Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(589,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.j (of order \(3\), degree \(2\), 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 589.5 | ||
Character | \(\chi\) | \(=\) | 1764.589 |
Dual form | 1764.2.j.i.1177.5 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.899846 | − | 1.47996i | −0.519526 | − | 0.854454i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.19243 | − | 2.06535i | 0.533271 | − | 0.923653i | −0.465974 | − | 0.884799i | \(-0.654296\pi\) |
0.999245 | − | 0.0388541i | \(-0.0123708\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.38055 | + | 2.66347i | −0.460185 | + | 0.887823i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.12978 | + | 1.95684i | 0.340642 | + | 0.590009i | 0.984552 | − | 0.175092i | \(-0.0560224\pi\) |
−0.643910 | + | 0.765101i | \(0.722689\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.37884 | − | 4.12027i | 0.659770 | − | 1.14276i | −0.320904 | − | 0.947112i | \(-0.603987\pi\) |
0.980675 | − | 0.195644i | \(-0.0626798\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.12964 | + | 0.0937498i | −1.06627 | + | 0.0242061i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.30404 | −1.04388 | −0.521941 | − | 0.852982i | \(-0.674792\pi\) | ||||
−0.521941 | + | 0.852982i | \(0.674792\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.59629 | −1.97212 | −0.986062 | − | 0.166378i | \(-0.946793\pi\) | ||||
−0.986062 | + | 0.166378i | \(0.946793\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.664550 | + | 1.15103i | −0.138568 | + | 0.240007i | −0.926955 | − | 0.375173i | \(-0.877583\pi\) |
0.788387 | + | 0.615180i | \(0.210917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.343781 | − | 0.595446i | −0.0687562 | − | 0.119089i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.18411 | − | 0.353550i | 0.997683 | − | 0.0680408i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.87886 | − | 6.71839i | −0.720287 | − | 1.24757i | −0.960885 | − | 0.276948i | \(-0.910677\pi\) |
0.240598 | − | 0.970625i | \(-0.422656\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.405320 | + | 0.702036i | −0.0727977 | + | 0.126089i | −0.900126 | − | 0.435629i | \(-0.856526\pi\) |
0.827329 | + | 0.561718i | \(0.189859\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.87941 | − | 3.43288i | 0.327163 | − | 0.597588i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.63226 | −0.761539 | −0.380770 | − | 0.924670i | \(-0.624341\pi\) | ||||
−0.380770 | + | 0.924670i | \(0.624341\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.23841 | + | 0.187026i | −1.31920 | + | 0.0299481i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00426 | − | 8.66764i | 0.781534 | − | 1.35366i | −0.149513 | − | 0.988760i | \(-0.547771\pi\) |
0.931048 | − | 0.364898i | \(-0.118896\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.74292 | − | 3.01883i | −0.265793 | − | 0.460367i | 0.701978 | − | 0.712199i | \(-0.252300\pi\) |
−0.967771 | + | 0.251831i | \(0.918967\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.85478 | + | 6.02733i | 0.574637 | + | 0.898501i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.18338 | + | 3.78173i | 0.318479 | + | 0.551622i | 0.980171 | − | 0.198154i | \(-0.0634946\pi\) |
−0.661692 | + | 0.749776i | \(0.730161\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.87297 | + | 6.36979i | 0.542324 | + | 0.891950i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6787 | −1.60419 | −0.802094 | − | 0.597197i | \(-0.796281\pi\) | ||||
−0.802094 | + | 0.597197i | \(0.796281\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.38874 | 0.726617 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.73534 | + | 12.7222i | 1.02457 | + | 1.68509i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.40463 | − | 4.16495i | 0.313056 | − | 0.542230i | −0.665966 | − | 0.745982i | \(-0.731980\pi\) |
0.979022 | + | 0.203752i | \(0.0653137\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.575967 | + | 0.997604i | 0.0737450 | + | 0.127730i | 0.900540 | − | 0.434774i | \(-0.143172\pi\) |
−0.826795 | + | 0.562504i | \(0.809838\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.67319 | − | 9.82626i | −0.703673 | − | 1.21880i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.06381 | − | 3.57463i | 0.252135 | − | 0.436710i | −0.711979 | − | 0.702201i | \(-0.752201\pi\) |
0.964113 | + | 0.265491i | \(0.0855341\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.30148 | − | 0.0522474i | 0.277065 | − | 0.00628985i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.41593 | −0.524074 | −0.262037 | − | 0.965058i | \(-0.584394\pi\) | ||||
−0.262037 | + | 0.965058i | \(0.584394\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1118 | −1.41758 | −0.708790 | − | 0.705420i | \(-0.750759\pi\) | ||||
−0.708790 | + | 0.705420i | \(0.750759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.571885 | + | 1.04459i | −0.0660356 | + | 0.120619i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.23312 | + | 7.33198i | 0.476263 | + | 0.824913i | 0.999630 | − | 0.0271950i | \(-0.00865752\pi\) |
−0.523367 | + | 0.852108i | \(0.675324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.18814 | − | 7.35413i | −0.576460 | − | 0.817125i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.817808 | + | 1.41648i | 0.0897661 | + | 0.155479i | 0.907412 | − | 0.420242i | \(-0.138055\pi\) |
−0.817646 | + | 0.575721i | \(0.804721\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.13226 | + | 8.88934i | −0.556672 | + | 0.964184i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −6.45255 | + | 11.7861i | −0.691786 | + | 1.26360i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.34310 | −0.672367 | −0.336184 | − | 0.941796i | \(-0.609136\pi\) | ||||
−0.336184 | + | 0.941796i | \(0.609136\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.40371 | − | 0.0318666i | 0.145558 | − | 0.00330441i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.2505 | + | 17.7543i | −1.05168 | + | 1.82156i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.98278 | + | 10.3625i | 0.607459 | + | 1.05215i | 0.991658 | + | 0.128900i | \(0.0411445\pi\) |
−0.384198 | + | 0.923251i | \(0.625522\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.77170 | + | 0.307617i | −0.680581 | + | 0.0309166i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.42348 | − | 9.39374i | −0.539656 | − | 0.934712i | −0.998922 | − | 0.0464132i | \(-0.985221\pi\) |
0.459266 | − | 0.888299i | \(-0.348112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.17226 | + | 15.8868i | −0.903769 | + | 1.56537i | −0.0812086 | + | 0.996697i | \(0.525878\pi\) |
−0.822561 | + | 0.568677i | \(0.807455\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.83412 | 0.370658 | 0.185329 | − | 0.982676i | \(-0.440665\pi\) | ||||
0.185329 | + | 0.982676i | \(0.440665\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.64496 | 0.253341 | 0.126671 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126671 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.16832 | + | 6.85556i | 0.395640 | + | 0.650701i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.64275 | + | 4.57738i | −0.248609 | + | 0.430603i | −0.963140 | − | 0.269000i | \(-0.913307\pi\) |
