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 | 55.4 | ||
Root | \(-0.780776 - 1.17915i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.2.b.a.55.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | \(-0.849514\pi\) | ||
0.890313 | − | 0.455350i | \(-0.150486\pi\) | |||||||
\(12\) | 0.780776 | − | 1.84130i | 0.225391 | − | 0.531538i | ||||
\(13\) | − | 6.04090i | − | 1.67544i | −0.546098 | − | 0.837722i | \(-0.683887\pi\) | ||
0.546098 | − | 0.837722i | \(-0.316113\pi\) | |||||||
\(14\) | 2.78078 | + | 2.50345i | 0.743194 | + | 0.669076i | ||||
\(15\) | − | 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 | \(-0.541122\pi\) | ||||
−0.128829 | + | 0.991667i | \(0.541122\pi\) | |||||||
\(20\) | −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 | \(0.101972\pi\) | ||||
−0.949124 | + | 0.314903i | \(0.898028\pi\) | |||||||
\(24\) | 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 | ||||||||
\(28\) | −0.780776 | + | 5.23358i | −0.147553 | + | 0.989054i | ||||
\(29\) | −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 | \(-0.206492\pi\) | |||||||
\(42\) | −2.78078 | − | 2.50345i | −0.429083 | − | 0.386291i | ||||
\(43\) | 8.10887i | 1.23659i | 0.785946 | + | 0.618296i | \(0.212177\pi\) | ||||
−0.785946 | + | 0.618296i | \(0.787823\pi\) | |||||||
\(44\) | 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 | \(-0.768641\pi\) | ||||
−0.747282 | + | 0.664507i | \(0.768641\pi\) | |||||||
\(48\) | 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 | ||||||||
\(56\) | −6.78078 | + | 3.16561i | −0.906119 | + | 0.423022i | ||||
\(57\) | 1.12311 | 0.148759 | ||||||||
\(58\) | −1.56155 | − | 2.35829i | −0.205042 | − | 0.309659i | ||||
\(59\) | 4.00000 | 0.520756 | 0.260378 | − | 0.965507i | \(-0.416153\pi\) | ||||
0.260378 | + | 0.965507i | \(0.416153\pi\) | |||||||
\(60\) | 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 | \(-0.959683\pi\) | ||
0.991989 | − | 0.126322i | \(-0.0403172\pi\) | |||||||
\(68\) | −8.00000 | − | 3.39228i | −0.970143 | − | 0.411375i | ||||
\(69\) | − | 3.02045i | − | 0.363619i | ||||||
\(70\) | −4.24621 | + | 4.71659i | −0.507519 | + | 0.563740i | ||||
\(71\) | − | 12.4536i | − | 1.47797i | −0.673720 | − | 0.738987i | \(-0.735305\pi\) | ||
0.673720 | − | 0.738987i | \(-0.264695\pi\) | |||||||
\(72\) | −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 | \(-0.914519\pi\) | ||
0.964158 | − | 0.265329i | \(-0.0854805\pi\) | |||||||
\(80\) | 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 | \(-0.388623\pi\) | ||||
0.342805 | + | 0.939406i | \(0.388623\pi\) | |||||||
\(84\) | 0.780776 | − | 5.23358i | 0.0851897 | − | 0.571031i | ||||
\(85\) | −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 | \(0.854573\pi\) | |||||||
\(98\) | 8.78078 | + | 4.57143i | 0.886992 | + | 0.461784i | ||||
\(99\) | − | 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 | \(-0.628955\pi\) | ||||
−0.394132 | + | 0.919054i | \(0.628955\pi\) | |||||||
\(104\) | 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 | \(0.0883549\pi\) | ||||
−0.961723 | + | 0.274024i | \(0.911645\pi\) | |||||||
