Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(53,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.ce (of order \(12\), 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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 107.6 | ||
Character | \(\chi\) | \(=\) | 630.107 |
Dual form | 630.2.ce.c.53.6 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.258819 | + | 0.965926i | 0.183013 | + | 0.683013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | −0.923861 | + | 2.03629i | −0.413163 | + | 0.910657i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.56861 | + | 0.634242i | −0.970842 | + | 0.239721i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.20602 | − | 0.365351i | −0.697604 | − | 0.115534i | ||||
\(11\) | 4.28438 | − | 2.47359i | 1.29179 | − | 0.745816i | 0.312819 | − | 0.949813i | \(-0.398727\pi\) |
0.978971 | + | 0.203997i | \(0.0653933\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.34735 | + | 4.34735i | −1.20574 | + | 1.20574i | −0.233344 | + | 0.972394i | \(0.574967\pi\) |
−0.972394 | + | 0.233344i | \(0.925033\pi\) | |||||||
\(14\) | −1.27744 | − | 2.31693i | −0.341409 | − | 0.619225i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −4.25035 | − | 1.13888i | −1.03086 | − | 0.276219i | −0.296541 | − | 0.955020i | \(-0.595833\pi\) |
−0.734322 | + | 0.678802i | \(0.762500\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.22874 | − | 1.86412i | −0.740725 | − | 0.427658i | 0.0816079 | − | 0.996665i | \(-0.473994\pi\) |
−0.822333 | + | 0.569007i | \(0.807328\pi\) | |||||||
\(20\) | −0.218058 | − | 2.22541i | −0.0487593 | − | 0.497617i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.49819 | + | 3.49819i | 0.745816 | + | 0.745816i | ||||
\(23\) | 1.87844 | − | 0.503327i | 0.391682 | − | 0.104951i | −0.0576026 | − | 0.998340i | \(-0.518346\pi\) |
0.449284 | + | 0.893389i | \(0.351679\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.29296 | − | 3.76250i | −0.658592 | − | 0.752500i | ||||
\(26\) | −5.32440 | − | 3.07404i | −1.04420 | − | 0.602869i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.90736 | − | 1.83357i | 0.360457 | − | 0.346513i | ||||
\(29\) | −3.56555 | −0.662105 | −0.331053 | − | 0.943612i | \(-0.607404\pi\) | ||||
−0.331053 | + | 0.943612i | \(0.607404\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.272207 | − | 0.471476i | −0.0488898 | − | 0.0846796i | 0.840545 | − | 0.541742i | \(-0.182235\pi\) |
−0.889435 | + | 0.457062i | \(0.848902\pi\) | |||||||
\(32\) | 0.965926 | + | 0.258819i | 0.170753 | + | 0.0457532i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.40029i | − | 0.754644i | ||||||
\(35\) | 1.08153 | − | 5.81638i | 0.182813 | − | 0.983148i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.62530 | + | 0.435499i | −0.267198 | + | 0.0715955i | −0.389931 | − | 0.920844i | \(-0.627501\pi\) |
0.122732 | + | 0.992440i | \(0.460834\pi\) | |||||||
\(38\) | 0.964938 | − | 3.60120i | 0.156534 | − | 0.584191i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.09314 | − | 0.786607i | 0.330955 | − | 0.124373i | ||||
\(41\) | − | 0.268424i | − | 0.0419208i | −0.999780 | − | 0.0209604i | \(-0.993328\pi\) | ||
0.999780 | − | 0.0209604i | \(-0.00667239\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.39666 | + | 8.39666i | −1.28048 | + | 1.28048i | −0.340084 | + | 0.940395i | \(0.610455\pi\) |
−0.940395 | + | 0.340084i | \(0.889545\pi\) | |||||||
\(44\) | −2.47359 | + | 4.28438i | −0.372908 | + | 0.645895i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.972352 | + | 1.68416i | 0.143366 | + | 0.248316i | ||||
\(47\) | 0.240094 | + | 0.896043i | 0.0350213 | + | 0.130701i | 0.981223 | − | 0.192875i | \(-0.0617813\pi\) |
−0.946202 | + | 0.323577i | \(0.895115\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.19547 | − | 3.25824i | 0.885068 | − | 0.465462i | ||||
\(50\) | 2.78202 | − | 4.15456i | 0.393436 | − | 0.587544i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.59124 | − | 5.93859i | 0.220665 | − | 0.823534i | ||||
\(53\) | 2.06426 | − | 7.70392i | 0.283548 | − | 1.05822i | −0.666346 | − | 0.745643i | \(-0.732143\pi\) |
0.949894 | − | 0.312573i | \(-0.101191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.07877 | + | 11.0095i | 0.145462 | + | 1.48452i | ||||
\(56\) | 2.26476 | + | 1.36780i | 0.302641 | + | 0.182780i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.922831 | − | 3.44405i | −0.121174 | − | 0.452226i | ||||
\(59\) | 4.90077 | + | 8.48838i | 0.638026 | + | 1.10509i | 0.985865 | + | 0.167539i | \(0.0535820\pi\) |
−0.347840 | + | 0.937554i | \(0.613085\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.71103 | + | 9.89179i | −0.731222 | + | 1.26651i | 0.225139 | + | 0.974327i | \(0.427716\pi\) |
−0.956361 | + | 0.292187i | \(0.905617\pi\) | |||||||
\(62\) | 0.384959 | − | 0.384959i | 0.0488898 | − | 0.0488898i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −4.83612 | − | 12.8688i | −0.599847 | − | 1.59618i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.0109452 | + | 0.0408482i | −0.00133717 | + | 0.00499040i | −0.966591 | − | 0.256323i | \(-0.917489\pi\) |
0.965254 | + | 0.261313i | \(0.0841556\pi\) | |||||||
\(68\) | 4.25035 | − | 1.13888i | 0.515431 | − | 0.138109i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.89811 | − | 0.460709i | 0.704959 | − | 0.0550652i | ||||
\(71\) | 16.3109i | 1.93574i | 0.251443 | + | 0.967872i | \(0.419095\pi\) | ||||
−0.251443 | + | 0.967872i | \(0.580905\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.42396 | + | 2.25719i | 0.985950 | + | 0.264185i | 0.715548 | − | 0.698563i | \(-0.246177\pi\) |
0.270402 | + | 0.962748i | \(0.412844\pi\) | |||||||
\(74\) | −0.841319 | − | 1.45721i | −0.0978013 | − | 0.169397i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.72823 | 0.427658 | ||||||||
\(77\) | −9.43604 | + | 9.07102i | −1.07534 | + | 1.03374i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.93305 | − | 4.00280i | −0.780029 | − | 0.450350i | 0.0564118 | − | 0.998408i | \(-0.482034\pi\) |
−0.836440 | + | 0.548058i | \(0.815367\pi\) | |||||||
\(80\) | 1.30155 | + | 1.81823i | 0.145518 | + | 0.203285i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.259278 | − | 0.0694733i | 0.0286324 | − | 0.00767204i | ||||
\(83\) | −1.30281 | − | 1.30281i | −0.143002 | − | 0.143002i | 0.631981 | − | 0.774984i | \(-0.282242\pi\) |
−0.774984 | + | 0.631981i | \(0.782242\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.24583 | − | 7.60279i | 0.677455 | − | 0.824639i | ||||
\(86\) | −10.2838 | − | 5.93734i | −1.10893 | − | 0.640239i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.77861 | − | 1.28042i | −0.509402 | − | 0.136494i | ||||
\(89\) | −0.229324 | + | 0.397201i | −0.0243083 | + | 0.0421033i | −0.877924 | − | 0.478801i | \(-0.841072\pi\) |
0.853615 | + | 0.520904i | \(0.174405\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.40936 | − | 13.9239i | 0.881540 | − | 1.45962i | ||||
\(92\) | −1.37511 | + | 1.37511i | −0.143366 | + | 0.143366i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.803371 | + | 0.463826i | −0.0828613 | + | 0.0478400i | ||||
\(95\) | 6.77880 | − | 4.85248i | 0.695490 | − | 0.497854i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.6198 | − | 10.6198i | −1.07828 | − | 1.07828i | −0.996664 | − | 0.0816181i | \(-0.973991\pi\) |
−0.0816181 | − | 0.996664i | \(-0.526009\pi\) | |||||||
\(98\) | 4.75072 | + | 5.14107i | 0.479895 | + | 0.519327i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.73304 | + | 1.61194i | 0.473304 | + | 0.161194i | ||||
\(101\) | 4.33656 | − | 2.50371i | 0.431504 | − | 0.249129i | −0.268483 | − | 0.963284i | \(-0.586522\pi\) |
0.699987 | + | 0.714156i | \(0.253189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.73881 | + | 17.6855i | 0.466929 | + | 1.74260i | 0.650415 | + | 0.759579i | \(0.274595\pi\) |
−0.183486 | + | 0.983022i | \(0.558738\pi\) | |||||||
\(104\) | 6.14808 | 0.602869 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.97569 | 0.774667 | ||||||||
\(107\) | 1.00810 | + | 3.76228i | 0.0974568 | + | 0.363714i | 0.997380 | − | 0.0723338i | \(-0.0230447\pi\) |
−0.899924 | + | 0.436047i | \(0.856378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.47396 | − | 4.31509i | 0.715875 | − | 0.413311i | −0.0973573 | − | 0.995249i | \(-0.531039\pi\) |
0.813233 | + | 0.581939i | \(0.197706\pi\) | |||||||
\(110\) | −10.3552 | + | 3.89148i | −0.987326 | + | 0.371039i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.735033 | + | 2.54160i | −0.0694541 | + | 0.240159i | ||||
\(113\) | 13.9091 | + | 13.9091i | 1.30845 | + | 1.30845i | 0.922530 | + | 0.385925i | \(0.126118\pi\) |
0.385925 | + | 0.922530i | \(0.373882\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.710499 | + | 4.29005i | −0.0662544 | + | 0.400050i | ||||
\(116\) | 3.08785 | − | 1.78277i | 0.286700 | − | 0.165526i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.93073 | + | 6.93073i | −0.638026 | + | 0.638026i | ||||
