Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [520,2,Mod(129,520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("520.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 520 = 2^{3} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 520.f (of order \(2\), degree \(1\), 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: | \(4.15222090511\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 11x^{8} + 36x^{6} + 42x^{4} + 13x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.4 | ||
Root | \(-2.50630i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 520.129 |
Dual form | 520.2.f.b.129.7 |
$q$-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 \(\left(\mathbb{Z}/520\mathbb{Z}\right)^\times\).
\(n\) | \(41\) | \(261\) | \(391\) | \(417\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 0.949078i | − | 0.547951i | −0.961737 | − | 0.273975i | \(-0.911661\pi\) | ||
0.961737 | − | 0.273975i | \(-0.0883387\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.108880 | − | 2.23342i | 0.0486926 | − | 0.998814i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.85660 | 1.45766 | 0.728830 | − | 0.684695i | \(-0.240065\pi\) | ||||
0.728830 | + | 0.684695i | \(0.240065\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.09925 | 0.699750 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 0.589684i | − | 0.177797i | −0.996041 | − | 0.0888983i | \(-0.971665\pi\) | ||
0.996041 | − | 0.0888983i | \(-0.0283346\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.32782 | + | 1.38767i | −0.922970 | + | 0.384871i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.11969 | − | 0.103336i | −0.547301 | − | 0.0266812i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.66022i | 0.887734i | 0.896093 | + | 0.443867i | \(0.146394\pi\) | ||||
−0.896093 | + | 0.443867i | \(0.853606\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.94139i | − | 1.36305i | −0.731796 | − | 0.681524i | \(-0.761317\pi\) | ||
0.731796 | − | 0.681524i | \(-0.238683\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 3.66022i | − | 0.798725i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.51775i | 0.733502i | 0.930319 | + | 0.366751i | \(0.119530\pi\) | ||||
−0.930319 | + | 0.366751i | \(0.880470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.97629 | − | 0.486349i | −0.995258 | − | 0.0972697i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.83959i | − | 0.931379i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.33862 | 0.991357 | 0.495679 | − | 0.868506i | \(-0.334919\pi\) | ||||
0.495679 | + | 0.868506i | \(0.334919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.71673i | − | 1.56557i | −0.622291 | − | 0.782786i | \(-0.713798\pi\) | ||
0.622291 | − | 0.782786i | \(-0.286202\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.559657 | −0.0974237 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.419907 | − | 8.61340i | 0.0709773 | − | 1.45593i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.85660 | 0.305224 | 0.152612 | − | 0.988286i | \(-0.451232\pi\) | ||||
0.152612 | + | 0.988286i | \(0.451232\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.31701 | + | 3.15836i | 0.210890 | + | 0.505742i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.63292i | 0.723540i | 0.932267 | + | 0.361770i | \(0.117827\pi\) | ||||
−0.932267 | + | 0.361770i | \(0.882173\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.30078i | − | 0.960860i | −0.877033 | − | 0.480430i | \(-0.840481\pi\) | ||
0.877033 | − | 0.480430i | \(-0.159519\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.228566 | − | 4.68850i | 0.0340727 | − | 0.698920i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.85660 | −0.562543 | −0.281272 | − | 0.959628i | \(-0.590756\pi\) | ||||
−0.281272 | + | 0.959628i | \(0.590756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.87339 | 1.12477 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.47383 | 0.486434 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7912i | 1.48229i | 0.671345 | + | 0.741145i | \(0.265717\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.31701 | − | 0.0642049i | −0.177586 | − | 0.00865738i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.63884 | −0.746883 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.3127i | 1.34260i | 0.741185 | + | 0.671300i | \(0.234264\pi\) | ||||
−0.741185 | + | 0.671300i | \(0.765736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.4874 | −1.72688 | −0.863439 | − | 0.504453i | \(-0.831694\pi\) | ||||
−0.863439 | + | 0.504453i | \(0.831694\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.09598 | 1.02000 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.73692 | + | 7.58349i | 0.339473 | + | 0.940616i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.09598 | −0.500403 | −0.250202 | − | 0.968194i | \(-0.580497\pi\) | ||||
−0.250202 | + | 0.968194i | \(0.580497\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.33862 | 0.401923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.34145i | 0.633913i | 0.948440 | + | 0.316957i | \(0.102661\pi\) | ||||
−0.948440 | + | 0.316957i | \(0.897339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.09598 | −0.713480 | −0.356740 | − | 0.934204i | \(-0.616112\pi\) | ||||
−0.356740 | + | 0.934204i | \(0.616112\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.461583 | + | 4.72289i | −0.0532990 | + | 0.545352i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 2.27418i | − | 0.259167i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1128 | 1.25028 | 0.625142 | − | 0.780511i | \(-0.285041\pi\) | ||||
0.625142 | + | 0.780511i | \(0.285041\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.70460 | 0.189400 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.77977 | 0.963705 | 0.481852 | − | 0.876252i | \(-0.339964\pi\) | ||||
0.481852 | + | 0.876252i | \(0.339964\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.17479 | + | 0.398525i | 0.886681 | + | 0.0432261i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.06677i | − | 0.543215i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.413343i | 0.0438142i | 0.999760 | + | 0.0219071i | \(0.00697381\pi\) | ||||
−0.999760 | + | 0.0219071i | \(0.993026\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.8341 | + | 5.35170i | −1.34538 | + | 0.561011i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.27286 | −0.857856 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −13.2696 | − | 0.646899i | −1.36143 | − | 0.0663704i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.45713 | 0.858692 | 0.429346 | − | 0.903140i | \(-0.358744\pi\) | ||||
0.429346 | + | 0.903140i | \(0.358744\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 1.23790i | − | 0.124413i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.4762 | −1.14192 | −0.570962 | − | 0.820977i | \(-0.693430\pi\) | ||||
−0.570962 | + | 0.820977i | \(0.693430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.28280i | 0.914661i | 0.889297 | + | 0.457331i | \(0.151194\pi\) | ||||
−0.889297 | + | 0.457331i | \(0.848806\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.17479 | − | 0.398525i | −0.797778 | − | 0.0388920i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.8788i | − | 1.05169i | −0.850580 | − | 0.525846i | \(-0.823749\pi\) | ||