\(108\) | 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 | ||||||||
\(112\) | −9.02699 | − | 5.52390i | −0.852970 | − | 0.521960i | ||||
\(113\) | 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 | ||||||||
\(126\) | 2.78078 | + | 2.50345i | 0.247731 | + | 0.223025i | ||||
\(127\) | 19.4470i | 1.72564i | 0.505510 | + | 0.862821i | \(0.331304\pi\) | ||||
−0.505510 | + | 0.862821i | \(0.668696\pi\) | |||||||
\(128\) | 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 | \(-0.0757323\pi\) | ||||
0.971830 | + | 0.235682i | \(0.0757323\pi\) | |||||||
\(132\) | −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 | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | −8.87689 | − | 1.32431i | −0.750235 | − | 0.111924i | ||||
\(141\) | 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 | \(-0.892970\pi\) | ||
0.944000 | − | 0.329945i | \(-0.107030\pi\) | |||||||
\(152\) | 3.12311 | − | 0.580639i | 0.253317 | − | 0.0470960i | ||||
\(153\) | 4.34475i | 0.351253i | ||||||||
\(154\) | 7.56155 | − | 8.39919i | 0.609327 | − | 0.676826i | ||||
\(155\) | 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 | \(0.148726\pi\) | ||||
−0.892817 | + | 0.450420i | \(0.851274\pi\) | |||||||
\(164\) | 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 | \(-0.527699\pi\) | ||||
−0.0869085 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(168\) | 6.78078 | − | 3.16561i | 0.523148 | − | 0.244232i | ||||
\(169\) | −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 | \(0.0271169\pi\) | ||||
−0.996374 | + | 0.0850873i | \(0.972883\pi\) | |||||||
\(180\) | −3.12311 | − | 1.32431i | −0.232783 | − | 0.0987080i | ||||
\(181\) | 6.04090i | 0.449016i | 0.974472 | + | 0.224508i | \(0.0720775\pi\) | ||||
−0.974472 | + | 0.224508i | \(0.927922\pi\) | |||||||
\(182\) | 15.1231 | − | 16.7984i | 1.12100 | − | 1.24518i | ||||
\(183\) | − | 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 | \(-0.893683\pi\) | ||
0.944737 | − | 0.327828i | \(-0.106317\pi\) | |||||||
\(192\) | −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 | ||||||||
\(196\) | 1.46543 | + | 13.9231i | 0.104674 | + | 0.994507i | ||||
\(197\) | 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 | \(-0.441878\pi\) | ||||
0.181584 | + | 0.983375i | \(0.441878\pi\) | |||||||
\(200\) | −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 | ||||||||
\(210\) | 4.24621 | − | 4.71659i | 0.293016 | − | 0.325476i | ||||
\(211\) | − | 3.97292i | − | 0.273507i | −0.990605 | − | 0.136754i | \(-0.956333\pi\) | ||
0.990605 | − | 0.136754i | \(-0.0436668\pi\) | |||||||
\(212\) | 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 | \(-0.282216\pi\) | ||||
0.632045 | + | 0.774932i | \(0.282216\pi\) | |||||||
\(224\) | −0.534565 | − | 14.9571i | −0.0357171 | − | 0.999362i | ||||
\(225\) | 2.12311 | 0.141540 | ||||||||
\(226\) | 9.56155 | + | 14.4401i | 0.636025 | + | 0.960540i | ||||
\(227\) | 16.4924 | 1.09464 | 0.547320 | − | 0.836923i | \(-0.315648\pi\) | ||||
0.547320 | + | 0.836923i | \(0.315648\pi\) | |||||||
\(228\) | −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 | ||||||||
\(238\) | −10.8769 | + | 12.0818i | −0.705044 | + | 0.783146i | ||||
