Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(107,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 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("504.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.bm (of order \(6\), 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: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.16 | ||
Character | \(\chi\) | \(=\) | 504.107 |
Dual form | 504.2.bm.c.179.16 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.648862 | + | 1.25657i | 0.458814 | + | 0.888532i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.15796 | + | 1.63069i | −0.578979 | + | 0.815343i | ||||
\(5\) | 1.02787 | − | 1.78033i | 0.459679 | − | 0.796188i | −0.539264 | − | 0.842137i | \(-0.681298\pi\) |
0.998944 | + | 0.0459483i | \(0.0146310\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.24680 | − | 2.33356i | 0.471248 | − | 0.882001i | ||||
\(8\) | −2.80043 | − | 0.396971i | −0.990102 | − | 0.140350i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.90407 | + | 0.136412i | 0.918346 | + | 0.0431374i | ||||
\(11\) | 5.24912 | − | 3.03058i | 1.58267 | − | 0.913754i | 0.588201 | − | 0.808715i | \(-0.299836\pi\) |
0.994468 | − | 0.105040i | \(-0.0334970\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.77772i | − | 0.493050i | −0.969136 | − | 0.246525i | \(-0.920711\pi\) | ||
0.969136 | − | 0.246525i | \(-0.0792887\pi\) | |||||||
\(14\) | 3.74129 | + | 0.0525476i | 0.999901 | + | 0.0140439i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.31827 | − | 3.77653i | −0.329567 | − | 0.944132i | ||||
\(17\) | 0.786233 | − | 0.453932i | 0.190690 | − | 0.110095i | −0.401616 | − | 0.915808i | \(-0.631551\pi\) |
0.592305 | + | 0.805714i | \(0.298218\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.37450 | + | 5.84481i | −0.774164 | + | 1.34089i | 0.161100 | + | 0.986938i | \(0.448496\pi\) |
−0.935263 | + | 0.353953i | \(0.884837\pi\) | |||||||
\(20\) | 1.71292 | + | 3.73769i | 0.383022 | + | 0.835772i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.21410 | + | 4.62948i | 1.53805 | + | 0.987009i | ||||
\(23\) | 0.351459 | − | 0.608746i | 0.0732843 | − | 0.126932i | −0.827055 | − | 0.562122i | \(-0.809985\pi\) |
0.900339 | + | 0.435189i | \(0.143319\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.386948 | + | 0.670213i | 0.0773896 | + | 0.134043i | ||||
\(26\) | 2.23383 | − | 1.15349i | 0.438090 | − | 0.226218i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.36155 | + | 4.73530i | 0.446291 | + | 0.894888i | ||||
\(29\) | 4.52576 | 0.840412 | 0.420206 | − | 0.907429i | \(-0.361958\pi\) | ||||
0.420206 | + | 0.907429i | \(0.361958\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.31501 | + | 4.22332i | −1.31381 | + | 0.758531i | −0.982726 | − | 0.185069i | \(-0.940749\pi\) |
−0.331088 | + | 0.943600i | \(0.607416\pi\) | |||||||
\(32\) | 3.89011 | − | 4.10695i | 0.687682 | − | 0.726012i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.08056 | + | 0.693421i | 0.185314 | + | 0.118921i | ||||
\(35\) | −2.87294 | − | 4.61833i | −0.485616 | − | 0.780640i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.07548 | + | 3.50768i | 0.998803 | + | 0.576659i | 0.907894 | − | 0.419200i | \(-0.137689\pi\) |
0.0909092 | + | 0.995859i | \(0.471023\pi\) | |||||||
\(38\) | −9.53402 | − | 0.447840i | −1.54662 | − | 0.0726493i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.58523 | + | 4.57766i | −0.566875 | + | 0.723791i | ||||
\(41\) | − | 11.6289i | − | 1.81613i | −0.418831 | − | 0.908064i | \(-0.637560\pi\) | ||
0.418831 | − | 0.908064i | \(-0.362440\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.69997 | −0.716739 | −0.358369 | − | 0.933580i | \(-0.616667\pi\) | ||||
−0.358369 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(44\) | −1.13633 | + | 12.0689i | −0.171309 | + | 1.81946i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.992982 | + | 0.0466433i | 0.146407 | + | 0.00687717i | ||||
\(47\) | −4.42306 | + | 7.66096i | −0.645169 | + | 1.11747i | 0.339093 | + | 0.940753i | \(0.389880\pi\) |
−0.984262 | + | 0.176713i | \(0.943453\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.89096 | − | 5.81897i | −0.555851 | − | 0.831282i | ||||
\(50\) | −0.591097 | + | 0.921104i | −0.0835937 | + | 0.130264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.89889 | + | 2.05852i | 0.402004 | + | 0.285465i | ||||
\(53\) | 3.31595 | + | 5.74340i | 0.455481 | + | 0.788917i | 0.998716 | − | 0.0506644i | \(-0.0161339\pi\) |
−0.543235 | + | 0.839581i | \(0.682801\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12.4602i | − | 1.68014i | ||||||
\(56\) | −4.41794 | + | 6.04002i | −0.590372 | + | 0.807131i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.93659 | + | 5.68695i | 0.385593 | + | 0.746733i | ||||
\(59\) | −1.11754 | + | 0.645211i | −0.145491 | + | 0.0839993i | −0.570978 | − | 0.820965i | \(-0.693436\pi\) |
0.425487 | + | 0.904964i | \(0.360103\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.95517 | + | 4.59292i | 1.01856 | + | 0.588063i | 0.913685 | − | 0.406422i | \(-0.133224\pi\) |
0.104870 | + | 0.994486i | \(0.466557\pi\) | |||||||
\(62\) | −10.0533 | − | 6.45150i | −1.27678 | − | 0.819341i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.68483 | + | 2.22338i | 0.960604 | + | 0.277922i | ||||
\(65\) | −3.16492 | − | 1.82727i | −0.392560 | − | 0.226645i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.562480 | − | 0.974244i | −0.0687179 | − | 0.119023i | 0.829619 | − | 0.558330i | \(-0.188558\pi\) |
−0.898337 | + | 0.439307i | \(0.855224\pi\) | |||||||
\(68\) | −0.170204 | + | 1.80773i | −0.0206403 | + | 0.219220i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.93913 | − | 6.60672i | 0.470816 | − | 0.789654i | ||||
\(71\) | 1.43897 | 0.170774 | 0.0853869 | − | 0.996348i | \(-0.472787\pi\) | ||||
0.0853869 | + | 0.996348i | \(0.472787\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.08692 | + | 3.61465i | 0.244255 | + | 0.423063i | 0.961922 | − | 0.273324i | \(-0.0881231\pi\) |
−0.717667 | + | 0.696387i | \(0.754790\pi\) | |||||||
\(74\) | −0.465515 | + | 9.91029i | −0.0541150 | + | 1.15205i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.62351 | − | 12.2708i | −0.645061 | − | 1.40756i | ||||
\(77\) | −0.527404 | − | 16.0277i | −0.0601032 | − | 1.82652i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6339 | − | 6.71681i | −1.30891 | − | 0.755701i | −0.326997 | − | 0.945025i | \(-0.606037\pi\) |
−0.981915 | + | 0.189325i | \(0.939370\pi\) | |||||||
\(80\) | −8.07849 | − | 1.53484i | −0.903202 | − | 0.171601i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.6126 | − | 7.54554i | 1.61369 | − | 0.833266i | ||||
\(83\) | 4.71682i | 0.517738i | 0.965912 | + | 0.258869i | \(0.0833499\pi\) | ||||
−0.965912 | + | 0.258869i | \(0.916650\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1.86634i | − | 0.202433i | ||||||
\(86\) | −3.04963 | − | 5.90586i | −0.328850 | − | 0.636846i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −15.9028 | + | 6.40319i | −1.69525 | + | 0.682582i | ||||
\(89\) | −4.08201 | − | 2.35675i | −0.432692 | − | 0.249815i | 0.267801 | − | 0.963474i | \(-0.413703\pi\) |
−0.700493 | + | 0.713660i | \(0.747036\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.14840 | − | 2.21646i | −0.434870 | − | 0.232348i | ||||
\(92\) | 0.585697 | + | 1.27802i | 0.0610632 | + | 0.133243i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.4965 | − | 0.586998i | −1.28892 | − | 0.0605442i | ||||
\(95\) | 6.93713 | + | 12.0155i | 0.711734 | + | 1.23276i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.2014 | −1.23886 | −0.619430 | − | 0.785052i | \(-0.712636\pi\) | ||||
−0.619430 | + | 0.785052i | \(0.712636\pi\) | |||||||
\(98\) | 4.78728 | − | 8.66499i | 0.483588 | − | 0.875296i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.54098 | − | 0.145088i | −0.154098 | − | 0.0145088i | ||||
\(101\) | −5.20672 | − | 9.01831i | −0.518088 | − | 0.897355i | −0.999779 | − | 0.0210140i | \(-0.993311\pi\) |
0.481691 | − | 0.876341i | \(-0.340023\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.65349 | + | 3.26404i | 0.557055 | + | 0.321616i | 0.751963 | − | 0.659206i | \(-0.229107\pi\) |
−0.194908 | + | 0.980822i | \(0.562441\pi\) | |||||||
\(104\) | −0.705701 | + | 4.97837i | −0.0691996 | + | 0.488169i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.06541 | + | 7.89341i | −0.491996 | + | 0.766676i | ||||
\(107\) | 8.00556 | + | 4.62201i | 0.773926 | + | 0.446827i | 0.834273 | − | 0.551351i | \(-0.185887\pi\) |
−0.0603472 | + | 0.998177i | \(0.519221\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.22453 | + | 2.43904i | −0.404637 | + | 0.233617i | −0.688483 | − | 0.725253i | \(-0.741723\pi\) |
0.283846 | + | 0.958870i | \(0.408390\pi\) | |||||||
\(110\) | 15.6572 | − | 8.08496i | 1.49286 | − | 0.770871i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.4564 | − | 1.63234i | −0.988033 | − | 0.154241i | ||||
