Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [288,2,Mod(35,288)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(288, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("288.35");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 288 = 2^{5} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 288.w (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.29969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 251.5 | ||
Character | \(\chi\) | \(=\) | 288.251 |
Dual form | 288.2.w.a.179.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/288\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.290763 | − | 1.38400i | −0.205600 | − | 0.978636i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.83091 | + | 0.804831i | −0.915457 | + | 0.402416i | ||||
\(5\) | −1.12344 | + | 2.71222i | −0.502418 | + | 1.21294i | 0.445745 | + | 0.895160i | \(0.352939\pi\) |
−0.948163 | + | 0.317784i | \(0.897061\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.03150 | − | 3.03150i | 1.14580 | − | 1.14580i | 0.158430 | − | 0.987370i | \(-0.449357\pi\) |
0.987370 | − | 0.158430i | \(-0.0506433\pi\) | |||||||
\(8\) | 1.64625 | + | 2.29997i | 0.582037 | + | 0.813163i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.08037 | + | 0.766228i | 1.29033 | + | 0.242303i | ||||
\(11\) | 0.616847 | − | 1.48920i | 0.185986 | − | 0.449011i | −0.803194 | − | 0.595718i | \(-0.796868\pi\) |
0.989180 | + | 0.146707i | \(0.0468676\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35133 | − | 1.38816i | 0.929490 | − | 0.385008i | 0.134005 | − | 0.990981i | \(-0.457216\pi\) |
0.795485 | + | 0.605973i | \(0.207216\pi\) | |||||||
\(14\) | −5.07705 | − | 3.31415i | −1.35690 | − | 0.885745i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.70449 | − | 2.94715i | 0.676123 | − | 0.736789i | ||||
\(17\) | 4.76709 | 1.15619 | 0.578094 | − | 0.815970i | \(-0.303797\pi\) | ||||
0.578094 | + | 0.815970i | \(0.303797\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.13264 | + | 2.73444i | 0.259846 | + | 0.627323i | 0.998928 | − | 0.0462921i | \(-0.0147405\pi\) |
−0.739082 | + | 0.673615i | \(0.764741\pi\) | |||||||
\(20\) | −0.125961 | − | 5.87003i | −0.0281657 | − | 1.31258i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.24041 | − | 0.420712i | −0.477657 | − | 0.0896962i | ||||
\(23\) | 4.11192 | − | 4.11192i | 0.857395 | − | 0.857395i | −0.133636 | − | 0.991031i | \(-0.542665\pi\) |
0.991031 | + | 0.133636i | \(0.0426652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.55851 | − | 2.55851i | −0.511702 | − | 0.511702i | ||||
\(26\) | −2.89566 | − | 4.23461i | −0.567886 | − | 0.830475i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.11057 | + | 7.99027i | −0.587843 | + | 1.51002i | ||||
\(29\) | −8.16664 | + | 3.38273i | −1.51651 | + | 0.628158i | −0.976888 | − | 0.213751i | \(-0.931432\pi\) |
−0.539620 | + | 0.841909i | \(0.681432\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.16305i | 1.10692i | 0.832877 | + | 0.553458i | \(0.186692\pi\) | ||||
−0.832877 | + | 0.553458i | \(0.813308\pi\) | |||||||
\(32\) | −4.86523 | − | 2.88610i | −0.860059 | − | 0.510195i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.38609 | − | 6.59765i | −0.237713 | − | 1.13149i | ||||
\(35\) | 4.81640 | + | 11.6278i | 0.814121 | + | 1.96546i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.38963 | − | 3.88931i | −1.54365 | − | 0.639399i | −0.561493 | − | 0.827482i | \(-0.689773\pi\) |
−0.982153 | + | 0.188083i | \(0.939773\pi\) | |||||||
\(38\) | 3.45513 | − | 2.36265i | 0.560497 | − | 0.383272i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.08750 | + | 1.88112i | −1.27875 | + | 0.297431i | ||||
\(41\) | −0.169917 | − | 0.169917i | −0.0265365 | − | 0.0265365i | 0.693714 | − | 0.720251i | \(-0.255973\pi\) |
−0.720251 | + | 0.693714i | \(0.755973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.57687 | + | 3.13844i | 1.15546 | + | 0.478608i | 0.876361 | − | 0.481654i | \(-0.159964\pi\) |
0.279100 | + | 0.960262i | \(0.409964\pi\) | |||||||
\(44\) | 0.0691613 | + | 3.22306i | 0.0104265 | + | 0.485894i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.88649 | − | 4.49531i | −1.01536 | − | 0.662797i | ||||
\(47\) | − | 2.44049i | − | 0.355981i | −0.984032 | − | 0.177991i | \(-0.943040\pi\) | ||
0.984032 | − | 0.177991i | \(-0.0569597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 11.3800i | − | 1.62572i | ||||||
\(50\) | −2.79706 | + | 4.28490i | −0.395564 | + | 0.605976i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.01875 | + | 5.23886i | −0.695976 | + | 0.726499i | ||||
\(53\) | 1.99073 | + | 0.824586i | 0.273447 | + | 0.113266i | 0.515193 | − | 0.857074i | \(-0.327720\pi\) |
−0.241746 | + | 0.970340i | \(0.577720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.34605 | + | 3.34605i | 0.451182 | + | 0.451182i | ||||
\(56\) | 11.9630 | + | 1.98176i | 1.59862 | + | 0.264824i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.05626 | + | 10.3191i | 0.926533 | + | 1.35496i | ||||
\(59\) | 1.21488 | + | 0.503218i | 0.158163 | + | 0.0655134i | 0.460361 | − | 0.887732i | \(-0.347720\pi\) |
−0.302197 | + | 0.953245i | \(0.597720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.04489 | + | 2.52258i | 0.133784 | + | 0.322983i | 0.976548 | − | 0.215300i | \(-0.0690731\pi\) |
−0.842764 | + | 0.538283i | \(0.819073\pi\) | |||||||
\(62\) | 8.52966 | − | 1.79198i | 1.08327 | − | 0.227582i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.57973 | + | 7.57265i | −0.322467 | + | 0.946581i | ||||
\(65\) | 10.6491i | 1.32085i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.91551 | − | 1.62186i | 0.478355 | − | 0.198141i | −0.130459 | − | 0.991454i | \(-0.541645\pi\) |
0.608815 | + | 0.793312i | \(0.291645\pi\) | |||||||
\(68\) | −8.72813 | + | 3.83670i | −1.05844 | + | 0.465268i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 14.6925 | − | 10.0468i | 1.75609 | − | 1.20083i | ||||
\(71\) | −5.28919 | − | 5.28919i | −0.627711 | − | 0.627711i | 0.319781 | − | 0.947492i | \(-0.396391\pi\) |
−0.947492 | + | 0.319781i | \(0.896391\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.57482 | + | 1.57482i | −0.184319 | + | 0.184319i | −0.793235 | − | 0.608916i | \(-0.791605\pi\) |
0.608916 | + | 0.793235i | \(0.291605\pi\) | |||||||
\(74\) | −2.65266 | + | 14.1261i | −0.308365 | + | 1.64213i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.27453 | − | 4.09494i | −0.490322 | − | 0.469721i | ||||
\(77\) | −2.64454 | − | 6.38449i | −0.301373 | − | 0.727580i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7711 | −1.54937 | −0.774684 | − | 0.632348i | \(-0.782091\pi\) | ||||
−0.774684 | + | 0.632348i | \(0.782091\pi\) | |||||||
\(80\) | 4.95501 | + | 10.6461i | 0.553987 | + | 1.19028i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.185759 | + | 0.284570i | −0.0205137 | + | 0.0314255i | ||||
\(83\) | 3.31934 | − | 1.37492i | 0.364345 | − | 0.150917i | −0.192997 | − | 0.981199i | \(-0.561821\pi\) |
0.557343 | + | 0.830282i | \(0.311821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.35554 | + | 12.9294i | −0.580890 | + | 1.40239i | ||||
\(86\) | 2.14053 | − | 11.3989i | 0.230820 | − | 1.22918i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.44060 | − | 1.03286i | 0.473370 | − | 0.110104i | ||||
\(89\) | 6.99010 | − | 6.99010i | 0.740949 | − | 0.740949i | −0.231811 | − | 0.972761i | \(-0.574465\pi\) |
0.972761 | + | 0.231811i | \(0.0744652\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.95133 | − | 14.3678i | 0.623869 | − | 1.50615i | ||||
\(92\) | −4.21917 | + | 10.8380i | −0.439879 | + | 1.12994i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.37763 | + | 0.709602i | −0.348376 | + | 0.0731899i | ||||
\(95\) | −8.68886 | −0.891459 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5584 | −1.37665 | −0.688323 | − | 0.725404i | \(-0.741653\pi\) | ||||
−0.688323 | + | 0.725404i | \(0.741653\pi\) | |||||||
\(98\) | −15.7499 | + | 3.30888i | −1.59099 | + | 0.334248i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.74358 | + | 2.62524i | 0.674358 | + | 0.262524i | ||||
\(101\) | −1.10479 | + | 2.66720i | −0.109931 | + | 0.265396i | −0.969265 | − | 0.246018i | \(-0.920878\pi\) |
0.859335 | + | 0.511413i | \(0.170878\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8009 | + | 12.8009i | −1.26131 | + | 1.26131i | −0.310851 | + | 0.950459i | \(0.600614\pi\) |
−0.950459 | + | 0.310851i | \(0.899386\pi\) | |||||||
\(104\) | 8.70985 | + | 5.42269i | 0.854071 | + | 0.531738i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.562398 | − | 2.99492i | 0.0546249 | − | 0.290893i | ||||
\(107\) | −0.720677 | + | 1.73987i | −0.0696704 | + | 0.168199i | −0.954879 | − | 0.296995i | \(-0.904016\pi\) |
0.885209 | + | 0.465194i | \(0.154016\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.45017 | − | 1.84332i | 0.426249 | − | 0.176558i | −0.159238 | − | 0.987240i | \(-0.550904\pi\) |
