Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6040,2,Mod(1,6040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6040, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6040.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6040 = 2^{3} \cdot 5 \cdot 151 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6040.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: | \(48.2296428209\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6040.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.161432 | 0.0932027 | 0.0466014 | − | 0.998914i | \(-0.485161\pi\) | ||||
0.0466014 | + | 0.998914i | \(0.485161\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.19061 | −1.58390 | −0.791950 | − | 0.610585i | \(-0.790934\pi\) | ||||
−0.791950 | + | 0.610585i | \(0.790934\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97394 | −0.991313 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12337 | −1.54475 | −0.772377 | − | 0.635165i | \(-0.780932\pi\) | ||||
−0.772377 | + | 0.635165i | \(0.780932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.40106 | 0.943285 | 0.471643 | − | 0.881790i | \(-0.343661\pi\) | ||||
0.471643 | + | 0.881790i | \(0.343661\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.161432 | 0.0416815 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.946395 | 0.229535 | 0.114767 | − | 0.993392i | \(-0.463388\pi\) | ||||
0.114767 | + | 0.993392i | \(0.463388\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.49403 | −1.71925 | −0.859624 | − | 0.510927i | \(-0.829302\pi\) | ||||
−0.859624 | + | 0.510927i | \(0.829302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.676498 | −0.147624 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0845329 | 0.0176263 | 0.00881316 | − | 0.999961i | \(-0.497195\pi\) | ||||
0.00881316 | + | 0.999961i | \(0.497195\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.964384 | −0.185596 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.04163 | −1.30760 | −0.653799 | − | 0.756669i | \(-0.726826\pi\) | ||||
−0.653799 | + | 0.756669i | \(0.726826\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.299430 | 0.0537793 | 0.0268896 | − | 0.999638i | \(-0.491440\pi\) | ||||
0.0268896 | + | 0.999638i | \(0.491440\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.827075 | −0.143975 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.19061 | −0.708342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.50414 | 1.06927 | 0.534637 | − | 0.845082i | \(-0.320448\pi\) | ||||
0.534637 | + | 0.845082i | \(0.320448\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.549040 | 0.0879168 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.06155 | 0.478133 | 0.239067 | − | 0.971003i | \(-0.423159\pi\) | ||||
0.239067 | + | 0.971003i | \(0.423159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.23185 | −0.492852 | −0.246426 | − | 0.969162i | \(-0.579256\pi\) | ||||
−0.246426 | + | 0.969162i | \(0.579256\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.97394 | −0.443329 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.8083 | 1.57656 | 0.788280 | − | 0.615317i | \(-0.210972\pi\) | ||||
0.788280 | + | 0.615317i | \(0.210972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.5612 | 1.50874 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.152778 | 0.0213932 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.20685 | 0.165773 | 0.0828867 | − | 0.996559i | \(-0.473586\pi\) | ||||
0.0828867 | + | 0.996559i | \(0.473586\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.12337 | −0.690835 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.20978 | −0.160239 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.73216 | −1.26702 | −0.633510 | − | 0.773735i | \(-0.718386\pi\) | ||||
−0.633510 | + | 0.773735i | \(0.718386\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.97977 | −0.253483 | −0.126742 | − | 0.991936i | \(-0.540452\pi\) | ||||
−0.126742 | + | 0.991936i | \(0.540452\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.4626 | 1.57014 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.40106 | 0.421850 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.22539 | −0.760552 | −0.380276 | − | 0.924873i | \(-0.624171\pi\) | ||||
−0.380276 | + | 0.924873i | \(0.624171\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.0136463 | 0.00164282 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.16645 | 0.613145 | 0.306572 | − | 0.951847i | \(-0.400818\pi\) | ||||
0.306572 | + | 0.951847i | \(0.400818\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.01109 | 0.820586 | 0.410293 | − | 0.911954i | \(-0.365427\pi\) | ||||
0.410293 | + | 0.911954i | \(0.365427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.161432 | 0.0186405 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 21.4700 | 2.44674 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.877371 | −0.0987119 | −0.0493560 | − | 0.998781i | \(-0.515717\pi\) | ||||
−0.0493560 | + | 0.998781i | \(0.515717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.76614 | 0.974015 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.30430 | −0.911515 | −0.455757 | − | 0.890104i | \(-0.650632\pi\) | ||||
−0.455757 | + | 0.890104i | \(0.650632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.946395 | 0.102651 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.13674 | −0.121872 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.68009 | −0.178089 | −0.0890446 | − | 0.996028i | \(-0.528381\pi\) | ||||
−0.0890446 | + | 0.996028i | \(0.528381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.2525 | −1.49407 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.0483376 | 0.00501238 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.49403 | −0.768871 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0683939 | −0.00694434 | −0.00347217 | − | 0.999994i | \(-0.501105\pi\) | ||||
−0.00347217 | + | 0.999994i | \(0.501105\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 15.2366 | 1.53133 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.5066 | 1.44346 | 0.721730 | − | 0.692175i | \(-0.243347\pi\) | ||||
0.721730 | + | 0.692175i | \(0.243347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.37358 | 0.430942 | 0.215471 | − | 0.976510i | \(-0.430871\pi\) | ||||
0.215471 | + | 0.976510i | \(0.430871\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.676498 | −0.0660194 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.34505 | 0.806746 | 0.403373 | − | 0.915036i | \(-0.367838\pi\) | ||||
