Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.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: | \(63.9122617778\) |
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: | \( x^{9} - x^{8} - 17x^{7} + 4x^{6} + 75x^{5} + x^{4} - 118x^{3} - 26x^{2} + 60x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.09926\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.09926 | 0.491604 | 0.245802 | − | 0.969320i | \(-0.420949\pi\) | ||||
0.245802 | + | 0.969320i | \(0.420949\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.62400 | −0.613814 | −0.306907 | − | 0.951740i | \(-0.599294\pi\) | ||||
−0.306907 | + | 0.951740i | \(0.599294\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.16402 | −1.25550 | −0.627750 | − | 0.778415i | \(-0.716024\pi\) | ||||
−0.627750 | + | 0.778415i | \(0.716024\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.95343 | 1.09648 | 0.548242 | − | 0.836320i | \(-0.315297\pi\) | ||||
0.548242 | + | 0.836320i | \(0.315297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.09926 | 0.283828 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.36393 | −0.573337 | −0.286668 | − | 0.958030i | \(-0.592548\pi\) | ||||
−0.286668 | + | 0.958030i | \(0.592548\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.37074 | 1.00272 | 0.501359 | − | 0.865240i | \(-0.332834\pi\) | ||||
0.501359 | + | 0.865240i | \(0.332834\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.62400 | −0.354386 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.79163 | −0.758325 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.09478 | −1.45387 | −0.726933 | − | 0.686708i | \(-0.759055\pi\) | ||||
−0.726933 | + | 0.686708i | \(0.759055\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.16402 | −0.724863 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.78520 | −0.301754 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.52968 | 0.580276 | 0.290138 | − | 0.956985i | \(-0.406299\pi\) | ||||
0.290138 | + | 0.956985i | \(0.406299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.95343 | 0.633055 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.81475 | −0.595764 | −0.297882 | − | 0.954603i | \(-0.596280\pi\) | ||||
−0.297882 | + | 0.954603i | \(0.596280\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.25079 | 0.190744 | 0.0953721 | − | 0.995442i | \(-0.469596\pi\) | ||||
0.0953721 | + | 0.995442i | \(0.469596\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.09926 | 0.163868 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.41448 | 0.935649 | 0.467824 | − | 0.883821i | \(-0.345038\pi\) | ||||
0.467824 | + | 0.883821i | \(0.345038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.36263 | −0.623233 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.36393 | −0.331016 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.55412 | −0.488196 | −0.244098 | − | 0.969751i | \(-0.578492\pi\) | ||||
−0.244098 | + | 0.969751i | \(0.578492\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.57734 | −0.617209 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.37074 | 0.578919 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.96232 | 0.776228 | 0.388114 | − | 0.921611i | \(-0.373127\pi\) | ||||
0.388114 | + | 0.921611i | \(0.373127\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.3425 | −1.58030 | −0.790149 | − | 0.612915i | \(-0.789997\pi\) | ||||
−0.790149 | + | 0.612915i | \(0.789997\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.62400 | −0.204605 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.34585 | 0.539036 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.8312 | −1.56758 | −0.783791 | − | 0.621024i | \(-0.786717\pi\) | ||||
−0.783791 | + | 0.621024i | \(0.786717\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.30445 | 0.985557 | 0.492778 | − | 0.870155i | \(-0.335981\pi\) | ||||
0.492778 | + | 0.870155i | \(0.335981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.26071 | −0.264596 | −0.132298 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132298 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.79163 | −0.437819 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.76236 | 0.770643 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.7456 | −1.65900 | −0.829502 | − | 0.558504i | \(-0.811376\pi\) | ||||
−0.829502 | + | 0.558504i | \(0.811376\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.49232 | 1.04192 | 0.520959 | − | 0.853582i | \(-0.325575\pi\) | ||||
0.520959 | + | 0.853582i | \(0.325575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.59857 | −0.281855 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.52312 | −0.479450 | −0.239725 | − | 0.970841i | \(-0.577057\pi\) | ||||
−0.239725 | + | 0.970841i | \(0.577057\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.42036 | −0.673036 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.09478 | −0.839390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.80459 | 0.492940 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.79546 | −0.283836 | −0.141918 | − | 0.989878i | \(-0.545327\pi\) | ||||
−0.141918 | + | 0.989878i | \(0.545327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.16402 | −0.418500 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.71767 | −0.270418 | −0.135209 | − | 0.990817i | \(-0.543171\pi\) | ||||
−0.135209 | + | 0.990817i | \(0.543171\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.577486 | 0.0569014 | 0.0284507 | − | 0.999595i | \(-0.490943\pi\) | ||||
0.0284507 | + | 0.999595i | \(0.490943\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.78520 | −0.174217 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.55434 | 0.730306 | 0.365153 | − | 0.930948i | \(-0.381017\pi\) | ||||
0.365153 | + | 0.930948i | \(0.381017\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.65806 | −0.541944 | −0.270972 | − | 0.962587i | \(-0.587345\pi\) | ||||
−0.270972 | + | 0.962587i | \(0.587345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.52968 | 0.335022 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.3321 | −0.971959 | −0.485979 | − | 0.873970i | \(-0.661537\pi\) | ||||
