Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8008,2,Mod(1,8008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8008, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8008.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: | \(63.9442019386\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 78 x^{11} + 273 x^{10} - 750 x^{9} - 1306 x^{8} + 3378 x^{7} + \cdots - 128 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-3.22058\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8008.1 |
$q$-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 | ||||||||
\(3\) | 3.22058 | 1.85940 | 0.929701 | − | 0.368316i | \(-0.120065\pi\) | ||||
0.929701 | + | 0.368316i | \(0.120065\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.58838 | −1.60477 | −0.802385 | − | 0.596806i | \(-0.796436\pi\) | ||||
−0.802385 | + | 0.596806i | \(0.796436\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.37212 | 2.45737 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −11.5566 | −2.98391 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.82146 | −1.16938 | −0.584688 | − | 0.811258i | \(-0.698783\pi\) | ||||
−0.584688 | + | 0.811258i | \(0.698783\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.88691 | −1.80938 | −0.904690 | − | 0.426070i | \(-0.859898\pi\) | ||||
−0.904690 | + | 0.426070i | \(0.859898\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.22058 | 0.702788 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.80149 | 1.00118 | 0.500590 | − | 0.865685i | \(-0.333116\pi\) | ||||
0.500590 | + | 0.865685i | \(0.333116\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.87644 | 1.57529 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 14.0808 | 2.70984 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.62720 | 1.78773 | 0.893863 | − | 0.448340i | \(-0.147985\pi\) | ||||
0.893863 | + | 0.448340i | \(0.147985\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.44581 | −0.978096 | −0.489048 | − | 0.872257i | \(-0.662656\pi\) | ||||
−0.489048 | + | 0.872257i | \(0.662656\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.22058 | −0.560631 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.58838 | −0.606546 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.187963 | 0.0309009 | 0.0154504 | − | 0.999881i | \(-0.495082\pi\) | ||||
0.0154504 | + | 0.999881i | \(0.495082\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.22058 | −0.515705 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50581 | 0.235169 | 0.117584 | − | 0.993063i | \(-0.462485\pi\) | ||||
0.117584 | + | 0.993063i | \(0.462485\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.53445 | −1.45399 | −0.726995 | − | 0.686643i | \(-0.759084\pi\) | ||||
−0.726995 | + | 0.686643i | \(0.759084\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −26.4539 | −3.94352 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.00380 | −0.438150 | −0.219075 | − | 0.975708i | \(-0.570304\pi\) | ||||
−0.219075 | + | 0.975708i | \(0.570304\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.5279 | −2.17434 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.34802 | −0.322526 | −0.161263 | − | 0.986911i | \(-0.551557\pi\) | ||||
−0.161263 | + | 0.986911i | \(0.551557\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.58838 | 0.483857 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −25.4004 | −3.36436 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.59689 | −0.598464 | −0.299232 | − | 0.954180i | \(-0.596731\pi\) | ||||
−0.299232 | + | 0.954180i | \(0.596731\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.05035 | 0.646632 | 0.323316 | − | 0.946291i | \(-0.395202\pi\) | ||||
0.323316 | + | 0.946291i | \(0.395202\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.37212 | 0.928800 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.58838 | 0.445083 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.9657 | −1.58401 | −0.792006 | − | 0.610513i | \(-0.790963\pi\) | ||||
−0.792006 | + | 0.610513i | \(0.790963\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.4636 | 1.86160 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.4722 | −1.59886 | −0.799430 | − | 0.600759i | \(-0.794865\pi\) | ||||
−0.799430 | + | 0.600759i | \(0.794865\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.2013 | 1.42805 | 0.714027 | − | 0.700118i | \(-0.246869\pi\) | ||||
0.714027 | + | 0.700118i | \(0.246869\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.3667 | 2.92909 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.0938 | 1.24815 | 0.624073 | − | 0.781366i | \(-0.285477\pi\) | ||||
0.624073 | + | 0.781366i | \(0.285477\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 23.2318 | 2.58131 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8010 | −1.51485 | −0.757427 | − | 0.652920i | \(-0.773544\pi\) | ||||
−0.757427 | + | 0.652920i | \(0.773544\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17.3012 | 1.87658 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 31.0052 | 3.32410 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.44120 | −1.00077 | −0.500383 | − | 0.865804i | \(-0.666807\pi\) | ||||
−0.500383 | + | 0.865804i | \(0.666807\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −17.5387 | −1.81867 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28.3012 | 2.90364 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.672558 | −0.0682879 | −0.0341439 | − | 0.999417i | \(-0.510870\pi\) | ||||
−0.0341439 | + | 0.999417i | \(0.510870\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.37212 | −0.740926 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.9285 | −1.68445 | −0.842223 | − | 0.539130i | \(-0.818753\pi\) | ||||
−0.842223 | + | 0.539130i | \(0.818753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.87422 | −0.972935 | −0.486468 | − | 0.873699i | \(-0.661715\pi\) | ||||
−0.486468 | + | 0.873699i | \(0.661715\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.5566 | −1.12781 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.81921 | −0.852585 | −0.426292 | − | 0.904585i | \(-0.640181\pi\) | ||||
−0.426292 | + | 0.904585i | \(0.640181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 19.4616 | 1.86409 | 0.932043 | − | 0.362347i | \(-0.118024\pi\) | ||||
