Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1336,2,Mod(1,1336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1336.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1336 = 2^{3} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1336.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: | \(10.6680137100\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} - 25 x^{10} + 20 x^{9} + 224 x^{8} - 135 x^{7} - 865 x^{6} + 330 x^{5} + 1341 x^{4} - 127 x^{3} - 652 x^{2} - 48 x + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-0.571891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1336.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.571891 | 0.330181 | 0.165091 | − | 0.986278i | \(-0.447208\pi\) | ||||
0.165091 | + | 0.986278i | \(0.447208\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.42234 | −1.08331 | −0.541653 | − | 0.840602i | \(-0.682201\pi\) | ||||
−0.541653 | + | 0.840602i | \(0.682201\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.89487 | −1.47212 | −0.736062 | − | 0.676914i | \(-0.763317\pi\) | ||||
−0.736062 | + | 0.676914i | \(0.763317\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.67294 | −0.890980 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.06107 | 0.319924 | 0.159962 | − | 0.987123i | \(-0.448863\pi\) | ||||
0.159962 | + | 0.987123i | \(0.448863\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.87406 | 1.62917 | 0.814585 | − | 0.580044i | \(-0.196965\pi\) | ||||
0.814585 | + | 0.580044i | \(0.196965\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.38532 | −0.357687 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.69476 | 1.13865 | 0.569324 | − | 0.822114i | \(-0.307205\pi\) | ||||
0.569324 | + | 0.822114i | \(0.307205\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.56178 | −1.04654 | −0.523272 | − | 0.852166i | \(-0.675289\pi\) | ||||
−0.523272 | + | 0.852166i | \(0.675289\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.22744 | −0.486068 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.88976 | 1.43661 | 0.718307 | − | 0.695726i | \(-0.244917\pi\) | ||||
0.718307 | + | 0.695726i | \(0.244917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.867754 | 0.173551 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.24430 | −0.624366 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.73271 | −0.878841 | −0.439421 | − | 0.898281i | \(-0.644816\pi\) | ||||
−0.439421 | + | 0.898281i | \(0.644816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.09371 | 0.914858 | 0.457429 | − | 0.889246i | \(-0.348770\pi\) | ||||
0.457429 | + | 0.889246i | \(0.348770\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.606816 | 0.105633 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.43473 | 1.59476 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.53085 | 1.23806 | 0.619032 | − | 0.785366i | \(-0.287525\pi\) | ||||
0.619032 | + | 0.785366i | \(0.287525\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.35932 | 0.537922 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.59931 | −0.718291 | −0.359145 | − | 0.933282i | \(-0.616932\pi\) | ||||
−0.359145 | + | 0.933282i | \(0.616932\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.94427 | 1.21149 | 0.605745 | − | 0.795659i | \(-0.292875\pi\) | ||||
0.605745 | + | 0.795659i | \(0.292875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.47478 | 0.965204 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0221 | 1.46188 | 0.730940 | − | 0.682442i | \(-0.239082\pi\) | ||||
0.730940 | + | 0.682442i | \(0.239082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 8.17004 | 1.16715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.68489 | 0.375960 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.90356 | 1.08564 | 0.542819 | − | 0.839850i | \(-0.317357\pi\) | ||||
0.542819 | + | 0.839850i | \(0.317357\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.57028 | −0.346576 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.60884 | −0.345549 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.93731 | −1.03335 | −0.516675 | − | 0.856182i | \(-0.672830\pi\) | ||||
−0.516675 | + | 0.856182i | \(0.672830\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.9263 | 1.65504 | 0.827518 | − | 0.561439i | \(-0.189752\pi\) | ||||
0.827518 | + | 0.561439i | \(0.189752\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 10.4108 | 1.31163 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.2290 | −1.76489 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.91109 | −0.844324 | −0.422162 | − | 0.906520i | \(-0.638729\pi\) | ||||
−0.422162 | + | 0.906520i | \(0.638729\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.94019 | 0.474343 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.67998 | −0.674090 | −0.337045 | − | 0.941489i | \(-0.609427\pi\) | ||||
−0.337045 | + | 0.941489i | \(0.609427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.1491 | 1.65603 | 0.828016 | − | 0.560705i | \(-0.189470\pi\) | ||||
0.828016 | + | 0.560705i | \(0.189470\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.496260 | 0.0573032 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.13273 | −0.470968 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.05349 | −0.568562 | −0.284281 | − | 0.958741i | \(-0.591755\pi\) | ||||
−0.284281 | + | 0.958741i | \(0.591755\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.16344 | 0.684826 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.2582 | −1.12599 | −0.562994 | − | 0.826461i | \(-0.690351\pi\) | ||||
−0.562994 | + | 0.826461i | \(0.690351\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.3723 | −1.23350 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.70659 | −0.290177 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.7067 | 1.34691 | 0.673453 | − | 0.739230i | \(-0.264810\pi\) | ||||
0.673453 | + | 0.739230i | \(0.264810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.8787 | −2.39834 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.91305 | 0.302069 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.0502 | 1.13373 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4437 | −1.06039 | −0.530197 | − | 0.847875i | \(-0.677882\pi\) | ||||
−0.530197 | + | 0.847875i | \(0.677882\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.83618 | −0.285046 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.1024 | 1.30374 | 0.651871 | − | 0.758330i | \(-0.273984\pi\) | ||||
