Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(37,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.k (of order \(4\), degree \(2\), 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: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.37 |
Dual form | 144.2.k.a.109.1 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.707107 | + | 0.707107i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000i | 1.00000i | ||||||||
\(5\) | 1.00000 | + | 1.00000i | 0.447214 | + | 0.447214i | 0.894427 | − | 0.447214i | \(-0.147584\pi\) |
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.00000i | − | 0.755929i | −0.925820 | − | 0.377964i | \(-0.876624\pi\) | ||
0.925820 | − | 0.377964i | \(-0.123376\pi\) | |||||||
\(8\) | −2.00000 | + | 2.00000i | −0.707107 | + | 0.707107i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.00000i | 0.632456i | ||||||||
\(11\) | −1.00000 | − | 1.00000i | −0.301511 | − | 0.301511i | 0.540094 | − | 0.841605i | \(-0.318389\pi\) |
−0.841605 | + | 0.540094i | \(0.818389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 1.00000i | −0.277350 | + | 0.277350i | −0.832050 | − | 0.554700i | \(-0.812833\pi\) |
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 2.00000 | − | 2.00000i | 0.534522 | − | 0.534522i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.00000 | − | 3.00000i | 0.688247 | − | 0.688247i | −0.273597 | − | 0.961844i | \(-0.588214\pi\) |
0.961844 | + | 0.273597i | \(0.0882135\pi\) | |||||||
\(20\) | −2.00000 | + | 2.00000i | −0.447214 | + | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 2.00000i | − | 0.426401i | ||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.00000i | − | 0.600000i | ||||||
\(26\) | −2.00000 | −0.392232 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.00000 | 0.755929 | ||||||||
\(29\) | −3.00000 | + | 3.00000i | −0.557086 | + | 0.557086i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) |
0.371391 | + | 0.928477i | \(0.378881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.00000 | −1.43684 | −0.718421 | − | 0.695608i | \(-0.755135\pi\) | ||||
−0.718421 | + | 0.695608i | \(0.755135\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.707107 | − | 0.707107i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 2.00000i | 0.342997 | + | 0.342997i | ||||
\(35\) | 2.00000 | − | 2.00000i | 0.338062 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | 6.00000 | 0.973329 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.00000 | −0.632456 | ||||||||
\(41\) | 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 | \(0.568740\pi\) | |||||||
\(44\) | 2.00000 | − | 2.00000i | 0.301511 | − | 0.301511i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | − | 6.00000i | 0.884652 | − | 0.884652i | ||||
\(47\) | −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 | ||||||||
\(50\) | 3.00000 | − | 3.00000i | 0.424264 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.00000 | − | 2.00000i | −0.277350 | − | 0.277350i | ||||
\(53\) | 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 | ||||||||
\(55\) | − | 2.00000i | − | 0.269680i | ||||||
\(56\) | 4.00000 | + | 4.00000i | 0.534522 | + | 0.534522i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.00000 | −0.787839 | ||||||||
\(59\) | 3.00000 | + | 3.00000i | 0.390567 | + | 0.390567i | 0.874889 | − | 0.484323i | \(-0.160934\pi\) |
−0.484323 | + | 0.874889i | \(0.660934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.00000 | + | 9.00000i | −1.15233 | + | 1.15233i | −0.166248 | + | 0.986084i | \(0.553165\pi\) |
−0.986084 | + | 0.166248i | \(0.946835\pi\) | |||||||
\(62\) | −8.00000 | − | 8.00000i | −1.01600 | − | 1.01600i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −2.00000 | −0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 5.00000i | −0.610847 | + | 0.610847i | −0.943167 | − | 0.332320i | \(-0.892169\pi\) |
0.332320 | + | 0.943167i | \(0.392169\pi\) | |||||||
\(68\) | 4.00000i | 0.485071i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.00000 | 0.478091 | ||||||||
\(71\) | 10.0000i | 1.18678i | 0.804914 | + | 0.593391i | \(0.202211\pi\) | ||||
−0.804914 | + | 0.593391i | \(0.797789\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | 6.00000i | 0.697486i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | + | 6.00000i | 0.688247 | + | 0.688247i | ||||
\(77\) | −2.00000 | + | 2.00000i | −0.227921 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −4.00000 | − | 4.00000i | −0.447214 | − | 0.447214i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 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 | ||||||||
\(85\) | 2.00000 | + | 2.00000i | 0.216930 | + | 0.216930i | ||||
\(86\) | 10.0000i | 1.07833i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | 0.426401 | ||||||||
\(89\) | − | 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 | ||||
\(92\) | 12.0000 | 1.25109 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | − | 8.00000i | −0.825137 | − | 0.825137i | ||||
\(95\) | 6.00000 | 0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.00000 | −0.203069 | −0.101535 | − | 0.994832i | \(-0.532375\pi\) | ||||
−0.101535 | + | 0.994832i | \(0.532375\pi\) | |||||||
\(98\) | 3.00000 | + | 3.00000i | 0.303046 | + | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.00000 | 0.600000 | ||||||||
\(101\) | −11.0000 | − | 11.0000i | −1.09454 | − | 1.09454i | −0.995037 | − | 0.0995037i | \(-0.968274\pi\) |
−0.0995037 | − | 0.995037i | \(-0.531726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.00000i | 0.591198i | 0.955312 | + | 0.295599i | \(0.0955191\pi\) | ||||
−0.955312 | + | 0.295599i | \(0.904481\pi\) | |||||||
\(104\) | − | 4.00000i | − | 0.392232i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000i | 0.971286i | ||||||||
\(107\) | 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 | \(-0.684871\pi\) |
0.836031 | + | 0.548683i | \(0.184871\pi\) | |||||||
\(110\) | 2.00000 | − | 2.00000i | 0.190693 | − | 0.190693i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.00000i | 0.755929i | ||||||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | − | 6.00000i | 0.559503 | − | 0.559503i | ||||
\(116\) | −6.00000 | − | 6.00000i | −0.557086 | − | 0.557086i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | − | 4.00000i | − | 0.366679i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 9.00000i | − | 0.818182i | ||||||
\(122\) | −18.0000 | −1.62964 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 16.0000i | − | 1.43684i | ||||||