0.932043 | + | 0.362347i | \(0.118024\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.605348 | 0.0574571 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −18.4208 | −1.73289 | −0.866444 | − | 0.499275i | \(-0.833600\pi\) | ||||
−0.866444 | + | 0.499275i | \(0.833600\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.2296 | −1.60666 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.37212 | −0.681553 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.82146 | −0.441982 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.84959 | 0.437273 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.3218 | −0.923207 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.56887 | −0.760364 | −0.380182 | − | 0.924912i | \(-0.624139\pi\) | ||||
−0.380182 | + | 0.924912i | \(0.624139\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −30.7064 | −2.70355 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.7365 | 0.938052 | 0.469026 | − | 0.883184i | \(-0.344605\pi\) | ||||
0.469026 | + | 0.883184i | \(0.344605\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.88691 | −0.683882 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −50.5271 | −4.34868 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.31232 | −0.368427 | −0.184213 | − | 0.982886i | \(-0.558974\pi\) | ||||
−0.184213 | + | 0.982886i | \(0.558974\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.63319 | −0.477801 | −0.238900 | − | 0.971044i | \(-0.576787\pi\) | ||||
−0.238900 | + | 0.971044i | \(0.576787\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.67398 | −0.814696 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −34.5460 | −2.86889 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.22058 | 0.265629 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.7571 | 1.45471 | 0.727357 | − | 0.686259i | \(-0.240748\pi\) | ||||
0.727357 | + | 0.686259i | \(0.240748\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.42961 | −0.604613 | −0.302307 | − | 0.953211i | \(-0.597757\pi\) | ||||
−0.302307 | + | 0.953211i | \(0.597757\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −35.5444 | −2.87359 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 19.5416 | 1.56962 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.8574 | −1.82422 | −0.912111 | − | 0.409944i | \(-0.865548\pi\) | ||||
−0.912111 | + | 0.409944i | \(0.865548\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.56200 | −0.599705 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.80149 | 0.378410 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0878 | −0.868463 | −0.434232 | − | 0.900801i | \(-0.642980\pi\) | ||||
−0.434232 | + | 0.900801i | \(0.642980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 11.5566 | 0.899684 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3294 | −1.34099 | −0.670495 | − | 0.741914i | \(-0.733918\pi\) | ||||
−0.670495 | + | 0.741914i | \(0.733918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −58.1432 | −4.44632 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.42083 | 0.108024 | 0.0540118 | − | 0.998540i | \(-0.482799\pi\) | ||||
0.0540118 | + | 0.998540i | \(0.482799\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.87644 | 0.595403 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.8046 | −1.11279 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.73218 | −0.652674 | −0.326337 | − | 0.945254i | \(-0.605814\pi\) | ||||
−0.326337 | + | 0.945254i | \(0.605814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.81515 | −0.209249 | −0.104624 | − | 0.994512i | \(-0.533364\pi\) | ||||
−0.104624 | + | 0.994512i | \(0.533364\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 16.2651 | 1.20235 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.674480 | −0.0495888 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.82146 | 0.352580 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.0808 | 1.02422 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.2757 | 1.90125 | 0.950623 | − | 0.310349i | \(-0.100446\pi\) | ||||
0.950623 | + | 0.310349i | \(0.100446\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.2260 | 1.52788 | 0.763941 | − | 0.645286i | \(-0.223262\pi\) | ||||
0.763941 | + | 0.645286i | \(0.223262\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.5566 | 0.827589 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.19961 | −0.227963 | −0.113982 | − | 0.993483i | \(-0.536360\pi\) | ||||
−0.113982 | + | 0.993483i | \(0.536360\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.44127 | 0.456609 | 0.228305 | − | 0.973590i | \(-0.426682\pi\) | ||||
0.228305 | + | 0.973590i | \(0.426682\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −41.7570 | −2.94532 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.62720 | 0.675697 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.40342 | −0.377392 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.3972 | 2.46027 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.88691 | 0.545549 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.29768 | −0.295864 | −0.147932 | − | 0.988998i | \(-0.547262\pi\) | ||||
−0.147932 | + | 0.988998i | \(0.547262\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −43.3884 | −2.97292 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 34.2132 | 2.33332 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.44581 | −0.369686 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.2952 | 2.65532 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.82146 | 0.324326 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.0231 | 1.13995 | 0.569974 | − | 0.821662i | \(-0.306953\pi\) | ||||
0.569974 | + | 0.821662i | \(0.306953\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 58.0661 | 3.87107 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.75499 | 0.581089 | 0.290545 | − | 0.956861i | \(-0.406164\pi\) | ||||
0.290545 | + | 0.956861i | \(0.406164\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.48184 | −0.164005 | −0.0820023 | − | 0.996632i | \(-0.526131\pi\) | ||||
−0.0820023 | + | 0.996632i | \(0.526131\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.22058 | −0.211898 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.5143 | −1.86804 | −0.934018 | − | 0.357225i | \(-0.883723\pi\) | ||||
−0.934018 | + | 0.357225i | \(0.883723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.7788 | 0.703130 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 35.7283 | 2.32080 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.4973 | 1.58460 | 0.792300 | − | 0.610131i | \(-0.208883\pi\) | ||||
