Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [828,2,Mod(73,828)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(828, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("828.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 828 = 2^{2} \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 828.q (of order \(11\), degree \(10\), 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: | \(6.61161328736\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{11})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + 15500 x^{12} - 28190 x^{11} + 41920 x^{10} - 33520 x^{9} - 13837 x^{8} + \cdots + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 276) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{11}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(1.84381 - 0.541390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 828.289 |
Dual form | 828.2.q.c.361.2 |
$q$-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 \(\left(\mathbb{Z}/828\mathbb{Z}\right)^\times\).
\(n\) | \(415\) | \(461\) | \(649\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{11}\right)\) |
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 | ||||||||
\(5\) | 1.21471 | − | 2.65985i | 0.543235 | − | 1.18952i | −0.416635 | − | 0.909074i | \(-0.636791\pi\) |
0.959870 | − | 0.280445i | \(-0.0904822\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.960219 | + | 0.281946i | 0.362929 | + | 0.106566i | 0.458113 | − | 0.888894i | \(-0.348526\pi\) |
−0.0951837 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.65056 | − | 1.90485i | 0.497662 | − | 0.574333i | −0.450235 | − | 0.892910i | \(-0.648660\pi\) |
0.947897 | + | 0.318578i | \(0.103205\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.463267 | − | 0.136028i | 0.128487 | − | 0.0377273i | −0.216857 | − | 0.976203i | \(-0.569580\pi\) |
0.345344 | + | 0.938476i | \(0.387762\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.446491 | − | 3.10542i | −0.108290 | − | 0.753174i | −0.969529 | − | 0.244975i | \(-0.921220\pi\) |
0.861239 | − | 0.508199i | \(-0.169689\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0786963 | + | 0.547345i | −0.0180542 | + | 0.125569i | −0.996855 | − | 0.0792435i | \(-0.974750\pi\) |
0.978801 | + | 0.204813i | \(0.0656586\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.87251 | + | 2.82908i | −0.807473 | + | 0.589904i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.32496 | − | 2.68314i | −0.464991 | − | 0.536628i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0173123 | + | 0.120410i | 0.00321482 | + | 0.0223596i | 0.991366 | − | 0.131126i | \(-0.0418592\pi\) |
−0.988151 | + | 0.153486i | \(0.950950\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92752 | − | 4.45205i | 1.24422 | − | 0.799611i | 0.258175 | − | 0.966098i | \(-0.416879\pi\) |
0.986044 | + | 0.166487i | \(0.0532424\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.91632 | − | 2.21155i | 0.323917 | − | 0.373821i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.95959 | − | 8.67029i | −0.650952 | − | 1.42539i | −0.890718 | − | 0.454556i | \(-0.849798\pi\) |
0.239766 | − | 0.970831i | \(-0.422929\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.578290 | − | 1.26628i | 0.0903137 | − | 0.197760i | −0.859085 | − | 0.511833i | \(-0.828967\pi\) |
0.949399 | + | 0.314074i | \(0.101694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.21923 | + | 3.35419i | 0.795925 | + | 0.511510i | 0.874284 | − | 0.485415i | \(-0.161332\pi\) |
−0.0783589 | + | 0.996925i | \(0.524968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.69831 | −1.26878 | −0.634389 | − | 0.773014i | \(-0.718748\pi\) | ||||
−0.634389 | + | 0.773014i | \(0.718748\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.04625 | − | 3.24303i | −0.720892 | − | 0.463289i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.41370 | + | 2.17686i | 1.01835 | + | 0.299015i | 0.747965 | − | 0.663738i | \(-0.231031\pi\) |
0.270385 | + | 0.962752i | \(0.412849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.06165 | − | 6.70407i | −0.412832 | − | 0.903976i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.227334 | + | 0.0667513i | −0.0295964 | + | 0.00869028i | −0.296497 | − | 0.955034i | \(-0.595819\pi\) |
0.266901 | + | 0.963724i | \(0.414000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.54102 | + | 0.990353i | −0.197307 | + | 0.126802i | −0.635564 | − | 0.772048i | \(-0.719232\pi\) |
0.438257 | + | 0.898850i | \(0.355596\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.200924 | − | 1.39745i | 0.0249215 | − | 0.173333i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.83195 | + | 2.11418i | 0.223808 | + | 0.258288i | 0.856538 | − | 0.516084i | \(-0.172611\pi\) |
−0.632730 | + | 0.774373i | \(0.718065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.51699 | + | 8.67507i | 0.892103 | + | 1.02954i | 0.999376 | + | 0.0353118i | \(0.0112424\pi\) |
−0.107274 | + | 0.994230i | \(0.534212\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.94856 | − | 13.5525i | 0.228061 | − | 1.58620i | −0.478200 | − | 0.878251i | \(-0.658711\pi\) |
0.706261 | − | 0.707951i | \(-0.250380\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.12196 | − | 1.36370i | 0.241820 | − | 0.155408i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.3977 | − | 4.81479i | 1.84488 | − | 0.541706i | 0.844903 | − | 0.534919i | \(-0.179658\pi\) |
0.999977 | − | 0.00678681i | \(-0.00216032\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.34983 | + | 7.33511i | 0.367692 | + | 0.805133i | 0.999548 | + | 0.0300477i | \(0.00956591\pi\) |
−0.631857 | + | 0.775085i | \(0.717707\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.80229 | − | 2.58458i | −0.954742 | − | 0.280338i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.15453 | − | 2.66995i | −0.440379 | − | 0.283015i | 0.301604 | − | 0.953433i | \(-0.402478\pi\) |
−0.741983 | + | 0.670419i | \(0.766114\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.483191 | 0.0506522 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.36026 | + | 0.874186i | 0.139560 | + | 0.0896896i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.49214 | + | 14.2158i | −0.659177 | + | 1.44340i | 0.224109 | + | 0.974564i | \(0.428053\pi\) |
