Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,3,Mod(3,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.3");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.h (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.871936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Character | \(\chi\) | \(=\) | 32.19 |
Dual form | 32.3.h.a.27.4 |
$q$-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 \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.108191 | − | 1.99707i | −0.0540954 | − | 0.998536i | ||||
\(3\) | 4.35131 | + | 1.80237i | 1.45044 | + | 0.600791i | 0.962304 | − | 0.271977i | \(-0.0876775\pi\) |
0.488135 | + | 0.872768i | \(0.337678\pi\) | |||||||
\(4\) | −3.97659 | + | 0.432130i | −0.994147 | + | 0.108032i | ||||
\(5\) | −2.81639 | + | 1.16659i | −0.563278 | + | 0.233318i | −0.646108 | − | 0.763246i | \(-0.723604\pi\) |
0.0828294 | + | 0.996564i | \(0.473604\pi\) | |||||||
\(6\) | 3.12870 | − | 8.88489i | 0.521449 | − | 1.48081i | ||||
\(7\) | −6.23443 | − | 6.23443i | −0.890633 | − | 0.890633i | 0.103950 | − | 0.994583i | \(-0.466852\pi\) |
−0.994583 | + | 0.103950i | \(0.966852\pi\) | |||||||
\(8\) | 1.29322 | + | 7.89478i | 0.161653 | + | 0.986848i | ||||
\(9\) | 9.32143 | + | 9.32143i | 1.03571 | + | 1.03571i | ||||
\(10\) | 2.63447 | + | 5.49832i | 0.263447 | + | 0.549832i | ||||
\(11\) | −8.06262 | + | 3.33965i | −0.732965 | + | 0.303604i | −0.717770 | − | 0.696280i | \(-0.754837\pi\) |
−0.0151955 | + | 0.999885i | \(0.504837\pi\) | |||||||
\(12\) | −18.0823 | − | 5.28697i | −1.50685 | − | 0.440581i | ||||
\(13\) | 13.3208 | + | 5.51766i | 1.02468 | + | 0.424436i | 0.830789 | − | 0.556588i | \(-0.187890\pi\) |
0.193889 | + | 0.981023i | \(0.437890\pi\) | |||||||
\(14\) | −11.7761 | + | 13.1251i | −0.841150 | + | 0.937508i | ||||
\(15\) | −14.3576 | −0.957176 | ||||||||
\(16\) | 15.6265 | − | 3.43680i | 0.976658 | − | 0.214800i | ||||
\(17\) | 4.56488i | 0.268522i | 0.990946 | + | 0.134261i | \(0.0428661\pi\) | ||||
−0.990946 | + | 0.134261i | \(0.957134\pi\) | |||||||
\(18\) | 17.6071 | − | 19.6241i | 0.978170 | − | 1.09023i | ||||
\(19\) | 13.4421 | − | 32.4522i | 0.707481 | − | 1.70801i | 0.00128016 | − | 0.999999i | \(-0.499593\pi\) |
0.706201 | − | 0.708011i | \(-0.250407\pi\) | |||||||
\(20\) | 10.6955 | − | 5.85609i | 0.534776 | − | 0.292804i | ||||
\(21\) | −15.8912 | − | 38.3647i | −0.756724 | − | 1.82689i | ||||
\(22\) | 7.54181 | + | 15.7403i | 0.342810 | + | 0.715469i | ||||
\(23\) | −6.75277 | + | 6.75277i | −0.293599 | + | 0.293599i | −0.838500 | − | 0.544901i | \(-0.816567\pi\) |
0.544901 | + | 0.838500i | \(0.316567\pi\) | |||||||
\(24\) | −8.60212 | + | 36.6836i | −0.358422 | + | 1.52848i | ||||
\(25\) | −11.1065 | + | 11.1065i | −0.444261 | + | 0.444261i | ||||
\(26\) | 9.57798 | − | 27.1996i | 0.368384 | − | 1.04614i | ||||
\(27\) | 7.53841 | + | 18.1993i | 0.279200 | + | 0.674050i | ||||
\(28\) | 27.4859 | + | 22.0977i | 0.981638 | + | 0.789203i | ||||
\(29\) | −0.266504 | + | 0.643399i | −0.00918981 | + | 0.0221862i | −0.928408 | − | 0.371563i | \(-0.878822\pi\) |
0.919218 | + | 0.393749i | \(0.128822\pi\) | |||||||
\(30\) | 1.55336 | + | 28.6732i | 0.0517788 | + | 0.955774i | ||||
\(31\) | 0.326715i | 0.0105392i | 0.999986 | + | 0.00526959i | \(0.00167737\pi\) | ||||
−0.999986 | + | 0.00526959i | \(0.998323\pi\) | |||||||
\(32\) | −8.55419 | − | 30.8355i | −0.267318 | − | 0.963608i | ||||
\(33\) | −41.1023 | −1.24552 | ||||||||
\(34\) | 9.11639 | − | 0.493878i | 0.268129 | − | 0.0145258i | ||||
\(35\) | 24.8316 | + | 10.2856i | 0.709475 | + | 0.293874i | ||||
\(36\) | −41.0956 | − | 33.0394i | −1.14154 | − | 0.917762i | ||||
\(37\) | 31.5133 | − | 13.0532i | 0.851710 | − | 0.352790i | 0.0862502 | − | 0.996274i | \(-0.472512\pi\) |
0.765460 | + | 0.643484i | \(0.222512\pi\) | |||||||
\(38\) | −66.2637 | − | 23.3339i | −1.74378 | − | 0.614050i | ||||
\(39\) | 48.0182 | + | 48.0182i | 1.23124 | + | 1.23124i | ||||
\(40\) | −12.8522 | − | 20.7261i | −0.321305 | − | 0.518153i | ||||
\(41\) | 15.7509 | + | 15.7509i | 0.384169 | + | 0.384169i | 0.872601 | − | 0.488433i | \(-0.162431\pi\) |
−0.488433 | + | 0.872601i | \(0.662431\pi\) | |||||||
\(42\) | −74.8979 | + | 35.8866i | −1.78328 | + | 0.854442i | ||||
\(43\) | 4.83274 | − | 2.00179i | 0.112389 | − | 0.0465531i | −0.325780 | − | 0.945446i | \(-0.605627\pi\) |
0.438170 | + | 0.898892i | \(0.355627\pi\) | |||||||
\(44\) | 30.6186 | − | 16.7645i | 0.695877 | − | 0.381011i | ||||
\(45\) | −37.1271 | − | 15.3785i | −0.825046 | − | 0.341745i | ||||
\(46\) | 14.2164 | + | 12.7552i | 0.309051 | + | 0.277287i | ||||
\(47\) | −49.7096 | −1.05765 | −0.528825 | − | 0.848731i | \(-0.677367\pi\) | ||||
−0.528825 | + | 0.848731i | \(0.677367\pi\) | |||||||
\(48\) | 74.1903 | + | 13.2102i | 1.54563 | + | 0.275213i | ||||
\(49\) | 28.7362i | 0.586454i | ||||||||
\(50\) | 23.3822 | + | 20.9789i | 0.467643 | + | 0.419578i | ||||
\(51\) | −8.22762 | + | 19.8632i | −0.161326 | + | 0.389475i | ||||
\(52\) | −55.3558 | − | 16.1852i | −1.06453 | − | 0.311253i | ||||
\(53\) | 4.45882 | + | 10.7645i | 0.0841286 | + | 0.203105i | 0.960346 | − | 0.278812i | \(-0.0899407\pi\) |
−0.876217 | + | 0.481917i | \(0.839941\pi\) | |||||||
\(54\) | 35.5298 | − | 17.0238i | 0.657959 | − | 0.315255i | ||||
\(55\) | 18.8115 | − | 18.8115i | 0.342027 | − | 0.342027i | ||||
\(56\) | 41.1569 | − | 57.2820i | 0.734946 | − | 1.02289i | ||||
\(57\) | 116.982 | − | 116.982i | 2.05232 | − | 2.05232i | ||||
\(58\) | 1.31375 | + | 0.462619i | 0.0226508 | + | 0.00797618i | ||||
\(59\) | 13.1268 | + | 31.6909i | 0.222488 | + | 0.537134i | 0.995227 | − | 0.0975907i | \(-0.0311136\pi\) |
−0.772739 | + | 0.634724i | \(0.781114\pi\) | |||||||
\(60\) | 57.0944 | − | 6.20436i | 0.951574 | − | 0.103406i | ||||
\(61\) | −35.4023 | + | 85.4687i | −0.580366 | + | 1.40113i | 0.312116 | + | 0.950044i | \(0.398962\pi\) |
−0.892482 | + | 0.451083i | \(0.851038\pi\) | |||||||
\(62\) | 0.652473 | − | 0.0353475i | 0.0105238 | − | 0.000570122i | ||||
\(63\) | − | 116.228i | − | 1.84488i | ||||||
\(64\) | −60.6551 | + | 20.4194i | −0.947737 | + | 0.319054i | ||||
\(65\) | −43.9535 | −0.676207 | ||||||||
\(66\) | 4.44689 | + | 82.0842i | 0.0673771 | + | 1.24370i | ||||
\(67\) | −41.3348 | − | 17.1214i | −0.616938 | − | 0.255544i | 0.0522539 | − | 0.998634i | \(-0.483359\pi\) |
−0.669192 | + | 0.743090i | \(0.733359\pi\) | |||||||
\(68\) | −1.97262 | − | 18.1527i | −0.0290091 | − | 0.266951i | ||||
\(69\) | −41.5545 | + | 17.2124i | −0.602239 | + | 0.249455i | ||||
\(70\) | 17.8545 | − | 50.7033i | 0.255064 | − | 0.724333i | ||||
\(71\) | 37.6381 | + | 37.6381i | 0.530114 | + | 0.530114i | 0.920606 | − | 0.390492i | \(-0.127695\pi\) |
−0.390492 | + | 0.920606i | \(0.627695\pi\) | |||||||
\(72\) | −61.5359 | + | 85.6453i | −0.854666 | + | 1.18952i | ||||
\(73\) | −52.2302 | − | 52.2302i | −0.715482 | − | 0.715482i | 0.252195 | − | 0.967677i | \(-0.418848\pi\) |
−0.967677 | + | 0.252195i | \(0.918848\pi\) | |||||||
\(74\) | −29.4777 | − | 61.5220i | −0.398347 | − | 0.831379i | ||||
\(75\) | −68.3461 | + | 28.3099i | −0.911282 | + | 0.377465i | ||||
\(76\) | −39.4303 | + | 134.858i | −0.518820 | + | 1.77445i | ||||
\(77\) | 71.0866 | + | 29.4450i | 0.923203 | + | 0.382403i | ||||
\(78\) | 90.7006 | − | 101.091i | 1.16283 | − | 1.29604i | ||||
\(79\) | 26.9061 | 0.340583 | 0.170292 | − | 0.985394i | \(-0.445529\pi\) | ||||
0.170292 | + | 0.985394i | \(0.445529\pi\) | |||||||
\(80\) | −40.0011 | + | 27.9091i | −0.500014 | + | 0.348864i | ||||
\(81\) | − | 25.8643i | − | 0.319313i | ||||||
\(82\) | 29.7516 | − | 33.1598i | 0.362824 | − | 0.404388i | ||||
\(83\) | 10.6315 | − | 25.6667i | 0.128090 | − | 0.309237i | −0.846804 | − | 0.531905i | \(-0.821476\pi\) |
0.974894 | + | 0.222667i | \(0.0714764\pi\) | |||||||
\(84\) | 79.7713 | + | 145.694i | 0.949658 | + | 1.73445i | ||||
\(85\) | −5.32533 | − | 12.8565i | −0.0626510 | − | 0.151253i | ||||
\(86\) | −4.52057 | − | 9.43475i | −0.0525647 | − | 0.109706i | ||||
\(87\) | −2.31929 | + | 2.31929i | −0.0266585 | + | 0.0266585i | ||||
\(88\) | −36.7926 | − | 59.3337i | −0.418097 | − | 0.674247i | ||||
\(89\) | −103.292 | + | 103.292i | −1.16058 | + | 1.16058i | −0.176234 | + | 0.984348i | \(0.556391\pi\) |
−0.984348 | + | 0.176234i | \(0.943609\pi\) | |||||||
\(90\) | −26.6952 | + | 75.8092i | −0.296614 | + | 0.842325i | ||||
\(91\) | −48.6482 | − | 117.447i | −0.534596 | − | 1.29063i | ||||
\(92\) | 23.9349 | − | 29.7711i | 0.260162 | − | 0.323599i | ||||
\(93\) | −0.588862 | + | 1.42164i | −0.00633185 | + | 0.0152864i | ||||
\(94\) | 5.37812 | + | 99.2736i | 0.0572140 | + | 1.05610i | ||||
\(95\) | 107.080i | 1.12715i | ||||||||
\(96\) | 18.3551 | − | 149.593i | 0.191198 | − | 1.55826i | ||||
\(97\) | 77.9778 | 0.803895 | 0.401948 | − | 0.915663i | \(-0.368333\pi\) | ||||
0.401948 | + | 0.915663i | \(0.368333\pi\) | |||||||
\(98\) | 57.3883 | − | 3.10900i | 0.585595 | − | 0.0317245i | ||||
\(99\) | −106.285 | − | 44.0249i | −1.07359 | − | 0.444696i | ||||
\(100\) | 39.3667 | − | 48.9656i | 0.393667 | − | 0.489656i | ||||
\(101\) | 104.064 | − | 43.1046i | 1.03033 | − | 0.426778i | 0.197500 | − | 0.980303i | \(-0.436718\pi\) |
0.832833 | + | 0.553525i | \(0.186718\pi\) | |||||||
\(102\) | 40.5585 | + | 14.2821i | 0.397632 | + | 0.140021i | ||||
\(103\) | −76.6571 | − | 76.6571i | −0.744243 | − | 0.744243i | 0.229148 | − | 0.973392i | \(-0.426406\pi\) |
−0.973392 | + | 0.229148i | \(0.926406\pi\) | |||||||
\(104\) | −26.3339 | + | 112.301i | −0.253211 | + | 1.07981i | ||||
\(105\) | 89.5117 | + | 89.5117i | 0.852492 | + | 0.852492i | ||||
\(106\) | 21.0152 | − | 10.0692i | 0.198256 | − | 0.0949925i | ||||
\(107\) | −40.9728 | + | 16.9715i | −0.382923 | + | 0.158612i | −0.565837 | − | 0.824517i | \(-0.691447\pi\) |
0.182914 | + | 0.983129i | \(0.441447\pi\) | |||||||
\(108\) | −37.8416 | − | 69.1137i | −0.350386 | − | 0.639942i | ||||
\(109\) | 102.183 | + | 42.3255i | 0.937456 | + | 0.388307i | 0.798502 | − | 0.601992i | \(-0.205626\pi\) |
0.138954 | + | 0.990299i | \(0.455626\pi\) | |||||||
\(110\) | −39.6032 | − | 35.5327i | −0.360029 | − | 0.323024i | ||||
\(111\) | 160.651 | 1.44731 | ||||||||
\(112\) | −118.849 | − | 75.9960i | −1.06115 | − | 0.678536i | ||||