\(119\) | 11.6398 | + | 0.229577i | 1.06702 | + | 0.0210453i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.73730 | − | 11.6693i | 0.612482 | − | 1.06085i | ||||
\(122\) | −11.0329 | − | 2.95625i | −0.998868 | − | 0.267646i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.471476 | + | 0.272207i | 0.0423398 | + | 0.0244449i | ||||
\(125\) | 10.7038 | − | 3.22940i | 0.957376 | − | 0.288846i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.200145 | − | 0.200145i | −0.0177600 | − | 0.0177600i | 0.698171 | − | 0.715931i | \(-0.253998\pi\) |
−0.715931 | + | 0.698171i | \(0.753998\pi\) | |||||||
\(128\) | −0.965926 | + | 0.258819i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.1786 | − | 8.00203i | 0.980432 | − | 0.701824i | ||||
\(131\) | −13.5876 | − | 7.84483i | −1.18716 | − | 0.685406i | −0.229498 | − | 0.973309i | \(-0.573709\pi\) |
−0.957660 | + | 0.287903i | \(0.907042\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.47568 | + | 2.74038i | 0.821645 | + | 0.237621i | ||||
\(134\) | −0.0422892 | −0.00365323 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.20015 | + | 3.81076i | 0.188661 | + | 0.326770i | ||||
\(137\) | 2.44530 | + | 0.655217i | 0.208916 | + | 0.0559789i | 0.361759 | − | 0.932272i | \(-0.382176\pi\) |
−0.152843 | + | 0.988250i | \(0.548843\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 2.80784i | − | 0.238158i | −0.992885 | − | 0.119079i | \(-0.962006\pi\) | ||
0.992885 | − | 0.119079i | \(-0.0379942\pi\) | |||||||
\(140\) | 1.97155 | + | 5.57790i | 0.166627 | + | 0.471419i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.7551 | + | 4.22156i | −1.32214 | + | 0.354266i | ||||
\(143\) | −7.87216 | + | 29.3793i | −0.658303 | + | 2.45682i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.29407 | − | 7.26049i | 0.273558 | − | 0.602951i | ||||
\(146\) | 8.72113i | 0.721766i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.18980 | − | 1.18980i | 0.0978013 | − | 0.0978013i | ||||
\(149\) | −9.80410 | + | 16.9812i | −0.803184 | + | 1.39115i | 0.114327 | + | 0.993443i | \(0.463529\pi\) |
−0.917510 | + | 0.397712i | \(0.869804\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.25264 | + | 2.16964i | 0.101939 | + | 0.176563i | 0.912483 | − | 0.409114i | \(-0.134162\pi\) |
−0.810545 | + | 0.585677i | \(0.800829\pi\) | |||||||
\(152\) | 0.964938 | + | 3.60120i | 0.0782668 | + | 0.292096i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.2042 | − | 6.76676i | −0.902857 | − | 0.545281i | ||||
\(155\) | 1.21154 | − | 0.118714i | 0.0973136 | − | 0.00953533i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.05560 | + | 18.8678i | −0.403481 | + | 1.50581i | 0.403360 | + | 0.915042i | \(0.367842\pi\) |
−0.806840 | + | 0.590770i | \(0.798824\pi\) | |||||||
\(158\) | 2.07200 | − | 7.73281i | 0.164839 | − | 0.615189i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.41941 | + | 1.72779i | −0.112214 | + | 0.136594i | ||||
\(161\) | −4.50574 | + | 2.48423i | −0.355102 | + | 0.195785i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.00961679 | + | 0.0358904i | 0.000753245 | + | 0.00281115i | 0.966301 | − | 0.257413i | \(-0.0828701\pi\) |
−0.965548 | + | 0.260224i | \(0.916203\pi\) | |||||||
\(164\) | 0.134212 | + | 0.232462i | 0.0104802 | + | 0.0181522i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.921227 | − | 1.59561i | 0.0715011 | − | 0.123844i | ||||
\(167\) | 9.26150 | − | 9.26150i | 0.716676 | − | 0.716676i | −0.251247 | − | 0.967923i | \(-0.580841\pi\) |
0.967923 | + | 0.251247i | \(0.0808405\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 24.7989i | − | 1.90761i | ||||||
\(170\) | 8.96027 | + | 4.06526i | 0.687221 | + | 0.311791i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.07339 | − | 11.4701i | 0.234344 | − | 0.874583i | ||||
\(173\) | 0.706925 | − | 0.189420i | 0.0537465 | − | 0.0144013i | −0.231846 | − | 0.972753i | \(-0.574476\pi\) |
0.285592 | + | 0.958351i | \(0.407810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8447 | + | 7.57585i | 0.819779 | + | 0.572680i | ||||
\(176\) | − | 4.94718i | − | 0.372908i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.443021 | − | 0.118707i | −0.0332058 | − | 0.00889747i | ||||
\(179\) | 3.20263 | + | 5.54712i | 0.239376 | + | 0.414611i | 0.960535 | − | 0.278158i | \(-0.0897238\pi\) |
−0.721159 | + | 0.692769i | \(0.756390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.70196 | −0.646812 | −0.323406 | − | 0.946260i | \(-0.604828\pi\) | ||||
−0.323406 | + | 0.946260i | \(0.604828\pi\) | |||||||
\(182\) | 15.6260 | + | 4.51904i | 1.15827 | + | 0.334974i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.68416 | − | 0.972352i | −0.124158 | − | 0.0716828i | ||||
\(185\) | 0.614753 | − | 3.71193i | 0.0451975 | − | 0.272907i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0273 | + | 5.63424i | −1.53767 | + | 0.412016i | ||||
\(188\) | −0.655949 | − | 0.655949i | −0.0478400 | − | 0.0478400i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.44162 | + | 5.29190i | 0.467324 | + | 0.383915i | ||||
\(191\) | 6.91128 | + | 3.99023i | 0.500083 | + | 0.288723i | 0.728748 | − | 0.684782i | \(-0.240103\pi\) |
−0.228665 | + | 0.973505i | \(0.573436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.8317 | − | 5.04593i | −1.35553 | − | 0.363214i | −0.493358 | − | 0.869826i | \(-0.664231\pi\) |
−0.862174 | + | 0.506612i | \(0.830898\pi\) | |||||||
\(194\) | 7.50936 | − | 13.0066i | 0.539141 | − | 0.933819i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.73632 | + | 5.91945i | −0.266880 | + | 0.422818i | ||||
\(197\) | −10.0960 | + | 10.0960i | −0.719312 | + | 0.719312i | −0.968464 | − | 0.249153i | \(-0.919848\pi\) |
0.249153 | + | 0.968464i | \(0.419848\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0002 | + | 6.35098i | −0.779785 | + | 0.450209i | −0.836354 | − | 0.548190i | \(-0.815317\pi\) |
0.0565691 | + | 0.998399i | \(0.481984\pi\) | |||||||
\(200\) | −0.332015 | + | 4.98896i | −0.0234770 | + | 0.352773i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.54078 | + | 3.54078i | 0.249129 | + | 0.249129i | ||||
\(203\) | 9.15848 | − | 2.26142i | 0.642800 | − | 0.158721i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.546590 | + | 0.247987i | 0.0381755 | + | 0.0173201i | ||||
\(206\) | −15.8564 | + | 9.15468i | −1.10477 | + | 0.637837i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.59124 | + | 5.93859i | 0.110333 | + | 0.411767i | ||||
\(209\) | −18.4442 | −1.27582 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.8900 | 1.30044 | 0.650220 | − | 0.759746i | \(-0.274677\pi\) | ||||
0.650220 | + | 0.759746i | \(0.274677\pi\) | |||||||
\(212\) | 2.06426 | + | 7.70392i | 0.141774 | + | 0.529108i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.37317 | + | 1.94750i | −0.230585 | + | 0.133128i | ||||
\(215\) | −9.34069 | − | 24.8554i | −0.637030 | − | 1.69512i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.998223 | + | 1.03839i | 0.0677638 | + | 0.0704906i | ||||
\(218\) | 6.10246 | + | 6.10246i | 0.413311 | + | 0.413311i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.43900 | − | 8.99513i | −0.434117 | − | 0.606451i | ||||
\(221\) | 23.4289 | − | 13.5267i | 1.57600 | − | 0.909903i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.93799 | − | 2.93799i | 0.196743 | − | 0.196743i | −0.601859 | − | 0.798602i | \(-0.705573\pi\) |
0.798602 | + | 0.601859i | \(0.205573\pi\) | |||||||
\(224\) | −2.64524 | − | 0.0521732i | −0.176742 | − | 0.00348597i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.83520 | + | 17.0351i | −0.654227 | + | 1.13316i | ||||
\(227\) | −0.861758 | − | 0.230907i | −0.0571969 | − | 0.0153259i | 0.230107 | − | 0.973165i | \(-0.426092\pi\) |
−0.287304 | + | 0.957839i | \(0.592759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8423 | + | 10.3013i | 1.17905 | + | 0.680728i | 0.955796 | − | 0.294032i | \(-0.0949971\pi\) |
0.223259 | + | 0.974759i | \(0.428330\pi\) | |||||||
\(230\) | −4.32777 | + | 0.424059i | −0.285364 | + | 0.0279616i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.52122 | + | 2.52122i | 0.165526 | + | 0.165526i | ||||
\(233\) | −4.65452 | + | 1.24718i | −0.304928 | + | 0.0817052i | −0.408038 | − | 0.912965i | \(-0.633787\pi\) |
0.103111 | + | 0.994670i | \(0.467120\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.04642 | − | 0.338918i | −0.133494 | − | 0.0221086i | ||||
\(236\) | −8.48838 | − | 4.90077i | −0.552547 | − | 0.319013i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.79085 | + | 11.3026i | 0.180904 | + | 0.732640i | ||||
\(239\) | −15.7251 | −1.01717 | −0.508585 | − | 0.861012i | \(-0.669831\pi\) | ||||
−0.508585 | + | 0.861012i | \(0.669831\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.64485 | − | 6.31306i | −0.234785 | − | 0.406660i | 0.724425 | − | 0.689354i | \(-0.242105\pi\) |
