Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,2,Mod(19,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.69520363885\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.562828176.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + x^{6} + 2x^{5} - 6x^{4} + 4x^{3} + 4x^{2} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(1.40376 + 0.171630i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.31 |
Dual form | 588.2.o.d.19.3 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.850516 | + | 1.12988i | 0.601406 | + | 0.798944i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.553244 | + | 1.92196i | −0.276622 | + | 0.960979i | ||||
\(5\) | −0.834598 | + | 0.481855i | −0.373244 | + | 0.215492i | −0.674875 | − | 0.737932i | \(-0.735802\pi\) |
0.301631 | + | 0.953425i | \(0.402469\pi\) | |||||||
\(6\) | 1.40376 | − | 0.171630i | 0.573083 | − | 0.0700677i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.64212 | + | 1.00956i | −0.934130 | + | 0.356933i | ||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.25428 | − | 0.533167i | −0.396637 | − | 0.168602i | ||||
\(11\) | 4.74861 | + | 2.74161i | 1.43176 | + | 0.826626i | 0.997255 | − | 0.0740437i | \(-0.0235904\pi\) |
0.434504 | + | 0.900670i | \(0.356924\pi\) | |||||||
\(12\) | 1.38784 | + | 1.44010i | 0.400636 | + | 0.415722i | ||||
\(13\) | 3.75117i | 1.04039i | 0.854048 | + | 0.520193i | \(0.174140\pi\) | ||||
−0.854048 | + | 0.520193i | \(0.825860\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.963711i | 0.248829i | ||||||||
\(16\) | −3.38784 | − | 2.12662i | −0.846961 | − | 0.531656i | ||||
\(17\) | 0.594545 | + | 0.343260i | 0.144198 | + | 0.0832529i | 0.570363 | − | 0.821393i | \(-0.306802\pi\) |
−0.426165 | + | 0.904645i | \(0.640136\pi\) | |||||||
\(18\) | 0.553244 | − | 1.30151i | 0.130401 | − | 0.306768i | ||||
\(19\) | 2.44109 | + | 4.22809i | 0.560024 | + | 0.969989i | 0.997494 | + | 0.0707563i | \(0.0225413\pi\) |
−0.437470 | + | 0.899233i | \(0.644125\pi\) | |||||||
\(20\) | −0.464369 | − | 1.87065i | −0.103836 | − | 0.418289i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.941086 | + | 7.69713i | 0.200640 | + | 1.64103i | ||||
\(23\) | −1.07465 | + | 0.620450i | −0.224080 | + | 0.129373i | −0.607838 | − | 0.794061i | \(-0.707963\pi\) |
0.383758 | + | 0.923434i | \(0.374630\pi\) | |||||||
\(24\) | −0.446756 | + | 2.79292i | −0.0911937 | + | 0.570103i | ||||
\(25\) | −2.03563 | + | 3.52582i | −0.407126 | + | 0.705163i | ||||
\(26\) | −4.23836 | + | 3.19043i | −0.831210 | + | 0.625695i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.48011 | −0.460544 | −0.230272 | − | 0.973126i | \(-0.573962\pi\) | ||||
−0.230272 | + | 0.973126i | \(0.573962\pi\) | |||||||
\(30\) | −1.08887 | + | 0.819652i | −0.198800 | + | 0.149647i | ||||
\(31\) | 2.41401 | − | 4.18119i | 0.433569 | − | 0.750963i | −0.563609 | − | 0.826042i | \(-0.690587\pi\) |
0.997178 | + | 0.0750787i | \(0.0239208\pi\) | |||||||
\(32\) | −0.478592 | − | 5.63657i | −0.0846040 | − | 0.996415i | ||||
\(33\) | 4.74861 | − | 2.74161i | 0.826626 | − | 0.477253i | ||||
\(34\) | 0.117828 | + | 0.963711i | 0.0202073 | + | 0.165275i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.94109 | − | 0.481855i | 0.323514 | − | 0.0803092i | ||||
\(37\) | 1.36643 | + | 2.36673i | 0.224640 | + | 0.389089i | 0.956212 | − | 0.292677i | \(-0.0945459\pi\) |
−0.731571 | + | 0.681765i | \(0.761213\pi\) | |||||||
\(38\) | −2.70103 | + | 6.35418i | −0.438165 | + | 1.03078i | ||||
\(39\) | 3.24861 | + | 1.87558i | 0.520193 | + | 0.300334i | ||||
\(40\) | 1.71865 | − | 2.11569i | 0.271742 | − | 0.334521i | ||||
\(41\) | − | 9.42976i | − | 1.47268i | −0.676611 | − | 0.736340i | \(-0.736552\pi\) | ||
0.676611 | − | 0.736340i | \(-0.263448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 5.97437i | − | 0.911083i | −0.890215 | − | 0.455541i | \(-0.849446\pi\) | ||
0.890215 | − | 0.455541i | \(-0.150554\pi\) | |||||||
\(44\) | −7.89640 | + | 7.60984i | −1.19043 | + | 1.14723i | ||||
\(45\) | 0.834598 | + | 0.481855i | 0.124415 | + | 0.0718308i | ||||
\(46\) | −1.61504 | − | 0.686521i | −0.238125 | − | 0.101222i | ||||
\(47\) | 1.80752 | + | 3.13072i | 0.263654 | + | 0.456662i | 0.967210 | − | 0.253978i | \(-0.0817390\pi\) |
−0.703556 | + | 0.710640i | \(0.748406\pi\) | |||||||
\(48\) | −3.53563 | + | 1.87065i | −0.510324 | + | 0.270004i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −5.71508 | + | 0.698752i | −0.808234 | + | 0.0988184i | ||||
\(51\) | 0.594545 | − | 0.343260i | 0.0832529 | − | 0.0480661i | ||||
\(52\) | −7.20959 | − | 2.07531i | −0.999790 | − | 0.287794i | ||||
\(53\) | 2.04757 | − | 3.54650i | 0.281256 | − | 0.487150i | −0.690438 | − | 0.723391i | \(-0.742582\pi\) |
0.971694 | + | 0.236242i | \(0.0759157\pi\) | |||||||
\(54\) | −0.850516 | − | 1.12988i | −0.115741 | − | 0.153757i | ||||
\(55\) | −5.28424 | −0.712526 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.88217 | 0.646660 | ||||||||
\(58\) | −2.10937 | − | 2.80222i | −0.276974 | − | 0.367949i | ||||
\(59\) | 6.34315 | − | 10.9867i | 0.825808 | − | 1.43034i | −0.0754923 | − | 0.997146i | \(-0.524053\pi\) |
0.901300 | − | 0.433195i | \(-0.142614\pi\) | |||||||
\(60\) | −1.85221 | − | 0.533167i | −0.239119 | − | 0.0688316i | ||||
\(61\) | −9.01711 | + | 5.20603i | −1.15452 | + | 0.666564i | −0.949985 | − | 0.312295i | \(-0.898902\pi\) |
−0.204537 | + | 0.978859i | \(0.565569\pi\) | |||||||
\(62\) | 6.77738 | − | 0.828634i | 0.860728 | − | 0.105237i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.96158 | − | 5.33475i | 0.745198 | − | 0.666843i | ||||
\(65\) | −1.80752 | − | 3.13072i | −0.224195 | − | 0.388318i | ||||
\(66\) | 7.13645 | + | 3.03356i | 0.878436 | + | 0.373405i | ||||
\(67\) | 8.17396 | + | 4.71924i | 0.998608 | + | 0.576546i | 0.907836 | − | 0.419325i | \(-0.137733\pi\) |
0.0907716 | + | 0.995872i | \(0.471067\pi\) | |||||||
\(68\) | −0.988660 | + | 0.952783i | −0.119893 | + | 0.115542i | ||||
\(69\) | 1.24090i | 0.149387i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.1163i | − | 1.20058i | −0.799782 | − | 0.600291i | \(-0.795052\pi\) | ||
0.799782 | − | 0.600291i | \(-0.204948\pi\) | |||||||
\(72\) | 2.19536 | + | 1.78336i | 0.258726 | + | 0.210171i | ||||
\(73\) | 5.76850 | + | 3.33044i | 0.675152 | + | 0.389799i | 0.798026 | − | 0.602623i | \(-0.205878\pi\) |
−0.122874 | + | 0.992422i | \(0.539211\pi\) | |||||||
\(74\) | −1.51194 | + | 3.55685i | −0.175760 | + | 0.413475i | ||||
\(75\) | 2.03563 | + | 3.52582i | 0.235054 | + | 0.407126i | ||||
\(76\) | −9.47672 | + | 2.35250i | −1.08705 | + | 0.269850i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.643814 | + | 5.26574i | 0.0728976 | + | 0.596228i | ||||
\(79\) | 1.22492 | − | 0.707208i | 0.137814 | − | 0.0795671i | −0.429508 | − | 0.903063i | \(-0.641313\pi\) |
0.567322 | + | 0.823496i | \(0.307980\pi\) | |||||||
\(80\) | 3.85221 | + | 0.142425i | 0.430690 | + | 0.0159237i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 10.6545 | − | 8.02016i | 1.17659 | − | 0.885679i | ||||
\(83\) | −0.543780 | −0.0596876 | −0.0298438 | − | 0.999555i | \(-0.509501\pi\) | ||||
−0.0298438 | + | 0.999555i | \(0.509501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.661608 | −0.0717614 | ||||||||
\(86\) | 6.75030 | − | 5.08130i | 0.727904 | − | 0.547930i | ||||
\(87\) | −1.24005 | + | 2.14784i | −0.132948 | + | 0.230272i | ||||
\(88\) | −15.3142 | − | 2.44966i | −1.63250 | − | 0.261135i | ||||
\(89\) | −0.480107 | + | 0.277190i | −0.0508912 | + | 0.0293821i | −0.525230 | − | 0.850960i | \(-0.676021\pi\) |
0.474339 | + | 0.880343i | \(0.342687\pi\) | |||||||
\(90\) | 0.165402 | + | 1.35282i | 0.0174349 | + | 0.142600i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.597935 | − | 2.40870i | −0.0623390 | − | 0.251124i | ||||
\(93\) | −2.41401 | − | 4.18119i | −0.250321 | − | 0.433569i | ||||
\(94\) | −2.00000 | + | 4.70500i | −0.206284 | + | 0.485284i | ||||
\(95\) | −4.07465 | − | 2.35250i | −0.418050 | − | 0.241362i | ||||
\(96\) | −5.12071 | − | 2.40381i | −0.522630 | − | 0.245338i | ||||
\(97\) | 10.8747i | 1.10416i | 0.833790 | + | 0.552081i | \(0.186166\pi\) | ||||
−0.833790 | + | 0.552081i | \(0.813834\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.48322i | − | 0.551084i | ||||||
\(100\) | −5.65027 | − | 5.86303i | −0.565027 | − | 0.586303i | ||||
\(101\) | −12.4972 | − | 7.21527i | −1.24352 | − | 0.717946i | −0.273710 | − | 0.961812i | \(-0.588251\pi\) |
−0.969809 | + | 0.243866i | \(0.921584\pi\) | |||||||
\(102\) | 0.893512 | + | 0.379814i | 0.0884709 | + | 0.0376072i | ||||
\(103\) | −7.51235 | − | 13.0118i | −0.740214 | − | 1.28209i | −0.952398 | − | 0.304858i | \(-0.901391\pi\) |
0.212184 | − | 0.977230i | \(-0.431942\pi\) | |||||||
\(104\) | −3.78702 | − | 9.91103i | −0.371348 | − | 0.971857i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.74861 | − | 0.702851i | 0.558354 | − | 0.0682669i | ||||
\(107\) | 10.4925 | − | 6.05782i | 1.01434 | − | 0.585632i | 0.101883 | − | 0.994796i | \(-0.467513\pi\) |
0.912461 | + | 0.409165i | \(0.134180\pi\) | |||||||
\(108\) | 0.553244 | − | 1.92196i | 0.0532359 | − | 0.184940i | ||||
\(109\) | 3.03563 | − | 5.25787i | 0.290761 | − | 0.503612i | −0.683229 | − | 0.730204i | \(-0.739425\pi\) |
0.973990 | + | 0.226592i | \(0.0727583\pi\) | |||||||
\(110\) | −4.49433 | − | 5.97054i | −0.428518 | − | 0.569268i | ||||
\(111\) | 2.73287 | 0.259392 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.37939 | −0.694194 | −0.347097 | − | 0.937829i | \(-0.612833\pi\) | ||||
−0.347097 | + | 0.937829i | \(0.612833\pi\) | |||||||
\(114\) | 4.15237 | + | 5.51625i | 0.388905 | + | 0.516645i | ||||
\(115\) | 0.597935 | − | 1.03565i | 0.0557577 | − | 0.0965752i | ||||
