Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(289,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.bo (of order \(9\), degree \(6\), 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: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.939693 - 0.342020i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.529 |
Dual form | 912.2.bo.d.481.1 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{9}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.939693 | + | 0.342020i | −0.542532 | + | 0.197465i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.613341 | + | 3.47843i | −0.274294 | + | 1.55560i | 0.466900 | + | 0.884310i | \(0.345371\pi\) |
−0.741194 | + | 0.671290i | \(0.765740\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.85844 | + | 3.21891i | 0.702425 | + | 1.21664i | 0.967613 | + | 0.252438i | \(0.0812325\pi\) |
−0.265188 | + | 0.964197i | \(0.585434\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.766044 | − | 0.642788i | 0.255348 | − | 0.214263i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.64543 | + | 4.58202i | −0.797627 | + | 1.38153i | 0.123531 | + | 0.992341i | \(0.460578\pi\) |
−0.921158 | + | 0.389190i | \(0.872755\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.213011 | + | 0.0775297i | 0.0590786 | + | 0.0215029i | 0.371390 | − | 0.928477i | \(-0.378881\pi\) |
−0.312312 | + | 0.949980i | \(0.601103\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.613341 | − | 3.47843i | −0.158364 | − | 0.898126i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.26604 | − | 1.06234i | −0.307061 | − | 0.257655i | 0.476215 | − | 0.879329i | \(-0.342008\pi\) |
−0.783276 | + | 0.621674i | \(0.786453\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.17752 | + | 1.24432i | 0.958388 | + | 0.285467i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.84730 | − | 2.38917i | −0.621331 | − | 0.521359i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.50727 | − | 8.54818i | −0.314288 | − | 1.78242i | −0.576182 | − | 0.817321i | \(-0.695458\pi\) |
0.261894 | − | 0.965097i | \(-0.415653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.02481 | − | 2.55682i | −1.40496 | − | 0.511365i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.500000 | + | 0.866025i | −0.0962250 | + | 0.166667i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0923963 | − | 0.0775297i | 0.0171576 | − | 0.0143969i | −0.634169 | − | 0.773195i | \(-0.718657\pi\) |
0.651326 | + | 0.758798i | \(0.274213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.56031 | + | 2.70253i | 0.280239 | + | 0.485389i | 0.971444 | − | 0.237271i | \(-0.0762528\pi\) |
−0.691204 | + | 0.722660i | \(0.742919\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.918748 | − | 5.21048i | 0.159934 | − | 0.907028i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12.3366 | + | 4.49016i | −2.08527 | + | 0.758976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.12836 | 0.843096 | 0.421548 | − | 0.906806i | \(-0.361487\pi\) | ||||
0.421548 | + | 0.906806i | \(0.361487\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.226682 | −0.0362981 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.67752 | + | 2.43042i | −1.04285 | + | 0.379568i | −0.805961 | − | 0.591968i | \(-0.798351\pi\) |
−0.236892 | + | 0.971536i | \(0.576129\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.929892 | − | 5.27368i | 0.141807 | − | 0.804229i | −0.828068 | − | 0.560627i | \(-0.810560\pi\) |
0.969875 | − | 0.243602i | \(-0.0783289\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.76604 | + | 3.05888i | 0.263266 | + | 0.455991i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.92262 | − | 1.61327i | 0.280443 | − | 0.235319i | −0.491706 | − | 0.870761i | \(-0.663626\pi\) |
0.772149 | + | 0.635442i | \(0.219182\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.40760 | + | 5.90214i | −0.486801 | + | 0.843163i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.55303 | + | 0.565258i | 0.217468 | + | 0.0791519i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.03074 | + | 5.84564i | 0.141584 | + | 0.802961i | 0.970047 | + | 0.242918i | \(0.0781044\pi\) |
−0.828463 | + | 0.560043i | \(0.810784\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −14.3157 | − | 12.0123i | −1.93033 | − | 1.61974i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.35117 | + | 0.259515i | −0.576326 | + | 0.0343736i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.167718 | − | 0.140732i | −0.0218351 | − | 0.0183218i | 0.631805 | − | 0.775128i | \(-0.282314\pi\) |
−0.653640 | + | 0.756806i | \(0.726759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.273318 | − | 1.55007i | −0.0349948 | − | 0.198466i | 0.962298 | − | 0.271997i | \(-0.0876841\pi\) |
−0.997293 | + | 0.0735316i | \(0.976573\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.49273 | + | 1.27125i | 0.440042 | + | 0.160162i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.400330 | + | 0.693392i | −0.0496548 | + | 0.0860046i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.8589 | + | 9.95080i | −1.44880 | + | 1.21568i | −0.515343 | + | 0.856984i | \(0.672336\pi\) |
−0.933453 | + | 0.358701i | \(0.883220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.34002 | + | 7.51714i | 0.522477 | + | 0.904957i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.235300 | − | 1.33445i | 0.0279249 | − | 0.158370i | −0.967657 | − | 0.252271i | \(-0.918823\pi\) |
0.995582 | + | 0.0939008i | \(0.0299337\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.27972 | + | 0.829748i | −0.266820 | + | 0.0971147i | −0.471966 | − | 0.881617i | \(-0.656455\pi\) |
0.205145 | + | 0.978731i | \(0.434233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.47565 | 0.863214 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.6655 | −2.24109 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.69207 | + | 0.979832i | −0.302881 | + | 0.110240i | −0.488990 | − | 0.872289i | \(-0.662635\pi\) |
0.186109 | + | 0.982529i | \(0.440412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.173648 | − | 0.984808i | 0.0192942 | − | 0.109423i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.960637 | + | 1.66387i | 0.105444 | + | 0.182634i | 0.913919 | − | 0.405896i | \(-0.133040\pi\) |
−0.808476 | + | 0.588530i | \(0.799707\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.47178 | − | 3.75227i | 0.485033 | − | 0.406991i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.0603074 | + | 0.104455i | −0.00646563 | + | 0.0111988i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.4226 | + | 4.15749i | 1.21080 | + | 0.440693i | 0.866980 | − | 0.498344i | \(-0.166058\pi\) |
0.343816 | + | 0.939037i | \(0.388280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.146307 | + | 0.829748i | 0.0153371 | + | 0.0869813i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.39053 | − | 2.00589i | −0.247886 | − | 0.208001i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.89053 | + | 13.7680i | −0.706953 | + | 1.41257i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.4081 | + | 11.2507i | 1.36138 | + | 1.14234i | 0.975552 | + | 0.219767i | \(0.0705296\pi\) |
0.385831 | + | 0.922570i | \(0.373915\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.918748 | + | 5.21048i | 0.0923377 | + | 0.523673i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.1099 | − | 5.13560i | −1.40399 | − | 0.511011i | −0.474631 | − | 0.880185i | \(-0.657418\pi\) |
−0.929360 | + | 0.369174i | \(0.879641\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.33022 | − | 5.76811i | 0.328137 | − | 0.568349i | −0.654006 | − | 0.756490i | \(-0.726913\pi\) |
0.982142 | + | 0.188141i | \(0.0602461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.0569 | − | 8.43874i | 0.981453 | − | 0.823537i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.04323 | + | 7.00309i | 0.390874 | + | 0.677014i | 0.992565 | − | 0.121715i | \(-0.0388394\pi\) |
−0.601691 | + | 0.798729i | \(0.705506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.64796 | − | 15.0173i | 0.253628 | − | 1.43840i | −0.545941 | − | 0.837823i | \(-0.683828\pi\) |
