Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,2,Mod(33,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.33");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.e (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: | \(1.02208514587\) |
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 | 33.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.33 |
Dual form | 128.2.e.a.97.1 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | \(-0.383860\pi\) |
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | − | 1.00000i | 0.447214 | − | 0.447214i | −0.447214 | − | 0.894427i | \(-0.647584\pi\) |
0.894427 | + | 0.447214i | \(0.147584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.00000i | − | 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.00000i | 0.301511 | − | 0.301511i | −0.540094 | − | 0.841605i | \(-0.681611\pi\) |
0.841605 | + | 0.540094i | \(0.181611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.00000i | 0.277350 | + | 0.277350i | 0.832050 | − | 0.554700i | \(-0.187167\pi\) |
−0.554700 | + | 0.832050i | \(0.687167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.00000 | −0.516398 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.00000i | 0.600000i | ||||||||
\(26\) | 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 | ||||||||
\(33\) | −2.00000 | −0.348155 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 2.00000i | −0.338062 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.00000 | + | 3.00000i | −0.493197 | + | 0.493197i | −0.909312 | − | 0.416115i | \(-0.863391\pi\) |
0.416115 | + | 0.909312i | \(0.363391\pi\) | |||||||
\(38\) | 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 | −0.214280 | − | 0.976772i | \(-0.568740\pi\) |
0.976772 | + | 0.214280i | \(0.0687403\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.00000i | −0.149071 | − | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 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 | −0.274721 | − | 0.961524i | \(-0.588586\pi\) |
0.961524 | + | 0.274721i | \(0.0885855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.00000i | − | 0.269680i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 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 | \(0.0531652\pi\) |
0.166248 | + | 0.986084i | \(0.446835\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | − | 5.00000i | −0.610847 | − | 0.610847i | 0.332320 | − | 0.943167i | \(-0.392169\pi\) |
−0.943167 | + | 0.332320i | \(0.892169\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 4.00000i | 0.468165i | 0.972217 | + | 0.234082i | \(0.0752085\pi\) | ||||
−0.972217 | + | 0.234082i | \(0.924791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.00000 | − | 3.00000i | 0.346410 | − | 0.346410i | ||||
\(76\) | 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 | \(-0.274731\pi\) |
−0.759856 | + | 0.650092i | \(0.774731\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | + | 2.00000i | −0.216930 | + | 0.216930i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.00000i | − | 0.423999i | −0.977270 | − | 0.212000i | \(-0.932002\pi\) | ||
0.977270 | − | 0.212000i | \(-0.0679975\pi\) | |||||||
\(90\) | 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 | ||||||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 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 | \(0.531726\pi\) |
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.00000i | 0.390360i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.00000 | + | 7.00000i | −0.676716 | + | 0.676716i | −0.959256 | − | 0.282540i | \(-0.908823\pi\) |
0.282540 | + | 0.959256i | \(0.408823\pi\) | |||||||
\(108\) | 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 | ||||||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | + | 6.00000i | 0.559503 | + | 0.559503i | ||||
\(116\) | 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 | ||||||||
\(125\) | 8.00000 | + | 8.00000i | 0.715542 | + | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.0000 | −0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0000 | + | 11.0000i | 0.961074 | + | 0.961074i | 0.999270 | − | 0.0381958i | \(-0.0121611\pi\) |
−0.0381958 | + | 0.999270i | \(0.512161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 6.00000i | 0.520266 | − | 0.520266i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.00000i | 0.688530i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 8.00000i | − | 0.683486i | −0.939793 | − | 0.341743i | \(-0.888983\pi\) | ||
0.939793 | − | 0.341743i | \(-0.111017\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 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 | ||||||||
\(153\) | 2.00000i | 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | − | 8.00000i | 0.642575 | − | 0.642575i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.0000 | − | 15.0000i | −1.19713 | − | 1.19713i | −0.975022 | − | 0.222108i | \(-0.928706\pi\) |
−0.222108 | − | 0.975022i | \(-0.571294\pi\) | |||||||
\(158\) | 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 | \(-0.267639\pi\) |
