Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9800,2,Mod(1,9800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9800, 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("9800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9800 = 2^{3} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9800.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: | \(78.2533939809\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 4 \) |
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 | 1.2 | ||
Root | \(-0.874032\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9800.1 |
$q$-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 | ||||||||
\(3\) | −0.874032 | −0.504623 | −0.252311 | − | 0.967646i | \(-0.581191\pi\) | ||||
−0.252311 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23607 | −0.745356 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | −0.150756 | − | 0.988571i | \(-0.548171\pi\) | ||||
−0.150756 | + | 0.988571i | \(0.548171\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.28825 | −0.634645 | −0.317323 | − | 0.948318i | \(-0.602784\pi\) | ||||
−0.317323 | + | 0.948318i | \(0.602784\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.74806 | 0.423968 | 0.211984 | − | 0.977273i | \(-0.432008\pi\) | ||||
0.211984 | + | 0.977273i | \(0.432008\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | −0.104257 | − | 0.994550i | \(-0.533247\pi\) | ||||
−0.104257 | + | 0.994550i | \(0.533247\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.57649 | 0.880746 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.70820 | 0.874292 | 0.437146 | − | 0.899391i | \(-0.355989\pi\) | ||||
0.437146 | + | 0.899391i | \(0.355989\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.86474 | 1.23294 | 0.616472 | − | 0.787377i | \(-0.288562\pi\) | ||||
0.616472 | + | 0.787377i | \(0.288562\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.874032 | 0.152149 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.23607 | 0.696405 | 0.348203 | − | 0.937419i | \(-0.386792\pi\) | ||||
0.348203 | + | 0.937419i | \(0.386792\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.206331 | −0.0322235 | −0.0161117 | − | 0.999870i | \(-0.505129\pi\) | ||||
−0.0161117 | + | 0.999870i | \(0.505129\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.23607 | −0.340997 | −0.170499 | − | 0.985358i | \(-0.554538\pi\) | ||||
−0.170499 | + | 0.985358i | \(0.554538\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.41421 | 0.206284 | 0.103142 | − | 0.994667i | \(-0.467110\pi\) | ||||
0.103142 | + | 0.994667i | \(0.467110\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.52786 | −0.213944 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.23607 | −0.444508 | −0.222254 | − | 0.974989i | \(-0.571341\pi\) | ||||
−0.222254 | + | 0.974989i | \(0.571341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.76393 | 0.366092 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.62054 | 0.210977 | 0.105488 | − | 0.994421i | \(-0.466359\pi\) | ||||
0.105488 | + | 0.994421i | \(0.466359\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.95440 | −0.250235 | −0.125117 | − | 0.992142i | \(-0.539931\pi\) | ||||
−0.125117 | + | 0.992142i | \(0.539931\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.47214 | 0.179850 | 0.0899250 | − | 0.995949i | \(-0.471337\pi\) | ||||
0.0899250 | + | 0.995949i | \(0.471337\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.874032 | 0.105221 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.70820 | −0.796117 | −0.398059 | − | 0.917360i | \(-0.630316\pi\) | ||||
−0.398059 | + | 0.917360i | \(0.630316\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.8554 | 1.50462 | 0.752308 | − | 0.658812i | \(-0.228941\pi\) | ||||
0.752308 | + | 0.658812i | \(0.228941\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.94427 | 0.668783 | 0.334391 | − | 0.942434i | \(-0.391469\pi\) | ||||
0.334391 | + | 0.942434i | \(0.391469\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.70820 | 0.300912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.20788 | 0.132582 | 0.0662912 | − | 0.997800i | \(-0.478883\pi\) | ||||
0.0662912 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.11512 | −0.441187 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.11667 | −0.542366 | −0.271183 | − | 0.962528i | \(-0.587415\pi\) | ||||
−0.271183 | + | 0.962528i | \(0.587415\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.95595 | 0.300131 | 0.150065 | − | 0.988676i | \(-0.452052\pi\) | ||||
0.150065 | + | 0.988676i | \(0.452052\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.23607 | 0.224733 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1877 | 1.21273 | 0.606363 | − | 0.795188i | \(-0.292628\pi\) | ||||
0.606363 | + | 0.795188i | \(0.292628\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.08191 | 0.205137 | 0.102569 | − | 0.994726i | \(-0.467294\pi\) | ||||
0.102569 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.4164 | 1.29701 | 0.648507 | − | 0.761209i | \(-0.275394\pi\) | ||||
