Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4864,2,Mod(1,4864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4864, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4864.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4864 = 2^{8} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4864.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: | \(38.8392355432\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 7x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1216) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-2.52434\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4864.1 |
$q$-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 | ||||||||
\(3\) | 2.37228 | 1.36964 | 0.684819 | − | 0.728714i | \(-0.259881\pi\) | ||||
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.792287 | 0.354322 | 0.177161 | − | 0.984182i | \(-0.443309\pi\) | ||||
0.177161 | + | 0.984182i | \(0.443309\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.31662 | 1.25357 | 0.626783 | − | 0.779194i | \(-0.284371\pi\) | ||||
0.626783 | + | 0.779194i | \(0.284371\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.62772 | 0.875906 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.37228 | 1.01678 | 0.508391 | − | 0.861127i | \(-0.330241\pi\) | ||||
0.508391 | + | 0.861127i | \(0.330241\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.10891 | −1.13961 | −0.569804 | − | 0.821781i | \(-0.692981\pi\) | ||||
−0.569804 | + | 0.821781i | \(0.692981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.87953 | 0.485292 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.00000 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292637\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.86797 | 1.71693 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.52434 | 0.526361 | 0.263180 | − | 0.964747i | \(-0.415229\pi\) | ||||
0.263180 | + | 0.964747i | \(0.415229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.37228 | −0.874456 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.883156 | −0.169963 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.98844 | −1.11203 | −0.556013 | − | 0.831174i | \(-0.687669\pi\) | ||||
−0.556013 | + | 0.831174i | \(0.687669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | 0.622171 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.00000 | 1.39262 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.62772 | 0.444166 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.16915 | 0.521005 | 0.260502 | − | 0.965473i | \(-0.416112\pi\) | ||||
0.260502 | + | 0.965473i | \(0.416112\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.74749 | −1.56085 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.37228 | 1.42926 | 0.714630 | − | 0.699503i | \(-0.246595\pi\) | ||||
0.714630 | + | 0.699503i | \(0.246595\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.08191 | 0.310352 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.30506 | 1.35728 | 0.678642 | − | 0.734470i | \(-0.262569\pi\) | ||||
0.678642 | + | 0.734470i | \(0.262569\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.00000 | 0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.8614 | 1.66093 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.45254 | −1.29841 | −0.649203 | − | 0.760615i | \(-0.724898\pi\) | ||||
−0.649203 | + | 0.760615i | \(0.724898\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.67181 | 0.360267 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.37228 | 0.314216 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.37228 | 0.569223 | 0.284611 | − | 0.958643i | \(-0.408135\pi\) | ||||
0.284611 | + | 0.958643i | \(0.408135\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.55134 | −0.582740 | −0.291370 | − | 0.956610i | \(-0.594111\pi\) | ||||
−0.291370 | + | 0.956610i | \(0.594111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.71516 | 1.09801 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.25544 | −0.403787 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.37228 | 1.02284 | 0.511418 | − | 0.859332i | \(-0.329120\pi\) | ||||
0.511418 | + | 0.859332i | \(0.329120\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.98844 | 0.720923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.63325 | −0.787222 | −0.393611 | − | 0.919277i | \(-0.628774\pi\) | ||||
−0.393611 | + | 0.919277i | \(0.628774\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4891 | 1.69582 | 0.847912 | − | 0.530137i | \(-0.177860\pi\) | ||||
0.847912 | + | 0.530137i | \(0.177860\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −10.3723 | −1.19769 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 11.1846 | 1.27460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.5615 | −1.52578 | −0.762891 | − | 0.646527i | \(-0.776221\pi\) | ||||
−0.762891 | + | 0.646527i | \(0.776221\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.97825 | −1.10869 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.00000 | −0.878114 | −0.439057 | − | 0.898459i | \(-0.644687\pi\) | ||||
−0.439057 | + | 0.898459i | \(0.644687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.96143 | 0.429678 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.2063 | −1.52307 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.48913 | −0.793846 | −0.396923 | − | 0.917852i | \(-0.629922\pi\) | ||||
−0.396923 | + | 0.917852i | \(0.629922\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.6277 | −1.42857 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.21782 | 0.852149 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.792287 | 0.0812869 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.74456 | 0.887876 | 0.443938 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443938 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.86141 | 0.890605 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.8564 | 1.37876 | 0.689382 | − | 0.724398i | \(-0.257882\pi\) | ||||
0.689382 | + | 0.724398i | \(0.257882\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.34363 | −0.526523 | −0.263262 | − | 0.964724i | \(-0.584798\pi\) | ||||
−0.263262 | + | 0.964724i | \(0.584798\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.23369 | 0.608346 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.62772 | 0.737399 | 0.368700 | − | 0.929549i | \(-0.379803\pi\) | ||||
