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: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - x^{8} - 15x^{7} + 15x^{6} + 66x^{5} - 59x^{4} - 77x^{3} + 34x^{2} + 11x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(0.141545\) 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 | ||||||||
\(3\) | 0.141545 | 0.0817212 | 0.0408606 | − | 0.999165i | \(-0.486990\pi\) | ||||
0.0408606 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.343768 | 0.153738 | 0.0768688 | − | 0.997041i | \(-0.475508\pi\) | ||||
0.0768688 | + | 0.997041i | \(0.475508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97996 | −0.993322 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0486587 | 0.0125636 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.94296 | −0.471238 | −0.235619 | − | 0.971846i | \(-0.575712\pi\) | ||||
−0.235619 | + | 0.971846i | \(0.575712\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.383972 | −0.0880892 | −0.0440446 | − | 0.999030i | \(-0.514024\pi\) | ||||
−0.0440446 | + | 0.999030i | \(0.514024\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.141545 | −0.0308877 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.66573 | −0.347328 | −0.173664 | − | 0.984805i | \(-0.555561\pi\) | ||||
−0.173664 | + | 0.984805i | \(0.555561\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.88182 | −0.976365 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.846436 | −0.162897 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.52781 | 0.655098 | 0.327549 | − | 0.944834i | \(-0.393777\pi\) | ||||
0.327549 | + | 0.944834i | \(0.393777\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.92433 | 1.60286 | 0.801429 | − | 0.598090i | \(-0.204074\pi\) | ||||
0.801429 | + | 0.598090i | \(0.204074\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.141545 | 0.0246399 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.343768 | −0.0581074 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.87381 | 0.965649 | 0.482825 | − | 0.875717i | \(-0.339611\pi\) | ||||
0.482825 | + | 0.875717i | \(0.339611\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.141545 | 0.0226654 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.78021 | 1.05889 | 0.529446 | − | 0.848344i | \(-0.322400\pi\) | ||||
0.529446 | + | 0.848344i | \(0.322400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.87960 | −0.286636 | −0.143318 | − | 0.989677i | \(-0.545777\pi\) | ||||
−0.143318 | + | 0.989677i | \(0.545777\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.02442 | −0.152711 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.51467 | 0.366803 | 0.183401 | − | 0.983038i | \(-0.441289\pi\) | ||||
0.183401 | + | 0.983038i | \(0.441289\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.275017 | −0.0385101 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.793466 | 0.108991 | 0.0544954 | − | 0.998514i | \(-0.482645\pi\) | ||||
0.0544954 | + | 0.998514i | \(0.482645\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.343768 | 0.0463536 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0543494 | −0.00719876 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.0287 | −1.82638 | −0.913191 | − | 0.407531i | \(-0.866390\pi\) | ||||
−0.913191 | + | 0.407531i | \(0.866390\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.36966 | 0.815551 | 0.407776 | − | 0.913082i | \(-0.366305\pi\) | ||||
0.407776 | + | 0.913082i | \(0.366305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.97996 | 0.375440 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.343768 | 0.0426392 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.05936 | −0.984607 | −0.492304 | − | 0.870423i | \(-0.663845\pi\) | ||||
−0.492304 | + | 0.870423i | \(0.663845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.235776 | −0.0283841 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.428251 | 0.0508241 | 0.0254120 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254120 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.1299 | −1.41970 | −0.709848 | − | 0.704354i | \(-0.751237\pi\) | ||||
−0.709848 | + | 0.704354i | \(0.751237\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.690999 | −0.0797897 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.37219 | 1.05445 | 0.527227 | − | 0.849725i | \(-0.323232\pi\) | ||||
0.527227 | + | 0.849725i | \(0.323232\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.82009 | 0.980010 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.37797 | −0.480544 | −0.240272 | − | 0.970706i | \(-0.577237\pi\) | ||||
−0.240272 | + | 0.970706i | \(0.577237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.667928 | −0.0724470 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.499346 | 0.0535355 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.95758 | −0.525502 | −0.262751 | − | 0.964864i | \(-0.584630\pi\) | ||||
−0.262751 | + | 0.964864i | \(0.584630\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.26320 | 0.130987 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.131997 | −0.0135426 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.5322 | −1.37399 | −0.686994 | − | 0.726664i | \(-0.741070\pi\) | ||||
−0.686994 | + | 0.726664i | \(0.741070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.97996 | −0.299498 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.38219 | −0.535548 | −0.267774 | − | 0.963482i | \(-0.586288\pi\) | ||||
−0.267774 | + | 0.963482i | \(0.586288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3682 | −1.21868 | −0.609339 | − | 0.792910i | \(-0.708565\pi\) | ||||
−0.609339 | + | 0.792910i | \(0.708565\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.0486587 | −0.00474861 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.508008 | −0.0491110 | −0.0245555 | − | 0.999698i | \(-0.507817\pi\) | ||||
−0.0245555 | + | 0.999698i | \(0.507817\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.42923 | 0.136896 | 0.0684478 | − | 0.997655i | \(-0.478195\pi\) | ||||
0.0684478 | + | 0.997655i | \(0.478195\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.831411 | 0.0789141 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.14399 | −0.860194 | −0.430097 | − | 0.902783i | \(-0.641521\pi\) | ||||