\(239\) | − | 2.27678i | − | 0.147273i | −0.997285 | − | 0.0736363i | \(-0.976540\pi\) | ||
0.997285 | − | 0.0736363i | \(-0.0234604\pi\) | |||||||
\(240\) | −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 | \(-0.747747\pi\) | ||||
−0.702084 | + | 0.712094i | \(0.747747\pi\) | |||||||
\(252\) | −0.780776 | + | 5.23358i | −0.0491843 | + | 0.329685i | ||||
\(253\) | 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 | \(0.0485251\pi\) | ||||
−0.988403 | + | 0.151856i | \(0.951475\pi\) | |||||||
\(264\) | −1.56155 | − | 8.39919i | −0.0961069 | − | 0.516934i | ||||
\(265\) | − | 7.20217i | − | 0.442426i | ||||||
\(266\) | −3.12311 | − | 2.81164i | −0.191490 | − | 0.172393i | ||||
\(267\) | − | 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 | \(-0.456431\pi\) | ||||
0.136448 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(272\) | 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 | ||||||||
\(280\) | −5.36932 | − | 11.5012i | −0.320878 | − | 0.687325i | ||||
\(281\) | −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 | \(-0.330041\pi\) | ||||
0.508931 | + | 0.860807i | \(0.330041\pi\) | |||||||
\(284\) | 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 | \(-0.0654848\pi\) | |||||||
\(294\) | −8.78078 | − | 4.57143i | −0.512105 | − | 0.266611i | ||||
\(295\) | 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 | \(-0.711584\pi\) | ||||
−0.616832 | + | 0.787095i | \(0.711584\pi\) | |||||||
\(308\) | 15.8078 | + | 2.35829i | 0.900731 | + | 0.134376i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | −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 | ||||||
\(322\) | −7.56155 | + | 8.39919i | −0.421389 | + | 0.468069i | ||||
\(323\) | − | 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 | \(-0.952053\pi\) | ||
0.988677 | − | 0.150061i | \(-0.0479472\pi\) | |||||||
\(332\) | −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 | ||||||||
\(336\) | 9.02699 | + | 5.52390i | 0.492463 | + | 0.301354i | ||||
\(337\) | −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 | \(0.381697\pi\) | ||||
−0.363162 | + | 0.931726i | \(0.618303\pi\) | |||||||
\(348\) | −1.56155 | + | 3.68260i | −0.0837080 | + | 0.197408i | ||||
\(349\) | − | 4.13595i | − | 0.221392i | −0.993854 | − | 0.110696i | \(-0.964692\pi\) | ||
0.993854 | − | 0.110696i | \(-0.0353080\pi\) | |||||||
\(350\) | 5.90388 | + | 5.31510i | 0.315576 | + | 0.284104i | ||||
\(351\) | 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 | \(0.00937144\pi\) | ||||
−0.999567 | + | 0.0294370i | \(0.990629\pi\) | |||||||
\(360\) | −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 | ||||||||
\(364\) | 31.6155 | + | 4.71659i | 1.65710 | + | 0.247216i | ||||
\(365\) | −5.75379 | −0.301167 | ||||||||
\(366\) | 11.1231 | − | 7.36520i | 0.581414 | − | 0.384985i | ||||
\(367\) | −8.63068 | −0.450518 | −0.225259 | − | 0.974299i | \(-0.572323\pi\) | ||||
−0.225259 | + | 0.974299i | \(0.572323\pi\) | |||||||
\(368\) | 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 | ||||||||
\(378\) | −2.78078 | − | 2.50345i | −0.143028 | − | 0.128764i | ||||
