Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8752,2,Mod(1,8752)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8752, 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("8752.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8752 = 2^{4} \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8752.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: | \(69.8850718490\) |
Analytic rank: | \(1\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 4 x^{17} - 18 x^{16} + 84 x^{15} + 116 x^{14} - 708 x^{13} - 282 x^{12} + 3104 x^{11} - 137 x^{10} - 7703 x^{9} + 2068 x^{8} + 11068 x^{7} - 4274 x^{6} - 9021 x^{5} + \cdots + 328 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 547) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Root | \(-2.50138\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8752.1 |
$q$-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 | ||||||||
\(3\) | 3.08733 | 1.78247 | 0.891235 | − | 0.453541i | \(-0.149840\pi\) | ||||
0.891235 | + | 0.453541i | \(0.149840\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.57921 | −1.60067 | −0.800336 | − | 0.599552i | \(-0.795346\pi\) | ||||
−0.800336 | + | 0.599552i | \(0.795346\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.44216 | −0.545085 | −0.272542 | − | 0.962144i | \(-0.587865\pi\) | ||||
−0.272542 | + | 0.962144i | \(0.587865\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.53160 | 2.17720 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.34528 | 1.61166 | 0.805831 | − | 0.592145i | \(-0.201719\pi\) | ||||
0.805831 | + | 0.592145i | \(0.201719\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.39279 | −1.49569 | −0.747845 | − | 0.663873i | \(-0.768911\pi\) | ||||
−0.747845 | + | 0.663873i | \(0.768911\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.0502 | −2.85315 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.31413 | −1.28887 | −0.644433 | − | 0.764661i | \(-0.722907\pi\) | ||||
−0.644433 | + | 0.764661i | \(0.722907\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.56610 | −0.588704 | −0.294352 | − | 0.955697i | \(-0.595104\pi\) | ||||
−0.294352 | + | 0.955697i | \(0.595104\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.45242 | −0.971598 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.63074 | 1.38260 | 0.691302 | − | 0.722566i | \(-0.257037\pi\) | ||||
0.691302 | + | 0.722566i | \(0.257037\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.81075 | 1.56215 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 10.9032 | 2.09832 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.19544 | 0.964768 | 0.482384 | − | 0.875960i | \(-0.339771\pi\) | ||||
0.482384 | + | 0.875960i | \(0.339771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.77081 | −0.856864 | −0.428432 | − | 0.903574i | \(-0.640934\pi\) | ||||
−0.428432 | + | 0.903574i | \(0.640934\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.5026 | 2.87274 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.16179 | 0.872502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.44033 | −0.565586 | −0.282793 | − | 0.959181i | \(-0.591261\pi\) | ||||
−0.282793 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16.6493 | −2.66602 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.38934 | 1.31019 | 0.655097 | − | 0.755545i | \(-0.272628\pi\) | ||||
0.655097 | + | 0.755545i | \(0.272628\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.49566 | −0.838080 | −0.419040 | − | 0.907968i | \(-0.637633\pi\) | ||||
−0.419040 | + | 0.907968i | \(0.637633\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −23.3780 | −3.48498 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.427891 | 0.0624143 | 0.0312072 | − | 0.999513i | \(-0.490065\pi\) | ||||
0.0312072 | + | 0.999513i | \(0.490065\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.92018 | −0.702882 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.4065 | −2.29737 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.73075 | −0.512458 | −0.256229 | − | 0.966616i | \(-0.582480\pi\) | ||||
−0.256229 | + | 0.966616i | \(0.582480\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19.1319 | −2.57974 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.92240 | −1.04935 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.87686 | −0.374535 | −0.187268 | − | 0.982309i | \(-0.559963\pi\) | ||||
−0.187268 | + | 0.982309i | \(0.559963\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.71286 | −0.475383 | −0.237691 | − | 0.971341i | \(-0.576391\pi\) | ||||
−0.237691 | + | 0.971341i | \(0.576391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −9.41961 | −1.18676 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 19.3019 | 2.39411 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.57367 | −0.803101 | −0.401551 | − | 0.915837i | \(-0.631529\pi\) | ||||
−0.401551 | + | 0.915837i | \(0.631529\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.4713 | 2.46445 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.1354 | 1.32153 | 0.660764 | − | 0.750594i | \(-0.270232\pi\) | ||||
0.660764 | + | 0.750594i | \(0.270232\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.468824 | −0.0548717 | −0.0274359 | − | 0.999624i | \(-0.508734\pi\) | ||||
−0.0274359 | + | 0.999624i | \(0.508734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 24.1144 | 2.78449 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.70874 | −0.878493 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.80618 | −0.653246 | −0.326623 | − | 0.945155i | \(-0.605911\pi\) | ||||
−0.326623 | + | 0.945155i | \(0.605911\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 14.0670 | 1.56300 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.338379 | −0.0371420 | −0.0185710 | − | 0.999828i | \(-0.505912\pi\) | ||||
−0.0185710 | + | 0.999828i | \(0.505912\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.0204 | 2.06305 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.0400 | 1.71967 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.79829 | 0.190618 | 0.0953091 | − | 0.995448i | \(-0.469616\pi\) | ||||
0.0953091 | + | 0.995448i | \(0.469616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.77726 | 0.815278 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.7291 | −1.52733 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.18462 | 0.942322 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.5278 | −1.17047 | −0.585234 | − | 0.810864i | \(-0.698997\pi\) | ||||
