Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3360,2,Mod(1,3360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3360, 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("3360.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3360 = 2^{5} \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3360.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: | \(26.8297350792\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(2.17009\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3360.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.41855 | 1.03073 | 0.515366 | − | 0.856970i | \(-0.327656\pi\) | ||||
0.515366 | + | 0.856970i | \(0.327656\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.26180 | 0.904659 | 0.452330 | − | 0.891851i | \(-0.350593\pi\) | ||||
0.452330 | + | 0.891851i | \(0.350593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.68035 | −1.62022 | −0.810111 | − | 0.586277i | \(-0.800593\pi\) | ||||
−0.810111 | + | 0.586277i | \(0.800593\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.41855 | −1.70193 | −0.850966 | − | 0.525221i | \(-0.823983\pi\) | ||||
−0.850966 | + | 0.525221i | \(0.823983\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.15676 | 0.449715 | 0.224857 | − | 0.974392i | \(-0.427808\pi\) | ||||
0.224857 | + | 0.974392i | \(0.427808\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.68035 | −1.24051 | −0.620255 | − | 0.784401i | \(-0.712971\pi\) | ||||
−0.620255 | + | 0.784401i | \(0.712971\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.57531 | −1.71978 | −0.859888 | − | 0.510483i | \(-0.829467\pi\) | ||||
−0.859888 | + | 0.510483i | \(0.829467\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.41855 | −0.595093 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.68035 | 1.09824 | 0.549121 | − | 0.835743i | \(-0.314963\pi\) | ||||
0.549121 | + | 0.835743i | \(0.314963\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.26180 | −0.522305 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.83710 | 1.38012 | 0.690062 | − | 0.723751i | \(-0.257583\pi\) | ||||
0.690062 | + | 0.723751i | \(0.257583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.68035 | −1.32374 | −0.661870 | − | 0.749618i | \(-0.730237\pi\) | ||||
−0.661870 | + | 0.749618i | \(0.730237\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.15676 | −0.314595 | −0.157298 | − | 0.987551i | \(-0.550278\pi\) | ||||
−0.157298 | + | 0.987551i | \(0.550278\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.68035 | 0.935436 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.41855 | 0.194853 | 0.0974265 | − | 0.995243i | \(-0.468939\pi\) | ||||
0.0974265 | + | 0.995243i | \(0.468939\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.41855 | 0.460957 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.41855 | 0.982611 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.00000 | −1.04151 | −0.520756 | − | 0.853706i | \(-0.674350\pi\) | ||||
−0.520756 | + | 0.853706i | \(0.674350\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.156755 | 0.0200705 | 0.0100352 | − | 0.999950i | \(-0.496806\pi\) | ||||
0.0100352 | + | 0.999950i | \(0.496806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.26180 | 0.404576 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.5174 | 1.89576 | 0.947879 | − | 0.318631i | \(-0.103223\pi\) | ||||
0.947879 | + | 0.318631i | \(0.103223\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.15676 | −0.259643 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.26180 | 0.149748 | 0.0748738 | − | 0.997193i | \(-0.476145\pi\) | ||||
0.0748738 | + | 0.997193i | \(0.476145\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.738205 | 0.0864003 | 0.0432002 | − | 0.999066i | \(-0.486245\pi\) | ||||
0.0432002 | + | 0.999066i | \(0.486245\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.41855 | −0.389580 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8371 | −1.18953 | −0.594763 | − | 0.803901i | \(-0.702754\pi\) | ||||
−0.594763 | + | 0.803901i | \(0.702754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.68035 | −0.724585 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.68035 | 0.716208 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.52359 | 0.479500 | 0.239750 | − | 0.970835i | \(-0.422935\pi\) | ||||
0.239750 | + | 0.970835i | \(0.422935\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.26180 | −0.341929 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.57531 | 0.992913 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.41855 | −0.761127 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.26180 | 0.331185 | 0.165593 | − | 0.986194i | \(-0.447046\pi\) | ||||
0.165593 | + | 0.986194i | \(0.447046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.41855 | 0.343577 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0000 | −0.995037 | −0.497519 | − | 0.867453i | \(-0.665755\pi\) | ||||
−0.497519 | + | 0.867453i | \(0.665755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00000 | 0.0975900 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.15676 | −0.595196 | −0.297598 | − | 0.954691i | \(-0.596186\pi\) | ||||
−0.297598 | + | 0.954691i | \(0.596186\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.3607 | −1.85442 | −0.927209 | − | 0.374544i | \(-0.877799\pi\) | ||||
−0.927209 | + | 0.374544i | \(0.877799\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.68035 | −0.634070 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.2557 | 1.52920 | 0.764602 | − | 0.644503i | \(-0.222936\pi\) | ||||
0.764602 | + | 0.644503i | \(0.222936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.15676 | 0.201118 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.26180 | 0.301553 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.68035 | 0.612386 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.686489 | 0.0624081 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.83710 | −0.796815 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.5236 | −0.933818 | −0.466909 | − | 0.884305i | \(-0.654632\pi\) | ||||
