Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 2 x^{12} - 49 x^{11} + 99 x^{10} + 901 x^{9} - 1879 x^{8} - 7582 x^{7} + 16968 x^{6} + 26911 x^{5} - 72240 x^{4} - 14532 x^{3} + 112850 x^{2} - 72184 x + 12144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(1.25667\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.25667 | 0.562000 | 0.281000 | − | 0.959708i | \(-0.409334\pi\) | ||||
0.281000 | + | 0.959708i | \(0.409334\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.55521 | −1.72171 | −0.860854 | − | 0.508852i | \(-0.830070\pi\) | ||||
−0.860854 | + | 0.508852i | \(0.830070\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23461 | −1.57829 | −0.789147 | − | 0.614204i | \(-0.789477\pi\) | ||||
−0.789147 | + | 0.614204i | \(0.789477\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.93555 | −0.536825 | −0.268412 | − | 0.963304i | \(-0.586499\pi\) | ||||
−0.268412 | + | 0.963304i | \(0.586499\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.25667 | 0.324471 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.59670 | 1.84247 | 0.921235 | − | 0.389007i | \(-0.127182\pi\) | ||||
0.921235 | + | 0.389007i | \(0.127182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.42731 | −1.01569 | −0.507847 | − | 0.861447i | \(-0.669558\pi\) | ||||
−0.507847 | + | 0.861447i | \(0.669558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.55521 | −0.994029 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.61071 | 1.37843 | 0.689214 | − | 0.724558i | \(-0.257956\pi\) | ||||
0.689214 | + | 0.724558i | \(0.257956\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.42078 | −0.684156 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.73263 | 0.693132 | 0.346566 | − | 0.938026i | \(-0.387348\pi\) | ||||
0.346566 | + | 0.938026i | \(0.387348\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.27190 | −0.228440 | −0.114220 | − | 0.993455i | \(-0.536437\pi\) | ||||
−0.114220 | + | 0.993455i | \(0.536437\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.23461 | −0.911229 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.72440 | −0.967601 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.87153 | 1.12967 | 0.564836 | − | 0.825203i | \(-0.308939\pi\) | ||||
0.564836 | + | 0.825203i | \(0.308939\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.93555 | −0.309936 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.71632 | 1.36126 | 0.680631 | − | 0.732627i | \(-0.261706\pi\) | ||||
0.680631 | + | 0.732627i | \(0.261706\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.25563 | 0.801476 | 0.400738 | − | 0.916193i | \(-0.368754\pi\) | ||||
0.400738 | + | 0.916193i | \(0.368754\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.25667 | 0.187333 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.55882 | −0.956702 | −0.478351 | − | 0.878169i | \(-0.658765\pi\) | ||||
−0.478351 | + | 0.878169i | \(0.658765\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.7500 | 1.96428 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.59670 | 1.06375 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.93979 | 0.541172 | 0.270586 | − | 0.962696i | \(-0.412783\pi\) | ||||
0.270586 | + | 0.962696i | \(0.412783\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.57819 | −0.887002 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.42731 | −0.586411 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 12.3546 | 1.60844 | 0.804218 | − | 0.594335i | \(-0.202584\pi\) | ||||
0.804218 | + | 0.594335i | \(0.202584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.282357 | −0.0361522 | −0.0180761 | − | 0.999837i | \(-0.505754\pi\) | ||||
−0.0180761 | + | 0.999837i | \(0.505754\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.55521 | −0.573903 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.43235 | −0.301696 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.25155 | −1.00809 | −0.504043 | − | 0.863678i | \(-0.668155\pi\) | ||||
−0.504043 | + | 0.863678i | \(0.668155\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.61071 | 0.795836 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.66362 | −0.197435 | −0.0987175 | − | 0.995115i | \(-0.531474\pi\) | ||||
−0.0987175 | + | 0.995115i | \(0.531474\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.89727 | −0.456141 | −0.228071 | − | 0.973645i | \(-0.573242\pi\) | ||||
−0.228071 | + | 0.973645i | \(0.573242\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.42078 | −0.394997 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23.8448 | 2.71736 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.21505 | 0.699248 | 0.349624 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349624 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.1118 | 1.54898 | 0.774488 | − | 0.632588i | \(-0.218007\pi\) | ||||
0.774488 | + | 0.632588i | \(0.218007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.54655 | 1.03547 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.73263 | 0.400180 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.93566 | −0.735178 | −0.367589 | − | 0.929988i | \(-0.619817\pi\) | ||||
−0.367589 | + | 0.929988i | \(0.619817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.81684 | 0.924256 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.27190 | −0.131890 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.56367 | −0.570820 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.11931 | −0.316718 | −0.158359 | − | 0.987382i | \(-0.550620\pi\) | ||||
−0.158359 | + | 0.987382i | \(0.550620\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.23461 | −0.526098 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8680 | 1.18091 | 0.590457 | − | 0.807069i | \(-0.298948\pi\) | ||||
0.590457 | + | 0.807069i | \(0.298948\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.31747 | −0.228347 | −0.114174 | − | 0.993461i | \(-0.536422\pi\) | ||||
−0.114174 | + | 0.993461i | \(0.536422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.72440 | −0.558645 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.55158 | −0.149997 | −0.0749985 | − | 0.997184i | \(-0.523895\pi\) | ||||
−0.0749985 | + | 0.997184i | \(0.523895\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.37197 | 0.514541 | 0.257271 | − | 0.966339i | \(-0.417177\pi\) | ||||
