Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3525,2,Mod(1,3525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3525, 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("3525.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3525 = 3 \cdot 5^{2} \cdot 47 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3525.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: | \(28.1472667125\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 3 x^{12} - 17 x^{11} + 51 x^{10} + 106 x^{9} - 316 x^{8} - 288 x^{7} + 852 x^{6} + 309 x^{5} - 923 x^{4} - 107 x^{3} + 293 x^{2} + 12 x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 705) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.105426\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3525.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.105426 | −0.0745472 | −0.0372736 | − | 0.999305i | \(-0.511867\pi\) | ||||
−0.0372736 | + | 0.999305i | \(0.511867\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.98889 | −0.994443 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.105426 | −0.0430398 | ||||||||
\(7\) | −3.91364 | −1.47922 | −0.739608 | − | 0.673038i | \(-0.764989\pi\) | ||||
−0.739608 | + | 0.673038i | \(0.764989\pi\) | |||||||
\(8\) | 0.420531 | 0.148680 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.01909 | 1.81482 | 0.907412 | − | 0.420242i | \(-0.138055\pi\) | ||||
0.907412 | + | 0.420242i | \(0.138055\pi\) | |||||||
\(12\) | −1.98889 | −0.574142 | ||||||||
\(13\) | −5.26742 | −1.46092 | −0.730460 | − | 0.682956i | \(-0.760694\pi\) | ||||
−0.730460 | + | 0.682956i | \(0.760694\pi\) | |||||||
\(14\) | 0.412598 | 0.110271 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.93344 | 0.983359 | ||||||||
\(17\) | −1.81336 | −0.439803 | −0.219902 | − | 0.975522i | \(-0.570574\pi\) | ||||
−0.219902 | + | 0.975522i | \(0.570574\pi\) | |||||||
\(18\) | −0.105426 | −0.0248491 | ||||||||
\(19\) | 8.19937 | 1.88106 | 0.940532 | − | 0.339704i | \(-0.110327\pi\) | ||||
0.940532 | + | 0.339704i | \(0.110327\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.91364 | −0.854025 | ||||||||
\(22\) | −0.634566 | −0.135290 | ||||||||
\(23\) | −4.74109 | −0.988585 | −0.494292 | − | 0.869296i | \(-0.664573\pi\) | ||||
−0.494292 | + | 0.869296i | \(0.664573\pi\) | |||||||
\(24\) | 0.420531 | 0.0858405 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.555321 | 0.108907 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 7.78377 | 1.47099 | ||||||||
\(29\) | −4.95306 | −0.919760 | −0.459880 | − | 0.887981i | \(-0.652108\pi\) | ||||
−0.459880 | + | 0.887981i | \(0.652108\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.06513 | −0.909723 | −0.454862 | − | 0.890562i | \(-0.650311\pi\) | ||||
−0.454862 | + | 0.890562i | \(0.650311\pi\) | |||||||
\(32\) | −1.25575 | −0.221987 | ||||||||
\(33\) | 6.01909 | 1.04779 | ||||||||
\(34\) | 0.191174 | 0.0327861 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.98889 | −0.331481 | ||||||||
\(37\) | 0.310810 | 0.0510968 | 0.0255484 | − | 0.999674i | \(-0.491867\pi\) | ||||
0.0255484 | + | 0.999674i | \(0.491867\pi\) | |||||||
\(38\) | −0.864424 | −0.140228 | ||||||||
\(39\) | −5.26742 | −0.843462 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.61857 | 0.408952 | 0.204476 | − | 0.978872i | \(-0.434451\pi\) | ||||
0.204476 | + | 0.978872i | \(0.434451\pi\) | |||||||
\(42\) | 0.412598 | 0.0636652 | ||||||||
\(43\) | −4.72384 | −0.720378 | −0.360189 | − | 0.932879i | \(-0.617288\pi\) | ||||
−0.360189 | + | 0.932879i | \(0.617288\pi\) | |||||||
\(44\) | −11.9713 | −1.80474 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.499832 | 0.0736962 | ||||||||
\(47\) | 1.00000 | 0.145865 | ||||||||
\(48\) | 3.93344 | 0.567743 | ||||||||
\(49\) | 8.31654 | 1.18808 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.81336 | −0.253921 | ||||||||
\(52\) | 10.4763 | 1.45280 | ||||||||
\(53\) | 3.05124 | 0.419120 | 0.209560 | − | 0.977796i | \(-0.432797\pi\) | ||||
0.209560 | + | 0.977796i | \(0.432797\pi\) | |||||||
\(54\) | −0.105426 | −0.0143466 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.64580 | −0.219930 | ||||||||
\(57\) | 8.19937 | 1.08603 | ||||||||
\(58\) | 0.522180 | 0.0685655 | ||||||||
\(59\) | −5.83634 | −0.759826 | −0.379913 | − | 0.925022i | \(-0.624046\pi\) | ||||
−0.379913 | + | 0.925022i | \(0.624046\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0059 | 1.28113 | 0.640564 | − | 0.767905i | \(-0.278701\pi\) | ||||
0.640564 | + | 0.767905i | \(0.278701\pi\) | |||||||
\(62\) | 0.533994 | 0.0678173 | ||||||||
\(63\) | −3.91364 | −0.493072 | ||||||||
\(64\) | −7.73448 | −0.966811 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.634566 | −0.0781097 | ||||||||
\(67\) | 8.37059 | 1.02263 | 0.511315 | − | 0.859393i | \(-0.329159\pi\) | ||||
0.511315 | + | 0.859393i | \(0.329159\pi\) | |||||||
\(68\) | 3.60656 | 0.437359 | ||||||||
\(69\) | −4.74109 | −0.570760 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.96991 | −1.18321 | −0.591606 | − | 0.806228i | \(-0.701506\pi\) | ||||
−0.591606 | + | 0.806228i | \(0.701506\pi\) | |||||||
\(72\) | 0.420531 | 0.0495600 | ||||||||
\(73\) | 3.65100 | 0.427317 | 0.213659 | − | 0.976908i | \(-0.431462\pi\) | ||||
0.213659 | + | 0.976908i | \(0.431462\pi\) | |||||||
\(74\) | −0.0327673 | −0.00380912 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.3076 | −1.87061 | ||||||||
\(77\) | −23.5565 | −2.68451 | ||||||||
\(78\) | 0.555321 | 0.0628777 | ||||||||
\(79\) | 9.00605 | 1.01326 | 0.506630 | − | 0.862163i | \(-0.330891\pi\) | ||||
0.506630 | + | 0.862163i | \(0.330891\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −0.276064 | −0.0304862 | ||||||||
\(83\) | 12.9270 | 1.41892 | 0.709462 | − | 0.704744i | \(-0.248938\pi\) | ||||
0.709462 | + | 0.704744i | \(0.248938\pi\) | |||||||
\(84\) | 7.78377 | 0.849279 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.498013 | 0.0537022 | ||||||||
\(87\) | −4.95306 | −0.531024 | ||||||||
\(88\) | 2.53121 | 0.269828 | ||||||||
\(89\) | 8.60225 | 0.911836 | 0.455918 | − | 0.890022i | \(-0.349311\pi\) | ||||
0.455918 | + | 0.890022i | \(0.349311\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.6148 | 2.16101 | ||||||||
\(92\) | 9.42948 | 0.983091 | ||||||||
\(93\) | −5.06513 | −0.525229 | ||||||||
\(94\) | −0.105426 | −0.0108738 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.25575 | −0.128164 | ||||||||
\(97\) | 8.42460 | 0.855388 | 0.427694 | − | 0.903924i | \(-0.359326\pi\) | ||||
0.427694 | + | 0.903924i | \(0.359326\pi\) | |||||||
\(98\) | −0.876777 | −0.0885679 | ||||||||
\(99\) | 6.01909 | 0.604941 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.0893 | 1.70045 | 0.850225 | − | 0.526420i | \(-0.176466\pi\) | ||||
0.850225 | + | 0.526420i | \(0.176466\pi\) | |||||||
\(102\) | 0.191174 | 0.0189291 | ||||||||
\(103\) | 11.9079 | 1.17332 | 0.586662 | − | 0.809832i | \(-0.300442\pi\) | ||||
0.586662 | + | 0.809832i | \(0.300442\pi\) | |||||||