0.368700 | + | 0.929549i | \(0.379803\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6217 | −1.20894 | −0.604469 | − | 0.796628i | \(-0.706615\pi\) | ||||
−0.604469 | + | 0.796628i | \(0.706615\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.51811 | 0.713587 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.25544 | −0.306246 | −0.153123 | − | 0.988207i | \(-0.548933\pi\) | ||||
−0.153123 | + | 0.988207i | \(0.548933\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.00000 | 0.186501 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7971 | −0.998189 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.5831 | 1.52017 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.372281 | 0.0338438 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.42554 | −0.664160 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.9051 | 1.67755 | 0.838777 | − | 0.544475i | \(-0.183271\pi\) | ||||
0.838777 | + | 0.544475i | \(0.183271\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 22.2337 | 1.95757 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.37228 | 0.119897 | 0.0599484 | − | 0.998201i | \(-0.480906\pi\) | ||||
0.0599484 | + | 0.998201i | \(0.480906\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.31662 | 0.287588 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.699713 | −0.0602217 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.00000 | −0.427179 | −0.213589 | − | 0.976924i | \(-0.568515\pi\) | ||||
−0.213589 | + | 0.976924i | \(0.568515\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.37228 | 0.794947 | 0.397473 | − | 0.917614i | \(-0.369887\pi\) | ||||
0.397473 | + | 0.917614i | \(0.369887\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 22.0742 | 1.85899 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.8564 | −1.15873 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.74456 | −0.394014 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.48913 | 0.782650 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.2819 | −1.74348 | −0.871742 | − | 0.489965i | \(-0.837010\pi\) | ||||
−0.871742 | + | 0.489965i | \(0.837010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.3692 | −1.82038 | −0.910189 | − | 0.414193i | \(-0.864064\pi\) | ||||
−0.910189 | + | 0.414193i | \(0.864064\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.1386 | 1.06219 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.74456 | 0.220449 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.28962 | 0.102923 | 0.0514615 | − | 0.998675i | \(-0.483612\pi\) | ||||
0.0514615 | + | 0.998675i | \(0.483612\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.4241 | −1.77835 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.37228 | 0.659828 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.744563 | −0.0583186 | −0.0291593 | − | 0.999575i | \(-0.509283\pi\) | ||||
−0.0291593 | + | 0.999575i | \(0.509283\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.33830 | 0.493436 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.1947 | 1.56271 | 0.781356 | − | 0.624085i | \(-0.214528\pi\) | ||||
0.781356 | + | 0.624085i | \(0.214528\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.88316 | 0.298704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.62772 | 0.200947 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.75372 | −0.361419 | −0.180709 | − | 0.983537i | \(-0.557839\pi\) | ||||
−0.180709 | + | 0.983537i | \(0.557839\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.5012 | −1.09619 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3723 | 0.779628 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.9783 | −1.71748 | −0.858738 | − | 0.512416i | \(-0.828751\pi\) | ||||
−0.858738 | + | 0.512416i | \(0.828751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 11.6819 | 0.868311 | 0.434155 | − | 0.900838i | \(-0.357047\pi\) | ||||
0.434155 | + | 0.900838i | \(0.357047\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.7971 | −0.798142 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.51087 | 0.184603 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.8614 | 1.23303 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.92910 | −0.213060 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.7089 | −0.991943 | −0.495972 | − | 0.868339i | \(-0.665188\pi\) | ||||
−0.495972 | + | 0.868339i | \(0.665188\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7446 | 1.06134 | 0.530668 | − | 0.847580i | \(-0.321941\pi\) | ||||
0.530668 | + | 0.847580i | \(0.321941\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.72281 | −0.553042 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.1947 | −1.43881 | −0.719406 | − | 0.694589i | \(-0.755586\pi\) | ||||
−0.719406 | + | 0.694589i | \(0.755586\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.78073 | 0.480673 | 0.240336 | − | 0.970690i | \(-0.422742\pi\) | ||||
0.240336 | + | 0.970690i | \(0.422742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 19.8614 | 1.40092 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −19.8614 | −1.39400 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.63325 | 0.461043 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.37228 | 0.233266 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.37228 | −0.576372 | −0.288186 | − | 0.957575i | \(-0.593052\pi\) | ||||
−0.288186 | + | 0.957575i | \(0.593052\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −15.7359 | −1.07821 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.42554 | 0.506417 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.4891 | 0.779933 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 34.3723 | 2.32266 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.5446 | −1.38198 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.92820 | −0.463947 | −0.231973 | − | 0.972722i | \(-0.574518\pi\) | ||||
−0.231973 | + | 0.972722i | \(0.574518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.4891 | −0.765942 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.11684 | 0.206872 | 0.103436 | − | 0.994636i | \(-0.467016\pi\) | ||||
0.103436 | + | 0.994636i | \(0.467016\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.96143 | 0.261779 | 0.130889 | − | 0.991397i | \(-0.458217\pi\) | ||||
