Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (of order \(4\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 849.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.849 |
Dual form | 1600.2.q.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | − | 1.00000i | 0.577350 | − | 0.577350i | −0.356822 | − | 0.934172i | \(-0.616140\pi\) |
0.934172 | + | 0.356822i | \(0.116140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | + | 1.00000i | −0.301511 | + | 0.301511i | −0.841605 | − | 0.540094i | \(-0.818389\pi\) |
0.540094 | + | 0.841605i | \(0.318389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.00000i | −0.277350 | + | 0.277350i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) |
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | + | 3.00000i | 0.688247 | + | 0.688247i | 0.961844 | − | 0.273597i | \(-0.0882135\pi\) |
−0.273597 | + | 0.961844i | \(0.588214\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | − | 2.00000i | 0.436436 | − | 0.436436i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.00000 | 1.25109 | 0.625543 | − | 0.780189i | \(-0.284877\pi\) | ||||
0.625543 | + | 0.780189i | \(0.284877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.00000 | − | 3.00000i | −0.557086 | − | 0.557086i | 0.371391 | − | 0.928477i | \(-0.378881\pi\) |
−0.928477 | + | 0.371391i | \(0.878881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.00000i | 0.348155i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000i | 0.320256i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.00000 | + | 5.00000i | 0.762493 | + | 0.762493i | 0.976772 | − | 0.214280i | \(-0.0687403\pi\) |
−0.214280 | + | 0.976772i | \(0.568740\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 2.00000i | −0.280056 | − | 0.280056i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | + | 5.00000i | 0.686803 | + | 0.686803i | 0.961524 | − | 0.274721i | \(-0.0885855\pi\) |
−0.274721 | + | 0.961524i | \(0.588586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | 0.794719 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | + | 3.00000i | −0.390567 | + | 0.390567i | −0.874889 | − | 0.484323i | \(-0.839066\pi\) |
0.484323 | + | 0.874889i | \(0.339066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | − | 9.00000i | −1.15233 | − | 1.15233i | −0.986084 | − | 0.166248i | \(-0.946835\pi\) |
−0.166248 | − | 0.986084i | \(-0.553165\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.00000i | 0.251976i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 5.00000i | −0.610847 | + | 0.610847i | −0.943167 | − | 0.332320i | \(-0.892169\pi\) |
0.332320 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | − | 6.00000i | 0.722315 | − | 0.722315i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.0000i | − | 1.18678i | −0.804914 | − | 0.593391i | \(-0.797789\pi\) | ||
0.804914 | − | 0.593391i | \(-0.202211\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.00000 | + | 2.00000i | −0.227921 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | − | 1.00000i | 0.109764 | − | 0.109764i | −0.650092 | − | 0.759856i | \(-0.725269\pi\) |
0.759856 | + | 0.650092i | \(0.225269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.00000 | −0.643268 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.00000i | 0.423999i | 0.977270 | + | 0.212000i | \(0.0679975\pi\) | ||||
−0.977270 | + | 0.212000i | \(0.932002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | + | 2.00000i | −0.209657 | + | 0.209657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.00000 | − | 8.00000i | 0.829561 | − | 0.829561i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.00000i | − | 0.203069i | −0.994832 | − | 0.101535i | \(-0.967625\pi\) | ||
0.994832 | − | 0.101535i | \(-0.0323753\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.00000 | − | 1.00000i | −0.100504 | − | 0.100504i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.0000 | − | 11.0000i | 1.09454 | − | 1.09454i | 0.0995037 | − | 0.995037i | \(-0.468274\pi\) |
0.995037 | − | 0.0995037i | \(-0.0317255\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000 | 0.591198 | 0.295599 | − | 0.955312i | \(-0.404481\pi\) | ||||
0.295599 | + | 0.955312i | \(0.404481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.00000 | + | 7.00000i | 0.676716 | + | 0.676716i | 0.959256 | − | 0.282540i | \(-0.0911770\pi\) |
−0.282540 | + | 0.959256i | \(0.591177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00000 | − | 3.00000i | −0.287348 | − | 0.287348i | 0.548683 | − | 0.836031i | \(-0.315129\pi\) |
−0.836031 | + | 0.548683i | \(0.815129\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | 0.569495 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | − | 1.00000i | −0.0924500 | − | 0.0924500i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 4.00000i | − | 0.366679i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000i | 0.818182i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.0000 | 0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.0000 | − | 11.0000i | −0.961074 | − | 0.961074i | 0.0381958 | − | 0.999270i | \(-0.487839\pi\) |
−0.999270 | + | 0.0381958i | \(0.987839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | + | 6.00000i | 0.520266 | + | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.00000 | 0.683486 | 0.341743 | − | 0.939793i | \(-0.388983\pi\) | ||||