0.651871 | + | 0.758330i | \(0.273984\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.0031 | −1.18270 | −0.591352 | − | 0.806413i | \(-0.701406\pi\) | ||||
−0.591352 | + | 0.806413i | \(0.701406\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.39563 | 0.526560 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.54799 | 0.923039 | 0.461519 | − | 0.887130i | \(-0.347304\pi\) | ||||
0.461519 | + | 0.887130i | \(0.347304\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.3174 | −1.56292 | −0.781461 | − | 0.623954i | \(-0.785525\pi\) | ||||
−0.781461 | + | 0.623954i | \(0.785525\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.30682 | 0.408786 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.43572 | 0.793566 | 0.396783 | − | 0.917912i | \(-0.370127\pi\) | ||||
0.396783 | + | 0.917912i | \(0.370127\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.6894 | −1.55629 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −15.7010 | −1.45156 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −18.2855 | −1.67623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.87413 | −0.897648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.63030 | −0.237166 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0097 | 0.895297 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.8782 | 1.49770 | 0.748849 | − | 0.662741i | \(-0.230607\pi\) | ||||
0.748849 | + | 0.662741i | \(0.230607\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.54325 | 0.400011 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0754 | 0.880292 | 0.440146 | − | 0.897926i | \(-0.354927\pi\) | ||||
0.440146 | + | 0.897926i | \(0.354927\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.7676 | 1.54064 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.85882 | 0.676379 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11.6192 | −0.992696 | −0.496348 | − | 0.868124i | \(-0.665326\pi\) | ||||
−0.496348 | + | 0.868124i | \(0.665326\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −19.7902 | −1.67859 | −0.839293 | − | 0.543679i | \(-0.817031\pi\) | ||||
−0.839293 | + | 0.543679i | \(0.817031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.73157 | 0.482685 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.23278 | 0.521212 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.4642 | 0.952054 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.67237 | 0.385371 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 18.7206 | 1.53365 | 0.766825 | − | 0.641857i | \(-0.221836\pi\) | ||||
0.766825 | + | 0.641857i | \(0.221836\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.14926 | −0.581799 | −0.290899 | − | 0.956754i | \(-0.593954\pi\) | ||||
−0.290899 | + | 0.956754i | \(0.593954\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.5488 | −1.01451 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.3387 | −0.991071 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.73863 | −0.378184 | −0.189092 | − | 0.981959i | \(-0.560554\pi\) | ||||
−0.189092 | + | 0.981959i | \(0.560554\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.51997 | 0.358457 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −26.8347 | −2.11487 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.04789 | 0.238729 | 0.119365 | − | 0.992850i | \(-0.461914\pi\) | ||||
0.119365 | + | 0.992850i | \(0.461914\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.46992 | −0.114433 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.5046 | 1.65420 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.1934 | 0.932451 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.6556 | 1.41836 | 0.709178 | − | 0.705030i | \(-0.249066\pi\) | ||||
0.709178 | + | 0.705030i | \(0.249066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.37979 | −0.255488 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.53927 | −0.341193 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.44709 | 0.257648 | 0.128824 | − | 0.991667i | \(-0.458880\pi\) | ||||
0.128824 | + | 0.991667i | \(0.458880\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.9657 | 1.11239 | 0.556195 | − | 0.831052i | \(-0.312261\pi\) | ||||
0.556195 | + | 0.831052i | \(0.312261\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.39240 | 0.546462 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −18.2423 | −1.34120 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.98147 | 0.364281 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.6361 | 0.919144 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.37740 | 0.316737 | 0.158369 | − | 0.987380i | \(-0.449377\pi\) | ||||
0.158369 | + | 0.987380i | \(0.449377\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.36494 | −0.674103 | −0.337052 | − | 0.941486i | \(-0.609430\pi\) | ||||
−0.337052 | + | 0.941486i | \(0.609430\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.13743 | −0.582734 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.30685 | −0.235603 | −0.117802 | − | 0.993037i | \(-0.537585\pi\) | ||||
−0.117802 | + | 0.993037i | \(0.537585\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.1610 | −1.14562 | −0.572810 | − | 0.819688i | \(-0.694147\pi\) | ||||
−0.572810 | + | 0.819688i | \(0.694147\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.95239 | −0.278780 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.4333 | 1.29376 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1411 | 0.778128 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.4159 | −1.28000 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.84037 | −0.334815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.54669 | 0.450693 | 0.225346 | − | 0.974279i | \(-0.427649\pi\) | ||||
0.225346 | + | 0.974279i | \(0.427649\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.24833 | −0.222572 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −19.2438 | −1.31241 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.8394 | −1.34678 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.09176 | 0.546791 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.5773 | 1.85505 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.5139 | −1.37371 | −0.686857 | − | 0.726793i | \(-0.741010\pi\) | ||||
−0.686857 | + | 0.726793i | \(0.741010\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.31945 | −0.154630 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −16.3625 | −1.08602 | −0.543009 | − | 0.839727i | \(-0.682715\pi\) | ||||
