Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [882,2,Mod(227,882)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(882, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("882.227");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 882.l (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: | \(7.04280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 227.19 | ||
Character | \(\chi\) | \(=\) | 882.227 |
Dual form | 882.2.l.c.509.7 |
$q$-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 \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(785\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.765075 | + | 1.55392i | 0.441716 | + | 0.897155i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.474556 | − | 0.821956i | 0.212228 | − | 0.367590i | −0.740183 | − | 0.672405i | \(-0.765261\pi\) |
0.952412 | + | 0.304815i | \(0.0985947\pi\) | |||||||
\(6\) | −1.55392 | + | 0.765075i | −0.634384 | + | 0.312341i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.82932 | + | 2.37773i | −0.609773 | + | 0.792576i | ||||
\(10\) | 0.821956 | + | 0.474556i | 0.259925 | + | 0.150068i | ||||
\(11\) | −1.51873 | + | 0.876838i | −0.457914 | + | 0.264377i | −0.711167 | − | 0.703024i | \(-0.751833\pi\) |
0.253253 | + | 0.967400i | \(0.418500\pi\) | |||||||
\(12\) | −0.765075 | − | 1.55392i | −0.220858 | − | 0.448577i | ||||
\(13\) | −0.720756 | + | 0.416129i | −0.199902 | + | 0.115413i | −0.596610 | − | 0.802532i | \(-0.703486\pi\) |
0.396708 | + | 0.917945i | \(0.370153\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.64032 | + | 0.108564i | 0.423530 | + | 0.0280310i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.73638 | + | 4.73955i | −0.663670 | + | 1.14951i | 0.315975 | + | 0.948768i | \(0.397669\pi\) |
−0.979644 | + | 0.200742i | \(0.935665\pi\) | |||||||
\(18\) | −2.37773 | − | 1.82932i | −0.560436 | − | 0.431175i | ||||
\(19\) | −3.21232 | + | 1.85463i | −0.736957 | + | 0.425482i | −0.820962 | − | 0.570983i | \(-0.806562\pi\) |
0.0840051 | + | 0.996465i | \(0.473229\pi\) | |||||||
\(20\) | −0.474556 | + | 0.821956i | −0.106114 | + | 0.183795i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.876838 | − | 1.51873i | −0.186942 | − | 0.323794i | ||||
\(23\) | 0.888998 | + | 0.513263i | 0.185369 | + | 0.107023i | 0.589813 | − | 0.807540i | \(-0.299202\pi\) |
−0.404444 | + | 0.914563i | \(0.632535\pi\) | |||||||
\(24\) | 1.55392 | − | 0.765075i | 0.317192 | − | 0.156170i | ||||
\(25\) | 2.04959 | + | 3.55000i | 0.409918 | + | 0.710000i | ||||
\(26\) | −0.416129 | − | 0.720756i | −0.0816096 | − | 0.141352i | ||||
\(27\) | −5.09436 | − | 1.02347i | −0.980410 | − | 0.196968i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.58867 | − | 3.80397i | −1.22348 | − | 0.706379i | −0.257826 | − | 0.966191i | \(-0.583006\pi\) |
−0.965659 | + | 0.259812i | \(0.916339\pi\) | |||||||
\(30\) | −0.108564 | + | 1.64032i | −0.0198209 | + | 0.299481i | ||||
\(31\) | 11.0016i | 1.97595i | 0.154602 | + | 0.987977i | \(0.450591\pi\) | ||||
−0.154602 | + | 0.987977i | \(0.549409\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −2.52447 | − | 1.68913i | −0.439455 | − | 0.294040i | ||||
\(34\) | −4.73955 | − | 2.73638i | −0.812826 | − | 0.469285i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.82932 | − | 2.37773i | 0.304887 | − | 0.396288i | ||||
\(37\) | −2.19830 | − | 3.80756i | −0.361398 | − | 0.625959i | 0.626794 | − | 0.779185i | \(-0.284367\pi\) |
−0.988191 | + | 0.153226i | \(0.951034\pi\) | |||||||
\(38\) | −1.85463 | − | 3.21232i | −0.300861 | − | 0.521107i | ||||
\(39\) | −1.19806 | − | 0.801626i | −0.191844 | − | 0.128363i | ||||
\(40\) | −0.821956 | − | 0.474556i | −0.129963 | − | 0.0750340i | ||||
\(41\) | 4.05647 | + | 7.02601i | 0.633514 | + | 1.09728i | 0.986828 | + | 0.161774i | \(0.0517216\pi\) |
−0.353314 | + | 0.935505i | \(0.614945\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.08463 | − | 5.34273i | 0.470401 | − | 0.814759i | −0.529026 | − | 0.848606i | \(-0.677443\pi\) |
0.999427 | + | 0.0338470i | \(0.0107759\pi\) | |||||||
\(44\) | 1.51873 | − | 0.876838i | 0.228957 | − | 0.132188i | ||||
\(45\) | 1.08627 | + | 2.63199i | 0.161932 | + | 0.392353i | ||||
\(46\) | −0.513263 | + | 0.888998i | −0.0756766 | + | 0.131076i | ||||
\(47\) | 6.80125 | 0.992064 | 0.496032 | − | 0.868304i | \(-0.334790\pi\) | ||||
0.496032 | + | 0.868304i | \(0.334790\pi\) | |||||||
\(48\) | 0.765075 | + | 1.55392i | 0.110429 | + | 0.224289i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.55000 | + | 2.04959i | −0.502046 | + | 0.289856i | ||||
\(51\) | −9.45841 | − | 0.625999i | −1.32444 | − | 0.0876573i | ||||
\(52\) | 0.720756 | − | 0.416129i | 0.0999509 | − | 0.0577067i | ||||
\(53\) | 1.88177 | + | 1.08644i | 0.258480 | + | 0.149234i | 0.623641 | − | 0.781711i | \(-0.285653\pi\) |
−0.365161 | + | 0.930944i | \(0.618986\pi\) | |||||||
\(54\) | 1.02347 | − | 5.09436i | 0.139277 | − | 0.693255i | ||||
\(55\) | 1.66444i | 0.224433i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.33961 | − | 3.57275i | −0.707249 | − | 0.473222i | ||||
\(58\) | 3.80397 | − | 6.58867i | 0.499486 | − | 0.865134i | ||||
\(59\) | −10.8659 | −1.41462 | −0.707311 | − | 0.706902i | \(-0.750092\pi\) | ||||
−0.707311 | + | 0.706902i | \(0.750092\pi\) | |||||||
\(60\) | −1.64032 | − | 0.108564i | −0.211765 | − | 0.0140155i | ||||
\(61\) | 1.09663i | 0.140409i | 0.997533 | + | 0.0702043i | \(0.0223651\pi\) | ||||
−0.997533 | + | 0.0702043i | \(0.977635\pi\) | |||||||
\(62\) | −11.0016 | −1.39721 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.789907i | 0.0979759i | ||||||||
\(66\) | 1.68913 | − | 2.52447i | 0.207918 | − | 0.310741i | ||||
\(67\) | 14.4481 | 1.76512 | 0.882559 | − | 0.470202i | \(-0.155819\pi\) | ||||
0.882559 | + | 0.470202i | \(0.155819\pi\) | |||||||
\(68\) | 2.73638 | − | 4.73955i | 0.331835 | − | 0.574755i | ||||
\(69\) | −0.117419 | + | 1.77412i | −0.0141355 | + | 0.213578i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 11.0131i | − | 1.30701i | −0.756922 | − | 0.653505i | \(-0.773298\pi\) | ||
0.756922 | − | 0.653505i | \(-0.226702\pi\) | |||||||
\(72\) | 2.37773 | + | 1.82932i | 0.280218 | + | 0.215587i | ||||
\(73\) | 3.16204 | + | 1.82561i | 0.370089 | + | 0.213671i | 0.673497 | − | 0.739190i | \(-0.264791\pi\) |
−0.303408 | + | 0.952861i | \(0.598125\pi\) | |||||||
\(74\) | 3.80756 | − | 2.19830i | 0.442620 | − | 0.255547i | ||||
\(75\) | −3.94831 | + | 5.90091i | −0.455912 | + | 0.681379i | ||||
\(76\) | 3.21232 | − | 1.85463i | 0.368478 | − | 0.212741i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.801626 | − | 1.19806i | 0.0907663 | − | 0.135654i | ||||
\(79\) | 9.84819 | 1.10801 | 0.554004 | − | 0.832514i | \(-0.313099\pi\) | ||||
0.554004 | + | 0.832514i | \(0.313099\pi\) | |||||||
\(80\) | 0.474556 | − | 0.821956i | 0.0530570 | − | 0.0918975i | ||||
\(81\) | −2.30717 | − | 8.69925i | −0.256353 | − | 0.966583i | ||||
\(82\) | −7.02601 | + | 4.05647i | −0.775893 | + | 0.447962i | ||||
\(83\) | 2.41103 | − | 4.17603i | 0.264645 | − | 0.458379i | −0.702825 | − | 0.711363i | \(-0.748078\pi\) |
0.967471 | + | 0.252983i | \(0.0814117\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.59713 | + | 4.49837i | 0.281699 | + | 0.487916i | ||||
\(86\) | 5.34273 | + | 3.08463i | 0.576121 | + | 0.332624i | ||||
\(87\) | 0.870230 | − | 13.1486i | 0.0932984 | − | 1.40967i | ||||
\(88\) | 0.876838 | + | 1.51873i | 0.0934712 | + | 0.161897i | ||||
\(89\) | −2.15943 | − | 3.74024i | −0.228899 | − | 0.396465i | 0.728583 | − | 0.684957i | \(-0.240179\pi\) |
−0.957482 | + | 0.288493i | \(0.906846\pi\) | |||||||
\(90\) | −2.63199 | + | 1.08627i | −0.277436 | + | 0.114503i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.888998 | − | 0.513263i | −0.0926845 | − | 0.0535114i | ||||
\(93\) | −17.0957 | + | 8.41708i | −1.77274 | + | 0.872811i | ||||
\(94\) | 6.80125i | 0.701495i | ||||||||
\(95\) | 3.52051i | 0.361197i | ||||||||
\(96\) | −1.55392 | + | 0.765075i | −0.158596 | + | 0.0780851i | ||||
\(97\) | 3.90396 | + | 2.25395i | 0.396387 | + | 0.228854i | 0.684924 | − | 0.728615i | \(-0.259836\pi\) |
−0.288537 | + | 0.957469i | \(0.593169\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.693358 | − | 5.21514i | 0.0696851 | − | 0.524141i | ||||
\(100\) | −2.04959 | − | 3.55000i | −0.204959 | − | 0.355000i | ||||
\(101\) | −6.33624 | − | 10.9747i | −0.630480 | − | 1.09202i | −0.987454 | − | 0.157909i | \(-0.949525\pi\) |
0.356974 | − | 0.934114i | \(-0.383808\pi\) | |||||||
\(102\) | 0.625999 | − | 9.45841i | 0.0619831 | − | 0.936522i | ||||
\(103\) | 7.33341 | + | 4.23394i | 0.722582 | + | 0.417183i | 0.815702 | − | 0.578472i | \(-0.196351\pi\) |
−0.0931202 | + | 0.995655i | \(0.529684\pi\) | |||||||
\(104\) | 0.416129 | + | 0.720756i | 0.0408048 | + | 0.0706760i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.08644 | + | 1.88177i | −0.105524 | + | 0.182773i | ||||
\(107\) | −1.28657 | + | 0.742804i | −0.124378 | + | 0.0718096i | −0.560898 | − | 0.827885i | \(-0.689544\pi\) |
0.436520 | + | 0.899694i | \(0.356211\pi\) | |||||||
\(108\) | 5.09436 | + | 1.02347i | 0.490205 | + | 0.0984838i | ||||
\(109\) | 7.60276 | − | 13.1684i | 0.728213 | − | 1.26130i | −0.229425 | − | 0.973326i | \(-0.573685\pi\) |
0.957638 | − | 0.287975i | \(-0.0929820\pi\) | |||||||
\(110\) | −1.66444 | −0.158698 | ||||||||
\(111\) | 4.23477 | − | 6.32904i | 0.401947 | − | 0.600726i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.0031 | + | 9.81676i | −1.59952 | + | 0.923483i | −0.607941 | + | 0.793982i | \(0.708004\pi\) |
−0.991579 | + | 0.129501i | \(0.958662\pi\) | |||||||
\(114\) | 3.57275 | − | 5.33961i | 0.334618 | − | 0.500101i | ||||
