Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3960,2,Mod(1,3960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3960.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3960 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3960.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: | \(31.6207592004\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3960.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.585786 | −0.221406 | −0.110703 | − | 0.993854i | \(-0.535310\pi\) | ||||
−0.110703 | + | 0.993854i | \(0.535310\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41421 | 0.392232 | 0.196116 | − | 0.980581i | \(-0.437167\pi\) | ||||
0.196116 | + | 0.980581i | \(0.437167\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.24264 | 1.02899 | 0.514496 | − | 0.857493i | \(-0.327979\pi\) | ||||
0.514496 | + | 0.857493i | \(0.327979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.17157 | −0.268777 | −0.134389 | − | 0.990929i | \(-0.542907\pi\) | ||||
−0.134389 | + | 0.990929i | \(0.542907\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843 | 0.589768 | 0.294884 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294884 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.65685 | 1.42184 | 0.710921 | − | 0.703272i | \(-0.248278\pi\) | ||||
0.710921 | + | 0.703272i | \(0.248278\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.82843 | −0.867211 | −0.433606 | − | 0.901103i | \(-0.642759\pi\) | ||||
−0.433606 | + | 0.901103i | \(0.642759\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.585786 | 0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.65685 | −0.601183 | −0.300592 | − | 0.953753i | \(-0.597184\pi\) | ||||
−0.300592 | + | 0.953753i | \(0.597184\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.65685 | −0.571105 | −0.285552 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285552 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.07107 | −1.38332 | −0.691662 | − | 0.722221i | \(-0.743121\pi\) | ||||
−0.691662 | + | 0.722221i | \(0.743121\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.48528 | −0.654246 | −0.327123 | − | 0.944982i | \(-0.606079\pi\) | ||||
−0.327123 | + | 0.944982i | \(0.606079\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.65685 | −0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.48528 | −0.890822 | −0.445411 | − | 0.895326i | \(-0.646942\pi\) | ||||
−0.445411 | + | 0.895326i | \(0.646942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.82843 | 1.14936 | 0.574682 | − | 0.818377i | \(-0.305126\pi\) | ||||
0.574682 | + | 0.818377i | \(0.305126\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82843 | 1.13036 | 0.565182 | − | 0.824966i | \(-0.308806\pi\) | ||||
0.565182 | + | 0.824966i | \(0.308806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.41421 | −0.175412 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.48528 | 1.03664 | 0.518321 | − | 0.855186i | \(-0.326557\pi\) | ||||
0.518321 | + | 0.855186i | \(0.326557\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.4853 | 1.24437 | 0.622187 | − | 0.782869i | \(-0.286244\pi\) | ||||
0.622187 | + | 0.782869i | \(0.286244\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.07107 | 0.827606 | 0.413803 | − | 0.910366i | \(-0.364200\pi\) | ||||
0.413803 | + | 0.910366i | \(0.364200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.585786 | 0.0667566 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.485281 | 0.0545984 | 0.0272992 | − | 0.999627i | \(-0.491309\pi\) | ||||
0.0272992 | + | 0.999627i | \(0.491309\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.2426 | 1.12428 | 0.562138 | − | 0.827043i | \(-0.309979\pi\) | ||||
0.562138 | + | 0.827043i | \(0.309979\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.24264 | −0.460179 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.828427 | −0.0868428 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.17157 | 0.120201 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.82843 | 0.896391 | 0.448195 | − | 0.893936i | \(-0.352067\pi\) | ||||
0.448195 | + | 0.893936i | \(0.352067\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.4853 | 1.83935 | 0.919677 | − | 0.392675i | \(-0.128450\pi\) | ||||
0.919677 | + | 0.392675i | \(0.128450\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.58579 | 0.443325 | 0.221662 | − | 0.975123i | \(-0.428852\pi\) | ||||
0.221662 | + | 0.975123i | \(0.428852\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.31371 | 0.892091 | 0.446046 | − | 0.895010i | \(-0.352832\pi\) | ||||
0.446046 | + | 0.895010i | \(0.352832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.65685 | 0.720296 | 0.360148 | − | 0.932895i | \(-0.382726\pi\) | ||||