−0.543009 | + | 0.839727i | \(0.682715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.74442 | −0.511766 | −0.255883 | − | 0.966708i | \(-0.582366\pi\) | ||||
−0.255883 | + | 0.966708i | \(0.582366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.36347 | −0.155505 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.83490 | −0.513281 | −0.256641 | − | 0.966507i | \(-0.582616\pi\) | ||||
−0.256641 | + | 0.966507i | \(0.582616\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.2771 | −1.58366 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.89004 | −0.187728 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.60183 | 0.427037 | 0.213518 | − | 0.976939i | \(-0.431508\pi\) | ||||
0.213518 | + | 0.976939i | \(0.431508\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.3394 | 1.31018 | 0.655089 | − | 0.755552i | \(-0.272631\pi\) | ||||
0.655089 | + | 0.755552i | \(0.272631\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.2577 | 0.850483 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −19.7906 | −1.26438 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.7962 | −1.70500 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.86659 | −0.371780 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.8497 | 1.37914 | 0.689572 | − | 0.724217i | \(-0.257799\pi\) | ||||
0.689572 | + | 0.724217i | \(0.257799\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.31052 | 0.459608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.50373 | −0.407279 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.922785 | −0.0575617 | −0.0287809 | − | 0.999586i | \(-0.509163\pi\) | ||||
−0.0287809 | + | 0.999586i | \(0.509163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.3317 | −1.82258 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.6502 | 0.783030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4243 | −0.642790 | −0.321395 | − | 0.946945i | \(-0.604152\pi\) | ||||
−0.321395 | + | 0.946945i | \(0.604152\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.1452 | −1.17608 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.26684 | 0.444723 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.1738 | 1.29099 | 0.645495 | − | 0.763764i | \(-0.276651\pi\) | ||||
0.645495 | + | 0.763764i | \(0.276651\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.48917 | 0.394189 | 0.197095 | − | 0.980384i | \(-0.436849\pi\) | ||||
0.197095 | + | 0.980384i | \(0.436849\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −13.0841 | −0.791887 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.920747 | 0.0555231 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.08812 | 0.185547 | 0.0927736 | − | 0.995687i | \(-0.470427\pi\) | ||||
0.0927736 | + | 0.995687i | \(0.470427\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −13.6152 | −0.815121 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.5330 | 1.82145 | 0.910724 | − | 0.413016i | \(-0.135525\pi\) | ||||
0.910724 | + | 0.413016i | \(0.135525\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.5616 | 0.925039 | 0.462519 | − | 0.886609i | \(-0.346946\pi\) | ||||
0.462519 | + | 0.886609i | \(0.346946\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.31951 | 0.374336 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.9137 | 1.05741 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.04079 | 0.296517 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.97264 | −0.350122 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.5838 | −0.735151 | −0.367575 | − | 0.929994i | \(-0.619812\pi\) | ||||
−0.367575 | + | 0.929994i | \(0.619812\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.2269 | 1.11943 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.44243 | −0.199750 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 40.4709 | 2.34049 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.9419 | −1.78346 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.49317 | 0.430471 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −31.3118 | −1.79291 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.5504 | 1.17287 | 0.586435 | − | 0.809996i | \(-0.300531\pi\) | ||||
0.586435 | + | 0.809996i | \(0.300531\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.86449 | −0.390507 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.9297 | −1.86727 | −0.933636 | − | 0.358222i | \(-0.883383\pi\) | ||||
−0.933636 | + | 0.358222i | \(0.883383\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.25293 | 0.523006 | 0.261503 | − | 0.965203i | \(-0.415782\pi\) | ||||
0.261503 | + | 0.965203i | \(0.415782\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.2185 | −1.42090 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.7853 | 1.27975 | 0.639875 | − | 0.768479i | \(-0.278986\pi\) | ||||
0.639875 | + | 0.768479i | \(0.278986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.02173 | −0.281163 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.46041 | 0.304770 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.4165 | −1.19164 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.09724 | 0.282744 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.33176 | −0.516048 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −39.0350 | −2.15207 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.6285 | 0.639162 | 0.319581 | − | 0.947559i | \(-0.396458\pi\) | ||||
0.319581 | + | 0.947559i | \(0.396458\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.1295 | −1.10309 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.7410 | 0.914660 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.5453 | −0.792331 | −0.396165 | − | 0.918179i | \(-0.629659\pi\) | ||||
−0.396165 | + | 0.918179i | \(0.629659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.82431 | 0.262021 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.40478 | 0.292685 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.55715 | −0.246063 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.54450 | −0.513859 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.30707 | 0.338581 | 0.169291 | − | 0.985566i | \(-0.445852\pi\) | ||||
0.169291 | + | 0.985566i | \(0.445852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.5992 | −1.04912 | −0.524561 | − | 0.851373i | \(-0.675770\pi\) | ||||
−0.524561 | + | 0.851373i | \(0.675770\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.0572 | −1.01720 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.14946 | −0.433752 | −0.216876 | − | 0.976199i | \(-0.569587\pi\) | ||||