0.403373 | + | 0.915036i | \(0.367838\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6827 | −1.21478 | −0.607390 | − | 0.794404i | \(-0.707784\pi\) | ||||
−0.607390 | + | 0.794404i | \(0.707784\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.04998 | 0.0996593 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.45054 | −0.794960 | −0.397480 | − | 0.917611i | \(-0.630115\pi\) | ||||
−0.397480 | + | 0.917611i | \(0.630115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0845329 | 0.00788273 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.1146 | −0.935091 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.96597 | −0.363560 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2489 | 1.38626 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.494231 | 0.0445633 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6730 | 1.30202 | 0.651009 | − | 0.759070i | \(-0.274346\pi\) | ||||
0.651009 | + | 0.759070i | \(0.274346\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.521723 | −0.0459351 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.5392 | 1.70715 | 0.853576 | − | 0.520969i | \(-0.174429\pi\) | ||||
0.853576 | + | 0.520969i | \(0.174429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 31.4045 | 2.72312 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.964384 | −0.0830010 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.978415 | −0.0835917 | −0.0417958 | − | 0.999126i | \(-0.513308\pi\) | ||||
−0.0417958 | + | 0.999126i | \(0.513308\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.63898 | 0.478292 | 0.239146 | − | 0.970984i | \(-0.423133\pi\) | ||||
0.239146 | + | 0.970984i | \(0.423133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.74481 | 0.146940 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −17.4249 | −1.45714 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.04163 | −0.584775 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.70491 | 0.140619 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.99834 | −0.655250 | −0.327625 | − | 0.944808i | \(-0.606248\pi\) | ||||
−0.327625 | + | 0.944808i | \(0.606248\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | 0.0813788 | ||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.81452 | −0.227541 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.299430 | 0.0240508 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.1455 | 1.60778 | 0.803892 | − | 0.594775i | \(-0.202759\pi\) | ||||
0.803892 | + | 0.594775i | \(0.202759\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.194824 | 0.0154505 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.354244 | −0.0279183 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.216522 | 0.0169593 | 0.00847964 | − | 0.999964i | \(-0.497301\pi\) | ||||
0.00847964 | + | 0.999964i | \(0.497301\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.827075 | −0.0643877 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1317 | 1.55784 | 0.778920 | − | 0.627123i | \(-0.215768\pi\) | ||||
0.778920 | + | 0.627123i | \(0.215768\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.43276 | −0.110212 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.2868 | 1.70431 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −18.0911 | −1.37544 | −0.687720 | − | 0.725976i | \(-0.741388\pi\) | ||||
−0.687720 | + | 0.725976i | \(0.741388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.19061 | −0.316780 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.57108 | −0.118090 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.74050 | 0.503809 | 0.251904 | − | 0.967752i | \(-0.418943\pi\) | ||||
0.251904 | + | 0.967752i | \(0.418943\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.26368 | 0.168258 | 0.0841289 | − | 0.996455i | \(-0.473189\pi\) | ||||
0.0841289 | + | 0.996455i | \(0.473189\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.319597 | −0.0236253 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.50414 | 0.478194 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.84873 | −0.354574 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.04136 | 0.293965 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.81958 | −0.493447 | −0.246724 | − | 0.969086i | \(-0.579354\pi\) | ||||
−0.246724 | + | 0.969086i | \(0.579354\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2436 | −1.16924 | −0.584619 | − | 0.811308i | \(-0.698756\pi\) | ||||
−0.584619 | + | 0.811308i | \(0.698756\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.549040 | 0.0393176 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 26.5182 | 1.88935 | 0.944673 | − | 0.328012i | \(-0.106379\pi\) | ||||
0.944673 | + | 0.328012i | \(0.106379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.7836 | −0.835318 | −0.417659 | − | 0.908604i | \(-0.637149\pi\) | ||||
−0.417659 | + | 0.908604i | \(0.637149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00498 | −0.0708856 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.5087 | 2.07110 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.06155 | 0.213828 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.251396 | −0.0174732 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.3947 | 2.65582 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.30468 | −0.0898176 | −0.0449088 | − | 0.998991i | \(-0.514300\pi\) | ||||
−0.0449088 | + | 0.998991i | \(0.514300\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.834029 | 0.0571468 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.23185 | −0.220410 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.25480 | −0.0851810 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.13181 | 0.0764808 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.21875 | 0.216517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.63488 | −0.243409 | −0.121705 | − | 0.992566i | \(-0.538836\pi\) | ||||
−0.121705 | + | 0.992566i | \(0.538836\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.97394 | −0.198263 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.3226 | 1.21612 | 0.608058 | − | 0.793892i | \(-0.291949\pi\) | ||||
0.608058 | + | 0.793892i | \(0.291949\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5483 | 0.961376 | 0.480688 | − | 0.876892i | \(-0.340387\pi\) | ||||
