Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6930,2,Mod(1,6930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6930, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6930.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6930 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6930.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: | \(55.3363286007\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 770) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6930.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.46410 | −0.406069 | −0.203034 | − | 0.979172i | \(-0.565080\pi\) | ||||
−0.203034 | + | 0.979172i | \(0.565080\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.73205 | 1.54444 | 0.772219 | − | 0.635356i | \(-0.219147\pi\) | ||||
0.772219 | + | 0.635356i | \(0.219147\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 8.19615 | 1.70902 | 0.854508 | − | 0.519438i | \(-0.173859\pi\) | ||||
0.854508 | + | 0.519438i | \(0.173859\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.46410 | 0.287134 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 4.73205 | 0.878720 | 0.439360 | − | 0.898311i | \(-0.355205\pi\) | ||||
0.439360 | + | 0.898311i | \(0.355205\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.46410 | −0.594089 | ||||||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.732051 | 0.120348 | 0.0601742 | − | 0.998188i | \(-0.480834\pi\) | ||||
0.0601742 | + | 0.998188i | \(0.480834\pi\) | |||||||
\(38\) | −6.73205 | −1.09208 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 2.19615 | 0.342981 | 0.171491 | − | 0.985186i | \(-0.445142\pi\) | ||||
0.171491 | + | 0.985186i | \(0.445142\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.19615 | −1.20846 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.46410 | −0.203034 | ||||||||
\(53\) | 7.26795 | 0.998330 | 0.499165 | − | 0.866507i | \(-0.333640\pi\) | ||||
0.499165 | + | 0.866507i | \(0.333640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.73205 | −0.621349 | ||||||||
\(59\) | −6.92820 | −0.901975 | −0.450988 | − | 0.892530i | \(-0.648928\pi\) | ||||
−0.450988 | + | 0.892530i | \(0.648928\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.46410 | −0.181599 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 3.46410 | 0.420084 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −9.46410 | −1.12318 | −0.561591 | − | 0.827415i | \(-0.689811\pi\) | ||||
−0.561591 | + | 0.827415i | \(0.689811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.3923 | −1.68449 | −0.842246 | − | 0.539093i | \(-0.818767\pi\) | ||||
−0.842246 | + | 0.539093i | \(0.818767\pi\) | |||||||
\(74\) | −0.732051 | −0.0850992 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.73205 | 0.772219 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.1962 | −1.37217 | −0.686087 | − | 0.727519i | \(-0.740673\pi\) | ||||
−0.686087 | + | 0.727519i | \(0.740673\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.19615 | −0.242524 | ||||||||
\(83\) | 16.3923 | 1.79929 | 0.899645 | − | 0.436623i | \(-0.143826\pi\) | ||||
0.899645 | + | 0.436623i | \(0.143826\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.46410 | 0.375735 | ||||||||
\(86\) | −2.00000 | −0.215666 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | −3.46410 | −0.367194 | −0.183597 | − | 0.983002i | \(-0.558774\pi\) | ||||
−0.183597 | + | 0.983002i | \(0.558774\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.46410 | −0.153480 | ||||||||
\(92\) | 8.19615 | 0.854508 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.92820 | 0.714590 | ||||||||
\(95\) | 6.73205 | 0.690694 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.5885 | 1.48123 | 0.740617 | − | 0.671928i | \(-0.234533\pi\) | ||||
0.740617 | + | 0.671928i | \(0.234533\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 7.85641 | 0.781742 | 0.390871 | − | 0.920446i | \(-0.372174\pi\) | ||||
0.390871 | + | 0.920446i | \(0.372174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.3923 | 1.22105 | 0.610525 | − | 0.791997i | \(-0.290958\pi\) | ||||
0.610525 | + | 0.791997i | \(0.290958\pi\) | |||||||
\(104\) | 1.46410 | 0.143567 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.26795 | −0.705926 | ||||||||
\(107\) | −7.85641 | −0.759507 | −0.379754 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.6603 | −1.49998 | −0.749990 | − | 0.661449i | \(-0.769942\pi\) | ||||
−0.749990 | + | 0.661449i | \(0.769942\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −7.85641 | −0.739069 | −0.369534 | − | 0.929217i | \(-0.620483\pi\) | ||||
−0.369534 | + | 0.929217i | \(0.620483\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.19615 | 0.764295 | ||||||||
\(116\) | 4.73205 | 0.439360 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.92820 | 0.637793 | ||||||||
\(119\) | 3.46410 | 0.317554 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.92820 | 0.446179 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.07180 | 0.0951066 | 0.0475533 | − | 0.998869i | \(-0.484858\pi\) | ||||
0.0475533 | + | 0.998869i | \(0.484858\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.46410 | 0.128410 | ||||||||
\(131\) | −5.66025 | −0.494539 | −0.247269 | − | 0.968947i | \(-0.579533\pi\) | ||||
−0.247269 | + | 0.968947i | \(0.579533\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.73205 | 0.583743 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.46410 | −0.297044 | ||||||||
\(137\) | 0.928203 | 0.0793018 | 0.0396509 | − | 0.999214i | \(-0.487375\pi\) | ||||
0.0396509 | + | 0.999214i | \(0.487375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.6603 | 1.15865 | 0.579324 | − | 0.815097i | \(-0.303317\pi\) | ||||
0.579324 | + | 0.815097i | \(0.303317\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.46410 | 0.794210 | ||||||||
\(143\) | 1.46410 | 0.122434 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.73205 | 0.392975 | ||||||||
\(146\) | 14.3923 | 1.19112 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.732051 | 0.0601742 | ||||||||
