Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −0.570351 | −0.329293 | −0.164646 | − | 0.986353i | \(-0.552648\pi\) | ||||
−0.164646 | + | 0.986353i | \(0.552648\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.34990 | −0.603694 | −0.301847 | − | 0.953356i | \(-0.597603\pi\) | ||||
−0.301847 | + | 0.953356i | \(0.597603\pi\) | |||||||
\(6\) | −0.570351 | −0.232845 | ||||||||
\(7\) | −5.21632 | −1.97158 | −0.985792 | − | 0.167971i | \(-0.946279\pi\) | ||||
−0.985792 | + | 0.167971i | \(0.946279\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.67470 | −0.891566 | ||||||||
\(10\) | −1.34990 | −0.426876 | ||||||||
\(11\) | 4.89676 | 1.47643 | 0.738215 | − | 0.674566i | \(-0.235669\pi\) | ||||
0.738215 | + | 0.674566i | \(0.235669\pi\) | |||||||
\(12\) | −0.570351 | −0.164646 | ||||||||
\(13\) | −1.50729 | −0.418048 | −0.209024 | − | 0.977910i | \(-0.567029\pi\) | ||||
−0.209024 | + | 0.977910i | \(0.567029\pi\) | |||||||
\(14\) | −5.21632 | −1.39412 | ||||||||
\(15\) | 0.769917 | 0.198792 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.322117 | 0.0781247 | 0.0390624 | − | 0.999237i | \(-0.487563\pi\) | ||||
0.0390624 | + | 0.999237i | \(0.487563\pi\) | |||||||
\(18\) | −2.67470 | −0.630433 | ||||||||
\(19\) | −4.66258 | −1.06967 | −0.534835 | − | 0.844956i | \(-0.679626\pi\) | ||||
−0.534835 | + | 0.844956i | \(0.679626\pi\) | |||||||
\(20\) | −1.34990 | −0.301847 | ||||||||
\(21\) | 2.97514 | 0.649228 | ||||||||
\(22\) | 4.89676 | 1.04399 | ||||||||
\(23\) | −9.15574 | −1.90910 | −0.954551 | − | 0.298046i | \(-0.903665\pi\) | ||||
−0.954551 | + | 0.298046i | \(0.903665\pi\) | |||||||
\(24\) | −0.570351 | −0.116422 | ||||||||
\(25\) | −3.17777 | −0.635554 | ||||||||
\(26\) | −1.50729 | −0.295605 | ||||||||
\(27\) | 3.23657 | 0.622879 | ||||||||
\(28\) | −5.21632 | −0.985792 | ||||||||
\(29\) | 2.96884 | 0.551300 | 0.275650 | − | 0.961258i | \(-0.411107\pi\) | ||||
0.275650 | + | 0.961258i | \(0.411107\pi\) | |||||||
\(30\) | 0.769917 | 0.140567 | ||||||||
\(31\) | 5.76322 | 1.03510 | 0.517552 | − | 0.855651i | \(-0.326843\pi\) | ||||
0.517552 | + | 0.855651i | \(0.326843\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.79288 | −0.486177 | ||||||||
\(34\) | 0.322117 | 0.0552425 | ||||||||
\(35\) | 7.04151 | 1.19023 | ||||||||
\(36\) | −2.67470 | −0.445783 | ||||||||
\(37\) | 8.51683 | 1.40016 | 0.700079 | − | 0.714065i | \(-0.253148\pi\) | ||||
0.700079 | + | 0.714065i | \(0.253148\pi\) | |||||||
\(38\) | −4.66258 | −0.756371 | ||||||||
\(39\) | 0.859688 | 0.137660 | ||||||||
\(40\) | −1.34990 | −0.213438 | ||||||||
\(41\) | 6.87743 | 1.07407 | 0.537037 | − | 0.843559i | \(-0.319544\pi\) | ||||
0.537037 | + | 0.843559i | \(0.319544\pi\) | |||||||
\(42\) | 2.97514 | 0.459073 | ||||||||
\(43\) | −1.22389 | −0.186641 | −0.0933207 | − | 0.995636i | \(-0.529748\pi\) | ||||
−0.0933207 | + | 0.995636i | \(0.529748\pi\) | |||||||
\(44\) | 4.89676 | 0.738215 | ||||||||
\(45\) | 3.61058 | 0.538233 | ||||||||
\(46\) | −9.15574 | −1.34994 | ||||||||
\(47\) | −4.13339 | −0.602917 | −0.301458 | − | 0.953479i | \(-0.597473\pi\) | ||||
−0.301458 | + | 0.953479i | \(0.597473\pi\) | |||||||
\(48\) | −0.570351 | −0.0823231 | ||||||||
\(49\) | 20.2100 | 2.88714 | ||||||||
\(50\) | −3.17777 | −0.449405 | ||||||||
\(51\) | −0.183720 | −0.0257259 | ||||||||
\(52\) | −1.50729 | −0.209024 | ||||||||
\(53\) | 11.4389 | 1.57126 | 0.785628 | − | 0.618699i | \(-0.212340\pi\) | ||||
0.785628 | + | 0.618699i | \(0.212340\pi\) | |||||||
\(54\) | 3.23657 | 0.440442 | ||||||||
\(55\) | −6.61014 | −0.891311 | ||||||||
\(56\) | −5.21632 | −0.697060 | ||||||||
\(57\) | 2.65931 | 0.352234 | ||||||||
\(58\) | 2.96884 | 0.389828 | ||||||||
\(59\) | 11.2413 | 1.46349 | 0.731747 | − | 0.681576i | \(-0.238705\pi\) | ||||
0.731747 | + | 0.681576i | \(0.238705\pi\) | |||||||
\(60\) | 0.769917 | 0.0993959 | ||||||||
\(61\) | −11.6601 | −1.49293 | −0.746463 | − | 0.665427i | \(-0.768250\pi\) | ||||
−0.746463 | + | 0.665427i | \(0.768250\pi\) | |||||||
\(62\) | 5.76322 | 0.731930 | ||||||||
\(63\) | 13.9521 | 1.75780 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.03470 | 0.252373 | ||||||||
\(66\) | −2.79288 | −0.343779 | ||||||||
\(67\) | −8.42595 | −1.02939 | −0.514697 | − | 0.857372i | \(-0.672096\pi\) | ||||
−0.514697 | + | 0.857372i | \(0.672096\pi\) | |||||||
\(68\) | 0.322117 | 0.0390624 | ||||||||
\(69\) | 5.22199 | 0.628653 | ||||||||
\(70\) | 7.04151 | 0.841622 | ||||||||
\(71\) | 6.79327 | 0.806212 | 0.403106 | − | 0.915153i | \(-0.367931\pi\) | ||||
0.403106 | + | 0.915153i | \(0.367931\pi\) | |||||||
\(72\) | −2.67470 | −0.315216 | ||||||||
\(73\) | −11.4400 | −1.33895 | −0.669476 | − | 0.742834i | \(-0.733481\pi\) | ||||
−0.669476 | + | 0.742834i | \(0.733481\pi\) | |||||||
\(74\) | 8.51683 | 0.990062 | ||||||||
\(75\) | 1.81245 | 0.209283 | ||||||||
\(76\) | −4.66258 | −0.534835 | ||||||||
\(77\) | −25.5431 | −2.91091 | ||||||||
\(78\) | 0.859688 | 0.0973404 | ||||||||
\(79\) | −7.18568 | −0.808452 | −0.404226 | − | 0.914659i | \(-0.632459\pi\) | ||||
−0.404226 | + | 0.914659i | \(0.632459\pi\) | |||||||
\(80\) | −1.34990 | −0.150923 | ||||||||
\(81\) | 6.17811 | 0.686457 | ||||||||
\(82\) | 6.87743 | 0.759485 | ||||||||
\(83\) | 0.615951 | 0.0676094 | 0.0338047 | − | 0.999428i | \(-0.489238\pi\) | ||||
0.0338047 | + | 0.999428i | \(0.489238\pi\) | |||||||
\(84\) | 2.97514 | 0.324614 | ||||||||
\(85\) | −0.434825 | −0.0471634 | ||||||||
\(86\) | −1.22389 | −0.131975 | ||||||||
\(87\) | −1.69328 | −0.181539 | ||||||||
\(88\) | 4.89676 | 0.521997 | ||||||||
\(89\) | 17.3622 | 1.84039 | 0.920197 | − | 0.391456i | \(-0.128028\pi\) | ||||
0.920197 | + | 0.391456i | \(0.128028\pi\) | |||||||
\(90\) | 3.61058 | 0.380588 | ||||||||
\(91\) | 7.86253 | 0.824217 | ||||||||
\(92\) | −9.15574 | −0.954551 | ||||||||
\(93\) | −3.28706 | −0.340852 | ||||||||
\(94\) | −4.13339 | −0.426326 | ||||||||
\(95\) | 6.29402 | 0.645753 | ||||||||
\(96\) | −0.570351 | −0.0582112 | ||||||||
\(97\) | 11.3356 | 1.15096 | 0.575479 | − | 0.817817i | \(-0.304816\pi\) | ||||
0.575479 | + | 0.817817i | \(0.304816\pi\) | |||||||
\(98\) | 20.2100 | 2.04152 | ||||||||
\(99\) | −13.0974 | −1.31634 | ||||||||
\(100\) | −3.17777 | −0.317777 | ||||||||
\(101\) | −8.87668 | −0.883263 | −0.441631 | − | 0.897197i | \(-0.645600\pi\) | ||||
−0.441631 | + | 0.897197i | \(0.645600\pi\) | |||||||
\(102\) | −0.183720 | −0.0181910 | ||||||||
\(103\) | 14.9086 | 1.46899 | 0.734496 | − | 0.678613i | \(-0.237419\pi\) | ||||
0.734496 | + | 0.678613i | \(0.237419\pi\) | |||||||
\(104\) | −1.50729 | −0.147802 | ||||||||
\(105\) | −4.01614 | −0.391935 | ||||||||
\(106\) | 11.4389 | 1.11105 | ||||||||
\(107\) | 4.02749 | 0.389352 | 0.194676 | − | 0.980868i | \(-0.437634\pi\) | ||||
0.194676 | + | 0.980868i | \(0.437634\pi\) | |||||||
\(108\) | 3.23657 | 0.311439 | ||||||||
\(109\) | −12.4478 | −1.19228 | −0.596139 | − | 0.802881i | \(-0.703299\pi\) | ||||
−0.596139 | + | 0.802881i | \(0.703299\pi\) | |||||||
\(110\) | −6.61014 | −0.630252 | ||||||||
\(111\) | −4.85759 | −0.461062 | ||||||||
\(112\) | −5.21632 | −0.492896 | ||||||||