−0.485979 | + | 0.873970i | \(0.661537\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.09926 | −0.102507 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.95343 | 0.365494 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.83902 | 0.351922 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.33907 | 0.576279 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.81475 | −0.343964 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.66429 | −0.864400 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.87590 | 0.521402 | 0.260701 | − | 0.965420i | \(-0.416046\pi\) | ||||
0.260701 | + | 0.965420i | \(0.416046\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.25079 | 0.110126 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.82339 | 0.421422 | 0.210711 | − | 0.977548i | \(-0.432422\pi\) | ||||
0.210711 | + | 0.977548i | \(0.432422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.09808 | −0.615482 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.09926 | 0.0946093 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.74001 | −0.404967 | −0.202483 | − | 0.979286i | \(-0.564901\pi\) | ||||
−0.202483 | + | 0.979286i | \(0.564901\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.2187 | 1.71492 | 0.857462 | − | 0.514547i | \(-0.172040\pi\) | ||||
0.857462 | + | 0.514547i | \(0.172040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.41448 | 0.540197 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.4621 | −1.37663 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.09926 | −0.0912886 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.36263 | −0.359824 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.49552 | −0.122518 | −0.0612588 | − | 0.998122i | \(-0.519512\pi\) | ||||
−0.0612588 | + | 0.998122i | \(0.519512\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.0744 | 1.06398 | 0.531988 | − | 0.846752i | \(-0.321445\pi\) | ||||
0.531988 | + | 0.846752i | \(0.321445\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.36393 | −0.191112 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.89828 | −0.714727 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.6257 | −1.00764 | −0.503819 | − | 0.863809i | \(-0.668072\pi\) | ||||
−0.503819 | + | 0.863809i | \(0.668072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.55412 | −0.281860 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.62400 | 0.127989 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.89587 | −0.461800 | −0.230900 | − | 0.972977i | \(-0.574167\pi\) | ||||
−0.230900 | + | 0.972977i | \(0.574167\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.57734 | −0.356346 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.7013 | −1.83406 | −0.917032 | − | 0.398813i | \(-0.869422\pi\) | ||||
−0.917032 | + | 0.398813i | \(0.869422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.62958 | 0.202275 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.37074 | 0.334239 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.81905 | 0.214328 | 0.107164 | − | 0.994241i | \(-0.465823\pi\) | ||||
0.107164 | + | 0.994241i | \(0.465823\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.15759 | 0.465470 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.96232 | 0.448155 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0776 | 0.902722 | 0.451361 | − | 0.892342i | \(-0.350939\pi\) | ||||
0.451361 | + | 0.892342i | \(0.350939\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.8023 | 1.76921 | 0.884606 | − | 0.466340i | \(-0.154428\pi\) | ||||
0.884606 | + | 0.466340i | \(0.154428\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −12.3425 | −0.912386 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.88004 | 0.285266 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.84345 | 0.719824 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.62400 | −0.118129 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.52735 | 0.255230 | 0.127615 | − | 0.991824i | \(-0.459268\pi\) | ||||
0.127615 | + | 0.991824i | \(0.459268\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.2610 | −1.89031 | −0.945153 | − | 0.326627i | \(-0.894088\pi\) | ||||
−0.945153 | + | 0.326627i | \(0.894088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.34585 | 0.311212 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.7606 | −1.19414 | −0.597072 | − | 0.802187i | \(-0.703669\pi\) | ||||
−0.597072 | + | 0.802187i | \(0.703669\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.9678 | −0.777489 | −0.388744 | − | 0.921346i | \(-0.627091\pi\) | ||||
−0.388744 | + | 0.921346i | \(0.627091\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.8312 | −0.905044 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.62400 | 0.113982 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.19340 | −0.292880 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.00000 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.1999 | −1.25891 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.67146 | 0.115068 | 0.0575341 | − | 0.998344i | \(-0.481676\pi\) | ||||
0.0575341 | + | 0.998344i | \(0.481676\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.30445 | 0.569011 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.37495 | 0.0937707 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.1459 | 0.892403 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.26071 | −0.152765 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.34562 | −0.628654 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.4523 | −0.766902 | −0.383451 | − | 0.923561i | \(-0.625264\pi\) | ||||
−0.383451 | + | 0.923561i | \(0.625264\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.79163 | −0.252775 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.3236 | 0.685201 | 0.342601 | − | 0.939481i | \(-0.388692\pi\) | ||||
0.342601 | + | 0.939481i | \(0.388692\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.4908 | −1.35407 | −0.677037 | − | 0.735949i | \(-0.736736\pi\) | ||||
−0.677037 | + | 0.735949i | \(0.736736\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.76236 | 0.444931 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.3015 | −1.06795 | −0.533974 | − | 0.845501i | \(-0.679302\pi\) | ||||
−0.533974 | + | 0.845501i | \(0.679302\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.05119 | 0.459969 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.7456 | −0.957827 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.9115 | −1.61139 | −0.805695 | − | 0.592331i | \(-0.798208\pi\) | ||||