0.130889 | + | 0.991397i | \(0.458217\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 26.5330 | 1.74574 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.1168 | 1.84200 | 0.920998 | − | 0.389568i | \(-0.127376\pi\) | ||||
0.920998 | + | 0.389568i | \(0.127376\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.37228 | 0.480915 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −32.1716 | −2.08977 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.1012 | −1.55898 | −0.779490 | − | 0.626415i | \(-0.784522\pi\) | ||||
−0.779490 | + | 0.626415i | \(0.784522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.0217 | −1.34855 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.16915 | 0.202469 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.10891 | −0.261444 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.9783 | −1.20270 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.8614 | −0.685566 | −0.342783 | − | 0.939415i | \(-0.611370\pi\) | ||||
−0.342783 | + | 0.939415i | \(0.611370\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.51278 | 0.535194 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.39764 | 0.588503 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 18.2337 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.5109 | 0.653114 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.7359 | −0.974030 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.1561 | 1.48953 | 0.744766 | − | 0.667326i | \(-0.232561\pi\) | ||||
0.744766 | + | 0.667326i | \(0.232561\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.48913 | −0.460053 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.7663 | −1.08728 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.51278 | 0.519033 | 0.259517 | − | 0.965739i | \(-0.416437\pi\) | ||||
0.259517 | + | 0.965739i | \(0.416437\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.57301 | −0.460028 | −0.230014 | − | 0.973187i | \(-0.573877\pi\) | ||||
−0.230014 | + | 0.973187i | \(0.573877\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −32.3288 | −1.95663 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.7446 | −0.889131 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 13.0641 | 0.784947 | 0.392473 | − | 0.919763i | \(-0.371619\pi\) | ||||
0.392473 | + | 0.919763i | \(0.371619\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.10268 | 0.544963 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.2337 | 1.68428 | 0.842140 | − | 0.539258i | \(-0.181295\pi\) | ||||
0.842140 | + | 0.539258i | \(0.181295\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.3723 | −1.38934 | −0.694669 | − | 0.719330i | \(-0.744449\pi\) | ||||
−0.694669 | + | 0.719330i | \(0.744449\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.87953 | 0.111334 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 20.7446 | 1.21607 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −28.0627 | −1.63944 | −0.819719 | − | 0.572765i | \(-0.805871\pi\) | ||||
−0.819719 | + | 0.572765i | \(0.805871\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410 | 0.201688 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.97825 | −0.172816 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.3723 | −0.599845 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 31.0843 | 1.79167 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 32.8713 | 1.88841 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.60597 | −0.206477 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.7446 | −1.52639 | −0.763196 | − | 0.646167i | \(-0.776371\pi\) | ||||
−0.763196 | + | 0.646167i | \(0.776371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.6766 | −0.721146 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.2164 | 1.31648 | 0.658240 | − | 0.752808i | \(-0.271301\pi\) | ||||
0.658240 | + | 0.752808i | \(0.271301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −21.1168 | −1.19359 | −0.596797 | − | 0.802392i | \(-0.703560\pi\) | ||||
−0.596797 | + | 0.802392i | \(0.703560\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.90491 | 0.389047 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.2603 | 1.02560 | 0.512800 | − | 0.858508i | \(-0.328608\pi\) | ||||
0.512800 | + | 0.858508i | \(0.328608\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.1947 | −1.13069 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0951 | 1.00997 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.00000 | 0.278207 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 17.9653 | 0.996537 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −29.9422 | −1.65581 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.8614 | 1.70144 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.8614 | −0.981752 | −0.490876 | − | 0.871230i | \(-0.663323\pi\) | ||||
−0.490876 | + | 0.871230i | \(0.663323\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.32763 | 0.456351 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.63325 | 0.362413 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.7446 | −1.34792 | −0.673961 | − | 0.738767i | \(-0.735408\pi\) | ||||
−0.673961 | + | 0.738767i | \(0.735408\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.72281 | −0.419446 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 11.6819 | 0.632612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −9.94987 | −0.537243 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.74456 | 0.255439 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.8832 | 1.06738 | 0.533692 | − | 0.845679i | \(-0.320804\pi\) | ||||
0.533692 | + | 0.845679i | \(0.320804\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1615 | 1.23981 | 0.619903 | − | 0.784679i | \(-0.287172\pi\) | ||||
0.619903 | + | 0.784679i | \(0.287172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.62881 | 0.193692 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1168 | 1.12394 | 0.561968 | − | 0.827159i | \(-0.310044\pi\) | ||||
0.561968 | + | 0.827159i | \(0.310044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.25544 | −0.278930 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 39.3398 | 2.08208 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.5831 | −0.875224 | −0.437612 | − | 0.899164i | \(-0.644176\pi\) | ||||
−0.437612 | + | 0.899164i | \(0.644176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.883156 | 0.0463537 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.4795 | 0.600867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 30.5870 | 1.59663 | 0.798314 | − | 0.602241i | \(-0.205725\pi\) | ||||
