Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6012,2,Mod(1,6012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6012, 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("6012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6012 = 2^{2} \cdot 3^{2} \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6012.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: | \(48.0060616952\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 4x^{9} - 26x^{8} + 82x^{7} + 211x^{6} - 340x^{5} - 593x^{4} + 192x^{3} + 423x^{2} + 126x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-2.20804\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6012.1 |
$q$-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 | ||||||||
\(5\) | 3.55061 | 1.58788 | 0.793941 | − | 0.607995i | \(-0.208026\pi\) | ||||
0.793941 | + | 0.607995i | \(0.208026\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.20804 | −0.834559 | −0.417280 | − | 0.908778i | \(-0.637016\pi\) | ||||
−0.417280 | + | 0.908778i | \(0.637016\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.03191 | 1.21567 | 0.607833 | − | 0.794065i | \(-0.292039\pi\) | ||||
0.607833 | + | 0.794065i | \(0.292039\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.294662 | 0.0817245 | 0.0408623 | − | 0.999165i | \(-0.486990\pi\) | ||||
0.0408623 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.93181 | −1.92375 | −0.961874 | − | 0.273494i | \(-0.911821\pi\) | ||||
−0.961874 | + | 0.273494i | \(0.911821\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.66885 | 0.382862 | 0.191431 | − | 0.981506i | \(-0.438687\pi\) | ||||
0.191431 | + | 0.981506i | \(0.438687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.24235 | −0.884591 | −0.442295 | − | 0.896869i | \(-0.645836\pi\) | ||||
−0.442295 | + | 0.896869i | \(0.645836\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.60685 | 1.52137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.37239 | 0.997628 | 0.498814 | − | 0.866709i | \(-0.333769\pi\) | ||||
0.498814 | + | 0.866709i | \(0.333769\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.91837 | −1.06297 | −0.531486 | − | 0.847067i | \(-0.678366\pi\) | ||||
−0.531486 | + | 0.847067i | \(0.678366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.83988 | −1.32518 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.66478 | 1.09568 | 0.547841 | − | 0.836582i | \(-0.315450\pi\) | ||||
0.547841 | + | 0.836582i | \(0.315450\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.87811 | −1.07418 | −0.537090 | − | 0.843525i | \(-0.680476\pi\) | ||||
−0.537090 | + | 0.843525i | \(0.680476\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.6835 | 1.78171 | 0.890857 | − | 0.454285i | \(-0.150105\pi\) | ||||
0.890857 | + | 0.454285i | \(0.150105\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.6994 | 1.70654 | 0.853270 | − | 0.521470i | \(-0.174616\pi\) | ||||
0.853270 | + | 0.521470i | \(0.174616\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.12457 | −0.303511 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.71086 | 0.235005 | 0.117502 | − | 0.993073i | \(-0.462511\pi\) | ||||
0.117502 | + | 0.993073i | \(0.462511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.3157 | 1.93033 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.53719 | 0.981258 | 0.490629 | − | 0.871369i | \(-0.336767\pi\) | ||||
0.490629 | + | 0.871369i | \(0.336767\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.37266 | 0.303788 | 0.151894 | − | 0.988397i | \(-0.451463\pi\) | ||||
0.151894 | + | 0.988397i | \(0.451463\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04623 | 0.129769 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.92029 | 1.08979 | 0.544893 | − | 0.838505i | \(-0.316570\pi\) | ||||
0.544893 | + | 0.838505i | \(0.316570\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.2771 | 1.69438 | 0.847191 | − | 0.531289i | \(-0.178292\pi\) | ||||
0.847191 | + | 0.531289i | \(0.178292\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0170 | 1.28944 | 0.644719 | − | 0.764419i | \(-0.276974\pi\) | ||||
0.644719 | + | 0.764419i | \(0.276974\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.90260 | −1.01454 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.32039 | 0.936117 | 0.468058 | − | 0.883698i | \(-0.344954\pi\) | ||||
0.468058 | + | 0.883698i | \(0.344954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.974422 | −0.106957 | −0.0534784 | − | 0.998569i | \(-0.517031\pi\) | ||||
−0.0534784 | + | 0.998569i | \(0.517031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −28.1628 | −3.05468 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.4831 | −1.42920 | −0.714602 | − | 0.699531i | \(-0.753392\pi\) | ||||
−0.714602 | + | 0.699531i | \(0.753392\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.650624 | −0.0682040 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.92546 | 0.607939 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.4003 | 1.25906 | 0.629532 | − | 0.776974i | \(-0.283247\pi\) | ||||
