Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(107,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.l (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.12 | ||
Character | \(\chi\) | \(=\) | 432.107 |
Dual form | 432.2.l.a.323.12 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.932009 | − | 1.06365i | 0.659030 | − | 0.752117i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.262720 | − | 1.98267i | −0.131360 | − | 0.991335i | ||||
\(5\) | −2.82387 | + | 2.82387i | −1.26288 | + | 1.26288i | −0.313182 | + | 0.949693i | \(0.601395\pi\) |
−0.949693 | + | 0.313182i | \(0.898605\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.49224 | −1.31994 | −0.659971 | − | 0.751291i | \(-0.729432\pi\) | ||||
−0.659971 | + | 0.751291i | \(0.729432\pi\) | |||||||
\(8\) | −2.35373 | − | 1.56842i | −0.832170 | − | 0.554521i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.371751 | + | 5.63550i | 0.117558 | + | 1.78210i | ||||
\(11\) | −1.04434 | − | 1.04434i | −0.314881 | − | 0.314881i | 0.531916 | − | 0.846797i | \(-0.321472\pi\) |
−0.846797 | + | 0.531916i | \(0.821472\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.232068 | − | 0.232068i | 0.0643640 | − | 0.0643640i | −0.674192 | − | 0.738556i | \(-0.735508\pi\) |
0.738556 | + | 0.674192i | \(0.235508\pi\) | |||||||
\(14\) | −3.25480 | + | 3.71453i | −0.869881 | + | 0.992751i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.86196 | + | 1.04177i | −0.965489 | + | 0.260444i | ||||
\(17\) | 6.83177i | 1.65695i | 0.560027 | + | 0.828474i | \(0.310791\pi\) | ||||
−0.560027 | + | 0.828474i | \(0.689209\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.59498 | − | 3.59498i | −0.824746 | − | 0.824746i | 0.162039 | − | 0.986784i | \(-0.448193\pi\) |
−0.986784 | + | 0.162039i | \(0.948193\pi\) | |||||||
\(20\) | 6.34070 | + | 4.85692i | 1.41782 | + | 1.08604i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.08416 | + | 0.137483i | −0.444344 | + | 0.0293115i | ||||
\(23\) | 3.02976i | 0.631748i | 0.948801 | + | 0.315874i | \(0.102298\pi\) | ||||
−0.948801 | + | 0.315874i | \(0.897702\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 10.9485i | − | 2.18971i | ||||||
\(26\) | −0.0305507 | − | 0.463129i | −0.00599149 | − | 0.0908271i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.917482 | + | 6.92396i | 0.173388 | + | 1.30850i | ||||
\(29\) | −4.56568 | − | 4.56568i | −0.847826 | − | 0.847826i | 0.142035 | − | 0.989862i | \(-0.454635\pi\) |
−0.989862 | + | 0.142035i | \(0.954635\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.60037i | 0.287435i | 0.989619 | + | 0.143717i | \(0.0459057\pi\) | ||||
−0.989619 | + | 0.143717i | \(0.954094\pi\) | |||||||
\(32\) | −2.49129 | + | 5.07873i | −0.440402 | + | 0.897801i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.26665 | + | 6.36727i | 1.24622 | + | 1.09198i | ||||
\(35\) | 9.86165 | − | 9.86165i | 1.66692 | − | 1.66692i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0478917 | + | 0.0478917i | 0.00787335 | + | 0.00787335i | 0.711032 | − | 0.703159i | \(-0.248228\pi\) |
−0.703159 | + | 0.711032i | \(0.748228\pi\) | |||||||
\(38\) | −7.17437 | + | 0.473264i | −1.16384 | + | 0.0767735i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 11.0757 | − | 2.21762i | 1.75122 | − | 0.350636i | ||||
\(41\) | 5.73402 | 0.895504 | 0.447752 | − | 0.894158i | \(-0.352225\pi\) | ||||
0.447752 | + | 0.894158i | \(0.352225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.10123 | − | 8.10123i | 1.23543 | − | 1.23543i | 0.273575 | − | 0.961851i | \(-0.411794\pi\) |
0.961851 | − | 0.273575i | \(-0.0882062\pi\) | |||||||
\(44\) | −1.79622 | + | 2.34496i | −0.270790 | + | 0.353516i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.22262 | + | 2.82376i | 0.475149 | + | 0.416341i | ||||
\(47\) | −4.46856 | −0.651806 | −0.325903 | − | 0.945403i | \(-0.605668\pi\) | ||||
−0.325903 | + | 0.945403i | \(0.605668\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.19573 | 0.742248 | ||||||||
\(50\) | −11.6455 | − | 10.2041i | −1.64692 | − | 1.44308i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.521083 | − | 0.399145i | −0.0722612 | − | 0.0553514i | ||||
\(53\) | −3.08126 | + | 3.08126i | −0.423243 | + | 0.423243i | −0.886319 | − | 0.463076i | \(-0.846746\pi\) |
0.463076 | + | 0.886319i | \(0.346746\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.89819 | 0.795312 | ||||||||
\(56\) | 8.21980 | + | 5.47730i | 1.09842 | + | 0.731935i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −9.11156 | + | 0.601052i | −1.19641 | + | 0.0789220i | ||||
\(59\) | −2.53529 | − | 2.53529i | −0.330067 | − | 0.330067i | 0.522545 | − | 0.852612i | \(-0.324983\pi\) |
−0.852612 | + | 0.522545i | \(0.824983\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.63186 | + | 5.63186i | −0.721085 | + | 0.721085i | −0.968826 | − | 0.247741i | \(-0.920312\pi\) |
0.247741 | + | 0.968826i | \(0.420312\pi\) | |||||||
\(62\) | 1.70224 | + | 1.49156i | 0.216185 | + | 0.189428i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.08011 | + | 7.38329i | 0.385014 | + | 0.922911i | ||||
\(65\) | 1.31066i | 0.162567i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.61823 | − | 4.61823i | −0.564207 | − | 0.564207i | 0.366293 | − | 0.930500i | \(-0.380627\pi\) |
−0.930500 | + | 0.366293i | \(0.880627\pi\) | |||||||
\(68\) | 13.5452 | − | 1.79485i | 1.64259 | − | 0.217657i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.29824 | − | 19.6805i | −0.155170 | − | 2.35227i | ||||
\(71\) | − | 5.63903i | − | 0.669230i | −0.942355 | − | 0.334615i | \(-0.891394\pi\) | ||
0.942355 | − | 0.334615i | \(-0.108606\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3342i | 1.32657i | 0.748369 | + | 0.663283i | \(0.230837\pi\) | ||||
−0.748369 | + | 0.663283i | \(0.769163\pi\) | |||||||
\(74\) | 0.0955757 | − | 0.00630473i | 0.0111105 | − | 0.000732910i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.18319 | + | 8.07214i | −0.709260 | + | 0.925938i | ||||
\(77\) | 3.64710 | + | 3.64710i | 0.415625 | + | 0.415625i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.86489i | 0.547343i | 0.961823 | + | 0.273672i | \(0.0882382\pi\) | ||||
−0.961823 | + | 0.273672i | \(0.911762\pi\) | |||||||
\(80\) | 7.96384 | − | 13.8475i | 0.890384 | − | 1.54820i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.34416 | − | 6.09902i | 0.590164 | − | 0.673524i | ||||
\(83\) | −0.847057 | + | 0.847057i | −0.0929766 | + | 0.0929766i | −0.752065 | − | 0.659089i | \(-0.770942\pi\) |
0.659089 | + | 0.752065i | \(0.270942\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −19.2921 | − | 19.2921i | −2.09252 | − | 2.09252i | ||||
\(86\) | −1.06649 | − | 16.1673i | −0.115003 | − | 1.74337i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.820134 | + | 4.09608i | 0.0874266 | + | 0.436643i | ||||
\(89\) | −13.9912 | −1.48306 | −0.741532 | − | 0.670917i | \(-0.765901\pi\) | ||||
−0.741532 | + | 0.670917i | \(0.765901\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.810436 | + | 0.810436i | −0.0849568 | + | 0.0849568i | ||||
\(92\) | 6.00701 | − | 0.795979i | 0.626274 | − | 0.0829865i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.16474 | + | 4.75300i | −0.429560 | + | 0.490235i | ||||
\(95\) | 20.3036 | 2.08310 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.87328 | 0.291738 | 0.145869 | − | 0.989304i | \(-0.453402\pi\) | ||||
0.145869 | + | 0.989304i | \(0.453402\pi\) | |||||||
\(98\) | 4.84247 | − | 5.52646i | 0.489163 | − | 0.558257i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −21.7073 | + | 2.87640i | −2.17073 | + | 0.287640i | ||||
\(101\) | −2.52589 | + | 2.52589i | −0.251335 | + | 0.251335i | −0.821518 | − | 0.570183i | \(-0.806872\pi\) |
0.570183 | + | 0.821518i | \(0.306872\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.9034 | 1.76408 | 0.882040 | − | 0.471175i | \(-0.156170\pi\) | ||||
0.882040 | + | 0.471175i | \(0.156170\pi\) | |||||||
\(104\) | −0.910206 | + | 0.182245i | −0.0892530 | + | 0.0178706i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.405634 | + | 6.14915i | 0.0393986 | + | 0.597258i | ||||
\(107\) | 2.33160 | + | 2.33160i | 0.225404 | + | 0.225404i | 0.810769 | − | 0.585366i | \(-0.199049\pi\) |
−0.585366 | + | 0.810769i | \(0.699049\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.4336 | + | 12.4336i | −1.19092 | + | 1.19092i | −0.214113 | + | 0.976809i | \(0.568686\pi\) |
−0.976809 | + | 0.214113i | \(0.931314\pi\) | |||||||
\(110\) | 5.49716 | − | 6.27364i | 0.524134 | − | 0.598168i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 13.4869 | − | 3.63813i | 1.27439 | − | 0.343771i | ||||
