Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.666016 | −0.384525 | −0.192262 | − | 0.981344i | \(-0.561582\pi\) | ||||
−0.192262 | + | 0.981344i | \(0.561582\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.513693 | 0.229730 | 0.114865 | − | 0.993381i | \(-0.463356\pi\) | ||||
0.114865 | + | 0.993381i | \(0.463356\pi\) | |||||||
\(6\) | 0.666016 | 0.271900 | ||||||||
\(7\) | 2.90198 | 1.09685 | 0.548423 | − | 0.836201i | \(-0.315228\pi\) | ||||
0.548423 | + | 0.836201i | \(0.315228\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.55642 | −0.852141 | ||||||||
\(10\) | −0.513693 | −0.162444 | ||||||||
\(11\) | 0.858892 | 0.258966 | 0.129483 | − | 0.991582i | \(-0.458668\pi\) | ||||
0.129483 | + | 0.991582i | \(0.458668\pi\) | |||||||
\(12\) | −0.666016 | −0.192262 | ||||||||
\(13\) | −5.16614 | −1.43283 | −0.716414 | − | 0.697675i | \(-0.754218\pi\) | ||||
−0.716414 | + | 0.697675i | \(0.754218\pi\) | |||||||
\(14\) | −2.90198 | −0.775588 | ||||||||
\(15\) | −0.342128 | −0.0883370 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.36731 | 1.05923 | 0.529614 | − | 0.848239i | \(-0.322337\pi\) | ||||
0.529614 | + | 0.848239i | \(0.322337\pi\) | |||||||
\(18\) | 2.55642 | 0.602555 | ||||||||
\(19\) | −1.53998 | −0.353295 | −0.176648 | − | 0.984274i | \(-0.556525\pi\) | ||||
−0.176648 | + | 0.984274i | \(0.556525\pi\) | |||||||
\(20\) | 0.513693 | 0.114865 | ||||||||
\(21\) | −1.93277 | −0.421765 | ||||||||
\(22\) | −0.858892 | −0.183116 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0.666016 | 0.135950 | ||||||||
\(25\) | −4.73612 | −0.947224 | ||||||||
\(26\) | 5.16614 | 1.01316 | ||||||||
\(27\) | 3.70067 | 0.712194 | ||||||||
\(28\) | 2.90198 | 0.548423 | ||||||||
\(29\) | −3.13545 | −0.582238 | −0.291119 | − | 0.956687i | \(-0.594028\pi\) | ||||
−0.291119 | + | 0.956687i | \(0.594028\pi\) | |||||||
\(30\) | 0.342128 | 0.0624637 | ||||||||
\(31\) | 9.58158 | 1.72090 | 0.860451 | − | 0.509532i | \(-0.170182\pi\) | ||||
0.860451 | + | 0.509532i | \(0.170182\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.572036 | −0.0995787 | ||||||||
\(34\) | −4.36731 | −0.748987 | ||||||||
\(35\) | 1.49073 | 0.251979 | ||||||||
\(36\) | −2.55642 | −0.426070 | ||||||||
\(37\) | −7.80219 | −1.28267 | −0.641336 | − | 0.767260i | \(-0.721619\pi\) | ||||
−0.641336 | + | 0.767260i | \(0.721619\pi\) | |||||||
\(38\) | 1.53998 | 0.249817 | ||||||||
\(39\) | 3.44073 | 0.550958 | ||||||||
\(40\) | −0.513693 | −0.0812219 | ||||||||
\(41\) | 4.19115 | 0.654547 | 0.327274 | − | 0.944930i | \(-0.393870\pi\) | ||||
0.327274 | + | 0.944930i | \(0.393870\pi\) | |||||||
\(42\) | 1.93277 | 0.298233 | ||||||||
\(43\) | 11.0431 | 1.68406 | 0.842029 | − | 0.539432i | \(-0.181361\pi\) | ||||
0.842029 | + | 0.539432i | \(0.181361\pi\) | |||||||
\(44\) | 0.858892 | 0.129483 | ||||||||
\(45\) | −1.31322 | −0.195763 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −1.61318 | −0.235306 | −0.117653 | − | 0.993055i | \(-0.537537\pi\) | ||||
−0.117653 | + | 0.993055i | \(0.537537\pi\) | |||||||
\(48\) | −0.666016 | −0.0961312 | ||||||||
\(49\) | 1.42151 | 0.203073 | ||||||||
\(50\) | 4.73612 | 0.669789 | ||||||||
\(51\) | −2.90870 | −0.407299 | ||||||||
\(52\) | −5.16614 | −0.716414 | ||||||||
\(53\) | −6.05418 | −0.831606 | −0.415803 | − | 0.909455i | \(-0.636499\pi\) | ||||
−0.415803 | + | 0.909455i | \(0.636499\pi\) | |||||||
\(54\) | −3.70067 | −0.503597 | ||||||||
\(55\) | 0.441207 | 0.0594923 | ||||||||
\(56\) | −2.90198 | −0.387794 | ||||||||
\(57\) | 1.02565 | 0.135851 | ||||||||
\(58\) | 3.13545 | 0.411704 | ||||||||
\(59\) | 3.21058 | 0.417982 | 0.208991 | − | 0.977918i | \(-0.432982\pi\) | ||||
0.208991 | + | 0.977918i | \(0.432982\pi\) | |||||||
\(60\) | −0.342128 | −0.0441685 | ||||||||
\(61\) | −6.32871 | −0.810309 | −0.405154 | − | 0.914248i | \(-0.632782\pi\) | ||||
−0.405154 | + | 0.914248i | \(0.632782\pi\) | |||||||
\(62\) | −9.58158 | −1.21686 | ||||||||
\(63\) | −7.41870 | −0.934668 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.65381 | −0.329164 | ||||||||
\(66\) | 0.572036 | 0.0704128 | ||||||||
\(67\) | −3.00309 | −0.366886 | −0.183443 | − | 0.983030i | \(-0.558724\pi\) | ||||
−0.183443 | + | 0.983030i | \(0.558724\pi\) | |||||||
\(68\) | 4.36731 | 0.529614 | ||||||||
\(69\) | 0.666016 | 0.0801789 | ||||||||
\(70\) | −1.49073 | −0.178176 | ||||||||
\(71\) | 2.11045 | 0.250464 | 0.125232 | − | 0.992127i | \(-0.460032\pi\) | ||||
0.125232 | + | 0.992127i | \(0.460032\pi\) | |||||||
\(72\) | 2.55642 | 0.301277 | ||||||||
\(73\) | 12.7851 | 1.49638 | 0.748189 | − | 0.663486i | \(-0.230924\pi\) | ||||
0.748189 | + | 0.663486i | \(0.230924\pi\) | |||||||
\(74\) | 7.80219 | 0.906986 | ||||||||
\(75\) | 3.15433 | 0.364231 | ||||||||
\(76\) | −1.53998 | −0.176648 | ||||||||
\(77\) | 2.49249 | 0.284046 | ||||||||
\(78\) | −3.44073 | −0.389586 | ||||||||
\(79\) | −2.80194 | −0.315242 | −0.157621 | − | 0.987500i | \(-0.550382\pi\) | ||||
−0.157621 | + | 0.987500i | \(0.550382\pi\) | |||||||
\(80\) | 0.513693 | 0.0574326 | ||||||||
\(81\) | 5.20456 | 0.578285 | ||||||||
\(82\) | −4.19115 | −0.462835 | ||||||||
\(83\) | −16.3424 | −1.79381 | −0.896907 | − | 0.442219i | \(-0.854192\pi\) | ||||
−0.896907 | + | 0.442219i | \(0.854192\pi\) | |||||||
\(84\) | −1.93277 | −0.210882 | ||||||||
\(85\) | 2.24345 | 0.243337 | ||||||||
\(86\) | −11.0431 | −1.19081 | ||||||||
\(87\) | 2.08826 | 0.223885 | ||||||||
\(88\) | −0.858892 | −0.0915582 | ||||||||
\(89\) | −10.3293 | −1.09490 | −0.547451 | − | 0.836837i | \(-0.684402\pi\) | ||||
−0.547451 | + | 0.836837i | \(0.684402\pi\) | |||||||
\(90\) | 1.31322 | 0.138425 | ||||||||
\(91\) | −14.9920 | −1.57159 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −6.38149 | −0.661730 | ||||||||
\(94\) | 1.61318 | 0.166386 | ||||||||
\(95\) | −0.791075 | −0.0811626 | ||||||||
\(96\) | 0.666016 | 0.0679750 | ||||||||
\(97\) | −13.5647 | −1.37729 | −0.688646 | − | 0.725098i | \(-0.741794\pi\) | ||||
−0.688646 | + | 0.725098i | \(0.741794\pi\) | |||||||
\(98\) | −1.42151 | −0.143594 | ||||||||
\(99\) | −2.19569 | −0.220675 | ||||||||
\(100\) | −4.73612 | −0.473612 | ||||||||
\(101\) | −12.3385 | −1.22773 | −0.613864 | − | 0.789411i | \(-0.710386\pi\) | ||||
−0.613864 | + | 0.789411i | \(0.710386\pi\) | |||||||
\(102\) | 2.90870 | 0.288004 | ||||||||
\(103\) | 13.5956 | 1.33962 | 0.669809 | − | 0.742533i | \(-0.266376\pi\) | ||||
0.669809 | + | 0.742533i | \(0.266376\pi\) | |||||||
\(104\) | 5.16614 | 0.506581 | ||||||||
\(105\) | −0.992849 | −0.0968921 | ||||||||
\(106\) | 6.05418 | 0.588034 | ||||||||
\(107\) | 2.09749 | 0.202772 | 0.101386 | − | 0.994847i | \(-0.467672\pi\) | ||||
0.101386 | + | 0.994847i | \(0.467672\pi\) | |||||||
\(108\) | 3.70067 | 0.356097 | ||||||||
\(109\) | −3.35144 | −0.321010 | −0.160505 | − | 0.987035i | \(-0.551312\pi\) | ||||
−0.160505 | + | 0.987035i | \(0.551312\pi\) | |||||||
\(110\) | −0.441207 | −0.0420674 | ||||||||
\(111\) | 5.19638 | 0.493219 | ||||||||
\(112\) | 2.90198 | 0.274212 | ||||||||
\(113\) | 2.60455 | 0.245016 | 0.122508 | − | 0.992468i | \(-0.460906\pi\) | ||||
0.122508 | + | 0.992468i | \(0.460906\pi\) | |||||||
