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 | 55.3 | ||
Root | \(-0.780776 + 1.17915i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.2.b.b.55.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.780776 | − | 1.17915i | 0.552092 | − | 0.833783i | ||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −0.780776 | − | 1.84130i | −0.390388 | − | 0.920650i | ||||
\(5\) | 1.69614i | 0.758537i | 0.925287 | + | 0.379269i | \(0.123824\pi\) | ||||
−0.925287 | + | 0.379269i | \(0.876176\pi\) | |||||||
\(6\) | 0.780776 | − | 1.17915i | 0.318751 | − | 0.481385i | ||||
\(7\) | −2.56155 | + | 0.662153i | −0.968176 | + | 0.250270i | ||||
\(8\) | −2.78078 | − | 0.516994i | −0.983153 | − | 0.182785i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.00000 | + | 1.32431i | 0.632456 | + | 0.418783i | ||||
\(11\) | 3.02045i | 0.910699i | 0.890313 | + | 0.455350i | \(0.150486\pi\) | ||||
−0.890313 | + | 0.455350i | \(0.849514\pi\) | |||||||
\(12\) | −0.780776 | − | 1.84130i | −0.225391 | − | 0.531538i | ||||
\(13\) | − | 6.04090i | − | 1.67544i | −0.546098 | − | 0.837722i | \(-0.683887\pi\) | ||
0.546098 | − | 0.837722i | \(-0.316113\pi\) | |||||||
\(14\) | −1.21922 | + | 3.53744i | −0.325851 | + | 0.945421i | ||||
\(15\) | 1.69614i | 0.437942i | ||||||||
\(16\) | −2.78078 | + | 2.87529i | −0.695194 | + | 0.718822i | ||||
\(17\) | 4.34475i | 1.05376i | 0.849940 | + | 0.526879i | \(0.176638\pi\) | ||||
−0.849940 | + | 0.526879i | \(0.823362\pi\) | |||||||
\(18\) | 0.780776 | − | 1.17915i | 0.184031 | − | 0.277928i | ||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 3.12311 | − | 1.32431i | 0.698348 | − | 0.296124i | ||||
\(21\) | −2.56155 | + | 0.662153i | −0.558977 | + | 0.144494i | ||||
\(22\) | 3.56155 | + | 2.35829i | 0.759326 | + | 0.502790i | ||||
\(23\) | − | 3.02045i | − | 0.629807i | −0.949124 | − | 0.314903i | \(-0.898028\pi\) | ||
0.949124 | − | 0.314903i | \(-0.101972\pi\) | |||||||
\(24\) | −2.78078 | − | 0.516994i | −0.567624 | − | 0.105531i | ||||
\(25\) | 2.12311 | 0.424621 | ||||||||
\(26\) | −7.12311 | − | 4.71659i | −1.39696 | − | 0.924999i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.21922 | + | 4.19960i | 0.608376 | + | 0.793649i | ||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 2.00000 | + | 1.32431i | 0.365148 | + | 0.241784i | ||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 1.21922 | + | 5.52390i | 0.215530 | + | 0.976497i | ||||
\(33\) | 3.02045i | 0.525792i | ||||||||
\(34\) | 5.12311 | + | 3.39228i | 0.878605 | + | 0.581772i | ||||
\(35\) | −1.12311 | − | 4.34475i | −0.189839 | − | 0.734398i | ||||
\(36\) | −0.780776 | − | 1.84130i | −0.130129 | − | 0.306883i | ||||
\(37\) | −7.12311 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(38\) | 0.876894 | − | 1.32431i | 0.142251 | − | 0.214831i | ||||
\(39\) | − | 6.04090i | − | 0.967317i | ||||||
\(40\) | 0.876894 | − | 4.71659i | 0.138649 | − | 0.745758i | ||||
\(41\) | − | 7.73704i | − | 1.20832i | −0.796862 | − | 0.604161i | \(-0.793508\pi\) | ||
0.796862 | − | 0.604161i | \(-0.206492\pi\) | |||||||
\(42\) | −1.21922 | + | 3.53744i | −0.188130 | + | 0.545839i | ||||
\(43\) | − | 8.10887i | − | 1.23659i | −0.785946 | − | 0.618296i | \(-0.787823\pi\) | ||
0.785946 | − | 0.618296i | \(-0.212177\pi\) | |||||||
\(44\) | 5.56155 | − | 2.35829i | 0.838436 | − | 0.355526i | ||||
\(45\) | 1.69614i | 0.252846i | ||||||||
\(46\) | −3.56155 | − | 2.35829i | −0.525122 | − | 0.347712i | ||||
\(47\) | 10.2462 | 1.49456 | 0.747282 | − | 0.664507i | \(-0.231359\pi\) | ||||
0.747282 | + | 0.664507i | \(0.231359\pi\) | |||||||
\(48\) | −2.78078 | + | 2.87529i | −0.401371 | + | 0.415012i | ||||
\(49\) | 6.12311 | − | 3.39228i | 0.874729 | − | 0.484612i | ||||
\(50\) | 1.65767 | − | 2.50345i | 0.234430 | − | 0.354042i | ||||
\(51\) | 4.34475i | 0.608387i | ||||||||
\(52\) | −11.1231 | + | 4.71659i | −1.54250 | + | 0.654073i | ||||
\(53\) | −4.24621 | −0.583262 | −0.291631 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291631 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(54\) | 0.780776 | − | 1.17915i | 0.106250 | − | 0.160462i | ||||
\(55\) | −5.12311 | −0.690799 | ||||||||
\(56\) | 7.46543 | − | 0.516994i | 0.997611 | − | 0.0690862i | ||||
\(57\) | 1.12311 | 0.148759 | ||||||||
\(58\) | −1.56155 | + | 2.35829i | −0.205042 | + | 0.309659i | ||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 3.12311 | − | 1.32431i | 0.403191 | − | 0.170967i | ||||
\(61\) | 9.43318i | 1.20779i | 0.797062 | + | 0.603897i | \(0.206386\pi\) | ||||
−0.797062 | + | 0.603897i | \(0.793614\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.56155 | + | 0.662153i | −0.322725 | + | 0.0834235i | ||||
\(64\) | 7.46543 | + | 2.87529i | 0.933179 | + | 0.359411i | ||||
\(65\) | 10.2462 | 1.27089 | ||||||||
\(66\) | 3.56155 | + | 2.35829i | 0.438397 | + | 0.290286i | ||||
\(67\) | 2.06798i | 0.252643i | 0.991989 | + | 0.126322i | \(0.0403172\pi\) | ||||
−0.991989 | + | 0.126322i | \(0.959683\pi\) | |||||||
\(68\) | 8.00000 | − | 3.39228i | 0.970143 | − | 0.411375i | ||||
\(69\) | − | 3.02045i | − | 0.363619i | ||||||
\(70\) | −6.00000 | − | 2.06798i | −0.717137 | − | 0.247170i | ||||
\(71\) | 12.4536i | 1.47797i | 0.673720 | + | 0.738987i | \(0.264695\pi\) | ||||
−0.673720 | + | 0.738987i | \(0.735305\pi\) | |||||||
\(72\) | −2.78078 | − | 0.516994i | −0.327718 | − | 0.0609283i | ||||
\(73\) | 3.39228i | 0.397037i | 0.980097 | + | 0.198518i | \(0.0636129\pi\) | ||||
−0.980097 | + | 0.198518i | \(0.936387\pi\) | |||||||
\(74\) | −5.56155 | + | 8.39919i | −0.646517 | + | 0.976386i | ||||
\(75\) | 2.12311 | 0.245155 | ||||||||
\(76\) | −0.876894 | − | 2.06798i | −0.100587 | − | 0.237213i | ||||
\(77\) | −2.00000 | − | 7.73704i | −0.227921 | − | 0.881717i | ||||
\(78\) | −7.12311 | − | 4.71659i | −0.806533 | − | 0.534049i | ||||
\(79\) | 4.71659i | 0.530658i | 0.964158 | + | 0.265329i | \(0.0854805\pi\) | ||||
−0.964158 | + | 0.265329i | \(0.914519\pi\) | |||||||
\(80\) | −4.87689 | − | 4.71659i | −0.545253 | − | 0.527331i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −9.12311 | − | 6.04090i | −1.00748 | − | 0.667105i | ||||
\(83\) | −6.24621 | −0.685611 | −0.342805 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342805 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(84\) | 3.21922 | + | 4.19960i | 0.351246 | + | 0.458213i | ||||
\(85\) | −7.36932 | −0.799315 | ||||||||
\(86\) | −9.56155 | − | 6.33122i | −1.03105 | − | 0.682712i | ||||
\(87\) | −2.00000 | −0.214423 | ||||||||
\(88\) | 1.56155 | − | 8.39919i | 0.166462 | − | 0.895357i | ||||
\(89\) | 7.73704i | 0.820124i | 0.912058 | + | 0.410062i | \(0.134493\pi\) | ||||
−0.912058 | + | 0.410062i | \(0.865507\pi\) | |||||||
\(90\) | 2.00000 | + | 1.32431i | 0.210819 | + | 0.139594i | ||||
\(91\) | 4.00000 | + | 15.4741i | 0.419314 | + | 1.62212i | ||||
\(92\) | −5.56155 | + | 2.35829i | −0.579832 | + | 0.245869i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.00000 | − | 12.0818i | 0.825137 | − | 1.24614i | ||||
\(95\) | 1.90495i | 0.195443i | ||||||||
\(96\) | 1.21922 | + | 5.52390i | 0.124436 | + | 0.563781i | ||||
\(97\) | 8.68951i | 0.882286i | 0.897437 | + | 0.441143i | \(0.145427\pi\) | ||||
−0.897437 | + | 0.441143i | \(0.854573\pi\) | |||||||
\(98\) | 0.780776 | − | 9.86866i | 0.0788703 | − | 0.996885i | ||||
\(99\) | 3.02045i | 0.303566i | ||||||||
\(100\) | −1.65767 | − | 3.90928i | −0.165767 | − | 0.390928i | ||||
\(101\) | − | 6.99337i | − | 0.695866i | −0.937519 | − | 0.347933i | \(-0.886884\pi\) | ||
0.937519 | − | 0.347933i | \(-0.113116\pi\) | |||||||
\(102\) | 5.12311 | + | 3.39228i | 0.507263 | + | 0.335886i | ||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | −3.12311 | + | 16.7984i | −0.306246 | + | 1.64722i | ||||
\(105\) | −1.12311 | − | 4.34475i | −0.109604 | − | 0.424005i | ||||
\(106\) | −3.31534 | + | 5.00691i | −0.322014 | + | 0.486314i | ||||
\(107\) | − | 5.66906i | − | 0.548049i | −0.961723 | − | 0.274024i | \(-0.911645\pi\) | ||
0.961723 | − | 0.274024i | \(-0.0883549\pi\) | |||||||
\(108\) | −0.780776 | − | 1.84130i | −0.0751302 | − | 0.177179i | ||||
\(109\) | 8.24621 | 0.789844 | 0.394922 | − | 0.918715i | \(-0.370772\pi\) | ||||
0.394922 | + | 0.918715i | \(0.370772\pi\) | |||||||
\(110\) | −4.00000 | + | 6.04090i | −0.381385 | + | 0.575977i | ||||
\(111\) | −7.12311 | −0.676095 | ||||||||
\(112\) | 5.21922 | − | 9.20650i | 0.493170 | − | 0.869933i | ||||
\(113\) | 12.2462 | 1.15203 | 0.576013 | − | 0.817440i | \(-0.304608\pi\) | ||||
0.576013 | + | 0.817440i | \(0.304608\pi\) | |||||||
\(114\) | 0.876894 | − | 1.32431i | 0.0821287 | − | 0.124033i | ||||
\(115\) | 5.12311 | 0.477732 | ||||||||
\(116\) | 1.56155 | + | 3.68260i | 0.144987 | + | 0.341921i | ||||
\(117\) | − | 6.04090i | − | 0.558481i | ||||||
\(118\) | −3.12311 | + | 4.71659i | −0.287505 | + | 0.434197i | ||||
\(119\) | −2.87689 | − | 11.1293i | −0.263724 | − | 1.02022i | ||||
\(120\) | 0.876894 | − | 4.71659i | 0.0800491 | − | 0.430564i | ||||
\(121\) | 1.87689 | 0.170627 | ||||||||
\(122\) | 11.1231 | + | 7.36520i | 1.00704 | + | 0.666814i | ||||
\(123\) | − | 7.73704i | − | 0.697625i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0818i | 1.08063i | ||||||||