0.792300 | + | 0.610131i | \(0.208883\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3070 | −1.05042 | −0.525212 | − | 0.850971i | \(-0.676014\pi\) | ||||
−0.525212 | + | 0.850971i | \(0.676014\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 32.5776 | 2.08985 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.58838 | −0.229253 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.88691 | 0.501832 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −44.4471 | −2.81672 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5380 | −0.980750 | −0.490375 | − | 0.871511i | \(-0.663140\pi\) | ||||
−0.490375 | + | 0.871511i | \(0.663140\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.80149 | −0.301867 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 55.7199 | 3.48931 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.16513 | −0.135057 | −0.0675285 | − | 0.997717i | \(-0.521511\pi\) | ||||
−0.0675285 | + | 0.997717i | \(0.521511\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.187963 | 0.0116794 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 70.9729 | 4.39311 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −24.7513 | −1.52623 | −0.763117 | − | 0.646261i | \(-0.776332\pi\) | ||||
−0.763117 | + | 0.646261i | \(0.776332\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.42560 | 0.517580 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −30.4061 | −1.86083 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.63021 | −0.526193 | −0.263097 | − | 0.964769i | \(-0.584744\pi\) | ||||
−0.263097 | + | 0.964769i | \(0.584744\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.5050 | 0.941860 | 0.470930 | − | 0.882171i | \(-0.343918\pi\) | ||||
0.470930 | + | 0.882171i | \(0.343918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.22058 | −0.194918 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.87644 | −0.474967 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.26881 | −0.256488 | −0.128244 | − | 0.991743i | \(-0.540934\pi\) | ||||
−0.128244 | + | 0.991743i | \(0.540934\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −40.1472 | −2.40355 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.5752 | 1.82397 | 0.911983 | − | 0.410228i | \(-0.134551\pi\) | ||||
0.911983 | + | 0.410228i | \(0.134551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.50838 | 0.565215 | 0.282607 | − | 0.959236i | \(-0.408801\pi\) | ||||
0.282607 | + | 0.959236i | \(0.408801\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 91.1462 | 5.39903 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.50581 | 0.0888853 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.24647 | 0.367439 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.16602 | −0.126975 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.94798 | 0.581167 | 0.290584 | − | 0.956850i | \(-0.406151\pi\) | ||||
0.290584 | + | 0.956850i | \(0.406151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.4954 | 0.960398 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −14.0808 | −0.817048 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.80149 | −0.277677 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.53445 | −0.549556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −54.5194 | −3.13206 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.1226 | −1.03770 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.51711 | 0.0865863 | 0.0432931 | − | 0.999062i | \(-0.486215\pi\) | ||||
0.0432931 | + | 0.999062i | \(0.486215\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.8007 | −1.80908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.5405 | −1.39156 | −0.695781 | − | 0.718254i | \(-0.744942\pi\) | ||||
−0.695781 | + | 0.718254i | \(0.744942\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.8630 | −0.953152 | −0.476576 | − | 0.879133i | \(-0.658122\pi\) | ||||
−0.476576 | + | 0.879133i | \(0.658122\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.4539 | −1.49051 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.33688 | −0.243583 | −0.121792 | − | 0.992556i | \(-0.538864\pi\) | ||||
−0.121792 | + | 0.992556i | \(0.538864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.62720 | −0.539020 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −28.4029 | −1.58530 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 38.0264 | 2.11585 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.87644 | −0.436906 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 62.6777 | 3.46609 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00380 | −0.165605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.17809 | 0.284613 | 0.142307 | − | 0.989823i | \(-0.454548\pi\) | ||||
0.142307 | + | 0.989823i | \(0.454548\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.38568 | 0.0759350 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 46.5258 | 2.54198 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9945 | 0.816801 | 0.408401 | − | 0.912803i | \(-0.366087\pi\) | ||||
0.408401 | + | 0.912803i | \(0.366087\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −59.3258 | −3.22213 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.44581 | 0.294907 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −55.4891 | −2.98743 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.8587 | 0.636607 | 0.318303 | − | 0.947989i | \(-0.396887\pi\) | ||||
0.318303 | + | 0.947989i | \(0.396887\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.50061 | 0.133854 | 0.0669272 | − | 0.997758i | \(-0.478680\pi\) | ||||
0.0669272 | + | 0.997758i | \(0.478680\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −14.0808 | −0.751575 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.57532 | −0.137071 | −0.0685353 | − | 0.997649i | \(-0.521833\pi\) | ||||
−0.0685353 | + | 0.997649i | \(0.521833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 48.3434 | 2.56580 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −15.5279 | −0.821823 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −27.7361 | −1.46386 | −0.731928 | − | 0.681382i | \(-0.761379\pi\) | ||||