\(114\) | −1.02565 | −0.0960610 | ||||||||
\(115\) | −0.513693 | −0.0479021 | ||||||||
\(116\) | −3.13545 | −0.291119 | ||||||||
\(117\) | 13.2068 | 1.22097 | ||||||||
\(118\) | −3.21058 | −0.295558 | ||||||||
\(119\) | 12.6739 | 1.16181 | ||||||||
\(120\) | 0.342128 | 0.0312318 | ||||||||
\(121\) | −10.2623 | −0.932937 | ||||||||
\(122\) | 6.32871 | 0.572975 | ||||||||
\(123\) | −2.79137 | −0.251690 | ||||||||
\(124\) | 9.58158 | 0.860451 | ||||||||
\(125\) | −5.00137 | −0.447336 | ||||||||
\(126\) | 7.41870 | 0.660910 | ||||||||
\(127\) | 8.95804 | 0.794898 | 0.397449 | − | 0.917624i | \(-0.369896\pi\) | ||||
0.397449 | + | 0.917624i | \(0.369896\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.35489 | −0.647562 | ||||||||
\(130\) | 2.65381 | 0.232754 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −0.572036 | −0.0497894 | ||||||||
\(133\) | −4.46899 | −0.387511 | ||||||||
\(134\) | 3.00309 | 0.259427 | ||||||||
\(135\) | 1.90101 | 0.163613 | ||||||||
\(136\) | −4.36731 | −0.374494 | ||||||||
\(137\) | −6.37224 | −0.544417 | −0.272209 | − | 0.962238i | \(-0.587754\pi\) | ||||
−0.272209 | + | 0.962238i | \(0.587754\pi\) | |||||||
\(138\) | −0.666016 | −0.0566951 | ||||||||
\(139\) | −3.38441 | −0.287062 | −0.143531 | − | 0.989646i | \(-0.545846\pi\) | ||||
−0.143531 | + | 0.989646i | \(0.545846\pi\) | |||||||
\(140\) | 1.49073 | 0.125989 | ||||||||
\(141\) | 1.07440 | 0.0904810 | ||||||||
\(142\) | −2.11045 | −0.177105 | ||||||||
\(143\) | −4.43716 | −0.371054 | ||||||||
\(144\) | −2.55642 | −0.213035 | ||||||||
\(145\) | −1.61066 | −0.133758 | ||||||||
\(146\) | −12.7851 | −1.05810 | ||||||||
\(147\) | −0.946748 | −0.0780864 | ||||||||
\(148\) | −7.80219 | −0.641336 | ||||||||
\(149\) | −8.77077 | −0.718529 | −0.359265 | − | 0.933236i | \(-0.616972\pi\) | ||||
−0.359265 | + | 0.933236i | \(0.616972\pi\) | |||||||
\(150\) | −3.15433 | −0.257550 | ||||||||
\(151\) | −8.39331 | −0.683038 | −0.341519 | − | 0.939875i | \(-0.610941\pi\) | ||||
−0.341519 | + | 0.939875i | \(0.610941\pi\) | |||||||
\(152\) | 1.53998 | 0.124909 | ||||||||
\(153\) | −11.1647 | −0.902612 | ||||||||
\(154\) | −2.49249 | −0.200851 | ||||||||
\(155\) | 4.92199 | 0.395344 | ||||||||
\(156\) | 3.44073 | 0.275479 | ||||||||
\(157\) | −18.6501 | −1.48844 | −0.744219 | − | 0.667936i | \(-0.767178\pi\) | ||||
−0.744219 | + | 0.667936i | \(0.767178\pi\) | |||||||
\(158\) | 2.80194 | 0.222910 | ||||||||
\(159\) | 4.03219 | 0.319773 | ||||||||
\(160\) | −0.513693 | −0.0406110 | ||||||||
\(161\) | −2.90198 | −0.228708 | ||||||||
\(162\) | −5.20456 | −0.408909 | ||||||||
\(163\) | −14.6796 | −1.14980 | −0.574898 | − | 0.818225i | \(-0.694958\pi\) | ||||
−0.574898 | + | 0.818225i | \(0.694958\pi\) | |||||||
\(164\) | 4.19115 | 0.327274 | ||||||||
\(165\) | −0.293851 | −0.0228763 | ||||||||
\(166\) | 16.3424 | 1.26842 | ||||||||
\(167\) | 18.8637 | 1.45972 | 0.729860 | − | 0.683597i | \(-0.239585\pi\) | ||||
0.729860 | + | 0.683597i | \(0.239585\pi\) | |||||||
\(168\) | 1.93277 | 0.149116 | ||||||||
\(169\) | 13.6890 | 1.05300 | ||||||||
\(170\) | −2.24345 | −0.172065 | ||||||||
\(171\) | 3.93683 | 0.301057 | ||||||||
\(172\) | 11.0431 | 0.842029 | ||||||||
\(173\) | −4.89372 | −0.372062 | −0.186031 | − | 0.982544i | \(-0.559563\pi\) | ||||
−0.186031 | + | 0.982544i | \(0.559563\pi\) | |||||||
\(174\) | −2.08826 | −0.158311 | ||||||||
\(175\) | −13.7441 | −1.03896 | ||||||||
\(176\) | 0.858892 | 0.0647414 | ||||||||
\(177\) | −2.13830 | −0.160724 | ||||||||
\(178\) | 10.3293 | 0.774213 | ||||||||
\(179\) | −6.04074 | −0.451506 | −0.225753 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225753 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(180\) | −1.31322 | −0.0978813 | ||||||||
\(181\) | 10.2860 | 0.764550 | 0.382275 | − | 0.924049i | \(-0.375141\pi\) | ||||
0.382275 | + | 0.924049i | \(0.375141\pi\) | |||||||
\(182\) | 14.9920 | 1.11128 | ||||||||
\(183\) | 4.21503 | 0.311584 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −4.00793 | −0.294669 | ||||||||
\(186\) | 6.38149 | 0.467914 | ||||||||
\(187\) | 3.75105 | 0.274304 | ||||||||
\(188\) | −1.61318 | −0.117653 | ||||||||
\(189\) | 10.7393 | 0.781167 | ||||||||
\(190\) | 0.791075 | 0.0573906 | ||||||||
\(191\) | 7.08976 | 0.512997 | 0.256498 | − | 0.966545i | \(-0.417431\pi\) | ||||
0.256498 | + | 0.966545i | \(0.417431\pi\) | |||||||
\(192\) | −0.666016 | −0.0480656 | ||||||||
\(193\) | 0.399230 | 0.0287372 | 0.0143686 | − | 0.999897i | \(-0.495426\pi\) | ||||
0.0143686 | + | 0.999897i | \(0.495426\pi\) | |||||||
\(194\) | 13.5647 | 0.973892 | ||||||||
\(195\) | 1.76748 | 0.126572 | ||||||||
\(196\) | 1.42151 | 0.101536 | ||||||||
\(197\) | 18.7880 | 1.33859 | 0.669294 | − | 0.742998i | \(-0.266597\pi\) | ||||
0.669294 | + | 0.742998i | \(0.266597\pi\) | |||||||
\(198\) | 2.19569 | 0.156041 | ||||||||
\(199\) | −2.56488 | −0.181820 | −0.0909099 | − | 0.995859i | \(-0.528978\pi\) | ||||
−0.0909099 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(200\) | 4.73612 | 0.334894 | ||||||||
\(201\) | 2.00011 | 0.141077 | ||||||||
\(202\) | 12.3385 | 0.868135 | ||||||||
\(203\) | −9.09902 | −0.638626 | ||||||||
\(204\) | −2.90870 | −0.203650 | ||||||||
\(205\) | 2.15296 | 0.150369 | ||||||||
\(206\) | −13.5956 | −0.947253 | ||||||||
\(207\) | 2.55642 | 0.177684 | ||||||||
\(208\) | −5.16614 | −0.358207 | ||||||||
\(209\) | −1.32268 | −0.0914914 | ||||||||
\(210\) | 0.992849 | 0.0685131 | ||||||||
\(211\) | 11.1136 | 0.765089 | 0.382544 | − | 0.923937i | \(-0.375048\pi\) | ||||
0.382544 | + | 0.923937i | \(0.375048\pi\) | |||||||
\(212\) | −6.05418 | −0.415803 | ||||||||
\(213\) | −1.40559 | −0.0963098 | ||||||||
\(214\) | −2.09749 | −0.143382 | ||||||||
\(215\) | 5.67277 | 0.386879 | ||||||||
\(216\) | −3.70067 | −0.251799 | ||||||||
\(217\) | 27.8056 | 1.88757 | ||||||||
\(218\) | 3.35144 | 0.226988 | ||||||||
\(219\) | −8.51506 | −0.575394 | ||||||||
\(220\) | 0.441207 | 0.0297461 | ||||||||
\(221\) | −22.5621 | −1.51769 | ||||||||
\(222\) | −5.19638 | −0.348759 | ||||||||
\(223\) | 4.48756 | 0.300509 | 0.150254 | − | 0.988647i | \(-0.451991\pi\) | ||||
0.150254 | + | 0.988647i | \(0.451991\pi\) | |||||||
\(224\) | −2.90198 | −0.193897 | ||||||||
\(225\) | 12.1075 | 0.807168 | ||||||||
\(226\) | −2.60455 | −0.173252 | ||||||||
\(227\) | −8.01551 | −0.532008 | −0.266004 | − | 0.963972i | \(-0.585703\pi\) | ||||
−0.266004 | + | 0.963972i | \(0.585703\pi\) | |||||||
\(228\) | 1.02565 | 0.0679254 | ||||||||
\(229\) | −15.9785 | −1.05589 | −0.527945 | − | 0.849278i | \(-0.677037\pi\) | ||||
−0.527945 | + | 0.849278i | \(0.677037\pi\) | |||||||
\(230\) | 0.513693 | 0.0338719 | ||||||||
\(231\) | −1.66004 | −0.109223 | ||||||||
\(232\) | 3.13545 | 0.205852 | ||||||||
\(233\) | −7.42163 | −0.486207 | −0.243104 | − | 0.970000i | \(-0.578166\pi\) | ||||
−0.243104 | + | 0.970000i | \(0.578166\pi\) | |||||||
\(234\) | −13.2068 | −0.863357 | ||||||||
\(235\) | −0.828677 | −0.0540569 | ||||||||
\(236\) | 3.21058 | 0.208991 | ||||||||
\(237\) | 1.86613 | 0.121218 | ||||||||
\(238\) | −12.6739 | −0.821524 | ||||||||