\(104\) | −2.21511 | −0.217210 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.321679 | −0.0312443 | ||||||||
\(107\) | 12.2483 | 1.18409 | 0.592045 | − | 0.805905i | \(-0.298321\pi\) | ||||
0.592045 | + | 0.805905i | \(0.298321\pi\) | |||||||
\(108\) | −1.98889 | −0.191381 | ||||||||
\(109\) | 8.14773 | 0.780411 | 0.390205 | − | 0.920728i | \(-0.372404\pi\) | ||||
0.390205 | + | 0.920728i | \(0.372404\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.310810 | 0.0295008 | ||||||||
\(112\) | −15.3940 | −1.45460 | ||||||||
\(113\) | −5.65228 | −0.531722 | −0.265861 | − | 0.964011i | \(-0.585656\pi\) | ||||
−0.265861 | + | 0.964011i | \(0.585656\pi\) | |||||||
\(114\) | −0.864424 | −0.0809607 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.85107 | 0.914649 | ||||||||
\(117\) | −5.26742 | −0.486973 | ||||||||
\(118\) | 0.615299 | 0.0566429 | ||||||||
\(119\) | 7.09681 | 0.650564 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 25.2294 | 2.29359 | ||||||||
\(122\) | −1.05488 | −0.0955045 | ||||||||
\(123\) | 2.61857 | 0.236108 | ||||||||
\(124\) | 10.0740 | 0.904668 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.412598 | 0.0367571 | ||||||||
\(127\) | −0.531624 | −0.0471740 | −0.0235870 | − | 0.999722i | \(-0.507509\pi\) | ||||
−0.0235870 | + | 0.999722i | \(0.507509\pi\) | |||||||
\(128\) | 3.32691 | 0.294060 | ||||||||
\(129\) | −4.72384 | −0.415911 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.63792 | −0.492587 | −0.246294 | − | 0.969195i | \(-0.579213\pi\) | ||||
−0.246294 | + | 0.969195i | \(0.579213\pi\) | |||||||
\(132\) | −11.9713 | −1.04197 | ||||||||
\(133\) | −32.0894 | −2.78250 | ||||||||
\(134\) | −0.882475 | −0.0762342 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.762572 | −0.0653900 | ||||||||
\(137\) | 8.43334 | 0.720509 | 0.360254 | − | 0.932854i | \(-0.382690\pi\) | ||||
0.360254 | + | 0.932854i | \(0.382690\pi\) | |||||||
\(138\) | 0.499832 | 0.0425485 | ||||||||
\(139\) | −8.77831 | −0.744566 | −0.372283 | − | 0.928119i | \(-0.621425\pi\) | ||||
−0.372283 | + | 0.928119i | \(0.621425\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | 1.05108 | 0.0882051 | ||||||||
\(143\) | −31.7051 | −2.65131 | ||||||||
\(144\) | 3.93344 | 0.327786 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.384909 | −0.0318553 | ||||||||
\(147\) | 8.31654 | 0.685937 | ||||||||
\(148\) | −0.618165 | −0.0508128 | ||||||||
\(149\) | −5.39214 | −0.441741 | −0.220871 | − | 0.975303i | \(-0.570890\pi\) | ||||
−0.220871 | + | 0.975303i | \(0.570890\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.79825 | −0.227718 | −0.113859 | − | 0.993497i | \(-0.536321\pi\) | ||||
−0.113859 | + | 0.993497i | \(0.536321\pi\) | |||||||
\(152\) | 3.44809 | 0.279677 | ||||||||
\(153\) | −1.81336 | −0.146601 | ||||||||
\(154\) | 2.48346 | 0.200123 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.4763 | 0.838775 | ||||||||
\(157\) | 24.1331 | 1.92603 | 0.963017 | − | 0.269442i | \(-0.0868392\pi\) | ||||
0.963017 | + | 0.269442i | \(0.0868392\pi\) | |||||||
\(158\) | −0.949469 | −0.0755357 | ||||||||
\(159\) | 3.05124 | 0.241979 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 18.5549 | 1.46233 | ||||||||
\(162\) | −0.105426 | −0.00828302 | ||||||||
\(163\) | 17.8940 | 1.40157 | 0.700783 | − | 0.713374i | \(-0.252834\pi\) | ||||
0.700783 | + | 0.713374i | \(0.252834\pi\) | |||||||
\(164\) | −5.20803 | −0.406679 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.36284 | −0.105777 | ||||||||
\(167\) | −0.300971 | −0.0232899 | −0.0116449 | − | 0.999932i | \(-0.503707\pi\) | ||||
−0.0116449 | + | 0.999932i | \(0.503707\pi\) | |||||||
\(168\) | −1.64580 | −0.126977 | ||||||||
\(169\) | 14.7457 | 1.13429 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.19937 | 0.627022 | ||||||||
\(172\) | 9.39517 | 0.716375 | ||||||||
\(173\) | 11.3416 | 0.862285 | 0.431143 | − | 0.902284i | \(-0.358111\pi\) | ||||
0.431143 | + | 0.902284i | \(0.358111\pi\) | |||||||
\(174\) | 0.522180 | 0.0395863 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 23.6757 | 1.78462 | ||||||||
\(177\) | −5.83634 | −0.438686 | ||||||||
\(178\) | −0.906898 | −0.0679748 | ||||||||
\(179\) | −2.95113 | −0.220577 | −0.110289 | − | 0.993900i | \(-0.535178\pi\) | ||||
−0.110289 | + | 0.993900i | \(0.535178\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.8185 | −0.952791 | −0.476396 | − | 0.879231i | \(-0.658057\pi\) | ||||
−0.476396 | + | 0.879231i | \(0.658057\pi\) | |||||||
\(182\) | −2.17332 | −0.161098 | ||||||||
\(183\) | 10.0059 | 0.739659 | ||||||||
\(184\) | −1.99377 | −0.146983 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.533994 | 0.0391544 | ||||||||
\(187\) | −10.9148 | −0.798166 | ||||||||
\(188\) | −1.98889 | −0.145054 | ||||||||
\(189\) | −3.91364 | −0.284675 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8899 | 1.14975 | 0.574876 | − | 0.818241i | \(-0.305050\pi\) | ||||
0.574876 | + | 0.818241i | \(0.305050\pi\) | |||||||
\(192\) | −7.73448 | −0.558188 | ||||||||
\(193\) | −15.7194 | −1.13151 | −0.565753 | − | 0.824575i | \(-0.691415\pi\) | ||||
−0.565753 | + | 0.824575i | \(0.691415\pi\) | |||||||
\(194\) | −0.888169 | −0.0637668 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −16.5407 | −1.18148 | ||||||||
\(197\) | 18.7134 | 1.33327 | 0.666636 | − | 0.745383i | \(-0.267733\pi\) | ||||
0.666636 | + | 0.745383i | \(0.267733\pi\) | |||||||
\(198\) | −0.634566 | −0.0450967 | ||||||||
\(199\) | −10.8238 | −0.767276 | −0.383638 | − | 0.923484i | \(-0.625329\pi\) | ||||
−0.383638 | + | 0.923484i | \(0.625329\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.37059 | 0.590416 | ||||||||
\(202\) | −1.80165 | −0.126764 | ||||||||
\(203\) | 19.3845 | 1.36052 | ||||||||
\(204\) | 3.60656 | 0.252510 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.25540 | −0.0874680 | ||||||||
\(207\) | −4.74109 | −0.329528 | ||||||||
\(208\) | −20.7191 | −1.43661 | ||||||||
\(209\) | 49.3528 | 3.41380 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.37231 | 0.576373 | 0.288187 | − | 0.957574i | \(-0.406948\pi\) | ||||
0.288187 | + | 0.957574i | \(0.406948\pi\) | |||||||
\(212\) | −6.06857 | −0.416791 | ||||||||
\(213\) | −9.96991 | −0.683127 | ||||||||
\(214\) | −1.29129 | −0.0882706 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0.420531 | 0.0286135 | ||||||||
\(217\) | 19.8231 | 1.34568 | ||||||||
\(218\) | −0.858979 | −0.0581774 | ||||||||
\(219\) | 3.65100 | 0.246712 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.55171 | 0.642517 | ||||||||
\(222\) | −0.0327673 | −0.00219920 | ||||||||
\(223\) | −1.53200 | −0.102590 | −0.0512950 | − | 0.998684i | \(-0.516335\pi\) | ||||
−0.0512950 | + | 0.998684i | \(0.516335\pi\) | |||||||
\(224\) | 4.91454 | 0.328366 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.595895 | 0.0396384 | ||||||||
\(227\) | −18.1538 | −1.20491 | −0.602454 | − | 0.798154i | \(-0.705810\pi\) | ||||
−0.602454 | + | 0.798154i | \(0.705810\pi\) | |||||||
\(228\) | −16.3076 | −1.08000 | ||||||||
\(229\) | 15.1187 | 0.999071 | 0.499536 | − | 0.866293i | \(-0.333504\pi\) | ||||
