Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(25,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.q (of order \(9\), degree \(6\), 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: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 97.2 | ||
Character | \(\chi\) | \(=\) | 216.97 |
Dual form | 216.2.q.a.49.2 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.278117 | + | 1.70958i | −0.160571 | + | 0.987024i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42978 | + | 0.884366i | 1.08663 | + | 0.395500i | 0.822371 | − | 0.568952i | \(-0.192651\pi\) |
0.264258 | + | 0.964452i | \(0.414873\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.245784 | + | 1.39391i | −0.0928975 | + | 0.526848i | 0.902474 | + | 0.430745i | \(0.141749\pi\) |
−0.995371 | + | 0.0961034i | \(0.969362\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.84530 | − | 0.950925i | −0.948434 | − | 0.316975i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.99234 | + | 0.725153i | −0.600714 | + | 0.218642i | −0.624435 | − | 0.781077i | \(-0.714671\pi\) |
0.0237215 | + | 0.999719i | \(0.492449\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.59088 | − | 1.33491i | 0.441231 | − | 0.370237i | −0.394939 | − | 0.918707i | \(-0.629234\pi\) |
0.836170 | + | 0.548471i | \(0.184790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.18765 | + | 3.90793i | −0.564850 | + | 1.00902i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.93552 | + | 3.35242i | 0.469433 | + | 0.813082i | 0.999389 | − | 0.0349427i | \(-0.0111249\pi\) |
−0.529956 | + | 0.848025i | \(0.677792\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.22285 | − | 2.11804i | 0.280542 | − | 0.485913i | −0.690976 | − | 0.722877i | \(-0.742819\pi\) |
0.971518 | + | 0.236964i | \(0.0761525\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.31464 | − | 0.807856i | −0.505095 | − | 0.176289i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.45350 | + | 8.24321i | 0.303076 | + | 1.71883i | 0.632426 | + | 0.774621i | \(0.282059\pi\) |
−0.329350 | + | 0.944208i | \(0.606830\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.29148 | + | 1.08368i | 0.258296 | + | 0.216736i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41701 | − | 4.59979i | 0.465153 | − | 0.885230i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.797932 | − | 0.669544i | −0.148172 | − | 0.124331i | 0.565688 | − | 0.824619i | \(-0.308611\pi\) |
−0.713861 | + | 0.700288i | \(0.753055\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.54023 | − | 8.73507i | −0.276633 | − | 1.56886i | −0.733726 | − | 0.679446i | \(-0.762220\pi\) |
0.457093 | − | 0.889419i | \(-0.348891\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.685600 | − | 3.60774i | −0.119348 | − | 0.628026i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.82993 | + | 3.16952i | −0.309314 | + | 0.535747i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.97082 | − | 8.60972i | −0.817198 | − | 1.41543i | −0.907739 | − | 0.419536i | \(-0.862193\pi\) |
0.0905404 | − | 0.995893i | \(-0.471141\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.83967 | + | 3.09099i | 0.294584 | + | 0.494955i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.25295 | − | 7.76415i | 1.44507 | − | 1.21256i | 0.508985 | − | 0.860775i | \(-0.330021\pi\) |
0.936083 | − | 0.351780i | \(-0.114424\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.70613 | − | 2.07686i | 0.870176 | − | 0.316718i | 0.131938 | − | 0.991258i | \(-0.457880\pi\) |
0.738239 | + | 0.674540i | \(0.235658\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.07248 | − | 4.82682i | −0.905231 | − | 0.719540i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.665477 | − | 3.77411i | 0.0970698 | − | 0.550510i | −0.897024 | − | 0.441983i | \(-0.854275\pi\) |
0.994093 | − | 0.108528i | \(-0.0346136\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.69528 | + | 1.70894i | 0.670754 | + | 0.244134i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.26953 | + | 2.37656i | −0.877910 | + | 0.332785i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.73190 | −0.512616 | −0.256308 | − | 0.966595i | \(-0.582506\pi\) | ||||
−0.256308 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.48224 | −0.739225 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.28086 | + | 2.67963i | 0.434561 | + | 0.354925i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.04377 | − | 1.83578i | −0.656643 | − | 0.238998i | −0.00785651 | − | 0.999969i | \(-0.502501\pi\) |
−0.648786 | + | 0.760971i | \(0.724723\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.85946 | + | 10.5455i | −0.238079 | + | 1.35021i | 0.597952 | + | 0.801532i | \(0.295981\pi\) |
−0.836031 | + | 0.548682i | \(0.815130\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.02483 | − | 3.73237i | 0.255105 | − | 0.470234i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.04603 | − | 1.83660i | 0.625883 | − | 0.227803i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3245 | − | 9.50236i | 1.38350 | − | 1.16090i | 0.415610 | − | 0.909543i | \(-0.363568\pi\) |
0.967895 | − | 0.251356i | \(-0.0808763\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.4966 | + | 0.192291i | −1.74519 | + | 0.0231491i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.68331 | + | 4.64763i | 0.318450 | + | 0.551572i | 0.980165 | − | 0.198184i | \(-0.0635043\pi\) |
−0.661715 | + | 0.749756i | \(0.730171\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.25081 | + | 9.09467i | −0.614561 | + | 1.06445i | 0.375901 | + | 0.926660i | \(0.377333\pi\) |
−0.990461 | + | 0.137791i | \(0.956000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.21182 | + | 1.90650i | −0.255399 | + | 0.220143i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.521112 | − | 2.95537i | −0.0593862 | − | 0.336796i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.10688 | − | 5.12428i | −0.687077 | − | 0.576526i | 0.230988 | − | 0.972957i | \(-0.425804\pi\) |
−0.918065 | + | 0.396431i | \(0.870249\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.19148 | + | 5.41134i | 0.799054 | + | 0.601260i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.32482 | − | 7.82445i | −1.02353 | − | 0.858845i | −0.0334649 | − | 0.999440i | \(-0.510654\pi\) |
−0.990067 | + | 0.140594i | \(0.955099\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73812 | + | 9.85735i | 0.188525 | + | 1.06918i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.36656 | − | 1.17791i | 0.146510 | − | 0.126286i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.20496 | + | 12.4794i | −0.763724 | + | 1.32281i | 0.177194 | + | 0.984176i | \(0.443298\pi\) |
−0.940918 | + | 0.338633i | \(0.890035\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.46973 | + | 2.54564i | 0.154069 | + | 0.266856i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.3616 | − | 0.203764i | 1.59293 | − | 0.0211294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.84439 | − | 4.06492i | 0.497024 | − | 0.417052i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.6595 | − | 3.87974i | 1.08231 | − | 0.393928i | 0.261541 | − | 0.965192i | \(-0.415769\pi\) |
0.820766 | + | 0.571265i | \(0.193547\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 6.35838 | − | 0.168711i | 0.639041 | − | 0.0169561i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0926500 | − | 0.525444i | 0.00921902 | − | 0.0522836i | −0.979851 | − | 0.199729i | \(-0.935994\pi\) |
0.989070 | + | 0.147445i | \(0.0471050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.39538 | + | 0.507876i | 0.137491 | + | 0.0500425i | 0.409849 | − | 0.912153i | \(-0.365581\pi\) |
−0.272358 | + | 0.962196i | \(0.587804\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.90961 | − | 4.00990i | −0.479129 | − | 0.391326i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.416489 | −0.0402635 | −0.0201317 | − | 0.999797i | \(-0.506409\pi\) | ||||
−0.0201317 | + | 0.999797i | \(0.506409\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.2057 | −1.64800 | −0.824002 | − | 0.566586i | \(-0.808264\pi\) | ||||
−0.824002 | + | 0.566586i | \(0.808264\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.1014 | − | 6.10349i | 1.52828 | − | 0.579318i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.1681 | + | 3.70087i | 0.956531 | + | 0.348149i | 0.772673 | − | 0.634804i | \(-0.218919\pi\) |