\(125\) | 8.00000 | − | 8.00000i | 0.715542 | − | 0.715542i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.707107 | − | 0.707107i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.00000 | − | 2.00000i | −0.175412 | − | 0.175412i | ||||
\(131\) | −11.0000 | + | 11.0000i | −0.961074 | + | 0.961074i | −0.999270 | − | 0.0381958i | \(-0.987839\pi\) |
0.0381958 | + | 0.999270i | \(0.487839\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 6.00000i | −0.520266 | − | 0.520266i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.00000 | + | 4.00000i | −0.342997 | + | 0.342997i | ||||
\(137\) | − | 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 | 0.568338 | − | 0.822795i | \(-0.307586\pi\) |
−0.822795 | + | 0.568338i | \(0.807586\pi\) | |||||||
\(140\) | 4.00000 | + | 4.00000i | 0.338062 | + | 0.338062i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.0000 | + | 10.0000i | −0.839181 | + | 0.839181i | ||||
\(143\) | 2.00000 | 0.167248 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 4.00000 | − | 4.00000i | 0.331042 | − | 0.331042i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.00000 | + | 6.00000i | −0.493197 | + | 0.493197i | ||||
\(149\) | −7.00000 | − | 7.00000i | −0.573462 | − | 0.573462i | 0.359632 | − | 0.933094i | \(-0.382902\pi\) |
−0.933094 | + | 0.359632i | \(0.882902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 12.0000i | 0.973329i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.00000 | −0.322329 | ||||||||
\(155\) | −8.00000 | − | 8.00000i | −0.642575 | − | 0.642575i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.0000 | − | 15.0000i | 1.19713 | − | 1.19713i | 0.222108 | − | 0.975022i | \(-0.428706\pi\) |
0.975022 | − | 0.222108i | \(-0.0712939\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 8.00000i | − | 0.632456i | ||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | + | 1.00000i | −0.0783260 | + | 0.0783260i | −0.745184 | − | 0.666858i | \(-0.767639\pi\) |
0.666858 | + | 0.745184i | \(0.267639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | 0.155230 | ||||||||
\(167\) | 2.00000i | 0.154765i | 0.997001 | + | 0.0773823i | \(0.0246562\pi\) | ||||
−0.997001 | + | 0.0773823i | \(0.975344\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000i | 0.846154i | ||||||||
\(170\) | 4.00000i | 0.306786i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.0000 | + | 10.0000i | −0.762493 | + | 0.762493i | ||||
\(173\) | 1.00000 | − | 1.00000i | 0.0760286 | − | 0.0760286i | −0.668070 | − | 0.744099i | \(-0.732879\pi\) |
0.744099 | + | 0.668070i | \(0.232879\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.00000 | −0.453557 | ||||||||
\(176\) | 4.00000 | + | 4.00000i | 0.301511 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.00000 | − | 4.00000i | 0.299813 | − | 0.299813i | ||||
\(179\) | 17.0000 | − | 17.0000i | 1.27064 | − | 1.27064i | 0.324887 | − | 0.945753i | \(-0.394674\pi\) |
0.945753 | − | 0.324887i | \(-0.105326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.00000 | − | 9.00000i | −0.668965 | − | 0.668965i | 0.288512 | − | 0.957476i | \(-0.406840\pi\) |
−0.957476 | + | 0.288512i | \(0.906840\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.0000 | + | 12.0000i | 0.884652 | + | 0.884652i | ||||
\(185\) | 6.00000i | 0.441129i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00000 | − | 2.00000i | −0.146254 | − | 0.146254i | ||||
\(188\) | − | 16.0000i | − | 1.16692i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.00000 | + | 6.00000i | 0.435286 | + | 0.435286i | ||||
\(191\) | 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 | \(0.331909\pi\) | |||||||
\(194\) | −2.00000 | − | 2.00000i | −0.143592 | − | 0.143592i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.00000i | 0.428571i | ||||||||
\(197\) | 17.0000 | + | 17.0000i | 1.21120 | + | 1.21120i | 0.970632 | + | 0.240567i | \(0.0773335\pi\) |
0.240567 | + | 0.970632i | \(0.422666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.0000i | 0.992434i | 0.868199 | + | 0.496217i | \(0.165278\pi\) | ||||
−0.868199 | + | 0.496217i | \(0.834722\pi\) | |||||||
\(200\) | 6.00000 | + | 6.00000i | 0.424264 | + | 0.424264i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 22.0000i | − | 1.54791i | ||||||
\(203\) | 6.00000 | + | 6.00000i | 0.421117 | + | 0.421117i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.00000 | + | 6.00000i | −0.418040 | + | 0.418040i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.00000 | − | 4.00000i | 0.277350 | − | 0.277350i | ||||
\(209\) | −6.00000 | −0.415029 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | + | 9.00000i | −0.619586 | + | 0.619586i | −0.945425 | − | 0.325840i | \(-0.894353\pi\) |
0.325840 | + | 0.945425i | \(0.394353\pi\) | |||||||
\(212\) | −10.0000 | + | 10.0000i | −0.686803 | + | 0.686803i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 14.0000i | 0.957020i | ||||||||
\(215\) | 10.0000i | 0.681994i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0000i | 1.08615i | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.00000 | 0.269680 | ||||||||
\(221\) | −2.00000 | + | 2.00000i | −0.134535 | + | 0.134535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 24.0000 | 1.60716 | 0.803579 | − | 0.595198i | \(-0.202926\pi\) | ||||
0.803579 | + | 0.595198i | \(0.202926\pi\) | |||||||
\(224\) | −8.00000 | + | 8.00000i | −0.534522 | + | 0.534522i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.00000 | + | 6.00000i | 0.399114 | + | 0.399114i | ||||
\(227\) | −15.0000 | + | 15.0000i | −0.995585 | + | 0.995585i | −0.999990 | − | 0.00440533i | \(-0.998598\pi\) |
0.00440533 | + | 0.999990i | \(0.498598\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.00000 | + | 7.00000i | 0.462573 | + | 0.462573i | 0.899498 | − | 0.436925i | \(-0.143932\pi\) |
−0.436925 | + | 0.899498i | \(0.643932\pi\) | |||||||
\(230\) | 12.0000 | 0.791257 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 12.0000i | − | 0.787839i | ||||||
\(233\) | 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 | ||||
\(236\) | −6.00000 | + | 6.00000i | −0.390567 | + | 0.390567i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000 | − | 4.00000i | 0.259281 | − | 0.259281i | ||||
\(239\) | 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 | \(0.696846\pi\) | |||||||
\(242\) | 9.00000 | − | 9.00000i | 0.578542 | − | 0.578542i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −18.0000 | − | 18.0000i | −1.15233 | − | 1.15233i | ||||