\(113\) | 2.39142i | 0.224966i | 0.993654 | + | 0.112483i | \(0.0358803\pi\) | ||||
−0.993654 | + | 0.112483i | \(0.964120\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.722512 | − | 1.25143i | −0.0673746 | − | 0.116696i | ||||
\(116\) | −5.24064 | + | 7.38009i | −0.486581 | + | 0.685224i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.53588 | − | 0.985617i | −0.141389 | − | 0.0907334i | ||||
\(119\) | −0.0789966 | − | 2.40068i | −0.00724160 | − | 0.220070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.8688 | − | 22.2895i | 1.16989 | − | 2.02632i | ||||
\(122\) | −0.609541 | + | 12.9764i | −0.0551852 | + | 1.17483i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.58356 | − | 16.8189i | 0.142208 | − | 1.51038i | ||||
\(125\) | 11.8697 | 1.06166 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.06366i | − | 0.360591i | −0.983612 | − | 0.180296i | \(-0.942295\pi\) | ||
0.983612 | − | 0.180296i | \(-0.0577055\pi\) | |||||||
\(128\) | 2.19255 | + | 11.0992i | 0.193796 | + | 0.981042i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.242502 | − | 5.16260i | 0.0212689 | − | 0.452790i | ||||
\(131\) | −0.208033 | − | 0.120108i | −0.0181760 | − | 0.0104939i | 0.490884 | − | 0.871225i | \(-0.336674\pi\) |
−0.509060 | + | 0.860731i | \(0.670007\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.43184 | + | 15.1619i | 0.817844 | + | 1.31470i | ||||
\(134\) | 0.859239 | − | 1.33895i | 0.0742269 | − | 0.115667i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.38199 | + | 0.959094i | −0.204254 | + | 0.0822416i | ||||
\(137\) | −13.2051 | + | 7.62397i | −1.12819 | + | 0.651360i | −0.943479 | − | 0.331434i | \(-0.892468\pi\) |
−0.184709 | + | 0.982793i | \(0.559134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.64300 | 0.648271 | 0.324135 | − | 0.946011i | \(-0.394927\pi\) | ||||
0.324135 | + | 0.946011i | \(0.394927\pi\) | |||||||
\(140\) | 10.8578 | + | 0.662960i | 0.917650 | + | 0.0560303i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.933690 | + | 1.80817i | 0.0783535 | + | 0.151738i | ||||
\(143\) | −5.38751 | − | 9.33144i | −0.450526 | − | 0.780334i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.65191 | − | 8.05735i | 0.386320 | − | 0.669126i | ||||
\(146\) | −3.18795 | + | 4.96778i | −0.263837 | + | 0.411136i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.7551 | + | 5.84545i | −1.04846 | + | 0.480493i | ||||
\(149\) | −8.37831 | + | 14.5117i | −0.686378 | + | 1.18884i | 0.286623 | + | 0.958043i | \(0.407467\pi\) |
−0.973002 | + | 0.230798i | \(0.925866\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.10302 | + | 4.10093i | −0.578036 | + | 0.333729i | −0.760352 | − | 0.649511i | \(-0.774974\pi\) |
0.182317 | + | 0.983240i | \(0.441640\pi\) | |||||||
\(152\) | 11.7703 | − | 15.0284i | 0.954695 | − | 1.21896i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 19.7977 | − | 11.0624i | 1.59535 | − | 0.891437i | ||||
\(155\) | 17.3642i | 1.39472i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.87900 | − | 1.08484i | 0.149961 | − | 0.0865798i | −0.423142 | − | 0.906063i | \(-0.639073\pi\) |
0.573103 | + | 0.819483i | \(0.305740\pi\) | |||||||
\(158\) | 0.891409 | − | 18.9771i | 0.0709167 | − | 1.50974i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.31318 | − | 11.1471i | −0.261930 | − | 0.881257i | ||||
\(161\) | −0.982340 | − | 1.57914i | −0.0774193 | − | 0.124453i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.29429 | + | 16.0982i | −0.727985 | + | 1.26091i | 0.229749 | + | 0.973250i | \(0.426210\pi\) |
−0.957734 | + | 0.287657i | \(0.907124\pi\) | |||||||
\(164\) | 18.9631 | + | 13.4658i | 1.48077 | + | 1.05150i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.92704 | + | 3.06056i | −0.460027 | + | 0.237546i | ||||
\(167\) | −22.6164 | −1.75011 | −0.875056 | − | 0.484022i | \(-0.839176\pi\) | ||||
−0.875056 | + | 0.484022i | \(0.839176\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.83973 | 0.756902 | ||||||||
\(170\) | 2.34520 | − | 1.21100i | 0.179868 | − | 0.0928792i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.44237 | − | 7.66417i | 0.414977 | − | 0.584388i | ||||
\(173\) | −0.544356 | + | 0.942851i | −0.0413866 | + | 0.0716837i | −0.885977 | − | 0.463730i | \(-0.846511\pi\) |
0.844590 | + | 0.535413i | \(0.179844\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.04643 | − | 0.0673395i | 0.154695 | − | 0.00509039i | ||||
\(176\) | −18.3648 | − | 15.8283i | −1.38430 | − | 1.19311i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.312771 | − | 6.65855i | 0.0234432 | − | 0.499079i | ||||
\(179\) | −5.20593 | + | 3.00564i | −0.389109 | + | 0.224652i | −0.681774 | − | 0.731563i | \(-0.738791\pi\) |
0.292665 | + | 0.956215i | \(0.405458\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.28891i | − | 0.541780i | −0.962610 | − | 0.270890i | \(-0.912682\pi\) | ||
0.962610 | − | 0.270890i | \(-0.0873180\pi\) | |||||||
\(182\) | 0.0934146 | − | 6.65095i | 0.00692435 | − | 0.493001i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.22589 | + | 1.56523i | −0.0903739 | + | 0.115390i | ||||
\(185\) | 12.4897 | − | 7.21091i | 0.918259 | − | 0.530157i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.75135 | − | 4.76549i | 0.201199 | − | 0.348487i | ||||
\(188\) | −7.37091 | − | 16.0837i | −0.537579 | − | 1.17302i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.5971 | + | 16.5134i | −0.768793 | + | 1.19801i | ||||
\(191\) | 2.21264 | − | 3.83240i | 0.160101 | − | 0.277303i | −0.774804 | − | 0.632202i | \(-0.782151\pi\) |
0.934905 | + | 0.354899i | \(0.115485\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.26476 | + | 2.19063i | 0.0910393 | + | 0.157685i | 0.907949 | − | 0.419081i | \(-0.137648\pi\) |
−0.816909 | + | 0.576766i | \(0.804314\pi\) | |||||||
\(194\) | −7.91699 | − | 15.3319i | −0.568407 | − | 1.10077i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.9945 | + | 0.393191i | 0.999606 | + | 0.0280851i | ||||
\(197\) | 11.6259 | 0.828314 | 0.414157 | − | 0.910205i | \(-0.364076\pi\) | ||||
0.414157 | + | 0.910205i | \(0.364076\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8071 | + | 9.70356i | −1.19142 | + | 0.687867i | −0.958629 | − | 0.284659i | \(-0.908120\pi\) |
−0.232792 | + | 0.972527i | \(0.574786\pi\) | |||||||
\(200\) | −0.817566 | − | 2.03049i | −0.0578106 | − | 0.143578i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.95373 | − | 12.3943i | 0.559623 | − | 0.872058i | ||||
\(203\) | 5.64273 | − | 10.5611i | 0.396042 | − | 0.741244i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.7033 | − | 11.9530i | −1.44598 | − | 0.834837i | ||||
\(206\) | −0.433181 | + | 9.22194i | −0.0301812 | + | 0.642523i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −6.71359 | + | 2.34351i | −0.465504 | + | 0.162493i | ||||
\(209\) | 40.9068i | 2.82958i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.73966 | 0.395135 | 0.197567 | − | 0.980289i | \(-0.436696\pi\) | ||||
0.197567 | + | 0.980289i | \(0.436696\pi\) | |||||||
\(212\) | −13.2054 | − | 1.24334i | −0.906951 | − | 0.0853927i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.613401 | + | 13.0586i | −0.0419312 | + | 0.892669i | ||||
\(215\) | −4.83098 | + | 8.36750i | −0.329470 | + | 0.570659i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.734973 | + | 22.3356i | 0.0498932 | + | 1.51624i | ||||
\(218\) | −5.80597 | − | 3.72584i | −0.393230 | − | 0.252346i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.3187 | + | 14.4284i | 1.36989 | + | 0.972763i | ||||
\(221\) | −0.806962 | − | 1.39770i | −0.0542821 | − | 0.0940194i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 5.21414i | − | 0.349164i | −0.984643 | − | 0.174582i | \(-0.944143\pi\) | ||
0.984643 | − | 0.174582i | \(-0.0558575\pi\) | |||||||
\(224\) | −4.73358 | − | 14.1984i | −0.316275 | − | 0.948667i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.00499 | + | 1.55170i | −0.199889 | + | 0.103217i | ||||
\(227\) | −6.08667 | + | 3.51414i | −0.403986 | + | 0.233242i | −0.688203 | − | 0.725519i | \(-0.741600\pi\) |
0.284216 | + | 0.958760i | \(0.408267\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0239 | + | 12.7155i | 1.45538 | + | 0.840264i | 0.998779 | − | 0.0494076i | \(-0.0157333\pi\) |
0.456601 | + | 0.889672i | \(0.349067\pi\) | |||||||
\(230\) | 1.10370 | − | 1.71989i | 0.0727759 | − | 0.113406i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.6741 | − | 1.79659i | −0.832094 | − | 0.117952i | ||||
\(233\) | 10.0196 | + | 5.78482i | 0.656406 | + | 0.378976i | 0.790906 | − | 0.611937i | \(-0.209610\pi\) |
−0.134500 | + | 0.990914i | \(0.542943\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.09270 | + | 15.7490i | 0.593142 | + | 1.02735i | ||||
\(236\) | 0.241926 | − | 2.56948i | 0.0157480 | − | 0.167259i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.96538 | − | 1.65698i | 0.192217 | − | 0.107406i | ||||
\(239\) | 17.2023 | 1.11272 | 0.556362 | − | 0.830940i | \(-0.312197\pi\) | ||||