\(149\) | 7.26795 | 0.595414 | 0.297707 | − | 0.954657i | \(-0.403778\pi\) | ||||
0.297707 | + | 0.954657i | \(0.403778\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.1244 | 0.905287 | 0.452644 | − | 0.891692i | \(-0.350481\pi\) | ||||
0.452644 | + | 0.891692i | \(0.350481\pi\) | |||||||
\(152\) | −6.73205 | −0.546041 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 2.00000 | 0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.53590 | 0.362004 | 0.181002 | − | 0.983483i | \(-0.442066\pi\) | ||||
0.181002 | + | 0.983483i | \(0.442066\pi\) | |||||||
\(158\) | 12.1962 | 0.970274 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 8.19615 | 0.645947 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 2.19615 | 0.171491 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.3923 | −1.27229 | ||||||||
\(167\) | −13.8564 | −1.07224 | −0.536120 | − | 0.844141i | \(-0.680111\pi\) | ||||
−0.536120 | + | 0.844141i | \(0.680111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8564 | −0.835108 | ||||||||
\(170\) | −3.46410 | −0.265684 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −0.928203 | −0.0705700 | −0.0352850 | − | 0.999377i | \(-0.511234\pi\) | ||||
−0.0352850 | + | 0.999377i | \(0.511234\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.46410 | 0.259645 | ||||||||
\(179\) | 6.00000 | 0.448461 | 0.224231 | − | 0.974536i | \(-0.428013\pi\) | ||||
0.224231 | + | 0.974536i | \(0.428013\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.0000 | 1.04061 | 0.520306 | − | 0.853980i | \(-0.325818\pi\) | ||||
0.520306 | + | 0.853980i | \(0.325818\pi\) | |||||||
\(182\) | 1.46410 | 0.108526 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.19615 | −0.604228 | ||||||||
\(185\) | 0.732051 | 0.0538214 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.46410 | −0.253320 | ||||||||
\(188\) | −6.92820 | −0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.73205 | −0.488394 | ||||||||
\(191\) | 12.0000 | 0.868290 | 0.434145 | − | 0.900843i | \(-0.357051\pi\) | ||||
0.434145 | + | 0.900843i | \(0.357051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.3923 | 0.892018 | 0.446009 | − | 0.895029i | \(-0.352845\pi\) | ||||
0.446009 | + | 0.895029i | \(0.352845\pi\) | |||||||
\(194\) | −14.5885 | −1.04739 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 24.2487 | 1.72765 | 0.863825 | − | 0.503793i | \(-0.168062\pi\) | ||||
0.863825 | + | 0.503793i | \(0.168062\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.92820 | 0.207575 | 0.103787 | − | 0.994600i | \(-0.466904\pi\) | ||||
0.103787 | + | 0.994600i | \(0.466904\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.85641 | −0.552775 | ||||||||
\(203\) | 4.73205 | 0.332125 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.19615 | 0.153386 | ||||||||
\(206\) | −12.3923 | −0.863413 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.46410 | −0.101517 | ||||||||
\(209\) | −6.73205 | −0.465666 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.9282 | 1.85381 | 0.926907 | − | 0.375291i | \(-0.122457\pi\) | ||||
0.926907 | + | 0.375291i | \(0.122457\pi\) | |||||||
\(212\) | 7.26795 | 0.499165 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.85641 | 0.537053 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | 15.6603 | 1.06065 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | −5.07180 | −0.341166 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −25.4641 | −1.70520 | −0.852601 | − | 0.522562i | \(-0.824976\pi\) | ||||
−0.852601 | + | 0.522562i | \(0.824976\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.85641 | 0.522600 | ||||||||
\(227\) | −6.92820 | −0.459841 | −0.229920 | − | 0.973209i | \(-0.573847\pi\) | ||||
−0.229920 | + | 0.973209i | \(0.573847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.3923 | 1.61189 | 0.805944 | − | 0.591991i | \(-0.201658\pi\) | ||||
0.805944 | + | 0.591991i | \(0.201658\pi\) | |||||||
\(230\) | −8.19615 | −0.540438 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.73205 | −0.310674 | ||||||||
\(233\) | 7.85641 | 0.514690 | 0.257345 | − | 0.966320i | \(-0.417152\pi\) | ||||
0.257345 | + | 0.966320i | \(0.417152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.92820 | −0.451946 | ||||||||
\(236\) | −6.92820 | −0.450988 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.46410 | −0.224544 | ||||||||
\(239\) | −1.26795 | −0.0820168 | −0.0410084 | − | 0.999159i | \(-0.513057\pi\) | ||||
−0.0410084 | + | 0.999159i | \(0.513057\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.26795 | 0.210507 | 0.105254 | − | 0.994445i | \(-0.466435\pi\) | ||||
0.105254 | + | 0.994445i | \(0.466435\pi\) | |||||||
\(242\) | −1.00000 | −0.0642824 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.92820 | −0.315496 | ||||||||
\(245\) | 1.00000 | 0.0638877 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.85641 | −0.627148 | ||||||||
\(248\) | −2.00000 | −0.127000 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.19615 | −0.515288 | ||||||||
\(254\) | −1.07180 | −0.0672505 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.6603 | 1.47589 | 0.737943 | − | 0.674863i | \(-0.235797\pi\) | ||||
0.737943 | + | 0.674863i | \(0.235797\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.732051 | 0.0454874 | ||||||||
\(260\) | −1.46410 | −0.0907997 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.66025 | 0.349692 | ||||||||
\(263\) | 24.0000 | 1.47990 | 0.739952 | − | 0.672660i | \(-0.234848\pi\) | ||||
0.739952 | + | 0.672660i | \(0.234848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.26795 | 0.446467 | ||||||||
\(266\) | −6.73205 | −0.412769 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.00000 | −0.244339 | ||||||||
\(269\) | −28.3923 | −1.73111 | −0.865555 | − | 0.500814i | \(-0.833034\pi\) | ||||
−0.865555 | + | 0.500814i | \(0.833034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.392305 | 0.0238308 | 0.0119154 | − | 0.999929i | \(-0.496207\pi\) | ||||
0.0119154 | + | 0.999929i | \(0.496207\pi\) | |||||||
