Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(35,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.l (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 71.4 | ||
Character | \(\chi\) | \(=\) | 324.71 |
Dual form | 324.2.l.a.251.4 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{17}{18}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.940037 | + | 1.05657i | −0.664707 | + | 0.747105i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.232661 | − | 1.98642i | −0.116330 | − | 0.993211i | ||||
\(5\) | −0.546554 | + | 0.651358i | −0.244426 | + | 0.291296i | −0.874284 | − | 0.485414i | \(-0.838669\pi\) |
0.629858 | + | 0.776710i | \(0.283113\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.348909 | + | 0.958618i | −0.131875 | + | 0.362324i | −0.988002 | − | 0.154442i | \(-0.950642\pi\) |
0.856127 | + | 0.516766i | \(0.172864\pi\) | |||||||
\(8\) | 2.31749 | + | 1.62149i | 0.819358 | + | 0.573283i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.174421 | − | 1.18977i | −0.0551568 | − | 0.376238i | ||||
\(11\) | −1.57259 | + | 1.31956i | −0.474155 | + | 0.397863i | −0.848307 | − | 0.529504i | \(-0.822378\pi\) |
0.374153 | + | 0.927367i | \(0.377934\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.374417 | + | 2.12343i | −0.103845 | + | 0.588933i | 0.887831 | + | 0.460170i | \(0.152212\pi\) |
−0.991675 | + | 0.128762i | \(0.958900\pi\) | |||||||
\(14\) | −0.684856 | − | 1.26978i | −0.183035 | − | 0.339363i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.89174 | + | 0.924324i | −0.972934 | + | 0.231081i | ||||
\(17\) | 6.34902 | + | 3.66561i | 1.53986 | + | 0.889041i | 0.998846 | + | 0.0480291i | \(0.0152940\pi\) |
0.541017 | + | 0.841011i | \(0.318039\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.39109 | + | 2.53520i | −1.00738 | + | 0.581614i | −0.910425 | − | 0.413675i | \(-0.864245\pi\) |
−0.0969597 | + | 0.995288i | \(0.530912\pi\) | |||||||
\(20\) | 1.42103 | + | 0.934141i | 0.317753 | + | 0.208880i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0840920 | − | 2.90198i | 0.0179285 | − | 0.618705i | ||||
\(23\) | −5.20278 | + | 1.89366i | −1.08486 | + | 0.394855i | −0.821713 | − | 0.569902i | \(-0.806981\pi\) |
−0.263142 | + | 0.964757i | \(0.584759\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.742695 | + | 4.21203i | 0.148539 | + | 0.842407i | ||||
\(26\) | −1.89157 | − | 2.39170i | −0.370968 | − | 0.469050i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.98540 | + | 0.470046i | 0.375205 | + | 0.0888304i | ||||
\(29\) | −3.64198 | + | 0.642180i | −0.676300 | + | 0.119250i | −0.501240 | − | 0.865308i | \(-0.667123\pi\) |
−0.175059 | + | 0.984558i | \(0.556012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.60292 | + | 4.40400i | 0.287894 | + | 0.790981i | 0.996361 | + | 0.0852374i | \(0.0271649\pi\) |
−0.708467 | + | 0.705744i | \(0.750613\pi\) | |||||||
\(32\) | 2.68177 | − | 4.98077i | 0.474074 | − | 0.880485i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.84127 | + | 3.26235i | −1.68776 | + | 0.559488i | ||||
\(35\) | −0.433706 | − | 0.751201i | −0.0733097 | − | 0.126976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.33157 | − | 9.23455i | 0.876504 | − | 1.51815i | 0.0213528 | − | 0.999772i | \(-0.493203\pi\) |
0.855152 | − | 0.518378i | \(-0.173464\pi\) | |||||||
\(38\) | 1.44919 | − | 7.02265i | 0.235089 | − | 1.13922i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.32280 | + | 0.623286i | −0.367268 | + | 0.0985502i | ||||
\(41\) | −4.00006 | − | 0.705319i | −0.624705 | − | 0.110152i | −0.147670 | − | 0.989037i | \(-0.547177\pi\) |
−0.477035 | + | 0.878884i | \(0.658288\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.51843 | − | 4.19310i | −0.536555 | − | 0.639441i | 0.427857 | − | 0.903847i | \(-0.359269\pi\) |
−0.964412 | + | 0.264405i | \(0.914824\pi\) | |||||||
\(44\) | 2.98709 | + | 2.81682i | 0.450320 | + | 0.424652i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.89003 | − | 7.27719i | 0.426112 | − | 1.07296i | ||||
\(47\) | −4.10423 | − | 1.49382i | −0.598663 | − | 0.217896i | 0.0248724 | − | 0.999691i | \(-0.492082\pi\) |
−0.623535 | + | 0.781795i | \(0.714304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.56510 | + | 3.83057i | 0.652157 | + | 0.547225i | ||||
\(50\) | −5.14845 | − | 3.17476i | −0.728101 | − | 0.448979i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.30513 | + | 0.249713i | 0.597014 | + | 0.0346289i | ||||
\(53\) | 5.55975i | 0.763690i | 0.924226 | + | 0.381845i | \(0.124711\pi\) | ||||
−0.924226 | + | 0.381845i | \(0.875289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.74553i | − | 0.235368i | ||||||
\(56\) | −2.36298 | + | 1.65584i | −0.315767 | + | 0.221271i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.74510 | − | 4.45167i | 0.360449 | − | 0.584533i | ||||
\(59\) | 9.24583 | + | 7.75817i | 1.20370 | + | 1.01003i | 0.999516 | + | 0.0310964i | \(0.00989987\pi\) |
0.204188 | + | 0.978932i | \(0.434545\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.502750 | − | 0.182986i | −0.0643705 | − | 0.0234290i | 0.309634 | − | 0.950856i | \(-0.399793\pi\) |
−0.374005 | + | 0.927427i | \(0.622016\pi\) | |||||||
\(62\) | −6.15992 | − | 2.44633i | −0.782311 | − | 0.310684i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.74155 | + | 7.51558i | 0.342694 | + | 0.939447i | ||||
\(65\) | −1.17847 | − | 1.40445i | −0.146171 | − | 0.174200i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.40223 | + | 1.12889i | 0.782157 | + | 0.137915i | 0.550448 | − | 0.834870i | \(-0.314457\pi\) |
0.231709 | + | 0.972785i | \(0.425568\pi\) | |||||||
\(68\) | 5.80427 | − | 13.4647i | 0.703872 | − | 1.63283i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.20139 | + | 0.247918i | 0.143594 | + | 0.0296319i | ||||
\(71\) | 5.86015 | − | 10.1501i | 0.695472 | − | 1.20459i | −0.274550 | − | 0.961573i | \(-0.588529\pi\) |
0.970021 | − | 0.243019i | \(-0.0781379\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.769587 | − | 1.33296i | −0.0900734 | − | 0.156012i | 0.817468 | − | 0.575973i | \(-0.195377\pi\) |
−0.907542 | + | 0.419962i | \(0.862043\pi\) | |||||||
\(74\) | 4.74503 | + | 14.3140i | 0.551599 | + | 1.66396i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.05760 | + | 8.13271i | 0.694854 | + | 0.932886i | ||||
\(77\) | −0.716265 | − | 1.96792i | −0.0816260 | − | 0.224266i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.2516 | − | 2.51294i | 1.60343 | − | 0.282728i | 0.700868 | − | 0.713291i | \(-0.252796\pi\) |
0.902560 | + | 0.430563i | \(0.141685\pi\) | |||||||
\(80\) | 1.52498 | − | 3.04011i | 0.170498 | − | 0.339894i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.50542 | − | 3.56330i | 0.497541 | − | 0.393501i | ||||
\(83\) | −0.916197 | − | 5.19601i | −0.100566 | − | 0.570337i | −0.992899 | − | 0.118960i | \(-0.962044\pi\) |
0.892333 | − | 0.451377i | \(-0.149067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.85770 | + | 2.13203i | −0.635357 | + | 0.231251i | ||||
\(86\) | 7.73773 | + | 0.224219i | 0.834381 | + | 0.0241782i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.78413 | + | 0.508136i | −0.616590 | + | 0.0541675i | ||||
\(89\) | 3.41168 | − | 1.96973i | 0.361637 | − | 0.208791i | −0.308162 | − | 0.951334i | \(-0.599714\pi\) |
0.669799 | + | 0.742543i | \(0.266380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.90492 | − | 1.09981i | −0.199690 | − | 0.115291i | ||||
\(92\) | 4.97208 | + | 9.89434i | 0.518376 | + | 1.03156i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.43644 | − | 2.93214i | 0.560726 | − | 0.302427i | ||||
\(95\) | 0.748647 | − | 4.24579i | 0.0768096 | − | 0.435609i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.35056 | − | 2.81145i | 0.340198 | − | 0.285460i | −0.456642 | − | 0.889651i | \(-0.650948\pi\) |
0.796840 | + | 0.604191i | \(0.206503\pi\) | |||||||
\(98\) | −8.33861 | + | 1.22245i | −0.842327 | + | 0.123486i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.19408 | − | 2.45528i | 0.819408 | − | 0.245528i | ||||
\(101\) | 2.06720 | − | 5.67959i | 0.205694 | − | 0.565140i | −0.793354 | − | 0.608760i | \(-0.791667\pi\) |
0.999048 | + | 0.0436206i | \(0.0138893\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.110043 | + | 0.131145i | −0.0108429 | + | 0.0129221i | −0.771439 | − | 0.636304i | \(-0.780463\pi\) |
0.760596 | + | 0.649226i | \(0.224907\pi\) | |||||||
\(104\) | −4.31082 | + | 4.31391i | −0.422711 | + | 0.423014i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.87423 | − | 5.22637i | −0.570556 | − | 0.507630i | ||||
\(107\) | 8.17263 | 0.790078 | 0.395039 | − | 0.918664i | \(-0.370731\pi\) | ||||
0.395039 | + | 0.918664i | \(0.370731\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.1819 | −1.83729 | −0.918646 | − | 0.395082i | \(-0.870716\pi\) | ||||
−0.918646 | + | 0.395082i | \(0.870716\pi\) | |||||||
\(110\) | 1.84427 | + | 1.64087i | 0.175844 | + | 0.156450i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.471786 | − | 4.05320i | 0.0445796 | − | 0.382991i | ||||
\(113\) | 3.19731 | − | 3.81040i | 0.300777 | − | 0.358452i | −0.594395 | − | 0.804174i | \(-0.702608\pi\) |
0.895172 | + | 0.445721i | \(0.147053\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.61015 | − | 4.42386i | 0.150148 | − | 0.412527i | ||||
