Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1000,2,Mod(1,1000)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1000, 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("1000.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1000 = 2^{3} \cdot 5^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1000.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: | \(7.98504020213\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.4400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.54336\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1000.1 |
$q$-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 | ||||||||
\(3\) | 2.54336 | 1.46841 | 0.734205 | − | 0.678927i | \(-0.237555\pi\) | ||||
0.734205 | + | 0.678927i | \(0.237555\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.87918 | 1.08823 | 0.544114 | − | 0.839012i | \(-0.316866\pi\) | ||||
0.544114 | + | 0.839012i | \(0.316866\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.46869 | 1.15623 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.99442 | 1.50588 | 0.752938 | − | 0.658092i | \(-0.228636\pi\) | ||||
0.752938 | + | 0.658092i | \(0.228636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.149344 | 0.0414206 | 0.0207103 | − | 0.999786i | \(-0.493407\pi\) | ||||
0.0207103 | + | 0.999786i | \(0.493407\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.23049 | −1.51112 | −0.755558 | − | 0.655082i | \(-0.772634\pi\) | ||||
−0.755558 | + | 0.655082i | \(0.772634\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.90770 | −0.437656 | −0.218828 | − | 0.975763i | \(-0.570223\pi\) | ||||
−0.218828 | + | 0.975763i | \(0.570223\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.32279 | 1.59796 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.35689 | 0.908474 | 0.454237 | − | 0.890881i | \(-0.349912\pi\) | ||||
0.454237 | + | 0.890881i | \(0.349912\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.19205 | 0.229410 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.93525 | −1.65923 | −0.829617 | − | 0.558333i | \(-0.811441\pi\) | ||||
−0.829617 | + | 0.558333i | \(0.811441\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.99442 | −1.61545 | −0.807723 | − | 0.589562i | \(-0.799300\pi\) | ||||
−0.807723 | + | 0.589562i | \(0.799300\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.7026 | 2.21124 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.56444 | −0.421591 | −0.210795 | − | 0.977530i | \(-0.567605\pi\) | ||||
−0.210795 | + | 0.977530i | \(0.567605\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.379836 | 0.0608225 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.99787 | 1.24906 | 0.624529 | − | 0.781002i | \(-0.285291\pi\) | ||||
0.624529 | + | 0.781002i | \(0.285291\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.54336 | 0.692856 | 0.346428 | − | 0.938077i | \(-0.387394\pi\) | ||||
0.346428 | + | 0.938077i | \(0.387394\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.68713 | 1.41301 | 0.706507 | − | 0.707706i | \(-0.250270\pi\) | ||||
0.706507 | + | 0.707706i | \(0.250270\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.28967 | 0.184238 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.8464 | −2.21894 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.52786 | 0.209868 | 0.104934 | − | 0.994479i | \(-0.466537\pi\) | ||||
0.104934 | + | 0.994479i | \(0.466537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.85197 | −0.642659 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.4666 | 1.49282 | 0.746409 | − | 0.665487i | \(-0.231776\pi\) | ||||
0.746409 | + | 0.665487i | \(0.231776\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.55541 | −0.455224 | −0.227612 | − | 0.973752i | \(-0.573092\pi\) | ||||
−0.227612 | + | 0.973752i | \(0.573092\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.98698 | 1.25824 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.08115 | 0.498592 | 0.249296 | − | 0.968427i | \(-0.419801\pi\) | ||||
0.249296 | + | 0.968427i | \(0.419801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.0811 | 1.33401 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.56444 | −1.01641 | −0.508206 | − | 0.861236i | \(-0.669691\pi\) | ||||
−0.508206 | + | 0.861236i | \(0.669691\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.2671 | 1.78687 | 0.893437 | − | 0.449188i | \(-0.148287\pi\) | ||||
0.893437 | + | 0.449188i | \(0.148287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.3798 | 1.63873 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −15.0867 | −1.69739 | −0.848695 | − | 0.528883i | \(-0.822611\pi\) | ||||
−0.848695 | + | 0.528883i | \(0.822611\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.37426 | −0.819362 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.96033 | −0.983524 | −0.491762 | − | 0.870730i | \(-0.663647\pi\) | ||||
−0.491762 | + | 0.870730i | \(0.663647\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22.7256 | −2.43644 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.26362 | −0.981942 | −0.490971 | − | 0.871176i | \(-0.663358\pi\) | ||||
−0.490971 | + | 0.871176i | \(0.663358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.429988 | 0.0450750 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −22.8761 | −2.37214 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.66606 | −0.372232 | −0.186116 | − | 0.982528i | \(-0.559590\pi\) | ||||
−0.186116 | + | 0.982528i | \(0.559590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 17.3241 | 1.74114 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.28409 | −0.227275 | −0.113638 | − | 0.993522i | \(-0.536250\pi\) | ||||
−0.113638 | + | 0.993522i | \(0.536250\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7379 | −1.45217 | −0.726083 | − | 0.687607i | \(-0.758661\pi\) | ||||