−0.216876 | + | 0.976199i | \(0.569587\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.7589 | 0.730245 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.4573 | −0.553460 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0437 | 1.26898 | 0.634490 | − | 0.772931i | \(-0.281210\pi\) | ||||
0.634490 | + | 0.772931i | \(0.281210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.80985 | 0.0952554 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.64692 | −0.296387 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −34.2741 | −1.79399 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6955 | −0.610499 | −0.305250 | − | 0.952272i | \(-0.598740\pi\) | ||||
−0.305250 | + | 0.952272i | \(0.598740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.2937 | 0.639983 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −30.7834 | −1.59819 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.35308 | −0.225394 | −0.112697 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112697 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.72447 | 0.295610 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −27.8002 | −1.43178 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.7673 | 0.861277 | 0.430638 | − | 0.902525i | \(-0.358288\pi\) | ||||
0.430638 | + | 0.902525i | \(0.358288\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.65248 | 0.494512 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.78673 | 0.397883 | 0.198942 | − | 0.980011i | \(-0.436250\pi\) | ||||
0.198942 | + | 0.980011i | \(0.436250\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0109 | 0.510203 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −21.2346 | −1.07941 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.32989 | −0.270236 | −0.135118 | − | 0.990830i | \(-0.543141\pi\) | ||||
−0.135118 | + | 0.990830i | \(0.543141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 32.3458 | 1.63580 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5.76203 | 0.290656 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.2413 | 0.615926 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.4029 | 0.973805 | 0.486903 | − | 0.873456i | \(-0.338127\pi\) | ||||
0.486903 | + | 0.873456i | \(0.338127\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.1611 | 0.508691 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 23.5610 | 1.17658 | 0.588291 | − | 0.808650i | \(-0.299801\pi\) | ||||
0.588291 | + | 0.808650i | \(0.299801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.9208 | 1.49046 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.9300 | −0.741876 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.99076 | 0.396087 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.0973 | −1.09264 | −0.546321 | − | 0.837576i | \(-0.683972\pi\) | ||||
−0.546321 | + | 0.837576i | \(0.683972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.64492 | −0.327770 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 30.9148 | 1.52122 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.8490 | 1.21979 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.3179 | −0.554238 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 38.5514 | 1.88336 | 0.941679 | − | 0.336514i | \(-0.109248\pi\) | ||||
0.941679 | + | 0.336514i | \(0.109248\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.3205 | −1.33152 | −0.665759 | − | 0.746167i | \(-0.731892\pi\) | ||||
−0.665759 | + | 0.746167i | \(0.731892\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −26.7886 | −1.30251 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.07390 | 0.197613 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −50.3461 | −2.43642 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.56447 | 0.172094 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.18336 | −0.201505 | −0.100753 | − | 0.994912i | \(-0.532125\pi\) | ||||
−0.100753 | + | 0.994912i | \(0.532125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.43297 | 0.0688641 | 0.0344320 | − | 0.999407i | \(-0.489038\pi\) | ||||
0.0344320 | + | 0.999407i | \(0.489038\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.55630 | 0.314350 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −31.4296 | −1.50348 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.5235 | −1.17044 | −0.585221 | − | 0.810874i | \(-0.698992\pi\) | ||||
−0.585221 | + | 0.810874i | \(0.698992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −21.8380 | −1.03991 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.2089 | −0.960156 | −0.480078 | − | 0.877226i | \(-0.659392\pi\) | ||||
−0.480078 | + | 0.877226i | \(0.659392\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −30.7800 | −1.45911 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.7061 | 0.506382 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.98049 | 0.282237 | 0.141118 | − | 0.989993i | \(-0.454930\pi\) | ||||
0.141118 | + | 0.989993i | \(0.454930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.88018 | −0.229799 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.08860 | −0.192099 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 55.4201 | 2.59814 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.13632 | −0.380601 | −0.190300 | − | 0.981726i | \(-0.560946\pi\) | ||||
−0.190300 | + | 0.981726i | \(0.560946\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −15.2312 | −0.710933 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.6806 | −0.544022 | −0.272011 | − | 0.962294i | \(-0.587689\pi\) | ||||
−0.272011 | + | 0.962294i | \(0.587689\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.62768 | 0.168592 | 0.0842962 | − | 0.996441i | \(-0.473136\pi\) | ||||
0.0842962 | + | 0.996441i | \(0.473136\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.05641 | −0.327233 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.3107 | 0.708496 | 0.354248 | − | 0.935152i | \(-0.384737\pi\) | ||||
0.354248 | + | 0.935152i | \(0.384737\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.9178 | 1.24295 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.70998 | −0.124869 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.42942 | 0.387585 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.95850 | −0.181629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −21.1258 | −0.967282 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.8901 | 1.68555 | 0.842777 | − | 0.538264i | \(-0.180920\pi\) | ||||
