Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2366,2,Mod(1,2366)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2366, 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("2366.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2366 = 2 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2366.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: | \(18.8926051182\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.285686784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 10x^{4} + 12x^{3} + 21x^{2} + 2x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.466545\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2366.1 |
$q$-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 | ||||||||
\(3\) | −0.466545 | −0.269360 | −0.134680 | − | 0.990889i | \(-0.543001\pi\) | ||||
−0.134680 | + | 0.990889i | \(0.543001\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.38938 | 1.51578 | 0.757888 | − | 0.652385i | \(-0.226232\pi\) | ||||
0.757888 | + | 0.652385i | \(0.226232\pi\) | |||||||
\(6\) | −0.466545 | −0.190466 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.78234 | −0.927445 | ||||||||
\(10\) | 3.38938 | 1.07181 | ||||||||
\(11\) | −0.822730 | −0.248063 | −0.124031 | − | 0.992278i | \(-0.539582\pi\) | ||||
−0.124031 | + | 0.992278i | \(0.539582\pi\) | |||||||
\(12\) | −0.466545 | −0.134680 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | −1.58130 | −0.408289 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.58130 | 1.11113 | 0.555564 | − | 0.831474i | \(-0.312502\pi\) | ||||
0.555564 | + | 0.831474i | \(0.312502\pi\) | |||||||
\(18\) | −2.78234 | −0.655803 | ||||||||
\(19\) | 5.90621 | 1.35498 | 0.677488 | − | 0.735534i | \(-0.263068\pi\) | ||||
0.677488 | + | 0.735534i | \(0.263068\pi\) | |||||||
\(20\) | 3.38938 | 0.757888 | ||||||||
\(21\) | −0.466545 | −0.101808 | ||||||||
\(22\) | −0.822730 | −0.175407 | ||||||||
\(23\) | −6.13055 | −1.27831 | −0.639154 | − | 0.769079i | \(-0.720715\pi\) | ||||
−0.639154 | + | 0.769079i | \(0.720715\pi\) | |||||||
\(24\) | −0.466545 | −0.0952331 | ||||||||
\(25\) | 6.48787 | 1.29757 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.69772 | 0.519176 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −6.86813 | −1.27538 | −0.637690 | − | 0.770293i | \(-0.720110\pi\) | ||||
−0.637690 | + | 0.770293i | \(0.720110\pi\) | |||||||
\(30\) | −1.58130 | −0.288704 | ||||||||
\(31\) | 4.28683 | 0.769938 | 0.384969 | − | 0.922930i | \(-0.374212\pi\) | ||||
0.384969 | + | 0.922930i | \(0.374212\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.383841 | 0.0668181 | ||||||||
\(34\) | 4.58130 | 0.785686 | ||||||||
\(35\) | 3.38938 | 0.572909 | ||||||||
\(36\) | −2.78234 | −0.463723 | ||||||||
\(37\) | 9.69086 | 1.59317 | 0.796584 | − | 0.604528i | \(-0.206638\pi\) | ||||
0.796584 | + | 0.604528i | \(0.206638\pi\) | |||||||
\(38\) | 5.90621 | 0.958113 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.38938 | 0.535907 | ||||||||
\(41\) | −0.0893760 | −0.0139582 | −0.00697909 | − | 0.999976i | \(-0.502222\pi\) | ||||
−0.00697909 | + | 0.999976i | \(0.502222\pi\) | |||||||
\(42\) | −0.466545 | −0.0719895 | ||||||||
\(43\) | 7.35374 | 1.12144 | 0.560718 | − | 0.828007i | \(-0.310525\pi\) | ||||
0.560718 | + | 0.828007i | \(0.310525\pi\) | |||||||
\(44\) | −0.822730 | −0.124031 | ||||||||
\(45\) | −9.43038 | −1.40580 | ||||||||
\(46\) | −6.13055 | −0.903900 | ||||||||
\(47\) | 11.1759 | 1.63018 | 0.815089 | − | 0.579335i | \(-0.196688\pi\) | ||||
0.815089 | + | 0.579335i | \(0.196688\pi\) | |||||||
\(48\) | −0.466545 | −0.0673400 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 6.48787 | 0.917524 | ||||||||
\(51\) | −2.13738 | −0.299293 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.01530 | −0.963625 | −0.481813 | − | 0.876274i | \(-0.660021\pi\) | ||||
−0.481813 | + | 0.876274i | \(0.660021\pi\) | |||||||
\(54\) | 2.69772 | 0.367113 | ||||||||
\(55\) | −2.78854 | −0.376007 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −2.75551 | −0.364976 | ||||||||
\(58\) | −6.86813 | −0.901829 | ||||||||
\(59\) | 1.74117 | 0.226681 | 0.113340 | − | 0.993556i | \(-0.463845\pi\) | ||||
0.113340 | + | 0.993556i | \(0.463845\pi\) | |||||||
\(60\) | −1.58130 | −0.204145 | ||||||||
\(61\) | 2.37945 | 0.304657 | 0.152329 | − | 0.988330i | \(-0.451323\pi\) | ||||
0.152329 | + | 0.988330i | \(0.451323\pi\) | |||||||
\(62\) | 4.28683 | 0.544428 | ||||||||
\(63\) | −2.78234 | −0.350541 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.383841 | 0.0472475 | ||||||||
\(67\) | 0.291719 | 0.0356391 | 0.0178196 | − | 0.999841i | \(-0.494328\pi\) | ||||
0.0178196 | + | 0.999841i | \(0.494328\pi\) | |||||||
\(68\) | 4.58130 | 0.555564 | ||||||||
\(69\) | 2.86018 | 0.344325 | ||||||||
\(70\) | 3.38938 | 0.405108 | ||||||||
\(71\) | −10.9484 | −1.29933 | −0.649667 | − | 0.760219i | \(-0.725092\pi\) | ||||
−0.649667 | + | 0.760219i | \(0.725092\pi\) | |||||||
\(72\) | −2.78234 | −0.327901 | ||||||||
\(73\) | −12.7187 | −1.48861 | −0.744304 | − | 0.667841i | \(-0.767219\pi\) | ||||
−0.744304 | + | 0.667841i | \(0.767219\pi\) | |||||||
\(74\) | 9.69086 | 1.12654 | ||||||||
\(75\) | −3.02688 | −0.349514 | ||||||||
\(76\) | 5.90621 | 0.677488 | ||||||||
\(77\) | −0.822730 | −0.0937588 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.95602 | 1.12014 | 0.560070 | − | 0.828445i | \(-0.310774\pi\) | ||||
0.560070 | + | 0.828445i | \(0.310774\pi\) | |||||||
\(80\) | 3.38938 | 0.378944 | ||||||||
\(81\) | 7.08840 | 0.787600 | ||||||||
\(82\) | −0.0893760 | −0.00986993 | ||||||||
\(83\) | −3.23553 | −0.355146 | −0.177573 | − | 0.984108i | \(-0.556825\pi\) | ||||
−0.177573 | + | 0.984108i | \(0.556825\pi\) | |||||||
\(84\) | −0.466545 | −0.0509042 | ||||||||
\(85\) | 15.5277 | 1.68422 | ||||||||
\(86\) | 7.35374 | 0.792974 | ||||||||
\(87\) | 3.20429 | 0.343536 | ||||||||
\(88\) | −0.822730 | −0.0877033 | ||||||||
\(89\) | −8.04265 | −0.852519 | −0.426260 | − | 0.904601i | \(-0.640169\pi\) | ||||
−0.426260 | + | 0.904601i | \(0.640169\pi\) | |||||||
\(90\) | −9.43038 | −0.994050 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.13055 | −0.639154 | ||||||||
\(93\) | −2.00000 | −0.207390 | ||||||||
\(94\) | 11.1759 | 1.15271 | ||||||||
\(95\) | 20.0184 | 2.05384 | ||||||||
\(96\) | −0.466545 | −0.0476166 | ||||||||
\(97\) | −14.7739 | −1.50006 | −0.750029 | − | 0.661405i | \(-0.769961\pi\) | ||||
−0.750029 | + | 0.661405i | \(0.769961\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 2.28911 | 0.230064 | ||||||||
\(100\) | 6.48787 | 0.648787 | ||||||||
\(101\) | −8.23976 | −0.819887 | −0.409943 | − | 0.912111i | \(-0.634452\pi\) | ||||
−0.409943 | + | 0.912111i | \(0.634452\pi\) | |||||||
\(102\) | −2.13738 | −0.211632 | ||||||||
\(103\) | 13.3231 | 1.31277 | 0.656383 | − | 0.754428i | \(-0.272086\pi\) | ||||
0.656383 | + | 0.754428i | \(0.272086\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.58130 | −0.154319 | ||||||||
\(106\) | −7.01530 | −0.681386 | ||||||||
\(107\) | −9.02649 | −0.872624 | −0.436312 | − | 0.899795i | \(-0.643716\pi\) | ||||
−0.436312 | + | 0.899795i | \(0.643716\pi\) | |||||||
\(108\) | 2.69772 | 0.259588 | ||||||||
\(109\) | 0.397192 | 0.0380441 | 0.0190220 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190220 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(110\) | −2.78854 | −0.265877 | ||||||||