0.360148 | + | 0.932895i | \(0.382726\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82843 | −0.263752 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.48528 | −0.227825 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.55635 | −0.847989 | −0.423994 | − | 0.905665i | \(-0.639372\pi\) | ||||
−0.423994 | + | 0.905665i | \(0.639372\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.17157 | 0.102361 | 0.0511804 | − | 0.998689i | \(-0.483702\pi\) | ||||
0.0511804 | + | 0.998689i | \(0.483702\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.686292 | 0.0595090 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.31371 | −0.453981 | −0.226990 | − | 0.973897i | \(-0.572889\pi\) | ||||
−0.226990 | + | 0.973897i | \(0.572889\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.0000 | −1.35710 | −0.678551 | − | 0.734553i | \(-0.737392\pi\) | ||||
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.41421 | −0.118262 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.65685 | −0.635867 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.48528 | −0.203602 | −0.101801 | − | 0.994805i | \(-0.532461\pi\) | ||||
−0.101801 | + | 0.994805i | \(0.532461\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1421 | 0.825355 | 0.412678 | − | 0.910877i | \(-0.364594\pi\) | ||||
0.412678 | + | 0.910877i | \(0.364594\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.82843 | 0.387829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.51472 | 0.440122 | 0.220061 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220061 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.65685 | −0.130578 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.3137 | 0.886158 | 0.443079 | − | 0.896483i | \(-0.353886\pi\) | ||||
0.443079 | + | 0.896483i | \(0.353886\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7279 | 1.44921 | 0.724605 | − | 0.689164i | \(-0.242022\pi\) | ||||
0.724605 | + | 0.689164i | \(0.242022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | −0.846154 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.8995 | 1.66499 | 0.832494 | − | 0.554034i | \(-0.186912\pi\) | ||||
0.832494 | + | 0.554034i | \(0.186912\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.585786 | −0.0442813 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.6569 | 1.31974 | 0.659868 | − | 0.751382i | \(-0.270612\pi\) | ||||
0.659868 | + | 0.751382i | \(0.270612\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.3137 | 1.73289 | 0.866447 | − | 0.499269i | \(-0.166398\pi\) | ||||
0.866447 | + | 0.499269i | \(0.166398\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.65685 | 0.268857 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.24264 | −0.310253 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.31371 | −0.239772 | −0.119886 | − | 0.992788i | \(-0.538253\pi\) | ||||
−0.119886 | + | 0.992788i | \(0.538253\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.8995 | 1.28843 | 0.644217 | − | 0.764843i | \(-0.277183\pi\) | ||||
0.644217 | + | 0.764843i | \(0.277183\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.24264 | 0.587264 | 0.293632 | − | 0.955919i | \(-0.405136\pi\) | ||||
0.293632 | + | 0.955919i | \(0.405136\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.9706 | −1.20301 | −0.601506 | − | 0.798869i | \(-0.705432\pi\) | ||||
−0.601506 | + | 0.798869i | \(0.705432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.48528 | −0.314805 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.65685 | 0.255406 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.17157 | 0.0810394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4853 | −1.41026 | −0.705132 | − | 0.709076i | \(-0.749112\pi\) | ||||
−0.705132 | + | 0.709076i | \(0.749112\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.07107 | 0.618642 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.82843 | 0.192006 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.8284 | 0.992985 | 0.496492 | − | 0.868041i | \(-0.334621\pi\) | ||||
0.496492 | + | 0.868041i | \(0.334621\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.07107 | −0.0710893 | −0.0355446 | − | 0.999368i | \(-0.511317\pi\) | ||||
−0.0355446 | + | 0.999368i | \(0.511317\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.31371 | −0.615467 | −0.307734 | − | 0.951473i | \(-0.599571\pi\) | ||||
−0.307734 | + | 0.951473i | \(0.599571\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.72792 | −0.571785 | −0.285893 | − | 0.958262i | \(-0.592290\pi\) | ||||
−0.285893 | + | 0.958262i | \(0.592290\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.48528 | 0.292587 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.1421 | −1.17352 | −0.586759 | − | 0.809762i | \(-0.699596\pi\) | ||||