−0.466909 | + | 0.884305i | \(0.654632\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.68035 | 0.764262 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.5236 | −0.919450 | −0.459725 | − | 0.888061i | \(-0.652052\pi\) | ||||
−0.459725 | + | 0.888061i | \(0.652052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.41855 | 0.643270 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −15.9421 | −1.36203 | −0.681015 | − | 0.732270i | \(-0.738461\pi\) | ||||
−0.681015 | + | 0.732270i | \(0.738461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.4186 | −1.30778 | −0.653892 | − | 0.756588i | \(-0.726865\pi\) | ||||
−0.653892 | + | 0.756588i | \(0.726865\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.15676 | 0.181632 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.1506 | 0.932461 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.68035 | −0.554773 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.1568 | −0.995920 | −0.497960 | − | 0.867200i | \(-0.665917\pi\) | ||||
−0.497960 | + | 0.867200i | \(0.665917\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.83710 | 0.230880 | 0.115440 | − | 0.993314i | \(-0.463172\pi\) | ||||
0.115440 | + | 0.993314i | \(0.463172\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.68035 | −0.540074 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.57531 | −0.769107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.26180 | −0.579554 | −0.289777 | − | 0.957094i | \(-0.593581\pi\) | ||||
−0.289777 | + | 0.957094i | \(0.593581\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.41855 | −0.112498 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.15676 | −0.169976 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.6803 | 1.30651 | 0.653253 | − | 0.757140i | \(-0.273404\pi\) | ||||
0.653253 | + | 0.757140i | \(0.273404\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.41855 | −0.266134 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.31965 | 0.256883 | 0.128441 | − | 0.991717i | \(-0.459003\pi\) | ||||
0.128441 | + | 0.991717i | \(0.459003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.36069 | −0.181592 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.41855 | −0.567311 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.83710 | −0.671872 | −0.335936 | − | 0.941885i | \(-0.609053\pi\) | ||||
−0.335936 | + | 0.941885i | \(0.609053\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.00000 | 0.601317 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.5814 | −0.940382 | −0.470191 | − | 0.882565i | \(-0.655815\pi\) | ||||
−0.470191 | + | 0.882565i | \(0.655815\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.6803 | −1.68582 | −0.842908 | − | 0.538057i | \(-0.819158\pi\) | ||||
−0.842908 | + | 0.538057i | \(0.819158\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.156755 | −0.0115877 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.68035 | 0.491149 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −22.8371 | −1.67001 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.26180 | −0.0913003 | −0.0456501 | − | 0.998957i | \(-0.514536\pi\) | ||||
−0.0456501 | + | 0.998957i | \(0.514536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3607 | 1.39361 | 0.696807 | − | 0.717259i | \(-0.254604\pi\) | ||||
0.696807 | + | 0.717259i | \(0.254604\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.26180 | −0.233582 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.94214 | 0.280866 | 0.140433 | − | 0.990090i | \(-0.455151\pi\) | ||||
0.140433 | + | 0.990090i | \(0.455151\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.90110 | −0.276542 | −0.138271 | − | 0.990394i | \(-0.544154\pi\) | ||||
−0.138271 | + | 0.990394i | \(0.544154\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.5174 | −1.09452 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.68035 | 0.468868 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.83710 | 0.617210 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.15676 | 0.149905 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −25.3607 | −1.75424 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.313511 | −0.0215830 | −0.0107915 | − | 0.999942i | \(-0.503435\pi\) | ||||
−0.0107915 | + | 0.999942i | \(0.503435\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.26180 | −0.0864568 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.68035 | −0.591995 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.57531 | 0.650014 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.738205 | −0.0498833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.7899 | −1.46575 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.8843 | 1.33155 | 0.665775 | − | 0.746153i | \(-0.268101\pi\) | ||||
0.665775 | + | 0.746153i | \(0.268101\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.8843 | −1.58526 | −0.792628 | − | 0.609706i | \(-0.791288\pi\) | ||||
−0.792628 | + | 0.609706i | \(0.791288\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.8781 | 1.77616 | 0.888079 | − | 0.459691i | \(-0.152040\pi\) | ||||
0.888079 | + | 0.459691i | \(0.152040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.41855 | 0.224924 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.7792 | −1.49232 | −0.746159 | − | 0.665768i | \(-0.768104\pi\) | ||||
−0.746159 | + | 0.665768i | \(0.768104\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.15676 | −0.140691 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.26180 | 0.0816187 | 0.0408094 | − | 0.999167i | \(-0.487006\pi\) | ||||
0.0408094 | + | 0.999167i | \(0.487006\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.83710 | −0.311585 | −0.155793 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155793 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.1978 | −1.53967 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.8371 | 0.686773 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.3607 | 1.09580 | 0.547899 | − | 0.836545i | \(-0.315428\pi\) | ||||