\(245\) | 3.00000 | + | 3.00000i | 0.191663 | + | 0.191663i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | 16.0000 | − | 16.0000i | 1.01600 | − | 1.01600i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 16.0000 | 1.01193 | ||||||||
\(251\) | −21.0000 | − | 21.0000i | −1.32551 | − | 1.32551i | −0.909243 | − | 0.416265i | \(-0.863339\pi\) |
−0.416265 | − | 0.909243i | \(-0.636661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.00000 | + | 6.00000i | −0.377217 | + | 0.377217i | ||||
\(254\) | 8.00000 | + | 8.00000i | 0.501965 | + | 0.501965i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 1.00000 | ||||||||
\(257\) | 22.0000 | 1.37232 | 0.686161 | − | 0.727450i | \(-0.259294\pi\) | ||||
0.686161 | + | 0.727450i | \(0.259294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | − | 6.00000i | 0.372822 | − | 0.372822i | ||||
\(260\) | − | 4.00000i | − | 0.248069i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −22.0000 | −1.35916 | ||||||||
\(263\) | − | 6.00000i | − | 0.369976i | −0.982741 | − | 0.184988i | \(-0.940775\pi\) | ||
0.982741 | − | 0.184988i | \(-0.0592246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000i | 0.614295i | ||||||||
\(266\) | − | 12.0000i | − | 0.735767i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0000 | − | 10.0000i | −0.610847 | − | 0.610847i | ||||
\(269\) | −3.00000 | + | 3.00000i | −0.182913 | + | 0.182913i | −0.792624 | − | 0.609711i | \(-0.791286\pi\) |
0.609711 | + | 0.792624i | \(0.291286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | −0.485965 | −0.242983 | − | 0.970031i | \(-0.578126\pi\) | ||||
−0.242983 | + | 0.970031i | \(0.578126\pi\) | |||||||
\(272\) | −8.00000 | −0.485071 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.00000 | − | 8.00000i | 0.483298 | − | 0.483298i | ||||
\(275\) | −3.00000 | + | 3.00000i | −0.180907 | + | 0.180907i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00000 | + | 3.00000i | 0.180253 | + | 0.180253i | 0.791466 | − | 0.611213i | \(-0.209318\pi\) |
−0.611213 | + | 0.791466i | \(0.709318\pi\) | |||||||
\(278\) | − | 6.00000i | − | 0.359856i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.00000i | 0.478091i | ||||||||
\(281\) | 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 | \(0.967149\pi\) | |||||||
\(284\) | −20.0000 | −1.18678 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.00000 | + | 2.00000i | 0.118262 | + | 0.118262i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −6.00000 | − | 6.00000i | −0.352332 | − | 0.352332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8.00000 | 0.468165 | ||||||||
\(293\) | −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 | ||||||||
\(295\) | 6.00000i | 0.349334i | ||||||||
\(296\) | −12.0000 | −0.697486 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 14.0000i | − | 0.810998i | ||||||
\(299\) | 6.00000 | + | 6.00000i | 0.346989 | + | 0.346989i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | − | 10.0000i | 0.576390 | − | 0.576390i | ||||
\(302\) | 10.0000 | − | 10.0000i | 0.575435 | − | 0.575435i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.0000 | + | 12.0000i | −0.688247 | + | 0.688247i | ||||
\(305\) | −18.0000 | −1.03068 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.00000 | + | 5.00000i | −0.285365 | + | 0.285365i | −0.835244 | − | 0.549879i | \(-0.814674\pi\) |
0.549879 | + | 0.835244i | \(0.314674\pi\) | |||||||
\(308\) | −4.00000 | − | 4.00000i | −0.227921 | − | 0.227921i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 16.0000i | − | 0.908739i | ||||||
\(311\) | − | 30.0000i | − | 1.70114i | −0.525859 | − | 0.850572i | \(-0.676256\pi\) | ||
0.525859 | − | 0.850572i | \(-0.323744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.0000i | 0.904373i | 0.891923 | + | 0.452187i | \(0.149356\pi\) | ||||
−0.891923 | + | 0.452187i | \(0.850644\pi\) | |||||||
\(314\) | 30.0000 | 1.69300 | ||||||||
\(315\) | 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 | ||||||||
\(320\) | 8.00000 | − | 8.00000i | 0.447214 | − | 0.447214i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.0000 | − | 12.0000i | −0.668734 | − | 0.668734i | ||||
\(323\) | 6.00000 | − | 6.00000i | 0.333849 | − | 0.333849i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | + | 3.00000i | 0.166410 | + | 0.166410i | ||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.0000i | 0.882109i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.00000 | + | 1.00000i | 0.0549650 | + | 0.0549650i | 0.734055 | − | 0.679090i | \(-0.237625\pi\) |
−0.679090 | + | 0.734055i | \(0.737625\pi\) | |||||||
\(332\) | 2.00000 | + | 2.00000i | 0.109764 | + | 0.109764i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.00000 | + | 2.00000i | −0.109435 | + | 0.109435i | ||||
\(335\) | −10.0000 | −0.546358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.0000 | 0.980522 | 0.490261 | − | 0.871576i | \(-0.336901\pi\) | ||||
0.490261 | + | 0.871576i | \(0.336901\pi\) | |||||||
\(338\) | −11.0000 | + | 11.0000i | −0.598321 | + | 0.598321i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | + | 4.00000i | −0.216930 | + | 0.216930i | ||||
\(341\) | 8.00000 | + | 8.00000i | 0.433224 | + | 0.433224i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.0000i | − | 1.07990i | ||||||
\(344\) | −20.0000 | −1.07833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | 0.107521 | ||||||||
\(347\) | −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 | \(-0.713777\pi\) |
0.782826 | + | 0.622240i | \(0.213777\pi\) | |||||||
\(350\) | −6.00000 | − | 6.00000i | −0.320713 | − | 0.320713i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.00000i | 0.426401i | ||||||||
\(353\) | 6.00000 | 0.319348 | 0.159674 | − | 0.987170i | \(-0.448956\pi\) | ||||
0.159674 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.0000 | + | 10.0000i | −0.530745 | + | 0.530745i | ||||
\(356\) | 8.00000 | 0.423999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 34.0000 | 1.79696 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | − | 18.0000i | − | 0.946059i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.00000 | + | 4.00000i | −0.209657 | + | 0.209657i | ||||
\(365\) | 4.00000 | − | 4.00000i | 0.209370 | − | 0.209370i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | 0.417597 | 0.208798 | − | 0.977959i | \(-0.433045\pi\) | ||||
0.208798 | + | 0.977959i | \(0.433045\pi\) | |||||||