\(113\) | 3.34233i | 0.314420i | 0.987565 | + | 0.157210i | \(0.0502499\pi\) | ||||
−0.987565 | + | 0.157210i | \(0.949750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.55566 | − | 8.55566i | −0.797819 | − | 0.797819i | ||||
\(116\) | −7.85274 | + | 10.2517i | −0.729109 | + | 0.951850i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.05959 | + | 0.333760i | −0.465773 | + | 0.0307251i | ||||
\(119\) | − | 23.8582i | − | 2.18708i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 8.81869i | − | 0.801699i | ||||||
\(122\) | 0.741409 | + | 11.2393i | 0.0671240 | + | 1.01756i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.17301 | − | 0.420450i | 0.284944 | − | 0.0377575i | ||||
\(125\) | 16.7979 | + | 16.7979i | 1.50245 | + | 1.50245i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.33827i | 0.651166i | 0.945513 | + | 0.325583i | \(0.105561\pi\) | ||||
−0.945513 | + | 0.325583i | \(0.894439\pi\) | |||||||
\(128\) | 10.7240 | + | 3.60512i | 0.947872 | + | 0.318650i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.39409 | + | 1.22155i | 0.122270 | + | 0.107137i | ||||
\(131\) | 1.31055 | − | 1.31055i | 0.114503 | − | 0.114503i | −0.647534 | − | 0.762037i | \(-0.724199\pi\) |
0.762037 | + | 0.647534i | \(0.224199\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.5545 | + | 12.5545i | 1.08862 | + | 1.08862i | ||||
\(134\) | −9.21643 | + | 0.607970i | −0.796178 | + | 0.0525206i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.7151 | − | 16.0802i | 0.918812 | − | 1.37886i | ||||
\(137\) | −9.34212 | −0.798151 | −0.399076 | − | 0.916918i | \(-0.630669\pi\) | ||||
−0.399076 | + | 0.916918i | \(0.630669\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2794 | + | 11.2794i | −0.956704 | + | 0.956704i | −0.999101 | − | 0.0423964i | \(-0.986501\pi\) |
0.0423964 | + | 0.999101i | \(0.486501\pi\) | |||||||
\(140\) | −22.1432 | − | 16.9615i | −1.87145 | − | 1.43351i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.99798 | − | 5.25563i | −0.503339 | − | 0.441042i | ||||
\(143\) | −0.484717 | −0.0405341 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.7858 | 2.14140 | ||||||||
\(146\) | 12.0556 | + | 10.5636i | 0.997732 | + | 0.874246i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.0823713 | − | 0.107536i | 0.00677088 | − | 0.00883937i | ||||
\(149\) | −2.91548 | + | 2.91548i | −0.238845 | + | 0.238845i | −0.816372 | − | 0.577527i | \(-0.804018\pi\) |
0.577527 | + | 0.816372i | \(0.304018\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.43937 | −0.768165 | −0.384083 | − | 0.923299i | \(-0.625482\pi\) | ||||
−0.384083 | + | 0.923299i | \(0.625482\pi\) | |||||||
\(152\) | 2.82318 | + | 14.1001i | 0.228990 | + | 1.14367i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.27838 | − | 0.480124i | 0.586508 | − | 0.0386895i | ||||
\(155\) | −4.51925 | − | 4.51925i | −0.362995 | − | 0.362995i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.77607 | − | 6.77607i | 0.540789 | − | 0.540789i | −0.382971 | − | 0.923760i | \(-0.625099\pi\) |
0.923760 | + | 0.382971i | \(0.125099\pi\) | |||||||
\(158\) | 5.17456 | + | 4.53412i | 0.411666 | + | 0.360715i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.30661 | − | 21.3768i | −0.577638 | − | 1.68998i | ||||
\(161\) | − | 10.5806i | − | 0.833872i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.01118 | − | 8.01118i | −0.627484 | − | 0.627484i | 0.319950 | − | 0.947434i | \(-0.396334\pi\) |
−0.947434 | + | 0.319950i | \(0.896334\pi\) | |||||||
\(164\) | −1.50644 | − | 11.3687i | −0.117633 | − | 0.887744i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.111511 | + | 1.69044i | 0.00865496 | + | 0.131204i | ||||
\(167\) | − | 19.7351i | − | 1.52715i | −0.645720 | − | 0.763575i | \(-0.723443\pi\) | ||
0.645720 | − | 0.763575i | \(-0.276557\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8923i | 0.991715i | ||||||||
\(170\) | −38.5005 | + | 2.53972i | −2.95285 | + | 0.194787i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −18.1904 | − | 13.9337i | −1.38701 | − | 1.06243i | ||||
\(173\) | −9.69695 | − | 9.69695i | −0.737246 | − | 0.737246i | 0.234798 | − | 0.972044i | \(-0.424557\pi\) |
−0.972044 | + | 0.234798i | \(0.924557\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 38.2349i | 2.89029i | ||||||||
\(176\) | 5.12118 | + | 2.94524i | 0.386023 | + | 0.222006i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.0399 | + | 14.8818i | −0.977383 | + | 1.11544i | ||||
\(179\) | −7.48591 | + | 7.48591i | −0.559523 | + | 0.559523i | −0.929172 | − | 0.369648i | \(-0.879478\pi\) |
0.369648 | + | 0.929172i | \(0.379478\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.99423 | + | 1.99423i | 0.148230 | + | 0.148230i | 0.777327 | − | 0.629097i | \(-0.216575\pi\) |
−0.629097 | + | 0.777327i | \(0.716575\pi\) | |||||||
\(182\) | 0.106690 | + | 1.61736i | 0.00790842 | + | 0.119887i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.75194 | − | 7.13124i | 0.350318 | − | 0.525722i | ||||
\(185\) | −0.270480 | −0.0198861 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.13472 | − | 7.13472i | 0.521742 | − | 0.521742i | ||||
\(188\) | 1.17398 | + | 8.85968i | 0.0856213 | + | 0.646158i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.9231 | − | 21.5960i | 1.37283 | − | 1.56674i | ||||
\(191\) | 3.21357 | 0.232526 | 0.116263 | − | 0.993218i | \(-0.462908\pi\) | ||||
0.116263 | + | 0.993218i | \(0.462908\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.64075 | 0.478012 | 0.239006 | − | 0.971018i | \(-0.423178\pi\) | ||||
0.239006 | + | 0.971018i | \(0.423178\pi\) | |||||||
\(194\) | 2.67792 | − | 3.05618i | 0.192264 | − | 0.219421i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.36502 | − | 10.3014i | −0.0975017 | − | 0.735816i | ||||
\(197\) | 16.0021 | − | 16.0021i | 1.14011 | − | 1.14011i | 0.151675 | − | 0.988430i | \(-0.451533\pi\) |
0.988430 | − | 0.151675i | \(-0.0484668\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.64621 | −0.542025 | −0.271013 | − | 0.962576i | \(-0.587359\pi\) | ||||
−0.271013 | + | 0.962576i | \(0.587359\pi\) | |||||||
\(200\) | −17.1719 | + | 25.7699i | −1.21424 | + | 1.82221i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.332522 | + | 5.04082i | 0.0233962 | + | 0.354671i | ||||
\(203\) | 15.9445 | + | 15.9445i | 1.11908 | + | 1.11908i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −16.1922 | + | 16.1922i | −1.13091 | + | 1.13091i | ||||
\(206\) | 16.6862 | − | 19.0431i | 1.16258 | − | 1.32679i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.654473 | + | 1.13800i | −0.0453796 | + | 0.0789060i | ||||
\(209\) | 7.50879i | 0.519394i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.6941 | + | 11.6941i | 0.805055 | + | 0.805055i | 0.983881 | − | 0.178825i | \(-0.0572297\pi\) |
−0.178825 | + | 0.983881i | \(0.557230\pi\) | |||||||
\(212\) | 6.91862 | + | 5.29960i | 0.475173 | + | 0.363978i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.65308 | − | 0.306944i | 0.318078 | − | 0.0209823i | ||||
\(215\) | 45.7537i | 3.12038i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.58888i | − | 0.379398i | ||||||
\(218\) | 1.63683 | + | 24.8133i | 0.110860 | + | 1.68057i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.54957 | − | 11.6942i | −0.104472 | − | 0.788420i | ||||
\(221\) | 1.58543 | + | 1.58543i | 0.106648 | + | 0.106648i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.1836i | 0.748909i | 0.927245 | + | 0.374454i | \(0.122170\pi\) | ||||
−0.927245 | + | 0.374454i | \(0.877830\pi\) | |||||||
\(224\) | 8.70017 | − | 17.7361i | 0.581305 | − | 1.18505i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.55508 | + | 3.11508i | 0.236481 | + | 0.207212i | ||||
\(227\) | −16.2484 | + | 16.2484i | −1.07844 | + | 1.07844i | −0.0817944 | + | 0.996649i | \(0.526065\pi\) |
−0.996649 | + | 0.0817944i | \(0.973935\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.86904 | + | 8.86904i | 0.586083 | + | 0.586083i | 0.936568 | − | 0.350485i | \(-0.113983\pi\) |
−0.350485 | + | 0.936568i | \(0.613983\pi\) | |||||||
\(230\) | −17.0742 | + | 1.12631i | −1.12584 | + | 0.0742670i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.58548 | + | 17.9073i | 0.235398 | + | 1.17567i | ||||
\(233\) | −1.62473 | −0.106440 | −0.0532199 | − | 0.998583i | \(-0.516948\pi\) | ||||
−0.0532199 | + | 0.998583i | \(0.516948\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.6187 | − | 12.6187i | 0.823150 | − | 0.823150i | ||||
\(236\) | −4.36058 | + | 5.69272i | −0.283849 | + | 0.370565i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −25.3769 | − | 22.2360i | −1.64494 | − | 1.44135i | ||||