0.499536 | + | 0.866293i | \(0.333504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.5565 | −1.54991 | ||||||||
\(232\) | −2.08291 | −0.136750 | ||||||||
\(233\) | 19.5817 | 1.28284 | 0.641419 | − | 0.767191i | \(-0.278346\pi\) | ||||
0.641419 | + | 0.767191i | \(0.278346\pi\) | |||||||
\(234\) | 0.555321 | 0.0363025 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.6078 | 0.755604 | ||||||||
\(237\) | 9.00605 | 0.585006 | ||||||||
\(238\) | −0.748186 | −0.0484977 | ||||||||
\(239\) | −9.11127 | −0.589359 | −0.294680 | − | 0.955596i | \(-0.595213\pi\) | ||||
−0.294680 | + | 0.955596i | \(0.595213\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −26.0653 | −1.67902 | −0.839508 | − | 0.543348i | \(-0.817156\pi\) | ||||
−0.839508 | + | 0.543348i | \(0.817156\pi\) | |||||||
\(242\) | −2.65983 | −0.170980 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −19.9006 | −1.27401 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.276064 | −0.0176012 | ||||||||
\(247\) | −43.1895 | −2.74808 | ||||||||
\(248\) | −2.13004 | −0.135258 | ||||||||
\(249\) | 12.9270 | 0.819216 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.4279 | −1.47876 | −0.739378 | − | 0.673290i | \(-0.764880\pi\) | ||||
−0.739378 | + | 0.673290i | \(0.764880\pi\) | |||||||
\(252\) | 7.78377 | 0.490332 | ||||||||
\(253\) | −28.5370 | −1.79411 | ||||||||
\(254\) | 0.0560468 | 0.00351669 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.1182 | 0.944889 | ||||||||
\(257\) | −1.10336 | −0.0688257 | −0.0344128 | − | 0.999408i | \(-0.510956\pi\) | ||||
−0.0344128 | + | 0.999408i | \(0.510956\pi\) | |||||||
\(258\) | 0.498013 | 0.0310050 | ||||||||
\(259\) | −1.21640 | −0.0755832 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.95306 | −0.306587 | ||||||||
\(262\) | 0.594381 | 0.0367210 | ||||||||
\(263\) | 9.70681 | 0.598548 | 0.299274 | − | 0.954167i | \(-0.403256\pi\) | ||||
0.299274 | + | 0.954167i | \(0.403256\pi\) | |||||||
\(264\) | 2.53121 | 0.155785 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.38304 | 0.207428 | ||||||||
\(267\) | 8.60225 | 0.526449 | ||||||||
\(268\) | −16.6481 | −1.01695 | ||||||||
\(269\) | −19.1818 | −1.16954 | −0.584768 | − | 0.811200i | \(-0.698815\pi\) | ||||
−0.584768 | + | 0.811200i | \(0.698815\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.39437 | 0.449176 | 0.224588 | − | 0.974454i | \(-0.427896\pi\) | ||||
0.224588 | + | 0.974454i | \(0.427896\pi\) | |||||||
\(272\) | −7.13272 | −0.432485 | ||||||||
\(273\) | 20.6148 | 1.24766 | ||||||||
\(274\) | −0.889090 | −0.0537119 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 9.42948 | 0.567588 | ||||||||
\(277\) | −4.95059 | −0.297452 | −0.148726 | − | 0.988878i | \(-0.547517\pi\) | ||||
−0.148726 | + | 0.988878i | \(0.547517\pi\) | |||||||
\(278\) | 0.925459 | 0.0555053 | ||||||||
\(279\) | −5.06513 | −0.303241 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.11672 | −0.126273 | −0.0631365 | − | 0.998005i | \(-0.520110\pi\) | ||||
−0.0631365 | + | 0.998005i | \(0.520110\pi\) | |||||||
\(282\) | −0.105426 | −0.00627801 | ||||||||
\(283\) | −8.64610 | −0.513957 | −0.256979 | − | 0.966417i | \(-0.582727\pi\) | ||||
−0.256979 | + | 0.966417i | \(0.582727\pi\) | |||||||
\(284\) | 19.8290 | 1.17664 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.34253 | 0.197648 | ||||||||
\(287\) | −10.2481 | −0.604928 | ||||||||
\(288\) | −1.25575 | −0.0739956 | ||||||||
\(289\) | −13.7117 | −0.806573 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.42460 | 0.493859 | ||||||||
\(292\) | −7.26142 | −0.424942 | ||||||||
\(293\) | 6.47739 | 0.378413 | 0.189207 | − | 0.981937i | \(-0.439408\pi\) | ||||
0.189207 | + | 0.981937i | \(0.439408\pi\) | |||||||
\(294\) | −0.876777 | −0.0511347 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.130705 | 0.00759708 | ||||||||
\(297\) | 6.01909 | 0.349263 | ||||||||
\(298\) | 0.568470 | 0.0329306 | ||||||||
\(299\) | 24.9733 | 1.44424 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.4874 | 1.06559 | ||||||||
\(302\) | 0.295007 | 0.0169757 | ||||||||
\(303\) | 17.0893 | 0.981755 | ||||||||
\(304\) | 32.2517 | 1.84976 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.191174 | 0.0109287 | ||||||||
\(307\) | −28.5347 | −1.62856 | −0.814279 | − | 0.580473i | \(-0.802868\pi\) | ||||
−0.814279 | + | 0.580473i | \(0.802868\pi\) | |||||||
\(308\) | 46.8512 | 2.66960 | ||||||||
\(309\) | 11.9079 | 0.677419 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.78357 | 0.327956 | 0.163978 | − | 0.986464i | \(-0.447567\pi\) | ||||
0.163978 | + | 0.986464i | \(0.447567\pi\) | |||||||
\(312\) | −2.21511 | −0.125406 | ||||||||
\(313\) | −7.35209 | −0.415565 | −0.207782 | − | 0.978175i | \(-0.566625\pi\) | ||||
−0.207782 | + | 0.978175i | \(0.566625\pi\) | |||||||
\(314\) | −2.54425 | −0.143580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.9120 | −1.00763 | ||||||||
\(317\) | 34.6205 | 1.94448 | 0.972242 | − | 0.233979i | \(-0.0751747\pi\) | ||||
0.972242 | + | 0.233979i | \(0.0751747\pi\) | |||||||
\(318\) | −0.321679 | −0.0180389 | ||||||||
\(319\) | −29.8129 | −1.66920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.2483 | 0.683635 | ||||||||
\(322\) | −1.95616 | −0.109013 | ||||||||
\(323\) | −14.8684 | −0.827299 | ||||||||
\(324\) | −1.98889 | −0.110494 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.88649 | −0.104483 | ||||||||
\(327\) | 8.14773 | 0.450570 | ||||||||
\(328\) | 1.10119 | 0.0608030 | ||||||||
\(329\) | −3.91364 | −0.215766 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.8888 | −0.928294 | −0.464147 | − | 0.885758i | \(-0.653639\pi\) | ||||
−0.464147 | + | 0.885758i | \(0.653639\pi\) | |||||||
\(332\) | −25.7103 | −1.41104 | ||||||||
\(333\) | 0.310810 | 0.0170323 | ||||||||
\(334\) | 0.0317301 | 0.00173619 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −15.3940 | −0.839814 | ||||||||
\(337\) | −21.8081 | −1.18797 | −0.593983 | − | 0.804478i | \(-0.702445\pi\) | ||||
−0.593983 | + | 0.804478i | \(0.702445\pi\) | |||||||
\(338\) | −1.55458 | −0.0845578 | ||||||||
\(339\) | −5.65228 | −0.306990 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −30.4874 | −1.65099 | ||||||||
\(342\) | −0.864424 | −0.0467427 | ||||||||
\(343\) | −5.15248 | −0.278208 | ||||||||
\(344\) | −1.98652 | −0.107106 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.19569 | −0.0642809 | ||||||||
\(347\) | 8.30860 | 0.446029 | 0.223015 | − | 0.974815i | \(-0.428410\pi\) | ||||
0.223015 | + | 0.974815i | \(0.428410\pi\) | |||||||
\(348\) | 9.85107 | 0.528073 | ||||||||
\(349\) | −31.0289 | −1.66094 | −0.830469 | − | 0.557065i | \(-0.811927\pi\) | ||||
−0.830469 | + | 0.557065i | \(0.811927\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.26742 | −0.281154 | ||||||||
\(352\) | −7.55845 | −0.402867 | ||||||||
\(353\) | 5.20699 | 0.277140 | 0.138570 | − | 0.990353i | \(-0.455749\pi\) | ||||
0.138570 | + | 0.990353i | \(0.455749\pi\) | |||||||
