Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(1\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.43 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 | ||||||||
\(3\) | 2.95352 | 1.70522 | 0.852609 | − | 0.522550i | \(-0.175019\pi\) | ||||
0.852609 | + | 0.522550i | \(0.175019\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.20957 | −0.988149 | −0.494074 | − | 0.869420i | \(-0.664493\pi\) | ||||
−0.494074 | + | 0.869420i | \(0.664493\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.79098 | 1.05489 | 0.527445 | − | 0.849589i | \(-0.323150\pi\) | ||||
0.527445 | + | 0.849589i | \(0.323150\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.72330 | 1.90777 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.59219 | −0.480064 | −0.240032 | − | 0.970765i | \(-0.577158\pi\) | ||||
−0.240032 | + | 0.970765i | \(0.577158\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.09648 | −0.858809 | −0.429405 | − | 0.903112i | \(-0.641277\pi\) | ||||
−0.429405 | + | 0.903112i | \(0.641277\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.52601 | −1.68501 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.40426 | −1.55326 | −0.776630 | − | 0.629957i | \(-0.783073\pi\) | ||||
−0.776630 | + | 0.629957i | \(0.783073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.68929 | −0.846381 | −0.423190 | − | 0.906041i | \(-0.639090\pi\) | ||||
−0.423190 | + | 0.906041i | \(0.639090\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.24322 | 1.79882 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.82834 | 0.798263 | 0.399132 | − | 0.916894i | \(-0.369312\pi\) | ||||
0.399132 | + | 0.916894i | \(0.369312\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.117811 | −0.0235621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 8.04333 | 1.54794 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.84859 | 0.343274 | 0.171637 | − | 0.985160i | \(-0.445094\pi\) | ||||
0.171637 | + | 0.985160i | \(0.445094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.59961 | −1.72414 | −0.862071 | − | 0.506788i | \(-0.830833\pi\) | ||||
−0.862071 | + | 0.506788i | \(0.830833\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.70258 | −0.818613 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.16685 | −1.04239 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.44224 | −1.55230 | −0.776148 | − | 0.630551i | \(-0.782829\pi\) | ||||
−0.776148 | + | 0.630551i | \(0.782829\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.14553 | −1.46446 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.33089 | −1.45724 | −0.728620 | − | 0.684918i | \(-0.759838\pi\) | ||||
−0.728620 | + | 0.684918i | \(0.759838\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.49925 | −0.381132 | −0.190566 | − | 0.981674i | \(-0.561032\pi\) | ||||
−0.190566 | + | 0.981674i | \(0.561032\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −12.6460 | −1.88516 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.81656 | −0.410838 | −0.205419 | − | 0.978674i | \(-0.565856\pi\) | ||||
−0.205419 | + | 0.978674i | \(0.565856\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.789558 | 0.112794 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.9151 | −2.64865 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.77002 | 0.243131 | 0.121565 | − | 0.992583i | \(-0.461209\pi\) | ||||
0.121565 | + | 0.992583i | \(0.461209\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.51806 | 0.474375 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8964 | −1.44326 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.74373 | 0.747770 | 0.373885 | − | 0.927475i | \(-0.378025\pi\) | ||||
0.373885 | + | 0.927475i | \(0.378025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.55137 | 0.326669 | 0.163334 | − | 0.986571i | \(-0.447775\pi\) | ||||
0.163334 | + | 0.986571i | \(0.447775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.9736 | 2.01249 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.84188 | 0.848631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.92611 | 0.968329 | 0.484164 | − | 0.874977i | \(-0.339124\pi\) | ||||
0.484164 | + | 0.874977i | \(0.339124\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.3071 | 1.36121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0832947 | 0.00988526 | 0.00494263 | − | 0.999988i | \(-0.498427\pi\) | ||||
0.00494263 | + | 0.999988i | \(0.498427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.15722 | −0.252484 | −0.126242 | − | 0.991999i | \(-0.540292\pi\) | ||||
−0.126242 | + | 0.991999i | \(0.540292\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.347957 | −0.0401786 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.44377 | −0.506415 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.81067 | 0.428734 | 0.214367 | − | 0.976753i | \(-0.431231\pi\) | ||||
0.214367 | + | 0.976753i | \(0.431231\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.58627 | 0.731808 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.22034 | −0.243714 | −0.121857 | − | 0.992548i | \(-0.538885\pi\) | ||||
−0.121857 | + | 0.992548i | \(0.538885\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.1506 | 1.53485 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.45984 | 0.585356 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.81827 | 0.828735 | 0.414367 | − | 0.910110i | \(-0.364003\pi\) | ||||
0.414367 | + | 0.910110i | \(0.364003\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.64221 | −0.905950 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −28.3527 | −2.94004 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.15173 | 0.836350 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.44586 | −0.959081 | −0.479541 | − | 0.877520i | \(-0.659197\pi\) | ||||
−0.479541 | + | 0.877520i | \(0.659197\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.11259 | −0.915850 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.00534 | −0.498050 | −0.249025 | − | 0.968497i | \(-0.580110\pi\) | ||||
−0.249025 | + | 0.968497i | \(0.580110\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.08879 | 0.501413 | 0.250707 | − | 0.968063i | \(-0.419337\pi\) | ||||
0.250707 | + | 0.968063i | \(0.419337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −18.2140 | −1.77750 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0939 | 1.26584 | 0.632918 | − | 0.774219i | \(-0.281857\pi\) | ||||
