Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(2591,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.2591");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.h (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2591.4 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.2591 |
Dual form | 6048.2.h.b.2591.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(5\) | − 2.96713i | − 1.32694i | −0.748203 | − | 0.663470i | \(-0.769083\pi\) | ||||
0.748203 | − | 0.663470i | \(-0.230917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.76028 | 1.43528 | 0.717639 | − | 0.696415i | \(-0.245223\pi\) | ||||
0.717639 | + | 0.696415i | \(0.245223\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.26795 | −0.351666 | −0.175833 | − | 0.984420i | \(-0.556262\pi\) | ||||
−0.175833 | + | 0.984420i | \(0.556262\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.378937i | 0.0919058i | 0.998944 | + | 0.0459529i | \(0.0146324\pi\) | ||||
−0.998944 | + | 0.0459529i | \(0.985368\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.00000i | 1.14708i | 0.819178 | + | 0.573539i | \(0.194430\pi\) | ||||
−0.819178 | + | 0.573539i | \(0.805570\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.93185 | −0.402819 | −0.201409 | − | 0.979507i | \(-0.564552\pi\) | ||||
−0.201409 | + | 0.979507i | \(0.564552\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.80385 | −0.760770 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 4.24264i | − 0.787839i | −0.919145 | − | 0.393919i | \(-0.871119\pi\) | ||||
0.919145 | − | 0.393919i | \(-0.128881\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4641i | 1.87941i | 0.341989 | + | 0.939704i | \(0.388900\pi\) | ||||
−0.341989 | + | 0.939704i | \(0.611100\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.96713 | 0.501536 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.46410 | 0.405096 | 0.202548 | − | 0.979272i | \(-0.435078\pi\) | ||||
0.202548 | + | 0.979272i | \(0.435078\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.6945i | 1.67021i | 0.550094 | + | 0.835103i | \(0.314592\pi\) | ||||
−0.550094 | + | 0.835103i | \(0.685408\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.73205i | 0.721631i | 0.932637 | + | 0.360815i | \(0.117502\pi\) | ||||
−0.932637 | + | 0.360815i | \(0.882498\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.20736 | −0.467842 | −0.233921 | − | 0.972256i | \(-0.575156\pi\) | ||||
−0.233921 | + | 0.972256i | \(0.575156\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.76268i | 1.20365i | 0.798629 | + | 0.601824i | \(0.205559\pi\) | ||||
−0.798629 | + | 0.601824i | \(0.794441\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 14.1244i | − 1.90453i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.48477 | 0.453678 | 0.226839 | − | 0.973932i | \(-0.427161\pi\) | ||||
0.226839 | + | 0.973932i | \(0.427161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.92820 | −0.630992 | −0.315496 | − | 0.948927i | \(-0.602171\pi\) | ||||
−0.315496 | + | 0.948927i | \(0.602171\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.76217i | 0.466639i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.66025i | 0.935849i | 0.883768 | + | 0.467924i | \(0.154998\pi\) | ||||
−0.883768 | + | 0.467924i | \(0.845002\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.240237 | −0.0285108 | −0.0142554 | − | 0.999898i | \(-0.504538\pi\) | ||||
−0.0142554 | + | 0.999898i | \(0.504538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.196152 | −0.0229579 | −0.0114790 | − | 0.999934i | \(-0.503654\pi\) | ||||
−0.0114790 | + | 0.999934i | \(0.503654\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.76028i | 0.542484i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.80385i | 0.202949i | 0.994838 | + | 0.101474i | \(0.0323560\pi\) | ||||
−0.994838 | + | 0.101474i | \(0.967644\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.82894 | 0.859338 | 0.429669 | − | 0.902986i | \(-0.358630\pi\) | ||||
0.429669 | + | 0.902986i | \(0.358630\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12436 | 0.121953 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.93185i | − 0.204776i | −0.994745 | − | 0.102388i | \(-0.967352\pi\) | ||||
0.994745 | − | 0.102388i | \(-0.0326483\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.26795i | − 0.132917i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 14.8356 | 1.52210 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.9282 | −1.31266 | −0.656330 | − | 0.754474i | \(-0.727892\pi\) | ||||
−0.656330 | + | 0.754474i | \(0.727892\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 4.52004i | − 0.449761i | −0.974386 | − | 0.224880i | \(-0.927801\pi\) | ||||