\(113\) | −12.5797 | −1.18340 | −0.591701 | − | 0.806157i | \(-0.701543\pi\) | ||||
−0.591701 | + | 0.806157i | \(0.701543\pi\) | |||||||
\(114\) | 2.65931 | 0.249067 | ||||||||
\(115\) | 12.3593 | 1.15251 | ||||||||
\(116\) | 2.96884 | 0.275650 | ||||||||
\(117\) | 4.03156 | 0.372718 | ||||||||
\(118\) | 11.2413 | 1.03485 | ||||||||
\(119\) | −1.68026 | −0.154029 | ||||||||
\(120\) | 0.769917 | 0.0702835 | ||||||||
\(121\) | 12.9783 | 1.17985 | ||||||||
\(122\) | −11.6601 | −1.05566 | ||||||||
\(123\) | −3.92255 | −0.353684 | ||||||||
\(124\) | 5.76322 | 0.517552 | ||||||||
\(125\) | 11.0392 | 0.987374 | ||||||||
\(126\) | 13.9521 | 1.24295 | ||||||||
\(127\) | −17.8995 | −1.58832 | −0.794161 | − | 0.607708i | \(-0.792089\pi\) | ||||
−0.794161 | + | 0.607708i | \(0.792089\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0.698047 | 0.0614596 | ||||||||
\(130\) | 2.03470 | 0.178455 | ||||||||
\(131\) | 13.7807 | 1.20402 | 0.602012 | − | 0.798487i | \(-0.294366\pi\) | ||||
0.602012 | + | 0.798487i | \(0.294366\pi\) | |||||||
\(132\) | −2.79288 | −0.243089 | ||||||||
\(133\) | 24.3215 | 2.10894 | ||||||||
\(134\) | −8.42595 | −0.727892 | ||||||||
\(135\) | −4.36905 | −0.376028 | ||||||||
\(136\) | 0.322117 | 0.0276213 | ||||||||
\(137\) | 19.1060 | 1.63234 | 0.816169 | − | 0.577814i | \(-0.196094\pi\) | ||||
0.816169 | + | 0.577814i | \(0.196094\pi\) | |||||||
\(138\) | 5.22199 | 0.444525 | ||||||||
\(139\) | 8.94678 | 0.758856 | 0.379428 | − | 0.925221i | \(-0.376121\pi\) | ||||
0.379428 | + | 0.925221i | \(0.376121\pi\) | |||||||
\(140\) | 7.04151 | 0.595116 | ||||||||
\(141\) | 2.35748 | 0.198536 | ||||||||
\(142\) | 6.79327 | 0.570078 | ||||||||
\(143\) | −7.38087 | −0.617219 | ||||||||
\(144\) | −2.67470 | −0.222892 | ||||||||
\(145\) | −4.00764 | −0.332816 | ||||||||
\(146\) | −11.4400 | −0.946782 | ||||||||
\(147\) | −11.5268 | −0.950715 | ||||||||
\(148\) | 8.51683 | 0.700079 | ||||||||
\(149\) | 4.04808 | 0.331632 | 0.165816 | − | 0.986157i | \(-0.446974\pi\) | ||||
0.165816 | + | 0.986157i | \(0.446974\pi\) | |||||||
\(150\) | 1.81245 | 0.147986 | ||||||||
\(151\) | 6.54005 | 0.532221 | 0.266111 | − | 0.963942i | \(-0.414261\pi\) | ||||
0.266111 | + | 0.963942i | \(0.414261\pi\) | |||||||
\(152\) | −4.66258 | −0.378186 | ||||||||
\(153\) | −0.861565 | −0.0696534 | ||||||||
\(154\) | −25.5431 | −2.05832 | ||||||||
\(155\) | −7.77977 | −0.624886 | ||||||||
\(156\) | 0.859688 | 0.0688301 | ||||||||
\(157\) | −5.48019 | −0.437367 | −0.218684 | − | 0.975796i | \(-0.570176\pi\) | ||||
−0.218684 | + | 0.975796i | \(0.570176\pi\) | |||||||
\(158\) | −7.18568 | −0.571662 | ||||||||
\(159\) | −6.52420 | −0.517403 | ||||||||
\(160\) | −1.34990 | −0.106719 | ||||||||
\(161\) | 47.7593 | 3.76396 | ||||||||
\(162\) | 6.17811 | 0.485399 | ||||||||
\(163\) | −1.13211 | −0.0886733 | −0.0443367 | − | 0.999017i | \(-0.514117\pi\) | ||||
−0.0443367 | + | 0.999017i | \(0.514117\pi\) | |||||||
\(164\) | 6.87743 | 0.537037 | ||||||||
\(165\) | 3.77010 | 0.293502 | ||||||||
\(166\) | 0.615951 | 0.0478071 | ||||||||
\(167\) | 5.63483 | 0.436036 | 0.218018 | − | 0.975945i | \(-0.430041\pi\) | ||||
0.218018 | + | 0.975945i | \(0.430041\pi\) | |||||||
\(168\) | 2.97514 | 0.229537 | ||||||||
\(169\) | −10.7281 | −0.825236 | ||||||||
\(170\) | −0.434825 | −0.0333496 | ||||||||
\(171\) | 12.4710 | 0.953682 | ||||||||
\(172\) | −1.22389 | −0.0933207 | ||||||||
\(173\) | 8.86807 | 0.674227 | 0.337113 | − | 0.941464i | \(-0.390549\pi\) | ||||
0.337113 | + | 0.941464i | \(0.390549\pi\) | |||||||
\(174\) | −1.69328 | −0.128367 | ||||||||
\(175\) | 16.5763 | 1.25305 | ||||||||
\(176\) | 4.89676 | 0.369107 | ||||||||
\(177\) | −6.41150 | −0.481918 | ||||||||
\(178\) | 17.3622 | 1.30136 | ||||||||
\(179\) | −0.744506 | −0.0556470 | −0.0278235 | − | 0.999613i | \(-0.508858\pi\) | ||||
−0.0278235 | + | 0.999613i | \(0.508858\pi\) | |||||||
\(180\) | 3.61058 | 0.269117 | ||||||||
\(181\) | −9.27992 | −0.689771 | −0.344885 | − | 0.938645i | \(-0.612082\pi\) | ||||
−0.344885 | + | 0.938645i | \(0.612082\pi\) | |||||||
\(182\) | 7.86253 | 0.582810 | ||||||||
\(183\) | 6.65037 | 0.491609 | ||||||||
\(184\) | −9.15574 | −0.674970 | ||||||||
\(185\) | −11.4969 | −0.845267 | ||||||||
\(186\) | −3.28706 | −0.241019 | ||||||||
\(187\) | 1.57733 | 0.115346 | ||||||||
\(188\) | −4.13339 | −0.301458 | ||||||||
\(189\) | −16.8830 | −1.22806 | ||||||||
\(190\) | 6.29402 | 0.456616 | ||||||||
\(191\) | 11.8110 | 0.854613 | 0.427307 | − | 0.904107i | \(-0.359463\pi\) | ||||
0.427307 | + | 0.904107i | \(0.359463\pi\) | |||||||
\(192\) | −0.570351 | −0.0411616 | ||||||||
\(193\) | −1.38758 | −0.0998804 | −0.0499402 | − | 0.998752i | \(-0.515903\pi\) | ||||
−0.0499402 | + | 0.998752i | \(0.515903\pi\) | |||||||
\(194\) | 11.3356 | 0.813850 | ||||||||
\(195\) | −1.16049 | −0.0831046 | ||||||||
\(196\) | 20.2100 | 1.44357 | ||||||||
\(197\) | −10.4728 | −0.746156 | −0.373078 | − | 0.927800i | \(-0.621698\pi\) | ||||
−0.373078 | + | 0.927800i | \(0.621698\pi\) | |||||||
\(198\) | −13.0974 | −0.930790 | ||||||||
\(199\) | 14.8353 | 1.05164 | 0.525822 | − | 0.850594i | \(-0.323758\pi\) | ||||
0.525822 | + | 0.850594i | \(0.323758\pi\) | |||||||
\(200\) | −3.17777 | −0.224702 | ||||||||
\(201\) | 4.80575 | 0.338972 | ||||||||
\(202\) | −8.87668 | −0.624561 | ||||||||
\(203\) | −15.4864 | −1.08693 | ||||||||
\(204\) | −0.183720 | −0.0128629 | ||||||||
\(205\) | −9.28384 | −0.648411 | ||||||||
\(206\) | 14.9086 | 1.03873 | ||||||||
\(207\) | 24.4888 | 1.70209 | ||||||||
\(208\) | −1.50729 | −0.104512 | ||||||||
\(209\) | −22.8316 | −1.57929 | ||||||||
\(210\) | −4.01614 | −0.277140 | ||||||||
\(211\) | 26.9035 | 1.85211 | 0.926057 | − | 0.377384i | \(-0.123176\pi\) | ||||
0.926057 | + | 0.377384i | \(0.123176\pi\) | |||||||
\(212\) | 11.4389 | 0.785628 | ||||||||
\(213\) | −3.87455 | −0.265480 | ||||||||
\(214\) | 4.02749 | 0.275314 | ||||||||
\(215\) | 1.65213 | 0.112674 | ||||||||
\(216\) | 3.23657 | 0.220221 | ||||||||
\(217\) | −30.0628 | −2.04080 | ||||||||
\(218\) | −12.4478 | −0.843068 | ||||||||
\(219\) | 6.52482 | 0.440907 | ||||||||
\(220\) | −6.61014 | −0.445656 | ||||||||
\(221\) | −0.485525 | −0.0326599 | ||||||||
\(222\) | −4.85759 | −0.326020 | ||||||||
\(223\) | 5.37965 | 0.360248 | 0.180124 | − | 0.983644i | \(-0.442350\pi\) | ||||
0.180124 | + | 0.983644i | \(0.442350\pi\) | |||||||
\(224\) | −5.21632 | −0.348530 | ||||||||
\(225\) | 8.49958 | 0.566639 | ||||||||
\(226\) | −12.5797 | −0.836792 | ||||||||
\(227\) | 17.7145 | 1.17576 | 0.587878 | − | 0.808950i | \(-0.299964\pi\) | ||||
0.587878 | + | 0.808950i | \(0.299964\pi\) | |||||||
\(228\) | 2.65931 | 0.176117 | ||||||||
\(229\) | 15.0714 | 0.995947 | 0.497974 | − | 0.867192i | \(-0.334078\pi\) | ||||
0.497974 | + | 0.867192i | \(0.334078\pi\) | |||||||
\(230\) | 12.3593 | 0.814950 | ||||||||
\(231\) | 14.5685 | 0.958539 | ||||||||
\(232\) | 2.96884 | 0.194914 | ||||||||
\(233\) | 2.85531 | 0.187057 | 0.0935287 | − | 0.995617i | \(-0.470185\pi\) | ||||
0.0935287 | + | 0.995617i | \(0.470185\pi\) | |||||||
\(234\) | 4.03156 | 0.263551 | ||||||||
\(235\) | 5.57966 | 0.363977 | ||||||||