0.547899 | + | 0.836545i | \(0.315428\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.37298 | 0.463535 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.68035 | 0.418339 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.5174 | 1.59173 | 0.795867 | − | 0.605471i | \(-0.207015\pi\) | ||||
0.795867 | + | 0.605471i | \(0.207015\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.68035 | −0.415096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.68035 | −0.413503 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −21.3074 | −1.31387 | −0.656934 | − | 0.753948i | \(-0.728147\pi\) | ||||
−0.656934 | + | 0.753948i | \(0.728147\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.41855 | 0.0871409 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.52359 | −0.276839 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.0349 | 1.28252 | 0.641260 | − | 0.767324i | \(-0.278412\pi\) | ||||
0.641260 | + | 0.767324i | \(0.278412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.57531 | 0.0956930 | 0.0478465 | − | 0.998855i | \(-0.484764\pi\) | ||||
0.0478465 | + | 0.998855i | \(0.484764\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.26180 | 0.197413 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.41855 | 0.206146 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.6803 | −1.60307 | −0.801533 | − | 0.597950i | \(-0.795982\pi\) | ||||
−0.801533 | + | 0.597950i | \(0.795982\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.57531 | −0.573259 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.83710 | 0.527177 | 0.263589 | − | 0.964635i | \(-0.415094\pi\) | ||||
0.263589 | + | 0.964635i | \(0.415094\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 25.6742 | 1.52617 | 0.763086 | − | 0.646296i | \(-0.223683\pi\) | ||||
0.763086 | + | 0.646296i | \(0.223683\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.41855 | 0.439437 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.83710 | −0.521638 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 27.6270 | 1.62512 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.26180 | −0.191210 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.5236 | −1.19900 | −0.599500 | − | 0.800374i | \(-0.704634\pi\) | ||||
−0.599500 | + | 0.800374i | \(0.704634\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.41855 | −0.198364 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.03489 | 0.406838 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.68035 | 0.500327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.0000 | 0.574485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.156755 | 0.00897579 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.1978 | 1.60933 | 0.804667 | − | 0.593727i | \(-0.202344\pi\) | ||||
0.804667 | + | 0.593727i | \(0.202344\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.6742 | −0.775393 | −0.387696 | − | 0.921787i | \(-0.626729\pi\) | ||||
−0.387696 | + | 0.921787i | \(0.626729\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.5753 | 1.33256 | 0.666278 | − | 0.745704i | \(-0.267887\pi\) | ||||
0.666278 | + | 0.745704i | \(0.267887\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.00000 | −0.0563436 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.6286 | −0.653129 | −0.326564 | − | 0.945175i | \(-0.605891\pi\) | ||||
−0.326564 | + | 0.945175i | \(0.605891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.8371 | −1.27863 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.15676 | 0.343637 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 49.5585 | 2.75751 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.26180 | 0.180932 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.3607 | 1.07065 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.15676 | 0.118906 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.3135 | 1.33639 | 0.668196 | − | 0.743986i | \(-0.267067\pi\) | ||||
0.668196 | + | 0.743986i | \(0.267067\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.68035 | 0.366081 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.5174 | 0.847809 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.68649 | 0.309763 | 0.154881 | − | 0.987933i | \(-0.450500\pi\) | ||||
0.154881 | + | 0.987933i | \(0.450500\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.2557 | −0.882886 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −32.7337 | −1.77263 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.15676 | −0.116116 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.68035 | −0.465985 | −0.232993 | − | 0.972478i | \(-0.574852\pi\) | ||||
−0.232993 | + | 0.972478i | \(0.574852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.47027 | 0.239288 | 0.119644 | − | 0.992817i | \(-0.461825\pi\) | ||||
0.119644 | + | 0.992817i | \(0.461825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.26180 | −0.174102 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.6681 | −1.73875 | −0.869373 | − | 0.494157i | \(-0.835477\pi\) | ||||
−0.869373 | + | 0.494157i | \(0.835477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.26180 | 0.0669691 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.68035 | −0.353561 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.94828 | −0.261160 | −0.130580 | − | 0.991438i | \(-0.541684\pi\) | ||||
−0.130580 | + | 0.991438i | \(0.541684\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.0349 | 1.89657 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.686489 | −0.0360313 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.738205 | 0.0386394 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4764 | −0.703463 | −0.351731 | − | 0.936101i | \(-0.614407\pi\) | ||||
−0.351731 | + | 0.936101i | \(0.614407\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8.83710 | 0.460041 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.41855 | −0.0736475 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.1917 | −1.61504 | −0.807521 | − | 0.589839i | \(-0.799191\pi\) | ||||
−0.807521 | + | 0.589839i | \(0.799191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −21.7899 | −1.12224 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.2101 | −0.524457 | −0.262228 | − | 0.965006i | \(-0.584457\pi\) | ||||
