Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5184,2,Mod(1,5184)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5184, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5184.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5184 = 2^{6} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5184.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: | \(41.3944484078\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 288) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5184.1 |
$q$-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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | 0.223607 | − | 0.974679i | \(-0.428217\pi\) | ||||
0.223607 | + | 0.974679i | \(0.428217\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.44949 | −1.30378 | −0.651892 | − | 0.758312i | \(-0.726025\pi\) | ||||
−0.651892 | + | 0.758312i | \(0.726025\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.44949 | 0.437038 | 0.218519 | − | 0.975833i | \(-0.429878\pi\) | ||||
0.218519 | + | 0.975833i | \(0.429878\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.89898 | −1.63608 | −0.818041 | − | 0.575160i | \(-0.804940\pi\) | ||||
−0.818041 | + | 0.575160i | \(0.804940\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.89898 | 1.18818 | 0.594089 | − | 0.804400i | \(-0.297513\pi\) | ||||
0.594089 | + | 0.804400i | \(0.297513\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.44949 | 1.13630 | 0.568149 | − | 0.822926i | \(-0.307660\pi\) | ||||
0.568149 | + | 0.822926i | \(0.307660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | −0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.101021 | −0.0187590 | −0.00937952 | − | 0.999956i | \(-0.502986\pi\) | ||||
−0.00937952 | + | 0.999956i | \(0.502986\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.55051 | −0.458085 | −0.229043 | − | 0.973416i | \(-0.573560\pi\) | ||||
−0.229043 | + | 0.973416i | \(0.573560\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.44949 | −0.583070 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.898979 | 0.147791 | 0.0738957 | − | 0.997266i | \(-0.476457\pi\) | ||||
0.0738957 | + | 0.997266i | \(0.476457\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.8990 | −1.85831 | −0.929154 | − | 0.369692i | \(-0.879463\pi\) | ||||
−0.929154 | + | 0.369692i | \(0.879463\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.34847 | −0.358138 | −0.179069 | − | 0.983836i | \(-0.557309\pi\) | ||||
−0.179069 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.34847 | 0.926019 | 0.463010 | − | 0.886353i | \(-0.346770\pi\) | ||||
0.463010 | + | 0.886353i | \(0.346770\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.89898 | 0.699854 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.89898 | −1.22237 | −0.611184 | − | 0.791488i | \(-0.709307\pi\) | ||||
−0.611184 | + | 0.791488i | \(0.709307\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.44949 | 0.195449 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.3485 | 1.86801 | 0.934006 | − | 0.357258i | \(-0.116288\pi\) | ||||
0.934006 | + | 0.357258i | \(0.116288\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.89898 | 1.01136 | 0.505680 | − | 0.862721i | \(-0.331242\pi\) | ||||
0.505680 | + | 0.862721i | \(0.331242\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −5.89898 | −0.731678 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3485 | 1.50861 | 0.754303 | − | 0.656527i | \(-0.227975\pi\) | ||||
0.754303 | + | 0.656527i | \(0.227975\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.79796 | −0.925447 | −0.462724 | − | 0.886503i | \(-0.653128\pi\) | ||||
−0.462724 | + | 0.886503i | \(0.653128\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.89898 | −0.573382 | −0.286691 | − | 0.958023i | \(-0.592555\pi\) | ||||
−0.286691 | + | 0.958023i | \(0.592555\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.00000 | −0.569803 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.4495 | −1.51319 | −0.756593 | − | 0.653886i | \(-0.773137\pi\) | ||||
−0.756593 | + | 0.653886i | \(0.773137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.550510 | −0.0604264 | −0.0302132 | − | 0.999543i | \(-0.509619\pi\) | ||||
−0.0302132 | + | 0.999543i | \(0.509619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.89898 | 0.531369 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.8990 | −1.36729 | −0.683645 | − | 0.729815i | \(-0.739606\pi\) | ||||
−0.683645 | + | 0.729815i | \(0.739606\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.3485 | 2.13310 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.89898 | −0.395881 | −0.197941 | − | 0.980214i | \(-0.563425\pi\) | ||||
−0.197941 | + | 0.980214i | \(0.563425\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7980 | −1.27344 | −0.636722 | − | 0.771093i | \(-0.719710\pi\) | ||||
−0.636722 | + | 0.771093i | \(0.719710\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.5505 | −1.23664 | −0.618319 | − | 0.785927i | \(-0.712186\pi\) | ||||
−0.618319 | + | 0.785927i | \(0.712186\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.79796 | −0.560510 | −0.280255 | − | 0.959926i | \(-0.590419\pi\) | ||||