0.257271 | + | 0.966339i | \(0.417177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.87153 | 0.652217 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.3036 | 1.62779 | 0.813893 | − | 0.581014i | \(-0.197344\pi\) | ||||
0.813893 | + | 0.581014i | \(0.197344\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.30748 | 0.774677 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.93555 | −0.178942 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −34.6046 | −3.17220 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4012 | 1.49101 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.71632 | 0.785925 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.5821 | −0.946496 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.88097 | 0.699323 | 0.349662 | − | 0.936876i | \(-0.386297\pi\) | ||||
0.349662 | + | 0.936876i | \(0.386297\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.25563 | 0.462732 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2297 | 1.76748 | 0.883739 | − | 0.467979i | \(-0.155018\pi\) | ||||
0.883739 | + | 0.467979i | \(0.155018\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.1673 | 1.74873 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.25667 | 0.108157 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.73853 | −0.319404 | −0.159702 | − | 0.987165i | \(-0.551053\pi\) | ||||
−0.159702 | + | 0.987165i | \(0.551053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1822 | 1.11810 | 0.559049 | − | 0.829135i | \(-0.311167\pi\) | ||||
0.559049 | + | 0.829135i | \(0.311167\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.55882 | −0.552352 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.1318 | 0.847268 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.69069 | 0.389540 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 13.7500 | 1.13408 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.0892 | −1.31808 | −0.659040 | − | 0.752108i | \(-0.729037\pi\) | ||||
−0.659040 | + | 0.752108i | \(0.729037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.2676 | 1.56797 | 0.783987 | − | 0.620778i | \(-0.213183\pi\) | ||||
0.783987 | + | 0.620778i | \(0.213183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.59670 | 0.614156 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.59836 | −0.128383 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.92368 | −0.712187 | −0.356094 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356094 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.93979 | 0.312446 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −30.1132 | −2.37325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.94760 | −0.230874 | −0.115437 | − | 0.993315i | \(-0.536827\pi\) | ||||
−0.115437 | + | 0.993315i | \(0.536827\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.57819 | −0.512111 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.25365 | −0.711819 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.42731 | −0.338564 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.5486 | −0.954055 | −0.477028 | − | 0.878888i | \(-0.658286\pi\) | ||||
−0.477028 | + | 0.878888i | \(0.658286\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.5824 | 1.17792 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.3546 | 0.928631 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.07676 | 0.229968 | 0.114984 | − | 0.993367i | \(-0.463318\pi\) | ||||
0.114984 | + | 0.993367i | \(0.463318\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.50830 | 0.186440 | 0.0932201 | − | 0.995646i | \(-0.470284\pi\) | ||||
0.0932201 | + | 0.995646i | \(0.470284\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.282357 | −0.0208725 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.63525 | 0.634877 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.7658 | −2.90796 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.55521 | −0.331343 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.30849 | −0.239394 | −0.119697 | − | 0.992810i | \(-0.538192\pi\) | ||||
−0.119697 | + | 0.992810i | \(0.538192\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.4096 | −1.32515 | −0.662577 | − | 0.748994i | \(-0.730537\pi\) | ||||
−0.662577 | + | 0.748994i | \(0.730537\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.43235 | −0.174184 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.0745 | −0.931520 | −0.465760 | − | 0.884911i | \(-0.654219\pi\) | ||||
−0.465760 | + | 0.884911i | \(0.654219\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.8563 | −1.33669 | −0.668343 | − | 0.743853i | \(-0.732996\pi\) | ||||
−0.668343 | + | 0.743853i | \(0.732996\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.25155 | −0.582019 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −17.0029 | −1.19337 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.9536 | 0.765029 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.61071 | 0.459476 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.1752 | 1.60306 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.39616 | 0.509173 | 0.254586 | − | 0.967050i | \(-0.418061\pi\) | ||||
0.254586 | + | 0.967050i | \(0.418061\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.66362 | −0.113989 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.60460 | 0.450430 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.79377 | 0.393307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.89727 | −0.263353 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.7038 | −0.989083 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.81997 | −0.121874 | −0.0609371 | − | 0.998142i | \(-0.519409\pi\) | ||||
−0.0609371 | + | 0.998142i | \(0.519409\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.42078 | −0.228052 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.8780 | 1.45209 | 0.726045 | − | 0.687647i | \(-0.241356\pi\) | ||||
0.726045 | + | 0.687647i | \(0.241356\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.04962 | 0.0693609 | 0.0346804 | − | 0.999398i | \(-0.488959\pi\) | ||||
0.0346804 | + | 0.999398i | \(0.488959\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 23.8448 | 1.56887 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.9898 | −1.17855 | −0.589274 | − | 0.807933i | \(-0.700586\pi\) | ||||
