Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3564,2,Mod(1189,3564)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3564, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3564.1189");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3564 = 2^{2} \cdot 3^{4} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3564.i (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.4586832804\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 18x^{9} + 152x^{8} - 204x^{7} + 162x^{6} - 408x^{5} + 2800x^{4} - 4422x^{3} + 3528x^{2} - 252x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2377.6 | ||
Root | \(1.48688 - 1.48688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3564.2377 |
Dual form | 3564.2.i.t.1189.6 |
$q$-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 \(\left(\mathbb{Z}/3564\mathbb{Z}\right)^\times\).
\(n\) | \(1541\) | \(1783\) | \(2917\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.03112 | − | 3.51801i | 0.908345 | − | 1.57330i | 0.0919827 | − | 0.995761i | \(-0.470680\pi\) |
0.816363 | − | 0.577540i | \(-0.195987\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.0326133 | + | 0.0564879i | 0.0123267 | + | 0.0213504i | 0.872123 | − | 0.489287i | \(-0.162743\pi\) |
−0.859796 | + | 0.510637i | \(0.829410\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.665097 | + | 1.15198i | −0.184465 | + | 0.319502i | −0.943396 | − | 0.331669i | \(-0.892388\pi\) |
0.758931 | + | 0.651171i | \(0.225722\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.03900 | 0.494529 | 0.247265 | − | 0.968948i | \(-0.420468\pi\) | ||||
0.247265 | + | 0.968948i | \(0.420468\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0245009 | −0.00562088 | −0.00281044 | − | 0.999996i | \(-0.500895\pi\) | ||||
−0.00281044 | + | 0.999996i | \(0.500895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.08825 | − | 1.88490i | 0.226915 | − | 0.393028i | −0.729977 | − | 0.683471i | \(-0.760469\pi\) |
0.956892 | + | 0.290443i | \(0.0938027\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.75091 | − | 9.96087i | −1.15018 | − | 1.99217i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00575 | − | 8.67021i | −0.929544 | − | 1.61002i | −0.784086 | − | 0.620653i | \(-0.786868\pi\) |
−0.145458 | − | 0.989364i | \(-0.546466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.22158 | + | 3.84790i | −0.399008 | + | 0.691103i | −0.993604 | − | 0.112922i | \(-0.963979\pi\) |
0.594595 | + | 0.804025i | \(0.297312\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.264966 | 0.0447875 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.48344 | 0.243875 | 0.121938 | − | 0.992538i | \(-0.461089\pi\) | ||||
0.121938 | + | 0.992538i | \(0.461089\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.77606 | − | 6.54033i | 0.589721 | − | 1.02143i | −0.404547 | − | 0.914517i | \(-0.632571\pi\) |
0.994269 | − | 0.106910i | \(-0.0340958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.82691 | − | 8.36045i | −0.736097 | − | 1.27496i | −0.954241 | − | 0.299040i | \(-0.903334\pi\) |
0.218144 | − | 0.975917i | \(-0.430000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.16360 | + | 10.6757i | 0.899053 | + | 1.55721i | 0.828707 | + | 0.559682i | \(0.189077\pi\) |
0.0703457 | + | 0.997523i | \(0.477590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.49787 | − | 6.05849i | 0.499696 | − | 0.865499i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.61780 | 0.496943 | 0.248472 | − | 0.968639i | \(-0.420072\pi\) | ||||
0.248472 | + | 0.968639i | \(0.420072\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.06224 | 0.547753 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.03922 | − | 8.72819i | 0.656051 | − | 1.13631i | −0.325578 | − | 0.945515i | \(-0.605559\pi\) |
0.981629 | − | 0.190799i | \(-0.0611078\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.07277 | + | 7.05424i | 0.521464 | + | 0.903203i | 0.999688 | + | 0.0249648i | \(0.00794738\pi\) |
−0.478224 | + | 0.878238i | \(0.658719\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.70178 | + | 4.67963i | 0.335115 | + | 0.580436i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.68781 | − | 2.92338i | 0.206199 | − | 0.357148i | −0.744315 | − | 0.667829i | \(-0.767224\pi\) |
0.950514 | + | 0.310681i | \(0.100557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.101239 | 0.0120149 | 0.00600745 | − | 0.999982i | \(-0.498088\pi\) | ||||
0.00600745 | + | 0.999982i | \(0.498088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.12217 | −0.950628 | −0.475314 | − | 0.879816i | \(-0.657666\pi\) | ||||
−0.475314 | + | 0.879816i | \(0.657666\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0326133 | + | 0.0564879i | −0.00371663 | + | 0.00643740i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.66096 | − | 6.34096i | −0.411890 | − | 0.713414i | 0.583207 | − | 0.812324i | \(-0.301798\pi\) |
−0.995096 | + | 0.0989099i | \(0.968464\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.94927 | + | 6.84033i | 0.433488 | + | 0.750824i | 0.997171 | − | 0.0751675i | \(-0.0239492\pi\) |
−0.563682 | + | 0.825992i | \(0.690616\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.14145 | − | 7.17320i | 0.449203 | − | 0.778043i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.48031 | −1.00491 | −0.502455 | − | 0.864603i | \(-0.667570\pi\) | ||||
−0.502455 | + | 0.864603i | \(0.667570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0867640 | −0.00909534 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0497642 | + | 0.0861942i | −0.00510570 | + | 0.00884334i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.31040 | − | 7.46583i | −0.437655 | − | 0.758040i | 0.559853 | − | 0.828592i | \(-0.310857\pi\) |
−0.997508 | + | 0.0705513i | \(0.977524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.11873 | − | 7.13385i | −0.409829 | − | 0.709845i | 0.585041 | − | 0.811004i | \(-0.301078\pi\) |