\(354\) | 0.615299 | 0.0327028 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.1089 | −0.906769 | ||||||||
\(357\) | 7.09681 | 0.375603 | ||||||||
\(358\) | 0.311124 | 0.0164434 | ||||||||
\(359\) | 10.4951 | 0.553908 | 0.276954 | − | 0.960883i | \(-0.410675\pi\) | ||||
0.276954 | + | 0.960883i | \(0.410675\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 48.2297 | 2.53841 | ||||||||
\(362\) | 1.35140 | 0.0710279 | ||||||||
\(363\) | 25.2294 | 1.32420 | ||||||||
\(364\) | −41.0004 | −2.14900 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.05488 | −0.0551395 | ||||||||
\(367\) | 9.10793 | 0.475430 | 0.237715 | − | 0.971335i | \(-0.423602\pi\) | ||||
0.237715 | + | 0.971335i | \(0.423602\pi\) | |||||||
\(368\) | −18.6488 | −0.972134 | ||||||||
\(369\) | 2.61857 | 0.136317 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.9415 | −0.619969 | ||||||||
\(372\) | 10.0740 | 0.522310 | ||||||||
\(373\) | −5.56531 | −0.288161 | −0.144080 | − | 0.989566i | \(-0.546022\pi\) | ||||
−0.144080 | + | 0.989566i | \(0.546022\pi\) | |||||||
\(374\) | 1.15069 | 0.0595010 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.420531 | 0.0216872 | ||||||||
\(377\) | 26.0898 | 1.34370 | ||||||||
\(378\) | 0.412598 | 0.0212217 | ||||||||
\(379\) | 29.4344 | 1.51194 | 0.755971 | − | 0.654605i | \(-0.227165\pi\) | ||||
0.755971 | + | 0.654605i | \(0.227165\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.531624 | −0.0272359 | ||||||||
\(382\) | −1.67520 | −0.0857108 | ||||||||
\(383\) | −20.1438 | −1.02930 | −0.514649 | − | 0.857401i | \(-0.672078\pi\) | ||||
−0.514649 | + | 0.857401i | \(0.672078\pi\) | |||||||
\(384\) | 3.32691 | 0.169776 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.65723 | 0.0843506 | ||||||||
\(387\) | −4.72384 | −0.240126 | ||||||||
\(388\) | −16.7556 | −0.850635 | ||||||||
\(389\) | −7.57089 | −0.383860 | −0.191930 | − | 0.981409i | \(-0.561475\pi\) | ||||
−0.191930 | + | 0.981409i | \(0.561475\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.59728 | 0.434783 | ||||||||
\(392\) | 3.49736 | 0.176644 | ||||||||
\(393\) | −5.63792 | −0.284395 | ||||||||
\(394\) | −1.97287 | −0.0993918 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.9713 | −0.601579 | ||||||||
\(397\) | 9.90230 | 0.496982 | 0.248491 | − | 0.968634i | \(-0.420065\pi\) | ||||
0.248491 | + | 0.968634i | \(0.420065\pi\) | |||||||
\(398\) | 1.14110 | 0.0571983 | ||||||||
\(399\) | −32.0894 | −1.60648 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.11343 | −0.205415 | −0.102707 | − | 0.994712i | \(-0.532751\pi\) | ||||
−0.102707 | + | 0.994712i | \(0.532751\pi\) | |||||||
\(402\) | −0.882475 | −0.0440138 | ||||||||
\(403\) | 26.6801 | 1.32903 | ||||||||
\(404\) | −33.9887 | −1.69100 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.04362 | −0.101423 | ||||||||
\(407\) | 1.87079 | 0.0927317 | ||||||||
\(408\) | −0.762572 | −0.0377529 | ||||||||
\(409\) | 9.70852 | 0.480056 | 0.240028 | − | 0.970766i | \(-0.422843\pi\) | ||||
0.240028 | + | 0.970766i | \(0.422843\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.43334 | 0.415986 | ||||||||
\(412\) | −23.6835 | −1.16680 | ||||||||
\(413\) | 22.8413 | 1.12395 | ||||||||
\(414\) | 0.499832 | 0.0245654 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6.61455 | 0.324305 | ||||||||
\(417\) | −8.77831 | −0.429876 | ||||||||
\(418\) | −5.20305 | −0.254489 | ||||||||
\(419\) | 11.7035 | 0.571753 | 0.285877 | − | 0.958266i | \(-0.407715\pi\) | ||||
0.285877 | + | 0.958266i | \(0.407715\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.14482 | 0.202006 | 0.101003 | − | 0.994886i | \(-0.467795\pi\) | ||||
0.101003 | + | 0.994886i | \(0.467795\pi\) | |||||||
\(422\) | −0.882656 | −0.0429670 | ||||||||
\(423\) | 1.00000 | 0.0486217 | ||||||||
\(424\) | 1.28314 | 0.0623149 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.05108 | 0.0509252 | ||||||||
\(427\) | −39.1596 | −1.89506 | ||||||||
\(428\) | −24.3605 | −1.17751 | ||||||||
\(429\) | −31.7051 | −1.53074 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.28815 | 0.302890 | 0.151445 | − | 0.988466i | \(-0.451607\pi\) | ||||
0.151445 | + | 0.988466i | \(0.451607\pi\) | |||||||
\(432\) | 3.93344 | 0.189248 | ||||||||
\(433\) | 9.10564 | 0.437589 | 0.218795 | − | 0.975771i | \(-0.429788\pi\) | ||||
0.218795 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(434\) | −2.08986 | −0.100316 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.2049 | −0.776074 | ||||||||
\(437\) | −38.8739 | −1.85959 | ||||||||
\(438\) | −0.384909 | −0.0183917 | ||||||||
\(439\) | 26.1154 | 1.24642 | 0.623210 | − | 0.782054i | \(-0.285828\pi\) | ||||
0.623210 | + | 0.782054i | \(0.285828\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.31654 | 0.396026 | ||||||||
\(442\) | −1.00700 | −0.0478979 | ||||||||
\(443\) | 22.6260 | 1.07499 | 0.537497 | − | 0.843266i | \(-0.319370\pi\) | ||||
0.537497 | + | 0.843266i | \(0.319370\pi\) | |||||||
\(444\) | −0.618165 | −0.0293368 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.161512 | 0.00764780 | ||||||||
\(447\) | −5.39214 | −0.255039 | ||||||||
\(448\) | 30.2700 | 1.43012 | ||||||||
\(449\) | 3.25384 | 0.153558 | 0.0767790 | − | 0.997048i | \(-0.475536\pi\) | ||||
0.0767790 | + | 0.997048i | \(0.475536\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7614 | 0.742175 | ||||||||
\(452\) | 11.2417 | 0.528767 | ||||||||
\(453\) | −2.79825 | −0.131473 | ||||||||
\(454\) | 1.91387 | 0.0898225 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.44809 | 0.161472 | ||||||||
\(457\) | −7.68301 | −0.359396 | −0.179698 | − | 0.983722i | \(-0.557512\pi\) | ||||
−0.179698 | + | 0.983722i | \(0.557512\pi\) | |||||||
\(458\) | −1.59390 | −0.0744780 | ||||||||
\(459\) | −1.81336 | −0.0846402 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.6542 | −1.61401 | −0.807004 | − | 0.590546i | \(-0.798913\pi\) | ||||
−0.807004 | + | 0.590546i | \(0.798913\pi\) | |||||||
\(462\) | 2.48346 | 0.115541 | ||||||||
\(463\) | 3.09033 | 0.143620 | 0.0718098 | − | 0.997418i | \(-0.477123\pi\) | ||||
0.0718098 | + | 0.997418i | \(0.477123\pi\) | |||||||
\(464\) | −19.4825 | −0.904454 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.06441 | −0.0956319 | ||||||||
\(467\) | −37.3216 | −1.72704 | −0.863520 | − | 0.504315i | \(-0.831745\pi\) | ||||
−0.863520 | + | 0.504315i | \(0.831745\pi\) | |||||||
\(468\) | 10.4763 | 0.484267 | ||||||||
\(469\) | −32.7594 | −1.51269 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.1331 | 1.11200 | ||||||||
\(472\) | −2.45436 | −0.112971 | ||||||||
\(473\) | −28.4332 | −1.30736 | ||||||||
\(474\) | −0.949469 | −0.0436106 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.1148 | −0.646949 | ||||||||
\(477\) | 3.05124 | 0.139707 | ||||||||
\(478\) | 0.960562 | 0.0439351 | ||||||||
\(479\) | 23.6474 | 1.08048 | 0.540239 | − | 0.841512i | \(-0.318334\pi\) | ||||
0.540239 | + | 0.841512i | \(0.318334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.63717 | −0.0746483 | ||||||||
\(482\) | 2.74795 | 0.125166 | ||||||||