−0.586759 | + | 0.809762i | \(0.699596\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.1421 | −0.782144 | −0.391072 | − | 0.920360i | \(-0.627896\pi\) | ||||
−0.391072 | + | 0.920360i | \(0.627896\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.65685 | 0.425291 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.65685 | −0.105423 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.51472 | −0.600564 | −0.300282 | − | 0.953851i | \(-0.597081\pi\) | ||||
−0.300282 | + | 0.953851i | \(0.597081\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.82843 | −0.177822 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.79899 | 0.611244 | 0.305622 | − | 0.952153i | \(-0.401136\pi\) | ||||
0.305622 | + | 0.952153i | \(0.401136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.14214 | 0.133106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.7279 | 1.15481 | 0.577407 | − | 0.816457i | \(-0.304065\pi\) | ||||
0.577407 | + | 0.816457i | \(0.304065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.48528 | 0.398388 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.65685 | 0.101020 | 0.0505101 | − | 0.998724i | \(-0.483915\pi\) | ||||
0.0505101 | + | 0.998724i | \(0.483915\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.4853 | −0.758427 | −0.379213 | − | 0.925309i | \(-0.623805\pi\) | ||||
−0.379213 | + | 0.925309i | \(0.623805\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.5858 | 0.876375 | 0.438187 | − | 0.898884i | \(-0.355621\pi\) | ||||
0.438187 | + | 0.898884i | \(0.355621\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.68629 | 0.398871 | 0.199435 | − | 0.979911i | \(-0.436089\pi\) | ||||
0.199435 | + | 0.979911i | \(0.436089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2426 | −0.608862 | −0.304431 | − | 0.952534i | \(-0.598466\pi\) | ||||
−0.304431 | + | 0.952534i | \(0.598466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.14214 | 0.126446 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.41421 | −0.549984 | −0.274992 | − | 0.961446i | \(-0.588675\pi\) | ||||
−0.274992 | + | 0.961446i | \(0.588675\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.82843 | −0.514011 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.00000 | 0.231326 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.31371 | 0.306277 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.82843 | −0.505514 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.2426 | −0.584578 | −0.292289 | − | 0.956330i | \(-0.594417\pi\) | ||||
−0.292289 | + | 0.956330i | \(0.594417\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.828427 | −0.0469758 | −0.0234879 | − | 0.999724i | \(-0.507477\pi\) | ||||
−0.0234879 | + | 0.999724i | \(0.507477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.0000 | 1.01742 | 0.508710 | − | 0.860938i | \(-0.330123\pi\) | ||||
0.508710 | + | 0.860938i | \(0.330123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.0000 | 1.46031 | 0.730153 | − | 0.683284i | \(-0.239449\pi\) | ||||
0.730153 | + | 0.683284i | \(0.239449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.65685 | −0.428702 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.97056 | −0.276570 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.41421 | 0.0784465 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.62742 | 0.144854 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.4853 | 0.796183 | 0.398092 | − | 0.917346i | \(-0.369673\pi\) | ||||
0.398092 | + | 0.917346i | \(0.369673\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.48528 | −0.463600 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.8701 | 1.02792 | 0.513959 | − | 0.857815i | \(-0.328178\pi\) | ||||
0.513959 | + | 0.857815i | \(0.328178\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.82843 | 0.261474 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000 | 0.431959 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.2426 | −0.979316 | −0.489658 | − | 0.871915i | \(-0.662878\pi\) | ||||
−0.489658 | + | 0.871915i | \(0.662878\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.1716 | −0.598001 | −0.299000 | − | 0.954253i | \(-0.596653\pi\) | ||||
−0.299000 | + | 0.954253i | \(0.596653\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4853 | −0.558075 | −0.279038 | − | 0.960280i | \(-0.590015\pi\) | ||||
−0.279038 | + | 0.960280i | \(0.590015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.4853 | −0.556501 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.48528 | 0.447836 | 0.223918 | − | 0.974608i | \(-0.428115\pi\) | ||||
0.223918 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6274 | −0.927759 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.07107 | −0.370117 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.1716 | −1.10515 | −0.552574 | − | 0.833464i | \(-0.686354\pi\) | ||||