\(236\) | 11.2413 | 0.731747 | ||||||||
\(237\) | 4.09836 | 0.266217 | ||||||||
\(238\) | −1.68026 | −0.108915 | ||||||||
\(239\) | 1.54106 | 0.0996831 | 0.0498415 | − | 0.998757i | \(-0.484128\pi\) | ||||
0.0498415 | + | 0.998757i | \(0.484128\pi\) | |||||||
\(240\) | 0.769917 | 0.0496979 | ||||||||
\(241\) | 2.05203 | 0.132183 | 0.0660914 | − | 0.997814i | \(-0.478947\pi\) | ||||
0.0660914 | + | 0.997814i | \(0.478947\pi\) | |||||||
\(242\) | 12.9783 | 0.834277 | ||||||||
\(243\) | −13.2334 | −0.848924 | ||||||||
\(244\) | −11.6601 | −0.746463 | ||||||||
\(245\) | −27.2815 | −1.74295 | ||||||||
\(246\) | −3.92255 | −0.250093 | ||||||||
\(247\) | 7.02789 | 0.447174 | ||||||||
\(248\) | 5.76322 | 0.365965 | ||||||||
\(249\) | −0.351308 | −0.0222633 | ||||||||
\(250\) | 11.0392 | 0.698179 | ||||||||
\(251\) | −21.3125 | −1.34523 | −0.672616 | − | 0.739992i | \(-0.734829\pi\) | ||||
−0.672616 | + | 0.739992i | \(0.734829\pi\) | |||||||
\(252\) | 13.9521 | 0.878899 | ||||||||
\(253\) | −44.8335 | −2.81866 | ||||||||
\(254\) | −17.8995 | −1.12311 | ||||||||
\(255\) | 0.248003 | 0.0155306 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.74967 | 0.109142 | 0.0545708 | − | 0.998510i | \(-0.482621\pi\) | ||||
0.0545708 | + | 0.998510i | \(0.482621\pi\) | |||||||
\(258\) | 0.698047 | 0.0434585 | ||||||||
\(259\) | −44.4265 | −2.76053 | ||||||||
\(260\) | 2.03470 | 0.126187 | ||||||||
\(261\) | −7.94075 | −0.491520 | ||||||||
\(262\) | 13.7807 | 0.851374 | ||||||||
\(263\) | −12.0852 | −0.745204 | −0.372602 | − | 0.927991i | \(-0.621534\pi\) | ||||
−0.372602 | + | 0.927991i | \(0.621534\pi\) | |||||||
\(264\) | −2.79288 | −0.171890 | ||||||||
\(265\) | −15.4414 | −0.948557 | ||||||||
\(266\) | 24.3215 | 1.49125 | ||||||||
\(267\) | −9.90258 | −0.606028 | ||||||||
\(268\) | −8.42595 | −0.514697 | ||||||||
\(269\) | 16.6643 | 1.01604 | 0.508020 | − | 0.861345i | \(-0.330377\pi\) | ||||
0.508020 | + | 0.861345i | \(0.330377\pi\) | |||||||
\(270\) | −4.36905 | −0.265892 | ||||||||
\(271\) | −14.5424 | −0.883387 | −0.441694 | − | 0.897166i | \(-0.645622\pi\) | ||||
−0.441694 | + | 0.897166i | \(0.645622\pi\) | |||||||
\(272\) | 0.322117 | 0.0195312 | ||||||||
\(273\) | −4.48441 | −0.271409 | ||||||||
\(274\) | 19.1060 | 1.15424 | ||||||||
\(275\) | −15.5608 | −0.938351 | ||||||||
\(276\) | 5.22199 | 0.314327 | ||||||||
\(277\) | −4.14787 | −0.249221 | −0.124611 | − | 0.992206i | \(-0.539768\pi\) | ||||
−0.124611 | + | 0.992206i | \(0.539768\pi\) | |||||||
\(278\) | 8.94678 | 0.536592 | ||||||||
\(279\) | −15.4149 | −0.922865 | ||||||||
\(280\) | 7.04151 | 0.420811 | ||||||||
\(281\) | 17.6806 | 1.05474 | 0.527368 | − | 0.849637i | \(-0.323179\pi\) | ||||
0.527368 | + | 0.849637i | \(0.323179\pi\) | |||||||
\(282\) | 2.35748 | 0.140386 | ||||||||
\(283\) | −20.8410 | −1.23887 | −0.619436 | − | 0.785048i | \(-0.712638\pi\) | ||||
−0.619436 | + | 0.785048i | \(0.712638\pi\) | |||||||
\(284\) | 6.79327 | 0.403106 | ||||||||
\(285\) | −3.58980 | −0.212642 | ||||||||
\(286\) | −7.38087 | −0.436440 | ||||||||
\(287\) | −35.8749 | −2.11763 | ||||||||
\(288\) | −2.67470 | −0.157608 | ||||||||
\(289\) | −16.8962 | −0.993897 | ||||||||
\(290\) | −4.00764 | −0.235336 | ||||||||
\(291\) | −6.46528 | −0.379002 | ||||||||
\(292\) | −11.4400 | −0.669476 | ||||||||
\(293\) | 11.4157 | 0.666911 | 0.333455 | − | 0.942766i | \(-0.391785\pi\) | ||||
0.333455 | + | 0.942766i | \(0.391785\pi\) | |||||||
\(294\) | −11.5268 | −0.672257 | ||||||||
\(295\) | −15.1747 | −0.883503 | ||||||||
\(296\) | 8.51683 | 0.495031 | ||||||||
\(297\) | 15.8487 | 0.919637 | ||||||||
\(298\) | 4.04808 | 0.234499 | ||||||||
\(299\) | 13.8004 | 0.798097 | ||||||||
\(300\) | 1.81245 | 0.104642 | ||||||||
\(301\) | 6.38420 | 0.367979 | ||||||||
\(302\) | 6.54005 | 0.376337 | ||||||||
\(303\) | 5.06283 | 0.290852 | ||||||||
\(304\) | −4.66258 | −0.267418 | ||||||||
\(305\) | 15.7400 | 0.901270 | ||||||||
\(306\) | −0.861565 | −0.0492524 | ||||||||
\(307\) | −1.95560 | −0.111612 | −0.0558059 | − | 0.998442i | \(-0.517773\pi\) | ||||
−0.0558059 | + | 0.998442i | \(0.517773\pi\) | |||||||
\(308\) | −25.5431 | −1.45545 | ||||||||
\(309\) | −8.50316 | −0.483728 | ||||||||
\(310\) | −7.77977 | −0.441861 | ||||||||
\(311\) | 20.7951 | 1.17918 | 0.589591 | − | 0.807702i | \(-0.299289\pi\) | ||||
0.589591 | + | 0.807702i | \(0.299289\pi\) | |||||||
\(312\) | 0.859688 | 0.0486702 | ||||||||
\(313\) | 9.78998 | 0.553363 | 0.276681 | − | 0.960962i | \(-0.410765\pi\) | ||||
0.276681 | + | 0.960962i | \(0.410765\pi\) | |||||||
\(314\) | −5.48019 | −0.309265 | ||||||||
\(315\) | −18.8339 | −1.06117 | ||||||||
\(316\) | −7.18568 | −0.404226 | ||||||||
\(317\) | 21.4136 | 1.20271 | 0.601355 | − | 0.798982i | \(-0.294628\pi\) | ||||
0.601355 | + | 0.798982i | \(0.294628\pi\) | |||||||
\(318\) | −6.52420 | −0.365859 | ||||||||
\(319\) | 14.5377 | 0.813955 | ||||||||
\(320\) | −1.34990 | −0.0754617 | ||||||||
\(321\) | −2.29709 | −0.128211 | ||||||||
\(322\) | 47.7593 | 2.66152 | ||||||||
\(323\) | −1.50190 | −0.0835677 | ||||||||
\(324\) | 6.17811 | 0.343229 | ||||||||
\(325\) | 4.78984 | 0.265692 | ||||||||
\(326\) | −1.13211 | −0.0627015 | ||||||||
\(327\) | 7.09959 | 0.392608 | ||||||||
\(328\) | 6.87743 | 0.379742 | ||||||||
\(329\) | 21.5611 | 1.18870 | ||||||||
\(330\) | 3.77010 | 0.207537 | ||||||||
\(331\) | 20.0123 | 1.09997 | 0.549986 | − | 0.835174i | \(-0.314633\pi\) | ||||
0.549986 | + | 0.835174i | \(0.314633\pi\) | |||||||
\(332\) | 0.615951 | 0.0338047 | ||||||||
\(333\) | −22.7800 | −1.24833 | ||||||||
\(334\) | 5.63483 | 0.308324 | ||||||||
\(335\) | 11.3742 | 0.621439 | ||||||||
\(336\) | 2.97514 | 0.162307 | ||||||||
\(337\) | 12.9771 | 0.706906 | 0.353453 | − | 0.935452i | \(-0.385007\pi\) | ||||
0.353453 | + | 0.935452i | \(0.385007\pi\) | |||||||
\(338\) | −10.7281 | −0.583530 | ||||||||
\(339\) | 7.17487 | 0.389685 | ||||||||
\(340\) | −0.434825 | −0.0235817 | ||||||||
\(341\) | 28.2211 | 1.52826 | ||||||||
\(342\) | 12.4710 | 0.674355 | ||||||||
\(343\) | −68.9076 | −3.72066 | ||||||||
\(344\) | −1.22389 | −0.0659877 | ||||||||
\(345\) | −7.04916 | −0.379514 | ||||||||
\(346\) | 8.86807 | 0.476750 | ||||||||
\(347\) | −31.8177 | −1.70806 | −0.854031 | − | 0.520221i | \(-0.825849\pi\) | ||||
−0.854031 | + | 0.520221i | \(0.825849\pi\) | |||||||
\(348\) | −1.69328 | −0.0907694 | ||||||||
\(349\) | −29.6834 | −1.58892 | −0.794459 | − | 0.607318i | \(-0.792245\pi\) | ||||
−0.794459 | + | 0.607318i | \(0.792245\pi\) | |||||||
\(350\) | 16.5763 | 0.886039 | ||||||||
\(351\) | −4.87847 | −0.260393 | ||||||||
\(352\) | 4.89676 | 0.260998 | ||||||||
\(353\) | 21.3908 | 1.13852 | 0.569258 | − | 0.822159i | \(-0.307231\pi\) | ||||
0.569258 | + | 0.822159i | \(0.307231\pi\) | |||||||
\(354\) | −6.41150 | −0.340767 | ||||||||
\(355\) | −9.17023 | −0.486705 | ||||||||
\(356\) | 17.3622 | 0.920197 | ||||||||
\(357\) | 0.958341 | 0.0507208 | ||||||||
\(358\) | −0.744506 | −0.0393483 | ||||||||
\(359\) | −33.2527 | −1.75501 | −0.877504 | − | 0.479568i | \(-0.840793\pi\) | ||||
−0.877504 | + | 0.479568i | \(0.840793\pi\) | |||||||
\(360\) | 3.61058 | 0.190294 | ||||||||