0.556362 | + | 0.830940i | \(0.312197\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.84594 | + | 11.8575i | 0.440986 | + | 0.763810i | 0.997763 | − | 0.0668522i | \(-0.0212956\pi\) |
−0.556777 | + | 0.830662i | \(0.687962\pi\) | |||||||
\(242\) | 36.3585 | + | 1.70786i | 2.33721 | + | 0.109786i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −16.7014 | + | 7.65398i | −1.06920 | + | 0.489996i | ||||
\(245\) | −14.3591 | + | 0.946023i | −0.917370 | + | 0.0604392i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.3904 | + | 5.99890i | 0.661126 | + | 0.381701i | ||||
\(248\) | 22.1617 | − | 8.92328i | 1.40727 | − | 0.566629i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.70178 | + | 14.9151i | 0.487103 | + | 0.943316i | ||||
\(251\) | − | 9.77570i | − | 0.617037i | −0.951218 | − | 0.308518i | \(-0.900167\pi\) | ||
0.951218 | − | 0.308518i | \(-0.0998332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.26050i | − | 0.267856i | ||||||
\(254\) | 5.10629 | − | 2.63675i | 0.320397 | − | 0.165445i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.5243 | + | 9.95696i | −0.782771 | + | 0.622310i | ||||
\(257\) | −17.9664 | − | 10.3729i | −1.12071 | − | 0.647043i | −0.179129 | − | 0.983826i | \(-0.557328\pi\) |
−0.941582 | + | 0.336783i | \(0.890661\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.7603 | − | 9.80408i | 0.979298 | − | 0.609196i | ||||
\(260\) | 6.64454 | − | 3.04509i | 0.412077 | − | 0.188849i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0159399 | − | 0.339343i | 0.000984772 | − | 0.0209647i | ||||
\(263\) | 6.61692 | + | 11.4608i | 0.408016 | + | 0.706705i | 0.994667 | − | 0.103135i | \(-0.0328873\pi\) |
−0.586651 | + | 0.809840i | \(0.699554\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.6335 | 0.837501 | ||||||||
\(266\) | −12.9321 | + | 21.6898i | −0.792919 | + | 1.32989i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.24001 | + | 0.210905i | 0.136831 | + | 0.0128831i | ||||
\(269\) | −6.00719 | − | 10.4048i | −0.366265 | − | 0.634390i | 0.622713 | − | 0.782450i | \(-0.286030\pi\) |
−0.988978 | + | 0.148060i | \(0.952697\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7592 | + | 14.8721i | 1.56476 | + | 0.903414i | 0.996764 | + | 0.0803814i | \(0.0256138\pi\) |
0.567994 | + | 0.823032i | \(0.307720\pi\) | |||||||
\(272\) | −2.75075 | − | 2.37083i | −0.166789 | − | 0.143753i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.1484 | − | 11.6463i | −1.09638 | − | 0.703578i | ||||
\(275\) | 4.06227 | + | 2.34535i | 0.244964 | + | 0.141430i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.23966 | + | 4.17982i | −0.434989 | + | 0.251141i | −0.701470 | − | 0.712699i | \(-0.747472\pi\) |
0.266481 | + | 0.963840i | \(0.414139\pi\) | |||||||
\(278\) | 4.95925 | + | 9.60400i | 0.297436 | + | 0.576010i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.21214 | + | 14.0738i | 0.371246 | + | 0.841069i | ||||
\(281\) | − | 3.58062i | − | 0.213602i | −0.994280 | − | 0.106801i | \(-0.965939\pi\) | ||
0.994280 | − | 0.106801i | \(-0.0340608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.8564 | − | 18.8038i | −0.645346 | − | 1.11777i | −0.984222 | − | 0.176940i | \(-0.943380\pi\) |
0.338876 | − | 0.940831i | \(-0.389953\pi\) | |||||||
\(284\) | −1.66626 | + | 2.34650i | −0.0988744 | + | 0.139239i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.22990 | − | 12.8246i | 0.486644 | − | 0.758336i | ||||
\(287\) | −27.1367 | − | 14.4990i | −1.60183 | − | 0.855846i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.08789 | + | 14.0086i | −0.475758 | + | 0.824038i | ||||
\(290\) | 13.1431 | + | 0.617370i | 0.771790 | + | 0.0362532i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.31092 | − | 0.782503i | −0.486360 | − | 0.0457925i | ||||
\(293\) | −14.2584 | −0.832986 | −0.416493 | − | 0.909139i | \(-0.636741\pi\) | ||||
−0.416493 | + | 0.909139i | \(0.636741\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.65278i | 0.154451i | ||||||||
\(296\) | −15.6215 | − | 12.2348i | −0.907983 | − | 0.711134i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23.6713 | − | 1.11191i | −1.37124 | − | 0.0644113i | ||||
\(299\) | −1.08218 | − | 0.624795i | −0.0625839 | − | 0.0361328i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.85994 | + | 10.9676i | −0.337762 | + | 0.632164i | ||||
\(302\) | −9.76200 | − | 6.26454i | −0.561740 | − | 0.360484i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 26.5216 | + | 5.03887i | 1.52112 | + | 0.288999i | ||||
\(305\) | 16.3538 | − | 9.44190i | 0.936418 | − | 0.540641i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0680 | 0.688757 | 0.344378 | − | 0.938831i | \(-0.388090\pi\) | ||||
0.344378 | + | 0.938831i | \(0.388090\pi\) | |||||||
\(308\) | 26.7468 | + | 17.6993i | 1.52404 | + | 1.00851i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.8194 | + | 11.2669i | −1.23926 | + | 0.639920i | ||||
\(311\) | 4.88095 | + | 8.45405i | 0.276773 | + | 0.479385i | 0.970581 | − | 0.240775i | \(-0.0774016\pi\) |
−0.693808 | + | 0.720160i | \(0.744068\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.1208 | + | 24.4580i | −0.798155 | + | 1.38245i | 0.122661 | + | 0.992449i | \(0.460857\pi\) |
−0.920816 | + | 0.389997i | \(0.872476\pi\) | |||||||
\(314\) | 2.58240 | + | 1.65719i | 0.145733 | + | 0.0935208i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.4245 | − | 11.1934i | 1.37399 | − | 0.629677i | ||||
\(317\) | 12.7790 | − | 22.1338i | 0.717738 | − | 1.24316i | −0.244157 | − | 0.969736i | \(-0.578511\pi\) |
0.961894 | − | 0.273422i | \(-0.0881556\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.7563 | − | 13.7157i | 1.33009 | − | 0.767931i | ||||
\(320\) | 11.8574 | − | 11.3962i | 0.662848 | − | 0.637066i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.34690 | − | 2.25902i | 0.0750597 | − | 0.125890i | ||||
\(323\) | 6.12718i | 0.340925i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.19145 | − | 0.687883i | 0.0660897 | − | 0.0381569i | ||||
\(326\) | −26.2593 | − | 1.23347i | −1.45437 | − | 0.0683158i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.61633 | + | 32.5659i | −0.254894 | + | 1.79815i | ||||
\(329\) | 12.3626 | + | 19.8732i | 0.681572 | + | 1.09564i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.83423 | + | 10.1052i | −0.320678 | + | 0.555431i | −0.980628 | − | 0.195879i | \(-0.937244\pi\) |
0.659950 | + | 0.751310i | \(0.270577\pi\) | |||||||
\(332\) | −7.69165 | − | 5.46188i | −0.422134 | − | 0.299760i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −14.6749 | − | 28.4192i | −0.802977 | − | 1.55503i | ||||
\(335\) | −2.31264 | −0.126353 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.5456 | 1.22814 | 0.614068 | − | 0.789253i | \(-0.289532\pi\) | ||||
0.614068 | + | 0.789253i | \(0.289532\pi\) | |||||||
\(338\) | 6.38462 | + | 12.3643i | 0.347278 | + | 0.672532i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.04341 | + | 2.16114i | 0.165052 | + | 0.117204i | ||||
\(341\) | −25.5982 | + | 44.3374i | −1.38622 | + | 2.40101i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4302 | + | 1.82465i | −0.995135 | + | 0.0985219i | ||||
\(344\) | 13.1619 | + | 1.86575i | 0.709645 | + | 0.100595i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.53797 | − | 0.0722431i | −0.0826820 | − | 0.00388381i | ||||
\(347\) | −6.94457 | + | 4.00945i | −0.372804 | + | 0.215238i | −0.674683 | − | 0.738108i | \(-0.735720\pi\) |
0.301879 | + | 0.953346i | \(0.402386\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.5648i | − | 0.993750i | −0.867822 | − | 0.496875i | \(-0.834481\pi\) | ||
0.867822 | − | 0.496875i | \(-0.165519\pi\) | |||||||
\(350\) | 1.41247 | + | 2.52779i | 0.0754994 | + | 0.135116i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.97324 | − | 33.3472i | 0.424975 | − | 1.77741i | ||||
\(353\) | 16.1137 | − | 9.30324i | 0.857645 | − | 0.495161i | −0.00557823 | − | 0.999984i | \(-0.501776\pi\) |
0.863223 | + | 0.504823i | \(0.168442\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.47908 | − | 2.56184i | 0.0785012 | − | 0.135968i | ||||
\(356\) | 8.56990 | − | 3.92746i | 0.454204 | − | 0.208155i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.15474 | − | 4.59139i | −0.378140 | − | 0.242662i | ||||
\(359\) | 16.9950 | − | 29.4361i | 0.896959 | − | 1.55358i | 0.0655985 | − | 0.997846i | \(-0.479104\pi\) |
0.831361 | − | 0.555733i | \(-0.187562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.2745 | − | 22.9921i | −0.698659 | − | 1.21011i | ||||
\(362\) | 9.15905 | − | 4.72949i | 0.481389 | − | 0.248577i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.41802 | − | 4.19816i | 0.441224 | − | 0.220043i | ||||
\(365\) | 8.58037 | 0.449117 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.41003 | + | 2.54613i | −0.230202 | + | 0.132907i | −0.610665 | − | 0.791889i | \(-0.709098\pi\) |
0.380463 | + | 0.924796i | \(0.375765\pi\) | |||||||