0.850580 | − | 0.525846i | \(-0.176251\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.8138i | 1.32313i | 0.749890 | + | 0.661563i | \(0.230106\pi\) | ||||
−0.749890 | + | 0.661563i | \(0.769894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.76206i | − | 0.167248i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 9.43809i | − | 0.887861i | −0.896061 | − | 0.443931i | \(-0.853584\pi\) | ||
0.896061 | − | 0.443931i | \(-0.146416\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.85660 | + | 0.383013i | 0.732632 | + | 0.0357161i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.98592 | + | 2.91307i | −0.645849 | + | 0.269314i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.1160i | 1.29401i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6523 | 0.968388 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.39700 | 0.396464 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.62804 | + | 11.0612i | −0.145616 | + | 0.989341i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1619i | 1.78908i | 0.446992 | + | 0.894538i | \(0.352495\pi\) | ||||
−0.446992 | + | 0.894538i | \(0.647505\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.97994 | −0.526504 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.18960 | 0.540788 | 0.270394 | − | 0.962750i | \(-0.412846\pi\) | ||||
0.270394 | + | 0.962750i | \(0.412846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 22.9136i | − | 1.98686i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −10.8088 | − | 0.526935i | −0.930274 | − | 0.0453513i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.50691 | 0.214179 | 0.107090 | − | 0.994249i | \(-0.465847\pi\) | ||||
0.107090 | + | 0.994249i | \(0.465847\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.71556 | 0.824063 | 0.412032 | − | 0.911170i | \(-0.364819\pi\) | ||||
0.412032 | + | 0.911170i | \(0.364819\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.66022i | 0.308246i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.818289 | + | 1.96236i | 0.0684288 | + | 0.164101i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.581269 | − | 11.9234i | 0.0482718 | − | 0.990181i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 7.47247i | − | 0.616319i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.8973i | 1.46621i | 0.680118 | + | 0.733103i | \(0.261929\pi\) | ||||
−0.680118 | + | 0.733103i | \(0.738071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.40398i | 0.114254i | 0.998367 | + | 0.0571272i | \(0.0181940\pi\) | ||||
−0.998367 | + | 0.0571272i | \(0.981806\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.68372i | 0.621192i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −19.4681 | − | 0.949078i | −1.56371 | − | 0.0762318i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.6161i | 1.48573i | 0.669443 | + | 0.742863i | \(0.266533\pi\) | ||||
−0.669443 | + | 0.742863i | \(0.733467\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.2417 | 0.812222 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.5666i | 1.06920i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.74619 | −0.215098 | −0.107549 | − | 0.994200i | \(-0.534300\pi\) | ||||
−0.107549 | + | 0.994200i | \(0.534300\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.0609354 | + | 1.24995i | −0.00474382 | + | 0.0973082i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.3304 | −1.18630 | −0.593152 | − | 0.805090i | \(-0.702117\pi\) | ||||
−0.593152 | + | 0.805090i | \(0.702117\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.14873 | − | 9.23584i | 0.703748 | − | 0.710449i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 12.4725i | − | 0.953793i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.5456i | − | 0.953825i | −0.878951 | − | 0.476913i | \(-0.841756\pi\) | ||
0.878951 | − | 0.476913i | \(-0.158244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −19.1916 | − | 1.87565i | −1.45075 | − | 0.141786i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.78757 | 0.735679 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.82362 | 0.659508 | 0.329754 | − | 0.944067i | \(-0.393034\pi\) | ||||
0.329754 | + | 0.944067i | \(0.393034\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.88929 | 0.586406 | 0.293203 | − | 0.956050i | \(-0.405279\pi\) | ||||
0.293203 | + | 0.956050i | \(0.405279\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.8006i | 0.946244i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.202147 | − | 4.14657i | 0.0148621 | − | 0.304862i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.15837 | 0.157836 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 18.6644i | − | 1.35763i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.2975 | −1.17924 | −0.589621 | − | 0.807680i | \(-0.700723\pi\) | ||||
−0.589621 | + | 0.807680i | \(0.700723\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8476 | −1.35668 | −0.678339 | − | 0.734749i | \(-0.737300\pi\) | ||||
−0.678339 | + | 0.734749i | \(0.737300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.19732 | − | 2.59755i | 0.515411 | − | 0.186014i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.1727 | 1.86473 | 0.932364 | − | 0.361522i | \(-0.117743\pi\) | ||||
0.932364 | + | 0.361522i | \(0.117743\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.02941 | −0.214749 | −0.107375 | − | 0.994219i | \(-0.534244\pi\) | ||||
−0.107375 | + | 0.994219i | \(0.534244\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.88740i | 0.274196i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.5890 | 1.44506 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3472 | + | 0.504432i | 0.722682 | + | 0.0352311i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.38464i | 0.513268i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.50354 | −0.242345 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.82362 | −0.607443 | −0.303722 | − | 0.952761i | \(-0.598229\pi\) | ||||
−0.303722 | + | 0.952761i | \(0.598229\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.06945 | 0.347353 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0723 | − | 0.686029i | −0.959721 | − | 0.0467868i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 33.6170i | − | 2.28207i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.78556i | 0.390952i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.07919 | − | 12.1805i | −0.341663 | − | 0.819352i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.27236 | −0.219133 | −0.109567 | − | 0.993979i | \(-0.534946\pi\) | ||||
−0.109567 | + | 0.993979i | \(0.534946\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −10.4465 | − | 1.02097i | −0.696432 | − | 0.0680645i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.12956 | −0.141344 | −0.0706718 | − | 0.997500i | \(-0.522514\pi\) | ||||
−0.0706718 | + | 0.997500i | \(0.522514\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.62136i | − | 0.173225i | −0.996242 | − | 0.0866123i | \(-0.972396\pi\) | ||
0.996242 | − | 0.0866123i | \(-0.0276041\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.15837 | −0.142011 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.3197i | − | 0.676066i | −0.941134 | − | 0.338033i | \(-0.890238\pi\) | ||