0.842777 | + | 0.538264i | \(0.180920\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.2367 | 2.01702 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.3465 | −0.698292 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 25.2982 | 1.14873 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.4148 | −0.607883 | −0.303941 | − | 0.952691i | \(-0.598303\pi\) | ||||
−0.303941 | + | 0.952691i | \(0.598303\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.74306 | 0.0788239 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0176 | −0.497218 | −0.248609 | − | 0.968604i | \(-0.579973\pi\) | ||||
−0.248609 | + | 0.968604i | \(0.579973\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −22.2189 | −1.00069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.87020 | 0.308792 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.1228 | 0.992343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.2887 | −1.31114 | −0.655570 | − | 0.755134i | \(-0.727572\pi\) | ||||
−0.655570 | + | 0.755134i | \(0.727572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.571891 | −0.0255502 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −44.1648 | −1.96921 | −0.984606 | − | 0.174788i | \(-0.944076\pi\) | ||||
−0.984606 | + | 0.174788i | \(0.944076\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −31.7386 | −1.41235 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.2983 | 0.546185 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 37.9725 | 1.68310 | 0.841550 | − | 0.540179i | \(-0.181643\pi\) | ||||
0.841550 | + | 0.540179i | \(0.181643\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −55.1091 | −2.43788 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14.7998 | 0.653427 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 29.0757 | 1.28123 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.6342 | 0.467691 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10.6689 | 0.468314 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.46873 | 0.414833 | 0.207416 | − | 0.978253i | \(-0.433495\pi\) | ||||
0.207416 | + | 0.978253i | \(0.433495\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0224 | −0.744337 | −0.372169 | − | 0.928165i | \(-0.621386\pi\) | ||||
−0.372169 | + | 0.928165i | \(0.621386\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.93287 | −0.0843574 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 23.9138 | 1.04170 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.4688 | 1.06386 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 21.2160 | 0.920694 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −27.0166 | −1.17022 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −23.1285 | −0.999933 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.97136 | 0.0850705 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.66898 | 0.373399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.15422 | −0.264591 | −0.132295 | − | 0.991210i | \(-0.542235\pi\) | ||||
−0.132295 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.55873 | 0.367290 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 39.5263 | 1.69312 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.7274 | 1.35656 | 0.678282 | − | 0.734801i | \(-0.262725\pi\) | ||||
0.678282 | + | 0.734801i | \(0.262725\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −34.5511 | −1.47461 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.5896 | 0.919747 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.6827 | 0.836993 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.4326 | −0.442840 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 26.8039 | 1.13572 | 0.567858 | − | 0.823127i | \(-0.307772\pi\) | ||||
0.567858 | + | 0.823127i | \(0.307772\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 46.6651 | 1.97372 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.84886 | 0.120279 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.48928 | −0.189201 | −0.0946003 | − | 0.995515i | \(-0.530157\pi\) | ||||
−0.0946003 | + | 0.995515i | \(0.530157\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.4342 | −0.859674 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.0058 | −1.00815 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.5245 | −0.734667 | −0.367333 | − | 0.930089i | \(-0.619729\pi\) | ||||
−0.367333 | + | 0.930089i | \(0.619729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.05790 | −0.211667 | −0.105833 | − | 0.994384i | \(-0.533751\pi\) | ||||
−0.105833 | + | 0.994384i | \(0.533751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.50339 | 0.104581 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.97862 | 0.249326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.91260 | −0.246145 | −0.123072 | − | 0.992398i | \(-0.539275\pi\) | ||||
−0.123072 | + | 0.992398i | \(0.539275\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.35572 | −0.222576 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 39.9545 | 1.65759 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.38623 | 0.347322 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 38.0333 | 1.57248 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.8702 | 0.613757 | 0.306878 | − | 0.951749i | \(-0.400715\pi\) | ||||
0.306878 | + | 0.951749i | \(0.400715\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −23.2364 | −0.957440 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.89116 | −0.0777919 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.7408 | −0.810659 | −0.405329 | − | 0.914171i | \(-0.632843\pi\) | ||||
−0.405329 | + | 0.914171i | \(0.632843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 44.2938 | 1.81587 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.24230 | −0.378262 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22.7370 | −0.929010 | −0.464505 | − | 0.885570i | \(-0.653768\pi\) | ||||
−0.464505 | + | 0.885570i | \(0.653768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0388 | 0.654238 | 0.327119 | − | 0.944983i | \(-0.393922\pi\) | ||||
0.327119 | + | 0.944983i | \(0.393922\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 18.4729 | 0.752276 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.9186 | 0.972427 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.35650 | 0.258002 | 0.129001 | − | 0.991644i | \(-0.458823\pi\) | ||||
0.129001 | + | 0.991644i | \(0.458823\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.5418 | 0.427176 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 58.8707 | 2.38165 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 41.1061 | 1.66026 | 0.830130 | − | 0.557570i | \(-0.188266\pi\) | ||||
