Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(169,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.169");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.j (of order \(5\), degree \(4\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.484000000.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 169.2 | ||
Root | \(0.476925 - 1.46782i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.169 |
Dual form | 462.2.j.e.421.2 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.809017 | − | 0.587785i | −0.572061 | − | 0.415627i | ||||
\(3\) | 0.309017 | − | 0.951057i | 0.178411 | − | 0.549093i | ||||
\(4\) | 0.309017 | + | 0.951057i | 0.154508 | + | 0.475528i | ||||
\(5\) | 2.52029 | − | 1.83110i | 1.12711 | − | 0.818891i | 0.141835 | − | 0.989890i | \(-0.454700\pi\) |
0.985271 | + | 0.170999i | \(0.0546996\pi\) | |||||||
\(6\) | −0.809017 | + | 0.587785i | −0.330280 | + | 0.239962i | ||||
\(7\) | 0.309017 | + | 0.951057i | 0.116797 | + | 0.359466i | ||||
\(8\) | 0.309017 | − | 0.951057i | 0.109254 | − | 0.336249i | ||||
\(9\) | −0.809017 | − | 0.587785i | −0.269672 | − | 0.195928i | ||||
\(10\) | −3.11525 | −0.985127 | ||||||||
\(11\) | 2.97414 | − | 1.46782i | 0.896736 | − | 0.442566i | ||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.74861 | + | 1.27044i | 0.484976 | + | 0.352356i | 0.803249 | − | 0.595643i | \(-0.203103\pi\) |
−0.318273 | + | 0.947999i | \(0.603103\pi\) | |||||||
\(14\) | 0.309017 | − | 0.951057i | 0.0825883 | − | 0.254181i | ||||
\(15\) | −0.962664 | − | 2.96278i | −0.248559 | − | 0.764985i | ||||
\(16\) | −0.809017 | + | 0.587785i | −0.202254 | + | 0.146946i | ||||
\(17\) | −0.574672 | + | 0.417524i | −0.139378 | + | 0.101264i | −0.655290 | − | 0.755378i | \(-0.727453\pi\) |
0.515911 | + | 0.856642i | \(0.327453\pi\) | |||||||
\(18\) | 0.309017 | + | 0.951057i | 0.0728360 | + | 0.224166i | ||||
\(19\) | 0.0949591 | − | 0.292254i | 0.0217851 | − | 0.0670476i | −0.939573 | − | 0.342349i | \(-0.888778\pi\) |
0.961358 | + | 0.275301i | \(0.0887776\pi\) | |||||||
\(20\) | 2.52029 | + | 1.83110i | 0.563553 | + | 0.409445i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −3.26889 | − | 0.560659i | −0.696930 | − | 0.119533i | ||||
\(23\) | 0.879178 | 0.183321 | 0.0916606 | − | 0.995790i | \(-0.470782\pi\) | ||||
0.0916606 | + | 0.995790i | \(0.470782\pi\) | |||||||
\(24\) | −0.809017 | − | 0.587785i | −0.165140 | − | 0.119981i | ||||
\(25\) | 1.45385 | − | 4.47449i | 0.290770 | − | 0.894898i | ||||
\(26\) | −0.667908 | − | 2.05561i | −0.130988 | − | 0.403138i | ||||
\(27\) | −0.809017 | + | 0.587785i | −0.155695 | + | 0.113119i | ||||
\(28\) | −0.809017 | + | 0.587785i | −0.152890 | + | 0.111081i | ||||
\(29\) | 2.03082 | + | 6.25023i | 0.377115 | + | 1.16064i | 0.942041 | + | 0.335498i | \(0.108905\pi\) |
−0.564926 | + | 0.825141i | \(0.691095\pi\) | |||||||
\(30\) | −0.962664 | + | 2.96278i | −0.175758 | + | 0.540926i | ||||
\(31\) | −6.21902 | − | 4.51838i | −1.11697 | − | 0.811525i | −0.133222 | − | 0.991086i | \(-0.542532\pi\) |
−0.983747 | + | 0.179561i | \(0.942532\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −0.476925 | − | 3.28216i | −0.0830220 | − | 0.571350i | ||||
\(34\) | 0.710334 | 0.121821 | ||||||||
\(35\) | 2.52029 | + | 1.83110i | 0.426006 | + | 0.309512i | ||||
\(36\) | 0.309017 | − | 0.951057i | 0.0515028 | − | 0.158509i | ||||
\(37\) | −1.19873 | − | 3.68932i | −0.197070 | − | 0.606520i | −0.999946 | − | 0.0103738i | \(-0.996698\pi\) |
0.802876 | − | 0.596146i | \(-0.203302\pi\) | |||||||
\(38\) | −0.248606 | + | 0.180623i | −0.0403292 | + | 0.0293009i | ||||
\(39\) | 1.74861 | − | 1.27044i | 0.280001 | − | 0.203433i | ||||
\(40\) | −0.962664 | − | 2.96278i | −0.152211 | − | 0.468456i | ||||
\(41\) | 1.32558 | − | 4.07972i | 0.207021 | − | 0.637144i | −0.792604 | − | 0.609737i | \(-0.791275\pi\) |
0.999624 | − | 0.0274071i | \(-0.00872506\pi\) | |||||||
\(42\) | −0.809017 | − | 0.587785i | −0.124834 | − | 0.0906972i | ||||
\(43\) | −8.24254 | −1.25698 | −0.628488 | − | 0.777819i | \(-0.716326\pi\) | ||||
−0.628488 | + | 0.777819i | \(0.716326\pi\) | |||||||
\(44\) | 2.31504 | + | 2.37499i | 0.349006 | + | 0.358043i | ||||
\(45\) | −3.11525 | −0.464393 | ||||||||
\(46\) | −0.711270 | − | 0.516768i | −0.104871 | − | 0.0761933i | ||||
\(47\) | 3.10205 | − | 9.54713i | 0.452480 | − | 1.39259i | −0.421587 | − | 0.906788i | \(-0.638527\pi\) |
0.874068 | − | 0.485804i | \(-0.161473\pi\) | |||||||
\(48\) | 0.309017 | + | 0.951057i | 0.0446028 | + | 0.137273i | ||||
\(49\) | −0.809017 | + | 0.587785i | −0.115574 | + | 0.0839693i | ||||
\(50\) | −3.80623 | + | 2.76539i | −0.538282 | + | 0.391085i | ||||
\(51\) | 0.219505 | + | 0.675568i | 0.0307369 | + | 0.0945984i | ||||
\(52\) | −0.667908 | + | 2.05561i | −0.0926222 | + | 0.285062i | ||||
\(53\) | 5.32652 | + | 3.86994i | 0.731653 | + | 0.531577i | 0.890086 | − | 0.455793i | \(-0.150644\pi\) |
−0.158433 | + | 0.987370i | \(0.550644\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.80795 | − | 9.14527i | 0.648304 | − | 1.23315i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −0.248606 | − | 0.180623i | −0.0329287 | − | 0.0239241i | ||||
\(58\) | 2.03082 | − | 6.25023i | 0.266660 | − | 0.820696i | ||||
\(59\) | −1.77713 | − | 5.46944i | −0.231362 | − | 0.712060i | −0.997583 | − | 0.0694828i | \(-0.977865\pi\) |
0.766221 | − | 0.642577i | \(-0.222135\pi\) | |||||||
\(60\) | 2.52029 | − | 1.83110i | 0.325368 | − | 0.236393i | ||||
\(61\) | −2.52759 | + | 1.83640i | −0.323624 | + | 0.235127i | −0.737720 | − | 0.675106i | \(-0.764098\pi\) |
0.414096 | + | 0.910233i | \(0.364098\pi\) | |||||||
\(62\) | 2.37545 | + | 7.31090i | 0.301683 | + | 0.928485i | ||||
\(63\) | 0.309017 | − | 0.951057i | 0.0389325 | − | 0.119822i | ||||
\(64\) | −0.809017 | − | 0.587785i | −0.101127 | − | 0.0734732i | ||||
\(65\) | 6.73328 | 0.835161 | ||||||||
\(66\) | −1.54336 | + | 2.93565i | −0.189975 | + | 0.361353i | ||||
\(67\) | −6.67624 | −0.815632 | −0.407816 | − | 0.913064i | \(-0.633710\pi\) | ||||
−0.407816 | + | 0.913064i | \(0.633710\pi\) | |||||||
\(68\) | −0.574672 | − | 0.417524i | −0.0696892 | − | 0.0506322i | ||||
\(69\) | 0.271681 | − | 0.836148i | 0.0327065 | − | 0.100660i | ||||
\(70\) | −0.962664 | − | 2.96278i | −0.115060 | − | 0.354119i | ||||
\(71\) | −8.77385 | + | 6.37458i | −1.04126 | + | 0.756523i | −0.970532 | − | 0.240972i | \(-0.922534\pi\) |
−0.0707328 | + | 0.997495i | \(0.522534\pi\) | |||||||
\(72\) | −0.809017 | + | 0.587785i | −0.0953436 | + | 0.0692712i | ||||
\(73\) | 3.32049 | + | 10.2194i | 0.388634 | + | 1.19609i | 0.933810 | + | 0.357770i | \(0.116463\pi\) |
−0.545176 | + | 0.838322i | \(0.683537\pi\) | |||||||
\(74\) | −1.19873 | + | 3.68932i | −0.139350 | + | 0.428874i | ||||
\(75\) | −3.80623 | − | 2.76539i | −0.439505 | − | 0.319319i | ||||
\(76\) | 0.307294 | 0.0352490 | ||||||||
\(77\) | 2.31504 | + | 2.37499i | 0.263824 | + | 0.270655i | ||||
\(78\) | −2.16140 | −0.244730 | ||||||||
\(79\) | 7.86013 | + | 5.71072i | 0.884333 | + | 0.642506i | 0.934394 | − | 0.356240i | \(-0.115942\pi\) |
−0.0500609 | + | 0.998746i | \(0.515942\pi\) | |||||||
\(80\) | −0.962664 | + | 2.96278i | −0.107629 | + | 0.331248i | ||||
\(81\) | 0.309017 | + | 0.951057i | 0.0343352 | + | 0.105673i | ||||
\(82\) | −3.47041 | + | 2.52140i | −0.383243 | + | 0.278442i | ||||
\(83\) | −12.7701 | + | 9.27804i | −1.40170 | + | 1.01840i | −0.407240 | + | 0.913321i | \(0.633509\pi\) |
−0.994464 | + | 0.105076i | \(0.966491\pi\) | |||||||
\(84\) | 0.309017 | + | 0.951057i | 0.0337165 | + | 0.103769i | ||||
\(85\) | −0.683813 | + | 2.10456i | −0.0741699 | + | 0.228271i | ||||
\(86\) | 6.66836 | + | 4.84485i | 0.719068 | + | 0.522433i | ||||
\(87\) | 6.57188 | 0.704580 | ||||||||
\(88\) | −0.476925 | − | 3.28216i | −0.0508404 | − | 0.349879i | ||||
\(89\) | 14.8726 | 1.57650 | 0.788248 | − | 0.615358i | \(-0.210989\pi\) | ||||
0.788248 | + | 0.615358i | \(0.210989\pi\) | |||||||
\(90\) | 2.52029 | + | 1.83110i | 0.265662 | + | 0.193014i | ||||
\(91\) | −0.667908 | + | 2.05561i | −0.0700158 | + | 0.215486i | ||||
\(92\) | 0.271681 | + | 0.836148i | 0.0283247 | + | 0.0871745i | ||||
\(93\) | −6.21902 | + | 4.51838i | −0.644882 | + | 0.468534i | ||||
\(94\) | −8.12127 | + | 5.90045i | −0.837645 | + | 0.608585i | ||||
\(95\) | −0.295821 | − | 0.910443i | −0.0303506 | − | 0.0934095i | ||||
\(96\) | 0.309017 | − | 0.951057i | 0.0315389 | − | 0.0970668i | ||||
\(97\) | 0.211270 | + | 0.153497i | 0.0214512 | + | 0.0155852i | 0.598459 | − | 0.801153i | \(-0.295780\pi\) |
−0.577008 | + | 0.816739i | \(0.695780\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | −3.26889 | − | 0.560659i | −0.328536 | − | 0.0563484i | ||||
\(100\) | 4.70476 | 0.470476 | ||||||||
\(101\) | −2.06365 | − | 1.49933i | −0.205341 | − | 0.149189i | 0.480362 | − | 0.877070i | \(-0.340505\pi\) |
−0.685703 | + | 0.727881i | \(0.740505\pi\) | |||||||
\(102\) | 0.219505 | − | 0.675568i | 0.0217343 | − | 0.0668912i | ||||
\(103\) | 5.82249 | + | 17.9198i | 0.573707 | + | 1.76569i | 0.640540 | + | 0.767925i | \(0.278711\pi\) |
−0.0668329 | + | 0.997764i | \(0.521289\pi\) | |||||||
\(104\) | 1.74861 | − | 1.27044i | 0.171465 | − | 0.124577i | ||||
\(105\) | 2.52029 | − | 1.83110i | 0.245955 | − | 0.178697i | ||||
\(106\) | −2.03455 | − | 6.26170i | −0.197613 | − | 0.608190i | ||||
\(107\) | −1.05094 | + | 3.23446i | −0.101598 | + | 0.312687i | −0.988917 | − | 0.148470i | \(-0.952565\pi\) |
0.887319 | + | 0.461156i | \(0.152565\pi\) | |||||||
\(108\) | −0.809017 | − | 0.587785i | −0.0778477 | − | 0.0565597i | ||||
\(109\) | 6.96590 | 0.667212 | 0.333606 | − | 0.942713i | \(-0.391734\pi\) | ||||
0.333606 | + | 0.942713i | \(0.391734\pi\) | |||||||
\(110\) | −9.26517 | + | 4.57263i | −0.883399 | + | 0.435984i | ||||
\(111\) | −3.87918 | −0.368195 | ||||||||
\(112\) | −0.809017 | − | 0.587785i | −0.0764449 | − | 0.0555405i | ||||
\(113\) | −0.432012 | + | 1.32960i | −0.0406403 | + | 0.125078i | −0.969318 | − | 0.245809i | \(-0.920946\pi\) |
0.928678 | + | 0.370887i | \(0.120946\pi\) | |||||||