0.714531 | + | 0.699604i | \(0.246640\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.58486 | + | 2.74506i | 0.147789 | + | 0.255978i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.69009 | + | 12.0242i | 0.710949 | + | 1.11164i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.94719 | − | 5.10469i | 0.267927 | − | 0.464062i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.3308 | + | 0.393439i | −1.56267 | + | 0.0354752i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.2846 | 0.919880 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.67115 | −0.680704 | −0.340352 | − | 0.940298i | \(-0.610546\pi\) | ||||
−0.340352 | + | 0.940298i | \(0.610546\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.89938 | + | 5.29593i | −0.255276 | + | 0.466281i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.69007 | − | 16.7837i | 0.846625 | − | 1.46640i | −0.0375770 | − | 0.999294i | \(-0.511964\pi\) |
0.884202 | − | 0.467104i | \(-0.154703\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.45149 | − | 11.1286i | 0.469189 | − | 0.957796i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.84498 | + | 8.39176i | 0.413935 | + | 0.716956i | 0.995316 | − | 0.0966750i | \(-0.0308208\pi\) |
−0.581381 | + | 0.813631i | \(0.697487\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.81197 | − | 6.60252i | 0.323327 | − | 0.560018i | −0.657846 | − | 0.753153i | \(-0.728532\pi\) |
0.981172 | + | 0.193135i | \(0.0618654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.63210 | − | 6.63429i | 0.305878 | − | 0.558708i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.7503 | 0.898981 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.5011 | −1.53643 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.54590 | − | 7.87372i | 0.372414 | − | 0.645041i | −0.617522 | − | 0.786554i | \(-0.711863\pi\) |
0.989936 | + | 0.141513i | \(0.0451967\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1291 | + | 17.5441i | 0.824294 | + | 1.42772i | 0.902457 | + | 0.430779i | \(0.141761\pi\) |
−0.0781631 | + | 0.996941i | \(0.524905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.94195 | − | 11.4637i | 0.480379 | − | 0.926783i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.966633 | + | 1.67426i | 0.0776418 | + | 0.134480i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.18075 | + | 7.24127i | −0.333660 | + | 0.577917i | −0.983227 | − | 0.182388i | \(-0.941617\pi\) |
0.649566 | + | 0.760305i | \(0.274951\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.5090 | + | 17.2839i | 0.833418 | + | 1.37071i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.3839 | −1.51826 | −0.759132 | − | 0.650937i | \(-0.774376\pi\) | ||||
−0.759132 | + | 0.650937i | \(0.774376\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.84904 | − | 7.97511i | −0.377497 | − | 0.620861i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.84158 | + | 15.3141i | −0.684182 | + | 1.18504i | 0.289511 | + | 0.957175i | \(0.406507\pi\) |
−0.973693 | + | 0.227864i | \(0.926826\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.81772 | − | 8.34454i | −0.370594 | − | 0.641888i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.8676 | − | 22.8960i | 0.907541 | − | 1.75090i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.5928 | − | 18.3473i | −0.805356 | − | 1.39492i | −0.916051 | − | 0.401063i | \(-0.868641\pi\) |
0.110695 | − | 0.993854i | \(-0.464692\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.32775 | + | 0.189054i | −0.625952 | + | 0.0142102i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.9878 | 0.970753 | 0.485376 | − | 0.874305i | \(-0.338683\pi\) | ||||
0.485376 | + | 0.874305i | \(0.338683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.8238 | −1.25050 | −0.625251 | − | 0.780423i | \(-0.715004\pi\) | ||||
−0.625251 | + | 0.780423i | \(0.715004\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.958131 | − | 1.75010i | 0.0708271 | − | 0.129371i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.52365 | + | 9.56725i | −0.406107 | + | 0.703398i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.86262 | − | 8.42230i | −0.355590 | − | 0.615899i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.58561 | − | 7.94251i | −0.331803 | − | 0.574700i | 0.651062 | − | 0.759024i | \(-0.274324\pi\) |
−0.982865 | + | 0.184324i | \(0.940990\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8153 | − | 22.1968i | 0.922466 | − | 1.59776i | 0.126880 | − | 0.991918i | \(-0.459504\pi\) |
0.795586 | − | 0.605840i | \(-0.207163\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −9.43745 | + | 17.2382i | −0.675830 | + | 1.23445i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.1036 | 1.14734 | 0.573668 | − | 0.819088i | \(-0.305520\pi\) | ||||
0.573668 | + | 0.819088i | \(0.305520\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.2282 | −1.36305 | −0.681526 | − | 0.731794i | \(-0.738683\pi\) | ||||
−0.681526 | + | 0.731794i | \(0.738683\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.14741 | + | 0.162258i | −0.504140 | + | 0.0114448i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.9345 | − | 20.6711i | −0.833540 | − | 1.44373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.14830 | − | 3.35907i | −0.149317 | − | 0.233472i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.71192 | − | 16.8215i | −0.671788 | − | 1.16357i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3251 | + | 21.3477i | −0.848496 | + | 1.46964i | 0.0340549 | + | 0.999420i | \(0.489158\pi\) |
−0.882551 | + | 0.470218i | \(0.844175\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.97365 | + | 6.53539i | 0.272270 | + | 0.447797i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.31325 | −0.566959 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.8988 | + | 17.9250i | 0.736470 | + | 1.21126i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.2386 | + | 17.7338i | −0.688723 | + | 1.19290i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.41074 | − | 12.8358i | −0.496260 | − | 0.859547i | 0.503731 | − | 0.863861i | \(-0.331960\pi\) |
−0.999991 | + | 0.00431335i | \(0.998627\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.06056 | − | 0.0936047i | 0.137371 | − | 0.00624031i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.07752 | − | 15.7227i | −0.602496 | − | 1.04355i | −0.992442 | − | 0.122716i | \(-0.960840\pi\) |
0.389946 | − | 0.920838i | \(-0.372494\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.75346 | − | 8.23323i | 0.314117 | − | 0.544067i | −0.665132 | − | 0.746726i | \(-0.731625\pi\) |
0.979249 | + | 0.202659i | \(0.0649581\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3431 | 1.33272 | 0.666360 | − | 0.745630i | \(-0.267851\pi\) | ||||
0.666360 | + | 0.745630i | \(0.267851\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.4141 | 0.679343 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.04187 | − | 12.8625i | 0.457419 | − | 0.835509i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.90544 | − | 15.4247i | 0.576045 | − | 0.997739i | −0.419882 | − | 0.907579i | \(-0.637929\pi\) |
0.995927 | − | 0.0901607i | \(-0.0287381\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.14437 | + | 5.44620i | 0.202546 | + | 0.350821i | 0.949348 | − | 0.314226i | \(-0.101745\pi\) |
