Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,2,Mod(177,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.177");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.t (of order \(6\), degree \(2\), 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: | \(12.5205430369\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 177.1 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.177 |
Dual form | 1568.2.t.c.753.1 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | + | 0.707107i | −0.707107 | + | 0.408248i | −0.809989 | − | 0.586445i | \(-0.800527\pi\) |
0.102882 | + | 0.994694i | \(0.467194\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.22474 | + | 0.707107i | 0.547723 | + | 0.316228i | 0.748203 | − | 0.663470i | \(-0.230917\pi\) |
−0.200480 | + | 0.979698i | \(0.564250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.44949 | + | 1.41421i | −0.738549 | + | 0.426401i | −0.821541 | − | 0.570149i | \(-0.806886\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.24264i | − | 1.17670i | −0.808608 | − | 0.588348i | \(-0.799778\pi\) | ||
0.808608 | − | 0.588348i | \(-0.200222\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.00000 | + | 5.19615i | 0.727607 | + | 1.26025i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) |
−0.230285 | + | 0.973123i | \(0.573966\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.67423 | − | 2.12132i | −0.842927 | − | 0.486664i | 0.0153309 | − | 0.999882i | \(-0.495120\pi\) |
−0.858258 | + | 0.513218i | \(0.828453\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.50000 | − | 2.59808i | −0.300000 | − | 0.519615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.65685i | − | 1.08866i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843i | 0.525226i | 0.964901 | + | 0.262613i | \(0.0845842\pi\) | ||||
−0.964901 | + | 0.262613i | \(0.915416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000 | − | 3.46410i | 0.348155 | − | 0.603023i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.34847 | − | 4.24264i | −1.20808 | − | 0.697486i | −0.245741 | − | 0.969335i | \(-0.579031\pi\) |
−0.962340 | + | 0.271850i | \(0.912365\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.00000 | + | 5.19615i | 0.480384 | + | 0.832050i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.48528i | 1.29399i | 0.762493 | + | 0.646997i | \(0.223975\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.22474 | + | 0.707107i | −0.182574 | + | 0.105409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.34847 | − | 4.24264i | −1.02899 | − | 0.594089i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.89898 | + | 2.82843i | −0.672927 | + | 0.388514i | −0.797185 | − | 0.603736i | \(-0.793678\pi\) |
0.124258 | + | 0.992250i | \(0.460345\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.22474 | − | 0.707107i | 0.159448 | − | 0.0920575i | −0.418153 | − | 0.908377i | \(-0.637322\pi\) |
0.577601 | + | 0.816319i | \(0.303989\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.0227 | − | 6.36396i | −1.41131 | − | 0.814822i | −0.415800 | − | 0.909456i | \(-0.636499\pi\) |
−0.995512 | + | 0.0946341i | \(0.969832\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8.48528i | − | 1.02151i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.67423 | + | 2.12132i | 0.424264 | + | 0.244949i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | − | 6.92820i | 0.450035 | − | 0.779484i | −0.548352 | − | 0.836247i | \(-0.684745\pi\) |
0.998388 | + | 0.0567635i | \(0.0180781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.5563i | − | 1.70753i | −0.520658 | − | 0.853766i | \(-0.674313\pi\) | ||
0.520658 | − | 0.853766i | \(-0.325687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.48528i | 0.920358i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.00000 | − | 3.46410i | −0.214423 | − | 0.371391i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.00000 | + | 5.19615i | −0.317999 | + | 0.550791i | −0.980071 | − | 0.198650i | \(-0.936344\pi\) |
0.662071 | + | 0.749441i | \(0.269678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.89898 | + | 2.82843i | 0.508001 | + | 0.293294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | − | 5.19615i | −0.307794 | − | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 2.82843i | − | 0.284268i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.57321 | + | 4.94975i | −0.853067 | + | 0.492518i | −0.861684 | − | 0.507445i | \(-0.830590\pi\) |
0.00861771 | + | 0.999963i | \(0.497257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | + | 3.46410i | −0.197066 | + | 0.341328i | −0.947576 | − | 0.319531i | \(-0.896475\pi\) |
0.750510 | + | 0.660859i | \(0.229808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.89898 | − | 2.82843i | −0.473602 | − | 0.273434i | 0.244144 | − | 0.969739i | \(-0.421493\pi\) |
−0.717746 | + | 0.696305i | \(0.754826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.34847 | + | 4.24264i | −0.703856 | + | 0.406371i | −0.808782 | − | 0.588109i | \(-0.799873\pi\) |
0.104926 | + | 0.994480i | \(0.466539\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | 1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.34847 | + | 4.24264i | −0.685248 | + | 0.395628i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.67423 | + | 2.12132i | 0.339683 | + | 0.196116i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.50000 | + | 2.59808i | −0.136364 | + | 0.236189i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.34847 | + | 4.24264i | −0.662589 | + | 0.382546i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 11.3137i | − | 1.01193i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | −0.177471 | −0.0887357 | − | 0.996055i | \(-0.528283\pi\) | ||||
