Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.a (trivial) |
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: | yes |
Analytic conductor: | \(64.2156933055\) |
Analytic rank: | \(1\) |
Dimension: | \(67\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.63 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 2.47283 | 1.42769 | 0.713843 | − | 0.700305i | \(-0.246953\pi\) | ||||
0.713843 | + | 0.700305i | \(0.246953\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.183201 | 0.0819301 | 0.0409650 | − | 0.999161i | \(-0.486957\pi\) | ||||
0.0409650 | + | 0.999161i | \(0.486957\pi\) | |||||||
\(6\) | 2.47283 | 1.00953 | ||||||||
\(7\) | −1.10885 | −0.419107 | −0.209553 | − | 0.977797i | \(-0.567201\pi\) | ||||
−0.209553 | + | 0.977797i | \(0.567201\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.11487 | 1.03829 | ||||||||
\(10\) | 0.183201 | 0.0579333 | ||||||||
\(11\) | −6.09305 | −1.83712 | −0.918562 | − | 0.395278i | \(-0.870648\pi\) | ||||
−0.918562 | + | 0.395278i | \(0.870648\pi\) | |||||||
\(12\) | 2.47283 | 0.713843 | ||||||||
\(13\) | 0.147267 | 0.0408445 | 0.0204222 | − | 0.999791i | \(-0.493499\pi\) | ||||
0.0204222 | + | 0.999791i | \(0.493499\pi\) | |||||||
\(14\) | −1.10885 | −0.296353 | ||||||||
\(15\) | 0.453025 | 0.116970 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.55699 | −0.620160 | −0.310080 | − | 0.950710i | \(-0.600356\pi\) | ||||
−0.310080 | + | 0.950710i | \(0.600356\pi\) | |||||||
\(18\) | 3.11487 | 0.734182 | ||||||||
\(19\) | −2.37200 | −0.544174 | −0.272087 | − | 0.962273i | \(-0.587714\pi\) | ||||
−0.272087 | + | 0.962273i | \(0.587714\pi\) | |||||||
\(20\) | 0.183201 | 0.0409650 | ||||||||
\(21\) | −2.74200 | −0.598353 | ||||||||
\(22\) | −6.09305 | −1.29904 | ||||||||
\(23\) | −3.26269 | −0.680318 | −0.340159 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340159 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(24\) | 2.47283 | 0.504764 | ||||||||
\(25\) | −4.96644 | −0.993287 | ||||||||
\(26\) | 0.147267 | 0.0288814 | ||||||||
\(27\) | 0.284055 | 0.0546664 | ||||||||
\(28\) | −1.10885 | −0.209553 | ||||||||
\(29\) | 1.03517 | 0.192225 | 0.0961127 | − | 0.995370i | \(-0.469359\pi\) | ||||
0.0961127 | + | 0.995370i | \(0.469359\pi\) | |||||||
\(30\) | 0.453025 | 0.0827106 | ||||||||
\(31\) | 3.46406 | 0.622164 | 0.311082 | − | 0.950383i | \(-0.399309\pi\) | ||||
0.311082 | + | 0.950383i | \(0.399309\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −15.0671 | −2.62284 | ||||||||
\(34\) | −2.55699 | −0.438520 | ||||||||
\(35\) | −0.203143 | −0.0343374 | ||||||||
\(36\) | 3.11487 | 0.519145 | ||||||||
\(37\) | 3.31986 | 0.545781 | 0.272891 | − | 0.962045i | \(-0.412020\pi\) | ||||
0.272891 | + | 0.962045i | \(0.412020\pi\) | |||||||
\(38\) | −2.37200 | −0.384789 | ||||||||
\(39\) | 0.364165 | 0.0583131 | ||||||||
\(40\) | 0.183201 | 0.0289667 | ||||||||
\(41\) | −10.1172 | −1.58005 | −0.790023 | − | 0.613077i | \(-0.789931\pi\) | ||||
−0.790023 | + | 0.613077i | \(0.789931\pi\) | |||||||
\(42\) | −2.74200 | −0.423099 | ||||||||
\(43\) | −5.55485 | −0.847107 | −0.423553 | − | 0.905871i | \(-0.639217\pi\) | ||||
−0.423553 | + | 0.905871i | \(0.639217\pi\) | |||||||
\(44\) | −6.09305 | −0.918562 | ||||||||
\(45\) | 0.570648 | 0.0850672 | ||||||||
\(46\) | −3.26269 | −0.481058 | ||||||||
\(47\) | 1.64994 | 0.240669 | 0.120334 | − | 0.992733i | \(-0.461603\pi\) | ||||
0.120334 | + | 0.992733i | \(0.461603\pi\) | |||||||
\(48\) | 2.47283 | 0.356922 | ||||||||
\(49\) | −5.77045 | −0.824350 | ||||||||
\(50\) | −4.96644 | −0.702360 | ||||||||
\(51\) | −6.32298 | −0.885395 | ||||||||
\(52\) | 0.147267 | 0.0204222 | ||||||||
\(53\) | 2.63040 | 0.361313 | 0.180657 | − | 0.983546i | \(-0.442178\pi\) | ||||
0.180657 | + | 0.983546i | \(0.442178\pi\) | |||||||
\(54\) | 0.284055 | 0.0386550 | ||||||||
\(55\) | −1.11625 | −0.150516 | ||||||||
\(56\) | −1.10885 | −0.148177 | ||||||||
\(57\) | −5.86554 | −0.776910 | ||||||||
\(58\) | 1.03517 | 0.135924 | ||||||||
\(59\) | −4.61993 | −0.601463 | −0.300732 | − | 0.953709i | \(-0.597231\pi\) | ||||
−0.300732 | + | 0.953709i | \(0.597231\pi\) | |||||||
\(60\) | 0.453025 | 0.0584852 | ||||||||
\(61\) | 6.45638 | 0.826654 | 0.413327 | − | 0.910583i | \(-0.364367\pi\) | ||||
0.413327 | + | 0.910583i | \(0.364367\pi\) | |||||||
\(62\) | 3.46406 | 0.439936 | ||||||||
\(63\) | −3.45393 | −0.435154 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.0269795 | 0.00334639 | ||||||||
\(66\) | −15.0671 | −1.85463 | ||||||||
\(67\) | 8.78722 | 1.07353 | 0.536765 | − | 0.843732i | \(-0.319646\pi\) | ||||
0.536765 | + | 0.843732i | \(0.319646\pi\) | |||||||
\(68\) | −2.55699 | −0.310080 | ||||||||
\(69\) | −8.06807 | −0.971282 | ||||||||
\(70\) | −0.203143 | −0.0242802 | ||||||||
\(71\) | −0.468330 | −0.0555806 | −0.0277903 | − | 0.999614i | \(-0.508847\pi\) | ||||
−0.0277903 | + | 0.999614i | \(0.508847\pi\) | |||||||
\(72\) | 3.11487 | 0.367091 | ||||||||
\(73\) | −13.3090 | −1.55770 | −0.778848 | − | 0.627213i | \(-0.784196\pi\) | ||||
−0.778848 | + | 0.627213i | \(0.784196\pi\) | |||||||
\(74\) | 3.31986 | 0.385926 | ||||||||
\(75\) | −12.2811 | −1.41810 | ||||||||
\(76\) | −2.37200 | −0.272087 | ||||||||
\(77\) | 6.75629 | 0.769950 | ||||||||
\(78\) | 0.364165 | 0.0412336 | ||||||||
\(79\) | 8.13638 | 0.915414 | 0.457707 | − | 0.889103i | \(-0.348671\pi\) | ||||
0.457707 | + | 0.889103i | \(0.348671\pi\) | |||||||
\(80\) | 0.183201 | 0.0204825 | ||||||||
\(81\) | −8.64219 | −0.960244 | ||||||||
\(82\) | −10.1172 | −1.11726 | ||||||||
\(83\) | −10.0982 | −1.10842 | −0.554211 | − | 0.832376i | \(-0.686980\pi\) | ||||
−0.554211 | + | 0.832376i | \(0.686980\pi\) | |||||||
\(84\) | −2.74200 | −0.299176 | ||||||||
\(85\) | −0.468443 | −0.0508098 | ||||||||
\(86\) | −5.55485 | −0.598995 | ||||||||
\(87\) | 2.55978 | 0.274438 | ||||||||
\(88\) | −6.09305 | −0.649521 | ||||||||
\(89\) | 17.2007 | 1.82327 | 0.911634 | − | 0.411004i | \(-0.134822\pi\) | ||||
0.911634 | + | 0.411004i | \(0.134822\pi\) | |||||||
\(90\) | 0.570648 | 0.0601516 | ||||||||
\(91\) | −0.163297 | −0.0171182 | ||||||||
\(92\) | −3.26269 | −0.340159 | ||||||||
\(93\) | 8.56602 | 0.888255 | ||||||||
\(94\) | 1.64994 | 0.170179 | ||||||||
\(95\) | −0.434553 | −0.0445842 | ||||||||
\(96\) | 2.47283 | 0.252382 | ||||||||
\(97\) | −9.50991 | −0.965585 | −0.482793 | − | 0.875735i | \(-0.660378\pi\) | ||||
−0.482793 | + | 0.875735i | \(0.660378\pi\) | |||||||
\(98\) | −5.77045 | −0.582903 | ||||||||
\(99\) | −18.9791 | −1.90747 | ||||||||
\(100\) | −4.96644 | −0.496644 | ||||||||
\(101\) | 16.1242 | 1.60442 | 0.802210 | − | 0.597042i | \(-0.203657\pi\) | ||||
0.802210 | + | 0.597042i | \(0.203657\pi\) | |||||||
\(102\) | −6.32298 | −0.626069 | ||||||||
\(103\) | −5.38319 | −0.530422 | −0.265211 | − | 0.964190i | \(-0.585442\pi\) | ||||
−0.265211 | + | 0.964190i | \(0.585442\pi\) | |||||||
\(104\) | 0.147267 | 0.0144407 | ||||||||
\(105\) | −0.502337 | −0.0490231 | ||||||||
\(106\) | 2.63040 | 0.255487 | ||||||||
\(107\) | −3.46803 | −0.335267 | −0.167634 | − | 0.985849i | \(-0.553613\pi\) | ||||
−0.167634 | + | 0.985849i | \(0.553613\pi\) | |||||||
\(108\) | 0.284055 | 0.0273332 | ||||||||
\(109\) | −7.14898 | −0.684748 | −0.342374 | − | 0.939564i | \(-0.611231\pi\) | ||||