\(111\) | −4.52122 | −0.429135 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 4.47322 | 0.420805 | 0.210402 | − | 0.977615i | \(-0.432523\pi\) | ||||
0.210402 | + | 0.977615i | \(0.432523\pi\) | |||||||
\(114\) | −2.75551 | −0.258077 | ||||||||
\(115\) | −20.7787 | −1.93763 | ||||||||
\(116\) | −6.86813 | −0.637690 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.74117 | 0.160288 | ||||||||
\(119\) | 4.58130 | 0.419967 | ||||||||
\(120\) | −1.58130 | −0.144352 | ||||||||
\(121\) | −10.3231 | −0.938465 | ||||||||
\(122\) | 2.37945 | 0.215425 | ||||||||
\(123\) | 0.0416979 | 0.00375978 | ||||||||
\(124\) | 4.28683 | 0.384969 | ||||||||
\(125\) | 5.04295 | 0.451056 | ||||||||
\(126\) | −2.78234 | −0.247870 | ||||||||
\(127\) | −0.540127 | −0.0479285 | −0.0239642 | − | 0.999713i | \(-0.507629\pi\) | ||||
−0.0239642 | + | 0.999713i | \(0.507629\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.43085 | −0.302070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.72615 | −0.675037 | −0.337518 | − | 0.941319i | \(-0.609587\pi\) | ||||
−0.337518 | + | 0.941319i | \(0.609587\pi\) | |||||||
\(132\) | 0.383841 | 0.0334090 | ||||||||
\(133\) | 5.90621 | 0.512133 | ||||||||
\(134\) | 0.291719 | 0.0252007 | ||||||||
\(135\) | 9.14359 | 0.786955 | ||||||||
\(136\) | 4.58130 | 0.392843 | ||||||||
\(137\) | 12.5401 | 1.07137 | 0.535687 | − | 0.844417i | \(-0.320053\pi\) | ||||
0.535687 | + | 0.844417i | \(0.320053\pi\) | |||||||
\(138\) | 2.86018 | 0.243474 | ||||||||
\(139\) | 12.0974 | 1.02608 | 0.513042 | − | 0.858363i | \(-0.328518\pi\) | ||||
0.513042 | + | 0.858363i | \(0.328518\pi\) | |||||||
\(140\) | 3.38938 | 0.286455 | ||||||||
\(141\) | −5.21408 | −0.439105 | ||||||||
\(142\) | −10.9484 | −0.918768 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.78234 | −0.231861 | ||||||||
\(145\) | −23.2787 | −1.93319 | ||||||||
\(146\) | −12.7187 | −1.05261 | ||||||||
\(147\) | −0.466545 | −0.0384800 | ||||||||
\(148\) | 9.69086 | 0.796584 | ||||||||
\(149\) | −17.0078 | −1.39333 | −0.696666 | − | 0.717395i | \(-0.745334\pi\) | ||||
−0.696666 | + | 0.717395i | \(0.745334\pi\) | |||||||
\(150\) | −3.02688 | −0.247144 | ||||||||
\(151\) | 5.54567 | 0.451300 | 0.225650 | − | 0.974208i | \(-0.427549\pi\) | ||||
0.225650 | + | 0.974208i | \(0.427549\pi\) | |||||||
\(152\) | 5.90621 | 0.479057 | ||||||||
\(153\) | −12.7467 | −1.03051 | ||||||||
\(154\) | −0.822730 | −0.0662975 | ||||||||
\(155\) | 14.5297 | 1.16705 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.29353 | 0.183044 | 0.0915218 | − | 0.995803i | \(-0.470827\pi\) | ||||
0.0915218 | + | 0.995803i | \(0.470827\pi\) | |||||||
\(158\) | 9.95602 | 0.792059 | ||||||||
\(159\) | 3.27295 | 0.259562 | ||||||||
\(160\) | 3.38938 | 0.267954 | ||||||||
\(161\) | −6.13055 | −0.483155 | ||||||||
\(162\) | 7.08840 | 0.556917 | ||||||||
\(163\) | −23.3560 | −1.82938 | −0.914691 | − | 0.404155i | \(-0.867566\pi\) | ||||
−0.914691 | + | 0.404155i | \(0.867566\pi\) | |||||||
\(164\) | −0.0893760 | −0.00697909 | ||||||||
\(165\) | 1.30098 | 0.101281 | ||||||||
\(166\) | −3.23553 | −0.251126 | ||||||||
\(167\) | 21.7780 | 1.68523 | 0.842614 | − | 0.538517i | \(-0.181015\pi\) | ||||
0.842614 | + | 0.538517i | \(0.181015\pi\) | |||||||
\(168\) | −0.466545 | −0.0359947 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 15.5277 | 1.19092 | ||||||||
\(171\) | −16.4330 | −1.25667 | ||||||||
\(172\) | 7.35374 | 0.560718 | ||||||||
\(173\) | 8.09733 | 0.615629 | 0.307814 | − | 0.951446i | \(-0.400402\pi\) | ||||
0.307814 | + | 0.951446i | \(0.400402\pi\) | |||||||
\(174\) | 3.20429 | 0.242917 | ||||||||
\(175\) | 6.48787 | 0.490437 | ||||||||
\(176\) | −0.822730 | −0.0620156 | ||||||||
\(177\) | −0.812334 | −0.0610588 | ||||||||
\(178\) | −8.04265 | −0.602822 | ||||||||
\(179\) | 9.90883 | 0.740621 | 0.370310 | − | 0.928908i | \(-0.379251\pi\) | ||||
0.370310 | + | 0.928908i | \(0.379251\pi\) | |||||||
\(180\) | −9.43038 | −0.702899 | ||||||||
\(181\) | −1.27902 | −0.0950685 | −0.0475343 | − | 0.998870i | \(-0.515136\pi\) | ||||
−0.0475343 | + | 0.998870i | \(0.515136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.11012 | −0.0820624 | ||||||||
\(184\) | −6.13055 | −0.451950 | ||||||||
\(185\) | 32.8460 | 2.41488 | ||||||||
\(186\) | −2.00000 | −0.146647 | ||||||||
\(187\) | −3.76917 | −0.275629 | ||||||||
\(188\) | 11.1759 | 0.815089 | ||||||||
\(189\) | 2.69772 | 0.196230 | ||||||||
\(190\) | 20.0184 | 1.45228 | ||||||||
\(191\) | −10.0342 | −0.726050 | −0.363025 | − | 0.931779i | \(-0.618256\pi\) | ||||
−0.363025 | + | 0.931779i | \(0.618256\pi\) | |||||||
\(192\) | −0.466545 | −0.0336700 | ||||||||
\(193\) | 15.8582 | 1.14150 | 0.570750 | − | 0.821124i | \(-0.306653\pi\) | ||||
0.570750 | + | 0.821124i | \(0.306653\pi\) | |||||||
\(194\) | −14.7739 | −1.06070 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 14.8081 | 1.05503 | 0.527515 | − | 0.849546i | \(-0.323124\pi\) | ||||
0.527515 | + | 0.849546i | \(0.323124\pi\) | |||||||
\(198\) | 2.28911 | 0.162680 | ||||||||
\(199\) | −2.55543 | −0.181149 | −0.0905747 | − | 0.995890i | \(-0.528870\pi\) | ||||
−0.0905747 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(200\) | 6.48787 | 0.458762 | ||||||||
\(201\) | −0.136100 | −0.00959974 | ||||||||
\(202\) | −8.23976 | −0.579748 | ||||||||
\(203\) | −6.86813 | −0.482048 | ||||||||
\(204\) | −2.13738 | −0.149647 | ||||||||
\(205\) | −0.302929 | −0.0211575 | ||||||||
\(206\) | 13.3231 | 0.928265 | ||||||||
\(207\) | 17.0572 | 1.18556 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.85921 | −0.336119 | ||||||||
\(210\) | −1.58130 | −0.109120 | ||||||||
\(211\) | −8.63648 | −0.594560 | −0.297280 | − | 0.954790i | \(-0.596080\pi\) | ||||
−0.297280 | + | 0.954790i | \(0.596080\pi\) | |||||||
\(212\) | −7.01530 | −0.481813 | ||||||||
\(213\) | 5.10792 | 0.349989 | ||||||||
\(214\) | −9.02649 | −0.617038 | ||||||||
\(215\) | 24.9246 | 1.69984 | ||||||||
\(216\) | 2.69772 | 0.183557 | ||||||||
\(217\) | 4.28683 | 0.291009 | ||||||||
\(218\) | 0.397192 | 0.0269012 | ||||||||
\(219\) | 5.93384 | 0.400971 | ||||||||
\(220\) | −2.78854 | −0.188003 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.52122 | −0.303445 | ||||||||
\(223\) | −19.9277 | −1.33446 | −0.667228 | − | 0.744854i | \(-0.732519\pi\) | ||||
−0.667228 | + | 0.744854i | \(0.732519\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | −18.0514 | −1.20343 | ||||||||
\(226\) | 4.47322 | 0.297554 | ||||||||
\(227\) | −0.352624 | −0.0234045 | −0.0117022 | − | 0.999932i | \(-0.503725\pi\) | ||||
−0.0117022 | + | 0.999932i | \(0.503725\pi\) | |||||||
\(228\) | −2.75551 | −0.182488 | ||||||||
\(229\) | −8.31317 | −0.549350 | −0.274675 | − | 0.961537i | \(-0.588570\pi\) | ||||
−0.274675 | + | 0.961537i | \(0.588570\pi\) | |||||||
\(230\) | −20.7787 | −1.37011 | ||||||||
\(231\) | 0.383841 | 0.0252549 | ||||||||
\(232\) | −6.86813 | −0.450915 | ||||||||
\(233\) | 15.3798 | 1.00756 | 0.503781 | − | 0.863831i | \(-0.331942\pi\) | ||||
0.503781 | + | 0.863831i | \(0.331942\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 37.8795 | 2.47098 | ||||||||
\(236\) | 1.74117 | 0.113340 | ||||||||
\(237\) | −4.64493 | −0.301721 | ||||||||
\(238\) | 4.58130 | 0.296961 | ||||||||
\(239\) | −2.88606 | −0.186684 | −0.0933418 | − | 0.995634i | \(-0.529755\pi\) | ||||