0.648507 | + | 0.761209i | \(0.275394\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.4721 | −1.09883 | −0.549416 | − | 0.835549i | \(-0.685150\pi\) | ||||
−0.549416 | + | 0.835549i | \(0.685150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.70246 | −0.351422 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.18034 | −0.675470 | −0.337735 | − | 0.941241i | \(-0.609661\pi\) | ||||
−0.337735 | + | 0.941241i | \(0.609661\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.11667 | 0.473037 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0000 | −0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.180340 | 0.0162607 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.1246 | −1.60830 | −0.804150 | − | 0.594427i | \(-0.797379\pi\) | ||||
−0.804150 | + | 0.594427i | \(0.797379\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.95440 | 0.172075 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.8098 | −1.29394 | −0.646971 | − | 0.762515i | \(-0.723964\pi\) | ||||
−0.646971 | + | 0.762515i | \(0.723964\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.9443 | 1.61852 | 0.809259 | − | 0.587452i | \(-0.199869\pi\) | ||||
0.809259 | + | 0.587452i | \(0.199869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5231 | −1.14702 | −0.573509 | − | 0.819199i | \(-0.694418\pi\) | ||||
−0.573509 | + | 0.819199i | \(0.694418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.23607 | −0.104096 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.28825 | 0.191353 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.6525 | −1.28230 | −0.641150 | − | 0.767415i | \(-0.721543\pi\) | ||||
−0.641150 | + | 0.767415i | \(0.721543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.2361 | −1.48403 | −0.742015 | − | 0.670383i | \(-0.766130\pi\) | ||||
−0.742015 | + | 0.670383i | \(0.766130\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.90879 | −0.316007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.461370 | 0.0368213 | 0.0184107 | − | 0.999831i | \(-0.494139\pi\) | ||||
0.0184107 | + | 0.999831i | \(0.494139\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.82843 | 0.224309 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.76393 | −0.686444 | −0.343222 | − | 0.939254i | \(-0.611518\pi\) | ||||
−0.343222 | + | 0.939254i | \(0.611518\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.27740 | 0.563142 | 0.281571 | − | 0.959540i | \(-0.409144\pi\) | ||||
0.281571 | + | 0.959540i | \(0.409144\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.76393 | −0.597226 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.07107 | 0.540738 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.8918 | −1.28426 | −0.642128 | − | 0.766597i | \(-0.721948\pi\) | ||||
−0.642128 | + | 0.766597i | \(0.721948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.41641 | −0.106464 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.18034 | −0.461940 | −0.230970 | − | 0.972961i | \(-0.574190\pi\) | ||||
−0.230970 | + | 0.972961i | \(0.574190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4397 | −0.775975 | −0.387988 | − | 0.921665i | \(-0.626830\pi\) | ||||
−0.387988 | + | 0.921665i | \(0.626830\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.70820 | 0.126274 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.74806 | −0.127831 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.2361 | −1.53659 | −0.768294 | − | 0.640097i | \(-0.778894\pi\) | ||||
−0.768294 | + | 0.640097i | \(0.778894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.23607 | 0.160956 | 0.0804778 | − | 0.996756i | \(-0.474355\pi\) | ||||
0.0804778 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.416408 | −0.0296678 | −0.0148339 | − | 0.999890i | \(-0.504722\pi\) | ||||
−0.0148339 | + | 0.999890i | \(0.504722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.03476 | 0.215128 | 0.107564 | − | 0.994198i | \(-0.465695\pi\) | ||||
0.107564 | + | 0.994198i | \(0.465695\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.28669 | −0.0907564 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.23607 | 0.155417 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.16228 | 0.218739 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.4721 | −0.720932 | −0.360466 | − | 0.932772i | \(-0.617382\pi\) | ||||
−0.360466 | + | 0.932772i | \(0.617382\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.86319 | 0.401739 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.2361 | −0.759263 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.00000 | −0.269069 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.19859 | 0.482053 | 0.241027 | − | 0.970519i | \(-0.422516\pi\) | ||||
0.241027 | + | 0.970519i | \(0.422516\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.5563 | −1.03251 | −0.516256 | − | 0.856435i | \(-0.672675\pi\) | ||||
−0.516256 | + | 0.856435i | \(0.672675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.74962 | 0.181700 | 0.0908499 | − | 0.995865i | \(-0.471042\pi\) | ||||