0.183858 | + | 0.982953i | \(0.441141\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.75834 | + | 21.3146i | −0.350467 | + | 1.98759i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.79593 | + | 2.28541i | −0.535834 | + | 0.211286i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.14870 | + | 1.87397i | −0.471980 | + | 0.171787i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.98291 | + | 4.18116i | −0.452992 | + | 0.380105i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.7000 | + | 17.9780i | 0.964786 | + | 1.62102i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.28464 | − | 7.42122i | −0.383230 | − | 0.663774i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0422583 | + | 0.0731936i | −0.00374982 | + | 0.00649488i | −0.867894 | − | 0.496749i | \(-0.834527\pi\) |
0.864144 | + | 0.503244i | \(0.167860\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.96358 | + | 10.3327i | 0.172884 | + | 0.909741i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.176083 | + | 0.998617i | 0.0153845 | + | 0.0872496i | 0.991533 | − | 0.129853i | \(-0.0414505\pi\) |
−0.976149 | + | 0.217102i | \(0.930339\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.65180 | + | 2.22513i | 0.229941 | + | 0.192943i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 9.94068 | − | 9.03894i | 0.855558 | − | 0.777948i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.572591 | − | 0.480461i | −0.0489198 | − | 0.0410486i | 0.618000 | − | 0.786178i | \(-0.287943\pi\) |
−0.666920 | + | 0.745130i | \(0.732388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.0126135 | − | 0.0715348i | −0.00106986 | − | 0.00606750i | 0.984268 | − | 0.176681i | \(-0.0565361\pi\) |
−0.985338 | + | 0.170614i | \(0.945425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.26704 | + | 2.18733i | 0.527780 | + | 0.184206i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.20157 | + | 3.81322i | −0.184104 | + | 0.318878i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.34667 | − | 2.33250i | −0.111835 | − | 0.193704i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.22740 | + | 7.55164i | −0.348670 | + | 0.622849i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.86114 | + | 4.91808i | −0.480163 | + | 0.402905i | −0.850485 | − | 0.525999i | \(-0.823692\pi\) |
0.370322 | + | 0.928903i | \(0.379247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.5372 | + | 5.29110i | −1.18302 | + | 0.430583i | −0.857267 | − | 0.514872i | \(-0.827839\pi\) |
−0.325751 | + | 0.945456i | \(0.605617\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.31924 | − | 11.3792i | −0.187500 | − | 0.919954i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.98259 | − | 22.5864i | 0.319889 | − | 1.81418i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.236318 | − | 0.0860127i | −0.0188602 | − | 0.00686456i | 0.332573 | − | 0.943078i | \(-0.392083\pi\) |
−0.351433 | + | 0.936213i | \(0.614306\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.03791 | − | 6.37997i | 0.0823113 | − | 0.505965i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.8475 | −0.933717 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.08013 | 0.162929 | 0.0814643 | − | 0.996676i | \(-0.474040\pi\) | ||||
0.0814643 | + | 0.996676i | \(0.474040\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.52471 | − | 9.37231i | 0.118698 | − | 0.729633i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.65547 | + | 0.966512i | 0.205486 | + | 0.0747910i | 0.442713 | − | 0.896663i | \(-0.354016\pi\) |
−0.237226 | + | 0.971454i | \(0.576238\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.50850 | + | 8.55514i | −0.116039 | + | 0.658088i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.49349 | + | 4.86363i | −0.420098 | + | 0.371931i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.27324 | + | 1.91930i | −0.400917 | + | 0.145922i | −0.534606 | − | 0.845102i | \(-0.679540\pi\) |
0.133689 | + | 0.991023i | \(0.457318\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.82798 | + | 1.53386i | −0.138182 | + | 0.115949i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.54117 | − | 8.11214i | 0.341335 | − | 0.609746i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.261810 | + | 0.453468i | 0.0195686 | + | 0.0338938i | 0.875644 | − | 0.482957i | \(-0.160437\pi\) |
−0.856075 | + | 0.516851i | \(0.827104\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.44721 | − | 4.23870i | 0.181900 | − | 0.315060i | −0.760628 | − | 0.649188i | \(-0.775109\pi\) |
0.942527 | + | 0.334129i | \(0.108442\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.5112 | − | 6.11177i | −1.29446 | − | 0.451795i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.46384 | − | 25.3157i | −0.328188 | − | 1.86125i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.28724 | − | 5.27562i | −0.459769 | − | 0.385792i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.81763 | + | 4.49964i | 0.423170 | + | 0.327301i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.8417 | − | 9.09725i | −0.784477 | − | 0.658254i | 0.159895 | − | 0.987134i | \(-0.448884\pi\) |
−0.944372 | + | 0.328880i | \(0.893329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.00475 | − | 11.3695i | −0.144305 | − | 0.818396i | −0.967922 | − | 0.251250i | \(-0.919158\pi\) |
0.823617 | − | 0.567146i | \(-0.191953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.73643 | + | 9.13736i | 0.124348 | + | 0.654340i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.58339 | − | 14.8669i | 0.611541 | − | 1.05922i | −0.379439 | − | 0.925217i | \(-0.623883\pi\) |
0.990981 | − | 0.134004i | \(-0.0427835\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.09229 | + | 12.2842i | 0.502759 | + | 0.870804i | 0.999995 | + | 0.00318864i | \(0.00101498\pi\) |
−0.497236 | + | 0.867615i | \(0.665652\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0955 | + | 22.0028i | 0.923684 | + | 1.55196i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.12940 | − | 0.947681i | 0.0792685 | − | 0.0665142i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 29.3489 | − | 10.6821i | 2.04982 | − | 0.746073i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.70303 | − | 24.8366i | 0.257378 | − | 1.72626i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.900436 | + | 5.10662i | −0.0622844 | + | 0.353233i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.69567 | − | 0.617173i | −0.116735 | − | 0.0424880i | 0.282992 | − | 0.959122i | \(-0.408673\pi\) |
−0.399727 | + | 0.916634i | \(0.630895\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.69175 | + | 3.29474i | −0.595549 | + | 0.225752i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 15.7013 | 1.07082 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.5545 | 0.852252 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.0877 | − | 11.5060i | −0.951958 | − | 0.777506i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.55436 | + | 2.74956i | 0.508162 | + | 0.184956i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.03626 | + | 22.8907i | −0.270288 | + | 1.53288i | 0.483256 | + | 0.875479i | \(0.339454\pi\) |
−0.753543 | + | 0.657398i | \(0.771657\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.64416 | − | 4.31151i | −0.176277 | − | 0.287434i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.33464 | + | 2.30562i | −0.420445 | + | 0.153029i | −0.543574 | − | 0.839361i | \(-0.682929\pi\) |
0.123129 | + | 0.992391i | \(0.460707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.87666 | + | 4.93111i | −0.388341 | + | 0.325857i | −0.815966 | − | 0.578099i | \(-0.803795\pi\) |
0.427626 | + | 0.903956i | \(0.359350\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.19737 | − | 0.0689404i | 0.341962 | − | 0.00453595i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.49573 | − | 9.51888i | −0.360037 | − | 0.623603i | 0.627929 | − | 0.778270i | \(-0.283903\pi\) |
−0.987967 | + | 0.154668i | \(0.950569\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.95465 | − | 8.58171i | 0.323206 | − | 0.559809i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.4588 | − | 9.01502i | 0.679370 | − | 0.585588i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.71043 | + | 21.0429i | 0.240008 | + | 1.36115i | 0.831806 | + | 0.555066i | \(0.187307\pi\) |