−0.0933418 | + | 0.995634i | \(0.529755\pi\) | |||||||
\(240\) | −1.58130 | −0.102072 | ||||||||
\(241\) | −6.26744 | −0.403722 | −0.201861 | − | 0.979414i | \(-0.564699\pi\) | ||||
−0.201861 | + | 0.979414i | \(0.564699\pi\) | |||||||
\(242\) | −10.3231 | −0.663595 | ||||||||
\(243\) | −11.4002 | −0.731324 | ||||||||
\(244\) | 2.37945 | 0.152329 | ||||||||
\(245\) | 3.38938 | 0.216539 | ||||||||
\(246\) | 0.0416979 | 0.00265856 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.28683 | 0.272214 | ||||||||
\(249\) | 1.50952 | 0.0956621 | ||||||||
\(250\) | 5.04295 | 0.318944 | ||||||||
\(251\) | 17.2665 | 1.08985 | 0.544926 | − | 0.838484i | \(-0.316558\pi\) | ||||
0.544926 | + | 0.838484i | \(0.316558\pi\) | |||||||
\(252\) | −2.78234 | −0.175271 | ||||||||
\(253\) | 5.04379 | 0.317100 | ||||||||
\(254\) | −0.540127 | −0.0338906 | ||||||||
\(255\) | −7.24439 | −0.453661 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.1931 | −0.698206 | −0.349103 | − | 0.937084i | \(-0.613514\pi\) | ||||
−0.349103 | + | 0.937084i | \(0.613514\pi\) | |||||||
\(258\) | −3.43085 | −0.213595 | ||||||||
\(259\) | 9.69086 | 0.602161 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.1094 | 1.18284 | ||||||||
\(262\) | −7.72615 | −0.477323 | ||||||||
\(263\) | −28.5826 | −1.76248 | −0.881240 | − | 0.472668i | \(-0.843291\pi\) | ||||
−0.881240 | + | 0.472668i | \(0.843291\pi\) | |||||||
\(264\) | 0.383841 | 0.0236238 | ||||||||
\(265\) | −23.7775 | −1.46064 | ||||||||
\(266\) | 5.90621 | 0.362133 | ||||||||
\(267\) | 3.75226 | 0.229635 | ||||||||
\(268\) | 0.291719 | 0.0178196 | ||||||||
\(269\) | −18.3754 | −1.12037 | −0.560183 | − | 0.828369i | \(-0.689269\pi\) | ||||
−0.560183 | + | 0.828369i | \(0.689269\pi\) | |||||||
\(270\) | 9.14359 | 0.556461 | ||||||||
\(271\) | −20.3825 | −1.23815 | −0.619075 | − | 0.785332i | \(-0.712492\pi\) | ||||
−0.619075 | + | 0.785332i | \(0.712492\pi\) | |||||||
\(272\) | 4.58130 | 0.277782 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.5401 | 0.757575 | ||||||||
\(275\) | −5.33777 | −0.321880 | ||||||||
\(276\) | 2.86018 | 0.172162 | ||||||||
\(277\) | 7.23219 | 0.434540 | 0.217270 | − | 0.976112i | \(-0.430285\pi\) | ||||
0.217270 | + | 0.976112i | \(0.430285\pi\) | |||||||
\(278\) | 12.0974 | 0.725551 | ||||||||
\(279\) | −11.9274 | −0.714075 | ||||||||
\(280\) | 3.38938 | 0.202554 | ||||||||
\(281\) | 12.4585 | 0.743215 | 0.371607 | − | 0.928390i | \(-0.378807\pi\) | ||||
0.371607 | + | 0.928390i | \(0.378807\pi\) | |||||||
\(282\) | −5.21408 | −0.310494 | ||||||||
\(283\) | 13.0607 | 0.776378 | 0.388189 | − | 0.921580i | \(-0.373101\pi\) | ||||
0.388189 | + | 0.921580i | \(0.373101\pi\) | |||||||
\(284\) | −10.9484 | −0.649667 | ||||||||
\(285\) | −9.33946 | −0.553222 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.0893760 | −0.00527570 | ||||||||
\(288\) | −2.78234 | −0.163951 | ||||||||
\(289\) | 3.98828 | 0.234605 | ||||||||
\(290\) | −23.2787 | −1.36697 | ||||||||
\(291\) | 6.89267 | 0.404056 | ||||||||
\(292\) | −12.7187 | −0.744304 | ||||||||
\(293\) | −14.5582 | −0.850498 | −0.425249 | − | 0.905076i | \(-0.639813\pi\) | ||||
−0.425249 | + | 0.905076i | \(0.639813\pi\) | |||||||
\(294\) | −0.466545 | −0.0272095 | ||||||||
\(295\) | 5.90148 | 0.343597 | ||||||||
\(296\) | 9.69086 | 0.563270 | ||||||||
\(297\) | −2.21950 | −0.128788 | ||||||||
\(298\) | −17.0078 | −0.985235 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.02688 | −0.174757 | ||||||||
\(301\) | 7.35374 | 0.423863 | ||||||||
\(302\) | 5.54567 | 0.319117 | ||||||||
\(303\) | 3.84422 | 0.220845 | ||||||||
\(304\) | 5.90621 | 0.338744 | ||||||||
\(305\) | 8.06485 | 0.461792 | ||||||||
\(306\) | −12.7467 | −0.728681 | ||||||||
\(307\) | −3.24267 | −0.185069 | −0.0925345 | − | 0.995709i | \(-0.529497\pi\) | ||||
−0.0925345 | + | 0.995709i | \(0.529497\pi\) | |||||||
\(308\) | −0.822730 | −0.0468794 | ||||||||
\(309\) | −6.21583 | −0.353606 | ||||||||
\(310\) | 14.5297 | 0.825231 | ||||||||
\(311\) | 10.2709 | 0.582408 | 0.291204 | − | 0.956661i | \(-0.405944\pi\) | ||||
0.291204 | + | 0.956661i | \(0.405944\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.13382 | −0.346704 | −0.173352 | − | 0.984860i | \(-0.555460\pi\) | ||||
−0.173352 | + | 0.984860i | \(0.555460\pi\) | |||||||
\(314\) | 2.29353 | 0.129431 | ||||||||
\(315\) | −9.43038 | −0.531342 | ||||||||
\(316\) | 9.95602 | 0.560070 | ||||||||
\(317\) | −5.04487 | −0.283348 | −0.141674 | − | 0.989913i | \(-0.545248\pi\) | ||||
−0.141674 | + | 0.989913i | \(0.545248\pi\) | |||||||
\(318\) | 3.27295 | 0.183538 | ||||||||
\(319\) | 5.65062 | 0.316374 | ||||||||
\(320\) | 3.38938 | 0.189472 | ||||||||
\(321\) | 4.21127 | 0.235050 | ||||||||
\(322\) | −6.13055 | −0.341642 | ||||||||
\(323\) | 27.0581 | 1.50555 | ||||||||
\(324\) | 7.08840 | 0.393800 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.3560 | −1.29357 | ||||||||
\(327\) | −0.185308 | −0.0102475 | ||||||||
\(328\) | −0.0893760 | −0.00493496 | ||||||||
\(329\) | 11.1759 | 0.616150 | ||||||||
\(330\) | 1.30098 | 0.0716166 | ||||||||
\(331\) | 23.0874 | 1.26900 | 0.634499 | − | 0.772924i | \(-0.281207\pi\) | ||||
0.634499 | + | 0.772924i | \(0.281207\pi\) | |||||||
\(332\) | −3.23553 | −0.177573 | ||||||||
\(333\) | −26.9632 | −1.47758 | ||||||||
\(334\) | 21.7780 | 1.19164 | ||||||||
\(335\) | 0.988744 | 0.0540209 | ||||||||
\(336\) | −0.466545 | −0.0254521 | ||||||||
\(337\) | −29.1429 | −1.58751 | −0.793757 | − | 0.608235i | \(-0.791878\pi\) | ||||
−0.793757 | + | 0.608235i | \(0.791878\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.08696 | −0.113348 | ||||||||
\(340\) | 15.5277 | 0.842110 | ||||||||
\(341\) | −3.52691 | −0.190993 | ||||||||
\(342\) | −16.4330 | −0.888597 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 7.35374 | 0.396487 | ||||||||
\(345\) | 9.69421 | 0.521919 | ||||||||
\(346\) | 8.09733 | 0.435315 | ||||||||
\(347\) | −29.1082 | −1.56261 | −0.781306 | − | 0.624148i | \(-0.785446\pi\) | ||||
−0.781306 | + | 0.624148i | \(0.785446\pi\) | |||||||
\(348\) | 3.20429 | 0.171768 | ||||||||
\(349\) | −25.7802 | −1.37998 | −0.689992 | − | 0.723817i | \(-0.742386\pi\) | ||||
−0.689992 | + | 0.723817i | \(0.742386\pi\) | |||||||
\(350\) | 6.48787 | 0.346791 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.822730 | −0.0438517 | ||||||||
\(353\) | −9.91779 | −0.527871 | −0.263935 | − | 0.964540i | \(-0.585021\pi\) | ||||
−0.263935 | + | 0.964540i | \(0.585021\pi\) | |||||||
\(354\) | −0.812334 | −0.0431751 | ||||||||
\(355\) | −37.1082 | −1.96950 | ||||||||
\(356\) | −8.04265 | −0.426260 | ||||||||
\(357\) | −2.13738 | −0.113122 | ||||||||
\(358\) | 9.90883 | 0.523698 | ||||||||
\(359\) | −25.2683 | −1.33361 | −0.666804 | − | 0.745233i | \(-0.732338\pi\) | ||||
−0.666804 | + | 0.745233i | \(0.732338\pi\) | |||||||
\(360\) | −9.43038 | −0.497025 | ||||||||
\(361\) | 15.8833 | 0.835962 | ||||||||
\(362\) | −1.27902 | −0.0672236 | ||||||||
\(363\) | 4.81620 | 0.252785 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.1084 | −2.25640 | ||||||||
\(366\) | −1.11012 | −0.0580269 | ||||||||
\(367\) | 35.7838 | 1.86790 | 0.933950 | − | 0.357404i | \(-0.116338\pi\) | ||||
0.933950 | + | 0.357404i | \(0.116338\pi\) | |||||||
\(368\) | −6.13055 | −0.319577 | ||||||||
