Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(81,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([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("605.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.g (of order \(5\), degree \(4\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{5})\) |
Coefficient field: | 8.0.324000000.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 9x^{4} + 27x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 251.1 | ||
Root | \(1.40126 - 1.01807i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.251 |
Dual form | 605.2.g.i.511.1 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.535233 | + | 1.64728i | −0.378467 | + | 1.16480i | 0.562643 | + | 0.826700i | \(0.309785\pi\) |
−0.941110 | + | 0.338101i | \(0.890215\pi\) | |||||||
\(3\) | 0.809017 | − | 0.587785i | 0.467086 | − | 0.339358i | −0.329218 | − | 0.944254i | \(-0.606785\pi\) |
0.796305 | + | 0.604896i | \(0.206785\pi\) | |||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | −0.309017 | − | 0.951057i | −0.138197 | − | 0.425325i | ||||
\(6\) | 0.535233 | + | 1.64728i | 0.218508 | + | 0.672499i | ||||
\(7\) | −1.40126 | − | 1.01807i | −0.529626 | − | 0.384796i | 0.290592 | − | 0.956847i | \(-0.406148\pi\) |
−0.820218 | + | 0.572051i | \(0.806148\pi\) | |||||||
\(8\) | −1.40126 | + | 1.01807i | −0.495420 | + | 0.359943i | ||||
\(9\) | −0.618034 | + | 1.90211i | −0.206011 | + | 0.634038i | ||||
\(10\) | 1.73205 | 0.547723 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −1.07047 | + | 3.29456i | −0.296894 | + | 0.913746i | 0.685685 | + | 0.727899i | \(0.259503\pi\) |
−0.982579 | + | 0.185847i | \(0.940497\pi\) | |||||||
\(14\) | 2.42705 | − | 1.76336i | 0.648657 | − | 0.471277i | ||||
\(15\) | −0.809017 | − | 0.587785i | −0.208887 | − | 0.151765i | ||||
\(16\) | −1.54508 | − | 4.75528i | −0.386271 | − | 1.18882i | ||||
\(17\) | 2.14093 | + | 6.58911i | 0.519252 | + | 1.59809i | 0.775409 | + | 0.631459i | \(0.217544\pi\) |
−0.256157 | + | 0.966635i | \(0.582456\pi\) | |||||||
\(18\) | −2.80252 | − | 2.03615i | −0.660560 | − | 0.479925i | ||||
\(19\) | −2.80252 | + | 2.03615i | −0.642942 | + | 0.467124i | −0.860859 | − | 0.508843i | \(-0.830073\pi\) |
0.217918 | + | 0.975967i | \(0.430073\pi\) | |||||||
\(20\) | −0.309017 | + | 0.951057i | −0.0690983 | + | 0.212663i | ||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | −0.535233 | + | 1.64728i | −0.109254 | + | 0.336249i | ||||
\(25\) | −0.809017 | + | 0.587785i | −0.161803 | + | 0.117557i | ||||
\(26\) | −4.85410 | − | 3.52671i | −0.951968 | − | 0.691645i | ||||
\(27\) | 1.54508 | + | 4.75528i | 0.297352 | + | 0.915155i | ||||
\(28\) | 0.535233 | + | 1.64728i | 0.101150 | + | 0.311306i | ||||
\(29\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(30\) | 1.40126 | − | 1.01807i | 0.255834 | − | 0.185874i | ||||
\(31\) | −2.47214 | + | 7.60845i | −0.444009 | + | 1.36652i | 0.439558 | + | 0.898214i | \(0.355135\pi\) |
−0.883567 | + | 0.468304i | \(0.844865\pi\) | |||||||
\(32\) | 5.19615 | 0.918559 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −12.0000 | −2.05798 | ||||||||
\(35\) | −0.535233 | + | 1.64728i | −0.0904709 | + | 0.278441i | ||||
\(36\) | 1.61803 | − | 1.17557i | 0.269672 | − | 0.195928i | ||||
\(37\) | 6.47214 | + | 4.70228i | 1.06401 | + | 0.773050i | 0.974827 | − | 0.222965i | \(-0.0715734\pi\) |
0.0891861 | + | 0.996015i | \(0.471573\pi\) | |||||||
\(38\) | −1.85410 | − | 5.70634i | −0.300775 | − | 0.925690i | ||||
\(39\) | 1.07047 | + | 3.29456i | 0.171412 | + | 0.527551i | ||||
\(40\) | 1.40126 | + | 1.01807i | 0.221558 | + | 0.160972i | ||||
\(41\) | 9.80881 | − | 7.12652i | 1.53188 | − | 1.11298i | 0.576696 | − | 0.816959i | \(-0.304342\pi\) |
0.955183 | − | 0.296016i | \(-0.0956582\pi\) | |||||||
\(42\) | 0.927051 | − | 2.85317i | 0.143047 | − | 0.440254i | ||||
\(43\) | −8.66025 | −1.32068 | −0.660338 | − | 0.750968i | \(-0.729587\pi\) | ||||
−0.660338 | + | 0.750968i | \(0.729587\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.28115 | + | 5.29007i | −1.06207 | + | 0.771636i | −0.974469 | − | 0.224520i | \(-0.927918\pi\) |
−0.0875959 | + | 0.996156i | \(0.527918\pi\) | |||||||
\(48\) | −4.04508 | − | 2.93893i | −0.583858 | − | 0.424197i | ||||
\(49\) | −1.23607 | − | 3.80423i | −0.176581 | − | 0.543461i | ||||
\(50\) | −0.535233 | − | 1.64728i | −0.0756934 | − | 0.232960i | ||||
\(51\) | 5.60503 | + | 4.07230i | 0.784862 | + | 0.570235i | ||||
\(52\) | 2.80252 | − | 2.03615i | 0.388639 | − | 0.282363i | ||||
\(53\) | 1.85410 | − | 5.70634i | 0.254680 | − | 0.783826i | −0.739212 | − | 0.673473i | \(-0.764802\pi\) |
0.993892 | − | 0.110353i | \(-0.0351982\pi\) | |||||||
\(54\) | −8.66025 | −1.17851 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | −1.07047 | + | 3.29456i | −0.141787 | + | 0.436375i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.70820 | + | 7.05342i | 1.26390 | + | 0.918277i | 0.998942 | − | 0.0459824i | \(-0.0146418\pi\) |
0.264958 | + | 0.964260i | \(0.414642\pi\) | |||||||
\(60\) | 0.309017 | + | 0.951057i | 0.0398939 | + | 0.122781i | ||||
\(61\) | −2.67617 | − | 8.23639i | −0.342648 | − | 1.05456i | −0.962831 | − | 0.270105i | \(-0.912942\pi\) |
0.620183 | − | 0.784457i | \(-0.287058\pi\) | |||||||
\(62\) | −11.2101 | − | 8.14459i | −1.42368 | − | 1.03436i | ||||
\(63\) | 2.80252 | − | 2.03615i | 0.353084 | − | 0.256531i | ||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | 3.46410 | 0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | −0.610847 | −0.305424 | − | 0.952217i | \(-0.598798\pi\) | ||||
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 2.14093 | − | 6.58911i | 0.259626 | − | 0.799047i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.42705 | − | 1.76336i | −0.290088 | − | 0.210761i | ||||
\(71\) | −3.70820 | − | 11.4127i | −0.440083 | − | 1.35444i | −0.887787 | − | 0.460254i | \(-0.847758\pi\) |
0.447704 | − | 0.894182i | \(-0.352242\pi\) | |||||||
\(72\) | −1.07047 | − | 3.29456i | −0.126156 | − | 0.388267i | ||||
\(73\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(74\) | −11.2101 | + | 8.14459i | −1.30314 | + | 0.946790i | ||||
\(75\) | −0.309017 | + | 0.951057i | −0.0356822 | + | 0.109819i | ||||
\(76\) | 3.46410 | 0.397360 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | 3.21140 | − | 9.88367i | 0.361311 | − | 1.11200i | −0.590949 | − | 0.806709i | \(-0.701246\pi\) |
0.952259 | − | 0.305291i | \(-0.0987536\pi\) | |||||||
\(80\) | −4.04508 | + | 2.93893i | −0.452254 | + | 0.328582i | ||||
\(81\) | −0.809017 | − | 0.587785i | −0.0898908 | − | 0.0653095i | ||||
\(82\) | 6.48936 | + | 19.9722i | 0.716630 | + | 2.20556i | ||||
\(83\) | −1.07047 | − | 3.29456i | −0.117499 | − | 0.361625i | 0.874961 | − | 0.484193i | \(-0.160887\pi\) |
−0.992460 | + | 0.122569i | \(0.960887\pi\) | |||||||
\(84\) | 1.40126 | + | 1.01807i | 0.152890 | + | 0.111081i | ||||
\(85\) | 5.60503 | − | 4.07230i | 0.607951 | − | 0.441702i | ||||
\(86\) | 4.63525 | − | 14.2658i | 0.499832 | − | 1.53833i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.00000 | 0.317999 | 0.159000 | − | 0.987279i | \(-0.449173\pi\) | ||||
0.159000 | + | 0.987279i | \(0.449173\pi\) | |||||||
\(90\) | −1.07047 | + | 3.29456i | −0.112837 | + | 0.347277i | ||||
\(91\) | 4.85410 | − | 3.52671i | 0.508848 | − | 0.369700i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.47214 | + | 7.60845i | 0.256349 | + | 0.788960i | ||||
\(94\) | −4.81710 | − | 14.8255i | −0.496846 | − | 1.52913i | ||||
\(95\) | 2.80252 | + | 2.03615i | 0.287532 | + | 0.208904i | ||||
\(96\) | 4.20378 | − | 3.05422i | 0.429046 | − | 0.311720i | ||||
\(97\) | −3.09017 | + | 9.51057i | −0.313759 | + | 0.965652i | 0.662503 | + | 0.749059i | \(0.269494\pi\) |
−0.976262 | + | 0.216592i | \(0.930506\pi\) | |||||||
\(98\) | 6.92820 | 0.699854 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 0.535233 | − | 1.64728i | 0.0532577 | − | 0.163910i | −0.920890 | − | 0.389823i | \(-0.872536\pi\) |
0.974148 | + | 0.225912i | \(0.0725363\pi\) | |||||||
\(102\) | −9.70820 | + | 7.05342i | −0.961255 | + | 0.698393i | ||||
\(103\) | 3.23607 | + | 2.35114i | 0.318859 | + | 0.231665i | 0.735689 | − | 0.677320i | \(-0.236859\pi\) |
−0.416829 | + | 0.908985i | \(0.636859\pi\) | |||||||
\(104\) | −1.85410 | − | 5.70634i | −0.181810 | − | 0.559553i | ||||
\(105\) | 0.535233 | + | 1.64728i | 0.0522334 | + | 0.160758i | ||||
\(106\) | 8.40755 | + | 6.10844i | 0.816614 | + | 0.593304i | ||||
\(107\) | 1.40126 | − | 1.01807i | 0.135465 | − | 0.0984209i | −0.517989 | − | 0.855387i | \(-0.673319\pi\) |
0.653454 | + | 0.756966i | \(0.273319\pi\) | |||||||
\(108\) | 1.54508 | − | 4.75528i | 0.148676 | − | 0.457577i | ||||
\(109\) | −1.73205 | −0.165900 | −0.0829502 | − | 0.996554i | \(-0.526434\pi\) | ||||
−0.0829502 | + | 0.996554i | \(0.526434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.00000 | 0.759326 | ||||||||
\(112\) | −2.67617 | + | 8.23639i | −0.252874 | + | 0.778266i | ||||
\(113\) | 4.85410 | − | 3.52671i | 0.456636 | − | 0.331765i | −0.335575 | − | 0.942014i | \(-0.608930\pi\) |