−0.585234 | + | 0.810864i | \(0.698997\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 34.9132 | 3.50891 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.15589 | −0.612534 | −0.306267 | − | 0.951946i | \(-0.599080\pi\) | ||||
−0.306267 | + | 0.951946i | \(0.599080\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.0271 | −1.57920 | −0.789601 | − | 0.613621i | \(-0.789712\pi\) | ||||
−0.789601 | + | 0.613621i | \(0.789712\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 15.9362 | 1.55521 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.286864 | −0.0277322 | −0.0138661 | − | 0.999904i | \(-0.504414\pi\) | ||||
−0.0138661 | + | 0.999904i | \(0.504414\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.7934 | −1.51273 | −0.756366 | − | 0.654149i | \(-0.773027\pi\) | ||||
−0.756366 | + | 0.654149i | \(0.773027\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.6214 | −1.00814 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.9488 | −1.21812 | −0.609058 | − | 0.793126i | \(-0.708452\pi\) | ||||
−0.609058 | + | 0.793126i | \(0.708452\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.7328 | −2.21310 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −35.2235 | −3.25642 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.66382 | 0.702541 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.5720 | 1.59746 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 25.9006 | 2.33538 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.0603 | −0.899818 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.62312 | 0.232764 | 0.116382 | − | 0.993205i | \(-0.462870\pi\) | ||||
0.116382 | + | 0.993205i | \(0.462870\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.9669 | −1.49385 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.96563 | −0.171738 | −0.0858691 | − | 0.996306i | \(-0.527367\pi\) | ||||
−0.0858691 | + | 0.996306i | \(0.527367\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.70073 | 0.320894 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −39.0249 | −3.35873 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.8493 | −1.18323 | −0.591614 | − | 0.806221i | \(-0.701509\pi\) | ||||
−0.591614 | + | 0.806221i | \(0.701509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.30984 | −0.280737 | −0.140368 | − | 0.990099i | \(-0.544829\pi\) | ||||
−0.140368 | + | 0.990099i | \(0.544829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.32104 | 0.111252 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −28.8260 | −2.41055 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.5956 | −1.54428 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −15.1902 | −1.25287 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.24371 | 0.101889 | 0.0509443 | − | 0.998701i | \(-0.483777\pi\) | ||||
0.0509443 | + | 0.998701i | \(0.483777\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.7224 | 1.60499 | 0.802494 | − | 0.596660i | \(-0.203506\pi\) | ||||
0.802494 | + | 0.596660i | \(0.203506\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −34.7098 | −2.80612 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.0758 | 1.37156 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.3800 | −0.908221 | −0.454110 | − | 0.890945i | \(-0.650043\pi\) | ||||
−0.454110 | + | 0.890945i | \(0.650043\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −11.5181 | −0.913441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.56258 | −0.753637 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.36146 | −0.184964 | −0.0924819 | − | 0.995714i | \(-0.529480\pi\) | ||||
−0.0924819 | + | 0.995714i | \(0.529480\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −59.0664 | −4.59832 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.39282 | −0.262544 | −0.131272 | − | 0.991346i | \(-0.541906\pi\) | ||||
−0.131272 | + | 0.991346i | \(0.541906\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.0822 | 1.23709 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −16.7607 | −1.28173 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.1775 | −1.83819 | −0.919093 | − | 0.394042i | \(-0.871077\pi\) | ||||
−0.919093 | + | 0.394042i | \(0.871077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2643 | −0.851505 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.88182 | −0.667598 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.73639 | 0.727732 | 0.363866 | − | 0.931451i | \(-0.381457\pi\) | ||||
0.363866 | + | 0.931451i | \(0.381457\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.08741 | −0.601133 | −0.300566 | − | 0.953761i | \(-0.597176\pi\) | ||||
−0.300566 | + | 0.953761i | \(0.597176\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −11.4628 | −0.847355 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.3137 | 0.905318 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −28.4055 | −2.07722 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.7242 | −1.14377 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.4764 | −1.69869 | −0.849347 | − | 0.527835i | \(-0.823004\pi\) | ||||
−0.849347 | + | 0.527835i | \(0.823004\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.846561 | 0.0609368 | 0.0304684 | − | 0.999536i | \(-0.490300\pi\) | ||||
0.0304684 | + | 0.999536i | \(0.490300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 59.5914 | 4.26743 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.5035 | 1.74580 | 0.872900 | − | 0.487900i | \(-0.162237\pi\) | ||||
0.872900 | + | 0.487900i | \(0.162237\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.60963 | 0.468544 | 0.234272 | − | 0.972171i | \(-0.424729\pi\) | ||||
0.234272 | + | 0.972171i | \(0.424729\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −20.2951 | −1.43150 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.49265 | −0.525881 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −30.0272 | −2.09719 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 43.3093 | 3.01021 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.7165 | −0.948792 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.49983 | −0.103253 | −0.0516264 | − | 0.998666i | \(-0.516441\pi\) | ||||
−0.0516264 | + | 0.998666i | \(0.516441\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.3786 | 2.35558 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.6701 | 1.34149 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.88027 | 0.467063 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.44741 | −0.0978072 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 28.6580 | 1.92774 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −22.0562 | −1.47699 | −0.738497 | − | 0.674257i | \(-0.764464\pi\) | ||||