0.629532 | + | 0.776974i | \(0.283247\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.93174 | −0.590230 | −0.295115 | − | 0.955462i | \(-0.595358\pi\) | ||||
−0.295115 | + | 0.955462i | \(0.595358\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.1541 | −1.39465 | −0.697324 | − | 0.716756i | \(-0.745626\pi\) | ||||
−0.697324 | + | 0.716756i | \(0.745626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.93955 | −0.187503 | −0.0937517 | − | 0.995596i | \(-0.529886\pi\) | ||||
−0.0937517 | + | 0.995596i | \(0.529886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8243 | −1.03678 | −0.518391 | − | 0.855144i | \(-0.673469\pi\) | ||||
−0.518391 | + | 0.855144i | \(0.673469\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.4515 | 1.07727 | 0.538635 | − | 0.842539i | \(-0.318940\pi\) | ||||
0.538635 | + | 0.842539i | \(0.318940\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15.0629 | −1.40463 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.5137 | 1.60548 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.25626 | 0.477842 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.25591 | 0.827874 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.28212 | 0.202506 | 0.101253 | − | 0.994861i | \(-0.467715\pi\) | ||||
0.101253 | + | 0.994861i | \(0.467715\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.0903 | 1.93004 | 0.965020 | − | 0.262177i | \(-0.0844405\pi\) | ||||
0.965020 | + | 0.262177i | \(0.0844405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.68489 | −0.319521 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3823 | 0.972452 | 0.486226 | − | 0.873833i | \(-0.338373\pi\) | ||||
0.486226 | + | 0.873833i | \(0.338373\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.21711 | −0.188053 | −0.0940266 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940266 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.18805 | 0.0993497 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.0753 | 1.58412 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.96062 | 0.734083 | 0.367041 | − | 0.930205i | \(-0.380371\pi\) | ||||
0.367041 | + | 0.930205i | \(0.380371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.29768 | 0.512498 | 0.256249 | − | 0.966611i | \(-0.417513\pi\) | ||||
0.256249 | + | 0.966611i | \(0.417513\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −21.0139 | −1.68787 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.25805 | 0.260021 | 0.130010 | − | 0.991513i | \(-0.458499\pi\) | ||||
0.130010 | + | 0.991513i | \(0.458499\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.36726 | 0.738243 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.09781 | −0.320965 | −0.160483 | − | 0.987039i | \(-0.551305\pi\) | ||||
−0.160483 | + | 0.987039i | \(0.551305\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9132 | −0.993321 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.21336 | 0.168279 | 0.0841394 | − | 0.996454i | \(-0.473186\pi\) | ||||
0.0841394 | + | 0.996454i | \(0.473186\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.7962 | −1.26967 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1599 | 0.908871 | 0.454436 | − | 0.890780i | \(-0.349841\pi\) | ||||
0.454436 | + | 0.890780i | \(0.349841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7837 | −0.875874 | −0.437937 | − | 0.899006i | \(-0.644291\pi\) | ||||
−0.437937 | + | 0.899006i | \(0.644291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 23.6640 | 1.73982 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31.9803 | −2.33863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.28053 | −0.382086 | −0.191043 | − | 0.981582i | \(-0.561187\pi\) | ||||
−0.191043 | + | 0.981582i | \(0.561187\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.96897 | −0.213711 | −0.106855 | − | 0.994275i | \(-0.534078\pi\) | ||||
−0.106855 | + | 0.994275i | \(0.534078\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.6973 | 1.04714 | 0.523571 | − | 0.851982i | \(-0.324600\pi\) | ||||
0.523571 | + | 0.851982i | \(0.324600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.70190 | −0.616861 | −0.308431 | − | 0.951247i | \(-0.599804\pi\) | ||||
−0.308431 | + | 0.951247i | \(0.599804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −11.8624 | −0.832579 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.4215 | −1.70567 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.72866 | 0.465431 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.97823 | −0.273873 | −0.136936 | − | 0.990580i | \(-0.543726\pi\) | ||||
−0.136936 | + | 0.990580i | \(0.543726\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 41.4835 | 2.82915 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.0680 | 0.887113 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.33720 | −0.157217 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.0052 | 1.47358 | 0.736790 | − | 0.676121i | \(-0.236341\pi\) | ||||
