Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,2,Mod(55,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.55");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.b (of order \(2\), degree \(1\), 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: | \(0.670743376979\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2312.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.2 | ||
Root | \(1.28078 - 0.599676i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.2.b.a.55.1 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28078 | + | 0.599676i | −0.905646 | + | 0.424035i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.28078 | − | 1.53610i | 0.640388 | − | 0.768051i | ||||
\(5\) | 3.33513i | 1.49152i | 0.666217 | + | 0.745758i | \(0.267913\pi\) | ||||
−0.666217 | + | 0.745758i | \(0.732087\pi\) | |||||||
\(6\) | 1.28078 | − | 0.599676i | 0.522875 | − | 0.244817i | ||||
\(7\) | −1.56155 | + | 2.13578i | −0.590211 | + | 0.807249i | ||||
\(8\) | −0.719224 | + | 2.73546i | −0.254284 | + | 0.967130i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −2.00000 | − | 4.27156i | −0.632456 | − | 1.35079i | ||||
\(11\) | 0.936426i | 0.282343i | 0.989985 | + | 0.141172i | \(0.0450869\pi\) | ||||
−0.989985 | + | 0.141172i | \(0.954913\pi\) | |||||||
\(12\) | −1.28078 | + | 1.53610i | −0.369728 | + | 0.443435i | ||||
\(13\) | 1.87285i | 0.519436i | 0.965685 | + | 0.259718i | \(0.0836296\pi\) | ||||
−0.965685 | + | 0.259718i | \(0.916370\pi\) | |||||||
\(14\) | 0.719224 | − | 3.67188i | 0.192221 | − | 0.981352i | ||||
\(15\) | − | 3.33513i | − | 0.861127i | ||||||
\(16\) | −0.719224 | − | 3.93481i | −0.179806 | − | 0.983702i | ||||
\(17\) | − | 5.20798i | − | 1.26312i | −0.775326 | − | 0.631561i | \(-0.782415\pi\) | ||
0.775326 | − | 0.631561i | \(-0.217585\pi\) | |||||||
\(18\) | −1.28078 | + | 0.599676i | −0.301882 | + | 0.141345i | ||||
\(19\) | 7.12311 | 1.63415 | 0.817076 | − | 0.576530i | \(-0.195593\pi\) | ||||
0.817076 | + | 0.576530i | \(0.195593\pi\) | |||||||
\(20\) | 5.12311 | + | 4.27156i | 1.14556 | + | 0.955149i | ||||
\(21\) | 1.56155 | − | 2.13578i | 0.340759 | − | 0.466065i | ||||
\(22\) | −0.561553 | − | 1.19935i | −0.119723 | − | 0.255703i | ||||
\(23\) | − | 0.936426i | − | 0.195258i | −0.995223 | − | 0.0976292i | \(-0.968874\pi\) | ||
0.995223 | − | 0.0976292i | \(-0.0311259\pi\) | |||||||
\(24\) | 0.719224 | − | 2.73546i | 0.146811 | − | 0.558373i | ||||
\(25\) | −6.12311 | −1.22462 | ||||||||
\(26\) | −1.12311 | − | 2.39871i | −0.220259 | − | 0.470425i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.28078 | + | 5.13416i | 0.242044 | + | 0.970265i | ||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 2.00000 | + | 4.27156i | 0.365148 | + | 0.779876i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 3.28078 | + | 4.60831i | 0.579965 | + | 0.814642i | ||||
\(33\) | − | 0.936426i | − | 0.163011i | ||||||
\(34\) | 3.12311 | + | 6.67026i | 0.535608 | + | 1.14394i | ||||
\(35\) | −7.12311 | − | 5.20798i | −1.20402 | − | 0.880310i | ||||
\(36\) | 1.28078 | − | 1.53610i | 0.213463 | − | 0.256017i | ||||
\(37\) | 1.12311 | 0.184637 | 0.0923187 | − | 0.995730i | \(-0.470572\pi\) | ||||
0.0923187 | + | 0.995730i | \(0.470572\pi\) | |||||||
\(38\) | −9.12311 | + | 4.27156i | −1.47996 | + | 0.692938i | ||||
\(39\) | − | 1.87285i | − | 0.299896i | ||||||
\(40\) | −9.12311 | − | 2.39871i | −1.44249 | − | 0.379269i | ||||
\(41\) | − | 1.46228i | − | 0.228370i | −0.993460 | − | 0.114185i | \(-0.963574\pi\) | ||
0.993460 | − | 0.114185i | \(-0.0364256\pi\) | |||||||
\(42\) | −0.719224 | + | 3.67188i | −0.110979 | + | 0.566584i | ||||
\(43\) | 9.06897i | 1.38300i | 0.722374 | + | 0.691502i | \(0.243051\pi\) | ||||
−0.722374 | + | 0.691502i | \(0.756949\pi\) | |||||||
\(44\) | 1.43845 | + | 1.19935i | 0.216854 | + | 0.180809i | ||||
\(45\) | 3.33513i | 0.497172i | ||||||||
\(46\) | 0.561553 | + | 1.19935i | 0.0827964 | + | 0.176835i | ||||
\(47\) | 6.24621 | 0.911104 | 0.455552 | − | 0.890209i | \(-0.349442\pi\) | ||||
0.455552 | + | 0.890209i | \(0.349442\pi\) | |||||||
\(48\) | 0.719224 | + | 3.93481i | 0.103811 | + | 0.567941i | ||||
\(49\) | −2.12311 | − | 6.67026i | −0.303301 | − | 0.952895i | ||||
\(50\) | 7.84233 | − | 3.67188i | 1.10907 | − | 0.519283i | ||||
\(51\) | 5.20798i | 0.729264i | ||||||||
\(52\) | 2.87689 | + | 2.39871i | 0.398953 | + | 0.332641i | ||||
\(53\) | 12.2462 | 1.68215 | 0.841073 | − | 0.540921i | \(-0.181924\pi\) | ||||
0.841073 | + | 0.540921i | \(0.181924\pi\) | |||||||
\(54\) | 1.28078 | − | 0.599676i | 0.174292 | − | 0.0816056i | ||||
\(55\) | −3.12311 | −0.421119 | ||||||||
\(56\) | −4.71922 | − | 5.80766i | −0.630633 | − | 0.776081i | ||||
\(57\) | −7.12311 | −0.943478 | ||||||||
\(58\) | 2.56155 | − | 1.19935i | 0.336348 | − | 0.157483i | ||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | −5.12311 | − | 4.27156i | −0.661390 | − | 0.551456i | ||||
\(61\) | 4.79741i | 0.614246i | 0.951670 | + | 0.307123i | \(0.0993662\pi\) | ||||
−0.951670 | + | 0.307123i | \(0.900634\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.56155 | + | 2.13578i | −0.196737 | + | 0.269083i | ||||
\(64\) | −6.96543 | − | 3.93481i | −0.870679 | − | 0.491851i | ||||
\(65\) | −6.24621 | −0.774747 | ||||||||
\(66\) | 0.561553 | + | 1.19935i | 0.0691224 | + | 0.147630i | ||||
\(67\) | − | 10.9418i | − | 1.33676i | −0.743822 | − | 0.668378i | \(-0.766989\pi\) | ||
0.743822 | − | 0.668378i | \(-0.233011\pi\) | |||||||
\(68\) | −8.00000 | − | 6.67026i | −0.970143 | − | 0.808888i | ||||
\(69\) | 0.936426i | 0.112732i | ||||||||
\(70\) | 12.2462 | + | 2.39871i | 1.46370 | + | 0.286700i | ||||
\(71\) | − | 3.86098i | − | 0.458215i | −0.973401 | − | 0.229107i | \(-0.926419\pi\) | ||
0.973401 | − | 0.229107i | \(-0.0735807\pi\) | |||||||
\(72\) | −0.719224 | + | 2.73546i | −0.0847613 | + | 0.322377i | ||||
\(73\) | 6.67026i | 0.780695i | 0.920668 | + | 0.390348i | \(0.127645\pi\) | ||||
−0.920668 | + | 0.390348i | \(0.872355\pi\) | |||||||
\(74\) | −1.43845 | + | 0.673500i | −0.167216 | + | 0.0782928i | ||||
\(75\) | 6.12311 | 0.707035 | ||||||||
\(76\) | 9.12311 | − | 10.9418i | 1.04649 | − | 1.25511i | ||||
\(77\) | −2.00000 | − | 1.46228i | −0.227921 | − | 0.166642i | ||||
\(78\) | 1.12311 | + | 2.39871i | 0.127167 | + | 0.271600i | ||||
\(79\) | − | 2.39871i | − | 0.269875i | −0.990854 | − | 0.134938i | \(-0.956917\pi\) | ||
0.990854 | − | 0.134938i | \(-0.0430834\pi\) | |||||||
\(80\) | 13.1231 | − | 2.39871i | 1.46721 | − | 0.268183i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.876894 | + | 1.87285i | 0.0968368 | + | 0.206822i | ||||
\(83\) | −10.2462 | −1.12467 | −0.562334 | − | 0.826910i | \(-0.690096\pi\) | ||||
−0.562334 | + | 0.826910i | \(0.690096\pi\) | |||||||
\(84\) | −1.28078 | − | 5.13416i | −0.139744 | − | 0.560183i | ||||
\(85\) | 17.3693 | 1.88397 | ||||||||
\(86\) | −5.43845 | − | 11.6153i | −0.586443 | − | 1.25251i | ||||
\(87\) | 2.00000 | 0.214423 | ||||||||
\(88\) | −2.56155 | − | 0.673500i | −0.273062 | − | 0.0717953i | ||||
\(89\) | 1.46228i | 0.155001i | 0.996992 | + | 0.0775006i | \(0.0246940\pi\) | ||||
−0.996992 | + | 0.0775006i | \(0.975306\pi\) | |||||||
\(90\) | −2.00000 | − | 4.27156i | −0.210819 | − | 0.450262i | ||||
\(91\) | −4.00000 | − | 2.92456i | −0.419314 | − | 0.306577i | ||||
\(92\) | −1.43845 | − | 1.19935i | −0.149968 | − | 0.125041i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.00000 | + | 3.74571i | −0.825137 | + | 0.386340i | ||||
\(95\) | 23.7565i | 2.43737i | ||||||||
\(96\) | −3.28078 | − | 4.60831i | −0.334843 | − | 0.470334i | ||||
\(97\) | − | 10.4160i | − | 1.05758i | −0.848752 | − | 0.528791i | \(-0.822646\pi\) | ||
0.848752 | − | 0.528791i | \(-0.177354\pi\) | |||||||
\(98\) | 6.71922 | + | 7.26994i | 0.678744 | + | 0.734375i | ||||
\(99\) | 0.936426i | 0.0941144i | ||||||||
\(100\) | −7.84233 | + | 9.40572i | −0.784233 | + | 0.940572i | ||||
\(101\) | 13.7511i | 1.36829i | 0.729348 | + | 0.684143i | \(0.239824\pi\) | ||||
−0.729348 | + | 0.684143i | \(0.760176\pi\) | |||||||
\(102\) | −3.12311 | − | 6.67026i | −0.309234 | − | 0.660455i | ||||
\(103\) | −8.00000 | −0.788263 | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | −5.12311 | − | 1.34700i | −0.502362 | − | 0.132084i | ||||
\(105\) | 7.12311 | + | 5.20798i | 0.695144 | + | 0.508247i | ||||
\(106\) | −15.6847 | + | 7.34376i | −1.52343 | + | 0.713289i | ||||
\(107\) | − | 9.47954i | − | 0.916422i | −0.888843 | − | 0.458211i | \(-0.848490\pi\) | ||
0.888843 | − | 0.458211i | \(-0.151510\pi\) | |||||||
\(108\) | −1.28078 | + | 1.53610i | −0.123243 | + | 0.147812i | ||||
\(109\) | −8.24621 | −0.789844 | −0.394922 | − | 0.918715i | \(-0.629228\pi\) | ||||
−0.394922 | + | 0.918715i | \(0.629228\pi\) | |||||||
\(110\) | 4.00000 | − | 1.87285i | 0.381385 | − | 0.178570i | ||||
\(111\) | −1.12311 | −0.106600 | ||||||||
\(112\) | 9.52699 | + | 4.60831i | 0.900216 | + | 0.435444i | ||||
\(113\) | −4.24621 | −0.399450 | −0.199725 | − | 0.979852i | \(-0.564005\pi\) | ||||
−0.199725 | + | 0.979852i | \(0.564005\pi\) | |||||||
\(114\) | 9.12311 | − | 4.27156i | 0.854457 | − | 0.400068i | ||||
\(115\) | 3.12311 | 0.291231 | ||||||||