0.799570 | − | 0.600573i | \(-0.205061\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.81908 | + | 1.75400i | −0.457407 | + | 0.166482i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.815207 | 0.0766883 | 0.0383441 | − | 0.999265i | \(-0.487792\pi\) | ||||
0.0383441 | + | 0.999265i | \(0.487792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 30.6587 | 2.85894 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.213011 | − | 0.0775297i | 0.0196929 | − | 0.00716762i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.06670 | − | 6.04958i | 0.0977846 | − | 0.554564i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.49660 | − | 14.7165i | −0.772418 | − | 1.33787i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.44356 | − | 4.56769i | 0.490830 | − | 0.411855i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.37211 | − | 7.57272i | 0.391054 | − | 0.677325i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.3969 | + | 3.78417i | 0.922578 | + | 0.335791i | 0.759264 | − | 0.650783i | \(-0.225559\pi\) |
0.163314 | + | 0.986574i | \(0.447782\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.929892 | + | 5.27368i | 0.0818725 | + | 0.464322i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.0307 | + | 9.25589i | 0.963761 | + | 0.808691i | 0.981561 | − | 0.191150i | \(-0.0612218\pi\) |
−0.0178001 | + | 0.999842i | \(0.505666\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.75830 | + | 15.7596i | 0.325886 | + | 1.36653i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.70574 | − | 2.27038i | −0.232873 | − | 0.195403i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.0821293 | − | 0.465778i | −0.00701678 | − | 0.0397941i | 0.981098 | − | 0.193510i | \(-0.0619871\pi\) |
−0.988115 | + | 0.153716i | \(0.950876\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.57057 | − | 3.48340i | −0.811766 | − | 0.295458i | −0.0974126 | − | 0.995244i | \(-0.531057\pi\) |
−0.714353 | + | 0.699786i | \(0.753279\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.25490 | + | 2.17355i | −0.105682 | + | 0.183046i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.918748 | + | 0.770921i | −0.0768296 | + | 0.0644677i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.213011 | + | 0.368946i | 0.0176896 | + | 0.0306393i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.18345 | − | 6.71167i | 0.0976092 | − | 0.553569i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.58987 | + | 1.67058i | −0.376017 | + | 0.136859i | −0.523113 | − | 0.852263i | \(-0.675229\pi\) |
0.147096 | + | 0.989122i | \(0.453007\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.04189 | −0.735818 | −0.367909 | − | 0.929862i | \(-0.619926\pi\) | ||||
−0.367909 | + | 0.929862i | \(0.619926\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.65270 | −0.133613 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3576 | + | 3.76984i | −0.831940 | + | 0.302801i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.0577812 | − | 0.327693i | 0.00461144 | − | 0.0261528i | −0.982415 | − | 0.186709i | \(-0.940218\pi\) |
0.987027 | + | 0.160556i | \(0.0513289\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.96791 | − | 5.14057i | −0.235371 | − | 0.407674i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.7147 | − | 20.7381i | 1.94779 | − | 1.63439i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.97044 | − | 3.41290i | 0.154337 | − | 0.267319i | −0.778481 | − | 0.627669i | \(-0.784009\pi\) |
0.932817 | + | 0.360350i | \(0.117343\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 17.5608 | + | 6.39160i | 1.36710 | + | 0.497585i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.04071 | − | 5.90214i | −0.0805323 | − | 0.456722i | −0.998232 | − | 0.0594456i | \(-0.981067\pi\) |
0.917699 | − | 0.397276i | \(-0.130044\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.91921 | − | 8.32321i | −0.763017 | − | 0.640247i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000 | − | 1.73205i | 0.305888 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.39306 | + | 7.88171i | 0.714141 | + | 0.599235i | 0.925758 | − | 0.378117i | \(-0.123428\pi\) |
−0.211617 | + | 0.977353i | \(0.567873\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.82501 | − | 27.3640i | −0.364736 | − | 2.06852i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.205737 | + | 0.0748822i | 0.0154641 | + | 0.00562849i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.03209 | − | 6.98378i | 0.301372 | − | 0.521992i | −0.675075 | − | 0.737749i | \(-0.735889\pi\) |
0.976447 | + | 0.215757i | \(0.0692219\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.145430 | − | 0.122030i | 0.0108097 | − | 0.00907042i | −0.637367 | − | 0.770561i | \(-0.719976\pi\) |
0.648176 | + | 0.761490i | \(0.275532\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.786989 | + | 1.36310i | 0.0581759 | + | 0.100764i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.14543 | + | 17.8386i | −0.231257 | + | 1.31152i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.21688 | − | 2.99070i | 0.600878 | − | 0.218702i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.71688 | −0.270363 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.0378 | −1.30517 | −0.652584 | − | 0.757717i | \(-0.726315\pi\) | ||||
−0.652584 | + | 0.757717i | \(0.726315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3871 | − | 5.96443i | 1.17957 | − | 0.429329i | 0.323521 | − | 0.946221i | \(-0.395133\pi\) |
0.856050 | + | 0.516892i | \(0.172911\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.139033 | − | 0.788496i | 0.00995637 | − | 0.0564654i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.24035 | + | 9.07656i | 0.373360 | + | 0.646678i | 0.990080 | − | 0.140504i | \(-0.0448724\pi\) |
−0.616720 | + | 0.787182i | \(0.711539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.4593 | − | 8.77639i | 0.741440 | − | 0.622142i | −0.191784 | − | 0.981437i | \(-0.561427\pi\) |
0.933224 | + | 0.359295i | \(0.116983\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.74035 | − | 13.4067i | 0.545962 | − | 0.945635i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.421274 | + | 0.153331i | 0.0295677 | + | 0.0107617i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.35844 | − | 24.7179i | −0.304407 | − | 1.72638i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.64930 | − | 5.57943i | −0.462158 | − | 0.387797i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.7528 | + | 15.8497i | −1.15882 | + | 1.09635i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.2023 | + | 10.2390i | 0.840043 | + | 0.704880i | 0.957573 | − | 0.288189i | \(-0.0930532\pi\) |
−0.117530 | + | 0.993069i | \(0.537498\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.235300 | + | 1.33445i | 0.0161225 | + | 0.0914351i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 17.7738 | + | 6.46913i | 1.21216 | + | 0.441191i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.79948 | + | 10.0450i | −0.393694 | + | 0.681898i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.85844 | − | 1.55942i | 0.125582 | − | 0.105376i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.187319 | − | 0.324446i | −0.0126004 | − | 0.0218246i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.23261 | + | 18.3331i | −0.216472 | + | 1.22767i | 0.661863 | + | 0.749625i | \(0.269766\pi\) |
−0.878334 | + | 0.478047i | \(0.841345\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.02481 | + | 2.55682i | −0.468321 | + | 0.170455i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.79292 | 0.384490 | 0.192245 | − | 0.981347i | \(-0.438423\pi\) | ||||
0.192245 | + | 0.981347i | \(0.438423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.12836 | −0.537137 | −0.268568 | − | 0.963261i | \(-0.586551\pi\) | ||||
−0.268568 | + | 0.963261i | \(0.586551\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.4795 | − | 6.72600i | 1.21586 | − | 0.442538i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.95677 | + | 16.7687i | −0.193704 | + | 1.09855i | 0.720548 | + | 0.693405i | \(0.243890\pi\) |
−0.914252 | + | 0.405146i | \(0.867221\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.43242 | + | 7.67717i | 0.289139 | + | 0.500804i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.19459 | − | 1.84148i | 0.142554 | − | 0.119617i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50980 | + | 13.0074i | −0.485769 | + | 0.841376i | −0.999866 | − | 0.0163558i | \(-0.994794\pi\) |
