Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [572,2,Mod(571,572)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(572, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("572.571");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 572 = 2^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 572.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.56744299562\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 571.8 | ||
Character | \(\chi\) | \(=\) | 572.571 |
Dual form | 572.2.b.c.571.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/572\mathbb{Z}\right)^\times\).
\(n\) | \(287\) | \(353\) | \(365\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30250 | + | 0.550896i | −0.921009 | + | 0.389542i | ||||
\(3\) | − | 0.566258i | − | 0.326929i | −0.986549 | − | 0.163465i | \(-0.947733\pi\) | ||
0.986549 | − | 0.163465i | \(-0.0522670\pi\) | |||||||
\(4\) | 1.39303 | − | 1.43509i | 0.696514 | − | 0.717543i | ||||
\(5\) | 3.29519i | 1.47365i | 0.676081 | + | 0.736827i | \(0.263677\pi\) | ||||
−0.676081 | + | 0.736827i | \(0.736323\pi\) | |||||||
\(6\) | 0.311949 | + | 0.737553i | 0.127353 | + | 0.301105i | ||||
\(7\) | − | 2.02255i | − | 0.764453i | −0.924069 | − | 0.382226i | \(-0.875157\pi\) | ||
0.924069 | − | 0.382226i | \(-0.124843\pi\) | |||||||
\(8\) | −1.02384 | + | 2.63662i | −0.361982 | + | 0.932185i | ||||
\(9\) | 2.67935 | 0.893117 | ||||||||
\(10\) | −1.81531 | − | 4.29199i | −0.574050 | − | 1.35725i | ||||
\(11\) | −0.176245 | − | 3.31194i | −0.0531398 | − | 0.998587i | ||||
\(12\) | −0.812629 | − | 0.788813i | −0.234586 | − | 0.227711i | ||||
\(13\) | 2.00264 | − | 2.99824i | 0.555432 | − | 0.831562i | ||||
\(14\) | 1.11422 | + | 2.63438i | 0.297787 | + | 0.704068i | ||||
\(15\) | 1.86593 | 0.481780 | ||||||||
\(16\) | −0.118946 | − | 3.99823i | −0.0297366 | − | 0.999558i | ||||
\(17\) | 1.97924i | 0.480037i | 0.970768 | + | 0.240018i | \(0.0771534\pi\) | ||||
−0.970768 | + | 0.240018i | \(0.922847\pi\) | |||||||
\(18\) | −3.48986 | + | 1.47604i | −0.822569 | + | 0.347907i | ||||
\(19\) | 2.68960i | 0.617036i | 0.951219 | + | 0.308518i | \(0.0998330\pi\) | ||||
−0.951219 | + | 0.308518i | \(0.900167\pi\) | |||||||
\(20\) | 4.72888 | + | 4.59029i | 1.05741 | + | 1.02642i | ||||
\(21\) | −1.14529 | −0.249922 | ||||||||
\(22\) | 2.05409 | + | 4.21672i | 0.437934 | + | 0.899007i | ||||
\(23\) | 0.308907i | 0.0644115i | 0.999481 | + | 0.0322057i | \(0.0102532\pi\) | ||||
−0.999481 | + | 0.0322057i | \(0.989747\pi\) | |||||||
\(24\) | 1.49301 | + | 0.579758i | 0.304759 | + | 0.118343i | ||||
\(25\) | −5.85828 | −1.17166 | ||||||||
\(26\) | −0.956723 | + | 5.00846i | −0.187629 | + | 0.982240i | ||||
\(27\) | − | 3.21598i | − | 0.618915i | ||||||
\(28\) | −2.90254 | − | 2.81747i | −0.548528 | − | 0.532452i | ||||
\(29\) | 4.88668i | 0.907433i | 0.891146 | + | 0.453716i | \(0.149902\pi\) | ||||
−0.891146 | + | 0.453716i | \(0.850098\pi\) | |||||||
\(30\) | −2.43038 | + | 1.02793i | −0.443724 | + | 0.187674i | ||||
\(31\) | 7.20359 | 1.29380 | 0.646902 | − | 0.762573i | \(-0.276064\pi\) | ||||
0.646902 | + | 0.762573i | \(0.276064\pi\) | |||||||
\(32\) | 2.35754 | + | 5.14218i | 0.416757 | + | 0.909018i | ||||
\(33\) | −1.87541 | + | 0.0998000i | −0.326467 | + | 0.0173730i | ||||
\(34\) | −1.09036 | − | 2.57797i | −0.186994 | − | 0.442118i | ||||
\(35\) | 6.66469 | 1.12654 | ||||||||
\(36\) | 3.73241 | − | 3.84510i | 0.622069 | − | 0.640850i | ||||
\(37\) | − | 6.85284i | − | 1.12660i | −0.826253 | − | 0.563300i | \(-0.809532\pi\) | ||
0.826253 | − | 0.563300i | \(-0.190468\pi\) | |||||||
\(38\) | −1.48169 | − | 3.50321i | −0.240361 | − | 0.568296i | ||||
\(39\) | −1.69778 | − | 1.13401i | −0.271862 | − | 0.181587i | ||||
\(40\) | −8.68816 | − | 3.37375i | −1.37372 | − | 0.533436i | ||||
\(41\) | 3.51069 | 0.548277 | 0.274138 | − | 0.961690i | \(-0.411607\pi\) | ||||
0.274138 | + | 0.961690i | \(0.411607\pi\) | |||||||
\(42\) | 1.49174 | − | 0.630933i | 0.230180 | − | 0.0973551i | ||||
\(43\) | 8.51358 | 1.29831 | 0.649154 | − | 0.760657i | \(-0.275123\pi\) | ||||
0.649154 | + | 0.760657i | \(0.275123\pi\) | |||||||
\(44\) | −4.99843 | − | 4.36070i | −0.753542 | − | 0.657400i | ||||
\(45\) | 8.82897i | 1.31615i | ||||||||
\(46\) | −0.170175 | − | 0.402352i | −0.0250910 | − | 0.0593235i | ||||
\(47\) | 3.39367 | 0.495017 | 0.247509 | − | 0.968886i | \(-0.420388\pi\) | ||||
0.247509 | + | 0.968886i | \(0.420388\pi\) | |||||||
\(48\) | −2.26403 | + | 0.0673543i | −0.326785 | + | 0.00972176i | ||||
\(49\) | 2.90928 | 0.415612 | ||||||||
\(50\) | 7.63043 | − | 3.22730i | 1.07911 | − | 0.456409i | ||||
\(51\) | 1.12076 | 0.156938 | ||||||||
\(52\) | −1.51300 | − | 7.05059i | −0.209816 | − | 0.977741i | ||||
\(53\) | 5.92430 | 0.813766 | 0.406883 | − | 0.913480i | \(-0.366616\pi\) | ||||
0.406883 | + | 0.913480i | \(0.366616\pi\) | |||||||
\(54\) | 1.77167 | + | 4.18882i | 0.241094 | + | 0.570026i | ||||
\(55\) | 10.9135 | − | 0.580760i | 1.47157 | − | 0.0783097i | ||||
\(56\) | 5.33270 | + | 2.07077i | 0.712612 | + | 0.276718i | ||||
\(57\) | 1.52301 | 0.201727 | ||||||||
\(58\) | −2.69205 | − | 6.36491i | −0.353483 | − | 0.835753i | ||||
\(59\) | −6.37888 | −0.830460 | −0.415230 | − | 0.909717i | \(-0.636299\pi\) | ||||
−0.415230 | + | 0.909717i | \(0.636299\pi\) | |||||||
\(60\) | 2.59929 | − | 2.67777i | 0.335567 | − | 0.345698i | ||||
\(61\) | 10.0713i | 1.28950i | 0.764392 | + | 0.644751i | \(0.223039\pi\) | ||||
−0.764392 | + | 0.644751i | \(0.776961\pi\) | |||||||
\(62\) | −9.38270 | + | 3.96843i | −1.19160 | + | 0.503991i | ||||
\(63\) | − | 5.41913i | − | 0.682746i | ||||||
\(64\) | −5.90350 | − | 5.39895i | −0.737938 | − | 0.674869i | ||||
\(65\) | 9.87977 | + | 6.59907i | 1.22543 | + | 0.818514i | ||||
\(66\) | 2.38775 | − | 1.16315i | 0.293912 | − | 0.143173i | ||||
\(67\) | −15.1432 | −1.85003 | −0.925015 | − | 0.379930i | \(-0.875948\pi\) | ||||
−0.925015 | + | 0.379930i | \(0.875948\pi\) | |||||||
\(68\) | 2.84038 | + | 2.75714i | 0.344447 | + | 0.334352i | ||||
\(69\) | 0.174921 | 0.0210580 | ||||||||
\(70\) | −8.68078 | + | 3.67155i | −1.03755 | + | 0.438834i | ||||
\(71\) | 11.2773 | 1.33836 | 0.669182 | − | 0.743098i | \(-0.266644\pi\) | ||||
0.669182 | + | 0.743098i | \(0.266644\pi\) | |||||||
\(72\) | −2.74323 | + | 7.06443i | −0.323293 | + | 0.832551i | ||||
\(73\) | −6.30410 | −0.737839 | −0.368920 | − | 0.929461i | \(-0.620272\pi\) | ||||
−0.368920 | + | 0.929461i | \(0.620272\pi\) | |||||||
\(74\) | 3.77520 | + | 8.92584i | 0.438858 | + | 1.03761i | ||||
\(75\) | 3.31730i | 0.383048i | ||||||||
\(76\) | 3.85981 | + | 3.74668i | 0.442750 | + | 0.429774i | ||||
\(77\) | −6.69857 | + | 0.356464i | −0.763373 | + | 0.0406229i | ||||
\(78\) | 2.83608 | + | 0.541752i | 0.321123 | + | 0.0613414i | ||||
\(79\) | 6.80153 | 0.765231 | 0.382616 | − | 0.923908i | \(-0.375023\pi\) | ||||
0.382616 | + | 0.923908i | \(0.375023\pi\) | |||||||
\(80\) | 13.1749 | − | 0.391951i | 1.47300 | − | 0.0438214i | ||||
\(81\) | 6.21698 | 0.690776 | ||||||||
\(82\) | −4.57268 | + | 1.93402i | −0.504968 | + | 0.213577i | ||||
\(83\) | − | 3.98900i | − | 0.437850i | −0.975742 | − | 0.218925i | \(-0.929745\pi\) | ||
0.975742 | − | 0.218925i | \(-0.0702549\pi\) | |||||||
\(84\) | −1.59542 | + | 1.64359i | −0.174074 | + | 0.179330i | ||||
\(85\) | −6.52198 | −0.707408 | ||||||||
\(86\) | −11.0890 | + | 4.69009i | −1.19575 | + | 0.505746i | ||||
\(87\) | 2.76712 | 0.296666 | ||||||||
\(88\) | 8.91276 | + | 2.92621i | 0.950104 | + | 0.311935i | ||||
\(89\) | 9.31924i | 0.987837i | 0.869508 | + | 0.493919i | \(0.164436\pi\) | ||||
−0.869508 | + | 0.493919i | \(0.835564\pi\) | |||||||
\(90\) | −4.86384 | − | 11.4998i | −0.512694 | − | 1.21218i | ||||
\(91\) | −6.06410 | − | 4.05044i | −0.635690 | − | 0.424601i | ||||
\(92\) | 0.443308 | + | 0.430316i | 0.0462180 | + | 0.0448635i | ||||
\(93\) | − | 4.07909i | − | 0.422982i | ||||||
\(94\) | −4.42026 | + | 1.86956i | −0.455915 | + | 0.192830i | ||||
\(95\) | −8.86274 | −0.909298 | ||||||||
\(96\) | 2.91180 | − | 1.33497i | 0.297184 | − | 0.136250i | ||||
\(97\) | − | 9.78624i | − | 0.993642i | −0.867853 | − | 0.496821i | \(-0.834501\pi\) | ||
0.867853 | − | 0.496821i | \(-0.165499\pi\) | |||||||
\(98\) | −3.78935 | + | 1.60271i | −0.382782 | + | 0.161898i | ||||
\(99\) | −0.472222 | − | 8.87385i | −0.0474601 | − | 0.891855i | ||||
\(100\) | −8.16075 | + | 8.40714i | −0.816075 | + | 0.840714i | ||||
\(101\) | − | 12.1164i | − | 1.20562i | −0.797883 | − | 0.602812i | \(-0.794047\pi\) | ||
0.797883 | − | 0.602812i | \(-0.205953\pi\) | |||||||
\(102\) | −1.45979 | + | 0.617422i | −0.144541 | + | 0.0611339i | ||||
\(103\) | 15.6340i | 1.54046i | 0.637764 | + | 0.770232i | \(0.279860\pi\) | ||||
−0.637764 | + | 0.770232i | \(0.720140\pi\) | |||||||
\(104\) | 5.85483 | + | 8.34991i | 0.574114 | + | 0.818776i | ||||
\(105\) | − | 3.77394i | − | 0.368299i | ||||||
\(106\) | −7.71642 | + | 3.26367i | −0.749485 | + | 0.316996i | ||||
\(107\) | −1.68984 | −0.163363 | −0.0816814 | − | 0.996658i | \(-0.526029\pi\) | ||||
−0.0816814 | + | 0.996658i | \(0.526029\pi\) | |||||||
\(108\) | −4.61521 | − | 4.47995i | −0.444099 | − | 0.431083i | ||||
\(109\) | 8.82859 | 0.845626 | 0.422813 | − | 0.906217i | \(-0.361043\pi\) | ||||
0.422813 | + | 0.906217i | \(0.361043\pi\) | |||||||
\(110\) | −13.8949 | + | 6.76862i | −1.32483 | + | 0.645363i | ||||