−0.959210 | + | 0.282693i | \(0.908772\pi\) | |||||||
\(242\) | 13.0155 | + | 3.48748i | 0.836666 | + | 0.224184i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 11.4221i | − | 0.731222i | ||||||
\(245\) | 0.910960 | + | 15.6259i | 0.0581991 | + | 0.998305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 22.1405 | − | 5.93252i | 1.40876 | − | 0.377477i | ||||
\(248\) | −0.140905 | + | 0.525863i | −0.00894746 | + | 0.0333924i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.88970 | + | 9.50323i | 0.372497 | + | 0.601037i | ||||
\(251\) | − | 8.22912i | − | 0.519418i | −0.965687 | − | 0.259709i | \(-0.916373\pi\) | ||
0.965687 | − | 0.259709i | \(-0.0836266\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.80294 | − | 6.80294i | 0.427697 | − | 0.427697i | ||||
\(254\) | 0.141524 | − | 0.245127i | 0.00888001 | − | 0.0153806i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0.337836 | + | 1.26082i | 0.0210736 | + | 0.0786479i | 0.975662 | − | 0.219281i | \(-0.0703710\pi\) |
−0.954588 | + | 0.297928i | \(0.903704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.89855 | − | 2.14946i | 0.242244 | − | 0.133561i | ||||
\(260\) | 10.6226 | + | 8.72666i | 0.658787 | + | 0.541205i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.06078 | − | 15.1550i | 0.250876 | − | 0.936282i | ||||
\(263\) | 3.82344 | − | 14.2693i | 0.235763 | − | 0.879881i | −0.742040 | − | 0.670356i | \(-0.766141\pi\) |
0.977803 | − | 0.209525i | \(-0.0671919\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.7803 | + | 11.3208i | 0.846520 | + | 0.695431i | ||||
\(266\) | −0.194514 | + | 9.86206i | −0.0119264 | + | 0.604682i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.0109452 | − | 0.0408482i | −0.000668587 | − | 0.00249520i | ||||
\(269\) | −10.5069 | − | 18.1984i | −0.640615 | − | 1.10958i | −0.985296 | − | 0.170858i | \(-0.945346\pi\) |
0.344680 | − | 0.938720i | \(-0.387987\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.95098 | − | 8.57534i | 0.300750 | − | 0.520915i | −0.675556 | − | 0.737309i | \(-0.736096\pi\) |
0.976306 | + | 0.216394i | \(0.0694296\pi\) | |||||||
\(272\) | −3.11148 | + | 3.11148i | −0.188661 | + | 0.188661i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.53156i | 0.152937i | ||||||||
\(275\) | −23.4152 | − | 7.97456i | −1.41199 | − | 0.480884i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.36596 | − | 20.0261i | 0.322410 | − | 1.20325i | −0.594481 | − | 0.804110i | \(-0.702642\pi\) |
0.916890 | − | 0.399139i | \(-0.130691\pi\) | |||||||
\(278\) | 2.71217 | − | 0.726722i | 0.162665 | − | 0.0435859i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.87756 | + | 3.34804i | −0.291490 | + | 0.200084i | ||||
\(281\) | − | 24.6495i | − | 1.47046i | −0.677816 | − | 0.735232i | \(-0.737073\pi\) | ||
0.677816 | − | 0.735232i | \(-0.262927\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.33016 | − | 1.42821i | −0.316845 | − | 0.0848985i | 0.0968916 | − | 0.995295i | \(-0.469110\pi\) |
−0.413737 | + | 0.910396i | \(0.635777\pi\) | |||||||
\(284\) | −8.15543 | − | 14.1256i | −0.483936 | − | 0.838202i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −30.4157 | −1.79852 | ||||||||
\(287\) | 0.170246 | + | 0.689476i | 0.0100493 | + | 0.0406985i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.04603 | + | 1.18128i | 0.120355 | + | 0.0694870i | ||||
\(290\) | 7.86566 | + | 1.30267i | 0.461888 | + | 0.0764957i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.42396 | + | 2.25719i | −0.492975 | + | 0.132092i | ||||
\(293\) | −13.1648 | − | 13.1648i | −0.769096 | − | 0.769096i | 0.208851 | − | 0.977947i | \(-0.433028\pi\) |
−0.977947 | + | 0.208851i | \(0.933028\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −21.8124 | + | 2.13731i | −1.26997 | + | 0.124439i | ||||
\(296\) | 1.45721 | + | 0.841319i | 0.0846984 | + | 0.0489007i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.9401 | − | 5.07498i | −1.09717 | − | 0.293986i | ||||
\(299\) | −5.97810 | + | 10.3544i | −0.345723 | + | 0.598809i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.2422 | − | 26.8932i | 0.936185 | − | 1.55010i | ||||
\(302\) | −1.77151 | + | 1.77151i | −0.101939 | + | 0.101939i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.22874 | + | 1.86412i | −0.185181 | + | 0.106914i | ||||
\(305\) | −14.8664 | − | 20.7680i | −0.851245 | − | 1.18917i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.9282 | + | 16.9282i | 0.966145 | + | 0.966145i | 0.999445 | − | 0.0333006i | \(-0.0106019\pi\) |
−0.0333006 | + | 0.999445i | \(0.510602\pi\) | |||||||
\(308\) | 3.63634 | − | 12.5738i | 0.207200 | − | 0.716456i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.428240 | + | 1.13954i | 0.0243224 | + | 0.0647213i | ||||
\(311\) | 23.6318 | − | 13.6438i | 1.34004 | − | 0.773671i | 0.353225 | − | 0.935539i | \(-0.385085\pi\) |
0.986812 | + | 0.161868i | \(0.0517518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.92449 | + | 7.18228i | 0.108778 | + | 0.405967i | 0.998746 | − | 0.0500564i | \(-0.0159401\pi\) |
−0.889968 | + | 0.456023i | \(0.849273\pi\) | |||||||
\(314\) | −19.5333 | −1.10233 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00559 | 0.450350 | ||||||||
\(317\) | −8.08855 | − | 30.1869i | −0.454298 | − | 1.69546i | −0.690143 | − | 0.723673i | \(-0.742452\pi\) |
0.235845 | − | 0.971791i | \(-0.424214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.2762 | + | 8.81970i | −0.855302 | + | 0.493809i | ||||
\(320\) | −2.03629 | − | 0.923861i | −0.113832 | − | 0.0516454i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.56576 | − | 3.70925i | −0.198712 | − | 0.206708i | ||||
\(323\) | 11.6003 | + | 11.6003i | 0.645458 | + | 0.645458i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.6726 | + | 2.04125i | 1.70141 | + | 0.113228i | ||||
\(326\) | −0.0321784 | + | 0.0185782i | −0.00178220 | + | 0.00102895i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.189805 | + | 0.189805i | −0.0104802 | + | 0.0104802i | ||||
\(329\) | −1.18502 | − | 2.14930i | −0.0653320 | − | 0.118495i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.38534 | + | 9.32768i | −0.296005 | + | 0.512696i | −0.975218 | − | 0.221245i | \(-0.928988\pi\) |
0.679213 | + | 0.733941i | \(0.262321\pi\) | |||||||
\(332\) | 1.77967 | + | 0.476862i | 0.0976723 | + | 0.0261712i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 11.3430 | + | 6.54887i | 0.620660 | + | 0.358338i | ||||
\(335\) | −0.0730669 | − | 0.0600258i | −0.00399207 | − | 0.00327956i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.8140 | − | 21.8140i | −1.18828 | − | 1.18828i | −0.977542 | − | 0.210740i | \(-0.932413\pi\) |
−0.210740 | − | 0.977542i | \(-0.567587\pi\) | |||||||
\(338\) | 23.9539 | − | 6.41843i | 1.30292 | − | 0.349117i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.60765 | + | 9.70712i | −0.0871870 | + | 0.526443i | ||||
\(341\) | −2.33248 | − | 1.34666i | −0.126311 | − | 0.0729256i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.8472 | + | 12.2986i | −0.747680 | + | 0.664060i | ||||
\(344\) | 11.8747 | 0.640239 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.365931 | + | 0.633812i | 0.0196726 | + | 0.0340739i | ||||
\(347\) | 5.94688 | + | 1.59346i | 0.319245 | + | 0.0855415i | 0.414883 | − | 0.909875i | \(-0.363822\pi\) |
−0.0956379 | + | 0.995416i | \(0.530489\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.197242i | 0.0105581i | 0.999986 | + | 0.00527907i | \(0.00168039\pi\) | ||||
−0.999986 | + | 0.00527907i | \(0.998320\pi\) | |||||||
\(350\) | −4.51090 | + | 12.4359i | −0.241118 | + | 0.664727i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.77861 | − | 1.28042i | 0.254701 | − | 0.0682469i | ||||
\(353\) | 2.64401 | − | 9.86759i | 0.140727 | − | 0.525199i | −0.859182 | − | 0.511670i | \(-0.829027\pi\) |
0.999908 | − | 0.0135287i | \(-0.00430643\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.2137 | − | 15.0690i | −1.76280 | − | 0.799778i | ||||
\(356\) | − | 0.458649i | − | 0.0243083i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.52921 | + | 4.52921i | −0.239376 | + | 0.239376i | ||||
\(359\) | 7.63203 | − | 13.2191i | 0.402803 | − | 0.697676i | −0.591260 | − | 0.806481i | \(-0.701369\pi\) |
0.994063 | + | 0.108805i | \(0.0347026\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.55014 | − | 4.41697i | −0.134218 | − | 0.232472i | ||||
\(362\) | −2.25223 | − | 8.40545i | −0.118375 | − | 0.441781i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.320765 | + | 16.2631i | −0.0168127 | + | 0.852420i | ||||
\(365\) | −12.3789 | + | 15.0683i | −0.647940 | + | 0.788711i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.14181 | + | 22.9216i | −0.320600 | + | 1.19650i | 0.598062 | + | 0.801450i | \(0.295938\pi\) |
−0.918662 | + | 0.395045i | \(0.870729\pi\) | |||||||