0.632918 | + | 0.774219i | \(0.281857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.5138 | −1.19860 | −0.599301 | − | 0.800523i | \(-0.704555\pi\) | ||||
−0.599301 | + | 0.800523i | \(0.704555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −27.8879 | −2.64700 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.39986 | 0.884265 | 0.442132 | − | 0.896950i | \(-0.354222\pi\) | ||||
0.442132 | + | 0.896950i | \(0.354222\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.45897 | −0.788803 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −17.7221 | −1.63841 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.8741 | −1.63852 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.46493 | −0.769539 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.5590 | −2.48491 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3081 | 1.01143 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.3179 | 1.89166 | 0.945830 | − | 0.324661i | \(-0.105250\pi\) | ||||
0.945830 | + | 0.324661i | \(0.105250\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −7.38160 | −0.649913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.57963 | −0.312754 | −0.156377 | − | 0.987697i | \(-0.549982\pi\) | ||||
−0.156377 | + | 0.987697i | \(0.549982\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2967 | −0.892839 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.7723 | −1.52959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.0256 | −1.88177 | −0.940886 | − | 0.338723i | \(-0.890005\pi\) | ||||
−0.940886 | + | 0.338723i | \(0.890005\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.3419 | 1.13164 | 0.565822 | − | 0.824527i | \(-0.308559\pi\) | ||||
0.565822 | + | 0.824527i | \(0.308559\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.31879 | −0.700568 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.93019 | 0.412283 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.08458 | −0.339206 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.33198 | 0.192338 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.8924 | −0.892339 | −0.446169 | − | 0.894949i | \(-0.647212\pi\) | ||||
−0.446169 | + | 0.894949i | \(0.647212\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.3935 | 1.65960 | 0.829800 | − | 0.558061i | \(-0.188455\pi\) | ||||
0.829800 | + | 0.558061i | \(0.188455\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −36.6535 | −2.96326 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.2110 | 1.70371 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.7969 | 1.65978 | 0.829888 | − | 0.557929i | \(-0.188404\pi\) | ||||
0.829888 | + | 0.557929i | \(0.188404\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.22779 | 0.414591 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.6848 | 0.842081 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.50279 | −0.509338 | −0.254669 | − | 0.967028i | \(-0.581966\pi\) | ||||
−0.254669 | + | 0.967028i | \(0.581966\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.3907 | 0.808912 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.59953 | 0.201158 | 0.100579 | − | 0.994929i | \(-0.467931\pi\) | ||||
0.100579 | + | 0.994929i | \(0.467931\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.41181 | −0.262447 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −21.1149 | −1.61470 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.08423 | −0.158461 | −0.0792306 | − | 0.996856i | \(-0.525246\pi\) | ||||
−0.0792306 | + | 0.996856i | \(0.525246\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.328807 | −0.0248555 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 16.9642 | 1.27511 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.99236 | −0.373147 | −0.186573 | − | 0.982441i | \(-0.559738\pi\) | ||||
−0.186573 | + | 0.982441i | \(0.559738\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.41894 | −0.477116 | −0.238558 | − | 0.971128i | \(-0.576675\pi\) | ||||
−0.238558 | + | 0.971128i | \(0.576675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.53552 | 0.557042 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.8633 | 1.53390 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.1968 | 0.745664 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 22.4488 | 1.63291 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.14655 | 0.517107 | 0.258553 | − | 0.965997i | \(-0.416754\pi\) | ||||
0.258553 | + | 0.965997i | \(0.416754\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.7630 | −0.774738 | −0.387369 | − | 0.921925i | \(-0.626616\pi\) | ||||
−0.387369 | + | 0.921925i | \(0.626616\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 20.2077 | 1.44710 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.15452 | 0.367244 | 0.183622 | − | 0.982997i | \(-0.441218\pi\) | ||||
0.183622 | + | 0.982997i | \(0.441218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.68144 | −0.686299 | −0.343150 | − | 0.939281i | \(-0.611494\pi\) | ||||
−0.343150 | + | 0.939281i | \(0.611494\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.4100 | 1.65121 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.15936 | 0.362116 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 20.6172 | 1.43997 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.9107 | 1.52290 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.87405 | 0.406317 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.36365 | −0.369249 | −0.184624 | − | 0.982809i | \(-0.559107\pi\) | ||||
−0.184624 | + | 0.982809i | \(0.559107\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.246013 | 0.0168565 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.52226 | 0.376615 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −26.7923 | −1.81878 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.37141 | −0.430540 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 19.8307 | 1.33395 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.71908 | 0.650838 | 0.325419 | − | 0.945570i | \(-0.394495\pi\) | ||||
0.325419 | + | 0.945570i | \(0.394495\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.674266 | −0.0449511 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.18543 | 0.277797 | 0.138898 | − | 0.990307i | \(-0.455644\pi\) | ||||
0.138898 | + | 0.990307i | \(0.455644\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3864 | −1.08285 | −0.541423 | − | 0.840750i | \(-0.682114\pi\) | ||||