\(116\) | −2.56155 | + | 3.07221i | −0.237834 | + | 0.285247i | ||||
\(117\) | 1.87285i | 0.173145i | ||||||||
\(118\) | −5.12311 | + | 2.39871i | −0.471620 | + | 0.220819i | ||||
\(119\) | 11.1231 | + | 8.13254i | 1.01965 | + | 0.745509i | ||||
\(120\) | 9.12311 | + | 2.39871i | 0.832822 | + | 0.218971i | ||||
\(121\) | 10.1231 | 0.920282 | ||||||||
\(122\) | −2.87689 | − | 6.14441i | −0.260462 | − | 0.556289i | ||||
\(123\) | 1.46228i | 0.131849i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3.74571i | − | 0.335026i | ||||||
\(126\) | 0.719224 | − | 3.67188i | 0.0640735 | − | 0.327117i | ||||
\(127\) | − | 9.89012i | − | 0.877606i | −0.898583 | − | 0.438803i | \(-0.855403\pi\) | ||
0.898583 | − | 0.438803i | \(-0.144597\pi\) | |||||||
\(128\) | 11.2808 | + | 0.862603i | 0.997089 | + | 0.0762440i | ||||
\(129\) | − | 9.06897i | − | 0.798478i | ||||||
\(130\) | 8.00000 | − | 3.74571i | 0.701646 | − | 0.328520i | ||||
\(131\) | 5.75379 | 0.502711 | 0.251355 | − | 0.967895i | \(-0.419124\pi\) | ||||
0.251355 | + | 0.967895i | \(0.419124\pi\) | |||||||
\(132\) | −1.43845 | − | 1.19935i | −0.125201 | − | 0.104390i | ||||
\(133\) | −11.1231 | + | 15.2134i | −0.964496 | + | 1.31917i | ||||
\(134\) | 6.56155 | + | 14.0140i | 0.566832 | + | 1.21063i | ||||
\(135\) | − | 3.33513i | − | 0.287042i | ||||||
\(136\) | 14.2462 | + | 3.74571i | 1.22160 | + | 0.321192i | ||||
\(137\) | 0.246211 | 0.0210352 | 0.0105176 | − | 0.999945i | \(-0.496652\pi\) | ||||
0.0105176 | + | 0.999945i | \(0.496652\pi\) | |||||||
\(138\) | −0.561553 | − | 1.19935i | −0.0478025 | − | 0.102096i | ||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | −17.1231 | + | 4.27156i | −1.44717 | + | 0.361013i | ||||
\(141\) | −6.24621 | −0.526026 | ||||||||
\(142\) | 2.31534 | + | 4.94506i | 0.194299 | + | 0.414980i | ||||
\(143\) | −1.75379 | −0.146659 | ||||||||
\(144\) | −0.719224 | − | 3.93481i | −0.0599353 | − | 0.327901i | ||||
\(145\) | − | 6.67026i | − | 0.553935i | ||||||
\(146\) | −4.00000 | − | 8.54312i | −0.331042 | − | 0.707033i | ||||
\(147\) | 2.12311 | + | 6.67026i | 0.175111 | + | 0.550154i | ||||
\(148\) | 1.43845 | − | 1.72521i | 0.118240 | − | 0.141811i | ||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | −7.84233 | + | 3.67188i | −0.640323 | + | 0.299808i | ||||
\(151\) | − | 9.06897i | − | 0.738022i | −0.929425 | − | 0.369011i | \(-0.879696\pi\) | ||
0.929425 | − | 0.369011i | \(-0.120304\pi\) | |||||||
\(152\) | −5.12311 | + | 19.4849i | −0.415539 | + | 1.58044i | ||||
\(153\) | − | 5.20798i | − | 0.421041i | ||||||
\(154\) | 3.43845 | + | 0.673500i | 0.277078 | + | 0.0542722i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.87689 | − | 2.39871i | −0.230336 | − | 0.192050i | ||||
\(157\) | − | 21.8836i | − | 1.74650i | −0.487268 | − | 0.873252i | \(-0.662007\pi\) | ||
0.487268 | − | 0.873252i | \(-0.337993\pi\) | |||||||
\(158\) | 1.43845 | + | 3.07221i | 0.114437 | + | 0.244412i | ||||
\(159\) | −12.2462 | −0.971188 | ||||||||
\(160\) | −15.3693 | + | 10.9418i | −1.21505 | + | 0.865027i | ||||
\(161\) | 2.00000 | + | 1.46228i | 0.157622 | + | 0.115244i | ||||
\(162\) | −1.28078 | + | 0.599676i | −0.100627 | + | 0.0471150i | ||||
\(163\) | 15.7392i | 1.23279i | 0.787436 | + | 0.616396i | \(0.211408\pi\) | ||||
−0.787436 | + | 0.616396i | \(0.788592\pi\) | |||||||
\(164\) | −2.24621 | − | 1.87285i | −0.175400 | − | 0.146245i | ||||
\(165\) | 3.12311 | 0.243133 | ||||||||
\(166\) | 13.1231 | − | 6.14441i | 1.01855 | − | 0.476899i | ||||
\(167\) | 14.2462 | 1.10240 | 0.551202 | − | 0.834372i | \(-0.314169\pi\) | ||||
0.551202 | + | 0.834372i | \(0.314169\pi\) | |||||||
\(168\) | 4.71922 | + | 5.80766i | 0.364096 | + | 0.448071i | ||||
\(169\) | 9.49242 | 0.730186 | ||||||||
\(170\) | −22.2462 | + | 10.4160i | −1.70621 | + | 0.798868i | ||||
\(171\) | 7.12311 | 0.544718 | ||||||||
\(172\) | 13.9309 | + | 11.6153i | 1.06222 | + | 0.885660i | ||||
\(173\) | − | 16.6757i | − | 1.26783i | −0.773404 | − | 0.633913i | \(-0.781448\pi\) | ||
0.773404 | − | 0.633913i | \(-0.218552\pi\) | |||||||
\(174\) | −2.56155 | + | 1.19935i | −0.194191 | + | 0.0909227i | ||||
\(175\) | 9.56155 | − | 13.0776i | 0.722785 | − | 0.988574i | ||||
\(176\) | 3.68466 | − | 0.673500i | 0.277742 | − | 0.0507670i | ||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | −0.876894 | − | 1.87285i | −0.0657260 | − | 0.140376i | ||||
\(179\) | − | 16.1498i | − | 1.20709i | −0.797328 | − | 0.603547i | \(-0.793754\pi\) | ||
0.797328 | − | 0.603547i | \(-0.206246\pi\) | |||||||
\(180\) | 5.12311 | + | 4.27156i | 0.381854 | + | 0.318383i | ||||
\(181\) | − | 1.87285i | − | 0.139208i | −0.997575 | − | 0.0696040i | \(-0.977826\pi\) | ||
0.997575 | − | 0.0696040i | \(-0.0221736\pi\) | |||||||
\(182\) | 6.87689 | + | 1.34700i | 0.509749 | + | 0.0998463i | ||||
\(183\) | − | 4.79741i | − | 0.354635i | ||||||
\(184\) | 2.56155 | + | 0.673500i | 0.188840 | + | 0.0496511i | ||||
\(185\) | 3.74571i | 0.275390i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.87689 | 0.356634 | ||||||||
\(188\) | 8.00000 | − | 9.59482i | 0.583460 | − | 0.699774i | ||||
\(189\) | 1.56155 | − | 2.13578i | 0.113586 | − | 0.155355i | ||||
\(190\) | −14.2462 | − | 30.4268i | −1.03353 | − | 2.20739i | ||||
\(191\) | 2.80928i | 0.203272i | 0.994822 | + | 0.101636i | \(0.0324078\pi\) | ||||
−0.994822 | + | 0.101636i | \(0.967592\pi\) | |||||||
\(192\) | 6.96543 | + | 3.93481i | 0.502687 | + | 0.283970i | ||||
\(193\) | −15.3693 | −1.10631 | −0.553154 | − | 0.833079i | \(-0.686576\pi\) | ||||
−0.553154 | + | 0.833079i | \(0.686576\pi\) | |||||||
\(194\) | 6.24621 | + | 13.3405i | 0.448452 | + | 0.957794i | ||||
\(195\) | 6.24621 | 0.447300 | ||||||||
\(196\) | −12.9654 | − | 5.28181i | −0.926102 | − | 0.377272i | ||||
\(197\) | −16.2462 | −1.15749 | −0.578747 | − | 0.815507i | \(-0.696458\pi\) | ||||
−0.578747 | + | 0.815507i | \(0.696458\pi\) | |||||||
\(198\) | −0.561553 | − | 1.19935i | −0.0399078 | − | 0.0852343i | ||||
\(199\) | −3.12311 | −0.221391 | −0.110696 | − | 0.993854i | \(-0.535308\pi\) | ||||
−0.110696 | + | 0.993854i | \(0.535308\pi\) | |||||||
\(200\) | 4.40388 | − | 16.7495i | 0.311401 | − | 1.18437i | ||||
\(201\) | 10.9418i | 0.771777i | ||||||||
\(202\) | −8.24621 | − | 17.6121i | −0.580201 | − | 1.23918i | ||||
\(203\) | 3.12311 | − | 4.27156i | 0.219199 | − | 0.299805i | ||||
\(204\) | 8.00000 | + | 6.67026i | 0.560112 | + | 0.467012i | ||||
\(205\) | 4.87689 | 0.340617 | ||||||||
\(206\) | 10.2462 | − | 4.79741i | 0.713887 | − | 0.334251i | ||||
\(207\) | − | 0.936426i | − | 0.0650861i | ||||||
\(208\) | 7.36932 | − | 1.34700i | 0.510970 | − | 0.0933976i | ||||
\(209\) | 6.67026i | 0.461392i | ||||||||
\(210\) | −12.2462 | − | 2.39871i | −0.845069 | − | 0.165526i | ||||
\(211\) | 12.8147i | 0.882199i | 0.897458 | + | 0.441099i | \(0.145411\pi\) | ||||
−0.897458 | + | 0.441099i | \(0.854589\pi\) | |||||||
\(212\) | 15.6847 | − | 18.8114i | 1.07723 | − | 1.29197i | ||||
\(213\) | 3.86098i | 0.264550i | ||||||||
\(214\) | 5.68466 | + | 12.1412i | 0.388595 | + | 0.829954i | ||||
\(215\) | −30.2462 | −2.06277 | ||||||||
\(216\) | 0.719224 | − | 2.73546i | 0.0489370 | − | 0.186124i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 10.5616 | − | 4.94506i | 0.715319 | − | 0.334922i | ||||
\(219\) | − | 6.67026i | − | 0.450735i | ||||||
\(220\) | −4.00000 | + | 4.79741i | −0.269680 | + | 0.323441i | ||||
\(221\) | 9.75379 | 0.656111 | ||||||||
\(222\) | 1.43845 | − | 0.673500i | 0.0965423 | − | 0.0452024i | ||||
\(223\) | 27.1231 | 1.81630 | 0.908149 | − | 0.418648i | \(-0.137496\pi\) | ||||
0.908149 | + | 0.418648i | \(0.137496\pi\) | |||||||
\(224\) | −14.9654 | − | 0.189103i | −0.999920 | − | 0.0126350i | ||||
\(225\) | −6.12311 | −0.408207 | ||||||||
\(226\) | 5.43845 | − | 2.54635i | 0.361760 | − | 0.169381i | ||||
\(227\) | −16.4924 | −1.09464 | −0.547320 | − | 0.836923i | \(-0.684352\pi\) | ||||
−0.547320 | + | 0.836923i | \(0.684352\pi\) | |||||||
\(228\) | −9.12311 | + | 10.9418i | −0.604192 | + | 0.724640i | ||||
\(229\) | 5.61856i | 0.371285i | 0.982617 | + | 0.185642i | \(0.0594366\pi\) | ||||
−0.982617 | + | 0.185642i | \(0.940563\pi\) | |||||||
\(230\) | −4.00000 | + | 1.87285i | −0.263752 | + | 0.123492i | ||||
\(231\) | 2.00000 | + | 1.46228i | 0.131590 | + | 0.0962109i | ||||
\(232\) | 1.43845 | − | 5.47091i | 0.0944387 | − | 0.359183i | ||||
\(233\) | 22.4924 | 1.47353 | 0.736764 | − | 0.676150i | \(-0.236353\pi\) | ||||
0.736764 | + | 0.676150i | \(0.236353\pi\) | |||||||
\(234\) | −1.12311 | − | 2.39871i | −0.0734197 | − | 0.156808i | ||||
\(235\) | 20.8319i | 1.35893i | ||||||||
\(236\) | 5.12311 | − | 6.14441i | 0.333486 | − | 0.399967i | ||||
\(237\) | 2.39871i | 0.155813i | ||||||||
\(238\) | −19.1231 | − | 3.74571i | −1.23957 | − | 0.242798i | ||||
\(239\) | 16.1498i | 1.04464i | 0.852748 | + | 0.522322i | \(0.174934\pi\) | ||||
−0.852748 | + | 0.522322i | \(0.825066\pi\) | |||||||
\(240\) | −13.1231 | + | 2.39871i | −0.847093 | + | 0.154836i | ||||
\(241\) | 23.7565i | 1.53029i | 0.643858 | + | 0.765145i | \(0.277333\pi\) | ||||
−0.643858 | + | 0.765145i | \(0.722667\pi\) | |||||||
\(242\) | −12.9654 | + | 6.07059i | −0.833450 | + | 0.390232i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 7.36932 | + | 6.14441i | 0.471772 | + | 0.393356i | ||||