−0.591799 | + | 0.806086i | \(0.701582\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4255 | − | 17.9781i | −1.38014 | − | 1.15807i | −0.969162 | − | 0.246424i | \(-0.920744\pi\) |
−0.410974 | − | 0.911647i | \(-0.634811\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.2512 | + | 10.7894i | −0.721763 | + | 0.692140i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.89713 | + | 8.30468i | 0.632305 | + | 0.530567i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.881979 | − | 5.00195i | −0.0561190 | − | 0.318267i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.9699 | − | 13.7654i | 1.01205 | − | 0.872345i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1783 | − | 19.3613i | 0.705565 | − | 1.22207i | −0.260922 | − | 0.965360i | \(-0.584027\pi\) |
0.966487 | − | 0.256715i | \(-0.0826400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.87346 | − | 15.3693i | −0.557870 | − | 0.966258i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −17.3353 | + | 0.229944i | −1.08558 | + | 0.0143996i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.7122 | + | 11.5059i | −0.855344 | + | 0.717719i | −0.960960 | − | 0.276688i | \(-0.910763\pi\) |
0.105616 | + | 0.994407i | \(0.466319\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.2229 | − | 4.81275i | 0.821632 | − | 0.299050i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.63367 | + | 2.66383i | 0.101122 | + | 0.164887i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.58969 | + | 26.0294i | −0.283013 | + | 1.60504i | 0.429286 | + | 0.903168i | \(0.358765\pi\) |
−0.712299 | + | 0.701876i | \(0.752346\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.06768 | − | 3.30037i | −0.557023 | − | 0.202740i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.3306 | − | 15.7882i | −1.18301 | − | 0.966219i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.30073 | −0.262220 | −0.131110 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131110 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.97894 | −0.180957 | −0.0904787 | − | 0.995898i | \(-0.528840\pi\) | ||||
−0.0904787 | + | 0.995898i | \(0.528840\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.76073 | + | 1.80462i | −0.288132 | + | 0.109221i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.35891 | − | 1.22254i | −0.202550 | − | 0.0737221i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.08403 | − | 6.14785i | 0.0651332 | − | 0.369389i | −0.934767 | − | 0.355261i | \(-0.884392\pi\) |
0.999900 | − | 0.0141273i | \(-0.00449702\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.92398 | + | 26.3185i | −0.234923 | + | 1.57565i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.23973 | − | 0.815197i | 0.133611 | − | 0.0486306i | −0.274349 | − | 0.961630i | \(-0.588462\pi\) |
0.407960 | + | 0.913000i | \(0.366240\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.00910269 | + | 0.00763807i | −0.000541099 | + | 0.000454036i | −0.643058 | − | 0.765817i | \(-0.722335\pi\) |
0.642517 | + | 0.766271i | \(0.277890\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.60199 | + | 9.41237i | 0.331833 | + | 0.557541i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.54829 | + | 14.8061i | 0.504590 | + | 0.873975i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00750 | − | 1.74504i | 0.0592646 | − | 0.102649i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.66812 | + | 19.3022i | 0.215029 | + | 1.13152i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.905379 | − | 5.13466i | −0.0528928 | − | 0.299970i | 0.946873 | − | 0.321607i | \(-0.104223\pi\) |
−0.999766 | + | 0.0216376i | \(0.993112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6317 | − | 8.92107i | −0.619003 | − | 0.519405i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.47995 | + | 10.9171i | −0.0858754 | + | 0.633472i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.3163 | + | 11.1737i | 0.770100 | + | 0.646190i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.49248 | + | 8.46428i | 0.0860252 | + | 0.487873i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.872519 | + | 0.304527i | 0.0501249 | + | 0.0174946i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.8441 | + | 23.9788i | −0.792713 | + | 1.37302i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.1440 | + | 17.5700i | 0.578951 | + | 1.00277i | 0.995600 | + | 0.0937049i | \(0.0298710\pi\) |
−0.416649 | + | 0.909067i | \(0.636796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.25633 | + | 2.24426i | −0.0714702 | + | 0.127671i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.13067 | + | 6.82244i | −0.461048 | + | 0.386865i | −0.843516 | − | 0.537103i | \(-0.819519\pi\) |
0.382468 | + | 0.923969i | \(0.375074\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.88285 | − | 2.14118i | 0.332518 | − | 0.121027i | −0.170365 | − | 0.985381i | \(-0.554495\pi\) |
0.502884 | + | 0.864354i | \(0.332272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.22067 | − | 7.27813i | 0.463182 | − | 0.410076i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.02412 | + | 17.1507i | −0.169852 | + | 0.963277i | 0.774068 | + | 0.633102i | \(0.218219\pi\) |
−0.943920 | + | 0.330175i | \(0.892892\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.07527 | + | 0.755338i | 0.116193 | + | 0.0422908i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.115833 | − | 0.712019i | 0.00646515 | − | 0.0397410i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.46745 | 0.526783 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.50121 | 0.194212 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.78519 | − | 29.4144i | 0.264622 | − | 1.62662i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.09720 | + | 1.85523i | 0.281018 | + | 0.102282i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.55468 | − | 20.1596i | 0.195383 | − | 1.10807i | −0.716489 | − | 0.697598i | \(-0.754252\pi\) |
0.911872 | − | 0.410474i | \(-0.134637\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.95629 | + | 29.2241i | 0.326403 | + | 1.60147i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 35.9195 | − | 13.0736i | 1.96249 | − | 0.714289i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.9649 | − | 14.2352i | 0.924136 | − | 0.775442i | −0.0506197 | − | 0.998718i | \(-0.516120\pi\) |
0.974755 | + | 0.223276i | \(0.0716752\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.15484 | + | 16.3538i | −0.497223 | + | 0.888217i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.40292 | + | 16.2863i | 0.509197 | + | 0.881955i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.49007 | + | 14.7052i | −0.458421 | + | 0.794008i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −35.3936 | − | 12.3531i | −1.90553 | − | 0.665069i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.196028 | − | 1.11173i | −0.0105234 | − | 0.0596809i | 0.979094 | − | 0.203409i | \(-0.0652021\pi\) |
−0.989617 | + | 0.143728i | \(0.954091\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.55881 | − | 8.02079i | −0.511671 | − | 0.429343i | 0.350046 | − | 0.936733i | \(-0.386166\pi\) |
−0.861717 | + | 0.507389i | \(0.830611\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.29513 | − | 10.5442i | −0.122505 | − | 0.562808i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 20.3466 | + | 17.0729i | 1.08294 | + | 0.908696i | 0.996162 | − | 0.0875314i | \(-0.0278978\pi\) |
0.0867801 | + | 0.996227i | \(0.472342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.40964 | + | 13.6657i | 0.127890 | + | 0.725301i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.77176 | − | 9.32327i | −0.0937713 | − | 0.493440i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.47495 | − | 12.9470i | 0.394513 | − | 0.683317i | −0.598526 | − | 0.801103i | \(-0.704247\pi\) |
0.993039 | + | 0.117787i | \(0.0375800\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.50926 | + | 11.2744i | 0.342592 | + | 0.593388i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.76218 | − | 9.68152i | −0.302436 | − | 0.508148i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.8013 | + | 17.4544i | −1.08879 | + | 0.913603i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7509 | − | 8.28066i | 1.18759 | − | 0.432247i | 0.328712 | − | 0.944430i | \(-0.393385\pi\) |