−0.0887357 | + | 0.996055i | \(0.528283\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.00000 | − | 10.3923i | −0.528271 | − | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.22474 | − | 0.707107i | −0.107006 | − | 0.0617802i | 0.445542 | − | 0.895261i | \(-0.353011\pi\) |
−0.552548 | + | 0.833481i | \(0.686344\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000 | − | 6.92820i | 0.344265 | − | 0.596285i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.00000 | − | 5.19615i | −0.256307 | − | 0.443937i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.965250 | + | 0.261329i | \(0.915839\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.24264i | 0.359856i | 0.983680 | + | 0.179928i | \(0.0575865\pi\) | ||||
−0.983680 | + | 0.179928i | \(0.942414\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.00000 | + | 10.3923i | 0.501745 | + | 0.869048i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | + | 3.46410i | −0.166091 | + | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.79796 | − | 5.65685i | −0.802680 | − | 0.463428i | 0.0417274 | − | 0.999129i | \(-0.486714\pi\) |
−0.844407 | + | 0.535701i | \(0.820047\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | − | 8.66025i | −0.406894 | − | 0.704761i | 0.587646 | − | 0.809118i | \(-0.300055\pi\) |
−0.994540 | + | 0.104357i | \(0.966722\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.65685i | − | 0.454369i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.0227 | − | 6.36396i | 0.879708 | − | 0.507899i | 0.00914557 | − | 0.999958i | \(-0.497089\pi\) |
0.870562 | + | 0.492059i | \(0.163756\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.00000 | − | 6.92820i | 0.317221 | − | 0.549442i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.34847 | + | 4.24264i | 0.575577 | + | 0.332309i | 0.759374 | − | 0.650655i | \(-0.225506\pi\) |
−0.183797 | + | 0.982964i | \(0.558839\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.89898 | − | 2.82843i | 0.381385 | − | 0.220193i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −24.0000 | −1.85718 | −0.928588 | − | 0.371113i | \(-0.878976\pi\) | ||||
−0.928588 | + | 0.371113i | \(0.878976\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.67423 | − | 2.12132i | 0.280976 | − | 0.162221i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.57321 | + | 4.94975i | 0.651809 | + | 0.376322i | 0.789149 | − | 0.614202i | \(-0.210522\pi\) |
−0.137340 | + | 0.990524i | \(0.543855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.00000 | + | 1.73205i | −0.0751646 | + | 0.130189i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.89898 | − | 2.82843i | 0.366167 | − | 0.211407i | −0.305616 | − | 0.952155i | \(-0.598862\pi\) |
0.671783 | + | 0.740748i | \(0.265529\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.7279i | 0.946059i | 0.881047 | + | 0.473029i | \(0.156840\pi\) | ||||
−0.881047 | + | 0.473029i | \(0.843160\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0000 | 1.33060 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.00000 | − | 10.3923i | −0.441129 | − | 0.764057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.6969 | − | 8.48528i | −1.07475 | − | 0.620505i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00000 | + | 3.46410i | 0.143963 | + | 0.249351i | 0.928986 | − | 0.370116i | \(-0.120682\pi\) |
−0.785022 | + | 0.619467i | \(0.787349\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.48528i | 0.607644i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 5.65685i | − | 0.403034i | −0.979485 | − | 0.201517i | \(-0.935413\pi\) | ||
0.979485 | − | 0.201517i | \(-0.0645872\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0000 | + | 17.3205i | 0.708881 | + | 1.22782i | 0.965272 | + | 0.261245i | \(0.0841331\pi\) |
−0.256391 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.34847 | + | 4.24264i | 0.513239 | + | 0.296319i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.00000 | − | 5.19615i | −0.208514 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.9706i | 1.16830i | 0.811645 | + | 0.584151i | \(0.198572\pi\) | ||||
−0.811645 | + | 0.584151i | \(0.801428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | + | 10.3923i | −0.409197 | + | 0.708749i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.44949 | + | 1.41421i | 0.165521 | + | 0.0955637i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.0454 | − | 12.7279i | 1.48293 | − | 0.856173i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 28.0000 | 1.87502 | 0.937509 | − | 0.347960i | \(-0.113126\pi\) | ||||
0.937509 | + | 0.347960i | \(0.113126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.57321 | − | 4.94975i | 0.569024 | − | 0.328526i | −0.187735 | − | 0.982220i | \(-0.560115\pi\) |
0.756760 | + | 0.653693i | \(0.226781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.67423 | − | 2.12132i | −0.242800 | − | 0.140181i | 0.373663 | − | 0.927565i | \(-0.378102\pi\) |
−0.616463 | + | 0.787384i | \(0.711435\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.3137i | 0.734904i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.00000 | + | 8.66025i | 0.322078 | + | 0.557856i | 0.980917 | − | 0.194429i | \(-0.0622852\pi\) |
−0.658838 | + | 0.752285i | \(0.728952\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.57321 | + | 4.94975i | 0.549972 | + | 0.317526i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.00000 | + | 15.5885i | −0.572656 | + | 0.991870i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.0000 | + | 19.0526i | 0.697097 | + | 1.20741i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.3848i | 1.16044i | 0.814461 | + | 0.580218i | \(0.197033\pi\) | ||||