\(369\) | 0.248674 | 0.0129455 | ||||||||
\(370\) | 32.8460 | 1.70758 | ||||||||
\(371\) | −7.01530 | −0.364216 | ||||||||
\(372\) | −2.00000 | −0.103695 | ||||||||
\(373\) | −23.3304 | −1.20800 | −0.604000 | − | 0.796984i | \(-0.706427\pi\) | ||||
−0.604000 | + | 0.796984i | \(0.706427\pi\) | |||||||
\(374\) | −3.76917 | −0.194899 | ||||||||
\(375\) | −2.35277 | −0.121496 | ||||||||
\(376\) | 11.1759 | 0.576355 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 2.69772 | 0.138756 | ||||||||
\(379\) | 24.3066 | 1.24855 | 0.624274 | − | 0.781206i | \(-0.285395\pi\) | ||||
0.624274 | + | 0.781206i | \(0.285395\pi\) | |||||||
\(380\) | 20.0184 | 1.02692 | ||||||||
\(381\) | 0.251993 | 0.0129100 | ||||||||
\(382\) | −10.0342 | −0.513395 | ||||||||
\(383\) | −4.91150 | −0.250966 | −0.125483 | − | 0.992096i | \(-0.540048\pi\) | ||||
−0.125483 | + | 0.992096i | \(0.540048\pi\) | |||||||
\(384\) | −0.466545 | −0.0238083 | ||||||||
\(385\) | −2.78854 | −0.142117 | ||||||||
\(386\) | 15.8582 | 0.807162 | ||||||||
\(387\) | −20.4606 | −1.04007 | ||||||||
\(388\) | −14.7739 | −0.750029 | ||||||||
\(389\) | 5.14522 | 0.260873 | 0.130437 | − | 0.991457i | \(-0.458362\pi\) | ||||
0.130437 | + | 0.991457i | \(0.458362\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −28.0858 | −1.42036 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 3.60460 | 0.181828 | ||||||||
\(394\) | 14.8081 | 0.746019 | ||||||||
\(395\) | 33.7447 | 1.69788 | ||||||||
\(396\) | 2.28911 | 0.115032 | ||||||||
\(397\) | −12.3500 | −0.619827 | −0.309913 | − | 0.950765i | \(-0.600300\pi\) | ||||
−0.309913 | + | 0.950765i | \(0.600300\pi\) | |||||||
\(398\) | −2.55543 | −0.128092 | ||||||||
\(399\) | −2.75551 | −0.137948 | ||||||||
\(400\) | 6.48787 | 0.324394 | ||||||||
\(401\) | −32.4894 | −1.62244 | −0.811221 | − | 0.584739i | \(-0.801197\pi\) | ||||
−0.811221 | + | 0.584739i | \(0.801197\pi\) | |||||||
\(402\) | −0.136100 | −0.00678804 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −8.23976 | −0.409943 | ||||||||
\(405\) | 24.0253 | 1.19382 | ||||||||
\(406\) | −6.86813 | −0.340859 | ||||||||
\(407\) | −7.97296 | −0.395205 | ||||||||
\(408\) | −2.13738 | −0.105816 | ||||||||
\(409\) | −3.76834 | −0.186332 | −0.0931662 | − | 0.995651i | \(-0.529699\pi\) | ||||
−0.0931662 | + | 0.995651i | \(0.529699\pi\) | |||||||
\(410\) | −0.302929 | −0.0149606 | ||||||||
\(411\) | −5.85052 | −0.288585 | ||||||||
\(412\) | 13.3231 | 0.656383 | ||||||||
\(413\) | 1.74117 | 0.0856774 | ||||||||
\(414\) | 17.0572 | 0.838317 | ||||||||
\(415\) | −10.9664 | −0.538321 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.64396 | −0.276386 | ||||||||
\(418\) | −4.85921 | −0.237672 | ||||||||
\(419\) | −10.5301 | −0.514428 | −0.257214 | − | 0.966354i | \(-0.582805\pi\) | ||||
−0.257214 | + | 0.966354i | \(0.582805\pi\) | |||||||
\(420\) | −1.58130 | −0.0771594 | ||||||||
\(421\) | −24.9973 | −1.21830 | −0.609148 | − | 0.793057i | \(-0.708488\pi\) | ||||
−0.609148 | + | 0.793057i | \(0.708488\pi\) | |||||||
\(422\) | −8.63648 | −0.420417 | ||||||||
\(423\) | −31.0952 | −1.51190 | ||||||||
\(424\) | −7.01530 | −0.340693 | ||||||||
\(425\) | 29.7229 | 1.44177 | ||||||||
\(426\) | 5.10792 | 0.247479 | ||||||||
\(427\) | 2.37945 | 0.115150 | ||||||||
\(428\) | −9.02649 | −0.436312 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 24.9246 | 1.20197 | ||||||||
\(431\) | 11.9784 | 0.576979 | 0.288489 | − | 0.957483i | \(-0.406847\pi\) | ||||
0.288489 | + | 0.957483i | \(0.406847\pi\) | |||||||
\(432\) | 2.69772 | 0.129794 | ||||||||
\(433\) | 7.96950 | 0.382990 | 0.191495 | − | 0.981494i | \(-0.438666\pi\) | ||||
0.191495 | + | 0.981494i | \(0.438666\pi\) | |||||||
\(434\) | 4.28683 | 0.205775 | ||||||||
\(435\) | 10.8605 | 0.520723 | ||||||||
\(436\) | 0.397192 | 0.0190220 | ||||||||
\(437\) | −36.2083 | −1.73208 | ||||||||
\(438\) | 5.93384 | 0.283530 | ||||||||
\(439\) | 4.35655 | 0.207927 | 0.103963 | − | 0.994581i | \(-0.466848\pi\) | ||||
0.103963 | + | 0.994581i | \(0.466848\pi\) | |||||||
\(440\) | −2.78854 | −0.132939 | ||||||||
\(441\) | −2.78234 | −0.132492 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −11.4823 | −0.545542 | −0.272771 | − | 0.962079i | \(-0.587940\pi\) | ||||
−0.272771 | + | 0.962079i | \(0.587940\pi\) | |||||||
\(444\) | −4.52122 | −0.214568 | ||||||||
\(445\) | −27.2596 | −1.29223 | ||||||||
\(446\) | −19.9277 | −0.943603 | ||||||||
\(447\) | 7.93490 | 0.375308 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −29.5248 | −1.39336 | −0.696680 | − | 0.717382i | \(-0.745340\pi\) | ||||
−0.696680 | + | 0.717382i | \(0.745340\pi\) | |||||||
\(450\) | −18.0514 | −0.850953 | ||||||||
\(451\) | 0.0735323 | 0.00346250 | ||||||||
\(452\) | 4.47322 | 0.210402 | ||||||||
\(453\) | −2.58730 | −0.121562 | ||||||||
\(454\) | −0.352624 | −0.0165495 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.75551 | −0.129039 | ||||||||
\(457\) | −16.5981 | −0.776428 | −0.388214 | − | 0.921569i | \(-0.626908\pi\) | ||||
−0.388214 | + | 0.921569i | \(0.626908\pi\) | |||||||
\(458\) | −8.31317 | −0.388449 | ||||||||
\(459\) | 12.3591 | 0.576871 | ||||||||
\(460\) | −20.7787 | −0.968813 | ||||||||
\(461\) | −26.4422 | −1.23154 | −0.615769 | − | 0.787927i | \(-0.711154\pi\) | ||||
−0.615769 | + | 0.787927i | \(0.711154\pi\) | |||||||
\(462\) | 0.383841 | 0.0178579 | ||||||||
\(463\) | 10.4717 | 0.486663 | 0.243331 | − | 0.969943i | \(-0.421760\pi\) | ||||
0.243331 | + | 0.969943i | \(0.421760\pi\) | |||||||
\(464\) | −6.86813 | −0.318845 | ||||||||
\(465\) | −6.77875 | −0.314357 | ||||||||
\(466\) | 15.3798 | 0.712454 | ||||||||
\(467\) | −27.9010 | −1.29110 | −0.645551 | − | 0.763717i | \(-0.723372\pi\) | ||||
−0.645551 | + | 0.763717i | \(0.723372\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.291719 | 0.0134703 | ||||||||
\(470\) | 37.8795 | 1.74725 | ||||||||
\(471\) | −1.07003 | −0.0493046 | ||||||||
\(472\) | 1.74117 | 0.0801438 | ||||||||
\(473\) | −6.05015 | −0.278186 | ||||||||
\(474\) | −4.64493 | −0.213349 | ||||||||
\(475\) | 38.3187 | 1.75818 | ||||||||
\(476\) | 4.58130 | 0.209983 | ||||||||
\(477\) | 19.5189 | 0.893710 | ||||||||
\(478\) | −2.88606 | −0.132005 | ||||||||
\(479\) | 6.88133 | 0.314416 | 0.157208 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157208 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(480\) | −1.58130 | −0.0721760 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −6.26744 | −0.285474 | ||||||||
\(483\) | 2.86018 | 0.130142 | ||||||||
\(484\) | −10.3231 | −0.469232 | ||||||||
\(485\) | −50.0742 | −2.27375 | ||||||||
\(486\) | −11.4002 | −0.517124 | ||||||||
\(487\) | 40.8062 | 1.84911 | 0.924553 | − | 0.381053i | \(-0.124438\pi\) | ||||
0.924553 | + | 0.381053i | \(0.124438\pi\) | |||||||
\(488\) | 2.37945 | 0.107713 | ||||||||
\(489\) | 10.8966 | 0.492762 | ||||||||
\(490\) | 3.38938 | 0.153116 | ||||||||
\(491\) | 6.72706 | 0.303588 | 0.151794 | − | 0.988412i | \(-0.451495\pi\) | ||||
0.151794 | + | 0.988412i | \(0.451495\pi\) | |||||||
\(492\) | 0.0416979 | 0.00187989 | ||||||||
\(493\) | −31.4649 | −1.41711 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.75866 | 0.348726 | ||||||||
\(496\) | 4.28683 | 0.192484 | ||||||||
\(497\) | −10.9484 | −0.491102 | ||||||||
\(498\) | 1.50952 | 0.0676433 | ||||||||