\(115\) | 0.843760 | − | 0.487145i | 0.0786810 | − | 0.0454265i | ||||
\(116\) | 6.58867 | + | 3.80397i | 0.611742 | + | 0.353190i | ||||
\(117\) | 0.329053 | − | 2.47500i | 0.0304210 | − | 0.228813i | ||||
\(118\) | − | 10.8659i | − | 1.00029i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.108564 | − | 1.64032i | 0.00991047 | − | 0.149740i | ||||
\(121\) | −3.96231 | + | 6.86292i | −0.360210 | + | 0.623902i | ||||
\(122\) | −1.09663 | −0.0992838 | ||||||||
\(123\) | −7.81434 | + | 11.6788i | −0.704595 | + | 1.05305i | ||||
\(124\) | − | 11.0016i | − | 0.987977i | ||||||
\(125\) | 8.63615 | 0.772441 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.7051 | 1.65981 | 0.829903 | − | 0.557907i | \(-0.188395\pi\) | ||||
0.829903 | + | 0.557907i | \(0.188395\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 10.6621 | + | 0.705666i | 0.938748 | + | 0.0621305i | ||||
\(130\) | −0.789907 | −0.0692794 | ||||||||
\(131\) | −3.32193 | + | 5.75375i | −0.290238 | + | 0.502707i | −0.973866 | − | 0.227124i | \(-0.927068\pi\) |
0.683628 | + | 0.729831i | \(0.260401\pi\) | |||||||
\(132\) | 2.52447 | + | 1.68913i | 0.219727 | + | 0.147020i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 14.4481i | 1.24813i | ||||||||
\(135\) | −3.25881 | + | 3.70164i | −0.280474 | + | 0.318587i | ||||
\(136\) | 4.73955 | + | 2.73638i | 0.406413 | + | 0.234643i | ||||
\(137\) | −17.6798 | + | 10.2074i | −1.51049 | + | 0.872080i | −0.510562 | + | 0.859841i | \(0.670563\pi\) |
−0.999925 | + | 0.0122395i | \(0.996104\pi\) | |||||||
\(138\) | −1.77412 | − | 0.117419i | −0.151023 | − | 0.00999534i | ||||
\(139\) | 10.9829 | − | 6.34099i | 0.931559 | − | 0.537836i | 0.0442550 | − | 0.999020i | \(-0.485909\pi\) |
0.887304 | + | 0.461184i | \(0.152575\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.20346 | + | 10.5686i | 0.438211 | + | 0.890035i | ||||
\(142\) | 11.0131 | 0.924196 | ||||||||
\(143\) | 0.729755 | − | 1.26397i | 0.0610252 | − | 0.105699i | ||||
\(144\) | −1.82932 | + | 2.37773i | −0.152443 | + | 0.198144i | ||||
\(145\) | −6.25339 | + | 3.61040i | −0.519316 | + | 0.299827i | ||||
\(146\) | −1.82561 | + | 3.16204i | −0.151088 | + | 0.261693i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.19830 | + | 3.80756i | 0.180699 | + | 0.312979i | ||||
\(149\) | 17.1827 | + | 9.92046i | 1.40767 | + | 0.812716i | 0.995163 | − | 0.0982404i | \(-0.0313214\pi\) |
0.412503 | + | 0.910956i | \(0.364655\pi\) | |||||||
\(150\) | −5.90091 | − | 3.94831i | −0.481807 | − | 0.322378i | ||||
\(151\) | −0.872422 | − | 1.51108i | −0.0709967 | − | 0.122970i | 0.828342 | − | 0.560223i | \(-0.189285\pi\) |
−0.899338 | + | 0.437253i | \(0.855951\pi\) | |||||||
\(152\) | 1.85463 | + | 3.21232i | 0.150431 | + | 0.260553i | ||||
\(153\) | −6.26364 | − | 15.1765i | −0.506385 | − | 1.22695i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.04287 | + | 5.22090i | 0.726341 | + | 0.419353i | ||||
\(156\) | 1.19806 | + | 0.801626i | 0.0959218 | + | 0.0641815i | ||||
\(157\) | 9.49564i | 0.757835i | 0.925431 | + | 0.378917i | \(0.123704\pi\) | ||||
−0.925431 | + | 0.378917i | \(0.876296\pi\) | |||||||
\(158\) | 9.84819i | 0.783480i | ||||||||
\(159\) | −0.248543 | + | 3.75532i | −0.0197108 | + | 0.297816i | ||||
\(160\) | 0.821956 | + | 0.474556i | 0.0649813 | + | 0.0375170i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 8.69925 | − | 2.30717i | 0.683478 | − | 0.181269i | ||||
\(163\) | −5.92061 | − | 10.2548i | −0.463738 | − | 0.803217i | 0.535406 | − | 0.844595i | \(-0.320159\pi\) |
−0.999144 | + | 0.0413777i | \(0.986825\pi\) | |||||||
\(164\) | −4.05647 | − | 7.02601i | −0.316757 | − | 0.548639i | ||||
\(165\) | −2.58640 | + | 1.27342i | −0.201351 | + | 0.0991355i | ||||
\(166\) | 4.17603 | + | 2.41103i | 0.324123 | + | 0.187133i | ||||
\(167\) | 1.73229 | + | 3.00041i | 0.134048 | + | 0.232179i | 0.925234 | − | 0.379398i | \(-0.123869\pi\) |
−0.791185 | + | 0.611577i | \(0.790536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.15367 | + | 10.6585i | −0.473359 | + | 0.819883i | ||||
\(170\) | −4.49837 | + | 2.59713i | −0.345009 | + | 0.199191i | ||||
\(171\) | 1.46655 | − | 11.0307i | 0.112150 | − | 0.843542i | ||||
\(172\) | −3.08463 | + | 5.34273i | −0.235201 | + | 0.407379i | ||||
\(173\) | 3.09982 | 0.235675 | 0.117838 | − | 0.993033i | \(-0.462404\pi\) | ||||
0.117838 | + | 0.993033i | \(0.462404\pi\) | |||||||
\(174\) | 13.1486 | + | 0.870230i | 0.996790 | + | 0.0659719i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.51873 | + | 0.876838i | −0.114478 | + | 0.0660941i | ||||
\(177\) | −8.31325 | − | 16.8848i | −0.624862 | − | 1.26914i | ||||
\(178\) | 3.74024 | − | 2.15943i | 0.280343 | − | 0.161856i | ||||
\(179\) | 0.500470 | + | 0.288947i | 0.0374069 | + | 0.0215969i | 0.518587 | − | 0.855025i | \(-0.326458\pi\) |
−0.481180 | + | 0.876622i | \(0.659792\pi\) | |||||||
\(180\) | −1.08627 | − | 2.63199i | −0.0809659 | − | 0.196177i | ||||
\(181\) | 26.0581i | 1.93688i | 0.249238 | + | 0.968442i | \(0.419820\pi\) | ||||
−0.249238 | + | 0.968442i | \(0.580180\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.70407 | + | 0.839001i | −0.125968 | + | 0.0620207i | ||||
\(184\) | 0.513263 | − | 0.888998i | 0.0378383 | − | 0.0655378i | ||||
\(185\) | −4.17286 | −0.306795 | ||||||||
\(186\) | −8.41708 | − | 17.0957i | −0.617171 | − | 1.25351i | ||||
\(187\) | − | 9.59745i | − | 0.701835i | ||||||
\(188\) | −6.80125 | −0.496032 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.52051 | −0.255405 | ||||||||
\(191\) | 1.77964i | 0.128770i | 0.997925 | + | 0.0643852i | \(0.0205086\pi\) | ||||
−0.997925 | + | 0.0643852i | \(0.979491\pi\) | |||||||
\(192\) | −0.765075 | − | 1.55392i | −0.0552145 | − | 0.112144i | ||||
\(193\) | −1.48335 | −0.106774 | −0.0533871 | − | 0.998574i | \(-0.517002\pi\) | ||||
−0.0533871 | + | 0.998574i | \(0.517002\pi\) | |||||||
\(194\) | −2.25395 | + | 3.90396i | −0.161824 | + | 0.280288i | ||||
\(195\) | −1.22745 | + | 0.604338i | −0.0878995 | + | 0.0432775i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.44809i | 0.174419i | 0.996190 | + | 0.0872096i | \(0.0277950\pi\) | ||||
−0.996190 | + | 0.0872096i | \(0.972205\pi\) | |||||||
\(198\) | 5.21514 | + | 0.693358i | 0.370624 | + | 0.0492748i | ||||
\(199\) | −9.47403 | − | 5.46984i | −0.671596 | − | 0.387746i | 0.125085 | − | 0.992146i | \(-0.460080\pi\) |
−0.796681 | + | 0.604400i | \(0.793413\pi\) | |||||||
\(200\) | 3.55000 | − | 2.04959i | 0.251023 | − | 0.144928i | ||||
\(201\) | 11.0539 | + | 22.4512i | 0.779681 | + | 1.58358i | ||||
\(202\) | 10.9747 | − | 6.33624i | 0.772177 | − | 0.445816i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 9.45841 | + | 0.625999i | 0.662221 | + | 0.0438287i | ||||
\(205\) | 7.70010 | 0.537798 | ||||||||
\(206\) | −4.23394 | + | 7.33341i | −0.294993 | + | 0.510943i | ||||
\(207\) | −2.84666 | + | 1.17487i | −0.197857 | + | 0.0816593i | ||||
\(208\) | −0.720756 | + | 0.416129i | −0.0499755 | + | 0.0288534i | ||||
\(209\) | 3.25243 | − | 5.63337i | 0.224975 | − | 0.389668i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.7481 | + | 22.0804i | 0.877617 | + | 1.52008i | 0.853949 | + | 0.520357i | \(0.174201\pi\) |
0.0236678 | + | 0.999720i | \(0.492466\pi\) | |||||||
\(212\) | −1.88177 | − | 1.08644i | −0.129240 | − | 0.0746169i | ||||
\(213\) | 17.1134 | − | 8.42582i | 1.17259 | − | 0.577328i | ||||
\(214\) | −0.742804 | − | 1.28657i | −0.0507770 | − | 0.0879484i | ||||
\(215\) | −2.92766 | − | 5.07085i | −0.199665 | − | 0.345829i | ||||
\(216\) | −1.02347 | + | 5.09436i | −0.0696386 | + | 0.346627i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 13.1684 | + | 7.60276i | 0.891875 | + | 0.514924i | ||||
\(219\) | −0.417642 | + | 6.31028i | −0.0282216 | + | 0.426409i | ||||
\(220\) | − | 1.66444i | − | 0.112216i | ||||||
\(221\) | − | 4.55475i | − | 0.306385i | ||||||
\(222\) | 6.32904 | + | 4.23477i | 0.424777 | + | 0.284219i | ||||
\(223\) | −13.3108 | − | 7.68501i | −0.891359 | − | 0.514626i | −0.0169720 | − | 0.999856i | \(-0.505403\pi\) |
−0.874387 | + | 0.485230i | \(0.838736\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.1903 | − | 1.62071i | −0.812686 | − | 0.108047i | ||||
\(226\) | −9.81676 | − | 17.0031i | −0.653001 | − | 1.13103i | ||||
\(227\) | −4.17388 | − | 7.22937i | −0.277030 | − | 0.479830i | 0.693615 | − | 0.720346i | \(-0.256017\pi\) |
−0.970645 | + | 0.240515i | \(0.922684\pi\) | |||||||
\(228\) | 5.33961 | + | 3.57275i | 0.353625 | + | 0.236611i | ||||
\(229\) | 11.3671 | + | 6.56281i | 0.751161 | + | 0.433683i | 0.826113 | − | 0.563504i | \(-0.190547\pi\) |
−0.0749523 | + | 0.997187i | \(0.523880\pi\) | |||||||
\(230\) | 0.487145 | + | 0.843760i | 0.0321214 | + | 0.0556359i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.80397 | + | 6.58867i | −0.249743 | + | 0.432567i | ||||
\(233\) | 9.84350 | − | 5.68315i | 0.644869 | − | 0.372315i | −0.141619 | − | 0.989921i | \(-0.545231\pi\) |
0.786488 | + | 0.617606i | \(0.211897\pi\) | |||||||
\(234\) | 2.47500 | + | 0.329053i | 0.161796 | + | 0.0215109i | ||||
\(235\) | 3.22758 | − | 5.59033i | 0.210544 | − | 0.364673i | ||||
\(236\) | 10.8659 | 0.707311 | ||||||||
\(237\) | 7.53460 | + | 15.3033i | 0.489425 | + | 0.994054i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.67039 | − | 2.69645i | 0.302102 | − | 0.174419i | −0.341285 | − | 0.939960i | \(-0.610862\pi\) |
0.643387 | + | 0.765541i | \(0.277529\pi\) | |||||||
\(240\) | 1.64032 | + | 0.108564i | 0.105882 | + | 0.00700776i | ||||
\(241\) | 12.1233 | − | 6.99936i | 0.780928 | − | 0.450869i | −0.0558314 | − | 0.998440i | \(-0.517781\pi\) |