0.792210 | + | 0.610249i | \(0.208930\pi\) | |||||||
\(114\) | −4.85410 | − | 3.52671i | −0.454628 | − | 0.330307i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.60503 | − | 4.07230i | −0.518186 | − | 0.376484i | ||||
\(118\) | −16.8151 | + | 12.2169i | −1.54796 | + | 1.12466i | ||||
\(119\) | 3.70820 | − | 11.4127i | 0.339930 | − | 1.04620i | ||||
\(120\) | 1.73205 | 0.158114 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 15.0000 | 1.35804 | ||||||||
\(123\) | 3.74663 | − | 11.5309i | 0.337822 | − | 1.03971i | ||||
\(124\) | 6.47214 | − | 4.70228i | 0.581215 | − | 0.422277i | ||||
\(125\) | 0.809017 | + | 0.587785i | 0.0723607 | + | 0.0525731i | ||||
\(126\) | 1.85410 | + | 5.70634i | 0.165177 | + | 0.508361i | ||||
\(127\) | −0.535233 | − | 1.64728i | −0.0474943 | − | 0.146172i | 0.924497 | − | 0.381189i | \(-0.124485\pi\) |
−0.971991 | + | 0.235017i | \(0.924485\pi\) | |||||||
\(128\) | 9.80881 | + | 7.12652i | 0.866984 | + | 0.629901i | ||||
\(129\) | −7.00629 | + | 5.09037i | −0.616870 | + | 0.448182i | ||||
\(130\) | −1.85410 | + | 5.70634i | −0.162615 | + | 0.500479i | ||||
\(131\) | 3.46410 | 0.302660 | 0.151330 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151330 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | 0.520266 | ||||||||
\(134\) | 2.67617 | − | 8.23639i | 0.231186 | − | 0.711516i | ||||
\(135\) | 4.04508 | − | 2.93893i | 0.348145 | − | 0.252942i | ||||
\(136\) | −9.70820 | − | 7.05342i | −0.832472 | − | 0.604826i | ||||
\(137\) | 5.56231 | + | 17.1190i | 0.475220 | + | 1.46258i | 0.845661 | + | 0.533720i | \(0.179207\pi\) |
−0.370441 | + | 0.928856i | \(0.620793\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2101 | + | 8.14459i | 0.950826 | + | 0.690815i | 0.951002 | − | 0.309185i | \(-0.100056\pi\) |
−0.000176405 | 1.00000i | \(0.500056\pi\) | ||||||||
\(140\) | 1.40126 | − | 1.01807i | 0.118428 | − | 0.0860430i | ||||
\(141\) | −2.78115 | + | 8.55951i | −0.234215 | + | 0.720841i | ||||
\(142\) | 20.7846 | 1.74421 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 10.0000 | 0.833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −3.23607 | − | 2.35114i | −0.266906 | − | 0.193919i | ||||
\(148\) | −2.47214 | − | 7.60845i | −0.203208 | − | 0.625411i | ||||
\(149\) | 5.88756 | + | 18.1201i | 0.482328 | + | 1.48445i | 0.835814 | + | 0.549013i | \(0.184996\pi\) |
−0.353486 | + | 0.935440i | \(0.615004\pi\) | |||||||
\(150\) | −1.40126 | − | 1.01807i | −0.114412 | − | 0.0831254i | ||||
\(151\) | −16.8151 | + | 12.2169i | −1.36839 | + | 0.994196i | −0.370533 | + | 0.928819i | \(0.620825\pi\) |
−0.997861 | + | 0.0653769i | \(0.979175\pi\) | |||||||
\(152\) | 1.85410 | − | 5.70634i | 0.150388 | − | 0.462845i | ||||
\(153\) | −13.8564 | −1.12022 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 1.07047 | − | 3.29456i | 0.0857059 | − | 0.263776i | ||||
\(157\) | −3.23607 | + | 2.35114i | −0.258266 | + | 0.187641i | −0.709382 | − | 0.704824i | \(-0.751026\pi\) |
0.451116 | + | 0.892465i | \(0.351026\pi\) | |||||||
\(158\) | 14.5623 | + | 10.5801i | 1.15851 | + | 0.841710i | ||||
\(159\) | −1.85410 | − | 5.70634i | −0.147040 | − | 0.452542i | ||||
\(160\) | −1.60570 | − | 4.94183i | −0.126942 | − | 0.390686i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.40126 | − | 1.01807i | 0.110093 | − | 0.0799874i | ||||
\(163\) | −5.87132 | + | 18.0701i | −0.459878 | + | 1.41536i | 0.405435 | + | 0.914124i | \(0.367120\pi\) |
−0.865312 | + | 0.501233i | \(0.832880\pi\) | |||||||
\(164\) | −12.1244 | −0.946753 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | 1.60570 | − | 4.94183i | 0.124253 | − | 0.382411i | −0.869511 | − | 0.493913i | \(-0.835566\pi\) |
0.993764 | + | 0.111502i | \(0.0355662\pi\) | |||||||
\(168\) | 2.42705 | − | 1.76336i | 0.187251 | − | 0.136046i | ||||
\(169\) | 0.809017 | + | 0.587785i | 0.0622321 | + | 0.0452143i | ||||
\(170\) | 3.70820 | + | 11.4127i | 0.284406 | + | 0.875312i | ||||
\(171\) | −2.14093 | − | 6.58911i | −0.163721 | − | 0.503882i | ||||
\(172\) | 7.00629 | + | 5.09037i | 0.534225 | + | 0.388137i | ||||
\(173\) | 8.40755 | − | 6.10844i | 0.639214 | − | 0.464416i | −0.220366 | − | 0.975417i | \(-0.570725\pi\) |
0.859580 | + | 0.511001i | \(0.170725\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | 0.130931 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | −1.60570 | + | 4.94183i | −0.120352 | + | 0.370406i | ||||
\(179\) | 14.5623 | − | 10.5801i | 1.08844 | − | 0.790796i | 0.109303 | − | 0.994008i | \(-0.465138\pi\) |
0.979135 | + | 0.203212i | \(0.0651381\pi\) | |||||||
\(180\) | −1.61803 | − | 1.17557i | −0.120601 | − | 0.0876219i | ||||
\(181\) | 3.39919 | + | 10.4616i | 0.252660 | + | 0.777606i | 0.994282 | + | 0.106788i | \(0.0340567\pi\) |
−0.741622 | + | 0.670818i | \(0.765943\pi\) | |||||||
\(182\) | 3.21140 | + | 9.88367i | 0.238045 | + | 0.732626i | ||||
\(183\) | −7.00629 | − | 5.09037i | −0.517920 | − | 0.376291i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.47214 | − | 7.60845i | 0.181755 | − | 0.559385i | ||||
\(186\) | −13.8564 | −1.01600 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 9.00000 | 0.656392 | ||||||||
\(189\) | 2.67617 | − | 8.23639i | 0.194662 | − | 0.599109i | ||||
\(190\) | −4.85410 | + | 3.52671i | −0.352154 | + | 0.255855i | ||||
\(191\) | 4.85410 | + | 3.52671i | 0.351230 | + | 0.255184i | 0.749385 | − | 0.662134i | \(-0.230349\pi\) |
−0.398155 | + | 0.917318i | \(0.630349\pi\) | |||||||
\(192\) | −0.309017 | − | 0.951057i | −0.0223014 | − | 0.0686366i | ||||
\(193\) | 1.07047 | + | 3.29456i | 0.0770538 | + | 0.237147i | 0.982163 | − | 0.188032i | \(-0.0602109\pi\) |
−0.905109 | + | 0.425180i | \(0.860211\pi\) | |||||||
\(194\) | −14.0126 | − | 10.1807i | −1.00605 | − | 0.730934i | ||||
\(195\) | 2.80252 | − | 2.03615i | 0.200692 | − | 0.145812i | ||||
\(196\) | −1.23607 | + | 3.80423i | −0.0882906 | + | 0.271730i | ||||
\(197\) | 10.3923 | 0.740421 | 0.370211 | − | 0.928948i | \(-0.379286\pi\) | ||||
0.370211 | + | 0.928948i | \(0.379286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0.535233 | − | 1.64728i | 0.0378467 | − | 0.116480i | ||||
\(201\) | −4.04508 | + | 2.93893i | −0.285318 | + | 0.207296i | ||||
\(202\) | 2.42705 | + | 1.76336i | 0.170767 | + | 0.124069i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.14093 | − | 6.58911i | −0.149895 | − | 0.461330i | ||||
\(205\) | −9.80881 | − | 7.12652i | −0.685077 | − | 0.497738i | ||||
\(206\) | −5.60503 | + | 4.07230i | −0.390521 | + | 0.283730i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 17.3205 | 1.20096 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.00000 | −0.207020 | ||||||||
\(211\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(212\) | −4.85410 | + | 3.52671i | −0.333381 | + | 0.242216i | ||||
\(213\) | −9.70820 | − | 7.05342i | −0.665195 | − | 0.483293i | ||||
\(214\) | 0.927051 | + | 2.85317i | 0.0633719 | + | 0.195039i | ||||
\(215\) | 2.67617 | + | 8.23639i | 0.182513 | + | 0.561717i | ||||
\(216\) | −7.00629 | − | 5.09037i | −0.476718 | − | 0.346356i | ||||
\(217\) | 11.2101 | − | 8.14459i | 0.760989 | − | 0.552891i | ||||
\(218\) | 0.927051 | − | 2.85317i | 0.0627878 | − | 0.193241i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.0000 | −1.61441 | ||||||||
\(222\) | −4.28187 | + | 13.1782i | −0.287380 | + | 0.884465i | ||||
\(223\) | 15.3713 | − | 11.1679i | 1.02934 | − | 0.747859i | 0.0611635 | − | 0.998128i | \(-0.480519\pi\) |
0.968176 | + | 0.250269i | \(0.0805189\pi\) | |||||||
\(224\) | −7.28115 | − | 5.29007i | −0.486492 | − | 0.353457i | ||||
\(225\) | −0.618034 | − | 1.90211i | −0.0412023 | − | 0.126808i | ||||
\(226\) | 3.21140 | + | 9.88367i | 0.213619 | + | 0.657452i | ||||
\(227\) | 15.4138 | + | 11.1988i | 1.02305 | + | 0.743291i | 0.966906 | − | 0.255131i | \(-0.0821187\pi\) |
0.0561463 | + | 0.998423i | \(0.482119\pi\) | |||||||
\(228\) | 2.80252 | − | 2.03615i | 0.185601 | − | 0.134847i | ||||
\(229\) | 2.16312 | − | 6.65740i | 0.142943 | − | 0.439933i | −0.853798 | − | 0.520605i | \(-0.825707\pi\) |
0.996741 | + | 0.0806717i | \(0.0257065\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.07047 | − | 3.29456i | 0.0701286 | − | 0.215834i | −0.909850 | − | 0.414938i | \(-0.863803\pi\) |
0.979978 | + | 0.199104i | \(0.0638033\pi\) | |||||||
\(234\) | 9.70820 | − | 7.05342i | 0.634645 | − | 0.461097i | ||||
\(235\) | 7.28115 | + | 5.29007i | 0.474970 | + | 0.345086i | ||||
\(236\) | −3.70820 | − | 11.4127i | −0.241384 | − | 0.742902i | ||||
\(237\) | −3.21140 | − | 9.88367i | −0.208603 | − | 0.642013i | ||||
\(238\) | 16.8151 | + | 12.2169i | 1.08996 | + | 0.791903i | ||||
\(239\) | 2.80252 | − | 2.03615i | 0.181280 | − | 0.131707i | −0.493445 | − | 0.869777i | \(-0.664262\pi\) |
0.674724 | + | 0.738070i | \(0.264262\pi\) | |||||||
\(240\) | −1.54508 | + | 4.75528i | −0.0997348 | + | 0.306952i | ||||
\(241\) | 19.0526 | 1.22728 | 0.613642 | − | 0.789585i | \(-0.289704\pi\) | ||||
0.613642 | + | 0.789585i | \(0.289704\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0000 | −1.02640 | ||||||||