\(126\) | −1.21922 | + | 3.53744i | −0.108617 | + | 0.315140i | ||||
\(127\) | − | 19.4470i | − | 1.72564i | −0.505510 | − | 0.862821i | \(-0.668696\pi\) | ||
0.505510 | − | 0.862821i | \(-0.331304\pi\) | |||||||
\(128\) | 9.21922 | − | 6.55789i | 0.814872 | − | 0.579641i | ||||
\(129\) | − | 8.10887i | − | 0.713946i | ||||||
\(130\) | 8.00000 | − | 12.0818i | 0.701646 | − | 1.05964i | ||||
\(131\) | −22.2462 | −1.94366 | −0.971830 | − | 0.235682i | \(-0.924268\pi\) | ||||
−0.971830 | + | 0.235682i | \(0.924268\pi\) | |||||||
\(132\) | 5.56155 | − | 2.35829i | 0.484071 | − | 0.205263i | ||||
\(133\) | −2.87689 | + | 0.743668i | −0.249458 | + | 0.0644842i | ||||
\(134\) | 2.43845 | + | 1.61463i | 0.210650 | + | 0.139482i | ||||
\(135\) | 1.69614i | 0.145981i | ||||||||
\(136\) | 2.24621 | − | 12.0818i | 0.192611 | − | 1.03601i | ||||
\(137\) | −16.2462 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(138\) | −3.56155 | − | 2.35829i | −0.303180 | − | 0.200751i | ||||
\(139\) | 12.0000 | 1.01783 | 0.508913 | − | 0.860818i | \(-0.330047\pi\) | ||||
0.508913 | + | 0.860818i | \(0.330047\pi\) | |||||||
\(140\) | −7.12311 | + | 5.46026i | −0.602012 | + | 0.461476i | ||||
\(141\) | 10.2462 | 0.862887 | ||||||||
\(142\) | 14.6847 | + | 9.72350i | 1.23231 | + | 0.815978i | ||||
\(143\) | 18.2462 | 1.52582 | ||||||||
\(144\) | −2.78078 | + | 2.87529i | −0.231731 | + | 0.239607i | ||||
\(145\) | − | 3.39228i | − | 0.281714i | ||||||
\(146\) | 4.00000 | + | 2.64861i | 0.331042 | + | 0.219201i | ||||
\(147\) | 6.12311 | − | 3.39228i | 0.505025 | − | 0.279791i | ||||
\(148\) | 5.56155 | + | 13.1158i | 0.457157 | + | 1.07811i | ||||
\(149\) | −10.0000 | −0.819232 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(150\) | 1.65767 | − | 2.50345i | 0.135348 | − | 0.204406i | ||||
\(151\) | 8.10887i | 0.659891i | 0.944000 | + | 0.329945i | \(0.107030\pi\) | ||||
−0.944000 | + | 0.329945i | \(0.892970\pi\) | |||||||
\(152\) | −3.12311 | − | 0.580639i | −0.253317 | − | 0.0470960i | ||||
\(153\) | 4.34475i | 0.351253i | ||||||||
\(154\) | −10.6847 | − | 3.68260i | −0.860994 | − | 0.296752i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −11.1231 | + | 4.71659i | −0.890561 | + | 0.377629i | ||||
\(157\) | − | 4.13595i | − | 0.330085i | −0.986286 | − | 0.165042i | \(-0.947224\pi\) | ||
0.986286 | − | 0.165042i | \(-0.0527761\pi\) | |||||||
\(158\) | 5.56155 | + | 3.68260i | 0.442453 | + | 0.292972i | ||||
\(159\) | −4.24621 | −0.336746 | ||||||||
\(160\) | −9.36932 | + | 2.06798i | −0.740710 | + | 0.163488i | ||||
\(161\) | 2.00000 | + | 7.73704i | 0.157622 | + | 0.609764i | ||||
\(162\) | 0.780776 | − | 1.17915i | 0.0613436 | − | 0.0926426i | ||||
\(163\) | − | 11.5012i | − | 0.900840i | −0.892817 | − | 0.450420i | \(-0.851274\pi\) | ||
0.892817 | − | 0.450420i | \(-0.148726\pi\) | |||||||
\(164\) | −14.2462 | + | 6.04090i | −1.11244 | + | 0.471715i | ||||
\(165\) | −5.12311 | −0.398833 | ||||||||
\(166\) | −4.87689 | + | 7.36520i | −0.378520 | + | 0.571651i | ||||
\(167\) | 2.24621 | 0.173817 | 0.0869085 | − | 0.996216i | \(-0.472301\pi\) | ||||
0.0869085 | + | 0.996216i | \(0.472301\pi\) | |||||||
\(168\) | 7.46543 | − | 0.516994i | 0.575971 | − | 0.0398869i | ||||
\(169\) | −23.4924 | −1.80711 | ||||||||
\(170\) | −5.75379 | + | 8.68951i | −0.441295 | + | 0.666455i | ||||
\(171\) | 1.12311 | 0.0858860 | ||||||||
\(172\) | −14.9309 | + | 6.33122i | −1.13847 | + | 0.482751i | ||||
\(173\) | − | 8.48071i | − | 0.644776i | −0.946608 | − | 0.322388i | \(-0.895514\pi\) | ||
0.946608 | − | 0.322388i | \(-0.104486\pi\) | |||||||
\(174\) | −1.56155 | + | 2.35829i | −0.118381 | + | 0.178782i | ||||
\(175\) | −5.43845 | + | 1.40582i | −0.411108 | + | 0.106270i | ||||
\(176\) | −8.68466 | − | 8.39919i | −0.654631 | − | 0.633113i | ||||
\(177\) | −4.00000 | −0.300658 | ||||||||
\(178\) | 9.12311 | + | 6.04090i | 0.683806 | + | 0.452784i | ||||
\(179\) | − | 2.27678i | − | 0.170175i | −0.996374 | − | 0.0850873i | \(-0.972883\pi\) | ||
0.996374 | − | 0.0850873i | \(-0.0271169\pi\) | |||||||
\(180\) | 3.12311 | − | 1.32431i | 0.232783 | − | 0.0987080i | ||||
\(181\) | 6.04090i | 0.449016i | 0.974472 | + | 0.224508i | \(0.0720775\pi\) | ||||
−0.974472 | + | 0.224508i | \(0.927922\pi\) | |||||||
\(182\) | 21.3693 | + | 7.36520i | 1.58400 | + | 0.545945i | ||||
\(183\) | 9.43318i | 0.697321i | ||||||||
\(184\) | −1.56155 | + | 8.39919i | −0.115119 | + | 0.619197i | ||||
\(185\) | − | 12.0818i | − | 0.888271i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.1231 | −0.959657 | ||||||||
\(188\) | −8.00000 | − | 18.8664i | −0.583460 | − | 1.37597i | ||||
\(189\) | −2.56155 | + | 0.662153i | −0.186326 | + | 0.0481646i | ||||
\(190\) | 2.24621 | + | 1.48734i | 0.162957 | + | 0.107903i | ||||
\(191\) | 9.06134i | 0.655656i | 0.944737 | + | 0.327828i | \(0.106317\pi\) | ||||
−0.944737 | + | 0.327828i | \(0.893683\pi\) | |||||||
\(192\) | 7.46543 | + | 2.87529i | 0.538771 | + | 0.207506i | ||||
\(193\) | 9.36932 | 0.674418 | 0.337209 | − | 0.941430i | \(-0.390517\pi\) | ||||
0.337209 | + | 0.941430i | \(0.390517\pi\) | |||||||
\(194\) | 10.2462 | + | 6.78456i | 0.735635 | + | 0.487103i | ||||
\(195\) | 10.2462 | 0.733746 | ||||||||
\(196\) | −11.0270 | − | 8.62586i | −0.787642 | − | 0.616133i | ||||
\(197\) | 0.246211 | 0.0175418 | 0.00877091 | − | 0.999962i | \(-0.497208\pi\) | ||||
0.00877091 | + | 0.999962i | \(0.497208\pi\) | |||||||
\(198\) | 3.56155 | + | 2.35829i | 0.253109 | + | 0.167597i | ||||
\(199\) | −5.12311 | −0.363167 | −0.181584 | − | 0.983375i | \(-0.558122\pi\) | ||||
−0.181584 | + | 0.983375i | \(0.558122\pi\) | |||||||
\(200\) | −5.90388 | − | 1.09763i | −0.417468 | − | 0.0776143i | ||||
\(201\) | 2.06798i | 0.145864i | ||||||||
\(202\) | −8.24621 | − | 5.46026i | −0.580201 | − | 0.384182i | ||||
\(203\) | 5.12311 | − | 1.32431i | 0.359572 | − | 0.0929481i | ||||
\(204\) | 8.00000 | − | 3.39228i | 0.560112 | − | 0.237507i | ||||
\(205\) | 13.1231 | 0.916557 | ||||||||
\(206\) | 6.24621 | − | 9.43318i | 0.435194 | − | 0.657241i | ||||
\(207\) | − | 3.02045i | − | 0.209936i | ||||||
\(208\) | 17.3693 | + | 16.7984i | 1.20435 | + | 1.16476i | ||||
\(209\) | 3.39228i | 0.234649i | ||||||||
\(210\) | −6.00000 | − | 2.06798i | −0.414039 | − | 0.142704i | ||||
\(211\) | 3.97292i | 0.273507i | 0.990605 | + | 0.136754i | \(0.0436668\pi\) | ||||
−0.990605 | + | 0.136754i | \(0.956333\pi\) | |||||||
\(212\) | 3.31534 | + | 7.81855i | 0.227699 | + | 0.536980i | ||||
\(213\) | 12.4536i | 0.853308i | ||||||||
\(214\) | −6.68466 | − | 4.42627i | −0.456954 | − | 0.302574i | ||||
\(215\) | 13.7538 | 0.938001 | ||||||||
\(216\) | −2.78078 | − | 0.516994i | −0.189208 | − | 0.0351770i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 6.43845 | − | 9.72350i | 0.436067 | − | 0.658558i | ||||
\(219\) | 3.39228i | 0.229229i | ||||||||
\(220\) | 4.00000 | + | 9.43318i | 0.269680 | + | 0.635985i | ||||
\(221\) | 26.2462 | 1.76551 | ||||||||
\(222\) | −5.56155 | + | 8.39919i | −0.373267 | + | 0.563717i | ||||
\(223\) | −18.8769 | −1.26409 | −0.632045 | − | 0.774932i | \(-0.717784\pi\) | ||||
−0.632045 | + | 0.774932i | \(0.717784\pi\) | |||||||
\(224\) | −6.78078 | − | 13.3425i | −0.453060 | − | 0.891480i | ||||
\(225\) | 2.12311 | 0.141540 | ||||||||
\(226\) | 9.56155 | − | 14.4401i | 0.636025 | − | 0.960540i | ||||
\(227\) | −16.4924 | −1.09464 | −0.547320 | − | 0.836923i | \(-0.684352\pi\) | ||||
−0.547320 | + | 0.836923i | \(0.684352\pi\) | |||||||
\(228\) | −0.876894 | − | 2.06798i | −0.0580737 | − | 0.136955i | ||||
\(229\) | − | 18.1227i | − | 1.19758i | −0.800906 | − | 0.598790i | \(-0.795648\pi\) | ||
0.800906 | − | 0.598790i | \(-0.204352\pi\) | |||||||
\(230\) | 4.00000 | − | 6.04090i | 0.263752 | − | 0.398325i | ||||
\(231\) | −2.00000 | − | 7.73704i | −0.131590 | − | 0.509060i | ||||
\(232\) | 5.56155 | + | 1.03399i | 0.365134 | + | 0.0678846i | ||||
\(233\) | −10.4924 | −0.687381 | −0.343691 | − | 0.939083i | \(-0.611677\pi\) | ||||
−0.343691 | + | 0.939083i | \(0.611677\pi\) | |||||||
\(234\) | −7.12311 | − | 4.71659i | −0.465652 | − | 0.308333i | ||||
\(235\) | 17.3790i | 1.13368i | ||||||||
\(236\) | 3.12311 | + | 7.36520i | 0.203297 | + | 0.479434i | ||||
\(237\) | 4.71659i | 0.306375i | ||||||||
\(238\) | −15.3693 | − | 5.29723i | −0.996245 | − | 0.343368i | ||||
\(239\) | 2.27678i | 0.147273i | 0.997285 | + | 0.0736363i | \(0.0234604\pi\) | ||||
−0.997285 | + | 0.0736363i | \(0.976540\pi\) | |||||||
\(240\) | −4.87689 | − | 4.71659i | −0.314802 | − | 0.304455i | ||||
\(241\) | − | 1.90495i | − | 0.122708i | −0.998116 | − | 0.0613542i | \(-0.980458\pi\) | ||
0.998116 | − | 0.0613542i | \(-0.0195419\pi\) | |||||||
\(242\) | 1.46543 | − | 2.21313i | 0.0942017 | − | 0.142266i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 17.3693 | − | 7.36520i | 1.11196 | − | 0.471509i | ||||
\(245\) | 5.75379 | + | 10.3857i | 0.367596 | + | 0.663515i | ||||
\(246\) | −9.12311 | − | 6.04090i | −0.581668 | − | 0.385153i | ||||
\(247\) | − | 6.78456i | − | 0.431691i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.24621 | −0.395838 | ||||||||
\(250\) | 14.2462 | + | 9.43318i | 0.901010 | + | 0.596607i | ||||
\(251\) | 22.2462 | 1.40417 | 0.702084 | − | 0.712094i | \(-0.252253\pi\) | ||||