\(379\) | 18.7033i | 0.960725i | 0.877070 | + | 0.480363i | \(0.159495\pi\) | ||||
−0.877070 | + | 0.480363i | \(0.840505\pi\) | |||||||
\(380\) | 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 | \(-0.733946\pi\) | ||||
−0.670559 | + | 0.741856i | \(0.733946\pi\) | |||||||
\(384\) | −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 | ||||||||
\(392\) | −15.2732 | + | 12.5988i | −0.771413 | + | 0.636335i | ||||
\(393\) | −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 | ||||||||
\(406\) | −5.56155 | − | 5.00691i | −0.276015 | − | 0.248489i | ||||
\(407\) | 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 | \(-0.368018\pi\) | ||||
0.402854 | + | 0.915264i | \(0.368018\pi\) | |||||||
\(420\) | 8.87689 | + | 1.32431i | 0.433148 | + | 0.0646196i | ||||
\(421\) | 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 | \(0.118495\pi\) | ||||
−0.931507 | + | 0.363725i | \(0.881505\pi\) | |||||||
\(432\) | 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 | \(-0.769268\pi\) | ||||
−0.748588 | + | 0.663036i | \(0.769268\pi\) | |||||||
\(440\) | −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 | \(-0.675267\pi\) | ||
0.523213 | − | 0.852202i | \(-0.324733\pi\) | |||||||
\(444\) | −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 | ||||||||
\(448\) | 17.2192 | − | 12.3085i | 0.813532 | − | 0.581520i | ||||
\(449\) | 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 | \(-0.130937\pi\) | |||||||
\(462\) | −7.56155 | + | 8.39919i | −0.351795 | + | 0.390766i | ||||
\(463\) | − | 39.4746i | − | 1.83454i | −0.398264 | − | 0.917271i | \(-0.630387\pi\) | ||
0.398264 | − | 0.917271i | \(-0.369613\pi\) | |||||||
\(464\) | 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 | \(-0.365259\pi\) | ||||
0.410774 | + | 0.911737i | \(0.365259\pi\) | |||||||
\(468\) | 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 | ||||||||
\(476\) | −22.7386 | − | 3.39228i | −1.04222 | − | 0.155485i | ||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | 2.68466 | − | 1.77766i | 0.122793 | − | 0.0813081i | ||||
\(479\) | −20.4924 | −0.936323 | −0.468161 | − | 0.883643i | \(-0.655083\pi\) | ||||
−0.468161 | + | 0.883643i | \(0.655083\pi\) | |||||||
\(480\) | −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 | \(-0.738960\pi\) | ||
0.682161 | − | 0.731202i | \(-0.261040\pi\) | |||||||
\(488\) | −4.87689 | − | 26.2316i | −0.220767 | − | 1.18745i | ||||
\(489\) | − | 11.5012i | − | 0.520100i | ||||||
\(490\) | −7.75379 | + | 14.8934i | −0.350280 | + | 0.672817i | ||||
\(491\) | − | 11.7100i | − | 0.528463i | −0.964459 | − | 0.264231i | \(-0.914882\pi\) | ||
0.964459 | − | 0.264231i | \(-0.0851183\pi\) | |||||||
\(492\) | −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 | \(-0.871560\pi\) | ||
0.919690 | − | 0.392645i | \(-0.128440\pi\) | |||||||
\(500\) | −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 | \(-0.330779\pi\) | ||||
0.506933 | + | 0.861986i | \(0.330779\pi\) | |||||||
\(504\) | −6.78078 | + | 3.16561i | −0.302040 | + | 0.141007i | ||||
\(505\) | 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 | ||||||||
\(518\) | −19.8078 | − | 17.8324i | −0.870303 | − | 0.783509i | ||||