−0.342374 | + | 0.939564i | \(0.611231\pi\) | |||||||
\(110\) | −1.11625 | −0.106431 | ||||||||
\(111\) | 8.20943 | 0.779205 | ||||||||
\(112\) | −1.10885 | −0.104777 | ||||||||
\(113\) | −4.43458 | −0.417170 | −0.208585 | − | 0.978004i | \(-0.566886\pi\) | ||||
−0.208585 | + | 0.978004i | \(0.566886\pi\) | |||||||
\(114\) | −5.86554 | −0.549359 | ||||||||
\(115\) | −0.597729 | −0.0557385 | ||||||||
\(116\) | 1.03517 | 0.0961127 | ||||||||
\(117\) | 0.458717 | 0.0424084 | ||||||||
\(118\) | −4.61993 | −0.425299 | ||||||||
\(119\) | 2.83532 | 0.259913 | ||||||||
\(120\) | 0.453025 | 0.0413553 | ||||||||
\(121\) | 26.1252 | 2.37502 | ||||||||
\(122\) | 6.45638 | 0.584533 | ||||||||
\(123\) | −25.0182 | −2.25581 | ||||||||
\(124\) | 3.46406 | 0.311082 | ||||||||
\(125\) | −1.82586 | −0.163310 | ||||||||
\(126\) | −3.45393 | −0.307700 | ||||||||
\(127\) | −20.5120 | −1.82014 | −0.910071 | − | 0.414453i | \(-0.863973\pi\) | ||||
−0.910071 | + | 0.414453i | \(0.863973\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −13.7362 | −1.20940 | ||||||||
\(130\) | 0.0269795 | 0.00236626 | ||||||||
\(131\) | 9.46249 | 0.826742 | 0.413371 | − | 0.910563i | \(-0.364351\pi\) | ||||
0.413371 | + | 0.910563i | \(0.364351\pi\) | |||||||
\(132\) | −15.0671 | −1.31142 | ||||||||
\(133\) | 2.63020 | 0.228067 | ||||||||
\(134\) | 8.78722 | 0.759100 | ||||||||
\(135\) | 0.0520392 | 0.00447882 | ||||||||
\(136\) | −2.55699 | −0.219260 | ||||||||
\(137\) | 6.24595 | 0.533627 | 0.266814 | − | 0.963748i | \(-0.414029\pi\) | ||||
0.266814 | + | 0.963748i | \(0.414029\pi\) | |||||||
\(138\) | −8.06807 | −0.686800 | ||||||||
\(139\) | 7.54672 | 0.640104 | 0.320052 | − | 0.947400i | \(-0.396300\pi\) | ||||
0.320052 | + | 0.947400i | \(0.396300\pi\) | |||||||
\(140\) | −0.203143 | −0.0171687 | ||||||||
\(141\) | 4.08002 | 0.343600 | ||||||||
\(142\) | −0.468330 | −0.0393014 | ||||||||
\(143\) | −0.897304 | −0.0750363 | ||||||||
\(144\) | 3.11487 | 0.259573 | ||||||||
\(145\) | 0.189643 | 0.0157490 | ||||||||
\(146\) | −13.3090 | −1.10146 | ||||||||
\(147\) | −14.2693 | −1.17691 | ||||||||
\(148\) | 3.31986 | 0.272891 | ||||||||
\(149\) | 6.14251 | 0.503214 | 0.251607 | − | 0.967829i | \(-0.419041\pi\) | ||||
0.251607 | + | 0.967829i | \(0.419041\pi\) | |||||||
\(150\) | −12.2811 | −1.00275 | ||||||||
\(151\) | 8.45338 | 0.687926 | 0.343963 | − | 0.938983i | \(-0.388231\pi\) | ||||
0.343963 | + | 0.938983i | \(0.388231\pi\) | |||||||
\(152\) | −2.37200 | −0.192395 | ||||||||
\(153\) | −7.96468 | −0.643906 | ||||||||
\(154\) | 6.75629 | 0.544437 | ||||||||
\(155\) | 0.634620 | 0.0509739 | ||||||||
\(156\) | 0.364165 | 0.0291566 | ||||||||
\(157\) | −14.5966 | −1.16493 | −0.582467 | − | 0.812855i | \(-0.697912\pi\) | ||||
−0.582467 | + | 0.812855i | \(0.697912\pi\) | |||||||
\(158\) | 8.13638 | 0.647295 | ||||||||
\(159\) | 6.50452 | 0.515842 | ||||||||
\(160\) | 0.183201 | 0.0144833 | ||||||||
\(161\) | 3.61784 | 0.285126 | ||||||||
\(162\) | −8.64219 | −0.678995 | ||||||||
\(163\) | −3.38562 | −0.265182 | −0.132591 | − | 0.991171i | \(-0.542330\pi\) | ||||
−0.132591 | + | 0.991171i | \(0.542330\pi\) | |||||||
\(164\) | −10.1172 | −0.790023 | ||||||||
\(165\) | −2.76030 | −0.214889 | ||||||||
\(166\) | −10.0982 | −0.783773 | ||||||||
\(167\) | 15.2464 | 1.17981 | 0.589903 | − | 0.807474i | \(-0.299166\pi\) | ||||
0.589903 | + | 0.807474i | \(0.299166\pi\) | |||||||
\(168\) | −2.74200 | −0.211550 | ||||||||
\(169\) | −12.9783 | −0.998332 | ||||||||
\(170\) | −0.468443 | −0.0359279 | ||||||||
\(171\) | −7.38847 | −0.565011 | ||||||||
\(172\) | −5.55485 | −0.423553 | ||||||||
\(173\) | −6.34616 | −0.482489 | −0.241245 | − | 0.970464i | \(-0.577556\pi\) | ||||
−0.241245 | + | 0.970464i | \(0.577556\pi\) | |||||||
\(174\) | 2.55978 | 0.194057 | ||||||||
\(175\) | 5.50704 | 0.416293 | ||||||||
\(176\) | −6.09305 | −0.459281 | ||||||||
\(177\) | −11.4243 | −0.858701 | ||||||||
\(178\) | 17.2007 | 1.28924 | ||||||||
\(179\) | 11.4406 | 0.855109 | 0.427555 | − | 0.903990i | \(-0.359375\pi\) | ||||
0.427555 | + | 0.903990i | \(0.359375\pi\) | |||||||
\(180\) | 0.570648 | 0.0425336 | ||||||||
\(181\) | 7.37118 | 0.547896 | 0.273948 | − | 0.961745i | \(-0.411670\pi\) | ||||
0.273948 | + | 0.961745i | \(0.411670\pi\) | |||||||
\(182\) | −0.163297 | −0.0121044 | ||||||||
\(183\) | 15.9655 | 1.18020 | ||||||||
\(184\) | −3.26269 | −0.240529 | ||||||||
\(185\) | 0.608202 | 0.0447159 | ||||||||
\(186\) | 8.56602 | 0.628091 | ||||||||
\(187\) | 15.5798 | 1.13931 | ||||||||
\(188\) | 1.64994 | 0.120334 | ||||||||
\(189\) | −0.314975 | −0.0229110 | ||||||||
\(190\) | −0.434553 | −0.0315258 | ||||||||
\(191\) | 12.3229 | 0.891656 | 0.445828 | − | 0.895119i | \(-0.352909\pi\) | ||||
0.445828 | + | 0.895119i | \(0.352909\pi\) | |||||||
\(192\) | 2.47283 | 0.178461 | ||||||||
\(193\) | −23.3237 | −1.67887 | −0.839437 | − | 0.543457i | \(-0.817115\pi\) | ||||
−0.839437 | + | 0.543457i | \(0.817115\pi\) | |||||||
\(194\) | −9.50991 | −0.682772 | ||||||||
\(195\) | 0.0667155 | 0.00477760 | ||||||||
\(196\) | −5.77045 | −0.412175 | ||||||||
\(197\) | −17.6664 | −1.25868 | −0.629341 | − | 0.777130i | \(-0.716675\pi\) | ||||
−0.629341 | + | 0.777130i | \(0.716675\pi\) | |||||||
\(198\) | −18.9791 | −1.34878 | ||||||||
\(199\) | −11.2536 | −0.797748 | −0.398874 | − | 0.917006i | \(-0.630599\pi\) | ||||
−0.398874 | + | 0.917006i | \(0.630599\pi\) | |||||||
\(200\) | −4.96644 | −0.351180 | ||||||||
\(201\) | 21.7293 | 1.53266 | ||||||||
\(202\) | 16.1242 | 1.13450 | ||||||||
\(203\) | −1.14784 | −0.0805629 | ||||||||
\(204\) | −6.32298 | −0.442697 | ||||||||
\(205\) | −1.85349 | −0.129453 | ||||||||
\(206\) | −5.38319 | −0.375065 | ||||||||
\(207\) | −10.1629 | −0.706368 | ||||||||
\(208\) | 0.147267 | 0.0102111 | ||||||||
\(209\) | 14.4527 | 0.999715 | ||||||||
\(210\) | −0.502337 | −0.0346646 | ||||||||
\(211\) | 10.2433 | 0.705177 | 0.352588 | − | 0.935779i | \(-0.385302\pi\) | ||||
0.352588 | + | 0.935779i | \(0.385302\pi\) | |||||||
\(212\) | 2.63040 | 0.180657 | ||||||||
\(213\) | −1.15810 | −0.0793517 | ||||||||
\(214\) | −3.46803 | −0.237070 | ||||||||
\(215\) | −1.01766 | −0.0694035 | ||||||||
\(216\) | 0.284055 | 0.0193275 | ||||||||
\(217\) | −3.84113 | −0.260753 | ||||||||
\(218\) | −7.14898 | −0.484190 | ||||||||
\(219\) | −32.9107 | −2.22390 | ||||||||
\(220\) | −1.11625 | −0.0752578 | ||||||||
\(221\) | −0.376559 | −0.0253301 | ||||||||
\(222\) | 8.20943 | 0.550981 | ||||||||
\(223\) | 12.9734 | 0.868760 | 0.434380 | − | 0.900730i | \(-0.356967\pi\) | ||||
0.434380 | + | 0.900730i | \(0.356967\pi\) | |||||||
\(224\) | −1.10885 | −0.0740883 | ||||||||
\(225\) | −15.4698 | −1.03132 | ||||||||
\(226\) | −4.43458 | −0.294984 | ||||||||
\(227\) | −22.7690 | −1.51123 | −0.755616 | − | 0.655015i | \(-0.772662\pi\) | ||||
−0.755616 | + | 0.655015i | \(0.772662\pi\) | |||||||
\(228\) | −5.86554 | −0.388455 | ||||||||
\(229\) | −2.30148 | −0.152086 | −0.0760430 | − | 0.997105i | \(-0.524229\pi\) | ||||
−0.0760430 | + | 0.997105i | \(0.524229\pi\) | |||||||
\(230\) | −0.597729 | −0.0394131 | ||||||||
\(231\) | 16.7071 | 1.09925 | ||||||||
\(232\) | 1.03517 | 0.0679619 | ||||||||