−0.552574 | + | 0.833464i | \(0.686354\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.79899 | 0.197234 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.7574 | 0.815885 | 0.407943 | − | 0.913008i | \(-0.366246\pi\) | ||||
0.407943 | + | 0.913008i | \(0.366246\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.8284 | 0.557692 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.31371 | 0.375680 | 0.187840 | − | 0.982200i | \(-0.439851\pi\) | ||||
0.187840 | + | 0.982200i | \(0.439851\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.970563 | 0.0495934 | 0.0247967 | − | 0.999693i | \(-0.492106\pi\) | ||||
0.0247967 | + | 0.999693i | \(0.492106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.585786 | −0.0298544 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.31371 | −0.168012 | −0.0840058 | − | 0.996465i | \(-0.526771\pi\) | ||||
−0.0840058 | + | 0.996465i | \(0.526771\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.0000 | 0.606866 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.485281 | −0.0244172 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4853 | 0.927750 | 0.463875 | − | 0.885901i | \(-0.346459\pi\) | ||||
0.463875 | + | 0.885901i | \(0.346459\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.31371 | 0.465104 | 0.232552 | − | 0.972584i | \(-0.425292\pi\) | ||||
0.232552 | + | 0.972584i | \(0.425292\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.82843 | −0.340148 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.65685 | 0.181264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.97056 | 0.344672 | 0.172336 | − | 0.985038i | \(-0.444868\pi\) | ||||
0.172336 | + | 0.985038i | \(0.444868\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.17157 | −0.254476 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.2426 | −0.502791 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.6274 | −1.30083 | −0.650417 | − | 0.759577i | \(-0.725406\pi\) | ||||
−0.650417 | + | 0.759577i | \(0.725406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.6569 | 1.64033 | 0.820167 | − | 0.572124i | \(-0.193880\pi\) | ||||
0.820167 | + | 0.572124i | \(0.193880\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24264 | 0.205798 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.17157 | −0.250270 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.97056 | −0.432097 | −0.216048 | − | 0.976383i | \(-0.569317\pi\) | ||||
−0.216048 | + | 0.976383i | \(0.569317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.1716 | −0.729099 | −0.364550 | − | 0.931184i | \(-0.618777\pi\) | ||||
−0.364550 | + | 0.931184i | \(0.618777\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.31371 | −0.158516 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.3137 | −1.87634 | −0.938170 | − | 0.346174i | \(-0.887481\pi\) | ||||
−0.938170 | + | 0.346174i | \(0.887481\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.0000 | 1.14027 | 0.570137 | − | 0.821549i | \(-0.306890\pi\) | ||||
0.570137 | + | 0.821549i | \(0.306890\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.00000 | −0.0948091 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.6569 | 0.738893 | 0.369446 | − | 0.929252i | \(-0.379547\pi\) | ||||
0.369446 | + | 0.929252i | \(0.379547\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.65685 | 0.172195 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.828427 | 0.0388373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.6985 | −1.57635 | −0.788174 | − | 0.615452i | \(-0.788973\pi\) | ||||
−0.788174 | + | 0.615452i | \(0.788973\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.4558 | −0.533552 | −0.266776 | − | 0.963759i | \(-0.585958\pi\) | ||||
−0.266776 | + | 0.963759i | \(0.585958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.51472 | 0.163343 | 0.0816714 | − | 0.996659i | \(-0.473974\pi\) | ||||
0.0816714 | + | 0.996659i | \(0.473974\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.82843 | 0.130884 | 0.0654420 | − | 0.997856i | \(-0.479154\pi\) | ||||
0.0654420 | + | 0.997856i | \(0.479154\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.97056 | −0.229519 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.07107 | 0.417088 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.17157 | −0.0537555 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.1421 | 1.19446 | 0.597232 | − | 0.802068i | \(-0.296267\pi\) | ||||
0.597232 | + | 0.802068i | \(0.296267\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.17157 | −0.235803 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.82843 | −0.400878 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.7990 | 1.25969 | 0.629846 | − | 0.776720i | \(-0.283118\pi\) | ||||
