Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5148,2,Mod(1,5148)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5148, 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("5148.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5148.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: | \(41.1069869606\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.90996.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 11x^{2} - 3x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1716) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.309233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5148.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.472388 | −0.211258 | −0.105629 | − | 0.994406i | \(-0.533686\pi\) | ||||
−0.105629 | + | 0.994406i | \(0.533686\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.15838 | −1.94969 | −0.974843 | − | 0.222893i | \(-0.928450\pi\) | ||||
−0.974843 | + | 0.222893i | \(0.928450\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.24924 | −1.51566 | −0.757831 | − | 0.652450i | \(-0.773741\pi\) | ||||
−0.757831 | + | 0.652450i | \(0.773741\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.15838 | −1.18341 | −0.591707 | − | 0.806153i | \(-0.701546\pi\) | ||||
−0.591707 | + | 0.806153i | \(0.701546\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.83207 | 1.42459 | 0.712293 | − | 0.701882i | \(-0.247657\pi\) | ||||
0.712293 | + | 0.701882i | \(0.247657\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.77685 | −0.955370 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.68600 | −1.61295 | −0.806474 | − | 0.591269i | \(-0.798627\pi\) | ||||
−0.806474 | + | 0.591269i | \(0.798627\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52761 | 0.274367 | 0.137184 | − | 0.990546i | \(-0.456195\pi\) | ||||
0.137184 | + | 0.990546i | \(0.456195\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.43676 | 0.411887 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.436758 | −0.0718026 | −0.0359013 | − | 0.999355i | \(-0.511430\pi\) | ||||
−0.0359013 | + | 0.999355i | \(0.511430\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.39532 | 0.686433 | 0.343216 | − | 0.939256i | \(-0.388484\pi\) | ||||
0.343216 | + | 0.939256i | \(0.388484\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.06753 | 0.925290 | 0.462645 | − | 0.886544i | \(-0.346901\pi\) | ||||
0.462645 | + | 0.886544i | \(0.346901\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.0457 | −1.90291 | −0.951454 | − | 0.307791i | \(-0.900410\pi\) | ||||
−0.951454 | + | 0.307791i | \(0.900410\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.6089 | 2.80127 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.05522 | 0.144946 | 0.0724731 | − | 0.997370i | \(-0.476911\pi\) | ||||
0.0724731 | + | 0.997370i | \(0.476911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.472388 | 0.0636968 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.944776 | 0.122999 | 0.0614997 | − | 0.998107i | \(-0.480412\pi\) | ||||
0.0614997 | + | 0.998107i | \(0.480412\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.38153 | 0.689035 | 0.344517 | − | 0.938780i | \(-0.388043\pi\) | ||||
0.344517 | + | 0.938780i | \(0.388043\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.472388 | −0.0585925 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13.0813 | 1.59814 | 0.799068 | − | 0.601240i | \(-0.205327\pi\) | ||||
0.799068 | + | 0.601240i | \(0.205327\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.67369 | −0.435987 | −0.217993 | − | 0.975950i | \(-0.569951\pi\) | ||||
−0.217993 | + | 0.975950i | \(0.569951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.21361 | −0.493166 | −0.246583 | − | 0.969122i | \(-0.579308\pi\) | ||||
−0.246583 | + | 0.969122i | \(0.579308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.15838 | 0.587852 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.12275 | 1.02639 | 0.513195 | − | 0.858272i | \(-0.328462\pi\) | ||||
0.513195 | + | 0.858272i | \(0.328462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.292156 | 0.0320683 | 0.0160341 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160341 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.95206 | 0.320196 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9091 | −1.15637 | −0.578184 | − | 0.815907i | \(-0.696238\pi\) | ||||
−0.578184 | + | 0.815907i | \(0.696238\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.15838 | −0.540746 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.43676 | 0.250006 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.3072 | −1.85882 | −0.929409 | − | 0.369053i | \(-0.879682\pi\) | ||||
−0.929409 | + | 0.369053i | \(0.879682\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.0675 | −1.20076 | −0.600382 | − | 0.799713i | \(-0.704985\pi\) | ||||
−0.600382 | + | 0.799713i | \(0.704985\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4272 | 1.22449 | 0.612245 | − | 0.790668i | \(-0.290267\pi\) | ||||