0.480688 | + | 0.876892i | \(0.340387\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.46595 | 0.228043 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.5748 | −1.74097 | −0.870485 | − | 0.492195i | \(-0.836195\pi\) | ||||
−0.870485 | + | 0.492195i | \(0.836195\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8083 | 0.705059 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.141636 | −0.00920022 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 28.8526 | 1.86632 | 0.933160 | − | 0.359461i | \(-0.117039\pi\) | ||||
0.933160 | + | 0.359461i | \(0.117039\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.9374 | 0.962205 | 0.481102 | − | 0.876664i | \(-0.340237\pi\) | ||||
0.481102 | + | 0.876664i | \(0.340237\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.30829 | 0.276377 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 10.5612 | 0.674730 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.4877 | −1.62174 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.34058 | −0.0849557 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.1778 | −1.52609 | −0.763044 | − | 0.646346i | \(-0.776296\pi\) | ||||
−0.763044 | + | 0.646346i | \(0.776296\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.433093 | −0.0272283 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.152778 | 0.00956735 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.16663 | 0.571799 | 0.285899 | − | 0.958260i | \(-0.407708\pi\) | ||||
0.285899 | + | 0.958260i | \(0.407708\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.2563 | −1.69362 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 20.9414 | 1.29624 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.3915 | 1.07241 | 0.536203 | − | 0.844089i | \(-0.319858\pi\) | ||||
0.536203 | + | 0.844089i | \(0.319858\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.20685 | 0.0741362 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.271220 | −0.0165984 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.9765 | −0.730218 | −0.365109 | − | 0.930965i | \(-0.618968\pi\) | ||||
−0.365109 | + | 0.930965i | \(0.618968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.5814 | 0.764267 | 0.382133 | − | 0.924107i | \(-0.375189\pi\) | ||||
0.382133 | + | 0.924107i | \(0.375189\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.30081 | −0.139251 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.12337 | −0.308951 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.98067 | −0.299259 | −0.149630 | − | 0.988742i | \(-0.547808\pi\) | ||||
−0.149630 | + | 0.988742i | \(0.547808\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.890488 | −0.0533121 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.8595 | −0.767133 | −0.383567 | − | 0.923513i | \(-0.625304\pi\) | ||||
−0.383567 | + | 0.923513i | \(0.625304\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.19862 | 0.546801 | 0.273401 | − | 0.961900i | \(-0.411852\pi\) | ||||
0.273401 | + | 0.961900i | \(0.411852\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.20978 | −0.0716609 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.8297 | −0.757316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.1043 | −0.947314 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0110409 | −0.000647232 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.1170 | −0.999988 | −0.499994 | − | 0.866029i | \(-0.666665\pi\) | ||||
−0.499994 | + | 0.866029i | \(0.666665\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.73216 | −0.566628 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.94090 | 0.286700 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.287502 | 0.0166267 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.5434 | 0.780628 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.34183 | 0.134534 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.97977 | −0.113361 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.2058 | −1.09614 | −0.548068 | − | 0.836434i | \(-0.684636\pi\) | ||||
−0.548068 | + | 0.836434i | \(0.684636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.706035 | 0.0401649 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.2230 | −1.31686 | −0.658428 | − | 0.752644i | \(-0.728778\pi\) | ||||
−0.658428 | + | 0.752644i | \(0.728778\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.5337 | −0.878016 | −0.439008 | − | 0.898483i | \(-0.644670\pi\) | ||||
−0.439008 | + | 0.898483i | \(0.644670\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.4626 | 0.702189 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −12.3799 | −0.695327 | −0.347664 | − | 0.937619i | \(-0.613025\pi\) | ||||
−0.347664 | + | 0.937619i | \(0.613025\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 36.0768 | 2.01992 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.34716 | 0.0751909 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.09232 | −0.394627 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.40106 | 0.188657 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.04739 | −0.113221 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −45.2935 | −2.49711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5304 | 0.743698 | 0.371849 | − | 0.928293i | \(-0.378724\pi\) | ||||
0.371849 | + | 0.928293i | \(0.378724\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −19.3429 | −1.05999 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.22539 | −0.340129 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.5353 | 1.11863 | 0.559315 | − | 0.828955i | \(-0.311064\pi\) | ||||
0.559315 | + | 0.828955i | \(0.311064\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.36419 | −0.0740924 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.53409 | −0.0830757 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.9236 | −0.805797 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.0136463 | 0.000734692 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.0348 | −0.860796 | −0.430398 | − | 0.902639i | \(-0.641627\pi\) | ||||
−0.430398 | + | 0.902639i | \(0.641627\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5976 | 1.10256 | 0.551282 | − | 0.834319i | \(-0.314139\pi\) | ||||
0.551282 | + | 0.834319i | \(0.314139\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.27993 | −0.175070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.38401 | 0.0736634 | 0.0368317 | − | 0.999321i | \(-0.488273\pi\) | ||||
0.0368317 | + | 0.999321i | \(0.488273\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16645 | 0.274207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.640234 | −0.0338848 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.24361 | 0.223969 | 0.111985 | − | 0.993710i | \(-0.464279\pi\) | ||||