0.736790 | + | 0.676121i | \(0.236341\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.76931 | 0.250178 | 0.125089 | − | 0.992146i | \(-0.460078\pi\) | ||||
0.125089 | + | 0.992146i | \(0.460078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.1199 | −1.13132 | −0.565658 | − | 0.824640i | \(-0.691378\pi\) | ||||
−0.565658 | + | 0.824640i | \(0.691378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.0631 | −1.31438 | −0.657190 | − | 0.753725i | \(-0.728255\pi\) | ||||
−0.657190 | + | 0.753725i | \(0.728255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 41.5402 | 2.70978 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.7343 | 0.759029 | 0.379515 | − | 0.925186i | \(-0.376091\pi\) | ||||
0.379515 | + | 0.925186i | \(0.376091\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −29.8701 | −1.92410 | −0.962051 | − | 0.272871i | \(-0.912027\pi\) | ||||
−0.962051 | + | 0.272871i | \(0.912027\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.54354 | −0.481939 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.491748 | 0.0312892 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6006 | −0.984703 | −0.492351 | − | 0.870397i | \(-0.663862\pi\) | ||||
−0.492351 | + | 0.870397i | \(0.663862\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.1047 | −1.07537 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.26641 | 0.203753 | 0.101876 | − | 0.994797i | \(-0.467515\pi\) | ||||
0.101876 | + | 0.994797i | \(0.467515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7161 | −0.914413 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.86610 | −0.608370 | −0.304185 | − | 0.952613i | \(-0.598384\pi\) | ||||
−0.304185 | + | 0.952613i | \(0.598384\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.07460 | 0.373160 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.55598 | −0.338754 | −0.169377 | − | 0.985551i | \(-0.554176\pi\) | ||||
−0.169377 | + | 0.985551i | \(0.554176\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.07130 | 0.186568 | 0.0932841 | − | 0.995640i | \(-0.470264\pi\) | ||||
0.0932841 | + | 0.995640i | \(0.470264\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 30.6701 | 1.84948 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.76698 | 0.406588 | 0.203294 | − | 0.979118i | \(-0.434835\pi\) | ||||
0.203294 | + | 0.979118i | \(0.434835\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0634 | 1.31619 | 0.658095 | − | 0.752935i | \(-0.271362\pi\) | ||||
0.658095 | + | 0.752935i | \(0.271362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.83028 | −0.227687 | −0.113843 | − | 0.993499i | \(-0.536316\pi\) | ||||
−0.113843 | + | 0.993499i | \(0.536316\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.1871 | 0.896467 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 45.9137 | 2.70080 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.96214 | 0.406733 | 0.203366 | − | 0.979103i | \(-0.434812\pi\) | ||||
0.203366 | + | 0.979103i | \(0.434812\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.7616 | 1.55812 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.25006 | −0.0722927 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.7975 | −1.48695 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.42441 | 0.482380 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −18.7402 | −1.06956 | −0.534779 | − | 0.844992i | \(-0.679605\pi\) | ||||
−0.534779 | + | 0.844992i | \(0.679605\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.4427 | −0.762263 | −0.381132 | − | 0.924521i | \(-0.624466\pi\) | ||||
−0.381132 | + | 0.924521i | \(0.624466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.4741 | −0.592033 | −0.296016 | − | 0.955183i | \(-0.595658\pi\) | ||||
−0.296016 | + | 0.955183i | \(0.595658\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.28731 | −0.409296 | −0.204648 | − | 0.978836i | \(-0.565605\pi\) | ||||
−0.204648 | + | 0.978836i | \(0.565605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.6610 | 1.21278 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.2370 | −0.736529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.24145 | 0.124333 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −25.8328 | −1.42421 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.5439 | −0.634508 | −0.317254 | − | 0.948341i | \(-0.602761\pi\) | ||||
−0.317254 | + | 0.948341i | \(0.602761\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 31.6725 | 1.73045 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.9308 | 1.19465 | 0.597324 | − | 0.802000i | \(-0.296231\pi\) | ||||
0.597324 | + | 0.802000i | \(0.296231\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.8623 | −1.29222 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1474 | 1.08786 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2498 | 0.764967 | 0.382484 | − | 0.923962i | \(-0.375069\pi\) | ||||
0.382484 | + | 0.923962i | \(0.375069\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.7841 | −1.27313 | −0.636566 | − | 0.771222i | \(-0.719646\pi\) | ||||