\(519\) | 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 | \(-0.503427\pi\) | ||||
−0.0107661 | + | 0.999942i | \(0.503427\pi\) | |||||||
\(524\) | −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 | ||||||||
\(532\) | 0.876894 | − | 5.87787i | 0.0380182 | − | 0.254838i | ||||
\(533\) | −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 | ||||||||
\(546\) | −15.1231 | + | 16.7984i | −0.647209 | + | 0.718904i | ||||
\(547\) | − | 33.0161i | − | 1.41167i | −0.708378 | − | 0.705834i | \(-0.750573\pi\) | ||
0.708378 | − | 0.705834i | \(-0.249427\pi\) | |||||||
\(548\) | 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 | ||||||||
\(560\) | 9.36932 | − | 15.3110i | 0.395926 | − | 0.647010i | ||||
\(561\) | −13.1231 | −0.554058 | ||||||||
\(562\) | −0.192236 | − | 0.290319i | −0.00810898 | − | 0.0122464i | ||||
\(563\) | −14.2462 | −0.600406 | −0.300203 | − | 0.953875i | \(-0.597054\pi\) | ||||
−0.300203 | + | 0.953875i | \(0.597054\pi\) | |||||||
\(564\) | −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 | \(0.327738\pi\) | ||||
−0.515146 | + | 0.857102i | \(0.672262\pi\) | |||||||
\(572\) | 14.2462 | − | 33.5968i | 0.595664 | − | 1.40475i | ||||
\(573\) | 9.06134i | 0.378543i | ||||||||
\(574\) | 19.3693 | − | 21.5150i | 0.808460 | − | 0.898017i | ||||
\(575\) | 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 | \(-0.789554\pi\) | ||||
−0.789295 | + | 0.614014i | \(0.789554\pi\) | |||||||
\(588\) | −1.46543 | − | 13.9231i | −0.0604335 | − | 0.574179i | ||||
\(589\) | 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 | \(-0.871428\pi\) | ||
0.919528 | − | 0.393026i | \(-0.128572\pi\) | |||||||
\(600\) | 5.90388 | − | 1.09763i | 0.241025 | − | 0.0448107i | ||||
\(601\) | 5.29723i | 0.216078i | 0.994147 | + | 0.108039i | \(0.0344572\pi\) | ||||
−0.994147 | + | 0.108039i | \(0.965543\pi\) | |||||||
\(602\) | −20.3002 | + | 22.5490i | −0.827374 | + | 0.919027i | ||||
\(603\) | − | 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 | \(-0.738979\pi\) | ||||
−0.682206 | + | 0.731160i | \(0.738979\pi\) | |||||||
\(608\) | −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 | ||||||||
\(616\) | 9.56155 | + | 20.4810i | 0.385246 | + | 0.825202i | ||||
\(617\) | 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 | \(-0.368338\pi\) | ||||
0.401934 | + | 0.915669i | \(0.368338\pi\) | |||||||
\(620\) | 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 | ||||||
\(630\) | −4.24621 | + | 4.71659i | −0.169173 | + | 0.187913i | ||||
\(631\) | 17.9597i | 0.714963i | 0.933920 | + | 0.357481i | \(0.116364\pi\) | ||||
−0.933920 | + | 0.357481i | \(0.883636\pi\) | |||||||
\(632\) | 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 | \(-0.301502\pi\) | ||||
0.583961 | + | 0.811782i | \(0.301502\pi\) | |||||||
\(644\) | −15.8078 | − | 2.35829i | −0.622913 | − | 0.0929298i | ||||
\(645\) | 13.7538 | 0.541555 | ||||||||
\(646\) | 5.75379 | − | 3.80989i | 0.226380 | − | 0.149898i | ||||
\(647\) | 32.9848 | 1.29677 | 0.648384 | − | 0.761313i | \(-0.275445\pi\) | ||||
0.648384 | + | 0.761313i | \(0.275445\pi\) | |||||||