\(114\) | 0.0949591 | + | 0.292254i | 0.00889373 | + | 0.0273721i | ||||
\(115\) | 2.21578 | − | 1.60986i | 0.206623 | − | 0.150120i | ||||
\(116\) | −5.31677 | + | 3.86286i | −0.493649 | + | 0.358657i | ||||
\(117\) | −0.667908 | − | 2.05561i | −0.0617481 | − | 0.190041i | ||||
\(118\) | −1.77713 | + | 5.46944i | −0.163598 | + | 0.503503i | ||||
\(119\) | −0.574672 | − | 0.417524i | −0.0526801 | − | 0.0382743i | ||||
\(120\) | −3.11525 | −0.284382 | ||||||||
\(121\) | 6.69098 | − | 8.73102i | 0.608271 | − | 0.793729i | ||||
\(122\) | 3.12427 | 0.282858 | ||||||||
\(123\) | −3.47041 | − | 2.52140i | −0.312917 | − | 0.227347i | ||||
\(124\) | 2.37545 | − | 7.31090i | 0.213322 | − | 0.656538i | ||||
\(125\) | 0.284219 | + | 0.874736i | 0.0254213 | + | 0.0782388i | ||||
\(126\) | −0.809017 | + | 0.587785i | −0.0720730 | + | 0.0523641i | ||||
\(127\) | −12.9791 | + | 9.42987i | −1.15171 | + | 0.836765i | −0.988707 | − | 0.149860i | \(-0.952118\pi\) |
−0.163002 | + | 0.986626i | \(0.552118\pi\) | |||||||
\(128\) | 0.309017 | + | 0.951057i | 0.0273135 | + | 0.0840623i | ||||
\(129\) | −2.54709 | + | 7.83913i | −0.224258 | + | 0.690196i | ||||
\(130\) | −5.44734 | − | 3.95772i | −0.477763 | − | 0.347115i | ||||
\(131\) | 19.8696 | 1.73601 | 0.868007 | − | 0.496551i | \(-0.165400\pi\) | ||||
0.868007 | + | 0.496551i | \(0.165400\pi\) | |||||||
\(132\) | 2.97414 | − | 1.46782i | 0.258865 | − | 0.127758i | ||||
\(133\) | 0.307294 | 0.0266458 | ||||||||
\(134\) | 5.40119 | + | 3.92419i | 0.466592 | + | 0.338999i | ||||
\(135\) | −0.962664 | + | 2.96278i | −0.0828529 | + | 0.254995i | ||||
\(136\) | 0.219505 | + | 0.675568i | 0.0188224 | + | 0.0579294i | ||||
\(137\) | −1.87963 | + | 1.36563i | −0.160587 | + | 0.116674i | −0.665177 | − | 0.746686i | \(-0.731644\pi\) |
0.504589 | + | 0.863359i | \(0.331644\pi\) | |||||||
\(138\) | −0.711270 | + | 0.516768i | −0.0605473 | + | 0.0439902i | ||||
\(139\) | 2.31208 | + | 7.11586i | 0.196108 | + | 0.603559i | 0.999962 | + | 0.00873210i | \(0.00277955\pi\) |
−0.803854 | + | 0.594827i | \(0.797220\pi\) | |||||||
\(140\) | −0.962664 | + | 2.96278i | −0.0813600 | + | 0.250400i | ||||
\(141\) | −8.12127 | − | 5.90045i | −0.683934 | − | 0.496907i | ||||
\(142\) | 10.8451 | 0.910099 | ||||||||
\(143\) | 7.06537 | + | 1.21181i | 0.590836 | + | 0.101336i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 16.5630 | + | 12.0337i | 1.37549 | + | 0.999348i | ||||
\(146\) | 3.32049 | − | 10.2194i | 0.274806 | − | 0.845765i | ||||
\(147\) | 0.309017 | + | 0.951057i | 0.0254873 | + | 0.0784418i | ||||
\(148\) | 3.13832 | − | 2.28012i | 0.257968 | − | 0.187425i | ||||
\(149\) | −1.15492 | + | 0.839099i | −0.0946147 | + | 0.0687416i | −0.634087 | − | 0.773262i | \(-0.718624\pi\) |
0.539472 | + | 0.842003i | \(0.318624\pi\) | |||||||
\(150\) | 1.45385 | + | 4.47449i | 0.118706 | + | 0.365341i | ||||
\(151\) | −3.07840 | + | 9.47433i | −0.250516 | + | 0.771010i | 0.744164 | + | 0.667997i | \(0.232848\pi\) |
−0.994680 | + | 0.103013i | \(0.967152\pi\) | |||||||
\(152\) | −0.248606 | − | 0.180623i | −0.0201646 | − | 0.0146504i | ||||
\(153\) | 0.710334 | 0.0574271 | ||||||||
\(154\) | −0.476925 | − | 3.28216i | −0.0384317 | − | 0.264484i | ||||
\(155\) | −23.9473 | −1.92349 | ||||||||
\(156\) | 1.74861 | + | 1.27044i | 0.140001 | + | 0.101716i | ||||
\(157\) | −7.61459 | + | 23.4353i | −0.607710 | + | 1.87034i | −0.130749 | + | 0.991415i | \(0.541738\pi\) |
−0.476961 | + | 0.878924i | \(0.658262\pi\) | |||||||
\(158\) | −3.00230 | − | 9.24013i | −0.238850 | − | 0.735106i | ||||
\(159\) | 5.32652 | − | 3.86994i | 0.422420 | − | 0.306906i | ||||
\(160\) | 2.52029 | − | 1.83110i | 0.199246 | − | 0.144761i | ||||
\(161\) | 0.271681 | + | 0.836148i | 0.0214115 | + | 0.0658977i | ||||
\(162\) | 0.309017 | − | 0.951057i | 0.0242787 | − | 0.0747221i | ||||
\(163\) | −11.6069 | − | 8.43289i | −0.909121 | − | 0.660515i | 0.0316713 | − | 0.999498i | \(-0.489917\pi\) |
−0.940792 | + | 0.338983i | \(0.889917\pi\) | |||||||
\(164\) | 4.28967 | 0.334967 | ||||||||
\(165\) | −7.21193 | − | 7.39868i | −0.561448 | − | 0.575986i | ||||
\(166\) | 15.7847 | 1.22513 | ||||||||
\(167\) | −11.3518 | − | 8.24754i | −0.878426 | − | 0.638214i | 0.0544087 | − | 0.998519i | \(-0.482673\pi\) |
−0.932835 | + | 0.360305i | \(0.882673\pi\) | |||||||
\(168\) | 0.309017 | − | 0.951057i | 0.0238412 | − | 0.0733756i | ||||
\(169\) | −2.57361 | − | 7.92075i | −0.197970 | − | 0.609288i | ||||
\(170\) | 1.79024 | − | 1.30069i | 0.137306 | − | 0.0997583i | ||||
\(171\) | −0.248606 | + | 0.180623i | −0.0190114 | + | 0.0138126i | ||||
\(172\) | −2.54709 | − | 7.83913i | −0.194213 | − | 0.597728i | ||||
\(173\) | 4.38107 | − | 13.4836i | 0.333087 | − | 1.02514i | −0.634570 | − | 0.772865i | \(-0.718823\pi\) |
0.967657 | − | 0.252270i | \(-0.0811772\pi\) | |||||||
\(174\) | −5.31677 | − | 3.86286i | −0.403063 | − | 0.292842i | ||||
\(175\) | 4.70476 | 0.355646 | ||||||||
\(176\) | −1.54336 | + | 2.93565i | −0.116335 | + | 0.221283i | ||||
\(177\) | −5.75091 | −0.432265 | ||||||||
\(178\) | −12.0322 | − | 8.74191i | −0.901852 | − | 0.655234i | ||||
\(179\) | −4.91066 | + | 15.1135i | −0.367040 | + | 1.12963i | 0.581654 | + | 0.813436i | \(0.302406\pi\) |
−0.948694 | + | 0.316196i | \(0.897594\pi\) | |||||||
\(180\) | −0.962664 | − | 2.96278i | −0.0717527 | − | 0.220832i | ||||
\(181\) | 14.3675 | − | 10.4386i | 1.06793 | − | 0.775897i | 0.0923916 | − | 0.995723i | \(-0.470549\pi\) |
0.975539 | + | 0.219826i | \(0.0705488\pi\) | |||||||
\(182\) | 1.74861 | − | 1.27044i | 0.129615 | − | 0.0941710i | ||||
\(183\) | 0.965452 | + | 2.97136i | 0.0713683 | + | 0.219649i | ||||
\(184\) | 0.271681 | − | 0.836148i | 0.0200286 | − | 0.0616416i | ||||
\(185\) | −9.77664 | − | 7.10315i | −0.718793 | − | 0.522234i | ||||
\(186\) | 7.68713 | 0.563648 | ||||||||
\(187\) | −1.09630 | + | 2.08529i | −0.0801695 | + | 0.152492i | ||||
\(188\) | 10.0384 | 0.732129 | ||||||||
\(189\) | −0.809017 | − | 0.587785i | −0.0588473 | − | 0.0427551i | ||||
\(190\) | −0.295821 | + | 0.910443i | −0.0214611 | + | 0.0660505i | ||||
\(191\) | −8.12423 | − | 25.0038i | −0.587849 | − | 1.80921i | −0.587516 | − | 0.809213i | \(-0.699894\pi\) |
−0.000332794 | − | 1.00000i | \(-0.500106\pi\) | |||||||
\(192\) | −0.809017 | + | 0.587785i | −0.0583858 | + | 0.0424197i | ||||
\(193\) | −4.50451 | + | 3.27272i | −0.324242 | + | 0.235575i | −0.737983 | − | 0.674819i | \(-0.764222\pi\) |
0.413742 | + | 0.910394i | \(0.364222\pi\) | |||||||
\(194\) | −0.0806980 | − | 0.248363i | −0.00579378 | − | 0.0178314i | ||||
\(195\) | 2.08070 | − | 6.40373i | 0.149002 | − | 0.458581i | ||||
\(196\) | −0.809017 | − | 0.587785i | −0.0577869 | − | 0.0419847i | ||||
\(197\) | −11.8089 | −0.841346 | −0.420673 | − | 0.907212i | \(-0.638206\pi\) | ||||
−0.420673 | + | 0.907212i | \(0.638206\pi\) | |||||||
\(198\) | 2.31504 | + | 2.37499i | 0.164523 | + | 0.168783i | ||||
\(199\) | 9.53591 | 0.675983 | 0.337991 | − | 0.941149i | \(-0.390252\pi\) | ||||
0.337991 | + | 0.941149i | \(0.390252\pi\) | |||||||
\(200\) | −3.80623 | − | 2.76539i | −0.269141 | − | 0.195542i | ||||
\(201\) | −2.06307 | + | 6.34948i | −0.145518 | + | 0.447858i | ||||
\(202\) | 0.788244 | + | 2.42596i | 0.0554606 | + | 0.170690i | ||||
\(203\) | −5.31677 | + | 3.86286i | −0.373164 | + | 0.271119i | ||||
\(204\) | −0.574672 | + | 0.417524i | −0.0402351 | + | 0.0292325i | ||||
\(205\) | −4.12951 | − | 12.7093i | −0.288417 | − | 0.887657i | ||||
\(206\) | 5.82249 | − | 17.9198i | 0.405672 | − | 1.24853i | ||||
\(207\) | −0.711270 | − | 0.516768i | −0.0494367 | − | 0.0359179i | ||||
\(208\) | −2.16140 | −0.149866 | ||||||||
\(209\) | −0.146556 | − | 1.00859i | −0.0101375 | − | 0.0697654i | ||||
\(210\) | −3.11525 | −0.214972 | ||||||||
\(211\) | 9.67135 | + | 7.02665i | 0.665803 | + | 0.483735i | 0.868618 | − | 0.495483i | \(-0.165009\pi\) |
−0.202814 | + | 0.979217i | \(0.565009\pi\) | |||||||
\(212\) | −2.03455 | + | 6.26170i | −0.139733 | + | 0.430055i | ||||
\(213\) | 3.35131 | + | 10.3143i | 0.229628 | + | 0.706723i | ||||
\(214\) | 2.75139 | − | 1.99900i | 0.188081 | − | 0.136649i | ||||
\(215\) | −20.7736 | + | 15.0929i | −1.41675 | + | 1.02933i | ||||
\(216\) | 0.309017 | + | 0.951057i | 0.0210259 | + | 0.0647112i | ||||
\(217\) | 2.37545 | − | 7.31090i | 0.161256 | − | 0.496296i | ||||
\(218\) | −5.63553 | − | 4.09445i | −0.381686 | − | 0.277311i | ||||
\(219\) | 10.7453 | 0.726102 | ||||||||
\(220\) | 10.1834 | + | 1.74659i | 0.686565 | + | 0.117755i | ||||
\(221\) | −1.53531 | −0.103276 | ||||||||
\(222\) | 3.13832 | + | 2.28012i | 0.210630 | + | 0.153032i | ||||
\(223\) | −2.71282 | + | 8.34921i | −0.181664 | + | 0.559104i | −0.999875 | − | 0.0158139i | \(-0.994966\pi\) |
0.818211 | + | 0.574918i | \(0.194966\pi\) | |||||||
\(224\) | 0.309017 | + | 0.951057i | 0.0206471 | + | 0.0635451i | ||||
\(225\) | −3.80623 | + | 2.76539i | −0.253749 | + | 0.184359i | ||||
\(226\) | 1.13102 | − | 0.821736i | 0.0752345 | − | 0.0546610i | ||||
\(227\) | −6.02667 | − | 18.5482i | −0.400004 | − | 1.23109i | −0.924995 | − | 0.379979i | \(-0.875931\pi\) |
0.524991 | − | 0.851108i | \(-0.324069\pi\) | |||||||
\(228\) | 0.0949591 | − | 0.292254i | 0.00628882 | − | 0.0193550i | ||||
\(229\) | 5.88938 | + | 4.27888i | 0.389181 | + | 0.282757i | 0.765120 | − | 0.643888i | \(-0.222680\pi\) |
−0.375939 | + | 0.926645i | \(0.622680\pi\) | |||||||
\(230\) | −2.73886 | −0.180595 | ||||||||
\(231\) | 2.97414 | − | 1.46782i | 0.195684 | − | 0.0965758i | ||||
\(232\) | 6.57188 | 0.431465 | ||||||||
\(233\) | 2.21054 | + | 1.60605i | 0.144817 | + | 0.105216i | 0.657835 | − | 0.753162i | \(-0.271472\pi\) |
−0.513018 | + | 0.858378i | \(0.671472\pi\) | |||||||
\(234\) | −0.667908 | + | 2.05561i | −0.0436625 | + | 0.134379i | ||||
\(235\) | −9.66365 | − | 29.7417i | −0.630387 | − | 1.94013i | ||||
\(236\) | 4.65258 | − | 3.38030i | 0.302857 | − | 0.220039i | ||||
\(237\) | 7.86013 | − | 5.71072i | 0.510570 | − | 0.370951i | ||||
\(238\) | 0.219505 | + | 0.675568i | 0.0142284 | + | 0.0437905i | ||||