0.629846 | + | 0.776720i | \(0.283118\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.02944 | −0.317234 | −0.158617 | − | 0.987340i | \(-0.550704\pi\) | ||||
−0.158617 | + | 0.987340i | \(0.550704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 32.4853 | 1.46306 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.14214 | −0.275512 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.0000 | −1.61158 | −0.805791 | − | 0.592200i | \(-0.798259\pi\) | ||||
−0.805791 | + | 0.592200i | \(0.798259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.92893 | 0.130595 | 0.0652973 | − | 0.997866i | \(-0.479200\pi\) | ||||
0.0652973 | + | 0.997866i | \(0.479200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.4853 | −0.822584 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −35.3137 | −1.56525 | −0.782626 | − | 0.622492i | \(-0.786120\pi\) | ||||
−0.782626 | + | 0.622492i | \(0.786120\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.14214 | −0.183237 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.48528 | 0.197262 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.6274 | 0.903704 | 0.451852 | − | 0.892093i | \(-0.350764\pi\) | ||||
0.451852 | + | 0.892093i | \(0.350764\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.8995 | 1.04505 | 0.522526 | − | 0.852623i | \(-0.324990\pi\) | ||||
0.522526 | + | 0.852623i | \(0.324990\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.4853 | −0.892353 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.0000 | −0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.17157 | −0.224006 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.58579 | −0.198261 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.65685 | 0.286731 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 20.3431 | 0.874620 | 0.437310 | − | 0.899311i | \(-0.355931\pi\) | ||||
0.437310 | + | 0.899311i | \(0.355931\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.31371 | −0.398955 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −38.7279 | −1.65589 | −0.827943 | − | 0.560812i | \(-0.810489\pi\) | ||||
−0.827943 | + | 0.560812i | \(0.810489\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.97056 | −0.382159 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.284271 | −0.0120884 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.21320 | −0.0514051 | −0.0257025 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257025 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.8284 | −0.542585 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.07107 | 0.382300 | 0.191150 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191150 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.65685 | −0.322126 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1421 | 1.01209 | 0.506045 | − | 0.862507i | \(-0.331107\pi\) | ||||
0.506045 | + | 0.862507i | \(0.331107\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.34315 | −0.265452 | −0.132726 | − | 0.991153i | \(-0.542373\pi\) | ||||
−0.132726 | + | 0.991153i | \(0.542373\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.82843 | 0.117954 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.17157 | 0.132034 | 0.0660172 | − | 0.997818i | \(-0.478971\pi\) | ||||
0.0660172 | + | 0.997818i | \(0.478971\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.48528 | 0.268593 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.51472 | −0.310166 | −0.155083 | − | 0.987901i | \(-0.549564\pi\) | ||||
−0.155083 | + | 0.987901i | \(0.549564\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.65685 | 0.233087 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.5858 | −1.25601 | −0.628004 | − | 0.778210i | \(-0.716128\pi\) | ||||
−0.628004 | + | 0.778210i | \(0.716128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.48528 | 0.101887 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −13.6569 | −0.558004 | −0.279002 | − | 0.960291i | \(-0.590004\pi\) | ||||
−0.279002 | + | 0.960291i | \(0.590004\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.14214 | −0.332125 | −0.166062 | − | 0.986115i | \(-0.553105\pi\) | ||||
−0.166062 | + | 0.986115i | \(0.553105\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.384776 | 0.0156176 | 0.00780879 | − | 0.999970i | \(-0.497514\pi\) | ||||
0.00780879 | + | 0.999970i | \(0.497514\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.34315 | −0.256616 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.5563 | 1.43611 | 0.718054 | − | 0.695988i | \(-0.245033\pi\) | ||||
0.718054 | + | 0.695988i | \(0.245033\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.6569 | −1.59652 | −0.798262 | − | 0.602310i | \(-0.794247\pi\) | ||||