\(116\) | 1.37210 | − | 4.76666i | 0.127397 | − | 0.442573i | ||||
\(117\) | 3.24861 | − | 1.87558i | 0.300334 | − | 0.173398i | ||||
\(118\) | 17.8085 | − | 2.17735i | 1.63941 | − | 0.200442i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.972923 | − | 2.54624i | −0.0888153 | − | 0.232439i | ||||
\(121\) | 9.53284 | + | 16.5114i | 0.866622 | + | 1.50103i | ||||
\(122\) | −13.5514 | − | 5.76041i | −1.22688 | − | 0.521523i | ||||
\(123\) | −8.16641 | − | 4.71488i | −0.736340 | − | 0.425126i | ||||
\(124\) | 6.70053 | + | 6.95284i | 0.601725 | + | 0.624383i | ||||
\(125\) | − | 8.74207i | − | 0.781915i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.6431i | 1.03316i | 0.856240 | + | 0.516578i | \(0.172794\pi\) | ||||
−0.856240 | + | 0.516578i | \(0.827206\pi\) | |||||||
\(128\) | 11.0980 | + | 2.19857i | 0.980937 | + | 0.194328i | ||||
\(129\) | −5.17396 | − | 2.98718i | −0.455541 | − | 0.263007i | ||||
\(130\) | 2.00000 | − | 4.70500i | 0.175412 | − | 0.412656i | ||||
\(131\) | −4.63078 | − | 8.02074i | −0.404593 | − | 0.700776i | 0.589681 | − | 0.807636i | \(-0.299253\pi\) |
−0.994274 | + | 0.106861i | \(0.965920\pi\) | |||||||
\(132\) | 2.64212 | + | 10.6434i | 0.229967 | + | 0.926389i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.61993 | + | 13.2494i | 0.139940 | + | 1.14457i | ||||
\(135\) | 0.834598 | − | 0.481855i | 0.0718308 | − | 0.0414715i | ||||
\(136\) | −1.91740 | − | 0.306707i | −0.164416 | − | 0.0262999i | ||||
\(137\) | −3.61504 | + | 6.26144i | −0.308854 | + | 0.534951i | −0.978112 | − | 0.208080i | \(-0.933279\pi\) |
0.669258 | + | 0.743030i | \(0.266612\pi\) | |||||||
\(138\) | −1.40207 | + | 1.05541i | −0.119352 | + | 0.0898422i | ||||
\(139\) | 5.30812 | 0.450229 | 0.225115 | − | 0.974332i | \(-0.427724\pi\) | ||||
0.225115 | + | 0.974332i | \(0.427724\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.61504 | 0.304441 | ||||||||
\(142\) | 11.4302 | − | 8.60406i | 0.959197 | − | 0.722037i | ||||
\(143\) | −10.2842 | + | 17.8128i | −0.860011 | + | 1.48958i | ||||
\(144\) | −0.147789 | + | 3.99727i | −0.0123157 | + | 0.333106i | ||||
\(145\) | 2.06989 | − | 1.19505i | 0.171895 | − | 0.0992438i | ||||
\(146\) | 1.14321 | + | 9.35029i | 0.0946127 | + | 0.773836i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.30473 | + | 1.31685i | −0.436046 | + | 0.108244i | ||||
\(149\) | −2.33080 | − | 4.03707i | −0.190947 | − | 0.330730i | 0.754617 | − | 0.656165i | \(-0.227822\pi\) |
−0.945564 | + | 0.325435i | \(0.894489\pi\) | |||||||
\(150\) | −2.25240 | + | 5.29878i | −0.183908 | + | 0.432643i | ||||
\(151\) | −10.5709 | − | 6.10309i | −0.860244 | − | 0.496662i | 0.00384988 | − | 0.999993i | \(-0.498775\pi\) |
−0.864094 | + | 0.503330i | \(0.832108\pi\) | |||||||
\(152\) | −10.7181 | − | 8.70668i | −0.869356 | − | 0.706205i | ||||
\(153\) | − | 0.686521i | − | 0.0555019i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.65281i | 0.373723i | ||||||||
\(156\) | −5.40207 | + | 5.20603i | −0.432511 | + | 0.416816i | ||||
\(157\) | 18.9944 | + | 10.9664i | 1.51592 | + | 0.875217i | 0.999825 | + | 0.0186856i | \(0.00594816\pi\) |
0.516095 | + | 0.856531i | \(0.327385\pi\) | |||||||
\(158\) | 1.84087 | + | 0.782517i | 0.146452 | + | 0.0622537i | ||||
\(159\) | −2.04757 | − | 3.54650i | −0.162383 | − | 0.281256i | ||||
\(160\) | 3.11545 | + | 4.47366i | 0.246298 | + | 0.353674i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.40376 | + | 0.171630i | −0.110290 | + | 0.0134845i | ||||
\(163\) | 3.48011 | − | 2.00924i | 0.272583 | − | 0.157376i | −0.357478 | − | 0.933922i | \(-0.616363\pi\) |
0.630061 | + | 0.776546i | \(0.283030\pi\) | |||||||
\(164\) | 18.1236 | + | 5.21696i | 1.41521 | + | 0.407376i | ||||
\(165\) | −2.64212 | + | 4.57628i | −0.205689 | + | 0.356263i | ||||
\(166\) | −0.462494 | − | 0.614404i | −0.0358965 | − | 0.0476870i | ||||
\(167\) | 14.7178 | 1.13890 | 0.569448 | − | 0.822027i | \(-0.307157\pi\) | ||||
0.569448 | + | 0.822027i | \(0.307157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.07126 | −0.0824047 | ||||||||
\(170\) | −0.562708 | − | 0.747535i | −0.0431577 | − | 0.0573333i | ||||
\(171\) | 2.44109 | − | 4.22809i | 0.186675 | − | 0.323330i | ||||
\(172\) | 11.4825 | + | 3.30528i | 0.875531 | + | 0.252026i | ||||
\(173\) | 10.0918 | − | 5.82648i | 0.767262 | − | 0.442979i | −0.0646349 | − | 0.997909i | \(-0.520588\pi\) |
0.831897 | + | 0.554930i | \(0.187255\pi\) | |||||||
\(174\) | −3.48148 | + | 0.425661i | −0.263930 | + | 0.0322693i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −10.2572 | − | 19.3866i | −0.773163 | − | 1.46132i | ||||
\(177\) | −6.34315 | − | 10.9867i | −0.476780 | − | 0.825808i | ||||
\(178\) | −0.721529 | − | 0.306707i | −0.0540809 | − | 0.0229887i | ||||
\(179\) | 2.24663 | + | 1.29709i | 0.167921 | + | 0.0969494i | 0.581605 | − | 0.813471i | \(-0.302425\pi\) |
−0.413684 | + | 0.910421i | \(0.635758\pi\) | |||||||
\(180\) | −1.38784 | + | 1.33748i | −0.103444 | + | 0.0996898i | ||||
\(181\) | − | 9.53343i | − | 0.708615i | −0.935129 | − | 0.354307i | \(-0.884717\pi\) | ||
0.935129 | − | 0.354307i | \(-0.115283\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4121i | 0.769681i | ||||||||
\(184\) | 2.21298 | − | 2.72423i | 0.163143 | − | 0.200833i | ||||
\(185\) | −2.28085 | − | 1.31685i | −0.167691 | − | 0.0968166i | ||||
\(186\) | 2.67107 | − | 6.28370i | 0.195852 | − | 0.460743i | ||||
\(187\) | 1.88217 | + | 3.26002i | 0.137638 | + | 0.238396i | ||||
\(188\) | −7.01711 | + | 1.74193i | −0.511775 | + | 0.127043i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.807521 | − | 6.60470i | −0.0585837 | − | 0.479155i | ||||
\(191\) | −7.21637 | + | 4.16637i | −0.522158 | + | 0.301468i | −0.737817 | − | 0.675001i | \(-0.764143\pi\) |
0.215659 | + | 0.976469i | \(0.430810\pi\) | |||||||
\(192\) | −1.63924 | − | 7.83026i | −0.118302 | − | 0.565100i | ||||
\(193\) | 6.18630 | − | 10.7150i | 0.445300 | − | 0.771282i | −0.552773 | − | 0.833332i | \(-0.686430\pi\) |
0.998073 | + | 0.0620498i | \(0.0197638\pi\) | |||||||
\(194\) | −12.2871 | + | 9.24915i | −0.882164 | + | 0.664050i | ||||
\(195\) | −3.61504 | −0.258878 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.23686 | 0.230617 | 0.115308 | − | 0.993330i | \(-0.463214\pi\) | ||||
0.115308 | + | 0.993330i | \(0.463214\pi\) | |||||||
\(198\) | 6.19536 | − | 4.66357i | 0.440285 | − | 0.331425i | ||||
\(199\) | −9.61504 | + | 16.6537i | −0.681592 | + | 1.18055i | 0.292903 | + | 0.956142i | \(0.405379\pi\) |
−0.974495 | + | 0.224410i | \(0.927955\pi\) | |||||||
\(200\) | 1.81886 | − | 11.3707i | 0.128613 | − | 0.804031i | ||||
\(201\) | 8.17396 | − | 4.71924i | 0.576546 | − | 0.332869i | ||||
\(202\) | −2.47672 | − | 20.2570i | −0.174261 | − | 1.42528i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.330804 | + | 1.33260i | 0.0231609 | + | 0.0933004i | ||||
\(205\) | 4.54378 | + | 7.87006i | 0.317351 | + | 0.549669i | ||||
\(206\) | 8.31232 | − | 19.5547i | 0.579147 | − | 1.36244i | ||||
\(207\) | 1.07465 | + | 0.620450i | 0.0746934 | + | 0.0431243i | ||||
\(208\) | 7.97732 | − | 12.7084i | 0.553128 | − | 0.881167i | ||||
\(209\) | 26.7700i | 1.85172i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 9.24637i | − | 0.636546i | −0.947999 | − | 0.318273i | \(-0.896897\pi\) | ||
0.947999 | − | 0.318273i | \(-0.103103\pi\) | |||||||
\(212\) | 5.68342 | + | 5.89743i | 0.390339 | + | 0.405037i | ||||
\(213\) | −8.76095 | − | 5.05814i | −0.600291 | − | 0.346578i | ||||
\(214\) | 15.7686 | + | 6.70291i | 1.07792 | + | 0.458201i | ||||
\(215\) | 2.87878 | + | 4.98620i | 0.196331 | + | 0.340056i | ||||
\(216\) | 2.64212 | − | 1.00956i | 0.179773 | − | 0.0686918i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.52260 | − | 1.04201i | 0.577223 | − | 0.0705740i | ||||
\(219\) | 5.76850 | − | 3.33044i | 0.389799 | − | 0.225051i | ||||
\(220\) | 2.92347 | − | 10.1561i | 0.197100 | − | 0.684723i | ||||
\(221\) | −1.28763 | + | 2.23024i | −0.0866152 | + | 0.150022i | ||||
\(222\) | 2.32435 | + | 3.08781i | 0.156000 | + | 0.207240i | ||||
\(223\) | 1.94585 | 0.130303 | 0.0651517 | − | 0.997875i | \(-0.479247\pi\) | ||||
0.0651517 | + | 0.997875i | \(0.479247\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.07126 | 0.271417 | ||||||||
\(226\) | −6.27629 | − | 8.33780i | −0.417492 | − | 0.554622i | ||||
\(227\) | 4.32265 | − | 7.48706i | 0.286905 | − | 0.496933i | −0.686165 | − | 0.727446i | \(-0.740707\pi\) |
0.973069 | + | 0.230513i | \(0.0740404\pi\) | |||||||
\(228\) | −2.70103 | + | 9.38333i | −0.178880 | + | 0.621426i | ||||
\(229\) | −14.5396 | + | 8.39446i | −0.960805 | + | 0.554721i | −0.896421 | − | 0.443204i | \(-0.853842\pi\) |
−0.0643846 | + | 0.997925i | \(0.520508\pi\) | |||||||
\(230\) | 1.67871 | − | 0.205247i | 0.110691 | − | 0.0135336i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.55274 | − | 2.50381i | 0.430208 | − | 0.164383i | ||||
\(233\) | 0.523283 | + | 0.906353i | 0.0342814 | + | 0.0593772i | 0.882657 | − | 0.470018i | \(-0.155752\pi\) |
−0.848376 | + | 0.529395i | \(0.822419\pi\) | |||||||
\(234\) | 4.88217 | + | 2.07531i | 0.319158 | + | 0.135667i | ||||
\(235\) | −3.01711 | − | 1.74193i | −0.196814 | − | 0.113631i | ||||
\(236\) | 17.6066 | + | 18.2696i | 1.14609 | + | 1.18925i | ||||
\(237\) | − | 1.41442i | − | 0.0918761i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.2479i | 1.24505i | 0.782602 | + | 0.622523i | \(0.213892\pi\) | ||||
−0.782602 | + | 0.622523i | \(0.786108\pi\) | |||||||
\(240\) | 2.04945 | − | 3.26490i | 0.132291 | − | 0.210748i | ||||
\(241\) | 2.38754 | + | 1.37844i | 0.153795 | + | 0.0887934i | 0.574922 | − | 0.818208i | \(-0.305032\pi\) |
−0.421128 | + | 0.907001i | \(0.638366\pi\) | |||||||