−0.746802 | + | 0.665047i | \(0.768412\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −6.21527 | + | 14.2958i | −0.398710 | + | 0.917077i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.4492 | + | 35.4190i | −1.30115 | + | 2.25366i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.36044 | − | 2.48494i | 0.0862142 | − | 0.157477i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 25.1868 | 1.58978 | 0.794889 | − | 0.606755i | \(-0.207529\pi\) | ||||
0.794889 | + | 0.606755i | \(0.207529\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.00318 | −0.188809 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 17.7741 | − | 0.403502i | 1.11306 | − | 0.0252683i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.3401 | − | 24.8379i | 0.894514 | − | 1.54934i | 0.0601087 | − | 0.998192i | \(-0.480855\pi\) |
0.834405 | − | 0.551152i | \(-0.185811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 23.2492 | − | 1.05614i | 1.43909 | − | 0.0653732i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.20840 | + | 12.4853i | 0.444489 | + | 0.769877i | 0.998016 | − | 0.0629537i | \(-0.0200520\pi\) |
−0.553528 | + | 0.832831i | \(0.686719\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −13.9260 | + | 24.1205i | −0.855468 | + | 1.48171i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.70782 | + | 9.38753i | 0.349313 | + | 0.574507i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.8999 | 0.786524 | 0.393262 | − | 0.919426i | \(-0.371347\pi\) | ||||
0.393262 | + | 0.919426i | \(0.371347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.4622 | 1.18224 | 0.591122 | − | 0.806582i | \(-0.298685\pi\) | ||||
0.591122 | + | 0.806582i | \(0.298685\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.776794 | − | 1.34545i | 0.0468424 | − | 0.0811335i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.95620 | − | 13.7805i | −0.478042 | − | 0.827993i | 0.521641 | − | 0.853165i | \(-0.325320\pi\) |
−0.999683 | + | 0.0251721i | \(0.991987\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.31028 | − | 2.04876i | −0.0784446 | − | 0.122656i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.9998 | − | 24.2484i | −0.835158 | − | 1.44654i | −0.893901 | − | 0.448263i | \(-0.852043\pi\) |
0.0587432 | − | 0.998273i | \(-0.481291\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.62345 | − | 4.54394i | 0.155948 | − | 0.270109i | −0.777456 | − | 0.628937i | \(-0.783490\pi\) |
0.933404 | + | 0.358828i | \(0.116824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 35.4996 | − | 0.805900i | 2.10281 | − | 0.0477374i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.52473 | 0.0896898 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.95246 | − | 18.1789i | 0.583423 | − | 1.06567i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.65939 | + | 2.87415i | −0.0969428 | + | 0.167910i | −0.910418 | − | 0.413690i | \(-0.864240\pi\) |
0.813475 | + | 0.581600i | \(0.197573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.73471 | − | 9.93282i | −0.333888 | − | 0.578311i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.54875 | + | 9.74503i | 0.379997 | + | 0.565464i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.16171 | + | 5.47625i | 0.182847 | + | 0.316700i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −9.02205 | + | 16.4794i | −0.518303 | + | 0.946719i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.74720 | 0.157304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.4703 | −0.711715 | −0.355857 | − | 0.934540i | \(-0.615811\pi\) | ||||
−0.355857 | + | 0.934540i | \(0.615811\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 31.7654 | − | 0.721130i | 1.80707 | − | 0.0410236i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3383 | − | 19.6385i | 0.642936 | − | 1.11360i | −0.341838 | − | 0.939759i | \(-0.611049\pi\) |
0.984774 | − | 0.173840i | \(-0.0556174\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.16108 | + | 5.47515i | 0.178675 | + | 0.309474i | 0.941427 | − | 0.337217i | \(-0.109486\pi\) |
−0.762752 | + | 0.646691i | \(0.776152\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.79041 | + | 13.4934i | 0.437553 | + | 0.757864i | 0.997500 | − | 0.0706643i | \(-0.0225119\pi\) |
−0.559947 | + | 0.828528i | \(0.689179\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.76453 | − | 15.1806i | 0.490719 | − | 0.849951i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.45012 | − | 5.67434i | −0.192567 | − | 0.316711i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 36.9987 | 2.05867 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.27119 | −0.181453 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.38006 | − | 3.91443i | −0.131618 | − | 0.216469i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.8634 | + | 18.8159i | 0.597104 | + | 1.03422i | 0.993246 | + | 0.116026i | \(0.0370155\pi\) |
−0.396142 | + | 0.918189i | \(0.629651\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.39509 | − | 12.3379i | 0.350449 | − | 0.676112i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.92190 | − | 8.52499i | −0.268912 | − | 0.465770i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.04329 | − | 7.00319i | 0.220252 | − | 0.381488i | −0.734632 | − | 0.678465i | \(-0.762645\pi\) |
0.954884 | + | 0.296977i | \(0.0959786\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.15239 | − | 0.207775i | 0.497090 | − | 0.0112848i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.83169 | −0.0991917 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.63644 | − | 4.81566i | 0.141941 | − | 0.259266i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.466877 | − | 0.808654i | 0.0250632 | − | 0.0434108i | −0.853222 | − | 0.521548i | \(-0.825355\pi\) |
0.878285 | + | 0.478138i | \(0.158688\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.90264 | − | 3.29548i | −0.101846 | − | 0.176403i | 0.810599 | − | 0.585601i | \(-0.199142\pi\) |
−0.912445 | + | 0.409199i | \(0.865808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10.8754 | − | 22.2009i | 0.580487 | − | 1.18500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.55974 | + | 11.3618i | 0.349140 | + | 0.604728i | 0.986097 | − | 0.166171i | \(-0.0531405\pi\) |
−0.636957 | + | 0.770899i | \(0.719807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.26569 | + | 9.12043i | −0.279474 | + | 0.484062i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.5658 | −1.13820 | −0.569100 | − | 0.822268i | \(-0.692708\pi\) | ||||
−0.569100 | + | 0.822268i | \(0.692708\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54.8962 | 2.88927 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −10.2067 | + | 0.231710i | −0.535715 | + | 0.0121616i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.4425 | + | 25.0151i | −0.755954 | + | 1.30935i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.33095 | − | 16.1617i | −0.487072 | − | 0.843633i | 0.512818 | − | 0.858497i | \(-0.328602\pi\) |
−0.999890 | + | 0.0148645i | \(0.995268\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.1773 | + | 25.2948i | 0.842158 | + | 1.31680i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0854 | − | 17.4684i | 0.522201 | − | 0.904478i | −0.477466 | − | 0.878650i | \(-0.658444\pi\) |
