Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1305,2,Mod(1,1305)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1305, 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("1305.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1305 = 3^{2} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1305.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: | \(10.4204774638\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{7} - x^{6} - 13x^{5} + 12x^{4} + 47x^{3} - 37x^{2} - 35x + 18 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.57501\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1305.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57501 | −1.82081 | −0.910404 | − | 0.413720i | \(-0.864229\pi\) | ||||
−0.910404 | + | 0.413720i | \(0.864229\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.63069 | 2.31534 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.24826 | −0.849762 | −0.424881 | − | 0.905249i | \(-0.639684\pi\) | ||||
−0.424881 | + | 0.905249i | \(0.639684\pi\) | |||||||
\(8\) | −6.77405 | −2.39499 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.57501 | 0.814290 | ||||||||
\(11\) | −3.75744 | −1.13291 | −0.566456 | − | 0.824092i | \(-0.691686\pi\) | ||||
−0.566456 | + | 0.824092i | \(0.691686\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55119 | −0.430223 | −0.215112 | − | 0.976589i | \(-0.569012\pi\) | ||||
−0.215112 | + | 0.976589i | \(0.569012\pi\) | |||||||
\(14\) | 5.78930 | 1.54725 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 8.18188 | 2.04547 | ||||||||
\(17\) | −3.55119 | −0.861291 | −0.430645 | − | 0.902521i | \(-0.641714\pi\) | ||||
−0.430645 | + | 0.902521i | \(0.641714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.18909 | −0.272796 | −0.136398 | − | 0.990654i | \(-0.543553\pi\) | ||||
−0.136398 | + | 0.990654i | \(0.543553\pi\) | |||||||
\(20\) | −4.63069 | −1.03545 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 9.67546 | 2.06281 | ||||||||
\(23\) | −3.67991 | −0.767314 | −0.383657 | − | 0.923476i | \(-0.625336\pi\) | ||||
−0.383657 | + | 0.923476i | \(0.625336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.99434 | 0.783354 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −10.4110 | −1.96749 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.18909 | 0.931988 | 0.465994 | − | 0.884788i | \(-0.345697\pi\) | ||||
0.465994 | + | 0.884788i | \(0.345697\pi\) | |||||||
\(32\) | −7.52034 | −1.32942 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 9.14436 | 1.56825 | ||||||||
\(35\) | 2.24826 | 0.380025 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.969518 | 0.159388 | 0.0796939 | − | 0.996819i | \(-0.474606\pi\) | ||||
0.0796939 | + | 0.996819i | \(0.474606\pi\) | |||||||
\(38\) | 3.06193 | 0.496710 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 6.77405 | 1.07107 | ||||||||
\(41\) | 11.3809 | 1.77740 | 0.888700 | − | 0.458489i | \(-0.151609\pi\) | ||||
0.888700 | + | 0.458489i | \(0.151609\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.884393 | −0.134869 | −0.0674343 | − | 0.997724i | \(-0.521481\pi\) | ||||
−0.0674343 | + | 0.997724i | \(0.521481\pi\) | |||||||
\(44\) | −17.3995 | −2.62308 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.47581 | 1.39713 | ||||||||
\(47\) | 11.2251 | 1.63734 | 0.818672 | − | 0.574262i | \(-0.194711\pi\) | ||||
0.818672 | + | 0.574262i | \(0.194711\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.94533 | −0.277904 | ||||||||
\(50\) | −2.57501 | −0.364162 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.18308 | −0.996115 | ||||||||
\(53\) | −10.6567 | −1.46381 | −0.731906 | − | 0.681406i | \(-0.761369\pi\) | ||||
−0.731906 | + | 0.681406i | \(0.761369\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.75744 | 0.506653 | ||||||||
\(56\) | 15.2298 | 2.03517 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.57501 | −0.338116 | ||||||||
\(59\) | 8.49652 | 1.10615 | 0.553076 | − | 0.833131i | \(-0.313454\pi\) | ||||
0.553076 | + | 0.833131i | \(0.313454\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8743 | −1.39231 | −0.696154 | − | 0.717892i | \(-0.745107\pi\) | ||||
−0.696154 | + | 0.717892i | \(0.745107\pi\) | |||||||
\(62\) | −13.3620 | −1.69697 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.00121 | 0.375151 | ||||||||
\(65\) | 1.55119 | 0.192402 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.05179 | −0.495005 | −0.247502 | − | 0.968887i | \(-0.579610\pi\) | ||||
−0.247502 | + | 0.968887i | \(0.579610\pi\) | |||||||
\(68\) | −16.4445 | −1.99418 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.78930 | −0.691953 | ||||||||
\(71\) | 6.37818 | 0.756951 | 0.378476 | − | 0.925611i | \(-0.376448\pi\) | ||||
0.378476 | + | 0.925611i | \(0.376448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.26017 | −0.381573 | −0.190787 | − | 0.981632i | \(-0.561104\pi\) | ||||
−0.190787 | + | 0.981632i | \(0.561104\pi\) | |||||||
\(74\) | −2.49652 | −0.290215 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.50631 | −0.631617 | ||||||||
\(77\) | 8.44770 | 0.962705 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.32579 | 0.711707 | 0.355854 | − | 0.934542i | \(-0.384190\pi\) | ||||
0.355854 | + | 0.934542i | \(0.384190\pi\) | |||||||
\(80\) | −8.18188 | −0.914762 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −29.3060 | −3.23630 | ||||||||
\(83\) | −9.03930 | −0.992193 | −0.496096 | − | 0.868268i | \(-0.665234\pi\) | ||||
−0.496096 | + | 0.868268i | \(0.665234\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.55119 | 0.385181 | ||||||||
\(86\) | 2.27732 | 0.245570 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 25.4531 | 2.71331 | ||||||||
\(89\) | 1.46717 | 0.155520 | 0.0777599 | − | 0.996972i | \(-0.475223\pi\) | ||||
0.0777599 | + | 0.996972i | \(0.475223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.48748 | 0.365588 | ||||||||
\(92\) | −17.0405 | −1.77660 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −28.9047 | −2.98129 | ||||||||
\(95\) | 1.18909 | 0.121998 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.3993 | 1.25896 | 0.629478 | − | 0.777018i | \(-0.283269\pi\) | ||||
0.629478 | + | 0.777018i | \(0.283269\pi\) | |||||||
\(98\) | 5.00924 | 0.506010 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.63069 | 0.463069 | ||||||||
\(101\) | 3.45196 | 0.343483 | 0.171742 | − | 0.985142i | \(-0.445061\pi\) | ||||
0.171742 | + | 0.985142i | \(0.445061\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.1975 | 1.79306 | 0.896528 | − | 0.442988i | \(-0.146082\pi\) | ||||
0.896528 | + | 0.442988i | \(0.146082\pi\) | |||||||
\(104\) | 10.5078 | 1.03038 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27.4412 | 2.66532 | ||||||||