\(368\) | −2.76226 | − | 0.524806i | −0.143993 | − | 0.0273574i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.1651 | + | 11.0153i | 0.892372 | + | 0.572659i | ||||
\(371\) | 17.5369 | − | 0.577066i | 0.910470 | − | 0.0299598i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7870 | − | 8.53728i | −0.765642 | − | 0.442044i | 0.0656756 | − | 0.997841i | \(-0.479080\pi\) |
−0.831318 | + | 0.555797i | \(0.812413\pi\) | |||||||
\(374\) | 7.77344 | + | 0.365141i | 0.401955 | + | 0.0188810i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 15.4276 | − | 19.6982i | 0.795620 | − | 1.01586i | ||||
\(377\) | − | 8.04551i | − | 0.414365i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.2872 | 0.579783 | 0.289892 | − | 0.957059i | \(-0.406381\pi\) | ||||
0.289892 | + | 0.957059i | \(0.406381\pi\) | |||||||
\(380\) | −27.6263 | − | 2.60112i | −1.41720 | − | 0.133434i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.25139 | + | 0.293646i | 0.319849 | + | 0.0150242i | ||||
\(383\) | 10.2813 | − | 17.8078i | 0.525352 | − | 0.909936i | −0.474212 | − | 0.880410i | \(-0.657267\pi\) |
0.999564 | − | 0.0295252i | \(-0.00939952\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29.0766 | − | 15.5355i | −1.48188 | − | 0.791760i | ||||
\(386\) | −1.93203 | + | 3.01068i | −0.0983378 | + | 0.153239i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.1287 | − | 19.8966i | 0.717274 | − | 1.01010i | ||||
\(389\) | 6.92881 | + | 12.0011i | 0.351305 | + | 0.608478i | 0.986478 | − | 0.163892i | \(-0.0524048\pi\) |
−0.635174 | + | 0.772369i | \(0.719071\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.638155i | − | 0.0322729i | ||||||
\(392\) | 8.58640 | + | 17.8402i | 0.433679 | + | 0.901067i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.54363 | + | 14.6089i | 0.380042 | + | 0.735984i | ||||
\(395\) | −23.9163 | + | 13.8081i | −1.20336 | + | 0.694760i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −29.9634 | − | 17.2993i | −1.50382 | − | 0.868229i | −0.999990 | − | 0.00442498i | \(-0.998591\pi\) |
−0.503827 | − | 0.863804i | \(-0.668075\pi\) | |||||||
\(398\) | −23.0987 | − | 14.8231i | −1.15783 | − | 0.743012i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.02098 | − | 2.34484i | 0.101049 | − | 0.117242i | ||||
\(401\) | −12.1249 | − | 7.00029i | −0.605486 | − | 0.349578i | 0.165711 | − | 0.986174i | \(-0.447008\pi\) |
−0.771197 | + | 0.636597i | \(0.780342\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.50786 | + | 13.0040i | 0.373993 | + | 0.647775i | ||||
\(404\) | 20.7352 | + | 1.95229i | 1.03161 | + | 0.0971301i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 16.9322 | + | 0.237818i | 0.840329 | + | 0.0118027i | ||||
\(407\) | 42.5212 | 2.10770 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.76388 | − | 4.78718i | −0.136665 | − | 0.236711i | 0.789567 | − | 0.613664i | \(-0.210305\pi\) |
−0.926232 | + | 0.376953i | \(0.876972\pi\) | |||||||
\(410\) | 1.58633 | − | 33.7711i | 0.0783430 | − | 1.66783i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11.8691 | + | 5.43944i | −0.584750 | + | 0.267982i | ||||
\(413\) | 0.112284 | + | 3.41229i | 0.00552515 | + | 0.167908i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.39750 | + | 4.84830i | 0.412217 | + | 0.237994i | ||||
\(416\) | −7.30098 | − | 6.91552i | −0.357960 | − | 0.339061i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −51.4024 | + | 26.5428i | −2.51417 | + | 1.29825i | ||||
\(419\) | − | 13.1122i | − | 0.640574i | −0.947320 | − | 0.320287i | \(-0.896221\pi\) | ||
0.947320 | − | 0.320287i | \(-0.103779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 22.0752i | − | 1.07588i | −0.842983 | − | 0.537941i | \(-0.819202\pi\) | ||
0.842983 | − | 0.537941i | \(-0.180798\pi\) | |||||||
\(422\) | 3.72424 | + | 7.21231i | 0.181293 | + | 0.351090i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.00614 | − | 17.4003i | −0.340248 | − | 0.845035i | ||||
\(425\) | 0.608462 | + | 0.351296i | 0.0295148 | + | 0.0170404i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.6364 | − | 12.8374i | 0.998664 | − | 0.621244i | ||||
\(428\) | −16.8071 | + | 7.70245i | −0.812404 | + | 0.372312i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −13.6490 | − | 0.641134i | −0.658215 | − | 0.0309182i | ||||
\(431\) | −12.9464 | − | 22.4237i | −0.623604 | − | 1.08011i | −0.988809 | − | 0.149187i | \(-0.952334\pi\) |
0.365205 | − | 0.930927i | \(-0.380999\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.4535 | −1.55961 | −0.779807 | − | 0.626020i | \(-0.784683\pi\) | ||||
−0.779807 | + | 0.626020i | \(0.784683\pi\) | |||||||
\(434\) | −27.5895 | + | 15.4163i | −1.32434 | + | 0.740005i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.914531 | − | 9.71318i | 0.0437981 | − | 0.465177i | ||||
\(437\) | 2.37200 | + | 4.10843i | 0.113468 | + | 0.196533i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7422 | + | 6.77937i | 0.560425 | + | 0.323561i | 0.753316 | − | 0.657659i | \(-0.228453\pi\) |
−0.192891 | + | 0.981220i | \(0.561786\pi\) | |||||||
\(440\) | −4.94634 | + | 34.8940i | −0.235808 | + | 1.66351i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.23271 | − | 1.92092i | 0.0586338 | − | 0.0913689i | ||||
\(443\) | −3.78628 | − | 2.18601i | −0.179892 | − | 0.103860i | 0.407350 | − | 0.913272i | \(-0.366453\pi\) |
−0.587242 | + | 0.809412i | \(0.699786\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.39158 | + | 4.84488i | −0.397799 | + | 0.229669i | ||||
\(446\) | 6.55195 | − | 3.38325i | 0.310244 | − | 0.160202i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 14.7698 | − | 15.1609i | 0.697810 | − | 0.716283i | ||||
\(449\) | − | 13.7570i | − | 0.649235i | −0.945845 | − | 0.324618i | \(-0.894764\pi\) | ||
0.945845 | − | 0.324618i | \(-0.105236\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −35.2423 | − | 61.0415i | −1.65950 | − | 2.87433i | ||||
\(452\) | −3.89965 | − | 2.76916i | −0.183424 | − | 0.130250i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −8.36518 | − | 5.36816i | −0.392598 | − | 0.251940i | ||||
\(455\) | −8.21007 | + | 5.10727i | −0.384894 | + | 0.239433i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.88182 | − | 10.1876i | 0.275140 | − | 0.476557i | −0.695030 | − | 0.718980i | \(-0.744609\pi\) |
0.970170 | + | 0.242424i | \(0.0779424\pi\) | |||||||
\(458\) | −1.68751 | + | 35.9253i | −0.0788523 | + | 1.67868i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.87732 | + | 0.270910i | 0.134156 | + | 0.0126313i | ||||
\(461\) | 11.1624 | 0.519887 | 0.259943 | − | 0.965624i | \(-0.416296\pi\) | ||||
0.259943 | + | 0.965624i | \(0.416296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.0864i | 0.747599i | 0.927510 | + | 0.373799i | \(0.121945\pi\) | ||||
−0.927510 | + | 0.373799i | \(0.878055\pi\) | |||||||
\(464\) | −5.96617 | − | 17.0917i | −0.276972 | − | 0.793460i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.767721 | + | 16.3439i | −0.0355640 | + | 0.757117i | ||||
\(467\) | −18.8715 | − | 10.8955i | −0.873268 | − | 0.504181i | −0.00483503 | − | 0.999988i | \(-0.501539\pi\) |
−0.868433 | + | 0.495807i | \(0.834872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.97476 | + | 0.0978869i | −0.137361 | + | 0.00452000i | ||||
\(470\) | −13.8899 | + | 21.6446i | −0.640694 | + | 0.998390i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.38572 | − | 1.36324i | 0.155840 | − | 0.0627482i | ||||
\(473\) | −24.6707 | + | 14.2436i | −1.13436 | + | 0.654923i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.22302 | −0.239649 | ||||||||
\(476\) | 4.00623 | + | 2.65107i | 0.183625 | + | 0.121512i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.1619 | + | 21.6160i | 0.510534 | + | 0.988691i | ||||
\(479\) | 10.9014 | + | 18.8818i | 0.498099 | + | 0.862734i | 0.999998 | − | 0.00219321i | \(-0.000698121\pi\) |
−0.501898 | + | 0.864927i | \(0.667365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.23566 | − | 10.8005i | 0.284322 | − | 0.492459i | ||||
\(482\) | −10.4578 | + | 16.2963i | −0.476339 | + | 0.742277i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.4456 | + | 46.7953i | 0.974798 | + | 2.12706i | ||||
\(485\) | −12.5415 | + | 21.7225i | −0.569479 | + | 0.986366i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.03965 | − | 2.90964i | 0.228368 | − | 0.131849i | −0.381451 | − | 0.924389i | \(-0.624575\pi\) |
0.609819 | + | 0.792541i | \(0.291242\pi\) | |||||||
\(488\) | −20.4547 | − | 16.0201i | −0.925939 | − | 0.725197i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −10.5058 | − | 17.4295i | −0.474605 | − | 0.787383i | ||||
\(491\) | − | 17.6807i | − | 0.797919i | −0.916969 | − | 0.398959i | \(-0.869371\pi\) | ||
0.916969 | − | 0.398959i | \(-0.130629\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.55830 | − | 2.05439i | 0.160258 | − | 0.0925249i | ||||
\(494\) | −0.796133 | + | 16.9488i | −0.0358197 | + | 0.762561i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 25.5926 | + | 22.0579i | 1.14914 | + | 0.990427i | ||||