\(361\) | 2.73969 | 0.144194 | ||||||||
\(362\) | −9.27992 | −0.487742 | ||||||||
\(363\) | −7.40219 | −0.388514 | ||||||||
\(364\) | 7.86253 | 0.412109 | ||||||||
\(365\) | 15.4429 | 0.808317 | ||||||||
\(366\) | 6.65037 | 0.347620 | ||||||||
\(367\) | −9.57219 | −0.499664 | −0.249832 | − | 0.968289i | \(-0.580375\pi\) | ||||
−0.249832 | + | 0.968289i | \(0.580375\pi\) | |||||||
\(368\) | −9.15574 | −0.477276 | ||||||||
\(369\) | −18.3950 | −0.957608 | ||||||||
\(370\) | −11.4969 | −0.597694 | ||||||||
\(371\) | −59.6691 | −3.09786 | ||||||||
\(372\) | −3.28706 | −0.170426 | ||||||||
\(373\) | −21.7305 | −1.12516 | −0.562582 | − | 0.826742i | \(-0.690192\pi\) | ||||
−0.562582 | + | 0.826742i | \(0.690192\pi\) | |||||||
\(374\) | 1.57733 | 0.0815617 | ||||||||
\(375\) | −6.29621 | −0.325135 | ||||||||
\(376\) | −4.13339 | −0.213163 | ||||||||
\(377\) | −4.47492 | −0.230470 | ||||||||
\(378\) | −16.8830 | −0.868368 | ||||||||
\(379\) | −31.9976 | −1.64361 | −0.821803 | − | 0.569771i | \(-0.807032\pi\) | ||||
−0.821803 | + | 0.569771i | \(0.807032\pi\) | |||||||
\(380\) | 6.29402 | 0.322877 | ||||||||
\(381\) | 10.2090 | 0.523022 | ||||||||
\(382\) | 11.8110 | 0.604303 | ||||||||
\(383\) | 16.0904 | 0.822183 | 0.411091 | − | 0.911594i | \(-0.365148\pi\) | ||||
0.411091 | + | 0.911594i | \(0.365148\pi\) | |||||||
\(384\) | −0.570351 | −0.0291056 | ||||||||
\(385\) | 34.4806 | 1.75730 | ||||||||
\(386\) | −1.38758 | −0.0706261 | ||||||||
\(387\) | 3.27354 | 0.166403 | ||||||||
\(388\) | 11.3356 | 0.575479 | ||||||||
\(389\) | 12.6861 | 0.643213 | 0.321607 | − | 0.946873i | \(-0.395777\pi\) | ||||
0.321607 | + | 0.946873i | \(0.395777\pi\) | |||||||
\(390\) | −1.16049 | −0.0587638 | ||||||||
\(391\) | −2.94921 | −0.149148 | ||||||||
\(392\) | 20.2100 | 1.02076 | ||||||||
\(393\) | −7.85983 | −0.396476 | ||||||||
\(394\) | −10.4728 | −0.527612 | ||||||||
\(395\) | 9.69995 | 0.488057 | ||||||||
\(396\) | −13.0974 | −0.658168 | ||||||||
\(397\) | −0.346410 | −0.0173858 | −0.00869291 | − | 0.999962i | \(-0.502767\pi\) | ||||
−0.00869291 | + | 0.999962i | \(0.502767\pi\) | |||||||
\(398\) | 14.8353 | 0.743625 | ||||||||
\(399\) | −13.8718 | −0.694460 | ||||||||
\(400\) | −3.17777 | −0.158888 | ||||||||
\(401\) | 23.8455 | 1.19079 | 0.595394 | − | 0.803434i | \(-0.296996\pi\) | ||||
0.595394 | + | 0.803434i | \(0.296996\pi\) | |||||||
\(402\) | 4.80575 | 0.239689 | ||||||||
\(403\) | −8.68687 | −0.432724 | ||||||||
\(404\) | −8.87668 | −0.441631 | ||||||||
\(405\) | −8.33984 | −0.414410 | ||||||||
\(406\) | −15.4864 | −0.768578 | ||||||||
\(407\) | 41.7049 | 2.06724 | ||||||||
\(408\) | −0.183720 | −0.00909548 | ||||||||
\(409\) | −1.11996 | −0.0553783 | −0.0276891 | − | 0.999617i | \(-0.508815\pi\) | ||||
−0.0276891 | + | 0.999617i | \(0.508815\pi\) | |||||||
\(410\) | −9.28384 | −0.458496 | ||||||||
\(411\) | −10.8971 | −0.537516 | ||||||||
\(412\) | 14.9086 | 0.734496 | ||||||||
\(413\) | −58.6383 | −2.88540 | ||||||||
\(414\) | 24.4888 | 1.20356 | ||||||||
\(415\) | −0.831472 | −0.0408154 | ||||||||
\(416\) | −1.50729 | −0.0739012 | ||||||||
\(417\) | −5.10281 | −0.249885 | ||||||||
\(418\) | −22.8316 | −1.11673 | ||||||||
\(419\) | −37.9806 | −1.85547 | −0.927737 | − | 0.373235i | \(-0.878249\pi\) | ||||
−0.927737 | + | 0.373235i | \(0.878249\pi\) | |||||||
\(420\) | −4.01614 | −0.195967 | ||||||||
\(421\) | −3.97835 | −0.193893 | −0.0969464 | − | 0.995290i | \(-0.530908\pi\) | ||||
−0.0969464 | + | 0.995290i | \(0.530908\pi\) | |||||||
\(422\) | 26.9035 | 1.30964 | ||||||||
\(423\) | 11.0556 | 0.537540 | ||||||||
\(424\) | 11.4389 | 0.555523 | ||||||||
\(425\) | −1.02361 | −0.0496525 | ||||||||
\(426\) | −3.87455 | −0.187722 | ||||||||
\(427\) | 60.8230 | 2.94343 | ||||||||
\(428\) | 4.02749 | 0.194676 | ||||||||
\(429\) | 4.20969 | 0.203246 | ||||||||
\(430\) | 1.65213 | 0.0796727 | ||||||||
\(431\) | 20.1325 | 0.969748 | 0.484874 | − | 0.874584i | \(-0.338865\pi\) | ||||
0.484874 | + | 0.874584i | \(0.338865\pi\) | |||||||
\(432\) | 3.23657 | 0.155720 | ||||||||
\(433\) | 36.4879 | 1.75350 | 0.876748 | − | 0.480949i | \(-0.159708\pi\) | ||||
0.876748 | + | 0.480949i | \(0.159708\pi\) | |||||||
\(434\) | −30.0628 | −1.44306 | ||||||||
\(435\) | 2.28576 | 0.109594 | ||||||||
\(436\) | −12.4478 | −0.596139 | ||||||||
\(437\) | 42.6894 | 2.04211 | ||||||||
\(438\) | 6.52482 | 0.311768 | ||||||||
\(439\) | −22.6093 | −1.07908 | −0.539541 | − | 0.841959i | \(-0.681402\pi\) | ||||
−0.539541 | + | 0.841959i | \(0.681402\pi\) | |||||||
\(440\) | −6.61014 | −0.315126 | ||||||||
\(441\) | −54.0557 | −2.57408 | ||||||||
\(442\) | −0.485525 | −0.0230940 | ||||||||
\(443\) | −20.8098 | −0.988705 | −0.494352 | − | 0.869262i | \(-0.664595\pi\) | ||||
−0.494352 | + | 0.869262i | \(0.664595\pi\) | |||||||
\(444\) | −4.85759 | −0.230531 | ||||||||
\(445\) | −23.4373 | −1.11103 | ||||||||
\(446\) | 5.37965 | 0.254734 | ||||||||
\(447\) | −2.30883 | −0.109204 | ||||||||
\(448\) | −5.21632 | −0.246448 | ||||||||
\(449\) | −38.4084 | −1.81260 | −0.906302 | − | 0.422630i | \(-0.861107\pi\) | ||||
−0.906302 | + | 0.422630i | \(0.861107\pi\) | |||||||
\(450\) | 8.49958 | 0.400674 | ||||||||
\(451\) | 33.6771 | 1.58579 | ||||||||
\(452\) | −12.5797 | −0.591701 | ||||||||
\(453\) | −3.73012 | −0.175257 | ||||||||
\(454\) | 17.7145 | 0.831385 | ||||||||
\(455\) | −10.6136 | −0.497575 | ||||||||
\(456\) | 2.65931 | 0.124534 | ||||||||
\(457\) | 22.2360 | 1.04016 | 0.520079 | − | 0.854118i | \(-0.325903\pi\) | ||||
0.520079 | + | 0.854118i | \(0.325903\pi\) | |||||||
\(458\) | 15.0714 | 0.704241 | ||||||||
\(459\) | 1.04255 | 0.0486622 | ||||||||
\(460\) | 12.3593 | 0.576257 | ||||||||
\(461\) | 8.26591 | 0.384982 | 0.192491 | − | 0.981299i | \(-0.438343\pi\) | ||||
0.192491 | + | 0.981299i | \(0.438343\pi\) | |||||||
\(462\) | 14.5685 | 0.677790 | ||||||||
\(463\) | −27.2271 | −1.26535 | −0.632675 | − | 0.774417i | \(-0.718043\pi\) | ||||
−0.632675 | + | 0.774417i | \(0.718043\pi\) | |||||||
\(464\) | 2.96884 | 0.137825 | ||||||||
\(465\) | 4.43720 | 0.205770 | ||||||||
\(466\) | 2.85531 | 0.132270 | ||||||||
\(467\) | −5.58987 | −0.258668 | −0.129334 | − | 0.991601i | \(-0.541284\pi\) | ||||
−0.129334 | + | 0.991601i | \(0.541284\pi\) | |||||||
\(468\) | 4.03156 | 0.186359 | ||||||||
\(469\) | 43.9525 | 2.02954 | ||||||||
\(470\) | 5.57966 | 0.257371 | ||||||||
\(471\) | 3.12564 | 0.144022 | ||||||||
\(472\) | 11.2413 | 0.517424 | ||||||||
\(473\) | −5.99310 | −0.275563 | ||||||||
\(474\) | 4.09836 | 0.188244 | ||||||||
\(475\) | 14.8166 | 0.679833 | ||||||||
\(476\) | −1.68026 | −0.0770147 | ||||||||
\(477\) | −30.5957 | −1.40088 | ||||||||
\(478\) | 1.54106 | 0.0704866 | ||||||||
\(479\) | 2.67407 | 0.122182 | 0.0610908 | − | 0.998132i | \(-0.480542\pi\) | ||||
0.0610908 | + | 0.998132i | \(0.480542\pi\) | |||||||
\(480\) | 0.769917 | 0.0351418 | ||||||||
\(481\) | −12.8374 | −0.585334 | ||||||||
\(482\) | 2.05203 | 0.0934673 | ||||||||
\(483\) | −27.2396 | −1.23944 | ||||||||
\(484\) | 12.9783 | 0.589923 | ||||||||
\(485\) | −15.3019 | −0.694826 | ||||||||
\(486\) | −13.2334 | −0.600280 | ||||||||