\(113\) | − | 123.602i | − | 1.09383i | −0.837190 | − | 0.546913i | \(-0.815803\pi\) | ||
0.837190 | − | 0.546913i | \(-0.184197\pi\) | |||||||
\(114\) | −246.278 | − | 220.965i | −2.16033 | − | 1.93829i | ||||
\(115\) | 11.1408 | − | 26.8962i | 0.0968761 | − | 0.233880i | ||||
\(116\) | 0.781747 | − | 2.67370i | 0.00673920 | − | 0.0230491i | ||||
\(117\) | 72.7365 | + | 175.602i | 0.621680 | + | 1.50087i | ||||
\(118\) | 61.8688 | − | 29.6438i | 0.524312 | − | 0.251219i | ||||
\(119\) | 28.4594 | − | 28.4594i | 0.239155 | − | 0.239155i | ||||
\(120\) | −18.5676 | − | 113.350i | −0.154730 | − | 0.944587i | ||||
\(121\) | −31.7073 | + | 31.7073i | −0.262044 | + | 0.262044i | ||||
\(122\) | 174.517 | + | 61.4540i | 1.43047 | + | 0.503721i | ||||
\(123\) | 40.1481 | + | 96.9262i | 0.326408 | + | 0.788018i | ||||
\(124\) | −0.141183 | − | 1.29921i | −0.00113857 | − | 0.0104775i | ||||
\(125\) | 47.4883 | − | 114.647i | 0.379906 | − | 0.917175i | ||||
\(126\) | −232.115 | + | 12.5748i | −1.84218 | + | 0.0997997i | ||||
\(127\) | 133.213i | 1.04892i | 0.851434 | + | 0.524462i | \(0.175734\pi\) | ||||
−0.851434 | + | 0.524462i | \(0.824266\pi\) | |||||||
\(128\) | 47.3414 | + | 118.923i | 0.369855 | + | 0.929090i | ||||
\(129\) | 24.6367 | 0.190982 | ||||||||
\(130\) | 4.75536 | + | 87.7782i | 0.0365797 | + | 0.675217i | ||||
\(131\) | 228.056 | + | 94.4640i | 1.74089 | + | 0.721100i | 0.998704 | + | 0.0509041i | \(0.0162103\pi\) |
0.742185 | + | 0.670195i | \(0.233790\pi\) | |||||||
\(132\) | 163.447 | − | 17.7615i | 1.23823 | − | 0.134557i | ||||
\(133\) | −286.125 | + | 118.517i | −2.15132 | + | 0.891104i | ||||
\(134\) | −29.7207 | + | 84.4010i | −0.221796 | + | 0.629858i | ||||
\(135\) | −42.4622 | − | 42.4622i | −0.314535 | − | 0.314535i | ||||
\(136\) | −36.0387 | + | 5.90341i | −0.264991 | + | 0.0434075i | ||||
\(137\) | −111.817 | − | 111.817i | −0.816180 | − | 0.816180i | 0.169372 | − | 0.985552i | \(-0.445826\pi\) |
−0.985552 | + | 0.169372i | \(0.945826\pi\) | |||||||
\(138\) | 38.8702 | + | 81.1250i | 0.281668 | + | 0.587862i | ||||
\(139\) | 31.7750 | − | 13.1616i | 0.228597 | − | 0.0946880i | −0.265445 | − | 0.964126i | \(-0.585519\pi\) |
0.494042 | + | 0.869438i | \(0.335519\pi\) | |||||||
\(140\) | −103.190 | − | 30.1711i | −0.737070 | − | 0.215508i | ||||
\(141\) | −216.302 | − | 89.5952i | −1.53406 | − | 0.635427i | ||||
\(142\) | 71.0939 | − | 79.2381i | 0.500661 | − | 0.558015i | ||||
\(143\) | −125.828 | −0.879914 | ||||||||
\(144\) | 177.698 | + | 113.626i | 1.23401 | + | 0.789067i | ||||
\(145\) | − | 2.12296i | − | 0.0146411i | ||||||
\(146\) | −98.6566 | + | 109.958i | −0.675730 | + | 0.753138i | ||||
\(147\) | −51.7934 | + | 125.040i | −0.352336 | + | 0.850615i | ||||
\(148\) | −119.675 | + | 65.5251i | −0.808613 | + | 0.442737i | ||||
\(149\) | −108.344 | − | 261.565i | −0.727140 | − | 1.75547i | −0.651898 | − | 0.758307i | \(-0.726027\pi\) |
−0.0752422 | − | 0.997165i | \(-0.523973\pi\) | |||||||
\(150\) | 63.9313 | + | 133.429i | 0.426209 | + | 0.889528i | ||||
\(151\) | 51.5292 | − | 51.5292i | 0.341253 | − | 0.341253i | −0.515585 | − | 0.856838i | \(-0.672425\pi\) |
0.856838 | + | 0.515585i | \(0.172425\pi\) | |||||||
\(152\) | 273.587 | + | 64.1548i | 1.79991 | + | 0.422071i | ||||
\(153\) | −42.5512 | + | 42.5512i | −0.278112 | + | 0.278112i | ||||
\(154\) | 51.1129 | − | 145.151i | 0.331902 | − | 0.942538i | ||||
\(155\) | −0.381142 | − | 0.920157i | −0.00245898 | − | 0.00593650i | ||||
\(156\) | −211.699 | − | 170.199i | −1.35704 | − | 1.09102i | ||||
\(157\) | 39.3450 | − | 94.9872i | 0.250605 | − | 0.605014i | −0.747648 | − | 0.664095i | \(-0.768817\pi\) |
0.998253 | + | 0.0590811i | \(0.0188171\pi\) | |||||||
\(158\) | −2.91099 | − | 53.7334i | −0.0184240 | − | 0.340085i | ||||
\(159\) | 54.8764i | 0.345134i | ||||||||
\(160\) | 60.0642 | + | 76.8655i | 0.375401 | + | 0.480410i | ||||
\(161\) | 84.1994 | 0.522978 | ||||||||
\(162\) | −51.6529 | + | 2.79828i | −0.318845 | + | 0.0172734i | ||||
\(163\) | −4.97467 | − | 2.06057i | −0.0305194 | − | 0.0126416i | 0.367372 | − | 0.930074i | \(-0.380258\pi\) |
−0.397891 | + | 0.917433i | \(0.630258\pi\) | |||||||
\(164\) | −69.4413 | − | 55.8285i | −0.423423 | − | 0.340417i | ||||
\(165\) | 115.760 | − | 47.9494i | 0.701577 | − | 0.290603i | ||||
\(166\) | −52.4085 | − | 18.4550i | −0.315714 | − | 0.111174i | ||||
\(167\) | −165.012 | − | 165.012i | −0.988097 | − | 0.988097i | 0.0118333 | − | 0.999930i | \(-0.496233\pi\) |
−0.999930 | + | 0.0118333i | \(0.996233\pi\) | |||||||
\(168\) | 282.330 | − | 175.072i | 1.68054 | − | 1.04209i | ||||
\(169\) | 27.4985 | + | 27.4985i | 0.162713 | + | 0.162713i | ||||
\(170\) | −25.0992 | + | 12.0260i | −0.147642 | + | 0.0707413i | ||||
\(171\) | 427.801 | − | 177.201i | 2.50176 | − | 1.03626i | ||||
\(172\) | −18.3528 | + | 10.0486i | −0.106702 | + | 0.0584224i | ||||
\(173\) | −115.760 | − | 47.9493i | −0.669132 | − | 0.277163i | 0.0221438 | − | 0.999755i | \(-0.492951\pi\) |
−0.691275 | + | 0.722591i | \(0.742951\pi\) | |||||||
\(174\) | 4.88271 | + | 4.38086i | 0.0280616 | + | 0.0251774i | ||||
\(175\) | 138.486 | 0.791348 | ||||||||
\(176\) | −114.513 | + | 79.8967i | −0.650642 | + | 0.453959i | ||||
\(177\) | 161.556i | 0.912748i | ||||||||
\(178\) | 217.456 | + | 195.106i | 1.22166 | + | 1.09610i | ||||
\(179\) | −44.8368 | + | 108.246i | −0.250485 | + | 0.604724i | −0.998243 | − | 0.0592467i | \(-0.981130\pi\) |
0.747758 | + | 0.663971i | \(0.231130\pi\) | |||||||
\(180\) | 154.285 | + | 45.1104i | 0.857137 | + | 0.250613i | ||||
\(181\) | 80.3652 | + | 194.019i | 0.444007 | + | 1.07193i | 0.974530 | + | 0.224256i | \(0.0719953\pi\) |
−0.530524 | + | 0.847670i | \(0.678005\pi\) | |||||||
\(182\) | −229.287 | + | 109.861i | −1.25982 | + | 0.603630i | ||||
\(183\) | −308.093 | + | 308.093i | −1.68357 | + | 1.68357i | ||||
\(184\) | −62.0445 | − | 44.5788i | −0.337198 | − | 0.242276i | ||||
\(185\) | −73.5260 | + | 73.5260i | −0.397438 | + | 0.397438i | ||||
\(186\) | 2.90282 | + | 1.02219i | 0.0156066 | + | 0.00549565i | ||||
\(187\) | −15.2451 | − | 36.8049i | −0.0815245 | − | 0.196818i | ||||
\(188\) | 197.675 | − | 21.4810i | 1.05146 | − | 0.114261i | ||||
\(189\) | 66.4648 | − | 160.460i | 0.351666 | − | 0.848996i | ||||
\(190\) | 213.846 | − | 11.5850i | 1.12550 | − | 0.0609738i | ||||
\(191\) | − | 338.117i | − | 1.77025i | −0.465357 | − | 0.885123i | \(-0.654074\pi\) | ||
0.465357 | − | 0.885123i | \(-0.345926\pi\) | |||||||
\(192\) | −300.733 | − | 20.4718i | −1.56632 | − | 0.106624i | ||||
\(193\) | 234.508 | 1.21507 | 0.607533 | − | 0.794295i | \(-0.292159\pi\) | ||||
0.607533 | + | 0.794295i | \(0.292159\pi\) | |||||||
\(194\) | −8.43648 | − | 155.727i | −0.0434870 | − | 0.802718i | ||||
\(195\) | −191.255 | − | 79.2206i | −0.980797 | − | 0.406259i | ||||
\(196\) | −12.4178 | − | 114.272i | −0.0633560 | − | 0.583022i | ||||
\(197\) | 237.007 | − | 98.1713i | 1.20308 | − | 0.498332i | 0.311086 | − | 0.950382i | \(-0.399307\pi\) |
0.891993 | + | 0.452050i | \(0.149307\pi\) | |||||||
\(198\) | −76.4217 | + | 217.023i | −0.385968 | + | 1.09607i | ||||
\(199\) | 39.2172 | + | 39.2172i | 0.197071 | + | 0.197071i | 0.798743 | − | 0.601672i | \(-0.205499\pi\) |
−0.601672 | + | 0.798743i | \(0.705499\pi\) | |||||||
\(200\) | −102.047 | − | 73.3204i | −0.510234 | − | 0.366602i | ||||
\(201\) | −149.002 | − | 149.002i | −0.741302 | − | 0.741302i | ||||
\(202\) | −97.3416 | − | 203.159i | −0.481889 | − | 1.00574i | ||||
\(203\) | 5.67273 | − | 2.34972i | 0.0279445 | − | 0.0115750i | ||||
\(204\) | 24.1344 | − | 82.5433i | 0.118306 | − | 0.404624i | ||||
\(205\) | −62.7356 | − | 25.9859i | −0.306027 | − | 0.126761i | ||||
\(206\) | −144.796 | + | 161.383i | −0.702894 | + | 0.783414i | ||||
\(207\) | −125.891 | −0.608169 | ||||||||
\(208\) | 227.121 | + | 40.4409i | 1.09193 | + | 0.194427i | ||||
\(209\) | 306.542i | 1.46671i | ||||||||
\(210\) | 169.077 | − | 188.446i | 0.805128 | − | 0.897360i | ||||
\(211\) | −79.9026 | + | 192.902i | −0.378685 | + | 0.914227i | 0.613528 | + | 0.789673i | \(0.289750\pi\) |
−0.992213 | + | 0.124554i | \(0.960250\pi\) | |||||||
\(212\) | −22.3826 | − | 40.8794i | −0.105578 | − | 0.192827i | ||||
\(213\) | 95.9373 | + | 231.613i | 0.450410 | + | 1.08739i | ||||
\(214\) | 38.3261 | + | 79.9894i | 0.179094 | + | 0.373782i | ||||
\(215\) | −11.2756 | + | 11.2756i | −0.0524448 | + | 0.0524448i | ||||
\(216\) | −133.931 | + | 83.0499i | −0.620051 | + | 0.384490i | ||||
\(217\) | 2.03688 | − | 2.03688i | 0.00938655 | − | 0.00938655i | ||||
\(218\) | 73.4718 | − | 208.645i | 0.337026 | − | 0.957089i | ||||
\(219\) | −133.132 | − | 321.408i | −0.607907 | − | 1.46762i | ||||
\(220\) | −66.6766 | + | 82.9346i | −0.303076 | + | 0.376976i | ||||
\(221\) | −25.1875 | + | 60.8079i | −0.113970 | + | 0.275149i | ||||
\(222\) | −17.3810 | − | 320.831i | −0.0782926 | − | 1.44519i | ||||
\(223\) | 344.421i | 1.54449i | 0.635326 | + | 0.772244i | \(0.280866\pi\) | ||||
−0.635326 | + | 0.772244i | \(0.719134\pi\) | |||||||
\(224\) | −138.911 | + | 245.572i | −0.620139 | + | 1.09630i | ||||
\(225\) | −207.058 | −0.920256 | ||||||||
\(226\) | −246.843 | + | 13.3726i | −1.09222 | + | 0.0591709i | ||||
\(227\) | 68.2639 | + | 28.2758i | 0.300722 | + | 0.124563i | 0.527942 | − | 0.849280i | \(-0.322964\pi\) |
−0.227220 | + | 0.973843i | \(0.572964\pi\) | |||||||
\(228\) | −414.638 | + | 515.741i | −1.81859 | + | 2.26202i | ||||
\(229\) | −41.8202 | + | 17.3225i | −0.182621 | + | 0.0756440i | −0.472120 | − | 0.881534i | \(-0.656511\pi\) |
0.289499 | + | 0.957178i | \(0.406511\pi\) | |||||||
\(230\) | −54.9189 | − | 19.3390i | −0.238778 | − | 0.0840824i | ||||
\(231\) | 256.249 | + | 256.249i | 1.10930 | + | 1.10930i | ||||
\(232\) | −5.42414 | − | 1.27194i | −0.0233799 | − | 0.00548248i | ||||
\(233\) | 203.044 | + | 203.044i | 0.871432 | + | 0.871432i | 0.992629 | − | 0.121197i | \(-0.0386731\pi\) |
−0.121197 | + | 0.992629i | \(0.538673\pi\) | |||||||
\(234\) | 342.819 | − | 164.259i | 1.46504 | − | 0.701960i | ||||
\(235\) | 140.002 | − | 57.9906i | 0.595752 | − | 0.246768i | ||||
\(236\) | −65.8944 | − | 120.349i | −0.279214 | − | 0.509954i | ||||
\(237\) | 117.077 | + | 48.4948i | 0.493995 | + | 0.204619i | ||||
\(238\) | −59.9146 | − | 53.7565i | −0.251742 | − | 0.225868i | ||||