0.514098 | + | 0.857732i | \(0.328127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.1596 | + | 7.33748i | 1.29859 | + | 0.472649i | 0.896538 | − | 0.442967i | \(-0.146074\pi\) |
0.402054 | + | 0.915616i | \(0.368296\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.173648 | + | 0.984808i | 0.0111395 | + | 0.0631754i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −18.4402 | − | 15.4731i | −1.17810 | − | 0.988542i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.793386 | + | 0.588936i | 0.0504819 | + | 0.0374731i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.47178 | − | 1.23497i | −0.0932704 | − | 0.0782631i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.43969 | + | 25.1787i | 0.280231 | + | 1.58927i | 0.721839 | + | 0.692061i | \(0.243297\pi\) |
−0.441608 | + | 0.897208i | \(0.645592\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 43.1553 | + | 15.7072i | 2.71315 | + | 0.987506i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.91875 | + | 5.05542i | −0.182779 | + | 0.316583i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.13950 | − | 1.79525i | 0.133458 | − | 0.111985i | −0.573615 | − | 0.819125i | \(-0.694459\pi\) |
0.707073 | + | 0.707140i | \(0.250015\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.53074 | + | 16.5077i | 0.592212 | + | 1.02574i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.0209445 | − | 0.118782i | 0.00129643 | − | 0.00735244i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.30066 | − | 0.473401i | 0.0802021 | − | 0.0291912i | −0.301608 | − | 0.953432i | \(-0.597523\pi\) |
0.381810 | + | 0.924241i | \(0.375301\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.9659 | −1.28792 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1557 | −0.743917 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0471 | − | 5.84067i | 0.978409 | − | 0.356112i | 0.197188 | − | 0.980366i | \(-0.436819\pi\) |
0.781221 | + | 0.624254i | \(0.214597\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.46064 | − | 25.2975i | 0.270964 | − | 1.53672i | −0.480531 | − | 0.876978i | \(-0.659556\pi\) |
0.751496 | − | 0.659738i | \(-0.229333\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.421274 | − | 0.729669i | −0.0254967 | − | 0.0441615i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.2991 | − | 25.4239i | 1.82710 | − | 1.53312i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.1125 | + | 19.2474i | −0.667683 | + | 1.15646i | 0.310867 | + | 0.950453i | \(0.399381\pi\) |
−0.978550 | + | 0.206008i | \(0.933953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.93242 | + | 1.06731i | 0.175559 | + | 0.0638984i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.268104 | + | 1.52049i | 0.0159937 | + | 0.0907050i | 0.991760 | − | 0.128111i | \(-0.0408915\pi\) |
−0.975766 | + | 0.218816i | \(0.929780\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.88326 | − | 6.61484i | −0.468611 | − | 0.393211i | 0.377677 | − | 0.925938i | \(-0.376723\pi\) |
−0.846288 | + | 0.532726i | \(0.821168\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.76604 | − | 15.2944i | 0.104611 | − | 0.905962i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.2331 | − | 16.9776i | −1.19432 | − | 1.00215i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.47771 | − | 14.0518i | −0.145748 | − | 0.826576i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.4474 | − | 5.98638i | −0.964166 | − | 0.350928i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.2515 | − | 24.6843i | 0.832581 | − | 1.44207i | −0.0634033 | − | 0.997988i | \(-0.520195\pi\) |
0.895985 | − | 0.444085i | \(-0.146471\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.592396 | − | 0.497079i | 0.0344906 | − | 0.0289411i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.64543 | − | 4.58202i | −0.153503 | − | 0.265876i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.341671 | − | 1.93771i | 0.0197594 | − | 0.112061i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.7037 | − | 6.80758i | 1.07806 | − | 0.392382i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.0155 | 0.862617 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.55943 | 0.318332 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.0180 | + | 8.74184i | −1.37078 | + | 0.498923i | −0.919370 | − | 0.393394i | \(-0.871301\pi\) |
−0.451410 | + | 0.892317i | \(0.649079\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.15657 | + | 6.55926i | −0.0657952 | + | 0.373143i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.18732 | + | 8.98470i | 0.294146 | + | 0.509476i | 0.974786 | − | 0.223142i | \(-0.0716315\pi\) |
−0.680640 | + | 0.732618i | \(0.738298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.8250 | + | 9.92236i | −0.668389 | + | 0.560845i | −0.912588 | − | 0.408880i | \(-0.865919\pi\) |
0.244199 | + | 0.969725i | \(0.421475\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.56418 | + | 11.3695i | −0.369850 | + | 0.640598i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.6844 | − | 9.71232i | −1.49874 | − | 0.545498i | −0.543009 | − | 0.839727i | \(-0.682715\pi\) |
−0.955735 | + | 0.294229i | \(0.904937\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.110815 | + | 0.628461i | 0.00620443 | + | 0.0351870i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.19459 | − | 5.19788i | −0.345748 | − | 0.290117i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.96703 | − | 6.01330i | −0.220732 | − | 0.334589i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.29813 | − | 1.08926i | −0.0720075 | − | 0.0604215i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.64796 | + | 15.0173i | 0.146432 | + | 0.830459i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.76604 | + | 3.19058i | 0.483288 | + | 0.175902i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.9611 | + | 22.4493i | −0.712407 | + | 1.23392i | 0.251545 | + | 0.967846i | \(0.419062\pi\) |
−0.963951 | + | 0.266079i | \(0.914272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.92855 | − | 3.29644i | 0.215283 | − | 0.180644i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −27.3396 | − | 47.3536i | −1.49372 | − | 2.58720i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.08260 | + | 23.1536i | −0.222393 | + | 1.26125i | 0.645213 | + | 0.764003i | \(0.276769\pi\) |
−0.867606 | + | 0.497252i | \(0.834343\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.766044 | + | 0.278817i | −0.0416058 | + | 0.0151433i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.5107 | −0.894106 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.686852 | 0.0370865 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −28.8097 | + | 10.4859i | −1.55106 | + | 0.564541i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.417566 | − | 2.36813i | 0.0224161 | − | 0.127128i | −0.971546 | − | 0.236850i | \(-0.923885\pi\) |
0.993962 | + | 0.109722i | \(0.0349961\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.59879 | − | 4.50124i | −0.139110 | − | 0.240946i | 0.788050 | − | 0.615611i | \(-0.211091\pi\) |
−0.927160 | + | 0.374665i | \(0.877758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.173648 | + | 0.145708i | −0.00926865 | + | 0.00777732i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.13816 | + | 7.16750i | −0.220252 | + | 0.381487i | −0.954884 | − | 0.296978i | \(-0.904021\pi\) |
0.734633 | + | 0.678465i | \(0.237355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.49747 | + | 1.63695i | 0.238701 | + | 0.0868801i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.06670 | + | 6.04958i | 0.0564560 | + | 0.320178i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.75877 | + | 1.47578i | 0.0928244 | + | 0.0778889i | 0.688019 | − | 0.725693i | \(-0.258481\pi\) |
−0.595195 | + | 0.803582i | \(0.702925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9033 | + | 10.3964i | 0.837017 | + | 0.547177i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 13.0175 | + | 10.9230i | 0.683244 | + | 0.573310i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.48798 | − | 8.43874i | −0.0778843 | − | 0.441704i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.0638 | + | 10.2144i | 1.46492 | + | 0.533186i | 0.946715 | − | 0.322072i | \(-0.104379\pi\) |