\(116\) | 2.12299 | + | 7.08511i | 0.197114 | + | 0.657836i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.8884 | + | 2.47585i | −1.55471 | + | 0.227921i | ||||
\(119\) | −5.72915 | + | 4.80732i | −0.525190 | + | 0.440687i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.17833 | + | 6.68262i | −0.107121 | + | 0.607511i | ||||
\(122\) | 0.665940 | − | 0.359175i | 0.0602914 | − | 0.0325181i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.37526 | − | 4.20872i | 0.752120 | − | 0.377954i | ||||
\(125\) | −6.83132 | − | 3.94406i | −0.611011 | − | 0.352768i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8653 | + | 7.42778i | −1.14161 | + | 0.659109i | −0.946829 | − | 0.321738i | \(-0.895733\pi\) |
−0.194781 | + | 0.980847i | \(0.562400\pi\) | |||||||
\(128\) | −10.5179 | − | 4.16829i | −0.929656 | − | 0.368428i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.59170 | + | 0.0751006i | 0.227307 | + | 0.00658676i | ||||
\(131\) | −2.94977 | + | 1.07363i | −0.257722 | + | 0.0938032i | −0.467650 | − | 0.883914i | \(-0.654899\pi\) |
0.209928 | + | 0.977717i | \(0.432677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.898197 | − | 5.09393i | −0.0778836 | − | 0.441700i | ||||
\(134\) | −7.21108 | + | 5.70318i | −0.622942 | + | 0.492680i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.77007 | + | 18.7899i | 0.752027 | + | 1.61122i | ||||
\(137\) | 11.8307 | − | 2.08607i | 1.01077 | − | 0.178225i | 0.356344 | − | 0.934355i | \(-0.384023\pi\) |
0.654422 | + | 0.756130i | \(0.272912\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.983129 | + | 2.70112i | 0.0833879 | + | 0.229106i | 0.974378 | − | 0.224916i | \(-0.0722108\pi\) |
−0.890990 | + | 0.454022i | \(0.849989\pi\) | |||||||
\(140\) | −1.39130 | + | 1.03630i | −0.117586 | + | 0.0875832i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.21546 | + | 15.7331i | 0.437672 | + | 1.32029i | ||||
\(143\) | −2.21319 | − | 3.83335i | −0.185076 | − | 0.320561i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.57225 | − | 2.72322i | 0.130568 | − | 0.226151i | ||||
\(146\) | 2.13180 | + | 0.439917i | 0.176429 | + | 0.0364078i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −19.5841 | − | 8.44222i | −1.60981 | − | 0.693946i | ||||
\(149\) | −10.9239 | − | 1.92617i | −0.894918 | − | 0.157798i | −0.292770 | − | 0.956183i | \(-0.594577\pi\) |
−0.602148 | + | 0.798385i | \(0.705688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.78495 | − | 4.51073i | −0.308015 | − | 0.367078i | 0.589725 | − | 0.807604i | \(-0.299236\pi\) |
−0.897740 | + | 0.440527i | \(0.854792\pi\) | |||||||
\(152\) | −14.2871 | − | 1.24480i | −1.15884 | − | 0.100966i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.75256 | + | 1.09314i | 0.221807 | + | 0.0880877i | ||||
\(155\) | −3.74466 | − | 1.36295i | −0.300779 | − | 0.109474i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.5896 | − | 11.4030i | −1.08456 | − | 0.910058i | −0.0882726 | − | 0.996096i | \(-0.528135\pi\) |
−0.996292 | + | 0.0860388i | \(0.972579\pi\) | |||||||
\(158\) | −10.7419 | + | 17.4200i | −0.854582 | + | 1.38586i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.77853 | + | 4.46905i | 0.140606 | + | 0.353310i | ||||
\(161\) | − | 5.64820i | − | 0.445140i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 18.0395i | − | 1.41296i | −0.707732 | − | 0.706481i | \(-0.750282\pi\) | ||
0.707732 | − | 0.706481i | \(-0.249718\pi\) | |||||||
\(164\) | −0.470403 | + | 8.10991i | −0.0367323 | + | 0.633277i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.35119 | + | 3.91642i | 0.492948 | + | 0.303973i | ||||
\(167\) | 12.3127 | + | 10.3316i | 0.952789 | + | 0.799485i | 0.979765 | − | 0.200151i | \(-0.0641433\pi\) |
−0.0269759 | + | 0.999636i | \(0.508588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.84725 | + | 2.85617i | 0.603635 | + | 0.219705i | ||||
\(170\) | 3.25383 | − | 8.19323i | 0.249557 | − | 0.628392i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.51066 | + | 7.96465i | −0.572682 | + | 0.607299i | ||||
\(173\) | −3.51165 | − | 4.18502i | −0.266986 | − | 0.318181i | 0.615850 | − | 0.787864i | \(-0.288813\pi\) |
−0.882835 | + | 0.469683i | \(0.844368\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.29687 | − | 0.757653i | −0.324813 | − | 0.0572732i | ||||
\(176\) | 4.90042 | − | 6.58898i | 0.369383 | − | 0.496663i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.12595 | + | 5.45628i | −0.0843936 | + | 0.408965i | ||||
\(179\) | −6.73827 | + | 11.6710i | −0.503642 | + | 0.872333i | 0.496349 | + | 0.868123i | \(0.334674\pi\) |
−0.999991 | + | 0.00421032i | \(0.998660\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.16955 | + | 12.4180i | 0.532909 | + | 0.923025i | 0.999261 | + | 0.0384262i | \(0.0122345\pi\) |
−0.466353 | + | 0.884599i | \(0.654432\pi\) | |||||||
\(182\) | 2.95271 | − | 0.978813i | 0.218869 | − | 0.0725545i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −15.1280 | − | 4.04771i | −1.11525 | − | 0.298401i | ||||
\(185\) | 3.10100 | + | 8.51994i | 0.227990 | + | 0.626398i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.8214 | + | 2.61342i | −1.08385 | + | 0.191112i | ||||
\(188\) | −2.01246 | + | 8.50028i | −0.146773 | + | 0.619946i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.78220 | + | 4.78219i | 0.274390 | + | 0.346937i | ||||
\(191\) | 1.45788 | + | 8.26803i | 0.105488 | + | 0.598254i | 0.991024 | + | 0.133683i | \(0.0426803\pi\) |
−0.885536 | + | 0.464571i | \(0.846209\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.16115 | + | 0.422623i | −0.0835812 | + | 0.0304211i | −0.383472 | − | 0.923552i | \(-0.625272\pi\) |
0.299891 | + | 0.953973i | \(0.403050\pi\) | |||||||
\(194\) | −0.179166 | + | 6.18296i | −0.0128634 | + | 0.443910i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.54701 | − | 9.95943i | 0.467644 | − | 0.711388i | ||||
\(197\) | −2.53158 | + | 1.46161i | −0.180368 | + | 0.104135i | −0.587466 | − | 0.809249i | \(-0.699874\pi\) |
0.407098 | + | 0.913385i | \(0.366541\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5012 | + | 7.21757i | 0.886186 | + | 0.511640i | 0.872693 | − | 0.488269i | \(-0.162372\pi\) |
0.0134930 | + | 0.999909i | \(0.495705\pi\) | |||||||
\(200\) | −5.10857 | + | 10.9656i | −0.361231 | + | 0.775387i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.05761 | + | 7.52315i | 0.285492 | + | 0.529327i | ||||
\(203\) | 0.655114 | − | 3.71534i | 0.0459800 | − | 0.260765i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.64567 | − | 2.21998i | 0.184781 | − | 0.155050i | ||||
\(206\) | −0.0351180 | − | 0.239549i | −0.00244679 | − | 0.0166902i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.505601 | − | 8.60990i | −0.0350571 | − | 0.596989i | ||||
\(209\) | 3.56005 | − | 9.78114i | 0.246253 | − | 0.676576i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.58544 | + | 4.27296i | −0.246832 | + | 0.294163i | −0.875208 | − | 0.483747i | \(-0.839276\pi\) |
0.628376 | + | 0.777910i | \(0.283720\pi\) | |||||||
\(212\) | 11.0440 | − | 1.29353i | 0.758505 | − | 0.0888403i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.68258 | + | 8.63492i | −0.525170 | + | 0.590271i | ||||
\(215\) | 4.65422 | 0.317415 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.78103 | −0.324557 | ||||||||
\(218\) | 18.0317 | − | 20.2669i | 1.22126 | − | 1.37265i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.46736 | + | 0.406117i | −0.233770 | + | 0.0273804i | ||||
\(221\) | −10.1608 | + | 12.1092i | −0.683492 | + | 0.814554i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.64768 | − | 12.7694i | 0.311231 | − | 0.855102i | −0.681177 | − | 0.732119i | \(-0.738532\pi\) |
0.992409 | − | 0.122983i | \(-0.0392461\pi\) | |||||||
\(224\) | 3.83897 | + | 4.30863i | 0.256502 | + | 0.287882i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.02035 | + | 6.96008i | 0.0678728 | + | 0.462978i | ||||
\(227\) | 13.7746 | − | 11.5582i | 0.914249 | − | 0.767146i | −0.0586732 | − | 0.998277i | \(-0.518687\pi\) |
0.972923 | + | 0.231131i | \(0.0742426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.41193 | − | 13.6787i | 0.159385 | − | 0.903916i | −0.795282 | − | 0.606240i | \(-0.792677\pi\) |
0.954667 | − | 0.297676i | \(-0.0962117\pi\) | |||||||
\(230\) | 3.16049 | + | 5.85982i | 0.208397 | + | 0.386385i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.48156 | − | 4.41719i | −0.622495 | − | 0.290003i | ||||
\(233\) | −2.12007 | − | 1.22403i | −0.138891 | − | 0.0801886i | 0.428945 | − | 0.903331i | \(-0.358886\pi\) |
−0.567835 | + | 0.823142i | \(0.692219\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.21619 | − | 1.85687i | 0.209801 | − | 0.121129i | ||||
\(236\) | 13.2599 | − | 20.1711i | 0.863143 | − | 1.31303i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.306357 | − | 10.5723i | 0.0198582 | − | 0.685299i | ||||
\(239\) | −14.4768 | + | 5.26911i | −0.936424 | + | 0.340831i | −0.764753 | − | 0.644324i | \(-0.777139\pi\) |
−0.171671 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.02973 | + | 11.5112i | 0.130747 | + | 0.741501i | 0.977728 | + | 0.209878i | \(0.0673067\pi\) |
−0.846981 | + | 0.531623i | \(0.821582\pi\) | |||||||