\(239\) | 87.6710 | 0.366824 | 0.183412 | − | 0.983036i | \(-0.441286\pi\) | ||||
0.183412 | + | 0.983036i | \(0.441286\pi\) | |||||||
\(240\) | −224.360 | + | 49.3444i | −0.934833 | + | 0.205602i | ||||
\(241\) | 15.4754i | 0.0642135i | 0.999484 | + | 0.0321067i | \(0.0102216\pi\) | ||||
−0.999484 | + | 0.0321067i | \(0.989778\pi\) | |||||||
\(242\) | 66.7522 | + | 59.8913i | 0.275836 | + | 0.247485i | ||||
\(243\) | 114.463 | − | 276.338i | 0.471041 | − | 1.13719i | ||||
\(244\) | 103.847 | − | 355.172i | 0.425602 | − | 1.45562i | ||||
\(245\) | −33.5233 | − | 80.9325i | −0.136830 | − | 0.330337i | ||||
\(246\) | 189.225 | − | 90.6652i | 0.769207 | − | 0.368558i | ||||
\(247\) | 358.121 | − | 358.121i | 1.44988 | − | 1.44988i | ||||
\(248\) | −2.57934 | + | 0.422516i | −0.0104006 | + | 0.00170369i | ||||
\(249\) | 92.5220 | − | 92.5220i | 0.371574 | − | 0.371574i | ||||
\(250\) | −234.096 | − | 82.4338i | −0.936383 | − | 0.329735i | ||||
\(251\) | 95.9530 | + | 231.651i | 0.382283 | + | 0.922913i | 0.991524 | + | 0.129927i | \(0.0414743\pi\) |
−0.609241 | + | 0.792985i | \(0.708526\pi\) | |||||||
\(252\) | 50.2254 | + | 462.189i | 0.199307 | + | 1.83409i | ||||
\(253\) | 31.8932 | − | 76.9969i | 0.126060 | − | 0.304336i | ||||
\(254\) | 266.037 | − | 14.4125i | 1.04739 | − | 0.0567420i | ||||
\(255\) | − | 65.5409i | − | 0.257023i | ||||||
\(256\) | 232.377 | − | 107.411i | 0.907722 | − | 0.419573i | ||||
\(257\) | −131.142 | −0.510282 | −0.255141 | − | 0.966904i | \(-0.582122\pi\) | ||||
−0.255141 | + | 0.966904i | \(0.582122\pi\) | |||||||
\(258\) | −2.66547 | − | 49.2013i | −0.0103313 | − | 0.190703i | ||||
\(259\) | −277.847 | − | 115.088i | −1.07277 | − | 0.444355i | ||||
\(260\) | 174.785 | − | 18.9936i | 0.672250 | − | 0.0730523i | ||||
\(261\) | −8.48160 | + | 3.51319i | −0.0324965 | + | 0.0134605i | ||||
\(262\) | 163.978 | − | 465.665i | 0.625870 | − | 1.77735i | ||||
\(263\) | −281.350 | − | 281.350i | −1.06977 | − | 1.06977i | −0.997376 | − | 0.0723955i | \(-0.976936\pi\) |
−0.0723955 | − | 0.997376i | \(-0.523064\pi\) | |||||||
\(264\) | −53.1545 | − | 324.494i | −0.201343 | − | 1.22914i | ||||
\(265\) | −25.1156 | − | 25.1156i | −0.0947757 | − | 0.0947757i | ||||
\(266\) | 267.643 | + | 558.590i | 1.00618 | + | 2.09996i | ||||
\(267\) | −635.626 | + | 263.285i | −2.38062 | + | 0.986085i | ||||
\(268\) | 171.770 | + | 50.2230i | 0.640934 | + | 0.187399i | ||||
\(269\) | 133.290 | + | 55.2107i | 0.495503 | + | 0.205244i | 0.616419 | − | 0.787419i | \(-0.288583\pi\) |
−0.120915 | + | 0.992663i | \(0.538583\pi\) | |||||||
\(270\) | −80.2061 | + | 89.3942i | −0.297060 | + | 0.331090i | ||||
\(271\) | −368.673 | −1.36042 | −0.680208 | − | 0.733019i | \(-0.738111\pi\) | ||||
−0.680208 | + | 0.733019i | \(0.738111\pi\) | |||||||
\(272\) | 15.6886 | + | 71.3332i | 0.0576787 | + | 0.262255i | ||||
\(273\) | − | 598.732i | − | 2.19316i | ||||||
\(274\) | −211.208 | + | 235.404i | −0.770834 | + | 0.859137i | ||||
\(275\) | 52.4559 | − | 126.640i | 0.190749 | − | 0.460508i | ||||
\(276\) | 157.807 | − | 86.4036i | 0.571765 | − | 0.313057i | ||||
\(277\) | 21.6001 | + | 52.1472i | 0.0779786 | + | 0.188257i | 0.958061 | − | 0.286564i | \(-0.0925130\pi\) |
−0.880083 | + | 0.474821i | \(0.842513\pi\) | |||||||
\(278\) | −29.7225 | − | 62.0329i | −0.106915 | − | 0.223140i | ||||
\(279\) | −3.04545 | + | 3.04545i | −0.0109156 | + | 0.0109156i | ||||
\(280\) | −49.0896 | + | 209.342i | −0.175320 | + | 0.747649i | ||||
\(281\) | 85.0605 | − | 85.0605i | 0.302706 | − | 0.302706i | −0.539365 | − | 0.842072i | \(-0.681336\pi\) |
0.842072 | + | 0.539365i | \(0.181336\pi\) | |||||||
\(282\) | −155.526 | + | 441.664i | −0.551511 | + | 1.56618i | ||||
\(283\) | 27.0948 | + | 65.4127i | 0.0957414 | + | 0.231140i | 0.964493 | − | 0.264107i | \(-0.0850773\pi\) |
−0.868752 | + | 0.495248i | \(0.835077\pi\) | |||||||
\(284\) | −165.936 | − | 133.407i | −0.584281 | − | 0.469742i | ||||
\(285\) | −192.997 | + | 465.937i | −0.677184 | + | 1.63487i | ||||
\(286\) | 13.6134 | + | 251.287i | 0.0475993 | + | 0.878626i | ||||
\(287\) | − | 196.396i | − | 0.684306i | ||||||
\(288\) | 207.693 | − | 367.168i | 0.721157 | − | 1.27489i | ||||
\(289\) | 268.162 | 0.927896 | ||||||||
\(290\) | −4.23971 | + | 0.229685i | −0.0146197 | + | 0.000792018i | ||||
\(291\) | 339.306 | + | 140.545i | 1.16600 | + | 0.482973i | ||||
\(292\) | 230.268 | + | 185.128i | 0.788590 | + | 0.633999i | ||||
\(293\) | −321.033 | + | 132.976i | −1.09568 | + | 0.453844i | −0.855983 | − | 0.517005i | \(-0.827047\pi\) |
−0.239694 | + | 0.970849i | \(0.577047\pi\) | |||||||
\(294\) | 255.318 | + | 89.9070i | 0.868430 | + | 0.305806i | ||||
\(295\) | −73.9404 | − | 73.9404i | −0.250645 | − | 0.250645i | ||||
\(296\) | 143.806 | + | 231.910i | 0.485831 | + | 0.783479i | ||||
\(297\) | −121.559 | − | 121.559i | −0.409289 | − | 0.409289i | ||||
\(298\) | −510.643 | + | 244.669i | −1.71357 | + | 0.821039i | ||||
\(299\) | −127.212 | + | 52.6929i | −0.425458 | + | 0.176231i | ||||
\(300\) | 259.551 | − | 142.111i | 0.865170 | − | 0.473704i | ||||
\(301\) | −42.6094 | − | 17.6494i | −0.141559 | − | 0.0586358i | ||||
\(302\) | −108.483 | − | 97.3326i | −0.359214 | − | 0.322293i | ||||
\(303\) | 530.504 | 1.75084 | ||||||||
\(304\) | 98.5222 | − | 553.313i | 0.324086 | − | 1.82011i | ||||
\(305\) | − | 282.013i | − | 0.924634i | ||||||
\(306\) | 89.5815 | + | 80.3742i | 0.292750 | + | 0.262661i | ||||
\(307\) | −92.6973 | + | 223.791i | −0.301946 | + | 0.728961i | 0.697972 | + | 0.716125i | \(0.254086\pi\) |
−0.999918 | + | 0.0128360i | \(0.995914\pi\) | |||||||
\(308\) | −295.406 | − | 86.3722i | −0.959112 | − | 0.280429i | ||||
\(309\) | −195.394 | − | 471.724i | −0.632344 | − | 1.52661i | ||||
\(310\) | −1.79638 | + | 0.860719i | −0.00579479 | + | 0.00277651i | ||||
\(311\) | −44.5768 | + | 44.5768i | −0.143334 | + | 0.143334i | −0.775133 | − | 0.631799i | \(-0.782317\pi\) |
0.631799 | + | 0.775133i | \(0.282317\pi\) | |||||||
\(312\) | −316.995 | + | 441.191i | −1.01601 | + | 1.41407i | ||||
\(313\) | −27.9303 | + | 27.9303i | −0.0892343 | + | 0.0892343i | −0.750315 | − | 0.661081i | \(-0.770098\pi\) |
0.661081 | + | 0.750315i | \(0.270098\pi\) | |||||||
\(314\) | −193.953 | − | 68.2980i | −0.617685 | − | 0.217510i | ||||
\(315\) | 135.590 | + | 327.342i | 0.430443 | + | 1.03918i | ||||
\(316\) | −106.994 | + | 11.6269i | −0.338590 | + | 0.0367940i | ||||
\(317\) | −125.850 | + | 303.829i | −0.397003 | + | 0.958450i | 0.591370 | + | 0.806400i | \(0.298587\pi\) |
−0.988373 | + | 0.152049i | \(0.951413\pi\) | |||||||
\(318\) | 109.592 | − | 5.93712i | 0.344629 | − | 0.0186702i | ||||
\(319\) | − | 6.07751i | − | 0.0190518i | ||||||
\(320\) | 147.008 | − | 128.269i | 0.459399 | − | 0.400840i | ||||
\(321\) | −208.874 | −0.650699 | ||||||||
\(322\) | −9.10960 | − | 168.152i | −0.0282907 | − | 0.522212i | ||||
\(323\) | 148.140 | + | 61.3618i | 0.458639 | + | 0.189975i | ||||
\(324\) | 11.1767 | + | 102.852i | 0.0344961 | + | 0.317444i | ||||
\(325\) | −209.230 | + | 86.6660i | −0.643785 | + | 0.266665i | ||||
\(326\) | −3.57690 | + | 10.1577i | −0.0109721 | + | 0.0311586i | ||||
\(327\) | 368.343 | + | 368.343i | 1.12643 | + | 1.12643i | ||||
\(328\) | −103.981 | + | 144.719i | −0.317014 | + | 0.441218i | ||||
\(329\) | 309.911 | + | 309.911i | 0.941978 | + | 0.941978i | ||||
\(330\) | −108.283 | − | 225.994i | −0.328129 | − | 0.684829i | ||||
\(331\) | −169.515 | + | 70.2155i | −0.512131 | + | 0.212131i | −0.623756 | − | 0.781619i | \(-0.714394\pi\) |
0.111626 | + | 0.993750i | \(0.464394\pi\) | |||||||
\(332\) | −31.1858 | + | 106.660i | −0.0939330 | + | 0.321265i | ||||
\(333\) | 415.423 | + | 172.074i | 1.24752 | + | 0.516739i | ||||
\(334\) | −311.688 | + | 347.394i | −0.933198 | + | 1.04010i | ||||
\(335\) | 136.389 | 0.407131 | ||||||||
\(336\) | −380.176 | − | 544.893i | −1.13148 | − | 1.62170i | ||||
\(337\) | − | 67.3116i | − | 0.199738i | −0.995001 | − | 0.0998689i | \(-0.968158\pi\) | ||
0.995001 | − | 0.0998689i | \(-0.0318423\pi\) | |||||||
\(338\) | 51.9414 | − | 57.8916i | 0.153673 | − | 0.171277i | ||||
\(339\) | 222.778 | − | 537.833i | 0.657161 | − | 1.58653i | ||||
\(340\) | 26.7323 | + | 48.8238i | 0.0786245 | + | 0.143599i | ||||
\(341\) | −1.09111 | − | 2.63418i | −0.00319974 | − | 0.00772486i | ||||
\(342\) | −400.167 | − | 835.177i | −1.17008 | − | 2.44204i | ||||
\(343\) | −126.333 | + | 126.333i | −0.368318 | + | 0.368318i | ||||
\(344\) | 22.0535 | + | 35.5646i | 0.0641089 | + | 0.103386i | ||||
\(345\) | 96.9538 | − | 96.9538i | 0.281026 | − | 0.281026i | ||||
\(346\) | −83.2340 | + | 236.368i | −0.240561 | + | 0.683145i | ||||
\(347\) | −107.157 | − | 258.699i | −0.308809 | − | 0.745530i | −0.999744 | − | 0.0226140i | \(-0.992801\pi\) |
0.690935 | − | 0.722916i | \(-0.257199\pi\) | |||||||
\(348\) | 8.22063 | − | 10.2251i | 0.0236225 | − | 0.0293825i | ||||
\(349\) | 165.558 | − | 399.692i | 0.474378 | − | 1.14525i | −0.487831 | − | 0.872938i | \(-0.662212\pi\) |
0.962209 | − | 0.272311i | \(-0.0877881\pi\) | |||||||
\(350\) | −14.9829 | − | 276.566i | −0.0428083 | − | 0.790189i | ||||
\(351\) | 284.024i | 0.809187i | ||||||||
\(352\) | 171.949 | + | 220.047i | 0.488491 | + | 0.625133i | ||||
\(353\) | −574.524 | −1.62755 | −0.813773 | − | 0.581183i | \(-0.802590\pi\) | ||||
−0.813773 | + | 0.581183i | \(0.802590\pi\) | |||||||
\(354\) | 322.640 | − | 17.4789i | 0.911412 | − | 0.0493755i | ||||
\(355\) | −149.912 | − | 62.0955i | −0.422287 | − | 0.174917i | ||||
\(356\) | 366.114 | − | 455.385i | 1.02841 | − | 1.27917i | ||||
\(357\) | 175.130 | − | 72.5414i | 0.490562 | − | 0.203197i | ||||
\(358\) | 221.025 | + | 77.8311i | 0.617389 | + | 0.217405i | ||||
\(359\) | 499.243 | + | 499.243i | 1.39065 | + | 1.39065i | 0.823868 | + | 0.566782i | \(0.191812\pi\) |
0.566782 | + | 0.823868i | \(0.308188\pi\) | |||||||
\(360\) | 73.3965 | − | 312.998i | 0.203879 | − | 0.869439i | ||||
\(361\) | −617.189 | − | 617.189i | −1.70966 | − | 1.70966i | ||||
\(362\) | 378.774 | − | 181.486i | 1.04634 | − | 0.501343i | ||||
\(363\) | −195.117 | + | 80.8201i | −0.537512 | + | 0.222645i | ||||
\(364\) | 244.206 | + | 446.017i | 0.670897 | + | 1.22532i | ||||
\(365\) | 208.032 | + | 86.1696i | 0.569950 | + | 0.236081i | ||||