\(368\) | 24.0000i | 1.25109i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.00000 | + | 6.00000i | −0.311925 | + | 0.311925i | ||||
\(371\) | 10.0000 | − | 10.0000i | 0.519174 | − | 0.519174i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.00000 | − | 5.00000i | −0.258890 | − | 0.258890i | 0.565712 | − | 0.824603i | \(-0.308601\pi\) |
−0.824603 | + | 0.565712i | \(0.808601\pi\) | |||||||
\(374\) | − | 4.00000i | − | 0.206835i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.0000 | − | 16.0000i | 0.825137 | − | 0.825137i | ||||
\(377\) | − | 6.00000i | − | 0.309016i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00000 | − | 3.00000i | −0.154100 | − | 0.154100i | 0.625847 | − | 0.779946i | \(-0.284754\pi\) |
−0.779946 | + | 0.625847i | \(0.784754\pi\) | |||||||
\(380\) | 12.0000i | 0.615587i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.00000 | + | 8.00000i | 0.409316 | + | 0.409316i | ||||
\(383\) | 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 | ||||||||
\(386\) | 14.0000 | + | 14.0000i | 0.712581 | + | 0.712581i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 4.00000i | − | 0.203069i | ||||||
\(389\) | 13.0000 | + | 13.0000i | 0.659126 | + | 0.659126i | 0.955173 | − | 0.296047i | \(-0.0956686\pi\) |
−0.296047 | + | 0.955173i | \(0.595669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | −6.00000 | + | 6.00000i | −0.303046 | + | 0.303046i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 34.0000i | 1.71290i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.00000 | + | 5.00000i | −0.250943 | + | 0.250943i | −0.821357 | − | 0.570414i | \(-0.806783\pi\) |
0.570414 | + | 0.821357i | \(0.306783\pi\) | |||||||
\(398\) | −14.0000 | + | 14.0000i | −0.701757 | + | 0.701757i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0000i | 0.600000i | ||||||||
\(401\) | 18.0000 | 0.898877 | 0.449439 | − | 0.893311i | \(-0.351624\pi\) | ||||
0.449439 | + | 0.893311i | \(0.351624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.00000 | − | 8.00000i | 0.398508 | − | 0.398508i | ||||
\(404\) | 22.0000 | − | 22.0000i | 1.09454 | − | 1.09454i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12.0000i | 0.595550i | ||||||||
\(407\) | − | 6.00000i | − | 0.297409i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.0000i | − | 0.791149i | −0.918434 | − | 0.395575i | \(-0.870545\pi\) | ||
0.918434 | − | 0.395575i | \(-0.129455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.0000 | −0.591198 | ||||||||
\(413\) | 6.00000 | − | 6.00000i | 0.295241 | − | 0.295241i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.00000 | 0.0981761 | ||||||||
\(416\) | 8.00000 | 0.392232 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −6.00000 | − | 6.00000i | −0.293470 | − | 0.293470i | ||||
\(419\) | −3.00000 | + | 3.00000i | −0.146560 | + | 0.146560i | −0.776579 | − | 0.630020i | \(-0.783047\pi\) |
0.630020 | + | 0.776579i | \(0.283047\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.00000 | − | 9.00000i | −0.438633 | − | 0.438633i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.891552 | + | 0.452919i | \(0.850383\pi\) | |||||||
\(422\) | −18.0000 | −0.876226 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.0000 | −0.971286 | ||||||||
\(425\) | − | 6.00000i | − | 0.291043i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | + | 18.0000i | 0.871081 | + | 0.871081i | ||||
\(428\) | −14.0000 | + | 14.0000i | −0.676716 | + | 0.676716i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.0000 | + | 10.0000i | −0.482243 | + | 0.482243i | ||||
\(431\) | −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 | \(0.390791\pi\) | |||||||
\(434\) | −16.0000 | + | 16.0000i | −0.768025 | + | 0.768025i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.00000 | + | 6.00000i | 0.287348 | + | 0.287348i | ||||
\(437\) | −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 | \(0.891570\pi\) | |||||||
\(440\) | 4.00000 | + | 4.00000i | 0.190693 | + | 0.190693i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.00000 | −0.190261 | ||||||||
\(443\) | 15.0000 | + | 15.0000i | 0.712672 | + | 0.712672i | 0.967093 | − | 0.254422i | \(-0.0818852\pi\) |
−0.254422 | + | 0.967093i | \(0.581885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.00000 | − | 4.00000i | 0.189618 | − | 0.189618i | ||||
\(446\) | 24.0000 | + | 24.0000i | 1.13643 | + | 1.13643i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.0000 | −0.755929 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 12.0000i | 0.564433i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −30.0000 | −1.40797 | ||||||||
\(455\) | 4.00000i | 0.187523i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 32.0000i | − | 1.49690i | −0.663193 | − | 0.748448i | \(-0.730799\pi\) | ||
0.663193 | − | 0.748448i | \(-0.269201\pi\) | |||||||
\(458\) | 14.0000i | 0.654177i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.0000 | + | 12.0000i | 0.559503 | + | 0.559503i | ||||
\(461\) | −11.0000 | + | 11.0000i | −0.512321 | + | 0.512321i | −0.915237 | − | 0.402916i | \(-0.867997\pi\) |
0.402916 | + | 0.915237i | \(0.367997\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 12.0000 | − | 12.0000i | 0.557086 | − | 0.557086i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00000 | + | 4.00000i | −0.185296 | + | 0.185296i | ||||
\(467\) | 5.00000 | − | 5.00000i | 0.231372 | − | 0.231372i | −0.581893 | − | 0.813265i | \(-0.697688\pi\) |
0.813265 | + | 0.581893i | \(0.197688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | + | 10.0000i | 0.461757 | + | 0.461757i | ||||
\(470\) | − | 16.0000i | − | 0.738025i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.0000 | −0.552345 | ||||||||
\(473\) | − | 10.0000i | − | 0.459800i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.00000 | − | 9.00000i | −0.412948 | − | 0.412948i | ||||
\(476\) | 8.00000 | 0.366679 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 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 | ||||||||
\(482\) | −18.0000 | − | 18.0000i | −0.819878 | − | 0.819878i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.0000 | 0.818182 | ||||||||
\(485\) | −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 | \(-0.0144289\pi\) | |||||||
\(488\) | − | 36.0000i | − | 1.62964i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.00000i | 0.271052i | ||||||||
\(491\) | 19.0000 | + | 19.0000i | 0.857458 | + | 0.857458i | 0.991038 | − | 0.133580i | \(-0.0426473\pi\) |