0.858876 | + | 0.512183i | \(0.171163\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −33.7105 | + | 13.2925i | −1.75490 | + | 0.691978i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.917241 | − | 5.20193i | 0.0476208 | − | 0.270071i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8087 | + | 6.11786i | 0.870320 | + | 0.316771i | 0.738297 | − | 0.674476i | \(-0.235630\pi\) |
0.132023 | + | 0.991247i | \(0.457853\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.8788 | − | 5.26095i | 0.716697 | − | 0.271674i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.16319 | −0.111410 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.2231 | 1.91202 | 0.956010 | − | 0.293334i | \(-0.0947648\pi\) | ||||
0.956010 | + | 0.293334i | \(0.0947648\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.113377 | − | 0.0926002i | −0.00580849 | − | 0.00474405i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.9881 | − | 8.00300i | −1.12354 | − | 0.408934i | −0.287595 | − | 0.957752i | \(-0.592856\pi\) |
−0.835942 | + | 0.548818i | \(0.815078\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.34745 | − | 7.64175i | 0.0686722 | − | 0.389460i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.2106 | + | 0.483194i | −0.925697 | + | 0.0245621i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.90844 | + | 1.78653i | −0.248868 | + | 0.0905805i | −0.463442 | − | 0.886127i | \(-0.653386\pi\) |
0.214574 | + | 0.976708i | \(0.431164\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.8215 | + | 20.8277i | −1.25528 | + | 1.05330i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.75618 | + | 0.0232949i | −0.0885877 | + | 0.00117507i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.3066 | − | 17.8516i | −0.518581 | − | 0.898209i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 17.1043 | − | 29.6256i | 0.858442 | − | 1.48686i | −0.0149734 | − | 0.999888i | \(-0.504766\pi\) |
0.873415 | − | 0.486977i | \(-0.161900\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.54154 | + | 3.91462i | −0.227361 | + | 0.195976i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.67724 | − | 32.1972i | −0.283508 | − | 1.60785i | −0.710567 | − | 0.703629i | \(-0.751562\pi\) |
0.427060 | − | 0.904223i | \(-0.359549\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.1108 | − | 11.8404i | −0.702910 | − | 0.589812i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.6881 | + | 19.5082i | 0.630476 | + | 0.969372i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.1469 | + | 13.5489i | 0.800374 | + | 0.671594i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.13626 | + | 17.7866i | 0.155078 | + | 0.879491i | 0.958714 | + | 0.284371i | \(0.0917846\pi\) |
−0.803636 | + | 0.595121i | \(0.797104\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.980632 | − | 0.845264i | 0.0483710 | − | 0.0416938i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.79859 | − | 6.57935i | 0.186916 | − | 0.323749i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.7375 | − | 27.2582i | −0.772525 | − | 1.33805i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.125802 | − | 0.00166870i | 0.00616056 | − | 8.17167e-5i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.10008 | − | 6.79677i | 0.395715 | − | 0.332044i | −0.423120 | − | 0.906074i | \(-0.639065\pi\) |
0.818835 | + | 0.574030i | \(0.194621\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.0408 | − | 5.11045i | 0.684309 | − | 0.249068i | 0.0236122 | − | 0.999721i | \(-0.492483\pi\) |
0.660696 | + | 0.750653i | \(0.270261\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.48238 | + | 10.1057i | −0.266562 | + | 0.491354i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.13327 | + | 6.42709i | −0.0549716 | + | 0.311760i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −14.2424 | − | 5.18383i | −0.689240 | − | 0.250863i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.90670 | − | 4.82427i | −0.285178 | − | 0.232918i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.20497 | 0.106210 | 0.0531048 | − | 0.998589i | \(-0.483088\pi\) | ||||
0.0531048 | + | 0.998589i | \(0.483088\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.38398 | −0.306794 | −0.153397 | − | 0.988165i | \(-0.549021\pi\) | ||||
−0.153397 | + | 0.988165i | \(0.549021\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.36213 | − | 1.65353i | 0.209148 | − | 0.0792807i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19.2369 | + | 7.00166i | 0.920226 | + | 0.334935i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.72428 | − | 9.77890i | 0.0822955 | − | 0.466721i | −0.915612 | − | 0.402063i | \(-0.868293\pi\) |
0.997907 | − | 0.0646581i | \(-0.0205957\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.7344 | − | 9.32731i | −0.558781 | − | 0.444157i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.82027 | + | 2.48238i | −0.324041 | + | 0.117941i | −0.498918 | − | 0.866649i | \(-0.666269\pi\) |
0.174877 | + | 0.984590i | \(0.444047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −28.5428 | + | 23.9502i | −1.35306 | + | 1.13535i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.77774 | − | 11.3879i | −0.320576 | − | 0.538627i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.51154 | − | 2.61806i | −0.0713339 | − | 0.123554i | 0.828152 | − | 0.560503i | \(-0.189392\pi\) |
−0.899486 | + | 0.436949i | \(0.856059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.8048 | + | 22.1786i | −0.602956 | + | 1.04435i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.00249 | − | 26.3239i | −0.235038 | − | 1.23681i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.31983 | + | 7.48511i | 0.0618745 | + | 0.350908i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.3187 | − | 17.8885i | −0.997248 | − | 0.836790i | −0.0106471 | − | 0.999943i | \(-0.503389\pi\) |
−0.986601 | + | 0.163153i | \(0.947834\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 20.0986 | − | 0.800170i | 0.938124 | − | 0.0373487i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.9390 | − | 17.5699i | −0.975227 | − | 0.818313i | 0.00813531 | − | 0.999967i | \(-0.497410\pi\) |
−0.983362 | + | 0.181654i | \(0.941855\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.60742 | − | 20.4587i | −0.167651 | − | 0.950795i | −0.946289 | − | 0.323322i | \(-0.895200\pi\) |
0.778638 | − | 0.627473i | \(-0.215911\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 37.5055 | + | 13.0902i | 1.73928 | + | 0.607043i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.66334 | + | 4.61304i | −0.123245 | + | 0.213466i | −0.921045 | − | 0.389455i | \(-0.872663\pi\) |
0.797801 | + | 0.602921i | \(0.205997\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.4621 | + | 18.1208i | 0.483093 | + | 0.836742i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.212769 | − | 0.380082i | 0.00980390 | − | 0.0175133i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.86251 | + | 8.27563i | −0.453479 | + | 0.380514i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.87458 | − | 1.41023i | 0.177778 | − | 0.0647059i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.6184 | + | 3.54876i | 0.486182 | + | 0.162487i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.43810 | + | 8.15589i | −0.0657086 | + | 0.372652i | 0.934166 | + | 0.356838i | \(0.116145\pi\) |
−0.999875 | + | 0.0158142i | \(0.994966\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.4012 | − | 7.06145i | −0.884617 | − | 0.321974i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.29500 | − | 20.2543i | 0.149928 | − | 0.921601i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 29.3313 | 1.33186 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.1730 | 1.09539 | 0.547693 | − | 0.836680i | \(-0.315506\pi\) | ||||
0.547693 | + | 0.836680i | \(0.315506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.578521 | + | 3.55614i | −0.0261616 | + | 0.160814i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.1657 | − | 13.8912i | −1.72239 | − | 0.626900i | −0.724350 | − | 0.689432i | \(-0.757860\pi\) |