\(239\) | 8.00283 | − | 24.6302i | 0.517660 | − | 1.59319i | −0.260729 | − | 0.965412i | \(-0.583963\pi\) |
0.778389 | − | 0.627782i | \(-0.216037\pi\) | |||||||
\(240\) | 2.52029 | + | 1.83110i | 0.162684 | + | 0.118197i | ||||
\(241\) | −6.36034 | −0.409705 | −0.204853 | − | 0.978793i | \(-0.565672\pi\) | ||||
−0.204853 | + | 0.978793i | \(0.565672\pi\) | |||||||
\(242\) | −10.5451 | + | 3.13068i | −0.677864 | + | 0.201248i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.52759 | − | 1.83640i | −0.161812 | − | 0.117563i | ||||
\(245\) | −0.962664 | + | 2.96278i | −0.0615023 | + | 0.189285i | ||||
\(246\) | 1.32558 | + | 4.07972i | 0.0845159 | + | 0.260113i | ||||
\(247\) | 0.537336 | − | 0.390397i | 0.0341899 | − | 0.0248404i | ||||
\(248\) | −6.21902 | + | 4.51838i | −0.394908 | + | 0.286918i | ||||
\(249\) | 4.87776 | + | 15.0122i | 0.309115 | + | 0.951359i | ||||
\(250\) | 0.284219 | − | 0.874736i | 0.0179756 | − | 0.0553232i | ||||
\(251\) | 10.4223 | + | 7.57222i | 0.657847 | + | 0.477954i | 0.865935 | − | 0.500156i | \(-0.166724\pi\) |
−0.208088 | + | 0.978110i | \(0.566724\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | 2.61480 | − | 1.29048i | 0.164391 | − | 0.0811317i | ||||
\(254\) | 16.0430 | 1.00663 | ||||||||
\(255\) | 1.79024 | + | 1.30069i | 0.112109 | + | 0.0814523i | ||||
\(256\) | 0.309017 | − | 0.951057i | 0.0193136 | − | 0.0594410i | ||||
\(257\) | 1.61565 | + | 4.97247i | 0.100782 | + | 0.310174i | 0.988717 | − | 0.149794i | \(-0.0478610\pi\) |
−0.887936 | + | 0.459968i | \(0.847861\pi\) | |||||||
\(258\) | 6.66836 | − | 4.84485i | 0.415154 | − | 0.301627i | ||||
\(259\) | 3.13832 | − | 2.28012i | 0.195006 | − | 0.141680i | ||||
\(260\) | 2.08070 | + | 6.40373i | 0.129039 | + | 0.397142i | ||||
\(261\) | 2.03082 | − | 6.25023i | 0.125705 | − | 0.386880i | ||||
\(262\) | −16.0748 | − | 11.6791i | −0.993107 | − | 0.721535i | ||||
\(263\) | 26.8248 | 1.65409 | 0.827043 | − | 0.562139i | \(-0.190021\pi\) | ||||
0.827043 | + | 0.562139i | \(0.190021\pi\) | |||||||
\(264\) | −3.26889 | − | 0.560659i | −0.201186 | − | 0.0345062i | ||||
\(265\) | 20.5106 | 1.25995 | ||||||||
\(266\) | −0.248606 | − | 0.180623i | −0.0152430 | − | 0.0110747i | ||||
\(267\) | 4.59590 | − | 14.1447i | 0.281264 | − | 0.865642i | ||||
\(268\) | −2.06307 | − | 6.34948i | −0.126022 | − | 0.387856i | ||||
\(269\) | 8.93180 | − | 6.48934i | 0.544582 | − | 0.395662i | −0.281202 | − | 0.959649i | \(-0.590733\pi\) |
0.825784 | + | 0.563987i | \(0.190733\pi\) | |||||||
\(270\) | 2.52029 | − | 1.83110i | 0.153380 | − | 0.111437i | ||||
\(271\) | −5.59734 | − | 17.2268i | −0.340014 | − | 1.04646i | −0.964199 | − | 0.265179i | \(-0.914569\pi\) |
0.624185 | − | 0.781277i | \(-0.285431\pi\) | |||||||
\(272\) | 0.219505 | − | 0.675568i | 0.0133095 | − | 0.0409623i | ||||
\(273\) | 1.74861 | + | 1.27044i | 0.105830 | + | 0.0768903i | ||||
\(274\) | 2.32335 | 0.140359 | ||||||||
\(275\) | −2.24382 | − | 15.4417i | −0.135307 | − | 0.931172i | ||||
\(276\) | 0.879178 | 0.0529203 | ||||||||
\(277\) | −9.15906 | − | 6.65445i | −0.550314 | − | 0.399827i | 0.277587 | − | 0.960701i | \(-0.410465\pi\) |
−0.827901 | + | 0.560874i | \(0.810465\pi\) | |||||||
\(278\) | 2.31208 | − | 7.11586i | 0.138670 | − | 0.426781i | ||||
\(279\) | 2.37545 | + | 7.31090i | 0.142215 | + | 0.437692i | ||||
\(280\) | 2.52029 | − | 1.83110i | 0.150616 | − | 0.109429i | ||||
\(281\) | −20.3541 | + | 14.7881i | −1.21422 | + | 0.882184i | −0.995607 | − | 0.0936276i | \(-0.970154\pi\) |
−0.218614 | + | 0.975811i | \(0.570154\pi\) | |||||||
\(282\) | 3.10205 | + | 9.54713i | 0.184724 | + | 0.568523i | ||||
\(283\) | 1.73590 | − | 5.34254i | 0.103188 | − | 0.317581i | −0.886113 | − | 0.463470i | \(-0.846604\pi\) |
0.989301 | + | 0.145889i | \(0.0466042\pi\) | |||||||
\(284\) | −8.77385 | − | 6.37458i | −0.520632 | − | 0.378262i | ||||
\(285\) | −0.957296 | −0.0567053 | ||||||||
\(286\) | −5.00372 | − | 5.13329i | −0.295876 | − | 0.303538i | ||||
\(287\) | 4.28967 | 0.253211 | ||||||||
\(288\) | −0.809017 | − | 0.587785i | −0.0476718 | − | 0.0346356i | ||||
\(289\) | −5.09737 | + | 15.6881i | −0.299845 | + | 0.922828i | ||||
\(290\) | −6.32652 | − | 19.4710i | −0.371506 | − | 1.14338i | ||||
\(291\) | 0.211270 | − | 0.153497i | 0.0123849 | − | 0.00899813i | ||||
\(292\) | −8.69316 | + | 6.31595i | −0.508728 | + | 0.369613i | ||||
\(293\) | 2.56520 | + | 7.89487i | 0.149861 | + | 0.461223i | 0.997604 | − | 0.0691831i | \(-0.0220393\pi\) |
−0.847743 | + | 0.530407i | \(0.822039\pi\) | |||||||
\(294\) | 0.309017 | − | 0.951057i | 0.0180222 | − | 0.0554667i | ||||
\(295\) | −14.4939 | − | 10.5305i | −0.843870 | − | 0.613107i | ||||
\(296\) | −3.87918 | −0.225473 | ||||||||
\(297\) | −1.54336 | + | 2.93565i | −0.0895549 | + | 0.170344i | ||||
\(298\) | 1.42756 | 0.0826963 | ||||||||
\(299\) | 1.53734 | + | 1.11694i | 0.0889064 | + | 0.0645943i | ||||
\(300\) | 1.45385 | − | 4.47449i | 0.0839381 | − | 0.258335i | ||||
\(301\) | −2.54709 | − | 7.83913i | −0.146812 | − | 0.451840i | ||||
\(302\) | 8.05935 | − | 5.85546i | 0.463763 | − | 0.336944i | ||||
\(303\) | −2.06365 | + | 1.49933i | −0.118554 | + | 0.0861342i | ||||
\(304\) | 0.0949591 | + | 0.292254i | 0.00544628 | + | 0.0167619i | ||||
\(305\) | −3.00762 | + | 9.25650i | −0.172216 | + | 0.530026i | ||||
\(306\) | −0.574672 | − | 0.417524i | −0.0328518 | − | 0.0238682i | ||||
\(307\) | 1.44088 | 0.0822355 | 0.0411178 | − | 0.999154i | \(-0.486908\pi\) | ||||
0.0411178 | + | 0.999154i | \(0.486908\pi\) | |||||||
\(308\) | −1.54336 | + | 2.93565i | −0.0879412 | + | 0.167274i | ||||
\(309\) | 18.8420 | 1.07188 | ||||||||
\(310\) | 19.3738 | + | 14.0759i | 1.10036 | + | 0.799456i | ||||
\(311\) | 3.05749 | − | 9.41000i | 0.173375 | − | 0.533592i | −0.826181 | − | 0.563405i | \(-0.809491\pi\) |
0.999556 | + | 0.0298128i | \(0.00949111\pi\) | |||||||
\(312\) | −0.667908 | − | 2.05561i | −0.0378128 | − | 0.116376i | ||||
\(313\) | 4.49721 | − | 3.26742i | 0.254197 | − | 0.184685i | −0.453388 | − | 0.891313i | \(-0.649785\pi\) |
0.707585 | + | 0.706628i | \(0.249785\pi\) | |||||||
\(314\) | 19.9352 | − | 14.4838i | 1.12501 | − | 0.817369i | ||||
\(315\) | −0.962664 | − | 2.96278i | −0.0542400 | − | 0.166933i | ||||
\(316\) | −3.00230 | + | 9.24013i | −0.168893 | + | 0.519798i | ||||
\(317\) | 0.561684 | + | 0.408087i | 0.0315473 | + | 0.0229205i | 0.603447 | − | 0.797403i | \(-0.293793\pi\) |
−0.571900 | + | 0.820323i | \(0.693793\pi\) | |||||||
\(318\) | −6.58394 | −0.369209 | ||||||||
\(319\) | 15.2142 | + | 15.6082i | 0.851831 | + | 0.873889i | ||||
\(320\) | −3.11525 | −0.174148 | ||||||||
\(321\) | 2.75139 | + | 1.99900i | 0.153568 | + | 0.111574i | ||||
\(322\) | 0.271681 | − | 0.836148i | 0.0151402 | − | 0.0465967i | ||||
\(323\) | 0.0674526 | + | 0.207598i | 0.00375316 | + | 0.0115511i | ||||
\(324\) | −0.809017 | + | 0.587785i | −0.0449454 | + | 0.0326547i | ||||
\(325\) | 8.22677 | − | 5.97710i | 0.456339 | − | 0.331550i | ||||
\(326\) | 4.43343 | + | 13.6447i | 0.245545 | + | 0.755710i | ||||
\(327\) | 2.15258 | − | 6.62497i | 0.119038 | − | 0.366361i | ||||
\(328\) | −3.47041 | − | 2.52140i | −0.191621 | − | 0.139221i | ||||
\(329\) | 10.0384 | 0.553437 | ||||||||
\(330\) | 1.48574 | + | 10.2247i | 0.0817872 | + | 0.562852i | ||||
\(331\) | −31.0269 | −1.70539 | −0.852696 | − | 0.522408i | \(-0.825034\pi\) | ||||
−0.852696 | + | 0.522408i | \(0.825034\pi\) | |||||||
\(332\) | −12.7701 | − | 9.27804i | −0.700852 | − | 0.509199i | ||||
\(333\) | −1.19873 | + | 3.68932i | −0.0656901 | + | 0.202173i | ||||
\(334\) | 4.33599 | + | 13.3448i | 0.237255 | + | 0.730195i | ||||
\(335\) | −16.8260 | + | 12.2248i | −0.919304 | + | 0.667914i | ||||
\(336\) | −0.809017 | + | 0.587785i | −0.0441355 | + | 0.0320663i | ||||
\(337\) | 5.07933 | + | 15.6326i | 0.276689 | + | 0.851561i | 0.988768 | + | 0.149461i | \(0.0477539\pi\) |
−0.712079 | + | 0.702100i | \(0.752246\pi\) | |||||||
\(338\) | −2.57361 | + | 7.92075i | −0.139986 | + | 0.430832i | ||||
\(339\) | 1.13102 | + | 0.821736i | 0.0614287 | + | 0.0446306i | ||||
\(340\) | −2.21286 | −0.120009 | ||||||||
\(341\) | −25.1284 | − | 4.30986i | −1.36078 | − | 0.233392i | ||||
\(342\) | 0.307294 | 0.0166166 | ||||||||
\(343\) | −0.809017 | − | 0.587785i | −0.0436828 | − | 0.0317374i | ||||
\(344\) | −2.54709 | + | 7.83913i | −0.137330 | + | 0.422657i | ||||
\(345\) | −0.846353 | − | 2.60481i | −0.0455661 | − | 0.140238i | ||||
\(346\) | −11.4698 | + | 8.33330i | −0.616620 | + | 0.448001i | ||||
\(347\) | −28.3634 | + | 20.6072i | −1.52263 | + | 1.10625i | −0.562462 | + | 0.826823i | \(0.690146\pi\) |
−0.960166 | + | 0.279430i | \(0.909854\pi\) | |||||||
\(348\) | 2.03082 | + | 6.25023i | 0.108864 | + | 0.335048i | ||||
\(349\) | 2.66588 | − | 8.20475i | 0.142702 | − | 0.439190i | −0.854007 | − | 0.520262i | \(-0.825834\pi\) |
0.996708 | + | 0.0810718i | \(0.0258343\pi\) | |||||||
\(350\) | −3.80623 | − | 2.76539i | −0.203451 | − | 0.147816i | ||||
\(351\) | −2.16140 | −0.115367 | ||||||||
\(352\) | 2.97414 | − | 1.46782i | 0.158522 | − | 0.0782353i | ||||
\(353\) | −28.0551 | −1.49322 | −0.746611 | − | 0.665261i | \(-0.768320\pi\) | ||||
−0.746611 | + | 0.665261i | \(0.768320\pi\) | |||||||
\(354\) | 4.65258 | + | 3.38030i | 0.247282 | + | 0.179661i | ||||
\(355\) | −10.4402 | + | 32.1315i | −0.554107 | + | 1.70536i | ||||
\(356\) | 4.59590 | + | 14.1447i | 0.243582 | + | 0.749668i | ||||
\(357\) | −0.574672 | + | 0.417524i | −0.0304149 | + | 0.0220977i | ||||
\(358\) | 12.8563 | − | 9.34063i | 0.679475 | − | 0.493668i | ||||
\(359\) | −5.76547 | − | 17.7443i | −0.304290 | − | 0.936508i | −0.979941 | − | 0.199287i | \(-0.936138\pi\) |
0.675651 | − | 0.737221i | \(-0.263862\pi\) | |||||||
\(360\) | −0.962664 | + | 2.96278i | −0.0507368 | + | 0.156152i | ||||
\(361\) | 15.2949 | + | 11.1124i | 0.804996 | + | 0.584864i | ||||
\(362\) | −17.7593 | −0.933406 | ||||||||
\(363\) | −6.23607 | − | 9.06154i | −0.327309 | − | 0.475607i | ||||
\(364\) | −2.16140 | −0.113288 | ||||||||
\(365\) | 27.0813 | + | 19.6757i | 1.41750 | + | 1.02987i | ||||