0.702084 | + | 0.712094i | \(0.252253\pi\) | |||||||
\(252\) | 3.21922 | + | 4.19960i | 0.202792 | + | 0.264550i | ||||
\(253\) | 9.12311 | 0.573565 | ||||||||
\(254\) | −22.9309 | − | 15.1838i | −1.43881 | − | 0.952713i | ||||
\(255\) | −7.36932 | −0.461485 | ||||||||
\(256\) | −0.534565 | − | 15.9911i | −0.0334103 | − | 0.999442i | ||||
\(257\) | − | 19.8188i | − | 1.23626i | −0.786074 | − | 0.618132i | \(-0.787890\pi\) | ||
0.786074 | − | 0.618132i | \(-0.212110\pi\) | |||||||
\(258\) | −9.56155 | − | 6.33122i | −0.595276 | − | 0.394164i | ||||
\(259\) | 18.2462 | − | 4.71659i | 1.13376 | − | 0.293075i | ||||
\(260\) | −8.00000 | − | 18.8664i | −0.496139 | − | 1.17004i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | −17.3693 | + | 26.2316i | −1.07308 | + | 1.62059i | ||||
\(263\) | − | 4.92539i | − | 0.303713i | −0.988403 | − | 0.151856i | \(-0.951475\pi\) | ||
0.988403 | − | 0.151856i | \(-0.0485251\pi\) | |||||||
\(264\) | 1.56155 | − | 8.39919i | 0.0961069 | − | 0.516934i | ||||
\(265\) | − | 7.20217i | − | 0.442426i | ||||||
\(266\) | −1.36932 | + | 3.97292i | −0.0839582 | + | 0.243595i | ||||
\(267\) | 7.73704i | 0.473499i | ||||||||
\(268\) | 3.80776 | − | 1.61463i | 0.232596 | − | 0.0986290i | ||||
\(269\) | 22.4674i | 1.36986i | 0.728607 | + | 0.684932i | \(0.240168\pi\) | ||||
−0.728607 | + | 0.684932i | \(0.759832\pi\) | |||||||
\(270\) | 2.00000 | + | 1.32431i | 0.121716 | + | 0.0805948i | ||||
\(271\) | −4.49242 | −0.272895 | −0.136448 | − | 0.990647i | \(-0.543569\pi\) | ||||
−0.136448 | + | 0.990647i | \(0.543569\pi\) | |||||||
\(272\) | −12.4924 | − | 12.0818i | −0.757464 | − | 0.732566i | ||||
\(273\) | 4.00000 | + | 15.4741i | 0.242091 | + | 0.936534i | ||||
\(274\) | −12.6847 | + | 19.1567i | −0.766308 | + | 1.15730i | ||||
\(275\) | 6.41273i | 0.386702i | ||||||||
\(276\) | −5.56155 | + | 2.35829i | −0.334766 | + | 0.141953i | ||||
\(277\) | 3.12311 | 0.187649 | 0.0938246 | − | 0.995589i | \(-0.470091\pi\) | ||||
0.0938246 | + | 0.995589i | \(0.470091\pi\) | |||||||
\(278\) | 9.36932 | − | 14.1498i | 0.561934 | − | 0.848647i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.876894 | + | 12.6624i | 0.0524045 | + | 0.756725i | ||||
\(281\) | −0.246211 | −0.0146877 | −0.00734387 | − | 0.999973i | \(-0.502338\pi\) | ||||
−0.00734387 | + | 0.999973i | \(0.502338\pi\) | |||||||
\(282\) | 8.00000 | − | 12.0818i | 0.476393 | − | 0.719460i | ||||
\(283\) | −17.1231 | −1.01786 | −0.508931 | − | 0.860807i | \(-0.669959\pi\) | ||||
−0.508931 | + | 0.860807i | \(0.669959\pi\) | |||||||
\(284\) | 22.9309 | − | 9.72350i | 1.36070 | − | 0.576983i | ||||
\(285\) | 1.90495i | 0.112839i | ||||||||
\(286\) | 14.2462 | − | 21.5150i | 0.842396 | − | 1.27221i | ||||
\(287\) | 5.12311 | + | 19.8188i | 0.302407 | + | 1.16987i | ||||
\(288\) | 1.21922 | + | 5.52390i | 0.0718434 | + | 0.325499i | ||||
\(289\) | −1.87689 | −0.110406 | ||||||||
\(290\) | −4.00000 | − | 2.64861i | −0.234888 | − | 0.155532i | ||||
\(291\) | 8.68951i | 0.509388i | ||||||||
\(292\) | 6.24621 | − | 2.64861i | 0.365532 | − | 0.154998i | ||||
\(293\) | − | 6.99337i | − | 0.408557i | −0.978913 | − | 0.204278i | \(-0.934515\pi\) | ||
0.978913 | − | 0.204278i | \(-0.0654848\pi\) | |||||||
\(294\) | 0.780776 | − | 9.86866i | 0.0455358 | − | 0.575552i | ||||
\(295\) | − | 6.78456i | − | 0.395013i | ||||||
\(296\) | 19.8078 | + | 3.68260i | 1.15130 | + | 0.214047i | ||||
\(297\) | 3.02045i | 0.175264i | ||||||||
\(298\) | −7.80776 | + | 11.7915i | −0.452292 | + | 0.683062i | ||||
\(299\) | −18.2462 | −1.05521 | ||||||||
\(300\) | −1.65767 | − | 3.90928i | −0.0957057 | − | 0.225702i | ||||
\(301\) | 5.36932 | + | 20.7713i | 0.309482 | + | 1.19724i | ||||
\(302\) | 9.56155 | + | 6.33122i | 0.550206 | + | 0.364320i | ||||
\(303\) | − | 6.99337i | − | 0.401759i | ||||||
\(304\) | −3.12311 | + | 3.22925i | −0.179122 | + | 0.185210i | ||||
\(305\) | −16.0000 | −0.916157 | ||||||||
\(306\) | 5.12311 | + | 3.39228i | 0.292868 | + | 0.193924i | ||||
\(307\) | 21.6155 | 1.23366 | 0.616832 | − | 0.787095i | \(-0.288416\pi\) | ||||
0.616832 | + | 0.787095i | \(0.288416\pi\) | |||||||
\(308\) | −12.6847 | + | 9.72350i | −0.722775 | + | 0.554048i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | −3.12311 | + | 16.7984i | −0.176811 | + | 0.951021i | ||||
\(313\) | − | 25.6509i | − | 1.44988i | −0.688814 | − | 0.724938i | \(-0.741868\pi\) | ||
0.688814 | − | 0.724938i | \(-0.258132\pi\) | |||||||
\(314\) | −4.87689 | − | 3.22925i | −0.275219 | − | 0.182237i | ||||
\(315\) | −1.12311 | − | 4.34475i | −0.0632798 | − | 0.244799i | ||||
\(316\) | 8.68466 | − | 3.68260i | 0.488550 | − | 0.207163i | ||||
\(317\) | 18.4924 | 1.03864 | 0.519319 | − | 0.854580i | \(-0.326186\pi\) | ||||
0.519319 | + | 0.854580i | \(0.326186\pi\) | |||||||
\(318\) | −3.31534 | + | 5.00691i | −0.185915 | + | 0.280773i | ||||
\(319\) | − | 6.04090i | − | 0.338225i | ||||||
\(320\) | −4.87689 | + | 12.6624i | −0.272627 | + | 0.707851i | ||||
\(321\) | − | 5.66906i | − | 0.316416i | ||||||
\(322\) | 10.6847 | + | 3.68260i | 0.595433 | + | 0.205223i | ||||
\(323\) | 4.87962i | 0.271509i | ||||||||
\(324\) | −0.780776 | − | 1.84130i | −0.0433765 | − | 0.102294i | ||||
\(325\) | − | 12.8255i | − | 0.711429i | ||||||
\(326\) | −13.5616 | − | 8.97983i | −0.751105 | − | 0.497347i | ||||
\(327\) | 8.24621 | 0.456017 | ||||||||
\(328\) | −4.00000 | + | 21.5150i | −0.220863 | + | 1.18797i | ||||
\(329\) | −26.2462 | + | 6.78456i | −1.44700 | + | 0.374045i | ||||
\(330\) | −4.00000 | + | 6.04090i | −0.220193 | + | 0.332540i | ||||
\(331\) | 5.46026i | 0.300123i | 0.988677 | + | 0.150061i | \(0.0479472\pi\) | ||||
−0.988677 | + | 0.150061i | \(0.952053\pi\) | |||||||
\(332\) | 4.87689 | + | 11.5012i | 0.267654 | + | 0.631208i | ||||
\(333\) | −7.12311 | −0.390344 | ||||||||
\(334\) | 1.75379 | − | 2.64861i | 0.0959631 | − | 0.144926i | ||||
\(335\) | −3.50758 | −0.191639 | ||||||||
\(336\) | 5.21922 | − | 9.20650i | 0.284732 | − | 0.502256i | ||||
\(337\) | −8.24621 | −0.449200 | −0.224600 | − | 0.974451i | \(-0.572108\pi\) | ||||
−0.224600 | + | 0.974451i | \(0.572108\pi\) | |||||||
\(338\) | −18.3423 | + | 27.7010i | −0.997691 | + | 1.50674i | ||||
\(339\) | 12.2462 | 0.665123 | ||||||||
\(340\) | 5.75379 | + | 13.5691i | 0.312043 | + | 0.735889i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.876894 | − | 1.32431i | 0.0474170 | − | 0.0716103i | ||||
\(343\) | −13.4384 | + | 12.7439i | −0.725608 | + | 0.688108i | ||||
\(344\) | −4.19224 | + | 22.5490i | −0.226030 | + | 1.21576i | ||||
\(345\) | 5.12311 | 0.275819 | ||||||||
\(346\) | −10.0000 | − | 6.62153i | −0.537603 | − | 0.355976i | ||||
\(347\) | − | 34.7123i | − | 1.86345i | −0.363162 | − | 0.931726i | \(-0.618303\pi\) | ||
0.363162 | − | 0.931726i | \(-0.381697\pi\) | |||||||
\(348\) | 1.56155 | + | 3.68260i | 0.0837080 | + | 0.197408i | ||||
\(349\) | − | 4.13595i | − | 0.221392i | −0.993854 | − | 0.110696i | \(-0.964692\pi\) | ||
0.993854 | − | 0.110696i | \(-0.0353080\pi\) | |||||||
\(350\) | −2.58854 | + | 7.51036i | −0.138363 | + | 0.401446i | ||||
\(351\) | − | 6.04090i | − | 0.322439i | ||||||
\(352\) | −16.6847 | + | 3.68260i | −0.889295 | + | 0.196283i | ||||
\(353\) | 6.24970i | 0.332638i | 0.986072 | + | 0.166319i | \(0.0531881\pi\) | ||||
−0.986072 | + | 0.166319i | \(0.946812\pi\) | |||||||
\(354\) | −3.12311 | + | 4.71659i | −0.165991 | + | 0.250684i | ||||
\(355\) | −21.1231 | −1.12110 | ||||||||
\(356\) | 14.2462 | − | 6.04090i | 0.755048 | − | 0.320167i | ||||
\(357\) | −2.87689 | − | 11.1293i | −0.152261 | − | 0.589026i | ||||
\(358\) | −2.68466 | − | 1.77766i | −0.141889 | − | 0.0939520i | ||||
\(359\) | − | 1.11550i | − | 0.0588740i | −0.999567 | − | 0.0294370i | \(-0.990629\pi\) | ||
0.999567 | − | 0.0294370i | \(-0.00937144\pi\) | |||||||
\(360\) | 0.876894 | − | 4.71659i | 0.0462164 | − | 0.248586i | ||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 7.12311 | + | 4.71659i | 0.374382 | + | 0.247898i | ||||
\(363\) | 1.87689 | 0.0985114 | ||||||||
\(364\) | 25.3693 | − | 19.4470i | 1.32971 | − | 1.01930i | ||||
\(365\) | −5.75379 | −0.301167 | ||||||||
\(366\) | 11.1231 | + | 7.36520i | 0.581414 | + | 0.384985i | ||||
\(367\) | 8.63068 | 0.450518 | 0.225259 | − | 0.974299i | \(-0.427677\pi\) | ||||
0.225259 | + | 0.974299i | \(0.427677\pi\) | |||||||
\(368\) | 8.68466 | + | 8.39919i | 0.452719 | + | 0.437838i | ||||
\(369\) | − | 7.73704i | − | 0.402774i | ||||||
\(370\) | −14.2462 | − | 9.43318i | −0.740625 | − | 0.490408i | ||||
\(371\) | 10.8769 | − | 2.81164i | 0.564700 | − | 0.145973i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.0000 | −0.517780 | −0.258890 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258890 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(374\) | −10.2462 | + | 15.4741i | −0.529819 | + | 0.800145i | ||||
\(375\) | 12.0818i | 0.623901i | ||||||||
\(376\) | −28.4924 | − | 5.29723i | −1.46938 | − | 0.273184i | ||||
\(377\) | 12.0818i | 0.622244i | ||||||||
\(378\) | −1.21922 | + | 3.53744i | −0.0627101 | + | 0.181946i | ||||
\(379\) | − | 18.7033i | − | 0.960725i | −0.877070 | − | 0.480363i | \(-0.840505\pi\) | ||
0.877070 | − | 0.480363i | \(-0.159495\pi\) | |||||||