−0.994870 | + | 0.101159i | \(0.967745\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.26052 | − | 10.8435i | 0.616868 | − | 1.06845i | −0.373186 | − | 0.927757i | \(-0.621735\pi\) |
0.990054 | − | 0.140690i | \(-0.0449320\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.79084 | −0.849843 | −0.424921 | − | 0.905230i | \(-0.639698\pi\) | ||||
−0.424921 | + | 0.905230i | \(0.639698\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.99172 | −0.957033 | −0.478517 | − | 0.878079i | \(-0.658825\pi\) | ||||
−0.478517 | + | 0.878079i | \(0.658825\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.06725 | + | 3.58058i | −0.194470 | + | 0.336832i | −0.946727 | − | 0.322038i | \(-0.895632\pi\) |
0.752256 | + | 0.658870i | \(0.228965\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.42072 | − | 7.65691i | −0.412234 | − | 0.714011i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.0664984 | + | 0.115179i | 0.00609590 | + | 0.0105584i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | + | 0.866025i | −0.0454545 | + | 0.0787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −26.4120 | −2.36236 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.9661 | 1.23929 | 0.619644 | − | 0.784883i | \(-0.287277\pi\) | ||||
0.619644 | + | 0.784883i | \(0.287277\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.75431 | + | 16.8950i | −0.852238 | + | 1.47612i | 0.0269455 | + | 0.999637i | \(0.491422\pi\) |
−0.879184 | + | 0.476483i | \(0.841911\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.000799054 | − | 0.00138400i | −6.92868e−5 | − | 0.000120008i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.39744 | + | 7.61659i | 0.375699 | + | 0.650729i | 0.990431 | − | 0.138006i | \(-0.0440694\pi\) |
−0.614733 | + | 0.788736i | \(0.710736\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.71853 | − | 8.17273i | 0.400220 | − | 0.693202i | −0.593532 | − | 0.804810i | \(-0.702267\pi\) |
0.993752 | + | 0.111608i | \(0.0356002\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.33019 | −0.111236 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.6691 | −3.37739 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.62138 | − | 6.27242i | 0.296675 | − | 0.513856i | −0.678698 | − | 0.734417i | \(-0.737455\pi\) |
0.975373 | + | 0.220561i | \(0.0707888\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.51708 | − | 9.55586i | −0.448973 | − | 0.777645i | 0.549346 | − | 0.835595i | \(-0.314877\pi\) |
−0.998319 | + | 0.0579502i | \(0.981544\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.02462 | + | 15.6311i | 0.724875 | + | 1.25552i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.25444 | − | 2.17276i | 0.100116 | − | 0.173405i | −0.811617 | − | 0.584190i | \(-0.801412\pi\) |
0.911732 | + | 0.410785i | \(0.134745\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.141965 | 0.0111884 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.6456 | −0.990484 | −0.495242 | − | 0.868755i | \(-0.664921\pi\) | ||||
−0.495242 | + | 0.868755i | \(0.664921\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.55833 | + | 9.62731i | −0.430117 | + | 0.744984i | −0.996883 | − | 0.0788947i | \(-0.974861\pi\) |
0.566766 | + | 0.823879i | \(0.308194\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.61529 | + | 9.72597i | 0.431946 | + | 0.748152i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.573346 | − | 0.993065i | −0.0435907 | − | 0.0755013i | 0.843407 | − | 0.537275i | \(-0.180546\pi\) |
−0.886998 | + | 0.461774i | \(0.847213\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.375113 | − | 0.649714i | 0.0283558 | − | 0.0491138i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.480893 | 0.0359436 | 0.0179718 | − | 0.999838i | \(-0.494279\pi\) | ||||
0.0179718 | + | 0.999838i | \(0.494279\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.754827 | 0.0561058 | 0.0280529 | − | 0.999606i | \(-0.491069\pi\) | ||||
0.0280529 | + | 0.999606i | \(0.491069\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.01304 | − | 5.21874i | 0.221523 | − | 0.383689i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.01950 | + | 1.76582i | 0.0745531 | + | 0.129130i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.0071 | + | 19.0649i | 0.796449 | + | 1.37949i | 0.921915 | + | 0.387392i | \(0.126624\pi\) |
−0.125466 | + | 0.992098i | \(0.540043\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2957 | − | 23.0288i | 0.957043 | − | 1.65765i | 0.227420 | − | 0.973797i | \(-0.426971\pi\) |
0.729622 | − | 0.683850i | \(-0.239696\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.25967 | −0.0897476 | −0.0448738 | − | 0.998993i | \(-0.514289\pi\) | ||||
−0.0448738 | + | 0.998993i | \(0.514289\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0762801 | 0.00540735 | 0.00270368 | − | 0.999996i | \(-0.499139\pi\) | ||||
0.00270368 | + | 0.999996i | \(0.499139\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.326508 | − | 0.565528i | 0.0229164 | − | 0.0396923i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3393 | − | 26.5684i | −1.07134 | − | 1.85562i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0122504 | − | 0.0212184i | −0.000847380 | − | 0.00146771i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.52933 | − | 7.84503i | 0.311812 | − | 0.540074i | −0.666943 | − | 0.745109i | \(-0.732397\pi\) |
0.978755 | + | 0.205035i | \(0.0657308\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −39.2162 | −2.67452 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.289813 | −0.0196738 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.35613 | + | 2.34888i | −0.0912231 | + | 0.158003i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3912 | + | 17.9980i | 0.695844 | + | 1.20524i | 0.969895 | + | 0.243522i | \(0.0783028\pi\) |