−0.814461 | + | 0.580218i | \(0.802967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.9706i | − | 1.06693i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.00000 | − | 10.3923i | −0.375735 | − | 0.650791i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.00000 | − | 5.19615i | 0.187135 | − | 0.324127i | −0.757159 | − | 0.653231i | \(-0.773413\pi\) |
0.944294 | + | 0.329104i | \(0.106747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.44949 | − | 1.41421i | −0.151620 | − | 0.0875376i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0000 | + | 20.7846i | 0.739952 | + | 1.28163i | 0.952517 | + | 0.304487i | \(0.0984850\pi\) |
−0.212565 | + | 0.977147i | \(0.568182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.00000 | −0.491436 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 8.48528i | − | 0.519291i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.12372 | − | 3.53553i | 0.373370 | − | 0.215565i | −0.301560 | − | 0.953447i | \(-0.597507\pi\) |
0.674930 | + | 0.737882i | \(0.264174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.0000 | − | 17.3205i | 0.607457 | − | 1.05215i | −0.384201 | − | 0.923249i | \(-0.625523\pi\) |
0.991658 | − | 0.128897i | \(-0.0411435\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.34847 | + | 4.24264i | 0.443129 | + | 0.255841i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.6969 | + | 8.48528i | −0.883053 | + | 0.509831i | −0.871664 | − | 0.490104i | \(-0.836959\pi\) |
−0.0113895 | + | 0.999935i | \(0.503625\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.00000 | 0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.0227 | + | 6.36396i | −0.655232 | + | 0.378298i | −0.790458 | − | 0.612517i | \(-0.790157\pi\) |
0.135226 | + | 0.990815i | \(0.456824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.34847 | + | 4.24264i | 0.435286 | + | 0.251312i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.50000 | + | 16.4545i | −0.558824 | + | 0.967911i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2474 | − | 7.07107i | 0.717958 | − | 0.414513i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.0416i | 1.40453i | 0.711917 | + | 0.702264i | \(0.247827\pi\) | ||||
−0.711917 | + | 0.702264i | \(0.752173\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.00000 | 0.116445 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.00000 | + | 13.8564i | 0.464207 | + | 0.804030i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 22.0454 | + | 12.7279i | 1.27492 | + | 0.736075i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.00000 | − | 12.1244i | 0.402139 | − | 0.696526i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.00000 | − | 15.5885i | −0.515339 | − | 0.892592i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7279i | 0.726421i | 0.931707 | + | 0.363210i | \(0.118319\pi\) | ||||
−0.931707 | + | 0.363210i | \(0.881681\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 5.65685i | − | 0.321807i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.5959 | + | 11.3137i | 1.10062 | + | 0.635441i | 0.936383 | − | 0.350980i | \(-0.114152\pi\) |
0.164234 | + | 0.986421i | \(0.447485\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.00000 | 0.446516 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 25.4558i | − | 1.41640i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.0227 | + | 6.36396i | −0.611430 | + | 0.353009i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.00000 | − | 10.3923i | 0.331801 | − | 0.574696i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0454 | + | 12.7279i | 1.21173 | + | 0.699590i | 0.963135 | − | 0.269019i | \(-0.0866994\pi\) |
0.248590 | + | 0.968609i | \(0.420033\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.34847 | − | 4.24264i | 0.402694 | − | 0.232495i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.0000 | 1.74315 | 0.871576 | − | 0.490261i | \(-0.163099\pi\) | ||||
0.871576 | + | 0.490261i | \(0.163099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.6969 | − | 8.48528i | 0.798228 | − | 0.460857i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.79796 | + | 5.65685i | 0.530589 | + | 0.306336i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.00000 | − | 10.3923i | 0.323029 | − | 0.559503i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2474 | − | 7.07107i | 0.657477 | − | 0.379595i | −0.133838 | − | 0.991003i | \(-0.542730\pi\) |
0.791315 | + | 0.611408i | \(0.209397\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.24264i | 0.227103i | 0.993532 | + | 0.113552i | \(0.0362227\pi\) | ||||
−0.993532 | + | 0.113552i | \(0.963777\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.0000 | −1.28103 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.00000 | − | 5.19615i | −0.159674 | − | 0.276563i | 0.775077 | − | 0.631867i | \(-0.217711\pi\) |
−0.934751 | + | 0.355303i | \(0.884378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0000 | + | 25.9808i | −0.791670 | + | 1.37121i | 0.133263 | + | 0.991081i | \(0.457455\pi\) |
−0.924932 | + | 0.380131i | \(0.875879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | − | 0.866025i | −0.0263158 | − | 0.0455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.24264i | − | 0.222681i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 2.82843i | − | 0.148047i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.0000 | − | 24.2487i | −0.730794 | − | 1.26577i | −0.956544 | − | 0.291587i | \(-0.905817\pi\) |
0.225750 | − | 0.974185i | \(-0.427517\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | + | 5.19615i | −0.156174 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.3939 | + | 16.9706i | 1.52196 | + | 0.878702i | 0.999664 | + | 0.0259367i | \(0.00825685\pi\) |