−0.636566 | + | 0.771222i | \(0.719646\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −20.2344 | −1.07697 | −0.538483 | − | 0.842636i | \(-0.681002\pi\) | ||||
−0.538483 | + | 0.842636i | \(0.681002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 50.6925 | 2.69048 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −11.2426 | −0.593360 | −0.296680 | − | 0.954977i | \(-0.595879\pi\) | ||||
−0.296680 | + | 0.954977i | \(0.595879\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.2149 | −0.853417 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 39.1170 | 2.04748 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.4318 | 1.17093 | 0.585466 | − | 0.810697i | \(-0.300912\pi\) | ||||
0.585466 | + | 0.810697i | \(0.300912\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.77764 | −0.196125 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7002 | 0.761148 | 0.380574 | − | 0.924751i | \(-0.375726\pi\) | ||||
0.380574 | + | 0.924751i | \(0.375726\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.58304 | 0.0815306 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.8018 | −0.554852 | −0.277426 | − | 0.960747i | \(-0.589481\pi\) | ||||
−0.277426 | + | 0.960747i | \(0.589481\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.4252 | 1.14587 | 0.572936 | − | 0.819600i | \(-0.305804\pi\) | ||||
0.572936 | + | 0.819600i | \(0.305804\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −31.6097 | −1.61098 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.31218 | −0.370742 | −0.185371 | − | 0.982669i | \(-0.559349\pi\) | ||||
−0.185371 | + | 0.982669i | \(0.559349\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.6495 | 1.70173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 29.5425 | 1.48644 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1341 | −1.06069 | −0.530345 | − | 0.847782i | \(-0.677938\pi\) | ||||
−0.530345 | + | 0.847782i | \(0.677938\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.71434 | 0.135548 | 0.0677738 | − | 0.997701i | \(-0.478410\pi\) | ||||
0.0677738 | + | 0.997701i | \(0.478410\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.74392 | −0.0868708 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.8718 | 1.33198 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.0922 | −1.83409 | −0.917047 | − | 0.398780i | \(-0.869434\pi\) | ||||
−0.917047 | + | 0.398780i | \(0.869434\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −16.6424 | −0.818918 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.45980 | −0.169835 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 33.2791 | 1.62579 | 0.812895 | − | 0.582411i | \(-0.197890\pi\) | ||||
0.812895 | + | 0.582411i | \(0.197890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.9871 | 0.681689 | 0.340845 | − | 0.940120i | \(-0.389287\pi\) | ||||
0.340845 | + | 0.940120i | \(0.389287\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −60.3361 | −2.92673 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.23893 | −0.253530 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.1646 | 0.585950 | 0.292975 | − | 0.956120i | \(-0.405355\pi\) | ||||
0.292975 | + | 0.956120i | \(0.405355\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.2617 | 1.02177 | 0.510886 | − | 0.859649i | \(-0.329318\pi\) | ||||
0.510886 | + | 0.859649i | \(0.329318\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.07986 | −0.338676 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.9982 | −1.47946 | −0.739731 | − | 0.672902i | \(-0.765047\pi\) | ||||
−0.739731 | + | 0.672902i | \(0.765047\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2547 | 1.15238 | 0.576189 | − | 0.817317i | \(-0.304539\pi\) | ||||
0.576189 | + | 0.817317i | \(0.304539\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −47.8732 | −2.26941 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.27291 | −0.154458 | −0.0772291 | − | 0.997013i | \(-0.524607\pi\) | ||||
−0.0772291 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.7319 | −1.30584 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.31012 | −0.108300 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.8794 | 0.602471 | 0.301235 | − | 0.953550i | \(-0.402601\pi\) | ||||
0.301235 | + | 0.953550i | \(0.402601\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.5766 | 1.65697 | 0.828483 | − | 0.560014i | \(-0.189204\pi\) | ||||
0.828483 | + | 0.560014i | \(0.189204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.4976 | 1.41734 | 0.708671 | − | 0.705539i | \(-0.249295\pi\) | ||||
0.708671 | + | 0.705539i | \(0.249295\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.09517 | −0.235776 | −0.117888 | − | 0.993027i | \(-0.537612\pi\) | ||||
−0.117888 | + | 0.993027i | \(0.537612\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −19.6963 | −0.909492 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 47.1067 | 2.16597 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.6947 | 0.582474 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.0421 | −1.50973 | −0.754865 | − | 0.655880i | \(-0.772298\pi\) | ||||