\(242\) | −5.95295 | − | 7.52688i | −0.382670 | − | 0.483846i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.246517 | + | 1.04125i | −0.0157816 | + | 0.0666590i | ||||
\(245\) | −4.99015 | + | 0.879897i | −0.318809 | + | 0.0562146i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.73920 | − | 10.2734i | −0.237920 | − | 0.653679i | ||||
\(248\) | −3.42626 | + | 12.8054i | −0.217568 | + | 0.813141i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.5888 | − | 3.51017i | 0.669698 | − | 0.222002i | ||||
\(251\) | 1.74376 | + | 3.02028i | 0.110065 | + | 0.190639i | 0.915796 | − | 0.401643i | \(-0.131561\pi\) |
−0.805731 | + | 0.592281i | \(0.798227\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.68306 | − | 9.84335i | 0.357291 | − | 0.618846i | ||||
\(254\) | 4.24591 | − | 20.5754i | 0.266412 | − | 1.29102i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.2912 | − | 7.19446i | 0.893203 | − | 0.449654i | ||||
\(257\) | 17.5820 | + | 3.10019i | 1.09674 | + | 0.193385i | 0.692606 | − | 0.721316i | \(-0.256463\pi\) |
0.404132 | + | 0.914701i | \(0.367574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.99218 | + | 8.33295i | 0.434473 | + | 0.517784i | ||||
\(260\) | −2.51564 | + | 2.66770i | −0.156013 | + | 0.165444i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.63853 | − | 4.12587i | 0.101229 | − | 0.254897i | ||||
\(263\) | 6.92028 | + | 2.51878i | 0.426723 | + | 0.155314i | 0.546449 | − | 0.837493i | \(-0.315979\pi\) |
−0.119726 | + | 0.992807i | \(0.538202\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.62138 | − | 3.03870i | −0.222460 | − | 0.186666i | ||||
\(266\) | 6.22641 | + | 3.83948i | 0.381765 | + | 0.235413i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.752896 | − | 12.9802i | 0.0459904 | − | 0.792891i | ||||
\(269\) | 0.906912i | 0.0552954i | 0.999618 | + | 0.0276477i | \(0.00880165\pi\) | ||||
−0.999618 | + | 0.0276477i | \(0.991198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.71551i | 0.407938i | 0.978977 | + | 0.203969i | \(0.0653842\pi\) | ||||
−0.978977 | + | 0.203969i | \(0.934616\pi\) | |||||||
\(272\) | −28.0969 | − | 8.39703i | −1.70363 | − | 0.509145i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.91723 | + | 14.4609i | −0.538709 | + | 0.873615i | ||||
\(275\) | −6.72600 | − | 5.64378i | −0.405593 | − | 0.340333i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.68312 | + | 0.612607i | 0.101129 | + | 0.0368080i | 0.392089 | − | 0.919927i | \(-0.371752\pi\) |
−0.290960 | + | 0.956735i | \(0.593975\pi\) | |||||||
\(278\) | −3.77809 | − | 1.50042i | −0.226595 | − | 0.0899890i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.212953 | − | 2.44415i | 0.0127263 | − | 0.146066i | ||||
\(281\) | 3.69638 | + | 4.40517i | 0.220508 | + | 0.262791i | 0.864945 | − | 0.501866i | \(-0.167353\pi\) |
−0.644438 | + | 0.764657i | \(0.722909\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.1948 | + | 1.79762i | 0.606019 | + | 0.106858i | 0.468234 | − | 0.883605i | \(-0.344890\pi\) |
0.137785 | + | 0.990462i | \(0.456002\pi\) | |||||||
\(284\) | −21.5258 | − | 9.27920i | −1.27732 | − | 0.550619i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.13067 | + | 1.26512i | 0.362514 | + | 0.0748079i | ||||
\(287\) | 2.07179 | − | 3.58844i | 0.122294 | − | 0.211819i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.3734 | + | 31.8236i | 1.08079 | + | 1.87198i | ||||
\(290\) | 1.39929 | + | 4.22112i | 0.0821689 | + | 0.247872i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.46878 | + | 1.83885i | −0.144474 | + | 0.107611i | ||||
\(293\) | 4.28880 | + | 11.7834i | 0.250555 | + | 0.688393i | 0.999663 | + | 0.0259461i | \(0.00825984\pi\) |
−0.749109 | + | 0.662447i | \(0.769518\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.1067 | + | 1.78208i | −0.588434 | + | 0.103757i | ||||
\(296\) | 27.3296 | − | 12.7559i | 1.58850 | − | 0.741423i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.3040 | − | 9.73111i | 0.712750 | − | 0.563708i | ||||
\(299\) | −2.07303 | − | 11.7567i | −0.119886 | − | 0.679910i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.24719 | − | 1.90982i | 0.302443 | − | 0.110080i | ||||
\(302\) | 8.32387 | + | 0.241204i | 0.478985 | + | 0.0138797i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.7456 | − | 13.9251i | 0.845719 | − | 0.798660i | ||||
\(305\) | 0.393969 | − | 0.227458i | 0.0225586 | − | 0.0130242i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.0184 | + | 13.2897i | 1.31373 | + | 0.758482i | 0.982712 | − | 0.185143i | \(-0.0592749\pi\) |
0.331017 | + | 0.943625i | \(0.392608\pi\) | |||||||
\(308\) | −3.74248 | + | 1.88066i | −0.213247 | + | 0.107161i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.96016 | − | 2.67526i | 0.281718 | − | 0.151945i | ||||
\(311\) | 3.84093 | − | 21.7830i | 0.217799 | − | 1.23520i | −0.658184 | − | 0.752857i | \(-0.728675\pi\) |
0.875983 | − | 0.482342i | \(-0.160214\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.20542 | + | 3.52877i | −0.237705 | + | 0.199458i | −0.753856 | − | 0.657039i | \(-0.771809\pi\) |
0.516152 | + | 0.856497i | \(0.327364\pi\) | |||||||
\(314\) | 24.8227 | − | 3.63902i | 1.40083 | − | 0.205362i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.30754 | − | 27.7250i | −0.467336 | − | 1.55965i | ||||
\(317\) | −6.85935 | + | 18.8459i | −0.385260 | + | 1.05849i | 0.583850 | + | 0.811862i | \(0.301546\pi\) |
−0.969110 | + | 0.246631i | \(0.920677\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.87996 | − | 5.81571i | 0.273225 | − | 0.325617i | ||||
\(320\) | −6.39374 | − | 2.32194i | −0.357421 | − | 0.129800i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.96769 | + | 5.30951i | 0.332566 | + | 0.295888i | ||||
\(323\) | −37.1721 | −2.06831 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.22202 | −0.511546 | ||||||||
\(326\) | 19.0599 | + | 16.9578i | 1.05563 | + | 0.939204i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.12645 | − | 8.12063i | −0.448708 | − | 0.448387i | ||||
\(329\) | 2.86400 | − | 3.41318i | 0.157897 | − | 0.188175i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.99263 | + | 21.9596i | −0.439315 | + | 1.20701i | 0.500624 | + | 0.865665i | \(0.333104\pi\) |
−0.939939 | + | 0.341343i | \(0.889118\pi\) | |||||||
\(332\) | −10.1083 | + | 3.02886i | −0.554766 | + | 0.166230i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.4905 | + | 3.29712i | −1.23062 | + | 0.180410i | ||||
\(335\) | −4.23448 | + | 3.55315i | −0.231354 | + | 0.194129i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.10728 | − | 6.27969i | 0.0603173 | − | 0.342076i | −0.939683 | − | 0.342047i | \(-0.888880\pi\) |
1.00000 | 2.90332e-5i | \(-9.24155e-6\pi\) | ||||||||
\(338\) | −10.3944 | + | 5.60623i | −0.565383 | + | 0.304939i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.59797 | + | 11.1398i | 0.303592 | + | 0.604142i | ||||
\(341\) | −8.33210 | − | 4.81054i | −0.451208 | − | 0.260505i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4491 | + | 6.61016i | −0.618195 | + | 0.356915i | ||||
\(344\) | −1.35487 | − | 15.4226i | −0.0730498 | − | 0.831529i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.72282 | + | 0.223787i | 0.415182 | + | 0.0120309i | ||||
\(347\) | 15.1793 | − | 5.52480i | 0.814866 | − | 0.296587i | 0.0992334 | − | 0.995064i | \(-0.468361\pi\) |
0.715632 | + | 0.698477i | \(0.246139\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.65392 | − | 20.7224i | −0.195590 | − | 1.10925i | −0.911576 | − | 0.411132i | \(-0.865134\pi\) |
0.715986 | − | 0.698115i | \(-0.245978\pi\) | |||||||
\(350\) | 4.83972 | − | 3.82770i | 0.258694 | − | 0.204599i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.35511 | + | 11.3715i | 0.125528 | + | 0.606103i | ||||
\(353\) | 9.47086 | − | 1.66997i | 0.504083 | − | 0.0888834i | 0.0841766 | − | 0.996451i | \(-0.473174\pi\) |
0.419906 | + | 0.907567i | \(0.362063\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.40844 | + | 9.36462i | 0.180901 | + | 0.497022i | ||||
\(356\) | −4.70648 | − | 6.31875i | −0.249443 | − | 0.334893i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.99698 | − | 18.0906i | −0.316950 | − | 0.956119i | ||||
\(359\) | 7.01604 | + | 12.1521i | 0.370292 | + | 0.641365i | 0.989610 | − | 0.143775i | \(-0.0459242\pi\) |
−0.619318 | + | 0.785140i | \(0.712591\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.35443 | − | 5.81005i | 0.176549 | − | 0.305792i | ||||
\(362\) | −19.8601 | − | 4.09831i | −1.04382 | − | 0.215402i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.74148 | + | 4.03985i | −0.0912782 | + | 0.211746i | ||||
\(365\) | 1.28886 | + | 0.227260i | 0.0674619 | + | 0.0118954i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.8419 | + | 28.4137i | 1.24454 | + | 1.48318i | 0.814276 | + | 0.580478i | \(0.197134\pi\) |
0.430261 | + | 0.902704i | \(0.358421\pi\) | |||||||
\(368\) | 18.4975 | − | 12.1787i | 0.964249 | − | 0.634857i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.9169 | − | 4.73264i | −0.619532 | − | 0.246038i | ||||
\(371\) | −5.32967 | − | 1.93984i | −0.276703 | − | 0.100712i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.7187 | + | 18.2242i | 1.12455 | + | 0.943611i | 0.998825 | − | 0.0484536i | \(-0.0154293\pi\) |