0.585486 | + | 0.810682i | \(0.300904\pi\) | |||||||
\(110\) | 3.65803 | − | 5.60385i | 0.348780 | − | 0.534306i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.735628 | − | 17.1330i | −0.0695104 | − | 1.61891i | ||||
\(113\) | −13.6612 | −1.28514 | −0.642568 | − | 0.766229i | \(-0.722131\pi\) | ||||
−0.642568 | + | 0.766229i | \(0.722131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.53296 | + | 15.7720i | 0.609201 | + | 1.47074i | ||||
\(116\) | 12.2299 | − | 12.7663i | 1.13552 | − | 1.18532i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.343213 | − | 1.82771i | 0.0315954 | − | 0.168254i | ||||
\(119\) | 14.4514 | − | 14.4514i | 1.32476 | − | 1.32476i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.94096 | + | 5.94096i | 0.540087 | + | 0.540087i | ||||
\(122\) | 3.18743 | − | 2.17959i | 0.288577 | − | 0.197331i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.96021 | − | 11.2840i | −0.445440 | − | 1.01333i | ||||
\(125\) | −3.74754 | + | 1.55228i | −0.335190 | + | 0.138840i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 13.2014i | − | 1.17143i | −0.810515 | − | 0.585717i | \(-0.800813\pi\) | ||
0.810515 | − | 0.585717i | \(-0.199187\pi\) | |||||||
\(128\) | 11.2306 | + | 1.36851i | 0.992657 | + | 0.120960i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.7383 | − | 3.09635i | 1.29264 | − | 0.271568i | ||||
\(131\) | −2.56553 | − | 6.19375i | −0.224152 | − | 0.541150i | 0.771294 | − | 0.636479i | \(-0.219610\pi\) |
−0.995446 | + | 0.0953287i | \(0.969610\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.7231 | + | 4.85585i | 1.01652 | + | 0.421056i | ||||
\(134\) | −3.38313 | − | 4.94749i | −0.292258 | − | 0.427398i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.84781 | + | 10.9642i | 0.672944 | + | 0.940169i | ||||
\(137\) | 9.77333 | + | 9.77333i | 0.834992 | + | 0.834992i | 0.988195 | − | 0.153203i | \(-0.0489587\pi\) |
−0.153203 | + | 0.988195i | \(0.548959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.26616 | − | 3.42396i | −0.701127 | − | 0.290416i | 0.00350050 | − | 0.999994i | \(-0.498886\pi\) |
−0.704627 | + | 0.709578i | \(0.748886\pi\) | |||||||
\(140\) | −18.1769 | − | 17.4132i | −1.53623 | − | 1.47168i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.78234 | + | 8.85814i | −0.485243 | + | 0.743358i | ||||
\(143\) | − | 5.84708i | − | 0.488957i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 25.9501i | − | 2.15504i | ||||||
\(146\) | 2.63745 | + | 1.72165i | 0.218277 | + | 0.142485i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.3219 | − | 0.436073i | 1.67045 | − | 0.0358449i | ||||
\(149\) | −18.9803 | − | 7.86190i | −1.55493 | − | 0.644072i | −0.570729 | − | 0.821139i | \(-0.693339\pi\) |
−0.984199 | + | 0.177066i | \(0.943339\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.83326 | + | 7.83326i | 0.637462 | + | 0.637462i | 0.949929 | − | 0.312467i | \(-0.101155\pi\) |
−0.312467 | + | 0.949929i | \(0.601155\pi\) | |||||||
\(152\) | −4.42452 | + | 7.10661i | −0.358876 | + | 0.576422i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.06720 | + | 5.51642i | −0.650073 | + | 0.444526i | ||||
\(155\) | −16.7156 | − | 6.92381i | −1.34263 | − | 0.556134i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.58014 | + | 8.64323i | 0.285727 | + | 0.689805i | 0.999949 | − | 0.0101140i | \(-0.00321944\pi\) |
−0.714222 | + | 0.699919i | \(0.753219\pi\) | |||||||
\(158\) | 4.00412 | + | 19.0592i | 0.318551 | + | 1.51627i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.2935 | − | 9.95323i | 1.05095 | − | 0.786872i | ||||
\(161\) | − | 24.9306i | − | 1.96481i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.73693 | + | 1.96210i | −0.371025 | + | 0.153684i | −0.560402 | − | 0.828221i | \(-0.689353\pi\) |
0.189377 | + | 0.981904i | \(0.439353\pi\) | |||||||
\(164\) | 0.447857 | + | 0.174349i | 0.0349718 | + | 0.0136143i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.86803 | − | 4.19420i | −0.222602 | − | 0.325533i | ||||
\(167\) | −4.55199 | − | 4.55199i | −0.352244 | − | 0.352244i | 0.508700 | − | 0.860944i | \(-0.330126\pi\) |
−0.860944 | + | 0.508700i | \(0.830126\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.111994 | − | 0.111994i | 0.00861490 | − | 0.00861490i | ||||
\(170\) | 19.4515 | + | 3.65268i | 1.49186 | + | 0.280147i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.3985 | + | 0.351884i | −1.25037 | + | 0.0268309i | ||||
\(173\) | −4.28444 | − | 10.3436i | −0.325740 | − | 0.786406i | −0.998899 | − | 0.0469083i | \(-0.985063\pi\) |
0.673159 | − | 0.739498i | \(-0.264937\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.5123 | −1.17262 | ||||||||
\(176\) | −2.72064 | − | 5.84547i | −0.205076 | − | 0.440619i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.7068 | − | 7.64184i | −0.877459 | − | 0.572780i | ||||
\(179\) | 10.2246 | − | 4.23519i | 0.764226 | − | 0.316553i | 0.0336946 | − | 0.999432i | \(-0.489273\pi\) |
0.730531 | + | 0.682880i | \(0.239273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.33358 | + | 3.21956i | −0.0991246 | + | 0.239308i | −0.965661 | − | 0.259806i | \(-0.916341\pi\) |
0.866536 | + | 0.499114i | \(0.166341\pi\) | |||||||
\(182\) | −21.6154 | − | 4.05903i | −1.60224 | − | 0.300875i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 16.2265 | + | 2.68806i | 1.19624 | + | 0.198166i | ||||
\(185\) | 21.0974 | − | 21.0974i | 1.55111 | − | 1.55111i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.94056 | − | 7.09915i | 0.215035 | − | 0.519141i | ||||
\(188\) | 1.96418 | + | 4.46832i | 0.143253 | + | 0.325886i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.52640 | + | 12.0254i | 0.183284 | + | 0.872414i | ||||
\(191\) | 4.82446 | 0.349085 | 0.174543 | − | 0.984650i | \(-0.444155\pi\) | ||||
0.174543 | + | 0.984650i | \(0.444155\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.222878 | 0.0160431 | 0.00802155 | − | 0.999968i | \(-0.497447\pi\) | ||||
0.00802155 | + | 0.999968i | \(0.497447\pi\) | |||||||
\(194\) | 3.94228 | + | 18.7648i | 0.283039 | + | 1.34724i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 9.15899 | + | 20.8358i | 0.654214 | + | 1.48827i | ||||
\(197\) | −9.44160 | + | 22.7940i | −0.672686 | + | 1.62401i | 0.104341 | + | 0.994542i | \(0.466727\pi\) |
−0.777028 | + | 0.629467i | \(0.783273\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8710 | − | 14.8710i | 1.05418 | − | 1.05418i | 0.0557310 | − | 0.998446i | \(-0.482251\pi\) |
0.998446 | − | 0.0557310i | \(-0.0177489\pi\) | |||||||
\(200\) | 1.67256 | − | 10.0964i | 0.118268 | − | 0.713926i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.01263 | + | 0.753507i | 0.282328 | + | 0.0530165i | ||||
\(203\) | −14.5024 | + | 35.0120i | −1.01787 | + | 2.45736i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.651743 | − | 0.269961i | 0.0455197 | − | 0.0188549i | ||||
\(206\) | 21.4385 | + | 13.9944i | 1.49369 | + | 0.975037i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.97250 | − | 13.6312i | 0.344781 | − | 0.945150i | ||||
\(209\) | 4.77079 | 0.330003 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.644000 | − | 1.55475i | −0.0443348 | − | 0.107034i | 0.900161 | − | 0.435558i | \(-0.143449\pi\) |
−0.944496 | + | 0.328524i | \(0.893449\pi\) | |||||||
\(212\) | −4.30850 | + | 0.0924532i | −0.295909 | + | 0.00634971i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.61752 | + | 0.491528i | 0.178930 | + | 0.0336002i | ||||
\(215\) | −17.0243 | + | 17.0243i | −1.16105 | + | 1.16105i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.6833 | + | 18.6833i | 1.26830 | + | 1.26830i | ||||
\(218\) | −3.84510 | − | 5.62306i | −0.260423 | − | 0.380842i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.81935 | − | 3.43333i | −0.594600 | − | 0.231475i | ||||
\(221\) | 15.9761 | − | 6.61750i | 1.07467 | − | 0.445141i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.4280i | − | 1.56885i | −0.620221 | − | 0.784427i | \(-0.712957\pi\) | ||
0.620221 | − | 0.784427i | \(-0.287043\pi\) | |||||||
\(224\) | −23.4982 | + | 5.99974i | −1.57004 | + | 0.400875i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.97216 | + | 18.9071i | 0.264224 | + | 1.25768i | ||||
\(227\) | 5.10690 | + | 12.3292i | 0.338957 | + | 0.818315i | 0.997816 | + | 0.0660486i | \(0.0210392\pi\) |
−0.658859 | + | 0.752266i | \(0.728961\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.82666 | − | 3.24191i | −0.517200 | − | 0.214231i | 0.108786 | − | 0.994065i | \(-0.465304\pi\) |
−0.625987 | + | 0.779834i | \(0.715304\pi\) | |||||||
\(230\) | 19.9288 | − | 13.6275i | 1.31407 | − | 0.898571i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −21.2245 | − | 13.2142i | −1.39346 | − | 0.867556i | ||||
\(233\) | 9.66805 | + | 9.66805i | 0.633375 | + | 0.633375i | 0.948913 | − | 0.315538i | \(-0.102185\pi\) |