0.836759 | + | 0.547572i | \(0.184448\pi\) | |||||||
\(242\) | −6.86292 | − | 3.96231i | −0.441165 | − | 0.254707i | ||||
\(243\) | 11.7528 | − | 10.2407i | 0.753940 | − | 0.656944i | ||||
\(244\) | − | 1.09663i | − | 0.0702043i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.6788 | − | 7.81434i | −0.744616 | − | 0.498224i | ||||
\(247\) | 1.54353 | − | 2.67348i | 0.0982127 | − | 0.170109i | ||||
\(248\) | 11.0016 | 0.698605 | ||||||||
\(249\) | 8.33384 | + | 0.551570i | 0.528135 | + | 0.0349543i | ||||
\(250\) | 8.63615i | 0.546198i | ||||||||
\(251\) | 16.5094 | 1.04207 | 0.521033 | − | 0.853536i | \(-0.325547\pi\) | ||||
0.521033 | + | 0.853536i | \(0.325547\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.80019 | −0.113177 | ||||||||
\(254\) | 18.7051i | 1.17366i | ||||||||
\(255\) | −5.00309 | + | 7.47732i | −0.313306 | + | 0.468248i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.06000 | + | 5.30007i | −0.190878 | + | 0.330610i | −0.945541 | − | 0.325502i | \(-0.894467\pi\) |
0.754664 | + | 0.656112i | \(0.227800\pi\) | |||||||
\(258\) | −0.705666 | + | 10.6621i | −0.0439329 | + | 0.663795i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 0.789907i | − | 0.0489879i | ||||||
\(261\) | 21.0976 | − | 8.70738i | 1.30591 | − | 0.538973i | ||||
\(262\) | −5.75375 | − | 3.32193i | −0.355468 | − | 0.205229i | ||||
\(263\) | −14.1668 | + | 8.17923i | −0.873565 | + | 0.504353i | −0.868531 | − | 0.495634i | \(-0.834936\pi\) |
−0.00503369 | + | 0.999987i | \(0.501602\pi\) | |||||||
\(264\) | −1.68913 | + | 2.52447i | −0.103959 | + | 0.155371i | ||||
\(265\) | 1.78601 | − | 1.03115i | 0.109714 | − | 0.0633432i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.15990 | − | 6.21714i | 0.254582 | − | 0.380483i | ||||
\(268\) | −14.4481 | −0.882559 | ||||||||
\(269\) | −2.65845 | + | 4.60457i | −0.162088 | + | 0.280745i | −0.935617 | − | 0.353015i | \(-0.885156\pi\) |
0.773529 | + | 0.633761i | \(0.218490\pi\) | |||||||
\(270\) | −3.70164 | − | 3.25881i | −0.225275 | − | 0.198325i | ||||
\(271\) | 14.2825 | − | 8.24602i | 0.867601 | − | 0.500910i | 0.00105086 | − | 0.999999i | \(-0.499666\pi\) |
0.866550 | + | 0.499090i | \(0.166332\pi\) | |||||||
\(272\) | −2.73638 | + | 4.73955i | −0.165917 | + | 0.287377i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.2074 | − | 17.6798i | −0.616654 | − | 1.06808i | ||||
\(275\) | −6.22554 | − | 3.59432i | −0.375414 | − | 0.216746i | ||||
\(276\) | 0.117419 | − | 1.77412i | 0.00706777 | − | 0.106789i | ||||
\(277\) | −7.31402 | − | 12.6682i | −0.439457 | − | 0.761161i | 0.558191 | − | 0.829713i | \(-0.311496\pi\) |
−0.997648 | + | 0.0685513i | \(0.978162\pi\) | |||||||
\(278\) | 6.34099 | + | 10.9829i | 0.380308 | + | 0.658712i | ||||
\(279\) | −26.1589 | − | 20.1255i | −1.56609 | − | 1.20488i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.62307 | + | 2.09178i | 0.216134 | + | 0.124785i | 0.604159 | − | 0.796864i | \(-0.293509\pi\) |
−0.388025 | + | 0.921649i | \(0.626842\pi\) | |||||||
\(282\) | −10.5686 | + | 5.20346i | −0.629350 | + | 0.309862i | ||||
\(283\) | 9.70591i | 0.576957i | 0.957486 | + | 0.288478i | \(0.0931493\pi\) | ||||
−0.957486 | + | 0.288478i | \(0.906851\pi\) | |||||||
\(284\) | 11.0131i | 0.653505i | ||||||||
\(285\) | −5.47059 | + | 2.69346i | −0.324050 | + | 0.159547i | ||||
\(286\) | 1.26397 | + | 0.729755i | 0.0747403 | + | 0.0431513i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.37773 | − | 1.82932i | −0.140109 | − | 0.107794i | ||||
\(289\) | −6.47555 | − | 11.2160i | −0.380915 | − | 0.659764i | ||||
\(290\) | −3.61040 | − | 6.25339i | −0.212010 | − | 0.367212i | ||||
\(291\) | −0.515633 | + | 7.79087i | −0.0302270 | + | 0.456709i | ||||
\(292\) | −3.16204 | − | 1.82561i | −0.185045 | − | 0.106836i | ||||
\(293\) | 1.01377 | + | 1.75591i | 0.0592253 | + | 0.102581i | 0.894118 | − | 0.447832i | \(-0.147804\pi\) |
−0.834893 | + | 0.550413i | \(0.814470\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.15650 | + | 8.93131i | −0.300223 | + | 0.520001i | ||||
\(296\) | −3.80756 | + | 2.19830i | −0.221310 | + | 0.127773i | ||||
\(297\) | 8.63437 | − | 2.91255i | 0.501017 | − | 0.169003i | ||||
\(298\) | −9.92046 | + | 17.1827i | −0.574677 | + | 0.995370i | ||||
\(299\) | −0.854335 | −0.0494075 | ||||||||
\(300\) | 3.94831 | − | 5.90091i | 0.227956 | − | 0.340689i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 1.51108 | − | 0.872422i | 0.0869528 | − | 0.0502022i | ||||
\(303\) | 12.2061 | − | 18.2425i | 0.701220 | − | 1.04800i | ||||
\(304\) | −3.21232 | + | 1.85463i | −0.184239 | + | 0.106371i | ||||
\(305\) | 0.901378 | + | 0.520411i | 0.0516128 | + | 0.0297986i | ||||
\(306\) | 15.1765 | − | 6.26364i | 0.867584 | − | 0.358068i | ||||
\(307\) | 9.79004i | 0.558747i | 0.960183 | + | 0.279374i | \(0.0901268\pi\) | ||||
−0.960183 | + | 0.279374i | \(0.909873\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.968595 | + | 14.6348i | −0.0551014 | + | 0.832545i | ||||
\(310\) | −5.22090 | + | 9.04287i | −0.296527 | + | 0.513600i | ||||
\(311\) | 13.7039 | 0.777076 | 0.388538 | − | 0.921433i | \(-0.372980\pi\) | ||||
0.388538 | + | 0.921433i | \(0.372980\pi\) | |||||||
\(312\) | −0.801626 | + | 1.19806i | −0.0453832 | + | 0.0678270i | ||||
\(313\) | − | 18.8585i | − | 1.06595i | −0.846132 | − | 0.532974i | \(-0.821074\pi\) | ||
0.846132 | − | 0.532974i | \(-0.178926\pi\) | |||||||
\(314\) | −9.49564 | −0.535870 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.84819 | −0.554004 | ||||||||
\(317\) | − | 7.86426i | − | 0.441701i | −0.975308 | − | 0.220850i | \(-0.929117\pi\) | ||
0.975308 | − | 0.220850i | \(-0.0708832\pi\) | |||||||
\(318\) | −3.75532 | − | 0.248543i | −0.210588 | − | 0.0139376i | ||||
\(319\) | 13.3419 | 0.747000 | ||||||||
\(320\) | −0.474556 | + | 0.821956i | −0.0265285 | + | 0.0459487i | ||||
\(321\) | −2.13858 | − | 1.43093i | −0.119364 | − | 0.0798667i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.2999i | − | 1.12952i | ||||||
\(324\) | 2.30717 | + | 8.69925i | 0.128176 | + | 0.483292i | ||||
\(325\) | −2.95451 | − | 1.70579i | −0.163887 | − | 0.0946202i | ||||
\(326\) | 10.2548 | − | 5.92061i | 0.567960 | − | 0.327912i | ||||
\(327\) | 26.2792 | + | 1.73928i | 1.45325 | + | 0.0961821i | ||||
\(328\) | 7.02601 | − | 4.05647i | 0.387947 | − | 0.223981i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.27342 | − | 2.58640i | −0.0700994 | − | 0.142376i | ||||
\(331\) | 22.7350 | 1.24963 | 0.624813 | − | 0.780774i | \(-0.285175\pi\) | ||||
0.624813 | + | 0.780774i | \(0.285175\pi\) | |||||||
\(332\) | −2.41103 | + | 4.17603i | −0.132323 | + | 0.229190i | ||||
\(333\) | 13.0747 | + | 1.73830i | 0.716490 | + | 0.0952582i | ||||
\(334\) | −3.00041 | + | 1.73229i | −0.164175 | + | 0.0947866i | ||||
\(335\) | 6.85644 | − | 11.8757i | 0.374608 | − | 0.648839i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.0639 | − | 17.4312i | −0.548217 | − | 0.949539i | −0.998397 | − | 0.0566014i | \(-0.981974\pi\) |
0.450180 | − | 0.892938i | \(-0.351360\pi\) | |||||||
\(338\) | −10.6585 | − | 6.15367i | −0.579745 | − | 0.334716i | ||||
\(339\) | −28.2631 | − | 18.9109i | −1.53504 | − | 1.02710i | ||||
\(340\) | −2.59713 | − | 4.49837i | −0.140849 | − | 0.243958i | ||||
\(341\) | −9.64666 | − | 16.7085i | −0.522396 | − | 0.904816i | ||||
\(342\) | 11.0307 | + | 1.46655i | 0.596474 | + | 0.0793019i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.34273 | − | 3.08463i | −0.288061 | − | 0.166312i | ||||
\(345\) | 1.40252 | + | 0.938431i | 0.0755093 | + | 0.0505234i | ||||
\(346\) | 3.09982i | 0.166647i | ||||||||
\(347\) | − | 22.6395i | − | 1.21535i | −0.794185 | − | 0.607677i | \(-0.792102\pi\) | ||
0.794185 | − | 0.607677i | \(-0.207898\pi\) | |||||||
\(348\) | −0.870230 | + | 13.1486i | −0.0466492 | + | 0.704837i | ||||
\(349\) | −13.3378 | − | 7.70058i | −0.713955 | − | 0.412202i | 0.0985684 | − | 0.995130i | \(-0.468574\pi\) |
−0.812524 | + | 0.582928i | \(0.801907\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.09769 | − | 1.38224i | 0.218719 | − | 0.0737783i | ||||
\(352\) | −0.876838 | − | 1.51873i | −0.0467356 | − | 0.0809485i | ||||
\(353\) | 15.6132 | + | 27.0429i | 0.831009 | + | 1.43935i | 0.897239 | + | 0.441545i | \(0.145570\pi\) |
−0.0662300 | + | 0.997804i | \(0.521097\pi\) | |||||||
\(354\) | 16.8848 | − | 8.31325i | 0.897414 | − | 0.441844i | ||||
\(355\) | −9.05225 | − | 5.22632i | −0.480444 | − | 0.277384i | ||||
\(356\) | 2.15943 | + | 3.74024i | 0.114449 | + | 0.198232i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.288947 | + | 0.500470i | −0.0152713 | + | 0.0264507i | ||||
\(359\) | 1.39179 | − | 0.803552i | 0.0734560 | − | 0.0424098i | −0.462822 | − | 0.886451i | \(-0.653163\pi\) |
0.536278 | + | 0.844041i | \(0.319830\pi\) | |||||||
\(360\) | 2.63199 | − | 1.08627i | 0.138718 | − | 0.0572515i | ||||
\(361\) | −2.62067 | + | 4.53913i | −0.137930 | + | 0.238902i | ||||
\(362\) | −26.0581 | −1.36958 | ||||||||
\(363\) | −13.6959 | − | 0.906453i | −0.718847 | − | 0.0475765i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.00114 | − | 1.73271i | 0.157087 | − | 0.0906941i | ||||
\(366\) | −0.839001 | − | 1.70407i | −0.0438553 | − | 0.0890730i | ||||
\(367\) | −16.1877 | + | 9.34599i | −0.844992 | + | 0.487856i | −0.858958 | − | 0.512046i | \(-0.828888\pi\) |
0.0139659 | + | 0.999902i | \(0.495554\pi\) | |||||||
\(368\) | 0.888998 | + | 0.513263i | 0.0463422 | + | 0.0267557i | ||||
\(369\) | −24.1265 | − | 3.20765i | −1.25598 | − | 0.166984i | ||||
\(370\) | − | 4.17286i | − | 0.216937i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 17.0957 | − | 8.41708i | 0.886368 | − | 0.436405i | ||||