\(272\) | 3.46410 | 0.210042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.928203 | −0.0560748 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.07180 | 0.424903 | 0.212452 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212452 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(278\) | −13.6603 | −0.819288 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −22.3923 | −1.33581 | −0.667906 | − | 0.744245i | \(-0.732809\pi\) | ||||
−0.667906 | + | 0.744245i | \(0.732809\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −31.7128 | −1.88513 | −0.942566 | − | 0.334021i | \(-0.891594\pi\) | ||||
−0.942566 | + | 0.334021i | \(0.891594\pi\) | |||||||
\(284\) | −9.46410 | −0.561591 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.46410 | −0.0865741 | ||||||||
\(287\) | 2.19615 | 0.129635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −4.73205 | −0.277876 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −14.3923 | −0.842246 | ||||||||
\(293\) | −21.4641 | −1.25395 | −0.626973 | − | 0.779041i | \(-0.715706\pi\) | ||||
−0.626973 | + | 0.779041i | \(0.715706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.92820 | −0.403376 | ||||||||
\(296\) | −0.732051 | −0.0425496 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.26795 | −0.421021 | ||||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | −11.1244 | −0.640135 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.73205 | 0.386110 | ||||||||
\(305\) | −4.92820 | −0.282188 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.3923 | 1.39214 | 0.696071 | − | 0.717973i | \(-0.254930\pi\) | ||||
0.696071 | + | 0.717973i | \(0.254930\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.00000 | −0.113592 | ||||||||
\(311\) | −24.9282 | −1.41355 | −0.706774 | − | 0.707439i | \(-0.749850\pi\) | ||||
−0.706774 | + | 0.707439i | \(0.749850\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.1962 | 1.25460 | 0.627300 | − | 0.778777i | \(-0.284160\pi\) | ||||
0.627300 | + | 0.778777i | \(0.284160\pi\) | |||||||
\(314\) | −4.53590 | −0.255976 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.1962 | −0.686087 | ||||||||
\(317\) | −30.5885 | −1.71802 | −0.859009 | − | 0.511960i | \(-0.828920\pi\) | ||||
−0.859009 | + | 0.511960i | \(0.828920\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.73205 | −0.264944 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −8.19615 | −0.456754 | ||||||||
\(323\) | 23.3205 | 1.29759 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.46410 | −0.0812137 | ||||||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.19615 | −0.121262 | ||||||||
\(329\) | −6.92820 | −0.381964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.7846 | −1.03250 | −0.516248 | − | 0.856439i | \(-0.672672\pi\) | ||||
−0.516248 | + | 0.856439i | \(0.672672\pi\) | |||||||
\(332\) | 16.3923 | 0.899645 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.8564 | 0.758189 | ||||||||
\(335\) | −4.00000 | −0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.7846 | 1.24116 | 0.620578 | − | 0.784144i | \(-0.286898\pi\) | ||||
0.620578 | + | 0.784144i | \(0.286898\pi\) | |||||||
\(338\) | 10.8564 | 0.590511 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.46410 | 0.187867 | ||||||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.928203 | 0.0499005 | ||||||||
\(347\) | 23.0718 | 1.23856 | 0.619279 | − | 0.785171i | \(-0.287425\pi\) | ||||
0.619279 | + | 0.785171i | \(0.287425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.60770 | −0.300173 | −0.150087 | − | 0.988673i | \(-0.547955\pi\) | ||||
−0.150087 | + | 0.988673i | \(0.547955\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −14.1962 | −0.755585 | −0.377792 | − | 0.925890i | \(-0.623317\pi\) | ||||
−0.377792 | + | 0.925890i | \(0.623317\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.46410 | −0.502302 | ||||||||
\(356\) | −3.46410 | −0.183597 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.00000 | −0.317110 | ||||||||
\(359\) | 34.0526 | 1.79723 | 0.898613 | − | 0.438743i | \(-0.144576\pi\) | ||||
0.898613 | + | 0.438743i | \(0.144576\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.3205 | 1.38529 | ||||||||
\(362\) | −14.0000 | −0.735824 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.46410 | −0.0767398 | ||||||||
\(365\) | −14.3923 | −0.753328 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.3923 | 0.646873 | 0.323437 | − | 0.946250i | \(-0.395162\pi\) | ||||
0.323437 | + | 0.946250i | \(0.395162\pi\) | |||||||
\(368\) | 8.19615 | 0.427254 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.732051 | −0.0380575 | ||||||||
\(371\) | 7.26795 | 0.377333 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.3923 | 0.952317 | 0.476159 | − | 0.879359i | \(-0.342029\pi\) | ||||
0.476159 | + | 0.879359i | \(0.342029\pi\) | |||||||
\(374\) | 3.46410 | 0.179124 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92820 | 0.357295 | ||||||||
\(377\) | −6.92820 | −0.356821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.14359 | 0.315575 | 0.157788 | − | 0.987473i | \(-0.449564\pi\) | ||||
0.157788 | + | 0.987473i | \(0.449564\pi\) | |||||||
\(380\) | 6.73205 | 0.345347 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | 33.4641 | 1.70994 | 0.854968 | − | 0.518681i | \(-0.173577\pi\) | ||||
0.854968 | + | 0.518681i | \(0.173577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.00000 | −0.0509647 | ||||||||
\(386\) | −12.3923 | −0.630752 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.5885 | 0.740617 | ||||||||
\(389\) | 1.60770 | 0.0815134 | 0.0407567 | − | 0.999169i | \(-0.487023\pi\) | ||||
0.0407567 | + | 0.999169i | \(0.487023\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.3923 | 1.43586 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.2487 | −1.22163 | ||||||||
\(395\) | −12.1962 | −0.613655 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3923 | 1.52535 | 0.762673 | − | 0.646784i | \(-0.223887\pi\) | ||||
0.762673 | + | 0.646784i | \(0.223887\pi\) | |||||||