−0.745184 | + | 0.666858i | \(0.767639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.00000 | + | 2.00000i | −0.155700 | + | 0.155700i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.00000i | − | 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(168\) | 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 | \(-0.232879\pi\) |
−0.668070 | + | 0.744099i | \(0.732879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.00000 | 0.453557 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | 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 | −0.288512 | − | 0.957476i | \(-0.593160\pi\) |
0.957476 | + | 0.288512i | \(0.0931604\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.0000i | − | 1.33060i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.00000i | 0.441129i | ||||||||
\(186\) | 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 | ||||||||
\(193\) | 14.0000 | 1.00774 | 0.503871 | − | 0.863779i | \(-0.331909\pi\) | ||||
0.503871 | + | 0.863779i | \(0.331909\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.00000 | − | 2.00000i | −0.143223 | − | 0.143223i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.0000 | − | 17.0000i | 1.21120 | − | 1.21120i | 0.240567 | − | 0.970632i | \(-0.422666\pi\) |
0.970632 | − | 0.240567i | \(-0.0773335\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000i | 0.992434i | 0.868199 | + | 0.496217i | \(0.165278\pi\) | ||||
−0.868199 | + | 0.496217i | \(0.834722\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | 0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | − | 9.00000i | −0.619586 | − | 0.619586i | 0.325840 | − | 0.945425i | \(-0.394353\pi\) |
−0.945425 | + | 0.325840i | \(0.894353\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.0000 | + | 10.0000i | −0.685189 | + | 0.685189i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 10.0000i | − | 0.681994i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.0000i | − | 1.08615i | ||||||
\(218\) | 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 | ||||||||
\(223\) | −24.0000 | −1.60716 | −0.803579 | − | 0.595198i | \(-0.797074\pi\) | ||||
−0.803579 | + | 0.595198i | \(0.797074\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | 0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.0000 | + | 15.0000i | 0.995585 | + | 0.995585i | 0.999990 | − | 0.00440533i | \(-0.00140226\pi\) |
−0.00440533 | + | 0.999990i | \(0.501402\pi\) | |||||||
\(228\) | 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 | ||||||||
\(233\) | 4.00000i | 0.262049i | 0.991379 | + | 0.131024i | \(0.0418266\pi\) | ||||
−0.991379 | + | 0.131024i | \(0.958173\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | + | 8.00000i | −0.521862 | + | 0.521862i | ||||
\(236\) | 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 | ||||||||
\(245\) | 3.00000 | − | 3.00000i | 0.191663 | − | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.00000i | 0.126745i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.0000 | − | 21.0000i | 1.32551 | − | 1.32551i | 0.416265 | − | 0.909243i | \(-0.363339\pi\) |
0.909243 | − | 0.416265i | \(-0.136661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | + | 6.00000i | 0.377217 | + | 0.377217i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.0000 | −1.37232 | −0.686161 | − | 0.727450i | \(-0.740706\pi\) | ||||
−0.686161 | + | 0.727450i | \(0.740706\pi\) | |||||||
\(258\) | 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 | ||||||||
\(263\) | 6.00000i | 0.369976i | 0.982741 | + | 0.184988i | \(0.0592246\pi\) | ||||
−0.982741 | + | 0.184988i | \(0.940775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 10.0000i | − | 0.614295i | ||||||
\(266\) | 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 | ||||||||
\(273\) | −4.00000 | −0.242091 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.00000 | + | 3.00000i | 0.180907 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.00000 | + | 3.00000i | −0.180253 | + | 0.180253i | −0.791466 | − | 0.611213i | \(-0.790682\pi\) |
0.611213 | + | 0.791466i | \(0.290682\pi\) | |||||||
\(278\) | 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 | −0.994679 | − | 0.103022i | \(-0.967149\pi\) |
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.00000 | − | 6.00000i | −0.355409 | − | 0.355409i | ||||
\(286\) | 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 | −0.993151 | − | 0.116841i | \(-0.962723\pi\) |
0.116841 | + | 0.993151i | \(0.462723\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000i | 0.349334i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.00000i | 0.464207i | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 22.0000 | 1.26387 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 18.0000 | 1.03068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00000 | − | 5.00000i | −0.285365 | − | 0.285365i | 0.549879 | − | 0.835244i | \(-0.314674\pi\) |
−0.835244 | + | 0.549879i | \(0.814674\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | − | 16.0000i | − | 0.904373i | −0.891923 | − | 0.452187i | \(-0.850644\pi\) | ||