\(368\) | 0.503327 | − | 1.87844i | 0.0262377 | − | 0.0979205i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.74456 | − | 0.366913i | 0.194670 | − | 0.0190749i | ||||
\(371\) | −0.416117 | + | 21.0976i | −0.0216037 | + | 1.09533i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.81825 | + | 17.9820i | 0.249480 | + | 0.931071i | 0.971079 | + | 0.238760i | \(0.0767408\pi\) |
−0.721599 | + | 0.692311i | \(0.756593\pi\) | |||||||
\(374\) | −10.8845 | − | 18.8525i | −0.562825 | − | 0.974841i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.463826 | − | 0.803371i | 0.0239200 | − | 0.0414307i | ||||
\(377\) | 15.5007 | − | 15.5007i | 0.798326 | − | 0.798326i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.8805i | 1.79169i | 0.444367 | + | 0.895845i | \(0.353429\pi\) | ||||
−0.444367 | + | 0.895845i | \(0.646571\pi\) | |||||||
\(380\) | −3.44437 | + | 7.59177i | −0.176692 | + | 0.389449i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.06549 | + | 7.70853i | −0.105680 | + | 0.394403i | ||||
\(383\) | −30.0303 | + | 8.04661i | −1.53448 | + | 0.411162i | −0.924477 | − | 0.381238i | \(-0.875498\pi\) |
−0.610002 | + | 0.792400i | \(0.708831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −9.75364 | − | 27.5949i | −0.497091 | − | 1.40637i | ||||
\(386\) | − | 19.4960i | − | 0.992319i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.5070 | + | 3.88713i | 0.736480 | + | 0.197339i | ||||
\(389\) | 9.96369 | + | 17.2576i | 0.505179 | + | 0.874996i | 0.999982 | + | 0.00599092i | \(0.00190698\pi\) |
−0.494803 | + | 0.869005i | \(0.664760\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.55726 | −0.432759 | ||||||||
\(392\) | −6.68478 | − | 2.07694i | −0.337633 | − | 0.104901i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.3651 | − | 7.13897i | −0.622942 | − | 0.359656i | ||||
\(395\) | 14.5560 | − | 10.4197i | 0.732393 | − | 0.524271i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.5094 | + | 3.35189i | −0.627831 | + | 0.168227i | −0.558685 | − | 0.829380i | \(-0.688694\pi\) |
−0.0691456 | + | 0.997607i | \(0.522027\pi\) | |||||||
\(398\) | −8.98164 | − | 8.98164i | −0.450209 | − | 0.450209i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.90490 | + | 0.970538i | −0.245245 | + | 0.0485269i | ||||
\(401\) | −1.57729 | − | 0.910650i | −0.0787662 | − | 0.0454757i | 0.460100 | − | 0.887867i | \(-0.347814\pi\) |
−0.538866 | + | 0.842392i | \(0.681147\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.23305 | + | 0.866294i | 0.161050 | + | 0.0431532i | ||||
\(404\) | −2.50371 | + | 4.33656i | −0.124564 | + | 0.215752i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.55475 | + | 8.26112i | 0.226049 | + | 0.409992i | ||||
\(407\) | −5.88618 | + | 5.88618i | −0.291767 | + | 0.291767i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.8771 | + | 10.3214i | −0.883967 | + | 0.510359i | −0.871964 | − | 0.489569i | \(-0.837154\pi\) |
−0.0120026 | + | 0.999928i | \(0.503821\pi\) | |||||||
\(410\) | −0.0980689 | + | 0.592149i | −0.00484328 | + | 0.0292441i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.9467 | − | 12.9467i | −0.637837 | − | 0.637837i | ||||
\(413\) | −17.9718 | − | 18.6950i | −0.884336 | − | 0.919922i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.85652 | − | 1.44929i | 0.189309 | − | 0.0711427i | ||||
\(416\) | −5.32440 | + | 3.07404i | −0.261050 | + | 0.150717i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4.77372 | − | 17.8158i | −0.233490 | − | 0.871398i | ||||
\(419\) | 12.8948 | 0.629954 | 0.314977 | − | 0.949099i | \(-0.398003\pi\) | ||||
0.314977 | + | 0.949099i | \(0.398003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9311 | −0.825170 | −0.412585 | − | 0.910919i | \(-0.635374\pi\) | ||||
−0.412585 | + | 0.910919i | \(0.635374\pi\) | |||||||
\(422\) | 4.88909 | + | 18.2463i | 0.237997 | + | 0.888217i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.90715 | + | 3.98784i | −0.335441 | + | 0.193667i | ||||
\(425\) | 9.71122 | + | 19.7422i | 0.471063 | + | 0.957639i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.39559 | − | 29.0303i | 0.406291 | − | 1.40487i | ||||
\(428\) | −2.75418 | − | 2.75418i | −0.133128 | − | 0.133128i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.5909 | − | 15.4555i | 1.04121 | − | 0.745329i | ||||
\(431\) | 25.7429 | − | 14.8627i | 1.23999 | − | 0.715910i | 0.270901 | − | 0.962607i | \(-0.412679\pi\) |
0.969093 | + | 0.246697i | \(0.0793452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.0190 | − | 20.0190i | 0.962052 | − | 0.962052i | −0.0372534 | − | 0.999306i | \(-0.511861\pi\) |
0.999306 | + | 0.0372534i | \(0.0118609\pi\) | |||||||
\(434\) | −0.744650 | + | 1.23296i | −0.0357444 | + | 0.0591842i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.31509 | + | 7.47396i | −0.206655 | + | 0.357938i | ||||
\(437\) | −7.00326 | − | 1.87652i | −0.335012 | − | 0.0897661i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.54137 | − | 3.19931i | −0.264475 | − | 0.152695i | 0.361899 | − | 0.932217i | \(-0.382128\pi\) |
−0.626374 | + | 0.779522i | \(0.715462\pi\) | |||||||
\(440\) | 7.02209 | − | 8.54771i | 0.334765 | − | 0.407496i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.1296 | + | 19.1296i | 0.909903 | + | 0.909903i | ||||
\(443\) | 0.328032 | − | 0.0878959i | 0.0155853 | − | 0.00417606i | −0.251018 | − | 0.967982i | \(-0.580765\pi\) |
0.266603 | + | 0.963806i | \(0.414099\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.596954 | − | 0.833930i | −0.0282983 | − | 0.0395321i | ||||
\(446\) | 3.59829 | + | 2.07747i | 0.170384 | + | 0.0983713i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.634242 | − | 2.56861i | −0.0299651 | − | 0.121355i | ||||
\(449\) | −11.8831 | −0.560800 | −0.280400 | − | 0.959883i | \(-0.590467\pi\) | ||||
−0.280400 | + | 0.959883i | \(0.590467\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.663971 | − | 1.15003i | −0.0312652 | − | 0.0541529i | ||||
\(452\) | −19.0001 | − | 5.09107i | −0.893691 | − | 0.239464i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 0.892157i | − | 0.0418710i | ||||||
\(455\) | 20.5840 | + | 29.9877i | 0.964995 | + | 1.40584i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.4777 | − | 5.21904i | 0.911129 | − | 0.244136i | 0.227340 | − | 0.973816i | \(-0.426997\pi\) |
0.683790 | + | 0.729679i | \(0.260331\pi\) | |||||||
\(458\) | −5.33233 | + | 19.9005i | −0.249164 | + | 0.929891i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.52972 | − | 4.07055i | −0.0713234 | − | 0.189790i | ||||
\(461\) | 19.5952i | 0.912638i | 0.889816 | + | 0.456319i | \(0.150832\pi\) | ||||
−0.889816 | + | 0.456319i | \(0.849168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.2239 | − | 19.2239i | 0.893411 | − | 0.893411i | −0.101432 | − | 0.994843i | \(-0.532342\pi\) |
0.994843 | + | 0.101432i | \(0.0323423\pi\) | |||||||
\(464\) | −1.78277 | + | 3.08785i | −0.0827632 | + | 0.143350i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.40936 | − | 4.17313i | −0.111611 | − | 0.193316i | ||||
\(467\) | 7.83232 | + | 29.2306i | 0.362437 | + | 1.35263i | 0.870863 | + | 0.491526i | \(0.163561\pi\) |
−0.508426 | + | 0.861105i | \(0.669773\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.00220636 | − | 0.111865i | 0.000101880 | − | 0.00516544i | ||||
\(470\) | −0.202282 | − | 2.06441i | −0.00933058 | − | 0.0952240i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.53682 | − | 9.46756i | 0.116767 | − | 0.435780i | ||||
\(473\) | −15.2046 | + | 56.7444i | −0.699109 | + | 2.60911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.61839 | + | 18.2866i | 0.166023 | + | 0.839048i | ||||
\(476\) | −10.1952 | + | 5.62109i | −0.467294 | + | 0.257642i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.06995 | − | 15.1892i | −0.186155 | − | 0.694740i | ||||
\(479\) | −0.818104 | − | 1.41700i | −0.0373801 | − | 0.0647443i | 0.846730 | − | 0.532023i | \(-0.178568\pi\) |
−0.884110 | + | 0.467278i | \(0.845235\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.17250 | − | 8.95903i | 0.235846 | − | 0.408497i | ||||
\(482\) | 5.15460 | − | 5.15460i | 0.234785 | − | 0.234785i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 13.4746i | 0.612482i | ||||||||
\(485\) | 31.4364 | − | 11.8138i | 1.42745 | − | 0.536438i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.86735 | + | 6.96906i | −0.0846178 | + | 0.315798i | −0.995242 | − | 0.0974385i | \(-0.968935\pi\) |
0.910624 | + | 0.413237i | \(0.135602\pi\) | |||||||
\(488\) | 11.0329 | − | 2.95625i | 0.499434 | − | 0.133823i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.8577 | + | 4.92421i | −0.671204 | + | 0.222453i | ||||
\(491\) | 23.4235i | 1.05709i | 0.848907 | + | 0.528543i | \(0.177261\pi\) | ||||
−0.848907 | + | 0.528543i | \(0.822739\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.1548 | + | 4.06073i | 0.682540 | + | 0.182886i | ||||
\(494\) | 11.4607 | + | 19.8506i | 0.515643 | + | 0.893120i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.544414 | −0.0244449 | ||||||||