\(245\) | 22.2462 | − | 7.08084i | 1.42126 | − | 0.452378i | ||||
\(246\) | −0.876894 | − | 1.87285i | −0.0559087 | − | 0.119409i | ||||
\(247\) | 13.3405i | 0.848837i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.2462 | 0.649327 | ||||||||
\(250\) | 2.24621 | + | 4.79741i | 0.142063 | + | 0.303415i | ||||
\(251\) | −5.75379 | −0.363176 | −0.181588 | − | 0.983375i | \(-0.558124\pi\) | ||||
−0.181588 | + | 0.983375i | \(0.558124\pi\) | |||||||
\(252\) | 1.28078 | + | 5.13416i | 0.0806813 | + | 0.323422i | ||||
\(253\) | 0.876894 | 0.0551299 | ||||||||
\(254\) | 5.93087 | + | 12.6670i | 0.372136 | + | 0.794800i | ||||
\(255\) | −17.3693 | −1.08771 | ||||||||
\(256\) | −14.9654 | + | 5.66001i | −0.935340 | + | 0.353751i | ||||
\(257\) | 2.28343i | 0.142436i | 0.997461 | + | 0.0712181i | \(0.0226886\pi\) | ||||
−0.997461 | + | 0.0712181i | \(0.977311\pi\) | |||||||
\(258\) | 5.43845 | + | 11.6153i | 0.338583 | + | 0.723138i | ||||
\(259\) | −1.75379 | + | 2.39871i | −0.108975 | + | 0.149048i | ||||
\(260\) | −8.00000 | + | 9.59482i | −0.496139 | + | 0.595046i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | −7.36932 | + | 3.45041i | −0.455278 | + | 0.213167i | ||||
\(263\) | − | 24.6929i | − | 1.52263i | −0.648382 | − | 0.761315i | \(-0.724554\pi\) | ||
0.648382 | − | 0.761315i | \(-0.275446\pi\) | |||||||
\(264\) | 2.56155 | + | 0.673500i | 0.157653 | + | 0.0414511i | ||||
\(265\) | 40.8427i | 2.50895i | ||||||||
\(266\) | 5.12311 | − | 26.1552i | 0.314118 | − | 1.60368i | ||||
\(267\) | − | 1.46228i | − | 0.0894900i | ||||||
\(268\) | −16.8078 | − | 14.0140i | −1.02670 | − | 0.856043i | ||||
\(269\) | − | 10.8265i | − | 0.660106i | −0.943962 | − | 0.330053i | \(-0.892933\pi\) | ||
0.943962 | − | 0.330053i | \(-0.107067\pi\) | |||||||
\(270\) | 2.00000 | + | 4.27156i | 0.121716 | + | 0.259959i | ||||
\(271\) | −28.4924 | −1.73079 | −0.865396 | − | 0.501089i | \(-0.832933\pi\) | ||||
−0.865396 | + | 0.501089i | \(0.832933\pi\) | |||||||
\(272\) | −20.4924 | + | 3.74571i | −1.24254 | + | 0.227117i | ||||
\(273\) | 4.00000 | + | 2.92456i | 0.242091 | + | 0.177002i | ||||
\(274\) | −0.315342 | + | 0.147647i | −0.0190505 | + | 0.00891969i | ||||
\(275\) | − | 5.73384i | − | 0.345763i | ||||||
\(276\) | 1.43845 | + | 1.19935i | 0.0865843 | + | 0.0721926i | ||||
\(277\) | −5.12311 | −0.307818 | −0.153909 | − | 0.988085i | \(-0.549186\pi\) | ||||
−0.153909 | + | 0.988085i | \(0.549186\pi\) | |||||||
\(278\) | 15.3693 | − | 7.19612i | 0.921790 | − | 0.431594i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 19.3693 | − | 15.7392i | 1.15754 | − | 0.940599i | ||||
\(281\) | 16.2462 | 0.969168 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(282\) | 8.00000 | − | 3.74571i | 0.476393 | − | 0.223054i | ||||
\(283\) | 8.87689 | 0.527677 | 0.263838 | − | 0.964567i | \(-0.415011\pi\) | ||||
0.263838 | + | 0.964567i | \(0.415011\pi\) | |||||||
\(284\) | −5.93087 | − | 4.94506i | −0.351932 | − | 0.293435i | ||||
\(285\) | − | 23.7565i | − | 1.40721i | ||||||
\(286\) | 2.24621 | − | 1.05171i | 0.132821 | − | 0.0621887i | ||||
\(287\) | 3.12311 | + | 2.28343i | 0.184351 | + | 0.134786i | ||||
\(288\) | 3.28078 | + | 4.60831i | 0.193322 | + | 0.271547i | ||||
\(289\) | −10.1231 | −0.595477 | ||||||||
\(290\) | 4.00000 | + | 8.54312i | 0.234888 | + | 0.501669i | ||||
\(291\) | 10.4160i | 0.610595i | ||||||||
\(292\) | 10.2462 | + | 8.54312i | 0.599614 | + | 0.499948i | ||||
\(293\) | 13.7511i | 0.803348i | 0.915783 | + | 0.401674i | \(0.131571\pi\) | ||||
−0.915783 | + | 0.401674i | \(0.868429\pi\) | |||||||
\(294\) | −6.71922 | − | 7.26994i | −0.391873 | − | 0.423992i | ||||
\(295\) | 13.3405i | 0.776716i | ||||||||
\(296\) | −0.807764 | + | 3.07221i | −0.0469503 | + | 0.178568i | ||||
\(297\) | − | 0.936426i | − | 0.0543370i | ||||||
\(298\) | 12.8078 | − | 5.99676i | 0.741934 | − | 0.347383i | ||||
\(299\) | 1.75379 | 0.101424 | ||||||||
\(300\) | 7.84233 | − | 9.40572i | 0.452777 | − | 0.543039i | ||||
\(301\) | −19.3693 | − | 14.1617i | −1.11643 | − | 0.816265i | ||||
\(302\) | 5.43845 | + | 11.6153i | 0.312947 | + | 0.668387i | ||||
\(303\) | − | 13.7511i | − | 0.789980i | ||||||
\(304\) | −5.12311 | − | 28.0281i | −0.293830 | − | 1.60752i | ||||
\(305\) | −16.0000 | −0.916157 | ||||||||
\(306\) | 3.12311 | + | 6.67026i | 0.178536 | + | 0.381314i | ||||
\(307\) | 19.6155 | 1.11952 | 0.559759 | − | 0.828656i | \(-0.310894\pi\) | ||||
0.559759 | + | 0.828656i | \(0.310894\pi\) | |||||||
\(308\) | −4.80776 | + | 1.19935i | −0.273948 | + | 0.0683395i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 5.12311 | + | 1.34700i | 0.290039 | + | 0.0762589i | ||||
\(313\) | − | 22.9354i | − | 1.29638i | −0.761478 | − | 0.648191i | \(-0.775526\pi\) | ||
0.761478 | − | 0.648191i | \(-0.224474\pi\) | |||||||
\(314\) | 13.1231 | + | 28.0281i | 0.740580 | + | 1.58171i | ||||
\(315\) | −7.12311 | − | 5.20798i | −0.401342 | − | 0.293437i | ||||
\(316\) | −3.68466 | − | 3.07221i | −0.207278 | − | 0.172825i | ||||
\(317\) | −14.4924 | −0.813976 | −0.406988 | − | 0.913434i | \(-0.633421\pi\) | ||||
−0.406988 | + | 0.913434i | \(0.633421\pi\) | |||||||
\(318\) | 15.6847 | − | 7.34376i | 0.879552 | − | 0.411818i | ||||
\(319\) | − | 1.87285i | − | 0.104860i | ||||||
\(320\) | 13.1231 | − | 23.2306i | 0.733604 | − | 1.29863i | ||||
\(321\) | 9.47954i | 0.529097i | ||||||||
\(322\) | −3.43845 | − | 0.673500i | −0.191617 | − | 0.0375327i | ||||
\(323\) | − | 37.0970i | − | 2.06413i | ||||||
\(324\) | 1.28078 | − | 1.53610i | 0.0711542 | − | 0.0853390i | ||||
\(325\) | − | 11.4677i | − | 0.636112i | ||||||
\(326\) | −9.43845 | − | 20.1584i | −0.522747 | − | 1.11647i | ||||
\(327\) | 8.24621 | 0.456017 | ||||||||
\(328\) | 4.00000 | + | 1.05171i | 0.220863 | + | 0.0580707i | ||||
\(329\) | −9.75379 | + | 13.3405i | −0.537744 | + | 0.735487i | ||||
\(330\) | −4.00000 | + | 1.87285i | −0.220193 | + | 0.103097i | ||||
\(331\) | − | 17.6121i | − | 0.968048i | −0.875055 | − | 0.484024i | \(-0.839175\pi\) | ||
0.875055 | − | 0.484024i | \(-0.160825\pi\) | |||||||
\(332\) | −13.1231 | + | 15.7392i | −0.720224 | + | 0.863803i | ||||
\(333\) | 1.12311 | 0.0615458 | ||||||||
\(334\) | −18.2462 | + | 8.54312i | −0.998388 | + | 0.467459i | ||||
\(335\) | 36.4924 | 1.99379 | ||||||||
\(336\) | −9.52699 | − | 4.60831i | −0.519740 | − | 0.251404i | ||||
\(337\) | 8.24621 | 0.449200 | 0.224600 | − | 0.974451i | \(-0.427892\pi\) | ||||
0.224600 | + | 0.974451i | \(0.427892\pi\) | |||||||
\(338\) | −12.1577 | + | 5.69238i | −0.661290 | + | 0.309625i | ||||
\(339\) | 4.24621 | 0.230623 | ||||||||
\(340\) | 22.2462 | − | 26.6811i | 1.20647 | − | 1.44698i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −9.12311 | + | 4.27156i | −0.493321 | + | 0.230979i | ||||
\(343\) | 17.5616 | + | 5.88148i | 0.948235 | + | 0.317570i | ||||
\(344\) | −24.8078 | − | 6.52262i | −1.33754 | − | 0.351676i | ||||
\(345\) | −3.12311 | −0.168142 | ||||||||
\(346\) | 10.0000 | + | 21.3578i | 0.537603 | + | 1.14820i | ||||
\(347\) | 20.1261i | 1.08042i | 0.841529 | + | 0.540212i | \(0.181656\pi\) | ||||
−0.841529 | + | 0.540212i | \(0.818344\pi\) | |||||||
\(348\) | 2.56155 | − | 3.07221i | 0.137314 | − | 0.164688i | ||||
\(349\) | − | 21.8836i | − | 1.17140i | −0.810526 | − | 0.585702i | \(-0.800819\pi\) | ||
0.810526 | − | 0.585702i | \(-0.199181\pi\) | |||||||
\(350\) | −4.40388 | + | 22.4833i | −0.235397 | + | 1.20178i | ||||
\(351\) | − | 1.87285i | − | 0.0999655i | ||||||
\(352\) | −4.31534 | + | 3.07221i | −0.230008 | + | 0.163749i | ||||
\(353\) | − | 28.9645i | − | 1.54162i | −0.637063 | − | 0.770812i | \(-0.719851\pi\) | ||
0.637063 | − | 0.770812i | \(-0.280149\pi\) | |||||||
\(354\) | 5.12311 | − | 2.39871i | 0.272290 | − | 0.127490i | ||||
\(355\) | 12.8769 | 0.683435 | ||||||||
\(356\) | 2.24621 | + | 1.87285i | 0.119049 | + | 0.0992610i | ||||
\(357\) | −11.1231 | − | 8.13254i | −0.588697 | − | 0.430420i | ||||
\(358\) | 9.68466 | + | 20.6843i | 0.511850 | + | 1.09320i | ||||
\(359\) | 22.8201i | 1.20440i | 0.798346 | + | 0.602199i | \(0.205708\pi\) | ||||
−0.798346 | + | 0.602199i | \(0.794292\pi\) | |||||||
\(360\) | −9.12311 | − | 2.39871i | −0.480830 | − | 0.126423i | ||||
\(361\) | 31.7386 | 1.67045 | ||||||||
\(362\) | 1.12311 | + | 2.39871i | 0.0590291 | + | 0.126073i | ||||
\(363\) | −10.1231 | −0.531325 | ||||||||
\(364\) | −9.61553 | + | 2.39871i | −0.503991 | + | 0.125726i | ||||
\(365\) | −22.2462 | −1.16442 | ||||||||
\(366\) | 2.87689 | + | 6.14441i | 0.150378 | + | 0.321174i | ||||
\(367\) | −33.3693 | −1.74186 | −0.870932 | − | 0.491403i | \(-0.836484\pi\) | ||||
−0.870932 | + | 0.491403i | \(0.836484\pi\) | |||||||
\(368\) | −3.68466 | + | 0.673500i | −0.192076 | + | 0.0351086i | ||||
\(369\) | − | 1.46228i | − | 0.0761232i | ||||||
\(370\) | −2.24621 | − | 4.79741i | −0.116775 | − | 0.249406i | ||||
\(371\) | −19.1231 | + | 26.1552i | −0.992822 | + | 1.35791i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | −6.24621 | + | 2.92456i | −0.322984 | + | 0.151225i | ||||
\(375\) | 3.74571i | 0.193427i | ||||||||
\(376\) | −4.49242 | + | 17.0862i | −0.231679 | + | 0.881155i | ||||