−0.883287 | + | 0.468833i | \(0.844675\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.35100 | + | 2.95829i | 0.134430 | + | 0.294361i | 0.964861 | − | 0.262761i | \(-0.0846330\pi\) |
−0.830431 | + | 0.557121i | \(0.811906\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.917997 | − | 1.05943i | 0.0904529 | − | 0.104388i | −0.708719 | − | 0.705491i | \(-0.750726\pi\) |
0.799172 | + | 0.601103i | \(0.205272\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.44978 | − | 5.43034i | 0.816871 | − | 0.524971i | −0.0642102 | − | 0.997936i | \(-0.520453\pi\) |
0.881081 | + | 0.472965i | \(0.156816\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.961777 | + | 6.68930i | 0.0921215 | + | 0.640719i | 0.982606 | + | 0.185705i | \(0.0594568\pi\) |
−0.890484 | + | 0.455014i | \(0.849634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.56447 | − | 7.57581i | −0.617534 | − | 0.712672i | 0.357703 | − | 0.933835i | \(-0.383560\pi\) |
−0.975237 | + | 0.221164i | \(0.929015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.82094 | + | 13.7368i | 0.263054 | + | 1.28096i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.446829 | − | 3.10777i | 0.0409608 | − | 0.284889i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.661368 | + | 4.59992i | 0.0601244 | + | 0.418174i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.06733 | − | 1.19428i | 0.363793 | − | 0.106819i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9350 | + | 12.6197i | −0.970327 | + | 1.11982i | 0.0224388 | + | 0.999748i | \(0.492857\pi\) |
−0.992766 | + | 0.120069i | \(0.961689\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.8070 | − | 4.05411i | −1.20633 | − | 0.354209i | −0.384057 | − | 0.923309i | \(-0.625474\pi\) |
−0.822268 | + | 0.569100i | \(0.807292\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.229887 | + | 0.503383i | −0.0199338 | + | 0.0436488i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.88176 | −0.160769 | −0.0803847 | − | 0.996764i | \(-0.525615\pi\) | ||||
−0.0803847 | + | 0.996764i | \(0.525615\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.46292 | 0.293721 | 0.146860 | − | 0.989157i | \(-0.453083\pi\) | ||||
0.146860 | + | 0.989157i | \(0.453083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.505538 | − | 1.10697i | 0.0422752 | − | 0.0925699i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.341302 | + | 0.100215i | 0.0283436 | + | 0.00832242i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.1256 | + | 16.3019i | −1.15722 | + | 1.33550i | −0.224678 | + | 0.974433i | \(0.572133\pi\) |
−0.932540 | + | 0.361067i | \(0.882412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.13983 | + | 0.921937i | −0.255516 | + | 0.0750262i | −0.406982 | − | 0.913436i | \(-0.633419\pi\) |
0.151466 | + | 0.988462i | \(0.451601\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.42682 | − | 23.8341i | −0.275249 | − | 1.91440i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.24424 | + | 22.5642i | −0.258919 | + | 1.80082i | 0.281649 | + | 0.959518i | \(0.409119\pi\) |
−0.540567 | + | 0.841301i | \(0.681790\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.51610 | + | 1.62470i | −0.355919 | + | 0.128044i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.91542 | + | 9.13488i | 0.619984 | + | 0.715499i | 0.975704 | − | 0.219093i | \(-0.0703099\pi\) |
−0.355720 | + | 0.934592i | \(0.615764\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.18059 | + | 8.21115i | 0.0913565 | + | 0.635398i | 0.983129 | + | 0.182914i | \(0.0585530\pi\) |
−0.891772 | + | 0.452484i | \(0.850538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7402 | + | 6.90230i | −0.826168 | + | 0.530946i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.5301 | + | 15.6146i | −1.02868 | + | 1.18716i | −0.0465543 | + | 0.998916i | \(0.514824\pi\) |
−0.982123 | + | 0.188241i | \(0.939721\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.47597 | − | 3.23192i | −0.111573 | − | 0.244310i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.61211 | + | 3.53002i | −0.120494 | + | 0.263846i | −0.960262 | − | 0.279100i | \(-0.909964\pi\) |
0.839768 | + | 0.542946i | \(0.182691\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.70576 | + | 4.30953i | 0.498435 | + | 0.320325i | 0.765590 | − | 0.643329i | \(-0.222447\pi\) |
−0.267155 | + | 0.963654i | \(0.586083\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −27.8714 | −2.04915 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.65230 | − | 4.27517i | −0.486464 | − | 0.312632i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2019 | + | 4.75730i | 1.17233 | + | 0.344226i | 0.809211 | − | 0.587518i | \(-0.199895\pi\) |
0.363116 | + | 0.931744i | \(0.381713\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.84842 | − | 19.3753i | −0.636923 | − | 1.39467i | −0.902547 | − | 0.430591i | \(-0.858305\pi\) |
0.265624 | − | 0.964077i | \(-0.414422\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 25.8424 | − | 7.58802i | 1.84120 | − | 0.540624i | 0.841196 | − | 0.540731i | \(-0.181852\pi\) |
1.00000 | 0.000106800i | \(3.39955e-5\pi\) | ||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.12918 | + | 3.93898i | −0.434486 | + | 0.279227i | −0.739546 | − | 0.673106i | \(-0.764960\pi\) |
0.305060 | + | 0.952333i | \(0.401323\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.0173255 | + | 0.120501i | −0.00121601 | + | 0.00845752i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.66565 | − | 3.07633i | −0.186177 | − | 0.214860i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.912714 | + | 1.05333i | 0.0631338 | + | 0.0728603i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.22131 | + | 15.4495i | −0.152921 | + | 1.06359i | 0.758369 | + | 0.651825i | \(0.225997\pi\) |
−0.911290 | + | 0.411765i | \(0.864913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.2615 | − | 9.80797i | 1.04083 | − | 0.668898i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.90717 | − | 2.32176i | 0.536774 | − | 0.157611i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.629267 | − | 1.37790i | −0.0423291 | − | 0.0926878i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.34888 | + | 0.396066i | 0.0903274 | + | 0.0265225i | 0.326584 | − | 0.945168i | \(-0.394102\pi\) |