−0.315538 | + | 0.948913i | \(0.602185\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.61915 | + | 2.74174i | 0.431785 | + | 0.178851i | ||||
\(236\) | −2.62934 | + | 0.0564212i | −0.171155 | + | 0.00367270i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −24.2027 | − | 15.7989i | −1.56883 | − | 1.02409i | ||||
\(239\) | 25.8579i | 1.67261i | 0.548268 | + | 0.836303i | \(0.315287\pi\) | ||||
−0.548268 | + | 0.836303i | \(0.684713\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.9358i | 1.60626i | 0.595805 | + | 0.803129i | \(0.296833\pi\) | ||||
−0.595805 | + | 0.803129i | \(0.703167\pi\) | |||||||
\(242\) | 6.49488 | − | 9.94970i | 0.417507 | − | 0.639591i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.94334 | − | 3.77766i | −0.252447 | − | 0.241840i | ||||
\(245\) | 30.8652 | + | 12.7848i | 1.97190 | + | 0.816789i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.59170 | + | 7.59170i | 0.483048 | + | 0.483048i | ||||
\(248\) | −14.1748 | + | 10.1459i | −0.900102 | + | 0.644266i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.23800 | + | 4.73525i | 0.204789 | + | 0.299483i | ||||
\(251\) | 11.5486 | + | 4.78358i | 0.728939 | + | 0.301937i | 0.716116 | − | 0.697981i | \(-0.245918\pi\) |
0.0128233 | + | 0.999918i | \(0.495918\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.58705 | − | 8.65990i | −0.225516 | − | 0.544443i | ||||
\(254\) | −18.2707 | + | 3.83848i | −1.14641 | + | 0.240847i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.37144 | − | 15.9411i | −0.0857148 | − | 0.996320i | ||||
\(257\) | 17.0780i | 1.06530i | 0.846337 | + | 0.532648i | \(0.178803\pi\) | ||||
−0.846337 | + | 0.532648i | \(0.821197\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40.2552 | + | 16.6742i | −2.50133 | + | 1.03609i | ||||
\(260\) | −8.57070 | − | 19.4975i | −0.531532 | − | 1.20919i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.82619 | + | 5.35161i | −0.483503 | + | 0.330624i | ||||
\(263\) | −10.4595 | − | 10.4595i | −0.644963 | − | 0.644963i | 0.306809 | − | 0.951771i | \(-0.400739\pi\) |
−0.951771 | + | 0.306809i | \(0.900739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.47292 | + | 4.47292i | −0.274770 | + | 0.274770i | ||||
\(266\) | 3.31187 | − | 17.6366i | 0.203064 | − | 1.08137i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.86364 | + | 6.12080i | −0.358179 | + | 0.373888i | ||||
\(269\) | −3.47587 | − | 8.39150i | −0.211928 | − | 0.511639i | 0.781792 | − | 0.623540i | \(-0.214306\pi\) |
−0.993719 | + | 0.111901i | \(0.964306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.66173 | −0.343925 | −0.171963 | − | 0.985103i | \(-0.555011\pi\) | ||||
−0.171963 | + | 0.985103i | \(0.555011\pi\) | |||||||
\(272\) | 12.8926 | − | 14.0493i | 0.781726 | − | 0.851866i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.6846 | − | 16.3680i | 0.645479 | − | 0.988828i | ||||
\(275\) | −5.38834 | + | 2.23192i | −0.324929 | + | 0.134590i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.27625 | + | 12.7380i | −0.317019 | + | 0.765352i | 0.682390 | + | 0.730988i | \(0.260940\pi\) |
−0.999409 | + | 0.0343637i | \(0.989060\pi\) | |||||||
\(278\) | −2.33527 | + | 12.4359i | −0.140060 | + | 0.745858i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −18.8147 | + | 30.2199i | −1.12439 | + | 1.80598i | ||||
\(281\) | −5.75892 | + | 5.75892i | −0.343548 | + | 0.343548i | −0.857700 | − | 0.514151i | \(-0.828107\pi\) |
0.514151 | + | 0.857700i | \(0.328107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.4136 | − | 25.1407i | 0.619025 | − | 1.49446i | −0.233812 | − | 0.972282i | \(-0.575120\pi\) |
0.852837 | − | 0.522177i | \(-0.174880\pi\) | |||||||
\(284\) | 13.9410 | + | 5.42714i | 0.827243 | + | 0.322042i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −8.09236 | + | 1.70011i | −0.478511 | + | 0.100530i | ||||
\(287\) | −1.03021 | −0.0608111 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.72512 | 0.336772 | ||||||||
\(290\) | −35.9149 | + | 7.54531i | −2.10900 | + | 0.443076i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.61590 | − | 4.15083i | 0.0945632 | − | 0.242909i | ||||
\(293\) | 5.21345 | − | 12.5864i | 0.304573 | − | 0.735304i | −0.695290 | − | 0.718729i | \(-0.744724\pi\) |
0.999863 | − | 0.0165743i | \(-0.00527600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.72968 | + | 2.72968i | −0.158928 | + | 0.158928i | ||||
\(296\) | −6.51236 | − | 27.9987i | −0.378523 | − | 1.62739i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.36211 | + | 28.5547i | −0.310619 | + | 1.65413i | ||||
\(299\) | 8.07236 | − | 19.4884i | 0.466837 | − | 1.12704i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 32.4835 | − | 13.4551i | 1.87232 | − | 0.775539i | ||||
\(302\) | 8.56362 | − | 13.1189i | 0.492781 | − | 0.754905i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.1220 | + | 4.05720i | 0.637892 | + | 0.232696i | ||||
\(305\) | −8.01566 | −0.458975 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.98052 | − | 21.6809i | −0.512545 | − | 1.23739i | −0.942398 | − | 0.334495i | \(-0.891434\pi\) |
0.429852 | − | 0.902899i | \(-0.358566\pi\) | |||||||
\(308\) | 9.98036 | + | 9.56104i | 0.568684 | + | 0.544791i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.72230 | + | 25.1475i | −0.268208 | + | 1.42828i | ||||
\(311\) | 12.7177 | − | 12.7177i | 0.721157 | − | 0.721157i | −0.247684 | − | 0.968841i | \(-0.579670\pi\) |
0.968841 | + | 0.247684i | \(0.0796695\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.1388 | + | 10.1388i | 0.573081 | + | 0.573081i | 0.932988 | − | 0.359907i | \(-0.117192\pi\) |
−0.359907 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(314\) | 10.9213 | − | 7.46805i | 0.616323 | − | 0.421446i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 25.2137 | − | 11.0834i | 1.41838 | − | 0.623490i | ||||
\(317\) | 2.52668 | − | 1.04659i | 0.141913 | − | 0.0587822i | −0.310597 | − | 0.950542i | \(-0.600529\pi\) |
0.452509 | + | 0.891760i | \(0.350529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.2484i | 0.797757i | ||||||||
\(320\) | −17.6405 | − | 15.5042i | −0.986136 | − | 0.866713i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −34.5040 | + | 7.24889i | −1.92283 | + | 0.403965i | ||||
\(323\) | 5.39940 | + | 13.0353i | 0.300431 | + | 0.725304i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −12.1260 | − | 5.02277i | −0.672631 | − | 0.278613i | ||||
\(326\) | 4.09287 | + | 5.98540i | 0.226683 | + | 0.331501i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.111078 | − | 0.670528i | 0.00613327 | − | 0.0370237i | ||||
\(329\) | −7.39834 | − | 7.39834i | −0.407884 | − | 0.407884i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.49794 | − | 2.27732i | −0.302194 | − | 0.125173i | 0.226434 | − | 0.974027i | \(-0.427293\pi\) |
−0.528628 | + | 0.848854i | \(0.677293\pi\) | |||||||
\(332\) | −4.97086 | + | 5.18887i | −0.272811 | + | 0.284776i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.97641 | + | 7.62351i | −0.272297 | + | 0.417140i | ||||
\(335\) | 12.4418i | 0.679768i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5.85273i | − | 0.318818i | −0.987213 | − | 0.159409i | \(-0.949041\pi\) | ||
0.987213 | − | 0.159409i | \(-0.0509589\pi\) | |||||||
\(338\) | −0.187563 | − | 0.122436i | −0.0102021 | − | 0.00665963i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.600467 | − | 27.9829i | −0.0325649 | − | 1.51759i | ||||
\(341\) | 9.17801 | + | 3.80166i | 0.497017 | + | 0.205871i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.2780 | − | 13.2780i | −0.716946 | − | 0.716946i | ||||
\(344\) | 5.25508 | + | 22.5932i | 0.283335 | + | 1.21815i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.0697 | + | 8.93719i | −0.702633 | + | 0.480466i | ||||
\(347\) | −7.23994 | − | 2.99888i | −0.388660 | − | 0.160988i | 0.179792 | − | 0.983705i | \(-0.442458\pi\) |
−0.568452 | + | 0.822716i | \(0.692458\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.01973 | − | 9.70449i | −0.215171 | − | 0.519469i | 0.779032 | − | 0.626984i | \(-0.215711\pi\) |
−0.994204 | + | 0.107515i | \(0.965711\pi\) | |||||||
\(350\) | 4.51039 | + | 21.4690i | 0.241090 | + | 1.14756i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −7.29908 | + | 5.46502i | −0.389042 | + | 0.291286i | ||||
\(353\) | 16.6657i | 0.887026i | 0.896268 | + | 0.443513i | \(0.146268\pi\) | ||||
−0.896268 | + | 0.443513i | \(0.853732\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.2875 | − | 8.40338i | 1.07675 | − | 0.446005i | ||||
\(356\) | −7.17242 | + | 18.4241i | −0.380138 | + | 0.976477i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.83444 | − | 12.9195i | −0.466915 | − | 0.682815i | ||||
\(359\) | 9.54649 | + | 9.54649i | 0.503845 | + | 0.503845i | 0.912630 | − | 0.408786i | \(-0.134048\pi\) |
−0.408786 | + | 0.912630i | \(0.634048\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.24075 | − | 7.24075i | 0.381092 | − | 0.381092i | ||||