−0.280255 | + | 0.959926i | \(0.590419\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.898979 | −0.0861066 | −0.0430533 | − | 0.999073i | \(-0.513709\pi\) | ||||
−0.0430533 | + | 0.999073i | \(0.513709\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.79796 | 0.827642 | 0.413821 | − | 0.910358i | \(-0.364194\pi\) | ||||
0.413821 | + | 0.910358i | \(0.364194\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.44949 | 0.508168 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.8990 | −1.54913 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.89898 | −0.808998 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.00000 | −0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.00000 | −0.709885 | −0.354943 | − | 0.934888i | \(-0.615500\pi\) | ||||
−0.354943 | + | 0.934888i | \(0.615500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.2474 | −1.15743 | −0.578717 | − | 0.815528i | \(-0.696447\pi\) | ||||
−0.578717 | + | 0.815528i | \(0.696447\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.7980 | −1.19643 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.1010 | −0.862988 | −0.431494 | − | 0.902116i | \(-0.642013\pi\) | ||||
−0.431494 | + | 0.902116i | \(0.642013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.44949 | −0.292582 | −0.146291 | − | 0.989242i | \(-0.546734\pi\) | ||||
−0.146291 | + | 0.989242i | \(0.546734\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.55051 | −0.715030 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.101021 | −0.00838930 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.10102 | −0.335969 | −0.167984 | − | 0.985790i | \(-0.553726\pi\) | ||||
−0.167984 | + | 0.985790i | \(0.553726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.2474 | −1.24082 | −0.620410 | − | 0.784278i | \(-0.713034\pi\) | ||||
−0.620410 | + | 0.784278i | \(0.713034\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.55051 | −0.204862 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7980 | 0.861771 | 0.430885 | − | 0.902407i | \(-0.358201\pi\) | ||||
0.430885 | + | 0.902407i | \(0.358201\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −18.7980 | −1.48149 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.79796 | −0.454131 | −0.227066 | − | 0.973879i | \(-0.572913\pi\) | ||||
−0.227066 | + | 0.973879i | \(0.572913\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.55051 | −0.352129 | −0.176065 | − | 0.984379i | \(-0.556337\pi\) | ||||
−0.176065 | + | 0.984379i | \(0.556337\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.7980 | 1.67677 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.00000 | −0.228086 | −0.114043 | − | 0.993476i | \(-0.536380\pi\) | ||||
−0.114043 | + | 0.993476i | \(0.536380\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.7980 | 1.04303 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6969 | −0.795097 | −0.397549 | − | 0.917581i | \(-0.630139\pi\) | ||||
−0.397549 | + | 0.917581i | \(0.630139\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.898979 | 0.0660943 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.10102 | 0.519278 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5505 | 0.908123 | 0.454062 | − | 0.890970i | \(-0.349975\pi\) | ||||
0.454062 | + | 0.890970i | \(0.349975\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.10102 | 0.295198 | 0.147599 | − | 0.989047i | \(-0.452846\pi\) | ||||
0.147599 | + | 0.989047i | \(0.452846\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5959 | 1.25366 | 0.626829 | − | 0.779157i | \(-0.284353\pi\) | ||||
0.626829 | + | 0.779157i | \(0.284353\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.79796 | 0.552783 | 0.276391 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276391 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.348469 | 0.0244577 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.8990 | −0.831061 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.79796 | 0.401053 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.5505 | 0.726327 | 0.363164 | − | 0.931725i | \(-0.381697\pi\) | ||||
0.363164 | + | 0.931725i | \(0.381697\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.34847 | −0.160164 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.79796 | 0.597244 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.8990 | −1.94396 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1464 | 1.08124 | 0.540622 | − | 0.841265i | \(-0.318189\pi\) | ||||
0.540622 | + | 0.841265i | \(0.318189\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.65153 | 0.507850 | 0.253925 | − | 0.967224i | \(-0.418278\pi\) | ||||
0.253925 | + | 0.967224i | \(0.418278\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.00000 | 0.0660819 | 0.0330409 | − | 0.999454i | \(-0.489481\pi\) | ||||
0.0330409 | + | 0.999454i | \(0.489481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.34847 | 0.414128 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −14.1464 | −0.915056 | −0.457528 | − | 0.889195i | \(-0.651265\pi\) | ||||