−0.236257 | + | 0.971691i | \(0.575921\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.73511 | + | 2.40041i | 0.247908 | + | 0.159321i | 0.658694 | − | 0.752411i | \(-0.271109\pi\) |
−0.410786 | + | 0.911732i | \(0.634746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.67523 | −0.110702 | −0.0553512 | − | 0.998467i | \(-0.517628\pi\) | ||||
−0.0553512 | + | 0.998467i | \(0.517628\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.3038 | + | 11.7632i | 1.19912 | + | 0.770630i | 0.978804 | − | 0.204798i | \(-0.0656538\pi\) |
0.220319 | + | 0.975428i | \(0.429290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.5659 | + | 23.1362i | −0.689245 | + | 1.50924i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.72594 | + | 19.1071i | 0.564434 | + | 1.23594i | 0.949708 | + | 0.313136i | \(0.101380\pi\) |
−0.385274 | + | 0.922802i | \(0.625893\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.2462 | − | 19.9032i | 1.11093 | − | 1.28208i | 0.155182 | − | 0.987886i | \(-0.450404\pi\) |
0.955746 | − | 0.294194i | \(-0.0950510\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.7557 | + | 9.48290i | −0.942706 | + | 0.605840i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0379966 | + | 0.264272i | 0.00241766 | + | 0.0168152i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.0613 | + | 19.6898i | 1.07690 | + | 1.24281i | 0.968582 | + | 0.248693i | \(0.0800011\pi\) |
0.108318 | + | 0.994116i | \(0.465453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00283 | + | 12.0461i | −0.0630476 | + | 0.757331i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.12414 | − | 7.81860i | 0.0701222 | − | 0.487711i | −0.924252 | − | 0.381784i | \(-0.875310\pi\) |
0.994374 | − | 0.105927i | \(-0.0337810\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.35752 | − | 9.44177i | −0.0843523 | − | 0.586683i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8421 | + | 3.47716i | −0.730216 | + | 0.214411i | −0.625646 | − | 0.780107i | \(-0.715165\pi\) |
−0.104570 | + | 0.994518i | \(0.533347\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.7956 | − | 17.0751i | 0.908888 | − | 1.04891i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.7364 | − | 3.15249i | −0.654610 | − | 0.192211i | −0.0624710 | − | 0.998047i | \(-0.519898\pi\) |
−0.592139 | + | 0.805836i | \(0.701716\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.90135 | − | 21.6809i | 0.601464 | − | 1.31702i | −0.326797 | − | 0.945095i | \(-0.605969\pi\) |
0.928261 | − | 0.371929i | \(-0.121303\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.94844 | −0.539612 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −17.8542 | −1.07275 | −0.536376 | − | 0.843979i | \(-0.680207\pi\) | ||||
−0.536376 | + | 0.843979i | \(0.680207\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.687581 | − | 1.50559i | 0.0410176 | − | 0.0898161i | −0.888014 | − | 0.459817i | \(-0.847915\pi\) |
0.929032 | + | 0.370000i | \(0.120642\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.30907 | + | 0.384378i | 0.0778161 | + | 0.0228489i | 0.320409 | − | 0.947279i | \(-0.396180\pi\) |
−0.242593 | + | 0.970128i | \(0.577998\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.912307 | − | 1.05286i | 0.0538518 | − | 0.0621483i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.86713 | − | 2.01637i | 0.403949 | − | 0.118610i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.50932 | − | 10.4975i | −0.0881752 | − | 0.613272i | −0.985215 | − | 0.171322i | \(-0.945196\pi\) |
0.897040 | − | 0.441950i | \(-0.145713\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0985970 | + | 0.685757i | −0.00574054 | + | 0.0399263i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.40917 | + | 1.83739i | −0.0814946 | + | 0.106259i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.06590 | + | 4.69230i | 0.234355 | + | 0.270460i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.762294 | + | 5.30187i | 0.0436488 | + | 0.303584i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.68375 | + | 5.58071i | −0.495608 | + | 0.318508i | −0.764457 | − | 0.644674i | \(-0.776993\pi\) |
0.268849 | + | 0.963182i | \(0.413357\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.61609 | + | 5.32725i | −0.261755 | + | 0.302081i | −0.871380 | − | 0.490609i | \(-0.836774\pi\) |
0.609625 | + | 0.792690i | \(0.291320\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.939900 | + | 2.05809i | 0.0531263 | + | 0.116330i | 0.934334 | − | 0.356400i | \(-0.115996\pi\) |
−0.881207 | + | 0.472730i | \(0.843269\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.31835 | − | 2.88679i | 0.0740460 | − | 0.162138i | −0.868989 | − | 0.494831i | \(-0.835230\pi\) |
0.943035 | + | 0.332693i | \(0.107957\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.257938 | + | 0.165766i | 0.0144417 | + | 0.00928114i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.73487 | 0.0965308 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.44206 | − | 0.926754i | −0.0799909 | − | 0.0514071i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.35228 | − | 2.45245i | −0.460476 | − | 0.135208i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.63436 | − | 18.9066i | −0.474587 | − | 1.03920i | −0.983916 | − | 0.178629i | \(-0.942834\pi\) |
0.509329 | − | 0.860572i | \(-0.329894\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.84869 | − | 2.30458i | 0.428820 | − | 0.125913i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.9636 | + | 14.1152i | −1.19644 | + | 0.768902i | −0.978336 | − | 0.207024i | \(-0.933622\pi\) |
−0.218099 | + | 0.975927i | \(0.569986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.95381 | − | 20.5442i | 0.159958 | − | 1.11253i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.51864 | − | 9.83104i | −0.459963 | − | 0.530826i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.52379 | − | 8.68291i | −0.403898 | − | 0.466123i | 0.516967 | − | 0.856006i | \(-0.327061\pi\) |
−0.920865 | + | 0.389882i | \(0.872516\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.15887 | − | 28.9256i | 0.222619 | − | 1.54835i | −0.505456 | − | 0.862852i | \(-0.668676\pi\) |