−0.731928 | + | 0.681382i | \(0.761379\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.2033 | 2.27386 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.22058 | 0.169036 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.7828 | −2.29170 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.26063 | −0.118004 | −0.0590019 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590019 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 11.1010 | 0.577897 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.34802 | −0.121903 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5037 | 0.802750 | 0.401375 | − | 0.915914i | \(-0.368532\pi\) | ||||
0.401375 | + | 0.915914i | \(0.368532\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −33.2420 | −1.71661 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.62720 | −0.495826 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.4062 | 0.945462 | 0.472731 | − | 0.881207i | \(-0.343268\pi\) | ||||
0.472731 | + | 0.881207i | \(0.343268\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.5967 | −1.41382 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6395 | 1.10573 | 0.552864 | − | 0.833272i | \(-0.313535\pi\) | ||||
0.552864 | + | 0.833272i | \(0.313535\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.58838 | 0.182881 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −70.2891 | −3.57300 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.7136 | −0.948816 | −0.474408 | − | 0.880305i | \(-0.657338\pi\) | ||||
−0.474408 | + | 0.880305i | \(0.657338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.1502 | −1.17076 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 34.5777 | 1.74422 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −39.8086 | −2.00299 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.96224 | −0.449802 | −0.224901 | − | 0.974382i | \(-0.572206\pi\) | ||||
−0.224901 | + | 0.974382i | \(0.572206\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −25.4004 | −1.27161 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 31.1663 | 1.55637 | 0.778186 | − | 0.628034i | \(-0.216140\pi\) | ||||
0.778186 | + | 0.628034i | \(0.216140\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.44581 | 0.271275 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −83.3645 | −4.14241 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.187963 | −0.00931696 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.9295 | 1.13379 | 0.566896 | − | 0.823789i | \(-0.308144\pi\) | ||||
0.566896 | + | 0.823789i | \(0.308144\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −13.8882 | −0.685053 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.59689 | −0.226198 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 49.5231 | 2.43099 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.1421 | −0.888423 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.40201 | 0.410465 | 0.205233 | − | 0.978713i | \(-0.434205\pi\) | ||||
0.205233 | + | 0.978713i | \(0.434205\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.9322 | 1.31260 | 0.656298 | − | 0.754502i | \(-0.272122\pi\) | ||||
0.656298 | + | 0.754502i | \(0.272122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −22.1444 | −1.07670 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −37.9760 | −1.84210 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.05035 | 0.244404 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.22058 | 0.155491 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −37.7147 | −1.81665 | −0.908326 | − | 0.418263i | \(-0.862639\pi\) | ||||
−0.908326 | + | 0.418263i | \(0.862639\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.03235 | 0.0976686 | 0.0488343 | − | 0.998807i | \(-0.484449\pi\) | ||||
0.0488343 | + | 0.998807i | \(0.484449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −111.258 | −5.33442 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.8689 | −1.81152 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.1673 | 1.63072 | 0.815358 | − | 0.578957i | \(-0.196540\pi\) | ||||
0.815358 | + | 0.578957i | \(0.196540\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.37212 | 0.351053 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13.1136 | −0.623045 | −0.311522 | − | 0.950239i | \(-0.600839\pi\) | ||||
−0.311522 | + | 0.950239i | \(0.600839\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.8786 | 1.60600 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 57.1880 | 2.70490 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −19.2230 | −0.907189 | −0.453595 | − | 0.891208i | \(-0.649859\pi\) | ||||
−0.453595 | + | 0.891208i | \(0.649859\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.50581 | −0.0709060 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.9276 | −1.12422 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.58838 | 0.168226 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.52855 | −0.0715024 | −0.0357512 | − | 0.999361i | \(-0.511382\pi\) | ||||
−0.0357512 | + | 0.999361i | \(0.511382\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −67.8898 | −3.16882 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.36243 | 0.249753 | 0.124877 | − | 0.992172i | \(-0.460147\pi\) | ||||
0.124877 | + | 0.992172i | \(0.460147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.2844 | 0.570906 | 0.285453 | − | 0.958393i | \(-0.407856\pi\) | ||||
0.285453 | + | 0.958393i | \(0.407856\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 62.9353 | 2.91855 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.8548 | −0.826221 | −0.413111 | − | 0.910681i | \(-0.635558\pi\) | ||||
−0.413111 | + | 0.910681i | \(0.635558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.9657 | −0.598700 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −73.6141 | −3.39196 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.53445 | 0.438394 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −62.1208 | −2.85030 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.3099 | −0.792567 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 24.1782 | 1.10473 | 0.552365 | − | 0.833602i | \(-0.313725\pi\) | ||||
0.552365 | + | 0.833602i | \(0.313725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.187963 | −0.00857036 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.4636 | 0.703617 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.41339 | 0.109586 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.1691 | 0.913950 | 0.456975 | − | 0.889480i | \(-0.348933\pi\) | ||||