−0.457528 | + | 0.889195i | \(0.651265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.89898 | 0.312984 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.5959 | −1.50137 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.7980 | 1.37587 | 0.687937 | − | 0.725770i | \(-0.258516\pi\) | ||||
0.687937 | + | 0.725770i | \(0.258516\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.89898 | 0.496605 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7980 | −0.673558 | −0.336779 | − | 0.941584i | \(-0.609338\pi\) | ||||
−0.336779 | + | 0.941584i | \(0.609338\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.10102 | −0.192688 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.44949 | −0.336030 | −0.168015 | − | 0.985784i | \(-0.553736\pi\) | ||||
−0.168015 | + | 0.985784i | \(0.553736\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.89898 | −0.546660 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.10102 | −0.432957 | −0.216478 | − | 0.976287i | \(-0.569457\pi\) | ||||
−0.216478 | + | 0.976287i | \(0.569457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −29.3939 | −1.78555 | −0.892775 | − | 0.450502i | \(-0.851245\pi\) | ||||
−0.892775 | + | 0.450502i | \(0.851245\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.79796 | −0.349630 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.7980 | 0.889123 | 0.444562 | − | 0.895748i | \(-0.353359\pi\) | ||||
0.444562 | + | 0.895748i | \(0.353359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.1010 | −0.602576 | −0.301288 | − | 0.953533i | \(-0.597417\pi\) | ||||
−0.301288 | + | 0.953533i | \(0.597417\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.44949 | −0.205051 | −0.102525 | − | 0.994730i | \(-0.532692\pi\) | ||||
−0.102525 | + | 0.994730i | \(0.532692\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 41.0454 | 2.42283 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.797959 | −0.0466173 | −0.0233086 | − | 0.999728i | \(-0.507420\pi\) | ||||
−0.0233086 | + | 0.999728i | \(0.507420\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.3485 | 0.835400 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −32.1464 | −1.85908 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.10102 | 0.466935 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.89898 | 0.452294 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −21.7980 | −1.24408 | −0.622038 | − | 0.782987i | \(-0.713695\pi\) | ||||
−0.622038 | + | 0.782987i | \(0.713695\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.2474 | 0.864603 | 0.432302 | − | 0.901729i | \(-0.357702\pi\) | ||||
0.432302 | + | 0.901729i | \(0.357702\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.0000 | −0.960897 | −0.480448 | − | 0.877023i | \(-0.659526\pi\) | ||||
−0.480448 | + | 0.877023i | \(0.659526\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.8990 | −1.45463 | −0.727316 | − | 0.686303i | \(-0.759232\pi\) | ||||
−0.727316 | + | 0.686303i | \(0.759232\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.146428 | −0.00819841 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.5959 | 1.09035 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 23.5959 | 1.30887 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.8990 | −1.20733 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.2474 | 0.618216 | 0.309108 | − | 0.951027i | \(-0.399970\pi\) | ||||
0.309108 | + | 0.951027i | \(0.399970\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.3485 | 0.674669 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.7980 | −0.588202 | −0.294101 | − | 0.955774i | \(-0.595020\pi\) | ||||
−0.294101 | + | 0.955774i | \(0.595020\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.69694 | −0.200200 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.24745 | 0.391325 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.14643 | 0.329958 | 0.164979 | − | 0.986297i | \(-0.447244\pi\) | ||||
0.164979 | + | 0.986297i | \(0.447244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7980 | 0.792117 | 0.396058 | − | 0.918225i | \(-0.370378\pi\) | ||||
0.396058 | + | 0.918225i | \(0.370378\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.6969 | −0.729014 | −0.364507 | − | 0.931201i | \(-0.618763\pi\) | ||||
−0.364507 | + | 0.931201i | \(0.618763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −7.79796 | −0.413873 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.79796 | 0.0948926 | 0.0474463 | − | 0.998874i | \(-0.484892\pi\) | ||||
0.0474463 | + | 0.998874i | \(0.484892\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.89898 | −0.256424 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.34847 | 0.226988 | 0.113494 | − | 0.993539i | \(-0.463796\pi\) | ||||
0.113494 | + | 0.993539i | \(0.463796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.6969 | 1.59371 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.6969 | −1.64121 | −0.820603 | − | 0.571499i | \(-0.806362\pi\) | ||||
