Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9680,2,Mod(1,9680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9680.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9680 = 2^{4} \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9680.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: | \(77.2951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.45753625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - x^{5} - 13x^{4} + 11x^{3} + 41x^{2} - 30x - 20 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 440) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.36422\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9680.1 |
$q$-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 | ||||||||
\(3\) | −0.843136 | −0.486785 | −0.243392 | − | 0.969928i | \(-0.578260\pi\) | ||||
−0.243392 | + | 0.969928i | \(0.578260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.75693 | 1.79795 | 0.898975 | − | 0.438000i | \(-0.144313\pi\) | ||||
0.898975 | + | 0.438000i | \(0.144313\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.28912 | −0.763040 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.78308 | −1.04924 | −0.524619 | − | 0.851337i | \(-0.675792\pi\) | ||||
−0.524619 | + | 0.851337i | \(0.675792\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.843136 | 0.217697 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.98203 | −1.20832 | −0.604160 | − | 0.796863i | \(-0.706491\pi\) | ||||
−0.604160 | + | 0.796863i | \(0.706491\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.12115 | 0.716041 | 0.358021 | − | 0.933714i | \(-0.383452\pi\) | ||||
0.358021 | + | 0.933714i | \(0.383452\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.01074 | −0.875215 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.39001 | −1.95795 | −0.978976 | − | 0.203975i | \(-0.934614\pi\) | ||||
−0.978976 | + | 0.203975i | \(0.934614\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.45945 | 0.858222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.60693 | 0.484095 | 0.242047 | − | 0.970264i | \(-0.422181\pi\) | ||||
0.242047 | + | 0.970264i | \(0.422181\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.68869 | 0.662508 | 0.331254 | − | 0.943542i | \(-0.392528\pi\) | ||||
0.331254 | + | 0.943542i | \(0.392528\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.75693 | −0.804068 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.44757 | −0.566776 | −0.283388 | − | 0.959005i | \(-0.591458\pi\) | ||||
−0.283388 | + | 0.959005i | \(0.591458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.18965 | 0.510753 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.32837 | −1.45685 | −0.728423 | − | 0.685127i | \(-0.759747\pi\) | ||||
−0.728423 | + | 0.685127i | \(0.759747\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.7051 | −1.78500 | −0.892502 | − | 0.451043i | \(-0.851052\pi\) | ||||
−0.892502 | + | 0.451043i | \(0.851052\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.28912 | 0.341242 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.66156 | 0.242364 | 0.121182 | − | 0.992630i | \(-0.461332\pi\) | ||||
0.121182 | + | 0.992630i | \(0.461332\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.6284 | 2.23262 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.20053 | 0.588192 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.93994 | −0.266472 | −0.133236 | − | 0.991084i | \(-0.542537\pi\) | ||||
−0.133236 | + | 0.991084i | \(0.542537\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.63156 | −0.348558 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.103915 | −0.0135285 | −0.00676427 | − | 0.999977i | \(-0.502153\pi\) | ||||
−0.00676427 | + | 0.999977i | \(0.502153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.1513 | 1.29974 | 0.649870 | − | 0.760045i | \(-0.274823\pi\) | ||||
0.649870 | + | 0.760045i | \(0.274823\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −10.8892 | −1.37191 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.78308 | 0.469233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.99277 | 0.609964 | 0.304982 | − | 0.952358i | \(-0.401350\pi\) | ||||
0.304982 | + | 0.952358i | \(0.401350\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.91706 | 0.953102 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.22929 | 0.739281 | 0.369640 | − | 0.929175i | \(-0.379481\pi\) | ||||
0.369640 | + | 0.929175i | \(0.379481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.30650 | 0.855161 | 0.427580 | − | 0.903977i | \(-0.359366\pi\) | ||||
0.427580 | + | 0.903977i | \(0.359366\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.843136 | −0.0973570 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.5445 | 1.18635 | 0.593175 | − | 0.805073i | \(-0.297874\pi\) | ||||
0.593175 | + | 0.805073i | \(0.297874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.10744 | 0.345271 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.69010 | 0.624569 | 0.312285 | − | 0.949989i | \(-0.398906\pi\) | ||||
0.312285 | + | 0.949989i | \(0.398906\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.98203 | 0.540377 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.19800 | −0.235650 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.6371 | 1.44553 | 0.722767 | − | 0.691091i | \(-0.242870\pi\) | ||||
0.722767 | + | 0.691091i | \(0.242870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.9958 | −1.88648 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.11007 | −0.322499 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.12115 | −0.320223 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6967 | 1.39069 | 0.695345 | − | 0.718676i | \(-0.255252\pi\) | ||||
0.695345 | + | 0.718676i | \(0.255252\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.84287 | −0.481884 | −0.240942 | − | 0.970540i | \(-0.577456\pi\) | ||||
−0.240942 | + | 0.970540i | \(0.577456\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.904576 | −0.0891305 | −0.0445653 | − | 0.999006i | \(-0.514190\pi\) | ||||
