0.909762 | − | 0.415130i | \(-0.863736\pi\) | ||
0.909762 | − | 0.415130i | \(-0.136264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.0000 | + | 26.0000i | −0.888662 | + | 0.888662i | ||||
\(857\) | 25.9808i | 0.887486i | 0.896154 | + | 0.443743i | \(0.146350\pi\) | ||||
−0.896154 | + | 0.443743i | \(0.853650\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.2295 | 1.71381 | 0.856904 | − | 0.515476i | \(-0.172385\pi\) | ||||
0.856904 | + | 0.515476i | \(0.172385\pi\) | |||||||
\(860\) | − | 6.92820i | − | 0.236250i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 23.0000 | + | 23.0000i | 0.783383 | + | 0.783383i | ||||
\(863\) | 35.0000i | 1.19141i | 0.803202 | + | 0.595707i | \(0.203128\pi\) | ||||
−0.803202 | + | 0.595707i | \(0.796872\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.0000 | −0.714021 | ||||||||
\(866\) | 10.3923 | + | 10.3923i | 0.353145 | + | 0.353145i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.00000 | −0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3923 | 0.352130 | ||||||||
\(872\) | 18.0000 | + | 18.0000i | 0.609557 | + | 0.609557i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.19615 | − | 5.19615i | −0.175762 | − | 0.175762i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.00000 | 0.0337676 | 0.0168838 | − | 0.999857i | \(-0.494625\pi\) | ||||
0.0168838 | + | 0.999857i | \(0.494625\pi\) | |||||||
\(878\) | −22.5167 | + | 22.5167i | −0.759900 | + | 0.759900i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.92820 | −0.233550 | ||||||||
\(881\) | − | 13.8564i | − | 0.466834i | −0.972377 | − | 0.233417i | \(-0.925009\pi\) | ||
0.972377 | − | 0.233417i | \(-0.0749907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 12.0000i | 0.403604i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.0000 | − | 17.0000i | −0.571126 | − | 0.571126i | ||||
\(887\) | 25.9808 | 0.872349 | 0.436174 | − | 0.899862i | \(-0.356333\pi\) | ||||
0.436174 | + | 0.899862i | \(0.356333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.0000 | + | 27.0000i | −0.905042 | + | 0.905042i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 13.8564i | − | 0.463947i | ||||||
\(893\) | 45.0000 | 1.50587 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.9090 | −1.10003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.00000 | − | 8.00000i | 0.266963 | − | 0.266963i | ||||
\(899\) | 6.92820 | 0.231069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.73205i | 0.0577030i | ||||||||
\(902\) | 3.46410 | − | 3.46410i | 0.115342 | − | 0.115342i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 32.0000 | + | 32.0000i | 1.06430 | + | 1.06430i | ||||
\(905\) | 12.0000 | 0.398893 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 7.00000i | − | 0.232431i | −0.993224 | − | 0.116216i | \(-0.962924\pi\) | ||
0.993224 | − | 0.116216i | \(-0.0370764\pi\) | |||||||
\(908\) | 38.1051i | 1.26456i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.0000i | 0.861418i | 0.902491 | + | 0.430709i | \(0.141737\pi\) | ||||
−0.902491 | + | 0.430709i | \(0.858263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 13.8564i | − | 0.458580i | ||||||
\(914\) | −15.0000 | + | 15.0000i | −0.496156 | + | 0.496156i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.1769 | 1.03011 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1.00000i | − | 0.0329870i | −0.999864 | − | 0.0164935i | \(-0.994750\pi\) | ||
0.999864 | − | 0.0164935i | \(-0.00525028\pi\) | |||||||
\(920\) | −3.46410 | − | 3.46410i | −0.114208 | − | 0.114208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −17.3205 | − | 17.3205i | −0.570421 | − | 0.570421i | ||||
\(923\) | −48.4974 | −1.59631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | 0.197279 | ||||||||