\(398\) | −2.92820 | −0.146778 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −2.53590 | −0.126637 | −0.0633184 | − | 0.997993i | \(-0.520168\pi\) | ||||
−0.0633184 | + | 0.997993i | \(0.520168\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.92820 | −0.145864 | ||||||||
\(404\) | 7.85641 | 0.390871 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.73205 | −0.234848 | ||||||||
\(407\) | −0.732051 | −0.0362864 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.8756 | 0.537766 | 0.268883 | − | 0.963173i | \(-0.413346\pi\) | ||||
0.268883 | + | 0.963173i | \(0.413346\pi\) | |||||||
\(410\) | −2.19615 | −0.108460 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.3923 | 0.610525 | ||||||||
\(413\) | −6.92820 | −0.340915 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 16.3923 | 0.804667 | ||||||||
\(416\) | 1.46410 | 0.0717835 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.73205 | 0.329275 | ||||||||
\(419\) | −30.9282 | −1.51094 | −0.755471 | − | 0.655182i | \(-0.772592\pi\) | ||||
−0.755471 | + | 0.655182i | \(0.772592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.8564 | −1.74753 | −0.873767 | − | 0.486344i | \(-0.838330\pi\) | ||||
−0.873767 | + | 0.486344i | \(0.838330\pi\) | |||||||
\(422\) | −26.9282 | −1.31084 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.26795 | −0.352963 | ||||||||
\(425\) | 3.46410 | 0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.92820 | −0.238492 | ||||||||
\(428\) | −7.85641 | −0.379754 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.00000 | −0.0964486 | ||||||||
\(431\) | −3.12436 | −0.150495 | −0.0752475 | − | 0.997165i | \(-0.523975\pi\) | ||||
−0.0752475 | + | 0.997165i | \(0.523975\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.1962 | −0.874451 | −0.437226 | − | 0.899352i | \(-0.644039\pi\) | ||||
−0.437226 | + | 0.899352i | \(0.644039\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.6603 | −0.749990 | ||||||||
\(437\) | 55.1769 | 2.63947 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.2487 | 1.25278 | 0.626391 | − | 0.779509i | \(-0.284531\pi\) | ||||
0.626391 | + | 0.779509i | \(0.284531\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.07180 | 0.241241 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.46410 | −0.164214 | ||||||||
\(446\) | 25.4641 | 1.20576 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −40.3923 | −1.90623 | −0.953115 | − | 0.302607i | \(-0.902143\pi\) | ||||
−0.953115 | + | 0.302607i | \(0.902143\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.19615 | −0.103413 | ||||||||
\(452\) | −7.85641 | −0.369534 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.92820 | 0.325157 | ||||||||
\(455\) | −1.46410 | −0.0686381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.00000 | 0.0935561 | 0.0467780 | − | 0.998905i | \(-0.485105\pi\) | ||||
0.0467780 | + | 0.998905i | \(0.485105\pi\) | |||||||
\(458\) | −24.3923 | −1.13978 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.19615 | 0.382148 | ||||||||
\(461\) | −22.3923 | −1.04291 | −0.521457 | − | 0.853278i | \(-0.674611\pi\) | ||||
−0.521457 | + | 0.853278i | \(0.674611\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.5167 | 1.27881 | 0.639404 | − | 0.768871i | \(-0.279181\pi\) | ||||
0.639404 | + | 0.768871i | \(0.279181\pi\) | |||||||
\(464\) | 4.73205 | 0.219680 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.85641 | −0.363941 | ||||||||
\(467\) | 34.0526 | 1.57576 | 0.787882 | − | 0.615826i | \(-0.211178\pi\) | ||||
0.787882 | + | 0.615826i | \(0.211178\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00000 | −0.184703 | ||||||||
\(470\) | 6.92820 | 0.319574 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.92820 | 0.318896 | ||||||||
\(473\) | −2.00000 | −0.0919601 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.73205 | 0.308888 | ||||||||
\(476\) | 3.46410 | 0.158777 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.26795 | 0.0579946 | ||||||||
\(479\) | 32.7846 | 1.49797 | 0.748984 | − | 0.662589i | \(-0.230542\pi\) | ||||
0.748984 | + | 0.662589i | \(0.230542\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.07180 | −0.0488697 | ||||||||
\(482\) | −3.26795 | −0.148851 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 14.5885 | 0.662428 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.19615 | 0.190146 | 0.0950729 | − | 0.995470i | \(-0.469692\pi\) | ||||
0.0950729 | + | 0.995470i | \(0.469692\pi\) | |||||||
\(488\) | 4.92820 | 0.223089 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.00000 | −0.0451754 | ||||||||
\(491\) | 27.7128 | 1.25066 | 0.625331 | − | 0.780360i | \(-0.284964\pi\) | ||||
0.625331 | + | 0.780360i | \(0.284964\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.3923 | 0.738272 | ||||||||
\(494\) | 9.85641 | 0.443461 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −9.46410 | −0.424523 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.1436 | 0.543622 | 0.271811 | − | 0.962351i | \(-0.412377\pi\) | ||||
0.271811 | + | 0.962351i | \(0.412377\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.0000 | 0.535586 | ||||||||
\(503\) | −8.78461 | −0.391686 | −0.195843 | − | 0.980635i | \(-0.562744\pi\) | ||||
−0.195843 | + | 0.980635i | \(0.562744\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.85641 | 0.349605 | ||||||||
\(506\) | 8.19615 | 0.364363 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.07180 | 0.0475533 | ||||||||
\(509\) | −11.0718 | −0.490749 | −0.245374 | − | 0.969428i | \(-0.578911\pi\) | ||||
−0.245374 | + | 0.969428i | \(0.578911\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.3923 | −0.636678 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −23.6603 | −1.04361 | ||||||||
\(515\) | 12.3923 | 0.546070 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.92820 | 0.304702 | ||||||||
\(518\) | −0.732051 | −0.0321645 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.46410 | 0.0642051 | ||||||||
\(521\) | −10.3923 | −0.455295 | −0.227648 | − | 0.973744i | \(-0.573103\pi\) | ||||