\(380\) | 3.50758 | − | 1.48734i | 0.179935 | − | 0.0762988i | ||||
\(381\) | − | 19.4470i | − | 0.996300i | ||||||
\(382\) | 10.6847 | + | 7.07488i | 0.546675 | + | 0.361983i | ||||
\(383\) | 26.2462 | 1.34112 | 0.670559 | − | 0.741856i | \(-0.266054\pi\) | ||||
0.670559 | + | 0.741856i | \(0.266054\pi\) | |||||||
\(384\) | 9.21922 | − | 6.55789i | 0.470467 | − | 0.334656i | ||||
\(385\) | 13.1231 | − | 3.39228i | 0.668815 | − | 0.172887i | ||||
\(386\) | 7.31534 | − | 11.0478i | 0.372341 | − | 0.562318i | ||||
\(387\) | − | 8.10887i | − | 0.412197i | ||||||
\(388\) | 16.0000 | − | 6.78456i | 0.812277 | − | 0.344434i | ||||
\(389\) | 0.246211 | 0.0124834 | 0.00624170 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624170 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(390\) | 8.00000 | − | 12.0818i | 0.405096 | − | 0.611785i | ||||
\(391\) | 13.1231 | 0.663664 | ||||||||
\(392\) | −18.7808 | + | 6.26757i | −0.948572 | + | 0.316560i | ||||
\(393\) | −22.2462 | −1.12217 | ||||||||
\(394\) | 0.192236 | − | 0.290319i | 0.00968471 | − | 0.0146261i | ||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 5.56155 | − | 2.35829i | 0.279479 | − | 0.118509i | ||||
\(397\) | 16.2177i | 0.813945i | 0.913440 | + | 0.406973i | \(0.133416\pi\) | ||||
−0.913440 | + | 0.406973i | \(0.866584\pi\) | |||||||
\(398\) | −4.00000 | + | 6.04090i | −0.200502 | + | 0.302803i | ||||
\(399\) | −2.87689 | + | 0.743668i | −0.144025 | + | 0.0372300i | ||||
\(400\) | −5.90388 | + | 6.10454i | −0.295194 | + | 0.305227i | ||||
\(401\) | −8.24621 | −0.411796 | −0.205898 | − | 0.978573i | \(-0.566012\pi\) | ||||
−0.205898 | + | 0.978573i | \(0.566012\pi\) | |||||||
\(402\) | 2.43845 | + | 1.61463i | 0.121619 | + | 0.0805302i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −12.8769 | + | 5.46026i | −0.640649 | + | 0.271658i | ||||
\(405\) | 1.69614i | 0.0842819i | ||||||||
\(406\) | 2.43845 | − | 7.07488i | 0.121018 | − | 0.351121i | ||||
\(407\) | − | 21.5150i | − | 1.06646i | ||||||
\(408\) | 2.24621 | − | 12.0818i | 0.111204 | − | 0.598138i | ||||
\(409\) | 27.5559i | 1.36255i | 0.732028 | + | 0.681275i | \(0.238574\pi\) | ||||
−0.732028 | + | 0.681275i | \(0.761426\pi\) | |||||||
\(410\) | 10.2462 | − | 15.4741i | 0.506024 | − | 0.764210i | ||||
\(411\) | −16.2462 | −0.801367 | ||||||||
\(412\) | −6.24621 | − | 14.7304i | −0.307729 | − | 0.725715i | ||||
\(413\) | 10.2462 | − | 2.64861i | 0.504183 | − | 0.130330i | ||||
\(414\) | −3.56155 | − | 2.35829i | −0.175041 | − | 0.115904i | ||||
\(415\) | − | 10.5945i | − | 0.520061i | ||||||
\(416\) | 33.3693 | − | 7.36520i | 1.63607 | − | 0.361109i | ||||
\(417\) | 12.0000 | 0.587643 | ||||||||
\(418\) | 4.00000 | + | 2.64861i | 0.195646 | + | 0.129548i | ||||
\(419\) | −16.4924 | −0.805708 | −0.402854 | − | 0.915264i | \(-0.631982\pi\) | ||||
−0.402854 | + | 0.915264i | \(0.631982\pi\) | |||||||
\(420\) | −7.12311 | + | 5.46026i | −0.347572 | + | 0.266433i | ||||
\(421\) | 19.1231 | 0.932003 | 0.466002 | − | 0.884784i | \(-0.345694\pi\) | ||||
0.466002 | + | 0.884784i | \(0.345694\pi\) | |||||||
\(422\) | 4.68466 | + | 3.10196i | 0.228046 | + | 0.151001i | ||||
\(423\) | 10.2462 | 0.498188 | ||||||||
\(424\) | 11.8078 | + | 2.19526i | 0.573436 | + | 0.106611i | ||||
\(425\) | 9.22437i | 0.447448i | ||||||||
\(426\) | 14.6847 | + | 9.72350i | 0.711474 | + | 0.471105i | ||||
\(427\) | −6.24621 | − | 24.1636i | −0.302275 | − | 1.16936i | ||||
\(428\) | −10.4384 | + | 4.42627i | −0.504561 | + | 0.213952i | ||||
\(429\) | 18.2462 | 0.880935 | ||||||||
\(430\) | 10.7386 | − | 16.2177i | 0.517863 | − | 0.782089i | ||||
\(431\) | − | 15.1022i | − | 0.727449i | −0.931507 | − | 0.363725i | \(-0.881505\pi\) | ||
0.931507 | − | 0.363725i | \(-0.118495\pi\) | |||||||
\(432\) | −2.78078 | + | 2.87529i | −0.133790 | + | 0.138337i | ||||
\(433\) | − | 6.78456i | − | 0.326045i | −0.986622 | − | 0.163023i | \(-0.947876\pi\) | ||
0.986622 | − | 0.163023i | \(-0.0521244\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 3.39228i | − | 0.162647i | ||||||
\(436\) | −6.43845 | − | 15.1838i | −0.308346 | − | 0.727170i | ||||
\(437\) | − | 3.39228i | − | 0.162275i | ||||||
\(438\) | 4.00000 | + | 2.64861i | 0.191127 | + | 0.126556i | ||||
\(439\) | 31.3693 | 1.49718 | 0.748588 | − | 0.663036i | \(-0.230732\pi\) | ||||
0.748588 | + | 0.663036i | \(0.230732\pi\) | |||||||
\(440\) | 14.2462 | + | 2.64861i | 0.679161 | + | 0.126268i | ||||
\(441\) | 6.12311 | − | 3.39228i | 0.291576 | − | 0.161537i | ||||
\(442\) | 20.4924 | − | 30.9481i | 0.974725 | − | 1.47205i | ||||
\(443\) | 35.8735i | 1.70440i | 0.523213 | + | 0.852202i | \(0.324733\pi\) | ||||
−0.523213 | + | 0.852202i | \(0.675267\pi\) | |||||||
\(444\) | 5.56155 | + | 13.1158i | 0.263940 | + | 0.622447i | ||||
\(445\) | −13.1231 | −0.622095 | ||||||||
\(446\) | −14.7386 | + | 22.2586i | −0.697895 | + | 1.05398i | ||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | −21.0270 | − | 2.42194i | −0.993432 | − | 0.114426i | ||||
\(449\) | 28.2462 | 1.33302 | 0.666511 | − | 0.745496i | \(-0.267787\pi\) | ||||
0.666511 | + | 0.745496i | \(0.267787\pi\) | |||||||
\(450\) | 1.65767 | − | 2.50345i | 0.0781434 | − | 0.118014i | ||||
\(451\) | 23.3693 | 1.10042 | ||||||||
\(452\) | −9.56155 | − | 22.5490i | −0.449738 | − | 1.06061i | ||||
\(453\) | 8.10887i | 0.380988i | ||||||||
\(454\) | −12.8769 | + | 19.4470i | −0.604343 | + | 0.912693i | ||||
\(455\) | −26.2462 | + | 6.78456i | −1.23044 | + | 0.318065i | ||||
\(456\) | −3.12311 | − | 0.580639i | −0.146253 | − | 0.0271909i | ||||
\(457\) | −16.2462 | −0.759966 | −0.379983 | − | 0.924994i | \(-0.624070\pi\) | ||||
−0.379983 | + | 0.924994i | \(0.624070\pi\) | |||||||
\(458\) | −21.3693 | − | 14.1498i | −0.998523 | − | 0.661175i | ||||
\(459\) | 4.34475i | 0.202796i | ||||||||
\(460\) | −4.00000 | − | 9.43318i | −0.186501 | − | 0.439824i | ||||
\(461\) | − | 17.1702i | − | 0.799697i | −0.916581 | − | 0.399848i | \(-0.869063\pi\) | ||
0.916581 | − | 0.399848i | \(-0.130937\pi\) | |||||||
\(462\) | −10.6847 | − | 3.68260i | −0.497095 | − | 0.171330i | ||||
\(463\) | 39.4746i | 1.83454i | 0.398264 | + | 0.917271i | \(0.369613\pi\) | ||||
−0.398264 | + | 0.917271i | \(0.630387\pi\) | |||||||
\(464\) | 5.56155 | − | 5.75058i | 0.258189 | − | 0.266964i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.19224 | + | 12.3721i | −0.379498 | + | 0.573127i | ||||
\(467\) | −17.7538 | −0.821547 | −0.410774 | − | 0.911737i | \(-0.634741\pi\) | ||||
−0.410774 | + | 0.911737i | \(0.634741\pi\) | |||||||
\(468\) | −11.1231 | + | 4.71659i | −0.514166 | + | 0.218024i | ||||
\(469\) | −1.36932 | − | 5.29723i | −0.0632292 | − | 0.244603i | ||||
\(470\) | 20.4924 | + | 13.5691i | 0.945245 | + | 0.625897i | ||||
\(471\) | − | 4.13595i | − | 0.190575i | ||||||
\(472\) | 11.1231 | + | 2.06798i | 0.511982 | + | 0.0951863i | ||||
\(473\) | 24.4924 | 1.12616 | ||||||||
\(474\) | 5.56155 | + | 3.68260i | 0.255451 | + | 0.169147i | ||||
\(475\) | 2.38447 | 0.109407 | ||||||||
\(476\) | −18.2462 | + | 13.9867i | −0.836314 | + | 0.641081i | ||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | 2.68466 | + | 1.77766i | 0.122793 | + | 0.0813081i | ||||
\(479\) | 20.4924 | 0.936323 | 0.468161 | − | 0.883643i | \(-0.344917\pi\) | ||||
0.468161 | + | 0.883643i | \(0.344917\pi\) | |||||||
\(480\) | −9.36932 | + | 2.06798i | −0.427649 | + | 0.0943897i | ||||
\(481\) | 43.0299i | 1.96200i | ||||||||
\(482\) | −2.24621 | − | 1.48734i | −0.102312 | − | 0.0677463i | ||||
\(483\) | 2.00000 | + | 7.73704i | 0.0910032 | + | 0.352047i | ||||
\(484\) | −1.46543 | − | 3.45593i | −0.0666107 | − | 0.157088i | ||||
\(485\) | −14.7386 | −0.669247 | ||||||||
\(486\) | 0.780776 | − | 1.17915i | 0.0354167 | − | 0.0534872i | ||||
\(487\) | 32.2725i | 1.46240i | 0.682161 | + | 0.731202i | \(0.261040\pi\) | ||||
−0.682161 | + | 0.731202i | \(0.738960\pi\) | |||||||
\(488\) | 4.87689 | − | 26.2316i | 0.220767 | − | 1.18745i | ||||
\(489\) | − | 11.5012i | − | 0.520100i | ||||||
\(490\) | 16.7386 | + | 1.32431i | 0.756174 | + | 0.0598261i | ||||
\(491\) | 11.7100i | 0.528463i | 0.964459 | + | 0.264231i | \(0.0851183\pi\) | ||||
−0.964459 | + | 0.264231i | \(0.914882\pi\) | |||||||
\(492\) | −14.2462 | + | 6.04090i | −0.642269 | + | 0.272345i | ||||
\(493\) | − | 8.68951i | − | 0.391356i | ||||||
\(494\) | −8.00000 | − | 5.29723i | −0.359937 | − | 0.238334i | ||||
\(495\) | −5.12311 | −0.230266 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.24621 | − | 31.9006i | −0.369893 | − | 1.43094i | ||||
\(498\) | −4.87689 | + | 7.36520i | −0.218539 | + | 0.330043i | ||||
\(499\) | 17.5420i | 0.785290i | 0.919690 | + | 0.392645i | \(0.128440\pi\) | ||||
−0.919690 | + | 0.392645i | \(0.871560\pi\) | |||||||
\(500\) | 22.2462 | − | 9.43318i | 0.994881 | − | 0.421865i | ||||
\(501\) | 2.24621 | 0.100353 | ||||||||
\(502\) | 17.3693 | − | 26.2316i | 0.775231 | − | 1.17077i | ||||
\(503\) | −22.7386 | −1.01387 | −0.506933 | − | 0.861986i | \(-0.669221\pi\) | ||||
−0.506933 | + | 0.861986i | \(0.669221\pi\) | |||||||
\(504\) | 7.46543 | − | 0.516994i | 0.332537 | − | 0.0230287i | ||||
\(505\) | 11.8617 | 0.527840 | ||||||||
\(506\) | 7.12311 | − | 10.7575i | 0.316661 | − | 0.478229i | ||||