−0.0445653 | + | 0.999006i | \(0.514190\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.01074 | 0.391408 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7915 | −1.42995 | −0.714974 | − | 0.699151i | \(-0.753561\pi\) | ||||
−0.714974 | + | 0.699151i | \(0.753561\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.39429 | −0.325114 | −0.162557 | − | 0.986699i | \(-0.551974\pi\) | ||||
−0.162557 | + | 0.986699i | \(0.551974\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.90677 | 0.275898 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1755 | −0.957231 | −0.478616 | − | 0.878025i | \(-0.658861\pi\) | ||||
−0.478616 | + | 0.878025i | \(0.658861\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.39001 | 0.875623 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.65993 | 0.800611 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −23.6992 | −2.17250 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.86509 | 0.709171 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.9587 | −0.972430 | −0.486215 | − | 0.873839i | \(-0.661623\pi\) | ||||
−0.486215 | + | 0.873839i | \(0.661623\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.86896 | 0.868913 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.9021 | 1.12726 | 0.563631 | − | 0.826027i | \(-0.309404\pi\) | ||||
0.563631 | + | 0.826027i | \(0.309404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.8471 | 1.28741 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.45945 | −0.383808 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.8824 | 1.61324 | 0.806618 | − | 0.591073i | \(-0.201295\pi\) | ||||
0.806618 | + | 0.591073i | \(0.201295\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8892 | 0.923611 | 0.461806 | − | 0.886981i | \(-0.347202\pi\) | ||||
0.461806 | + | 0.886981i | \(0.347202\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.40092 | −0.117979 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.60693 | −0.216494 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −13.1768 | −1.08681 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.69412 | −0.138788 | −0.0693941 | − | 0.997589i | \(-0.522107\pi\) | ||||
−0.0693941 | + | 0.997589i | \(0.522107\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.48984 | −0.283999 | −0.142000 | − | 0.989867i | \(-0.545353\pi\) | ||||
−0.142000 | + | 0.989867i | \(0.545353\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.4045 | 0.921997 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.68869 | −0.296283 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.7003 | 1.65207 | 0.826033 | − | 0.563622i | \(-0.190592\pi\) | ||||
0.826033 | + | 0.563622i | \(0.190592\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.63564 | 0.129714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −44.6676 | −3.52030 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.3831 | −1.28323 | −0.641613 | − | 0.767028i | \(-0.721735\pi\) | ||||
−0.641613 | + | 0.767028i | \(0.721735\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 14.4012 | 1.11440 | 0.557199 | − | 0.830379i | \(-0.311876\pi\) | ||||
0.557199 | + | 0.830379i | \(0.311876\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.31169 | 0.100900 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.14470 | −0.546369 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.12354 | 0.617621 | 0.308811 | − | 0.951124i | \(-0.400069\pi\) | ||||
0.308811 | + | 0.951124i | \(0.400069\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.75693 | 0.359590 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.0876143 | 0.00658549 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.99340 | −0.223737 | −0.111869 | − | 0.993723i | \(-0.535684\pi\) | ||||
−0.111869 | + | 0.993723i | \(0.535684\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.5264 | −1.07974 | −0.539870 | − | 0.841749i | \(-0.681526\pi\) | ||||
−0.539870 | + | 0.841749i | \(0.681526\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.55893 | −0.632694 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.44757 | 0.253470 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 21.2133 | 1.54304 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.96741 | 0.576502 | 0.288251 | − | 0.957555i | \(-0.406926\pi\) | ||||
0.288251 | + | 0.957555i | \(0.406926\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.4962 | 1.40337 | 0.701684 | − | 0.712489i | \(-0.252432\pi\) | ||||
0.701684 | + | 0.712489i | \(0.252432\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.18965 | −0.228416 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.9751 | −1.28067 | −0.640336 | − | 0.768095i | \(-0.721205\pi\) | ||||
−0.640336 | + | 0.768095i | \(0.721205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.17717 | 0.508776 | 0.254388 | − | 0.967102i | \(-0.418126\pi\) | ||||
0.254388 | + | 0.967102i | \(0.418126\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.20959 | −0.296921 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.4010 | 0.870378 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.32837 | 0.651522 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 21.4949 | 1.49400 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.43285 | −0.305170 | −0.152585 | − | 0.988290i | \(-0.548760\pi\) | ||||
−0.152585 | + | 0.988290i | \(0.548760\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.25214 | −0.359871 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 11.7051 | 0.798278 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 17.5468 | 1.19116 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.16037 | −0.416280 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.8474 | 1.26781 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.2105 | 1.01857 | 0.509286 | − | 0.860597i | \(-0.329909\pi\) | ||||
0.509286 | + | 0.860597i | \(0.329909\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.28912 | −0.152608 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.28398 | 0.284338 | 0.142169 | − | 0.989842i | \(-0.454592\pi\) | ||||
0.142169 | + | 0.989842i | \(0.454592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.09655 | −0.270708 | −0.135354 | − | 0.990797i | \(-0.543217\pi\) | ||||