−0.805695 | + | 0.592331i | \(0.798208\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.5384 | −1.32300 | −0.661498 | − | 0.749947i | \(-0.730079\pi\) | ||||
−0.661498 | + | 0.749947i | \(0.730079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.79567 | −0.306384 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 17.2794 | 1.09946 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.49232 | 0.601551 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.15343 | 0.325281 | 0.162641 | − | 0.986685i | \(-0.447999\pi\) | ||||
0.162641 | + | 0.986685i | \(0.447999\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.16402 | 0.261790 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.59857 | −0.162729 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3581 | 0.770878 | 0.385439 | − | 0.922733i | \(-0.374050\pi\) | ||||
0.385439 | + | 0.922733i | \(0.374050\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.73219 | −0.356181 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.61176 | −0.346036 | −0.173018 | − | 0.984919i | \(-0.555352\pi\) | ||||
−0.173018 | + | 0.984919i | \(0.555352\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.90690 | −0.239999 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.52312 | −0.276811 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.50357 | 0.152645 | 0.0763226 | − | 0.997083i | \(-0.475682\pi\) | ||||
0.0763226 | + | 0.997083i | \(0.475682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.01951 | 0.487151 | 0.243575 | − | 0.969882i | \(-0.421680\pi\) | ||||
0.243575 | + | 0.969882i | \(0.421680\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.42036 | −0.388578 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.7884 | 0.952077 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −15.3260 | −0.920850 | −0.460425 | − | 0.887699i | \(-0.652303\pi\) | ||||
−0.460425 | + | 0.887699i | \(0.652303\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.09478 | −0.484622 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.6963 | 1.23464 | 0.617319 | − | 0.786713i | \(-0.288219\pi\) | ||||
0.617319 | + | 0.786713i | \(0.288219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.2936 | −0.730780 | −0.365390 | − | 0.930855i | \(-0.619064\pi\) | ||||
−0.365390 | + | 0.930855i | \(0.619064\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.80459 | 0.284599 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.19515 | 0.365688 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.4118 | −0.671285 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.79546 | −0.163873 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −26.5827 | −1.55298 | −0.776489 | − | 0.630131i | \(-0.783001\pi\) | ||||
−0.776489 | + | 0.630131i | \(0.783001\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.55414 | 0.381597 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.16402 | −0.241621 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.95343 | −0.228633 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.03129 | −0.117081 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.71767 | −0.156126 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.5677 | −0.776882 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.50926 | −0.200284 | −0.100142 | − | 0.994973i | \(-0.531930\pi\) | ||||
−0.100142 | + | 0.994973i | \(0.531930\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.577486 | 0.0328520 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.88485 | −0.447109 | −0.223554 | − | 0.974691i | \(-0.571766\pi\) | ||||
−0.223554 | + | 0.974691i | \(0.571766\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.5619 | −1.55789 | −0.778946 | − | 0.627091i | \(-0.784246\pi\) | ||||
−0.778946 | + | 0.627091i | \(0.784246\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.78520 | −0.100585 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.95975 | 0.334733 | 0.167366 | − | 0.985895i | \(-0.446474\pi\) | ||||
0.167366 | + | 0.985895i | \(0.446474\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.16402 | 0.233140 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.55434 | 0.421642 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10.3321 | −0.574895 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.9899 | −0.831491 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.65806 | −0.312891 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.4171 | −0.574314 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.9771 | −0.603356 | −0.301678 | − | 0.953410i | \(-0.597547\pi\) | ||||
−0.301678 | + | 0.953410i | \(0.597547\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.52968 | 0.193425 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.1049 | −0.770631 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2823 | −1.21379 | −0.606897 | − | 0.794781i | \(-0.707586\pi\) | ||||
−0.606897 | + | 0.794781i | \(0.707586\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.3321 | −0.561161 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 33.7068 | 1.82533 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4529 | 0.996363 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.09926 | −0.0591822 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0078 | 0.966709 | 0.483355 | − | 0.875425i | \(-0.339418\pi\) | ||||
0.483355 | + | 0.875425i | \(0.339418\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.3714 | 1.25104 | 0.625521 | − | 0.780208i | \(-0.284887\pi\) | ||||
0.625521 | + | 0.780208i | \(0.284887\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.95343 | 0.211018 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.85756 | −0.418216 | −0.209108 | − | 0.977893i | \(-0.567056\pi\) | ||||
−0.209108 | + | 0.977893i | \(0.567056\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.12875 | 0.484504 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.83902 | 0.203182 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.9850 | 1.37143 | 0.685717 | − | 0.727868i | \(-0.259489\pi\) | ||||