\(499\) | −1.16200 | −0.0520184 | −0.0260092 | − | 0.999662i | \(-0.508280\pi\) | ||||
−0.0260092 | + | 0.999662i | \(0.508280\pi\) | |||||||
\(500\) | 5.04295 | 0.225528 | ||||||||
\(501\) | −10.1604 | −0.453933 | ||||||||
\(502\) | 17.2665 | 0.770641 | ||||||||
\(503\) | 9.95053 | 0.443672 | 0.221836 | − | 0.975084i | \(-0.428795\pi\) | ||||
0.221836 | + | 0.975084i | \(0.428795\pi\) | |||||||
\(504\) | −2.78234 | −0.123935 | ||||||||
\(505\) | −27.9277 | −1.24276 | ||||||||
\(506\) | 5.04379 | 0.224224 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.540127 | −0.0239642 | ||||||||
\(509\) | −0.0522003 | −0.00231374 | −0.00115687 | − | 0.999999i | \(-0.500368\pi\) | ||||
−0.00115687 | + | 0.999999i | \(0.500368\pi\) | |||||||
\(510\) | −7.24439 | −0.320787 | ||||||||
\(511\) | −12.7187 | −0.562641 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 15.9333 | 0.703472 | ||||||||
\(514\) | −11.1931 | −0.493706 | ||||||||
\(515\) | 45.1570 | 1.98986 | ||||||||
\(516\) | −3.43085 | −0.151035 | ||||||||
\(517\) | −9.19479 | −0.404386 | ||||||||
\(518\) | 9.69086 | 0.425792 | ||||||||
\(519\) | −3.77777 | −0.165826 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.0984 | 1.14339 | 0.571695 | − | 0.820466i | \(-0.306286\pi\) | ||||
0.571695 | + | 0.820466i | \(0.306286\pi\) | |||||||
\(522\) | 19.1094 | 0.836397 | ||||||||
\(523\) | −19.5321 | −0.854080 | −0.427040 | − | 0.904233i | \(-0.640444\pi\) | ||||
−0.427040 | + | 0.904233i | \(0.640444\pi\) | |||||||
\(524\) | −7.72615 | −0.337518 | ||||||||
\(525\) | −3.02688 | −0.132104 | ||||||||
\(526\) | −28.5826 | −1.24626 | ||||||||
\(527\) | 19.6392 | 0.855499 | ||||||||
\(528\) | 0.383841 | 0.0167045 | ||||||||
\(529\) | 14.5836 | 0.634069 | ||||||||
\(530\) | −23.7775 | −1.03283 | ||||||||
\(531\) | −4.84452 | −0.210234 | ||||||||
\(532\) | 5.90621 | 0.256067 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 3.75226 | 0.162376 | ||||||||
\(535\) | −30.5942 | −1.32270 | ||||||||
\(536\) | 0.291719 | 0.0126003 | ||||||||
\(537\) | −4.62292 | −0.199494 | ||||||||
\(538\) | −18.3754 | −0.792219 | ||||||||
\(539\) | −0.822730 | −0.0354375 | ||||||||
\(540\) | 9.14359 | 0.393477 | ||||||||
\(541\) | −32.8802 | −1.41363 | −0.706814 | − | 0.707399i | \(-0.749868\pi\) | ||||
−0.706814 | + | 0.707399i | \(0.749868\pi\) | |||||||
\(542\) | −20.3825 | −0.875504 | ||||||||
\(543\) | 0.596719 | 0.0256077 | ||||||||
\(544\) | 4.58130 | 0.196421 | ||||||||
\(545\) | 1.34623 | 0.0576662 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.0180 | −1.66829 | −0.834144 | − | 0.551546i | \(-0.814038\pi\) | ||||
−0.834144 | + | 0.551546i | \(0.814038\pi\) | |||||||
\(548\) | 12.5401 | 0.535687 | ||||||||
\(549\) | −6.62043 | −0.282553 | ||||||||
\(550\) | −5.33777 | −0.227603 | ||||||||
\(551\) | −40.5646 | −1.72811 | ||||||||
\(552\) | 2.86018 | 0.121737 | ||||||||
\(553\) | 9.95602 | 0.423373 | ||||||||
\(554\) | 7.23219 | 0.307266 | ||||||||
\(555\) | −15.3241 | −0.650473 | ||||||||
\(556\) | 12.0974 | 0.513042 | ||||||||
\(557\) | 29.5492 | 1.25204 | 0.626020 | − | 0.779807i | \(-0.284683\pi\) | ||||
0.626020 | + | 0.779807i | \(0.284683\pi\) | |||||||
\(558\) | −11.9274 | −0.504927 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.38938 | 0.143227 | ||||||||
\(561\) | 1.75849 | 0.0742434 | ||||||||
\(562\) | 12.4585 | 0.525532 | ||||||||
\(563\) | −27.1323 | −1.14349 | −0.571745 | − | 0.820431i | \(-0.693733\pi\) | ||||
−0.571745 | + | 0.820431i | \(0.693733\pi\) | |||||||
\(564\) | −5.21408 | −0.219552 | ||||||||
\(565\) | 15.1614 | 0.637845 | ||||||||
\(566\) | 13.0607 | 0.548982 | ||||||||
\(567\) | 7.08840 | 0.297685 | ||||||||
\(568\) | −10.9484 | −0.459384 | ||||||||
\(569\) | 42.4594 | 1.77999 | 0.889996 | − | 0.455969i | \(-0.150707\pi\) | ||||
0.889996 | + | 0.455969i | \(0.150707\pi\) | |||||||
\(570\) | −9.33946 | −0.391187 | ||||||||
\(571\) | 11.2678 | 0.471543 | 0.235771 | − | 0.971809i | \(-0.424238\pi\) | ||||
0.235771 | + | 0.971809i | \(0.424238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.68141 | 0.195569 | ||||||||
\(574\) | −0.0893760 | −0.00373048 | ||||||||
\(575\) | −39.7742 | −1.65870 | ||||||||
\(576\) | −2.78234 | −0.115931 | ||||||||
\(577\) | −22.8987 | −0.953286 | −0.476643 | − | 0.879097i | \(-0.658147\pi\) | ||||
−0.476643 | + | 0.879097i | \(0.658147\pi\) | |||||||
\(578\) | 3.98828 | 0.165890 | ||||||||
\(579\) | −7.39857 | −0.307474 | ||||||||
\(580\) | −23.2787 | −0.966594 | ||||||||
\(581\) | −3.23553 | −0.134233 | ||||||||
\(582\) | 6.89267 | 0.285710 | ||||||||
\(583\) | 5.77170 | 0.239039 | ||||||||
\(584\) | −12.7187 | −0.526303 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.5582 | −0.601393 | ||||||||
\(587\) | 35.8019 | 1.47770 | 0.738852 | − | 0.673868i | \(-0.235368\pi\) | ||||
0.738852 | + | 0.673868i | \(0.235368\pi\) | |||||||
\(588\) | −0.466545 | −0.0192400 | ||||||||
\(589\) | 25.3189 | 1.04325 | ||||||||
\(590\) | 5.90148 | 0.242960 | ||||||||
\(591\) | −6.90862 | −0.284183 | ||||||||
\(592\) | 9.69086 | 0.398292 | ||||||||
\(593\) | 14.6093 | 0.599931 | 0.299965 | − | 0.953950i | \(-0.403025\pi\) | ||||
0.299965 | + | 0.953950i | \(0.403025\pi\) | |||||||
\(594\) | −2.21950 | −0.0910670 | ||||||||
\(595\) | 15.5277 | 0.636575 | ||||||||
\(596\) | −17.0078 | −0.696666 | ||||||||
\(597\) | 1.19222 | 0.0487944 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.5729 | −1.53519 | −0.767594 | − | 0.640936i | \(-0.778546\pi\) | ||||
−0.767594 | + | 0.640936i | \(0.778546\pi\) | |||||||
\(600\) | −3.02688 | −0.123572 | ||||||||
\(601\) | −5.45158 | −0.222375 | −0.111187 | − | 0.993799i | \(-0.535465\pi\) | ||||
−0.111187 | + | 0.993799i | \(0.535465\pi\) | |||||||
\(602\) | 7.35374 | 0.299716 | ||||||||
\(603\) | −0.811659 | −0.0330533 | ||||||||
\(604\) | 5.54567 | 0.225650 | ||||||||
\(605\) | −34.9889 | −1.42250 | ||||||||
\(606\) | 3.84422 | 0.156161 | ||||||||
\(607\) | −39.9387 | −1.62106 | −0.810531 | − | 0.585696i | \(-0.800821\pi\) | ||||
−0.810531 | + | 0.585696i | \(0.800821\pi\) | |||||||
\(608\) | 5.90621 | 0.239528 | ||||||||
\(609\) | 3.20429 | 0.129844 | ||||||||
\(610\) | 8.06485 | 0.326536 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12.7467 | −0.515255 | ||||||||
\(613\) | 16.6552 | 0.672696 | 0.336348 | − | 0.941738i | \(-0.390808\pi\) | ||||
0.336348 | + | 0.941738i | \(0.390808\pi\) | |||||||
\(614\) | −3.24267 | −0.130864 | ||||||||
\(615\) | 0.141330 | 0.00569897 | ||||||||
\(616\) | −0.822730 | −0.0331487 | ||||||||
\(617\) | 26.9652 | 1.08558 | 0.542788 | − | 0.839869i | \(-0.317369\pi\) | ||||
0.542788 | + | 0.839869i | \(0.317369\pi\) | |||||||
\(618\) | −6.21583 | −0.250037 | ||||||||
\(619\) | 12.7533 | 0.512597 | 0.256298 | − | 0.966598i | \(-0.417497\pi\) | ||||
0.256298 | + | 0.966598i | \(0.417497\pi\) | |||||||
\(620\) | 14.5297 | 0.583526 | ||||||||
\(621\) | −16.5385 | −0.663667 | ||||||||
\(622\) | 10.2709 | 0.411825 | ||||||||
\(623\) | −8.04265 | −0.322222 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.3469 | −0.613875 | ||||||||
\(626\) | −6.13382 | −0.245157 | ||||||||
\(627\) | 2.26704 | 0.0905369 | ||||||||
\(628\) | 2.29353 | 0.0915218 | ||||||||
\(629\) | 44.3967 | 1.77021 | ||||||||
\(630\) | −9.43038 | −0.375715 | ||||||||
\(631\) | 37.5529 | 1.49496 | 0.747479 | − | 0.664286i | \(-0.231264\pi\) | ||||