0.0908499 | + | 0.995865i | \(0.471042\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.58359 | −0.103745 | −0.0518723 | − | 0.998654i | \(-0.516519\pi\) | ||||
−0.0518723 | + | 0.998654i | \(0.516519\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.19548 | −0.337483 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.76393 | 0.308153 | 0.154077 | − | 0.988059i | \(-0.450760\pi\) | ||||
0.154077 | + | 0.988059i | \(0.450760\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.2055 | 1.81687 | 0.908437 | − | 0.418022i | \(-0.137277\pi\) | ||||
0.908437 | + | 0.418022i | \(0.137277\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.0965 | −1.03259 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.23607 | 0.460420 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.05573 | −0.0669040 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.57649 | 0.288866 | 0.144433 | − | 0.989515i | \(-0.453864\pi\) | ||||
0.144433 | + | 0.989515i | \(0.453864\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.6746 | 1.35202 | 0.676011 | − | 0.736891i | \(-0.263707\pi\) | ||||
0.676011 | + | 0.736891i | \(0.263707\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −10.5279 | −0.651658 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.7082 | −1.03027 | −0.515136 | − | 0.857108i | \(-0.672259\pi\) | ||||
−0.515136 | + | 0.857108i | \(0.672259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.47214 | 0.273690 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.127520 | −0.00777500 | −0.00388750 | − | 0.999992i | \(-0.501237\pi\) | ||||
−0.00388750 | + | 0.999992i | \(0.501237\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.60970 | −0.401511 | −0.200755 | − | 0.979641i | \(-0.564340\pi\) | ||||
−0.200755 | + | 0.979641i | \(0.564340\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.9443 | 1.25842 | 0.629210 | − | 0.777236i | \(-0.283379\pi\) | ||||
0.629210 | + | 0.777236i | \(0.283379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −15.3500 | −0.918982 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6525 | −0.695128 | −0.347564 | − | 0.937656i | \(-0.612991\pi\) | ||||
−0.347564 | + | 0.937656i | \(0.612991\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.0339 | 1.84477 | 0.922387 | − | 0.386268i | \(-0.126236\pi\) | ||||
0.922387 | + | 0.386268i | \(0.126236\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.9443 | −0.820251 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.58359 | −0.151453 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.2619 | −1.24213 | −0.621067 | − | 0.783757i | \(-0.713301\pi\) | ||||
−0.621067 | + | 0.783757i | \(0.713301\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.57649 | −0.265555 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.28825 | 0.132333 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.6525 | −0.611969 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.7078 | 1.35307 | 0.676537 | − | 0.736408i | \(-0.263480\pi\) | ||||
0.676537 | + | 0.736408i | \(0.263480\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.81966 | −0.103517 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.3755 | 1.38221 | 0.691103 | − | 0.722756i | \(-0.257125\pi\) | ||||
0.691103 | + | 0.722756i | \(0.257125\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.08191 | −0.117677 | −0.0588384 | − | 0.998268i | \(-0.518740\pi\) | ||||
−0.0588384 | + | 0.998268i | \(0.518740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.4721 | 1.09366 | 0.546832 | − | 0.837242i | \(-0.315834\pi\) | ||||
0.546832 | + | 0.837242i | \(0.315834\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.70820 | −0.263609 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.7264 | −0.654502 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.52786 | −0.307579 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.0270 | 0.554495 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.0000 | −0.824475 | −0.412237 | − | 0.911077i | \(-0.635253\pi\) | ||||
−0.412237 | + | 0.911077i | \(0.635253\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −9.47214 | −0.519070 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.6525 | 0.689224 | 0.344612 | − | 0.938745i | \(-0.388010\pi\) | ||||
0.344612 | + | 0.938745i | \(0.388010\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.27585 | 0.340857 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.86474 | −0.371746 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.8885 | −1.33609 | −0.668044 | − | 0.744122i | \(-0.732868\pi\) | ||||
−0.668044 | + | 0.744122i | \(0.732868\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.6290 | 1.26483 | 0.632415 | − | 0.774630i | \(-0.282064\pi\) | ||||
0.632415 | + | 0.774630i | \(0.282064\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −10.4721 | −0.558961 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.1058 | 0.537879 | 0.268939 | − | 0.963157i | \(-0.413327\pi\) | ||||