\(483\) | 18.5549 | 0.844276 | ||||||||
\(484\) | −50.1785 | −2.28084 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.105426 | −0.00478220 | ||||||||
\(487\) | 20.9636 | 0.949953 | 0.474977 | − | 0.879998i | \(-0.342457\pi\) | ||||
0.474977 | + | 0.879998i | \(0.342457\pi\) | |||||||
\(488\) | 4.20780 | 0.190478 | ||||||||
\(489\) | 17.8940 | 0.809195 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.3991 | 0.514432 | 0.257216 | − | 0.966354i | \(-0.417195\pi\) | ||||
0.257216 | + | 0.966354i | \(0.417195\pi\) | |||||||
\(492\) | −5.20803 | −0.234796 | ||||||||
\(493\) | 8.98166 | 0.404514 | ||||||||
\(494\) | 4.55329 | 0.204862 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −19.9233 | −0.894585 | ||||||||
\(497\) | 39.0186 | 1.75022 | ||||||||
\(498\) | −1.36284 | −0.0610702 | ||||||||
\(499\) | 5.18330 | 0.232036 | 0.116018 | − | 0.993247i | \(-0.462987\pi\) | ||||
0.116018 | + | 0.993247i | \(0.462987\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.300971 | −0.0134464 | ||||||||
\(502\) | 2.46990 | 0.110237 | ||||||||
\(503\) | 31.1393 | 1.38843 | 0.694217 | − | 0.719766i | \(-0.255751\pi\) | ||||
0.694217 | + | 0.719766i | \(0.255751\pi\) | |||||||
\(504\) | −1.64580 | −0.0733100 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.00853 | 0.133746 | ||||||||
\(507\) | 14.7457 | 0.654880 | ||||||||
\(508\) | 1.05734 | 0.0469119 | ||||||||
\(509\) | 23.8471 | 1.05700 | 0.528502 | − | 0.848932i | \(-0.322754\pi\) | ||||
0.528502 | + | 0.848932i | \(0.322754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.2887 | −0.632094 | ||||||||
\(512\) | −8.24766 | −0.364499 | ||||||||
\(513\) | 8.19937 | 0.362011 | ||||||||
\(514\) | 0.116322 | 0.00513076 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.39517 | 0.413599 | ||||||||
\(517\) | 6.01909 | 0.264719 | ||||||||
\(518\) | 0.128239 | 0.00563451 | ||||||||
\(519\) | 11.3416 | 0.497841 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.8990 | −1.57276 | −0.786382 | − | 0.617741i | \(-0.788048\pi\) | ||||
−0.786382 | + | 0.617741i | \(0.788048\pi\) | |||||||
\(522\) | 0.522180 | 0.0228552 | ||||||||
\(523\) | −1.71087 | −0.0748113 | −0.0374057 | − | 0.999300i | \(-0.511909\pi\) | ||||
−0.0374057 | + | 0.999300i | \(0.511909\pi\) | |||||||
\(524\) | 11.2132 | 0.489850 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.02335 | −0.0446200 | ||||||||
\(527\) | 9.18487 | 0.400099 | ||||||||
\(528\) | 23.6757 | 1.03035 | ||||||||
\(529\) | −0.522109 | −0.0227004 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.83634 | −0.253275 | ||||||||
\(532\) | 63.8221 | 2.76704 | ||||||||
\(533\) | −13.7931 | −0.597446 | ||||||||
\(534\) | −0.906898 | −0.0392453 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.52009 | 0.152045 | ||||||||
\(537\) | −2.95113 | −0.127350 | ||||||||
\(538\) | 2.02226 | 0.0871857 | ||||||||
\(539\) | 50.0580 | 2.15615 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.3408 | 0.487577 | 0.243788 | − | 0.969828i | \(-0.421610\pi\) | ||||
0.243788 | + | 0.969828i | \(0.421610\pi\) | |||||||
\(542\) | −0.779556 | −0.0334848 | ||||||||
\(543\) | −12.8185 | −0.550094 | ||||||||
\(544\) | 2.27712 | 0.0976305 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.17332 | −0.0930097 | ||||||||
\(547\) | −0.484399 | −0.0207114 | −0.0103557 | − | 0.999946i | \(-0.503296\pi\) | ||||
−0.0103557 | + | 0.999946i | \(0.503296\pi\) | |||||||
\(548\) | −16.7729 | −0.716505 | ||||||||
\(549\) | 10.0059 | 0.427043 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −40.6120 | −1.73013 | ||||||||
\(552\) | −1.99377 | −0.0848606 | ||||||||
\(553\) | −35.2464 | −1.49883 | ||||||||
\(554\) | 0.521920 | 0.0221742 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.4590 | 0.740428 | ||||||||
\(557\) | −21.3581 | −0.904970 | −0.452485 | − | 0.891772i | \(-0.649462\pi\) | ||||
−0.452485 | + | 0.891772i | \(0.649462\pi\) | |||||||
\(558\) | 0.533994 | 0.0226058 | ||||||||
\(559\) | 24.8824 | 1.05241 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.9148 | −0.460821 | ||||||||
\(562\) | 0.223157 | 0.00941330 | ||||||||
\(563\) | 11.0818 | 0.467044 | 0.233522 | − | 0.972352i | \(-0.424975\pi\) | ||||
0.233522 | + | 0.972352i | \(0.424975\pi\) | |||||||
\(564\) | −1.98889 | −0.0837472 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.911521 | 0.0383141 | ||||||||
\(567\) | −3.91364 | −0.164357 | ||||||||
\(568\) | −4.19266 | −0.175920 | ||||||||
\(569\) | −25.7144 | −1.07800 | −0.539001 | − | 0.842305i | \(-0.681198\pi\) | ||||
−0.539001 | + | 0.842305i | \(0.681198\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.26461 | 0.178468 | 0.0892342 | − | 0.996011i | \(-0.471558\pi\) | ||||
0.0892342 | + | 0.996011i | \(0.471558\pi\) | |||||||
\(572\) | 63.0578 | 2.63658 | ||||||||
\(573\) | 15.8899 | 0.663810 | ||||||||
\(574\) | 1.08042 | 0.0450957 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.73448 | −0.322270 | ||||||||
\(577\) | 16.2722 | 0.677422 | 0.338711 | − | 0.940890i | \(-0.390009\pi\) | ||||
0.338711 | + | 0.940890i | \(0.390009\pi\) | |||||||
\(578\) | 1.44557 | 0.0601278 | ||||||||
\(579\) | −15.7194 | −0.653276 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −50.5916 | −2.09889 | ||||||||
\(582\) | −0.888169 | −0.0368158 | ||||||||
\(583\) | 18.3657 | 0.760630 | ||||||||
\(584\) | 1.53536 | 0.0635336 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.682883 | −0.0282097 | ||||||||
\(587\) | 16.0920 | 0.664189 | 0.332094 | − | 0.943246i | \(-0.392245\pi\) | ||||
0.332094 | + | 0.943246i | \(0.392245\pi\) | |||||||
\(588\) | −16.5407 | −0.682125 | ||||||||
\(589\) | −41.5308 | −1.71125 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.7134 | 0.769765 | ||||||||
\(592\) | 1.22255 | 0.0502465 | ||||||||
\(593\) | 34.4845 | 1.41611 | 0.708055 | − | 0.706157i | \(-0.249573\pi\) | ||||
0.708055 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(594\) | −0.634566 | −0.0260366 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.7243 | 0.439286 | ||||||||
\(597\) | −10.8238 | −0.442987 | ||||||||
\(598\) | −2.63283 | −0.107664 | ||||||||
\(599\) | −25.1565 | −1.02787 | −0.513934 | − | 0.857830i | \(-0.671812\pi\) | ||||
−0.513934 | + | 0.857830i | \(0.671812\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.3707 | 0.830937 | 0.415469 | − | 0.909608i | \(-0.363618\pi\) | ||||
0.415469 | + | 0.909608i | \(0.363618\pi\) | |||||||
\(602\) | −1.94904 | −0.0794371 | ||||||||
\(603\) | 8.37059 | 0.340877 | ||||||||
\(604\) | 5.56539 | 0.226453 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.80165 | −0.0731871 | ||||||||
\(607\) | 35.8381 | 1.45462 | 0.727312 | − | 0.686307i | \(-0.240769\pi\) | ||||
0.727312 | + | 0.686307i | \(0.240769\pi\) | |||||||
\(608\) | −10.2963 | −0.417572 | ||||||||
\(609\) | 19.3845 | 0.785499 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.26742 | −0.213097 | ||||||||
\(612\) | 3.60656 | 0.145786 | ||||||||
\(613\) | −15.4848 | −0.625426 | −0.312713 | − | 0.949848i | \(-0.601238\pi\) | ||||