0.798314 | + | 0.602241i | \(0.205725\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.3505 | −1.62764 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.8935 | −1.28894 | −0.644469 | − | 0.764631i | \(-0.722921\pi\) | ||||
−0.644469 | + | 0.764631i | \(0.722921\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.6155 | −0.909659 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 24.6060 | 1.26727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.3505 | −0.788504 | −0.394252 | − | 0.919002i | \(-0.628996\pi\) | ||||
−0.394252 | + | 0.919002i | \(0.628996\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 44.8482 | 2.29764 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.92287 | 0.404840 | 0.202420 | − | 0.979299i | \(-0.435119\pi\) | ||||
0.202420 | + | 0.979299i | \(0.435119\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.86141 | 0.451619 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.6277 | 1.25190 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.1793 | 0.617513 | 0.308756 | − | 0.951141i | \(-0.400087\pi\) | ||||
0.308756 | + | 0.951141i | \(0.400087\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.6217 | 0.638306 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.25544 | 0.164215 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.7446 | −0.540618 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.30506 | −0.467008 | −0.233504 | − | 0.972356i | \(-0.575019\pi\) | ||||
−0.233504 | + | 0.972356i | \(0.575019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.86797 | 0.393891 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −21.7228 | −1.08479 | −0.542393 | − | 0.840125i | \(-0.682482\pi\) | ||||
−0.542393 | + | 0.840125i | \(0.682482\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.2337 | −0.709030 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.90564 | −0.392834 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.6873 | 0.529748 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.00000 | 0.296681 | 0.148340 | − | 0.988936i | \(-0.452607\pi\) | ||||
0.148340 | + | 0.988936i | \(0.452607\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8614 | −0.585080 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.5012 | 0.713558 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.33830 | −0.311135 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.2337 | 1.08879 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.2337 | −1.67243 | −0.836213 | − | 0.548405i | \(-0.815235\pi\) | ||||
−0.836213 | + | 0.548405i | \(0.815235\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.9855 | −1.75383 | −0.876914 | − | 0.480647i | \(-0.840402\pi\) | ||||
−0.876914 | + | 0.480647i | \(0.840402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.4511 | 1.18885 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −21.8614 | −1.06043 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.0951 | −0.730503 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −32.8713 | −1.58704 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.3870 | 0.548491 | 0.274246 | − | 0.961660i | \(-0.411572\pi\) | ||||
0.274246 | + | 0.961660i | \(0.411572\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 21.4891 | 1.03270 | 0.516351 | − | 0.856377i | \(-0.327290\pi\) | ||||
0.516351 | + | 0.856377i | \(0.327290\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −11.2554 | −0.539657 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.52434 | 0.120755 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.92820 | 0.330665 | 0.165333 | − | 0.986238i | \(-0.447130\pi\) | ||||
0.165333 | + | 0.986238i | \(0.447130\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.5109 | 0.500518 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3505 | −0.491769 | −0.245884 | − | 0.969299i | \(-0.579078\pi\) | ||||
−0.245884 | + | 0.969299i | \(0.579078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.93354 | −0.281277 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −50.4868 | −2.38794 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.5109 | 0.684811 | 0.342405 | − | 0.939552i | \(-0.388758\pi\) | ||||
0.342405 | + | 0.939552i | \(0.388758\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −53.0660 | −2.49326 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.7971 | −0.506174 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −31.0000 | −1.45012 | −0.725059 | − | 0.688686i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688686i | \(0.758188\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.41578 | −0.206111 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.1846 | 0.520918 | 0.260459 | − | 0.965485i | \(-0.416126\pi\) | ||||
0.260459 | + | 0.965485i | \(0.416126\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.31040 | 0.386217 | 0.193108 | − | 0.981177i | \(-0.438143\pi\) | ||||
0.193108 | + | 0.981177i | \(0.438143\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.51087 | 0.301935 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 28.1168 | 1.30109 | 0.650546 | − | 0.759467i | \(-0.274540\pi\) | ||||
0.650546 | + | 0.759467i | \(0.274540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 27.7677 | 1.28219 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.05934 | 0.140967 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 31.6060 | 1.45324 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.37228 | −0.200614 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.8386 | −1.13728 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.1514 | 0.646592 | 0.323296 | − | 0.946298i | \(-0.395209\pi\) | ||||
0.323296 | + | 0.946298i | \(0.395209\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.0217 | −0.593741 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.8614 | 0.903725 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.92820 | 0.314594 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.2974 | −1.32759 | −0.663796 | − | 0.747914i | \(-0.731056\pi\) | ||||
−0.663796 | + | 0.747914i | \(0.731056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.76631 | −0.0798754 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.9783 | −0.675959 | −0.337979 | − | 0.941153i | \(-0.609743\pi\) | ||||