\(233\) | 21.4748 | 1.40686 | 0.703430 | − | 0.710764i | \(-0.251651\pi\) | ||||
0.703430 | + | 0.710764i | \(0.251651\pi\) | |||||||
\(234\) | 0.458717 | 0.0299873 | ||||||||
\(235\) | 0.302272 | 0.0197180 | ||||||||
\(236\) | −4.61993 | −0.300732 | ||||||||
\(237\) | 20.1198 | 1.30692 | ||||||||
\(238\) | 2.83532 | 0.183786 | ||||||||
\(239\) | −7.14563 | −0.462213 | −0.231106 | − | 0.972929i | \(-0.574235\pi\) | ||||
−0.231106 | + | 0.972929i | \(0.574235\pi\) | |||||||
\(240\) | 0.453025 | 0.0292426 | ||||||||
\(241\) | 0.514479 | 0.0331405 | 0.0165703 | − | 0.999863i | \(-0.494725\pi\) | ||||
0.0165703 | + | 0.999863i | \(0.494725\pi\) | |||||||
\(242\) | 26.1252 | 1.67939 | ||||||||
\(243\) | −22.2228 | −1.42559 | ||||||||
\(244\) | 6.45638 | 0.413327 | ||||||||
\(245\) | −1.05715 | −0.0675390 | ||||||||
\(246\) | −25.0182 | −1.59510 | ||||||||
\(247\) | −0.349317 | −0.0222265 | ||||||||
\(248\) | 3.46406 | 0.219968 | ||||||||
\(249\) | −24.9711 | −1.58248 | ||||||||
\(250\) | −1.82586 | −0.115478 | ||||||||
\(251\) | −8.33417 | −0.526048 | −0.263024 | − | 0.964789i | \(-0.584720\pi\) | ||||
−0.263024 | + | 0.964789i | \(0.584720\pi\) | |||||||
\(252\) | −3.45393 | −0.217577 | ||||||||
\(253\) | 19.8797 | 1.24983 | ||||||||
\(254\) | −20.5120 | −1.28703 | ||||||||
\(255\) | −1.15838 | −0.0725405 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.2387 | 1.76148 | 0.880742 | − | 0.473596i | \(-0.157044\pi\) | ||||
0.880742 | + | 0.473596i | \(0.157044\pi\) | |||||||
\(258\) | −13.7362 | −0.855177 | ||||||||
\(259\) | −3.68123 | −0.228741 | ||||||||
\(260\) | 0.0269795 | 0.00167320 | ||||||||
\(261\) | 3.22441 | 0.199586 | ||||||||
\(262\) | 9.46249 | 0.584595 | ||||||||
\(263\) | 17.7534 | 1.09472 | 0.547360 | − | 0.836897i | \(-0.315633\pi\) | ||||
0.547360 | + | 0.836897i | \(0.315633\pi\) | |||||||
\(264\) | −15.0671 | −0.927313 | ||||||||
\(265\) | 0.481893 | 0.0296024 | ||||||||
\(266\) | 2.63020 | 0.161268 | ||||||||
\(267\) | 42.5343 | 2.60306 | ||||||||
\(268\) | 8.78722 | 0.536765 | ||||||||
\(269\) | 6.26438 | 0.381946 | 0.190973 | − | 0.981595i | \(-0.438836\pi\) | ||||
0.190973 | + | 0.981595i | \(0.438836\pi\) | |||||||
\(270\) | 0.0520392 | 0.00316700 | ||||||||
\(271\) | 10.3591 | 0.629271 | 0.314636 | − | 0.949212i | \(-0.398118\pi\) | ||||
0.314636 | + | 0.949212i | \(0.398118\pi\) | |||||||
\(272\) | −2.55699 | −0.155040 | ||||||||
\(273\) | −0.403805 | −0.0244394 | ||||||||
\(274\) | 6.24595 | 0.377332 | ||||||||
\(275\) | 30.2607 | 1.82479 | ||||||||
\(276\) | −8.06807 | −0.485641 | ||||||||
\(277\) | −23.9326 | −1.43797 | −0.718985 | − | 0.695026i | \(-0.755393\pi\) | ||||
−0.718985 | + | 0.695026i | \(0.755393\pi\) | |||||||
\(278\) | 7.54672 | 0.452622 | ||||||||
\(279\) | 10.7901 | 0.645986 | ||||||||
\(280\) | −0.203143 | −0.0121401 | ||||||||
\(281\) | −7.88074 | −0.470126 | −0.235063 | − | 0.971980i | \(-0.575530\pi\) | ||||
−0.235063 | + | 0.971980i | \(0.575530\pi\) | |||||||
\(282\) | 4.08002 | 0.242962 | ||||||||
\(283\) | −9.88057 | −0.587339 | −0.293669 | − | 0.955907i | \(-0.594876\pi\) | ||||
−0.293669 | + | 0.955907i | \(0.594876\pi\) | |||||||
\(284\) | −0.468330 | −0.0277903 | ||||||||
\(285\) | −1.07457 | −0.0636523 | ||||||||
\(286\) | −0.897304 | −0.0530587 | ||||||||
\(287\) | 11.2185 | 0.662208 | ||||||||
\(288\) | 3.11487 | 0.183546 | ||||||||
\(289\) | −10.4618 | −0.615401 | ||||||||
\(290\) | 0.189643 | 0.0111362 | ||||||||
\(291\) | −23.5164 | −1.37855 | ||||||||
\(292\) | −13.3090 | −0.778848 | ||||||||
\(293\) | −1.56316 | −0.0913210 | −0.0456605 | − | 0.998957i | \(-0.514539\pi\) | ||||
−0.0456605 | + | 0.998957i | \(0.514539\pi\) | |||||||
\(294\) | −14.2693 | −0.832203 | ||||||||
\(295\) | −0.846376 | −0.0492779 | ||||||||
\(296\) | 3.31986 | 0.192963 | ||||||||
\(297\) | −1.73076 | −0.100429 | ||||||||
\(298\) | 6.14251 | 0.355826 | ||||||||
\(299\) | −0.480486 | −0.0277872 | ||||||||
\(300\) | −12.2811 | −0.709052 | ||||||||
\(301\) | 6.15951 | 0.355028 | ||||||||
\(302\) | 8.45338 | 0.486437 | ||||||||
\(303\) | 39.8724 | 2.29061 | ||||||||
\(304\) | −2.37200 | −0.136044 | ||||||||
\(305\) | 1.18282 | 0.0677278 | ||||||||
\(306\) | −7.96468 | −0.455311 | ||||||||
\(307\) | −1.67312 | −0.0954899 | −0.0477450 | − | 0.998860i | \(-0.515203\pi\) | ||||
−0.0477450 | + | 0.998860i | \(0.515203\pi\) | |||||||
\(308\) | 6.75629 | 0.384975 | ||||||||
\(309\) | −13.3117 | −0.757276 | ||||||||
\(310\) | 0.634620 | 0.0360440 | ||||||||
\(311\) | 8.55050 | 0.484854 | 0.242427 | − | 0.970170i | \(-0.422056\pi\) | ||||
0.242427 | + | 0.970170i | \(0.422056\pi\) | |||||||
\(312\) | 0.364165 | 0.0206168 | ||||||||
\(313\) | −5.99853 | −0.339057 | −0.169528 | − | 0.985525i | \(-0.554224\pi\) | ||||
−0.169528 | + | 0.985525i | \(0.554224\pi\) | |||||||
\(314\) | −14.5966 | −0.823732 | ||||||||
\(315\) | −0.632764 | −0.0356522 | ||||||||
\(316\) | 8.13638 | 0.457707 | ||||||||
\(317\) | −19.4961 | −1.09501 | −0.547505 | − | 0.836802i | \(-0.684422\pi\) | ||||
−0.547505 | + | 0.836802i | \(0.684422\pi\) | |||||||
\(318\) | 6.50452 | 0.364756 | ||||||||
\(319\) | −6.30731 | −0.353142 | ||||||||
\(320\) | 0.183201 | 0.0102413 | ||||||||
\(321\) | −8.57584 | −0.478657 | ||||||||
\(322\) | 3.61784 | 0.201614 | ||||||||
\(323\) | 6.06517 | 0.337475 | ||||||||
\(324\) | −8.64219 | −0.480122 | ||||||||
\(325\) | −0.731392 | −0.0405703 | ||||||||
\(326\) | −3.38562 | −0.187512 | ||||||||
\(327\) | −17.6782 | −0.977606 | ||||||||
\(328\) | −10.1172 | −0.558631 | ||||||||
\(329\) | −1.82954 | −0.100866 | ||||||||
\(330\) | −2.76030 | −0.151950 | ||||||||
\(331\) | 3.23070 | 0.177575 | 0.0887876 | − | 0.996051i | \(-0.471701\pi\) | ||||
0.0887876 | + | 0.996051i | \(0.471701\pi\) | |||||||
\(332\) | −10.0982 | −0.554211 | ||||||||
\(333\) | 10.3409 | 0.566679 | ||||||||
\(334\) | 15.2464 | 0.834248 | ||||||||
\(335\) | 1.60983 | 0.0879543 | ||||||||
\(336\) | −2.74200 | −0.149588 | ||||||||
\(337\) | 12.9842 | 0.707292 | 0.353646 | − | 0.935379i | \(-0.384942\pi\) | ||||
0.353646 | + | 0.935379i | \(0.384942\pi\) | |||||||
\(338\) | −12.9783 | −0.705927 | ||||||||
\(339\) | −10.9659 | −0.595588 | ||||||||
\(340\) | −0.468443 | −0.0254049 | ||||||||
\(341\) | −21.1067 | −1.14299 | ||||||||
\(342\) | −7.38847 | −0.399523 | ||||||||
\(343\) | 14.1605 | 0.764597 | ||||||||
\(344\) | −5.55485 | −0.299497 | ||||||||
\(345\) | −1.47808 | −0.0795772 | ||||||||
\(346\) | −6.34616 | −0.341171 | ||||||||
\(347\) | −2.32541 | −0.124834 | −0.0624172 | − | 0.998050i | \(-0.519881\pi\) | ||||
−0.0624172 | + | 0.998050i | \(0.519881\pi\) | |||||||
\(348\) | 2.55978 | 0.137219 | ||||||||
\(349\) | 22.9593 | 1.22898 | 0.614491 | − | 0.788924i | \(-0.289362\pi\) | ||||
0.614491 | + | 0.788924i | \(0.289362\pi\) | |||||||
\(350\) | 5.50704 | 0.294364 | ||||||||
\(351\) | 0.0418318 | 0.00223282 | ||||||||
\(352\) | −6.09305 | −0.324761 | ||||||||
\(353\) | −17.7095 | −0.942581 | −0.471291 | − | 0.881978i | \(-0.656212\pi\) | ||||
−0.471291 | + | 0.881978i | \(0.656212\pi\) | |||||||
\(354\) | −11.4243 | −0.607193 | ||||||||
\(355\) | −0.0857987 | −0.00455372 | ||||||||
\(356\) | 17.2007 | 0.911634 | ||||||||
\(357\) | 7.01125 | 0.371075 | ||||||||
\(358\) | 11.4406 | 0.604654 | ||||||||