0.999666 | − | 0.0258279i | \(-0.00822218\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.25453 | − | 15.2207i | −0.477902 | − | 0.785995i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −36.9087 | −1.90090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2436 | 0.937110 | 0.468555 | − | 0.883434i | \(-0.344775\pi\) | ||||
0.468555 | + | 0.883434i | \(0.344775\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.90285 | + | 11.3530i | 0.353644 | + | 0.581631i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.4282 | − | 19.7942i | 0.583952 | − | 1.01143i | −0.411053 | − | 0.911611i | \(-0.634839\pi\) |
0.995005 | − | 0.0998233i | \(-0.0318278\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4468 | − | 0.474563i | 0.531039 | − | 0.0241234i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.17146 | − | 10.6893i | −0.312905 | − | 0.541968i | 0.666085 | − | 0.745876i | \(-0.267969\pi\) |
−0.978990 | + | 0.203908i | \(0.934636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.86025 | − | 4.95410i | 0.144649 | − | 0.250539i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −33.5587 | + | 0.761840i | −1.69281 | + | 0.0384298i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.1908 | 1.01591 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.2032 | −1.31510 | −0.657551 | − | 0.753410i | \(-0.728408\pi\) | ||||
−0.657551 | + | 0.753410i | \(0.728408\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.95559 | + | 3.38718i | −0.0976575 | + | 0.169148i | −0.910715 | − | 0.413036i | \(-0.864468\pi\) |
0.813057 | + | 0.582184i | \(0.197802\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.92838 | + | 3.34006i | 0.0960596 | + | 0.166380i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.3753 | + | 1.94604i | −1.06215 | + | 0.0966997i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.23344 | − | 9.06459i | −0.259412 | − | 0.449315i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.05065 | + | 1.81978i | −0.0519513 | + | 0.0899823i | −0.890832 | − | 0.454334i | \(-0.849877\pi\) |
0.838880 | + | 0.544316i | \(0.183211\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.05971 | − | 14.7217i | 0.397556 | − | 0.726166i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.90072 | 0.191479 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.2016 | + | 0.299700i | −0.646487 | + | 0.0146763i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.7017 | + | 20.2679i | −0.571664 | + | 0.990150i | 0.424732 | + | 0.905319i | \(0.360368\pi\) |
−0.996395 | + | 0.0848311i | \(0.972965\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.78341 | + | 16.9454i | 0.476814 | + | 0.825866i | 0.999647 | − | 0.0265688i | \(-0.00845812\pi\) |
−0.522833 | + | 0.852435i | \(0.675125\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.0868 | + | 0.594492i | −0.636302 | + | 0.0289052i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.47965 | + | 2.56282i | 0.0717733 | + | 0.124315i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.67357 | − | 15.9099i | −0.467044 | − | 0.768138i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.70877 | 0.323150 | 0.161575 | − | 0.986860i | \(-0.448343\pi\) | ||||
0.161575 | + | 0.986860i | \(0.448343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.46607 | 0.454910 | 0.227455 | − | 0.973789i | \(-0.426959\pi\) | ||||
0.227455 | + | 0.973789i | \(0.426959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.6481 | + | 27.3809i | 0.798217 | + | 1.31281i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.71267 | − | 9.89463i | 0.273274 | − | 0.473324i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.82386 | − | 6.62312i | −0.182503 | − | 0.316104i | 0.760229 | − | 0.649655i | \(-0.225087\pi\) |
−0.942732 | + | 0.333550i | \(0.891753\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.0763 | − | 31.3091i | −0.858833 | − | 1.48754i | −0.873043 | − | 0.487643i | \(-0.837857\pi\) |
0.0142102 | − | 0.999899i | \(-0.495477\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.56371 | + | 13.1007i | −0.358554 | + | 0.621034i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.7434 | + | 0.357402i | −0.744637 | + | 0.0169045i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.7337 | 0.648132 | 0.324066 | − | 0.946034i | \(-0.394950\pi\) | ||||
0.324066 | + | 0.946034i | \(0.394950\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 22.6149 | 1.06489 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 16.8499 | − | 30.7776i | 0.791679 | − | 1.44606i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.213109 | + | 0.369115i | 0.00996881 | + | 0.0172665i | 0.870967 | − | 0.491342i | \(-0.163493\pi\) |
−0.860998 | + | 0.508608i | \(0.830160\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.3126 | + | 1.52169i | −1.04146 | + | 0.0710266i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.26453 | − | 3.92228i | −0.105470 | − | 0.182679i | 0.808460 | − | 0.588551i | \(-0.200301\pi\) |
−0.913930 | + | 0.405872i | \(0.866968\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.5598 | − | 28.6825i | 0.769600 | − | 1.33299i | −0.168179 | − | 0.985756i | \(-0.553789\pi\) |
0.937780 | − | 0.347230i | \(-0.112878\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.60801 | − | 2.93715i | 0.0745697 | − | 0.136207i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.51332 | −0.0700281 | −0.0350140 | − | 0.999387i | \(-0.511148\pi\) | ||||
−0.0350140 | + | 0.999387i | \(0.511148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.4788 | − | 0.328694i | 0.667149 | − | 0.0151454i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.93824 | − | 6.82123i | 0.181080 | − | 0.313640i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.95524 | + | 5.11863i | 0.135596 | + | 0.234859i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.1230 | − | 31.1058i | 0.738223 | − | 1.42424i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.1463 | − | 19.3060i | −0.509288 | − | 0.882112i | −0.999942 | − | 0.0107580i | \(-0.996576\pi\) |
0.490654 | − | 0.871354i | \(-0.336758\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.0194 | + | 19.0862i | −0.502441 | + | 0.870254i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 28.5362 | 1.29576 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.63353 | 0.209965 | 0.104983 | − | 0.994474i | \(-0.466521\pi\) | ||||
0.104983 | + | 0.994474i | \(0.466521\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.4425 | + | 28.6874i | 0.788778 | + | 1.29729i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.5858 | + | 21.7993i | −0.567990 | + | 0.983788i | 0.428774 | + | 0.903412i | \(0.358946\pi\) |
−0.996765 | + | 0.0803766i | \(0.974388\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.6948 | + | 28.9162i | 0.751894 | + | 1.30232i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.43944 | + | 14.3527i | −0.334378 | + | 0.645108i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.13727 | − | 1.96982i | 0.0509114 | − | 0.0881811i | −0.839447 | − | 0.543442i | \(-0.817121\pi\) |
0.890358 | + | 0.455261i | \(0.150454\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 30.6203 | − | 0.695132i | 1.36801 | − | 0.0310562i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −8.94793 | −0.398968 | −0.199484 | − | 0.979901i | \(-0.563927\pi\) | ||||