\(107\) | 8.07919 | 0.781044 | 0.390522 | − | 0.920594i | \(-0.372294\pi\) | ||||
0.390522 | + | 0.920594i | \(0.372294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.0114 | −1.34205 | −0.671026 | − | 0.741434i | \(-0.734146\pi\) | ||||
−0.671026 | + | 0.741434i | \(0.734146\pi\) | |||||||
\(110\) | −9.67546 | −0.922518 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.3950 | −1.73816 | ||||||||
\(113\) | −0.678491 | −0.0638270 | −0.0319135 | − | 0.999491i | \(-0.510160\pi\) | ||||
−0.0319135 | + | 0.999491i | \(0.510160\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.67991 | 0.343153 | ||||||||
\(116\) | 4.63069 | 0.429948 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −21.8786 | −2.01409 | ||||||||
\(119\) | 7.98400 | 0.731892 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.11836 | 0.283488 | ||||||||
\(122\) | 28.0014 | 2.53513 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.0291 | 2.15787 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.39928 | −0.745315 | −0.372658 | − | 0.927969i | \(-0.621553\pi\) | ||||
−0.372658 | + | 0.927969i | \(0.621553\pi\) | |||||||
\(128\) | 7.31254 | 0.646343 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.99434 | −0.350327 | ||||||||
\(131\) | 7.34298 | 0.641559 | 0.320779 | − | 0.947154i | \(-0.396055\pi\) | ||||
0.320779 | + | 0.947154i | \(0.396055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.67339 | 0.231812 | ||||||||
\(134\) | 10.4334 | 0.901308 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24.0559 | 2.06278 | ||||||||
\(137\) | 1.80353 | 0.154086 | 0.0770429 | − | 0.997028i | \(-0.475452\pi\) | ||||
0.0770429 | + | 0.997028i | \(0.475452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.707451 | 0.0600052 | 0.0300026 | − | 0.999550i | \(-0.490448\pi\) | ||||
0.0300026 | + | 0.999550i | \(0.490448\pi\) | |||||||
\(140\) | 10.4110 | 0.879889 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.4239 | −1.37826 | ||||||||
\(143\) | 5.82851 | 0.487405 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.00000 | −0.0830455 | ||||||||
\(146\) | 8.39496 | 0.694772 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.48953 | 0.369037 | ||||||||
\(149\) | 16.9930 | 1.39212 | 0.696062 | − | 0.717982i | \(-0.254934\pi\) | ||||
0.696062 | + | 0.717982i | \(0.254934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.86646 | 0.640163 | 0.320082 | − | 0.947390i | \(-0.396290\pi\) | ||||
0.320082 | + | 0.947390i | \(0.396290\pi\) | |||||||
\(152\) | 8.05497 | 0.653344 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −21.7529 | −1.75290 | ||||||||
\(155\) | −5.18909 | −0.416798 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.85591 | 0.786588 | 0.393294 | − | 0.919413i | \(-0.371336\pi\) | ||||
0.393294 | + | 0.919413i | \(0.371336\pi\) | |||||||
\(158\) | −16.2890 | −1.29588 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.52034 | 0.594535 | ||||||||
\(161\) | 8.27340 | 0.652035 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.5786 | 1.29853 | 0.649267 | − | 0.760560i | \(-0.275076\pi\) | ||||
0.649267 | + | 0.760560i | \(0.275076\pi\) | |||||||
\(164\) | 52.7014 | 4.11529 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.2763 | 1.80659 | ||||||||
\(167\) | 4.74360 | 0.367071 | 0.183536 | − | 0.983013i | \(-0.441246\pi\) | ||||
0.183536 | + | 0.983013i | \(0.441246\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.5938 | −0.814908 | ||||||||
\(170\) | −9.14436 | −0.701341 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.09534 | −0.312267 | ||||||||
\(173\) | 19.8201 | 1.50689 | 0.753446 | − | 0.657510i | \(-0.228390\pi\) | ||||
0.753446 | + | 0.657510i | \(0.228390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.24826 | −0.169952 | ||||||||
\(176\) | −30.7429 | −2.31734 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.77798 | −0.283172 | ||||||||
\(179\) | −7.42036 | −0.554624 | −0.277312 | − | 0.960780i | \(-0.589443\pi\) | ||||
−0.277312 | + | 0.960780i | \(0.589443\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8411 | 1.47478 | 0.737390 | − | 0.675468i | \(-0.236058\pi\) | ||||
0.737390 | + | 0.675468i | \(0.236058\pi\) | |||||||
\(182\) | −8.98031 | −0.665665 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 24.9279 | 1.83771 | ||||||||
\(185\) | −0.969518 | −0.0712804 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.3434 | 0.975766 | ||||||||
\(188\) | 51.9797 | 3.79101 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.06193 | −0.222136 | ||||||||
\(191\) | −5.66409 | −0.409839 | −0.204920 | − | 0.978779i | \(-0.565693\pi\) | ||||
−0.204920 | + | 0.978779i | \(0.565693\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.7896 | 1.06458 | 0.532289 | − | 0.846563i | \(-0.321332\pi\) | ||||
0.532289 | + | 0.846563i | \(0.321332\pi\) | |||||||
\(194\) | −31.9283 | −2.29232 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.00820 | −0.643443 | ||||||||
\(197\) | −27.1349 | −1.93328 | −0.966640 | − | 0.256139i | \(-0.917550\pi\) | ||||
−0.966640 | + | 0.256139i | \(0.917550\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.53523 | −0.675934 | −0.337967 | − | 0.941158i | \(-0.609739\pi\) | ||||
−0.337967 | + | 0.941158i | \(0.609739\pi\) | |||||||
\(200\) | −6.77405 | −0.478997 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.88885 | −0.625417 | ||||||||
\(203\) | −2.24826 | −0.157797 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3809 | −0.794877 | ||||||||
\(206\) | −46.8588 | −3.26481 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.6917 | −0.880009 | ||||||||
\(209\) | 4.46794 | 0.309054 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5727 | 1.48513 | 0.742564 | − | 0.669775i | \(-0.233609\pi\) | ||||
0.742564 | + | 0.669775i | \(0.233609\pi\) | |||||||
\(212\) | −49.3479 | −3.38923 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −20.8040 | −1.42213 | ||||||||
\(215\) | 0.884393 | 0.0603151 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.6664 | −0.791969 | ||||||||
\(218\) | 36.0796 | 2.44362 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 17.3995 | 1.17308 | ||||||||
\(221\) | 5.50858 | 0.370547 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.5140 | 1.50765 | 0.753824 | − | 0.657076i | \(-0.228207\pi\) | ||||
0.753824 | + | 0.657076i | \(0.228207\pi\) | |||||||
\(224\) | 16.9077 | 1.12969 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.74712 | 0.116217 | ||||||||
\(227\) | −8.38063 | −0.556242 | −0.278121 | − | 0.960546i | \(-0.589712\pi\) | ||||
−0.278121 | + | 0.960546i | \(0.589712\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5492 | −0.763192 | −0.381596 | − | 0.924329i | \(-0.624625\pi\) | ||||
−0.381596 | + | 0.924329i | \(0.624625\pi\) | |||||||