−0.274051 | + | 0.961715i | \(0.588364\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.63856 | + | 16.6945i | 0.639734 | + | 1.10805i | 0.985491 | + | 0.169728i | \(0.0542888\pi\) |
−0.345757 | + | 0.938324i | \(0.612378\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.92345 | + | 5.06357i | −0.193187 | + | 0.334610i | −0.946305 | − | 0.323276i | \(-0.895216\pi\) |
0.753118 | + | 0.657886i | \(0.228549\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.58641 | 0.431490 | 0.215745 | − | 0.976450i | \(-0.430782\pi\) | ||||
0.215745 | + | 0.976450i | \(0.430782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 50.0761 | 3.26660 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.33037 | − | 5.76836i | 0.215423 | − | 0.373124i | −0.737980 | − | 0.674823i | \(-0.764220\pi\) |
0.953403 | + | 0.301698i | \(0.0975535\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.27308 | − | 3.93708i | −0.146422 | − | 0.253610i | 0.783481 | − | 0.621416i | \(-0.213442\pi\) |
−0.929902 | + | 0.367806i | \(0.880109\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.2092 | − | 24.6111i | −0.907793 | − | 1.57234i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0162954 | − | 0.0282245i | 0.00103685 | − | 0.00179588i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6963 | 0.675144 | 0.337572 | − | 0.941300i | \(-0.390394\pi\) | ||||
0.337572 | + | 0.941300i | \(0.390394\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.17649 | 0.136835 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.04104 | − | 10.4634i | 0.376829 | − | 0.652688i | −0.613770 | − | 0.789485i | \(-0.710348\pi\) |
0.990599 | + | 0.136797i | \(0.0436810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0483798 | + | 0.0837962i | 0.00300617 | + | 0.00520684i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.0327 | − | 17.3772i | −0.618643 | − | 1.07152i | −0.989734 | − | 0.142925i | \(-0.954349\pi\) |
0.371090 | − | 0.928597i | \(-0.378984\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.34820 | − | 12.7275i | 0.451396 | − | 0.781841i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.65060 | 0.100639 | 0.0503194 | − | 0.998733i | \(-0.483976\pi\) | ||||
0.0503194 | + | 0.998733i | \(0.483976\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.5070 | −1.30646 | −0.653229 | − | 0.757160i | \(-0.726586\pi\) | ||||
−0.653229 | + | 0.757160i | \(0.726586\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.75091 | − | 9.96087i | 0.346793 | − | 0.600663i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.1750 | − | 26.2839i | −0.911779 | − | 1.57925i | −0.811549 | − | 0.584284i | \(-0.801376\pi\) |
−0.100230 | − | 0.994964i | \(-0.531958\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5791 | + | 18.3235i | 0.631096 | + | 1.09309i | 0.987328 | + | 0.158693i | \(0.0507281\pi\) |
−0.356232 | + | 0.934398i | \(0.615939\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.6096 | + | 25.3046i | −0.868453 | + | 1.50420i | −0.00487508 | + | 0.999988i | \(0.501552\pi\) |
−0.863578 | + | 0.504216i | \(0.831782\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.492599 | 0.0290772 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8425 | −0.755441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.00172 | + | 8.66323i | −0.292204 | + | 0.506112i | −0.974331 | − | 0.225122i | \(-0.927722\pi\) |
0.682127 | + | 0.731234i | \(0.261055\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.4706 | − | 35.4560i | −1.19184 | − | 2.06433i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.44758 | + | 2.50728i | 0.0837155 | + | 0.145000i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.314843 | − | 0.545324i | 0.0181472 | − | 0.0314319i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 33.0891 | 1.89468 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.8466 | −1.64636 | −0.823182 | − | 0.567777i | \(-0.807804\pi\) | ||||
−0.823182 | + | 0.567777i | \(0.807804\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.5377 | − | 25.1801i | 0.824360 | − | 1.42783i | −0.0780481 | − | 0.996950i | \(-0.524869\pi\) |
0.902408 | − | 0.430883i | \(-0.141798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.82932 | + | 8.36462i | 0.272969 | + | 0.472797i | 0.969621 | − | 0.244613i | \(-0.0786610\pi\) |
−0.696652 | + | 0.717410i | \(0.745328\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.77307 | − | 16.9274i | −0.548910 | − | 0.950740i | −0.998350 | − | 0.0574294i | \(-0.981710\pi\) |
0.449439 | − | 0.893311i | \(-0.351624\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.00575 | − | 8.67021i | 0.280268 | − | 0.485438i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.0499571 | −0.00277969 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.2996 | 0.848672 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.402031 | + | 0.696337i | −0.0221647 | + | 0.0383903i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3490 | + | 17.9250i | 0.568832 | + | 0.985247i | 0.996682 | + | 0.0813966i | \(0.0259380\pi\) |
−0.427849 | + | 0.903850i | \(0.640729\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.85631 | − | 11.8755i | −0.374600 | − | 0.648827i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.8104 | + | 18.7242i | −0.588880 | + | 1.01997i | 0.405499 | + | 0.914095i | \(0.367098\pi\) |
−0.994379 | + | 0.105875i | \(0.966236\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.44317 | −0.240611 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.912895 | 0.0492917 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.9751 | − | 22.4735i | 0.696540 | − | 1.20644i | −0.273119 | − | 0.961980i | \(-0.588055\pi\) |
0.969659 | − | 0.244462i | \(-0.0786113\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.81880 | − | 15.2746i | −0.472059 | − | 0.817631i | 0.527430 | − | 0.849599i | \(-0.323156\pi\) |