0.111985 | + | 0.993710i | \(0.464279\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 37.1605 | 1.95582 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.46166 | 0.129204 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.01109 | 0.366977 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.7777 | −0.771388 | −0.385694 | − | 0.922627i | \(-0.626038\pi\) | ||||
−0.385694 | + | 0.922627i | \(0.626038\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.10485 | −0.473980 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.05743 | −0.262569 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −11.5535 | −0.598218 | −0.299109 | − | 0.954219i | \(-0.596689\pi\) | ||||
−0.299109 | + | 0.954219i | \(0.596689\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.161432 | 0.00833630 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.9490 | −1.23344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.1521 | 1.03514 | 0.517571 | − | 0.855640i | \(-0.326836\pi\) | ||||
0.517571 | + | 0.855640i | \(0.326836\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.36869 | 0.121352 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.49393 | −0.229629 | −0.114814 | − | 0.993387i | \(-0.536627\pi\) | ||||
−0.114814 | + | 0.993387i | \(0.536627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.4700 | 1.09421 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.61131 | 0.488570 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.85928 | −0.347779 | −0.173890 | − | 0.984765i | \(-0.555634\pi\) | ||||
−0.173890 | + | 0.984765i | \(0.555634\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0800015 | 0.00404585 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.15426 | 0.159111 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.877371 | −0.0441453 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.7721 | −0.891954 | −0.445977 | − | 0.895044i | \(-0.647144\pi\) | ||||
−0.445977 | + | 0.895044i | \(0.647144\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.06969 | 0.253802 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9637 | 0.996940 | 0.498470 | − | 0.866907i | \(-0.333895\pi\) | ||||
0.498470 | + | 0.866907i | \(0.333895\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.01838 | 0.0507292 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.76614 | 0.435593 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.3231 | −1.65177 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6507 | 0.773875 | 0.386938 | − | 0.922106i | \(-0.373533\pi\) | ||||
0.386938 | + | 0.922106i | \(0.373533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.157947 | −0.00779097 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.7837 | 2.00683 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.30430 | −0.407642 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.910310 | 0.0445781 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −25.8757 | −1.26411 | −0.632056 | − | 0.774923i | \(-0.717789\pi\) | ||||
−0.632056 | + | 0.774923i | \(0.717789\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.79000 | 0.428398 | 0.214199 | − | 0.976790i | \(-0.431286\pi\) | ||||
0.214199 | + | 0.976790i | \(0.431286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −32.1434 | −1.56286 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.946395 | 0.0459069 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.29643 | 0.401492 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.81293 | −0.135810 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4202 | 0.598261 | 0.299131 | − | 0.954212i | \(-0.403303\pi\) | ||||
0.299131 | + | 0.954212i | \(0.403303\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.44335 | 0.453819 | 0.226909 | − | 0.973916i | \(-0.427138\pi\) | ||||
0.226909 | + | 0.973916i | \(0.427138\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.13674 | −0.0545026 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.633492 | −0.0303040 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.6942 | 0.939953 | 0.469977 | − | 0.882679i | \(-0.344262\pi\) | ||||
0.469977 | + | 0.882679i | \(0.344262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −31.4084 | −1.49564 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.3873 | −0.731072 | −0.365536 | − | 0.930797i | \(-0.619114\pi\) | ||||
−0.365536 | + | 0.930797i | \(0.619114\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.68009 | −0.0796439 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.29119 | −0.0610710 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9276 | 0.798863 | 0.399432 | − | 0.916763i | \(-0.369208\pi\) | ||||
0.399432 | + | 0.916763i | \(0.369208\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.6854 | −0.738598 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.161432 | 0.00758473 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −14.2525 | −0.668169 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.23431 | −0.338407 | −0.169203 | − | 0.985581i | \(-0.554119\pi\) | ||||
−0.169203 | + | 0.985581i | \(0.554119\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.912689 | −0.0426007 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.6230 | 1.05366 | 0.526829 | − | 0.849971i | \(-0.323381\pi\) | ||||
0.526829 | + | 0.849971i | \(0.323381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −36.7217 | −1.70660 | −0.853302 | − | 0.521418i | \(-0.825403\pi\) | ||||
−0.853302 | + | 0.521418i | \(0.825403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.0483376 | 0.00224160 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.6994 | −0.633932 | −0.316966 | − | 0.948437i | \(-0.602664\pi\) | ||||
−0.316966 | + | 0.948437i | \(0.602664\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.0882 | 1.20464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.25212 | 0.149850 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.5579 | 0.761335 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.49403 | −0.343850 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.58910 | −0.164333 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.7364 | 1.40438 | 0.702191 | − | 0.711989i | \(-0.252205\pi\) | ||||