−0.589274 | + | 0.807933i | \(0.700586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.24227 | −0.537667 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.21505 | 0.403711 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −27.1655 | −1.75719 | −0.878596 | − | 0.477565i | \(-0.841519\pi\) | ||||
−0.878596 | + | 0.477565i | \(0.841519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.7168 | 1.39890 | 0.699451 | − | 0.714680i | \(-0.253428\pi\) | ||||
0.699451 | + | 0.714680i | \(0.253428\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.2792 | 1.10393 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.56927 | 0.545249 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.1118 | 0.894302 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.4390 | 1.92130 | 0.960648 | − | 0.277770i | \(-0.0895952\pi\) | ||||
0.960648 | + | 0.277770i | \(0.0895952\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.6045 | −2.17557 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.54655 | 0.597828 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.0748 | −1.43937 | −0.719684 | − | 0.694301i | \(-0.755714\pi\) | ||||
−0.719684 | + | 0.694301i | \(0.755714\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.3013 | −1.94497 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.73263 | 0.231044 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.5164 | 1.32676 | 0.663379 | − | 0.748284i | \(-0.269122\pi\) | ||||
0.663379 | + | 0.748284i | \(0.269122\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.95102 | 0.304139 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.93566 | −0.424455 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.2955 | 0.993554 | 0.496777 | − | 0.867878i | \(-0.334517\pi\) | ||||
0.496777 | + | 0.867878i | \(0.334517\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.9830 | −1.57835 | −0.789177 | − | 0.614166i | \(-0.789493\pi\) | ||||
−0.789177 | + | 0.614166i | \(0.789493\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.81684 | 0.533619 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.9064 | 1.07980 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.26377 | −0.496522 | −0.248261 | − | 0.968693i | \(-0.579859\pi\) | ||||
−0.248261 | + | 0.968693i | \(0.579859\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.27190 | −0.0761466 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.956330 | −0.0570499 | −0.0285249 | − | 0.999593i | \(-0.509081\pi\) | ||||
−0.0285249 | + | 0.999593i | \(0.509081\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.81438 | 0.464517 | 0.232258 | − | 0.972654i | \(-0.425389\pi\) | ||||
0.232258 | + | 0.972654i | \(0.425389\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.56367 | −0.329563 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −39.7047 | −2.34369 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 40.7098 | 2.39469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.11931 | −0.182857 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0569 | −1.05490 | −0.527448 | − | 0.849587i | \(-0.676851\pi\) | ||||
−0.527448 | + | 0.849587i | \(0.676851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5257 | 0.903942 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.23461 | −0.303743 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.7954 | −0.739974 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.9405 | −1.37991 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.8680 | 0.681801 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.354830 | −0.0203175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.9495 | −1.53809 | −0.769046 | − | 0.639193i | \(-0.779268\pi\) | ||||
−0.769046 | + | 0.639193i | \(0.779268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.31747 | −0.131836 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.51738 | −0.426272 | −0.213136 | − | 0.977023i | \(-0.568368\pi\) | ||||
−0.213136 | + | 0.977023i | \(0.568368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9480 | 1.41015 | 0.705073 | − | 0.709135i | \(-0.250914\pi\) | ||||
0.705073 | + | 0.709135i | \(0.250914\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5.72440 | −0.322534 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.0071 | 1.57303 | 0.786517 | − | 0.617569i | \(-0.211882\pi\) | ||||
0.786517 | + | 0.617569i | \(0.211882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.5389 | −1.09397 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.55158 | −0.0866008 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −33.6329 | −1.87138 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.62108 | 0.367272 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.37197 | 0.297071 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.8768 | 1.64716 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.36380 | 0.404751 | 0.202375 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202375 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.87153 | 0.376558 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.3695 | −0.566545 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2355 | 0.666512 | 0.333256 | − | 0.942836i | \(-0.391853\pi\) | ||||
0.333256 | + | 0.942836i | \(0.391853\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.3036 | 0.939803 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.65789 | 0.360545 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −30.7475 | −1.66021 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.30748 | 0.447260 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.3771 | 1.04022 | 0.520109 | − | 0.854100i | \(-0.325891\pi\) | ||||
0.520109 | + | 0.854100i | \(0.325891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.13099 | −0.381713 | −0.190857 | − | 0.981618i | \(-0.561127\pi\) | ||||
−0.190857 | + | 0.981618i | \(0.561127\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.93555 | −0.103312 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.7743 | 0.573457 | 0.286729 | − | 0.958012i | \(-0.407432\pi\) | ||||
0.286729 | + | 0.958012i | \(0.407432\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.09062 | −0.110959 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −34.6046 | −1.83147 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.8570 | −1.15357 | −0.576784 | − | 0.816896i | \(-0.695693\pi\) | ||||