\(497\) | −10.3450 | − | 41.8962i | −0.464039 | − | 1.87930i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.5933 | + | 14.7763i | 1.14571 | + | 0.661477i | 0.947838 | − | 0.318751i | \(-0.103263\pi\) |
0.197873 | + | 0.980228i | \(0.436597\pi\) | |||||||
\(500\) | −7.65505 | + | 8.14863i | −0.342344 | + | 0.364418i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.94872 | − | 2.12985i | 0.354769 | − | 0.0950600i | ||||
\(503\) | −16.6368 | − | 16.6368i | −0.741797 | − | 0.741797i | 0.231127 | − | 0.972924i | \(-0.425759\pi\) |
−0.972924 | + | 0.231127i | \(0.925759\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.09191 | + | 11.1436i | 0.0485893 | + | 0.495883i | ||||
\(506\) | 8.33186 | + | 4.81040i | 0.370396 | + | 0.213848i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.273404 | + | 0.0732583i | 0.0121303 | + | 0.00325031i | ||||
\(509\) | 4.84247 | − | 8.38740i | 0.214639 | − | 0.371765i | −0.738522 | − | 0.674229i | \(-0.764476\pi\) |
0.953161 | + | 0.302464i | \(0.0978093\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.0694 | − | 0.455009i | −1.02053 | − | 0.0201284i | ||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.13042 | + | 0.652649i | −0.0498608 | + | 0.0287871i | ||||
\(515\) | −40.3908 | − | 6.68933i | −1.77983 | − | 0.294767i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.24510 | + | 3.24510i | 0.142719 | + | 0.142719i | ||||
\(518\) | 3.08524 | + | 3.20939i | 0.135558 | + | 0.141013i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.67997 | + | 12.5193i | −0.249083 | + | 0.549007i | ||||
\(521\) | −18.3916 | + | 10.6184i | −0.805750 | + | 0.465200i | −0.845478 | − | 0.534011i | \(-0.820684\pi\) |
0.0397281 | + | 0.999211i | \(0.487351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0569475 | + | 0.212531i | 0.00249014 | + | 0.00929332i | 0.967160 | − | 0.254169i | \(-0.0818021\pi\) |
−0.964670 | + | 0.263463i | \(0.915135\pi\) | |||||||
\(524\) | 15.6897 | 0.685406 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.7726 | 0.644118 | ||||||||
\(527\) | 0.620022 | + | 2.31395i | 0.0270086 | + | 0.100797i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6434 | + | 9.60906i | −0.723625 | + | 0.417785i | ||||
\(530\) | −7.36843 | + | 16.2408i | −0.320064 | + | 0.705456i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −9.57636 | + | 2.36460i | −0.415188 | + | 0.102519i | ||||
\(533\) | 1.16693 | + | 1.16693i | 0.0505455 | + | 0.0505455i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.59245 | − | 1.42304i | −0.371484 | − | 0.0615234i | ||||
\(536\) | 0.0366235 | − | 0.0211446i | 0.00158189 | − | 0.000913307i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.8590 | − | 14.8590i | 0.640615 | − | 0.640615i | ||||
\(539\) | 18.4842 | − | 29.2846i | 0.796173 | − | 1.26138i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.0652 | + | 36.4861i | −0.905666 | + | 1.56866i | −0.0856442 | + | 0.996326i | \(0.527295\pi\) |
−0.820021 | + | 0.572333i | \(0.806038\pi\) | |||||||
\(542\) | 9.56455 | + | 2.56281i | 0.410833 | + | 0.110082i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.81076 | − | 2.20015i | −0.163385 | − | 0.0943305i | ||||
\(545\) | 1.88188 | + | 19.2057i | 0.0806110 | + | 0.822682i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.6450 | + | 10.6450i | 0.455147 | + | 0.455147i | 0.897059 | − | 0.441911i | \(-0.145699\pi\) |
−0.441911 | + | 0.897059i | \(0.645699\pi\) | |||||||
\(548\) | −2.44530 | + | 0.655217i | −0.104458 | + | 0.0279895i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.64254 | − | 24.6813i | 0.0700380 | − | 1.05241i | ||||
\(551\) | 11.5122 | + | 6.64660i | 0.490438 | + | 0.283154i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.3470 | + | 5.88438i | 0.865243 | + | 0.250229i | ||||
\(554\) | 20.7325 | 0.880839 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.40392 | + | 2.43166i | 0.0595395 | + | 0.103125i | ||||
\(557\) | 30.4049 | + | 8.14696i | 1.28830 | + | 0.345198i | 0.837013 | − | 0.547183i | \(-0.184300\pi\) |
0.451283 | + | 0.892381i | \(0.350967\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 73.0065i | − | 3.08784i | ||||||
\(560\) | −4.49637 | − | 3.84483i | −0.190006 | − | 0.162474i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.8096 | − | 6.37975i | 1.00435 | − | 0.269114i | ||||
\(563\) | 0.0168462 | − | 0.0628710i | 0.000709984 | − | 0.00264969i | −0.965570 | − | 0.260144i | \(-0.916230\pi\) |
0.966280 | + | 0.257494i | \(0.0828967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −41.1730 | + | 15.4729i | −1.73216 | + | 0.650948i | ||||
\(566\) | − | 5.51819i | − | 0.231947i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.5335 | − | 11.5335i | 0.483936 | − | 0.483936i | ||||
\(569\) | −13.5754 | + | 23.5133i | −0.569110 | + | 0.985728i | 0.427544 | + | 0.903995i | \(0.359379\pi\) |
−0.996654 | + | 0.0817335i | \(0.973954\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.3600 | + | 23.1403i | 0.559101 | + | 0.968391i | 0.997572 | + | 0.0696454i | \(0.0221868\pi\) |
−0.438471 | + | 0.898745i | \(0.644480\pi\) | |||||||
\(572\) | −7.87216 | − | 29.3793i | −0.329151 | − | 1.22841i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.621920 | + | 0.342894i | −0.0259584 | + | 0.0143121i | ||||
\(575\) | −8.07940 | − | 5.41020i | −0.336934 | − | 0.225621i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.91412 | − | 14.6077i | 0.162947 | − | 0.608127i | −0.835346 | − | 0.549724i | \(-0.814733\pi\) |
0.998293 | − | 0.0584023i | \(-0.0186006\pi\) | |||||||
\(578\) | −0.611475 | + | 2.28205i | −0.0254340 | + | 0.0949210i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.777496 | + | 7.93480i | 0.0322838 | + | 0.329475i | ||||
\(581\) | 4.17271 | + | 2.52011i | 0.173113 | + | 0.104552i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.2123 | − | 38.1127i | −0.422949 | − | 1.57847i | ||||
\(584\) | −4.36056 | − | 7.55272i | −0.180441 | − | 0.312534i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.30892 | − | 16.1235i | 0.384548 | − | 0.666057i | ||||
\(587\) | −0.814359 | + | 0.814359i | −0.0336122 | + | 0.0336122i | −0.723713 | − | 0.690101i | \(-0.757566\pi\) |
0.690101 | + | 0.723713i | \(0.257566\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.02970i | 0.0836324i | ||||||||
\(590\) | −7.70995 | − | 20.5160i | −0.317414 | − | 0.844631i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.435499 | + | 1.62530i | −0.0178989 | + | 0.0667996i | ||||
\(593\) | −0.591195 | + | 0.158410i | −0.0242775 | + | 0.00650513i | −0.270937 | − | 0.962597i | \(-0.587334\pi\) |
0.246660 | + | 0.969102i | \(0.420667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.2211 | + | 23.4899i | −0.460018 | + | 0.962994i | ||||
\(596\) | − | 19.6082i | − | 0.803184i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.5488 | − | 3.09449i | −0.472266 | − | 0.126543i | ||||
\(599\) | 6.50281 | + | 11.2632i | 0.265698 | + | 0.460202i | 0.967746 | − | 0.251927i | \(-0.0810644\pi\) |
−0.702049 | + | 0.712129i | \(0.747731\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.4846 | −0.509258 | −0.254629 | − | 0.967039i | \(-0.581953\pi\) | ||||
−0.254629 | + | 0.967039i | \(0.581953\pi\) | |||||||
\(602\) | 30.1807 | + | 8.72828i | 1.23007 | + | 0.355738i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.16964 | − | 1.25264i | −0.0882816 | − | 0.0509694i | ||||
\(605\) | 17.5379 | + | 24.5000i | 0.713015 | + | 0.996065i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.60280 | − | 2.30511i | 0.349177 | − | 0.0935616i | −0.0799678 | − | 0.996797i | \(-0.525482\pi\) |
0.429145 | + | 0.903236i | \(0.358815\pi\) | |||||||
\(608\) | −2.63626 | − | 2.63626i | −0.106914 | − | 0.106914i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 16.2126 | − | 19.7349i | 0.656429 | − | 0.799045i | ||||
\(611\) | −4.93919 | − | 2.85164i | −0.199818 | − | 0.115365i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.7729 | − | 7.44173i | −1.12174 | − | 0.300569i | −0.350151 | − | 0.936693i | \(-0.613870\pi\) |
−0.771586 | + | 0.636125i | \(0.780536\pi\) | |||||||
\(614\) | −11.9701 | + | 20.7328i | −0.483072 | + | 0.836706i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.0865 | + | 0.258110i | 0.527269 | + | 0.0103996i | ||||
\(617\) | 3.97067 | − | 3.97067i | 0.159853 | − | 0.159853i | −0.622649 | − | 0.782502i | \(-0.713943\pi\) |
0.782502 | + | 0.622649i | \(0.213943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.1348 | − | 16.8210i | 1.17103 | − | 0.676092i | 0.217104 | − | 0.976148i | \(-0.430339\pi\) |
0.953921 | + | 0.300057i | \(0.0970056\pi\) | |||||||
\(620\) | −0.989871 | + | 0.708581i | −0.0397542 | + | 0.0284573i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.2953 | + | 19.2953i | 0.773671 | + | 0.773671i | ||||