0.522294 | + | 0.852766i | \(0.325076\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.00000 | + | 13.8564i | 0.413118 | + | 0.715542i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000 | 0.618031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 25.4558i | − | 1.30758i | −0.756677 | − | 0.653789i | \(-0.773178\pi\) | ||
0.756677 | − | 0.653789i | \(-0.226822\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.44949 | − | 1.41421i | 0.125491 | − | 0.0724524i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.0000 | + | 20.7846i | −0.613171 | + | 1.06204i | 0.377531 | + | 0.925997i | \(0.376773\pi\) |
−0.990702 | + | 0.136047i | \(0.956560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.34847 | − | 4.24264i | −0.373544 | − | 0.215666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.44949 | − | 1.41421i | 0.124194 | − | 0.0717035i | −0.436616 | − | 0.899648i | \(-0.643823\pi\) |
0.560810 | + | 0.827945i | \(0.310490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.00000 | 0.100887 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.79796 | − | 5.65685i | 0.492989 | − | 0.284627i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3712 | − | 10.6066i | −0.922023 | − | 0.532330i | −0.0377429 | − | 0.999287i | \(-0.512017\pi\) |
−0.884280 | + | 0.466957i | \(0.845350\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000 | − | 20.7846i | 0.599251 | − | 1.03793i | −0.393680 | − | 0.919247i | \(-0.628798\pi\) |
0.992932 | − | 0.118686i | \(-0.0378683\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.6969 | + | 8.48528i | −0.732107 | + | 0.422682i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.07107i | 0.351364i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.0000 | 1.18964 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0000 | + | 19.0526i | 0.543915 | + | 0.942088i | 0.998674 | + | 0.0514740i | \(0.0163919\pi\) |
−0.454759 | + | 0.890614i | \(0.650275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.34847 | + | 4.24264i | 0.362473 | + | 0.209274i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.0000 | − | 19.0526i | 0.539969 | − | 0.935253i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.00000 | − | 5.19615i | −0.146911 | − | 0.254457i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8701i | 1.31269i | 0.754462 | + | 0.656344i | \(0.227898\pi\) | ||||
−0.754462 | + | 0.656344i | \(0.772102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.9706i | 0.827095i | 0.910483 | + | 0.413547i | \(0.135710\pi\) | ||||
−0.910483 | + | 0.413547i | \(0.864290\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.00000 | − | 15.5885i | 0.436564 | − | 0.756151i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.6969 | − | 8.48528i | −0.709575 | − | 0.409673i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.00000 | 0.0961139 | 0.0480569 | − | 0.998845i | \(-0.484697\pi\) | ||||
0.0480569 | + | 0.998845i | \(0.484697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 5.65685i | − | 0.271225i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 22.0454 | − | 12.7279i | 1.05457 | − | 0.608859i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.0000 | + | 24.2487i | −0.668184 | + | 1.15733i | 0.310228 | + | 0.950662i | \(0.399595\pi\) |
−0.978412 | + | 0.206666i | \(0.933739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5959 | − | 11.3137i | −0.931030 | − | 0.537531i | −0.0438929 | − | 0.999036i | \(-0.513976\pi\) |
−0.887137 | + | 0.461506i | \(0.847309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.34847 | + | 4.24264i | −0.348351 | + | 0.201120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.0000 | 0.756774 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.6969 | + | 8.48528i | −0.692052 | + | 0.399556i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.2474 | + | 7.07107i | 0.575435 | + | 0.332228i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.0000 | − | 24.2487i | 0.654892 | − | 1.13431i | −0.327028 | − | 0.945015i | \(-0.606047\pi\) |
0.981921 | − | 0.189292i | \(-0.0606194\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 29.3939 | − | 16.9706i | 1.37199 | − | 0.792118i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.5563i | 0.724531i | 0.932075 | + | 0.362266i | \(0.117997\pi\) | ||||
−0.932075 | + | 0.362266i | \(0.882003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −32.0000 | −1.48717 | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743583 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.00000 | + | 6.92820i | 0.185496 | + | 0.321288i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.12372 | + | 3.53553i | 0.283372 | + | 0.163605i | 0.634949 | − | 0.772554i | \(-0.281021\pi\) |
−0.351577 | + | 0.936159i | \(0.614354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.00000 | + | 15.5885i | −0.414698 | + | 0.718278i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −12.0000 | − | 20.7846i | −0.551761 | − | 0.955677i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.7279i | 0.583997i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 5.65685i | − | 0.259010i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.00000 | − | 10.3923i | −0.274147 | − | 0.474837i | 0.695773 | − | 0.718262i | \(-0.255062\pi\) |
−0.969920 | + | 0.243426i | \(0.921729\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.0000 | + | 31.1769i | −0.820729 | + | 1.42154i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.2474 | − | 7.07107i | −0.556128 | − | 0.321081i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | + | 1.73205i | 0.0453143 | + | 0.0784867i | 0.887793 | − | 0.460243i | \(-0.152238\pi\) |