−0.133580 | + | 0.991038i | \(0.542647\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.00000 | + | 6.00000i | −0.270226 | + | 0.270226i | ||||
\(494\) | −6.00000 | + | 6.00000i | −0.269953 | + | 0.269953i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.0000 | 1.43684 | ||||||||
\(497\) | 20.0000 | 0.897123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.0000 | − | 23.0000i | 1.02962 | − | 1.02962i | 0.0300737 | − | 0.999548i | \(-0.490426\pi\) |
0.999548 | − | 0.0300737i | \(-0.00957421\pi\) | |||||||
\(500\) | 16.0000 | + | 16.0000i | 0.715542 | + | 0.715542i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 42.0000i | − | 1.87455i | ||||||
\(503\) | − | 6.00000i | − | 0.267527i | −0.991013 | − | 0.133763i | \(-0.957294\pi\) | ||
0.991013 | − | 0.133763i | \(-0.0427062\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 22.0000i | − | 0.978987i | ||||||
\(506\) | −12.0000 | −0.533465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.0000i | 0.709885i | ||||||||
\(509\) | −23.0000 | + | 23.0000i | −1.01946 | + | 1.01946i | −0.0196502 | + | 0.999807i | \(0.506255\pi\) |
−0.999807 | + | 0.0196502i | \(0.993745\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.00000 | −0.353899 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.707107 | + | 0.707107i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 22.0000 | + | 22.0000i | 0.970378 | + | 0.970378i | ||||
\(515\) | −6.00000 | + | 6.00000i | −0.264392 | + | 0.264392i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.00000 | + | 8.00000i | 0.351840 | + | 0.351840i | ||||
\(518\) | 12.0000 | 0.527250 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.00000 | − | 4.00000i | 0.175412 | − | 0.175412i | ||||
\(521\) | − | 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 | \(0.468760\pi\) | |||||||
\(524\) | −22.0000 | − | 22.0000i | −0.961074 | − | 0.961074i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.00000 | − | 6.00000i | 0.261612 | − | 0.261612i | ||||
\(527\) | −16.0000 | −0.696971 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −10.0000 | + | 10.0000i | −0.434372 | + | 0.434372i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | − | 12.0000i | 0.520266 | − | 0.520266i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.0000i | 0.605273i | ||||||||
\(536\) | − | 20.0000i | − | 0.863868i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.00000 | −0.258678 | ||||||||
\(539\) | −3.00000 | − | 3.00000i | −0.129219 | − | 0.129219i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.00000 | + | 9.00000i | −0.386940 | + | 0.386940i | −0.873595 | − | 0.486654i | \(-0.838217\pi\) |
0.486654 | + | 0.873595i | \(0.338217\pi\) | |||||||
\(542\) | −8.00000 | − | 8.00000i | −0.343629 | − | 0.343629i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −8.00000 | − | 8.00000i | −0.342997 | − | 0.342997i | ||||
\(545\) | 6.00000 | 0.257012 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00000 | + | 5.00000i | −0.213785 | + | 0.213785i | −0.805873 | − | 0.592088i | \(-0.798304\pi\) |
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(548\) | 16.0000 | 0.683486 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.00000 | −0.255841 | ||||||||
\(551\) | 18.0000i | 0.766826i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.00000i | 0.254916i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.00000 | − | 6.00000i | 0.254457 | − | 0.254457i | ||||
\(557\) | 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 | ||||||||
\(560\) | −8.00000 | + | 8.00000i | −0.338062 | + | 0.338062i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.0000 | + | 20.0000i | −0.843649 | + | 0.843649i | ||||
\(563\) | −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 | ||||||||
\(565\) | 6.00000 | + | 6.00000i | 0.252422 | + | 0.252422i | ||||
\(566\) | − | 30.0000i | − | 1.26099i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.0000 | − | 20.0000i | −0.839181 | − | 0.839181i | ||||
\(569\) | − | 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 | 0.727721 | − | 0.685873i | \(-0.240579\pi\) |
−0.685873 | + | 0.727721i | \(0.740579\pi\) | |||||||
\(572\) | 4.00000i | 0.167248i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 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 | \(0.377754\pi\) | |||||||
\(578\) | −13.0000 | − | 13.0000i | −0.540729 | − | 0.540729i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 12.0000i | − | 0.498273i | ||||||
\(581\) | −2.00000 | − | 2.00000i | −0.0829740 | − | 0.0829740i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.0000i | − | 0.414158i | ||||||
\(584\) | 8.00000 | + | 8.00000i | 0.331042 | + | 0.331042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 30.0000i | − | 1.23929i | ||||||
\(587\) | 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 | ||||
\(590\) | −6.00000 | + | 6.00000i | −0.247016 | + | 0.247016i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0000 | − | 12.0000i | −0.493197 | − | 0.493197i | ||||
\(593\) | −34.0000 | −1.39621 | −0.698106 | − | 0.715994i | \(-0.745974\pi\) | ||||
−0.698106 | + | 0.715994i | \(0.745974\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 4.00000i | 0.163984 | − | 0.163984i | ||||
\(596\) | 14.0000 | − | 14.0000i | 0.573462 | − | 0.573462i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000i | 0.490716i | ||||||||
\(599\) | − | 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 | \(0.133742\pi\) | ||||
−0.913023 | + | 0.407909i | \(0.866258\pi\) | |||||||
\(602\) | 20.0000 | 0.815139 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.0000 | 0.813788 | ||||||||
\(605\) | 9.00000 | − | 9.00000i | 0.365902 | − | 0.365902i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −32.0000 | −1.29884 | −0.649420 | − | 0.760430i | \(-0.724988\pi\) | ||||
−0.649420 | + | 0.760430i | \(0.724988\pi\) | |||||||
\(608\) | −24.0000 | −0.973329 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18.0000 | − | 18.0000i | −0.728799 | − | 0.728799i | ||||
\(611\) | 8.00000 | − | 8.00000i | 0.323645 | − | 0.323645i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25.0000 | − | 25.0000i | −1.00974 | − | 1.00974i | −0.999952 | − | 0.00978840i | \(-0.996884\pi\) |
−0.00978840 | − | 0.999952i | \(-0.503116\pi\) | |||||||
\(614\) | −10.0000 | −0.403567 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 8.00000i | − | 0.322329i | ||||||
\(617\) | 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 | 0.960740 | − | 0.277452i | \(-0.0894899\pi\) |
−0.277452 | + | 0.960740i | \(0.589490\pi\) | |||||||