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | + | 3.00000i | −0.254457 | + | 0.254457i | −0.822795 | − | 0.568338i | \(-0.807586\pi\) |
0.568338 | + | 0.822795i | \(0.307586\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.00000 | − | 8.00000i | −0.673722 | − | 0.673722i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.00000i | − | 0.167248i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.00000 | + | 3.00000i | −0.247436 | + | 0.247436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.00000 | + | 7.00000i | −0.573462 | + | 0.573462i | −0.933094 | − | 0.359632i | \(-0.882902\pi\) |
0.359632 | + | 0.933094i | \(0.382902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0000 | + | 15.0000i | −1.19713 | + | 1.19713i | −0.222108 | + | 0.975022i | \(0.571294\pi\) |
−0.975022 | + | 0.222108i | \(0.928706\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.00000 | − | 1.00000i | 0.0783260 | − | 0.0783260i | −0.666858 | − | 0.745184i | \(-0.732361\pi\) |
0.745184 | + | 0.666858i | \(0.232361\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.00000 | 0.154765 | 0.0773823 | − | 0.997001i | \(-0.475344\pi\) | ||||
0.0773823 | + | 0.997001i | \(0.475344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | + | 3.00000i | −0.229416 | + | 0.229416i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.00000 | + | 1.00000i | −0.0760286 | + | 0.0760286i | −0.744099 | − | 0.668070i | \(-0.767121\pi\) |
0.668070 | + | 0.744099i | \(0.267121\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.0000 | − | 17.0000i | −1.27064 | − | 1.27064i | −0.945753 | − | 0.324887i | \(-0.894674\pi\) |
−0.324887 | − | 0.945753i | \(-0.605326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | + | 9.00000i | −0.668965 | + | 0.668965i | −0.957476 | − | 0.288512i | \(-0.906840\pi\) |
0.288512 | + | 0.957476i | \(0.406840\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −18.0000 | −1.33060 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | + | 2.00000i | 0.146254 | + | 0.146254i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | + | 8.00000i | 0.581914 | + | 0.581914i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 14.0000i | − | 1.00774i | −0.863779 | − | 0.503871i | \(-0.831909\pi\) | ||
0.863779 | − | 0.503871i | \(-0.168091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.0000 | − | 17.0000i | −1.21120 | − | 1.21120i | −0.970632 | − | 0.240567i | \(-0.922666\pi\) |
−0.240567 | − | 0.970632i | \(-0.577334\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 14.0000i | − | 0.992434i | −0.868199 | − | 0.496217i | \(-0.834722\pi\) | ||
0.868199 | − | 0.496217i | \(-0.165278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.0000i | 0.705346i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | − | 6.00000i | −0.421117 | − | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000i | 0.417029i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.00000 | + | 9.00000i | 0.619586 | + | 0.619586i | 0.945425 | − | 0.325840i | \(-0.105647\pi\) |
−0.325840 | + | 0.945425i | \(0.605647\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0000 | − | 10.0000i | −0.685189 | − | 0.685189i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000 | 1.08615 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.00000 | − | 4.00000i | 0.270295 | − | 0.270295i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | + | 2.00000i | 0.134535 | + | 0.134535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000i | 1.60716i | 0.595198 | + | 0.803579i | \(0.297074\pi\) | ||||
−0.595198 | + | 0.803579i | \(0.702926\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0000 | − | 15.0000i | 0.995585 | − | 0.995585i | −0.00440533 | − | 0.999990i | \(-0.501402\pi\) |
0.999990 | + | 0.00440533i | \(0.00140226\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | + | 7.00000i | −0.462573 | + | 0.462573i | −0.899498 | − | 0.436925i | \(-0.856068\pi\) |
0.436925 | + | 0.899498i | \(0.356068\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000i | 0.263181i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.00000 | 0.262049 | 0.131024 | − | 0.991379i | \(-0.458173\pi\) | ||||
0.131024 | + | 0.991379i | \(0.458173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.0000 | −1.15948 | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.00000 | + | 7.00000i | −0.449050 | + | 0.449050i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | −0.381771 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 2.00000i | − | 0.126745i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.0000 | + | 21.0000i | −1.32551 | + | 1.32551i | −0.416265 | + | 0.909243i | \(0.636661\pi\) |
−0.909243 | + | 0.416265i | \(0.863339\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | + | 6.00000i | −0.377217 | + | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.0000i | − | 1.37232i | −0.727450 | − | 0.686161i | \(-0.759294\pi\) | ||
0.727450 | − | 0.686161i | \(-0.240706\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | + | 6.00000i | 0.372822 | + | 0.372822i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 3.00000i | 0.185695 | − | 0.185695i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | 0.369976 | 0.184988 | − | 0.982741i | \(-0.440775\pi\) | ||||