−0.820603 | + | 0.571499i | \(0.806362\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.595918 | 0.0306913 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.0000 | −1.33553 | −0.667765 | − | 0.744372i | \(-0.732749\pi\) | ||||
−0.667765 | + | 0.744372i | \(0.732749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −28.5505 | −1.45886 | −0.729431 | − | 0.684054i | \(-0.760215\pi\) | ||||
−0.729431 | + | 0.684054i | \(0.760215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.00000 | −0.254824 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.79796 | 0.344670 | 0.172335 | − | 0.985038i | \(-0.444869\pi\) | ||||
0.172335 | + | 0.985038i | \(0.444869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 26.6969 | 1.35012 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.4495 | −0.676717 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.6969 | 0.536864 | 0.268432 | − | 0.963299i | \(-0.413495\pi\) | ||||
0.268432 | + | 0.963299i | \(0.413495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.6969 | −0.683992 | −0.341996 | − | 0.939701i | \(-0.611103\pi\) | ||||
−0.341996 | + | 0.939701i | \(0.611103\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.0454 | 0.749465 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.30306 | 0.0645904 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.5959 | 1.31508 | 0.657542 | − | 0.753418i | \(-0.271596\pi\) | ||||
0.657542 | + | 0.753418i | \(0.271596\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −49.4949 | −2.43548 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.550510 | −0.0270235 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −31.2474 | −1.52654 | −0.763269 | − | 0.646081i | \(-0.776407\pi\) | ||||
−0.763269 | + | 0.646081i | \(0.776407\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.101021 | −0.00492344 | −0.00246172 | − | 0.999997i | \(-0.500784\pi\) | ||||
−0.00246172 | + | 0.999997i | \(0.500784\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −19.5959 | −0.950542 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.2474 | −1.31860 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.2020 | −0.684088 | −0.342044 | − | 0.939684i | \(-0.611119\pi\) | ||||
−0.342044 | + | 0.939684i | \(0.611119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.49490 | −0.408239 | −0.204119 | − | 0.978946i | \(-0.565433\pi\) | ||||
−0.204119 | + | 0.978946i | \(0.565433\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 21.7980 | 1.04274 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.3485 | 1.73482 | 0.867409 | − | 0.497596i | \(-0.165784\pi\) | ||||
0.867409 | + | 0.497596i | \(0.165784\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.4495 | 1.11412 | 0.557059 | − | 0.830473i | \(-0.311930\pi\) | ||||
0.557059 | + | 0.830473i | \(0.311930\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.8990 | −0.611470 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.1010 | 0.523890 | 0.261945 | − | 0.965083i | \(-0.415636\pi\) | ||||
0.261945 | + | 0.965083i | \(0.415636\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.2474 | −0.812151 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.3485 | 0.953951 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.4949 | −1.47327 | −0.736635 | − | 0.676291i | \(-0.763586\pi\) | ||||
−0.736635 | + | 0.676291i | \(0.763586\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.6969 | −1.66257 | −0.831286 | − | 0.555845i | \(-0.812395\pi\) | ||||
−0.831286 | + | 0.555845i | \(0.812395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.2474 | 1.45219 | 0.726096 | − | 0.687593i | \(-0.241333\pi\) | ||||
0.726096 | + | 0.687593i | \(0.241333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 39.5959 | 1.83228 | 0.916140 | − | 0.400858i | \(-0.131288\pi\) | ||||
0.916140 | + | 0.400858i | \(0.131288\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −42.5959 | −1.96690 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.40408 | −0.156520 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.0000 | −0.734130 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.0454 | −1.14435 | −0.572177 | − | 0.820130i | \(-0.693901\pi\) | ||||
−0.572177 | + | 0.820130i | \(0.693901\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.30306 | −0.241799 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.89898 | −0.177044 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7980 | 0.806503 | 0.403251 | − | 0.915089i | \(-0.367880\pi\) | ||||
0.403251 | + | 0.915089i | \(0.367880\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.7526 | 0.485256 | 0.242628 | − | 0.970119i | \(-0.421991\pi\) | ||||
0.242628 | + | 0.970119i | \(0.421991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.494897 | −0.0222891 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 26.8990 | 1.20658 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.65153 | −0.0739327 | −0.0369663 | − | 0.999317i | \(-0.511769\pi\) | ||||
−0.0369663 | + | 0.999317i | \(0.511769\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 39.7980 | 1.77450 | 0.887252 | − | 0.461286i | \(-0.152612\pi\) | ||||