\(507\) | −23.4924 | −1.04334 | ||||||||
\(508\) | −35.8078 | + | 15.1838i | −1.58871 | + | 0.673670i | ||||
\(509\) | − | 1.69614i | − | 0.0751801i | −0.999293 | − | 0.0375901i | \(-0.988032\pi\) | ||
0.999293 | − | 0.0375901i | \(-0.0119681\pi\) | |||||||
\(510\) | −5.75379 | + | 8.68951i | −0.254782 | + | 0.384778i | ||||
\(511\) | −2.24621 | − | 8.68951i | −0.0993665 | − | 0.384401i | ||||
\(512\) | −19.2732 | − | 11.8551i | −0.851763 | − | 0.523927i | ||||
\(513\) | 1.12311 | 0.0495863 | ||||||||
\(514\) | −23.3693 | − | 15.4741i | −1.03078 | − | 0.682532i | ||||
\(515\) | 13.5691i | 0.597927i | ||||||||
\(516\) | −14.9309 | + | 6.33122i | −0.657295 | + | 0.278716i | ||||
\(517\) | 30.9481i | 1.36110i | ||||||||
\(518\) | 8.68466 | − | 25.1976i | 0.381582 | − | 1.10712i | ||||
\(519\) | − | 8.48071i | − | 0.372262i | ||||||
\(520\) | −28.4924 | − | 5.29723i | −1.24948 | − | 0.232299i | ||||
\(521\) | − | 33.8056i | − | 1.48105i | −0.672030 | − | 0.740524i | \(-0.734577\pi\) | ||
0.672030 | − | 0.740524i | \(-0.265423\pi\) | |||||||
\(522\) | −1.56155 | + | 2.35829i | −0.0683473 | + | 0.103220i | ||||
\(523\) | 0.492423 | 0.0215321 | 0.0107661 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107661 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(524\) | 17.3693 | + | 40.9620i | 0.758782 | + | 1.78943i | ||||
\(525\) | −5.43845 | + | 1.40582i | −0.237353 | + | 0.0613551i | ||||
\(526\) | −5.80776 | − | 3.84563i | −0.253231 | − | 0.167677i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −8.68466 | − | 8.39919i | −0.377951 | − | 0.365528i | ||||
\(529\) | 13.8769 | 0.603343 | ||||||||
\(530\) | −8.49242 | − | 5.62329i | −0.368887 | − | 0.244260i | ||||
\(531\) | −4.00000 | −0.173585 | ||||||||
\(532\) | 3.61553 | + | 4.71659i | 0.156753 | + | 0.204490i | ||||
\(533\) | −46.7386 | −2.02447 | ||||||||
\(534\) | 9.12311 | + | 6.04090i | 0.394795 | + | 0.261415i | ||||
\(535\) | 9.61553 | 0.415716 | ||||||||
\(536\) | 1.06913 | − | 5.75058i | 0.0461794 | − | 0.248387i | ||||
\(537\) | − | 2.27678i | − | 0.0982503i | ||||||
\(538\) | 26.4924 | + | 17.5420i | 1.14217 | + | 0.756291i | ||||
\(539\) | 10.2462 | + | 18.4945i | 0.441336 | + | 0.796615i | ||||
\(540\) | 3.12311 | − | 1.32431i | 0.134397 | − | 0.0569891i | ||||
\(541\) | 11.1231 | 0.478220 | 0.239110 | − | 0.970993i | \(-0.423144\pi\) | ||||
0.239110 | + | 0.970993i | \(0.423144\pi\) | |||||||
\(542\) | −3.50758 | + | 5.29723i | −0.150663 | + | 0.227535i | ||||
\(543\) | 6.04090i | 0.259240i | ||||||||
\(544\) | −24.0000 | + | 5.29723i | −1.02899 | + | 0.227117i | ||||
\(545\) | 13.9867i | 0.599126i | ||||||||
\(546\) | 21.3693 | + | 7.36520i | 0.914522 | + | 0.315202i | ||||
\(547\) | 33.0161i | 1.41167i | 0.708378 | + | 0.705834i | \(0.249427\pi\) | ||||
−0.708378 | + | 0.705834i | \(0.750573\pi\) | |||||||
\(548\) | 12.6847 | + | 29.9142i | 0.541862 | + | 1.27787i | ||||
\(549\) | 9.43318i | 0.402598i | ||||||||
\(550\) | 7.56155 | + | 5.00691i | 0.322426 | + | 0.213495i | ||||
\(551\) | −2.24621 | −0.0956918 | ||||||||
\(552\) | −1.56155 | + | 8.39919i | −0.0664641 | + | 0.357493i | ||||
\(553\) | −3.12311 | − | 12.0818i | −0.132808 | − | 0.513770i | ||||
\(554\) | 2.43845 | − | 3.68260i | 0.103600 | − | 0.156459i | ||||
\(555\) | − | 12.0818i | − | 0.512843i | ||||||
\(556\) | −9.36932 | − | 22.0956i | −0.397348 | − | 0.937063i | ||||
\(557\) | 14.0000 | 0.593199 | 0.296600 | − | 0.955002i | \(-0.404147\pi\) | ||||
0.296600 | + | 0.955002i | \(0.404147\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.9848 | −2.07184 | ||||||||
\(560\) | 15.6155 | + | 8.85254i | 0.659877 | + | 0.374088i | ||||
\(561\) | −13.1231 | −0.554058 | ||||||||
\(562\) | −0.192236 | + | 0.290319i | −0.00810898 | + | 0.0122464i | ||||
\(563\) | 14.2462 | 0.600406 | 0.300203 | − | 0.953875i | \(-0.402946\pi\) | ||||
0.300203 | + | 0.953875i | \(0.402946\pi\) | |||||||
\(564\) | −8.00000 | − | 18.8664i | −0.336861 | − | 0.794417i | ||||
\(565\) | 20.7713i | 0.873855i | ||||||||
\(566\) | −13.3693 | + | 20.1907i | −0.561954 | + | 0.848677i | ||||
\(567\) | −2.56155 | + | 0.662153i | −0.107575 | + | 0.0278078i | ||||
\(568\) | 6.43845 | − | 34.6307i | 0.270151 | − | 1.45307i | ||||
\(569\) | 34.9848 | 1.46664 | 0.733320 | − | 0.679883i | \(-0.237969\pi\) | ||||
0.733320 | + | 0.679883i | \(0.237969\pi\) | |||||||
\(570\) | 2.24621 | + | 1.48734i | 0.0940834 | + | 0.0622977i | ||||
\(571\) | − | 40.9620i | − | 1.71420i | −0.515146 | − | 0.857102i | \(-0.672262\pi\) | ||
0.515146 | − | 0.857102i | \(-0.327738\pi\) | |||||||
\(572\) | −14.2462 | − | 33.5968i | −0.595664 | − | 1.40475i | ||||
\(573\) | 9.06134i | 0.378543i | ||||||||
\(574\) | 27.3693 | + | 9.43318i | 1.14237 | + | 0.393733i | ||||
\(575\) | − | 6.41273i | − | 0.267429i | ||||||
\(576\) | 7.46543 | + | 2.87529i | 0.311060 | + | 0.119804i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | −1.46543 | + | 2.21313i | −0.0609541 | + | 0.0920543i | ||||
\(579\) | 9.36932 | 0.389376 | ||||||||
\(580\) | −6.24621 | + | 2.64861i | −0.259360 | + | 0.109978i | ||||
\(581\) | 16.0000 | − | 4.13595i | 0.663792 | − | 0.171588i | ||||
\(582\) | 10.2462 | + | 6.78456i | 0.424719 | + | 0.281229i | ||||
\(583\) | − | 12.8255i | − | 0.531176i | ||||||
\(584\) | 1.75379 | − | 9.43318i | 0.0725723 | − | 0.390348i | ||||
\(585\) | 10.2462 | 0.423629 | ||||||||
\(586\) | −8.24621 | − | 5.46026i | −0.340648 | − | 0.225561i | ||||
\(587\) | 38.2462 | 1.57859 | 0.789295 | − | 0.614014i | \(-0.210446\pi\) | ||||
0.789295 | + | 0.614014i | \(0.210446\pi\) | |||||||
\(588\) | −11.0270 | − | 8.62586i | −0.454745 | − | 0.355725i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −8.00000 | − | 5.29723i | −0.329355 | − | 0.218083i | ||||
\(591\) | 0.246211 | 0.0101278 | ||||||||
\(592\) | 19.8078 | − | 20.4810i | 0.814094 | − | 0.841763i | ||||
\(593\) | 21.7238i | 0.892088i | 0.895011 | + | 0.446044i | \(0.147168\pi\) | ||||
−0.895011 | + | 0.446044i | \(0.852832\pi\) | |||||||
\(594\) | 3.56155 | + | 2.35829i | 0.146132 | + | 0.0967620i | ||||
\(595\) | 18.8769 | − | 4.87962i | 0.773877 | − | 0.200045i | ||||
\(596\) | 7.80776 | + | 18.4130i | 0.319818 | + | 0.754226i | ||||
\(597\) | −5.12311 | −0.209675 | ||||||||
\(598\) | −14.2462 | + | 21.5150i | −0.582571 | + | 0.879813i | ||||
\(599\) | 19.2382i | 0.786051i | 0.919528 | + | 0.393026i | \(0.128572\pi\) | ||||
−0.919528 | + | 0.393026i | \(0.871428\pi\) | |||||||
\(600\) | −5.90388 | − | 1.09763i | −0.241025 | − | 0.0448107i | ||||
\(601\) | 5.29723i | 0.216078i | 0.994147 | + | 0.108039i | \(0.0344572\pi\) | ||||
−0.994147 | + | 0.108039i | \(0.965543\pi\) | |||||||
\(602\) | 28.6847 | + | 9.88653i | 1.16910 | + | 0.402945i | ||||
\(603\) | 2.06798i | 0.0842145i | ||||||||
\(604\) | 14.9309 | − | 6.33122i | 0.607528 | − | 0.257613i | ||||
\(605\) | 3.18348i | 0.129427i | ||||||||
\(606\) | −8.24621 | − | 5.46026i | −0.334979 | − | 0.221808i | ||||
\(607\) | 33.6155 | 1.36441 | 0.682206 | − | 0.731160i | \(-0.261021\pi\) | ||||
0.682206 | + | 0.731160i | \(0.261021\pi\) | |||||||
\(608\) | 1.36932 | + | 6.20393i | 0.0555331 | + | 0.251602i | ||||
\(609\) | 5.12311 | − | 1.32431i | 0.207599 | − | 0.0536636i | ||||
\(610\) | −12.4924 | + | 18.8664i | −0.505803 | + | 0.763876i | ||||
\(611\) | − | 61.8963i | − | 2.50406i | ||||||
\(612\) | 8.00000 | − | 3.39228i | 0.323381 | − | 0.137125i | ||||
\(613\) | −40.7386 | −1.64542 | −0.822709 | − | 0.568463i | \(-0.807538\pi\) | ||||
−0.822709 | + | 0.568463i | \(0.807538\pi\) | |||||||
\(614\) | 16.8769 | − | 25.4879i | 0.681096 | − | 1.02861i | ||||
\(615\) | 13.1231 | 0.529175 | ||||||||
\(616\) | 1.56155 | + | 22.5490i | 0.0629168 | + | 0.908523i | ||||
\(617\) | 15.7538 | 0.634224 | 0.317112 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317112 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(618\) | 6.24621 | − | 9.43318i | 0.251259 | − | 0.379458i | ||||
\(619\) | −20.0000 | −0.803868 | −0.401934 | − | 0.915669i | \(-0.631662\pi\) | ||||
−0.401934 | + | 0.915669i | \(0.631662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 3.02045i | − | 0.121206i | ||||||
\(622\) | −6.24621 | + | 9.43318i | −0.250450 | + | 0.378236i | ||||
\(623\) | −5.12311 | − | 19.8188i | −0.205253 | − | 0.794025i | ||||
\(624\) | 17.3693 | + | 16.7984i | 0.695329 | + | 0.672473i | ||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | −30.2462 | − | 20.0276i | −1.20888 | − | 0.800465i | ||||
\(627\) | 3.39228i | 0.135475i | ||||||||
\(628\) | −7.61553 | + | 3.22925i | −0.303893 | + | 0.128861i | ||||
\(629\) | − | 30.9481i | − | 1.23398i | ||||||
\(630\) | −6.00000 | − | 2.06798i | −0.239046 | − | 0.0823901i | ||||
\(631\) | − | 17.9597i | − | 0.714963i | −0.933920 | − | 0.357481i | \(-0.883636\pi\) | ||
0.933920 | − | 0.357481i | \(-0.116364\pi\) | |||||||
\(632\) | 2.43845 | − | 13.1158i | 0.0969962 | − | 0.521718i | ||||
\(633\) | 3.97292i | 0.157909i | ||||||||
\(634\) | 14.4384 | − | 21.8053i | 0.573424 | − | 0.865999i | ||||
\(635\) | 32.9848 | 1.30896 | ||||||||
\(636\) | 3.31534 | + | 7.81855i | 0.131462 | + | 0.310026i | ||||
\(637\) | −20.4924 | − | 36.9890i | −0.811939 | − | 1.46556i | ||||