−0.842479 | + | 0.538730i | \(0.818904\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.5980i | 1.78703i | 0.449032 | + | 0.893516i | \(0.351769\pi\) | ||||
−0.449032 | + | 0.893516i | \(0.648231\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.6969 | + | 8.48528i | −0.661917 | + | 0.382158i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | − | 3.46410i | 0.0898933 | − | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.6969 | + | 8.48528i | 0.657925 | + | 0.379853i | 0.791486 | − | 0.611187i | \(-0.209308\pi\) |
−0.133561 | + | 0.991041i | \(0.542641\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.3939 | − | 16.9706i | 1.31322 | − | 0.758189i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.0000 | −1.60516 | −0.802580 | − | 0.596544i | \(-0.796540\pi\) | ||||
−0.802580 | + | 0.596544i | \(0.796540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −14.0000 | −0.622992 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.12372 | − | 3.53553i | 0.271964 | − | 0.157019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.22474 | + | 0.707107i | 0.0542859 | + | 0.0313420i | 0.526897 | − | 0.849929i | \(-0.323355\pi\) |
−0.472611 | + | 0.881271i | \(0.656689\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.0000 | + | 20.7846i | −0.529813 | + | 0.917663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.89898 | + | 2.82843i | −0.215875 | + | 0.124635i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | + | 5.19615i | 0.131432 | + | 0.227648i | 0.924229 | − | 0.381839i | \(-0.124709\pi\) |
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.7196 | − | 14.8492i | −1.12464 | − | 0.649312i | −0.182060 | − | 0.983287i | \(-0.558276\pi\) |
−0.942582 | + | 0.333975i | \(0.891610\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.41421i | 0.0613716i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 25.4558i | − | 1.10262i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | − | 6.92820i | −0.172935 | − | 0.299532i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.00000 | + | 6.92820i | −0.172613 | + | 0.298974i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6969 | + | 8.48528i | 0.631871 | + | 0.364811i | 0.781476 | − | 0.623935i | \(-0.214467\pi\) |
−0.149605 | + | 0.988746i | \(0.547800\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.00000 | − | 15.5885i | −0.386227 | − | 0.668965i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.0000 | −0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.48528i | 0.362804i | 0.983409 | + | 0.181402i | \(0.0580636\pi\) | ||||
−0.983409 | + | 0.181402i | \(0.941936\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.0227 | − | 6.36396i | 0.470438 | − | 0.271607i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | − | 10.3923i | 0.255609 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.6969 | + | 8.48528i | 0.623850 | + | 0.360180i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.89898 | + | 2.82843i | −0.207576 | + | 0.119844i | −0.600185 | − | 0.799862i | \(-0.704906\pi\) |
0.392608 | + | 0.919706i | \(0.371573\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 36.0000 | 1.52264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 24.0000 | 1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.22474 | − | 0.707107i | 0.0516168 | − | 0.0298010i | −0.473970 | − | 0.880541i | \(-0.657179\pi\) |
0.525586 | + | 0.850740i | \(0.323846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.6969 | − | 8.48528i | −0.618305 | − | 0.356978i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0454 | + | 12.7279i | −0.922572 | + | 0.532647i | −0.884455 | − | 0.466626i | \(-0.845469\pi\) |
−0.0381170 | + | 0.999273i | \(0.512136\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18.0000 | 0.750652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.0000 | − | 32.9090i | −0.790980 | − | 1.37002i | −0.925361 | − | 0.379088i | \(-0.876238\pi\) |
0.134380 | − | 0.990930i | \(-0.457096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.89898 | − | 2.82843i | −0.203595 | − | 0.117545i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.00000 | − | 13.8564i | 0.331326 | − | 0.573874i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | + | 5.19615i | 0.124035 | + | 0.214834i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 41.0122i | − | 1.69275i | −0.532584 | − | 0.846377i | \(-0.678779\pi\) | ||
0.532584 | − | 0.846377i | \(-0.321221\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.9706i | 0.699260i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.00000 | + | 6.92820i | 0.164538 | + | 0.284988i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.0000 | − | 25.9808i | 0.615976 | − | 1.06690i | −0.374236 | − | 0.927333i | \(-0.622095\pi\) |
0.990212 | − | 0.139569i | \(-0.0445716\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −24.4949 | − | 14.1421i | −1.00251 | − | 0.578799i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.67423 | + | 2.12132i | −0.149379 | + | 0.0862439i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0000 | − | 27.7128i | 0.649420 | − | 1.12483i | −0.333842 | − | 0.942629i | \(-0.608345\pi\) |
0.983262 | − | 0.182199i | \(-0.0583216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.34847 | + | 4.24264i | −0.296802 | + | 0.171359i | −0.641005 | − | 0.767536i | \(-0.721482\pi\) |
0.344203 | + | 0.938895i | \(0.388149\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −12.0000 | −0.483887 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0000 | 0.966204 | 0.483102 | − | 0.875564i | \(-0.339510\pi\) | ||||
0.483102 | + | 0.875564i | \(0.339510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.67423 | − | 2.12132i | 0.147680 | − | 0.0852631i | −0.424339 | − | 0.905503i | \(-0.639494\pi\) |
