Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(8,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(36))
chi = DirichletCharacter(H, H._module([2, 27]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.r (of order \(36\), degree \(12\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{36})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{36}]$ |
Embedding invariants
Embedding label | 197.15 | ||
Character | \(\chi\) | \(=\) | 405.197 |
Dual form | 405.2.r.a.368.15 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{13}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.45457 | − | 0.214747i | 1.73564 | − | 0.151849i | 0.825024 | − | 0.565098i | \(-0.191162\pi\) |
0.910618 | + | 0.413249i | \(0.135606\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00918 | − | 0.706926i | 2.00459 | − | 0.353463i | ||||
\(5\) | −1.21103 | − | 1.87974i | −0.541587 | − | 0.840645i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.02748 | − | 0.719449i | 0.388351 | − | 0.271926i | −0.363054 | − | 0.931768i | \(-0.618266\pi\) |
0.751404 | + | 0.659842i | \(0.229377\pi\) | |||||||
\(8\) | 4.92901 | − | 1.32073i | 1.74267 | − | 0.466947i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.37621 | − | 4.35388i | −1.06765 | − | 1.37682i | ||||
\(11\) | −0.955177 | − | 2.62433i | −0.287997 | − | 0.791264i | −0.996347 | − | 0.0854029i | \(-0.972782\pi\) |
0.708350 | − | 0.705862i | \(-0.249440\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.519069 | + | 5.93299i | −0.143964 | + | 1.64552i | 0.489688 | + | 0.871898i | \(0.337111\pi\) |
−0.633652 | + | 0.773618i | \(0.718445\pi\) | |||||||
\(14\) | 2.36752 | − | 1.98658i | 0.632746 | − | 0.530937i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.16396 | − | 1.51556i | 1.04099 | − | 0.378889i | ||||
\(17\) | 5.37628 | + | 1.44057i | 1.30394 | + | 0.349390i | 0.842938 | − | 0.538010i | \(-0.180824\pi\) |
0.461001 | + | 0.887400i | \(0.347490\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.75284 | − | 1.01200i | −0.402128 | − | 0.232169i | 0.285274 | − | 0.958446i | \(-0.407916\pi\) |
−0.687402 | + | 0.726277i | \(0.741249\pi\) | |||||||
\(20\) | −6.18405 | − | 6.68010i | −1.38280 | − | 1.49372i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.90811 | − | 6.23647i | −0.620012 | − | 1.32962i | ||||
\(23\) | −2.67978 | + | 3.82712i | −0.558772 | + | 0.798009i | −0.994792 | − | 0.101928i | \(-0.967499\pi\) |
0.436020 | + | 0.899937i | \(0.356388\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.06683 | + | 4.55282i | −0.413367 | + | 0.910565i | ||||
\(26\) | 14.6744i | 2.87789i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.61075 | − | 3.61075i | 0.682367 | − | 0.682367i | ||||
\(29\) | −2.13514 | − | 1.79159i | −0.396485 | − | 0.332691i | 0.422648 | − | 0.906294i | \(-0.361101\pi\) |
−0.819133 | + | 0.573603i | \(0.805545\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.860131 | + | 4.87805i | 0.154484 | + | 0.876123i | 0.959256 | + | 0.282539i | \(0.0911765\pi\) |
−0.804772 | + | 0.593584i | \(0.797712\pi\) | |||||||
\(32\) | 0.645681 | − | 0.301086i | 0.114141 | − | 0.0532250i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 13.5058 | + | 2.38144i | 2.31623 | + | 0.408413i | ||||
\(35\) | −2.59668 | − | 1.06012i | −0.438919 | − | 0.179193i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.354589 | − | 1.32334i | 0.0582941 | − | 0.217556i | −0.930634 | − | 0.365951i | \(-0.880744\pi\) |
0.988928 | + | 0.148394i | \(0.0474105\pi\) | |||||||
\(38\) | −4.51978 | − | 2.10761i | −0.733206 | − | 0.341899i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.45178 | − | 7.66582i | −1.33634 | − | 1.21207i | ||||
\(41\) | 0.207426 | + | 0.247201i | 0.0323945 | + | 0.0386063i | 0.781998 | − | 0.623280i | \(-0.214200\pi\) |
−0.749604 | + | 0.661887i | \(0.769756\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.79373 | − | 8.13568i | 0.578538 | − | 1.24068i | −0.371467 | − | 0.928446i | \(-0.621145\pi\) |
0.950005 | − | 0.312234i | \(-0.101077\pi\) | |||||||
\(44\) | −5.68468 | − | 9.84615i | −0.856997 | − | 1.48436i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.75583 | + | 9.96940i | −0.848652 | + | 1.46991i | ||||
\(47\) | 0.213694 | + | 0.305187i | 0.0311705 | + | 0.0445161i | 0.834435 | − | 0.551107i | \(-0.185794\pi\) |
−0.803264 | + | 0.595623i | \(0.796905\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.85603 | + | 5.09941i | −0.265148 | + | 0.728487i | ||||
\(50\) | −4.09548 | + | 11.6191i | −0.579188 | + | 1.64318i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.11314 | + | 24.1534i | 0.293040 | + | 3.34947i | ||||
\(53\) | −7.96878 | − | 7.96878i | −1.09460 | − | 1.09460i | −0.995031 | − | 0.0995653i | \(-0.968255\pi\) |
−0.0995653 | − | 0.995031i | \(-0.531745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.77630 | + | 4.97361i | −0.509197 | + | 0.670642i | ||||
\(56\) | 4.11426 | − | 4.90319i | 0.549792 | − | 0.655216i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.62558 | − | 3.93908i | −0.738675 | − | 0.517226i | ||||
\(59\) | −2.97238 | − | 1.08186i | −0.386971 | − | 0.140846i | 0.141206 | − | 0.989980i | \(-0.454902\pi\) |
−0.528177 | + | 0.849134i | \(0.677124\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.0275256 | + | 0.156106i | −0.00352429 | + | 0.0199873i | −0.986519 | − | 0.163646i | \(-0.947675\pi\) |
0.982995 | + | 0.183633i | \(0.0587858\pi\) | |||||||
\(62\) | 3.15880 | + | 11.7888i | 0.401168 | + | 1.49718i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.15484 | + | 3.55350i | −0.769355 | + | 0.444187i | ||||
\(65\) | 11.7811 | − | 6.20929i | 1.46126 | − | 0.770168i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.09208 | + | 0.707965i | 0.988605 | + | 0.0864917i | 0.569972 | − | 0.821664i | \(-0.306954\pi\) |
0.418633 | + | 0.908156i | \(0.362509\pi\) | |||||||
\(68\) | 22.5728 | + | 1.97487i | 2.73736 | + | 0.239488i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.60139 | − | 2.04451i | −0.789017 | − | 0.244366i | ||||
\(71\) | −7.01095 | + | 4.04777i | −0.832046 | + | 0.480382i | −0.854553 | − | 0.519365i | \(-0.826169\pi\) |
0.0225065 | + | 0.999747i | \(0.492835\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.41949 | − | 5.29760i | −0.166139 | − | 0.620037i | −0.997892 | − | 0.0648926i | \(-0.979330\pi\) |
0.831754 | − | 0.555145i | \(-0.187337\pi\) | |||||||
\(74\) | 0.586179 | − | 3.32439i | 0.0681419 | − | 0.386452i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.74284 | − | 2.81816i | −0.888165 | − | 0.323266i | ||||
\(77\) | −2.86949 | − | 2.00924i | −0.327009 | − | 0.228974i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.3148 | − | 12.2927i | 1.16051 | − | 1.38304i | 0.250668 | − | 0.968073i | \(-0.419350\pi\) |
0.909838 | − | 0.414964i | \(-0.136206\pi\) | |||||||
\(80\) | −7.89151 | − | 5.99177i | −0.882298 | − | 0.669900i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.562227 | + | 0.562227i | 0.0620876 | + | 0.0620876i | ||||
\(83\) | 0.151375 | + | 1.73023i | 0.0166156 | + | 0.189917i | 0.999966 | + | 0.00819974i | \(0.00261009\pi\) |
−0.983351 | + | 0.181718i | \(0.941834\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.80292 | − | 11.8506i | −0.412485 | − | 1.28537i | ||||
\(86\) | 7.56486 | − | 20.7843i | 0.815740 | − | 2.24123i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.17410 | − | 11.6738i | −0.871361 | − | 1.24443i | ||||
\(89\) | −6.44892 | + | 11.1699i | −0.683584 | + | 1.18400i | 0.290295 | + | 0.956937i | \(0.406247\pi\) |
−0.973879 | + | 0.227066i | \(0.927087\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.73515 | + | 6.46947i | 0.391550 | + | 0.678185i | ||||
\(92\) | −8.03821 | + | 17.2380i | −0.838041 | + | 1.79719i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.590066 | + | 0.703213i | 0.0608606 | + | 0.0725309i | ||||
\(95\) | 0.220434 | + | 4.52043i | 0.0226161 | + | 0.463787i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.21455 | − | 1.49897i | −0.326388 | − | 0.152197i | 0.252517 | − | 0.967593i | \(-0.418742\pi\) |
−0.578904 | + | 0.815395i | \(0.696520\pi\) | |||||||
\(98\) | −3.46068 | + | 12.9154i | −0.349581 | + | 1.30466i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.06779 | + | 19.7142i | −0.506779 | + | 1.97142i | ||||
\(101\) | 9.18834 | + | 1.62015i | 0.914274 | + | 0.161211i | 0.610943 | − | 0.791674i | \(-0.290790\pi\) |
0.303330 | + | 0.952885i | \(0.401901\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.625323 | + | 0.291593i | −0.0616149 | + | 0.0287315i | −0.453181 | − | 0.891418i | \(-0.649711\pi\) |
0.391567 | + | 0.920150i | \(0.371933\pi\) | |||||||
\(104\) | 5.27735 | + | 29.9293i | 0.517487 | + | 2.93481i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −21.2712 | − | 17.8487i | −2.06604 | − | 1.73361i | ||||
\(107\) | 7.01111 | − | 7.01111i | 0.677790 | − | 0.677790i | −0.281710 | − | 0.959500i | \(-0.590902\pi\) |
0.959500 | + | 0.281710i | \(0.0909016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.98129i | − | 0.381339i | −0.981654 | − | 0.190669i | \(-0.938934\pi\) | ||
0.981654 | − | 0.190669i | \(-0.0610658\pi\) | |||||||