0.184988 | + | 0.982741i | \(0.440775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000 | + | 4.00000i | 0.244796 | + | 0.244796i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.00000 | − | 3.00000i | −0.182913 | − | 0.182913i | 0.609711 | − | 0.792624i | \(-0.291286\pi\) |
−0.792624 | + | 0.609711i | \(0.791286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000i | 0.242091i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | + | 3.00000i | 0.180253 | + | 0.180253i | 0.791466 | − | 0.611213i | \(-0.209318\pi\) |
−0.611213 | + | 0.791466i | \(0.709318\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.00000i | 0.478947i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.0000i | 1.19310i | 0.802576 | + | 0.596550i | \(0.203462\pi\) | ||||
−0.802576 | + | 0.596550i | \(0.796538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.0000 | − | 15.0000i | −0.891657 | − | 0.891657i | 0.103022 | − | 0.994679i | \(-0.467149\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.00000 | − | 2.00000i | −0.117242 | − | 0.117242i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.0000 | − | 15.0000i | −0.876309 | − | 0.876309i | 0.116841 | − | 0.993151i | \(-0.462723\pi\) |
−0.993151 | + | 0.116841i | \(0.962723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00000 | + | 6.00000i | −0.346989 | + | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | + | 10.0000i | 0.576390 | + | 0.576390i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 22.0000i | − | 1.26387i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00000 | + | 5.00000i | −0.285365 | + | 0.285365i | −0.835244 | − | 0.549879i | \(-0.814674\pi\) |
0.549879 | + | 0.835244i | \(0.314674\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.00000 | − | 6.00000i | 0.341328 | − | 0.341328i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000i | 1.70114i | 0.525859 | + | 0.850572i | \(0.323744\pi\) | ||||
−0.525859 | + | 0.850572i | \(0.676256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.0000 | −0.904373 | −0.452187 | − | 0.891923i | \(-0.649356\pi\) | ||||
−0.452187 | + | 0.891923i | \(0.649356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.00000 | − | 5.00000i | 0.280828 | − | 0.280828i | −0.552611 | − | 0.833439i | \(-0.686369\pi\) |
0.833439 | + | 0.552611i | \(0.186369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.0000 | 0.781404 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000 | − | 6.00000i | 0.333849 | − | 0.333849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.00000 | −0.331801 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 16.0000i | − | 0.882109i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00000 | + | 1.00000i | −0.0549650 | + | 0.0549650i | −0.734055 | − | 0.679090i | \(-0.762375\pi\) |
0.679090 | + | 0.734055i | \(0.262375\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.00000 | + | 3.00000i | −0.164399 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000i | 0.980522i | 0.871576 | + | 0.490261i | \(0.163099\pi\) | ||||
−0.871576 | + | 0.490261i | \(0.836901\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | + | 6.00000i | 0.325875 | + | 0.325875i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.00000 | + | 8.00000i | −0.433224 | + | 0.433224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.0000 | − | 13.0000i | −0.697877 | − | 0.697877i | 0.266076 | − | 0.963952i | \(-0.414273\pi\) |
−0.963952 | + | 0.266076i | \(0.914273\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.00000 | − | 3.00000i | −0.160586 | − | 0.160586i | 0.622240 | − | 0.782826i | \(-0.286223\pi\) |
−0.782826 | + | 0.622240i | \(0.786223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | −0.427008 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | − | 4.00000i | −0.211702 | − | 0.211702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.0000i | 1.37223i | 0.727494 | + | 0.686114i | \(0.240685\pi\) | ||||
−0.727494 | + | 0.686114i | \(0.759315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.00000 | + | 9.00000i | 0.472377 | + | 0.472377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.00000i | − | 0.417597i | −0.977959 | − | 0.208798i | \(-0.933045\pi\) | ||
0.977959 | − | 0.208798i | \(-0.0669552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 10.0000 | + | 10.0000i | 0.519174 | + | 0.519174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.00000 | + | 5.00000i | 0.258890 | + | 0.258890i | 0.824603 | − | 0.565712i | \(-0.191399\pi\) |
−0.565712 | + | 0.824603i | \(0.691399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.00000 | 0.309016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00000 | + | 3.00000i | −0.154100 | + | 0.154100i | −0.779946 | − | 0.625847i | \(-0.784754\pi\) |
0.625847 | + | 0.779946i | \(0.284754\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.00000 | − | 8.00000i | −0.409852 | − | 0.409852i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.0000i | − | 0.817562i | −0.912633 | − | 0.408781i | \(-0.865954\pi\) | ||