\(638\) | −7.12311 | − | 4.71659i | −0.282006 | − | 0.186732i | ||||
\(639\) | 12.4536i | 0.492658i | ||||||||
\(640\) | 11.1231 | + | 15.6371i | 0.439679 | + | 0.618111i | ||||
\(641\) | −9.50758 | −0.375527 | −0.187763 | − | 0.982214i | \(-0.560124\pi\) | ||||
−0.187763 | + | 0.982214i | \(0.560124\pi\) | |||||||
\(642\) | −6.68466 | − | 4.42627i | −0.263822 | − | 0.174691i | ||||
\(643\) | −29.6155 | −1.16792 | −0.583961 | − | 0.811782i | \(-0.698498\pi\) | ||||
−0.583961 | + | 0.811782i | \(0.698498\pi\) | |||||||
\(644\) | 12.6847 | − | 9.72350i | 0.499846 | − | 0.383159i | ||||
\(645\) | 13.7538 | 0.541555 | ||||||||
\(646\) | 5.75379 | + | 3.80989i | 0.226380 | + | 0.149898i | ||||
\(647\) | −32.9848 | −1.29677 | −0.648384 | − | 0.761313i | \(-0.724555\pi\) | ||||
−0.648384 | + | 0.761313i | \(0.724555\pi\) | |||||||
\(648\) | −2.78078 | − | 0.516994i | −0.109239 | − | 0.0203094i | ||||
\(649\) | − | 12.0818i | − | 0.474252i | ||||||
\(650\) | −15.1231 | − | 10.0138i | −0.593177 | − | 0.392774i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.1771 | + | 8.97983i | −0.829358 | + | 0.351677i | ||||
\(653\) | −32.7386 | −1.28116 | −0.640581 | − | 0.767891i | \(-0.721306\pi\) | ||||
−0.640581 | + | 0.767891i | \(0.721306\pi\) | |||||||
\(654\) | 6.43845 | − | 9.72350i | 0.251763 | − | 0.380219i | ||||
\(655\) | − | 37.7327i | − | 1.47434i | ||||||
\(656\) | 22.2462 | + | 21.5150i | 0.868569 | + | 0.840018i | ||||
\(657\) | 3.39228i | 0.132346i | ||||||||
\(658\) | −12.4924 | + | 36.2454i | −0.487005 | + | 1.41299i | ||||
\(659\) | − | 38.1045i | − | 1.48434i | −0.670210 | − | 0.742171i | \(-0.733796\pi\) | ||
0.670210 | − | 0.742171i | \(-0.266204\pi\) | |||||||
\(660\) | 4.00000 | + | 9.43318i | 0.155700 | + | 0.367186i | ||||
\(661\) | − | 2.64861i | − | 0.103019i | −0.998673 | − | 0.0515096i | \(-0.983597\pi\) | ||
0.998673 | − | 0.0515096i | \(-0.0164033\pi\) | |||||||
\(662\) | 6.43845 | + | 4.26324i | 0.250237 | + | 0.165696i | ||||
\(663\) | 26.2462 | 1.01932 | ||||||||
\(664\) | 17.3693 | + | 3.22925i | 0.674060 | + | 0.125319i | ||||
\(665\) | −1.26137 | − | 4.87962i | −0.0489137 | − | 0.189223i | ||||
\(666\) | −5.56155 | + | 8.39919i | −0.215506 | + | 0.325462i | ||||
\(667\) | 6.04090i | 0.233904i | ||||||||
\(668\) | −1.75379 | − | 4.13595i | −0.0678561 | − | 0.160025i | ||||
\(669\) | −18.8769 | −0.729823 | ||||||||
\(670\) | −2.73863 | + | 4.13595i | −0.105803 | + | 0.159786i | ||||
\(671\) | −28.4924 | −1.09994 | ||||||||
\(672\) | −6.78078 | − | 13.3425i | −0.261574 | − | 0.514696i | ||||
\(673\) | 29.8617 | 1.15109 | 0.575543 | − | 0.817772i | \(-0.304791\pi\) | ||||
0.575543 | + | 0.817772i | \(0.304791\pi\) | |||||||
\(674\) | −6.43845 | + | 9.72350i | −0.248000 | + | 0.374535i | ||||
\(675\) | 2.12311 | 0.0817184 | ||||||||
\(676\) | 18.3423 | + | 43.2566i | 0.705474 | + | 1.66372i | ||||
\(677\) | 32.6443i | 1.25462i | 0.778769 | + | 0.627311i | \(0.215844\pi\) | ||||
−0.778769 | + | 0.627311i | \(0.784156\pi\) | |||||||
\(678\) | 9.56155 | − | 14.4401i | 0.367209 | − | 0.554568i | ||||
\(679\) | −5.75379 | − | 22.2586i | −0.220810 | − | 0.854208i | ||||
\(680\) | 20.4924 | + | 3.80989i | 0.785849 | + | 0.146103i | ||||
\(681\) | −16.4924 | −0.631991 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.0890i | 1.11306i | 0.830828 | + | 0.556529i | \(0.187867\pi\) | ||||
−0.830828 | + | 0.556529i | \(0.812133\pi\) | |||||||
\(684\) | −0.876894 | − | 2.06798i | −0.0335289 | − | 0.0790710i | ||||
\(685\) | − | 27.5559i | − | 1.05286i | ||||||
\(686\) | 4.53457 | + | 25.7961i | 0.173131 | + | 0.984899i | ||||
\(687\) | − | 18.1227i | − | 0.691424i | ||||||
\(688\) | 23.3153 | + | 22.5490i | 0.888889 | + | 0.859671i | ||||
\(689\) | 25.6509i | 0.977222i | ||||||||
\(690\) | 4.00000 | − | 6.04090i | 0.152277 | − | 0.229973i | ||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | −15.6155 | + | 6.62153i | −0.593613 | + | 0.251713i | ||||
\(693\) | −2.00000 | − | 7.73704i | −0.0759737 | − | 0.293906i | ||||
\(694\) | −40.9309 | − | 27.1025i | −1.55371 | − | 1.02880i | ||||
\(695\) | 20.3537i | 0.772060i | ||||||||
\(696\) | 5.56155 | + | 1.03399i | 0.210810 | + | 0.0391932i | ||||
\(697\) | 33.6155 | 1.27328 | ||||||||
\(698\) | −4.87689 | − | 3.22925i | −0.184593 | − | 0.122229i | ||||
\(699\) | −10.4924 | −0.396860 | ||||||||
\(700\) | 6.83475 | + | 8.91618i | 0.258329 | + | 0.337000i | ||||
\(701\) | −34.0000 | −1.28416 | −0.642081 | − | 0.766637i | \(-0.721929\pi\) | ||||
−0.642081 | + | 0.766637i | \(0.721929\pi\) | |||||||
\(702\) | −7.12311 | − | 4.71659i | −0.268844 | − | 0.178016i | ||||
\(703\) | −8.00000 | −0.301726 | ||||||||
\(704\) | −8.68466 | + | 22.5490i | −0.327315 | + | 0.849846i | ||||
\(705\) | 17.3790i | 0.654532i | ||||||||
\(706\) | 7.36932 | + | 4.87962i | 0.277348 | + | 0.183647i | ||||
\(707\) | 4.63068 | + | 17.9139i | 0.174155 | + | 0.673721i | ||||
\(708\) | 3.12311 | + | 7.36520i | 0.117373 | + | 0.276801i | ||||
\(709\) | 6.00000 | 0.225335 | 0.112667 | − | 0.993633i | \(-0.464061\pi\) | ||||
0.112667 | + | 0.993633i | \(0.464061\pi\) | |||||||
\(710\) | −16.4924 | + | 24.9073i | −0.618950 | + | 0.934752i | ||||
\(711\) | 4.71659i | 0.176886i | ||||||||
\(712\) | 4.00000 | − | 21.5150i | 0.149906 | − | 0.806308i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −15.3693 | − | 5.29723i | −0.575182 | − | 0.198244i | ||||
\(715\) | 30.9481i | 1.15740i | ||||||||
\(716\) | −4.19224 | + | 1.77766i | −0.156671 | + | 0.0664341i | ||||
\(717\) | 2.27678i | 0.0850279i | ||||||||
\(718\) | −1.31534 | − | 0.870958i | −0.0490881 | − | 0.0325039i | ||||
\(719\) | 4.49242 | 0.167539 | 0.0837695 | − | 0.996485i | \(-0.473304\pi\) | ||||
0.0837695 | + | 0.996485i | \(0.473304\pi\) | |||||||
\(720\) | −4.87689 | − | 4.71659i | −0.181751 | − | 0.175777i | ||||
\(721\) | −20.4924 | + | 5.29723i | −0.763178 | + | 0.197279i | ||||
\(722\) | −13.8499 | + | 20.9165i | −0.515440 | + | 0.778430i | ||||
\(723\) | − | 1.90495i | − | 0.0708457i | ||||||
\(724\) | 11.1231 | − | 4.71659i | 0.413387 | − | 0.175291i | ||||
\(725\) | −4.24621 | −0.157700 | ||||||||
\(726\) | 1.46543 | − | 2.21313i | 0.0543874 | − | 0.0821371i | ||||
\(727\) | 32.9848 | 1.22334 | 0.611670 | − | 0.791113i | \(-0.290498\pi\) | ||||
0.611670 | + | 0.791113i | \(0.290498\pi\) | |||||||
\(728\) | −3.12311 | − | 45.0979i | −0.115750 | − | 1.67144i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −4.49242 | + | 6.78456i | −0.166272 | + | 0.251108i | ||||
\(731\) | 35.2311 | 1.30307 | ||||||||
\(732\) | 17.3693 | − | 7.36520i | 0.641988 | − | 0.272226i | ||||
\(733\) | − | 16.6354i | − | 0.614441i | −0.951638 | − | 0.307220i | \(-0.900601\pi\) | ||
0.951638 | − | 0.307220i | \(-0.0993989\pi\) | |||||||
\(734\) | 6.73863 | − | 10.1768i | 0.248728 | − | 0.375634i | ||||
\(735\) | 5.75379 | + | 10.3857i | 0.212232 | + | 0.383080i | ||||
\(736\) | 16.6847 | − | 3.68260i | 0.615005 | − | 0.135742i | ||||
\(737\) | −6.24621 | −0.230082 | ||||||||
\(738\) | −9.12311 | − | 6.04090i | −0.335826 | − | 0.222368i | ||||
\(739\) | 5.87787i | 0.216221i | 0.994139 | + | 0.108110i | \(0.0344800\pi\) | ||||
−0.994139 | + | 0.108110i | \(0.965520\pi\) | |||||||
\(740\) | −22.2462 | + | 9.43318i | −0.817787 | + | 0.346771i | ||||
\(741\) | − | 6.78456i | − | 0.249237i | ||||||
\(742\) | 5.17708 | − | 15.0207i | 0.190057 | − | 0.551428i | ||||
\(743\) | − | 13.6149i | − | 0.499482i | −0.968313 | − | 0.249741i | \(-0.919654\pi\) | ||
0.968313 | − | 0.249741i | \(-0.0803455\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.9614i | − | 0.621418i | ||||||
\(746\) | −7.80776 | + | 11.7915i | −0.285863 | + | 0.431716i | ||||
\(747\) | −6.24621 | −0.228537 | ||||||||
\(748\) | 10.2462 | + | 24.1636i | 0.374639 | + | 0.883508i | ||||
\(749\) | 3.75379 | + | 14.5216i | 0.137160 | + | 0.530608i | ||||
\(750\) | 14.2462 | + | 9.43318i | 0.520198 | + | 0.344451i | ||||
\(751\) | 30.7851i | 1.12336i | 0.827353 | + | 0.561682i | \(0.189846\pi\) | ||||
−0.827353 | + | 0.561682i | \(0.810154\pi\) | |||||||
\(752\) | −28.4924 | + | 29.4608i | −1.03901 | + | 1.07433i | ||||
\(753\) | 22.2462 | 0.810697 | ||||||||
\(754\) | 14.2462 | + | 9.43318i | 0.518816 | + | 0.343536i | ||||
\(755\) | −13.7538 | −0.500552 | ||||||||
\(756\) | 3.21922 | + | 4.19960i | 0.117082 | + | 0.152738i | ||||
\(757\) | 30.9848 | 1.12616 | 0.563082 | − | 0.826401i | \(-0.309616\pi\) | ||||
0.563082 | + | 0.826401i | \(0.309616\pi\) | |||||||
\(758\) | −22.0540 | − | 14.6031i | −0.801036 | − | 0.530409i | ||||
\(759\) | 9.12311 | 0.331148 | ||||||||
\(760\) | 0.984845 | − | 5.29723i | 0.0357241 | − | 0.192151i | ||||
\(761\) | 33.8056i | 1.22545i | 0.790296 | + | 0.612725i | \(0.209927\pi\) | ||||
−0.790296 | + | 0.612725i | \(0.790073\pi\) | |||||||
\(762\) | −22.9309 | − | 15.1838i | −0.830698 | − | 0.550049i | ||||
\(763\) | −21.1231 | + | 5.46026i | −0.764708 | + | 0.197675i | ||||
\(764\) | 16.6847 | − | 7.07488i | 0.603630 | − | 0.255960i | ||||
\(765\) | −7.36932 | −0.266438 | ||||||||
\(766\) | 20.4924 | − | 30.9481i | 0.740421 | − | 1.11820i | ||||
\(767\) | 24.1636i | 0.872496i | ||||||||
\(768\) | −0.534565 | − | 15.9911i | −0.0192895 | − | 0.577028i | ||||