\(110\) | −8.20113 | + | 13.0190i | −0.781947 | + | 1.24131i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.18801 | − | 4.55296i | 0.301239 | − | 0.430214i | ||||
\(113\) | −5.38280 | − | 11.5434i | −0.506371 | − | 1.08592i | −0.978851 | − | 0.204575i | \(-0.934419\pi\) |
0.472480 | − | 0.881341i | \(-0.343359\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.4393 | + | 0.402540i | 0.973466 | + | 0.0375371i | ||||
\(116\) | −9.82667 | − | 5.67343i | −0.912383 | − | 0.526765i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.52823 | − | 2.01718i | −0.693030 | − | 0.185697i | ||||
\(119\) | 6.56043 | − | 2.38780i | 0.601394 | − | 0.218889i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.45176 | − | 2.05727i | 0.222887 | − | 0.187024i | ||||
\(122\) | −0.0340403 | + | 0.389083i | −0.00308187 | + | 0.0352259i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.89684 | + | 18.9489i | 0.619354 | + | 1.70166i | ||||
\(125\) | 11.0611 | − | 1.62848i | 0.989335 | − | 0.145656i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.43624 | + | 0.384839i | −0.127445 | + | 0.0341489i | −0.321978 | − | 0.946747i | \(-0.604348\pi\) |
0.194532 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(128\) | −15.5115 | + | 10.8613i | −1.37104 | + | 0.960012i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 27.5840 | − | 17.7711i | 2.41928 | − | 1.55863i | ||||
\(131\) | 4.86082 | − | 0.857093i | 0.424691 | − | 0.0748846i | 0.0427823 | − | 0.999084i | \(-0.486378\pi\) |
0.381909 | + | 0.924200i | \(0.375267\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.52909 | + | 0.221266i | −0.219300 | + | 0.0191862i | ||||
\(134\) | 20.0146 | 1.72900 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 28.4024 | 2.43548 | ||||||||
\(137\) | −9.23718 | + | 0.808148i | −0.789185 | + | 0.0690448i | −0.474620 | − | 0.880191i | \(-0.657414\pi\) |
−0.314566 | + | 0.949236i | \(0.601859\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.653880 | − | 0.115297i | 0.0554614 | − | 0.00977934i | −0.145849 | − | 0.989307i | \(-0.546591\pi\) |
0.201310 | + | 0.979528i | \(0.435480\pi\) | |||||||
\(140\) | −11.1600 | − | 2.41455i | −0.943190 | − | 0.204067i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.3396 | + | 11.4411i | −1.37119 | + | 0.960117i | ||||
\(143\) | 16.0659 | − | 4.30485i | 1.34350 | − | 0.359990i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.782020 | + | 6.18317i | −0.0649432 | + | 0.513484i | ||||
\(146\) | −4.62188 | − | 12.6985i | −0.382509 | − | 1.05094i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.486104 | − | 5.55619i | 0.0399575 | − | 0.456716i | ||||
\(149\) | −3.98025 | + | 3.33983i | −0.326075 | + | 0.273610i | −0.791098 | − | 0.611689i | \(-0.790490\pi\) |
0.465023 | + | 0.885298i | \(0.346046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.92942 | − | 1.43019i | 0.319772 | − | 0.116387i | −0.177147 | − | 0.984184i | \(-0.556687\pi\) |
0.496919 | + | 0.867797i | \(0.334465\pi\) | |||||||
\(152\) | −9.97633 | − | 2.67315i | −0.809187 | − | 0.216821i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −7.47485 | − | 4.31561i | −0.602340 | − | 0.347761i | ||||
\(155\) | 8.12781 | − | 7.52426i | 0.652841 | − | 0.604363i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.80347 | + | 12.4456i | 0.463168 | + | 0.993266i | 0.989706 | + | 0.143115i | \(0.0457119\pi\) |
−0.526538 | + | 0.850151i | \(0.676510\pi\) | |||||||
\(158\) | 22.6786 | − | 32.3884i | 1.80421 | − | 2.57668i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.34790 | − | 0.849088i | −0.106561 | − | 0.0671263i | ||||
\(161\) | 5.86025i | 0.461852i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.8723 | − | 14.8723i | 1.16489 | − | 1.16489i | 0.181498 | − | 0.983391i | \(-0.441905\pi\) |
0.983391 | − | 0.181498i | \(-0.0580947\pi\) | |||||||
\(164\) | 1.00636 | + | 0.844437i | 0.0785835 | + | 0.0659394i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.743123 | + | 4.21446i | 0.0576775 | + | 0.327105i | ||||
\(167\) | 3.30546 | − | 1.54136i | 0.255784 | − | 0.119274i | −0.290497 | − | 0.956876i | \(-0.593821\pi\) |
0.546281 | + | 0.837602i | \(0.316043\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −22.1284 | − | 3.90184i | −1.70219 | − | 0.300142i | ||||
\(170\) | −11.8794 | − | 28.2714i | −0.911109 | − | 2.16831i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.45841 | − | 35.2993i | 0.721197 | − | 2.69154i | ||||
\(173\) | 7.42544 | + | 3.46254i | 0.564546 | + | 0.263252i | 0.683871 | − | 0.729603i | \(-0.260295\pi\) |
−0.119325 | + | 0.992855i | \(0.538073\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.15190 | + | 6.16491i | 0.0870751 | + | 0.466024i | ||||
\(176\) | −7.95463 | − | 9.47996i | −0.599603 | − | 0.714579i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.4306 | + | 28.8021i | −1.00667 | + | 2.15881i | ||||
\(179\) | −3.07632 | − | 5.32834i | −0.229935 | − | 0.398259i | 0.727854 | − | 0.685732i | \(-0.240518\pi\) |
−0.957789 | + | 0.287474i | \(0.907185\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.75332 | + | 8.23298i | −0.353311 | + | 0.611953i | −0.986827 | − | 0.161777i | \(-0.948278\pi\) |
0.633516 | + | 0.773729i | \(0.281611\pi\) | |||||||
\(182\) | 10.5575 | + | 15.0776i | 0.782573 | + | 1.11763i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.15408 | + | 22.4032i | −0.601127 | + | 1.65158i | ||||
\(185\) | −2.91696 | + | 0.936070i | −0.214459 | + | 0.0688212i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.35477 | − | 15.4851i | −0.0990708 | − | 1.13238i | ||||
\(188\) | 1.07248 | + | 1.07248i | 0.0782189 | + | 0.0782189i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.51182 | + | 11.0484i | 0.109679 | + | 0.801534i | ||||
\(191\) | −8.71630 | + | 10.3877i | −0.630690 | + | 0.751627i | −0.982869 | − | 0.184306i | \(-0.940996\pi\) |
0.352179 | + | 0.935933i | \(0.385441\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.3226 | + | 10.0288i | 1.03096 | + | 0.721888i | 0.961250 | − | 0.275679i | \(-0.0889026\pi\) |
0.0697136 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(194\) | −8.21222 | − | 2.98900i | −0.589603 | − | 0.214598i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.83626 | + | 21.7565i | −0.274019 | + | 1.55404i | ||||
\(197\) | 0.482608 | + | 1.80112i | 0.0343844 | + | 0.128324i | 0.980985 | − | 0.194085i | \(-0.0621739\pi\) |
−0.946600 | + | 0.322410i | \(0.895507\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.71379 | + | 3.87621i | −0.475928 | + | 0.274777i | −0.718718 | − | 0.695302i | \(-0.755271\pi\) |
0.242790 | + | 0.970079i | \(0.421937\pi\) | |||||||
\(200\) | −4.17442 | + | 25.1706i | −0.295176 | + | 1.77983i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 22.9013 | + | 2.00361i | 1.61133 | + | 0.140973i | ||||
\(203\) | −3.48277 | − | 0.304703i | −0.244443 | − | 0.0213859i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.213474 | − | 0.689273i | 0.0149097 | − | 0.0481409i | ||||
\(206\) | −1.47228 | + | 0.850021i | −0.102579 | + | 0.0592237i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.83040 | + | 25.4914i | 0.473603 | + | 1.76751i | ||||
\(209\) | −0.981552 | + | 5.56666i | −0.0678954 | + | 0.385054i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.1076 | − | 7.31857i | −1.38426 | − | 0.503831i | −0.460796 | − | 0.887506i | \(-0.652436\pi\) |
−0.923468 | + | 0.383675i | \(0.874658\pi\) | |||||||
\(212\) | −37.5816 | − | 26.3149i | −2.58111 | − | 1.80732i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.7036 | − | 18.7149i | 1.07348 | − | 1.27932i | ||||
\(215\) | −19.8873 | + | 2.72130i | −1.35630 | + | 0.185591i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.39327 | + | 4.39327i | 0.298235 | + | 0.298235i | ||||
\(218\) | −0.854971 | − | 9.77236i | −0.0579059 | − | 0.661868i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.6239 | + | 22.6097i | −0.783683 | + | 1.52434i | ||||
\(221\) | −11.3376 | + | 31.1497i | −0.762646 | + | 2.09535i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2104 | − | 18.8664i | −0.884633 | − | 1.26339i | −0.963827 | − | 0.266528i | \(-0.914124\pi\) |
0.0791939 | − | 0.996859i | \(-0.474765\pi\) | |||||||
\(224\) | 0.446808 | − | 0.773894i | 0.0298536 | − | 0.0517079i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.6914 | − | 27.1782i | −1.04377 | − | 1.80787i | ||||
\(227\) | 10.0438 | − | 21.5391i | 0.666633 | − | 1.42960i | −0.223869 | − | 0.974619i | \(-0.571869\pi\) |
0.890502 | − | 0.454979i | \(-0.150353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.86052 | − | 11.7513i | −0.651602 | − | 0.776549i | 0.334553 | − | 0.942377i | \(-0.391415\pi\) |
−0.986155 | + | 0.165828i | \(0.946970\pi\) | |||||||
\(230\) | 25.7103 | − | 1.25374i | 1.69529 | − | 0.0826689i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.8903 | − | 6.01086i | −0.846291 | − | 0.394632i | ||||
\(233\) | −3.29342 | + | 12.2912i | −0.215759 | + | 0.805223i | 0.770139 | + | 0.637876i | \(0.220187\pi\) |
−0.985898 | + | 0.167347i | \(0.946480\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.314883 | − | 0.771279i | 0.0205407 | − | 0.0503127i | ||||