\(242\) | −10.5480 | + | 24.8141i | −0.678050 | + | 1.59511i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −5.01711 | − | 20.2107i | −0.321187 | − | 1.29386i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.61843 | − | 13.2371i | −0.103187 | − | 0.843968i | ||||
\(247\) | −15.8603 | + | 9.15692i | −1.00916 | + | 0.582641i | ||||
\(248\) | −2.15695 | + | 13.4843i | −0.136966 | + | 0.856252i | ||||
\(249\) | −0.271890 | + | 0.470927i | −0.0172303 | + | 0.0298438i | ||||
\(250\) | 9.87747 | − | 7.43528i | 0.624706 | − | 0.470248i | ||||
\(251\) | −20.7493 | −1.30968 | −0.654841 | − | 0.755767i | \(-0.727264\pi\) | ||||
−0.654841 | + | 0.755767i | \(0.727264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.80413 | −0.427772 | ||||||||
\(254\) | −13.1553 | + | 9.90263i | −0.825434 | + | 0.621346i | ||||
\(255\) | −0.330804 | + | 0.572969i | −0.0207157 | + | 0.0358807i | ||||
\(256\) | 6.95495 | + | 14.4093i | 0.434684 | + | 0.900583i | ||||
\(257\) | −6.45283 | + | 3.72554i | −0.402516 | + | 0.232393i | −0.687569 | − | 0.726119i | \(-0.741322\pi\) |
0.285053 | + | 0.958512i | \(0.407989\pi\) | |||||||
\(258\) | −1.02538 | − | 8.38658i | −0.0638375 | − | 0.522126i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 7.01711 | − | 1.74193i | 0.435182 | − | 0.108030i | ||||
\(261\) | 1.24005 | + | 2.14784i | 0.0767574 | + | 0.132948i | ||||
\(262\) | 5.12390 | − | 12.0540i | 0.316556 | − | 0.744698i | ||||
\(263\) | −25.7034 | − | 14.8399i | −1.58494 | − | 0.915066i | −0.994123 | − | 0.108260i | \(-0.965472\pi\) |
−0.590818 | − | 0.806805i | \(-0.701195\pi\) | |||||||
\(264\) | −9.77857 | + | 12.0377i | −0.601829 | + | 0.740866i | ||||
\(265\) | 3.94654i | 0.242434i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.554380i | 0.0339275i | ||||||||
\(268\) | −13.5924 | + | 13.0991i | −0.830286 | + | 0.800155i | ||||
\(269\) | 3.73727 | + | 2.15771i | 0.227865 | + | 0.131558i | 0.609587 | − | 0.792719i | \(-0.291335\pi\) |
−0.381722 | + | 0.924277i | \(0.624669\pi\) | |||||||
\(270\) | 1.25428 | + | 0.533167i | 0.0763328 | + | 0.0324475i | ||||
\(271\) | 6.79142 | + | 11.7631i | 0.412550 | + | 0.714557i | 0.995168 | − | 0.0981892i | \(-0.0313050\pi\) |
−0.582618 | + | 0.812746i | \(0.697972\pi\) | |||||||
\(272\) | −1.28424 | − | 2.42728i | −0.0778683 | − | 0.147176i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.1493 | + | 1.24090i | −0.613142 | + | 0.0749656i | ||||
\(275\) | −19.3328 | + | 11.1618i | −1.16581 | + | 0.673082i | ||||
\(276\) | −2.38496 | − | 0.686521i | −0.143558 | − | 0.0413237i | ||||
\(277\) | −1.03563 | + | 1.79376i | −0.0622250 | + | 0.107777i | −0.895460 | − | 0.445143i | \(-0.853153\pi\) |
0.833235 | + | 0.552920i | \(0.186486\pi\) | |||||||
\(278\) | 4.51465 | + | 5.99753i | 0.270770 | + | 0.359708i | ||||
\(279\) | −4.82802 | −0.289046 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.7122 | 1.41455 | 0.707276 | − | 0.706938i | \(-0.249924\pi\) | ||||
0.707276 | + | 0.706938i | \(0.249924\pi\) | |||||||
\(282\) | 3.07465 | + | 4.08455i | 0.183093 | + | 0.243232i | ||||
\(283\) | −6.12739 | + | 10.6129i | −0.364235 | + | 0.630874i | −0.988653 | − | 0.150216i | \(-0.952003\pi\) |
0.624418 | + | 0.781091i | \(0.285336\pi\) | |||||||
\(284\) | 19.4431 | + | 5.59677i | 1.15373 | + | 0.332107i | ||||
\(285\) | −4.07465 | + | 2.35250i | −0.241362 | + | 0.139350i | ||||
\(286\) | −28.8732 | + | 3.53017i | −1.70731 | + | 0.208743i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4.64212 | + | 3.23276i | −0.273539 | + | 0.190492i | ||||
\(289\) | −8.26434 | − | 14.3143i | −0.486138 | − | 0.842016i | ||||
\(290\) | 3.11074 | + | 1.32231i | 0.182669 | + | 0.0776488i | ||||
\(291\) | 9.41780 | + | 5.43737i | 0.552081 | + | 0.318744i | ||||
\(292\) | −9.59236 | + | 9.24426i | −0.561351 | + | 0.540980i | ||||
\(293\) | − | 10.7090i | − | 0.625626i | −0.949815 | − | 0.312813i | \(-0.898729\pi\) | ||
0.949815 | − | 0.312813i | \(-0.101271\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.2259i | 0.711821i | ||||||||
\(296\) | −5.99964 | − | 4.87370i | −0.348722 | − | 0.283278i | ||||
\(297\) | −4.74861 | − | 2.74161i | −0.275542 | − | 0.159084i | ||||
\(298\) | 2.57901 | − | 6.06712i | 0.149398 | − | 0.351459i | ||||
\(299\) | −2.32741 | − | 4.03120i | −0.134598 | − | 0.233130i | ||||
\(300\) | −7.90267 | + | 1.96176i | −0.456261 | + | 0.113262i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.09495 | − | 17.1345i | −0.120551 | − | 0.985982i | ||||
\(303\) | −12.4972 | + | 7.21527i | −0.717946 | + | 0.414506i | ||||
\(304\) | 0.721529 | − | 19.5154i | 0.0413825 | − | 1.11928i | ||||
\(305\) | 5.01711 | − | 8.68988i | 0.287279 | − | 0.497581i | ||||
\(306\) | 0.775684 | − | 0.583897i | 0.0443429 | − | 0.0333792i | ||||
\(307\) | 4.22056 | 0.240880 | 0.120440 | − | 0.992721i | \(-0.461569\pi\) | ||||
0.120440 | + | 0.992721i | \(0.461569\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −15.0247 | −0.854725 | ||||||||
\(310\) | −5.25711 | + | 3.95729i | −0.298584 | + | 0.224759i | ||||
\(311\) | −4.85070 | + | 8.40165i | −0.275058 | + | 0.476414i | −0.970150 | − | 0.242507i | \(-0.922030\pi\) |
0.695092 | + | 0.718921i | \(0.255364\pi\) | |||||||
\(312\) | −10.4767 | − | 1.67586i | −0.593127 | − | 0.0948767i | ||||
\(313\) | −11.8328 | + | 6.83168i | −0.668831 | + | 0.386149i | −0.795633 | − | 0.605778i | \(-0.792862\pi\) |
0.126803 | + | 0.991928i | \(0.459528\pi\) | |||||||
\(314\) | 3.76434 | + | 30.7885i | 0.212434 | + | 1.73750i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.681544 | + | 2.74550i | 0.0383398 | + | 0.154447i | ||||
\(317\) | −10.0442 | − | 17.3970i | −0.564138 | − | 0.977115i | −0.997129 | − | 0.0757171i | \(-0.975875\pi\) |
0.432992 | − | 0.901398i | \(-0.357458\pi\) | |||||||
\(318\) | 2.26562 | − | 5.32987i | 0.127049 | − | 0.298884i | ||||
\(319\) | −11.7771 | − | 6.79948i | −0.659388 | − | 0.380698i | ||||
\(320\) | −2.40495 | + | 7.32499i | −0.134441 | + | 0.409479i | ||||
\(321\) | − | 12.1156i | − | 0.676229i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.35171i | 0.186494i | ||||||||
\(324\) | −1.38784 | − | 1.44010i | −0.0771023 | − | 0.0800057i | ||||
\(325\) | −13.2259 | − | 7.63599i | −0.733642 | − | 0.423569i | ||||
\(326\) | 5.23008 | + | 2.22320i | 0.289667 | + | 0.123132i | ||||
\(327\) | −3.03563 | − | 5.25787i | −0.167871 | − | 0.290761i | ||||
\(328\) | 9.51989 | + | 24.9145i | 0.525648 | + | 1.37568i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.41780 | + | 0.906935i | −0.408337 | + | 0.0499251i | ||||
\(331\) | −8.15886 | + | 4.71052i | −0.448452 | + | 0.258914i | −0.707176 | − | 0.707037i | \(-0.750031\pi\) |
0.258724 | + | 0.965951i | \(0.416698\pi\) | |||||||
\(332\) | 0.300843 | − | 1.04512i | 0.0165109 | − | 0.0573585i | ||||
\(333\) | 1.36643 | − | 2.36673i | 0.0748802 | − | 0.129696i | ||||
\(334\) | 12.5177 | + | 16.6293i | 0.684939 | + | 0.909914i | ||||
\(335\) | −9.09596 | −0.496965 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.4411 | −0.732185 | −0.366092 | − | 0.930578i | \(-0.619305\pi\) | ||||
−0.366092 | + | 0.930578i | \(0.619305\pi\) | |||||||
\(338\) | −0.911125 | − | 1.21039i | −0.0495587 | − | 0.0658367i | ||||
\(339\) | −3.68969 | + | 6.39074i | −0.200397 | + | 0.347097i | ||||
\(340\) | 0.366030 | − | 1.27158i | 0.0198508 | − | 0.0689612i | ||||
\(341\) | 22.9264 | − | 13.2365i | 1.24153 | − | 0.716799i | ||||
\(342\) | 6.85340 | − | 0.837928i | 0.370589 | − | 0.0453100i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.03148 | + | 15.7850i | 0.325195 | + | 0.851070i | ||||
\(345\) | −0.597935 | − | 1.03565i | −0.0321917 | − | 0.0557577i | ||||
\(346\) | 15.1664 | + | 6.44693i | 0.815351 | + | 0.346589i | ||||
\(347\) | 19.5890 | + | 11.3097i | 1.05159 | + | 0.607136i | 0.923094 | − | 0.384574i | \(-0.125651\pi\) |
0.128497 | + | 0.991710i | \(0.458985\pi\) | |||||||
\(348\) | −3.44200 | − | 3.57161i | −0.184510 | − | 0.191458i | ||||
\(349\) | − | 2.48180i | − | 0.132848i | −0.997791 | − | 0.0664239i | \(-0.978841\pi\) | ||
0.997791 | − | 0.0664239i | \(-0.0211590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 3.75117i | − | 0.200223i | ||||||
\(352\) | 13.1806 | − | 28.0780i | 0.702530 | − | 1.49656i | ||||
\(353\) | 7.89315 | + | 4.55711i | 0.420110 | + | 0.242551i | 0.695124 | − | 0.718889i | \(-0.255349\pi\) |
−0.275014 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(354\) | 7.01862 | − | 16.5113i | 0.373036 | − | 0.877566i | ||||
\(355\) | 4.87458 | + | 8.44303i | 0.258716 | + | 0.448109i | ||||
\(356\) | −0.267131 | − | 1.07610i | −0.0141579 | − | 0.0570331i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.445241 | + | 3.64162i | 0.0235317 | + | 0.192466i | ||||
\(359\) | 6.00000 | − | 3.46410i | 0.316668 | − | 0.182828i | −0.333238 | − | 0.942843i | \(-0.608141\pi\) |
0.649906 | + | 0.760014i | \(0.274808\pi\) | |||||||
\(360\) | −2.69157 | − | 0.430544i | −0.141858 | − | 0.0226916i | ||||
\(361\) | −2.41780 | + | 4.18776i | −0.127253 | + | 0.220408i | ||||
\(362\) | 10.7716 | − | 8.10834i | 0.566143 | − | 0.426165i | ||||
\(363\) | 19.0657 | 1.00069 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.41917 | −0.335995 | ||||||||
\(366\) | −11.7643 | + | 8.85562i | −0.614932 | + | 0.462891i | ||||
\(367\) | −1.91680 | + | 3.31999i | −0.100056 | + | 0.173302i | −0.911707 | − | 0.410840i | \(-0.865235\pi\) |
0.811652 | + | 0.584142i | \(0.198569\pi\) | |||||||
\(368\) | 4.96021 | + | 0.183391i | 0.258569 | + | 0.00955992i | ||||
\(369\) | −8.16641 | + | 4.71488i | −0.425126 | + | 0.245447i | ||||
\(370\) | −0.452022 | − | 3.69708i | −0.0234995 | − | 0.192202i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.37160 | − | 2.32641i | 0.485895 | − | 0.120619i | ||||
\(373\) | 13.4150 | + | 23.2355i | 0.694603 | + | 1.20309i | 0.970314 | + | 0.241848i | \(0.0777534\pi\) |