−0.430097 | + | 0.902783i | \(0.641521\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.572623 | −0.0533974 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.97996 | −0.275498 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.94296 | 0.178111 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.959707 | 0.0865339 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.39705 | −0.303842 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2998 | −1.18017 | −0.590083 | − | 0.807343i | \(-0.700905\pi\) | ||||
−0.590083 | + | 0.807343i | \(0.700905\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.266048 | −0.0234242 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.2076 | 1.50344 | 0.751719 | − | 0.659483i | \(-0.229225\pi\) | ||||
0.751719 | + | 0.659483i | \(0.229225\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.383972 | 0.0332946 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.290978 | −0.0250434 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.9509 | −1.44822 | −0.724109 | − | 0.689686i | \(-0.757749\pi\) | ||||
−0.724109 | + | 0.689686i | \(0.757749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0975 | −0.941275 | −0.470638 | − | 0.882327i | \(-0.655976\pi\) | ||||
−0.470638 | + | 0.882327i | \(0.655976\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.355940 | 0.0299756 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.00000 | 0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.21275 | 0.100713 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.141545 | 0.0116745 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.3649 | −0.849127 | −0.424563 | − | 0.905398i | \(-0.639572\pi\) | ||||
−0.424563 | + | 0.905398i | \(0.639572\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.99428 | 0.569187 | 0.284593 | − | 0.958648i | \(-0.408141\pi\) | ||||
0.284593 | + | 0.958648i | \(0.408141\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.78996 | 0.468091 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.06790 | 0.246420 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.89153 | −0.470195 | −0.235098 | − | 0.971972i | \(-0.575541\pi\) | ||||
−0.235098 | + | 0.971972i | \(0.575541\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.112311 | 0.00890687 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.66573 | 0.131278 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.13057 | 0.0885533 | 0.0442767 | − | 0.999019i | \(-0.485902\pi\) | ||||
0.0442767 | + | 0.999019i | \(0.485902\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.0486587 | 0.00378808 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.9501 | −1.23425 | −0.617127 | − | 0.786864i | \(-0.711703\pi\) | ||||
−0.617127 | + | 0.786864i | \(0.711703\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.14422 | 0.0875009 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.4356 | −1.70574 | −0.852872 | − | 0.522120i | \(-0.825141\pi\) | ||||
−0.852872 | + | 0.522120i | \(0.825141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.88182 | 0.369031 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.98570 | −0.149254 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.9674 | 0.969228 | 0.484614 | − | 0.874728i | \(-0.338960\pi\) | ||||
0.484614 | + | 0.874728i | \(0.338960\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.833575 | −0.0619591 | −0.0309796 | − | 0.999520i | \(-0.509863\pi\) | ||||
−0.0309796 | + | 0.999520i | \(0.509863\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.901595 | 0.0666478 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.01923 | 0.148457 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.94296 | −0.142084 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.846436 | 0.0615692 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.3507 | 1.18309 | 0.591547 | − | 0.806271i | \(-0.298517\pi\) | ||||
0.591547 | + | 0.806271i | \(0.298517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.1486 | 1.30636 | 0.653182 | − | 0.757201i | \(-0.273434\pi\) | ||||
0.653182 | + | 0.757201i | \(0.273434\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0486587 | 0.00348452 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.4904 | −1.60237 | −0.801186 | − | 0.598416i | \(-0.795797\pi\) | ||||
−0.801186 | + | 0.598416i | \(0.795797\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.1359 | 0.931182 | 0.465591 | − | 0.885000i | \(-0.345842\pi\) | ||||
0.465591 | + | 0.885000i | \(0.345842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.14076 | −0.0804633 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.52781 | −0.247604 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.33082 | 0.162791 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.96380 | 0.345008 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.383972 | −0.0265599 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0317 | −1.24135 | −0.620677 | − | 0.784066i | \(-0.713142\pi\) | ||||
−0.620677 | + | 0.784066i | \(0.713142\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.0606170 | 0.00415341 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.646145 | −0.0440667 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.92433 | −0.605823 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.71693 | −0.116019 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.94296 | −0.130698 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.34803 | 0.425096 | 0.212548 | − | 0.977151i | \(-0.431824\pi\) | ||||
0.212548 | + | 0.977151i | \(0.431824\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 14.5477 | 0.969844 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.57190 | −0.237075 | −0.118538 | − | 0.992950i | \(-0.537821\pi\) | ||||
−0.118538 | + | 0.992950i | \(0.537821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.43178 | −0.425024 | −0.212512 | − | 0.977158i | \(-0.568164\pi\) | ||||
−0.212512 | + | 0.977158i | \(0.568164\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.141545 | −0.00931300 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.7243 | 0.768085 | 0.384043 | − | 0.923315i | \(-0.374532\pi\) | ||||
0.384043 | + | 0.923315i | \(0.374532\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.864463 | 0.0563914 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.32659 | 0.0861713 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.8255 | −0.894299 | −0.447150 | − | 0.894459i | \(-0.647561\pi\) | ||||