\(236\) | −12.6816 | − | 2.23611i | −0.825501 | − | 0.145558i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 15.5903 | − | 7.26986i | 1.01057 | − | 0.471235i | ||||
\(239\) | 0.944310 | + | 5.35545i | 0.0610824 | + | 0.346415i | 0.999997 | + | 0.00226637i | \(0.000721408\pi\) |
−0.938915 | + | 0.344149i | \(0.888167\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.71656 | + | 4.79676i | 0.368236 | + | 0.308987i | 0.808063 | − | 0.589096i | \(-0.200516\pi\) |
−0.439827 | + | 0.898082i | \(0.644960\pi\) | |||||||
\(242\) | 5.57622 | − | 5.57622i | 0.358453 | − | 0.358453i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.645313i | 0.0413119i | ||||||||
\(245\) | 11.8333 | − | 2.68666i | 0.755999 | − | 0.171644i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.91404 | − | 9.87427i | 0.439930 | − | 0.628285i | ||||
\(248\) | 10.6822 | + | 22.9080i | 0.678318 | + | 1.45466i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 26.8005 | − | 6.37256i | 1.69501 | − | 0.403036i | ||||
\(251\) | −4.37402 | − | 2.52534i | −0.276086 | − | 0.159398i | 0.355564 | − | 0.934652i | \(-0.384289\pi\) |
−0.631650 | + | 0.775254i | \(0.717622\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.6033 | + | 3.37704i | 0.792361 | + | 0.212312i | ||||
\(254\) | −3.44270 | + | 1.25304i | −0.216014 | + | 0.0786228i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.8532 | + | 20.8543i | −1.55332 | + | 1.30339i | ||||
\(257\) | 2.32628 | − | 26.5895i | 0.145109 | − | 1.65861i | −0.479405 | − | 0.877594i | \(-0.659147\pi\) |
0.624514 | − | 0.781013i | \(-0.285297\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.587745 | − | 1.61482i | −0.0365207 | − | 0.100340i | ||||
\(260\) | 42.8429 | − | 33.2225i | 2.65700 | − | 2.06037i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.7471 | − | 3.14764i | 0.725741 | − | 0.194462i | ||||
\(263\) | 21.4619 | − | 15.0278i | 1.32340 | − | 0.926654i | 0.323590 | − | 0.946197i | \(-0.395110\pi\) |
0.999809 | + | 0.0195432i | \(0.00622118\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.32882 | + | 24.6296i | −0.327347 | + | 1.51299i | ||||
\(266\) | −6.16030 | + | 1.08623i | −0.377712 | + | 0.0666009i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 32.9431 | − | 2.88214i | 2.01232 | − | 0.176055i | ||||
\(269\) | 2.30251 | 0.140387 | 0.0701934 | − | 0.997533i | \(-0.477638\pi\) | ||||
0.0701934 | + | 0.997533i | \(0.477638\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.12068 | 0.371805 | 0.185902 | − | 0.982568i | \(-0.440479\pi\) | ||||
0.185902 | + | 0.982568i | \(0.440479\pi\) | |||||||
\(272\) | 24.5699 | − | 2.14958i | 1.48977 | − | 0.130338i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −22.4997 | + | 3.96731i | −1.35926 | + | 0.239674i | ||||
\(275\) | 13.9223 | + | 1.07529i | 0.839546 | + | 0.0648426i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.67336 | − | 6.07315i | 0.521132 | − | 0.364901i | −0.283219 | − | 0.959055i | \(-0.591402\pi\) |
0.804351 | + | 0.594155i | \(0.202513\pi\) | |||||||
\(278\) | 1.58023 | − | 0.423423i | 0.0947762 | − | 0.0253952i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −14.1992 | − | 1.79585i | −0.848564 | − | 0.107323i | ||||
\(281\) | 2.07965 | + | 5.71378i | 0.124061 | + | 0.340856i | 0.986139 | − | 0.165920i | \(-0.0530594\pi\) |
−0.862078 | + | 0.506776i | \(0.830837\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.312211 | − | 3.56859i | 0.0185590 | − | 0.212131i | −0.981253 | − | 0.192726i | \(-0.938267\pi\) |
0.999812 | − | 0.0194049i | \(-0.00617717\pi\) | |||||||
\(284\) | −25.2466 | + | 21.1845i | −1.49811 | + | 1.25707i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 38.5104 | − | 14.0167i | 2.27717 | − | 0.828822i | ||||
\(287\) | 0.390974 | + | 0.104761i | 0.0230785 | + | 0.00618386i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.1067 | + | 6.98981i | 0.712160 | + | 0.411166i | ||||
\(290\) | −0.591705 | + | 15.3449i | −0.0347461 | + | 0.901086i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.43599 | − | 20.2355i | −0.552200 | − | 1.18420i | ||||
\(293\) | −15.2979 | + | 21.8477i | −0.893714 | + | 1.27636i | 0.0666984 | + | 0.997773i | \(0.478753\pi\) |
−0.960412 | + | 0.278582i | \(0.910135\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.56602 | + | 6.89745i | 0.0911771 | + | 0.401585i | ||||
\(296\) | − | 6.99110i | − | 0.406349i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.05259 | + | 9.05259i | −0.524403 | + | 0.524403i | ||||
\(299\) | −21.3153 | − | 17.8856i | −1.23269 | − | 1.03435i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.95523 | − | 11.0886i | −0.112697 | − | 0.639138i | ||||
\(302\) | 9.33791 | − | 4.35434i | 0.537336 | − | 0.250564i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.83248 | − | 1.55741i | −0.506578 | − | 0.0893233i | ||||
\(305\) | 0.326772 | − | 0.137307i | 0.0187109 | − | 0.00786217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.38428 | − | 12.6303i | 0.193151 | − | 0.720850i | −0.799586 | − | 0.600551i | \(-0.794948\pi\) |
0.992738 | − | 0.120299i | \(-0.0383854\pi\) | |||||||
\(308\) | −12.9247 | − | 6.02688i | −0.736453 | − | 0.343413i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 18.3345 | − | 20.2142i | 1.04133 | − | 1.14809i | ||||
\(311\) | 7.01743 | + | 8.36305i | 0.397922 | + | 0.474225i | 0.927385 | − | 0.374108i | \(-0.122051\pi\) |
−0.529463 | + | 0.848333i | \(0.677607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.03021 | + | 4.35380i | −0.114754 | + | 0.246091i | −0.955293 | − | 0.295660i | \(-0.904461\pi\) |
0.840539 | + | 0.541751i | \(0.182238\pi\) | |||||||
\(314\) | 16.9177 | + | 29.3023i | 0.954720 | + | 1.65362i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 32.6638 | − | 56.5754i | 1.83748 | − | 3.18262i | ||||
\(317\) | 18.1287 | + | 25.8905i | 1.01821 | + | 1.45415i | 0.886423 | + | 0.462876i | \(0.153182\pi\) |
0.131787 | + | 0.991278i | \(0.457929\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.66229 | + | 7.31459i | −0.149060 | + | 0.409538i | ||||
\(320\) | 14.1333 | + | 7.26611i | 0.790076 | + | 0.406188i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.25847 | + | 14.3844i | 0.0701318 | + | 0.801610i | ||||
\(323\) | −7.96588 | − | 7.96588i | −0.443234 | − | 0.443234i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −25.9390 | − | 14.6257i | −1.43884 | − | 0.811290i | ||||
\(326\) | 33.3113 | − | 39.6989i | 1.84494 | − | 2.19872i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.34889 | + | 0.944503i | 0.0744800 | + | 0.0521515i | ||||
\(329\) | 0.439133 | + | 0.159831i | 0.0242102 | + | 0.00881179i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.86664 | + | 27.6001i | −0.267495 | + | 1.51704i | 0.494340 | + | 0.869268i | \(0.335410\pi\) |
−0.761835 | + | 0.647771i | \(0.775701\pi\) | |||||||
\(332\) | 1.83003 | + | 6.82978i | 0.100436 | + | 0.374833i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.78247 | − | 4.49321i | 0.425838 | − | 0.245858i | ||||
\(335\) | −8.46893 | − | 16.0684i | −0.462707 | − | 0.877908i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −35.9100 | − | 3.14172i | −1.95614 | − | 0.171140i | −0.961522 | − | 0.274727i | \(-0.911413\pi\) |
−0.994620 | + | 0.103586i | \(0.966968\pi\) | |||||||
\(338\) | −55.1537 | − | 4.82532i | −2.99997 | − | 0.262463i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −23.6240 | − | 44.8226i | −1.28119 | − | 2.43085i | ||||
\(341\) | 11.9800 | − | 6.91666i | 0.648754 | − | 0.374558i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.03422 | + | 15.0559i | 0.217828 | + | 0.812944i | ||||
\(344\) | 7.95435 | − | 45.1114i | 0.428870 | − | 2.43224i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.9698 | + | 6.90445i | 1.01982 | + | 0.371186i | ||||
\(347\) | −13.1696 | − | 9.22149i | −0.706984 | − | 0.495035i | 0.163930 | − | 0.986472i | \(-0.447583\pi\) |
−0.870913 | + | 0.491437i | \(0.836472\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.65928 | + | 4.36096i | −0.195877 | + | 0.233437i | −0.855039 | − | 0.518564i | \(-0.826467\pi\) |
0.659162 | + | 0.752001i | \(0.270911\pi\) | |||||||
\(350\) | 4.15130 | + | 14.8848i | 0.221896 | + | 0.795628i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.40689 | − | 1.40689i | −0.0749873 | − | 0.0749873i | ||||
\(353\) | 1.22287 | + | 13.9775i | 0.0650869 | + | 0.743946i | 0.956686 | + | 0.291121i | \(0.0940282\pi\) |
−0.891599 | + | 0.452825i | \(0.850416\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0992 | + | 8.27679i | 0.854456 | + | 0.439286i | ||||
\(356\) | −17.9586 | + | 49.3408i | −0.951804 | + | 2.61506i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.69528 | − | 12.4181i | −0.459560 | − | 0.656319i | ||||
\(359\) | 3.44870 | − | 5.97333i | 0.182016 | − | 0.315260i | −0.760551 | − | 0.649278i | \(-0.775071\pi\) |
0.942567 | + | 0.334018i | \(0.108405\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.45171 | − | 12.9067i | −0.392195 | − | 0.679302i | ||||
\(362\) | −9.89933 | + | 21.2292i | −0.520297 | + | 1.11578i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 19.5483 | + | 23.2968i | 1.02461 | + | 1.22108i | ||||
