Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(149,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.r (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 149.5 | ||
Root | \(1.65604 + 0.956115i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 700.149 |
Dual form | 700.2.r.d.249.5 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.22469 | − | 1.28442i | 1.28442 | − | 0.741563i | 0.306771 | − | 0.951783i | \(-0.400751\pi\) |
0.977654 | + | 0.210220i | \(0.0674182\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.568650 | + | 2.58392i | −0.214929 | + | 0.976630i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.79949 | − | 3.11682i | 0.599831 | − | 1.03894i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.784425 | + | 1.35866i | 0.236513 | + | 0.409652i | 0.959711 | − | 0.280988i | \(-0.0906621\pi\) |
−0.723198 | + | 0.690640i | \(0.757329\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.56885i | − | 1.54452i | −0.635306 | − | 0.772260i | \(-0.719126\pi\) | ||
0.635306 | − | 0.772260i | \(-0.280874\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.20753 | − | 3.58392i | 1.50555 | − | 0.869228i | 0.505568 | − | 0.862787i | \(-0.331283\pi\) |
0.999979 | − | 0.00644117i | \(-0.00205030\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.58392 | − | 2.74343i | 0.363376 | − | 0.629386i | −0.625138 | − | 0.780514i | \(-0.714957\pi\) |
0.988514 | + | 0.151129i | \(0.0482907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.05378 | + | 6.47880i | 0.448172 | + | 1.41379i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.96812 | + | 2.86834i | 1.03592 | + | 0.598091i | 0.918676 | − | 0.395012i | \(-0.129259\pi\) |
0.117248 | + | 0.993103i | \(0.462593\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.53871i | − | 0.296125i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.96986 | −0.365794 | −0.182897 | − | 0.983132i | \(-0.558547\pi\) | ||||
−0.182897 | + | 0.983132i | \(0.558547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.484931 | − | 0.839925i | −0.0870961 | − | 0.150855i | 0.819186 | − | 0.573527i | \(-0.194425\pi\) |
−0.906282 | + | 0.422673i | \(0.861092\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.49020 | + | 2.01507i | 0.607566 | + | 0.350779i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.80804 | + | 3.35327i | 0.954836 | + | 0.551275i | 0.894580 | − | 0.446908i | \(-0.147475\pi\) |
0.0602563 | + | 0.998183i | \(0.480808\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.15277 | − | 12.3890i | −1.14536 | − | 1.98382i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.87439 | −1.38595 | −0.692973 | − | 0.720963i | \(-0.743700\pi\) | ||||
−0.692973 | + | 0.720963i | \(0.743700\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.59899i | 0.701339i | 0.936499 | + | 0.350670i | \(0.114046\pi\) | ||||
−0.936499 | + | 0.350670i | \(0.885954\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.347286 | − | 0.200506i | −0.0506569 | − | 0.0292468i | 0.474458 | − | 0.880278i | \(-0.342644\pi\) |
−0.525115 | + | 0.851032i | \(0.675978\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.35327 | − | 2.93869i | −0.907611 | − | 0.419813i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.20655 | − | 15.9462i | 1.28917 | − | 2.23292i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.26077 | + | 4.76936i | −1.13470 | + | 0.655121i | −0.945114 | − | 0.326742i | \(-0.894049\pi\) |
−0.189590 | + | 0.981863i | \(0.560716\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 8.13770i | − | 1.07786i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.28442 | − | 3.95674i | −0.297407 | − | 0.515124i | 0.678135 | − | 0.734937i | \(-0.262788\pi\) |
−0.975542 | + | 0.219814i | \(0.929455\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.65277 | + | 13.2550i | −0.979837 | + | 1.69713i | −0.316886 | + | 0.948464i | \(0.602637\pi\) |
−0.662951 | + | 0.748663i | \(0.730696\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.03032 | + | 6.42212i | 0.885737 | + | 0.809112i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.746774 | − | 0.431150i | 0.0912330 | − | 0.0526734i | −0.453689 | − | 0.891160i | \(-0.649892\pi\) |
0.544922 | + | 0.838486i | \(0.316559\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.7367 | 1.77409 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.1377 | −1.44048 | −0.720240 | − | 0.693725i | \(-0.755968\pi\) | ||||
−0.720240 | + | 0.693725i | \(0.755968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.46410 | + | 2.00000i | −0.405442 | + | 0.234082i | −0.688830 | − | 0.724923i | \(-0.741875\pi\) |
0.283387 | + | 0.959006i | \(0.408542\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.95674 | + | 1.25429i | −0.450912 | + | 0.142939i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.43719 | + | 11.1495i | −0.724241 | + | 1.25442i | 0.235045 | + | 0.971985i | \(0.424476\pi\) |
−0.959286 | + | 0.282437i | \(0.908857\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.42212 | + | 5.92729i | 0.380236 | + | 0.658588i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 17.1076i | − | 1.87780i | −0.344192 | − | 0.938899i | \(-0.611847\pi\) | ||
0.344192 | − | 0.938899i | \(-0.388153\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.38233 | + | 2.53014i | −0.469835 | + | 0.271259i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.79949 | + | 4.84887i | −0.296746 | + | 0.513979i | −0.975389 | − | 0.220489i | \(-0.929235\pi\) |
0.678644 | + | 0.734468i | \(0.262568\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.3895 | + | 3.16673i | 1.50842 | + | 0.331963i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.15764 | − | 1.24571i | −0.223737 | − | 0.129175i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.233174i | 0.0236752i | 0.999930 | + | 0.0118376i | \(0.00376811\pi\) | ||||
−0.999930 | + | 0.0118376i | \(0.996232\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.64627 | 0.567472 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.25176 | − | 10.8284i | −0.622073 | − | 1.07746i | −0.989099 | − | 0.147251i | \(-0.952957\pi\) |
0.367026 | − | 0.930211i | \(-0.380376\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.91926 | + | 1.68544i | 0.287643 | + | 0.166071i | 0.636879 | − | 0.770964i | \(-0.280225\pi\) |
−0.349235 | + | 0.937035i | \(0.613559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3604 | + | 8.86834i | 1.48495 | + | 0.857335i | 0.999853 | − | 0.0171265i | \(-0.00545179\pi\) |
0.485095 | + | 0.874462i | \(0.338785\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.95226 | + | 5.11347i | 0.282775 | + | 0.489782i | 0.972067 | − | 0.234702i | \(-0.0754115\pi\) |