−0.738497 | + | 0.674257i | \(0.764464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 51.0167 | 3.40111 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.69637 | −0.643571 | −0.321785 | − | 0.946813i | \(-0.604283\pi\) | ||||
−0.321785 | + | 0.946813i | \(0.604283\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.6579 | 0.836460 | 0.418230 | − | 0.908341i | \(-0.362651\pi\) | ||||
0.418230 | + | 0.908341i | \(0.362651\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.7994 | −1.56589 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.4477 | 0.815473 | 0.407736 | − | 0.913100i | \(-0.366318\pi\) | ||||
0.407736 | + | 0.913100i | \(0.366318\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.53151 | −0.0999049 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −17.9256 | −1.16439 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.95816 | −0.126663 | −0.0633314 | − | 0.997993i | \(-0.520173\pi\) | ||||
−0.0633314 | + | 0.997993i | \(0.520173\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −17.4587 | −1.12462 | −0.562308 | − | 0.826928i | \(-0.690086\pi\) | ||||
−0.562308 | + | 0.826928i | \(0.690086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 10.7199 | 0.687679 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.6104 | 1.12508 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.8384 | 0.880519 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.04469 | −0.0662044 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.61597 | −0.228238 | −0.114119 | − | 0.993467i | \(-0.536405\pi\) | ||||
−0.114119 | + | 0.993467i | \(0.536405\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 35.4432 | 2.22829 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 58.7222 | 3.67733 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.0934 | −0.629606 | −0.314803 | − | 0.949157i | \(-0.601939\pi\) | ||||
−0.314803 | + | 0.949157i | \(0.601939\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.96150 | 0.308293 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 33.9345 | 2.10049 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.71252 | 0.352249 | 0.176124 | − | 0.984368i | \(-0.443644\pi\) | ||||
0.176124 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.3531 | 0.820277 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.55191 | 0.339771 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.2319 | −0.684820 | −0.342410 | − | 0.939551i | \(-0.611243\pi\) | ||||
−0.342410 | + | 0.939551i | \(0.611243\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.7123 | 1.56191 | 0.780954 | − | 0.624588i | \(-0.214733\pi\) | ||||
0.780954 | + | 0.624588i | \(0.214733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.0110 | 1.45321 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 41.7507 | 2.51766 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.7925 | 0.648461 | 0.324231 | − | 0.945978i | \(-0.394895\pi\) | ||||
0.324231 | + | 0.945978i | \(0.394895\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −31.1611 | −1.86556 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.316572 | 0.0188851 | 0.00944256 | − | 0.999955i | \(-0.496994\pi\) | ||||
0.00944256 | + | 0.999955i | \(0.496994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 30.9827 | 1.84173 | 0.920864 | − | 0.389883i | \(-0.127485\pi\) | ||||
0.920864 | + | 0.389883i | \(0.127485\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 28.3559 | 1.67966 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.0988 | −0.714167 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.2400 | 0.661175 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −35.5900 | −2.08632 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.7659 | −1.27158 | −0.635789 | − | 0.771863i | \(-0.719325\pi\) | ||||
−0.635789 | + | 0.771863i | \(0.719325\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2969 | 0.599508 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 58.2807 | 3.38179 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.7582 | −2.06795 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.92561 | 0.456825 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.0053 | −1.09182 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.2891 | 0.760932 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.11297 | −0.177667 | −0.0888334 | − | 0.996046i | \(-0.528314\pi\) | ||||
−0.0888334 | + | 0.996046i | \(0.528314\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −49.4811 | −2.81488 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −27.3164 | −1.54897 | −0.774485 | − | 0.632592i | \(-0.781991\pi\) | ||||
−0.774485 | + | 0.632592i | \(0.781991\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.8638 | 0.783630 | 0.391815 | − | 0.920044i | \(-0.371847\pi\) | ||||
0.391815 | + | 0.920044i | \(0.371847\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 33.7148 | 1.89961 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.2600 | −0.800923 | −0.400461 | − | 0.916314i | \(-0.631150\pi\) | ||||
−0.400461 | + | 0.916314i | \(0.631150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.7711 | 1.55488 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.885643 | −0.0494318 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.6366 | 0.758761 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −42.1217 | −2.33649 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −48.7594 | −2.69640 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.617087 | −0.0340211 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0211 | 0.770667 | 0.385334 | − | 0.922777i | \(-0.374086\pi\) | ||||
0.385334 | + | 0.922777i | \(0.374086\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −22.4709 | −1.23140 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.5285 | 1.28550 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.77663 | −0.151253 | −0.0756263 | − | 0.997136i | \(-0.524096\pi\) | ||||
−0.0756263 | + | 0.997136i | \(0.524096\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −39.9771 | −2.17126 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −25.5013 | −1.38098 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1908 | 0.928216 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −73.2710 | −3.94478 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −34.2051 | −1.83623 | −0.918114 | − | 0.396317i | \(-0.870288\pi\) | ||||
−0.918114 | + | 0.396317i | \(0.870288\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.8576 | 1.70530 | 0.852649 | − | 0.522485i | \(-0.174995\pi\) | ||||