−0.798262 | + | 0.602310i | \(0.794247\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.4558 | −1.42509 | −0.712545 | − | 0.701626i | \(-0.752458\pi\) | ||||
−0.712545 | + | 0.701626i | \(0.752458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.17157 | −0.0469381 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.5147 | −0.618612 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.6274 | 0.900783 | 0.450392 | − | 0.892831i | \(-0.351284\pi\) | ||||
0.450392 | + | 0.892831i | \(0.351284\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.55635 | 0.379232 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.41421 | −0.373005 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.68629 | 0.106102 | 0.0530511 | − | 0.998592i | \(-0.483105\pi\) | ||||
0.0530511 | + | 0.998592i | \(0.483105\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.6569 | 1.16955 | 0.584776 | − | 0.811195i | \(-0.301182\pi\) | ||||
0.584776 | + | 0.811195i | \(0.301182\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.6274 | −1.51860 | −0.759300 | − | 0.650740i | \(-0.774459\pi\) | ||||
−0.759300 | + | 0.650740i | \(0.774459\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.82843 | −0.346546 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.7990 | −1.32266 | −0.661328 | − | 0.750097i | \(-0.730007\pi\) | ||||
−0.661328 | + | 0.750097i | \(0.730007\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.17157 | −0.0457771 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.6274 | −0.881439 | −0.440720 | − | 0.897645i | \(-0.645277\pi\) | ||||
−0.440720 | + | 0.897645i | \(0.645277\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.3431 | 1.10242 | 0.551210 | − | 0.834366i | \(-0.314166\pi\) | ||||
0.551210 | + | 0.834366i | \(0.314166\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.686292 | −0.0266132 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.6569 | 0.838557 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.82843 | −0.340818 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.10051 | 0.235157 | 0.117579 | − | 0.993064i | \(-0.462487\pi\) | ||||
0.117579 | + | 0.993064i | \(0.462487\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.10051 | −0.234461 | −0.117231 | − | 0.993105i | \(-0.537402\pi\) | ||||
−0.117231 | + | 0.993105i | \(0.537402\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.17157 | −0.198467 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.7990 | 1.36981 | 0.684905 | − | 0.728632i | \(-0.259844\pi\) | ||||
0.684905 | + | 0.728632i | \(0.259844\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.31371 | 0.203026 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.17157 | −0.349409 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6569 | 0.671698 | 0.335849 | − | 0.941916i | \(-0.390977\pi\) | ||||
0.335849 | + | 0.941916i | \(0.390977\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000 | 0.606915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.5147 | −0.587662 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.2843 | 0.992743 | 0.496372 | − | 0.868110i | \(-0.334665\pi\) | ||||
0.496372 | + | 0.868110i | \(0.334665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.28427 | 0.161584 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.8284 | −0.407245 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.3137 | 1.32623 | 0.663117 | − | 0.748516i | \(-0.269233\pi\) | ||||
0.663117 | + | 0.748516i | \(0.269233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.6569 | −0.511453 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.41421 | 0.0528886 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.65685 | 0.210965 | 0.105483 | − | 0.994421i | \(-0.466361\pi\) | ||||
0.105483 | + | 0.994421i | \(0.466361\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.65685 | 0.284368 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.2843 | 1.04901 | 0.524503 | − | 0.851409i | \(-0.324251\pi\) | ||||
0.524503 | + | 0.851409i | \(0.324251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.4853 | −1.42343 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.44365 | 0.164130 | 0.0820650 | − | 0.996627i | \(-0.473848\pi\) | ||||
0.0820650 | + | 0.996627i | \(0.473848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.48528 | −0.312559 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.2843 | −0.746169 | −0.373084 | − | 0.927797i | \(-0.621700\pi\) | ||||
−0.373084 | + | 0.927797i | \(0.621700\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.5269 | −1.56016 | −0.780081 | − | 0.625679i | \(-0.784822\pi\) | ||||
−0.780081 | + | 0.625679i | \(0.784822\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.48528 | 0.0910537 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.68629 | −0.0981550 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.34315 | 0.0855026 | 0.0427513 | − | 0.999086i | \(-0.486388\pi\) | ||||