−0.726083 | + | 0.687607i | \(0.758661\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.71681 | −0.262644 | −0.131322 | − | 0.991340i | \(-0.541922\pi\) | ||||
−0.131322 | + | 0.991340i | \(0.541922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.381966 | 0.0365857 | 0.0182929 | − | 0.999833i | \(-0.494177\pi\) | ||||
0.0182929 | + | 0.999833i | \(0.494177\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.52229 | −0.619068 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.8395 | 1.67820 | 0.839100 | − | 0.543978i | \(-0.183082\pi\) | ||||
0.839100 | + | 0.543978i | \(0.183082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.518029 | 0.0478918 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −17.9387 | −1.64444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.9443 | 1.26766 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.3415 | 1.83413 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.77385 | −0.246140 | −0.123070 | − | 0.992398i | \(-0.539274\pi\) | ||||
−0.123070 | + | 0.992398i | \(0.539274\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.5554 | 1.01740 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.08672 | −0.269688 | −0.134844 | − | 0.990867i | \(-0.543053\pi\) | ||||
−0.134844 | + | 0.990867i | \(0.543053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.49261 | −0.476270 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.5774 | 1.58717 | 0.793587 | − | 0.608457i | \(-0.208211\pi\) | ||||
0.793587 | + | 0.608457i | \(0.208211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.6034 | −0.899372 | −0.449686 | − | 0.893187i | \(-0.648464\pi\) | ||||
−0.449686 | + | 0.893187i | \(0.648464\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 24.6379 | 2.07488 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.745888 | 0.0623743 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.28009 | 0.270537 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.91672 | −0.238947 | −0.119474 | − | 0.992837i | \(-0.538121\pi\) | ||||
−0.119474 | + | 0.992837i | \(0.538121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0198 | 0.815403 | 0.407702 | − | 0.913115i | \(-0.366330\pi\) | ||||
0.407702 | + | 0.913115i | \(0.366330\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.6116 | −1.74720 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.2305 | −0.816482 | −0.408241 | − | 0.912874i | \(-0.633858\pi\) | ||||
−0.408241 | + | 0.912874i | \(0.633858\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.88591 | 0.308173 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.5443 | 0.988626 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.49508 | −0.665386 | −0.332693 | − | 0.943035i | \(-0.607957\pi\) | ||||
−0.332693 | + | 0.943035i | \(0.607957\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.35745 | −0.414572 | −0.207286 | − | 0.978280i | \(-0.566463\pi\) | ||||
−0.207286 | + | 0.978280i | \(0.566463\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9777 | −0.998284 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.61722 | −0.506031 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.2193 | −1.23313 | −0.616567 | − | 0.787303i | \(-0.711477\pi\) | ||||
−0.616567 | + | 0.787303i | \(0.711477\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 29.1636 | 2.19207 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.65116 | 0.272900 | 0.136450 | − | 0.990647i | \(-0.456431\pi\) | ||||
0.136450 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.33424 | 0.396491 | 0.198246 | − | 0.980152i | \(-0.436476\pi\) | ||||
0.198246 | + | 0.980152i | \(0.436476\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.04270 | −0.668456 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.1177 | −2.27555 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.43212 | 0.249650 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.09230 | 0.151393 | 0.0756967 | − | 0.997131i | \(-0.475882\pi\) | ||||
0.0756967 | + | 0.997131i | \(0.475882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.0366 | −1.22632 | −0.613160 | − | 0.789959i | \(-0.710102\pi\) | ||||
−0.613160 | + | 0.789959i | \(0.710102\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8315 | 1.55543 | 0.777715 | − | 0.628617i | \(-0.216379\pi\) | ||||
0.777715 | + | 0.628617i | \(0.216379\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.31032 | 0.376439 | 0.188219 | − | 0.982127i | \(-0.439728\pi\) | ||||
0.188219 | + | 0.982127i | \(0.439728\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3798 | 0.732137 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −25.7262 | −1.80562 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.1127 | 1.05041 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −9.52786 | −0.659056 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.21196 | 0.358806 | 0.179403 | − | 0.983776i | \(-0.442583\pi\) | ||||
0.179403 | + | 0.983776i | \(0.442583\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −21.7825 | −1.49251 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −25.8965 | −1.75797 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 38.8297 | 2.62387 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.930487 | −0.0625914 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.72928 | 0.249731 | 0.124865 | − | 0.992174i | \(-0.460150\pi\) | ||||
0.124865 | + | 0.992174i | \(0.460150\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5725 | 1.23270 | 0.616350 | − | 0.787473i | \(-0.288611\pi\) | ||||
0.616350 | + | 0.787473i | \(0.288611\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.7005 | 1.69834 | 0.849168 | − | 0.528122i | \(-0.177104\pi\) | ||||