0.912633 | − | 0.408781i | \(-0.134046\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.00000 | + | 5.00000i | −0.254164 | + | 0.254164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0000 | − | 13.0000i | 0.659126 | − | 0.659126i | −0.296047 | − | 0.955173i | \(-0.595669\pi\) |
0.955173 | + | 0.296047i | \(0.0956686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −22.0000 | −1.10975 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00000 | − | 5.00000i | 0.250943 | − | 0.250943i | −0.570414 | − | 0.821357i | \(-0.693217\pi\) |
0.821357 | + | 0.570414i | \(0.193217\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.0000 | 0.600751 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.00000 | + | 8.00000i | −0.398508 | + | 0.398508i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.00000 | −0.297409 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.0000i | − | 0.791149i | −0.918434 | − | 0.395575i | \(-0.870545\pi\) | ||
0.918434 | − | 0.395575i | \(-0.129455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.00000 | − | 8.00000i | 0.394611 | − | 0.394611i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | + | 6.00000i | −0.295241 | + | 0.295241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000i | 0.293821i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.00000 | + | 3.00000i | 0.146560 | + | 0.146560i | 0.776579 | − | 0.630020i | \(-0.216953\pi\) |
−0.630020 | + | 0.776579i | \(0.716953\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | + | 9.00000i | −0.438633 | + | 0.438633i | −0.891552 | − | 0.452919i | \(-0.850383\pi\) |
0.452919 | + | 0.891552i | \(0.350383\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000 | 0.388973 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.0000 | − | 18.0000i | −0.871081 | − | 0.871081i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00000 | − | 2.00000i | −0.0965609 | − | 0.0965609i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −32.0000 | −1.54139 | −0.770693 | − | 0.637207i | \(-0.780090\pi\) | ||||
−0.770693 | + | 0.637207i | \(0.780090\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.0000 | + | 18.0000i | 0.861057 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.0000i | − | 0.668184i | −0.942541 | − | 0.334092i | \(-0.891570\pi\) | ||
0.942541 | − | 0.334092i | \(-0.108430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.00000i | − | 0.142857i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0000 | − | 15.0000i | −0.712672 | − | 0.712672i | 0.254422 | − | 0.967093i | \(-0.418115\pi\) |
−0.967093 | + | 0.254422i | \(0.918115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0000i | 0.662177i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0000 | − | 10.0000i | −0.469841 | − | 0.469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.0000 | −1.49690 | −0.748448 | − | 0.663193i | \(-0.769201\pi\) | ||||
−0.748448 | + | 0.663193i | \(0.769201\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | − | 8.00000i | 0.373408 | − | 0.373408i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.0000 | + | 11.0000i | 0.512321 | + | 0.512321i | 0.915237 | − | 0.402916i | \(-0.132003\pi\) |
−0.402916 | + | 0.915237i | \(0.632003\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.0000i | − | 0.743583i | −0.928316 | − | 0.371792i | \(-0.878744\pi\) | ||
0.928316 | − | 0.371792i | \(-0.121256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | + | 5.00000i | −0.231372 | + | 0.231372i | −0.813265 | − | 0.581893i | \(-0.802312\pi\) |
0.581893 | + | 0.813265i | \(0.302312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | + | 10.0000i | −0.461757 | + | 0.461757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.0000i | 1.38233i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.0000 | −0.459800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.00000 | + | 5.00000i | −0.228934 | + | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −40.0000 | −1.82765 | −0.913823 | − | 0.406112i | \(-0.866884\pi\) | ||||
−0.913823 | + | 0.406112i | \(0.866884\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | −0.273576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.0000 | − | 12.0000i | 0.546019 | − | 0.546019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 2.00000i | − | 0.0904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.0000 | − | 19.0000i | 0.857458 | − | 0.857458i | −0.133580 | − | 0.991038i | \(-0.542647\pi\) |
0.991038 | + | 0.133580i | \(0.0426473\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 6.00000i | −0.270226 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 20.0000i | − | 0.897123i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0000 | + | 23.0000i | 1.02962 | + | 1.02962i | 0.999548 | + | 0.0300737i | \(0.00957421\pi\) |
0.0300737 | + | 0.999548i | \(0.490426\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.00000 | − | 2.00000i | 0.0893534 | − | 0.0893534i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.00000 | 0.267527 | 0.133763 | − | 0.991013i | \(-0.457294\pi\) | ||||
0.133763 | + | 0.991013i | \(0.457294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0000 | + | 11.0000i | 0.488527 | + | 0.488527i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.0000 | − | 23.0000i | −1.01946 | − | 1.01946i | −0.999807 | − | 0.0196502i | \(-0.993745\pi\) |