0.612245 | + | 0.790668i | \(0.290267\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.05522 | −0.295360 | −0.147680 | − | 0.989035i | \(-0.547181\pi\) | ||||
−0.147680 | + | 0.989035i | \(0.547181\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1032 | 0.967707 | 0.483854 | − | 0.875149i | \(-0.339237\pi\) | ||||
0.483854 | + | 0.875149i | \(0.339237\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.26154 | 0.871253 | 0.435626 | − | 0.900128i | \(-0.356527\pi\) | ||||
0.435626 | + | 0.900128i | \(0.356527\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.22739 | −0.300956 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 32.2360 | 2.95507 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.61847 | 0.413088 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.5755 | 1.11590 | 0.557950 | − | 0.829875i | \(-0.311588\pi\) | ||||
0.557950 | + | 0.829875i | \(0.311588\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.55370 | −0.310488 | −0.155244 | − | 0.987876i | \(-0.549616\pi\) | ||||
−0.155244 | + | 0.987876i | \(0.549616\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.6089 | 2.30729 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 21.7244 | 1.85604 | 0.928020 | − | 0.372531i | \(-0.121510\pi\) | ||||
0.928020 | + | 0.372531i | \(0.121510\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.74122 | −0.486964 | −0.243482 | − | 0.969905i | \(-0.578290\pi\) | ||||
−0.243482 | + | 0.969905i | \(0.578290\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.00000 | −0.0836242 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.10316 | 0.340749 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3953 | −1.01546 | −0.507732 | − | 0.861515i | \(-0.669516\pi\) | ||||
−0.507732 | + | 0.861515i | \(0.669516\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.03190 | −0.490869 | −0.245435 | − | 0.969413i | \(-0.578931\pi\) | ||||
−0.245435 | + | 0.969413i | \(0.578931\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.721626 | −0.0579624 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.0936 | −1.60365 | −0.801823 | − | 0.597562i | \(-0.796136\pi\) | ||||
−0.801823 | + | 0.597562i | \(0.796136\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −35.2425 | −2.77749 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5733 | 1.14147 | 0.570734 | − | 0.821135i | \(-0.306659\pi\) | ||||
0.570734 | + | 0.821135i | \(0.306659\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.31677 | 0.179277 | 0.0896384 | − | 0.995974i | \(-0.471429\pi\) | ||||
0.0896384 | + | 0.995974i | \(0.471429\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −17.7317 | −1.34811 | −0.674057 | − | 0.738679i | \(-0.735450\pi\) | ||||
−0.674057 | + | 0.738679i | \(0.735450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 24.6408 | 1.86267 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.1242 | 0.831464 | 0.415732 | − | 0.909487i | \(-0.363525\pi\) | ||||
0.415732 | + | 0.909487i | \(0.363525\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0936 | 1.79086 | 0.895432 | − | 0.445198i | \(-0.146867\pi\) | ||||
0.895432 | + | 0.445198i | \(0.146867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.206319 | 0.0151689 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.24924 | 0.456990 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9448 | 1.22608 | 0.613040 | − | 0.790052i | \(-0.289946\pi\) | ||||
0.613040 | + | 0.790052i | \(0.289946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.22964 | 0.664364 | 0.332182 | − | 0.943215i | \(-0.392215\pi\) | ||||
0.332182 | + | 0.943215i | \(0.392215\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.78639 | 0.127275 | 0.0636376 | − | 0.997973i | \(-0.479730\pi\) | ||||
0.0636376 | + | 0.997973i | \(0.479730\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.0798 | 1.21076 | 0.605379 | − | 0.795938i | \(-0.293022\pi\) | ||||
0.605379 | + | 0.795938i | \(0.293022\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 44.8057 | 3.14474 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.07629 | −0.145015 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.15838 | 0.356813 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.541393 | −0.0372711 | −0.0186355 | − | 0.999826i | \(-0.505932\pi\) | ||||
−0.0186355 | + | 0.999826i | \(0.505932\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.86623 | −0.195475 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.88001 | −0.534930 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.24924 | −0.420369 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.1059 | 1.01157 | 0.505784 | − | 0.862660i | \(-0.331203\pi\) | ||||
0.505784 | + | 0.862660i | \(0.331203\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 30.0595 | 1.99512 | 0.997558 | − | 0.0698384i | \(-0.0222484\pi\) | ||||