\(239\) | 7.94904 | 0.514181 | 0.257090 | − | 0.966387i | \(-0.417236\pi\) | ||||
0.257090 | + | 0.966387i | \(0.417236\pi\) | |||||||
\(240\) | −0.342128 | −0.0220842 | ||||||||
\(241\) | −18.9159 | −1.21848 | −0.609239 | − | 0.792986i | \(-0.708525\pi\) | ||||
−0.609239 | + | 0.792986i | \(0.708525\pi\) | |||||||
\(242\) | 10.2623 | 0.659686 | ||||||||
\(243\) | −14.5683 | −0.934559 | ||||||||
\(244\) | −6.32871 | −0.405154 | ||||||||
\(245\) | 0.730218 | 0.0466519 | ||||||||
\(246\) | 2.79137 | 0.177971 | ||||||||
\(247\) | 7.95574 | 0.506212 | ||||||||
\(248\) | −9.58158 | −0.608431 | ||||||||
\(249\) | 10.8843 | 0.689766 | ||||||||
\(250\) | 5.00137 | 0.316315 | ||||||||
\(251\) | 20.4684 | 1.29195 | 0.645976 | − | 0.763358i | \(-0.276451\pi\) | ||||
0.645976 | + | 0.763358i | \(0.276451\pi\) | |||||||
\(252\) | −7.41870 | −0.467334 | ||||||||
\(253\) | −0.858892 | −0.0539981 | ||||||||
\(254\) | −8.95804 | −0.562077 | ||||||||
\(255\) | −1.49418 | −0.0935690 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.0534 | −1.06376 | −0.531882 | − | 0.846818i | \(-0.678515\pi\) | ||||
−0.531882 | + | 0.846818i | \(0.678515\pi\) | |||||||
\(258\) | 7.35489 | 0.457896 | ||||||||
\(259\) | −22.6418 | −1.40689 | ||||||||
\(260\) | −2.65381 | −0.164582 | ||||||||
\(261\) | 8.01553 | 0.496149 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −12.6819 | −0.781997 | −0.390998 | − | 0.920391i | \(-0.627870\pi\) | ||||
−0.390998 | + | 0.920391i | \(0.627870\pi\) | |||||||
\(264\) | 0.572036 | 0.0352064 | ||||||||
\(265\) | −3.10999 | −0.191045 | ||||||||
\(266\) | 4.46899 | 0.274011 | ||||||||
\(267\) | 6.87948 | 0.421017 | ||||||||
\(268\) | −3.00309 | −0.183443 | ||||||||
\(269\) | −3.85121 | −0.234812 | −0.117406 | − | 0.993084i | \(-0.537458\pi\) | ||||
−0.117406 | + | 0.993084i | \(0.537458\pi\) | |||||||
\(270\) | −1.90101 | −0.115692 | ||||||||
\(271\) | −18.3602 | −1.11530 | −0.557650 | − | 0.830076i | \(-0.688297\pi\) | ||||
−0.557650 | + | 0.830076i | \(0.688297\pi\) | |||||||
\(272\) | 4.36731 | 0.264807 | ||||||||
\(273\) | 9.98495 | 0.604316 | ||||||||
\(274\) | 6.37224 | 0.384961 | ||||||||
\(275\) | −4.06782 | −0.245299 | ||||||||
\(276\) | 0.666016 | 0.0400895 | ||||||||
\(277\) | −8.48390 | −0.509748 | −0.254874 | − | 0.966974i | \(-0.582034\pi\) | ||||
−0.254874 | + | 0.966974i | \(0.582034\pi\) | |||||||
\(278\) | 3.38441 | 0.202983 | ||||||||
\(279\) | −24.4946 | −1.46645 | ||||||||
\(280\) | −1.49073 | −0.0890880 | ||||||||
\(281\) | 25.6835 | 1.53215 | 0.766074 | − | 0.642753i | \(-0.222208\pi\) | ||||
0.766074 | + | 0.642753i | \(0.222208\pi\) | |||||||
\(282\) | −1.07440 | −0.0639797 | ||||||||
\(283\) | −4.17828 | −0.248373 | −0.124186 | − | 0.992259i | \(-0.539632\pi\) | ||||
−0.124186 | + | 0.992259i | \(0.539632\pi\) | |||||||
\(284\) | 2.11045 | 0.125232 | ||||||||
\(285\) | 0.526869 | 0.0312090 | ||||||||
\(286\) | 4.43716 | 0.262374 | ||||||||
\(287\) | 12.1626 | 0.717938 | ||||||||
\(288\) | 2.55642 | 0.150639 | ||||||||
\(289\) | 2.07339 | 0.121964 | ||||||||
\(290\) | 1.61066 | 0.0945810 | ||||||||
\(291\) | 9.03434 | 0.529603 | ||||||||
\(292\) | 12.7851 | 0.748189 | ||||||||
\(293\) | 6.81701 | 0.398254 | 0.199127 | − | 0.979974i | \(-0.436189\pi\) | ||||
0.199127 | + | 0.979974i | \(0.436189\pi\) | |||||||
\(294\) | 0.946748 | 0.0552155 | ||||||||
\(295\) | 1.64925 | 0.0960231 | ||||||||
\(296\) | 7.80219 | 0.453493 | ||||||||
\(297\) | 3.17847 | 0.184434 | ||||||||
\(298\) | 8.77077 | 0.508077 | ||||||||
\(299\) | 5.16614 | 0.298765 | ||||||||
\(300\) | 3.15433 | 0.182116 | ||||||||
\(301\) | 32.0469 | 1.84715 | ||||||||
\(302\) | 8.39331 | 0.482981 | ||||||||
\(303\) | 8.21766 | 0.472092 | ||||||||
\(304\) | −1.53998 | −0.0883238 | ||||||||
\(305\) | −3.25101 | −0.186153 | ||||||||
\(306\) | 11.1647 | 0.638243 | ||||||||
\(307\) | −3.01812 | −0.172253 | −0.0861266 | − | 0.996284i | \(-0.527449\pi\) | ||||
−0.0861266 | + | 0.996284i | \(0.527449\pi\) | |||||||
\(308\) | 2.49249 | 0.142023 | ||||||||
\(309\) | −9.05492 | −0.515116 | ||||||||
\(310\) | −4.92199 | −0.279550 | ||||||||
\(311\) | 18.3068 | 1.03809 | 0.519043 | − | 0.854748i | \(-0.326289\pi\) | ||||
0.519043 | + | 0.854748i | \(0.326289\pi\) | |||||||
\(312\) | −3.44073 | −0.194793 | ||||||||
\(313\) | −14.1283 | −0.798579 | −0.399289 | − | 0.916825i | \(-0.630743\pi\) | ||||
−0.399289 | + | 0.916825i | \(0.630743\pi\) | |||||||
\(314\) | 18.6501 | 1.05248 | ||||||||
\(315\) | −3.81093 | −0.214722 | ||||||||
\(316\) | −2.80194 | −0.157621 | ||||||||
\(317\) | 23.2730 | 1.30714 | 0.653572 | − | 0.756865i | \(-0.273270\pi\) | ||||
0.653572 | + | 0.756865i | \(0.273270\pi\) | |||||||
\(318\) | −4.03219 | −0.226114 | ||||||||
\(319\) | −2.69301 | −0.150780 | ||||||||
\(320\) | 0.513693 | 0.0287163 | ||||||||
\(321\) | −1.39696 | −0.0779710 | ||||||||
\(322\) | 2.90198 | 0.161721 | ||||||||
\(323\) | −6.72556 | −0.374220 | ||||||||
\(324\) | 5.20456 | 0.289142 | ||||||||
\(325\) | 24.4674 | 1.35721 | ||||||||
\(326\) | 14.6796 | 0.813028 | ||||||||
\(327\) | 2.23211 | 0.123436 | ||||||||
\(328\) | −4.19115 | −0.231417 | ||||||||
\(329\) | −4.68141 | −0.258095 | ||||||||
\(330\) | 0.293851 | 0.0161760 | ||||||||
\(331\) | −13.3253 | −0.732427 | −0.366213 | − | 0.930531i | \(-0.619346\pi\) | ||||
−0.366213 | + | 0.930531i | \(0.619346\pi\) | |||||||
\(332\) | −16.3424 | −0.896907 | ||||||||
\(333\) | 19.9457 | 1.09302 | ||||||||
\(334\) | −18.8637 | −1.03218 | ||||||||
\(335\) | −1.54267 | −0.0842848 | ||||||||
\(336\) | −1.93277 | −0.105441 | ||||||||
\(337\) | 19.3494 | 1.05403 | 0.527016 | − | 0.849856i | \(-0.323311\pi\) | ||||
0.527016 | + | 0.849856i | \(0.323311\pi\) | |||||||
\(338\) | −13.6890 | −0.744582 | ||||||||
\(339\) | −1.73467 | −0.0942146 | ||||||||
\(340\) | 2.24345 | 0.121668 | ||||||||
\(341\) | 8.22955 | 0.445655 | ||||||||
\(342\) | −3.93683 | −0.212880 | ||||||||
\(343\) | −16.1887 | −0.874107 | ||||||||
\(344\) | −11.0431 | −0.595405 | ||||||||
\(345\) | 0.342128 | 0.0184195 | ||||||||
\(346\) | 4.89372 | 0.263088 | ||||||||
\(347\) | 12.7515 | 0.684535 | 0.342268 | − | 0.939602i | \(-0.388805\pi\) | ||||
0.342268 | + | 0.939602i | \(0.388805\pi\) | |||||||
\(348\) | 2.08826 | 0.111942 | ||||||||
\(349\) | 4.42521 | 0.236876 | 0.118438 | − | 0.992961i | \(-0.462211\pi\) | ||||
0.118438 | + | 0.992961i | \(0.462211\pi\) | |||||||
\(350\) | 13.7441 | 0.734655 | ||||||||
\(351\) | −19.1182 | −1.02045 | ||||||||
\(352\) | −0.858892 | −0.0457791 | ||||||||
\(353\) | −21.3505 | −1.13637 | −0.568185 | − | 0.822901i | \(-0.692354\pi\) | ||||
−0.568185 | + | 0.822901i | \(0.692354\pi\) | |||||||
\(354\) | 2.13830 | 0.113649 | ||||||||
\(355\) | 1.08412 | 0.0575393 | ||||||||
\(356\) | −10.3293 | −0.547451 | ||||||||
\(357\) | −8.44100 | −0.446745 | ||||||||
\(358\) | 6.04074 | 0.319263 | ||||||||
\(359\) | −6.08122 | −0.320954 | −0.160477 | − | 0.987040i | \(-0.551303\pi\) | ||||
−0.160477 | + | 0.987040i | \(0.551303\pi\) | |||||||
\(360\) | 1.31322 | 0.0692125 | ||||||||
\(361\) | −16.6285 | −0.875182 | ||||||||
\(362\) | −10.2860 | −0.540619 | ||||||||
\(363\) | 6.83486 | 0.358737 | ||||||||
\(364\) | −14.9920 | −0.785797 | ||||||||