\(230\) | −9.47581 | −0.624817 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.77405 | −0.444738 | ||||||||
\(233\) | 8.85319 | 0.579991 | 0.289996 | − | 0.957028i | \(-0.406346\pi\) | ||||
0.289996 | + | 0.957028i | \(0.406346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.2251 | −0.732242 | ||||||||
\(236\) | 39.3447 | 2.56112 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −20.5589 | −1.33264 | ||||||||
\(239\) | −13.9536 | −0.902584 | −0.451292 | − | 0.892376i | \(-0.649037\pi\) | ||||
−0.451292 | + | 0.892376i | \(0.649037\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.2138 | −1.55975 | −0.779874 | − | 0.625937i | \(-0.784717\pi\) | ||||
−0.779874 | + | 0.625937i | \(0.784717\pi\) | |||||||
\(242\) | −8.02983 | −0.516177 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −50.3554 | −3.22367 | ||||||||
\(245\) | 1.94533 | 0.124282 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.84451 | 0.117363 | ||||||||
\(248\) | −35.1512 | −2.23210 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.57501 | 0.162858 | ||||||||
\(251\) | 10.1141 | 0.638397 | 0.319198 | − | 0.947688i | \(-0.396586\pi\) | ||||
0.319198 | + | 0.947688i | \(0.396586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 13.8270 | 0.869299 | ||||||||
\(254\) | 21.6282 | 1.35708 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −24.8323 | −1.55202 | ||||||||
\(257\) | 18.2290 | 1.13709 | 0.568546 | − | 0.822652i | \(-0.307506\pi\) | ||||
0.568546 | + | 0.822652i | \(0.307506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.17973 | −0.135442 | ||||||||
\(260\) | 7.18308 | 0.445476 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.9083 | −1.16816 | ||||||||
\(263\) | −4.26573 | −0.263036 | −0.131518 | − | 0.991314i | \(-0.541985\pi\) | ||||
−0.131518 | + | 0.991314i | \(0.541985\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.6567 | 0.654637 | ||||||||
\(266\) | −6.88401 | −0.422086 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.7626 | −1.14611 | ||||||||
\(269\) | −8.10868 | −0.494395 | −0.247197 | − | 0.968965i | \(-0.579510\pi\) | ||||
−0.247197 | + | 0.968965i | \(0.579510\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 26.9259 | 1.63563 | 0.817815 | − | 0.575481i | \(-0.195185\pi\) | ||||
0.817815 | + | 0.575481i | \(0.195185\pi\) | |||||||
\(272\) | −29.0554 | −1.76174 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.64410 | −0.280561 | ||||||||
\(275\) | −3.75744 | −0.226582 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 29.1380 | 1.75073 | 0.875367 | − | 0.483459i | \(-0.160620\pi\) | ||||
0.875367 | + | 0.483459i | \(0.160620\pi\) | |||||||
\(278\) | −1.82169 | −0.109258 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.2298 | −0.910156 | ||||||||
\(281\) | −21.6594 | −1.29209 | −0.646047 | − | 0.763298i | \(-0.723579\pi\) | ||||
−0.646047 | + | 0.763298i | \(0.723579\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.1608 | −0.960660 | −0.480330 | − | 0.877088i | \(-0.659483\pi\) | ||||
−0.480330 | + | 0.877088i | \(0.659483\pi\) | |||||||
\(284\) | 29.5354 | 1.75260 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.0085 | −0.887471 | ||||||||
\(287\) | −25.5872 | −1.51037 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.38903 | −0.258178 | ||||||||
\(290\) | 2.57501 | 0.151210 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −15.0968 | −0.883473 | ||||||||
\(293\) | −16.5348 | −0.965975 | −0.482988 | − | 0.875627i | \(-0.660448\pi\) | ||||
−0.482988 | + | 0.875627i | \(0.660448\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.49652 | −0.494687 | ||||||||
\(296\) | −6.56756 | −0.381732 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −43.7573 | −2.53479 | ||||||||
\(299\) | 5.70825 | 0.330117 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.98834 | 0.114606 | ||||||||
\(302\) | −20.2562 | −1.16561 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −9.72901 | −0.557997 | ||||||||
\(305\) | 10.8743 | 0.622659 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.3923 | −1.44922 | −0.724608 | − | 0.689161i | \(-0.757979\pi\) | ||||
−0.724608 | + | 0.689161i | \(0.757979\pi\) | |||||||
\(308\) | 39.1187 | 2.22899 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.3620 | 0.758909 | ||||||||
\(311\) | −16.8950 | −0.958030 | −0.479015 | − | 0.877807i | \(-0.659006\pi\) | ||||
−0.479015 | + | 0.877807i | \(0.659006\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.1978 | −1.25469 | −0.627347 | − | 0.778740i | \(-0.715859\pi\) | ||||
−0.627347 | + | 0.778740i | \(0.715859\pi\) | |||||||
\(314\) | −25.3791 | −1.43223 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 29.2927 | 1.64785 | ||||||||
\(317\) | 26.1161 | 1.46683 | 0.733414 | − | 0.679783i | \(-0.237926\pi\) | ||||
0.733414 | + | 0.679783i | \(0.237926\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.75744 | −0.210376 | ||||||||
\(320\) | −3.00121 | −0.167773 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −21.3041 | −1.18723 | ||||||||
\(323\) | 4.22270 | 0.234957 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.55119 | −0.0860447 | ||||||||
\(326\) | −42.6900 | −2.36438 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −77.0948 | −4.25685 | ||||||||
\(329\) | −25.2369 | −1.39135 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.3439 | 1.33806 | 0.669030 | − | 0.743236i | \(-0.266710\pi\) | ||||
0.669030 | + | 0.743236i | \(0.266710\pi\) | |||||||
\(332\) | −41.8582 | −2.29727 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −12.2148 | −0.668366 | ||||||||
\(335\) | 4.05179 | 0.221373 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.5099 | −1.28067 | −0.640333 | − | 0.768098i | \(-0.721204\pi\) | ||||
−0.640333 | + | 0.768098i | \(0.721204\pi\) | |||||||
\(338\) | 27.2792 | 1.48379 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 16.4445 | 0.891826 | ||||||||
\(341\) | −19.4977 | −1.05586 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1114 | 1.08591 | ||||||||
\(344\) | 5.99092 | 0.323009 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −51.0369 | −2.74376 | ||||||||
\(347\) | 29.9492 | 1.60776 | 0.803879 | − | 0.594793i | \(-0.202766\pi\) | ||||
0.803879 | + | 0.594793i | \(0.202766\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.0927 | −0.914951 | −0.457476 | − | 0.889222i | \(-0.651246\pi\) | ||||
−0.457476 | + | 0.889222i | \(0.651246\pi\) | |||||||
\(350\) | 5.78930 | 0.309451 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 28.2572 | 1.50612 | ||||||||
\(353\) | 6.40124 | 0.340704 | 0.170352 | − | 0.985383i | \(-0.445510\pi\) | ||||
0.170352 | + | 0.985383i | \(0.445510\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.37818 | −0.338519 | ||||||||