0.852649 | + | 0.522485i | \(0.174995\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −58.7987 | −3.13844 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7596 | 1.05170 | 0.525849 | − | 0.850578i | \(-0.323748\pi\) | ||||
0.525849 | + | 0.850578i | \(0.323748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.8559 | −2.11533 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 23.6607 | 1.25226 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.12948 | −0.323501 | −0.161751 | − | 0.986832i | \(-0.551714\pi\) | ||||
−0.161751 | + | 0.986832i | \(0.551714\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4151 | −0.653428 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 54.2506 | 2.84742 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.67802 | 0.0878316 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.4451 | 0.701828 | 0.350914 | − | 0.936408i | \(-0.385871\pi\) | ||||
0.350914 | + | 0.936408i | \(0.385871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 54.7958 | 2.85256 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.38034 | 0.279333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5335 | 0.648963 | 0.324481 | − | 0.945892i | \(-0.394810\pi\) | ||||
0.324481 | + | 0.945892i | \(0.394810\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −31.0594 | −1.60390 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −28.0179 | −1.44299 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.91515 | 0.457940 | 0.228970 | − | 0.973433i | \(-0.426464\pi\) | ||||
0.228970 | + | 0.973433i | \(0.426464\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.09843 | 0.414895 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.41053 | 0.429758 | 0.214879 | − | 0.976641i | \(-0.431064\pi\) | ||||
0.214879 | + | 0.976641i | \(0.431064\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.5912 | 1.40618 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −35.8954 | −1.82467 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.85721 | −0.347674 | −0.173837 | − | 0.984774i | \(-0.555617\pi\) | ||||
−0.173837 | + | 0.984774i | \(0.555617\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.2366 | −1.78199 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.06855 | −0.306118 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.7815 | 1.04563 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.82424 | −0.392688 | −0.196344 | − | 0.980535i | \(-0.562907\pi\) | ||||
−0.196344 | + | 0.980535i | \(0.562907\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.4254 | 0.571983 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.2178 | −0.809879 | −0.404939 | − | 0.914344i | \(-0.632707\pi\) | ||||
−0.404939 | + | 0.914344i | \(0.632707\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.7280 | 1.28160 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −50.3488 | −2.50185 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.3895 | −0.911535 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.0577 | 0.497322 | 0.248661 | − | 0.968591i | \(-0.420009\pi\) | ||||
0.248661 | + | 0.968591i | \(0.420009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −42.7574 | −2.10907 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.14889 | 0.204154 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.21113 | 0.0594521 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.2186 | −0.500405 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.3701 | −1.43482 | −0.717412 | − | 0.696649i | \(-0.754673\pi\) | ||||
−0.717412 | + | 0.696649i | \(0.754673\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −28.4591 | −1.38701 | −0.693507 | − | 0.720450i | \(-0.743935\pi\) | ||||
−0.693507 | + | 0.720450i | \(0.743935\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.79481 | 0.135889 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −41.5074 | −2.01340 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.35453 | 0.259124 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −88.9952 | −4.29673 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.8736 | 0.812772 | 0.406386 | − | 0.913701i | \(-0.366789\pi\) | ||||
0.406386 | + | 0.913701i | \(0.366789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.5129 | −0.841615 | −0.420807 | − | 0.907150i | \(-0.638253\pi\) | ||||
−0.420807 | + | 0.907150i | \(0.638253\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −57.4106 | −2.75263 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −17.0151 | −0.813945 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.19663 | 0.0571120 | 0.0285560 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285560 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −32.1366 | −1.53032 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.77986 | 0.0845637 | 0.0422819 | − | 0.999106i | \(-0.486537\pi\) | ||||
0.0422819 | + | 0.999106i | \(0.486537\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.43646 | −0.305117 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.83974 | 0.181614 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 35.7981 | 1.68942 | 0.844708 | − | 0.535227i | \(-0.179774\pi\) | ||||
0.844708 | + | 0.535227i | \(0.179774\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 44.8433 | 2.11159 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 60.8896 | 2.86084 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −27.8364 | −1.30499 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.01813 | −0.421850 | −0.210925 | − | 0.977502i | \(-0.567648\pi\) | ||||
−0.210925 | + | 0.977502i | \(0.567648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −57.9411 | −2.70446 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.8599 | −1.43729 | −0.718646 | − | 0.695377i | \(-0.755238\pi\) | ||||
−0.718646 | + | 0.695377i | \(0.755238\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.05816 | 0.0491767 | 0.0245884 | − | 0.999698i | \(-0.492172\pi\) | ||||
0.0245884 | + | 0.999698i | \(0.492172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 52.7185 | 2.44476 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 34.1893 | 1.58209 | 0.791047 | − | 0.611755i | \(-0.209536\pi\) | ||||
0.791047 | + | 0.611755i | \(0.209536\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.48027 | 0.437758 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −35.1337 | −1.61888 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.3758 | −1.35070 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.0432 | −0.919644 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.3678 | −1.11572 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.8709 | 1.41053 | 0.705265 | − | 0.708944i | \(-0.250828\pi\) | ||||