\(623\) | 0.337122 | − | 1.16570i | 0.0135065 | − | 0.0467028i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.31282 | + | 24.7795i | −0.132513 | + | 0.991181i | ||||
\(626\) | −6.43946 | + | 3.71782i | −0.257373 | + | 0.148594i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.05560 | − | 18.8678i | −0.201740 | − | 0.752906i | ||||
\(629\) | 7.40409 | 0.295221 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.9081 | −0.633292 | −0.316646 | − | 0.948544i | \(-0.602557\pi\) | ||||
−0.316646 | + | 0.948544i | \(0.602557\pi\) | |||||||
\(632\) | 2.07200 | + | 7.73281i | 0.0824197 | + | 0.307595i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 27.0648 | − | 15.6259i | 1.07488 | − | 0.620583i | ||||
\(635\) | 0.592460 | − | 0.222648i | 0.0235111 | − | 0.00883550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.7692 | + | 41.0986i | −0.505934 | + | 1.62839i | ||||
\(638\) | −12.4729 | − | 12.4729i | −0.493809 | − | 0.493809i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.365351 | − | 2.20602i | 0.0144417 | − | 0.0872005i | ||||
\(641\) | −31.4224 | + | 18.1417i | −1.24111 | + | 0.716555i | −0.969320 | − | 0.245802i | \(-0.920949\pi\) |
−0.271789 | + | 0.962357i | \(0.587615\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.60079 | − | 2.60079i | 0.102565 | − | 0.102565i | −0.653962 | − | 0.756527i | \(-0.726894\pi\) |
0.756527 | + | 0.653962i | \(0.226894\pi\) | |||||||
\(644\) | 2.65997 | − | 4.40428i | 0.104818 | − | 0.173553i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.20266 | + | 14.2074i | −0.322729 | + | 0.558983i | ||||
\(647\) | −7.66073 | − | 2.05269i | −0.301174 | − | 0.0806994i | 0.105067 | − | 0.994465i | \(-0.466494\pi\) |
−0.406242 | + | 0.913766i | \(0.633161\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 41.9936 | + | 24.2450i | 1.64839 | + | 0.951699i | ||||
\(650\) | 5.96694 | + | 30.1557i | 0.234043 | + | 1.18281i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.0262736 | − | 0.0262736i | −0.00102895 | − | 0.00102895i | ||||
\(653\) | 45.9484 | − | 12.3118i | 1.79810 | − | 0.481799i | 0.804421 | − | 0.594060i | \(-0.202476\pi\) |
0.993679 | + | 0.112260i | \(0.0358090\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.5275 | − | 20.4209i | 1.11466 | − | 0.797909i | ||||
\(656\) | −0.232462 | − | 0.134212i | −0.00907612 | − | 0.00524010i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.76936 | − | 1.70092i | 0.0689770 | − | 0.0663087i | ||||
\(659\) | 40.4379 | 1.57524 | 0.787618 | − | 0.616164i | \(-0.211314\pi\) | ||||
0.787618 | + | 0.616164i | \(0.211314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.3620 | + | 26.6078i | 0.597513 | + | 1.03492i | 0.993187 | + | 0.116532i | \(0.0371777\pi\) |
−0.395674 | + | 0.918391i | \(0.629489\pi\) | |||||||
\(662\) | −10.4037 | − | 2.78766i | −0.404350 | − | 0.108345i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.84245i | 0.0715011i | ||||||||
\(665\) | −14.3344 | + | 16.7635i | −0.555865 | + | 0.650061i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.69767 | + | 1.79463i | −0.259335 | + | 0.0694885i | ||||
\(668\) | −3.38994 | + | 12.6514i | −0.131161 | + | 0.489499i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.0390693 | − | 0.0861130i | 0.00150938 | − | 0.00332684i | ||||
\(671\) | 56.5070i | 2.18143i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.13524 | − | 2.13524i | 0.0823073 | − | 0.0823073i | −0.664755 | − | 0.747062i | \(-0.731464\pi\) |
0.747062 | + | 0.664755i | \(0.231464\pi\) | |||||||
\(674\) | 15.4248 | − | 26.7165i | 0.594141 | − | 1.02908i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3995 | + | 21.4765i | 0.476902 | + | 0.826019i | ||||
\(677\) | 0.625198 | + | 2.33327i | 0.0240283 | + | 0.0896749i | 0.976899 | − | 0.213703i | \(-0.0685523\pi\) |
−0.952870 | + | 0.303378i | \(0.901886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.0137 | + | 20.5426i | 1.30533 | + | 0.788354i | ||||
\(680\) | −9.79245 | + | 0.959519i | −0.375523 | + | 0.0367959i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.697081 | − | 2.60154i | 0.0266926 | − | 0.0996182i | ||||
\(683\) | −5.33754 | + | 19.9200i | −0.204235 | + | 0.762216i | 0.785446 | + | 0.618930i | \(0.212434\pi\) |
−0.989681 | + | 0.143286i | \(0.954233\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.59333 | + | 4.37402i | −0.137294 | + | 0.167123i | ||||
\(686\) | −15.4634 | − | 10.1923i | −0.590396 | − | 0.389143i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.07339 | + | 11.4701i | 0.117172 | + | 0.437292i | ||||
\(689\) | 24.5176 | + | 42.4657i | 0.934046 | + | 1.61782i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.3078 | − | 35.1742i | 0.772546 | − | 1.33809i | −0.163617 | − | 0.986524i | \(-0.552316\pi\) |
0.936163 | − | 0.351566i | \(-0.114351\pi\) | |||||||
\(692\) | −0.517505 | + | 0.517505i | −0.0196726 | + | 0.0196726i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.15667i | 0.233704i | ||||||||
\(695\) | 5.71758 | + | 2.59405i | 0.216880 | + | 0.0983981i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.305703 | + | 1.14090i | −0.0115793 | + | 0.0432146i | ||||
\(698\) | −0.190521 | + | 0.0510501i | −0.00721134 | + | 0.00193227i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.1797 | − | 1.13855i | −0.498145 | − | 0.0430330i | ||||
\(701\) | − | 16.4455i | − | 0.621140i | −0.950551 | − | 0.310570i | \(-0.899480\pi\) | ||
0.950551 | − | 0.310570i | \(-0.100520\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.05951 | + | 1.62364i | 0.228539 | + | 0.0612368i | ||||
\(704\) | 2.47359 | + | 4.28438i | 0.0932270 | + | 0.161474i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.2157 | 0.384472 | ||||||||
\(707\) | −9.55095 | + | 9.18148i | −0.359200 | + | 0.345305i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.3375 | + | 10.0098i | 0.651122 | + | 0.375926i | 0.788886 | − | 0.614539i | \(-0.210658\pi\) |
−0.137764 | + | 0.990465i | \(0.543991\pi\) | |||||||
\(710\) | 5.95919 | − | 35.9821i | 0.223644 | − | 1.35038i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.443021 | − | 0.118707i | 0.0166029 | − | 0.00444873i | ||||
\(713\) | −0.748631 | − | 0.748631i | −0.0280365 | − | 0.0280365i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −52.5520 | − | 43.1724i | −1.96533 | − | 1.61456i | ||||
\(716\) | −5.54712 | − | 3.20263i | −0.207306 | − | 0.119688i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.7440 | + | 3.95063i | 0.550239 | + | 0.147436i | ||||
\(719\) | 20.2948 | − | 35.1516i | 0.756868 | − | 1.31093i | −0.187572 | − | 0.982251i | \(-0.560062\pi\) |
0.944440 | − | 0.328683i | \(-0.106605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.3890 | − | 42.4215i | −0.871052 | − | 1.57986i | ||||
\(722\) | 3.60644 | − | 3.60644i | 0.134218 | − | 0.134218i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.53612 | − | 4.35098i | 0.280078 | − | 0.161703i | ||||
\(725\) | 11.7412 | + | 13.4154i | 0.436057 | + | 0.498234i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.5089 | + | 17.5089i | 0.649368 | + | 0.649368i | 0.952840 | − | 0.303473i | \(-0.0981461\pi\) |
−0.303473 | + | 0.952840i | \(0.598146\pi\) | |||||||
\(728\) | −15.7920 | + | 3.89937i | −0.585290 | + | 0.144520i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −17.7587 | − | 8.05711i | −0.657281 | − | 0.298207i | ||||
\(731\) | 45.2516 | − | 26.1260i | 1.67369 | − | 0.966305i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.36477 | + | 5.09340i | 0.0504090 | + | 0.188129i | 0.986539 | − | 0.163524i | \(-0.0522862\pi\) |
−0.936130 | + | 0.351653i | \(0.885620\pi\) | |||||||
\(734\) | −23.7301 | −0.875896 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.94470 | 0.0716828 | ||||||||
\(737\) | 0.0541481 | + | 0.202083i | 0.00199457 | + | 0.00744384i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.95782 | − | 2.28505i | 0.145591 | − | 0.0840570i | −0.425435 | − | 0.904989i | \(-0.639879\pi\) |
0.571026 | + | 0.820932i | \(0.306546\pi\) | |||||||
\(740\) | 1.32357 | + | 3.52200i | 0.0486555 | + | 0.129471i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −20.4864 | + | 5.05852i | −0.752080 | + | 0.185704i | ||||
\(743\) | −12.0060 | − | 12.0060i | −0.440459 | − | 0.440459i | 0.451707 | − | 0.892166i | \(-0.350815\pi\) |
−0.892166 | + | 0.451707i | \(0.850815\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.5210 | − | 35.6523i | −0.935019 | − | 1.30620i | ||||
\(746\) | −16.1222 | + | 9.30815i | −0.590275 | + | 0.340796i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 15.3930 | − | 15.3930i | 0.562825 | − | 0.562825i | ||||
\(749\) | −4.97561 | − | 9.02444i | −0.181805 | − | 0.329746i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.40868 | − | 12.8322i | 0.270347 | − | 0.468254i | −0.698604 | − | 0.715509i | \(-0.746195\pi\) |
0.968951 | + | 0.247255i | \(0.0795284\pi\) | |||||||