\(373\) | −18.7682 | + | 32.5075i | −0.971781 | + | 1.68317i | −0.281609 | + | 0.959529i | \(0.590868\pi\) |
−0.690173 | + | 0.723645i | \(0.742465\pi\) | |||||||
\(374\) | 9.59745 | 0.496272 | ||||||||
\(375\) | 6.60731 | + | 13.4199i | 0.341200 | + | 0.692999i | ||||
\(376\) | − | 6.80125i | − | 0.350748i | ||||||
\(377\) | 6.33177 | 0.326103 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.63192 | −0.443392 | −0.221696 | − | 0.975116i | \(-0.571159\pi\) | ||||
−0.221696 | + | 0.975116i | \(0.571159\pi\) | |||||||
\(380\) | − | 3.52051i | − | 0.180599i | ||||||
\(381\) | 14.3108 | + | 29.0661i | 0.733164 | + | 1.48910i | ||||
\(382\) | −1.77964 | −0.0910545 | ||||||||
\(383\) | −4.19997 | + | 7.27456i | −0.214608 | + | 0.371713i | −0.953151 | − | 0.302494i | \(-0.902181\pi\) |
0.738543 | + | 0.674206i | \(0.235514\pi\) | |||||||
\(384\) | 1.55392 | − | 0.765075i | 0.0792980 | − | 0.0390426i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1.48335i | − | 0.0755007i | ||||||
\(387\) | 7.06078 | + | 17.1080i | 0.358920 | + | 0.869647i | ||||
\(388\) | −3.90396 | − | 2.25395i | −0.198193 | − | 0.114427i | ||||
\(389\) | 12.3475 | − | 7.12883i | 0.626043 | − | 0.361446i | −0.153175 | − | 0.988199i | \(-0.548950\pi\) |
0.779218 | + | 0.626753i | \(0.215617\pi\) | |||||||
\(390\) | −0.604338 | − | 1.22745i | −0.0306018 | − | 0.0621544i | ||||
\(391\) | −4.86527 | + | 2.80897i | −0.246047 | + | 0.142056i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.4824 | − | 0.759954i | −0.579209 | − | 0.0383346i | ||||
\(394\) | −2.44809 | −0.123333 | ||||||||
\(395\) | 4.67352 | − | 8.09477i | 0.235150 | − | 0.407292i | ||||
\(396\) | −0.693358 | + | 5.21514i | −0.0348426 | + | 0.262071i | ||||
\(397\) | −22.2162 | + | 12.8265i | −1.11500 | + | 0.643744i | −0.940119 | − | 0.340846i | \(-0.889287\pi\) |
−0.174879 | + | 0.984590i | \(0.555953\pi\) | |||||||
\(398\) | 5.46984 | − | 9.47403i | 0.274178 | − | 0.474890i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.04959 | + | 3.55000i | 0.102480 | + | 0.177500i | ||||
\(401\) | 22.5981 | + | 13.0470i | 1.12849 | + | 0.651536i | 0.943556 | − | 0.331214i | \(-0.107458\pi\) |
0.184938 | + | 0.982750i | \(0.440791\pi\) | |||||||
\(402\) | −22.4512 | + | 11.0539i | −1.11976 | + | 0.551318i | ||||
\(403\) | −4.57810 | − | 7.92951i | −0.228052 | − | 0.394997i | ||||
\(404\) | 6.33624 | + | 10.9747i | 0.315240 | + | 0.546011i | ||||
\(405\) | −8.24528 | − | 2.23189i | −0.409711 | − | 0.110904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.67722 | + | 3.85510i | 0.330978 | + | 0.191090i | ||||
\(408\) | −0.625999 | + | 9.45841i | −0.0309915 | + | 0.468261i | ||||
\(409\) | − | 30.8308i | − | 1.52448i | −0.647292 | − | 0.762242i | \(-0.724099\pi\) | ||
0.647292 | − | 0.762242i | \(-0.275901\pi\) | |||||||
\(410\) | 7.70010i | 0.380281i | ||||||||
\(411\) | −29.3879 | − | 19.6635i | −1.44960 | − | 0.969929i | ||||
\(412\) | −7.33341 | − | 4.23394i | −0.361291 | − | 0.208591i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −1.17487 | − | 2.84666i | −0.0577418 | − | 0.139906i | ||||
\(415\) | −2.28834 | − | 3.96353i | −0.112330 | − | 0.194562i | ||||
\(416\) | −0.416129 | − | 0.720756i | −0.0204024 | − | 0.0353380i | ||||
\(417\) | 18.2561 | + | 12.2152i | 0.894007 | + | 0.598182i | ||||
\(418\) | 5.63337 | + | 3.25243i | 0.275537 | + | 0.159081i | ||||
\(419\) | −13.9168 | − | 24.1047i | −0.679883 | − | 1.17759i | −0.975016 | − | 0.222135i | \(-0.928697\pi\) |
0.295133 | − | 0.955456i | \(-0.404636\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.39960 | − | 12.8165i | 0.360634 | − | 0.624637i | −0.627431 | − | 0.778672i | \(-0.715894\pi\) |
0.988065 | + | 0.154035i | \(0.0492269\pi\) | |||||||
\(422\) | −22.0804 | + | 12.7481i | −1.07486 | + | 0.620569i | ||||
\(423\) | −12.4417 | + | 16.1715i | −0.604934 | + | 0.786286i | ||||
\(424\) | 1.08644 | − | 1.88177i | 0.0527621 | − | 0.0913866i | ||||
\(425\) | −22.4339 | −1.08820 | ||||||||
\(426\) | 8.42582 | + | 17.1134i | 0.408232 | + | 0.829147i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.28657 | − | 0.742804i | 0.0621889 | − | 0.0359048i | ||||
\(429\) | 2.52243 | + | 0.166945i | 0.121784 | + | 0.00806019i | ||||
\(430\) | 5.07085 | − | 2.92766i | 0.244538 | − | 0.141184i | ||||
\(431\) | −24.7338 | − | 14.2801i | −1.19139 | − | 0.687847i | −0.232765 | − | 0.972533i | \(-0.574777\pi\) |
−0.958621 | + | 0.284686i | \(0.908111\pi\) | |||||||
\(432\) | −5.09436 | − | 1.02347i | −0.245103 | − | 0.0492419i | ||||
\(433\) | 18.0220i | 0.866080i | 0.901375 | + | 0.433040i | \(0.142559\pi\) | ||||
−0.901375 | + | 0.433040i | \(0.857441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.3946 | − | 6.95503i | −0.498382 | − | 0.333468i | ||||
\(436\) | −7.60276 | + | 13.1684i | −0.364106 | + | 0.630651i | ||||
\(437\) | −3.80766 | −0.182145 | ||||||||
\(438\) | −6.31028 | − | 0.417642i | −0.301517 | − | 0.0199557i | ||||
\(439\) | − | 24.5104i | − | 1.16982i | −0.811099 | − | 0.584909i | \(-0.801130\pi\) | ||
0.811099 | − | 0.584909i | \(-0.198870\pi\) | |||||||
\(440\) | 1.66444 | 0.0793489 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.55475 | 0.216647 | ||||||||
\(443\) | − | 10.5547i | − | 0.501469i | −0.968056 | − | 0.250734i | \(-0.919328\pi\) | ||
0.968056 | − | 0.250734i | \(-0.0806720\pi\) | |||||||
\(444\) | −4.23477 | + | 6.32904i | −0.200973 | + | 0.300363i | ||||
\(445\) | −4.09908 | −0.194315 | ||||||||
\(446\) | 7.68501 | − | 13.3108i | 0.363896 | − | 0.630286i | ||||
\(447\) | −2.26949 | + | 34.2905i | −0.107343 | + | 1.62188i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.2540i | − | 0.814267i | −0.913369 | − | 0.407133i | \(-0.866528\pi\) | ||
0.913369 | − | 0.407133i | \(-0.133472\pi\) | |||||||
\(450\) | 1.62071 | − | 12.1903i | 0.0764011 | − | 0.574656i | ||||
\(451\) | −12.3213 | − | 7.11373i | −0.580190 | − | 0.334973i | ||||
\(452\) | 17.0031 | − | 9.81676i | 0.799760 | − | 0.461742i | ||||
\(453\) | 1.68062 | − | 2.51176i | 0.0789626 | − | 0.118013i | ||||
\(454\) | 7.22937 | − | 4.17388i | 0.339291 | − | 0.195890i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.57275 | + | 5.33961i | −0.167309 | + | 0.250050i | ||||
\(457\) | 1.37536 | 0.0643368 | 0.0321684 | − | 0.999482i | \(-0.489759\pi\) | ||||
0.0321684 | + | 0.999482i | \(0.489759\pi\) | |||||||
\(458\) | −6.56281 | + | 11.3671i | −0.306660 | + | 0.531151i | ||||
\(459\) | 18.7909 | − | 21.3444i | 0.877084 | − | 0.996269i | ||||
\(460\) | −0.843760 | + | 0.487145i | −0.0393405 | + | 0.0227132i | ||||
\(461\) | −18.7031 | + | 32.3947i | −0.871088 | + | 1.50877i | −0.0102165 | + | 0.999948i | \(0.503252\pi\) |
−0.860872 | + | 0.508822i | \(0.830081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.18312 | − | 8.97742i | −0.240880 | − | 0.417216i | 0.720085 | − | 0.693886i | \(-0.244103\pi\) |
−0.960965 | + | 0.276669i | \(0.910769\pi\) | |||||||
\(464\) | −6.58867 | − | 3.80397i | −0.305871 | − | 0.176595i | ||||
\(465\) | −1.19438 | + | 18.0463i | −0.0553880 | + | 0.836875i | ||||
\(466\) | 5.68315 | + | 9.84350i | 0.263267 | + | 0.455991i | ||||
\(467\) | −18.1423 | − | 31.4234i | −0.839527 | − | 1.45410i | −0.890291 | − | 0.455393i | \(-0.849499\pi\) |
0.0507637 | − | 0.998711i | \(-0.483834\pi\) | |||||||
\(468\) | −0.329053 | + | 2.47500i | −0.0152105 | + | 0.114407i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.59033 | + | 3.22758i | 0.257862 | + | 0.148877i | ||||
\(471\) | −14.7554 | + | 7.26488i | −0.679895 | + | 0.334748i | ||||
\(472\) | 10.8659i | 0.500145i | ||||||||
\(473\) | 10.8189i | 0.497452i | ||||||||
\(474\) | −15.3033 | + | 7.53460i | −0.702902 | + | 0.346076i | ||||
\(475\) | −13.1679 | − | 7.60248i | −0.604184 | − | 0.348826i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.02561 | + | 2.48688i | −0.275894 | + | 0.113867i | ||||
\(478\) | 2.69645 | + | 4.67039i | 0.123333 | + | 0.213619i | ||||
\(479\) | 11.5975 | + | 20.0875i | 0.529905 | + | 0.917822i | 0.999391 | + | 0.0348822i | \(0.0111056\pi\) |
−0.469487 | + | 0.882939i | \(0.655561\pi\) | |||||||
\(480\) | −0.108564 | + | 1.64032i | −0.00495523 | + | 0.0748702i | ||||
\(481\) | 3.16887 | + | 1.82955i | 0.144488 | + | 0.0834202i | ||||
\(482\) | 6.99936 | + | 12.1233i | 0.318812 | + | 0.552199i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.96231 | − | 6.86292i | 0.180105 | − | 0.311951i | ||||
\(485\) | 3.70529 | − | 2.13925i | 0.168249 | − | 0.0971385i | ||||
\(486\) | 10.2407 | + | 11.7528i | 0.464529 | + | 0.533116i | ||||
\(487\) | −14.3695 | + | 24.8887i | −0.651144 | + | 1.12781i | 0.331701 | + | 0.943384i | \(0.392377\pi\) |
−0.982846 | + | 0.184430i | \(0.940956\pi\) | |||||||
\(488\) | 1.09663 | 0.0496419 | ||||||||
\(489\) | 11.4054 | − | 17.0458i | 0.515770 | − | 0.770839i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 21.0143 | − | 12.1326i | 0.948364 | − | 0.547538i | 0.0557919 | − | 0.998442i | \(-0.482232\pi\) |
0.892572 | + | 0.450904i | \(0.148898\pi\) | |||||||
\(492\) | 7.81434 | − | 11.6788i | 0.352298 | − | 0.526523i | ||||
\(493\) | 36.0582 | − | 20.8182i | 1.62398 | − | 0.937605i | ||||
\(494\) | 2.67348 | + | 1.54353i | 0.120285 | + | 0.0694468i | ||||
\(495\) | −3.95758 | − | 3.04479i | −0.177880 | − | 0.136853i | ||||
\(496\) | 11.0016i | 0.493988i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.551570 | + | 8.33384i | −0.0247164 | + | 0.373448i | ||||
\(499\) | −13.2911 | + | 23.0209i | −0.594992 | + | 1.03056i | 0.398556 | + | 0.917144i | \(0.369511\pi\) |
−0.993548 | + | 0.113412i | \(0.963822\pi\) | |||||||
\(500\) | −8.63615 | −0.386221 | ||||||||