\(359\) | 30.8355 | 1.62744 | 0.813719 | − | 0.581259i | \(-0.197440\pi\) | ||||
0.813719 | + | 0.581259i | \(0.197440\pi\) | |||||||
\(360\) | 0.570648 | 0.0300758 | ||||||||
\(361\) | −13.3736 | −0.703875 | ||||||||
\(362\) | 7.37118 | 0.387421 | ||||||||
\(363\) | 64.6032 | 3.39079 | ||||||||
\(364\) | −0.163297 | −0.00855909 | ||||||||
\(365\) | −2.43822 | −0.127622 | ||||||||
\(366\) | 15.9655 | 0.834530 | ||||||||
\(367\) | 12.9844 | 0.677779 | 0.338889 | − | 0.940826i | \(-0.389949\pi\) | ||||
0.338889 | + | 0.940826i | \(0.389949\pi\) | |||||||
\(368\) | −3.26269 | −0.170080 | ||||||||
\(369\) | −31.5139 | −1.64055 | ||||||||
\(370\) | 0.608202 | 0.0316189 | ||||||||
\(371\) | −2.91672 | −0.151429 | ||||||||
\(372\) | 8.56602 | 0.444128 | ||||||||
\(373\) | −16.8227 | −0.871047 | −0.435523 | − | 0.900177i | \(-0.643437\pi\) | ||||
−0.435523 | + | 0.900177i | \(0.643437\pi\) | |||||||
\(374\) | 15.5798 | 0.805615 | ||||||||
\(375\) | −4.51504 | −0.233156 | ||||||||
\(376\) | 1.64994 | 0.0850893 | ||||||||
\(377\) | 0.152445 | 0.00785134 | ||||||||
\(378\) | −0.314975 | −0.0162005 | ||||||||
\(379\) | 25.8009 | 1.32531 | 0.662653 | − | 0.748927i | \(-0.269431\pi\) | ||||
0.662653 | + | 0.748927i | \(0.269431\pi\) | |||||||
\(380\) | −0.434553 | −0.0222921 | ||||||||
\(381\) | −50.7225 | −2.59859 | ||||||||
\(382\) | 12.3229 | 0.630496 | ||||||||
\(383\) | 2.87242 | 0.146774 | 0.0733869 | − | 0.997304i | \(-0.476619\pi\) | ||||
0.0733869 | + | 0.997304i | \(0.476619\pi\) | |||||||
\(384\) | 2.47283 | 0.126191 | ||||||||
\(385\) | 1.23776 | 0.0630821 | ||||||||
\(386\) | −23.3237 | −1.18714 | ||||||||
\(387\) | −17.3026 | −0.879543 | ||||||||
\(388\) | −9.50991 | −0.482793 | ||||||||
\(389\) | −31.4507 | −1.59461 | −0.797306 | − | 0.603575i | \(-0.793742\pi\) | ||||
−0.797306 | + | 0.603575i | \(0.793742\pi\) | |||||||
\(390\) | 0.0667155 | 0.00337827 | ||||||||
\(391\) | 8.34266 | 0.421906 | ||||||||
\(392\) | −5.77045 | −0.291452 | ||||||||
\(393\) | 23.3991 | 1.18033 | ||||||||
\(394\) | −17.6664 | −0.890022 | ||||||||
\(395\) | 1.49059 | 0.0749999 | ||||||||
\(396\) | −18.9791 | −0.953733 | ||||||||
\(397\) | −1.11182 | −0.0558008 | −0.0279004 | − | 0.999611i | \(-0.508882\pi\) | ||||
−0.0279004 | + | 0.999611i | \(0.508882\pi\) | |||||||
\(398\) | −11.2536 | −0.564093 | ||||||||
\(399\) | 6.50402 | 0.325608 | ||||||||
\(400\) | −4.96644 | −0.248322 | ||||||||
\(401\) | −12.7527 | −0.636839 | −0.318419 | − | 0.947950i | \(-0.603152\pi\) | ||||
−0.318419 | + | 0.947950i | \(0.603152\pi\) | |||||||
\(402\) | 21.7293 | 1.08376 | ||||||||
\(403\) | 0.510141 | 0.0254119 | ||||||||
\(404\) | 16.1242 | 0.802210 | ||||||||
\(405\) | −1.58326 | −0.0786728 | ||||||||
\(406\) | −1.14784 | −0.0569666 | ||||||||
\(407\) | −20.2281 | −1.00267 | ||||||||
\(408\) | −6.32298 | −0.313034 | ||||||||
\(409\) | −27.3108 | −1.35043 | −0.675217 | − | 0.737620i | \(-0.735950\pi\) | ||||
−0.675217 | + | 0.737620i | \(0.735950\pi\) | |||||||
\(410\) | −1.85349 | −0.0915373 | ||||||||
\(411\) | 15.4451 | 0.761853 | ||||||||
\(412\) | −5.38319 | −0.265211 | ||||||||
\(413\) | 5.12281 | 0.252077 | ||||||||
\(414\) | −10.1629 | −0.499477 | ||||||||
\(415\) | −1.85000 | −0.0908132 | ||||||||
\(416\) | 0.147267 | 0.00722035 | ||||||||
\(417\) | 18.6617 | 0.913869 | ||||||||
\(418\) | 14.4527 | 0.706905 | ||||||||
\(419\) | −12.6594 | −0.618454 | −0.309227 | − | 0.950988i | \(-0.600070\pi\) | ||||
−0.309227 | + | 0.950988i | \(0.600070\pi\) | |||||||
\(420\) | −0.502337 | −0.0245115 | ||||||||
\(421\) | 12.2017 | 0.594675 | 0.297337 | − | 0.954772i | \(-0.403901\pi\) | ||||
0.297337 | + | 0.954772i | \(0.403901\pi\) | |||||||
\(422\) | 10.2433 | 0.498635 | ||||||||
\(423\) | 5.13936 | 0.249884 | ||||||||
\(424\) | 2.63040 | 0.127744 | ||||||||
\(425\) | 12.6991 | 0.615998 | ||||||||
\(426\) | −1.15810 | −0.0561101 | ||||||||
\(427\) | −7.15916 | −0.346456 | ||||||||
\(428\) | −3.46803 | −0.167634 | ||||||||
\(429\) | −2.21888 | −0.107128 | ||||||||
\(430\) | −1.01766 | −0.0490757 | ||||||||
\(431\) | −6.39065 | −0.307827 | −0.153913 | − | 0.988084i | \(-0.549188\pi\) | ||||
−0.153913 | + | 0.988084i | \(0.549188\pi\) | |||||||
\(432\) | 0.284055 | 0.0136666 | ||||||||
\(433\) | 8.54652 | 0.410720 | 0.205360 | − | 0.978687i | \(-0.434164\pi\) | ||||
0.205360 | + | 0.978687i | \(0.434164\pi\) | |||||||
\(434\) | −3.84113 | −0.184380 | ||||||||
\(435\) | 0.468955 | 0.0224847 | ||||||||
\(436\) | −7.14898 | −0.342374 | ||||||||
\(437\) | 7.73911 | 0.370212 | ||||||||
\(438\) | −32.9107 | −1.57254 | ||||||||
\(439\) | −0.779523 | −0.0372046 | −0.0186023 | − | 0.999827i | \(-0.505922\pi\) | ||||
−0.0186023 | + | 0.999827i | \(0.505922\pi\) | |||||||
\(440\) | −1.11625 | −0.0532153 | ||||||||
\(441\) | −17.9742 | −0.855914 | ||||||||
\(442\) | −0.376559 | −0.0179111 | ||||||||
\(443\) | −2.87892 | −0.136782 | −0.0683909 | − | 0.997659i | \(-0.521786\pi\) | ||||
−0.0683909 | + | 0.997659i | \(0.521786\pi\) | |||||||
\(444\) | 8.20943 | 0.389602 | ||||||||
\(445\) | 3.15118 | 0.149380 | ||||||||
\(446\) | 12.9734 | 0.614306 | ||||||||
\(447\) | 15.1894 | 0.718432 | ||||||||
\(448\) | −1.10885 | −0.0523883 | ||||||||
\(449\) | 1.51382 | 0.0714418 | 0.0357209 | − | 0.999362i | \(-0.488627\pi\) | ||||
0.0357209 | + | 0.999362i | \(0.488627\pi\) | |||||||
\(450\) | −15.4698 | −0.729254 | ||||||||
\(451\) | 61.6448 | 2.90274 | ||||||||
\(452\) | −4.43458 | −0.208585 | ||||||||
\(453\) | 20.9037 | 0.982143 | ||||||||
\(454\) | −22.7690 | −1.06860 | ||||||||
\(455\) | −0.0299162 | −0.00140249 | ||||||||
\(456\) | −5.86554 | −0.274679 | ||||||||
\(457\) | −5.83393 | −0.272900 | −0.136450 | − | 0.990647i | \(-0.543569\pi\) | ||||
−0.136450 | + | 0.990647i | \(0.543569\pi\) | |||||||
\(458\) | −2.30148 | −0.107541 | ||||||||
\(459\) | −0.726324 | −0.0339019 | ||||||||
\(460\) | −0.597729 | −0.0278693 | ||||||||
\(461\) | −14.3110 | −0.666530 | −0.333265 | − | 0.942833i | \(-0.608150\pi\) | ||||
−0.333265 | + | 0.942833i | \(0.608150\pi\) | |||||||
\(462\) | 16.7071 | 0.777286 | ||||||||
\(463\) | −21.2913 | −0.989490 | −0.494745 | − | 0.869038i | \(-0.664739\pi\) | ||||
−0.494745 | + | 0.869038i | \(0.664739\pi\) | |||||||
\(464\) | 1.03517 | 0.0480563 | ||||||||
\(465\) | 1.56931 | 0.0727748 | ||||||||
\(466\) | 21.4748 | 0.994801 | ||||||||
\(467\) | −11.1190 | −0.514528 | −0.257264 | − | 0.966341i | \(-0.582821\pi\) | ||||
−0.257264 | + | 0.966341i | \(0.582821\pi\) | |||||||
\(468\) | 0.458717 | 0.0212042 | ||||||||
\(469\) | −9.74372 | −0.449923 | ||||||||
\(470\) | 0.302272 | 0.0139427 | ||||||||
\(471\) | −36.0948 | −1.66316 | ||||||||
\(472\) | −4.61993 | −0.212649 | ||||||||
\(473\) | 33.8460 | 1.55624 | ||||||||
\(474\) | 20.1198 | 0.924135 | ||||||||
\(475\) | 11.7804 | 0.540521 | ||||||||
\(476\) | 2.83532 | 0.129957 | ||||||||
\(477\) | 8.19336 | 0.375148 | ||||||||
\(478\) | −7.14563 | −0.326834 | ||||||||
\(479\) | 28.7405 | 1.31319 | 0.656593 | − | 0.754245i | \(-0.271997\pi\) | ||||
0.656593 | + | 0.754245i | \(0.271997\pi\) | |||||||
\(480\) | 0.453025 | 0.0206777 | ||||||||
\(481\) | 0.488905 | 0.0222922 | ||||||||
\(482\) | 0.514479 | 0.0234339 | ||||||||
\(483\) | 8.94629 | 0.407070 | ||||||||
\(484\) | 26.1252 | 1.18751 | ||||||||