0.125727 | + | 0.992065i | \(0.459874\pi\) | |||||||
\(374\) | 11.1714 | − | 18.1165i | 0.577661 | − | 0.936782i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.08931 | − | 10.1169i | −0.365603 | − | 0.521737i | ||||
\(377\) | − | 7.97393i | − | 0.410678i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.3245i | − | 0.787168i | −0.919289 | − | 0.393584i | \(-0.871235\pi\) | ||
0.919289 | − | 0.393584i | \(-0.128765\pi\) | |||||||
\(380\) | −8.60811 | − | 0.499300i | −0.441587 | − | 0.0256136i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.1062 | − | 6.23191i | −0.517077 | − | 0.318852i | ||||
\(383\) | −28.1952 | − | 23.6586i | −1.44071 | − | 1.20890i | −0.939028 | − | 0.343841i | \(-0.888272\pi\) |
−0.501678 | − | 0.865055i | \(-0.667284\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.67330 | + | 0.609031i | 0.0852792 | + | 0.0310391i | ||||
\(386\) | 0.644992 | − | 1.62411i | 0.0328292 | − | 0.0826650i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.36428 | − | 6.00151i | −0.323097 | − | 0.304681i | ||||
\(389\) | 5.77806 | + | 6.88602i | 0.292959 | + | 0.349135i | 0.892369 | − | 0.451307i | \(-0.149042\pi\) |
−0.599409 | + | 0.800443i | \(0.704598\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −39.9740 | − | 7.04849i | −2.02157 | − | 0.356457i | ||||
\(392\) | 4.36836 | + | 16.2796i | 0.220635 | + | 0.822243i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.835495 | − | 4.04875i | 0.0420917 | − | 0.203973i | ||||
\(395\) | −6.15244 | + | 10.6563i | −0.309563 | + | 0.536178i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.35735 | − | 4.08305i | −0.118312 | − | 0.204922i | 0.800787 | − | 0.598949i | \(-0.204415\pi\) |
−0.919099 | + | 0.394027i | \(0.871082\pi\) | |||||||
\(398\) | −19.3774 | + | 6.42355i | −0.971302 | + | 0.321983i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.78366 | − | 15.7056i | −0.339183 | − | 0.785282i | ||||
\(401\) | −5.87724 | − | 16.1476i | −0.293495 | − | 0.806372i | −0.995549 | − | 0.0942475i | \(-0.969955\pi\) |
0.702053 | − | 0.712124i | \(-0.252267\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.95173 | + | 1.75476i | −0.495731 | + | 0.0874107i | ||||
\(404\) | −11.7630 | − | 2.78491i | −0.585231 | − | 0.138555i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.30966 | + | 4.18472i | 0.164256 | + | 0.207684i | ||||
\(407\) | 3.80117 | + | 21.5575i | 0.188417 | + | 1.06857i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1511 | − | 6.60646i | 0.897514 | − | 0.326668i | 0.148258 | − | 0.988949i | \(-0.452633\pi\) |
0.749256 | + | 0.662280i | \(0.230411\pi\) | |||||||
\(410\) | −0.141473 | + | 4.88218i | −0.00698684 | + | 0.241114i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.286111 | + | 0.188080i | 0.0140957 | + | 0.00926605i | ||||
\(413\) | −10.6631 | + | 6.15633i | −0.524696 | + | 0.302933i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.88522 | + | 2.24313i | 0.190718 | + | 0.110111i | ||||
\(416\) | 9.57221 | + | 7.55943i | 0.469316 | + | 0.370631i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.98784 | + | 12.9561i | 0.341787 | + | 0.633702i | ||||
\(419\) | −2.66451 | + | 15.1112i | −0.130170 | + | 0.738230i | 0.847932 | + | 0.530105i | \(0.177847\pi\) |
−0.978102 | + | 0.208126i | \(0.933264\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.8213 | + | 14.9539i | −0.868558 | + | 0.728807i | −0.963794 | − | 0.266648i | \(-0.914084\pi\) |
0.0952359 | + | 0.995455i | \(0.469639\pi\) | |||||||
\(422\) | −1.14422 | − | 7.80500i | −0.0556996 | − | 0.379941i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.01506 | + | 12.8847i | −0.437810 | + | 0.625735i | ||||
\(425\) | −10.7243 | + | 29.4647i | −0.520204 | + | 1.42925i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.350828 | − | 0.418100i | 0.0169777 | − | 0.0202333i | ||||
\(428\) | −1.90145 | − | 16.2343i | −0.0919101 | − | 0.784714i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.37514 | + | 4.91748i | −0.210988 | + | 0.237142i | ||||
\(431\) | 16.8732 | 0.812754 | 0.406377 | − | 0.913706i | \(-0.366792\pi\) | ||||
0.406377 | + | 0.913706i | \(0.366792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.79450 | −0.134295 | −0.0671475 | − | 0.997743i | \(-0.521390\pi\) | ||||
−0.0671475 | + | 0.997743i | \(0.521390\pi\) | |||||||
\(434\) | 4.49434 | − | 5.05147i | 0.215735 | − | 0.242478i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.46287 | + | 38.1033i | 0.213733 | + | 1.82482i | ||||
\(437\) | 18.0451 | − | 21.5053i | 0.863213 | − | 1.02874i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.92679 | − | 5.29380i | 0.0919605 | − | 0.252659i | −0.885182 | − | 0.465245i | \(-0.845966\pi\) |
0.977142 | + | 0.212586i | \(0.0681884\pi\) | |||||||
\(440\) | 2.83036 | − | 4.04526i | 0.134932 | − | 0.192850i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.24261 | − | 22.1187i | −0.154235 | − | 1.05208i | ||||
\(443\) | −4.19281 | + | 3.51819i | −0.199206 | + | 0.167154i | −0.736934 | − | 0.675964i | \(-0.763727\pi\) |
0.537728 | + | 0.843119i | \(0.319283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.581665 | + | 3.29879i | −0.0275736 | + | 0.156377i | ||||
\(446\) | 9.12270 | + | 16.9143i | 0.431973 | + | 0.800914i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −8.16112 | + | 0.00585318i | −0.385577 | + | 0.000276537i | ||||
\(449\) | 21.3460 | + | 12.3241i | 1.00738 | + | 0.581612i | 0.910424 | − | 0.413676i | \(-0.135755\pi\) |
0.0969581 | + | 0.995288i | \(0.469089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.22118 | − | 4.16915i | 0.340032 | − | 0.196318i | ||||
\(452\) | −8.31295 | − | 5.46467i | −0.391008 | − | 0.257036i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.736573 | + | 25.4189i | −0.0345691 | + | 1.19297i | ||||
\(455\) | 1.75751 | − | 0.639680i | 0.0823932 | − | 0.0299887i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.98007 | − | 11.2295i | −0.0926236 | − | 0.525294i | −0.995450 | − | 0.0952886i | \(-0.969623\pi\) |
0.902826 | − | 0.430006i | \(-0.141489\pi\) | |||||||
\(458\) | 12.1852 | + | 15.4069i | 0.569376 | + | 0.719916i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.16227 | − | 2.16918i | −0.427193 | − | 0.101139i | ||||
\(461\) | −18.4150 | + | 3.24705i | −0.857670 | + | 0.151230i | −0.585155 | − | 0.810921i | \(-0.698966\pi\) |
−0.272515 | + | 0.962152i | \(0.587855\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1162 | − | 33.2889i | −0.563086 | − | 1.54707i | −0.815086 | − | 0.579340i | \(-0.803310\pi\) |
0.252000 | − | 0.967727i | \(-0.418912\pi\) | |||||||
\(464\) | 13.5801 | − | 5.86557i | 0.630439 | − | 0.272302i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.28621 | − | 1.08937i | 0.152231 | − | 0.0504640i | ||||
\(467\) | −1.62531 | − | 2.81512i | −0.0752103 | − | 0.130268i | 0.825967 | − | 0.563718i | \(-0.190629\pi\) |
−0.901178 | + | 0.433450i | \(0.857296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.31596 | + | 5.74342i | −0.153117 | + | 0.265206i | ||||
\(470\) | −1.06144 | + | 5.14364i | −0.0489604 | + | 0.237258i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.84737 | + | 32.9715i | 0.407233 | + | 1.51764i | ||||
\(473\) | 11.0661 | + | 1.95125i | 0.508820 | + | 0.0897187i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.9396 | − | 16.6125i | −0.639591 | − | 0.762235i | ||||
\(476\) | 10.8823 | + | 10.2620i | 0.498790 | + | 0.470359i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.04154 | − | 20.2488i | 0.367811 | − | 0.926159i | ||||
\(479\) | 36.5463 | + | 13.3018i | 1.66984 | + | 0.607774i | 0.991864 | − | 0.127306i | \(-0.0406329\pi\) |
0.677981 | + | 0.735079i | \(0.262855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.6126 | + | 14.7788i | 0.803068 | + | 0.673854i | ||||
\(482\) | −14.0704 | − | 8.67640i | −0.640887 | − | 0.395199i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.5486 | + | 0.785868i | 0.615847 | + | 0.0357213i | ||||
\(485\) | 3.71903i | 0.168872i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 14.4854i | − | 0.656395i | −0.944609 | − | 0.328198i | \(-0.893559\pi\) | ||
0.944609 | − | 0.328198i | \(-0.106441\pi\) | |||||||
\(488\) | −0.868410 | − | 1.23927i | −0.0393111 | − | 0.0560992i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.76125 | − | 6.09955i | 0.169916 | − | 0.275550i | ||||
\(491\) | 5.58619 | + | 4.68737i | 0.252101 | + | 0.211538i | 0.760076 | − | 0.649834i | \(-0.225161\pi\) |
−0.507975 | + | 0.861372i | \(0.669606\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.4770 | − | 9.27287i | −1.14743 | − | 0.417629i | ||||
\(494\) | 14.3695 | + | 5.70664i | 0.646513 | + | 0.256754i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.3089 | − | 15.6576i | −0.462882 | − | 0.703046i | ||||
\(497\) | 7.68539 | + | 9.15909i | 0.344737 | + | 0.410842i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.1578 | + | 2.49639i | 0.633788 | + | 0.111754i | 0.481307 | − | 0.876552i | \(-0.340162\pi\) |
0.152482 | + | 0.988306i | \(0.451274\pi\) | |||||||
\(500\) | −6.24519 | + | 14.4875i | −0.279293 | + | 0.647901i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.83033 | − | 0.996780i | −0.215588 | − | 0.0444885i | ||||