0.849168 | + | 0.528122i | \(0.177104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 36.5731 | 2.40634 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 21.5626 | 1.41261 | 0.706307 | − | 0.707906i | \(-0.250360\pi\) | ||||
0.706307 | + | 0.707906i | \(0.250360\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −38.3710 | −2.49246 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.91328 | −0.317813 | −0.158907 | − | 0.987294i | \(-0.550797\pi\) | ||||
−0.158907 | + | 0.987294i | \(0.550797\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.2172 | −1.75321 | −0.876607 | − | 0.481206i | \(-0.840199\pi\) | ||||
−0.876607 | + | 0.481206i | \(0.840199\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.3316 | −1.43257 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.284904 | −0.0181280 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.7894 | −1.44422 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1177 | −0.701744 | −0.350872 | − | 0.936423i | \(-0.614115\pi\) | ||||
−0.350872 | + | 0.936423i | \(0.614115\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.7602 | 1.36805 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.52786 | 0.344819 | 0.172409 | − | 0.985025i | \(-0.444845\pi\) | ||||
0.172409 | + | 0.985025i | \(0.444845\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.38347 | −0.458786 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.9936 | −1.91846 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.3327 | −0.760468 | −0.380234 | − | 0.924890i | \(-0.624156\pi\) | ||||
−0.380234 | + | 0.924890i | \(0.624156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −23.5607 | −1.44189 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.94427 | 0.179515 | 0.0897577 | − | 0.995964i | \(-0.471391\pi\) | ||||
0.0897577 | + | 0.995964i | \(0.471391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0000 | −0.971931 | −0.485965 | − | 0.873978i | \(-0.661532\pi\) | ||||
−0.485965 | + | 0.873978i | \(0.661532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.09362 | 0.0661887 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.17476 | −0.431090 | −0.215545 | − | 0.976494i | \(-0.569153\pi\) | ||||
−0.215545 | + | 0.976494i | \(0.569153\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −31.1989 | −1.86783 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1143 | −1.25957 | −0.629786 | − | 0.776769i | \(-0.716857\pi\) | ||||
−0.629786 | + | 0.776769i | \(0.716857\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.44672 | −0.0859983 | −0.0429992 | − | 0.999075i | \(-0.513691\pi\) | ||||
−0.0429992 | + | 0.999075i | \(0.513691\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23.0273 | 1.35926 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.8190 | 1.28347 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.32411 | −0.546589 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.5658 | −0.675678 | −0.337839 | − | 0.941204i | \(-0.609696\pi\) | ||||
−0.337839 | + | 0.941204i | \(0.609696\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.95359 | 0.345462 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.650676 | 0.0376296 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.0811 | 0.753985 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.80927 | −0.333734 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.6574 | 1.63556 | 0.817781 | − | 0.575529i | \(-0.195204\pi\) | ||||
0.817781 | + | 0.575529i | \(0.195204\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37.4838 | −2.13238 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.60658 | 0.147806 | 0.0739029 | − | 0.997265i | \(-0.476455\pi\) | ||||
0.0739029 | + | 0.997265i | \(0.476455\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.298688 | 0.0168829 | 0.00844143 | − | 0.999964i | \(-0.497313\pi\) | ||||
0.00844143 | + | 0.999964i | \(0.497313\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.2100 | 0.854280 | 0.427140 | − | 0.904186i | \(-0.359521\pi\) | ||||
0.427140 | + | 0.904186i | \(0.359521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −44.6264 | −2.49860 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.90983 | −0.385669 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.8859 | 0.661350 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.971478 | 0.0537228 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 27.8910 | 1.53768 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.4586 | 0.739749 | 0.369875 | − | 0.929082i | \(-0.379401\pi\) | ||||
0.369875 | + | 0.929082i | \(0.379401\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.89523 | −0.487456 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.50508 | −0.463301 | −0.231651 | − | 0.972799i | \(-0.574413\pi\) | ||||
−0.231651 | + | 0.972799i | \(0.574413\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 45.3723 | 2.46429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −44.9220 | −2.43266 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4411 | −0.887734 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.6797 | 0.895412 | 0.447706 | − | 0.894181i | \(-0.352241\pi\) | ||||
0.447706 | + | 0.894181i | \(0.352241\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.1657 | −1.07945 | −0.539724 | − | 0.841842i | \(-0.681471\pi\) | ||||
−0.539724 | + | 0.841842i | \(0.681471\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.178025 | 0.00950229 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.2448 | −1.23719 | −0.618597 | − | 0.785709i | \(-0.712299\pi\) | ||||
−0.618597 | + | 0.785709i | \(0.712299\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −45.6246 | −2.41471 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.35247 | −0.176937 | −0.0884683 | − | 0.996079i | \(-0.528197\pi\) | ||||