0.705265 | + | 0.708944i | \(0.250828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 18.5530 | 0.845942 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −29.5228 | −1.34334 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.2603 | 1.87354 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.2537 | 1.05373 | 0.526863 | − | 0.849950i | \(-0.323368\pi\) | ||||
0.526863 | + | 0.849950i | \(0.323368\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.29061 | −0.329693 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.10242 | 0.410786 | 0.205393 | − | 0.978680i | \(-0.434153\pi\) | ||||
0.205393 | + | 0.978680i | \(0.434153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −27.6092 | −1.24346 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −124.962 | −5.61662 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −16.0590 | −0.720345 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.0594 | −1.12181 | −0.560907 | − | 0.827879i | \(-0.689548\pi\) | ||||
−0.560907 | + | 0.827879i | \(0.689548\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.4748 | −0.467978 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.25454 | 0.323464 | 0.161732 | − | 0.986835i | \(-0.448292\pi\) | ||||
0.161732 | + | 0.986835i | \(0.448292\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 22.0332 | 0.980467 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 49.6509 | 2.20507 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.63509 | 0.0724740 | 0.0362370 | − | 0.999343i | \(-0.488463\pi\) | ||||
0.0362370 | + | 0.999343i | \(0.488463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.676119 | 0.0299098 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.9788 | −1.23529 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 57.3645 | 2.52778 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.28720 | 0.100591 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −74.6441 | −3.27651 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.4953 | 1.42365 | 0.711823 | − | 0.702359i | \(-0.247870\pi\) | ||||
0.711823 | + | 0.702359i | \(0.247870\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −42.1414 | −1.84272 | −0.921358 | − | 0.388714i | \(-0.872919\pi\) | ||||
−0.921358 | + | 0.388714i | \(0.872919\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −34.7767 | −1.51778 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.3527 | 1.10438 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.9667 | 0.911595 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −18.7905 | −0.815439 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −45.2419 | −1.95964 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.02675 | 0.0443901 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 30.0595 | 1.29716 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.2997 | −1.13281 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.3831 | 1.86519 | 0.932593 | − | 0.360930i | \(-0.117541\pi\) | ||||
0.932593 | + | 0.360930i | \(0.117541\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −24.9685 | −1.07150 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 56.5278 | 2.42139 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.2509 | −1.03500 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.3320 | −0.567963 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.37344 | 0.356075 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 38.0163 | 1.61370 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.5599 | −1.12538 | −0.562689 | − | 0.826669i | \(-0.690233\pi\) | ||||
−0.562689 | + | 0.826669i | \(0.690233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.6369 | 1.25351 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −87.6972 | −3.70258 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.6328 | 1.75461 | 0.877306 | − | 0.479931i | \(-0.159338\pi\) | ||||
0.877306 | + | 0.479931i | \(0.159338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 46.3463 | 1.94980 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.2869 | −0.851969 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.6265 | 0.655097 | 0.327549 | − | 0.944834i | \(-0.393777\pi\) | ||||
0.327549 | + | 0.944834i | \(0.393777\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −37.2288 | −1.55798 | −0.778988 | − | 0.627038i | \(-0.784267\pi\) | ||||
−0.778988 | + | 0.627038i | \(0.784267\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −72.4794 | −3.02787 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 51.7911 | 2.15984 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.81210 | −0.408483 | −0.204242 | − | 0.978921i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978921i | \(0.565473\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.61361 | 0.108618 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.487997 | 0.0202455 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.9419 | −0.825909 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 126.072 | 5.21246 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.72834 | −0.401532 | −0.200766 | − | 0.979639i | \(-0.564343\pi\) | ||||
−0.200766 | + | 0.979639i | \(0.564343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.2424 | 0.504439 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 75.6503 | 3.11184 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.2791 | 1.16128 | 0.580642 | − | 0.814159i | \(-0.302802\pi\) | ||||
0.580642 | + | 0.814159i | \(0.302802\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.4304 | −1.12454 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.4061 | 0.835166 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.5093 | −1.32830 | −0.664148 | − | 0.747601i | \(-0.731205\pi\) | ||||
−0.664148 | + | 0.747601i | \(0.731205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.09124 | 0.207676 | 0.103838 | − | 0.994594i | \(-0.466888\pi\) | ||||
0.103838 | + | 0.994594i | \(0.466888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −42.9366 | −1.74851 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −62.8940 | −2.55700 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.8978 | −1.09175 | −0.545875 | − | 0.837867i | \(-0.683803\pi\) | ||||