\(356\) | 6.79400 | 0.360082 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.1075 | 1.00986 | ||||||||
\(359\) | 29.2509 | 1.54380 | 0.771902 | − | 0.635741i | \(-0.219306\pi\) | ||||
0.771902 | + | 0.635741i | \(0.219306\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5861 | −0.925582 | ||||||||
\(362\) | −51.0911 | −2.68529 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.1494 | 0.846461 | ||||||||
\(365\) | 3.26017 | 0.170645 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.2919 | −0.693832 | −0.346916 | − | 0.937896i | \(-0.612771\pi\) | ||||
−0.346916 | + | 0.937896i | \(0.612771\pi\) | |||||||
\(368\) | −30.1086 | −1.56952 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.49652 | 0.129788 | ||||||||
\(371\) | 23.9591 | 1.24389 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7309 | −1.02163 | −0.510814 | − | 0.859691i | \(-0.670656\pi\) | ||||
−0.510814 | + | 0.859691i | \(0.670656\pi\) | |||||||
\(374\) | −34.3594 | −1.77668 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −76.0391 | −3.92142 | ||||||||
\(377\) | −1.55119 | −0.0798905 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.4806 | 1.30885 | 0.654424 | − | 0.756128i | \(-0.272911\pi\) | ||||
0.654424 | + | 0.756128i | \(0.272911\pi\) | |||||||
\(380\) | 5.50631 | 0.282468 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 14.5851 | 0.746239 | ||||||||
\(383\) | 0.542784 | 0.0277350 | 0.0138675 | − | 0.999904i | \(-0.495586\pi\) | ||||
0.0138675 | + | 0.999904i | \(0.495586\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.44770 | −0.430535 | ||||||||
\(386\) | −38.0833 | −1.93839 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 57.4171 | 2.91491 | ||||||||
\(389\) | −19.9301 | −1.01050 | −0.505249 | − | 0.862974i | \(-0.668599\pi\) | ||||
−0.505249 | + | 0.862974i | \(0.668599\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.0681 | 0.660881 | ||||||||
\(392\) | 13.1777 | 0.665576 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 69.8726 | 3.52013 | ||||||||
\(395\) | −6.32579 | −0.318285 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.40286 | 0.471916 | 0.235958 | − | 0.971763i | \(-0.424177\pi\) | ||||
0.235958 | + | 0.971763i | \(0.424177\pi\) | |||||||
\(398\) | 24.5533 | 1.23075 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.18188 | 0.409094 | ||||||||
\(401\) | 9.37578 | 0.468204 | 0.234102 | − | 0.972212i | \(-0.424785\pi\) | ||||
0.234102 | + | 0.972212i | \(0.424785\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.04928 | −0.400963 | ||||||||
\(404\) | 15.9850 | 0.795282 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.78930 | 0.287318 | ||||||||
\(407\) | −3.64291 | −0.180572 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.7204 | 0.975111 | 0.487556 | − | 0.873092i | \(-0.337889\pi\) | ||||
0.487556 | + | 0.873092i | \(0.337889\pi\) | |||||||
\(410\) | 29.3060 | 1.44732 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 84.2670 | 4.15154 | ||||||||
\(413\) | −19.1024 | −0.939967 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.03930 | 0.443722 | ||||||||
\(416\) | 11.6655 | 0.571948 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −11.5050 | −0.562728 | ||||||||
\(419\) | −6.24026 | −0.304857 | −0.152428 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152428 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.31722 | 0.307882 | 0.153941 | − | 0.988080i | \(-0.450803\pi\) | ||||
0.153941 | + | 0.988080i | \(0.450803\pi\) | |||||||
\(422\) | −55.5500 | −2.70413 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 72.1891 | 3.50581 | ||||||||
\(425\) | −3.55119 | −0.172258 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.4482 | 1.18313 | ||||||||
\(428\) | 37.4122 | 1.80839 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.27732 | −0.109822 | ||||||||
\(431\) | −37.8006 | −1.82079 | −0.910396 | − | 0.413737i | \(-0.864223\pi\) | ||||
−0.910396 | + | 0.413737i | \(0.864223\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.8447 | 1.81870 | 0.909350 | − | 0.416032i | \(-0.136580\pi\) | ||||
0.909350 | + | 0.416032i | \(0.136580\pi\) | |||||||
\(434\) | 30.0412 | 1.44202 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −64.8825 | −3.10731 | ||||||||
\(437\) | 4.37575 | 0.209321 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.5318 | −0.741291 | −0.370646 | − | 0.928774i | \(-0.620864\pi\) | ||||
−0.370646 | + | 0.928774i | \(0.620864\pi\) | |||||||
\(440\) | −25.4531 | −1.21343 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.1847 | −0.674696 | ||||||||
\(443\) | −5.24223 | −0.249066 | −0.124533 | − | 0.992215i | \(-0.539743\pi\) | ||||
−0.124533 | + | 0.992215i | \(0.539743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.46717 | −0.0695505 | ||||||||
\(446\) | −57.9738 | −2.74514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.74749 | −0.318789 | ||||||||
\(449\) | −28.0123 | −1.32198 | −0.660992 | − | 0.750393i | \(-0.729864\pi\) | ||||
−0.660992 | + | 0.750393i | \(0.729864\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −42.7631 | −2.01364 | ||||||||
\(452\) | −3.14188 | −0.147781 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.5802 | 1.01281 | ||||||||
\(455\) | −3.48748 | −0.163496 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.90391 | 0.0890610 | 0.0445305 | − | 0.999008i | \(-0.485821\pi\) | ||||
0.0445305 | + | 0.999008i | \(0.485821\pi\) | |||||||
\(458\) | 29.7393 | 1.38963 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17.0405 | 0.794518 | ||||||||
\(461\) | 30.5294 | 1.42190 | 0.710949 | − | 0.703244i | \(-0.248266\pi\) | ||||
0.710949 | + | 0.703244i | \(0.248266\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.9230 | 1.53006 | 0.765030 | − | 0.643995i | \(-0.222724\pi\) | ||||
0.765030 | + | 0.643995i | \(0.222724\pi\) | |||||||
\(464\) | 8.18188 | 0.379834 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.7971 | −1.05605 | ||||||||
\(467\) | −4.42775 | −0.204892 | −0.102446 | − | 0.994739i | \(-0.532667\pi\) | ||||
−0.102446 | + | 0.994739i | \(0.532667\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.10947 | 0.420636 | ||||||||
\(470\) | 28.9047 | 1.33327 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −57.5558 | −2.64922 | ||||||||
\(473\) | 3.32305 | 0.152794 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.18909 | −0.0545593 | ||||||||
\(476\) | 36.9714 | 1.69458 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 35.9307 | 1.64343 | ||||||||
\(479\) | −8.27071 | −0.377898 | −0.188949 | − | 0.981987i | \(-0.560508\pi\) | ||||
−0.188949 | + | 0.981987i | \(0.560508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50391 | −0.0685723 | ||||||||
\(482\) | 62.3508 | 2.84000 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.4402 | 0.656371 | ||||||||