−0.754865 | + | 0.655880i | \(0.772298\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.96386 | 0.0895442 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 44.0288 | 1.99925 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.5450 | 1.11224 | 0.556120 | − | 0.831102i | \(-0.312289\pi\) | ||||
0.556120 | + | 0.831102i | \(0.312289\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.313854 | −0.0141641 | −0.00708203 | − | 0.999975i | \(-0.502254\pi\) | ||||
−0.00708203 | + | 0.999975i | \(0.502254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −42.6128 | −1.91918 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −31.5244 | −1.41406 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.37644 | 0.419747 | 0.209874 | − | 0.977729i | \(-0.432695\pi\) | ||||
0.209874 | + | 0.977729i | \(0.432695\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −36.3288 | −1.61982 | −0.809910 | − | 0.586554i | \(-0.800484\pi\) | ||||
−0.809910 | + | 0.586554i | \(0.800484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.0613 | −0.937216 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.7895 | −1.23175 | −0.615874 | − | 0.787844i | \(-0.711197\pi\) | ||||
−0.615874 | + | 0.787844i | \(0.711197\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.3259 | −1.07611 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −50.2558 | −2.21454 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 47.1711 | 2.07458 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6428 | −1.38630 | −0.693149 | − | 0.720795i | \(-0.743777\pi\) | ||||
−0.693149 | + | 0.720795i | \(0.743777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9004 | −1.26372 | −0.631862 | − | 0.775081i | \(-0.717709\pi\) | ||||
−0.631862 | + | 0.775081i | \(0.717709\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 46.9434 | 2.04489 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.00249 | −0.217499 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.02672 | −0.0877868 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.88659 | −0.297733 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.56608 | −0.368967 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.9331 | −0.985970 | −0.492985 | − | 0.870038i | \(-0.664094\pi\) | ||||
−0.492985 | + | 0.870038i | \(0.664094\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.4330 | −1.64629 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.8027 | −1.70184 | −0.850920 | − | 0.525295i | \(-0.823955\pi\) | ||||
−0.850920 | + | 0.525295i | \(0.823955\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.96574 | 0.381953 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.3717 | −0.781245 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.4714 | 0.655545 | 0.327772 | − | 0.944757i | \(-0.393702\pi\) | ||||
0.327772 | + | 0.944757i | \(0.393702\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.44268 | 0.145610 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.4599 | 0.525120 | 0.262560 | − | 0.964916i | \(-0.415433\pi\) | ||||
0.262560 | + | 0.964916i | \(0.415433\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 40.6600 | 1.71058 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.9960 | −1.38326 | −0.691632 | − | 0.722250i | \(-0.743108\pi\) | ||||
−0.691632 | + | 0.722250i | \(0.743108\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.0059 | 1.21386 | 0.606929 | − | 0.794756i | \(-0.292401\pi\) | ||||
0.606929 | + | 0.794756i | \(0.292401\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.2709 | −1.34579 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 44.3082 | 1.84458 | 0.922288 | − | 0.386505i | \(-0.126318\pi\) | ||||
0.922288 | + | 0.386505i | \(0.126318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.15156 | 0.0892618 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.89803 | 0.285687 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0664 | 0.498035 | 0.249018 | − | 0.968499i | \(-0.419892\pi\) | ||||
0.249018 | + | 0.968499i | \(0.419892\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.87691 | −0.406971 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.1853 | 0.541457 | 0.270728 | − | 0.962656i | \(-0.412736\pi\) | ||||
0.270728 | + | 0.962656i | \(0.412736\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 62.1845 | 2.54932 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.1252 | 0.863151 | 0.431575 | − | 0.902077i | \(-0.357958\pi\) | ||||
0.431575 | + | 0.902077i | \(0.357958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.6746 | 1.25124 | 0.625621 | − | 0.780127i | \(-0.284846\pi\) | ||||
0.625621 | + | 0.780127i | \(0.284846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.6629 | 0.758757 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.8394 | −0.642903 | −0.321451 | − | 0.946926i | \(-0.604171\pi\) | ||||