0.268939 | + | 0.963157i | \(0.413327\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.18034 | 0.273408 | 0.136704 | − | 0.990612i | \(-0.456349\pi\) | ||||
0.136704 | + | 0.990612i | \(0.456349\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.74032 | 0.458748 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.4025 | −1.79580 | −0.897898 | − | 0.440204i | \(-0.854906\pi\) | ||||
−0.897898 | + | 0.440204i | \(0.854906\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.461370 | 0.0240180 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.18034 | 0.0611157 | 0.0305578 | − | 0.999533i | \(-0.490272\pi\) | ||||
0.0305578 | + | 0.999533i | \(0.490272\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.7735 | −0.554865 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.1803 | −0.574295 | −0.287148 | − | 0.957886i | \(-0.592707\pi\) | ||||
−0.287148 | + | 0.957886i | \(0.592707\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.8415 | 0.811584 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.11667 | 0.261450 | 0.130725 | − | 0.991419i | \(-0.458270\pi\) | ||||
0.130725 | + | 0.991419i | \(0.458270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.00000 | 0.254164 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.819660 | −0.0415584 | −0.0207792 | − | 0.999784i | \(-0.506615\pi\) | ||||
−0.0207792 | + | 0.999784i | \(0.506615\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.74806 | −0.0884034 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.9443 | 0.652952 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.8809 | 1.09817 | 0.549086 | − | 0.835766i | \(-0.314976\pi\) | ||||
0.549086 | + | 0.835766i | \(0.314976\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.7082 | −1.03412 | −0.517059 | − | 0.855950i | \(-0.672973\pi\) | ||||
−0.517059 | + | 0.855950i | \(0.672973\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.7082 | −0.782481 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.23607 | −0.209974 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.57804 | 0.275816 | 0.137908 | − | 0.990445i | \(-0.455962\pi\) | ||||
0.137908 | + | 0.990445i | \(0.455962\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.5579 | −0.816741 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 11.8197 | 0.578811 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.7363 | −1.69698 | −0.848491 | − | 0.529210i | \(-0.822488\pi\) | ||||
−0.848491 | + | 0.529210i | \(0.822488\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.0689 | 1.12431 | 0.562154 | − | 0.827032i | \(-0.309973\pi\) | ||||
0.562154 | + | 0.827032i | \(0.309973\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.16228 | −0.153755 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.00000 | −0.0965609 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.1803 | −1.45374 | −0.726868 | − | 0.686777i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686777i | \(0.759025\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −24.3755 | −1.17141 | −0.585705 | − | 0.810524i | \(-0.699182\pi\) | ||||
−0.585705 | + | 0.810524i | \(0.699182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.16228 | 0.151272 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.6777 | −1.13007 | −0.565037 | − | 0.825066i | \(-0.691138\pi\) | ||||
−0.565037 | + | 0.825066i | \(0.691138\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.1803 | −1.71898 | −0.859490 | − | 0.511153i | \(-0.829219\pi\) | ||||
−0.859490 | + | 0.511153i | \(0.829219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.6808 | 0.647078 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.29180 | 0.0609636 | 0.0304818 | − | 0.999535i | \(-0.490296\pi\) | ||||
0.0304818 | + | 0.999535i | \(0.490296\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.206331 | 0.00971575 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.9389 | 0.748875 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.2361 | 0.946603 | 0.473302 | − | 0.880900i | \(-0.343062\pi\) | ||||
0.473302 | + | 0.880900i | \(0.343062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.00000 | 0.373408 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −42.1413 | −1.96271 | −0.981357 | − | 0.192193i | \(-0.938440\pi\) | ||||
−0.981357 | + | 0.192193i | \(0.938440\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.4164 | −0.623513 | −0.311757 | − | 0.950162i | \(-0.600917\pi\) | ||||
−0.311757 | + | 0.950162i | \(0.600917\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7124 | −1.23610 | −0.618052 | − | 0.786137i | \(-0.712078\pi\) | ||||
−0.618052 | + | 0.786137i | \(0.712078\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.403252 | −0.0185809 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.23607 | 0.102815 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.23607 | 0.331317 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.5865 | 1.26046 | 0.630229 | − | 0.776409i | \(-0.282961\pi\) | ||||