0.456975 | + | 0.889480i | \(0.348933\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.7091 | −1.61482 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.2466 | −1.50040 | −0.750199 | − | 0.661212i | \(-0.770042\pi\) | ||||
−0.750199 | + | 0.661212i | \(0.770042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −46.4172 | −2.09052 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 26.4539 | 1.18902 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4722 | −0.604312 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.2438 | 0.727174 | 0.363587 | − | 0.931560i | \(-0.381552\pi\) | ||||
0.363587 | + | 0.931560i | \(0.381552\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55.8107 | −2.49344 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.01690 | −0.223692 | −0.111846 | − | 0.993726i | \(-0.535676\pi\) | ||||
−0.111846 | + | 0.993726i | \(0.535676\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 60.7457 | 2.70315 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.22058 | 0.143031 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.55308 | 0.201812 | 0.100906 | − | 0.994896i | \(-0.467826\pi\) | ||||
0.100906 | + | 0.994896i | \(0.467826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.2013 | 0.539753 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −111.054 | −4.90314 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 35.4324 | 1.56134 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.00380 | 0.132107 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.57589 | 0.200859 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.492144 | −0.0215612 | −0.0107806 | − | 0.999942i | \(-0.503432\pi\) | ||||
−0.0107806 | + | 0.999942i | \(0.503432\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −25.6861 | −1.12317 | −0.561587 | − | 0.827418i | \(-0.689809\pi\) | ||||
−0.561587 | + | 0.827418i | \(0.689809\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 25.3667 | 1.10709 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.2568 | 1.14376 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0543117 | 0.00236138 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −33.8888 | −1.47065 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.50581 | −0.0652240 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31.6466 | 1.36820 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.1227 | −1.21358 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.1339 | −0.951612 | −0.475806 | − | 0.879550i | \(-0.657844\pi\) | ||||
−0.475806 | + | 0.879550i | \(0.657844\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.06642 | −0.389077 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −69.8357 | −2.99143 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.06333 | −0.130979 | −0.0654893 | − | 0.997853i | \(-0.520861\pi\) | ||||
−0.0654893 | + | 0.997853i | \(0.520861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.2318 | 1.58902 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −75.9288 | −3.23468 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.0938 | 0.471755 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.17222 | −0.0922055 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.2576 | −1.23969 | −0.619843 | − | 0.784726i | \(-0.712804\pi\) | ||||
−0.619843 | + | 0.784726i | \(0.712804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.53445 | 0.403264 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.5279 | 0.655588 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.6837 | 0.576701 | 0.288350 | − | 0.957525i | \(-0.406893\pi\) | ||||
0.288350 | + | 0.957525i | \(0.406893\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 66.1009 | 2.78089 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.2318 | 0.975644 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.2646 | 1.39452 | 0.697261 | − | 0.716817i | \(-0.254402\pi\) | ||||
0.697261 | + | 0.716817i | \(0.254402\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.90886 | −0.414673 | −0.207336 | − | 0.978270i | \(-0.566479\pi\) | ||||
−0.207336 | + | 0.978270i | \(0.566479\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 84.6231 | 3.53518 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 37.8187 | 1.57715 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.2505 | 0.509996 | 0.254998 | − | 0.966942i | \(-0.417925\pi\) | ||||
0.254998 | + | 0.966942i | \(0.417925\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 68.3600 | 2.84095 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.8010 | −0.572561 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.34802 | 0.0972452 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 26.4539 | 1.09374 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −34.6030 | −1.42822 | −0.714110 | − | 0.700034i | \(-0.753168\pi\) | ||||
−0.714110 | + | 0.700034i | \(0.753168\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 42.9506 | 1.76975 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.3046 | −0.423875 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.5812 | 0.886234 | 0.443117 | − | 0.896464i | \(-0.353873\pi\) | ||||
0.443117 | + | 0.896464i | \(0.353873\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.3012 | 0.709280 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.7446 | 0.849020 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.49682 | 0.306312 | 0.153156 | − | 0.988202i | \(-0.451056\pi\) | ||||
0.153156 | + | 0.988202i | \(0.451056\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.9034 | 1.75007 | 0.875034 | − | 0.484062i | \(-0.160839\pi\) | ||||
0.875034 | + | 0.484062i | \(0.160839\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −95.5847 | −3.89251 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.58838 | −0.145888 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.2793 | −0.741934 | −0.370967 | − | 0.928646i | \(-0.620974\pi\) | ||||
−0.370967 | + | 0.928646i | \(0.620974\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 31.0052 | 1.25639 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.00380 | 0.121521 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.1318 | −0.530387 | −0.265193 | − | 0.964195i | \(-0.585436\pi\) | ||||