−0.998043 | + | 0.0625322i | \(0.980082\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.700181 | − | 3.97092i | 0.0315346 | − | 0.178841i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.5986 | + | 5.21320i | 0.701106 | + | 0.234316i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.13789 | + | 2.59798i | −0.320178 | + | 0.116535i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8373 | − | 17.4846i | 0.932806 | − | 0.782717i | −0.0435134 | − | 0.999053i | \(-0.513855\pi\) |
0.976319 | + | 0.216336i | \(0.0694107\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.39086 | + | 4.27092i | −0.106816 | + | 0.190811i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.4402 | − | 23.2791i | −0.599270 | − | 1.03797i | −0.992929 | − | 0.118709i | \(-0.962124\pi\) |
0.393659 | − | 0.919256i | \(-0.371209\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.689803 | − | 1.19477i | 0.0306959 | − | 0.0531668i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.2061 | − | 4.95823i | −0.630916 | − | 0.220203i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.15594 | + | 29.2408i | 0.228533 | + | 1.29608i | 0.855814 | + | 0.517283i | \(0.173057\pi\) |
−0.627281 | + | 0.778793i | \(0.715832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.3866 | − | 9.55448i | −0.503713 | − | 0.422665i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.78692 | − | 10.7442i | −0.299650 | − | 0.474368i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.94131 | + | 2.46805i | 0.129609 | + | 0.108755i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.41095 | + | 8.00188i | 0.0620534 | + | 0.351922i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.81461 | − | 9.54879i | −0.0796527 | − | 0.419145i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.7615 | − | 34.2280i | 0.865769 | − | 1.49956i | −0.000512875 | − | 1.00000i | \(-0.500163\pi\) |
0.866282 | − | 0.499556i | \(-0.166503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.77869 | − | 6.54488i | −0.165231 | − | 0.286188i | 0.771507 | − | 0.636221i | \(-0.219503\pi\) |
−0.936737 | + | 0.350034i | \(0.886170\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.11385 | − | 3.55166i | −0.0922561 | − | 0.155007i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.3025 | − | 22.0704i | 1.14576 | − | 0.961403i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.2249 | + | 16.0966i | −1.92282 | + | 0.699851i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6054 | + | 10.0196i | 0.547026 | + | 0.434814i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.35592 | − | 24.7037i | 0.188676 | − | 1.07003i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.01197 | − | 0.368328i | −0.0437515 | − | 0.0159242i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.848051 | + | 0.321466i | −0.0365961 | + | 0.0138723i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.5938 | −0.456309 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.89649 | 0.124530 | 0.0622650 | − | 0.998060i | \(-0.480168\pi\) | ||||
0.0622650 | + | 0.998060i | \(0.480168\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.56576 | + | 5.36255i | 0.281764 | + | 0.230129i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.8059 | − | 15.2161i | −1.79077 | − | 0.651787i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.59815 | + | 14.7349i | −0.111089 | + | 0.630017i | 0.877524 | + | 0.479533i | \(0.159194\pi\) |
−0.988613 | + | 0.150483i | \(0.951917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 15.3187 | − | 28.2369i | 0.653786 | − | 1.20512i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.39388 | + | 0.871300i | −0.101983 | + | 0.0371186i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.64375 | − | 7.25297i | 0.367570 | − | 0.308427i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 44.5206 | − | 0.590543i | 1.88979 | − | 0.0250672i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.7114 | − | 18.5527i | −0.453856 | − | 0.786102i | 0.544766 | − | 0.838588i | \(-0.316619\pi\) |
−0.998622 | + | 0.0524865i | \(0.983285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.30535 | − | 10.9212i | 0.266688 | − | 0.461917i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.7677 | − | 9.28128i | 0.454611 | − | 0.391856i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.65262 | + | 43.4002i | 0.322520 | + | 1.82910i | 0.526561 | + | 0.850137i | \(0.323481\pi\) |
−0.204042 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.4332 | + | 17.9846i | 0.901701 | + | 0.756617i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.31046 | + | 8.69425i | −0.391003 | + | 0.365124i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.4926 | + | 18.8735i | 0.942940 | + | 0.791220i | 0.978094 | − | 0.208162i | \(-0.0667480\pi\) |
−0.0351549 | + | 0.999382i | \(0.511192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.20125 | + | 29.4977i | 0.217665 | + | 1.23444i | 0.876221 | + | 0.481910i | \(0.160057\pi\) |
−0.658555 | + | 0.752532i | \(0.728832\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5677 | − | 16.0046i | 0.775677 | − | 0.668601i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.05585 | + | 12.2211i | −0.294249 | + | 0.509655i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7784 | + | 32.5251i | 0.781755 | + | 1.35404i | 0.930919 | + | 0.365226i | \(0.119008\pi\) |
−0.149164 | + | 0.988812i | \(0.547658\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 19.9946 | − | 0.265219i | 0.830948 | − | 0.0110221i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.1985 | − | 11.0748i | 0.547565 | − | 0.459461i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.43522 | − | 2.70620i | 0.307935 | − | 0.112079i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.1039 | + | 0.427297i | −0.665816 | + | 0.0176665i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.06466 | + | 23.0518i | −0.167766 | + | 0.951451i | 0.778400 | + | 0.627769i | \(0.216032\pi\) |
−0.946166 | + | 0.323682i | \(0.895079\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.3847 | − | 7.41944i | −0.839939 | − | 0.305713i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.0289 | + | 18.8087i | 0.947281 | + | 0.773686i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.10744 | −0.127607 | −0.0638037 | − | 0.997962i | \(-0.520323\pi\) | ||||
−0.0638037 | + | 0.997962i | \(0.520323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.1675 | −0.580809 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.9733 | + | 8.70836i | −0.940233 | + | 0.356409i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −18.8508 | − | 6.86114i | −0.770224 | − | 0.280339i | −0.0731340 | − | 0.997322i | \(-0.523300\pi\) |
−0.697090 | + | 0.716983i | \(0.745522\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.44368 | + | 36.5439i | −0.262843 | + | 1.49066i | 0.512264 | + | 0.858828i | \(0.328807\pi\) |
−0.775107 | + | 0.631829i | \(0.782304\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −41.2576 | + | 16.2684i | −1.68014 | + | 0.662499i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.8050 | + | 5.75256i | −0.642566 | + | 0.233875i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.1436 | + | 20.2588i | −0.979957 | + | 0.822281i | −0.984083 | − | 0.177710i | \(-0.943131\pi\) |
0.00412615 | + | 0.999991i | \(0.498687\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.30603 | + | 2.19437i | 0.0529229 | + | 0.0889202i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.97939 | − | 6.89251i | −0.160989 | − | 0.278841i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.5827 | + | 28.7220i | −0.669767 | + | 1.16007i | 0.308202 | + | 0.951321i | \(0.400273\pi\) |
−0.977969 | + | 0.208750i | \(0.933061\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0995 | + | 53.1451i | 0.407250 | + | 2.14302i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.65400 | − | 9.38030i | −0.0665875 | − | 0.377636i | −0.999831 | − | 0.0183917i | \(-0.994145\pi\) |
0.933243 | − | 0.359245i | \(-0.116966\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.2981 | + | 18.7103i | 0.896237 | + | 0.752032i | 0.969451 | − | 0.245284i | \(-0.0788812\pi\) |