0.630229 | + | 0.776409i | \(0.282961\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.69316 | −0.441970 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0000 | −0.589086 | −0.294543 | − | 0.955638i | \(-0.595167\pi\) | ||||
−0.294543 | + | 0.955638i | \(0.595167\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.65996 | 0.346395 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.1246 | 0.637435 | 0.318717 | − | 0.947850i | \(-0.396748\pi\) | ||||
0.318717 | + | 0.947850i | \(0.396748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.23024 | 0.370671 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0557 | −0.584455 | −0.292227 | − | 0.956349i | \(-0.594396\pi\) | ||||
−0.292227 | + | 0.956349i | \(0.594396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.36068 | −0.284174 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.49768 | −0.200542 | −0.100271 | − | 0.994960i | \(-0.531971\pi\) | ||||
−0.100271 | + | 0.994960i | \(0.531971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.78593 | 0.301374 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.0795 | −1.28893 | −0.644463 | − | 0.764636i | \(-0.722919\pi\) | ||||
−0.644463 | + | 0.764636i | \(0.722919\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.4721 | −0.638960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.41421 | −0.0621970 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7639 | 0.648065 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.1869 | 1.76062 | 0.880309 | − | 0.474400i | \(-0.157335\pi\) | ||||
0.880309 | + | 0.474400i | \(0.157335\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.7000 | −1.34242 | −0.671209 | − | 0.741268i | \(-0.734225\pi\) | ||||
−0.671209 | + | 0.741268i | \(0.734225\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.62365 | −0.157253 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.472136 | 0.0204505 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.40182 | 0.233106 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −42.0132 | −1.80629 | −0.903143 | − | 0.429339i | \(-0.858746\pi\) | ||||
−0.903143 | + | 0.429339i | \(0.858746\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.12461 | 0.391575 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.34752 | −0.185887 | −0.0929434 | − | 0.995671i | \(-0.529628\pi\) | ||||
−0.0929434 | + | 0.995671i | \(0.529628\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.37016 | 0.186514 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.8886 | −0.634278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.2361 | 1.36589 | 0.682943 | − | 0.730472i | \(-0.260700\pi\) | ||||
0.682943 | + | 0.730472i | \(0.260700\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.11667 | 0.216412 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.52786 | 0.0645065 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.7279 | 0.536418 | 0.268209 | − | 0.963361i | \(-0.413568\pi\) | ||||
0.268209 | + | 0.963361i | \(0.413568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.8885 | 0.540316 | 0.270158 | − | 0.962816i | \(-0.412924\pi\) | ||||
0.270158 | + | 0.962816i | \(0.412924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.1246 | −1.26068 | −0.630338 | − | 0.776321i | \(-0.717084\pi\) | ||||
−0.630338 | + | 0.776321i | \(0.717084\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.5610 | 0.775397 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.8840 | −0.994304 | −0.497152 | − | 0.867663i | \(-0.665621\pi\) | ||||
−0.497152 | + | 0.867663i | \(0.665621\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.95440 | −0.0812219 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.23607 | 0.134024 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.77198 | 0.403333 | 0.201666 | − | 0.979454i | \(-0.435364\pi\) | ||||
0.201666 | + | 0.979454i | \(0.435364\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.7082 | −0.894471 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.363954 | 0.0149711 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.73722 | −0.276664 | −0.138332 | − | 0.990386i | \(-0.544174\pi\) | ||||
−0.138332 | + | 0.990386i | \(0.544174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.65248 | −0.108559 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.9443 | 1.06005 | 0.530027 | − | 0.847981i | \(-0.322182\pi\) | ||||
0.530027 | + | 0.847981i | \(0.322182\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.49302 | −0.0609018 | −0.0304509 | − | 0.999536i | \(-0.509694\pi\) | ||||
−0.0304509 | + | 0.999536i | \(0.509694\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.29180 | −0.134052 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.7735 | −0.437284 | −0.218642 | − | 0.975805i | \(-0.570163\pi\) | ||||
−0.218642 | + | 0.975805i | \(0.570163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.23607 | −0.130917 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.05573 | 0.244589 | 0.122294 | − | 0.992494i | \(-0.460975\pi\) | ||||
0.122294 | + | 0.992494i | \(0.460975\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.3050 | 1.94468 | 0.972342 | − | 0.233561i | \(-0.0750380\pi\) | ||||