−0.447150 | + | 0.894459i | \(0.647561\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.5623 | −0.938040 | −0.469020 | − | 0.883187i | \(-0.655393\pi\) | ||||
−0.469020 | + | 0.883187i | \(0.655393\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.78775 | 0.242984 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.343768 | 0.0219625 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.383972 | −0.0244315 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.619681 | −0.0392707 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.48632 | 0.598771 | 0.299386 | − | 0.954132i | \(-0.403218\pi\) | ||||
0.299386 | + | 0.954132i | \(0.403218\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.66573 | −0.104723 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.0945421 | −0.00592046 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0937 | 0.879143 | 0.439572 | − | 0.898208i | \(-0.355130\pi\) | ||||
0.439572 | + | 0.898208i | \(0.355130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.87381 | −0.364981 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.5128 | −0.650723 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5786 | 0.960615 | 0.480307 | − | 0.877100i | \(-0.340525\pi\) | ||||
0.480307 | + | 0.877100i | \(0.340525\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.272768 | 0.0167560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.701722 | −0.0429447 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16.3016 | −0.993924 | −0.496962 | − | 0.867772i | \(-0.665551\pi\) | ||||
−0.496962 | + | 0.867772i | \(0.665551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.78877 | 0.230151 | 0.115076 | − | 0.993357i | \(-0.463289\pi\) | ||||
0.115076 | + | 0.993357i | \(0.463289\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.141545 | −0.00856671 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.88182 | −0.294385 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.7291 | −1.18541 | −0.592703 | − | 0.805421i | \(-0.701939\pi\) | ||||
−0.592703 | + | 0.805421i | \(0.701939\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −26.5942 | −1.59215 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.8178 | −1.12257 | −0.561286 | − | 0.827622i | \(-0.689693\pi\) | ||||
−0.561286 | + | 0.827622i | \(0.689693\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.57588 | −0.390895 | −0.195448 | − | 0.980714i | \(-0.562616\pi\) | ||||
−0.195448 | + | 0.980714i | \(0.562616\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0186836 | −0.00110672 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.78021 | −0.400223 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2249 | −0.777935 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.91542 | −0.112284 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.44965 | 0.493634 | 0.246817 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246817 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.82262 | −0.280784 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.846436 | −0.0491152 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.66573 | −0.0963314 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.87960 | 0.108338 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.761824 | −0.0437656 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.18968 | 0.125381 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.311354 | −0.0177699 | −0.00888496 | − | 0.999961i | \(-0.502828\pi\) | ||||
−0.00888496 | + | 0.999961i | \(0.502828\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.75067 | −0.0995919 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.0877 | −0.912249 | −0.456125 | − | 0.889916i | \(-0.650763\pi\) | ||||
−0.456125 | + | 0.889916i | \(0.650763\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.5991 | 0.994758 | 0.497379 | − | 0.867533i | \(-0.334296\pi\) | ||||
0.497379 | + | 0.867533i | \(0.334296\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.02442 | 0.0577193 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.0753 | −1.07138 | −0.535688 | − | 0.844416i | \(-0.679948\pi\) | ||||
−0.535688 | + | 0.844416i | \(0.679948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.52781 | 0.197520 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.0719061 | −0.00401341 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.746043 | 0.0415109 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.88182 | −0.270795 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.202301 | 0.0111873 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.51467 | −0.138638 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.2735 | −1.88384 | −0.941922 | − | 0.335832i | \(-0.890983\pi\) | ||||
−0.941922 | + | 0.335832i | \(0.890983\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.5038 | −0.959200 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.77055 | −0.151371 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.3206 | 1.10693 | 0.553466 | − | 0.832872i | \(-0.313305\pi\) | ||||
0.553466 | + | 0.832872i | \(0.313305\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.29429 | −0.0702961 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.92433 | 0.483280 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.0810521 | −0.00436370 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.03772 | −0.0557080 | −0.0278540 | − | 0.999612i | \(-0.508867\pi\) | ||||
−0.0278540 | + | 0.999612i | \(0.508867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.8448 | −0.741096 | −0.370548 | − | 0.928813i | \(-0.620830\pi\) | ||||
−0.370548 | + | 0.928813i | \(0.620830\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.846436 | −0.0451794 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −16.0955 | −0.856678 | −0.428339 | − | 0.903618i | \(-0.640901\pi\) | ||||
−0.428339 | + | 0.903618i | \(0.640901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.147219 | 0.00781357 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.275017 | 0.0145555 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.89822 | 0.205740 | 0.102870 | − | 0.994695i | \(-0.467197\pi\) | ||||
0.102870 | + | 0.994695i | \(0.467197\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8526 | −0.992240 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.141545 | 0.00742920 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.16987 | −0.218261 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 35.9022 | 1.87408 | 0.937041 | − | 0.349220i | \(-0.113553\pi\) | ||||