−0.689292 | + | 0.724484i | \(0.742078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 17.2281 | 1.63522 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.6412i | − | 1.47140i | −0.677307 | − | 0.735701i | \(-0.736853\pi\) | ||
0.677307 | − | 0.735701i | \(-0.263147\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.3571 | − | 10.0211i | −1.60466 | − | 0.926452i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.73064 | + | 18.0777i | 0.525327 | + | 1.65718i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.26936 | − | 7.39474i | 0.388123 | − | 0.672249i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −19.7428 | + | 11.3985i | −1.78014 | + | 1.02777i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.8744i | 1.14242i | 0.820805 | + | 0.571209i | \(0.193525\pi\) | ||||
−0.820805 | + | 0.571209i | \(0.806475\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.90705 | + | 10.2313i | 0.520087 | + | 0.900817i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.114058 | − | 0.197554i | 0.00996526 | − | 0.0172603i | −0.861000 | − | 0.508605i | \(-0.830161\pi\) |
0.870965 | + | 0.491345i | \(0.163495\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.18810 | + | 5.65277i | 0.536576 | + | 0.490157i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.38002 | + | 4.83821i | −0.715953 | + | 0.413356i | −0.813261 | − | 0.581899i | \(-0.802310\pi\) |
0.0973082 | + | 0.995254i | \(0.468977\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.3709 | 1.04928 | 0.524642 | − | 0.851323i | \(-0.324199\pi\) | ||||
0.524642 | + | 0.851323i | \(0.324199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.03014 | −0.0867533 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.56619 | − | 4.36834i | 0.632717 | − | 0.365299i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.9086 | + | 1.62263i | −1.47708 | + | 0.133832i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.95479 | − | 10.3140i | 0.487836 | − | 0.844956i | −0.512067 | − | 0.858946i | \(-0.671120\pi\) |
0.999902 | + | 0.0139898i | \(0.00445323\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.98493 | − | 8.63415i | −0.405668 | − | 0.702637i | 0.588731 | − | 0.808329i | \(-0.299628\pi\) |
−0.994399 | + | 0.105692i | \(0.966294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 25.7970i | − | 2.08556i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.4289 | + | 6.02111i | −0.832315 | + | 0.480537i | −0.854645 | − | 0.519214i | \(-0.826225\pi\) |
0.0223299 | + | 0.999751i | \(0.492892\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2518 | + | 21.2207i | −0.971628 | + | 1.68291i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2367 | + | 11.2061i | −0.806764 | + | 0.883167i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.4944 | − | 8.36834i | −1.13529 | − | 0.655459i | −0.190029 | − | 0.981778i | \(-0.560858\pi\) |
−0.945260 | + | 0.326319i | \(0.894192\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 6.76683i | − | 0.523633i | −0.965118 | − | 0.261816i | \(-0.915679\pi\) | ||
0.965118 | − | 0.261816i | \(-0.0843215\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.0121 | −1.38555 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.70051 | − | 9.87357i | −0.435929 | − | 0.755050i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.06552 | + | 2.34723i | 0.309096 | + | 0.178457i | 0.646522 | − | 0.762895i | \(-0.276223\pi\) |
−0.337426 | + | 0.941352i | \(0.609556\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.1643 | − | 5.86834i | −0.763993 | − | 0.441092i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.73669 | + | 9.93623i | 0.428780 | + | 0.742669i | 0.996765 | − | 0.0803699i | \(-0.0256102\pi\) |
−0.567985 | + | 0.823039i | \(0.692277\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.832162 | 0.0618541 | 0.0309271 | − | 0.999522i | \(-0.490154\pi\) | ||||
0.0309271 | + | 0.999522i | \(0.490154\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 39.3176i | 2.90644i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.73868 | + | 5.62263i | 0.712163 | + | 0.411167i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.97590 | + | 0.874988i | 0.289204 | + | 0.0636460i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.46986 | + | 6.00998i | −0.251070 | + | 0.434867i | −0.963821 | − | 0.266551i | \(-0.914116\pi\) |
0.712750 | + | 0.701418i | \(0.247449\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.0403 | + | 9.83821i | −1.22659 | + | 0.708169i | −0.966314 | − | 0.257366i | \(-0.917145\pi\) |
−0.260272 | + | 0.965535i | \(0.583812\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 16.0422i | − | 1.14296i | −0.820616 | − | 0.571481i | \(-0.806369\pi\) | ||
0.820616 | − | 0.571481i | \(-0.193631\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.33821 | − | 9.24604i | −0.378415 | − | 0.655435i | 0.612417 | − | 0.790535i | \(-0.290198\pi\) |
−0.990832 | + | 0.135101i | \(0.956864\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.10756 | − | 1.91835i | 0.0781213 | − | 0.135310i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.12016 | − | 5.08996i | 0.0786199 | − | 0.357245i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 17.8802 | − | 10.3231i | 1.24276 | − | 0.717508i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.96986 | 0.343772 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.3658 | 0.782455 | 0.391227 | − | 0.920294i | \(-0.372051\pi\) | ||||
0.391227 | + | 0.920294i | \(0.372051\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.0026 | + | 15.5900i | −1.85019 | + | 1.06821i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.44605 | − | 0.775398i | 0.166049 | − | 0.0526375i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.13770 | + | 8.89876i | −0.347174 | + | 0.601322i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.9583 | − | 34.5688i | −1.34254 | − | 2.32535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.04222i | 0.404617i | 0.979322 | + | 0.202309i | \(0.0648444\pi\) | ||||
−0.979322 | + | 0.202309i | \(0.935156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.7418 | − | 10.8206i | 1.24394 | − | 0.718189i | 0.274046 | − | 0.961717i | \(-0.411638\pi\) |
0.969894 | + | 0.243528i | \(0.0783047\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.71558 | + | 4.70351i | −0.179450 | + | 0.310817i | −0.941692 | − | 0.336475i | \(-0.890765\pi\) |
0.762242 | + | 0.647292i | \(0.224099\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.19148 | + | 7.87253i | −0.473165 | + | 0.517975i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00998 | − | 3.46986i | −0.393727 | − | 0.227318i | 0.290047 | − | 0.957012i | \(-0.406329\pi\) |
−0.683774 | + | 0.729694i | \(0.739662\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.0724i | 2.14828i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.69446 | −0.109606 | −0.0548028 | − | 0.998497i | \(-0.517453\pi\) | ||||