\(244\) | −2.67617 | + | 8.23639i | −0.171324 | + | 0.527281i | ||||
\(245\) | −3.23607 | + | 2.35114i | −0.206745 | + | 0.150209i | ||||
\(246\) | 16.9894 | + | 12.3435i | 1.08320 | + | 0.786992i | ||||
\(247\) | −3.70820 | − | 11.4127i | −0.235947 | − | 0.726171i | ||||
\(248\) | −4.28187 | − | 13.1782i | −0.271899 | − | 0.836818i | ||||
\(249\) | −2.80252 | − | 2.03615i | −0.177602 | − | 0.129036i | ||||
\(250\) | −1.40126 | + | 1.01807i | −0.0886234 | + | 0.0643886i | ||||
\(251\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(252\) | −3.46410 | −0.218218 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 3.00000 | 0.188237 | ||||||||
\(255\) | 2.14093 | − | 6.58911i | 0.134070 | − | 0.412626i | ||||
\(256\) | −15.3713 | + | 11.1679i | −0.960708 | + | 0.697995i | ||||
\(257\) | −9.70820 | − | 7.05342i | −0.605581 | − | 0.439980i | 0.242274 | − | 0.970208i | \(-0.422107\pi\) |
−0.847856 | + | 0.530227i | \(0.822107\pi\) | |||||||
\(258\) | −4.63525 | − | 14.2658i | −0.288578 | − | 0.888153i | ||||
\(259\) | −4.28187 | − | 13.1782i | −0.266062 | − | 0.818855i | ||||
\(260\) | −2.80252 | − | 2.03615i | −0.173805 | − | 0.126277i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.85410 | + | 5.70634i | −0.114547 | + | 0.352539i | ||||
\(263\) | −24.2487 | −1.49524 | −0.747620 | − | 0.664127i | \(-0.768803\pi\) | ||||
−0.747620 | + | 0.664127i | \(0.768803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | −3.21140 | + | 9.88367i | −0.196903 | + | 0.606007i | ||||
\(267\) | 2.42705 | − | 1.76336i | 0.148533 | − | 0.107916i | ||||
\(268\) | 4.04508 | + | 2.93893i | 0.247093 | + | 0.179523i | ||||
\(269\) | −4.63525 | − | 14.2658i | −0.282616 | − | 0.869804i | −0.987103 | − | 0.160087i | \(-0.948823\pi\) |
0.704486 | − | 0.709717i | \(-0.251177\pi\) | |||||||
\(270\) | 2.67617 | + | 8.23639i | 0.162866 | + | 0.501251i | ||||
\(271\) | −11.2101 | − | 8.14459i | −0.680963 | − | 0.494749i | 0.192714 | − | 0.981255i | \(-0.438271\pi\) |
−0.873677 | + | 0.486506i | \(0.838271\pi\) | |||||||
\(272\) | 28.0252 | − | 20.3615i | 1.69928 | − | 1.23460i | ||||
\(273\) | 1.85410 | − | 5.70634i | 0.112215 | − | 0.345363i | ||||
\(274\) | −31.1769 | −1.88347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.21140 | + | 9.88367i | −0.192954 | + | 0.593852i | 0.807040 | + | 0.590497i | \(0.201068\pi\) |
−0.999994 | + | 0.00335552i | \(0.998932\pi\) | |||||||
\(278\) | −19.4164 | + | 14.1068i | −1.16452 | + | 0.846072i | ||||
\(279\) | −12.9443 | − | 9.40456i | −0.774953 | − | 0.563037i | ||||
\(280\) | −0.927051 | − | 2.85317i | −0.0554019 | − | 0.170509i | ||||
\(281\) | 2.14093 | + | 6.58911i | 0.127717 | + | 0.393074i | 0.994386 | − | 0.105810i | \(-0.0337435\pi\) |
−0.866669 | + | 0.498884i | \(0.833744\pi\) | |||||||
\(282\) | −12.6113 | − | 9.16267i | −0.750994 | − | 0.545629i | ||||
\(283\) | −4.20378 | + | 3.05422i | −0.249889 | + | 0.181555i | −0.705677 | − | 0.708533i | \(-0.749357\pi\) |
0.455789 | + | 0.890088i | \(0.349357\pi\) | |||||||
\(284\) | −3.70820 | + | 11.4127i | −0.220041 | + | 0.677218i | ||||
\(285\) | 3.46410 | 0.205196 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −21.0000 | −1.23959 | ||||||||
\(288\) | −3.21140 | + | 9.88367i | −0.189233 | + | 0.582401i | ||||
\(289\) | −25.0795 | + | 18.2213i | −1.47527 | + | 1.07184i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.09017 | + | 9.51057i | 0.181149 | + | 0.557519i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.60503 | − | 4.07230i | −0.327450 | − | 0.237906i | 0.411898 | − | 0.911230i | \(-0.364866\pi\) |
−0.739348 | + | 0.673324i | \(0.764866\pi\) | |||||||
\(294\) | 5.60503 | − | 4.07230i | 0.326892 | − | 0.237501i | ||||
\(295\) | 3.70820 | − | 11.4127i | 0.215900 | − | 0.664472i | ||||
\(296\) | −13.8564 | −0.805387 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −33.0000 | −1.91164 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.809017 | − | 0.587785i | 0.0467086 | − | 0.0339358i | ||||
\(301\) | 12.1353 | + | 8.81678i | 0.699464 | + | 0.508191i | ||||
\(302\) | −11.1246 | − | 34.2380i | −0.640149 | − | 1.97018i | ||||
\(303\) | −0.535233 | − | 1.64728i | −0.0307483 | − | 0.0946337i | ||||
\(304\) | 14.0126 | + | 10.1807i | 0.803677 | + | 0.583905i | ||||
\(305\) | −7.00629 | + | 5.09037i | −0.401179 | + | 0.291474i | ||||
\(306\) | 7.41641 | − | 22.8254i | 0.423968 | − | 1.30484i | ||||
\(307\) | 10.3923 | 0.593120 | 0.296560 | − | 0.955014i | \(-0.404160\pi\) | ||||
0.296560 | + | 0.955014i | \(0.404160\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | −4.28187 | + | 13.1782i | −0.243194 | + | 0.748473i | ||||
\(311\) | 4.85410 | − | 3.52671i | 0.275251 | − | 0.199981i | −0.441592 | − | 0.897216i | \(-0.645586\pi\) |
0.716843 | + | 0.697234i | \(0.245586\pi\) | |||||||
\(312\) | −4.85410 | − | 3.52671i | −0.274809 | − | 0.199661i | ||||
\(313\) | 3.09017 | + | 9.51057i | 0.174667 | + | 0.537569i | 0.999618 | − | 0.0276348i | \(-0.00879755\pi\) |
−0.824951 | + | 0.565204i | \(0.808798\pi\) | |||||||
\(314\) | −2.14093 | − | 6.58911i | −0.120820 | − | 0.371845i | ||||
\(315\) | −2.80252 | − | 2.03615i | −0.157904 | − | 0.114724i | ||||
\(316\) | −8.40755 | + | 6.10844i | −0.472962 | + | 0.343627i | ||||
\(317\) | −1.85410 | + | 5.70634i | −0.104137 | + | 0.320500i | −0.989527 | − | 0.144349i | \(-0.953891\pi\) |
0.885390 | + | 0.464849i | \(0.153891\pi\) | |||||||
\(318\) | 10.3923 | 0.582772 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0.535233 | − | 1.64728i | 0.0298738 | − | 0.0919421i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.4164 | − | 14.1068i | −1.08036 | − | 0.784926i | ||||
\(324\) | 0.309017 | + | 0.951057i | 0.0171676 | + | 0.0528365i | ||||
\(325\) | −1.07047 | − | 3.29456i | −0.0593788 | − | 0.182749i | ||||
\(326\) | −26.6239 | − | 19.3434i | −1.47456 | − | 1.07133i | ||||
\(327\) | −1.40126 | + | 1.01807i | −0.0774898 | + | 0.0562996i | ||||
\(328\) | −6.48936 | + | 19.9722i | −0.358315 | + | 1.10278i | ||||
\(329\) | 15.5885 | 0.859419 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.0000 | −1.86881 | −0.934405 | − | 0.356214i | \(-0.884068\pi\) | ||||
−0.934405 | + | 0.356214i | \(0.884068\pi\) | |||||||
\(332\) | −1.07047 | + | 3.29456i | −0.0587495 | + | 0.180812i | ||||
\(333\) | −12.9443 | + | 9.40456i | −0.709342 | + | 0.515367i | ||||
\(334\) | 7.28115 | + | 5.29007i | 0.398407 | + | 0.289460i | ||||
\(335\) | 1.54508 | + | 4.75528i | 0.0844170 | + | 0.259809i | ||||
\(336\) | 2.67617 | + | 8.23639i | 0.145997 | + | 0.449332i | ||||
\(337\) | 8.40755 | + | 6.10844i | 0.457988 | + | 0.332748i | 0.792742 | − | 0.609558i | \(-0.208653\pi\) |
−0.334753 | + | 0.942306i | \(0.608653\pi\) | |||||||
\(338\) | −1.40126 | + | 1.01807i | −0.0762184 | + | 0.0553759i | ||||
\(339\) | 1.85410 | − | 5.70634i | 0.100701 | − | 0.309926i | ||||
\(340\) | −6.92820 | −0.375735 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 12.0000 | 0.648886 | ||||||||
\(343\) | −5.88756 | + | 18.1201i | −0.317899 | + | 0.978391i | ||||
\(344\) | 12.1353 | − | 8.81678i | 0.654289 | − | 0.475369i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.56231 | + | 17.1190i | 0.299031 | + | 0.920324i | ||||
\(347\) | 3.74663 | + | 11.5309i | 0.201130 | + | 0.619014i | 0.999850 | + | 0.0173113i | \(0.00551065\pi\) |
−0.798720 | + | 0.601702i | \(0.794489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.0252 | − | 20.3615i | 1.50015 | − | 1.08992i | 0.529833 | − | 0.848102i | \(-0.322255\pi\) |
0.970320 | − | 0.241823i | \(-0.0777452\pi\) | |||||||
\(350\) | −0.927051 | + | 2.85317i | −0.0495530 | + | 0.152508i | ||||
\(351\) | −17.3205 | −0.924500 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.0000 | 1.27739 | 0.638696 | − | 0.769460i | \(-0.279474\pi\) | ||||
0.638696 | + | 0.769460i | \(0.279474\pi\) | |||||||
\(354\) | −6.42280 | + | 19.7673i | −0.341368 | + | 1.05062i | ||||
\(355\) | −9.70820 | + | 7.05342i | −0.515258 | + | 0.374357i | ||||
\(356\) | −2.42705 | − | 1.76336i | −0.128633 | − | 0.0934577i | ||||
\(357\) | −3.70820 | − | 11.4127i | −0.196259 | − | 0.604023i | ||||
\(358\) | 9.63420 | + | 29.6510i | 0.509183 | + | 1.56710i | ||||
\(359\) | −2.80252 | − | 2.03615i | −0.147911 | − | 0.107464i | 0.511369 | − | 0.859361i | \(-0.329139\pi\) |
−0.659280 | + | 0.751898i | \(0.729139\pi\) | |||||||
\(360\) | −2.80252 | + | 2.03615i | −0.147706 | + | 0.107314i | ||||
\(361\) | −2.16312 | + | 6.65740i | −0.113848 | + | 0.350389i | ||||
\(362\) | −19.0526 | −1.00138 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.00000 | −0.314485 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 12.1353 | − | 8.81678i | 0.634320 | − | 0.460860i | ||||
\(367\) | −13.7533 | − | 9.99235i | −0.717916 | − | 0.521596i | 0.167802 | − | 0.985821i | \(-0.446333\pi\) |
−0.885718 | + | 0.464224i | \(0.846333\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.49326 | + | 23.0619i | 0.390084 | + | 1.20055i | ||||
\(370\) | 11.2101 | + | 8.14459i | 0.582784 | + | 0.423417i | ||||