\(497\) | 1.79411 | − | 3.35791i | 0.0804768 | − | 0.150623i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.79931 | − | 8.31264i | 0.214846 | − | 0.372125i | −0.738379 | − | 0.674386i | \(-0.764408\pi\) |
0.953225 | + | 0.302261i | \(0.0977416\pi\) | |||||||
\(500\) | −13.7446 | + | 19.3557i | −0.614677 | + | 0.865614i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.2839 | − | 6.34308i | 0.548257 | − | 0.283105i | ||||
\(503\) | 21.6062 | 0.963375 | 0.481687 | − | 0.876343i | \(-0.340024\pi\) | ||||
0.481687 | + | 0.876343i | \(0.340024\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.4074 | −0.952618 | ||||||||
\(506\) | 5.35364 | − | 2.76448i | 0.237998 | − | 0.122896i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.62655 | + | 4.70554i | 0.294006 | + | 0.208775i | ||||
\(509\) | 8.22302 | − | 14.2427i | 0.364479 | − | 0.631296i | −0.624213 | − | 0.781254i | \(-0.714580\pi\) |
0.988692 | + | 0.149958i | \(0.0479138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.0370 | − | 0.363181i | 0.488247 | − | 0.0160662i | ||||
\(512\) | −20.6382 | − | 9.27706i | −0.912089 | − | 0.409992i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.37662 | − | 29.3066i | 0.0607200 | − | 1.29266i | ||||
\(515\) | 11.6222 | − | 6.71006i | 0.512133 | − | 0.295680i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 53.6178i | 2.35811i | ||||||||
\(518\) | 22.5458 | + | 13.4425i | 0.990606 | + | 0.590630i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.13777 | + | 6.37352i | 0.356865 | + | 0.279497i | ||||
\(521\) | 22.2819 | − | 12.8645i | 0.976189 | − | 0.563603i | 0.0750717 | − | 0.997178i | \(-0.476081\pi\) |
0.901117 | + | 0.433575i | \(0.142748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.2515 | + | 33.3445i | −0.841808 | + | 1.45805i | 0.0465564 | + | 0.998916i | \(0.485175\pi\) |
−0.888365 | + | 0.459139i | \(0.848158\pi\) | |||||||
\(524\) | 0.436752 | − | 0.200157i | 0.0190796 | − | 0.00874389i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −10.1079 | + | 15.7511i | −0.440727 | + | 0.686782i | ||||
\(527\) | −3.83420 | + | 6.64103i | −0.167020 | + | 0.289288i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2530 | + | 19.4907i | 0.489259 | + | 0.847421i | ||||
\(530\) | 8.84628 | + | 17.1315i | 0.384258 | + | 0.744147i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −35.6460 | − | 2.17649i | −1.54545 | − | 0.0943628i | ||||
\(533\) | −20.6729 | −0.895441 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.4574 | − | 9.50169i | 0.711516 | − | 0.410794i | ||||
\(536\) | 1.18844 | + | 2.95159i | 0.0513328 | + | 0.127489i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.17652 | − | 14.2997i | 0.395628 | − | 0.616505i | ||||
\(539\) | −38.0590 | − | 18.7526i | −1.63932 | − | 0.807732i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.4037 | − | 18.7083i | −1.39314 | − | 0.804331i | −0.399481 | − | 0.916741i | \(-0.630810\pi\) |
−0.993662 | + | 0.112410i | \(0.964143\pi\) | |||||||
\(542\) | −1.97372 | + | 42.0182i | −0.0847784 | + | 1.80484i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.19426 | − | 4.99486i | 0.0512036 | − | 0.214153i | ||||
\(545\) | 10.0281i | 0.429556i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.1153 | −1.33039 | −0.665197 | − | 0.746668i | \(-0.731652\pi\) | ||||
−0.665197 | + | 0.746668i | \(0.731652\pi\) | |||||||
\(548\) | 2.85865 | − | 30.3616i | 0.122116 | − | 1.29698i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.311259 | + | 6.62635i | −0.0132721 | + | 0.282549i | ||||
\(551\) | −15.2722 | + | 26.4522i | −0.650617 | + | 1.12690i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.1792 | + | 18.7737i | −1.28335 | + | 0.798339i | ||||
\(554\) | −9.94978 | − | 6.38504i | −0.422726 | − | 0.271274i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.85027 | + | 12.4633i | −0.375335 | + | 0.528563i | ||||
\(557\) | 15.0725 | + | 26.1063i | 0.638641 | + | 1.10616i | 0.985731 | + | 0.168327i | \(0.0538364\pi\) |
−0.347090 | + | 0.937832i | \(0.612830\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.35521i | 0.353388i | ||||||||
\(560\) | −13.6539 | + | 16.9379i | −0.576984 | + | 0.715759i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.49932 | − | 2.32333i | 0.189792 | − | 0.0980037i | ||||
\(563\) | 26.6333 | − | 15.3767i | 1.12246 | − | 0.648051i | 0.180431 | − | 0.983588i | \(-0.442251\pi\) |
0.942027 | + | 0.335536i | \(0.108918\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.25752 | + | 2.45808i | 0.179115 | + | 0.103412i | ||||
\(566\) | 16.5841 | − | 25.8429i | 0.697082 | − | 1.08626i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.02973 | − | 0.571227i | −0.169084 | − | 0.0239682i | ||||
\(569\) | −38.4227 | − | 22.1833i | −1.61076 | − | 0.929974i | −0.989194 | − | 0.146613i | \(-0.953163\pi\) |
−0.621568 | − | 0.783361i | \(-0.713504\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2431 | − | 28.1338i | −0.679751 | − | 1.17736i | −0.975056 | − | 0.221961i | \(-0.928754\pi\) |
0.295304 | − | 0.955403i | \(-0.404579\pi\) | |||||||
\(572\) | 21.4552 | + | 2.02008i | 0.897085 | + | 0.0844637i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.611070 | − | 43.5070i | 0.0255056 | − | 1.81595i | ||||
\(575\) | 0.543986 | 0.0226858 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 19.6946 | + | 34.1120i | 0.819896 | + | 1.42010i | 0.905758 | + | 0.423795i | \(0.139302\pi\) |
−0.0858615 | + | 0.996307i | \(0.527364\pi\) | |||||||
\(578\) | −22.8508 | − | 1.07337i | −0.950469 | − | 0.0446463i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.75228 | + | 16.9159i | 0.321896 | + | 0.702393i | ||||
\(581\) | 11.0070 | + | 5.88095i | 0.456646 | + | 0.243983i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.8117 | + | 20.0985i | 1.44175 | + | 0.832396i | ||||
\(584\) | −4.40936 | − | 10.9510i | −0.182461 | − | 0.453157i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.25174 | − | 17.9168i | −0.382186 | − | 0.740134i | ||||
\(587\) | − | 24.9178i | − | 1.02847i | −0.857650 | − | 0.514233i | \(-0.828077\pi\) | ||
0.857650 | − | 0.514233i | \(-0.171923\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 57.0064i | − | 2.34891i | ||||||
\(590\) | −3.33342 | + | 1.72129i | −0.137235 | + | 0.0708644i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.23774 | − | 27.5683i | 0.215270 | − | 1.13305i | ||||
\(593\) | 12.1405 | + | 7.00931i | 0.498550 | + | 0.287838i | 0.728114 | − | 0.685456i | \(-0.240397\pi\) |
−0.229565 | + | 0.973293i | \(0.573730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4.35521 | − | 2.32696i | −0.178546 | − | 0.0953961i | ||||
\(596\) | −13.9622 | − | 30.4663i | −0.571915 | − | 1.24795i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.0829184 | − | 1.76524i | 0.00339079 | − | 0.0721860i | ||||
\(599\) | −12.2437 | − | 21.2067i | −0.500264 | − | 0.866483i | −1.00000 | 0.000304857i | \(-0.999903\pi\) | |
0.499736 | − | 0.866178i | \(-0.333430\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.0204 | −0.694275 | −0.347138 | − | 0.937814i | \(-0.612846\pi\) | ||||
−0.347138 | + | 0.937814i | \(0.612846\pi\) | |||||||
\(602\) | −17.5839 | − | 0.246972i | −0.716668 | − | 0.0100658i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.53767 | − | 16.3315i | 0.0625668 | − | 0.664519i | ||||
\(605\) | −26.4551 | − | 45.8216i | −1.07555 | − | 1.86291i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21.1481 | − | 12.2099i | −0.858375 | − | 0.495583i | 0.00509301 | − | 0.999987i | \(-0.498379\pi\) |
−0.863468 | + | 0.504404i | \(0.831712\pi\) | |||||||
\(608\) | 10.8771 | + | 36.5959i | 0.441125 | + | 1.48416i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.4758 | + | 14.4233i | 0.910019 | + | 0.583984i | ||||
\(611\) | 13.6190 | + | 7.86294i | 0.550966 | + | 0.318101i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.0566 | − | 19.6626i | 1.37553 | − | 0.794164i | 0.383915 | − | 0.923369i | \(-0.374576\pi\) |
0.991618 | + | 0.129205i | \(0.0412424\pi\) | |||||||
\(614\) | 7.83045 | + | 15.1643i | 0.316011 | + | 0.611982i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.88555 | + | 45.0937i | −0.196844 | + | 1.81688i | ||||
\(617\) | 14.5542i | 0.585932i | 0.956123 | + | 0.292966i | \(0.0946422\pi\) | ||||
−0.956123 | + | 0.292966i | \(0.905358\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.16451 | + | 14.1413i | 0.328159 | + | 0.568389i | 0.982147 | − | 0.188117i | \(-0.0602383\pi\) |
−0.653987 | + | 0.756506i | \(0.726905\pi\) | |||||||
\(620\) | −28.3155 | − | 20.1070i | −1.13718 | − | 0.807516i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.45608 | + | 11.6188i | −0.298962 | + | 0.465871i | ||||
\(623\) | −10.5891 | + | 6.58719i | −0.424242 | + | 0.263910i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.2658 | − | 17.7809i | 0.410632 | − | 0.711236i | ||||
\(626\) | −39.8957 | − | 1.87402i | −1.59455 | − | 0.0749007i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.406768 | + | 4.32026i | −0.0162318 | + | 0.172397i | ||||