−0.0548028 | + | 0.998497i | \(0.517453\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.46733 | + | 12.9338i | 0.481013 | + | 0.833139i | 0.999763 | − | 0.0217871i | \(-0.00693559\pi\) |
−0.518749 | + | 0.854926i | \(0.673602\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 19.2240 | + | 11.0990i | 1.23322 | + | 0.712000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −15.2777 | − | 8.82061i | −0.972099 | − | 0.561242i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.9734 | − | 38.0590i | −1.39251 | − | 2.41189i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.90958 | 0.562368 | 0.281184 | − | 0.959654i | \(-0.409273\pi\) | ||||
0.281184 | + | 0.959654i | \(0.409273\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000i | 0.565825i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.36955 | − | 4.83216i | −0.522078 | − | 0.301422i | 0.215706 | − | 0.976458i | \(-0.430795\pi\) |
−0.737785 | + | 0.675036i | \(0.764128\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.9673 | + | 13.1007i | −0.743614 | + | 0.814036i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.54475 | + | 6.13969i | −0.219415 | + | 0.380038i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.28492 | − | 3.05125i | 0.325882 | − | 0.188148i | −0.328129 | − | 0.944633i | \(-0.606418\pi\) |
0.654011 | + | 0.756485i | \(0.273085\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.3830i | 0.880223i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2668 | + | 19.5147i | 0.686951 | + | 1.18983i | 0.972820 | + | 0.231565i | \(0.0743844\pi\) |
−0.285869 | + | 0.958269i | \(0.592282\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.23064 | + | 3.86359i | −0.135502 | + | 0.234696i | −0.925789 | − | 0.378040i | \(-0.876598\pi\) |
0.790287 | + | 0.612737i | \(0.209931\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 36.0795 | − | 11.4372i | 2.18363 | − | 0.692210i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.63659 | − | 3.25429i | 0.338670 | − | 0.195531i | −0.321014 | − | 0.947074i | \(-0.604024\pi\) |
0.659684 | + | 0.751543i | \(0.270690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.49052 | −0.208972 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.1980 | −0.668015 | −0.334008 | − | 0.942570i | \(-0.608401\pi\) | ||||
−0.334008 | + | 0.942570i | \(0.608401\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.62187 | − | 3.82314i | 0.393629 | − | 0.227262i | −0.290102 | − | 0.956996i | \(-0.593689\pi\) |
0.683731 | + | 0.729734i | \(0.260356\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.04642 | − | 22.9307i | 0.297881 | − | 1.35356i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.1890 | − | 29.7721i | 1.01111 | − | 1.75130i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.299494 | + | 0.518739i | 0.0175567 | + | 0.0304090i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 6.12561i | − | 0.357862i | −0.983862 | − | 0.178931i | \(-0.942736\pi\) | ||
0.983862 | − | 0.178931i | \(-0.0572639\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.09059 | − | 1.20700i | 0.121308 | − | 0.0700374i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.9734 | − | 27.6667i | 0.923764 | − | 1.60001i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.8834 | − | 2.61521i | −0.684949 | − | 0.150738i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −27.8164 | − | 16.0598i | −1.59801 | − | 0.922613i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.4080i | 1.50719i | 0.657341 | + | 0.753593i | \(0.271681\pi\) | ||||
−0.657341 | + | 0.753593i | \(0.728319\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.65927 | 0.492608 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.67641 | + | 16.7600i | 0.548699 | + | 0.950374i | 0.998364 | + | 0.0571771i | \(0.0182100\pi\) |
−0.449665 | + | 0.893197i | \(0.648457\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.54009 | + | 4.35327i | 0.426191 | + | 0.246062i | 0.697723 | − | 0.716368i | \(-0.254197\pi\) |
−0.271531 | + | 0.962430i | \(0.587530\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.2289 | − | 7.63770i | −0.743008 | − | 0.428976i | 0.0801539 | − | 0.996782i | \(-0.474459\pi\) |
−0.823162 | + | 0.567807i | \(0.807792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.54521 | − | 2.67638i | −0.0865150 | − | 0.149848i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 45.5629 | 2.54307 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 22.7065i | − | 1.26343i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.1357 | + | 7.58392i | 0.726408 | + | 0.419392i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.715575 | − | 0.783342i | 0.0394509 | − | 0.0431870i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.37439 | + | 14.5049i | −0.460298 | + | 0.797259i | −0.998976 | − | 0.0452526i | \(-0.985591\pi\) |
0.538678 | + | 0.842512i | \(0.318924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 20.9031 | − | 12.0684i | 1.14548 | − | 0.661344i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 31.2453i | − | 1.70204i | −0.525135 | − | 0.851019i | \(-0.675985\pi\) | ||
0.525135 | − | 0.851019i | \(-0.324015\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −20.0900 | − | 34.7968i | −1.09114 | − | 1.88990i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.760783 | − | 1.31772i | 0.0411987 | − | 0.0713583i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.2061 | − | 14.7453i | 0.605074 | − | 0.796169i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.4811 | − | 6.05125i | 0.562654 | − | 0.324848i | −0.191556 | − | 0.981482i | \(-0.561353\pi\) |
0.754210 | + | 0.656633i | \(0.228020\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.87439 | 0.207391 | 0.103696 | − | 0.994609i | \(-0.466933\pi\) | ||||
0.103696 | + | 0.994609i | \(0.466933\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.56885 | −0.457371 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.22031 | − | 1.28190i | 0.118175 | − | 0.0682284i | −0.439747 | − | 0.898122i | \(-0.644932\pi\) |
0.557922 | + | 0.829893i | \(0.311599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 35.9684 | + | 32.8568i | 1.90365 | + | 1.73897i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4196 | − | 18.0473i | 0.549925 | − | 0.952498i | −0.448354 | − | 0.893856i | \(-0.647990\pi\) |
0.998279 | − | 0.0586422i | \(-0.0186771\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.48240 | + | 7.76375i | 0.235916 | + | 0.408618i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 21.9347i | − | 1.15127i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.7111 | + | 7.91608i | −0.715711 | + | 0.413216i | −0.813172 | − | 0.582023i | \(-0.802261\pi\) |