0.974386 | − | 0.224880i | \(-0.0721992\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.53590i | 0.348402i | 0.984710 | + | 0.174201i | \(0.0557343\pi\) | ||||
−0.984710 | + | 0.174201i | \(0.944266\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.86422 | 0.856936 | 0.428468 | − | 0.903557i | \(-0.359053\pi\) | ||||
0.428468 | + | 0.903557i | \(0.359053\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.5885 | −1.68467 | −0.842334 | − | 0.538955i | \(-0.818819\pi\) | ||||
−0.842334 | + | 0.538955i | \(0.818819\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.48528i | 0.798228i | 0.916901 | + | 0.399114i | \(0.130682\pi\) | ||||
−0.916901 | + | 0.399114i | \(0.869318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.73205i | 0.534516i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.378937 | −0.0347371 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.6603 | 1.06002 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 3.54914i | − 0.317444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 17.6603i | − 1.56709i | −0.621332 | − | 0.783547i | \(-0.713408\pi\) | ||||
0.621332 | − | 0.783547i | \(-0.286592\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.41421 | 0.123560 | 0.0617802 | − | 0.998090i | \(-0.480322\pi\) | ||||
0.0617802 | + | 0.998090i | \(0.480322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.00000 | −0.433555 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.48477i | 0.297724i | 0.988858 | + | 0.148862i | \(0.0475610\pi\) | ||||
−0.988858 | + | 0.148862i | \(0.952439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.3205i | 0.960193i | 0.877216 | + | 0.480096i | \(0.159398\pi\) | ||||
−0.877216 | + | 0.480096i | \(0.840602\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.03579 | −0.504738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.5885 | −1.04541 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 19.7990i | 1.62200i | 0.585049 | + | 0.810998i | \(0.301075\pi\) | ||||
−0.585049 | + | 0.810998i | \(0.698925\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 14.9282i | − 1.21484i | −0.794381 | − | 0.607420i | \(-0.792205\pi\) | ||||
0.794381 | − | 0.607420i | \(-0.207795\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 31.0483 | 2.49386 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.73205 | 0.537276 | 0.268638 | − | 0.963241i | \(-0.413426\pi\) | ||||
0.268638 | + | 0.963241i | \(0.413426\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 1.93185i | − 0.152251i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 18.0526i | − 1.41399i | −0.707221 | − | 0.706993i | \(-0.750051\pi\) | ||||
0.707221 | − | 0.706993i | \(-0.249949\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −22.9048 | −1.77243 | −0.886214 | − | 0.463276i | \(-0.846674\pi\) | ||||
−0.886214 | + | 0.463276i | \(0.846674\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3923 | −0.876331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.3156i | 0.784280i | 0.919905 | + | 0.392140i | \(0.128265\pi\) | ||||
−0.919905 | + | 0.392140i | \(0.871735\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.80385i | − 0.287544i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.9700 | −0.894683 | −0.447342 | − | 0.894363i | \(-0.647629\pi\) | ||||
−0.447342 | + | 0.894363i | \(0.647629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.7846 | 1.84223 | 0.921113 | − | 0.389296i | \(-0.127282\pi\) | ||||
0.921113 | + | 0.389296i | \(0.127282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 7.31130i | − 0.537538i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.80385i | 0.131910i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.03768 | 0.364514 | 0.182257 | − | 0.983251i | \(-0.441660\pi\) | ||||
0.182257 | + | 0.983251i | \(0.441660\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.32051 | 0.670905 | 0.335452 | − | 0.942057i | \(-0.391111\pi\) | ||||
0.335452 | + | 0.942057i | \(0.391111\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.0764i | 1.43038i | 0.698928 | + | 0.715192i | \(0.253661\pi\) | ||||
−0.698928 | + | 0.715192i | \(0.746339\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2679i | 1.01143i | 0.862701 | + | 0.505714i | \(0.168771\pi\) | ||||
−0.862701 | + | 0.505714i | \(0.831229\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.24264 | 0.297775 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.7321 | 2.21626 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.8014i | 1.64638i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 14.5359i | − 1.00069i | −0.865825 | − | 0.500346i | \(-0.833206\pi\) | ||||