0.937041 | + | 0.349220i | \(0.113553\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.2048 | −1.05182 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.793466 | −0.0411947 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.8176 | −0.922563 | −0.461281 | − | 0.887254i | \(-0.652610\pi\) | ||||
−0.461281 | + | 0.887254i | \(0.652610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.480837 | −0.0248303 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.52781 | 0.181692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.508512 | 0.0261205 | 0.0130603 | − | 0.999915i | \(-0.495843\pi\) | ||||
0.0130603 | + | 0.999915i | \(0.495843\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.88252 | −0.0964446 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.2777 | 1.59822 | 0.799109 | − | 0.601187i | \(-0.205305\pi\) | ||||
0.799109 | + | 0.601187i | \(0.205305\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.343768 | −0.0175200 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.60114 | 0.284722 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.1369 | −0.513963 | −0.256981 | − | 0.966416i | \(-0.582728\pi\) | ||||
−0.256981 | + | 0.966416i | \(0.582728\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.23644 | 0.163674 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.43566 | 0.122863 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.22186 | 0.162109 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.86914 | −0.143998 | −0.0719989 | − | 0.997405i | \(-0.522938\pi\) | ||||
−0.0719989 | + | 0.997405i | \(0.522938\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0543494 | 0.00272087 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.7925 | 1.23808 | 0.619040 | − | 0.785359i | \(-0.287522\pi\) | ||||
0.619040 | + | 0.785359i | \(0.287522\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.92433 | 0.444553 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.03206 | 0.150664 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.87381 | 0.291154 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.9450 | 0.936769 | 0.468384 | − | 0.883525i | \(-0.344836\pi\) | ||||
0.468384 | + | 0.883525i | \(0.344836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.39933 | −0.118350 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.0287 | 0.690308 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.50500 | −0.0738778 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.57080 | −0.0769222 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.32966 | 0.0649579 | 0.0324790 | − | 0.999472i | \(-0.489660\pi\) | ||||
0.0324790 | + | 0.999472i | \(0.489660\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.02264 | −0.390999 | −0.195500 | − | 0.980704i | \(-0.562633\pi\) | ||||
−0.195500 | + | 0.980704i | \(0.562633\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.49363 | −0.364353 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.48520 | 0.460100 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.36966 | −0.308249 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.141545 | 0.00683387 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.68512 | −0.466516 | −0.233258 | − | 0.972415i | \(-0.574939\pi\) | ||||
−0.233258 | + | 0.972415i | \(0.574939\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.7157 | −1.37999 | −0.689994 | − | 0.723815i | \(-0.742387\pi\) | ||||
−0.689994 | + | 0.723815i | \(0.742387\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.171659 | 0.00823042 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.639592 | 0.0305958 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.65803 | −0.413225 | −0.206613 | − | 0.978423i | \(-0.566244\pi\) | ||||
−0.206613 | + | 0.978423i | \(0.566244\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.97996 | −0.141903 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.9580 | −0.995745 | −0.497872 | − | 0.867250i | \(-0.665885\pi\) | ||||
−0.497872 | + | 0.867250i | \(0.665885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.70426 | −0.0807895 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.46710 | −0.0693917 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.5646 | −1.58401 | −0.792006 | − | 0.610513i | \(-0.790963\pi\) | ||||
−0.792006 | + | 0.610513i | \(0.790963\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.78021 | 0.319268 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.990008 | 0.0465146 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.343768 | −0.0161161 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.1902 | −0.991235 | −0.495617 | − | 0.868541i | \(-0.665058\pi\) | ||||
−0.495617 | + | 0.868541i | \(0.665058\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.64459 | 0.0767631 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.6365 | 1.70633 | 0.853166 | − | 0.521640i | \(-0.174680\pi\) | ||||
0.853166 | + | 0.521640i | \(0.174680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3814 | −0.807782 | −0.403891 | − | 0.914807i | \(-0.632342\pi\) | ||||
−0.403891 | + | 0.914807i | \(0.632342\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.434247 | 0.0201377 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.9327 | 1.20002 | 0.600012 | − | 0.799991i | \(-0.295163\pi\) | ||||
0.600012 | + | 0.799991i | \(0.295163\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.05936 | 0.372147 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.833919 | −0.0384250 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.87960 | −0.0864240 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.87448 | 0.0860072 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.36450 | −0.108263 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.2850 | −0.972537 | −0.486268 | − | 0.873810i | \(-0.661642\pi\) | ||||
−0.486268 | + | 0.873810i | \(0.661642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.87381 | 0.267823 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.235776 | 0.0107282 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.65194 | −0.211234 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 29.4443 | 1.33425 | 0.667123 | − | 0.744947i | \(-0.267525\pi\) | ||||