\(371\) | −8.40755 | + | 6.10844i | −0.436498 | + | 0.317135i | ||||
\(372\) | 2.47214 | − | 7.60845i | 0.128174 | − | 0.394480i | ||||
\(373\) | 13.8564 | 0.717458 | 0.358729 | − | 0.933442i | \(-0.383210\pi\) | ||||
0.358729 | + | 0.933442i | \(0.383210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 4.81710 | − | 14.8255i | 0.248423 | − | 0.764567i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 12.1353 | + | 8.81678i | 0.624170 | + | 0.453486i | ||||
\(379\) | −10.5066 | − | 32.3359i | −0.539687 | − | 1.66098i | −0.733299 | − | 0.679907i | \(-0.762020\pi\) |
0.193612 | − | 0.981078i | \(-0.437980\pi\) | |||||||
\(380\) | −1.07047 | − | 3.29456i | −0.0549138 | − | 0.169007i | ||||
\(381\) | −1.40126 | − | 1.01807i | −0.0717886 | − | 0.0521575i | ||||
\(382\) | −8.40755 | + | 6.10844i | −0.430168 | + | 0.312535i | ||||
\(383\) | 7.41641 | − | 22.8254i | 0.378961 | − | 1.16632i | −0.561807 | − | 0.827269i | \(-0.689894\pi\) |
0.940767 | − | 0.339053i | \(-0.110106\pi\) | |||||||
\(384\) | 12.1244 | 0.618718 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.00000 | −0.305392 | ||||||||
\(387\) | 5.35233 | − | 16.4728i | 0.272074 | − | 0.837359i | ||||
\(388\) | 8.09017 | − | 5.87785i | 0.410716 | − | 0.298403i | ||||
\(389\) | −2.42705 | − | 1.76336i | −0.123056 | − | 0.0894057i | 0.524555 | − | 0.851377i | \(-0.324232\pi\) |
−0.647611 | + | 0.761971i | \(0.724232\pi\) | |||||||
\(390\) | 1.85410 | + | 5.70634i | 0.0938861 | + | 0.288952i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 5.60503 | + | 4.07230i | 0.283097 | + | 0.205682i | ||||
\(393\) | 2.80252 | − | 2.03615i | 0.141368 | − | 0.102710i | ||||
\(394\) | −5.56231 | + | 17.1190i | −0.280225 | + | 0.862444i | ||||
\(395\) | −10.3923 | −0.522894 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0000 | 1.00377 | 0.501886 | − | 0.864934i | \(-0.332640\pi\) | ||||
0.501886 | + | 0.864934i | \(0.332640\pi\) | |||||||
\(398\) | 7.49326 | − | 23.0619i | 0.375603 | − | 1.15599i | ||||
\(399\) | 4.85410 | − | 3.52671i | 0.243009 | − | 0.176556i | ||||
\(400\) | 4.04508 | + | 2.93893i | 0.202254 | + | 0.146946i | ||||
\(401\) | 8.34346 | + | 25.6785i | 0.416652 | + | 1.28232i | 0.910765 | + | 0.412926i | \(0.135493\pi\) |
−0.494112 | + | 0.869398i | \(0.664507\pi\) | |||||||
\(402\) | −2.67617 | − | 8.23639i | −0.133475 | − | 0.410794i | ||||
\(403\) | −22.4201 | − | 16.2892i | −1.11683 | − | 0.811422i | ||||
\(404\) | −1.40126 | + | 1.01807i | −0.0697152 | + | 0.0506511i | ||||
\(405\) | −0.309017 | + | 0.951057i | −0.0153552 | + | 0.0472584i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −12.0000 | −0.594089 | ||||||||
\(409\) | −1.60570 | + | 4.94183i | −0.0793967 | + | 0.244358i | −0.982874 | − | 0.184277i | \(-0.941006\pi\) |
0.903478 | + | 0.428635i | \(0.141006\pi\) | |||||||
\(410\) | 16.9894 | − | 12.3435i | 0.839045 | − | 0.609602i | ||||
\(411\) | 14.5623 | + | 10.5801i | 0.718306 | + | 0.521880i | ||||
\(412\) | −1.23607 | − | 3.80423i | −0.0608967 | − | 0.187421i | ||||
\(413\) | −6.42280 | − | 19.7673i | −0.316045 | − | 0.972687i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.80252 | + | 2.03615i | −0.137570 | + | 0.0999506i | ||||
\(416\) | −5.56231 | + | 17.1190i | −0.272714 | + | 0.839329i | ||||
\(417\) | 13.8564 | 0.678551 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | 0.535233 | − | 1.64728i | 0.0261167 | − | 0.0803789i | ||||
\(421\) | 13.7533 | − | 9.99235i | 0.670294 | − | 0.486997i | −0.199829 | − | 0.979831i | \(-0.564039\pi\) |
0.870124 | + | 0.492833i | \(0.164039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.56231 | − | 17.1190i | −0.270449 | − | 0.832355i | ||||
\(424\) | 3.21140 | + | 9.88367i | 0.155959 | + | 0.479993i | ||||
\(425\) | −5.60503 | − | 4.07230i | −0.271884 | − | 0.197535i | ||||
\(426\) | 16.8151 | − | 12.2169i | 0.814694 | − | 0.591910i | ||||
\(427\) | −4.63525 | + | 14.2658i | −0.224316 | + | 0.690373i | ||||
\(428\) | −1.73205 | −0.0837218 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.0000 | −0.723364 | ||||||||
\(431\) | −11.7751 | + | 36.2401i | −0.567188 | + | 1.74563i | 0.0941714 | + | 0.995556i | \(0.469980\pi\) |
−0.661359 | + | 0.750069i | \(0.730020\pi\) | |||||||
\(432\) | 20.2254 | − | 14.6946i | 0.973096 | − | 0.706996i | ||||
\(433\) | −25.8885 | − | 18.8091i | −1.24412 | − | 0.903909i | −0.246258 | − | 0.969204i | \(-0.579201\pi\) |
−0.997866 | + | 0.0652953i | \(0.979201\pi\) | |||||||
\(434\) | 7.41641 | + | 22.8254i | 0.355999 | + | 1.09565i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.40126 | + | 1.01807i | 0.0671081 | + | 0.0487569i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.7128 | 1.32266 | 0.661330 | − | 0.750095i | \(-0.269992\pi\) | ||||
0.661330 | + | 0.750095i | \(0.269992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.00000 | 0.380952 | ||||||||
\(442\) | 12.8456 | − | 39.5347i | 0.611003 | − | 1.88047i | ||||
\(443\) | 12.1353 | − | 8.81678i | 0.576563 | − | 0.418898i | −0.260920 | − | 0.965360i | \(-0.584026\pi\) |
0.837484 | + | 0.546463i | \(0.184026\pi\) | |||||||
\(444\) | −6.47214 | − | 4.70228i | −0.307154 | − | 0.223160i | ||||
\(445\) | −0.927051 | − | 2.85317i | −0.0439464 | − | 0.135253i | ||||
\(446\) | 10.1694 | + | 31.2983i | 0.481536 | + | 1.48202i | ||||
\(447\) | 15.4138 | + | 11.1988i | 0.729050 | + | 0.529686i | ||||
\(448\) | −1.40126 | + | 1.01807i | −0.0662032 | + | 0.0480995i | ||||
\(449\) | −4.63525 | + | 14.2658i | −0.218751 | + | 0.673247i | 0.780115 | + | 0.625636i | \(0.215161\pi\) |
−0.998866 | + | 0.0476105i | \(0.984839\pi\) | |||||||
\(450\) | 3.46410 | 0.163299 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −6.00000 | −0.282216 | ||||||||
\(453\) | −6.42280 | + | 19.7673i | −0.301769 | + | 0.928751i | ||||
\(454\) | −26.6976 | + | 19.3969i | −1.25298 | + | 0.910342i | ||||
\(455\) | −4.85410 | − | 3.52671i | −0.227564 | − | 0.165335i | ||||
\(456\) | −1.85410 | − | 5.70634i | −0.0868263 | − | 0.267224i | ||||
\(457\) | −6.42280 | − | 19.7673i | −0.300446 | − | 0.924677i | −0.981338 | − | 0.192293i | \(-0.938408\pi\) |
0.680892 | − | 0.732384i | \(-0.261592\pi\) | |||||||
\(458\) | 9.80881 | + | 7.12652i | 0.458336 | + | 0.333000i | ||||
\(459\) | −28.0252 | + | 20.3615i | −1.30810 | + | 0.950392i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.1244 | 0.564688 | 0.282344 | − | 0.959313i | \(-0.408888\pi\) | ||||
0.282344 | + | 0.959313i | \(0.408888\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 41.0000 | 1.90543 | 0.952716 | − | 0.303863i | \(-0.0982765\pi\) | ||||
0.952716 | + | 0.303863i | \(0.0982765\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.47214 | − | 4.70228i | 0.300138 | − | 0.218063i | ||||
\(466\) | 4.85410 | + | 3.52671i | 0.224862 | + | 0.163372i | ||||
\(467\) | 0.927051 | + | 2.85317i | 0.0428988 | + | 0.132029i | 0.970212 | − | 0.242257i | \(-0.0778878\pi\) |
−0.927313 | + | 0.374286i | \(0.877888\pi\) | |||||||
\(468\) | 2.14093 | + | 6.58911i | 0.0989646 | + | 0.304582i | ||||
\(469\) | 7.00629 | + | 5.09037i | 0.323521 | + | 0.235051i | ||||
\(470\) | −12.6113 | + | 9.16267i | −0.581717 | + | 0.422642i | ||||
\(471\) | −1.23607 | + | 3.80423i | −0.0569550 | + | 0.175289i | ||||
\(472\) | −20.7846 | −0.956689 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 18.0000 | 0.826767 | ||||||||
\(475\) | 1.07047 | − | 3.29456i | 0.0491164 | − | 0.151165i | ||||
\(476\) | −9.70820 | + | 7.05342i | −0.444975 | + | 0.323293i | ||||
\(477\) | 9.70820 | + | 7.05342i | 0.444508 | + | 0.322954i | ||||
\(478\) | 1.85410 | + | 5.70634i | 0.0848047 | + | 0.261002i | ||||
\(479\) | −3.21140 | − | 9.88367i | −0.146733 | − | 0.451596i | 0.850497 | − | 0.525980i | \(-0.176301\pi\) |
−0.997230 | + | 0.0743832i | \(0.976301\pi\) | |||||||
\(480\) | −4.20378 | − | 3.05422i | −0.191875 | − | 0.139406i | ||||
\(481\) | −22.4201 | + | 16.2892i | −1.02227 | + | 0.742723i | ||||
\(482\) | −10.1976 | + | 31.3849i | −0.464486 | + | 1.42954i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 10.0000 | 0.454077 | ||||||||
\(486\) | 8.56373 | − | 26.3565i | 0.388459 | − | 1.19555i | ||||
\(487\) | 16.1803 | − | 11.7557i | 0.733201 | − | 0.532702i | −0.157373 | − | 0.987539i | \(-0.550303\pi\) |
0.890575 | + | 0.454837i | \(0.150303\pi\) | |||||||
\(488\) | 12.1353 | + | 8.81678i | 0.549337 | + | 0.399117i | ||||
\(489\) | 5.87132 | + | 18.0701i | 0.265510 | + | 0.817157i | ||||
\(490\) | −2.14093 | − | 6.58911i | −0.0967175 | − | 0.297666i | ||||
\(491\) | 19.6176 | + | 14.2530i | 0.885331 | + | 0.643230i | 0.934656 | − | 0.355552i | \(-0.115707\pi\) |
−0.0493256 | + | 0.998783i | \(0.515707\pi\) | |||||||
\(492\) | −9.80881 | + | 7.12652i | −0.442215 | + | 0.321288i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 20.7846 | 0.935144 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 40.0000 | 1.79605 | ||||||||
\(497\) | −6.42280 | + | 19.7673i | −0.288102 | + | 0.886686i | ||||
\(498\) | 4.85410 | − | 3.52671i | 0.217518 | − | 0.158036i | ||||
\(499\) | 30.7426 | + | 22.3358i | 1.37623 | + | 0.999890i | 0.997221 | + | 0.0744963i | \(0.0237349\pi\) |