\(377\) | − | 3.74571i | − | 0.192914i | ||||||
\(378\) | −0.719224 | + | 3.67188i | −0.0369929 | + | 0.188861i | ||||
\(379\) | − | 25.1035i | − | 1.28948i | −0.764402 | − | 0.644740i | \(-0.776966\pi\) | ||
0.764402 | − | 0.644740i | \(-0.223034\pi\) | |||||||
\(380\) | 36.4924 | + | 30.4268i | 1.87202 | + | 1.56086i | ||||
\(381\) | 9.89012i | 0.506686i | ||||||||
\(382\) | −1.68466 | − | 3.59806i | −0.0861946 | − | 0.184093i | ||||
\(383\) | −9.75379 | −0.498395 | −0.249198 | − | 0.968453i | \(-0.580167\pi\) | ||||
−0.249198 | + | 0.968453i | \(0.580167\pi\) | |||||||
\(384\) | −11.2808 | − | 0.862603i | −0.575670 | − | 0.0440195i | ||||
\(385\) | 4.87689 | − | 6.67026i | 0.248550 | − | 0.339948i | ||||
\(386\) | 19.6847 | − | 9.21662i | 1.00192 | − | 0.469113i | ||||
\(387\) | 9.06897i | 0.461002i | ||||||||
\(388\) | −16.0000 | − | 13.3405i | −0.812277 | − | 0.677263i | ||||
\(389\) | −16.2462 | −0.823716 | −0.411858 | − | 0.911248i | \(-0.635120\pi\) | ||||
−0.411858 | + | 0.911248i | \(0.635120\pi\) | |||||||
\(390\) | −8.00000 | + | 3.74571i | −0.405096 | + | 0.189671i | ||||
\(391\) | −4.87689 | −0.246635 | ||||||||
\(392\) | 19.7732 | − | 1.01025i | 0.998697 | − | 0.0510253i | ||||
\(393\) | −5.75379 | −0.290240 | ||||||||
\(394\) | 20.8078 | − | 9.74247i | 1.04828 | − | 0.490819i | ||||
\(395\) | 8.00000 | 0.402524 | ||||||||
\(396\) | 1.43845 | + | 1.19935i | 0.0722847 | + | 0.0602697i | ||||
\(397\) | 18.1379i | 0.910317i | 0.890410 | + | 0.455159i | \(0.150417\pi\) | ||||
−0.890410 | + | 0.455159i | \(0.849583\pi\) | |||||||
\(398\) | 4.00000 | − | 1.87285i | 0.200502 | − | 0.0938776i | ||||
\(399\) | 11.1231 | − | 15.2134i | 0.556852 | − | 0.761622i | ||||
\(400\) | 4.40388 | + | 24.0932i | 0.220194 | + | 1.20466i | ||||
\(401\) | 8.24621 | 0.411796 | 0.205898 | − | 0.978573i | \(-0.433988\pi\) | ||||
0.205898 | + | 0.978573i | \(0.433988\pi\) | |||||||
\(402\) | −6.56155 | − | 14.0140i | −0.327261 | − | 0.698956i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 21.1231 | + | 17.6121i | 1.05091 | + | 0.876234i | ||||
\(405\) | 3.33513i | 0.165724i | ||||||||
\(406\) | −1.43845 | + | 7.34376i | −0.0713889 | + | 0.364465i | ||||
\(407\) | 1.05171i | 0.0521311i | ||||||||
\(408\) | −14.2462 | − | 3.74571i | −0.705293 | − | 0.185440i | ||||
\(409\) | − | 0.821147i | − | 0.0406031i | −0.999794 | − | 0.0203016i | \(-0.993537\pi\) | ||
0.999794 | − | 0.0203016i | \(-0.00646263\pi\) | |||||||
\(410\) | −6.24621 | + | 2.92456i | −0.308478 | + | 0.144434i | ||||
\(411\) | −0.246211 | −0.0121447 | ||||||||
\(412\) | −10.2462 | + | 12.2888i | −0.504795 | + | 0.605427i | ||||
\(413\) | −6.24621 | + | 8.54312i | −0.307356 | + | 0.420379i | ||||
\(414\) | 0.561553 | + | 1.19935i | 0.0275988 | + | 0.0589450i | ||||
\(415\) | − | 34.1725i | − | 1.67746i | ||||||
\(416\) | −8.63068 | + | 6.14441i | −0.423154 | + | 0.301255i | ||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | −4.00000 | − | 8.54312i | −0.195646 | − | 0.417858i | ||||
\(419\) | −16.4924 | −0.805708 | −0.402854 | − | 0.915264i | \(-0.631982\pi\) | ||||
−0.402854 | + | 0.915264i | \(0.631982\pi\) | |||||||
\(420\) | 17.1231 | − | 4.27156i | 0.835522 | − | 0.208431i | ||||
\(421\) | 10.8769 | 0.530107 | 0.265054 | − | 0.964234i | \(-0.414610\pi\) | ||||
0.265054 | + | 0.964234i | \(0.414610\pi\) | |||||||
\(422\) | −7.68466 | − | 16.4127i | −0.374083 | − | 0.798959i | ||||
\(423\) | 6.24621 | 0.303701 | ||||||||
\(424\) | −8.80776 | + | 33.4990i | −0.427743 | + | 1.62685i | ||||
\(425\) | 31.8890i | 1.54685i | ||||||||
\(426\) | −2.31534 | − | 4.94506i | −0.112179 | − | 0.239589i | ||||
\(427\) | −10.2462 | − | 7.49141i | −0.495849 | − | 0.362535i | ||||
\(428\) | −14.5616 | − | 12.1412i | −0.703859 | − | 0.586866i | ||||
\(429\) | 1.75379 | 0.0846737 | ||||||||
\(430\) | 38.7386 | − | 18.1379i | 1.86814 | − | 0.874689i | ||||
\(431\) | − | 4.68213i | − | 0.225530i | −0.993622 | − | 0.112765i | \(-0.964029\pi\) | ||
0.993622 | − | 0.112765i | \(-0.0359708\pi\) | |||||||
\(432\) | 0.719224 | + | 3.93481i | 0.0346037 | + | 0.189314i | ||||
\(433\) | − | 13.3405i | − | 0.641105i | −0.947231 | − | 0.320552i | \(-0.896131\pi\) | ||
0.947231 | − | 0.320552i | \(-0.103869\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.67026i | 0.319815i | ||||||||
\(436\) | −10.5616 | + | 12.6670i | −0.505807 | + | 0.606641i | ||||
\(437\) | − | 6.67026i | − | 0.319082i | ||||||
\(438\) | 4.00000 | + | 8.54312i | 0.191127 | + | 0.408206i | ||||
\(439\) | −6.63068 | −0.316465 | −0.158233 | − | 0.987402i | \(-0.550580\pi\) | ||||
−0.158233 | + | 0.987402i | \(0.550580\pi\) | |||||||
\(440\) | 2.24621 | − | 8.54312i | 0.107084 | − | 0.407277i | ||||
\(441\) | −2.12311 | − | 6.67026i | −0.101100 | − | 0.317632i | ||||
\(442\) | −12.4924 | + | 5.84912i | −0.594204 | + | 0.278214i | ||||
\(443\) | 18.8438i | 0.895296i | 0.894210 | + | 0.447648i | \(0.147738\pi\) | ||||
−0.894210 | + | 0.447648i | \(0.852262\pi\) | |||||||
\(444\) | −1.43845 | + | 1.72521i | −0.0682657 | + | 0.0818746i | ||||
\(445\) | −4.87689 | −0.231187 | ||||||||
\(446\) | −34.7386 | + | 16.2651i | −1.64492 | + | 0.770174i | ||||
\(447\) | 10.0000 | 0.472984 | ||||||||
\(448\) | 19.2808 | − | 8.73222i | 0.910931 | − | 0.412559i | ||||
\(449\) | 11.7538 | 0.554696 | 0.277348 | − | 0.960770i | \(-0.410545\pi\) | ||||
0.277348 | + | 0.960770i | \(0.410545\pi\) | |||||||
\(450\) | 7.84233 | − | 3.67188i | 0.369691 | − | 0.173094i | ||||
\(451\) | 1.36932 | 0.0644786 | ||||||||
\(452\) | −5.43845 | + | 6.52262i | −0.255803 | + | 0.306798i | ||||
\(453\) | 9.06897i | 0.426097i | ||||||||
\(454\) | 21.1231 | − | 9.89012i | 0.991356 | − | 0.464166i | ||||
\(455\) | 9.75379 | − | 13.3405i | 0.457265 | − | 0.625414i | ||||
\(456\) | 5.12311 | − | 19.4849i | 0.239911 | − | 0.912466i | ||||
\(457\) | 0.246211 | 0.0115173 | 0.00575864 | − | 0.999983i | \(-0.498167\pi\) | ||||
0.00575864 | + | 0.999983i | \(0.498167\pi\) | |||||||
\(458\) | −3.36932 | − | 7.19612i | −0.157438 | − | 0.336252i | ||||
\(459\) | 5.20798i | 0.243088i | ||||||||
\(460\) | 4.00000 | − | 4.79741i | 0.186501 | − | 0.223680i | ||||
\(461\) | − | 6.25969i | − | 0.291543i | −0.989318 | − | 0.145771i | \(-0.953434\pi\) | ||
0.989318 | − | 0.145771i | \(-0.0465664\pi\) | |||||||
\(462\) | −3.43845 | − | 0.673500i | −0.159971 | − | 0.0313341i | ||||
\(463\) | 39.2652i | 1.82481i | 0.409292 | + | 0.912404i | \(0.365776\pi\) | ||||
−0.409292 | + | 0.912404i | \(0.634224\pi\) | |||||||
\(464\) | 1.43845 | + | 7.86962i | 0.0667782 | + | 0.365338i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28.8078 | + | 13.4882i | −1.33449 | + | 0.624828i | ||||
\(467\) | 34.2462 | 1.58473 | 0.792363 | − | 0.610050i | \(-0.208851\pi\) | ||||
0.792363 | + | 0.610050i | \(0.208851\pi\) | |||||||
\(468\) | 2.87689 | + | 2.39871i | 0.132984 | + | 0.110880i | ||||
\(469\) | 23.3693 | + | 17.0862i | 1.07909 | + | 0.788969i | ||||
\(470\) | −12.4924 | − | 26.6811i | −0.576232 | − | 1.23071i | ||||
\(471\) | 21.8836i | 1.00835i | ||||||||
\(472\) | −2.87689 | + | 10.9418i | −0.132420 | + | 0.503638i | ||||
\(473\) | −8.49242 | −0.390482 | ||||||||
\(474\) | −1.43845 | − | 3.07221i | −0.0660701 | − | 0.141111i | ||||
\(475\) | −43.6155 | −2.00122 | ||||||||
\(476\) | 26.7386 | − | 6.67026i | 1.22556 | − | 0.305731i | ||||
\(477\) | 12.2462 | 0.560715 | ||||||||
\(478\) | −9.68466 | − | 20.6843i | −0.442966 | − | 0.946077i | ||||
\(479\) | 12.4924 | 0.570793 | 0.285397 | − | 0.958409i | \(-0.407875\pi\) | ||||
0.285397 | + | 0.958409i | \(0.407875\pi\) | |||||||
\(480\) | 15.3693 | − | 10.9418i | 0.701510 | − | 0.499424i | ||||
\(481\) | 2.10341i | 0.0959073i | ||||||||
\(482\) | −14.2462 | − | 30.4268i | −0.648897 | − | 1.38590i | ||||
\(483\) | −2.00000 | − | 1.46228i | −0.0910032 | − | 0.0665360i | ||||
\(484\) | 12.9654 | − | 15.5501i | 0.589338 | − | 0.706824i | ||||
\(485\) | 34.7386 | 1.57740 | ||||||||
\(486\) | 1.28078 | − | 0.599676i | 0.0580972 | − | 0.0272019i | ||||
\(487\) | − | 1.57756i | − | 0.0714860i | −0.999361 | − | 0.0357430i | \(-0.988620\pi\) | ||
0.999361 | − | 0.0357430i | \(-0.0113798\pi\) | |||||||
\(488\) | −13.1231 | − | 3.45041i | −0.594055 | − | 0.156193i | ||||
\(489\) | − | 15.7392i | − | 0.711753i | ||||||
\(490\) | −24.2462 | + | 22.4095i | −1.09533 | + | 1.01236i | ||||
\(491\) | 11.3524i | 0.512326i | 0.966634 | + | 0.256163i | \(0.0824585\pi\) | ||||
−0.966634 | + | 0.256163i | \(0.917542\pi\) | |||||||
\(492\) | 2.24621 | + | 1.87285i | 0.101267 | + | 0.0844347i | ||||
\(493\) | 10.4160i | 0.469112i | ||||||||
\(494\) | −8.00000 | − | 17.0862i | −0.359937 | − | 0.768746i | ||||
\(495\) | −3.12311 | −0.140373 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.24621 | + | 6.02913i | 0.369893 | + | 0.270444i | ||||
\(498\) | −13.1231 | + | 6.14441i | −0.588060 | + | 0.275338i | ||||
\(499\) | − | 13.8664i | − | 0.620744i | −0.950615 | − | 0.310372i | \(-0.899546\pi\) | ||
0.950615 | − | 0.310372i | \(-0.100454\pi\) | |||||||
\(500\) | −5.75379 | − | 4.79741i | −0.257317 | − | 0.214547i | ||||
\(501\) | −14.2462 | −0.636474 | ||||||||
\(502\) | 7.36932 | − | 3.45041i | 0.328909 | − | 0.153999i | ||||