−0.275711 | + | 0.961241i | \(0.588913\pi\) | |||||||
\(374\) | −2.08260 | + | 4.89932i | −0.107689 | + | 0.253338i | ||||
\(375\) | −7.57086 | − | 4.37104i | −0.390957 | − | 0.225719i | ||||
\(376\) | −7.93633 | − | 6.44693i | −0.409285 | − | 0.332475i | ||||
\(377\) | − | 9.30330i | − | 0.479144i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 6.93692i | − | 0.356325i | −0.984001 | − | 0.178163i | \(-0.942985\pi\) | ||
0.984001 | − | 0.178163i | \(-0.0570153\pi\) | |||||||
\(380\) | 6.77568 | − | 6.52980i | 0.347585 | − | 0.334972i | ||||
\(381\) | 10.0832 | + | 5.82154i | 0.516578 | + | 0.298247i | ||||
\(382\) | −10.8451 | − | 4.61004i | −0.554885 | − | 0.235870i | ||||
\(383\) | 1.12881 | + | 1.95515i | 0.0576793 | + | 0.0999035i | 0.893423 | − | 0.449216i | \(-0.148297\pi\) |
−0.835744 | + | 0.549119i | \(0.814963\pi\) | |||||||
\(384\) | 7.45303 | − | 8.51189i | 0.380336 | − | 0.434371i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.3682 | − | 2.12351i | 0.884017 | − | 0.108084i | ||||
\(387\) | −5.17396 | + | 2.98718i | −0.263007 | + | 0.151847i | ||||
\(388\) | −20.9008 | − | 6.01639i | −1.06108 | − | 0.305436i | ||||
\(389\) | −15.3047 | + | 26.5086i | −0.775981 | + | 1.34404i | 0.158261 | + | 0.987397i | \(0.449411\pi\) |
−0.934242 | + | 0.356641i | \(0.883922\pi\) | |||||||
\(390\) | −3.07465 | − | 4.08455i | −0.155691 | − | 0.206829i | ||||
\(391\) | −0.851904 | −0.0430827 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.26156 | −0.467184 | ||||||||
\(394\) | 2.75300 | + | 3.65726i | 0.138694 | + | 0.184250i | ||||
\(395\) | −0.681544 | + | 1.18047i | −0.0342922 | + | 0.0593958i | ||||
\(396\) | 10.5385 | + | 3.03356i | 0.529580 | + | 0.152442i | ||||
\(397\) | 12.0368 | − | 6.94947i | 0.604112 | − | 0.348784i | −0.166546 | − | 0.986034i | \(-0.553261\pi\) |
0.770657 | + | 0.637250i | \(0.219928\pi\) | |||||||
\(398\) | −26.9944 | + | 3.30046i | −1.35311 | + | 0.165437i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14.3945 | − | 7.61589i | 0.719724 | − | 0.380794i | ||||
\(401\) | 5.13832 | + | 8.89984i | 0.256596 | + | 0.444437i | 0.965328 | − | 0.261041i | \(-0.0840658\pi\) |
−0.708732 | + | 0.705478i | \(0.750732\pi\) | |||||||
\(402\) | 12.2842 | + | 5.22178i | 0.612682 | + | 0.260439i | ||||
\(403\) | 15.6843 | + | 9.05535i | 0.781292 | + | 0.451079i | ||||
\(404\) | 20.7815 | − | 20.0273i | 1.03392 | − | 0.996396i | ||||
\(405\) | − | 0.963711i | − | 0.0478872i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14.9849i | 0.742775i | ||||||||
\(408\) | −1.22432 | + | 1.50716i | −0.0606127 | + | 0.0746157i | ||||
\(409\) | −10.5342 | − | 6.08193i | −0.520883 | − | 0.300732i | 0.216413 | − | 0.976302i | \(-0.430564\pi\) |
−0.737296 | + | 0.675570i | \(0.763898\pi\) | |||||||
\(410\) | −5.02764 | + | 11.8275i | −0.248297 | + | 0.584120i | ||||
\(411\) | 3.61504 | + | 6.26144i | 0.178317 | + | 0.308854i | ||||
\(412\) | 29.1642 | − | 7.23973i | 1.43682 | − | 0.356676i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.212976 | + | 1.74193i | 0.0104672 | + | 0.0856111i | ||||
\(415\) | 0.453838 | − | 0.262023i | 0.0222780 | − | 0.0128622i | ||||
\(416\) | 21.1437 | − | 1.79528i | 1.03666 | − | 0.0880209i | ||||
\(417\) | 2.65406 | − | 4.59697i | 0.129970 | − | 0.225115i | ||||
\(418\) | −30.2468 | + | 22.7683i | −1.47942 | + | 1.11364i | ||||
\(419\) | 16.2245 | 0.792619 | 0.396310 | − | 0.918117i | \(-0.370291\pi\) | ||||
0.396310 | + | 0.918117i | \(0.370291\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.58477 | −0.467133 | −0.233567 | − | 0.972341i | \(-0.575040\pi\) | ||||
−0.233567 | + | 0.972341i | \(0.575040\pi\) | |||||||
\(422\) | 10.4473 | − | 7.86419i | 0.508565 | − | 0.382823i | ||||
\(423\) | 1.80752 | − | 3.13072i | 0.0878847 | − | 0.152221i | ||||
\(424\) | −1.82953 | + | 11.4374i | −0.0888499 | + | 0.555451i | ||||
\(425\) | −2.42055 | + | 1.39750i | −0.117414 | + | 0.0677889i | ||||
\(426\) | −1.73626 | − | 14.2008i | −0.0841220 | − | 0.688032i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 5.83799 | + | 23.5175i | 0.282190 | + | 1.13676i | ||||
\(429\) | 10.2842 | + | 17.8128i | 0.496528 | + | 0.860011i | ||||
\(430\) | −3.18534 | + | 7.49351i | −0.153611 | + | 0.361369i | ||||
\(431\) | 0.131544 | + | 0.0759470i | 0.00633626 | + | 0.00365824i | 0.503165 | − | 0.864190i | \(-0.332169\pi\) |
−0.496829 | + | 0.867849i | \(0.665502\pi\) | |||||||
\(432\) | 3.38784 | + | 2.12662i | 0.162998 | + | 0.102317i | ||||
\(433\) | − | 9.46997i | − | 0.455098i | −0.973767 | − | 0.227549i | \(-0.926929\pi\) | ||
0.973767 | − | 0.227549i | \(-0.0730711\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 2.39011i | − | 0.114597i | ||||||
\(436\) | 8.42595 | + | 8.74324i | 0.403530 | + | 0.418725i | ||||
\(437\) | −5.24663 | − | 3.02915i | −0.250981 | − | 0.144904i | ||||
\(438\) | 8.66920 | + | 3.68510i | 0.414230 | + | 0.176081i | ||||
\(439\) | −16.7373 | − | 28.9898i | −0.798826 | − | 1.38361i | −0.920381 | − | 0.391023i | \(-0.872121\pi\) |
0.121555 | − | 0.992585i | \(-0.461212\pi\) | |||||||
\(440\) | 13.9616 | − | 5.33475i | 0.665592 | − | 0.254324i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.61504 | + | 0.441992i | −0.171950 | + | 0.0210234i | ||||
\(443\) | 22.6513 | − | 13.0777i | 1.07619 | − | 0.621341i | 0.146327 | − | 0.989236i | \(-0.453255\pi\) |
0.929867 | + | 0.367895i | \(0.119921\pi\) | |||||||
\(444\) | −1.51194 | + | 5.25246i | −0.0717537 | + | 0.249271i | ||||
\(445\) | 0.267131 | − | 0.462684i | 0.0126632 | − | 0.0219333i | ||||
\(446\) | 1.65497 | + | 2.19857i | 0.0783652 | + | 0.104105i | ||||
\(447\) | −4.66161 | −0.220486 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2918 | 0.485701 | 0.242851 | − | 0.970064i | \(-0.421918\pi\) | ||||
0.242851 | + | 0.970064i | \(0.421918\pi\) | |||||||
\(450\) | 3.46267 | + | 4.60002i | 0.163232 | + | 0.216847i | ||||
\(451\) | 25.8527 | − | 44.7782i | 1.21736 | − | 2.10852i | ||||
\(452\) | 4.08260 | − | 14.1829i | 0.192029 | − | 0.667106i | ||||
\(453\) | −10.5709 | + | 6.10309i | −0.496662 | + | 0.286748i | ||||
\(454\) | 12.1359 | − | 1.48380i | 0.569568 | − | 0.0696380i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.8993 | + | 4.92884i | −0.604064 | + | 0.230814i | ||||
\(457\) | −5.96574 | − | 10.3330i | −0.279065 | − | 0.483356i | 0.692087 | − | 0.721814i | \(-0.256691\pi\) |
−0.971153 | + | 0.238458i | \(0.923358\pi\) | |||||||
\(458\) | −21.8509 | − | 9.28837i | −1.02103 | − | 0.434017i | ||||
\(459\) | −0.594545 | − | 0.343260i | −0.0277510 | − | 0.0160220i | ||||
\(460\) | 1.65968 | + | 1.72217i | 0.0773829 | + | 0.0802968i | ||||
\(461\) | 30.0093i | 1.39767i | 0.715281 | + | 0.698837i | \(0.246299\pi\) | ||||
−0.715281 | + | 0.698837i | \(0.753701\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2736i | 0.616875i | 0.951245 | + | 0.308437i | \(0.0998060\pi\) | ||||
−0.951245 | + | 0.308437i | \(0.900194\pi\) | |||||||
\(464\) | 8.40221 | + | 5.27425i | 0.390063 | + | 0.244851i | ||||
\(465\) | 4.02945 | + | 2.32641i | 0.186861 | + | 0.107885i | ||||
\(466\) | −0.579007 | + | 1.36211i | −0.0268220 | + | 0.0630987i | ||||
\(467\) | 14.8246 | + | 25.6770i | 0.686002 | + | 1.18819i | 0.973121 | + | 0.230295i | \(0.0739692\pi\) |
−0.287119 | + | 0.957895i | \(0.592697\pi\) | |||||||
\(468\) | 1.80752 | + | 7.28134i | 0.0835527 | + | 0.336580i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.597935 | − | 4.89050i | −0.0275807 | − | 0.225582i | ||||
\(471\) | 18.9944 | − | 10.9664i | 0.875217 | − | 0.505307i | ||||
\(472\) | −5.66768 | + | 35.4318i | −0.260876 | + | 1.63088i | ||||
\(473\) | 16.3794 | − | 28.3699i | 0.753125 | − | 1.30445i | ||||
\(474\) | 1.59812 | − | 1.20298i | 0.0734039 | − | 0.0552549i | ||||
\(475\) | −19.8766 | −0.912001 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.09515 | −0.187504 | ||||||||
\(478\) | −21.7478 | + | 16.3707i | −0.994721 | + | 0.748777i | ||||
\(479\) | −5.76773 | + | 9.99001i | −0.263535 | + | 0.456455i | −0.967179 | − | 0.254097i | \(-0.918222\pi\) |
0.703644 | + | 0.710553i | \(0.251555\pi\) | |||||||
\(480\) | 5.43203 | − | 0.461225i | 0.247937 | − | 0.0210519i | ||||
\(481\) | −8.87802 | + | 5.12573i | −0.404803 | + | 0.233713i | ||||
\(482\) | 0.473165 | + | 3.87001i | 0.0215521 | + | 0.176274i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −37.0081 | + | 9.18691i | −1.68219 | + | 0.417587i | ||||
\(485\) | −5.24005 | − | 9.07604i | −0.237939 | − | 0.412122i | ||||
\(486\) | −0.553244 | + | 1.30151i | −0.0250957 | + | 0.0590376i | ||||
\(487\) | 8.44822 | + | 4.87758i | 0.382825 | + | 0.221024i | 0.679047 | − | 0.734095i | \(-0.262393\pi\) |
−0.296221 | + | 0.955119i | \(0.595727\pi\) | |||||||
\(488\) | 18.5685 | − | 22.8582i | 0.840555 | − | 1.03474i | ||||
\(489\) | − | 4.01848i | − | 0.181722i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 40.4736i | − | 1.82655i | −0.407346 | − | 0.913274i | \(-0.633546\pi\) | ||
0.407346 | − | 0.913274i | \(-0.366454\pi\) | |||||||
\(492\) | 13.5798 | − | 13.0870i | 0.612225 | − | 0.590008i | ||||
\(493\) | −1.47453 | − | 0.851323i | −0.0664097 | − | 0.0383416i | ||||
\(494\) | −23.8356 | − | 10.1320i | −1.07241 | − | 0.455861i | ||||
\(495\) | 2.64212 | + | 4.57628i | 0.118754 | + | 0.205689i | ||||
\(496\) | −17.0701 | + | 9.03151i | −0.766470 | + | 0.405527i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.763337 | + | 0.0933291i | −0.0342059 | + | 0.00418218i | ||||
\(499\) | 27.6827 | − | 15.9826i | 1.23925 | − | 0.715480i | 0.270307 | − | 0.962774i | \(-0.412875\pi\) |
0.968941 | + | 0.247294i | \(0.0795413\pi\) | |||||||
\(500\) | 16.8019 | + | 4.83650i | 0.751404 | + | 0.216295i | ||||
\(501\) | 7.35889 | − | 12.7460i | 0.328771 | − | 0.569448i | ||||