0.830130 | + | 0.557570i | \(0.188266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.37149 | 0.256923 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00777 | −0.362639 | −0.181320 | − | 0.983424i | \(-0.558037\pi\) | ||||
−0.181320 | + | 0.983424i | \(0.558037\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.0370 | 0.845547 | 0.422774 | − | 0.906235i | \(-0.361057\pi\) | ||||
0.422774 | + | 0.906235i | \(0.361057\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.3525 | −0.896974 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.4909 | −1.98281 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.5858 | −1.14343 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.76816 | −0.110550 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.3556 | 1.40972 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 36.8742 | 1.46794 | 0.733969 | − | 0.679182i | \(-0.237666\pi\) | ||||
0.733969 | + | 0.679182i | \(0.237666\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.74399 | 0.148810 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −40.8848 | −1.62246 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 47.9913 | 1.90148 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.1823 | 0.600601 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.7992 | −1.53248 | −0.766239 | − | 0.642556i | \(-0.777874\pi\) | ||||
−0.766239 | + | 0.642556i | \(0.777874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.42249 | 0.371587 | 0.185793 | − | 0.982589i | \(-0.440514\pi\) | ||||
0.185793 | + | 0.982589i | \(0.440514\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.0053 | −0.433334 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.3331 | −0.760064 | −0.380032 | − | 0.924973i | \(-0.624087\pi\) | ||||
−0.380032 | + | 0.924973i | \(0.624087\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.42204 | −0.330594 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.3460 | −0.444683 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3499 | 0.444157 | 0.222078 | − | 0.975029i | \(-0.428716\pi\) | ||||
0.222078 | + | 0.975029i | \(0.428716\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −24.4061 | −0.953625 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.8198 | −1.47549 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09087 | 0.0424944 | 0.0212472 | − | 0.999774i | \(-0.493236\pi\) | ||||
0.0212472 | + | 0.999774i | \(0.493236\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.28977 | 0.283539 | 0.141770 | − | 0.989900i | \(-0.454721\pi\) | ||||
0.141770 | + | 0.989900i | \(0.454721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.7712 | 0.612503 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −43.0392 | −1.66899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −32.6072 | −1.26256 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.7317 | −0.453575 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 13.7156 | 0.529487 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1157 | −0.659760 | −0.329880 | − | 0.944023i | \(-0.607008\pi\) | ||||
−0.329880 | + | 0.944023i | \(0.607008\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.81526 | −0.108359 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.2655 | 0.932599 | 0.466299 | − | 0.884627i | \(-0.345587\pi\) | ||||
0.466299 | + | 0.884627i | \(0.345587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 40.6768 | 1.56103 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.35756 | −0.358583 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.6640 | 1.21159 | 0.605794 | − | 0.795621i | \(-0.292855\pi\) | ||||
0.605794 | + | 0.795621i | \(0.292855\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 28.1457 | 1.07539 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.42896 | −0.168975 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 46.4260 | 1.76869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.4115 | −0.814531 | −0.407265 | − | 0.913310i | \(-0.633518\pi\) | ||||
−0.407265 | + | 0.913310i | \(0.633518\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.0465 | 0.419624 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 47.9388 | 1.81842 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −21.5926 | −0.817880 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.48071 | −0.169476 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.17654 | −0.233285 | −0.116642 | − | 0.993174i | \(-0.537213\pi\) | ||||
−0.116642 | + | 0.993174i | \(0.537213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.3541 | −1.29569 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8838 | −0.522896 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −51.0324 | −1.91927 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.8554 | 1.08369 | 0.541844 | − | 0.840479i | \(-0.317727\pi\) | ||||
0.541844 | + | 0.840479i | \(0.317727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13.5077 | 0.506577 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 35.0945 | 1.31430 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0980 | −0.564631 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.77552 | 0.141000 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −28.0992 | −1.04792 | −0.523962 | − | 0.851742i | \(-0.675547\pi\) | ||||
−0.523962 | + | 0.851742i | \(0.675547\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 46.7507 | 1.74109 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.6319 | 0.432596 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.10682 | −0.152524 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.6298 | 1.43270 | 0.716350 | − | 0.697741i | \(-0.245811\pi\) | ||||
0.716350 | + | 0.697741i | \(0.245811\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −10.9083 | −0.404013 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.2964 | 1.37946 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.6843 | −1.61352 | −0.806759 | − | 0.590881i | \(-0.798780\pi\) | ||||
−0.806759 | + | 0.590881i | \(0.798780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.3181 | −0.417474 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.33314 | −0.270120 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −43.7643 | −1.60990 | −0.804949 | − | 0.593345i | \(-0.797807\pi\) | ||||