\(362\) | 4.84363 | + | 0.909554i | 0.254575 | + | 0.0478051i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.667267 | + | 31.0960i | 0.0349743 | + | 1.62987i | ||||
\(365\) | −2.50205 | − | 6.04049i | −0.130963 | − | 0.316173i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.31072 | −0.329417 | −0.164708 | − | 0.986342i | \(-0.552668\pi\) | ||||
−0.164708 | + | 0.986342i | \(0.552668\pi\) | |||||||
\(368\) | −0.997804 | − | 23.2391i | −0.0520141 | − | 1.21142i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −35.3331 | − | 23.0644i | −1.83688 | − | 1.19906i | ||||
\(371\) | 8.53463 | − | 3.53516i | 0.443096 | − | 0.183536i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.06259 | + | 7.39375i | −0.158575 | + | 0.382834i | −0.983120 | − | 0.182963i | \(-0.941431\pi\) |
0.824545 | + | 0.565797i | \(0.191431\pi\) | |||||||
\(374\) | −10.6802 | − | 2.00557i | −0.552261 | − | 0.103706i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.61305 | − | 4.01765i | 0.289471 | − | 0.207194i | ||||
\(377\) | −22.6733 | + | 22.6733i | −1.16773 | + | 1.16773i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.31838 | + | 20.0823i | −0.427286 | + | 1.03156i | 0.552858 | + | 0.833275i | \(0.313537\pi\) |
−0.980144 | + | 0.198285i | \(0.936463\pi\) | |||||||
\(380\) | 15.9086 | − | 6.99307i | 0.816092 | − | 0.358737i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.40277 | − | 6.67705i | −0.0717720 | − | 0.341627i | ||||
\(383\) | −7.95308 | −0.406383 | −0.203192 | − | 0.979139i | \(-0.565131\pi\) | ||||
−0.203192 | + | 0.979139i | \(0.565131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.2871 | 1.03393 | ||||||||
\(386\) | −0.0648046 | − | 0.308463i | −0.00329847 | − | 0.0157004i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 24.8243 | − | 10.9122i | 1.26026 | − | 0.553984i | ||||
\(389\) | −2.38215 | + | 5.75102i | −0.120780 | + | 0.291588i | −0.972693 | − | 0.232094i | \(-0.925442\pi\) |
0.851913 | + | 0.523683i | \(0.175442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.6019 | − | 19.6019i | 0.991310 | − | 0.991310i | ||||
\(392\) | 26.1737 | − | 18.7343i | 1.32197 | − | 0.946227i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 34.2922 | + | 6.43952i | 1.72762 | + | 0.324418i | ||||
\(395\) | 15.4710 | − | 37.3503i | 0.778430 | − | 1.87930i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.3118 | − | 10.4845i | 1.27036 | − | 0.526202i | 0.357288 | − | 0.933994i | \(-0.383701\pi\) |
0.913075 | + | 0.407792i | \(0.133701\pi\) | |||||||
\(398\) | −24.9054 | − | 16.2575i | −1.24839 | − | 0.814916i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −14.4598 | + | 0.620851i | −0.722990 | + | 0.0310426i | ||||
\(401\) | −1.81017 | −0.0903954 | −0.0451977 | − | 0.998978i | \(-0.514392\pi\) | ||||
−0.0451977 | + | 0.998978i | \(0.514392\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.55532 | + | 20.6544i | 0.426171 | + | 1.02887i | ||||
\(404\) | −0.123870 | − | 5.77257i | −0.00616275 | − | 0.287196i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 52.6734 | + | 9.89120i | 2.61413 | + | 0.490892i | ||||
\(407\) | −11.5839 | + | 11.5839i | −0.574194 | + | 0.574194i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.4331 | − | 14.4331i | −0.713672 | − | 0.713672i | 0.253630 | − | 0.967301i | \(-0.418376\pi\) |
−0.967301 | + | 0.253630i | \(0.918376\pi\) | |||||||
\(410\) | −0.563129 | − | 0.823518i | −0.0278109 | − | 0.0406707i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 13.1348 | − | 33.7399i | 0.647104 | − | 1.66225i | ||||
\(413\) | 5.20841 | − | 2.15739i | 0.256289 | − | 0.106158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.5474i | 0.517754i | ||||||||
\(416\) | −20.3113 | − | 2.91851i | −0.995845 | − | 0.143092i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.38717 | − | 6.60278i | −0.0678486 | − | 0.322952i | ||||
\(419\) | −1.33902 | − | 3.23269i | −0.0654155 | − | 0.157927i | 0.887791 | − | 0.460247i | \(-0.152239\pi\) |
−0.953207 | + | 0.302320i | \(0.902239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.5557 | − | 4.37232i | −0.514454 | − | 0.213094i | 0.110325 | − | 0.993896i | \(-0.464811\pi\) |
−0.624779 | + | 0.780802i | \(0.714811\pi\) | |||||||
\(422\) | −1.96453 | + | 1.34336i | −0.0956318 | + | 0.0653938i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.38071 | + | 5.93609i | 0.0670530 | + | 0.288282i | ||||
\(425\) | −12.1966 | − | 12.1966i | −0.591624 | − | 0.591624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.8148 | + | 4.47963i | 0.523364 | + | 0.216784i | ||||
\(428\) | −0.0808028 | − | 3.76557i | −0.00390575 | − | 0.182016i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 28.5117 | + | 18.6116i | 1.37496 | + | 0.897532i | ||||
\(431\) | 3.31967i | 0.159903i | 0.996799 | + | 0.0799513i | \(0.0254765\pi\) | ||||
−0.996799 | + | 0.0799513i | \(0.974524\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.53298i | 0.217841i | 0.994050 | + | 0.108921i | \(0.0347394\pi\) | ||||
−0.994050 | + | 0.108921i | \(0.965261\pi\) | |||||||
\(434\) | 20.4253 | − | 31.2901i | 0.980445 | − | 1.50197i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −6.66431 | + | 6.95659i | −0.319163 | + | 0.333160i | ||||
\(437\) | 15.9011 | + | 6.58646i | 0.760654 | + | 0.315073i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9703 | + | 20.9703i | 1.00086 | + | 1.00086i | 1.00000 | 0.000858061i | \(0.000273129\pi\) | |
0.000858061 | 1.00000i | \(0.499727\pi\) | ||||||||
\(440\) | −2.18739 | + | 13.2043i | −0.104280 | + | 0.629489i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.8039 | − | 20.1868i | −0.656583 | − | 0.960186i | ||||
\(443\) | −31.9708 | − | 13.2427i | −1.51898 | − | 0.629181i | −0.541590 | − | 0.840643i | \(-0.682178\pi\) |
−0.977386 | + | 0.211462i | \(0.932178\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.1058 | + | 26.8117i | 0.526464 | + | 1.27100i | ||||
\(446\) | −32.4243 | + | 6.81198i | −1.53534 | + | 0.322557i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 15.1360 | + | 30.7770i | 0.715110 | + | 1.45407i | ||||
\(449\) | − | 21.0485i | − | 0.993340i | −0.867940 | − | 0.496670i | \(-0.834556\pi\) | ||
0.867940 | − | 0.496670i | \(-0.165444\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.357852 | + | 0.148227i | −0.0168506 | + | 0.00697975i | ||||
\(452\) | 25.0125 | − | 10.9950i | 1.17649 | − | 0.517159i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 15.5787 | − | 10.6528i | 0.731143 | − | 0.499961i | ||||
\(455\) | 32.2827 | + | 32.2827i | 1.51344 | + | 1.51344i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.62656 | + | 4.62656i | −0.216421 | + | 0.216421i | −0.806988 | − | 0.590567i | \(-0.798904\pi\) |
0.590567 | + | 0.806988i | \(0.298904\pi\) | |||||||
\(458\) | −2.21110 | + | 11.7747i | −0.103318 | + | 0.550197i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −24.6550 | − | 23.6192i | −1.14955 | − | 1.10125i | ||||
\(461\) | 4.84388 | + | 11.6942i | 0.225602 | + | 0.544652i | 0.995633 | − | 0.0933550i | \(-0.0297592\pi\) |
−0.770031 | + | 0.638007i | \(0.779759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.2219 | 0.660950 | 0.330475 | − | 0.943815i | \(-0.392791\pi\) | ||||
0.330475 | + | 0.943815i | \(0.392791\pi\) | |||||||
\(464\) | −12.1172 | + | 33.2169i | −0.562526 | + | 1.54206i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.5695 | − | 16.1917i | 0.489622 | − | 0.750066i | ||||
\(467\) | −34.5241 | + | 14.3003i | −1.59758 | + | 0.661741i | −0.991071 | − | 0.133333i | \(-0.957432\pi\) |
−0.606512 | + | 0.795074i | \(0.707432\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.95321 | − | 16.7865i | 0.321069 | − | 0.775130i | ||||
\(470\) | 1.86997 | − | 9.95809i | 0.0862552 | − | 0.459333i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.842601 | + | 3.62260i | 0.0387838 | + | 0.166744i | ||||
\(473\) | 9.34754 | − | 9.34754i | 0.429800 | − | 0.429800i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.09821 | − | 9.89396i | 0.188039 | − | 0.453966i | ||||
\(476\) | −14.8284 | + | 38.0903i | −0.679657 | + | 1.74587i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.7873 | − | 7.51850i | 1.63687 | − | 0.343888i | ||||
\(479\) | 13.4016 | 0.612333 | 0.306167 | − | 0.951978i | \(-0.400954\pi\) | ||||
0.306167 | + | 0.951978i | \(0.400954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −36.8667 | −1.68098 | ||||||||
\(482\) | 34.5112 | − | 7.25041i | 1.57194 | − | 0.330247i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −15.6589 | − | 6.09591i | −0.711766 | − | 0.277087i | ||||
\(485\) | 15.2320 | − | 36.7734i | 0.691652 | − | 1.66979i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.26750 | − | 1.26750i | 0.0574358 | − | 0.0574358i | −0.677805 | − | 0.735241i | \(-0.737069\pi\) |
0.735241 | + | 0.677805i | \(0.237069\pi\) | |||||||