−0.262228 | + | 0.965006i | \(0.584457\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.5236 | 0.539140 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.3545 | −0.529093 | −0.264546 | − | 0.964373i | \(-0.585222\pi\) | ||||
−0.264546 | + | 0.964373i | \(0.585222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.41855 | −0.174225 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.68035 | −0.441247 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −23.8432 | −1.20890 | −0.604450 | − | 0.796643i | \(-0.706607\pi\) | ||||
−0.604450 | + | 0.796643i | \(0.706607\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.4079 | −0.728637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.5236 | 0.530845 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | −0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.7259 | −1.54209 | −0.771045 | − | 0.636781i | \(-0.780266\pi\) | ||||
−0.771045 | + | 0.636781i | \(0.780266\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.41855 | −0.371392 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.63931 | 0.431426 | 0.215713 | − | 0.976457i | \(-0.430792\pi\) | ||||
0.215713 | + | 0.976457i | \(0.430792\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.2327 | −1.55581 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 22.8371 | 1.13199 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.7337 | 0.530746 | 0.265373 | − | 0.964146i | \(-0.414505\pi\) | ||||
0.265373 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.9421 | 0.786368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.00000 | 0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.8371 | −0.531972 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.4186 | 0.755050 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −32.1978 | −1.57297 | −0.786483 | − | 0.617612i | \(-0.788100\pi\) | ||||
−0.786483 | + | 0.617612i | \(0.788100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.67420 | −0.374018 | −0.187009 | − | 0.982358i | \(-0.559879\pi\) | ||||
−0.187009 | + | 0.982358i | \(0.559879\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.15676 | −0.104865 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.68035 | −0.324044 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.156755 | −0.00758593 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1506 | −0.538357 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.06400 | −0.0512512 | −0.0256256 | − | 0.999672i | \(-0.508158\pi\) | ||||
−0.0256256 | + | 0.999672i | \(0.508158\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.62249 | 0.222143 | 0.111071 | − | 0.993812i | \(-0.464572\pi\) | ||||
0.111071 | + | 0.993812i | \(0.464572\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.68035 | 0.320298 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2618 | −0.632951 | −0.316475 | − | 0.948601i | \(-0.602499\pi\) | ||||
−0.316475 | + | 0.948601i | \(0.602499\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.35455 | −0.301914 | −0.150957 | − | 0.988540i | \(-0.548235\pi\) | ||||
−0.150957 | + | 0.988540i | \(0.548235\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.52359 | 0.214439 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.1568 | 0.574995 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.31351 | −0.109181 | −0.0545907 | − | 0.998509i | \(-0.517385\pi\) | ||||
−0.0545907 | + | 0.998509i | \(0.517385\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.2101 | 1.42254 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.83710 | −0.133299 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.26180 | −0.152915 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.47641 | 0.349732 | 0.174866 | − | 0.984592i | \(-0.444051\pi\) | ||||
0.174866 | + | 0.984592i | \(0.444051\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.68035 | 0.311812 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.3135 | −1.03924 | −0.519622 | − | 0.854396i | \(-0.673927\pi\) | ||||
−0.519622 | + | 0.854396i | \(0.673927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.78992 | 0.0831847 | 0.0415923 | − | 0.999135i | \(-0.486757\pi\) | ||||
0.0415923 | + | 0.999135i | \(0.486757\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 9.57531 | 0.444044 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.5236 | −1.04227 | −0.521134 | − | 0.853475i | \(-0.674491\pi\) | ||||
−0.521134 | + | 0.853475i | \(0.674491\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.5174 | −0.716529 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.26180 | 0.334606 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −29.6742 | −1.36442 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.41855 | −0.340386 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.41855 | 0.0649510 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.7214 | −1.58646 | −0.793230 | − | 0.608922i | \(-0.791602\pi\) | ||||
−0.793230 | + | 0.608922i | \(0.791602\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.7899 | 0.993535 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.15676 | 0.0981358 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.26180 | 0.148110 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.8371 | 1.03485 | 0.517424 | − | 0.855729i | \(-0.326891\pi\) | ||||
0.517424 | + | 0.855729i | \(0.326891\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.6803 | −0.754311 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.3028 | −0.690607 | −0.345304 | − | 0.938491i | \(-0.612224\pi\) | ||||
−0.345304 | + | 0.938491i | \(0.612224\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 44.6270 | 2.00990 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.41855 | 0.153652 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.26180 | −0.0565993 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 39.8843 | 1.78547 | 0.892733 | − | 0.450586i | \(-0.148785\pi\) | ||||
0.892733 | + | 0.450586i | \(0.148785\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.31965 | −0.148311 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 37.3074 | 1.66345 | 0.831727 | − | 0.555185i | \(-0.187353\pi\) | ||||