−0.0196502 | − | 0.999807i | \(-0.506255\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | 0.353899 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 24.0000i | 1.05963i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 8.00000i | 0.351840 | + | 0.351840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000i | 0.0877903i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 40.0000i | − | 1.75243i | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||
0.481919 | − | 0.876216i | \(-0.339940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 25.0000 | + | 25.0000i | 1.09317 | + | 1.09317i | 0.995188 | + | 0.0979859i | \(0.0312400\pi\) |
0.0979859 | + | 0.995188i | \(0.468760\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 16.0000i | − | 0.696971i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.00000 | − | 3.00000i | −0.130189 | − | 0.130189i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −34.0000 | −1.46721 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | − | 3.00000i | 0.129219 | − | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | − | 9.00000i | −0.386940 | − | 0.386940i | 0.486654 | − | 0.873595i | \(-0.338217\pi\) |
−0.873595 | + | 0.486654i | \(0.838217\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 18.0000i | 0.772454i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | + | 5.00000i | −0.213785 | + | 0.213785i | −0.805873 | − | 0.592088i | \(-0.798304\pi\) |
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.00000 | − | 9.00000i | 0.384111 | − | 0.384111i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 18.0000i | − | 0.766826i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0000 | − | 25.0000i | 1.05928 | − | 1.05928i | 0.0611558 | − | 0.998128i | \(-0.480521\pi\) |
0.998128 | − | 0.0611558i | \(-0.0194786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.0000 | −0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.0000 | + | 19.0000i | −0.800755 | + | 0.800755i | −0.983213 | − | 0.182459i | \(-0.941594\pi\) |
0.182459 | + | 0.983213i | \(0.441594\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.0000 | 0.419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.0000i | 1.00613i | 0.864248 | + | 0.503066i | \(0.167795\pi\) | ||||
−0.864248 | + | 0.503066i | \(0.832205\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00000 | + | 1.00000i | −0.0418487 | + | 0.0418487i | −0.727721 | − | 0.685873i | \(-0.759421\pi\) |
0.685873 | + | 0.727721i | \(0.259421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.00000 | − | 8.00000i | 0.334205 | − | 0.334205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000i | 0.749350i | 0.927156 | + | 0.374675i | \(0.122246\pi\) | ||||
−0.927156 | + | 0.374675i | \(0.877754\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.0000 | − | 14.0000i | −0.581820 | − | 0.581820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.00000 | − | 2.00000i | 0.0829740 | − | 0.0829740i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0000 | −0.414158 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.00000 | + | 7.00000i | 0.288921 | + | 0.288921i | 0.836653 | − | 0.547733i | \(-0.184509\pi\) |
−0.547733 | + | 0.836653i | \(0.684509\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | + | 24.0000i | 0.988903 | + | 0.988903i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.0000 | −1.39857 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 34.0000i | − | 1.39621i | −0.715994 | − | 0.698106i | \(-0.754026\pi\) | ||
0.715994 | − | 0.698106i | \(-0.245974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.0000 | − | 14.0000i | −0.572982 | − | 0.572982i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.0000i | − | 0.572024i | −0.958226 | − | 0.286012i | \(-0.907670\pi\) | ||
0.958226 | − | 0.286012i | \(-0.0923298\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.0000i | − | 0.815817i | −0.913023 | − | 0.407909i | \(-0.866258\pi\) | ||
0.913023 | − | 0.407909i | \(-0.133742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.00000 | − | 5.00000i | −0.203616 | − | 0.203616i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0000i | 1.29884i | 0.760430 | + | 0.649420i | \(0.224988\pi\) | ||||
−0.760430 | + | 0.649420i | \(0.775012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0000 | −0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | + | 8.00000i | 0.323645 | + | 0.323645i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.0000 | + | 25.0000i | 1.00974 | + | 1.00974i | 0.999952 | + | 0.00978840i | \(0.00311579\pi\) |
0.00978840 | + | 0.999952i | \(0.496884\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0000 | − | 17.0000i | 0.683288 | − | 0.683288i | −0.277452 | − | 0.960740i | \(-0.589490\pi\) |
0.960740 | + | 0.277452i | \(0.0894899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 24.0000 | + | 24.0000i | 0.963087 | + | 0.963087i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.00000i | 0.320513i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.00000 | + | 6.00000i | −0.239617 | + | 0.239617i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.00000 | − | 6.00000i | 0.239236 | − | 0.239236i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 10.0000i | − | 0.398094i | −0.979990 | − | 0.199047i | \(-0.936215\pi\) | ||