0.972342 | + | 0.233561i | \(0.0750380\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 30.8276 | 1.23906 | 0.619532 | − | 0.784971i | \(-0.287322\pi\) | ||||
0.619532 | + | 0.784971i | \(0.287322\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.57649 | −0.183648 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.76393 | −0.110381 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.40492 | 0.295253 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.5279 | −0.657964 | −0.328982 | − | 0.944336i | \(-0.606706\pi\) | ||||
−0.328982 | + | 0.944336i | \(0.606706\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.15298 | 0.363798 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.0000 | 0.593391 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.3050 | 1.03898 | 0.519492 | − | 0.854476i | \(-0.326121\pi\) | ||||
0.519492 | + | 0.854476i | \(0.326121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −32.7031 | −1.28969 | −0.644843 | − | 0.764315i | \(-0.723077\pi\) | ||||
−0.644843 | + | 0.764315i | \(0.723077\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.9272 | −1.92353 | −0.961763 | − | 0.273883i | \(-0.911692\pi\) | ||||
−0.961763 | + | 0.273883i | \(0.911692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.62054 | −0.0636119 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.47214 | −0.175008 | −0.0875041 | − | 0.996164i | \(-0.527889\pi\) | ||||
−0.0875041 | + | 0.996164i | \(0.527889\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −28.7456 | −1.12147 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.41641 | −0.0551754 | −0.0275877 | − | 0.999619i | \(-0.508783\pi\) | ||||
−0.0275877 | + | 0.999619i | \(0.508783\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.14833 | 0.239142 | 0.119571 | − | 0.992826i | \(-0.461848\pi\) | ||||
0.119571 | + | 0.992826i | \(0.461848\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.49613 | 0.135778 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.70820 | −0.182302 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.29180 | −0.243255 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.95440 | 0.0754486 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.0689 | −0.542316 | −0.271158 | − | 0.962535i | \(-0.587407\pi\) | ||||
−0.271158 | + | 0.962535i | \(0.587407\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.49458 | 0.0958744 | 0.0479372 | − | 0.998850i | \(-0.484735\pi\) | ||||
0.0479372 | + | 0.998850i | \(0.484735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.5967 | 0.521029 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33.9443 | −1.29884 | −0.649421 | − | 0.760429i | \(-0.724989\pi\) | ||||
−0.649421 | + | 0.760429i | \(0.724989\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.40325 | −0.0916898 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.40492 | 0.282105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.9281 | −0.796141 | −0.398070 | − | 0.917355i | \(-0.630320\pi\) | ||||
−0.398070 | + | 0.917355i | \(0.630320\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.360680 | −0.0136617 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.38411 | 0.0523519 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.3050 | 0.653599 | 0.326800 | − | 0.945094i | \(-0.394030\pi\) | ||||
0.326800 | + | 0.945094i | \(0.394030\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.3956 | −0.505225 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.05573 | −0.340095 | −0.170048 | − | 0.985436i | \(-0.554392\pi\) | ||||
−0.170048 | + | 0.985436i | \(0.554392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.2918 | −0.498481 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.86474 | −0.257086 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.16383 | −0.155501 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.9172 | 0.966549 | 0.483274 | − | 0.875469i | \(-0.339447\pi\) | ||||
0.483274 | + | 0.875469i | \(0.339447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.6525 | −0.916835 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.5980 | 1.46861 | 0.734304 | − | 0.678821i | \(-0.237509\pi\) | ||||
0.734304 | + | 0.678821i | \(0.237509\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.94427 | 0.220158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.90879 | −0.144572 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.48218 | 0.239425 | 0.119712 | − | 0.992809i | \(-0.461803\pi\) | ||||
0.119712 | + | 0.992809i | \(0.461803\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.47214 | −0.0542268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.63932 | −0.170660 | −0.0853301 | − | 0.996353i | \(-0.527194\pi\) | ||||
−0.0853301 | + | 0.996353i | \(0.527194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.32456 | −0.232338 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.180340 | 0.00661603 | 0.00330801 | − | 0.999995i | \(-0.498947\pi\) | ||||