\(366\) | 648.617 | + | 581.951i | 1.77218 | + | 1.59003i | ||||
\(367\) | 295.566 | 0.805357 | 0.402679 | − | 0.915341i | \(-0.368079\pi\) | ||||
0.402679 | + | 0.915341i | \(0.368079\pi\) | |||||||
\(368\) | −82.3144 | + | 128.730i | −0.223681 | + | 0.349811i | ||||
\(369\) | 293.642i | 0.795778i | ||||||||
\(370\) | 154.792 | + | 138.882i | 0.418355 | + | 0.375356i | ||||
\(371\) | 39.3126 | − | 94.9090i | 0.105964 | − | 0.255819i | ||||
\(372\) | 1.72733 | − | 5.90774i | 0.00464336 | − | 0.0158810i | ||||
\(373\) | −133.878 | − | 323.209i | −0.358921 | − | 0.866512i | −0.995452 | − | 0.0952612i | \(-0.969631\pi\) |
0.636531 | − | 0.771251i | \(-0.280369\pi\) | |||||||
\(374\) | −71.8526 | + | 34.4275i | −0.192119 | + | 0.0920521i | ||||
\(375\) | 413.273 | − | 413.273i | 1.10206 | − | 1.10206i | ||||
\(376\) | −64.2856 | − | 392.446i | −0.170972 | − | 1.04374i | ||||
\(377\) | −7.10011 | + | 7.10011i | −0.0188332 | + | 0.0188332i | ||||
\(378\) | −327.641 | − | 115.375i | −0.866776 | − | 0.305224i | ||||
\(379\) | 170.642 | + | 411.967i | 0.450244 | + | 1.08698i | 0.972229 | + | 0.234030i | \(0.0751915\pi\) |
−0.521986 | + | 0.852954i | \(0.674809\pi\) | |||||||
\(380\) | −46.2722 | − | 425.811i | −0.121769 | − | 1.12056i | ||||
\(381\) | −240.100 | + | 579.654i | −0.630185 | + | 1.52140i | ||||
\(382\) | −675.244 | + | 36.5812i | −1.76765 | + | 0.0957622i | ||||
\(383\) | − | 254.902i | − | 0.665540i | −0.943008 | − | 0.332770i | \(-0.892017\pi\) | ||
0.943008 | − | 0.332770i | \(-0.107983\pi\) | |||||||
\(384\) | −8.34710 | + | 602.800i | −0.0217372 | + | 1.56979i | ||||
\(385\) | −234.558 | −0.609242 | ||||||||
\(386\) | −25.3716 | − | 468.328i | −0.0657294 | − | 1.21329i | ||||
\(387\) | 63.7075 | + | 26.3885i | 0.164619 | + | 0.0681874i | ||||
\(388\) | −310.086 | + | 33.6965i | −0.799190 | + | 0.0868467i | ||||
\(389\) | 687.246 | − | 284.667i | 1.76670 | − | 0.731791i | 0.771247 | − | 0.636536i | \(-0.219633\pi\) |
0.995453 | − | 0.0952550i | \(-0.0303666\pi\) | |||||||
\(390\) | −137.517 | + | 390.522i | −0.352608 | + | 1.00134i | ||||
\(391\) | −30.8256 | − | 30.8256i | −0.0788379 | − | 0.0788379i | ||||
\(392\) | −226.866 | + | 37.1624i | −0.578741 | + | 0.0948020i | ||||
\(393\) | 822.086 | + | 822.086i | 2.09182 | + | 2.09182i | ||||
\(394\) | −221.697 | − | 462.698i | −0.562683 | − | 1.17436i | ||||
\(395\) | −75.7781 | + | 31.3883i | −0.191843 | + | 0.0794640i | ||||
\(396\) | 441.678 | + | 129.140i | 1.11535 | + | 0.326110i | ||||
\(397\) | −56.8981 | − | 23.5679i | −0.143320 | − | 0.0593651i | 0.309871 | − | 0.950779i | \(-0.399714\pi\) |
−0.453191 | + | 0.891414i | \(0.649714\pi\) | |||||||
\(398\) | 74.0766 | − | 82.5625i | 0.186122 | − | 0.207443i | ||||
\(399\) | −1458.63 | −3.65572 | ||||||||
\(400\) | −135.386 | + | 211.728i | −0.338464 | + | 0.529319i | ||||
\(401\) | 704.010i | 1.75564i | 0.478994 | + | 0.877818i | \(0.341001\pi\) | ||||
−0.478994 | + | 0.877818i | \(0.658999\pi\) | |||||||
\(402\) | −281.446 | + | 313.687i | −0.700115 | + | 0.780317i | ||||
\(403\) | −1.80270 | + | 4.35211i | −0.00447321 | + | 0.0107993i | ||||
\(404\) | −395.192 | + | 216.378i | −0.978197 | + | 0.535589i | ||||
\(405\) | 30.1730 | + | 72.8441i | 0.0745013 | + | 0.179862i | ||||
\(406\) | −5.30630 | − | 11.0746i | −0.0130697 | − | 0.0272774i | ||||
\(407\) | −210.486 | + | 210.486i | −0.517166 | + | 0.517166i | ||||
\(408\) | −167.456 | − | 39.2677i | −0.410431 | − | 0.0962442i | ||||
\(409\) | 528.488 | − | 528.488i | 1.29215 | − | 1.29215i | 0.358690 | − | 0.933457i | \(-0.383224\pi\) |
0.933457 | − | 0.358690i | \(-0.116776\pi\) | |||||||
\(410\) | −45.1083 | + | 128.099i | −0.110020 | + | 0.312436i | ||||
\(411\) | −285.014 | − | 688.085i | −0.693465 | − | 1.67417i | ||||
\(412\) | 337.959 | + | 271.708i | 0.820290 | + | 0.659485i | ||||
\(413\) | 115.737 | − | 279.413i | 0.280234 | − | 0.676544i | ||||
\(414\) | 13.6202 | + | 251.413i | 0.0328991 | + | 0.607278i | ||||
\(415\) | 84.6901i | 0.204072i | ||||||||
\(416\) | 56.1909 | − | 457.953i | 0.135074 | − | 1.10085i | ||||
\(417\) | 161.985 | 0.388453 | ||||||||
\(418\) | 612.186 | − | 33.1650i | 1.46456 | − | 0.0793421i | ||||
\(419\) | −153.485 | − | 63.5754i | −0.366312 | − | 0.151731i | 0.191932 | − | 0.981408i | \(-0.438525\pi\) |
−0.558244 | + | 0.829677i | \(0.688525\pi\) | |||||||
\(420\) | −394.632 | − | 317.271i | −0.939600 | − | 0.755406i | ||||
\(421\) | −240.175 | + | 99.4838i | −0.570487 | + | 0.236304i | −0.649231 | − | 0.760591i | \(-0.724909\pi\) |
0.0787437 | + | 0.996895i | \(0.474909\pi\) | |||||||
\(422\) | 393.884 | + | 138.701i | 0.933373 | + | 0.328675i | ||||
\(423\) | −463.364 | − | 463.364i | −1.09542 | − | 1.09542i | ||||
\(424\) | −79.2174 | + | 49.1224i | −0.186834 | + | 0.115855i | ||||
\(425\) | −50.7000 | − | 50.7000i | −0.119294 | − | 0.119294i | ||||
\(426\) | 452.168 | − | 216.652i | 1.06143 | − | 0.508573i | ||||
\(427\) | 753.562 | − | 312.136i | 1.76478 | − | 0.730997i | ||||
\(428\) | 155.598 | − | 85.1941i | 0.363547 | − | 0.199052i | ||||
\(429\) | −547.516 | − | 226.789i | −1.27626 | − | 0.528645i | ||||
\(430\) | 23.7381 | + | 21.2983i | 0.0552050 | + | 0.0495310i | ||||
\(431\) | −607.318 | −1.40909 | −0.704546 | − | 0.709659i | \(-0.748849\pi\) | ||||
−0.704546 | + | 0.709659i | \(0.748849\pi\) | |||||||
\(432\) | 180.347 | + | 258.484i | 0.417469 | + | 0.598344i | ||||
\(433\) | 233.380i | 0.538984i | 0.963003 | + | 0.269492i | \(0.0868557\pi\) | ||||
−0.963003 | + | 0.269492i | \(0.913144\pi\) | |||||||
\(434\) | −4.28817 | − | 3.84743i | −0.00988057 | − | 0.00886504i | ||||
\(435\) | 3.82637 | − | 9.23768i | 0.00879626 | − | 0.0212361i | ||||
\(436\) | −424.629 | − | 124.155i | −0.973919 | − | 0.284759i | ||||
\(437\) | 128.371 | + | 309.914i | 0.293754 | + | 0.709185i | ||||
\(438\) | −627.472 | + | 300.647i | −1.43258 | + | 0.686408i | ||||
\(439\) | −496.850 | + | 496.850i | −1.13178 | + | 1.13178i | −0.141896 | + | 0.989882i | \(0.545320\pi\) |
−0.989882 | + | 0.141896i | \(0.954680\pi\) | |||||||
\(440\) | 172.840 | + | 124.185i | 0.392819 | + | 0.282239i | ||||
\(441\) | −267.863 | + | 267.863i | −0.607399 | + | 0.607399i | ||||
\(442\) | 124.163 | + | 43.7223i | 0.280911 | + | 0.0989193i | ||||
\(443\) | 59.8483 | + | 144.487i | 0.135098 | + | 0.326155i | 0.976922 | − | 0.213597i | \(-0.0685180\pi\) |
−0.841824 | + | 0.539752i | \(0.818518\pi\) | |||||||
\(444\) | −638.843 | + | 69.4220i | −1.43884 | + | 0.156356i | ||||
\(445\) | 170.411 | − | 411.409i | 0.382947 | − | 0.924515i | ||||
\(446\) | 687.833 | − | 37.2632i | 1.54223 | − | 0.0835497i | ||||
\(447\) | − | 1333.43i | − | 2.98306i | ||||||
\(448\) | 505.454 | + | 250.847i | 1.12825 | + | 0.559926i | ||||
\(449\) | −15.4530 | −0.0344165 | −0.0172082 | − | 0.999852i | \(-0.505478\pi\) | ||||
−0.0172082 | + | 0.999852i | \(0.505478\pi\) | |||||||
\(450\) | 22.4017 | + | 413.509i | 0.0497816 | + | 0.918908i | ||||
\(451\) | −179.596 | − | 74.3911i | −0.398217 | − | 0.164947i | ||||
\(452\) | 53.4122 | + | 491.516i | 0.118169 | + | 1.08742i | ||||
\(453\) | 317.095 | − | 131.345i | 0.699989 | − | 0.289945i | ||||
\(454\) | 49.0833 | − | 139.387i | 0.108113 | − | 0.307020i | ||||
\(455\) | 274.025 | + | 274.025i | 0.602253 | + | 0.602253i | ||||
\(456\) | 1074.83 | + | 772.263i | 2.35709 | + | 1.69356i | ||||
\(457\) | −93.8365 | − | 93.8365i | −0.205332 | − | 0.205332i | 0.596948 | − | 0.802280i | \(-0.296380\pi\) |
−0.802280 | + | 0.596948i | \(0.796380\pi\) | |||||||
\(458\) | 39.1188 | + | 81.6438i | 0.0854122 | + | 0.178261i | ||||
\(459\) | −83.0778 | + | 34.4120i | −0.180997 | + | 0.0749716i | ||||
\(460\) | −32.6796 | + | 111.769i | −0.0710426 | + | 0.242977i | ||||
\(461\) | −574.348 | − | 237.903i | −1.24588 | − | 0.516058i | −0.340329 | − | 0.940306i | \(-0.610538\pi\) |
−0.905546 | + | 0.424248i | \(0.860538\pi\) | |||||||
\(462\) | 484.024 | − | 539.472i | 1.04767 | − | 1.16769i | ||||
\(463\) | 568.089 | 1.22697 | 0.613487 | − | 0.789705i | \(-0.289766\pi\) | ||||
0.613487 | + | 0.789705i | \(0.289766\pi\) | |||||||
\(464\) | −1.95330 | + | 10.9700i | −0.00420971 | + | 0.0236423i | ||||
\(465\) | − | 4.69085i | − | 0.0100879i | ||||||
\(466\) | 383.525 | − | 427.460i | 0.823016 | − | 0.917296i | ||||
\(467\) | −156.459 | + | 377.726i | −0.335030 | + | 0.808835i | 0.663147 | + | 0.748489i | \(0.269220\pi\) |
−0.998178 | + | 0.0603459i | \(0.980780\pi\) | |||||||
\(468\) | −365.126 | − | 666.864i | −0.780184 | − | 1.42492i | ||||
\(469\) | 150.957 | + | 364.442i | 0.321869 | + | 0.777061i | ||||
\(470\) | −130.958 | − | 273.319i | −0.278635 | − | 0.581530i | ||||
\(471\) | 342.405 | − | 342.405i | 0.726974 | − | 0.726974i | ||||
\(472\) | −233.217 | + | 144.617i | −0.494103 | + | 0.306391i | ||||
\(473\) | −32.2793 | + | 32.2793i | −0.0682437 | + | 0.0682437i | ||||
\(474\) | 84.1810 | − | 239.057i | 0.177597 | − | 0.504341i | ||||
\(475\) | 211.136 | + | 509.727i | 0.444497 | + | 1.07311i | ||||
\(476\) | −100.873 | + | 125.470i | −0.211919 | + | 0.263592i | ||||
\(477\) | −58.7783 | + | 141.903i | −0.123225 | + | 0.297492i | ||||
\(478\) | −9.48520 | − | 175.085i | −0.0198435 | − | 0.366287i | ||||
\(479\) | 327.880i | 0.684509i | 0.939607 | + | 0.342254i | \(0.111190\pi\) | ||||
−0.939607 | + | 0.342254i | \(0.888810\pi\) | |||||||
\(480\) | 122.818 | + | 442.724i | 0.255871 | + | 0.922342i | ||||
\(481\) | 491.806 | 1.02247 | ||||||||
\(482\) | 30.9056 | − | 1.67430i | 0.0641194 | − | 0.00347365i | ||||
\(483\) | 366.378 | + | 151.759i | 0.758547 | + | 0.314200i | ||||
\(484\) | 112.385 | − | 139.789i | 0.232201 | − | 0.288820i | ||||
\(485\) | −219.616 | + | 90.9680i | −0.452817 | + | 0.187563i | ||||
\(486\) | −564.250 | − | 198.693i | −1.16101 | − | 0.408834i | ||||
\(487\) | −147.493 | − | 147.493i | −0.302861 | − | 0.302861i | 0.539271 | − | 0.842132i | \(-0.318700\pi\) |
−0.842132 | + | 0.539271i | \(0.818700\pi\) | |||||||
\(488\) | −720.540 | − | 168.963i | −1.47652 | − | 0.346236i | ||||
\(489\) | −17.9324 | − | 17.9324i | −0.0366716 | − | 0.0366716i | ||||
\(490\) | −158.001 | + | 75.7047i | −0.322451 | + | 0.154499i | ||||
\(491\) | 598.802 | − | 248.032i | 1.21956 | − | 0.505157i | 0.322288 | − | 0.946642i | \(-0.395548\pi\) |
0.897269 | + | 0.441485i | \(0.145548\pi\) | |||||||