0.0427513 | + | 0.999086i | \(0.486388\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.1421 | −0.369110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.51472 | 0.200436 | 0.100218 | − | 0.994966i | \(-0.468046\pi\) | ||||
0.100218 | + | 0.994966i | \(0.468046\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.828427 | 0.0300305 | 0.0150152 | − | 0.999887i | \(-0.495220\pi\) | ||||
0.0150152 | + | 0.999887i | \(0.495220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.45584 | −0.197515 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4853 | 0.450817 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27.1716 | −0.979832 | −0.489916 | − | 0.871770i | \(-0.662973\pi\) | ||||
−0.489916 | + | 0.871770i | \(0.662973\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.8579 | −0.426498 | −0.213249 | − | 0.976998i | \(-0.568405\pi\) | ||||
−0.213249 | + | 0.976998i | \(0.568405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.82843 | −0.173442 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.28427 | 0.153500 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4853 | −0.375193 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.51472 | −0.196829 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.8995 | 0.851925 | 0.425962 | − | 0.904741i | \(-0.359936\pi\) | ||||
0.425962 | + | 0.904741i | \(0.359936\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.48528 | −0.159478 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.4853 | 0.443365 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.6274 | 0.588973 | 0.294487 | − | 0.955656i | \(-0.404851\pi\) | ||||
0.294487 | + | 0.955656i | \(0.404851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.0294 | −0.673213 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.07107 | −0.249533 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.65685 | 0.0583964 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.0294 | 0.739356 | 0.369678 | − | 0.929160i | \(-0.379468\pi\) | ||||
0.369678 | + | 0.929160i | \(0.379468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.6274 | −0.513638 | −0.256819 | − | 0.966460i | \(-0.582674\pi\) | ||||
−0.256819 | + | 0.966460i | \(0.582674\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.3137 | −0.396302 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.6274 | 0.371806 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.3137 | 0.743854 | 0.371927 | − | 0.928262i | \(-0.378697\pi\) | ||||
0.371927 | + | 0.928262i | \(0.378697\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.62742 | −0.0915860 | −0.0457930 | − | 0.998951i | \(-0.514581\pi\) | ||||
−0.0457930 | + | 0.998951i | \(0.514581\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −16.8701 | −0.586629 | −0.293315 | − | 0.956016i | \(-0.594758\pi\) | ||||
−0.293315 | + | 0.956016i | \(0.594758\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −38.6274 | −1.34159 | −0.670793 | − | 0.741645i | \(-0.734046\pi\) | ||||
−0.670793 | + | 0.741645i | \(0.734046\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.2426 | −0.978550 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.7279 | −0.648106 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.8579 | −0.547474 | −0.273737 | − | 0.961805i | \(-0.588260\pi\) | ||||
−0.273737 | + | 0.961805i | \(0.588260\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.0000 | 0.378412 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.585786 | −0.0201279 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.3431 | −0.354558 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.4142 | 1.28104 | 0.640519 | − | 0.767942i | \(-0.278719\pi\) | ||||
0.640519 | + | 0.767942i | \(0.278719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −41.8995 | −1.43126 | −0.715630 | − | 0.698480i | \(-0.753860\pi\) | ||||
−0.715630 | + | 0.698480i | \(0.753860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.85786 | 0.268107 | 0.134053 | − | 0.990974i | \(-0.457201\pi\) | ||||
0.134053 | + | 0.990974i | \(0.457201\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.3137 | 0.929769 | 0.464885 | − | 0.885371i | \(-0.346096\pi\) | ||||
0.464885 | + | 0.885371i | \(0.346096\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21.8995 | −0.744605 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.485281 | −0.0164620 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.585786 | 0.0198032 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14.3848 | −0.485739 | −0.242870 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242870 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.34315 | −0.0789426 | −0.0394713 | − | 0.999221i | \(-0.512567\pi\) | ||||