0.887252 | + | 0.461286i | \(0.152612\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.7980 | −0.569502 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.4949 | 0.686799 | 0.343400 | − | 0.939189i | \(-0.388421\pi\) | ||||
0.343400 | + | 0.939189i | \(0.388421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.8990 | 0.747567 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.5505 | −0.553042 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.20204 | 0.404705 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.5959 | 0.594508 | 0.297254 | − | 0.954798i | \(-0.403929\pi\) | ||||
0.297254 | + | 0.954798i | \(0.403929\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.4949 | −0.544286 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.69694 | 0.291171 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 70.1918 | 3.04035 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.79796 | −0.250668 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 7.10102 | 0.305863 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −29.5959 | −1.27243 | −0.636214 | − | 0.771513i | \(-0.719500\pi\) | ||||
−0.636214 | + | 0.771513i | \(0.719500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.898979 | −0.0385081 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.55051 | −0.280080 | −0.140040 | − | 0.990146i | \(-0.544723\pi\) | ||||
−0.140040 | + | 0.990146i | \(0.544723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.404082 | −0.0172145 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 46.3939 | 1.97287 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.6969 | 0.792215 | 0.396107 | − | 0.918204i | \(-0.370361\pi\) | ||||
0.396107 | + | 0.918204i | \(0.370361\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.8536 | 0.585944 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.34847 | 0.183266 | 0.0916331 | − | 0.995793i | \(-0.470791\pi\) | ||||
0.0916331 | + | 0.995793i | \(0.470791\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.79796 | 0.370133 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.00000 | −0.0419222 | −0.0209611 | − | 0.999780i | \(-0.506673\pi\) | ||||
−0.0209611 | + | 0.999780i | \(0.506673\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.65153 | −0.152812 | −0.0764059 | − | 0.997077i | \(-0.524344\pi\) | ||||
−0.0764059 | + | 0.997077i | \(0.524344\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −21.7980 | −0.909038 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −19.1010 | −0.795186 | −0.397593 | − | 0.917562i | \(-0.630154\pi\) | ||||
−0.397593 | + | 0.917562i | \(0.630154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.89898 | 0.0787829 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.8990 | −0.534221 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −29.9444 | −1.23594 | −0.617969 | − | 0.786203i | \(-0.712044\pi\) | ||||
−0.617969 | + | 0.786203i | \(0.712044\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.2020 | −0.420368 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.8990 | 1.18674 | 0.593369 | − | 0.804930i | \(-0.297797\pi\) | ||||
0.593369 | + | 0.804930i | \(0.297797\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.8990 | −0.692791 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.5505 | −1.16654 | −0.583271 | − | 0.812278i | \(-0.698227\pi\) | ||||
−0.583271 | + | 0.812278i | \(0.698227\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.3031 | 0.420271 | 0.210135 | − | 0.977672i | \(-0.432610\pi\) | ||||
0.210135 | + | 0.977672i | \(0.432610\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.89898 | −0.361795 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.9444 | −1.05305 | −0.526525 | − | 0.850160i | \(-0.676505\pi\) | ||||
−0.526525 | + | 0.850160i | \(0.676505\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −37.4495 | −1.51504 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6969 | 1.07828 | 0.539140 | − | 0.842216i | \(-0.318750\pi\) | ||||
0.539140 | + | 0.842216i | \(0.318750\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.6969 | 0.954003 | 0.477001 | − | 0.878903i | \(-0.341724\pi\) | ||||
0.477001 | + | 0.878903i | \(0.341724\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26.1464 | −1.05091 | −0.525457 | − | 0.850820i | \(-0.676106\pi\) | ||||
−0.525457 | + | 0.850820i | \(0.676106\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.4949 | 1.78265 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.0000 | 0.440000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.40408 | 0.175602 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.20204 | 0.246899 | 0.123450 | − | 0.992351i | \(-0.460604\pi\) | ||||
0.123450 | + | 0.992351i | \(0.460604\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −8.00000 | −0.317470 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.8990 | −1.14502 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.5959 | 1.05048 | 0.525238 | − | 0.850955i | \(-0.323976\pi\) | ||||
0.525238 | + | 0.850955i | \(0.323976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.34847 | 0.171487 | 0.0857434 | − | 0.996317i | \(-0.472673\pi\) | ||||