0.728075 | − | 0.685497i | \(-0.240415\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.4206 | − | 17.6221i | 1.45945 | − | 0.937932i | 0.460721 | − | 0.887545i | \(-0.347591\pi\) |
0.998730 | − | 0.0503875i | \(-0.0160456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.2053 | − | 9.45634i | 1.70928 | − | 0.501890i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.1092 | + | 26.5155i | 0.639101 | + | 1.39944i | 0.900778 | + | 0.434280i | \(0.142997\pi\) |
−0.261678 | + | 0.965155i | \(0.584276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.9370 | + | 5.26677i | 0.944051 | + | 0.277198i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.6807 | − | 21.6453i | −1.76293 | − | 1.13296i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.4367 | −1.17119 | −0.585593 | − | 0.810605i | \(-0.699138\pi\) | ||||
−0.585593 | + | 0.810605i | \(0.699138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.50502 | + | 4.18053i | 0.337724 | + | 0.217042i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.65832 | + | 12.3900i | −0.292977 | + | 0.641530i | −0.997688 | − | 0.0679649i | \(-0.978349\pi\) |
0.704711 | + | 0.709495i | \(0.251077\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.0243993 | + | 0.0534271i | 0.00125663 | + | 0.00275163i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.03505 | + | 3.50264i | −0.155900 | + | 0.179918i | −0.828327 | − | 0.560246i | \(-0.810707\pi\) |
0.672426 | + | 0.740164i | \(0.265252\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −25.6052 | + | 16.4555i | −1.30837 | + | 0.840836i | −0.994097 | − | 0.108498i | \(-0.965396\pi\) |
−0.314269 | + | 0.949334i | \(0.601759\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.04967 | − | 7.30060i | −0.0534960 | − | 0.372073i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.96796 | + | 2.27115i | 0.0997797 | + | 0.115152i | 0.803443 | − | 0.595382i | \(-0.202999\pi\) |
−0.703663 | + | 0.710534i | \(0.748454\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5145 | + | 10.7626i | 0.531742 | + | 0.544287i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.11182 | − | 49.4638i | 0.357835 | − | 2.48879i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.38627 | + | 9.64170i | 0.0695747 | + | 0.483903i | 0.994582 | + | 0.103954i | \(0.0331494\pi\) |
−0.925007 | + | 0.379949i | \(0.875942\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.1560 | − | 5.62470i | 0.956603 | − | 0.280884i | 0.234069 | − | 0.972220i | \(-0.424796\pi\) |
0.722533 | + | 0.691336i | \(0.242978\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.60369 | − | 3.00482i | 0.129699 | − | 0.149681i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.0511 | − | 6.76841i | −1.14260 | − | 0.335498i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.1075 | − | 22.1323i | 0.499784 | − | 1.09437i | −0.476756 | − | 0.879036i | \(-0.658187\pi\) |
0.976540 | − | 0.215338i | \(-0.0690853\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.237111 | −0.0116675 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.5793 | 1.15746 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.43702 | + | 11.9054i | −0.265616 | + | 0.581618i | −0.994702 | − | 0.102805i | \(-0.967218\pi\) |
0.729086 | + | 0.684422i | \(0.239946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.86675 | + | 1.72263i | 0.285928 | + | 0.0839560i | 0.421552 | − | 0.906804i | \(-0.361486\pi\) |
−0.135624 | + | 0.990760i | \(0.543304\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.29420 | + | 8.41795i | −0.353821 | + | 0.408331i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.75894 | + | 0.516472i | −0.0851212 | + | 0.0249938i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.47655 | − | 24.1799i | −0.167459 | − | 1.16471i | −0.884112 | − | 0.467275i | \(-0.845236\pi\) |
0.716653 | − | 0.697430i | \(-0.245673\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.34204 | − | 16.2892i | 0.112551 | − | 0.782810i | −0.852872 | − | 0.522121i | \(-0.825141\pi\) |
0.965423 | − | 0.260690i | \(-0.0839499\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.24373 | − | 2.34223i | −0.0594957 | − | 0.112044i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.691787 | + | 0.798365i | 0.0330172 | + | 0.0381039i | 0.772018 | − | 0.635601i | \(-0.219247\pi\) |
−0.739001 | + | 0.673705i | \(0.764702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.83450 | − | 19.7144i | −0.134671 | − | 0.936659i | −0.939353 | − | 0.342953i | \(-0.888573\pi\) |
0.804681 | − | 0.593707i | \(-0.202336\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.1482 | + | 7.80719i | −0.575881 | + | 0.370096i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0130 | − | 18.4800i | 0.755702 | − | 0.872127i | −0.239406 | − | 0.970920i | \(-0.576953\pi\) |
0.995108 | + | 0.0987927i | \(0.0314981\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.45756 | − | 3.19162i | −0.0686340 | − | 0.150288i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.586937 | − | 1.28521i | 0.0275160 | − | 0.0602517i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.21331 | + | 5.27838i | 0.384203 | + | 0.246912i | 0.718458 | − | 0.695571i | \(-0.244848\pi\) |
−0.334255 | + | 0.942483i | \(0.608485\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.8585 | −1.34408 | −0.672038 | − | 0.740517i | \(-0.734581\pi\) | ||||
−0.672038 | + | 0.740517i | \(0.734581\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.0636 | + | 10.9661i | 0.793014 | + | 0.509639i | 0.873329 | − | 0.487130i | \(-0.161956\pi\) |
−0.0803151 | + | 0.996770i | \(0.525593\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.5386 | + | 7.79244i | 1.22806 | + | 0.360591i | 0.830518 | − | 0.556993i | \(-0.188045\pi\) |
0.397543 | + | 0.917584i | \(0.369863\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.16299 | + | 2.54659i | 0.0537018 | + | 0.117591i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15.0039 | − | 4.40553i | 0.689878 | − | 0.202567i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.65157 | − | 1.06140i | 0.0757792 | − | 0.0487003i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.91070 | − | 20.2444i | 0.132993 | − | 0.924988i | −0.808630 | − | 0.588318i | \(-0.799790\pi\) |