−0.199484 | + | 0.979901i | \(0.563927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −25.8685 | −1.15113 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.01437 | + | 14.6388i | −0.355930 | + | 0.650133i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.6343 | − | 28.8115i | 0.737304 | − | 1.27705i | −0.216402 | − | 0.976304i | \(-0.569432\pi\) |
0.953705 | − | 0.300743i | \(-0.0972346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −44.5641 | + | 3.03922i | −1.96755 | + | 0.134185i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 21.8746 | + | 37.8878i | 0.963908 | + | 1.66954i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.93349 | + | 8.54505i | −0.216975 | + | 0.375811i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.6213 | + | 32.1866i | −0.773490 | + | 1.41284i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.1479 | −0.663642 | −0.331821 | − | 0.943342i | \(-0.607663\pi\) | ||||
−0.331821 | + | 0.943342i | \(0.607663\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.4790 | −0.458217 | −0.229108 | − | 0.973401i | \(-0.573581\pi\) | ||||
−0.229108 | + | 0.973401i | \(0.573581\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.74451 | − | 3.02159i | 0.0759922 | − | 0.131622i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6167 | + | 18.3887i | 0.461598 | + | 0.799511i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.77348 | + | 12.1546i | 0.337340 | + | 0.527465i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.8086 | − | 41.2378i | −1.03127 | − | 1.78621i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.57192 | − | 7.91880i | 0.197661 | − | 0.342360i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −11.6870 | − | 19.2214i | −0.504332 | − | 0.829464i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.87748 | 0.209699 | 0.104850 | − | 0.994488i | \(-0.466564\pi\) | ||||
0.104850 | + | 0.994488i | \(0.466564\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1388 | + | 24.8985i | 0.649669 | + | 1.06850i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.15393 | − | 5.46277i | 0.135100 | − | 0.234000i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.62179 | + | 16.6654i | 0.411398 | + | 0.712562i | 0.995043 | − | 0.0994468i | \(-0.0317073\pi\) |
−0.583645 | + | 0.812009i | \(0.698374\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.45224 | + | 0.156824i | −0.147338 | + | 0.00669310i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.3438 | + | 57.7532i | 1.42049 | + | 2.46037i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 19.1296 | − | 0.434274i | 0.812005 | − | 0.0184339i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.6478 | 0.620646 | 0.310323 | − | 0.950631i | \(-0.399563\pi\) | ||||
0.310323 | + | 0.950631i | \(0.399563\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.5845 | −0.701450 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.08905 | + | 14.7752i | −0.341520 | + | 0.623811i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.85335 | + | 3.21010i | −0.0781095 | + | 0.135290i | −0.902434 | − | 0.430828i | \(-0.858222\pi\) |
0.824325 | + | 0.566117i | \(0.191555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.30259 | + | 10.9164i | 0.265152 | + | 0.459257i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.1768 | − | 26.2871i | −0.636246 | − | 1.10201i | −0.986250 | − | 0.165262i | \(-0.947153\pi\) |
0.350004 | − | 0.936748i | \(-0.386180\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.88458 | − | 10.1924i | 0.246262 | − | 0.426539i | −0.716224 | − | 0.697871i | \(-0.754131\pi\) |
0.962486 | + | 0.271332i | \(0.0874642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.62825 | + | 13.9336i | −0.318675 | + | 0.582083i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.913839 | 0.0381097 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.59281 | −0.149570 | −0.0747852 | − | 0.997200i | \(-0.523827\pi\) | ||||
−0.0747852 | + | 0.997200i | \(0.523827\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −44.3821 | + | 1.00755i | −1.84446 | + | 0.0418723i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.1943 | − | 22.8533i | −0.546454 | − | 0.946485i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 34.0041 | − | 1.54470i | 1.40590 | − | 0.0638654i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.62298 | − | 8.00724i | −0.190811 | − | 0.330494i | 0.754708 | − | 0.656060i | \(-0.227778\pi\) |
−0.945519 | + | 0.325566i | \(0.894445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.48425 | − | 6.03490i | 0.143566 | − | 0.248664i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.4908 | − | 23.8327i | −0.596071 | − | 0.980346i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −34.0793 | −1.39947 | −0.699735 | − | 0.714403i | \(-0.746698\pi\) | ||||
−0.699735 | + | 0.714403i | \(0.746698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 17.3024 | + | 28.4570i | 0.708142 | + | 1.16467i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.51340 | − | 6.08539i | 0.143554 | − | 0.248642i | −0.785279 | − | 0.619142i | \(-0.787480\pi\) |
0.928832 | + | 0.370500i | \(0.120814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.31218 | + | 4.00481i | 0.0943158 | + | 0.163360i | 0.909323 | − | 0.416091i | \(-0.136600\pi\) |
−0.815007 | + | 0.579451i | \(0.803267\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.67171 | + | 10.4319i | 0.271693 | + | 0.424818i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.02864 | − | 12.1740i | −0.285755 | − | 0.494942i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.1041 | − | 17.5007i | 0.410111 | − | 0.710333i | −0.584791 | − | 0.811184i | \(-0.698823\pi\) |
0.994901 | + | 0.100852i | \(0.0321567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.7756 | 0.840493 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −17.8207 | −0.719773 | −0.359887 | − | 0.932996i | \(-0.617185\pi\) | ||||
−0.359887 | + | 0.932996i | \(0.617185\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −19.8532 | + | 36.2633i | −0.800558 | + | 1.46228i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.0671 | − | 26.0969i | 0.606577 | − | 1.05062i | −0.385223 | − | 0.922824i | \(-0.625875\pi\) |
0.991800 | − | 0.127799i | \(-0.0407913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −15.9558 | − | 27.6363i | −0.641318 | − | 1.11080i | −0.985139 | − | 0.171760i | \(-0.945055\pi\) |
0.343821 | − | 0.939035i | \(-0.388279\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.03815 | + | 6.20204i | −0.121917 | + | 0.248879i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.9825 | − | 24.2185i | 0.559301 | − | 0.968738i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.1559 | + | 29.5100i | −0.645206 | + | 1.17852i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.9374 | 0.794957 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.1430 | −0.403788 | −0.201894 | − | 0.979407i | \(-0.564710\pi\) | ||||
−0.201894 | + | 0.979407i | \(0.564710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 42.6844 | − | 0.969009i | 1.69655 | − | 0.0385147i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.14731 | + | 15.8436i | −0.363000 | + | 0.628734i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.09643 | − | 11.7617i | 0.241171 | − | 0.465285i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.9256 | − | 37.9762i | −0.866009 | − | 1.49997i | −0.866042 | − | 0.499972i | \(-0.833344\pi\) |