0.518202 | + | 0.855258i | \(0.326602\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.55303 | + | 6.15403i | −0.184964 | + | 0.320366i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9010 | + | 14.1817i | −0.877459 | + | 0.736275i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.92649 | + | 17.1932i | 0.513974 | + | 0.890229i | 0.999869 | + | 0.0162118i | \(0.00516060\pi\) |
−0.485894 | + | 0.874017i | \(0.661506\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.51842 | + | 8.61138i | −0.0784108 | + | 0.444690i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0256923 | − | 0.00935122i | 0.00132322 | − | 0.000481612i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.8256 | −1.32657 | −0.663287 | − | 0.748365i | \(-0.730839\pi\) | ||||
−0.663287 | + | 0.748365i | \(0.730839\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −11.0642 | −0.566835 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.9201 | − | 6.88635i | 0.966772 | − | 0.351876i | 0.190088 | − | 0.981767i | \(-0.439123\pi\) |
0.776684 | + | 0.629891i | \(0.216900\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.0617 | − | 68.4050i | 0.614719 | − | 3.48624i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.67752 | − | 4.63760i | −0.136106 | − | 0.235742i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.68139 | − | 7.28455i | 0.440164 | − | 0.369341i | −0.395607 | − | 0.918420i | \(-0.629466\pi\) |
0.835771 | + | 0.549079i | \(0.185021\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.17277 | + | 12.4236i | −0.362743 | + | 0.628289i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −13.5312 | − | 4.92496i | −0.682559 | − | 0.248431i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.75712 | − | 9.96513i | −0.0884104 | − | 0.501400i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0307 | + | 8.41679i | 0.503429 | + | 0.422427i | 0.858810 | − | 0.512295i | \(-0.171204\pi\) |
−0.355381 | + | 0.934722i | \(0.615649\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.92174 | − | 13.5237i | −0.446646 | − | 0.677034i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.2554 | + | 13.6399i | 0.811754 | + | 0.681143i | 0.951026 | − | 0.309112i | \(-0.100032\pi\) |
−0.139272 | + | 0.990254i | \(0.544476\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.122836 | + | 0.696639i | 0.00611891 | + | 0.0347021i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.31908 | + | 1.20805i | 0.164926 | + | 0.0600283i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.5667 | + | 23.4982i | −0.672477 | + | 1.16476i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.2763 | + | 18.6920i | −1.10149 | + | 0.924262i | −0.997525 | − | 0.0703185i | \(-0.977598\pi\) |
−0.103968 | + | 0.994581i | \(0.533154\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.236482 | + | 0.409598i | 0.0116648 | + | 0.0202040i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.141311 | − | 0.801414i | 0.00695345 | − | 0.0394350i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.37686 | + | 2.32099i | −0.313028 | + | 0.113933i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.1848 | 0.498751 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −40.4962 | −1.97837 | −0.989184 | − | 0.146679i | \(-0.953141\pi\) | ||||
−0.989184 | + | 0.146679i | \(0.953141\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3491 | + | 10.6822i | −1.43039 | + | 0.520619i | −0.937043 | − | 0.349215i | \(-0.886448\pi\) |
−0.493345 | + | 0.869834i | \(0.664226\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.435822 | − | 2.47167i | 0.0211904 | − | 0.120177i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.17752 | + | 10.6998i | 0.299654 | + | 0.519015i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.48158 | − | 3.76049i | 0.216879 | − | 0.181983i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.599670 | − | 1.03866i | 0.0289524 | − | 0.0501469i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.4513 | + | 8.89955i | 1.17778 | + | 0.428676i | 0.855417 | − | 0.517941i | \(-0.173301\pi\) |
0.322361 | + | 0.946617i | \(0.395523\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.69965 | − | 26.6530i | −0.225851 | − | 1.28086i | −0.861053 | − | 0.508516i | \(-0.830194\pi\) |
0.635202 | − | 0.772346i | \(-0.280917\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.326352 | − | 0.273842i | −0.0156474 | − | 0.0131297i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.34002 | − | 37.5857i | 0.207611 | − | 1.79797i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.25284 | + | 1.89036i | 0.107522 | + | 0.0902219i | 0.694964 | − | 0.719045i | \(-0.255420\pi\) |
−0.587442 | + | 0.809267i | \(0.699865\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.18345 | + | 6.71167i | 0.0563547 | + | 0.319603i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.9402 | + | 9.44145i | 1.23245 | + | 0.448577i | 0.874437 | − | 0.485138i | \(-0.161231\pi\) |
0.358017 | + | 0.933715i | \(0.383453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −21.4675 | + | 37.1828i | −1.01766 | + | 1.76263i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.74170 | − | 3.13966i | 0.176976 | − | 0.148501i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.46110 | − | 14.6551i | −0.399304 | − | 0.691615i | 0.594336 | − | 0.804217i | \(-0.297415\pi\) |
−0.993640 | + | 0.112602i | \(0.964082\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.52869 | − | 37.0260i | 0.307424 | − | 1.74349i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.49660 | − | 3.09251i | 0.399205 | − | 0.145299i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.97596 | −0.139515 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.19160 | 0.429965 | 0.214982 | − | 0.976618i | \(-0.431031\pi\) | ||||
0.214982 | + | 0.976618i | \(0.431031\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.55303 | − | 0.565258i | 0.0724894 | − | 0.0263840i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.68210 | + | 15.2110i | −0.124918 | + | 0.708445i | 0.856438 | + | 0.516249i | \(0.172672\pi\) |
−0.981357 | + | 0.192196i | \(0.938439\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.9907 | + | 25.9646i | 0.696675 | + | 1.20668i | 0.969613 | + | 0.244645i | \(0.0786715\pi\) |
−0.272937 | + | 0.962032i | \(0.587995\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.44356 | − | 7.08499i | 0.391561 | − | 0.328559i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.4427 | − | 25.0155i | 0.668328 | − | 1.15758i | −0.310044 | − | 0.950722i | \(-0.600344\pi\) |
0.978372 | − | 0.206855i | \(-0.0663230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.0699 | − | 19.6798i | −2.49671 | − | 0.908730i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.0577812 | + | 0.327693i | 0.00266242 | + | 0.0150993i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.7041 | + | 18.2119i | 0.997958 | + | 0.837386i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −26.1648 | − | 19.4223i | −1.20052 | − | 0.891157i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.54710 | + | 3.81547i | 0.208198 | + | 0.174699i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.37211 | − | 13.4529i | −0.108385 | − | 0.614679i | −0.989814 | − | 0.142364i | \(-0.954530\pi\) |
0.881430 | − | 0.472315i | \(-0.156582\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.09240 | + | 0.397600i | 0.0498090 | + | 0.0181290i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −16.1313 | + | 27.9403i | −0.734002 | + | 1.27133i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −47.3585 | + | 39.7385i | −2.15044 | + | 1.80443i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.08899 | − | 5.35029i | −0.139976 | − | 0.242445i | 0.787512 | − | 0.616300i | \(-0.211369\pi\) |
−0.927487 | + | 0.373855i | \(0.878036\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.684326 | + | 3.88100i | −0.0309463 | + | 0.175505i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.85591 | − | 1.40344i | 0.174015 | − | 0.0633363i | −0.253543 | − | 0.967324i | \(-0.581596\pi\) |