0.865825 | − | 0.500346i | \(-0.166794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.0406 | 0.957561 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4641 | −0.710350 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 0.480473i | − 0.0323201i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 24.1244i | − 1.61549i | −0.589535 | − | 0.807743i | \(-0.700689\pi\) | ||||
0.589535 | − | 0.807743i | \(-0.299311\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22.6274 | 1.50183 | 0.750917 | − | 0.660396i | \(-0.229612\pi\) | ||||
0.750917 | + | 0.660396i | \(0.229612\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.46410 | 0.493242 | 0.246621 | − | 0.969112i | \(-0.420680\pi\) | ||||
0.246621 | + | 0.969112i | \(0.420680\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 10.5558i | − 0.691536i | −0.938320 | − | 0.345768i | \(-0.887618\pi\) | ||||
0.938320 | − | 0.345768i | \(-0.112382\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.51666i | 0.620798i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 21.7680 | 1.40806 | 0.704028 | − | 0.710173i | \(-0.251383\pi\) | ||||
0.704028 | + | 0.710173i | \(0.251383\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 17.8038 | 1.14685 | 0.573423 | − | 0.819259i | \(-0.305615\pi\) | ||||
0.573423 | + | 0.819259i | \(0.305615\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.96713i | 0.189563i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.33975i | − 0.403388i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.04008 | 0.570605 | 0.285303 | − | 0.958438i | \(-0.407906\pi\) | ||||
0.285303 | + | 0.958438i | \(0.407906\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.19615 | −0.578157 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 20.8714i | 1.30192i | 0.759110 | + | 0.650962i | \(0.225634\pi\) | ||||
−0.759110 | + | 0.650962i | \(0.774366\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.46410i | 0.153112i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4171 | 0.642348 | 0.321174 | − | 0.947020i | \(-0.395923\pi\) | ||||
0.321174 | + | 0.947020i | \(0.395923\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.0000 | 1.59717 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.2146i | 0.927649i | 0.885927 | + | 0.463825i | \(0.153523\pi\) | ||||
−0.885927 | + | 0.463825i | \(0.846477\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8564i | 0.720225i | 0.932909 | + | 0.360113i | \(0.117262\pi\) | ||||
−0.932909 | + | 0.360113i | \(0.882738\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.1074 | −1.09192 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.92820 | −0.476360 | −0.238180 | − | 0.971221i | \(-0.576551\pi\) | ||||
−0.238180 | + | 0.971221i | \(0.576551\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 29.6985i | − 1.77166i | −0.464007 | − | 0.885832i | \(-0.653589\pi\) | ||||
0.464007 | − | 0.885832i | \(-0.346411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.4641i | 1.87035i | 0.354190 | + | 0.935173i | \(0.384756\pi\) | ||||
−0.354190 | + | 0.935173i | \(0.615244\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.6945 | −0.631278 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8564 | 0.991553 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.62587i | 0.445508i | 0.974875 | + | 0.222754i | \(0.0715047\pi\) | ||||
−0.974875 | + | 0.222754i | \(0.928495\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 10.3397i | − 0.602003i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44949 | 0.141658 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.73205 | −0.272751 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 14.6226i | 0.837288i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.00000i | 0.513657i | 0.966457 | + | 0.256829i | \(0.0826776\pi\) | ||||
−0.966457 | + | 0.256829i | \(0.917322\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.378937 | 0.0214876 | 0.0107438 | − | 0.999942i | \(-0.496580\pi\) | ||||
0.0107438 | + | 0.999942i | \(0.496580\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.0526 | 1.69867 | 0.849336 | − | 0.527853i | \(-0.177003\pi\) | ||||
0.849336 | + | 0.527853i | \(0.177003\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 16.8690i | − 0.947459i | −0.880670 | − | 0.473729i | \(-0.842907\pi\) | ||||
0.880670 | − | 0.473729i | \(-0.157093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 20.1962i | − 1.13077i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.89469 | −0.105423 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.82309 | 0.267537 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 3.20736i | − 0.176828i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.7846i | 1.36229i | 0.732151 | + | 0.681143i | \(0.238517\pi\) | ||||