\(485\) | −1.74223 | −0.0791105 | ||||||||
\(486\) | −22.2228 | −1.00805 | ||||||||
\(487\) | 16.5753 | 0.751100 | 0.375550 | − | 0.926802i | \(-0.377454\pi\) | ||||
0.375550 | + | 0.926802i | \(0.377454\pi\) | |||||||
\(488\) | 6.45638 | 0.292266 | ||||||||
\(489\) | −8.37205 | −0.378597 | ||||||||
\(490\) | −1.05715 | −0.0477573 | ||||||||
\(491\) | −29.4508 | −1.32910 | −0.664548 | − | 0.747246i | \(-0.731376\pi\) | ||||
−0.664548 | + | 0.747246i | \(0.731376\pi\) | |||||||
\(492\) | −25.0182 | −1.12791 | ||||||||
\(493\) | −2.64690 | −0.119211 | ||||||||
\(494\) | −0.349317 | −0.0157165 | ||||||||
\(495\) | −3.47699 | −0.156279 | ||||||||
\(496\) | 3.46406 | 0.155541 | ||||||||
\(497\) | 0.519309 | 0.0232942 | ||||||||
\(498\) | −24.9711 | −1.11898 | ||||||||
\(499\) | −3.93211 | −0.176026 | −0.0880128 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880128 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(500\) | −1.82586 | −0.0816551 | ||||||||
\(501\) | 37.7018 | 1.68439 | ||||||||
\(502\) | −8.33417 | −0.371972 | ||||||||
\(503\) | 38.5297 | 1.71796 | 0.858978 | − | 0.512013i | \(-0.171100\pi\) | ||||
0.858978 | + | 0.512013i | \(0.171100\pi\) | |||||||
\(504\) | −3.45393 | −0.153850 | ||||||||
\(505\) | 2.95398 | 0.131450 | ||||||||
\(506\) | 19.8797 | 0.883762 | ||||||||
\(507\) | −32.0931 | −1.42531 | ||||||||
\(508\) | −20.5120 | −0.910071 | ||||||||
\(509\) | 35.2800 | 1.56376 | 0.781879 | − | 0.623430i | \(-0.214261\pi\) | ||||
0.781879 | + | 0.623430i | \(0.214261\pi\) | |||||||
\(510\) | −1.15838 | −0.0512939 | ||||||||
\(511\) | 14.7577 | 0.652840 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.673778 | −0.0297480 | ||||||||
\(514\) | 28.2387 | 1.24556 | ||||||||
\(515\) | −0.986207 | −0.0434575 | ||||||||
\(516\) | −13.7362 | −0.604702 | ||||||||
\(517\) | −10.0532 | −0.442138 | ||||||||
\(518\) | −3.68123 | −0.161744 | ||||||||
\(519\) | −15.6929 | −0.688844 | ||||||||
\(520\) | 0.0269795 | 0.00118313 | ||||||||
\(521\) | 23.9501 | 1.04927 | 0.524636 | − | 0.851326i | \(-0.324201\pi\) | ||||
0.524636 | + | 0.851326i | \(0.324201\pi\) | |||||||
\(522\) | 3.22441 | 0.141128 | ||||||||
\(523\) | −39.3010 | −1.71851 | −0.859257 | − | 0.511545i | \(-0.829074\pi\) | ||||
−0.859257 | + | 0.511545i | \(0.829074\pi\) | |||||||
\(524\) | 9.46249 | 0.413371 | ||||||||
\(525\) | 13.6180 | 0.594336 | ||||||||
\(526\) | 17.7534 | 0.774084 | ||||||||
\(527\) | −8.85756 | −0.385841 | ||||||||
\(528\) | −15.0671 | −0.655709 | ||||||||
\(529\) | −12.3548 | −0.537167 | ||||||||
\(530\) | 0.481893 | 0.0209321 | ||||||||
\(531\) | −14.3905 | −0.624493 | ||||||||
\(532\) | 2.63020 | 0.114033 | ||||||||
\(533\) | −1.48993 | −0.0645361 | ||||||||
\(534\) | 42.5343 | 1.84064 | ||||||||
\(535\) | −0.635347 | −0.0274685 | ||||||||
\(536\) | 8.78722 | 0.379550 | ||||||||
\(537\) | 28.2906 | 1.22083 | ||||||||
\(538\) | 6.26438 | 0.270077 | ||||||||
\(539\) | 35.1596 | 1.51443 | ||||||||
\(540\) | 0.0520392 | 0.00223941 | ||||||||
\(541\) | −29.7835 | −1.28049 | −0.640246 | − | 0.768170i | \(-0.721168\pi\) | ||||
−0.640246 | + | 0.768170i | \(0.721168\pi\) | |||||||
\(542\) | 10.3591 | 0.444962 | ||||||||
\(543\) | 18.2277 | 0.782224 | ||||||||
\(544\) | −2.55699 | −0.109630 | ||||||||
\(545\) | −1.30970 | −0.0561015 | ||||||||
\(546\) | −0.403805 | −0.0172813 | ||||||||
\(547\) | −10.1833 | −0.435408 | −0.217704 | − | 0.976015i | \(-0.569857\pi\) | ||||
−0.217704 | + | 0.976015i | \(0.569857\pi\) | |||||||
\(548\) | 6.24595 | 0.266814 | ||||||||
\(549\) | 20.1108 | 0.858307 | ||||||||
\(550\) | 30.2607 | 1.29032 | ||||||||
\(551\) | −2.45541 | −0.104604 | ||||||||
\(552\) | −8.06807 | −0.343400 | ||||||||
\(553\) | −9.02203 | −0.383656 | ||||||||
\(554\) | −23.9326 | −1.01680 | ||||||||
\(555\) | 1.50398 | 0.0638403 | ||||||||
\(556\) | 7.54672 | 0.320052 | ||||||||
\(557\) | 22.8626 | 0.968718 | 0.484359 | − | 0.874869i | \(-0.339053\pi\) | ||||
0.484359 | + | 0.874869i | \(0.339053\pi\) | |||||||
\(558\) | 10.7901 | 0.456781 | ||||||||
\(559\) | −0.818045 | −0.0345996 | ||||||||
\(560\) | −0.203143 | −0.00858436 | ||||||||
\(561\) | 38.5263 | 1.62658 | ||||||||
\(562\) | −7.88074 | −0.332429 | ||||||||
\(563\) | 9.38563 | 0.395557 | 0.197779 | − | 0.980247i | \(-0.436627\pi\) | ||||
0.197779 | + | 0.980247i | \(0.436627\pi\) | |||||||
\(564\) | 4.08002 | 0.171800 | ||||||||
\(565\) | −0.812420 | −0.0341788 | ||||||||
\(566\) | −9.88057 | −0.415311 | ||||||||
\(567\) | 9.58291 | 0.402444 | ||||||||
\(568\) | −0.468330 | −0.0196507 | ||||||||
\(569\) | 22.8722 | 0.958851 | 0.479425 | − | 0.877583i | \(-0.340845\pi\) | ||||
0.479425 | + | 0.877583i | \(0.340845\pi\) | |||||||
\(570\) | −1.07457 | −0.0450090 | ||||||||
\(571\) | 19.9195 | 0.833604 | 0.416802 | − | 0.908997i | \(-0.363151\pi\) | ||||
0.416802 | + | 0.908997i | \(0.363151\pi\) | |||||||
\(572\) | −0.897304 | −0.0375182 | ||||||||
\(573\) | 30.4725 | 1.27301 | ||||||||
\(574\) | 11.2185 | 0.468251 | ||||||||
\(575\) | 16.2040 | 0.675752 | ||||||||
\(576\) | 3.11487 | 0.129786 | ||||||||
\(577\) | −26.3043 | −1.09506 | −0.547531 | − | 0.836786i | \(-0.684432\pi\) | ||||
−0.547531 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(578\) | −10.4618 | −0.435154 | ||||||||
\(579\) | −57.6754 | −2.39691 | ||||||||
\(580\) | 0.189643 | 0.00787452 | ||||||||
\(581\) | 11.1974 | 0.464547 | ||||||||
\(582\) | −23.5164 | −0.974785 | ||||||||
\(583\) | −16.0272 | −0.663777 | ||||||||
\(584\) | −13.3090 | −0.550729 | ||||||||
\(585\) | 0.0840375 | 0.00347452 | ||||||||
\(586\) | −1.56316 | −0.0645737 | ||||||||
\(587\) | 0.955976 | 0.0394574 | 0.0197287 | − | 0.999805i | \(-0.493720\pi\) | ||||
0.0197287 | + | 0.999805i | \(0.493720\pi\) | |||||||
\(588\) | −14.2693 | −0.588457 | ||||||||
\(589\) | −8.21675 | −0.338565 | ||||||||
\(590\) | −0.846376 | −0.0348447 | ||||||||
\(591\) | −43.6860 | −1.79700 | ||||||||
\(592\) | 3.31986 | 0.136445 | ||||||||
\(593\) | −11.7470 | −0.482393 | −0.241197 | − | 0.970476i | \(-0.577540\pi\) | ||||
−0.241197 | + | 0.970476i | \(0.577540\pi\) | |||||||
\(594\) | −1.73076 | −0.0710139 | ||||||||
\(595\) | 0.519434 | 0.0212947 | ||||||||
\(596\) | 6.14251 | 0.251607 | ||||||||
\(597\) | −27.8283 | −1.13893 | ||||||||
\(598\) | −0.480486 | −0.0196485 | ||||||||
\(599\) | 25.2248 | 1.03066 | 0.515329 | − | 0.856993i | \(-0.327670\pi\) | ||||
0.515329 | + | 0.856993i | \(0.327670\pi\) | |||||||
\(600\) | −12.2811 | −0.501375 | ||||||||
\(601\) | −16.7051 | −0.681417 | −0.340709 | − | 0.940169i | \(-0.610667\pi\) | ||||
−0.340709 | + | 0.940169i | \(0.610667\pi\) | |||||||
\(602\) | 6.15951 | 0.251043 | ||||||||
\(603\) | 27.3710 | 1.11464 | ||||||||
\(604\) | 8.45338 | 0.343963 | ||||||||
\(605\) | 4.78618 | 0.194586 | ||||||||
\(606\) | 39.8724 | 1.61971 | ||||||||
\(607\) | −8.60323 | −0.349194 | −0.174597 | − | 0.984640i | \(-0.555862\pi\) | ||||
−0.174597 | + | 0.984640i | \(0.555862\pi\) | |||||||
\(608\) | −2.37200 | −0.0961973 | ||||||||
\(609\) | −2.83842 | −0.115019 | ||||||||
\(610\) | 1.18282 | 0.0478908 | ||||||||
\(611\) | 0.242982 | 0.00982999 | ||||||||
\(612\) | −7.96468 | −0.321953 | ||||||||
\(613\) | −32.3558 | −1.30684 | −0.653420 | − | 0.756996i | \(-0.726666\pi\) | ||||