0.685717 | + | 0.727868i | \(0.259489\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.103389 | 0.00544152 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.33907 | 0.332715 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.48511 | −0.130077 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.7725 | 0.771117 | 0.385559 | − | 0.922683i | \(-0.374009\pi\) | ||||
0.385559 | + | 0.922683i | \(0.374009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.81475 | −0.198588 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.77189 | 0.299661 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.5103 | 1.42443 | 0.712215 | − | 0.701962i | \(-0.247692\pi\) | ||||
0.712215 | + | 0.701962i | \(0.247692\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.66429 | −0.499062 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.95343 | −0.203612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.8568 | 1.27681 | 0.638404 | − | 0.769701i | \(-0.279595\pi\) | ||||
0.638404 | + | 0.769701i | \(0.279595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.87590 | 0.301032 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.3583 | −1.04026 | −0.520131 | − | 0.854087i | \(-0.674117\pi\) | ||||
−0.520131 | + | 0.854087i | \(0.674117\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.43360 | 0.378851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.25079 | 0.0635814 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.10949 | −0.309764 | −0.154882 | − | 0.987933i | \(-0.549500\pi\) | ||||
−0.154882 | + | 0.987933i | \(0.549500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.36393 | 0.119549 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.82339 | 0.243308 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −16.2092 | −0.815574 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.6577 | 0.735650 | 0.367825 | − | 0.929895i | \(-0.380103\pi\) | ||||
0.367825 | + | 0.929895i | \(0.380103\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.09808 | −0.355348 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.7090 | 0.834410 | 0.417205 | − | 0.908812i | \(-0.363010\pi\) | ||||
0.417205 | + | 0.908812i | \(0.363010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.0021 | −1.59414 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.09926 | 0.0546227 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.6977 | −0.728536 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.84895 | −0.289212 | −0.144606 | − | 0.989489i | \(-0.546191\pi\) | ||||
−0.144606 | + | 0.989489i | \(0.546191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.74001 | −0.233808 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.68280 | −0.476459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 10.4345 | 0.512211 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 20.2187 | 0.990112 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.8906 | 1.06943 | 0.534714 | − | 0.845033i | \(-0.320419\pi\) | ||||
0.534714 | + | 0.845033i | \(0.320419\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.1392 | 1.37142 | 0.685710 | − | 0.727875i | \(-0.259492\pi\) | ||||
0.685710 | + | 0.727875i | \(0.259492\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.41448 | 0.311883 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.96313 | 0.434776 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0442 | 0.970009 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −16.4621 | −0.794800 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0315 | −0.675873 | −0.337937 | − | 0.941169i | \(-0.609729\pi\) | ||||
−0.337937 | + | 0.941169i | \(0.609729\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.07861 | 0.0998917 | 0.0499459 | − | 0.998752i | \(-0.484095\pi\) | ||||
0.0499459 | + | 0.998752i | \(0.484095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.09926 | −0.0527055 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.37074 | −0.209081 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −27.1515 | −1.29587 | −0.647935 | − | 0.761695i | \(-0.724367\pi\) | ||||
−0.647935 | + | 0.761695i | \(0.724367\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.36263 | −0.207744 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.9145 | 1.04119 | 0.520595 | − | 0.853804i | \(-0.325710\pi\) | ||||
0.520595 | + | 0.853804i | \(0.325710\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.97209 | −0.235700 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.49552 | −0.0707356 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5385 | 0.544537 | 0.272268 | − | 0.962221i | \(-0.412226\pi\) | ||||
0.272268 | + | 0.962221i | \(0.412226\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.8847 | 0.747981 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.0744 | 0.614287 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.05765 | −0.330868 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7409 | −0.736326 | −0.368163 | − | 0.929761i | \(-0.620013\pi\) | ||||
−0.368163 | + | 0.929761i | \(0.620013\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.36393 | −0.110339 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.0594 | 1.40001 | 0.700003 | − | 0.714140i | \(-0.253182\pi\) | ||||
0.700003 | + | 0.714140i | \(0.253182\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.3524 | 0.574064 | 0.287032 | − | 0.957921i | \(-0.407331\pi\) | ||||
0.287032 | + | 0.957921i | \(0.407331\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.89828 | −0.412648 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.95785 | 0.460794 | 0.230397 | − | 0.973097i | \(-0.425997\pi\) | ||||
0.230397 | + | 0.973097i | \(0.425997\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.8379 | 0.962204 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.6257 | −0.581761 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.20833 | −0.239479 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.5722 | −0.760386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.55412 | −0.162732 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −29.1940 | −1.33391 | −0.666953 | − | 0.745099i | \(-0.732402\pi\) | ||||
−0.666953 | + | 0.745099i | \(0.732402\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9543 | 0.636262 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.62400 | 0.0738945 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.07294 | −0.139535 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.9615 | −0.677969 | −0.338985 | − | 0.940792i | \(-0.610083\pi\) | ||||