0.667123 | + | 0.744947i | \(0.267525\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.160027 | 0.00723669 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.7655 | 1.07252 | 0.536261 | − | 0.844053i | \(-0.319836\pi\) | ||||
0.536261 | + | 0.844053i | \(0.319836\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.85441 | −0.308707 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.02442 | −0.0460441 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.428251 | −0.0192097 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.2462 | 1.75690 | 0.878451 | − | 0.477833i | \(-0.158578\pi\) | ||||
0.878451 | + | 0.477833i | \(0.158578\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.25766 | −0.100865 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.9003 | −0.664370 | −0.332185 | − | 0.943214i | \(-0.607786\pi\) | ||||
−0.332185 | + | 0.943214i | \(0.607786\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.85022 | −0.0823339 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.141545 | 0.00628625 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.3793 | 0.681677 | 0.340838 | − | 0.940122i | \(-0.389289\pi\) | ||||
0.340838 | + | 0.940122i | \(0.389289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.1299 | 0.536595 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.325008 | 0.0143494 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.25180 | −0.187357 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.51467 | 0.110595 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.17565 | −0.139396 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.8745 | −1.96599 | −0.982994 | − | 0.183636i | \(-0.941213\pi\) | ||||
−0.982994 | + | 0.183636i | \(0.941213\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.0853 | 1.53417 | 0.767086 | − | 0.641544i | \(-0.221706\pi\) | ||||
0.767086 | + | 0.641544i | \(0.221706\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.690999 | 0.0301577 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.3396 | −0.755327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2254 | −0.879363 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.8051 | 1.81419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.78021 | 0.293684 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.174637 | −0.00755021 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.83547 | 0.0792065 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.41564 | 0.232836 | 0.116418 | − | 0.993200i | \(-0.462859\pi\) | ||||
0.116418 | + | 0.993200i | \(0.462859\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.117989 | −0.00506338 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.491324 | 0.0210460 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.15207 | 0.348557 | 0.174279 | − | 0.984696i | \(-0.444241\pi\) | ||||
0.174279 | + | 0.984696i | \(0.444241\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −18.9814 | −0.810104 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.35458 | −0.0577071 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.37219 | −0.398546 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.285812 | 0.0121321 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 41.6501 | 1.76477 | 0.882385 | − | 0.470528i | \(-0.155937\pi\) | ||||
0.882385 | + | 0.470528i | \(0.155937\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.87960 | −0.0794985 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.275017 | −0.0116112 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.1701 | −1.01865 | −0.509324 | − | 0.860575i | \(-0.670105\pi\) | ||||
−0.509324 | + | 0.860575i | \(0.670105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.14341 | −0.132244 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.82009 | −0.370409 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.0116 | 0.461631 | 0.230815 | − | 0.972998i | \(-0.425861\pi\) | ||||
0.230815 | + | 0.972998i | \(0.425861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.2224 | −0.678885 | −0.339443 | − | 0.940627i | \(-0.610238\pi\) | ||||
−0.339443 | + | 0.940627i | \(0.610238\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.31436 | 0.0966839 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.13178 | 0.339119 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.16422 | 0.381512 | 0.190756 | − | 0.981638i | \(-0.438906\pi\) | ||||
0.190756 | + | 0.981638i | \(0.438906\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.56885 | 0.106758 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.37797 | 0.181629 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.793466 | 0.0328620 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.02442 | −0.0423544 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.4842 | −1.17567 | −0.587834 | − | 0.808982i | \(-0.700019\pi\) | ||||
−0.587834 | + | 0.808982i | \(0.700019\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.42669 | −0.141194 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.18341 | −0.130948 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.2059 | 0.460172 | 0.230086 | − | 0.973170i | \(-0.426099\pi\) | ||||
0.230086 | + | 0.973170i | \(0.426099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.667928 | 0.0273824 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.85933 | 0.0760974 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8800 | 0.567123 | 0.283561 | − | 0.958954i | \(-0.408484\pi\) | ||||
0.283561 | + | 0.958954i | \(0.408484\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7232 | 0.478200 | 0.239100 | − | 0.970995i | \(-0.423148\pi\) | ||||
0.239100 | + | 0.970995i | \(0.423148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.0166 | 0.978032 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.343768 | 0.0139762 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.3454 | −0.744618 | −0.372309 | − | 0.928109i | \(-0.621434\pi\) | ||||
−0.372309 | + | 0.928109i | \(0.621434\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.499346 | −0.0202345 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.51467 | 0.101733 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.2327 | −0.413296 | −0.206648 | − | 0.978415i | \(-0.566255\pi\) | ||||
−0.206648 | + | 0.978415i | \(0.566255\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.329917 | 0.0133035 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.92459 | 0.117739 | 0.0588697 | − | 0.998266i | \(-0.481250\pi\) | ||||