−0.265193 | + | 0.964195i | \(0.585436\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −17.4021 | −0.701722 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −28.6665 | −1.15407 | −0.577035 | − | 0.816719i | \(-0.695791\pi\) | ||||
−0.577035 | + | 0.816719i | \(0.695791\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.00413 | −0.321713 | −0.160856 | − | 0.986978i | \(-0.551426\pi\) | ||||
−0.160856 | + | 0.986978i | \(0.551426\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 67.6086 | 2.71304 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.44120 | −0.378254 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.34385 | −0.0937541 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.4004 | 1.01439 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.906254 | −0.0361347 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.94503 | −0.117240 | −0.0586198 | − | 0.998280i | \(-0.518670\pi\) | ||||
−0.0586198 | + | 0.998280i | \(0.518670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −13.8410 | −0.550131 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 30.7483 | 1.22021 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −99.3189 | −3.92900 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.80551 | 0.268802 | 0.134401 | − | 0.990927i | \(-0.457089\pi\) | ||||
0.134401 | + | 0.990927i | \(0.457089\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.83786 | −0.230223 | −0.115111 | − | 0.993353i | \(-0.536722\pi\) | ||||
−0.115111 | + | 0.993353i | \(0.536722\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 110.186 | 4.33858 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 25.5786 | 1.00560 | 0.502800 | − | 0.864403i | \(-0.332303\pi\) | ||||
0.502800 | + | 0.864403i | \(0.332303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.59689 | 0.180444 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −17.5387 | −0.687394 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.7271 | −0.537183 | −0.268592 | − | 0.963254i | \(-0.586558\pi\) | ||||
−0.268592 | + | 0.963254i | \(0.586558\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −38.5266 | −1.50536 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 89.9494 | 3.50926 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9970 | 0.662109 | 0.331054 | − | 0.943612i | \(-0.392596\pi\) | ||||
0.331054 | + | 0.943612i | \(0.392596\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9076 | −0.579839 | −0.289920 | − | 0.957051i | \(-0.593629\pi\) | ||||
−0.289920 | + | 0.957051i | \(0.593629\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 15.5279 | 0.603053 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 28.3012 | 1.09747 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 46.2249 | 1.78984 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 54.8241 | 2.11962 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.05035 | −0.194967 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 43.1293 | 1.66251 | 0.831256 | − | 0.555889i | \(-0.187622\pi\) | ||||
0.831256 | + | 0.555889i | \(0.187622\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 110.906 | 4.26879 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.9025 | −0.880213 | −0.440107 | − | 0.897946i | \(-0.645059\pi\) | ||||
−0.440107 | + | 0.897946i | \(0.645059\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.672558 | −0.0258104 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 28.1961 | 1.08048 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.1717 | 1.15449 | 0.577245 | − | 0.816571i | \(-0.304128\pi\) | ||||
0.577245 | + | 0.816571i | \(0.304128\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.4742 | 0.591240 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.99296 | −0.304950 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.34802 | 0.0894526 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.3464 | −1.64897 | −0.824487 | − | 0.565881i | \(-0.808536\pi\) | ||||
−0.824487 | + | 0.565881i | \(0.808536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.37212 | −0.280044 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.2140 | 0.766760 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.26022 | −0.275000 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −91.8326 | −3.47343 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.2983 | 0.766655 | 0.383327 | − | 0.923613i | \(-0.374778\pi\) | ||||
0.383327 | + | 0.923613i | \(0.374778\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.48244 | −0.0559114 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 34.7139 | 1.30740 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.9285 | −0.636661 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.3039 | −1.32587 | −0.662933 | − | 0.748679i | \(-0.730689\pi\) | ||||
−0.662933 | + | 0.748679i | \(0.730689\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 81.7846 | 3.06716 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −26.1480 | −0.979250 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.58838 | −0.134198 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 78.8956 | 2.94641 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.25158 | −0.307732 | −0.153866 | − | 0.988092i | \(-0.549172\pi\) | ||||
−0.153866 | + | 0.988092i | \(0.549172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.87422 | −0.367735 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −52.5178 | −1.95316 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 75.8281 | 2.81619 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.8606 | 0.847852 | 0.423926 | − | 0.905697i | \(-0.360652\pi\) | ||||
0.423926 | + | 0.905697i | \(0.360652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 35.2232 | 1.30456 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45.9700 | 1.70026 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.50689 | 0.351145 | 0.175572 | − | 0.984467i | \(-0.443822\pi\) | ||||
0.175572 | + | 0.984467i | \(0.443822\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.5566 | −0.426273 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9657 | 0.477598 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.9610 | −0.734277 | −0.367139 | − | 0.930166i | \(-0.619663\pi\) | ||||
−0.367139 | + | 0.930166i | \(0.619663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25.4004 | 0.933107 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.175889 | 0.00645274 | 0.00322637 | − | 0.999995i | \(-0.498973\pi\) | ||||