0.0857434 | + | 0.996317i | \(0.472673\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.79796 | −0.385198 | −0.192599 | − | 0.981278i | \(-0.561692\pi\) | ||||
−0.192599 | + | 0.981278i | \(0.561692\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7980 | 0.816391 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0000 | 0.665261 | 0.332631 | − | 0.943057i | \(-0.392064\pi\) | ||||
0.332631 | + | 0.943057i | \(0.392064\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2474 | −0.517621 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.65153 | 0.298061 | 0.149031 | − | 0.988833i | \(-0.452385\pi\) | ||||
0.149031 | + | 0.988833i | \(0.452385\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.3939 | 1.18218 | 0.591092 | − | 0.806604i | \(-0.298697\pi\) | ||||
0.591092 | + | 0.806604i | \(0.298697\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.7980 | −0.535062 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.550510 | −0.0213158 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4495 | 0.442003 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.2929 | 1.05206 | 0.526031 | − | 0.850465i | \(-0.323680\pi\) | ||||
0.526031 | + | 0.850465i | \(0.323680\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.3939 | −0.937533 | −0.468766 | − | 0.883322i | \(-0.655301\pi\) | ||||
−0.468766 | + | 0.883322i | \(0.655301\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.4495 | 0.516144 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.3939 | −0.665558 | −0.332779 | − | 0.943005i | \(-0.607986\pi\) | ||||
−0.332779 | + | 0.943005i | \(0.607986\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.1010 | −0.385940 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 52.4949 | 1.99990 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.9444 | −1.44347 | −0.721736 | − | 0.692168i | \(-0.756656\pi\) | ||||
−0.721736 | + | 0.692168i | \(0.756656\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.44949 | −0.130847 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −58.2929 | −2.20800 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.4949 | 0.471926 | 0.235963 | − | 0.971762i | \(-0.424176\pi\) | ||||
0.235963 | + | 0.971762i | \(0.424176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.59592 | 0.135623 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 44.1464 | 1.66030 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.00000 | 0.187779 | 0.0938895 | − | 0.995583i | \(-0.470070\pi\) | ||||
0.0938895 | + | 0.995583i | \(0.470070\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.8990 | −0.520521 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.55051 | −0.319771 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −31.1918 | −1.16326 | −0.581630 | − | 0.813454i | \(-0.697585\pi\) | ||||
−0.581630 | + | 0.813454i | \(0.697585\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 43.2929 | 1.61231 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.404082 | 0.0150072 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.5505 | 0.688000 | 0.344000 | − | 0.938970i | \(-0.388218\pi\) | ||||
0.344000 | + | 0.938970i | \(0.388218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.5051 | −0.425532 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8990 | 0.439499 | 0.219749 | − | 0.975556i | \(-0.429476\pi\) | ||||
0.219749 | + | 0.975556i | \(0.429476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.8990 | 0.659317 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.0000 | −0.514998 | −0.257499 | − | 0.966279i | \(-0.582898\pi\) | ||||
−0.257499 | + | 0.966279i | \(0.582898\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.4495 | 1.30052 | 0.650258 | − | 0.759714i | \(-0.274661\pi\) | ||||
0.650258 | + | 0.759714i | \(0.274661\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.10102 | −0.150250 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 42.6413 | 1.55600 | 0.778002 | − | 0.628262i | \(-0.216233\pi\) | ||||
0.778002 | + | 0.628262i | \(0.216233\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.2474 | −0.554911 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.0000 | 1.52652 | 0.763258 | − | 0.646094i | \(-0.223599\pi\) | ||||
0.763258 | + | 0.646094i | \(0.223599\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.2929 | −0.916865 | −0.458433 | − | 0.888729i | \(-0.651589\pi\) | ||||
−0.458433 | + | 0.888729i | \(0.651589\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.10102 | 0.112264 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −84.6413 | −3.05622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.5959 | −1.31968 | −0.659841 | − | 0.751405i | \(-0.729376\pi\) | ||||
−0.659841 | + | 0.751405i | \(0.729376\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 36.4949 | 1.31263 | 0.656315 | − | 0.754487i | \(-0.272114\pi\) | ||||
0.656315 | + | 0.754487i | \(0.272114\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2020 | 0.366468 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −47.5959 | −1.70530 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.3031 | −0.404455 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.7980 | 0.385396 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2474 | −0.757390 | −0.378695 | − | 0.925522i | \(-0.623627\pi\) | ||||