−0.0732141 | + | 0.997316i | \(0.523326\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 41.4302 | + | 13.2381i | 1.66254 | + | 0.531227i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15.6242 | − | 13.1103i | −0.625971 | − | 0.525252i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.31142 | − | 30.1226i | −0.212457 | − | 1.20490i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.47974 | − | 2.95960i | −0.338648 | − | 0.118195i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.2423 | − | 33.3286i | 0.767240 | − | 1.32890i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.17030 | + | 7.22318i | 0.166017 | + | 0.287550i | 0.937016 | − | 0.349286i | \(-0.113576\pi\) |
−0.770999 | + | 0.636837i | \(0.780243\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.52670 | − | 2.72723i | 0.0606809 | − | 0.108398i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.167408 | + | 0.140472i | −0.00664339 | + | 0.00557446i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.75090 | − | 3.54904i | 0.386345 | − | 0.140618i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.21528 | − | 15.7755i | −0.127194 | − | 0.624071i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.90981 | − | 10.8311i | 0.0754330 | − | 0.427802i | −0.923581 | − | 0.383404i | \(-0.874752\pi\) |
0.999014 | − | 0.0443983i | \(-0.0141371\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.45557 | − | 2.71361i | −0.294019 | − | 0.107014i | 0.190799 | − | 0.981629i | \(-0.438892\pi\) |
−0.484818 | + | 0.874615i | \(0.661114\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.36681 | + | 26.8426i | −0.171943 | + | 1.05693i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.52146 | −0.295699 | −0.147849 | − | 0.989010i | \(-0.547235\pi\) | ||||
−0.147849 | + | 0.989010i | \(0.547235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.3801 | 0.446709 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.49161 | + | 21.4628i | −0.136847 | + | 0.841193i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.5518 | + | 8.57214i | 0.921652 | + | 0.335454i | 0.758896 | − | 0.651212i | \(-0.225739\pi\) |
0.162757 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.455300 | + | 2.58214i | −0.0177901 | + | 0.100892i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 23.5885 | − | 20.8840i | 0.920275 | − | 0.814761i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.5262 | + | 11.1106i | −1.18913 | + | 0.432808i | −0.859418 | − | 0.511273i | \(-0.829174\pi\) |
−0.329712 | + | 0.944081i | \(0.606952\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.7123 | + | 20.7361i | −0.961197 | + | 0.806540i | −0.981147 | − | 0.193261i | \(-0.938094\pi\) |
0.0199502 | + | 0.999801i | \(0.493649\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.80159 | + | 12.1501i | −0.264152 | + | 0.471869i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.47546 | + | 7.75173i | 0.173551 | + | 0.300599i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.35940 | − | 7.55070i | 0.168797 | − | 0.292364i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.0109 | − | 13.2666i | −1.46959 | − | 0.512916i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.94243 | − | 22.3586i | −0.152196 | − | 0.863145i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.1895 | + | 13.5846i | 0.624061 | + | 0.523649i | 0.899077 | − | 0.437790i | \(-0.144239\pi\) |
−0.275016 | + | 0.961440i | \(0.588683\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.10623 | − | 3.32128i | 0.312009 | − | 0.127836i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −39.0139 | − | 32.7366i | −1.49943 | − | 1.25817i | −0.881731 | − | 0.471752i | \(-0.843622\pi\) |
−0.617696 | − | 0.786417i | \(-0.711934\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.78807 | + | 15.8119i | 0.106996 | + | 0.606807i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.17986 | − | 11.4708i | −0.0835324 | − | 0.439561i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.73422 | + | 8.19991i | −0.181150 | + | 0.313761i | −0.942272 | − | 0.334847i | \(-0.891315\pi\) |
0.761123 | + | 0.648608i | \(0.224649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.966365 | − | 1.67379i | −0.0369229 | − | 0.0639523i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.79570 | − | 11.4180i | −0.259272 | − | 0.435625i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.93701 | + | 4.98174i | −0.226182 | + | 0.189789i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.4877 | + | 5.63705i | −0.589179 | + | 0.214444i | −0.619368 | − | 0.785101i | \(-0.712611\pi\) |
0.0301894 | + | 0.999544i | \(0.490389\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.32762 | + | 8.90447i | −0.0504321 | + | 0.338253i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0326149 | − | 0.184968i | 0.00123715 | − | 0.00701625i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.9380 | + | 15.9921i | 1.66427 | + | 0.605745i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 17.8017 | − | 6.74800i | 0.673323 | − | 0.255233i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.6066 | 0.891607 | 0.445804 | − | 0.895131i | \(-0.352918\pi\) | ||||
0.445804 | + | 0.895131i | \(0.352918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −24.3144 | −0.917033 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.2931 | + | 10.8571i | 0.500648 | + | 0.408901i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.709650 | + | 0.258291i | 0.0266891 | + | 0.00971404i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.0376114 | − | 0.213305i | 0.00141253 | − | 0.00801083i | −0.984093 | − | 0.177652i | \(-0.943150\pi\) |
0.985506 | + | 0.169641i | \(0.0542609\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.5031 | + | 20.3873i | 0.468903 | + | 0.764583i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 69.7663 | − | 25.3929i | 2.61277 | − | 0.950970i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.72159 | + | 7.31829i | −0.326169 | + | 0.273688i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.0064 | + | 0.490871i | −1.38203 | + | 0.0183319i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.99911 | + | 10.3908i | 0.223729 | + | 0.387510i | 0.955937 | − | 0.293571i | \(-0.0948435\pi\) |
−0.732208 | + | 0.681081i | \(0.761510\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.05089 | + | 1.82020i | −0.0391374 | + | 0.0677879i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.6937 | − | 31.6285i | 1.36465 | − | 1.17627i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.304941 | − | 1.72941i | −0.0113252 | − | 0.0642286i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.3729 | − | 8.70393i | −0.384711 | − | 0.322811i | 0.429838 | − | 0.902906i | \(-0.358571\pi\) |
−0.814548 | + | 0.580095i | \(0.803015\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.3162 | − | 22.2355i | −0.567265 | − | 0.823535i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.0069 | + | 15.1096i | 0.666008 | + | 0.558847i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.82017 | − | 10.3227i | −0.0672296 | − | 0.381278i | −0.999794 | − | 0.0202755i | \(-0.993546\pi\) |
0.932565 | − | 0.361003i | \(-0.117565\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.9501 | + | 14.6102i | −0.625212 | + | 0.538906i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.6716 | + | 27.1439i | −0.577269 | + | 0.999859i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.2321 | − | 33.3110i | −0.707465 | − | 1.22537i | −0.965794 | − | 0.259309i | \(-0.916505\pi\) |
0.258329 | − | 0.966057i | \(-0.416828\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.79651 | − | 0.116681i | 0.323148 | − | 0.00428639i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.10477 | − | 5.12251i | 0.223962 | − | 0.187927i | −0.523901 | − | 0.851779i | \(-0.675524\pi\) |
0.747864 | + | 0.663852i | \(0.231080\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.5906 | + | 6.76643i | −0.681108 | + | 0.247903i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.0915 | + | 31.1301i | 0.698520 | + | 1.13899i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.102366 | − | 0.580548i | 0.00374038 | − | 0.0212127i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.2299 | + | 12.0947i | 1.21258 | + | 0.441341i | 0.867596 | − | 0.497269i | \(-0.165664\pi\) |