\(366\) | 0.965452 | − | 2.97136i | 0.0504650 | − | 0.155315i | ||||
\(367\) | −0.465624 | − | 1.43304i | −0.0243054 | − | 0.0748042i | 0.938168 | − | 0.346180i | \(-0.112521\pi\) |
−0.962473 | + | 0.271376i | \(0.912521\pi\) | |||||||
\(368\) | −0.711270 | + | 0.516768i | −0.0370775 | + | 0.0269384i | ||||
\(369\) | −3.47041 | + | 2.52140i | −0.180662 | + | 0.131259i | ||||
\(370\) | 3.73434 | + | 11.4931i | 0.194139 | + | 0.597499i | ||||
\(371\) | −2.03455 | + | 6.26170i | −0.105628 | + | 0.325091i | ||||
\(372\) | −6.21902 | − | 4.51838i | −0.322441 | − | 0.234267i | ||||
\(373\) | −34.9467 | −1.80947 | −0.904737 | − | 0.425971i | \(-0.859933\pi\) | ||||
−0.904737 | + | 0.425971i | \(0.859933\pi\) | |||||||
\(374\) | 2.11263 | − | 1.04265i | 0.109241 | − | 0.0539139i | ||||
\(375\) | 0.919752 | 0.0474958 | ||||||||
\(376\) | −8.12127 | − | 5.90045i | −0.418823 | − | 0.304292i | ||||
\(377\) | −4.38941 | + | 13.5092i | −0.226066 | + | 0.695761i | ||||
\(378\) | 0.309017 | + | 0.951057i | 0.0158941 | + | 0.0489171i | ||||
\(379\) | −9.65258 | + | 7.01301i | −0.495820 | + | 0.360234i | −0.807418 | − | 0.589980i | \(-0.799136\pi\) |
0.311598 | + | 0.950214i | \(0.399136\pi\) | |||||||
\(380\) | 0.774469 | − | 0.562685i | 0.0397294 | − | 0.0288651i | ||||
\(381\) | 4.95757 | + | 15.2578i | 0.253984 | + | 0.781683i | ||||
\(382\) | −8.12423 | + | 25.0038i | −0.415672 | + | 1.27931i | ||||
\(383\) | −14.6245 | − | 10.6253i | −0.747278 | − | 0.542929i | 0.147704 | − | 0.989032i | \(-0.452812\pi\) |
−0.894982 | + | 0.446103i | \(0.852812\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 10.1834 | + | 1.74659i | 0.518994 | + | 0.0890145i | ||||
\(386\) | 5.56788 | 0.283398 | ||||||||
\(387\) | 6.66836 | + | 4.84485i | 0.338972 | + | 0.246277i | ||||
\(388\) | −0.0806980 | + | 0.248363i | −0.00409682 | + | 0.0126087i | ||||
\(389\) | −0.468412 | − | 1.44162i | −0.0237494 | − | 0.0730932i | 0.938479 | − | 0.345335i | \(-0.112235\pi\) |
−0.962229 | + | 0.272242i | \(0.912235\pi\) | |||||||
\(390\) | −5.44734 | + | 3.95772i | −0.275837 | + | 0.200407i | ||||
\(391\) | −0.505239 | + | 0.367078i | −0.0255510 | + | 0.0185639i | ||||
\(392\) | 0.309017 | + | 0.951057i | 0.0156077 | + | 0.0480356i | ||||
\(393\) | 6.14004 | − | 18.8971i | 0.309724 | − | 0.953233i | ||||
\(394\) | 9.55356 | + | 6.94107i | 0.481301 | + | 0.349686i | ||||
\(395\) | 30.2666 | 1.52288 | ||||||||
\(396\) | −0.476925 | − | 3.28216i | −0.0239664 | − | 0.164935i | ||||
\(397\) | 32.2351 | 1.61783 | 0.808917 | − | 0.587924i | \(-0.200054\pi\) | ||||
0.808917 | + | 0.587924i | \(0.200054\pi\) | |||||||
\(398\) | −7.71472 | − | 5.60507i | −0.386704 | − | 0.280957i | ||||
\(399\) | 0.0949591 | − | 0.292254i | 0.00475390 | − | 0.0146310i | ||||
\(400\) | 1.45385 | + | 4.47449i | 0.0726925 | + | 0.223725i | ||||
\(401\) | −7.22677 | + | 5.25055i | −0.360888 | + | 0.262200i | −0.753422 | − | 0.657537i | \(-0.771598\pi\) |
0.392535 | + | 0.919737i | \(0.371598\pi\) | |||||||
\(402\) | 5.40119 | − | 3.92419i | 0.269387 | − | 0.195721i | ||||
\(403\) | −5.13430 | − | 15.8017i | −0.255758 | − | 0.787141i | ||||
\(404\) | 0.788244 | − | 2.42596i | 0.0392166 | − | 0.120696i | ||||
\(405\) | 2.52029 | + | 1.83110i | 0.125234 | + | 0.0909879i | ||||
\(406\) | 6.57188 | 0.326157 | ||||||||
\(407\) | −8.98046 | − | 9.21301i | −0.445145 | − | 0.456672i | ||||
\(408\) | 0.710334 | 0.0351668 | ||||||||
\(409\) | 17.3829 | + | 12.6294i | 0.859527 | + | 0.624483i | 0.927756 | − | 0.373186i | \(-0.121735\pi\) |
−0.0682290 | + | 0.997670i | \(0.521735\pi\) | |||||||
\(410\) | −4.12951 | + | 12.7093i | −0.203942 | + | 0.627668i | ||||
\(411\) | 0.717954 | + | 2.20964i | 0.0354141 | + | 0.108993i | ||||
\(412\) | −15.2435 | + | 11.0750i | −0.750992 | + | 0.545628i | ||||
\(413\) | 4.65258 | − | 3.38030i | 0.228939 | − | 0.166334i | ||||
\(414\) | 0.271681 | + | 0.836148i | 0.0133524 | + | 0.0410944i | ||||
\(415\) | −15.1954 | + | 46.7667i | −0.745913 | + | 2.29568i | ||||
\(416\) | 1.74861 | + | 1.27044i | 0.0857325 | + | 0.0622883i | ||||
\(417\) | 7.48206 | 0.366398 | ||||||||
\(418\) | −0.474266 | + | 0.902107i | −0.0231971 | + | 0.0441235i | ||||
\(419\) | 22.3380 | 1.09128 | 0.545642 | − | 0.838018i | \(-0.316286\pi\) | ||||
0.545642 | + | 0.838018i | \(0.316286\pi\) | |||||||
\(420\) | 2.52029 | + | 1.83110i | 0.122977 | + | 0.0893483i | ||||
\(421\) | 3.05944 | − | 9.41598i | 0.149108 | − | 0.458907i | −0.848408 | − | 0.529342i | \(-0.822439\pi\) |
0.997516 | + | 0.0704352i | \(0.0224388\pi\) | |||||||
\(422\) | −3.69413 | − | 11.3694i | −0.179827 | − | 0.553452i | ||||
\(423\) | −8.12127 | + | 5.90045i | −0.394870 | + | 0.286890i | ||||
\(424\) | 5.32652 | − | 3.86994i | 0.258678 | − | 0.187941i | ||||
\(425\) | 1.03272 | + | 3.17838i | 0.0500942 | + | 0.154174i | ||||
\(426\) | 3.35131 | − | 10.3143i | 0.162372 | − | 0.499729i | ||||
\(427\) | −2.52759 | − | 1.83640i | −0.122318 | − | 0.0888696i | ||||
\(428\) | −3.40091 | −0.164389 | ||||||||
\(429\) | 3.33582 | − | 6.34510i | 0.161055 | − | 0.306344i | ||||
\(430\) | 25.6776 | 1.23828 | ||||||||
\(431\) | −1.31574 | − | 0.955939i | −0.0633768 | − | 0.0460460i | 0.555646 | − | 0.831419i | \(-0.312471\pi\) |
−0.619023 | + | 0.785373i | \(0.712471\pi\) | |||||||
\(432\) | 0.309017 | − | 0.951057i | 0.0148676 | − | 0.0457577i | ||||
\(433\) | −5.08416 | − | 15.6474i | −0.244329 | − | 0.751967i | −0.995746 | − | 0.0921398i | \(-0.970629\pi\) |
0.751417 | − | 0.659828i | \(-0.229371\pi\) | |||||||
\(434\) | −6.21902 | + | 4.51838i | −0.298522 | + | 0.216889i | ||||
\(435\) | 16.5630 | − | 12.0337i | 0.794137 | − | 0.576974i | ||||
\(436\) | 2.15258 | + | 6.62497i | 0.103090 | + | 0.317278i | ||||
\(437\) | 0.0834859 | − | 0.256943i | 0.00399367 | − | 0.0122913i | ||||
\(438\) | −8.69316 | − | 6.31595i | −0.415375 | − | 0.301788i | ||||
\(439\) | −6.45481 | −0.308071 | −0.154036 | − | 0.988065i | \(-0.549227\pi\) | ||||
−0.154036 | + | 0.988065i | \(0.549227\pi\) | |||||||
\(440\) | −7.21193 | − | 7.39868i | −0.343815 | − | 0.352718i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 1.24209 | + | 0.902434i | 0.0590804 | + | 0.0429244i | ||||
\(443\) | 10.7204 | − | 32.9941i | 0.509344 | − | 1.56760i | −0.284000 | − | 0.958824i | \(-0.591662\pi\) |
0.793344 | − | 0.608774i | \(-0.208338\pi\) | |||||||
\(444\) | −1.19873 | − | 3.68932i | −0.0568893 | − | 0.175087i | ||||
\(445\) | 37.4833 | − | 27.2332i | 1.77688 | − | 1.29098i | ||||
\(446\) | 7.10226 | − | 5.16009i | 0.336302 | − | 0.244337i | ||||
\(447\) | 0.441140 | + | 1.35769i | 0.0208652 | + | 0.0642165i | ||||
\(448\) | 0.309017 | − | 0.951057i | 0.0145997 | − | 0.0449332i | ||||
\(449\) | 29.3647 | + | 21.3347i | 1.38581 | + | 1.00685i | 0.996311 | + | 0.0858192i | \(0.0273508\pi\) |
0.389496 | + | 0.921028i | \(0.372649\pi\) | |||||||
\(450\) | 4.70476 | 0.221784 | ||||||||
\(451\) | −2.04585 | − | 14.0794i | −0.0963353 | − | 0.662971i | ||||
\(452\) | −1.39802 | −0.0657573 | ||||||||
\(453\) | 8.05935 | + | 5.85546i | 0.378661 | + | 0.275113i | ||||
\(454\) | −6.02667 | + | 18.5482i | −0.282846 | + | 0.870509i | ||||
\(455\) | 2.08070 | + | 6.40373i | 0.0975446 | + | 0.300211i | ||||
\(456\) | −0.248606 | + | 0.180623i | −0.0116420 | + | 0.00845844i | ||||
\(457\) | −17.2230 | + | 12.5133i | −0.805660 | + | 0.585346i | −0.912569 | − | 0.408923i | \(-0.865905\pi\) |
0.106909 | + | 0.994269i | \(0.465905\pi\) | |||||||
\(458\) | −2.24954 | − | 6.92338i | −0.105114 | − | 0.323508i | ||||
\(459\) | 0.219505 | − | 0.675568i | 0.0102456 | − | 0.0315328i | ||||
\(460\) | 2.21578 | + | 1.60986i | 0.103311 | + | 0.0750601i | ||||
\(461\) | −34.3997 | −1.60215 | −0.801076 | − | 0.598562i | \(-0.795739\pi\) | ||||
−0.801076 | + | 0.598562i | \(0.795739\pi\) | |||||||
\(462\) | −3.26889 | − | 0.560659i | −0.152083 | − | 0.0260842i | ||||
\(463\) | 33.4916 | 1.55648 | 0.778242 | − | 0.627964i | \(-0.216111\pi\) | ||||
0.778242 | + | 0.627964i | \(0.216111\pi\) | |||||||
\(464\) | −5.31677 | − | 3.86286i | −0.246825 | − | 0.179329i | ||||
\(465\) | −7.40012 | + | 22.7752i | −0.343172 | + | 1.05618i | ||||
\(466\) | −0.844352 | − | 2.59865i | −0.0391138 | − | 0.120380i | ||||
\(467\) | 20.1500 | − | 14.6398i | 0.932429 | − | 0.677449i | −0.0141572 | − | 0.999900i | \(-0.504507\pi\) |
0.946586 | + | 0.322450i | \(0.104507\pi\) | |||||||
\(468\) | 1.74861 | − | 1.27044i | 0.0808293 | − | 0.0587260i | ||||
\(469\) | −2.06307 | − | 6.34948i | −0.0952637 | − | 0.293192i | ||||
\(470\) | −9.66365 | + | 29.7417i | −0.445751 | + | 1.37188i | ||||
\(471\) | 19.9352 | + | 14.4838i | 0.918568 | + | 0.667379i | ||||
\(472\) | −5.75091 | −0.264707 | ||||||||
\(473\) | −24.5145 | + | 12.0986i | −1.12718 | + | 0.556295i | ||||
\(474\) | −9.71565 | −0.446255 | ||||||||
\(475\) | −1.16963 | − | 0.849787i | −0.0536664 | − | 0.0389909i | ||||
\(476\) | 0.219505 | − | 0.675568i | 0.0100610 | − | 0.0309646i | ||||
\(477\) | −2.03455 | − | 6.26170i | −0.0931556 | − | 0.286703i | ||||
\(478\) | −20.9517 | + | 15.2223i | −0.958308 | + | 0.696251i | ||||
\(479\) | 21.0876 | − | 15.3211i | 0.963518 | − | 0.700037i | 0.00955297 | − | 0.999954i | \(-0.496959\pi\) |
0.953965 | + | 0.299917i | \(0.0969591\pi\) | |||||||
\(480\) | −0.962664 | − | 2.96278i | −0.0439394 | − | 0.135232i | ||||
\(481\) | 2.59093 | − | 7.97408i | 0.118136 | − | 0.363587i | ||||
\(482\) | 5.14562 | + | 3.73851i | 0.234377 | + | 0.170285i | ||||
\(483\) | 0.879178 | 0.0400040 | ||||||||
\(484\) | 10.3713 | + | 3.66547i | 0.471424 | + | 0.166612i | ||||
\(485\) | 0.813528 | 0.0369404 | ||||||||
\(486\) | −0.809017 | − | 0.587785i | −0.0366978 | − | 0.0266625i | ||||
\(487\) | −3.41038 | + | 10.4961i | −0.154539 | + | 0.475623i | −0.998114 | − | 0.0613891i | \(-0.980447\pi\) |
0.843575 | + | 0.537012i | \(0.180447\pi\) | |||||||
\(488\) | 0.965452 | + | 2.97136i | 0.0437040 | + | 0.134507i | ||||
\(489\) | −11.6069 | + | 8.43289i | −0.524881 | + | 0.381349i | ||||
\(490\) | 2.52029 | − | 1.83110i | 0.113855 | − | 0.0827205i | ||||