0.831727 | + | 0.555185i | \(0.187353\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0000 | −0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.36069 | 0.104842 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.0349 | −1.10965 | −0.554826 | − | 0.831966i | \(-0.687215\pi\) | ||||
−0.554826 | + | 0.831966i | \(0.687215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.738205 | −0.0326563 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.41855 | 0.327537 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.37298 | −0.324263 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.83710 | 0.387906 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.15061 | 0.225652 | 0.112826 | − | 0.993615i | \(-0.464010\pi\) | ||||
0.112826 | + | 0.993615i | \(0.464010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.52359 | 0.285257 | 0.142628 | − | 0.989776i | \(-0.454445\pi\) | ||||
0.142628 | + | 0.989776i | \(0.454445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 63.9664 | 2.78642 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.3484 | −0.797757 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.00000 | −0.347170 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.8248 | 1.24854 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.15676 | −0.266180 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.5814 | 0.542930 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.41855 | 0.147247 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.0349 | 1.93620 | 0.968101 | − | 0.250562i | \(-0.0806152\pi\) | ||||
0.968101 | + | 0.250562i | \(0.0806152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 22.6803 | 0.973307 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.3607 | −0.829321 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.8904 | 0.978724 | 0.489362 | − | 0.872081i | \(-0.337230\pi\) | ||||
0.489362 | + | 0.872081i | \(0.337230\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.156755 | 0.00669016 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 49.5585 | 2.11126 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | 0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.68035 | −0.283565 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 15.0928 | 0.639500 | 0.319750 | − | 0.947502i | \(-0.396401\pi\) | ||||
0.319750 | + | 0.947502i | \(0.396401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.3135 | −1.19753 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 22.8371 | 0.964183 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.0472 | 1.05561 | 0.527806 | − | 0.849365i | \(-0.323015\pi\) | ||||
0.527806 | + | 0.849365i | \(0.323015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 16.2557 | 0.683880 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.0349 | 1.38489 | 0.692447 | − | 0.721468i | \(-0.256532\pi\) | ||||
0.692447 | + | 0.721468i | \(0.256532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.8371 | 1.79268 | 0.896338 | − | 0.443370i | \(-0.146217\pi\) | ||||
0.896338 | + | 0.443370i | \(0.146217\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.26180 | 0.0527123 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.15676 | 0.0899429 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.42469 | −0.350725 | −0.175362 | − | 0.984504i | \(-0.556110\pi\) | ||||
−0.175362 | + | 0.984504i | \(0.556110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.3607 | −0.804603 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 10.8371 | 0.449599 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.84939 | 0.200841 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.26180 | 0.134859 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.0472 | 1.36400 | 0.682002 | − | 0.731351i | \(-0.261110\pi\) | ||||
0.682002 | + | 0.731351i | \(0.261110\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 71.0349 | 2.92694 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.94214 | −0.162158 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.7152 | 1.71304 | 0.856520 | − | 0.516114i | \(-0.172622\pi\) | ||||
0.856520 | + | 0.516114i | \(0.172622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.68035 | 0.273867 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.90110 | 0.159662 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.21461 | −0.172204 | −0.0861022 | − | 0.996286i | \(-0.527441\pi\) | ||||
−0.0861022 | + | 0.996286i | \(0.527441\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.1978 | −0.905467 | −0.452733 | − | 0.891646i | \(-0.649551\pi\) | ||||
−0.452733 | + | 0.891646i | \(0.649551\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 15.5174 | 0.631919 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.686489 | 0.0279097 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.5113 | 1.48195 | 0.740974 | − | 0.671534i | \(-0.234364\pi\) | ||||
0.740974 | + | 0.671534i | \(0.234364\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.68035 | −0.270701 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.03489 | −0.284601 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.63317 | 0.0659629 | 0.0329815 | − | 0.999456i | \(-0.489500\pi\) | ||||
0.0329815 | + | 0.999456i | \(0.489500\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.83710 | −0.356346 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.73206 | −0.0697302 | −0.0348651 | − | 0.999392i | \(-0.511100\pi\) | ||||
−0.0348651 | + | 0.999392i | \(0.511100\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.7321 | −0.793099 | −0.396549 | − | 0.918013i | \(-0.629792\pi\) | ||||
−0.396549 | + | 0.918013i | \(0.629792\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.15676 | −0.0865476 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.52359 | −0.181234 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.3607 | 1.01281 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −44.6270 | −1.77940 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.73367 | 0.188444 | 0.0942222 | − | 0.995551i | \(-0.469964\pi\) | ||||