0.997558 | + | 0.0698384i | \(0.0222484\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.1722 | −0.936523 | −0.468262 | − | 0.883590i | \(-0.655119\pi\) | ||||
−0.468262 | + | 0.883590i | \(0.655119\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9782 | −0.850227 | −0.425113 | − | 0.905140i | \(-0.639766\pi\) | ||||
−0.425113 | + | 0.905140i | \(0.639766\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.16262 | 0.402005 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.9490 | −1.29039 | −0.645197 | − | 0.764016i | \(-0.723225\pi\) | ||||
−0.645197 | + | 0.764016i | \(0.723225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.2455 | −1.30413 | −0.652064 | − | 0.758164i | \(-0.726097\pi\) | ||||
−0.652064 | + | 0.758164i | \(0.726097\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.26302 | −0.591793 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.15838 | −0.328220 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.6888 | −0.990266 | −0.495133 | − | 0.868817i | \(-0.664881\pi\) | ||||
−0.495133 | + | 0.868817i | \(0.664881\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.83207 | −0.429529 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.76307 | 0.546625 | 0.273313 | − | 0.961925i | \(-0.411881\pi\) | ||||
0.273313 | + | 0.961925i | \(0.411881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.25297 | 0.139993 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.07126 | 0.251045 | 0.125522 | − | 0.992091i | \(-0.459939\pi\) | ||||
0.125522 | + | 0.992091i | \(0.459939\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.498475 | −0.0306211 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.1511 | 0.923779 | 0.461889 | − | 0.886938i | \(-0.347172\pi\) | ||||
0.461889 | + | 0.886938i | \(0.347172\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.8778 | 1.81494 | 0.907472 | − | 0.420112i | \(-0.138009\pi\) | ||||
0.907472 | + | 0.420112i | \(0.138009\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.77685 | 0.288055 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.4272 | 0.626511 | 0.313255 | − | 0.949669i | \(-0.398580\pi\) | ||||
0.313255 | + | 0.949669i | \(0.398580\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.21361 | −0.132053 | −0.0660264 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660264 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.31400 | 0.0781094 | 0.0390547 | − | 0.999237i | \(-0.487565\pi\) | ||||
0.0390547 | + | 0.999237i | \(0.487565\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.6727 | −1.33833 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.0530 | 1.29723 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 13.7864 | 0.805410 | 0.402705 | − | 0.915330i | \(-0.368070\pi\) | ||||
0.402705 | + | 0.915330i | \(0.368070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.446301 | −0.0259846 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.83207 | 0.395109 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.2986 | −1.80402 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.54217 | −0.145564 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.4752 | −1.11151 | −0.555753 | − | 0.831348i | \(-0.687570\pi\) | ||||
−0.555753 | + | 0.831348i | \(0.687570\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.59514 | −0.317271 | −0.158636 | − | 0.987337i | \(-0.550710\pi\) | ||||
−0.158636 | + | 0.987337i | \(0.550710\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.48469 | −0.310013 | −0.155007 | − | 0.987913i | \(-0.549540\pi\) | ||||
−0.155007 | + | 0.987913i | \(0.549540\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.9644 | 1.00898 | 0.504490 | − | 0.863418i | \(-0.331681\pi\) | ||||
0.504490 | + | 0.863418i | \(0.331681\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.68600 | 0.486322 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 32.2360 | 1.79366 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.77685 | −0.264972 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 67.2946 | 3.71007 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.8348 | −1.42001 | −0.710006 | − | 0.704196i | \(-0.751308\pi\) | ||||
−0.710006 | + | 0.704196i | \(0.751308\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.17945 | −0.337620 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.94478 | −0.378306 | −0.189153 | − | 0.981948i | \(-0.560574\pi\) | ||||
−0.189153 | + | 0.981948i | \(0.560574\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.52761 | −0.0827248 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −65.0417 | −3.51192 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0095 | 0.537340 | 0.268670 | − | 0.963232i | \(-0.413416\pi\) | ||||
0.268670 | + | 0.963232i | \(0.413416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.4824 | 1.57816 | 0.789079 | − | 0.614291i | \(-0.210558\pi\) | ||||
0.789079 | + | 0.614291i | \(0.210558\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.76454 | −0.253591 | −0.126796 | − | 0.991929i | \(-0.540469\pi\) | ||||