−0.732151 | + | 0.681143i | \(0.761483\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.7290 | 1.24182 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.4641 | −0.678963 | −0.339481 | − | 0.940613i | \(-0.610252\pi\) | ||||
−0.339481 | + | 0.940613i | \(0.610252\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 49.8120i | 2.69747i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.00000i | − 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −20.1136 | −1.07975 | −0.539876 | − | 0.841744i | \(-0.681529\pi\) | ||||
−0.539876 | + | 0.841744i | \(0.681529\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.4641 | −1.47012 | −0.735060 | − | 0.678002i | \(-0.762846\pi\) | ||||
−0.735060 | + | 0.678002i | \(0.762846\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.4219i | 0.980501i | 0.871582 | + | 0.490250i | \(0.163095\pi\) | ||||
−0.871582 | + | 0.490250i | \(0.836905\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.712813i | 0.0378322i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.2827 | 0.701035 | 0.350518 | − | 0.936556i | \(-0.386006\pi\) | ||||
0.350518 | + | 0.936556i | \(0.386006\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.00000 | −0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.582009i | 0.0304638i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 14.5167i | − 0.757764i | −0.925445 | − | 0.378882i | \(-0.876309\pi\) | ||||
0.925445 | − | 0.378882i | \(-0.123691\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.76268 | −0.454936 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6603 | −0.655523 | −0.327762 | − | 0.944760i | \(-0.606294\pi\) | ||||
−0.327762 | + | 0.944760i | \(0.606294\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.37945i | 0.277056i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 17.8038i | − 0.914522i | −0.889332 | − | 0.457261i | \(-0.848830\pi\) | ||||
0.889332 | − | 0.457261i | \(-0.151170\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.82843 | 0.144526 | 0.0722629 | − | 0.997386i | \(-0.476978\pi\) | ||||
0.0722629 | + | 0.997386i | \(0.476978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.1244 | 0.719844 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 29.3195i | − 1.48656i | −0.668980 | − | 0.743280i | \(-0.733269\pi\) | ||||
0.668980 | − | 0.743280i | \(-0.266731\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 0.732051i | − 0.0370214i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.35225 | 0.269301 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.92820 | −0.448094 | −0.224047 | − | 0.974578i | \(-0.571927\pi\) | ||||
−0.224047 | + | 0.974578i | \(0.571927\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.0759i | 0.752853i | 0.926446 | + | 0.376427i | \(0.122847\pi\) | ||||
−0.926446 | + | 0.376427i | \(0.877153\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 13.2679i | − 0.660924i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7298 | 0.581425 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.5885 | 1.71029 | 0.855145 | − | 0.518390i | \(-0.173468\pi\) | ||||
0.855145 | + | 0.518390i | \(0.173468\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.48477i | 0.171474i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 23.2295i | − 1.14029i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.9086 | 1.02145 | 0.510726 | − | 0.859744i | \(-0.329377\pi\) | ||||
0.510726 | + | 0.859744i | \(0.329377\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.3205 | 0.697939 | 0.348969 | − | 0.937134i | \(-0.386532\pi\) | ||||
0.348969 | + | 0.937134i | \(0.386532\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 1.44142i | − 0.0699191i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.92820i | − 0.238492i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.7356 | 1.43232 | 0.716158 | − | 0.697938i | \(-0.245899\pi\) | ||||
0.716158 | + | 0.697938i | \(0.245899\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.2679 | −1.21430 | −0.607150 | − | 0.794587i | \(-0.707687\pi\) | ||||
−0.607150 | + | 0.794587i | \(0.707687\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 9.65926i | − 0.462065i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 10.2487i | − 0.489144i | −0.969631 | − | 0.244572i | \(-0.921352\pi\) | ||||
0.969631 | − | 0.244572i | \(-0.0786475\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.93666 | 0.472105 | 0.236052 | − | 0.971740i | \(-0.424146\pi\) | ||||