\(503\) | −9.08769 | + | 15.7403i | −0.405200 | + | 0.701827i | −0.994345 | − | 0.106200i | \(-0.966132\pi\) |
0.589145 | + | 0.808028i | \(0.299465\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.56961 | + | 4.45069i | 0.114346 | + | 0.198053i | ||||
\(506\) | 5.05785 | + | 15.2576i | 0.224849 | + | 0.678285i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.7479 | + | 23.8277i | 0.787437 | + | 1.05718i | ||||
\(509\) | −6.60337 | − | 18.1426i | −0.292689 | − | 0.804157i | −0.995671 | − | 0.0929491i | \(-0.970371\pi\) |
0.702982 | − | 0.711208i | \(-0.251852\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.54632 | − | 0.272658i | 0.0684052 | − | 0.0120617i | ||||
\(512\) | −5.83289 | + | 21.8627i | −0.257780 | + | 0.966204i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −19.8033 | + | 15.6623i | −0.873487 | + | 0.690834i | ||||
\(515\) | −0.0252774 | − | 0.143355i | −0.00111386 | − | 0.00631699i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.42546 | − | 3.06662i | 0.370551 | − | 0.134870i | ||||
\(518\) | −15.3772 | − | 0.445592i | −0.675636 | − | 0.0195782i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.453805 | − | 5.16567i | −0.0199006 | − | 0.226530i | ||||
\(521\) | −24.7853 | + | 14.3098i | −1.08586 | + | 0.626924i | −0.932472 | − | 0.361241i | \(-0.882353\pi\) |
−0.153392 | + | 0.988165i | \(0.549020\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.5509 | − | 6.09156i | −0.461359 | − | 0.266365i | 0.251257 | − | 0.967920i | \(-0.419156\pi\) |
−0.712615 | + | 0.701555i | \(0.752489\pi\) | |||||||
\(524\) | 2.81897 | + | 5.60969i | 0.123147 | + | 0.245060i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.16657 | + | 4.94399i | −0.399682 | + | 0.215568i | ||||
\(527\) | −5.96633 | + | 33.8368i | −0.259898 | + | 1.47395i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.86398 | − | 4.92046i | 0.254956 | − | 0.213933i | ||||
\(530\) | 6.61482 | − | 0.969736i | 0.287329 | − | 0.0421227i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.90971 | + | 2.96935i | −0.429641 | + | 0.128738i | ||||
\(533\) | 2.99539 | − | 8.22975i | 0.129745 | − | 0.356470i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.46679 | + | 5.32331i | −0.193116 | + | 0.230147i | ||||
\(536\) | 13.0067 | + | 12.9973i | 0.561802 | + | 0.561399i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.958211 | − | 0.852531i | −0.0413114 | − | 0.0367552i | ||||
\(539\) | −12.2337 | −0.526944 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.27951 | 0.269977 | 0.134989 | − | 0.990847i | \(-0.456900\pi\) | ||||
0.134989 | + | 0.990847i | \(0.456900\pi\) | |||||||
\(542\) | −7.09538 | − | 6.31283i | −0.304773 | − | 0.271159i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 35.2842 | − | 21.7927i | 1.51280 | − | 0.934355i | ||||
\(545\) | 10.4839 | − | 12.4943i | 0.449083 | − | 0.535196i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.59471 | + | 23.6138i | −0.367483 | + | 1.00965i | 0.608832 | + | 0.793299i | \(0.291638\pi\) |
−0.976315 | + | 0.216353i | \(0.930584\pi\) | |||||||
\(548\) | −6.89636 | − | 23.0154i | −0.294598 | − | 0.983170i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 12.2857 | − | 1.80109i | 0.523865 | − | 0.0767988i | ||||
\(551\) | 14.3642 | − | 12.0530i | 0.611936 | − | 0.513476i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.56355 | + | 14.5386i | −0.109013 | + | 0.618245i | ||||
\(554\) | −2.22946 | + | 1.20246i | −0.0947206 | + | 0.0510875i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.13683 | − | 2.58135i | 0.217850 | − | 0.109474i | ||||
\(557\) | −17.6052 | − | 10.1644i | −0.745958 | − | 0.430679i | 0.0782737 | − | 0.996932i | \(-0.475059\pi\) |
−0.824232 | + | 0.566253i | \(0.808393\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.2211 | − | 5.90115i | 0.432306 | − | 0.249592i | ||||
\(560\) | 2.38222 | + | 2.52259i | 0.100667 | + | 0.106599i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.12909 | − | 0.235560i | −0.342905 | − | 0.00993649i | ||||
\(563\) | 33.7274 | − | 12.2758i | 1.42144 | − | 0.517362i | 0.486976 | − | 0.873416i | \(-0.338100\pi\) |
0.934466 | + | 0.356053i | \(0.115878\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.734434 | + | 4.16518i | 0.0308979 | + | 0.175230i | ||||
\(566\) | −11.4828 | + | 9.08166i | −0.482659 | + | 0.381731i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 30.0391 | − | 14.0206i | 1.26041 | − | 0.588290i | ||||
\(569\) | −37.1364 | + | 6.54816i | −1.55684 | + | 0.274513i | −0.884789 | − | 0.465992i | \(-0.845698\pi\) |
−0.672051 | + | 0.740505i | \(0.734587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.67247 | + | 12.8375i | 0.195537 | + | 0.537233i | 0.998250 | − | 0.0591320i | \(-0.0188333\pi\) |
−0.802713 | + | 0.596365i | \(0.796611\pi\) | |||||||
\(572\) | −7.09973 | + | 5.28819i | −0.296855 | + | 0.221110i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.84387 | + | 5.56225i | 0.0769615 | + | 0.232164i | ||||
\(575\) | −11.8402 | − | 20.5079i | −0.493772 | − | 0.855238i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.52845 | − | 14.7717i | 0.355044 | − | 0.614954i | −0.632082 | − | 0.774902i | \(-0.717799\pi\) |
0.987125 | + | 0.159948i | \(0.0511326\pi\) | |||||||
\(578\) | −50.8954 | − | 10.5027i | −2.11697 | − | 0.436855i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −5.77527 | − | 2.48957i | −0.239805 | − | 0.103374i | ||||
\(581\) | 5.30066 | + | 0.934650i | 0.219909 | + | 0.0387758i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.33643 | − | 8.74322i | −0.303844 | − | 0.362107i | ||||
\(584\) | 0.377872 | − | 4.33701i | 0.0156365 | − | 0.179467i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.4816 | − | 6.54542i | −0.680847 | − | 0.270389i | ||||
\(587\) | −5.94463 | − | 2.16367i | −0.245361 | − | 0.0893041i | 0.216412 | − | 0.976302i | \(-0.430564\pi\) |
−0.461773 | + | 0.886998i | \(0.652787\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.2036 | − | 15.2746i | −0.750065 | − | 0.629379i | ||||
\(590\) | 7.61778 | − | 12.3536i | 0.313619 | − | 0.508590i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.2133 | + | 40.8665i | −0.501966 | + | 1.67960i | ||||
\(593\) | − | 28.7935i | − | 1.18241i | −0.806523 | − | 0.591203i | \(-0.798653\pi\) | ||
0.806523 | − | 0.591203i | \(-0.201347\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 6.35919i | − | 0.260701i | ||||||
\(596\) | −1.28464 | + | 22.1476i | −0.0526207 | + | 0.907199i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 14.3705 | + | 8.86148i | 0.587653 | + | 0.362373i | ||||
\(599\) | −36.9656 | − | 31.0178i | −1.51037 | − | 1.26735i | −0.863024 | − | 0.505163i | \(-0.831433\pi\) |
−0.647351 | − | 0.762192i | \(-0.724123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.1432 | − | 14.9749i | −1.67827 | − | 0.610839i | −0.685196 | − | 0.728358i | \(-0.740284\pi\) |
−0.993071 | + | 0.117519i | \(0.962506\pi\) | |||||||
\(602\) | −2.91470 | + | 7.33930i | −0.118794 | + | 0.299128i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.07959 | + | 8.56797i | −0.328754 | + | 0.348626i | ||||
\(605\) | −3.70876 | − | 4.41992i | −0.150782 | − | 0.179695i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.37632 | − | 0.242682i | −0.0558630 | − | 0.00985015i | 0.145647 | − | 0.989337i | \(-0.453474\pi\) |
−0.201510 | + | 0.979486i | \(0.564585\pi\) | |||||||
\(608\) | 0.851357 | + | 28.6698i | 0.0345271 | + | 1.16271i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.130021 | + | 0.630074i | −0.00526441 | + | 0.0255109i | ||||
\(611\) | 4.70870 | − | 8.15571i | 0.190494 | − | 0.329945i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.57422 | − | 16.5830i | −0.386699 | − | 0.669782i | 0.605304 | − | 0.795994i | \(-0.293051\pi\) |
−0.992003 | + | 0.126212i | \(0.959718\pi\) | |||||||
\(614\) | −35.6795 | + | 11.8276i | −1.43991 | + | 0.477325i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.53102 | − | 5.72206i | 0.0616867 | − | 0.230549i | ||||
\(617\) | −2.45052 | − | 6.73275i | −0.0986543 | − | 0.271050i | 0.880541 | − | 0.473970i | \(-0.157179\pi\) |
−0.979195 | + | 0.202919i | \(0.934957\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.559347 | − | 0.0986280i | 0.0224821 | − | 0.00396419i | −0.162396 | − | 0.986726i | \(-0.551922\pi\) |
0.184878 | + | 0.982761i | \(0.440811\pi\) | |||||||
\(620\) | −1.83615 | + | 7.75558i | −0.0737415 | + | 0.311472i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.4045 | + | 24.5350i | 0.778051 | + | 0.983764i | ||||
\(623\) | 0.697858 | + | 3.95775i | 0.0279591 | + | 0.158564i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.7927 | + | 5.02013i | −0.551708 | + | 0.200805i | ||||
\(626\) | 0.224878 | − | 7.76048i | 0.00898795 | − | 0.310171i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −19.4894 | + | 29.6476i | −0.777711 | + | 1.18307i | ||||
\(629\) | 67.7005 | − | 39.0869i | 2.69939 | − | 1.55850i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.0510 | + | 9.26705i | 0.638980 | + | 0.368915i | 0.784222 | − | 0.620481i | \(-0.213063\pi\) |
−0.145242 | + | 0.989396i | \(0.546396\pi\) | |||||||
\(632\) | 37.1027 | + | 17.2851i | 1.47586 | + | 0.687563i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.4639 | − | 24.9632i | −0.534720 | − | 0.991416i | ||||