0.0588697 | + | 0.998266i | \(0.481250\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 38.5588 | 1.54981 | 0.774904 | − | 0.632079i | \(-0.217798\pi\) | ||||
0.774904 | + | 0.632079i | \(0.217798\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.40993 | 0.0565786 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.95758 | 0.198621 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.2413 | 0.929653 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.0543494 | −0.00217051 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −11.4126 | −0.455050 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.8716 | 1.26879 | 0.634395 | − | 0.773009i | \(-0.281249\pi\) | ||||
0.634395 | + | 0.773009i | \(0.281249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.55230 | −0.101445 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.57204 | −0.181436 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.27617 | −0.0504846 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.7019 | 1.60763 | 0.803815 | − | 0.594879i | \(-0.202800\pi\) | ||||
0.803815 | + | 0.594879i | \(0.202800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.5035 | −1.12407 | −0.562033 | − | 0.827114i | \(-0.689981\pi\) | ||||
−0.562033 | + | 0.827114i | \(0.689981\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.0914589 | −0.00360119 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.3960 | −1.50950 | −0.754751 | − | 0.656012i | \(-0.772242\pi\) | ||||
−0.754751 | + | 0.656012i | \(0.772242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14.0287 | −0.550675 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.26320 | −0.0495086 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.3523 | −0.992111 | −0.496055 | − | 0.868291i | \(-0.665219\pi\) | ||||
−0.496055 | + | 0.868291i | \(0.665219\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.91543 | 0.231135 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.1467 | 1.41022 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.42625 | −0.133468 | −0.0667339 | − | 0.997771i | \(-0.521258\pi\) | ||||
−0.0667339 | + | 0.997771i | \(0.521258\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.9669 | −0.854413 | −0.427207 | − | 0.904154i | \(-0.640502\pi\) | ||||
−0.427207 | + | 0.904154i | \(0.640502\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.275017 | −0.0106808 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.131997 | 0.00511863 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.87637 | −0.227534 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.898534 | 0.0347393 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.36966 | 0.245898 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.5578 | −0.908087 | −0.454044 | − | 0.890979i | \(-0.650019\pi\) | ||||
−0.454044 | + | 0.890979i | \(0.650019\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.13215 | 0.159047 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.9949 | −1.76773 | −0.883863 | − | 0.467745i | \(-0.845066\pi\) | ||||
−0.883863 | + | 0.467745i | \(0.845066\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5322 | 0.519318 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.505586 | −0.0193741 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.43705 | −0.208043 | −0.104021 | − | 0.994575i | \(-0.533171\pi\) | ||||
−0.104021 | + | 0.994575i | \(0.533171\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.82719 | −0.222646 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.910388 | −0.0347335 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.793466 | 0.0302286 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.9640 | 1.02576 | 0.512880 | − | 0.858460i | \(-0.328579\pi\) | ||||
0.512880 | + | 0.858460i | \(0.328579\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.97996 | 0.113200 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.81495 | −0.144709 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.1737 | −0.498989 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.65952 | 0.0627689 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.3979 | −1.63911 | −0.819557 | − | 0.572997i | \(-0.805781\pi\) | ||||
−0.819557 | + | 0.572997i | \(0.805781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.25538 | −0.0850632 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.122361 | 0.00460837 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.38219 | 0.202418 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 48.5676 | 1.82399 | 0.911997 | − | 0.410196i | \(-0.134540\pi\) | ||||
0.911997 | + | 0.410196i | \(0.134540\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.9288 | −1.04741 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.8655 | −0.556717 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.343768 | 0.0128562 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.95694 | −0.0730833 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.5701 | −1.51301 | −0.756504 | − | 0.653989i | \(-0.773094\pi\) | ||||
−0.756504 | + | 0.653989i | \(0.773094\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3682 | 0.460617 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.06123 | −0.0766578 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.2222 | −0.639615 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.9922 | 0.593117 | 0.296559 | − | 0.955015i | \(-0.404161\pi\) | ||||
0.296559 | + | 0.955015i | \(0.404161\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.9241 | −0.960153 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.65199 | 0.135074 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −17.4403 | −0.644172 | −0.322086 | − | 0.946710i | \(-0.604384\pi\) | ||||
−0.322086 | + | 0.946710i | \(0.604384\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.0486587 | 0.00179480 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.05936 | −0.296870 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.7320 | −0.983352 | −0.491676 | − | 0.870778i | \(-0.663616\pi\) | ||||
−0.491676 | + | 0.870778i | \(0.663616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0543494 | −0.00199658 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.12671 | 0.298140 | 0.149070 | − | 0.988827i | \(-0.452372\pi\) | ||||