0.236052 | + | 0.971740i | \(0.424146\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.73205 | −0.271725 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 34.7733i | − 1.64105i | −0.571607 | − | 0.820527i | \(-0.693680\pi\) | ||||
0.571607 | − | 0.820527i | \(-0.306320\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 50.9090i | 2.39721i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.76217 | −0.176373 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.1769 | −1.22450 | −0.612252 | − | 0.790663i | \(-0.709736\pi\) | ||||
−0.612252 | + | 0.790663i | \(0.709736\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 20.3166i | − 0.946240i | −0.880998 | − | 0.473120i | \(-0.843128\pi\) | ||||
0.880998 | − | 0.473120i | \(-0.156872\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 12.2487i | − 0.569246i | −0.958640 | − | 0.284623i | \(-0.908132\pi\) | ||||
0.958640 | − | 0.284623i | \(-0.0918684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.1817 | −0.841349 | −0.420674 | − | 0.907212i | \(-0.638207\pi\) | ||||
−0.420674 | + | 0.907212i | \(0.638207\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.66025 | −0.353718 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.5259i | 1.03574i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 19.0192i | − 0.872662i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.9096 | 1.41230 | 0.706148 | − | 0.708064i | \(-0.250431\pi\) | ||||
0.706148 | + | 0.708064i | \(0.250431\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.12436 | −0.142458 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 38.3596i | 1.74182i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 16.5885i | − 0.751695i | −0.926682 | − | 0.375847i | \(-0.877352\pi\) | ||||
0.926682 | − | 0.375847i | \(-0.122648\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4214 | 0.605700 | 0.302850 | − | 0.953038i | \(-0.402062\pi\) | ||||
0.302850 | + | 0.953038i | \(0.402062\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.60770 | 0.0724069 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 0.240237i | − 0.0107761i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.6603i | 1.50684i | 0.657540 | + | 0.753420i | \(0.271597\pi\) | ||||
−0.657540 | + | 0.753420i | \(0.728403\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −19.4201 | −0.865897 | −0.432949 | − | 0.901419i | \(-0.642527\pi\) | ||||
−0.432949 | + | 0.901419i | \(0.642527\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.4115 | −0.596806 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00429i | 0.133163i | 0.997781 | + | 0.0665815i | \(0.0212092\pi\) | ||||
−0.997781 | + | 0.0665815i | \(0.978791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 0.196152i | − 0.00867727i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.4915 | 0.462309 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.2679 | −0.671484 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.0793i | 1.27399i | 0.770869 | + | 0.636994i | \(0.219822\pi\) | ||||
−0.770869 | + | 0.636994i | \(0.780178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.6603i | 1.25323i | 0.779331 | + | 0.626613i | \(0.215559\pi\) | ||||
−0.779331 | + | 0.626613i | \(0.784441\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.96524 | −0.172729 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.2679 | −0.837737 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 13.5601i | − 0.587354i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 26.3013i | − 1.13710i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.76028 | −0.205040 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.1051 | 1.42330 | 0.711650 | − | 0.702534i | \(-0.247948\pi\) | ||||
0.711650 | + | 0.702534i | \(0.247948\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 52.1872i | 2.23545i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.2132 | 0.903713 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.80385 | −0.0767074 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 35.5312i | − 1.50551i | −0.658303 | − | 0.752753i | \(-0.728726\pi\) | ||||
0.658303 | − | 0.752753i | \(-0.271274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 6.00000i | − 0.253773i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.4944 | 0.821590 | 0.410795 | − | 0.911728i | \(-0.365251\pi\) | ||||
0.410795 | + | 0.911728i | \(0.365251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.1769 | 1.05920 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 20.2795i | − 0.850159i | −0.905156 | − | 0.425080i | \(-0.860246\pi\) | ||||
0.905156 | − | 0.425080i | \(-0.139754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.24871i | − 0.0941056i | −0.998892 | − | 0.0470528i | \(-0.985017\pi\) | ||||