\(635\) | 2.19343 | − | 12.4396i | 0.0870438 | − | 0.493650i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.84319 | + | 8.25942i | −0.390002 | + | 0.327250i | ||||
\(638\) | 1.55734 | + | 10.6230i | 0.0616555 | + | 0.420568i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 8.46363 | − | 4.57269i | 0.334554 | − | 0.180752i | ||||
\(641\) | 8.67287 | − | 23.8285i | 0.342558 | − | 0.941170i | −0.642092 | − | 0.766628i | \(-0.721933\pi\) |
0.984650 | − | 0.174542i | \(-0.0558446\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.0729 | − | 21.5384i | 0.712725 | − | 0.849392i | −0.281178 | − | 0.959656i | \(-0.590725\pi\) |
0.993902 | + | 0.110263i | \(0.0351694\pi\) | |||||||
\(644\) | −11.2197 | + | 1.31411i | −0.442118 | + | 0.0517833i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.9432 | − | 39.2748i | 1.37482 | − | 1.54525i | ||||
\(647\) | 26.2892 | 1.03353 | 0.516767 | − | 0.856126i | \(-0.327135\pi\) | ||||
0.516767 | + | 0.856126i | \(0.327135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.7773 | −0.972595 | ||||||||
\(650\) | 8.66904 | − | 9.74367i | 0.340028 | − | 0.382178i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −35.8340 | + | 4.19708i | −1.40337 | + | 0.164370i | ||||
\(653\) | −3.30137 | + | 3.93442i | −0.129193 | + | 0.153966i | −0.826763 | − | 0.562551i | \(-0.809820\pi\) |
0.697570 | + | 0.716516i | \(0.254265\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.912891 | − | 2.50815i | 0.0356696 | − | 0.0980014i | ||||
\(656\) | 16.2191 | − | 0.952439i | 0.633251 | − | 0.0371865i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.913984 | + | 6.23452i | 0.0356308 | + | 0.243047i | ||||
\(659\) | 6.33669 | − | 5.31712i | 0.246842 | − | 0.207125i | −0.510969 | − | 0.859599i | \(-0.670713\pi\) |
0.757811 | + | 0.652474i | \(0.226269\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.914795 | − | 5.18806i | 0.0355814 | − | 0.201792i | −0.961835 | − | 0.273630i | \(-0.911775\pi\) |
0.997416 | + | 0.0718384i | \(0.0228866\pi\) | |||||||
\(662\) | −15.6884 | − | 29.0876i | −0.609745 | − | 1.13052i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.30199 | − | 13.5273i | 0.244565 | − | 0.524962i | ||||
\(665\) | 3.80888 | + | 2.19906i | 0.147702 | + | 0.0852759i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.7324 | − | 10.2378i | 0.686601 | − | 0.396409i | ||||
\(668\) | 17.6583 | − | 26.8621i | 0.683219 | − | 1.03932i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.226432 | − | 7.81409i | 0.00874783 | − | 0.301885i | ||||
\(671\) | 1.03208 | − | 0.375647i | 0.0398431 | − | 0.0145017i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.65489 | + | 15.0566i | 0.102338 | + | 0.580390i | 0.992250 | + | 0.124257i | \(0.0396547\pi\) |
−0.889912 | + | 0.456133i | \(0.849234\pi\) | |||||||
\(674\) | 5.59402 | + | 7.07305i | 0.215474 | + | 0.272444i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.84780 | − | 16.2525i | 0.147992 | − | 0.625095i | ||||
\(677\) | 24.0011 | − | 4.23205i | 0.922439 | − | 0.162651i | 0.307792 | − | 0.951454i | \(-0.400410\pi\) |
0.614647 | + | 0.788803i | \(0.289299\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.52607 | + | 4.19285i | 0.0585653 | + | 0.160907i | ||||
\(680\) | −17.0323 | − | 4.55723i | −0.653157 | − | 0.174762i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 12.9151 | − | 4.28132i | 0.494546 | − | 0.163940i | ||||
\(683\) | 12.9096 | + | 22.3600i | 0.493971 | + | 0.855582i | 0.999976 | − | 0.00694804i | \(-0.00221165\pi\) |
−0.506005 | + | 0.862530i | \(0.668878\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.10734 | + | 8.84617i | −0.195141 | + | 0.337995i | ||||
\(686\) | 3.77854 | − | 18.3106i | 0.144265 | − | 0.699100i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.5686 | + | 13.0663i | 0.669796 | + | 0.498147i | ||||
\(689\) | −11.8057 | − | 2.08167i | −0.449762 | − | 0.0793051i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.26030 | + | 7.46074i | 0.238153 | + | 0.283820i | 0.871862 | − | 0.489752i | \(-0.162913\pi\) |
−0.633709 | + | 0.773572i | \(0.718468\pi\) | |||||||
\(692\) | −7.49619 | + | 7.94930i | −0.284962 | + | 0.302187i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.43176 | + | 21.2314i | −0.320065 | + | 0.805933i | ||||
\(695\) | −2.29673 | − | 0.835942i | −0.0871200 | − | 0.0317091i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.8110 | − | 19.1407i | −0.864030 | − | 0.725007i | ||||
\(698\) | 25.3294 | + | 15.6192i | 0.958733 | + | 0.591197i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.505307 | + | 8.71166i | −0.0190988 | + | 0.329270i | ||||
\(701\) | 46.8518i | 1.76957i | 0.466000 | + | 0.884785i | \(0.345695\pi\) | ||||
−0.466000 | + | 0.884785i | \(0.654305\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.0663i | 2.03915i | ||||||||
\(704\) | −14.2286 | − | 8.20130i | −0.536261 | − | 0.309098i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.13853 | + | 11.5764i | −0.268662 | + | 0.435684i | ||||
\(707\) | 4.72329 | + | 3.96331i | 0.177638 | + | 0.149056i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.0301 | + | 9.11022i | 0.940026 | + | 0.342142i | 0.766176 | − | 0.642631i | \(-0.222157\pi\) |
0.173850 | + | 0.984772i | \(0.444379\pi\) | |||||||
\(710\) | −13.0984 | − | 5.20185i | −0.491574 | − | 0.195222i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.1004 | + | 0.967151i | 0.416006 | + | 0.0362455i | ||||
\(713\) | −16.6793 | − | 19.8776i | −0.624646 | − | 0.744424i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.70651 | + | 0.653558i | 0.138616 | + | 0.0244417i | ||||
\(716\) | 24.7513 | + | 10.6696i | 0.924999 | + | 0.398744i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −19.4349 | − | 4.01055i | −0.725303 | − | 0.149673i | ||||
\(719\) | 19.9787 | − | 34.6042i | 0.745081 | − | 1.29052i | −0.205076 | − | 0.978746i | \(-0.565744\pi\) |
0.950157 | − | 0.311772i | \(-0.100922\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0873226 | − | 0.151247i | −0.00325206 | − | 0.00563274i | ||||
\(722\) | 2.98540 | + | 9.00584i | 0.111105 | + | 0.335163i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 22.9994 | − | 17.1309i | 0.854765 | − | 0.636666i | ||||
\(725\) | −5.40977 | − | 14.8632i | −0.200914 | − | 0.552006i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.3051 | − | 8.16484i | 1.71736 | − | 0.302817i | 0.773657 | − | 0.633605i | \(-0.218426\pi\) |
0.943705 | + | 0.330788i | \(0.107314\pi\) | |||||||
\(728\) | −2.63131 | − | 5.63759i | −0.0975230 | − | 0.208943i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.45169 | + | 1.14813i | −0.0537294 | + | 0.0424942i | ||||
\(731\) | −6.96831 | − | 39.5192i | −0.257732 | − | 1.46167i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.6192 | + | 3.86508i | −0.392230 | + | 0.142760i | −0.530604 | − | 0.847620i | \(-0.678035\pi\) |
0.138374 | + | 0.990380i | \(0.455812\pi\) | |||||||
\(734\) | −52.4332 | − | 1.51938i | −1.93534 | − | 0.0560812i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.52078 | + | 30.9922i | −0.166638 | + | 1.14239i | ||||
\(737\) | −11.5577 | + | 6.67287i | −0.425735 | + | 0.245798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.1693 | − | 15.6862i | −0.999438 | − | 0.577026i | −0.0913557 | − | 0.995818i | \(-0.529120\pi\) |
−0.908082 | + | 0.418793i | \(0.862453\pi\) | |||||||
\(740\) | 16.2027 | − | 8.14215i | 0.595623 | − | 0.299311i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.05966 | − | 3.80762i | 0.259168 | − | 0.139782i | ||||
\(743\) | 1.81455 | − | 10.2908i | 0.0665695 | − | 0.377535i | −0.933262 | − | 0.359196i | \(-0.883051\pi\) |
0.999832 | − | 0.0183390i | \(-0.00583781\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.22511 | − | 6.06259i | 0.264708 | − | 0.222116i | ||||
\(746\) | −39.6714 | + | 5.81585i | −1.45247 | + | 0.212933i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.63971 | + | 28.8335i | 0.315899 | + | 1.05426i | ||||
\(749\) | −2.85150 | + | 7.83444i | −0.104192 | + | 0.286264i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.54549 | − | 7.80061i | 0.238848 | − | 0.284648i | −0.633283 | − | 0.773920i | \(-0.718293\pi\) |
0.872131 | + | 0.489272i | \(0.162737\pi\) | |||||||
\(752\) | 17.3533 | + | 2.01991i | 0.632811 | + | 0.0736584i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.42498 | + | 7.49579i | 0.306820 | + | 0.272981i | ||||
\(755\) | 5.00678 | 0.182215 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 46.4748 | 1.68916 | 0.844578 | − | 0.535433i | \(-0.179851\pi\) | ||||
0.844578 | + | 0.535433i | \(0.179851\pi\) | |||||||
\(758\) | 16.1914 | + | 14.4056i | 0.588097 | + | 0.523236i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.61948 | − | 8.62567i | 0.312662 | − | 0.312886i | ||||
\(761\) | −34.3388 | + | 40.9234i | −1.24478 | + | 1.48347i | −0.430942 | + | 0.902380i | \(0.641819\pi\) |
−0.813838 | + | 0.581092i | \(0.802626\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.69273 | − | 18.3881i | 0.242293 | − | 0.665694i | ||||
\(764\) | 16.0846 | − | 4.81960i | 0.581921 | − | 0.174367i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 51.5013 | − | 7.55012i | 1.86082 | − | 0.272797i | ||||