\(487\) | 40.4979 | 1.83513 | 0.917567 | − | 0.397581i | \(-0.130150\pi\) | ||||
0.917567 | + | 0.397581i | \(0.130150\pi\) | |||||||
\(488\) | −11.6601 | −0.527829 | ||||||||
\(489\) | 0.645698 | 0.0291995 | ||||||||
\(490\) | −27.2815 | −1.23245 | ||||||||
\(491\) | 18.4772 | 0.833865 | 0.416932 | − | 0.908938i | \(-0.363105\pi\) | ||||
0.416932 | + | 0.908938i | \(0.363105\pi\) | |||||||
\(492\) | −3.92255 | −0.176842 | ||||||||
\(493\) | 0.956312 | 0.0430701 | ||||||||
\(494\) | 7.02789 | 0.316200 | ||||||||
\(495\) | 17.6801 | 0.794663 | ||||||||
\(496\) | 5.76322 | 0.258776 | ||||||||
\(497\) | −35.4359 | −1.58952 | ||||||||
\(498\) | −0.351308 | −0.0157425 | ||||||||
\(499\) | −29.2974 | −1.31153 | −0.655766 | − | 0.754964i | \(-0.727654\pi\) | ||||
−0.655766 | + | 0.754964i | \(0.727654\pi\) | |||||||
\(500\) | 11.0392 | 0.493687 | ||||||||
\(501\) | −3.21383 | −0.143583 | ||||||||
\(502\) | −21.3125 | −0.951222 | ||||||||
\(503\) | −0.315857 | −0.0140834 | −0.00704169 | − | 0.999975i | \(-0.502241\pi\) | ||||
−0.00704169 | + | 0.999975i | \(0.502241\pi\) | |||||||
\(504\) | 13.9521 | 0.621475 | ||||||||
\(505\) | 11.9826 | 0.533220 | ||||||||
\(506\) | −44.8335 | −1.99309 | ||||||||
\(507\) | 6.11877 | 0.271744 | ||||||||
\(508\) | −17.8995 | −0.794161 | ||||||||
\(509\) | 42.7339 | 1.89415 | 0.947074 | − | 0.321016i | \(-0.104024\pi\) | ||||
0.947074 | + | 0.321016i | \(0.104024\pi\) | |||||||
\(510\) | 0.248003 | 0.0109818 | ||||||||
\(511\) | 59.6747 | 2.63986 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −15.0908 | −0.666275 | ||||||||
\(514\) | 1.74967 | 0.0771748 | ||||||||
\(515\) | −20.1252 | −0.886821 | ||||||||
\(516\) | 0.698047 | 0.0307298 | ||||||||
\(517\) | −20.2402 | −0.890164 | ||||||||
\(518\) | −44.4265 | −1.95199 | ||||||||
\(519\) | −5.05792 | −0.222018 | ||||||||
\(520\) | 2.03470 | 0.0892274 | ||||||||
\(521\) | 7.72520 | 0.338447 | 0.169224 | − | 0.985578i | \(-0.445874\pi\) | ||||
0.169224 | + | 0.985578i | \(0.445874\pi\) | |||||||
\(522\) | −7.94075 | −0.347557 | ||||||||
\(523\) | −4.49738 | −0.196657 | −0.0983283 | − | 0.995154i | \(-0.531350\pi\) | ||||
−0.0983283 | + | 0.995154i | \(0.531350\pi\) | |||||||
\(524\) | 13.7807 | 0.602012 | ||||||||
\(525\) | −9.45430 | −0.412619 | ||||||||
\(526\) | −12.0852 | −0.526939 | ||||||||
\(527\) | 1.85643 | 0.0808673 | ||||||||
\(528\) | −2.79288 | −0.121544 | ||||||||
\(529\) | 60.8275 | 2.64467 | ||||||||
\(530\) | −15.4414 | −0.670731 | ||||||||
\(531\) | −30.0671 | −1.30480 | ||||||||
\(532\) | 24.3215 | 1.05447 | ||||||||
\(533\) | −10.3663 | −0.449015 | ||||||||
\(534\) | −9.90258 | −0.428526 | ||||||||
\(535\) | −5.43671 | −0.235050 | ||||||||
\(536\) | −8.42595 | −0.363946 | ||||||||
\(537\) | 0.424630 | 0.0183241 | ||||||||
\(538\) | 16.6643 | 0.718449 | ||||||||
\(539\) | 98.9636 | 4.26267 | ||||||||
\(540\) | −4.36905 | −0.188014 | ||||||||
\(541\) | −23.9482 | −1.02962 | −0.514808 | − | 0.857306i | \(-0.672137\pi\) | ||||
−0.514808 | + | 0.857306i | \(0.672137\pi\) | |||||||
\(542\) | −14.5424 | −0.624649 | ||||||||
\(543\) | 5.29281 | 0.227136 | ||||||||
\(544\) | 0.322117 | 0.0138106 | ||||||||
\(545\) | 16.8032 | 0.719771 | ||||||||
\(546\) | −4.48441 | −0.191915 | ||||||||
\(547\) | −28.8409 | −1.23315 | −0.616573 | − | 0.787298i | \(-0.711480\pi\) | ||||
−0.616573 | + | 0.787298i | \(0.711480\pi\) | |||||||
\(548\) | 19.1060 | 0.816169 | ||||||||
\(549\) | 31.1873 | 1.33104 | ||||||||
\(550\) | −15.5608 | −0.663514 | ||||||||
\(551\) | −13.8425 | −0.589709 | ||||||||
\(552\) | 5.22199 | 0.222262 | ||||||||
\(553\) | 37.4828 | 1.59393 | ||||||||
\(554\) | −4.14787 | −0.176226 | ||||||||
\(555\) | 6.55726 | 0.278340 | ||||||||
\(556\) | 8.94678 | 0.379428 | ||||||||
\(557\) | −29.5672 | −1.25280 | −0.626402 | − | 0.779500i | \(-0.715473\pi\) | ||||
−0.626402 | + | 0.779500i | \(0.715473\pi\) | |||||||
\(558\) | −15.4149 | −0.652564 | ||||||||
\(559\) | 1.84476 | 0.0780251 | ||||||||
\(560\) | 7.04151 | 0.297558 | ||||||||
\(561\) | −0.899632 | −0.0379825 | ||||||||
\(562\) | 17.6806 | 0.745811 | ||||||||
\(563\) | −25.6045 | −1.07910 | −0.539551 | − | 0.841953i | \(-0.681406\pi\) | ||||
−0.539551 | + | 0.841953i | \(0.681406\pi\) | |||||||
\(564\) | 2.35748 | 0.0992679 | ||||||||
\(565\) | 16.9814 | 0.714412 | ||||||||
\(566\) | −20.8410 | −0.876014 | ||||||||
\(567\) | −32.2270 | −1.35341 | ||||||||
\(568\) | 6.79327 | 0.285039 | ||||||||
\(569\) | 29.7372 | 1.24665 | 0.623325 | − | 0.781963i | \(-0.285782\pi\) | ||||
0.623325 | + | 0.781963i | \(0.285782\pi\) | |||||||
\(570\) | −3.58980 | −0.150360 | ||||||||
\(571\) | 28.3577 | 1.18673 | 0.593367 | − | 0.804932i | \(-0.297798\pi\) | ||||
0.593367 | + | 0.804932i | \(0.297798\pi\) | |||||||
\(572\) | −7.38087 | −0.308610 | ||||||||
\(573\) | −6.73641 | −0.281418 | ||||||||
\(574\) | −35.8749 | −1.49739 | ||||||||
\(575\) | 29.0948 | 1.21334 | ||||||||
\(576\) | −2.67470 | −0.111446 | ||||||||
\(577\) | 37.8697 | 1.57653 | 0.788267 | − | 0.615333i | \(-0.210978\pi\) | ||||
0.788267 | + | 0.615333i | \(0.210978\pi\) | |||||||
\(578\) | −16.8962 | −0.702791 | ||||||||
\(579\) | 0.791410 | 0.0328899 | ||||||||
\(580\) | −4.00764 | −0.166408 | ||||||||
\(581\) | −3.21300 | −0.133298 | ||||||||
\(582\) | −6.46528 | −0.267995 | ||||||||
\(583\) | 56.0137 | 2.31985 | ||||||||
\(584\) | −11.4400 | −0.473391 | ||||||||
\(585\) | −5.44220 | −0.225007 | ||||||||
\(586\) | 11.4157 | 0.471577 | ||||||||
\(587\) | −15.5658 | −0.642470 | −0.321235 | − | 0.947000i | \(-0.604098\pi\) | ||||
−0.321235 | + | 0.947000i | \(0.604098\pi\) | |||||||
\(588\) | −11.5268 | −0.475357 | ||||||||
\(589\) | −26.8715 | −1.10722 | ||||||||
\(590\) | −15.1747 | −0.624731 | ||||||||
\(591\) | 5.97318 | 0.245704 | ||||||||
\(592\) | 8.51683 | 0.350040 | ||||||||
\(593\) | 33.2364 | 1.36486 | 0.682428 | − | 0.730953i | \(-0.260924\pi\) | ||||
0.682428 | + | 0.730953i | \(0.260924\pi\) | |||||||
\(594\) | 15.8487 | 0.650281 | ||||||||
\(595\) | 2.26819 | 0.0929866 | ||||||||
\(596\) | 4.04808 | 0.165816 | ||||||||
\(597\) | −8.46132 | −0.346299 | ||||||||
\(598\) | 13.8004 | 0.564340 | ||||||||
\(599\) | −34.2324 | −1.39870 | −0.699349 | − | 0.714781i | \(-0.746527\pi\) | ||||
−0.699349 | + | 0.714781i | \(0.746527\pi\) | |||||||
\(600\) | 1.81245 | 0.0739928 | ||||||||
\(601\) | −0.459329 | −0.0187364 | −0.00936821 | − | 0.999956i | \(-0.502982\pi\) | ||||
−0.00936821 | + | 0.999956i | \(0.502982\pi\) | |||||||
\(602\) | 6.38420 | 0.260201 | ||||||||
\(603\) | 22.5369 | 0.917773 | ||||||||
\(604\) | 6.54005 | 0.266111 | ||||||||
\(605\) | −17.5194 | −0.712265 | ||||||||
\(606\) | 5.06283 | 0.205663 | ||||||||
\(607\) | −39.7664 | −1.61407 | −0.807034 | − | 0.590506i | \(-0.798928\pi\) | ||||
−0.807034 | + | 0.590506i | \(0.798928\pi\) | |||||||
\(608\) | −4.66258 | −0.189093 | ||||||||
\(609\) | 8.83270 | 0.357919 | ||||||||
\(610\) | 15.7400 | 0.637294 | ||||||||
\(611\) | 6.23023 | 0.252048 | ||||||||
\(612\) | −0.861565 | −0.0348267 | ||||||||
\(613\) | −24.6191 | −0.994358 | −0.497179 | − | 0.867648i | \(-0.665631\pi\) | ||||
−0.497179 | + | 0.867648i | \(0.665631\pi\) | |||||||