\(485\) | −12.3993 | −0.563022 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.9284 | 1.80933 | 0.904665 | − | 0.426124i | \(-0.140121\pi\) | ||||
0.904665 | + | 0.426124i | \(0.140121\pi\) | |||||||
\(488\) | 73.6628 | 3.33456 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.00924 | −0.226294 | ||||||||
\(491\) | −33.3896 | −1.50685 | −0.753427 | − | 0.657532i | \(-0.771601\pi\) | ||||
−0.753427 | + | 0.657532i | \(0.771601\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.55119 | −0.159938 | ||||||||
\(494\) | −4.74964 | −0.213696 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.4565 | 1.90635 | ||||||||
\(497\) | −14.3398 | −0.643229 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.12737 | −0.140000 | −0.0700002 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0700002 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(500\) | −4.63069 | −0.207091 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26.0439 | −1.16240 | ||||||||
\(503\) | −17.2563 | −0.769419 | −0.384710 | − | 0.923038i | \(-0.625698\pi\) | ||||
−0.384710 | + | 0.923038i | \(0.625698\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.45196 | −0.153610 | ||||||||
\(506\) | −35.6048 | −1.58283 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −38.8944 | −1.72566 | ||||||||
\(509\) | −4.71879 | −0.209157 | −0.104578 | − | 0.994517i | \(-0.533349\pi\) | ||||
−0.104578 | + | 0.994517i | \(0.533349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.32970 | 0.324247 | ||||||||
\(512\) | 49.3183 | 2.17958 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −46.9398 | −2.07043 | ||||||||
\(515\) | −18.1975 | −0.801879 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.1775 | −1.85496 | ||||||||
\(518\) | 5.61283 | 0.246613 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.5078 | −0.460800 | ||||||||
\(521\) | 40.0385 | 1.75412 | 0.877060 | − | 0.480381i | \(-0.159502\pi\) | ||||
0.877060 | + | 0.480381i | \(0.159502\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.38694 | −0.235555 | −0.117777 | − | 0.993040i | \(-0.537577\pi\) | ||||
−0.117777 | + | 0.993040i | \(0.537577\pi\) | |||||||
\(524\) | 34.0030 | 1.48543 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.9843 | 0.478939 | ||||||||
\(527\) | −18.4275 | −0.802713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.45826 | −0.411229 | ||||||||
\(530\) | −27.4412 | −1.19197 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.3796 | 0.536725 | ||||||||
\(533\) | −17.6540 | −0.764679 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.07919 | −0.349294 | ||||||||
\(536\) | 27.4470 | 1.18553 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 20.8799 | 0.900198 | ||||||||
\(539\) | 7.30945 | 0.314840 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9892 | 1.54730 | 0.773649 | − | 0.633614i | \(-0.218429\pi\) | ||||
0.773649 | + | 0.633614i | \(0.218429\pi\) | |||||||
\(542\) | −69.3345 | −2.97817 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 26.7062 | 1.14502 | ||||||||
\(545\) | 14.0114 | 0.600184 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.2745 | 1.03790 | 0.518951 | − | 0.854804i | \(-0.326323\pi\) | ||||
0.518951 | + | 0.854804i | \(0.326323\pi\) | |||||||
\(548\) | 8.35157 | 0.356761 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.67546 | 0.412563 | ||||||||
\(551\) | −1.18909 | −0.0506570 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.2220 | −0.604782 | ||||||||
\(554\) | −75.0307 | −3.18775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.27598 | 0.138933 | ||||||||
\(557\) | −4.93097 | −0.208932 | −0.104466 | − | 0.994528i | \(-0.533313\pi\) | ||||
−0.104466 | + | 0.994528i | \(0.533313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.37186 | 0.0580236 | ||||||||
\(560\) | 18.3950 | 0.777330 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 55.7733 | 2.35266 | ||||||||
\(563\) | −34.7020 | −1.46252 | −0.731258 | − | 0.682101i | \(-0.761067\pi\) | ||||
−0.731258 | + | 0.682101i | \(0.761067\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.678491 | 0.0285443 | ||||||||
\(566\) | 41.6142 | 1.74918 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −43.2061 | −1.81289 | ||||||||
\(569\) | 19.9633 | 0.836903 | 0.418452 | − | 0.908239i | \(-0.362573\pi\) | ||||
0.418452 | + | 0.908239i | \(0.362573\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.22542 | −0.302375 | −0.151187 | − | 0.988505i | \(-0.548310\pi\) | ||||
−0.151187 | + | 0.988505i | \(0.548310\pi\) | |||||||
\(572\) | 26.9900 | 1.12851 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 65.8875 | 2.75009 | ||||||||
\(575\) | −3.67991 | −0.153463 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6693 | 0.735581 | 0.367791 | − | 0.929909i | \(-0.380114\pi\) | ||||
0.367791 | + | 0.929909i | \(0.380114\pi\) | |||||||
\(578\) | 11.3018 | 0.470093 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.63069 | −0.192279 | ||||||||
\(581\) | 20.3227 | 0.843128 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.0420 | 1.65837 | ||||||||
\(584\) | 22.0845 | 0.913864 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 42.5774 | 1.75886 | ||||||||
\(587\) | −13.1365 | −0.542203 | −0.271102 | − | 0.962551i | \(-0.587388\pi\) | ||||
−0.271102 | + | 0.962551i | \(0.587388\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.17031 | −0.254243 | ||||||||
\(590\) | 21.8786 | 0.900729 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.93248 | 0.326023 | ||||||||
\(593\) | −11.3675 | −0.466807 | −0.233403 | − | 0.972380i | \(-0.574986\pi\) | ||||
−0.233403 | + | 0.972380i | \(0.574986\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.98400 | −0.327312 | ||||||||
\(596\) | 78.6894 | 3.22324 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −14.6988 | −0.601079 | ||||||||
\(599\) | 8.98828 | 0.367251 | 0.183626 | − | 0.982996i | \(-0.441217\pi\) | ||||
0.183626 | + | 0.982996i | \(0.441217\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.15704 | −0.210360 | −0.105180 | − | 0.994453i | \(-0.533542\pi\) | ||||
−0.105180 | + | 0.994453i | \(0.533542\pi\) | |||||||
\(602\) | −5.12001 | −0.208676 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36.4271 | 1.48220 | ||||||||
\(605\) | −3.11836 | −0.126780 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.3436 | −1.47514 | −0.737570 | − | 0.675271i | \(-0.764027\pi\) | ||||
−0.737570 | + | 0.675271i | \(0.764027\pi\) | |||||||
\(608\) | 8.94238 | 0.362661 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.0014 | −1.13374 | ||||||||
\(611\) | −17.4122 | −0.704423 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.9943 | 0.767171 | 0.383585 | − | 0.923505i | \(-0.374689\pi\) | ||||