0.891923 | − | 0.452187i | \(-0.149356\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.00000 | + | 2.00000i | −0.112687 | + | 0.112687i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.00000 | + | 5.00000i | 0.280828 | + | 0.280828i | 0.833439 | − | 0.552611i | \(-0.186369\pi\) |
−0.552611 | + | 0.833439i | \(0.686369\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | −3.00000 | + | 3.00000i | −0.166410 | + | 0.166410i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.00000i | 0.331801i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.0000i | 0.882109i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | − | 1.00000i | 0.0549650 | − | 0.0549650i | −0.679090 | − | 0.734055i | \(-0.737625\pi\) |
0.734055 | + | 0.679090i | \(0.237625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.00000 | + | 3.00000i | 0.164399 | + | 0.164399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.0000 | −0.546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | 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 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 12.0000i | − | 0.646058i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.0000 | − | 13.0000i | 0.697877 | − | 0.697877i | −0.266076 | − | 0.963952i | \(-0.585727\pi\) |
0.963952 | + | 0.266076i | \(0.0857271\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0000 | − | 10.0000i | −0.530745 | − | 0.530745i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.00000 | − | 4.00000i | 0.211702 | − | 0.211702i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.0000i | − | 1.37223i | −0.727494 | − | 0.686114i | \(-0.759315\pi\) | ||
0.727494 | − | 0.686114i | \(-0.240685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.00000i | − | 0.0526316i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.00000 | − | 9.00000i | 0.472377 | − | 0.472377i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | + | 4.00000i | 0.209370 | + | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 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 | −0.565712 | − | 0.824603i | \(-0.691399\pi\) |
0.824603 | + | 0.565712i | \(0.191399\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 16.0000i | − | 0.826236i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 6.00000i | − | 0.309016i | ||||||
\(378\) | 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 | ||||||||
\(383\) | 16.0000 | 0.817562 | 0.408781 | − | 0.912633i | \(-0.365954\pi\) | ||||
0.408781 | + | 0.912633i | \(0.365954\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 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 | ||||||||
\(393\) | − | 22.0000i | − | 1.10975i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00000 | + | 5.00000i | 0.250943 | + | 0.250943i | 0.821357 | − | 0.570414i | \(-0.193217\pi\) |
−0.570414 | + | 0.821357i | \(0.693217\pi\) | |||||||
\(398\) | 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 | ||||||||
\(405\) | 5.00000 | − | 5.00000i | 0.248452 | − | 0.248452i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.00000i | 0.297409i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0000i | 0.791149i | 0.918434 | + | 0.395575i | \(0.129455\pi\) | ||||
−0.918434 | + | 0.395575i | \(0.870545\pi\) | |||||||
\(410\) | 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 | ||||||||
\(415\) | −2.00000 | −0.0981761 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 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 | −0.452919 | − | 0.891552i | \(-0.649617\pi\) |
0.891552 | + | 0.452919i | \(0.149617\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 6.00000i | − | 0.291043i | ||||||
\(426\) | 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 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000 | + | 6.00000i | 0.287678 | + | 0.287678i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.0000 | + | 18.0000i | −0.861057 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000i | 0.668184i | 0.942541 | + | 0.334092i | \(0.108430\pi\) | ||||
−0.942541 | + | 0.334092i | \(0.891570\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 3.00000i | − | 0.142857i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0000 | + | 15.0000i | −0.712672 | + | 0.712672i | −0.967093 | − | 0.254422i | \(-0.918115\pi\) |
0.254422 | + | 0.967093i | \(0.418115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.00000 | − | 4.00000i | −0.189618 | − | 0.189618i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.0000 | 0.662177 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −10.0000 | + | 10.0000i | −0.469841 | + | 0.469841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 4.00000i | − | 0.187523i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.0000i | 1.49690i | 0.663193 | + | 0.748448i | \(0.269201\pi\) | ||||
−0.663193 | + | 0.748448i | \(0.730799\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | − | 8.00000i | 0.373408 | − | 0.373408i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.0000 | − | 11.0000i | −0.512321 | − | 0.512321i | 0.402916 | − | 0.915237i | \(-0.367997\pi\) |