−0.653420 | + | 0.756996i | \(0.726666\pi\) | |||||||
\(614\) | −1.67312 | −0.0675216 | ||||||||
\(615\) | −4.58336 | −0.184819 | ||||||||
\(616\) | 6.75629 | 0.272219 | ||||||||
\(617\) | 19.6209 | 0.789908 | 0.394954 | − | 0.918701i | \(-0.370761\pi\) | ||||
0.394954 | + | 0.918701i | \(0.370761\pi\) | |||||||
\(618\) | −13.3117 | −0.535475 | ||||||||
\(619\) | −0.598669 | −0.0240626 | −0.0120313 | − | 0.999928i | \(-0.503830\pi\) | ||||
−0.0120313 | + | 0.999928i | \(0.503830\pi\) | |||||||
\(620\) | 0.634620 | 0.0254870 | ||||||||
\(621\) | −0.926783 | −0.0371905 | ||||||||
\(622\) | 8.55050 | 0.342844 | ||||||||
\(623\) | −19.0730 | −0.764143 | ||||||||
\(624\) | 0.364165 | 0.0145783 | ||||||||
\(625\) | 24.4977 | 0.979907 | ||||||||
\(626\) | −5.99853 | −0.239749 | ||||||||
\(627\) | 35.7390 | 1.42728 | ||||||||
\(628\) | −14.5966 | −0.582467 | ||||||||
\(629\) | −8.48883 | −0.338472 | ||||||||
\(630\) | −0.632764 | −0.0252099 | ||||||||
\(631\) | 9.43387 | 0.375557 | 0.187778 | − | 0.982211i | \(-0.439871\pi\) | ||||
0.187778 | + | 0.982211i | \(0.439871\pi\) | |||||||
\(632\) | 8.13638 | 0.323648 | ||||||||
\(633\) | 25.3299 | 1.00677 | ||||||||
\(634\) | −19.4961 | −0.774289 | ||||||||
\(635\) | −3.75781 | −0.149124 | ||||||||
\(636\) | 6.50452 | 0.257921 | ||||||||
\(637\) | −0.849796 | −0.0336701 | ||||||||
\(638\) | −6.30731 | −0.249709 | ||||||||
\(639\) | −1.45879 | −0.0577088 | ||||||||
\(640\) | 0.183201 | 0.00724166 | ||||||||
\(641\) | 24.6998 | 0.975583 | 0.487792 | − | 0.872960i | \(-0.337803\pi\) | ||||
0.487792 | + | 0.872960i | \(0.337803\pi\) | |||||||
\(642\) | −8.57584 | −0.338461 | ||||||||
\(643\) | 16.3325 | 0.644091 | 0.322045 | − | 0.946724i | \(-0.395630\pi\) | ||||
0.322045 | + | 0.946724i | \(0.395630\pi\) | |||||||
\(644\) | 3.61784 | 0.142563 | ||||||||
\(645\) | −2.51649 | −0.0990865 | ||||||||
\(646\) | 6.06517 | 0.238631 | ||||||||
\(647\) | −23.1810 | −0.911339 | −0.455670 | − | 0.890149i | \(-0.650600\pi\) | ||||
−0.455670 | + | 0.890149i | \(0.650600\pi\) | |||||||
\(648\) | −8.64219 | −0.339497 | ||||||||
\(649\) | 28.1494 | 1.10496 | ||||||||
\(650\) | −0.731392 | −0.0286875 | ||||||||
\(651\) | −9.49845 | −0.372273 | ||||||||
\(652\) | −3.38562 | −0.132591 | ||||||||
\(653\) | 32.5455 | 1.27360 | 0.636801 | − | 0.771028i | \(-0.280257\pi\) | ||||
0.636801 | + | 0.771028i | \(0.280257\pi\) | |||||||
\(654\) | −17.6782 | −0.691272 | ||||||||
\(655\) | 1.73354 | 0.0677350 | ||||||||
\(656\) | −10.1172 | −0.395011 | ||||||||
\(657\) | −41.4557 | −1.61734 | ||||||||
\(658\) | −1.82954 | −0.0713230 | ||||||||
\(659\) | −31.2204 | −1.21618 | −0.608088 | − | 0.793870i | \(-0.708063\pi\) | ||||
−0.608088 | + | 0.793870i | \(0.708063\pi\) | |||||||
\(660\) | −2.76030 | −0.107445 | ||||||||
\(661\) | −17.0012 | −0.661271 | −0.330636 | − | 0.943759i | \(-0.607263\pi\) | ||||
−0.330636 | + | 0.943759i | \(0.607263\pi\) | |||||||
\(662\) | 3.23070 | 0.125565 | ||||||||
\(663\) | −0.931166 | −0.0361635 | ||||||||
\(664\) | −10.0982 | −0.391887 | ||||||||
\(665\) | 0.481855 | 0.0186855 | ||||||||
\(666\) | 10.3409 | 0.400703 | ||||||||
\(667\) | −3.37742 | −0.130774 | ||||||||
\(668\) | 15.2464 | 0.589903 | ||||||||
\(669\) | 32.0809 | 1.24032 | ||||||||
\(670\) | 1.60983 | 0.0621931 | ||||||||
\(671\) | −39.3390 | −1.51867 | ||||||||
\(672\) | −2.74200 | −0.105775 | ||||||||
\(673\) | 5.41016 | 0.208546 | 0.104273 | − | 0.994549i | \(-0.466748\pi\) | ||||
0.104273 | + | 0.994549i | \(0.466748\pi\) | |||||||
\(674\) | 12.9842 | 0.500131 | ||||||||
\(675\) | −1.41074 | −0.0542994 | ||||||||
\(676\) | −12.9783 | −0.499166 | ||||||||
\(677\) | −6.64408 | −0.255353 | −0.127676 | − | 0.991816i | \(-0.540752\pi\) | ||||
−0.127676 | + | 0.991816i | \(0.540752\pi\) | |||||||
\(678\) | −10.9659 | −0.421144 | ||||||||
\(679\) | 10.5451 | 0.404683 | ||||||||
\(680\) | −0.468443 | −0.0179640 | ||||||||
\(681\) | −56.3038 | −2.15757 | ||||||||
\(682\) | −21.1067 | −0.808217 | ||||||||
\(683\) | 7.56452 | 0.289448 | 0.144724 | − | 0.989472i | \(-0.453771\pi\) | ||||
0.144724 | + | 0.989472i | \(0.453771\pi\) | |||||||
\(684\) | −7.38847 | −0.282505 | ||||||||
\(685\) | 1.14427 | 0.0437201 | ||||||||
\(686\) | 14.1605 | 0.540652 | ||||||||
\(687\) | −5.69116 | −0.217131 | ||||||||
\(688\) | −5.55485 | −0.211777 | ||||||||
\(689\) | 0.387371 | 0.0147577 | ||||||||
\(690\) | −1.47808 | −0.0562696 | ||||||||
\(691\) | −5.35303 | −0.203639 | −0.101819 | − | 0.994803i | \(-0.532466\pi\) | ||||
−0.101819 | + | 0.994803i | \(0.532466\pi\) | |||||||
\(692\) | −6.34616 | −0.241245 | ||||||||
\(693\) | 21.0450 | 0.799432 | ||||||||
\(694\) | −2.32541 | −0.0882712 | ||||||||
\(695\) | 1.38257 | 0.0524438 | ||||||||
\(696\) | 2.55978 | 0.0970283 | ||||||||
\(697\) | 25.8696 | 0.979882 | ||||||||
\(698\) | 22.9593 | 0.869021 | ||||||||
\(699\) | 53.1034 | 2.00856 | ||||||||
\(700\) | 5.50704 | 0.208147 | ||||||||
\(701\) | −21.3549 | −0.806563 | −0.403282 | − | 0.915076i | \(-0.632131\pi\) | ||||
−0.403282 | + | 0.915076i | \(0.632131\pi\) | |||||||
\(702\) | 0.0418318 | 0.00157884 | ||||||||
\(703\) | −7.87470 | −0.297000 | ||||||||
\(704\) | −6.09305 | −0.229640 | ||||||||
\(705\) | 0.747465 | 0.0281512 | ||||||||
\(706\) | −17.7095 | −0.666506 | ||||||||
\(707\) | −17.8794 | −0.672423 | ||||||||
\(708\) | −11.4243 | −0.429350 | ||||||||
\(709\) | 49.1276 | 1.84503 | 0.922513 | − | 0.385965i | \(-0.126132\pi\) | ||||
0.922513 | + | 0.385965i | \(0.126132\pi\) | |||||||
\(710\) | −0.0857987 | −0.00321997 | ||||||||
\(711\) | 25.3438 | 0.950465 | ||||||||
\(712\) | 17.2007 | 0.644622 | ||||||||
\(713\) | −11.3022 | −0.423269 | ||||||||
\(714\) | 7.01125 | 0.262389 | ||||||||
\(715\) | −0.164387 | −0.00614773 | ||||||||
\(716\) | 11.4406 | 0.427555 | ||||||||
\(717\) | −17.6699 | −0.659895 | ||||||||
\(718\) | 30.8355 | 1.15077 | ||||||||
\(719\) | −23.2540 | −0.867229 | −0.433615 | − | 0.901098i | \(-0.642762\pi\) | ||||
−0.433615 | + | 0.901098i | \(0.642762\pi\) | |||||||
\(720\) | 0.570648 | 0.0212668 | ||||||||
\(721\) | 5.96916 | 0.222303 | ||||||||
\(722\) | −13.3736 | −0.497714 | ||||||||
\(723\) | 1.27222 | 0.0473143 | ||||||||
\(724\) | 7.37118 | 0.273948 | ||||||||
\(725\) | −5.14108 | −0.190935 | ||||||||
\(726\) | 64.6032 | 2.39765 | ||||||||
\(727\) | −10.5130 | −0.389904 | −0.194952 | − | 0.980813i | \(-0.562455\pi\) | ||||
−0.194952 | + | 0.980813i | \(0.562455\pi\) | |||||||
\(728\) | −0.163297 | −0.00605219 | ||||||||
\(729\) | −29.0266 | −1.07506 | ||||||||
\(730\) | −2.43822 | −0.0902425 | ||||||||
\(731\) | 14.2037 | 0.525342 | ||||||||
\(732\) | 15.9655 | 0.590102 | ||||||||
\(733\) | −23.3493 | −0.862427 | −0.431214 | − | 0.902250i | \(-0.641914\pi\) | ||||
−0.431214 | + | 0.902250i | \(0.641914\pi\) | |||||||
\(734\) | 12.9844 | 0.479262 | ||||||||
\(735\) | −2.61416 | −0.0964246 | ||||||||
\(736\) | −3.26269 | −0.120264 | ||||||||
\(737\) | −53.5409 | −1.97221 | ||||||||
\(738\) | −31.5139 | −1.16004 | ||||||||
\(739\) | −5.69260 | −0.209406 | −0.104703 | − | 0.994504i | \(-0.533389\pi\) | ||||
−0.104703 | + | 0.994504i | \(0.533389\pi\) | |||||||
\(740\) | 0.608202 | 0.0223580 | ||||||||
\(741\) | −0.863800 | −0.0317325 | ||||||||