\(767\) | −19.9357 | + | 16.7280i | −0.719837 | + | 0.604015i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.11818 | − | 23.3554i | 0.148506 | − | 0.842217i | −0.815980 | − | 0.578080i | \(-0.803802\pi\) |
0.964485 | − | 0.264136i | \(-0.0850869\pi\) | |||||||
\(770\) | −2.21645 | + | 1.19544i | −0.0798751 | + | 0.0430806i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.10966 | + | 2.20820i | 0.0399376 | + | 0.0794748i | ||||
\(773\) | −24.4917 | − | 14.1403i | −0.880907 | − | 0.508592i | −0.00994940 | − | 0.999951i | \(-0.503167\pi\) |
−0.870957 | + | 0.491359i | \(0.836500\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.3593 | + | 10.0224i | −0.623565 | + | 0.360015i | ||||
\(776\) | 12.3236 | − | 1.08263i | 0.442393 | − | 0.0388642i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −12.7071 | − | 0.368219i | −0.455572 | − | 0.0132013i | ||||
\(779\) | 19.3527 | − | 7.04382i | 0.693384 | − | 0.252371i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.17803 | + | 23.6948i | 0.149502 | + | 0.847866i | ||||
\(782\) | 45.0242 | − | 35.6093i | 1.61006 | − | 1.27338i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −21.3069 | − | 10.6880i | −0.760959 | − | 0.381713i | ||||
\(785\) | 14.8548 | − | 2.61931i | 0.530192 | − | 0.0934872i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.69409 | − | 7.40195i | −0.0960339 | − | 0.263851i | 0.882369 | − | 0.470558i | \(-0.155947\pi\) |
−0.978403 | + | 0.206707i | \(0.933725\pi\) | |||||||
\(788\) | 3.49237 | + | 4.68873i | 0.124411 | + | 0.167029i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.47560 | − | 16.5178i | −0.194813 | − | 0.587677i | ||||
\(791\) | 2.53715 | + | 4.39448i | 0.0902108 | + | 0.156250i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.576796 | − | 0.999040i | 0.0204826 | − | 0.0354769i | ||||
\(794\) | 6.53000 | + | 1.34752i | 0.231741 | + | 0.0478218i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.4286 | − | 26.5119i | 0.405076 | − | 0.939689i | ||||
\(797\) | −1.80271 | − | 0.317867i | −0.0638553 | − | 0.0112594i | 0.141629 | − | 0.989920i | \(-0.454766\pi\) |
−0.205485 | + | 0.978660i | \(0.565877\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.5821 | − | 24.5288i | −0.728141 | − | 0.867765i | ||||
\(800\) | 22.9709 | + | 7.59650i | 0.812145 | + | 0.268577i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 22.5858 | + | 8.96964i | 0.797532 | + | 0.316729i | ||||
\(803\) | 2.96918 | + | 1.08069i | 0.104780 | + | 0.0381368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.67900 | + | 3.08704i | 0.129668 | + | 0.108804i | ||||
\(806\) | 7.50098 | − | 12.1642i | 0.264211 | − | 0.428465i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.0001 | − | 9.81046i | 0.492522 | − | 0.345131i | ||||
\(809\) | 0.784403i | 0.0275781i | 0.999905 | + | 0.0137891i | \(0.00438933\pi\) | ||||
−0.999905 | + | 0.0137891i | \(0.995611\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.4637i | − | 1.45599i | −0.685584 | − | 0.727994i | \(-0.740453\pi\) | ||
0.685584 | − | 0.727994i | \(-0.259547\pi\) | |||||||
\(812\) | −7.53264 | − | 0.436919i | −0.264344 | − | 0.0153329i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −26.3502 | − | 16.2487i | −0.923573 | − | 0.569516i | ||||
\(815\) | 11.7502 | + | 9.85955i | 0.411590 | + | 0.345365i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0800 | + | 9.49236i | 0.912425 | + | 0.332096i | ||||
\(818\) | −10.0825 | + | 25.3881i | −0.352528 | + | 0.887675i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.02535 | − | 4.73890i | −0.175493 | − | 0.165490i | ||||
\(821\) | 1.49518 | + | 1.78189i | 0.0521823 | + | 0.0621884i | 0.791504 | − | 0.611164i | \(-0.209298\pi\) |
−0.739322 | + | 0.673352i | \(0.764854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.3729 | + | 7.82414i | 1.54674 | + | 0.272732i | 0.880879 | − | 0.473341i | \(-0.156952\pi\) |
0.665863 | + | 0.746074i | \(0.268063\pi\) | |||||||
\(824\) | −0.467674 | + | 0.125493i | −0.0162922 | + | 0.00437175i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.51912 | − | 17.0534i | 0.122446 | − | 0.593364i | ||||
\(827\) | −20.6443 | + | 35.7571i | −0.717874 | + | 1.24339i | 0.243966 | + | 0.969784i | \(0.421551\pi\) |
−0.961840 | + | 0.273611i | \(0.911782\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.75417 | − | 4.77037i | −0.0956564 | − | 0.165682i | 0.814226 | − | 0.580548i | \(-0.197162\pi\) |
−0.909882 | + | 0.414866i | \(0.863828\pi\) | |||||||
\(830\) | −6.02226 | + | 1.99636i | −0.209036 | + | 0.0692946i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −16.9853 | + | 3.00752i | −0.588858 | + | 0.104267i | ||||
\(833\) | 14.9425 | + | 41.0542i | 0.517728 | + | 1.42245i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.4592 | + | 2.37321i | −0.465774 | + | 0.0821285i | ||||
\(836\) | −20.2578 | − | 4.79606i | −0.700629 | − | 0.165875i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.4612 | − | 17.0203i | −0.465011 | − | 0.587957i | ||||
\(839\) | 4.43317 | + | 25.1418i | 0.153050 | + | 0.867990i | 0.960547 | + | 0.278118i | \(0.0897107\pi\) |
−0.807497 | + | 0.589872i | \(0.799178\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.3994 | + | 5.24096i | −0.496532 | + | 0.180723i | ||||
\(842\) | 0.952967 | − | 32.8866i | 0.0328414 | − | 1.13335i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.32209 | + | 6.12805i | 0.320880 | + | 0.210936i | ||||
\(845\) | −6.14933 | + | 3.55032i | −0.211543 | + | 0.122135i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.99495 | − | 3.46119i | −0.205989 | − | 0.118928i | ||||
\(848\) | −5.13901 | − | 21.6371i | −0.176474 | − | 0.743020i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −21.0502 | − | 39.0288i | −0.722015 | − | 1.33868i | ||||
\(851\) | −10.2519 | + | 58.1415i | −0.351431 | + | 1.99306i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.0320 | − | 29.3953i | 1.19947 | − | 1.00648i | 0.199827 | − | 0.979831i | \(-0.435962\pi\) |
0.999645 | − | 0.0266448i | \(-0.00848230\pi\) | |||||||
\(854\) | 0.111959 | + | 0.763702i | 0.00383116 | + | 0.0261333i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.9400 | + | 13.2518i | 0.647357 | + | 0.452938i | ||||
\(857\) | 14.1429 | − | 38.8574i | 0.483113 | − | 1.32734i | −0.423697 | − | 0.905804i | \(-0.639268\pi\) |
0.906810 | − | 0.421539i | \(-0.138510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.1399 | + | 43.0699i | −1.23308 | + | 1.46953i | −0.399866 | + | 0.916574i | \(0.630943\pi\) |
−0.833213 | + | 0.552952i | \(0.813501\pi\) | |||||||
\(860\) | −1.08285 | − | 9.24524i | −0.0369250 | − | 0.315260i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.8614 | + | 17.8276i | −0.540243 | + | 0.607212i | ||||
\(863\) | −12.4602 | −0.424150 | −0.212075 | − | 0.977253i | \(-0.568022\pi\) | ||||
−0.212075 | + | 0.977253i | \(0.568022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.64525 | 0.157943 | ||||||||
\(866\) | 2.62693 | − | 2.95257i | 0.0892668 | − | 0.100332i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.11236 | + | 9.49713i | 0.0377559 | + | 0.322354i | ||||
\(869\) | −19.0960 | + | 22.7577i | −0.647786 | + | 0.772002i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.79421 | + | 13.1720i | −0.162446 | + | 0.446316i | ||||
\(872\) | −44.4539 | − | 31.1032i | −1.50540 | − | 1.05329i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.75870 | + | 39.2816i | 0.194791 | + | 1.32872i | ||||
\(875\) | 6.16435 | − | 5.17251i | 0.208393 | − | 0.174863i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.26229 | + | 18.5014i | −0.110160 | + | 0.624747i | 0.878873 | + | 0.477055i | \(0.158296\pi\) |
−0.989033 | + | 0.147693i | \(0.952815\pi\) | |||||||
\(878\) | 3.78200 | + | 7.01215i | 0.127636 | + | 0.236649i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.61344 | + | 6.79316i | 0.0543890 | + | 0.228997i | ||||
\(881\) | 13.9892 | + | 8.07667i | 0.471308 | + | 0.272110i | 0.716787 | − | 0.697292i | \(-0.245612\pi\) |
−0.245479 | + | 0.969402i | \(0.578945\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.99218 | + | 1.15019i | −0.0670423 | + | 0.0387069i | −0.533146 | − | 0.846023i | \(-0.678991\pi\) |
0.466104 | + | 0.884730i | \(0.345657\pi\) | |||||||
\(884\) | 26.4180 | + | 17.3664i | 0.888534 | + | 0.584094i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.224204 | − | 7.73720i | 0.00753228 | − | 0.259936i | ||||
\(887\) | −9.36820 | + | 3.40975i | −0.314553 | + | 0.114488i | −0.494472 | − | 0.869193i | \(-0.664639\pi\) |
0.179919 | + | 0.983681i | \(0.442416\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.63159 | − | 14.9245i | −0.0882608 | − | 0.500552i | ||||
\(890\) | −2.93860 | − | 3.71555i | −0.0985020 | − | 0.124545i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −26.4467 | − | 6.26131i | −0.885502 | − | 0.209644i | ||||
\(893\) | 21.8091 | − | 3.84554i | 0.729815 | − | 0.128686i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.91918 | − | 10.7679i | −0.131004 | − | 0.359930i | ||||
\(896\) | 7.66557 | − | 8.62826i | 0.256089 | − | 0.288250i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −33.0873 | + | 10.9683i | −1.10414 | + | 0.366018i | ||||