−0.576784 | + | 0.816896i | \(0.695693\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.601031 | 0.0316332 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.4012 | 0.860838 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.89759 | −0.256352 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.0341568 | −0.00178297 | −0.000891485 | − | 1.00000i | \(-0.500284\pi\) | ||||
−0.000891485 | 1.00000i | \(0.500284\pi\) | ||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.71632 | 0.453754 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.9466 | −0.931740 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.34690 | −0.225074 | −0.112537 | − | 0.993648i | \(-0.535898\pi\) | ||||
−0.112537 | + | 0.993648i | \(0.535898\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.5821 | −0.546460 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.22469 | −0.372090 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 32.2351 | 1.65581 | 0.827904 | − | 0.560870i | \(-0.189533\pi\) | ||||
0.827904 | + | 0.560870i | \(0.189533\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.88097 | 0.403754 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.6117 | 1.20650 | 0.603250 | − | 0.797552i | \(-0.293872\pi\) | ||||
0.603250 | + | 0.797552i | \(0.293872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 29.9650 | 1.52716 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.25563 | 0.267159 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −31.0376 | −1.57367 | −0.786834 | − | 0.617164i | \(-0.788281\pi\) | ||||
−0.786834 | + | 0.617164i | \(0.788281\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 50.2195 | 2.53971 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 20.2297 | 1.02045 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.81028 | 0.392978 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.95462 | 0.198476 | 0.0992382 | − | 0.995064i | \(-0.468359\pi\) | ||||
0.0992382 | + | 0.995064i | \(0.468359\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 20.1673 | 1.00963 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 19.9560 | 0.996556 | 0.498278 | − | 0.867017i | \(-0.333966\pi\) | ||||
0.498278 | + | 0.867017i | \(0.333966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.46182 | 0.122632 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.25667 | 0.0624445 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −35.9698 | −1.78296 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 38.6158 | 1.90943 | 0.954714 | − | 0.297524i | \(-0.0961607\pi\) | ||||
0.954714 | + | 0.297524i | \(0.0961607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.73853 | −0.184408 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −56.2780 | −2.76926 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7340 | 0.870526 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.1822 | 0.645534 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.87110 | 0.237969 | 0.118984 | − | 0.992896i | \(-0.462036\pi\) | ||||
0.118984 | + | 0.992896i | \(0.462036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.1671 | 0.495512 | 0.247756 | − | 0.968822i | \(-0.420307\pi\) | ||||
0.247756 | + | 0.968822i | \(0.420307\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.55882 | −0.318901 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −25.9866 | −1.26054 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.28620 | 0.0622435 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 10.1318 | 0.489170 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.5825 | −1.66578 | −0.832890 | − | 0.553438i | \(-0.813315\pi\) | ||||
−0.832890 | + | 0.553438i | \(0.813315\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.2208 | −1.45232 | −0.726160 | − | 0.687526i | \(-0.758697\pi\) | ||||
−0.726160 | + | 0.687526i | \(0.758697\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.69069 | 0.224901 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.2676 | −1.40006 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.35552 | 0.160150 | 0.0800751 | − | 0.996789i | \(-0.474484\pi\) | ||||
0.0800751 | + | 0.996789i | \(0.474484\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.7500 | 0.654760 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.9007 | 1.18307 | 0.591533 | − | 0.806281i | \(-0.298523\pi\) | ||||
0.591533 | + | 0.806281i | \(0.298523\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.71584 | −0.413170 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −16.0892 | −0.760993 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 23.2157 | 1.09562 | 0.547808 | − | 0.836604i | \(-0.315463\pi\) | ||||
0.547808 | + | 0.836604i | \(0.315463\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −45.6266 | −2.14847 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 19.2676 | 0.905270 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.0799 | 0.519432 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.56399 | −0.0731602 | −0.0365801 | − | 0.999331i | \(-0.511646\pi\) | ||||
−0.0365801 | + | 0.999331i | \(0.511646\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.59670 | 0.354583 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.9153 | −0.927550 | −0.463775 | − | 0.885953i | \(-0.653505\pi\) | ||||
−0.463775 | + | 0.885953i | \(0.653505\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.9153 | 1.25086 | 0.625431 | − | 0.780280i | \(-0.284923\pi\) | ||||
0.625431 | + | 0.780280i | \(0.284923\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.59836 | −0.0741221 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.6163 | −1.83322 | −0.916611 | − | 0.399780i | \(-0.869087\pi\) | ||||
−0.916611 | + | 0.399780i | \(0.869087\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.5875 | 1.73563 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.92368 | −0.411182 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −27.5112 | −1.26497 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.1448 | 0.694892 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.93979 | 0.180391 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 38.0876 | 1.74027 | 0.870134 | − | 0.492815i | \(-0.164032\pi\) | ||||
0.870134 | + | 0.492815i | \(0.164032\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.3002 | −0.606436 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.1132 | −1.37020 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.91994 | −0.177995 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.70083 | −0.213015 | −0.106508 | − | 0.994312i | \(-0.533967\pi\) | ||||