\(491\) | 0.0565149 | + | 0.173935i | 0.00255048 | + | 0.00784958i | 0.952324 | − | 0.305090i | \(-0.0986864\pi\) |
−0.949773 | + | 0.312939i | \(0.898686\pi\) | |||||||
\(492\) | 1.32558 | − | 4.07972i | 0.0597618 | − | 0.183928i | ||||
\(493\) | −3.77668 | − | 2.74392i | −0.170093 | − | 0.123580i | ||||
\(494\) | −0.664184 | −0.0298830 | ||||||||
\(495\) | −9.26517 | + | 4.57263i | −0.416438 | + | 0.205525i | ||||
\(496\) | 7.68713 | 0.345162 | ||||||||
\(497\) | −8.77385 | − | 6.37458i | −0.393561 | − | 0.285939i | ||||
\(498\) | 4.87776 | − | 15.0122i | 0.218577 | − | 0.672712i | ||||
\(499\) | 5.21872 | + | 16.0616i | 0.233622 | + | 0.719014i | 0.997301 | + | 0.0734185i | \(0.0233909\pi\) |
−0.763679 | + | 0.645596i | \(0.776609\pi\) | |||||||
\(500\) | −0.744095 | + | 0.540617i | −0.0332769 | + | 0.0241771i | ||||
\(501\) | −11.3518 | + | 8.24754i | −0.507159 | + | 0.368473i | ||||
\(502\) | −3.98095 | − | 12.2521i | −0.177678 | − | 0.546838i | ||||
\(503\) | 1.26201 | − | 3.88407i | 0.0562703 | − | 0.173182i | −0.918971 | − | 0.394325i | \(-0.870979\pi\) |
0.975242 | + | 0.221142i | \(0.0709786\pi\) | |||||||
\(504\) | −0.809017 | − | 0.587785i | −0.0360365 | − | 0.0261820i | ||||
\(505\) | −7.94640 | −0.353610 | ||||||||
\(506\) | −2.87394 | − | 0.492919i | −0.127762 | − | 0.0219129i | ||||
\(507\) | −8.32837 | −0.369876 | ||||||||
\(508\) | −12.9791 | − | 9.42987i | −0.575854 | − | 0.418383i | ||||
\(509\) | 11.5255 | − | 35.4719i | 0.510860 | − | 1.57227i | −0.279831 | − | 0.960049i | \(-0.590278\pi\) |
0.790691 | − | 0.612216i | \(-0.209722\pi\) | |||||||
\(510\) | −0.683813 | − | 2.10456i | −0.0302797 | − | 0.0931914i | ||||
\(511\) | −8.69316 | + | 6.31595i | −0.384563 | + | 0.279401i | ||||
\(512\) | −0.809017 | + | 0.587785i | −0.0357538 | + | 0.0259767i | ||||
\(513\) | 0.0949591 | + | 0.292254i | 0.00419254 | + | 0.0129033i | ||||
\(514\) | 1.61565 | − | 4.97247i | 0.0712634 | − | 0.219326i | ||||
\(515\) | 47.4872 | + | 34.5015i | 2.09254 | + | 1.52032i | ||||
\(516\) | −8.24254 | −0.362858 | ||||||||
\(517\) | −4.78759 | − | 32.9477i | −0.210558 | − | 1.44904i | ||||
\(518\) | −3.87918 | −0.170441 | ||||||||
\(519\) | −11.4698 | − | 8.33330i | −0.503468 | − | 0.365791i | ||||
\(520\) | 2.08070 | − | 6.40373i | 0.0912446 | − | 0.280822i | ||||
\(521\) | −0.291138 | − | 0.896030i | −0.0127550 | − | 0.0392558i | 0.944476 | − | 0.328579i | \(-0.106570\pi\) |
−0.957231 | + | 0.289323i | \(0.906570\pi\) | |||||||
\(522\) | −5.31677 | + | 3.86286i | −0.232709 | + | 0.169073i | ||||
\(523\) | −18.6008 | + | 13.5143i | −0.813357 | + | 0.590938i | −0.914802 | − | 0.403903i | \(-0.867653\pi\) |
0.101445 | + | 0.994841i | \(0.467653\pi\) | |||||||
\(524\) | 6.14004 | + | 18.8971i | 0.268229 | + | 0.825524i | ||||
\(525\) | 1.45385 | − | 4.47449i | 0.0634512 | − | 0.195283i | ||||
\(526\) | −21.7017 | − | 15.7672i | −0.946239 | − | 0.687483i | ||||
\(527\) | 5.46043 | 0.237860 | ||||||||
\(528\) | 2.31504 | + | 2.37499i | 0.100749 | + | 0.103358i | ||||
\(529\) | −22.2270 | −0.966393 | ||||||||
\(530\) | −16.5934 | − | 12.0558i | −0.720772 | − | 0.523671i | ||||
\(531\) | −1.77713 | + | 5.46944i | −0.0771208 | + | 0.237353i | ||||
\(532\) | 0.0949591 | + | 0.292254i | 0.00411700 | + | 0.0126708i | ||||
\(533\) | 7.50094 | − | 5.44975i | 0.324902 | − | 0.236055i | ||||
\(534\) | −12.0322 | + | 8.74191i | −0.520685 | + | 0.378300i | ||||
\(535\) | 3.27393 | + | 10.0761i | 0.141544 | + | 0.435629i | ||||
\(536\) | −2.06307 | + | 6.34948i | −0.0891111 | + | 0.274256i | ||||
\(537\) | 12.8563 | + | 9.34063i | 0.554789 | + | 0.403078i | ||||
\(538\) | −11.0403 | −0.475982 | ||||||||
\(539\) | −1.54336 | + | 2.93565i | −0.0664773 | + | 0.126447i | ||||
\(540\) | −3.11525 | −0.134059 | ||||||||
\(541\) | −15.1643 | − | 11.0175i | −0.651964 | − | 0.473680i | 0.211976 | − | 0.977275i | \(-0.432010\pi\) |
−0.863940 | + | 0.503595i | \(0.832010\pi\) | |||||||
\(542\) | −5.59734 | + | 17.2268i | −0.240426 | + | 0.739956i | ||||
\(543\) | −5.48791 | − | 16.8901i | −0.235509 | − | 0.724822i | ||||
\(544\) | −0.574672 | + | 0.417524i | −0.0246389 | + | 0.0179012i | ||||
\(545\) | 17.5561 | − | 12.7552i | 0.752019 | − | 0.546374i | ||||
\(546\) | −0.667908 | − | 2.05561i | −0.0285838 | − | 0.0879720i | ||||
\(547\) | 8.12818 | − | 25.0160i | 0.347536 | − | 1.06961i | −0.612676 | − | 0.790334i | \(-0.709907\pi\) |
0.960212 | − | 0.279271i | \(-0.0900929\pi\) | |||||||
\(548\) | −1.87963 | − | 1.36563i | −0.0802937 | − | 0.0583368i | ||||
\(549\) | 3.12427 | 0.133341 | ||||||||
\(550\) | −7.26114 | + | 13.8115i | −0.309616 | + | 0.588925i | ||||
\(551\) | 2.01950 | 0.0860336 | ||||||||
\(552\) | −0.711270 | − | 0.516768i | −0.0302737 | − | 0.0219951i | ||||
\(553\) | −3.00230 | + | 9.24013i | −0.127671 | + | 0.392930i | ||||
\(554\) | 3.49845 | + | 10.7671i | 0.148635 | + | 0.457451i | ||||
\(555\) | −9.77664 | + | 7.10315i | −0.414995 | + | 0.301512i | ||||
\(556\) | −6.05311 | + | 4.39784i | −0.256709 | + | 0.186510i | ||||
\(557\) | −2.36860 | − | 7.28979i | −0.100361 | − | 0.308879i | 0.888253 | − | 0.459355i | \(-0.151919\pi\) |
−0.988614 | + | 0.150476i | \(0.951919\pi\) | |||||||
\(558\) | 2.37545 | − | 7.31090i | 0.100561 | − | 0.309495i | ||||
\(559\) | −14.4130 | − | 10.4716i | −0.609603 | − | 0.442903i | ||||
\(560\) | −3.11525 | −0.131643 | ||||||||
\(561\) | 1.64445 | + | 1.68704i | 0.0694289 | + | 0.0712267i | ||||
\(562\) | 25.1590 | 1.06127 | ||||||||
\(563\) | 32.5519 | + | 23.6503i | 1.37190 | + | 0.996742i | 0.997586 | + | 0.0694397i | \(0.0221211\pi\) |
0.374312 | + | 0.927303i | \(0.377879\pi\) | |||||||
\(564\) | 3.10205 | − | 9.54713i | 0.130620 | − | 0.402007i | ||||
\(565\) | 1.34582 | + | 4.14202i | 0.0566192 | + | 0.174256i | ||||
\(566\) | −4.54464 | + | 3.30187i | −0.191025 | + | 0.138788i | ||||
\(567\) | −0.809017 | + | 0.587785i | −0.0339755 | + | 0.0246847i | ||||
\(568\) | 3.35131 | + | 10.3143i | 0.140618 | + | 0.432778i | ||||
\(569\) | −9.29055 | + | 28.5934i | −0.389480 | + | 1.19870i | 0.543698 | + | 0.839281i | \(0.317024\pi\) |
−0.933178 | + | 0.359415i | \(0.882976\pi\) | |||||||
\(570\) | 0.774469 | + | 0.562685i | 0.0324389 | + | 0.0235683i | ||||
\(571\) | −21.9318 | −0.917817 | −0.458909 | − | 0.888483i | \(-0.651760\pi\) | ||||
−0.458909 | + | 0.888483i | \(0.651760\pi\) | |||||||
\(572\) | 1.03082 | + | 7.09404i | 0.0431009 | + | 0.296617i | ||||
\(573\) | −26.2906 | −1.09830 | ||||||||
\(574\) | −3.47041 | − | 2.52140i | −0.144852 | − | 0.105241i | ||||
\(575\) | 1.27819 | − | 3.93387i | 0.0533043 | − | 0.164054i | ||||
\(576\) | 0.309017 | + | 0.951057i | 0.0128757 | + | 0.0396274i | ||||
\(577\) | 29.3684 | − | 21.3374i | 1.22262 | − | 0.888287i | 0.226308 | − | 0.974056i | \(-0.427335\pi\) |
0.996315 | + | 0.0857685i | \(0.0273345\pi\) | |||||||
\(578\) | 13.3451 | − | 9.69577i | 0.555082 | − | 0.403291i | ||||
\(579\) | 1.72057 | + | 5.29537i | 0.0715045 | + | 0.220068i | ||||
\(580\) | −6.32652 | + | 19.4710i | −0.262694 | + | 0.808490i | ||||
\(581\) | −12.7701 | − | 9.27804i | −0.529794 | − | 0.384918i | ||||
\(582\) | −0.261144 | −0.0108248 | ||||||||
\(583\) | 21.5222 | + | 3.69134i | 0.891358 | + | 0.152880i | ||||
\(584\) | 10.7453 | 0.444645 | ||||||||
\(585\) | −5.44734 | − | 3.95772i | −0.225220 | − | 0.163632i | ||||
\(586\) | 2.56520 | − | 7.89487i | 0.105967 | − | 0.326134i | ||||
\(587\) | −1.81885 | − | 5.59783i | −0.0750718 | − | 0.231047i | 0.906478 | − | 0.422252i | \(-0.138760\pi\) |
−0.981550 | + | 0.191205i | \(0.938760\pi\) | |||||||
\(588\) | −0.809017 | + | 0.587785i | −0.0333633 | + | 0.0242399i | ||||
\(589\) | −1.91107 | + | 1.38847i | −0.0787441 | + | 0.0572110i | ||||
\(590\) | 5.53619 | + | 17.0386i | 0.227921 | + | 0.701470i | ||||
\(591\) | −3.64914 | + | 11.2309i | −0.150105 | + | 0.461977i | ||||
\(592\) | 3.13832 | + | 2.28012i | 0.128984 | + | 0.0937125i | ||||
\(593\) | −10.5795 | −0.434449 | −0.217224 | − | 0.976122i | \(-0.569700\pi\) | ||||
−0.217224 | + | 0.976122i | \(0.569700\pi\) | |||||||
\(594\) | 2.97414 | − | 1.46782i | 0.122030 | − | 0.0602256i | ||||
\(595\) | −2.21286 | −0.0907186 | ||||||||
\(596\) | −1.15492 | − | 0.839099i | −0.0473074 | − | 0.0343708i | ||||
\(597\) | 2.94676 | − | 9.06919i | 0.120603 | − | 0.371177i | ||||
\(598\) | −0.587210 | − | 1.80725i | −0.0240128 | − | 0.0739038i | ||||
\(599\) | 9.76734 | − | 7.09639i | 0.399083 | − | 0.289951i | −0.370085 | − | 0.928998i | \(-0.620671\pi\) |
0.769167 | + | 0.639047i | \(0.220671\pi\) | |||||||
\(600\) | −3.80623 | + | 2.76539i | −0.155389 | + | 0.112896i | ||||
\(601\) | −13.3021 | − | 40.9395i | −0.542602 | − | 1.66996i | −0.726623 | − | 0.687036i | \(-0.758911\pi\) |
0.184021 | − | 0.982922i | \(-0.441089\pi\) | |||||||
\(602\) | −2.54709 | + | 7.83913i | −0.103811 | + | 0.319499i | ||||
\(603\) | 5.40119 | + | 3.92419i | 0.219953 | + | 0.159805i | ||||
\(604\) | −9.96190 | −0.405344 | ||||||||
\(605\) | 0.875861 | − | 34.2565i | 0.0356088 | − | 1.39273i | ||||
\(606\) | 2.55081 | 0.103620 | ||||||||
\(607\) | −9.57439 | − | 6.95620i | −0.388613 | − | 0.282344i | 0.376274 | − | 0.926508i | \(-0.377205\pi\) |
−0.764887 | + | 0.644165i | \(0.777205\pi\) | |||||||
\(608\) | 0.0949591 | − | 0.292254i | 0.00385110 | − | 0.0118525i | ||||
\(609\) | 2.03082 | + | 6.25023i | 0.0822931 | + | 0.253272i | ||||
\(610\) | 7.87405 | − | 5.72083i | 0.318811 | − | 0.231630i | ||||
\(611\) | 17.5533 | − | 12.7532i | 0.710130 | − | 0.515940i | ||||
\(612\) | 0.219505 | + | 0.675568i | 0.00887297 | + | 0.0273082i | ||||
\(613\) | 11.6416 | − | 35.8292i | 0.470200 | − | 1.44713i | −0.382122 | − | 0.924112i | \(-0.624807\pi\) |
0.852323 | − | 0.523016i | \(-0.175193\pi\) | |||||||
\(614\) | −1.16570 | − | 0.846930i | −0.0470438 | − | 0.0341793i | ||||
\(615\) | −13.3634 | −0.538863 | ||||||||
\(616\) | 2.97414 | − | 1.46782i | 0.119831 | − | 0.0591403i | ||||
\(617\) | −40.5797 | −1.63368 | −0.816838 | − | 0.576867i | \(-0.804275\pi\) | ||||
−0.816838 | + | 0.576867i | \(0.804275\pi\) | |||||||
\(618\) | −15.2435 | − | 11.0750i | −0.613183 | − | 0.445503i | ||||