\(488\) | −4.08171 | + | 6.55599i | −0.184770 | + | 0.296776i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.71969 | − | 46.4347i | 0.393915 | − | 2.09771i | ||||
\(491\) | 8.81902 | − | 21.2910i | 0.397997 | − | 0.960849i | −0.590144 | − | 0.807298i | \(-0.700929\pi\) |
0.988141 | − | 0.153551i | \(-0.0490710\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.9311 | + | 16.1258i | −1.75337 | + | 0.726269i | ||||
\(494\) | 8.29953 | − | 12.7143i | 0.373414 | − | 0.572043i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.1634 | + | 16.6679i | 0.815563 | + | 0.748411i | ||||
\(497\) | −32.0684 | −1.43846 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.76574 | − | 6.67709i | −0.123812 | − | 0.298908i | 0.849805 | − | 0.527097i | \(-0.176719\pi\) |
−0.973617 | + | 0.228189i | \(0.926719\pi\) | |||||||
\(500\) | 5.61209 | − | 5.85823i | 0.250980 | − | 0.261988i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.26258 | − | 17.3741i | 0.145616 | − | 0.775445i | ||||
\(503\) | 17.1789 | − | 17.1789i | 0.765968 | − | 0.765968i | −0.211426 | − | 0.977394i | \(-0.567811\pi\) |
0.977394 | + | 0.211426i | \(0.0678108\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.99287 | − | 5.99287i | −0.266679 | − | 0.266679i | ||||
\(506\) | −10.9423 | + | 7.48245i | −0.486446 | + | 0.332636i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.6249 | + | 24.1706i | 0.471404 | + | 1.07240i | ||||
\(509\) | 0.432418 | − | 0.179113i | 0.0191666 | − | 0.00793905i | −0.373080 | − | 0.927799i | \(-0.621698\pi\) |
0.392246 | + | 0.919860i | \(0.371698\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.54815i | 0.422385i | ||||||||
\(512\) | −21.6637 | + | 6.53315i | −0.957411 | + | 0.288727i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 23.6359 | − | 4.96564i | 1.04254 | − | 0.219025i | ||||
\(515\) | −20.3379 | − | 49.0999i | −0.896193 | − | 2.16360i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.63437 | − | 1.50541i | −0.159839 | − | 0.0662077i | ||||
\(518\) | 34.7818 | + | 50.8649i | 1.52823 | + | 2.23488i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −24.4925 | + | 17.5310i | −1.07407 | + | 0.768786i | ||||
\(521\) | −20.6495 | − | 20.6495i | −0.904670 | − | 0.904670i | 0.0911655 | − | 0.995836i | \(-0.470941\pi\) |
−0.995836 | + | 0.0911655i | \(0.970941\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.6453 | − | 16.8358i | −1.77729 | − | 0.736180i | −0.993321 | − | 0.115386i | \(-0.963190\pi\) |
−0.783974 | − | 0.620794i | \(-0.786810\pi\) | |||||||
\(524\) | 9.68219 | + | 9.27540i | 0.422969 | + | 0.405198i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.4348 | + | 17.5172i | −0.498579 | + | 0.763788i | ||||
\(527\) | 29.3798i | 1.27980i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 10.8158i | − | 0.470252i | ||||||
\(530\) | 7.49109 | + | 4.88997i | 0.325392 | + | 0.212407i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −25.3721 | + | 0.544441i | −1.10002 | + | 0.0236045i | ||||
\(533\) | −0.805318 | − | 0.333574i | −0.0348822 | − | 0.0144487i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.90927 | − | 3.90927i | −0.169013 | − | 0.169013i | ||||
\(536\) | 10.1761 | + | 6.33557i | 0.439541 | + | 0.273655i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.6032 | + | 7.25055i | −0.457136 | + | 0.312593i | ||||
\(539\) | −16.9471 | − | 7.01973i | −0.729964 | − | 0.302361i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.26862 | − | 17.5480i | −0.312502 | − | 0.754447i | −0.999611 | − | 0.0278925i | \(-0.991120\pi\) |
0.687109 | − | 0.726555i | \(-0.258880\pi\) | |||||||
\(542\) | 1.64622 | + | 7.83583i | 0.0707111 | + | 0.336578i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23.1930 | − | 13.7583i | −0.994390 | − | 0.589881i | ||||
\(545\) | 14.1407i | 0.605721i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.22407 | + | 2.16388i | −0.223365 | + | 0.0925208i | −0.491560 | − | 0.870844i | \(-0.663573\pi\) |
0.268195 | + | 0.963365i | \(0.413573\pi\) | |||||||
\(548\) | −25.7600 | − | 10.0282i | −1.10041 | − | 0.428386i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.65571 | + | 6.80851i | 0.198520 | + | 0.290316i | ||||
\(551\) | −18.4998 | − | 18.4998i | −0.788116 | − | 0.788116i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −41.7471 | + | 41.7471i | −1.77527 | + | 1.77527i | ||||
\(554\) | 19.1635 | + | 3.59860i | 0.814180 | + | 0.152890i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.8903 | − | 0.383896i | 0.758719 | − | 0.0162808i | ||||
\(557\) | 7.20051 | + | 17.3836i | 0.305095 | + | 0.736565i | 0.999850 | + | 0.0173184i | \(0.00551288\pi\) |
−0.694755 | + | 0.719247i | \(0.744487\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.7492 | 1.25826 | ||||||||
\(560\) | 47.2949 | + | 17.2527i | 1.99858 | + | 0.729059i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.64483 | + | 6.29587i | 0.406843 | + | 0.265575i | ||||
\(563\) | 43.4445 | − | 17.9953i | 1.83097 | − | 0.758411i | 0.864007 | − | 0.503479i | \(-0.167947\pi\) |
0.966959 | − | 0.254932i | \(-0.0820530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.3475 | − | 37.0522i | 0.645675 | − | 1.55880i | ||||
\(566\) | −37.8226 | − | 7.10247i | −1.58980 | − | 0.298539i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.45766 | − | 20.8723i | 0.145080 | − | 0.875782i | ||||
\(569\) | −5.66061 | + | 5.66061i | −0.237305 | + | 0.237305i | −0.815733 | − | 0.578428i | \(-0.803666\pi\) |
0.578428 | + | 0.815733i | \(0.303666\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.7365 | + | 33.1629i | −0.574856 | + | 1.38783i | 0.322522 | + | 0.946562i | \(0.395469\pi\) |
−0.897378 | + | 0.441263i | \(0.854531\pi\) | |||||||
\(572\) | 4.70591 | + | 10.7055i | 0.196764 | + | 0.447619i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.299545 | + | 1.42581i | 0.0125028 | + | 0.0595120i | ||||
\(575\) | −21.0408 | −0.877461 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.38583 | 0.182584 | 0.0912922 | − | 0.995824i | \(-0.470900\pi\) | ||||
0.0912922 | + | 0.995824i | \(0.470900\pi\) | |||||||
\(578\) | −1.66465 | − | 7.92357i | −0.0692404 | − | 0.329577i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.8854 | + | 47.5124i | 0.867220 | + | 1.97284i | ||||
\(581\) | 5.89454 | − | 14.2307i | 0.244547 | − | 0.590388i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.45595 | − | 2.45595i | 0.101715 | − | 0.101715i | ||||
\(584\) | −6.21459 | − | 1.02950i | −0.257162 | − | 0.0426008i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.9354 | − | 3.55576i | −0.782215 | − | 0.146887i | ||||
\(587\) | −4.24918 | + | 10.2584i | −0.175382 | + | 0.423411i | −0.986988 | − | 0.160795i | \(-0.948594\pi\) |
0.811605 | + | 0.584206i | \(0.198594\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.8525 | + | 6.98052i | −0.694394 | + | 0.287627i | ||||
\(590\) | 4.57157 | + | 2.98419i | 0.188208 | + | 0.122857i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −36.8566 | + | 17.1541i | −1.51480 | + | 0.705028i | ||||
\(593\) | 5.76763 | 0.236848 | 0.118424 | − | 0.992963i | \(-0.462216\pi\) | ||||
0.118424 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.9602 | + | 55.4309i | 0.941277 | + | 2.27244i | ||||
\(596\) | 41.0788 | − | 0.881482i | 1.68265 | − | 0.0361069i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −29.3191 | − | 5.50565i | −1.19895 | − | 0.225143i | ||||
\(599\) | −13.4401 | + | 13.4401i | −0.549149 | + | 0.549149i | −0.926195 | − | 0.377045i | \(-0.876940\pi\) |
0.377045 | + | 0.926195i | \(0.376940\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.58677 | + | 8.58677i | 0.350262 | + | 0.350262i | 0.860207 | − | 0.509945i | \(-0.170334\pi\) |
−0.509945 | + | 0.860207i | \(0.670334\pi\) | |||||||
\(602\) | −28.0669 | − | 41.0449i | −1.14392 | − | 1.67287i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.6465 | − | 8.03757i | −0.840093 | − | 0.327044i | ||||
\(605\) | −22.7875 | + | 9.43890i | −0.926444 | + | 0.383746i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3743i | 0.542847i | 0.962460 | + | 0.271424i | \(0.0874944\pi\) | ||||
−0.962460 | + | 0.271424i | \(0.912506\pi\) | |||||||
\(608\) | 2.38129 | − | 16.5726i | 0.0965742 | − | 0.672107i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.33066 | + | 11.0937i | 0.0943655 | + | 0.449170i | ||||
\(611\) | −3.38780 | − | 8.17886i | −0.137056 | − | 0.330881i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.6749 | − | 4.42168i | −0.431154 | − | 0.178590i | 0.156542 | − | 0.987671i | \(-0.449965\pi\) |
−0.587697 | + | 0.809081i | \(0.699965\pi\) | |||||||
\(614\) | −27.3952 | + | 18.7330i | −1.10558 | + | 0.756004i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 10.3306 | − | 16.5928i | 0.416230 | − | 0.668544i | ||||
\(617\) | −14.8713 | − | 14.8713i | −0.598695 | − | 0.598695i | 0.341270 | − | 0.939965i | \(-0.389143\pi\) |