0.00322637 | + | 0.999995i | \(0.498973\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −63.7190 | −2.33448 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −101.742 | −3.72256 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −8.81921 | −0.322247 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.57364 | 0.0574228 | 0.0287114 | − | 0.999588i | \(-0.490860\pi\) | ||||
0.0287114 | + | 0.999588i | \(0.490860\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −50.0414 | −1.82361 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 26.6602 | 0.970266 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 50.0158 | 1.81785 | 0.908927 | − | 0.416955i | \(-0.136903\pi\) | ||||
0.908927 | + | 0.416955i | \(0.136903\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.4636 | −0.561292 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.8031 | −0.609110 | −0.304555 | − | 0.952495i | \(-0.598508\pi\) | ||||
−0.304555 | + | 0.952495i | \(0.598508\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.4616 | 0.704558 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 127.547 | 4.61146 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.59689 | 0.165984 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.5212 | 1.28093 | 0.640463 | − | 0.767989i | \(-0.278742\pi\) | ||||
0.640463 | + | 0.767989i | \(0.278742\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.97297 | −0.251125 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −16.8047 | −0.604422 | −0.302211 | − | 0.953241i | \(-0.597725\pi\) | ||||
−0.302211 | + | 0.953241i | \(0.597725\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.8936 | −1.54078 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.605348 | 0.0217167 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.8762 | −0.425509 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.4722 | 0.482074 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 135.558 | 4.84446 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 82.0210 | 2.92746 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42.6983 | −1.52203 | −0.761015 | − | 0.648734i | \(-0.775299\pi\) | ||||
−0.761015 | + | 0.648734i | \(0.775299\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −79.7136 | −2.83788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.4208 | −0.654970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.05035 | −0.179343 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.1353 | 0.962389 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.5422 | 1.93198 | 0.965992 | − | 0.258573i | \(-0.0832523\pi\) | ||||
0.965992 | + | 0.258573i | \(0.0832523\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4827 | 0.512361 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −69.6017 | −2.45926 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.2013 | −0.430574 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.2296 | −0.607262 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.7943 | −0.978405 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −20.7298 | −0.728822 | −0.364411 | − | 0.931238i | \(-0.618730\pi\) | ||||
−0.364411 | + | 0.931238i | \(0.618730\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3286 | 0.608490 | 0.304245 | − | 0.952594i | \(-0.401596\pi\) | ||||
0.304245 | + | 0.952594i | \(0.401596\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 49.9350 | 1.75130 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 39.7872 | 1.39368 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 75.1973 | 2.63082 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.37212 | −0.257603 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.2760 | −0.812337 | −0.406169 | − | 0.913798i | \(-0.633135\pi\) | ||||
−0.406169 | + | 0.913798i | \(0.633135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21.3793 | −0.745237 | −0.372618 | − | 0.927985i | \(-0.621540\pi\) | ||||
−0.372618 | + | 0.927985i | \(0.621540\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.3667 | −0.883155 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.61740 | 0.125789 | 0.0628947 | − | 0.998020i | \(-0.479967\pi\) | ||||
0.0628947 | + | 0.998020i | \(0.479967\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.0455 | 1.11299 | 0.556493 | − | 0.830852i | \(-0.312147\pi\) | ||||
0.556493 | + | 0.830852i | \(0.312147\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.7480 | −0.476914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.82146 | −0.167054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 62.1844 | 2.15198 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −76.6811 | −2.65049 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.9950 | 0.690305 | 0.345152 | − | 0.938547i | \(-0.387827\pi\) | ||||
0.345152 | + | 0.938547i | \(0.387827\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 63.6830 | 2.19597 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 98.4699 | 3.39148 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.58838 | −0.123444 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 30.6225 | 1.05096 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.902501 | 0.0309373 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.80987 | −0.0962080 | −0.0481040 | − | 0.998842i | \(-0.515318\pi\) | ||||
−0.0481040 | + | 0.998842i | \(0.515318\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 208.640 | 7.13533 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.6433 | −1.72994 | −0.864971 | − | 0.501822i | \(-0.832663\pi\) | ||||
−0.864971 | + | 0.501822i | \(0.832663\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.6529 | −1.01174 | −0.505871 | − | 0.862609i | \(-0.668829\pi\) | ||||
−0.505871 | + | 0.862609i | \(0.668829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.84959 | 0.165274 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.5305 | −1.44776 | −0.723878 | − | 0.689928i | \(-0.757642\pi\) | ||||
−0.723878 | + | 0.689928i | \(0.757642\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.09847 | −0.173353 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 20.1172 | 0.683217 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.0938 | −0.376330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.9657 | 0.439326 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.95818 | −0.167809 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.3218 | −0.348939 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.2810 | 0.718610 | 0.359305 | − | 0.933220i | \(-0.383014\pi\) | ||||