\(501\) | −3.33706 | + | 4.98737i | −0.149089 | + | 0.222819i | ||||
\(502\) | 16.5094i | 0.736852i | ||||||||
\(503\) | −33.9478 | −1.51366 | −0.756829 | − | 0.653613i | \(-0.773252\pi\) | ||||
−0.756829 | + | 0.653613i | \(0.773252\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.0276 | −0.535222 | ||||||||
\(506\) | − | 1.80019i | − | 0.0800284i | ||||||
\(507\) | −21.2704 | − | 1.40777i | −0.944652 | − | 0.0625212i | ||||
\(508\) | −18.7051 | −0.829903 | ||||||||
\(509\) | −5.70574 | + | 9.88263i | −0.252902 | + | 0.438040i | −0.964324 | − | 0.264726i | \(-0.914719\pi\) |
0.711421 | + | 0.702766i | \(0.248052\pi\) | |||||||
\(510\) | −7.47732 | − | 5.00309i | −0.331101 | − | 0.221541i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 18.2629 | − | 6.16045i | 0.806326 | − | 0.271990i | ||||
\(514\) | −5.30007 | − | 3.06000i | −0.233776 | − | 0.134971i | ||||
\(515\) | 6.96023 | − | 4.01849i | 0.306704 | − | 0.177076i | ||||
\(516\) | −10.6621 | − | 0.705666i | −0.469374 | − | 0.0310652i | ||||
\(517\) | −10.3292 | + | 5.96359i | −0.454280 | + | 0.262278i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.37160 | + | 4.81687i | 0.104101 | + | 0.211437i | ||||
\(520\) | 0.789907 | 0.0346397 | ||||||||
\(521\) | 9.24387 | − | 16.0108i | 0.404981 | − | 0.701448i | −0.589338 | − | 0.807887i | \(-0.700611\pi\) |
0.994319 | + | 0.106439i | \(0.0339447\pi\) | |||||||
\(522\) | 8.70738 | + | 21.0976i | 0.381112 | + | 0.923416i | ||||
\(523\) | −0.133147 | + | 0.0768726i | −0.00582212 | + | 0.00336140i | −0.502908 | − | 0.864340i | \(-0.667737\pi\) |
0.497086 | + | 0.867701i | \(0.334403\pi\) | |||||||
\(524\) | 3.32193 | − | 5.75375i | 0.145119 | − | 0.251354i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.17923 | − | 14.1668i | −0.356631 | − | 0.617704i | ||||
\(527\) | −52.1428 | − | 30.1047i | −2.27138 | − | 1.31138i | ||||
\(528\) | −2.52447 | − | 1.68913i | −0.109864 | − | 0.0735100i | ||||
\(529\) | −10.9731 | − | 19.0060i | −0.477092 | − | 0.826348i | ||||
\(530\) | 1.03115 | + | 1.78601i | 0.0447904 | + | 0.0775792i | ||||
\(531\) | 19.8773 | − | 25.8362i | 0.862600 | − | 1.12120i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.84746 | − | 3.37603i | −0.253281 | − | 0.146232i | ||||
\(534\) | 6.21714 | + | 4.15990i | 0.269042 | + | 0.180016i | ||||
\(535\) | 1.41001i | 0.0609600i | ||||||||
\(536\) | − | 14.4481i | − | 0.624063i | ||||||
\(537\) | −0.0661020 | + | 0.998756i | −0.00285251 | + | 0.0430995i | ||||
\(538\) | −4.60457 | − | 2.65845i | −0.198517 | − | 0.114614i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 3.25881 | − | 3.70164i | 0.140237 | − | 0.159293i | ||||
\(541\) | 17.9635 | + | 31.1136i | 0.772309 | + | 1.33768i | 0.936294 | + | 0.351216i | \(0.114232\pi\) |
−0.163985 | + | 0.986463i | \(0.552435\pi\) | |||||||
\(542\) | 8.24602 | + | 14.2825i | 0.354197 | + | 0.613487i | ||||
\(543\) | −40.4922 | + | 19.9364i | −1.73769 | + | 0.855553i | ||||
\(544\) | −4.73955 | − | 2.73638i | −0.203206 | − | 0.117321i | ||||
\(545\) | −7.21588 | − | 12.4983i | −0.309094 | − | 0.535367i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.2216 | − | 17.7043i | 0.437044 | − | 0.756983i | −0.560416 | − | 0.828211i | \(-0.689359\pi\) |
0.997460 | + | 0.0712286i | \(0.0226920\pi\) | |||||||
\(548\) | 17.6798 | − | 10.2074i | 0.755244 | − | 0.436040i | ||||
\(549\) | −2.60748 | − | 2.00608i | −0.111284 | − | 0.0856174i | ||||
\(550\) | 3.59432 | − | 6.22554i | 0.153262 | − | 0.265458i | ||||
\(551\) | 28.2199 | 1.20221 | ||||||||
\(552\) | 1.77412 | + | 0.117419i | 0.0755114 | + | 0.00499767i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 12.6682 | − | 7.31402i | 0.538222 | − | 0.310743i | ||||
\(555\) | −3.19255 | − | 6.48428i | −0.135516 | − | 0.275242i | ||||
\(556\) | −10.9829 | + | 6.34099i | −0.465780 | + | 0.268918i | ||||
\(557\) | 18.8181 | + | 10.8646i | 0.797348 | + | 0.460349i | 0.842543 | − | 0.538629i | \(-0.181058\pi\) |
−0.0451952 | + | 0.998978i | \(0.514391\pi\) | |||||||
\(558\) | 20.1255 | − | 26.1589i | 0.851982 | − | 1.10739i | ||||
\(559\) | 5.13441i | 0.217162i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 14.9136 | − | 7.34277i | 0.629654 | − | 0.310012i | ||||
\(562\) | −2.09178 | + | 3.62307i | −0.0882365 | + | 0.152830i | ||||
\(563\) | 20.8519 | 0.878805 | 0.439402 | − | 0.898290i | \(-0.355190\pi\) | ||||
0.439402 | + | 0.898290i | \(0.355190\pi\) | |||||||
\(564\) | −5.20346 | − | 10.5686i | −0.219105 | − | 0.445017i | ||||
\(565\) | 18.6344i | 0.783957i | ||||||||
\(566\) | −9.70591 | −0.407970 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.0131 | −0.462098 | ||||||||
\(569\) | − | 11.6914i | − | 0.490128i | −0.969507 | − | 0.245064i | \(-0.921191\pi\) | ||
0.969507 | − | 0.245064i | \(-0.0788090\pi\) | |||||||
\(570\) | −2.69346 | − | 5.47059i | −0.112816 | − | 0.229138i | ||||
\(571\) | 13.5544 | 0.567235 | 0.283617 | − | 0.958938i | \(-0.408465\pi\) | ||||
0.283617 | + | 0.958938i | \(0.408465\pi\) | |||||||
\(572\) | −0.729755 | + | 1.26397i | −0.0305126 | + | 0.0528494i | ||||
\(573\) | −2.76542 | + | 1.36156i | −0.115527 | + | 0.0568800i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.20792i | 0.175483i | ||||||||
\(576\) | 1.82932 | − | 2.37773i | 0.0762217 | − | 0.0990720i | ||||
\(577\) | −20.0748 | − | 11.5902i | −0.835727 | − | 0.482507i | 0.0200828 | − | 0.999798i | \(-0.493607\pi\) |
−0.855809 | + | 0.517291i | \(0.826940\pi\) | |||||||
\(578\) | 11.2160 | − | 6.47555i | 0.466523 | − | 0.269347i | ||||
\(579\) | −1.13488 | − | 2.30501i | −0.0471639 | − | 0.0957929i | ||||
\(580\) | 6.25339 | − | 3.61040i | 0.259658 | − | 0.149914i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.79087 | − | 0.515633i | −0.322942 | − | 0.0213737i | ||||
\(583\) | −3.81052 | −0.157816 | ||||||||
\(584\) | 1.82561 | − | 3.16204i | 0.0755442 | − | 0.130846i | ||||
\(585\) | −1.87818 | − | 1.44499i | −0.0776533 | − | 0.0597431i | ||||
\(586\) | −1.75591 | + | 1.01377i | −0.0725358 | + | 0.0418786i | ||||
\(587\) | 4.22194 | − | 7.31262i | 0.174258 | − | 0.301824i | −0.765646 | − | 0.643262i | \(-0.777581\pi\) |
0.939904 | + | 0.341438i | \(0.110914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.4040 | − | 35.3408i | −0.840733 | − | 1.45619i | ||||
\(590\) | −8.93131 | − | 5.15650i | −0.367696 | − | 0.212290i | ||||
\(591\) | −3.80413 | + | 1.87297i | −0.156481 | + | 0.0770438i | ||||
\(592\) | −2.19830 | − | 3.80756i | −0.0903494 | − | 0.156490i | ||||
\(593\) | 16.3255 | + | 28.2765i | 0.670407 | + | 1.16118i | 0.977789 | + | 0.209592i | \(0.0672136\pi\) |
−0.307382 | + | 0.951586i | \(0.599453\pi\) | |||||||
\(594\) | 2.91255 | + | 8.63437i | 0.119503 | + | 0.354272i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −17.1827 | − | 9.92046i | −0.703833 | − | 0.406358i | ||||
\(597\) | 1.25133 | − | 18.9067i | 0.0512134 | − | 0.773800i | ||||
\(598\) | − | 0.854335i | − | 0.0349364i | ||||||
\(599\) | − | 47.9900i | − | 1.96082i | −0.196974 | − | 0.980409i | \(-0.563112\pi\) | ||
0.196974 | − | 0.980409i | \(-0.436888\pi\) | |||||||
\(600\) | 5.90091 | + | 3.94831i | 0.240904 | + | 0.161189i | ||||
\(601\) | −20.1783 | − | 11.6499i | −0.823090 | − | 0.475211i | 0.0283909 | − | 0.999597i | \(-0.490962\pi\) |
−0.851481 | + | 0.524386i | \(0.824295\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −26.4302 | + | 34.3537i | −1.07632 | + | 1.39899i | ||||
\(604\) | 0.872422 | + | 1.51108i | 0.0354983 | + | 0.0614849i | ||||
\(605\) | 3.76068 | + | 6.51369i | 0.152893 | + | 0.264819i | ||||
\(606\) | 18.2425 | + | 12.2061i | 0.741049 | + | 0.495838i | ||||
\(607\) | 21.3385 | + | 12.3198i | 0.866101 | + | 0.500044i | 0.866051 | − | 0.499956i | \(-0.166651\pi\) |
5.03773e−5 | 1.00000i | \(0.499984\pi\) | ||||||||
\(608\) | −1.85463 | − | 3.21232i | −0.0752153 | − | 0.130277i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.520411 | + | 0.901378i | −0.0210708 | + | 0.0364957i | ||||
\(611\) | −4.90204 | + | 2.83020i | −0.198315 | + | 0.114497i | ||||
\(612\) | 6.26364 | + | 15.1765i | 0.253193 | + | 0.613474i | ||||
\(613\) | −17.2009 | + | 29.7928i | −0.694736 | + | 1.20332i | 0.275533 | + | 0.961291i | \(0.411146\pi\) |
−0.970270 | + | 0.242027i | \(0.922188\pi\) | |||||||
\(614\) | −9.79004 | −0.395094 | ||||||||
\(615\) | 5.89115 | + | 11.9653i | 0.237554 | + | 0.482488i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −22.4321 | + | 12.9512i | −0.903083 | + | 0.521395i | −0.878199 | − | 0.478295i | \(-0.841255\pi\) |
−0.0248838 | + | 0.999690i | \(0.507922\pi\) | |||||||
\(618\) | −14.6348 | − | 0.968595i | −0.588698 | − | 0.0389626i | ||||
\(619\) | −10.1907 | + | 5.88361i | −0.409599 | + | 0.236482i | −0.690618 | − | 0.723220i | \(-0.742661\pi\) |
0.281018 | + | 0.959702i | \(0.409328\pi\) | |||||||
\(620\) | −9.04287 | − | 5.22090i | −0.363170 | − | 0.209676i | ||||
\(621\) | −4.00357 | − | 3.52461i | −0.160658 | − | 0.141438i | ||||
\(622\) | 13.7039i | 0.549476i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.19806 | − | 0.801626i | −0.0479609 | − | 0.0320907i | ||||
\(625\) | −6.14962 | + | 10.6515i | −0.245985 | + | 0.426058i | ||||
\(626\) | 18.8585 | 0.753739 | ||||||||
\(627\) | 11.2421 | + | 0.744054i | 0.448968 | + | 0.0297146i | ||||
\(628\) | − | 9.49564i | − | 0.378917i | ||||||
\(629\) | 24.0615 | 0.959394 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4353 | 0.654277 | 0.327139 | − | 0.944976i | \(-0.393916\pi\) | ||||
0.327139 | + | 0.944976i | \(0.393916\pi\) | |||||||
\(632\) | − | 9.84819i | − | 0.391740i | ||||||
\(633\) | −24.5578 | + | 36.7027i | −0.976087 | + | 1.45880i | ||||
\(634\) | 7.86426 | 0.312329 | ||||||||