−0.135354 | + | 0.990797i | \(0.543217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.2531 | 1.13029 | 0.565143 | − | 0.824993i | \(-0.308821\pi\) | ||||
0.565143 | + | 0.824993i | \(0.308821\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.66156 | −0.108388 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.89046 | −0.577498 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.40626 | −0.220332 | −0.110166 | − | 0.993913i | \(-0.535138\pi\) | ||||
−0.110166 | + | 0.993913i | \(0.535138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.1839 | 1.30016 | 0.650080 | − | 0.759866i | \(-0.274735\pi\) | ||||
0.650080 | + | 0.759866i | \(0.274735\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.9983 | −1.02629 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.6284 | −0.998460 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.8076 | −0.751298 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.79753 | −0.304031 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.6971 | −1.24327 | −0.621635 | − | 0.783307i | \(-0.713531\pi\) | ||||
−0.621635 | + | 0.783307i | \(0.713531\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.20053 | −0.263047 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.7134 | −0.668285 | −0.334143 | − | 0.942523i | \(-0.608447\pi\) | ||||
−0.334143 | + | 0.942523i | \(0.608447\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.3998 | −1.01904 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.96758 | −0.369384 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.86317 | 0.546527 | 0.273263 | − | 0.961939i | \(-0.411897\pi\) | ||||
0.273263 | + | 0.961939i | \(0.411897\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.93994 | 0.119170 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.4980 | −0.703665 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.15481 | −0.131381 | −0.0656905 | − | 0.997840i | \(-0.520925\pi\) | ||||
−0.0656905 | + | 0.997840i | \(0.520925\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2552 | 0.622961 | 0.311481 | − | 0.950252i | \(-0.399175\pi\) | ||||
0.311481 | + | 0.950252i | \(0.399175\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.1729 | 0.918309 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.8253 | −0.890766 | −0.445383 | − | 0.895340i | \(-0.646933\pi\) | ||||
−0.445383 | + | 0.895340i | \(0.646933\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.44386 | −0.505521 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 16.8470 | 1.00501 | 0.502504 | − | 0.864575i | \(-0.332412\pi\) | ||||
0.502504 | + | 0.864575i | \(0.332412\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.89422 | −0.290931 | −0.145466 | − | 0.989363i | \(-0.546468\pi\) | ||||
−0.145466 | + | 0.989363i | \(0.546468\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.63156 | 0.155880 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −44.3744 | −2.61934 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.82064 | 0.460037 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.5482 | −0.676967 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.9575 | −0.698565 | −0.349283 | − | 0.937017i | \(-0.613575\pi\) | ||||
−0.349283 | + | 0.937017i | \(0.613575\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.103915 | 0.00605015 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.5232 | 2.05436 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −55.6801 | −3.20935 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.08320 | 0.234574 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −10.1513 | −0.581262 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.8325 | 0.960680 | 0.480340 | − | 0.877082i | \(-0.340513\pi\) | ||||
0.480340 | + | 0.877082i | \(0.340513\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.762681 | 0.0433874 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −24.5949 | −1.39465 | −0.697324 | − | 0.716756i | \(-0.745626\pi\) | ||||
−0.697324 | + | 0.716756i | \(0.745626\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.20995 | 0.407530 | 0.203765 | − | 0.979020i | \(-0.434682\pi\) | ||||
0.203765 | + | 0.979020i | \(0.434682\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.8892 | 0.613536 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.55901 | −0.480722 | −0.240361 | − | 0.970684i | \(-0.577266\pi\) | ||||
−0.240361 | + | 0.970684i | \(0.577266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.4712 | 0.696077 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.5497 | −0.865207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.78308 | −0.209848 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.86185 | 0.158260 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.90393 | 0.435758 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.4094 | 1.39662 | 0.698312 | − | 0.715793i | \(-0.253935\pi\) | ||||
0.698312 | + | 0.715793i | \(0.253935\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.89189 | 0.432473 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.99277 | −0.272784 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.9403 | 1.03175 | 0.515873 | − | 0.856665i | \(-0.327468\pi\) | ||||
0.515873 | + | 0.856665i | \(0.327468\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.57934 | 0.465966 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 41.0446 | 2.21620 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7.91706 | −0.426240 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.89209 | −0.423670 | −0.211835 | − | 0.977305i | \(-0.567944\pi\) | ||||
−0.211835 | + | 0.977305i | \(0.567944\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.45858 | −0.399249 | −0.199624 | − | 0.979873i | \(-0.563972\pi\) | ||||
−0.199624 | + | 0.979873i | \(0.563972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.8705 | −0.900478 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.03405 | −0.108262 | −0.0541308 | − | 0.998534i | \(-0.517239\pi\) | ||||
−0.0541308 | + | 0.998534i | \(0.517239\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.22929 | −0.330616 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 19.9816 | 1.05754 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.3025 | 0.860413 | 0.430206 | − | 0.902731i | \(-0.358441\pi\) | ||||