3.28428e−5 | − | 1.00000i | \(-0.499990\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.10737 | + | 1.91802i | −0.0436704 | + | 0.0756394i | −0.887034 | − | 0.461703i | \(-0.847238\pi\) |
0.843364 | + | 0.537343i | \(0.180572\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.48065 | + | 12.3033i | 0.294550 | + | 0.484441i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −20.9266 | −0.822710 | −0.411355 | − | 0.911475i | \(-0.634944\pi\) | ||||
−0.411355 | + | 0.911475i | \(0.634944\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.8668 | 0.426560 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.01442 | + | 6.95317i | −0.157096 | + | 0.272099i | −0.933820 | − | 0.357742i | \(-0.883547\pi\) |
0.776724 | + | 0.629841i | \(0.216880\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −23.1095 | − | 40.0268i | −0.902962 | − | 1.56398i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.7210 | − | 32.2594i | 0.652348 | − | 1.25856i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.25793 | + | 16.0352i | 0.360638 | + | 0.624643i | 0.988066 | − | 0.154031i | \(-0.0492257\pi\) |
−0.627428 | + | 0.778675i | \(0.715892\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.4273 | + | 18.0606i | −0.405574 | + | 0.702474i | −0.994388 | − | 0.105794i | \(-0.966262\pi\) |
0.588814 | + | 0.808268i | \(0.299595\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 35.4584 | − | 0.804966i | 1.37709 | − | 0.0312623i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.3108 | 0.399236 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.3279 | + | 22.5178i | −0.476624 | + | 0.870589i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.30143 | + | 2.25415i | −0.0502412 | + | 0.0870204i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.4484 | + | 19.8292i | 0.441303 | + | 0.764360i | 0.997786 | − | 0.0664992i | \(-0.0211830\pi\) |
−0.556483 | + | 0.830859i | \(0.687850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.99272 | − | 2.96531i | −0.0766998 | − | 0.114135i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.3119 | + | 40.3774i | 0.895948 | + | 1.55183i | 0.832627 | + | 0.553835i | \(0.186836\pi\) |
0.0633218 | + | 0.997993i | \(0.479831\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.1006 | + | 27.5824i | −0.578656 | + | 1.05696i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −36.6203 | −1.40124 | −0.700618 | − | 0.713536i | \(-0.747092\pi\) | ||||
−0.700618 | + | 0.713536i | \(0.747092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.1092 | 0.882958 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.4622 | + | 0.373720i | −0.628073 | + | 0.0142583i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −27.7816 | + | 48.1192i | −1.05840 | + | 1.83320i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.2586 | − | 22.9645i | −0.504380 | − | 0.873611i | −0.999987 | − | 0.00506472i | \(-0.998388\pi\) |
0.495607 | − | 0.868547i | \(-0.334945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.09101 | − | 15.7461i | −0.344842 | − | 0.597283i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.5385 | + | 37.3058i | −0.815830 | + | 1.41306i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.3057 | − | 30.1069i | −0.692383 | − | 1.13875i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.9931 | −1.13282 | −0.566411 | − | 0.824123i | \(-0.691669\pi\) | ||||
−0.566411 | + | 0.824123i | \(0.691669\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 39.8203 | 1.50185 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.37111 | − | 15.4125i | −0.352937 | − | 0.580468i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.48805 | − | 9.50558i | −0.206108 | − | 0.356990i | 0.744377 | − | 0.667759i | \(-0.232746\pi\) |
−0.950485 | + | 0.310770i | \(0.899413\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −25.3726 | + | 1.15259i | −0.951546 | + | 0.0432257i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.538712 | − | 0.933076i | −0.0201749 | − | 0.0349440i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.8189 | − | 22.2030i | 0.479401 | − | 0.830346i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.8414 | + | 0.700152i | −1.15179 | + | 0.0261477i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.1042 | −0.488705 | −0.244352 | − | 0.969687i | \(-0.578575\pi\) | ||||
−0.244352 | + | 0.969687i | \(0.578575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.23071 | − | 9.55427i | 0.194532 | − | 0.355327i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.66696 | + | 4.61931i | −0.0990483 | + | 0.171557i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.96026 | − | 15.5196i | −0.332318 | − | 0.575591i | 0.650648 | − | 0.759379i | \(-0.274497\pi\) |
−0.982966 | + | 0.183788i | \(0.941164\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.7500 | − | 3.66569i | 0.990741 | − | 0.135766i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.50160 | + | 12.9932i | 0.277457 | + | 0.480569i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.95660 | + | 5.12098i | −0.109204 | + | 0.189148i | −0.915448 | − | 0.402436i | \(-0.868164\pi\) |
0.806244 | + | 0.591583i | \(0.201497\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.32662 | 0.343550 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.1774 | −1.07331 | −0.536653 | − | 0.843803i | \(-0.680312\pi\) | ||||
−0.536653 | + | 0.843803i | \(0.680312\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 70.8197 | − | 1.60773i | 2.60163 | − | 0.0590614i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.8512 | + | 32.6513i | −0.691584 | + | 1.19786i | 0.279735 | + | 0.960077i | \(0.409753\pi\) |
−0.971319 | + | 0.237781i | \(0.923580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.8413 | − | 18.7777i | −0.397196 | − | 0.687963i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.90179 | + | 0.222673i | −0.179347 | + | 0.00814717i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.3277 | + | 35.2085i | −0.741767 | + | 1.28478i | 0.209923 | + | 0.977718i | \(0.432679\pi\) |
−0.951690 | + | 0.307060i | \(0.900655\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.6643 | − | 37.2755i | −0.825932 | − | 1.35839i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 48.3130 | 1.75829 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.6704 | 0.642241 | 0.321120 | − | 0.947038i | \(-0.395941\pi\) | ||||
0.321120 | + | 0.947038i | \(0.395941\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.70240 | + | 4.44459i | 0.0980910 | + | 0.161328i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.644183 | − | 1.11576i | 0.0233516 | − | 0.0404462i | −0.854113 | − | 0.520087i | \(-0.825900\pi\) |
0.877465 | + | 0.479641i | \(0.159233\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.5911 | − | 25.9418i | −0.599853 | − | 0.937929i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −11.4405 | − | 19.8154i | −0.413091 | − | 0.715494i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.19275 | − | 7.26205i | 0.151194 | − | 0.261876i | −0.780472 | − | 0.625190i | \(-0.785021\pi\) |
0.931667 | + | 0.363314i | \(0.118355\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −49.6629 | + | 1.12743i | −1.78857 | + | 0.0406035i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 50.3060 | 1.80938 | 0.904691 | − | 0.426068i | \(-0.140102\pi\) | ||||