0.427558 | + | 0.903988i | \(0.359374\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.199340 | −0.00897784 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.6878 | −0.839953 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.73277 | − | 1.72259i | 0.212294 | − | 0.0772687i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.61540 | + | 26.1752i | −0.206614 | + | 1.17176i | 0.688266 | + | 0.725458i | \(0.258372\pi\) |
−0.894880 | + | 0.446306i | \(0.852739\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.99660 | + | 5.19026i | 0.133878 | + | 0.231884i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.8746 | − | 16.6768i | 0.886166 | − | 0.743582i | −0.0812712 | − | 0.996692i | \(-0.525898\pi\) |
0.967437 | + | 0.253110i | \(0.0814535\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.5180 | − | 45.9305i | 1.18004 | − | 2.04388i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1677 | + | 4.42869i | 0.540387 | + | 0.196685i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.37551 | − | 24.8148i | −0.193941 | − | 1.09990i | −0.913918 | − | 0.405898i | \(-0.866959\pi\) |
0.719977 | − | 0.693998i | \(-0.244152\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.90760 | − | 5.79617i | −0.305574 | − | 0.256407i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.16637 | + | 2.99568i | −0.139799 | + | 0.132262i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 18.0214 | + | 15.1218i | 0.794118 | + | 0.666344i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.30587 | + | 13.0773i | 0.101412 | + | 0.575137i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.5223 | − | 4.19377i | −0.505772 | − | 0.184086i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.38800 | − | 2.40409i | 0.0608095 | − | 0.105325i | −0.834018 | − | 0.551737i | \(-0.813965\pi\) |
0.894827 | + | 0.446412i | \(0.147298\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.60678 | + | 7.22195i | −0.376348 | + | 0.315794i | −0.811267 | − | 0.584676i | \(-0.801222\pi\) |
0.434919 | + | 0.900470i | \(0.356777\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.8931 | + | 24.0635i | 0.606343 | + | 1.05022i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.895582 | − | 5.07910i | 0.0390122 | − | 0.221249i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −49.1865 | + | 17.9024i | −2.13854 | + | 0.778366i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.218941 | −0.00950122 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.61081 | −0.0697721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −26.8396 | + | 9.76882i | −1.16038 | + | 0.422343i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.40033 | + | 7.94166i | −0.0604287 | + | 0.342708i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.0292 | − | 31.2274i | −0.776571 | − | 1.34506i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.8628 | + | 14.1496i | −0.724987 | + | 0.608337i | −0.928760 | − | 0.370682i | \(-0.879124\pi\) |
0.203773 | + | 0.979018i | \(0.434680\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.0949225 | + | 0.164411i | −0.00407351 | + | 0.00705553i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 50.6125 | + | 18.4215i | 2.16800 | + | 0.789088i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.93107 | − | 33.6368i | −0.253594 | − | 1.43821i | −0.799655 | − | 0.600460i | \(-0.794984\pi\) |
0.546061 | − | 0.837746i | \(-0.316127\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.20574 | − | 1.01173i | −0.0514596 | − | 0.0431797i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.482459 | − | 0.208911i | 0.0205534 | − | 0.00889990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.15704 | − | 6.84457i | −0.346873 | − | 0.291061i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.14543 | − | 17.8386i | −0.133516 | − | 0.757207i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.5774 | + | 12.9491i | 1.50746 | + | 0.548672i | 0.957981 | − | 0.286832i | \(-0.0926023\pi\) |
0.549484 | + | 0.835504i | \(0.314824\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.606944 | − | 1.05126i | 0.0256710 | − | 0.0444635i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.69846 | + | 5.62068i | −0.282809 | + | 0.237305i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.86231 | + | 10.1538i | 0.247067 | + | 0.427933i | 0.962711 | − | 0.270533i | \(-0.0871999\pi\) |
−0.715644 | + | 0.698465i | \(0.753867\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.500000 | + | 2.83564i | −0.0210352 | + | 0.119296i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.49273 | − | 1.27125i | 0.146681 | − | 0.0533874i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.8972 | 0.624524 | 0.312262 | − | 0.949996i | \(-0.398913\pi\) | ||||
0.312262 | + | 0.949996i | \(0.398913\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.9409 | −0.541559 | −0.270779 | − | 0.962641i | \(-0.587281\pi\) | ||||
−0.270779 | + | 0.962641i | \(0.587281\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.9500 | − | 6.16928i | 0.708095 | − | 0.257725i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.2679 | + | 63.9032i | −0.469902 | + | 2.66495i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.3657 | − | 19.6860i | −0.473161 | − | 0.819539i | 0.526367 | − | 0.850257i | \(-0.323554\pi\) |
−0.999528 | + | 0.0307187i | \(0.990220\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.3589 | + | 11.2095i | −0.555177 | + | 0.465849i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.57057 | + | 6.18442i | −0.148132 | + | 0.256573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.5116 | − | 10.7413i | −1.22225 | − | 0.444861i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.139033 | + | 0.788496i | 0.00574831 | + | 0.0326003i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.08899 | + | 6.78747i | 0.333868 | + | 0.280149i | 0.794274 | − | 0.607560i | \(-0.207852\pi\) |
−0.460405 | + | 0.887709i | \(0.652296\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.15539 | + | 13.2314i | 0.130016 | + | 0.545190i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.02869 | − | 6.73687i | −0.330256 | − | 0.277118i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.86808 | − | 10.5944i | −0.0767128 | − | 0.435060i | −0.998839 | − | 0.0481709i | \(-0.984661\pi\) |
0.922126 | − | 0.386889i | \(-0.126450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 20.3888 | + | 7.42091i | 0.835858 | + | 0.304228i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.82682 | + | 11.8244i | −0.279403 | + | 0.483940i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.7153 | − | 15.7040i | 0.764686 | − | 0.641648i | −0.174656 | − | 0.984630i | \(-0.555881\pi\) |
0.939342 | + | 0.342982i | \(0.111437\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.2057 | + | 22.8730i | 0.538673 | + | 0.933009i | 0.998976 | + | 0.0452473i | \(0.0144076\pi\) |
−0.460303 | + | 0.887762i | \(0.652259\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.68820 | + | 15.2455i | −0.109472 | + | 0.620845i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 56.4017 | − | 20.5286i | 2.29306 | − | 0.834604i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3618 | 0.664107 | 0.332053 | − | 0.943261i | \(-0.392259\pi\) | ||||
0.332053 | + | 0.943261i | \(0.392259\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.448311 | −0.0181665 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.534615 | − | 0.194584i | 0.0216282 | − | 0.00787203i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.03162 | − | 5.85062i | 0.0416668 | − | 0.236304i | −0.956861 | − | 0.290546i | \(-0.906163\pi\) |
0.998528 | + | 0.0542418i | \(0.0172742\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.5496 | + | 21.7366i | 0.506050 | + | 0.876504i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −26.1438 | + | 21.9373i | −1.05251 | + | 0.883162i | −0.993355 | − | 0.115087i | \(-0.963285\pi\) |
−0.0591558 | + | 0.998249i | \(0.518841\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.1506 | − | 27.9737i | 0.649149 | − | 1.12436i | −0.334177 | − | 0.942510i | \(-0.608458\pi\) |