−0.0884683 | + | 0.996079i | \(0.528197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3607 | −0.808457 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 35.4653 | 1.86145 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.15982 | 0.373740 | 0.186870 | − | 0.982385i | \(-0.440166\pi\) | ||||
0.186870 | + | 0.982385i | \(0.440166\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 27.7421 | 1.44420 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.39899 | 0.228384 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.8520 | 0.872562 | 0.436281 | − | 0.899810i | \(-0.356295\pi\) | ||||
0.436281 | + | 0.899810i | \(0.356295\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.33443 | −0.0687265 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.3915 | 0.687874 | 0.343937 | − | 0.938993i | \(-0.388239\pi\) | ||||
0.343937 | + | 0.938993i | \(0.388239\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.05491 | −0.361434 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.1431 | 0.569383 | 0.284692 | − | 0.958619i | \(-0.408109\pi\) | ||||
0.284692 | + | 0.958619i | \(0.408109\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 15.7595 | 0.801101 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.96130 | −0.251548 | −0.125774 | − | 0.992059i | \(-0.540141\pi\) | ||||
−0.125774 | + | 0.992059i | \(0.540141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.1456 | −1.37281 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.85066 | −0.396013 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.5408 | 0.679594 | 0.339797 | − | 0.940499i | \(-0.389642\pi\) | ||||
0.339797 | + | 0.940499i | \(0.389642\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −13.9697 | −0.699359 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6515 | 0.581846 | 0.290923 | − | 0.956746i | \(-0.406038\pi\) | ||||
0.290923 | + | 0.956746i | \(0.406038\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.34326 | −0.0669128 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.8079 | −0.634863 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.2172 | 0.950230 | 0.475115 | − | 0.879924i | \(-0.342406\pi\) | ||||
0.475115 | + | 0.879924i | \(0.342406\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47.2490 | 2.33062 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.0143 | 1.62453 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −26.9684 | −1.32065 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.48329 | 0.414436 | 0.207218 | − | 0.978295i | \(-0.433559\pi\) | ||||
0.207218 | + | 0.978295i | \(0.433559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.7803 | 0.574138 | 0.287069 | − | 0.957910i | \(-0.407319\pi\) | ||||
0.287069 | + | 0.957910i | \(0.407319\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 33.6016 | 1.63377 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.2367 | −0.495387 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.89706 | 0.0915911 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.8018 | 1.09833 | 0.549163 | − | 0.835716i | \(-0.314947\pi\) | ||||
0.549163 | + | 0.835716i | \(0.314947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.9559 | −0.959020 | −0.479510 | − | 0.877536i | \(-0.659186\pi\) | ||||
−0.479510 | + | 0.877536i | \(0.659186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.31164 | −0.397600 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.74540 | −0.0833036 | −0.0416518 | − | 0.999132i | \(-0.513262\pi\) | ||||
−0.0416518 | + | 0.999132i | \(0.513262\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.47345 | 0.213022 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.198339 | 0.00942337 | 0.00471169 | − | 0.999989i | \(-0.498500\pi\) | ||||
0.00471169 | + | 0.999989i | \(0.498500\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.41828 | −0.350873 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.5751 | −1.63170 | −0.815849 | − | 0.578265i | \(-0.803730\pi\) | ||||
−0.815849 | + | 0.578265i | \(0.803730\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 39.9448 | 1.88093 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 25.4841 | 1.19735 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7597 | 0.971097 | 0.485548 | − | 0.874210i | \(-0.338620\pi\) | ||||
0.485548 | + | 0.874210i | \(0.338620\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.42705 | −0.346665 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.52016 | 0.350249 | 0.175124 | − | 0.984546i | \(-0.443967\pi\) | ||||
0.175124 | + | 0.984546i | \(0.443967\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.05820 | 0.374496 | 0.187248 | − | 0.982313i | \(-0.440043\pi\) | ||||
0.187248 | + | 0.982313i | \(0.440043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.2993 | 1.21699 | 0.608494 | − | 0.793559i | \(-0.291774\pi\) | ||||
0.608494 | + | 0.793559i | \(0.291774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.7504 | 0.542581 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.0198 | −1.19893 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.6915 | 1.04336 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.29969 | 0.242656 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.0533 | 1.69301 | 0.846504 | − | 0.532383i | \(-0.178703\pi\) | ||||
0.846504 | + | 0.532383i | \(0.178703\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.382983 | −0.0174625 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 31.9046 | 1.45171 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −40.6512 | −1.84208 | −0.921042 | − | 0.389464i | \(-0.872660\pi\) | ||||