\(239\) | −23.4506 | −1.51690 | −0.758448 | − | 0.651734i | \(-0.774042\pi\) | ||||
−0.758448 | + | 0.651734i | \(0.774042\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.3544 | 1.43998 | 0.719988 | − | 0.693986i | \(-0.244147\pi\) | ||||
0.719988 | + | 0.693986i | \(0.244147\pi\) | |||||||
\(242\) | −9.38004 | − | 8.21910i | −0.602972 | − | 0.528344i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6457 | + | 9.68651i | 0.809559 | + | 0.620115i | ||||
\(245\) | −14.6721 | + | 14.6721i | −0.937366 | + | 0.937366i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.66856 | −0.106168 | ||||||||
\(248\) | 2.51006 | − | 3.76684i | 0.159389 | − | 0.239195i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 33.5230 | − | 2.21137i | 2.12018 | − | 0.139860i | ||||
\(251\) | −7.46789 | − | 7.46789i | −0.471369 | − | 0.471369i | 0.430988 | − | 0.902357i | \(-0.358165\pi\) |
−0.902357 | + | 0.430988i | \(0.858165\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.16411 | − | 3.16411i | 0.198926 | − | 0.198926i | ||||
\(254\) | 7.80538 | + | 6.83933i | 0.489753 | + | 0.429138i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 13.8294 | − | 8.04658i | 0.864338 | − | 0.502911i | ||||
\(257\) | 7.42519i | 0.463171i | 0.972815 | + | 0.231585i | \(0.0743913\pi\) | ||||
−0.972815 | + | 0.231585i | \(0.925609\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.167249 | − | 0.167249i | −0.0103924 | − | 0.0103924i | ||||
\(260\) | 2.59861 | − | 0.344337i | 0.161159 | − | 0.0213549i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.172528 | − | 2.61541i | −0.0106588 | − | 0.161581i | ||||
\(263\) | 3.59594i | 0.221735i | 0.993835 | + | 0.110868i | \(0.0353629\pi\) | ||||
−0.993835 | + | 0.110868i | \(0.964637\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 17.4022i | − | 1.06901i | ||||||
\(266\) | 25.0546 | − | 1.65275i | 1.53620 | − | 0.101337i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.94312 | + | 10.3697i | −0.485203 | + | 0.633432i | ||||
\(269\) | −0.0462496 | − | 0.0462496i | −0.00281989 | − | 0.00281989i | 0.705695 | − | 0.708515i | \(-0.250635\pi\) |
−0.708515 | + | 0.705695i | \(0.750635\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 20.4615i | − | 1.24294i | −0.783436 | − | 0.621472i | \(-0.786535\pi\) | ||
0.783436 | − | 0.621472i | \(-0.213465\pi\) | |||||||
\(272\) | −7.11717 | − | 26.3840i | −0.431542 | − | 1.59977i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.70693 | + | 9.93678i | −0.526005 | + | 0.600303i | ||||
\(275\) | −11.4340 | + | 11.4340i | −0.689498 | + | 0.689498i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.75384 | − | 6.75384i | −0.405799 | − | 0.405799i | 0.474472 | − | 0.880271i | \(-0.342639\pi\) |
−0.880271 | + | 0.474472i | \(0.842639\pi\) | |||||||
\(278\) | 1.48488 | + | 22.5098i | 0.0890572 | + | 1.35005i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −38.6789 | + | 7.74445i | −2.31151 | + | 0.462820i | ||||
\(281\) | 16.1522 | 0.963558 | 0.481779 | − | 0.876293i | \(-0.339991\pi\) | ||||
0.481779 | + | 0.876293i | \(0.339991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.06204 | − | 2.06204i | 0.122575 | − | 0.122575i | −0.643158 | − | 0.765733i | \(-0.722376\pi\) |
0.765733 | + | 0.643158i | \(0.222376\pi\) | |||||||
\(284\) | −11.1803 | + | 1.48149i | −0.663431 | + | 0.0879101i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.451760 | + | 0.515571i | −0.0267132 | + | 0.0304864i | ||||
\(287\) | −20.0246 | −1.18201 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6731 | −1.74548 | ||||||||
\(290\) | 24.0326 | − | 27.4272i | 1.41124 | − | 1.61058i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.4719 | − | 2.97772i | 1.31507 | − | 0.174258i | ||||
\(293\) | 9.16203 | − | 9.16203i | 0.535251 | − | 0.535251i | −0.386879 | − | 0.922130i | \(-0.626447\pi\) |
0.922130 | + | 0.386879i | \(0.126447\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3187 | 0.833667 | ||||||||
\(296\) | −0.0376099 | − | 0.187839i | −0.00218603 | − | 0.0109179i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.383810 | + | 5.81831i | 0.0222335 | + | 0.337045i | ||||
\(299\) | 0.703110 | + | 0.703110i | 0.0406619 | + | 0.0406619i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.2914 | + | 28.2914i | −1.63069 | + | 1.63069i | ||||
\(302\) | −8.79758 | + | 10.0402i | −0.506244 | + | 0.577750i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.6288 | + | 10.1385i | 1.01108 | + | 0.581483i | ||||
\(305\) | − | 31.8073i | − | 1.82128i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.2013 | − | 18.2013i | −1.03880 | − | 1.03880i | −0.999216 | − | 0.0395861i | \(-0.987396\pi\) |
−0.0395861 | − | 0.999216i | \(-0.512604\pi\) | |||||||
\(308\) | 6.27282 | − | 8.18915i | 0.357427 | − | 0.466620i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.01889 | + | 0.594939i | −0.512239 | + | 0.0337902i | ||||
\(311\) | 17.7227i | 1.00496i | 0.864589 | + | 0.502480i | \(0.167579\pi\) | ||||
−0.864589 | + | 0.502480i | \(0.832421\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.370162i | 0.0209228i | 0.999945 | + | 0.0104614i | \(0.00333003\pi\) | ||||
−0.999945 | + | 0.0104614i | \(0.996670\pi\) | |||||||
\(314\) | −0.892040 | − | 13.5228i | −0.0503407 | − | 0.763133i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.64548 | − | 1.27811i | 0.542600 | − | 0.0718991i | ||||
\(317\) | −3.06429 | − | 3.06429i | −0.172108 | − | 0.172108i | 0.615797 | − | 0.787905i | \(-0.288834\pi\) |
−0.787905 | + | 0.615797i | \(0.788834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.53628i | 0.533929i | ||||||||
\(320\) | −29.5473 | − | 12.1516i | −1.65175 | − | 0.679297i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.2541 | − | 9.86125i | −0.627169 | − | 0.549546i | ||||
\(323\) | 24.5601 | − | 24.5601i | 1.36656 | − | 1.36656i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.54080 | − | 2.54080i | −0.140938 | − | 0.140938i | ||||
\(326\) | −15.9876 | + | 1.05464i | −0.885472 | + | 0.0584109i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −13.4964 | − | 8.99337i | −0.745212 | − | 0.496576i | ||||
\(329\) | 15.6053 | 0.860347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.48964 | + | 8.48964i | −0.466633 | + | 0.466633i | −0.900822 | − | 0.434189i | \(-0.857035\pi\) |
0.434189 | + | 0.900822i | \(0.357035\pi\) | |||||||
\(332\) | 1.90197 | + | 1.45690i | 0.104384 | + | 0.0799575i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.9913 | − | 18.3933i | −1.14859 | − | 1.00644i | ||||
\(335\) | 26.0826 | 1.42505 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.7714 | −0.641230 | −0.320615 | − | 0.947210i | \(-0.603890\pi\) | ||||
−0.320615 | + | 0.947210i | \(0.603890\pi\) | |||||||
\(338\) | 13.7129 | + | 12.0157i | 0.745885 | + | 0.653569i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −33.1814 | + | 43.3182i | −1.79951 | + | 2.34926i | ||||
\(341\) | 1.67134 | − | 1.67134i | 0.0905079 | − | 0.0905079i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.30093 | 0.340218 | ||||||||
\(344\) | −31.7743 | + | 6.36198i | −1.71315 | + | 0.343015i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.3518 | + | 1.27656i | −1.04036 | + | 0.0686283i | ||||
\(347\) | −8.81089 | − | 8.81089i | −0.472994 | − | 0.472994i | 0.429888 | − | 0.902882i | \(-0.358553\pi\) |
−0.902882 | + | 0.429888i | \(0.858553\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.43832 | − | 9.43832i | 0.505222 | − | 0.505222i | −0.407834 | − | 0.913056i | \(-0.633716\pi\) |
0.913056 | + | 0.407834i | \(0.133716\pi\) | |||||||
\(350\) | 40.6687 | + | 35.6353i | 2.17383 | + | 1.90479i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.90570 | − | 2.70218i | 0.421375 | − | 0.144026i | ||||
\(353\) | − | 13.1519i | − | 0.700007i | −0.936748 | − | 0.350004i | \(-0.886180\pi\) | ||
0.936748 | − | 0.350004i | \(-0.113820\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.9239 | + | 15.9239i | 0.845154 | + | 0.845154i | ||||
\(356\) | 3.67577 | + | 27.7399i | 0.194815 | + | 1.47021i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.985487 | + | 14.9394i | 0.0520846 | + | 0.789570i | ||||
\(359\) | 17.2661i | 0.911269i | 0.890167 | + | 0.455634i | \(0.150588\pi\) | ||||
−0.890167 | + | 0.455634i | \(0.849412\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.84780i | 0.360411i | ||||||||
\(362\) | 3.97981 | − | 0.262532i | 0.209174 | − | 0.0137984i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.81975 | + | 1.39391i | 0.0953806 | + | 0.0730607i | ||||