\(629\) | 6.36899 | 0.253948 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 32.9828i | − | 1.31302i | −0.754315 | − | 0.656512i | \(-0.772031\pi\) | ||
0.754315 | − | 0.656512i | \(-0.227969\pi\) | |||||||
\(632\) | 29.9135 | + | 23.4283i | 1.18989 | + | 0.931927i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.1045 | + | 1.69593i | 1.43389 | + | 0.0673542i | ||||
\(635\) | −7.23466 | − | 4.17693i | −0.287099 | − | 0.165756i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.3445 | + | 6.91702i | −0.409863 | + | 0.274062i | ||||
\(638\) | 32.6493 | + | 20.9519i | 1.29260 | + | 0.829494i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 22.0140 | + | 7.50514i | 0.870178 | + | 0.296667i | ||||
\(641\) | 11.8256 | − | 6.82749i | 0.467081 | − | 0.269669i | −0.247936 | − | 0.968776i | \(-0.579752\pi\) |
0.715017 | + | 0.699107i | \(0.246419\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 46.5621 | 1.83623 | 0.918115 | − | 0.396315i | \(-0.129711\pi\) | ||||
0.918115 | + | 0.396315i | \(0.129711\pi\) | |||||||
\(644\) | 3.71258 | + | 0.226685i | 0.146296 | + | 0.00893263i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.69925 | + | 3.97569i | −0.302923 | + | 0.156421i | ||||
\(647\) | −17.7299 | − | 30.7090i | −0.697033 | − | 1.20730i | −0.969491 | − | 0.245128i | \(-0.921170\pi\) |
0.272458 | − | 0.962168i | \(-0.412163\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.91073 | + | 6.77358i | −0.153509 | + | 0.265886i | ||||
\(650\) | 1.63746 | + | 1.05080i | 0.0642265 | + | 0.0412159i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.4887 | − | 33.7971i | −0.606583 | − | 1.32360i | ||||
\(653\) | 10.6086 | − | 18.3747i | 0.415148 | − | 0.719057i | −0.580296 | − | 0.814405i | \(-0.697063\pi\) |
0.995444 | + | 0.0953486i | \(0.0303966\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.427664 | + | 0.246912i | −0.0167102 | + | 0.00964766i | ||||
\(656\) | −43.9168 | + | 15.3300i | −1.71466 | + | 0.598536i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16.9505 | + | 28.4295i | −0.660799 | + | 1.10830i | ||||
\(659\) | − | 7.62196i | − | 0.296909i | −0.988919 | − | 0.148455i | \(-0.952570\pi\) | ||
0.988919 | − | 0.148455i | \(-0.0474299\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1044 | − | 20.2675i | 1.36540 | − | 0.788315i | 0.375065 | − | 0.926998i | \(-0.377620\pi\) |
0.990337 | + | 0.138683i | \(0.0442869\pi\) | |||||||
\(662\) | −16.4835 | − | 0.774278i | −0.640650 | − | 0.0300932i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.87244 | − | 13.2091i | 0.0726647 | − | 0.512614i | ||||
\(665\) | 36.6880 | − | 1.20725i | 1.42270 | − | 0.0468151i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.59062 | − | 2.75504i | 0.0615891 | − | 0.106675i | ||||
\(668\) | 26.1889 | − | 36.8803i | 1.01328 | − | 1.42694i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.50058 | − | 2.90600i | −0.0579725 | − | 0.112269i | ||||
\(671\) | 55.6769 | 2.14938 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 25.1754 | 0.970440 | 0.485220 | − | 0.874392i | \(-0.338739\pi\) | ||||
0.485220 | + | 0.874392i | \(0.338739\pi\) | |||||||
\(674\) | 14.6289 | + | 28.3302i | 0.563486 | + | 1.09124i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.3940 | + | 16.0455i | −0.438230 | + | 0.617135i | ||||
\(677\) | −18.0389 | + | 31.2442i | −0.693290 | + | 1.20081i | 0.277464 | + | 0.960736i | \(0.410506\pi\) |
−0.970754 | + | 0.240077i | \(0.922827\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.2127 | + | 28.4726i | −0.583810 | + | 1.09268i | ||||
\(680\) | −0.740882 | + | 5.22656i | −0.0284115 | + | 0.200429i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −72.3230 | − | 3.39722i | −2.76939 | − | 0.130086i | ||||
\(683\) | 2.69000 | − | 1.55307i | 0.102930 | − | 0.0594268i | −0.447651 | − | 0.894208i | \(-0.647739\pi\) |
0.550581 | + | 0.834781i | \(0.314406\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.3459i | 1.19767i | ||||||||
\(686\) | −14.2514 | − | 21.9749i | −0.544122 | − | 0.839006i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.19583 | + | 17.7496i | 0.236214 | + | 0.676696i | ||||
\(689\) | 10.2101 | − | 5.89482i | 0.388975 | − | 0.224575i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.31148 | − | 5.73566i | 0.125975 | − | 0.218195i | −0.796139 | − | 0.605114i | \(-0.793128\pi\) |
0.922114 | + | 0.386919i | \(0.126461\pi\) | |||||||
\(692\) | −0.907153 | − | 1.97945i | −0.0344848 | − | 0.0752476i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.54423 | − | 6.12479i | −0.362294 | − | 0.232494i | ||||
\(695\) | 7.85605 | − | 13.6071i | 0.297997 | − | 0.516146i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.27873 | − | 9.14302i | −0.199946 | − | 0.346317i | ||||
\(698\) | 23.3280 | − | 12.0460i | 0.882978 | − | 0.455947i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.25987 | + | 3.41506i | −0.0854149 | + | 0.129077i | ||||
\(701\) | 30.4248 | 1.14913 | 0.574565 | − | 0.818459i | \(-0.305171\pi\) | ||||
0.574565 | + | 0.818459i | \(0.305171\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −41.0034 | + | 23.6734i | −1.54647 | + | 0.892857i | ||||
\(704\) | 47.0767 | − | 11.6187i | 1.77427 | − | 0.437897i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 22.1458 | + | 14.2115i | 0.833466 | + | 0.534858i | ||||
\(707\) | −27.5365 | + | 0.906112i | −1.03562 | + | 0.0340778i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.73691 | − | 2.73486i | −0.177899 | − | 0.102710i | 0.408406 | − | 0.912800i | \(-0.366085\pi\) |
−0.586305 | + | 0.810090i | \(0.699418\pi\) | |||||||
\(710\) | 4.17885 | + | 0.196293i | 0.156830 | + | 0.00736674i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.4958 | + | 8.22035i | 0.393347 | + | 0.308070i | ||||
\(713\) | 5.93730i | 0.222354i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −22.1507 | −0.828391 | ||||||||
\(716\) | 1.12698 | − | 11.9696i | 0.0421173 | − | 0.447326i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 48.0160 | + | 2.25545i | 1.79194 | + | 0.0841727i | ||||
\(719\) | −4.25219 | + | 7.36501i | −0.158580 | + | 0.274669i | −0.934357 | − | 0.356339i | \(-0.884025\pi\) |
0.775777 | + | 0.631007i | \(0.217358\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.6656 | − | 9.12311i | 0.546176 | − | 0.339762i | ||||
\(722\) | 20.2780 | − | 31.5991i | 0.754669 | − | 1.17600i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.8859 | + | 8.44025i | 0.441737 | + | 0.313679i | ||||
\(725\) | 1.75123 | + | 3.03322i | 0.0650391 | + | 0.112651i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.9931i | − | 1.18656i | −0.804997 | − | 0.593280i | \(-0.797833\pi\) | ||
0.804997 | − | 0.593280i | \(-0.202167\pi\) | |||||||
\(728\) | 10.7374 | + | 7.85384i | 0.397956 | + | 0.291083i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 5.56747 | + | 10.7819i | 0.206061 | + | 0.399055i | ||||
\(731\) | −3.69527 | + | 2.13347i | −0.136675 | + | 0.0789091i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.6276 | − | 7.29054i | −0.466411 | − | 0.269282i | 0.248325 | − | 0.968677i | \(-0.420120\pi\) |
−0.714736 | + | 0.699394i | \(0.753453\pi\) | |||||||
\(734\) | −6.06091 | − | 3.88945i | −0.223712 | − | 0.143562i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.13287 | − | 3.81151i | −0.0417581 | − | 0.140494i | ||||
\(737\) | −5.90505 | − | 3.40928i | −0.217515 | − | 0.125583i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.3199 | + | 21.3387i | 0.453194 | + | 0.784955i | 0.998582 | − | 0.0532282i | \(-0.0169511\pi\) |
−0.545388 | + | 0.838184i | \(0.683618\pi\) | |||||||
\(740\) | −2.70377 | + | 28.7166i | −0.0993927 | + | 1.05565i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.1041 | + | 21.6620i | 0.444357 | + | 0.795235i | ||||
\(743\) | −44.0203 | −1.61495 | −0.807474 | − | 0.589903i | \(-0.799166\pi\) | ||||
−0.807474 | + | 0.589903i | \(0.799166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.2237 | + | 29.8323i | 0.631028 | + | 1.09297i | ||||
\(746\) | 1.13301 | − | 24.1205i | 0.0414824 | − | 0.883114i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.58506 | + | 10.0048i | 0.167646 | + | 0.365813i | ||||
\(749\) | 20.7671 | − | 12.9187i | 0.758812 | − | 0.472038i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.28019 | + | 4.20322i | 0.265658 | + | 0.153378i | 0.626913 | − | 0.779089i | \(-0.284318\pi\) |
−0.361255 | + | 0.932467i | \(0.617652\pi\) | |||||||
\(752\) | 34.7626 | + | 6.60460i | 1.26766 | + | 0.240845i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 10.1098 | − | 5.22042i | 0.368177 | − | 0.190117i | ||||
\(755\) | 16.8610i | 0.613634i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.5161i | 1.61797i | 0.587831 | + | 0.808983i | \(0.299982\pi\) | ||||
−0.587831 | + | 0.808983i | \(0.700018\pi\) | |||||||
\(758\) | 7.32381 | + | 14.1832i | 0.266013 | + | 0.515156i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.6572 | − | 36.4023i | −0.531671 | − | 1.32045i | ||||