\(742\) | −2.91672 | −0.107076 | ||||||||
\(743\) | −3.76103 | −0.137979 | −0.0689894 | − | 0.997617i | \(-0.521977\pi\) | ||||
−0.0689894 | + | 0.997617i | \(0.521977\pi\) | |||||||
\(744\) | 8.56602 | 0.314046 | ||||||||
\(745\) | 1.12532 | 0.0412284 | ||||||||
\(746\) | −16.8227 | −0.615923 | ||||||||
\(747\) | −31.4546 | −1.15086 | ||||||||
\(748\) | 15.5798 | 0.569656 | ||||||||
\(749\) | 3.84553 | 0.140513 | ||||||||
\(750\) | −4.51504 | −0.164866 | ||||||||
\(751\) | −23.6062 | −0.861404 | −0.430702 | − | 0.902494i | \(-0.641734\pi\) | ||||
−0.430702 | + | 0.902494i | \(0.641734\pi\) | |||||||
\(752\) | 1.64994 | 0.0601672 | ||||||||
\(753\) | −20.6089 | −0.751032 | ||||||||
\(754\) | 0.152445 | 0.00555174 | ||||||||
\(755\) | 1.54867 | 0.0563618 | ||||||||
\(756\) | −0.314975 | −0.0114555 | ||||||||
\(757\) | −33.0172 | −1.20003 | −0.600016 | − | 0.799988i | \(-0.704839\pi\) | ||||
−0.600016 | + | 0.799988i | \(0.704839\pi\) | |||||||
\(758\) | 25.8009 | 0.937132 | ||||||||
\(759\) | 49.1591 | 1.78436 | ||||||||
\(760\) | −0.434553 | −0.0157629 | ||||||||
\(761\) | −27.7048 | −1.00430 | −0.502148 | − | 0.864782i | \(-0.667457\pi\) | ||||
−0.502148 | + | 0.864782i | \(0.667457\pi\) | |||||||
\(762\) | −50.7225 | −1.83748 | ||||||||
\(763\) | 7.92716 | 0.286982 | ||||||||
\(764\) | 12.3229 | 0.445828 | ||||||||
\(765\) | −1.45914 | −0.0527553 | ||||||||
\(766\) | 2.87242 | 0.103785 | ||||||||
\(767\) | −0.680362 | −0.0245664 | ||||||||
\(768\) | 2.47283 | 0.0892304 | ||||||||
\(769\) | −21.3734 | −0.770743 | −0.385372 | − | 0.922761i | \(-0.625927\pi\) | ||||
−0.385372 | + | 0.922761i | \(0.625927\pi\) | |||||||
\(770\) | 1.23776 | 0.0446058 | ||||||||
\(771\) | 69.8295 | 2.51485 | ||||||||
\(772\) | −23.3237 | −0.839437 | ||||||||
\(773\) | −22.4101 | −0.806035 | −0.403018 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403018 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(774\) | −17.3026 | −0.621931 | ||||||||
\(775\) | −17.2040 | −0.617987 | ||||||||
\(776\) | −9.50991 | −0.341386 | ||||||||
\(777\) | −9.10304 | −0.326570 | ||||||||
\(778\) | −31.4507 | −1.12756 | ||||||||
\(779\) | 23.9981 | 0.859820 | ||||||||
\(780\) | 0.0667155 | 0.00238880 | ||||||||
\(781\) | 2.85356 | 0.102108 | ||||||||
\(782\) | 8.34266 | 0.298333 | ||||||||
\(783\) | 0.294044 | 0.0105083 | ||||||||
\(784\) | −5.77045 | −0.206087 | ||||||||
\(785\) | −2.67411 | −0.0954431 | ||||||||
\(786\) | 23.3991 | 0.834618 | ||||||||
\(787\) | −10.6122 | −0.378285 | −0.189143 | − | 0.981950i | \(-0.560571\pi\) | ||||
−0.189143 | + | 0.981950i | \(0.560571\pi\) | |||||||
\(788\) | −17.6664 | −0.629341 | ||||||||
\(789\) | 43.9010 | 1.56292 | ||||||||
\(790\) | 1.49059 | 0.0530330 | ||||||||
\(791\) | 4.91729 | 0.174839 | ||||||||
\(792\) | −18.9791 | −0.674391 | ||||||||
\(793\) | 0.950810 | 0.0337643 | ||||||||
\(794\) | −1.11182 | −0.0394571 | ||||||||
\(795\) | 1.19164 | 0.0422630 | ||||||||
\(796\) | −11.2536 | −0.398874 | ||||||||
\(797\) | −9.84951 | −0.348888 | −0.174444 | − | 0.984667i | \(-0.555813\pi\) | ||||
−0.174444 | + | 0.984667i | \(0.555813\pi\) | |||||||
\(798\) | 6.50402 | 0.230240 | ||||||||
\(799\) | −4.21888 | −0.149253 | ||||||||
\(800\) | −4.96644 | −0.175590 | ||||||||
\(801\) | 53.5779 | 1.89308 | ||||||||
\(802\) | −12.7527 | −0.450313 | ||||||||
\(803\) | 81.0921 | 2.86168 | ||||||||
\(804\) | 21.7293 | 0.766332 | ||||||||
\(805\) | 0.662793 | 0.0233604 | ||||||||
\(806\) | 0.510141 | 0.0179690 | ||||||||
\(807\) | 15.4907 | 0.545300 | ||||||||
\(808\) | 16.1242 | 0.567248 | ||||||||
\(809\) | 27.9025 | 0.981001 | 0.490501 | − | 0.871441i | \(-0.336814\pi\) | ||||
0.490501 | + | 0.871441i | \(0.336814\pi\) | |||||||
\(810\) | −1.58326 | −0.0556301 | ||||||||
\(811\) | 4.47359 | 0.157089 | 0.0785445 | − | 0.996911i | \(-0.474973\pi\) | ||||
0.0785445 | + | 0.996911i | \(0.474973\pi\) | |||||||
\(812\) | −1.14784 | −0.0402814 | ||||||||
\(813\) | 25.6163 | 0.898403 | ||||||||
\(814\) | −20.2281 | −0.708993 | ||||||||
\(815\) | −0.620250 | −0.0217264 | ||||||||
\(816\) | −6.32298 | −0.221349 | ||||||||
\(817\) | 13.1761 | 0.460974 | ||||||||
\(818\) | −27.3108 | −0.954900 | ||||||||
\(819\) | −0.508649 | −0.0177736 | ||||||||
\(820\) | −1.85349 | −0.0647266 | ||||||||
\(821\) | −4.66110 | −0.162673 | −0.0813367 | − | 0.996687i | \(-0.525919\pi\) | ||||
−0.0813367 | + | 0.996687i | \(0.525919\pi\) | |||||||
\(822\) | 15.4451 | 0.538711 | ||||||||
\(823\) | −2.98327 | −0.103990 | −0.0519951 | − | 0.998647i | \(-0.516558\pi\) | ||||
−0.0519951 | + | 0.998647i | \(0.516558\pi\) | |||||||
\(824\) | −5.38319 | −0.187532 | ||||||||
\(825\) | 74.8296 | 2.60523 | ||||||||
\(826\) | 5.12281 | 0.178245 | ||||||||
\(827\) | −39.6207 | −1.37775 | −0.688874 | − | 0.724881i | \(-0.741895\pi\) | ||||
−0.688874 | + | 0.724881i | \(0.741895\pi\) | |||||||
\(828\) | −10.1629 | −0.353184 | ||||||||
\(829\) | −37.6711 | −1.30837 | −0.654186 | − | 0.756333i | \(-0.726989\pi\) | ||||
−0.654186 | + | 0.756333i | \(0.726989\pi\) | |||||||
\(830\) | −1.85000 | −0.0642146 | ||||||||
\(831\) | −59.1811 | −2.05297 | ||||||||
\(832\) | 0.147267 | 0.00510556 | ||||||||
\(833\) | 14.7550 | 0.511229 | ||||||||
\(834\) | 18.6617 | 0.646203 | ||||||||
\(835\) | 2.79317 | 0.0966615 | ||||||||
\(836\) | 14.4527 | 0.499857 | ||||||||
\(837\) | 0.983983 | 0.0340114 | ||||||||
\(838\) | −12.6594 | −0.437313 | ||||||||
\(839\) | 44.0077 | 1.51932 | 0.759658 | − | 0.650323i | \(-0.225366\pi\) | ||||
0.759658 | + | 0.650323i | \(0.225366\pi\) | |||||||
\(840\) | −0.502337 | −0.0173323 | ||||||||
\(841\) | −27.9284 | −0.963049 | ||||||||
\(842\) | 12.2017 | 0.420499 | ||||||||
\(843\) | −19.4877 | −0.671192 | ||||||||
\(844\) | 10.2433 | 0.352588 | ||||||||
\(845\) | −2.37764 | −0.0817934 | ||||||||
\(846\) | 5.13936 | 0.176695 | ||||||||
\(847\) | −28.9690 | −0.995387 | ||||||||
\(848\) | 2.63040 | 0.0903283 | ||||||||
\(849\) | −24.4329 | −0.838536 | ||||||||
\(850\) | 12.6991 | 0.435576 | ||||||||
\(851\) | −10.8317 | −0.371305 | ||||||||
\(852\) | −1.15810 | −0.0396758 | ||||||||
\(853\) | −2.83934 | −0.0972171 | −0.0486086 | − | 0.998818i | \(-0.515479\pi\) | ||||
−0.0486086 | + | 0.998818i | \(0.515479\pi\) | |||||||
\(854\) | −7.15916 | −0.244982 | ||||||||
\(855\) | −1.35358 | −0.0462914 | ||||||||
\(856\) | −3.46803 | −0.118535 | ||||||||
\(857\) | −2.26847 | −0.0774894 | −0.0387447 | − | 0.999249i | \(-0.512336\pi\) | ||||
−0.0387447 | + | 0.999249i | \(0.512336\pi\) | |||||||
\(858\) | −2.21888 | −0.0757512 | ||||||||
\(859\) | 29.5917 | 1.00966 | 0.504828 | − | 0.863220i | \(-0.331556\pi\) | ||||
0.504828 | + | 0.863220i | \(0.331556\pi\) | |||||||
\(860\) | −1.01766 | −0.0347018 | ||||||||
\(861\) | 27.7414 | 0.945425 | ||||||||
\(862\) | −6.39065 | −0.217666 | ||||||||
\(863\) | 2.62119 | 0.0892263 | 0.0446132 | − | 0.999004i | \(-0.485794\pi\) | ||||
0.0446132 | + | 0.999004i | \(0.485794\pi\) | |||||||
\(864\) | 0.284055 | 0.00966374 | ||||||||
\(865\) | −1.16262 | −0.0395304 | ||||||||
\(866\) | 8.54652 | 0.290423 | ||||||||
\(867\) | −25.8703 | −0.878600 | ||||||||
\(868\) | −3.84113 | −0.130376 | ||||||||
\(869\) | −49.5753 | −1.68173 | ||||||||
\(870\) | 0.468955 | 0.0158991 | ||||||||
\(871\) | 1.29407 | 0.0438477 | ||||||||