0.702191 | + | 0.711989i | \(0.252205\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.1210 | 1.00863 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.0571863 | −0.00260207 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0683939 | −0.00310560 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.1333 | −1.45610 | −0.728050 | − | 0.685524i | \(-0.759573\pi\) | ||||
−0.728050 | + | 0.685524i | \(0.759573\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0349535 | 0.00158065 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −27.3982 | −1.23646 | −0.618232 | − | 0.785996i | \(-0.712151\pi\) | ||||
−0.618232 | + | 0.785996i | \(0.712151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.66416 | −0.300139 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 15.2366 | 0.684834 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.6506 | −0.971160 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.7573 | 1.15305 | 0.576527 | − | 0.817078i | \(-0.304408\pi\) | ||||
0.576527 | + | 0.817078i | \(0.304408\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.24990 | 0.145195 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 40.6555 | 1.81274 | 0.906370 | − | 0.422486i | \(-0.138842\pi\) | ||||
0.906370 | + | 0.422486i | \(0.138842\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.5066 | 0.645535 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.231293 | −0.0102721 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −37.1664 | −1.64737 | −0.823687 | − | 0.567045i | \(-0.808086\pi\) | ||||
−0.823687 | + | 0.567045i | \(0.808086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.3807 | −1.29973 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.22713 | 0.319085 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.37358 | 0.192723 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −55.3751 | −2.43540 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.92048 | −0.128195 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8001 | 0.779835 | 0.389918 | − | 0.920850i | \(-0.372503\pi\) | ||||
0.389918 | + | 0.920850i | \(0.372503\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9113 | 0.520846 | 0.260423 | − | 0.965495i | \(-0.416138\pi\) | ||||
0.260423 | + | 0.965495i | \(0.416138\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.676498 | −0.0295248 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.283379 | 0.0123442 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9929 | −0.999689 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 28.9429 | 1.25601 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.4125 | 0.451016 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.34505 | 0.360788 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.08813 | 0.0469563 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −54.1089 | −2.33063 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.0172 | −1.54850 | −0.774250 | − | 0.632880i | \(-0.781873\pi\) | ||||
−0.774250 | + | 0.632880i | \(0.781873\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.365430 | 0.0156821 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.6827 | −0.543266 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.1274 | 0.988857 | 0.494429 | − | 0.869218i | \(-0.335377\pi\) | ||||
0.494429 | + | 0.869218i | \(0.335377\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.88771 | 0.251281 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 52.7702 | 2.24808 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.67672 | 0.156350 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.04998 | 0.0445690 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.7989 | 0.584679 | 0.292339 | − | 0.956315i | \(-0.405566\pi\) | ||||
0.292339 | + | 0.956315i | \(0.405566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.9917 | −0.464900 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.782740 | −0.0330473 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.3822 | 0.774717 | 0.387358 | − | 0.921929i | \(-0.373388\pi\) | ||||
0.387358 | + | 0.921929i | \(0.373388\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.45054 | −0.355517 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −36.7354 | −1.54274 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.06642 | −0.170473 | −0.0852366 | − | 0.996361i | \(-0.527165\pi\) | ||||
−0.0852366 | + | 0.996361i | \(0.527165\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.78702 | −0.367725 | −0.183863 | − | 0.982952i | \(-0.558860\pi\) | ||||
−0.183863 | + | 0.982952i | \(0.558860\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.10090 | −0.0459906 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.0845329 | 0.00352526 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.1665 | −0.881173 | −0.440587 | − | 0.897710i | \(-0.645229\pi\) | ||||
−0.440587 | + | 0.897710i | \(0.645229\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.62223 | −0.108976 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 34.8000 | 1.44375 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.18313 | −0.256079 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.1146 | −0.418186 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 42.9895 | 1.77437 | 0.887184 | − | 0.461416i | \(-0.152658\pi\) | ||||
0.887184 | + | 0.461416i | \(0.152658\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.24394 | −0.0924600 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.28089 | 0.176092 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.7723 | 0.442363 | 0.221182 | − | 0.975233i | \(-0.429009\pi\) | ||||
0.221182 | + | 0.975233i | \(0.429009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.96597 | −0.162589 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.90225 | −0.0778539 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.7694 | −0.807756 | −0.403878 | − | 0.914813i | \(-0.632338\pi\) | ||||
−0.403878 | + | 0.914813i | \(0.632338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.8725 | 1.34090 | 0.670449 | − | 0.741956i | \(-0.266102\pi\) | ||||
0.670449 | + | 0.741956i | \(0.266102\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.5139 | 0.753946 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.2489 | 0.619956 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.7733 | 0.640217 | 0.320108 | − | 0.947381i | \(-0.396281\pi\) | ||||
0.320108 | + | 0.947381i | \(0.396281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.76364 | 0.193033 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.7599 | 1.48715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.83510 | 0.195288 | 0.0976439 | − | 0.995221i | \(-0.468869\pi\) | ||||