\(111\) | −3.88048 | −0.368318 | ||||||||
\(112\) | −8.08663 | + | 0.240575i | −0.764115 | + | 0.0227322i | ||||
\(113\) | −13.7534 | −1.29381 | −0.646905 | − | 0.762571i | \(-0.723937\pi\) | ||||
−0.646905 | + | 0.762571i | \(0.723937\pi\) | |||||||
\(114\) | −1.98372 | + | 0.839017i | −0.185792 | + | 0.0785812i | ||||
\(115\) | −1.01791 | −0.0949202 | ||||||||
\(116\) | 7.01280 | + | 6.80727i | 0.651122 | + | 0.632040i | ||||
\(117\) | 5.36577 | − | 8.03334i | 0.496066 | − | 0.742683i | ||||
\(118\) | 8.30851 | − | 3.51410i | 0.764860 | − | 0.323499i | ||||
\(119\) | 4.00312 | 0.366965 | ||||||||
\(120\) | −1.91041 | + | 4.91974i | −0.174396 | + | 0.449109i | ||||
\(121\) | −10.9379 | + | 1.16742i | −0.994352 | + | 0.106129i | ||||
\(122\) | −5.54826 | − | 13.1179i | −0.502316 | − | 1.18764i | ||||
\(123\) | − | 1.98795i | − | 0.179248i | ||||||
\(124\) | 10.0348 | − | 10.3378i | 0.901152 | − | 0.928360i | ||||
\(125\) | − | 2.82819i | − | 0.252961i | ||||||
\(126\) | 2.98537 | + | 7.05843i | 0.265958 | + | 0.628815i | ||||
\(127\) | −6.09562 | −0.540899 | −0.270449 | − | 0.962734i | \(-0.587172\pi\) | ||||
−0.270449 | + | 0.962734i | \(0.587172\pi\) | |||||||
\(128\) | 10.6636 | + | 3.77993i | 0.942537 | + | 0.334102i | ||||
\(129\) | − | 4.82088i | − | 0.424455i | ||||||
\(130\) | −16.5038 | − | 3.15259i | −1.44748 | − | 0.276500i | ||||
\(131\) | −16.2333 | −1.41831 | −0.709157 | − | 0.705051i | \(-0.750924\pi\) | ||||
−0.709157 | + | 0.705051i | \(0.750924\pi\) | |||||||
\(132\) | −2.46928 | + | 2.83040i | −0.214923 | + | 0.246355i | ||||
\(133\) | 5.43985 | 0.471695 | ||||||||
\(134\) | 19.7240 | − | 8.34230i | 1.70389 | − | 0.720665i | ||||
\(135\) | 10.5973 | 0.912067 | ||||||||
\(136\) | −5.21850 | − | 2.02643i | −0.447483 | − | 0.173765i | ||||
\(137\) | − | 14.5906i | − | 1.24656i | −0.782000 | − | 0.623278i | \(-0.785801\pi\) | ||
0.782000 | − | 0.623278i | \(-0.214199\pi\) | |||||||
\(138\) | −0.227835 | + | 0.0963631i | −0.0193946 | + | 0.00820298i | ||||
\(139\) | −6.82374 | −0.578782 | −0.289391 | − | 0.957211i | \(-0.593453\pi\) | ||||
−0.289391 | + | 0.957211i | \(0.593453\pi\) | |||||||
\(140\) | 9.28411 | − | 9.56441i | 0.784650 | − | 0.808340i | ||||
\(141\) | − | 1.92169i | − | 0.161836i | ||||||
\(142\) | −14.6887 | + | 6.21259i | −1.23265 | + | 0.521349i | ||||
\(143\) | −10.2829 | − | 6.10419i | −0.859903 | − | 0.510458i | ||||
\(144\) | −0.318699 | − | 10.7127i | −0.0265583 | − | 0.892722i | ||||
\(145\) | −16.1025 | −1.33724 | ||||||||
\(146\) | 8.21111 | − | 3.47290i | 0.679556 | − | 0.287419i | ||||
\(147\) | − | 1.64740i | − | 0.135876i | ||||||
\(148\) | −9.83442 | − | 9.54620i | −0.808384 | − | 0.784693i | ||||
\(149\) | −2.32447 | −0.190428 | −0.0952142 | − | 0.995457i | \(-0.530354\pi\) | ||||
−0.0952142 | + | 0.995457i | \(0.530354\pi\) | |||||||
\(150\) | −1.82748 | − | 4.32079i | −0.149213 | − | 0.352791i | ||||
\(151\) | 13.1052i | 1.06649i | 0.845962 | + | 0.533244i | \(0.179027\pi\) | ||||
−0.845962 | + | 0.533244i | \(0.820973\pi\) | |||||||
\(152\) | −7.09144 | − | 2.75372i | −0.575192 | − | 0.223356i | ||||
\(153\) | 5.30308i | 0.428729i | ||||||||
\(154\) | 8.52853 | − | 4.15451i | 0.687249 | − | 0.334780i | ||||
\(155\) | 23.7372i | 1.90662i | ||||||||
\(156\) | −3.99245 | + | 0.856751i | −0.319652 | + | 0.0685950i | ||||
\(157\) | −0.476003 | −0.0379891 | −0.0189946 | − | 0.999820i | \(-0.506047\pi\) | ||||
−0.0189946 | + | 0.999820i | \(0.506047\pi\) | |||||||
\(158\) | −8.85901 | + | 3.74693i | −0.704785 | + | 0.298090i | ||||
\(159\) | − | 3.35468i | − | 0.266044i | ||||||
\(160\) | −16.9445 | + | 7.76853i | −1.33958 | + | 0.614156i | ||||
\(161\) | 0.624780 | 0.0492395 | ||||||||
\(162\) | −8.09764 | + | 3.42491i | −0.636211 | + | 0.269086i | ||||
\(163\) | −19.3878 | −1.51857 | −0.759283 | − | 0.650761i | \(-0.774450\pi\) | ||||
−0.759283 | + | 0.650761i | \(0.774450\pi\) | |||||||
\(164\) | 4.89048 | − | 5.03814i | 0.381883 | − | 0.393412i | ||||
\(165\) | −0.328860 | − | 6.17984i | −0.0256017 | − | 0.481100i | ||||
\(166\) | 2.19752 | + | 5.19568i | 0.170561 | + | 0.403263i | ||||
\(167\) | − | 10.7009i | − | 0.828063i | −0.910262 | − | 0.414032i | \(-0.864120\pi\) | ||
0.910262 | − | 0.414032i | \(-0.135880\pi\) | |||||||
\(168\) | 1.17259 | − | 3.01968i | 0.0904673 | − | 0.232974i | ||||
\(169\) | −4.97889 | − | 12.0088i | −0.382991 | − | 0.923752i | ||||
\(170\) | 8.49489 | − | 3.59293i | 0.651529 | − | 0.275565i | ||||
\(171\) | 7.20638i | 0.551086i | ||||||||
\(172\) | 11.8596 | − | 12.2177i | 0.904290 | − | 0.931592i | ||||
\(173\) | − | 2.43341i | − | 0.185008i | −0.995712 | − | 0.0925042i | \(-0.970513\pi\) | ||
0.995712 | − | 0.0925042i | \(-0.0294872\pi\) | |||||||
\(174\) | −3.60418 | + | 1.52439i | −0.273232 | + | 0.115564i | ||||
\(175\) | 11.8487i | 0.895676i | ||||||||
\(176\) | −13.2209 | + | 1.09861i | −0.996565 | + | 0.0828109i | ||||
\(177\) | 3.61209i | 0.271501i | ||||||||
\(178\) | −5.13393 | − | 12.1383i | −0.384804 | − | 0.909807i | ||||
\(179\) | − | 22.7340i | − | 1.69922i | −0.527414 | − | 0.849609i | \(-0.676838\pi\) | ||
0.527414 | − | 0.849609i | \(-0.323162\pi\) | |||||||
\(180\) | 12.6703 | + | 12.2990i | 0.944391 | + | 0.916714i | ||||
\(181\) | −5.87335 | −0.436563 | −0.218281 | − | 0.975886i | \(-0.570045\pi\) | ||||
−0.218281 | + | 0.975886i | \(0.570045\pi\) | |||||||
\(182\) | 10.1299 | + | 1.93502i | 0.750876 | + | 0.143433i | ||||
\(183\) | 5.70298 | 0.421576 | ||||||||
\(184\) | −0.814469 | − | 0.316271i | −0.0600434 | − | 0.0233158i | ||||
\(185\) | 22.5814 | 1.66022 | ||||||||
\(186\) | 2.24715 | + | 5.31303i | 0.164769 | + | 0.389570i | ||||
\(187\) | 6.55513 | − | 0.348831i | 0.479358 | − | 0.0255091i | ||||
\(188\) | 4.72747 | − | 4.87021i | 0.344786 | − | 0.355196i | ||||
\(189\) | −6.50448 | −0.473132 | ||||||||
\(190\) | 11.5437 | − | 4.88244i | 0.837471 | − | 0.354210i | ||||
\(191\) | − | 14.5141i | − | 1.05020i | −0.851039 | − | 0.525102i | \(-0.824027\pi\) | ||
0.851039 | − | 0.525102i | \(-0.175973\pi\) | |||||||
\(192\) | −3.05720 | + | 3.34291i | −0.220634 | + | 0.241253i | ||||
\(193\) | 17.5788 | 1.26535 | 0.632673 | − | 0.774419i | \(-0.281958\pi\) | ||||
0.632673 | + | 0.774419i | \(0.281958\pi\) | |||||||
\(194\) | 5.39120 | + | 12.7466i | 0.387065 | + | 0.915153i | ||||
\(195\) | 3.73678 | − | 5.59450i | 0.267596 | − | 0.400630i | ||||
\(196\) | 4.05271 | − | 4.17507i | 0.289479 | − | 0.298219i | ||||
\(197\) | −19.2340 | −1.37037 | −0.685183 | − | 0.728371i | \(-0.740278\pi\) | ||||
−0.685183 | + | 0.728371i | \(0.740278\pi\) | |||||||
\(198\) | 5.50364 | + | 11.2981i | 0.391126 | + | 0.802919i | ||||
\(199\) | 3.92359i | 0.278136i | 0.990283 | + | 0.139068i | \(0.0444107\pi\) | ||||
−0.990283 | + | 0.139068i | \(0.955589\pi\) | |||||||
\(200\) | 5.99794 | − | 15.4460i | 0.424118 | − | 1.09220i | ||||
\(201\) | 8.57493i | 0.604829i | ||||||||
\(202\) | 6.67486 | + | 15.7816i | 0.469641 | + | 1.11039i | ||||
\(203\) | 9.88356 | 0.693690 | ||||||||
\(204\) | 1.56125 | − | 1.60839i | 0.109309 | − | 0.112610i | ||||
\(205\) | 11.5684i | 0.807970i | ||||||||
\(206\) | −8.61271 | − | 20.3633i | −0.600076 | − | 1.41878i | ||||
\(207\) | 0.827670i | 0.0575270i | ||||||||
\(208\) | −12.2259 | − | 7.65038i | −0.847711 | − | 0.530458i | ||||
\(209\) | 8.90778 | − | 0.474028i | 0.616164 | − | 0.0327892i | ||||
\(210\) | 2.07905 | + | 4.91556i | 0.143468 | + | 0.339206i | ||||
\(211\) | −12.5108 | −0.861281 | −0.430641 | − | 0.902523i | \(-0.641712\pi\) | ||||
−0.430641 | + | 0.902523i | \(0.641712\pi\) | |||||||
\(212\) | 8.25272 | − | 8.50189i | 0.566799 | − | 0.583912i | ||||
\(213\) | − | 6.38584i | − | 0.437551i | ||||||
\(214\) | 2.20102 | − | 0.930925i | 0.150459 | − | 0.0636367i | ||||
\(215\) | 28.0539i | 1.91326i | ||||||||
\(216\) | 8.47930 | + | 3.29265i | 0.576944 | + | 0.224036i | ||||
\(217\) | − | 14.5696i | − | 0.989052i | ||||||
\(218\) | −11.4993 | + | 4.86363i | −0.778829 | + | 0.329407i | ||||
\(219\) | 3.56975i | 0.241221i | ||||||||
\(220\) | 14.3693 | − | 16.4708i | 0.968780 | − | 1.11046i | ||||
\(221\) | 5.93424 | + | 3.96370i | 0.399180 | + | 0.266627i | ||||
\(222\) | 5.05433 | − | 2.13774i | 0.339224 | − | 0.143476i | ||||
\(223\) | −2.86548 | −0.191887 | −0.0959434 | − | 0.995387i | \(-0.530587\pi\) | ||||
−0.0959434 | + | 0.995387i | \(0.530587\pi\) | |||||||
\(224\) | 10.4003 | − | 4.76824i | 0.694901 | − | 0.318591i | ||||
\(225\) | −15.6964 | −1.04643 | ||||||||
\(226\) | 17.9138 | − | 7.57668i | 1.19161 | − | 0.503993i | ||||
\(227\) | 25.7142i | 1.70671i | 0.521331 | + | 0.853355i | \(0.325436\pi\) | ||||
−0.521331 | + | 0.853355i | \(0.674564\pi\) | |||||||
\(228\) | 2.12159 | − | 2.18565i | 0.140506 | − | 0.144748i | ||||
\(229\) | 21.1894i | 1.40023i | 0.714029 | + | 0.700116i | \(0.246868\pi\) | ||||
−0.714029 | + | 0.700116i | \(0.753132\pi\) | |||||||
\(230\) | 1.32583 | − | 0.560760i | 0.0874224 | − | 0.0369754i | ||||
\(231\) | 0.201851 | + | 3.79312i | 0.0132808 | + | 0.249569i | ||||
\(232\) | −12.8843 | − | 5.00317i | −0.845895 | − | 0.328474i | ||||
\(233\) | 13.0405i | 0.854311i | 0.904178 | + | 0.427156i | \(0.140484\pi\) | ||||
−0.904178 | + | 0.427156i | \(0.859516\pi\) | |||||||
\(234\) | −2.56340 | + | 13.4194i | −0.167575 | + | 0.877256i | ||||
\(235\) | 11.1828i | 0.729484i | ||||||||
\(236\) | −8.88596 | + | 9.15425i | −0.578427 | + | 0.595891i | ||||