−0.915237 | + | 0.402916i | \(0.867997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −16.0000 | −0.741982 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.00000 | − | 5.00000i | −0.231372 | − | 0.231372i | 0.581893 | − | 0.813265i | \(-0.302312\pi\) |
−0.813265 | + | 0.581893i | \(0.802312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | + | 10.0000i | −0.461757 | + | 0.461757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 30.0000i | 1.38233i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 10.0000i | − | 0.459800i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.00000 | + | 9.00000i | −0.412948 | + | 0.412948i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.00000 | − | 5.00000i | −0.228934 | − | 0.228934i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 40.0000 | 1.82765 | 0.913823 | − | 0.406112i | \(-0.133116\pi\) | ||||
0.913823 | + | 0.406112i | \(0.133116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | −0.273576 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −12.0000 | − | 12.0000i | −0.546019 | − | 0.546019i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.00000 | + | 2.00000i | −0.0908153 | + | 0.0908153i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.00000i | − | 0.0906287i | −0.998973 | − | 0.0453143i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453143i | \(-0.0144289\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.00000i | 0.0904431i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.0000 | + | 19.0000i | −0.857458 | + | 0.857458i | −0.991038 | − | 0.133580i | \(-0.957353\pi\) |
0.133580 | + | 0.991038i | \(0.457353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 6.00000i | 0.270226 | + | 0.270226i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | −0.0898933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.0000 | −0.897123 | ||||||||
\(498\) | 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 | ||||||||
\(503\) | 6.00000i | 0.267527i | 0.991013 | + | 0.133763i | \(0.0427062\pi\) | ||||
−0.991013 | + | 0.133763i | \(0.957294\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0000i | 0.978987i | ||||||||
\(506\) | 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 | ||||||||
\(513\) | −24.0000 | −1.05963 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.00000 | + | 6.00000i | 0.264392 | + | 0.264392i | ||||
\(516\) | 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 | 0.0979859 | − | 0.995188i | \(-0.468760\pi\) |
0.995188 | − | 0.0979859i | \(-0.0312400\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.00000 | − | 6.00000i | −0.261861 | − | 0.261861i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.0000 | −0.696971 | ||||||||
\(528\) | 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 | ||||||||
\(535\) | 14.0000i | 0.605273i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.0000i | 1.46721i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.00000 | − | 3.00000i | 0.129219 | − | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.00000 | + | 9.00000i | 0.386940 | + | 0.386940i | 0.873595 | − | 0.486654i | \(-0.161783\pi\) |
−0.486654 | + | 0.873595i | \(0.661783\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.0000 | −0.772454 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.00000 | −0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | − | 5.00000i | −0.213785 | − | 0.213785i | 0.592088 | − | 0.805873i | \(-0.298304\pi\) |
−0.805873 | + | 0.592088i | \(0.798304\pi\) | |||||||
\(548\) | 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 | ||||||||
\(555\) | 6.00000 | − | 6.00000i | 0.254686 | − | 0.254686i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.0000 | + | 25.0000i | 1.05928 | + | 1.05928i | 0.998128 | + | 0.0611558i | \(0.0194786\pi\) |
0.0611558 | + | 0.998128i | \(0.480521\pi\) | |||||||
\(558\) | 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 | \(-0.0584057\pi\) |
−0.182459 | + | 0.983213i | \(0.558406\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.00000 | + | 6.00000i | −0.252422 | + | 0.252422i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 10.0000i | − | 0.419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 24.0000i | − | 1.00613i | −0.864248 | − | 0.503066i | \(-0.832205\pi\) | ||
0.864248 | − | 0.503066i | \(-0.167795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.00000 | − | 1.00000i | 0.0418487 | − | 0.0418487i | −0.685873 | − | 0.727721i | \(-0.740579\pi\) |
0.727721 | + | 0.685873i | \(0.240579\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.00000 | − | 8.00000i | −0.334205 | − | 0.334205i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.0000 | −0.750652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0000 | 0.749350 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(578\) | 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 | ||||||||
\(583\) | − | 10.0000i | − | 0.414158i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.00000i | − | 0.0826898i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.00000 | + | 7.00000i | −0.288921 | + | 0.288921i | −0.836653 | − | 0.547733i | \(-0.815491\pi\) |