0.941134 | − | 0.338033i | \(-0.109762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.419907 | + | 8.61340i | −0.0273917 | + | 0.561876i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.5469i | − | 0.685094i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1.76463i | − | 0.114145i | −0.998370 | − | 0.0570723i | \(-0.981823\pi\) | ||
0.998370 | − | 0.0570723i | \(-0.0181766\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.9136i | − | 1.47599i | −0.674804 | − | 0.737997i | \(-0.735772\pi\) | ||
0.674804 | − | 0.737997i | \(-0.264228\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 16.1366i | − | 1.03516i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.857255 | − | 17.5846i | 0.0547680 | − | 1.12344i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.24470 | + | 19.7719i | 0.524598 | + | 1.25805i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 8.33269i | − | 0.528063i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.79239 | 0.554971 | 0.277486 | − | 0.960730i | \(-0.410499\pi\) | ||||
0.277486 | + | 0.960730i | \(0.410499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.07436 | 0.130414 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.378231 | − | 7.75852i | 0.0236858 | − | 0.485857i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.3907i | 1.52145i | 0.649074 | + | 0.760725i | \(0.275157\pi\) | ||||
−0.649074 | + | 0.760725i | \(0.724843\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.16019 | 0.444912 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.2071 | 0.693702 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.14545i | 0.255619i | 0.991799 | + | 0.127810i | \(0.0407947\pi\) | ||||
−0.991799 | + | 0.127810i | \(0.959205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.1013 | + | 1.17495i | 1.48053 | + | 0.0721766i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.392295 | 0.0240080 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.2081 | 0.622402 | 0.311201 | − | 0.950344i | \(-0.399269\pi\) | ||||
0.311201 | + | 0.950344i | \(0.399269\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 3.82991i | − | 0.232650i | −0.993211 | − | 0.116325i | \(-0.962889\pi\) | ||
0.993211 | − | 0.116325i | \(-0.0371115\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.07919 | + | 12.1805i | 0.307406 | + | 0.737200i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.286792 | + | 2.93444i | −0.0172942 | + | 0.176953i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.9080i | − | 1.31632i | −0.752877 | − | 0.658162i | \(-0.771334\pi\) | ||
0.752877 | − | 0.658162i | \(-0.228666\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 18.2986i | − | 1.09551i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0345i | 0.717920i | 0.933353 | + | 0.358960i | \(0.116869\pi\) | ||||
−0.933353 | + | 0.358960i | \(0.883131\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.1180i | 0.839226i | 0.907703 | + | 0.419613i | \(0.137834\pi\) | ||||
−0.907703 | + | 0.419613i | \(0.862166\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.613957 | + | 12.5939i | −0.0363677 | + | 0.745997i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.8673i | 1.05467i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.60279 | 0.211929 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 8.02648i | − | 0.470521i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.3166 | −1.59585 | −0.797926 | − | 0.602755i | \(-0.794070\pi\) | ||||
−0.797926 | + | 0.602755i | \(0.794070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.0326 | + | 1.12285i | 1.34101 | + | 0.0653748i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.85383 | −0.165596 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.88149 | − | 11.7064i | −0.282304 | − | 0.677001i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 24.2996i | − | 1.40061i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.8918i | 0.625718i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.46850 | + | 30.1229i | −0.0840862 | + | 1.72483i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.0772 | −1.43123 | −0.715616 | − | 0.698493i | \(-0.753854\pi\) | ||||
−0.715616 | + | 0.698493i | \(0.753854\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.81010 | 0.501189 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.3022 | 1.60487 | 0.802434 | − | 0.596741i | \(-0.203538\pi\) | ||||
0.802434 | + | 0.596741i | \(0.203538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.0428i | − | 1.35898i | −0.733685 | − | 0.679490i | \(-0.762201\pi\) | ||
0.733685 | − | 0.679490i | \(-0.237799\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.881490 | − | 18.0817i | 0.0496663 | − | 1.01879i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −32.6514 | −1.83388 | −0.916941 | − | 0.399022i | \(-0.869350\pi\) | ||||
−0.916941 | + | 0.399022i | \(0.869350\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 3.14810i | − | 0.176260i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.3248 | −0.576275 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.7468 | 1.21002 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.2351 | − | 5.28698i | 0.956030 | − | 0.293269i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1104 | 0.725007 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.8734 | −0.819997 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20.3679i | − | 1.11952i | −0.828654 | − | 0.559761i | \(-0.810893\pi\) | ||
0.828654 | − | 0.559761i | \(-0.189107\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.89748 | 0.213580 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.445970 | + | 9.14802i | −0.0243659 | + | 0.499810i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.1805i | 0.663516i | 0.943364 | + | 0.331758i | \(0.107642\pi\) | ||||
−0.943364 | + | 0.331758i | \(0.892358\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.95749 | −0.486504 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.14012 | −0.278353 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.36833 | 0.181873 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.363509 | − | 7.45653i | 0.0195707 | − | 0.401446i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 20.9841i | − | 1.12649i | −0.826291 | − | 0.563243i | \(-0.809553\pi\) | ||
0.826291 | − | 0.563243i | \(-0.190447\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.8415i | 0.794445i | 0.917722 | + | 0.397222i | \(0.130026\pi\) | ||||
−0.917722 | + | 0.397222i | \(0.869974\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.71577 | + | 16.1053i | 0.358461 | + | 0.859635i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.93760 | −0.209577 | −0.104789 | − | 0.994495i | \(-0.533417\pi\) | ||||
−0.104789 | + | 0.994495i | \(0.533417\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.9297 | + | 0.581577i | 0.633161 | + | 0.0308669i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.3972 | 0.709055 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 18.2781i | − | 0.964681i | −0.875984 | − | 0.482340i | \(-0.839787\pi\) | ||