−0.804949 | + | 0.593345i | \(0.797807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −15.3245 | −0.562959 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.8756 | 0.839223 | 0.419612 | − | 0.907704i | \(-0.362166\pi\) | ||||
0.419612 | + | 0.907704i | \(0.362166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −45.3477 | −1.66141 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.4197 | 1.00323 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −37.1882 | −1.35883 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 43.4421 | 1.58523 | 0.792613 | − | 0.609726i | \(-0.208720\pi\) | ||||
0.792613 | + | 0.609726i | \(0.208720\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.4957 | 0.455367 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.3180 | 0.630266 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.0801 | 1.05693 | 0.528467 | − | 0.848954i | \(-0.322767\pi\) | ||||
0.528467 | + | 0.848954i | \(0.322767\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.18082 | 0.151754 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.2027 | −0.877349 | −0.438674 | − | 0.898646i | \(-0.644552\pi\) | ||||
−0.438674 | + | 0.898646i | \(0.644552\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 63.5541 | 2.30081 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 30.3976 | 1.09903 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.6242 | −1.68350 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −19.7954 | −0.713842 | −0.356921 | − | 0.934135i | \(-0.616173\pi\) | ||||
−0.356921 | + | 0.934135i | \(0.616173\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.527732 | −0.0190058 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.49477 | −0.197633 | −0.0988166 | − | 0.995106i | \(-0.531506\pi\) | ||||
−0.0988166 | + | 0.995106i | \(0.531506\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.42009 | 0.158774 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.7745 | −0.601783 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.9810 | 0.751723 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.02685 | −0.215658 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 15.3543 | 0.548719 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.4786 | 0.409689 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10.8772 | −0.387731 | −0.193865 | − | 0.981028i | \(-0.562103\pi\) | ||||
−0.193865 | + | 0.981028i | \(0.562103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.96156 | −0.212237 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.8561 | −1.16823 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 75.9296 | 2.69634 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.9489 | −0.388319 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −7.62805 | −0.270199 | −0.135100 | − | 0.990832i | \(-0.543135\pi\) | ||||
−0.135100 | + | 0.990832i | \(0.543135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.0516 | 1.66457 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.9642 | −1.20007 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.0132 | 0.529805 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 65.0030 | 2.29106 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.1091 | 0.426261 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 46.5151 | 1.63539 | 0.817693 | − | 0.575655i | \(-0.195253\pi\) | ||||
0.817693 | + | 0.575655i | \(0.195253\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.6127 | −1.67191 | −0.835954 | − | 0.548799i | \(-0.815085\pi\) | ||||
−0.835954 | + | 0.548799i | \(0.815085\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.71110 | 0.130154 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.38304 | −0.258617 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.2400 | −1.26788 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 61.1535 | 2.13687 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.54536 | −0.333135 | −0.166568 | − | 0.986030i | \(-0.553268\pi\) | ||||
−0.166568 | + | 0.986030i | \(0.553268\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 47.1124 | 1.64223 | 0.821117 | − | 0.570760i | \(-0.193351\pi\) | ||||
0.821117 | + | 0.570760i | \(0.193351\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.526567 | 0.0183327 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 13.6412 | 0.474352 | 0.237176 | − | 0.971467i | \(-0.423778\pi\) | ||||
0.237176 | + | 0.971467i | \(0.423778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23.4729 | −0.815247 | −0.407623 | − | 0.913150i | \(-0.633642\pi\) | ||||
−0.407623 | + | 0.913150i | \(0.633642\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.76607 | 0.0612642 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.3564 | 1.32897 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.42234 | 0.0838287 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16.5255 | −0.571207 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.4753 | −0.430694 | −0.215347 | − | 0.976538i | \(-0.569088\pi\) | ||||
−0.215347 | + | 0.976538i | \(0.569088\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.60149 | −0.227638 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 17.4616 | 0.601408 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −52.0915 | −1.79200 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 38.4585 | 1.32145 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.89951 | 0.305431 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 51.8858 | 1.77862 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.5347 | −1.07973 | −0.539863 | − | 0.841753i | \(-0.681524\pi\) | ||||
−0.539863 | + | 0.841753i | \(0.681524\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −29.5366 | −1.01013 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.19401 | 0.0407868 | 0.0203934 | − | 0.999792i | \(-0.493508\pi\) | ||||
0.0203934 | + | 0.999792i | \(0.493508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.35552 | −0.0462496 | −0.0231248 | − | 0.999733i | \(-0.507362\pi\) | ||||
−0.0231248 | + | 0.999733i | \(0.507362\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.2447 | 0.349138 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.6022 | −0.394945 | −0.197473 | − | 0.980308i | \(-0.563273\pi\) | ||||
−0.197473 | + | 0.980308i | \(0.563273\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.1902 | −1.53651 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.88278 | 0.0979044 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.36210 | −0.181897 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −40.5961 | −1.37555 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.9153 | 0.944790 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.9866 | −1.31799 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −23.1480 | −0.781653 | −0.390826 | − | 0.920464i | \(-0.627811\pi\) | ||||