\(365\) | −8.23907 | + | 9.08380i | −0.431253 | + | 0.475468i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.23085 | − | 1.50657i | −0.168649 | − | 0.0786424i | 0.336460 | − | 0.941698i | \(-0.390770\pi\) |
−0.505110 | + | 0.863055i | \(0.668548\pi\) | |||||||
\(368\) | −5.35826 | + | 19.9973i | −0.279319 | + | 1.04243i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.95886 | + | 2.92406i | −0.361774 | + | 0.152014i | ||||
\(371\) | −13.9209 | − | 2.45463i | −0.722736 | − | 0.127438i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.1529 | + | 5.20069i | −0.577476 | + | 0.269282i | −0.689335 | − | 0.724443i | \(-0.742097\pi\) |
0.111859 | + | 0.993724i | \(0.464319\pi\) | |||||||
\(374\) | −6.65076 | − | 37.7184i | −0.343903 | − | 1.95037i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.45637 | + | 1.22204i | 0.0751066 | + | 0.0630219i | ||||
\(377\) | 11.7378 | − | 11.7378i | 0.604527 | − | 0.604527i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.9996i | 0.821843i | 0.911671 | + | 0.410922i | \(0.134793\pi\) | ||||
−0.911671 | + | 0.410922i | \(0.865207\pi\) | |||||||
\(380\) | 4.07937 | + | 17.9674i | 0.209267 | + | 0.921708i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.1640 | + | 27.3691i | −0.980518 | + | 1.40032i | ||||
\(383\) | 10.5466 | + | 22.6172i | 0.538904 | + | 1.15568i | 0.967659 | + | 0.252262i | \(0.0811746\pi\) |
−0.428755 | + | 0.903421i | \(0.641048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.301816 | + | 7.82714i | −0.0153820 | + | 0.398908i | ||||
\(386\) | 37.3095 | + | 21.5406i | 1.89900 | + | 1.09639i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.9473 | − | 3.73718i | −0.708069 | − | 0.189726i | ||||
\(389\) | −17.5837 | + | 6.39994i | −0.891529 | + | 0.324490i | −0.746853 | − | 0.664989i | \(-0.768436\pi\) |
−0.144676 | + | 0.989479i | \(0.546214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.9205 | + | 16.7153i | −1.00742 | + | 0.845327i | ||||
\(392\) | −2.41350 | + | 27.5864i | −0.121900 | + | 1.39332i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.57138 | + | 4.31732i | 0.0791649 | + | 0.217504i | ||||
\(395\) | −35.5986 | − | 4.50235i | −1.79116 | − | 0.226538i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.00214 | + | 2.41212i | −0.451805 | + | 0.121061i | −0.477544 | − | 0.878608i | \(-0.658473\pi\) |
0.0257391 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(398\) | −15.6471 | + | 10.9562i | −0.784316 | + | 0.549184i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.70614 | + | 22.0902i | −0.0853070 | + | 1.10451i | ||||
\(401\) | 21.8705 | − | 3.85636i | 1.09216 | − | 0.192578i | 0.401575 | − | 0.915826i | \(-0.368463\pi\) |
0.690588 | + | 0.723249i | \(0.257352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.3879 | + | 2.57111i | −1.46391 | + | 0.128076i | ||||
\(404\) | 37.9830 | 1.88972 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −8.61413 | −0.427512 | ||||||||
\(407\) | −3.81158 | + | 0.333470i | −0.188933 | + | 0.0165295i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.79062 | + | 0.492062i | −0.137987 | + | 0.0243309i | −0.242215 | − | 0.970223i | \(-0.577874\pi\) |
0.104228 | + | 0.994553i | \(0.466763\pi\) | |||||||
\(410\) | 0.375968 | − | 1.73771i | 0.0185678 | − | 0.0858195i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.30089 | + | 1.61110i | −0.113357 | + | 0.0793734i | ||||
\(413\) | −3.83240 | + | 1.02689i | −0.188580 | + | 0.0505299i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.06906 | − | 2.37990i | 0.150654 | − | 0.116825i | ||||
\(416\) | 1.45119 | + | 3.98710i | 0.0711503 | + | 0.195484i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.21386 | + | 13.8745i | −0.0593720 | + | 0.678626i | ||||
\(419\) | −3.08697 | + | 2.59027i | −0.150808 | + | 0.126543i | −0.715070 | − | 0.699053i | \(-0.753605\pi\) |
0.564262 | + | 0.825596i | \(0.309161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.12343 | + | 1.50080i | −0.200964 | + | 0.0731448i | −0.440541 | − | 0.897733i | \(-0.645213\pi\) |
0.239577 | + | 0.970877i | \(0.422991\pi\) | |||||||
\(422\) | −50.9271 | − | 13.6459i | −2.47909 | − | 0.664271i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −49.8028 | − | 28.7537i | −2.41864 | − | 1.39640i | ||||
\(425\) | −17.6705 | + | 21.4998i | −0.857147 | + | 1.04290i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0840279 | + | 0.180198i | 0.00406640 | + | 0.00872041i | ||||
\(428\) | 23.1524 | − | 33.0651i | 1.11912 | − | 1.59826i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −48.2302 | + | 10.9503i | −2.32587 | + | 0.528073i | ||||
\(431\) | 14.3108i | 0.689325i | 0.938727 | + | 0.344662i | \(0.112007\pi\) | ||||
−0.938727 | + | 0.344662i | \(0.887993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.5706 | + | 10.5706i | −0.507988 | + | 0.507988i | −0.913909 | − | 0.405920i | \(-0.866951\pi\) |
0.405920 | + | 0.913909i | \(0.366951\pi\) | |||||||
\(434\) | 11.7270 | + | 9.84015i | 0.562915 | + | 0.472342i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.81448 | − | 15.9617i | −0.134789 | − | 0.764427i | ||||
\(437\) | 8.57026 | − | 3.99638i | 0.409971 | − | 0.191173i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9432 | + | 4.22183i | 1.14275 | + | 0.201497i | 0.712807 | − | 0.701360i | \(-0.247424\pi\) |
0.429940 | + | 0.902857i | \(0.358535\pi\) | |||||||
\(440\) | −12.0447 | + | 29.5025i | −0.574208 | + | 1.40647i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.1395 | + | 78.8937i | −1.00550 | + | 3.75259i | ||||
\(443\) | 6.12987 | + | 2.85840i | 0.291239 | + | 0.135807i | 0.562747 | − | 0.826629i | \(-0.309745\pi\) |
−0.271508 | + | 0.962436i | \(0.587522\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 28.8062 | − | 1.40470i | 1.36555 | − | 0.0665894i | ||||
\(446\) | −36.4773 | − | 43.4720i | −1.72725 | − | 2.05846i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.76741 | + | 8.07923i | −0.177993 | + | 0.381708i | ||||
\(449\) | −1.79424 | − | 3.10771i | −0.0846753 | − | 0.146662i | 0.820577 | − | 0.571535i | \(-0.193652\pi\) |
−0.905253 | + | 0.424873i | \(0.860319\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.450607 | − | 0.780474i | 0.0212183 | − | 0.0367511i | ||||
\(452\) | −29.7409 | − | 42.4745i | −1.39890 | − | 1.99783i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 20.0278 | − | 55.0260i | 0.939953 | − | 2.58250i | ||||
\(455\) | 7.63755 | − | 14.8558i | 0.358054 | − | 0.696451i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.64330 | + | 30.2131i | 0.123648 | + | 1.41331i | 0.763995 | + | 0.645222i | \(0.223235\pi\) |
−0.640347 | + | 0.768086i | \(0.721209\pi\) | |||||||
\(458\) | −26.7269 | − | 26.7269i | −1.24887 | − | 1.24887i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 42.1374 | − | 5.76593i | 1.96467 | − | 0.268838i | ||||
\(461\) | −25.6308 | + | 30.5456i | −1.19375 | + | 1.42265i | −0.312550 | + | 0.949901i | \(0.601183\pi\) |
−0.881197 | + | 0.472750i | \(0.843261\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0626 | + | 9.84673i | 0.653544 | + | 0.457616i | 0.852735 | − | 0.522344i | \(-0.174942\pi\) |
−0.199191 | + | 0.979961i | \(0.563831\pi\) | |||||||
\(464\) | −11.6059 | − | 4.22420i | −0.538790 | − | 0.196103i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.44442 | + | 30.8768i | −0.252208 | + | 1.43034i | ||||
\(467\) | 4.75144 | + | 17.7326i | 0.219870 | + | 0.820568i | 0.984395 | + | 0.175973i | \(0.0563072\pi\) |
−0.764525 | + | 0.644595i | \(0.777026\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.82379 | − | 5.09442i | 0.407445 | − | 0.235238i | ||||
\(470\) | 0.607271 | − | 1.96078i | 0.0280113 | − | 0.0904439i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.0797 | − | 1.40679i | −0.740129 | − | 0.0647529i | ||||
\(473\) | −24.9744 | − | 2.18497i | −1.14832 | − | 0.100465i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.23028 | − | 5.88872i | 0.377631 | − | 0.270193i | ||||
\(476\) | 24.6139 | − | 14.2109i | 1.12818 | − | 0.651354i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.46794 | + | 12.9425i | 0.158620 | + | 0.591978i | ||||
\(479\) | −4.07702 | + | 23.1219i | −0.186284 | + | 1.05647i | 0.738011 | + | 0.674789i | \(0.235765\pi\) |
−0.924295 | + | 0.381679i | \(0.875346\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.66733 | + | 2.79068i | 0.349600 | + | 0.127244i | ||||
\(482\) | 15.0618 | + | 10.5464i | 0.686046 | + | 0.480374i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.37519 | − | 9.98117i | 0.380691 | − | 0.453689i | ||||
\(485\) | 1.07523 | + | 7.85779i | 0.0488238 | + | 0.356804i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.21511 | + | 7.21511i | 0.326948 | + | 0.326948i | 0.851425 | − | 0.524477i | \(-0.175739\pi\) |
−0.524477 | + | 0.851425i | \(0.675739\pi\) | |||||||
\(488\) | 0.0704984 | + | 0.805800i | 0.00319131 | + | 0.0364768i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 28.4686 | − | 9.13575i | 1.28608 | − | 0.412711i | ||||
\(491\) | 11.3506 | − | 31.1854i | 0.512243 | − | 1.40738i | −0.366650 | − | 0.930359i | \(-0.619495\pi\) |