\(614\) | −1.95560 | −0.0789215 | ||||||||
\(615\) | 5.29505 | 0.213517 | ||||||||
\(616\) | −25.5431 | −1.02916 | ||||||||
\(617\) | 34.4311 | 1.38614 | 0.693071 | − | 0.720869i | \(-0.256257\pi\) | ||||
0.693071 | + | 0.720869i | \(0.256257\pi\) | |||||||
\(618\) | −8.50316 | −0.342047 | ||||||||
\(619\) | 10.0546 | 0.404128 | 0.202064 | − | 0.979372i | \(-0.435235\pi\) | ||||
0.202064 | + | 0.979372i | \(0.435235\pi\) | |||||||
\(620\) | −7.77977 | −0.312443 | ||||||||
\(621\) | −29.6332 | −1.18914 | ||||||||
\(622\) | 20.7951 | 0.833808 | ||||||||
\(623\) | −90.5670 | −3.62849 | ||||||||
\(624\) | 0.859688 | 0.0344150 | ||||||||
\(625\) | 0.987070 | 0.0394828 | ||||||||
\(626\) | 9.78998 | 0.391286 | ||||||||
\(627\) | 13.0220 | 0.520049 | ||||||||
\(628\) | −5.48019 | −0.218684 | ||||||||
\(629\) | 2.74341 | 0.109387 | ||||||||
\(630\) | −18.8339 | −0.750362 | ||||||||
\(631\) | 11.3772 | 0.452920 | 0.226460 | − | 0.974020i | \(-0.427285\pi\) | ||||
0.226460 | + | 0.974020i | \(0.427285\pi\) | |||||||
\(632\) | −7.18568 | −0.285831 | ||||||||
\(633\) | −15.3444 | −0.609887 | ||||||||
\(634\) | 21.4136 | 0.850444 | ||||||||
\(635\) | 24.1625 | 0.958859 | ||||||||
\(636\) | −6.52420 | −0.258701 | ||||||||
\(637\) | −30.4624 | −1.20697 | ||||||||
\(638\) | 14.5377 | 0.575553 | ||||||||
\(639\) | −18.1699 | −0.718792 | ||||||||
\(640\) | −1.34990 | −0.0533595 | ||||||||
\(641\) | 45.9301 | 1.81413 | 0.907065 | − | 0.420991i | \(-0.138318\pi\) | ||||
0.907065 | + | 0.420991i | \(0.138318\pi\) | |||||||
\(642\) | −2.29709 | −0.0906587 | ||||||||
\(643\) | 23.6098 | 0.931079 | 0.465540 | − | 0.885027i | \(-0.345860\pi\) | ||||
0.465540 | + | 0.885027i | \(0.345860\pi\) | |||||||
\(644\) | 47.7593 | 1.88198 | ||||||||
\(645\) | −0.942293 | −0.0371028 | ||||||||
\(646\) | −1.50190 | −0.0590913 | ||||||||
\(647\) | 14.5105 | 0.570468 | 0.285234 | − | 0.958458i | \(-0.407929\pi\) | ||||
0.285234 | + | 0.958458i | \(0.407929\pi\) | |||||||
\(648\) | 6.17811 | 0.242699 | ||||||||
\(649\) | 55.0461 | 2.16075 | ||||||||
\(650\) | 4.78984 | 0.187873 | ||||||||
\(651\) | 17.1464 | 0.672019 | ||||||||
\(652\) | −1.13211 | −0.0443367 | ||||||||
\(653\) | 32.5732 | 1.27469 | 0.637344 | − | 0.770579i | \(-0.280033\pi\) | ||||
0.637344 | + | 0.770579i | \(0.280033\pi\) | |||||||
\(654\) | 7.09959 | 0.277616 | ||||||||
\(655\) | −18.6026 | −0.726862 | ||||||||
\(656\) | 6.87743 | 0.268518 | ||||||||
\(657\) | 30.5986 | 1.19376 | ||||||||
\(658\) | 21.5611 | 0.840538 | ||||||||
\(659\) | −9.88742 | −0.385159 | −0.192580 | − | 0.981281i | \(-0.561685\pi\) | ||||
−0.192580 | + | 0.981281i | \(0.561685\pi\) | |||||||
\(660\) | 3.77010 | 0.146751 | ||||||||
\(661\) | 35.1654 | 1.36777 | 0.683887 | − | 0.729588i | \(-0.260288\pi\) | ||||
0.683887 | + | 0.729588i | \(0.260288\pi\) | |||||||
\(662\) | 20.0123 | 0.777798 | ||||||||
\(663\) | 0.276920 | 0.0107547 | ||||||||
\(664\) | 0.615951 | 0.0239035 | ||||||||
\(665\) | −32.8316 | −1.27316 | ||||||||
\(666\) | −22.7800 | −0.882706 | ||||||||
\(667\) | −27.1819 | −1.05249 | ||||||||
\(668\) | 5.63483 | 0.218018 | ||||||||
\(669\) | −3.06829 | −0.118627 | ||||||||
\(670\) | 11.3742 | 0.439424 | ||||||||
\(671\) | −57.0969 | −2.20420 | ||||||||
\(672\) | 2.97514 | 0.114768 | ||||||||
\(673\) | −23.4595 | −0.904296 | −0.452148 | − | 0.891943i | \(-0.649342\pi\) | ||||
−0.452148 | + | 0.891943i | \(0.649342\pi\) | |||||||
\(674\) | 12.9771 | 0.499858 | ||||||||
\(675\) | −10.2851 | −0.395873 | ||||||||
\(676\) | −10.7281 | −0.412618 | ||||||||
\(677\) | 22.5313 | 0.865947 | 0.432974 | − | 0.901407i | \(-0.357464\pi\) | ||||
0.432974 | + | 0.901407i | \(0.357464\pi\) | |||||||
\(678\) | 7.17487 | 0.275549 | ||||||||
\(679\) | −59.1302 | −2.26921 | ||||||||
\(680\) | −0.434825 | −0.0166748 | ||||||||
\(681\) | −10.1035 | −0.387167 | ||||||||
\(682\) | 28.2211 | 1.08064 | ||||||||
\(683\) | 35.8628 | 1.37225 | 0.686127 | − | 0.727482i | \(-0.259310\pi\) | ||||
0.686127 | + | 0.727482i | \(0.259310\pi\) | |||||||
\(684\) | 12.4710 | 0.476841 | ||||||||
\(685\) | −25.7912 | −0.985432 | ||||||||
\(686\) | −68.9076 | −2.63091 | ||||||||
\(687\) | −8.59600 | −0.327958 | ||||||||
\(688\) | −1.22389 | −0.0466603 | ||||||||
\(689\) | −17.2418 | −0.656861 | ||||||||
\(690\) | −7.04916 | −0.268357 | ||||||||
\(691\) | −26.4427 | −1.00593 | −0.502964 | − | 0.864308i | \(-0.667757\pi\) | ||||
−0.502964 | + | 0.864308i | \(0.667757\pi\) | |||||||
\(692\) | 8.86807 | 0.337113 | ||||||||
\(693\) | 68.3201 | 2.59527 | ||||||||
\(694\) | −31.8177 | −1.20778 | ||||||||
\(695\) | −12.0773 | −0.458116 | ||||||||
\(696\) | −1.69328 | −0.0641837 | ||||||||
\(697\) | 2.21533 | 0.0839117 | ||||||||
\(698\) | −29.6834 | −1.12353 | ||||||||
\(699\) | −1.62853 | −0.0615966 | ||||||||
\(700\) | 16.5763 | 0.626524 | ||||||||
\(701\) | 1.80863 | 0.0683109 | 0.0341555 | − | 0.999417i | \(-0.489126\pi\) | ||||
0.0341555 | + | 0.999417i | \(0.489126\pi\) | |||||||
\(702\) | −4.87847 | −0.184126 | ||||||||
\(703\) | −39.7105 | −1.49771 | ||||||||
\(704\) | 4.89676 | 0.184554 | ||||||||
\(705\) | −3.18237 | −0.119855 | ||||||||
\(706\) | 21.3908 | 0.805052 | ||||||||
\(707\) | 46.3036 | 1.74143 | ||||||||
\(708\) | −6.41150 | −0.240959 | ||||||||
\(709\) | 12.8308 | 0.481869 | 0.240935 | − | 0.970541i | \(-0.422546\pi\) | ||||
0.240935 | + | 0.970541i | \(0.422546\pi\) | |||||||
\(710\) | −9.17023 | −0.344153 | ||||||||
\(711\) | 19.2195 | 0.720789 | ||||||||
\(712\) | 17.3622 | 0.650678 | ||||||||
\(713\) | −52.7665 | −1.97612 | ||||||||
\(714\) | 0.958341 | 0.0358650 | ||||||||
\(715\) | 9.96343 | 0.372611 | ||||||||
\(716\) | −0.744506 | −0.0278235 | ||||||||
\(717\) | −0.878947 | −0.0328249 | ||||||||
\(718\) | −33.2527 | −1.24098 | ||||||||
\(719\) | 15.9441 | 0.594616 | 0.297308 | − | 0.954782i | \(-0.403911\pi\) | ||||
0.297308 | + | 0.954782i | \(0.403911\pi\) | |||||||
\(720\) | 3.61058 | 0.134558 | ||||||||
\(721\) | −77.7683 | −2.89624 | ||||||||
\(722\) | 2.73969 | 0.101961 | ||||||||
\(723\) | −1.17038 | −0.0435268 | ||||||||
\(724\) | −9.27992 | −0.344885 | ||||||||
\(725\) | −9.43429 | −0.350381 | ||||||||
\(726\) | −7.40219 | −0.274721 | ||||||||
\(727\) | −42.8669 | −1.58985 | −0.794923 | − | 0.606710i | \(-0.792489\pi\) | ||||
−0.794923 | + | 0.606710i | \(0.792489\pi\) | |||||||
\(728\) | 7.86253 | 0.291405 | ||||||||
\(729\) | −10.9866 | −0.406913 | ||||||||
\(730\) | 15.4429 | 0.571566 | ||||||||
\(731\) | −0.394235 | −0.0145813 | ||||||||
\(732\) | 6.65037 | 0.245805 | ||||||||
\(733\) | 18.1886 | 0.671810 | 0.335905 | − | 0.941896i | \(-0.390958\pi\) | ||||
0.335905 | + | 0.941896i | \(0.390958\pi\) | |||||||
\(734\) | −9.57219 | −0.353316 | ||||||||
\(735\) | 15.5600 | 0.573940 | ||||||||
\(736\) | −9.15574 | −0.337485 | ||||||||
\(737\) | −41.2599 | −1.51983 | ||||||||
\(738\) | −18.3950 | −0.677131 | ||||||||
\(739\) | −28.1395 | −1.03513 | −0.517565 | − | 0.855644i | \(-0.673161\pi\) | ||||
−0.517565 | + | 0.855644i | \(0.673161\pi\) | |||||||
\(740\) | −11.4969 | −0.422633 | ||||||||
\(741\) | −4.00837 | −0.147251 | ||||||||
\(742\) | −59.6691 | −2.19052 | ||||||||