\(503\) | −26.7386 | −1.19222 | −0.596108 | − | 0.802904i | \(-0.703287\pi\) | ||||
−0.596108 | + | 0.802904i | \(0.703287\pi\) | |||||||
\(504\) | −4.71922 | − | 5.80766i | −0.210211 | − | 0.258694i | ||||
\(505\) | −45.8617 | −2.04082 | ||||||||
\(506\) | −1.12311 | + | 0.525853i | −0.0499281 | + | 0.0233770i | ||||
\(507\) | −9.49242 | −0.421573 | ||||||||
\(508\) | −15.1922 | − | 12.6670i | −0.674046 | − | 0.562008i | ||||
\(509\) | − | 3.33513i | − | 0.147827i | −0.997265 | − | 0.0739136i | \(-0.976451\pi\) | ||
0.997265 | − | 0.0739136i | \(-0.0235489\pi\) | |||||||
\(510\) | 22.2462 | − | 10.4160i | 0.985079 | − | 0.461227i | ||||
\(511\) | −14.2462 | − | 10.4160i | −0.630215 | − | 0.460775i | ||||
\(512\) | 15.7732 | − | 16.2236i | 0.697083 | − | 0.716990i | ||||
\(513\) | −7.12311 | −0.314493 | ||||||||
\(514\) | −1.36932 | − | 2.92456i | −0.0603980 | − | 0.128997i | ||||
\(515\) | − | 26.6811i | − | 1.17571i | ||||||
\(516\) | −13.9309 | − | 11.6153i | −0.613272 | − | 0.511336i | ||||
\(517\) | 5.84912i | 0.257244i | ||||||||
\(518\) | 0.807764 | − | 4.12391i | 0.0354911 | − | 0.181194i | ||||
\(519\) | 16.6757i | 0.731980i | ||||||||
\(520\) | 4.49242 | − | 17.0862i | 0.197006 | − | 0.749281i | ||||
\(521\) | 29.7856i | 1.30493i | 0.757818 | + | 0.652466i | \(0.226266\pi\) | ||||
−0.757818 | + | 0.652466i | \(0.773734\pi\) | |||||||
\(522\) | 2.56155 | − | 1.19935i | 0.112116 | − | 0.0524942i | ||||
\(523\) | 32.4924 | 1.42079 | 0.710397 | − | 0.703801i | \(-0.248515\pi\) | ||||
0.710397 | + | 0.703801i | \(0.248515\pi\) | |||||||
\(524\) | 7.36932 | − | 8.83841i | 0.321930 | − | 0.386108i | ||||
\(525\) | −9.56155 | + | 13.0776i | −0.417300 | + | 0.570753i | ||||
\(526\) | 14.8078 | + | 31.6261i | 0.645649 | + | 1.37896i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −3.68466 | + | 0.673500i | −0.160354 | + | 0.0293103i | ||||
\(529\) | 22.1231 | 0.961874 | ||||||||
\(530\) | −24.4924 | − | 52.3104i | −1.06388 | − | 2.27222i | ||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 9.12311 | + | 36.5712i | 0.395537 | + | 1.58556i | ||||
\(533\) | 2.73863 | 0.118623 | ||||||||
\(534\) | 0.876894 | + | 1.87285i | 0.0379469 | + | 0.0810463i | ||||
\(535\) | 31.6155 | 1.36686 | ||||||||
\(536\) | 29.9309 | + | 7.86962i | 1.29282 | + | 0.339916i | ||||
\(537\) | 16.1498i | 0.696916i | ||||||||
\(538\) | 6.49242 | + | 13.8664i | 0.279908 | + | 0.597822i | ||||
\(539\) | 6.24621 | − | 1.98813i | 0.269043 | − | 0.0856349i | ||||
\(540\) | −5.12311 | − | 4.27156i | −0.220463 | − | 0.183819i | ||||
\(541\) | 2.87689 | 0.123687 | 0.0618437 | − | 0.998086i | \(-0.480302\pi\) | ||||
0.0618437 | + | 0.998086i | \(0.480302\pi\) | |||||||
\(542\) | 36.4924 | − | 17.0862i | 1.56748 | − | 0.733917i | ||||
\(543\) | 1.87285i | 0.0803718i | ||||||||
\(544\) | 24.0000 | − | 17.0862i | 1.02899 | − | 0.732566i | ||||
\(545\) | − | 27.5022i | − | 1.17806i | ||||||
\(546\) | −6.87689 | − | 1.34700i | −0.294304 | − | 0.0576463i | ||||
\(547\) | − | 16.7909i | − | 0.717929i | −0.933351 | − | 0.358964i | \(-0.883130\pi\) | ||
0.933351 | − | 0.358964i | \(-0.116870\pi\) | |||||||
\(548\) | 0.315342 | − | 0.378206i | 0.0134707 | − | 0.0161562i | ||||
\(549\) | 4.79741i | 0.204749i | ||||||||
\(550\) | 3.43845 | + | 7.34376i | 0.146616 | + | 0.313139i | ||||
\(551\) | −14.2462 | −0.606909 | ||||||||
\(552\) | −2.56155 | − | 0.673500i | −0.109027 | − | 0.0286661i | ||||
\(553\) | 5.12311 | + | 3.74571i | 0.217857 | + | 0.159284i | ||||
\(554\) | 6.56155 | − | 3.07221i | 0.278774 | − | 0.130526i | ||||
\(555\) | − | 3.74571i | − | 0.158996i | ||||||
\(556\) | −15.3693 | + | 18.4332i | −0.651804 | + | 0.781743i | ||||
\(557\) | 14.0000 | 0.593199 | 0.296600 | − | 0.955002i | \(-0.404147\pi\) | ||||
0.296600 | + | 0.955002i | \(0.404147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −16.9848 | −0.718382 | ||||||||
\(560\) | −15.3693 | + | 31.7738i | −0.649472 | + | 1.34269i | ||||
\(561\) | −4.87689 | −0.205903 | ||||||||
\(562\) | −20.8078 | + | 9.74247i | −0.877723 | + | 0.410961i | ||||
\(563\) | 2.24621 | 0.0946665 | 0.0473333 | − | 0.998879i | \(-0.484928\pi\) | ||||
0.0473333 | + | 0.998879i | \(0.484928\pi\) | |||||||
\(564\) | −8.00000 | + | 9.59482i | −0.336861 | + | 0.404015i | ||||
\(565\) | − | 14.1617i | − | 0.595786i | ||||||
\(566\) | −11.3693 | + | 5.32326i | −0.477888 | + | 0.223753i | ||||
\(567\) | −1.56155 | + | 2.13578i | −0.0655791 | + | 0.0896943i | ||||
\(568\) | 10.5616 | + | 2.77691i | 0.443153 | + | 0.116517i | ||||
\(569\) | −30.9848 | −1.29895 | −0.649476 | − | 0.760382i | \(-0.725012\pi\) | ||||
−0.649476 | + | 0.760382i | \(0.725012\pi\) | |||||||
\(570\) | 14.2462 | + | 30.4268i | 0.596708 | + | 1.27444i | ||||
\(571\) | − | 8.83841i | − | 0.369876i | −0.982750 | − | 0.184938i | \(-0.940792\pi\) | ||
0.982750 | − | 0.184938i | \(-0.0592084\pi\) | |||||||
\(572\) | −2.24621 | + | 2.69400i | −0.0939188 | + | 0.112642i | ||||
\(573\) | − | 2.80928i | − | 0.117359i | ||||||
\(574\) | −5.36932 | − | 1.05171i | −0.224111 | − | 0.0438973i | ||||
\(575\) | 5.73384i | 0.239118i | ||||||||
\(576\) | −6.96543 | − | 3.93481i | −0.290226 | − | 0.163950i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 12.9654 | − | 6.07059i | 0.539291 | − | 0.252503i | ||||
\(579\) | 15.3693 | 0.638727 | ||||||||
\(580\) | −10.2462 | − | 8.54312i | −0.425451 | − | 0.354734i | ||||
\(581\) | 16.0000 | − | 21.8836i | 0.663792 | − | 0.907887i | ||||
\(582\) | −6.24621 | − | 13.3405i | −0.258914 | − | 0.552983i | ||||
\(583\) | 11.4677i | 0.474943i | ||||||||
\(584\) | −18.2462 | − | 4.79741i | −0.755034 | − | 0.198518i | ||||
\(585\) | −6.24621 | −0.258249 | ||||||||
\(586\) | −8.24621 | − | 17.6121i | −0.340648 | − | 0.727549i | ||||
\(587\) | −21.7538 | −0.897875 | −0.448937 | − | 0.893563i | \(-0.648197\pi\) | ||||
−0.448937 | + | 0.893563i | \(0.648197\pi\) | |||||||
\(588\) | 12.9654 | + | 5.28181i | 0.534686 | + | 0.217818i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −8.00000 | − | 17.0862i | −0.329355 | − | 0.703429i | ||||
\(591\) | 16.2462 | 0.668280 | ||||||||
\(592\) | −0.807764 | − | 4.41921i | −0.0331989 | − | 0.181628i | ||||
\(593\) | − | 26.0399i | − | 1.06933i | −0.845064 | − | 0.534666i | \(-0.820438\pi\) | ||
0.845064 | − | 0.534666i | \(-0.179562\pi\) | |||||||
\(594\) | 0.561553 | + | 1.19935i | 0.0230408 | + | 0.0492100i | ||||
\(595\) | −27.1231 | + | 37.0970i | −1.11194 | + | 1.52083i | ||||
\(596\) | −12.8078 | + | 15.3610i | −0.524626 | + | 0.629212i | ||||
\(597\) | 3.12311 | 0.127820 | ||||||||
\(598\) | −2.24621 | + | 1.05171i | −0.0918544 | + | 0.0430074i | ||||
\(599\) | − | 17.2015i | − | 0.702835i | −0.936219 | − | 0.351417i | \(-0.885700\pi\) | ||
0.936219 | − | 0.351417i | \(-0.114300\pi\) | |||||||
\(600\) | −4.40388 | + | 16.7495i | −0.179788 | + | 0.683795i | ||||
\(601\) | − | 17.0862i | − | 0.696962i | −0.937316 | − | 0.348481i | \(-0.886698\pi\) | ||
0.937316 | − | 0.348481i | \(-0.113302\pi\) | |||||||
\(602\) | 33.3002 | + | 6.52262i | 1.35721 | + | 0.265842i | ||||
\(603\) | − | 10.9418i | − | 0.445585i | ||||||
\(604\) | −13.9309 | − | 11.6153i | −0.566839 | − | 0.472621i | ||||
\(605\) | 33.7619i | 1.37262i | ||||||||
\(606\) | 8.24621 | + | 17.6121i | 0.334979 | + | 0.715442i | ||||
\(607\) | 7.61553 | 0.309105 | 0.154552 | − | 0.987985i | \(-0.450606\pi\) | ||||
0.154552 | + | 0.987985i | \(0.450606\pi\) | |||||||
\(608\) | 23.3693 | + | 32.8255i | 0.947751 | + | 1.33125i | ||||
\(609\) | −3.12311 | + | 4.27156i | −0.126555 | + | 0.173092i | ||||
\(610\) | 20.4924 | − | 9.59482i | 0.829714 | − | 0.388483i | ||||
\(611\) | 11.6982i | 0.473260i | ||||||||
\(612\) | −8.00000 | − | 6.67026i | −0.323381 | − | 0.269629i | ||||
\(613\) | 8.73863 | 0.352950 | 0.176475 | − | 0.984305i | \(-0.443531\pi\) | ||||
0.176475 | + | 0.984305i | \(0.443531\pi\) | |||||||
\(614\) | −25.1231 | + | 11.7630i | −1.01389 | + | 0.474715i | ||||
\(615\) | −4.87689 | −0.196655 | ||||||||
\(616\) | 5.43845 | − | 4.41921i | 0.219121 | − | 0.178055i | ||||
\(617\) | 32.2462 | 1.29818 | 0.649092 | − | 0.760710i | \(-0.275149\pi\) | ||||
0.649092 | + | 0.760710i | \(0.275149\pi\) | |||||||
\(618\) | −10.2462 | + | 4.79741i | −0.412163 | + | 0.192980i | ||||
\(619\) | 20.0000 | 0.803868 | 0.401934 | − | 0.915669i | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.936426i | 0.0375775i | ||||||||
\(622\) | −10.2462 | + | 4.79741i | −0.410836 | + | 0.192359i | ||||
\(623\) | −3.12311 | − | 2.28343i | −0.125125 | − | 0.0914835i | ||||
\(624\) | −7.36932 | + | 1.34700i | −0.295009 | + | 0.0539232i | ||||
\(625\) | −18.1231 | −0.724924 | ||||||||
\(626\) | 13.7538 | + | 29.3751i | 0.549712 | + | 1.17406i | ||||
\(627\) | − | 6.67026i | − | 0.266385i | ||||||
\(628\) | −33.6155 | − | 28.0281i | −1.34141 | − | 1.11844i | ||||
\(629\) | − | 5.84912i | − | 0.233220i | ||||||
\(630\) | 12.2462 | + | 2.39871i | 0.487901 | + | 0.0955667i | ||||
\(631\) | − | 40.3169i | − | 1.60499i | −0.596659 | − | 0.802495i | \(-0.703506\pi\) | ||
0.596659 | − | 0.802495i | \(-0.296494\pi\) | |||||||
\(632\) | 6.56155 | + | 1.72521i | 0.261005 | + | 0.0686250i | ||||
\(633\) | − | 12.8147i | − | 0.509338i | ||||||
\(634\) | 18.5616 | − | 8.69076i | 0.737173 | − | 0.345154i | ||||