0.979990 | − | 0.199047i | \(-0.0637846\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 18.0000 | 0.715436 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.00000 | − | 3.00000i | 0.118864 | − | 0.118864i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.0000 | 0.395594 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.0000 | −0.710957 | −0.355479 | − | 0.934684i | \(-0.615682\pi\) | ||||
−0.355479 | + | 0.934684i | \(0.615682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.0000 | − | 21.0000i | 0.828159 | − | 0.828159i | −0.159103 | − | 0.987262i | \(-0.550860\pi\) |
0.987262 | + | 0.159103i | \(0.0508601\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 42.0000 | 1.65119 | 0.825595 | − | 0.564263i | \(-0.190840\pi\) | ||||
0.825595 | + | 0.564263i | \(0.190840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.00000i | − | 0.235521i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.0000 | − | 16.0000i | 0.627089 | − | 0.627089i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.0000 | − | 19.0000i | 0.743527 | − | 0.743527i | −0.229728 | − | 0.973255i | \(-0.573784\pi\) |
0.973255 | + | 0.229728i | \(0.0737835\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0000 | − | 17.0000i | −0.662226 | − | 0.662226i | 0.293678 | − | 0.955904i | \(-0.405121\pi\) |
−0.955904 | + | 0.293678i | \(0.905121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | + | 9.00000i | −0.350059 | + | 0.350059i | −0.860132 | − | 0.510072i | \(-0.829619\pi\) |
0.510072 | + | 0.860132i | \(0.329619\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00000 | 0.155347 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.0000 | − | 18.0000i | −0.696963 | − | 0.696963i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.0000 | + | 24.0000i | 0.927894 | + | 0.927894i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 14.0000i | − | 0.539660i | −0.962908 | − | 0.269830i | \(-0.913032\pi\) | ||
0.962908 | − | 0.269830i | \(-0.0869676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.00000 | + | 3.00000i | 0.115299 | + | 0.115299i | 0.762402 | − | 0.647103i | \(-0.224020\pi\) |
−0.647103 | + | 0.762402i | \(0.724020\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.00000i | − | 0.153506i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 30.0000i | − | 1.14960i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.00000 | + | 5.00000i | 0.191320 | + | 0.191320i | 0.796266 | − | 0.604946i | \(-0.206805\pi\) |
−0.604946 | + | 0.796266i | \(0.706805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0000i | 0.534133i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.0000 | −0.380970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | + | 9.00000i | 0.342376 | + | 0.342376i | 0.857260 | − | 0.514884i | \(-0.172165\pi\) |
−0.514884 | + | 0.857260i | \(0.672165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | − | 2.00000i | −0.0759737 | − | 0.0759737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.00000 | − | 4.00000i | 0.151294 | − | 0.151294i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.0000 | + | 31.0000i | 1.17085 | + | 1.17085i | 0.982006 | + | 0.188847i | \(0.0604752\pi\) |
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000i | 0.678883i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 22.0000 | − | 22.0000i | 0.827395 | − | 0.827395i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.0000 | + | 27.0000i | −1.01401 | + | 1.01401i | −0.0141058 | + | 0.999901i | \(0.504490\pi\) |
−0.999901 | + | 0.0141058i | \(0.995510\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0000 | 1.79761 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −18.0000 | + | 18.0000i | −0.669427 | + | 0.669427i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.00000 | 0.0741759 | 0.0370879 | − | 0.999312i | \(-0.488192\pi\) | ||||
0.0370879 | + | 0.999312i | \(0.488192\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000i | 1.07407i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0000 | − | 10.0000i | 0.369863 | − | 0.369863i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.0000 | + | 21.0000i | −0.775653 | + | 0.775653i | −0.979088 | − | 0.203436i | \(-0.934789\pi\) |
0.203436 | + | 0.979088i | \(0.434789\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 10.0000i | − | 0.368355i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.0000 | + | 23.0000i | 0.846069 | + | 0.846069i | 0.989640 | − | 0.143571i | \(-0.0458586\pi\) |
−0.143571 | + | 0.989640i | \(0.545859\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.00000 | + | 6.00000i | −0.220416 | + | 0.220416i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 46.0000 | 1.68758 | 0.843788 | − | 0.536676i | \(-0.180320\pi\) | ||||
0.843788 | + | 0.536676i | \(0.180320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.00000 | + | 1.00000i | 0.0365881 | + | 0.0365881i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.0000 | + | 14.0000i | 0.511549 | + | 0.511549i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 42.0000i | 1.53057i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0000 | + | 23.0000i | 0.835949 | + | 0.835949i | 0.988323 | − | 0.152374i | \(-0.0486917\pi\) |