−0.999489 | + | 0.0319680i | \(0.989823\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.728839 | + | 1.26239i | 0.0387922 | + | 0.0671900i | 0.884770 | − | 0.466029i | \(-0.154316\pi\) |
−0.845977 | + | 0.533219i | \(0.820982\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.205630 | − | 0.356161i | 0.0109137 | − | 0.0189031i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.4306 | 1.44773 | 0.723867 | − | 0.689940i | \(-0.242363\pi\) | ||||
0.723867 | + | 0.689940i | \(0.242363\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9994 | −0.999968 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −16.4971 | + | 28.5739i | −0.863499 | + | 1.49562i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7642 | + | 25.5724i | 0.770685 | + | 1.33487i | 0.937188 | + | 0.348825i | \(0.113419\pi\) |
−0.166503 | + | 0.986041i | \(0.553247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.117989 | + | 0.204362i | 0.00612566 | + | 0.0106100i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.60267 | − | 9.70410i | 0.290095 | − | 0.502459i | −0.683737 | − | 0.729729i | \(-0.739646\pi\) |
0.973832 | + | 0.227269i | \(0.0729797\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 13.3172 | 0.685872 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.5553 | 1.56952 | 0.784760 | − | 0.619799i | \(-0.212786\pi\) | ||||
0.784760 | + | 0.619799i | \(0.212786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.4138 | − | 24.9655i | 0.736512 | − | 1.27568i | −0.217545 | − | 0.976050i | \(-0.569805\pi\) |
0.954057 | − | 0.299626i | \(-0.0968618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.132483 | + | 0.229468i | 0.00675197 | + | 0.0116948i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.4694 | + | 26.7938i | 0.784329 | + | 1.35850i | 0.929399 | + | 0.369076i | \(0.120326\pi\) |
−0.145070 | + | 0.989421i | \(0.546341\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.21893 | − | 3.84330i | 0.112216 | − | 0.194364i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −29.7434 | −1.49655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.7282 | 1.09050 | 0.545252 | − | 0.838272i | \(-0.316434\pi\) | ||||
0.545252 | + | 0.838272i | \(0.316434\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5328 | − | 23.4396i | 0.675798 | − | 1.17052i | −0.300438 | − | 0.953801i | \(-0.597133\pi\) |
0.976235 | − | 0.216714i | \(-0.0695340\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.95514 | − | 5.11845i | −0.147206 | − | 0.254968i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.741718 | + | 1.28469i | 0.0367656 | + | 0.0636799i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.8406 | + | 32.6329i | −0.931610 | + | 1.61360i | −0.151039 | + | 0.988528i | \(0.548262\pi\) |
−0.780570 | + | 0.625068i | \(0.785071\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.657383 | 0.0323477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 32.0858 | 1.57503 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.14703 | − | 14.1111i | 0.398009 | − | 0.689371i | −0.595471 | − | 0.803376i | \(-0.703035\pi\) |
0.993480 | + | 0.114005i | \(0.0363681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.8369 | − | 22.2342i | −0.625633 | − | 1.08363i | −0.988418 | − | 0.151756i | \(-0.951507\pi\) |
0.362785 | − | 0.931873i | \(-0.381826\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.7261 | − | 20.3102i | −0.568799 | − | 0.985188i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.265653 | + | 0.460124i | −0.0128558 | + | 0.0222670i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2321 | 0.492861 | 0.246431 | − | 0.969160i | \(-0.420742\pi\) | ||||
0.246431 | + | 0.969160i | \(0.420742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.6352 | 0.943606 | 0.471803 | − | 0.881704i | \(-0.343603\pi\) | ||||
0.471803 | + | 0.881704i | \(0.343603\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.0266630 | + | 0.0461816i | −0.00127546 | + | 0.00220917i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.42212 | + | 14.5875i | 0.401966 | + | 0.696226i | 0.993963 | − | 0.109715i | \(-0.0349937\pi\) |
−0.591997 | + | 0.805940i | \(0.701660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.88022 | − | 10.1848i | −0.279378 | − | 0.483897i | 0.691852 | − | 0.722039i | \(-0.256795\pi\) |
−0.971230 | + | 0.238142i | \(0.923462\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −19.2557 | + | 33.3518i | −0.912806 | + | 1.58103i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 29.4906 | 1.39175 | 0.695873 | − | 0.718165i | \(-0.255018\pi\) | ||||
0.695873 | + | 0.718165i | \(0.255018\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.55212 | 0.355615 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.176228 | + | 0.305236i | −0.00826171 | + | 0.0143097i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5520 | + | 18.2766i | 0.493602 | + | 0.854944i | 0.999973 | − | 0.00737216i | \(-0.00234665\pi\) |
−0.506371 | + | 0.862316i | \(0.669013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.94710 | − | 8.56863i | −0.230409 | − | 0.399081i | 0.727519 | − | 0.686087i | \(-0.240673\pi\) |
−0.957929 | + | 0.287007i | \(0.907340\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6411 | − | 18.4308i | 0.494532 | − | 0.856554i | −0.505449 | − | 0.862857i | \(-0.668673\pi\) |
0.999980 | + | 0.00630289i | \(0.00200629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.29453 | 0.291276 | 0.145638 | − | 0.989338i | \(-0.453477\pi\) | ||||
0.145638 | + | 0.989338i | \(0.453477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.220181 | 0.0101670 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.82691 | − | 8.36045i | 0.221941 | − | 0.384414i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.140902 | + | 0.244050i | 0.00646504 | + | 0.0111978i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.0492 | + | 20.8699i | 0.550544 | + | 0.953570i | 0.998235 | + | 0.0593816i | \(0.0189129\pi\) |