\(635\) | 32.9848 | 1.30896 | ||||||||
\(636\) | −15.6847 | + | 18.8114i | −0.621937 | + | 0.745922i | ||||
\(637\) | 12.4924 | − | 3.97626i | 0.494968 | − | 0.157545i | ||||
\(638\) | 1.12311 | + | 2.39871i | 0.0444642 | + | 0.0949657i | ||||
\(639\) | − | 3.86098i | − | 0.152738i | ||||||
\(640\) | −2.87689 | + | 37.6229i | −0.113719 | + | 1.48717i | ||||
\(641\) | −42.4924 | −1.67835 | −0.839175 | − | 0.543862i | \(-0.816962\pi\) | ||||
−0.839175 | + | 0.543862i | \(0.816962\pi\) | |||||||
\(642\) | −5.68466 | − | 12.1412i | −0.224356 | − | 0.479174i | ||||
\(643\) | −11.6155 | −0.458072 | −0.229036 | − | 0.973418i | \(-0.573557\pi\) | ||||
−0.229036 | + | 0.973418i | \(0.573557\pi\) | |||||||
\(644\) | 4.80776 | − | 1.19935i | 0.189452 | − | 0.0472611i | ||||
\(645\) | 30.2462 | 1.19094 | ||||||||
\(646\) | 22.2462 | + | 47.5130i | 0.875265 | + | 1.86937i | ||||
\(647\) | −32.9848 | −1.29677 | −0.648384 | − | 0.761313i | \(-0.724555\pi\) | ||||
−0.648384 | + | 0.761313i | \(0.724555\pi\) | |||||||
\(648\) | −0.719224 | + | 2.73546i | −0.0282538 | + | 0.107459i | ||||
\(649\) | 3.74571i | 0.147032i | ||||||||
\(650\) | 6.87689 | + | 14.6875i | 0.269734 | + | 0.576092i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.1771 | + | 20.1584i | 0.946848 | + | 0.789465i | ||||
\(653\) | 16.7386 | 0.655033 | 0.327517 | − | 0.944845i | \(-0.393788\pi\) | ||||
0.327517 | + | 0.944845i | \(0.393788\pi\) | |||||||
\(654\) | −10.5616 | + | 4.94506i | −0.412989 | + | 0.193367i | ||||
\(655\) | 19.1896i | 0.749801i | ||||||||
\(656\) | −5.75379 | + | 1.05171i | −0.224648 | + | 0.0410622i | ||||
\(657\) | 6.67026i | 0.260232i | ||||||||
\(658\) | 4.49242 | − | 22.9354i | 0.175133 | − | 0.894113i | ||||
\(659\) | 26.7963i | 1.04384i | 0.852995 | + | 0.521919i | \(0.174783\pi\) | ||||
−0.852995 | + | 0.521919i | \(0.825217\pi\) | |||||||
\(660\) | 4.00000 | − | 4.79741i | 0.155700 | − | 0.186739i | ||||
\(661\) | 8.54312i | 0.332289i | 0.986101 | + | 0.166144i | \(0.0531318\pi\) | ||||
−0.986101 | + | 0.166144i | \(0.946868\pi\) | |||||||
\(662\) | 10.5616 | + | 22.5571i | 0.410486 | + | 0.876708i | ||||
\(663\) | −9.75379 | −0.378806 | ||||||||
\(664\) | 7.36932 | − | 28.0281i | 0.285985 | − | 1.08770i | ||||
\(665\) | −50.7386 | − | 37.0970i | −1.96756 | − | 1.43856i | ||||
\(666\) | −1.43845 | + | 0.673500i | −0.0557387 | + | 0.0260976i | ||||
\(667\) | 1.87285i | 0.0725171i | ||||||||
\(668\) | 18.2462 | − | 21.8836i | 0.705967 | − | 0.846704i | ||||
\(669\) | −27.1231 | −1.04864 | ||||||||
\(670\) | −46.7386 | + | 21.8836i | −1.80567 | + | 0.845439i | ||||
\(671\) | −4.49242 | −0.173428 | ||||||||
\(672\) | 14.9654 | + | 0.189103i | 0.577304 | + | 0.00729480i | ||||
\(673\) | −27.8617 | −1.07399 | −0.536996 | − | 0.843585i | \(-0.680441\pi\) | ||||
−0.536996 | + | 0.843585i | \(0.680441\pi\) | |||||||
\(674\) | −10.5616 | + | 4.94506i | −0.406816 | + | 0.190477i | ||||
\(675\) | 6.12311 | 0.235678 | ||||||||
\(676\) | 12.1577 | − | 14.5813i | 0.467603 | − | 0.560821i | ||||
\(677\) | 9.18425i | 0.352979i | 0.984302 | + | 0.176490i | \(0.0564742\pi\) | ||||
−0.984302 | + | 0.176490i | \(0.943526\pi\) | |||||||
\(678\) | −5.43845 | + | 2.54635i | −0.208862 | + | 0.0977921i | ||||
\(679\) | 22.2462 | + | 16.2651i | 0.853731 | + | 0.624197i | ||||
\(680\) | −12.4924 | + | 47.5130i | −0.479063 | + | 1.82204i | ||||
\(681\) | 16.4924 | 0.631991 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.1843i | 1.23150i | 0.787942 | + | 0.615750i | \(0.211147\pi\) | ||||
−0.787942 | + | 0.615750i | \(0.788853\pi\) | |||||||
\(684\) | 9.12311 | − | 10.9418i | 0.348831 | − | 0.418371i | ||||
\(685\) | 0.821147i | 0.0313744i | ||||||||
\(686\) | −26.0194 | + | 2.99838i | −0.993426 | + | 0.114479i | ||||
\(687\) | − | 5.61856i | − | 0.214361i | ||||||
\(688\) | 35.6847 | − | 6.52262i | 1.36046 | − | 0.248672i | ||||
\(689\) | 22.9354i | 0.873767i | ||||||||
\(690\) | 4.00000 | − | 1.87285i | 0.152277 | − | 0.0712983i | ||||
\(691\) | 12.0000 | 0.456502 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(692\) | −25.6155 | − | 21.3578i | −0.973756 | − | 0.811901i | ||||
\(693\) | −2.00000 | − | 1.46228i | −0.0759737 | − | 0.0555474i | ||||
\(694\) | −12.0691 | − | 25.7770i | −0.458138 | − | 0.978481i | ||||
\(695\) | − | 40.0216i | − | 1.51811i | ||||||
\(696\) | −1.43845 | + | 5.47091i | −0.0545242 | + | 0.207374i | ||||
\(697\) | −7.61553 | −0.288459 | ||||||||
\(698\) | 13.1231 | + | 28.0281i | 0.496717 | + | 1.06088i | ||||
\(699\) | −22.4924 | −0.850742 | ||||||||
\(700\) | −7.84233 | − | 31.4370i | −0.296412 | − | 1.18821i | ||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | 1.12311 | + | 2.39871i | 0.0423889 | + | 0.0905333i | ||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 3.68466 | − | 6.52262i | 0.138871 | − | 0.245830i | ||||
\(705\) | − | 20.8319i | − | 0.784576i | ||||||
\(706\) | 17.3693 | + | 37.0970i | 0.653703 | + | 1.39616i | ||||
\(707\) | −29.3693 | − | 21.4731i | −1.10455 | − | 0.807578i | ||||
\(708\) | −5.12311 | + | 6.14441i | −0.192538 | + | 0.230921i | ||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | −16.4924 | + | 7.72197i | −0.618950 | + | 0.289800i | ||||
\(711\) | − | 2.39871i | − | 0.0899585i | ||||||
\(712\) | −4.00000 | − | 1.05171i | −0.149906 | − | 0.0394143i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 19.1231 | + | 3.74571i | 0.715664 | + | 0.140180i | ||||
\(715\) | − | 5.84912i | − | 0.218745i | ||||||
\(716\) | −24.8078 | − | 20.6843i | −0.927110 | − | 0.773008i | ||||
\(717\) | − | 16.1498i | − | 0.603126i | ||||||
\(718\) | −13.6847 | − | 29.2274i | −0.510707 | − | 1.09076i | ||||
\(719\) | 28.4924 | 1.06259 | 0.531294 | − | 0.847187i | \(-0.321706\pi\) | ||||
0.531294 | + | 0.847187i | \(0.321706\pi\) | |||||||
\(720\) | 13.1231 | − | 2.39871i | 0.489069 | − | 0.0893945i | ||||
\(721\) | 12.4924 | − | 17.0862i | 0.465242 | − | 0.636325i | ||||
\(722\) | −40.6501 | + | 19.0329i | −1.51284 | + | 0.708332i | ||||
\(723\) | − | 23.7565i | − | 0.883514i | ||||||
\(724\) | −2.87689 | − | 2.39871i | −0.106919 | − | 0.0891472i | ||||
\(725\) | 12.2462 | 0.454813 | ||||||||
\(726\) | 12.9654 | − | 6.07059i | 0.481192 | − | 0.225301i | ||||
\(727\) | 32.9848 | 1.22334 | 0.611670 | − | 0.791113i | \(-0.290498\pi\) | ||||
0.611670 | + | 0.791113i | \(0.290498\pi\) | |||||||
\(728\) | 10.8769 | − | 8.83841i | 0.403125 | − | 0.327573i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 28.4924 | − | 13.3405i | 1.05455 | − | 0.493755i | ||||
\(731\) | 47.2311 | 1.74690 | ||||||||
\(732\) | −7.36932 | − | 6.14441i | −0.272378 | − | 0.227104i | ||||
\(733\) | 36.0453i | 1.33136i | 0.746235 | + | 0.665682i | \(0.231859\pi\) | ||||
−0.746235 | + | 0.665682i | \(0.768141\pi\) | |||||||
\(734\) | 42.7386 | − | 20.0108i | 1.57751 | − | 0.738612i | ||||
\(735\) | −22.2462 | + | 7.08084i | −0.820564 | + | 0.261181i | ||||
\(736\) | 4.31534 | − | 3.07221i | 0.159066 | − | 0.113243i | ||||
\(737\) | 10.2462 | 0.377424 | ||||||||
\(738\) | 0.876894 | + | 1.87285i | 0.0322789 | + | 0.0689407i | ||||
\(739\) | 36.5712i | 1.34529i | 0.739964 | + | 0.672646i | \(0.234842\pi\) | ||||
−0.739964 | + | 0.672646i | \(0.765158\pi\) | |||||||
\(740\) | 5.75379 | + | 4.79741i | 0.211513 | + | 0.176356i | ||||
\(741\) | − | 13.3405i | − | 0.490077i | ||||||
\(742\) | 8.80776 | − | 44.9666i | 0.323343 | − | 1.65078i | ||||
\(743\) | − | 35.1089i | − | 1.28802i | −0.765017 | − | 0.644010i | \(-0.777269\pi\) | ||
0.765017 | − | 0.644010i | \(-0.222731\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 33.3513i | − | 1.22190i | ||||||
\(746\) | 12.8078 | − | 5.99676i | 0.468926 | − | 0.219557i | ||||
\(747\) | −10.2462 | −0.374889 | ||||||||
\(748\) | 6.24621 | − | 7.49141i | 0.228384 | − | 0.273913i | ||||
\(749\) | 20.2462 | + | 14.8028i | 0.739780 | + | 0.540883i | ||||
\(750\) | −2.24621 | − | 4.79741i | −0.0820200 | − | 0.175177i | ||||
\(751\) | 28.8492i | 1.05272i | 0.850261 | + | 0.526361i | \(0.176444\pi\) | ||||
−0.850261 | + | 0.526361i | \(0.823556\pi\) | |||||||
\(752\) | −4.49242 | − | 24.5776i | −0.163822 | − | 0.896254i | ||||
\(753\) | 5.75379 | 0.209680 | ||||||||
\(754\) | 2.24621 | + | 4.79741i | 0.0818022 | + | 0.174711i | ||||
\(755\) | 30.2462 | 1.10077 | ||||||||
\(756\) | −1.28078 | − | 5.13416i | −0.0465814 | − | 0.186728i | ||||
\(757\) | −34.9848 | −1.27155 | −0.635773 | − | 0.771876i | \(-0.719319\pi\) | ||||
−0.635773 | + | 0.771876i | \(0.719319\pi\) | |||||||
\(758\) | 15.0540 | + | 32.1520i | 0.546785 | + | 1.16781i | ||||
\(759\) | −0.876894 | −0.0318292 | ||||||||
\(760\) | −64.9848 | − | 17.0862i | −2.35725 | − | 0.619783i | ||||
\(761\) | − | 29.7856i | − | 1.07973i | −0.841752 | − | 0.539864i | \(-0.818476\pi\) | ||
0.841752 | − | 0.539864i | \(-0.181524\pi\) | |||||||
\(762\) | −5.93087 | − | 12.6670i | −0.214853 | − | 0.458878i | ||||
\(763\) | 12.8769 | − | 17.6121i | 0.466175 | − | 0.637600i | ||||
\(764\) | 4.31534 | + | 3.59806i | 0.156124 | + | 0.130173i | ||||
\(765\) | 17.3693 | 0.627989 | ||||||||
\(766\) | 12.4924 | − | 5.84912i | 0.451370 | − | 0.211337i | ||||
\(767\) | 7.49141i | 0.270499i | ||||||||