0.878893 | − | 0.477018i | \(-0.158282\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.89818 | − | 12.7079i | −0.400754 | − | 0.572336i | ||||
\(494\) | 14.8505 | − | 25.7218i | 0.668156 | − | 1.15728i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.9745 | + | 19.0084i | 0.492770 | + | 0.853502i | ||||
\(497\) | −4.29144 | + | 9.20302i | −0.192497 | + | 0.412812i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.7113 | − | 18.7240i | −0.703333 | − | 0.838200i | 0.289566 | − | 0.957158i | \(-0.406489\pi\) |
−0.992899 | + | 0.118958i | \(0.962044\pi\) | |||||||
\(500\) | 43.1947 | − | 14.3483i | 1.93173 | − | 0.641674i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11.2786 | − | 5.25932i | −0.503391 | − | 0.234735i | ||||
\(503\) | 9.98672 | − | 37.2709i | 0.445286 | − | 1.66183i | −0.269896 | − | 0.962890i | \(-0.586989\pi\) |
0.715181 | − | 0.698939i | \(-0.246344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.08185 | − | 19.2337i | −0.359638 | − | 0.855889i | ||||
\(506\) | 31.6608 | + | 5.58265i | 1.40749 | + | 0.248179i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.48608 | + | 2.55820i | −0.243405 | + | 0.113502i | ||||
\(509\) | −0.294649 | − | 1.67104i | −0.0130601 | − | 0.0740674i | 0.977581 | − | 0.210559i | \(-0.0675284\pi\) |
−0.990641 | + | 0.136492i | \(0.956417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.26985 | − | 4.42193i | −0.233124 | − | 0.195615i | ||||
\(512\) | −29.7458 | + | 29.7458i | −1.31459 | + | 1.31459i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 65.7653i | − | 2.90078i | ||||||
\(515\) | 1.30540 | + | 0.822317i | 0.0575228 | + | 0.0362356i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.596795 | − | 0.852312i | 0.0262470 | − | 0.0374846i | ||||
\(518\) | −1.78944 | − | 3.83746i | −0.0786234 | − | 0.168608i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 49.8683 | − | 46.1652i | 2.18687 | − | 2.02448i | ||||
\(521\) | −22.9824 | − | 13.2689i | −1.00688 | − | 0.581322i | −0.0966024 | − | 0.995323i | \(-0.530798\pi\) |
−0.910276 | + | 0.414001i | \(0.864131\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6802 | + | 3.93354i | 0.641920 | + | 0.172002i | 0.565073 | − | 0.825041i | \(-0.308848\pi\) |
0.0768469 | + | 0.997043i | \(0.475515\pi\) | |||||||
\(524\) | 18.8820 | − | 6.87247i | 0.824863 | − | 0.300225i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 49.4526 | − | 41.4957i | 2.15624 | − | 1.80930i | ||||
\(527\) | −2.40286 | + | 27.4648i | −0.104670 | + | 1.19639i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.400836 | + | 1.10129i | 0.0174277 | + | 0.0478821i | ||||
\(530\) | −7.79083 | + | 61.5995i | −0.338412 | + | 2.67571i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.98314 | + | 2.67497i | −0.432824 | + | 0.115975i | ||||
\(533\) | −1.57431 | + | 1.10234i | −0.0681909 | + | 0.0477478i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −21.6697 | − | 4.68842i | −0.936862 | − | 0.202698i | ||||
\(536\) | 40.8210 | − | 7.19784i | 1.76320 | − | 0.310900i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.65168 | − | 0.494458i | 0.243661 | − | 0.0213176i | ||||
\(539\) | 15.1554 | 0.652788 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.56072 | 0.282068 | 0.141034 | − | 0.990005i | \(-0.454957\pi\) | ||||
0.141034 | + | 0.990005i | \(0.454957\pi\) | |||||||
\(542\) | 15.0236 | − | 1.31440i | 0.645320 | − | 0.0564582i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.90510 | − | 0.688574i | 0.167430 | − | 0.0295224i | ||||
\(545\) | −7.48379 | + | 4.82145i | −0.320570 | + | 0.206528i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4654 | − | 20.6319i | 1.25985 | − | 0.882156i | 0.263264 | − | 0.964724i | \(-0.415201\pi\) |
0.996585 | + | 0.0825680i | \(0.0263122\pi\) | |||||||
\(548\) | −36.4622 | + | 9.77001i | −1.55759 | + | 0.417354i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 34.4041 | − | 0.350390i | 1.46700 | − | 0.0149407i | ||||
\(551\) | 1.92945 | + | 5.30113i | 0.0821975 | + | 0.225836i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.75428 | − | 20.0515i | 0.0745994 | − | 0.852675i | ||||
\(554\) | 19.9852 | − | 16.7696i | 0.849089 | − | 0.712470i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.54002 | − | 0.924490i | 0.107721 | − | 0.0392071i | ||||
\(557\) | 4.37675 | + | 1.17275i | 0.185449 | + | 0.0496908i | 0.350348 | − | 0.936620i | \(-0.386063\pi\) |
−0.164899 | + | 0.986310i | \(0.552730\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.2997 | + | 26.7312i | 1.95827 | + | 1.13061i | ||||
\(560\) | −12.4191 | − | 0.478885i | −0.524804 | − | 0.0202366i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.33165 | + | 13.5783i | 0.267085 | + | 0.572765i | ||||
\(563\) | −1.52340 | + | 2.17564i | −0.0642037 | + | 0.0916924i | −0.849970 | − | 0.526831i | \(-0.823380\pi\) |
0.785766 | + | 0.618524i | \(0.212269\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −15.1800 | + | 24.0977i | −0.638625 | + | 1.01380i | ||||
\(566\) | − | 8.82639i | − | 0.371001i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −29.2111 | + | 29.2111i | −1.22567 | + | 1.22567i | ||||
\(569\) | −22.4581 | − | 18.8446i | −0.941494 | − | 0.790007i | 0.0363507 | − | 0.999339i | \(-0.488427\pi\) |
−0.977845 | + | 0.209332i | \(0.932871\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.73020 | − | 15.4837i | −0.114255 | − | 0.647973i | −0.987116 | − | 0.160004i | \(-0.948849\pi\) |
0.872861 | − | 0.487969i | \(-0.162262\pi\) | |||||||
\(572\) | 61.3679 | − | 28.6163i | 2.56592 | − | 1.19651i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.982170 | + | 0.173183i | 0.0409950 | + | 0.00722852i | ||||
\(575\) | −11.8855 | − | 20.1106i | −0.495661 | − | 0.838668i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.02870 | − | 26.2315i | 0.292609 | − | 1.09203i | −0.650489 | − | 0.759515i | \(-0.725436\pi\) |
0.943098 | − | 0.332515i | \(-0.107897\pi\) | |||||||
\(578\) | 31.2178 | + | 14.5571i | 1.29849 | + | 0.605496i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.23579 | + | 25.3422i | 0.0513133 | + | 1.05228i | ||||
\(581\) | 1.40035 | + | 1.66887i | 0.0580961 | + | 0.0692363i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3011 | + | 28.5243i | −0.550875 | + | 1.18136i | ||||
\(584\) | −13.9934 | − | 24.2372i | −0.579049 | − | 1.00294i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32.8581 | + | 56.9118i | −1.35735 | + | 2.35101i | ||||
\(587\) | −0.208890 | − | 0.298326i | −0.00862180 | − | 0.0123132i | 0.814818 | − | 0.579717i | \(-0.196837\pi\) |
−0.823440 | + | 0.567404i | \(0.807948\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.42892 | − | 9.42087i | 0.141286 | − | 0.388180i | ||||
\(590\) | 5.32511 | + | 16.5940i | 0.219231 | + | 0.683163i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.529109 | − | 6.04775i | −0.0217463 | − | 0.248561i | ||||
\(593\) | 5.77411 | + | 5.77411i | 0.237114 | + | 0.237114i | 0.815654 | − | 0.578540i | \(-0.196377\pi\) |
−0.578540 | + | 0.815654i | \(0.696377\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.4333 | − | 9.44021i | −0.509715 | − | 0.387011i | ||||
\(596\) | −13.5965 | + | 16.2037i | −0.556936 | + | 0.663730i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −56.1607 | − | 39.3241i | −2.29658 | − | 1.60808i | ||||
\(599\) | 22.4110 | + | 8.15692i | 0.915687 | + | 0.333283i | 0.756521 | − | 0.653969i | \(-0.226897\pi\) |
0.159166 | + | 0.987252i | \(0.449120\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.792095 | + | 4.49219i | −0.0323102 | + | 0.183240i | −0.996692 | − | 0.0812748i | \(-0.974101\pi\) |
0.964381 | + | 0.264515i | \(0.0852120\pi\) | |||||||
\(602\) | −7.18049 | − | 26.7979i | −0.292655 | − | 1.09220i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.7427 | − | 8.51171i | 0.599872 | − | 0.346336i | ||||
\(605\) | −6.83627 | − | 2.11726i | −0.277934 | − | 0.0860788i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.4825 | − | 3.54176i | −1.64313 | − | 0.143756i | −0.772275 | − | 0.635289i | \(-0.780881\pi\) |
−0.870859 | + | 0.491533i | \(0.836437\pi\) | |||||||
\(608\) | −1.43647 | − | 0.125675i | −0.0582566 | − | 0.00509680i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.772598 | − | 0.407202i | 0.0312816 | − | 0.0164871i | ||||
\(611\) | −1.92160 | + | 1.10943i | −0.0777394 | + | 0.0448829i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.74347 | − | 21.4349i | −0.231977 | − | 0.865749i | −0.979488 | − | 0.201500i | \(-0.935418\pi\) |
0.747512 | − | 0.664249i | \(-0.231248\pi\) | |||||||
\(614\) | 5.59463 | − | 31.7288i | 0.225781 | − | 1.28047i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −16.7974 | − | 6.11376i | −0.676788 | − | 0.246331i | ||||
\(617\) | 10.6418 | + | 7.45148i | 0.428423 | + | 0.299985i | 0.767829 | − | 0.640655i | \(-0.221337\pi\) |
−0.339406 | + | 0.940640i | \(0.610226\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.80404 | + | 9.30049i | −0.313671 | + | 0.373818i | −0.899728 | − | 0.436452i | \(-0.856235\pi\) |
0.586057 | + | 0.810270i | \(0.300679\pi\) | |||||||