−0.447692 | + | 0.894188i | \(0.647754\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.986628 | + | 1.70889i | −0.0449864 | + | 0.0779187i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −35.0198 | −1.59017 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0710 | −0.456359 | −0.228180 | − | 0.973619i | \(-0.573277\pi\) | ||||
−0.228180 | + | 0.973619i | \(0.573277\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0667 | + | 17.4361i | −0.454305 | + | 0.786879i | −0.998648 | − | 0.0519833i | \(-0.983446\pi\) |
0.544343 | + | 0.838863i | \(0.316779\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2067 | − | 17.6785i | −0.459686 | − | 0.796200i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.00330175 | + | 0.00571880i | 0.000148104 | + | 0.000256523i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.65567 | − | 13.2600i | 0.342715 | − | 0.593600i | −0.642221 | − | 0.766520i | \(-0.721987\pi\) |
0.984936 | + | 0.172920i | \(0.0553201\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.52374 | −0.0679401 | −0.0339701 | − | 0.999423i | \(-0.510815\pi\) | ||||
−0.0339701 | + | 0.999423i | \(0.510815\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.4626 | −1.48907 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.1477 | + | 27.9687i | −0.715736 | + | 1.23969i | 0.246939 | + | 0.969031i | \(0.420575\pi\) |
−0.962675 | + | 0.270660i | \(0.912758\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.264891 | − | 0.458805i | −0.0117181 | − | 0.0202963i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.4318 | − | 44.0491i | −1.12066 | − | 1.94104i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.16360 | + | 10.6757i | −0.271075 | + | 0.469515i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.21862 | 0.403875 | 0.201937 | − | 0.979398i | \(-0.435276\pi\) | ||||
0.201937 | + | 0.979398i | \(0.435276\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.5934 | 1.07539 | 0.537697 | − | 0.843138i | \(-0.319295\pi\) | ||||
0.537697 | + | 0.843138i | \(0.319295\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.52980 | + | 7.84585i | −0.197321 | + | 0.341770i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.13144 | + | 15.8161i | 0.397019 | + | 0.687657i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.02289 | + | 8.69990i | 0.217565 | + | 0.376834i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −17.8553 | + | 30.9262i | −0.771951 | + | 1.33706i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.99575 | 0.301328 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.7563 | −1.27933 | −0.639663 | − | 0.768656i | \(-0.720926\pi\) | ||||
−0.639663 | + | 0.768656i | \(0.720926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.2944 | + | 35.1509i | −0.869317 | + | 1.50570i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8796 | + | 25.7722i | 0.636206 | + | 1.10194i | 0.986258 | + | 0.165211i | \(0.0528304\pi\) |
−0.350053 | + | 0.936730i | \(0.613836\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.122645 | + | 0.212428i | 0.00522486 | + | 0.00904972i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.238792 | − | 0.413600i | 0.0101545 | − | 0.0175880i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.85395 | 0.120926 | 0.0604628 | − | 0.998170i | \(-0.480742\pi\) | ||||
0.0604628 | + | 0.998170i | \(0.480742\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.8414 | 0.543135 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.4188 | + | 35.3664i | −0.860551 | + | 1.49052i | 0.0108475 | + | 0.999941i | \(0.496547\pi\) |
−0.871398 | + | 0.490576i | \(0.836786\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.39766 | + | 14.5452i | 0.353292 | + | 0.611920i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.02267 | − | 10.4316i | −0.252483 | − | 0.437314i | 0.711726 | − | 0.702458i | \(-0.247914\pi\) |
−0.964209 | + | 0.265144i | \(0.914581\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.28430 | − | 12.6168i | 0.304839 | − | 0.527996i | −0.672387 | − | 0.740200i | \(-0.734731\pi\) |
0.977225 | + | 0.212204i | \(0.0680642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.0336 | −1.04397 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.5694 | −1.60567 | −0.802834 | − | 0.596203i | \(-0.796675\pi\) | ||||
−0.802834 | + | 0.596203i | \(0.796675\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.257597 | + | 0.446172i | −0.0106869 | + | 0.0185103i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.80890 | + | 3.13311i | 0.0749170 | + | 0.129760i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.47077 | − | 16.4039i | −0.390900 | − | 0.677060i | 0.601668 | − | 0.798746i | \(-0.294503\pi\) |
−0.992569 | + | 0.121687i | \(0.961170\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.0544307 | − | 0.0942768i | 0.00224278 | − | 0.00388461i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.4929 | 1.21113 | 0.605564 | − | 0.795797i | \(-0.292948\pi\) | ||||
0.605564 | + | 0.795797i | \(0.292948\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.540265 | 0.0221487 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.95571 | + | 12.0476i | −0.284202 | + | 0.492253i | −0.972415 | − | 0.233256i | \(-0.925062\pi\) |
0.688213 | + | 0.725509i | \(0.258395\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.57465 | + | 14.8517i | 0.349767 | + | 0.605815i | 0.986208 | − | 0.165511i | \(-0.0529274\pi\) |
−0.636441 | + | 0.771326i | \(0.719594\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.03112 | + | 3.51801i | 0.0825768 | + | 0.143027i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0161 | − | 31.2047i | 0.731249 | − | 1.26656i | −0.225101 | − | 0.974336i | \(-0.572271\pi\) |
0.956350 | − | 0.292225i | \(-0.0943956\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.3975 | −0.663374 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.24646 | 0.211903 | 0.105951 | − | 0.994371i | \(-0.466211\pi\) | ||||