\(620\) | 16.0000 | − | 16.0000i | 0.642575 | − | 0.642575i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.0000 | − | 30.0000i | 1.20289 | − | 1.20289i | ||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −16.0000 | + | 16.0000i | −0.639489 | + | 0.639489i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.0000 | + | 30.0000i | 1.19713 | + | 1.19713i | ||||
\(629\) | 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 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.0000 | 0.397151 | ||||||||
\(635\) | 8.00000 | + | 8.00000i | 0.317470 | + | 0.317470i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | + | 3.00000i | −0.118864 | + | 0.118864i | ||||
\(638\) | 6.00000 | + | 6.00000i | 0.237542 | + | 0.237542i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 16.0000 | 0.632456 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.0000 | + | 21.0000i | −0.828159 | + | 0.828159i | −0.987262 | − | 0.159103i | \(-0.949140\pi\) |
0.159103 | + | 0.987262i | \(0.449140\pi\) | |||||||
\(644\) | − | 24.0000i | − | 0.945732i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 42.0000i | 1.65119i | 0.564263 | + | 0.825595i | \(0.309160\pi\) | ||||
−0.564263 | + | 0.825595i | \(0.690840\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.00000i | − | 0.235521i | ||||||
\(650\) | 6.00000i | 0.235339i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.00000 | − | 2.00000i | −0.0783260 | − | 0.0783260i | ||||
\(653\) | −19.0000 | + | 19.0000i | −0.743527 | + | 0.743527i | −0.973255 | − | 0.229728i | \(-0.926216\pi\) |
0.229728 | + | 0.973255i | \(0.426216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.0000 | −0.859611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.0000 | + | 16.0000i | −0.623745 | + | 0.623745i | ||||
\(659\) | 17.0000 | − | 17.0000i | 0.662226 | − | 0.662226i | −0.293678 | − | 0.955904i | \(-0.594879\pi\) |
0.955904 | + | 0.293678i | \(0.0948794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.00000 | − | 9.00000i | −0.350059 | − | 0.350059i | 0.510072 | − | 0.860132i | \(-0.329619\pi\) |
−0.860132 | + | 0.510072i | \(0.829619\pi\) | |||||||
\(662\) | 2.00000i | 0.0777322i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.00000i | 0.155230i | ||||||||
\(665\) | − | 12.0000i | − | 0.465340i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.0000 | + | 18.0000i | 0.696963 | + | 0.696963i | ||||
\(668\) | −4.00000 | −0.154765 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.0000 | − | 10.0000i | −0.386334 | − | 0.386334i | ||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.0000 | 0.539660 | 0.269830 | − | 0.962908i | \(-0.413032\pi\) | ||||
0.269830 | + | 0.962908i | \(0.413032\pi\) | |||||||
\(674\) | 18.0000 | + | 18.0000i | 0.693334 | + | 0.693334i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.0000 | −0.846154 | ||||||||
\(677\) | −3.00000 | − | 3.00000i | −0.115299 | − | 0.115299i | 0.647103 | − | 0.762402i | \(-0.275980\pi\) |
−0.762402 | + | 0.647103i | \(0.775980\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00000i | 0.153506i | ||||||||
\(680\) | −8.00000 | −0.306786 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.0000i | 0.612672i | ||||||||
\(683\) | −5.00000 | − | 5.00000i | −0.191320 | − | 0.191320i | 0.604946 | − | 0.796266i | \(-0.293195\pi\) |
−0.796266 | + | 0.604946i | \(0.793195\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.00000 | − | 8.00000i | 0.305664 | − | 0.305664i | ||||
\(686\) | 20.0000 | − | 20.0000i | 0.763604 | − | 0.763604i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0000 | − | 20.0000i | −0.762493 | − | 0.762493i | ||||
\(689\) | −10.0000 | −0.380970 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.00000 | + | 9.00000i | −0.342376 | + | 0.342376i | −0.857260 | − | 0.514884i | \(-0.827835\pi\) |
0.514884 | + | 0.857260i | \(0.327835\pi\) | |||||||
\(692\) | 2.00000 | + | 2.00000i | 0.0760286 | + | 0.0760286i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 26.0000i | − | 0.986947i | ||||||
\(695\) | − | 6.00000i | − | 0.227593i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.00000 | 0.227103 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 12.0000i | − | 0.453557i | ||||||
\(701\) | −31.0000 | + | 31.0000i | −1.17085 | + | 1.17085i | −0.188847 | + | 0.982006i | \(0.560475\pi\) |
−0.982006 | + | 0.188847i | \(0.939525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.0000 | 0.678883 | ||||||||
\(704\) | −8.00000 | + | 8.00000i | −0.301511 | + | 0.301511i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00000 | + | 6.00000i | 0.225813 | + | 0.225813i | ||||
\(707\) | −22.0000 | + | 22.0000i | −0.827395 | + | 0.827395i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27.0000 | + | 27.0000i | 1.01401 | + | 1.01401i | 0.999901 | + | 0.0141058i | \(0.00449016\pi\) |
0.0141058 | + | 0.999901i | \(0.495510\pi\) | |||||||
\(710\) | −20.0000 | −0.750587 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 8.00000 | + | 8.00000i | 0.299813 | + | 0.299813i | ||||
\(713\) | 48.0000i | 1.79761i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.00000 | + | 2.00000i | 0.0747958 | + | 0.0747958i | ||||
\(716\) | 34.0000 | + | 34.0000i | 1.27064 | + | 1.27064i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −26.0000 | + | 26.0000i | −0.970311 | + | 0.970311i | ||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | −1.00000 | + | 1.00000i | −0.0372161 | + | 0.0372161i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 18.0000 | − | 18.0000i | 0.668965 | − | 0.668965i | ||||
\(725\) | 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 | \(-0.0118082\pi\) | |||||||
\(728\) | −8.00000 | −0.296500 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.00000 | 0.296093 | ||||||||
\(731\) | 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 | \(0.434789\pi\) | |||||||
\(734\) | 8.00000 | + | 8.00000i | 0.295285 | + | 0.295285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −24.0000 | + | 24.0000i | −0.884652 | + | 0.884652i | ||||
\(737\) | 10.0000 | 0.368355 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.0000 | − | 23.0000i | 0.846069 | − | 0.846069i | −0.143571 | − | 0.989640i | \(-0.545859\pi\) |
0.989640 | + | 0.143571i | \(0.0458586\pi\) | |||||||
\(740\) | −12.0000 | −0.441129 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.0000 | 0.734223 | ||||||||
\(743\) | − | 46.0000i | − | 1.68758i | −0.536676 | − | 0.843788i | \(-0.680320\pi\) | ||