0.379009 | + | 0.925393i | \(0.376265\pi\) | |||||||
\(500\) | −0.309017 | − | 0.951057i | −0.0138197 | − | 0.0425325i | ||||
\(501\) | −1.60570 | − | 4.94183i | −0.0717374 | − | 0.220785i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.00629 | − | 5.09037i | 0.312395 | − | 0.226968i | −0.420528 | − | 0.907279i | \(-0.638155\pi\) |
0.732924 | + | 0.680311i | \(0.238155\pi\) | |||||||
\(504\) | −1.85410 | + | 5.70634i | −0.0825883 | + | 0.254181i | ||||
\(505\) | −1.73205 | −0.0770752 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −0.535233 | + | 1.64728i | −0.0237471 | + | 0.0730862i | ||||
\(509\) | −12.1353 | + | 8.81678i | −0.537886 | + | 0.390797i | −0.823299 | − | 0.567608i | \(-0.807869\pi\) |
0.285413 | + | 0.958404i | \(0.407869\pi\) | |||||||
\(510\) | 9.70820 | + | 7.05342i | 0.429886 | + | 0.312331i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −2.67617 | − | 8.23639i | −0.118271 | − | 0.364000i | ||||
\(513\) | −14.0126 | − | 10.1807i | −0.618671 | − | 0.449491i | ||||
\(514\) | 16.8151 | − | 12.2169i | 0.741682 | − | 0.538864i | ||||
\(515\) | 1.23607 | − | 3.80423i | 0.0544677 | − | 0.167634i | ||||
\(516\) | 8.66025 | 0.381246 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 24.0000 | 1.05450 | ||||||||
\(519\) | 3.21140 | − | 9.88367i | 0.140965 | − | 0.433845i | ||||
\(520\) | −4.85410 | + | 3.52671i | −0.212866 | + | 0.154657i | ||||
\(521\) | −12.1353 | − | 8.81678i | −0.531655 | − | 0.386270i | 0.289321 | − | 0.957232i | \(-0.406570\pi\) |
−0.820977 | + | 0.570962i | \(0.806570\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.35233 | + | 16.4728i | 0.234041 | + | 0.720304i | 0.997247 | + | 0.0741493i | \(0.0236241\pi\) |
−0.763206 | + | 0.646155i | \(0.776376\pi\) | |||||||
\(524\) | −2.80252 | − | 2.03615i | −0.122429 | − | 0.0889495i | ||||
\(525\) | 1.40126 | − | 1.01807i | 0.0611559 | − | 0.0444324i | ||||
\(526\) | 12.9787 | − | 39.9444i | 0.565899 | − | 1.74166i | ||||
\(527\) | −55.4256 | −2.41438 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 3.21140 | − | 9.88367i | 0.139494 | − | 0.429319i | ||||
\(531\) | −19.4164 | + | 14.1068i | −0.842600 | + | 0.612185i | ||||
\(532\) | −4.85410 | − | 3.52671i | −0.210452 | − | 0.152902i | ||||
\(533\) | 12.9787 | + | 39.9444i | 0.562170 | + | 1.73018i | ||||
\(534\) | 1.60570 | + | 4.94183i | 0.0694854 | + | 0.213854i | ||||
\(535\) | −1.40126 | − | 1.01807i | −0.0605817 | − | 0.0440152i | ||||
\(536\) | 7.00629 | − | 5.09037i | 0.302626 | − | 0.219870i | ||||
\(537\) | 5.56231 | − | 17.1190i | 0.240031 | − | 0.738740i | ||||
\(538\) | 25.9808 | 1.12011 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.00000 | −0.215166 | ||||||||
\(541\) | 1.60570 | − | 4.94183i | 0.0690344 | − | 0.212466i | −0.910588 | − | 0.413316i | \(-0.864370\pi\) |
0.979622 | + | 0.200850i | \(0.0643704\pi\) | |||||||
\(542\) | 19.4164 | − | 14.1068i | 0.834006 | − | 0.605941i | ||||
\(543\) | 8.89919 | + | 6.46564i | 0.381901 | + | 0.277467i | ||||
\(544\) | 11.1246 | + | 34.2380i | 0.476964 | + | 1.46794i | ||||
\(545\) | 0.535233 | + | 1.64728i | 0.0229269 | + | 0.0705616i | ||||
\(546\) | 8.40755 | + | 6.10844i | 0.359810 | + | 0.261417i | ||||
\(547\) | −36.4327 | + | 26.4699i | −1.55775 | + | 1.13177i | −0.619927 | + | 0.784659i | \(0.712838\pi\) |
−0.937823 | + | 0.347113i | \(0.887162\pi\) | |||||||
\(548\) | 5.56231 | − | 17.1190i | 0.237610 | − | 0.731288i | ||||
\(549\) | 17.3205 | 0.739221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.5623 | + | 10.5801i | −0.619252 | + | 0.449913i | ||||
\(554\) | −14.5623 | − | 10.5801i | −0.618693 | − | 0.449507i | ||||
\(555\) | −2.47214 | − | 7.60845i | −0.104936 | − | 0.322961i | ||||
\(556\) | −4.28187 | − | 13.1782i | −0.181592 | − | 0.558881i | ||||
\(557\) | −5.60503 | − | 4.07230i | −0.237493 | − | 0.172549i | 0.462673 | − | 0.886529i | \(-0.346891\pi\) |
−0.700166 | + | 0.713980i | \(0.746891\pi\) | |||||||
\(558\) | 22.4201 | − | 16.2892i | 0.949120 | − | 0.689576i | ||||
\(559\) | 9.27051 | − | 28.5317i | 0.392101 | − | 1.20676i | ||||
\(560\) | 8.66025 | 0.365963 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0000 | −0.506189 | ||||||||
\(563\) | 4.81710 | − | 14.8255i | 0.203016 | − | 0.624820i | −0.796773 | − | 0.604279i | \(-0.793461\pi\) |
0.999789 | − | 0.0205411i | \(-0.00653891\pi\) | |||||||
\(564\) | 7.28115 | − | 5.29007i | 0.306592 | − | 0.222752i | ||||
\(565\) | −4.85410 | − | 3.52671i | −0.204214 | − | 0.148370i | ||||
\(566\) | −2.78115 | − | 8.55951i | −0.116901 | − | 0.359783i | ||||
\(567\) | 0.535233 | + | 1.64728i | 0.0224777 | + | 0.0691792i | ||||
\(568\) | 16.8151 | + | 12.2169i | 0.705546 | + | 0.512609i | ||||
\(569\) | −1.40126 | + | 1.01807i | −0.0587438 | + | 0.0426799i | −0.616770 | − | 0.787144i | \(-0.711559\pi\) |
0.558026 | + | 0.829824i | \(0.311559\pi\) | |||||||
\(570\) | −1.85410 | + | 5.70634i | −0.0776598 | + | 0.239012i | ||||
\(571\) | 3.46410 | 0.144968 | 0.0724841 | − | 0.997370i | \(-0.476907\pi\) | ||||
0.0724841 | + | 0.997370i | \(0.476907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 11.2399 | − | 34.5928i | 0.469144 | − | 1.44388i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.61803 | + | 1.17557i | 0.0674181 | + | 0.0489821i | ||||
\(577\) | −6.18034 | − | 19.0211i | −0.257291 | − | 0.791860i | −0.993370 | − | 0.114964i | \(-0.963325\pi\) |
0.736079 | − | 0.676896i | \(-0.236675\pi\) | |||||||
\(578\) | −16.5922 | − | 51.0656i | −0.690146 | − | 2.12405i | ||||
\(579\) | 2.80252 | + | 2.03615i | 0.116469 | + | 0.0846194i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.85410 | + | 5.70634i | −0.0769211 | + | 0.236739i | ||||
\(582\) | −17.3205 | −0.717958 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.14093 | + | 6.58911i | −0.0885167 | + | 0.272426i | ||||
\(586\) | 9.70820 | − | 7.05342i | 0.401042 | − | 0.291374i | ||||
\(587\) | −16.9894 | − | 12.3435i | −0.701226 | − | 0.509470i | 0.179105 | − | 0.983830i | \(-0.442680\pi\) |
−0.880331 | + | 0.474360i | \(0.842680\pi\) | |||||||
\(588\) | 1.23607 | + | 3.80423i | 0.0509746 | + | 0.156884i | ||||
\(589\) | −8.56373 | − | 26.3565i | −0.352862 | − | 1.08600i | ||||
\(590\) | 16.8151 | + | 12.2169i | 0.692267 | + | 0.502961i | ||||
\(591\) | 8.40755 | − | 6.10844i | 0.345840 | − | 0.251268i | ||||
\(592\) | 12.3607 | − | 38.0423i | 0.508021 | − | 1.56353i | ||||
\(593\) | −24.2487 | −0.995775 | −0.497888 | − | 0.867242i | \(-0.665891\pi\) | ||||
−0.497888 | + | 0.867242i | \(0.665891\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | −0.491952 | ||||||||
\(596\) | 5.88756 | − | 18.1201i | 0.241164 | − | 0.742227i | ||||
\(597\) | −11.3262 | + | 8.22899i | −0.463552 | + | 0.336790i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.27051 | + | 28.5317i | 0.378783 | + | 1.16577i | 0.940891 | + | 0.338710i | \(0.109990\pi\) |
−0.562108 | + | 0.827064i | \(0.690010\pi\) | |||||||
\(600\) | −0.535233 | − | 1.64728i | −0.0218508 | − | 0.0672499i | ||||
\(601\) | 16.8151 | + | 12.2169i | 0.685902 | + | 0.498337i | 0.875311 | − | 0.483561i | \(-0.160657\pi\) |
−0.189408 | + | 0.981898i | \(0.560657\pi\) | |||||||
\(602\) | −21.0189 | + | 15.2711i | −0.856666 | + | 0.622404i | ||||
\(603\) | 3.09017 | − | 9.51057i | 0.125841 | − | 0.387300i | ||||
\(604\) | 20.7846 | 0.845714 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 3.00000 | 0.121867 | ||||||||
\(607\) | 1.07047 | − | 3.29456i | 0.0434489 | − | 0.133722i | −0.926979 | − | 0.375113i | \(-0.877604\pi\) |
0.970428 | + | 0.241391i | \(0.0776038\pi\) | |||||||
\(608\) | −14.5623 | + | 10.5801i | −0.590579 | + | 0.429081i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.63525 | − | 14.2658i | −0.187676 | − | 0.577607i | ||||
\(611\) | −9.63420 | − | 29.6510i | −0.389758 | − | 1.19955i | ||||
\(612\) | 11.2101 | + | 8.14459i | 0.453140 | + | 0.329226i | ||||
\(613\) | −8.40755 | + | 6.10844i | −0.339578 | + | 0.246718i | −0.744484 | − | 0.667641i | \(-0.767304\pi\) |
0.404906 | + | 0.914358i | \(0.367304\pi\) | |||||||
\(614\) | −5.56231 | + | 17.1190i | −0.224476 | + | 0.690867i | ||||
\(615\) | −12.1244 | −0.488901 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −36.0000 | −1.44931 | −0.724653 | − | 0.689114i | \(-0.758000\pi\) | ||||
−0.724653 | + | 0.689114i | \(0.758000\pi\) | |||||||
\(618\) | −2.14093 | + | 6.58911i | −0.0861209 | + | 0.265053i | ||||
\(619\) | −16.1803 | + | 11.7557i | −0.650343 | + | 0.472502i | −0.863388 | − | 0.504541i | \(-0.831662\pi\) |
0.213045 | + | 0.977042i | \(0.431662\pi\) | |||||||
\(620\) | −6.47214 | − | 4.70228i | −0.259927 | − | 0.188848i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.21140 | + | 9.88367i | 0.128765 | + | 0.396299i | ||||
\(623\) | −4.20378 | − | 3.05422i | −0.168421 | − | 0.122365i | ||||
\(624\) | 14.0126 | − | 10.1807i | 0.560952 | − | 0.407556i | ||||
\(625\) | 0.309017 | − | 0.951057i | 0.0123607 | − | 0.0380423i | ||||
\(626\) | −17.3205 | −0.692267 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | 0.159617 | ||||||||