−0.337979 | + | 0.941153i | \(0.609743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −29.9422 | −1.34853 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.02078 | 0.315560 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.0000 | −0.986835 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.37228 | 0.0614317 | 0.0307159 | − | 0.999528i | \(-0.490221\pi\) | ||||
0.0307159 | + | 0.999528i | \(0.490221\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 47.9075 | 2.14035 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.4294 | 0.955491 | 0.477745 | − | 0.878498i | \(-0.341454\pi\) | ||||
0.477745 | + | 0.878498i | \(0.341454\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.9783 | 0.488526 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.21194 | 0.409117 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −24.5437 | −1.08788 | −0.543939 | − | 0.839124i | \(-0.683068\pi\) | ||||
−0.543939 | + | 0.839124i | \(0.683068\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.0550 | 2.12583 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.883156 | −0.0389923 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.23369 | −0.186559 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 31.3793 | 1.38006 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2772 | −0.495013 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 40.2337 | 1.76267 | 0.881335 | − | 0.472492i | \(-0.156645\pi\) | ||||
0.881335 | + | 0.472492i | \(0.156645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.6277 | −0.858260 | −0.429130 | − | 0.903243i | \(-0.641180\pi\) | ||||
−0.429130 | + | 0.903243i | \(0.641180\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −34.4010 | −1.50138 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.3205 | 0.754493 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6277 | −0.722944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.4891 | 0.498586 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.04334 | 0.261276 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −54.5109 | −2.35232 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.4891 | 0.581018 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.5538 | −1.44259 | −0.721295 | − | 0.692628i | \(-0.756453\pi\) | ||||
−0.721295 | + | 0.692628i | \(0.756453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 27.7128 | 1.18927 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −25.4891 | −1.08984 | −0.544918 | − | 0.838489i | \(-0.683439\pi\) | ||||
−0.544918 | + | 0.838489i | \(0.683439\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.9596 | −0.510425 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.98844 | −0.255116 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.9783 | −1.91267 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.95650 | 0.252839 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 28.5051 | 1.20780 | 0.603900 | − | 0.797060i | \(-0.293613\pi\) | ||||
0.603900 | + | 0.797060i | \(0.293613\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.5099 | −1.62879 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.0000 | 1.68880 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.48913 | 0.399919 | 0.199959 | − | 0.979804i | \(-0.435919\pi\) | ||||
0.199959 | + | 0.979804i | \(0.435919\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.57924 | −0.108509 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −33.0941 | −1.38982 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −18.9783 | −0.795610 | −0.397805 | − | 0.917470i | \(-0.630228\pi\) | ||||
−0.397805 | + | 0.917470i | \(0.630228\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.97825 | −0.124636 | −0.0623180 | − | 0.998056i | \(-0.519849\pi\) | ||||
−0.0623180 | + | 0.998056i | \(0.519849\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.5214 | −1.35860 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.0371 | −0.460280 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.4674 | −1.47653 | −0.738263 | − | 0.674513i | \(-0.764354\pi\) | ||||
−0.738263 | + | 0.674513i | \(0.764354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 34.9783 | 1.45365 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −26.5330 | −1.10077 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.8766 | −1.32020 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.55437 | −0.353680 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.13859 | −0.129544 | −0.0647718 | − | 0.997900i | \(-0.520632\pi\) | ||||
−0.0647718 | + | 0.997900i | \(0.520632\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.46410 | 0.142736 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.9075 | −1.97065 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.9783 | −1.68278 | −0.841388 | − | 0.540432i | \(-0.818261\pi\) | ||||
−0.841388 | + | 0.540432i | \(0.818261\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1386 | 0.538630 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 16.0858 | 0.658348 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.0564 | 1.35065 | 0.675325 | − | 0.737520i | \(-0.264003\pi\) | ||||
0.675325 | + | 0.737520i | \(0.264003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.4674 | −1.89544 | −0.947722 | − | 0.319097i | \(-0.896620\pi\) | ||||
−0.947722 | + | 0.319097i | \(0.896620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.0000 | 0.895909 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.294954 | 0.0119916 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.62792 | 0.309608 | 0.154804 | − | 0.987945i | \(-0.450525\pi\) | ||||
0.154804 | + | 0.987945i | \(0.450525\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −47.1168 | −1.90927 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.2337 | −1.54677 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1383 | 1.41922 | 0.709612 | − | 0.704592i | \(-0.248870\pi\) | ||||
0.709612 | + | 0.704592i | \(0.248870\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.8397 | −1.36233 | −0.681167 | − | 0.732128i | \(-0.738527\pi\) | ||||
−0.681167 | + | 0.732128i | \(0.738527\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.2337 | 0.732874 | 0.366437 | − | 0.930443i | \(-0.380578\pi\) | ||||