0.983326 | − | 0.181849i | \(-0.0582083\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.15657 | + | 2.96875i | 0.327312 | + | 0.119132i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.84565 | + | 44.4949i | 0.314329 | + | 1.78265i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.97384 | − | 4.17355i | −0.198954 | − | 0.166942i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3216 | − | 20.6237i | 0.412205 | − | 0.823629i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.49273 | − | 5.44804i | −0.258882 | − | 0.217228i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.13058 | − | 17.7544i | −0.124626 | − | 0.706791i | −0.981529 | − | 0.191313i | \(-0.938725\pi\) |
0.856903 | − | 0.515478i | \(-0.172386\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.9684 | − | 5.44804i | −0.594940 | − | 0.216540i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.5398 | + | 33.8440i | −0.775414 | + | 1.34306i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.18345 | + | 0.993031i | −0.0468899 | + | 0.0393453i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.677519 | − | 1.17350i | −0.0268022 | − | 0.0464228i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.449493 | − | 2.54920i | 0.0177539 | − | 0.100687i | −0.974643 | − | 0.223765i | \(-0.928165\pi\) |
0.992397 | + | 0.123077i | \(0.0392764\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.2160 | − | 5.53817i | 0.600061 | − | 0.218404i | −0.0240880 | − | 0.999710i | \(-0.507668\pi\) |
0.624149 | + | 0.781306i | \(0.285446\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.9145 | −0.744756 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.477407 | −0.0187688 | −0.00938439 | − | 0.999956i | \(-0.502987\pi\) | ||||
−0.00938439 | + | 0.999956i | \(0.502987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.08853 | − | 0.396191i | 0.0427284 | − | 0.0155519i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.01414 | − | 11.4227i | 0.0789403 | − | 0.447693i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.05097 | − | 13.9447i | −0.315059 | − | 0.545698i | 0.664391 | − | 0.747385i | \(-0.268691\pi\) |
−0.979450 | + | 0.201687i | \(0.935358\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.9616 | + | 32.6926i | −1.52235 | + | 1.27741i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.21301 | + | 2.10100i | −0.0473241 | + | 0.0819677i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.6630 | − | 4.97291i | −0.532234 | − | 0.193717i | 0.0619017 | − | 0.998082i | \(-0.480283\pi\) |
−0.594135 | + | 0.804365i | \(0.702506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.52915 | − | 14.3435i | −0.0983726 | − | 0.557899i | −0.993662 | − | 0.112413i | \(-0.964142\pi\) |
0.895289 | − | 0.445486i | \(-0.146969\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.286989 | + | 0.240812i | 0.0111457 | + | 0.00935238i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −57.1237 | + | 3.40700i | −2.21516 | + | 0.132118i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.802004 | − | 0.672961i | −0.0310537 | − | 0.0260572i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.23261 | − | 18.3331i | −0.124980 | − | 0.708797i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.82547 | + | 2.84824i | 0.302099 | + | 0.109955i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4324 | + | 21.5336i | −0.479235 | + | 0.830059i | −0.999716 | − | 0.0238142i | \(-0.992419\pi\) |
0.520482 | + | 0.853873i | \(0.325752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.72668 | − | 4.80526i | 0.220420 | − | 0.184954i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −23.2271 | − | 40.2306i | −0.892692 | − | 1.54619i | −0.836636 | − | 0.547760i | \(-0.815481\pi\) |
−0.0560563 | − | 0.998428i | \(-0.517853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.2970 | + | 64.0682i | −0.433537 | + | 2.45871i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.44356 | + | 1.98129i | −0.208598 | + | 0.0759234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 26.0000 | 0.994862 | 0.497431 | − | 0.867503i | \(-0.334277\pi\) | ||||
0.497431 | + | 0.867503i | \(0.334277\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.67055 | 0.0638284 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.63816 | − | 2.78006i | 0.291414 | − | 0.106066i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.233651 | + | 1.32510i | −0.00890139 | + | 0.0504823i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.03478 | − | 13.9166i | −0.305657 | − | 0.529414i | 0.671750 | − | 0.740778i | \(-0.265543\pi\) |
−0.977407 | + | 0.211364i | \(0.932210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −15.0646 | + | 12.6407i | −0.572259 | + | 0.480182i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17.9868 | − | 31.1540i | 0.682278 | − | 1.18174i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0360 | + | 4.01676i | 0.418017 | + | 0.152146i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.95677 | − | 16.7687i | −0.111835 | − | 0.634249i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.59240 | − | 6.37078i | −0.286761 | − | 0.240621i | 0.488048 | − | 0.872817i | \(-0.337709\pi\) |
−0.774808 | + | 0.632196i | \(0.782154\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.4238 | + | 6.38133i | 0.808014 | + | 0.240676i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.79086 | − | 5.69821i | −0.255759 | − | 0.214607i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.69144 | − | 54.9629i | −0.364484 | − | 2.06709i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8148 | + | 9.39582i | 0.969495 | + | 0.352867i | 0.777747 | − | 0.628577i | \(-0.216362\pi\) |
0.191748 | + | 0.981444i | \(0.438584\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.43242 | + | 2.48102i | −0.0537199 | + | 0.0930456i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.7499 | − | 17.4112i | 0.777090 | − | 0.652056i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.11809 | − | 3.66864i | −0.0792120 | − | 0.137199i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.60813 | − | 14.7914i | 0.0974023 | − | 0.552396i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 11.5239 | − | 4.19437i | 0.429770 | − | 0.156424i | −0.118072 | − | 0.993005i | \(-0.537671\pi\) |
0.547843 | + | 0.836581i | \(0.315449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.7561 | 0.921965 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.4534 | −0.797859 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.847296 | + | 0.308391i | −0.0314678 | + | 0.0114533i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.90719 | + | 27.8301i | −0.181998 | + | 1.03216i | 0.747755 | + | 0.663975i | \(0.231132\pi\) |
−0.929752 | + | 0.368185i | \(0.879979\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.500000 | − | 0.866025i | −0.0185185 | − | 0.0320750i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.77972 | + | 5.68886i | −0.250757 | + | 0.210410i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.2883 | − | 19.5520i | 0.416944 | − | 0.722168i | −0.578686 | − | 0.815550i | \(-0.696434\pi\) |
0.995630 | + | 0.0933819i | \(0.0297677\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.6202 | + | 8.23308i | 0.834359 | + | 0.303682i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.2229 | − | 80.6619i | −0.523906 | − | 2.97122i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2986 | − | 17.0325i | −0.746696 | − | 0.626552i | 0.187931 | − | 0.982182i | \(-0.439822\pi\) |
−0.934627 | + | 0.355630i | \(0.884266\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.946967 | − | 0.282065i | −0.0347877 | − | 0.0103619i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.1536 | + | 17.7500i | 0.776052 | + | 0.651185i | 0.942251 | − | 0.334907i | \(-0.108705\pi\) |
−0.166199 | + | 0.986092i | \(0.553150\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.99582 | − | 16.9902i | −0.109759 | − | 0.622472i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.80541 | + | 0.657115i | 0.0660564 | + | 0.0240426i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.0282 | + | 26.0296i | −0.549119 | + | 0.951102i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.988140 | + | 0.829148i | −0.0360578 | + | 0.0302561i | −0.660638 | − | 0.750704i | \(-0.729714\pi\) |