−0.545875 | + | 0.837867i | \(0.683803\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −23.1323 | −0.937367 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.30753 | −0.0933525 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.32992 | −0.255663 | −0.127832 | − | 0.991796i | \(-0.540802\pi\) | ||||
−0.127832 | + | 0.991796i | \(0.540802\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −92.7039 | −3.73818 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.5277 | −0.504344 | −0.252172 | − | 0.967682i | \(-0.581145\pi\) | ||||
−0.252172 | + | 0.967682i | \(0.581145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −30.6964 | −1.23379 | −0.616897 | − | 0.787044i | \(-0.711611\pi\) | ||||
−0.616897 | + | 0.787044i | \(0.711611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 72.2964 | 2.90115 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.59342 | −0.103903 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.04591 | −0.121837 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −42.3474 | −1.69119 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.2824 | 0.728965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2190 | −0.924334 | −0.462167 | − | 0.886793i | \(-0.652928\pi\) | ||||
−0.462167 | + | 0.886793i | \(0.652928\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.63048 | −0.184045 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.38870 | −0.372579 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.5335 | 1.05129 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 72.7319 | 2.87723 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2964 | 0.406681 | 0.203341 | − | 0.979108i | \(-0.434820\pi\) | ||||
0.203341 | + | 0.979108i | \(0.434820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 49.1690 | 1.93903 | 0.969517 | − | 0.245022i | \(-0.0787952\pi\) | ||||
0.969517 | + | 0.245022i | \(0.0787952\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 60.7281 | 2.39117 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.1501 | 0.477668 | 0.238834 | − | 0.971060i | \(-0.423235\pi\) | ||||
0.238834 | + | 0.971060i | \(0.423235\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.3776 | −0.603625 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.2417 | 0.832527 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.9760 | 1.25132 | 0.625658 | − | 0.780097i | \(-0.284830\pi\) | ||||
0.625658 | + | 0.780097i | \(0.284830\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.03541 | 0.274896 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.06217 | −0.119467 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.5352 | 0.644120 | 0.322060 | − | 0.946719i | \(-0.395625\pi\) | ||||
0.322060 | + | 0.946719i | \(0.395625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.40089 | 0.171175 | 0.0855873 | − | 0.996331i | \(-0.472723\pi\) | ||||
0.0855873 | + | 0.996331i | \(0.472723\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 88.4766 | 3.43615 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.2457 | −0.513645 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.4496 | 1.33389 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −68.0948 | −2.63270 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.8463 | −0.766156 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −28.2504 | −1.08897 | −0.544487 | − | 0.838769i | \(-0.683276\pi\) | ||||
−0.544487 | + | 0.838769i | \(0.683276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 85.1623 | 3.27790 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.1494 | 0.582240 | 0.291120 | − | 0.956687i | \(-0.405972\pi\) | ||||
0.291120 | + | 0.956687i | \(0.405972\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.6249 | 0.638004 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.9359 | −1.14715 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.816285 | 0.0312343 | 0.0156171 | − | 0.999878i | \(-0.495029\pi\) | ||||
0.0156171 | + | 0.999878i | \(0.495029\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 49.5697 | 1.89396 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.0792 | 1.49097 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.1191 | 0.766478 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8709 | −0.717882 | −0.358941 | − | 0.933360i | \(-0.616862\pi\) | ||||
−0.358941 | + | 0.933360i | \(0.616862\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −50.3504 | −1.91266 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 11.8466 | 0.449367 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −44.5820 | −1.68866 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.4300 | 1.45356 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.2476 | 1.10467 | 0.552334 | − | 0.833623i | \(-0.313737\pi\) | ||||
0.552334 | + | 0.833623i | \(0.313737\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.82823 | 0.332963 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.72828 | −0.178077 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.87778 | 0.333883 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.19560 | −0.195125 | −0.0975625 | − | 0.995229i | \(-0.531105\pi\) | ||||
−0.0975625 | + | 0.995229i | \(0.531105\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −37.9237 | −1.42225 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.6340 | −1.18470 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 103.174 | 3.85850 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.04548 | −0.225773 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.5079 | 0.951286 | 0.475643 | − | 0.879638i | \(-0.342215\pi\) | ||||
0.475643 | + | 0.879638i | \(0.342215\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.1137 | 0.860799 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −53.9009 | −2.00459 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.5803 | 1.50711 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.2744 | −0.677761 | −0.338881 | − | 0.940829i | \(-0.610048\pi\) | ||||
−0.338881 | + | 0.940829i | \(0.610048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.10533 | −0.337234 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.2046 | 1.08017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4034 | 0.421195 | 0.210597 | − | 0.977573i | \(-0.432459\pi\) | ||||
0.210597 | + | 0.977573i | \(0.432459\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 54.3690 | 2.00543 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −35.1381 | −1.29433 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.2708 | 0.819246 | 0.409623 | − | 0.912255i | \(-0.365660\pi\) | ||||