−0.227648 | + | 0.973744i | \(0.573103\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −29.1769 | −1.27582 | −0.637909 | − | 0.770112i | \(-0.720200\pi\) | ||||
−0.637909 | + | 0.770112i | \(0.720200\pi\) | |||||||
\(524\) | −5.66025 | −0.247269 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 6.92820 | 0.301797 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 44.1769 | 1.92074 | ||||||||
\(530\) | −7.26795 | −0.315700 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.73205 | 0.291871 | ||||||||
\(533\) | −3.21539 | −0.139274 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.85641 | −0.339662 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 28.3923 | 1.22408 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.7321 | −0.891340 | −0.445670 | − | 0.895197i | \(-0.647035\pi\) | ||||
−0.445670 | + | 0.895197i | \(0.647035\pi\) | |||||||
\(542\) | −0.392305 | −0.0168509 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.46410 | −0.148522 | ||||||||
\(545\) | −15.6603 | −0.670812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.7846 | 1.23074 | 0.615371 | − | 0.788238i | \(-0.289006\pi\) | ||||
0.615371 | + | 0.788238i | \(0.289006\pi\) | |||||||
\(548\) | 0.928203 | 0.0396509 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 31.8564 | 1.35713 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.1962 | −0.518633 | ||||||||
\(554\) | −7.07180 | −0.300452 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.6603 | 0.579324 | ||||||||
\(557\) | 25.6077 | 1.08503 | 0.542516 | − | 0.840045i | \(-0.317472\pi\) | ||||
0.542516 | + | 0.840045i | \(0.317472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.92820 | −0.123850 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.3923 | 0.944562 | ||||||||
\(563\) | −5.07180 | −0.213751 | −0.106875 | − | 0.994272i | \(-0.534085\pi\) | ||||
−0.106875 | + | 0.994272i | \(0.534085\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.85641 | −0.330522 | ||||||||
\(566\) | 31.7128 | 1.33299 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.46410 | 0.397105 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.60770 | 0.150977 | 0.0754887 | − | 0.997147i | \(-0.475948\pi\) | ||||
0.0754887 | + | 0.997147i | \(0.475948\pi\) | |||||||
\(572\) | 1.46410 | 0.0612172 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.19615 | −0.0916656 | ||||||||
\(575\) | 8.19615 | 0.341803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −34.5885 | −1.43994 | −0.719968 | − | 0.694007i | \(-0.755844\pi\) | ||||
−0.719968 | + | 0.694007i | \(0.755844\pi\) | |||||||
\(578\) | 5.00000 | 0.207973 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.73205 | 0.196488 | ||||||||
\(581\) | 16.3923 | 0.680067 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.26795 | −0.301008 | ||||||||
\(584\) | 14.3923 | 0.595558 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.4641 | 0.886674 | ||||||||
\(587\) | 11.4115 | 0.471005 | 0.235502 | − | 0.971874i | \(-0.424326\pi\) | ||||
0.235502 | + | 0.971874i | \(0.424326\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.4641 | 0.554779 | ||||||||
\(590\) | 6.92820 | 0.285230 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.732051 | 0.0300871 | ||||||||
\(593\) | −0.248711 | −0.0102133 | −0.00510667 | − | 0.999987i | \(-0.501626\pi\) | ||||
−0.00510667 | + | 0.999987i | \(0.501626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.46410 | 0.142014 | ||||||||
\(596\) | 7.26795 | 0.297707 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | 0.490716 | ||||||||
\(599\) | −37.1769 | −1.51901 | −0.759504 | − | 0.650503i | \(-0.774558\pi\) | ||||
−0.759504 | + | 0.650503i | \(0.774558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.51666 | −0.225029 | −0.112515 | − | 0.993650i | \(-0.535891\pi\) | ||||
−0.112515 | + | 0.993650i | \(0.535891\pi\) | |||||||
\(602\) | −2.00000 | −0.0815139 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 11.1244 | 0.452644 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.9282 | 0.849450 | 0.424725 | − | 0.905323i | \(-0.360371\pi\) | ||||
0.424725 | + | 0.905323i | \(0.360371\pi\) | |||||||
\(608\) | −6.73205 | −0.273021 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.92820 | 0.199537 | ||||||||
\(611\) | 10.1436 | 0.410366 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.1769 | −1.42078 | −0.710391 | − | 0.703807i | \(-0.751482\pi\) | ||||
−0.710391 | + | 0.703807i | \(0.751482\pi\) | |||||||
\(614\) | −24.3923 | −0.984393 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | −17.3205 | −0.697297 | −0.348649 | − | 0.937253i | \(-0.613359\pi\) | ||||
−0.348649 | + | 0.937253i | \(0.613359\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.7846 | 1.15695 | 0.578476 | − | 0.815700i | \(-0.303648\pi\) | ||||
0.578476 | + | 0.815700i | \(0.303648\pi\) | |||||||
\(620\) | 2.00000 | 0.0803219 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 24.9282 | 0.999530 | ||||||||
\(623\) | −3.46410 | −0.138786 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −22.1962 | −0.887137 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.53590 | 0.181002 | ||||||||
\(629\) | 2.53590 | 0.101113 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.9282 | −1.86818 | −0.934091 | − | 0.357035i | \(-0.883788\pi\) | ||||
−0.934091 | + | 0.357035i | \(0.883788\pi\) | |||||||
\(632\) | 12.1962 | 0.485137 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.5885 | 1.21482 | ||||||||
\(635\) | 1.07180 | 0.0425330 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.46410 | −0.0580098 | ||||||||
\(638\) | 4.73205 | 0.187344 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 35.5692 | 1.40490 | 0.702450 | − | 0.711733i | \(-0.252090\pi\) | ||||
0.702450 | + | 0.711733i | \(0.252090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 33.2679 | 1.31196 | 0.655980 | − | 0.754778i | \(-0.272256\pi\) | ||||
0.655980 | + | 0.754778i | \(0.272256\pi\) | |||||||
\(644\) | 8.19615 | 0.322974 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −23.3205 | −0.917533 | ||||||||