\(899\) | −8.66598 | − | 15.0099i | −0.289027 | − | 0.500609i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20.3798 | + | 35.2989i | −0.678951 | + | 1.17598i | ||||
\(902\) | −2.38320 | + | 11.5488i | −0.0793518 | + | 0.384533i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.5883 | − | 3.64618i | 0.451939 | − | 0.121270i | ||||
\(905\) | −12.0071 | − | 2.11718i | −0.399131 | − | 0.0703775i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.6103 | − | 20.9872i | −0.584741 | − | 0.696868i | 0.389845 | − | 0.920881i | \(-0.372529\pi\) |
−0.974586 | + | 0.224013i | \(0.928084\pi\) | |||||||
\(908\) | −26.1643 | − | 24.6729i | −0.868293 | − | 0.818800i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.976258 | + | 2.45824i | −0.0323626 | + | 0.0814900i | ||||
\(911\) | −43.0029 | − | 15.6518i | −1.42475 | − | 0.518566i | −0.489327 | − | 0.872100i | \(-0.662758\pi\) |
−0.935422 | + | 0.353534i | \(0.884980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.29727 | + | 6.96224i | 0.274600 | + | 0.230416i | ||||
\(914\) | 13.7260 | + | 8.46409i | 0.454017 | + | 0.279967i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −27.7329 | − | 1.60860i | −0.916320 | − | 0.0531498i | ||||
\(917\) | − | 3.20230i | − | 0.105749i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.8178i | 1.18152i | 0.806847 | + | 0.590760i | \(0.201172\pi\) | ||||
−0.806847 | + | 0.590760i | \(0.798828\pi\) | |||||||
\(920\) | 10.9048 | − | 7.64142i | 0.359519 | − | 0.251930i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.8800 | − | 22.5090i | 0.457114 | − | 0.741293i | ||||
\(923\) | 19.3588 | + | 16.2440i | 0.637203 | + | 0.534676i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.8560 | + | 15.5983i | 1.40910 | + | 0.512869i | ||||
\(926\) | 46.5616 | + | 18.4913i | 1.53011 | + | 0.607661i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.56841 | + | 19.8621i | −0.215618 | + | 0.652005i | ||||
\(929\) | 9.73496 | + | 11.6017i | 0.319394 | + | 0.380639i | 0.901723 | − | 0.432314i | \(-0.142303\pi\) |
−0.582329 | + | 0.812953i | \(0.697859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29.7570 | − | 5.24696i | −0.975246 | − | 0.171962i | ||||
\(932\) | −1.93817 | + | 4.49614i | −0.0634869 | + | 0.147276i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.50221 | + | 0.929069i | 0.147317 | + | 0.0304001i | ||||
\(935\) | 6.39844 | − | 11.0824i | 0.209251 | − | 0.362434i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −20.1768 | − | 34.9472i | −0.659147 | − | 1.14168i | −0.980837 | − | 0.194831i | \(-0.937584\pi\) |
0.321690 | − | 0.946845i | \(-0.395749\pi\) | |||||||
\(938\) | −2.95117 | − | 8.90256i | −0.0963591 | − | 0.290679i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.43680 | − | 5.95669i | −0.144713 | − | 0.194286i | ||||
\(941\) | 12.8302 | + | 35.2506i | 0.418252 | + | 1.14914i | 0.952694 | + | 0.303932i | \(0.0982995\pi\) |
−0.534442 | + | 0.845205i | \(0.679478\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 22.1471 | − | 3.90513i | 0.721208 | − | 0.127168i | ||||
\(944\) | −43.1534 | − | 21.6466i | −1.40452 | − | 0.704538i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.4642 | + | 9.85782i | −0.405245 | + | 0.320505i | ||||
\(947\) | −1.96803 | − | 11.1613i | −0.0639525 | − | 0.362693i | −0.999943 | − | 0.0106676i | \(-0.996604\pi\) |
0.935991 | − | 0.352025i | \(-0.114507\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.11860 | − | 1.13508i | 0.101234 | − | 0.0368462i | ||||
\(950\) | 30.6559 | + | 0.888329i | 0.994610 | + | 0.0288212i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.0723 | + | 1.85120i | −0.682956 | + | 0.0599977i | ||||
\(953\) | −34.5149 | + | 19.9272i | −1.11805 | + | 0.645505i | −0.940902 | − | 0.338680i | \(-0.890020\pi\) |
−0.177145 | + | 0.984185i | \(0.556686\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.18226 | − | 3.56933i | −0.200053 | − | 0.115501i | ||||
\(956\) | 13.8349 | + | 27.5310i | 0.447451 | + | 0.890418i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −48.4091 | + | 26.1094i | −1.56403 | + | 0.843557i | ||||
\(959\) | −2.12809 | + | 12.0690i | −0.0687195 | + | 0.389728i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.92155 | − | 5.80787i | 0.223276 | − | 0.187351i | ||||
\(962\) | −32.1713 | + | 4.71633i | −1.03724 | + | 0.152060i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.3938 | − | 6.71011i | 0.721257 | − | 0.216118i | ||||
\(965\) | 0.359351 | − | 0.987308i | 0.0115679 | − | 0.0317826i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.8413 | + | 15.3037i | −0.412948 | + | 0.492132i | −0.931923 | − | 0.362657i | \(-0.881870\pi\) |
0.518974 | + | 0.854790i | \(0.326314\pi\) | |||||||
\(968\) | −13.5665 | + | 13.5763i | −0.436045 | + | 0.436358i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.92939 | − | 3.49602i | −0.126165 | − | 0.112250i | ||||
\(971\) | −7.27802 | −0.233563 | −0.116781 | − | 0.993158i | \(-0.537258\pi\) | ||||
−0.116781 | + | 0.993158i | \(0.537258\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.93237 | −0.0940074 | ||||||||
\(974\) | 15.3048 | + | 13.6168i | 0.490396 | + | 0.436310i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.12571 | + | 0.247430i | 0.0680423 | + | 0.00792003i | ||||
\(977\) | 11.3127 | − | 13.4819i | 0.361925 | − | 0.431325i | −0.554098 | − | 0.832451i | \(-0.686937\pi\) |
0.916023 | + | 0.401126i | \(0.131381\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.76599 | + | 7.59951i | −0.0884015 | + | 0.242881i | ||||
\(980\) | 2.90886 | + | 9.70782i | 0.0929201 | + | 0.310105i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.2037 | + | 1.49587i | −0.325614 | + | 0.0477352i | ||||
\(983\) | −30.8633 | + | 25.8973i | −0.984385 | + | 0.825997i | −0.984745 | − | 0.174003i | \(-0.944330\pi\) |
0.000360257 | 1.00000i | \(0.499885\pi\) | ||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.431616 | − | 2.44782i | 0.0137524 | − | 0.0779939i | ||||
\(986\) | 33.7467 | − | 18.2013i | 1.07471 | − | 0.579647i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −19.5373 | + | 9.81784i | −0.621564 | + | 0.312347i | ||||
\(989\) | 26.2459 | + | 15.1531i | 0.834571 | + | 0.481840i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.6152 | + | 19.9851i | −1.09959 | + | 0.634848i | −0.936113 | − | 0.351700i | \(-0.885604\pi\) |
−0.163476 | + | 0.986547i | \(0.552271\pi\) | |||||||
\(992\) | 26.2340 | + | 3.82670i | 0.832930 | + | 0.121498i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −16.9017 | − | 0.489768i | −0.536091 | − | 0.0155345i | ||||
\(995\) | −11.5338 | + | 4.19796i | −0.365646 | + | 0.133084i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.92799 | + | 27.9480i | 0.156071 | + | 0.885123i | 0.957800 | + | 0.287435i | \(0.0928026\pi\) |
−0.801729 | + | 0.597688i | \(0.796086\pi\) | |||||||
\(998\) | −15.9464 | + | 12.6119i | −0.504775 | + | 0.399222i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.2.l.a.71.4 | 96 | ||
3.2 | odd | 2 | 108.2.l.a.95.13 | yes | 96 | ||
4.3 | odd | 2 | inner | 324.2.l.a.71.3 | 96 | ||
9.2 | odd | 6 | 972.2.l.c.863.1 | 96 | |||
9.4 | even | 3 | 972.2.l.a.539.7 | 96 | |||
9.5 | odd | 6 | 972.2.l.d.539.10 | 96 | |||
9.7 | even | 3 | 972.2.l.b.863.16 | 96 | |||
12.11 | even | 2 | 108.2.l.a.95.14 | yes | 96 | ||
27.2 | odd | 18 | inner | 324.2.l.a.251.3 | 96 | ||
27.7 | even | 9 | 972.2.l.c.107.8 | 96 | |||
27.11 | odd | 18 | 972.2.l.a.431.14 | 96 | |||
27.16 | even | 9 | 972.2.l.d.431.3 | 96 | |||
27.20 | odd | 18 | 972.2.l.b.107.9 | 96 | |||
27.25 | even | 9 | 108.2.l.a.83.14 | yes | 96 | ||
36.7 | odd | 6 | 972.2.l.b.863.9 | 96 | |||
36.11 | even | 6 | 972.2.l.c.863.8 | 96 | |||
36.23 | even | 6 | 972.2.l.d.539.3 | 96 | |||
36.31 | odd | 6 | 972.2.l.a.539.14 | 96 | |||
108.7 | odd | 18 | 972.2.l.c.107.1 | 96 | |||
108.11 | even | 18 | 972.2.l.a.431.7 | 96 | |||
108.43 | odd | 18 | 972.2.l.d.431.10 | 96 | |||
108.47 | even | 18 | 972.2.l.b.107.16 | 96 | |||
108.79 | odd | 18 | 108.2.l.a.83.13 | ✓ | 96 | ||
108.83 | even | 18 | inner | 324.2.l.a.251.4 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.l.a.83.13 | ✓ | 96 | 108.79 | odd | 18 | ||
108.2.l.a.83.14 | yes | 96 | 27.25 | even | 9 | ||
108.2.l.a.95.13 | yes | 96 | 3.2 | odd | 2 | ||
108.2.l.a.95.14 | yes | 96 | 12.11 | even | 2 | ||
324.2.l.a.71.3 | 96 | 4.3 | odd | 2 | inner | ||
324.2.l.a.71.4 | 96 | 1.1 | even | 1 | trivial | ||
324.2.l.a.251.3 | 96 | 27.2 | odd | 18 | inner | ||
324.2.l.a.251.4 | 96 | 108.83 | even | 18 | inner | ||
972.2.l.a.431.7 | 96 | 108.11 | even | 18 | |||
972.2.l.a.431.14 | 96 | 27.11 | odd | 18 | |||
972.2.l.a.539.7 | 96 | 9.4 | even | 3 | |||
972.2.l.a.539.14 | 96 | 36.31 | odd | 6 | |||
972.2.l.b.107.9 | 96 | 27.20 | odd | 18 | |||
972.2.l.b.107.16 | 96 | 108.47 | even | 18 | |||
972.2.l.b.863.9 | 96 | 36.7 | odd | 6 | |||
972.2.l.b.863.16 | 96 | 9.7 | even | 3 | |||
972.2.l.c.107.1 | 96 | 108.7 | odd | 18 | |||
972.2.l.c.107.8 | 96 | 27.7 | even | 9 | |||
972.2.l.c.863.1 | 96 | 9.2 | odd | 6 | |||
972.2.l.c.863.8 | 96 | 36.11 | even | 6 | |||
972.2.l.d.431.3 | 96 | 27.16 | even | 9 | |||
972.2.l.d.431.10 | 96 | 108.43 | odd | 18 | |||
972.2.l.d.539.3 | 96 | 36.23 | even | 6 | |||
972.2.l.d.539.10 | 96 | 9.5 | odd | 6 |