0.998892 | − | 0.0470528i | \(-0.0149829\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.34847 | 0.306452 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −26.3923 | −1.09873 | −0.549363 | − | 0.835584i | \(-0.685130\pi\) | ||||
−0.549363 | + | 0.835584i | \(0.685130\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.82894i | 0.324799i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 41.7128i | 1.72757i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −32.9802 | −1.36124 | −0.680619 | − | 0.732638i | \(-0.738289\pi\) | ||||
−0.680619 | + | 0.732638i | \(0.738289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −52.3205 | −2.15583 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 22.3872i | − 0.919331i | −0.888092 | − | 0.459666i | \(-0.847969\pi\) | ||||
0.888092 | − | 0.459666i | \(-0.152031\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12436i | 0.0460941i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 8.14351 | 0.332735 | 0.166367 | − | 0.986064i | \(-0.446796\pi\) | ||||
0.166367 | + | 0.986064i | \(0.446796\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −47.6603 | −1.94410 | −0.972051 | − | 0.234769i | \(-0.924567\pi\) | ||||
−0.972051 | + | 0.234769i | \(0.924567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 34.5975i | − 1.40659i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 23.1769i | − 0.940722i | −0.882474 | − | 0.470361i | \(-0.844124\pi\) | ||||
0.882474 | − | 0.470361i | \(-0.155876\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.06678 | 0.164524 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.58846 | 0.0641572 | 0.0320786 | − | 0.999485i | \(-0.489787\pi\) | ||||
0.0320786 | + | 0.999485i | \(0.489787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 10.4543i | − 0.420874i | −0.977607 | − | 0.210437i | \(-0.932511\pi\) | ||||
0.977607 | − | 0.210437i | \(-0.0674887\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.3397i | 0.455783i | 0.973687 | + | 0.227891i | \(0.0731831\pi\) | ||||
−0.973687 | + | 0.227891i | \(0.926817\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.93185 | 0.0773980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.5500 | −1.18200 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.933740i | 0.0372307i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.0526i | 0.877899i | 0.898512 | + | 0.438949i | \(0.144649\pi\) | ||||
−0.898512 | + | 0.438949i | \(0.855351\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −52.4002 | −2.07944 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.26795 | 0.0502380 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 7.72741i | − 0.305214i | −0.988287 | − | 0.152607i | \(-0.951233\pi\) | ||||
0.988287 | − | 0.152607i | \(-0.0487669\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 4.85641i | − 0.191518i | −0.995405 | − | 0.0957590i | \(-0.969472\pi\) | ||||
0.995405 | − | 0.0957590i | \(-0.0305278\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 22.7290 | 0.893567 | 0.446784 | − | 0.894642i | \(-0.352569\pi\) | ||||
0.446784 | + | 0.894642i | \(0.352569\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 16.5885 | 0.651154 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.7738i | 1.55647i | 0.627973 | + | 0.778235i | \(0.283885\pi\) | ||||
−0.627973 | + | 0.778235i | \(0.716115\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 4.19615i | − 0.163957i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.0072 | −0.467735 | −0.233867 | − | 0.972269i | \(-0.575138\pi\) | ||||
−0.233867 | + | 0.972269i | \(0.575138\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.73205 | −0.339637 | −0.169819 | − | 0.985475i | \(-0.554318\pi\) | ||||
−0.169819 | + | 0.985475i | \(0.554318\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.8356i | 0.575301i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.19615i | 0.317356i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −23.4596 | −0.905649 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.928203 | 0.0357796 | 0.0178898 | − | 0.999840i | \(-0.494305\pi\) | ||||
0.0178898 | + | 0.999840i | \(0.494305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 12.2846i | − 0.472136i | −0.971737 | − | 0.236068i | \(-0.924141\pi\) | ||||
0.971737 | − | 0.236068i | \(-0.0758588\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 12.9282i | − 0.496139i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.83083 | −0.261374 | −0.130687 | − | 0.991424i | \(-0.541718\pi\) | ||||