\(237\) | − | 3.85142i | − | 0.250177i | ||||||
\(238\) | −5.21407 | + | 2.20530i | −0.337978 | + | 0.142948i | ||||
\(239\) | − | 10.9316i | − | 0.707106i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(240\) | −0.221945 | − | 7.46041i | −0.0143265 | − | 0.481567i | ||||
\(241\) | 3.82015 | 0.246078 | 0.123039 | − | 0.992402i | \(-0.460736\pi\) | ||||
0.123039 | + | 0.992402i | \(0.460736\pi\) | |||||||
\(242\) | 13.6035 | − | 7.54620i | 0.874465 | − | 0.485088i | ||||
\(243\) | − | 13.1684i | − | 0.844750i | ||||||
\(244\) | 14.4532 | + | 14.0297i | 0.925274 | + | 0.898157i | ||||
\(245\) | 9.58664i | 0.612468i | ||||||||
\(246\) | 1.09516 | + | 2.58932i | 0.0698245 | + | 0.165089i | ||||
\(247\) | 8.06406 | + | 5.38629i | 0.513104 | + | 0.342721i | ||||
\(248\) | −7.37533 | + | 18.9931i | −0.468334 | + | 1.20606i | ||||
\(249\) | −2.25880 | −0.143146 | ||||||||
\(250\) | 1.55804 | + | 3.68373i | 0.0985390 | + | 0.232979i | ||||
\(251\) | 21.9902i | 1.38801i | 0.719969 | + | 0.694006i | \(0.244156\pi\) | ||||
−0.719969 | + | 0.694006i | \(0.755844\pi\) | |||||||
\(252\) | −7.77692 | − | 7.54900i | −0.489900 | − | 0.475542i | ||||
\(253\) | 1.02308 | − | 0.0544432i | 0.0643205 | − | 0.00342281i | ||||
\(254\) | 7.93956 | − | 3.35805i | 0.498172 | − | 0.210703i | ||||
\(255\) | 3.69312i | 0.231272i | ||||||||
\(256\) | −15.9717 | + | 0.951150i | −0.998231 | + | 0.0594469i | ||||
\(257\) | −7.77431 | −0.484948 | −0.242474 | − | 0.970158i | \(-0.577959\pi\) | ||||
−0.242474 | + | 0.970158i | \(0.577959\pi\) | |||||||
\(258\) | 2.65580 | + | 6.27921i | 0.165343 | + | 0.390927i | ||||
\(259\) | −13.8602 | −0.861233 | ||||||||
\(260\) | 23.2330 | − | 4.98564i | 1.44085 | − | 0.309196i | ||||
\(261\) | 13.0931i | 0.810444i | ||||||||
\(262\) | 21.1440 | − | 8.94288i | 1.30628 | − | 0.552493i | ||||
\(263\) | −30.2037 | −1.86244 | −0.931219 | − | 0.364459i | \(-0.881254\pi\) | ||||
−0.931219 | + | 0.364459i | \(0.881254\pi\) | |||||||
\(264\) | 1.65699 | − | 5.04692i | 0.101981 | − | 0.310617i | ||||
\(265\) | 19.5217i | 1.19921i | ||||||||
\(266\) | −7.08542 | + | 2.99679i | −0.434435 | + | 0.183745i | ||||
\(267\) | 5.27709 | 0.322953 | ||||||||
\(268\) | −21.0948 | + | 21.7317i | −1.28857 | + | 1.32748i | ||||
\(269\) | 10.1042 | 0.616063 | 0.308031 | − | 0.951376i | \(-0.400330\pi\) | ||||
0.308031 | + | 0.951376i | \(0.400330\pi\) | |||||||
\(270\) | −13.8030 | + | 5.83798i | −0.840022 | + | 0.355288i | ||||
\(271\) | − | 10.2931i | − | 0.625262i | −0.949875 | − | 0.312631i | \(-0.898790\pi\) | ||
0.949875 | − | 0.312631i | \(-0.101210\pi\) | |||||||
\(272\) | 7.91346 | − | 0.235424i | 0.479824 | − | 0.0142746i | ||||
\(273\) | −2.29359 | + | 3.43384i | −0.138815 | + | 0.207826i | ||||
\(274\) | 8.03788 | + | 19.0043i | 0.485586 | + | 1.14809i | ||||
\(275\) | 1.03249 | + | 19.4023i | 0.0622616 | + | 1.17000i | ||||
\(276\) | 0.243670 | − | 0.251027i | 0.0146672 | − | 0.0151100i | ||||
\(277\) | − | 7.47366i | − | 0.449048i | −0.974469 | − | 0.224524i | \(-0.927917\pi\) | ||
0.974469 | − | 0.224524i | \(-0.0720828\pi\) | |||||||
\(278\) | 8.88794 | − | 3.75917i | 0.533063 | − | 0.225460i | ||||
\(279\) | 19.3010 | 1.15552 | ||||||||
\(280\) | −6.82358 | + | 17.5723i | −0.407787 | + | 1.05014i | ||||
\(281\) | 15.6582 | 0.934092 | 0.467046 | − | 0.884233i | \(-0.345318\pi\) | ||||
0.467046 | + | 0.884233i | \(0.345318\pi\) | |||||||
\(282\) | 1.05865 | + | 2.50301i | 0.0630418 | + | 0.149052i | ||||
\(283\) | 5.54393 | 0.329553 | 0.164776 | − | 0.986331i | \(-0.447310\pi\) | ||||
0.164776 | + | 0.986331i | \(0.447310\pi\) | |||||||
\(284\) | 15.7095 | − | 16.1838i | 0.932190 | − | 0.960335i | ||||
\(285\) | 5.01860i | 0.297276i | ||||||||
\(286\) | 16.7563 | + | 2.28589i | 0.990823 | + | 0.135168i | ||||
\(287\) | − | 7.10055i | − | 0.419132i | ||||||
\(288\) | 6.31667 | + | 13.7777i | 0.372213 | + | 0.811859i | ||||
\(289\) | 13.0826 | 0.769565 | ||||||||
\(290\) | 20.9736 | − | 8.87081i | 1.23161 | − | 0.520912i | ||||
\(291\) | −5.54154 | −0.324851 | ||||||||
\(292\) | −8.78179 | + | 9.04693i | −0.513915 | + | 0.529432i | ||||
\(293\) | 15.9521 | 0.931933 | 0.465966 | − | 0.884802i | \(-0.345707\pi\) | ||||
0.465966 | + | 0.884802i | \(0.345707\pi\) | |||||||
\(294\) | 0.907548 | + | 2.14575i | 0.0529293 | + | 0.125143i | ||||
\(295\) | − | 21.0196i | − | 1.22381i | ||||||
\(296\) | 18.0683 | + | 7.01621i | 1.05020 | + | 0.407809i | ||||
\(297\) | −10.6511 | + | 0.566800i | −0.618041 | + | 0.0328890i | ||||
\(298\) | 3.02764 | − | 1.28054i | 0.175386 | − | 0.0741799i | ||||
\(299\) | 0.926176 | + | 0.618628i | 0.0535622 | + | 0.0357762i | ||||
\(300\) | 4.76061 | + | 4.62109i | 0.274854 | + | 0.266799i | ||||
\(301\) | − | 17.2192i | − | 0.992495i | ||||||
\(302\) | −7.21961 | − | 17.0696i | −0.415442 | − | 0.982244i | ||||
\(303\) | −6.86099 | −0.394154 | ||||||||
\(304\) | 10.7536 | − | 0.319918i | 0.616763 | − | 0.0183485i | ||||
\(305\) | −33.1870 | −1.90028 | ||||||||
\(306\) | −2.92145 | − | 6.90728i | −0.167008 | − | 0.394863i | ||||
\(307\) | − | 16.7983i | − | 0.958732i | −0.877615 | − | 0.479366i | \(-0.840867\pi\) | ||
0.877615 | − | 0.479366i | \(-0.159133\pi\) | |||||||
\(308\) | −8.81974 | + | 10.1096i | −0.502551 | + | 0.576047i | ||||
\(309\) | 8.85288 | 0.503623 | ||||||||
\(310\) | −13.0767 | − | 30.9178i | −0.742708 | − | 1.75601i | ||||
\(311\) | − | 2.05498i | − | 0.116527i | −0.998301 | − | 0.0582637i | \(-0.981444\pi\) | ||
0.998301 | − | 0.0582637i | \(-0.0185564\pi\) | |||||||
\(312\) | 4.72820 | − | 3.31535i | 0.267682 | − | 0.187694i | ||||
\(313\) | −0.656102 | −0.0370851 | −0.0185425 | − | 0.999828i | \(-0.505903\pi\) | ||||
−0.0185425 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(314\) | 0.619995 | − | 0.262228i | 0.0349883 | − | 0.0147984i | ||||
\(315\) | 17.8571 | 1.00613 | ||||||||
\(316\) | 9.47472 | − | 9.76078i | 0.532994 | − | 0.549087i | ||||
\(317\) | 12.6773i | 0.712027i | 0.934481 | + | 0.356014i | \(0.115864\pi\) | ||||
−0.934481 | + | 0.356014i | \(0.884136\pi\) | |||||||
\(318\) | 1.84808 | + | 4.36949i | 0.103635 | + | 0.245029i | ||||
\(319\) | 16.1844 | − | 0.861251i | 0.906151 | − | 0.0482208i | ||||
\(320\) | 17.7906 | − | 19.4532i | 0.994523 | − | 1.08746i | ||||
\(321\) | 0.956885i | 0.0534081i | ||||||||
\(322\) | −0.813778 | + | 0.344189i | −0.0453501 | + | 0.0191809i | ||||
\(323\) | −5.32336 | −0.296200 | ||||||||
\(324\) | 8.66043 | − | 8.92191i | 0.481135 | − | 0.495662i | ||||
\(325\) | −11.7320 | + | 17.5645i | −0.650775 | + | 0.974305i | ||||
\(326\) | 25.2526 | − | 10.6806i | 1.39861 | − | 0.591545i | ||||
\(327\) | − | 4.99926i | − | 0.276460i | ||||||
\(328\) | −3.59438 | + | 9.25633i | −0.198466 | + | 0.511096i | ||||
\(329\) | − | 6.86387i | − | 0.378417i | ||||||
\(330\) | 3.83279 | + | 7.86809i | 0.210988 | + | 0.433124i | ||||
\(331\) | −19.2651 | −1.05891 | −0.529453 | − | 0.848339i | \(-0.677603\pi\) | ||||
−0.529453 | + | 0.848339i | \(0.677603\pi\) | |||||||
\(332\) | −5.72456 | − | 5.55679i | −0.314176 | − | 0.304968i | ||||
\(333\) | − | 18.3612i | − | 1.00619i | ||||||
\(334\) | 5.89510 | + | 13.9380i | 0.322566 | + | 0.762654i | ||||
\(335\) | − | 49.8996i | − | 2.72630i | ||||||
\(336\) | 0.136228 | + | 4.57912i | 0.00743183 | + | 0.249811i | ||||
\(337\) | − | 29.1905i | − | 1.59011i | −0.606538 | − | 0.795054i | \(-0.707442\pi\) | ||
0.606538 | − | 0.795054i | \(-0.292558\pi\) | |||||||
\(338\) | 13.1006 | + | 12.8986i | 0.712579 | + | 0.701592i | ||||
\(339\) | 7.78796i | 0.422984i | ||||||||
\(340\) | −9.08530 | + | 9.35960i | −0.492719 | + | 0.507596i | ||||
\(341\) | −1.26960 | − | 23.8579i | −0.0687525 | − | 1.29198i | ||||
\(342\) | −3.96996 | − | 9.38633i | −0.214671 | − | 0.507555i | ||||
\(343\) | − | 20.0420i | − | 1.08217i | ||||||
\(344\) | −8.71654 | + | 22.4470i | −0.469964 | + | 1.21026i | ||||
\(345\) | 0.576397i | 0.0310322i | ||||||||
\(346\) | 1.34055 | + | 3.16952i | 0.0720686 | + | 0.170394i | ||||
\(347\) | −33.2976 | −1.78751 | −0.893755 | − | 0.448555i | \(-0.851939\pi\) | ||||
−0.893755 | + | 0.448555i | \(0.851939\pi\) | |||||||
\(348\) | 3.85467 | − | 3.97105i | 0.206632 | − | 0.212871i | ||||
\(349\) | 33.9879 | 1.81933 | 0.909666 | − | 0.415340i | \(-0.136337\pi\) | ||||
0.909666 | + | 0.415340i | \(0.136337\pi\) | |||||||
\(350\) | −6.52738 | − | 15.4329i | −0.348903 | − | 0.824925i | ||||
\(351\) | −9.64228 | − | 6.44044i | −0.514667 | − | 0.343765i | ||||
\(352\) | 16.6151 | − | 8.71430i | 0.885587 | − | 0.464474i | ||||
\(353\) | 2.40079i | 0.127781i | 0.997957 | + | 0.0638905i | \(0.0203508\pi\) | ||||
−0.997957 | + | 0.0638905i | \(0.979649\pi\) | |||||||
\(354\) | −1.98989 | − | 4.70476i | −0.105761 | − | 0.250055i | ||||
\(355\) | 37.1607i | 1.97229i | ||||||||
\(356\) | 13.3739 | + | 12.9820i | 0.708816 | + | 0.688042i | ||||
\(357\) | − | 2.26680i | − | 0.119972i | ||||||
\(358\) | 12.5241 | + | 29.6111i | 0.661917 | + | 1.56499i | ||||
\(359\) | 6.66503i | 0.351767i | 0.984411 | + | 0.175884i | \(0.0562782\pi\) | ||||
−0.984411 | + | 0.175884i | \(0.943722\pi\) | |||||||
\(360\) | −23.2786 | − | 9.03946i | −1.22689 | − | 0.476421i | ||||
\(361\) | 11.7661 | 0.619267 | ||||||||
\(362\) | 7.65005 | − | 3.23560i | 0.402078 | − | 0.170059i | ||||
\(363\) | 0.661063 | + | 6.19366i | 0.0346968 | + | 0.325083i | ||||