−0.541423 | + | 0.840750i | \(0.682114\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.1248 | −0.863547 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.39839 | −0.615709 | −0.307855 | − | 0.951433i | \(-0.599611\pi\) | ||||
−0.307855 | + | 0.951433i | \(0.599611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.22339 | 0.405969 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.2549 | 0.731085 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.1810 | 1.49946 | 0.749728 | − | 0.661746i | \(-0.230184\pi\) | ||||
0.749728 | + | 0.661746i | \(0.230184\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6968 | −1.07554 | −0.537768 | − | 0.843093i | \(-0.680732\pi\) | ||||
−0.537768 | + | 0.843093i | \(0.680732\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.67730 | −0.300049 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.74458 | −0.111457 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.4238 | 0.726880 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.55782 | −0.415585 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.8438 | 1.25253 | 0.626265 | − | 0.779610i | \(-0.284583\pi\) | ||||
0.626265 | + | 0.779610i | \(0.284583\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.09545 | −0.383217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 41.7942 | 2.61726 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.77049 | −0.422332 | −0.211166 | − | 0.977450i | \(-0.567726\pi\) | ||||
−0.211166 | + | 0.977450i | \(0.567726\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −26.3531 | −1.63750 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.5800 | 0.654886 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.61357 | −0.161160 | −0.0805798 | − | 0.996748i | \(-0.525677\pi\) | ||||
−0.0805798 | + | 0.996748i | \(0.525677\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.91098 | −0.240249 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.0914 | 1.41317 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.39158 | 0.389701 | 0.194851 | − | 0.980833i | \(-0.437578\pi\) | ||||
0.194851 | + | 0.980833i | \(0.437578\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.56193 | 0.398609 | 0.199305 | − | 0.979938i | \(-0.436132\pi\) | ||||
0.199305 | + | 0.979938i | \(0.436132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.5250 | −1.54484 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.187577 | 0.0113113 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.47130 | −0.328739 | −0.164369 | − | 0.986399i | \(-0.552559\pi\) | ||||
−0.164369 | + | 0.986399i | \(0.552559\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −54.9415 | −3.28926 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.7471 | −1.23767 | −0.618833 | − | 0.785523i | \(-0.712394\pi\) | ||||
−0.618833 | + | 0.785523i | \(0.712394\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.53526 | −0.388481 | −0.194240 | − | 0.980954i | \(-0.562224\pi\) | ||||
−0.194240 | + | 0.980954i | \(0.562224\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0763 | 1.42616 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −26.0423 | −1.53723 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24.0145 | 1.41262 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.8986 | −1.63544 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.0638 | 1.17214 | 0.586071 | − | 0.810260i | \(-0.300674\pi\) | ||||
0.586071 | + | 0.810260i | \(0.300674\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.6912 | −0.738908 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.8065 | −0.743110 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.8544 | −0.685556 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.97535 | −0.402053 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −14.7834 | −0.849283 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.63742 | −0.322797 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.2533 | 0.756405 | 0.378202 | − | 0.925723i | \(-0.376542\pi\) | ||||
0.378202 | + | 0.925723i | \(0.376542\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0299 | 0.855018 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.7386 | −1.17598 | −0.587990 | − | 0.808869i | \(-0.700080\pi\) | ||||
−0.587990 | + | 0.808869i | \(0.700080\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.4283 | −0.702489 | −0.351244 | − | 0.936284i | \(-0.614241\pi\) | ||||
−0.351244 | + | 0.936284i | \(0.614241\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35.2948 | −1.98863 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.73239 | −0.434295 | −0.217147 | − | 0.976139i | \(-0.569675\pi\) | ||||
−0.217147 | + | 0.976139i | \(0.569675\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.94330 | −0.164793 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.6732 | 2.15853 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 23.6271 | 1.31465 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.364798 | 0.0202354 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −36.9597 | −2.04388 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.86097 | −0.433389 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.796235 | −0.0437650 | −0.0218825 | − | 0.999761i | \(-0.506966\pi\) | ||||
−0.0218825 | + | 0.999761i | \(0.506966\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −54.0408 | −2.96142 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −17.5133 | −0.956853 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.3093 | −1.37868 | −0.689342 | − | 0.724437i | \(-0.742100\pi\) | ||||
−0.689342 | + | 0.724437i | \(0.742100\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 27.7627 | 1.50786 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.2844 | 0.827698 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3332 | −0.935905 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −24.9838 | −1.34508 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.11729 | −0.113662 | −0.0568310 | − | 0.998384i | \(-0.518100\pi\) | ||||
−0.0568310 | + | 0.998384i | \(0.518100\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.59151 | 0.406364 | 0.203182 | − | 0.979141i | \(-0.434872\pi\) | ||||
0.203182 | + | 0.979141i | \(0.434872\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −24.9060 | −1.32939 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.83946 | 0.310803 | 0.155401 | − | 0.987851i | \(-0.450333\pi\) | ||||