\(743\) | 24.1449 | 0.885791 | 0.442895 | − | 0.896573i | \(-0.353951\pi\) | ||||
0.442895 | + | 0.896573i | \(0.353951\pi\) | |||||||
\(744\) | −3.28706 | −0.120509 | ||||||||
\(745\) | −5.46451 | −0.200204 | ||||||||
\(746\) | −21.7305 | −0.795611 | ||||||||
\(747\) | −1.64748 | −0.0602783 | ||||||||
\(748\) | 1.57733 | 0.0576729 | ||||||||
\(749\) | −21.0087 | −0.767641 | ||||||||
\(750\) | −6.29621 | −0.229905 | ||||||||
\(751\) | −4.34927 | −0.158707 | −0.0793536 | − | 0.996847i | \(-0.525286\pi\) | ||||
−0.0793536 | + | 0.996847i | \(0.525286\pi\) | |||||||
\(752\) | −4.13339 | −0.150729 | ||||||||
\(753\) | 12.1556 | 0.442975 | ||||||||
\(754\) | −4.47492 | −0.162967 | ||||||||
\(755\) | −8.82841 | −0.321299 | ||||||||
\(756\) | −16.8830 | −0.614029 | ||||||||
\(757\) | −29.4399 | −1.07001 | −0.535005 | − | 0.844849i | \(-0.679690\pi\) | ||||
−0.535005 | + | 0.844849i | \(0.679690\pi\) | |||||||
\(758\) | −31.9976 | −1.16221 | ||||||||
\(759\) | 25.5708 | 0.928163 | ||||||||
\(760\) | 6.29402 | 0.228308 | ||||||||
\(761\) | −4.73746 | −0.171733 | −0.0858665 | − | 0.996307i | \(-0.527366\pi\) | ||||
−0.0858665 | + | 0.996307i | \(0.527366\pi\) | |||||||
\(762\) | 10.2090 | 0.369833 | ||||||||
\(763\) | 64.9315 | 2.35068 | ||||||||
\(764\) | 11.8110 | 0.427307 | ||||||||
\(765\) | 1.16303 | 0.0420493 | ||||||||
\(766\) | 16.0904 | 0.581371 | ||||||||
\(767\) | −16.9440 | −0.611812 | ||||||||
\(768\) | −0.570351 | −0.0205808 | ||||||||
\(769\) | 7.09119 | 0.255715 | 0.127857 | − | 0.991793i | \(-0.459190\pi\) | ||||
0.127857 | + | 0.991793i | \(0.459190\pi\) | |||||||
\(770\) | 34.4806 | 1.24260 | ||||||||
\(771\) | −0.997929 | −0.0359395 | ||||||||
\(772\) | −1.38758 | −0.0499402 | ||||||||
\(773\) | −48.2015 | −1.73369 | −0.866844 | − | 0.498579i | \(-0.833856\pi\) | ||||
−0.866844 | + | 0.498579i | \(0.833856\pi\) | |||||||
\(774\) | 3.27354 | 0.117665 | ||||||||
\(775\) | −18.3142 | −0.657865 | ||||||||
\(776\) | 11.3356 | 0.406925 | ||||||||
\(777\) | 25.3387 | 0.909022 | ||||||||
\(778\) | 12.6861 | 0.454820 | ||||||||
\(779\) | −32.0666 | −1.14890 | ||||||||
\(780\) | −1.16049 | −0.0415523 | ||||||||
\(781\) | 33.2650 | 1.19032 | ||||||||
\(782\) | −2.94921 | −0.105464 | ||||||||
\(783\) | 9.60886 | 0.343393 | ||||||||
\(784\) | 20.2100 | 0.721786 | ||||||||
\(785\) | 7.39772 | 0.264036 | ||||||||
\(786\) | −7.85983 | −0.280351 | ||||||||
\(787\) | 42.7134 | 1.52257 | 0.761284 | − | 0.648419i | \(-0.224569\pi\) | ||||
0.761284 | + | 0.648419i | \(0.224569\pi\) | |||||||
\(788\) | −10.4728 | −0.373078 | ||||||||
\(789\) | 6.89280 | 0.245390 | ||||||||
\(790\) | 9.69995 | 0.345109 | ||||||||
\(791\) | 65.6199 | 2.33318 | ||||||||
\(792\) | −13.0974 | −0.465395 | ||||||||
\(793\) | 17.5752 | 0.624115 | ||||||||
\(794\) | −0.346410 | −0.0122936 | ||||||||
\(795\) | 8.80702 | 0.312353 | ||||||||
\(796\) | 14.8353 | 0.525822 | ||||||||
\(797\) | 33.1497 | 1.17422 | 0.587111 | − | 0.809506i | \(-0.300265\pi\) | ||||
0.587111 | + | 0.809506i | \(0.300265\pi\) | |||||||
\(798\) | −13.8718 | −0.491057 | ||||||||
\(799\) | −1.33143 | −0.0471027 | ||||||||
\(800\) | −3.17777 | −0.112351 | ||||||||
\(801\) | −46.4388 | −1.64083 | ||||||||
\(802\) | 23.8455 | 0.842015 | ||||||||
\(803\) | −56.0190 | −1.97687 | ||||||||
\(804\) | 4.80575 | 0.169486 | ||||||||
\(805\) | −64.4702 | −2.27228 | ||||||||
\(806\) | −8.68687 | −0.305982 | ||||||||
\(807\) | −9.50451 | −0.334575 | ||||||||
\(808\) | −8.87668 | −0.312280 | ||||||||
\(809\) | −35.0877 | −1.23362 | −0.616810 | − | 0.787112i | \(-0.711575\pi\) | ||||
−0.616810 | + | 0.787112i | \(0.711575\pi\) | |||||||
\(810\) | −8.33984 | −0.293032 | ||||||||
\(811\) | 7.14130 | 0.250765 | 0.125382 | − | 0.992108i | \(-0.459984\pi\) | ||||
0.125382 | + | 0.992108i | \(0.459984\pi\) | |||||||
\(812\) | −15.4864 | −0.543467 | ||||||||
\(813\) | 8.29427 | 0.290893 | ||||||||
\(814\) | 41.7049 | 1.46176 | ||||||||
\(815\) | 1.52823 | 0.0535315 | ||||||||
\(816\) | −0.183720 | −0.00643147 | ||||||||
\(817\) | 5.70649 | 0.199645 | ||||||||
\(818\) | −1.11996 | −0.0391583 | ||||||||
\(819\) | −21.0299 | −0.734845 | ||||||||
\(820\) | −9.28384 | −0.324206 | ||||||||
\(821\) | −12.4706 | −0.435226 | −0.217613 | − | 0.976035i | \(-0.569827\pi\) | ||||
−0.217613 | + | 0.976035i | \(0.569827\pi\) | |||||||
\(822\) | −10.8971 | −0.380082 | ||||||||
\(823\) | 7.16190 | 0.249648 | 0.124824 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124824 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(824\) | 14.9086 | 0.519367 | ||||||||
\(825\) | 8.87512 | 0.308992 | ||||||||
\(826\) | −58.6383 | −2.04029 | ||||||||
\(827\) | −51.1621 | −1.77908 | −0.889541 | − | 0.456856i | \(-0.848976\pi\) | ||||
−0.889541 | + | 0.456856i | \(0.848976\pi\) | |||||||
\(828\) | 24.4888 | 0.851046 | ||||||||
\(829\) | 40.4277 | 1.40411 | 0.702056 | − | 0.712122i | \(-0.252266\pi\) | ||||
0.702056 | + | 0.712122i | \(0.252266\pi\) | |||||||
\(830\) | −0.831472 | −0.0288608 | ||||||||
\(831\) | 2.36574 | 0.0820667 | ||||||||
\(832\) | −1.50729 | −0.0522560 | ||||||||
\(833\) | 6.50998 | 0.225557 | ||||||||
\(834\) | −5.10281 | −0.176696 | ||||||||
\(835\) | −7.60646 | −0.263232 | ||||||||
\(836\) | −22.8316 | −0.789647 | ||||||||
\(837\) | 18.6531 | 0.644745 | ||||||||
\(838\) | −37.9806 | −1.31202 | ||||||||
\(839\) | −32.1188 | −1.10887 | −0.554433 | − | 0.832229i | \(-0.687065\pi\) | ||||
−0.554433 | + | 0.832229i | \(0.687065\pi\) | |||||||
\(840\) | −4.01614 | −0.138570 | ||||||||
\(841\) | −20.1860 | −0.696069 | ||||||||
\(842\) | −3.97835 | −0.137103 | ||||||||
\(843\) | −10.0842 | −0.347317 | ||||||||
\(844\) | 26.9035 | 0.926057 | ||||||||
\(845\) | 14.4818 | 0.498190 | ||||||||
\(846\) | 11.0556 | 0.380098 | ||||||||
\(847\) | −67.6990 | −2.32616 | ||||||||
\(848\) | 11.4389 | 0.392814 | ||||||||
\(849\) | 11.8867 | 0.407951 | ||||||||
\(850\) | −1.02361 | −0.0351096 | ||||||||
\(851\) | −77.9779 | −2.67305 | ||||||||
\(852\) | −3.87455 | −0.132740 | ||||||||
\(853\) | 29.8726 | 1.02282 | 0.511409 | − | 0.859337i | \(-0.329124\pi\) | ||||
0.511409 | + | 0.859337i | \(0.329124\pi\) | |||||||
\(854\) | 60.8230 | 2.08132 | ||||||||
\(855\) | −16.8346 | −0.575732 | ||||||||
\(856\) | 4.02749 | 0.137657 | ||||||||
\(857\) | −36.3366 | −1.24124 | −0.620618 | − | 0.784113i | \(-0.713118\pi\) | ||||
−0.620618 | + | 0.784113i | \(0.713118\pi\) | |||||||
\(858\) | 4.20969 | 0.143716 | ||||||||
\(859\) | 16.2362 | 0.553973 | 0.276986 | − | 0.960874i | \(-0.410664\pi\) | ||||
0.276986 | + | 0.960874i | \(0.410664\pi\) | |||||||
\(860\) | 1.65213 | 0.0563371 | ||||||||
\(861\) | 20.4613 | 0.697318 | ||||||||
\(862\) | 20.1325 | 0.685715 | ||||||||
\(863\) | 21.2757 | 0.724233 | 0.362117 | − | 0.932133i | \(-0.382054\pi\) | ||||
0.362117 | + | 0.932133i | \(0.382054\pi\) | |||||||
\(864\) | 3.23657 | 0.110110 | ||||||||
\(865\) | −11.9710 | −0.407026 | ||||||||
\(866\) | 36.4879 | 1.23991 | ||||||||
\(867\) | 9.63679 | 0.327283 | ||||||||
\(868\) | −30.0628 | −1.02040 | ||||||||
\(869\) | −35.1866 | −1.19362 | ||||||||
\(870\) | 2.28576 | 0.0774945 | ||||||||