0.572019 | + | 0.820240i | \(0.306160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 29.3939 | + | 16.9706i | 1.17954 | + | 0.681005i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.500000 | − | 0.866025i | 0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −14.6969 | + | 8.48528i | −0.586939 | + | 0.338869i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 50.9117i | − | 2.02998i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0000 | 0.636950 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.0000 | − | 20.7846i | −0.476957 | − | 0.826114i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.44949 | − | 1.41421i | −0.0972050 | − | 0.0561214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 24.0000 | + | 41.5692i | 0.947943 | + | 1.64189i | 0.749749 | + | 0.661723i | \(0.230174\pi\) |
0.198194 | + | 0.980163i | \(0.436492\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 21.2132i | − | 0.836567i | −0.908317 | − | 0.418284i | \(-0.862632\pi\) | ||
0.908317 | − | 0.418284i | \(-0.137368\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 16.9706i | − | 0.668215i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.00000 | + | 10.3923i | 0.235884 | + | 0.408564i | 0.959529 | − | 0.281609i | \(-0.0908680\pi\) |
−0.723645 | + | 0.690172i | \(0.757535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00000 | + | 3.46410i | −0.0785069 | + | 0.135978i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.8434 | − | 18.3848i | −1.24613 | − | 0.719452i | −0.275792 | − | 0.961217i | \(-0.588940\pi\) |
−0.970335 | + | 0.241765i | \(0.922274\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.00000 | − | 1.73205i | −0.0390732 | − | 0.0676768i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.82843i | − | 0.110180i | −0.998481 | − | 0.0550899i | \(-0.982455\pi\) | ||
0.998481 | − | 0.0550899i | \(-0.0175446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −33.0681 | + | 19.0919i | −1.28620 | + | 0.742588i | −0.977974 | − | 0.208725i | \(-0.933069\pi\) |
−0.308226 | + | 0.951313i | \(0.599735\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.0000 | + | 31.1769i | −0.699062 | + | 1.21081i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.6969 | − | 8.48528i | −0.569068 | − | 0.328551i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −34.2929 | + | 19.7990i | −1.32584 | + | 0.765473i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.0000 | 1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −46.0000 | −1.77317 | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.6969 | + | 8.48528i | −0.565685 | + | 0.326599i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.57321 | + | 4.94975i | 0.329495 | + | 0.190234i | 0.655617 | − | 0.755094i | \(-0.272409\pi\) |
−0.326122 | + | 0.945328i | \(0.605742\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00000 | + | 12.1244i | −0.268241 | + | 0.464606i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.89898 | − | 2.82843i | 0.187454 | − | 0.108227i | −0.403336 | − | 0.915052i | \(-0.632149\pi\) |
0.590790 | + | 0.806825i | \(0.298816\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 8.48528i | − | 0.324206i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.0000 | + | 20.7846i | 0.457164 | + | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.0227 | − | 6.36396i | −0.419323 | − | 0.242096i | 0.275464 | − | 0.961311i | \(-0.411168\pi\) |
−0.694788 | + | 0.719215i | \(0.744502\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.00000 | + | 5.19615i | −0.113796 | + | 0.197101i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 8.48528i | − | 0.320943i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.7990i | 0.747798i | 0.927470 | + | 0.373899i | \(0.121979\pi\) | ||||
−0.927470 | + | 0.373899i | \(0.878021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | + | 31.1769i | 0.678883 | + | 1.17586i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 22.0454 | + | 12.7279i | 0.827933 | + | 0.478007i | 0.853144 | − | 0.521675i | \(-0.174693\pi\) |
−0.0252116 | + | 0.999682i | \(0.508026\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.00000 | + | 6.92820i | 0.150012 | + | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.0000 | 0.898807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.9706i | 0.634663i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.34847 | − | 4.24264i | 0.274434 | − | 0.158444i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0000 | − | 20.7846i | 0.447524 | − | 0.775135i | −0.550700 | − | 0.834703i | \(-0.685639\pi\) |
0.998224 | + | 0.0595683i | \(0.0189724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −12.2474 | − | 7.07107i | −0.455488 | − | 0.262976i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.34847 | − | 4.24264i | 0.272915 | − | 0.157568i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.0000 | −1.07407 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −44.0908 | + | 25.4558i | −1.63076 | + | 0.941518i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.7196 | − | 14.8492i | −0.949977 | − | 0.548469i | −0.0569030 | − | 0.998380i | \(-0.518123\pi\) |
−0.893074 | + | 0.449910i | \(0.851456\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.7423 | + | 21.2132i | −1.35159 | + | 0.780340i | −0.988472 | − | 0.151403i | \(-0.951621\pi\) |
−0.363117 | + | 0.931744i | \(0.618287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 25.4558i | − | 0.935144i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000 | 1.10059 | 0.550297 | − | 0.834969i | \(-0.314515\pi\) | ||||