0.155401 | + | 0.987851i | \(0.450333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.184045 | −0.00976811 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −52.7917 | −2.79403 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.8687 | 1.36530 | 0.682649 | − | 0.730746i | \(-0.260828\pi\) | ||||
0.682649 | + | 0.730746i | \(0.260828\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.38915 | −0.283639 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.0014 | −1.31223 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.76653 | 0.249492 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.50518 | −0.130769 | −0.0653846 | − | 0.997860i | \(-0.520827\pi\) | ||||
−0.0653846 | + | 0.997860i | \(0.520827\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −53.4035 | −2.78007 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.94008 | 0.256476 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.7541 | 1.33350 | 0.666748 | − | 0.745283i | \(-0.267686\pi\) | ||||
0.666748 | + | 0.745283i | \(0.267686\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 33.3989 | 1.72471 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.72411 | −0.294807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.75495 | 0.295612 | 0.147806 | − | 0.989016i | \(-0.452779\pi\) | ||||
0.147806 | + | 0.989016i | \(0.452779\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 62.9630 | 3.22569 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.4505 | 0.789483 | 0.394741 | − | 0.918792i | \(-0.370834\pi\) | ||||
0.394741 | + | 0.918792i | \(0.370834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.81882 | 0.500413 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −14.3040 | −0.727111 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.6086 | 1.65332 | 0.826662 | − | 0.562699i | \(-0.190237\pi\) | ||||
0.826662 | + | 0.562699i | \(0.190237\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.5177 | −1.23991 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.5725 | −0.533314 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.41994 | −0.423653 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5235 | −0.979858 | −0.489929 | − | 0.871762i | \(-0.662977\pi\) | ||||
−0.489929 | + | 0.871762i | \(0.662977\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −30.4116 | −1.52249 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −36.1517 | −1.80533 | −0.902666 | − | 0.430342i | \(-0.858393\pi\) | ||||
−0.902666 | + | 0.430342i | \(0.858393\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.7250 | 1.48071 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.5528 | −0.723135 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 15.0339 | 0.745201 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.8489 | −1.03091 | −0.515456 | − | 0.856916i | \(-0.672377\pi\) | ||||
−0.515456 | + | 0.856916i | \(0.672377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −65.0531 | −3.20883 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.0306 | 0.788816 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.90599 | 0.240825 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 39.4056 | 1.92970 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.6753 | −0.961200 | −0.480600 | − | 0.876940i | \(-0.659581\pi\) | ||||
−0.480600 | + | 0.876940i | \(0.659581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.1107 | −1.71119 | −0.855594 | − | 0.517647i | \(-0.826808\pi\) | ||||
−0.855594 | + | 0.517647i | \(0.826808\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −16.1200 | −0.783783 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.754490 | 0.0365981 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.12081 | 0.344600 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.5614 | 0.703033 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.91371 | −0.333022 | −0.166511 | − | 0.986040i | \(-0.553250\pi\) | ||||
−0.166511 | + | 0.986040i | \(0.553250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.01226 | 0.0967030 | 0.0483515 | − | 0.998830i | \(-0.484603\pi\) | ||||
0.0483515 | + | 0.998830i | \(0.484603\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0639 | −0.578419 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.1238 | −0.675635 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.9694 | −1.90763 | −0.953817 | − | 0.300387i | \(-0.902884\pi\) | ||||
−0.953817 | + | 0.300387i | \(0.902884\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.51888 | 0.215185 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.6185 | 0.884590 | 0.442295 | − | 0.896870i | \(-0.354164\pi\) | ||||
0.442295 | + | 0.896870i | \(0.354164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −17.2750 | −0.818913 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −32.1709 | −1.52163 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.16958 | −0.149582 | −0.0747909 | − | 0.997199i | \(-0.523829\pi\) | ||||
−0.0747909 | + | 0.997199i | \(0.523829\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.8566 | 0.699568 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.2327 | 2.82998 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 19.0955 | 0.895213 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.36090 | 0.203994 | 0.101997 | − | 0.994785i | \(-0.467477\pi\) | ||||
0.101997 | + | 0.994785i | \(0.467477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −51.5116 | −2.40435 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.1343 | 0.751451 | 0.375725 | − | 0.926731i | \(-0.377394\pi\) | ||||
0.375725 | + | 0.926731i | \(0.377394\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.0431464 | −0.00200518 | −0.00100259 | − | 0.999999i | \(-0.500319\pi\) | ||||
−0.00100259 | + | 0.999999i | \(0.500319\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 62.6472 | 2.90519 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.9118 | 0.597485 | 0.298743 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298743 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.1216 | 1.02148 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 61.4243 | 2.83028 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.97929 | 0.182968 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.434637 | 0.0199425 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.1304 | 0.463837 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 21.4679 | 0.980893 | 0.490447 | − | 0.871471i | \(-0.336834\pi\) | ||||