0.430206 | + | 0.902731i | \(0.358441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.25841 | −0.487285 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.30650 | −0.382440 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.770896 | 0.0402404 | 0.0201202 | − | 0.999798i | \(-0.493595\pi\) | ||||
0.0201202 | + | 0.999798i | \(0.493595\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.3538 | 1.11163 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.22817 | −0.479103 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.01958 | 0.259904 | 0.129952 | − | 0.991520i | \(-0.458518\pi\) | ||||
0.129952 | + | 0.991520i | \(0.458518\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.843136 | 0.0435394 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.86222 | −0.507930 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.65481 | −0.187735 | −0.0938676 | − | 0.995585i | \(-0.529923\pi\) | ||||
−0.0938676 | + | 0.995585i | \(0.529923\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.23970 | 0.473364 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.48146 | −0.280090 | −0.140045 | − | 0.990145i | \(-0.544725\pi\) | ||||
−0.140045 | + | 0.990145i | \(0.544725\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.7943 | 1.36203 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.840557 | 0.0426179 | 0.0213090 | − | 0.999773i | \(-0.493217\pi\) | ||||
0.0213090 | + | 0.999773i | \(0.493217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 46.7813 | 2.36583 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −10.8782 | −0.548734 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.5445 | −0.530552 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.61935 | 0.181650 | 0.0908249 | − | 0.995867i | \(-0.471050\pi\) | ||||
0.0908249 | + | 0.995867i | \(0.471050\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.5181 | −0.626690 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.0879 | 0.503768 | 0.251884 | − | 0.967757i | \(-0.418950\pi\) | ||||
0.251884 | + | 0.967757i | \(0.418950\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.9546 | −0.695129 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.10744 | −0.154410 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3840 | −0.612352 | −0.306176 | − | 0.951975i | \(-0.599050\pi\) | ||||
−0.306176 | + | 0.951975i | \(0.599050\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.9205 | −0.785299 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.494315 | −0.0243237 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.69010 | −0.279316 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.18109 | −0.449600 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.612942 | 0.0299442 | 0.0149721 | − | 0.999888i | \(-0.495234\pi\) | ||||
0.0149721 | + | 0.999888i | \(0.495234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.5449 | −1.63488 | −0.817440 | − | 0.576013i | \(-0.804608\pi\) | ||||
−0.817440 | + | 0.576013i | \(0.804608\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.80352 | −0.184933 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.98203 | −0.241664 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 48.2890 | 2.33687 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.72012 | 0.420034 | 0.210017 | − | 0.977698i | \(-0.432648\pi\) | ||||
0.210017 | + | 0.977698i | \(0.432648\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.3703 | −0.546420 | −0.273210 | − | 0.961954i | \(-0.588085\pi\) | ||||
−0.273210 | + | 0.961954i | \(0.588085\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.19800 | 0.105386 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −29.3076 | −1.40197 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.3176 | 1.16061 | 0.580307 | − | 0.814398i | \(-0.302933\pi\) | ||||
0.580307 | + | 0.814398i | \(0.302933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −35.7752 | −1.70358 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.227915 | 0.0108285 | 0.00541427 | − | 0.999985i | \(-0.498277\pi\) | ||||
0.00541427 | + | 0.999985i | \(0.498277\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.6371 | −0.646463 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.42838 | 0.0675600 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.4036 | 1.90676 | 0.953382 | − | 0.301767i | \(-0.0975764\pi\) | ||||
0.953382 | + | 0.301767i | \(0.0975764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.94241 | 0.138247 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 17.9958 | 0.843658 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.54698 | −0.212699 | −0.106349 | − | 0.994329i | \(-0.533916\pi\) | ||||
−0.106349 | + | 0.994329i | \(0.533916\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.2171 | −1.03701 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.5792 | 1.70366 | 0.851832 | − | 0.523815i | \(-0.175492\pi\) | ||||
0.851832 | + | 0.523815i | \(0.175492\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.18502 | 0.240968 | 0.120484 | − | 0.992715i | \(-0.461555\pi\) | ||||
0.120484 | + | 0.992715i | \(0.461555\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.11007 | 0.144226 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.0802 | 0.466454 | 0.233227 | − | 0.972422i | \(-0.425071\pi\) | ||||
0.233227 | + | 0.972422i | \(0.425071\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 23.7503 | 1.09668 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4532 | −0.804201 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.12115 | 0.143208 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.44077 | 0.203329 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.56337 | 0.117123 | 0.0585617 | − | 0.998284i | \(-0.481349\pi\) | ||||
0.0585617 | + | 0.998284i | \(0.481349\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.0424 | 0.594683 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.6609 | 1.71363 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.6967 | −0.621935 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.41271 | −0.109330 | −0.0546651 | − | 0.998505i | \(-0.517409\pi\) | ||||