0.875984 | − | 0.482340i | \(-0.160213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.3001 | −0.857900 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.1098i | − | 0.530629i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.663730 | + | 13.6148i | −0.0347412 | + | 0.712634i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 25.0296i | − | 1.30654i | −0.757126 | − | 0.653268i | \(-0.773397\pi\) | ||
0.757126 | − | 0.653268i | \(-0.226603\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.72565i | 0.506297i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 41.6175i | 2.16067i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 21.3882i | − | 1.10744i | −0.832704 | − | 0.553719i | \(-0.813208\pi\) | ||
0.832704 | − | 0.553719i | \(-0.186792\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 10.4979 | + | 1.54514i | 0.542110 | + | 0.0797904i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.7660 | + | 7.40826i | −0.914993 | + | 0.381545i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.4784i | 1.05191i | 0.850514 | + | 0.525953i | \(0.176291\pi\) | ||||
−0.850514 | + | 0.525953i | \(0.823709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 19.1352 | 0.980325 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −12.7276 | −0.650352 | −0.325176 | − | 0.945653i | \(-0.605424\pi\) | ||||
−0.325176 | + | 0.945653i | \(0.605424\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.07919 | − | 0.247613i | −0.258859 | − | 0.0126195i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 13.2269i | − | 0.672362i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15.2680 | −0.774120 | −0.387060 | − | 0.922054i | \(-0.626509\pi\) | ||||
−0.387060 | + | 0.922054i | \(0.626509\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.8757 | −0.651154 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.87442i | − | 0.296325i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.20996 | − | 24.8194i | 0.0608796 | − | 1.24880i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.96702 | −0.148910 | −0.0744552 | − | 0.997224i | \(-0.523722\pi\) | ||||
−0.0744552 | + | 0.997224i | \(0.523722\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21.7468 | −1.08870 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 15.8408i | − | 0.791050i | −0.918455 | − | 0.395525i | \(-0.870563\pi\) | ||
0.918455 | − | 0.395525i | \(-0.129437\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0960 | + | 29.0077i | 0.602544 | + | 1.44498i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.185597 | − | 3.80709i | 0.00922240 | − | 0.189176i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.09481i | − | 0.0542677i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 19.5460i | − | 0.966487i | −0.875486 | − | 0.483243i | \(-0.839459\pi\) | ||
0.875486 | − | 0.483243i | \(-0.160541\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 2.37925i | − | 0.117360i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 39.7720i | 1.95705i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.955942 | − | 19.6089i | 0.0469253 | − | 0.962562i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.22083i | − | 0.451546i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −39.9411 | −1.95125 | −0.975625 | − | 0.219444i | \(-0.929576\pi\) | ||||
−0.975625 | + | 0.219444i | \(0.929576\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.4551i | 0.558287i | 0.960249 | + | 0.279144i | \(0.0900506\pi\) | ||||
−0.960249 | + | 0.279144i | \(0.909949\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.09598 | −0.393640 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.78014 | − | 18.2143i | 0.0863496 | − | 0.883524i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −52.0154 | −2.51720 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.86243 | − | 0.776620i | 0.0899192 | − | 0.0374956i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.4522i | 1.70767i | 0.520542 | + | 0.853836i | \(0.325730\pi\) | ||||
−0.520542 | + | 0.853836i | \(0.674270\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9479i | 1.39115i | 0.718455 | + | 0.695574i | \(0.244850\pi\) | ||||
−0.718455 | + | 0.695574i | \(0.755150\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.3162 | − | 0.551670i | −0.542571 | − | 0.0264506i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.9003 | 0.999799 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.6681 | −1.60689 | −0.803446 | − | 0.595377i | \(-0.797003\pi\) | ||||
−0.803446 | + | 0.595377i | \(0.797003\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.5282 | 0.787058 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.1485i | 0.719727i | 0.933005 | + | 0.359863i | \(0.117177\pi\) | ||||
−0.933005 | + | 0.359863i | \(0.882823\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.923166 | + | 0.0450048i | 0.0437623 | + | 0.00213343i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.9860 | 0.803408 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.5311i | 0.496996i | 0.968632 | + | 0.248498i | \(0.0799369\pi\) | ||||
−0.968632 | + | 0.248498i | \(0.920063\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.73196 | 0.128643 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.33249 | 0.0626057 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.5552 | + | 29.2465i | 0.494836 | + | 1.37110i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.1073 | 0.706692 | 0.353346 | − | 0.935493i | \(-0.385044\pi\) | ||||
0.353346 | + | 0.935493i | \(0.385044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.7140 | 0.826817 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.9226i | 0.695016i | 0.937677 | + | 0.347508i | \(0.112972\pi\) | ||||
−0.937677 | + | 0.347508i | \(0.887028\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0959767 | −0.00446041 | −0.00223021 | − | 0.999998i | \(-0.500710\pi\) | ||||
−0.00223021 | + | 0.999998i | \(0.500710\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.900750 | + | 18.4767i | −0.0417713 | + | 0.856839i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 7.55364i | − | 0.349541i | −0.984609 | − | 0.174770i | \(-0.944082\pi\) | ||
0.984609 | − | 0.174770i | \(-0.0559183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.7966 | −0.729417 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 17.6681 | 0.814105 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.71547 | −0.170838 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.88959 | + | 29.5661i | −0.132583 | + | 1.35658i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.6535i | 1.03723i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2.15464i | − | 0.0984479i | −0.998788 | − | 0.0492240i | \(-0.984325\pi\) | ||
0.998788 | − | 0.0492240i | \(-0.0156748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.17844 | + | 2.57636i | −0.281712 | + | 0.117472i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.8757 | 0.585867 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.920813 | − | 18.8883i | 0.0418120 | − | 0.857673i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.6555 | 1.88759 | 0.943796 | − | 0.330529i | \(-0.107227\pi\) | ||||
0.943796 | + | 0.330529i | \(0.107227\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.60635i | 0.117863i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2206 | 0.596638 | 0.298319 | − | 0.954466i | \(-0.403574\pi\) | ||||