\(365\) | −32.0063 | − | 32.0063i | −1.67529 | − | 1.67529i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10.5034i | − | 0.548272i | −0.961691 | − | 0.274136i | \(-0.911608\pi\) | ||
0.961691 | − | 0.274136i | \(-0.0883919\pi\) | |||||||
\(368\) | −3.15633 | − | 11.7008i | −0.164535 | − | 0.609946i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.252090 | + | 0.287698i | −0.0131055 | + | 0.0149567i | ||||
\(371\) | 10.7605 | − | 10.7605i | 0.558656 | − | 0.558656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.07410 | − | 8.07410i | −0.418061 | − | 0.418061i | 0.466474 | − | 0.884535i | \(-0.345524\pi\) |
−0.884535 | + | 0.466474i | \(0.845524\pi\) | |||||||
\(374\) | −0.939254 | − | 14.2385i | −0.0485677 | − | 0.736255i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 10.5178 | + | 7.00858i | 0.542414 | + | 0.361440i | ||||
\(377\) | −2.11910 | −0.109139 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.2056 | − | 15.2056i | 0.781061 | − | 0.781061i | −0.198949 | − | 0.980010i | \(-0.563753\pi\) |
0.980010 | + | 0.198949i | \(0.0637528\pi\) | |||||||
\(380\) | −5.33416 | − | 40.2553i | −0.273636 | − | 2.06505i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.99507 | − | 3.41813i | 0.153241 | − | 0.174887i | ||||
\(383\) | −4.56566 | −0.233295 | −0.116647 | − | 0.993173i | \(-0.537215\pi\) | ||||
−0.116647 | + | 0.993173i | \(0.537215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.5979 | −1.04977 | ||||||||
\(386\) | 6.18924 | − | 7.06347i | 0.315024 | − | 0.359521i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.754869 | − | 5.69677i | −0.0383227 | − | 0.289210i | ||||
\(389\) | 19.8480 | − | 19.8480i | 1.00633 | − | 1.00633i | 0.00635288 | − | 0.999980i | \(-0.497978\pi\) |
0.999980 | − | 0.00635288i | \(-0.00202220\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −20.6986 | −1.04677 | ||||||||
\(392\) | −12.2294 | − | 8.14910i | −0.617676 | − | 0.411592i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.10661 | − | 31.9349i | −0.106130 | − | 1.60886i | ||||
\(395\) | −13.7379 | − | 13.7379i | −0.691226 | − | 0.691226i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.43072 | − | 3.43072i | 0.172183 | − | 0.172183i | −0.615755 | − | 0.787938i | \(-0.711149\pi\) |
0.787938 | + | 0.615755i | \(0.211149\pi\) | |||||||
\(398\) | −7.12633 | + | 8.13292i | −0.357211 | + | 0.407666i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 11.4059 | + | 42.2828i | 0.570295 | + | 2.11414i | ||||
\(401\) | 27.7827i | 1.38740i | 0.720263 | + | 0.693701i | \(0.244021\pi\) | ||||
−0.720263 | + | 0.693701i | \(0.755979\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.371394 | + | 0.371394i | 0.0185005 | + | 0.0185005i | ||||
\(404\) | 5.67160 | + | 4.34440i | 0.282173 | + | 0.216142i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 31.8198 | − | 2.09902i | 1.57919 | − | 0.104173i | ||||
\(407\) | − | 0.100031i | − | 0.00495834i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 15.4360i | − | 0.763259i | −0.924315 | − | 0.381629i | \(-0.875363\pi\) | ||
0.924315 | − | 0.381629i | \(-0.124637\pi\) | |||||||
\(410\) | 2.13163 | + | 32.3141i | 0.105274 | + | 1.59588i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.70360 | − | 35.4966i | −0.231730 | − | 1.74879i | ||||
\(413\) | 8.85385 | + | 8.85385i | 0.435669 | + | 0.435669i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 4.78397i | − | 0.234836i | ||||||
\(416\) | 0.600462 | + | 1.75676i | 0.0294400 | + | 0.0861321i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.98676 | + | 6.99826i | 0.390645 | + | 0.342296i | ||||
\(419\) | 3.80731 | − | 3.80731i | 0.186000 | − | 0.186000i | −0.607965 | − | 0.793964i | \(-0.708014\pi\) |
0.793964 | + | 0.607965i | \(0.208014\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −21.9222 | − | 21.9222i | −1.06842 | − | 1.06842i | −0.997480 | − | 0.0709444i | \(-0.977399\pi\) |
−0.0709444 | − | 0.997480i | \(-0.522601\pi\) | |||||||
\(422\) | 23.3375 | − | 1.53948i | 1.13605 | − | 0.0749406i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.0852 | − | 2.41974i | 0.586907 | − | 0.117513i | ||||
\(425\) | 74.7980 | 3.62823 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 19.6678 | − | 19.6678i | 0.951791 | − | 0.951791i | ||||
\(428\) | 4.01023 | − | 5.23534i | 0.193842 | − | 0.253060i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.6661 | + | 42.6429i | 2.34689 | + | 2.05642i | ||||
\(431\) | −13.7104 | −0.660409 | −0.330204 | − | 0.943909i | \(-0.607118\pi\) | ||||
−0.330204 | + | 0.943909i | \(0.607118\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.9638 | 1.39191 | 0.695956 | − | 0.718085i | \(-0.254981\pi\) | ||||
0.695956 | + | 0.718085i | \(0.254981\pi\) | |||||||
\(434\) | −5.94463 | − | 5.20888i | −0.285351 | − | 0.250034i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 27.9183 | + | 21.3851i | 1.33704 | + | 1.02416i | ||||
\(437\) | 10.8919 | − | 10.8919i | 0.521032 | − | 0.521032i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.5288 | 1.40933 | 0.704666 | − | 0.709539i | \(-0.251097\pi\) | ||||
0.704666 | + | 0.709539i | \(0.251097\pi\) | |||||||
\(440\) | −13.8828 | − | 9.25085i | −0.661835 | − | 0.441017i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.16399 | − | 0.208716i | 0.150496 | − | 0.00992758i | ||||
\(443\) | 24.5661 | + | 24.5661i | 1.16717 | + | 1.16717i | 0.982870 | + | 0.184303i | \(0.0590026\pi\) |
0.184303 | + | 0.982870i | \(0.440997\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 39.5094 | − | 39.5094i | 1.87293 | − | 1.87293i | ||||
\(446\) | 11.8955 | + | 10.4232i | 0.563267 | + | 0.493553i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.7565 | − | 25.7842i | −0.508196 | − | 1.21819i | ||||
\(449\) | − | 17.2682i | − | 0.814938i | −0.913219 | − | 0.407469i | \(-0.866411\pi\) | ||
0.913219 | − | 0.407469i | \(-0.133589\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.98829 | − | 5.98829i | −0.281978 | − | 0.281978i | ||||
\(452\) | 6.62674 | − | 0.878098i | 0.311695 | − | 0.0413022i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.13903 | + | 32.4263i | 0.100390 | + | 1.52184i | ||||
\(455\) | − | 4.57714i | − | 0.214580i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.6182i | 1.43226i | 0.697968 | + | 0.716129i | \(0.254088\pi\) | ||||
−0.697968 | + | 0.716129i | \(0.745912\pi\) | |||||||
\(458\) | 17.6996 | − | 1.16757i | 0.827049 | − | 0.0545570i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.7153 | + | 19.2108i | −0.686104 | + | 0.895708i | ||||
\(461\) | −17.6631 | − | 17.6631i | −0.822654 | − | 0.822654i | 0.163834 | − | 0.986488i | \(-0.447614\pi\) |
−0.986488 | + | 0.163834i | \(0.947614\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 34.1440i | − | 1.58680i | −0.608697 | − | 0.793402i | \(-0.708308\pi\) | ||
0.608697 | − | 0.793402i | \(-0.291692\pi\) | |||||||
\(464\) | 22.3889 | + | 12.8761i | 1.03938 | + | 0.597756i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.51426 | + | 1.72815i | −0.0701470 | + | 0.0800552i | ||||
\(467\) | 12.8687 | − | 12.8687i | 0.595492 | − | 0.595492i | −0.343618 | − | 0.939110i | \(-0.611652\pi\) |
0.939110 | + | 0.343618i | \(0.111652\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.1280 | + | 16.1280i | 0.744720 | + | 0.744720i | ||||
\(470\) | −1.66119 | − | 25.1826i | −0.0766250 | − | 1.16159i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.99099 | + | 9.94381i | 0.0916429 | + | 0.457701i | ||||
\(473\) | −16.9209 | −0.778025 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −39.3598 | + | 39.3598i | −1.80595 | + | 1.80595i | ||||
\(476\) | −47.3029 | + | 6.26803i | −2.16813 | + | 0.287295i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −21.8562 | + | 24.9434i | −0.999679 | + | 1.14088i | ||||
\(479\) | −27.7604 | −1.26841 | −0.634204 | − | 0.773166i | \(-0.718672\pi\) | ||||
−0.634204 | + | 0.773166i | \(0.718672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.0222283 | 0.00101352 | ||||||||
\(482\) | 20.8345 | − | 23.7774i | 0.948987 | − | 1.08303i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.4846 | + | 2.31685i | −0.794752 | + | 0.105311i | ||||
\(485\) | −8.11379 | + | 8.11379i | −0.368428 | + | 0.368428i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.7274 | −0.848620 | −0.424310 | − | 0.905517i | \(-0.639483\pi\) | ||||
−0.424310 | + | 0.905517i | \(0.639483\pi\) | |||||||
\(488\) | 22.0890 | − | 4.42276i | 0.999922 | − | 0.200209i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.93152 | + | 29.2806i | 0.0872571 | + | 1.32276i | ||||
\(491\) | 13.1322 | + | 13.1322i | 0.592650 | + | 0.592650i | 0.938346 | − | 0.345696i | \(-0.112357\pi\) |