\(871\) | 12.7004 | 0.430336 | ||||||||
\(872\) | −12.4478 | −0.421534 | ||||||||
\(873\) | −30.3194 | −1.02615 | ||||||||
\(874\) | 42.6894 | 1.44399 | ||||||||
\(875\) | −57.5839 | −1.94669 | ||||||||
\(876\) | 6.52482 | 0.220453 | ||||||||
\(877\) | 34.6583 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(878\) | −22.6093 | −0.763026 | ||||||||
\(879\) | −6.51094 | −0.219609 | ||||||||
\(880\) | −6.61014 | −0.222828 | ||||||||
\(881\) | −35.0066 | −1.17940 | −0.589701 | − | 0.807622i | \(-0.700754\pi\) | ||||
−0.589701 | + | 0.807622i | \(0.700754\pi\) | |||||||
\(882\) | −54.0557 | −1.82015 | ||||||||
\(883\) | 23.4321 | 0.788553 | 0.394277 | − | 0.918992i | \(-0.370995\pi\) | ||||
0.394277 | + | 0.918992i | \(0.370995\pi\) | |||||||
\(884\) | −0.485525 | −0.0163300 | ||||||||
\(885\) | 8.65488 | 0.290931 | ||||||||
\(886\) | −20.8098 | −0.699120 | ||||||||
\(887\) | −53.8044 | −1.80658 | −0.903288 | − | 0.429035i | \(-0.858854\pi\) | ||||
−0.903288 | + | 0.429035i | \(0.858854\pi\) | |||||||
\(888\) | −4.85759 | −0.163010 | ||||||||
\(889\) | 93.3694 | 3.13151 | ||||||||
\(890\) | −23.4373 | −0.785620 | ||||||||
\(891\) | 30.2528 | 1.01351 | ||||||||
\(892\) | 5.37965 | 0.180124 | ||||||||
\(893\) | 19.2723 | 0.644922 | ||||||||
\(894\) | −2.30883 | −0.0772188 | ||||||||
\(895\) | 1.00501 | 0.0335937 | ||||||||
\(896\) | −5.21632 | −0.174265 | ||||||||
\(897\) | −7.87107 | −0.262807 | ||||||||
\(898\) | −38.4084 | −1.28170 | ||||||||
\(899\) | 17.1101 | 0.570653 | ||||||||
\(900\) | 8.49958 | 0.283319 | ||||||||
\(901\) | 3.68466 | 0.122754 | ||||||||
\(902\) | 33.6771 | 1.12133 | ||||||||
\(903\) | −3.64124 | −0.121173 | ||||||||
\(904\) | −12.5797 | −0.418396 | ||||||||
\(905\) | 12.5270 | 0.416410 | ||||||||
\(906\) | −3.73012 | −0.123925 | ||||||||
\(907\) | 13.1054 | 0.435157 | 0.217578 | − | 0.976043i | \(-0.430184\pi\) | ||||
0.217578 | + | 0.976043i | \(0.430184\pi\) | |||||||
\(908\) | 17.7145 | 0.587878 | ||||||||
\(909\) | 23.7424 | 0.787487 | ||||||||
\(910\) | −10.6136 | −0.351839 | ||||||||
\(911\) | −4.35027 | −0.144131 | −0.0720654 | − | 0.997400i | \(-0.522959\pi\) | ||||
−0.0720654 | + | 0.997400i | \(0.522959\pi\) | |||||||
\(912\) | 2.65931 | 0.0880586 | ||||||||
\(913\) | 3.01617 | 0.0998205 | ||||||||
\(914\) | 22.2360 | 0.735503 | ||||||||
\(915\) | −8.97733 | −0.296781 | ||||||||
\(916\) | 15.0714 | 0.497974 | ||||||||
\(917\) | −71.8845 | −2.37384 | ||||||||
\(918\) | 1.04255 | 0.0344094 | ||||||||
\(919\) | 51.8873 | 1.71160 | 0.855802 | − | 0.517303i | \(-0.173064\pi\) | ||||
0.855802 | + | 0.517303i | \(0.173064\pi\) | |||||||
\(920\) | 12.3593 | 0.407475 | ||||||||
\(921\) | 1.11538 | 0.0367529 | ||||||||
\(922\) | 8.26591 | 0.272223 | ||||||||
\(923\) | −10.2395 | −0.337036 | ||||||||
\(924\) | 14.5685 | 0.479270 | ||||||||
\(925\) | −27.0645 | −0.889876 | ||||||||
\(926\) | −27.2271 | −0.894738 | ||||||||
\(927\) | −39.8761 | −1.30970 | ||||||||
\(928\) | 2.96884 | 0.0974569 | ||||||||
\(929\) | 31.6185 | 1.03737 | 0.518684 | − | 0.854966i | \(-0.326422\pi\) | ||||
0.518684 | + | 0.854966i | \(0.326422\pi\) | |||||||
\(930\) | 4.43720 | 0.145502 | ||||||||
\(931\) | −94.2309 | −3.08829 | ||||||||
\(932\) | 2.85531 | 0.0935287 | ||||||||
\(933\) | −11.8605 | −0.388296 | ||||||||
\(934\) | −5.58987 | −0.182906 | ||||||||
\(935\) | −2.12924 | −0.0696335 | ||||||||
\(936\) | 4.03156 | 0.131776 | ||||||||
\(937\) | 29.0006 | 0.947407 | 0.473704 | − | 0.880684i | \(-0.342917\pi\) | ||||
0.473704 | + | 0.880684i | \(0.342917\pi\) | |||||||
\(938\) | 43.9525 | 1.43510 | ||||||||
\(939\) | −5.58373 | −0.182218 | ||||||||
\(940\) | 5.57966 | 0.181988 | ||||||||
\(941\) | −1.22096 | −0.0398021 | −0.0199011 | − | 0.999802i | \(-0.506335\pi\) | ||||
−0.0199011 | + | 0.999802i | \(0.506335\pi\) | |||||||
\(942\) | 3.12564 | 0.101839 | ||||||||
\(943\) | −62.9679 | −2.05052 | ||||||||
\(944\) | 11.2413 | 0.365874 | ||||||||
\(945\) | 22.7904 | 0.741371 | ||||||||
\(946\) | −5.99310 | −0.194852 | ||||||||
\(947\) | 45.0609 | 1.46428 | 0.732141 | − | 0.681154i | \(-0.238521\pi\) | ||||
0.732141 | + | 0.681154i | \(0.238521\pi\) | |||||||
\(948\) | 4.09836 | 0.133109 | ||||||||
\(949\) | 17.2435 | 0.559746 | ||||||||
\(950\) | 14.8166 | 0.480715 | ||||||||
\(951\) | −12.2133 | −0.396043 | ||||||||
\(952\) | −1.68026 | −0.0544576 | ||||||||
\(953\) | −19.2424 | −0.623323 | −0.311661 | − | 0.950193i | \(-0.600885\pi\) | ||||
−0.311661 | + | 0.950193i | \(0.600885\pi\) | |||||||
\(954\) | −30.5957 | −0.990571 | ||||||||
\(955\) | −15.9437 | −0.515925 | ||||||||
\(956\) | 1.54106 | 0.0498415 | ||||||||
\(957\) | −8.29160 | −0.268029 | ||||||||
\(958\) | 2.67407 | 0.0863954 | ||||||||
\(959\) | −99.6631 | −3.21829 | ||||||||
\(960\) | 0.769917 | 0.0248490 | ||||||||
\(961\) | 2.21470 | 0.0714421 | ||||||||
\(962\) | −12.8374 | −0.413894 | ||||||||
\(963\) | −10.7723 | −0.347133 | ||||||||
\(964\) | 2.05203 | 0.0660914 | ||||||||
\(965\) | 1.87310 | 0.0602972 | ||||||||
\(966\) | −27.2396 | −0.876418 | ||||||||
\(967\) | −5.11420 | −0.164462 | −0.0822309 | − | 0.996613i | \(-0.526204\pi\) | ||||
−0.0822309 | + | 0.996613i | \(0.526204\pi\) | |||||||
\(968\) | 12.9783 | 0.417138 | ||||||||
\(969\) | 0.856608 | 0.0275182 | ||||||||
\(970\) | −15.3019 | −0.491316 | ||||||||
\(971\) | 51.4507 | 1.65113 | 0.825566 | − | 0.564306i | \(-0.190856\pi\) | ||||
0.825566 | + | 0.564306i | \(0.190856\pi\) | |||||||
\(972\) | −13.2334 | −0.424462 | ||||||||
\(973\) | −46.6693 | −1.49615 | ||||||||
\(974\) | 40.4979 | 1.29764 | ||||||||
\(975\) | −2.73189 | −0.0874905 | ||||||||
\(976\) | −11.6601 | −0.373232 | ||||||||
\(977\) | −16.9760 | −0.543110 | −0.271555 | − | 0.962423i | \(-0.587538\pi\) | ||||
−0.271555 | + | 0.962423i | \(0.587538\pi\) | |||||||
\(978\) | 0.645698 | 0.0206471 | ||||||||
\(979\) | 85.0188 | 2.71721 | ||||||||
\(980\) | −27.2815 | −0.871475 | ||||||||
\(981\) | 33.2940 | 1.06300 | ||||||||
\(982\) | 18.4772 | 0.589631 | ||||||||
\(983\) | −0.922623 | −0.0294271 | −0.0147135 | − | 0.999892i | \(-0.504684\pi\) | ||||
−0.0147135 | + | 0.999892i | \(0.504684\pi\) | |||||||
\(984\) | −3.92255 | −0.125046 | ||||||||
\(985\) | 14.1372 | 0.450450 | ||||||||
\(986\) | 0.956312 | 0.0304552 | ||||||||
\(987\) | −12.2974 | −0.391430 | ||||||||
\(988\) | 7.02789 | 0.223587 | ||||||||
\(989\) | 11.2056 | 0.356318 | ||||||||
\(990\) | 17.6801 | 0.561912 | ||||||||
\(991\) | 26.2547 | 0.834008 | 0.417004 | − | 0.908905i | \(-0.363080\pi\) | ||||
0.417004 | + | 0.908905i | \(0.363080\pi\) | |||||||
\(992\) | 5.76322 | 0.182982 | ||||||||
\(993\) | −11.4140 | −0.362213 | ||||||||
\(994\) | −35.4359 | −1.12396 | ||||||||
\(995\) | −20.0261 | −0.634871 | ||||||||
\(996\) | −0.351308 | −0.0111316 | ||||||||
\(997\) | 29.4017 | 0.931160 | 0.465580 | − | 0.885006i | \(-0.345846\pi\) | ||||
0.465580 | + | 0.885006i | \(0.345846\pi\) | |||||||
\(998\) | −29.2974 | −0.927393 | ||||||||
\(999\) | 27.5653 | 0.872129 |
(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 | 4034.2.a.d.1.19 | ✓ | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.d.1.19 | ✓ | 52 | 1.1 | even | 1 | trivial |