0.105951 | + | 0.994371i | \(0.466211\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.9328 | + | 37.9886i | −0.882979 | + | 1.52937i | −0.0349672 | + | 0.999388i | \(0.511133\pi\) |
−0.848012 | + | 0.529977i | \(0.822201\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.75213 | + | 3.03477i | 0.0704240 | + | 0.121978i | 0.899087 | − | 0.437770i | \(-0.144231\pi\) |
−0.828663 | + | 0.559748i | \(0.810898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.309184 | − | 0.535523i | −0.0123872 | − | 0.0214553i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.8914 | + | 43.1132i | −0.995657 | + | 1.72453i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.02472 | 0.120603 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.01155 | 0.0402690 | 0.0201345 | − | 0.999797i | \(-0.493591\pi\) | ||||
0.0201345 | + | 0.999797i | \(0.493591\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.3668 | − | 49.1327i | 1.12570 | − | 1.94977i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.65285 | + | 8.05897i | 0.184352 | + | 0.319308i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22.0619 | + | 38.2124i | 0.871394 | + | 1.50930i | 0.860555 | + | 0.509357i | \(0.170117\pi\) |
0.0108390 | + | 0.999941i | \(0.496550\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.4009 | − | 37.0674i | 0.843969 | − | 1.46180i | −0.0425451 | − | 0.999095i | \(-0.513547\pi\) |
0.886514 | − | 0.462702i | \(-0.153120\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.3725 | 1.46926 | 0.734632 | − | 0.678466i | \(-0.237355\pi\) | ||||
0.734632 | + | 0.678466i | \(0.237355\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0784 | 0.395614 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.997227 | − | 1.72725i | 0.0390245 | − | 0.0675924i | −0.845853 | − | 0.533415i | \(-0.820908\pi\) |
0.884878 | + | 0.465823i | \(0.154242\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 39.6244 | + | 68.6315i | 1.54825 | + | 2.68165i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.8763 | + | 37.8909i | 0.852180 | + | 1.47602i | 0.879237 | + | 0.476385i | \(0.158053\pi\) |
−0.0270565 | + | 0.999634i | \(0.508613\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.94013 | + | 8.55656i | −0.192149 | + | 0.332811i | −0.945962 | − | 0.324277i | \(-0.894879\pi\) |
0.753813 | + | 0.657089i | \(0.228212\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.00649191 | −0.000251745 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.7899 | −0.843709 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.07277 | + | 7.05424i | −0.157227 | + | 0.272326i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.9386 | + | 34.5347i | 0.768578 | + | 1.33122i | 0.938334 | + | 0.345730i | \(0.112369\pi\) |
−0.169757 | + | 0.985486i | \(0.554298\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −14.6321 | − | 25.3436i | −0.562358 | − | 0.974033i | −0.997290 | − | 0.0735697i | \(-0.976561\pi\) |
0.434932 | − | 0.900463i | \(-0.356772\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.281153 | − | 0.486971i | 0.0107897 | − | 0.0186882i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.8274 | −0.605618 | −0.302809 | − | 0.953051i | \(-0.597924\pi\) | ||||
−0.302809 | + | 0.953051i | \(0.597924\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.7269 | 1.36506 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.40619 | + | 4.16764i | −0.0916685 | + | 0.158774i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.5082 | + | 33.7891i | 0.742126 | + | 1.28540i | 0.951526 | + | 0.307569i | \(0.0995157\pi\) |
−0.209400 | + | 0.977830i | \(0.567151\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.1678 | − | 33.1996i | −0.727077 | − | 1.25933i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.69937 | − | 13.3357i | 0.291634 | − | 0.505125i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.8646 | 0.410350 | 0.205175 | − | 0.978725i | \(-0.434224\pi\) | ||||
0.205175 | + | 0.978725i | \(0.434224\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.0363455 | −0.00137079 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.268651 | − | 0.465317i | 0.0101037 | − | 0.0175001i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.3842 | − | 21.4501i | −0.465099 | − | 0.805575i | 0.534107 | − | 0.845417i | \(-0.320648\pi\) |
−0.999206 | + | 0.0398420i | \(0.987315\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.83526 | + | 8.37492i | 0.181082 | + | 0.313643i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.70178 | + | 4.67963i | −0.101041 | + | 0.175008i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.2606 | −1.68794 | −0.843968 | − | 0.536393i | \(-0.819787\pi\) | ||||
−0.843968 | + | 0.536393i | \(0.819787\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.816706 | 0.0304157 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −57.5752 | + | 99.7232i | −2.13829 | + | 3.70363i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2434 | + | 21.2062i | 0.454082 | + | 0.786493i | 0.998635 | − | 0.0522333i | \(-0.0166339\pi\) |
−0.544553 | + | 0.838727i | \(0.683301\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.84204 | − | 17.0469i | −0.364021 | − | 0.630503i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.1709 | − | 29.7409i | 0.634221 | − | 1.09850i | −0.352458 | − | 0.935828i | \(-0.614654\pi\) |
0.986680 | − | 0.162676i | \(-0.0520126\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.37563 | 0.124343 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.6418 | −0.943250 | −0.471625 | − | 0.881799i | \(-0.656332\pi\) | ||||
−0.471625 | + | 0.881799i | \(0.656332\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −12.6008 | + | 21.8252i | −0.462277 | + | 0.800688i | −0.999074 | − | 0.0430239i | \(-0.986301\pi\) |