0.550297 | + | 0.834969i | \(0.314515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.00000 | − | 13.8564i | −0.293097 | − | 0.507659i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.4722 | + | 7.77817i | 0.492922 | + | 0.284589i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.0000 | + | 19.0526i | −0.401396 | + | 0.695238i | −0.993895 | − | 0.110333i | \(-0.964808\pi\) |
0.592499 | + | 0.805571i | \(0.298141\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.0000 | − | 22.5167i | −0.473746 | − | 0.820553i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 14.1421i | − | 0.514685i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.4558i | 0.925208i | 0.886565 | + | 0.462604i | \(0.153085\pi\) | ||||
−0.886565 | + | 0.462604i | \(0.846915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.0000 | + | 20.7846i | 0.435572 | + | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | + | 25.9808i | −0.543750 | + | 0.941802i | 0.454935 | + | 0.890525i | \(0.349663\pi\) |
−0.998684 | + | 0.0512772i | \(0.983671\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.34847 | − | 4.24264i | −0.265684 | − | 0.153393i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.00000 | − | 5.19615i | −0.108324 | − | 0.187622i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.48528i | 0.305590i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.1691 | − | 16.2635i | 1.01317 | − | 0.584956i | 0.101054 | − | 0.994881i | \(-0.467778\pi\) |
0.912119 | + | 0.409925i | \(0.134445\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | + | 10.3923i | −0.215526 | + | 0.373303i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.0454 | − | 12.7279i | −0.789859 | − | 0.456025i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.0000 | 0.571793 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.0000 | 0.642448 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.0681 | − | 19.0919i | 1.17875 | − | 0.680552i | 0.223026 | − | 0.974813i | \(-0.428407\pi\) |
0.955725 | + | 0.294260i | \(0.0950733\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.3939 | − | 16.9706i | −1.04645 | − | 0.604168i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27.0000 | + | 46.7654i | −0.958798 | + | 1.66069i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.79796 | − | 5.65685i | 0.347498 | − | 0.200628i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 26.8701i | − | 0.951786i | −0.879503 | − | 0.475893i | \(-0.842125\pi\) | ||
0.879503 | − | 0.475893i | \(-0.157875\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.00000 | − | 5.19615i | −0.106000 | − | 0.183597i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.89898 | + | 2.82843i | 0.172881 | + | 0.0998130i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.00000 | + | 8.66025i | −0.176008 | + | 0.304855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.00000 | − | 10.3923i | −0.210949 | − | 0.365374i | 0.741063 | − | 0.671436i | \(-0.234322\pi\) |
−0.952012 | + | 0.306062i | \(0.900989\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.7279i | − | 0.446938i | −0.974711 | − | 0.223469i | \(-0.928262\pi\) | ||
0.974711 | − | 0.223469i | \(-0.0717381\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.2843i | 0.991973i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.00000 | + | 10.3923i | 0.210171 | + | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.0000 | − | 31.1769i | 0.629740 | − | 1.09074i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.5959 | + | 11.3137i | 0.683902 | + | 0.394851i | 0.801324 | − | 0.598231i | \(-0.204129\pi\) |
−0.117421 | + | 0.993082i | \(0.537463\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.0000 | + | 27.7128i | 0.557725 | + | 0.966008i | 0.997686 | + | 0.0679910i | \(0.0216589\pi\) |
−0.439961 | + | 0.898017i | \(0.645008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | −0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 45.2548i | − | 1.57366i | −0.617167 | − | 0.786832i | \(-0.711720\pi\) | ||
0.617167 | − | 0.786832i | \(-0.288280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.3712 | + | 10.6066i | −0.638057 | + | 0.368383i | −0.783866 | − | 0.620930i | \(-0.786755\pi\) |
0.145809 | + | 0.989313i | \(0.453422\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.0000 | − | 20.7846i | 0.416275 | − | 0.721010i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.3939 | − | 16.9706i | −1.01722 | − | 0.587291i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.5959 | + | 11.3137i | −0.677334 | + | 0.391059i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.34847 | − | 4.24264i | 0.253095 | − | 0.146124i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.12372 | − | 3.53553i | −0.210663 | − | 0.121626i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.00000 | − | 15.5885i | 0.308879 | − | 0.534994i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.0908 | − | 25.4558i | 1.51141 | − | 0.872615i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.24264i | 0.145265i | 0.997359 | + | 0.0726326i | \(0.0231401\pi\) | ||||
−0.997359 | + | 0.0726326i | \(0.976860\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | 0.205196 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −21.0000 | − | 36.3731i | −0.717346 | − | 1.24248i | −0.962048 | − | 0.272882i | \(-0.912023\pi\) |
0.244701 | − | 0.969599i | \(-0.421310\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.4166 | − | 23.3345i | −1.37900 | − | 0.796164i | −0.386957 | − | 0.922098i | \(-0.626474\pi\) |
−0.992039 | + | 0.125934i | \(0.959807\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.0000 | − | 20.7846i | 0.408485 | − | 0.707516i | −0.586235 | − | 0.810141i | \(-0.699391\pi\) |