0.747479 | + | 0.664286i | \(0.231264\pi\) | |||||||
\(632\) | 9.95602 | 0.396029 | ||||||||
\(633\) | 4.02931 | 0.160151 | ||||||||
\(634\) | −5.04487 | −0.200357 | ||||||||
\(635\) | −1.83069 | −0.0726488 | ||||||||
\(636\) | 3.27295 | 0.129781 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.65062 | 0.223710 | ||||||||
\(639\) | 30.4621 | 1.20506 | ||||||||
\(640\) | 3.38938 | 0.133977 | ||||||||
\(641\) | 1.97623 | 0.0780564 | 0.0390282 | − | 0.999238i | \(-0.487574\pi\) | ||||
0.0390282 | + | 0.999238i | \(0.487574\pi\) | |||||||
\(642\) | 4.21127 | 0.166205 | ||||||||
\(643\) | 39.0704 | 1.54079 | 0.770394 | − | 0.637568i | \(-0.220060\pi\) | ||||
0.770394 | + | 0.637568i | \(0.220060\pi\) | |||||||
\(644\) | −6.13055 | −0.241577 | ||||||||
\(645\) | −11.6284 | −0.457870 | ||||||||
\(646\) | 27.0581 | 1.06459 | ||||||||
\(647\) | 12.1051 | 0.475900 | 0.237950 | − | 0.971277i | \(-0.423525\pi\) | ||||
0.237950 | + | 0.971277i | \(0.423525\pi\) | |||||||
\(648\) | 7.08840 | 0.278459 | ||||||||
\(649\) | −1.43251 | −0.0562311 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.00000 | −0.0783862 | ||||||||
\(652\) | −23.3560 | −0.914691 | ||||||||
\(653\) | 40.2464 | 1.57496 | 0.787481 | − | 0.616338i | \(-0.211385\pi\) | ||||
0.787481 | + | 0.616338i | \(0.211385\pi\) | |||||||
\(654\) | −0.185308 | −0.00724611 | ||||||||
\(655\) | −26.1868 | −1.02320 | ||||||||
\(656\) | −0.0893760 | −0.00348955 | ||||||||
\(657\) | 35.3876 | 1.38060 | ||||||||
\(658\) | 11.1759 | 0.435684 | ||||||||
\(659\) | −3.62327 | −0.141143 | −0.0705714 | − | 0.997507i | \(-0.522482\pi\) | ||||
−0.0705714 | + | 0.997507i | \(0.522482\pi\) | |||||||
\(660\) | 1.30098 | 0.0506406 | ||||||||
\(661\) | 23.6365 | 0.919352 | 0.459676 | − | 0.888087i | \(-0.347965\pi\) | ||||
0.459676 | + | 0.888087i | \(0.347965\pi\) | |||||||
\(662\) | 23.0874 | 0.897317 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.23553 | −0.125563 | ||||||||
\(665\) | 20.0184 | 0.776278 | ||||||||
\(666\) | −26.9632 | −1.04480 | ||||||||
\(667\) | 42.1054 | 1.63033 | ||||||||
\(668\) | 21.7780 | 0.842614 | ||||||||
\(669\) | 9.29716 | 0.359449 | ||||||||
\(670\) | 0.988744 | 0.0381985 | ||||||||
\(671\) | −1.95764 | −0.0755740 | ||||||||
\(672\) | −0.466545 | −0.0179974 | ||||||||
\(673\) | 46.8710 | 1.80674 | 0.903372 | − | 0.428859i | \(-0.141084\pi\) | ||||
0.903372 | + | 0.428859i | \(0.141084\pi\) | |||||||
\(674\) | −29.1429 | −1.12254 | ||||||||
\(675\) | 17.5025 | 0.673670 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.7304 | −0.527704 | −0.263852 | − | 0.964563i | \(-0.584993\pi\) | ||||
−0.263852 | + | 0.964563i | \(0.584993\pi\) | |||||||
\(678\) | −2.08696 | −0.0801491 | ||||||||
\(679\) | −14.7739 | −0.566969 | ||||||||
\(680\) | 15.5277 | 0.595462 | ||||||||
\(681\) | 0.164515 | 0.00630423 | ||||||||
\(682\) | −3.52691 | −0.135052 | ||||||||
\(683\) | 3.50578 | 0.134145 | 0.0670725 | − | 0.997748i | \(-0.478634\pi\) | ||||
0.0670725 | + | 0.997748i | \(0.478634\pi\) | |||||||
\(684\) | −16.4330 | −0.628333 | ||||||||
\(685\) | 42.5031 | 1.62396 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 3.87847 | 0.147973 | ||||||||
\(688\) | 7.35374 | 0.280359 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 9.69421 | 0.369052 | ||||||||
\(691\) | −31.7769 | −1.20885 | −0.604426 | − | 0.796662i | \(-0.706597\pi\) | ||||
−0.604426 | + | 0.796662i | \(0.706597\pi\) | |||||||
\(692\) | 8.09733 | 0.307814 | ||||||||
\(693\) | 2.28911 | 0.0869562 | ||||||||
\(694\) | −29.1082 | −1.10493 | ||||||||
\(695\) | 41.0025 | 1.55531 | ||||||||
\(696\) | 3.20429 | 0.121458 | ||||||||
\(697\) | −0.409458 | −0.0155093 | ||||||||
\(698\) | −25.7802 | −0.975796 | ||||||||
\(699\) | −7.17535 | −0.271397 | ||||||||
\(700\) | 6.48787 | 0.245218 | ||||||||
\(701\) | 31.6828 | 1.19664 | 0.598322 | − | 0.801256i | \(-0.295834\pi\) | ||||
0.598322 | + | 0.801256i | \(0.295834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 57.2362 | 2.15870 | ||||||||
\(704\) | −0.822730 | −0.0310078 | ||||||||
\(705\) | −17.6725 | −0.665584 | ||||||||
\(706\) | −9.91779 | −0.373261 | ||||||||
\(707\) | −8.23976 | −0.309888 | ||||||||
\(708\) | −0.812334 | −0.0305294 | ||||||||
\(709\) | −35.3147 | −1.32627 | −0.663137 | − | 0.748498i | \(-0.730775\pi\) | ||||
−0.663137 | + | 0.748498i | \(0.730775\pi\) | |||||||
\(710\) | −37.1082 | −1.39265 | ||||||||
\(711\) | −27.7010 | −1.03887 | ||||||||
\(712\) | −8.04265 | −0.301411 | ||||||||
\(713\) | −26.2806 | −0.984217 | ||||||||
\(714\) | −2.13738 | −0.0799895 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.90883 | 0.370310 | ||||||||
\(717\) | 1.34648 | 0.0502850 | ||||||||
\(718\) | −25.2683 | −0.943003 | ||||||||
\(719\) | −1.21956 | −0.0454818 | −0.0227409 | − | 0.999741i | \(-0.507239\pi\) | ||||
−0.0227409 | + | 0.999741i | \(0.507239\pi\) | |||||||
\(720\) | −9.43038 | −0.351450 | ||||||||
\(721\) | 13.3231 | 0.496179 | ||||||||
\(722\) | 15.8833 | 0.591114 | ||||||||
\(723\) | 2.92404 | 0.108746 | ||||||||
\(724\) | −1.27902 | −0.0475343 | ||||||||
\(725\) | −44.5595 | −1.65490 | ||||||||
\(726\) | 4.81620 | 0.178746 | ||||||||
\(727\) | −5.75380 | −0.213397 | −0.106698 | − | 0.994291i | \(-0.534028\pi\) | ||||
−0.106698 | + | 0.994291i | \(0.534028\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.9465 | −0.590611 | ||||||||
\(730\) | −43.1084 | −1.59551 | ||||||||
\(731\) | 33.6897 | 1.24606 | ||||||||
\(732\) | −1.11012 | −0.0410312 | ||||||||
\(733\) | 35.2258 | 1.30110 | 0.650548 | − | 0.759466i | \(-0.274539\pi\) | ||||
0.650548 | + | 0.759466i | \(0.274539\pi\) | |||||||
\(734\) | 35.7838 | 1.32080 | ||||||||
\(735\) | −1.58130 | −0.0583270 | ||||||||
\(736\) | −6.13055 | −0.225975 | ||||||||
\(737\) | −0.240006 | −0.00884073 | ||||||||
\(738\) | 0.248674 | 0.00915382 | ||||||||
\(739\) | 29.3524 | 1.07975 | 0.539873 | − | 0.841746i | \(-0.318472\pi\) | ||||
0.539873 | + | 0.841746i | \(0.318472\pi\) | |||||||
\(740\) | 32.8460 | 1.20744 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.01530 | −0.257540 | ||||||||
\(743\) | −14.9838 | −0.549702 | −0.274851 | − | 0.961487i | \(-0.588629\pi\) | ||||
−0.274851 | + | 0.961487i | \(0.588629\pi\) | |||||||
\(744\) | −2.00000 | −0.0733236 | ||||||||
\(745\) | −57.6458 | −2.11198 | ||||||||
\(746\) | −23.3304 | −0.854185 | ||||||||
\(747\) | 9.00234 | 0.329378 | ||||||||
\(748\) | −3.76917 | −0.137815 | ||||||||
\(749\) | −9.02649 | −0.329821 | ||||||||
\(750\) | −2.35277 | −0.0859108 | ||||||||
\(751\) | 43.8390 | 1.59971 | 0.799855 | − | 0.600194i | \(-0.204910\pi\) | ||||
0.799855 | + | 0.600194i | \(0.204910\pi\) | |||||||
\(752\) | 11.1759 | 0.407545 | ||||||||
\(753\) | −8.05560 | −0.293562 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.7963 | 0.684069 | ||||||||
\(756\) | 2.69772 | 0.0981151 | ||||||||
\(757\) | −36.3597 | −1.32152 | −0.660758 | − | 0.750599i | \(-0.729765\pi\) | ||||
−0.660758 | + | 0.750599i | \(0.729765\pi\) | |||||||
\(758\) | 24.3066 | 0.882856 | ||||||||
\(759\) | −2.35315 | −0.0854140 | ||||||||
\(760\) | 20.0184 | 0.726142 | ||||||||
\(761\) | −18.2335 | −0.660962 | −0.330481 | − | 0.943813i | \(-0.607211\pi\) | ||||
−0.330481 | + | 0.943813i | \(0.607211\pi\) | |||||||
\(762\) | 0.251993 | 0.00912876 | ||||||||
\(763\) | 0.397192 | 0.0143793 | ||||||||