0.941623 | − | 0.336670i | \(-0.109301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.01375 | − | 3.47805i | −0.137415 | − | 0.158585i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.9258 | + | 34.5362i | 1.35886 | + | 1.56821i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.443196 | + | 3.08250i | −0.0200831 | + | 0.139681i | −0.997396 | − | 0.0721195i | \(-0.977024\pi\) |
0.977313 | + | 0.211801i | \(0.0679328\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.62679 | − | 2.97346i | 0.208804 | − | 0.134190i | −0.432059 | − | 0.901845i | \(-0.642213\pi\) |
0.640863 | + | 0.767655i | \(0.278576\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.366193 | − | 0.107524i | 0.0164925 | − | 0.00484264i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.77206 | + | 10.4494i | 0.214056 | + | 0.468718i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.04956 | − | 2.36356i | −0.360348 | − | 0.105808i | 0.0965470 | − | 0.995328i | \(-0.469220\pi\) |
−0.456895 | + | 0.889521i | \(0.651038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.42347 | + | 0.914807i | 0.0634693 | + | 0.0407892i | 0.571991 | − | 0.820260i | \(-0.306171\pi\) |
−0.508521 | + | 0.861049i | \(0.669808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.50967 | 0.423175 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.2843 | + | 7.89467i | 0.544494 | + | 0.349925i | 0.783794 | − | 0.621021i | \(-0.213282\pi\) |
−0.239300 | + | 0.970946i | \(0.576918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.69212 | − | 12.4640i | 0.251805 | − | 0.551375i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.70281 | − | 3.72863i | −0.0750346 | − | 0.164303i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.3571 | + | 16.5689i | −0.631423 | + | 0.728701i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.6860 | − | 13.9368i | 0.950083 | − | 0.610581i | 0.0288462 | − | 0.999584i | \(-0.490817\pi\) |
0.921237 | + | 0.389003i | \(0.127180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.00234 | − | 13.9266i | −0.0875563 | − | 0.608967i | −0.985604 | − | 0.169070i | \(-0.945924\pi\) |
0.898048 | − | 0.439898i | \(-0.144985\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −16.9185 | − | 19.5250i | −0.736983 | − | 0.850524i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.99260 | − | 21.9113i | 0.304026 | − | 0.952664i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.0956541 | − | 0.665289i | 0.00414324 | − | 0.0288169i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.17984 | − | 29.0714i | −0.180710 | − | 1.25687i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.5066 | + | 4.25952i | −0.624843 | + | 0.183470i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8199 | − | 13.6409i | 0.508177 | − | 0.586468i | −0.442454 | − | 0.896791i | \(-0.645892\pi\) |
0.950631 | + | 0.310324i | \(0.100437\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.9608 | + | 5.56739i | 0.812191 | + | 0.238481i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.77596 | + | 14.8373i | −0.289719 | + | 0.634396i | −0.997394 | − | 0.0721416i | \(-0.977017\pi\) |
0.707675 | + | 0.706538i | \(0.249744\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.0672682 | −0.00286572 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.1029 | 0.727287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.28190 | + | 20.3245i | −0.393287 | + | 0.861178i | 0.604620 | + | 0.796514i | \(0.293325\pi\) |
−0.997907 | + | 0.0646639i | \(0.979402\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.87416 | + | 0.843930i | 0.121564 | + | 0.0356944i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.19015 | + | 10.6060i | −0.387318 | + | 0.446989i | −0.915606 | − | 0.402076i | \(-0.868289\pi\) |
0.528288 | + | 0.849065i | \(0.322834\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.1244 | + | 8.25807i | −1.18320 | + | 0.347420i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.30762 | + | 36.9153i | 0.222507 | + | 1.54757i | 0.728509 | + | 0.685037i | \(0.240214\pi\) |
−0.506002 | + | 0.862532i | \(0.668877\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.24484 | − | 36.4787i | 0.219490 | − | 1.52659i | −0.520438 | − | 0.853899i | \(-0.674231\pi\) |
0.739928 | − | 0.672686i | \(-0.234860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 16.5942 | + | 3.81299i | 0.692027 | + | 0.159013i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7946 | − | 15.9198i | −0.574278 | − | 0.662752i | 0.392087 | − | 0.919928i | \(-0.371753\pi\) |
−0.966364 | + | 0.257177i | \(0.917208\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.14847 | + | 7.98779i | 0.0476466 | + | 0.331389i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.3833 | − | 10.5289i | 0.678528 | − | 0.436064i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.0269562 | − | 0.0311092i | 0.00111260 | − | 0.00128401i | −0.755193 | − | 0.655503i | \(-0.772457\pi\) |
0.756306 | + | 0.654218i | \(0.227002\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.89163 | + | 4.14210i | 0.0779434 | + | 0.170672i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.17509 | + | 13.5216i | −0.253580 | + | 0.555264i | −0.993018 | − | 0.117961i | \(-0.962364\pi\) |
0.739438 | + | 0.673225i | \(0.235091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.72341 | − | 4.96354i | −0.316629 | − | 0.203485i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.0448 | −1.79962 | −0.899811 | − | 0.436280i | \(-0.856296\pi\) | ||||
−0.899811 | + | 0.436280i | \(0.856296\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.1322 | + | 23.8634i | 1.51465 | + | 0.973409i | 0.992723 | + | 0.120422i | \(0.0384248\pi\) |
0.521932 | + | 0.852987i | \(0.325212\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.0384 | + | 3.82843i | 0.530088 | + | 0.155648i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.82155 | − | 19.3165i | −0.358056 | − | 0.784032i | −0.999853 | − | 0.0171579i | \(-0.994538\pi\) |