\(620\) | 27.2667 | − | 35.9119i | 1.09506 | − | 1.44225i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.0207 | + | 19.0207i | 0.762661 | + | 0.762661i | ||||
\(623\) | 1.41001 | + | 16.1165i | 0.0564908 | + | 0.645693i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.4564 | − | 18.8198i | −0.658256 | − | 0.752794i | ||||
\(626\) | −4.04832 | + | 11.1227i | −0.161804 | + | 0.444552i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 32.0653 | + | 45.7939i | 1.27954 | + | 1.82738i | ||||
\(629\) | 3.81274 | − | 6.60386i | 0.152024 | − | 0.263313i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.6365 | + | 20.1551i | 0.463243 | + | 0.802360i | 0.999120 | − | 0.0419354i | \(-0.0133524\pi\) |
−0.535877 | + | 0.844296i | \(0.680019\pi\) | |||||||
\(632\) | 34.6065 | − | 74.2139i | 1.37657 | − | 2.95207i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 50.0581 | + | 59.6569i | 1.98806 | + | 2.36928i | ||||
\(635\) | 2.46272 | + | 2.23370i | 0.0977299 | + | 0.0886417i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.2913 | − | 13.6588i | −1.16057 | − | 0.541181i | ||||
\(638\) | −4.96400 | + | 18.5259i | −0.196526 | + | 0.733447i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 39.2013 | + | 16.0043i | 1.54957 | + | 0.632627i | ||||
\(641\) | 36.8613 | + | 6.49963i | 1.45593 | + | 0.256720i | 0.844916 | − | 0.534898i | \(-0.179650\pi\) |
0.611016 | + | 0.791618i | \(0.290761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.5339 | − | 13.7719i | 1.16470 | − | 0.543110i | 0.258524 | − | 0.966005i | \(-0.416764\pi\) |
0.906179 | + | 0.422895i | \(0.138986\pi\) | |||||||
\(644\) | 4.14276 | + | 23.4948i | 0.163248 | + | 0.925823i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.2635 | − | 17.8422i | −0.836600 | − | 0.701991i | ||||
\(647\) | −25.9188 | + | 25.9188i | −1.01897 | + | 1.01897i | −0.0191583 | + | 0.999816i | \(0.506099\pi\) |
−0.999816 | + | 0.0191583i | \(0.993901\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.83386i | 0.346759i | ||||||||
\(650\) | −66.8100 | − | 30.3295i | −2.62050 | − | 1.18962i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 49.1121 | − | 70.1394i | 1.92338 | − | 2.74687i | ||||
\(653\) | 14.6418 | + | 31.3994i | 0.572978 | + | 1.22875i | 0.952773 | + | 0.303684i | \(0.0982167\pi\) |
−0.379795 | + | 0.925071i | \(0.624006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.49768 | − | 8.09910i | −0.292959 | − | 0.316458i | ||||
\(656\) | 1.23836 | + | 0.714967i | 0.0483498 | + | 0.0279148i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.11221 | + | 0.298015i | 0.0433583 | + | 0.0116178i | ||||
\(659\) | 14.1890 | − | 5.16436i | 0.552723 | − | 0.201175i | −0.0505327 | − | 0.998722i | \(-0.516092\pi\) |
0.603256 | + | 0.797548i | \(0.293870\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.1426 | − | 21.9363i | 1.01683 | − | 0.853222i | 0.0276043 | − | 0.999619i | \(-0.491212\pi\) |
0.989226 | + | 0.146397i | \(0.0467677\pi\) | |||||||
\(662\) | −6.01847 | + | 68.7915i | −0.233915 | + | 2.67366i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.03129 | + | 8.32839i | 0.117637 | + | 0.323204i | ||||
\(665\) | 3.47871 | + | 4.48606i | 0.134899 | + | 0.173962i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.5783 | − | 3.37035i | 0.487035 | − | 0.130501i | ||||
\(668\) | 12.1625 | − | 8.51630i | 0.470582 | − | 0.329505i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −24.2382 | − | 37.6222i | −0.936404 | − | 1.45347i | ||||
\(671\) | 0.435964 | − | 0.0768722i | 0.0168302 | − | 0.00296762i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.9802 | − | 3.93526i | 1.73386 | − | 0.151693i | 0.823995 | − | 0.566598i | \(-0.191741\pi\) |
0.909865 | + | 0.414905i | \(0.136185\pi\) | |||||||
\(674\) | −88.8183 | −3.42115 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −91.4752 | −3.51828 | ||||||||
\(677\) | −15.7890 | + | 1.38136i | −0.606822 | + | 0.0530900i | −0.386426 | − | 0.922321i | \(-0.626290\pi\) |
−0.220396 | + | 0.975411i | \(0.570735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.38131 | + | 0.772543i | −0.168139 | + | 0.0296475i | ||||
\(680\) | −34.3960 | − | 53.3890i | −1.31903 | − | 2.04737i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.9204 | − | 19.5501i | 1.06913 | − | 0.748612i | ||||
\(683\) | 7.02767 | − | 1.88306i | 0.268906 | − | 0.0720532i | −0.121846 | − | 0.992549i | \(-0.538881\pi\) |
0.390753 | + | 0.920496i | \(0.372215\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.7056 | + | 16.3848i | 0.485455 | + | 0.626030i | ||||
\(686\) | 13.1355 | + | 36.0895i | 0.501515 | + | 1.37790i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.46685 | − | 39.6262i | 0.132172 | − | 1.51074i | ||||
\(689\) | 51.4151 | − | 43.1424i | 1.95876 | − | 1.64359i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 42.1583 | − | 15.3444i | 1.60378 | − | 0.583728i | 0.623582 | − | 0.781758i | \(-0.285677\pi\) |
0.980196 | + | 0.198030i | \(0.0634544\pi\) | |||||||
\(692\) | 32.2177 | + | 8.63269i | 1.22473 | + | 0.328166i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.3061 | − | 19.8066i | −1.30224 | − | 0.751849i | ||||
\(695\) | −1.00859 | − | 1.08950i | −0.0382581 | − | 0.0413270i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.759071 | + | 1.62783i | 0.0287519 | + | 0.0616585i | ||||
\(698\) | −8.04544 | + | 11.4901i | −0.304525 | + | 0.434906i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.97629 | + | 23.9019i | 0.339272 | + | 0.903407i | ||||
\(701\) | − | 23.7146i | − | 0.895688i | −0.894112 | − | 0.447844i | \(-0.852192\pi\) | ||
0.894112 | − | 0.447844i | \(-0.147808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.96076 | + | 1.96076i | −0.0739516 | + | 0.0739516i | ||||
\(704\) | 15.2045 | + | 12.7581i | 0.573041 | + | 0.480839i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.00324 | + | 34.0461i | 0.225935 | + | 1.28134i | ||||
\(707\) | 10.6064 | − | 4.94586i | 0.398896 | − | 0.186008i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.6845 | − | 6.29214i | −1.34016 | − | 0.236306i | −0.542826 | − | 0.839845i | \(-0.682646\pi\) |
−0.797334 | + | 0.603539i | \(0.793757\pi\) | |||||||
\(710\) | 41.2940 | + | 16.8587i | 1.54974 | + | 0.632696i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17.0345 | + | 63.5736i | −0.638395 | + | 2.38252i | ||||
\(713\) | −20.9738 | − | 9.78025i | −0.785476 | − | 0.366273i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −27.5482 | − | 24.9864i | −1.03025 | − | 0.934439i | ||||
\(716\) | −16.1002 | − | 19.1875i | −0.601694 | − | 0.717071i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.18233 | − | 15.4026i | 0.268042 | − | 0.574818i | ||||
\(719\) | 3.82026 | + | 6.61689i | 0.142472 | + | 0.246768i | 0.928427 | − | 0.371515i | \(-0.121162\pi\) |
−0.785955 | + | 0.618284i | \(0.787828\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.432720 | + | 0.749493i | −0.0161153 | + | 0.0279126i | ||||
\(722\) | −21.0624 | − | 30.0802i | −0.783862 | − | 1.11947i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.2368 | + | 36.3677i | −0.491941 | + | 1.35160i | ||||
\(725\) | 12.5698 | − | 6.01798i | 0.466830 | − | 0.223502i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.09954 | − | 46.8579i | −0.152043 | − | 1.73786i | −0.563218 | − | 0.826308i | \(-0.690437\pi\) |
0.411175 | − | 0.911557i | \(-0.365119\pi\) | |||||||
\(728\) | 26.9550 | + | 26.9550i | 0.999018 | + | 0.999018i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18.2726 | + | 24.0661i | −0.676301 | + | 0.890727i | ||||
\(731\) | 32.1162 | − | 38.2746i | 1.18786 | − | 1.41564i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5374 | + | 26.9842i | 1.42341 | + | 0.996682i | 0.995687 | + | 0.0927724i | \(0.0295729\pi\) |
0.427723 | + | 0.903910i | \(0.359316\pi\) | |||||||
\(734\) | −8.25389 | − | 3.00417i | −0.304657 | − | 0.110886i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.577989 | + | 3.27794i | −0.0213050 | + | 0.120826i | ||||
\(737\) | −5.87144 | − | 21.9125i | −0.216277 | − | 0.807157i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.7581 | + | 23.5317i | −1.49931 | + | 0.865628i | −1.00000 | 0.000795196i | \(-0.999747\pi\) | |
−0.499311 | + | 0.866423i | \(0.666414\pi\) | |||||||
\(740\) | −11.0329 | + | 5.81494i | −0.405576 | + | 0.213761i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −34.6969 | − | 3.03559i | −1.27376 | − | 0.111440i | ||||
\(743\) | 5.97266 | + | 0.522540i | 0.219115 | + | 0.0191701i | 0.196185 | − | 0.980567i | \(-0.437145\pi\) |
0.0229307 | + | 0.999737i | \(0.492700\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.0982 | + | 3.43722i | 0.406607 | + | 0.125930i | ||||
\(746\) | −26.2588 | + | 15.1605i | −0.961402 | + | 0.555066i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.3784 | − | 61.1248i | −0.598852 | − | 2.23495i | ||||
\(749\) | 2.15964 | − | 12.2479i | 0.0789114 | − | 0.447529i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.7152 | + | 11.1794i | 1.12081 | + | 0.407943i | 0.834949 | − | 0.550327i | \(-0.185497\pi\) |
0.285865 | + | 0.958270i | \(0.407719\pi\) | |||||||
\(752\) | 1.35234 | + | 0.946921i | 0.0493149 | + | 0.0345306i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 26.2906 | − | 31.3319i | 0.957446 | − | 1.14104i | ||||