0.0974609 | + | 0.995239i | \(0.468928\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.9694 | + | 27.6598i | −0.831334 | + | 1.43991i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.62614 | − | 24.0572i | −0.395930 | − | 1.24899i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.4886 | + | 11.2518i | 1.00908 | + | 0.582594i | 0.910923 | − | 0.412577i | \(-0.135371\pi\) |
0.0981594 | + | 0.995171i | \(0.468704\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.9699i | 0.564977i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.36581 | 0.378356 | 0.189178 | − | 0.981943i | \(-0.439418\pi\) | ||||
0.189178 | + | 0.981943i | \(0.439418\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.5362 | + | 28.6415i | 0.847174 | + | 1.46735i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.1446 | + | 16.8266i | 1.48922 | + | 0.859802i | 0.999924 | − | 0.0123162i | \(-0.00392046\pi\) |
0.489296 | + | 0.872118i | \(0.337254\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.3342 | + | 8.27585i | 0.728648 | + | 0.420685i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.74273 | + | 15.1429i | 0.443274 | + | 0.767773i | 0.997930 | − | 0.0643065i | \(-0.0204835\pi\) |
−0.554656 | + | 0.832080i | \(0.687150\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.1196 | 2.07951 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.585994i | − | 0.0295595i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.58092 | + | 3.79949i | 0.330287 | + | 0.190691i | 0.655968 | − | 0.754788i | \(-0.272260\pi\) |
−0.325682 | + | 0.945479i | \(0.605594\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.0272 | + | 4.62750i | 1.05267 | + | 0.231665i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.42212 | + | 9.39139i | −0.270768 | + | 0.468984i | −0.969059 | − | 0.246830i | \(-0.920611\pi\) |
0.698291 | + | 0.715814i | \(0.253944\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.67741 | + | 2.70051i | −0.232999 | + | 0.134522i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.5216i | 0.521535i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.43466 | − | 14.6093i | −0.417067 | − | 0.722382i | 0.578576 | − | 0.815629i | \(-0.303609\pi\) |
−0.995643 | + | 0.0932469i | \(0.970275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.4286 | + | 21.5270i | −0.613059 | + | 1.06185i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.5229 | − | 3.65277i | 0.567006 | − | 0.179741i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.5213 | − | 15.8895i | 1.34773 | − | 0.778110i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.03014 | 0.196885 | 0.0984426 | − | 0.995143i | \(-0.468614\pi\) | ||||
0.0984426 | + | 0.995143i | \(0.468614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.1196 | 1.22426 | 0.612128 | − | 0.790758i | \(-0.290314\pi\) | ||||
0.612128 | + | 0.790758i | \(0.290314\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.24988 | + | 0.721618i | −0.0607712 | + | 0.0350863i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.8981 | − | 27.3116i | −1.44687 | − | 1.32170i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 11.2216 | − | 19.4364i | 0.541785 | − | 0.938399i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.1201 | − | 26.1888i | −0.728310 | − | 1.26147i | −0.957597 | − | 0.288111i | \(-0.906973\pi\) |
0.229288 | − | 0.973359i | \(-0.426360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.9769i | 1.10420i | 0.833778 | + | 0.552099i | \(0.186173\pi\) | ||||
−0.833778 | + | 0.552099i | \(0.813827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.7382 | − | 9.08645i | 0.752860 | − | 0.434664i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.97590 | − | 10.3506i | 0.285214 | − | 0.494006i | −0.687447 | − | 0.726235i | \(-0.741269\pi\) |
0.972661 | + | 0.232229i | \(0.0746019\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.5920 | + | 14.5138i | −0.980573 | + | 0.691135i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.2175 | − | 7.05378i | −0.580471 | − | 0.335135i | 0.180849 | − | 0.983511i | \(-0.442115\pi\) |
−0.761321 | + | 0.648376i | \(0.775449\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 30.5939i | − | 1.44704i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −37.9468 | −1.79082 | −0.895409 | − | 0.445245i | \(-0.853117\pi\) | ||||
−0.895409 | + | 0.445245i | \(0.853117\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.96129 | − | 12.0573i | −0.327794 | − | 0.567756i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.1798 | − | 12.8055i | −1.04210 | − | 0.601657i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.0611 | + | 9.27287i | 0.751306 | + | 0.433767i | 0.826165 | − | 0.563428i | \(-0.190518\pi\) |
−0.0748598 | + | 0.997194i | \(0.523851\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.51462 | − | 9.55159i | −0.257400 | − | 0.445830i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −23.2453 | −1.08264 | −0.541320 | − | 0.840817i | \(-0.682075\pi\) | ||||
−0.541320 | + | 0.840817i | \(0.682075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.59393i | − | 0.352920i | −0.984308 | − | 0.176460i | \(-0.943535\pi\) | ||
0.984308 | − | 0.176460i | \(-0.0564646\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −24.3941 | − | 14.0839i | −1.12882 | − | 0.651726i | −0.185184 | − | 0.982704i | \(-0.559288\pi\) |
−0.943639 | + | 0.330978i | \(0.892621\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.689404 | + | 2.17478i | 0.0318337 | + | 0.100422i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.4673 | + | 26.7902i | −0.712697 | + | 1.23443i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.24848 | + | 3.60756i | −0.287305 | + | 0.165876i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.3297i | 1.57185i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0900 | − | 29.6007i | −0.780860 | − | 1.35249i | −0.931441 | − | 0.363892i | \(-0.881448\pi\) |
0.150581 | − | 0.988598i | \(-0.451886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.6739 | − | 32.3441i | 0.851456 | − | 1.47476i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.38002 | + | 38.0784i | −0.381304 | + | 1.73263i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.96234 | + | 5.75176i | −0.451436 | + | 0.260637i | −0.708437 | − | 0.705774i | \(-0.750599\pi\) |
0.257000 | + | 0.966411i | \(0.417266\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −42.9940 | −1.94426 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.5337 | −1.15232 | −0.576159 | − | 0.817338i | \(-0.695449\pi\) | ||||
−0.576159 | + | 0.817338i | \(0.695449\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.2280 | + | 7.05982i | −0.550720 | + | 0.317958i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.90210 | − | 31.3628i | 0.309602 | − | 1.40682i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.69798 | + | 9.86919i | −0.255076 | + | 0.441805i | −0.964916 | − | 0.262558i | \(-0.915434\pi\) |