−0.312713 | + | 0.949848i | \(0.601238\pi\) | |||||||
\(614\) | 3.00828 | 0.121404 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.90625 | −0.399134 | ||||||||
\(617\) | −2.17201 | −0.0874418 | −0.0437209 | − | 0.999044i | \(-0.513921\pi\) | ||||
−0.0437209 | + | 0.999044i | \(0.513921\pi\) | |||||||
\(618\) | −1.25540 | −0.0504997 | ||||||||
\(619\) | 48.9908 | 1.96911 | 0.984553 | − | 0.175088i | \(-0.0560210\pi\) | ||||
0.984553 | + | 0.175088i | \(0.0560210\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.74109 | −0.190253 | ||||||||
\(622\) | −0.609736 | −0.0244482 | ||||||||
\(623\) | −33.6661 | −1.34880 | ||||||||
\(624\) | −20.7191 | −0.829426 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.775099 | 0.0309792 | ||||||||
\(627\) | 49.3528 | 1.97096 | ||||||||
\(628\) | −47.9980 | −1.91533 | ||||||||
\(629\) | −0.563609 | −0.0224725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.3727 | −1.56740 | −0.783701 | − | 0.621138i | \(-0.786670\pi\) | ||||
−0.783701 | + | 0.621138i | \(0.786670\pi\) | |||||||
\(632\) | 3.78732 | 0.150652 | ||||||||
\(633\) | 8.37231 | 0.332769 | ||||||||
\(634\) | −3.64989 | −0.144956 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6.06857 | −0.240635 | ||||||||
\(637\) | −43.8067 | −1.73569 | ||||||||
\(638\) | 3.14305 | 0.124434 | ||||||||
\(639\) | −9.96991 | −0.394404 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.26333 | 0.247387 | 0.123693 | − | 0.992320i | \(-0.460526\pi\) | ||||
0.123693 | + | 0.992320i | \(0.460526\pi\) | |||||||
\(642\) | −1.29129 | −0.0509631 | ||||||||
\(643\) | −9.33050 | −0.367959 | −0.183980 | − | 0.982930i | \(-0.558898\pi\) | ||||
−0.183980 | + | 0.982930i | \(0.558898\pi\) | |||||||
\(644\) | −36.9035 | −1.45420 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.56751 | 0.0616728 | ||||||||
\(647\) | 39.0295 | 1.53441 | 0.767204 | − | 0.641404i | \(-0.221648\pi\) | ||||
0.767204 | + | 0.641404i | \(0.221648\pi\) | |||||||
\(648\) | 0.420531 | 0.0165200 | ||||||||
\(649\) | −35.1294 | −1.37895 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 19.8231 | 0.776927 | ||||||||
\(652\) | −35.5891 | −1.39378 | ||||||||
\(653\) | 0.459927 | 0.0179983 | 0.00899916 | − | 0.999960i | \(-0.497135\pi\) | ||||
0.00899916 | + | 0.999960i | \(0.497135\pi\) | |||||||
\(654\) | −0.858979 | −0.0335888 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 10.3000 | 0.402146 | ||||||||
\(657\) | 3.65100 | 0.142439 | ||||||||
\(658\) | 0.412598 | 0.0160847 | ||||||||
\(659\) | 24.7401 | 0.963738 | 0.481869 | − | 0.876243i | \(-0.339958\pi\) | ||||
0.481869 | + | 0.876243i | \(0.339958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.4421 | −0.406149 | −0.203075 | − | 0.979163i | \(-0.565093\pi\) | ||||
−0.203075 | + | 0.979163i | \(0.565093\pi\) | |||||||
\(662\) | 1.78052 | 0.0692017 | ||||||||
\(663\) | 9.55171 | 0.370958 | ||||||||
\(664\) | 5.43621 | 0.210966 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.0327673 | −0.00126971 | ||||||||
\(667\) | 23.4829 | 0.909261 | ||||||||
\(668\) | 0.598598 | 0.0231604 | ||||||||
\(669\) | −1.53200 | −0.0592304 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 60.2266 | 2.32502 | ||||||||
\(672\) | 4.91454 | 0.189582 | ||||||||
\(673\) | 0.153505 | 0.00591720 | 0.00295860 | − | 0.999996i | \(-0.499058\pi\) | ||||
0.00295860 | + | 0.999996i | \(0.499058\pi\) | |||||||
\(674\) | 2.29914 | 0.0885595 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.3275 | −1.12798 | ||||||||
\(677\) | 35.9544 | 1.38184 | 0.690920 | − | 0.722931i | \(-0.257206\pi\) | ||||
0.690920 | + | 0.722931i | \(0.257206\pi\) | |||||||
\(678\) | 0.595895 | 0.0228852 | ||||||||
\(679\) | −32.9708 | −1.26530 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.1538 | −0.695654 | ||||||||
\(682\) | 3.21416 | 0.123076 | ||||||||
\(683\) | 2.63818 | 0.100947 | 0.0504736 | − | 0.998725i | \(-0.483927\pi\) | ||||
0.0504736 | + | 0.998725i | \(0.483927\pi\) | |||||||
\(684\) | −16.3076 | −0.623537 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.543203 | 0.0207396 | ||||||||
\(687\) | 15.1187 | 0.576814 | ||||||||
\(688\) | −18.5809 | −0.708390 | ||||||||
\(689\) | −16.0722 | −0.612301 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.92106 | 0.225248 | 0.112624 | − | 0.993638i | \(-0.464074\pi\) | ||||
0.112624 | + | 0.993638i | \(0.464074\pi\) | |||||||
\(692\) | −22.5571 | −0.857493 | ||||||||
\(693\) | −23.5565 | −0.894838 | ||||||||
\(694\) | −0.875940 | −0.0332502 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.08291 | −0.0789527 | ||||||||
\(697\) | −4.74840 | −0.179858 | ||||||||
\(698\) | 3.27124 | 0.123818 | ||||||||
\(699\) | 19.5817 | 0.740646 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.9641 | −1.16950 | −0.584749 | − | 0.811214i | \(-0.698807\pi\) | ||||
−0.584749 | + | 0.811214i | \(0.698807\pi\) | |||||||
\(702\) | 0.555321 | 0.0209592 | ||||||||
\(703\) | 2.54844 | 0.0961164 | ||||||||
\(704\) | −46.5546 | −1.75459 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.548950 | −0.0206600 | ||||||||
\(707\) | −66.8813 | −2.51533 | ||||||||
\(708\) | 11.6078 | 0.436248 | ||||||||
\(709\) | 15.6593 | 0.588096 | 0.294048 | − | 0.955791i | \(-0.404998\pi\) | ||||
0.294048 | + | 0.955791i | \(0.404998\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.00605 | 0.337753 | ||||||||
\(712\) | 3.61751 | 0.135572 | ||||||||
\(713\) | 24.0142 | 0.899339 | ||||||||
\(714\) | −0.748186 | −0.0280002 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.86945 | 0.219352 | ||||||||
\(717\) | −9.11127 | −0.340267 | ||||||||
\(718\) | −1.10645 | −0.0412923 | ||||||||
\(719\) | 31.2286 | 1.16463 | 0.582315 | − | 0.812963i | \(-0.302147\pi\) | ||||
0.582315 | + | 0.812963i | \(0.302147\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −46.6033 | −1.73560 | ||||||||
\(722\) | −5.08465 | −0.189231 | ||||||||
\(723\) | −26.0653 | −0.969380 | ||||||||
\(724\) | 25.4945 | 0.947496 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.65983 | −0.0987155 | ||||||||
\(727\) | −0.383501 | −0.0142233 | −0.00711163 | − | 0.999975i | \(-0.502264\pi\) | ||||
−0.00711163 | + | 0.999975i | \(0.502264\pi\) | |||||||
\(728\) | 8.66914 | 0.321300 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.56600 | 0.316825 | ||||||||
\(732\) | −19.9006 | −0.735549 | ||||||||
\(733\) | −41.5815 | −1.53585 | −0.767924 | − | 0.640541i | \(-0.778710\pi\) | ||||
−0.767924 | + | 0.640541i | \(0.778710\pi\) | |||||||
\(734\) | −0.960210 | −0.0354420 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.95360 | 0.219453 | ||||||||
\(737\) | 50.3833 | 1.85589 | ||||||||
\(738\) | −0.276064 | −0.0101621 | ||||||||
\(739\) | 16.4098 | 0.603645 | 0.301822 | − | 0.953364i | \(-0.402405\pi\) | ||||
0.301822 | + | 0.953364i | \(0.402405\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −43.1895 | −1.58661 | ||||||||
\(742\) | 1.25894 | 0.0462170 | ||||||||
\(743\) | −5.59200 | −0.205151 | −0.102575 | − | 0.994725i | \(-0.532708\pi\) | ||||