0.366437 | + | 0.930443i | \(0.380578\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.22938 | −0.0894621 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.8386 | −0.995138 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.9783 | 0.639130 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.00000 | 0.319489 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.8457 | 0.631811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8843 | −0.473107 | −0.236553 | − | 0.971619i | \(-0.576018\pi\) | ||||
−0.236553 | + | 0.971619i | \(0.576018\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −19.8614 | −0.789420 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.9783 | 0.594394 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.4356 | −0.651204 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −17.4303 | −0.689533 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.9783 | 1.38156 | 0.690779 | − | 0.723066i | \(-0.257268\pi\) | ||||
0.690779 | + | 0.723066i | \(0.257268\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30.6277 | 1.20784 | 0.603920 | − | 0.797045i | \(-0.293605\pi\) | ||||
0.603920 | + | 0.797045i | \(0.293605\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 17.6155 | 0.693608 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.5831 | −0.651950 | −0.325975 | − | 0.945378i | \(-0.605693\pi\) | ||||
−0.325975 | + | 0.945378i | \(0.605693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.7446 | 0.578775 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.2554 | 1.06822 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.5200 | 1.85960 | 0.929800 | − | 0.368064i | \(-0.119979\pi\) | ||||
0.929800 | + | 0.368064i | \(0.119979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.08724 | 0.0424820 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 38.0733 | 1.48538 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.1386 | −0.706579 | −0.353290 | − | 0.935514i | \(-0.614937\pi\) | ||||
−0.353290 | + | 0.935514i | \(0.614937\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.2549 | 0.748930 | 0.374465 | − | 0.927241i | \(-0.377826\pi\) | ||||
0.374465 | + | 0.927241i | \(0.377826\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −48.7375 | −1.89281 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.62772 | 0.101899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.1168 | −0.585327 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.4356 | −0.635439 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.3484 | −0.592519 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.25544 | 0.202582 | 0.101291 | − | 0.994857i | \(-0.467703\pi\) | ||||
0.101291 | + | 0.994857i | \(0.467703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.86141 | 0.148626 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.10891 | −0.157918 | −0.0789592 | − | 0.996878i | \(-0.525160\pi\) | ||||
−0.0789592 | + | 0.996878i | \(0.525160\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.0024 | 1.11301 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.39403 | 0.283340 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.0000 | −0.459167 | −0.229584 | − | 0.973289i | \(-0.573736\pi\) | ||||
−0.229584 | + | 0.973289i | \(0.573736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.96143 | −0.151359 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.39764 | 0.358542 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.8397 | 1.47967 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.8614 | −0.413187 | −0.206594 | − | 0.978427i | \(-0.566238\pi\) | ||||
−0.206594 | + | 0.978427i | \(0.566238\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 29.3900 | 1.11643 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.42554 | 0.281667 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 66.7011 | 2.52287 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7128 | 1.04670 | 0.523349 | − | 0.852118i | \(-0.324682\pi\) | ||||
0.523349 | + | 0.852118i | \(0.324682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.16915 | 0.119527 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.4891 | 0.658679 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.9565 | 1.72837 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.699713 | −0.0262783 | −0.0131391 | − | 0.999914i | \(-0.504182\pi\) | ||||
−0.0131391 | + | 0.999914i | \(0.504182\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −35.6357 | −1.33644 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.74456 | 0.327486 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.9783 | −0.410563 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −57.1749 | −2.13524 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.89587 | 0.219879 | 0.109939 | − | 0.993938i | \(-0.464934\pi\) | ||||
0.109939 | + | 0.993938i | \(0.464934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.7228 | −0.660032 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 18.9783 | 0.705809 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 26.1831 | 0.972417 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6371 | 0.765389 | 0.382694 | − | 0.923875i | \(-0.374996\pi\) | ||||
0.382694 | + | 0.923875i | \(0.374996\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.9348 | −0.738324 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 46.8614 | 1.73323 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5099 | 1.42239 | 0.711197 | − | 0.702992i | \(-0.248153\pi\) | ||||
0.711197 | + | 0.702992i | \(0.248153\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.51811 | 0.277310 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 28.2337 | 1.04000 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.6060 | 1.01550 | 0.507751 | − | 0.861504i | \(-0.330477\pi\) | ||||
0.507751 | + | 0.861504i | \(0.330477\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.74749 | −0.358083 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.63325 | −0.243350 | −0.121675 | − | 0.992570i | \(-0.538827\pi\) | ||||
−0.121675 | + | 0.992570i | \(0.538827\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.8614 | −0.617754 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −21.0217 | −0.769146 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.2983 | 0.924379 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.2921 | 1.10537 | 0.552686 | − | 0.833389i | \(-0.313603\pi\) | ||||