0.383585 | + | 0.923505i | \(0.374689\pi\) | |||||||
\(614\) | 65.3855 | 2.63874 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −57.2251 | −2.30567 | ||||||||
\(617\) | 24.5060 | 0.986574 | 0.493287 | − | 0.869867i | \(-0.335795\pi\) | ||||
0.493287 | + | 0.869867i | \(0.335795\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5314 | 0.503680 | 0.251840 | − | 0.967769i | \(-0.418964\pi\) | ||||
0.251840 | + | 0.967769i | \(0.418964\pi\) | |||||||
\(620\) | −24.0291 | −0.965030 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 43.5049 | 1.74439 | ||||||||
\(623\) | −3.29858 | −0.132155 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 57.1596 | 2.28456 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 45.6396 | 1.82122 | ||||||||
\(629\) | −3.44294 | −0.137279 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.8019 | 0.708681 | 0.354340 | − | 0.935116i | \(-0.384705\pi\) | ||||
0.354340 | + | 0.935116i | \(0.384705\pi\) | |||||||
\(632\) | −42.8512 | −1.70453 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −67.2493 | −2.67081 | ||||||||
\(635\) | 8.39928 | 0.333315 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.01758 | 0.119561 | ||||||||
\(638\) | 9.67546 | 0.383055 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.31254 | −0.289053 | ||||||||
\(641\) | −20.3973 | −0.805644 | −0.402822 | − | 0.915278i | \(-0.631971\pi\) | ||||
−0.402822 | + | 0.915278i | \(0.631971\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.6531 | −0.932787 | −0.466394 | − | 0.884577i | \(-0.654447\pi\) | ||||
−0.466394 | + | 0.884577i | \(0.654447\pi\) | |||||||
\(644\) | 38.3115 | 1.50968 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.8735 | −0.427812 | ||||||||
\(647\) | 17.5789 | 0.691096 | 0.345548 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345548 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.9252 | −1.25317 | ||||||||
\(650\) | 3.99434 | 0.156671 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 76.7702 | 3.00655 | ||||||||
\(653\) | −10.4035 | −0.407121 | −0.203560 | − | 0.979062i | \(-0.565251\pi\) | ||||
−0.203560 | + | 0.979062i | \(0.565251\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.34298 | −0.286914 | ||||||||
\(656\) | 93.1172 | 3.63562 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 64.9852 | 2.53339 | ||||||||
\(659\) | 43.5638 | 1.69700 | 0.848502 | − | 0.529192i | \(-0.177505\pi\) | ||||
0.848502 | + | 0.529192i | \(0.177505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.2404 | 0.709469 | 0.354734 | − | 0.934967i | \(-0.384571\pi\) | ||||
0.354734 | + | 0.934967i | \(0.384571\pi\) | |||||||
\(662\) | −62.6857 | −2.43635 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 61.2327 | 2.37629 | ||||||||
\(665\) | −2.67339 | −0.103670 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.67991 | −0.142487 | ||||||||
\(668\) | 21.9661 | 0.849895 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.4334 | −0.403077 | ||||||||
\(671\) | 40.8595 | 1.57736 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.8626 | −0.996929 | −0.498464 | − | 0.866910i | \(-0.666103\pi\) | ||||
−0.498464 | + | 0.866910i | \(0.666103\pi\) | |||||||
\(674\) | 60.5383 | 2.33185 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −49.0566 | −1.88679 | ||||||||
\(677\) | −30.3287 | −1.16563 | −0.582813 | − | 0.812606i | \(-0.698048\pi\) | ||||
−0.582813 | + | 0.812606i | \(0.698048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.8768 | −1.06981 | ||||||||
\(680\) | −24.0559 | −0.922503 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 50.2068 | 1.92252 | ||||||||
\(683\) | −39.4637 | −1.51004 | −0.755018 | − | 0.655704i | \(-0.772372\pi\) | ||||
−0.755018 | + | 0.655704i | \(0.772372\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.80353 | −0.0689092 | ||||||||
\(686\) | −51.7871 | −1.97724 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.23599 | −0.275870 | ||||||||
\(689\) | 16.5306 | 0.629766 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24.5853 | −0.935269 | −0.467635 | − | 0.883922i | \(-0.654894\pi\) | ||||
−0.467635 | + | 0.883922i | \(0.654894\pi\) | |||||||
\(692\) | 91.7805 | 3.48897 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −77.1196 | −2.92742 | ||||||||
\(695\) | −0.707451 | −0.0268351 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −40.4158 | −1.53086 | ||||||||
\(698\) | 44.0139 | 1.66595 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −10.4110 | −0.393498 | ||||||||
\(701\) | −34.8635 | −1.31678 | −0.658388 | − | 0.752678i | \(-0.728762\pi\) | ||||
−0.658388 | + | 0.752678i | \(0.728762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.15285 | −0.0434804 | ||||||||
\(704\) | −11.2769 | −0.425012 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.4833 | −0.620356 | ||||||||
\(707\) | −7.76091 | −0.291879 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.4622 | −0.918698 | −0.459349 | − | 0.888256i | \(-0.651917\pi\) | ||||
−0.459349 | + | 0.888256i | \(0.651917\pi\) | |||||||
\(710\) | 16.4239 | 0.616378 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.93868 | −0.372468 | ||||||||
\(713\) | −19.0954 | −0.715128 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.82851 | −0.217974 | ||||||||
\(716\) | −34.3613 | −1.28414 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −75.3214 | −2.81097 | ||||||||
\(719\) | −27.1333 | −1.01190 | −0.505951 | − | 0.862562i | \(-0.668858\pi\) | ||||
−0.505951 | + | 0.862562i | \(0.668858\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.9128 | −1.52367 | ||||||||
\(722\) | 45.2843 | 1.68531 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 91.8780 | 3.41462 | ||||||||
\(725\) | 1.00000 | 0.0371391 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.9854 | 1.26045 | 0.630224 | − | 0.776413i | \(-0.282963\pi\) | ||||
0.630224 | + | 0.776413i | \(0.282963\pi\) | |||||||
\(728\) | −23.6244 | −0.875578 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −8.39496 | −0.310712 | ||||||||
\(731\) | 3.14065 | 0.116161 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.2131 | 0.635779 | 0.317889 | − | 0.948128i | \(-0.397026\pi\) | ||||
0.317889 | + | 0.948128i | \(0.397026\pi\) | |||||||
\(734\) | 34.2268 | 1.26333 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.6742 | 1.02008 | ||||||||
\(737\) | 15.2244 | 0.560796 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5603 | −0.462039 | −0.231019 | − | 0.972949i | \(-0.574206\pi\) | ||||
−0.231019 | + | 0.972949i | \(0.574206\pi\) | |||||||
\(740\) | −4.48953 | −0.165038 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −61.6949 | −2.26489 | ||||||||
\(743\) | 43.0323 | 1.57870 | 0.789350 | − | 0.613943i | \(-0.210418\pi\) | ||||