−0.338985 | + | 0.940792i | \(0.610083\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.89587 | −0.266621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4089 | −0.875910 | −0.437955 | − | 0.898997i | \(-0.644297\pi\) | ||||
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.36393 | 0.106466 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.57734 | −0.205736 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4864 | −0.604948 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.6996 | 0.613278 | 0.306639 | − | 0.951826i | \(-0.400796\pi\) | ||||
0.306639 | + | 0.951826i | \(0.400796\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −23.7013 | −1.05890 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.8413 | 0.617152 | 0.308576 | − | 0.951200i | \(-0.400148\pi\) | ||||
0.308576 | + | 0.951200i | \(0.400148\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.98743 | −0.132939 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.62958 | 0.116784 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.8823 | 1.05857 | 0.529283 | − | 0.848446i | \(-0.322461\pi\) | ||||
0.529283 | + | 0.848446i | \(0.322461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.67139 | 0.162413 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.37074 | 0.192973 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.634808 | 0.0279730 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.7100 | −1.17471 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.81905 | 0.123743 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.9572 | −1.00577 | −0.502887 | − | 0.864352i | \(-0.667729\pi\) | ||||
−0.502887 | + | 0.864352i | \(0.667729\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.15498 | −0.181685 | −0.0908423 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908423 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.15759 | 0.268739 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.1355 | 0.833555 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.96232 | 0.258743 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.0813 | −0.653245 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.30419 | 0.359021 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.0776 | 0.521187 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.1661 | 0.782468 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.5952 | −0.670492 | −0.335246 | − | 0.942131i | \(-0.608819\pi\) | ||||
−0.335246 | + | 0.942131i | \(0.608819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.8023 | 1.02145 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.21968 | −0.266422 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.3173 | −0.526650 | −0.263325 | − | 0.964707i | \(-0.584819\pi\) | ||||
−0.263325 | + | 0.964707i | \(0.584819\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.3425 | −0.526766 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.37074 | −0.186200 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.9468 | 1.01832 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.88004 | 0.164698 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.4030 | 1.24584 | 0.622922 | − | 0.782284i | \(-0.285946\pi\) | ||||
0.622922 | + | 0.782284i | \(0.285946\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.94492 | 0.209148 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.84345 | 0.415591 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.67982 | −0.323666 | −0.161833 | − | 0.986818i | \(-0.551741\pi\) | ||||
−0.161833 | + | 0.986818i | \(0.551741\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.3576 | −0.477819 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.62400 | −0.0682015 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.7619 | −1.96036 | −0.980180 | − | 0.198109i | \(-0.936520\pi\) | ||||
−0.980180 | + | 0.198109i | \(0.936520\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7497 | −0.952044 | −0.476022 | − | 0.879433i | \(-0.657922\pi\) | ||||
−0.476022 | + | 0.879433i | \(0.657922\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.52735 | 0.147357 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.79163 | 0.158122 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4667 | 1.35161 | 0.675803 | − | 0.737082i | \(-0.263797\pi\) | ||||
0.675803 | + | 0.737082i | \(0.263797\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −26.2610 | −1.09137 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.4155 | −0.639543 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.7994 | 0.612930 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.34585 | 0.179679 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 44.9305 | 1.85448 | 0.927240 | − | 0.374467i | \(-0.122174\pi\) | ||||
0.927240 | + | 0.374467i | \(0.122174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −35.3802 | −1.45782 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.7606 | −0.689440 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −19.3818 | −0.795914 | −0.397957 | − | 0.917404i | \(-0.630281\pi\) | ||||
−0.397957 | + | 0.917404i | \(0.630281\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.22008 | 0.173006 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.9678 | −0.448883 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.0213 | −0.532035 | −0.266018 | − | 0.963968i | \(-0.585708\pi\) | ||||
−0.266018 | + | 0.963968i | \(0.585708\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.0563 | 1.42997 | 0.714987 | − | 0.699137i | \(-0.246432\pi\) | ||||
0.714987 | + | 0.699137i | \(0.246432\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −12.8312 | −0.522528 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.96829 | 0.283301 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.13500 | −0.330190 | −0.165095 | − | 0.986278i | \(-0.552793\pi\) | ||||
−0.165095 | + | 0.986278i | \(0.552793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.62400 | 0.0658077 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.3592 | 1.02592 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.2074 | −1.38162 | −0.690812 | − | 0.723034i | \(-0.742747\pi\) | ||||