0.0942222 | + | 0.995551i | \(0.469964\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.313511 | 0.0124609 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.5236 | −0.417616 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.26180 | 0.129237 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.26180 | 0.0499158 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1506 | −0.677408 | −0.338704 | − | 0.940893i | \(-0.609989\pi\) | ||||
−0.338704 | + | 0.940893i | \(0.609989\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7899 | 0.543821 | 0.271911 | − | 0.962322i | \(-0.412344\pi\) | ||||
0.271911 | + | 0.962322i | \(0.412344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.68035 | 0.341788 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.993857 | −0.0390725 | −0.0195363 | − | 0.999809i | \(-0.506219\pi\) | ||||
−0.0195363 | + | 0.999809i | \(0.506219\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.3484 | −1.07352 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.57531 | −0.375286 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.3028 | 1.14671 | 0.573354 | − | 0.819308i | \(-0.305642\pi\) | ||||
0.573354 | + | 0.819308i | \(0.305642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.5236 | −0.411191 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.738205 | 0.0288001 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7792 | −0.809444 | −0.404722 | − | 0.914440i | \(-0.632632\pi\) | ||||
−0.404722 | + | 0.914440i | \(0.632632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.1445 | −1.79481 | −0.897406 | − | 0.441206i | \(-0.854551\pi\) | ||||
−0.897406 | + | 0.441206i | \(0.854551\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.7899 | 0.846250 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.41855 | 0.287679 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.4079 | −0.557875 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.8843 | −0.768771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.535877 | 0.0206873 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.8843 | −0.689388 | −0.344694 | − | 0.938715i | \(-0.612017\pi\) | ||||
−0.344694 | + | 0.938715i | \(0.612017\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.21008 | 0.161806 | 0.0809032 | − | 0.996722i | \(-0.474220\pi\) | ||||
0.0809032 | + | 0.996722i | \(0.474220\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.26180 | −0.125176 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.8843 | 0.915248 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 33.3074 | 1.27447 | 0.637236 | − | 0.770669i | \(-0.280078\pi\) | ||||
0.637236 | + | 0.770669i | \(0.280078\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.9421 | −0.609118 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.8781 | −1.02546 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.62702 | 0.176275 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0456 | 0.914737 | 0.457368 | − | 0.889277i | \(-0.348792\pi\) | ||||
0.457368 | + | 0.889277i | \(0.348792\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.41855 | −0.129860 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.4186 | −0.584859 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −59.0349 | −2.23611 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.7792 | 0.861590 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −20.3545 | −0.768781 | −0.384390 | − | 0.923171i | \(-0.625588\pi\) | ||||
−0.384390 | + | 0.923171i | \(0.625588\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.5585 | −1.86913 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.15676 | 0.0812281 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0000 | 0.376089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.3607 | 1.77867 | 0.889334 | − | 0.457258i | \(-0.151168\pi\) | ||||
0.889334 | + | 0.457258i | \(0.151168\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | −0.150012 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.6516 | −0.773408 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.1506 | 0.417009 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.26180 | −0.0471226 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.8371 | 1.15003 | 0.575015 | − | 0.818143i | \(-0.304996\pi\) | ||||
0.575015 | + | 0.818143i | \(0.304996\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.83710 | 0.179894 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.68035 | −0.248102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.1978 | −0.600743 | −0.300371 | − | 0.953822i | \(-0.597111\pi\) | ||||
−0.300371 | + | 0.953822i | \(0.597111\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 57.9877 | 2.14475 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2146 | 0.820516 | 0.410258 | − | 0.911970i | \(-0.365439\pi\) | ||||
0.410258 | + | 0.911970i | \(0.365439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.00000 | −0.0368856 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 53.0472 | 1.95402 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.47641 | 0.348595 | 0.174298 | − | 0.984693i | \(-0.444234\pi\) | ||||
0.174298 | + | 0.984693i | \(0.444234\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.1978 | 0.888928 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.3197 | 1.00226 | 0.501130 | − | 0.865372i | \(-0.332918\pi\) | ||||
0.501130 | + | 0.865372i | \(0.332918\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1568 | −0.445389 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.8371 | −0.396509 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.15676 | 0.224963 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.7214 | 1.12104 | 0.560520 | − | 0.828141i | \(-0.310601\pi\) | ||||
0.560520 | + | 0.828141i | \(0.310601\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −17.3607 | −0.632659 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.83710 | 0.103253 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.83096 | 0.357312 | 0.178656 | − | 0.983912i | \(-0.442825\pi\) | ||||