0.994720 | + | 0.102624i | \(0.0327240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.00000 | + | 12.1244i | 0.238007 | + | 0.412240i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 26.8701i | − | 0.912555i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 22.6274i | 0.767583i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.00000 | − | 8.66025i | 0.169224 | − | 0.293105i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.7423 | − | 21.2132i | −1.24070 | − | 0.716319i | −0.271464 | − | 0.962449i | \(-0.587508\pi\) |
−0.969237 | + | 0.246130i | \(0.920841\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.0000 | − | 29.4449i | −0.573396 | − | 0.993151i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 50.9117i | 1.71331i | 0.515886 | + | 0.856657i | \(0.327463\pi\) | ||||
−0.515886 | + | 0.856657i | \(0.672537\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.44949 | + | 1.41421i | −0.0823387 | + | 0.0475383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.0000 | − | 41.5692i | 0.805841 | − | 1.39576i | −0.109881 | − | 0.993945i | \(-0.535047\pi\) |
0.915722 | − | 0.401813i | \(-0.131620\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.2474 | − | 7.07107i | −0.410305 | − | 0.236890i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36.0000 | −1.20201 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.79796 | − | 5.65685i | 0.326780 | − | 0.188667i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.3939 | − | 16.9706i | −0.979252 | − | 0.565371i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.00000 | + | 15.5885i | −0.299170 | + | 0.518178i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.3939 | + | 16.9706i | −0.976008 | + | 0.563498i | −0.901062 | − | 0.433689i | \(-0.857212\pi\) |
−0.0749452 | + | 0.997188i | \(0.523878\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 9.89949i | − | 0.328346i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.0000 | + | 38.1051i | 0.728094 | + | 1.26110i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.0454 | + | 12.7279i | 0.728799 | + | 0.420772i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | + | 13.8564i | −0.263896 | + | 0.457081i | −0.967274 | − | 0.253735i | \(-0.918341\pi\) |
0.703378 | + | 0.710816i | \(0.251674\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.00000 | − | 15.5885i | −0.296560 | − | 0.513657i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.4558i | 0.836983i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.00000 | − | 3.46410i | −0.0656886 | − | 0.113776i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.00000 | + | 15.5885i | −0.295280 | + | 0.511441i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) |
0.679770 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0000 | − | 20.7846i | −0.392442 | − | 0.679729i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.00000 | 0.0653372 | 0.0326686 | − | 0.999466i | \(-0.489599\pi\) | ||||
0.0326686 | + | 0.999466i | \(0.489599\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.1421i | 0.461511i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.3156 | + | 26.1630i | −1.47725 | + | 0.852888i | −0.999670 | − | 0.0257029i | \(-0.991818\pi\) |
−0.477575 | + | 0.878591i | \(0.658484\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 31.1769i | −0.586161 | + | 1.01526i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.44949 | + | 1.41421i | 0.0795977 | + | 0.0459558i | 0.539271 | − | 0.842133i | \(-0.318700\pi\) |
−0.459673 | + | 0.888088i | \(0.652033\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.34847 | + | 4.24264i | −0.238541 | + | 0.137722i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.0000 | −1.03767 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.79796 | + | 5.65685i | 0.316723 | + | 0.182860i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.89898 | − | 2.82843i | 0.157867 | − | 0.0911448i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.65685i | 0.182101i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 18.0000 | + | 31.1769i | 0.578243 | + | 1.00155i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.1691 | + | 16.2635i | 0.903990 | + | 0.521919i | 0.878493 | − | 0.477756i | \(-0.158550\pi\) |
0.0254978 | + | 0.999675i | \(0.491883\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 9.00000 | − | 15.5885i | 0.288231 | − | 0.499230i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00000 | + | 15.5885i | 0.287936 | + | 0.498719i | 0.973317 | − | 0.229465i | \(-0.0736978\pi\) |
−0.685381 | + | 0.728184i | \(0.740364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 16.9706i | − | 0.542382i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 8.48528i | − | 0.270914i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.00000 | − | 10.3923i | −0.191370 | − | 0.331463i | 0.754334 | − | 0.656490i | \(-0.227960\pi\) |
−0.945705 | + | 0.325027i | \(0.894626\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | − | 6.92820i | 0.127451 | − | 0.220751i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.0908 | − | 25.4558i | −1.40201 | − | 0.809449i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.00000 | − | 13.8564i | −0.254128 | − | 0.440163i | 0.710530 | − | 0.703667i | \(-0.248455\pi\) |
−0.964658 | + | 0.263504i | \(0.915122\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −36.0000 | −1.14243 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 28.2843i | 0.896672i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.3712 | − | 10.6066i | 0.581821 | − | 0.335914i | −0.180036 | − | 0.983660i | \(-0.557621\pi\) |
0.761857 | + | 0.647746i | \(0.224288\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0000 | + | 41.5692i | −0.759326 | + | 1.31519i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))