−0.921042 | + | 0.389464i | \(0.872660\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.6061 | −0.977060 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.15066 | −0.142187 | −0.0710937 | − | 0.997470i | \(-0.522649\pi\) | ||||
−0.0710937 | + | 0.997470i | \(0.522649\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 55.6710 | 2.50730 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.6585 | −1.10609 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 32.7267 | 1.46505 | 0.732525 | − | 0.680740i | \(-0.238342\pi\) | ||||
0.732525 | + | 0.680740i | \(0.238342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.6259 | −0.608761 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.1097 | 1.03041 | 0.515205 | − | 0.857067i | \(-0.327716\pi\) | ||||
0.515205 | + | 0.857067i | \(0.327716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.0070 | −1.46589 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.87476 | 0.171746 | 0.0858728 | − | 0.996306i | \(-0.472632\pi\) | ||||
0.0858728 | + | 0.996306i | \(0.472632\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.9566 | 1.94453 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.27407 | −0.100403 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 48.3816 | 2.12782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −41.2517 | −1.81075 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.8020 | 1.43708 | 0.718541 | − | 0.695485i | \(-0.244810\pi\) | ||||
0.718541 | + | 0.695485i | \(0.244810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.8927 | −0.957300 | −0.478650 | − | 0.878006i | \(-0.658874\pi\) | ||||
−0.478650 | + | 0.878006i | \(0.658874\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.0397 | 2.44113 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.01751 | −0.174674 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.7739 | 1.72604 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.19444 | 0.0517367 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.28622 | 0.400730 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.44114 | 0.277440 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6477 | 0.801728 | 0.400864 | − | 0.916138i | \(-0.368710\pi\) | ||||
0.400864 | + | 0.916138i | \(0.368710\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 13.5669 | 0.582212 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.73673 | −0.117014 | −0.0585070 | − | 0.998287i | \(-0.518634\pi\) | ||||
−0.0585070 | + | 0.998287i | \(0.518634\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.3326 | −0.526344 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.0458 | 0.726175 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −43.4374 | −1.84714 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.3816 | 1.54154 | 0.770770 | − | 0.637114i | \(-0.219872\pi\) | ||||
0.770770 | + | 0.637114i | \(0.219872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.678524 | 0.0286985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −79.1436 | −3.34145 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −17.7713 | −0.748971 | −0.374486 | − | 0.927233i | \(-0.622181\pi\) | ||||
−0.374486 | + | 0.927233i | \(0.622181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −21.2318 | −0.891652 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.1644 | 0.677648 | 0.338824 | − | 0.940850i | \(-0.389971\pi\) | ||||
0.338824 | + | 0.940850i | \(0.389971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.10394 | −0.129896 | −0.0649478 | − | 0.997889i | \(-0.520688\pi\) | ||||
−0.0649478 | + | 0.997889i | \(0.520688\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.32148 | 0.222308 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.6122 | −0.733204 | −0.366602 | − | 0.930378i | \(-0.619479\pi\) | ||||
−0.366602 | + | 0.930378i | \(0.619479\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −43.3302 | −1.80074 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.7984 | −1.07030 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.63080 | 0.316035 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.16181 | 0.378148 | 0.189074 | − | 0.981963i | \(-0.439451\pi\) | ||||
0.189074 | + | 0.981963i | \(0.439451\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.1587 | 0.707010 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 55.5254 | 2.28401 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.25096 | −0.215631 | −0.107816 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107816 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5061 | 0.552767 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.14245 | 0.0875382 | 0.0437691 | − | 0.999042i | \(-0.486063\pi\) | ||||
0.0437691 | + | 0.999042i | \(0.486063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.13849 | −0.372767 | −0.186383 | − | 0.982477i | \(-0.559677\pi\) | ||||
−0.186383 | + | 0.982477i | \(0.559677\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 14.1562 | 0.576487 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −45.1034 | −1.83069 | −0.915346 | − | 0.402669i | \(-0.868083\pi\) | ||||
−0.915346 | + | 0.402669i | \(0.868083\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −65.4310 | −2.65140 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.44672 | 0.0585279 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.6902 | 1.03762 | 0.518808 | − | 0.854891i | \(-0.326376\pi\) | ||||
0.518808 | + | 0.854891i | \(0.326376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.2974 | 0.454815 | 0.227408 | − | 0.973800i | \(-0.426975\pi\) | ||||
0.227408 | + | 0.973800i | \(0.426975\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.36868 | −0.255979 | −0.127990 | − | 0.991776i | \(-0.540852\pi\) | ||||