0.641797 | − | 0.766874i | \(-0.278189\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.02964 | + | 1.18321i | −0.163022 | + | 0.0478676i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.7218 | + | 18.4584i | −1.16006 | + | 0.745527i | −0.971618 | − | 0.236557i | \(-0.923981\pi\) |
−0.188445 | + | 0.982084i | \(0.560345\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.83677 | − | 40.5956i | 0.234980 | − | 1.63432i | −0.441077 | − | 0.897469i | \(-0.645404\pi\) |
0.676057 | − | 0.736849i | \(-0.263687\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.61337 | − | 5.32411i | −0.185427 | − | 0.213994i | 0.655424 | − | 0.755262i | \(-0.272490\pi\) |
−0.840851 | + | 0.541267i | \(0.817945\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.23648 | − | 3.73510i | −0.129667 | − | 0.149643i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.29035 | − | 29.8400i | 0.171614 | − | 1.19360i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25.1569 | + | 16.1674i | −1.00307 | + | 0.644636i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.4420 | + | 6.58958i | −0.893403 | + | 0.262327i | −0.696040 | − | 0.718003i | \(-0.745056\pi\) |
−0.197364 | + | 0.980330i | \(0.563238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 20.2835 | + | 44.4148i | 0.804928 | + | 1.76255i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.77890 | − | 0.815959i | −0.110104 | − | 0.0323295i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.9034 | − | 8.93518i | −0.549152 | − | 0.352919i | 0.236457 | − | 0.971642i | \(-0.424014\pi\) |
−0.785609 | + | 0.618723i | \(0.787650\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −34.1400 | −1.34635 | −0.673176 | − | 0.739482i | \(-0.735070\pi\) | ||||
−0.673176 | + | 0.739482i | \(0.735070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.12978 | + | 5.22469i | 0.319614 | + | 0.205404i | 0.690604 | − | 0.723233i | \(-0.257345\pi\) |
−0.370989 | + | 0.928637i | \(0.620981\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.248077 | + | 0.543213i | −0.00973788 | + | 0.0213230i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.47632 | − | 5.42237i | −0.0969057 | − | 0.212194i | 0.854971 | − | 0.518677i | \(-0.173575\pi\) |
−0.951876 | + | 0.306483i | \(0.900848\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.5549 | + | 31.8000i | −1.07666 | + | 1.24253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.7171 | + | 20.3833i | −1.23552 | + | 0.794021i | −0.984742 | − | 0.174023i | \(-0.944323\pi\) |
−0.250780 | + | 0.968044i | \(0.580687\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.57689 | + | 31.8330i | 0.178020 | + | 1.23816i | 0.861336 | + | 0.508036i | \(0.169628\pi\) |
−0.683316 | + | 0.730123i | \(0.739463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.05967 | + | 1.22293i | 0.0410924 | + | 0.0474232i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.407692 | − | 0.417310i | −0.0157859 | − | 0.0161583i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.657073 | + | 4.57004i | −0.0253660 | + | 0.176424i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.44939 | + | 30.9462i | 0.171511 | + | 1.19289i | 0.875693 | + | 0.482868i | \(0.160405\pi\) |
−0.704181 | + | 0.710020i | \(0.748686\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.24755 | − | 1.54082i | 0.201680 | − | 0.0592185i | −0.179332 | − | 0.983789i | \(-0.557394\pi\) |
0.381012 | + | 0.924570i | \(0.375576\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.2420 | + | 11.8199i | −0.393051 | + | 0.453605i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −31.9778 | − | 9.38953i | −1.22360 | − | 0.359280i | −0.394767 | − | 0.918781i | \(-0.629175\pi\) |
−0.828830 | + | 0.559501i | \(0.810993\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.28579 | + | 5.00518i | −0.0873356 | + | 0.191238i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.73064 | 0.142126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4533 | 0.892206 | 0.446103 | − | 0.894982i | \(-0.352811\pi\) | ||||
0.446103 | + | 0.894982i | \(0.352811\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.20644 | − | 9.21083i | 0.159560 | − | 0.349387i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.19052 | − | 1.23045i | −0.158727 | − | 0.0466066i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.67059 | − | 11.1605i | 0.365253 | − | 0.421525i | −0.543140 | − | 0.839642i | \(-0.682765\pi\) |
0.908393 | + | 0.418118i | \(0.137310\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.05724 | − | 1.48494i | 0.190737 | − | 0.0560056i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.463184 | + | 3.22152i | 0.0174198 | + | 0.121158i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.84594 | + | 12.8388i | −0.0693258 | + | 0.482172i | 0.925350 | + | 0.379115i | \(0.123771\pi\) |
−0.994675 | + | 0.103057i | \(0.967138\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.2317 | + | 36.8391i | −0.532980 | + | 1.37963i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.33030 | − | 2.68931i | −0.0871482 | − | 0.100574i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.59209 | − | 18.0284i | −0.0966687 | − | 0.672345i | −0.979320 | − | 0.202317i | \(-0.935153\pi\) |
0.882651 | − | 0.470028i | \(-0.155756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.18018 | − | 0.758455i | 0.0439522 | − | 0.0282463i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.282827 | − | 0.326399i | 0.0105039 | − | 0.0121222i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.56341 | + | 7.80279i | 0.132160 | + | 0.289389i | 0.964130 | − | 0.265431i | \(-0.0855143\pi\) |
−0.831970 | + | 0.554820i | \(0.812787\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.08583 | − | 17.7055i | 0.299065 | − | 0.654861i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.64399 | − | 1.69919i | −0.0976579 | − | 0.0627609i | 0.490900 | − | 0.871216i | \(-0.336668\pi\) |
−0.588558 | + | 0.808455i | \(0.700304\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.05093 | 0.259724 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.9339 | + | 12.1681i | 0.696494 | + | 0.447610i | 0.840389 | − | 0.541983i | \(-0.182326\pi\) |
−0.143895 | + | 0.989593i | \(0.545963\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.72970 | + | 1.38877i | 0.173516 | + | 0.0509489i | 0.367336 | − | 0.930088i | \(-0.380270\pi\) |