−0.106508 | + | 0.994312i | \(0.533967\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.94760 | −0.133295 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9587 | 1.21663 | 0.608315 | − | 0.793696i | \(-0.291846\pi\) | ||||
0.608315 | + | 0.793696i | \(0.291846\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 28.3556 | 1.27707 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.57819 | −0.295667 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.57813 | 0.339926 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −29.4450 | −1.31814 | −0.659069 | − | 0.752082i | \(-0.729050\pi\) | ||||
−0.659069 | + | 0.752082i | \(0.729050\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.2438 | 1.21474 | 0.607371 | − | 0.794418i | \(-0.292224\pi\) | ||||
0.607371 | + | 0.794418i | \(0.292224\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.9142 | 0.663674 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.25365 | −0.410969 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.63468 | 0.249753 | 0.124876 | − | 0.992172i | \(-0.460147\pi\) | ||||
0.124876 | + | 0.992172i | \(0.460147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7529 | 0.785342 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.42731 | −0.195470 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.91230 | −0.128331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 34.3329 | 1.50996 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.5486 | −0.550824 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.45179 | −0.282658 | −0.141329 | − | 0.989963i | \(-0.545138\pi\) | ||||
−0.141329 | + | 0.989963i | \(0.545138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.82181 | 0.210843 | 0.105422 | − | 0.994428i | \(-0.466381\pi\) | ||||
0.105422 | + | 0.994428i | \(0.466381\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.5824 | 0.680070 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.66222 | −0.420893 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.7015 | 0.900063 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.3546 | 0.536145 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.8709 | −0.730759 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.94983 | −0.0842984 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.07676 | 0.132772 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −71.9757 | −3.10021 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.7479 | 1.53692 | 0.768461 | − | 0.639896i | \(-0.221023\pi\) | ||||
0.768461 | + | 0.639896i | \(0.221023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.50830 | 0.107641 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.75080 | 0.289172 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.22907 | 0.0953084 | 0.0476542 | − | 0.998864i | \(-0.484825\pi\) | ||||
0.0476542 | + | 0.998864i | \(0.484825\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.282357 | −0.0120507 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.5255 | −0.704009 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −28.3109 | −1.20390 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.63525 | 0.366546 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.8215 | 0.628008 | 0.314004 | − | 0.949422i | \(-0.398330\pi\) | ||||
0.314004 | + | 0.949422i | \(0.398330\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1725 | −0.430252 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −39.7658 | −1.67891 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.1799 | −0.892627 | −0.446314 | − | 0.894877i | \(-0.647263\pi\) | ||||
−0.446314 | + | 0.894877i | \(0.647263\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.7449 | 0.914817 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.55521 | −0.191301 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.59884 | −0.318560 | −0.159280 | − | 0.987233i | \(-0.550917\pi\) | ||||
−0.159280 | + | 0.987233i | \(0.550917\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.3154 | −0.431688 | −0.215844 | − | 0.976428i | \(-0.569250\pi\) | ||||
−0.215844 | + | 0.976428i | \(0.569250\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.30849 | −0.138214 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.6138 | −0.943059 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2672 | 0.677211 | 0.338605 | − | 0.940928i | \(-0.390045\pi\) | ||||
0.338605 | + | 0.940928i | \(0.390045\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.4096 | −0.765078 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −64.2825 | −2.66689 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −20.6233 | −0.854129 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.43235 | −0.100565 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.5861 | −1.09733 | −0.548664 | − | 0.836043i | \(-0.684863\pi\) | ||||
−0.548664 | + | 0.836043i | \(0.684863\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.63108 | 0.232025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.0745 | −0.537813 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.4438 | 0.469939 | 0.234969 | − | 0.972003i | \(-0.424501\pi\) | ||||
0.234969 | + | 0.972003i | \(0.424501\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −43.4866 | −1.78277 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.8563 | −0.771736 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17.6317 | 0.720410 | 0.360205 | − | 0.932873i | \(-0.382707\pi\) | ||||
0.360205 | + | 0.932873i | \(0.382707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.54770 | −0.226295 | −0.113148 | − | 0.993578i | \(-0.536093\pi\) | ||||
−0.113148 | + | 0.993578i | \(0.536093\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.25155 | −0.336029 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.6109 | 0.837951 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5641 | 0.875259 | 0.437630 | − | 0.899155i | \(-0.355818\pi\) | ||||
0.437630 | + | 0.899155i | \(0.355818\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.0029 | −0.688993 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6949 | 0.513581 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.5125 | 1.91901 | 0.959506 | − | 0.281687i | \(-0.0908939\pi\) | ||||
0.959506 | + | 0.281687i | \(0.0908939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.9536 | 0.441690 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3.79509 | −0.152785 | −0.0763923 | − | 0.997078i | \(-0.524340\pi\) | ||||