−0.127990 | + | 0.991776i | \(0.540852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.19362 | 0.208413 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −26.6716 | −1.06858 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.2328 | −0.967765 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.9777 | 0.637072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.5148 | −1.41382 | −0.706910 | − | 0.707303i | \(-0.749912\pi\) | ||||
−0.706910 | + | 0.707303i | \(0.749912\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.2559 | 0.526875 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.192604 | 0.00763125 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −29.7074 | −1.17521 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5628 | 0.614693 | 0.307347 | − | 0.951598i | \(-0.400559\pi\) | ||||
0.307347 | + | 0.951598i | \(0.400559\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.8252 | 1.57055 | 0.785277 | − | 0.619144i | \(-0.212520\pi\) | ||||
0.785277 | + | 0.619144i | \(0.212520\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.0949 | −0.632757 | −0.316379 | − | 0.948633i | \(-0.602467\pi\) | ||||
−0.316379 | + | 0.948633i | \(0.602467\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 57.2689 | 2.24800 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −65.8643 | −2.58143 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.0700 | 1.72459 | 0.862296 | − | 0.506404i | \(-0.169026\pi\) | ||||
0.862296 | + | 0.506404i | \(0.169026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 52.9567 | 2.06604 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 23.4133 | 0.912051 | 0.456026 | − | 0.889967i | \(-0.349273\pi\) | ||||
0.456026 | + | 0.889967i | \(0.349273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8679 | −0.578294 | −0.289147 | − | 0.957285i | \(-0.593372\pi\) | ||||
−0.289147 | + | 0.957285i | \(0.593372\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.36657 | −0.0919098 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.9299 | −1.50737 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 9.48490 | 0.366708 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −17.7572 | −0.685511 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.8979 | 0.882648 | 0.441324 | − | 0.897348i | \(-0.354509\pi\) | ||||
0.441324 | + | 0.897348i | \(0.354509\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.9295 | −0.612220 | −0.306110 | − | 0.951996i | \(-0.599028\pi\) | ||||
−0.306110 | + | 0.951996i | \(0.599028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.5552 | −0.405073 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 47.2366 | 1.81011 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.8309 | 0.490961 | 0.245480 | − | 0.969402i | \(-0.421054\pi\) | ||||
0.245480 | + | 0.969402i | \(0.421054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 65.3657 | 2.49386 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.228178 | 0.00869287 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.0756 | −1.25825 | −0.629127 | − | 0.777303i | \(-0.716587\pi\) | ||||
−0.629127 | + | 0.777303i | \(0.716587\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 49.8792 | 1.89475 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −49.8307 | −1.88747 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 54.8415 | 2.07430 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.3469 | 0.995109 | 0.497554 | − | 0.867433i | \(-0.334232\pi\) | ||||
0.497554 | + | 0.867433i | \(0.334232\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.89217 | 0.184512 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.57630 | −0.247327 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 49.1651 | 1.84643 | 0.923217 | − | 0.384278i | \(-0.125550\pi\) | ||||
0.923217 | + | 0.384278i | \(0.125550\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −52.3312 | −1.96257 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −39.1877 | −1.46759 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.4962 | −0.466681 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.5785 | 0.767449 | 0.383724 | − | 0.923448i | \(-0.374641\pi\) | ||||
0.383724 | + | 0.923448i | \(0.374641\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.4330 | −1.58029 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −69.2232 | −2.57444 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.9611 | −0.703228 | −0.351614 | − | 0.936145i | \(-0.614367\pi\) | ||||
−0.351614 | + | 0.936145i | \(0.614367\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −34.6744 | −1.28424 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −28.3074 | −1.04699 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −40.6241 | −1.50049 | −0.750243 | − | 0.661162i | \(-0.770063\pi\) | ||||
−0.750243 | + | 0.661162i | \(0.770063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.3830 | 0.750817 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.5625 | −1.34497 | −0.672486 | − | 0.740109i | \(-0.734774\pi\) | ||||
−0.672486 | + | 0.740109i | \(0.734774\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.724614 | −0.0266193 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36.8890 | −1.35333 | −0.676664 | − | 0.736292i | \(-0.736575\pi\) | ||||
−0.676664 | + | 0.736292i | \(0.736575\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −31.0806 | −1.13718 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.82218 | −0.285816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.0051 | −1.05841 | −0.529205 | − | 0.848494i | \(-0.677510\pi\) | ||||
−0.529205 | + | 0.848494i | \(0.677510\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.2764 | −1.03045 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.7976 | 1.11936 | 0.559678 | − | 0.828710i | \(-0.310925\pi\) | ||||