0.298319 | + | 0.954466i | \(0.403574\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.5405i | 0.880061i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.76473 | − | 0.134782i | −0.124266 | − | 0.00605800i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 20.5999i | 0.924030i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 21.3534i | − | 0.955911i | −0.878384 | − | 0.477956i | \(-0.841378\pi\) | ||
0.878384 | − | 0.477956i | \(-0.158622\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.5498i | 0.650037i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 39.7750i | − | 1.77348i | −0.462268 | − | 0.886740i | \(-0.652964\pi\) | ||
0.462268 | − | 0.886740i | \(-0.347036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.24953 | + | 25.6311i | −0.0556033 | + | 1.14057i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.76554 | − | 8.68286i | −0.389291 | − | 0.385619i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.9107i | 0.705229i | 0.935769 | + | 0.352615i | \(0.114707\pi\) | ||||
−0.935769 | + | 0.352615i | \(0.885293\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.5098 | −1.04001 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.7539 | −1.26951 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 20.7324 | + | 1.01071i | 0.913577 | + | 0.0445373i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.27418i | 0.100018i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.9068 | −0.522649 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.7669 | 0.603137 | 0.301568 | − | 0.953445i | \(-0.402490\pi\) | ||||
0.301568 | + | 0.953445i | \(0.402490\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 6.04142i | − | 0.264173i | −0.991238 | − | 0.132086i | \(-0.957832\pi\) | ||
0.991238 | − | 0.132086i | \(-0.0421677\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.78014 | + | 18.2143i | −0.0776918 | + | 0.794938i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.9052 | 1.38981 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6254 | 0.461975 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.6490i | 0.939485i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.42897 | − | 15.4175i | −0.278470 | − | 0.667806i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.2968 | − | 1.18448i | −1.05044 | − | 0.0512096i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 8.37431i | − | 0.361378i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 4.64282i | − | 0.199980i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.4075i | 0.877388i | 0.898637 | + | 0.438694i | \(0.144559\pi\) | ||||
−0.898637 | + | 0.438694i | \(0.855441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 7.48756i | − | 0.321322i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.8520 | + | 1.50405i | 1.32156 | + | 0.0644265i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.8898i | 0.465616i | 0.972523 | + | 0.232808i | \(0.0747914\pi\) | ||||
−0.972523 | + | 0.232808i | \(0.925209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −28.3133 | −1.20838 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 31.7188i | − | 1.35127i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.8575 | 1.82249 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.93542 | − | 0.191853i | −0.167049 | − | 0.00814372i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2405 | 0.433904 | 0.216952 | − | 0.976182i | \(-0.430388\pi\) | ||||
0.216952 | + | 0.976182i | \(0.430388\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.74343 | + | 20.9679i | 0.369808 | + | 0.886846i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 2.04847i | − | 0.0864863i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 25.5180i | − | 1.07545i | −0.843119 | − | 0.537727i | \(-0.819283\pi\) | ||
0.843119 | − | 0.537727i | \(-0.180717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.0792 | − | 1.02762i | −0.886808 | − | 0.0432323i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.57398 | 0.276081 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.25524 | −0.346078 | −0.173039 | − | 0.984915i | \(-0.555359\pi\) | ||||
−0.173039 | + | 0.984915i | \(0.555359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.2662 | −0.848115 | −0.424058 | − | 0.905635i | \(-0.639395\pi\) | ||||
−0.424058 | + | 0.905635i | \(0.639395\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.4676i | 0.646167i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.71085 | − | 17.5054i | 0.0713476 | − | 0.730024i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.26745 | −0.177656 | −0.0888280 | − | 0.996047i | \(-0.528312\pi\) | ||||
−0.0888280 | + | 0.996047i | \(0.528312\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 17.8878i | 0.743393i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 33.8601 | 1.40475 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.36342 | 0.263546 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.74547 | + | 15.9196i | 0.237546 | + | 0.658196i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.84276 | −0.0760590 | −0.0380295 | − | 0.999277i | \(-0.512108\pi\) | ||||
−0.0380295 | + | 0.999277i | \(0.512108\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.7895 | −2.13395 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 24.8399i | − | 1.02178i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −36.3238 | −1.49164 | −0.745819 | − | 0.666148i | \(-0.767942\pi\) | ||||
−0.745819 | + | 0.666148i | \(0.767942\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 31.5269 | + | 1.53695i | 1.29248 | + | 0.0630089i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.87515i | 0.117672i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.2727 | −0.705745 | −0.352873 | − | 0.935671i | \(-0.614795\pi\) | ||||
−0.352873 | + | 0.935671i | \(0.614795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.1781 | −1.31257 | −0.656286 | − | 0.754512i | \(-0.727874\pi\) | ||||
−0.656286 | + | 0.754512i | \(0.727874\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.59848 | −0.350157 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.15982 | − | 23.7910i | 0.0471534 | − | 0.967240i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.88535i | 0.279468i | 0.990189 | + | 0.139734i | \(0.0446247\pi\) | ||||
−0.990189 | + | 0.139734i | \(0.955375\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 19.5405i | − | 0.791822i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.8341 | − | 5.35170i | 0.519211 | − | 0.216507i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.1565 | −0.935283 | −0.467642 | − | 0.883918i | \(-0.654896\pi\) | ||||
−0.467642 | + | 0.883918i | \(0.654896\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.478746 | − | 9.82033i | 0.0193049 | − | 0.395994i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.3256 | 1.38190 | 0.690949 | − | 0.722904i | \(-0.257193\pi\) | ||||
0.690949 | + | 0.722904i | \(0.257193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.0066i | − | 1.40704i | −0.710678 | − | 0.703518i | \(-0.751612\pi\) | ||