\(768\) | 14.9654 | − | 5.66001i | 0.540019 | − | 0.204238i | ||||
\(769\) | − | 32.5302i | − | 1.17307i | −0.809925 | − | 0.586534i | \(-0.800492\pi\) | ||
0.809925 | − | 0.586534i | \(-0.199508\pi\) | |||||||
\(770\) | −2.24621 | + | 11.4677i | −0.0809478 | + | 0.413266i | ||||
\(771\) | − | 2.28343i | − | 0.0822356i | ||||||
\(772\) | −19.6847 | + | 23.6089i | −0.708466 | + | 0.849701i | ||||
\(773\) | 3.33513i | 0.119956i | 0.998200 | + | 0.0599782i | \(0.0191031\pi\) | ||||
−0.998200 | + | 0.0599782i | \(0.980897\pi\) | |||||||
\(774\) | −5.43845 | − | 11.6153i | −0.195481 | − | 0.417504i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28.4924 | + | 7.49141i | 1.02282 | + | 0.268926i | ||||
\(777\) | 1.75379 | − | 2.39871i | 0.0629168 | − | 0.0860531i | ||||
\(778\) | 20.8078 | − | 9.74247i | 0.745994 | − | 0.349284i | ||||
\(779\) | − | 10.4160i | − | 0.373191i | ||||||
\(780\) | 8.00000 | − | 9.59482i | 0.286446 | − | 0.343550i | ||||
\(781\) | 3.61553 | 0.129374 | ||||||||
\(782\) | 6.24621 | − | 2.92456i | 0.223364 | − | 0.104582i | ||||
\(783\) | 2.00000 | 0.0714742 | ||||||||
\(784\) | −24.7192 | + | 13.1514i | −0.882829 | + | 0.469694i | ||||
\(785\) | 72.9848 | 2.60494 | ||||||||
\(786\) | 7.36932 | − | 3.45041i | 0.262855 | − | 0.123072i | ||||
\(787\) | −44.9848 | −1.60354 | −0.801768 | − | 0.597635i | \(-0.796107\pi\) | ||||
−0.801768 | + | 0.597635i | \(0.796107\pi\) | |||||||
\(788\) | −20.8078 | + | 24.9559i | −0.741246 | + | 0.889015i | ||||
\(789\) | 24.6929i | 0.879091i | ||||||||
\(790\) | −10.2462 | + | 4.79741i | −0.364544 | + | 0.170684i | ||||
\(791\) | 6.63068 | − | 9.06897i | 0.235760 | − | 0.322455i | ||||
\(792\) | −2.56155 | − | 0.673500i | −0.0910208 | − | 0.0239318i | ||||
\(793\) | −8.98485 | −0.319061 | ||||||||
\(794\) | −10.8769 | − | 23.2306i | −0.386007 | − | 0.824425i | ||||
\(795\) | − | 40.8427i | − | 1.44854i | ||||||
\(796\) | −4.00000 | + | 4.79741i | −0.141776 | + | 0.170040i | ||||
\(797\) | 39.6110i | 1.40309i | 0.712623 | + | 0.701547i | \(0.247507\pi\) | ||||
−0.712623 | + | 0.701547i | \(0.752493\pi\) | |||||||
\(798\) | −5.12311 | + | 26.1552i | −0.181356 | + | 0.925884i | ||||
\(799\) | − | 32.5302i | − | 1.15083i | ||||||
\(800\) | −20.0885 | − | 28.2172i | −0.710237 | − | 0.997627i | ||||
\(801\) | 1.46228i | 0.0516671i | ||||||||
\(802\) | −10.5616 | + | 4.94506i | −0.372941 | + | 0.174616i | ||||
\(803\) | −6.24621 | −0.220424 | ||||||||
\(804\) | 16.8078 | + | 14.0140i | 0.592764 | + | 0.494237i | ||||
\(805\) | −4.87689 | + | 6.67026i | −0.171888 | + | 0.235096i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.8265i | 0.381112i | ||||||||
\(808\) | −37.6155 | − | 9.89012i | −1.32331 | − | 0.347933i | ||||
\(809\) | 22.4924 | 0.790791 | 0.395396 | − | 0.918511i | \(-0.370607\pi\) | ||||
0.395396 | + | 0.918511i | \(0.370607\pi\) | |||||||
\(810\) | −2.00000 | − | 4.27156i | −0.0702728 | − | 0.150087i | ||||
\(811\) | 0.492423 | 0.0172913 | 0.00864565 | − | 0.999963i | \(-0.497248\pi\) | ||||
0.00864565 | + | 0.999963i | \(0.497248\pi\) | |||||||
\(812\) | −2.56155 | − | 10.2683i | −0.0898929 | − | 0.360347i | ||||
\(813\) | 28.4924 | 0.999273 | ||||||||
\(814\) | −0.630683 | − | 1.34700i | −0.0221054 | − | 0.0472123i | ||||
\(815\) | −52.4924 | −1.83873 | ||||||||
\(816\) | 20.4924 | − | 3.74571i | 0.717378 | − | 0.131126i | ||||
\(817\) | 64.5992i | 2.26004i | ||||||||
\(818\) | 0.492423 | + | 1.05171i | 0.0172171 | + | 0.0367720i | ||||
\(819\) | −4.00000 | − | 2.92456i | −0.139771 | − | 0.102192i | ||||
\(820\) | 6.24621 | − | 7.49141i | 0.218127 | − | 0.261611i | ||||
\(821\) | −57.2311 | −1.99738 | −0.998689 | − | 0.0511922i | \(-0.983698\pi\) | ||||
−0.998689 | + | 0.0511922i | \(0.983698\pi\) | |||||||
\(822\) | 0.315342 | − | 0.147647i | 0.0109988 | − | 0.00514978i | ||||
\(823\) | 13.0452i | 0.454728i | 0.973810 | + | 0.227364i | \(0.0730108\pi\) | ||||
−0.973810 | + | 0.227364i | \(0.926989\pi\) | |||||||
\(824\) | 5.75379 | − | 21.8836i | 0.200443 | − | 0.762353i | ||||
\(825\) | 5.73384i | 0.199627i | ||||||||
\(826\) | 2.87689 | − | 14.6875i | 0.100100 | − | 0.511044i | ||||
\(827\) | 55.9408i | 1.94525i | 0.232373 | + | 0.972627i | \(0.425351\pi\) | ||||
−0.232373 | + | 0.972627i | \(0.574649\pi\) | |||||||
\(828\) | −1.43845 | − | 1.19935i | −0.0499895 | − | 0.0416804i | ||||
\(829\) | 21.0625i | 0.731531i | 0.930707 | + | 0.365765i | \(0.119193\pi\) | ||||
−0.930707 | + | 0.365765i | \(0.880807\pi\) | |||||||
\(830\) | 20.4924 | + | 43.7673i | 0.711302 | + | 1.51918i | ||||
\(831\) | 5.12311 | 0.177719 | ||||||||
\(832\) | 7.36932 | − | 13.0452i | 0.255485 | − | 0.452262i | ||||
\(833\) | −34.7386 | + | 11.0571i | −1.20362 | + | 0.383106i | ||||
\(834\) | −15.3693 | + | 7.19612i | −0.532196 | + | 0.249181i | ||||
\(835\) | 47.5130i | 1.64426i | ||||||||
\(836\) | 10.2462 | + | 8.54312i | 0.354373 | + | 0.295470i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 21.1231 | − | 9.89012i | 0.729686 | − | 0.341648i | ||||
\(839\) | −42.7386 | −1.47550 | −0.737751 | − | 0.675073i | \(-0.764112\pi\) | ||||
−0.737751 | + | 0.675073i | \(0.764112\pi\) | |||||||
\(840\) | −19.3693 | + | 15.7392i | −0.668305 | + | 0.543055i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | −13.9309 | + | 6.52262i | −0.480089 | + | 0.224784i | ||||
\(843\) | −16.2462 | −0.559549 | ||||||||
\(844\) | 19.6847 | + | 16.4127i | 0.677574 | + | 0.564950i | ||||
\(845\) | 31.6585i | 1.08908i | ||||||||
\(846\) | −8.00000 | + | 3.74571i | −0.275046 | + | 0.128780i | ||||
\(847\) | −15.8078 | + | 21.6207i | −0.543161 | + | 0.742897i | ||||
\(848\) | −8.80776 | − | 48.1865i | −0.302460 | − | 1.65473i | ||||
\(849\) | −8.87689 | −0.304654 | ||||||||
\(850\) | −19.1231 | − | 40.8427i | −0.655917 | − | 1.40089i | ||||
\(851\) | − | 1.05171i | − | 0.0360520i | ||||||
\(852\) | 5.93087 | + | 4.94506i | 0.203188 | + | 0.169415i | ||||
\(853\) | 50.2070i | 1.71905i | 0.511090 | + | 0.859527i | \(0.329242\pi\) | ||||
−0.511090 | + | 0.859527i | \(0.670758\pi\) | |||||||
\(854\) | 17.6155 | + | 3.45041i | 0.602791 | + | 0.118071i | ||||
\(855\) | 23.7565i | 0.812455i | ||||||||
\(856\) | 25.9309 | + | 6.81791i | 0.886299 | + | 0.233031i | ||||
\(857\) | − | 56.4667i | − | 1.92887i | −0.264329 | − | 0.964433i | \(-0.585150\pi\) | ||
0.264329 | − | 0.964433i | \(-0.414850\pi\) | |||||||
\(858\) | −2.24621 | + | 1.05171i | −0.0766844 | + | 0.0359046i | ||||
\(859\) | −25.8617 | −0.882391 | −0.441196 | − | 0.897411i | \(-0.645445\pi\) | ||||
−0.441196 | + | 0.897411i | \(0.645445\pi\) | |||||||
\(860\) | −38.7386 | + | 46.4613i | −1.32098 | + | 1.58432i | ||||
\(861\) | −3.12311 | − | 2.28343i | −0.106435 | − | 0.0778190i | ||||
\(862\) | 2.80776 | + | 5.99676i | 0.0956328 | + | 0.204251i | ||||
\(863\) | 8.65840i | 0.294735i | 0.989082 | + | 0.147368i | \(0.0470800\pi\) | ||||
−0.989082 | + | 0.147368i | \(0.952920\pi\) | |||||||
\(864\) | −3.28078 | − | 4.60831i | −0.111614 | − | 0.156778i | ||||
\(865\) | 55.6155 | 1.89098 | ||||||||
\(866\) | 8.00000 | + | 17.0862i | 0.271851 | + | 0.580614i | ||||
\(867\) | 10.1231 | 0.343799 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.24621 | 0.0761975 | ||||||||
\(870\) | −4.00000 | − | 8.54312i | −0.135613 | − | 0.289639i | ||||
\(871\) | 20.4924 | 0.694359 | ||||||||
\(872\) | 5.93087 | − | 22.5571i | 0.200845 | − | 0.763881i | ||||
\(873\) | − | 10.4160i | − | 0.352527i | ||||||
\(874\) | 4.00000 | + | 8.54312i | 0.135302 | + | 0.288975i | ||||
\(875\) | 8.00000 | + | 5.84912i | 0.270449 | + | 0.197736i | ||||
\(876\) | −10.2462 | − | 8.54312i | −0.346187 | − | 0.288645i | ||||
\(877\) | 36.2462 | 1.22395 | 0.611974 | − | 0.790878i | \(-0.290376\pi\) | ||||
0.611974 | + | 0.790878i | \(0.290376\pi\) | |||||||
\(878\) | 8.49242 | − | 3.97626i | 0.286605 | − | 0.134192i | ||||
\(879\) | − | 13.7511i | − | 0.463813i | ||||||
\(880\) | 2.24621 | + | 12.2888i | 0.0757198 | + | 0.414256i | ||||
\(881\) | 46.8719i | 1.57915i | 0.613652 | + | 0.789577i | \(0.289700\pi\) | ||||
−0.613652 | + | 0.789577i | \(0.710300\pi\) | |||||||
\(882\) | 6.71922 | + | 7.26994i | 0.226248 | + | 0.244792i | ||||
\(883\) | 18.6638i | 0.628087i | 0.949409 | + | 0.314043i | \(0.101684\pi\) | ||||
−0.949409 | + | 0.314043i | \(0.898316\pi\) | |||||||
\(884\) | 12.4924 | − | 14.9828i | 0.420166 | − | 0.503927i | ||||
\(885\) | − | 13.3405i | − | 0.448437i | ||||||
\(886\) | −11.3002 | − | 24.1347i | −0.379637 | − | 0.810821i | ||||
\(887\) | −26.7386 | −0.897795 | −0.448898 | − | 0.893583i | \(-0.648183\pi\) | ||||
−0.448898 | + | 0.893583i | \(0.648183\pi\) | |||||||
\(888\) | 0.807764 | − | 3.07221i | 0.0271068 | − | 0.103096i | ||||
\(889\) | 21.1231 | + | 15.4439i | 0.708446 | + | 0.517973i | ||||
\(890\) | 6.24621 | − | 2.92456i | 0.209373 | − | 0.0980314i | ||||
\(891\) | 0.936426i | 0.0313715i | ||||||||
\(892\) | 34.7386 | − | 41.6639i | 1.16314 | − | 1.39501i | ||||
\(893\) | 44.4924 | 1.48888 | ||||||||
\(894\) | −12.8078 | + | 5.99676i | −0.428356 | + | 0.200562i | ||||
\(895\) | 53.8617 | 1.80040 | ||||||||
\(896\) | −19.4579 | + | 22.7462i | −0.650041 | + | 0.759899i | ||||
\(897\) | −1.75379 | −0.0585573 | ||||||||