−0.321451 | + | 0.946926i | \(0.604171\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.44738 | 0.139466 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 49.1558 | 1.98538 | 0.992692 | − | 0.120672i | \(-0.0385050\pi\) | ||||
0.992692 | + | 0.120672i | \(0.0385050\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −34.9563 | −1.40729 | −0.703644 | − | 0.710552i | \(-0.748445\pi\) | ||||
−0.703644 | + | 0.710552i | \(0.748445\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.5675 | −1.14823 | −0.574113 | − | 0.818776i | \(-0.694653\pi\) | ||||
−0.574113 | + | 0.818776i | \(0.694653\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 29.7712 | 1.19276 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.17008 | −0.206803 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.8638 | −2.10782 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.4630 | −0.535955 | −0.267977 | − | 0.963425i | \(-0.586355\pi\) | ||||
−0.267977 | + | 0.963425i | \(0.586355\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.10293 | 0.321555 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.626031 | −0.0248043 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 25.7483 | 1.01700 | 0.508498 | − | 0.861063i | \(-0.330201\pi\) | ||||
0.508498 | + | 0.861063i | \(0.330201\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.7685 | 1.17396 | 0.586978 | − | 0.809603i | \(-0.300318\pi\) | ||||
0.586978 | + | 0.809603i | \(0.300318\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −17.7282 | −0.696966 | −0.348483 | − | 0.937315i | \(-0.613303\pi\) | ||||
−0.348483 | + | 0.937315i | \(0.613303\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3892 | 1.19288 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.5359 | 1.03843 | 0.519216 | − | 0.854643i | \(-0.326224\pi\) | ||||
0.519216 | + | 0.854643i | \(0.326224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 78.4341 | 3.06468 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.886549 | −0.0345350 | −0.0172675 | − | 0.999851i | \(-0.505497\pi\) | ||||
−0.0172675 | + | 0.999851i | \(0.505497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.1798 | 0.901588 | 0.450794 | − | 0.892628i | \(-0.351141\pi\) | ||||
0.450794 | + | 0.892628i | \(0.351141\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −13.0836 | −0.507361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.7915 | −0.882492 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.56636 | 0.369305 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.8011 | −1.26439 | −0.632195 | − | 0.774809i | \(-0.717846\pi\) | ||||
−0.632195 | + | 0.774809i | \(0.717846\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.9458 | 1.22778 | 0.613888 | − | 0.789393i | \(-0.289605\pi\) | ||||
0.613888 | + | 0.789393i | \(0.289605\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.3804 | −1.05076 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.4310 | 1.20267 | 0.601336 | − | 0.798996i | \(-0.294635\pi\) | ||||
0.601336 | + | 0.798996i | \(0.294635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.4140 | 1.54414 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.504126 | 0.0192057 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6651 | 0.633972 | 0.316986 | − | 0.948430i | \(-0.397329\pi\) | ||||
0.316986 | + | 0.948430i | \(0.397329\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.87211 | −0.298606 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 54.5559 | 2.06645 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.20372 | −0.309850 | −0.154925 | − | 0.987926i | \(-0.549514\pi\) | ||||
−0.154925 | + | 0.987926i | \(0.549514\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.1225 | 0.419495 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 13.0975 | 0.492582 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −46.1822 | −1.73441 | −0.867204 | − | 0.497953i | \(-0.834085\pi\) | ||||
−0.867204 | + | 0.497953i | \(0.834085\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.1078 | 0.940295 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.21830 | 0.157756 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.24550 | 0.0837430 | 0.0418715 | − | 0.999123i | \(-0.486668\pi\) | ||||
0.0418715 | + | 0.999123i | \(0.486668\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 31.2528 | 1.16392 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.8670 | 1.51776 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.4556 | −0.610306 | −0.305153 | − | 0.952303i | \(-0.598708\pi\) | ||||
−0.305153 | + | 0.952303i | \(0.598708\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −92.6711 | −3.42757 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −45.4200 | −1.67763 | −0.838813 | − | 0.544420i | \(-0.816750\pi\) | ||||
−0.838813 | + | 0.544420i | \(0.816750\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.9658 | 1.32482 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.7343 | −1.75594 | −0.877968 | − | 0.478720i | \(-0.841101\pi\) | ||||