0.547733 | + | 0.836653i | \(0.315491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.0000 | + | 24.0000i | 0.988903 | + | 0.988903i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −34.0000 | −1.39857 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.0000 | 1.39621 | 0.698106 | − | 0.715994i | \(-0.254026\pi\) | ||||
0.698106 | + | 0.715994i | \(0.254026\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | + | 4.00000i | 0.163984 | + | 0.163984i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0000 | − | 14.0000i | 0.572982 | − | 0.572982i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.0000i | 0.572024i | 0.958226 | + | 0.286012i | \(0.0923298\pi\) | ||||
−0.958226 | + | 0.286012i | \(0.907670\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 9.00000 | + | 9.00000i | 0.365902 | + | 0.365902i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.0000 | 1.29884 | 0.649420 | − | 0.760430i | \(-0.275012\pi\) | ||||
0.649420 | + | 0.760430i | \(0.275012\pi\) | |||||||
\(608\) | 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 | 0.00978840 | − | 0.999952i | \(-0.496884\pi\) |
0.999952 | − | 0.00978840i | \(-0.00311579\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.0000i | 0.483102i | 0.970388 | + | 0.241551i | \(0.0776561\pi\) | ||||
−0.970388 | + | 0.241551i | \(0.922344\pi\) | |||||||
\(618\) | 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 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 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 | ||||||||
\(633\) | 18.0000i | 0.715436i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | + | 8.00000i | −0.317470 | + | 0.317470i | ||||
\(636\) | 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 | \(-0.449140\pi\) |
−0.987262 | + | 0.159103i | \(0.949140\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.0000 | + | 10.0000i | −0.393750 | + | 0.393750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 42.0000i | − | 1.65119i | −0.564263 | − | 0.825595i | \(-0.690840\pi\) | ||
0.564263 | − | 0.825595i | \(-0.309160\pi\) | |||||||
\(648\) | 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 | \(-0.426216\pi\) |
−0.973255 | + | 0.229728i | \(0.926216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 22.0000 | 0.859611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.00000 | 0.156055 | ||||||||
\(658\) | 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 | −0.510072 | − | 0.860132i | \(-0.670381\pi\) |
0.860132 | + | 0.510072i | \(0.170381\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.00000i | 0.155347i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 12.0000i | − | 0.465340i | ||||||
\(666\) | 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 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.0000 | − | 12.0000i | −0.461880 | − | 0.461880i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | + | 3.00000i | −0.115299 | + | 0.115299i | −0.762402 | − | 0.647103i | \(-0.775980\pi\) |
0.647103 | + | 0.762402i | \(0.275980\pi\) | |||||||
\(678\) | 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 | −0.604946 | − | 0.796266i | \(-0.706805\pi\) |
0.796266 | + | 0.604946i | \(0.206805\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.00000 | − | 8.00000i | −0.305664 | − | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.0000 | 0.534133 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 10.0000 | 0.380970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | − | 9.00000i | −0.342376 | − | 0.342376i | 0.514884 | − | 0.857260i | \(-0.327835\pi\) |
−0.857260 | + | 0.514884i | \(0.827835\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | + | 2.00000i | −0.0759737 | + | 0.0759737i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000i | 0.227593i | ||||||||
\(696\) | 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 | \(-0.939525\pi\) |
−0.188847 | − | 0.982006i | \(-0.560475\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.0000 | −0.678883 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.0000 | 0.602595 | ||||||||
\(706\) | 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 | ||||||||
\(713\) | 48.0000i | 1.79761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | − | 2.00000i | 0.0747958 | − | 0.0747958i | ||||
\(716\) | 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 | ||||||||
\(725\) | 9.00000 | − | 9.00000i | 0.334252 | − | 0.334252i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.00000i | − | 0.0741759i | −0.999312 | − | 0.0370879i | \(-0.988192\pi\) | ||
0.999312 | − | 0.0370879i | \(-0.0118082\pi\) | |||||||
\(728\) | 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 | \(-0.0652108\pi\) |
−0.203436 | + | 0.979088i | \(0.565211\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.00000 | −0.221313 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.0000 | −0.368355 | ||||||||
\(738\) | 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 | ||||||||
\(743\) | 46.0000i | 1.68758i | 0.536676 | + | 0.843788i | \(0.319680\pi\) | ||||