0.789350 | + | 0.613943i | \(0.210418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.9930 | −0.622577 | ||||||||
\(746\) | 50.8073 | 1.86019 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 61.7891 | 2.25923 | ||||||||
\(749\) | −18.1641 | −0.663702 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.4133 | −0.452969 | −0.226485 | − | 0.974015i | \(-0.572723\pi\) | ||||
−0.226485 | + | 0.974015i | \(0.572723\pi\) | |||||||
\(752\) | 91.8421 | 3.34914 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.99434 | 0.145465 | ||||||||
\(755\) | −7.86646 | −0.286290 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.0439 | 0.655815 | 0.327907 | − | 0.944710i | \(-0.393657\pi\) | ||||
0.327907 | + | 0.944710i | \(0.393657\pi\) | |||||||
\(758\) | −65.6127 | −2.38316 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.05497 | −0.292184 | ||||||||
\(761\) | −8.20477 | −0.297423 | −0.148711 | − | 0.988881i | \(-0.547513\pi\) | ||||
−0.148711 | + | 0.988881i | \(0.547513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 31.5013 | 1.14043 | ||||||||
\(764\) | −26.2286 | −0.948919 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.39768 | −0.0505001 | ||||||||
\(767\) | −13.1797 | −0.475893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23.5524 | −0.849320 | −0.424660 | − | 0.905353i | \(-0.639606\pi\) | ||||
−0.424660 | + | 0.905353i | \(0.639606\pi\) | |||||||
\(770\) | 21.7529 | 0.783921 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 68.4859 | 2.46486 | ||||||||
\(773\) | −27.2326 | −0.979487 | −0.489743 | − | 0.871867i | \(-0.662910\pi\) | ||||
−0.489743 | + | 0.871867i | \(0.662910\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.18909 | 0.186398 | ||||||||
\(776\) | −83.9933 | −3.01518 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 51.3203 | 1.83992 | ||||||||
\(779\) | −13.5330 | −0.484868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.9657 | −0.857559 | ||||||||
\(782\) | −33.6504 | −1.20334 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −15.9164 | −0.568444 | ||||||||
\(785\) | −9.85591 | −0.351773 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.2585 | 0.722137 | 0.361069 | − | 0.932539i | \(-0.382412\pi\) | ||||
0.361069 | + | 0.932539i | \(0.382412\pi\) | |||||||
\(788\) | −125.653 | −4.47621 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.2890 | 0.579536 | ||||||||
\(791\) | 1.52542 | 0.0542378 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.8681 | 0.599004 | ||||||||
\(794\) | −24.2125 | −0.859269 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −44.1546 | −1.56502 | ||||||||
\(797\) | 27.8574 | 0.986761 | 0.493381 | − | 0.869814i | \(-0.335761\pi\) | ||||
0.493381 | + | 0.869814i | \(0.335761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.8624 | −1.41023 | ||||||||
\(800\) | −7.52034 | −0.265884 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.1427 | −0.852510 | ||||||||
\(803\) | 12.2499 | 0.432289 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.27340 | −0.291599 | ||||||||
\(806\) | 20.7270 | 0.730077 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.3838 | −0.822638 | ||||||||
\(809\) | −17.5060 | −0.615477 | −0.307739 | − | 0.951471i | \(-0.599572\pi\) | ||||
−0.307739 | + | 0.951471i | \(0.599572\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.1690 | 1.37541 | 0.687704 | − | 0.725991i | \(-0.258619\pi\) | ||||
0.687704 | + | 0.725991i | \(0.258619\pi\) | |||||||
\(812\) | −10.4110 | −0.365354 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.38053 | 0.328787 | ||||||||
\(815\) | −16.5786 | −0.580722 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.05162 | 0.0367917 | ||||||||
\(818\) | −50.7803 | −1.77549 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −52.7014 | −1.84041 | ||||||||
\(821\) | 19.8338 | 0.692203 | 0.346101 | − | 0.938197i | \(-0.387505\pi\) | ||||
0.346101 | + | 0.938197i | \(0.387505\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.3727 | 0.361568 | 0.180784 | − | 0.983523i | \(-0.442136\pi\) | ||||
0.180784 | + | 0.983523i | \(0.442136\pi\) | |||||||
\(824\) | −123.271 | −4.29434 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 49.1889 | 1.71150 | ||||||||
\(827\) | −3.35272 | −0.116586 | −0.0582928 | − | 0.998300i | \(-0.518566\pi\) | ||||
−0.0582928 | + | 0.998300i | \(0.518566\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.0572 | −1.49544 | −0.747719 | − | 0.664015i | \(-0.768851\pi\) | ||||
−0.747719 | + | 0.664015i | \(0.768851\pi\) | |||||||
\(830\) | −23.2763 | −0.807933 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.65545 | −0.161399 | ||||||||
\(833\) | 6.90823 | 0.239356 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.74360 | −0.164159 | ||||||||
\(836\) | 20.6896 | 0.715566 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.0688 | 0.555086 | ||||||||
\(839\) | 39.3736 | 1.35933 | 0.679664 | − | 0.733523i | \(-0.262125\pi\) | ||||
0.679664 | + | 0.733523i | \(0.262125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −16.2669 | −0.560595 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 99.8965 | 3.43858 | ||||||||
\(845\) | 10.5938 | 0.364438 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.01089 | −0.240897 | ||||||||
\(848\) | −87.1919 | −2.99418 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.14436 | 0.313649 | ||||||||
\(851\) | −3.56774 | −0.122301 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.2743 | −1.55016 | −0.775081 | − | 0.631862i | \(-0.782291\pi\) | ||||
−0.775081 | + | 0.631862i | \(0.782291\pi\) | |||||||
\(854\) | −62.9544 | −2.15426 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −54.7288 | −1.87059 | ||||||||
\(857\) | −24.1619 | −0.825353 | −0.412677 | − | 0.910878i | \(-0.635406\pi\) | ||||
−0.412677 | + | 0.910878i | \(0.635406\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.3680 | −0.763185 | −0.381593 | − | 0.924331i | \(-0.624624\pi\) | ||||
−0.381593 | + | 0.924331i | \(0.624624\pi\) | |||||||
\(860\) | 4.09534 | 0.139650 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 97.3371 | 3.31531 | ||||||||
\(863\) | 2.98467 | 0.101599 | 0.0507997 | − | 0.998709i | \(-0.483823\pi\) | ||||
0.0507997 | + | 0.998709i | \(0.483823\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19.8201 | −0.673902 | ||||||||
\(866\) | −97.4505 | −3.31150 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −54.0236 | −1.83368 | ||||||||
\(869\) | −23.7688 | −0.806301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.28510 | 0.212963 | ||||||||
\(872\) | 94.9141 | 3.21420 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.2676 | −0.381133 | ||||||||
\(875\) | 2.24826 | 0.0760051 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29.5037 | 0.996269 | 0.498135 | − | 0.867100i | \(-0.334019\pi\) | ||||