0.624581 | + | 0.780960i | \(0.285270\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.7836 | − | 22.1418i | −0.465860 | − | 0.806893i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.54576 | − | 31.4516i | 0.201831 | − | 1.14464i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.3259 | − | 8.85392i | 0.884141 | − | 0.321801i | 0.140262 | − | 0.990114i | \(-0.455206\pi\) |
0.743880 | + | 0.668313i | \(0.232983\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −45.9249 | −1.66697 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3396 | 0.411059 | 0.205529 | − | 0.978651i | \(-0.434108\pi\) | ||||
0.205529 | + | 0.978651i | \(0.434108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.2605 | − | 19.3852i | 1.92816 | − | 0.701792i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.01367 | − | 5.74881i | 0.0366493 | − | 0.207849i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0248149 | − | 0.0429807i | −0.000896015 | − | 0.00155194i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.4283 | − | 13.7850i | 0.592420 | − | 0.497099i | −0.296579 | − | 0.955008i | \(-0.595846\pi\) |
0.888999 | + | 0.457909i | \(0.151401\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.39646 | + | 2.41874i | −0.0502923 | + | 0.0871087i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.99108 | − | 1.45263i | −0.143549 | − | 0.0522476i | 0.269246 | − | 0.963071i | \(-0.413225\pi\) |
−0.412796 | + | 0.910824i | \(0.635448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.05097 | − | 22.9742i | −0.145515 | − | 0.825258i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −14.6019 | − | 12.2525i | −0.523842 | − | 0.439556i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −30.9197 | + | 1.84413i | −1.10781 | + | 0.0660728i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.49201 | + | 4.60834i | 0.196520 | + | 0.164900i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.0209445 | + | 0.118782i | 0.000748497 | + | 0.00424493i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.10442 | + | 0.401975i | 0.0394184 | + | 0.0143471i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.41013 | + | 9.37062i | −0.192850 | + | 0.334027i | −0.946194 | − | 0.323601i | \(-0.895107\pi\) |
0.753343 | + | 0.657627i | \(0.228440\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.06031 | + | 0.889704i | −0.0377479 | + | 0.0316743i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.51501 | + | 2.62408i | 0.0538677 | + | 0.0933016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.0619563 | − | 0.351371i | 0.00220013 | − | 0.0124776i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 19.7015 | − | 7.17074i | 0.698739 | − | 0.254320i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.0327 | 0.780439 | 0.390219 | − | 0.920722i | \(-0.372399\pi\) | ||||
0.390219 | + | 0.920722i | \(0.372399\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.14796 | −0.146744 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.4226 | − | 4.15749i | 0.403598 | − | 0.146898i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.22890 | − | 12.6407i | 0.0786563 | − | 0.446082i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 56.9774 | + | 98.6877i | 2.00819 | + | 3.47828i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −13.0817 | + | 10.9769i | −0.460498 | + | 0.386404i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.34343 | + | 5.79098i | −0.117549 | + | 0.203600i | −0.918796 | − | 0.394733i | \(-0.870837\pi\) |
0.801247 | + | 0.598334i | \(0.204170\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.9530 | + | 8.71816i | 0.841102 | + | 0.306136i | 0.726407 | − | 0.687265i | \(-0.241189\pi\) |
0.114695 | + | 0.993401i | \(0.463411\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.46064 | + | 25.2975i | 0.156441 | + | 0.887223i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.6630 | + | 8.94729i | 0.373508 | + | 0.313410i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4468 | − | 20.8738i | 0.365487 | − | 0.730282i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.645430 | + | 0.541580i | 0.0225531 | + | 0.0189243i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.34348 | − | 41.6470i | −0.256289 | − | 1.45349i | −0.792741 | − | 0.609558i | \(-0.791347\pi\) |
0.536452 | − | 0.843931i | \(-0.319764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.506397 | − | 0.184313i | −0.0176519 | − | 0.00642476i | 0.333179 | − | 0.942864i | \(-0.391879\pi\) |
−0.350831 | + | 0.936439i | \(0.614101\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −19.7763 | + | 34.2536i | −0.688523 | + | 1.19256i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.2745 | − | 10.2995i | 0.426826 | − | 0.358150i | −0.403926 | − | 0.914791i | \(-0.632355\pi\) |
0.830753 | + | 0.556642i | \(0.187910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0517 | + | 17.4100i | 0.349110 | + | 0.604676i | 0.986092 | − | 0.166203i | \(-0.0531508\pi\) |
−0.636982 | + | 0.770879i | \(0.719817\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.85932 | − | 21.8873i | 0.133878 | − | 0.759261i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5842 | − | 3.85235i | 0.366722 | − | 0.133476i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.1685 | 0.732566 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.12061 | −0.107864 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.1031 | − | 10.5927i | 1.00475 | − | 0.365700i | 0.213337 | − | 0.976979i | \(-0.431567\pi\) |
0.791415 | + | 0.611279i | \(0.209345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.03327 | + | 28.5451i | −0.173561 | + | 0.984314i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.771974 | − | 1.33710i | −0.0265882 | − | 0.0460521i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 35.0355 | − | 29.3983i | 1.20526 | − | 1.01133i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.5808 | − | 54.6996i | 1.08513 | − | 1.87950i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.67024 | + | 3.51968i | 0.331882 | + | 0.120795i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.72984 | − | 43.8381i | −0.264975 | − | 1.50275i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.3209 | − | 13.6949i | −0.558817 | − | 0.468903i | 0.319097 | − | 0.947722i | \(-0.396620\pi\) |
−0.877913 | + | 0.478819i | \(0.841065\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.57145 | + | 14.9761i | 0.122141 | + | 0.512170i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.5551 | + | 35.7080i | 1.45366 | + | 1.21976i | 0.929857 | + | 0.367920i | \(0.119930\pi\) |
0.523799 | + | 0.851842i | \(0.324514\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.11902 | + | 23.3601i | 0.140539 | + | 0.797038i | 0.970841 | + | 0.239724i | \(0.0770569\pi\) |
−0.830302 | + | 0.557314i | \(0.811832\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.8195 | + | 9.03358i | 0.845848 | + | 0.307863i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.5410 | − | 18.2576i | 0.358820 | − | 0.621495i | −0.628944 | − | 0.777451i | \(-0.716512\pi\) |
0.987764 | + | 0.155956i | \(0.0498458\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −33.1771 | + | 27.8389i | −1.12806 | + | 0.946551i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.13429 | + | 12.3569i | 0.242293 | + | 0.419664i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.63206 | − | 14.9272i | 0.0892866 | − | 0.506370i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.29756 | + | 1.20021i | −0.111734 | + | 0.0406677i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.5030 | 0.592387 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 32.5012 | 1.09874 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 48.1134 | − | 17.5118i | 1.62467 | − | 0.591333i | 0.640409 | − | 0.768034i | \(-0.278765\pi\) |
0.984265 | + | 0.176701i | \(0.0565425\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.94949 | + | 28.0700i | −0.166942 | + | 0.946777i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0804 | + | 29.5841i | 0.575452 | + | 0.996713i | 0.995992 | + | 0.0894388i | \(0.0285074\pi\) |
−0.420540 | + | 0.907274i | \(0.638159\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −21.5403 | + | 18.0745i | −0.724889 | + | 0.608254i | −0.928733 | − | 0.370750i | \(-0.879101\pi\) |