−0.345696 | + | 0.938346i | \(0.612357\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.1917 | − | 31.1917i | 1.40480 | − | 1.40480i | ||||
\(494\) | −1.55511 | + | 1.77477i | −0.0699678 | + | 0.0798507i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.66723 | − | 6.18056i | −0.0748606 | − | 0.277515i | ||||
\(497\) | 19.6929i | 0.883345i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.7298 | − | 21.7298i | −0.972762 | − | 0.972762i | 0.0268772 | − | 0.999639i | \(-0.491444\pi\) |
−0.999639 | + | 0.0268772i | \(0.991444\pi\) | |||||||
\(500\) | 28.8916 | − | 37.7179i | 1.29207 | − | 1.68680i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −14.9034 | + | 0.983115i | −0.665171 | + | 0.0438786i | ||||
\(503\) | 4.25454i | 0.189701i | 0.995492 | + | 0.0948504i | \(0.0302373\pi\) | ||||
−0.995492 | + | 0.0948504i | \(0.969763\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 14.2656i | − | 0.634810i | ||||||
\(506\) | −0.416541 | − | 6.31449i | −0.0185175 | − | 0.280714i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.5494 | − | 1.92791i | 0.645524 | − | 0.0855373i | ||||
\(509\) | −6.41057 | − | 6.41057i | −0.284144 | − | 0.284144i | 0.550615 | − | 0.834759i | \(-0.314393\pi\) |
−0.834759 | + | 0.550615i | \(0.814393\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 39.5817i | − | 1.75099i | ||||||
\(512\) | 4.33036 | − | 22.2092i | 0.191377 | − | 0.981517i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.89784 | + | 6.92034i | 0.348359 | + | 0.305243i | ||||
\(515\) | −50.5571 | + | 50.5571i | −2.22781 | + | 2.22781i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.66671 | + | 4.66671i | 0.205242 | + | 0.205242i | ||||
\(518\) | −0.333773 | + | 0.0220176i | −0.0146652 | + | 0.000967399i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.05567 | − | 3.08494i | 0.0901470 | − | 0.135284i | ||||
\(521\) | −39.1263 | −1.71415 | −0.857077 | − | 0.515188i | \(-0.827722\pi\) | ||||
−0.857077 | + | 0.515188i | \(0.827722\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.3283 | + | 29.3283i | −1.28244 | + | 1.28244i | −0.343159 | + | 0.939277i | \(0.611497\pi\) |
−0.939277 | + | 0.343159i | \(0.888503\pi\) | |||||||
\(524\) | −2.94269 | − | 2.25408i | −0.128552 | − | 0.0984698i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.82484 | + | 3.35145i | 0.166771 | + | 0.146130i | ||||
\(527\) | −10.9334 | −0.476265 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.8206 | 0.600894 | ||||||||
\(530\) | −18.5099 | − | 16.2190i | −0.804018 | − | 0.704507i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 21.5932 | − | 28.1898i | 0.936183 | − | 1.22218i | ||||
\(533\) | 1.33068 | − | 1.33068i | 0.0576382 | − | 0.0576382i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.1683 | −0.569314 | ||||||||
\(536\) | 3.62675 | + | 18.1134i | 0.156652 | + | 0.782380i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.0922986 | + | 0.00608856i | −0.00397928 | + | 0.000262496i | ||||
\(539\) | −5.42613 | − | 5.42613i | −0.233720 | − | 0.233720i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5493 | + | 15.5493i | −0.668517 | + | 0.668517i | −0.957373 | − | 0.288856i | \(-0.906725\pi\) |
0.288856 | + | 0.957373i | \(0.406725\pi\) | |||||||
\(542\) | −21.7639 | − | 19.0702i | −0.934840 | − | 0.819137i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −34.6967 | − | 17.0199i | −1.48761 | − | 0.729723i | ||||
\(545\) | − | 70.2218i | − | 3.00797i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.0243 | − | 17.0243i | −0.727908 | − | 0.727908i | 0.242294 | − | 0.970203i | \(-0.422100\pi\) |
−0.970203 | + | 0.242294i | \(0.922100\pi\) | |||||||
\(548\) | 2.45436 | + | 18.5223i | 0.104845 | + | 0.791235i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.50524 | + | 22.8185i | 0.0641837 | + | 0.972983i | ||||
\(551\) | 32.8271i | 1.39848i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 16.9894i | − | 0.722462i | ||||||
\(554\) | −13.4784 | + | 0.889114i | −0.572642 | + | 0.0377748i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 25.3266 | + | 19.4000i | 1.07409 | + | 0.822742i | ||||
\(557\) | 31.8390 | + | 31.8390i | 1.34906 | + | 1.34906i | 0.886683 | + | 0.462378i | \(0.153004\pi\) |
0.462378 | + | 0.886683i | \(0.346996\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3.76007i | − | 0.159034i | ||||||
\(560\) | −27.8116 | + | 48.3589i | −1.17526 | + | 2.04353i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.0540 | − | 17.1803i | 0.635013 | − | 0.724709i | ||||
\(563\) | −31.4611 | + | 31.4611i | −1.32593 | + | 1.32593i | −0.417039 | + | 0.908889i | \(0.636932\pi\) |
−0.908889 | + | 0.417039i | \(0.863068\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.43832 | − | 9.43832i | −0.397073 | − | 0.397073i | ||||
\(566\) | −0.271458 | − | 4.11513i | −0.0114102 | − | 0.172972i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.84438 | + | 13.2728i | −0.371102 | + | 0.556913i | ||||
\(569\) | −29.9445 | −1.25534 | −0.627668 | − | 0.778481i | \(-0.715991\pi\) | ||||
−0.627668 | + | 0.778481i | \(0.715991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.15810 | + | 5.15810i | −0.215860 | + | 0.215860i | −0.806751 | − | 0.590891i | \(-0.798776\pi\) |
0.590891 | + | 0.806751i | \(0.298776\pi\) | |||||||
\(572\) | 0.127345 | + | 0.961034i | 0.00532456 | + | 0.0401828i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −18.6631 | + | 21.2992i | −0.778982 | + | 0.889013i | ||||
\(575\) | 33.1714 | 1.38334 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.1629 | −0.922653 | −0.461326 | − | 0.887230i | \(-0.652626\pi\) | ||||
−0.461326 | + | 0.887230i | \(0.652626\pi\) | |||||||
\(578\) | −27.6556 | + | 31.5620i | −1.15032 | + | 1.31280i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.77446 | − | 51.1248i | −0.281294 | − | 2.12284i | ||||
\(581\) | 2.95813 | − | 2.95813i | 0.122724 | − | 0.122724i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.43578 | 0.266543 | ||||||||
\(584\) | 17.7768 | − | 26.6776i | 0.735608 | − | 1.10393i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.20614 | − | 18.2843i | −0.0498252 | − | 0.755318i | ||||
\(587\) | −5.63868 | − | 5.63868i | −0.232733 | − | 0.232733i | 0.581099 | − | 0.813833i | \(-0.302623\pi\) |
−0.813833 | + | 0.581099i | \(0.802623\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.75330 | − | 5.75330i | 0.237061 | − | 0.237061i | ||||
\(590\) | 13.3452 | − | 15.2301i | 0.549411 | − | 0.627015i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.234848 | − | 0.135063i | −0.00965220 | − | 0.00555107i | ||||
\(593\) | 32.1028i | 1.31830i | 0.752011 | + | 0.659151i | \(0.229084\pi\) | ||||
−0.752011 | + | 0.659151i | \(0.770916\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 67.3726 | + | 67.3726i | 2.76201 | + | 2.76201i | ||||
\(596\) | 6.54638 | + | 5.01447i | 0.268150 | + | 0.205401i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.40317 | − | 0.0925613i | 0.0573799 | − | 0.00378511i | ||||
\(599\) | − | 36.1364i | − | 1.47649i | −0.674530 | − | 0.738247i | \(-0.735654\pi\) | ||
0.674530 | − | 0.738247i | \(-0.264346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.7508i | 0.601699i | 0.953672 | + | 0.300850i | \(0.0972703\pi\) | ||||
−0.953672 | + | 0.300850i | \(0.902730\pi\) | |||||||
\(602\) | 3.72444 | + | 56.4601i | 0.151797 | + | 2.30114i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.47991 | + | 18.7152i | 0.100906 | + | 0.761509i | ||||
\(605\) | 24.9029 | + | 24.9029i | 1.01245 | + | 1.01245i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.70271i | 0.272054i | 0.990705 | + | 0.136027i | \(0.0434335\pi\) | ||||
−0.990705 | + | 0.136027i | \(0.956567\pi\) | |||||||
\(608\) | 27.2141 | − | 9.30180i | 1.10368 | − | 0.377238i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −33.8320 | − | 29.6447i | −1.36982 | − | 1.20028i | ||||
\(611\) | −1.03701 | + | 1.03701i | −0.0419529 | + | 0.0419529i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.5746 | + | 13.5746i | 0.548273 | + | 0.548273i | 0.925941 | − | 0.377668i | \(-0.123274\pi\) |
−0.377668 | + | 0.925941i | \(0.623274\pi\) | |||||||
\(614\) | −36.3236 | + | 2.39612i | −1.46590 | + | 0.0966995i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.86410 | − | 14.3045i | −0.115398 | − | 0.576344i | ||||
\(617\) | 29.4666 | 1.18628 | 0.593141 | − | 0.805099i | \(-0.297888\pi\) | ||||
0.593141 | + | 0.805099i | \(0.297888\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.12555 | − | 8.12555i | 0.326593 | − | 0.326593i | −0.524696 | − | 0.851290i | \(-0.675821\pi\) |