0.552686 | + | 0.833389i | \(0.313603\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.7663 | −0.938977 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −17.7228 | −0.644999 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.6998 | −1.77002 | −0.885012 | − | 0.465568i | \(-0.845850\pi\) | ||||
−0.885012 | + | 0.465568i | \(0.845850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.1947 | 0.733021 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.0000 | 0.398750 | 0.199375 | − | 0.979923i | \(-0.436109\pi\) | ||||
0.199375 | + | 0.979923i | \(0.436109\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −41.8614 | −1.51548 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 10.4095 | 0.376358 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −17.9653 | −0.648690 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −31.4674 | −1.13474 | −0.567371 | − | 0.823462i | \(-0.692040\pi\) | ||||
−0.567371 | + | 0.823462i | \(0.692040\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 43.2554 | 1.55781 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.9600 | −0.681943 | −0.340972 | − | 0.940074i | \(-0.610756\pi\) | ||||
−0.340972 | + | 0.940074i | \(0.610756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.1460 | −0.544061 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 24.9348 | 0.894529 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.3692 | −0.800432 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.28873 | 0.189004 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.02175 | 0.0364678 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.6060 | 0.734523 | 0.367262 | − | 0.930118i | \(-0.380295\pi\) | ||||
0.367262 | + | 0.930118i | \(0.380295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 57.3052 | 2.04012 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7971 | −0.383899 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.7011 | 0.664094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −17.7663 | −0.630106 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.3321 | −0.401402 | −0.200701 | − | 0.979652i | \(-0.564322\pi\) | ||||
−0.200701 | + | 0.979652i | \(0.564322\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 46.5253 | 1.64595 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.6793 | −0.695334 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 48.8614 | 1.72428 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 6.63325 | 0.233791 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.1947 | 0.710887 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.97825 | −0.280500 | −0.140250 | − | 0.990116i | \(-0.544791\pi\) | ||||
−0.140250 | + | 0.990116i | \(0.544791\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.138593 | 0.00486667 | 0.00243334 | − | 0.999997i | \(-0.499225\pi\) | ||||
0.00243334 | + | 0.999997i | \(0.499225\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.9653 | −0.630071 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.589907 | −0.0206636 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.37228 | 0.327895 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.8098 | −1.25130 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.0179 | −1.29193 | −0.645966 | − | 0.763366i | \(-0.723545\pi\) | ||||
−0.645966 | + | 0.763366i | \(0.723545\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2704 | −0.950586 | −0.475293 | − | 0.879828i | \(-0.657658\pi\) | ||||
−0.475293 | + | 0.879828i | \(0.657658\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.9783 | −1.21779 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.3505 | −0.394697 | −0.197348 | − | 0.980333i | \(-0.563233\pi\) | ||||
−0.197348 | + | 0.980333i | \(0.563233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1113 | 1.15000 | 0.575002 | − | 0.818152i | \(-0.305001\pi\) | ||||
0.575002 | + | 0.818152i | \(0.305001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.9918 | 1.07509 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.0000 | 0.692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000 | 0.553703 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.05934 | −0.105746 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.7306 | −0.577604 | −0.288802 | − | 0.957389i | \(-0.593257\pi\) | ||||
−0.288802 | + | 0.957389i | \(0.593257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.86141 | 0.236600 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 66.9783 | 2.30685 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.07657 | 0.105837 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.23472 | 0.0424254 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −55.4456 | −1.90289 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.00000 | 0.274236 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.6766 | −0.434038 | −0.217019 | − | 0.976167i | \(-0.569633\pi\) | ||||
−0.217019 | + | 0.976167i | \(0.569633\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.08191 | 0.0711997 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.2337 | 0.417895 | 0.208947 | − | 0.977927i | \(-0.432996\pi\) | ||||
0.208947 | + | 0.977927i | \(0.432996\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.6060 | 1.07838 | 0.539191 | − | 0.842184i | \(-0.318730\pi\) | ||||
0.539191 | + | 0.842184i | \(0.318730\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 49.1971 | 1.67469 | 0.837345 | − | 0.546675i | \(-0.184107\pi\) | ||||
0.837345 | + | 0.546675i | \(0.184107\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.76631 | −0.128058 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.9783 | 0.644535 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.7330 | −1.55139 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.4010 | −1.16563 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 22.9783 | 0.777696 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −24.6277 | −0.832569 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.5986 | −0.830635 | −0.415317 | − | 0.909677i | \(-0.636329\pi\) | ||||
−0.415317 | + | 0.909677i | \(0.636329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −66.5725 | −2.24544 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37228 | 0.0462333 | 0.0231167 | − | 0.999733i | \(-0.492641\pi\) | ||||
0.0231167 | + | 0.999733i | \(0.492641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.1168 | −1.21543 | −0.607714 | − | 0.794156i | \(-0.707913\pi\) | ||||