\(365\) | 6.56759 | 0.343763 | ||||||||
\(366\) | −4.21503 | −0.220323 | ||||||||
\(367\) | −9.33388 | −0.487225 | −0.243612 | − | 0.969873i | \(-0.578332\pi\) | ||||
−0.243612 | + | 0.969873i | \(0.578332\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | −10.7143 | −0.557767 | ||||||||
\(370\) | 4.00793 | 0.208362 | ||||||||
\(371\) | −17.5691 | −0.912145 | ||||||||
\(372\) | −6.38149 | −0.330865 | ||||||||
\(373\) | −1.57892 | −0.0817533 | −0.0408767 | − | 0.999164i | \(-0.513015\pi\) | ||||
−0.0408767 | + | 0.999164i | \(0.513015\pi\) | |||||||
\(374\) | −3.75105 | −0.193962 | ||||||||
\(375\) | 3.33100 | 0.172012 | ||||||||
\(376\) | 1.61318 | 0.0831932 | ||||||||
\(377\) | 16.1982 | 0.834247 | ||||||||
\(378\) | −10.7393 | −0.552369 | ||||||||
\(379\) | −20.0720 | −1.03103 | −0.515513 | − | 0.856882i | \(-0.672399\pi\) | ||||
−0.515513 | + | 0.856882i | \(0.672399\pi\) | |||||||
\(380\) | −0.791075 | −0.0405813 | ||||||||
\(381\) | −5.96620 | −0.305658 | ||||||||
\(382\) | −7.08976 | −0.362743 | ||||||||
\(383\) | 1.58508 | 0.0809937 | 0.0404969 | − | 0.999180i | \(-0.487106\pi\) | ||||
0.0404969 | + | 0.999180i | \(0.487106\pi\) | |||||||
\(384\) | 0.666016 | 0.0339875 | ||||||||
\(385\) | 1.28037 | 0.0652539 | ||||||||
\(386\) | −0.399230 | −0.0203203 | ||||||||
\(387\) | −28.2309 | −1.43506 | ||||||||
\(388\) | −13.5647 | −0.688646 | ||||||||
\(389\) | 21.8900 | 1.10987 | 0.554934 | − | 0.831895i | \(-0.312744\pi\) | ||||
0.554934 | + | 0.831895i | \(0.312744\pi\) | |||||||
\(390\) | −1.76748 | −0.0894998 | ||||||||
\(391\) | −4.36731 | −0.220864 | ||||||||
\(392\) | −1.42151 | −0.0717970 | ||||||||
\(393\) | 0.666016 | 0.0335961 | ||||||||
\(394\) | −18.7880 | −0.946524 | ||||||||
\(395\) | −1.43933 | −0.0724207 | ||||||||
\(396\) | −2.19569 | −0.110338 | ||||||||
\(397\) | −31.5986 | −1.58589 | −0.792944 | − | 0.609294i | \(-0.791453\pi\) | ||||
−0.792944 | + | 0.609294i | \(0.791453\pi\) | |||||||
\(398\) | 2.56488 | 0.128566 | ||||||||
\(399\) | 2.97642 | 0.149007 | ||||||||
\(400\) | −4.73612 | −0.236806 | ||||||||
\(401\) | 38.0434 | 1.89980 | 0.949898 | − | 0.312561i | \(-0.101187\pi\) | ||||
0.949898 | + | 0.312561i | \(0.101187\pi\) | |||||||
\(402\) | −2.00011 | −0.0997563 | ||||||||
\(403\) | −49.4998 | −2.46576 | ||||||||
\(404\) | −12.3385 | −0.613864 | ||||||||
\(405\) | 2.67354 | 0.132850 | ||||||||
\(406\) | 9.09902 | 0.451577 | ||||||||
\(407\) | −6.70124 | −0.332168 | ||||||||
\(408\) | 2.90870 | 0.144002 | ||||||||
\(409\) | −9.93846 | −0.491425 | −0.245713 | − | 0.969343i | \(-0.579022\pi\) | ||||
−0.245713 | + | 0.969343i | \(0.579022\pi\) | |||||||
\(410\) | −2.15296 | −0.106327 | ||||||||
\(411\) | 4.24401 | 0.209342 | ||||||||
\(412\) | 13.5956 | 0.669809 | ||||||||
\(413\) | 9.31705 | 0.458462 | ||||||||
\(414\) | −2.55642 | −0.125641 | ||||||||
\(415\) | −8.39499 | −0.412094 | ||||||||
\(416\) | 5.16614 | 0.253291 | ||||||||
\(417\) | 2.25407 | 0.110382 | ||||||||
\(418\) | 1.32268 | 0.0646942 | ||||||||
\(419\) | −7.55580 | −0.369125 | −0.184563 | − | 0.982821i | \(-0.559087\pi\) | ||||
−0.184563 | + | 0.982821i | \(0.559087\pi\) | |||||||
\(420\) | −0.992849 | −0.0484461 | ||||||||
\(421\) | −8.23841 | −0.401515 | −0.200758 | − | 0.979641i | \(-0.564340\pi\) | ||||
−0.200758 | + | 0.979641i | \(0.564340\pi\) | |||||||
\(422\) | −11.1136 | −0.540999 | ||||||||
\(423\) | 4.12396 | 0.200514 | ||||||||
\(424\) | 6.05418 | 0.294017 | ||||||||
\(425\) | −20.6841 | −1.00333 | ||||||||
\(426\) | 1.40559 | 0.0681013 | ||||||||
\(427\) | −18.3658 | −0.888785 | ||||||||
\(428\) | 2.09749 | 0.101386 | ||||||||
\(429\) | 2.95522 | 0.142679 | ||||||||
\(430\) | −5.67277 | −0.273565 | ||||||||
\(431\) | 6.15658 | 0.296552 | 0.148276 | − | 0.988946i | \(-0.452628\pi\) | ||||
0.148276 | + | 0.988946i | \(0.452628\pi\) | |||||||
\(432\) | 3.70067 | 0.178048 | ||||||||
\(433\) | −32.2890 | −1.55171 | −0.775855 | − | 0.630912i | \(-0.782681\pi\) | ||||
−0.775855 | + | 0.630912i | \(0.782681\pi\) | |||||||
\(434\) | −27.8056 | −1.33471 | ||||||||
\(435\) | 1.07272 | 0.0514331 | ||||||||
\(436\) | −3.35144 | −0.160505 | ||||||||
\(437\) | 1.53998 | 0.0736672 | ||||||||
\(438\) | 8.51506 | 0.406865 | ||||||||
\(439\) | −20.6909 | −0.987525 | −0.493762 | − | 0.869597i | \(-0.664379\pi\) | ||||
−0.493762 | + | 0.869597i | \(0.664379\pi\) | |||||||
\(440\) | −0.441207 | −0.0210337 | ||||||||
\(441\) | −3.63398 | −0.173046 | ||||||||
\(442\) | 22.5621 | 1.07317 | ||||||||
\(443\) | −13.7282 | −0.652246 | −0.326123 | − | 0.945327i | \(-0.605742\pi\) | ||||
−0.326123 | + | 0.945327i | \(0.605742\pi\) | |||||||
\(444\) | 5.19638 | 0.246610 | ||||||||
\(445\) | −5.30608 | −0.251532 | ||||||||
\(446\) | −4.48756 | −0.212492 | ||||||||
\(447\) | 5.84147 | 0.276292 | ||||||||
\(448\) | 2.90198 | 0.137106 | ||||||||
\(449\) | −22.8131 | −1.07662 | −0.538309 | − | 0.842748i | \(-0.680936\pi\) | ||||
−0.538309 | + | 0.842748i | \(0.680936\pi\) | |||||||
\(450\) | −12.1075 | −0.570754 | ||||||||
\(451\) | 3.59974 | 0.169505 | ||||||||
\(452\) | 2.60455 | 0.122508 | ||||||||
\(453\) | 5.59008 | 0.262645 | ||||||||
\(454\) | 8.01551 | 0.376186 | ||||||||
\(455\) | −7.70130 | −0.361043 | ||||||||
\(456\) | −1.02565 | −0.0480305 | ||||||||
\(457\) | −24.2316 | −1.13351 | −0.566753 | − | 0.823888i | \(-0.691800\pi\) | ||||
−0.566753 | + | 0.823888i | \(0.691800\pi\) | |||||||
\(458\) | 15.9785 | 0.746627 | ||||||||
\(459\) | 16.1620 | 0.754376 | ||||||||
\(460\) | −0.513693 | −0.0239510 | ||||||||
\(461\) | −3.90091 | −0.181683 | −0.0908417 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908417 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(462\) | 1.66004 | 0.0772320 | ||||||||
\(463\) | −0.835677 | −0.0388372 | −0.0194186 | − | 0.999811i | \(-0.506182\pi\) | ||||
−0.0194186 | + | 0.999811i | \(0.506182\pi\) | |||||||
\(464\) | −3.13545 | −0.145559 | ||||||||
\(465\) | −3.27812 | −0.152019 | ||||||||
\(466\) | 7.42163 | 0.343801 | ||||||||
\(467\) | −5.54999 | −0.256823 | −0.128411 | − | 0.991721i | \(-0.540988\pi\) | ||||
−0.128411 | + | 0.991721i | \(0.540988\pi\) | |||||||
\(468\) | 13.2068 | 0.610486 | ||||||||
\(469\) | −8.71492 | −0.402418 | ||||||||
\(470\) | 0.828677 | 0.0382240 | ||||||||
\(471\) | 12.4212 | 0.572341 | ||||||||
\(472\) | −3.21058 | −0.147779 | ||||||||
\(473\) | 9.48484 | 0.436114 | ||||||||
\(474\) | −1.86613 | −0.0857144 | ||||||||
\(475\) | 7.29352 | 0.334650 | ||||||||
\(476\) | 12.6739 | 0.580905 | ||||||||
\(477\) | 15.4771 | 0.708646 | ||||||||
\(478\) | −7.94904 | −0.363581 | ||||||||
\(479\) | −7.49287 | −0.342358 | −0.171179 | − | 0.985240i | \(-0.554758\pi\) | ||||
−0.171179 | + | 0.985240i | \(0.554758\pi\) | |||||||
\(480\) | 0.342128 | 0.0156159 | ||||||||
\(481\) | 40.3072 | 1.83785 | ||||||||
\(482\) | 18.9159 | 0.861594 | ||||||||
\(483\) | 1.93277 | 0.0879440 | ||||||||
\(484\) | −10.2623 | −0.466468 | ||||||||
\(485\) | −6.96811 | −0.316406 | ||||||||
\(486\) | 14.5683 | 0.660833 | ||||||||
\(487\) | −15.4115 | −0.698361 | −0.349181 | − | 0.937055i | \(-0.613540\pi\) | ||||
−0.349181 | + | 0.937055i | \(0.613540\pi\) | |||||||