−0.126796 | + | 0.991929i | \(0.540469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.73541 | 0.0921058 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.37928 | −0.178352 | −0.0891758 | − | 0.996016i | \(-0.528423\pi\) | ||||
−0.0891758 | + | 0.996016i | \(0.528423\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.60892 | 0.400470 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.99046 | 0.104185 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −24.9257 | −1.30111 | −0.650555 | − | 0.759459i | \(-0.725464\pi\) | ||||
−0.650555 | + | 0.759459i | \(0.725464\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.44325 | −0.282600 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −15.8183 | −0.819040 | −0.409520 | − | 0.912301i | \(-0.634304\pi\) | ||||
−0.409520 | + | 0.912301i | \(0.634304\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.68600 | −0.447352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.06024 | 0.311294 | 0.155647 | − | 0.987813i | \(-0.450254\pi\) | ||||
0.155647 | + | 0.987813i | \(0.450254\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.4985 | 0.638642 | 0.319321 | − | 0.947647i | \(-0.396545\pi\) | ||||
0.319321 | + | 0.947647i | \(0.396545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.43676 | −0.124189 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.0522 | 1.72651 | 0.863257 | − | 0.504765i | \(-0.168421\pi\) | ||||
0.863257 | + | 0.504765i | \(0.168421\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.6953 | −2.15919 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.30948 | −0.216833 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9598 | −1.15232 | −0.576161 | − | 0.817336i | \(-0.695450\pi\) | ||||
−0.576161 | + | 0.817336i | \(0.695450\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4970 | −0.723946 | −0.361973 | − | 0.932189i | \(-0.617897\pi\) | ||||
−0.361973 | + | 0.932189i | \(0.617897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.52761 | 0.0760958 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.436758 | 0.0216493 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.2251 | 1.44509 | 0.722545 | − | 0.691324i | \(-0.242972\pi\) | ||||
0.722545 | + | 0.691324i | \(0.242972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.87352 | −0.239810 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.138011 | −0.00677469 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.586565 | −0.0286556 | −0.0143278 | − | 0.999897i | \(-0.504561\pi\) | ||||
−0.0143278 | + | 0.999897i | \(0.504561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.0798 | −0.734946 | −0.367473 | − | 0.930034i | \(-0.619777\pi\) | ||||
−0.367473 | + | 0.930034i | \(0.619777\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 29.8517 | 1.44802 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.7600 | −1.34340 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.53766 | 0.314908 | 0.157454 | − | 0.987526i | \(-0.449671\pi\) | ||||
0.157454 | + | 0.987526i | \(0.449671\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 22.8544 | 1.09831 | 0.549157 | − | 0.835719i | \(-0.314949\pi\) | ||||
0.549157 | + | 0.835719i | \(0.314949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −35.2425 | −1.68588 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.43399 | 0.259350 | 0.129675 | − | 0.991557i | \(-0.458607\pi\) | ||||
0.129675 | + | 0.991557i | \(0.458607\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.63354 | −0.410192 | −0.205096 | − | 0.978742i | \(-0.565751\pi\) | ||||
−0.205096 | + | 0.978742i | \(0.565751\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.15335 | 0.244292 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.4418 | −0.728742 | −0.364371 | − | 0.931254i | \(-0.618716\pi\) | ||||
−0.364371 | + | 0.931254i | \(0.618716\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.39532 | −0.206967 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.43676 | 0.114237 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.33585 | −0.202823 | −0.101411 | − | 0.994845i | \(-0.532336\pi\) | ||||
−0.101411 | + | 0.994845i | \(0.532336\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.1859 | −0.800429 | −0.400215 | − | 0.916421i | \(-0.631064\pi\) | ||||
−0.400215 | + | 0.916421i | \(0.631064\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.1461 | 0.657424 | 0.328712 | − | 0.944430i | \(-0.393385\pi\) | ||||
0.328712 | + | 0.944430i | \(0.393385\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.7492 | −0.682511 | −0.341256 | − | 0.939971i | \(-0.610852\pi\) | ||||
−0.341256 | + | 0.939971i | \(0.610852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −67.4784 | −3.11586 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.06753 | −0.278985 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.6408 | 1.13060 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.0479 | −0.961705 | −0.480852 | − | 0.876802i | \(-0.659673\pi\) | ||||