0.00330801 | + | 0.999995i | \(0.498947\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.70091 | −0.0988210 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.8885 | −1.52853 | −0.764267 | − | 0.644900i | \(-0.776899\pi\) | ||||
−0.764267 | + | 0.644900i | \(0.776899\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.00000 | −0.145768 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.9443 | 0.870269 | 0.435135 | − | 0.900365i | \(-0.356701\pi\) | ||||
0.435135 | + | 0.900365i | \(0.356701\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.874032 | −0.0317254 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.667701 | 0.0242041 | 0.0121021 | − | 0.999927i | \(-0.496148\pi\) | ||||
0.0121021 | + | 0.999927i | \(0.496148\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.70820 | −0.133895 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.8878 | 1.54657 | 0.773286 | − | 0.634057i | \(-0.218612\pi\) | ||||
0.773286 | + | 0.634057i | \(0.218612\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.9443 | −0.682261 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.7627 | 0.566944 | 0.283472 | − | 0.958980i | \(-0.408514\pi\) | ||||
0.283472 | + | 0.958980i | \(0.408514\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.652476 | 0.0233774 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.70820 | 0.240038 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.5471 | 0.770029 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.2604 | −0.722204 | −0.361102 | − | 0.932526i | \(-0.617599\pi\) | ||||
−0.361102 | + | 0.932526i | \(0.617599\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.6035 | 0.519899 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.47214 | 0.158810 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.7078 | −0.839773 | −0.419886 | − | 0.907577i | \(-0.637930\pi\) | ||||
−0.419886 | + | 0.907577i | \(0.637930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.47214 | 0.0874579 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.4412 | 0.404256 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.8554 | −0.453659 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.111456 | 0.00392344 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.7082 | −0.657745 | −0.328873 | − | 0.944374i | \(-0.606669\pi\) | ||||
−0.328873 | + | 0.944374i | \(0.606669\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.2858 | 1.02836 | 0.514182 | − | 0.857681i | \(-0.328096\pi\) | ||||
0.514182 | + | 0.857681i | \(0.328096\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.77709 | 0.202611 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.07107 | 0.247385 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.41641 | −0.328635 | −0.164317 | − | 0.986408i | \(-0.552542\pi\) | ||||
−0.164317 | + | 0.986408i | \(0.552542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.3050 | −0.359208 | −0.179604 | − | 0.983739i | \(-0.557482\pi\) | ||||
−0.179604 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.7639 | −0.548166 | −0.274083 | − | 0.961706i | \(-0.588374\pi\) | ||||
−0.274083 | + | 0.961706i | \(0.588374\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.8716 | −0.968021 | −0.484011 | − | 0.875062i | \(-0.660820\pi\) | ||||
−0.484011 | + | 0.875062i | \(0.660820\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −18.3060 | −0.635027 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 31.4164 | 1.08591 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19.5927 | −0.676414 | −0.338207 | − | 0.941072i | \(-0.609820\pi\) | ||||
−0.338207 | + | 0.941072i | \(0.609820\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.83282 | −0.235614 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.1846 | 0.350778 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −27.1246 | −0.930914 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.23607 | −0.145211 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −41.8561 | −1.43313 | −0.716563 | − | 0.697522i | \(-0.754286\pi\) | ||||
−0.716563 | + | 0.697522i | \(0.754286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.2650 | 0.384805 | 0.192403 | − | 0.981316i | \(-0.438372\pi\) | ||||
0.192403 | + | 0.981316i | \(0.438372\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.08502 | 0.139379 | 0.0696895 | − | 0.997569i | \(-0.477799\pi\) | ||||
0.0696895 | + | 0.997569i | \(0.477799\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 16.1246 | 0.548888 | 0.274444 | − | 0.961603i | \(-0.411506\pi\) | ||||
0.274444 | + | 0.961603i | \(0.411506\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.1877 | 0.413917 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.94427 | −0.201646 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.36861 | −0.114141 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.60970 | −0.223704 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.70820 | 0.0576819 | 0.0288410 | − | 0.999584i | \(-0.490818\pi\) | ||||