\(629\) | −17.1275 | + | 52.7129i | −0.682917 | + | 2.10180i | ||||
\(630\) | 4.85410 | − | 3.52671i | 0.193392 | − | 0.140508i | ||||
\(631\) | −22.6525 | − | 16.4580i | −0.901781 | − | 0.655182i | 0.0371420 | − | 0.999310i | \(-0.488175\pi\) |
−0.938923 | + | 0.344128i | \(0.888175\pi\) | |||||||
\(632\) | 5.56231 | + | 17.1190i | 0.221257 | + | 0.680958i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.40755 | − | 6.10844i | −0.333907 | − | 0.242597i | ||||
\(635\) | −1.40126 | + | 1.01807i | −0.0556072 | + | 0.0404010i | ||||
\(636\) | −1.85410 | + | 5.70634i | −0.0735199 | + | 0.226271i | ||||
\(637\) | 13.8564 | 0.549011 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0000 | 0.949425 | ||||||||
\(640\) | 3.74663 | − | 11.5309i | 0.148099 | − | 0.455801i | ||||
\(641\) | −24.2705 | + | 17.6336i | −0.958628 | + | 0.696484i | −0.952832 | − | 0.303500i | \(-0.901845\pi\) |
−0.00579592 | + | 0.999983i | \(0.501845\pi\) | |||||||
\(642\) | 2.42705 | + | 1.76336i | 0.0957881 | + | 0.0695941i | ||||
\(643\) | −9.57953 | − | 29.4828i | −0.377780 | − | 1.16269i | −0.941584 | − | 0.336778i | \(-0.890663\pi\) |
0.563804 | − | 0.825908i | \(-0.309337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7.00629 | + | 5.09037i | 0.275873 | + | 0.200433i | ||||
\(646\) | 33.6302 | − | 24.4338i | 1.32316 | − | 0.961334i | ||||
\(647\) | 10.1976 | − | 31.3849i | 0.400907 | − | 1.23387i | −0.523357 | − | 0.852114i | \(-0.675321\pi\) |
0.924264 | − | 0.381753i | \(-0.124679\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.00000 | 0.235339 | ||||||||
\(651\) | 4.28187 | − | 13.1782i | 0.167820 | − | 0.516495i | ||||
\(652\) | 15.3713 | − | 11.1679i | 0.601987 | − | 0.437369i | ||||
\(653\) | 24.2705 | + | 17.6336i | 0.949778 | + | 0.690054i | 0.950754 | − | 0.309945i | \(-0.100311\pi\) |
−0.000976014 | 1.00000i | \(0.500311\pi\) | ||||||||
\(654\) | −0.927051 | − | 2.85317i | −0.0362506 | − | 0.111568i | ||||
\(655\) | −1.07047 | − | 3.29456i | −0.0418266 | − | 0.128729i | ||||
\(656\) | −49.0440 | − | 35.6326i | −1.91485 | − | 1.39122i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.34346 | + | 25.6785i | −0.325262 | + | 1.00105i | ||||
\(659\) | −3.46410 | −0.134942 | −0.0674711 | − | 0.997721i | \(-0.521493\pi\) | ||||
−0.0674711 | + | 0.997721i | \(0.521493\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.0000 | 1.43913 | 0.719567 | − | 0.694423i | \(-0.244340\pi\) | ||||
0.719567 | + | 0.694423i | \(0.244340\pi\) | |||||||
\(662\) | 18.1979 | − | 56.0075i | 0.707283 | − | 2.17679i | ||||
\(663\) | −19.4164 | + | 14.1068i | −0.754071 | + | 0.547865i | ||||
\(664\) | 4.85410 | + | 3.52671i | 0.188376 | + | 0.136863i | ||||
\(665\) | −1.85410 | − | 5.70634i | −0.0718990 | − | 0.221282i | ||||
\(666\) | −8.56373 | − | 26.3565i | −0.331838 | − | 1.02129i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −4.20378 | + | 3.05422i | −0.162649 | + | 0.118171i | ||||
\(669\) | 5.87132 | − | 18.0701i | 0.226998 | − | 0.698629i | ||||
\(670\) | −8.66025 | −0.334575 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −9.00000 | −0.347183 | ||||||||
\(673\) | 6.42280 | − | 19.7673i | 0.247581 | − | 0.761975i | −0.747621 | − | 0.664126i | \(-0.768804\pi\) |
0.995201 | − | 0.0978489i | \(-0.0311962\pi\) | |||||||
\(674\) | −14.5623 | + | 10.5801i | −0.560919 | + | 0.407532i | ||||
\(675\) | −4.04508 | − | 2.93893i | −0.155695 | − | 0.113119i | ||||
\(676\) | −0.309017 | − | 0.951057i | −0.0118853 | − | 0.0365791i | ||||
\(677\) | −8.56373 | − | 26.3565i | −0.329131 | − | 1.01296i | −0.969541 | − | 0.244928i | \(-0.921236\pi\) |
0.640410 | − | 0.768033i | \(-0.278764\pi\) | |||||||
\(678\) | 8.40755 | + | 6.10844i | 0.322890 | + | 0.234593i | ||||
\(679\) | 14.0126 | − | 10.1807i | 0.537754 | − | 0.390701i | ||||
\(680\) | −3.70820 | + | 11.4127i | −0.142203 | + | 0.437656i | ||||
\(681\) | 19.0526 | 0.730096 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.0000 | −0.803543 | −0.401771 | − | 0.915740i | \(-0.631605\pi\) | ||||
−0.401771 | + | 0.915740i | \(0.631605\pi\) | |||||||
\(684\) | −2.14093 | + | 6.58911i | −0.0818606 | + | 0.251941i | ||||
\(685\) | 14.5623 | − | 10.5801i | 0.556397 | − | 0.404246i | ||||
\(686\) | −26.6976 | − | 19.3969i | −1.01932 | − | 0.740578i | ||||
\(687\) | −2.16312 | − | 6.65740i | −0.0825281 | − | 0.253995i | ||||
\(688\) | 13.3808 | + | 41.1820i | 0.510139 | + | 1.57005i | ||||
\(689\) | 16.8151 | + | 12.2169i | 0.640604 | + | 0.465426i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.09017 | + | 9.51057i | −0.117556 | + | 0.361799i | −0.992471 | − | 0.122476i | \(-0.960917\pi\) |
0.874916 | + | 0.484275i | \(0.160917\pi\) | |||||||
\(692\) | −10.3923 | −0.395056 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.0000 | −0.797149 | ||||||||
\(695\) | 4.28187 | − | 13.1782i | 0.162420 | − | 0.499879i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 67.9574 | + | 49.3740i | 2.57407 | + | 1.87017i | ||||
\(698\) | 18.5410 | + | 57.0634i | 0.701788 | + | 2.15988i | ||||
\(699\) | −1.07047 | − | 3.29456i | −0.0404888 | − | 0.124612i | ||||
\(700\) | −1.40126 | − | 1.01807i | −0.0529626 | − | 0.0384796i | ||||
\(701\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(702\) | 9.27051 | − | 28.5317i | 0.349893 | − | 1.07686i | ||||
\(703\) | −27.7128 | −1.04521 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.00000 | 0.338960 | ||||||||
\(706\) | −12.8456 | + | 39.5347i | −0.483450 | + | 1.48791i | ||||
\(707\) | −2.42705 | + | 1.76336i | −0.0912786 | + | 0.0663178i | ||||
\(708\) | −9.70820 | − | 7.05342i | −0.364857 | − | 0.265084i | ||||
\(709\) | 7.72542 | + | 23.7764i | 0.290134 | + | 0.892942i | 0.984813 | + | 0.173621i | \(0.0555468\pi\) |
−0.694678 | + | 0.719321i | \(0.744453\pi\) | |||||||
\(710\) | −6.42280 | − | 19.7673i | −0.241043 | − | 0.741855i | ||||
\(711\) | 16.8151 | + | 12.2169i | 0.630616 | + | 0.458169i | ||||
\(712\) | −4.20378 | + | 3.05422i | −0.157543 | + | 0.114462i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 20.7846 | 0.777844 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.0000 | −0.672692 | ||||||||
\(717\) | 1.07047 | − | 3.29456i | 0.0399773 | − | 0.123037i | ||||
\(718\) | 4.85410 | − | 3.52671i | 0.181153 | − | 0.131616i | ||||
\(719\) | −4.85410 | − | 3.52671i | −0.181027 | − | 0.131524i | 0.493581 | − | 0.869700i | \(-0.335688\pi\) |
−0.674609 | + | 0.738176i | \(0.735688\pi\) | |||||||
\(720\) | −3.09017 | − | 9.51057i | −0.115164 | − | 0.354438i | ||||
\(721\) | −2.14093 | − | 6.58911i | −0.0797325 | − | 0.245391i | ||||
\(722\) | −9.80881 | − | 7.12652i | −0.365046 | − | 0.265222i | ||||
\(723\) | 15.4138 | − | 11.1988i | 0.573247 | − | 0.416488i | ||||
\(724\) | 3.39919 | − | 10.4616i | 0.126330 | − | 0.388803i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.00000 | 0.0370879 | 0.0185440 | − | 0.999828i | \(-0.494097\pi\) | ||||
0.0185440 | + | 0.999828i | \(0.494097\pi\) | |||||||
\(728\) | −3.21140 | + | 9.88367i | −0.119022 | + | 0.366313i | ||||
\(729\) | −10.5172 | + | 7.64121i | −0.389527 | + | 0.283008i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.5410 | − | 57.0634i | −0.685764 | − | 2.11057i | ||||
\(732\) | 2.67617 | + | 8.23639i | 0.0989139 | + | 0.304426i | ||||
\(733\) | −16.8151 | − | 12.2169i | −0.621080 | − | 0.451241i | 0.232219 | − | 0.972664i | \(-0.425402\pi\) |
−0.853299 | + | 0.521423i | \(0.825402\pi\) | |||||||
\(734\) | 23.8214 | − | 17.3073i | 0.879264 | − | 0.638823i | ||||
\(735\) | −1.23607 | + | 3.80423i | −0.0455931 | + | 0.140321i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −42.0000 | −1.54604 | ||||||||
\(739\) | −1.07047 | + | 3.29456i | −0.0393777 | + | 0.121192i | −0.968813 | − | 0.247793i | \(-0.920295\pi\) |
0.929435 | + | 0.368985i | \(0.120295\pi\) | |||||||
\(740\) | −6.47214 | + | 4.70228i | −0.237920 | + | 0.172859i | ||||
\(741\) | −9.70820 | − | 7.05342i | −0.356640 | − | 0.259114i | ||||
\(742\) | −5.56231 | − | 17.1190i | −0.204199 | − | 0.628459i | ||||
\(743\) | −1.60570 | − | 4.94183i | −0.0589074 | − | 0.181298i | 0.917273 | − | 0.398259i | \(-0.130386\pi\) |
−0.976180 | + | 0.216961i | \(0.930386\pi\) | |||||||
\(744\) | −11.2101 | − | 8.14459i | −0.410981 | − | 0.298595i | ||||
\(745\) | 15.4138 | − | 11.1988i | 0.564720 | − | 0.410293i | ||||
\(746\) | −7.41641 | + | 22.8254i | −0.271534 | + | 0.835696i | ||||
\(747\) | 6.92820 | 0.253490 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.00000 | −0.109618 | ||||||||
\(750\) | −0.535233 | + | 1.64728i | −0.0195440 | + | 0.0601501i | ||||
\(751\) | 11.3262 | − | 8.22899i | 0.413300 | − | 0.300280i | −0.361636 | − | 0.932319i | \(-0.617782\pi\) |
0.774937 | + | 0.632039i | \(0.217782\pi\) | |||||||
\(752\) | 36.4058 | + | 26.4503i | 1.32758 | + | 0.964545i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.8151 | + | 12.2169i | 0.611964 | + | 0.444618i | ||||
\(756\) | −7.00629 | + | 5.09037i | −0.254816 | + | 0.185135i | ||||
\(757\) | −0.618034 | + | 1.90211i | −0.0224628 | + | 0.0691335i | −0.961660 | − | 0.274246i | \(-0.911572\pi\) |