0.559678 | + | 0.828710i | \(0.310925\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 55.3440 | 2.00886 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.9315 | 0.650017 | 0.325008 | − | 0.945711i | \(-0.394633\pi\) | ||||
0.325008 | + | 0.945711i | \(0.394633\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.09975 | 0.0398136 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.71246 | 0.0618335 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.274769 | 0.00990844 | 0.00495422 | − | 0.999988i | \(-0.498423\pi\) | ||||
0.00495422 | + | 0.999988i | \(0.498423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0594 | 0.506335 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −40.0620 | −1.44093 | −0.720465 | − | 0.693491i | \(-0.756072\pi\) | ||||
−0.720465 | + | 0.693491i | \(0.756072\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −18.7788 | −0.673687 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.2575 | −0.546658 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −42.7744 | −1.53059 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.6512 | −0.380644 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.0911 | 0.431000 | 0.215500 | − | 0.976504i | \(-0.430862\pi\) | ||||
0.215500 | + | 0.976504i | \(0.430862\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −31.3666 | −1.11668 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.3631 | 1.82626 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.530980 | −0.0188557 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 37.4182 | 1.32542 | 0.662710 | − | 0.748876i | \(-0.269406\pi\) | ||||
0.662710 | + | 0.748876i | \(0.269406\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.3556 | −2.13523 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −32.1326 | −1.13535 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 76.2502 | 2.69081 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.48835 | 0.263602 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.80589 | 0.0634919 | 0.0317459 | − | 0.999496i | \(-0.489893\pi\) | ||||
0.0317459 | + | 0.999496i | \(0.489893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6623 | 0.479749 | 0.239874 | − | 0.970804i | \(-0.422894\pi\) | ||||
0.239874 | + | 0.970804i | \(0.422894\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −40.6938 | −1.42719 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.66737 | −0.303233 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.49150 | 0.0521171 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.50658 | 0.296882 | 0.148441 | − | 0.988921i | \(-0.452575\pi\) | ||||
0.148441 | + | 0.988921i | \(0.452575\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.897547 | 0.0312865 | 0.0156433 | − | 0.999878i | \(-0.495020\pi\) | ||||
0.0156433 | + | 0.999878i | \(0.495020\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.48640 | 0.329875 | 0.164937 | − | 0.986304i | \(-0.447258\pi\) | ||||
0.164937 | + | 0.986304i | \(0.447258\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 36.5443 | 1.26923 | 0.634617 | − | 0.772827i | \(-0.281158\pi\) | ||||
0.634617 | + | 0.772827i | \(0.281158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.2480 | −0.633017 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −8.03526 | −0.278405 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.7218 | −0.370599 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.24539 | −0.146567 | −0.0732836 | − | 0.997311i | \(-0.523348\pi\) | ||||
−0.0732836 | + | 0.997311i | \(0.523348\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 50.8387 | 1.75306 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −53.7012 | −1.84957 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 40.1480 | 1.37950 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.67952 | −0.126281 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.1730 | −0.383004 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.4472 | −0.563141 | −0.281571 | − | 0.959540i | \(-0.590855\pi\) | ||||
−0.281571 | + | 0.959540i | \(0.590855\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.5917 | 0.669238 | 0.334619 | − | 0.942353i | \(-0.391392\pi\) | ||||
0.334619 | + | 0.942353i | \(0.391392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.49707 | −0.289916 | −0.144958 | − | 0.989438i | \(-0.546305\pi\) | ||||
−0.144958 | + | 0.989438i | \(0.546305\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 58.5667 | 1.99595 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27.1736 | −0.925000 | −0.462500 | − | 0.886619i | \(-0.653048\pi\) | ||||
−0.462500 | + | 0.886619i | \(0.653048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 55.4937 | 1.88466 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −75.3495 | −2.55606 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.609496 | 0.0206520 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.7164 | −0.430385 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.7008 | −1.20553 | −0.602765 | − | 0.797919i | \(-0.705934\pi\) | ||||
−0.602765 | + | 0.797919i | \(0.705934\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29.4159 | −0.992173 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.1477 | −1.89166 | −0.945832 | − | 0.324656i | \(-0.894751\pi\) | ||||
−0.945832 | + | 0.324656i | \(0.894751\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26.2876 | −0.884648 | −0.442324 | − | 0.896855i | \(-0.645846\pi\) | ||||
−0.442324 | + | 0.896855i | \(0.645846\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.03327 | −0.202577 | −0.101289 | − | 0.994857i | \(-0.532297\pi\) | ||||