\(488\) | 6.32871 | 0.286487 | ||||||||
\(489\) | 9.77685 | 0.442125 | ||||||||
\(490\) | −0.730218 | −0.0329879 | ||||||||
\(491\) | −17.3428 | −0.782670 | −0.391335 | − | 0.920248i | \(-0.627987\pi\) | ||||
−0.391335 | + | 0.920248i | \(0.627987\pi\) | |||||||
\(492\) | −2.79137 | −0.125845 | ||||||||
\(493\) | −13.6935 | −0.616723 | ||||||||
\(494\) | −7.95574 | −0.357946 | ||||||||
\(495\) | −1.12791 | −0.0506958 | ||||||||
\(496\) | 9.58158 | 0.430226 | ||||||||
\(497\) | 6.12449 | 0.274721 | ||||||||
\(498\) | −10.8843 | −0.487738 | ||||||||
\(499\) | −24.4498 | −1.09452 | −0.547262 | − | 0.836961i | \(-0.684330\pi\) | ||||
−0.547262 | + | 0.836961i | \(0.684330\pi\) | |||||||
\(500\) | −5.00137 | −0.223668 | ||||||||
\(501\) | −12.5636 | −0.561298 | ||||||||
\(502\) | −20.4684 | −0.913548 | ||||||||
\(503\) | 20.8743 | 0.930740 | 0.465370 | − | 0.885116i | \(-0.345921\pi\) | ||||
0.465370 | + | 0.885116i | \(0.345921\pi\) | |||||||
\(504\) | 7.41870 | 0.330455 | ||||||||
\(505\) | −6.33821 | −0.282047 | ||||||||
\(506\) | 0.858892 | 0.0381824 | ||||||||
\(507\) | −9.11708 | −0.404904 | ||||||||
\(508\) | 8.95804 | 0.397449 | ||||||||
\(509\) | −41.7327 | −1.84977 | −0.924886 | − | 0.380245i | \(-0.875840\pi\) | ||||
−0.924886 | + | 0.380245i | \(0.875840\pi\) | |||||||
\(510\) | 1.49418 | 0.0661633 | ||||||||
\(511\) | 37.1020 | 1.64130 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −5.69895 | −0.251615 | ||||||||
\(514\) | 17.0534 | 0.752195 | ||||||||
\(515\) | 6.98398 | 0.307751 | ||||||||
\(516\) | −7.35489 | −0.323781 | ||||||||
\(517\) | −1.38555 | −0.0609362 | ||||||||
\(518\) | 22.6418 | 0.994825 | ||||||||
\(519\) | 3.25929 | 0.143067 | ||||||||
\(520\) | 2.65381 | 0.116377 | ||||||||
\(521\) | −37.4460 | −1.64054 | −0.820269 | − | 0.571978i | \(-0.806176\pi\) | ||||
−0.820269 | + | 0.571978i | \(0.806176\pi\) | |||||||
\(522\) | −8.01553 | −0.350830 | ||||||||
\(523\) | −28.7944 | −1.25909 | −0.629545 | − | 0.776964i | \(-0.716759\pi\) | ||||
−0.629545 | + | 0.776964i | \(0.716759\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | 9.15382 | 0.399506 | ||||||||
\(526\) | 12.6819 | 0.552955 | ||||||||
\(527\) | 41.8457 | 1.82283 | ||||||||
\(528\) | −0.572036 | −0.0248947 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 3.10999 | 0.135089 | ||||||||
\(531\) | −8.20760 | −0.356179 | ||||||||
\(532\) | −4.46899 | −0.193755 | ||||||||
\(533\) | −21.6521 | −0.937854 | ||||||||
\(534\) | −6.87948 | −0.297704 | ||||||||
\(535\) | 1.07747 | 0.0465830 | ||||||||
\(536\) | 3.00309 | 0.129714 | ||||||||
\(537\) | 4.02323 | 0.173615 | ||||||||
\(538\) | 3.85121 | 0.166037 | ||||||||
\(539\) | 1.22092 | 0.0525889 | ||||||||
\(540\) | 1.90101 | 0.0818063 | ||||||||
\(541\) | 22.8379 | 0.981879 | 0.490939 | − | 0.871194i | \(-0.336654\pi\) | ||||
0.490939 | + | 0.871194i | \(0.336654\pi\) | |||||||
\(542\) | 18.3602 | 0.788636 | ||||||||
\(543\) | −6.85062 | −0.293988 | ||||||||
\(544\) | −4.36731 | −0.187247 | ||||||||
\(545\) | −1.72161 | −0.0737457 | ||||||||
\(546\) | −9.98495 | −0.427316 | ||||||||
\(547\) | 9.08995 | 0.388658 | 0.194329 | − | 0.980936i | \(-0.437747\pi\) | ||||
0.194329 | + | 0.980936i | \(0.437747\pi\) | |||||||
\(548\) | −6.37224 | −0.272209 | ||||||||
\(549\) | 16.1789 | 0.690497 | ||||||||
\(550\) | 4.06782 | 0.173452 | ||||||||
\(551\) | 4.82852 | 0.205702 | ||||||||
\(552\) | −0.666016 | −0.0283475 | ||||||||
\(553\) | −8.13117 | −0.345773 | ||||||||
\(554\) | 8.48390 | 0.360446 | ||||||||
\(555\) | 2.66934 | 0.113307 | ||||||||
\(556\) | −3.38441 | −0.143531 | ||||||||
\(557\) | −28.5010 | −1.20763 | −0.603813 | − | 0.797126i | \(-0.706353\pi\) | ||||
−0.603813 | + | 0.797126i | \(0.706353\pi\) | |||||||
\(558\) | 24.4946 | 1.03694 | ||||||||
\(559\) | −57.0502 | −2.41297 | ||||||||
\(560\) | 1.49073 | 0.0629947 | ||||||||
\(561\) | −2.49826 | −0.105477 | ||||||||
\(562\) | −25.6835 | −1.08339 | ||||||||
\(563\) | 4.56056 | 0.192205 | 0.0961024 | − | 0.995371i | \(-0.469362\pi\) | ||||
0.0961024 | + | 0.995371i | \(0.469362\pi\) | |||||||
\(564\) | 1.07440 | 0.0452405 | ||||||||
\(565\) | 1.33794 | 0.0562875 | ||||||||
\(566\) | 4.17828 | 0.175626 | ||||||||
\(567\) | 15.1036 | 0.634290 | ||||||||
\(568\) | −2.11045 | −0.0885526 | ||||||||
\(569\) | −9.59342 | −0.402177 | −0.201088 | − | 0.979573i | \(-0.564448\pi\) | ||||
−0.201088 | + | 0.979573i | \(0.564448\pi\) | |||||||
\(570\) | −0.526869 | −0.0220681 | ||||||||
\(571\) | −32.7726 | −1.37149 | −0.685745 | − | 0.727841i | \(-0.740524\pi\) | ||||
−0.685745 | + | 0.727841i | \(0.740524\pi\) | |||||||
\(572\) | −4.43716 | −0.185527 | ||||||||
\(573\) | −4.72189 | −0.197260 | ||||||||
\(574\) | −12.1626 | −0.507659 | ||||||||
\(575\) | 4.73612 | 0.197510 | ||||||||
\(576\) | −2.55642 | −0.106518 | ||||||||
\(577\) | −47.0143 | −1.95723 | −0.978616 | − | 0.205696i | \(-0.934054\pi\) | ||||
−0.978616 | + | 0.205696i | \(0.934054\pi\) | |||||||
\(578\) | −2.07339 | −0.0862418 | ||||||||
\(579\) | −0.265894 | −0.0110502 | ||||||||
\(580\) | −1.61066 | −0.0668789 | ||||||||
\(581\) | −47.4255 | −1.96754 | ||||||||
\(582\) | −9.03434 | −0.374486 | ||||||||
\(583\) | −5.19989 | −0.215358 | ||||||||
\(584\) | −12.7851 | −0.529049 | ||||||||
\(585\) | 6.78425 | 0.280494 | ||||||||
\(586\) | −6.81701 | −0.281608 | ||||||||
\(587\) | 43.3384 | 1.78877 | 0.894383 | − | 0.447302i | \(-0.147615\pi\) | ||||
0.894383 | + | 0.447302i | \(0.147615\pi\) | |||||||
\(588\) | −0.946748 | −0.0390432 | ||||||||
\(589\) | −14.7554 | −0.607987 | ||||||||
\(590\) | −1.64925 | −0.0678986 | ||||||||
\(591\) | −12.5131 | −0.514720 | ||||||||
\(592\) | −7.80219 | −0.320668 | ||||||||
\(593\) | 18.7496 | 0.769955 | 0.384977 | − | 0.922926i | \(-0.374209\pi\) | ||||
0.384977 | + | 0.922926i | \(0.374209\pi\) | |||||||
\(594\) | −3.17847 | −0.130414 | ||||||||
\(595\) | 6.51047 | 0.266903 | ||||||||
\(596\) | −8.77077 | −0.359265 | ||||||||
\(597\) | 1.70825 | 0.0699142 | ||||||||
\(598\) | −5.16614 | −0.211259 | ||||||||
\(599\) | 21.9935 | 0.898631 | 0.449315 | − | 0.893373i | \(-0.351668\pi\) | ||||
0.449315 | + | 0.893373i | \(0.351668\pi\) | |||||||
\(600\) | −3.15433 | −0.128775 | ||||||||
\(601\) | 26.7252 | 1.09014 | 0.545071 | − | 0.838390i | \(-0.316503\pi\) | ||||
0.545071 | + | 0.838390i | \(0.316503\pi\) | |||||||
\(602\) | −32.0469 | −1.30614 | ||||||||
\(603\) | 7.67717 | 0.312638 | ||||||||
\(604\) | −8.39331 | −0.341519 | ||||||||
\(605\) | −5.27167 | −0.214324 | ||||||||
\(606\) | −8.21766 | −0.333820 | ||||||||
\(607\) | −28.6155 | −1.16147 | −0.580734 | − | 0.814093i | \(-0.697235\pi\) | ||||
−0.580734 | + | 0.814093i | \(0.697235\pi\) | |||||||
\(608\) | 1.53998 | 0.0624544 | ||||||||
\(609\) | 6.06009 | 0.245567 | ||||||||
\(610\) | 3.25101 | 0.131630 | ||||||||
\(611\) | 8.33389 | 0.337153 | ||||||||
\(612\) | −11.1647 | −0.451306 | ||||||||
\(613\) | −6.18020 | −0.249616 | −0.124808 | − | 0.992181i | \(-0.539831\pi\) | ||||
−0.124808 | + | 0.992181i | \(0.539831\pi\) | |||||||
\(614\) | 3.01812 | 0.121801 | ||||||||
\(615\) | −1.43391 | −0.0578207 | ||||||||
\(616\) | −2.49249 | −0.100425 | ||||||||