\(619\) | −7.14425 | + | 21.9878i | −0.287152 | + | 0.883762i | 0.698594 | + | 0.715519i | \(0.253810\pi\) |
−0.985745 | + | 0.168244i | \(0.946190\pi\) | |||||||
\(620\) | −7.40012 | − | 22.7752i | −0.297196 | − | 0.914676i | ||||
\(621\) | −0.711270 | + | 0.516768i | −0.0285423 | + | 0.0207372i | ||||
\(622\) | −8.00462 | + | 5.81570i | −0.320956 | + | 0.233188i | ||||
\(623\) | 4.59590 | + | 14.1447i | 0.184131 | + | 0.566696i | ||||
\(624\) | −0.667908 | + | 2.05561i | −0.0267377 | + | 0.0822902i | ||||
\(625\) | 21.3492 | + | 15.5111i | 0.853967 | + | 0.620444i | ||||
\(626\) | −5.55886 | −0.222177 | ||||||||
\(627\) | −1.00451 | − | 0.172287i | −0.0401163 | − | 0.00688048i | ||||
\(628\) | −24.6413 | −0.983296 | ||||||||
\(629\) | 2.22926 | + | 1.61965i | 0.0888862 | + | 0.0645796i | ||||
\(630\) | −0.962664 | + | 2.96278i | −0.0383535 | + | 0.118040i | ||||
\(631\) | −5.69945 | − | 17.5411i | −0.226891 | − | 0.698300i | −0.998094 | − | 0.0617103i | \(-0.980345\pi\) |
0.771203 | − | 0.636590i | \(-0.219655\pi\) | |||||||
\(632\) | 7.86013 | − | 5.71072i | 0.312659 | − | 0.227160i | ||||
\(633\) | 9.67135 | − | 7.02665i | 0.384402 | − | 0.279284i | ||||
\(634\) | −0.214544 | − | 0.660299i | −0.00852064 | − | 0.0262238i | ||||
\(635\) | −15.4441 | + | 47.5319i | −0.612879 | + | 1.88625i | ||||
\(636\) | 5.32652 | + | 3.86994i | 0.211210 | + | 0.153453i | ||||
\(637\) | −2.16140 | −0.0856376 | ||||||||
\(638\) | −3.13430 | − | 21.5699i | −0.124088 | − | 0.853962i | ||||
\(639\) | 10.8451 | 0.429025 | ||||||||
\(640\) | 2.52029 | + | 1.83110i | 0.0996231 | + | 0.0723804i | ||||
\(641\) | −2.37656 | + | 7.31431i | −0.0938686 | + | 0.288898i | −0.986957 | − | 0.160983i | \(-0.948534\pi\) |
0.893089 | + | 0.449881i | \(0.148534\pi\) | |||||||
\(642\) | −1.05094 | − | 3.23446i | −0.0414773 | − | 0.127654i | ||||
\(643\) | −13.1343 | + | 9.54260i | −0.517965 | + | 0.376323i | −0.815837 | − | 0.578282i | \(-0.803723\pi\) |
0.297872 | + | 0.954606i | \(0.403723\pi\) | |||||||
\(644\) | −0.711270 | + | 0.516768i | −0.0280280 | + | 0.0203635i | ||||
\(645\) | 7.93480 | + | 24.4208i | 0.312432 | + | 0.961568i | ||||
\(646\) | 0.0674526 | − | 0.207598i | 0.00265389 | − | 0.00816783i | ||||
\(647\) | 11.8174 | + | 8.58586i | 0.464591 | + | 0.337545i | 0.795329 | − | 0.606177i | \(-0.207298\pi\) |
−0.330739 | + | 0.943722i | \(0.607298\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −13.3136 | − | 13.6583i | −0.522604 | − | 0.536137i | ||||
\(650\) | −10.1688 | −0.398855 | ||||||||
\(651\) | −6.21902 | − | 4.51838i | −0.243743 | − | 0.177089i | ||||
\(652\) | 4.43343 | − | 13.6447i | 0.173627 | − | 0.534368i | ||||
\(653\) | −4.36249 | − | 13.4264i | −0.170717 | − | 0.525414i | 0.828695 | − | 0.559701i | \(-0.189084\pi\) |
−0.999412 | + | 0.0342870i | \(0.989084\pi\) | |||||||
\(654\) | −5.63553 | + | 4.09445i | −0.220367 | + | 0.160106i | ||||
\(655\) | 50.0771 | − | 36.3831i | 1.95667 | − | 1.42161i | ||||
\(656\) | 1.32558 | + | 4.07972i | 0.0517552 | + | 0.159286i | ||||
\(657\) | 3.32049 | − | 10.2194i | 0.129545 | − | 0.398697i | ||||
\(658\) | −8.12127 | − | 5.90045i | −0.316600 | − | 0.230023i | ||||
\(659\) | 33.9283 | 1.32166 | 0.660829 | − | 0.750536i | \(-0.270205\pi\) | ||||
0.660829 | + | 0.750536i | \(0.270205\pi\) | |||||||
\(660\) | 4.80795 | − | 9.14527i | 0.187149 | − | 0.355979i | ||||
\(661\) | 18.7723 | 0.730157 | 0.365079 | − | 0.930977i | \(-0.381042\pi\) | ||||
0.365079 | + | 0.930977i | \(0.381042\pi\) | |||||||
\(662\) | 25.1013 | + | 18.2371i | 0.975589 | + | 0.708807i | ||||
\(663\) | −0.474438 | + | 1.46017i | −0.0184256 | + | 0.0567083i | ||||
\(664\) | 4.87776 | + | 15.0122i | 0.189294 | + | 0.582586i | ||||
\(665\) | 0.774469 | − | 0.562685i | 0.0300326 | − | 0.0218200i | ||||
\(666\) | 3.13832 | − | 2.28012i | 0.121607 | − | 0.0883530i | ||||
\(667\) | 1.78546 | + | 5.49507i | 0.0691331 | + | 0.212770i | ||||
\(668\) | 4.33599 | − | 13.3448i | 0.167764 | − | 0.516326i | ||||
\(669\) | 7.10226 | + | 5.16009i | 0.274589 | + | 0.199501i | ||||
\(670\) | 20.7981 | 0.803501 | ||||||||
\(671\) | −4.82188 | + | 9.17175i | −0.186146 | + | 0.354072i | ||||
\(672\) | 1.00000 | 0.0385758 | ||||||||
\(673\) | −21.4093 | − | 15.5547i | −0.825266 | − | 0.599591i | 0.0929499 | − | 0.995671i | \(-0.470370\pi\) |
−0.918216 | + | 0.396080i | \(0.870370\pi\) | |||||||
\(674\) | 5.07933 | − | 15.6326i | 0.195649 | − | 0.602144i | ||||
\(675\) | 1.45385 | + | 4.47449i | 0.0559587 | + | 0.172223i | ||||
\(676\) | 6.73779 | − | 4.89529i | 0.259146 | − | 0.188280i | ||||
\(677\) | −9.60943 | + | 6.98166i | −0.369320 | + | 0.268327i | −0.756929 | − | 0.653497i | \(-0.773301\pi\) |
0.387609 | + | 0.921824i | \(0.373301\pi\) | |||||||
\(678\) | −0.432012 | − | 1.32960i | −0.0165913 | − | 0.0510628i | ||||
\(679\) | −0.0806980 | + | 0.248363i | −0.00309690 | + | 0.00953129i | ||||
\(680\) | 1.79024 | + | 1.30069i | 0.0686528 | + | 0.0498791i | ||||
\(681\) | −19.5027 | −0.747346 | ||||||||
\(682\) | 17.7960 | + | 18.2569i | 0.681445 | + | 0.699091i | ||||
\(683\) | −35.6132 | −1.36270 | −0.681351 | − | 0.731957i | \(-0.738607\pi\) | ||||
−0.681351 | + | 0.731957i | \(0.738607\pi\) | |||||||
\(684\) | −0.248606 | − | 0.180623i | −0.00950569 | − | 0.00690629i | ||||
\(685\) | −2.23660 | + | 6.88356i | −0.0854562 | + | 0.263007i | ||||
\(686\) | 0.309017 | + | 0.951057i | 0.0117983 | + | 0.0363115i | ||||
\(687\) | 5.88938 | − | 4.27888i | 0.224694 | − | 0.163250i | ||||
\(688\) | 6.66836 | − | 4.84485i | 0.254229 | − | 0.184708i | ||||
\(689\) | 4.39746 | + | 13.5340i | 0.167530 | + | 0.515604i | ||||
\(690\) | −0.846353 | + | 2.60481i | −0.0322201 | + | 0.0991633i | ||||
\(691\) | −3.14171 | − | 2.28258i | −0.119516 | − | 0.0868336i | 0.526421 | − | 0.850224i | \(-0.323533\pi\) |
−0.645938 | + | 0.763390i | \(0.723533\pi\) | |||||||
\(692\) | 14.1774 | 0.538946 | ||||||||
\(693\) | −0.476925 | − | 3.28216i | −0.0181169 | − | 0.124679i | ||||
\(694\) | 35.0591 | 1.33083 | ||||||||
\(695\) | 18.8569 | + | 13.7004i | 0.715284 | + | 0.519684i | ||||
\(696\) | 2.03082 | − | 6.25023i | 0.0769782 | − | 0.236914i | ||||
\(697\) | 0.941604 | + | 2.89796i | 0.0356658 | + | 0.109768i | ||||
\(698\) | −6.97938 | + | 5.07081i | −0.264173 | + | 0.191933i | ||||
\(699\) | 2.21054 | − | 1.60605i | 0.0836104 | − | 0.0607465i | ||||
\(700\) | 1.45385 | + | 4.47449i | 0.0549504 | + | 0.169120i | ||||
\(701\) | 10.5574 | − | 32.4925i | 0.398749 | − | 1.22722i | −0.527254 | − | 0.849707i | \(-0.676779\pi\) |
0.926003 | − | 0.377515i | \(-0.123221\pi\) | |||||||
\(702\) | 1.74861 | + | 1.27044i | 0.0659969 | + | 0.0479495i | ||||
\(703\) | −1.19205 | −0.0449589 | ||||||||
\(704\) | −3.26889 | − | 0.560659i | −0.123201 | − | 0.0211306i | ||||
\(705\) | −31.2722 | −1.17778 | ||||||||
\(706\) | 22.6971 | + | 16.4904i | 0.854215 | + | 0.620623i | ||||
\(707\) | 0.788244 | − | 2.42596i | 0.0296450 | − | 0.0912378i | ||||
\(708\) | −1.77713 | − | 5.46944i | −0.0667886 | − | 0.205554i | ||||
\(709\) | 38.6479 | − | 28.0794i | 1.45145 | − | 1.05454i | 0.465964 | − | 0.884803i | \(-0.345707\pi\) |
0.985489 | − | 0.169739i | \(-0.0542925\pi\) | |||||||
\(710\) | 27.3327 | − | 19.8584i | 1.02578 | − | 0.745272i | ||||
\(711\) | −3.00230 | − | 9.24013i | −0.112595 | − | 0.346532i | ||||
\(712\) | 4.59590 | − | 14.1447i | 0.172238 | − | 0.530095i | ||||
\(713\) | −5.46762 | − | 3.97246i | −0.204764 | − | 0.148770i | ||||
\(714\) | 0.710334 | 0.0265836 | ||||||||
\(715\) | 20.0257 | − | 9.88327i | 0.748919 | − | 0.369613i | ||||
\(716\) | −15.8912 | −0.593883 | ||||||||
\(717\) | −20.9517 | − | 15.2223i | −0.782455 | − | 0.568487i | ||||
\(718\) | −5.76547 | + | 17.7443i | −0.215165 | + | 0.662211i | ||||
\(719\) | 1.01560 | + | 3.12571i | 0.0378756 | + | 0.116569i | 0.968207 | − | 0.250152i | \(-0.0804804\pi\) |
−0.930331 | + | 0.366721i | \(0.880480\pi\) | |||||||
\(720\) | 2.52029 | − | 1.83110i | 0.0939256 | − | 0.0682409i | ||||
\(721\) | −15.2435 | + | 11.0750i | −0.567697 | + | 0.412456i | ||||
\(722\) | −5.84214 | − | 17.9803i | −0.217422 | − | 0.669156i | ||||
\(723\) | −1.96545 | + | 6.04904i | −0.0730959 | + | 0.224966i | ||||
\(724\) | 14.3675 | + | 10.4386i | 0.533965 | + | 0.387949i | ||||
\(725\) | 30.9191 | 1.14831 | ||||||||
\(726\) | −0.281153 | + | 10.9964i | −0.0104346 | + | 0.408115i | ||||
\(727\) | −6.49508 | −0.240889 | −0.120445 | − | 0.992720i | \(-0.538432\pi\) | ||||
−0.120445 | + | 0.992720i | \(0.538432\pi\) | |||||||
\(728\) | 1.74861 | + | 1.27044i | 0.0648077 | + | 0.0470855i | ||||
\(729\) | 0.309017 | − | 0.951057i | 0.0114451 | − | 0.0352243i | ||||
\(730\) | −10.3441 | − | 31.8360i | −0.382854 | − | 1.17830i | ||||
\(731\) | 4.73676 | − | 3.44146i | 0.175195 | − | 0.127287i | ||||
\(732\) | −2.52759 | + | 1.83640i | −0.0934223 | + | 0.0678752i | ||||
\(733\) | −15.4915 | − | 47.6778i | −0.572190 | − | 1.76102i | −0.645553 | − | 0.763715i | \(-0.723373\pi\) |
0.0733629 | − | 0.997305i | \(-0.476627\pi\) | |||||||
\(734\) | −0.465624 | + | 1.43304i | −0.0171865 | + | 0.0528946i | ||||
\(735\) | 2.52029 | + | 1.83110i | 0.0929622 | + | 0.0675410i | ||||
\(736\) | 0.879178 | 0.0324069 | ||||||||
\(737\) | −19.8560 | + | 9.79954i | −0.731407 | + | 0.360971i | ||||
\(738\) | 4.28967 | 0.157905 | ||||||||
\(739\) | −12.3163 | − | 8.94833i | −0.453063 | − | 0.329170i | 0.337741 | − | 0.941239i | \(-0.390337\pi\) |
−0.790804 | + | 0.612070i | \(0.790337\pi\) | |||||||
\(740\) | 3.73434 | − | 11.4931i | 0.137277 | − | 0.422496i | ||||
\(741\) | −0.205244 | − | 0.631676i | −0.00753983 | − | 0.0232052i | ||||
\(742\) | 5.32652 | − | 3.86994i | 0.195543 | − | 0.142070i | ||||
\(743\) | 19.0139 | − | 13.8144i | 0.697554 | − | 0.506803i | −0.181581 | − | 0.983376i | \(-0.558121\pi\) |
0.879135 | + | 0.476573i | \(0.158121\pi\) | |||||||
\(744\) | 2.37545 | + | 7.31090i | 0.0870884 | + | 0.268030i | ||||
\(745\) | −1.37426 | + | 4.22954i | −0.0503490 | + | 0.154958i | ||||
\(746\) | 28.2725 | + | 20.5412i | 1.03513 | + | 0.752066i | ||||
\(747\) | 15.7847 | 0.577534 | ||||||||