−0.193821 | + | 0.981037i | \(0.562088\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.2019 | + | 57.3741i | 0.959962 | + | 2.10202i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.64470 | − | 2.83194i | 0.352410 | − | 0.103477i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.881369 | − | 0.566421i | 0.0321616 | − | 0.0206690i | −0.524461 | − | 0.851434i | \(-0.675733\pi\) |
0.556623 | + | 0.830765i | \(0.312097\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.36178 | + | 9.47135i | −0.0495601 | + | 0.344698i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.85765 | + | 2.14384i | 0.0675173 | + | 0.0779192i | 0.788503 | − | 0.615030i | \(-0.210856\pi\) |
−0.720986 | + | 0.692950i | \(0.756311\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.1081 | − | 22.0519i | −0.692666 | − | 0.799380i | 0.295076 | − | 0.955474i | \(-0.404655\pi\) |
−0.987742 | + | 0.156094i | \(0.950110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.962505 | + | 6.69437i | −0.0348450 | + | 0.242352i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.0962364 | + | 0.0618474i | −0.00347490 | + | 0.00223318i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.4993 | + | 5.72551i | −0.703163 | + | 0.206467i | −0.613719 | − | 0.789525i | \(-0.710327\pi\) |
−0.0894441 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.32220 | + | 20.4128i | 0.335296 | + | 0.734196i | 0.999916 | − | 0.0129858i | \(-0.00413362\pi\) |
−0.664620 | + | 0.747182i | \(0.731406\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −28.0516 | − | 8.23670i | −1.00764 | − | 0.295871i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.647582 | + | 0.416175i | 0.0232020 | + | 0.0149110i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 28.9319 | 1.03526 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 56.0765 | + | 36.0382i | 2.00145 | + | 1.28626i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.82947 | + | 12.7648i | −0.207798 | + | 0.455015i | −0.984621 | − | 0.174705i | \(-0.944103\pi\) |
0.776823 | + | 0.629720i | \(0.216830\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.16737 | − | 9.12526i | −0.148175 | − | 0.324457i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.579189 | + | 0.668420i | −0.0205676 | + | 0.0237363i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −44.3146 | + | 28.4792i | −1.56970 | + | 1.00879i | −0.590224 | + | 0.807240i | \(0.700960\pi\) |
−0.979479 | + | 0.201547i | \(0.935403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.88372 | + | 27.0119i | 0.137396 | + | 0.955611i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.5993 | − | 26.0809i | −0.797510 | − | 0.920376i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.16430 | + | 13.9857i | −0.0410363 | + | 0.492931i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.51836 | − | 52.2913i | 0.264331 | − | 1.83847i | −0.234927 | − | 0.972013i | \(-0.575485\pi\) |
0.499259 | − | 0.866453i | \(-0.333606\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.05545 | − | 42.1166i | −0.212636 | − | 1.47891i | −0.764307 | − | 0.644852i | \(-0.776919\pi\) |
0.551672 | − | 0.834061i | \(-0.313990\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33.9123 | − | 9.95756i | 1.18790 | − | 0.348798i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.24663 | + | 2.59275i | −0.0785998 | + | 0.0907090i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.90317 | + | 2.90783i | 0.345623 | + | 0.101484i | 0.449937 | − | 0.893060i | \(-0.351446\pi\) |
−0.104314 | + | 0.994544i | \(0.533265\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.5958 | + | 49.4779i | −0.787640 | + | 1.72469i | −0.104355 | + | 0.994540i | \(0.533278\pi\) |
−0.683285 | + | 0.730151i | \(0.739450\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −27.7576 | −0.965227 | −0.482613 | − | 0.875834i | \(-0.660312\pi\) | ||||
−0.482613 | + | 0.875834i | \(0.660312\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.3925 | −1.09031 | −0.545153 | − | 0.838336i | \(-0.683529\pi\) | ||||
−0.545153 | + | 0.838336i | \(0.683529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.81784 | + | 17.1187i | −0.270872 | + | 0.593127i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.2745 | + | 6.83400i | 0.805446 | + | 0.236500i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.24487 | − | 2.59072i | 0.0775017 | − | 0.0894417i | −0.715674 | − | 0.698434i | \(-0.753881\pi\) |
0.793176 | + | 0.608992i | \(0.208426\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.8111 | − | 8.16607i | 0.959003 | − | 0.281589i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.31283 | + | 36.9515i | 0.182767 | + | 1.27117i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.661869 | + | 4.60340i | −0.0227421 | + | 0.158175i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.8625 | + | 22.3738i | 1.36647 | + | 0.766962i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.3027 | − | 24.5846i | −0.729390 | − | 0.841760i | 0.263013 | − | 0.964792i | \(-0.415284\pi\) |
−0.992403 | + | 0.123032i | \(0.960738\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.10290 | − | 35.4914i | −0.174312 | − | 1.21236i | −0.869645 | − | 0.493677i | \(-0.835652\pi\) |
0.695334 | − | 0.718687i | \(-0.255257\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.63096 | − | 4.90412i | 0.260365 | − | 0.167326i | −0.403946 | − | 0.914783i | \(-0.632362\pi\) |
0.664311 | + | 0.747456i | \(0.268725\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.7686 | − | 32.0467i | 0.945255 | − | 1.09088i | −0.0504891 | − | 0.998725i | \(-0.516078\pi\) |
0.995744 | − | 0.0921581i | \(-0.0293765\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.0973 | + | 54.9553i | 0.853332 | + | 1.86854i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17.8939 | − | 39.1821i | 0.607008 | − | 1.32916i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.13627 | + | 0.730236i | 0.0385010 | + | 0.0247431i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.24225 | 0.143414 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.8182 | + | 22.3763i | 1.17573 | + | 0.755594i | 0.974596 | − | 0.223970i | \(-0.0719017\pi\) |