−0.480852 | + | 0.876802i | \(0.659673\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.436758 | −0.0199145 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.64811 | 0.392691 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.702827 | −0.0318481 | −0.0159241 | − | 0.999873i | \(-0.505069\pi\) | ||||
−0.0159241 | + | 0.999873i | \(0.505069\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.14755 | −0.0969177 | −0.0484589 | − | 0.998825i | \(-0.515431\pi\) | ||||
−0.0484589 | + | 0.998825i | \(0.515431\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.2809 | 2.44469 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.9503 | 0.850037 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.7585 | −1.42171 | −0.710854 | − | 0.703340i | \(-0.751691\pi\) | ||||
−0.710854 | + | 0.703340i | \(0.751691\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.69181 | −0.120022 | −0.0600109 | − | 0.998198i | \(-0.519114\pi\) | ||||
−0.0600109 | + | 0.998198i | \(0.519114\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.70056 | 0.253671 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −23.8348 | −1.05646 | −0.528230 | − | 0.849101i | \(-0.677144\pi\) | ||||
−0.528230 | + | 0.849101i | \(0.677144\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7354 | 0.961518 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.87047 | −0.258684 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.0457 | 0.573748 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −28.5231 | −1.24962 | −0.624810 | − | 0.780777i | \(-0.714823\pi\) | ||||
−0.624810 | + | 0.780777i | \(0.714823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.5500 | 1.29213 | 0.646065 | − | 0.763282i | \(-0.276413\pi\) | ||||
0.646065 | + | 0.763282i | \(0.276413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.54641 | −0.415848 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6772 | 1.02944 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.39532 | 0.190382 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.44325 | 0.0623972 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −19.6089 | −0.844616 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.8514 | 1.36940 | 0.684699 | − | 0.728826i | \(-0.259934\pi\) | ||||
0.684699 | + | 0.728826i | \(0.259934\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.77261 | −0.204436 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.47663 | −0.319677 | −0.159839 | − | 0.987143i | \(-0.551097\pi\) | ||||
−0.159839 | + | 0.987143i | \(0.551097\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 44.8057 | 1.90879 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −47.0587 | −2.00114 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.7759 | −1.13453 | −0.567265 | − | 0.823535i | \(-0.691999\pi\) | ||||
−0.567265 | + | 0.823535i | \(0.691999\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.06753 | 0.256629 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.809716 | −0.0341255 | −0.0170627 | − | 0.999854i | \(-0.505431\pi\) | ||||
−0.0170627 | + | 0.999854i | \(0.505431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.37504 | −0.184059 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −32.2738 | −1.35299 | −0.676495 | − | 0.736447i | \(-0.736502\pi\) | ||||
−0.676495 | + | 0.736447i | \(0.736502\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.2055 | −0.427089 | −0.213544 | − | 0.976933i | \(-0.568501\pi\) | ||||
−0.213544 | + | 0.976933i | \(0.568501\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −32.6358 | −1.36101 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.73246 | 0.321906 | 0.160953 | − | 0.986962i | \(-0.448543\pi\) | ||||
0.160953 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.50705 | −0.0625230 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05522 | −0.0437029 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.0713 | 0.498234 | 0.249117 | − | 0.968473i | \(-0.419860\pi\) | ||||
0.249117 | + | 0.968473i | \(0.419860\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.88001 | −0.324690 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.1830 | 0.541361 | 0.270680 | − | 0.962669i | \(-0.412751\pi\) | ||||
0.270680 | + | 0.962669i | \(0.412751\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.2279 | −0.624282 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.7962 | 1.74860 | 0.874302 | − | 0.485383i | \(-0.161320\pi\) | ||||
0.874302 | + | 0.485383i | \(0.161320\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.3936 | 1.89243 | 0.946216 | − | 0.323535i | \(-0.104871\pi\) | ||||
0.946216 | + | 0.323535i | \(0.104871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.472388 | −0.0192053 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.9038 | 0.970227 | 0.485114 | − | 0.874451i | \(-0.338778\pi\) | ||||