\(748\) | −2.32201 | − | 0.398255i | −0.0849009 | − | 0.0145616i | ||||
\(749\) | −3.40091 | −0.124267 | ||||||||
\(750\) | −0.744095 | − | 0.540617i | −0.0271705 | − | 0.0197405i | ||||
\(751\) | 5.12915 | − | 15.7859i | 0.187165 | − | 0.576036i | −0.812814 | − | 0.582524i | \(-0.802065\pi\) |
0.999979 | + | 0.00648819i | \(0.00206527\pi\) | |||||||
\(752\) | 3.10205 | + | 9.54713i | 0.113120 | + | 0.348148i | ||||
\(753\) | 10.4223 | − | 7.57222i | 0.379808 | − | 0.275947i | ||||
\(754\) | 11.4916 | − | 8.34916i | 0.418501 | − | 0.304059i | ||||
\(755\) | 9.58996 | + | 29.5149i | 0.349014 | + | 1.07416i | ||||
\(756\) | 0.309017 | − | 0.951057i | 0.0112388 | − | 0.0345896i | ||||
\(757\) | 1.29103 | + | 0.937989i | 0.0469233 | + | 0.0340918i | 0.611000 | − | 0.791631i | \(-0.290768\pi\) |
−0.564076 | + | 0.825723i | \(0.690768\pi\) | |||||||
\(758\) | 11.9312 | 0.433362 | ||||||||
\(759\) | −0.419302 | − | 2.88560i | −0.0152197 | − | 0.104741i | ||||
\(760\) | −0.957296 | −0.0347248 | ||||||||
\(761\) | −2.91975 | − | 2.12132i | −0.105841 | − | 0.0768979i | 0.533606 | − | 0.845733i | \(-0.320837\pi\) |
−0.639447 | + | 0.768835i | \(0.720837\pi\) | |||||||
\(762\) | 4.95757 | − | 15.2578i | 0.179594 | − | 0.552733i | ||||
\(763\) | 2.15258 | + | 6.62497i | 0.0779287 | + | 0.239840i | ||||
\(764\) | 21.2695 | − | 15.4532i | 0.769504 | − | 0.559077i | ||||
\(765\) | 1.79024 | − | 1.30069i | 0.0647264 | − | 0.0470265i | ||||
\(766\) | 5.58607 | + | 17.1921i | 0.201833 | + | 0.621177i | ||||
\(767\) | 3.84108 | − | 11.8216i | 0.138693 | − | 0.426854i | ||||
\(768\) | −0.809017 | − | 0.587785i | −0.0291929 | − | 0.0212099i | ||||
\(769\) | −38.6906 | −1.39522 | −0.697609 | − | 0.716479i | \(-0.745753\pi\) | ||||
−0.697609 | + | 0.716479i | \(0.745753\pi\) | |||||||
\(770\) | −7.21193 | − | 7.39868i | −0.259900 | − | 0.266630i | ||||
\(771\) | 5.22836 | 0.188295 | ||||||||
\(772\) | −4.50451 | − | 3.27272i | −0.162121 | − | 0.117788i | ||||
\(773\) | 0.534756 | − | 1.64581i | 0.0192338 | − | 0.0591957i | −0.940979 | − | 0.338465i | \(-0.890092\pi\) |
0.960213 | + | 0.279269i | \(0.0900923\pi\) | |||||||
\(774\) | −2.54709 | − | 7.83913i | −0.0915531 | − | 0.281772i | ||||
\(775\) | −29.2590 | + | 21.2579i | −1.05101 | + | 0.763606i | ||||
\(776\) | 0.211270 | − | 0.153497i | 0.00758415 | − | 0.00551021i | ||||
\(777\) | −1.19873 | − | 3.68932i | −0.0430043 | − | 0.132354i | ||||
\(778\) | −0.468412 | + | 1.44162i | −0.0167934 | + | 0.0516847i | ||||
\(779\) | −1.06644 | − | 0.774812i | −0.0382091 | − | 0.0277605i | ||||
\(780\) | 6.73328 | 0.241090 | ||||||||
\(781\) | −16.7379 | + | 31.8373i | −0.598929 | + | 1.13923i | ||||
\(782\) | 0.624510 | 0.0223324 | ||||||||
\(783\) | −5.31677 | − | 3.86286i | −0.190006 | − | 0.138047i | ||||
\(784\) | 0.309017 | − | 0.951057i | 0.0110363 | − | 0.0339663i | ||||
\(785\) | 23.7213 | + | 73.0067i | 0.846650 | + | 2.60572i | ||||
\(786\) | −16.0748 | + | 11.6791i | −0.573371 | + | 0.416578i | ||||
\(787\) | −2.10005 | + | 1.52577i | −0.0748587 | + | 0.0543880i | −0.624585 | − | 0.780957i | \(-0.714732\pi\) |
0.549727 | + | 0.835345i | \(0.314732\pi\) | |||||||
\(788\) | −3.64914 | − | 11.2309i | −0.129995 | − | 0.400084i | ||||
\(789\) | 8.28931 | − | 25.5119i | 0.295107 | − | 0.908247i | ||||
\(790\) | −24.4862 | − | 17.7903i | −0.871181 | − | 0.632950i | ||||
\(791\) | −1.39802 | −0.0497079 | ||||||||
\(792\) | −1.54336 | + | 2.93565i | −0.0548410 | + | 0.104314i | ||||
\(793\) | −6.75278 | −0.239798 | ||||||||
\(794\) | −26.0787 | − | 18.9473i | −0.925500 | − | 0.672415i | ||||
\(795\) | 6.33812 | − | 19.5067i | 0.224790 | − | 0.691832i | ||||
\(796\) | 2.94676 | + | 9.06919i | 0.104445 | + | 0.321449i | ||||
\(797\) | −24.3171 | + | 17.6674i | −0.861355 | + | 0.625811i | −0.928253 | − | 0.371948i | \(-0.878690\pi\) |
0.0668980 | + | 0.997760i | \(0.478690\pi\) | |||||||
\(798\) | −0.248606 | + | 0.180623i | −0.00880056 | + | 0.00639398i | ||||
\(799\) | 2.20349 | + | 6.78165i | 0.0779539 | + | 0.239917i | ||||
\(800\) | 1.45385 | − | 4.47449i | 0.0514014 | − | 0.158197i | ||||
\(801\) | −12.0322 | − | 8.74191i | −0.425137 | − | 0.308880i | ||||
\(802\) | 8.93278 | 0.315427 | ||||||||
\(803\) | 24.8759 | + | 25.5201i | 0.877852 | + | 0.900583i | ||||
\(804\) | −6.67624 | −0.235453 | ||||||||
\(805\) | 2.21578 | + | 1.60986i | 0.0780960 | + | 0.0567401i | ||||
\(806\) | −5.13430 | + | 15.8017i | −0.180848 | + | 0.556593i | ||||
\(807\) | −3.41165 | − | 10.5000i | −0.120096 | − | 0.369616i | ||||
\(808\) | −2.06365 | + | 1.49933i | −0.0725989 | + | 0.0527462i | ||||
\(809\) | −25.0367 | + | 18.1903i | −0.880245 | + | 0.639535i | −0.933316 | − | 0.359055i | \(-0.883099\pi\) |
0.0530713 | + | 0.998591i | \(0.483099\pi\) | |||||||
\(810\) | −0.962664 | − | 2.96278i | −0.0338246 | − | 0.104101i | ||||
\(811\) | 3.91631 | − | 12.0532i | 0.137520 | − | 0.423243i | −0.858453 | − | 0.512892i | \(-0.828574\pi\) |
0.995973 | + | 0.0896482i | \(0.0285743\pi\) | |||||||
\(812\) | −5.31677 | − | 3.86286i | −0.186582 | − | 0.135560i | ||||
\(813\) | −18.1134 | −0.635264 | ||||||||
\(814\) | 1.85008 | + | 12.7321i | 0.0648452 | + | 0.446259i | ||||
\(815\) | −44.6941 | −1.56557 | ||||||||
\(816\) | −0.574672 | − | 0.417524i | −0.0201175 | − | 0.0146163i | ||||
\(817\) | −0.782704 | + | 2.40892i | −0.0273834 | + | 0.0842773i | ||||
\(818\) | −6.63966 | − | 20.4348i | −0.232150 | − | 0.714485i | ||||
\(819\) | 1.74861 | − | 1.27044i | 0.0611012 | − | 0.0443926i | ||||
\(820\) | 10.8112 | − | 7.85479i | 0.377543 | − | 0.274301i | ||||
\(821\) | −1.18204 | − | 3.63795i | −0.0412535 | − | 0.126965i | 0.928309 | − | 0.371810i | \(-0.121263\pi\) |
−0.969562 | + | 0.244845i | \(0.921263\pi\) | |||||||
\(822\) | 0.717954 | − | 2.20964i | 0.0250415 | − | 0.0770699i | ||||
\(823\) | 38.8927 | + | 28.2572i | 1.35571 | + | 0.984985i | 0.998705 | + | 0.0508841i | \(0.0162039\pi\) |
0.357010 | + | 0.934100i | \(0.383796\pi\) | |||||||
\(824\) | 18.8420 | 0.656391 | ||||||||
\(825\) | −15.3793 | − | 2.63776i | −0.535440 | − | 0.0918352i | ||||
\(826\) | −5.75091 | −0.200100 | ||||||||
\(827\) | 35.4298 | + | 25.7413i | 1.23202 | + | 0.895112i | 0.997040 | − | 0.0768886i | \(-0.0244986\pi\) |
0.234977 | + | 0.972001i | \(0.424499\pi\) | |||||||
\(828\) | 0.271681 | − | 0.836148i | 0.00944157 | − | 0.0290582i | ||||
\(829\) | 15.3747 | + | 47.3184i | 0.533985 | + | 1.64344i | 0.745832 | + | 0.666134i | \(0.232052\pi\) |
−0.211847 | + | 0.977303i | \(0.567948\pi\) | |||||||
\(830\) | 39.7821 | − | 28.9034i | 1.38086 | − | 1.00325i | ||||
\(831\) | −9.15906 | + | 6.65445i | −0.317724 | + | 0.230840i | ||||
\(832\) | −0.667908 | − | 2.05561i | −0.0231555 | − | 0.0712654i | ||||
\(833\) | 0.219505 | − | 0.675568i | 0.00760540 | − | 0.0234070i | ||||
\(834\) | −6.05311 | − | 4.39784i | −0.209602 | − | 0.152285i | ||||
\(835\) | −43.7117 | −1.51271 | ||||||||
\(836\) | 0.913934 | − | 0.451054i | 0.0316091 | − | 0.0156000i | ||||
\(837\) | 7.68713 | 0.265706 | ||||||||
\(838\) | −18.0718 | − | 13.1300i | −0.624282 | − | 0.453567i | ||||
\(839\) | −5.92774 | + | 18.2437i | −0.204648 | + | 0.629842i | 0.795079 | + | 0.606505i | \(0.207429\pi\) |
−0.999728 | + | 0.0233371i | \(0.992571\pi\) | |||||||
\(840\) | −0.962664 | − | 2.96278i | −0.0332151 | − | 0.102225i | ||||
\(841\) | −11.4797 | + | 8.34047i | −0.395851 | + | 0.287603i | ||||
\(842\) | −8.00971 | + | 5.81940i | −0.276033 | + | 0.200550i | ||||
\(843\) | 7.77456 | + | 23.9276i | 0.267770 | + | 0.824112i | ||||
\(844\) | −3.69413 | + | 11.3694i | −0.127157 | + | 0.391349i | ||||
\(845\) | −20.9899 | − | 15.2500i | −0.722074 | − | 0.524617i | ||||
\(846\) | 10.0384 | 0.345129 | ||||||||
\(847\) | 10.3713 | + | 3.66547i | 0.356363 | + | 0.125947i | ||||
\(848\) | −6.58394 | −0.226093 | ||||||||
\(849\) | −4.54464 | − | 3.30187i | −0.155971 | − | 0.113320i | ||||
\(850\) | 1.03272 | − | 3.17838i | 0.0354220 | − | 0.109018i | ||||
\(851\) | −1.05390 | − | 3.24357i | −0.0361272 | − | 0.111188i | ||||
\(852\) | −8.77385 | + | 6.37458i | −0.300587 | + | 0.218389i | ||||
\(853\) | 27.9632 | − | 20.3165i | 0.957442 | − | 0.695623i | 0.00488696 | − | 0.999988i | \(-0.498444\pi\) |
0.952555 | + | 0.304366i | \(0.0984444\pi\) | |||||||
\(854\) | 0.965452 | + | 2.97136i | 0.0330371 | + | 0.101678i | ||||
\(855\) | −0.295821 | + | 0.910443i | −0.0101169 | + | 0.0311365i | ||||
\(856\) | 2.75139 | + | 1.99900i | 0.0940407 | + | 0.0683246i | ||||
\(857\) | −1.15867 | −0.0395792 | −0.0197896 | − | 0.999804i | \(-0.506300\pi\) | ||||
−0.0197896 | + | 0.999804i | \(0.506300\pi\) | |||||||
\(858\) | −6.42829 | + | 3.17255i | −0.219458 | + | 0.108309i | ||||
\(859\) | −13.5036 | −0.460737 | −0.230369 | − | 0.973103i | \(-0.573993\pi\) | ||||
−0.230369 | + | 0.973103i | \(0.573993\pi\) | |||||||
\(860\) | −20.7736 | − | 15.0929i | −0.708373 | − | 0.514663i | ||||
\(861\) | 1.32558 | − | 4.07972i | 0.0451756 | − | 0.139036i | ||||
\(862\) | 0.502567 | + | 1.54674i | 0.0171175 | + | 0.0526822i | ||||
\(863\) | −25.2030 | + | 18.3110i | −0.857919 | + | 0.623315i | −0.927318 | − | 0.374274i | \(-0.877892\pi\) |
0.0693991 | + | 0.997589i | \(0.477892\pi\) | |||||||
\(864\) | −0.809017 | + | 0.587785i | −0.0275233 | + | 0.0199969i | ||||
\(865\) | −13.6481 | − | 42.0046i | −0.464050 | − | 1.42820i | ||||
\(866\) | −5.08416 | + | 15.6474i | −0.172767 | + | 0.531721i | ||||
\(867\) | 13.3451 | + | 9.69577i | 0.453223 | + | 0.329286i | ||||
\(868\) | 7.68713 | 0.260918 | ||||||||
\(869\) | 31.7594 | + | 5.44717i | 1.07736 | + | 0.184783i | ||||
\(870\) | −20.4730 | −0.694101 | ||||||||
\(871\) | −11.6741 | − | 8.48173i | −0.395562 | − | 0.287393i | ||||
\(872\) | 2.15258 | − | 6.62497i | 0.0728956 | − | 0.224350i | ||||
\(873\) | −0.0806980 | − | 0.248363i | −0.00273121 | − | 0.00840581i | ||||
\(874\) | −0.218569 | + | 0.158800i | −0.00739321 | + | 0.00537148i | ||||
\(875\) | −0.744095 | + | 0.540617i | −0.0251550 | + | 0.0182762i | ||||
\(876\) | 3.32049 | + | 10.2194i | 0.112189 | + | 0.345282i | ||||