−0.0394713 | + | 0.999221i | \(0.512567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.2843 | −0.548009 | −0.274005 | − | 0.961728i | \(-0.588348\pi\) | ||||
−0.274005 | + | 0.961728i | \(0.588348\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.10051 | −0.137681 | −0.0688407 | − | 0.997628i | \(-0.521930\pi\) | ||||
−0.0688407 | + | 0.997628i | \(0.521930\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.59798 | 0.187750 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.25483 | 0.175846 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −17.6569 | −0.590204 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.9706 | −1.23304 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.5147 | −0.916648 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23.3137 | −0.774974 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39.5147 | 1.31206 | 0.656032 | − | 0.754733i | \(-0.272233\pi\) | ||||
0.656032 | + | 0.754733i | \(0.272233\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.6863 | −1.21547 | −0.607736 | − | 0.794139i | \(-0.707922\pi\) | ||||
−0.607736 | + | 0.794139i | \(0.707922\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.2426 | −0.338982 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.686292 | −0.0226633 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6863 | 0.418482 | 0.209241 | − | 0.977864i | \(-0.432901\pi\) | ||||
0.209241 | + | 0.977864i | \(0.432901\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.8284 | 0.488084 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.65685 | −0.120237 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.34315 | 0.208112 | 0.104056 | − | 0.994571i | \(-0.466818\pi\) | ||||
0.104056 | + | 0.994571i | \(0.466818\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.79899 | 0.255602 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.24264 | 0.138749 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.0711 | 0.361676 | 0.180838 | − | 0.983513i | \(-0.442119\pi\) | ||||
0.180838 | + | 0.983513i | \(0.442119\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.4853 | −1.12419 | −0.562094 | − | 0.827073i | \(-0.690004\pi\) | ||||
−0.562094 | + | 0.827073i | \(0.690004\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.3431 | −0.336819 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.4558 | 1.21715 | 0.608576 | − | 0.793496i | \(-0.291741\pi\) | ||||
0.608576 | + | 0.793496i | \(0.291741\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0000 | 0.324614 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.8995 | −0.709394 | −0.354697 | − | 0.934981i | \(-0.615416\pi\) | ||||
−0.354697 | + | 0.934981i | \(0.615416\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.31371 | 0.107229 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.11270 | 0.100514 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.68629 | −0.247945 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.8995 | −0.576205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.8701 | −1.44292 | −0.721462 | − | 0.692454i | \(-0.756529\pi\) | ||||
−0.721462 | + | 0.692454i | \(0.756529\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.9411 | −1.21759 | −0.608794 | − | 0.793328i | \(-0.708347\pi\) | ||||
−0.608794 | + | 0.793328i | \(0.708347\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.37258 | 0.300471 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.28427 | −0.201052 | −0.100526 | − | 0.994934i | \(-0.532053\pi\) | ||||
−0.100526 | + | 0.994934i | \(0.532053\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.9706 | 1.81708 | 0.908539 | − | 0.417799i | \(-0.137198\pi\) | ||||
0.908539 | + | 0.417799i | \(0.137198\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.24264 | −0.262632 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.6569 | −0.815841 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.4558 | −0.490971 | −0.245486 | − | 0.969400i | \(-0.578947\pi\) | ||||
−0.245486 | + | 0.969400i | \(0.578947\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16.9706 | 0.538003 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.242641 | 0.00768451 | 0.00384225 | − | 0.999993i | \(-0.498777\pi\) | ||||
0.00384225 | + | 0.999993i | \(0.498777\pi\) | |||||||
\(998\) | 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 | 3960.2.a.u.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 3960.2.a.bb.1.2 | yes | 2 | ||
4.3 | odd | 2 | 7920.2.a.bx.1.1 | 2 | |||
12.11 | even | 2 | 7920.2.a.cf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3960.2.a.u.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
3960.2.a.bb.1.2 | yes | 2 | 3.2 | odd | 2 | ||
7920.2.a.bx.1.1 | 2 | 4.3 | odd | 2 | |||
7920.2.a.cf.1.1 | 2 | 12.11 | even | 2 |