0.939197 | + | 0.343380i | \(0.111572\pi\) | |||||||
\(758\) | 58.8897 | 2.13897 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | −0.217643 | ||||||||
\(761\) | −10.7047 | + | 32.9456i | −0.388044 | + | 1.19428i | 0.546204 | + | 0.837652i | \(0.316072\pi\) |
−0.934248 | + | 0.356624i | \(0.883928\pi\) | |||||||
\(762\) | 2.42705 | − | 1.76336i | 0.0879228 | − | 0.0638796i | ||||
\(763\) | 2.42705 | + | 1.76336i | 0.0878651 | + | 0.0638378i | ||||
\(764\) | −1.85410 | − | 5.70634i | −0.0670791 | − | 0.206448i | ||||
\(765\) | 4.28187 | + | 13.1782i | 0.154811 | + | 0.476460i | ||||
\(766\) | 33.6302 | + | 24.4338i | 1.21511 | + | 0.882828i | ||||
\(767\) | −33.6302 | + | 24.4338i | −1.21432 | + | 0.882252i | ||||
\(768\) | −5.87132 | + | 18.0701i | −0.211863 | + | 0.652048i | ||||
\(769\) | −27.7128 | −0.999350 | −0.499675 | − | 0.866213i | \(-0.666547\pi\) | ||||
−0.499675 | + | 0.866213i | \(0.666547\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −12.0000 | −0.432169 | ||||||||
\(772\) | 1.07047 | − | 3.29456i | 0.0385269 | − | 0.118574i | ||||
\(773\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(774\) | 24.2705 | + | 17.6336i | 0.872385 | + | 0.633825i | ||||
\(775\) | −2.47214 | − | 7.60845i | −0.0888017 | − | 0.273304i | ||||
\(776\) | −5.35233 | − | 16.4728i | −0.192137 | − | 0.591338i | ||||
\(777\) | −11.2101 | − | 8.14459i | −0.402159 | − | 0.292186i | ||||
\(778\) | 4.20378 | − | 3.05422i | 0.150713 | − | 0.109499i | ||||
\(779\) | −12.9787 | + | 39.9444i | −0.465011 | + | 1.43116i | ||||
\(780\) | −3.46410 | −0.124035 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −16.1803 | + | 11.7557i | −0.577869 | + | 0.419847i | ||||
\(785\) | 3.23607 | + | 2.35114i | 0.115500 | + | 0.0839158i | ||||
\(786\) | 1.85410 | + | 5.70634i | 0.0661336 | + | 0.203538i | ||||
\(787\) | 8.02850 | + | 24.7092i | 0.286185 | + | 0.880787i | 0.986041 | + | 0.166503i | \(0.0532475\pi\) |
−0.699856 | + | 0.714284i | \(0.746752\pi\) | |||||||
\(788\) | −8.40755 | − | 6.10844i | −0.299507 | − | 0.217604i | ||||
\(789\) | −19.6176 | + | 14.2530i | −0.698406 | + | 0.507421i | ||||
\(790\) | 5.56231 | − | 17.1190i | 0.197898 | − | 0.609067i | ||||
\(791\) | −10.3923 | −0.369508 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.0000 | 1.06533 | ||||||||
\(794\) | −10.7047 | + | 32.9456i | −0.379894 | + | 1.16919i | ||||
\(795\) | −4.85410 | + | 3.52671i | −0.172157 | + | 0.125080i | ||||
\(796\) | 11.3262 | + | 8.22899i | 0.401448 | + | 0.291669i | ||||
\(797\) | −3.70820 | − | 11.4127i | −0.131351 | − | 0.404258i | 0.863653 | − | 0.504086i | \(-0.168171\pi\) |
−0.995005 | + | 0.0998284i | \(0.968171\pi\) | |||||||
\(798\) | 3.21140 | + | 9.88367i | 0.113682 | + | 0.349878i | ||||
\(799\) | −50.4453 | − | 36.6507i | −1.78463 | − | 1.29661i | ||||
\(800\) | −4.20378 | + | 3.05422i | −0.148626 | + | 0.107983i | ||||
\(801\) | −1.85410 | + | 5.70634i | −0.0655115 | + | 0.201624i | ||||
\(802\) | −46.7654 | −1.65134 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.00000 | 0.176336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 38.8328 | − | 28.2137i | 1.36783 | − | 0.993785i | ||||
\(807\) | −12.1353 | − | 8.81678i | −0.427181 | − | 0.310365i | ||||
\(808\) | 0.927051 | + | 2.85317i | 0.0326135 | + | 0.100374i | ||||
\(809\) | 14.9865 | + | 46.1238i | 0.526898 | + | 1.62163i | 0.760531 | + | 0.649301i | \(0.224939\pi\) |
−0.233633 | + | 0.972325i | \(0.575061\pi\) | |||||||
\(810\) | −1.40126 | − | 1.01807i | −0.0492352 | − | 0.0357715i | ||||
\(811\) | 5.60503 | − | 4.07230i | 0.196819 | − | 0.142998i | −0.485011 | − | 0.874508i | \(-0.661184\pi\) |
0.681830 | + | 0.731511i | \(0.261184\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.8564 | −0.485965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.0000 | 0.665541 | ||||||||
\(816\) | 10.7047 | − | 32.9456i | 0.374738 | − | 1.15333i | ||||
\(817\) | 24.2705 | − | 17.6336i | 0.849118 | − | 0.616920i | ||||
\(818\) | −7.28115 | − | 5.29007i | −0.254580 | − | 0.184963i | ||||
\(819\) | 3.70820 | + | 11.4127i | 0.129575 | + | 0.398791i | ||||
\(820\) | 3.74663 | + | 11.5309i | 0.130838 | + | 0.402678i | ||||
\(821\) | 23.8214 | + | 17.3073i | 0.831372 | + | 0.604027i | 0.919947 | − | 0.392042i | \(-0.128231\pi\) |
−0.0885749 | + | 0.996070i | \(0.528231\pi\) | |||||||
\(822\) | −25.2227 | + | 18.3253i | −0.879741 | + | 0.639169i | ||||
\(823\) | 5.25329 | − | 16.1680i | 0.183118 | − | 0.563580i | −0.816793 | − | 0.576931i | \(-0.804250\pi\) |
0.999911 | + | 0.0133515i | \(0.00425006\pi\) | |||||||
\(824\) | −6.92820 | −0.241355 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 36.0000 | 1.25260 | ||||||||
\(827\) | −9.09896 | + | 28.0037i | −0.316402 | + | 0.973785i | 0.658772 | + | 0.752343i | \(0.271076\pi\) |
−0.975174 | + | 0.221442i | \(0.928924\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.4615 | − | 17.0458i | −0.814851 | − | 0.592024i | 0.100382 | − | 0.994949i | \(-0.467994\pi\) |
−0.915233 | + | 0.402925i | \(0.867994\pi\) | |||||||
\(830\) | −1.85410 | − | 5.70634i | −0.0643568 | − | 0.198070i | ||||
\(831\) | 3.21140 | + | 9.88367i | 0.111402 | + | 0.342861i | ||||
\(832\) | 2.80252 | + | 2.03615i | 0.0971598 | + | 0.0705907i | ||||
\(833\) | 22.4201 | − | 16.2892i | 0.776812 | − | 0.564387i | ||||
\(834\) | −7.41641 | + | 22.8254i | −0.256809 | + | 0.790377i | ||||
\(835\) | −5.19615 | −0.179820 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −40.0000 | −1.38260 | ||||||||
\(838\) | −9.63420 | + | 29.6510i | −0.332808 | + | 1.02428i | ||||
\(839\) | 33.9787 | − | 24.6870i | 1.17308 | − | 0.852289i | 0.181702 | − | 0.983354i | \(-0.441839\pi\) |
0.991374 | + | 0.131064i | \(0.0418395\pi\) | |||||||
\(840\) | −2.42705 | − | 1.76336i | −0.0837412 | − | 0.0608416i | ||||
\(841\) | −8.96149 | − | 27.5806i | −0.309017 | − | 0.951057i | ||||
\(842\) | 9.09896 | + | 28.0037i | 0.313571 | + | 0.965072i | ||||
\(843\) | 5.60503 | + | 4.07230i | 0.193048 | + | 0.140257i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.309017 | − | 0.951057i | 0.0106305 | − | 0.0327173i | ||||
\(846\) | 31.1769 | 1.07188 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −30.0000 | −1.03020 | ||||||||
\(849\) | −1.60570 | + | 4.94183i | −0.0551075 | + | 0.169603i | ||||
\(850\) | 9.70820 | − | 7.05342i | 0.332989 | − | 0.241930i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 3.70820 | + | 11.4127i | 0.127041 | + | 0.390992i | ||||
\(853\) | 10.7047 | + | 32.9456i | 0.366521 | + | 1.12803i | 0.949023 | + | 0.315206i | \(0.102074\pi\) |
−0.582503 | + | 0.812829i | \(0.697926\pi\) | |||||||
\(854\) | −21.0189 | − | 15.2711i | −0.719251 | − | 0.522567i | ||||
\(855\) | −5.60503 | + | 4.07230i | −0.191688 | + | 0.139270i | ||||
\(856\) | −0.927051 | + | 2.85317i | −0.0316860 | + | 0.0975193i | ||||
\(857\) | 10.3923 | 0.354994 | 0.177497 | − | 0.984121i | \(-0.443200\pi\) | ||||
0.177497 | + | 0.984121i | \(0.443200\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | 2.67617 | − | 8.23639i | 0.0912565 | − | 0.280859i | ||||
\(861\) | −16.9894 | + | 12.3435i | −0.578996 | + | 0.420665i | ||||
\(862\) | −53.3951 | − | 38.7938i | −1.81865 | − | 1.32132i | ||||
\(863\) | 6.48936 | + | 19.9722i | 0.220900 | + | 0.679861i | 0.998682 | + | 0.0513266i | \(0.0163449\pi\) |
−0.777782 | + | 0.628535i | \(0.783655\pi\) | |||||||
\(864\) | 8.02850 | + | 24.7092i | 0.273135 | + | 0.840623i | ||||
\(865\) | −8.40755 | − | 6.10844i | −0.285865 | − | 0.207693i | ||||
\(866\) | 44.8403 | − | 32.5784i | 1.52373 | − | 1.10706i | ||||
\(867\) | −9.57953 | + | 29.4828i | −0.325338 | + | 1.00129i | ||||
\(868\) | −13.8564 | −0.470317 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.35233 | − | 16.4728i | 0.181357 | − | 0.558159i | ||||
\(872\) | 2.42705 | − | 1.76336i | 0.0821903 | − | 0.0597148i | ||||
\(873\) | −16.1803 | − | 11.7557i | −0.547622 | − | 0.397870i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.535233 | − | 1.64728i | −0.0180942 | − | 0.0556882i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.4201 | + | 16.2892i | −0.757074 | + | 0.550047i | −0.898012 | − | 0.439972i | \(-0.854988\pi\) |
0.140937 | + | 0.990019i | \(0.454988\pi\) | |||||||
\(878\) | −14.8328 | + | 45.6507i | −0.500583 | + | 1.54064i | ||||
\(879\) | −6.92820 | −0.233682 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −21.0000 | −0.707508 | −0.353754 | − | 0.935339i | \(-0.615095\pi\) | ||||
−0.353754 | + | 0.935339i | \(0.615095\pi\) | |||||||
\(882\) | −4.28187 | + | 13.1782i | −0.144178 | + | 0.443734i | ||||
\(883\) | 45.3050 | − | 32.9160i | 1.52463 | − | 1.10771i | 0.565503 | − | 0.824747i | \(-0.308682\pi\) |
0.959130 | − | 0.282964i | \(-0.0913178\pi\) | |||||||
\(884\) | 19.4164 | + | 14.1068i | 0.653044 | + | 0.474465i | ||||
\(885\) | −3.70820 | − | 11.4127i | −0.124650 | − | 0.383633i | ||||
\(886\) | 8.02850 | + | 24.7092i | 0.269723 | + | 0.830121i | ||||
\(887\) | −26.6239 | − | 19.3434i | −0.893943 | − | 0.649488i | 0.0429597 | − | 0.999077i | \(-0.486321\pi\) |