0.490447 | + | 0.871471i | \(0.336834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 29.2377 | 1.33313 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 31.5578 | 1.43593 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.8713 | 0.947715 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −38.2038 | −1.73118 | −0.865590 | − | 0.500754i | \(-0.833056\pi\) | ||||
−0.865590 | + | 0.500754i | \(0.833056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.2061 | −0.868532 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.1385 | −1.76630 | −0.883148 | − | 0.469094i | \(-0.844580\pi\) | ||||
−0.883148 | + | 0.469094i | \(0.844580\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.8388 | −0.533193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.1349 | 0.904996 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.232474 | 0.0104279 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.40982 | −0.331709 | −0.165854 | − | 0.986150i | \(-0.553038\pi\) | ||||
−0.165854 | + | 0.986150i | \(0.553038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.67778 | 0.343018 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.40546 | −0.330193 | −0.165096 | − | 0.986277i | \(-0.552794\pi\) | ||||
−0.165096 | + | 0.986277i | \(0.552794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.0596 | 0.492147 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.0769 | −0.447529 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.1793 | 1.82524 | 0.912620 | − | 0.408809i | \(-0.134056\pi\) | ||||
0.912620 | + | 0.408809i | \(0.134056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.02076 | −0.266343 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.6742 | −1.31015 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.2440 | −0.495471 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.48451 | 0.197229 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.15582 | −0.270211 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.3037 | 0.626657 | 0.313329 | − | 0.949645i | \(-0.398556\pi\) | ||||
0.313329 | + | 0.949645i | \(0.398556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −36.1029 | −1.57867 | −0.789336 | − | 0.613962i | \(-0.789575\pi\) | ||||
−0.789336 | + | 0.613962i | \(0.789575\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.971139 | −0.0423840 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 61.4784 | 2.67804 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.34383 | −0.362775 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.8731 | 1.42657 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.8929 | 1.25149 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.9319 | −1.25083 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.7451 | −0.636296 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.25713 | −0.0541484 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.7919 | 1.23786 | 0.618930 | − | 0.785446i | \(-0.287567\pi\) | ||||
0.618930 | + | 0.785446i | \(0.287567\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.9585 | −0.813586 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 27.6500 | 1.18440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.12238 | 0.390045 | 0.195022 | − | 0.980799i | \(-0.437522\pi\) | ||||
0.195022 | + | 0.980799i | \(0.437522\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.6022 | 0.623208 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.81997 | −0.290540 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6355 | 0.452267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 61.6202 | 2.61563 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.1915 | 1.57585 | 0.787927 | − | 0.615769i | \(-0.211155\pi\) | ||||
0.787927 | + | 0.615769i | \(0.211155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.73888 | 0.327320 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.1165 | 1.27152 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 38.4653 | 1.62112 | 0.810559 | − | 0.585657i | \(-0.199164\pi\) | ||||
0.810559 | + | 0.585657i | \(0.199164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.7696 | −0.873785 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 18.3821 | 0.771977 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.1036 | 0.633178 | 0.316589 | − | 0.948563i | \(-0.397462\pi\) | ||||
0.316589 | + | 0.948563i | \(0.397462\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.5136 | −1.48620 | −0.743100 | − | 0.669181i | \(-0.766645\pi\) | ||||
−0.743100 | + | 0.669181i | \(0.766645\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.1075 | 0.881779 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.451019 | −0.0188088 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.28053 | −0.344723 | −0.172362 | − | 0.985034i | \(-0.555140\pi\) | ||||
−0.172362 | + | 0.985034i | \(0.555140\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −31.7888 | −1.32110 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.19691 | −0.257091 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.81821 | −0.116718 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 39.1582 | 1.61899 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.17101 | −0.337254 | −0.168627 | − | 0.985680i | \(-0.553933\pi\) | ||||
−0.168627 | + | 0.985680i | \(0.553933\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.4157 | 1.45928 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.2240 | 0.626231 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.96319 | −0.409139 | −0.204570 | − | 0.978852i | \(-0.565579\pi\) | ||||
−0.204570 | + | 0.978852i | \(0.565579\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 39.4941 | 1.61910 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.5944 | −1.17029 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8594 | 0.811433 | 0.405717 | − | 0.913999i | \(-0.367022\pi\) | ||||
0.405717 | + | 0.913999i | \(0.367022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.1165 | 0.861361 | 0.430680 | − | 0.902504i | \(-0.358274\pi\) | ||||
0.430680 | + | 0.902504i | \(0.358274\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 45.3635 | 1.84735 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.7038 | 0.760419 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.1420 | −0.939305 | −0.469653 | − | 0.882851i | \(-0.655621\pi\) | ||||
−0.469653 | + | 0.882851i | \(0.655621\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 15.2383 | 0.617487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.72144 | 0.352832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.0338 | −1.25344 | −0.626721 | − | 0.779244i | \(-0.715603\pi\) | ||||