0.0976439 | + | 0.995221i | \(0.468869\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.494231 | 0.0199293 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.7533 | 1.19782 | 0.598912 | − | 0.800815i | \(-0.295600\pi\) | ||||
0.598912 | + | 0.800815i | \(0.295600\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 29.4984 | 1.18564 | 0.592820 | − | 0.805335i | \(-0.298014\pi\) | ||||
0.592820 | + | 0.805335i | \(0.298014\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.0815222 | −0.00327137 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.04059 | 0.282075 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.19813 | 0.247529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.15549 | 0.245435 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.40356 | −0.254922 | −0.127461 | − | 0.991844i | \(-0.540683\pi\) | ||||
−0.127461 | + | 0.991844i | \(0.540683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.210616 | −0.00837124 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.6730 | 0.582280 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.9193 | 1.42317 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.3647 | −0.607818 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.1471 | 1.78320 | 0.891601 | − | 0.452822i | \(-0.149583\pi\) | ||||
0.891601 | + | 0.452822i | \(0.149583\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.76855 | −0.109181 | −0.0545905 | − | 0.998509i | \(-0.517385\pi\) | ||||
−0.0545905 | + | 0.998509i | \(0.517385\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.521723 | −0.0205428 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.3507 | −1.50772 | −0.753861 | − | 0.657034i | \(-0.771811\pi\) | ||||
−0.753861 | + | 0.657034i | \(0.771811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 49.8615 | 1.95723 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.202564 | −0.00793911 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.4333 | 0.838749 | 0.419375 | − | 0.907813i | \(-0.362249\pi\) | ||||
0.419375 | + | 0.907813i | \(0.362249\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.5392 | 0.763461 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.8505 | −0.813457 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.68358 | 0.221401 | 0.110701 | − | 0.993854i | \(-0.464691\pi\) | ||||
0.110701 | + | 0.993854i | \(0.464691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.80659 | 0.186955 | 0.0934774 | − | 0.995621i | \(-0.470202\pi\) | ||||
0.0934774 | + | 0.995621i | \(0.470202\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.519609 | 0.0201799 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31.4045 | 1.21782 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.595249 | −0.0230481 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −0.586785 | −0.0226864 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.1431 | 0.391569 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.42751 | 0.286309 | 0.143155 | − | 0.989700i | \(-0.454275\pi\) | ||||
0.143155 | + | 0.989700i | \(0.454275\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.964384 | −0.0371192 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.88835 | 0.226308 | 0.113154 | − | 0.993577i | \(-0.463905\pi\) | ||||
0.113154 | + | 0.993577i | \(0.463905\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.286612 | 0.0109992 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.95786 | 0.113345 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.9378 | 1.60471 | 0.802353 | − | 0.596849i | \(-0.203581\pi\) | ||||
0.802353 | + | 0.596849i | \(0.203581\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.978415 | −0.0373833 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.34855 | 0.0896029 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.10457 | 0.156372 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 37.3562 | 1.42110 | 0.710549 | − | 0.703648i | \(-0.248447\pi\) | ||||
0.710549 | + | 0.703648i | \(0.248447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −63.8506 | −2.42548 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.63898 | 0.213899 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.89743 | 0.109748 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.29001 | −0.162263 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.1798 | −1.89526 | −0.947632 | − | 0.319366i | \(-0.896530\pi\) | ||||
−0.947632 | + | 0.319366i | \(0.896530\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −48.7422 | −1.83835 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.74481 | 0.0657134 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −60.7914 | −2.28630 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.4870 | −0.619182 | −0.309591 | − | 0.950870i | \(-0.600192\pi\) | ||||
−0.309591 | + | 0.950870i | \(0.600192\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.60925 | 0.0978544 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.0253117 | 0.000947931 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.4249 | −0.651655 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.65773 | 0.173946 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.3085 | −1.09302 | −0.546512 | − | 0.837451i | \(-0.684045\pi\) | ||||
−0.546512 | + | 0.837451i | \(0.684045\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.3280 | −0.682569 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.41138 | 0.0896801 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.04163 | −0.261519 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2952 | 0.456004 | 0.228002 | − | 0.973661i | \(-0.426781\pi\) | ||||
0.228002 | + | 0.973661i | \(0.426781\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.6029 | −0.948256 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.05860 | −0.113127 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.6390 | 1.31636 | 0.658179 | − | 0.752862i | \(-0.271327\pi\) | ||||
0.658179 | + | 0.752862i | \(0.271327\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.70491 | 0.0628867 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 31.8950 | 1.17487 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.0036 | −1.61870 | −0.809349 | − | 0.587328i | \(-0.800180\pi\) | ||||
−0.809349 | + | 0.587328i | \(0.800180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.11452 | −0.151151 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.19041 | −0.227104 | −0.113552 | − | 0.993532i | \(-0.536223\pi\) | ||||