0.904691 | + | 0.426068i | \(0.140102\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.557366 | 0.0200212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −43.0181 | + | 74.5095i | −1.54128 | + | 2.66958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.98903 | − | 8.64125i | −0.178521 | − | 0.309208i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.4837 | − | 33.4575i | −0.803503 | − | 1.19567i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.97051 | + | 17.2694i | 0.355863 | + | 0.616373i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.1922 | + | 19.3855i | −0.398960 | + | 0.691020i | −0.993598 | − | 0.112974i | \(-0.963962\pi\) |
0.594638 | + | 0.803994i | \(0.297296\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 11.9913 | − | 21.9030i | 0.426901 | − | 0.779767i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.48052 | 0.194619 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 48.2287 | − | 1.09487i | 1.71049 | − | 0.0388311i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.706182 | + | 1.22314i | −0.0250143 | + | 0.0433260i | −0.878262 | − | 0.478181i | \(-0.841296\pi\) |
0.853247 | + | 0.521507i | \(0.174630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.39736 | − | 16.2767i | −0.332455 | − | 0.575828i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.75699 | − | 16.8947i | 0.309413 | − | 0.596943i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.6837 | − | 23.7008i | −0.482887 | − | 0.836384i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.6080 | − | 19.0914i | −0.408620 | − | 0.672049i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 20.0848 | 0.706142 | 0.353071 | − | 0.935596i | \(-0.385137\pi\) | ||||
0.353071 | + | 0.935596i | \(0.385137\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.7821 | 1.95878 | 0.979388 | − | 0.201988i | \(-0.0647401\pi\) | ||||
0.979388 | + | 0.201988i | \(0.0647401\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.5130 | − | 28.8033i | −0.614207 | − | 1.01017i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.1140 | + | 40.0345i | −0.809646 | + | 1.40235i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.9827 | + | 25.9507i | 0.524177 | + | 0.907901i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 24.4346 | + | 42.3219i | 0.852772 | + | 1.47704i | 0.878697 | + | 0.477380i | \(0.158414\pi\) |
−0.0259249 | + | 0.999664i | \(0.508253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.266319 | − | 0.461277i | 0.00928328 | − | 0.0160791i | −0.861346 | − | 0.508018i | \(-0.830378\pi\) |
0.870630 | + | 0.491939i | \(0.163712\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.69020 | + | 0.0610721i | −0.0936607 | + | 0.00212626i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1951 | 0.354518 | 0.177259 | − | 0.984164i | \(-0.443277\pi\) | ||||
0.177259 | + | 0.984164i | \(0.443277\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.2692 | 0.738711 | 0.369355 | − | 0.929288i | \(-0.379579\pi\) | ||||
0.369355 | + | 0.929288i | \(0.379579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.2353 | + | 24.1752i | −0.459127 | + | 0.838629i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.0859 | + | 36.5219i | 0.729709 | + | 1.26389i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.85302 | + | 3.78273i | −0.0640498 | + | 0.130750i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.47717 | + | 16.4149i | 0.327188 | + | 0.566707i | 0.981953 | − | 0.189126i | \(-0.0605655\pi\) |
−0.654765 | + | 0.755833i | \(0.727232\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.5912 | + | 27.0047i | −0.537626 | + | 0.931196i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.2889 | + | 42.5389i | −0.802113 | + | 1.46512i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.9792 | −0.790509 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.08555 | + | 0.206257i | −0.311815 | + | 0.00707873i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.07837 | − | 5.33190i | 0.105525 | − | 0.182775i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.75811 | − | 4.77718i | −0.0944358 | − | 0.163568i | 0.814937 | − | 0.579549i | \(-0.196771\pi\) |
−0.909373 | + | 0.415982i | \(0.863438\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −33.1368 | − | 51.8127i | −1.13326 | − | 1.77196i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.92471 | − | 13.7260i | −0.270703 | − | 0.468871i | 0.698339 | − | 0.715767i | \(-0.253923\pi\) |
−0.969042 | + | 0.246896i | \(0.920589\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.7004 | − | 18.5337i | 0.365095 | − | 0.632362i | −0.623697 | − | 0.781666i | \(-0.714370\pi\) |
0.988791 | + | 0.149304i | \(0.0477033\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.03720 | −0.137428 | −0.0687140 | − | 0.997636i | \(-0.521890\pi\) | ||||
−0.0687140 | + | 0.997636i | \(0.521890\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.5247 | −1.71789 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.37202 | − | 2.25653i | −0.0465962 | − | 0.0766358i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.56500 | + | 16.5671i | −0.324470 | + | 0.561999i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.81894 | − | 17.0069i | −0.332702 | − | 0.576257i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.8597 | + | 1.62899i | −1.21367 | + | 0.0551330i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.6905 | − | 21.9806i | 0.428529 | − | 0.742233i | −0.568214 | − | 0.822881i | \(-0.692365\pi\) |
0.996743 | + | 0.0806475i | \(0.0256988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.74683 | − | 0.130463i | 0.193836 | − | 0.00440040i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.7755 | −0.632561 | −0.316281 | − | 0.948666i | \(-0.602434\pi\) | ||||
−0.316281 | + | 0.948666i | \(0.602434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.52167 | 0.286777 | 0.143388 | − | 0.989666i | \(-0.454200\pi\) | ||||
0.143388 | + | 0.989666i | \(0.454200\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.53980 | + | 17.4251i | −0.320677 | + | 0.585740i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.05040 | − | 8.74755i | 0.169576 | − | 0.293714i | −0.768695 | − | 0.639616i | \(-0.779094\pi\) |
0.938271 | + | 0.345902i | \(0.112427\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.52937 | − | 18.4609i | 0.285745 | − | 0.618463i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.7690 | − | 32.5089i | −0.628080 | − | 1.08787i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4870 | − | 26.8243i | 0.517674 | − | 0.896638i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.25956 | − | 9.60698i | 0.175612 | − | 0.320768i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.28873 | 0.209741 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50.2654 | 1.67458 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.0612 | + | 34.7470i | −0.666857 | + | 1.15503i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.6088 | + | 18.3750i | 0.352260 | + | 0.610131i | 0.986645 | − | 0.162885i | \(-0.0520801\pi\) |
−0.634385 | + | 0.773017i | \(0.718747\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 32.5073 | − | 1.47670i | 1.07820 | − | 0.0489792i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.46609 | − | 7.73550i | −0.147968 | − | 0.256289i | 0.782508 | − | 0.622640i | \(-0.213940\pi\) |