\(492\) | −201.537 | − | 368.086i | −0.409629 | − | 0.748143i | ||||
\(493\) | −2.93704 | − | 1.21656i | −0.00595748 | − | 0.00246767i | ||||
\(494\) | −753.938 | − | 676.447i | −1.52619 | − | 1.36933i | ||||
\(495\) | 350.700 | 0.708485 | ||||||||
\(496\) | 1.12285 | + | 5.10542i | 0.00226382 | + | 0.0102932i | ||||
\(497\) | − | 469.304i | − | 0.944274i | ||||||
\(498\) | −194.783 | − | 174.763i | −0.391131 | − | 0.350930i | ||||
\(499\) | 58.1446 | − | 140.373i | 0.116522 | − | 0.281309i | −0.854849 | − | 0.518877i | \(-0.826350\pi\) |
0.971371 | + | 0.237568i | \(0.0763502\pi\) | |||||||
\(500\) | −139.299 | + | 476.425i | −0.278598 | + | 0.952849i | ||||
\(501\) | −420.606 | − | 1015.43i | −0.839533 | − | 2.02681i | ||||
\(502\) | 452.242 | − | 216.688i | 0.900881 | − | 0.431648i | ||||
\(503\) | −256.204 | + | 256.204i | −0.509351 | + | 0.509351i | −0.914327 | − | 0.404976i | \(-0.867280\pi\) |
0.404976 | + | 0.914327i | \(0.367280\pi\) | |||||||
\(504\) | 917.592 | − | 150.308i | 1.82062 | − | 0.298231i | ||||
\(505\) | −242.799 | + | 242.799i | −0.480789 | + | 0.480789i | ||||
\(506\) | −157.219 | − | 55.3626i | −0.310709 | − | 0.109412i | ||||
\(507\) | 70.0921 | + | 169.217i | 0.138249 | + | 0.333762i | ||||
\(508\) | −57.5655 | − | 529.735i | −0.113318 | − | 1.04279i | ||||
\(509\) | −229.271 | + | 553.510i | −0.450435 | + | 1.08745i | 0.521722 | + | 0.853115i | \(0.325290\pi\) |
−0.972157 | + | 0.234331i | \(0.924710\pi\) | |||||||
\(510\) | −130.890 | + | 7.09092i | −0.256647 | + | 0.0139038i | ||||
\(511\) | 651.251i | 1.27446i | ||||||||
\(512\) | −239.648 | − | 452.452i | −0.468062 | − | 0.883696i | ||||
\(513\) | 691.941 | 1.34881 | ||||||||
\(514\) | 14.1884 | + | 261.901i | 0.0276039 | + | 0.509534i | ||||
\(515\) | 305.324 | + | 126.469i | 0.592861 | + | 0.245571i | ||||
\(516\) | −97.9702 | + | 10.6463i | −0.189865 | + | 0.0206323i | ||||
\(517\) | 400.789 | − | 166.012i | 0.775221 | − | 0.321107i | ||||
\(518\) | −199.778 | + | 567.331i | −0.385672 | + | 1.09523i | ||||
\(519\) | −417.285 | − | 417.285i | −0.804017 | − | 0.804017i | ||||
\(520\) | −56.8417 | − | 347.003i | −0.109311 | − | 0.667314i | ||||
\(521\) | 80.7376 | + | 80.7376i | 0.154967 | + | 0.154967i | 0.780332 | − | 0.625365i | \(-0.215050\pi\) |
−0.625365 | + | 0.780332i | \(0.715050\pi\) | |||||||
\(522\) | 7.93373 | + | 16.5583i | 0.0151987 | + | 0.0317208i | ||||
\(523\) | 123.197 | − | 51.0300i | 0.235559 | − | 0.0975717i | −0.261781 | − | 0.965127i | \(-0.584310\pi\) |
0.497341 | + | 0.867555i | \(0.334310\pi\) | |||||||
\(524\) | −947.707 | − | 277.095i | −1.80860 | − | 0.528807i | ||||
\(525\) | 602.595 | + | 249.603i | 1.14780 | + | 0.475435i | ||||
\(526\) | −531.436 | + | 592.315i | −1.01034 | + | 1.12607i | ||||
\(527\) | −1.49141 | −0.00283001 | ||||||||
\(528\) | −642.286 | + | 141.261i | −1.21645 | + | 0.267539i | ||||
\(529\) | 437.800i | 0.827599i | ||||||||
\(530\) | −47.4403 | + | 52.8748i | −0.0895100 | + | 0.0997639i | ||||
\(531\) | −173.044 | + | 417.765i | −0.325883 | + | 0.786751i | ||||
\(532\) | 1086.59 | − | 594.936i | 2.04246 | − | 1.11830i | ||||
\(533\) | 122.907 | + | 296.723i | 0.230594 | + | 0.556704i | ||||
\(534\) | 594.567 | + | 1240.90i | 1.11342 | + | 2.32379i | ||||
\(535\) | 95.5966 | − | 95.5966i | 0.178685 | − | 0.178685i | ||||
\(536\) | 81.7149 | − | 348.471i | 0.152453 | − | 0.650133i | ||||
\(537\) | −390.198 | + | 390.198i | −0.726626 | + | 0.726626i | ||||
\(538\) | 95.8389 | − | 272.164i | 0.178139 | − | 0.505881i | ||||
\(539\) | −95.9689 | − | 231.689i | −0.178050 | − | 0.429850i | ||||
\(540\) | 187.204 | + | 150.506i | 0.346674 | + | 0.278714i | ||||
\(541\) | 184.993 | − | 446.613i | 0.341947 | − | 0.825532i | −0.655572 | − | 0.755132i | \(-0.727573\pi\) |
0.997519 | − | 0.0703996i | \(-0.0224275\pi\) | |||||||
\(542\) | 39.8870 | + | 736.266i | 0.0735923 | + | 1.35842i | ||||
\(543\) | 989.085i | 1.82152i | ||||||||
\(544\) | 140.760 | − | 39.0489i | 0.258750 | − | 0.0717810i | ||||
\(545\) | −337.163 | −0.618648 | ||||||||
\(546\) | −1195.71 | + | 64.7773i | −2.18995 | + | 0.118640i | ||||
\(547\) | −570.529 | − | 236.321i | −1.04302 | − | 0.432031i | −0.205622 | − | 0.978632i | \(-0.565922\pi\) |
−0.837394 | + | 0.546600i | \(0.815922\pi\) | |||||||
\(548\) | 492.968 | + | 396.330i | 0.899577 | + | 0.723230i | ||||
\(549\) | −1126.69 | + | 466.691i | −2.05226 | + | 0.850074i | ||||
\(550\) | −258.584 | − | 91.0569i | −0.470152 | − | 0.165558i | ||||
\(551\) | 17.2973 | + | 17.2973i | 0.0313926 | + | 0.0313926i | ||||
\(552\) | −189.628 | − | 305.804i | −0.343528 | − | 0.553992i | ||||
\(553\) | −167.744 | − | 167.744i | −0.303335 | − | 0.303335i | ||||
\(554\) | 101.805 | − | 48.7787i | 0.183763 | − | 0.0880482i | ||||
\(555\) | −452.456 | + | 187.413i | −0.815236 | + | 0.337682i | ||||
\(556\) | −120.669 | + | 66.0693i | −0.217030 | + | 0.118830i | ||||
\(557\) | 340.362 | + | 140.983i | 0.611063 | + | 0.253111i | 0.666683 | − | 0.745341i | \(-0.267714\pi\) |
−0.0556199 | + | 0.998452i | \(0.517714\pi\) | |||||||
\(558\) | 6.41147 | + | 5.75249i | 0.0114901 | + | 0.0103091i | ||||
\(559\) | 75.4212 | 0.134922 | ||||||||
\(560\) | 423.381 | + | 75.3867i | 0.756038 | + | 0.134619i | ||||
\(561\) | − | 187.627i | − | 0.334451i | ||||||
\(562\) | −179.075 | − | 160.669i | −0.318638 | − | 0.285888i | ||||
\(563\) | 241.885 | − | 583.963i | 0.429637 | − | 1.03723i | −0.549766 | − | 0.835319i | \(-0.685283\pi\) |
0.979403 | − | 0.201916i | \(-0.0647168\pi\) | |||||||
\(564\) | 898.861 | + | 262.813i | 1.59373 | + | 0.465980i | ||||
\(565\) | 144.193 | + | 348.113i | 0.255209 | + | 0.616128i | ||||
\(566\) | 127.702 | − | 61.1873i | 0.225623 | − | 0.108105i | ||||
\(567\) | −161.249 | + | 161.249i | −0.284390 | + | 0.284390i | ||||
\(568\) | −248.470 | + | 345.819i | −0.437447 | + | 0.608836i | ||||
\(569\) | 88.6373 | − | 88.6373i | 0.155777 | − | 0.155777i | −0.624915 | − | 0.780693i | \(-0.714866\pi\) |
0.780693 | + | 0.624915i | \(0.214866\pi\) | |||||||
\(570\) | 951.390 | + | 335.019i | 1.66910 | + | 0.587753i | ||||
\(571\) | −160.453 | − | 387.367i | −0.281003 | − | 0.678401i | 0.718857 | − | 0.695158i | \(-0.244666\pi\) |
−0.999860 | + | 0.0167573i | \(0.994666\pi\) | |||||||
\(572\) | 500.365 | − | 54.3739i | 0.874764 | − | 0.0950592i | ||||
\(573\) | 609.413 | − | 1471.25i | 1.06355 | − | 2.56763i | ||||
\(574\) | −392.217 | + | 21.2482i | −0.683304 | + | 0.0370178i | ||||
\(575\) | − | 150.000i | − | 0.260869i | ||||||
\(576\) | −755.731 | − | 375.054i | −1.31203 | − | 0.651136i | ||||
\(577\) | −501.285 | −0.868778 | −0.434389 | − | 0.900725i | \(-0.643036\pi\) | ||||
−0.434389 | + | 0.900725i | \(0.643036\pi\) | |||||||
\(578\) | −29.0126 | − | 535.538i | −0.0501949 | − | 0.926537i | ||||
\(579\) | 1020.42 | + | 422.670i | 1.76238 | + | 0.730000i | ||||
\(580\) | 0.917395 | + | 8.44215i | 0.00158172 | + | 0.0145554i | ||||
\(581\) | −226.299 | + | 93.7360i | −0.389498 | + | 0.161336i | ||||
\(582\) | 243.969 | − | 692.824i | 0.419191 | − | 1.19042i | ||||
\(583\) | −71.8995 | − | 71.8995i | −0.123327 | − | 0.123327i | ||||
\(584\) | 344.800 | − | 479.891i | 0.590412 | − | 0.821731i | ||||
\(585\) | −409.709 | − | 409.709i | −0.700358 | − | 0.700358i | ||||
\(586\) | 300.296 | + | 626.739i | 0.512451 | + | 1.06952i | ||||
\(587\) | −805.600 | + | 333.691i | −1.37240 | + | 0.568468i | −0.942439 | − | 0.334378i | \(-0.891474\pi\) |
−0.429964 | + | 0.902846i | \(0.641474\pi\) | |||||||
\(588\) | 151.928 | − | 519.616i | 0.258380 | − | 0.883701i | ||||
\(589\) | 10.6026 | + | 4.39175i | 0.0180010 | + | 0.00745628i | ||||
\(590\) | −139.665 | + | 155.664i | −0.236720 | + | 0.263837i | ||||
\(591\) | 1208.23 | 2.04438 | ||||||||
\(592\) | 447.582 | − | 312.282i | 0.756050 | − | 0.527503i | ||||
\(593\) | − | 1035.33i | − | 1.74591i | −0.487798 | − | 0.872957i | \(-0.662200\pi\) | ||
0.487798 | − | 0.872957i | \(-0.337800\pi\) | |||||||
\(594\) | −229.610 | + | 255.913i | −0.386549 | + | 0.430830i | ||||
\(595\) | −46.9525 | + | 113.353i | −0.0789117 | + | 0.190510i | ||||
\(596\) | 543.869 | + | 993.319i | 0.912532 | + | 1.66664i | ||||
\(597\) | 99.9623 | + | 241.330i | 0.167441 | + | 0.404238i | ||||
\(598\) | 118.995 | + | 248.351i | 0.198988 | + | 0.415302i | ||||
\(599\) | 361.938 | − | 361.938i | 0.604237 | − | 0.604237i | −0.337197 | − | 0.941434i | \(-0.609479\pi\) |
0.941434 | + | 0.337197i | \(0.109479\pi\) | |||||||
\(600\) | −311.887 | − | 502.967i | −0.519812 | − | 0.838278i | ||||
\(601\) | −221.839 | + | 221.839i | −0.369116 | + | 0.369116i | −0.867155 | − | 0.498039i | \(-0.834054\pi\) |
0.498039 | + | 0.867155i | \(0.334054\pi\) | |||||||
\(602\) | −30.6371 | + | 87.0034i | −0.0508922 | + | 0.144524i | ||||
\(603\) | −225.703 | − | 544.896i | −0.374301 | − | 0.903642i | ||||
\(604\) | −182.643 | + | 227.178i | −0.302390 | + | 0.376122i | ||||
\(605\) | 52.3109 | − | 126.290i | 0.0864642 | − | 0.208743i | ||||
\(606\) | −57.3957 | − | 1059.45i | −0.0947123 | − | 1.74828i | ||||
\(607\) | 465.834i | 0.767437i | 0.923450 | + | 0.383719i | \(0.125357\pi\) | ||||
−0.923450 | + | 0.383719i | \(0.874643\pi\) | |||||||
\(608\) | −1115.67 | − | 136.892i | −1.83498 | − | 0.225152i | ||||
\(609\) | 28.9189 | 0.0474859 | ||||||||
\(610\) | −563.201 | + | 30.5113i | −0.923280 | + | 0.0500185i | ||||
\(611\) | −662.172 | − | 274.281i | −1.08375 | − | 0.448905i | ||||
\(612\) | 150.821 | − | 187.596i | 0.246440 | − | 0.306530i | ||||
\(613\) | 292.579 | − | 121.190i | 0.477290 | − | 0.197700i | −0.131051 | − | 0.991376i | \(-0.541835\pi\) |
0.608341 | + | 0.793676i | \(0.291835\pi\) | |||||||
\(614\) | 456.956 | + | 160.911i | 0.744227 | + | 0.262070i | ||||
\(615\) | −226.146 | − | 226.146i | −0.367717 | − | 0.367717i | ||||
\(616\) | −140.531 | + | 599.292i | −0.228135 | + | 0.972877i | ||||
\(617\) | −226.657 | − | 226.657i | −0.367354 | − | 0.367354i | 0.499158 | − | 0.866511i | \(-0.333643\pi\) |
−0.866511 | + | 0.499158i | \(0.833643\pi\) | |||||||
\(618\) | −920.926 | + | 441.253i | −1.49017 | + | 0.714001i | ||||
\(619\) | 756.530 | − | 313.365i | 1.22218 | − | 0.506244i | 0.324078 | − | 0.946030i | \(-0.394946\pi\) |
0.898102 | + | 0.439787i | \(0.144946\pi\) | |||||||