\(769\) | − | 44.5173i | − | 1.60533i | −0.596427 | − | 0.802667i | \(-0.703414\pi\) | ||
0.596427 | − | 0.802667i | \(-0.296586\pi\) | |||||||
\(770\) | 6.24621 | − | 18.1227i | 0.225098 | − | 0.653096i | ||||
\(771\) | − | 19.8188i | − | 0.713758i | ||||||
\(772\) | −7.31534 | − | 17.2517i | −0.263285 | − | 0.620903i | ||||
\(773\) | 1.69614i | 0.0610060i | 0.999535 | + | 0.0305030i | \(0.00971091\pi\) | ||||
−0.999535 | + | 0.0305030i | \(0.990289\pi\) | |||||||
\(774\) | −9.56155 | − | 6.33122i | −0.343683 | − | 0.227571i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.49242 | − | 24.1636i | 0.161269 | − | 0.867422i | ||||
\(777\) | 18.2462 | − | 4.71659i | 0.654579 | − | 0.169207i | ||||
\(778\) | 0.192236 | − | 0.290319i | 0.00689199 | − | 0.0104085i | ||||
\(779\) | − | 8.68951i | − | 0.311334i | ||||||
\(780\) | −8.00000 | − | 18.8664i | −0.286446 | − | 0.675524i | ||||
\(781\) | −37.6155 | −1.34599 | ||||||||
\(782\) | 10.2462 | − | 15.4741i | 0.366404 | − | 0.553352i | ||||
\(783\) | −2.00000 | −0.0714742 | ||||||||
\(784\) | −7.27320 | + | 27.0389i | −0.259757 | + | 0.965674i | ||||
\(785\) | 7.01515 | 0.250382 | ||||||||
\(786\) | −17.3693 | + | 26.2316i | −0.619543 | + | 0.935649i | ||||
\(787\) | −20.9848 | −0.748029 | −0.374014 | − | 0.927423i | \(-0.622019\pi\) | ||||
−0.374014 | + | 0.927423i | \(0.622019\pi\) | |||||||
\(788\) | −0.192236 | − | 0.453349i | −0.00684812 | − | 0.0161499i | ||||
\(789\) | − | 4.92539i | − | 0.175349i | ||||||
\(790\) | −6.24621 | + | 9.43318i | −0.222230 | + | 0.335617i | ||||
\(791\) | −31.3693 | + | 8.10887i | −1.11536 | + | 0.288318i | ||||
\(792\) | 1.56155 | − | 8.39919i | 0.0554874 | − | 0.298452i | ||||
\(793\) | 56.9848 | 2.02359 | ||||||||
\(794\) | 19.1231 | + | 12.6624i | 0.678654 | + | 0.449373i | ||||
\(795\) | − | 7.20217i | − | 0.255435i | ||||||
\(796\) | 4.00000 | + | 9.43318i | 0.141776 | + | 0.334350i | ||||
\(797\) | 34.1316i | 1.20900i | 0.796604 | + | 0.604502i | \(0.206628\pi\) | ||||
−0.796604 | + | 0.604502i | \(0.793372\pi\) | |||||||
\(798\) | −1.36932 | + | 3.97292i | −0.0484733 | + | 0.140640i | ||||
\(799\) | 44.5173i | 1.57491i | ||||||||
\(800\) | 2.58854 | + | 11.7278i | 0.0915187 | + | 0.414641i | ||||
\(801\) | 7.73704i | 0.273375i | ||||||||
\(802\) | −6.43845 | + | 9.72350i | −0.227349 | + | 0.343349i | ||||
\(803\) | −10.2462 | −0.361581 | ||||||||
\(804\) | 3.80776 | − | 1.61463i | 0.134289 | − | 0.0569435i | ||||
\(805\) | −13.1231 | + | 3.39228i | −0.462529 | + | 0.119562i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.4674i | 0.790891i | ||||||||
\(808\) | −3.61553 | + | 19.4470i | −0.127194 | + | 0.684143i | ||||
\(809\) | −10.4924 | −0.368894 | −0.184447 | − | 0.982842i | \(-0.559049\pi\) | ||||
−0.184447 | + | 0.982842i | \(0.559049\pi\) | |||||||
\(810\) | 2.00000 | + | 1.32431i | 0.0702728 | + | 0.0465314i | ||||
\(811\) | 32.4924 | 1.14096 | 0.570482 | − | 0.821310i | \(-0.306757\pi\) | ||||
0.570482 | + | 0.821310i | \(0.306757\pi\) | |||||||
\(812\) | −6.43845 | − | 8.39919i | −0.225945 | − | 0.294754i | ||||
\(813\) | −4.49242 | −0.157556 | ||||||||
\(814\) | −25.3693 | − | 16.7984i | −0.889194 | − | 0.588783i | ||||
\(815\) | 19.5076 | 0.683321 | ||||||||
\(816\) | −12.4924 | − | 12.0818i | −0.437322 | − | 0.422947i | ||||
\(817\) | − | 9.10712i | − | 0.318618i | ||||||
\(818\) | 32.4924 | + | 21.5150i | 1.13607 | + | 0.752253i | ||||
\(819\) | 4.00000 | + | 15.4741i | 0.139771 | + | 0.540708i | ||||
\(820\) | −10.2462 | − | 24.1636i | −0.357813 | − | 0.843829i | ||||
\(821\) | 25.2311 | 0.880570 | 0.440285 | − | 0.897858i | \(-0.354877\pi\) | ||||
0.440285 | + | 0.897858i | \(0.354877\pi\) | |||||||
\(822\) | −12.6847 | + | 19.1567i | −0.442428 | + | 0.668166i | ||||
\(823\) | − | 45.0979i | − | 1.57201i | −0.618217 | − | 0.786007i | \(-0.712145\pi\) | ||
0.618217 | − | 0.786007i | \(-0.287855\pi\) | |||||||
\(824\) | −22.2462 | − | 4.13595i | −0.774983 | − | 0.144083i | ||||
\(825\) | 6.41273i | 0.223263i | ||||||||
\(826\) | 4.87689 | − | 14.1498i | 0.169689 | − | 0.492333i | ||||
\(827\) | 30.9939i | 1.07776i | 0.842381 | + | 0.538882i | \(0.181153\pi\) | ||||
−0.842381 | + | 0.538882i | \(0.818847\pi\) | |||||||
\(828\) | −5.56155 | + | 2.35829i | −0.193277 | + | 0.0819564i | ||||
\(829\) | 31.6918i | 1.10070i | 0.834933 | + | 0.550351i | \(0.185506\pi\) | ||||
−0.834933 | + | 0.550351i | \(0.814494\pi\) | |||||||
\(830\) | −12.4924 | − | 8.27190i | −0.433618 | − | 0.287122i | ||||
\(831\) | 3.12311 | 0.108339 | ||||||||
\(832\) | 17.3693 | − | 45.0979i | 0.602173 | − | 1.56349i | ||||
\(833\) | 14.7386 | + | 26.6034i | 0.510663 | + | 0.921753i | ||||
\(834\) | 9.36932 | − | 14.1498i | 0.324433 | − | 0.489966i | ||||
\(835\) | 3.80989i | 0.131847i | ||||||||
\(836\) | 6.24621 | − | 2.64861i | 0.216030 | − | 0.0916042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.8769 | + | 19.4470i | −0.444825 | + | 0.671785i | ||||
\(839\) | −6.73863 | −0.232643 | −0.116322 | − | 0.993212i | \(-0.537110\pi\) | ||||
−0.116322 | + | 0.993212i | \(0.537110\pi\) | |||||||
\(840\) | 0.876894 | + | 12.6624i | 0.0302557 | + | 0.436895i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 14.9309 | − | 22.5490i | 0.514552 | − | 0.777088i | ||||
\(843\) | −0.246211 | −0.00847997 | ||||||||
\(844\) | 7.31534 | − | 3.10196i | 0.251804 | − | 0.106774i | ||||
\(845\) | − | 39.8465i | − | 1.37076i | ||||||
\(846\) | 8.00000 | − | 12.0818i | 0.275046 | − | 0.415381i | ||||
\(847\) | −4.80776 | + | 1.24279i | −0.165197 | + | 0.0427028i | ||||
\(848\) | 11.8078 | − | 12.2091i | 0.405480 | − | 0.419262i | ||||
\(849\) | −17.1231 | −0.587663 | ||||||||
\(850\) | 10.8769 | + | 7.20217i | 0.373074 | + | 0.247032i | ||||
\(851\) | 21.5150i | 0.737524i | ||||||||
\(852\) | 22.9309 | − | 9.72350i | 0.785599 | − | 0.333122i | ||||
\(853\) | − | 37.4067i | − | 1.28078i | −0.768050 | − | 0.640390i | \(-0.778773\pi\) | ||
0.768050 | − | 0.640390i | \(-0.221227\pi\) | |||||||
\(854\) | −33.3693 | − | 11.5012i | −1.14187 | − | 0.393561i | ||||
\(855\) | 1.90495i | 0.0651478i | ||||||||
\(856\) | −2.93087 | + | 15.7644i | −0.100175 | + | 0.538816i | ||||
\(857\) | 20.2364i | 0.691264i | 0.938370 | + | 0.345632i | \(0.112335\pi\) | ||||
−0.938370 | + | 0.345632i | \(0.887665\pi\) | |||||||
\(858\) | 14.2462 | − | 21.5150i | 0.486358 | − | 0.734509i | ||||
\(859\) | −31.8617 | −1.08711 | −0.543554 | − | 0.839374i | \(-0.682922\pi\) | ||||
−0.543554 | + | 0.839374i | \(0.682922\pi\) | |||||||
\(860\) | −10.7386 | − | 25.3249i | −0.366184 | − | 0.863571i | ||||
\(861\) | 5.12311 | + | 19.8188i | 0.174595 | + | 0.675424i | ||||
\(862\) | −17.8078 | − | 11.7915i | −0.606535 | − | 0.401619i | ||||
\(863\) | − | 21.8868i | − | 0.745035i | −0.928025 | − | 0.372518i | \(-0.878495\pi\) | ||
0.928025 | − | 0.372518i | \(-0.121505\pi\) | |||||||
\(864\) | 1.21922 | + | 5.52390i | 0.0414788 | + | 0.187927i | ||||
\(865\) | 14.3845 | 0.489087 | ||||||||
\(866\) | −8.00000 | − | 5.29723i | −0.271851 | − | 0.180007i | ||||
\(867\) | −1.87689 | −0.0637427 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.2462 | −0.483270 | ||||||||
\(870\) | −4.00000 | − | 2.64861i | −0.135613 | − | 0.0897964i | ||||
\(871\) | 12.4924 | 0.423290 | ||||||||
\(872\) | −22.9309 | − | 4.26324i | −0.776537 | − | 0.144372i | ||||
\(873\) | 8.68951i | 0.294095i | ||||||||
\(874\) | −4.00000 | − | 2.64861i | −0.135302 | − | 0.0895907i | ||||
\(875\) | −8.00000 | − | 30.9481i | −0.270449 | − | 1.04624i | ||||
\(876\) | 6.24621 | − | 2.64861i | 0.211040 | − | 0.0894884i | ||||
\(877\) | 19.7538 | 0.667038 | 0.333519 | − | 0.942743i | \(-0.391764\pi\) | ||||
0.333519 | + | 0.942743i | \(0.391764\pi\) | |||||||
\(878\) | 24.4924 | − | 36.9890i | 0.826579 | − | 1.24832i | ||||
\(879\) | − | 6.99337i | − | 0.235880i | ||||||
\(880\) | 14.2462 | − | 14.7304i | 0.480240 | − | 0.496562i | ||||
\(881\) | − | 39.1028i | − | 1.31741i | −0.752403 | − | 0.658703i | \(-0.771105\pi\) | ||
0.752403 | − | 0.658703i | \(-0.228895\pi\) | |||||||
\(882\) | 0.780776 | − | 9.86866i | 0.0262901 | − | 0.332295i | ||||
\(883\) | − | 26.9752i | − | 0.907789i | −0.891056 | − | 0.453894i | \(-0.850034\pi\) | ||
0.891056 | − | 0.453894i | \(-0.149966\pi\) | |||||||
\(884\) | −20.4924 | − | 48.3272i | −0.689235 | − | 1.62542i | ||||
\(885\) | − | 6.78456i | − | 0.228061i | ||||||
\(886\) | 42.3002 | + | 28.0092i | 1.42110 | + | 0.940988i | ||||
\(887\) | −22.7386 | −0.763489 | −0.381744 | − | 0.924268i | \(-0.624677\pi\) | ||||
−0.381744 | + | 0.924268i | \(0.624677\pi\) | |||||||
\(888\) | 19.8078 | + | 3.68260i | 0.664705 | + | 0.123580i | ||||
\(889\) | 12.8769 | + | 49.8145i | 0.431877 | + | 1.67072i | ||||
\(890\) | −10.2462 | + | 15.4741i | −0.343454 | + | 0.518692i | ||||
\(891\) | 3.02045i | 0.101189i | ||||||||
\(892\) | 14.7386 | + | 34.7580i | 0.493486 | + | 1.16379i | ||||
\(893\) | 11.5076 | 0.385086 | ||||||||
\(894\) | −7.80776 | + | 11.7915i | −0.261131 | + | 0.394366i | ||||
\(895\) | 3.86174 | 0.129084 | ||||||||
\(896\) | −19.2732 | + | 22.9029i | −0.643872 | + | 0.765133i | ||||
\(897\) | −18.2462 | −0.609223 | ||||||||
\(898\) | 22.0540 | − | 33.3064i | 0.735951 | − | 1.11145i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −1.65767 | − | 3.90928i | −0.0552557 | − | 0.130309i | ||||