−0.877968 | + | 0.478720i | \(0.841101\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.1583 | −0.996341 | −0.498170 | − | 0.867079i | \(-0.665995\pi\) | ||||
−0.498170 | + | 0.867079i | \(0.665995\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.8157 | 1.16564 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.28260 | 0.156483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.1521 | 0.771851 | 0.385925 | − | 0.922530i | \(-0.373882\pi\) | ||||
0.385925 | + | 0.922530i | \(0.373882\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 22.3606 | 0.813786 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.7840 | 1.40963 | 0.704815 | − | 0.709391i | \(-0.251030\pi\) | ||||
0.704815 | + | 0.709391i | \(0.251030\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.21024 | −0.0438710 | −0.0219355 | − | 0.999759i | \(-0.506983\pi\) | ||||
−0.0219355 | + | 0.999759i | \(0.506983\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.9005 | 0.865257 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.22092 | 0.0801928 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.0314 | 0.361740 | 0.180870 | − | 0.983507i | \(-0.442109\pi\) | ||||
0.180870 | + | 0.983507i | \(0.442109\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −20.0328 | −0.720529 | −0.360265 | − | 0.932850i | \(-0.617314\pi\) | ||||
−0.360265 | + | 0.932850i | \(0.617314\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −45.0202 | −1.61717 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4786 | −0.411262 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.5640 | 2.05980 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.5681 | 0.412882 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.8024 | −1.06234 | −0.531171 | − | 0.847265i | \(-0.678248\pi\) | ||||
−0.531171 | + | 0.847265i | \(0.678248\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −25.2854 | −0.899046 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.699134 | 0.0248270 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.3543 | −0.614720 | −0.307360 | − | 0.951593i | \(-0.599446\pi\) | ||||
−0.307360 | + | 0.951593i | \(0.599446\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −92.7978 | −3.28295 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.4194 | 1.56753 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 33.2595 | 1.17224 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.8720 | 1.05024 | 0.525121 | − | 0.851027i | \(-0.324020\pi\) | ||||
0.525121 | + | 0.851027i | \(0.324020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.8357 | −1.50416 | −0.752082 | − | 0.659069i | \(-0.770950\pi\) | ||||
−0.752082 | + | 0.659069i | \(0.770950\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.5497 | −0.509655 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.4980 | 0.682149 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.61185 | −0.230755 | −0.115378 | − | 0.993322i | \(-0.536808\pi\) | ||||
−0.115378 | + | 0.993322i | \(0.536808\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.03393 | −0.210330 | −0.105165 | − | 0.994455i | \(-0.533537\pi\) | ||||
−0.105165 | + | 0.994455i | \(0.533537\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 20.4064 | 0.709599 | 0.354800 | − | 0.934942i | \(-0.384549\pi\) | ||||
0.354800 | + | 0.934942i | \(0.384549\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.6242 | 1.58459 | 0.792297 | − | 0.610136i | \(-0.208885\pi\) | ||||
0.792297 | + | 0.610136i | \(0.208885\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.8517 | 0.583878 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.55061 | −0.122874 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 36.8866 | 1.27347 | 0.636733 | − | 0.771084i | \(-0.280285\pi\) | ||||
0.636733 | + | 0.771084i | \(0.280285\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.137440 | −0.00473933 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −45.8497 | −1.57728 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.6060 | −0.398787 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.2743 | −0.969231 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.36938 | −0.0468867 | −0.0234433 | − | 0.999725i | \(-0.507463\pi\) | ||||
−0.0234433 | + | 0.999725i | \(0.507463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 57.7831 | 1.97383 | 0.986916 | − | 0.161237i | \(-0.0515484\pi\) | ||||
0.986916 | + | 0.161237i | \(0.0515484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29.3215 | 1.00044 | 0.500219 | − | 0.865899i | \(-0.333253\pi\) | ||||
0.500219 | + | 0.865899i | \(0.333253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.25132 | 0.314919 | 0.157459 | − | 0.987525i | \(-0.449670\pi\) | ||||
0.157459 | + | 0.987525i | \(0.449670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.85879 | 0.267207 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 33.5470 | 1.13800 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.62847 | 0.0890623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −20.4374 | −0.690910 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8933 | −1.54971 | −0.774853 | − | 0.632141i | \(-0.782176\pi\) | ||||