0.409623 | + | 0.912255i | \(0.365660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 42.7238 | 1.56950 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −37.4127 | −1.37254 | −0.686270 | − | 0.727347i | \(-0.740753\pi\) | ||||
−0.686270 | + | 0.727347i | \(0.740753\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.45150 | −0.163090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.21016 | −0.0808655 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.413703 | 0.0151164 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.9303 | −0.763758 | −0.381879 | − | 0.924212i | \(-0.624723\pi\) | ||||
−0.381879 | + | 0.924212i | \(0.624723\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.1637 | −0.406828 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −70.5907 | −2.56906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.08103 | 0.0392907 | 0.0196454 | − | 0.999807i | \(-0.493746\pi\) | ||||
0.0196454 | + | 0.999807i | \(0.493746\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 109.425 | 3.97186 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −38.7659 | −1.40526 | −0.702631 | − | 0.711554i | \(-0.747992\pi\) | ||||
−0.702631 | + | 0.711554i | \(0.747992\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.7766 | 0.824567 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 124.234 | 4.49168 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.5143 | 0.560189 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.8853 | −1.76285 | −0.881424 | − | 0.472326i | \(-0.843415\pi\) | ||||
−0.881424 | + | 0.472326i | \(0.843415\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.1615 | −1.12225 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.06901 | 0.254255 | 0.127127 | − | 0.991886i | \(-0.459424\pi\) | ||||
0.127127 | + | 0.991886i | \(0.459424\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.2637 | −1.33855 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.3178 | 0.549523 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −21.5279 | −0.771316 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.5218 | 2.12986 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 56.6470 | 2.02440 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.7313 | 1.45376 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.3453 | −1.08169 | −0.540847 | − | 0.841121i | \(-0.681896\pi\) | ||||
−0.540847 | + | 0.841121i | \(0.681896\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.6364 | 0.627873 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.6742 | 0.663977 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.0226 | 0.711025 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 41.2256 | 1.46212 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.9392 | −1.30845 | −0.654227 | − | 0.756299i | \(-0.727006\pi\) | ||||
−0.654227 | + | 0.756299i | \(0.727006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.27387 | −0.0804437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.7457 | 0.415014 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.50600 | −0.0884347 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 34.2265 | 1.20633 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.6765 | −1.22067 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.3975 | −1.24451 | −0.622255 | − | 0.782815i | \(-0.713783\pi\) | ||||
−0.622255 | + | 0.782815i | \(0.713783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.8628 | 0.943281 | 0.471641 | − | 0.881791i | \(-0.343662\pi\) | ||||
0.471641 | + | 0.881791i | \(0.343662\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 79.3822 | 2.78406 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.45217 | 0.296066 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.1024 | 0.493381 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 50.7979 | 1.77502 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.5285 | 1.17015 | 0.585077 | − | 0.810978i | \(-0.301064\pi\) | ||||
0.585077 | + | 0.810978i | \(0.301064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.8795 | 0.623240 | 0.311620 | − | 0.950207i | \(-0.399128\pi\) | ||||
0.311620 | + | 0.950207i | \(0.399128\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 128.898 | 4.48765 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −23.8898 | −0.830729 | −0.415364 | − | 0.909655i | \(-0.636346\pi\) | ||||
−0.415364 | + | 0.909655i | \(0.636346\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.2441 | 1.01569 | 0.507844 | − | 0.861449i | \(-0.330443\pi\) | ||||
0.507844 | + | 0.861449i | \(0.330443\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.3201 | 1.15586 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.1465 | 0.905921 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.1436 | 0.420248 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −52.0172 | −1.79798 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 50.1966 | 1.73298 | 0.866489 | − | 0.499196i | \(-0.166371\pi\) | ||||
0.866489 | + | 0.499196i | \(0.166371\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00744 | −0.0692221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.977363 | 0.0336622 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −57.5614 | −1.98017 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.3416 | −0.870749 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 95.6537 | 3.28283 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.8119 | −0.781982 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.6698 | 1.66642 | 0.833212 | − | 0.552954i | \(-0.186499\pi\) | ||||
0.833212 | + | 0.552954i | \(0.186499\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 59.9903 | 2.05162 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.2395 | 0.725528 | 0.362764 | − | 0.931881i | \(-0.381833\pi\) | ||||
0.362764 | + | 0.931881i | \(0.381833\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.2261 | −0.553626 | −0.276813 | − | 0.960924i | \(-0.589278\pi\) | ||||
−0.276813 | + | 0.960924i | \(0.589278\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −37.3528 | −1.27298 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.9330 | 0.440243 | 0.220122 | − | 0.975472i | \(-0.429355\pi\) | ||||
0.220122 | + | 0.975472i | \(0.429355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 86.5366 | 2.94233 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 34.7015 | 1.17853 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −31.0357 | −1.05281 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 35.4504 | 1.20119 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −75.2948 | −2.54834 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.5085 | 0.490477 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.82463 | −0.162916 | −0.0814581 | − | 0.996677i | \(-0.525958\pi\) | ||||