0.709840 | + | 0.704363i | \(0.248767\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.69148 | − | 15.0541i | −0.388307 | − | 0.672567i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.49649i | 0.111313i | 0.998450 | + | 0.0556564i | \(0.0177251\pi\) | ||||
−0.998450 | + | 0.0556564i | \(0.982275\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −40.0713 | + | 23.1352i | −1.77963 | + | 1.02747i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.77188 | − | 9.99720i | 0.255834 | − | 0.443118i | −0.709287 | − | 0.704919i | \(-0.750983\pi\) |
0.965122 | + | 0.261801i | \(0.0843165\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.19798 | − | 10.0883i | −0.141470 | − | 0.446278i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.22134 | − | 2.43719i | −0.186377 | − | 0.107605i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 0.629127i | − | 0.0276690i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.0594 | 0.529348 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11.8744 | − | 20.5670i | −0.520226 | − | 0.901058i | −0.999723 | − | 0.0235150i | \(-0.992514\pi\) |
0.479497 | − | 0.877543i | \(-0.340819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.9757 | + | 8.06885i | 0.611113 | + | 0.352826i | 0.773401 | − | 0.633917i | \(-0.218554\pi\) |
−0.162288 | + | 0.986743i | \(0.551887\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.02044 | − | 3.47590i | −0.262255 | − | 0.151413i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.95479 | + | 8.58195i | 0.215426 | + | 0.373128i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.4432 | −0.713576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 49.4201i | 2.14062i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.5247 | + | 14.7367i | 1.10147 | + | 0.635935i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.990974 | − | 10.9371i | −0.0426843 | − | 0.471096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.769355 | − | 1.33256i | 0.0330772 | − | 0.0572913i | −0.849013 | − | 0.528372i | \(-0.822803\pi\) |
0.882090 | + | 0.471081i | \(0.156136\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.85130 | − | 1.06885i | 0.0794470 | − | 0.0458687i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.3779i | − | 0.614755i | −0.951588 | − | 0.307377i | \(-0.900549\pi\) | ||
0.951588 | − | 0.307377i | \(-0.0994514\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.5422 | + | 47.7045i | 1.17547 | + | 2.03598i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.12010 | + | 5.40417i | −0.132921 | + | 0.230226i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.1490 | − | 22.9734i | −1.06944 | − | 0.976927i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.6658 | + | 8.46733i | −0.621412 | + | 0.358772i | −0.777419 | − | 0.628984i | \(-0.783471\pi\) |
0.156007 | + | 0.987756i | \(0.450138\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 25.6111 | 1.08323 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 28.8874 | 1.21963 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.575322 | + | 0.332162i | −0.0242469 | + | 0.0139990i | −0.512074 | − | 0.858941i | \(-0.671123\pi\) |
0.487828 | + | 0.872940i | \(0.337789\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.2616 | + | 5.47194i | −0.724921 | + | 0.229800i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.5186 | + | 35.5392i | −0.860184 | + | 1.48988i | 0.0115674 | + | 0.999933i | \(0.496318\pi\) |
−0.871751 | + | 0.489949i | \(0.837015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.3146 | + | 24.7936i | 0.599046 | + | 1.03758i | 0.992962 | + | 0.118432i | \(0.0377866\pi\) |
−0.393916 | + | 0.919146i | \(0.628880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.8271i | 0.744738i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.2455 | − | 15.7302i | 1.13424 | − | 0.654856i | 0.189246 | − | 0.981930i | \(-0.439396\pi\) |
0.944999 | + | 0.327073i | \(0.106062\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −25.2729 | + | 43.7739i | −1.05030 | + | 1.81918i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 44.2046 | + | 9.72821i | 1.83391 | + | 0.403594i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.9599 | − | 7.48240i | −0.536744 | − | 0.309889i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 9.53871i | − | 0.393705i | −0.980433 | − | 0.196852i | \(-0.936928\pi\) | ||
0.980433 | − | 0.196852i | \(-0.0630720\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.07236 | −0.126595 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.6050 | − | 35.6890i | −0.847578 | − | 1.46805i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.60805 | + | 4.96986i | 0.353490 | + | 0.204088i | 0.666221 | − | 0.745754i | \(-0.267911\pi\) |
−0.312731 | + | 0.949842i | \(0.601244\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.7517 | − | 13.7130i | −0.972092 | − | 0.561238i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4.70655 | + | 8.15198i | 0.192304 | + | 0.333081i | 0.946014 | − | 0.324127i | \(-0.105071\pi\) |
−0.753709 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.00506 | −0.122579 | −0.0612894 | − | 0.998120i | \(-0.519521\pi\) | ||||
−0.0612894 | + | 0.998120i | \(0.519521\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 3.10341i | − | 0.126381i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.3091 | + | 9.41608i | 0.661967 | + | 0.382187i | 0.793026 | − | 0.609188i | \(-0.208504\pi\) |
−0.131059 | + | 0.991375i | \(0.541838\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.04566 | − | 12.7623i | −0.163939 | − | 0.517156i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.11659 | + | 1.93399i | −0.0451723 | + | 0.0782407i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.7171 | + | 7.91959i | −0.554030 | + | 0.319869i | −0.750746 | − | 0.660591i | \(-0.770306\pi\) |
0.196716 | + | 0.980461i | \(0.436972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 0.778912i | − | 0.0313578i | −0.999877 | − | 0.0156789i | \(-0.995009\pi\) | ||
0.999877 | − | 0.0156789i | \(-0.00499096\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.97338 | + | 8.61414i | 0.199897 | + | 0.346231i | 0.948495 | − | 0.316793i | \(-0.102606\pi\) |
−0.748598 | + | 0.663024i | \(0.769273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.41355 | − | 7.64450i | 0.177110 | − | 0.306763i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.9371 | − | 9.99097i | −0.438187 | − | 0.400280i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.0564 | − | 6.38341i | 0.441550 | − | 0.254929i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 48.0715 | 1.91673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5638 | −0.500157 | −0.250078 | − | 0.968226i | \(-0.580456\pi\) | ||||