0.851290 | + | 0.524696i | \(0.175821\pi\) | |||||||
\(620\) | −7.77287 | + | 10.1475i | −0.312166 | + | 0.407532i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.8508 | + | 16.5177i | 0.755848 | + | 0.662299i | ||||
\(623\) | 48.8606 | 1.95756 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −40.1278 | −1.60511 | ||||||||
\(626\) | 0.393725 | + | 0.344995i | 0.0157364 | + | 0.0137888i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.2149 | − | 11.6545i | −0.607141 | − | 0.465065i | ||||
\(629\) | −0.327185 | + | 0.327185i | −0.0130457 | + | 0.0130457i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.5182 | −0.816816 | −0.408408 | − | 0.912800i | \(-0.633916\pi\) | ||||
−0.408408 | + | 0.912800i | \(0.633916\pi\) | |||||||
\(632\) | 7.63020 | − | 11.4507i | 0.303513 | − | 0.455483i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.11529 | + | 0.403400i | −0.242869 | + | 0.0160211i | ||||
\(635\) | −20.7224 | − | 20.7224i | −0.822342 | − | 0.822342i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.20576 | − | 1.20576i | 0.0477741 | − | 0.0477741i | ||||
\(638\) | 10.1433 | + | 8.88790i | 0.401577 | + | 0.351875i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −40.4635 | + | 20.1027i | −1.59946 | + | 0.794629i | ||||
\(641\) | 0.543078i | 0.0214503i | 0.999942 | + | 0.0107251i | \(0.00341398\pi\) | ||||
−0.999942 | + | 0.0107251i | \(0.996586\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.7586 | + | 18.7586i | 0.739768 | + | 0.739768i | 0.972533 | − | 0.232765i | \(-0.0747772\pi\) |
−0.232765 | + | 0.972533i | \(0.574777\pi\) | |||||||
\(644\) | −20.9779 | + | 2.77975i | −0.826646 | + | 0.109537i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.23323 | − | 49.0137i | −0.127210 | − | 1.92842i | ||||
\(647\) | − | 12.4062i | − | 0.487739i | −0.969808 | − | 0.243870i | \(-0.921583\pi\) | ||
0.969808 | − | 0.243870i | \(-0.0784169\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.29543i | 0.207864i | ||||||||
\(650\) | −5.07059 | + | 0.334486i | −0.198885 | + | 0.0131196i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −13.7788 | + | 17.9882i | −0.539620 | + | 0.704473i | ||||
\(653\) | 15.5300 | + | 15.5300i | 0.607734 | + | 0.607734i | 0.942353 | − | 0.334619i | \(-0.108608\pi\) |
−0.334619 | + | 0.942353i | \(0.608608\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.40165i | 0.289206i | ||||||||
\(656\) | −22.1445 | + | 5.97356i | −0.864599 | + | 0.233228i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 14.5443 | − | 16.5986i | 0.566994 | − | 0.647081i | ||||
\(659\) | 8.80210 | − | 8.80210i | 0.342881 | − | 0.342881i | −0.514568 | − | 0.857449i | \(-0.672048\pi\) |
0.857449 | + | 0.514568i | \(0.172048\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.6925 | + | 11.6925i | 0.454786 | + | 0.454786i | 0.896939 | − | 0.442153i | \(-0.145785\pi\) |
−0.442153 | + | 0.896939i | \(0.645785\pi\) | |||||||
\(662\) | 1.11762 | + | 16.9425i | 0.0434377 | + | 0.658487i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.32229 | − | 0.665203i | 0.128930 | − | 0.0258149i | ||||
\(665\) | −70.9049 | −2.74957 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 13.8329 | − | 13.8329i | 0.535613 | − | 0.535613i | ||||
\(668\) | −39.1282 | + | 5.18481i | −1.51392 | + | 0.200606i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.3092 | − | 27.7429i | 0.939147 | − | 1.07180i | ||||
\(671\) | 11.7632 | 0.454113 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.5944 | −0.562571 | −0.281286 | − | 0.959624i | \(-0.590761\pi\) | ||||
−0.281286 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(674\) | −10.9711 | + | 12.5207i | −0.422589 | + | 0.482280i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.5611 | − | 3.38706i | 0.983121 | − | 0.130272i | ||||
\(677\) | 2.61762 | − | 2.61762i | 0.100603 | − | 0.100603i | −0.655014 | − | 0.755617i | \(-0.727337\pi\) |
0.755617 | + | 0.655014i | \(0.227337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0342 | −0.385077 | ||||||||
\(680\) | 15.1503 | + | 75.6665i | 0.580986 | + | 2.90168i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.220024 | − | 3.33542i | −0.00842516 | − | 0.127720i | ||||
\(683\) | 1.82014 | + | 1.82014i | 0.0696456 | + | 0.0696456i | 0.741072 | − | 0.671426i | \(-0.234318\pi\) |
−0.671426 | + | 0.741072i | \(0.734318\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.3810 | − | 26.3810i | 1.00797 | − | 1.00797i | ||||
\(686\) | 5.87252 | − | 6.70201i | 0.224214 | − | 0.255884i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −22.8469 | + | 39.7262i | −0.871031 | + | 1.51455i | ||||
\(689\) | 1.43012i | 0.0544832i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.06909 | + | 1.06909i | 0.0406700 | + | 0.0406700i | 0.727149 | − | 0.686479i | \(-0.240845\pi\) |
−0.686479 | + | 0.727149i | \(0.740845\pi\) | |||||||
\(692\) | −16.6783 | + | 21.7734i | −0.634013 | + | 0.827702i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.5836 | + | 1.15992i | −0.667463 | + | 0.0440298i | ||||
\(695\) | − | 63.7031i | − | 2.41640i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.1736i | 1.48380i | ||||||||
\(698\) | −1.24251 | − | 18.8357i | −0.0470298 | − | 0.712942i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 75.8072 | − | 10.0451i | 2.86524 | − | 0.379668i | ||||
\(701\) | 9.02410 | + | 9.02410i | 0.340835 | + | 0.340835i | 0.856681 | − | 0.515846i | \(-0.172522\pi\) |
−0.515846 | + | 0.856681i | \(0.672522\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.344340i | − | 0.0129870i | ||||||
\(704\) | 4.49400 | − | 10.9274i | 0.169374 | − | 0.411841i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.9891 | − | 12.2577i | −0.526487 | − | 0.461326i | ||||
\(707\) | 8.82100 | − | 8.82100i | 0.331748 | − | 0.331748i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0427 | + | 18.0427i | 0.677609 | + | 0.677609i | 0.959459 | − | 0.281850i | \(-0.0909480\pi\) |
−0.281850 | + | 0.959459i | \(0.590948\pi\) | |||||||
\(710\) | 31.7788 | − | 2.09631i | 1.19264 | − | 0.0786733i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 32.9315 | + | 21.9441i | 1.23416 | + | 0.822390i | ||||
\(713\) | −4.84874 | −0.181587 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.36878 | − | 1.36878i | 0.0511895 | − | 0.0511895i | ||||
\(716\) | 16.8088 | + | 12.8754i | 0.628174 | + | 0.481176i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.3651 | + | 16.0921i | 0.685381 | + | 0.600553i | ||||
\(719\) | −50.7768 | −1.89365 | −0.946827 | − | 0.321742i | \(-0.895732\pi\) | ||||
−0.946827 | + | 0.321742i | \(0.895732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −62.5231 | −2.32848 | ||||||||
\(722\) | 7.28369 | + | 6.38221i | 0.271071 | + | 0.237521i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.42998 | − | 4.47782i | 0.127474 | − | 0.166417i | ||||
\(725\) | −49.9876 | + | 49.9876i | −1.85649 | + | 1.85649i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33.9843 | −1.26041 | −0.630204 | − | 0.776430i | \(-0.717029\pi\) | ||||
−0.630204 | + | 0.776430i | \(0.717029\pi\) | |||||||
\(728\) | 3.17866 | − | 0.636444i | 0.117809 | − | 0.0235882i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −63.8738 | + | 4.21349i | −2.36408 | + | 0.155948i | ||||
\(731\) | 55.3458 | + | 55.3458i | 2.04704 | + | 2.04704i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.7181 | + | 29.7181i | −1.09766 | + | 1.09766i | −0.102979 | + | 0.994684i | \(0.532837\pi\) |
−0.994684 | + | 0.102979i | \(0.967163\pi\) | |||||||
\(734\) | −11.1720 | − | 9.78924i | −0.412365 | − | 0.361328i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.3873 | − | 7.54800i | −0.567184 | − | 0.278223i | ||||
\(737\) | 9.64604i | 0.355316i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.21758 | − | 5.21758i | −0.191932 | − | 0.191932i | 0.604599 | − | 0.796530i | \(-0.293334\pi\) |
−0.796530 | + | 0.604599i | \(0.793334\pi\) | |||||||
\(740\) | 0.0710607 | + | 0.536273i | 0.00261224 | + | 0.0197138i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.41657 | − | 21.4743i | −0.0520039 | − | 0.788346i | ||||
\(743\) | − | 4.21791i | − | 0.154740i | −0.997002 | − | 0.0773701i | \(-0.975348\pi\) | ||
0.997002 | − | 0.0773701i | \(-0.0246523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.4659i | − | 0.603263i | ||||||
\(746\) | −16.1132 | + | 1.06292i | −0.589945 | + | 0.0389162i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −16.0202 | − | 12.2714i | −0.585757 | − | 0.448685i | ||||
\(749\) | −8.14249 | − | 8.14249i | −0.297520 | − | 0.297520i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 18.8637i | − | 0.688346i | −0.938906 | − | 0.344173i | \(-0.888159\pi\) | ||