\(620\) | 1.91327 | + | 3.49438i | 0.00308592 | + | 0.00563610i | ||||
\(621\) | −173.801 | − | 71.9908i | −0.279873 | − | 0.115927i | ||||
\(622\) | 93.8459 | + | 84.2003i | 0.150878 | + | 0.135370i | ||||
\(623\) | 1287.93 | 2.06730 | ||||||||
\(624\) | 915.386 | + | 585.328i | 1.46697 | + | 0.938026i | ||||
\(625\) | − | 14.3854i | − | 0.0230167i | ||||||
\(626\) | 58.8007 | + | 52.7570i | 0.0939308 | + | 0.0842764i | ||||
\(627\) | −552.503 | + | 1333.86i | −0.881185 | + | 2.12737i | ||||
\(628\) | −115.412 | + | 394.727i | −0.183777 | + | 0.628546i | ||||
\(629\) | 59.5864 | + | 143.854i | 0.0947320 | + | 0.228703i | ||||
\(630\) | 639.057 | − | 306.198i | 1.01438 | − | 0.486028i | ||||
\(631\) | 338.810 | − | 338.810i | 0.536941 | − | 0.536941i | −0.385688 | − | 0.922629i | \(-0.626036\pi\) |
0.922629 | + | 0.385688i | \(0.126036\pi\) | |||||||
\(632\) | 34.7956 | + | 212.418i | 0.0550563 | + | 0.336104i | ||||
\(633\) | −695.363 | + | 695.363i | −1.09852 | + | 1.09852i | ||||
\(634\) | 620.383 | + | 218.460i | 0.978522 | + | 0.344574i | ||||
\(635\) | −155.405 | − | 375.181i | −0.244733 | − | 0.590837i | ||||
\(636\) | −23.7137 | − | 218.221i | −0.0372857 | − | 0.343114i | ||||
\(637\) | −158.557 | + | 382.790i | −0.248912 | + | 0.600927i | ||||
\(638\) | −12.1372 | + | 0.657531i | −0.0190239 | + | 0.00103061i | ||||
\(639\) | 701.682i | 1.09809i | ||||||||
\(640\) | −272.067 | − | 279.707i | −0.425104 | − | 0.437042i | ||||
\(641\) | 729.839 | 1.13859 | 0.569297 | − | 0.822132i | \(-0.307215\pi\) | ||||
0.569297 | + | 0.822132i | \(0.307215\pi\) | |||||||
\(642\) | 22.5983 | + | 417.137i | 0.0351998 | + | 0.649746i | ||||
\(643\) | −370.578 | − | 153.498i | −0.576327 | − | 0.238722i | 0.0754293 | − | 0.997151i | \(-0.475967\pi\) |
−0.651756 | + | 0.758429i | \(0.725967\pi\) | |||||||
\(644\) | −334.826 | + | 36.3850i | −0.519917 | + | 0.0564985i | ||||
\(645\) | −69.3867 | + | 28.7409i | −0.107576 | + | 0.0445595i | ||||
\(646\) | 106.516 | − | 302.486i | 0.164886 | − | 0.468244i | ||||
\(647\) | −179.567 | − | 179.567i | −0.277538 | − | 0.277538i | 0.554587 | − | 0.832126i | \(-0.312876\pi\) |
−0.832126 | + | 0.554587i | \(0.812876\pi\) | |||||||
\(648\) | 204.193 | − | 33.4484i | 0.315113 | − | 0.0516179i | ||||
\(649\) | −211.673 | − | 211.673i | −0.326152 | − | 0.326152i | ||||
\(650\) | 195.715 | + | 408.471i | 0.301100 | + | 0.628417i | ||||
\(651\) | 12.5343 | − | 5.19189i | 0.0192540 | − | 0.00797525i | ||||
\(652\) | 20.6726 | + | 6.04436i | 0.0317065 | + | 0.00927049i | ||||
\(653\) | −964.894 | − | 399.672i | −1.47763 | − | 0.612056i | −0.509048 | − | 0.860738i | \(-0.670002\pi\) |
−0.968585 | + | 0.248683i | \(0.920002\pi\) | |||||||
\(654\) | 695.756 | − | 775.458i | 1.06385 | − | 1.18572i | ||||
\(655\) | −752.497 | −1.14885 | ||||||||
\(656\) | 300.265 | + | 191.999i | 0.457721 | + | 0.292682i | ||||
\(657\) | − | 973.720i | − | 1.48207i | ||||||
\(658\) | 585.385 | − | 652.444i | 0.889642 | − | 0.991556i | ||||
\(659\) | 233.939 | − | 564.778i | 0.354990 | − | 0.857023i | −0.640998 | − | 0.767542i | \(-0.721479\pi\) |
0.995989 | − | 0.0894804i | \(-0.0285206\pi\) | |||||||
\(660\) | −439.610 | + | 240.699i | −0.666076 | + | 0.364695i | ||||
\(661\) | 281.181 | + | 678.831i | 0.425387 | + | 1.02698i | 0.980732 | + | 0.195356i | \(0.0625862\pi\) |
−0.555345 | + | 0.831620i | \(0.687414\pi\) | |||||||
\(662\) | 158.565 | + | 330.937i | 0.239525 | + | 0.499905i | ||||
\(663\) | −219.197 | + | 219.197i | −0.330614 | + | 0.330614i | ||||
\(664\) | 216.382 | + | 50.7405i | 0.325876 | + | 0.0764165i | ||||
\(665\) | 667.580 | − | 667.580i | 1.00388 | − | 1.00388i | ||||
\(666\) | 298.699 | − | 848.247i | 0.448497 | − | 1.27364i | ||||
\(667\) | −2.54508 | − | 6.14437i | −0.00381571 | − | 0.00921195i | ||||
\(668\) | 727.492 | + | 584.879i | 1.08906 | + | 0.875567i | ||||
\(669\) | −620.775 | + | 1498.68i | −0.927915 | + | 2.24018i | ||||
\(670\) | −14.7560 | − | 272.378i | −0.0220239 | − | 0.406534i | ||||
\(671\) | − | 807.333i | − | 1.20318i | ||||||
\(672\) | −1047.06 | + | 818.192i | −1.55812 | + | 1.21755i | ||||
\(673\) | 705.345 | 1.04806 | 0.524031 | − | 0.851699i | \(-0.324428\pi\) | ||||
0.524031 | + | 0.851699i | \(0.324428\pi\) | |||||||
\(674\) | −134.426 | + | 7.28250i | −0.199445 | + | 0.0108049i | ||||
\(675\) | −285.857 | − | 118.406i | −0.423492 | − | 0.175416i | ||||
\(676\) | −121.233 | − | 97.4673i | −0.179339 | − | 0.144182i | ||||
\(677\) | −10.4550 | + | 4.33061i | −0.0154432 | + | 0.00639676i | −0.390392 | − | 0.920649i | \(-0.627660\pi\) |
0.374948 | + | 0.927046i | \(0.377660\pi\) | |||||||
\(678\) | −1098.19 | − | 386.714i | −1.61975 | − | 0.570375i | ||||
\(679\) | −486.147 | − | 486.147i | −0.715976 | − | 0.715976i | ||||
\(680\) | 94.6123 | − | 58.6687i | 0.139136 | − | 0.0862775i | ||||
\(681\) | 246.074 | + | 246.074i | 0.361342 | + | 0.361342i | ||||
\(682\) | −5.14259 | + | 2.46402i | −0.00754046 | + | 0.00361294i | ||||
\(683\) | −307.101 | + | 127.205i | −0.449635 | + | 0.186245i | −0.595998 | − | 0.802986i | \(-0.703243\pi\) |
0.146363 | + | 0.989231i | \(0.453243\pi\) | |||||||
\(684\) | −1624.61 | + | 889.521i | −2.37517 | + | 1.30047i | ||||
\(685\) | 445.364 | + | 184.476i | 0.650166 | + | 0.269308i | ||||
\(686\) | 265.964 | + | 238.628i | 0.387703 | + | 0.347854i | ||||
\(687\) | −213.194 | −0.310327 | ||||||||
\(688\) | 68.6392 | − | 47.8901i | 0.0997662 | − | 0.0696077i | ||||
\(689\) | 167.995i | 0.243824i | ||||||||
\(690\) | −204.113 | − | 183.134i | −0.295816 | − | 0.265412i | ||||
\(691\) | −243.176 | + | 587.078i | −0.351919 | + | 0.849607i | 0.644465 | + | 0.764634i | \(0.277080\pi\) |
−0.996383 | + | 0.0849727i | \(0.972920\pi\) | |||||||
\(692\) | 481.049 | + | 140.651i | 0.695158 | + | 0.203253i | ||||
\(693\) | 388.159 | + | 937.099i | 0.560114 | + | 1.35224i | ||||
\(694\) | −505.047 | + | 241.988i | −0.727734 | + | 0.348686i | ||||
\(695\) | −74.1366 | + | 74.1366i | −0.106671 | + | 0.106671i | ||||
\(696\) | −21.3096 | − | 15.3109i | −0.0306173 | − | 0.0219985i | ||||
\(697\) | −71.9010 | + | 71.9010i | −0.103158 | + | 0.103158i | ||||
\(698\) | −816.125 | − | 287.388i | −1.16923 | − | 0.411730i | ||||
\(699\) | 517.546 | + | 1249.47i | 0.740410 | + | 1.78751i | ||||
\(700\) | −550.701 | + | 59.8438i | −0.786716 | + | 0.0854912i | ||||
\(701\) | 65.7383 | − | 158.706i | 0.0937779 | − | 0.226400i | −0.870029 | − | 0.493000i | \(-0.835900\pi\) |
0.963807 | + | 0.266600i | \(0.0859003\pi\) | |||||||
\(702\) | 567.217 | − | 30.7288i | 0.808002 | − | 0.0437733i | ||||
\(703\) | − | 1198.14i | − | 1.70432i | ||||||
\(704\) | 420.846 | − | 367.201i | 0.597792 | − | 0.521592i | ||||
\(705\) | 713.712 | 1.01236 | ||||||||
\(706\) | 62.1582 | + | 1147.37i | 0.0880428 | + | 1.62516i | ||||
\(707\) | −917.510 | − | 380.045i | −1.29775 | − | 0.537546i | ||||
\(708\) | −69.8133 | − | 642.444i | −0.0986064 | − | 0.907406i | ||||
\(709\) | −1029.00 | + | 426.228i | −1.45135 | + | 0.601167i | −0.962519 | − | 0.271214i | \(-0.912575\pi\) |
−0.488827 | + | 0.872381i | \(0.662575\pi\) | |||||||
\(710\) | −107.790 | + | 306.103i | −0.151817 | + | 0.431131i | ||||
\(711\) | 250.803 | + | 250.803i | 0.352747 | + | 0.352747i | ||||
\(712\) | −949.046 | − | 681.887i | −1.33293 | − | 0.957706i | ||||
\(713\) | −2.20623 | − | 2.20623i | −0.00309429 | − | 0.00309429i | ||||
\(714\) | −163.818 | − | 341.900i | −0.229437 | − | 0.478851i | ||||
\(715\) | 354.380 | − | 146.789i | 0.495637 | − | 0.205299i | ||||
\(716\) | 131.521 | − | 449.824i | 0.183689 | − | 0.628245i | ||||
\(717\) | 381.484 | + | 158.016i | 0.532056 | + | 0.220385i | ||||
\(718\) | 943.011 | − | 1051.04i | 1.31339 | − | 1.46384i | ||||
\(719\) | −439.735 | −0.611592 | −0.305796 | − | 0.952097i | \(-0.598923\pi\) | ||||
−0.305796 | + | 0.952097i | \(0.598923\pi\) | |||||||
\(720\) | −633.020 | − | 112.715i | −0.879195 | − | 0.156548i | ||||
\(721\) | 955.826i | 1.32570i | ||||||||
\(722\) | −1165.80 | + | 1299.34i | −1.61468 | + | 1.79965i | ||||
\(723\) | −27.8925 | + | 67.3385i | −0.0385789 | + | 0.0931377i | ||||
\(724\) | −403.421 | − | 736.805i | −0.557211 | − | 1.01769i | ||||
\(725\) | −4.18599 | − | 10.1059i | −0.00577378 | − | 0.0139391i | ||||
\(726\) | 182.513 | + | 380.919i | 0.251396 | + | 0.524681i | ||||
\(727\) | 137.308 | − | 137.308i | 0.188869 | − | 0.188869i | −0.606338 | − | 0.795207i | \(-0.707362\pi\) |
0.795207 | + | 0.606338i | \(0.207362\pi\) | |||||||
\(728\) | 864.307 | − | 535.953i | 1.18723 | − | 0.736199i | ||||
\(729\) | 831.529 | − | 831.529i | 1.14064 | − | 1.14064i | ||||
\(730\) | 149.580 | − | 424.777i | 0.204904 | − | 0.581886i | ||||
\(731\) | 9.13791 | + | 22.0609i | 0.0125006 | + | 0.0301790i | ||||
\(732\) | 1092.02 | − | 1358.30i | 1.49184 | − | 1.85560i | ||||
\(733\) | 57.7693 | − | 139.467i | 0.0788121 | − | 0.190269i | −0.879562 | − | 0.475784i | \(-0.842164\pi\) |
0.958374 | + | 0.285514i | \(0.0921645\pi\) | |||||||
\(734\) | −31.9775 | − | 590.267i | −0.0435661 | − | 0.804178i | ||||
\(735\) | − | 412.584i | − | 0.561339i | ||||||
\(736\) | 265.989 | + | 150.460i | 0.361399 | + | 0.204430i | ||||
\(737\) | 390.447 | 0.529778 | ||||||||
\(738\) | 586.424 | − | 31.7694i | 0.794613 | − | 0.0430479i | ||||
\(739\) | 536.590 | + | 222.263i | 0.726103 | + | 0.300762i | 0.714950 | − | 0.699176i | \(-0.246450\pi\) |
0.0111538 | + | 0.999938i | \(0.496450\pi\) | |||||||
\(740\) | 260.610 | − | 324.155i | 0.352176 | − | 0.438048i | ||||
\(741\) | 2203.76 | − | 912.828i | 2.97404 | − | 1.23189i | ||||
\(742\) | −193.793 | − | 68.2418i | −0.261177 | − | 0.0919700i | ||||
\(743\) | 907.324 | + | 907.324i | 1.22116 | + | 1.22116i | 0.967219 | + | 0.253944i | \(0.0817279\pi\) |
0.253944 | + | 0.967219i | \(0.418272\pi\) | |||||||
\(744\) | −11.9851 | − | 2.81044i | −0.0161090 | − | 0.00377747i | ||||
\(745\) | 610.278 | + | 610.278i | 0.819165 | + | 0.819165i | ||||
\(746\) | −630.987 | + | 302.331i | −0.845827 | + | 0.405270i | ||||
\(747\) | 338.351 | − | 140.150i | 0.452947 | − | 0.187617i | ||||
\(748\) | 76.5279 | + | 139.770i | 0.102310 | + | 0.186858i | ||||
\(749\) | 361.249 | + | 149.634i | 0.482309 | + | 0.199779i | ||||
\(750\) | −870.048 | − | 780.624i | −1.16006 | − | 1.04083i | ||||
\(751\) | −662.862 | −0.882639 | −0.441320 | − | 0.897350i | \(-0.645489\pi\) | ||||