−0.101289 | + | 0.994857i | \(0.532297\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.98642 | −0.267856 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −36.8302 | −1.23386 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.4801 | −0.618414 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.65490 | 0.0552557 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 80.3674 | 2.68040 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.51934 | −0.317135 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.2701 | 1.10716 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.46094 | −0.148123 | −0.0740615 | − | 0.997254i | \(-0.523596\pi\) | ||||
−0.0740615 | + | 0.997254i | \(0.523596\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.92280 | −0.262783 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.61407 | 0.219134 | 0.109567 | − | 0.993979i | \(-0.465054\pi\) | ||||
0.109567 | + | 0.993979i | \(0.465054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.7517 | −1.48106 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.88723 | −0.293482 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.77131 | 0.0584301 | 0.0292150 | − | 0.999573i | \(-0.490699\pi\) | ||||
0.0292150 | + | 0.999573i | \(0.490699\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 72.8861 | 2.40168 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.27905 | −0.0421004 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −51.1211 | −1.67904 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.5785 | −0.478306 | −0.239153 | − | 0.970982i | \(-0.576870\pi\) | ||||
−0.239153 | + | 0.970982i | \(0.576870\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.46030 | −0.0806330 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.62948 | 0.217040 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −14.6344 | −0.478086 | −0.239043 | − | 0.971009i | \(-0.576834\pi\) | ||||
−0.239043 | + | 0.971009i | \(0.576834\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.759672 | 0.0247910 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.7856 | 0.840587 | 0.420293 | − | 0.907388i | \(-0.361927\pi\) | ||||
0.420293 | + | 0.907388i | \(0.361927\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.8458 | 1.13474 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.45301 | 0.209695 | 0.104847 | − | 0.994488i | \(-0.466565\pi\) | ||||
0.104847 | + | 0.994488i | \(0.466565\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.28005 | 0.0740134 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 38.6846 | 1.25443 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.84133 | −0.221613 | −0.110806 | − | 0.993842i | \(-0.535343\pi\) | ||||
−0.110806 | + | 0.993842i | \(0.535343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −113.501 | −3.66897 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.4876 | 1.72720 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 49.8997 | 1.60967 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.42377 | −0.303677 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.1953 | 1.38907 | 0.694534 | − | 0.719460i | \(-0.255611\pi\) | ||||
0.694534 | + | 0.719460i | \(0.255611\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 30.2302 | 0.971133 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.3074 | 1.03679 | 0.518397 | − | 0.855140i | \(-0.326529\pi\) | ||||
0.518397 | + | 0.855140i | \(0.326529\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.5292 | −0.978721 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −44.9354 | −1.43761 | −0.718806 | − | 0.695211i | \(-0.755311\pi\) | ||||
−0.718806 | + | 0.695211i | \(0.755311\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −46.2664 | −1.47868 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.32492 | 0.0423015 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.9585 | 1.01932 | 0.509660 | − | 0.860376i | \(-0.329771\pi\) | ||||
0.509660 | + | 0.860376i | \(0.329771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 70.9368 | 2.25794 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19.7949 | 0.629442 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.4498 | 0.586078 | 0.293039 | − | 0.956100i | \(-0.405333\pi\) | ||||
0.293039 | + | 0.956100i | \(0.405333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 34.2300 | 1.08626 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.0718 | −0.667351 | −0.333676 | − | 0.942688i | \(-0.608289\pi\) | ||||
−0.333676 | + | 0.942688i | \(0.608289\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.05693 | −0.0967170 |
(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 | 1000.2.a.h.1.3 | yes | 4 | |
3.2 | odd | 2 | 9000.2.a.ba.1.3 | 4 | |||
4.3 | odd | 2 | 2000.2.a.m.1.2 | 4 | |||
5.2 | odd | 4 | 1000.2.c.d.249.2 | 8 | |||
5.3 | odd | 4 | 1000.2.c.d.249.7 | 8 | |||
5.4 | even | 2 | 1000.2.a.e.1.2 | ✓ | 4 | ||
8.3 | odd | 2 | 8000.2.a.bq.1.3 | 4 | |||
8.5 | even | 2 | 8000.2.a.ba.1.2 | 4 | |||
15.14 | odd | 2 | 9000.2.a.r.1.2 | 4 | |||
20.3 | even | 4 | 2000.2.c.j.1249.2 | 8 | |||
20.7 | even | 4 | 2000.2.c.j.1249.7 | 8 | |||
20.19 | odd | 2 | 2000.2.a.r.1.3 | 4 | |||
40.19 | odd | 2 | 8000.2.a.bb.1.2 | 4 | |||
40.29 | even | 2 | 8000.2.a.br.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1000.2.a.e.1.2 | ✓ | 4 | 5.4 | even | 2 | ||
1000.2.a.h.1.3 | yes | 4 | 1.1 | even | 1 | trivial | |
1000.2.c.d.249.2 | 8 | 5.2 | odd | 4 | |||
1000.2.c.d.249.7 | 8 | 5.3 | odd | 4 | |||
2000.2.a.m.1.2 | 4 | 4.3 | odd | 2 | |||
2000.2.a.r.1.3 | 4 | 20.19 | odd | 2 | |||
2000.2.c.j.1249.2 | 8 | 20.3 | even | 4 | |||
2000.2.c.j.1249.7 | 8 | 20.7 | even | 4 | |||
8000.2.a.ba.1.2 | 4 | 8.5 | even | 2 | |||
8000.2.a.bb.1.2 | 4 | 40.19 | odd | 2 | |||
8000.2.a.bq.1.3 | 4 | 8.3 | odd | 2 | |||
8000.2.a.br.1.3 | 4 | 40.29 | even | 2 | |||
9000.2.a.r.1.2 | 4 | 15.14 | odd | 2 | |||
9000.2.a.ba.1.3 | 4 | 3.2 | odd | 2 |