−0.690812 | + | 0.723034i | \(0.742747\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.19340 | −0.169094 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6354 | −0.548940 | −0.274470 | − | 0.961596i | \(-0.588502\pi\) | ||||
−0.274470 | + | 0.961596i | \(0.588502\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.8104 | −0.997213 | −0.498606 | − | 0.866829i | \(-0.666155\pi\) | ||||
−0.498606 | + | 0.866829i | \(0.666155\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.34554 | 0.294293 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.33456 | 0.333382 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.1999 | −0.726832 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.34391 | −0.332693 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.51667 | 0.259425 | 0.129712 | − | 0.991552i | \(-0.458595\pi\) | ||||
0.129712 | + | 0.991552i | \(0.458595\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.67146 | 0.0664346 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.45915 | 0.256323 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.2473 | −0.683364 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.30445 | 0.328519 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.7254 | 1.29258 | 0.646289 | − | 0.763093i | \(-0.276320\pi\) | ||||
0.646289 | + | 0.763093i | \(0.276320\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9951 | −0.473039 | −0.236519 | − | 0.971627i | \(-0.576007\pi\) | ||||
−0.236519 | + | 0.971627i | \(0.576007\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.37495 | 0.0541385 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.83271 | −0.229308 | −0.114654 | − | 0.993406i | \(-0.536576\pi\) | ||||
−0.114654 | + | 0.993406i | \(0.536576\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.8272 | −0.974554 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.1459 | 0.515229 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −15.8443 | −0.620034 | −0.310017 | − | 0.950731i | \(-0.600335\pi\) | ||||
−0.310017 | + | 0.950731i | \(0.600335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.30217 | 0.207173 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.26071 | −0.0881986 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.25099 | −0.126641 | −0.0633203 | − | 0.997993i | \(-0.520169\pi\) | ||||
−0.0633203 | + | 0.997993i | \(0.520169\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.29424 | −0.0892357 | −0.0446179 | − | 0.999004i | \(-0.514207\pi\) | ||||
−0.0446179 | + | 0.999004i | \(0.514207\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −9.34562 | −0.362954 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.80264 | −0.302573 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −11.4523 | −0.442771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 51.3945 | 1.98406 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3973 | 0.901901 | 0.450951 | − | 0.892549i | \(-0.351085\pi\) | ||||
0.450951 | + | 0.892549i | \(0.351085\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.79163 | −0.145940 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0661 | 1.57830 | 0.789150 | − | 0.614201i | \(-0.210522\pi\) | ||||
0.789150 | + | 0.614201i | \(0.210522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.53982 | 0.174222 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.3236 | 0.395601 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.0729842 | 0.00279266 | 0.00139633 | − | 0.999999i | \(-0.499556\pi\) | ||||
0.00139633 | + | 0.999999i | \(0.499556\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.21051 | −0.199083 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.4908 | −0.781774 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.0510 | −0.535299 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.0332 | −0.914264 | −0.457132 | − | 0.889399i | \(-0.651123\pi\) | ||||
−0.457132 | + | 0.889399i | \(0.651123\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.76236 | 0.256881 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.2256 | 0.843065 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.01780 | 0.341573 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.3015 | −0.616580 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.4959 | 1.22735 | 0.613676 | − | 0.789558i | \(-0.289690\pi\) | ||||
0.613676 | + | 0.789558i | \(0.289690\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.4273 | 0.581852 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.05119 | 0.265563 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.41349 | 0.165986 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.31742 | 0.312367 | 0.156184 | − | 0.987728i | \(-0.450081\pi\) | ||||
0.156184 | + | 0.987728i | \(0.450081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.7456 | −0.553001 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.09478 | 0.303152 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −18.0962 | −0.676759 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.9115 | −0.930336 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.29581 | 0.160207 | 0.0801034 | − | 0.996787i | \(-0.474475\pi\) | ||||
0.0801034 | + | 0.996787i | \(0.474475\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.937837 | −0.0349269 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.5384 | −0.763833 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.79163 | 0.140817 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.2693 | −0.714658 | −0.357329 | − | 0.933979i | \(-0.616312\pi\) | ||||
−0.357329 | + | 0.933979i | \(0.616312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.95679 | −0.109361 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.0166 | 0.739332 | 0.369666 | − | 0.929165i | \(-0.379472\pi\) | ||||
0.369666 | + | 0.929165i | \(0.379472\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.79567 | −0.176891 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.4295 | 1.96810 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.9829 | −0.771868 | −0.385934 | − | 0.922526i | \(-0.626121\pi\) | ||||
−0.385934 | + | 0.922526i | \(0.626121\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 17.2794 | 0.634775 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.9474 | −0.548366 | −0.274183 | − | 0.961678i | \(-0.588407\pi\) | ||||