−0.0546651 | + | 0.998505i | \(0.517409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.8132 | 0.624656 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.0326 | 0.678412 | 0.339206 | − | 0.940712i | \(-0.389842\pi\) | ||||
0.339206 | + | 0.940712i | \(0.389842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.9878 | −0.584941 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.6323 | 1.32919 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.43047 | −0.332634 | −0.166317 | − | 0.986072i | \(-0.553187\pi\) | ||||
−0.166317 | + | 0.986072i | \(0.553187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.1422 | −0.542472 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.1978 | 0.677637 | 0.338818 | − | 0.940852i | \(-0.389973\pi\) | ||||
0.338818 | + | 0.940852i | \(0.389973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.84287 | 0.215505 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.10594 | −0.0491164 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.0293 | −1.02076 | −0.510379 | − | 0.859950i | \(-0.670495\pi\) | ||||
−0.510379 | + | 0.859950i | \(0.670495\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.7565 | 1.53754 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.9186 | 0.614522 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.904576 | 0.0398604 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.84925 | −0.300649 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.10634 | 0.0484698 | 0.0242349 | − | 0.999706i | \(-0.492285\pi\) | ||||
0.0242349 | + | 0.999706i | \(0.492285\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.16929 | −0.0511294 | −0.0255647 | − | 0.999673i | \(-0.508138\pi\) | ||||
−0.0255647 | + | 0.999673i | \(0.508138\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.01074 | −0.175043 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.3772 | −0.800522 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 65.1723 | 2.83358 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.237873 | 0.0103228 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 35.2900 | 1.52858 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 14.7915 | 0.639492 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.52384 | 0.108912 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.43127 | 0.147522 | 0.0737609 | − | 0.997276i | \(-0.476500\pi\) | ||||
0.0737609 | + | 0.997276i | \(0.476500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.2477 | 0.525601 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.39429 | 0.145395 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.9440 | −1.79340 | −0.896699 | − | 0.442642i | \(-0.854041\pi\) | ||||
−0.896699 | + | 0.442642i | \(0.854041\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −23.2376 | −0.991755 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.13662 | 0.346632 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.1595 | 2.13300 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.90677 | −0.123385 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.5066 | 1.37735 | 0.688675 | − | 0.725070i | \(-0.258193\pi\) | ||||
0.688675 | + | 0.725070i | \(0.258193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 44.2812 | 1.87289 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −37.2583 | −1.57025 | −0.785124 | − | 0.619338i | \(-0.787401\pi\) | ||||
−0.785124 | + | 0.619338i | \(0.787401\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.1755 | 0.428087 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 14.7819 | 0.620780 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.5360 | 1.57359 | 0.786796 | − | 0.617213i | \(-0.211738\pi\) | ||||
0.786796 | + | 0.617213i | \(0.211738\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.6905 | −0.907718 | −0.453859 | − | 0.891073i | \(-0.649953\pi\) | ||||
−0.453859 | + | 0.891073i | \(0.649953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.71762 | −0.280632 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.39001 | −0.391590 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.9306 | −1.12114 | −0.560568 | − | 0.828108i | \(-0.689417\pi\) | ||||
−0.560568 | + | 0.828108i | \(0.689417\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.4380 | −0.683138 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.0674 | 1.12294 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.65993 | −0.358044 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.4757 | 0.638751 | 0.319376 | − | 0.947628i | \(-0.396527\pi\) | ||||
0.319376 | + | 0.947628i | \(0.396527\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.5130 | 0.474383 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.1554 | 0.623412 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −24.7646 | −1.01696 | −0.508481 | − | 0.861073i | \(-0.669793\pi\) | ||||
−0.508481 | + | 0.861073i | \(0.669793\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23.6992 | 0.971571 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.05133 | −0.247665 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.9401 | −0.528716 | −0.264358 | − | 0.964425i | \(-0.585160\pi\) | ||||
−0.264358 | + | 0.964425i | \(0.585160\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.7917 | 0.766531 | 0.383266 | − | 0.923638i | \(-0.374799\pi\) | ||||
0.383266 | + | 0.923638i | \(0.374799\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −11.4291 | −0.465427 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.3465 | −0.582308 | −0.291154 | − | 0.956676i | \(-0.594039\pi\) | ||||
−0.291154 | + | 0.956676i | \(0.594039\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.4557 | −0.423687 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.28582 | −0.254297 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.4276 | 1.59247 | 0.796233 | − | 0.604990i | \(-0.206823\pi\) | ||||
0.796233 | + | 0.604990i | \(0.206823\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.86509 | −0.317151 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.9316 | 1.32578 | 0.662888 | − | 0.748718i | \(-0.269330\pi\) | ||||