\(635\) | 8.87661 | − | 15.3747i | 0.352258 | − | 0.610128i | ||||
\(636\) | 0.248543 | − | 3.75532i | 0.00985538 | − | 0.148908i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 13.3419i | 0.528209i | ||||||||
\(639\) | 26.1861 | + | 20.1464i | 1.03590 | + | 0.796980i | ||||
\(640\) | −0.821956 | − | 0.474556i | −0.0324907 | − | 0.0187585i | ||||
\(641\) | −13.4048 | + | 7.73929i | −0.529460 | + | 0.305684i | −0.740796 | − | 0.671730i | \(-0.765552\pi\) |
0.211337 | + | 0.977413i | \(0.432218\pi\) | |||||||
\(642\) | 1.43093 | − | 2.13858i | 0.0564743 | − | 0.0844031i | ||||
\(643\) | 3.28185 | − | 1.89478i | 0.129423 | − | 0.0747226i | −0.433890 | − | 0.900966i | \(-0.642860\pi\) |
0.563314 | + | 0.826243i | \(0.309526\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.63981 | − | 8.42893i | 0.222067 | − | 0.331889i | ||||
\(646\) | 20.2999 | 0.798690 | ||||||||
\(647\) | 11.0730 | − | 19.1789i | 0.435323 | − | 0.754002i | −0.561999 | − | 0.827138i | \(-0.689967\pi\) |
0.997322 | + | 0.0731360i | \(0.0233007\pi\) | |||||||
\(648\) | −8.69925 | + | 2.30717i | −0.341739 | + | 0.0906343i | ||||
\(649\) | 16.5024 | − | 9.52765i | 0.647775 | − | 0.373993i | ||||
\(650\) | 1.70579 | − | 2.95451i | 0.0669066 | − | 0.115886i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.92061 | + | 10.2548i | 0.231869 | + | 0.401609i | ||||
\(653\) | −6.54842 | − | 3.78073i | −0.256259 | − | 0.147951i | 0.366368 | − | 0.930470i | \(-0.380601\pi\) |
−0.622627 | + | 0.782519i | \(0.713935\pi\) | |||||||
\(654\) | −1.73928 | + | 26.2792i | −0.0680110 | + | 1.02760i | ||||
\(655\) | 3.15289 | + | 5.46096i | 0.123193 | + | 0.213377i | ||||
\(656\) | 4.05647 | + | 7.02601i | 0.158379 | + | 0.274320i | ||||
\(657\) | −10.1252 | + | 4.17886i | −0.395021 | + | 0.163033i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.2514 | − | 7.07334i | −0.477246 | − | 0.275538i | 0.242022 | − | 0.970271i | \(-0.422189\pi\) |
−0.719268 | + | 0.694733i | \(0.755523\pi\) | |||||||
\(660\) | 2.58640 | − | 1.27342i | 0.100675 | − | 0.0495678i | ||||
\(661\) | − | 22.9586i | − | 0.892985i | −0.894787 | − | 0.446492i | \(-0.852673\pi\) | ||
0.894787 | − | 0.446492i | \(-0.147327\pi\) | |||||||
\(662\) | 22.7350i | 0.883620i | ||||||||
\(663\) | 7.07770 | − | 3.48472i | 0.274875 | − | 0.135335i | ||||
\(664\) | −4.17603 | − | 2.41103i | −0.162062 | − | 0.0935663i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.73830 | + | 13.0747i | −0.0673577 | + | 0.506635i | ||||
\(667\) | −3.90488 | − | 6.76344i | −0.151197 | − | 0.261882i | ||||
\(668\) | −1.73229 | − | 3.00041i | −0.0670242 | − | 0.116089i | ||||
\(669\) | 1.75809 | − | 26.5635i | 0.0679717 | − | 1.02701i | ||||
\(670\) | 11.8757 | + | 6.85644i | 0.458799 | + | 0.264888i | ||||
\(671\) | −0.961563 | − | 1.66548i | −0.0371207 | − | 0.0642950i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.86542 | + | 3.23100i | −0.0719066 | + | 0.124546i | −0.899737 | − | 0.436433i | \(-0.856242\pi\) |
0.827830 | + | 0.560979i | \(0.189575\pi\) | |||||||
\(674\) | 17.4312 | − | 10.0639i | 0.671426 | − | 0.387648i | ||||
\(675\) | −6.80803 | − | 20.1827i | −0.262041 | − | 0.776831i | ||||
\(676\) | 6.15367 | − | 10.6585i | 0.236680 | − | 0.409941i | ||||
\(677\) | 47.5314 | 1.82678 | 0.913390 | − | 0.407087i | \(-0.133455\pi\) | ||||
0.913390 | + | 0.407087i | \(0.133455\pi\) | |||||||
\(678\) | 18.9109 | − | 28.2631i | 0.726269 | − | 1.08544i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.49837 | − | 2.59713i | 0.172505 | − | 0.0995955i | ||||
\(681\) | 8.04052 | − | 12.0169i | 0.308113 | − | 0.460488i | ||||
\(682\) | 16.7085 | − | 9.64666i | 0.639802 | − | 0.369390i | ||||
\(683\) | 28.5275 | + | 16.4704i | 1.09158 | + | 0.630222i | 0.933996 | − | 0.357284i | \(-0.116297\pi\) |
0.157580 | + | 0.987506i | \(0.449631\pi\) | |||||||
\(684\) | −1.46655 | + | 11.0307i | −0.0560749 | + | 0.421771i | ||||
\(685\) | 19.3760i | 0.740320i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.50137 | + | 22.6846i | −0.0572807 | + | 0.865472i | ||||
\(688\) | 3.08463 | − | 5.34273i | 0.117600 | − | 0.203690i | ||||
\(689\) | −1.80839 | −0.0688943 | ||||||||
\(690\) | −0.938431 | + | 1.40252i | −0.0357254 | + | 0.0533931i | ||||
\(691\) | 7.93611i | 0.301904i | 0.988541 | + | 0.150952i | \(0.0482339\pi\) | ||||
−0.988541 | + | 0.150952i | \(0.951766\pi\) | |||||||
\(692\) | −3.09982 | −0.117838 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 22.6395 | 0.859385 | ||||||||
\(695\) | − | 12.0366i | − | 0.456576i | ||||||
\(696\) | −13.1486 | − | 0.870230i | −0.498395 | − | 0.0329860i | ||||
\(697\) | −44.4002 | −1.68178 | ||||||||
\(698\) | 7.70058 | − | 13.3378i | 0.291471 | − | 0.504843i | ||||
\(699\) | 16.3622 | + | 10.9480i | 0.618874 | + | 0.414090i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.1838i | 0.951180i | 0.879667 | + | 0.475590i | \(0.157765\pi\) | ||||
−0.879667 | + | 0.475590i | \(0.842235\pi\) | |||||||
\(702\) | 1.38224 | + | 4.09769i | 0.0521691 | + | 0.154657i | ||||
\(703\) | 14.1233 | + | 8.15406i | 0.532669 | + | 0.307536i | ||||
\(704\) | 1.51873 | − | 0.876838i | 0.0572392 | − | 0.0330471i | ||||
\(705\) | 11.1562 | + | 0.738369i | 0.420168 | + | 0.0278086i | ||||
\(706\) | −27.0429 | + | 15.6132i | −1.01777 | + | 0.587612i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.31325 | + | 16.8848i | 0.312431 | + | 0.634568i | ||||
\(709\) | 21.5021 | 0.807530 | 0.403765 | − | 0.914863i | \(-0.367701\pi\) | ||||
0.403765 | + | 0.914863i | \(0.367701\pi\) | |||||||
\(710\) | 5.22632 | − | 9.05225i | 0.196140 | − | 0.339725i | ||||
\(711\) | −18.0155 | + | 23.4163i | −0.675634 | + | 0.878180i | ||||
\(712\) | −3.74024 | + | 2.15943i | −0.140171 | + | 0.0809280i | ||||
\(713\) | −5.64674 | + | 9.78044i | −0.211472 | + | 0.366280i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.692620 | − | 1.19965i | −0.0259025 | − | 0.0448645i | ||||
\(716\) | −0.500470 | − | 0.288947i | −0.0187035 | − | 0.0107984i | ||||
\(717\) | 7.76326 | + | 5.19441i | 0.289924 | + | 0.193989i | ||||
\(718\) | 0.803552 | + | 1.39179i | 0.0299883 | + | 0.0519412i | ||||
\(719\) | 8.30671 | + | 14.3876i | 0.309788 | + | 0.536569i | 0.978316 | − | 0.207119i | \(-0.0664086\pi\) |
−0.668528 | + | 0.743687i | \(0.733075\pi\) | |||||||
\(720\) | 1.08627 | + | 2.63199i | 0.0404829 | + | 0.0980884i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.53913 | − | 2.62067i | −0.168929 | − | 0.0975312i | ||||
\(723\) | 20.1516 | + | 13.4835i | 0.749447 | + | 0.501457i | ||||
\(724\) | − | 26.0581i | − | 0.968442i | ||||||
\(725\) | − | 31.1863i | − | 1.15823i | ||||||
\(726\) | 0.906453 | − | 13.6959i | 0.0336416 | − | 0.508302i | ||||
\(727\) | 39.4866 | + | 22.7976i | 1.46448 | + | 0.845517i | 0.999213 | − | 0.0396542i | \(-0.0126256\pi\) |
0.465265 | + | 0.885171i | \(0.345959\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.9050 | + | 10.4279i | 0.922408 | + | 0.386218i | ||||
\(730\) | 1.73271 | + | 3.00114i | 0.0641304 | + | 0.111077i | ||||
\(731\) | 16.8814 | + | 29.2395i | 0.624382 | + | 1.08146i | ||||
\(732\) | 1.70407 | − | 0.839001i | 0.0629841 | − | 0.0310104i | ||||
\(733\) | 14.3262 | + | 8.27123i | 0.529150 | + | 0.305505i | 0.740670 | − | 0.671869i | \(-0.234508\pi\) |
−0.211520 | + | 0.977374i | \(0.567841\pi\) | |||||||
\(734\) | −9.34599 | − | 16.1877i | −0.344967 | − | 0.597500i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.513263 | + | 0.888998i | −0.0189191 | + | 0.0327689i | ||||
\(737\) | −21.9427 | + | 12.6686i | −0.808271 | + | 0.466656i | ||||
\(738\) | 3.20765 | − | 24.1265i | 0.118075 | − | 0.888110i | ||||
\(739\) | 7.75506 | − | 13.4322i | 0.285274 | − | 0.494110i | −0.687401 | − | 0.726278i | \(-0.741249\pi\) |
0.972676 | + | 0.232168i | \(0.0745819\pi\) | |||||||
\(740\) | 4.17286 | 0.153397 | ||||||||
\(741\) | 5.33528 | + | 0.353112i | 0.195997 | + | 0.0129719i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.0654 | − | 20.8224i | 1.32311 | − | 0.763899i | 0.338888 | − | 0.940827i | \(-0.389949\pi\) |
0.984224 | + | 0.176928i | \(0.0566160\pi\) | |||||||
\(744\) | 8.41708 | + | 17.0957i | 0.308585 | + | 0.626757i | ||||
\(745\) | 16.3084 | − | 9.41564i | 0.597492 | − | 0.344962i | ||||
\(746\) | −32.5075 | − | 18.7682i | −1.19018 | − | 0.687153i | ||||
\(747\) | 5.51892 | + | 13.3721i | 0.201927 | + | 0.489259i | ||||
\(748\) | 9.59745i | 0.350917i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −13.4199 | + | 6.60731i | −0.490024 | + | 0.241265i | ||||
\(751\) | 6.21569 | − | 10.7659i | 0.226814 | − | 0.392853i | −0.730048 | − | 0.683395i | \(-0.760503\pi\) |
0.956862 | + | 0.290543i | \(0.0938359\pi\) | |||||||
\(752\) | 6.80125 | 0.248016 | ||||||||
\(753\) | 12.6310 | + | 25.6543i | 0.460298 | + | 0.934895i | ||||
\(754\) | 6.33177i | 0.230589i | ||||||||
\(755\) | −1.65605 | −0.0602699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.8661 | 0.903775 | 0.451887 | − | 0.892075i | \(-0.350751\pi\) | ||||
0.451887 | + | 0.892075i | \(0.350751\pi\) | |||||||
\(758\) | − | 8.63192i | − | 0.313526i | ||||||
\(759\) | −1.37728 | − | 2.79735i | −0.0499922 | − | 0.101538i | ||||
\(760\) | 3.52051 | 0.127702 | ||||||||
\(761\) | −5.68277 | + | 9.84285i | −0.206000 | + | 0.356803i | −0.950451 | − | 0.310874i | \(-0.899378\pi\) |
0.744451 | + | 0.667678i | \(0.232711\pi\) | |||||||
\(762\) | −29.0661 | + | 14.3108i | −1.05296 | + | 0.518425i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 1.77964i | − | 0.0643852i | ||||||
\(765\) | −15.4469 | − | 2.05368i | −0.558483 | − | 0.0742509i | ||||
\(766\) | −7.27456 | − | 4.19997i | −0.262841 | − | 0.151751i | ||||