\(502\) | −17.6476 | − | 23.4441i | −0.787650 | − | 1.04636i | ||||
\(503\) | 22.7110 | 1.01263 | 0.506317 | − | 0.862348i | \(-0.331007\pi\) | ||||
0.506317 | + | 0.862348i | \(0.331007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.9069 | 0.618847 | ||||||||
\(506\) | −5.78702 | − | 7.68783i | −0.257265 | − | 0.341766i | ||||
\(507\) | −0.535631 | + | 0.927740i | −0.0237882 | + | 0.0412024i | ||||
\(508\) | −22.3775 | − | 6.44147i | −0.992841 | − | 0.285794i | ||||
\(509\) | 1.98947 | − | 1.14862i | 0.0881819 | − | 0.0509118i | −0.455261 | − | 0.890358i | \(-0.650454\pi\) |
0.543443 | + | 0.839446i | \(0.317121\pi\) | |||||||
\(510\) | −0.928739 | + | 0.113552i | −0.0411252 | + | 0.00502816i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −10.3655 | + | 20.1136i | −0.458093 | + | 0.888904i | ||||
\(513\) | −2.44109 | − | 4.22809i | −0.107777 | − | 0.186675i | ||||
\(514\) | −9.69764 | − | 4.12227i | −0.427745 | − | 0.181825i | ||||
\(515\) | 12.5396 | + | 7.23973i | 0.552560 | + | 0.319021i | ||||
\(516\) | 8.60370 | − | 8.29148i | 0.378757 | − | 0.365012i | ||||
\(517\) | 19.8221i | 0.871773i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 11.6530i | − | 0.511508i | ||||||
\(520\) | 7.93633 | + | 6.44693i | 0.348031 | + | 0.282717i | ||||
\(521\) | 32.5712 | + | 18.8050i | 1.42697 | + | 0.823862i | 0.996881 | − | 0.0789240i | \(-0.0251485\pi\) |
0.430090 | + | 0.902786i | \(0.358482\pi\) | |||||||
\(522\) | −1.37210 | + | 3.22788i | −0.0600554 | + | 0.141280i | ||||
\(523\) | −17.8444 | − | 30.9073i | −0.780279 | − | 1.35148i | −0.931779 | − | 0.363026i | \(-0.881744\pi\) |
0.151500 | − | 0.988457i | \(-0.451590\pi\) | |||||||
\(524\) | 17.9775 | − | 4.46273i | 0.785350 | − | 0.194955i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.09394 | − | 41.6632i | −0.222106 | − | 1.81660i | ||||
\(527\) | 2.87047 | − | 1.65727i | 0.125040 | − | 0.0721917i | ||||
\(528\) | −21.9179 | − | 0.810357i | −0.953854 | − | 0.0352663i | ||||
\(529\) | −10.7301 | + | 18.5850i | −0.466525 | + | 0.808046i | ||||
\(530\) | −4.45910 | + | 3.35660i | −0.193691 | + | 0.145801i | ||||
\(531\) | −12.6863 | −0.550539 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.3726 | 1.53216 | ||||||||
\(534\) | −0.626381 | + | 0.471509i | −0.0271062 | + | 0.0204042i | ||||
\(535\) | −5.83799 | + | 10.1117i | −0.252398 | + | 0.437167i | ||||
\(536\) | −26.3609 | − | 4.21669i | −1.13862 | − | 0.182133i | ||||
\(537\) | 2.24663 | − | 1.29709i | 0.0969494 | − | 0.0559738i | ||||
\(538\) | 0.740657 | + | 6.05782i | 0.0319320 | + | 0.261171i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.464369 | + | 1.87065i | 0.0199833 | + | 0.0804998i | ||||
\(541\) | −18.5102 | − | 32.0605i | −0.795814 | − | 1.37839i | −0.922321 | − | 0.386425i | \(-0.873710\pi\) |
0.126507 | − | 0.991966i | \(-0.459623\pi\) | |||||||
\(542\) | −7.51463 | + | 17.6782i | −0.322781 | + | 0.759342i | ||||
\(543\) | −8.25620 | − | 4.76672i | −0.354307 | − | 0.204559i | ||||
\(544\) | 1.65027 | − | 3.51548i | 0.0707547 | − | 0.150725i | ||||
\(545\) | 5.85094i | 0.250627i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.09106i | − | 0.0894073i | −0.999000 | − | 0.0447036i | \(-0.985766\pi\) | ||
0.999000 | − | 0.0447036i | \(-0.0142344\pi\) | |||||||
\(548\) | −10.0342 | − | 10.4121i | −0.428640 | − | 0.444781i | ||||
\(549\) | 9.01711 | + | 5.20603i | 0.384841 | + | 0.222188i | ||||
\(550\) | −29.0543 | − | 12.3504i | −1.23888 | − | 0.526623i | ||||
\(551\) | −6.05415 | − | 10.4861i | −0.257916 | − | 0.446723i | ||||
\(552\) | −1.25276 | − | 3.27861i | −0.0533211 | − | 0.139547i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.90755 | + | 0.355491i | −0.123530 | + | 0.0151034i | ||||
\(555\) | −2.28085 | + | 1.31685i | −0.0968166 | + | 0.0558971i | ||||
\(556\) | −2.93669 | + | 10.2020i | −0.124543 | + | 0.432661i | ||||
\(557\) | 8.39887 | − | 14.5473i | 0.355872 | − | 0.616388i | −0.631395 | − | 0.775461i | \(-0.717517\pi\) |
0.987267 | + | 0.159073i | \(0.0508507\pi\) | |||||||
\(558\) | −4.10631 | − | 5.45507i | −0.173834 | − | 0.230931i | ||||
\(559\) | 22.4109 | 0.947878 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.76434 | 0.158931 | ||||||||
\(562\) | 20.1676 | + | 26.7919i | 0.850720 | + | 1.13015i | ||||
\(563\) | 8.69784 | − | 15.0651i | 0.366570 | − | 0.634918i | −0.622456 | − | 0.782654i | \(-0.713865\pi\) |
0.989027 | + | 0.147736i | \(0.0471986\pi\) | |||||||
\(564\) | −2.00000 | + | 6.94796i | −0.0842152 | + | 0.292562i | ||||
\(565\) | 6.15882 | − | 3.55580i | 0.259104 | − | 0.149594i | ||||
\(566\) | −17.2028 | + | 2.10329i | −0.723086 | + | 0.0884079i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2130 | + | 26.7284i | 0.428527 | + | 1.12150i | ||||
\(569\) | 17.1425 | + | 29.6917i | 0.718652 | + | 1.24474i | 0.961534 | + | 0.274686i | \(0.0885739\pi\) |
−0.242882 | + | 0.970056i | \(0.578093\pi\) | |||||||
\(570\) | −6.12359 | − | 2.60301i | −0.256489 | − | 0.109028i | ||||
\(571\) | −5.14176 | − | 2.96860i | −0.215176 | − | 0.124232i | 0.388539 | − | 0.921432i | \(-0.372980\pi\) |
−0.603715 | + | 0.797201i | \(0.706313\pi\) | |||||||
\(572\) | −28.5458 | − | 29.6207i | −1.19356 | − | 1.23850i | ||||
\(573\) | 8.33274i | 0.348105i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 5.05203i | − | 0.210684i | ||||||
\(576\) | −7.60082 | − | 2.49551i | −0.316701 | − | 0.103980i | ||||
\(577\) | −33.7930 | − | 19.5104i | −1.40682 | − | 0.812229i | −0.411742 | − | 0.911300i | \(-0.635080\pi\) |
−0.995080 | + | 0.0990712i | \(0.968413\pi\) | |||||||
\(578\) | 9.14440 | − | 21.5122i | 0.380357 | − | 0.894790i | ||||
\(579\) | −6.18630 | − | 10.7150i | −0.257094 | − | 0.445300i | ||||
\(580\) | 1.15169 | + | 4.63940i | 0.0478211 | + | 0.192641i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.86643 | + | 15.2655i | 0.0773662 | + | 0.632777i | ||||
\(583\) | 19.4462 | − | 11.2273i | 0.805381 | − | 0.464987i | ||||
\(584\) | −18.6033 | − | 2.97579i | −0.769812 | − | 0.123139i | ||||
\(585\) | −1.80752 | + | 3.13072i | −0.0747318 | + | 0.129439i | ||||
\(586\) | 12.0999 | − | 9.10818i | 0.499840 | − | 0.376255i | ||||
\(587\) | −7.71931 | −0.318610 | −0.159305 | − | 0.987229i | \(-0.550925\pi\) | ||||
−0.159305 | + | 0.987229i | \(0.550925\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.5712 | 0.971235 | ||||||||
\(590\) | −13.8138 | + | 10.3984i | −0.568705 | + | 0.428093i | ||||
\(591\) | 1.61843 | − | 2.80321i | 0.0665734 | − | 0.115308i | ||||
\(592\) | 0.403887 | − | 10.9240i | 0.0165996 | − | 0.448974i | ||||
\(593\) | −0.336377 | + | 0.194207i | −0.0138133 | + | 0.00797513i | −0.506891 | − | 0.862010i | \(-0.669205\pi\) |
0.493077 | + | 0.869985i | \(0.335872\pi\) | |||||||
\(594\) | −0.941086 | − | 7.69713i | −0.0386132 | − | 0.315817i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.04858 | − | 2.24622i | 0.370644 | − | 0.0920088i | ||||
\(597\) | 9.61504 | + | 16.6537i | 0.393517 | + | 0.681592i | ||||
\(598\) | 2.57526 | − | 6.05829i | 0.105310 | − | 0.247742i | ||||
\(599\) | −18.0000 | − | 10.3923i | −0.735460 | − | 0.424618i | 0.0849563 | − | 0.996385i | \(-0.472925\pi\) |
−0.820416 | + | 0.571767i | \(0.806258\pi\) | |||||||
\(600\) | −8.93790 | − | 7.26054i | −0.364888 | − | 0.296410i | ||||
\(601\) | − | 26.4110i | − | 1.07733i | −0.842521 | − | 0.538664i | \(-0.818929\pi\) | ||
0.842521 | − | 0.538664i | \(-0.181071\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 9.43847i | − | 0.384364i | ||||||
\(604\) | 17.5781 | − | 16.9402i | 0.715244 | − | 0.689289i | ||||
\(605\) | −15.9122 | − | 9.18691i | −0.646922 | − | 0.373501i | ||||
\(606\) | −18.7815 | − | 7.98361i | −0.762944 | − | 0.324312i | ||||
\(607\) | 20.3531 | + | 35.2526i | 0.826106 | + | 1.43086i | 0.901071 | + | 0.433671i | \(0.142782\pi\) |
−0.0749655 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(608\) | 22.6636 | − | 15.7829i | 0.919131 | − | 0.640081i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.0856 | − | 1.72217i | 0.570310 | − | 0.0697288i | ||||
\(611\) | −11.7438 | + | 6.78031i | −0.475105 | + | 0.274302i | ||||
\(612\) | 1.31946 | + | 0.379814i | 0.0533362 | + | 0.0153531i | ||||
\(613\) | −8.66920 | + | 15.0155i | −0.350146 | + | 0.606470i | −0.986275 | − | 0.165113i | \(-0.947201\pi\) |
0.636129 | + | 0.771583i | \(0.280535\pi\) | |||||||
\(614\) | 3.58966 | + | 4.76872i | 0.144867 | + | 0.192450i | ||||
\(615\) | 9.08756 | 0.366446 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.4753 | −1.87103 | −0.935513 | − | 0.353291i | \(-0.885062\pi\) | ||||
−0.935513 | + | 0.353291i | \(0.885062\pi\) | |||||||
\(618\) | −12.7787 | − | 16.9761i | −0.514037 | − | 0.682877i | ||||
\(619\) | 13.1911 | − | 22.8476i | 0.530194 | − | 0.918322i | −0.469186 | − | 0.883099i | \(-0.655453\pi\) |
0.999379 | − | 0.0352227i | \(-0.0112141\pi\) | |||||||
\(620\) | −8.94251 | − | 2.57414i | −0.359140 | − | 0.103380i | ||||
\(621\) | 1.07465 | − | 0.620450i | 0.0431243 | − | 0.0248978i | ||||
\(622\) | −13.6184 | + | 1.66505i | −0.546049 | + | 0.0667625i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.01711 | − | 13.2627i | −0.280909 | − | 0.530935i | ||||
\(625\) | −5.96574 | − | 10.3330i | −0.238630 | − | 0.413318i | ||||
\(626\) | −17.7830 | − | 7.55917i | −0.710750 | − | 0.302125i | ||||
\(627\) | 23.1835 | + | 13.3850i | 0.925860 | + | 0.534546i | ||||
\(628\) | −31.5856 | + | 30.4394i | −1.26040 | + | 1.21466i | ||||
\(629\) | 1.87617i | 0.0748079i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 41.0696i | − | 1.63495i | −0.575961 | − | 0.817477i | \(-0.695372\pi\) | ||
0.575961 | − | 0.817477i | \(-0.304628\pi\) | |||||||
\(632\) | −2.52242 | + | 3.10515i | −0.100336 | + | 0.123516i | ||||