−0.113552 | + | 0.993532i | \(0.536223\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.99834 | −0.293037 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.6965 | 0.903597 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.9708 | −1.27781 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.56892 | 0.312685 | 0.156342 | − | 0.987703i | \(-0.450030\pi\) | ||||
0.156342 | + | 0.987703i | \(0.450030\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.90307 | −0.142236 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.00000 | 0.0363937 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.56594 | −0.311335 | −0.155667 | − | 0.987810i | \(-0.549753\pi\) | ||||
−0.155667 | + | 0.987810i | \(0.549753\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.0699150 | −0.00253775 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 41.4229 | 1.50158 | 0.750789 | − | 0.660542i | \(-0.229674\pi\) | ||||
0.750789 | + | 0.660542i | \(0.229674\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.1481 | 1.92409 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.81452 | −0.101759 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −33.0997 | −1.19516 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9301 | −0.610516 | −0.305258 | − | 0.952270i | \(-0.598743\pi\) | ||||
−0.305258 | + | 0.952270i | \(0.598743\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.47979 | 0.0532932 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.46937 | −0.196719 | −0.0983597 | − | 0.995151i | \(-0.531360\pi\) | ||||
−0.0983597 | + | 0.995151i | \(0.531360\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.299430 | 0.0107559 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.40004 | −0.157850 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.9433 | −0.822030 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26.4696 | −0.947158 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.79083 | 0.242685 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 20.1455 | 0.719023 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.9943 | 0.712719 | 0.356359 | − | 0.934349i | \(-0.384018\pi\) | ||||
0.356359 | + | 0.934349i | \(0.384018\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.80754 | 0.0999512 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.4129 | 1.25914 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.73332 | −0.239107 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.194824 | 0.00690969 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.4212 | 1.43179 | 0.715896 | − | 0.698206i | \(-0.246018\pi\) | ||||
0.715896 | + | 0.698206i | \(0.246018\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2290 | 0.361875 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.99648 | 0.176542 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.9204 | −1.26760 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.354244 | −0.0124855 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.93338 | −0.0680583 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.0223 | −0.879736 | −0.439868 | − | 0.898062i | \(-0.644975\pi\) | ||||
−0.439868 | + | 0.898062i | \(0.644975\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.6427 | 0.549290 | 0.274645 | − | 0.961546i | \(-0.411440\pi\) | ||||
0.274645 | + | 0.961546i | \(0.411440\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.03104 | 0.0712317 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.216522 | 0.00758442 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.2195 | 0.847335 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 42.3862 | 1.48109 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.8869 | 1.49676 | 0.748381 | − | 0.663269i | \(-0.230832\pi\) | ||||
0.748381 | + | 0.663269i | \(0.230832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −41.4506 | −1.44488 | −0.722439 | − | 0.691434i | \(-0.756979\pi\) | ||||
−0.722439 | + | 0.691434i | \(0.756979\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.827075 | −0.0287951 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.4717 | −0.572777 | −0.286389 | − | 0.958114i | \(-0.592455\pi\) | ||||
−0.286389 | + | 0.958114i | \(0.592455\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 42.5502 | 1.47783 | 0.738915 | − | 0.673798i | \(-0.235338\pi\) | ||||
0.738915 | + | 0.673798i | \(0.235338\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.804039 | −0.0278918 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.99506 | 0.346308 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 20.1317 | 0.696687 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.288766 | −0.00998121 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.51874 | 0.190528 | 0.0952640 | − | 0.995452i | \(-0.469630\pi\) | ||||
0.0952640 | + | 0.995452i | \(0.469630\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.5845 | 0.709811 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.07593 | −0.0714989 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.43276 | −0.0492885 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −63.9022 | −2.19570 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.48495 | 0.0509634 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.549814 | 0.0188474 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.6688 | 1.66639 | 0.833193 | − | 0.552982i | \(-0.186510\pi\) | ||||
0.833193 | + | 0.552982i | \(0.186510\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.2868 | 0.762192 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.8795 | 0.747391 | 0.373695 | − | 0.927552i | \(-0.378091\pi\) | ||||
0.373695 | + | 0.927552i | \(0.378091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.56079 | 0.121493 | 0.0607463 | − | 0.998153i | \(-0.480652\pi\) | ||||
0.0607463 | + | 0.998153i | \(0.480652\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.07113 | −0.0705839 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.8993 | 1.15395 | 0.576973 | − | 0.816763i | \(-0.304234\pi\) | ||||
0.576973 | + | 0.816763i | \(0.304234\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.0911 | −0.615116 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.59975 | −0.0882922 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.49509 | 0.152486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.1730 | −0.717418 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.203399 | 0.00688402 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.19061 | −0.141668 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.83378 | −0.163225 | −0.0816126 | − | 0.996664i | \(-0.526007\pi\) | ||||