\(764\) | −10.0342 | −0.363025 | ||||||||
\(765\) | −43.2034 | −1.56202 | ||||||||
\(766\) | −4.91150 | −0.177460 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.466545 | −0.0168350 | ||||||||
\(769\) | −6.54565 | −0.236042 | −0.118021 | − | 0.993011i | \(-0.537655\pi\) | ||||
−0.118021 | + | 0.993011i | \(0.537655\pi\) | |||||||
\(770\) | −2.78854 | −0.100492 | ||||||||
\(771\) | 5.22208 | 0.188069 | ||||||||
\(772\) | 15.8582 | 0.570750 | ||||||||
\(773\) | −44.6466 | −1.60583 | −0.802913 | − | 0.596097i | \(-0.796718\pi\) | ||||
−0.802913 | + | 0.596097i | \(0.796718\pi\) | |||||||
\(774\) | −20.4606 | −0.735440 | ||||||||
\(775\) | 27.8124 | 0.999051 | ||||||||
\(776\) | −14.7739 | −0.530351 | ||||||||
\(777\) | −4.52122 | −0.162198 | ||||||||
\(778\) | 5.14522 | 0.184465 | ||||||||
\(779\) | −0.527873 | −0.0189130 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00757 | 0.322316 | ||||||||
\(782\) | −28.0858 | −1.00435 | ||||||||
\(783\) | −18.5283 | −0.662147 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 7.77363 | 0.277453 | ||||||||
\(786\) | 3.60460 | 0.128572 | ||||||||
\(787\) | 25.0526 | 0.893028 | 0.446514 | − | 0.894777i | \(-0.352665\pi\) | ||||
0.446514 | + | 0.894777i | \(0.352665\pi\) | |||||||
\(788\) | 14.8081 | 0.527515 | ||||||||
\(789\) | 13.3351 | 0.474742 | ||||||||
\(790\) | 33.7447 | 1.20058 | ||||||||
\(791\) | 4.47322 | 0.159049 | ||||||||
\(792\) | 2.28911 | 0.0813400 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.3500 | −0.438284 | ||||||||
\(795\) | 11.0933 | 0.393438 | ||||||||
\(796\) | −2.55543 | −0.0905747 | ||||||||
\(797\) | 27.8264 | 0.985662 | 0.492831 | − | 0.870125i | \(-0.335962\pi\) | ||||
0.492831 | + | 0.870125i | \(0.335962\pi\) | |||||||
\(798\) | −2.75551 | −0.0975440 | ||||||||
\(799\) | 51.2003 | 1.81134 | ||||||||
\(800\) | 6.48787 | 0.229381 | ||||||||
\(801\) | 22.3774 | 0.790665 | ||||||||
\(802\) | −32.4894 | −1.14724 | ||||||||
\(803\) | 10.4640 | 0.369268 | ||||||||
\(804\) | −0.136100 | −0.00479987 | ||||||||
\(805\) | −20.7787 | −0.732354 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.57294 | 0.301782 | ||||||||
\(808\) | −8.23976 | −0.289874 | ||||||||
\(809\) | 7.49650 | 0.263563 | 0.131781 | − | 0.991279i | \(-0.457930\pi\) | ||||
0.131781 | + | 0.991279i | \(0.457930\pi\) | |||||||
\(810\) | 24.0253 | 0.844161 | ||||||||
\(811\) | −9.88726 | −0.347189 | −0.173594 | − | 0.984817i | \(-0.555538\pi\) | ||||
−0.173594 | + | 0.984817i | \(0.555538\pi\) | |||||||
\(812\) | −6.86813 | −0.241024 | ||||||||
\(813\) | 9.50936 | 0.333508 | ||||||||
\(814\) | −7.97296 | −0.279452 | ||||||||
\(815\) | −79.1622 | −2.77293 | ||||||||
\(816\) | −2.13738 | −0.0748233 | ||||||||
\(817\) | 43.4327 | 1.51952 | ||||||||
\(818\) | −3.76834 | −0.131757 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.302929 | −0.0105787 | ||||||||
\(821\) | 14.3675 | 0.501430 | 0.250715 | − | 0.968061i | \(-0.419334\pi\) | ||||
0.250715 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(822\) | −5.85052 | −0.204060 | ||||||||
\(823\) | 11.8869 | 0.414350 | 0.207175 | − | 0.978304i | \(-0.433573\pi\) | ||||
0.207175 | + | 0.978304i | \(0.433573\pi\) | |||||||
\(824\) | 13.3231 | 0.464133 | ||||||||
\(825\) | 2.49031 | 0.0867014 | ||||||||
\(826\) | 1.74117 | 0.0605830 | ||||||||
\(827\) | −29.0884 | −1.01150 | −0.505752 | − | 0.862679i | \(-0.668785\pi\) | ||||
−0.505752 | + | 0.862679i | \(0.668785\pi\) | |||||||
\(828\) | 17.0572 | 0.592780 | ||||||||
\(829\) | −49.6286 | −1.72367 | −0.861836 | − | 0.507187i | \(-0.830685\pi\) | ||||
−0.861836 | + | 0.507187i | \(0.830685\pi\) | |||||||
\(830\) | −10.9664 | −0.380651 | ||||||||
\(831\) | −3.37414 | −0.117048 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.58130 | 0.158733 | ||||||||
\(834\) | −5.64396 | −0.195434 | ||||||||
\(835\) | 73.8137 | 2.55443 | ||||||||
\(836\) | −4.85921 | −0.168059 | ||||||||
\(837\) | 11.5647 | 0.399734 | ||||||||
\(838\) | −10.5301 | −0.363755 | ||||||||
\(839\) | −4.61692 | −0.159394 | −0.0796969 | − | 0.996819i | \(-0.525395\pi\) | ||||
−0.0796969 | + | 0.996819i | \(0.525395\pi\) | |||||||
\(840\) | −1.58130 | −0.0545599 | ||||||||
\(841\) | 18.1712 | 0.626593 | ||||||||
\(842\) | −24.9973 | −0.861465 | ||||||||
\(843\) | −5.81247 | −0.200192 | ||||||||
\(844\) | −8.63648 | −0.297280 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −31.0952 | −1.06908 | ||||||||
\(847\) | −10.3231 | −0.354706 | ||||||||
\(848\) | −7.01530 | −0.240906 | ||||||||
\(849\) | −6.09341 | −0.209125 | ||||||||
\(850\) | 29.7229 | 1.01949 | ||||||||
\(851\) | −59.4103 | −2.03656 | ||||||||
\(852\) | 5.10792 | 0.174994 | ||||||||
\(853\) | 37.8266 | 1.29516 | 0.647579 | − | 0.761999i | \(-0.275782\pi\) | ||||
0.647579 | + | 0.761999i | \(0.275782\pi\) | |||||||
\(854\) | 2.37945 | 0.0814231 | ||||||||
\(855\) | −55.6978 | −1.90482 | ||||||||
\(856\) | −9.02649 | −0.308519 | ||||||||
\(857\) | −30.1652 | −1.03042 | −0.515211 | − | 0.857063i | \(-0.672287\pi\) | ||||
−0.515211 | + | 0.857063i | \(0.672287\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.6316 | 0.362745 | 0.181372 | − | 0.983414i | \(-0.441946\pi\) | ||||
0.181372 | + | 0.983414i | \(0.441946\pi\) | |||||||
\(860\) | 24.9246 | 0.849922 | ||||||||
\(861\) | 0.0416979 | 0.00142106 | ||||||||
\(862\) | 11.9784 | 0.407986 | ||||||||
\(863\) | 23.8352 | 0.811360 | 0.405680 | − | 0.914015i | \(-0.367035\pi\) | ||||
0.405680 | + | 0.914015i | \(0.367035\pi\) | |||||||
\(864\) | 2.69772 | 0.0917783 | ||||||||
\(865\) | 27.4449 | 0.933154 | ||||||||
\(866\) | 7.96950 | 0.270814 | ||||||||
\(867\) | −1.86071 | −0.0631931 | ||||||||
\(868\) | 4.28683 | 0.145505 | ||||||||
\(869\) | −8.19112 | −0.277865 | ||||||||
\(870\) | 10.8605 | 0.368207 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.397192 | 0.0134506 | ||||||||
\(873\) | 41.1059 | 1.39122 | ||||||||
\(874\) | −36.2083 | −1.22476 | ||||||||
\(875\) | 5.04295 | 0.170483 | ||||||||
\(876\) | 5.93384 | 0.200486 | ||||||||
\(877\) | −28.4246 | −0.959829 | −0.479915 | − | 0.877315i | \(-0.659332\pi\) | ||||
−0.479915 | + | 0.877315i | \(0.659332\pi\) | |||||||
\(878\) | 4.35655 | 0.147026 | ||||||||
\(879\) | 6.79205 | 0.229090 | ||||||||
\(880\) | −2.78854 | −0.0940017 | ||||||||
\(881\) | 55.1829 | 1.85916 | 0.929580 | − | 0.368621i | \(-0.120170\pi\) | ||||
0.929580 | + | 0.368621i | \(0.120170\pi\) | |||||||
\(882\) | −2.78234 | −0.0936861 | ||||||||
\(883\) | −9.18216 | −0.309004 | −0.154502 | − | 0.987992i | \(-0.549377\pi\) | ||||
−0.154502 | + | 0.987992i | \(0.549377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.75331 | −0.0925514 | ||||||||
\(886\) | −11.4823 | −0.385757 | ||||||||
\(887\) | 33.5715 | 1.12722 | 0.563610 | − | 0.826041i | \(-0.309412\pi\) | ||||
0.563610 | + | 0.826041i | \(0.309412\pi\) | |||||||
\(888\) | −4.52122 | −0.151722 | ||||||||
\(889\) | −0.540127 | −0.0181153 | ||||||||
\(890\) | −27.2596 | −0.913743 | ||||||||
\(891\) | −5.83184 | −0.195374 | ||||||||
\(892\) | −19.9277 | −0.667228 | ||||||||
\(893\) | 66.0074 | 2.20885 | ||||||||
\(894\) | 7.93490 | 0.265383 | ||||||||
\(895\) | 33.5848 | 1.12261 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.5248 | −0.985255 | ||||||||
\(899\) | −29.4425 | −0.981963 | ||||||||
\(900\) | −18.0514 | −0.601715 | ||||||||
\(901\) | −32.1392 | −1.07071 | ||||||||