\(633\) | −8.00759 | − | 4.62318i | −0.318273 | − | 0.183755i | ||||
\(634\) | 11.1138 | − | 26.1452i | 0.441384 | − | 1.03836i | ||||
\(635\) | −5.61028 | − | 9.71729i | −0.222637 | − | 0.385619i | ||||
\(636\) | 7.94904 | − | 1.97327i | 0.315200 | − | 0.0782452i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −2.33399 | − | 19.0897i | −0.0924037 | − | 0.755768i | ||||
\(639\) | −8.76095 | + | 5.05814i | −0.346578 | + | 0.200097i | ||||
\(640\) | −10.3218 | + | 3.51273i | −0.408004 | + | 0.138853i | ||||
\(641\) | −22.7239 | + | 39.3590i | −0.897540 | + | 1.55459i | −0.0669115 | + | 0.997759i | \(0.521315\pi\) |
−0.830629 | + | 0.556827i | \(0.812019\pi\) | |||||||
\(642\) | 13.6892 | − | 10.3046i | 0.540269 | − | 0.406688i | ||||
\(643\) | −30.5534 | −1.20491 | −0.602454 | − | 0.798154i | \(-0.705810\pi\) | ||||
−0.602454 | + | 0.798154i | \(0.705810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.75756 | 0.226704 | ||||||||
\(646\) | −3.78702 | + | 2.85069i | −0.148998 | + | 0.112159i | ||||
\(647\) | 18.0896 | − | 31.3321i | 0.711175 | − | 1.23179i | −0.253242 | − | 0.967403i | \(-0.581497\pi\) |
0.964417 | − | 0.264388i | \(-0.0851698\pi\) | |||||||
\(648\) | 0.446756 | − | 2.79292i | 0.0175502 | − | 0.109716i | ||||
\(649\) | 60.2423 | − | 34.7809i | 2.36472 | − | 1.36527i | ||||
\(650\) | −2.62113 | − | 21.4382i | −0.102809 | − | 0.840876i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.93633 | + | 7.80022i | 0.0758324 | + | 0.305480i | ||||
\(653\) | 4.11545 | + | 7.12816i | 0.161050 | + | 0.278946i | 0.935245 | − | 0.354000i | \(-0.115179\pi\) |
−0.774196 | + | 0.632946i | \(0.781845\pi\) | |||||||
\(654\) | 3.35889 | − | 7.90179i | 0.131343 | − | 0.308984i | ||||
\(655\) | 7.72968 | + | 4.46273i | 0.302024 | + | 0.174373i | ||||
\(656\) | −20.0535 | + | 31.9465i | −0.782959 | + | 1.24730i | ||||
\(657\) | − | 6.66089i | − | 0.259866i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.8837i | − | 0.891422i | −0.895177 | − | 0.445711i | \(-0.852951\pi\) | ||
0.895177 | − | 0.445711i | \(-0.147049\pi\) | |||||||
\(660\) | −7.33369 | − | 7.60984i | −0.285463 | − | 0.296213i | ||||
\(661\) | 17.7212 | + | 10.2313i | 0.689275 | + | 0.397953i | 0.803340 | − | 0.595520i | \(-0.203054\pi\) |
−0.114065 | + | 0.993473i | \(0.536387\pi\) | |||||||
\(662\) | −12.2616 | − | 5.21214i | −0.476559 | − | 0.202575i | ||||
\(663\) | 1.28763 | + | 2.23024i | 0.0500073 | + | 0.0866152i | ||||
\(664\) | 1.43673 | − | 0.548978i | 0.0557560 | − | 0.0213045i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.83629 | − | 0.469043i | 0.148653 | − | 0.0181750i | ||||
\(667\) | 2.66525 | − | 1.53878i | 0.103199 | − | 0.0595819i | ||||
\(668\) | −8.14252 | + | 28.2869i | −0.315044 | + | 1.09445i | ||||
\(669\) | 0.972923 | − | 1.68515i | 0.0376154 | − | 0.0651517i | ||||
\(670\) | −7.73626 | − | 10.2773i | −0.298878 | − | 0.397047i | ||||
\(671\) | −57.0916 | −2.20400 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.23008 | 0.163058 | 0.0815289 | − | 0.996671i | \(-0.474020\pi\) | ||||
0.0815289 | + | 0.996671i | \(0.474020\pi\) | |||||||
\(674\) | −11.4319 | − | 15.1868i | −0.440340 | − | 0.584975i | ||||
\(675\) | 2.03563 | − | 3.52582i | 0.0783515 | − | 0.135709i | ||||
\(676\) | 0.592669 | − | 2.05892i | 0.0227950 | − | 0.0791892i | ||||
\(677\) | −20.7962 | + | 12.0067i | −0.799262 | + | 0.461454i | −0.843213 | − | 0.537580i | \(-0.819339\pi\) |
0.0439511 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(678\) | −10.3589 | + | 1.26653i | −0.397831 | + | 0.0486406i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.74805 | − | 0.667932i | 0.0670345 | − | 0.0256140i | ||||
\(681\) | −4.32265 | − | 7.48706i | −0.165644 | − | 0.286905i | ||||
\(682\) | 34.4549 | + | 14.6461i | 1.31935 | + | 0.560827i | ||||
\(683\) | 7.09951 | + | 4.09890i | 0.271655 | + | 0.156840i | 0.629640 | − | 0.776887i | \(-0.283203\pi\) |
−0.357984 | + | 0.933728i | \(0.616536\pi\) | |||||||
\(684\) | 6.77568 | + | 7.03083i | 0.259075 | + | 0.268830i | ||||
\(685\) | − | 6.96771i | − | 0.266222i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.7889i | 0.640537i | ||||||||
\(688\) | −12.7052 | + | 20.2402i | −0.484382 | + | 0.771651i | ||||
\(689\) | 13.3035 | + | 7.68079i | 0.506824 | + | 0.292615i | ||||
\(690\) | 0.661608 | − | 1.55643i | 0.0251870 | − | 0.0592524i | ||||
\(691\) | 17.9925 | + | 31.1638i | 0.684465 | + | 1.18553i | 0.973605 | + | 0.228242i | \(0.0732976\pi\) |
−0.289139 | + | 0.957287i | \(0.593369\pi\) | |||||||
\(692\) | 5.61504 | + | 22.6194i | 0.213452 | + | 0.859860i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.88217 | + | 31.7522i | 0.147365 | + | 1.20530i | ||||
\(695\) | −4.43015 | + | 2.55775i | −0.168045 | + | 0.0970209i | ||||
\(696\) | 1.10800 | − | 6.92674i | 0.0419987 | − | 0.262558i | ||||
\(697\) | 3.23686 | − | 5.60641i | 0.122605 | − | 0.212358i | ||||
\(698\) | 2.80413 | − | 2.11081i | 0.106138 | − | 0.0798954i | ||||
\(699\) | 1.04657 | 0.0395848 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.9471 | −0.489003 | −0.244502 | − | 0.969649i | \(-0.578624\pi\) | ||||
−0.244502 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(702\) | 4.23836 | − | 3.19043i | 0.159967 | − | 0.120415i | ||||
\(703\) | −6.67117 | + | 11.5548i | −0.251608 | + | 0.435798i | ||||
\(704\) | 42.9350 | − | 8.98829i | 1.61817 | − | 0.338759i | ||||
\(705\) | −3.01711 | + | 1.74193i | −0.113631 | + | 0.0656048i | ||||
\(706\) | 1.56428 | + | 12.7942i | 0.0588723 | + | 0.481516i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 24.6252 | − | 6.11296i | 0.925472 | − | 0.229739i | ||||
\(709\) | −6.65603 | − | 11.5286i | −0.249973 | − | 0.432965i | 0.713545 | − | 0.700609i | \(-0.247088\pi\) |
−0.963518 | + | 0.267644i | \(0.913755\pi\) | |||||||
\(710\) | −5.39367 | + | 12.6886i | −0.202421 | + | 0.476195i | ||||
\(711\) | −1.22492 | − | 0.707208i | −0.0459381 | − | 0.0265224i | ||||
\(712\) | 0.988660 | − | 1.21706i | 0.0370516 | − | 0.0456114i | ||||
\(713\) | 5.99109i | 0.224368i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 19.8221i | − | 0.741303i | ||||||
\(716\) | −3.73590 | + | 3.60033i | −0.139617 | + | 0.134550i | ||||
\(717\) | 16.6692 | + | 9.62396i | 0.622523 | + | 0.359414i | ||||
\(718\) | 9.01711 | + | 3.83299i | 0.336515 | + | 0.143046i | ||||
\(719\) | −23.7520 | − | 41.1397i | −0.885800 | − | 1.53425i | −0.844794 | − | 0.535091i | \(-0.820277\pi\) |
−0.0410056 | − | 0.999159i | \(-0.513056\pi\) | |||||||
\(720\) | −1.80276 | − | 3.40733i | −0.0671850 | − | 0.126984i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −6.78803 | + | 0.829936i | −0.252624 | + | 0.0308870i | ||||
\(723\) | 2.38754 | − | 1.37844i | 0.0887934 | − | 0.0512649i | ||||
\(724\) | 18.3229 | + | 5.27431i | 0.680964 | + | 0.196018i | ||||
\(725\) | 5.04858 | − | 8.74440i | 0.187500 | − | 0.324759i | ||||
\(726\) | 16.2157 | + | 21.5419i | 0.601820 | + | 0.799494i | ||||
\(727\) | 24.3567 | 0.903340 | 0.451670 | − | 0.892185i | \(-0.350828\pi\) | ||||
0.451670 | + | 0.892185i | \(0.350828\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.45961 | − | 7.25287i | −0.202069 | − | 0.268441i | ||||
\(731\) | 2.05076 | − | 3.55203i | 0.0758503 | − | 0.131377i | ||||
\(732\) | −20.0115 | − | 5.76041i | −0.739648 | − | 0.212911i | ||||
\(733\) | −3.35812 | + | 1.93881i | −0.124035 | + | 0.0716117i | −0.560734 | − | 0.827996i | \(-0.689481\pi\) |
0.436699 | + | 0.899608i | \(0.356148\pi\) | |||||||
\(734\) | −5.38144 | + | 0.657960i | −0.198633 | + | 0.0242857i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.01153 | + | 5.76041i | 0.147867 | + | 0.212331i | ||||
\(737\) | 25.8766 | + | 44.8196i | 0.953177 | + | 1.65095i | ||||
\(738\) | −12.2729 | − | 5.21696i | −0.451772 | − | 0.192039i | ||||
\(739\) | 7.46497 | + | 4.30990i | 0.274603 | + | 0.158542i | 0.630978 | − | 0.775801i | \(-0.282654\pi\) |
−0.356374 | + | 0.934343i | \(0.615987\pi\) | |||||||
\(740\) | 3.79279 | − | 3.65515i | 0.139426 | − | 0.134366i | ||||
\(741\) | 18.3138i | 0.672776i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.12929i | 0.224862i | 0.993660 | + | 0.112431i | \(0.0358637\pi\) | ||||
−0.993660 | + | 0.112431i | \(0.964136\pi\) | |||||||
\(744\) | 10.5992 | + | 8.61011i | 0.388587 | + | 0.315662i | ||||
\(745\) | 3.89057 | + | 2.24622i | 0.142539 | + | 0.0822952i | ||||
\(746\) | −14.8436 | + | 34.9195i | −0.543461 | + | 1.27849i | ||||
\(747\) | 0.271890 | + | 0.470927i | 0.00994793 | + | 0.0172303i | ||||
\(748\) | −7.30692 | + | 1.81387i | −0.267167 | + | 0.0663216i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50040 | − | 12.2718i | −0.0547870 | − | 0.448102i | ||||
\(751\) | −30.7146 | + | 17.7331i | −1.12079 | + | 0.647090i | −0.941603 | − | 0.336725i | \(-0.890681\pi\) |
−0.179190 | + | 0.983815i | \(0.557348\pi\) | |||||||
\(752\) | 0.534262 | − | 14.4503i | 0.0194825 | − | 0.526948i | ||||
\(753\) | −10.3746 | + | 17.9694i | −0.378072 | + | 0.654841i | ||||
\(754\) | 10.5116 | − | 7.91261i | 0.382809 | − | 0.288160i | ||||
\(755\) | 11.7632 | 0.428108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.4204 | 1.06930 | 0.534651 | − | 0.845073i | \(-0.320443\pi\) | ||||
0.534651 | + | 0.845073i | \(0.320443\pi\) | |||||||
\(758\) | 7.83786 | − | 5.89996i | 0.284684 | − | 0.214296i | ||||
\(759\) | −3.40207 | + | 5.89255i | −0.123487 | + | 0.213886i | ||||
\(760\) | 13.1407 | + | 2.10199i | 0.476663 | + | 0.0762471i | ||||
\(761\) | −43.5568 | + | 25.1475i | −1.57893 | + | 0.911597i | −0.583923 | + | 0.811809i | \(0.698483\pi\) |
−0.995009 | + | 0.0997877i | \(0.968184\pi\) | |||||||
\(762\) | 1.99830 | + | 16.3441i | 0.0723909 | + | 0.592084i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −4.01518 | − | 16.1746i | −0.145264 | − | 0.585175i | ||||