\(648\) | −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 | ||||||||
\(658\) | −28.4924 | − | 25.6509i | −1.11075 | − | 0.999977i | ||||
\(659\) | 38.1045i | 1.48434i | 0.670210 | + | 0.742171i | \(0.266204\pi\) | ||||
−0.670210 | + | 0.742171i | \(0.733796\pi\) | |||||||
\(660\) | 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 | ||||||||
\(672\) | 0.534565 | + | 14.9571i | 0.0206213 | + | 0.576982i | ||||
\(673\) | 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 | \(-0.812133\pi\) | ||
0.830828 | − | 0.556529i | \(-0.187867\pi\) | |||||||
\(684\) | 0.876894 | − | 2.06798i | 0.0335289 | − | 0.0790710i | ||||
\(685\) | − | 27.5559i | − | 1.05286i | ||||||
\(686\) | 25.5194 | + | 5.89574i | 0.974336 | + | 0.225100i | ||||
\(687\) | 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 | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(692\) | 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 | ||||||||
\(700\) | −1.65767 | + | 11.1114i | −0.0626541 | + | 0.419973i | ||||
\(701\) | −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 | ||||||||
\(714\) | 10.8769 | − | 12.0818i | 0.407058 | − | 0.452150i | ||||
\(715\) | − | 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 | \(-0.526696\pi\) | ||||
−0.0837695 | + | 0.996485i | \(0.526696\pi\) | |||||||
\(720\) | 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 | \(-0.709502\pi\) | ||||
−0.611670 | + | 0.791113i | \(0.709502\pi\) | |||||||
\(728\) | 19.1231 | + | 40.9620i | 0.708749 | + | 1.51815i | ||||
\(729\) | 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 | \(-0.965520\pi\) | ||
0.994139 | − | 0.108110i | \(-0.0344800\pi\) | |||||||
\(740\) | 22.2462 | + | 9.43318i | 0.817787 | + | 0.346771i | ||||
\(741\) | − | 6.78456i | − | 0.249237i | ||||||
\(742\) | −11.8078 | − | 10.6302i | −0.433477 | − | 0.390247i | ||||
\(743\) | 13.6149i | 0.499482i | 0.968313 | + | 0.249741i | \(0.0803455\pi\) | ||||
−0.968313 | + | 0.249741i | \(0.919654\pi\) | |||||||
\(744\) | 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 | \(-0.810154\pi\) | ||
0.827353 | − | 0.561682i | \(-0.189846\pi\) | |||||||
\(752\) | 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 | ||||||||
\(756\) | 0.780776 | − | 5.23358i | 0.0283966 | − | 0.190344i | ||||
\(757\) | 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 | \(-0.296586\pi\) | |||||||
\(770\) | 14.2462 | + | 12.8255i | 0.513398 | + | 0.462197i | ||||
\(771\) | 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 | ||||||||
\(784\) | −26.7808 | − | 8.17252i | −0.956456 | − | 0.291876i | ||||
\(785\) | 7.01515 | 0.250382 | ||||||||
\(786\) | −17.3693 | − | 26.2316i | −0.619543 | − | 0.935649i | ||||
\(787\) | 20.9848 | 0.748029 | 0.374014 | − | 0.927423i | \(-0.377981\pi\) | ||||
0.374014 | + | 0.927423i | \(0.377981\pi\) | |||||||
\(788\) | −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 | \(0.793372\pi\) | |||||||
\(798\) | 3.12311 | + | 2.81164i | 0.110557 | + | 0.0995311i | ||||
\(799\) | − | 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 | \(-0.693243\pi\) | ||||
−0.570482 | + | 0.821310i | \(0.693243\pi\) | |||||||