\(898\) | −15.0540 | + | 7.04847i | −0.502358 | + | 0.235210i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −7.84233 | + | 9.40572i | −0.261411 | + | 0.313524i | ||||
\(901\) | − | 63.7781i | − | 2.12476i | ||||||
\(902\) | −1.75379 | + | 0.821147i | −0.0583948 | + | 0.0273412i | ||||
\(903\) | 19.3693 | + | 14.1617i | 0.644571 | + | 0.471271i | ||||
\(904\) | 3.05398 | − | 11.6153i | 0.101574 | − | 0.386320i | ||||
\(905\) | 6.24621 | 0.207631 | ||||||||
\(906\) | −5.43845 | − | 11.6153i | −0.180680 | − | 0.385893i | ||||
\(907\) | − | 38.4440i | − | 1.27651i | −0.769824 | − | 0.638256i | \(-0.779656\pi\) | ||
0.769824 | − | 0.638256i | \(-0.220344\pi\) | |||||||
\(908\) | −21.1231 | + | 25.3341i | −0.700995 | + | 0.840740i | ||||
\(909\) | 13.7511i | 0.456095i | ||||||||
\(910\) | −4.49242 | + | 22.9354i | −0.148922 | + | 0.760299i | ||||
\(911\) | 5.73384i | 0.189971i | 0.995479 | + | 0.0949853i | \(0.0302804\pi\) | ||||
−0.995479 | + | 0.0949853i | \(0.969720\pi\) | |||||||
\(912\) | 5.12311 | + | 28.0281i | 0.169643 | + | 0.928102i | ||||
\(913\) | − | 9.59482i | − | 0.317542i | ||||||
\(914\) | −0.315342 | + | 0.147647i | −0.0104306 | + | 0.00488373i | ||||
\(915\) | 16.0000 | 0.528944 | ||||||||
\(916\) | 8.63068 | + | 7.19612i | 0.285166 | + | 0.237766i | ||||
\(917\) | −8.98485 | + | 12.2888i | −0.296706 | + | 0.405813i | ||||
\(918\) | −3.12311 | − | 6.67026i | −0.103078 | − | 0.220152i | ||||
\(919\) | − | 9.06897i | − | 0.299158i | −0.988750 | − | 0.149579i | \(-0.952208\pi\) | ||
0.988750 | − | 0.149579i | \(-0.0477918\pi\) | |||||||
\(920\) | −2.24621 | + | 8.54312i | −0.0740554 | + | 0.281658i | ||||
\(921\) | −19.6155 | −0.646354 | ||||||||
\(922\) | 3.75379 | + | 8.01726i | 0.123624 | + | 0.264035i | ||||
\(923\) | 7.23106 | 0.238013 | ||||||||
\(924\) | 4.80776 | − | 1.19935i | 0.158164 | − | 0.0394558i | ||||
\(925\) | −6.87689 | −0.226111 | ||||||||
\(926\) | −23.5464 | − | 50.2899i | −0.773783 | − | 1.65263i | ||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | −6.56155 | − | 9.21662i | −0.215394 | − | 0.302550i | ||||
\(929\) | − | 3.56569i | − | 0.116987i | −0.998288 | − | 0.0584933i | \(-0.981370\pi\) | ||
0.998288 | − | 0.0584933i | \(-0.0186296\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1231 | − | 47.5130i | −0.495640 | − | 1.55718i | ||||
\(932\) | 28.8078 | − | 34.5507i | 0.943630 | − | 1.13174i | ||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | −43.8617 | + | 20.5366i | −1.43520 | + | 0.671980i | ||||
\(935\) | 16.2651i | 0.531925i | ||||||||
\(936\) | −5.12311 | − | 1.34700i | −0.167454 | − | 0.0440281i | ||||
\(937\) | 28.7845i | 0.940348i | 0.882574 | + | 0.470174i | \(0.155809\pi\) | ||||
−0.882574 | + | 0.470174i | \(0.844191\pi\) | |||||||
\(938\) | −40.1771 | − | 7.86962i | −1.31183 | − | 0.256952i | ||||
\(939\) | 22.9354i | 0.748467i | ||||||||
\(940\) | 32.0000 | + | 26.6811i | 1.04372 | + | 0.870240i | ||||
\(941\) | − | 53.7727i | − | 1.75294i | −0.481457 | − | 0.876470i | \(-0.659892\pi\) | ||
0.481457 | − | 0.876470i | \(-0.340108\pi\) | |||||||
\(942\) | −13.1231 | − | 28.0281i | −0.427574 | − | 0.913203i | ||||
\(943\) | −1.36932 | −0.0445911 | ||||||||
\(944\) | −2.87689 | − | 15.7392i | −0.0936349 | − | 0.512268i | ||||
\(945\) | 7.12311 | + | 5.20798i | 0.231715 | + | 0.169416i | ||||
\(946\) | 10.8769 | − | 5.09271i | 0.353638 | − | 0.165578i | ||||
\(947\) | − | 48.6800i | − | 1.58189i | −0.611889 | − | 0.790943i | \(-0.709590\pi\) | ||
0.611889 | − | 0.790943i | \(-0.290410\pi\) | |||||||
\(948\) | 3.68466 | + | 3.07221i | 0.119672 | + | 0.0997806i | ||||
\(949\) | −12.4924 | −0.405521 | ||||||||
\(950\) | 55.8617 | − | 26.1552i | 1.81239 | − | 0.848587i | ||||
\(951\) | 14.4924 | 0.469949 | ||||||||
\(952\) | −30.2462 | + | 24.5776i | −0.980285 | + | 0.796566i | ||||
\(953\) | −21.2311 | −0.687741 | −0.343871 | − | 0.939017i | \(-0.611738\pi\) | ||||
−0.343871 | + | 0.939017i | \(0.611738\pi\) | |||||||
\(954\) | −15.6847 | + | 7.34376i | −0.507810 | + | 0.237763i | ||||
\(955\) | −9.36932 | −0.303184 | ||||||||
\(956\) | 24.8078 | + | 20.6843i | 0.802340 | + | 0.668978i | ||||
\(957\) | 1.87285i | 0.0605407i | ||||||||
\(958\) | −16.0000 | + | 7.49141i | −0.516937 | + | 0.242037i | ||||
\(959\) | −0.384472 | + | 0.525853i | −0.0124152 | + | 0.0169807i | ||||
\(960\) | −13.1231 | + | 23.2306i | −0.423546 | + | 0.749766i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | −1.26137 | − | 2.69400i | −0.0406681 | − | 0.0868580i | ||||
\(963\) | − | 9.47954i | − | 0.305474i | ||||||
\(964\) | 36.4924 | + | 30.4268i | 1.17534 | + | 0.979980i | ||||
\(965\) | − | 51.2587i | − | 1.65008i | ||||||
\(966\) | 3.43845 | + | 0.673500i | 0.110630 | + | 0.0216695i | ||||
\(967\) | 8.83841i | 0.284224i | 0.989851 | + | 0.142112i | \(0.0453893\pi\) | ||||
−0.989851 | + | 0.142112i | \(0.954611\pi\) | |||||||
\(968\) | −7.28078 | + | 27.6913i | −0.234013 | + | 0.890032i | ||||
\(969\) | 37.0970i | 1.19173i | ||||||||
\(970\) | −44.4924 | + | 20.8319i | −1.42857 | + | 0.668873i | ||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | −1.28078 | + | 1.53610i | −0.0410809 | + | 0.0492705i | ||||
\(973\) | 18.7386 | − | 25.6294i | 0.600733 | − | 0.821639i | ||||
\(974\) | 0.946025 | + | 2.02050i | 0.0303126 | + | 0.0647410i | ||||
\(975\) | 11.4677i | 0.367260i | ||||||||
\(976\) | 18.8769 | − | 3.45041i | 0.604235 | − | 0.110445i | ||||
\(977\) | −11.2614 | −0.360283 | −0.180142 | − | 0.983641i | \(-0.557656\pi\) | ||||
−0.180142 | + | 0.983641i | \(0.557656\pi\) | |||||||
\(978\) | 9.43845 | + | 20.1584i | 0.301808 | + | 0.644596i | ||||
\(979\) | −1.36932 | −0.0437636 | ||||||||
\(980\) | 17.6155 | − | 43.2414i | 0.562707 | − | 1.38130i | ||||
\(981\) | −8.24621 | −0.263281 | ||||||||
\(982\) | −6.80776 | − | 14.5399i | −0.217244 | − | 0.463986i | ||||
\(983\) | 5.26137 | 0.167812 | 0.0839058 | − | 0.996474i | \(-0.473261\pi\) | ||||
0.0839058 | + | 0.996474i | \(0.473261\pi\) | |||||||
\(984\) | −4.00000 | − | 1.05171i | −0.127515 | − | 0.0335272i | ||||
\(985\) | − | 54.1833i | − | 1.72642i | ||||||
\(986\) | −6.24621 | − | 13.3405i | −0.198920 | − | 0.424849i | ||||
\(987\) | 9.75379 | − | 13.3405i | 0.310467 | − | 0.424634i | ||||
\(988\) | 20.4924 | + | 17.0862i | 0.651951 | + | 0.543586i | ||||
\(989\) | 8.49242 | 0.270043 | ||||||||
\(990\) | 4.00000 | − | 1.87285i | 0.127128 | − | 0.0595232i | ||||
\(991\) | 0.525853i | 0.0167043i | 0.999965 | + | 0.00835213i | \(0.00265860\pi\) | ||||
−0.999965 | + | 0.00835213i | \(0.997341\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.6121i | 0.558903i | ||||||||
\(994\) | −14.1771 | − | 2.77691i | −0.449670 | − | 0.0880783i | ||||
\(995\) | − | 10.4160i | − | 0.330208i | ||||||
\(996\) | 13.1231 | − | 15.7392i | 0.415822 | − | 0.498717i | ||||
\(997\) | − | 19.7802i | − | 0.626446i | −0.949680 | − | 0.313223i | \(-0.898591\pi\) | ||
0.949680 | − | 0.313223i | \(-0.101409\pi\) | |||||||
\(998\) | 8.31534 | + | 17.7597i | 0.263218 | + | 0.562175i | ||||
\(999\) | −1.12311 | −0.0355335 |
(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 | 84.2.b.a.55.2 | yes | 4 | |
3.2 | odd | 2 | 252.2.b.e.55.3 | 4 | |||
4.3 | odd | 2 | 84.2.b.b.55.1 | yes | 4 | ||
7.2 | even | 3 | 588.2.o.c.31.4 | 8 | |||
7.3 | odd | 6 | 588.2.o.a.19.2 | 8 | |||
7.4 | even | 3 | 588.2.o.c.19.2 | 8 | |||
7.5 | odd | 6 | 588.2.o.a.31.4 | 8 | |||
7.6 | odd | 2 | 84.2.b.b.55.2 | yes | 4 | ||
8.3 | odd | 2 | 1344.2.b.e.895.1 | 4 | |||
8.5 | even | 2 | 1344.2.b.f.895.1 | 4 | |||
12.11 | even | 2 | 252.2.b.d.55.4 | 4 | |||
21.20 | even | 2 | 252.2.b.d.55.3 | 4 | |||
24.5 | odd | 2 | 4032.2.b.n.3583.4 | 4 | |||
24.11 | even | 2 | 4032.2.b.j.3583.4 | 4 | |||
28.3 | even | 6 | 588.2.o.c.19.4 | 8 | |||
28.11 | odd | 6 | 588.2.o.a.19.4 | 8 | |||
28.19 | even | 6 | 588.2.o.c.31.2 | 8 | |||
28.23 | odd | 6 | 588.2.o.a.31.2 | 8 | |||
28.27 | even | 2 | inner | 84.2.b.a.55.1 | ✓ | 4 | |
56.13 | odd | 2 | 1344.2.b.e.895.4 | 4 | |||
56.27 | even | 2 | 1344.2.b.f.895.4 | 4 | |||
84.83 | odd | 2 | 252.2.b.e.55.4 | 4 | |||
168.83 | odd | 2 | 4032.2.b.n.3583.1 | 4 | |||
168.125 | even | 2 | 4032.2.b.j.3583.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.b.a.55.1 | ✓ | 4 | 28.27 | even | 2 | inner | |
84.2.b.a.55.2 | yes | 4 | 1.1 | even | 1 | trivial | |
84.2.b.b.55.1 | yes | 4 | 4.3 | odd | 2 | ||
84.2.b.b.55.2 | yes | 4 | 7.6 | odd | 2 | ||
252.2.b.d.55.3 | 4 | 21.20 | even | 2 | |||
252.2.b.d.55.4 | 4 | 12.11 | even | 2 | |||
252.2.b.e.55.3 | 4 | 3.2 | odd | 2 | |||
252.2.b.e.55.4 | 4 | 84.83 | odd | 2 | |||
588.2.o.a.19.2 | 8 | 7.3 | odd | 6 | |||
588.2.o.a.19.4 | 8 | 28.11 | odd | 6 | |||
588.2.o.a.31.2 | 8 | 28.23 | odd | 6 | |||
588.2.o.a.31.4 | 8 | 7.5 | odd | 6 | |||
588.2.o.c.19.2 | 8 | 7.4 | even | 3 | |||
588.2.o.c.19.4 | 8 | 28.3 | even | 6 | |||
588.2.o.c.31.2 | 8 | 28.19 | even | 6 | |||
588.2.o.c.31.4 | 8 | 7.2 | even | 3 | |||
1344.2.b.e.895.1 | 4 | 8.3 | odd | 2 | |||
1344.2.b.e.895.4 | 4 | 56.13 | odd | 2 | |||
1344.2.b.f.895.1 | 4 | 8.5 | even | 2 | |||
1344.2.b.f.895.4 | 4 | 56.27 | even | 2 | |||
4032.2.b.j.3583.1 | 4 | 168.125 | even | 2 | |||
4032.2.b.j.3583.4 | 4 | 24.11 | even | 2 | |||
4032.2.b.n.3583.1 | 4 | 168.83 | odd | 2 | |||
4032.2.b.n.3583.4 | 4 | 24.5 | odd | 2 |