−0.378695 | + | 0.925522i | \(0.623627\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30.3485 | −1.07907 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −46.5959 | −1.65467 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.6969 | −1.68951 | −0.844756 | − | 0.535151i | \(-0.820255\pi\) | ||||
−0.844756 | + | 0.535151i | \(0.820255\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.1010 | 1.10028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.10102 | −0.250590 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.7980 | −0.662541 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −32.4949 | −1.14246 | −0.571230 | − | 0.820790i | \(-0.693534\pi\) | ||||
−0.571230 | + | 0.820790i | \(0.693534\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.40408 | 0.295107 | 0.147554 | − | 0.989054i | \(-0.452860\pi\) | ||||
0.147554 | + | 0.989054i | \(0.452860\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.79796 | −0.203094 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.39388 | −0.328650 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.2929 | −0.533724 | −0.266862 | − | 0.963735i | \(-0.585987\pi\) | ||||
−0.266862 | + | 0.963735i | \(0.585987\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.5505 | −0.367768 | −0.183884 | − | 0.982948i | \(-0.558867\pi\) | ||||
−0.183884 | + | 0.982948i | \(0.558867\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.0000 | −0.973655 | −0.486828 | − | 0.873498i | \(-0.661846\pi\) | ||||
−0.486828 | + | 0.873498i | \(0.661846\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.1010 | 0.802332 | 0.401166 | − | 0.916005i | \(-0.368605\pi\) | ||||
0.401166 | + | 0.916005i | \(0.368605\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.0000 | 0.831551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.55051 | −0.157477 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.3485 | 1.04775 | 0.523873 | − | 0.851797i | \(-0.324487\pi\) | ||||
0.523873 | + | 0.851797i | \(0.324487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9898 | −0.999648 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 21.7980 | 0.749873 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 30.6969 | 1.05476 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.89898 | 0.167935 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.89898 | 0.270456 | 0.135228 | − | 0.990815i | \(-0.456823\pi\) | ||||
0.135228 | + | 0.990815i | \(0.456823\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.8990 | −0.953011 | −0.476505 | − | 0.879171i | \(-0.658097\pi\) | ||||
−0.476505 | + | 0.879171i | \(0.658097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.4495 | −0.731847 | −0.365924 | − | 0.930645i | \(-0.619247\pi\) | ||||
−0.365924 | + | 0.930645i | \(0.619247\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.7980 | 0.605850 | 0.302925 | − | 0.953014i | \(-0.402037\pi\) | ||||
0.302925 | + | 0.953014i | \(0.402037\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | −0.102003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.4949 | −0.661319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −72.8434 | −2.46820 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 31.0454 | 1.04953 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.8990 | 0.942082 | 0.471041 | − | 0.882111i | \(-0.343878\pi\) | ||||
0.471041 | + | 0.882111i | \(0.343878\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4949 | −0.825254 | −0.412627 | − | 0.910900i | \(-0.635389\pi\) | ||||
−0.412627 | + | 0.910900i | \(0.635389\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.5959 | 1.33251 | 0.666254 | − | 0.745725i | \(-0.267897\pi\) | ||||
0.666254 | + | 0.745725i | \(0.267897\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.8434 | 1.16993 | 0.584963 | − | 0.811060i | \(-0.301109\pi\) | ||||
0.584963 | + | 0.811060i | \(0.301109\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 27.5959 | 0.925537 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.3939 | 0.849774 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.257654 | 0.00859324 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.5959 | −1.45239 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.6969 | −0.355578 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.2474 | 0.838328 | 0.419164 | − | 0.907911i | \(-0.362323\pi\) | ||||
0.419164 | + | 0.907911i | \(0.362323\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.5403 | 1.44255 | 0.721277 | − | 0.692646i | \(-0.243555\pi\) | ||||
0.721277 | + | 0.692646i | \(0.243555\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.797959 | −0.0264086 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.6969 | 1.50905 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.79796 | 0.323205 | 0.161602 | − | 0.986856i | \(-0.448334\pi\) | ||||