−0.250078 | + | 0.968226i | \(0.580456\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 25.2854 | − | 14.5985i | 1.00500 | − | 0.580240i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3651 | + | 35.3804i | −0.648410 | + | 1.40182i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −21.8417 | + | 37.8310i | −0.864045 | + | 1.49657i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.76033 | + | 9.97718i | 0.227519 | + | 0.394075i | 0.957072 | − | 0.289849i | \(-0.0936052\pi\) |
−0.729553 | + | 0.683924i | \(0.760272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.74175i | 0.384177i | 0.981378 | + | 0.192088i | \(0.0615261\pi\) | ||||
−0.981378 | + | 0.192088i | \(0.938474\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −22.3035 | + | 12.8769i | −0.876840 | + | 0.506244i | −0.869615 | − | 0.493730i | \(-0.835633\pi\) |
−0.00722479 | + | 0.999974i | \(0.502300\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.58392 | − | 6.20753i | 0.140681 | − | 0.243667i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.44577 | − | 4.86679i | 0.174243 | − | 0.190745i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.1575 | − | 7.59646i | −0.514891 | − | 0.297272i | 0.219951 | − | 0.975511i | \(-0.429410\pi\) |
−0.734842 | + | 0.678239i | \(0.762744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.3960i | 0.561640i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.6894 | 0.572218 | 0.286109 | − | 0.958197i | \(-0.407638\pi\) | ||||
0.286109 | + | 0.958197i | \(0.407638\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.16784 | − | 3.75481i | −0.0843191 | − | 0.146045i | 0.820782 | − | 0.571242i | \(-0.193538\pi\) |
−0.905101 | + | 0.425197i | \(0.860205\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −88.8020 | − | 51.2699i | −3.44879 | − | 1.99116i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.78650 | − | 5.65024i | −0.378935 | − | 0.218778i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.76078 | + | 13.4421i | 0.300049 | + | 0.519700i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −24.0121 | −0.926976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 34.1971i | − | 1.31820i | −0.752055 | − | 0.659100i | \(-0.770937\pi\) | ||
0.752055 | − | 0.659100i | \(-0.229063\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6668 | − | 9.04521i | −0.602122 | − | 0.347636i | 0.167754 | − | 0.985829i | \(-0.446349\pi\) |
−0.769876 | + | 0.638193i | \(0.779682\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.602502 | − | 0.132594i | −0.0231219 | − | 0.00508850i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.7965 | − | 48.1450i | 1.06516 | − | 1.84492i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.8934 | − | 12.0628i | 0.799464 | − | 0.461570i | −0.0438200 | − | 0.999039i | \(-0.513953\pi\) |
0.843284 | + | 0.537469i | \(0.180619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 13.9518i | 0.532295i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.5598 | + | 46.0030i | 1.01185 | + | 1.75257i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.72415 | + | 15.1107i | −0.331882 | + | 0.574837i | −0.982881 | − | 0.184242i | \(-0.941017\pi\) |
0.650999 | + | 0.759079i | \(0.274350\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.21075 | + | 14.5895i | −0.121966 | + | 0.554210i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −55.0880 | + | 31.8051i | −2.08661 | + | 1.20470i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.8271 | −0.674283 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7015 | 0.781885 | 0.390942 | − | 0.920415i | \(-0.372149\pi\) | ||||
0.390942 | + | 0.920415i | \(0.372149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3989 | − | 10.6226i | 0.693929 | − | 0.400640i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 31.5347 | − | 9.99649i | 1.18598 | − | 0.375957i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.54774 | − | 6.14486i | 0.133238 | − | 0.230775i | −0.791685 | − | 0.610930i | \(-0.790796\pi\) |
0.924923 | + | 0.380154i | \(0.124129\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.1674 | + | 40.1271i | 0.868845 | + | 1.50488i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.56379i | − | 0.208366i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.76965 | + | 2.17641i | −0.140780 | + | 0.0812795i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.2216 | − | 45.4172i | 0.977901 | − | 1.69377i | 0.307893 | − | 0.951421i | \(-0.400376\pi\) |
0.670008 | − | 0.742354i | \(-0.266291\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.01507 | + | 6.58471i | −0.224013 | + | 0.245227i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 33.2250 | + | 19.1825i | 1.23565 | + | 0.713403i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 29.9045i | − | 1.10910i | −0.832151 | − | 0.554549i | \(-0.812891\pi\) | ||
0.832151 | − | 0.554549i | \(-0.187109\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.4905 | 1.35150 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.4824 | + | 28.5484i | 0.609624 | + | 1.05590i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.83323 | + | 2.79047i | 0.178519 | + | 0.103068i | 0.586597 | − | 0.809879i | \(-0.300467\pi\) |
−0.408077 | + | 0.912947i | \(0.633801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.17158 | + | 0.676410i | 0.0431556 | + | 0.0249159i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.3744 | + | 35.2895i | 0.749484 | + | 1.29814i | 0.948070 | + | 0.318061i | \(0.103032\pi\) |
−0.198586 | + | 0.980083i | \(0.563635\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −45.3176 | −1.66478 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 50.5327i | − | 1.85387i | −0.375226 | − | 0.926933i | \(-0.622435\pi\) | ||
0.375226 | − | 0.926933i | \(-0.377565\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −53.3211 | − | 30.7850i | −1.95092 | − | 1.12636i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.6498 | + | 34.6471i | −1.15646 | + | 1.26598i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.3568 | − | 26.5987i | 0.560377 | − | 0.970602i | −0.437086 | − | 0.899420i | \(-0.643990\pi\) |
0.997463 | − | 0.0711821i | \(-0.0226771\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.8211 | − | 11.4437i | 0.722319 | − | 0.417031i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 20.7116i | − | 0.752776i | −0.926462 | − | 0.376388i | \(-0.877166\pi\) | ||
0.926462 | − | 0.376388i | \(-0.122834\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 11.5598 | + | 20.0222i | 0.419595 | + | 0.726760i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.1764 | − | 29.7504i | 0.622644 | − | 1.07845i | −0.366347 | − | 0.930478i | \(-0.619392\pi\) |