−0.102575 | + | 0.994725i | \(0.532708\pi\) | |||||||
\(744\) | −2.13004 | −0.0780911 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0.586727 | 0.0214816 | ||||||||
\(747\) | 12.9270 | 0.472975 | ||||||||
\(748\) | 21.7082 | 0.793730 | ||||||||
\(749\) | −47.9355 | −1.75152 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6322 | 1.22725 | 0.613627 | − | 0.789596i | \(-0.289710\pi\) | ||||
0.613627 | + | 0.789596i | \(0.289710\pi\) | |||||||
\(752\) | 3.93344 | 0.143438 | ||||||||
\(753\) | −23.4279 | −0.853761 | ||||||||
\(754\) | −2.75054 | −0.100169 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.78377 | 0.283093 | ||||||||
\(757\) | −19.9225 | −0.724095 | −0.362048 | − | 0.932160i | \(-0.617922\pi\) | ||||
−0.362048 | + | 0.932160i | \(0.617922\pi\) | |||||||
\(758\) | −3.10314 | −0.112711 | ||||||||
\(759\) | −28.5370 | −1.03583 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.15807 | 0.186980 | 0.0934899 | − | 0.995620i | \(-0.470198\pi\) | ||||
0.0934899 | + | 0.995620i | \(0.470198\pi\) | |||||||
\(762\) | 0.0560468 | 0.00203036 | ||||||||
\(763\) | −31.8872 | −1.15440 | ||||||||
\(764\) | −31.6032 | −1.14336 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.12367 | 0.0767313 | ||||||||
\(767\) | 30.7424 | 1.11004 | ||||||||
\(768\) | 15.1182 | 0.545532 | ||||||||
\(769\) | 32.8776 | 1.18560 | 0.592799 | − | 0.805351i | \(-0.298023\pi\) | ||||
0.592799 | + | 0.805351i | \(0.298023\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.10336 | −0.0397365 | ||||||||
\(772\) | 31.2641 | 1.12522 | ||||||||
\(773\) | −15.8051 | −0.568471 | −0.284236 | − | 0.958754i | \(-0.591740\pi\) | ||||
−0.284236 | + | 0.958754i | \(0.591740\pi\) | |||||||
\(774\) | 0.498013 | 0.0179007 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.54280 | 0.127179 | ||||||||
\(777\) | −1.21640 | −0.0436380 | ||||||||
\(778\) | 0.798166 | 0.0286157 | ||||||||
\(779\) | 21.4706 | 0.769265 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −60.0098 | −2.14732 | ||||||||
\(782\) | −0.906373 | −0.0324118 | ||||||||
\(783\) | −4.95306 | −0.177008 | ||||||||
\(784\) | 32.7126 | 1.16831 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.594381 | 0.0212009 | ||||||||
\(787\) | −41.2581 | −1.47069 | −0.735346 | − | 0.677692i | \(-0.762980\pi\) | ||||
−0.735346 | + | 0.677692i | \(0.762980\pi\) | |||||||
\(788\) | −37.2188 | −1.32586 | ||||||||
\(789\) | 9.70681 | 0.345572 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 22.1210 | 0.786531 | ||||||||
\(792\) | 2.53121 | 0.0899427 | ||||||||
\(793\) | −52.7054 | −1.87162 | ||||||||
\(794\) | −1.04396 | −0.0370486 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.5272 | 0.763012 | ||||||||
\(797\) | −12.4799 | −0.442060 | −0.221030 | − | 0.975267i | \(-0.570942\pi\) | ||||
−0.221030 | + | 0.975267i | \(0.570942\pi\) | |||||||
\(798\) | 3.38304 | 0.119758 | ||||||||
\(799\) | −1.81336 | −0.0641519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.60225 | 0.303945 | ||||||||
\(802\) | 0.433661 | 0.0153131 | ||||||||
\(803\) | 21.9757 | 0.775505 | ||||||||
\(804\) | −16.6481 | −0.587135 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.81277 | −0.0990756 | ||||||||
\(807\) | −19.1818 | −0.675232 | ||||||||
\(808\) | 7.18658 | 0.252823 | ||||||||
\(809\) | −24.9414 | −0.876893 | −0.438446 | − | 0.898757i | \(-0.644471\pi\) | ||||
−0.438446 | + | 0.898757i | \(0.644471\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.1982 | −0.639026 | −0.319513 | − | 0.947582i | \(-0.603519\pi\) | ||||
−0.319513 | + | 0.947582i | \(0.603519\pi\) | |||||||
\(812\) | −38.5535 | −1.35296 | ||||||||
\(813\) | 7.39437 | 0.259332 | ||||||||
\(814\) | −0.197229 | −0.00691289 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.13272 | −0.249695 | ||||||||
\(817\) | −38.7325 | −1.35508 | ||||||||
\(818\) | −1.02353 | −0.0357868 | ||||||||
\(819\) | 20.6148 | 0.720338 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.753591 | 0.0263005 | 0.0131502 | − | 0.999914i | \(-0.495814\pi\) | ||||
0.0131502 | + | 0.999914i | \(0.495814\pi\) | |||||||
\(822\) | −0.889090 | −0.0310106 | ||||||||
\(823\) | −15.9465 | −0.555860 | −0.277930 | − | 0.960601i | \(-0.589648\pi\) | ||||
−0.277930 | + | 0.960601i | \(0.589648\pi\) | |||||||
\(824\) | 5.00765 | 0.174450 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.40806 | −0.0837871 | ||||||||
\(827\) | −33.2977 | −1.15788 | −0.578938 | − | 0.815372i | \(-0.696533\pi\) | ||||
−0.578938 | + | 0.815372i | \(0.696533\pi\) | |||||||
\(828\) | 9.42948 | 0.327697 | ||||||||
\(829\) | 22.2704 | 0.773484 | 0.386742 | − | 0.922188i | \(-0.373600\pi\) | ||||
0.386742 | + | 0.922188i | \(0.373600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.95059 | −0.171734 | ||||||||
\(832\) | 40.7408 | 1.41243 | ||||||||
\(833\) | −15.0809 | −0.522521 | ||||||||
\(834\) | 0.925459 | 0.0320460 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −98.1570 | −3.39483 | ||||||||
\(837\) | −5.06513 | −0.175076 | ||||||||
\(838\) | −1.23385 | −0.0426226 | ||||||||
\(839\) | −33.0485 | −1.14096 | −0.570480 | − | 0.821311i | \(-0.693243\pi\) | ||||
−0.570480 | + | 0.821311i | \(0.693243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.46719 | −0.154041 | ||||||||
\(842\) | −0.436970 | −0.0150590 | ||||||||
\(843\) | −2.11672 | −0.0729038 | ||||||||
\(844\) | −16.6516 | −0.573170 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.105426 | −0.00362461 | ||||||||
\(847\) | −98.7388 | −3.39271 | ||||||||
\(848\) | 12.0019 | 0.412146 | ||||||||
\(849\) | −8.64610 | −0.296733 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.47358 | −0.0505135 | ||||||||
\(852\) | 19.8290 | 0.679331 | ||||||||
\(853\) | −54.0166 | −1.84949 | −0.924746 | − | 0.380584i | \(-0.875723\pi\) | ||||
−0.924746 | + | 0.380584i | \(0.875723\pi\) | |||||||
\(854\) | 4.12842 | 0.141272 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.15080 | 0.176051 | ||||||||
\(857\) | −5.71466 | −0.195209 | −0.0976045 | − | 0.995225i | \(-0.531118\pi\) | ||||
−0.0976045 | + | 0.995225i | \(0.531118\pi\) | |||||||
\(858\) | 3.34253 | 0.114112 | ||||||||
\(859\) | −8.70298 | −0.296942 | −0.148471 | − | 0.988917i | \(-0.547435\pi\) | ||||
−0.148471 | + | 0.988917i | \(0.547435\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.2481 | −0.349255 | ||||||||
\(862\) | −0.662933 | −0.0225796 | ||||||||
\(863\) | 31.9407 | 1.08727 | 0.543637 | − | 0.839321i | \(-0.317047\pi\) | ||||
0.543637 | + | 0.839321i | \(0.317047\pi\) | |||||||
\(864\) | −1.25575 | −0.0427214 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −0.959968 | −0.0326210 | ||||||||
\(867\) | −13.7117 | −0.465675 | ||||||||
\(868\) | −39.4258 | −1.33820 | ||||||||
\(869\) | 54.2082 | 1.83889 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −44.0914 | −1.49398 | ||||||||
\(872\) | 3.42637 | 0.116032 | ||||||||
\(873\) | 8.42460 | 0.285129 | ||||||||
\(874\) | 4.09831 | 0.138627 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −7.26142 | −0.245341 | ||||||||