−0.441320 | + | 0.897350i | \(0.645489\pi\) | |||||||
\(752\) | −776.788 | + | 170.842i | −1.03296 | + | 0.227184i | ||||
\(753\) | 1180.93i | 1.56830i | ||||||||
\(754\) | 14.9476 | + | 13.4113i | 0.0198244 | + | 0.0177868i | ||||
\(755\) | −85.0132 | + | 205.240i | −0.112600 | + | 0.271841i | ||||
\(756\) | −194.964 | + | 666.806i | −0.257888 | + | 0.882018i | ||||
\(757\) | 76.1190 | + | 183.767i | 0.100553 | + | 0.242757i | 0.966148 | − | 0.257988i | \(-0.0830594\pi\) |
−0.865595 | + | 0.500745i | \(0.833059\pi\) | |||||||
\(758\) | 804.266 | − | 385.356i | 1.06104 | − | 0.508385i | ||||
\(759\) | 277.554 | − | 277.554i | 0.365684 | − | 0.365684i | ||||
\(760\) | −845.370 | + | 138.478i | −1.11233 | + | 0.182208i | ||||
\(761\) | 435.811 | − | 435.811i | 0.572683 | − | 0.572683i | −0.360195 | − | 0.932877i | \(-0.617290\pi\) |
0.932877 | + | 0.360195i | \(0.117290\pi\) | |||||||
\(762\) | 1183.59 | + | 416.784i | 1.55326 | + | 0.546961i | ||||
\(763\) | −373.176 | − | 900.926i | −0.489090 | − | 1.18077i | ||||
\(764\) | 146.110 | + | 1344.55i | 0.191244 | + | 1.75989i | ||||
\(765\) | 70.2012 | − | 169.481i | 0.0917662 | − | 0.221543i | ||||
\(766\) | −509.057 | + | 27.5780i | −0.664565 | + | 0.0360026i | ||||
\(767\) | 494.578i | 0.644821i | ||||||||
\(768\) | 1204.74 | − | 48.5477i | 1.56867 | − | 0.0632131i | ||||
\(769\) | −1422.48 | −1.84978 | −0.924889 | − | 0.380237i | \(-0.875843\pi\) | ||||
−0.924889 | + | 0.380237i | \(0.875843\pi\) | |||||||
\(770\) | 25.3770 | + | 468.429i | 0.0329572 | + | 0.608350i | ||||
\(771\) | −570.642 | − | 236.368i | −0.740132 | − | 0.306573i | ||||
\(772\) | −932.540 | + | 101.338i | −1.20795 | + | 0.131266i | ||||
\(773\) | −0.439715 | + | 0.182136i | −0.000568842 | + | 0.000235622i | −0.382968 | − | 0.923762i | \(-0.625098\pi\) |
0.382399 | + | 0.923997i | \(0.375098\pi\) | |||||||
\(774\) | 45.8072 | − | 130.083i | 0.0591824 | − | 0.168067i | ||||
\(775\) | −3.62867 | − | 3.62867i | −0.00468215 | − | 0.00468215i | ||||
\(776\) | 100.843 | + | 615.618i | 0.129952 | + | 0.793322i | ||||
\(777\) | −1001.57 | − | 1001.57i | −1.28902 | − | 1.28902i | ||||
\(778\) | −642.854 | − | 1341.68i | −0.826290 | − | 1.72453i | ||||
\(779\) | 722.878 | − | 299.426i | 0.927956 | − | 0.384372i | ||||
\(780\) | 794.778 | + | 232.381i | 1.01895 | + | 0.297924i | ||||
\(781\) | −429.160 | − | 177.764i | −0.549500 | − | 0.227610i | ||||
\(782\) | −58.2259 | + | 64.8960i | −0.0744576 | + | 0.0829872i | ||||
\(783\) | −13.7184 | −0.0175204 | ||||||||
\(784\) | 98.7608 | + | 449.048i | 0.125970 | + | 0.572765i | ||||
\(785\) | 313.420i | 0.399262i | ||||||||
\(786\) | 1552.82 | − | 1730.71i | 1.97560 | − | 2.20192i | ||||
\(787\) | 23.0303 | − | 55.6002i | 0.0292635 | − | 0.0706482i | −0.908572 | − | 0.417728i | \(-0.862827\pi\) |
0.937836 | + | 0.347079i | \(0.112827\pi\) | |||||||
\(788\) | −900.055 | + | 492.805i | −1.14220 | + | 0.625386i | ||||
\(789\) | −717.144 | − | 1731.34i | −0.908928 | − | 2.19435i | ||||
\(790\) | 70.8832 | + | 147.938i | 0.0897255 | + | 0.187264i | ||||
\(791\) | −770.590 | + | 770.590i | −0.974197 | + | 0.974197i | ||||
\(792\) | 210.116 | − | 896.034i | 0.265298 | − | 1.13136i | ||||
\(793\) | −943.175 | + | 943.175i | −1.18938 | + | 1.18938i | ||||
\(794\) | −40.9110 | + | 116.179i | −0.0515252 | + | 0.146322i | ||||
\(795\) | −64.0181 | − | 154.553i | −0.0805259 | − | 0.194407i | ||||
\(796\) | −172.898 | − | 139.004i | −0.217208 | − | 0.174628i | ||||
\(797\) | 49.3444 | − | 119.128i | 0.0619127 | − | 0.149470i | −0.889895 | − | 0.456165i | \(-0.849223\pi\) |
0.951808 | + | 0.306694i | \(0.0992229\pi\) | |||||||
\(798\) | 157.811 | + | 2912.99i | 0.197758 | + | 3.65037i | ||||
\(799\) | − | 226.918i | − | 0.284003i | ||||||
\(800\) | 437.482 | + | 247.468i | 0.546853 | + | 0.309335i | ||||
\(801\) | −1925.65 | −2.40406 | ||||||||
\(802\) | 1405.96 | − | 76.1674i | 1.75307 | − | 0.0949718i | ||||
\(803\) | 595.542 | + | 246.682i | 0.741647 | + | 0.307200i | ||||
\(804\) | 656.906 | + | 528.130i | 0.817048 | + | 0.656878i | ||||
\(805\) | −237.138 | + | 98.2260i | −0.294582 | + | 0.122020i | ||||
\(806\) | 8.88651 | + | 3.12927i | 0.0110254 | + | 0.00388247i | ||||
\(807\) | 480.478 | + | 480.478i | 0.595388 | + | 0.595388i | ||||
\(808\) | 474.879 | + | 765.816i | 0.587721 | + | 0.947792i | ||||
\(809\) | 29.6470 | + | 29.6470i | 0.0366465 | + | 0.0366465i | 0.725193 | − | 0.688546i | \(-0.241751\pi\) |
−0.688546 | + | 0.725193i | \(0.741751\pi\) | |||||||
\(810\) | 142.210 | − | 68.1387i | 0.175568 | − | 0.0841219i | ||||
\(811\) | −755.209 | + | 312.818i | −0.931207 | + | 0.385719i | −0.796136 | − | 0.605117i | \(-0.793126\pi\) |
−0.135071 | + | 0.990836i | \(0.543126\pi\) | |||||||
\(812\) | −21.5427 | + | 11.7952i | −0.0265304 | + | 0.0145261i | ||||
\(813\) | −1604.21 | − | 664.486i | −1.97320 | − | 0.817326i | ||||
\(814\) | 443.129 | + | 397.584i | 0.544385 | + | 0.488432i | ||||
\(815\) | 16.4144 | 0.0201404 | ||||||||
\(816\) | −60.3031 | + | 338.670i | −0.0739009 | + | 0.415037i | ||||
\(817\) | − | 183.741i | − | 0.224897i | ||||||
\(818\) | −1112.61 | − | 998.251i | −1.36015 | − | 1.22036i | ||||
\(819\) | 641.305 | − | 1548.25i | 0.783034 | − | 1.89041i | ||||
\(820\) | 260.703 | + | 76.2254i | 0.317930 | + | 0.0929578i | ||||
\(821\) | 120.712 | + | 291.425i | 0.147031 | + | 0.354964i | 0.980187 | − | 0.198074i | \(-0.0634685\pi\) |
−0.833156 | + | 0.553038i | \(0.813469\pi\) | |||||||
\(822\) | −1343.32 | + | 643.638i | −1.63421 | + | 0.783015i | ||||
\(823\) | 173.105 | − | 173.105i | 0.210334 | − | 0.210334i | −0.594076 | − | 0.804409i | \(-0.702482\pi\) |
0.804409 | + | 0.594076i | \(0.202482\pi\) | |||||||
\(824\) | 506.056 | − | 704.326i | 0.614146 | − | 0.854764i | ||||
\(825\) | 456.504 | − | 456.504i | 0.553338 | − | 0.553338i | ||||
\(826\) | −570.529 | − | 200.904i | −0.690713 | − | 0.243225i | ||||
\(827\) | −59.9551 | − | 144.744i | −0.0724971 | − | 0.175023i | 0.883477 | − | 0.468475i | \(-0.155196\pi\) |
−0.955974 | + | 0.293451i | \(0.905196\pi\) | |||||||
\(828\) | 500.617 | − | 54.4012i | 0.604610 | − | 0.0657020i | ||||
\(829\) | 259.829 | − | 627.283i | 0.313425 | − | 0.756674i | −0.686149 | − | 0.727461i | \(-0.740700\pi\) |
0.999573 | − | 0.0292124i | \(-0.00929993\pi\) | |||||||
\(830\) | 169.132 | − | 9.16269i | 0.203774 | − | 0.0110394i | ||||
\(831\) | 265.840i | 0.319904i | ||||||||
\(832\) | −920.644 | − | 62.6710i | −1.10654 | − | 0.0753257i | ||||
\(833\) | −131.178 | −0.157476 | ||||||||
\(834\) | −17.5253 | − | 323.496i | −0.0210135 | − | 0.387885i | ||||
\(835\) | 657.240 | + | 272.238i | 0.787114 | + | 0.326033i | ||||
\(836\) | −132.466 | − | 1218.99i | −0.158452 | − | 1.45812i | ||||
\(837\) | −5.94599 | + | 2.46291i | −0.00710394 | + | 0.00294255i | ||||
\(838\) | −110.359 | + | 313.398i | −0.131693 | + | 0.373983i | ||||
\(839\) | 182.343 | + | 182.343i | 0.217333 | + | 0.217333i | 0.807374 | − | 0.590040i | \(-0.200888\pi\) |
−0.590040 | + | 0.807374i | \(0.700888\pi\) | |||||||
\(840\) | −590.916 | + | 822.434i | −0.703472 | + | 0.979088i | ||||
\(841\) | 594.334 | + | 594.334i | 0.706699 | + | 0.706699i | ||||
\(842\) | 224.661 | + | 468.884i | 0.266818 | + | 0.556869i | ||||
\(843\) | 523.436 | − | 216.814i | 0.620920 | − | 0.257194i | ||||
\(844\) | 234.381 | − | 801.620i | 0.277703 | − | 0.949787i | ||||
\(845\) | −109.526 | − | 45.3671i | −0.129617 | − | 0.0536889i | ||||
\(846\) | −875.240 | + | 975.503i | −1.03456 | + | 1.15308i | ||||
\(847\) | 395.354 | 0.466770 | ||||||||
\(848\) | 106.671 | + | 152.888i | 0.125792 | + | 0.180293i | ||||
\(849\) | 333.466i | 0.392775i | ||||||||
\(850\) | −95.7663 | + | 106.737i | −0.112666 | + | 0.125573i | ||||
\(851\) | −124.657 | + | 300.947i | −0.146482 | + | 0.353640i | ||||
\(852\) | −481.590 | − | 879.573i | −0.565247 | − | 1.03236i | ||||
\(853\) | −300.757 | − | 726.092i | −0.352588 | − | 0.851222i | −0.996299 | − | 0.0859535i | \(-0.972606\pi\) |
0.643712 | − | 0.765268i | \(-0.277394\pi\) | |||||||
\(854\) | −704.886 | − | 1471.15i | −0.825393 | − | 1.72266i | ||||
\(855\) | −998.134 | + | 998.134i | −1.16741 | + | 1.16741i | ||||
\(856\) | −186.973 | − | 301.523i | −0.218426 | − | 0.352247i | ||||
\(857\) | −545.430 | + | 545.430i | −0.636441 | + | 0.636441i | −0.949676 | − | 0.313235i | \(-0.898587\pi\) |
0.313235 | + | 0.949676i | \(0.398587\pi\) | |||||||
\(858\) | −393.677 | + | 1117.97i | −0.458831 | + | 1.30299i | ||||
\(859\) | 230.652 | + | 556.843i | 0.268512 | + | 0.648246i | 0.999414 | − | 0.0342370i | \(-0.0109001\pi\) |
−0.730901 | + | 0.682483i | \(0.760900\pi\) | |||||||
\(860\) | 39.9660 | − | 49.7111i | 0.0464721 | − | 0.0578036i | ||||
\(861\) | 353.979 | − | 854.580i | 0.411125 | − | 0.992544i | ||||
\(862\) | 65.7063 | + | 1212.86i | 0.0762254 | + | 1.40703i | ||||
\(863\) | 980.846i | 1.13655i | 0.822837 | + | 0.568277i | \(0.192390\pi\) | ||||
−0.822837 | + | 0.568277i | \(0.807610\pi\) | |||||||
\(864\) | 496.700 | − | 388.131i | 0.574884 | − | 0.449226i | ||||
\(865\) | 381.962 | 0.441574 | ||||||||
\(866\) | 466.076 | − | 25.2496i | 0.538195 | − | 0.0291565i | ||||
\(867\) | 1166.86 | + | 483.328i | 1.34586 | + | 0.557472i | ||||
\(868\) | −7.21964 | + | 8.98004i | −0.00831756 | + | 0.0103457i | ||||
\(869\) | −216.933 | + | 89.8568i | −0.249636 | + | 0.103403i | ||||
\(870\) | −18.8623 | − | 6.64211i | −0.0216808 | − | 0.00763461i | ||||
\(871\) | −456.143 | − | 456.143i | −0.523701 | − | 0.523701i | ||||
\(872\) | −202.005 | + | 861.446i | −0.231657 | + | 0.987897i | ||||
\(873\) | 726.865 | + | 726.865i | 0.832606 | + | 0.832606i | ||||
\(874\) | 605.032 | − | 289.895i | 0.692256 | − | 0.331688i | ||||
\(875\) | −1010.82 | + | 418.696i | −1.15522 | + | 0.478509i | ||||
\(876\) | 668.300 | + | 1220.58i | 0.762899 | + | 1.39335i | ||||
\(877\) | 1395.56 | + | 578.059i | 1.59129 | + | 0.659132i | 0.990150 | − | 0.140014i | \(-0.0447146\pi\) |
0.601137 | + | 0.799146i | \(0.294715\pi\) | |||||||
\(878\) | 1046.00 | + | 938.491i | 1.19134 | + | 1.06890i | ||||
\(879\) | −1636.59 | −1.86188 | ||||||||
\(880\) | 229.307 | − | 358.610i | 0.260576 | − | 0.407511i | ||||
\(881\) | − | 1513.62i | − | 1.71807i | −0.511914 | − | 0.859037i | \(-0.671063\pi\) | ||