\(755\) | −7.44702 | − | 5.65429i | −0.271025 | − | 0.205781i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.11549 | − | 6.11549i | −0.222271 | − | 0.222271i | 0.587183 | − | 0.809454i | \(-0.300237\pi\) |
−0.809454 | + | 0.587183i | \(0.800237\pi\) | |||||||
\(758\) | 3.43586 | + | 39.2721i | 0.124796 | + | 1.42643i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.05677 | + | 21.9901i | 0.255976 | + | 0.797667i | ||||
\(761\) | 8.81390 | − | 24.2160i | 0.319503 | − | 0.877829i | −0.671137 | − | 0.741333i | \(-0.734194\pi\) |
0.990641 | − | 0.136495i | \(-0.0435839\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.86434 | − | 4.09070i | −0.103696 | − | 0.148093i | ||||
\(764\) | −27.6019 | + | 47.8078i | −0.998601 | + | 1.72963i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.7442 | + | 53.2505i | 1.11083 | + | 1.92402i | ||||
\(767\) | 7.96152 | − | 17.0735i | 0.287474 | − | 0.616490i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.3950 | + | 20.7306i | 0.627281 | + | 0.747565i | 0.982304 | − | 0.187293i | \(-0.0599713\pi\) |
−0.355023 | + | 0.934858i | \(0.615527\pi\) | |||||||
\(770\) | 0.940025 | + | 19.2771i | 0.0338762 | + | 0.694697i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 64.5115 | + | 30.0822i | 2.32182 | + | 1.08268i | ||||
\(773\) | 11.1567 | − | 41.6374i | 0.401279 | − | 1.49759i | −0.409539 | − | 0.912293i | \(-0.634310\pi\) |
0.810817 | − | 0.585299i | \(-0.199023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −23.9866 | − | 6.16608i | −0.861625 | − | 0.221492i | ||||
\(776\) | −17.8243 | − | 3.14290i | −0.639854 | − | 0.112823i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −41.7860 | + | 19.4851i | −1.49810 | + | 0.698576i | ||||
\(779\) | −0.113417 | − | 0.643218i | −0.00406357 | − | 0.0230457i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.3194 | + | 14.5327i | 0.619736 | + | 0.520020i | ||||
\(782\) | −45.3066 | + | 45.3066i | −1.62016 | + | 1.62016i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 24.0467i | 0.858809i | ||||||||
\(785\) | 16.3663 | − | 25.9809i | 0.584138 | − | 0.927300i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.3355 | + | 20.4732i | −0.511006 | + | 0.729792i | −0.988893 | − | 0.148629i | \(-0.952514\pi\) |
0.477887 | + | 0.878421i | \(0.341403\pi\) | |||||||
\(788\) | 3.20811 | + | 6.87982i | 0.114284 | + | 0.245084i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −88.3460 | − | 3.40664i | −3.14321 | − | 0.121203i | ||||
\(791\) | −13.8356 | − | 7.98800i | −0.491938 | − | 0.284021i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.911885 | − | 0.244339i | −0.0323820 | − | 0.00867673i | ||||
\(794\) | −21.5784 | + | 7.85389i | −0.765788 | + | 0.278724i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.1766 | + | 20.2866i | −0.856916 | + | 0.719038i | ||||
\(797\) | 2.62328 | − | 29.9842i | 0.0929213 | − | 1.06210i | −0.796387 | − | 0.604787i | \(-0.793258\pi\) |
0.889308 | − | 0.457308i | \(-0.151186\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.709237 | + | 1.94861i | 0.0250910 | + | 0.0689370i | ||||
\(800\) | 0.0362769 | + | 3.56196i | 0.00128258 | + | 0.125934i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 52.8546 | − | 14.1623i | 1.86636 | − | 0.500090i | ||||
\(803\) | −12.5468 | + | 8.78535i | −0.442766 | + | 0.310028i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.0157 | − | 7.09691i | 0.388253 | − | 0.250133i | ||||
\(806\) | −71.5824 | + | 12.6219i | −2.52138 | + | 0.444588i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 47.4292 | − | 4.14952i | 1.66855 | − | 0.145980i | ||||
\(809\) | 28.4904 | 1.00167 | 0.500835 | − | 0.865543i | \(-0.333026\pi\) | ||||
0.500835 | + | 0.865543i | \(0.333026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.4508 | 1.10439 | 0.552193 | − | 0.833716i | \(-0.313791\pi\) | ||||
0.552193 | + | 0.833716i | \(0.313791\pi\) | |||||||
\(812\) | −14.1784 | + | 1.24045i | −0.497566 | + | 0.0435314i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.28418 | + | 1.63705i | −0.325410 | + | 0.0573786i | ||||
\(815\) | −45.9668 | − | 9.94530i | −1.61015 | − | 0.348369i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.8831 | + | 10.4213i | −0.520694 | + | 0.364594i | ||||
\(818\) | −6.74411 | + | 1.80708i | −0.235802 | + | 0.0631830i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.368591 | − | 2.91433i | 0.0128718 | − | 0.101773i | ||||
\(821\) | −2.19118 | − | 6.02021i | −0.0764726 | − | 0.210107i | 0.895566 | − | 0.444929i | \(-0.146771\pi\) |
−0.972038 | + | 0.234823i | \(0.924549\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.506891 | − | 5.79379i | 0.0176691 | − | 0.201959i | −0.982229 | − | 0.187686i | \(-0.939901\pi\) |
0.999898 | − | 0.0142726i | \(-0.00454327\pi\) | |||||||
\(824\) | −2.69711 | + | 2.26314i | −0.0939583 | + | 0.0788404i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.18636 | + | 3.34356i | −0.319634 | + | 0.116337i | ||||
\(827\) | 15.0650 | + | 4.03665i | 0.523861 | + | 0.140368i | 0.511052 | − | 0.859550i | \(-0.329256\pi\) |
0.0128090 | + | 0.999918i | \(0.495923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.41349 | − | 0.816079i | −0.0490925 | − | 0.0283436i | 0.475253 | − | 0.879849i | \(-0.342357\pi\) |
−0.524345 | + | 0.851506i | \(0.675690\pi\) | |||||||
\(830\) | 7.02214 | − | 6.50069i | 0.243742 | − | 0.225642i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −17.8881 | − | 38.3611i | −0.620157 | − | 1.32993i | ||||
\(833\) | −17.3246 | + | 24.7421i | −0.600262 | + | 0.857263i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.90035 | − | 4.34677i | −0.238796 | − | 0.150426i | ||||
\(836\) | 23.0116i | 0.795873i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.02092 | + | 7.02092i | −0.242534 | + | 0.242534i | ||||
\(839\) | 0.322591 | + | 0.270686i | 0.0111371 | + | 0.00934513i | 0.648339 | − | 0.761352i | \(-0.275464\pi\) |
−0.637202 | + | 0.770697i | \(0.719908\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.68679 | − | 20.9088i | −0.127131 | − | 0.720994i | ||||
\(842\) | −9.79894 | + | 4.56932i | −0.337694 | + | 0.157469i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −85.7886 | − | 15.1268i | −2.95296 | − | 0.520687i | ||||
\(845\) | 19.4637 | + | 46.3209i | 0.669571 | + | 1.59349i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.03903 | − | 3.87772i | 0.0357015 | − | 0.133240i | ||||
\(848\) | −45.2588 | − | 21.1045i | −1.55419 | − | 0.724732i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −38.7565 | + | 56.5675i | −1.32934 | + | 1.94025i | ||||
\(851\) | 4.11438 | + | 4.90332i | 0.141039 | + | 0.168084i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.5905 | + | 37.7230i | −0.602288 | + | 1.29161i | 0.334725 | + | 0.942316i | \(0.391356\pi\) |
−0.937013 | + | 0.349294i | \(0.886421\pi\) | |||||||
\(854\) | 0.244949 | + | 0.424265i | 0.00838200 | + | 0.0145180i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.2981 | − | 43.8176i | 0.864671 | − | 1.49765i | ||||
\(857\) | 6.12897 | + | 8.75307i | 0.209362 | + | 0.298999i | 0.910075 | − | 0.414444i | \(-0.136024\pi\) |
−0.700714 | + | 0.713443i | \(0.747135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.91450 | + | 18.9974i | −0.235920 | + | 0.648184i | 0.764075 | + | 0.645127i | \(0.223195\pi\) |
−0.999995 | + | 0.00305761i | \(0.999027\pi\) | |||||||
\(860\) | −77.8078 | + | 24.9690i | −2.65322 | + | 0.851435i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.07319 | + | 35.1267i | 0.104673 | + | 1.19642i | ||||
\(863\) | 41.4293 | + | 41.4293i | 1.41027 | + | 1.41027i | 0.757901 | + | 0.652370i | \(0.226225\pi\) |
0.652370 | + | 0.757901i | \(0.273775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.48373 | − | 18.1511i | −0.0844494 | − | 0.617156i | ||||
\(866\) | −23.6762 | + | 28.2161i | −0.804548 | + | 0.958824i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.7191 | + | 14.5077i | 0.703253 | + | 0.492423i | ||||
\(869\) | −42.1125 | − | 15.3277i | −1.42857 | − | 0.519957i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.40070 | + | 47.6428i | −0.284647 | + | 1.61431i | ||||
\(872\) | −5.25819 | − | 19.6239i | −0.178065 | − | 0.664547i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 20.1781 | − | 11.6498i | 0.682534 | − | 0.394061i | ||||
\(875\) | 10.1934 | − | 9.63113i | 0.344601 | − | 0.325592i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.2279 | + | 3.25702i | 1.25710 | + | 0.109982i | 0.696166 | − | 0.717881i | \(-0.254888\pi\) |
0.560931 | + | 0.827863i | \(0.310443\pi\) | |||||||
\(878\) | 59.6769 | + | 5.22105i | 2.01400 | + | 0.176202i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.18658 | + | 26.4331i | −0.275970 | + | 0.891060i | ||||
\(881\) | −22.2691 | + | 12.8571i | −0.750267 | + | 0.433167i | −0.825790 | − | 0.563977i | \(-0.809271\pi\) |
0.0755236 | + | 0.997144i | \(0.475937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.4426 | − | 46.4363i | −0.418726 | − | 1.56271i | −0.777253 | − | 0.629188i | \(-0.783388\pi\) |
0.358527 | − | 0.933519i | \(-0.383279\pi\) | |||||||