\(364\) | −14.2602 | + | 3.06013i | −0.747437 | + | 0.160394i | ||||
\(365\) | − | 20.7732i | − | 1.08732i | ||||||
\(366\) | −7.42814 | + | 3.14174i | −0.388275 | + | 0.164222i | ||||
\(367\) | − | 20.5750i | − | 1.07401i | −0.843580 | − | 0.537003i | \(-0.819556\pi\) | ||
0.843580 | − | 0.537003i | \(-0.180444\pi\) | |||||||
\(368\) | 1.23508 | − | 0.0367433i | 0.0643830 | − | 0.00191538i | ||||
\(369\) | 9.40636 | 0.489676 | ||||||||
\(370\) | −29.4124 | + | 12.4400i | −1.52908 | + | 0.646725i | ||||
\(371\) | − | 11.9822i | − | 0.622086i | ||||||
\(372\) | −5.85385 | − | 5.68229i | −0.303508 | − | 0.294613i | ||||
\(373\) | 4.70653i | 0.243695i | 0.992549 | + | 0.121847i | \(0.0388819\pi\) | ||||
−0.992549 | + | 0.121847i | \(0.961118\pi\) | |||||||
\(374\) | −8.34590 | + | 4.06554i | −0.431556 | + | 0.210224i | ||||
\(375\) | −1.60149 | −0.0827004 | ||||||||
\(376\) | −3.47457 | + | 8.94780i | −0.179187 | + | 0.461448i | ||||
\(377\) | 14.6514 | + | 9.78624i | 0.754587 | + | 0.504017i | ||||
\(378\) | 8.47211 | − | 3.58329i | 0.435758 | − | 0.184305i | ||||
\(379\) | 0.898174 | 0.0461361 | 0.0230680 | − | 0.999734i | \(-0.492657\pi\) | ||||
0.0230680 | + | 0.999734i | \(0.492657\pi\) | |||||||
\(380\) | −12.3460 | + | 12.7188i | −0.633338 | + | 0.652460i | ||||
\(381\) | 3.45169i | 0.176836i | ||||||||
\(382\) | 7.99576 | + | 18.9047i | 0.409099 | + | 0.967247i | ||||
\(383\) | 6.62328 | 0.338434 | 0.169217 | − | 0.985579i | \(-0.445876\pi\) | ||||
0.169217 | + | 0.985579i | \(0.445876\pi\) | |||||||
\(384\) | 2.14042 | − | 6.03834i | 0.109228 | − | 0.308143i | ||||
\(385\) | −1.17462 | − | 22.0731i | −0.0598641 | − | 1.12495i | ||||
\(386\) | −22.8964 | + | 9.68406i | −1.16539 | + | 0.492906i | ||||
\(387\) | 22.8109 | 1.15954 | ||||||||
\(388\) | −14.0441 | − | 13.6325i | −0.712981 | − | 0.692085i | ||||
\(389\) | −25.4959 | −1.29269 | −0.646346 | − | 0.763044i | \(-0.723704\pi\) | ||||
−0.646346 | + | 0.763044i | \(0.723704\pi\) | |||||||
\(390\) | −1.78518 | + | 9.34543i | −0.0903959 | + | 0.473224i | ||||
\(391\) | −0.611401 | −0.0309199 | ||||||||
\(392\) | −2.97864 | + | 7.67066i | −0.150444 | + | 0.387427i | ||||
\(393\) | 9.19226i | 0.463688i | ||||||||
\(394\) | 25.0523 | − | 10.5959i | 1.26212 | − | 0.533815i | ||||
\(395\) | 22.4123i | 1.12769i | ||||||||
\(396\) | −13.3926 | − | 11.6838i | −0.673001 | − | 0.587135i | ||||
\(397\) | 7.89497i | 0.396237i | 0.980178 | + | 0.198119i | \(0.0634832\pi\) | ||||
−0.980178 | + | 0.198119i | \(0.936517\pi\) | |||||||
\(398\) | −2.16149 | − | 5.11049i | −0.108346 | − | 0.256166i | ||||
\(399\) | − | 3.08036i | − | 0.154211i | ||||||
\(400\) | 0.696821 | + | 23.4228i | 0.0348410 | + | 1.17114i | ||||
\(401\) | − | 22.6985i | − | 1.13351i | −0.823887 | − | 0.566754i | \(-0.808199\pi\) | ||
0.823887 | − | 0.566754i | \(-0.191801\pi\) | |||||||
\(402\) | −4.72389 | − | 11.1689i | −0.235606 | − | 0.557053i | ||||
\(403\) | 14.4262 | − | 21.5981i | 0.718619 | − | 1.07588i | ||||
\(404\) | −17.3880 | − | 16.8784i | −0.865088 | − | 0.839734i | ||||
\(405\) | 20.4861i | 1.01796i | ||||||||
\(406\) | −12.8734 | + | 5.44481i | −0.638894 | + | 0.270221i | ||||
\(407\) | −22.6962 | + | 1.20778i | −1.12501 | + | 0.0598673i | ||||
\(408\) | −1.14748 | + | 2.95502i | −0.0568087 | + | 0.146295i | ||||
\(409\) | −26.1421 | −1.29264 | −0.646321 | − | 0.763065i | \(-0.723693\pi\) | ||||
−0.646321 | + | 0.763065i | \(0.723693\pi\) | |||||||
\(410\) | −6.37297 | − | 15.0678i | −0.314738 | − | 0.744148i | ||||
\(411\) | −8.26202 | −0.407536 | ||||||||
\(412\) | 22.4362 | + | 21.7786i | 1.10535 | + | 1.07295i | ||||
\(413\) | 12.9016i | 0.634847i | ||||||||
\(414\) | −0.455960 | − | 1.07804i | −0.0224092 | − | 0.0529829i | ||||
\(415\) | 13.1445 | 0.645239 | ||||||||
\(416\) | 20.1388 | + | 3.22946i | 0.987385 | + | 0.158337i | ||||
\(417\) | 3.86400i | 0.189221i | ||||||||
\(418\) | −11.3413 | + | 5.52468i | −0.554720 | + | 0.270221i | ||||
\(419\) | 10.2084i | 0.498715i | 0.968411 | + | 0.249358i | \(0.0802195\pi\) | ||||
−0.968411 | + | 0.249358i | \(0.919781\pi\) | |||||||
\(420\) | −5.41593 | − | 5.25720i | −0.264270 | − | 0.256525i | ||||
\(421\) | − | 12.0697i | − | 0.588242i | −0.955768 | − | 0.294121i | \(-0.904973\pi\) | ||
0.955768 | − | 0.294121i | \(-0.0950269\pi\) | |||||||
\(422\) | 16.2954 | − | 6.89217i | 0.793248 | − | 0.335505i | ||||
\(423\) | 9.09283 | 0.442109 | ||||||||
\(424\) | −6.06554 | + | 15.6201i | −0.294569 | + | 0.758580i | ||||
\(425\) | − | 11.5949i | − | 0.562438i | ||||||
\(426\) | 3.51793 | + | 8.31758i | 0.170444 | + | 0.402988i | ||||
\(427\) | 20.3698 | 0.985764 | ||||||||
\(428\) | −2.35399 | + | 2.42506i | −0.113785 | + | 0.117220i | ||||
\(429\) | −3.45654 | + | 5.82280i | −0.166884 | + | 0.281127i | ||||
\(430\) | −15.4547 | − | 36.5402i | −0.745294 | − | 1.76213i | ||||
\(431\) | 23.2473i | 1.11978i | 0.828566 | + | 0.559892i | \(0.189157\pi\) | ||||
−0.828566 | + | 0.559892i | \(0.810843\pi\) | |||||||
\(432\) | −12.8582 | + | 0.382529i | −0.618642 | + | 0.0184044i | ||||
\(433\) | −24.0625 | −1.15637 | −0.578186 | − | 0.815905i | \(-0.696239\pi\) | ||||
−0.578186 | + | 0.815905i | \(0.696239\pi\) | |||||||
\(434\) | 8.02635 | + | 18.9770i | 0.385277 | + | 0.910925i | ||||
\(435\) | 9.11818i | 0.437183i | ||||||||
\(436\) | 12.2985 | − | 12.6698i | 0.588990 | − | 0.606773i | ||||
\(437\) | −0.830835 | −0.0397442 | ||||||||
\(438\) | −1.96656 | − | 4.64961i | −0.0939658 | − | 0.222167i | ||||
\(439\) | 14.5498 | 0.694426 | 0.347213 | − | 0.937786i | \(-0.387128\pi\) | ||||
0.347213 | + | 0.937786i | \(0.387128\pi\) | |||||||
\(440\) | −9.64240 | + | 29.3692i | −0.459684 | + | 1.40012i | ||||
\(441\) | 7.79499 | 0.371190 | ||||||||
\(442\) | −9.91295 | − | 1.89359i | −0.471511 | − | 0.0900687i | ||||
\(443\) | 31.6516i | 1.50381i | 0.659271 | + | 0.751905i | \(0.270865\pi\) | ||||
−0.659271 | + | 0.751905i | \(0.729135\pi\) | |||||||
\(444\) | −5.40561 | + | 5.56882i | −0.256539 | + | 0.264284i | ||||
\(445\) | −30.7087 | −1.45573 | ||||||||
\(446\) | 3.73230 | − | 1.57858i | 0.176729 | − | 0.0747480i | ||||
\(447\) | 1.31625i | 0.0622566i | ||||||||
\(448\) | −10.9197 | + | 11.9401i | −0.515905 | + | 0.564119i | ||||
\(449\) | 40.9503i | 1.93256i | 0.257489 | + | 0.966281i | \(0.417105\pi\) | ||||
−0.257489 | + | 0.966281i | \(0.582895\pi\) | |||||||
\(450\) | 20.4446 | − | 8.64707i | 0.963767 | − | 0.407627i | ||||
\(451\) | −0.618740 | − | 11.6272i | −0.0291353 | − | 0.547502i | ||||
\(452\) | −19.1588 | + | 19.7373i | −0.901156 | + | 0.928364i | ||||
\(453\) | 7.42093 | 0.348666 | ||||||||
\(454\) | −14.1658 | − | 33.4928i | −0.664835 | − | 1.57189i | ||||
\(455\) | 13.3470 | − | 19.9824i | 0.625715 | − | 0.936787i | ||||
\(456\) | −1.55931 | + | 4.01558i | −0.0730216 | + | 0.188047i | ||||
\(457\) | −1.93438 | −0.0904867 | −0.0452434 | − | 0.998976i | \(-0.514406\pi\) | ||||
−0.0452434 | + | 0.998976i | \(0.514406\pi\) | |||||||
\(458\) | −11.6731 | − | 27.5992i | −0.545449 | − | 1.28963i | ||||
\(459\) | 6.36520 | 0.297102 | ||||||||
\(460\) | −1.41797 | + | 1.46078i | −0.0661133 | + | 0.0681094i | ||||
\(461\) | −29.1988 | −1.35992 | −0.679962 | − | 0.733247i | \(-0.738004\pi\) | ||||
−0.679962 | + | 0.733247i | \(0.738004\pi\) | |||||||
\(462\) | −2.35252 | − | 4.82935i | −0.109449 | − | 0.224682i | ||||
\(463\) | 6.18860 | 0.287609 | 0.143804 | − | 0.989606i | \(-0.454066\pi\) | ||||
0.143804 | + | 0.989606i | \(0.454066\pi\) | |||||||
\(464\) | 19.5381 | − | 0.581252i | 0.907031 | − | 0.0269840i | ||||
\(465\) | 13.4414 | 0.623329 | ||||||||
\(466\) | −7.18395 | − | 16.9853i | −0.332790 | − | 0.786828i | ||||
\(467\) | 36.0734i | 1.66928i | 0.550798 | + | 0.834639i | \(0.314323\pi\) | ||||
−0.550798 | + | 0.834639i | \(0.685677\pi\) | |||||||
\(468\) | −4.05387 | − | 18.8910i | −0.187390 | − | 0.873237i | ||||
\(469\) | 30.6278i | 1.41426i | ||||||||
\(470\) | −6.16055 | − | 14.5656i | −0.284165 | − | 0.671861i | ||||
\(471\) | 0.269540i | 0.0124198i | ||||||||
\(472\) | 6.53095 | − | 16.8187i | 0.300612 | − | 0.774142i | ||||
\(473\) | −1.50047 | − | 28.1964i | −0.0689919 | − | 1.29647i | ||||
\(474\) | 2.12173 | + | 5.01648i | 0.0974543 | + | 0.230415i | ||||
\(475\) | − | 15.7564i | − | 0.722954i | ||||||
\(476\) | 5.57646 | − | 5.74482i | 0.255596 | − | 0.263313i | ||||
\(477\) | 15.8733 | 0.726788 | ||||||||
\(478\) | 6.02217 | + | 14.2384i | 0.275448 | + | 0.651251i | ||||
\(479\) | 8.54198i | 0.390293i | 0.980774 | + | 0.195146i | \(0.0625182\pi\) | ||||
−0.980774 | + | 0.195146i | \(0.937482\pi\) | |||||||
\(480\) | 4.39899 | + | 9.59494i | 0.200786 | + | 0.437947i | ||||
\(481\) | −20.5465 | − | 13.7238i | −0.936838 | − | 0.625749i | ||||
\(482\) | −4.97576 | + | 2.10450i | −0.226640 | + | 0.0958575i | ||||
\(483\) | − | 0.353787i | − | 0.0160978i | ||||||
\(484\) | −13.5614 | + | 17.3231i | −0.616428 | + | 0.787411i | ||||
\(485\) | 32.2475 | 1.46428 | ||||||||
\(486\) | 7.25439 | + | 17.1518i | 0.329066 | + | 0.778022i | ||||
\(487\) | −34.2160 | −1.55048 | −0.775238 | − | 0.631669i | \(-0.782370\pi\) | ||||
−0.775238 | + | 0.631669i | \(0.782370\pi\) | |||||||
\(488\) | −26.5543 | − | 10.3114i | −1.20206 | − | 0.466777i | ||||
\(489\) | 10.9785i | 0.496464i | ||||||||
\(490\) | −5.28124 | − | 12.4866i | −0.238582 | − | 0.564088i | ||||
\(491\) | −29.8149 | −1.34553 | −0.672764 | − | 0.739857i | \(-0.734893\pi\) | ||||