\(812\) | 1.56155 | − | 10.4672i | 0.0547998 | − | 0.367325i | ||||
\(813\) | −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 | \(0.287855\pi\) | ||||
−0.618217 | + | 0.786007i | \(0.712145\pi\) | |||||||
\(824\) | 22.2462 | − | 4.13595i | 0.774983 | − | 0.144083i | ||||
\(825\) | 6.41273i | 0.223263i | ||||||||
\(826\) | 11.1231 | + | 10.0138i | 0.387022 | + | 0.348425i | ||||
\(827\) | − | 30.9939i | − | 1.07776i | −0.842381 | − | 0.538882i | \(-0.818847\pi\) | ||
0.842381 | − | 0.538882i | \(-0.181153\pi\) | |||||||
\(828\) | −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 | \(-0.462890\pi\) | ||||
0.116322 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(840\) | 5.36932 | + | 11.5012i | 0.185259 | + | 0.396827i | ||||
\(841\) | −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 | \(-0.221227\pi\) | |||||||
\(854\) | −23.6155 | + | 26.2316i | −0.808107 | + | 0.897625i | ||||
\(855\) | − | 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 | \(-0.317078\pi\) | ||||
0.543554 | + | 0.839374i | \(0.317078\pi\) | |||||||
\(860\) | 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 | \(0.121505\pi\) | ||||
−0.928025 | + | 0.372518i | \(0.878495\pi\) | |||||||
\(864\) | −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 | \(-0.228895\pi\) | |||||||
\(882\) | 8.78078 | + | 4.57143i | 0.295664 | + | 0.153928i | ||||
\(883\) | 26.9752i | 0.907789i | 0.891056 | + | 0.453894i | \(0.149966\pi\) | ||||
−0.891056 | + | 0.453894i | \(0.850034\pi\) | |||||||
\(884\) | −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 | \(-0.375323\pi\) | ||||
0.381744 | + | 0.924268i | \(0.375323\pi\) | |||||||
\(888\) | −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 | ||||||||
\(896\) | 27.9579 | + | 10.6938i | 0.934006 | + | 0.357256i | ||||
\(897\) | −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 | \(0.0634050\pi\) | ||||
−0.980227 | + | 0.197878i | \(0.936595\pi\) | |||||||
\(908\) | −12.8769 | + | 30.3675i | −0.427335 | + | 1.00778i | ||||
\(909\) | − | 6.99337i | − | 0.231955i | ||||||
\(910\) | 28.4924 | + | 25.6509i | 0.944515 | + | 0.850320i | ||||
\(911\) | 6.41273i | 0.212463i | 0.994341 | + | 0.106232i | \(0.0338785\pi\) | ||||
−0.994341 | + | 0.106232i | \(0.966122\pi\) | |||||||
\(912\) | −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 | \(-0.957300\pi\) | ||
0.991016 | − | 0.133743i | \(-0.0426998\pi\) | |||||||
\(920\) | 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 | ||||||||
\(924\) | −15.8078 | − | 2.35829i | −0.520037 | − | 0.0775822i | ||||
\(925\) | −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 | \(0.624478\pi\) | |||||||
\(938\) | 5.17708 | − | 5.75058i | 0.169038 | − | 0.187763i | ||||
\(939\) | 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 | \(-0.759227\pi\) | ||
0.727304 | − | 0.686316i | \(-0.240773\pi\) | |||||||
\(948\) | −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 | ||||||||
\(952\) | −13.7538 | − | 29.4608i | −0.445763 | − | 0.954830i | ||||
\(953\) | 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 | ||||||||
\(966\) | 7.56155 | − | 8.39919i | 0.243289 | − | 0.270240i | ||||