−0.536676 | + | 0.843788i | \(0.680320\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.0000i | 0.512920i | ||||||||
\(746\) | 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 | ||||||||
\(753\) | −42.0000 | −1.53057 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.0000 | − | 10.0000i | −0.363937 | − | 0.363937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.0000 | + | 23.0000i | −0.835949 | + | 0.835949i | −0.988323 | − | 0.152374i | \(-0.951308\pi\) |
0.152374 | + | 0.988323i | \(0.451308\pi\) | |||||||
\(758\) | 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 | ||||||||
\(765\) | 2.00000 | + | 2.00000i | 0.0723102 | + | 0.0723102i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.0000 | −1.80305 | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 22.0000 | + | 22.0000i | 0.792311 | + | 0.792311i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.00000 | − | 5.00000i | 0.179838 | − | 0.179838i | −0.611448 | − | 0.791285i | \(-0.709412\pi\) |
0.791285 | + | 0.611448i | \(0.209412\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.0000i | 0.862105i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 12.0000i | − | 0.430498i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.0000 | − | 10.0000i | −0.357828 | − | 0.357828i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 24.0000 | 0.857690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.0000 | −1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | + | 15.0000i | 0.534692 | + | 0.534692i | 0.921965 | − | 0.387273i | \(-0.126583\pi\) |
−0.387273 | + | 0.921965i | \(0.626583\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | − | 6.00000i | 0.213606 | − | 0.213606i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000i | 0.426671i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000i | 0.639199i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.0000 | + | 10.0000i | −0.354663 | + | 0.354663i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.0000 | + | 25.0000i | 0.885545 | + | 0.885545i | 0.994091 | − | 0.108546i | \(-0.0346195\pi\) |
−0.108546 | + | 0.994091i | \(0.534619\pi\) | |||||||
\(798\) | 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 | ||||||||
\(805\) | 12.0000 | − | 12.0000i | 0.422944 | − | 0.422944i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.00000i | 0.211210i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16.0000i | 0.562530i | 0.959630 | + | 0.281265i | \(0.0907540\pi\) | ||||
−0.959630 | + | 0.281265i | \(0.909246\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −39.0000 | + | 39.0000i | −1.36948 | + | 1.36948i | −0.508288 | + | 0.861187i | \(0.669722\pi\) |
−0.861187 | + | 0.508288i | \(0.830278\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.00000 | − | 8.00000i | −0.280572 | − | 0.280572i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | 1.04957 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.00000 | − | 2.00000i | −0.0698857 | − | 0.0698857i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.0000 | + | 11.0000i | −0.383903 | + | 0.383903i | −0.872506 | − | 0.488603i | \(-0.837507\pi\) |
0.488603 | + | 0.872506i | \(0.337507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.0000i | − | 1.18517i | −0.805510 | − | 0.592583i | \(-0.798108\pi\) | ||
0.805510 | − | 0.592583i | \(-0.201892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 6.00000i | − | 0.208893i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.0000 | − | 33.0000i | 1.14752 | − | 1.14752i | 0.160484 | − | 0.987038i | \(-0.448695\pi\) |
0.987038 | − | 0.160484i | \(-0.0513055\pi\) | |||||||
\(828\) | 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 | ||||||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | − | 2.00000i | −0.0692129 | − | 0.0692129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −32.0000 | + | 32.0000i | −1.10608 | + | 1.10608i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 14.0000i | 0.483334i | 0.970359 | + | 0.241667i | \(0.0776941\pi\) | ||||
−0.970359 | + | 0.241667i | \(0.922306\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 11.0000i | − | 0.379310i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.0000 | − | 20.0000i | 0.688837 | − | 0.688837i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.0000 | − | 11.0000i | −0.378412 | − | 0.378412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.0000 | 0.618487 | ||||||||
\(848\) | 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 | −0.616308 | − | 0.787505i | \(-0.711372\pi\) |
0.787505 | + | 0.616308i | \(0.211372\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.00000i | − | 0.205196i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 8.00000i | − | 0.273275i | −0.990621 | − | 0.136637i | \(-0.956370\pi\) | ||
0.990621 | − | 0.136637i | \(-0.0436295\pi\) | |||||||
\(858\) | 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 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 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 | ||||||||