−0.130687 | + | 0.991424i | \(0.541718\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.3397 | 0.395061 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 11.1106i | − 0.423282i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.3205i | 1.49582i | 0.663799 | + | 0.747911i | \(0.268943\pi\) | ||||
−0.663799 | + | 0.747911i | \(0.731057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.5894 | 1.27412 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.05256 | −0.153502 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 27.1475i | − 1.02535i | −0.858584 | − | 0.512673i | \(-0.828655\pi\) | ||||
0.858584 | − | 0.512673i | \(-0.171345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3205i | 0.464677i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.52004 | 0.169994 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.660254 | −0.0247964 | −0.0123982 | − | 0.999923i | \(-0.503947\pi\) | ||||
−0.0123982 | + | 0.999923i | \(0.503947\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 20.2151i | − 0.757061i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.9090i | 0.669757i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −35.9845 | −1.34199 | −0.670997 | − | 0.741460i | \(-0.734134\pi\) | ||||
−0.670997 | + | 0.741460i | \(0.734134\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.53590 | −0.131684 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 16.1384i | 0.599364i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.9282i | 0.702008i | 0.936374 | + | 0.351004i | \(0.114160\pi\) | ||||
−0.936374 | + | 0.351004i | \(0.885840\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.79315 | −0.0663221 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.1962 | −1.33694 | −0.668468 | − | 0.743741i | \(-0.733050\pi\) | ||||
−0.668468 | + | 0.743741i | \(0.733050\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 36.4649i | 1.34320i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.07180i | − 0.0394267i | −0.999806 | − | 0.0197133i | \(-0.993725\pi\) | ||||
0.999806 | − | 0.0197133i | \(-0.00627536\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0430 | −0.661934 | −0.330967 | − | 0.943642i | \(-0.607375\pi\) | ||||
−0.330967 | + | 0.943642i | \(0.607375\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58.7461 | 2.15229 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.86422i | 0.323892i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 3.66025i | − 0.133565i | −0.997768 | − | 0.0667823i | \(-0.978727\pi\) | ||||
0.997768 | − | 0.0667823i | \(-0.0212733\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −44.2939 | −1.61202 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 52.6410 | 1.91327 | 0.956635 | − | 0.291289i | \(-0.0940841\pi\) | ||||
0.956635 | + | 0.291289i | \(0.0940841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.2533i | 1.09668i | 0.836255 | + | 0.548340i | \(0.184740\pi\) | ||||
−0.836255 | + | 0.548340i | \(0.815260\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 17.5885i | − 0.636745i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.41851 | −0.159543 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.339746 | 0.0122516 | 0.00612578 | − | 0.999981i | \(-0.498050\pi\) | ||||
0.00612578 | + | 0.999981i | \(0.498050\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 22.5630i | − 0.811536i | −0.913976 | − | 0.405768i | \(-0.867004\pi\) | ||||
0.913976 | − | 0.405768i | \(-0.132996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 39.8038i | − 1.42980i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −53.4727 | −1.91586 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.14359 | −0.0409210 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 19.9749i | − 0.712933i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 27.3205i | − 0.973871i | −0.873438 | − | 0.486935i | \(-0.838115\pi\) | ||||
0.873438 | − | 0.486935i | \(-0.161885\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.48528 | −0.301702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.24871 | 0.221898 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 45.9483i | − 1.62757i | −0.581164 | − | 0.813787i | \(-0.697402\pi\) | ||||
0.581164 | − | 0.813787i | \(-0.302598\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 1.21539i | − 0.0429974i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.933740 | −0.0329510 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.73205 | −0.202028 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.58682i | 0.301896i | 0.988542 | + | 0.150948i | \(0.0482327\pi\) | ||||
−0.988542 | + | 0.150948i | \(0.951767\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.3397i | 0.960028i | 0.877261 | + | 0.480014i | \(0.159368\pi\) | ||||