0.344979 | + | 0.938610i | \(0.387886\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.9908 | + | 24.4948i | 1.09292 | + | 0.892640i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.0013 | −1.45580 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.27205 | −0.0825791 | −0.0412895 | − | 0.999147i | \(-0.513147\pi\) | ||||
−0.0412895 | + | 0.999147i | \(0.513147\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.7428 | − | 10.8954i | 1.04330 | − | 0.395478i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7690 | + | 6.83137i | 0.680377 | + | 0.247637i | 0.659009 | − | 0.752135i | \(-0.270976\pi\) |
0.0213676 | + | 0.999772i | \(0.493198\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.22888 | − | 23.9831i | 0.153096 | − | 0.868248i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.42814 | − | 29.7000i | 0.160100 | − | 1.07380i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −10.4746 | + | 3.81245i | −0.378217 | + | 0.137660i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.6676 | − | 20.6986i | 0.889537 | − | 0.746410i | −0.0785806 | − | 0.996908i | \(-0.525039\pi\) |
0.968117 | + | 0.250498i | \(0.0805943\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.8566 | − | 26.6420i | −0.571062 | − | 0.959490i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.04006 | + | 8.72964i | 0.181278 | + | 0.313983i | 0.942316 | − | 0.334724i | \(-0.108643\pi\) |
−0.761038 | + | 0.648708i | \(0.775310\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.47686 | − | 12.9503i | 0.268577 | − | 0.465189i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.55024 | + | 23.9441i | 0.163239 | + | 0.858989i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.12981 | − | 29.0926i | −0.183794 | − | 1.04235i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.71631 | − | 7.31385i | −0.311894 | − | 0.261710i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.00837 | + | 2.05203i | −0.178984 | + | 0.0733334i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.498133 | − | 0.417983i | −0.0177791 | − | 0.0149185i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.0850424 | − | 0.482300i | −0.00303144 | − | 0.0171921i | 0.983255 | − | 0.182238i | \(-0.0583340\pi\) |
−0.986286 | + | 0.165045i | \(0.947223\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.2229 | − | 15.0857i | −1.53877 | − | 0.537064i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.65783 | + | 13.2637i | −0.272281 | + | 0.471605i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1191 | + | 19.2588i | 0.394851 | + | 0.683901i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.16411 | − | 14.5840i | 0.289551 | − | 0.517241i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33.1609 | + | 27.8253i | −1.17462 | + | 0.985623i | −0.174621 | + | 0.984636i | \(0.555870\pi\) |
−1.00000 | 0.000987700i | \(0.999686\pi\) | ||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.9405 | − | 5.07391i | 0.493178 | − | 0.179502i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32.3672 | − | 28.6562i | 1.14364 | − | 1.01252i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.86638 | − | 21.9273i | 0.136442 | − | 0.773799i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.7868 | − | 10.4776i | −1.01460 | − | 0.369285i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.19611 | − | 7.35242i | 0.0421049 | − | 0.258817i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.01221 | −0.0355874 | −0.0177937 | − | 0.999842i | \(-0.505664\pi\) | ||||
−0.0177937 | + | 0.999842i | \(0.505664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.1980 | −1.76269 | −0.881346 | − | 0.472472i | \(-0.843362\pi\) | ||||
−0.881346 | + | 0.472472i | \(0.843362\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.828493 | − | 5.09272i | 0.0290565 | − | 0.178609i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.05425 | + | 1.83960i | 0.177043 | + | 0.0644383i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.57888 | − | 14.6255i | 0.0902235 | − | 0.511683i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.76110 | − | 8.64072i | −0.0615379 | − | 0.301931i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.40675 | + | 3.42378i | −0.328298 | + | 0.119491i | −0.500910 | − | 0.865499i | \(-0.667001\pi\) |
0.172613 | + | 0.984990i | \(0.444779\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.5812 | − | 23.1434i | 0.961421 | − | 0.806728i | −0.0197629 | − | 0.999805i | \(-0.506291\pi\) |
0.981184 | + | 0.193077i | \(0.0618467\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.02420 | − | 5.40230i | 0.105289 | − | 0.188084i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 27.1307 | + | 46.9918i | 0.943428 | + | 1.63407i | 0.758868 | + | 0.651245i | \(0.225753\pi\) |
0.184561 | + | 0.982821i | \(0.440914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.48912 | − | 2.57923i | 0.0517192 | − | 0.0895803i | −0.839007 | − | 0.544121i | \(-0.816863\pi\) |
0.890726 | + | 0.454541i | \(0.150197\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.2087 | + | 3.56306i | 0.354137 | + | 0.123601i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.35872 | + | 19.0483i | 0.116373 | + | 0.659983i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.59745 | + | 4.69681i | 0.193708 | + | 0.162540i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −43.9022 | − | 14.0280i | −1.51748 | − | 0.484878i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.2584 | − | 19.5161i | −0.802967 | − | 0.673770i | 0.145951 | − | 0.989292i | \(-0.453376\pi\) |
−0.948918 | + | 0.315522i | \(0.897820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.84739 | − | 27.4909i | −0.167151 | − | 0.947963i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.770732 | + | 4.05572i | 0.0265454 | + | 0.139686i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.2312 | + | 19.4530i | −0.386365 | + | 0.669204i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.60344 | − | 7.97339i | −0.158176 | − | 0.273969i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.0105262 | − | 0.0176860i | −0.000361260 | − | 0.000606983i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 63.7466 | − | 53.4898i | 2.18521 | − | 1.83361i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.5715 | + | 5.66757i | −0.533159 | + | 0.194054i | −0.594548 | − | 0.804060i | \(-0.702669\pi\) |
0.0613893 | + | 0.998114i | \(0.480447\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −17.6492 | + | 6.95928i | −0.603589 | + | 0.238002i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.658235 | − | 3.73303i | 0.0224849 | − | 0.127518i | −0.971499 | − | 0.237043i | \(-0.923822\pi\) |
0.993984 | + | 0.109525i | \(0.0349329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.87400 | − | 2.50193i | −0.234538 | − | 0.0853647i | 0.222078 | − | 0.975029i | \(-0.428716\pi\) |
−0.456615 | + | 0.889664i | \(0.650938\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.6895 | + | 10.4961i | −0.943657 | + | 0.357707i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.3163 | −1.67875 | −0.839373 | − | 0.543557i | \(-0.817077\pi\) | ||||
−0.839373 | + | 0.543557i | \(0.817077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.5101 | −0.493360 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.70307 | + | 2.20772i | 0.0918012 | + | 0.0749781i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.8829 | + | 5.78089i | 0.538789 | + | 0.196103i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.33111 | − | 30.2343i | 0.180638 | − | 1.02445i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −34.0188 | + | 0.902643i | −1.15136 | + | 0.0305498i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3976 | − | 4.14839i | 0.385309 | − | 0.140241i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 30.8256 | − | 25.8658i | 1.04091 | − | 0.873425i | 0.0487991 | − | 0.998809i | \(-0.484461\pi\) |
0.992108 | + | 0.125384i | \(0.0400161\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.02989 | − | 0.119777i | 0.304571 | − | 0.00403997i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.03667 | − | 6.99172i | −0.135999 | − | 0.235557i | 0.789980 | − | 0.613133i | \(-0.210091\pi\) |