−0.0763923 | + | 0.997078i | \(0.524340\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.0986 | 0.405898 | 0.202949 | − | 0.979189i | \(-0.434947\pi\) | ||||
0.202949 | + | 0.979189i | \(0.434947\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.61071 | 0.265279 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 31.5934 | 1.26576 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.80561 | 0.152224 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.1752 | 0.925529 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.2009 | 2.08139 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.5310 | −1.21542 | −0.607709 | − | 0.794160i | \(-0.707911\pi\) | ||||
−0.607709 | + | 0.794160i | \(0.707911\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.39616 | 0.293971 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.90379 | 0.393020 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.6137 | −1.05447 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.66362 | −0.0658117 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.23785 | −0.127887 | −0.0639437 | − | 0.997954i | \(-0.520368\pi\) | ||||
−0.0639437 | + | 0.997954i | \(0.520368\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.2108 | −1.19140 | −0.595698 | − | 0.803209i | \(-0.703124\pi\) | ||||
−0.595698 | + | 0.803209i | \(0.703124\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.60460 | 0.260056 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −31.9382 | −1.25562 | −0.627810 | − | 0.778367i | \(-0.716048\pi\) | ||||
−0.627810 | + | 0.778367i | \(0.716048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −64.6717 | −2.53859 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.79377 | 0.227076 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.2765 | −0.832613 | −0.416307 | − | 0.909224i | \(-0.636676\pi\) | ||||
−0.416307 | + | 0.909224i | \(0.636676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 25.4221 | 0.993324 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.89727 | −0.152047 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.4493 | −0.796593 | −0.398297 | − | 0.917257i | \(-0.630399\pi\) | ||||
−0.398297 | + | 0.917257i | \(0.630399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.9118 | 0.891165 | 0.445582 | − | 0.895241i | \(-0.352997\pi\) | ||||
0.445582 | + | 0.895241i | \(0.352997\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.7038 | −0.571047 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.3437 | 0.982786 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.6753 | 0.955432 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.81997 | −0.0703641 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.47803 | 0.0570588 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.8721 | 1.15149 | 0.575743 | − | 0.817630i | \(-0.304713\pi\) | ||||
0.575743 | + | 0.817630i | \(0.304713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.42078 | −0.131666 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −10.0786 | −0.387353 | −0.193676 | − | 0.981065i | \(-0.562041\pi\) | ||||
−0.193676 | + | 0.981065i | \(0.562041\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.2091 | 0.545295 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 21.8780 | 0.838365 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 17.1938 | 0.657901 | 0.328951 | − | 0.944347i | \(-0.393305\pi\) | ||||
0.328951 | + | 0.944347i | \(0.393305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.69810 | −0.179505 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.04962 | 0.0400455 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.62566 | −0.290515 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.30843 | 0.163900 | 0.0819502 | − | 0.996636i | \(-0.473885\pi\) | ||||
0.0819502 | + | 0.996636i | \(0.473885\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 23.8448 | 0.905788 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.5657 | 0.628371 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 66.2153 | 2.50808 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −17.9898 | −0.680435 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.4059 | −0.770720 | −0.385360 | − | 0.922766i | \(-0.625923\pi\) | ||||
−0.385360 | + | 0.922766i | \(0.625923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.4224 | −1.14740 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.24227 | −0.310422 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −54.0614 | −2.03319 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −8.65515 | −0.325051 | −0.162525 | − | 0.986704i | \(-0.551964\pi\) | ||||
−0.162525 | + | 0.986704i | \(0.551964\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.21505 | 0.233083 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.40815 | −0.314888 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.7324 | 0.476165 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.1655 | −1.01452 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −37.7603 | −1.40822 | −0.704111 | − | 0.710090i | \(-0.748654\pi\) | ||||
−0.704111 | + | 0.710090i | \(0.748654\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.5566 | 0.393148 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.7168 | 0.807657 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.7685 | −0.474210 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.5464 | 1.87466 | 0.937332 | − | 0.348438i | \(-0.113288\pi\) | ||||
0.937332 | + | 0.348438i | \(0.113288\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.9254 | 1.47669 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.7422 | 1.68953 | 0.844763 | − | 0.535140i | \(-0.179741\pi\) | ||||
0.844763 | + | 0.535140i | \(0.179741\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 17.2792 | 0.637352 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.1936 | 1.59106 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.01671 | 0.331685 | 0.165842 | − | 0.986152i | \(-0.446966\pi\) | ||||
0.165842 | + | 0.986152i | \(0.446966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.56927 | 0.314800 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.8707 | 0.912416 | 0.456208 | − | 0.889873i | \(-0.349207\pi\) | ||||