0.485114 | + | 0.874451i | \(0.338778\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0457 | −0.527772 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.6378 | 0.712383 | 0.356191 | − | 0.934413i | \(-0.384075\pi\) | ||||
0.356191 | + | 0.934413i | \(0.384075\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.5683 | −1.23063 | −0.615316 | − | 0.788281i | \(-0.710972\pi\) | ||||
−0.615316 | + | 0.788281i | \(0.710972\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.38301 | −0.135975 | −0.0679873 | − | 0.997686i | \(-0.521658\pi\) | ||||
−0.0679873 | + | 0.997686i | \(0.521658\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 56.2736 | 2.25455 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.7025 | 0.868102 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.72941 | 0.108829 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.67221 | 0.305426 | 0.152713 | − | 0.988271i | \(-0.451199\pi\) | ||||
0.152713 | + | 0.988271i | \(0.451199\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.94054 | −0.235743 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.6089 | 0.776934 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 39.6451 | 1.56589 | 0.782943 | − | 0.622094i | \(-0.213718\pi\) | ||||
0.782943 | + | 0.622094i | \(0.213718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.6596 | 1.05135 | 0.525676 | − | 0.850685i | \(-0.323812\pi\) | ||||
0.525676 | + | 0.850685i | \(0.323812\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.7992 | 1.64330 | 0.821648 | − | 0.569995i | \(-0.193055\pi\) | ||||
0.821648 | + | 0.569995i | \(0.193055\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.944776 | −0.0370857 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.2862 | 0.754726 | 0.377363 | − | 0.926066i | \(-0.376831\pi\) | ||||
0.377363 | + | 0.926066i | \(0.376831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.67872 | 0.0655932 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.2169 | −1.41081 | −0.705405 | − | 0.708805i | \(-0.749235\pi\) | ||||
−0.705405 | + | 0.708805i | \(0.749235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.84890 | 0.344183 | 0.172091 | − | 0.985081i | \(-0.444948\pi\) | ||||
0.172091 | + | 0.985081i | \(0.444948\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.5697 | −0.487433 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −59.3434 | −2.29778 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.38153 | −0.207752 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.2114 | −0.624902 | −0.312451 | − | 0.949934i | \(-0.601150\pi\) | ||||
−0.312451 | + | 0.949934i | \(0.601150\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 28.0826 | 1.07930 | 0.539651 | − | 0.841889i | \(-0.318556\pi\) | ||||
0.539651 | + | 0.841889i | \(0.318556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 94.4357 | 3.62411 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10.2159 | 0.390899 | 0.195450 | − | 0.980714i | \(-0.437383\pi\) | ||||
0.195450 | + | 0.980714i | \(0.437383\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.2623 | −0.392104 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.05522 | 0.0402008 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.1069 | −0.764902 | −0.382451 | − | 0.923976i | \(-0.624920\pi\) | ||||
−0.382451 | + | 0.923976i | \(0.624920\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.71208 | 0.102875 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.4674 | −1.04040 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.32355 | −0.201068 | −0.100534 | − | 0.994934i | \(-0.532055\pi\) | ||||
−0.100534 | + | 0.994934i | \(0.532055\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.25297 | 0.0849723 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 62.2490 | 2.34111 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.4538 | −1.33150 | −0.665748 | − | 0.746177i | \(-0.731887\pi\) | ||||
−0.665748 | + | 0.746177i | \(0.731887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.4368 | 0.390860 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.472388 | 0.0176663 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0753 | 0.785977 | 0.392989 | − | 0.919543i | \(-0.371441\pi\) | ||||
0.392989 | + | 0.919543i | \(0.371441\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −64.1043 | −2.38737 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 41.4917 | 1.54096 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.2264 | 1.86279 | 0.931397 | − | 0.364004i | \(-0.118590\pi\) | ||||
0.931397 | + | 0.364004i | \(0.118590\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.9174 | −1.40243 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.70656 | −0.0999689 | −0.0499845 | − | 0.998750i | \(-0.515917\pi\) | ||||
−0.0499845 | + | 0.998750i | \(0.515917\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.0813 | −0.481856 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.9796 | 0.698177 | 0.349088 | − | 0.937090i | \(-0.386491\pi\) | ||||