0.536676 | − | 0.843788i | \(-0.319680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 14.0000i | − | 0.512920i | ||||||
\(746\) | − | 10.0000i | − | 0.366126i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.00000 | − | 4.00000i | 0.146254 | − | 0.146254i | ||||
\(749\) | 14.0000 | − | 14.0000i | 0.511549 | − | 0.511549i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | 32.0000 | 1.16692 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.00000 | − | 6.00000i | 0.218507 | − | 0.218507i | ||||
\(755\) | 10.0000 | − | 10.0000i | 0.363937 | − | 0.363937i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.0000 | + | 23.0000i | 0.835949 | + | 0.835949i | 0.988323 | − | 0.152374i | \(-0.0486917\pi\) |
−0.152374 | + | 0.988323i | \(0.548692\pi\) | |||||||
\(758\) | − | 6.00000i | − | 0.217930i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0000 | + | 12.0000i | −0.435286 | + | 0.435286i | ||||
\(761\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.00000 | − | 6.00000i | −0.217215 | − | 0.217215i | ||||
\(764\) | 16.0000i | 0.578860i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.0000 | + | 16.0000i | 0.578103 | + | 0.578103i | ||||
\(767\) | −6.00000 | −0.216647 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −50.0000 | −1.80305 | −0.901523 | − | 0.432731i | \(-0.857550\pi\) | ||||
−0.901523 | + | 0.432731i | \(0.857550\pi\) | |||||||
\(770\) | −4.00000 | − | 4.00000i | −0.144150 | − | 0.144150i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.0000i | 1.00774i | ||||||||
\(773\) | 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 | ||||||||
\(775\) | 24.0000i | 0.862105i | ||||||||
\(776\) | 4.00000 | − | 4.00000i | 0.143592 | − | 0.143592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.0000i | 0.932145i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | − | 10.0000i | 0.357828 | − | 0.357828i | ||||
\(782\) | 12.0000 | − | 12.0000i | 0.429119 | − | 0.429119i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.0000 | −0.428571 | ||||||||
\(785\) | 30.0000 | 1.07075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.0000 | − | 15.0000i | 0.534692 | − | 0.534692i | −0.387273 | − | 0.921965i | \(-0.626583\pi\) |
0.921965 | + | 0.387273i | \(0.126583\pi\) | |||||||
\(788\) | −34.0000 | + | 34.0000i | −1.21120 | + | 1.21120i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 12.0000i | − | 0.426671i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 18.0000i | − | 0.639199i | ||||||
\(794\) | −10.0000 | −0.354887 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −28.0000 | −0.992434 | ||||||||
\(797\) | 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 | ||||||||
\(800\) | −12.0000 | + | 12.0000i | −0.424264 | + | 0.424264i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0000 | + | 18.0000i | 0.635602 | + | 0.635602i | ||||
\(803\) | −4.00000 | + | 4.00000i | −0.141157 | + | 0.141157i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.0000 | − | 12.0000i | −0.422944 | − | 0.422944i | ||||
\(806\) | 16.0000 | 0.563576 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 44.0000 | 1.54791 | ||||||||
\(809\) | 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 | −0.861187 | − | 0.508288i | \(-0.830278\pi\) |
−0.508288 | − | 0.861187i | \(-0.669722\pi\) | |||||||
\(812\) | −12.0000 | + | 12.0000i | −0.421117 | + | 0.421117i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | − | 6.00000i | 0.210300 | − | 0.210300i | ||||
\(815\) | −2.00000 | −0.0700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.0000 | 1.04957 | ||||||||
\(818\) | 16.0000 | − | 16.0000i | 0.559427 | − | 0.559427i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.0000 | − | 11.0000i | −0.383903 | − | 0.383903i | 0.488603 | − | 0.872506i | \(-0.337507\pi\) |
−0.872506 | + | 0.488603i | \(0.837507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 34.0000i | − | 1.18517i | −0.805510 | − | 0.592583i | \(-0.798108\pi\) | ||
0.805510 | − | 0.592583i | \(-0.201892\pi\) | |||||||
\(824\) | −12.0000 | − | 12.0000i | −0.418040 | − | 0.418040i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | −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 | \(-0.558933\pi\) |
0.982910 | + | 0.184087i | \(0.0589328\pi\) | |||||||
\(830\) | 2.00000 | + | 2.00000i | 0.0694210 | + | 0.0694210i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.00000 | + | 8.00000i | 0.277350 | + | 0.277350i | ||||
\(833\) | 6.00000 | 0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.00000 | + | 2.00000i | −0.0692129 | + | 0.0692129i | ||||
\(836\) | − | 12.0000i | − | 0.415029i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | −0.207267 | ||||||||
\(839\) | − | 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 | ||||||||
\(842\) | − | 18.0000i | − | 0.620321i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.0000 | − | 18.0000i | −0.619586 | − | 0.619586i | ||||
\(845\) | −11.0000 | + | 11.0000i | −0.378412 | + | 0.378412i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0000 | −0.618487 | ||||||||
\(848\) | −20.0000 | − | 20.0000i | −0.686803 | − | 0.686803i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.00000 | − | 6.00000i | 0.205798 | − | 0.205798i | ||||
\(851\) | 18.0000 | − | 18.0000i | 0.617032 | − | 0.617032i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.00000 | − | 5.00000i | −0.171197 | − | 0.171197i | 0.616308 | − | 0.787505i | \(-0.288628\pi\) |
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | 36.0000i | 1.23189i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.0000 | −0.957020 | ||||||||
\(857\) | − | 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 | 0.654073 | − | 0.756432i | \(-0.273059\pi\) |
−0.756432 | + | 0.654073i | \(0.773059\pi\) | |||||||
\(860\) | −20.0000 | −0.681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −32.0000 | − | 32.0000i | −1.08992 | − | 1.08992i | ||||
\(863\) | −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 | ||||||||
\(866\) | 14.0000 | + | 14.0000i | 0.475739 | + | 0.475739i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −32.0000 | −1.08615 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.0000i | − | 0.338837i | ||||||
\(872\) | 12.0000i | 0.406371i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 36.0000i | − | 1.21772i | ||||||
\(875\) | −16.0000 | − | 16.0000i | −0.540899 | − | 0.540899i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.00000 | + | 5.00000i | −0.168838 | + | 0.168838i | −0.786468 | − | 0.617630i | \(-0.788093\pi\) |