0.536797 | + | 0.843712i | \(0.319634\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.7109 | − | 25.4801i | −0.538967 | − | 0.933518i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.286698 | − | 0.496576i | −0.0104757 | − | 0.0181445i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.4245 | + | 37.1084i | −0.781792 | + | 1.35410i | 0.149105 | + | 0.988821i | \(0.452361\pi\) |
−0.930897 | + | 0.365282i | \(0.880973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.8234 | −1.63129 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.4265 | 1.17856 | 0.589280 | − | 0.807929i | \(-0.299412\pi\) | ||||
0.589280 | + | 0.807929i | \(0.299412\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.121551 | − | 0.210533i | 0.00440623 | − | 0.00763182i | −0.863814 | − | 0.503811i | \(-0.831931\pi\) |
0.868220 | + | 0.496179i | \(0.165264\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.325863 | − | 0.564411i | −0.0117970 | − | 0.0204331i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.70314 | + | 11.6102i | 0.242036 | + | 0.419219i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.99151 | + | 13.8417i | −0.288181 | + | 0.499145i | −0.973376 | − | 0.229216i | \(-0.926384\pi\) |
0.685194 | + | 0.728360i | \(0.259717\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 27.0172 | 0.971740 | 0.485870 | − | 0.874031i | \(-0.338503\pi\) | ||||
0.485870 | + | 0.874031i | \(0.338503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 51.1046 | 1.83573 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0925167 | + | 0.160244i | −0.00331475 | + | 0.00574132i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0506197 | + | 0.0876759i | 0.00181132 | + | 0.00313729i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.09586 | − | 8.82628i | −0.181879 | − | 0.315024i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.58984 | + | 6.21779i | −0.127964 | + | 0.221640i | −0.922888 | − | 0.385069i | \(-0.874178\pi\) |
0.794924 | + | 0.606710i | \(0.207511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.269679 | −0.00958868 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.8351 | −0.384767 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 17.9938 | − | 31.1662i | 0.637374 | − | 1.10396i | −0.348632 | − | 0.937260i | \(-0.613354\pi\) |
0.986007 | − | 0.166705i | \(-0.0533129\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.5675 | + | 21.7676i | 0.444608 | + | 0.770083i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.06109 | − | 7.03401i | −0.143313 | − | 0.248225i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.288349 | − | 0.499434i | 0.0101630 | − | 0.0176028i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.20307 | 0.288405 | 0.144202 | − | 0.989548i | \(-0.453938\pi\) | ||||
0.144202 | + | 0.989548i | \(0.453938\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.6156 | −0.864371 | −0.432185 | − | 0.901785i | \(-0.642257\pi\) | ||||
−0.432185 | + | 0.901785i | \(0.642257\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.6849 | + | 44.4875i | −0.899701 | + | 1.55833i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.118263 | + | 0.204838i | 0.00413751 | + | 0.00716638i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.8497 | − | 27.4524i | −0.553157 | − | 0.958096i | −0.998044 | − | 0.0625094i | \(-0.980090\pi\) |
0.444887 | − | 0.895586i | \(-0.353244\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1219 | + | 24.4598i | −0.492257 | + | 0.852615i | −0.999960 | − | 0.00891743i | \(-0.997161\pi\) |
0.507703 | + | 0.861532i | \(0.330495\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.57682 | −0.333019 | −0.166509 | − | 0.986040i | \(-0.553250\pi\) | ||||
−0.166509 | + | 0.986040i | \(0.553250\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.0188 | −0.799478 | −0.399739 | − | 0.916629i | \(-0.630899\pi\) | ||||
−0.399739 | + | 0.916629i | \(0.630899\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.13215 | − | 12.3532i | 0.247114 | − | 0.428014i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.5793 | + | 39.1085i | 0.781389 | + | 1.35341i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9156 | − | 22.3704i | −0.445895 | − | 0.772313i | 0.552219 | − | 0.833699i | \(-0.313781\pi\) |
−0.998114 | + | 0.0613862i | \(0.980448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.6150 | + | 61.6870i | −1.22810 | + | 2.12714i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.6214 | 1.56942 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0652266 | −0.00224121 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.61434 | − | 2.79612i | 0.0553390 | − | 0.0958499i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.47755 | − | 9.48739i | −0.187548 | − | 0.324842i | 0.756884 | − | 0.653549i | \(-0.226721\pi\) |
−0.944432 | + | 0.328707i | \(0.893387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.8972 | + | 37.9271i | 0.747994 | + | 1.29556i | 0.948783 | + | 0.315929i | \(0.102316\pi\) |
−0.200789 | + | 0.979635i | \(0.564350\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5803 | + | 21.7897i | −0.429233 | + | 0.743454i | −0.996805 | − | 0.0798697i | \(-0.974550\pi\) |
0.567572 | + | 0.823324i | \(0.307883\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 10.9731 | 0.373528 | 0.186764 | − | 0.982405i | \(-0.440200\pi\) | ||||
0.186764 | + | 0.982405i | \(0.440200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.65814 | −0.158382 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.66096 | − | 6.34096i | 0.124189 | − | 0.215102i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.24512 | + | 3.88866i | 0.0760729 | + | 0.131762i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.861383 | − | 1.49196i | −0.0291201 | − | 0.0504374i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.9602 | − | 18.9836i | 0.370099 | − | 0.641031i | −0.619481 | − | 0.785011i | \(-0.712657\pi\) |