−0.774853 | + | 0.632141i | \(0.782176\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.88681 | 0.0635683 | 0.0317842 | − | 0.999495i | \(-0.489881\pi\) | ||||
0.0317842 | + | 0.999495i | \(0.489881\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.7750 | 0.564523 | 0.282261 | − | 0.959338i | \(-0.408915\pi\) | ||||
0.282261 | + | 0.959338i | \(0.408915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.6974 | −0.762103 | −0.381051 | − | 0.924554i | \(-0.624438\pi\) | ||||
−0.381051 | + | 0.924554i | \(0.624438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.03901 | −0.169003 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19.5247 | 0.653368 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 43.1750 | 1.44318 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.7958 | −1.06045 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −13.5702 | −0.452090 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −41.8393 | −1.39078 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.54330 | 0.316880 | 0.158440 | − | 0.987369i | \(-0.449354\pi\) | ||||
0.158440 | + | 0.987369i | \(0.449354\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.9918 | 1.29186 | 0.645928 | − | 0.763398i | \(-0.276471\pi\) | ||||
0.645928 | + | 0.763398i | \(0.276471\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.92878 | −0.130024 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −48.7762 | −1.61073 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.8168 | −1.31344 | −0.656718 | − | 0.754136i | \(-0.728056\pi\) | ||||
−0.656718 | + | 0.754136i | \(0.728056\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.20692 | 0.138473 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 50.6980 | 1.66694 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.5575 | −1.42907 | −0.714537 | − | 0.699598i | \(-0.753363\pi\) | ||||
−0.714537 | + | 0.699598i | \(0.753363\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.54560 | −0.116202 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −113.550 | −3.71347 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 10.9873 | 0.358938 | 0.179469 | − | 0.983764i | \(-0.442562\pi\) | ||||
0.179469 | + | 0.983764i | \(0.442562\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.6826 | −1.13062 | −0.565310 | − | 0.824878i | \(-0.691244\pi\) | ||||
−0.565310 | + | 0.824878i | \(0.691244\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.1793 | 0.950209 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.5561 | 1.09043 | 0.545213 | − | 0.838298i | \(-0.316449\pi\) | ||||
0.545213 | + | 0.838298i | \(0.316449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.24628 | 0.105379 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.5724 | −1.05512 | −0.527562 | − | 0.849516i | \(-0.676894\pi\) | ||||
−0.527562 | + | 0.849516i | \(0.676894\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.7491 | −0.606707 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −25.1325 | −0.811569 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.02715 | 0.129908 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −10.5416 | −0.339348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.25726 | −0.0404308 | −0.0202154 | − | 0.999796i | \(-0.506435\pi\) | ||||
−0.0202154 | + | 0.999796i | \(0.506435\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.4861 | 1.49181 | 0.745905 | − | 0.666053i | \(-0.232017\pi\) | ||||
0.745905 | + | 0.666053i | \(0.232017\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.89547 | 0.156942 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.2762 | −1.67246 | −0.836232 | − | 0.548376i | \(-0.815246\pi\) | ||||
−0.836232 | + | 0.548376i | \(0.815246\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.3625 | −1.73743 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.9641 | 1.05139 | 0.525696 | − | 0.850673i | \(-0.323805\pi\) | ||||
0.525696 | + | 0.850673i | \(0.323805\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 52.1845 | 1.66274 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.5654 | −1.57609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −38.7317 | −1.23035 | −0.615177 | − | 0.788389i | \(-0.710915\pi\) | ||||
−0.615177 | + | 0.788389i | \(0.710915\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.8971 | −0.979503 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −51.9696 | −1.64589 | −0.822947 | − | 0.568119i | \(-0.807671\pi\) | ||||
−0.822947 | + | 0.568119i | \(0.807671\pi\) | |||||||
\(998\) | 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 | 6012.2.a.k.1.8 | yes | 10 | |
3.2 | odd | 2 | 6012.2.a.j.1.3 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6012.2.a.j.1.3 | ✓ | 10 | 3.2 | odd | 2 | ||
6012.2.a.k.1.8 | yes | 10 | 1.1 | even | 1 | trivial |