\(617\) | 47.4025 | 1.90835 | 0.954176 | − | 0.299246i | \(-0.0967350\pi\) | ||||
0.954176 | + | 0.299246i | \(0.0967350\pi\) | |||||||
\(618\) | 9.05492 | 0.364242 | ||||||||
\(619\) | 5.78694 | 0.232597 | 0.116298 | − | 0.993214i | \(-0.462897\pi\) | ||||
0.116298 | + | 0.993214i | \(0.462897\pi\) | |||||||
\(620\) | 4.92199 | 0.197672 | ||||||||
\(621\) | −3.70067 | −0.148503 | ||||||||
\(622\) | −18.3068 | −0.734037 | ||||||||
\(623\) | −29.9754 | −1.20094 | ||||||||
\(624\) | 3.44073 | 0.137740 | ||||||||
\(625\) | 21.1114 | 0.844457 | ||||||||
\(626\) | 14.1283 | 0.564681 | ||||||||
\(627\) | 0.880923 | 0.0351807 | ||||||||
\(628\) | −18.6501 | −0.744219 | ||||||||
\(629\) | −34.0746 | −1.35864 | ||||||||
\(630\) | 3.81093 | 0.151831 | ||||||||
\(631\) | −0.0535723 | −0.00213268 | −0.00106634 | − | 0.999999i | \(-0.500339\pi\) | ||||
−0.00106634 | + | 0.999999i | \(0.500339\pi\) | |||||||
\(632\) | 2.80194 | 0.111455 | ||||||||
\(633\) | −7.40181 | −0.294195 | ||||||||
\(634\) | −23.2730 | −0.924290 | ||||||||
\(635\) | 4.60168 | 0.182612 | ||||||||
\(636\) | 4.03219 | 0.159887 | ||||||||
\(637\) | −7.34371 | −0.290968 | ||||||||
\(638\) | 2.69301 | 0.106617 | ||||||||
\(639\) | −5.39520 | −0.213431 | ||||||||
\(640\) | −0.513693 | −0.0203055 | ||||||||
\(641\) | −25.7287 | −1.01622 | −0.508112 | − | 0.861291i | \(-0.669656\pi\) | ||||
−0.508112 | + | 0.861291i | \(0.669656\pi\) | |||||||
\(642\) | 1.39696 | 0.0551338 | ||||||||
\(643\) | 21.7189 | 0.856510 | 0.428255 | − | 0.903658i | \(-0.359128\pi\) | ||||
0.428255 | + | 0.903658i | \(0.359128\pi\) | |||||||
\(644\) | −2.90198 | −0.114354 | ||||||||
\(645\) | −3.77815 | −0.148765 | ||||||||
\(646\) | 6.72556 | 0.264614 | ||||||||
\(647\) | 23.6323 | 0.929082 | 0.464541 | − | 0.885552i | \(-0.346219\pi\) | ||||
0.464541 | + | 0.885552i | \(0.346219\pi\) | |||||||
\(648\) | −5.20456 | −0.204454 | ||||||||
\(649\) | 2.75754 | 0.108243 | ||||||||
\(650\) | −24.4674 | −0.959692 | ||||||||
\(651\) | −18.5190 | −0.725816 | ||||||||
\(652\) | −14.6796 | −0.574898 | ||||||||
\(653\) | −42.1204 | −1.64830 | −0.824150 | − | 0.566372i | \(-0.808347\pi\) | ||||
−0.824150 | + | 0.566372i | \(0.808347\pi\) | |||||||
\(654\) | −2.23211 | −0.0872826 | ||||||||
\(655\) | −0.513693 | −0.0200716 | ||||||||
\(656\) | 4.19115 | 0.163637 | ||||||||
\(657\) | −32.6840 | −1.27512 | ||||||||
\(658\) | 4.68141 | 0.182500 | ||||||||
\(659\) | −14.7719 | −0.575433 | −0.287717 | − | 0.957716i | \(-0.592896\pi\) | ||||
−0.287717 | + | 0.957716i | \(0.592896\pi\) | |||||||
\(660\) | −0.293851 | −0.0114381 | ||||||||
\(661\) | 6.11864 | 0.237988 | 0.118994 | − | 0.992895i | \(-0.462033\pi\) | ||||
0.118994 | + | 0.992895i | \(0.462033\pi\) | |||||||
\(662\) | 13.3253 | 0.517904 | ||||||||
\(663\) | 15.0267 | 0.583590 | ||||||||
\(664\) | 16.3424 | 0.634209 | ||||||||
\(665\) | −2.29569 | −0.0890230 | ||||||||
\(666\) | −19.9457 | −0.772880 | ||||||||
\(667\) | 3.13545 | 0.121405 | ||||||||
\(668\) | 18.8637 | 0.729860 | ||||||||
\(669\) | −2.98878 | −0.115553 | ||||||||
\(670\) | 1.54267 | 0.0595984 | ||||||||
\(671\) | −5.43568 | −0.209842 | ||||||||
\(672\) | 1.93277 | 0.0745582 | ||||||||
\(673\) | 0.223478 | 0.00861445 | 0.00430722 | − | 0.999991i | \(-0.498629\pi\) | ||||
0.00430722 | + | 0.999991i | \(0.498629\pi\) | |||||||
\(674\) | −19.3494 | −0.745313 | ||||||||
\(675\) | −17.5268 | −0.674607 | ||||||||
\(676\) | 13.6890 | 0.526499 | ||||||||
\(677\) | −5.64093 | −0.216799 | −0.108399 | − | 0.994107i | \(-0.534573\pi\) | ||||
−0.108399 | + | 0.994107i | \(0.534573\pi\) | |||||||
\(678\) | 1.73467 | 0.0666198 | ||||||||
\(679\) | −39.3647 | −1.51068 | ||||||||
\(680\) | −2.24345 | −0.0860326 | ||||||||
\(681\) | 5.33846 | 0.204570 | ||||||||
\(682\) | −8.22955 | −0.315126 | ||||||||
\(683\) | 31.1038 | 1.19015 | 0.595077 | − | 0.803669i | \(-0.297122\pi\) | ||||
0.595077 | + | 0.803669i | \(0.297122\pi\) | |||||||
\(684\) | 3.93683 | 0.150529 | ||||||||
\(685\) | −3.27337 | −0.125069 | ||||||||
\(686\) | 16.1887 | 0.618087 | ||||||||
\(687\) | 10.6420 | 0.406016 | ||||||||
\(688\) | 11.0431 | 0.421015 | ||||||||
\(689\) | 31.2768 | 1.19155 | ||||||||
\(690\) | −0.342128 | −0.0130246 | ||||||||
\(691\) | 15.1637 | 0.576855 | 0.288427 | − | 0.957502i | \(-0.406868\pi\) | ||||
0.288427 | + | 0.957502i | \(0.406868\pi\) | |||||||
\(692\) | −4.89372 | −0.186031 | ||||||||
\(693\) | −6.37186 | −0.242047 | ||||||||
\(694\) | −12.7515 | −0.484040 | ||||||||
\(695\) | −1.73855 | −0.0659468 | ||||||||
\(696\) | −2.08826 | −0.0791553 | ||||||||
\(697\) | 18.3040 | 0.693315 | ||||||||
\(698\) | −4.42521 | −0.167497 | ||||||||
\(699\) | 4.94293 | 0.186959 | ||||||||
\(700\) | −13.7441 | −0.519480 | ||||||||
\(701\) | 22.8260 | 0.862126 | 0.431063 | − | 0.902322i | \(-0.358139\pi\) | ||||
0.431063 | + | 0.902322i | \(0.358139\pi\) | |||||||
\(702\) | 19.1182 | 0.721568 | ||||||||
\(703\) | 12.0152 | 0.453162 | ||||||||
\(704\) | 0.858892 | 0.0323707 | ||||||||
\(705\) | 0.551912 | 0.0207862 | ||||||||
\(706\) | 21.3505 | 0.803535 | ||||||||
\(707\) | −35.8062 | −1.34663 | ||||||||
\(708\) | −2.13830 | −0.0803622 | ||||||||
\(709\) | 27.0077 | 1.01430 | 0.507149 | − | 0.861859i | \(-0.330700\pi\) | ||||
0.507149 | + | 0.861859i | \(0.330700\pi\) | |||||||
\(710\) | −1.08412 | −0.0406864 | ||||||||
\(711\) | 7.16293 | 0.268631 | ||||||||
\(712\) | 10.3293 | 0.387107 | ||||||||
\(713\) | −9.58158 | −0.358833 | ||||||||
\(714\) | 8.44100 | 0.315896 | ||||||||
\(715\) | −2.27933 | −0.0852423 | ||||||||
\(716\) | −6.04074 | −0.225753 | ||||||||
\(717\) | −5.29419 | −0.197715 | ||||||||
\(718\) | 6.08122 | 0.226949 | ||||||||
\(719\) | 30.9376 | 1.15378 | 0.576888 | − | 0.816823i | \(-0.304267\pi\) | ||||
0.576888 | + | 0.816823i | \(0.304267\pi\) | |||||||
\(720\) | −1.31322 | −0.0489406 | ||||||||
\(721\) | 39.4543 | 1.46936 | ||||||||
\(722\) | 16.6285 | 0.618847 | ||||||||
\(723\) | 12.5983 | 0.468535 | ||||||||
\(724\) | 10.2860 | 0.382275 | ||||||||
\(725\) | 14.8499 | 0.551510 | ||||||||
\(726\) | −6.83486 | −0.253666 | ||||||||
\(727\) | −19.7288 | −0.731700 | −0.365850 | − | 0.930674i | \(-0.619222\pi\) | ||||
−0.365850 | + | 0.930674i | \(0.619222\pi\) | |||||||
\(728\) | 14.9920 | 0.555642 | ||||||||
\(729\) | −5.91094 | −0.218924 | ||||||||
\(730\) | −6.56759 | −0.243077 | ||||||||
\(731\) | 48.2287 | 1.78380 | ||||||||
\(732\) | 4.21503 | 0.155792 | ||||||||
\(733\) | 13.5687 | 0.501172 | 0.250586 | − | 0.968094i | \(-0.419377\pi\) | ||||
0.250586 | + | 0.968094i | \(0.419377\pi\) | |||||||
\(734\) | 9.33388 | 0.344520 | ||||||||
\(735\) | −0.486337 | −0.0179388 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −2.57933 | −0.0950109 | ||||||||
\(738\) | 10.7143 | 0.394401 | ||||||||
\(739\) | −7.09977 | −0.261169 | −0.130585 | − | 0.991437i | \(-0.541685\pi\) | ||||
−0.130585 | + | 0.991437i | \(0.541685\pi\) | |||||||
\(740\) | −4.00793 | −0.147334 | ||||||||
\(741\) | −5.29865 | −0.194651 | ||||||||
\(742\) | 17.5691 | 0.644984 | ||||||||
\(743\) | −11.4226 | −0.419056 | −0.209528 | − | 0.977803i | \(-0.567193\pi\) | ||||