−0.152374 | + | 0.988323i | \(0.548692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.0000i | 0.435572i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.00000 | − | 6.00000i | −0.217215 | − | 0.217215i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.00000i | − | 0.216647i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 50.0000 | 1.80305 | 0.901523 | − | 0.432731i | \(-0.142450\pi\) | ||||
0.901523 | + | 0.432731i | \(0.142450\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0000 | − | 22.0000i | −0.792311 | − | 0.792311i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.00000 | + | 5.00000i | 0.179838 | + | 0.179838i | 0.791285 | − | 0.611448i | \(-0.209412\pi\) |
−0.611448 | + | 0.791285i | \(0.709412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.0000 | 0.430498 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 10.0000i | 0.357828 | + | 0.357828i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 24.0000i | − | 0.857690i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | − | 15.0000i | 0.534692 | − | 0.534692i | −0.387273 | − | 0.921965i | \(-0.626583\pi\) |
0.921965 | + | 0.387273i | \(0.126583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | − | 6.00000i | 0.213606 | − | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000i | 0.426671i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | 0.639199 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0000 | − | 25.0000i | 0.885545 | − | 0.885545i | −0.108546 | − | 0.994091i | \(-0.534619\pi\) |
0.994091 | + | 0.108546i | \(0.0346195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.0000 | −0.566039 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.00000 | −0.141333 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.00000 | + | 4.00000i | −0.141157 | + | 0.141157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 16.0000i | − | 0.562530i | −0.959630 | − | 0.281265i | \(-0.909246\pi\) | ||
0.959630 | − | 0.281265i | \(-0.0907540\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.0000 | − | 39.0000i | 1.36948 | − | 1.36948i | 0.508288 | − | 0.861187i | \(-0.330278\pi\) |
0.861187 | − | 0.508288i | \(-0.169722\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | − | 8.00000i | 0.280572 | − | 0.280572i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000i | 1.04957i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | − | 2.00000i | −0.0698857 | − | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.0000 | − | 11.0000i | 0.383903 | − | 0.383903i | −0.488603 | − | 0.872506i | \(-0.662493\pi\) |
0.872506 | + | 0.488603i | \(0.162493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −34.0000 | −1.18517 | −0.592583 | − | 0.805510i | \(-0.701892\pi\) | ||||
−0.592583 | + | 0.805510i | \(0.701892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.0000 | − | 33.0000i | −1.14752 | − | 1.14752i | −0.987038 | − | 0.160484i | \(-0.948695\pi\) |
−0.160484 | − | 0.987038i | \(-0.551305\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0000 | − | 23.0000i | −0.798823 | − | 0.798823i | 0.184087 | − | 0.982910i | \(-0.441067\pi\) |
−0.982910 | + | 0.184087i | \(0.941067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000i | 0.207888i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.0000 | + | 32.0000i | 1.10608 | + | 1.10608i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 14.0000i | − | 0.483334i | −0.970359 | − | 0.241667i | \(-0.922306\pi\) | ||
0.970359 | − | 0.241667i | \(-0.0776941\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.0000 | + | 20.0000i | 0.688837 | + | 0.688837i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.0000i | 0.618487i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −30.0000 | −1.02960 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.0000 | + | 18.0000i | 0.617032 | + | 0.617032i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.00000 | + | 5.00000i | 0.171197 | + | 0.171197i | 0.787505 | − | 0.616308i | \(-0.211372\pi\) |
−0.616308 | + | 0.787505i | \(0.711372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.00000 | 0.273275 | 0.136637 | − | 0.990621i | \(-0.456370\pi\) | ||||
0.136637 | + | 0.990621i | \(0.456370\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.00000 | + | 3.00000i | −0.102359 | + | 0.102359i | −0.756432 | − | 0.654073i | \(-0.773059\pi\) |
0.654073 | + | 0.756432i | \(0.273059\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.0000i | 0.816970i | 0.912765 | + | 0.408485i | \(0.133943\pi\) | ||||
−0.912765 | + | 0.408485i | \(0.866057\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | − | 13.0000i | 0.441503 | − | 0.441503i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.0000i | − | 0.338837i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.00000 | 0.0676897 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.00000 | − | 5.00000i | 0.168838 | − | 0.168838i | −0.617630 | − | 0.786468i | \(-0.711907\pi\) |
0.786468 | + | 0.617630i | \(0.211907\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.0000 | −1.01187 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.00000 | 0.0673817 | 0.0336909 | − | 0.999432i | \(-0.489274\pi\) | ||||