−0.390826 | + | 0.920464i | \(0.627811\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.19653 | −0.242733 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.8493 | −1.17410 | −0.587051 | − | 0.809550i | \(-0.699711\pi\) | ||||
−0.587051 | + | 0.809550i | \(0.699711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 27.3131 | 0.919158 | 0.459579 | − | 0.888137i | \(-0.348000\pi\) | ||||
0.459579 | + | 0.888137i | \(0.348000\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.9957 | 0.369616 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 30.3880 | 1.02033 | 0.510165 | − | 0.860077i | \(-0.329584\pi\) | ||||
0.510165 | + | 0.860077i | \(0.329584\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −65.7384 | −2.20480 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.53983 | 0.219093 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −45.7188 | −1.52992 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.35005 | −0.279111 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.1449 | 0.772786 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.1071 | −0.804015 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.1053 | 1.23616 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −17.6954 | −0.588866 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −36.2520 | −1.20506 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.45970 | 0.181287 | 0.0906433 | − | 0.995883i | \(-0.471108\pi\) | ||||
0.0906433 | + | 0.995883i | \(0.471108\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −35.0221 | −1.16161 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.2698 | −0.439648 | −0.219824 | − | 0.975540i | \(-0.570548\pi\) | ||||
−0.219824 | + | 0.975540i | \(0.570548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.8847 | −0.360231 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.9069 | −0.591985 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −39.2424 | −1.29590 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.9992 | 1.45140 | 0.725699 | − | 0.688012i | \(-0.241516\pi\) | ||||
0.725699 | + | 0.688012i | \(0.241516\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.7526 | 0.387260 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.3645 | −1.09821 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.53493 | 0.214867 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.0837 | 1.05377 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.2648 | −1.64913 | −0.824567 | − | 0.565765i | \(-0.808581\pi\) | ||||
−0.824567 | + | 0.565765i | \(0.808581\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.2699 | −1.22147 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.8322 | −0.616538 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12.0668 | −0.394628 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.8524 | −1.62861 | −0.814304 | − | 0.580439i | \(-0.802881\pi\) | ||||
−0.814304 | + | 0.580439i | \(0.802881\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.29166 | 0.172687 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.194970 | 0.00635584 | 0.00317792 | − | 0.999995i | \(-0.498988\pi\) | ||||
0.00317792 | + | 0.999995i | \(0.498988\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.6881 | −1.03191 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −30.6091 | −0.995714 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.3319 | 0.400732 | 0.200366 | − | 0.979721i | \(-0.435787\pi\) | ||||
0.200366 | + | 0.979721i | \(0.435787\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 83.1129 | 2.69796 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 13.0307 | 0.422550 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.29690 | −0.106797 | −0.0533985 | − | 0.998573i | \(-0.517005\pi\) | ||||
−0.0533985 | + | 0.998573i | \(0.517005\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.6036 | −0.343123 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.87188 | −0.0928347 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 45.2553 | 1.46137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.05408 | −0.163035 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.5212 | −0.822409 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.6851 | 0.730260 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.24763 | −0.136594 | −0.0682972 | − | 0.997665i | \(-0.521757\pi\) | ||||
−0.0682972 | + | 0.997665i | \(0.521757\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.2479 | −0.393459 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.3992 | −1.55320 | −0.776602 | − | 0.629992i | \(-0.783058\pi\) | ||||
−0.776602 | + | 0.629992i | \(0.783058\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 77.0805 | 2.47109 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.91506 | 0.0933567 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.6611 | 0.788979 | 0.394489 | − | 0.918900i | \(-0.370921\pi\) | ||||
0.394489 | + | 0.918900i | \(0.370921\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.4827 | 0.430908 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.6154 | 1.39253 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.0710 | 0.640166 | 0.320083 | − | 0.947390i | \(-0.396289\pi\) | ||||
0.320083 | + | 0.947390i | \(0.396289\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.01034 | 0.255231 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.3237 | −0.710572 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 54.7341 | 1.74044 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.5808 | −1.03496 | −0.517481 | − | 0.855695i | \(-0.673130\pi\) | ||||
−0.517481 | + | 0.855695i | \(0.673130\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.65025 | 0.211039 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.1474 | 1.24106 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.5379 | 1.72723 | 0.863617 | − | 0.504149i | \(-0.168194\pi\) | ||||
0.863617 | + | 0.504149i | \(0.168194\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −24.4324 | −0.773006 |
(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 | 1336.2.a.d.1.8 | ✓ | 12 | |
4.3 | odd | 2 | 2672.2.a.p.1.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1336.2.a.d.1.8 | ✓ | 12 | 1.1 | even | 1 | trivial | |
2672.2.a.p.1.5 | 12 | 4.3 | odd | 2 |