0.178656 | + | 0.983912i | \(0.442825\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −7.37298 | −0.267622 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.5113 | −0.961034 | −0.480517 | − | 0.876985i | \(-0.659551\pi\) | ||||
−0.480517 | + | 0.876985i | \(0.659551\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.3607 | 0.700904 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.68035 | −0.241528 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −26.0944 | −0.942213 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 43.5585 | 1.57076 | 0.785380 | − | 0.619014i | \(-0.212468\pi\) | ||||
0.785380 | + | 0.619014i | \(0.212468\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.5174 | −0.918988 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −26.8248 | −0.964822 | −0.482411 | − | 0.875945i | \(-0.660239\pi\) | ||||
−0.482411 | + | 0.875945i | \(0.660239\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.57531 | −0.343955 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.68035 | 0.239656 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −65.5585 | −2.34888 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.31351 | 0.154350 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.68035 | 0.238736 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.26180 | −0.259185 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.115718 | 0.00412489 | 0.00206244 | − | 0.999998i | \(-0.499344\pi\) | ||||
0.00206244 | + | 0.999998i | \(0.499344\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.3074 | 0.758562 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.2557 | −0.577984 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.511304 | 0.0181569 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.41855 | −0.0503108 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.83710 | −0.313026 | −0.156513 | − | 0.987676i | \(-0.550025\pi\) | ||||
−0.156513 | + | 0.987676i | \(0.550025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.4079 | 0.509714 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.52359 | 0.159833 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.52359 | 0.0890556 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.15676 | −0.0760156 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −21.0349 | −0.740463 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.8248 | 0.943110 | 0.471555 | − | 0.881837i | \(-0.343693\pi\) | ||||
0.471555 | + | 0.881837i | \(0.343693\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.0456 | −0.563436 | −0.281718 | − | 0.959497i | \(-0.590904\pi\) | ||||
−0.281718 | + | 0.959497i | \(0.590904\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.57531 | −0.0552484 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.6803 | 0.584287 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 64.3956 | 2.25292 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.26180 | −0.113976 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 45.4017 | 1.58453 | 0.792266 | − | 0.610176i | \(-0.208901\pi\) | ||||
0.792266 | + | 0.610176i | \(0.208901\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.5113 | 1.83043 | 0.915215 | − | 0.402967i | \(-0.132021\pi\) | ||||
0.915215 | + | 0.402967i | \(0.132021\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.41855 | −0.119019 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.47027 | −0.0858996 | −0.0429498 | − | 0.999077i | \(-0.513676\pi\) | ||||
−0.0429498 | + | 0.999077i | \(0.513676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.7152 | −0.754201 | −0.377101 | − | 0.926172i | \(-0.623079\pi\) | ||||
−0.377101 | + | 0.926172i | \(0.623079\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.6803 | 0.925531 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.68035 | −0.231460 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.31965 | 0.114881 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.57531 | 0.330971 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.8371 | 1.34081 | 0.670403 | − | 0.741997i | \(-0.266121\pi\) | ||||
0.670403 | + | 0.741997i | \(0.266121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6270 | 0.538863 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.83710 | −0.304366 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.36069 | −0.0812103 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.686489 | −0.0235880 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −25.6742 | −0.881136 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.4079 | 0.493896 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.0517 | −0.857754 | −0.428877 | − | 0.903363i | \(-0.641091\pi\) | ||||
−0.428877 | + | 0.903363i | \(0.641091\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.41855 | −0.253709 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.52973 | −0.120573 | −0.0602867 | − | 0.998181i | \(-0.519201\pi\) | ||||
−0.0602867 | + | 0.998181i | \(0.519201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.8950 | −0.712927 | −0.356463 | − | 0.934309i | \(-0.616018\pi\) | ||||
−0.356463 | + | 0.934309i | \(0.616018\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.83710 | 0.301168 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.8781 | −0.710700 | −0.355350 | − | 0.934733i | \(-0.615638\pi\) | ||||
−0.355350 | + | 0.934733i | \(0.615638\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.83710 | −0.300470 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −27.6270 | −0.938263 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6742 | −0.463866 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 50.6147 | 1.71501 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.26180 | 0.110395 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −32.3545 | −1.09254 | −0.546268 | − | 0.837611i | \(-0.683952\pi\) | ||||
−0.546268 | + | 0.837611i | \(0.683952\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.5236 | 0.692244 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.1978 | −1.28692 | −0.643458 | − | 0.765481i | \(-0.722501\pi\) | ||||