\(752\) | 0.896043 | + | 0.240094i | 0.0326753 | + | 0.00875533i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 18.9844 | + | 10.9606i | 0.691370 | + | 0.399163i | ||||
\(755\) | −5.57530 | + | 0.546299i | −0.202906 | + | 0.0198818i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.0073 | − | 15.0073i | −0.545448 | − | 0.545448i | 0.379673 | − | 0.925121i | \(-0.376037\pi\) |
−0.925121 | + | 0.379673i | \(0.876037\pi\) | |||||||
\(758\) | −33.6920 | + | 9.02773i | −1.22375 | + | 0.327902i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.22455 | − | 1.36211i | −0.298336 | − | 0.0494090i | ||||
\(761\) | 2.48525 | + | 1.43486i | 0.0900904 | + | 0.0520137i | 0.544368 | − | 0.838846i | \(-0.316769\pi\) |
−0.454278 | + | 0.890860i | \(0.650103\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.4608 | + | 15.8241i | −0.595922 | + | 0.572870i | ||||
\(764\) | −7.98046 | −0.288723 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −15.5448 | − | 26.9245i | −0.561658 | − | 0.972821i | ||||
\(767\) | −58.2073 | − | 15.5966i | −2.10174 | − | 0.563161i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.3321i | 1.27411i | 0.770819 | + | 0.637055i | \(0.219847\pi\) | ||||
−0.770819 | + | 0.637055i | \(0.780153\pi\) | |||||||
\(770\) | 24.1302 | − | 16.5634i | 0.869591 | − | 0.596902i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 18.8317 | − | 5.04593i | 0.677766 | − | 0.181607i | ||||
\(773\) | 3.63582 | − | 13.5691i | 0.130771 | − | 0.488045i | −0.869208 | − | 0.494446i | \(-0.835371\pi\) |
0.999980 | + | 0.00640103i | \(0.00203753\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.877563 | + | 2.57673i | −0.0315230 | + | 0.0925589i | ||||
\(776\) | 15.0187i | 0.539141i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −14.0908 | + | 14.0908i | −0.505179 | + | 0.505179i | ||||
\(779\) | −0.500374 | + | 0.866673i | −0.0179278 | + | 0.0310518i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.3464 | + | 69.8820i | 1.44371 | + | 2.50058i | ||||
\(782\) | −2.21478 | − | 8.26568i | −0.0792005 | − | 0.295580i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.276021 | − | 6.99456i | 0.00985789 | − | 0.249806i | ||||
\(785\) | −33.7496 | − | 27.7259i | −1.20457 | − | 0.989579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.81054 | + | 14.2211i | −0.135831 | + | 0.506929i | 0.864162 | + | 0.503214i | \(0.167849\pi\) |
−0.999993 | + | 0.00371495i | \(0.998817\pi\) | |||||||
\(788\) | 3.69540 | − | 13.7914i | 0.131643 | − | 0.491299i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.8320 | + | 11.3632i | 0.492121 | + | 0.404286i | ||||
\(791\) | −44.5486 | − | 26.9052i | −1.58397 | − | 0.956639i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −18.1752 | − | 67.8309i | −0.645422 | − | 2.40875i | ||||
\(794\) | −6.47536 | − | 11.2157i | −0.229802 | − | 0.398029i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.35098 | − | 11.0002i | 0.225105 | − | 0.389892i | ||||
\(797\) | 17.8544 | − | 17.8544i | 0.632437 | − | 0.632437i | −0.316242 | − | 0.948679i | \(-0.602421\pi\) |
0.948679 | + | 0.316242i | \(0.102421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.08194i | − | 0.144409i | ||||||
\(800\) | −2.20695 | − | 4.48658i | −0.0780274 | − | 0.158624i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0.471387 | − | 1.75924i | 0.0166453 | − | 0.0621210i | ||||
\(803\) | 41.6749 | − | 11.1667i | 1.47067 | − | 0.394066i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.895942 | − | 11.4701i | −0.0315778 | − | 0.404268i | ||||
\(806\) | 3.34710i | 0.117897i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.83680 | − | 1.29602i | −0.170158 | − | 0.0455937i | ||||
\(809\) | −8.23813 | − | 14.2689i | −0.289637 | − | 0.501666i | 0.684086 | − | 0.729401i | \(-0.260201\pi\) |
−0.973723 | + | 0.227735i | \(0.926868\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.1358 | −0.847522 | −0.423761 | − | 0.905774i | \(-0.639290\pi\) | ||||
−0.423761 | + | 0.905774i | \(0.639290\pi\) | |||||||
\(812\) | −6.80077 | + | 6.53769i | −0.238660 | + | 0.229428i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.20907 | − | 4.16216i | −0.252678 | − | 0.145884i | ||||
\(815\) | −0.0819678 | − | 0.0135751i | −0.00287121 | − | 0.000475516i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 42.7630 | − | 11.4583i | 1.49609 | − | 0.400876i | ||||
\(818\) | −14.5966 | − | 14.5966i | −0.510359 | − | 0.510359i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.597354 | + | 0.0585321i | −0.0208605 | + | 0.00204403i | ||||
\(821\) | 22.7639 | + | 13.1427i | 0.794464 | + | 0.458684i | 0.841532 | − | 0.540207i | \(-0.181654\pi\) |
−0.0470674 | + | 0.998892i | \(0.514988\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4829 | + | 6.02428i | 0.783705 | + | 0.209993i | 0.628417 | − | 0.777876i | \(-0.283703\pi\) |
0.155287 | + | 0.987869i | \(0.450370\pi\) | |||||||
\(824\) | 9.15468 | − | 15.8564i | 0.318918 | − | 0.552383i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.4066 | − | 22.1981i | 0.466474 | − | 0.772370i | ||||
\(827\) | 3.56023 | − | 3.56023i | 0.123801 | − | 0.123801i | −0.642492 | − | 0.766293i | \(-0.722099\pi\) |
0.766293 | + | 0.642492i | \(0.222099\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.5490 | + | 14.7507i | −0.887354 | + | 0.512314i | −0.873076 | − | 0.487584i | \(-0.837878\pi\) |
−0.0142776 | + | 0.999898i | \(0.504545\pi\) | |||||||
\(830\) | 2.39804 | + | 3.35001i | 0.0832373 | + | 0.116281i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.34735 | − | 4.34735i | −0.150717 | − | 0.150717i | ||||
\(833\) | −30.0437 | + | 6.79277i | −1.04095 | + | 0.235355i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.3028 | + | 27.4155i | 0.356542 | + | 0.948751i | ||||
\(836\) | 15.9732 | − | 9.22212i | 0.552444 | − | 0.318954i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.33743 | + | 12.4555i | 0.115290 | + | 0.430267i | ||||
\(839\) | 18.9600 | 0.654573 | 0.327286 | − | 0.944925i | \(-0.393866\pi\) | ||||
0.327286 | + | 0.944925i | \(0.393866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.2869 | −0.561616 | ||||||||
\(842\) | −4.38208 | − | 16.3542i | −0.151017 | − | 0.563601i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.3592 | + | 9.44499i | −0.563107 | + | 0.325110i | ||||
\(845\) | 50.4978 | + | 22.9108i | 1.73718 | + | 0.788154i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.90428 | + | 34.2470i | −0.340315 | + | 1.17674i | ||||
\(848\) | −5.63966 | − | 5.63966i | −0.193667 | − | 0.193667i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −16.5561 | + | 14.4900i | −0.567869 | + | 0.497002i | ||||
\(851\) | −2.83384 | + | 1.63612i | −0.0971427 | + | 0.0560854i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2865 | − | 14.2865i | 0.489159 | − | 0.489159i | −0.418882 | − | 0.908041i | \(-0.637578\pi\) |
0.908041 | + | 0.418882i | \(0.137578\pi\) | |||||||
\(854\) | 30.2140 | + | 0.595925i | 1.03390 | + | 0.0203921i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.94750 | − | 3.37317i | 0.0665642 | − | 0.115293i | ||||
\(857\) | −14.9651 | − | 4.00989i | −0.511199 | − | 0.136975i | −0.00600644 | − | 0.999982i | \(-0.501912\pi\) |
−0.505193 | + | 0.863007i | \(0.668579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −42.4333 | − | 24.4989i | −1.44781 | − | 0.835891i | −0.449455 | − | 0.893303i | \(-0.648382\pi\) |
−0.998351 | + | 0.0574123i | \(0.981715\pi\) | |||||||
\(860\) | 20.5170 | + | 16.8551i | 0.699623 | + | 0.574753i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.0190 | + | 21.0190i | 0.715910 | + | 0.715910i | ||||
\(863\) | −50.5379 | + | 13.5416i | −1.72033 | + | 0.460961i | −0.977919 | − | 0.208984i | \(-0.932984\pi\) |
−0.742411 | + | 0.669945i | \(0.766318\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.267387 | + | 1.61450i | −0.00909142 | + | 0.0548948i | ||||
\(866\) | 24.5182 | + | 14.1556i | 0.833162 | + | 0.481026i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.38368 | − | 0.400162i | −0.0469652 | − | 0.0135824i | ||||
\(869\) | −39.6051 | −1.34351 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.129999 | − | 0.225164i | −0.00440484 | − | 0.00762940i | ||||
\(872\) | −8.33612 | − | 2.23366i | −0.282297 | − | 0.0756411i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 7.25031i | − | 0.245245i | ||||||
\(875\) | −25.4456 | + | 15.0838i | −0.860218 | + | 0.509927i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.1533 | + | 5.13210i | −0.646760 | + | 0.173299i | −0.567264 | − | 0.823536i | \(-0.691998\pi\) |
−0.0794965 | + | 0.996835i | \(0.525331\pi\) | |||||||
\(878\) | 1.65609 | − | 6.18060i | 0.0558902 | − | 0.208585i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.0739 | + | 4.57051i | 0.339591 | + | 0.154072i | ||||
\(881\) | 22.4079i | 0.754943i | 0.926021 | + | 0.377471i | \(0.123206\pi\) | ||||
−0.926021 | + | 0.377471i | \(0.876794\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.7816 | + | 24.7816i | −0.833966 | + | 0.833966i | −0.988057 | − | 0.154091i | \(-0.950755\pi\) |