\(765\) | 0.330804 | + | 0.572969i | 0.0119602 | + | 0.0207157i | ||||
\(766\) | −1.24901 | + | 2.93830i | −0.0451286 | + | 0.106165i | ||||
\(767\) | 41.2128 | + | 23.7942i | 1.48811 | + | 0.859160i | ||||
\(768\) | 15.9563 | + | 1.18150i | 0.575774 | + | 0.0426338i | ||||
\(769\) | − | 20.2817i | − | 0.731377i | −0.930737 | − | 0.365689i | \(-0.880833\pi\) | ||
0.930737 | − | 0.365689i | \(-0.119167\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.45109i | 0.268344i | ||||||||
\(772\) | 17.1712 | + | 17.8178i | 0.618006 | + | 0.641277i | ||||
\(773\) | 18.8149 | + | 10.8628i | 0.676723 | + | 0.390706i | 0.798619 | − | 0.601836i | \(-0.205564\pi\) |
−0.121896 | + | 0.992543i | \(0.538897\pi\) | |||||||
\(774\) | −7.77568 | − | 3.30528i | −0.279491 | − | 0.118806i | ||||
\(775\) | 9.82806 | + | 17.0227i | 0.353034 | + | 0.611473i | ||||
\(776\) | −10.9787 | − | 28.7324i | −0.394112 | − | 1.03143i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −42.9684 | + | 5.25351i | −1.54049 | + | 0.188347i | ||||
\(779\) | 39.8698 | − | 23.0189i | 1.42848 | − | 0.824736i | ||||
\(780\) | 2.00000 | − | 6.94796i | 0.0716115 | − | 0.248777i | ||||
\(781\) | 27.7349 | − | 48.0382i | 0.992432 | − | 1.71894i | ||||
\(782\) | −0.724559 | − | 0.962547i | −0.0259102 | − | 0.0344206i | ||||
\(783\) | 2.48011 | 0.0886318 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −21.1369 | −0.754410 | ||||||||
\(786\) | −7.87711 | − | 10.4644i | −0.280967 | − | 0.373254i | ||||
\(787\) | 0.299328 | − | 0.518452i | 0.0106699 | − | 0.0184808i | −0.860641 | − | 0.509212i | \(-0.829937\pi\) |
0.871311 | + | 0.490731i | \(0.163270\pi\) | |||||||
\(788\) | −1.79078 | + | 6.22111i | −0.0637937 | + | 0.221618i | ||||
\(789\) | −25.7034 | + | 14.8399i | −0.915066 | + | 0.528313i | ||||
\(790\) | −1.91345 | + | 0.233947i | −0.0680774 | + | 0.00832346i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5.53563 | + | 14.4873i | 0.196700 | + | 0.514784i | ||||
\(793\) | −19.5287 | − | 33.8247i | −0.693484 | − | 1.20115i | ||||
\(794\) | 18.0896 | + | 7.68951i | 0.641975 | + | 0.272890i | ||||
\(795\) | 3.41780 | + | 1.97327i | 0.121217 | + | 0.0699847i | ||||
\(796\) | −26.6883 | − | 27.6933i | −0.945942 | − | 0.981562i | ||||
\(797\) | − | 36.1789i | − | 1.28152i | −0.767741 | − | 0.640760i | \(-0.778619\pi\) | ||
0.767741 | − | 0.640760i | \(-0.221381\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.48180i | 0.0877998i | ||||||||
\(800\) | 20.8478 | + | 9.78655i | 0.737079 | + | 0.346007i | ||||
\(801\) | 0.480107 | + | 0.277190i | 0.0169637 | + | 0.00979402i | ||||
\(802\) | −5.68549 | + | 13.3751i | −0.200762 | + | 0.472292i | ||||
\(803\) | 18.2616 | + | 31.6299i | 0.644436 | + | 1.11620i | ||||
\(804\) | 4.54798 | + | 18.3209i | 0.160395 | + | 0.646128i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.10834 | + | 25.4231i | 0.109487 | + | 0.895490i | ||||
\(807\) | 3.73727 | − | 2.15771i | 0.131558 | − | 0.0759551i | ||||
\(808\) | 40.3034 | + | 6.44693i | 1.41787 | + | 0.226802i | ||||
\(809\) | 15.0603 | − | 26.0852i | 0.529491 | − | 0.917106i | −0.469917 | − | 0.882711i | \(-0.655716\pi\) |
0.999408 | − | 0.0343953i | \(-0.0109505\pi\) | |||||||
\(810\) | 1.08887 | − | 0.819652i | 0.0382592 | − | 0.0287996i | ||||
\(811\) | 21.5947 | 0.758292 | 0.379146 | − | 0.925337i | \(-0.376218\pi\) | ||||
0.379146 | + | 0.925337i | \(0.376218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.5828 | 0.476371 | ||||||||
\(814\) | −16.9311 | + | 12.7449i | −0.593435 | + | 0.446709i | ||||
\(815\) | −1.93633 | + | 3.35382i | −0.0678266 | + | 0.117479i | ||||
\(816\) | −2.74421 | − | 0.101460i | −0.0960665 | − | 0.00355181i | ||||
\(817\) | 25.2601 | − | 14.5839i | 0.883740 | − | 0.510228i | ||||
\(818\) | −2.08769 | − | 17.0751i | −0.0729942 | − | 0.597018i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.6397 | + | 4.37889i | −0.616006 | + | 0.152917i | ||||
\(821\) | −25.1264 | − | 43.5202i | −0.876918 | − | 1.51887i | −0.854705 | − | 0.519114i | \(-0.826262\pi\) |
−0.0222131 | − | 0.999753i | \(-0.507071\pi\) | |||||||
\(822\) | −4.00000 | + | 9.41000i | −0.139516 | + | 0.328212i | ||||
\(823\) | −2.87338 | − | 1.65894i | −0.100160 | − | 0.0578272i | 0.449084 | − | 0.893490i | \(-0.351751\pi\) |
−0.549243 | + | 0.835663i | \(0.685084\pi\) | |||||||
\(824\) | 32.9847 | + | 26.7945i | 1.14907 | + | 0.933430i | ||||
\(825\) | 22.3236i | 0.777209i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.3948i | 1.02216i | 0.859534 | + | 0.511078i | \(0.170754\pi\) | ||||
−0.859534 | + | 0.511078i | \(0.829246\pi\) | |||||||
\(828\) | −1.78702 | + | 1.72217i | −0.0621034 | + | 0.0598497i | ||||
\(829\) | −28.2980 | − | 16.3379i | −0.982830 | − | 0.567437i | −0.0797067 | − | 0.996818i | \(-0.525398\pi\) |
−0.903123 | + | 0.429381i | \(0.858732\pi\) | |||||||
\(830\) | 0.682050 | + | 0.289926i | 0.0236743 | + | 0.0100635i | ||||
\(831\) | 1.03563 | + | 1.79376i | 0.0359256 | + | 0.0622250i | ||||
\(832\) | 20.0115 | + | 22.3629i | 0.693775 | + | 0.775294i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 7.45133 | − | 0.911035i | 0.258019 | − | 0.0315465i | ||||
\(835\) | −12.2834 | + | 7.09184i | −0.425086 | + | 0.245423i | ||||
\(836\) | −51.4508 | − | 14.8104i | −1.77946 | − | 0.512227i | ||||
\(837\) | −2.41401 | + | 4.18119i | −0.0834403 | + | 0.144523i | ||||
\(838\) | 13.7992 | + | 18.3317i | 0.476686 | + | 0.633258i | ||||
\(839\) | 8.66161 | 0.299032 | 0.149516 | − | 0.988759i | \(-0.452228\pi\) | ||||
0.149516 | + | 0.988759i | \(0.452228\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.8491 | −0.787899 | ||||||||
\(842\) | −8.15201 | − | 10.8296i | −0.280937 | − | 0.373213i | ||||
\(843\) | 11.8561 | − | 20.5354i | 0.408346 | − | 0.707276i | ||||
\(844\) | 17.7711 | + | 5.11550i | 0.611707 | + | 0.176083i | ||||
\(845\) | 0.894073 | − | 0.516193i | 0.0307570 | − | 0.0177576i | ||||
\(846\) | 5.07465 | − | 0.620450i | 0.174470 | − | 0.0213315i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −14.4789 | + | 7.66057i | −0.497209 | + | 0.263065i | ||||
\(849\) | 6.12739 | + | 10.6129i | 0.210291 | + | 0.364235i | ||||
\(850\) | −3.63772 | − | 1.54632i | −0.124773 | − | 0.0530384i | ||||
\(851\) | −2.93688 | − | 1.69561i | −0.100675 | − | 0.0581248i | ||||
\(852\) | 14.5685 | − | 14.0398i | 0.499108 | − | 0.480996i | ||||
\(853\) | 7.17809i | 0.245773i | 0.992421 | + | 0.122887i | \(0.0392151\pi\) | ||||
−0.992421 | + | 0.122887i | \(0.960785\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.70500i | 0.160908i | ||||||||
\(856\) | −21.6066 | + | 26.5982i | −0.738498 | + | 0.909109i | ||||
\(857\) | −39.5334 | − | 22.8246i | −1.35044 | − | 0.779675i | −0.362126 | − | 0.932129i | \(-0.617949\pi\) |
−0.988311 | + | 0.152454i | \(0.951282\pi\) | |||||||
\(858\) | −11.3794 | + | 26.7700i | −0.388486 | + | 0.913913i | ||||
\(859\) | −6.77944 | − | 11.7423i | −0.231311 | − | 0.400643i | 0.726883 | − | 0.686761i | \(-0.240968\pi\) |
−0.958194 | + | 0.286118i | \(0.907635\pi\) | |||||||
\(860\) | −11.1759 | + | 2.77431i | −0.381096 | + | 0.0946033i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0260696 | + | 0.213223i | 0.000887934 | + | 0.00726240i | ||||
\(863\) | −36.0550 | + | 20.8163i | −1.22733 | + | 0.708597i | −0.966470 | − | 0.256781i | \(-0.917338\pi\) |
−0.260856 | + | 0.965378i | \(0.584005\pi\) | |||||||
\(864\) | 0.478592 | + | 5.63657i | 0.0162820 | + | 0.191760i | ||||
\(865\) | −5.61504 | + | 9.72554i | −0.190917 | + | 0.330678i | ||||
\(866\) | 10.6999 | − | 8.05436i | 0.363597 | − | 0.273698i | ||||
\(867\) | −16.5287 | −0.561344 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.75555 | 0.263089 | ||||||||
\(870\) | 2.70053 | − | 2.03282i | 0.0915564 | − | 0.0689192i | ||||
\(871\) | −17.7026 | + | 30.6619i | −0.599831 | + | 1.03894i | ||||
\(872\) | −2.71237 | + | 16.9566i | −0.0918525 | + | 0.574221i | ||||
\(873\) | 9.41780 | − | 5.43737i | 0.318744 | − | 0.184027i | ||||
\(874\) | −1.03979 | − | 8.50439i | −0.0351713 | − | 0.287665i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.20959 | + | 12.9294i | 0.108442 | + | 0.436843i | ||||
\(877\) | 9.84239 | + | 17.0475i | 0.332354 | + | 0.575654i | 0.982973 | − | 0.183751i | \(-0.0588239\pi\) |
−0.650619 | + | 0.759404i | \(0.725491\pi\) | |||||||
\(878\) | 18.5196 | − | 43.5673i | 0.625006 | − | 1.47033i | ||||
\(879\) | −9.27427 | − | 5.35450i | −0.312813 | − | 0.180603i | ||||
\(880\) | 17.9022 | + | 11.2376i | 0.603482 | + | 0.378819i | ||||
\(881\) | − | 7.24606i | − | 0.244126i | −0.992522 | − | 0.122063i | \(-0.961049\pi\) | ||
0.992522 | − | 0.122063i | \(-0.0389510\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4533i | 1.19310i | 0.802577 | + | 0.596549i | \(0.203462\pi\) | ||||
−0.802577 | + | 0.596549i | \(0.796538\pi\) | |||||||
\(884\) | −3.57405 | − | 3.70863i | −0.120208 | − | 0.124735i | ||||
\(885\) | 10.5880 | + | 6.11296i | 0.355911 | + | 0.205485i | ||||
\(886\) | 34.0415 | + | 14.4703i | 1.14365 | + | 0.486141i | ||||
\(887\) | 8.98684 | + | 15.5657i | 0.301749 | + | 0.522644i | 0.976532 | − | 0.215372i | \(-0.0690964\pi\) |
−0.674784 | + | 0.738016i | \(0.735763\pi\) | |||||||
\(888\) | −7.22056 | + | 2.75899i | −0.242306 | + | 0.0925857i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.749976 | − | 0.0916955i | 0.0251392 | − | 0.00307364i | ||||
\(891\) | −4.74861 | + | 2.74161i | −0.159084 | + | 0.0918474i | ||||
\(892\) | −1.07653 | + | 3.73983i | −0.0360448 | + | 0.125219i | ||||
\(893\) | −8.82463 | + | 15.2847i | −0.295305 | + | 0.511483i | ||||
\(894\) | −3.96477 | − | 5.26704i | −0.132602 | − | 0.176156i | ||||
\(895\) | −2.50005 | −0.0835674 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.65483 | −0.155420 | ||||||||