\(767\) | 7.83169 | − | 4.52163i | 0.282786 | − | 0.163266i | ||||
\(768\) | 0.765075 | + | 1.55392i | 0.0276073 | + | 0.0560722i | ||||
\(769\) | 29.8857 | − | 17.2545i | 1.07771 | − | 0.622214i | 0.147429 | − | 0.989073i | \(-0.452900\pi\) |
0.930277 | + | 0.366859i | \(0.119567\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.5770 | − | 0.700033i | −0.380922 | − | 0.0252111i | ||||
\(772\) | 1.48335 | 0.0533871 | ||||||||
\(773\) | −10.6262 | + | 18.4051i | −0.382197 | + | 0.661984i | −0.991376 | − | 0.131048i | \(-0.958166\pi\) |
0.609179 | + | 0.793033i | \(0.291499\pi\) | |||||||
\(774\) | −17.1080 | + | 7.06078i | −0.614933 | + | 0.253795i | ||||
\(775\) | −39.0558 | + | 22.5489i | −1.40293 | + | 0.809980i | ||||
\(776\) | 2.25395 | − | 3.90396i | 0.0809121 | − | 0.140144i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.12883 | + | 12.3475i | 0.255581 | + | 0.442679i | ||||
\(779\) | −26.0614 | − | 15.0465i | −0.933745 | − | 0.539098i | ||||
\(780\) | 1.22745 | − | 0.604338i | 0.0439498 | − | 0.0216388i | ||||
\(781\) | 9.65667 | + | 16.7258i | 0.345543 | + | 0.598498i | ||||
\(782\) | −2.80897 | − | 4.86527i | −0.100448 | − | 0.173982i | ||||
\(783\) | 29.6718 | + | 26.1221i | 1.06038 | + | 0.933528i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.80500 | + | 4.50622i | 0.278572 | + | 0.160834i | ||||
\(786\) | 0.759954 | − | 11.4824i | 0.0271067 | − | 0.409563i | ||||
\(787\) | − | 11.9663i | − | 0.426551i | −0.976992 | − | 0.213276i | \(-0.931587\pi\) | ||
0.976992 | − | 0.213276i | \(-0.0684132\pi\) | |||||||
\(788\) | − | 2.44809i | − | 0.0872096i | ||||||
\(789\) | −23.5485 | − | 15.7564i | −0.838351 | − | 0.560942i | ||||
\(790\) | 8.09477 | + | 4.67352i | 0.287999 | + | 0.166276i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.21514 | − | 0.693358i | −0.185312 | − | 0.0246374i | ||||
\(793\) | −0.456338 | − | 0.790400i | −0.0162050 | − | 0.0280679i | ||||
\(794\) | −12.8265 | − | 22.2162i | −0.455196 | − | 0.788422i | ||||
\(795\) | 2.96876 | + | 1.98640i | 0.105291 | + | 0.0704504i | ||||
\(796\) | 9.47403 | + | 5.46984i | 0.335798 | + | 0.193873i | ||||
\(797\) | −2.86820 | − | 4.96786i | −0.101597 | − | 0.175971i | 0.810746 | − | 0.585398i | \(-0.199062\pi\) |
−0.912343 | + | 0.409427i | \(0.865728\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.6108 | + | 32.2348i | −0.658403 | + | 1.14039i | ||||
\(800\) | −3.55000 | + | 2.04959i | −0.125511 | + | 0.0724640i | ||||
\(801\) | 12.8436 | + | 1.70756i | 0.453805 | + | 0.0603338i | ||||
\(802\) | −13.0470 | + | 22.5981i | −0.460706 | + | 0.797966i | ||||
\(803\) | −6.40305 | −0.225959 | ||||||||
\(804\) | −11.0539 | − | 22.4512i | −0.389841 | − | 0.791792i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.92951 | − | 4.57810i | 0.279305 | − | 0.161257i | ||||
\(807\) | −9.18903 | − | 0.608170i | −0.323469 | − | 0.0214086i | ||||
\(808\) | −10.9747 | + | 6.33624i | −0.386088 | + | 0.222908i | ||||
\(809\) | 27.5185 | + | 15.8878i | 0.967500 | + | 0.558586i | 0.898473 | − | 0.439028i | \(-0.144677\pi\) |
0.0690269 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(810\) | 2.23189 | − | 8.24528i | 0.0784206 | − | 0.289710i | ||||
\(811\) | − | 41.2541i | − | 1.44863i | −0.689471 | − | 0.724314i | \(-0.742157\pi\) | ||
0.689471 | − | 0.724314i | \(-0.257843\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.7408 | + | 15.8850i | 0.832627 | + | 0.557113i | ||||
\(814\) | −3.85510 | + | 6.67722i | −0.135121 | + | 0.234037i | ||||
\(815\) | −11.2386 | −0.393673 | ||||||||
\(816\) | −9.45841 | − | 0.625999i | −0.331110 | − | 0.0219143i | ||||
\(817\) | 22.8834i | 0.800589i | ||||||||
\(818\) | 30.8308 | 1.07797 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.70010 | −0.268899 | ||||||||
\(821\) | − | 13.5045i | − | 0.471309i | −0.971837 | − | 0.235655i | \(-0.924277\pi\) | ||
0.971837 | − | 0.235655i | \(-0.0757234\pi\) | |||||||
\(822\) | 19.6635 | − | 29.3879i | 0.685843 | − | 1.02502i | ||||
\(823\) | −18.9133 | −0.659277 | −0.329638 | − | 0.944107i | \(-0.606927\pi\) | ||||
−0.329638 | + | 0.944107i | \(0.606927\pi\) | |||||||
\(824\) | 4.23394 | − | 7.33341i | 0.147496 | − | 0.255471i | ||||
\(825\) | 0.822268 | − | 12.4239i | 0.0286277 | − | 0.432545i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 33.8495i | 1.17706i | 0.808475 | + | 0.588531i | \(0.200293\pi\) | ||||
−0.808475 | + | 0.588531i | \(0.799707\pi\) | |||||||
\(828\) | 2.84666 | − | 1.17487i | 0.0989284 | − | 0.0408296i | ||||
\(829\) | −21.8963 | − | 12.6418i | −0.760489 | − | 0.439068i | 0.0689825 | − | 0.997618i | \(-0.478025\pi\) |
−0.829471 | + | 0.558550i | \(0.811358\pi\) | |||||||
\(830\) | 3.96353 | − | 2.28834i | 0.137576 | − | 0.0794296i | ||||
\(831\) | 14.0896 | − | 21.0575i | 0.488764 | − | 0.730478i | ||||
\(832\) | 0.720756 | − | 0.416129i | 0.0249877 | − | 0.0144267i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.2152 | + | 18.2561i | −0.422979 | + | 0.632159i | ||||
\(835\) | 3.28827 | 0.113795 | ||||||||
\(836\) | −3.25243 | + | 5.63337i | −0.112487 | + | 0.194834i | ||||
\(837\) | 11.2599 | − | 56.0463i | 0.389199 | − | 1.93724i | ||||
\(838\) | 24.1047 | − | 13.9168i | 0.832683 | − | 0.480750i | ||||
\(839\) | −1.28248 | + | 2.22133i | −0.0442763 | + | 0.0766888i | −0.887314 | − | 0.461165i | \(-0.847432\pi\) |
0.843038 | + | 0.537854i | \(0.180765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4404 | + | 25.0114i | 0.497943 | + | 0.862463i | ||||
\(842\) | 12.8165 | + | 7.39960i | 0.441685 | + | 0.255007i | ||||
\(843\) | −0.478535 | + | 7.23033i | −0.0164816 | + | 0.249026i | ||||
\(844\) | −12.7481 | − | 22.0804i | −0.438808 | − | 0.760038i | ||||
\(845\) | 5.84053 | + | 10.1161i | 0.200920 | + | 0.348004i | ||||
\(846\) | −16.1715 | − | 12.4417i | −0.555988 | − | 0.427753i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.88177 | + | 1.08644i | 0.0646201 | + | 0.0373084i | ||||
\(849\) | −15.0822 | + | 7.42575i | −0.517619 | + | 0.254851i | ||||
\(850\) | − | 22.4339i | − | 0.769475i | ||||||
\(851\) | − | 4.51322i | − | 0.154711i | ||||||
\(852\) | −17.1134 | + | 8.42582i | −0.586295 | + | 0.288664i | ||||
\(853\) | 1.98108 | + | 1.14378i | 0.0678310 | + | 0.0391622i | 0.533532 | − | 0.845780i | \(-0.320864\pi\) |
−0.465701 | + | 0.884942i | \(0.654198\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.37082 | − | 6.44015i | −0.286276 | − | 0.220248i | ||||
\(856\) | 0.742804 | + | 1.28657i | 0.0253885 | + | 0.0439742i | ||||
\(857\) | −10.3313 | − | 17.8943i | −0.352911 | − | 0.611259i | 0.633847 | − | 0.773458i | \(-0.281475\pi\) |
−0.986758 | + | 0.162199i | \(0.948141\pi\) | |||||||
\(858\) | −0.166945 | + | 2.52243i | −0.00569942 | + | 0.0861143i | ||||
\(859\) | −14.3879 | − | 8.30688i | −0.490910 | − | 0.283427i | 0.234042 | − | 0.972226i | \(-0.424805\pi\) |
−0.724952 | + | 0.688800i | \(0.758138\pi\) | |||||||
\(860\) | 2.92766 | + | 5.07085i | 0.0998323 | + | 0.172915i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.2801 | − | 24.7338i | 0.486381 | − | 0.842437i | ||||
\(863\) | −5.54125 | + | 3.19924i | −0.188626 | + | 0.108904i | −0.591339 | − | 0.806423i | \(-0.701401\pi\) |
0.402713 | + | 0.915326i | \(0.368067\pi\) | |||||||
\(864\) | 1.02347 | − | 5.09436i | 0.0348193 | − | 0.173314i | ||||
\(865\) | 1.47104 | − | 2.54792i | 0.0500169 | − | 0.0866318i | ||||
\(866\) | −18.0220 | −0.612411 | ||||||||
\(867\) | 12.4744 | − | 18.6435i | 0.423654 | − | 0.633168i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.9567 | + | 8.63526i | −0.507372 | + | 0.292931i | ||||
\(870\) | 6.95503 | − | 10.3946i | 0.235798 | − | 0.352409i | ||||
\(871\) | −10.4136 | + | 6.01228i | −0.352850 | + | 0.203718i | ||||
\(872\) | −13.1684 | − | 7.60276i | −0.445937 | − | 0.257462i | ||||
\(873\) | −12.5009 | + | 5.15934i | −0.423090 | + | 0.174617i | ||||
\(874\) | − | 3.80766i | − | 0.128796i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.417642 | − | 6.31028i | 0.0141108 | − | 0.213205i | ||||
\(877\) | −5.08369 | + | 8.80522i | −0.171664 | + | 0.297331i | −0.939002 | − | 0.343912i | \(-0.888248\pi\) |
0.767338 | + | 0.641243i | \(0.221581\pi\) | |||||||
\(878\) | 24.5104 | 0.827187 | ||||||||
\(879\) | −1.95292 | + | 2.91872i | −0.0658704 | + | 0.0984460i | ||||
\(880\) | 1.66444i | 0.0561081i | ||||||||
\(881\) | 47.2933 | 1.59335 | 0.796675 | − | 0.604407i | \(-0.206590\pi\) | ||||
0.796675 | + | 0.604407i | \(0.206590\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5706 | −0.557645 | −0.278822 | − | 0.960343i | \(-0.589944\pi\) | ||||
−0.278822 | + | 0.960343i | \(0.589944\pi\) | |||||||
\(884\) | 4.55475i | 0.153193i | ||||||||
\(885\) | −17.8236 | − | 1.17965i | −0.599135 | − | 0.0396533i | ||||
\(886\) | 10.5547 | 0.354592 | ||||||||
\(887\) | −11.3965 | + | 19.7393i | −0.382656 | + | 0.662780i | −0.991441 | − | 0.130556i | \(-0.958324\pi\) |
0.608785 | + | 0.793335i | \(0.291657\pi\) | |||||||
\(888\) | −6.32904 | − | 4.23477i | −0.212389 | − | 0.142110i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 4.09908i | − | 0.137402i | ||||||
\(891\) | 11.1318 | + | 11.1888i | 0.372929 | + | 0.374838i | ||||
\(892\) | 13.3108 | + | 7.68501i | 0.445679 | + | 0.257313i | ||||
\(893\) | −21.8478 | + | 12.6138i | −0.731108 | + | 0.422105i | ||||
\(894\) | −34.2905 | − | 2.26949i | −1.14684 | − | 0.0759032i | ||||
\(895\) | 0.475003 | − | 0.274243i | 0.0158776 | − | 0.00916694i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.653630 | − | 1.32757i | −0.0218241 | − | 0.0443261i | ||||
\(898\) | 17.2540 | 0.575774 | ||||||||
\(899\) | 41.8499 | − | 72.4862i | 1.39577 | − | 2.41755i | ||||