0.498135 | + | 0.867100i | \(0.334019\pi\) | |||||||
\(878\) | 39.9945 | 1.34975 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 30.7429 | 1.03634 | ||||||||
\(881\) | 52.0937 | 1.75508 | 0.877541 | − | 0.479502i | \(-0.159183\pi\) | ||||
0.877541 | + | 0.479502i | \(0.159183\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.2221 | 0.747832 | 0.373916 | − | 0.927463i | \(-0.378015\pi\) | ||||
0.373916 | + | 0.927463i | \(0.378015\pi\) | |||||||
\(884\) | 25.5085 | 0.857944 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 13.4988 | 0.453502 | ||||||||
\(887\) | 38.6220 | 1.29680 | 0.648400 | − | 0.761300i | \(-0.275438\pi\) | ||||
0.648400 | + | 0.761300i | \(0.275438\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.8838 | 0.633341 | ||||||||
\(890\) | 3.77798 | 0.126638 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 104.255 | 3.49072 | ||||||||
\(893\) | −13.3476 | −0.446662 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.42036 | 0.248035 | ||||||||
\(896\) | −16.4405 | −0.549238 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 72.1321 | 2.40708 | ||||||||
\(899\) | 5.18909 | 0.173066 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.8440 | 1.26077 | ||||||||
\(902\) | 110.116 | 3.66645 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.59613 | 0.152865 | ||||||||
\(905\) | −19.8411 | −0.659541 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.7861 | −0.989030 | −0.494515 | − | 0.869169i | \(-0.664654\pi\) | ||||
−0.494515 | + | 0.869169i | \(0.664654\pi\) | |||||||
\(908\) | −38.8080 | −1.28789 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.98031 | 0.297694 | ||||||||
\(911\) | 53.7163 | 1.77970 | 0.889850 | − | 0.456254i | \(-0.150809\pi\) | ||||
0.889850 | + | 0.456254i | \(0.150809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.9647 | 1.12407 | ||||||||
\(914\) | −4.90258 | −0.162163 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −53.4807 | −1.76705 | ||||||||
\(917\) | −16.5089 | −0.545173 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.0358 | 1.71650 | 0.858251 | − | 0.513231i | \(-0.171551\pi\) | ||||
0.858251 | + | 0.513231i | \(0.171551\pi\) | |||||||
\(920\) | −24.9279 | −0.821848 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −78.6137 | −2.58900 | ||||||||
\(923\) | −9.89379 | −0.325658 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.969518 | 0.0318775 | ||||||||
\(926\) | −84.7770 | −2.78595 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.52034 | −0.246867 | ||||||||
\(929\) | −52.5081 | −1.72273 | −0.861367 | − | 0.507982i | \(-0.830391\pi\) | ||||
−0.861367 | + | 0.507982i | \(0.830391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.31317 | 0.0758112 | ||||||||
\(932\) | 40.9963 | 1.34288 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.4015 | 0.373068 | ||||||||
\(935\) | −13.3434 | −0.436376 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 46.1947 | 1.50912 | 0.754558 | − | 0.656233i | \(-0.227851\pi\) | ||||
0.754558 | + | 0.656233i | \(0.227851\pi\) | |||||||
\(938\) | −23.4570 | −0.765898 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −51.9797 | −1.69539 | ||||||||
\(941\) | 29.8642 | 0.973545 | 0.486773 | − | 0.873529i | \(-0.338174\pi\) | ||||
0.486773 | + | 0.873529i | \(0.338174\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −41.8807 | −1.36382 | ||||||||
\(944\) | 69.5175 | 2.26260 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.55690 | −0.278209 | ||||||||
\(947\) | 11.7523 | 0.381898 | 0.190949 | − | 0.981600i | \(-0.438843\pi\) | ||||
0.190949 | + | 0.981600i | \(0.438843\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.05714 | 0.164162 | ||||||||
\(950\) | 3.06193 | 0.0993420 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −54.0840 | −1.75287 | ||||||||
\(953\) | −17.1653 | −0.556040 | −0.278020 | − | 0.960575i | \(-0.589678\pi\) | ||||
−0.278020 | + | 0.960575i | \(0.589678\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.66409 | 0.183286 | ||||||||
\(956\) | −64.6147 | −2.08979 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.2972 | 0.688081 | ||||||||
\(959\) | −4.05480 | −0.130936 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.07332 | −0.131397 | ||||||||
\(962\) | 3.87258 | 0.124857 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −112.126 | −3.61135 | ||||||||
\(965\) | −14.7896 | −0.476093 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.2076 | 0.649831 | 0.324916 | − | 0.945743i | \(-0.394664\pi\) | ||||
0.324916 | + | 0.945743i | \(0.394664\pi\) | |||||||
\(968\) | −21.1239 | −0.678949 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 31.9283 | 1.02516 | ||||||||
\(971\) | 24.7827 | 0.795315 | 0.397658 | − | 0.917534i | \(-0.369823\pi\) | ||||
0.397658 | + | 0.917534i | \(0.369823\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.59053 | −0.0509902 | ||||||||
\(974\) | −102.816 | −3.29444 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −88.9720 | −2.84792 | ||||||||
\(977\) | 38.5423 | 1.23308 | 0.616539 | − | 0.787324i | \(-0.288534\pi\) | ||||
0.616539 | + | 0.787324i | \(0.288534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.51281 | −0.176190 | ||||||||
\(980\) | 9.00820 | 0.287756 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 85.9787 | 2.74369 | ||||||||
\(983\) | 13.0762 | 0.417065 | 0.208532 | − | 0.978015i | \(-0.433131\pi\) | ||||
0.208532 | + | 0.978015i | \(0.433131\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.1349 | 0.864589 | ||||||||
\(986\) | 9.14436 | 0.291216 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.54135 | 0.271737 | ||||||||
\(989\) | 3.25449 | 0.103487 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.8186 | −1.16958 | −0.584791 | − | 0.811184i | \(-0.698823\pi\) | ||||
−0.584791 | + | 0.811184i | \(0.698823\pi\) | |||||||
\(992\) | −39.0237 | −1.23900 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.9252 | 1.17120 | ||||||||
\(995\) | 9.53523 | 0.302287 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.5570 | −0.587707 | −0.293854 | − | 0.955850i | \(-0.594938\pi\) | ||||
−0.293854 | + | 0.955850i | \(0.594938\pi\) | |||||||
\(998\) | 8.05302 | 0.254914 | ||||||||
\(999\) | 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 | 1305.2.a.s.1.1 | ✓ | 7 | |
3.2 | odd | 2 | 1305.2.a.t.1.7 | yes | 7 | ||
5.4 | even | 2 | 6525.2.a.bw.1.7 | 7 | |||
15.14 | odd | 2 | 6525.2.a.bv.1.1 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1305.2.a.s.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
1305.2.a.t.1.7 | yes | 7 | 3.2 | odd | 2 | ||
6525.2.a.bv.1.1 | 7 | 15.14 | odd | 2 | |||
6525.2.a.bw.1.7 | 7 | 5.4 | even | 2 |