0.0288410 | + | 0.999584i | \(0.490818\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 18.5836 | 0.626809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −29.4922 | −0.993616 | −0.496808 | − | 0.867861i | \(-0.665495\pi\) | ||||
−0.496808 | + | 0.867861i | \(0.665495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.3607 | 0.584233 | 0.292117 | − | 0.956383i | \(-0.405640\pi\) | ||||
0.292117 | + | 0.956383i | \(0.405640\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.8260 | 1.00146 | 0.500730 | − | 0.865604i | \(-0.333065\pi\) | ||||
0.500730 | + | 0.865604i | \(0.333065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.70820 | −0.0907282 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.47214 | −0.149654 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 32.3206 | 1.07795 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.65685 | −0.188457 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −32.0000 | −1.06254 | −0.531271 | − | 0.847202i | \(-0.678286\pi\) | ||||
−0.531271 | + | 0.847202i | \(0.678286\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −27.2526 | −0.903912 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.36068 | 0.310133 | 0.155067 | − | 0.987904i | \(-0.450441\pi\) | ||||
0.155067 | + | 0.987904i | \(0.450441\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.20788 | −0.0399751 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.59675 | −0.0856588 | −0.0428294 | − | 0.999082i | \(-0.513637\pi\) | ||||
−0.0428294 | + | 0.999082i | \(0.513637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.7214 | −0.682792 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.3500 | 0.505252 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.65530 | −0.152900 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.35931 | −0.307069 | −0.153535 | − | 0.988143i | \(-0.549066\pi\) | ||||
−0.153535 | + | 0.988143i | \(0.549066\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.3050 | −0.697493 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.2185 | −1.73857 | −0.869287 | − | 0.494308i | \(-0.835422\pi\) | ||||
−0.869287 | + | 0.494308i | \(0.835422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.81966 | 0.0593824 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −22.5973 | −0.736651 | −0.368326 | − | 0.929697i | \(-0.620069\pi\) | ||||
−0.368326 | + | 0.929697i | \(0.620069\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.206331 | 0.00671906 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29.8885 | −0.971247 | −0.485624 | − | 0.874168i | \(-0.661407\pi\) | ||||
−0.485624 | + | 0.874168i | \(0.661407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.4164 | −0.954897 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0193 | −0.551888 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.2361 | 0.590724 | 0.295362 | − | 0.955385i | \(-0.404560\pi\) | ||||
0.295362 | + | 0.955385i | \(0.404560\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.11512 | 0.133023 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1246 | 0.520149 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −30.0000 | −0.966736 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.52786 | −0.177764 | −0.0888821 | − | 0.996042i | \(-0.528329\pi\) | ||||
−0.0888821 | + | 0.996042i | \(0.528329\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.83153 | 0.155211 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.6243 | 1.04696 | 0.523482 | − | 0.852037i | \(-0.324633\pi\) | ||||
0.523482 | + | 0.852037i | \(0.324633\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.40325 | 0.172865 | 0.0864327 | − | 0.996258i | \(-0.472453\pi\) | ||||
0.0864327 | + | 0.996258i | \(0.472453\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.11667 | 0.163530 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.6525 | 0.819021 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −54.9480 | −1.75257 | −0.876284 | − | 0.481794i | \(-0.839985\pi\) | ||||
−0.876284 | + | 0.481794i | \(0.839985\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.23607 | 0.0711028 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.3475 | −0.455764 | −0.227882 | − | 0.973689i | \(-0.573180\pi\) | ||||
−0.227882 | + | 0.973689i | \(0.573180\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.1105 | 0.416049 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.3879 | 0.645691 | 0.322845 | − | 0.946452i | \(-0.395361\pi\) | ||||
0.322845 | + | 0.946452i | \(0.395361\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 19.3863 | 0.613356 |
(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 | 9800.2.a.cm.1.2 | ✓ | 4 | |
5.4 | even | 2 | 9800.2.a.cn.1.3 | yes | 4 | ||
7.6 | odd | 2 | inner | 9800.2.a.cm.1.3 | yes | 4 | |
35.34 | odd | 2 | 9800.2.a.cn.1.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9800.2.a.cm.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9800.2.a.cm.1.3 | yes | 4 | 7.6 | odd | 2 | inner | |
9800.2.a.cn.1.2 | yes | 4 | 35.34 | odd | 2 | ||
9800.2.a.cn.1.3 | yes | 4 | 5.4 | even | 2 |