0.989580 | + | 0.143981i | \(0.0459903\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.9225 | 0.671205 | 0.335602 | − | 0.942004i | \(-0.391060\pi\) | ||||
0.335602 | + | 0.942004i | \(0.391060\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.61989 | 0.155472 | 0.0777359 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777359 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.3789 | − | 45.6896i | 0.885717 | − | 1.53411i | 0.0408269 | − | 0.999166i | \(-0.487001\pi\) |
0.844890 | − | 0.534940i | \(-0.179666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.455480 | + | 0.788914i | 0.0152763 | + | 0.0264593i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.151013 | − | 0.261563i | −0.00505347 | − | 0.00875287i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.976752 | − | 1.69178i | 0.0326492 | − | 0.0565501i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.4828 | 1.48358 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.37668 | 0.245753 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.53314 | − | 2.65548i | 0.0509635 | − | 0.0882713i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1686 | + | 19.3446i | 0.370848 | + | 0.642328i | 0.989696 | − | 0.143183i | \(-0.0457337\pi\) |
−0.618848 | + | 0.785511i | \(0.712400\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2343 | + | 26.3865i | 0.504733 | + | 0.874224i | 0.999985 | + | 0.00547419i | \(0.00174250\pi\) |
−0.495252 | + | 0.868750i | \(0.664924\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.94927 | + | 6.84033i | −0.130702 | + | 0.226382i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.27248 | −0.0420210 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.9543 | −1.25200 | −0.625998 | − | 0.779824i | \(-0.715308\pi\) | ||||
−0.625998 | + | 0.779824i | \(0.715308\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.0673340 | + | 0.116626i | −0.00221633 | + | 0.00383879i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.53111 | − | 14.7763i | −0.280501 | − | 0.485842i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.36910 | − | 4.10341i | −0.0777278 | − | 0.134628i | 0.824541 | − | 0.565802i | \(-0.191433\pi\) |
−0.902269 | + | 0.431173i | \(0.858100\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.0857009 | + | 0.148438i | −0.00280873 | + | 0.00486487i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.28290 | 0.270880 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.7283 | −0.840507 | −0.420254 | − | 0.907407i | \(-0.638059\pi\) | ||||
−0.420254 | + | 0.907407i | \(0.638059\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0752 | + | 34.7712i | −0.654432 | + | 1.13351i | 0.327603 | + | 0.944815i | \(0.393759\pi\) |
−0.982036 | + | 0.188695i | \(0.939574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −8.21856 | − | 14.2350i | −0.267633 | − | 0.463554i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.05784 | + | 1.83224i | 0.0343753 | + | 0.0595397i | 0.882701 | − | 0.469935i | \(-0.155723\pi\) |
−0.848326 | + | 0.529474i | \(0.822389\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.40203 | − | 9.35659i | 0.175357 | − | 0.303728i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0206 | 1.94426 | 0.972129 | − | 0.234448i | \(-0.0753282\pi\) | ||||
0.972129 | + | 0.234448i | \(0.0753282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 89.4274 | 2.89380 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.286830 | + | 0.496804i | −0.00926223 | + | 0.0160427i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.62913 | + | 9.74993i | 0.181585 | + | 0.314514i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.0102 | − | 93.5485i | −1.73865 | − | 3.01143i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.12794 | + | 5.41776i | −0.100588 | + | 0.174223i | −0.911927 | − | 0.410352i | \(-0.865406\pi\) |
0.811339 | + | 0.584576i | \(0.198739\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5467 | 0.755649 | 0.377825 | − | 0.925877i | \(-0.376672\pi\) | ||||
0.377825 | + | 0.925877i | \(0.376672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.615547 | 0.0197335 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.6751 | − | 41.0065i | 0.757434 | − | 1.31191i | −0.186721 | − | 0.982413i | \(-0.559786\pi\) |
0.944155 | − | 0.329501i | \(-0.106881\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.74015 | − | 8.21019i | −0.151496 | − | 0.262399i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.35029 | + | 9.26698i | 0.170648 | + | 0.295571i | 0.938647 | − | 0.344881i | \(-0.112081\pi\) |
−0.767999 | + | 0.640451i | \(0.778747\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.55854 | + | 4.43152i | −0.0815218 | + | 0.141200i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.0114 | −0.668125 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.54573 | −0.271464 | −0.135732 | − | 0.990746i | \(-0.543339\pi\) | ||||
−0.135732 | + | 0.990746i | \(0.543339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.154934 | − | 0.268354i | 0.00491174 | − | 0.00850739i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.3913 | + | 21.4623i | 0.392436 | + | 0.679719i | 0.992770 | − | 0.120030i | \(-0.0382992\pi\) |
−0.600334 | + | 0.799749i | \(0.704966\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3564.2.i.t.2377.6 | 12 | ||
3.2 | odd | 2 | 3564.2.i.s.2377.1 | 12 | |||
9.2 | odd | 6 | 3564.2.i.s.1189.1 | 12 | |||
9.4 | even | 3 | 3564.2.a.o.1.1 | ✓ | 6 | ||
9.5 | odd | 6 | 3564.2.a.p.1.6 | yes | 6 | ||
9.7 | even | 3 | inner | 3564.2.i.t.1189.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3564.2.a.o.1.1 | ✓ | 6 | 9.4 | even | 3 | ||
3564.2.a.p.1.6 | yes | 6 | 9.5 | odd | 6 | ||
3564.2.i.s.1189.1 | 12 | 9.2 | odd | 6 | |||
3564.2.i.s.2377.1 | 12 | 3.2 | odd | 2 | |||
3564.2.i.t.1189.6 | 12 | 9.7 | even | 3 | inner | ||
3564.2.i.t.2377.6 | 12 | 1.1 | even | 1 | trivial |