0.511914 | − | 0.859037i | \(-0.328937\pi\) | |||||||
\(882\) | 563.922 | + | 505.961i | 0.639367 | + | 0.573652i | ||||
\(883\) | −91.3318 | + | 220.494i | −0.103434 | + | 0.249711i | −0.967121 | − | 0.254317i | \(-0.918149\pi\) |
0.863687 | + | 0.504028i | \(0.168149\pi\) | |||||||
\(884\) | 73.8833 | − | 252.692i | 0.0835784 | − | 0.285851i | ||||
\(885\) | −188.470 | − | 455.006i | −0.212960 | − | 0.514131i | ||||
\(886\) | 282.075 | − | 135.153i | 0.318369 | − | 0.152543i | ||||
\(887\) | 892.828 | − | 892.828i | 1.00657 | − | 1.00657i | 0.00659168 | − | 0.999978i | \(-0.497902\pi\) |
0.999978 | − | 0.00659168i | \(-0.00209821\pi\) | |||||||
\(888\) | 207.758 | + | 1268.30i | 0.233961 | + | 1.42827i | ||||
\(889\) | 830.510 | − | 830.510i | 0.934207 | − | 0.934207i | ||||
\(890\) | −840.050 | − | 295.813i | −0.943877 | − | 0.332374i | ||||
\(891\) | 86.3777 | + | 208.534i | 0.0969447 | + | 0.234045i | ||||
\(892\) | −148.834 | − | 1369.62i | −0.166855 | − | 1.53545i | ||||
\(893\) | −668.203 | + | 1613.19i | −0.748268 | + | 1.80648i | ||||
\(894\) | −2662.95 | + | 144.265i | −2.97870 | + | 0.161370i | ||||
\(895\) | − | 357.168i | − | 0.399071i | ||||||
\(896\) | 446.273 | − | 1036.57i | 0.498073 | − | 1.15688i | ||||
\(897\) | −648.512 | −0.722978 | ||||||||
\(898\) | 1.67187 | + | 30.8608i | 0.00186177 | + | 0.0343661i | ||||
\(899\) | −0.210208 | − | 0.0870710i | −0.000233824 | − | 9.68531e-5i | ||||
\(900\) | 823.383 | − | 89.4757i | 0.914870 | − | 0.0994174i | ||||
\(901\) | −49.1388 | + | 20.3540i | −0.0545381 | + | 0.0225904i | ||||
\(902\) | −129.134 | + | 366.715i | −0.143164 | + | 0.406557i | ||||
\(903\) | −153.596 | − | 153.596i | −0.170095 | − | 0.170095i | ||||
\(904\) | 975.813 | − | 159.845i | 1.07944 | − | 0.176820i | ||||
\(905\) | −452.680 | − | 452.680i | −0.500199 | − | 0.500199i | ||||
\(906\) | −296.612 | − | 619.051i | −0.327386 | − | 0.683279i | ||||
\(907\) | −469.078 | + | 194.298i | −0.517175 | + | 0.214221i | −0.625976 | − | 0.779843i | \(-0.715299\pi\) |
0.108800 | + | 0.994064i | \(0.465299\pi\) | |||||||
\(908\) | −283.676 | − | 82.9425i | −0.312419 | − | 0.0913464i | ||||
\(909\) | 1371.82 | + | 568.226i | 1.50915 | + | 0.625111i | ||||
\(910\) | 517.600 | − | 576.894i | 0.568792 | − | 0.633950i | ||||
\(911\) | 469.566 | 0.515441 | 0.257720 | − | 0.966220i | \(-0.417029\pi\) | ||||
0.257720 | + | 0.966220i | \(0.417029\pi\) | |||||||
\(912\) | 1425.98 | − | 2230.07i | 1.56357 | − | 2.44525i | ||||
\(913\) | 242.446i | 0.265549i | ||||||||
\(914\) | −177.246 | + | 197.550i | −0.193923 | + | 0.216138i | ||||
\(915\) | 508.293 | − | 1227.13i | 0.555512 | − | 1.34112i | ||||
\(916\) | 158.816 | − | 86.9562i | 0.173380 | − | 0.0949303i | ||||
\(917\) | −832.872 | − | 2010.73i | −0.908257 | − | 2.19273i | ||||
\(918\) | 77.7114 | + | 162.189i | 0.0846529 | + | 0.176677i | ||||
\(919\) | 737.868 | − | 737.868i | 0.802903 | − | 0.802903i | −0.180645 | − | 0.983548i | \(-0.557819\pi\) |
0.983548 | + | 0.180645i | \(0.0578186\pi\) | |||||||
\(920\) | 226.747 | + | 53.1710i | 0.246464 | + | 0.0577946i | ||||
\(921\) | −806.710 | + | 806.710i | −0.875907 | + | 0.875907i | ||||
\(922\) | −412.970 | + | 1172.75i | −0.447907 | + | 1.27197i | ||||
\(923\) | 293.696 | + | 709.045i | 0.318197 | + | 0.768196i | ||||
\(924\) | −1129.73 | − | 908.266i | −1.22265 | − | 0.982971i | ||||
\(925\) | −205.027 | + | 494.979i | −0.221651 | + | 0.535113i | ||||
\(926\) | −61.4620 | − | 1134.51i | −0.0663736 | − | 1.22518i | ||||
\(927\) | − | 1429.11i | − | 1.54165i | ||||||
\(928\) | 22.1192 | + | 2.71403i | 0.0238354 | + | 0.00292461i | ||||
\(929\) | 796.539 | 0.857416 | 0.428708 | − | 0.903443i | \(-0.358969\pi\) | ||||
0.428708 | + | 0.903443i | \(0.358969\pi\) | |||||||
\(930\) | −9.36797 | + | 0.507507i | −0.0100731 | + | 0.000545707i | ||||
\(931\) | 932.554 | + | 386.277i | 1.00167 | + | 0.414905i | ||||
\(932\) | −895.162 | − | 719.680i | −0.960475 | − | 0.772189i | ||||
\(933\) | −274.312 | + | 113.624i | −0.294011 | + | 0.121783i | ||||
\(934\) | 771.273 | + | 271.594i | 0.825774 | + | 0.290786i | ||||
\(935\) | 85.8723 | + | 85.8723i | 0.0918420 | + | 0.0918420i | ||||
\(936\) | −1292.27 | + | 801.331i | −1.38063 | + | 0.856123i | ||||
\(937\) | 764.262 | + | 764.262i | 0.815648 | + | 0.815648i | 0.985474 | − | 0.169826i | \(-0.0543206\pi\) |
−0.169826 | + | 0.985474i | \(0.554321\pi\) | |||||||
\(938\) | 711.484 | − | 340.900i | 0.758511 | − | 0.363433i | ||||
\(939\) | −171.875 | + | 71.1927i | −0.183040 | + | 0.0758176i | ||||
\(940\) | −531.670 | + | 291.104i | −0.565606 | + | 0.309685i | ||||
\(941\) | 113.549 | + | 47.0336i | 0.120669 | + | 0.0499826i | 0.442201 | − | 0.896916i | \(-0.354198\pi\) |
−0.321532 | + | 0.946899i | \(0.604198\pi\) | |||||||
\(942\) | −720.852 | − | 646.762i | −0.765235 | − | 0.686584i | ||||
\(943\) | −212.725 | −0.225583 | ||||||||
\(944\) | 314.042 | + | 450.104i | 0.332671 | + | 0.476805i | ||||
\(945\) | 529.456i | 0.560271i | ||||||||
\(946\) | 67.9563 | + | 60.9717i | 0.0718354 | + | 0.0644521i | ||||
\(947\) | 396.726 | − | 957.782i | 0.418930 | − | 1.01139i | −0.563729 | − | 0.825960i | \(-0.690634\pi\) |
0.982658 | − | 0.185425i | \(-0.0593663\pi\) | |||||||
\(948\) | −486.522 | − | 142.252i | −0.513209 | − | 0.150054i | ||||
\(949\) | −407.560 | − | 983.937i | −0.429463 | − | 1.03681i | ||||
\(950\) | 995.118 | − | 476.801i | 1.04749 | − | 0.501896i | ||||
\(951\) | −1095.23 | + | 1095.23i | −1.15166 | + | 1.15166i | ||||
\(952\) | 261.485 | + | 187.877i | 0.274670 | + | 0.197349i | ||||
\(953\) | 391.136 | − | 391.136i | 0.410426 | − | 0.410426i | −0.471461 | − | 0.881887i | \(-0.656273\pi\) |
0.881887 | + | 0.471461i | \(0.156273\pi\) | |||||||
\(954\) | 289.751 | + | 102.032i | 0.303722 | + | 0.106952i | ||||
\(955\) | 394.443 | + | 952.270i | 0.413030 | + | 0.997142i | ||||
\(956\) | −348.632 | + | 37.8852i | −0.364677 | + | 0.0396289i | ||||
\(957\) | 10.9539 | − | 26.4452i | 0.0114461 | − | 0.0276334i | ||||
\(958\) | 654.799 | − | 35.4736i | 0.683506 | − | 0.0370288i | ||||
\(959\) | 1394.23i | 1.45383i | ||||||||
\(960\) | 870.864 | − | 293.175i | 0.907150 | − | 0.305391i | ||||
\(961\) | 960.893 | 0.999889 | ||||||||
\(962\) | −53.2089 | − | 982.171i | −0.0553107 | − | 1.02097i | ||||
\(963\) | −540.123 | − | 223.726i | −0.560875 | − | 0.232322i | ||||
\(964\) | −6.68740 | − | 61.5395i | −0.00693713 | − | 0.0638377i | ||||
\(965\) | −660.465 | + | 273.574i | −0.684420 | + | 0.283496i | ||||
\(966\) | 263.434 | − | 748.102i | 0.272706 | − | 0.774433i | ||||
\(967\) | −22.8939 | − | 22.8939i | −0.0236752 | − | 0.0236752i | 0.695170 | − | 0.718845i | \(-0.255329\pi\) |
−0.718845 | + | 0.695170i | \(0.755329\pi\) | |||||||
\(968\) | −291.327 | − | 209.318i | −0.300958 | − | 0.216237i | ||||
\(969\) | 534.009 | + | 534.009i | 0.551093 | + | 0.551093i | ||||
\(970\) | 205.430 | + | 428.747i | 0.211784 | + | 0.442007i | ||||
\(971\) | −619.006 | + | 256.401i | −0.637493 | + | 0.264058i | −0.677933 | − | 0.735124i | \(-0.737124\pi\) |
0.0404399 | + | 0.999182i | \(0.487124\pi\) | |||||||
\(972\) | −335.758 | + | 1148.35i | −0.345430 | + | 1.18143i | ||||
\(973\) | −280.154 | − | 116.044i | −0.287928 | − | 0.119264i | ||||
\(974\) | −278.597 | + | 310.512i | −0.286034 | + | 0.318801i | ||||
\(975\) | −1066.63 | −1.09398 | ||||||||
\(976\) | −259.476 | + | 1457.25i | −0.265856 | + | 1.49308i | ||||
\(977\) | 430.856i | 0.440999i | 0.975387 | + | 0.220500i | \(0.0707688\pi\) | ||||
−0.975387 | + | 0.220500i | \(0.929231\pi\) | |||||||
\(978\) | −33.8722 | + | 37.7524i | −0.0346341 | + | 0.0386017i | ||||
\(979\) | 487.844 | − | 1177.76i | 0.498309 | − | 1.20302i | ||||
\(980\) | 168.282 | + | 307.349i | 0.171716 | + | 0.313621i | ||||
\(981\) | 557.955 | + | 1347.02i | 0.568762 | + | 1.37311i | ||||
\(982\) | −560.123 | − | 1169.02i | −0.570390 | − | 1.19044i | ||||
\(983\) | 154.209 | − | 154.209i | 0.156876 | − | 0.156876i | −0.624305 | − | 0.781181i | \(-0.714618\pi\) |
0.781181 | + | 0.624305i | \(0.214618\pi\) | |||||||
\(984\) | −713.291 | + | 442.308i | −0.724889 | + | 0.449500i | ||||
\(985\) | −552.978 | + | 552.978i | −0.561399 | + | 0.561399i | ||||
\(986\) | −2.11180 | + | 5.99710i | −0.00214178 | + | 0.00608225i | ||||
\(987\) | 789.945 | + | 1907.09i | 0.800349 | + | 1.93221i | ||||
\(988\) | −1269.34 | + | 1578.85i | −1.28476 | + | 1.59803i | ||||
\(989\) | −19.1168 | + | 46.1520i | −0.0193294 | + | 0.0466653i | ||||
\(990\) | −37.9425 | − | 700.374i | −0.0383258 | − | 0.707448i | ||||
\(991\) | − | 966.543i | − | 0.975320i | −0.873033 | − | 0.487660i | \(-0.837850\pi\) | ||
0.873033 | − | 0.487660i | \(-0.162150\pi\) | |||||||
\(992\) | 10.0744 | − | 2.79478i | 0.0101556 | − | 0.00281732i | ||||
\(993\) | −864.169 | −0.870260 | ||||||||
\(994\) | −937.234 | + | 50.7744i | −0.942891 | + | 0.0510809i | ||||
\(995\) | −156.201 | − | 64.7007i | −0.156986 | − | 0.0650258i | ||||
\(996\) | −327.940 | + | 407.903i | −0.329258 | + | 0.409542i | ||||
\(997\) | 732.694 | − | 303.492i | 0.734899 | − | 0.304405i | 0.0163357 | − | 0.999867i | \(-0.494800\pi\) |
0.718564 | + | 0.695461i | \(0.244800\pi\) | |||||||
\(998\) | −286.626 | − | 100.932i | −0.287201 | − | 0.101134i | ||||
\(999\) | 475.120 | + | 475.120i | 0.475596 | + | 0.475596i |
(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 | 32.3.h.a.19.4 | ✓ | 28 | |
3.2 | odd | 2 | 288.3.u.a.19.4 | 28 | |||
4.3 | odd | 2 | 128.3.h.a.111.1 | 28 | |||
8.3 | odd | 2 | 256.3.h.a.223.7 | 28 | |||
8.5 | even | 2 | 256.3.h.b.223.1 | 28 | |||
32.5 | even | 8 | 128.3.h.a.15.1 | 28 | |||
32.11 | odd | 8 | 256.3.h.b.31.1 | 28 | |||
32.21 | even | 8 | 256.3.h.a.31.7 | 28 | |||
32.27 | odd | 8 | inner | 32.3.h.a.27.4 | yes | 28 | |
96.59 | even | 8 | 288.3.u.a.91.4 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.4 | ✓ | 28 | 1.1 | even | 1 | trivial | |
32.3.h.a.27.4 | yes | 28 | 32.27 | odd | 8 | inner | |
128.3.h.a.15.1 | 28 | 32.5 | even | 8 | |||
128.3.h.a.111.1 | 28 | 4.3 | odd | 2 | |||
256.3.h.a.31.7 | 28 | 32.21 | even | 8 | |||
256.3.h.a.223.7 | 28 | 8.3 | odd | 2 | |||
256.3.h.b.31.1 | 28 | 32.11 | odd | 8 | |||
256.3.h.b.223.1 | 28 | 8.5 | even | 2 | |||
288.3.u.a.19.4 | 28 | 3.2 | odd | 2 | |||
288.3.u.a.91.4 | 28 | 96.59 | even | 8 |