\(898\) | 8.75337 | + | 11.6285i | 0.292104 | + | 0.388048i | ||||
\(899\) | −5.98700 | + | 10.3698i | −0.199678 | + | 0.345852i | ||||
\(900\) | −2.25240 | + | 7.82479i | −0.0750800 | + | 0.260826i | ||||
\(901\) | 2.43475 | − | 1.40570i | 0.0811132 | − | 0.0468307i | ||||
\(902\) | 72.5820 | − | 8.87421i | 2.41672 | − | 0.295479i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.4972 | − | 7.44992i | 0.648468 | − | 0.247781i | ||||
\(905\) | 4.59374 | + | 7.95658i | 0.152701 | + | 0.264486i | ||||
\(906\) | −15.8864 | − | 6.75299i | −0.527791 | − | 0.224353i | ||||
\(907\) | 7.60870 | + | 4.39289i | 0.252643 | + | 0.145863i | 0.620974 | − | 0.783831i | \(-0.286737\pi\) |
−0.368331 | + | 0.929695i | \(0.620071\pi\) | |||||||
\(908\) | 11.9983 | + | 12.4501i | 0.398178 | + | 0.413172i | ||||
\(909\) | 14.4305i | 0.478631i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21.5478i | 0.713911i | 0.934121 | + | 0.356955i | \(0.116185\pi\) | ||||
−0.934121 | + | 0.356955i | \(0.883815\pi\) | |||||||
\(912\) | −16.5400 | − | 10.3825i | −0.547695 | − | 0.343800i | ||||
\(913\) | −2.58220 | − | 1.49083i | −0.0854582 | − | 0.0493393i | ||||
\(914\) | 6.60102 | − | 15.5289i | 0.218342 | − | 0.513650i | ||||
\(915\) | −5.01711 | − | 8.68988i | −0.165860 | − | 0.287279i | ||||
\(916\) | −8.08983 | − | 32.5887i | −0.267295 | − | 1.07676i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.117828 | − | 0.963711i | −0.00388890 | − | 0.0318072i | ||||
\(919\) | 27.5939 | − | 15.9314i | 0.910240 | − | 0.525527i | 0.0297316 | − | 0.999558i | \(-0.490535\pi\) |
0.880508 | + | 0.474031i | \(0.157201\pi\) | |||||||
\(920\) | −0.534262 | + | 3.33997i | −0.0176141 | + | 0.110116i | ||||
\(921\) | 2.11028 | − | 3.65512i | 0.0695362 | − | 0.120440i | ||||
\(922\) | −33.9069 | + | 25.5234i | −1.11666 | + | 0.840570i | ||||
\(923\) | 37.9479 | 1.24907 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.1262 | −0.365828 | ||||||||
\(926\) | −14.9975 | + | 11.2894i | −0.492848 | + | 0.370992i | ||||
\(927\) | −7.51235 | + | 13.0118i | −0.246738 | + | 0.427363i | ||||
\(928\) | 1.18696 | + | 13.9793i | 0.0389639 | + | 0.458893i | ||||
\(929\) | −44.1750 | + | 25.5044i | −1.44933 | + | 0.836773i | −0.998442 | − | 0.0558058i | \(-0.982227\pi\) |
−0.450892 | + | 0.892579i | \(0.648894\pi\) | |||||||
\(930\) | 0.798563 | + | 6.53143i | 0.0261859 | + | 0.214174i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.03148 | + | 0.504294i | −0.0665432 | + | 0.0165187i | ||||
\(933\) | 4.85070 | + | 8.40165i | 0.158805 | + | 0.275058i | ||||
\(934\) | −16.4033 | + | 38.5887i | −0.536731 | + | 1.26266i | ||||
\(935\) | −3.14171 | − | 1.81387i | −0.102745 | − | 0.0593199i | ||||
\(936\) | −6.68969 | + | 8.23517i | −0.218659 | + | 0.269175i | ||||
\(937\) | − | 2.65742i | − | 0.0868141i | −0.999057 | − | 0.0434071i | \(-0.986179\pi\) | ||
0.999057 | − | 0.0434071i | \(-0.0138212\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.6634i | 0.445887i | ||||||||
\(940\) | 5.01711 | − | 4.83504i | 0.163640 | − | 0.157702i | ||||
\(941\) | −26.2920 | − | 15.1797i | −0.857096 | − | 0.494844i | 0.00594304 | − | 0.999982i | \(-0.498108\pi\) |
−0.863039 | + | 0.505138i | \(0.831442\pi\) | |||||||
\(942\) | 28.5458 | + | 12.1342i | 0.930072 | + | 0.395355i | ||||
\(943\) | 5.85070 | + | 10.1337i | 0.190525 | + | 0.329999i | ||||
\(944\) | −44.8541 | + | 23.7316i | −1.45988 | + | 0.772397i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 45.9855 | − | 5.62240i | 1.49512 | − | 0.182800i | ||||
\(947\) | −37.6505 | + | 21.7375i | −1.22348 | + | 0.706374i | −0.965657 | − | 0.259819i | \(-0.916337\pi\) |
−0.257818 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(948\) | 2.71845 | + | 0.782517i | 0.0882910 | + | 0.0254150i | ||||
\(949\) | −12.4931 | + | 21.6386i | −0.405542 | + | 0.702419i | ||||
\(950\) | −16.9054 | − | 22.4581i | −0.548483 | − | 0.728637i | ||||
\(951\) | −20.0884 | −0.651410 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −53.8683 | −1.74497 | −0.872483 | − | 0.488645i | \(-0.837491\pi\) | ||||
−0.872483 | + | 0.488645i | \(0.837491\pi\) | |||||||
\(954\) | −3.48299 | − | 4.62701i | −0.112766 | − | 0.149805i | ||||
\(955\) | 4.01518 | − | 6.95449i | 0.129928 | − | 0.225042i | ||||
\(956\) | −36.9937 | − | 10.6488i | −1.19646 | − | 0.344407i | ||||
\(957\) | −11.7771 | + | 6.79948i | −0.380698 | + | 0.219796i | ||||
\(958\) | −16.1930 | + | 1.97984i | −0.523173 | + | 0.0639656i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 5.14115 | + | 5.74524i | 0.165930 | + | 0.185427i | ||||
\(961\) | 3.84512 | + | 6.65995i | 0.124036 | + | 0.214837i | ||||
\(962\) | −13.3423 | − | 5.67155i | −0.430174 | − | 0.182858i | ||||
\(963\) | −10.4925 | − | 6.05782i | −0.338115 | − | 0.195211i | ||||
\(964\) | −3.97020 | + | 3.82613i | −0.127872 | + | 0.123231i | ||||
\(965\) | 11.9236i | 0.383835i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 44.9529i | 1.44559i | 0.691064 | + | 0.722794i | \(0.257142\pi\) | ||||
−0.691064 | + | 0.722794i | \(0.742858\pi\) | |||||||
\(968\) | −41.8561 | − | 34.0010i | −1.34531 | − | 1.09283i | ||||
\(969\) | 2.90267 | + | 1.67586i | 0.0932472 | + | 0.0538363i | ||||
\(970\) | 5.79806 | − | 13.6399i | 0.186164 | − | 0.437952i | ||||
\(971\) | 0.641758 | + | 1.11156i | 0.0205950 | + | 0.0356716i | 0.876139 | − | 0.482058i | \(-0.160111\pi\) |
−0.855544 | + | 0.517730i | \(0.826777\pi\) | |||||||
\(972\) | −1.94109 | + | 0.481855i | −0.0622604 | + | 0.0154555i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.67428 | + | 13.6939i | 0.0536474 | + | 0.438781i | ||||
\(975\) | −13.2259 | + | 7.63599i | −0.423569 | + | 0.244547i | ||||
\(976\) | 41.6198 | + | 1.53878i | 1.33222 | + | 0.0492553i | ||||
\(977\) | −9.67678 | + | 16.7607i | −0.309588 | + | 0.536222i | −0.978272 | − | 0.207325i | \(-0.933524\pi\) |
0.668684 | + | 0.743546i | \(0.266858\pi\) | |||||||
\(978\) | 4.54039 | − | 3.41778i | 0.145186 | − | 0.109289i | ||||
\(979\) | −3.03979 | −0.0971520 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.07126 | −0.193840 | ||||||||
\(982\) | 45.7302 | − | 34.4234i | 1.45931 | − | 1.09850i | ||||
\(983\) | −4.21637 | + | 7.30296i | −0.134481 | + | 0.232928i | −0.925399 | − | 0.378994i | \(-0.876270\pi\) |
0.790918 | + | 0.611922i | \(0.209603\pi\) | |||||||
\(984\) | 26.3366 | + | 4.21280i | 0.839579 | + | 0.134299i | ||||
\(985\) | −2.70148 | + | 1.55970i | −0.0860763 | + | 0.0496962i | ||||
\(986\) | −0.292225 | − | 2.39011i | −0.00930635 | − | 0.0761165i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −8.82463 | − | 35.5488i | −0.280749 | − | 1.13096i | ||||
\(989\) | 3.70680 | + | 6.42036i | 0.117869 | + | 0.204156i | ||||
\(990\) | −2.92347 | + | 6.87747i | −0.0929141 | + | 0.218580i | ||||
\(991\) | −21.1967 | − | 12.2379i | −0.673334 | − | 0.388750i | 0.124005 | − | 0.992282i | \(-0.460426\pi\) |
−0.797339 | + | 0.603532i | \(0.793760\pi\) | |||||||
\(992\) | −24.7229 | − | 11.6057i | −0.784952 | − | 0.368480i | ||||
\(993\) | 9.42104i | 0.298968i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 18.5322i | − | 0.587511i | ||||||
\(996\) | −0.754681 | − | 0.783099i | −0.0239130 | − | 0.0248134i | ||||
\(997\) | 29.0273 | + | 16.7589i | 0.919304 | + | 0.530761i | 0.883413 | − | 0.468595i | \(-0.155240\pi\) |
0.0358914 | + | 0.999356i | \(0.488573\pi\) | |||||||
\(998\) | 41.6030 | + | 17.6846i | 1.31692 | + | 0.559795i | ||||
\(999\) | −1.36643 | − | 2.36673i | −0.0432321 | − | 0.0748802i |
(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 | 588.2.o.d.31.3 | 8 | ||
4.3 | odd | 2 | 588.2.o.b.31.3 | 8 | |||
7.2 | even | 3 | 84.2.o.b.19.3 | yes | 8 | ||
7.3 | odd | 6 | 588.2.b.b.391.2 | 8 | |||
7.4 | even | 3 | 588.2.b.a.391.2 | 8 | |||
7.5 | odd | 6 | 588.2.o.b.19.3 | 8 | |||
7.6 | odd | 2 | 84.2.o.a.31.3 | yes | 8 | ||
21.2 | odd | 6 | 252.2.bf.f.19.2 | 8 | |||
21.11 | odd | 6 | 1764.2.b.j.1567.7 | 8 | |||
21.17 | even | 6 | 1764.2.b.i.1567.7 | 8 | |||
21.20 | even | 2 | 252.2.bf.g.199.2 | 8 | |||
28.3 | even | 6 | 588.2.b.a.391.1 | 8 | |||
28.11 | odd | 6 | 588.2.b.b.391.1 | 8 | |||
28.19 | even | 6 | inner | 588.2.o.d.19.3 | 8 | ||
28.23 | odd | 6 | 84.2.o.a.19.3 | ✓ | 8 | ||
28.27 | even | 2 | 84.2.o.b.31.3 | yes | 8 | ||
56.13 | odd | 2 | 1344.2.bl.j.703.2 | 8 | |||
56.27 | even | 2 | 1344.2.bl.i.703.2 | 8 | |||
56.37 | even | 6 | 1344.2.bl.i.1279.2 | 8 | |||
56.51 | odd | 6 | 1344.2.bl.j.1279.2 | 8 | |||
84.11 | even | 6 | 1764.2.b.i.1567.8 | 8 | |||
84.23 | even | 6 | 252.2.bf.g.19.2 | 8 | |||
84.59 | odd | 6 | 1764.2.b.j.1567.8 | 8 | |||
84.83 | odd | 2 | 252.2.bf.f.199.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.o.a.19.3 | ✓ | 8 | 28.23 | odd | 6 | ||
84.2.o.a.31.3 | yes | 8 | 7.6 | odd | 2 | ||
84.2.o.b.19.3 | yes | 8 | 7.2 | even | 3 | ||
84.2.o.b.31.3 | yes | 8 | 28.27 | even | 2 | ||
252.2.bf.f.19.2 | 8 | 21.2 | odd | 6 | |||
252.2.bf.f.199.2 | 8 | 84.83 | odd | 2 | |||
252.2.bf.g.19.2 | 8 | 84.23 | even | 6 | |||
252.2.bf.g.199.2 | 8 | 21.20 | even | 2 | |||
588.2.b.a.391.1 | 8 | 28.3 | even | 6 | |||
588.2.b.a.391.2 | 8 | 7.4 | even | 3 | |||
588.2.b.b.391.1 | 8 | 28.11 | odd | 6 | |||
588.2.b.b.391.2 | 8 | 7.3 | odd | 6 | |||
588.2.o.b.19.3 | 8 | 7.5 | odd | 6 | |||
588.2.o.b.31.3 | 8 | 4.3 | odd | 2 | |||
588.2.o.d.19.3 | 8 | 28.19 | even | 6 | inner | ||
588.2.o.d.31.3 | 8 | 1.1 | even | 1 | trivial | ||
1344.2.bl.i.703.2 | 8 | 56.27 | even | 2 | |||
1344.2.bl.i.1279.2 | 8 | 56.37 | even | 6 | |||
1344.2.bl.j.703.2 | 8 | 56.13 | odd | 2 | |||
1344.2.bl.j.1279.2 | 8 | 56.51 | odd | 6 | |||
1764.2.b.i.1567.7 | 8 | 21.17 | even | 6 | |||
1764.2.b.i.1567.8 | 8 | 84.11 | even | 6 | |||
1764.2.b.j.1567.7 | 8 | 21.11 | odd | 6 | |||
1764.2.b.j.1567.8 | 8 | 84.59 | odd | 6 |