\(884\) | −23.4337 | + | 132.899i | −0.788162 | + | 4.46989i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.6600 | + | 5.69978i | 0.526109 | + | 0.191488i | ||||
\(887\) | 10.3392 | + | 7.23961i | 0.347158 | + | 0.243082i | 0.734130 | − | 0.679009i | \(-0.237590\pi\) |
−0.386972 | + | 0.922091i | \(0.626479\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.19883 | + | 1.42871i | −0.0402076 | + | 0.0479175i | ||||
\(890\) | 70.4052 | − | 9.63399i | 2.35999 | − | 0.322932i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −66.2999 | − | 66.2999i | −2.21989 | − | 2.21989i | ||||
\(893\) | −0.0657217 | − | 0.751202i | −0.00219929 | − | 0.0251380i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.29038 | + | 12.2354i | −0.210264 | + | 0.408985i | ||||
\(896\) | −8.12364 | + | 22.3195i | −0.271392 | + | 0.745643i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.07145 | − | 7.24279i | −0.169237 | − | 0.241695i | ||||
\(899\) | 6.90298 | − | 11.9563i | 0.230227 | − | 0.398765i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.3628 | − | 54.3220i | −1.04485 | − | 1.80973i | ||||
\(902\) | 0.938442 | − | 2.01249i | 0.0312467 | − | 0.0670087i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −41.7776 | − | 49.7886i | −1.38950 | − | 1.65594i | ||||
\(905\) | 21.2322 | − | 1.03537i | 0.705784 | − | 0.0344168i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 34.9158 | + | 16.2815i | 1.15936 | + | 0.540618i | 0.904548 | − | 0.426373i | \(-0.140209\pi\) |
0.254812 | + | 0.966991i | \(0.417987\pi\) | |||||||
\(908\) | 25.0410 | − | 93.4542i | 0.831014 | − | 3.10139i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.5566 | − | 38.1047i | 0.515698 | − | 1.26316i | ||||
\(911\) | −34.0239 | − | 5.99934i | −1.12726 | − | 0.198767i | −0.421236 | − | 0.906951i | \(-0.638403\pi\) |
−0.706028 | + | 0.708184i | \(0.749515\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.39610 | − | 2.04993i | 0.145490 | − | 0.0678429i | ||||
\(914\) | 12.9763 | + | 73.5924i | 0.429219 | + | 2.43422i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −47.8399 | − | 40.1424i | −1.58067 | − | 1.32634i | ||||
\(917\) | 4.37775 | − | 4.37775i | 0.144566 | − | 0.144566i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 29.7574i | − | 0.981607i | −0.871270 | − | 0.490804i | \(-0.836703\pi\) | ||
0.871270 | − | 0.490804i | \(-0.163297\pi\) | |||||||
\(920\) | 51.9869 | − | 11.8033i | 1.71396 | − | 0.389142i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −56.3530 | + | 80.4805i | −1.85589 | + | 2.65048i | ||||
\(923\) | −20.3762 | − | 43.6970i | −0.670692 | − | 1.43830i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.29208 | + | 4.34951i | 0.174002 | + | 0.143011i | ||||
\(926\) | 36.6321 | + | 21.1496i | 1.20381 | + | 0.695018i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.91804 | − | 0.513938i | −0.0629628 | − | 0.0168708i | ||||
\(929\) | −38.4305 | + | 13.9876i | −1.26086 | + | 0.458917i | −0.884059 | − | 0.467375i | \(-0.845200\pi\) |
−0.376806 | + | 0.926292i | \(0.622978\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.41393 | − | 7.06013i | 0.275756 | − | 0.231386i | ||||
\(932\) | −4.51492 | + | 51.6058i | −0.147891 | + | 1.69040i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 15.4708 | + | 42.5056i | 0.506219 | + | 1.39082i | ||||
\(935\) | −27.4673 | + | 21.2995i | −0.898277 | + | 0.696568i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.0128 | + | 6.43422i | −0.784465 | + | 0.210197i | −0.628752 | − | 0.777606i | \(-0.716434\pi\) |
−0.155713 | + | 0.987802i | \(0.549767\pi\) | |||||||
\(938\) | 20.5646 | − | 14.3995i | 0.671458 | − | 0.470160i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.717183 | − | 3.31479i | 0.0233919 | − | 0.108117i | ||||
\(941\) | −5.63001 | + | 0.992723i | −0.183533 | + | 0.0323619i | −0.264659 | − | 0.964342i | \(-0.585259\pi\) |
0.0811261 | + | 0.996704i | \(0.474148\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.50192 | + | 0.131401i | −0.0489093 | + | 0.00427901i | ||||
\(944\) | −14.0165 | −0.456197 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −61.7705 | −2.00833 | ||||||||
\(947\) | 19.0429 | − | 1.66603i | 0.618810 | − | 0.0541389i | 0.226560 | − | 0.973997i | \(-0.427252\pi\) |
0.392250 | + | 0.919858i | \(0.371697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.1674 | − | 5.67199i | 1.04420 | − | 0.184120i | ||||
\(950\) | 18.9372 | − | 16.2217i | 0.614404 | − | 0.526301i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 29.1828 | − | 20.4340i | 0.945821 | − | 0.662271i | ||||
\(953\) | 30.4309 | − | 8.15394i | 0.985755 | − | 0.264132i | 0.270288 | − | 0.962779i | \(-0.412881\pi\) |
0.715466 | + | 0.698647i | \(0.246214\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 30.0818 | + | 3.80461i | 0.973424 | + | 0.123114i | ||||
\(956\) | 7.57181 | + | 20.8034i | 0.244890 | + | 0.672830i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.04196 | + | 57.6299i | −0.162898 | + | 1.86194i | ||||
\(959\) | −8.90959 | + | 7.47603i | −0.287706 | + | 0.241414i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.07496 | − | 2.21110i | 0.195966 | − | 0.0713260i | ||||
\(962\) | 19.4193 | + | 5.20338i | 0.626103 | + | 0.167764i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.3097 | + | 15.1899i | 0.847377 | + | 0.489233i | ||||
\(965\) | 1.50647 | − | 39.0679i | 0.0484949 | − | 1.25764i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.05757 | − | 19.4240i | −0.291272 | − | 0.624635i | 0.705159 | − | 0.709049i | \(-0.250876\pi\) |
−0.996431 | + | 0.0844147i | \(0.973098\pi\) | |||||||
\(968\) | 9.36766 | − | 13.3784i | 0.301088 | − | 0.429998i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.32667 | + | 19.0566i | 0.138921 | + | 0.611870i | ||||
\(971\) | − | 28.3706i | − | 0.910457i | −0.890375 | − | 0.455228i | \(-0.849558\pi\) | ||
0.890375 | − | 0.455228i | \(-0.150442\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.588898 | − | 0.588898i | 0.0188792 | − | 0.0188792i | ||||
\(974\) | 19.2594 | + | 16.1606i | 0.617111 | + | 0.517818i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.121971 | + | 0.691733i | 0.00390420 | + | 0.0221418i | ||||
\(977\) | −26.7114 | + | 12.4557i | −0.854573 | + | 0.398494i | −0.799988 | − | 0.600015i | \(-0.795161\pi\) |
−0.0545842 | + | 0.998509i | \(0.517383\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.4732 | + | 6.25489i | 1.13373 | + | 0.199907i | ||||
\(980\) | 45.5424 | − | 19.1365i | 1.45480 | − | 0.611294i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.1637 | − | 78.9842i | 0.675362 | − | 2.52049i | ||||
\(983\) | 9.83346 | + | 4.58542i | 0.313639 | + | 0.146252i | 0.573063 | − | 0.819511i | \(-0.305755\pi\) |
−0.259424 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.80118 | − | 3.08837i | 0.0892529 | − | 0.0984038i | ||||
\(986\) | −24.5702 | − | 29.2816i | −0.782474 | − | 0.932517i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.7392 | − | 44.4754i | 0.659802 | − | 1.41495i | ||||
\(989\) | 20.9699 | + | 36.3209i | 0.666803 | + | 1.15494i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.0170972 | + | 0.0296132i | −0.000543110 | + | 0.000940694i | −0.866297 | − | 0.499530i | \(-0.833506\pi\) |
0.865754 | + | 0.500470i | \(0.166840\pi\) | |||||||
\(992\) | 2.02408 | + | 2.89069i | 0.0642646 | + | 0.0917794i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.55731 | + | 23.5110i | −0.271421 | + | 0.745724i | ||||
\(995\) | 15.4168 | + | 7.92598i | 0.488747 | + | 0.251271i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.74457 | − | 31.3705i | −0.0869213 | − | 0.993515i | −0.906963 | − | 0.421211i | \(-0.861605\pi\) |
0.820041 | − | 0.572304i | \(-0.193950\pi\) | |||||||
\(998\) | −42.5853 | − | 42.5853i | −1.34801 | − | 1.34801i | ||||
\(999\) | 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 | 405.2.r.a.197.15 | 192 | ||
3.2 | odd | 2 | 135.2.q.a.92.2 | yes | 192 | ||
5.3 | odd | 4 | inner | 405.2.r.a.278.2 | 192 | ||
15.2 | even | 4 | 675.2.ba.b.443.2 | 192 | |||
15.8 | even | 4 | 135.2.q.a.38.15 | yes | 192 | ||
15.14 | odd | 2 | 675.2.ba.b.632.15 | 192 | |||
27.5 | odd | 18 | inner | 405.2.r.a.287.2 | 192 | ||
27.22 | even | 9 | 135.2.q.a.32.15 | ✓ | 192 | ||
135.22 | odd | 36 | 675.2.ba.b.518.15 | 192 | |||
135.49 | even | 18 | 675.2.ba.b.32.2 | 192 | |||
135.103 | odd | 36 | 135.2.q.a.113.2 | yes | 192 | ||
135.113 | even | 36 | inner | 405.2.r.a.368.15 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.q.a.32.15 | ✓ | 192 | 27.22 | even | 9 | ||
135.2.q.a.38.15 | yes | 192 | 15.8 | even | 4 | ||
135.2.q.a.92.2 | yes | 192 | 3.2 | odd | 2 | ||
135.2.q.a.113.2 | yes | 192 | 135.103 | odd | 36 | ||
405.2.r.a.197.15 | 192 | 1.1 | even | 1 | trivial | ||
405.2.r.a.278.2 | 192 | 5.3 | odd | 4 | inner | ||
405.2.r.a.287.2 | 192 | 27.5 | odd | 18 | inner | ||
405.2.r.a.368.15 | 192 | 135.113 | even | 36 | inner | ||
675.2.ba.b.32.2 | 192 | 135.49 | even | 18 | |||
675.2.ba.b.443.2 | 192 | 15.2 | even | 4 | |||
675.2.ba.b.518.15 | 192 | 135.22 | odd | 36 | |||
675.2.ba.b.632.15 | 192 | 15.14 | odd | 2 |