0.710678 | − | 0.703518i | \(-0.248388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 17.0245 | 0.683169 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.59410i | 0.0638662i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.5269 | + | 4.84042i | 0.981077 | + | 0.193617i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.32514i | 0.132793i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.79558i | 0.270957i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.95144i | 0.197114i | 0.995131 | + | 0.0985570i | \(0.0314227\pi\) | ||||
−0.995131 | + | 0.0985570i | \(0.968577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.37431i | 0.332849i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 45.0298 | + | 2.19522i | 1.78695 | + | 0.0871148i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.2012 | + | 10.9257i | −1.03813 | + | 0.432892i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 11.2130i | 0.443581i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.02941 | −0.0406594 | −0.0203297 | − | 0.999793i | \(-0.506472\pi\) | ||||
−0.0203297 | + | 0.999793i | \(0.506472\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.30102 | −0.327360 | −0.163680 | − | 0.986513i | \(-0.552337\pi\) | ||||
−0.163680 | + | 0.986513i | \(0.552337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.651096 | + | 13.3557i | −0.0256369 | + | 0.525880i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.13808i | − | 0.241313i | −0.992694 | − | 0.120656i | \(-0.961500\pi\) | ||
0.992694 | − | 0.120656i | \(-0.0385000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.08125 | 0.238710 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −31.9052 | −1.25046 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.78421i | 0.148088i | 0.997255 | + | 0.0740438i | \(0.0235905\pi\) | ||||
−0.997255 | + | 0.0740438i | \(0.976410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.673924 | − | 13.8239i | 0.0263324 | − | 0.540146i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.7970 | −0.499258 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.6634 | −0.999705 | −0.499853 | − | 0.866110i | \(-0.666613\pi\) | ||||
−0.499853 | + | 0.866110i | \(0.666613\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 10.8080i | − | 0.420384i | −0.977660 | − | 0.210192i | \(-0.932591\pi\) | ||
0.977660 | − | 0.210192i | \(-0.0674089\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −11.5603 | + | 4.82055i | −0.448964 | + | 0.187215i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −51.1756 | − | 2.49483i | −1.98450 | − | 0.0967454i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.7800i | 0.727163i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.10572i | 0.120074i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.95328i | 0.307033i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.8803i | − | 0.612141i | −0.952009 | − | 0.306071i | \(-0.900986\pi\) | ||
0.952009 | − | 0.306071i | \(-0.0990143\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.35373 | + | 24.0832i | −0.0905950 | + | 0.926963i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 0.340888i | − | 0.0131014i | −0.999979 | − | 0.00655069i | \(-0.997915\pi\) | ||
0.999979 | − | 0.00655069i | \(-0.00208516\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 32.6158 | 1.25168 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.02112i | 0.0774493i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.9483 | 0.686771 | 0.343386 | − | 0.939194i | \(-0.388426\pi\) | ||||
0.343386 | + | 0.939194i | \(0.388426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.272952 | − | 5.59896i | 0.0104290 | − | 0.213925i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.48788 | −0.0949185 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.9747 | − | 35.9112i | −0.570491 | − | 1.36811i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.24959i | − | 0.0855783i | −0.999084 | − | 0.0427891i | \(-0.986376\pi\) | ||
0.999084 | − | 0.0427891i | \(-0.0136244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 4.77407i | − | 0.181352i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.05783 | − | 21.6989i | 0.0401258 | − | 0.823086i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16.9575 | −0.642311 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.79421 | −0.370451 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.89790 | −0.260530 | −0.130265 | − | 0.991479i | \(-0.541583\pi\) | ||||
−0.130265 | + | 0.991479i | \(0.541583\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 11.0308i | − | 0.416035i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 8.17479 | + | 0.398525i | 0.307880 | + | 0.0150093i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −44.2591 | −1.66454 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 35.4512i | − | 1.33140i | −0.746220 | − | 0.665699i | \(-0.768133\pi\) | ||
0.746220 | − | 0.665699i | \(-0.231867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.3285 | 0.874886 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 30.6633 | 1.14835 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.47186 | − | 1.61392i | 0.167238 | − | 0.0603571i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.67478 | −0.0625457 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.2319 | 0.903698 | 0.451849 | − | 0.892095i | \(-0.350765\pi\) | ||||
0.451849 | + | 0.892095i | \(0.350765\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35.8001i | 1.33326i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.7468 | −0.808772 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −26.5665 | − | 2.59643i | −0.986656 | − | 0.0964291i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 13.4972i | − | 0.500585i | −0.968170 | − | 0.250292i | \(-0.919473\pi\) | ||
0.968170 | − | 0.250292i | \(-0.0805267\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.2011 | −0.377817 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 23.0622 | 0.852988 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.3706 | 1.41725 | 0.708625 | − | 0.705585i | \(-0.249316\pi\) | ||||
0.708625 | + | 0.705585i | \(0.249316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.6891 | − | 0.813602i | −0.615588 | − | 0.0300102i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.41533i | 0.0889700i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.36168i | 0.344375i | 0.985064 | + | 0.172187i | \(0.0550835\pi\) | ||||
−0.985064 | + | 0.172187i | \(0.944917\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 18.7650 | − | 7.82487i | 0.689351 | − | 0.287454i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −11.4643 | −0.420585 | −0.210292 | − | 0.977639i | \(-0.567442\pi\) | ||||
−0.210292 | + | 0.977639i | \(0.567442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 39.9721 | + | 1.94866i | 1.46447 | + | 0.0713934i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.4309 | 0.674353 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 41.9551i | − | 1.53301i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.56686 | 0.239628 | 0.119814 | − | 0.992796i | \(-0.461770\pi\) | ||||
0.119814 | + | 0.992796i | \(0.461770\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 8.34467i | − | 0.304097i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.13567 | + | 0.152865i | 0.114119 | + | 0.00556334i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.6035i | − | 1.25768i | −0.777533 | − | 0.628842i | \(-0.783529\pi\) | ||