\(877\) | −3.18040 | −0.107395 | −0.0536973 | − | 0.998557i | \(-0.517101\pi\) | ||||
−0.0536973 | + | 0.998557i | \(0.517101\pi\) | |||||||
\(878\) | −2.75323 | −0.0929172 | ||||||||
\(879\) | 6.47739 | 0.218477 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.8243 | 1.00481 | 0.502403 | − | 0.864634i | \(-0.332449\pi\) | ||||
0.502403 | + | 0.864634i | \(0.332449\pi\) | |||||||
\(882\) | −0.876777 | −0.0295226 | ||||||||
\(883\) | 16.0274 | 0.539365 | 0.269682 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269682 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(884\) | −18.9973 | −0.638947 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.38536 | −0.0801378 | ||||||||
\(887\) | 43.7250 | 1.46814 | 0.734071 | − | 0.679073i | \(-0.237618\pi\) | ||||
0.734071 | + | 0.679073i | \(0.237618\pi\) | |||||||
\(888\) | 0.130705 | 0.00438618 | ||||||||
\(889\) | 2.08058 | 0.0697805 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.01909 | 0.201647 | ||||||||
\(892\) | 3.04697 | 0.102020 | ||||||||
\(893\) | 8.19937 | 0.274382 | ||||||||
\(894\) | 0.568470 | 0.0190125 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.0203 | −0.434978 | ||||||||
\(897\) | 24.9733 | 0.833834 | ||||||||
\(898\) | −0.343038 | −0.0114473 | ||||||||
\(899\) | 25.0879 | 0.836727 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.53299 | −0.184331 | ||||||||
\(902\) | −1.66166 | −0.0553271 | ||||||||
\(903\) | 18.4874 | 0.615221 | ||||||||
\(904\) | −2.37696 | −0.0790564 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.295007 | 0.00980095 | ||||||||
\(907\) | −32.2224 | −1.06993 | −0.534963 | − | 0.844875i | \(-0.679675\pi\) | ||||
−0.534963 | + | 0.844875i | \(0.679675\pi\) | |||||||
\(908\) | 36.1058 | 1.19821 | ||||||||
\(909\) | 17.0893 | 0.566816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.9641 | −1.72165 | −0.860823 | − | 0.508904i | \(-0.830051\pi\) | ||||
−0.860823 | + | 0.508904i | \(0.830051\pi\) | |||||||
\(912\) | 32.2517 | 1.06796 | ||||||||
\(913\) | 77.8088 | 2.57510 | ||||||||
\(914\) | 0.809987 | 0.0267920 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.0693 | −0.993519 | ||||||||
\(917\) | 22.0647 | 0.728642 | ||||||||
\(918\) | 0.191174 | 0.00630969 | ||||||||
\(919\) | 56.4042 | 1.86060 | 0.930301 | − | 0.366796i | \(-0.119545\pi\) | ||||
0.930301 | + | 0.366796i | \(0.119545\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.5347 | −0.940249 | ||||||||
\(922\) | 3.65345 | 0.120320 | ||||||||
\(923\) | 52.5157 | 1.72858 | ||||||||
\(924\) | 46.8512 | 1.54129 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.325800 | −0.0107064 | ||||||||
\(927\) | 11.9079 | 0.391108 | ||||||||
\(928\) | 6.21979 | 0.204175 | ||||||||
\(929\) | 10.3110 | 0.338292 | 0.169146 | − | 0.985591i | \(-0.445899\pi\) | ||||
0.169146 | + | 0.985591i | \(0.445899\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 68.1904 | 2.23485 | ||||||||
\(932\) | −38.9457 | −1.27571 | ||||||||
\(933\) | 5.78357 | 0.189345 | ||||||||
\(934\) | 3.93466 | 0.128746 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.21511 | −0.0724032 | ||||||||
\(937\) | −2.05321 | −0.0670756 | −0.0335378 | − | 0.999437i | \(-0.510677\pi\) | ||||
−0.0335378 | + | 0.999437i | \(0.510677\pi\) | |||||||
\(938\) | 3.45368 | 0.112767 | ||||||||
\(939\) | −7.35209 | −0.239926 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.5244 | 1.22326 | 0.611631 | − | 0.791143i | \(-0.290514\pi\) | ||||
0.611631 | + | 0.791143i | \(0.290514\pi\) | |||||||
\(942\) | −2.54425 | −0.0828962 | ||||||||
\(943\) | −12.4149 | −0.404283 | ||||||||
\(944\) | −22.9569 | −0.747182 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.99759 | 0.0974600 | ||||||||
\(947\) | −15.9626 | −0.518714 | −0.259357 | − | 0.965782i | \(-0.583511\pi\) | ||||
−0.259357 | + | 0.965782i | \(0.583511\pi\) | |||||||
\(948\) | −17.9120 | −0.581755 | ||||||||
\(949\) | −19.2313 | −0.624276 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.6205 | 1.12265 | ||||||||
\(952\) | 2.98443 | 0.0967259 | ||||||||
\(953\) | 12.3043 | 0.398575 | 0.199287 | − | 0.979941i | \(-0.436137\pi\) | ||||
0.199287 | + | 0.979941i | \(0.436137\pi\) | |||||||
\(954\) | −0.321679 | −0.0104148 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 18.1213 | 0.586084 | ||||||||
\(957\) | −29.8129 | −0.963715 | ||||||||
\(958\) | −2.49304 | −0.0805465 | ||||||||
\(959\) | −33.0050 | −1.06579 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.34451 | −0.172403 | ||||||||
\(962\) | 0.172599 | 0.00556482 | ||||||||
\(963\) | 12.2483 | 0.394697 | ||||||||
\(964\) | 51.8410 | 1.66968 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.95616 | −0.0629384 | ||||||||
\(967\) | −24.7346 | −0.795411 | −0.397705 | − | 0.917513i | \(-0.630193\pi\) | ||||
−0.397705 | + | 0.917513i | \(0.630193\pi\) | |||||||
\(968\) | 10.6098 | 0.341010 | ||||||||
\(969\) | −14.8684 | −0.477641 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.5319 | −0.498442 | −0.249221 | − | 0.968447i | \(-0.580175\pi\) | ||||
−0.249221 | + | 0.968447i | \(0.580175\pi\) | |||||||
\(972\) | −1.98889 | −0.0637935 | ||||||||
\(973\) | 34.3551 | 1.10137 | ||||||||
\(974\) | −2.21011 | −0.0708163 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 39.3577 | 1.25981 | ||||||||
\(977\) | 60.0176 | 1.92013 | 0.960066 | − | 0.279773i | \(-0.0902593\pi\) | ||||
0.960066 | + | 0.279773i | \(0.0902593\pi\) | |||||||
\(978\) | −1.88649 | −0.0603232 | ||||||||
\(979\) | 51.7777 | 1.65482 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.14773 | 0.260137 | ||||||||
\(982\) | −1.20175 | −0.0383495 | ||||||||
\(983\) | −59.1158 | −1.88550 | −0.942751 | − | 0.333498i | \(-0.891771\pi\) | ||||
−0.942751 | + | 0.333498i | \(0.891771\pi\) | |||||||
\(984\) | 1.10119 | 0.0351046 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −0.946898 | −0.0301554 | ||||||||
\(987\) | −3.91364 | −0.124572 | ||||||||
\(988\) | 85.8990 | 2.73281 | ||||||||
\(989\) | 22.3961 | 0.712155 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.32558 | 0.296237 | 0.148118 | − | 0.988970i | \(-0.452678\pi\) | ||||
0.148118 | + | 0.988970i | \(0.452678\pi\) | |||||||
\(992\) | 6.36051 | 0.201947 | ||||||||
\(993\) | −16.8888 | −0.535951 | ||||||||
\(994\) | −4.11356 | −0.130474 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −25.7103 | −0.814663 | ||||||||
\(997\) | −25.8977 | −0.820188 | −0.410094 | − | 0.912043i | \(-0.634504\pi\) | ||||
−0.410094 | + | 0.912043i | \(0.634504\pi\) | |||||||
\(998\) | −0.546453 | −0.0172977 | ||||||||
\(999\) | 0.310810 | 0.00983358 |
(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 | 3525.2.a.bi.1.6 | 13 | ||
5.2 | odd | 4 | 705.2.c.c.424.12 | ✓ | 26 | ||
5.3 | odd | 4 | 705.2.c.c.424.15 | yes | 26 | ||
5.4 | even | 2 | 3525.2.a.bh.1.8 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
705.2.c.c.424.12 | ✓ | 26 | 5.2 | odd | 4 | ||
705.2.c.c.424.15 | yes | 26 | 5.3 | odd | 4 | ||
3525.2.a.bh.1.8 | 13 | 5.4 | even | 2 | |||
3525.2.a.bi.1.6 | 13 | 1.1 | even | 1 | trivial |