−0.939965 | + | 0.341270i | \(0.889143\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.25062 | − | 2.58909i | −0.251234 | − | 0.104064i | 0.253513 | − | 0.967332i | \(-0.418414\pi\) |
−0.504746 | + | 0.863268i | \(0.668414\pi\) | |||||||
\(620\) | 36.1773 | − | 0.776303i | 1.45291 | − | 0.0311771i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −21.2992 | − | 13.9035i | −0.854020 | − | 0.557480i | ||||
\(623\) | − | 42.3810i | − | 1.69796i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 29.9995i | − | 1.19998i | ||||||
\(626\) | 11.0842 | − | 16.9801i | 0.443012 | − | 0.678663i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.5113 | − | 12.9436i | −0.539159 | − | 0.516506i | ||||
\(629\) | −44.7612 | − | 18.5407i | −1.78475 | − | 0.739266i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.78346 | − | 5.78346i | −0.230236 | − | 0.230236i | 0.582555 | − | 0.812791i | \(-0.302053\pi\) |
−0.812791 | + | 0.582555i | \(0.802053\pi\) | |||||||
\(632\) | −22.6706 | − | 31.6731i | −0.901789 | − | 1.25989i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.18314 | − | 3.19262i | −0.0867037 | − | 0.126795i | ||||
\(635\) | 35.8052 | + | 14.8310i | 1.42088 | + | 0.588550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.7973 | − | 38.1381i | −0.625913 | − | 1.51109i | ||||
\(638\) | 19.7198 | − | 4.14290i | 0.780714 | − | 0.164019i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.3286 | + | 28.9226i | −0.645446 | + | 1.14327i | ||||
\(641\) | 29.5203i | 1.16598i | 0.812479 | + | 0.582990i | \(0.198117\pi\) | ||||
−0.812479 | + | 0.582990i | \(0.801883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.0660 | − | 4.16947i | 0.396964 | − | 0.164428i | −0.175266 | − | 0.984521i | \(-0.556079\pi\) |
0.572230 | + | 0.820093i | \(0.306079\pi\) | |||||||
\(644\) | 20.0649 | + | 45.6458i | 0.790669 | + | 1.79870i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.4709 | − | 11.2630i | 0.648040 | − | 0.443135i | ||||
\(647\) | 31.9256 | + | 31.9256i | 1.25512 | + | 1.25512i | 0.953393 | + | 0.301730i | \(0.0975641\pi\) |
0.301730 | + | 0.953393i | \(0.402436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.49878 | − | 1.49878i | 0.0588324 | − | 0.0588324i | ||||
\(650\) | −3.42571 | + | 18.2429i | −0.134368 | + | 0.715544i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.09375 | − | 7.40486i | 0.277813 | − | 0.289997i | ||||
\(653\) | 6.05626 | + | 14.6211i | 0.237000 | + | 0.572168i | 0.996970 | − | 0.0777900i | \(-0.0247864\pi\) |
−0.759970 | + | 0.649958i | \(0.774786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.6811 | 0.769002 | ||||||||
\(656\) | −0.960309 | + | 0.0412322i | −0.0374938 | + | 0.00160985i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.08814 | + | 12.3905i | −0.315309 | + | 0.483031i | ||||
\(659\) | 28.2612 | − | 11.7062i | 1.10090 | − | 0.456008i | 0.243106 | − | 0.970000i | \(-0.421834\pi\) |
0.857795 | + | 0.513992i | \(0.171834\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.64573 | − | 16.0442i | 0.258489 | − | 0.624047i | −0.740350 | − | 0.672221i | \(-0.765340\pi\) |
0.998839 | + | 0.0481743i | \(0.0153403\pi\) | |||||||
\(662\) | −1.55322 | + | 8.27131i | −0.0603675 | + | 0.321474i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.62674 | + | 5.37094i | 0.334782 | + | 0.208433i | ||||
\(665\) | −26.3403 | + | 26.3403i | −1.02143 | + | 1.02143i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.6711 | + | 47.4901i | −0.761666 | + | 1.83883i | ||||
\(668\) | 11.9979 | + | 4.67072i | 0.464212 | + | 0.180716i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.2194 | − | 3.61761i | 0.665245 | − | 0.139760i | ||||
\(671\) | 4.40116 | 0.169905 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.2884 | 1.32172 | 0.660860 | − | 0.750509i | \(-0.270192\pi\) | ||||
0.660860 | + | 0.750509i | \(0.270192\pi\) | |||||||
\(674\) | −8.10018 | + | 1.70176i | −0.312007 | + | 0.0655492i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.114915 | + | 0.295187i | −0.00441980 | + | 0.0113533i | ||||
\(677\) | −16.6560 | + | 40.2112i | −0.640142 | + | 1.54544i | 0.186345 | + | 0.982484i | \(0.440336\pi\) |
−0.826487 | + | 0.562956i | \(0.809664\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.1023 | + | 41.1023i | −1.57736 | + | 1.57736i | ||||
\(680\) | −38.5538 | + | 8.96744i | −1.47847 | + | 0.343886i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.59287 | − | 13.8077i | 0.0992861 | − | 0.528726i | ||||
\(683\) | −5.35596 | + | 12.9304i | −0.204940 | + | 0.494769i | −0.992613 | − | 0.121325i | \(-0.961286\pi\) |
0.787673 | + | 0.616094i | \(0.211286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4872 | + | 15.5277i | −1.43231 | + | 0.593284i | ||||
\(686\) | −14.5160 | + | 22.2376i | −0.554225 | + | 0.849034i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 29.7411 | − | 13.8423i | 1.13387 | − | 0.527733i | ||||
\(689\) | 7.81623 | 0.297775 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.9998 | − | 48.2837i | −0.760826 | − | 1.83680i | −0.480898 | − | 0.876777i | \(-0.659689\pi\) |
−0.279929 | − | 0.960021i | \(-0.590311\pi\) | |||||||
\(692\) | 16.1693 | + | 15.4899i | 0.614663 | + | 0.588838i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.04535 | + | 10.8920i | −0.0776404 | + | 0.413456i | ||||
\(695\) | 18.5731 | − | 18.5731i | 0.704517 | − | 0.704517i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.810008 | − | 0.810008i | −0.0306812 | − | 0.0306812i | ||||
\(698\) | −12.2622 | + | 8.38501i | −0.464132 | + | 0.317377i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28.4016 | − | 12.4848i | 1.07348 | − | 0.471879i | ||||
\(701\) | 22.6661 | − | 9.38859i | 0.856085 | − | 0.354602i | 0.0889098 | − | 0.996040i | \(-0.471662\pi\) |
0.767175 | + | 0.641438i | \(0.221662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 30.0806i | − | 1.13451i | ||||||
\(704\) | 9.68589 | + | 8.51290i | 0.365051 | + | 0.320842i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.0653 | − | 4.84577i | 0.868076 | − | 0.182373i | ||||
\(707\) | 4.73644 | + | 11.4348i | 0.178132 | + | 0.430049i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.91323 | − | 2.86355i | −0.259632 | − | 0.107543i | 0.249071 | − | 0.968485i | \(-0.419875\pi\) |
−0.508703 | + | 0.860942i | \(0.669875\pi\) | |||||||
\(710\) | −17.5291 | − | 25.6346i | −0.657857 | − | 0.962049i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 27.5845 | + | 4.56959i | 1.03377 | + | 0.171253i | ||||
\(713\) | 25.3420 | + | 25.3420i | 0.949064 | + | 0.949064i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 15.8586 | + | 6.56884i | 0.593078 | + | 0.245661i | ||||
\(716\) | −15.3118 | + | 15.9834i | −0.572230 | + | 0.597327i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.4366 | − | 15.9881i | 0.389490 | − | 0.596671i | ||||
\(719\) | − | 32.1395i | − | 1.19860i | −0.800525 | − | 0.599300i | \(-0.795446\pi\) | ||
0.800525 | − | 0.599300i | \(-0.204554\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.6119i | 2.89042i | ||||||||
\(722\) | −12.1265 | − | 7.91587i | −0.451303 | − | 0.294598i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.149522 | − | 6.96805i | −0.00555696 | − | 0.258965i | ||||
\(725\) | 29.5492 | + | 12.2397i | 1.09743 | + | 0.454570i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.0313 | + | 24.0313i | 0.891271 | + | 0.891271i | 0.994643 | − | 0.103372i | \(-0.0329632\pi\) |
−0.103372 | + | 0.994643i | \(0.532963\pi\) | |||||||
\(728\) | 42.8428 | − | 9.96505i | 1.58786 | − | 0.369329i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.63253 | + | 5.21919i | −0.282493 | + | 0.193171i | ||||
\(731\) | 36.1196 | + | 14.9612i | 1.33593 | + | 0.553361i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.28110 | − | 7.92127i | −0.121190 | − | 0.292579i | 0.851629 | − | 0.524145i | \(-0.175615\pi\) |
−0.972819 | + | 0.231566i | \(0.925615\pi\) | |||||||
\(734\) | 1.83492 | + | 8.73404i | 0.0677282 | + | 0.322379i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −31.8728 | + | 8.13803i | −1.17485 | + | 0.299972i | ||||
\(737\) | − | 6.83141i | − | 0.251638i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.01435 | − | 1.66280i | 0.147670 | − | 0.0611671i | −0.307624 | − | 0.951508i | \(-0.599534\pi\) |
0.455295 | + | 0.890341i | \(0.349534\pi\) | |||||||
\(740\) | −21.6477 | + | 55.6073i | −0.795784 | + | 2.04417i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.37421 | − | 10.7840i | −0.270716 | − | 0.395894i | ||||
\(743\) | −20.6253 | − | 20.6253i | −0.756669 | − | 0.756669i | 0.219046 | − | 0.975715i | \(-0.429706\pi\) |
−0.975715 | + | 0.219046i | \(0.929706\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 42.6465 | − | 42.6465i | 1.56245 | − | 1.56245i | ||||
\(746\) | 11.1234 | + | 2.08880i | 0.407258 | + | 0.0764765i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.329698 | + | 15.3646i | 0.0120550 | + | 0.561785i | ||||