−0.672764 | + | 0.739857i | \(0.734893\pi\) | |||||||
\(492\) | −2.85289 | − | 2.76927i | −0.128618 | − | 0.124849i | ||||
\(493\) | −9.67191 | −0.435601 | ||||||||
\(494\) | −13.4707 | − | 2.57320i | −0.606077 | − | 0.115774i | ||||
\(495\) | 29.2410 | − | 1.55606i | 1.31429 | − | 0.0699397i | ||||
\(496\) | −0.856841 | − | 28.8016i | −0.0384733 | − | 1.29323i | ||||
\(497\) | − | 22.8089i | − | 1.02312i | ||||||
\(498\) | 2.94210 | − | 1.24436i | 0.131839 | − | 0.0557613i | ||||
\(499\) | −7.20650 | −0.322607 | −0.161304 | − | 0.986905i | \(-0.551570\pi\) | ||||
−0.161304 | + | 0.986905i | \(0.551570\pi\) | |||||||
\(500\) | −4.05870 | − | 3.93975i | −0.181510 | − | 0.176191i | ||||
\(501\) | −6.05949 | −0.270718 | ||||||||
\(502\) | −12.1143 | − | 28.6424i | −0.540689 | − | 1.27837i | ||||
\(503\) | 31.0775 | 1.38568 | 0.692839 | − | 0.721093i | \(-0.256360\pi\) | ||||
0.692839 | + | 0.721093i | \(0.256360\pi\) | |||||||
\(504\) | 14.2882 | + | 5.54832i | 0.636446 | + | 0.247142i | ||||
\(505\) | 39.9258 | 1.77667 | ||||||||
\(506\) | −1.30257 | + | 0.634523i | −0.0579064 | + | 0.0282080i | ||||
\(507\) | −6.80006 | + | 2.81934i | −0.302001 | + | 0.125211i | ||||
\(508\) | −8.49136 | + | 8.74774i | −0.376743 | + | 0.388118i | ||||
\(509\) | 3.26699i | 0.144807i | 0.997375 | + | 0.0724033i | \(0.0230669\pi\) | ||||
−0.997375 | + | 0.0724033i | \(0.976933\pi\) | |||||||
\(510\) | −2.03452 | − | 4.81030i | −0.0900903 | − | 0.213004i | ||||
\(511\) | 12.7504i | 0.564043i | ||||||||
\(512\) | 20.2792 | − | 10.0376i | 0.896223 | − | 0.443604i | ||||
\(513\) | 8.64969 | 0.381893 | ||||||||
\(514\) | 10.1261 | − | 4.28283i | 0.446641 | − | 0.188908i | ||||
\(515\) | −51.5170 | −2.27011 | ||||||||
\(516\) | −6.91838 | − | 6.71562i | −0.304565 | − | 0.295639i | ||||
\(517\) | −0.598116 | − | 11.2396i | −0.0263051 | − | 0.494318i | ||||
\(518\) | 18.0530 | − | 7.63554i | 0.793203 | − | 0.335486i | ||||
\(519\) | −1.37794 | −0.0604847 | ||||||||
\(520\) | −27.5145 | + | 19.2928i | −1.20659 | + | 0.846045i | ||||
\(521\) | −35.9580 | −1.57535 | −0.787675 | − | 0.616091i | \(-0.788715\pi\) | ||||
−0.787675 | + | 0.616091i | \(0.788715\pi\) | |||||||
\(522\) | −7.21294 | − | 17.0538i | −0.315702 | − | 0.746426i | ||||
\(523\) | 37.7227 | 1.64950 | 0.824749 | − | 0.565499i | \(-0.191316\pi\) | ||||
0.824749 | + | 0.565499i | \(0.191316\pi\) | |||||||
\(524\) | −22.6135 | + | 23.2962i | −0.987875 | + | 1.01770i | ||||
\(525\) | 6.70941 | 0.292823 | ||||||||
\(526\) | 39.3404 | − | 16.6391i | 1.71532 | − | 0.725498i | ||||
\(527\) | 14.2576i | 0.621073i | ||||||||
\(528\) | 0.622097 | + | 7.48646i | 0.0270733 | + | 0.325806i | ||||
\(529\) | 22.9046 | 0.995851 | ||||||||
\(530\) | −10.7544 | − | 25.4271i | −0.467142 | − | 1.10448i | ||||
\(531\) | −17.0913 | −0.741698 | ||||||||
\(532\) | 7.57787 | − | 7.80666i | 0.328542 | − | 0.338462i | ||||
\(533\) | 7.03063 | − | 10.5259i | 0.304530 | − | 0.455926i | ||||
\(534\) | −6.87343 | + | 2.90713i | −0.297442 | + | 0.125804i | ||||
\(535\) | − | 5.56834i | − | 0.240740i | ||||||
\(536\) | 15.5042 | − | 39.9267i | 0.669678 | − | 1.72457i | ||||
\(537\) | −12.8733 | −0.555524 | ||||||||
\(538\) | −13.1607 | + | 5.56635i | −0.567399 | + | 0.239982i | ||||
\(539\) | −0.512746 | − | 9.63536i | −0.0220855 | − | 0.415024i | ||||
\(540\) | 14.7623 | − | 15.2080i | 0.635267 | − | 0.654447i | ||||
\(541\) | 23.5890 | 1.01417 | 0.507085 | − | 0.861896i | \(-0.330723\pi\) | ||||
0.507085 | + | 0.861896i | \(0.330723\pi\) | |||||||
\(542\) | 5.67043 | + | 13.4068i | 0.243566 | + | 0.575871i | ||||
\(543\) | 3.32583i | 0.142725i | ||||||||
\(544\) | −10.1776 | + | 4.66613i | −0.436362 | + | 0.200059i | ||||
\(545\) | 29.0919i | 1.24616i | ||||||||
\(546\) | 1.09572 | − | 5.73612i | 0.0468926 | − | 0.245483i | ||||
\(547\) | −7.67744 | −0.328264 | −0.164132 | − | 0.986438i | \(-0.552482\pi\) | ||||
−0.164132 | + | 0.986438i | \(0.552482\pi\) | |||||||
\(548\) | −20.9387 | − | 20.3251i | −0.894458 | − | 0.868244i | ||||
\(549\) | 26.9847i | 1.15168i | ||||||||
\(550\) | −12.0334 | − | 24.7027i | −0.513108 | − | 1.05333i | ||||
\(551\) | −13.1432 | −0.559919 | ||||||||
\(552\) | −0.179091 | + | 0.461199i | −0.00762262 | + | 0.0196299i | ||||
\(553\) | − | 13.7564i | − | 0.584983i | ||||||
\(554\) | 4.11720 | + | 9.73446i | 0.174923 | + | 0.413577i | ||||
\(555\) | − | 12.7869i | − | 0.542774i | ||||||
\(556\) | −9.50566 | + | 9.79265i | −0.403130 | + | 0.415301i | ||||
\(557\) | −32.6865 | −1.38497 | −0.692487 | − | 0.721431i | \(-0.743485\pi\) | ||||
−0.692487 | + | 0.721431i | \(0.743485\pi\) | |||||||
\(558\) | −25.1396 | + | 10.6328i | −1.06424 | + | 0.450123i | ||||
\(559\) | 17.0496 | − | 25.5257i | 0.721121 | − | 1.07962i | ||||
\(560\) | −0.792741 | − | 26.6470i | −0.0334994 | − | 1.12604i | ||||
\(561\) | −0.197528 | − | 3.71189i | −0.00833965 | − | 0.156716i | ||||
\(562\) | −20.3949 | + | 8.62605i | −0.860307 | + | 0.363868i | ||||
\(563\) | 33.1892 | 1.39876 | 0.699379 | − | 0.714751i | \(-0.253460\pi\) | ||||
0.699379 | + | 0.714751i | \(0.253460\pi\) | |||||||
\(564\) | −2.75779 | − | 2.67697i | −0.116124 | − | 0.112721i | ||||
\(565\) | − | 45.3200i | − | 1.90663i | ||||||
\(566\) | −7.22099 | + | 3.05413i | −0.303521 | + | 0.128375i | ||||
\(567\) | − | 12.5742i | − | 0.528066i | ||||||
\(568\) | −11.5461 | + | 29.7338i | −0.484464 | + | 1.24760i | ||||
\(569\) | − | 0.0743011i | − | 0.00311487i | −0.999999 | − | 0.00155743i | \(-0.999504\pi\) | ||
0.999999 | − | 0.00155743i | \(-0.000495746\pi\) | |||||||
\(570\) | −2.76472 | − | 6.53673i | −0.115801 | − | 0.273794i | ||||
\(571\) | −13.0501 | −0.546130 | −0.273065 | − | 0.961996i | \(-0.588037\pi\) | ||||
−0.273065 | + | 0.961996i | \(0.588037\pi\) | |||||||
\(572\) | −23.0845 | + | 6.25361i | −0.965210 | + | 0.261476i | ||||
\(573\) | −8.21873 | −0.343342 | ||||||||
\(574\) | 3.91166 | + | 9.24848i | 0.163270 | + | 0.386024i | ||||
\(575\) | − | 1.80966i | − | 0.0754681i | ||||||
\(576\) | −15.8176 | − | 14.4657i | −0.659065 | − | 0.602737i | ||||
\(577\) | − | 10.3102i | − | 0.429220i | −0.976700 | − | 0.214610i | \(-0.931152\pi\) | ||
0.976700 | − | 0.214610i | \(-0.0688481\pi\) | |||||||
\(578\) | −17.0401 | + | 7.20715i | −0.708776 | + | 0.299778i | ||||
\(579\) | − | 9.95411i | − | 0.413679i | ||||||
\(580\) | −22.4313 | + | 23.1085i | −0.931408 | + | 0.959529i | ||||
\(581\) | −8.06796 | −0.334715 | ||||||||
\(582\) | 7.21787 | − | 3.05281i | 0.299190 | − | 0.126543i | ||||
\(583\) | −1.04413 | − | 19.6209i | −0.0432434 | − | 0.812616i | ||||
\(584\) | 6.45439 | − | 16.6215i | 0.267085 | − | 0.687803i | ||||
\(585\) | 26.4714 | + | 17.6812i | 1.09446 | + | 0.731029i | ||||
\(586\) | −20.7777 | + | 8.78795i | −0.858318 | + | 0.363027i | ||||
\(587\) | 21.1204 | 0.871731 | 0.435865 | − | 0.900012i | \(-0.356442\pi\) | ||||
0.435865 | + | 0.900012i | \(0.356442\pi\) | |||||||
\(588\) | −2.36417 | − | 2.29488i | −0.0974966 | − | 0.0946393i | ||||
\(589\) | 19.3748i | 0.798323i | ||||||||
\(590\) | 11.5796 | + | 27.3781i | 0.476725 | + | 1.12714i | ||||
\(591\) | 10.8914i | 0.448013i | ||||||||
\(592\) | −27.3992 | + | 0.815120i | −1.12610 | + | 0.0335012i | ||||
\(593\) | 8.87584 | 0.364487 | 0.182243 | − | 0.983253i | \(-0.441664\pi\) | ||||
0.182243 | + | 0.983253i | \(0.441664\pi\) | |||||||
\(594\) | 13.5609 | − | 6.60592i | 0.556409 | − | 0.271044i | ||||
\(595\) | 13.1910i | 0.540780i | ||||||||
\(596\) | −3.23806 | + | 3.33582i | −0.132636 | + | 0.136641i | ||||
\(597\) | 2.22176 | 0.0909308 | ||||||||
\(598\) | −1.54715 | − | 0.295538i | −0.0632675 | − | 0.0120855i | ||||
\(599\) | 29.4065i | 1.20152i | 0.799430 | + | 0.600759i | \(0.205135\pi\) | ||||
−0.799430 | + | 0.600759i | \(0.794865\pi\) | |||||||
\(600\) | −8.74644 | − | 3.39638i | −0.357072 | − | 0.138657i | ||||
\(601\) | 43.4130i | 1.77085i | 0.464780 | + | 0.885426i | \(0.346133\pi\) | ||||
−0.464780 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(602\) | 9.48596 | + | 22.4280i | 0.386619 | + | 0.914097i | ||||
\(603\) | −40.5738 | −1.65229 | ||||||||
\(604\) | 18.8071 | + | 18.2559i | 0.765251 | + | 0.742823i | ||||
\(605\) | −3.84688 | − | 36.0424i | −0.156398 | − | 1.46533i | ||||
\(606\) | 8.93646 | − | 3.77969i | 0.363019 | − | 0.153539i | ||||
\(607\) | 12.7943 | 0.519305 | 0.259652 | − | 0.965702i | \(-0.416392\pi\) | ||||
0.259652 | + | 0.965702i | \(0.416392\pi\) | |||||||
\(608\) | −13.8304 | + | 6.34082i | −0.560897 | + | 0.257154i | ||||
\(609\) | − | 5.59664i | − | 0.226787i | ||||||
\(610\) | 43.2261 | − | 18.2826i | 1.75017 | − | 0.740239i | ||||
\(611\) | 6.79629 | − | 10.1750i | 0.274948 | − | 0.411638i | ||||
\(612\) | 7.61038 | + | 7.38734i | 0.307632 | + | 0.298616i | ||||
\(613\) | 31.6996 | 1.28033 | 0.640167 | − | 0.768236i | \(-0.278865\pi\) | ||||
0.640167 | + | 0.768236i | \(0.278865\pi\) | |||||||
\(614\) | 9.25413 | + | 21.8799i | 0.373466 | + | 0.883000i | ||||
\(615\) | 6.55069 | 0.264149 | ||||||||
\(616\) | 5.91840 | − | 18.0265i | 0.238459 | − | 0.726309i | ||||
\(617\) | 18.5466i | 0.746659i | 0.927699 | + | 0.373329i | \(0.121784\pi\) | ||||
−0.927699 | + | 0.373329i | \(0.878216\pi\) | |||||||
\(618\) | −11.5309 | + | 4.87701i | −0.463841 | + | 0.196182i | ||||
\(619\) | 28.9557 | 1.16383 | 0.581914 | − | 0.813250i | \(-0.302304\pi\) | ||||
0.581914 | + | 0.813250i | \(0.302304\pi\) | |||||||