0.161602 | + | 0.986856i | \(0.448334\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 46.0000 | 1.51411 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.59592 | −0.118233 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.6969 | 1.56489 | 0.782443 | − | 0.622722i | \(-0.213973\pi\) | ||||
0.782443 | + | 0.622722i | \(0.213973\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5959 | 0.642230 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.10102 | 0.232228 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.4949 | 1.84561 | 0.922804 | − | 0.385270i | \(-0.125892\pi\) | ||||
0.922804 | + | 0.385270i | \(0.125892\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.00000 | −0.228193 | −0.114097 | − | 0.993470i | \(-0.536397\pi\) | ||||
−0.114097 | + | 0.993470i | \(0.536397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −64.8434 | −2.11159 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −20.7526 | −0.674367 | −0.337184 | − | 0.941439i | \(-0.609474\pi\) | ||||
−0.337184 | + | 0.941439i | \(0.609474\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.8990 | 0.938101 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 43.1010 | 1.39618 | 0.698090 | − | 0.716011i | \(-0.254034\pi\) | ||||
0.698090 | + | 0.716011i | \(0.254034\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.5505 | 0.406125 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 34.8434 | 1.12515 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.4949 | −0.790158 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.10102 | 0.132017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.2474 | 0.490325 | 0.245162 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245162 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −10.0000 | −0.320915 | −0.160458 | − | 0.987043i | \(-0.551297\pi\) | ||||
−0.160458 | + | 0.987043i | \(0.551297\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8990 | 0.381464 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13.2020 | 0.422371 | 0.211185 | − | 0.977446i | \(-0.432268\pi\) | ||||
0.211185 | + | 0.977446i | \(0.432268\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.6969 | −0.597557 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19.6515 | −0.626786 | −0.313393 | − | 0.949623i | \(-0.601466\pi\) | ||||
−0.313393 | + | 0.949623i | \(0.601466\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.5959 | 0.560653 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −12.7980 | −0.406951 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.3939 | 0.679599 | 0.339799 | − | 0.940498i | \(-0.389641\pi\) | ||||
0.339799 | + | 0.940498i | \(0.389641\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.79796 | 0.247212 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.3939 | −1.02592 | −0.512962 | − | 0.858411i | \(-0.671452\pi\) | ||||
−0.512962 | + | 0.858411i | \(0.671452\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 5184.2.a.bu.1.1 | 2 | ||
3.2 | odd | 2 | 5184.2.a.bj.1.1 | 2 | |||
4.3 | odd | 2 | 5184.2.a.by.1.2 | 2 | |||
8.3 | odd | 2 | 2592.2.a.n.1.2 | 2 | |||
8.5 | even | 2 | 2592.2.a.j.1.1 | 2 | |||
9.2 | odd | 6 | 1728.2.i.m.577.2 | 4 | |||
9.4 | even | 3 | 576.2.i.m.385.2 | 4 | |||
9.5 | odd | 6 | 1728.2.i.m.1153.2 | 4 | |||
9.7 | even | 3 | 576.2.i.m.193.1 | 4 | |||
12.11 | even | 2 | 5184.2.a.bn.1.2 | 2 | |||
24.5 | odd | 2 | 2592.2.a.o.1.1 | 2 | |||
24.11 | even | 2 | 2592.2.a.s.1.2 | 2 | |||
36.7 | odd | 6 | 576.2.i.i.193.2 | 4 | |||
36.11 | even | 6 | 1728.2.i.k.577.1 | 4 | |||
36.23 | even | 6 | 1728.2.i.k.1153.1 | 4 | |||
36.31 | odd | 6 | 576.2.i.i.385.1 | 4 | |||
72.5 | odd | 6 | 864.2.i.e.289.2 | 4 | |||
72.11 | even | 6 | 864.2.i.c.577.1 | 4 | |||
72.13 | even | 6 | 288.2.i.c.97.1 | ✓ | 4 | ||
72.29 | odd | 6 | 864.2.i.e.577.2 | 4 | |||
72.43 | odd | 6 | 288.2.i.e.193.1 | yes | 4 | ||
72.59 | even | 6 | 864.2.i.c.289.1 | 4 | |||
72.61 | even | 6 | 288.2.i.c.193.2 | yes | 4 | ||
72.67 | odd | 6 | 288.2.i.e.97.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
288.2.i.c.97.1 | ✓ | 4 | 72.13 | even | 6 | ||
288.2.i.c.193.2 | yes | 4 | 72.61 | even | 6 | ||
288.2.i.e.97.2 | yes | 4 | 72.67 | odd | 6 | ||
288.2.i.e.193.1 | yes | 4 | 72.43 | odd | 6 | ||
576.2.i.i.193.2 | 4 | 36.7 | odd | 6 | |||
576.2.i.i.385.1 | 4 | 36.31 | odd | 6 | |||
576.2.i.m.193.1 | 4 | 9.7 | even | 3 | |||
576.2.i.m.385.2 | 4 | 9.4 | even | 3 | |||
864.2.i.c.289.1 | 4 | 72.59 | even | 6 | |||
864.2.i.c.577.1 | 4 | 72.11 | even | 6 | |||
864.2.i.e.289.2 | 4 | 72.5 | odd | 6 | |||
864.2.i.e.577.2 | 4 | 72.29 | odd | 6 | |||
1728.2.i.k.577.1 | 4 | 36.11 | even | 6 | |||
1728.2.i.k.1153.1 | 4 | 36.23 | even | 6 | |||
1728.2.i.m.577.2 | 4 | 9.2 | odd | 6 | |||
1728.2.i.m.1153.2 | 4 | 9.5 | odd | 6 | |||
2592.2.a.j.1.1 | 2 | 8.5 | even | 2 | |||
2592.2.a.n.1.2 | 2 | 8.3 | odd | 2 | |||
2592.2.a.o.1.1 | 2 | 24.5 | odd | 2 | |||
2592.2.a.s.1.2 | 2 | 24.11 | even | 2 | |||
5184.2.a.bj.1.1 | 2 | 3.2 | odd | 2 | |||
5184.2.a.bn.1.2 | 2 | 12.11 | even | 2 | |||
5184.2.a.bu.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5184.2.a.by.1.2 | 2 | 4.3 | odd | 2 |