0.0336909 | + | 0.999432i | \(0.489274\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.0000 | − | 21.0000i | 0.706706 | − | 0.706706i | −0.259135 | − | 0.965841i | \(-0.583437\pi\) |
0.965841 | + | 0.259135i | \(0.0834374\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.00000 | 0.0671534 | 0.0335767 | − | 0.999436i | \(-0.489310\pi\) | ||||
0.0335767 | + | 0.999436i | \(0.489310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.0000i | − | 0.536623i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.00000 | + | 5.00000i | −0.167506 | + | 0.167506i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.0000 | − | 24.0000i | 0.803129 | − | 0.803129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000i | 0.400668i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.0000 | − | 24.0000i | −0.800445 | − | 0.800445i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | − | 10.0000i | 0.333148 | − | 0.333148i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 20.0000 | 0.665558 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.0000 | + | 27.0000i | 0.896520 | + | 0.896520i | 0.995127 | − | 0.0986062i | \(-0.0314384\pi\) |
−0.0986062 | + | 0.995127i | \(0.531438\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0000 | + | 11.0000i | 0.364847 | + | 0.364847i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.00000 | 0.265052 | 0.132526 | − | 0.991180i | \(-0.457691\pi\) | ||||
0.132526 | + | 0.991180i | \(0.457691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000i | 0.0661903i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.0000 | − | 22.0000i | −0.726504 | − | 0.726504i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.0000i | 0.857661i | 0.903385 | + | 0.428830i | \(0.141074\pi\) | ||||
−0.903385 | + | 0.428830i | \(0.858926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000i | 0.329511i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0000 | + | 10.0000i | 0.329154 | + | 0.329154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00000i | 0.197066i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −30.0000 | −0.984268 | −0.492134 | − | 0.870519i | \(-0.663783\pi\) | ||||
−0.492134 | + | 0.870519i | \(0.663783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | − | 9.00000i | −0.294963 | − | 0.294963i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 30.0000 | + | 30.0000i | 0.982156 | + | 0.982156i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.0000 | 0.914720 | 0.457360 | − | 0.889282i | \(-0.348795\pi\) | ||||
0.457360 | + | 0.889282i | \(0.348795\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | + | 16.0000i | −0.522140 | + | 0.522140i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.0000 | − | 29.0000i | −0.945373 | − | 0.945373i | 0.0532103 | − | 0.998583i | \(-0.483055\pi\) |
−0.998583 | + | 0.0532103i | \(0.983055\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.00000 | + | 5.00000i | −0.162478 | + | 0.162478i | −0.783664 | − | 0.621185i | \(-0.786651\pi\) |
0.621185 | + | 0.783664i | \(0.286651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | + | 4.00000i | −0.129845 | + | 0.129845i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.0000i | − | 0.324272i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.00000 | − | 6.00000i | 0.193952 | − | 0.193952i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.0000 | 0.516667 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.00000 | + | 7.00000i | −0.225572 | + | 0.225572i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.00000 | 0.0643157 | 0.0321578 | − | 0.999483i | \(-0.489762\pi\) | ||||
0.0321578 | + | 0.999483i | \(0.489762\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 12.0000i | − | 0.385496i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0000 | − | 19.0000i | 0.609739 | − | 0.609739i | −0.333139 | − | 0.942878i | \(-0.608108\pi\) |
0.942878 | + | 0.333139i | \(0.108108\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.00000 | + | 6.00000i | −0.192351 | + | 0.192351i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.00000i | − | 0.0639857i | −0.999488 | − | 0.0319928i | \(-0.989815\pi\) | ||
0.999488 | − | 0.0319928i | \(-0.0101854\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | − | 4.00000i | −0.127841 | − | 0.127841i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.00000 | − | 3.00000i | 0.0957826 | − | 0.0957826i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.0000 | −1.08443 | −0.542216 | − | 0.840239i | \(-0.682414\pi\) | ||||
−0.542216 | + | 0.840239i | \(0.682414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16.0000 | − | 16.0000i | −0.509286 | − | 0.509286i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.0000 | + | 30.0000i | 0.953945 | + | 0.953945i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.0000 | −1.01651 | −0.508257 | − | 0.861206i | \(-0.669710\pi\) | ||||
−0.508257 | + | 0.861206i | \(0.669710\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.00000i | 0.0634681i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.0000 | − | 37.0000i | −1.17180 | − | 1.17180i | −0.981780 | − | 0.190022i | \(-0.939144\pi\) |
−0.190022 | − | 0.981780i | \(-0.560856\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 24.0000i | 0.759326i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))