−0.925979 | + | 0.377576i | \(0.876758\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.05527 | − | 15.6842i | 0.304734 | − | 0.527815i | −0.672468 | − | 0.740126i | \(-0.734766\pi\) |
0.977202 | + | 0.212311i | \(0.0680991\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.2081 | − | 15.6946i | 0.612059 | − | 0.527569i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.38170 | + | 19.1786i | 0.113546 | + | 0.643954i | 0.987460 | + | 0.157872i | \(0.0504633\pi\) |
−0.873913 | + | 0.486082i | \(0.838426\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.0916388 | − | 0.0768940i | −0.00307347 | − | 0.00257894i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.2519 | − | 5.56631i | −0.611463 | − | 0.186478i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.17995 | − | 6.02469i | −0.240268 | − | 0.201609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.235107 | + | 1.33336i | 0.00785877 | + | 0.0445693i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.8057 | + | 19.6576i | −0.761461 | + | 0.656348i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.61952 | + | 8.00124i | −0.154069 | + | 0.266856i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.22318 | − | 12.5109i | −0.240639 | − | 0.416799i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.8854 | + | 0.197448i | −0.495356 | + | 0.00657064i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.69474 | − | 8.13485i | 0.322264 | − | 0.270412i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.68496 | + | 1.34122i | −0.122357 | + | 0.0445344i | −0.402473 | − | 0.915432i | \(-0.631849\pi\) |
0.280116 | + | 0.959966i | \(0.409627\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.763275 | + | 1.40694i | −0.0253162 | + | 0.0466654i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.15327 | + | 17.8831i | −0.104473 | + | 0.592493i | 0.886957 | + | 0.461852i | \(0.152815\pi\) |
−0.991430 | + | 0.130642i | \(0.958296\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.2522 | + | 8.82706i | 0.802629 | + | 0.292133i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37.1432 | − | 30.3365i | −1.22792 | − | 1.00289i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.43526 | −0.0473964 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.65763 | 0.186628 | 0.0933140 | − | 0.995637i | \(-0.470254\pi\) | ||||
0.0933140 | + | 0.995637i | \(0.470254\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −32.8585 | + | 12.4555i | −1.08272 | + | 0.410422i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10.4730 | + | 3.81185i | 0.344722 | + | 0.125469i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.91047 | − | 16.5061i | 0.0956956 | − | 0.542717i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.48732 | − | 2.77196i | −0.114539 | − | 0.0910431i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.1286 | + | 5.87034i | −0.529163 | + | 0.192600i | −0.592765 | − | 0.805376i | \(-0.701964\pi\) |
0.0636016 | + | 0.997975i | \(0.479741\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.36125 | − | 7.85502i | 0.306802 | − | 0.257438i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.40221 | − | 15.7974i | −0.307814 | − | 0.517185i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.6110 | − | 18.3788i | −0.347017 | − | 0.601051i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.09417 | + | 15.7516i | −0.297094 | + | 0.514581i | −0.975470 | − | 0.220134i | \(-0.929351\pi\) |
0.678376 | + | 0.734715i | \(0.262684\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.02439 | + | 10.6527i | 0.0660636 | + | 0.347637i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.33218 | − | 24.5690i | −0.141225 | − | 0.800928i | −0.970321 | − | 0.241821i | \(-0.922255\pi\) |
0.829096 | − | 0.559107i | \(-0.188856\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 77.4507 | + | 64.9888i | 2.52214 | + | 2.11633i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.1562 | + | 16.0780i | 0.330381 | + | 0.523018i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 32.2233 | + | 27.0386i | 1.04712 | + | 0.878636i | 0.992788 | − | 0.119887i | \(-0.0382531\pi\) |
0.0543305 | + | 0.998523i | \(0.482698\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.78713 | + | 21.4779i | 0.122935 | + | 0.697202i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −28.4793 | − | 9.93987i | −0.923505 | − | 0.322322i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.09208 | + | 15.7479i | −0.294521 | + | 0.510126i | −0.974873 | − | 0.222759i | \(-0.928494\pi\) |
0.680352 | + | 0.732885i | \(0.261827\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.2976 | − | 31.6923i | −0.592095 | − | 1.02554i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.86848 | + | 3.33777i | −0.0603993 | + | 0.107895i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.810453 | − | 0.680051i | 0.0261709 | − | 0.0219600i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.7986 | + | 16.3054i | −1.44512 | + | 0.525980i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.18504 | + | 0.396050i | 0.0381873 | + | 0.0127625i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.18372 | − | 29.3983i | 0.166870 | − | 0.946365i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8221 | + | 6.48673i | 0.573121 | + | 0.208599i | 0.612290 | − | 0.790634i | \(-0.290249\pi\) |
−0.0391685 | + | 0.999233i | \(0.512471\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.63306 | + | 16.1853i | −0.0845861 | + | 0.519948i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 51.8323 | 1.66338 | 0.831688 | − | 0.555243i | \(-0.187375\pi\) | ||||
0.831688 | + | 0.555243i | \(0.187375\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.102813 | 0.00329604 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.973747 | + | 5.98558i | −0.0311849 | + | 0.191692i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.8109 | + | 10.4863i | 0.921744 | + | 0.335487i | 0.758932 | − | 0.651170i | \(-0.225721\pi\) |
0.162812 | + | 0.986657i | \(0.447944\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.30530 | − | 30.0878i | 0.169558 | − | 0.961611i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 48.9553 | + | 16.3613i | 1.56302 | + | 0.522376i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.3321 | − | 14.3157i | 1.25450 | − | 0.456600i | 0.372579 | − | 0.928001i | \(-0.378474\pi\) |
0.881919 | + | 0.471401i | \(0.156251\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.0035 | − | 28.5323i | 1.08344 | − | 0.909115i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.58928 | + | 8.19808i | −0.146078 | + | 0.260948i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 25.4139 | + | 44.0181i | 0.808114 | + | 1.39969i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.830287 | − | 1.43810i | 0.0263749 | − | 0.0456827i | −0.852537 | − | 0.522667i | \(-0.824937\pi\) |
0.878912 | + | 0.476985i | \(0.158270\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.4758 | + | 11.6837i | 1.06232 | + | 0.370772i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.36893 | + | 36.1200i | 0.201909 | + | 1.14508i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0498 | + | 24.3756i | 0.920015 | + | 0.771984i | 0.973998 | − | 0.226558i | \(-0.0727472\pi\) |
−0.0539828 | + | 0.998542i | \(0.517192\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −51.6174 | + | 2.05500i | −1.63310 | + | 0.0650173i |
(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 | 216.2.q.a.97.2 | yes | 24 | |
3.2 | odd | 2 | 648.2.q.a.289.1 | 24 | |||
4.3 | odd | 2 | 432.2.u.e.97.3 | 24 | |||
27.5 | odd | 18 | 648.2.q.a.361.1 | 24 | |||
27.7 | even | 9 | 5832.2.a.h.1.3 | 12 | |||
27.20 | odd | 18 | 5832.2.a.i.1.10 | 12 | |||
27.22 | even | 9 | inner | 216.2.q.a.49.2 | ✓ | 24 | |
108.103 | odd | 18 | 432.2.u.e.49.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.q.a.49.2 | ✓ | 24 | 27.22 | even | 9 | inner | |
216.2.q.a.97.2 | yes | 24 | 1.1 | even | 1 | trivial | |
432.2.u.e.49.3 | 24 | 108.103 | odd | 18 | |||
432.2.u.e.97.3 | 24 | 4.3 | odd | 2 | |||
648.2.q.a.289.1 | 24 | 3.2 | odd | 2 | |||
648.2.q.a.361.1 | 24 | 27.5 | odd | 18 | |||
5832.2.a.h.1.3 | 12 | 27.7 | even | 9 | |||
5832.2.a.i.1.10 | 12 | 27.20 | odd | 18 |