0.149070 | + | 0.988827i | \(0.452372\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.56312 | −0.130543 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.0462 | 0.477335 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.508008 | 0.0185622 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.68036 | 0.207279 | 0.103640 | − | 0.994615i | \(-0.466951\pi\) | ||||
0.103640 | + | 0.994615i | \(0.466951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.34274 | 0.0489323 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.40441 | 0.0875054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −30.9880 | −1.12628 | −0.563138 | − | 0.826363i | \(-0.690406\pi\) | ||||
−0.563138 | + | 0.826363i | \(0.690406\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.235776 | −0.00855812 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.4708 | −0.379566 | −0.189783 | − | 0.981826i | \(-0.560778\pi\) | ||||
−0.189783 | + | 0.981826i | \(0.560778\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.42923 | −0.0517417 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.99040 | 0.0719632 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0287 | −0.506547 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.0177 | −1.51520 | −0.757599 | − | 0.652720i | \(-0.773628\pi\) | ||||
−0.757599 | + | 0.652720i | \(0.773628\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.99490 | 0.0718447 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 25.6652 | 0.923113 | 0.461557 | − | 0.887111i | \(-0.347291\pi\) | ||||
0.461557 | + | 0.887111i | \(0.347291\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −43.5670 | −1.56497 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.831411 | −0.0298267 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.60341 | −0.0932768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.428251 | 0.0153240 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.98607 | −0.106713 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.02532 | −0.0722868 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.4566 | 1.40648 | 0.703238 | − | 0.710955i | \(-0.251737\pi\) | ||||
0.703238 | + | 0.710955i | \(0.251737\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.20507 | 0.0785026 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.14399 | 0.325123 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.36966 | 0.226193 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.0386090 | 0.00136932 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.454799 | 0.0161098 | 0.00805490 | − | 0.999968i | \(-0.497436\pi\) | ||||
0.00805490 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.88591 | −0.172851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.7734 | 0.521993 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1299 | −0.428055 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.572623 | 0.0201823 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.30741 | −0.0812247 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.6757 | 1.00818 | 0.504092 | − | 0.863650i | \(-0.331827\pi\) | ||||
0.504092 | + | 0.863650i | \(0.331827\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.3682 | 0.855682 | 0.427841 | − | 0.903854i | \(-0.359274\pi\) | ||||
0.427841 | + | 0.903854i | \(0.359274\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.536282 | 0.0188082 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.388655 | 0.0136140 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.721712 | 0.0252495 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.97996 | 0.104128 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.7715 | 1.35313 | 0.676567 | − | 0.736381i | \(-0.263467\pi\) | ||||
0.676567 | + | 0.736381i | \(0.263467\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.94497 | 0.276944 | 0.138472 | − | 0.990366i | \(-0.455781\pi\) | ||||
0.138472 | + | 0.990366i | \(0.455781\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.690999 | −0.0240575 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.1512 | 0.596406 | 0.298203 | − | 0.954502i | \(-0.403613\pi\) | ||||
0.298203 | + | 0.954502i | \(0.403613\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.6830 | 0.509961 | 0.254981 | − | 0.966946i | \(-0.417931\pi\) | ||||
0.254981 | + | 0.966946i | \(0.417931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.79256 | −0.0968729 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.94296 | −0.0673197 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.48312 | −0.189751 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.55388 | −0.261100 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.17883 | 0.178793 | 0.0893966 | − | 0.995996i | \(-0.471506\pi\) | ||||
0.0893966 | + | 0.995996i | \(0.471506\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.5545 | −0.570846 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.66357 | −0.0917381 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.343768 | 0.0118260 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.00000 | −0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.930785 | −0.0319444 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.78417 | −0.335397 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.44234 | 0.117864 | 0.0589318 | − | 0.998262i | \(-0.481231\pi\) | ||||
0.0589318 | + | 0.998262i | \(0.481231\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.393347 | 0.0134522 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −16.5475 | −0.565252 | −0.282626 | − | 0.959230i | \(-0.591206\pi\) | ||||
−0.282626 | + | 0.959230i | \(0.591206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9475 | −1.29475 | −0.647376 | − | 0.762171i | \(-0.724133\pi\) | ||||
−0.647376 | + | 0.762171i | \(0.724133\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.959707 | −0.0327067 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 21.1359 | 0.719476 | 0.359738 | − | 0.933053i | \(-0.382866\pi\) | ||||
0.359738 | + | 0.933053i | \(0.382866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.71262 | −0.262237 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.87192 | −0.0635738 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.37219 | 0.317930 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.05936 | −0.273081 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 40.3255 | 1.36481 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.39705 | 0.114841 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.7514 | −1.07217 | −0.536085 | − | 0.844164i | \(-0.680097\pi\) | ||||