0.938906 | − | 0.344173i | \(-0.111841\pi\) | |||||||
\(752\) | 17.2574 | − | 4.65523i | 0.629312 | − | 0.169759i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.97502 | + | 2.25399i | −0.0719258 | + | 0.0820853i | ||||
\(755\) | 26.6556 | − | 26.6556i | 0.970097 | − | 0.970097i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.56895 | − | 1.56895i | −0.0570243 | − | 0.0570243i | 0.678020 | − | 0.735044i | \(-0.262838\pi\) |
−0.735044 | + | 0.678020i | \(0.762838\pi\) | |||||||
\(758\) | −2.00175 | − | 30.3453i | −0.0727070 | − | 1.10219i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −47.7891 | − | 31.8445i | −1.73349 | − | 1.15512i | ||||
\(761\) | −22.6380 | −0.820626 | −0.410313 | − | 0.911945i | \(-0.634581\pi\) | ||||
−0.410313 | + | 0.911945i | \(0.634581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 43.4211 | − | 43.4211i | 1.57195 | − | 1.57195i | ||||
\(764\) | −0.844270 | − | 6.37145i | −0.0305446 | − | 0.230511i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.25524 | + | 4.85629i | −0.153748 | + | 0.175465i | ||||
\(767\) | −1.17672 | −0.0424889 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.26910 | 0.298191 | 0.149096 | − | 0.988823i | \(-0.452364\pi\) | ||||
0.149096 | + | 0.988823i | \(0.452364\pi\) | |||||||
\(770\) | −19.1974 | + | 21.9090i | −0.691827 | + | 0.789547i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.74466 | − | 13.1664i | −0.0627917 | − | 0.473870i | ||||
\(773\) | 17.5970 | − | 17.5970i | 0.632920 | − | 0.632920i | −0.315880 | − | 0.948799i | \(-0.602300\pi\) |
0.948799 | + | 0.315880i | \(0.102300\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.5217 | 0.629399 | ||||||||
\(776\) | −6.76294 | − | 4.50652i | −0.242775 | − | 0.161775i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.61290 | − | 39.6099i | −0.0936770 | − | 1.42008i | ||||
\(779\) | −20.6137 | − | 20.6137i | −0.738563 | − | 0.738563i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.88909 | + | 5.88909i | −0.210728 | + | 0.210728i | ||||
\(782\) | −19.2913 | + | 22.0162i | −0.689856 | + | 0.787297i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.0657 | + | 5.41278i | −0.716632 | + | 0.193314i | ||||
\(785\) | 38.2696i | 1.36590i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.0406 | + | 34.0406i | 1.21342 | + | 1.21342i | 0.969896 | + | 0.243519i | \(0.0783018\pi\) |
0.243519 | + | 0.969896i | \(0.421698\pi\) | |||||||
\(788\) | −35.9311 | − | 27.5229i | −1.27999 | − | 0.980462i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −27.4161 | + | 1.80853i | −0.975422 | + | 0.0643445i | ||||
\(791\) | − | 11.6722i | − | 0.415016i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.61395i | 0.0928239i | ||||||||
\(794\) | −0.451639 | − | 6.84656i | −0.0160281 | − | 0.242975i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00881 | + | 15.1599i | 0.0712005 | + | 0.537328i | ||||
\(797\) | 8.72498 | + | 8.72498i | 0.309055 | + | 0.309055i | 0.844543 | − | 0.535488i | \(-0.179872\pi\) |
−0.535488 | + | 0.844543i | \(0.679872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.5282i | − | 1.08001i | ||||||
\(800\) | 55.6047 | + | 27.2760i | 1.96592 | + | 0.964351i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.5512 | + | 25.8937i | 1.04349 | + | 0.914339i | ||||
\(803\) | 11.8368 | − | 11.8368i | 0.417711 | − | 0.417711i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 29.8784 | + | 29.8784i | 1.05308 | + | 1.05308i | ||||
\(806\) | 0.741178 | − | 0.0488924i | 0.0261069 | − | 0.00172216i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.90692 | − | 1.98361i | 0.348524 | − | 0.0697830i | ||||
\(809\) | 14.0389 | 0.493583 | 0.246792 | − | 0.969069i | \(-0.420624\pi\) | ||||
0.246792 | + | 0.969069i | \(0.420624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −25.7221 | + | 25.7221i | −0.903226 | + | 0.903226i | −0.995714 | − | 0.0924881i | \(-0.970518\pi\) |
0.0924881 | + | 0.995714i | \(0.470518\pi\) | |||||||
\(812\) | 27.4237 | − | 35.8015i | 0.962382 | − | 1.25639i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −0.106398 | − | 0.0932296i | −0.00372925 | − | 0.00326769i | ||||
\(815\) | 45.2451 | 1.58487 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −58.2476 | −2.03782 | ||||||||
\(818\) | −16.4185 | − | 14.3864i | −0.574060 | − | 0.503010i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 36.3577 | + | 27.8497i | 1.26967 | + | 0.972554i | ||||
\(821\) | −17.2882 | + | 17.2882i | −0.603363 | + | 0.603363i | −0.941203 | − | 0.337841i | \(-0.890304\pi\) |
0.337841 | + | 0.941203i | \(0.390304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.0410 | 0.977448 | 0.488724 | − | 0.872438i | \(-0.337462\pi\) | ||||
0.488724 | + | 0.872438i | \(0.337462\pi\) | |||||||
\(824\) | −42.1399 | − | 28.0802i | −1.46801 | − | 0.978218i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.6693 | − | 1.16557i | 0.614794 | − | 0.0405554i | ||||
\(827\) | 2.47300 | + | 2.47300i | 0.0859945 | + | 0.0859945i | 0.748796 | − | 0.662801i | \(-0.230632\pi\) |
−0.662801 | + | 0.748796i | \(0.730632\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.56384 | + | 1.56384i | −0.0543144 | + | 0.0543144i | −0.733742 | − | 0.679428i | \(-0.762228\pi\) |
0.679428 | + | 0.733742i | \(0.262228\pi\) | |||||||
\(830\) | −5.08849 | − | 4.45870i | −0.176624 | − | 0.154764i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.42822 | + | 0.998629i | 0.0841833 | + | 0.0346212i | ||||
\(833\) | 35.4961i | 1.22987i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 55.7295 | + | 55.7295i | 1.92860 | + | 1.92860i | ||||
\(836\) | 14.8875 | − | 1.97271i | 0.514893 | − | 0.0682277i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.501216 | − | 7.59812i | −0.0173142 | − | 0.262473i | ||||
\(839\) | − | 2.11605i | − | 0.0730540i | −0.999333 | − | 0.0365270i | \(-0.988371\pi\) | ||
0.999333 | − | 0.0365270i | \(-0.0116295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.6909i | 0.437619i | ||||||||
\(842\) | −43.7494 | + | 2.88597i | −1.50770 | + | 0.0994570i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.1133 | − | 26.2578i | 0.692327 | − | 0.903832i | ||||
\(845\) | −36.4062 | − | 36.4062i | −1.25241 | − | 1.25241i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.7970i | 1.05820i | ||||||||
\(848\) | 8.68970 | − | 15.1096i | 0.298406 | − | 0.518867i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 69.7123 | − | 79.5592i | 2.39111 | − | 2.72886i | ||||
\(851\) | −0.145100 | + | 0.145100i | −0.00497398 | + | 0.00497398i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.0512 | + | 39.0512i | 1.33709 | + | 1.33709i | 0.898866 | + | 0.438223i | \(0.144392\pi\) |
0.438223 | + | 0.898866i | \(0.355608\pi\) | |||||||
\(854\) | −2.58918 | − | 39.2503i | −0.0885998 | − | 1.34312i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.83103 | − | 9.14488i | −0.0625832 | − | 0.312566i | ||||
\(857\) | 21.9751 | 0.750654 | 0.375327 | − | 0.926893i | \(-0.377530\pi\) | ||||
0.375327 | + | 0.926893i | \(0.377530\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.5462 | + | 34.5462i | −1.17870 | + | 1.17870i | −0.198627 | + | 0.980075i | \(0.563648\pi\) |
−0.980075 | + | 0.198627i | \(0.936352\pi\) | |||||||
\(860\) | 90.7145 | − | 12.0204i | 3.09334 | − | 0.409893i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.7783 | + | 14.5832i | −0.435229 | + | 0.496705i | ||||
\(863\) | −35.3792 | −1.20432 | −0.602161 | − | 0.798375i | \(-0.705693\pi\) | ||||
−0.602161 | + | 0.798375i | \(0.705693\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.7660 | 1.86210 | ||||||||
\(866\) | 26.9945 | − | 30.8075i | 0.917311 | − | 1.04688i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.0809 | + | 1.46831i | −0.376110 | + | 0.0498377i | ||||
\(869\) | 5.08062 | − | 5.08062i | 0.172348 | − | 0.172348i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.14349 | −0.0726292 | ||||||||
\(872\) | 48.7665 | − | 9.76423i | 1.65144 | − | 0.330659i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.43387 | − | 21.7366i | −0.0485015 | − | 0.735252i | ||||
\(875\) | −58.6624 | − | 58.6624i | −1.98315 | − | 1.98315i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.4117 | − | 18.4117i | 0.621719 | − | 0.621719i | −0.324252 | − | 0.945971i | \(-0.605113\pi\) |
0.945971 | + | 0.324252i | \(0.105113\pi\) | |||||||
\(878\) | 27.5211 | − | 31.4084i | 0.928792 | − | 1.05998i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −22.7786 | + | 6.14459i | −0.767865 | + | 0.207134i | ||||