\(877\) | 9.55294 | − | 29.4009i | 0.322580 | − | 0.992799i | −0.649941 | − | 0.759984i | \(-0.725207\pi\) |
0.972521 | − | 0.232814i | \(-0.0747935\pi\) | |||||||
\(878\) | 5.22205 | + | 3.79404i | 0.176236 | + | 0.128043i | ||||
\(879\) | 8.30116 | 0.279991 | ||||||||
\(880\) | 1.48574 | + | 10.2247i | 0.0500842 | + | 0.344675i | ||||
\(881\) | 23.1676 | 0.780535 | 0.390268 | − | 0.920701i | \(-0.372382\pi\) | ||||
0.390268 | + | 0.920701i | \(0.372382\pi\) | |||||||
\(882\) | −0.809017 | − | 0.587785i | −0.0272410 | − | 0.0197918i | ||||
\(883\) | −4.67092 | + | 14.3756i | −0.157189 | + | 0.483778i | −0.998376 | − | 0.0569659i | \(-0.981857\pi\) |
0.841187 | + | 0.540744i | \(0.181857\pi\) | |||||||
\(884\) | −0.474438 | − | 1.46017i | −0.0159571 | − | 0.0491108i | ||||
\(885\) | −14.4939 | + | 10.5305i | −0.487208 | + | 0.353978i | ||||
\(886\) | −28.0665 | + | 20.3915i | −0.942912 | + | 0.685066i | ||||
\(887\) | −2.97262 | − | 9.14879i | −0.0998109 | − | 0.307186i | 0.888667 | − | 0.458554i | \(-0.151632\pi\) |
−0.988478 | + | 0.151367i | \(0.951632\pi\) | |||||||
\(888\) | −1.19873 | + | 3.68932i | −0.0402268 | + | 0.123805i | ||||
\(889\) | −12.9791 | − | 9.42987i | −0.435305 | − | 0.316268i | ||||
\(890\) | −46.3319 | −1.55305 | ||||||||
\(891\) | 2.31504 | + | 2.37499i | 0.0775569 | + | 0.0795652i | ||||
\(892\) | −8.77887 | −0.293938 | ||||||||
\(893\) | −2.49562 | − | 1.81317i | −0.0835127 | − | 0.0606755i | ||||
\(894\) | 0.441140 | − | 1.35769i | 0.0147539 | − | 0.0454079i | ||||
\(895\) | 15.2979 | + | 47.0821i | 0.511353 | + | 1.57378i | ||||
\(896\) | −0.809017 | + | 0.587785i | −0.0270274 | + | 0.0196365i | ||||
\(897\) | 1.53734 | − | 1.11694i | 0.0513302 | − | 0.0372935i | ||||
\(898\) | −11.2163 | − | 34.5203i | −0.374294 | − | 1.15196i | ||||
\(899\) | 15.6112 | − | 48.0464i | 0.520663 | − | 1.60244i | ||||
\(900\) | −3.80623 | − | 2.76539i | −0.126874 | − | 0.0921796i | ||||
\(901\) | −4.67679 | −0.155807 | ||||||||
\(902\) | −6.62051 | + | 12.5930i | −0.220439 | + | 0.419299i | ||||
\(903\) | −8.24254 | −0.274295 | ||||||||
\(904\) | 1.13102 | + | 0.821736i | 0.0376172 | + | 0.0273305i | ||||
\(905\) | 17.0962 | − | 52.6167i | 0.568297 | − | 1.74904i | ||||
\(906\) | −3.07840 | − | 9.47433i | −0.102273 | − | 0.314764i | ||||
\(907\) | 18.5057 | − | 13.4452i | 0.614471 | − | 0.446439i | −0.236515 | − | 0.971628i | \(-0.576005\pi\) |
0.850986 | + | 0.525189i | \(0.176005\pi\) | |||||||
\(908\) | 15.7780 | − | 11.4634i | 0.523612 | − | 0.380427i | ||||
\(909\) | 0.788244 | + | 2.42596i | 0.0261444 | + | 0.0804642i | ||||
\(910\) | 2.08070 | − | 6.40373i | 0.0689745 | − | 0.212282i | ||||
\(911\) | −19.0630 | − | 13.8501i | −0.631584 | − | 0.458873i | 0.225364 | − | 0.974275i | \(-0.427643\pi\) |
−0.856949 | + | 0.515402i | \(0.827643\pi\) | |||||||
\(912\) | 0.307294 | 0.0101755 | ||||||||
\(913\) | −24.3616 | + | 46.3385i | −0.806251 | + | 1.53358i | ||||
\(914\) | 21.2889 | 0.704173 | ||||||||
\(915\) | 7.87405 | + | 5.72083i | 0.260308 | + | 0.189125i | ||||
\(916\) | −2.24954 | + | 6.92338i | −0.0743270 | + | 0.228755i | ||||
\(917\) | 6.14004 | + | 18.8971i | 0.202762 | + | 0.624038i | ||||
\(918\) | −0.574672 | + | 0.417524i | −0.0189670 | + | 0.0137803i | ||||
\(919\) | −24.9845 | + | 18.1523i | −0.824161 | + | 0.598788i | −0.917901 | − | 0.396809i | \(-0.870118\pi\) |
0.0937404 | + | 0.995597i | \(0.470118\pi\) | |||||||
\(920\) | −0.846353 | − | 2.60481i | −0.0279034 | − | 0.0858779i | ||||
\(921\) | 0.445257 | − | 1.37036i | 0.0146717 | − | 0.0451549i | ||||
\(922\) | 27.8299 | + | 20.2196i | 0.916530 | + | 0.665898i | ||||
\(923\) | −23.4405 | −0.771554 | ||||||||
\(924\) | 2.31504 | + | 2.37499i | 0.0761593 | + | 0.0781314i | ||||
\(925\) | −18.2506 | −0.600076 | ||||||||
\(926\) | −27.0952 | − | 19.6858i | −0.890405 | − | 0.646917i | ||||
\(927\) | 5.82249 | − | 17.9198i | 0.191236 | − | 0.588563i | ||||
\(928\) | 2.03082 | + | 6.25023i | 0.0666651 | + | 0.205174i | ||||
\(929\) | 33.1831 | − | 24.1090i | 1.08870 | − | 0.790989i | 0.109523 | − | 0.993984i | \(-0.465068\pi\) |
0.979180 | + | 0.202995i | \(0.0650676\pi\) | |||||||
\(930\) | 19.3738 | − | 14.0759i | 0.635291 | − | 0.461566i | ||||
\(931\) | 0.0949591 | + | 0.292254i | 0.00311216 | + | 0.00957823i | ||||
\(932\) | −0.844352 | + | 2.59865i | −0.0276577 | + | 0.0851215i | ||||
\(933\) | −8.00462 | − | 5.81570i | −0.262060 | − | 0.190397i | ||||
\(934\) | −24.9067 | −0.814973 | ||||||||
\(935\) | 1.05537 | + | 7.26296i | 0.0345143 | + | 0.237524i | ||||
\(936\) | −2.16140 | −0.0706474 | ||||||||
\(937\) | 2.92275 | + | 2.12350i | 0.0954820 | + | 0.0693717i | 0.634502 | − | 0.772921i | \(-0.281205\pi\) |
−0.539020 | + | 0.842293i | \(0.681205\pi\) | |||||||
\(938\) | −2.06307 | + | 6.34948i | −0.0673616 | + | 0.207318i | ||||
\(939\) | −1.71778 | − | 5.28679i | −0.0560577 | − | 0.172528i | ||||
\(940\) | 25.2998 | − | 18.3814i | 0.825187 | − | 0.599534i | ||||
\(941\) | 32.4823 | − | 23.5997i | 1.05889 | − | 0.769330i | 0.0850086 | − | 0.996380i | \(-0.472908\pi\) |
0.973883 | + | 0.227050i | \(0.0729082\pi\) | |||||||
\(942\) | −7.61459 | − | 23.4353i | −0.248097 | − | 0.763563i | ||||
\(943\) | 1.16542 | − | 3.58680i | 0.0379513 | − | 0.116802i | ||||
\(944\) | 4.65258 | + | 3.38030i | 0.151429 | + | 0.110019i | ||||
\(945\) | −3.11525 | −0.101339 | ||||||||
\(946\) | 26.9440 | + | 4.62126i | 0.876025 | + | 0.150250i | ||||
\(947\) | −33.8239 | −1.09913 | −0.549564 | − | 0.835452i | \(-0.685206\pi\) | ||||
−0.549564 | + | 0.835452i | \(0.685206\pi\) | |||||||
\(948\) | 7.86013 | + | 5.71072i | 0.255285 | + | 0.185475i | ||||
\(949\) | −7.17689 | + | 22.0882i | −0.232972 | + | 0.717014i | ||||
\(950\) | 0.446759 | + | 1.37498i | 0.0144948 | + | 0.0446104i | ||||
\(951\) | 0.561684 | − | 0.408087i | 0.0182139 | − | 0.0132331i | ||||
\(952\) | −0.574672 | + | 0.417524i | −0.0186252 | + | 0.0135320i | ||||
\(953\) | 10.3116 | + | 31.7359i | 0.334026 | + | 1.02803i | 0.967200 | + | 0.254017i | \(0.0817520\pi\) |
−0.633173 | + | 0.774010i | \(0.718248\pi\) | |||||||
\(954\) | −2.03455 | + | 6.26170i | −0.0658709 | + | 0.202730i | ||||
\(955\) | −66.2598 | − | 48.1405i | −2.14412 | − | 1.55779i | ||||
\(956\) | 25.8977 | 0.837592 | ||||||||
\(957\) | 19.5457 | − | 9.64637i | 0.631822 | − | 0.311823i | ||||
\(958\) | −26.0657 | −0.842146 | ||||||||
\(959\) | −1.87963 | − | 1.36563i | −0.0606964 | − | 0.0440985i | ||||
\(960\) | −0.962664 | + | 2.96278i | −0.0310698 | + | 0.0956232i | ||||
\(961\) | 8.68090 | + | 26.7171i | 0.280029 | + | 0.861840i | ||||
\(962\) | −6.78315 | + | 4.92825i | −0.218698 | + | 0.158893i | ||||
\(963\) | 2.75139 | − | 1.99900i | 0.0886624 | − | 0.0644170i | ||||
\(964\) | −1.96545 | − | 6.04904i | −0.0633029 | − | 0.194826i | ||||
\(965\) | −5.36000 | + | 16.4964i | −0.172544 | + | 0.531037i | ||||
\(966\) | −0.711270 | − | 0.516768i | −0.0228847 | − | 0.0166267i | ||||
\(967\) | 48.0391 | 1.54483 | 0.772417 | − | 0.635116i | \(-0.219048\pi\) | ||||
0.772417 | + | 0.635116i | \(0.219048\pi\) | |||||||
\(968\) | −6.23607 | − | 9.06154i | −0.200435 | − | 0.291249i | ||||
\(969\) | 0.218281 | 0.00701220 | ||||||||
\(970\) | −0.658158 | − | 0.478180i | −0.0211322 | − | 0.0153534i | ||||
\(971\) | −12.5807 | + | 38.7193i | −0.403733 | + | 1.24256i | 0.518216 | + | 0.855250i | \(0.326596\pi\) |
−0.921949 | + | 0.387312i | \(0.873404\pi\) | |||||||
\(972\) | 0.309017 | + | 0.951057i | 0.00991172 | + | 0.0305052i | ||||
\(973\) | −6.05311 | + | 4.39784i | −0.194054 | + | 0.140988i | ||||
\(974\) | 8.92850 | − | 6.48693i | 0.286087 | − | 0.207855i | ||||
\(975\) | −3.14235 | − | 9.67115i | −0.100636 | − | 0.309725i | ||||
\(976\) | 0.965452 | − | 2.97136i | 0.0309034 | − | 0.0951108i | ||||
\(977\) | −2.26347 | − | 1.64450i | −0.0724147 | − | 0.0526124i | 0.550989 | − | 0.834513i | \(-0.314251\pi\) |
−0.623404 | + | 0.781900i | \(0.714251\pi\) | |||||||
\(978\) | 14.3469 | 0.458763 | ||||||||
\(979\) | 44.2332 | − | 21.8304i | 1.41370 | − | 0.697703i | ||||
\(980\) | −3.11525 | −0.0995129 | ||||||||
\(981\) | −5.63553 | − | 4.09445i | −0.179929 | − | 0.130726i | ||||
\(982\) | 0.0565149 | − | 0.173935i | 0.00180346 | − | 0.00555049i | ||||
\(983\) | 9.02142 | + | 27.7651i | 0.287739 | + | 0.885568i | 0.985564 | + | 0.169301i | \(0.0541509\pi\) |
−0.697826 | + | 0.716267i | \(0.745849\pi\) | |||||||
\(984\) | −3.47041 | + | 2.52140i | −0.110633 | + | 0.0803794i | ||||
\(985\) | −29.7617 | + | 21.6231i | −0.948286 | + | 0.688970i | ||||
\(986\) | 1.44256 | + | 4.43975i | 0.0459406 | + | 0.141390i | ||||
\(987\) | 3.10205 | − | 9.54713i | 0.0987393 | − | 0.303888i | ||||
\(988\) | 0.537336 | + | 0.390397i | 0.0170949 | + | 0.0124202i | ||||
\(989\) | −7.24666 | −0.230430 | ||||||||
\(990\) | 10.1834 | + | 1.74659i | 0.323650 | + | 0.0555103i | ||||
\(991\) | 49.6877 | 1.57838 | 0.789191 | − | 0.614148i | \(-0.210500\pi\) | ||||
0.789191 | + | 0.614148i | \(0.210500\pi\) | |||||||
\(992\) | −6.21902 | − | 4.51838i | −0.197454 | − | 0.143459i | ||||
\(993\) | −9.58783 | + | 29.5083i | −0.304261 | + | 0.936418i | ||||
\(994\) | 3.35131 | + | 10.3143i | 0.106297 | + | 0.327149i | ||||
\(995\) | 24.0332 | − | 17.4612i | 0.761905 | − | 0.553556i | ||||
\(996\) | −12.7701 | + | 9.27804i | −0.404637 | + | 0.293986i | ||||
\(997\) | −10.1095 | − | 31.1138i | −0.320171 | − | 0.985385i | −0.973573 | − | 0.228374i | \(-0.926659\pi\) |
0.653402 | − | 0.757011i | \(-0.273341\pi\) | |||||||
\(998\) | 5.21872 | − | 16.0616i | 0.165196 | − | 0.508420i | ||||
\(999\) | 3.13832 | + | 2.28012i | 0.0992921 | + | 0.0721399i |
(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 | 462.2.j.e.169.2 | ✓ | 8 | |
11.3 | even | 5 | inner | 462.2.j.e.421.2 | yes | 8 | |
11.5 | even | 5 | 5082.2.a.cf.1.1 | 4 | |||
11.6 | odd | 10 | 5082.2.a.ca.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.j.e.169.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
462.2.j.e.421.2 | yes | 8 | 11.3 | even | 5 | inner | |
5082.2.a.ca.1.1 | 4 | 11.6 | odd | 10 | |||
5082.2.a.cf.1.1 | 4 | 11.5 | even | 5 |