0.203844 | + | 0.979003i | \(0.434656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.386659 | + | 0.669713i | −0.0129974 | + | 0.0225122i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.4298 | − | 12.1674i | −1.12246 | − | 0.408543i | −0.286912 | − | 0.957957i | \(-0.592629\pi\) |
−0.835550 | + | 0.549414i | \(0.814851\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.14115 | + | 40.4995i | 0.239506 | + | 1.35831i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.05303 | + | 3.40090i | 0.135782 | + | 0.113934i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.0392 | − | 4.34710i | 0.335949 | − | 0.145470i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.8195 | + | 18.3088i | 0.729347 | + | 0.611995i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.341671 | + | 1.93771i | 0.0114081 | + | 0.0646984i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.353693 | + | 0.128734i | 0.0117963 | + | 0.00429351i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.90508 | − | 8.49584i | 0.163412 | − | 0.283038i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.2474 | + | 12.7941i | −0.507401 | + | 0.425760i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.335275 | + | 0.580713i | 0.0111449 | + | 0.0193035i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.61422 | − | 9.15469i | 0.0535992 | − | 0.303976i | −0.946209 | − | 0.323556i | \(-0.895122\pi\) |
0.999808 | + | 0.0195795i | \(0.00623275\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −14.1099 | + | 5.13560i | −0.467997 | + | 0.170337i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.79055 | −0.125587 | −0.0627933 | − | 0.998027i | \(-0.520001\pi\) | ||||
−0.0627933 | + | 0.998027i | \(0.520001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.1652 | −0.336419 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.22416 | + | 1.90144i | −0.172705 | + | 0.0628596i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.29394 | + | 52.7085i | −0.306913 | + | 1.74059i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.21554 | − | 3.83742i | −0.0730838 | − | 0.126585i | 0.827168 | − | 0.561955i | \(-0.189951\pi\) |
−0.900251 | + | 0.435370i | \(0.856617\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.5797 | − | 16.4293i | 0.645172 | − | 0.541363i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.153581 | − | 0.266010i | 0.00505518 | − | 0.00875583i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.0257 | − | 13.1123i | −1.18452 | − | 0.431130i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.15657 | − | 6.55926i | −0.0379869 | − | 0.215434i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3384 | + | 19.5833i | 0.765709 | + | 0.642506i | 0.939606 | − | 0.342258i | \(-0.111192\pi\) |
−0.173897 | + | 0.984764i | \(0.555636\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.5795 | + | 20.4162i | −0.707239 | + | 0.669112i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.94743 | − | 6.66869i | −0.260187 | − | 0.218323i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.36319 | + | 30.4162i | 0.175395 | + | 0.994715i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.34477 | + | 0.489456i | 0.0439317 | + | 0.0159898i | 0.363893 | − | 0.931441i | \(-0.381448\pi\) |
−0.319961 | + | 0.947431i | \(0.603670\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.71823 | − | 13.3684i | 0.251875 | − | 0.436260i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.47384 | − | 2.91490i | 0.113244 | − | 0.0950230i | −0.584407 | − | 0.811460i | \(-0.698673\pi\) |
0.697651 | + | 0.716437i | \(0.254229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.8405 | + | 53.4173i | 1.00430 | + | 1.73951i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.27972 | − | 12.9289i | 0.0741591 | − | 0.420577i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.388881 | − | 0.141541i | 0.0126369 | − | 0.00459946i | −0.335694 | − | 0.941971i | \(-0.608971\pi\) |
0.348331 | + | 0.937372i | \(0.386749\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.549935 | −0.0178516 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.3969 | 0.920833 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.3678 | + | 4.86549i | −0.433027 | + | 0.157609i | −0.549331 | − | 0.835605i | \(-0.685117\pi\) |
0.116304 | + | 0.993214i | \(0.462895\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.0633 | − | 62.7431i | 0.358000 | − | 2.03032i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −0.319078 | − | 0.552659i | −0.0103143 | − | 0.0178649i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.34667 | − | 1.12999i | 0.0434862 | − | 0.0364892i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.6309 | − | 18.4132i | 0.342932 | − | 0.593975i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.59879 | + | 2.76573i | 0.244868 | + | 0.0891245i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.6959 | + | 60.6597i | 0.344314 | + | 1.95270i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5376 | + | 36.5324i | 1.40008 | + | 1.17480i | 0.961066 | + | 0.276320i | \(0.0891150\pi\) |
0.439009 | + | 0.898482i | \(0.355329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.78446 | + | 4.29385i | 0.185824 | + | 0.137938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.94356 | + | 5.82634i | 0.222830 | + | 0.186976i | 0.747368 | − | 0.664411i | \(-0.231317\pi\) |
−0.524538 | + | 0.851387i | \(0.675762\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.57357 | − | 37.2806i | −0.210739 | − | 1.19516i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.59240 | + | 0.579585i | 0.0509975 | + | 0.0185616i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.32635 | − | 2.29731i | 0.0424338 | − | 0.0734974i | −0.844028 | − | 0.536298i | \(-0.819822\pi\) |
0.886462 | + | 0.462801i | \(0.153156\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −49.2674 | + | 41.3403i | −1.57459 | + | 1.32124i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.62449 | − | 13.2060i | −0.243431 | − | 0.421635i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.34183 | − | 52.9802i | 0.297958 | − | 1.68980i | −0.356972 | − | 0.934115i | \(-0.616191\pi\) |
0.654930 | − | 0.755690i | \(-0.272698\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −34.7863 | + | 12.6612i | −1.10838 | + | 0.403418i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.32863 | −0.296934 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −46.4820 | −1.47804 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.3598 | − | 18.3295i | 1.59973 | − | 0.582255i | 0.620360 | − | 0.784317i | \(-0.286986\pi\) |
0.979373 | + | 0.202062i | \(0.0647642\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.50134 | − | 25.5284i | 0.142846 | − | 0.810119i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.1129 | + | 41.7648i | 0.764431 | + | 1.32403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.8938 | − | 11.6583i | 0.440020 | − | 0.369221i | −0.395697 | − | 0.918381i | \(-0.629497\pi\) |
0.835717 | + | 0.549160i | \(0.185052\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.56418 | + | 4.44129i | −0.0811270 | + | 0.140516i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 912.2.bo.d.529.1 | 6 | ||
4.3 | odd | 2 | 114.2.i.c.73.1 | yes | 6 | ||
12.11 | even | 2 | 342.2.u.b.73.1 | 6 | |||
19.6 | even | 9 | inner | 912.2.bo.d.481.1 | 6 | ||
76.43 | odd | 18 | 2166.2.a.r.1.1 | 3 | |||
76.63 | odd | 18 | 114.2.i.c.25.1 | ✓ | 6 | ||
76.71 | even | 18 | 2166.2.a.p.1.1 | 3 | |||
228.71 | odd | 18 | 6498.2.a.bu.1.3 | 3 | |||
228.119 | even | 18 | 6498.2.a.bp.1.3 | 3 | |||
228.215 | even | 18 | 342.2.u.b.253.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.i.c.25.1 | ✓ | 6 | 76.63 | odd | 18 | ||
114.2.i.c.73.1 | yes | 6 | 4.3 | odd | 2 | ||
342.2.u.b.73.1 | 6 | 12.11 | even | 2 | |||
342.2.u.b.253.1 | 6 | 228.215 | even | 18 | |||
912.2.bo.d.481.1 | 6 | 19.6 | even | 9 | inner | ||
912.2.bo.d.529.1 | 6 | 1.1 | even | 1 | trivial | ||
2166.2.a.p.1.1 | 3 | 76.71 | even | 18 | |||
2166.2.a.r.1.1 | 3 | 76.43 | odd | 18 | |||
6498.2.a.bp.1.3 | 3 | 228.119 | even | 18 | |||
6498.2.a.bu.1.3 | 3 | 228.71 | odd | 18 |