\(881\) | − | 4.20444i | − | 0.141651i | −0.997489 | − | 0.0708256i | \(-0.977437\pi\) | ||
0.997489 | − | 0.0708256i | \(-0.0225634\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.790399 | − | 0.790399i | −0.0265990 | − | 0.0265990i | 0.693682 | − | 0.720281i | \(-0.255987\pi\) |
−0.720281 | + | 0.693682i | \(0.755987\pi\) | |||||||
\(884\) | 2.72687 | − | 3.55992i | 0.0917145 | − | 0.119733i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 49.0257 | − | 3.23402i | 1.64705 | − | 0.108649i | ||||
\(887\) | 23.5992i | 0.792382i | 0.918168 | + | 0.396191i | \(0.129668\pi\) | ||||
−0.918168 | + | 0.396191i | \(0.870332\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 25.6270i | − | 0.859502i | ||||||
\(890\) | −5.20124 | − | 78.8474i | −0.174346 | − | 2.64297i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 22.1734 | − | 2.93816i | 0.742419 | − | 0.0983767i | ||||
\(893\) | 16.0644 | + | 16.0644i | 0.537574 | + | 0.537574i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 42.2786i | − | 1.41322i | ||||||
\(896\) | −37.4506 | − | 12.5899i | −1.25114 | − | 0.420600i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.3674 | − | 16.0941i | −0.612929 | − | 0.537068i | ||||
\(899\) | 7.30678 | − | 7.30678i | 0.243695 | − | 0.243695i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.0504 | − | 21.0504i | −0.701292 | − | 0.701292i | ||||
\(902\) | −11.9506 | + | 0.788332i | −0.397912 | + | 0.0262486i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.24218 | − | 7.86695i | 0.174352 | − | 0.261651i | ||||
\(905\) | −11.2629 | −0.374392 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6842 | + | 22.6842i | −0.753216 | + | 0.753216i | −0.975078 | − | 0.221862i | \(-0.928787\pi\) |
0.221862 | + | 0.975078i | \(0.428787\pi\) | |||||||
\(908\) | 36.4840 | + | 27.9464i | 1.21076 | + | 0.927434i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.86850 | − | 4.26593i | −0.161389 | − | 0.141414i | ||||
\(911\) | 27.0633 | 0.896647 | 0.448324 | − | 0.893871i | \(-0.352021\pi\) | ||||
0.448324 | + | 0.893871i | \(0.352021\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.76924 | 0.0585532 | ||||||||
\(914\) | 32.5671 | + | 28.5364i | 1.07723 | + | 0.943900i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.2543 | − | 19.9145i | 0.504016 | − | 0.657992i | ||||
\(917\) | −4.57675 | + | 4.57675i | −0.151138 | + | 0.151138i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.1750 | 1.49018 | 0.745092 | − | 0.666962i | \(-0.232405\pi\) | ||||
0.745092 | + | 0.666962i | \(0.232405\pi\) | |||||||
\(920\) | 6.71885 | + | 33.5566i | 0.221514 | + | 1.10633i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −35.2497 | + | 2.32527i | −1.16089 | + | 0.0765788i | ||||
\(923\) | −1.30864 | − | 1.30864i | −0.0430744 | − | 0.0430744i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.524344 | − | 0.524344i | 0.0172403 | − | 0.0172403i | ||||
\(926\) | −36.3174 | − | 31.8225i | −1.19346 | − | 1.04575i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 34.5623 | − | 11.8134i | 1.13456 | − | 0.387795i | ||||
\(929\) | 2.53089i | 0.0830358i | 0.999138 | + | 0.0415179i | \(0.0132194\pi\) | ||||
−0.999138 | + | 0.0415179i | \(0.986781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.6786 | − | 18.6786i | −0.612166 | − | 0.612166i | ||||
\(932\) | 0.426850 | + | 3.22131i | 0.0139819 | + | 0.105517i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.69411 | − | 25.6816i | −0.0554329 | − | 0.840327i | ||||
\(935\) | 40.2951i | 1.31779i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.3441i | 1.35065i | 0.737519 | + | 0.675326i | \(0.235997\pi\) | ||||
−0.737519 | + | 0.675326i | \(0.764003\pi\) | |||||||
\(938\) | 32.1860 | − | 2.12318i | 1.05091 | − | 0.0693242i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −28.3338 | − | 21.7034i | −0.924146 | − | 0.707888i | ||||
\(941\) | −28.2951 | − | 28.2951i | −0.922393 | − | 0.922393i | 0.0748056 | − | 0.997198i | \(-0.476166\pi\) |
−0.997198 | + | 0.0748056i | \(0.976166\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.3727i | 0.565733i | ||||||||
\(944\) | 12.4324 | + | 7.14999i | 0.404640 | + | 0.232712i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.7705 | + | 17.9980i | −0.512742 | + | 0.585166i | ||||
\(947\) | 27.4370 | − | 27.4370i | 0.891584 | − | 0.891584i | −0.103088 | − | 0.994672i | \(-0.532872\pi\) |
0.994672 | + | 0.103088i | \(0.0328724\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.63030 | + | 2.63030i | 0.0853831 | + | 0.0853831i | ||||
\(950\) | 5.18154 | + | 78.5489i | 0.168112 | + | 2.54846i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −37.4197 | + | 56.1558i | −1.21278 | + | 1.82002i | ||||
\(953\) | 49.7428 | 1.61133 | 0.805664 | − | 0.592373i | \(-0.201809\pi\) | ||||
0.805664 | + | 0.592373i | \(0.201809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.07472 | + | 9.07472i | −0.293651 | + | 0.293651i | ||||
\(956\) | 6.16095 | + | 46.4949i | 0.199260 | + | 1.50375i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.8730 | + | 29.5275i | −0.835918 | + | 0.953991i | ||||
\(959\) | 32.6249 | 1.05351 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.4388 | 0.917381 | ||||||||
\(962\) | 0.0207169 | − | 0.0236432i | 0.000667940 | − | 0.000762286i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.87296 | − | 44.3215i | −0.189155 | − | 1.42750i | ||||
\(965\) | −18.7527 | + | 18.7527i | −0.603669 | + | 0.603669i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.28275 | −0.266355 | −0.133178 | − | 0.991092i | \(-0.542518\pi\) | ||||
−0.133178 | + | 0.991092i | \(0.542518\pi\) | |||||||
\(968\) | −13.8314 | + | 20.7568i | −0.444559 | + | 0.667150i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.06814 | + | 16.1924i | 0.0342961 | + | 0.519906i | ||||
\(971\) | 24.2318 | + | 24.2318i | 0.777635 | + | 0.777635i | 0.979428 | − | 0.201793i | \(-0.0646768\pi\) |
−0.201793 | + | 0.979428i | \(0.564677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.3903 | − | 39.3903i | 1.26279 | − | 1.26279i | ||||
\(974\) | −17.4541 | + | 19.9195i | −0.559265 | + | 0.638261i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.8829 | − | 27.6171i | 0.508398 | − | 0.884002i | ||||
\(977\) | 16.9430i | 0.542055i | 0.962572 | + | 0.271027i | \(0.0873634\pi\) | ||||
−0.962572 | + | 0.271027i | \(0.912637\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.6116 | + | 14.6116i | 0.466989 | + | 0.466989i | ||||
\(980\) | 32.9446 | + | 25.2353i | 1.05238 | + | 0.806111i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 26.2075 | − | 1.72880i | 0.836316 | − | 0.0551683i | ||||
\(983\) | − | 32.4955i | − | 1.03645i | −0.855246 | − | 0.518223i | \(-0.826594\pi\) | ||
0.855246 | − | 0.518223i | \(-0.173406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 90.3761i | 2.87962i | ||||||||
\(986\) | −4.10625 | − | 62.2482i | −0.130770 | − | 1.98239i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.438364 | + | 3.30820i | 0.0139462 | + | 0.105248i | ||||
\(989\) | 24.5448 | + | 24.5448i | 0.780478 | + | 0.780478i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.3636i | 0.805700i | 0.915266 | + | 0.402850i | \(0.131980\pi\) | ||||
−0.915266 | + | 0.402850i | \(0.868020\pi\) | |||||||
\(992\) | −8.12785 | − | 3.98698i | −0.258059 | − | 0.126587i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.9464 | + | 18.3539i | 0.664379 | + | 0.582151i | ||||
\(995\) | 21.5919 | − | 21.5919i | 0.684510 | − | 0.684510i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.7251 | − | 22.7251i | −0.719712 | − | 0.719712i | 0.248834 | − | 0.968546i | \(-0.419953\pi\) |
−0.968546 | + | 0.248834i | \(0.919953\pi\) | |||||||
\(998\) | −43.3654 | + | 2.86064i | −1.37271 | + | 0.0905519i | ||||
\(999\) | 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 | 432.2.l.a.107.12 | yes | 32 | |
3.2 | odd | 2 | inner | 432.2.l.a.107.5 | ✓ | 32 | |
4.3 | odd | 2 | 1728.2.l.a.1295.1 | 32 | |||
12.11 | even | 2 | 1728.2.l.a.1295.16 | 32 | |||
16.3 | odd | 4 | inner | 432.2.l.a.323.5 | yes | 32 | |
16.13 | even | 4 | 1728.2.l.a.431.16 | 32 | |||
48.29 | odd | 4 | 1728.2.l.a.431.1 | 32 | |||
48.35 | even | 4 | inner | 432.2.l.a.323.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.l.a.107.5 | ✓ | 32 | 3.2 | odd | 2 | inner | |
432.2.l.a.107.12 | yes | 32 | 1.1 | even | 1 | trivial | |
432.2.l.a.323.5 | yes | 32 | 16.3 | odd | 4 | inner | |
432.2.l.a.323.12 | yes | 32 | 48.35 | even | 4 | inner | |
1728.2.l.a.431.1 | 32 | 48.29 | odd | 4 | |||
1728.2.l.a.431.16 | 32 | 16.13 | even | 4 | |||
1728.2.l.a.1295.1 | 32 | 4.3 | odd | 2 | |||
1728.2.l.a.1295.16 | 32 | 12.11 | even | 2 |