0.988991 | − | 0.147973i | \(-0.0472750\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.8916 | + | 4.72063i | −0.539112 | + | 0.170898i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22.0345 | + | 12.7216i | −0.795619 | + | 0.459351i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.8392 | −1.68906 | −0.844532 | − | 0.535505i | \(-0.820121\pi\) | ||||
−0.844532 | + | 0.535505i | \(0.820121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.8262 | −0.894094 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.8652 | + | 16.6653i | −1.03821 | + | 0.599409i | −0.919325 | − | 0.393499i | \(-0.871265\pi\) |
−0.118883 | + | 0.992908i | \(0.537931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −9.79677 | + | 44.5161i | −0.351457 | + | 1.59700i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.0563 | + | 24.3462i | −0.503620 | + | 0.872295i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.52111 | − | 16.4911i | −0.340692 | − | 0.590096i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.03105i | 0.108321i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.28158 | − | 4.20402i | 0.259560 | − | 0.149857i | −0.364574 | − | 0.931175i | \(-0.618785\pi\) |
0.624134 | + | 0.781317i | \(0.285452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.83821 | − | 13.5762i | 0.279047 | − | 0.483324i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 40.4156 | + | 8.89438i | 1.43701 | + | 0.316248i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 73.8150 | + | 42.6171i | 2.62125 | + | 1.51338i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.2935i | 0.577144i | 0.957458 | + | 0.288572i | \(0.0931804\pi\) | ||||
−0.957458 | + | 0.288572i | \(0.906820\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.87439 | −0.101688 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.0753 | + | 17.4510i | 0.355995 | + | 0.616601i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.43465 | − | 3.13770i | −0.191785 | − | 0.110727i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 50.1304 | + | 28.9428i | 1.76467 | + | 1.01883i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.75176 | − | 13.4264i | −0.272537 | − | 0.472048i | 0.696974 | − | 0.717097i | \(-0.254529\pi\) |
−0.969511 | + | 0.245048i | \(0.921196\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.6232 | −1.28601 | −0.643007 | − | 0.765861i | \(-0.722313\pi\) | ||||
−0.643007 | + | 0.765861i | \(0.722313\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11.4604i | 0.401933i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.6170 | + | 7.28442i | 0.441413 | + | 0.254850i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.7638 | − | 39.1508i | 1.24969 | − | 1.36804i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.6649 | − | 37.5246i | 0.756109 | − | 1.30962i | −0.188713 | − | 0.982032i | \(-0.560431\pi\) |
0.944821 | − | 0.327586i | \(-0.106235\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.5541 | + | 20.5272i | −1.23934 | + | 0.715532i | −0.968959 | − | 0.247222i | \(-0.920482\pi\) |
−0.270378 | + | 0.962754i | \(0.587149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0473i | 1.04485i | 0.852686 | + | 0.522423i | \(0.174972\pi\) | ||||
−0.852686 | + | 0.522423i | \(0.825028\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.0146 | − | 36.3984i | −0.729868 | − | 1.26417i | −0.956939 | − | 0.290290i | \(-0.906248\pi\) |
0.227071 | − | 0.973878i | \(-0.427085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.35977 | − | 14.4795i | 0.289997 | − | 0.502290i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.9702 | + | 4.52761i | −1.73136 | + | 0.156872i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.29240 | + | 0.746168i | −0.0446719 | + | 0.0257913i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.38893 | −0.116999 | −0.0584994 | − | 0.998287i | \(-0.518632\pi\) | ||||
−0.0584994 | + | 0.998287i | \(0.518632\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.1196 | −0.866195 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −24.9120 | + | 14.3830i | −0.858015 | + | 0.495375i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.6796 | + | 15.2367i | 0.573119 | + | 0.523539i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.82106 | − | 17.0106i | 0.337058 | − | 0.583801i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.2367 | + | 33.3189i | 0.659425 | + | 1.14216i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.1267i | − | 0.860321i | −0.902752 | − | 0.430160i | \(-0.858457\pi\) | ||
0.902752 | − | 0.430160i | \(-0.141543\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.3412 | − | 23.8683i | 1.41219 | − | 0.815327i | 0.416594 | − | 0.909093i | \(-0.363224\pi\) |
0.995594 | + | 0.0937657i | \(0.0298905\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5211 | + | 35.5436i | −0.700171 | + | 1.21273i | 0.268235 | + | 0.963354i | \(0.413560\pi\) |
−0.968406 | + | 0.249379i | \(0.919774\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −18.2260 | − | 57.4954i | −0.621142 | − | 1.95944i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.9617 | + | 15.5663i | 0.917786 | + | 0.529884i | 0.882928 | − | 0.469509i | \(-0.155569\pi\) |
0.0348576 | + | 0.999392i | \(0.488902\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 88.3117i | − | 2.99922i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.1980 | −0.685169 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.40101 | − | 4.15867i | −0.0813552 | − | 0.140911i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.726760 | + | 0.419595i | 0.0245971 | + | 0.0142011i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.87600 | − | 3.96986i | −0.232186 | − | 0.134053i | 0.379394 | − | 0.925235i | \(-0.376132\pi\) |
−0.611580 | + | 0.791182i | \(0.709466\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.86789 | − | 13.6276i | −0.265377 | − | 0.459647i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.3709 | −0.989530 | −0.494765 | − | 0.869027i | \(-0.664746\pi\) | ||||
−0.494765 | + | 0.869027i | \(0.664746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.9718i | 0.907674i | 0.891085 | + | 0.453837i | \(0.149945\pi\) | ||||
−0.891085 | + | 0.453837i | \(0.850055\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.3390 | + | 11.7427i | 0.682917 | + | 0.394282i | 0.800953 | − | 0.598727i | \(-0.204327\pi\) |