−0.274183 | + | 0.961678i | \(0.588407\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.64397 | −0.0602302 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9.49232 | 0.347306 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.2682 | −0.448272 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.1871 | −1.61241 | −0.806205 | − | 0.591636i | \(-0.798482\pi\) | ||||
−0.806205 | + | 0.591636i | \(0.798482\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.15343 | 0.187801 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.3721 | 0.523056 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.5638 | 0.602021 | 0.301011 | − | 0.953621i | \(-0.402676\pi\) | ||||
0.301011 | + | 0.953621i | \(0.402676\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.16402 | 0.151144 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.04978 | 0.255554 | 0.127777 | − | 0.991803i | \(-0.459216\pi\) | ||||
0.127777 | + | 0.991803i | \(0.459216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.18868 | 0.332653 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.59857 | −0.0939516 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 23.5716 | 0.851121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.0490 | −1.19178 | −0.595889 | − | 0.803067i | \(-0.703200\pi\) | ||||
−0.595889 | + | 0.803067i | \(0.703200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.3581 | 0.445067 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 42.7305 | 1.53691 | 0.768454 | − | 0.639904i | \(-0.221026\pi\) | ||||
0.768454 | + | 0.639904i | \(0.221026\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.6924 | 1.10250 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.73219 | −0.205641 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.6733 | −0.597383 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.5799 | −1.23737 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.8789 | −0.495360 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.7655 | −1.41749 | −0.708744 | − | 0.705466i | \(-0.750738\pi\) | ||||
−0.708744 | + | 0.705466i | \(0.750738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.61176 | −0.199784 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16.7793 | 0.596602 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −48.7953 | −1.73277 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.90690 | −0.138564 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.66395 | −0.342315 | −0.171157 | − | 0.985244i | \(-0.554751\pi\) | ||||
−0.171157 | + | 0.985244i | \(0.554751\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.1634 | −0.536442 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.52312 | −0.159817 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.41364 | 0.332200 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.78520 | 0.0629200 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.50357 | 0.0881297 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.85384 | 0.276126 | 0.138063 | − | 0.990423i | \(-0.455912\pi\) | ||||
0.138063 | + | 0.990423i | \(0.455912\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.7017 | −0.972738 | −0.486369 | − | 0.873753i | \(-0.661679\pi\) | ||||
−0.486369 | + | 0.873753i | \(0.661679\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.01951 | 0.281257 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.48110 | −0.227023 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.46689 | 0.191262 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.42036 | −0.224345 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.4164 | −0.991738 | −0.495869 | − | 0.868397i | \(-0.665150\pi\) | ||||
−0.495869 | + | 0.868397i | \(0.665150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.9282 | 0.659796 | 0.329898 | − | 0.944017i | \(-0.392986\pi\) | ||||
0.329898 | + | 0.944017i | \(0.392986\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15.7884 | 0.549682 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.4745 | 0.433779 | 0.216890 | − | 0.976196i | \(-0.430409\pi\) | ||||
0.216890 | + | 0.976196i | \(0.430409\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.06835 | −0.245494 | −0.122747 | − | 0.992438i | \(-0.539170\pi\) | ||||
−0.122747 | + | 0.992438i | \(0.539170\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.3260 | −0.531653 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.3129 | 0.357322 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.0540 | −0.901634 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.09478 | −0.279797 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.30055 | 0.286567 | 0.143283 | − | 0.989682i | \(-0.454234\pi\) | ||||
0.143283 | + | 0.989682i | \(0.454234\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 20.6963 | 0.712818 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.89059 | 0.0994394 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.2946 | −0.353728 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.2936 | −0.421916 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.52968 | −0.120996 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.3189 | 1.65441 | 0.827205 | − | 0.561901i | \(-0.189930\pi\) | ||||
0.827205 | + | 0.561901i | \(0.189930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.80459 | 0.164313 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 35.7504 | 1.22121 | 0.610606 | − | 0.791935i | \(-0.290926\pi\) | ||||
0.610606 | + | 0.791935i | \(0.290926\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.9841 | −1.43248 | −0.716239 | − | 0.697855i | \(-0.754138\pi\) | ||||
−0.716239 | + | 0.697855i | \(0.754138\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.19515 | 0.211130 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 31.7225 | 1.07984 | 0.539922 | − | 0.841715i | \(-0.318454\pi\) | ||||
0.539922 | + | 0.841715i | \(0.318454\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.09887 | 0.105365 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.4118 | −0.387566 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 61.4008 | 2.08288 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −50.7273 | −1.71883 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.79546 | −0.0946120 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.6948 | 0.530581 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.7023 | −0.631531 | −0.315765 | − | 0.948837i | \(-0.602261\pi\) | ||||