\(872\) | −7.14898 | −0.242095 | ||||||||
\(873\) | −29.6221 | −1.00256 | ||||||||
\(874\) | 7.73911 | 0.261779 | ||||||||
\(875\) | 2.02461 | 0.0684444 | ||||||||
\(876\) | −32.9107 | −1.11195 | ||||||||
\(877\) | 33.5166 | 1.13177 | 0.565887 | − | 0.824483i | \(-0.308534\pi\) | ||||
0.565887 | + | 0.824483i | \(0.308534\pi\) | |||||||
\(878\) | −0.779523 | −0.0263076 | ||||||||
\(879\) | −3.86543 | −0.130378 | ||||||||
\(880\) | −1.11625 | −0.0376289 | ||||||||
\(881\) | 16.6790 | 0.561931 | 0.280966 | − | 0.959718i | \(-0.409345\pi\) | ||||
0.280966 | + | 0.959718i | \(0.409345\pi\) | |||||||
\(882\) | −17.9742 | −0.605223 | ||||||||
\(883\) | 15.6322 | 0.526066 | 0.263033 | − | 0.964787i | \(-0.415277\pi\) | ||||
0.263033 | + | 0.964787i | \(0.415277\pi\) | |||||||
\(884\) | −0.376559 | −0.0126651 | ||||||||
\(885\) | −2.09294 | −0.0703534 | ||||||||
\(886\) | −2.87892 | −0.0967193 | ||||||||
\(887\) | −1.39451 | −0.0468229 | −0.0234115 | − | 0.999726i | \(-0.507453\pi\) | ||||
−0.0234115 | + | 0.999726i | \(0.507453\pi\) | |||||||
\(888\) | 8.20943 | 0.275491 | ||||||||
\(889\) | 22.7447 | 0.762833 | ||||||||
\(890\) | 3.15118 | 0.105628 | ||||||||
\(891\) | 52.6573 | 1.76409 | ||||||||
\(892\) | 12.9734 | 0.434380 | ||||||||
\(893\) | −3.91366 | −0.130966 | ||||||||
\(894\) | 15.1894 | 0.508008 | ||||||||
\(895\) | 2.09593 | 0.0700592 | ||||||||
\(896\) | −1.10885 | −0.0370441 | ||||||||
\(897\) | −1.18816 | −0.0396715 | ||||||||
\(898\) | 1.51382 | 0.0505170 | ||||||||
\(899\) | 3.58587 | 0.119596 | ||||||||
\(900\) | −15.4698 | −0.515660 | ||||||||
\(901\) | −6.72590 | −0.224072 | ||||||||
\(902\) | 61.6448 | 2.05255 | ||||||||
\(903\) | 15.2314 | 0.506869 | ||||||||
\(904\) | −4.43458 | −0.147492 | ||||||||
\(905\) | 1.35041 | 0.0448891 | ||||||||
\(906\) | 20.9037 | 0.694480 | ||||||||
\(907\) | 42.4405 | 1.40921 | 0.704607 | − | 0.709597i | \(-0.251123\pi\) | ||||
0.704607 | + | 0.709597i | \(0.251123\pi\) | |||||||
\(908\) | −22.7690 | −0.755616 | ||||||||
\(909\) | 50.2249 | 1.66585 | ||||||||
\(910\) | −0.0299162 | −0.000991713 0 | ||||||||
\(911\) | 17.7487 | 0.588041 | 0.294020 | − | 0.955799i | \(-0.405007\pi\) | ||||
0.294020 | + | 0.955799i | \(0.405007\pi\) | |||||||
\(912\) | −5.86554 | −0.194228 | ||||||||
\(913\) | 61.5289 | 2.03631 | ||||||||
\(914\) | −5.83393 | −0.192969 | ||||||||
\(915\) | 2.92490 | 0.0966942 | ||||||||
\(916\) | −2.30148 | −0.0760430 | ||||||||
\(917\) | −10.4925 | −0.346493 | ||||||||
\(918\) | −0.726324 | −0.0239723 | ||||||||
\(919\) | −46.2309 | −1.52502 | −0.762508 | − | 0.646979i | \(-0.776032\pi\) | ||||
−0.762508 | + | 0.646979i | \(0.776032\pi\) | |||||||
\(920\) | −0.597729 | −0.0197065 | ||||||||
\(921\) | −4.13733 | −0.136330 | ||||||||
\(922\) | −14.3110 | −0.471308 | ||||||||
\(923\) | −0.0689695 | −0.00227016 | ||||||||
\(924\) | 16.7071 | 0.549624 | ||||||||
\(925\) | −16.4879 | −0.542118 | ||||||||
\(926\) | −21.2913 | −0.699675 | ||||||||
\(927\) | −16.7679 | −0.550732 | ||||||||
\(928\) | 1.03517 | 0.0339810 | ||||||||
\(929\) | −10.1976 | −0.334573 | −0.167286 | − | 0.985908i | \(-0.553500\pi\) | ||||
−0.167286 | + | 0.985908i | \(0.553500\pi\) | |||||||
\(930\) | 1.56931 | 0.0514596 | ||||||||
\(931\) | 13.6875 | 0.448590 | ||||||||
\(932\) | 21.4748 | 0.703430 | ||||||||
\(933\) | 21.1439 | 0.692220 | ||||||||
\(934\) | −11.1190 | −0.363826 | ||||||||
\(935\) | 2.85425 | 0.0933438 | ||||||||
\(936\) | 0.458717 | 0.0149936 | ||||||||
\(937\) | 33.0387 | 1.07933 | 0.539664 | − | 0.841880i | \(-0.318551\pi\) | ||||
0.539664 | + | 0.841880i | \(0.318551\pi\) | |||||||
\(938\) | −9.74372 | −0.318144 | ||||||||
\(939\) | −14.8333 | −0.484067 | ||||||||
\(940\) | 0.302272 | 0.00985901 | ||||||||
\(941\) | −45.2092 | −1.47378 | −0.736890 | − | 0.676013i | \(-0.763706\pi\) | ||||
−0.736890 | + | 0.676013i | \(0.763706\pi\) | |||||||
\(942\) | −36.0948 | −1.17603 | ||||||||
\(943\) | 33.0094 | 1.07493 | ||||||||
\(944\) | −4.61993 | −0.150366 | ||||||||
\(945\) | −0.0577037 | −0.00187710 | ||||||||
\(946\) | 33.8460 | 1.10043 | ||||||||
\(947\) | −8.73369 | −0.283807 | −0.141903 | − | 0.989881i | \(-0.545322\pi\) | ||||
−0.141903 | + | 0.989881i | \(0.545322\pi\) | |||||||
\(948\) | 20.1198 | 0.653462 | ||||||||
\(949\) | −1.95997 | −0.0636233 | ||||||||
\(950\) | 11.7804 | 0.382206 | ||||||||
\(951\) | −48.2105 | −1.56333 | ||||||||
\(952\) | 2.83532 | 0.0918932 | ||||||||
\(953\) | 50.7558 | 1.64414 | 0.822070 | − | 0.569386i | \(-0.192819\pi\) | ||||
0.822070 | + | 0.569386i | \(0.192819\pi\) | |||||||
\(954\) | 8.19336 | 0.265270 | ||||||||
\(955\) | 2.25758 | 0.0730535 | ||||||||
\(956\) | −7.14563 | −0.231106 | ||||||||
\(957\) | −15.5969 | −0.504176 | ||||||||
\(958\) | 28.7405 | 0.928563 | ||||||||
\(959\) | −6.92583 | −0.223647 | ||||||||
\(960\) | 0.453025 | 0.0146213 | ||||||||
\(961\) | −19.0003 | −0.612912 | ||||||||
\(962\) | 0.488905 | 0.0157629 | ||||||||
\(963\) | −10.8025 | −0.348105 | ||||||||
\(964\) | 0.514479 | 0.0165703 | ||||||||
\(965\) | −4.27292 | −0.137550 | ||||||||
\(966\) | 8.94629 | 0.287842 | ||||||||
\(967\) | −25.1397 | −0.808437 | −0.404218 | − | 0.914663i | \(-0.632456\pi\) | ||||
−0.404218 | + | 0.914663i | \(0.632456\pi\) | |||||||
\(968\) | 26.1252 | 0.839697 | ||||||||
\(969\) | 14.9981 | 0.481809 | ||||||||
\(970\) | −1.74223 | −0.0559396 | ||||||||
\(971\) | 3.33687 | 0.107085 | 0.0535426 | − | 0.998566i | \(-0.482949\pi\) | ||||
0.0535426 | + | 0.998566i | \(0.482949\pi\) | |||||||
\(972\) | −22.2228 | −0.712797 | ||||||||
\(973\) | −8.36819 | −0.268272 | ||||||||
\(974\) | 16.5753 | 0.531108 | ||||||||
\(975\) | −1.80860 | −0.0579217 | ||||||||
\(976\) | 6.45638 | 0.206664 | ||||||||
\(977\) | −31.8464 | −1.01886 | −0.509429 | − | 0.860513i | \(-0.670143\pi\) | ||||
−0.509429 | + | 0.860513i | \(0.670143\pi\) | |||||||
\(978\) | −8.37205 | −0.267709 | ||||||||
\(979\) | −104.805 | −3.34957 | ||||||||
\(980\) | −1.05715 | −0.0337695 | ||||||||
\(981\) | −22.2682 | −0.710967 | ||||||||
\(982\) | −29.4508 | −0.939812 | ||||||||
\(983\) | −34.0752 | −1.08683 | −0.543415 | − | 0.839464i | \(-0.682869\pi\) | ||||
−0.543415 | + | 0.839464i | \(0.682869\pi\) | |||||||
\(984\) | −25.0182 | −0.797550 | ||||||||
\(985\) | −3.23651 | −0.103124 | ||||||||
\(986\) | −2.64690 | −0.0842946 | ||||||||
\(987\) | −4.52414 | −0.144005 | ||||||||
\(988\) | −0.349317 | −0.0111133 | ||||||||
\(989\) | 18.1238 | 0.576302 | ||||||||
\(990\) | −3.47699 | −0.110506 | ||||||||
\(991\) | 10.4713 | 0.332631 | 0.166315 | − | 0.986073i | \(-0.446813\pi\) | ||||
0.166315 | + | 0.986073i | \(0.446813\pi\) | |||||||
\(992\) | 3.46406 | 0.109984 | ||||||||
\(993\) | 7.98895 | 0.253522 | ||||||||
\(994\) | 0.519309 | 0.0164715 | ||||||||
\(995\) | −2.06168 | −0.0653596 | ||||||||
\(996\) | −24.9711 | −0.791240 | ||||||||
\(997\) | −19.2060 | −0.608259 | −0.304130 | − | 0.952631i | \(-0.598366\pi\) | ||||
−0.304130 | + | 0.952631i | \(0.598366\pi\) | |||||||
\(998\) | −3.93211 | −0.124469 | ||||||||
\(999\) | 0.943021 | 0.0298359 |
(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 | 8042.2.a.a.1.63 | ✓ | 67 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.a.1.63 | ✓ | 67 | 1.1 | even | 1 | trivial |