0.777533 | − | 0.628842i | \(-0.216471\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.96873i | − | 0.0714605i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 40.4330i | − | 1.46570i | −0.680393 | − | 0.732848i | \(-0.738191\pi\) | ||
0.680393 | − | 0.732848i | \(-0.261809\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.2745i | 1.92867i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.1609 | + | 0.836603i | 0.620455 | + | 0.0302475i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.3107 | − | 34.3188i | −0.516728 | − | 1.23918i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 9.52918i | − | 0.343631i | −0.985129 | − | 0.171816i | \(-0.945037\pi\) | ||
0.985129 | − | 0.171816i | \(-0.0549633\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.1487 | 0.833680 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.70473 | 0.169217 | 0.0846087 | − | 0.996414i | \(-0.473036\pi\) | ||||
0.0846087 | + | 0.996414i | \(0.473036\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.23937 | + | 43.3770i | −0.152283 | + | 1.55815i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 6.79558i | − | 0.243790i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.5260 | 0.986220 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.14977 | 0.112708 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 25.8367i | − | 0.923330i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.5775 | + | 2.02692i | 1.48396 | + | 0.0723439i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 24.8675 | 0.886430 | 0.443215 | − | 0.896415i | \(-0.353838\pi\) | ||||
0.443215 | + | 0.896415i | \(0.353838\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.93436 | 0.140067 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 36.3990i | − | 1.29420i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.8834 | − | 18.7160i | 1.59386 | − | 0.664626i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.11512 | − | 22.8740i | 0.0395492 | − | 0.811258i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.3616i | 0.685824i | 0.939368 | + | 0.342912i | \(0.111413\pi\) | ||||
−0.939368 | + | 0.342912i | \(0.888587\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 14.1160i | − | 0.499389i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.867710i | 0.0306590i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.59470i | 0.126854i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30.2998 | + | 1.47713i | 1.06793 | + | 0.0520620i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.68833i | − | 0.341045i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.50590 | −0.123261 | −0.0616304 | − | 0.998099i | \(-0.519630\pi\) | ||||
−0.0616304 | + | 0.998099i | \(0.519630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.32489i | − | 0.257212i | −0.991696 | − | 0.128606i | \(-0.958950\pi\) | ||
0.991696 | − | 0.128606i | \(-0.0410502\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.63488 | −0.127481 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.299005 | + | 6.13339i | −0.0104737 | + | 0.214843i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −37.4354 | −1.30970 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.9419 | + | 11.2346i | −0.941427 | + | 0.392568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 30.8633i | − | 1.07714i | −0.842582 | − | 0.538569i | \(-0.818965\pi\) | ||
0.842582 | − | 0.538569i | \(-0.181035\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 49.4309i | − | 1.72305i | −0.507714 | − | 0.861526i | \(-0.669509\pi\) | ||
0.507714 | − | 0.861526i | \(-0.330491\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.78501 | + | 0.272188i | 0.0969617 | + | 0.00947638i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.1108 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681922\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681922\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.440726 | 0.0153070 | 0.00765352 | − | 0.999971i | \(-0.497564\pi\) | ||||
0.00765352 | + | 0.999971i | \(0.497564\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −20.7924 | −0.721280 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 28.8183i | 0.998497i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.66918 | + | 34.2392i | −0.0577643 | + | 1.18490i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −42.1854 | −1.45814 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 21.0334i | − | 0.726153i | −0.931759 | − | 0.363076i | \(-0.881726\pi\) | ||
0.931759 | − | 0.363076i | \(-0.118274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.499104 | −0.0172105 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 11.4217 | 0.393385 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −19.6314 | − | 21.4385i | −0.675339 | − | 0.737507i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.0816 | 1.41158 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13.3991 | 0.459855 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.53107i | 0.223882i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.6034 | 1.08208 | 0.541040 | − | 0.840997i | \(-0.318031\pi\) | ||||
0.541040 | + | 0.840997i | \(0.318031\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −27.8562 | − | 1.35800i | −0.952662 | − | 0.0464427i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 29.1751i | − | 0.996602i | −0.867004 | − | 0.498301i | \(-0.833957\pi\) | ||
0.867004 | − | 0.498301i | \(-0.166043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7221 | 1.18470 | 0.592351 | − | 0.805680i | \(-0.298200\pi\) | ||||
0.592351 | + | 0.805680i | \(0.298200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 16.9575 | 0.577910 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −23.2447 | −0.791258 | −0.395629 | − | 0.918410i | \(-0.629473\pi\) | ||||
−0.395629 | + | 0.918410i | \(0.629473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.0196 | − | 1.36597i | −0.952694 | − | 0.0464443i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 3.41933i | − | 0.116127i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 6.55302i | − | 0.222296i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.6307 | − | 5.68388i | 0.461857 | − | 0.192591i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.7536 | 0.600870 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.27870 | + | 42.6586i | −0.212259 | + | 1.44212i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.3892 | 0.485890 | 0.242945 | − | 0.970040i | \(-0.421887\pi\) | ||||
0.242945 | + | 0.970040i | \(0.421887\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 25.9256i | 0.874449i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.9750 | 0.605593 | 0.302797 | − | 0.953055i | \(-0.402080\pi\) | ||||
0.302797 | + | 0.953055i | \(0.402080\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.2125i | 1.05038i | 0.850984 | + | 0.525191i | \(0.176006\pi\) | ||||
−0.850984 | + | 0.525191i | \(0.823994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.06567 | − | 21.8597i | 0.0358221 | − | 0.734806i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 53.2656i | 1.78848i | 0.447585 | + | 0.894242i | \(0.352284\pi\) | ||||