\(926\) | 30.0000 | + | 30.0000i | 0.985861 | + | 0.985861i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −16.0000 | + | 16.0000i | −0.525226 | + | 0.525226i | ||||
\(929\) | 8.66025i | 0.284134i | 0.989857 | + | 0.142067i | \(0.0453748\pi\) | ||||
−0.989857 | + | 0.142067i | \(0.954625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 14.0000i | − | 0.458585i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.66025 | + | 8.66025i | −0.283372 | + | 0.283372i | ||||
\(935\) | 3.00000i | 0.0981105i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 30.0000 | 0.978492 | ||||||||
\(941\) | − | 57.1577i | − | 1.86329i | −0.363374 | − | 0.931644i | \(-0.618375\pi\) | ||
0.363374 | − | 0.931644i | \(-0.381625\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.46410 | 0.112807 | ||||||||
\(944\) | −20.7846 | −0.676481 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | − | 2.00000i | 0.0650256 | − | 0.0650256i | ||||
\(947\) | − | 29.0000i | − | 0.942373i | −0.882034 | − | 0.471187i | \(-0.843826\pi\) | ||
0.882034 | − | 0.471187i | \(-0.156174\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −30.0000 | −0.973841 | ||||||||
\(950\) | 10.3923 | − | 10.3923i | 0.337171 | − | 0.337171i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.00000 | 0.259145 | 0.129573 | − | 0.991570i | \(-0.458639\pi\) | ||||
0.129573 | + | 0.991570i | \(0.458639\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.73205 | 0.0560478 | ||||||||
\(956\) | −40.0000 | −1.29369 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.1244 | + | 12.1244i | −0.391720 | + | 0.391720i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0000 | −0.903226 | ||||||||
\(962\) | −10.3923 | − | 10.3923i | −0.335061 | − | 0.335061i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.3923 | −0.334714 | ||||||||
\(965\) | 25.9808i | 0.836350i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.00000i | − | 0.192947i | −0.995336 | − | 0.0964735i | \(-0.969244\pi\) | ||
0.995336 | − | 0.0964735i | \(-0.0307563\pi\) | |||||||
\(968\) | 20.0000 | + | 20.0000i | 0.642824 | + | 0.642824i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 30.0000 | − | 30.0000i | 0.963242 | − | 0.963242i | ||||
\(971\) | −60.6218 | −1.94545 | −0.972723 | − | 0.231971i | \(-0.925483\pi\) | ||||
−0.972723 | + | 0.231971i | \(0.925483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 31.0000 | + | 31.0000i | 0.993304 | + | 0.993304i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 20.7846i | − | 0.665299i | ||||||
\(977\) | 31.0000 | 0.991778 | 0.495889 | − | 0.868386i | \(-0.334842\pi\) | ||||
0.495889 | + | 0.868386i | \(0.334842\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.5885 | −0.498209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32.0000 | + | 32.0000i | 1.02116 | + | 1.02116i | ||||
\(983\) | −60.6218 | −1.93353 | −0.966767 | − | 0.255658i | \(-0.917708\pi\) | ||||
−0.966767 | + | 0.255658i | \(0.917708\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.7128i | 0.883004i | ||||||||
\(986\) | 6.92820 | + | 6.92820i | 0.220639 | + | 0.220639i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −36.0000 | −1.14531 | ||||||||
\(989\) | 2.00000 | 0.0635963 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 23.0000i | − | 0.730619i | −0.930886 | − | 0.365310i | \(-0.880963\pi\) | ||
0.930886 | − | 0.365310i | \(-0.119037\pi\) | |||||||
\(992\) | −6.92820 | + | 6.92820i | −0.219971 | + | 0.219971i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.0000i | 1.23638i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.5167i | 0.713110i | 0.934274 | + | 0.356555i | \(0.116049\pi\) | ||||
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | 35.0000 | + | 35.0000i | 1.10791 | + | 1.10791i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))