0.456208 | + | 0.889873i | \(0.349207\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20.2188 | −0.740761 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.1118 | 0.516326 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.06778 | 0.258251 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −50.0545 | −1.82652 | −0.913258 | − | 0.407382i | \(-0.866442\pi\) | ||||
−0.913258 | + | 0.407382i | \(0.866442\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.4390 | 1.10926 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.2130 | 0.881201 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.17487 | 0.224430 | 0.112215 | − | 0.993684i | \(-0.464206\pi\) | ||||
0.112215 | + | 0.993684i | \(0.464206\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −34.6045 | −1.25606 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.9236 | −1.08473 | −0.542365 | − | 0.840143i | \(-0.682471\pi\) | ||||
−0.542365 | + | 0.840143i | \(0.682471\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −24.4705 | −0.885890 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.54655 | 0.345156 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.9130 | −0.863448 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.6073 | −0.670995 | −0.335497 | − | 0.942041i | \(-0.608904\pi\) | ||||
−0.335497 | + | 0.942041i | \(0.608904\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.0748 | −0.831020 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.9797 | 1.07830 | 0.539148 | − | 0.842211i | \(-0.318746\pi\) | ||||
0.539148 | + | 0.842211i | \(0.318746\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.35088 | 0.156288 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −31.3013 | −1.12293 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.5898 | −1.38262 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.70839 | 0.311611 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.73263 | 0.133393 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −11.2141 | −0.400250 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.9894 | 1.35417 | 0.677087 | − | 0.735903i | \(-0.263242\pi\) | ||||
0.677087 | + | 0.735903i | \(0.263242\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.5164 | 0.766004 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −78.8216 | −2.80257 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.546517 | 0.0194074 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.95102 | 0.175595 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.2033 | 0.786483 | 0.393242 | − | 0.919435i | \(-0.371354\pi\) | ||||
0.393242 | + | 0.919435i | \(0.371354\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −49.8253 | −1.76269 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.93566 | −0.245059 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.4007 | 0.719925 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −37.8424 | −1.33377 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.2955 | 0.573629 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15.6829 | −0.551380 | −0.275690 | − | 0.961247i | \(-0.588906\pi\) | ||||
−0.275690 | + | 0.961247i | \(0.588906\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.4336 | 0.506834 | 0.253417 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253417 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.9830 | −0.911263 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.70417 | −0.129751 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.2683 | −0.814054 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.81684 | 0.308085 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.25042 | 0.322842 | 0.161421 | − | 0.986886i | \(-0.448392\pi\) | ||||
0.161421 | + | 0.986886i | \(0.448392\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.7006 | −0.547290 | −0.273645 | − | 0.961831i | \(-0.588229\pi\) | ||||
−0.273645 | + | 0.961831i | \(0.588229\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17.9064 | 0.623422 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.4073 | 1.05737 | 0.528683 | − | 0.848819i | \(-0.322686\pi\) | ||||
0.528683 | + | 0.848819i | \(0.322686\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.7371 | −1.34539 | −0.672697 | − | 0.739918i | \(-0.734864\pi\) | ||||
−0.672697 | + | 0.739918i | \(0.734864\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.26377 | −0.286667 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 104.454 | 3.61913 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.25667 | −0.0434889 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.27190 | −0.0439632 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −32.4743 | −1.12114 | −0.560568 | − | 0.828108i | \(-0.689417\pi\) | ||||
−0.560568 | + | 0.828108i | \(0.689417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0675 | −0.519568 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.956330 | −0.0329378 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6288 | −0.400043 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −74.7108 | −2.56709 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.81438 | 0.268189 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.4257 | 1.55717 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.3706 | −0.731716 | −0.365858 | − | 0.930671i | \(-0.619224\pi\) | ||||
−0.365858 | + | 0.930671i | \(0.619224\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.56367 | −0.190273 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.7853 | −1.32488 | −0.662440 | − | 0.749115i | \(-0.730479\pi\) | ||||
−0.662440 | + | 0.749115i | \(0.730479\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.2770 | 1.40835 | 0.704176 | − | 0.710025i | \(-0.251317\pi\) | ||||
0.704176 | + | 0.710025i | \(0.251317\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −39.7047 | −1.35313 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.03297 | 0.103244 | 0.0516218 | − | 0.998667i | \(-0.483561\pi\) | ||||
0.0516218 | + | 0.998667i | \(0.483561\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.7695 | −0.536179 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 40.7098 | 1.38258 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −32.5334 | −1.10362 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.9713 | 0.541166 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.11931 | −0.105573 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 48.2039 | 1.62959 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.2512 | 0.886439 | 0.443220 | − | 0.896413i | \(-0.353836\pi\) | ||||