0.201132 | + | 0.979564i | \(0.435538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0646 | + | 5.01061i | 0.574920 | + | 0.168812i | 0.556252 | − | 0.831014i | \(-0.312239\pi\) |
0.0186687 | + | 0.999826i | \(0.494057\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.41762 | + | 7.48354i | 0.115012 | + | 0.251841i | 0.958380 | − | 0.285495i | \(-0.0921580\pi\) |
−0.843368 | + | 0.537336i | \(0.819431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42.8259 | + | 12.5748i | −1.43795 | + | 0.422221i | −0.905539 | − | 0.424263i | \(-0.860533\pi\) |
−0.532414 | + | 0.846484i | \(0.678715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.0581 | + | 9.03459i | −0.471493 | + | 0.303010i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.684525 | − | 4.76097i | 0.0229067 | − | 0.159320i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.43107 | + | 8.57591i | 0.248393 | + | 0.286661i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.656002 | + | 0.757067i | 0.0218789 | + | 0.0252496i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.44990 | − | 23.9946i | 0.114933 | − | 0.799375i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19.6083 | − | 12.6015i | 0.651800 | − | 0.418887i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.2401 | + | 11.5219i | −1.30295 | + | 0.382580i | −0.858310 | − | 0.513131i | \(-0.828486\pi\) |
−0.444637 | + | 0.895711i | \(0.646667\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.360612 | − | 0.789631i | −0.0119476 | − | 0.0261616i | 0.903564 | − | 0.428453i | \(-0.140941\pi\) |
−0.915512 | + | 0.402291i | \(0.868214\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.5014 | + | 5.72611i | 0.645401 | + | 0.189507i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.1147 | − | 7.78567i | −0.400064 | − | 0.257105i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −53.6469 | −1.76965 | −0.884824 | − | 0.465926i | \(-0.845721\pi\) | ||||
−0.884824 | + | 0.465926i | \(0.845721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.66243 | + | 2.99636i | 0.153466 | + | 0.0986264i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −14.0577 | + | 30.7822i | −0.462216 | + | 1.01211i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.81781 | + | 3.98044i | 0.0596403 | + | 0.130594i | 0.937105 | − | 0.349046i | \(-0.113494\pi\) |
−0.877465 | + | 0.479640i | \(0.840767\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.17217 | − | 2.50682i | 0.0711901 | − | 0.0821578i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.4519 | + | 12.5010i | −0.636146 | + | 0.408826i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.811889 | − | 5.64681i | −0.0265232 | − | 0.184473i | 0.972253 | − | 0.233932i | \(-0.0751594\pi\) |
−0.998776 | + | 0.0494590i | \(0.984250\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.27395 | − | 8.39458i | −0.237124 | − | 0.273656i | 0.624698 | − | 0.780866i | \(-0.285222\pi\) |
−0.861822 | + | 0.507211i | \(0.830677\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.34297 | + | 6.53970i | 0.0437332 | + | 0.212962i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.12760 | + | 14.7978i | −0.0691376 | + | 0.480863i | 0.925608 | + | 0.378484i | \(0.123554\pi\) |
−0.994745 | + | 0.102379i | \(0.967355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.940813 | − | 6.54350i | −0.0305401 | − | 0.212411i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.3258 | + | 8.31722i | −0.917564 | + | 0.269421i | −0.706221 | − | 0.707991i | \(-0.749602\pi\) |
−0.211343 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.3343 | − | 37.3158i | 1.04631 | − | 1.20751i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.80690 | − | 0.530554i | −0.0583478 | − | 0.0171325i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.2919 | − | 33.4847i | 0.493288 | − | 1.08015i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −62.2837 | −2.00498 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.5676 | −1.43320 | −0.716598 | − | 0.697486i | \(-0.754302\pi\) | ||||
−0.716598 | + | 0.697486i | \(0.754302\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.1020 | + | 48.3967i | −0.709288 | + | 1.55312i | 0.119046 | + | 0.992889i | \(0.462017\pi\) |
−0.828334 | + | 0.560235i | \(0.810711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.32516 | + | 0.976355i | 0.106600 | + | 0.0313005i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.1039 | + | 27.8174i | −0.771151 | + | 0.889956i | −0.996437 | − | 0.0843367i | \(-0.973123\pi\) |
0.225286 | + | 0.974293i | \(0.427668\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.9431 | + | 3.50682i | −0.381705 | + | 0.112079i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.86774 | − | 40.8111i | −0.187152 | − | 1.30167i | −0.839337 | − | 0.543611i | \(-0.817057\pi\) |
0.652185 | − | 0.758059i | \(-0.273852\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.2081 | − | 77.9541i | 0.357120 | − | 2.48382i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −29.7008 | + | 1.77648i | −0.944430 | + | 0.0564888i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4437 | + | 30.5176i | 0.840011 | + | 0.969425i | 0.999843 | − | 0.0177197i | \(-0.00564066\pi\) |
−0.159832 | + | 0.987144i | \(0.551095\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.03191 | + | 21.0874i | 0.0961180 | + | 0.668515i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.2576 | − | 14.3041i | 0.704905 | − | 0.453015i | −0.138451 | − | 0.990369i | \(-0.544212\pi\) |
0.843357 | + | 0.537354i | \(0.180576\pi\) | |||||||
\(998\) | 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 | 828.2.q.c.289.2 | 20 | ||
3.2 | odd | 2 | 276.2.i.a.13.1 | ✓ | 20 | ||
23.16 | even | 11 | inner | 828.2.q.c.361.2 | 20 | ||
69.50 | odd | 22 | 6348.2.a.s.1.2 | 10 | |||
69.62 | odd | 22 | 276.2.i.a.85.1 | yes | 20 | ||
69.65 | even | 22 | 6348.2.a.t.1.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.i.a.13.1 | ✓ | 20 | 3.2 | odd | 2 | ||
276.2.i.a.85.1 | yes | 20 | 69.62 | odd | 22 | ||
828.2.q.c.289.2 | 20 | 1.1 | even | 1 | trivial | ||
828.2.q.c.361.2 | 20 | 23.16 | even | 11 | inner | ||
6348.2.a.s.1.2 | 10 | 69.50 | odd | 22 | |||
6348.2.a.t.1.9 | 10 | 69.65 | even | 22 |