−0.0814581 | + | 0.996677i | \(0.525958\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −67.1985 | −2.26655 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.5509 | 1.06298 | 0.531489 | − | 0.847065i | \(-0.321633\pi\) | ||||
0.531489 | + | 0.847065i | \(0.321633\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.4305 | −1.36059 | −0.680297 | − | 0.732937i | \(-0.738149\pi\) | ||||
−0.680297 | + | 0.732937i | \(0.738149\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 31.7899 | 1.06861 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.6420 | −1.02886 | −0.514428 | − | 0.857534i | \(-0.671996\pi\) | ||||
−0.514428 | + | 0.857534i | \(0.671996\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.78295 | −0.126876 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 75.1921 | 2.51903 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.09801 | −0.0367436 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.8486 | −1.16486 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −110.397 | −3.68606 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −24.7865 | −0.826675 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.8257 | 0.660490 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.4690 | 0.814277 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.9466 | 0.962216 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.9314 | −1.06026 | −0.530132 | − | 0.847915i | \(-0.677858\pi\) | ||||
−0.530132 | + | 0.847915i | \(0.677858\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40.2079 | −1.33361 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.929435 | 0.0307936 | 0.0153968 | − | 0.999881i | \(-0.495099\pi\) | ||||
0.0153968 | + | 0.999881i | \(0.495099\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.80873 | −0.0598603 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 41.0278 | 1.35634 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.83475 | 0.0936119 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.0653 | 1.91540 | 0.957698 | − | 0.287775i | \(-0.0929155\pi\) | ||||
0.957698 | + | 0.287775i | \(0.0929155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.61078 | −0.316686 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.0508 | −1.97660 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.8716 | −0.883531 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −104.683 | −3.43824 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.9547 | −1.44211 | −0.721054 | − | 0.692879i | \(-0.756342\pi\) | ||||
−0.721054 | + | 0.692879i | \(0.756342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.6257 | 0.413790 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −84.3347 | −2.76099 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 101.669 | 3.32494 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.6735 | −1.32875 | −0.664373 | − | 0.747401i | \(-0.731301\pi\) | ||||
−0.664373 | + | 0.747401i | \(0.731301\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.8022 | 1.39680 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.6479 | 1.06429 | 0.532146 | − | 0.846653i | \(-0.321386\pi\) | ||||
0.532146 | + | 0.846653i | \(0.321386\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 55.6275 | 1.81148 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 56.2801 | 1.83079 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.2833 | −0.756605 | −0.378303 | − | 0.925682i | \(-0.623492\pi\) | ||||
−0.378303 | + | 0.925682i | \(0.623492\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.52827 | 0.0820711 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −44.0254 | −1.42762 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.41717 | 0.305052 | 0.152526 | − | 0.988299i | \(-0.451259\pi\) | ||||
0.152526 | + | 0.988299i | \(0.451259\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 84.0270 | 2.71905 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 85.7384 | 2.77153 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 19.9729 | 0.644960 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.23933 | −0.265785 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.87368 | −0.0603785 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −3.03002 | −0.0975398 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0391 | 0.451467 | 0.225734 | − | 0.974189i | \(-0.427522\pi\) | ||||
0.225734 | + | 0.974189i | \(0.427522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.1007 | 1.35247 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.1363 | −0.517838 | −0.258919 | − | 0.965899i | \(-0.583366\pi\) | ||||
−0.258919 | + | 0.965899i | \(0.583366\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.77331 | 0.153025 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −130.044 | −4.16473 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.00176 | 0.287992 | 0.143996 | − | 0.989578i | \(-0.454005\pi\) | ||||
0.143996 | + | 0.989578i | \(0.454005\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.61236 | 0.307212 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −103.156 | −3.29352 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 50.8826 | 1.62290 | 0.811451 | − | 0.584421i | \(-0.198678\pi\) | ||||
0.811451 | + | 0.584421i | \(0.198678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −87.7031 | −2.79445 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.90515 | −0.0606416 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.4403 | −1.15873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2975 | 0.644772 | 0.322386 | − | 0.946608i | \(-0.395515\pi\) | ||||
0.322386 | + | 0.946608i | \(0.395515\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43.2876 | 1.37369 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.6573 | −0.749985 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.1716 | −1.43060 | −0.715300 | − | 0.698817i | \(-0.753710\pi\) | ||||
−0.715300 | + | 0.698817i | \(0.753710\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −37.5106 | −1.18678 |
(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 | 8752.2.a.s.1.16 | 18 | ||
4.3 | odd | 2 | 547.2.a.b.1.18 | ✓ | 18 | ||
12.11 | even | 2 | 4923.2.a.l.1.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.2.a.b.1.18 | ✓ | 18 | 4.3 | odd | 2 | ||
4923.2.a.l.1.1 | 18 | 12.11 | even | 2 | |||
8752.2.a.s.1.16 | 18 | 1.1 | even | 1 | trivial |