0.617630 | + | 0.786468i | \(0.288093\pi\) | |||||||
\(878\) | −14.0000 | + | 14.0000i | −0.472477 | + | 0.472477i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.00000i | 0.269680i | ||||||||
\(881\) | −2.00000 | −0.0673817 | −0.0336909 | − | 0.999432i | \(-0.510726\pi\) | ||||
−0.0336909 | + | 0.999432i | \(0.510726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.0000 | + | 21.0000i | −0.706706 | + | 0.706706i | −0.965841 | − | 0.259135i | \(-0.916563\pi\) |
0.259135 | + | 0.965841i | \(0.416563\pi\) | |||||||
\(884\) | −4.00000 | − | 4.00000i | −0.134535 | − | 0.134535i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 30.0000i | 1.00787i | ||||||||
\(887\) | 2.00000i | 0.0671534i | 0.999436 | + | 0.0335767i | \(0.0106898\pi\) | ||||
−0.999436 | + | 0.0335767i | \(0.989310\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 16.0000i | − | 0.536623i | ||||||
\(890\) | 8.00000 | 0.268161 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48.0000i | 1.60716i | ||||||||
\(893\) | −24.0000 | + | 24.0000i | −0.803129 | + | 0.803129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.0000 | 1.13649 | ||||||||
\(896\) | −16.0000 | − | 16.0000i | −0.534522 | − | 0.534522i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.0000 | − | 30.0000i | −1.00111 | − | 1.00111i | ||||
\(899\) | 24.0000 | − | 24.0000i | 0.800445 | − | 0.800445i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0000 | + | 10.0000i | 0.333148 | + | 0.333148i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −12.0000 | + | 12.0000i | −0.399114 | + | 0.399114i | ||||
\(905\) | − | 18.0000i | − | 0.598340i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.0000 | − | 27.0000i | −0.896520 | − | 0.896520i | 0.0986062 | − | 0.995127i | \(-0.468562\pi\) |
−0.995127 | + | 0.0986062i | \(0.968562\pi\) | |||||||
\(908\) | −30.0000 | − | 30.0000i | −0.995585 | − | 0.995585i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | + | 4.00000i | −0.132599 | + | 0.132599i | ||||
\(911\) | 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 | ||||||||
\(914\) | 32.0000 | − | 32.0000i | 1.05847 | − | 1.05847i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.0000 | + | 14.0000i | −0.462573 | + | 0.462573i | ||||
\(917\) | 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 | \(-0.141074\pi\) | |||||||
\(920\) | 24.0000i | 0.791257i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.0000 | −0.724531 | ||||||||
\(923\) | −10.0000 | − | 10.0000i | −0.329154 | − | 0.329154i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.00000 | − | 9.00000i | 0.295918 | − | 0.295918i | ||||
\(926\) | −16.0000 | − | 16.0000i | −0.525793 | − | 0.525793i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.0000 | 0.787839 | ||||||||
\(929\) | −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 | ||||
\(932\) | −8.00000 | −0.262049 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.0000 | 0.327210 | ||||||||
\(935\) | − | 4.00000i | − | 0.130814i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28.0000i | 0.914720i | 0.889282 | + | 0.457360i | \(0.151205\pi\) | ||||
−0.889282 | + | 0.457360i | \(0.848795\pi\) | |||||||
\(938\) | 20.0000i | 0.653023i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.0000 | − | 16.0000i | 0.521862 | − | 0.521862i | ||||
\(941\) | 29.0000 | − | 29.0000i | 0.945373 | − | 0.945373i | −0.0532103 | − | 0.998583i | \(-0.516945\pi\) |
0.998583 | + | 0.0532103i | \(0.0169454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −12.0000 | − | 12.0000i | −0.390567 | − | 0.390567i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 10.0000 | − | 10.0000i | 0.325128 | − | 0.325128i | ||||
\(947\) | 5.00000 | − | 5.00000i | 0.162478 | − | 0.162478i | −0.621185 | − | 0.783664i | \(-0.713349\pi\) |
0.783664 | + | 0.621185i | \(0.213349\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | + | 4.00000i | 0.129845 | + | 0.129845i | ||||
\(950\) | − | 18.0000i | − | 0.583997i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.00000 | + | 8.00000i | 0.259281 | + | 0.259281i | ||||
\(953\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 40.0000 | + | 40.0000i | 1.29234 | + | 1.29234i | ||||
\(959\) | −16.0000 | −0.516667 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | −6.00000 | − | 6.00000i | −0.193448 | − | 0.193448i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 36.0000i | − | 1.15948i | ||||||
\(965\) | 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 | \(-0.0102379\pi\) | |||||||
\(968\) | 18.0000 | + | 18.0000i | 0.578542 | + | 0.578542i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 4.00000i | − | 0.128432i | ||||||
\(971\) | 19.0000 | + | 19.0000i | 0.609739 | + | 0.609739i | 0.942878 | − | 0.333139i | \(-0.108108\pi\) |
−0.333139 | + | 0.942878i | \(0.608108\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.00000 | + | 6.00000i | −0.192351 | + | 0.192351i | ||||
\(974\) | 2.00000 | − | 2.00000i | 0.0640841 | − | 0.0640841i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 36.0000 | − | 36.0000i | 1.15233 | − | 1.15233i | ||||
\(977\) | 2.00000 | 0.0639857 | 0.0319928 | − | 0.999488i | \(-0.489815\pi\) | ||||
0.0319928 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.00000 | + | 4.00000i | −0.127841 | + | 0.127841i | ||||
\(980\) | −6.00000 | + | 6.00000i | −0.191663 | + | 0.191663i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 38.0000i | 1.21263i | ||||||||
\(983\) | 34.0000i | 1.08443i | 0.840239 | + | 0.542216i | \(0.182414\pi\) | ||||
−0.840239 | + | 0.542216i | \(0.817586\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.0000i | 1.08333i | ||||||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | 30.0000 | − | 30.0000i | 0.953945 | − | 0.953945i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0000 | 1.01651 | 0.508257 | − | 0.861206i | \(-0.330290\pi\) | ||||
0.508257 | + | 0.861206i | \(0.330290\pi\) | |||||||
\(992\) | 32.0000 | + | 32.0000i | 1.01600 | + | 1.01600i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.0000 | + | 20.0000i | 0.634361 | + | 0.634361i | ||||
\(995\) | −14.0000 | + | 14.0000i | −0.443830 | + | 0.443830i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.0000 | − | 37.0000i | −1.17180 | − | 1.17180i | −0.981780 | − | 0.190022i | \(-0.939144\pi\) |
−0.190022 | − | 0.981780i | \(-0.560856\pi\) | |||||||
\(998\) | 46.0000 | 1.45610 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))