−0.0816126 | + | 0.996664i | \(0.526007\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.76324 | −0.0932016 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0.347938 | 0.0117223 | 0.00586116 | − | 0.999983i | \(-0.498134\pi\) | ||||
0.00586116 | + | 0.999983i | \(0.498134\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.71668 | −0.158729 | −0.0793644 | − | 0.996846i | \(-0.525289\pi\) | ||||
−0.0793644 | + | 0.996846i | \(0.525289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.57108 | −0.0528113 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.3660 | −0.750977 | −0.375489 | − | 0.926827i | \(-0.622525\pi\) | ||||
−0.375489 | + | 0.926827i | \(0.622525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −61.4887 | −2.06227 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −44.9122 | −1.50461 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −80.9981 | −2.71050 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.74050 | 0.225310 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0464119 | 0.00154965 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.10848 | −0.0703216 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.14216 | 0.0380507 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.18634 | 0.0727567 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.26368 | 0.0752472 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.4408 | −1.50884 | −0.754419 | − | 0.656393i | \(-0.772081\pi\) | ||||
−0.754419 | + | 0.656393i | \(0.772081\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −43.1417 | −1.43092 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3315 | −0.971798 | −0.485899 | − | 0.874015i | \(-0.661508\pi\) | ||||
−0.485899 | + | 0.874015i | \(0.661508\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 42.5460 | 1.40807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.319597 | −0.0105656 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −81.8813 | −2.70396 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.7346 | 1.54163 | 0.770816 | − | 0.637057i | \(-0.219849\pi\) | ||||
0.770816 | + | 0.637057i | \(0.219849\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.10044 | −0.102163 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.5714 | 0.578370 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.50414 | 0.213855 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.0068 | −0.427198 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.9530 | 0.753062 | 0.376531 | − | 0.926404i | \(-0.377117\pi\) | ||||
0.376531 | + | 0.926404i | \(0.377117\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −79.1459 | −2.59390 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.74893 | −0.122735 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.84873 | −0.158570 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.7330 | −0.513976 | −0.256988 | − | 0.966415i | \(-0.582730\pi\) | ||||
−0.256988 | + | 0.966415i | \(0.582730\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.50763 | −0.0818335 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −42.5723 | −1.38782 | −0.693908 | − | 0.720064i | \(-0.744113\pi\) | ||||
−0.693908 | + | 0.720064i | \(0.744113\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.258801 | 0.00842773 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.04136 | 0.131465 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −52.1864 | −1.69583 | −0.847916 | − | 0.530131i | \(-0.822143\pi\) | ||||
−0.847916 | + | 0.530131i | \(0.822143\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.8452 | 0.774046 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.99852 | −0.0648064 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.38819 | −0.206934 | −0.103467 | − | 0.994633i | \(-0.532994\pi\) | ||||
−0.103467 | + | 0.994633i | \(0.532994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.81958 | −0.220676 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.82395 | 0.188262 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.10015 | 0.132401 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9103 | −0.997108 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.8177 | −0.799738 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.2436 | −0.522900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.07412 | 0.0666992 | 0.0333496 | − | 0.999444i | \(-0.489383\pi\) | ||||
0.0333496 | + | 0.999444i | \(0.489383\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.14493 | −0.0367803 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.8743 | −1.18335 | −0.591676 | − | 0.806176i | \(-0.701534\pi\) | ||||
−0.591676 | + | 0.806176i | \(0.701534\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −23.6307 | −0.757567 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.549040 | 0.0175834 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −16.8655 | −0.539576 | −0.269788 | − | 0.962920i | \(-0.586954\pi\) | ||||
−0.269788 | + | 0.962920i | \(0.586954\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.60772 | 0.275104 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.7175 | 1.20423 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.8953 | 0.379402 | 0.189701 | − | 0.981842i | \(-0.439248\pi\) | ||||
0.189701 | + | 0.981842i | \(0.439248\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.5182 | 0.844942 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.31182 | −0.232738 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.273197 | −0.00868716 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.0984 | −1.49613 | −0.748066 | − | 0.663625i | \(-0.769017\pi\) | ||||
−0.748066 | + | 0.663625i | \(0.769017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.18424 | 0.0693147 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.7836 | −0.373566 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −37.6403 | −1.19208 | −0.596041 | − | 0.802954i | \(-0.703260\pi\) | ||||
−0.596041 | + | 0.802954i | \(0.703260\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.27249 | −0.198453 |
(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 | 6040.2.a.s.1.12 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6040.2.a.s.1.12 | ✓ | 24 | 1.1 | even | 1 | trivial |