\(620\) | 34.0649 | + | 33.0666i | 1.36808 | + | 1.32799i | ||||
\(621\) | 0.993437 | 0.0398653 | ||||||||
\(622\) | 1.13208 | + | 2.67662i | 0.0453923 | + | 0.107323i | ||||
\(623\) | 18.8486 | 0.755155 | ||||||||
\(624\) | −4.33209 | + | 6.92299i | −0.173422 | + | 0.277142i | ||||
\(625\) | −19.9720 | −0.798879 | ||||||||
\(626\) | 0.854574 | − | 0.361444i | 0.0341557 | − | 0.0144462i | ||||
\(627\) | −0.268422 | − | 5.04410i | −0.0107197 | − | 0.201442i | ||||
\(628\) | −0.663085 | + | 0.683105i | −0.0264600 | + | 0.0272588i | ||||
\(629\) | 13.5634 | 0.540809 | ||||||||
\(630\) | −23.2589 | + | 9.83738i | −0.926656 | + | 0.391931i | ||||
\(631\) | 8.22541 | 0.327448 | 0.163724 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163724 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(632\) | −6.96368 | + | 17.9330i | −0.277000 | + | 0.713337i | ||||
\(633\) | 7.08436i | 0.281578i | ||||||||
\(634\) | −6.98386 | − | 16.5122i | −0.277365 | − | 0.655783i | ||||
\(635\) | − | 20.0862i | − | 0.797097i | ||||||
\(636\) | −4.81426 | − | 4.67317i | −0.190898 | − | 0.185303i | ||||
\(637\) | 5.82624 | − | 8.72273i | 0.230844 | − | 0.345607i | ||||
\(638\) | −20.6057 | + | 10.0377i | −0.815789 | + | 0.397396i | ||||
\(639\) | 30.2158 | 1.19532 | ||||||||
\(640\) | −12.4556 | + | 35.1385i | −0.492351 | + | 1.38897i | ||||
\(641\) | −9.12648 | −0.360474 | −0.180237 | − | 0.983623i | \(-0.557687\pi\) | ||||
−0.180237 | + | 0.983623i | \(0.557687\pi\) | |||||||
\(642\) | −0.527144 | − | 1.24635i | −0.0208047 | − | 0.0491893i | ||||
\(643\) | −34.7576 | −1.37071 | −0.685353 | − | 0.728211i | \(-0.740352\pi\) | ||||
−0.685353 | + | 0.728211i | \(0.740352\pi\) | |||||||
\(644\) | 0.870336 | − | 0.896613i | 0.0342960 | − | 0.0353315i | ||||
\(645\) | 15.8857 | 0.625500 | ||||||||
\(646\) | 6.93370 | − | 2.93262i | 0.272803 | − | 0.115382i | ||||
\(647\) | − | 6.29445i | − | 0.247461i | −0.992316 | − | 0.123730i | \(-0.960514\pi\) | ||
0.992316 | − | 0.123730i | \(-0.0394858\pi\) | |||||||
\(648\) | −6.36520 | + | 16.3918i | −0.250049 | + | 0.643931i | ||||
\(649\) | 1.12424 | + | 21.1265i | 0.0441305 | + | 0.829286i | ||||
\(650\) | 5.60475 | − | 29.3410i | 0.219836 | − | 1.15085i | ||||
\(651\) | −8.25018 | −0.323350 | ||||||||
\(652\) | −27.0077 | + | 27.8231i | −1.05770 | + | 1.08964i | ||||
\(653\) | −32.3299 | −1.26517 | −0.632584 | − | 0.774492i | \(-0.718005\pi\) | ||||
−0.632584 | + | 0.774492i | \(0.718005\pi\) | |||||||
\(654\) | 2.75407 | + | 6.51155i | 0.107693 | + | 0.254622i | ||||
\(655\) | − | 53.4919i | − | 2.09010i | ||||||
\(656\) | −0.417583 | − | 14.0365i | −0.0163039 | − | 0.548034i | ||||
\(657\) | −16.8909 | −0.658977 | ||||||||
\(658\) | 3.78128 | + | 8.94021i | 0.147410 | + | 0.348526i | ||||
\(659\) | 1.75900 | 0.0685210 | 0.0342605 | − | 0.999413i | \(-0.489092\pi\) | ||||
0.0342605 | + | 0.999413i | \(0.489092\pi\) | |||||||
\(660\) | −9.32671 | − | 8.13674i | −0.363042 | − | 0.316722i | ||||
\(661\) | 28.7803i | 1.11942i | 0.828688 | + | 0.559712i | \(0.189088\pi\) | ||||
−0.828688 | + | 0.559712i | \(0.810912\pi\) | |||||||
\(662\) | 25.0929 | − | 10.6131i | 0.975262 | − | 0.412488i | ||||
\(663\) | 2.24448 | − | 3.36031i | 0.0871683 | − | 0.130504i | ||||
\(664\) | 10.5175 | + | 4.08410i | 0.408157 | + | 0.158494i | ||||
\(665\) | 17.9253i | 0.695115i | ||||||||
\(666\) | 10.1151 | + | 23.9155i | 0.391952 | + | 0.926706i | ||||
\(667\) | −1.50953 | −0.0584491 | ||||||||
\(668\) | −15.3568 | − | 14.9067i | −0.594171 | − | 0.576758i | ||||
\(669\) | 1.62260i | 0.0627334i | ||||||||
\(670\) | 27.4895 | + | 64.9943i | 1.06201 | + | 2.51095i | ||||
\(671\) | 33.3557 | − | 1.77502i | 1.28768 | − | 0.0685239i | ||||
\(672\) | −2.70005 | − | 5.88927i | −0.104157 | − | 0.227184i | ||||
\(673\) | 12.9869i | 0.500610i | 0.968167 | + | 0.250305i | \(0.0805309\pi\) | ||||
−0.968167 | + | 0.250305i | \(0.919469\pi\) | |||||||
\(674\) | 16.0809 | + | 38.0207i | 0.619414 | + | 1.46450i | ||||
\(675\) | 18.8401i | 0.725156i | ||||||||
\(676\) | −24.1694 | − | 9.58342i | −0.929591 | − | 0.368593i | ||||
\(677\) | − | 28.3135i | − | 1.08818i | −0.839028 | − | 0.544088i | \(-0.816876\pi\) | ||
0.839028 | − | 0.544088i | \(-0.183124\pi\) | |||||||
\(678\) | −4.29036 | − | 10.1438i | −0.164770 | − | 0.389572i | ||||
\(679\) | −19.7932 | −0.759592 | ||||||||
\(680\) | 6.67746 | − | 17.1960i | 0.256069 | − | 0.659435i | ||||
\(681\) | 14.5609 | 0.557973 | ||||||||
\(682\) | 14.7968 | + | 30.3755i | 0.566600 | + | 1.16314i | ||||
\(683\) | 36.1620 | 1.38370 | 0.691850 | − | 0.722041i | \(-0.256796\pi\) | ||||
0.691850 | + | 0.722041i | \(0.256796\pi\) | |||||||
\(684\) | 10.3418 | + | 10.0387i | 0.395428 | + | 0.383839i | ||||
\(685\) | 48.0787 | 1.83699 | ||||||||
\(686\) | 11.0411 | + | 26.1048i | 0.421550 | + | 0.996687i | ||||
\(687\) | 11.9986 | 0.457777 | ||||||||
\(688\) | −1.01266 | − | 34.0392i | −0.0386073 | − | 1.29773i | ||||
\(689\) | 11.8642 | − | 17.7625i | 0.451991 | − | 0.676697i | ||||
\(690\) | −0.317535 | − | 0.750759i | −0.0120883 | − | 0.0285809i | ||||
\(691\) | −20.2513 | −0.770394 | −0.385197 | − | 0.922834i | \(-0.625867\pi\) | ||||
−0.385197 | + | 0.922834i | \(0.625867\pi\) | |||||||
\(692\) | −3.49215 | − | 3.38980i | −0.132752 | − | 0.128861i | ||||
\(693\) | −17.9478 | + | 0.955094i | −0.681781 | + | 0.0362810i | ||||
\(694\) | 43.3703 | − | 18.3435i | 1.64631 | − | 0.696311i | ||||
\(695\) | − | 22.4855i | − | 0.852924i | ||||||
\(696\) | −2.83309 | + | 7.29583i | −0.107388 | + | 0.276548i | ||||
\(697\) | 6.94849i | 0.263193i | ||||||||
\(698\) | −44.2694 | + | 18.7238i | −1.67562 | + | 0.708707i | ||||
\(699\) | 7.38429 | 0.279299 | ||||||||
\(700\) | 17.0039 | + | 16.5055i | 0.642686 | + | 0.623851i | ||||
\(701\) | − | 29.5458i | − | 1.11593i | −0.829865 | − | 0.557965i | \(-0.811582\pi\) | ||
0.829865 | − | 0.557965i | \(-0.188418\pi\) | |||||||
\(702\) | 16.1071 | + | 3.07680i | 0.607923 | + | 0.116126i | ||||
\(703\) | 18.4314 | 0.695153 | ||||||||
\(704\) | −16.8405 | + | 20.5036i | −0.634701 | + | 0.772758i | ||||
\(705\) | 6.33234 | 0.238490 | ||||||||
\(706\) | −1.32258 | − | 3.12703i | −0.0497761 | − | 0.117687i | ||||
\(707\) | −24.5060 | −0.921643 | ||||||||
\(708\) | 5.18366 | + | 5.03175i | 0.194814 | + | 0.189105i | ||||
\(709\) | 17.9628i | 0.674605i | 0.941396 | + | 0.337303i | \(0.109515\pi\) | ||||
−0.941396 | + | 0.337303i | \(0.890485\pi\) | |||||||
\(710\) | −20.4717 | − | 48.4020i | −0.768289 | − | 1.81649i | ||||
\(711\) | 18.2237 | 0.683441 | ||||||||
\(712\) | −24.5713 | − | 9.54141i | −0.920847 | − | 0.357579i | ||||
\(713\) | 2.22524i | 0.0833358i | ||||||||
\(714\) | 1.24877 | + | 2.95251i | 0.0467340 | + | 0.110495i | ||||
\(715\) | 20.1145 | − | 33.8843i | 0.752238 | − | 1.26720i | ||||
\(716\) | −32.6252 | − | 31.6691i | −1.21926 | − | 1.18353i | ||||
\(717\) | −6.19011 | −0.231174 | ||||||||
\(718\) | −3.67174 | − | 8.68123i | −0.137028 | − | 0.323981i | ||||
\(719\) | − | 31.1311i | − | 1.16099i | −0.814262 | − | 0.580497i | \(-0.802858\pi\) | ||
0.814262 | − | 0.580497i | \(-0.197142\pi\) | |||||||
\(720\) | 35.3003 | − | 1.05017i | 1.31556 | − | 0.0391377i | ||||
\(721\) | 31.6206 | 1.17761 | ||||||||
\(722\) | −15.3253 | + | 6.48187i | −0.570350 | + | 0.241230i | ||||
\(723\) | − | 2.16319i | − | 0.0804499i | ||||||
\(724\) | −8.18174 | + | 8.42876i | −0.304072 | + | 0.313253i | ||||
\(725\) | − | 28.6275i | − | 1.06320i | ||||||
\(726\) | −4.27310 | − | 7.70308i | −0.158590 | − | 0.285888i | ||||
\(727\) | 43.4457i | 1.61131i | 0.592385 | + | 0.805655i | \(0.298186\pi\) | ||||
−0.592385 | + | 0.805655i | \(0.701814\pi\) | |||||||
\(728\) | 16.8881 | − | 11.8417i | 0.625916 | − | 0.438883i | ||||
\(729\) | 11.1943 | 0.414602 | ||||||||
\(730\) | 11.4439 | + | 27.0572i | 0.423557 | + | 1.00143i | ||||
\(731\) | 16.8504i | 0.623235i | ||||||||
\(732\) | 7.94440 | − | 8.18426i | 0.293634 | − | 0.302499i | ||||
\(733\) | −34.3465 | −1.26862 | −0.634308 | − | 0.773081i | \(-0.718715\pi\) | ||||
−0.634308 | + | 0.773081i | \(0.718715\pi\) | |||||||
\(734\) | 11.3347 | + | 26.7990i | 0.418370 | + | 0.989169i | ||||
\(735\) | 5.42851 | 0.200234 | ||||||||
\(736\) | −1.58845 | + | 0.728259i | −0.0585512 | + | 0.0268440i | ||||
\(737\) | 2.66890 | + | 50.1532i | 0.0983103 | + | 1.84742i | ||||
\(738\) | −12.2518 | + | 5.18192i | −0.450995 | + | 0.190749i | ||||
\(739\) | − | 11.9060i | − | 0.437971i | −0.975728 | − | 0.218985i | \(-0.929725\pi\) | ||
0.975728 | − | 0.218985i | \(-0.0702747\pi\) | |||||||
\(740\) | 31.4565 | − | 32.4063i | 1.15637 | − | 1.19128i | ||||
\(741\) | 3.05003 | − | 4.56634i | 0.112046 | − | 0.167749i | ||||
\(742\) | 6.60095 | + | 15.6069i | 0.242329 | + | 0.572946i | ||||
\(743\) | − | 14.5869i | − | 0.535140i | −0.963538 | − | 0.267570i | \(-0.913779\pi\) | ||
0.963538 | − | 0.267570i | \(-0.0862207\pi\) | |||||||
\(744\) | 10.7550 | + | 4.17634i | 0.394298 | + | 0.153112i | ||||
\(745\) | − | 7.65959i | − | 0.280626i | ||||||
\(746\) | −2.59281 | − | 6.13027i | −0.0949294 | − | 0.224445i | ||||
\(747\) | − | 10.6879i | − | 0.391051i | ||||||
\(748\) | 8.63087 | − | 9.89310i | 0.315576 | − | 0.361728i | ||||
\(749\) | 3.41779i | 0.124883i | ||||||||
\(750\) | 2.08594 | − | 0.882251i | 0.0761677 | − | 0.0322153i | ||||
\(751\) | − | 12.0462i | − | 0.439570i | −0.975548 | − | 0.219785i | \(-0.929464\pi\) | ||