\(647\) | 26.5359 | 1.04323 | 0.521617 | − | 0.853180i | \(-0.325329\pi\) | ||||
0.521617 | + | 0.853180i | \(0.325329\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.92820 | 0.271956 | ||||||||
\(650\) | 1.46410 | 0.0574268 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4.00000 | −0.156652 | ||||||||
\(653\) | −11.6603 | −0.456301 | −0.228151 | − | 0.973626i | \(-0.573268\pi\) | ||||
−0.228151 | + | 0.973626i | \(0.573268\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.66025 | −0.221164 | ||||||||
\(656\) | 2.19615 | 0.0857453 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.92820 | 0.270089 | ||||||||
\(659\) | −30.2487 | −1.17832 | −0.589161 | − | 0.808015i | \(-0.700542\pi\) | ||||
−0.589161 | + | 0.808015i | \(0.700542\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −46.0000 | −1.78919 | −0.894596 | − | 0.446875i | \(-0.852537\pi\) | ||||
−0.894596 | + | 0.446875i | \(0.852537\pi\) | |||||||
\(662\) | 18.7846 | 0.730085 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −16.3923 | −0.636145 | ||||||||
\(665\) | 6.73205 | 0.261058 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 38.7846 | 1.50175 | ||||||||
\(668\) | −13.8564 | −0.536120 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | 4.92820 | 0.190251 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | −22.7846 | −0.877630 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.8564 | −0.417554 | ||||||||
\(677\) | 4.14359 | 0.159251 | 0.0796256 | − | 0.996825i | \(-0.474628\pi\) | ||||
0.0796256 | + | 0.996825i | \(0.474628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.5885 | 0.559854 | ||||||||
\(680\) | −3.46410 | −0.132842 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.00000 | 0.0765840 | ||||||||
\(683\) | −6.24871 | −0.239100 | −0.119550 | − | 0.992828i | \(-0.538145\pi\) | ||||
−0.119550 | + | 0.992828i | \(0.538145\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.928203 | 0.0354648 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | −10.6410 | −0.405390 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4641 | −0.512199 | −0.256099 | − | 0.966650i | \(-0.582437\pi\) | ||||
−0.256099 | + | 0.966650i | \(0.582437\pi\) | |||||||
\(692\) | −0.928203 | −0.0352850 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −23.0718 | −0.875793 | ||||||||
\(695\) | 13.6603 | 0.518163 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.60770 | 0.288162 | ||||||||
\(698\) | 5.60770 | 0.212254 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −41.9090 | −1.58288 | −0.791440 | − | 0.611247i | \(-0.790668\pi\) | ||||
−0.791440 | + | 0.611247i | \(0.790668\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.92820 | 0.185871 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.1962 | 0.534279 | ||||||||
\(707\) | 7.85641 | 0.295471 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.3205 | 0.950932 | 0.475466 | − | 0.879734i | \(-0.342280\pi\) | ||||
0.475466 | + | 0.879734i | \(0.342280\pi\) | |||||||
\(710\) | 9.46410 | 0.355181 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.46410 | 0.129823 | ||||||||
\(713\) | 16.3923 | 0.613897 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.46410 | 0.0547543 | ||||||||
\(716\) | 6.00000 | 0.224231 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −34.0526 | −1.27083 | ||||||||
\(719\) | 27.7128 | 1.03351 | 0.516757 | − | 0.856132i | \(-0.327139\pi\) | ||||
0.516757 | + | 0.856132i | \(0.327139\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.3923 | 0.461514 | ||||||||
\(722\) | −26.3205 | −0.979548 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.0000 | 0.520306 | ||||||||
\(725\) | 4.73205 | 0.175744 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.00000 | −0.148352 | −0.0741759 | − | 0.997245i | \(-0.523633\pi\) | ||||
−0.0741759 | + | 0.997245i | \(0.523633\pi\) | |||||||
\(728\) | 1.46410 | 0.0542632 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 14.3923 | 0.532683 | ||||||||
\(731\) | 6.92820 | 0.256249 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26.0000 | 0.960332 | 0.480166 | − | 0.877178i | \(-0.340576\pi\) | ||||
0.480166 | + | 0.877178i | \(0.340576\pi\) | |||||||
\(734\) | −12.3923 | −0.457408 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.19615 | −0.302114 | ||||||||
\(737\) | 4.00000 | 0.147342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.7128 | 0.430863 | 0.215431 | − | 0.976519i | \(-0.430884\pi\) | ||||
0.215431 | + | 0.976519i | \(0.430884\pi\) | |||||||
\(740\) | 0.732051 | 0.0269107 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.26795 | −0.266815 | ||||||||
\(743\) | 32.7846 | 1.20275 | 0.601375 | − | 0.798967i | \(-0.294620\pi\) | ||||
0.601375 | + | 0.798967i | \(0.294620\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.26795 | 0.266277 | ||||||||
\(746\) | −18.3923 | −0.673390 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.46410 | −0.126660 | ||||||||
\(749\) | −7.85641 | −0.287067 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.6077 | −0.423571 | −0.211785 | − | 0.977316i | \(-0.567928\pi\) | ||||
−0.211785 | + | 0.977316i | \(0.567928\pi\) | |||||||
\(752\) | −6.92820 | −0.252646 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.92820 | 0.252310 | ||||||||
\(755\) | 11.1244 | 0.404857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.3731 | −1.57642 | −0.788210 | − | 0.615406i | \(-0.788992\pi\) | ||||
−0.788210 | + | 0.615406i | \(0.788992\pi\) | |||||||
\(758\) | −6.14359 | −0.223145 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.73205 | −0.244197 | ||||||||
\(761\) | 12.3397 | 0.447315 | 0.223658 | − | 0.974668i | \(-0.428200\pi\) | ||||
0.223658 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.6603 | −0.566939 | ||||||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −33.4641 | −1.20911 | ||||||||
\(767\) | 10.1436 | 0.366264 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.1962 | −0.656170 | −0.328085 | − | 0.944648i | \(-0.606403\pi\) | ||||
−0.328085 | + | 0.944648i | \(0.606403\pi\) | |||||||