\(749\) | 3.08968 | + | 7.45915i | 0.112894 | + | 0.272551i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.6475 | 0.498004 | 0.249002 | − | 0.968503i | \(-0.419897\pi\) | ||||
0.249002 | + | 0.968503i | \(0.419897\pi\) | |||||||
\(752\) | −7.19249 | − | 6.60028i | −0.262283 | − | 0.240687i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.9724 | + | 24.7873i | 1.38287 | + | 0.902700i | ||||
\(755\) | −30.0458 | + | 12.4454i | −1.09348 | + | 0.452933i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50145 | − | 3.62481i | 0.0545710 | − | 0.131746i | −0.894243 | − | 0.447582i | \(-0.852285\pi\) |
0.948814 | + | 0.315836i | \(0.102285\pi\) | |||||||
\(758\) | 30.2126 | + | 5.67344i | 1.09737 | + | 0.206069i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.3040 | − | 19.9841i | −0.518862 | − | 0.724901i | ||||
\(761\) | −10.5824 | + | 10.5824i | −0.383612 | + | 0.383612i | −0.872402 | − | 0.488790i | \(-0.837438\pi\) |
0.488790 | + | 0.872402i | \(0.337438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.90266 | − | 19.0787i | 0.286096 | − | 0.690696i | ||||
\(764\) | −8.83316 | + | 3.88287i | −0.319573 | + | 0.140477i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.31246 | + | 11.0071i | 0.0835525 | + | 0.397701i | ||||
\(767\) | 4.76999 | 0.172234 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.6343 | −1.53743 | −0.768715 | − | 0.639591i | \(-0.779104\pi\) | ||||
−0.768715 | + | 0.639591i | \(0.779104\pi\) | |||||||
\(770\) | −5.89875 | − | 28.0774i | −0.212576 | − | 1.01184i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.408070 | + | 0.179379i | −0.0146868 | + | 0.00645600i | ||||
\(773\) | 13.5374 | − | 32.6822i | 0.486906 | − | 1.17550i | −0.469362 | − | 0.883006i | \(-0.655516\pi\) |
0.956268 | − | 0.292490i | \(-0.0944839\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.7682 | − | 15.7682i | 0.566411 | − | 0.566411i | ||||
\(776\) | −22.3205 | − | 31.1839i | −0.801259 | − | 1.11944i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.65206 | + | 1.62472i | 0.310191 | + | 0.0582489i | ||||
\(779\) | 0.272172 | − | 0.657081i | 0.00975157 | − | 0.0235424i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1393 | + | 4.61404i | −0.398595 | + | 0.165103i | ||||
\(782\) | −32.8285 | − | 21.4295i | −1.17395 | − | 0.766318i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −33.5387 | − | 30.7772i | −1.19781 | − | 1.09918i | ||||
\(785\) | −27.4645 | −0.980249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −11.1547 | − | 26.9298i | −0.397622 | − | 0.959945i | −0.988228 | − | 0.152985i | \(-0.951111\pi\) |
0.590606 | − | 0.806960i | \(-0.298889\pi\) | |||||||
\(788\) | −1.05860 | − | 49.3328i | −0.0377110 | − | 1.75741i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −56.1912 | − | 10.5518i | −1.99919 | − | 0.375416i | ||||
\(791\) | −41.4139 | + | 41.4139i | −1.47251 | + | 1.47251i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.00350 | + | 7.00350i | 0.248702 | + | 0.248702i | ||||
\(794\) | −21.8703 | − | 31.9830i | −0.776147 | − | 1.13504i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −15.2589 | + | 39.1962i | −0.540836 | + | 1.38927i | ||||
\(797\) | 3.44606 | − | 1.42740i | 0.122066 | − | 0.0505612i | −0.320815 | − | 0.947142i | \(-0.603957\pi\) |
0.442880 | + | 0.896581i | \(0.353957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.6340i | − | 0.411582i | ||||||
\(800\) | 5.06363 | + | 19.8318i | 0.179026 | + | 0.701162i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.526329 | + | 2.50527i | 0.0185853 | + | 0.0884642i | ||||
\(803\) | 1.37380 | + | 3.31665i | 0.0484804 | + | 0.117042i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 67.6174 | + | 28.0080i | 2.38320 | + | 0.987154i | ||||
\(806\) | 26.0981 | − | 17.8461i | 0.919266 | − | 0.628602i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.95323 | + | 1.84988i | −0.279794 | + | 0.0650787i | ||||
\(809\) | 27.7746 | + | 27.7746i | 0.976503 | + | 0.976503i | 0.999730 | − | 0.0232274i | \(-0.00739419\pi\) |
−0.0232274 | + | 0.999730i | \(0.507394\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.7402 | + | 5.69137i | 0.482483 | + | 0.199851i | 0.610649 | − | 0.791902i | \(-0.290909\pi\) |
−0.128165 | + | 0.991753i | \(0.540909\pi\) | |||||||
\(812\) | −1.62602 | − | 75.7759i | −0.0570622 | − | 2.65921i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 19.4003 | + | 12.6640i | 0.679982 | + | 0.443873i | ||||
\(815\) | − | 15.0519i | − | 0.527246i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.2732i | 0.849212i | ||||||||
\(818\) | −15.7788 | + | 24.1721i | −0.551694 | + | 0.845156i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.976013 | + | 1.01882i | −0.0340839 | + | 0.0355787i | ||||
\(821\) | −9.08495 | − | 3.76311i | −0.317067 | − | 0.131333i | 0.218474 | − | 0.975843i | \(-0.429892\pi\) |
−0.535541 | + | 0.844509i | \(0.679892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −37.7132 | − | 37.7132i | −1.31460 | − | 1.31460i | −0.917985 | − | 0.396615i | \(-0.870185\pi\) |
−0.396615 | − | 0.917985i | \(-0.629815\pi\) | |||||||
\(824\) | −50.5151 | − | 8.36823i | −1.75978 | − | 0.291521i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.50024 | − | 6.58115i | −0.156583 | − | 0.228987i | ||||
\(827\) | 23.6871 | + | 9.81150i | 0.823680 | + | 0.341179i | 0.754398 | − | 0.656418i | \(-0.227929\pi\) |
0.0692824 | + | 0.997597i | \(0.477929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.99320 | − | 16.8831i | −0.242884 | − | 0.586374i | 0.754683 | − | 0.656090i | \(-0.227791\pi\) |
−0.997567 | + | 0.0697159i | \(0.977791\pi\) | |||||||
\(830\) | 14.5977 | − | 3.06680i | 0.506692 | − | 0.106450i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.86656 | + | 28.9595i | 0.0647112 | + | 1.00399i | ||||
\(833\) | − | 54.2495i | − | 1.87964i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.4599 | − | 7.23214i | 0.604225 | − | 0.250278i | ||||
\(836\) | −8.73491 | + | 3.83968i | −0.302103 | + | 0.132798i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.08470 | + | 2.79315i | −0.141104 | + | 0.0964879i | ||||
\(839\) | −9.56749 | − | 9.56749i | −0.330306 | − | 0.330306i | 0.522396 | − | 0.852703i | \(-0.325038\pi\) |
−0.852703 | + | 0.522396i | \(0.825038\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 34.7451 | − | 34.7451i | 1.19811 | − | 1.19811i | ||||
\(842\) | −2.98209 | + | 15.8804i | −0.102769 | + | 0.547276i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.43042 | + | 2.32831i | 0.0836586 | + | 0.0801437i | ||||
\(845\) | 0.177934 | + | 0.429570i | 0.00612111 | + | 0.0147777i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.0201 | 1.23766 | ||||||||
\(848\) | 7.81409 | − | 3.63689i | 0.268337 | − | 0.124891i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −13.3338 | + | 20.4265i | −0.457347 | + | 0.700623i | ||||
\(851\) | −54.6020 | + | 22.6169i | −1.87173 | + | 0.775297i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.73365 | + | 9.01383i | −0.127838 | + | 0.308628i | −0.974820 | − | 0.222994i | \(-0.928417\pi\) |
0.846982 | + | 0.531621i | \(0.178417\pi\) | |||||||
\(854\) | 3.05527 | − | 16.2702i | 0.104549 | − | 0.556753i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.18806 | + | 1.20672i | −0.177324 | + | 0.0412448i | ||||
\(857\) | 19.7027 | − | 19.7027i | 0.673032 | − | 0.673032i | −0.285382 | − | 0.958414i | \(-0.592120\pi\) |
0.958414 | + | 0.285382i | \(0.0921204\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.30760 | − | 20.0563i | 0.283452 | − | 0.684313i | −0.716460 | − | 0.697629i | \(-0.754239\pi\) |
0.999911 | + | 0.0133155i | \(0.00423857\pi\) | |||||||
\(860\) | 17.4684 | − | 44.8718i | 0.595666 | − | 1.53011i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.59442 | − | 0.965235i | 0.156487 | − | 0.0328760i | ||||
\(863\) | 29.3303 | 0.998415 | 0.499207 | − | 0.866483i | \(-0.333625\pi\) | ||||
0.499207 | + | 0.866483i | \(0.333625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.8674 | 1.11752 | ||||||||
\(866\) | 6.27364 | − | 1.31802i | 0.213187 | − | 0.0447882i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −49.2444 | − | 19.1706i | −1.67146 | − | 0.650693i | ||||
\(869\) | −8.49465 | + | 20.5079i | −0.288161 | + | 0.695683i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.8707 | − | 10.8707i | 0.368341 | − | 0.368341i | ||||
\(872\) | 11.5657 | + | 7.20069i | 0.391663 | + | 0.243846i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.49221 | − | 23.9223i | 0.151951 | − | 0.809183i | ||||
\(875\) | −6.65492 | + | 16.0664i | −0.224977 | + | 0.543144i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43.0165 | − | 17.8180i | 1.45256 | − | 0.601672i | 0.489756 | − | 0.871859i | \(-0.337086\pi\) |
0.962808 | + | 0.270188i | \(0.0870858\pi\) | |||||||
\(878\) | 22.9255 | − | 35.1203i | 0.773699 | − | 1.18525i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18.9107 | − | 0.811958i | 0.637480 | − | 0.0273711i | ||||