−0.607714 | + | 0.794156i | \(0.707913\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.21782 | 0.276239 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.0333 | −1.51207 | −0.756035 | − | 0.654531i | \(-0.772866\pi\) | ||||
−0.756035 | + | 0.654531i | \(0.772866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 62.7011 | 2.10293 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −33.6495 | −1.12730 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.30506 | 0.311382 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.2054 | −0.608538 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.6060 | −0.821569 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.7446 | −0.691870 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −47.2627 | −1.57455 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 73.7408 | 2.45394 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.25544 | 0.307661 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.1386 | −0.602282 | −0.301141 | − | 0.953580i | \(-0.597368\pi\) | ||||
−0.301141 | + | 0.953580i | \(0.597368\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.4107 | 1.20767 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.81306 | 0.258858 | 0.129429 | − | 0.991589i | \(-0.458686\pi\) | ||||
0.129429 | + | 0.991589i | \(0.458686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.9783 | −0.892850 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.55437 | −0.282799 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.55134 | 0.150299 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.7677 | −0.915972 | −0.457986 | − | 0.888959i | \(-0.651429\pi\) | ||||
−0.457986 | + | 0.888959i | \(0.651429\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −63.4456 | −2.09060 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.2554 | 0.897124 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.8564 | −0.455596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.0416 | −0.461185 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.1168 | −1.48024 | −0.740118 | − | 0.672477i | \(-0.765230\pi\) | ||||
−0.740118 | + | 0.672477i | \(0.765230\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.00000 | 0.131095 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 55.0758 | 1.80310 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 13.3591 | 0.436888 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9783 | −0.783335 | −0.391668 | − | 0.920107i | \(-0.628102\pi\) | ||||
−0.391668 | + | 0.920107i | \(0.628102\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −50.0951 | −1.63479 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.69349 | −0.185602 | −0.0928012 | − | 0.995685i | \(-0.529582\pi\) | ||||
−0.0928012 | + | 0.995685i | \(0.529582\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.32069 | −0.0754919 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 37.2119 | 1.20923 | 0.604613 | − | 0.796520i | \(-0.293328\pi\) | ||||
0.604613 | + | 0.796520i | \(0.293328\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −59.5345 | −1.93257 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 43.3185 | 1.40470 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.23369 | 0.266715 | 0.133358 | − | 0.991068i | \(-0.457424\pi\) | ||||
0.133358 | + | 0.991068i | \(0.457424\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.8614 | −0.351467 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.9075 | −1.54863 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.5831 | −0.535497 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 20.0435 | 0.645893 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.6819 | 0.376054 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8642 | 1.34626 | 0.673131 | − | 0.739524i | \(-0.264949\pi\) | ||||
0.673131 | + | 0.739524i | \(0.264949\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 11.8614 | 0.381043 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | 0.128366 | 0.0641831 | − | 0.997938i | \(-0.479556\pi\) | ||||
0.0641831 | + | 0.997938i | \(0.479556\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.0843 | 0.996518 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 42.6188 | 1.36489 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.51087 | 0.144316 | 0.0721578 | − | 0.997393i | \(-0.477011\pi\) | ||||
0.0721578 | + | 0.997393i | \(0.477011\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.2554 | −0.807167 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −33.1662 | −1.05892 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.22849 | 0.198658 | 0.0993290 | − | 0.995055i | \(-0.468330\pi\) | ||||
0.0993290 | + | 0.995055i | \(0.468330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0000 | −0.509802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 73.2119 | 2.33036 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 23.6588 | 0.752306 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.2434 | −0.801882 | −0.400941 | − | 0.916104i | \(-0.631317\pi\) | ||||
−0.400941 | + | 0.916104i | \(0.631317\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.3723 | −1.34464 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.37228 | 0.170313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.2997 | −0.326196 | −0.163098 | − | 0.986610i | \(-0.552149\pi\) | ||||
−0.163098 | + | 0.986610i | \(0.552149\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.79885 | −0.0885518 |
(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 | 4864.2.a.bi.1.4 | 4 | ||
4.3 | odd | 2 | 4864.2.a.bl.1.2 | 4 | |||
8.3 | odd | 2 | inner | 4864.2.a.bi.1.3 | 4 | ||
8.5 | even | 2 | 4864.2.a.bl.1.1 | 4 | |||
16.3 | odd | 4 | 1216.2.c.h.609.3 | ✓ | 8 | ||
16.5 | even | 4 | 1216.2.c.h.609.4 | yes | 8 | ||
16.11 | odd | 4 | 1216.2.c.h.609.6 | yes | 8 | ||
16.13 | even | 4 | 1216.2.c.h.609.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1216.2.c.h.609.3 | ✓ | 8 | 16.3 | odd | 4 | ||
1216.2.c.h.609.4 | yes | 8 | 16.5 | even | 4 | ||
1216.2.c.h.609.5 | yes | 8 | 16.13 | even | 4 | ||
1216.2.c.h.609.6 | yes | 8 | 16.11 | odd | 4 | ||
4864.2.a.bi.1.3 | 4 | 8.3 | odd | 2 | inner | ||
4864.2.a.bi.1.4 | 4 | 1.1 | even | 1 | trivial | ||
4864.2.a.bl.1.1 | 4 | 8.5 | even | 2 | |||
4864.2.a.bl.1.2 | 4 | 4.3 | odd | 2 |