0.975548 | − | 0.219785i | \(-0.0705357\pi\) | |||||||
\(752\) | −0.403664 | − | 13.5687i | −0.0147201 | − | 0.494798i | ||||
\(753\) | 12.4522 | 0.453782 | ||||||||
\(754\) | −24.4747 | − | 4.67520i | −0.891317 | − | 0.170261i | ||||
\(755\) | −43.1842 | −1.57163 | ||||||||
\(756\) | −9.06093 | + | 9.33450i | −0.329543 | + | 0.339492i | ||||
\(757\) | −5.92237 | −0.215252 | −0.107626 | − | 0.994191i | \(-0.534325\pi\) | ||||
−0.107626 | + | 0.994191i | \(0.534325\pi\) | |||||||
\(758\) | −1.16987 | + | 0.494800i | −0.0424917 | + | 0.0179719i | ||||
\(759\) | −0.0308289 | − | 0.579327i | −0.00111902 | − | 0.0210282i | ||||
\(760\) | 9.07402 | − | 23.3676i | 0.329149 | − | 0.847634i | ||||
\(761\) | −36.3042 | −1.31603 | −0.658013 | − | 0.753007i | \(-0.728603\pi\) | ||||
−0.658013 | + | 0.753007i | \(0.728603\pi\) | |||||||
\(762\) | −1.90152 | − | 4.49584i | −0.0688849 | − | 0.162867i | ||||
\(763\) | − | 17.8563i | − | 0.646441i | ||||||
\(764\) | −20.8290 | − | 20.2186i | −0.753567 | − | 0.731482i | ||||
\(765\) | −17.4747 | −0.631798 | ||||||||
\(766\) | −8.62684 | + | 3.64873i | −0.311700 | + | 0.131834i | ||||
\(767\) | −12.7746 | + | 19.1254i | −0.461264 | + | 0.690579i | ||||
\(768\) | 0.538596 | + | 9.04410i | 0.0194349 | + | 0.326351i | ||||
\(769\) | −5.56848 | −0.200805 | −0.100402 | − | 0.994947i | \(-0.532013\pi\) | ||||
−0.100402 | + | 0.994947i | \(0.532013\pi\) | |||||||
\(770\) | 13.6899 | + | 28.1031i | 0.493350 | + | 1.01277i | ||||
\(771\) | 4.40226i | 0.158544i | ||||||||
\(772\) | 24.4877 | − | 25.2270i | 0.881331 | − | 0.907941i | ||||
\(773\) | 21.0272i | 0.756295i | 0.925745 | + | 0.378147i | \(0.123439\pi\) | ||||
−0.925745 | + | 0.378147i | \(0.876561\pi\) | |||||||
\(774\) | −29.7112 | + | 12.5664i | −1.06795 | + | 0.451690i | ||||
\(775\) | −42.2007 | −1.51589 | ||||||||
\(776\) | 25.8026 | + | 10.0195i | 0.926258 | + | 0.359681i | ||||
\(777\) | 7.84846i | 0.281562i | ||||||||
\(778\) | 33.2085 | − | 14.0456i | 1.19058 | − | 0.503558i | ||||
\(779\) | 9.44233i | 0.338307i | ||||||||
\(780\) | −2.82316 | − | 13.1559i | −0.101085 | − | 0.471056i | ||||
\(781\) | −1.98756 | − | 37.3496i | −0.0711205 | − | 1.33647i | ||||
\(782\) | 0.796351 | − | 0.336818i | 0.0284775 | − | 0.0120446i | ||||
\(783\) | 15.7154 | 0.561624 | ||||||||
\(784\) | −0.346048 | − | 11.6320i | −0.0123589 | − | 0.415428i | ||||
\(785\) | − | 1.56852i | − | 0.0559828i | ||||||
\(786\) | −5.06398 | − | 11.9729i | −0.180626 | − | 0.427061i | ||||
\(787\) | 30.8979i | 1.10139i | 0.834706 | + | 0.550695i | \(0.185637\pi\) | ||||
−0.834706 | + | 0.550695i | \(0.814363\pi\) | |||||||
\(788\) | −26.7935 | + | 27.6025i | −0.954479 | + | 0.983297i | ||||
\(789\) | 17.1031i | 0.608886i | ||||||||
\(790\) | −12.3469 | − | 29.1921i | −0.439281 | − | 1.03861i | ||||
\(791\) | 27.8169i | 0.989057i | ||||||||
\(792\) | 23.8804 | + | 7.84033i | 0.848554 | + | 0.278594i | ||||
\(793\) | 30.1963 | + | 20.1692i | 1.07230 | + | 0.716231i | ||||
\(794\) | −4.34931 | − | 10.2832i | −0.154351 | − | 0.364938i | ||||
\(795\) | 11.0543 | 0.392056 | ||||||||
\(796\) | 5.63069 | + | 5.46567i | 0.199575 | + | 0.193726i | ||||
\(797\) | 9.20602 | 0.326094 | 0.163047 | − | 0.986618i | \(-0.447868\pi\) | ||||
0.163047 | + | 0.986618i | \(0.447868\pi\) | |||||||
\(798\) | 1.69696 | + | 4.01218i | 0.0600716 | + | 0.142030i | ||||
\(799\) | 6.71689i | 0.237626i | ||||||||
\(800\) | −13.8111 | − | 30.1243i | −0.488296 | − | 1.06506i | ||||
\(801\) | 24.9695i | 0.882255i | ||||||||
\(802\) | 12.5045 | + | 29.5649i | 0.441549 | + | 1.04397i | ||||
\(803\) | 1.11107 | + | 20.8788i | 0.0392086 | + | 0.736797i | ||||
\(804\) | 12.3058 | + | 11.9451i | 0.433991 | + | 0.421272i | ||||
\(805\) | 2.05877i | 0.0725621i | ||||||||
\(806\) | −6.89185 | + | 36.0789i | −0.242755 | + | 1.27083i | ||||
\(807\) | − | 5.72157i | − | 0.201409i | ||||||
\(808\) | 31.9462 | + | 12.4052i | 1.12386 | + | 0.436414i | ||||
\(809\) | − | 55.5715i | − | 1.95379i | −0.213719 | − | 0.976895i | \(-0.568558\pi\) | ||
0.213719 | − | 0.976895i | \(-0.431442\pi\) | |||||||
\(810\) | −11.2857 | − | 26.6833i | −0.396540 | − | 0.937554i | ||||
\(811\) | 15.0233i | 0.527538i | 0.964586 | + | 0.263769i | \(0.0849657\pi\) | ||||
−0.964586 | + | 0.263769i | \(0.915034\pi\) | |||||||
\(812\) | 13.7681 | − | 14.1838i | 0.483165 | − | 0.497752i | ||||
\(813\) | −5.82855 | −0.204416 | ||||||||
\(814\) | 28.8965 | − | 14.0764i | 1.01282 | − | 0.493376i | ||||
\(815\) | − | 63.8863i | − | 2.23784i | ||||||
\(816\) | −0.133310 | − | 4.48106i | −0.00466680 | − | 0.156869i | ||||
\(817\) | 22.8981i | 0.801103i | ||||||||
\(818\) | 34.0501 | − | 14.4016i | 1.19054 | − | 0.503539i | ||||
\(819\) | −16.2479 | − | 10.8526i | −0.567746 | − | 0.379219i | ||||
\(820\) | 16.6016 | + | 16.1151i | 0.579754 | + | 0.562763i | ||||
\(821\) | −8.14200 | −0.284158 | −0.142079 | − | 0.989855i | \(-0.545379\pi\) | ||||
−0.142079 | + | 0.989855i | \(0.545379\pi\) | |||||||
\(822\) | 10.7613 | − | 4.55151i | 0.375344 | − | 0.158752i | ||||
\(823\) | 55.2299i | 1.92519i | 0.270940 | + | 0.962596i | \(0.412666\pi\) | ||||
−0.270940 | + | 0.962596i | \(0.587334\pi\) | |||||||
\(824\) | −41.2209 | − | 16.0067i | −1.43600 | − | 0.557621i | ||||
\(825\) | 10.9867 | − | 0.584656i | 0.382507 | − | 0.0203551i | ||||
\(826\) | −7.10745 | − | 16.8044i | −0.247300 | − | 0.584700i | ||||
\(827\) | 22.3027i | 0.775542i | 0.921756 | + | 0.387771i | \(0.126755\pi\) | ||||
−0.921756 | + | 0.387771i | \(0.873245\pi\) | |||||||
\(828\) | 1.18778 | + | 1.15297i | 0.0412781 | + | 0.0400684i | ||||
\(829\) | −11.0651 | −0.384308 | −0.192154 | − | 0.981365i | \(-0.561547\pi\) | ||||
−0.192154 | + | 0.981365i | \(0.561547\pi\) | |||||||
\(830\) | −17.1208 | + | 7.24125i | −0.594270 | + | 0.251348i | ||||
\(831\) | −4.23202 | −0.146807 | ||||||||
\(832\) | −28.0099 | + | 6.88798i | −0.971069 | + | 0.238798i | ||||
\(833\) | 5.75817i | 0.199509i | ||||||||
\(834\) | −2.12866 | − | 5.03287i | −0.0737094 | − | 0.174274i | ||||
\(835\) | 35.2616 | 1.22028 | ||||||||
\(836\) | 11.7285 | − | 13.4438i | 0.405639 | − | 0.464963i | ||||
\(837\) | − | 23.1666i | − | 0.800755i | ||||||
\(838\) | −5.62379 | − | 13.2965i | −0.194271 | − | 0.459321i | ||||
\(839\) | 17.6559 | 0.609548 | 0.304774 | − | 0.952425i | \(-0.401419\pi\) | ||||
0.304774 | + | 0.952425i | \(0.401419\pi\) | |||||||
\(840\) | 9.95043 | + | 3.86391i | 0.343322 | + | 0.133317i | ||||
\(841\) | 5.12041 | 0.176566 | ||||||||
\(842\) | 6.64916 | + | 15.7208i | 0.229145 | + | 0.541776i | ||||
\(843\) | − | 8.86660i | − | 0.305382i | ||||||
\(844\) | −17.4279 | + | 17.9541i | −0.599895 | + | 0.618007i | ||||
\(845\) | 39.5712 | − | 16.4064i | 1.36129 | − | 0.564397i | ||||
\(846\) | −11.8434 | + | 5.00920i | −0.407186 | + | 0.172220i | ||||
\(847\) | 2.36118 | + | 22.1224i | 0.0811310 | + | 0.760136i | ||||
\(848\) | −0.704674 | − | 23.6867i | −0.0241986 | − | 0.813406i | ||||
\(849\) | − | 3.13930i | − | 0.107740i | ||||||
\(850\) | 6.38761 | + | 15.1025i | 0.219093 | + | 0.518010i | ||||
\(851\) | 2.11689 | 0.0725660 | ||||||||
\(852\) | −9.16423 | − | 8.89565i | −0.313961 | − | 0.304760i | ||||
\(853\) | −52.2246 | −1.78814 | −0.894069 | − | 0.447929i | \(-0.852162\pi\) | ||||
−0.894069 | + | 0.447929i | \(0.852162\pi\) | |||||||
\(854\) | −26.5317 | + | 11.2216i | −0.907897 | + | 0.383997i | ||||
\(855\) | −23.7464 | −0.812109 | ||||||||
\(856\) | 1.73012 | − | 4.45546i | 0.0591344 | − | 0.152284i | ||||
\(857\) | − | 11.0774i | − | 0.378397i | −0.981939 | − | 0.189199i | \(-0.939411\pi\) | ||
0.981939 | − | 0.189199i | \(-0.0605890\pi\) | |||||||
\(858\) | 1.29441 | − | 9.48841i | 0.0441903 | − | 0.323929i | ||||
\(859\) | − | 47.0064i | − | 1.60384i | −0.597433 | − | 0.801919i | \(-0.703813\pi\) | ||
0.597433 | − | 0.801919i | \(-0.296187\pi\) | |||||||
\(860\) | 40.2597 | + | 39.0798i | 1.37284 | + | 1.33261i | ||||
\(861\) | −4.02074 | −0.137026 | ||||||||
\(862\) | −12.8068 | − | 30.2797i | −0.436203 | − | 1.03133i | ||||
\(863\) | 9.40938 | 0.320299 | 0.160149 | − | 0.987093i | \(-0.448802\pi\) | ||||
0.160149 | + | 0.987093i | \(0.448802\pi\) | |||||||
\(864\) | 16.5371 | − | 7.58179i | 0.562605 | − | 0.257938i | ||||
\(865\) | 8.01854 | 0.272638 | ||||||||
\(866\) | 31.3415 | − | 13.2559i | 1.06503 | − | 0.450455i | ||||
\(867\) | − | 7.40813i | − | 0.251593i | ||||||
\(868\) | −20.9087 | − | 20.2959i | −0.709687 | − | 0.688888i | ||||
\(869\) | −1.19873 | − | 22.5262i | −0.0406643 | − | 0.764150i | ||||
\(870\) | −5.02317 | − | 11.8765i | −0.170301 | − | 0.402650i | ||||
\(871\) | −30.3262 | + | 45.4028i | −1.02757 | + | 1.53842i | ||||
\(872\) | −9.03907 | + | 23.2776i | −0.306101 | + | 0.788280i | ||||
\(873\) | − | 26.2208i | − | 0.887439i | ||||||
\(874\) | 1.08216 | − | 0.457703i | 0.0366048 | − | 0.0154820i | ||||
\(875\) | −5.72016 | −0.193377 | ||||||||
\(876\) | 5.12290 | + | 4.97276i | 0.173087 | + | 0.168014i | ||||
\(877\) | 8.80058 | 0.297174 | 0.148587 | − | 0.988899i | \(-0.452527\pi\) | ||||
0.148587 | + | 0.988899i | \(0.452527\pi\) | |||||||
\(878\) | −18.9512 | + | 8.01544i | −0.639572 | + | 0.270508i | ||||
\(879\) | − | 9.03302i | − | 0.304676i | ||||||
\(880\) | −3.62013 | − | 43.5655i | −0.122035 | − | 1.46859i | ||||
\(881\) | 9.21479 | 0.310454 | 0.155227 | − | 0.987879i | \(-0.450389\pi\) | ||||