\(761\) | 21.8857 | + | 12.6357i | 0.793357 | + | 0.458045i | 0.841143 | − | 0.540813i | \(-0.181883\pi\) |
−0.0477862 | + | 0.998858i | \(0.515217\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.424459 | + | 12.8992i | 0.0153664 | + | 0.466982i | ||||
\(764\) | 3.68730 | + | 8.04588i | 0.133402 | + | 0.291090i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 29.0480 | + | 1.36447i | 1.04955 | + | 0.0493002i | ||||
\(767\) | 1.14700 | + | 1.98666i | 0.0414158 | + | 0.0717343i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.1185 | −0.437005 | −0.218502 | − | 0.975836i | \(-0.570117\pi\) | ||||
−0.218502 | + | 0.975836i | \(0.570117\pi\) | |||||||
\(770\) | 0.654755 | − | 46.6173i | 0.0235957 | − | 1.67997i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.03676 | − | 0.474229i | −0.181277 | − | 0.0170679i | ||||
\(773\) | 9.15261 | + | 15.8528i | 0.329196 | + | 0.570185i | 0.982353 | − | 0.187038i | \(-0.0598888\pi\) |
−0.653156 | + | 0.757223i | \(0.726555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.66105 | − | 3.26841i | −0.203351 | − | 0.117405i | ||||
\(776\) | 34.1691 | + | 4.84358i | 1.22660 | + | 0.173874i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10.5844 | + | 16.4936i | −0.379468 | + | 0.591324i | ||||
\(779\) | 67.9687 | + | 39.2417i | 2.43523 | + | 1.40598i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.55330 | − | 4.36090i | 0.270278 | − | 0.156045i | ||||
\(782\) | 0.801889 | − | 0.414074i | 0.0286755 | − | 0.0148073i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.8462 | + | 22.3653i | −0.601649 | + | 0.798760i | ||||
\(785\) | − | 4.46033i | − | 0.159196i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.0540 | + | 19.1461i | 0.394033 | + | 0.682485i | 0.992977 | − | 0.118306i | \(-0.0377462\pi\) |
−0.598944 | + | 0.800791i | \(0.704413\pi\) | |||||||
\(788\) | −13.4623 | + | 18.9583i | −0.479576 | + | 0.675360i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −32.8692 | − | 21.0931i | −1.16944 | − | 0.750458i | ||||
\(791\) | 5.58051 | + | 2.98163i | 0.198420 | + | 0.106015i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.16491 | − | 14.1420i | 0.289944 | − | 0.502198i | ||||
\(794\) | 2.29585 | − | 48.8761i | 0.0814767 | − | 1.73455i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.63841 | − | 38.6433i | 0.128960 | − | 1.36968i | ||||
\(797\) | 11.9294 | 0.422563 | 0.211281 | − | 0.977425i | \(-0.432236\pi\) | ||||
0.211281 | + | 0.977425i | \(0.432236\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.03107i | 0.284119i | ||||||||
\(800\) | 4.25780 | + | 1.01803i | 0.150536 | + | 0.0359929i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.929030 | − | 19.7780i | 0.0328052 | − | 0.698385i | ||||
\(803\) | 21.9090 | + | 12.6492i | 0.773151 | + | 0.446379i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.82111 | + | 0.125737i | −0.134676 | + | 0.00443164i | ||||
\(806\) | −11.4689 | + | 17.8720i | −0.403976 | + | 0.629514i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.0011 | + | 27.3221i | 0.387016 | + | 0.961187i | ||||
\(809\) | −13.1494 | + | 7.59184i | −0.462310 | + | 0.266915i | −0.713015 | − | 0.701149i | \(-0.752671\pi\) |
0.250705 | + | 0.968064i | \(0.419338\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1176 | 1.09269 | 0.546344 | − | 0.837561i | \(-0.316019\pi\) | ||||
0.546344 | + | 0.837561i | \(0.316019\pi\) | |||||||
\(812\) | 10.6878 | + | 21.4308i | 0.375068 | + | 0.752075i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.5904 | + | 53.4311i | 0.967043 | + | 1.87276i | ||||
\(815\) | 19.1067 | + | 33.0938i | 0.669279 | + | 1.15923i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.8601 | − | 27.4704i | 0.554873 | − | 0.961069i | ||||
\(818\) | 4.22207 | − | 6.57923i | 0.147621 | − | 0.230037i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 43.4652 | − | 19.9194i | 1.51787 | − | 0.695616i | ||||
\(821\) | −2.78548 | + | 4.82459i | −0.0972139 | + | 0.168379i | −0.910530 | − | 0.413442i | \(-0.864326\pi\) |
0.813317 | + | 0.581821i | \(0.197660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.34067 | − | 4.81549i | 0.290737 | − | 0.167857i | −0.347537 | − | 0.937666i | \(-0.612982\pi\) |
0.638274 | + | 0.769809i | \(0.279649\pi\) | |||||||
\(824\) | −14.5365 | − | 11.3850i | −0.506402 | − | 0.396615i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.21494 | + | 2.35520i | −0.146656 | + | 0.0819478i | ||||
\(827\) | 52.4810i | 1.82494i | 0.409139 | + | 0.912472i | \(0.365829\pi\) | ||||
−0.409139 | + | 0.912472i | \(0.634171\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.0623 | + | 13.8924i | −0.835717 | + | 0.482501i | −0.855806 | − | 0.517297i | \(-0.826938\pi\) |
0.0200891 | + | 0.999798i | \(0.493605\pi\) | |||||||
\(830\) | −0.643433 | + | 13.6980i | −0.0223339 | + | 0.475463i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.95253 | − | 13.6614i | 0.137029 | − | 0.473625i | ||||
\(833\) | −5.70062 | − | 2.80884i | −0.197515 | − | 0.0973205i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −23.2469 | + | 40.2647i | −0.804491 | + | 1.39342i | ||||
\(836\) | −66.7061 | − | 47.3683i | −2.30708 | − | 1.63827i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.4765 | − | 8.50802i | 0.569171 | − | 0.293905i | ||||
\(839\) | −22.6418 | −0.781681 | −0.390841 | − | 0.920458i | \(-0.627816\pi\) | ||||
−0.390841 | + | 0.920458i | \(0.627816\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.51751 | −0.293707 | ||||||||
\(842\) | 27.7392 | − | 14.3238i | 0.955956 | − | 0.493630i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.64628 | + | 9.35958i | −0.228774 | + | 0.322170i | ||||
\(845\) | 10.1140 | − | 17.5180i | 0.347932 | − | 0.602637i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.9688 | − | 57.8208i | −1.23590 | − | 1.98674i | ||||
\(848\) | 17.3188 | − | 20.0941i | 0.594730 | − | 0.690035i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.0466216 | + | 0.992520i | −0.00159911 | + | 0.0340432i | ||||
\(851\) | 4.27057 | − | 2.46562i | 0.146393 | − | 0.0845202i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2579i | 0.899053i | 0.893267 | + | 0.449526i | \(0.148407\pi\) | ||||
−0.893267 | + | 0.449526i | \(0.851593\pi\) | |||||||
\(854\) | 29.5213 | + | 17.6015i | 1.01020 | + | 0.602310i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −20.5842 | − | 16.1216i | −0.703554 | − | 0.551025i | ||||
\(857\) | −23.8430 | + | 13.7658i | −0.814461 | + | 0.470229i | −0.848503 | − | 0.529191i | \(-0.822495\pi\) |
0.0340416 | + | 0.999420i | \(0.489162\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.71373 | − | 8.16443i | 0.160831 | − | 0.278567i | −0.774336 | − | 0.632774i | \(-0.781916\pi\) |
0.935167 | + | 0.354208i | \(0.115249\pi\) | |||||||
\(860\) | −8.05070 | − | 17.5670i | −0.274526 | − | 0.599031i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.7767 | − | 30.8180i | 0.673597 | − | 1.04966i | ||||
\(863\) | −2.57590 | + | 4.46158i | −0.0876846 | + | 0.151874i | −0.906532 | − | 0.422137i | \(-0.861280\pi\) |
0.818847 | + | 0.574011i | \(0.194613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.11906 | + | 1.93827i | 0.0380491 | + | 0.0659030i | ||||
\(866\) | −21.0578 | − | 40.7802i | −0.715573 | − | 1.38577i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −37.2734 | − | 24.6652i | −1.26514 | − | 0.837191i | ||||
\(869\) | −81.4234 | −2.76210 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.73193 | + | 0.999930i | −0.0586842 | + | 0.0338813i | ||||
\(872\) | 12.7987 | − | 5.15334i | 0.433420 | − | 0.174514i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.62344 | + | 5.64639i | −0.122565 | + | 0.190992i | ||||
\(875\) | 14.7992 | − | 27.6986i | 0.500303 | − | 0.936382i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.4832 | + | 19.3315i | 1.13065 | + | 0.652779i | 0.944098 | − | 0.329666i | \(-0.106936\pi\) |
0.186550 | + | 0.982446i | \(0.440270\pi\) | |||||||
\(878\) | −0.899710 | + | 19.1538i | −0.0303638 | + | 0.646410i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −47.0564 | + | 16.4259i | −1.58627 | + | 0.553718i | ||||
\(881\) | − | 19.8610i | − | 0.669134i | −0.942372 | − | 0.334567i | \(-0.891410\pi\) | ||
0.942372 | − | 0.334567i | \(-0.108590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.9587 | −0.570707 | −0.285353 | − | 0.958422i | \(-0.592111\pi\) | ||||
−0.285353 | + | 0.958422i | \(0.592111\pi\) | |||||||
\(884\) | 3.21363 | + | 0.302575i | 0.108086 | + | 0.0101767i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.290112 | − | 6.17616i | 0.00974650 | − | 0.207492i | ||||
\(887\) | 1.65637 | − | 2.86892i | 0.0556154 | − | 0.0963287i | −0.836877 | − | 0.547391i | \(-0.815621\pi\) |
0.892493 | + | 0.451062i | \(0.148955\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.48277 | − | 5.06659i | −0.318042 | − | 0.169928i | ||||