\(770\) | 1.00000 | 0.0360375 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 12.3923 | 0.446009 | ||||||||
\(773\) | 0.928203 | 0.0333851 | 0.0166926 | − | 0.999861i | \(-0.494686\pi\) | ||||
0.0166926 | + | 0.999861i | \(0.494686\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | −14.5885 | −0.523695 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.60770 | −0.0576387 | ||||||||
\(779\) | 14.7846 | 0.529714 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.46410 | 0.338652 | ||||||||
\(782\) | −28.3923 | −1.01531 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 4.53590 | 0.161893 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.1436 | 0.646749 | 0.323375 | − | 0.946271i | \(-0.395183\pi\) | ||||
0.323375 | + | 0.946271i | \(0.395183\pi\) | |||||||
\(788\) | 24.2487 | 0.863825 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.1962 | 0.433920 | ||||||||
\(791\) | −7.85641 | −0.279342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.21539 | 0.256226 | ||||||||
\(794\) | −30.3923 | −1.07858 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.92820 | 0.103787 | ||||||||
\(797\) | 25.6077 | 0.907071 | 0.453536 | − | 0.891238i | \(-0.350163\pi\) | ||||
0.453536 | + | 0.891238i | \(0.350163\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −24.0000 | −0.849059 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.53590 | 0.0895457 | ||||||||
\(803\) | 14.3923 | 0.507893 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.19615 | 0.288876 | ||||||||
\(806\) | 2.92820 | 0.103142 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.85641 | −0.276387 | ||||||||
\(809\) | 31.1769 | 1.09612 | 0.548061 | − | 0.836438i | \(-0.315366\pi\) | ||||
0.548061 | + | 0.836438i | \(0.315366\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.1244 | −1.51430 | −0.757150 | − | 0.653241i | \(-0.773409\pi\) | ||||
−0.757150 | + | 0.653241i | \(0.773409\pi\) | |||||||
\(812\) | 4.73205 | 0.166062 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.732051 | 0.0256584 | ||||||||
\(815\) | −4.00000 | −0.140114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.4641 | 0.471049 | ||||||||
\(818\) | −10.8756 | −0.380258 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.19615 | 0.0766930 | ||||||||
\(821\) | −17.9090 | −0.625027 | −0.312514 | − | 0.949913i | \(-0.601171\pi\) | ||||
−0.312514 | + | 0.949913i | \(0.601171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.875644 | −0.0305230 | −0.0152615 | − | 0.999884i | \(-0.504858\pi\) | ||||
−0.0152615 | + | 0.999884i | \(0.504858\pi\) | |||||||
\(824\) | −12.3923 | −0.431706 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.92820 | 0.241063 | ||||||||
\(827\) | 25.8564 | 0.899115 | 0.449558 | − | 0.893251i | \(-0.351582\pi\) | ||||
0.449558 | + | 0.893251i | \(0.351582\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.24871 | 0.0781010 | 0.0390505 | − | 0.999237i | \(-0.487567\pi\) | ||||
0.0390505 | + | 0.999237i | \(0.487567\pi\) | |||||||
\(830\) | −16.3923 | −0.568985 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.46410 | −0.0507586 | ||||||||
\(833\) | 3.46410 | 0.120024 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −13.8564 | −0.479521 | ||||||||
\(836\) | −6.73205 | −0.232833 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.9282 | 1.06840 | ||||||||
\(839\) | 31.8564 | 1.09981 | 0.549903 | − | 0.835229i | \(-0.314665\pi\) | ||||
0.549903 | + | 0.835229i | \(0.314665\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.60770 | −0.227852 | ||||||||
\(842\) | 35.8564 | 1.23569 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.9282 | 0.926907 | ||||||||
\(845\) | −10.8564 | −0.373472 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 7.26795 | 0.249582 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −3.46410 | −0.118818 | ||||||||
\(851\) | 6.00000 | 0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −54.7846 | −1.87579 | −0.937895 | − | 0.346920i | \(-0.887227\pi\) | ||||
−0.937895 | + | 0.346920i | \(0.887227\pi\) | |||||||
\(854\) | 4.92820 | 0.168640 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.85641 | 0.268526 | ||||||||
\(857\) | 27.4641 | 0.938156 | 0.469078 | − | 0.883157i | \(-0.344586\pi\) | ||||
0.469078 | + | 0.883157i | \(0.344586\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.7846 | −0.436205 | −0.218103 | − | 0.975926i | \(-0.569987\pi\) | ||||
−0.218103 | + | 0.975926i | \(0.569987\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.12436 | 0.106416 | ||||||||
\(863\) | 7.51666 | 0.255870 | 0.127935 | − | 0.991783i | \(-0.459165\pi\) | ||||
0.127935 | + | 0.991783i | \(0.459165\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.928203 | −0.0315599 | ||||||||
\(866\) | 18.1962 | 0.618330 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.00000 | 0.0678844 | ||||||||
\(869\) | 12.1962 | 0.413726 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.85641 | 0.198437 | ||||||||
\(872\) | 15.6603 | 0.530323 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −55.1769 | −1.86639 | ||||||||
\(875\) | 1.00000 | 0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.3205 | −0.719942 | −0.359971 | − | 0.932963i | \(-0.617213\pi\) | ||||
−0.359971 | + | 0.932963i | \(0.617213\pi\) | |||||||
\(878\) | −26.2487 | −0.885851 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −11.0718 | −0.373018 | −0.186509 | − | 0.982453i | \(-0.559717\pi\) | ||||
−0.186509 | + | 0.982453i | \(0.559717\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.6077 | −1.19829 | −0.599147 | − | 0.800639i | \(-0.704494\pi\) | ||||
−0.599147 | + | 0.800639i | \(0.704494\pi\) | |||||||
\(884\) | −5.07180 | −0.170583 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.8564 | −0.465253 | −0.232626 | − | 0.972566i | \(-0.574732\pi\) | ||||
−0.232626 | + | 0.972566i | \(0.574732\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07180 | 0.0359469 | ||||||||
\(890\) | 3.46410 | 0.116117 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.4641 | −0.852601 | ||||||||