−0.536085 | + | 0.844164i | \(0.680097\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.19601 | 0.0403404 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.7648 | −0.901729 | −0.450864 | − | 0.892593i | \(-0.648884\pi\) | ||||
−0.450864 | + | 0.892593i | \(0.648884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.5131 | −1.36338 | −0.681688 | − | 0.731643i | \(-0.738754\pi\) | ||||
−0.681688 | + | 0.731643i | \(0.738754\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.682619 | −0.0229460 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 27.5458 | 0.924897 | 0.462448 | − | 0.886646i | \(-0.346971\pi\) | ||||
0.462448 | + | 0.886646i | \(0.346971\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.2998 | 0.446061 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.82009 | 0.295484 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −0.965563 | −0.0323113 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.45777 | 0.149007 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.235776 | −0.00787232 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.4834 | 1.05003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.54167 | −0.0513606 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.266048 | 0.00885353 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.286556 | −0.00952545 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21.6514 | 0.718925 | 0.359462 | − | 0.933160i | \(-0.382960\pi\) | ||||
0.359462 | + | 0.933160i | \(0.382960\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.0387 | 0.531971 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.6600 | −1.24773 | −0.623866 | − | 0.781532i | \(-0.714439\pi\) | ||||
−0.623866 | + | 0.781532i | \(0.714439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.37797 | −0.144890 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.309940 | 0.0102463 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.2076 | −0.568246 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −45.8544 | −1.51260 | −0.756298 | − | 0.654227i | \(-0.772994\pi\) | ||||
−0.756298 | + | 0.654227i | \(0.772994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.0440707 | −0.00145218 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.428251 | 0.0140961 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −28.6749 | −0.942826 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 36.8569 | 1.21054 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.81073 | 0.125026 | 0.0625130 | − | 0.998044i | \(-0.480089\pi\) | ||||
0.0625130 | + | 0.998044i | \(0.480089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.383972 | −0.0125842 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.27714 | −0.0745501 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.667928 | −0.0218436 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 30.5064 | 0.996600 | 0.498300 | − | 0.867005i | \(-0.333958\pi\) | ||||
0.498300 | + | 0.867005i | \(0.333958\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.49107 | 0.0812929 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.0054 | 1.17374 | 0.586871 | − | 0.809681i | \(-0.300360\pi\) | ||||
0.586871 | + | 0.809681i | \(0.300360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.2940 | −0.367782 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.290978 | 0.00946550 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.75429 | 0.0895023 | 0.0447512 | − | 0.998998i | \(-0.485751\pi\) | ||||
0.0447512 | + | 0.998998i | \(0.485751\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.1299 | −0.393753 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.70002 | −0.0875543 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.0079 | −1.81427 | −0.907137 | − | 0.420836i | \(-0.861737\pi\) | ||||
−0.907137 | + | 0.420836i | \(0.861737\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.62084 | 0.181886 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.499346 | 0.0161415 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.9509 | 0.547375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.6437 | 1.56915 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.51385 | 0.0487830 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.23890 | 0.200837 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.0658 | −1.48138 | −0.740688 | − | 0.671849i | \(-0.765500\pi\) | ||||
−0.740688 | + | 0.671849i | \(0.765500\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.105599 | 0.00339233 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −20.6368 | −0.662268 | −0.331134 | − | 0.943584i | \(-0.607431\pi\) | ||||
−0.331134 | + | 0.943584i | \(0.607431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0975 | 0.355769 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.690999 | −0.0221297 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.08573 | 0.194700 | 0.0973498 | − | 0.995250i | \(-0.468963\pi\) | ||||
0.0973498 | + | 0.995250i | \(0.468963\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.95758 | −0.158445 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.25906 | −0.135981 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.52353 | 0.144278 | 0.0721391 | − | 0.997395i | \(-0.477017\pi\) | ||||
0.0721391 | + | 0.997395i | \(0.477017\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.73146 | −0.246345 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.355940 | −0.0113297 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.13089 | 0.0995567 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.0636 | −0.383212 | −0.191606 | − | 0.981472i | \(-0.561370\pi\) | ||||
−0.191606 | + | 0.981472i | \(0.561370\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.85126 | −0.153950 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.51572 | 0.143158 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.8318 | 0.343045 | 0.171523 | − | 0.985180i | \(-0.445131\pi\) | ||||
0.171523 | + | 0.985180i | \(0.445131\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.97181 | −0.157301 |
(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.p.1.5 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8008.2.a.p.1.5 | ✓ | 9 | 1.1 | even | 1 | trivial |