0.443220 | + | 0.896413i | \(0.353836\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.0569 | −0.609045 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.69895 | 0.124621 | 0.0623104 | − | 0.998057i | \(-0.480153\pi\) | ||||
0.0623104 | + | 0.998057i | \(0.480153\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.7365 | −1.60646 | −0.803230 | − | 0.595669i | \(-0.796887\pi\) | ||||
−0.803230 | + | 0.595669i | \(0.796887\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15.5257 | 0.521891 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.04390 | 0.0350508 | 0.0175254 | − | 0.999846i | \(-0.494421\pi\) | ||||
0.0175254 | + | 0.999846i | \(0.494421\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.8995 | −1.20403 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.23461 | −0.175366 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 29.0379 | 0.971716 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.86647 | 0.129242 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.7954 | −0.427224 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.74752 | −0.158339 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.9294 | 0.997093 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.9405 | −0.796690 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.15210 | 0.104779 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.2974 | −0.507943 | −0.253971 | − | 0.967212i | \(-0.581737\pi\) | ||||
−0.253971 | + | 0.967212i | \(0.581737\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.8680 | 0.393638 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.8233 | −1.12062 | −0.560308 | − | 0.828285i | \(-0.689317\pi\) | ||||
−0.560308 | + | 0.828285i | \(0.689317\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −73.8701 | −2.44474 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.354830 | −0.0117303 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −92.1507 | −3.04308 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1404 | −0.598396 | −0.299198 | − | 0.954191i | \(-0.596719\pi\) | ||||
−0.299198 | + | 0.954191i | \(0.596719\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.9495 | −0.888018 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.22001 | 0.105988 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −23.5060 | −0.772872 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.31747 | −0.0761158 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.9152 | −1.63767 | −0.818833 | − | 0.574032i | \(-0.805378\pi\) | ||||
−0.818833 | + | 0.574032i | \(0.805378\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −60.8753 | −1.99511 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.51738 | −0.246108 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −49.9725 | −1.63427 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.2081 | −1.47689 | −0.738443 | − | 0.674316i | \(-0.764438\pi\) | ||||
−0.738443 | + | 0.674316i | \(0.764438\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.9480 | 0.814148 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.416944 | 0.0135920 | 0.00679599 | − | 0.999977i | \(-0.497837\pi\) | ||||
0.00679599 | + | 0.999977i | \(0.497837\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 57.6211 | 1.87640 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.72440 | −0.186215 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −40.5028 | −1.31616 | −0.658082 | − | 0.752946i | \(-0.728632\pi\) | ||||
−0.658082 | + | 0.752946i | \(0.728632\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.54336 | 0.244868 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 28.0071 | 0.908192 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 46.8908 | 1.51894 | 0.759470 | − | 0.650542i | \(-0.225458\pi\) | ||||
0.759470 | + | 0.650542i | \(0.225458\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.15768 | −0.134539 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.5389 | −0.631602 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.0298 | 0.549920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.3823 | −0.947815 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.55158 | −0.0499990 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.1349 | −0.744737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.5237 | −0.917262 | −0.458631 | − | 0.888627i | \(-0.651660\pi\) | ||||
−0.458631 | + | 0.888627i | \(0.651660\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −33.6329 | −1.08044 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.4613 | 1.04173 | 0.520867 | − | 0.853638i | \(-0.325609\pi\) | ||||
0.520867 | + | 0.853638i | \(0.325609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −60.0476 | −1.92504 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.62108 | 0.212044 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.7999 | 0.953382 | 0.476691 | − | 0.879071i | \(-0.341836\pi\) | ||||
0.476691 | + | 0.879071i | \(0.341836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.3055 | 1.16033 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.37197 | 0.171514 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.3606 | −0.553717 | −0.276859 | − | 0.960911i | \(-0.589293\pi\) | ||||
−0.276859 | + | 0.960911i | \(0.589293\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.4304 | −0.523515 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.8768 | 0.950989 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.7434 | 1.10478 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.60573 | −0.209838 | −0.104919 | − | 0.994481i | \(-0.533458\pi\) | ||||
−0.104919 | + | 0.994481i | \(0.533458\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.36380 | 0.233683 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6961 | −0.751218 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.907767 | 0.0287493 | 0.0143746 | − | 0.999897i | \(-0.495424\pi\) | ||||
0.0143746 | + | 0.999897i | \(0.495424\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.87153 | 0.217406 |
(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 | 4008.2.a.m.1.8 | ✓ | 13 | |
4.3 | odd | 2 | 8016.2.a.bg.1.8 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.m.1.8 | ✓ | 13 | 1.1 | even | 1 | trivial | |
8016.2.a.bg.1.8 | 13 | 4.3 | odd | 2 |