\(893\) | −46.6410 | −1.56078 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.00000 | 0.200558 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 40.3923 | 1.34791 | ||||||||
\(899\) | 9.46410 | 0.315645 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1769 | 0.838765 | ||||||||
\(902\) | 2.19615 | 0.0731239 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.85641 | 0.261300 | ||||||||
\(905\) | 14.0000 | 0.465376 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.0333 | −1.03044 | −0.515222 | − | 0.857057i | \(-0.672291\pi\) | ||||
−0.515222 | + | 0.857057i | \(0.672291\pi\) | |||||||
\(908\) | −6.92820 | −0.229920 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.46410 | 0.0485345 | ||||||||
\(911\) | −9.46410 | −0.313560 | −0.156780 | − | 0.987634i | \(-0.550111\pi\) | ||||
−0.156780 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.3923 | −0.542506 | ||||||||
\(914\) | −2.00000 | −0.0661541 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.3923 | 0.805944 | ||||||||
\(917\) | −5.66025 | −0.186918 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.3731 | −0.836980 | −0.418490 | − | 0.908221i | \(-0.637441\pi\) | ||||
−0.418490 | + | 0.908221i | \(0.637441\pi\) | |||||||
\(920\) | −8.19615 | −0.270219 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 22.3923 | 0.737451 | ||||||||
\(923\) | 13.8564 | 0.456089 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.732051 | 0.0240697 | ||||||||
\(926\) | −27.5167 | −0.904254 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.73205 | −0.155337 | ||||||||
\(929\) | 25.6077 | 0.840161 | 0.420081 | − | 0.907487i | \(-0.362002\pi\) | ||||
0.420081 | + | 0.907487i | \(0.362002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.73205 | 0.220634 | ||||||||
\(932\) | 7.85641 | 0.257345 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −34.0526 | −1.11423 | ||||||||
\(935\) | −3.46410 | −0.113288 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.21539 | −0.0397051 | −0.0198525 | − | 0.999803i | \(-0.506320\pi\) | ||||
−0.0198525 | + | 0.999803i | \(0.506320\pi\) | |||||||
\(938\) | 4.00000 | 0.130605 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.92820 | −0.225973 | ||||||||
\(941\) | 14.7846 | 0.481965 | 0.240982 | − | 0.970530i | \(-0.422530\pi\) | ||||
0.240982 | + | 0.970530i | \(0.422530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0000 | 0.586161 | ||||||||
\(944\) | −6.92820 | −0.225494 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.00000 | 0.0650256 | ||||||||
\(947\) | −47.3205 | −1.53771 | −0.768855 | − | 0.639423i | \(-0.779173\pi\) | ||||
−0.768855 | + | 0.639423i | \(0.779173\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0718 | 0.684019 | ||||||||
\(950\) | −6.73205 | −0.218417 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.46410 | −0.112272 | ||||||||
\(953\) | −26.5359 | −0.859582 | −0.429791 | − | 0.902928i | \(-0.641413\pi\) | ||||
−0.429791 | + | 0.902928i | \(0.641413\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000 | 0.388311 | ||||||||
\(956\) | −1.26795 | −0.0410084 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −32.7846 | −1.05922 | ||||||||
\(959\) | 0.928203 | 0.0299732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 1.07180 | 0.0345561 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.26795 | 0.105254 | ||||||||
\(965\) | 12.3923 | 0.398922 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.9282 | 0.865953 | 0.432976 | − | 0.901405i | \(-0.357463\pi\) | ||||
0.432976 | + | 0.901405i | \(0.357463\pi\) | |||||||
\(968\) | −1.00000 | −0.0321412 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −14.5885 | −0.468407 | ||||||||
\(971\) | −42.9282 | −1.37763 | −0.688816 | − | 0.724936i | \(-0.741869\pi\) | ||||
−0.688816 | + | 0.724936i | \(0.741869\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6603 | 0.437928 | ||||||||
\(974\) | −4.19615 | −0.134453 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.92820 | −0.157748 | ||||||||
\(977\) | 33.7128 | 1.07857 | 0.539284 | − | 0.842124i | \(-0.318695\pi\) | ||||
0.539284 | + | 0.842124i | \(0.318695\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.46410 | 0.110713 | ||||||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.7128 | −0.884351 | ||||||||
\(983\) | 37.1769 | 1.18576 | 0.592880 | − | 0.805291i | \(-0.297991\pi\) | ||||
0.592880 | + | 0.805291i | \(0.297991\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 24.2487 | 0.772628 | ||||||||
\(986\) | −16.3923 | −0.522037 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.85641 | −0.313574 | ||||||||
\(989\) | 16.3923 | 0.521245 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | −0.127064 | −0.0635321 | − | 0.997980i | \(-0.520237\pi\) | ||||
−0.0635321 | + | 0.997980i | \(0.520237\pi\) | |||||||
\(992\) | −2.00000 | −0.0635001 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.46410 | 0.300183 | ||||||||
\(995\) | 2.92820 | 0.0928303 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.7128 | 0.560970 | 0.280485 | − | 0.959858i | \(-0.409505\pi\) | ||||
0.280485 | + | 0.959858i | \(0.409505\pi\) | |||||||
\(998\) | −12.1436 | −0.384399 | ||||||||
\(999\) | 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 | 6930.2.a.bv.1.1 | 2 | ||
3.2 | odd | 2 | 770.2.a.j.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 6160.2.a.t.1.1 | 2 | |||
15.2 | even | 4 | 3850.2.c.x.1849.3 | 4 | |||
15.8 | even | 4 | 3850.2.c.x.1849.2 | 4 | |||
15.14 | odd | 2 | 3850.2.a.bd.1.1 | 2 | |||
21.20 | even | 2 | 5390.2.a.bs.1.1 | 2 | |||
33.32 | even | 2 | 8470.2.a.br.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.a.j.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
3850.2.a.bd.1.1 | 2 | 15.14 | odd | 2 | |||
3850.2.c.x.1849.2 | 4 | 15.8 | even | 4 | |||
3850.2.c.x.1849.3 | 4 | 15.2 | even | 4 | |||
5390.2.a.bs.1.1 | 2 | 21.20 | even | 2 | |||
6160.2.a.t.1.1 | 2 | 12.11 | even | 2 | |||
6930.2.a.bv.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8470.2.a.br.1.2 | 2 | 33.32 | even | 2 |