0.349088 | + | 0.937090i | \(0.386491\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.8981 | 0.399814 | 0.199907 | − | 0.979815i | \(-0.435936\pi\) | ||||
0.199907 | + | 0.979815i | \(0.435936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.85540 | 0.214525 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.7600 | 0.575859 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.41864 | 0.124748 | 0.0623740 | − | 0.998053i | \(-0.480133\pi\) | ||||
0.0623740 | + | 0.998053i | \(0.480133\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.84940 | 0.103700 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0745 | −0.875004 | −0.437502 | − | 0.899217i | \(-0.644137\pi\) | ||||
−0.437502 | + | 0.899217i | \(0.644137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.5464 | −0.781057 | −0.390528 | − | 0.920591i | \(-0.627708\pi\) | ||||
−0.390528 | + | 0.920591i | \(0.627708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −52.1160 | −1.88672 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.944776 | 0.0341139 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.8865 | −0.897430 | −0.448715 | − | 0.893675i | \(-0.648118\pi\) | ||||
−0.448715 | + | 0.893675i | \(0.648118\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −50.3057 | −1.80937 | −0.904686 | − | 0.426079i | \(-0.859895\pi\) | ||||
−0.904686 | + | 0.426079i | \(0.859895\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.29717 | −0.262122 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.6727 | −0.812335 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.67369 | 0.131455 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.49198 | 0.338783 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.71513 | −0.132430 | −0.0662151 | − | 0.997805i | \(-0.521092\pi\) | ||||
−0.0662151 | + | 0.997805i | \(0.521092\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.7746 | −1.69867 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.38153 | 0.191104 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.267544 | −0.00947690 | −0.00473845 | − | 0.999989i | \(-0.501508\pi\) | ||||
−0.00473845 | + | 0.999989i | \(0.501508\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 81.5256 | 2.88417 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.21361 | 0.148695 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.6481 | 0.586769 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.4264 | −1.28069 | −0.640343 | − | 0.768089i | \(-0.721208\pi\) | ||||
−0.640343 | + | 0.768089i | \(0.721208\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.36775 | −0.153373 | −0.0766863 | − | 0.997055i | \(-0.524434\pi\) | ||||
−0.0766863 | + | 0.997055i | \(0.524434\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.88425 | −0.241145 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.2986 | −1.09500 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.7833 | 1.63275 | 0.816375 | − | 0.577522i | \(-0.195980\pi\) | ||||
0.816375 | + | 0.577522i | \(0.195980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.8790 | 1.07638 | 0.538188 | − | 0.842825i | \(-0.319109\pi\) | ||||
0.538188 | + | 0.842825i | \(0.319109\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.55804 | −0.0541783 | −0.0270891 | − | 0.999633i | \(-0.508624\pi\) | ||||
−0.0270891 | + | 0.999633i | \(0.508624\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2178 | 1.08424 | 0.542120 | − | 0.840301i | \(-0.317622\pi\) | ||||
0.542120 | + | 0.840301i | \(0.317622\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −122.541 | −4.24579 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.09441 | −0.0378737 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −41.7876 | −1.44267 | −0.721334 | − | 0.692588i | \(-0.756471\pi\) | ||||
−0.721334 | + | 0.692588i | \(0.756471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.4465 | 1.60160 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.472388 | −0.0162506 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.15838 | −0.177244 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.98396 | −0.102289 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.5346 | −1.14820 | −0.574102 | − | 0.818784i | \(-0.694649\pi\) | ||||
−0.574102 | + | 0.818784i | \(0.694649\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.6915 | 1.45831 | 0.729157 | − | 0.684346i | \(-0.239912\pi\) | ||||
0.729157 | + | 0.684346i | \(0.239912\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23.4824 | −0.801211 | −0.400605 | − | 0.916251i | \(-0.631200\pi\) | ||||
−0.400605 | + | 0.916251i | \(0.631200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5145 | 0.596201 | 0.298100 | − | 0.954535i | \(-0.403647\pi\) | ||||
0.298100 | + | 0.954535i | \(0.403647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.37623 | 0.284800 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.12275 | −0.309468 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.0813 | 0.443243 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −23.8238 | −0.805392 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.7514 | −0.700726 | −0.350363 | − | 0.936614i | \(-0.613942\pi\) | ||||