\(890\) | −11.5329 | − | 7.40099i | −0.386585 | − | 0.248082i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.50262 | + | 6.03775i | 0.284689 | + | 0.202159i | ||||
\(893\) | −29.8512 | − | 51.7039i | −0.998934 | − | 1.73020i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12.3577i | 0.413072i | ||||||||
\(896\) | 28.6343 | + | 8.72211i | 0.956606 | + | 0.291385i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 17.2867 | − | 8.92642i | 0.576866 | − | 0.297878i | ||||
\(899\) | −33.1060 | + | 19.1137i | −1.10415 | + | 0.637479i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.21422 | + | 3.01043i | 0.173711 | + | 0.100292i | ||||
\(902\) | 53.8357 | − | 83.8920i | 1.79253 | − | 2.79330i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.949322 | − | 6.69700i | 0.0315740 | − | 0.222739i | ||||
\(905\) | −12.9767 | − | 7.49208i | −0.431359 | − | 0.249045i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.58088 | + | 14.8625i | 0.284923 | + | 0.493502i | 0.972591 | − | 0.232524i | \(-0.0746985\pi\) |
−0.687667 | + | 0.726026i | \(0.741365\pi\) | |||||||
\(908\) | 1.31765 | − | 13.9947i | 0.0437277 | − | 0.464429i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.7449 | − | 7.00265i | −0.389339 | − | 0.232135i | ||||
\(911\) | −12.8972 | −0.427303 | −0.213652 | − | 0.976910i | \(-0.568536\pi\) | ||||
−0.213652 | + | 0.976910i | \(0.568536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 14.2947 | + | 24.7592i | 0.473086 | + | 0.819409i | ||||
\(914\) | 16.6180 | + | 0.780595i | 0.549674 | + | 0.0258198i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.2377 | + | 21.1900i | −1.52774 | + | 0.700138i | ||||
\(917\) | −0.539656 | + | 0.335706i | −0.0178210 | + | 0.0110860i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.2492 | + | 18.0418i | 1.03082 | + | 0.595142i | 0.917219 | − | 0.398384i | \(-0.130429\pi\) |
0.113598 | + | 0.993527i | \(0.463762\pi\) | |||||||
\(920\) | 1.52657 | + | 3.79135i | 0.0503294 | + | 0.124997i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.24288 | + | 14.0264i | 0.238532 | + | 0.461936i | ||||
\(923\) | − | 2.55807i | − | 0.0842000i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.42916i | 0.178510i | ||||||||
\(926\) | −20.2138 | + | 10.4379i | −0.664266 | + | 0.343009i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 17.6057 | − | 18.5871i | 0.577936 | − | 0.610150i | ||||
\(929\) | −32.7215 | − | 18.8918i | −1.07356 | − | 0.619818i | −0.144406 | − | 0.989519i | \(-0.546127\pi\) |
−0.929151 | + | 0.369700i | \(0.879460\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 47.1408 | − | 3.10578i | 1.54498 | − | 0.101788i | ||||
\(932\) | −21.0355 | + | 9.64024i | −0.689040 | + | 0.315777i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.44597 | − | 30.7831i | 0.0473136 | − | 1.00725i | ||||
\(935\) | −5.65610 | − | 9.79664i | −0.184974 | − | 0.320385i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6280 | 0.869899 | 0.434949 | − | 0.900455i | \(-0.356766\pi\) | ||||
0.434949 | + | 0.900455i | \(0.356766\pi\) | |||||||
\(938\) | −2.05321 | − | 3.67449i | −0.0670396 | − | 0.119976i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −36.2107 | − | 3.40936i | −1.18106 | − | 0.111201i | ||||
\(941\) | −5.35475 | − | 9.27469i | −0.174560 | − | 0.302346i | 0.765449 | − | 0.643496i | \(-0.222517\pi\) |
−0.940009 | + | 0.341150i | \(0.889184\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.07904 | − | 4.08708i | −0.230525 | − | 0.133094i | ||||
\(944\) | 3.90987 | + | 3.36985i | 0.127256 | + | 0.109679i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −33.9061 | − | 21.7584i | −1.10238 | − | 0.707428i | ||||
\(947\) | −24.4571 | − | 14.1203i | −0.794749 | − | 0.458849i | 0.0468825 | − | 0.998900i | \(-0.485071\pi\) |
−0.841632 | + | 0.540052i | \(0.818405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.42582 | − | 3.70995i | 0.208591 | − | 0.120430i | ||||
\(950\) | −3.38902 | − | 6.56312i | −0.109954 | − | 0.212936i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.731776 | + | 6.75431i | −0.0237170 | + | 0.218908i | ||||
\(953\) | 21.4320i | 0.694250i | 0.937819 | + | 0.347125i | \(0.112842\pi\) | ||||
−0.937819 | + | 0.347125i | \(0.887158\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.54863 | − | 7.87846i | −0.147190 | − | 0.254941i | ||||
\(956\) | −19.9195 | + | 28.0515i | −0.644244 | + | 0.907252i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −16.6529 | + | 25.9502i | −0.538031 | + | 0.838412i | ||||
\(959\) | 1.32678 | + | 40.3204i | 0.0428439 | + | 1.30201i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.1729 | − | 34.9405i | 0.650738 | − | 1.12711i | ||||
\(962\) | 17.6177 | + | 0.827554i | 0.568017 | + | 0.0266814i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −27.2632 | − | 2.56693i | −0.878088 | − | 0.0826751i | ||||
\(965\) | 5.20005 | 0.167396 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5003i | 0.530613i | 0.964164 | + | 0.265307i | \(0.0854732\pi\) | ||||
−0.964164 | + | 0.265307i | \(0.914527\pi\) | |||||||
\(968\) | −44.8866 | + | 57.3116i | −1.44271 | + | 1.84206i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −35.4336 | − | 1.66442i | −1.13770 | − | 0.0534412i | ||||
\(971\) | 20.4371 | + | 11.7994i | 0.655858 | + | 0.378660i | 0.790697 | − | 0.612208i | \(-0.209718\pi\) |
−0.134839 | + | 0.990868i | \(0.543052\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.52933 | − | 17.8354i | 0.305496 | − | 0.571776i | ||||
\(974\) | 6.92622 | + | 4.44474i | 0.221930 | + | 0.142419i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.85824 | − | 36.0976i | 0.219527 | − | 1.15546i | ||||
\(977\) | −26.7355 | + | 15.4358i | −0.855346 | + | 0.493834i | −0.862451 | − | 0.506141i | \(-0.831072\pi\) |
0.00710519 | + | 0.999975i | \(0.497738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.5693 | −0.913077 | ||||||||
\(980\) | 15.0846 | − | 24.5107i | 0.481859 | − | 0.782964i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 22.2171 | − | 11.4723i | 0.708976 | − | 0.366097i | ||||
\(983\) | 9.83164 | + | 17.0289i | 0.313581 | + | 0.543138i | 0.979135 | − | 0.203212i | \(-0.0651381\pi\) |
−0.665554 | + | 0.746350i | \(0.731805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9500 | − | 20.6980i | 0.380759 | − | 0.659494i | ||||
\(986\) | 4.89033 | + | 3.13826i | 0.155740 | + | 0.0999425i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.8140 | + | 9.99701i | −0.693995 | + | 0.318047i | ||||
\(989\) | −1.65185 | + | 2.86109i | −0.0525257 | + | 0.0909773i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.9635 | − | 16.7221i | 0.920057 | − | 0.531195i | 0.0364036 | − | 0.999337i | \(-0.488410\pi\) |
0.883653 | + | 0.468142i | \(0.155076\pi\) | |||||||
\(992\) | −11.1113 | + | 46.4715i | −0.352783 | + | 1.47547i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.38359 | + | 0.0756142i | 0.170757 | + | 0.00239834i | ||||
\(995\) | 39.8962i | 1.26479i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.84528 | − | 4.52948i | 0.248463 | − | 0.143450i | −0.370597 | − | 0.928794i | \(-0.620847\pi\) |
0.619060 | + | 0.785344i | \(0.287514\pi\) | |||||||
\(998\) | 13.5595 | + | 0.636931i | 0.429220 | + | 0.0201617i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.bm.c.107.16 | yes | 48 | |
3.2 | odd | 2 | inner | 504.2.bm.c.107.9 | yes | 48 | |
4.3 | odd | 2 | 2016.2.bu.c.1871.19 | 48 | |||
7.4 | even | 3 | inner | 504.2.bm.c.179.1 | yes | 48 | |
8.3 | odd | 2 | inner | 504.2.bm.c.107.24 | yes | 48 | |
8.5 | even | 2 | 2016.2.bu.c.1871.5 | 48 | |||
12.11 | even | 2 | 2016.2.bu.c.1871.6 | 48 | |||
21.11 | odd | 6 | inner | 504.2.bm.c.179.24 | yes | 48 | |
24.5 | odd | 2 | 2016.2.bu.c.1871.20 | 48 | |||
24.11 | even | 2 | inner | 504.2.bm.c.107.1 | ✓ | 48 | |
28.11 | odd | 6 | 2016.2.bu.c.431.20 | 48 | |||
56.11 | odd | 6 | inner | 504.2.bm.c.179.9 | yes | 48 | |
56.53 | even | 6 | 2016.2.bu.c.431.6 | 48 | |||
84.11 | even | 6 | 2016.2.bu.c.431.5 | 48 | |||
168.11 | even | 6 | inner | 504.2.bm.c.179.16 | yes | 48 | |
168.53 | odd | 6 | 2016.2.bu.c.431.19 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.bm.c.107.1 | ✓ | 48 | 24.11 | even | 2 | inner | |
504.2.bm.c.107.9 | yes | 48 | 3.2 | odd | 2 | inner | |
504.2.bm.c.107.16 | yes | 48 | 1.1 | even | 1 | trivial | |
504.2.bm.c.107.24 | yes | 48 | 8.3 | odd | 2 | inner | |
504.2.bm.c.179.1 | yes | 48 | 7.4 | even | 3 | inner | |
504.2.bm.c.179.9 | yes | 48 | 56.11 | odd | 6 | inner | |
504.2.bm.c.179.16 | yes | 48 | 168.11 | even | 6 | inner | |
504.2.bm.c.179.24 | yes | 48 | 21.11 | odd | 6 | inner | |
2016.2.bu.c.431.5 | 48 | 84.11 | even | 6 | |||
2016.2.bu.c.431.6 | 48 | 56.53 | even | 6 | |||
2016.2.bu.c.431.19 | 48 | 168.53 | odd | 6 | |||
2016.2.bu.c.431.20 | 48 | 28.11 | odd | 6 | |||
2016.2.bu.c.1871.5 | 48 | 8.5 | even | 2 | |||
2016.2.bu.c.1871.6 | 48 | 12.11 | even | 2 | |||
2016.2.bu.c.1871.19 | 48 | 4.3 | odd | 2 | |||
2016.2.bu.c.1871.20 | 48 | 24.5 | odd | 2 |