−0.447585 | + | 0.894242i | \(0.647716\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 77.7563i | 2.60786i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 1.00518i | − | 0.0336747i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 22.9136i | 0.766774i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.960716 | − | 19.7068i | 0.0321132 | − | 0.658726i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −11.1103 | + | 4.63292i | −0.370963 | + | 0.154689i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 46.5354i | − | 1.55204i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.4983 | −1.31588 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.0622 | −0.767464 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.858986 | − | 17.6201i | 0.0285537 | − | 0.585711i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.5858i | 1.38084i | 0.723411 | + | 0.690418i | \(0.242573\pi\) | ||||
−0.723411 | + | 0.690418i | \(0.757427\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −24.0914 | −0.799061 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6225 | 1.14710 | 0.573548 | − | 0.819172i | \(-0.305567\pi\) | ||||
0.573548 | + | 0.819172i | \(0.305567\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.17729i | − | 0.171343i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.5890 | + | 1.39372i | 0.945122 | + | 0.0460751i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.8708 | 0.788284 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.3494 | −1.56191 | −0.780956 | − | 0.624586i | \(-0.785268\pi\) | ||||
−0.780956 | + | 0.624586i | \(0.785268\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.8003i | 0.784245i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.41218 | − | 17.7754i | −0.243975 | − | 0.585083i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.23900 | − | 0.902957i | −0.303776 | − | 0.0296890i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.4869i | 0.640034i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.83607i | 0.322711i | 0.986896 | + | 0.161355i | \(0.0515866\pi\) | ||||
−0.986896 | + | 0.161355i | \(0.948413\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 46.7789i | − | 1.53312i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 26.8610i | − | 0.879389i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.235004 | − | 4.82055i | 0.00768545 | − | 0.157649i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.96076i | 0.0640554i | 0.999487 | + | 0.0320277i | \(0.0101965\pi\) | ||||
−0.999487 | + | 0.0320277i | \(0.989804\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.8185 | −0.744654 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.2254i | 0.691927i | 0.938248 | + | 0.345964i | \(0.112448\pi\) | ||||
−0.938248 | + | 0.345964i | \(0.887552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.2975 | −0.530718 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −41.6853 | − | 2.03218i | −1.35602 | − | 0.0661067i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −53.5500 | −1.74014 | −0.870071 | − | 0.492927i | \(-0.835927\pi\) | ||||
−0.870071 | + | 0.492927i | \(0.835927\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.2863 | − | 8.45922i | 0.658521 | − | 0.274598i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 30.9887i | 1.00488i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.13504i | 0.0367676i | 0.999831 | + | 0.0183838i | \(0.00585207\pi\) | ||||
−0.999831 | + | 0.0183838i | \(0.994148\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.77447 | + | 36.3990i | −0.0574204 | + | 1.17784i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.98780 | −0.0965817 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.66814 | 0.312201 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.9815 | −1.45102 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 22.8373i | − | 0.735921i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.05213 | + | 42.0945i | −0.0660603 | + | 1.35507i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3213 | 0.685647 | 0.342823 | − | 0.939400i | \(-0.388617\pi\) | ||||
0.342823 | + | 0.939400i | \(0.388617\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 20.6394i | − | 0.663033i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.2206 | 1.19447 | 0.597233 | − | 0.802068i | \(-0.296267\pi\) | ||||
0.597233 | + | 0.802068i | \(0.296267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.4691 | 1.20120 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.01776 | − | 16.3574i | −0.160697 | − | 0.523857i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.7798 | 0.728789 | 0.364395 | − | 0.931245i | \(-0.381276\pi\) | ||||
0.364395 | + | 0.931245i | \(0.381276\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.243742 | 0.00779002 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 28.9987i | 0.925857i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.48902 | 0.0793873 | 0.0396937 | − | 0.999212i | \(-0.487362\pi\) | ||||
0.0396937 | + | 0.999212i | \(0.487362\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.84968 | − | 58.4545i | 0.0907985 | − | 1.86252i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.1160i | 0.449318i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.1646 | 0.704793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.9068 | −1.14062 | −0.570308 | − | 0.821431i | \(-0.693176\pi\) | ||||
−0.570308 | + | 0.821431i | \(0.693176\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −19.3307 | −0.613443 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.329843 | + | 6.76594i | −0.0104567 | + | 0.214495i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 15.0609i | − | 0.476983i | −0.971145 | − | 0.238491i | \(-0.923347\pi\) | ||
0.971145 | − | 0.238491i | \(-0.0766529\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 8.98520i | − | 0.284279i |
(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 | 520.2.f.b.129.4 | yes | 10 | |
4.3 | odd | 2 | 1040.2.f.g.129.7 | 10 | |||
5.2 | odd | 4 | 2600.2.k.f.2001.8 | 20 | |||
5.3 | odd | 4 | 2600.2.k.f.2001.13 | 20 | |||
5.4 | even | 2 | 520.2.f.a.129.7 | yes | 10 | ||
13.12 | even | 2 | 520.2.f.a.129.4 | ✓ | 10 | ||
20.19 | odd | 2 | 1040.2.f.f.129.4 | 10 | |||
52.51 | odd | 2 | 1040.2.f.f.129.7 | 10 | |||
65.12 | odd | 4 | 2600.2.k.f.2001.7 | 20 | |||
65.38 | odd | 4 | 2600.2.k.f.2001.14 | 20 | |||
65.64 | even | 2 | inner | 520.2.f.b.129.7 | yes | 10 | |
260.259 | odd | 2 | 1040.2.f.g.129.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
520.2.f.a.129.4 | ✓ | 10 | 13.12 | even | 2 | ||
520.2.f.a.129.7 | yes | 10 | 5.4 | even | 2 | ||
520.2.f.b.129.4 | yes | 10 | 1.1 | even | 1 | trivial | |
520.2.f.b.129.7 | yes | 10 | 65.64 | even | 2 | inner | |
1040.2.f.f.129.4 | 10 | 20.19 | odd | 2 | |||
1040.2.f.f.129.7 | 10 | 52.51 | odd | 2 | |||
1040.2.f.g.129.4 | 10 | 260.259 | odd | 2 | |||
1040.2.f.g.129.7 | 10 | 4.3 | odd | 2 | |||
2600.2.k.f.2001.7 | 20 | 65.12 | odd | 4 | |||
2600.2.k.f.2001.8 | 20 | 5.2 | odd | 4 | |||
2600.2.k.f.2001.13 | 20 | 5.3 | odd | 4 | |||
2600.2.k.f.2001.14 | 20 | 65.38 | odd | 4 |