0.662888 | + | 0.748718i | \(0.269330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.2089 | 1.65632 | 0.828162 | − | 0.560489i | \(-0.189387\pi\) | ||||
0.828162 | + | 0.560489i | \(0.189387\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −41.8743 | −1.68036 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 64.8709 | 2.59900 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 17.1759 | 0.684847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.79380 | −0.310266 | −0.155133 | − | 0.987894i | \(-0.549581\pi\) | ||||
−0.155133 | + | 0.987894i | \(0.549581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.73749 | 0.148552 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.9587 | 0.434884 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −59.1234 | −2.34255 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.2596 | −0.564101 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −16.9699 | −0.670269 | −0.335135 | − | 0.942170i | \(-0.608782\pi\) | ||||
−0.335135 | + | 0.942170i | \(0.608782\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.346553 | −0.0136667 | −0.00683336 | − | 0.999977i | \(-0.502175\pi\) | ||||
−0.00683336 | + | 0.999977i | \(0.502175\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.86896 | −0.388590 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.23214 | −0.323639 | −0.161819 | − | 0.986820i | \(-0.551736\pi\) | ||||
−0.161819 | + | 0.986820i | \(0.551736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.7944 | −0.579837 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 32.9455 | 1.28926 | 0.644629 | − | 0.764496i | \(-0.277012\pi\) | ||||
0.644629 | + | 0.764496i | \(0.277012\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.9021 | −0.504127 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −16.7255 | −0.652522 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.7687 | 0.731127 | 0.365563 | − | 0.930786i | \(-0.380876\pi\) | ||||
0.365563 | + | 0.930786i | \(0.380876\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.66066 | 0.336860 | 0.168430 | − | 0.985714i | \(-0.446130\pi\) | ||||
0.168430 | + | 0.985714i | \(0.446130\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.8909 | −0.617153 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.8471 | −0.575746 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.4791 | −0.947834 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.8246 | −0.495826 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.7088 | 0.451341 | 0.225670 | − | 0.974204i | \(-0.427543\pi\) | ||||
0.225670 | + | 0.974204i | \(0.427543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.45945 | 0.171644 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 31.0721 | 1.19420 | 0.597099 | − | 0.802167i | \(-0.296320\pi\) | ||||
0.597099 | + | 0.802167i | \(0.296320\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 65.1542 | 2.50039 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.61198 | −0.138411 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.0210 | 1.18698 | 0.593492 | − | 0.804840i | \(-0.297749\pi\) | ||||
0.593492 | + | 0.804840i | \(0.297749\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.8824 | −0.721461 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.45395 | 0.131776 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.33896 | 0.279592 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.9523 | −1.59594 | −0.797969 | − | 0.602698i | \(-0.794092\pi\) | ||||
−0.797969 | + | 0.602698i | \(0.794092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −10.8892 | −0.413051 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.4742 | 1.76034 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.5467 | −0.550206 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.77487 | 0.369192 | 0.184596 | − | 0.982815i | \(-0.440902\pi\) | ||||
0.184596 | + | 0.982815i | \(0.440902\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.7604 | −0.405835 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.40092 | 0.0527618 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.0372 | −0.866404 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.6328 | 0.662214 | 0.331107 | − | 0.943593i | \(-0.392578\pi\) | ||||
0.331107 | + | 0.943593i | \(0.392578\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.1377 | −0.905233 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −34.6368 | −1.29716 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.87194 | 0.107255 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −51.4088 | −1.91723 | −0.958613 | − | 0.284713i | \(-0.908102\pi\) | ||||
−0.958613 | + | 0.284713i | \(0.908102\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.30300 | −0.160252 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.0178 | −0.632898 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.60693 | 0.0968189 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3527 | 0.643577 | 0.321788 | − | 0.946812i | \(-0.395716\pi\) | ||||
0.321788 | + | 0.946812i | \(0.395716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.16647 | 0.154314 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 58.3150 | 2.15686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −42.8536 | −1.58284 | −0.791418 | − | 0.611276i | \(-0.790657\pi\) | ||||
−0.791418 | + | 0.611276i | \(0.790657\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.1768 | 0.486035 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24.5873 | −0.904458 | −0.452229 | − | 0.891902i | \(-0.649371\pi\) | ||||
−0.452229 | + | 0.891902i | \(0.649371\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.95539 | 0.365720 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.69027 | −0.172069 | −0.0860347 | − | 0.996292i | \(-0.527420\pi\) | ||||
−0.0860347 | + | 0.996292i | \(0.527420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.69412 | 0.0620679 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.0253 | −0.476571 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −70.3621 | −2.57097 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.2922 | 1.76221 | 0.881103 | − | 0.472924i | \(-0.156801\pi\) | ||||