−0.643458 | + | 0.765481i | \(0.722501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.89043 | −0.231881 | −0.115941 | − | 0.993256i | \(-0.536988\pi\) | ||||
−0.115941 | + | 0.993256i | \(0.536988\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.00000 | 0.268917 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.56463 | −0.287572 | −0.143786 | − | 0.989609i | \(-0.545928\pi\) | ||||
−0.143786 | + | 0.989609i | \(0.545928\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.5236 | 0.352950 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.41855 | 0.114526 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.0000 | 0.535420 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.5814 | −0.420551 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.03489 | −0.234888 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 63.9664 | 2.13340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.47641 | −0.315705 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.68035 | −0.288864 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.6803 | −0.753920 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 35.2039 | 1.16893 | 0.584464 | − | 0.811420i | \(-0.301305\pi\) | ||||
0.584464 | + | 0.811420i | \(0.301305\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.0000 | −0.331679 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.69102 | 0.0560261 | 0.0280131 | − | 0.999608i | \(-0.491082\pi\) | ||||
0.0280131 | + | 0.999608i | \(0.491082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.0472 | −1.22608 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.156755 | −0.00518218 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.5236 | 0.347520 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3258 | −0.472564 | −0.236282 | − | 0.971684i | \(-0.575929\pi\) | ||||
−0.236282 | + | 0.971684i | \(0.575929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.1978 | −0.929149 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.11572 | 0.135470 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.68035 | 0.219648 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.5113 | −1.13228 | −0.566140 | − | 0.824309i | \(-0.691564\pi\) | ||||
−0.566140 | + | 0.824309i | \(0.691564\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.41855 | −0.243133 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.6742 | 0.447673 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22.8371 | −0.746853 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.9011 | −0.976826 | −0.488413 | − | 0.872612i | \(-0.662424\pi\) | ||||
−0.488413 | + | 0.872612i | \(0.662424\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.5753 | −0.769351 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −28.0944 | −0.915850 | −0.457925 | − | 0.888991i | \(-0.651407\pi\) | ||||
−0.457925 | + | 0.888991i | \(0.651407\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 19.0595 | 0.620662 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 48.3423 | 1.57091 | 0.785456 | − | 0.618917i | \(-0.212428\pi\) | ||||
0.785456 | + | 0.618917i | \(0.212428\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.40787 | 0.0781629 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.6286 | 0.377084 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.0928 | −1.39591 | −0.697956 | − | 0.716141i | \(-0.745907\pi\) | ||||
−0.697956 | + | 0.716141i | \(0.745907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.26180 | −0.0408307 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.8371 | 0.738219 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.9421 | 0.514799 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.6865 | 1.95763 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.15676 | −0.198399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.3607 | 0.623243 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.7337 | 0.538119 | 0.269059 | − | 0.963124i | \(-0.413287\pi\) | ||||
0.269059 | + | 0.963124i | \(0.413287\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −49.5585 | −1.59205 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −30.3012 | −0.972413 | −0.486206 | − | 0.873844i | \(-0.661620\pi\) | ||||
−0.486206 | + | 0.873844i | \(0.661620\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.4186 | 0.494296 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.26180 | −0.104461 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.6163 | 1.33142 | 0.665712 | − | 0.746208i | \(-0.268128\pi\) | ||||
0.665712 | + | 0.746208i | \(0.268128\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.4641 | 0.494236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.3607 | −0.618139 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.2511 | 0.901071 | 0.450535 | − | 0.892759i | \(-0.351233\pi\) | ||||
0.450535 | + | 0.892759i | \(0.351233\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.94214 | 0.125607 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.15676 | −0.0686503 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −18.7214 | −0.595305 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.6742 | −1.32382 | −0.661912 | − | 0.749581i | \(-0.730255\pi\) | ||||
−0.661912 | + | 0.749581i | \(0.730255\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −24.3135 | −0.771566 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.90110 | −0.123673 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.6225 | 0.399758 | 0.199879 | − | 0.979821i | \(-0.435945\pi\) | ||||
0.199879 | + | 0.979821i | \(0.435945\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.68035 | −0.211357 |
(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 | 3360.2.a.bi.1.3 | ✓ | 3 | |
4.3 | odd | 2 | 3360.2.a.bj.1.1 | yes | 3 | ||
8.3 | odd | 2 | 6720.2.a.da.1.3 | 3 | |||
8.5 | even | 2 | 6720.2.a.db.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3360.2.a.bi.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
3360.2.a.bj.1.1 | yes | 3 | 4.3 | odd | 2 | ||
6720.2.a.da.1.3 | 3 | 8.3 | odd | 2 | |||
6720.2.a.db.1.1 | 3 | 8.5 | even | 2 |