−0.209528 | + | 0.977803i | \(0.567193\pi\) | |||||||
\(744\) | 6.38149 | 0.233957 | ||||||||
\(745\) | −4.50548 | −0.165068 | ||||||||
\(746\) | 1.57892 | 0.0578083 | ||||||||
\(747\) | 41.7782 | 1.52858 | ||||||||
\(748\) | 3.75105 | 0.137152 | ||||||||
\(749\) | 6.08689 | 0.222410 | ||||||||
\(750\) | −3.33100 | −0.121631 | ||||||||
\(751\) | −6.92083 | −0.252545 | −0.126272 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126272 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(752\) | −1.61318 | −0.0588265 | ||||||||
\(753\) | −13.6323 | −0.496787 | ||||||||
\(754\) | −16.1982 | −0.589902 | ||||||||
\(755\) | −4.31158 | −0.156915 | ||||||||
\(756\) | 10.7393 | 0.390584 | ||||||||
\(757\) | −17.5699 | −0.638589 | −0.319295 | − | 0.947656i | \(-0.603446\pi\) | ||||
−0.319295 | + | 0.947656i | \(0.603446\pi\) | |||||||
\(758\) | 20.0720 | 0.729046 | ||||||||
\(759\) | 0.572036 | 0.0207636 | ||||||||
\(760\) | 0.791075 | 0.0286953 | ||||||||
\(761\) | 16.0153 | 0.580553 | 0.290276 | − | 0.956943i | \(-0.406253\pi\) | ||||
0.290276 | + | 0.956943i | \(0.406253\pi\) | |||||||
\(762\) | 5.96620 | 0.216133 | ||||||||
\(763\) | −9.72583 | −0.352099 | ||||||||
\(764\) | 7.08976 | 0.256498 | ||||||||
\(765\) | −5.73522 | −0.207357 | ||||||||
\(766\) | −1.58508 | −0.0572712 | ||||||||
\(767\) | −16.5863 | −0.598897 | ||||||||
\(768\) | −0.666016 | −0.0240328 | ||||||||
\(769\) | −38.5446 | −1.38996 | −0.694978 | − | 0.719031i | \(-0.744586\pi\) | ||||
−0.694978 | + | 0.719031i | \(0.744586\pi\) | |||||||
\(770\) | −1.28037 | −0.0461415 | ||||||||
\(771\) | 11.3579 | 0.409044 | ||||||||
\(772\) | 0.399230 | 0.0143686 | ||||||||
\(773\) | −1.30869 | −0.0470705 | −0.0235352 | − | 0.999723i | \(-0.507492\pi\) | ||||
−0.0235352 | + | 0.999723i | \(0.507492\pi\) | |||||||
\(774\) | 28.2309 | 1.01474 | ||||||||
\(775\) | −45.3795 | −1.63008 | ||||||||
\(776\) | 13.5647 | 0.486946 | ||||||||
\(777\) | 15.0798 | 0.540986 | ||||||||
\(778\) | −21.8900 | −0.784795 | ||||||||
\(779\) | −6.45428 | −0.231249 | ||||||||
\(780\) | 1.76748 | 0.0632859 | ||||||||
\(781\) | 1.81265 | 0.0648617 | ||||||||
\(782\) | 4.36731 | 0.156175 | ||||||||
\(783\) | −11.6032 | −0.414666 | ||||||||
\(784\) | 1.42151 | 0.0507682 | ||||||||
\(785\) | −9.58040 | −0.341939 | ||||||||
\(786\) | −0.666016 | −0.0237560 | ||||||||
\(787\) | −30.3100 | −1.08043 | −0.540217 | − | 0.841526i | \(-0.681658\pi\) | ||||
−0.540217 | + | 0.841526i | \(0.681658\pi\) | |||||||
\(788\) | 18.7880 | 0.669294 | ||||||||
\(789\) | 8.44632 | 0.300697 | ||||||||
\(790\) | 1.43933 | 0.0512092 | ||||||||
\(791\) | 7.55837 | 0.268745 | ||||||||
\(792\) | 2.19569 | 0.0780205 | ||||||||
\(793\) | 32.6950 | 1.16103 | ||||||||
\(794\) | 31.5986 | 1.12139 | ||||||||
\(795\) | 2.07130 | 0.0734616 | ||||||||
\(796\) | −2.56488 | −0.0909099 | ||||||||
\(797\) | 19.3895 | 0.686811 | 0.343405 | − | 0.939187i | \(-0.388420\pi\) | ||||
0.343405 | + | 0.939187i | \(0.388420\pi\) | |||||||
\(798\) | −2.97642 | −0.105364 | ||||||||
\(799\) | −7.04524 | −0.249243 | ||||||||
\(800\) | 4.73612 | 0.167447 | ||||||||
\(801\) | 26.4060 | 0.933011 | ||||||||
\(802\) | −38.0434 | −1.34336 | ||||||||
\(803\) | 10.9810 | 0.387511 | ||||||||
\(804\) | 2.00011 | 0.0705383 | ||||||||
\(805\) | −1.49073 | −0.0525412 | ||||||||
\(806\) | 49.4998 | 1.74355 | ||||||||
\(807\) | 2.56497 | 0.0902911 | ||||||||
\(808\) | 12.3385 | 0.434068 | ||||||||
\(809\) | 29.7412 | 1.04564 | 0.522822 | − | 0.852442i | \(-0.324879\pi\) | ||||
0.522822 | + | 0.852442i | \(0.324879\pi\) | |||||||
\(810\) | −2.67354 | −0.0939388 | ||||||||
\(811\) | −19.6730 | −0.690812 | −0.345406 | − | 0.938453i | \(-0.612259\pi\) | ||||
−0.345406 | + | 0.938453i | \(0.612259\pi\) | |||||||
\(812\) | −9.09902 | −0.319313 | ||||||||
\(813\) | 12.2282 | 0.428861 | ||||||||
\(814\) | 6.70124 | 0.234878 | ||||||||
\(815\) | −7.54080 | −0.264143 | ||||||||
\(816\) | −2.90870 | −0.101825 | ||||||||
\(817\) | −17.0062 | −0.594970 | ||||||||
\(818\) | 9.93846 | 0.347490 | ||||||||
\(819\) | 38.3260 | 1.33922 | ||||||||
\(820\) | 2.15296 | 0.0751847 | ||||||||
\(821\) | −33.2545 | −1.16059 | −0.580295 | − | 0.814407i | \(-0.697063\pi\) | ||||
−0.580295 | + | 0.814407i | \(0.697063\pi\) | |||||||
\(822\) | −4.24401 | −0.148027 | ||||||||
\(823\) | −12.4927 | −0.435468 | −0.217734 | − | 0.976008i | \(-0.569867\pi\) | ||||
−0.217734 | + | 0.976008i | \(0.569867\pi\) | |||||||
\(824\) | −13.5956 | −0.473627 | ||||||||
\(825\) | 2.70923 | 0.0943234 | ||||||||
\(826\) | −9.31705 | −0.324182 | ||||||||
\(827\) | 18.5792 | 0.646063 | 0.323031 | − | 0.946388i | \(-0.395298\pi\) | ||||
0.323031 | + | 0.946388i | \(0.395298\pi\) | |||||||
\(828\) | 2.55642 | 0.0888418 | ||||||||
\(829\) | −13.2394 | −0.459823 | −0.229912 | − | 0.973211i | \(-0.573844\pi\) | ||||
−0.229912 | + | 0.973211i | \(0.573844\pi\) | |||||||
\(830\) | 8.39499 | 0.291394 | ||||||||
\(831\) | 5.65042 | 0.196011 | ||||||||
\(832\) | −5.16614 | −0.179104 | ||||||||
\(833\) | 6.20817 | 0.215100 | ||||||||
\(834\) | −2.25407 | −0.0780521 | ||||||||
\(835\) | 9.69016 | 0.335342 | ||||||||
\(836\) | −1.32268 | −0.0457457 | ||||||||
\(837\) | 35.4583 | 1.22562 | ||||||||
\(838\) | 7.55580 | 0.261011 | ||||||||
\(839\) | −36.1690 | −1.24869 | −0.624346 | − | 0.781148i | \(-0.714635\pi\) | ||||
−0.624346 | + | 0.781148i | \(0.714635\pi\) | |||||||
\(840\) | 0.992849 | 0.0342565 | ||||||||
\(841\) | −19.1690 | −0.660999 | ||||||||
\(842\) | 8.23841 | 0.283914 | ||||||||
\(843\) | −17.1056 | −0.589149 | ||||||||
\(844\) | 11.1136 | 0.382544 | ||||||||
\(845\) | 7.03193 | 0.241906 | ||||||||
\(846\) | −4.12396 | −0.141785 | ||||||||
\(847\) | −29.7810 | −1.02329 | ||||||||
\(848\) | −6.05418 | −0.207902 | ||||||||
\(849\) | 2.78280 | 0.0955055 | ||||||||
\(850\) | 20.6841 | 0.709459 | ||||||||
\(851\) | 7.80219 | 0.267456 | ||||||||
\(852\) | −1.40559 | −0.0481549 | ||||||||
\(853\) | −14.0142 | −0.479837 | −0.239919 | − | 0.970793i | \(-0.577121\pi\) | ||||
−0.239919 | + | 0.970793i | \(0.577121\pi\) | |||||||
\(854\) | 18.3658 | 0.628466 | ||||||||
\(855\) | 2.02232 | 0.0691620 | ||||||||
\(856\) | −2.09749 | −0.0716908 | ||||||||
\(857\) | 45.7166 | 1.56165 | 0.780824 | − | 0.624751i | \(-0.214800\pi\) | ||||
0.780824 | + | 0.624751i | \(0.214800\pi\) | |||||||
\(858\) | −2.95522 | −0.100889 | ||||||||
\(859\) | −12.3005 | −0.419689 | −0.209845 | − | 0.977735i | \(-0.567296\pi\) | ||||
−0.209845 | + | 0.977735i | \(0.567296\pi\) | |||||||
\(860\) | 5.67277 | 0.193440 | ||||||||
\(861\) | −8.10052 | −0.276065 | ||||||||
\(862\) | −6.15658 | −0.209694 | ||||||||
\(863\) | −10.6679 | −0.363140 | −0.181570 | − | 0.983378i | \(-0.558118\pi\) | ||||
−0.181570 | + | 0.983378i | \(0.558118\pi\) | |||||||
\(864\) | −3.70067 | −0.125899 | ||||||||
\(865\) | −2.51387 | −0.0854740 | ||||||||
\(866\) | 32.2890 | 1.09722 | ||||||||
\(867\) | −1.38091 | −0.0468983 | ||||||||
\(868\) | 27.8056 | 0.943783 | ||||||||
\(869\) | −2.40656 | −0.0816370 | ||||||||
\(870\) | −1.07272 | −0.0363687 | ||||||||
\(871\) | 15.5144 | 0.525685 | ||||||||
\(872\) | 3.35144 | 0.113494 | ||||||||