−0.936903 | + | 0.349589i | \(0.886321\pi\) | |||||||
\(888\) | −11.2101 | + | 8.14459i | −0.376185 | + | 0.273315i | ||||
\(889\) | −0.927051 | + | 2.85317i | −0.0310923 | + | 0.0956922i | ||||
\(890\) | 5.19615 | 0.174175 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.0000 | −0.636167 | ||||||||
\(893\) | 9.63420 | − | 29.6510i | 0.322396 | − | 0.992233i | ||||
\(894\) | −26.6976 | + | 19.3969i | −0.892900 | + | 0.648730i | ||||
\(895\) | −14.5623 | − | 10.5801i | −0.486764 | − | 0.353655i | ||||
\(896\) | −6.48936 | − | 19.9722i | −0.216794 | − | 0.667224i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −21.0189 | − | 15.2711i | −0.701409 | − | 0.509604i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.618034 | + | 1.90211i | −0.0206011 | + | 0.0634038i | ||||
\(901\) | 41.5692 | 1.38487 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.0000 | 0.499169 | ||||||||
\(904\) | −3.21140 | + | 9.88367i | −0.106810 | + | 0.328726i | ||||
\(905\) | 8.89919 | − | 6.46564i | 0.295819 | − | 0.214925i | ||||
\(906\) | −29.1246 | − | 21.1603i | −0.967600 | − | 0.703003i | ||||
\(907\) | 5.25329 | + | 16.1680i | 0.174433 | + | 0.536848i | 0.999607 | − | 0.0280296i | \(-0.00892326\pi\) |
−0.825174 | + | 0.564878i | \(0.808923\pi\) | |||||||
\(908\) | −5.88756 | − | 18.1201i | −0.195386 | − | 0.601335i | ||||
\(909\) | 2.80252 | + | 2.03615i | 0.0929536 | + | 0.0675348i | ||||
\(910\) | 8.40755 | − | 6.10844i | 0.278708 | − | 0.202493i | ||||
\(911\) | 1.85410 | − | 5.70634i | 0.0614291 | − | 0.189059i | −0.915632 | − | 0.402017i | \(-0.868309\pi\) |
0.977062 | + | 0.212957i | \(0.0683094\pi\) | |||||||
\(912\) | 17.3205 | 0.573539 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 36.0000 | 1.19077 | ||||||||
\(915\) | −2.67617 | + | 8.23639i | −0.0884713 | + | 0.272287i | ||||
\(916\) | −5.66312 | + | 4.11450i | −0.187115 | + | 0.135947i | ||||
\(917\) | −4.85410 | − | 3.52671i | −0.160297 | − | 0.116462i | ||||
\(918\) | −18.5410 | − | 57.0634i | −0.611945 | − | 1.88337i | ||||
\(919\) | −11.7751 | − | 36.2401i | −0.388426 | − | 1.19545i | −0.933965 | − | 0.357366i | \(-0.883675\pi\) |
0.545539 | − | 0.838086i | \(-0.316325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.40755 | − | 6.10844i | 0.277038 | − | 0.201280i | ||||
\(922\) | −6.48936 | + | 19.9722i | −0.213716 | + | 0.657749i | ||||
\(923\) | 41.5692 | 1.36827 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | −0.263038 | ||||||||
\(926\) | −21.9446 | + | 67.5384i | −0.721143 | + | 2.21945i | ||||
\(927\) | −6.47214 | + | 4.70228i | −0.212573 | + | 0.154443i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.56231 | + | 17.1190i | 0.182493 | + | 0.561657i | 0.999896 | − | 0.0144098i | \(-0.00458693\pi\) |
−0.817403 | + | 0.576066i | \(0.804587\pi\) | |||||||
\(930\) | 4.28187 | + | 13.1782i | 0.140408 | + | 0.432131i | ||||
\(931\) | 11.2101 | + | 8.14459i | 0.367395 | + | 0.266928i | ||||
\(932\) | −2.80252 | + | 2.03615i | −0.0917995 | + | 0.0666962i | ||||
\(933\) | 1.85410 | − | 5.70634i | 0.0607006 | − | 0.186817i | ||||
\(934\) | −5.19615 | −0.170023 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.0000 | 0.392232 | ||||||||
\(937\) | 7.49326 | − | 23.0619i | 0.244794 | − | 0.753399i | −0.750876 | − | 0.660443i | \(-0.770368\pi\) |
0.995670 | − | 0.0929560i | \(-0.0296316\pi\) | |||||||
\(938\) | −12.1353 | + | 8.81678i | −0.396230 | + | 0.287878i | ||||
\(939\) | 8.09017 | + | 5.87785i | 0.264013 | + | 0.191816i | ||||
\(940\) | −2.78115 | − | 8.55951i | −0.0907112 | − | 0.279180i | ||||
\(941\) | 15.5218 | + | 47.7711i | 0.505995 | + | 1.55729i | 0.799091 | + | 0.601209i | \(0.205314\pi\) |
−0.293097 | + | 0.956083i | \(0.594686\pi\) | |||||||
\(942\) | −5.60503 | − | 4.07230i | −0.182622 | − | 0.132683i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 18.5410 | − | 57.0634i | 0.603459 | − | 1.85726i | ||||
\(945\) | −8.66025 | −0.281718 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −12.0000 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(948\) | −3.21140 | + | 9.88367i | −0.104301 | + | 0.321007i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.85410 | + | 3.52671i | 0.157488 | + | 0.114422i | ||||
\(951\) | 1.85410 | + | 5.70634i | 0.0601234 | + | 0.185041i | ||||
\(952\) | 6.42280 | + | 19.7673i | 0.208164 | + | 0.640663i | ||||
\(953\) | 44.8403 | + | 32.5784i | 1.45252 | + | 1.05532i | 0.985235 | + | 0.171210i | \(0.0547676\pi\) |
0.467284 | + | 0.884107i | \(0.345232\pi\) | |||||||
\(954\) | −16.8151 | + | 12.2169i | −0.544409 | + | 0.395536i | ||||
\(955\) | 1.85410 | − | 5.70634i | 0.0599973 | − | 0.184653i | ||||
\(956\) | −3.46410 | −0.112037 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0000 | 0.581554 | ||||||||
\(959\) | 9.63420 | − | 29.6510i | 0.311104 | − | 0.957481i | ||||
\(960\) | −0.809017 | + | 0.587785i | −0.0261109 | + | 0.0189707i | ||||
\(961\) | −26.6976 | − | 19.3969i | −0.861212 | − | 0.625707i | ||||
\(962\) | −14.8328 | − | 45.6507i | −0.478229 | − | 1.47184i | ||||
\(963\) | 1.07047 | + | 3.29456i | 0.0344953 | + | 0.106166i | ||||
\(964\) | −15.4138 | − | 11.1988i | −0.496446 | − | 0.360689i | ||||
\(965\) | 2.80252 | − | 2.03615i | 0.0902162 | − | 0.0655459i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.1051 | −1.22538 | −0.612689 | − | 0.790324i | \(-0.709912\pi\) | ||||
−0.612689 | + | 0.790324i | \(0.709912\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | −5.35233 | + | 16.4728i | −0.171853 | + | 0.528909i | ||||
\(971\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(972\) | 12.9443 | + | 9.40456i | 0.415188 | + | 0.301652i | ||||
\(973\) | −7.41641 | − | 22.8254i | −0.237759 | − | 0.731747i | ||||
\(974\) | 10.7047 | + | 32.9456i | 0.343000 | + | 1.05564i | ||||
\(975\) | −2.80252 | − | 2.03615i | −0.0897524 | − | 0.0652089i | ||||
\(976\) | −35.0315 | + | 25.4518i | −1.12133 | + | 0.814694i | ||||
\(977\) | −7.41641 | + | 22.8254i | −0.237272 | + | 0.730248i | 0.759540 | + | 0.650461i | \(0.225424\pi\) |
−0.996812 | + | 0.0797873i | \(0.974576\pi\) | |||||||
\(978\) | −32.9090 | −1.05231 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.00000 | 0.127775 | ||||||||
\(981\) | 1.07047 | − | 3.29456i | 0.0341774 | − | 0.105187i | ||||
\(982\) | −33.9787 | + | 24.6870i | −1.08430 | + | 0.787793i | ||||
\(983\) | 2.42705 | + | 1.76336i | 0.0774109 | + | 0.0562423i | 0.625818 | − | 0.779969i | \(-0.284765\pi\) |
−0.548407 | + | 0.836212i | \(0.684765\pi\) | |||||||
\(984\) | 6.48936 | + | 19.9722i | 0.206873 | + | 0.636690i | ||||
\(985\) | −3.21140 | − | 9.88367i | −0.102324 | − | 0.314920i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.6113 | − | 9.16267i | 0.401423 | − | 0.291651i | ||||
\(988\) | −3.70820 | + | 11.4127i | −0.117974 | + | 0.363086i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | −12.8456 | + | 39.5347i | −0.407848 | + | 1.25523i | ||||
\(993\) | −27.5066 | + | 19.9847i | −0.872895 | + | 0.634195i | ||||
\(994\) | −29.1246 | − | 21.1603i | −0.923777 | − | 0.671163i | ||||
\(995\) | 4.32624 | + | 13.3148i | 0.137151 | + | 0.422107i | ||||
\(996\) | 1.07047 | + | 3.29456i | 0.0339190 | + | 0.104392i | ||||
\(997\) | −36.4327 | − | 26.4699i | −1.15384 | − | 0.838311i | −0.164850 | − | 0.986319i | \(-0.552714\pi\) |
−0.988986 | + | 0.148008i | \(0.952714\pi\) | |||||||
\(998\) | −53.2478 | + | 38.6868i | −1.68553 | + | 1.22461i | ||||
\(999\) | −12.3607 | + | 38.0423i | −0.391075 | + | 1.20360i |
(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 | 605.2.g.i.251.1 | 8 | ||
11.2 | odd | 10 | inner | 605.2.g.i.366.1 | 8 | ||
11.3 | even | 5 | inner | 605.2.g.i.81.2 | 8 | ||
11.4 | even | 5 | 605.2.a.e.1.1 | ✓ | 2 | ||
11.5 | even | 5 | inner | 605.2.g.i.511.1 | 8 | ||
11.6 | odd | 10 | inner | 605.2.g.i.511.2 | 8 | ||
11.7 | odd | 10 | 605.2.a.e.1.2 | yes | 2 | ||
11.8 | odd | 10 | inner | 605.2.g.i.81.1 | 8 | ||
11.9 | even | 5 | inner | 605.2.g.i.366.2 | 8 | ||
11.10 | odd | 2 | inner | 605.2.g.i.251.2 | 8 | ||
33.26 | odd | 10 | 5445.2.a.u.1.2 | 2 | |||
33.29 | even | 10 | 5445.2.a.u.1.1 | 2 | |||
44.7 | even | 10 | 9680.2.a.bu.1.2 | 2 | |||
44.15 | odd | 10 | 9680.2.a.bu.1.1 | 2 | |||
55.4 | even | 10 | 3025.2.a.l.1.2 | 2 | |||
55.29 | odd | 10 | 3025.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.a.e.1.1 | ✓ | 2 | 11.4 | even | 5 | ||
605.2.a.e.1.2 | yes | 2 | 11.7 | odd | 10 | ||
605.2.g.i.81.1 | 8 | 11.8 | odd | 10 | inner | ||
605.2.g.i.81.2 | 8 | 11.3 | even | 5 | inner | ||
605.2.g.i.251.1 | 8 | 1.1 | even | 1 | trivial | ||
605.2.g.i.251.2 | 8 | 11.10 | odd | 2 | inner | ||
605.2.g.i.366.1 | 8 | 11.2 | odd | 10 | inner | ||
605.2.g.i.366.2 | 8 | 11.9 | even | 5 | inner | ||
605.2.g.i.511.1 | 8 | 11.5 | even | 5 | inner | ||
605.2.g.i.511.2 | 8 | 11.6 | odd | 10 | inner | ||
3025.2.a.l.1.1 | 2 | 55.29 | odd | 10 | |||
3025.2.a.l.1.2 | 2 | 55.4 | even | 10 | |||
5445.2.a.u.1.1 | 2 | 33.29 | even | 10 | |||
5445.2.a.u.1.2 | 2 | 33.26 | odd | 10 | |||
9680.2.a.bu.1.1 | 2 | 44.15 | odd | 10 | |||
9680.2.a.bu.1.2 | 2 | 44.7 | even | 10 |