0.881103 | + | 0.472924i | \(0.156801\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.6073 | 0.605205 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.48984 | 0.127008 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38.8242 | 1.41109 | 0.705544 | − | 0.708666i | \(-0.250703\pi\) | ||||
0.705544 | + | 0.708666i | \(0.250703\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.8876 | 1.01093 | 0.505463 | − | 0.862848i | \(-0.331322\pi\) | ||||
0.505463 | + | 0.862848i | \(0.331322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.1464 | −0.584538 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.4045 | −0.412330 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.393118 | 0.0141947 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.2240 | 1.37839 | 0.689197 | − | 0.724574i | \(-0.257964\pi\) | ||||
0.689197 | + | 0.724574i | \(0.257964\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.03288 | 0.325311 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.39582 | 0.301977 | 0.150988 | − | 0.988536i | \(-0.451754\pi\) | ||||
0.150988 | + | 0.988536i | \(0.451754\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.68869 | 0.132502 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13.8273 | 0.496051 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29.1153 | −1.04316 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.6255 | 0.415460 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −20.7003 | −0.738826 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.4248 | 1.26276 | 0.631379 | − | 0.775474i | \(-0.282489\pi\) | ||||
0.631379 | + | 0.775474i | \(0.282489\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.47286 | −0.266041 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −48.4042 | −1.72105 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38.4032 | −1.36374 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.63564 | −0.0580101 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 53.3896 | 1.89116 | 0.945579 | − | 0.325392i | \(-0.105496\pi\) | ||||
0.945579 | + | 0.325392i | \(0.105496\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.27796 | −0.292853 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −31.2171 | −1.10300 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 44.6676 | 1.57433 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.81680 | 0.0639543 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.84086 | 0.135038 | 0.0675188 | − | 0.997718i | \(-0.478492\pi\) | ||||
0.0675188 | + | 0.997718i | \(0.478492\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.7250 | 0.833097 | 0.416548 | − | 0.909114i | \(-0.363240\pi\) | ||||
0.416548 | + | 0.909114i | \(0.363240\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.64657 | −0.303248 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.3831 | 0.573877 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.5333 | −1.27814 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 41.1947 | 1.43946 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.152300 | −0.00531531 | −0.00265765 | − | 0.999996i | \(-0.500846\pi\) | ||||
−0.00265765 | + | 0.999996i | \(0.500846\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.1736 | 1.74894 | 0.874472 | − | 0.485077i | \(-0.161208\pi\) | ||||
0.874472 | + | 0.485077i | \(0.161208\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.2010 | 0.772006 | 0.386003 | − | 0.922498i | \(-0.373856\pi\) | ||||
0.386003 | + | 0.922498i | \(0.373856\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.18588 | 0.284307 | 0.142154 | − | 0.989845i | \(-0.454597\pi\) | ||||
0.142154 | + | 0.989845i | \(0.454597\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12.4998 | 0.433612 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −77.8610 | −2.69773 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.4012 | −0.498374 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.4495 | 0.568579 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.95392 | −0.274600 | −0.137300 | − | 0.990530i | \(-0.543842\pi\) | ||||
−0.137300 | + | 0.990530i | \(0.543842\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2039 | −0.765653 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −14.2043 | −0.489223 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.31169 | −0.0451237 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.12650 | 0.141621 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.3727 | 1.10972 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.87193 | 0.201051 | 0.100525 | − | 0.994934i | \(-0.467948\pi\) | ||||
0.100525 | + | 0.994934i | \(0.467948\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.14470 | 0.244343 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.9089 | −1.05583 | −0.527914 | − | 0.849298i | \(-0.677026\pi\) | ||||
−0.527914 | + | 0.849298i | \(0.677026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9133 | 0.372358 | 0.186179 | − | 0.982516i | \(-0.440390\pi\) | ||||
0.186179 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 37.4137 | 1.27505 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.3339 | 0.419850 | 0.209925 | − | 0.977718i | \(-0.432678\pi\) | ||||
0.209925 | + | 0.977718i | \(0.432678\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.12354 | −0.276209 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.59386 | −0.223939 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.8881 | −0.639997 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.3534 | −1.06115 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.75693 | −0.160814 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.3557 | 1.53155 | 0.765777 | − | 0.643106i | \(-0.222355\pi\) | ||||
0.765777 | + | 0.643106i | \(0.222355\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.0818 | 0.340051 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.4098 | −0.822388 | −0.411194 | − | 0.911548i | \(-0.634888\pi\) | ||||
−0.411194 | + | 0.911548i | \(0.634888\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.9932 | −1.17761 | −0.588807 | − | 0.808274i | \(-0.700402\pi\) | ||||