\(900\) | 12.1903 | + | 1.62071i | 0.406343 | + | 0.0540237i | ||||
\(901\) | −10.2985 | + | 5.94581i | −0.343091 | + | 0.198084i | ||||
\(902\) | 7.11373 | − | 12.3213i | 0.236861 | − | 0.410256i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.81676 | + | 17.0031i | 0.326501 | + | 0.565516i | ||||
\(905\) | 21.4186 | + | 12.3660i | 0.711979 | + | 0.411061i | ||||
\(906\) | 2.51176 | + | 1.68062i | 0.0834476 | + | 0.0558350i | ||||
\(907\) | 24.0653 | + | 41.6824i | 0.799077 | + | 1.38404i | 0.920218 | + | 0.391406i | \(0.128011\pi\) |
−0.121142 | + | 0.992635i | \(0.538656\pi\) | |||||||
\(908\) | 4.17388 | + | 7.22937i | 0.138515 | + | 0.239915i | ||||
\(909\) | 37.6858 | + | 5.01037i | 1.24996 | + | 0.166184i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.5958 | + | 11.8910i | 0.682368 | + | 0.393966i | 0.800747 | − | 0.599003i | \(-0.204436\pi\) |
−0.118378 | + | 0.992969i | \(0.537770\pi\) | |||||||
\(912\) | −5.33961 | − | 3.57275i | −0.176812 | − | 0.118305i | ||||
\(913\) | 8.45635i | 0.279864i | ||||||||
\(914\) | 1.37536i | 0.0454930i | ||||||||
\(915\) | −0.119054 | + | 1.79882i | −0.00393580 | + | 0.0594672i | ||||
\(916\) | −11.3671 | − | 6.56281i | −0.375580 | − | 0.216841i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 21.3444 | + | 18.7909i | 0.704469 | + | 0.620192i | ||||
\(919\) | −10.9692 | − | 18.9992i | −0.361841 | − | 0.626727i | 0.626423 | − | 0.779483i | \(-0.284518\pi\) |
−0.988264 | + | 0.152757i | \(0.951185\pi\) | |||||||
\(920\) | −0.487145 | − | 0.843760i | −0.0160607 | − | 0.0278179i | ||||
\(921\) | −15.2129 | + | 7.49011i | −0.501283 | + | 0.246808i | ||||
\(922\) | −32.3947 | − | 18.7031i | −1.06686 | − | 0.615953i | ||||
\(923\) | 4.58286 | + | 7.93774i | 0.150847 | + | 0.261274i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.01122 | − | 15.6079i | 0.296287 | − | 0.513184i | ||||
\(926\) | 8.97742 | − | 5.18312i | 0.295016 | − | 0.170328i | ||||
\(927\) | −23.4823 | + | 9.69160i | −0.771261 | + | 0.318314i | ||||
\(928\) | 3.80397 | − | 6.58867i | 0.124871 | − | 0.216284i | ||||
\(929\) | −50.4538 | −1.65534 | −0.827668 | − | 0.561217i | \(-0.810333\pi\) | ||||
−0.827668 | + | 0.561217i | \(0.810333\pi\) | |||||||
\(930\) | −18.0463 | − | 1.19438i | −0.591760 | − | 0.0391653i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −9.84350 | + | 5.68315i | −0.322435 | + | 0.186158i | ||||
\(933\) | 10.4845 | + | 21.2947i | 0.343247 | + | 0.697158i | ||||
\(934\) | 31.4234 | − | 18.1423i | 1.02821 | − | 0.593635i | ||||
\(935\) | −7.88868 | − | 4.55453i | −0.257987 | − | 0.148949i | ||||
\(936\) | −2.47500 | − | 0.329053i | −0.0808978 | − | 0.0107554i | ||||
\(937\) | − | 42.6251i | − | 1.39250i | −0.717799 | − | 0.696250i | \(-0.754850\pi\) | ||
0.717799 | − | 0.696250i | \(-0.245150\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.3046 | − | 14.4282i | 0.956320 | − | 0.470847i | ||||
\(940\) | −3.22758 | + | 5.59033i | −0.105272 | + | 0.182336i | ||||
\(941\) | −55.0404 | −1.79427 | −0.897133 | − | 0.441761i | \(-0.854354\pi\) | ||||
−0.897133 | + | 0.441761i | \(0.854354\pi\) | |||||||
\(942\) | −7.26488 | − | 14.7554i | −0.236703 | − | 0.480758i | ||||
\(943\) | 8.32815i | 0.271202i | ||||||||
\(944\) | −10.8659 | −0.353656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.8189 | −0.351752 | ||||||||
\(947\) | 25.6884i | 0.834760i | 0.908732 | + | 0.417380i | \(0.137052\pi\) | ||||
−0.908732 | + | 0.417380i | \(0.862948\pi\) | |||||||
\(948\) | −7.53460 | − | 15.3033i | −0.244712 | − | 0.497027i | ||||
\(949\) | −3.03875 | −0.0986421 | ||||||||
\(950\) | 7.60248 | − | 13.1679i | 0.246657 | − | 0.427223i | ||||
\(951\) | 12.2204 | − | 6.01675i | 0.396274 | − | 0.195106i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.3463i | 0.561903i | 0.959722 | + | 0.280952i | \(0.0906500\pi\) | ||||
−0.959722 | + | 0.280952i | \(0.909350\pi\) | |||||||
\(954\) | −2.48688 | − | 6.02561i | −0.0805158 | − | 0.195086i | ||||
\(955\) | 1.46279 | + | 0.844541i | 0.0473347 | + | 0.0273287i | ||||
\(956\) | −4.67039 | + | 2.69645i | −0.151051 | + | 0.0872094i | ||||
\(957\) | 10.2075 | + | 20.7321i | 0.329962 | + | 0.670175i | ||||
\(958\) | −20.0875 | + | 11.5975i | −0.648998 | + | 0.374699i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.64032 | − | 0.108564i | −0.0529412 | − | 0.00350388i | ||||
\(961\) | −90.0362 | −2.90439 | ||||||||
\(962\) | −1.82955 | + | 3.16887i | −0.0589870 | + | 0.102169i | ||||
\(963\) | 0.587371 | − | 4.41795i | 0.0189278 | − | 0.142366i | ||||
\(964\) | −12.1233 | + | 6.99936i | −0.390464 | + | 0.225434i | ||||
\(965\) | −0.703935 | + | 1.21925i | −0.0226605 | + | 0.0392491i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.61334 | + | 4.52644i | 0.0840393 | + | 0.145560i | 0.904981 | − | 0.425451i | \(-0.139885\pi\) |
−0.820942 | + | 0.571011i | \(0.806551\pi\) | |||||||
\(968\) | 6.86292 | + | 3.96231i | 0.220583 | + | 0.127353i | ||||
\(969\) | 31.5444 | − | 15.5310i | 1.01335 | − | 0.498927i | ||||
\(970\) | 2.13925 | + | 3.70529i | 0.0686873 | + | 0.118970i | ||||
\(971\) | 14.2195 | + | 24.6289i | 0.456326 | + | 0.790379i | 0.998763 | − | 0.0497167i | \(-0.0158319\pi\) |
−0.542438 | + | 0.840096i | \(0.682499\pi\) | |||||||
\(972\) | −11.7528 | + | 10.2407i | −0.376970 | + | 0.328472i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.8887 | − | 14.3695i | −0.797485 | − | 0.460428i | ||||
\(975\) | 0.390231 | − | 5.89613i | 0.0124974 | − | 0.188827i | ||||
\(976\) | 1.09663i | 0.0351021i | ||||||||
\(977\) | 24.3217i | 0.778119i | 0.921213 | + | 0.389059i | \(0.127200\pi\) | ||||
−0.921213 | + | 0.389059i | \(0.872800\pi\) | |||||||
\(978\) | 17.0458 | + | 11.4054i | 0.545065 | + | 0.364704i | ||||
\(979\) | 6.55917 | + | 3.78694i | 0.209632 | + | 0.121031i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.4029 | + | 42.1665i | 0.555632 | + | 1.34627i | ||||
\(982\) | 12.1326 | + | 21.0143i | 0.387168 | + | 0.670595i | ||||
\(983\) | 13.4186 | + | 23.2417i | 0.427987 | + | 0.741295i | 0.996694 | − | 0.0812449i | \(-0.0258896\pi\) |
−0.568707 | + | 0.822540i | \(0.692556\pi\) | |||||||
\(984\) | 11.6788 | + | 7.81434i | 0.372308 | + | 0.249112i | ||||
\(985\) | 2.01222 | + | 1.16176i | 0.0641147 | + | 0.0370166i | ||||
\(986\) | 20.8182 | + | 36.0582i | 0.662987 | + | 1.14833i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.54353 | + | 2.67348i | −0.0491063 | + | 0.0850547i | ||||
\(989\) | 5.48446 | − | 3.16645i | 0.174396 | − | 0.100687i | ||||
\(990\) | 3.04479 | − | 3.95758i | 0.0967697 | − | 0.125780i | ||||
\(991\) | −3.51093 | + | 6.08111i | −0.111528 | + | 0.193173i | −0.916387 | − | 0.400294i | \(-0.868908\pi\) |
0.804858 | + | 0.593467i | \(0.202241\pi\) | |||||||
\(992\) | −11.0016 | −0.349303 | ||||||||
\(993\) | 17.3940 | + | 35.3283i | 0.551980 | + | 1.12111i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.99193 | + | 5.19149i | −0.285063 | + | 0.164581i | ||||
\(996\) | −8.33384 | − | 0.551570i | −0.264068 | − | 0.0174772i | ||||
\(997\) | 9.60463 | − | 5.54524i | 0.304182 | − | 0.175619i | −0.340138 | − | 0.940375i | \(-0.610474\pi\) |
0.644320 | + | 0.764756i | \(0.277141\pi\) | |||||||
\(998\) | −23.0209 | − | 13.2911i | −0.728713 | − | 0.420723i | ||||
\(999\) | 7.30197 | + | 21.6470i | 0.231024 | + | 0.684880i |
(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 | 882.2.l.c.227.19 | 48 | ||
3.2 | odd | 2 | 2646.2.l.c.521.5 | 48 | |||
7.2 | even | 3 | 882.2.t.c.803.13 | 48 | |||
7.3 | odd | 6 | 882.2.m.c.587.3 | yes | 48 | ||
7.4 | even | 3 | 882.2.m.c.587.10 | yes | 48 | ||
7.5 | odd | 6 | 882.2.t.c.803.24 | 48 | |||
7.6 | odd | 2 | inner | 882.2.l.c.227.18 | 48 | ||
9.4 | even | 3 | 2646.2.t.c.2285.7 | 48 | |||
9.5 | odd | 6 | 882.2.t.c.815.24 | 48 | |||
21.2 | odd | 6 | 2646.2.t.c.1979.8 | 48 | |||
21.5 | even | 6 | 2646.2.t.c.1979.7 | 48 | |||
21.11 | odd | 6 | 2646.2.m.c.1763.15 | 48 | |||
21.17 | even | 6 | 2646.2.m.c.1763.16 | 48 | |||
21.20 | even | 2 | 2646.2.l.c.521.6 | 48 | |||
63.4 | even | 3 | 2646.2.m.c.881.16 | 48 | |||
63.5 | even | 6 | inner | 882.2.l.c.509.7 | 48 | ||
63.13 | odd | 6 | 2646.2.t.c.2285.8 | 48 | |||
63.23 | odd | 6 | inner | 882.2.l.c.509.6 | 48 | ||
63.31 | odd | 6 | 2646.2.m.c.881.15 | 48 | |||
63.32 | odd | 6 | 882.2.m.c.293.3 | ✓ | 48 | ||
63.40 | odd | 6 | 2646.2.l.c.1097.5 | 48 | |||
63.41 | even | 6 | 882.2.t.c.815.13 | 48 | |||
63.58 | even | 3 | 2646.2.l.c.1097.6 | 48 | |||
63.59 | even | 6 | 882.2.m.c.293.10 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
882.2.l.c.227.18 | 48 | 7.6 | odd | 2 | inner | ||
882.2.l.c.227.19 | 48 | 1.1 | even | 1 | trivial | ||
882.2.l.c.509.6 | 48 | 63.23 | odd | 6 | inner | ||
882.2.l.c.509.7 | 48 | 63.5 | even | 6 | inner | ||
882.2.m.c.293.3 | ✓ | 48 | 63.32 | odd | 6 | ||
882.2.m.c.293.10 | yes | 48 | 63.59 | even | 6 | ||
882.2.m.c.587.3 | yes | 48 | 7.3 | odd | 6 | ||
882.2.m.c.587.10 | yes | 48 | 7.4 | even | 3 | ||
882.2.t.c.803.13 | 48 | 7.2 | even | 3 | |||
882.2.t.c.803.24 | 48 | 7.5 | odd | 6 | |||
882.2.t.c.815.13 | 48 | 63.41 | even | 6 | |||
882.2.t.c.815.24 | 48 | 9.5 | odd | 6 | |||
2646.2.l.c.521.5 | 48 | 3.2 | odd | 2 | |||
2646.2.l.c.521.6 | 48 | 21.20 | even | 2 | |||
2646.2.l.c.1097.5 | 48 | 63.40 | odd | 6 | |||
2646.2.l.c.1097.6 | 48 | 63.58 | even | 3 | |||
2646.2.m.c.881.15 | 48 | 63.31 | odd | 6 | |||
2646.2.m.c.881.16 | 48 | 63.4 | even | 3 | |||
2646.2.m.c.1763.15 | 48 | 21.11 | odd | 6 | |||
2646.2.m.c.1763.16 | 48 | 21.17 | even | 6 | |||
2646.2.t.c.1979.7 | 48 | 21.5 | even | 6 | |||
2646.2.t.c.1979.8 | 48 | 21.2 | odd | 6 | |||
2646.2.t.c.2285.7 | 48 | 9.4 | even | 3 | |||
2646.2.t.c.2285.8 | 48 | 63.13 | odd | 6 |