−0.930476 | + | 0.366352i | \(0.880607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.84789 | + | 3.20063i | −0.0611561 | + | 0.105925i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.47206 | − | 4.06574i | −0.0817237 | − | 0.134409i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.9129 | 1.15167 | 0.575834 | − | 0.817566i | \(-0.304677\pi\) | ||||
0.575834 | + | 0.817566i | \(0.304677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.2213 | + | 18.4555i | 0.369755 | + | 0.608128i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.5048 | + | 18.1948i | −0.345769 | + | 0.598889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.59248 | + | 2.75826i | 0.0523605 | + | 0.0906911i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.6513 | − | 46.3626i | −0.973875 | − | 1.52275i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.51692 | − | 9.55559i | −0.181004 | − | 0.313509i | 0.761218 | − | 0.648496i | \(-0.224601\pi\) |
−0.942223 | + | 0.334987i | \(0.891268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −39.2669 | + | 0.891426i | −1.28554 | + | 0.0291840i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.1933 | −0.758503 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.6426 | 0.445686 | 0.222843 | − | 0.974854i | \(-0.428466\pi\) | ||||
0.222843 | + | 0.974854i | \(0.428466\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.25851 | − | 9.60506i | 0.171605 | − | 0.313449i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0278 | − | 20.8328i | 0.392095 | − | 0.679129i | −0.600630 | − | 0.799527i | \(-0.705084\pi\) |
0.992726 | + | 0.120398i | \(0.0384170\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.65117 | + | 11.5202i | 0.216592 | + | 0.375148i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6.69602 | − | 11.5978i | −0.217591 | − | 0.376879i | 0.736480 | − | 0.676460i | \(-0.236487\pi\) |
−0.954071 | + | 0.299580i | \(0.903153\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.8120 | + | 49.9038i | −0.935277 | + | 1.61995i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12.9595 | − | 23.6715i | 0.420240 | − | 0.767600i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.3444 | 1.17731 | 0.588655 | − | 0.808384i | \(-0.299658\pi\) | ||||
0.588655 | + | 0.808384i | \(0.299658\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.8721 | −0.707764 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −30.3534 | + | 0.689074i | −0.981186 | + | 0.0222746i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.1714 | + | 26.2777i | 0.489401 | + | 0.847667i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.29321 | + | 10.2121i | −0.170571 | + | 0.329079i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −30.5627 | − | 52.9362i | −0.983849 | − | 1.70408i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.82455 | − | 8.35637i | 0.155147 | − | 0.268723i | −0.777965 | − | 0.628307i | \(-0.783748\pi\) |
0.933113 | + | 0.359584i | \(0.117082\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.2932 | − | 54.7566i | −1.06953 | − | 1.75904i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43.3775 | −1.39205 | −0.696025 | − | 0.718017i | \(-0.745050\pi\) | ||||
−0.696025 | + | 0.718017i | \(0.745050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.94357 | + | 4.84123i | 0.0942697 | + | 0.155043i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.60004 | + | 4.50340i | −0.0831826 | + | 0.144076i | −0.904615 | − | 0.426229i | \(-0.859842\pi\) |
0.821433 | + | 0.570305i | \(0.193175\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.16631 | − | 12.4124i | −0.229036 | − | 0.396703i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65151 | + | 7.04478i | −0.116584 | + | 0.224922i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.6349 | + | 20.1522i | 0.371095 | + | 0.642755i | 0.989734 | − | 0.142920i | \(-0.0456491\pi\) |
−0.618639 | + | 0.785675i | \(0.712316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.2025 | − | 33.2596i | 0.611841 | − | 1.05974i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.63304 | 0.147322 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.0382 | −1.24009 | −0.620044 | − | 0.784567i | \(-0.712885\pi\) | ||||
−0.620044 | + | 0.784567i | \(0.712885\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.0714 | − | 33.0087i | 0.573478 | − | 1.04750i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.9283 | + | 39.7130i | −0.726877 | + | 1.25899i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0905 | − | 20.9413i | −0.382909 | − | 0.663218i | 0.608568 | − | 0.793502i | \(-0.291744\pi\) |
−0.991477 | + | 0.130284i | \(0.958411\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.0142 | + | 1.63774i | −0.759775 | + | 0.0518157i |
(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 | 1764.2.j.i.589.5 | ✓ | 24 | |
3.2 | odd | 2 | 5292.2.j.i.1765.3 | 24 | |||
7.2 | even | 3 | 1764.2.l.j.949.12 | 24 | |||
7.3 | odd | 6 | 1764.2.i.j.373.8 | 24 | |||
7.4 | even | 3 | 1764.2.i.j.373.5 | 24 | |||
7.5 | odd | 6 | 1764.2.l.j.949.1 | 24 | |||
7.6 | odd | 2 | inner | 1764.2.j.i.589.8 | yes | 24 | |
9.2 | odd | 6 | 5292.2.j.i.3529.3 | 24 | |||
9.7 | even | 3 | inner | 1764.2.j.i.1177.5 | yes | 24 | |
21.2 | odd | 6 | 5292.2.l.j.361.10 | 24 | |||
21.5 | even | 6 | 5292.2.l.j.361.3 | 24 | |||
21.11 | odd | 6 | 5292.2.i.j.1549.3 | 24 | |||
21.17 | even | 6 | 5292.2.i.j.1549.10 | 24 | |||
21.20 | even | 2 | 5292.2.j.i.1765.10 | 24 | |||
63.2 | odd | 6 | 5292.2.i.j.2125.3 | 24 | |||
63.11 | odd | 6 | 5292.2.l.j.3313.10 | 24 | |||
63.16 | even | 3 | 1764.2.i.j.1537.5 | 24 | |||
63.20 | even | 6 | 5292.2.j.i.3529.10 | 24 | |||
63.25 | even | 3 | 1764.2.l.j.961.12 | 24 | |||
63.34 | odd | 6 | inner | 1764.2.j.i.1177.8 | yes | 24 | |
63.38 | even | 6 | 5292.2.l.j.3313.3 | 24 | |||
63.47 | even | 6 | 5292.2.i.j.2125.10 | 24 | |||
63.52 | odd | 6 | 1764.2.l.j.961.1 | 24 | |||
63.61 | odd | 6 | 1764.2.i.j.1537.8 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.2.i.j.373.5 | 24 | 7.4 | even | 3 | |||
1764.2.i.j.373.8 | 24 | 7.3 | odd | 6 | |||
1764.2.i.j.1537.5 | 24 | 63.16 | even | 3 | |||
1764.2.i.j.1537.8 | 24 | 63.61 | odd | 6 | |||
1764.2.j.i.589.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
1764.2.j.i.589.8 | yes | 24 | 7.6 | odd | 2 | inner | |
1764.2.j.i.1177.5 | yes | 24 | 9.7 | even | 3 | inner | |
1764.2.j.i.1177.8 | yes | 24 | 63.34 | odd | 6 | inner | |
1764.2.l.j.949.1 | 24 | 7.5 | odd | 6 | |||
1764.2.l.j.949.12 | 24 | 7.2 | even | 3 | |||
1764.2.l.j.961.1 | 24 | 63.52 | odd | 6 | |||
1764.2.l.j.961.12 | 24 | 63.25 | even | 3 | |||
5292.2.i.j.1549.3 | 24 | 21.11 | odd | 6 | |||
5292.2.i.j.1549.10 | 24 | 21.17 | even | 6 | |||
5292.2.i.j.2125.3 | 24 | 63.2 | odd | 6 | |||
5292.2.i.j.2125.10 | 24 | 63.47 | even | 6 | |||
5292.2.j.i.1765.3 | 24 | 3.2 | odd | 2 | |||
5292.2.j.i.1765.10 | 24 | 21.20 | even | 2 | |||
5292.2.j.i.3529.3 | 24 | 9.2 | odd | 6 | |||
5292.2.j.i.3529.10 | 24 | 63.20 | even | 6 | |||
5292.2.l.j.361.3 | 24 | 21.5 | even | 6 | |||
5292.2.l.j.361.10 | 24 | 21.2 | odd | 6 | |||
5292.2.l.j.3313.3 | 24 | 63.38 | even | 6 | |||
5292.2.l.j.3313.10 | 24 | 63.11 | odd | 6 |