\(881\) | 54.5605 | 1.83819 | 0.919095 | − | 0.394035i | \(-0.128921\pi\) | ||||
0.919095 | + | 0.394035i | \(0.128921\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.61420 | − | 11.1397i | −0.155280 | − | 0.374879i | 0.827026 | − | 0.562164i | \(-0.190031\pi\) |
−0.982306 | + | 0.187285i | \(0.940031\pi\) | |||||||
\(884\) | −23.9248 | + | 24.9741i | −0.804679 | + | 0.839970i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.03203 | + | 48.0980i | −0.303437 | + | 1.61588i | ||||
\(887\) | −20.2635 | + | 20.2635i | −0.680383 | + | 0.680383i | −0.960086 | − | 0.279704i | \(-0.909764\pi\) |
0.279704 | + | 0.960086i | \(0.409764\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −40.0201 | − | 40.0201i | −1.34223 | − | 1.34223i | ||||
\(890\) | 33.8782 | − | 23.1662i | 1.13560 | − | 0.776534i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.8556 | + | 42.8946i | 0.631331 | + | 1.43622i | ||||
\(893\) | 6.67336 | − | 2.76419i | 0.223315 | − | 0.0925003i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.4895i | 1.08600i | ||||||||
\(896\) | 38.1943 | − | 29.8971i | 1.27598 | − | 0.998791i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.1311 | + | 6.12012i | −0.972118 | + | 0.204231i | ||||
\(899\) | −20.8479 | − | 50.3314i | −0.695318 | − | 1.67865i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.48997 | + | 3.93087i | 0.316157 | + | 0.130956i | ||||
\(902\) | 0.309197 | + | 0.452169i | 0.0102951 | + | 0.0150556i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −22.4897 | − | 31.4203i | −0.747997 | − | 1.04502i | ||||
\(905\) | −7.23396 | − | 7.23396i | −0.240465 | − | 0.240465i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3520 | + | 12.9864i | 1.04103 | + | 0.431208i | 0.836681 | − | 0.547691i | \(-0.184493\pi\) |
0.204347 | + | 0.978899i | \(0.434493\pi\) | |||||||
\(908\) | −19.2732 | − | 18.4634i | −0.639603 | − | 0.612730i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 35.2926 | − | 54.0658i | 1.16994 | − | 1.79226i | ||||
\(911\) | 44.6280i | 1.47859i | 0.673380 | + | 0.739296i | \(0.264842\pi\) | ||||
−0.673380 | + | 0.739296i | \(0.735158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 5.79128i | − | 0.191663i | ||||||
\(914\) | 7.74839 | + | 5.05793i | 0.256294 | + | 0.167301i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 16.9391 | − | 0.363485i | 0.559685 | − | 0.0120099i | ||||
\(917\) | −26.5538 | − | 10.9989i | −0.876883 | − | 0.363217i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.85821 | + | 7.85821i | 0.259219 | + | 0.259219i | 0.824736 | − | 0.565518i | \(-0.191324\pi\) |
−0.565518 | + | 0.824736i | \(0.691324\pi\) | |||||||
\(920\) | −25.5202 | + | 40.9902i | −0.841375 | + | 1.35141i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.7763 | − | 10.1042i | 0.486632 | − | 0.332763i | ||||
\(923\) | −25.0680 | − | 10.3835i | −0.825125 | − | 0.341778i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0726 | + | 33.9743i | 0.462705 | + | 1.11707i | ||||
\(926\) | −4.13521 | − | 19.6832i | −0.135892 | − | 0.646830i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 49.4955 | + | 7.11195i | 1.62477 | + | 0.233461i | ||||
\(929\) | − | 14.8136i | − | 0.486018i | −0.970024 | − | 0.243009i | \(-0.921866\pi\) | ||
0.970024 | − | 0.243009i | \(-0.0781344\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.1180 | − | 12.8895i | 1.01985 | − | 0.422436i | ||||
\(932\) | −25.4825 | − | 9.92022i | −0.834708 | − | 0.324948i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.8300 | + | 43.6233i | 0.976067 | + | 1.42740i | ||||
\(935\) | 15.9509 | + | 15.9509i | 0.521651 | + | 0.521651i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.7125 | + | 10.7125i | −0.349961 | + | 0.349961i | −0.860095 | − | 0.510134i | \(-0.829596\pi\) |
0.510134 | + | 0.860095i | \(0.329596\pi\) | |||||||
\(938\) | −25.2543 | − | 4.74235i | −0.824582 | − | 0.154843i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.3257 | + | 0.307406i | −0.467254 | + | 0.0100265i | ||||
\(941\) | −1.84380 | − | 4.45134i | −0.0601063 | − | 0.145109i | 0.890973 | − | 0.454056i | \(-0.150023\pi\) |
−0.951079 | + | 0.308947i | \(0.900023\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.39737 | −0.0455046 | ||||||||
\(944\) | 4.76868 | − | 2.21948i | 0.155207 | − | 0.0722378i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.6549 | − | 10.2191i | −0.508985 | − | 0.332251i | ||||
\(947\) | 46.3221 | − | 19.1872i | 1.50527 | − | 0.623501i | 0.530691 | − | 0.847565i | \(-0.321932\pi\) |
0.974574 | + | 0.224064i | \(0.0719324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.09163 | + | 7.46385i | −0.100358 | + | 0.242287i | ||||
\(950\) | −14.8849 | − | 2.79513i | −0.482928 | − | 0.0906861i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 57.0285 | + | 9.44723i | 1.84831 | + | 0.306186i | ||||
\(953\) | −2.40430 | + | 2.40430i | −0.0778828 | + | 0.0778828i | −0.744975 | − | 0.667092i | \(-0.767539\pi\) |
0.667092 | + | 0.744975i | \(0.267539\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.41999 | + | 13.0850i | −0.175387 | + | 0.423421i | ||||
\(956\) | −20.8112 | − | 47.3435i | −0.673083 | − | 1.53120i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.89668 | − | 18.5478i | −0.125896 | − | 0.599251i | ||||
\(959\) | 59.2558 | 1.91347 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.98312 | −0.225262 | ||||||||
\(962\) | 10.7195 | + | 51.0236i | 0.345609 | + | 1.64507i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −20.0691 | − | 45.6554i | −0.646383 | − | 1.47046i | ||||
\(965\) | −0.250390 | + | 0.604495i | −0.00806034 | + | 0.0194594i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.6984 | + | 12.6984i | −0.408354 | + | 0.408354i | −0.881164 | − | 0.472811i | \(-0.843239\pi\) |
0.472811 | + | 0.881164i | \(0.343239\pi\) | |||||||
\(968\) | −3.88374 | + | 23.4443i | −0.124828 | + | 0.753529i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −55.3233 | − | 10.3888i | −1.77633 | − | 0.333565i | ||||
\(971\) | −5.19719 | + | 12.5471i | −0.166786 | + | 0.402657i | −0.985069 | − | 0.172158i | \(-0.944926\pi\) |
0.818283 | + | 0.574815i | \(0.194926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.4386 | + | 14.6792i | −1.13611 | + | 0.470592i | ||||
\(974\) | −2.12276 | − | 1.38568i | −0.0680175 | − | 0.0443999i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.2603 | + | 3.74285i | 0.328424 | + | 0.119806i | ||||
\(977\) | 20.3021 | 0.649521 | 0.324761 | − | 0.945796i | \(-0.394716\pi\) | ||||
0.324761 | + | 0.945796i | \(0.394716\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.09784 | − | 14.7215i | −0.194888 | − | 0.470501i | ||||
\(980\) | −66.8010 | + | 1.43344i | −2.13388 | + | 0.0457895i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −32.0310 | − | 6.01490i | −1.02215 | − | 0.191943i | ||||
\(983\) | −11.4130 | + | 11.4130i | −0.364017 | + | 0.364017i | −0.865290 | − | 0.501272i | \(-0.832866\pi\) |
0.501272 | + | 0.865290i | \(0.332866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.2155 | − | 51.2155i | −1.63186 | − | 1.63186i | ||||
\(986\) | 33.6378 | + | 49.1919i | 1.07125 | + | 1.56659i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −20.0098 | − | 7.78971i | −0.636596 | − | 0.247824i | ||||
\(989\) | 44.0605 | − | 18.2505i | 1.40104 | − | 0.580331i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.0390i | 0.382431i | 0.981548 | + | 0.191216i | \(0.0612430\pi\) | ||||
−0.981548 | + | 0.191216i | \(0.938757\pi\) | |||||||
\(992\) | 17.7871 | − | 29.9846i | 0.564742 | − | 0.952013i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.32429 | + | 44.3826i | 0.295748 | + | 1.40773i | ||||
\(995\) | 23.6268 | + | 57.0401i | 0.749020 | + | 1.80829i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.2248 | + | 7.13474i | 0.545514 | + | 0.225959i | 0.638383 | − | 0.769719i | \(-0.279604\pi\) |
−0.0928685 | + | 0.995678i | \(0.529604\pi\) | |||||||
\(998\) | −8.43692 | + | 5.76923i | −0.267066 | + | 0.182622i | ||||
\(999\) | 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 | 288.2.w.a.251.5 | yes | 32 | |
3.2 | odd | 2 | 288.2.w.b.251.4 | yes | 32 | ||
4.3 | odd | 2 | 1152.2.w.b.143.2 | 32 | |||
12.11 | even | 2 | 1152.2.w.a.143.7 | 32 | |||
32.13 | even | 8 | 1152.2.w.a.1007.7 | 32 | |||
32.19 | odd | 8 | 288.2.w.b.179.4 | yes | 32 | ||
96.77 | odd | 8 | 1152.2.w.b.1007.2 | 32 | |||
96.83 | even | 8 | inner | 288.2.w.a.179.5 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.w.a.179.5 | ✓ | 32 | 96.83 | even | 8 | inner | |
288.2.w.a.251.5 | yes | 32 | 1.1 | even | 1 | trivial | |
288.2.w.b.179.4 | yes | 32 | 32.19 | odd | 8 | ||
288.2.w.b.251.4 | yes | 32 | 3.2 | odd | 2 | ||
1152.2.w.a.143.7 | 32 | 12.11 | even | 2 | |||
1152.2.w.a.1007.7 | 32 | 32.13 | even | 8 | |||
1152.2.w.b.143.2 | 32 | 4.3 | odd | 2 | |||
1152.2.w.b.1007.2 | 32 | 96.77 | odd | 8 |