−0.350363 | + | 0.936614i | \(0.613942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −45.1074 | −1.51971 | −0.759853 | − | 0.650094i | \(-0.774729\pi\) | ||||
−0.759853 | + | 0.650094i | \(0.774729\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.2224 | 0.714189 | 0.357095 | − | 0.934068i | \(-0.383767\pi\) | ||||
0.357095 | + | 0.934068i | \(0.383767\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −53.3012 | −1.78968 | −0.894840 | − | 0.446387i | \(-0.852710\pi\) | ||||
−0.894840 | + | 0.446387i | \(0.852710\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −64.8695 | −2.17565 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 67.2946 | 2.25193 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.25495 | −0.175654 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.2688 | −0.442540 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.59435 | −0.219690 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.3815 | −0.378335 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −37.9226 | −1.25920 | −0.629600 | − | 0.776919i | \(-0.716781\pi\) | ||||
−0.629600 | + | 0.776919i | \(0.716781\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.5623 | −1.07884 | −0.539418 | − | 0.842038i | \(-0.681356\pi\) | ||||
−0.539418 | + | 0.842038i | \(0.681356\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.292156 | −0.00966895 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.3313 | 0.605354 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.7879 | −0.388846 | −0.194423 | − | 0.980918i | \(-0.562283\pi\) | ||||
−0.194423 | + | 0.980918i | \(0.562283\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.67369 | −0.120921 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.08633 | 0.0685981 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.0964 | −1.41395 | −0.706973 | − | 0.707240i | \(-0.749940\pi\) | ||||
−0.706973 | + | 0.707240i | \(0.749940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −101.150 | −3.31507 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.95206 | −0.0965428 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.8002 | −0.548838 | −0.274419 | − | 0.961610i | \(-0.588485\pi\) | ||||
−0.274419 | + | 0.961610i | \(0.588485\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.8833 | 1.88694 | 0.943471 | − | 0.331456i | \(-0.107540\pi\) | ||||
0.943471 | + | 0.331456i | \(0.107540\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.0291 | 0.977883 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 13.2711 | 0.431252 | 0.215626 | − | 0.976476i | \(-0.430821\pi\) | ||||
0.215626 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.21361 | −0.136780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.63077 | 0.0528259 | 0.0264129 | − | 0.999651i | \(-0.491592\pi\) | ||||
0.0264129 | + | 0.999651i | \(0.491592\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.00451 | −0.259020 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −112.063 | −3.61869 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.6664 | −0.924723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.35997 | −0.140352 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.6759 | 0.439789 | 0.219894 | − | 0.975524i | \(-0.429429\pi\) | ||||
0.219894 | + | 0.975524i | \(0.429429\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.6750 | 0.727675 | 0.363837 | − | 0.931463i | \(-0.381466\pi\) | ||||
0.363837 | + | 0.931463i | \(0.381466\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.6154 | 0.949427 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.18222 | −0.229779 | −0.114890 | − | 0.993378i | \(-0.536651\pi\) | ||||
−0.114890 | + | 0.993378i | \(0.536651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.9091 | 0.348658 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.6771 | −1.13792 | −0.568962 | − | 0.822364i | \(-0.692655\pi\) | ||||
−0.568962 | + | 0.822364i | \(0.692655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.843870 | −0.0268879 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.4538 | 1.31815 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.0201 | −0.572427 | −0.286214 | − | 0.958166i | \(-0.592397\pi\) | ||||
−0.286214 | + | 0.958166i | \(0.592397\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.06831 | −0.255783 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 56.7962 | 1.79875 | 0.899376 | − | 0.437176i | \(-0.144021\pi\) | ||||
0.899376 | + | 0.437176i | \(0.144021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 5148.2.a.q.1.3 | 4 | ||
3.2 | odd | 2 | 1716.2.a.i.1.2 | ✓ | 4 | ||
12.11 | even | 2 | 6864.2.a.cb.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1716.2.a.i.1.2 | ✓ | 4 | 3.2 | odd | 2 | ||
5148.2.a.q.1.3 | 4 | 1.1 | even | 1 | trivial | ||
6864.2.a.cb.1.2 | 4 | 12.11 | even | 2 |