0.359305 | + | 0.933220i | \(0.383014\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 32.0383 | 1.08062 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.6285 | −0.425466 | −0.212733 | − | 0.977110i | \(-0.568236\pi\) | ||||
−0.212733 | + | 0.977110i | \(0.568236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.7754 | 1.27124 | 0.635621 | − | 0.772001i | \(-0.280744\pi\) | ||||
0.635621 | + | 0.772001i | \(0.280744\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 53.1247 | 1.78577 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.70061 | −0.224984 | −0.112492 | − | 0.993653i | \(-0.535883\pi\) | ||||
−0.112492 | + | 0.993653i | \(0.535883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.56887 | −0.287391 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.2318 | −0.778295 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.6907 | 0.792779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.3343 | 1.04739 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.4636 | −0.516314 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −52.4279 | −1.74857 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3209 | 0.377154 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.7064 | −1.02185 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.1018 | 0.335796 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.0193 | −1.22920 | −0.614602 | − | 0.788837i | \(-0.710683\pi\) | ||||
−0.614602 | + | 0.788837i | \(0.710683\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −124.799 | −4.13931 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.08133 | −0.168352 | −0.0841760 | − | 0.996451i | \(-0.526826\pi\) | ||||
−0.0841760 | + | 0.996451i | \(0.526826\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8010 | 0.456745 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −58.3652 | −1.92949 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7365 | 0.354550 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.40857 | −0.0794514 | −0.0397257 | − | 0.999211i | \(-0.512648\pi\) | ||||
−0.0397257 | + | 0.999211i | \(0.512648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.88599 | 0.160999 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.4722 | 0.443444 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.48048 | 0.0486778 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −72.7939 | −2.39087 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 49.1507 | 1.61258 | 0.806291 | − | 0.591519i | \(-0.201471\pi\) | ||||
0.806291 | + | 0.591519i | \(0.201471\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.88691 | −0.258483 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −79.0345 | −2.58747 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.3012 | −0.565810 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9279 | 0.651016 | 0.325508 | − | 0.945539i | \(-0.394465\pi\) | ||||
0.325508 | + | 0.945539i | \(0.394465\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −54.3086 | −1.77229 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.6058 | 0.606531 | 0.303266 | − | 0.952906i | \(-0.401923\pi\) | ||||
0.303266 | + | 0.952906i | \(0.401923\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.23015 | 0.235446 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −50.5271 | −1.64365 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.0457 | 0.781380 | 0.390690 | − | 0.920522i | \(-0.372236\pi\) | ||||
0.390690 | + | 0.920522i | \(0.372236\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.2013 | −0.396071 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −13.9672 | −0.452919 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.8193 | −0.382865 | −0.191432 | − | 0.981506i | \(-0.561313\pi\) | ||||
−0.191432 | + | 0.981506i | \(0.561313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −94.2872 | −3.05106 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −31.0052 | −1.00225 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.31232 | −0.139252 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.34315 | −0.0433276 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −65.0163 | −2.09512 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −76.1669 | −2.45190 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.52709 | −0.0812657 | −0.0406329 | − | 0.999174i | \(-0.512937\pi\) | ||||
−0.0406329 | + | 0.999174i | \(0.512937\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 122.467 | 3.93421 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.9102 | −0.799407 | −0.399703 | − | 0.916645i | \(-0.630887\pi\) | ||||
−0.399703 | + | 0.916645i | \(0.630887\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.63319 | −0.180592 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.3667 | −0.812385 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.1903 | 0.581960 | 0.290980 | − | 0.956729i | \(-0.406019\pi\) | ||||
0.290980 | + | 0.956729i | \(0.406019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.44120 | 0.301742 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 143.474 | 4.58076 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −41.7039 | −1.33015 | −0.665074 | − | 0.746778i | \(-0.731600\pi\) | ||||
−0.665074 | + | 0.746778i | \(0.731600\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.4814 | 0.365828 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.67398 | −0.307926 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.7796 | −1.45571 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.8239 | 1.51918 | 0.759589 | − | 0.650404i | \(-0.225400\pi\) | ||||
0.759589 | + | 0.650404i | \(0.225400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.6764 | 0.529210 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −23.1137 | −0.732753 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.8654 | −0.534134 | −0.267067 | − | 0.963678i | \(-0.586055\pi\) | ||||
−0.267067 | + | 0.963678i | \(0.586055\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.64666 | 0.0837365 |
(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 | 8008.2.a.y.1.14 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.y.1.14 | ✓ | 14 | 1.1 | even | 1 | trivial |