\(873\) | 2.00000i | 0.0676897i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.0000 | − | 16.0000i | 0.540899 | − | 0.540899i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.00000 | + | 5.00000i | 0.168838 | + | 0.168838i | 0.786468 | − | 0.617630i | \(-0.211907\pi\) |
−0.617630 | + | 0.786468i | \(0.711907\pi\) | |||||||
\(878\) | 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 | \(-0.416563\pi\) |
−0.965841 | + | 0.259135i | \(0.916563\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00000 | − | 6.00000i | 0.201688 | − | 0.201688i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.00000i | − | 0.0671534i | −0.999436 | − | 0.0335767i | \(-0.989310\pi\) | ||
0.999436 | − | 0.0335767i | \(-0.0106898\pi\) | |||||||
\(888\) | 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 | ||||||||
\(895\) | −34.0000 | −1.13649 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 20.0000i | 0.665558i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.0000i | − | 0.598340i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0000 | + | 27.0000i | −0.896520 | + | 0.896520i | −0.995127 | − | 0.0986062i | \(-0.968562\pi\) |
0.0986062 | + | 0.995127i | \(0.468562\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | −2.00000 | −0.0661903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.0000 | − | 18.0000i | −0.595062 | − | 0.595062i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 22.0000 | − | 22.0000i | 0.726504 | − | 0.726504i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 26.0000i | − | 0.857661i | −0.903385 | − | 0.428830i | \(-0.858926\pi\) | ||
0.903385 | − | 0.428830i | \(-0.141074\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0000i | 0.329511i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.0000 | − | 10.0000i | 0.329154 | − | 0.329154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.00000 | − | 9.00000i | −0.295918 | − | 0.295918i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.00000 | 0.197066 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0000 | 0.984268 | 0.492134 | − | 0.870519i | \(-0.336217\pi\) | ||||
0.492134 | + | 0.870519i | \(0.336217\pi\) | |||||||
\(930\) | 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 | ||||||||
\(935\) | 4.00000i | 0.130814i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 28.0000i | − | 0.914720i | −0.889282 | − | 0.457360i | \(-0.848795\pi\) | ||
0.889282 | − | 0.457360i | \(-0.151205\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.0000 | + | 16.0000i | −0.522140 | + | 0.522140i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 29.0000 | + | 29.0000i | 0.945373 | + | 0.945373i | 0.998583 | − | 0.0532103i | \(-0.0169454\pi\) |
−0.0532103 | + | 0.998583i | \(0.516945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.0000 | 0.520480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.00000 | − | 5.00000i | −0.162478 | − | 0.162478i | 0.621185 | − | 0.783664i | \(-0.286651\pi\) |
−0.783664 | + | 0.621185i | \(0.786651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | + | 4.00000i | −0.129845 | + | 0.129845i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.0000i | − | 0.324272i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.0000i | 0.777436i | 0.921357 | + | 0.388718i | \(0.127082\pi\) | ||||
−0.921357 | + | 0.388718i | \(0.872918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.00000 | − | 8.00000i | 0.258874 | − | 0.258874i | ||||
\(956\) | 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 | ||||||||
\(965\) | 14.0000 | − | 14.0000i | 0.450676 | − | 0.450676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.00000i | − | 0.0643157i | −0.999483 | − | 0.0321578i | \(-0.989762\pi\) | ||
0.999483 | − | 0.0321578i | \(-0.0102379\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.0000i | 0.385496i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.0000 | + | 19.0000i | −0.609739 | + | 0.609739i | −0.942878 | − | 0.333139i | \(-0.891892\pi\) |
0.333139 | + | 0.942878i | \(0.391892\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | + | 6.00000i | 0.192351 | + | 0.192351i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.00000 | 0.192154 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.00000 | −0.0639857 | −0.0319928 | − | 0.999488i | \(-0.510185\pi\) | ||||
−0.0319928 | + | 0.999488i | \(0.510185\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | − | 34.0000i | − | 1.08443i | −0.840239 | − | 0.542216i | \(-0.817586\pi\) | ||
0.840239 | − | 0.542216i | \(-0.182414\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 34.0000i | − | 1.08333i | ||||||
\(986\) | 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 | ||||||||
\(993\) | −2.00000 | −0.0634681 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.0000 | + | 14.0000i | 0.443830 | + | 0.443830i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.0000 | − | 37.0000i | 1.17180 | − | 1.17180i | 0.190022 | − | 0.981780i | \(-0.439144\pi\) |
0.981780 | − | 0.190022i | \(-0.0608559\pi\) | |||||||
\(998\) | 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 \(a_p\))