0.154091 | + | 0.988057i | \(0.450755\pi\) | |||||||
\(884\) | −13.5267 | + | 23.4289i | −0.454951 | + | 0.787999i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.169802 | + | 0.294105i | 0.00570460 | + | 0.00988066i | ||||
\(887\) | 9.95542 | + | 37.1542i | 0.334270 | + | 1.24751i | 0.904658 | + | 0.426139i | \(0.140126\pi\) |
−0.570387 | + | 0.821376i | \(0.693207\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.641035 | + | 0.387154i | 0.0214996 | + | 0.0129847i | ||||
\(890\) | 0.651012 | − | 0.792450i | 0.0218220 | − | 0.0265630i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.07538 | + | 4.01337i | −0.0360064 | + | 0.134378i | ||||
\(893\) | 0.895127 | − | 3.34066i | 0.0299543 | − | 0.111791i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2543 | + | 1.39672i | −0.476470 | + | 0.0466872i | ||||
\(896\) | 2.31693 | − | 1.27744i | 0.0774032 | − | 0.0426761i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.07558 | − | 11.4782i | −0.102633 | − | 0.383033i | ||||
\(899\) | 0.970567 | + | 1.68107i | 0.0323702 | + | 0.0560668i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.5477 | + | 30.3935i | −0.584598 | + | 1.01255i | ||||
\(902\) | 0.938997 | − | 0.938997i | 0.0312652 | − | 0.0312652i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 19.6704i | − | 0.654227i | ||||||
\(905\) | 8.03940 | − | 17.7197i | 0.267239 | − | 0.589023i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.21125 | − | 30.6448i | 0.272650 | − | 1.01754i | −0.684750 | − | 0.728778i | \(-0.740089\pi\) |
0.957400 | − | 0.288766i | \(-0.0932448\pi\) | |||||||
\(908\) | 0.861758 | − | 0.230907i | 0.0285984 | − | 0.00766293i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −23.6383 | + | 27.6440i | −0.783602 | + | 0.916391i | ||||
\(911\) | 38.5994i | 1.27886i | 0.768851 | + | 0.639428i | \(0.220829\pi\) | ||||
−0.768851 | + | 0.639428i | \(0.779171\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.80437 | − | 2.35912i | −0.291382 | − | 0.0780756i | ||||
\(914\) | 10.0824 | + | 17.4632i | 0.333496 | + | 0.577633i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −20.6026 | −0.680728 | ||||||||
\(917\) | 39.8768 | + | 11.5324i | 1.31685 | + | 0.380834i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.71713 | − | 2.14609i | −0.122617 | − | 0.0707928i | 0.437437 | − | 0.899249i | \(-0.355886\pi\) |
−0.560054 | + | 0.828456i | \(0.689220\pi\) | |||||||
\(920\) | 3.53593 | − | 2.53113i | 0.116576 | − | 0.0834488i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −18.9275 | + | 5.07160i | −0.623343 | + | 0.167024i | ||||
\(923\) | −70.9091 | − | 70.9091i | −2.33400 | − | 2.33400i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.99062 | + | 4.68112i | 0.229850 | + | 0.153914i | ||||
\(926\) | 23.5444 | + | 13.5934i | 0.773716 | + | 0.446705i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.44405 | − | 0.922831i | −0.113057 | − | 0.0302934i | ||||
\(929\) | 8.99774 | − | 15.5845i | 0.295206 | − | 0.511312i | −0.679827 | − | 0.733373i | \(-0.737945\pi\) |
0.975033 | + | 0.222061i | \(0.0712783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −26.0773 | − | 1.02907i | −0.854650 | − | 0.0337264i | ||||
\(932\) | 3.40735 | − | 3.40735i | 0.111611 | − | 0.111611i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.2075 | + | 15.1309i | −0.857534 | + | 0.495098i | ||||
\(935\) | 7.95333 | − | 48.0229i | 0.260102 | − | 1.57052i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 25.1463 | + | 25.1463i | 0.821495 | + | 0.821495i | 0.986322 | − | 0.164828i | \(-0.0527068\pi\) |
−0.164828 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(938\) | 0.108624 | − | 0.0268216i | 0.00354671 | − | 0.000875756i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.94171 | − | 0.729697i | 0.0633316 | − | 0.0238001i | ||||
\(941\) | 19.8371 | − | 11.4529i | 0.646670 | − | 0.373355i | −0.140509 | − | 0.990079i | \(-0.544874\pi\) |
0.787179 | + | 0.616724i | \(0.211541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.135105 | − | 0.504219i | −0.00439962 | − | 0.0164196i | ||||
\(944\) | 9.80154 | 0.319013 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −58.7462 | −1.91000 | ||||||||
\(947\) | 5.17572 | + | 19.3161i | 0.168188 | + | 0.627687i | 0.997612 | + | 0.0690674i | \(0.0220023\pi\) |
−0.829424 | + | 0.558620i | \(0.811331\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −46.4347 | + | 26.8091i | −1.50733 | + | 0.870260i | ||||
\(950\) | −16.7270 | + | 8.22802i | −0.542696 | + | 0.266952i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.06825 | − | 8.39292i | −0.261494 | − | 0.272016i | ||||
\(953\) | 5.12950 | + | 5.12950i | 0.166161 | + | 0.166161i | 0.785289 | − | 0.619129i | \(-0.212514\pi\) |
−0.619129 | + | 0.785289i | \(0.712514\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.5103 | + | 10.3870i | −0.469543 | + | 0.336114i | ||||
\(956\) | 13.6183 | − | 7.86253i | 0.440448 | − | 0.254293i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.15697 | − | 1.15697i | 0.0373801 | − | 0.0373801i | ||||
\(959\) | −6.69658 | − | 0.132080i | −0.216244 | − | 0.00426508i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3518 | − | 26.5901i | 0.495220 | − | 0.857745i | ||||
\(962\) | 9.99250 | + | 2.67748i | 0.322171 | + | 0.0863255i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.31306 | + | 3.64485i | 0.203330 | + | 0.117393i | ||||
\(965\) | 27.6728 | − | 33.6850i | 0.890819 | − | 1.08436i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.0930 | − | 19.0930i | −0.613989 | − | 0.613989i | 0.329994 | − | 0.943983i | \(-0.392953\pi\) |
−0.943983 | + | 0.329994i | \(0.892953\pi\) | |||||||
\(968\) | −13.0155 | + | 3.48748i | −0.418333 | + | 0.112092i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.5476 | + | 27.3075i | 0.627636 | + | 0.876792i | ||||
\(971\) | −38.4438 | − | 22.1955i | −1.23372 | − | 0.712289i | −0.265917 | − | 0.963996i | \(-0.585675\pi\) |
−0.967804 | + | 0.251707i | \(0.919008\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.78085 | + | 7.21223i | 0.0570915 | + | 0.231214i | ||||
\(974\) | −7.21490 | −0.231180 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.71103 | + | 9.89179i | 0.182806 | + | 0.316628i | ||||
\(977\) | −8.10250 | − | 2.17106i | −0.259222 | − | 0.0694583i | 0.126868 | − | 0.991920i | \(-0.459508\pi\) |
−0.386089 | + | 0.922461i | \(0.626174\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.26902i | 0.0725181i | ||||||||
\(980\) | −8.60189 | − | 13.0770i | −0.274777 | − | 0.417729i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −22.6253 | + | 6.06244i | −0.722003 | + | 0.193460i | ||||
\(983\) | −0.734462 | + | 2.74105i | −0.0234257 | + | 0.0874259i | −0.976649 | − | 0.214841i | \(-0.931077\pi\) |
0.953223 | + | 0.302267i | \(0.0977434\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.2311 | − | 29.8858i | −0.357853 | − | 0.952239i | ||||
\(986\) | 15.6894i | 0.499654i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.2079 | + | 16.2079i | −0.515643 | + | 0.515643i | ||||
\(989\) | −11.5464 | + | 19.9989i | −0.367153 | + | 0.635928i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.4678 | + | 30.2552i | 0.554884 | + | 0.961088i | 0.997913 | + | 0.0645801i | \(0.0205708\pi\) |
−0.443028 | + | 0.896508i | \(0.646096\pi\) | |||||||
\(992\) | −0.140905 | − | 0.525863i | −0.00447373 | − | 0.0166962i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 37.7911 | − | 20.8361i | 1.19866 | − | 0.660880i | ||||
\(995\) | −2.76977 | − | 28.2671i | −0.0878075 | − | 0.896126i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.417054 | + | 1.55647i | −0.0132082 | + | 0.0492938i | −0.972215 | − | 0.234088i | \(-0.924790\pi\) |
0.959007 | + | 0.283382i | \(0.0914563\pi\) | |||||||
\(998\) | −7.64876 | + | 28.5456i | −0.242117 | + | 0.903594i | ||||
\(999\) | 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 | 630.2.ce.c.107.6 | yes | 32 | |
3.2 | odd | 2 | inner | 630.2.ce.c.107.3 | yes | 32 | |
5.3 | odd | 4 | inner | 630.2.ce.c.233.7 | yes | 32 | |
7.4 | even | 3 | inner | 630.2.ce.c.557.2 | yes | 32 | |
15.8 | even | 4 | inner | 630.2.ce.c.233.2 | yes | 32 | |
21.11 | odd | 6 | inner | 630.2.ce.c.557.7 | yes | 32 | |
35.18 | odd | 12 | inner | 630.2.ce.c.53.3 | ✓ | 32 | |
105.53 | even | 12 | inner | 630.2.ce.c.53.6 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.ce.c.53.3 | ✓ | 32 | 35.18 | odd | 12 | inner | |
630.2.ce.c.53.6 | yes | 32 | 105.53 | even | 12 | inner | |
630.2.ce.c.107.3 | yes | 32 | 3.2 | odd | 2 | inner | |
630.2.ce.c.107.6 | yes | 32 | 1.1 | even | 1 | trivial | |
630.2.ce.c.233.2 | yes | 32 | 15.8 | even | 4 | inner | |
630.2.ce.c.233.7 | yes | 32 | 5.3 | odd | 4 | inner | |
630.2.ce.c.557.2 | yes | 32 | 7.4 | even | 3 | inner | |
630.2.ce.c.557.7 | yes | 32 | 21.11 | odd | 6 | inner |