−0.626721 | + | 0.779244i | \(0.715603\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 60.8935 | 2.45546 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21.7744 | −0.876606 | −0.438303 | − | 0.898827i | \(-0.644420\pi\) | ||||
−0.438303 | + | 0.898827i | \(0.644420\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.3890 | 1.22144 | 0.610719 | − | 0.791848i | \(-0.290881\pi\) | ||||
0.610719 | + | 0.791848i | \(0.290881\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 30.7926 | 1.23566 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 21.8206 | 0.874225 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3971 | −0.975883 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 17.3492 | 0.692859 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 60.4705 | 2.41112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.5313 | 0.896958 | 0.448479 | − | 0.893793i | \(-0.351966\pi\) | ||||
0.448479 | + | 0.893793i | \(0.351966\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.8417 | −0.629649 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −47.1034 | −1.86924 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.44485 | −0.0968686 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.476721 | 0.0188588 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −14.4396 | −0.570331 | −0.285165 | − | 0.958478i | \(-0.592048\pi\) | ||||
−0.285165 | + | 0.958478i | \(0.592048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.9112 | −1.02184 | −0.510920 | − | 0.859629i | \(-0.670695\pi\) | ||||
−0.510920 | + | 0.859629i | \(0.670695\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.3101 | 0.642211 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −27.6243 | −1.08602 | −0.543012 | − | 0.839725i | \(-0.682716\pi\) | ||||
−0.543012 | + | 0.839725i | \(0.682716\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.14512 | −0.358977 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −79.1317 | −3.10142 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.3271 | −0.834595 | −0.417297 | − | 0.908770i | \(-0.637023\pi\) | ||||
−0.417297 | + | 0.908770i | \(0.637023\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.90945 | 0.309048 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −12.3464 | −0.481681 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.0886 | 0.899406 | 0.449703 | − | 0.893178i | \(-0.351530\pi\) | ||||
0.449703 | + | 0.893178i | \(0.351530\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.1231 | −1.36613 | −0.683066 | − | 0.730357i | \(-0.739354\pi\) | ||||
−0.683066 | + | 0.730357i | \(0.739354\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 58.5703 | 2.27468 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.7513 | 0.882258 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.07701 | 0.274023 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.7055 | 1.10982 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.06226 | −0.156822 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.258351 | 0.00995868 | 0.00497934 | − | 0.999988i | \(-0.498415\pi\) | ||||
0.00497934 | + | 0.999988i | \(0.498415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.947590 | −0.0364728 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.2964 | 0.434155 | 0.217077 | − | 0.976154i | \(-0.430348\pi\) | ||||
0.217077 | + | 0.976154i | \(0.430348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.3632 | −1.01173 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.3618 | 0.473704 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.0402 | −1.11119 | −0.555597 | − | 0.831452i | \(-0.687510\pi\) | ||||
−0.555597 | + | 0.831452i | \(0.687510\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.6670 | 1.85947 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.3977 | −1.84649 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.48083 | −0.208803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.4622 | −1.42513 | −0.712565 | − | 0.701606i | \(-0.752467\pi\) | ||||
−0.712565 | + | 0.701606i | \(0.752467\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −25.4330 | −0.966121 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.4798 | −1.11823 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 59.7574 | 2.26347 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.7584 | −1.04992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3760 | 0.505204 | 0.252602 | − | 0.967570i | \(-0.418714\pi\) | ||||
0.252602 | + | 0.967570i | \(0.418714\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.8352 | 1.31383 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.3809 | 0.692266 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.9698 | −0.525388 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.4683 | −0.843815 | −0.421907 | − | 0.906639i | \(-0.638639\pi\) | ||||
−0.421907 | + | 0.906639i | \(0.638639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.8096 | 0.817925 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −36.7506 | −1.37632 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.8936 | −0.407397 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 68.4658 | 2.55690 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.2297 | −0.866320 | −0.433160 | − | 0.901317i | \(-0.642601\pi\) | ||||
−0.433160 | + | 0.901317i | \(0.642601\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.2027 | 0.528936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −49.3144 | −1.83402 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.217783 | −0.00808826 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.2597 | −0.899742 | −0.449871 | − | 0.893094i | \(-0.648530\pi\) | ||||
−0.449871 | + | 0.893094i | \(0.648530\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −33.5733 | −1.24346 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.0058 | 0.591997 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.52348 | 0.314822 | 0.157411 | − | 0.987533i | \(-0.449685\pi\) | ||||
0.157411 | + | 0.987533i | \(0.449685\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.15267 | −0.190059 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.6199 | −0.464860 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.3144 | −0.710493 | −0.355246 | − | 0.934773i | \(-0.615603\pi\) | ||||