\(902\) | 0.0735323 | 0.00244836 | ||||||||
\(903\) | −3.43085 | −0.114172 | ||||||||
\(904\) | 4.47322 | 0.148777 | ||||||||
\(905\) | −4.33507 | −0.144103 | ||||||||
\(906\) | −2.58730 | −0.0859574 | ||||||||
\(907\) | 11.0349 | 0.366409 | 0.183205 | − | 0.983075i | \(-0.441353\pi\) | ||||
0.183205 | + | 0.983075i | \(0.441353\pi\) | |||||||
\(908\) | −0.352624 | −0.0117022 | ||||||||
\(909\) | 22.9258 | 0.760400 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 59.9931 | 1.98766 | 0.993830 | − | 0.110917i | \(-0.0353789\pi\) | ||||
0.993830 | + | 0.110917i | \(0.0353789\pi\) | |||||||
\(912\) | −2.75551 | −0.0912441 | ||||||||
\(913\) | 2.66197 | 0.0880984 | ||||||||
\(914\) | −16.5981 | −0.549018 | ||||||||
\(915\) | −3.76261 | −0.124388 | ||||||||
\(916\) | −8.31317 | −0.274675 | ||||||||
\(917\) | −7.72615 | −0.255140 | ||||||||
\(918\) | 12.3591 | 0.407910 | ||||||||
\(919\) | 35.6537 | 1.17611 | 0.588053 | − | 0.808822i | \(-0.299895\pi\) | ||||
0.588053 | + | 0.808822i | \(0.299895\pi\) | |||||||
\(920\) | −20.7787 | −0.685054 | ||||||||
\(921\) | 1.51285 | 0.0498502 | ||||||||
\(922\) | −26.4422 | −0.870828 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.383841 | 0.0126274 | ||||||||
\(925\) | 62.8730 | 2.06725 | ||||||||
\(926\) | 10.4717 | 0.344123 | ||||||||
\(927\) | −37.0694 | −1.21752 | ||||||||
\(928\) | −6.86813 | −0.225457 | ||||||||
\(929\) | −29.0302 | −0.952450 | −0.476225 | − | 0.879324i | \(-0.657995\pi\) | ||||
−0.476225 | + | 0.879324i | \(0.657995\pi\) | |||||||
\(930\) | −6.77875 | −0.222284 | ||||||||
\(931\) | 5.90621 | 0.193568 | ||||||||
\(932\) | 15.3798 | 0.503781 | ||||||||
\(933\) | −4.79183 | −0.156877 | ||||||||
\(934\) | −27.9010 | −0.912947 | ||||||||
\(935\) | −12.7751 | −0.417792 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.2635 | 1.25001 | 0.625006 | − | 0.780620i | \(-0.285096\pi\) | ||||
0.625006 | + | 0.780620i | \(0.285096\pi\) | |||||||
\(938\) | 0.291719 | 0.00952495 | ||||||||
\(939\) | 2.86170 | 0.0933882 | ||||||||
\(940\) | 37.8795 | 1.23549 | ||||||||
\(941\) | 4.14746 | 0.135203 | 0.0676017 | − | 0.997712i | \(-0.478465\pi\) | ||||
0.0676017 | + | 0.997712i | \(0.478465\pi\) | |||||||
\(942\) | −1.07003 | −0.0348636 | ||||||||
\(943\) | 0.547924 | 0.0178428 | ||||||||
\(944\) | 1.74117 | 0.0566702 | ||||||||
\(945\) | 9.14359 | 0.297441 | ||||||||
\(946\) | −6.05015 | −0.196707 | ||||||||
\(947\) | −1.00792 | −0.0327530 | −0.0163765 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163765 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(948\) | −4.64493 | −0.150860 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 38.3187 | 1.24322 | ||||||||
\(951\) | 2.35366 | 0.0763226 | ||||||||
\(952\) | 4.58130 | 0.148481 | ||||||||
\(953\) | 16.5029 | 0.534582 | 0.267291 | − | 0.963616i | \(-0.413871\pi\) | ||||
0.267291 | + | 0.963616i | \(0.413871\pi\) | |||||||
\(954\) | 19.5189 | 0.631948 | ||||||||
\(955\) | −34.0097 | −1.10053 | ||||||||
\(956\) | −2.88606 | −0.0933418 | ||||||||
\(957\) | −2.63627 | −0.0852184 | ||||||||
\(958\) | 6.88133 | 0.222326 | ||||||||
\(959\) | 12.5401 | 0.404941 | ||||||||
\(960\) | −1.58130 | −0.0510361 | ||||||||
\(961\) | −12.6231 | −0.407196 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 25.1147 | 0.809311 | ||||||||
\(964\) | −6.26744 | −0.201861 | ||||||||
\(965\) | 53.7495 | 1.73026 | ||||||||
\(966\) | 2.86018 | 0.0920246 | ||||||||
\(967\) | −37.7765 | −1.21481 | −0.607406 | − | 0.794392i | \(-0.707790\pi\) | ||||
−0.607406 | + | 0.794392i | \(0.707790\pi\) | |||||||
\(968\) | −10.3231 | −0.331797 | ||||||||
\(969\) | −12.6238 | −0.405535 | ||||||||
\(970\) | −50.0742 | −1.60779 | ||||||||
\(971\) | −48.3122 | −1.55041 | −0.775206 | − | 0.631709i | \(-0.782354\pi\) | ||||
−0.775206 | + | 0.631709i | \(0.782354\pi\) | |||||||
\(972\) | −11.4002 | −0.365662 | ||||||||
\(973\) | 12.0974 | 0.387823 | ||||||||
\(974\) | 40.8062 | 1.30752 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.37945 | 0.0761643 | ||||||||
\(977\) | −16.3041 | −0.521615 | −0.260807 | − | 0.965391i | \(-0.583989\pi\) | ||||
−0.260807 | + | 0.965391i | \(0.583989\pi\) | |||||||
\(978\) | 10.8966 | 0.348435 | ||||||||
\(979\) | 6.61693 | 0.211478 | ||||||||
\(980\) | 3.38938 | 0.108270 | ||||||||
\(981\) | −1.10512 | −0.0352838 | ||||||||
\(982\) | 6.72706 | 0.214669 | ||||||||
\(983\) | −29.5121 | −0.941291 | −0.470645 | − | 0.882322i | \(-0.655979\pi\) | ||||
−0.470645 | + | 0.882322i | \(0.655979\pi\) | |||||||
\(984\) | 0.0416979 | 0.00132928 | ||||||||
\(985\) | 50.1901 | 1.59919 | ||||||||
\(986\) | −31.4649 | −1.00205 | ||||||||
\(987\) | −5.21408 | −0.165966 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.0825 | −1.43354 | ||||||||
\(990\) | 7.75866 | 0.246586 | ||||||||
\(991\) | 4.39245 | 0.139531 | 0.0697653 | − | 0.997563i | \(-0.477775\pi\) | ||||
0.0697653 | + | 0.997563i | \(0.477775\pi\) | |||||||
\(992\) | 4.28683 | 0.136107 | ||||||||
\(993\) | −10.7713 | −0.341817 | ||||||||
\(994\) | −10.9484 | −0.347262 | ||||||||
\(995\) | −8.66130 | −0.274582 | ||||||||
\(996\) | 1.50952 | 0.0478310 | ||||||||
\(997\) | 46.3338 | 1.46741 | 0.733704 | − | 0.679470i | \(-0.237790\pi\) | ||||
0.733704 | + | 0.679470i | \(0.237790\pi\) | |||||||
\(998\) | −1.16200 | −0.0367826 | ||||||||
\(999\) | 26.1432 | 0.827135 |
(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 | 2366.2.a.bh.1.3 | 6 | ||
13.2 | odd | 12 | 182.2.m.b.43.5 | ✓ | 12 | ||
13.5 | odd | 4 | 2366.2.d.r.337.3 | 12 | |||
13.7 | odd | 12 | 182.2.m.b.127.5 | yes | 12 | ||
13.8 | odd | 4 | 2366.2.d.r.337.9 | 12 | |||
13.12 | even | 2 | 2366.2.a.bf.1.3 | 6 | |||
39.2 | even | 12 | 1638.2.bj.g.1135.3 | 12 | |||
39.20 | even | 12 | 1638.2.bj.g.127.1 | 12 | |||
52.7 | even | 12 | 1456.2.cc.d.673.3 | 12 | |||
52.15 | even | 12 | 1456.2.cc.d.225.3 | 12 | |||
91.2 | odd | 12 | 1274.2.o.d.459.2 | 12 | |||
91.20 | even | 12 | 1274.2.m.c.491.5 | 12 | |||
91.33 | even | 12 | 1274.2.v.d.361.2 | 12 | |||
91.41 | even | 12 | 1274.2.m.c.589.5 | 12 | |||
91.46 | odd | 12 | 1274.2.o.d.569.5 | 12 | |||
91.54 | even | 12 | 1274.2.o.e.459.2 | 12 | |||
91.59 | even | 12 | 1274.2.o.e.569.5 | 12 | |||
91.67 | odd | 12 | 1274.2.v.e.667.2 | 12 | |||
91.72 | odd | 12 | 1274.2.v.e.361.2 | 12 | |||
91.80 | even | 12 | 1274.2.v.d.667.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.5 | ✓ | 12 | 13.2 | odd | 12 | ||
182.2.m.b.127.5 | yes | 12 | 13.7 | odd | 12 | ||
1274.2.m.c.491.5 | 12 | 91.20 | even | 12 | |||
1274.2.m.c.589.5 | 12 | 91.41 | even | 12 | |||
1274.2.o.d.459.2 | 12 | 91.2 | odd | 12 | |||
1274.2.o.d.569.5 | 12 | 91.46 | odd | 12 | |||
1274.2.o.e.459.2 | 12 | 91.54 | even | 12 | |||
1274.2.o.e.569.5 | 12 | 91.59 | even | 12 | |||
1274.2.v.d.361.2 | 12 | 91.33 | even | 12 | |||
1274.2.v.d.667.2 | 12 | 91.80 | even | 12 | |||
1274.2.v.e.361.2 | 12 | 91.72 | odd | 12 | |||
1274.2.v.e.667.2 | 12 | 91.67 | odd | 12 | |||
1456.2.cc.d.225.3 | 12 | 52.15 | even | 12 | |||
1456.2.cc.d.673.3 | 12 | 52.7 | even | 12 | |||
1638.2.bj.g.127.1 | 12 | 39.20 | even | 12 | |||
1638.2.bj.g.1135.3 | 12 | 39.2 | even | 12 | |||
2366.2.a.bf.1.3 | 6 | 13.12 | even | 2 | |||
2366.2.a.bh.1.3 | 6 | 1.1 | even | 1 | trivial | ||
2366.2.d.r.337.3 | 12 | 13.5 | odd | 4 | |||
2366.2.d.r.337.9 | 12 | 13.8 | odd | 4 |