−0.315765 | + | 0.948837i | \(0.602261\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.5827 | −0.896612 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.4113 | −0.923510 | −0.461755 | − | 0.887008i | \(-0.652780\pi\) | ||||
−0.461755 | + | 0.887008i | \(0.652780\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.94240 | 0.199978 | 0.0999889 | − | 0.994989i | \(-0.468119\pi\) | ||||
0.0999889 | + | 0.994989i | \(0.468119\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.55414 | 0.220315 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −41.6929 | −1.39991 | −0.699956 | − | 0.714186i | \(-0.746797\pi\) | ||||
−0.699956 | + | 0.714186i | \(0.746797\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.54246 | −0.320044 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.16402 | −0.139500 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 28.0361 | 0.938191 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.2764 | 0.443782 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.95343 | −0.132001 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.09478 | 0.269976 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.40169 | 0.279901 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.03129 | −0.0675970 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 26.1649 | 0.869752 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 47.3811 | 1.57326 | 0.786632 | − | 0.617422i | \(-0.211823\pi\) | ||||
0.786632 | + | 0.617422i | \(0.211823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.71767 | −0.0901394 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.9539 | 0.793627 | 0.396814 | − | 0.917899i | \(-0.370116\pi\) | ||||
0.396814 | + | 0.917899i | \(0.370116\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.5262 | −1.30813 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.5677 | −0.448533 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.83319 | −0.258675 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 50.7326 | 1.67351 | 0.836757 | − | 0.547574i | \(-0.184449\pi\) | ||||
0.836757 | + | 0.547574i | \(0.184449\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.50926 | −0.115634 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 32.8310 | 1.08065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.3832 | −0.440038 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.577486 | 0.0189671 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.26851 | −0.140045 | −0.0700226 | − | 0.997545i | \(-0.522307\pi\) | ||||
−0.0700226 | + | 0.997545i | \(0.522307\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0679 | −0.624926 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.88485 | −0.258138 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.8205 | 0.353869 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.9332 | 0.357171 | 0.178586 | − | 0.983924i | \(-0.442848\pi\) | ||||
0.178586 | + | 0.983924i | \(0.442848\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.5619 | −0.899450 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 31.1352 | 1.01498 | 0.507489 | − | 0.861658i | \(-0.330574\pi\) | ||||
0.507489 | + | 0.861658i | \(0.330574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.81475 | 0.124225 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.78520 | −0.0580725 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.71474 | 0.153209 | 0.0766043 | − | 0.997062i | \(-0.475592\pi\) | ||||
0.0766043 | + | 0.997062i | \(0.475592\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.93754 | −0.290125 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.95975 | 0.193258 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 55.1516 | 1.78653 | 0.893267 | − | 0.449526i | \(-0.148407\pi\) | ||||
0.893267 | + | 0.449526i | \(0.148407\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.87747 | 0.125472 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.16402 | 0.134604 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.69777 | 0.248574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.5255 | 1.11373 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.55434 | 0.243435 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.8677 | −0.929283 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −23.9274 | −0.769453 | −0.384727 | − | 0.923031i | \(-0.625704\pi\) | ||||
−0.384727 | + | 0.923031i | \(0.625704\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.3321 | −0.331916 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.7441 | −1.05081 | −0.525404 | − | 0.850853i | \(-0.676086\pi\) | ||||
−0.525404 | + | 0.850853i | \(0.676086\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.8351 | −1.05264 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.9899 | −0.480061 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −32.5643 | −1.04183 | −0.520913 | − | 0.853610i | \(-0.674408\pi\) | ||||
−0.520913 | + | 0.853610i | \(0.674408\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.8344 | 0.601949 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65806 | −0.180648 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61.7387 | −1.96916 | −0.984580 | − | 0.174935i | \(-0.944029\pi\) | ||||
−0.984580 | + | 0.174935i | \(0.944029\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.4243 | −0.587047 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10.4171 | −0.331580 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.25079 | −0.0397729 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.3446 | 0.836864 | 0.418432 | − | 0.908248i | \(-0.362580\pi\) | ||||
0.418432 | + | 0.908248i | \(0.362580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.9771 | −0.348348 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.0565 | −0.382217 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.02186 | −0.0957032 | −0.0478516 | − | 0.998854i | \(-0.515237\pi\) | ||||
−0.0478516 | + | 0.998854i | \(0.515237\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.52968 | 0.111674 |
(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 | 8004.2.a.f.1.7 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.f.1.7 | ✓ | 9 | 1.1 | even | 1 | trivial |