−0.355246 | + | 0.934773i | \(0.615603\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.7405 | 1.23949 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.5656 | −0.717793 | −0.358897 | − | 0.933377i | \(-0.616847\pi\) | ||||
−0.358897 | + | 0.933377i | \(0.616847\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.0675 | 0.881763 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.7077 | −0.464949 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.5448 | 1.33532 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.00000 | −0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58.6092 | 2.13584 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.0608 | −1.63993 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.8637 | 1.26714 | 0.633572 | − | 0.773684i | \(-0.281588\pi\) | ||||
0.633572 | + | 0.773684i | \(0.281588\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.0030 | −0.653469 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.0128 | −1.74046 | −0.870231 | − | 0.492644i | \(-0.836030\pi\) | ||||
−0.870231 | + | 0.492644i | \(0.836030\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.9257 | −1.26439 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 80.9884 | 2.92814 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.7854 | −0.642192 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.08806 | −0.327724 | −0.163862 | − | 0.986483i | \(-0.552395\pi\) | ||||
−0.163862 | + | 0.986483i | \(0.552395\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.9968 | −0.720167 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8463 | −0.426082 | −0.213041 | − | 0.977043i | \(-0.568337\pi\) | ||||
−0.213041 | + | 0.977043i | \(0.568337\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.13094 | 0.0406244 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −77.8345 | −2.79230 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 34.4243 | 1.23338 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.132621 | −0.00474556 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.8688 | 0.531367 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −45.9523 | −1.64011 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.0222 | 1.39099 | 0.695496 | − | 0.718530i | \(-0.255185\pi\) | ||||
0.695496 | + | 0.718530i | \(0.255185\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.71924 | −0.274812 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.2348 | 0.932802 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.90026 | −0.280546 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.5512 | −0.409677 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −25.5010 | −0.903292 | −0.451646 | − | 0.892197i | \(-0.649163\pi\) | ||||
−0.451646 | + | 0.892197i | \(0.649163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.0380 | 0.638138 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 44.7463 | 1.58103 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.43471 | 0.121208 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −23.6088 | −0.832101 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.8777 | 0.664526 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 48.1735 | 1.69369 | 0.846844 | − | 0.531841i | \(-0.178500\pi\) | ||||
0.846844 | + | 0.531841i | \(0.178500\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.9614 | 1.29789 | 0.648945 | − | 0.760835i | \(-0.275211\pi\) | ||||
0.648945 | + | 0.760835i | \(0.275211\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19.3808 | 0.679715 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.3684 | 0.503301 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.22046 | 0.322583 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −49.4620 | −1.72834 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.5519 | 1.03137 | 0.515684 | − | 0.856779i | \(-0.327538\pi\) | ||||
0.515684 | + | 0.856779i | \(0.327538\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.1257 | 0.980401 | 0.490201 | − | 0.871610i | \(-0.336923\pi\) | ||||
0.490201 | + | 0.871610i | \(0.336923\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.554013 | 0.0192883 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4000 | −0.639832 | −0.319916 | − | 0.947446i | \(-0.603655\pi\) | ||||
−0.319916 | + | 0.947446i | \(0.603655\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.5514 | 0.366465 | 0.183233 | − | 0.983070i | \(-0.441344\pi\) | ||||
0.183233 | + | 0.983070i | \(0.441344\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.1596 | −0.560571 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.05653 | −0.175199 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.74384 | −0.198774 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −77.2129 | −2.66887 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.9931 | −0.586668 | −0.293334 | − | 0.956010i | \(-0.594765\pi\) | ||||
−0.293334 | + | 0.956010i | \(0.594765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.5827 | −0.882163 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −61.2769 | −2.11049 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.53862 | 0.259336 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.6254 | −0.811779 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19.3020 | −0.662444 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.1481 | −1.23914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.2185 | −1.10314 | −0.551569 | − | 0.834129i | \(-0.685971\pi\) | ||||
−0.551569 | + | 0.834129i | \(0.685971\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 46.6548 | 1.59556 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.1617 | 0.927825 | 0.463912 | − | 0.885881i | \(-0.346445\pi\) | ||||
0.463912 | + | 0.885881i | \(0.346445\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0978 | 0.822207 | 0.411103 | − | 0.911589i | \(-0.365144\pi\) | ||||
0.411103 | + | 0.911589i | \(0.365144\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −76.9165 | −2.62131 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.0759 | 1.33016 | 0.665079 | − | 0.746773i | \(-0.268398\pi\) | ||||
0.665079 | + | 0.746773i | \(0.268398\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.60525 | 0.156583 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 70.9274 | 2.40882 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.06732 | −0.205820 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.5431 | −0.831610 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −54.0615 | −1.82970 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.5608 | 1.06695 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.5102 | 1.50300 | 0.751501 | − | 0.659732i | \(-0.229330\pi\) | ||||