0.155227 | + | 0.987879i | \(0.450389\pi\) | |||||||
\(882\) | −10.1530 | + | 4.29423i | −0.341869 | + | 0.144594i | ||||
\(883\) | − | 14.2442i | − | 0.479356i | −0.970852 | − | 0.239678i | \(-0.922958\pi\) | ||
0.970852 | − | 0.239678i | \(-0.0770418\pi\) | |||||||
\(884\) | 13.9548 | − | 2.99460i | 0.469351 | − | 0.100719i | ||||
\(885\) | −11.9025 | −0.400099 | ||||||||
\(886\) | −17.4367 | − | 41.2262i | −0.585798 | − | 1.38502i | ||||
\(887\) | −46.1304 | −1.54891 | −0.774453 | − | 0.632632i | \(-0.781975\pi\) | ||||
−0.774453 | + | 0.632632i | \(0.781975\pi\) | |||||||
\(888\) | 3.97299 | − | 10.2313i | 0.133325 | − | 0.343341i | ||||
\(889\) | 12.3287i | 0.413491i | ||||||||
\(890\) | 39.9981 | − | 16.9173i | 1.34074 | − | 0.567068i | ||||
\(891\) | −1.09571 | − | 20.5903i | −0.0367077 | − | 0.689800i | ||||
\(892\) | −3.99169 | + | 4.11221i | −0.133652 | + | 0.137687i | ||||
\(893\) | 9.12760i | 0.305444i | ||||||||
\(894\) | −0.725118 | − | 1.71442i | −0.0242516 | − | 0.0573389i | ||||
\(895\) | 74.9128 | 2.50406 | ||||||||
\(896\) | 7.64511 | − | 21.5677i | 0.255405 | − | 0.720525i | ||||
\(897\) | 0.350303 | − | 0.524455i | 0.0116963 | − | 0.0175110i | ||||
\(898\) | −22.5593 | − | 53.3378i | −0.752814 | − | 1.77991i | ||||
\(899\) | 35.2016i | 1.17404i | ||||||||
\(900\) | −21.8655 | + | 22.5257i | −0.728850 | + | 0.750856i | ||||
\(901\) | 11.7256i | 0.390637i | ||||||||
\(902\) | 7.21127 | + | 14.8036i | 0.240109 | + | 0.492905i | ||||
\(903\) | −9.75048 | −0.324476 | ||||||||
\(904\) | 14.0813 | − | 36.2624i | 0.468336 | − | 1.20607i | ||||
\(905\) | − | 19.3538i | − | 0.643342i | ||||||
\(906\) | −9.66579 | + | 4.08816i | −0.321124 | + | 0.135820i | ||||
\(907\) | − | 44.7921i | − | 1.48730i | −0.668570 | − | 0.743649i | \(-0.733093\pi\) | ||
0.668570 | − | 0.743649i | \(-0.266907\pi\) | |||||||
\(908\) | 36.9021 | + | 35.8206i | 1.22464 | + | 1.18875i | ||||
\(909\) | − | 32.4640i | − | 1.07676i | ||||||
\(910\) | −6.37627 | + | 33.3799i | −0.211371 | + | 1.10653i | ||||
\(911\) | 2.41882i | 0.0801390i | 0.999197 | + | 0.0400695i | \(0.0127579\pi\) | ||||
−0.999197 | + | 0.0400695i | \(0.987242\pi\) | |||||||
\(912\) | −0.181156 | − | 6.08933i | −0.00599868 | − | 0.201638i | ||||
\(913\) | −13.2113 | + | 0.703041i | −0.437231 | + | 0.0232672i | ||||
\(914\) | 2.51954 | − | 1.06564i | 0.0833390 | − | 0.0352484i | ||||
\(915\) | 18.7924i | 0.621257i | ||||||||
\(916\) | 30.4086 | + | 29.5174i | 1.00473 | + | 0.975281i | ||||
\(917\) | 32.8328i | 1.08423i | ||||||||
\(918\) | −8.29069 | + | 3.50656i | −0.273633 | + | 0.115734i | ||||
\(919\) | 41.2404 | 1.36039 | 0.680197 | − | 0.733029i | \(-0.261894\pi\) | ||||
0.680197 | + | 0.733029i | \(0.261894\pi\) | |||||||
\(920\) | 1.04217 | − | 2.68383i | 0.0343594 | − | 0.0884832i | ||||
\(921\) | −9.51219 | −0.313437 | ||||||||
\(922\) | 38.0316 | − | 16.0855i | 1.25250 | − | 0.529748i | ||||
\(923\) | 22.5843 | − | 33.8119i | 0.743370 | − | 1.11293i | ||||
\(924\) | 5.72464 | + | 4.99425i | 0.188327 | + | 0.164299i | ||||
\(925\) | 40.1458i | 1.31999i | ||||||||
\(926\) | −8.06067 | + | 3.40927i | −0.264890 | + | 0.112036i | ||||
\(927\) | 41.8890i | 1.37582i | ||||||||
\(928\) | −25.1282 | + | 11.5205i | −0.824872 | + | 0.378179i | ||||
\(929\) | − | 32.8823i | − | 1.07883i | −0.842039 | − | 0.539416i | \(-0.818645\pi\) | ||
0.842039 | − | 0.539416i | \(-0.181355\pi\) | |||||||
\(930\) | −17.5074 | + | 7.40480i | −0.574092 | + | 0.242813i | ||||
\(931\) | 7.82480i | 0.256447i | ||||||||
\(932\) | 18.7142 | + | 18.1658i | 0.613005 | + | 0.595040i | ||||
\(933\) | −1.16365 | −0.0380962 | ||||||||
\(934\) | −19.8727 | − | 46.9857i | −0.650254 | − | 1.53742i | ||||
\(935\) | 1.14946 | + | 21.6004i | 0.0375915 | + | 0.706408i | ||||
\(936\) | 15.6872 | + | 22.3723i | 0.512751 | + | 0.731263i | ||||
\(937\) | 24.7005i | 0.806929i | 0.914995 | + | 0.403465i | \(0.132194\pi\) | ||||
−0.914995 | + | 0.403465i | \(0.867806\pi\) | |||||||
\(938\) | −16.8727 | − | 39.8928i | −0.550914 | − | 1.30255i | ||||
\(939\) | 0.371523i | 0.0121242i | ||||||||
\(940\) | 16.0483 | + | 15.5779i | 0.523436 | + | 0.508096i | ||||
\(941\) | −2.48844 | −0.0811210 | −0.0405605 | − | 0.999177i | \(-0.512914\pi\) | ||||
−0.0405605 | + | 0.999177i | \(0.512914\pi\) | |||||||
\(942\) | −0.148489 | − | 0.351077i | −0.00483802 | − | 0.0114387i | ||||
\(943\) | 1.08447i | 0.0353153i | ||||||||
\(944\) | 0.758745 | + | 25.5042i | 0.0246950 | + | 0.830092i | ||||
\(945\) | − | 21.4335i | − | 0.697232i | ||||||
\(946\) | 17.4877 | + | 35.8993i | 0.568573 | + | 1.16719i | ||||
\(947\) | −39.8617 | −1.29533 | −0.647666 | − | 0.761924i | \(-0.724255\pi\) | ||||
−0.647666 | + | 0.761924i | \(0.724255\pi\) | |||||||
\(948\) | −5.52712 | − | 5.36513i | −0.179512 | − | 0.174251i | ||||
\(949\) | −12.6248 | + | 18.9012i | −0.409819 | + | 0.613559i | ||||
\(950\) | 8.68014 | + | 20.5228i | 0.281621 | + | 0.665847i | ||||
\(951\) | 7.17861 | 0.232783 | ||||||||
\(952\) | −4.09855 | + | 10.5547i | −0.132835 | + | 0.342080i | ||||
\(953\) | 2.43748i | 0.0789576i | 0.999220 | + | 0.0394788i | \(0.0125698\pi\) | ||||
−0.999220 | + | 0.0394788i | \(0.987430\pi\) | |||||||
\(954\) | −20.6750 | + | 8.74453i | −0.669378 | + | 0.283115i | ||||
\(955\) | 47.8268 | 1.54764 | ||||||||
\(956\) | −15.6878 | − | 15.2280i | −0.507379 | − | 0.492509i | ||||
\(957\) | −0.487690 | − | 9.16453i | −0.0157648 | − | 0.296247i | ||||
\(958\) | −4.70574 | − | 11.1260i | −0.152036 | − | 0.359463i | ||||
\(959\) | −29.5102 | −0.952933 | ||||||||
\(960\) | −11.0155 | − | 10.0740i | −0.355524 | − | 0.325139i | ||||
\(961\) | 20.8917 | 0.673927 | ||||||||
\(962\) | 34.3222 | + | 6.55627i | 1.10659 | + | 0.211383i | ||||
\(963\) | −4.52767 | −0.145902 | ||||||||
\(964\) | 5.32158 | − | 5.48225i | 0.171396 | − | 0.176571i | ||||
\(965\) | 57.9253i | 1.86468i | ||||||||
\(966\) | 0.194899 | + | 0.460808i | 0.00627079 | + | 0.0148263i | ||||
\(967\) | 6.50738i | 0.209263i | 0.994511 | + | 0.104632i | \(0.0333664\pi\) | ||||
−0.994511 | + | 0.104632i | \(0.966634\pi\) | |||||||
\(968\) | 8.12058 | − | 30.0342i | 0.261005 | − | 0.965337i | ||||
\(969\) | 3.01440i | 0.0968364i | ||||||||
\(970\) | −42.0025 | + | 17.7650i | −1.34862 | + | 0.570400i | ||||
\(971\) | − | 32.9668i | − | 1.05795i | −0.848636 | − | 0.528977i | \(-0.822576\pi\) | ||
0.848636 | − | 0.528977i | \(-0.177424\pi\) | |||||||
\(972\) | −18.8977 | − | 18.3439i | −0.606145 | − | 0.588380i | ||||
\(973\) | 13.8014i | 0.442451i | ||||||||
\(974\) | 44.5665 | − | 18.8495i | 1.42800 | − | 0.603976i | ||||
\(975\) | 9.94605 | + | 6.64334i | 0.318529 | + | 0.212757i | ||||
\(976\) | 40.2675 | − | 1.19795i | 1.28893 | − | 0.0383454i | ||||
\(977\) | − | 14.4762i | − | 0.463136i | −0.972819 | − | 0.231568i | \(-0.925614\pi\) | ||
0.972819 | − | 0.231568i | \(-0.0743855\pi\) | |||||||
\(978\) | −6.04799 | − | 14.2995i | −0.193393 | − | 0.457247i | ||||
\(979\) | 30.8647 | − | 1.64247i | 0.986441 | − | 0.0524935i | ||||
\(980\) | 13.7577 | + | 13.3545i | 0.439472 | + | 0.426592i | ||||
\(981\) | 23.6549 | 0.755243 | ||||||||
\(982\) | 38.8340 | − | 16.4249i | 1.23924 | − | 0.524140i | ||||
\(983\) | −16.7264 | −0.533490 | −0.266745 | − | 0.963767i | \(-0.585948\pi\) | ||||
−0.266745 | + | 0.963767i | \(0.585948\pi\) | |||||||
\(984\) | 5.24147 | + | 2.03535i | 0.167092 | + | 0.0648845i | ||||
\(985\) | − | 63.3797i | − | 2.01945i | ||||||
\(986\) | 12.5977 | − | 5.32821i | 0.401192 | − | 0.169685i | ||||
\(987\) | −3.88672 | −0.123716 | ||||||||
\(988\) | 18.9633 | − | 4.06937i | 0.603301 | − | 0.129464i | ||||
\(989\) | 2.62990i | 0.0836260i | ||||||||
\(990\) | −37.2293 | + | 18.1355i | −1.18322 | + | 0.576385i | ||||
\(991\) | 49.2134i | 1.56332i | 0.623707 | + | 0.781658i | \(0.285626\pi\) | ||||
−0.623707 | + | 0.781658i | \(0.714374\pi\) | |||||||
\(992\) | 16.9827 | + | 37.0422i | 0.539202 | + | 1.17609i | ||||
\(993\) | 10.9090i | 0.346187i | ||||||||
\(994\) | 12.5653 | + | 29.7086i | 0.398547 | + | 0.942300i | ||||
\(995\) | −12.9290 | −0.409876 | ||||||||
\(996\) | −3.14658 | + | 3.24158i | −0.0997031 | + | 0.102713i | ||||
\(997\) | − | 43.9297i | − | 1.39127i | −0.718397 | − | 0.695634i | \(-0.755124\pi\) | ||
0.718397 | − | 0.695634i | \(-0.244876\pi\) | |||||||
\(998\) | 9.38649 | − | 3.97003i | 0.297124 | − | 0.125669i | ||||
\(999\) | −22.0386 | −0.697270 |
(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 | 572.2.b.c.571.8 | yes | 56 | |
4.3 | odd | 2 | inner | 572.2.b.c.571.6 | yes | 56 | |
11.10 | odd | 2 | inner | 572.2.b.c.571.50 | yes | 56 | |
13.12 | even | 2 | inner | 572.2.b.c.571.49 | yes | 56 | |
44.43 | even | 2 | inner | 572.2.b.c.571.52 | yes | 56 | |
52.51 | odd | 2 | inner | 572.2.b.c.571.51 | yes | 56 | |
143.142 | odd | 2 | inner | 572.2.b.c.571.7 | yes | 56 | |
572.571 | even | 2 | inner | 572.2.b.c.571.5 | ✓ | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
572.2.b.c.571.5 | ✓ | 56 | 572.571 | even | 2 | inner | |
572.2.b.c.571.6 | yes | 56 | 4.3 | odd | 2 | inner | |
572.2.b.c.571.7 | yes | 56 | 143.142 | odd | 2 | inner | |
572.2.b.c.571.8 | yes | 56 | 1.1 | even | 1 | trivial | |
572.2.b.c.571.49 | yes | 56 | 13.12 | even | 2 | inner | |
572.2.b.c.571.50 | yes | 56 | 11.10 | odd | 2 | inner | |
572.2.b.c.571.51 | yes | 56 | 52.51 | odd | 2 | inner | |
572.2.b.c.571.52 | yes | 56 | 44.43 | even | 2 | inner |