−0.118036 | + | 0.993009i | \(0.537660\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −33.2664 | − | 7.32102i | −1.11572 | − | 0.245539i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.36880 | + | 9.29903i | −0.179861 | + | 0.311529i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.10015 | + | 0.635170i | −0.0368150 | + | 0.0212552i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 82.0664i | − | 2.74012i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.955246 | + | 1.65453i | 0.0318592 | + | 0.0551818i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −34.1860 | + | 59.2118i | −1.13890 | + | 1.97263i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −29.7959 | + | 9.44531i | −0.991547 | + | 0.314320i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.30250 | − | 4.79345i | 0.275680 | − | 0.159164i | −0.355786 | − | 0.934567i | \(-0.615787\pi\) |
0.631466 | + | 0.775403i | \(0.282453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −45.0000 | −1.49256 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.78994 | −0.125566 | −0.0627831 | − | 0.998027i | \(-0.519998\pi\) | ||||
−0.0627831 | + | 0.998027i | \(0.519998\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.2434 | − | 13.4196i | 0.769245 | − | 0.444124i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.445604 | + | 0.407055i | 0.0147151 | + | 0.0134421i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.6950 | − | 20.2563i | 0.385782 | − | 0.668194i | −0.606095 | − | 0.795392i | \(-0.707265\pi\) |
0.991877 | + | 0.127198i | \(0.0405983\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 33.9191 | + | 58.7497i | 1.11767 | + | 1.93587i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 67.5930i | 2.22485i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.5064 | − | 6.06587i | 0.345075 | − | 0.199229i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 25.1287 | − | 43.5241i | 0.824445 | − | 1.42798i | −0.0778977 | − | 0.996961i | \(-0.524821\pi\) |
0.902343 | − | 0.431019i | \(-0.141846\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.1252 | + | 12.7751i | −0.594028 | + | 0.418687i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 43.0540 | + | 24.8572i | 1.40952 | + | 0.813790i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 2.43621i | − | 0.0795875i | −0.999208 | − | 0.0397937i | \(-0.987330\pi\) | ||
0.999208 | − | 0.0397937i | \(-0.0126701\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.3658 | 0.729881 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.9824 | + | 20.7541i | 0.390615 | + | 0.676565i | 0.992531 | − | 0.121994i | \(-0.0389290\pi\) |
−0.601916 | + | 0.798560i | \(0.705596\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.0890 | − | 25.4548i | −1.43574 | − | 0.828922i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.3075 | + | 25.5809i | 1.43980 | + | 0.831269i | 0.997835 | − | 0.0657639i | \(-0.0209484\pi\) |
0.441964 | + | 0.897033i | \(0.354282\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.1377 | + | 19.2911i | 0.361545 | + | 0.626214i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −39.2402 | −1.27245 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33.3306i | − | 1.07968i | −0.841766 | − | 0.539842i | \(-0.818484\pi\) | ||
0.841766 | − | 0.539842i | \(-0.181516\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.87521 | − | 3.96941i | −0.222244 | − | 0.128313i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.73623 | − | 24.4045i | −0.249816 | − | 0.788063i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0297 | − | 26.0322i | 0.484829 | − | 0.839748i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 55.2820 | − | 31.9171i | 1.78144 | − | 1.02851i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.8392i | − | 1.02388i | −0.859021 | − | 0.511940i | \(-0.828927\pi\) | ||
0.859021 | − | 0.511940i | \(-0.171073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −29.1649 | − | 50.5150i | −0.936910 | − | 1.62278i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.973375 | + | 1.68594i | −0.0312371 | + | 0.0541042i | −0.881221 | − | 0.472704i | \(-0.843278\pi\) |
0.849984 | + | 0.526808i | \(0.176611\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.03470 | + | 31.9653i | −0.225522 | + | 1.02476i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.4049 | + | 25.0598i | −1.38865 | + | 0.801735i | −0.993163 | − | 0.116739i | \(-0.962756\pi\) |
−0.395483 | + | 0.918473i | \(0.629423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.78397 | −0.280737 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.2503 | 0.678470 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.5014 | − | 23.9608i | 1.32369 | − | 0.764232i | 0.339374 | − | 0.940652i | \(-0.389785\pi\) |
0.984315 | + | 0.176420i | \(0.0564516\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.585788 | − | 2.66179i | 0.0186458 | − | 0.0847259i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.1915 | + | 22.8483i | −0.419465 | + | 0.726534i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.43466 | − | 7.68106i | −0.140872 | − | 0.243997i | 0.786953 | − | 0.617012i | \(-0.211657\pi\) |
−0.927825 | + | 0.373015i | \(0.878324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.0251i | 1.36536i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5742 | − | 6.10503i | 0.334889 | − | 0.193348i | −0.323121 | − | 0.946358i | \(-0.604732\pi\) |
0.658010 | + | 0.753010i | \(0.271399\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.15972 | − | 8.93690i | 0.163246 | − | 0.282751i |
(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 | 700.2.r.d.149.5 | 12 | ||
5.2 | odd | 4 | 700.2.i.e.401.1 | yes | 6 | ||
5.3 | odd | 4 | 700.2.i.d.401.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 700.2.r.d.149.2 | 12 | ||
7.2 | even | 3 | 4900.2.e.t.2549.5 | 6 | |||
7.4 | even | 3 | inner | 700.2.r.d.249.2 | 12 | ||
7.5 | odd | 6 | 4900.2.e.s.2549.2 | 6 | |||
35.2 | odd | 12 | 4900.2.a.ba.1.3 | 3 | |||
35.4 | even | 6 | inner | 700.2.r.d.249.5 | 12 | ||
35.9 | even | 6 | 4900.2.e.t.2549.2 | 6 | |||
35.12 | even | 12 | 4900.2.a.bd.1.1 | 3 | |||
35.18 | odd | 12 | 700.2.i.d.501.3 | yes | 6 | ||
35.19 | odd | 6 | 4900.2.e.s.2549.5 | 6 | |||
35.23 | odd | 12 | 4900.2.a.bc.1.1 | 3 | |||
35.32 | odd | 12 | 700.2.i.e.501.1 | yes | 6 | ||
35.33 | even | 12 | 4900.2.a.bb.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
700.2.i.d.401.3 | ✓ | 6 | 5.3 | odd | 4 | ||
700.2.i.d.501.3 | yes | 6 | 35.18 | odd | 12 | ||
700.2.i.e.401.1 | yes | 6 | 5.2 | odd | 4 | ||
700.2.i.e.501.1 | yes | 6 | 35.32 | odd | 12 | ||
700.2.r.d.149.2 | 12 | 5.4 | even | 2 | inner | ||
700.2.r.d.149.5 | 12 | 1.1 | even | 1 | trivial | ||
700.2.r.d.249.2 | 12 | 7.4 | even | 3 | inner | ||
700.2.r.d.249.5 | 12 | 35.4 | even | 6 | inner | ||
4900.2.a.ba.1.3 | 3 | 35.2 | odd | 12 | |||
4900.2.a.bb.1.3 | 3 | 35.33 | even | 12 | |||
4900.2.a.bc.1.1 | 3 | 35.23 | odd | 12 | |||
4900.2.a.bd.1.1 | 3 | 35.12 | even | 12 | |||
4900.2.e.s.2549.2 | 6 | 7.5 | odd | 6 | |||
4900.2.e.s.2549.5 | 6 | 35.19 | odd | 6 | |||
4900.2.e.t.2549.2 | 6 | 35.9 | even | 6 | |||
4900.2.e.t.2549.5 | 6 | 7.2 | even | 3 |