\(873\) | 34.6772 | 1.17365 | ||||||||
\(874\) | −1.53998 | −0.0520905 | ||||||||
\(875\) | −14.5139 | −0.490659 | ||||||||
\(876\) | −8.51506 | −0.287697 | ||||||||
\(877\) | 29.8997 | 1.00964 | 0.504821 | − | 0.863224i | \(-0.331558\pi\) | ||||
0.504821 | + | 0.863224i | \(0.331558\pi\) | |||||||
\(878\) | 20.6909 | 0.698286 | ||||||||
\(879\) | −4.54024 | −0.153138 | ||||||||
\(880\) | 0.441207 | 0.0148731 | ||||||||
\(881\) | −18.0201 | −0.607112 | −0.303556 | − | 0.952814i | \(-0.598174\pi\) | ||||
−0.303556 | + | 0.952814i | \(0.598174\pi\) | |||||||
\(882\) | 3.63398 | 0.122362 | ||||||||
\(883\) | −9.96290 | −0.335278 | −0.167639 | − | 0.985848i | \(-0.553614\pi\) | ||||
−0.167639 | + | 0.985848i | \(0.553614\pi\) | |||||||
\(884\) | −22.5621 | −0.758846 | ||||||||
\(885\) | −1.09843 | −0.0369233 | ||||||||
\(886\) | 13.7282 | 0.461208 | ||||||||
\(887\) | 14.7481 | 0.495193 | 0.247596 | − | 0.968863i | \(-0.420359\pi\) | ||||
0.247596 | + | 0.968863i | \(0.420359\pi\) | |||||||
\(888\) | −5.19638 | −0.174379 | ||||||||
\(889\) | 25.9961 | 0.871881 | ||||||||
\(890\) | 5.30608 | 0.177860 | ||||||||
\(891\) | 4.47016 | 0.149756 | ||||||||
\(892\) | 4.48756 | 0.150254 | ||||||||
\(893\) | 2.48426 | 0.0831325 | ||||||||
\(894\) | −5.84147 | −0.195368 | ||||||||
\(895\) | −3.10308 | −0.103725 | ||||||||
\(896\) | −2.90198 | −0.0969485 | ||||||||
\(897\) | −3.44073 | −0.114883 | ||||||||
\(898\) | 22.8131 | 0.761283 | ||||||||
\(899\) | −30.0425 | −1.00197 | ||||||||
\(900\) | 12.1075 | 0.403584 | ||||||||
\(901\) | −26.4405 | −0.880861 | ||||||||
\(902\) | −3.59974 | −0.119858 | ||||||||
\(903\) | −21.3438 | −0.710276 | ||||||||
\(904\) | −2.60455 | −0.0866262 | ||||||||
\(905\) | 5.28383 | 0.175640 | ||||||||
\(906\) | −5.59008 | −0.185718 | ||||||||
\(907\) | 25.8084 | 0.856953 | 0.428477 | − | 0.903553i | \(-0.359050\pi\) | ||||
0.428477 | + | 0.903553i | \(0.359050\pi\) | |||||||
\(908\) | −8.01551 | −0.266004 | ||||||||
\(909\) | 31.5425 | 1.04620 | ||||||||
\(910\) | 7.70130 | 0.255296 | ||||||||
\(911\) | 54.2863 | 1.79859 | 0.899293 | − | 0.437347i | \(-0.144082\pi\) | ||||
0.899293 | + | 0.437347i | \(0.144082\pi\) | |||||||
\(912\) | 1.02565 | 0.0339627 | ||||||||
\(913\) | −14.0364 | −0.464537 | ||||||||
\(914\) | 24.2316 | 0.801509 | ||||||||
\(915\) | 2.16523 | 0.0715802 | ||||||||
\(916\) | −15.9785 | −0.527945 | ||||||||
\(917\) | −2.90198 | −0.0958319 | ||||||||
\(918\) | −16.1620 | −0.533424 | ||||||||
\(919\) | 41.7515 | 1.37726 | 0.688628 | − | 0.725115i | \(-0.258213\pi\) | ||||
0.688628 | + | 0.725115i | \(0.258213\pi\) | |||||||
\(920\) | 0.513693 | 0.0169359 | ||||||||
\(921\) | 2.01012 | 0.0662356 | ||||||||
\(922\) | 3.90091 | 0.128470 | ||||||||
\(923\) | −10.9029 | −0.358873 | ||||||||
\(924\) | −1.66004 | −0.0546113 | ||||||||
\(925\) | 36.9521 | 1.21498 | ||||||||
\(926\) | 0.835677 | 0.0274621 | ||||||||
\(927\) | −34.7562 | −1.14154 | ||||||||
\(928\) | 3.13545 | 0.102926 | ||||||||
\(929\) | −16.8914 | −0.554190 | −0.277095 | − | 0.960843i | \(-0.589372\pi\) | ||||
−0.277095 | + | 0.960843i | \(0.589372\pi\) | |||||||
\(930\) | 3.27812 | 0.107494 | ||||||||
\(931\) | −2.18909 | −0.0717446 | ||||||||
\(932\) | −7.42163 | −0.243104 | ||||||||
\(933\) | −12.1927 | −0.399170 | ||||||||
\(934\) | 5.54999 | 0.181601 | ||||||||
\(935\) | 1.92689 | 0.0630159 | ||||||||
\(936\) | −13.2068 | −0.431679 | ||||||||
\(937\) | 44.7518 | 1.46198 | 0.730989 | − | 0.682389i | \(-0.239059\pi\) | ||||
0.730989 | + | 0.682389i | \(0.239059\pi\) | |||||||
\(938\) | 8.71492 | 0.284552 | ||||||||
\(939\) | 9.40968 | 0.307073 | ||||||||
\(940\) | −0.828677 | −0.0270285 | ||||||||
\(941\) | 57.9392 | 1.88876 | 0.944382 | − | 0.328850i | \(-0.106661\pi\) | ||||
0.944382 | + | 0.328850i | \(0.106661\pi\) | |||||||
\(942\) | −12.4212 | −0.404706 | ||||||||
\(943\) | −4.19115 | −0.136483 | ||||||||
\(944\) | 3.21058 | 0.104495 | ||||||||
\(945\) | 5.51669 | 0.179458 | ||||||||
\(946\) | −9.48484 | −0.308379 | ||||||||
\(947\) | −4.25048 | −0.138122 | −0.0690610 | − | 0.997612i | \(-0.522000\pi\) | ||||
−0.0690610 | + | 0.997612i | \(0.522000\pi\) | |||||||
\(948\) | 1.86613 | 0.0606092 | ||||||||
\(949\) | −66.0494 | −2.14405 | ||||||||
\(950\) | −7.29352 | −0.236633 | ||||||||
\(951\) | −15.5002 | −0.502629 | ||||||||
\(952\) | −12.6739 | −0.410762 | ||||||||
\(953\) | −1.61863 | −0.0524327 | −0.0262163 | − | 0.999656i | \(-0.508346\pi\) | ||||
−0.0262163 | + | 0.999656i | \(0.508346\pi\) | |||||||
\(954\) | −15.4771 | −0.501088 | ||||||||
\(955\) | 3.64196 | 0.117851 | ||||||||
\(956\) | 7.94904 | 0.257090 | ||||||||
\(957\) | 1.79359 | 0.0579785 | ||||||||
\(958\) | 7.49287 | 0.242084 | ||||||||
\(959\) | −18.4921 | −0.597142 | ||||||||
\(960\) | −0.342128 | −0.0110421 | ||||||||
\(961\) | 60.8067 | 1.96151 | ||||||||
\(962\) | −40.3072 | −1.29956 | ||||||||
\(963\) | −5.36208 | −0.172791 | ||||||||
\(964\) | −18.9159 | −0.609239 | ||||||||
\(965\) | 0.205082 | 0.00660181 | ||||||||
\(966\) | −1.93277 | −0.0621858 | ||||||||
\(967\) | −37.7757 | −1.21478 | −0.607392 | − | 0.794402i | \(-0.707784\pi\) | ||||
−0.607392 | + | 0.794402i | \(0.707784\pi\) | |||||||
\(968\) | 10.2623 | 0.329843 | ||||||||
\(969\) | 4.47933 | 0.143897 | ||||||||
\(970\) | 6.96811 | 0.223733 | ||||||||
\(971\) | −34.3508 | −1.10237 | −0.551185 | − | 0.834383i | \(-0.685824\pi\) | ||||
−0.551185 | + | 0.834383i | \(0.685824\pi\) | |||||||
\(972\) | −14.5683 | −0.467279 | ||||||||
\(973\) | −9.82150 | −0.314863 | ||||||||
\(974\) | 15.4115 | 0.493816 | ||||||||
\(975\) | −16.2957 | −0.521881 | ||||||||
\(976\) | −6.32871 | −0.202577 | ||||||||
\(977\) | 4.60066 | 0.147188 | 0.0735941 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735941 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(978\) | −9.77685 | −0.312629 | ||||||||
\(979\) | −8.87175 | −0.283542 | ||||||||
\(980\) | 0.730218 | 0.0233260 | ||||||||
\(981\) | 8.56770 | 0.273546 | ||||||||
\(982\) | 17.3428 | 0.553431 | ||||||||
\(983\) | 35.4909 | 1.13198 | 0.565991 | − | 0.824411i | \(-0.308494\pi\) | ||||
0.565991 | + | 0.824411i | \(0.308494\pi\) | |||||||
\(984\) | 2.79137 | 0.0889857 | ||||||||
\(985\) | 9.65124 | 0.307514 | ||||||||
\(986\) | 13.6935 | 0.436089 | ||||||||
\(987\) | 3.11790 | 0.0992438 | ||||||||
\(988\) | 7.95574 | 0.253106 | ||||||||
\(989\) | −11.0431 | −0.351151 | ||||||||
\(990\) | 1.12791 | 0.0358473 | ||||||||
\(991\) | −1.36860 | −0.0434749 | −0.0217375 | − | 0.999764i | \(-0.506920\pi\) | ||||
−0.0217375 | + | 0.999764i | \(0.506920\pi\) | |||||||
\(992\) | −9.58158 | −0.304216 | ||||||||
\(993\) | 8.87489 | 0.281636 | ||||||||
\(994\) | −6.12449 | −0.194257 | ||||||||
\(995\) | −1.31756 | −0.0417695 | ||||||||
\(996\) | 10.8843 | 0.344883 | ||||||||
\(997\) | 3.55884 | 0.112710 | 0.0563548 | − | 0.998411i | \(-0.482052\pi\) | ||||
0.0563548 | + | 0.998411i | \(0.482052\pi\) | |||||||
\(998\) | 24.4498 | 0.773945 | ||||||||
\(999\) | −28.8733 | −0.913511 |
(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 | 6026.2.a.h.1.12 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.12 | ✓ | 24 | 1.1 | even | 1 | trivial |