0.751501 | + | 0.659732i | \(0.229330\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 59.2590 | 1.99876 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.5078 | 1.83641 | 0.918206 | − | 0.396102i | \(-0.129637\pi\) | ||||
0.918206 | + | 0.396102i | \(0.129637\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.4818 | 0.453699 | 0.226849 | − | 0.973930i | \(-0.427158\pi\) | ||||
0.226849 | + | 0.973930i | \(0.427158\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −37.4837 | −1.26000 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.3814 | −0.550034 | −0.275017 | − | 0.961439i | \(-0.588684\pi\) | ||||
−0.275017 | + | 0.961439i | \(0.588684\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.4979 | 1.99550 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.4866 | −0.351314 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.3911 | 0.347725 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.0310 | 0.368725 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −35.0122 | −1.16902 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.7457 | −0.591852 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11.3357 | −0.377645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −20.6019 | −0.685587 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.1831 | 0.471461 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −19.3793 | −0.643479 | −0.321739 | − | 0.946828i | \(-0.604268\pi\) | ||||
−0.321739 | + | 0.946828i | \(0.604268\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.6470 | −0.950162 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 52.5920 | 1.74245 | 0.871225 | − | 0.490883i | \(-0.163326\pi\) | ||||
0.871225 | + | 0.490883i | \(0.163326\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.53520 | 0.116998 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −16.6502 | −0.550440 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.99068 | −0.329921 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.06710 | 0.167148 | 0.0835741 | − | 0.996502i | \(-0.473366\pi\) | ||||
0.0835741 | + | 0.996502i | \(0.473366\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 39.1439 | 1.28983 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.257920 | −0.00848956 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.11240 | 0.0365754 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 29.1247 | 0.956579 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.4490 | −0.736528 | −0.368264 | − | 0.929721i | \(-0.620048\pi\) | ||||
−0.368264 | + | 0.929721i | \(0.620048\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.91291 | −0.0954667 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −61.2520 | −2.00530 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.5305 | −0.736827 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.9615 | −0.848124 | −0.424062 | − | 0.905633i | \(-0.639396\pi\) | ||||
−0.424062 | + | 0.905633i | \(0.639396\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −36.7073 | −1.19790 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.7081 | −1.03365 | −0.516827 | − | 0.856090i | \(-0.672887\pi\) | ||||
−0.516827 | + | 0.856090i | \(0.672887\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.7218 | −1.16326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −49.6021 | −1.61356 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.16446 | −0.102831 | −0.0514155 | − | 0.998677i | \(-0.516373\pi\) | ||||
−0.0514155 | + | 0.998677i | \(0.516373\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.67980 | 0.216836 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.8378 | −0.740567 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.6308 | 0.895049 | 0.447525 | − | 0.894272i | \(-0.352306\pi\) | ||||
0.447525 | + | 0.894272i | \(0.352306\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −15.7908 | −0.510978 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.69311 | −0.281008 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −61.4729 | −1.98506 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.1525 | 1.97266 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 74.9404 | 2.41492 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.7816 | 0.765556 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −43.9255 | −1.41255 | −0.706275 | − | 0.707938i | \(-0.749626\pi\) | ||||
−0.706275 | + | 0.707938i | \(0.749626\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 69.7833 | 2.24176 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.8322 | 0.700630 | 0.350315 | − | 0.936632i | \(-0.386075\pi\) | ||||
0.350315 | + | 0.936632i | \(0.386075\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.2369 | 1.19376 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.07744 | 0.0345057 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0.468434 | 0.0149865 | 0.00749326 | − | 0.999972i | \(-0.497615\pi\) | ||||
0.00749326 | + | 0.999972i | \(0.497615\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −12.4482 | −0.397846 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −71.6201 | −2.28665 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.1145 | −0.705342 | −0.352671 | − | 0.935747i | \(-0.614727\pi\) | ||||
−0.352671 | + | 0.935747i | \(0.614727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.3893 | −0.362892 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −23.2176 | −0.739023 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.56798 | −0.304244 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 58.1206 | 1.84626 | 0.923130 | − | 0.384488i | \(-0.125622\pi\) | ||||
0.923130 | + | 0.384488i | \(0.125622\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.35170 | −0.0746289 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 21.3918 | 0.678166 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.2231 | −0.323769 | −0.161885 | − | 0.986810i | \(-0.551757\pi\) | ||||
−0.161885 | + | 0.986810i | \(0.551757\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −75.9471 | −2.40286 |
(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 | 6008.2.a.b.1.43 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.b.1.43 | ✓ | 44 | 1.1 | even | 1 | trivial |