\(967\) | − | 40.9620i | − | 1.31725i | −0.752472 | − | 0.658624i | \(-0.771139\pi\) | ||
0.752472 | − | 0.658624i | \(-0.228861\pi\) | |||||||
\(968\) | −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 | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 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 | ||||||||
\(980\) | −23.6155 | + | 2.48558i | −0.754370 | + | 0.0793991i | ||||
\(981\) | 8.24621 | 0.263281 | ||||||||
\(982\) | 13.8078 | − | 9.14286i | 0.440623 | − | 0.291760i | ||||
\(983\) | 54.7386 | 1.74589 | 0.872946 | − | 0.487818i | \(-0.162207\pi\) | ||||
0.872946 | + | 0.487818i | \(0.162207\pi\) | |||||||
\(984\) | −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 | \(0.0546550\pi\) | ||||
−0.985295 | + | 0.170861i | \(0.945345\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.46026i | 0.173276i | ||||||||
\(994\) | 31.1771 | − | 34.6307i | 0.988877 | − | 1.09842i | ||||
\(995\) | 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.a.55.4 | yes | 4 | |
3.2 | odd | 2 | 252.2.b.e.55.1 | 4 | |||
4.3 | odd | 2 | 84.2.b.b.55.3 | yes | 4 | ||
7.2 | even | 3 | 588.2.o.c.31.3 | 8 | |||
7.3 | odd | 6 | 588.2.o.a.19.1 | 8 | |||
7.4 | even | 3 | 588.2.o.c.19.1 | 8 | |||
7.5 | odd | 6 | 588.2.o.a.31.3 | 8 | |||
7.6 | odd | 2 | 84.2.b.b.55.4 | yes | 4 | ||
8.3 | odd | 2 | 1344.2.b.e.895.2 | 4 | |||
8.5 | even | 2 | 1344.2.b.f.895.2 | 4 | |||
12.11 | even | 2 | 252.2.b.d.55.2 | 4 | |||
21.20 | even | 2 | 252.2.b.d.55.1 | 4 | |||
24.5 | odd | 2 | 4032.2.b.n.3583.3 | 4 | |||
24.11 | even | 2 | 4032.2.b.j.3583.3 | 4 | |||
28.3 | even | 6 | 588.2.o.c.19.3 | 8 | |||
28.11 | odd | 6 | 588.2.o.a.19.3 | 8 | |||
28.19 | even | 6 | 588.2.o.c.31.1 | 8 | |||
28.23 | odd | 6 | 588.2.o.a.31.1 | 8 | |||
28.27 | even | 2 | inner | 84.2.b.a.55.3 | ✓ | 4 | |
56.13 | odd | 2 | 1344.2.b.e.895.3 | 4 | |||
56.27 | even | 2 | 1344.2.b.f.895.3 | 4 | |||
84.83 | odd | 2 | 252.2.b.e.55.2 | 4 | |||
168.83 | odd | 2 | 4032.2.b.n.3583.2 | 4 | |||
168.125 | even | 2 | 4032.2.b.j.3583.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.2.b.a.55.3 | ✓ | 4 | 28.27 | even | 2 | inner | |
84.2.b.a.55.4 | yes | 4 | 1.1 | even | 1 | trivial | |
84.2.b.b.55.3 | yes | 4 | 4.3 | odd | 2 | ||
84.2.b.b.55.4 | yes | 4 | 7.6 | odd | 2 | ||
252.2.b.d.55.1 | 4 | 21.20 | even | 2 | |||
252.2.b.d.55.2 | 4 | 12.11 | even | 2 | |||
252.2.b.e.55.1 | 4 | 3.2 | odd | 2 | |||
252.2.b.e.55.2 | 4 | 84.83 | odd | 2 | |||
588.2.o.a.19.1 | 8 | 7.3 | odd | 6 | |||
588.2.o.a.19.3 | 8 | 28.11 | odd | 6 | |||
588.2.o.a.31.1 | 8 | 28.23 | odd | 6 | |||
588.2.o.a.31.3 | 8 | 7.5 | odd | 6 | |||
588.2.o.c.19.1 | 8 | 7.4 | even | 3 | |||
588.2.o.c.19.3 | 8 | 28.3 | even | 6 | |||
588.2.o.c.31.1 | 8 | 28.19 | even | 6 | |||
588.2.o.c.31.3 | 8 | 7.2 | even | 3 | |||
1344.2.b.e.895.2 | 4 | 8.3 | odd | 2 | |||
1344.2.b.e.895.3 | 4 | 56.13 | odd | 2 | |||
1344.2.b.f.895.2 | 4 | 8.5 | even | 2 | |||
1344.2.b.f.895.3 | 4 | 56.27 | even | 2 | |||
4032.2.b.j.3583.2 | 4 | 168.125 | even | 2 | |||
4032.2.b.j.3583.3 | 4 | 24.11 | even | 2 | |||
4032.2.b.n.3583.2 | 4 | 168.83 | odd | 2 | |||
4032.2.b.n.3583.3 | 4 | 24.5 | odd | 2 |