−0.588807 | + | 0.808274i | \(0.700402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0876143 | −0.00294512 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −44.8014 | −1.50428 | −0.752142 | − | 0.659001i | \(-0.770979\pi\) | ||||
−0.752142 | + | 0.659001i | \(0.770979\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.1299 | −1.74838 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.18599 | 0.173542 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.99340 | 0.100058 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.9509 | −1.00003 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9.61615 | 0.320717 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.66486 | 0.321983 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 46.9459 | 1.56226 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 14.5264 | 0.482874 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.93726 | −0.230348 | −0.115174 | − | 0.993345i | \(-0.536743\pi\) | ||||
−0.115174 | + | 0.993345i | \(0.536743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 11.0859 | 0.367697 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.7451 | 0.886106 | 0.443053 | − | 0.896496i | \(-0.353895\pi\) | ||||
0.443053 | + | 0.896496i | \(0.353895\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.55893 | 0.282950 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 61.3744 | 2.02676 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.1263 | 1.81845 | 0.909225 | − | 0.416305i | \(-0.136675\pi\) | ||||
0.909225 | + | 0.416305i | \(0.136675\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −14.1921 | −0.467645 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.5659 | −0.775681 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.44757 | −0.113355 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.07068 | 0.0680102 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.6870 | 0.449054 | 0.224527 | − | 0.974468i | \(-0.427916\pi\) | ||||
0.224527 | + | 0.974468i | \(0.427916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 48.7785 | 1.59865 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.7368 | 0.678894 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.9104 | −0.617774 | −0.308887 | − | 0.951099i | \(-0.599957\pi\) | ||||
−0.308887 | + | 0.951099i | \(0.599957\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.07897 | −0.198380 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.9993 | 0.358569 | 0.179284 | − | 0.983797i | \(-0.442622\pi\) | ||||
0.179284 | + | 0.983797i | \(0.442622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 87.5935 | 2.85244 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −21.2133 | −0.690068 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.9776 | 0.389219 | 0.194610 | − | 0.980881i | \(-0.437656\pi\) | ||||
0.194610 | + | 0.980881i | \(0.437656\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.6411 | −0.897267 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.21642 | 0.234008 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.2762 | 0.851170 | 0.425585 | − | 0.904918i | \(-0.360068\pi\) | ||||
0.425585 | + | 0.904918i | \(0.360068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7.96741 | −0.257819 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 89.8224 | 2.90052 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.3936 | −0.561083 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.8595 | 1.09111 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −19.4962 | −0.627605 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.2656 | −0.362277 | −0.181138 | − | 0.983458i | \(-0.557978\pi\) | ||||
−0.181138 | + | 0.983458i | \(0.557978\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.1105 | 0.421170 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0037 | 1.82934 | 0.914669 | − | 0.404204i | \(-0.132452\pi\) | ||||
0.914669 | + | 0.404204i | \(0.132452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 51.7992 | 1.66061 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.18965 | 0.102151 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.9823 | −1.11918 | −0.559591 | − | 0.828769i | \(-0.689042\pi\) | ||||
−0.559591 | + | 0.828769i | \(0.689042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.76993 | 0.248075 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.9629 | −0.572927 | −0.286464 | − | 0.958091i | \(-0.592480\pi\) | ||||
−0.286464 | + | 0.958091i | \(0.592480\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.9751 | 0.572734 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.66409 | −0.212120 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 109.911 | 3.49495 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −47.2159 | −1.49986 | −0.749931 | − | 0.661516i | \(-0.769913\pi\) | ||||
−0.749931 | + | 0.661516i | \(0.769913\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.4235 | −0.679856 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.17717 | −0.227532 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.1669 | 0.638693 | 0.319347 | − | 0.947638i | \(-0.396537\pi\) | ||||
0.319347 | + | 0.947638i | \(0.396537\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −15.3742 | −0.486420 |
(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 | 9680.2.a.cy.1.3 | 6 | ||
4.3 | odd | 2 | 4840.2.a.be.1.4 | 6 | |||
11.2 | odd | 10 | 880.2.bo.j.81.2 | 12 | |||
11.6 | odd | 10 | 880.2.bo.j.641.2 | 12 | |||
11.10 | odd | 2 | 9680.2.a.cx.1.3 | 6 | |||
44.35 | even | 10 | 440.2.y.b.81.2 | ✓ | 12 | ||
44.39 | even | 10 | 440.2.y.b.201.2 | yes | 12 | ||
44.43 | even | 2 | 4840.2.a.bf.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
440.2.y.b.81.2 | ✓ | 12 | 44.35 | even | 10 | ||
440.2.y.b.201.2 | yes | 12 | 44.39 | even | 10 | ||
880.2.bo.j.81.2 | 12 | 11.2 | odd | 10 | |||
880.2.bo.j.641.2 | 12 | 11.6 | odd | 10 | |||
4840.2.a.be.1.4 | 6 | 4.3 | odd | 2 | |||
4840.2.a.bf.1.4 | 6 | 44.43 | even | 2 | |||
9680.2.a.cx.1.3 | 6 | 11.10 | odd | 2 | |||
9680.2.a.cy.1.3 | 6 | 1.1 | even | 1 | trivial |