\(901\) | − | 18.4487i | − | 0.614617i | ||||||
\(902\) | 18.2462 | − | 27.5559i | 0.607532 | − | 0.917510i | ||||
\(903\) | 5.36932 | + | 20.7713i | 0.178680 | + | 0.691226i | ||||
\(904\) | −34.0540 | − | 6.33122i | −1.13262 | − | 0.210573i | ||||
\(905\) | −10.2462 | −0.340596 | ||||||||
\(906\) | 9.56155 | + | 6.33122i | 0.317661 | + | 0.210341i | ||||
\(907\) | − | 11.9188i | − | 0.395756i | −0.980227 | − | 0.197878i | \(-0.936595\pi\) | ||
0.980227 | − | 0.197878i | \(-0.0634050\pi\) | |||||||
\(908\) | 12.8769 | + | 30.3675i | 0.427335 | + | 1.00778i | ||||
\(909\) | − | 6.99337i | − | 0.231955i | ||||||
\(910\) | −12.4924 | + | 36.2454i | −0.414120 | + | 1.20152i | ||||
\(911\) | − | 6.41273i | − | 0.212463i | −0.994341 | − | 0.106232i | \(-0.966122\pi\) | ||
0.994341 | − | 0.106232i | \(-0.0338785\pi\) | |||||||
\(912\) | −3.12311 | + | 3.22925i | −0.103416 | + | 0.106931i | ||||
\(913\) | − | 18.8664i | − | 0.624385i | ||||||
\(914\) | −12.6847 | + | 19.1567i | −0.419571 | + | 0.633646i | ||||
\(915\) | −16.0000 | −0.528944 | ||||||||
\(916\) | −33.3693 | + | 14.1498i | −1.10255 | + | 0.467521i | ||||
\(917\) | 56.9848 | − | 14.7304i | 1.88181 | − | 0.486441i | ||||
\(918\) | 5.12311 | + | 3.39228i | 0.169088 | + | 0.111962i | ||||
\(919\) | 8.10887i | 0.267487i | 0.991016 | + | 0.133743i | \(0.0426998\pi\) | ||||
−0.991016 | + | 0.133743i | \(0.957300\pi\) | |||||||
\(920\) | −14.2462 | − | 2.64861i | −0.469684 | − | 0.0873222i | ||||
\(921\) | 21.6155 | 0.712256 | ||||||||
\(922\) | −20.2462 | − | 13.4061i | −0.666773 | − | 0.441506i | ||||
\(923\) | 75.2311 | 2.47626 | ||||||||
\(924\) | −12.6847 | + | 9.72350i | −0.417295 | + | 0.319880i | ||||
\(925\) | −15.1231 | −0.497245 | ||||||||
\(926\) | 46.5464 | + | 30.8209i | 1.52961 | + | 1.01284i | ||||
\(927\) | 8.00000 | 0.262754 | ||||||||
\(928\) | −2.43845 | − | 11.0478i | −0.0800460 | − | 0.362662i | ||||
\(929\) | − | 50.7670i | − | 1.66561i | −0.553566 | − | 0.832805i | \(-0.686733\pi\) | ||
0.553566 | − | 0.832805i | \(-0.313267\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.87689 | − | 3.80989i | 0.225381 | − | 0.124864i | ||||
\(932\) | 8.19224 | + | 19.3197i | 0.268346 | + | 0.632838i | ||||
\(933\) | −8.00000 | −0.261908 | ||||||||
\(934\) | −13.8617 | + | 20.9343i | −0.453570 | + | 0.684992i | ||||
\(935\) | − | 22.2586i | − | 0.727935i | ||||||
\(936\) | −3.12311 | + | 16.7984i | −0.102082 | + | 0.549072i | ||||
\(937\) | 56.5991i | 1.84901i | 0.381169 | + | 0.924505i | \(0.375522\pi\) | ||||
−0.381169 | + | 0.924505i | \(0.624478\pi\) | |||||||
\(938\) | −7.31534 | − | 2.52132i | −0.238854 | − | 0.0823242i | ||||
\(939\) | − | 25.6509i | − | 0.837086i | ||||||
\(940\) | 32.0000 | − | 13.5691i | 1.04372 | − | 0.442576i | ||||
\(941\) | − | 13.3603i | − | 0.435534i | −0.976001 | − | 0.217767i | \(-0.930123\pi\) | ||
0.976001 | − | 0.217767i | \(-0.0698773\pi\) | |||||||
\(942\) | −4.87689 | − | 3.22925i | −0.158898 | − | 0.105215i | ||||
\(943\) | −23.3693 | −0.761010 | ||||||||
\(944\) | 11.1231 | − | 11.5012i | 0.362026 | − | 0.374331i | ||||
\(945\) | −1.12311 | − | 4.34475i | −0.0365346 | − | 0.141335i | ||||
\(946\) | 19.1231 | − | 28.8802i | 0.621746 | − | 0.938975i | ||||
\(947\) | 42.2405i | 1.37263i | 0.727304 | + | 0.686316i | \(0.240773\pi\) | ||||
−0.727304 | + | 0.686316i | \(0.759227\pi\) | |||||||
\(948\) | 8.68466 | − | 3.68260i | 0.282065 | − | 0.119605i | ||||
\(949\) | 20.4924 | 0.665212 | ||||||||
\(950\) | 1.86174 | − | 2.81164i | 0.0604028 | − | 0.0912218i | ||||
\(951\) | 18.4924 | 0.599658 | ||||||||
\(952\) | 2.24621 | + | 32.4355i | 0.0728001 | + | 1.05124i | ||||
\(953\) | 61.2311 | 1.98347 | 0.991734 | − | 0.128309i | \(-0.0409549\pi\) | ||||
0.991734 | + | 0.128309i | \(0.0409549\pi\) | |||||||
\(954\) | −3.31534 | + | 5.00691i | −0.107338 | + | 0.162105i | ||||
\(955\) | −15.3693 | −0.497339 | ||||||||
\(956\) | 4.19224 | − | 1.77766i | 0.135587 | − | 0.0574935i | ||||
\(957\) | − | 6.04090i | − | 0.195274i | ||||||
\(958\) | 16.0000 | − | 24.1636i | 0.516937 | − | 0.780690i | ||||
\(959\) | 41.6155 | − | 10.7575i | 1.34384 | − | 0.347377i | ||||
\(960\) | −4.87689 | + | 12.6624i | −0.157401 | + | 0.408678i | ||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 50.7386 | + | 33.5968i | 1.63588 | + | 1.08320i | ||||
\(963\) | − | 5.66906i | − | 0.182683i | ||||||
\(964\) | −3.50758 | + | 1.48734i | −0.112971 | + | 0.0479039i | ||||
\(965\) | 15.8917i | 0.511571i | ||||||||
\(966\) | 10.6847 | + | 3.68260i | 0.343773 | + | 0.118486i | ||||
\(967\) | 40.9620i | 1.31725i | 0.752472 | + | 0.658624i | \(0.228861\pi\) | ||||
−0.752472 | + | 0.658624i | \(0.771139\pi\) | |||||||
\(968\) | −5.21922 | − | 0.970343i | −0.167752 | − | 0.0311880i | ||||
\(969\) | 4.87962i | 0.156756i | ||||||||
\(970\) | −11.5076 | + | 17.3790i | −0.369486 | + | 0.558007i | ||||
\(971\) | 12.0000 | 0.385098 | 0.192549 | − | 0.981287i | \(-0.438325\pi\) | ||||
0.192549 | + | 0.981287i | \(0.438325\pi\) | |||||||
\(972\) | −0.780776 | − | 1.84130i | −0.0250434 | − | 0.0590597i | ||||
\(973\) | −30.7386 | + | 7.94584i | −0.985435 | + | 0.254732i | ||||
\(974\) | 38.0540 | + | 25.1976i | 1.21933 | + | 0.807382i | ||||
\(975\) | − | 12.8255i | − | 0.410743i | ||||||
\(976\) | −27.1231 | − | 26.2316i | −0.868189 | − | 0.839652i | ||||
\(977\) | −60.7386 | −1.94320 | −0.971601 | − | 0.236627i | \(-0.923958\pi\) | ||||
−0.971601 | + | 0.236627i | \(0.923958\pi\) | |||||||
\(978\) | −13.5616 | − | 8.97983i | −0.433651 | − | 0.287143i | ||||
\(979\) | −23.3693 | −0.746887 | ||||||||
\(980\) | 14.6307 | − | 18.7033i | 0.467360 | − | 0.597456i | ||||
\(981\) | 8.24621 | 0.263281 | ||||||||
\(982\) | 13.8078 | + | 9.14286i | 0.440623 | + | 0.291760i | ||||
\(983\) | −54.7386 | −1.74589 | −0.872946 | − | 0.487818i | \(-0.837793\pi\) | ||||
−0.872946 | + | 0.487818i | \(0.837793\pi\) | |||||||
\(984\) | −4.00000 | + | 21.5150i | −0.127515 | + | 0.685872i | ||||
\(985\) | 0.417609i | 0.0133061i | ||||||||
\(986\) | −10.2462 | − | 6.78456i | −0.326306 | − | 0.216065i | ||||
\(987\) | −26.2462 | + | 6.78456i | −0.835426 | + | 0.215955i | ||||
\(988\) | −12.4924 | + | 5.29723i | −0.397437 | + | 0.168527i | ||||
\(989\) | −24.4924 | −0.778814 | ||||||||
\(990\) | −4.00000 | + | 6.04090i | −0.127128 | + | 0.191992i | ||||
\(991\) | − | 10.7575i | − | 0.341723i | −0.985295 | − | 0.170861i | \(-0.945345\pi\) | ||
0.985295 | − | 0.170861i | \(-0.0546550\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.46026i | 0.173276i | ||||||||
\(994\) | −44.0540 | − | 15.1838i | −1.39731 | − | 0.481599i | ||||
\(995\) | − | 8.68951i | − | 0.275476i | ||||||
\(996\) | 4.87689 | + | 11.5012i | 0.154530 | + | 0.364428i | ||||
\(997\) | 38.8940i | 1.23178i | 0.787830 | + | 0.615892i | \(0.211204\pi\) | ||||
−0.787830 | + | 0.615892i | \(0.788796\pi\) | |||||||
\(998\) | 20.6847 | + | 13.6964i | 0.654761 | + | 0.433553i | ||||
\(999\) | −7.12311 | −0.225365 |
(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.b.55.3 | yes | 4 | |
3.2 | odd | 2 | 252.2.b.d.55.2 | 4 | |||
4.3 | odd | 2 | 84.2.b.a.55.4 | yes | 4 | ||
7.2 | even | 3 | 588.2.o.a.31.1 | 8 | |||
7.3 | odd | 6 | 588.2.o.c.19.3 | 8 | |||
7.4 | even | 3 | 588.2.o.a.19.3 | 8 | |||
7.5 | odd | 6 | 588.2.o.c.31.1 | 8 | |||
7.6 | odd | 2 | 84.2.b.a.55.3 | ✓ | 4 | ||
8.3 | odd | 2 | 1344.2.b.f.895.2 | 4 | |||
8.5 | even | 2 | 1344.2.b.e.895.2 | 4 | |||
12.11 | even | 2 | 252.2.b.e.55.1 | 4 | |||
21.20 | even | 2 | 252.2.b.e.55.2 | 4 | |||
24.5 | odd | 2 | 4032.2.b.j.3583.3 | 4 | |||
24.11 | even | 2 | 4032.2.b.n.3583.3 | 4 | |||
28.3 | even | 6 | 588.2.o.a.19.1 | 8 | |||
28.11 | odd | 6 | 588.2.o.c.19.1 | 8 | |||
28.19 | even | 6 | 588.2.o.a.31.3 | 8 | |||
28.23 | odd | 6 | 588.2.o.c.31.3 | 8 | |||
28.27 | even | 2 | inner | 84.2.b.b.55.4 | yes | 4 | |
56.13 | odd | 2 | 1344.2.b.f.895.3 | 4 | |||
56.27 | even | 2 | 1344.2.b.e.895.3 | 4 | |||
84.83 | odd | 2 | 252.2.b.d.55.1 | 4 | |||
168.83 | odd | 2 | 4032.2.b.j.3583.2 | 4 | |||
168.125 | even | 2 | 4032.2.b.n.3583.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.b.a.55.3 | ✓ | 4 | 7.6 | odd | 2 | ||
84.2.b.a.55.4 | yes | 4 | 4.3 | odd | 2 | ||
84.2.b.b.55.3 | yes | 4 | 1.1 | even | 1 | trivial | |
84.2.b.b.55.4 | yes | 4 | 28.27 | even | 2 | inner | |
252.2.b.d.55.1 | 4 | 84.83 | odd | 2 | |||
252.2.b.d.55.2 | 4 | 3.2 | odd | 2 | |||
252.2.b.e.55.1 | 4 | 12.11 | even | 2 | |||
252.2.b.e.55.2 | 4 | 21.20 | even | 2 | |||
588.2.o.a.19.1 | 8 | 28.3 | even | 6 | |||
588.2.o.a.19.3 | 8 | 7.4 | even | 3 | |||
588.2.o.a.31.1 | 8 | 7.2 | even | 3 | |||
588.2.o.a.31.3 | 8 | 28.19 | even | 6 | |||
588.2.o.c.19.1 | 8 | 28.11 | odd | 6 | |||
588.2.o.c.19.3 | 8 | 7.3 | odd | 6 | |||
588.2.o.c.31.1 | 8 | 7.5 | odd | 6 | |||
588.2.o.c.31.3 | 8 | 28.23 | odd | 6 | |||
1344.2.b.e.895.2 | 4 | 8.5 | even | 2 | |||
1344.2.b.e.895.3 | 4 | 56.27 | even | 2 | |||
1344.2.b.f.895.2 | 4 | 8.3 | odd | 2 | |||
1344.2.b.f.895.3 | 4 | 56.13 | odd | 2 | |||
4032.2.b.j.3583.2 | 4 | 168.83 | odd | 2 | |||
4032.2.b.j.3583.3 | 4 | 24.5 | odd | 2 | |||
4032.2.b.n.3583.2 | 4 | 168.125 | even | 2 | |||
4032.2.b.n.3583.3 | 4 | 24.11 | even | 2 |