−0.877261 | + | 0.480014i | \(0.840632\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −53.5642 | −1.87627 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.6603 | −0.827768 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.4698i | 1.55201i | 0.630730 | + | 0.776003i | \(0.282756\pi\) | ||||
−0.630730 | + | 0.776003i | \(0.717244\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20.9282i | 0.729511i | 0.931103 | + | 0.364756i | \(0.118847\pi\) | ||||
−0.931103 | + | 0.364756i | \(0.881153\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 53.2968 | 1.85331 | 0.926656 | − | 0.375911i | \(-0.122670\pi\) | ||||
0.926656 | + | 0.375911i | \(0.122670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 25.8038 | 0.896205 | 0.448102 | − | 0.893982i | \(-0.352100\pi\) | ||||
0.448102 | + | 0.893982i | \(0.352100\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 0.378937i | − 0.0131294i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 67.9615i | 2.35191i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.0797 | 0.451560 | 0.225780 | − | 0.974178i | \(-0.427507\pi\) | ||||
0.225780 | + | 0.974178i | \(0.427507\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.0000 | 0.379310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.8024i | 1.16284i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.6603i | 0.400651i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.76028 | −0.163180 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.0000 | 0.616308 | 0.308154 | − | 0.951336i | \(-0.400289\pi\) | ||||
0.308154 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 14.3552i | − 0.490363i | −0.969477 | − | 0.245182i | \(-0.921152\pi\) | ||||
0.969477 | − | 0.245182i | \(-0.0788476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 21.1051i | − 0.720097i | −0.932934 | − | 0.360049i | \(-0.882760\pi\) | ||||
0.932934 | − | 0.360049i | \(-0.117240\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.0512 | −1.36336 | −0.681680 | − | 0.731650i | \(-0.738750\pi\) | ||||
−0.681680 | + | 0.731650i | \(0.738750\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 30.6077 | 1.04069 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.58682i | 0.291288i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 9.71281i | − 0.329106i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.54914 | 0.119983 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8564 | −1.54846 | −0.774230 | − | 0.632904i | \(-0.781863\pi\) | ||||
−0.774230 | + | 0.632904i | \(0.781863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.3973i | 1.46209i | 0.682328 | + | 0.731046i | \(0.260968\pi\) | ||||
−0.682328 | + | 0.731046i | \(0.739032\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.3923i | 0.349729i | 0.984593 | + | 0.174864i | \(0.0559487\pi\) | ||||
−0.984593 | + | 0.174864i | \(0.944051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −25.5574 | −0.858133 | −0.429066 | − | 0.903273i | \(-0.641157\pi\) | ||||
−0.429066 | + | 0.903273i | \(0.641157\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.6603 | 0.592306 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 16.0368i | − 0.536652i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 35.5167i | 1.18719i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 44.3954 | 1.48067 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.32051 | −0.110622 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 73.5391i | − 2.44452i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 15.0718i | − 0.500451i | −0.968188 | − | 0.250225i | \(-0.919495\pi\) | ||||
0.968188 | − | 0.250225i | \(-0.0805047\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.6023 | 1.41148 | 0.705738 | − | 0.708473i | \(-0.250616\pi\) | ||||
0.705738 | + | 0.708473i | \(0.250616\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.2679 | 1.23339 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.41421i | 0.0467014i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 25.7128i | − 0.848187i | −0.905618 | − | 0.424094i | \(-0.860593\pi\) | ||||
0.905618 | − | 0.424094i | \(-0.139407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.304608 | 0.0100263 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.37307 | −0.308185 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 40.0512i | − 1.31404i | −0.753874 | − | 0.657019i | \(-0.771817\pi\) | ||||
0.753874 | − | 0.657019i | \(-0.228183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 5.00000i | − 0.163868i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.35225 | 0.175037 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.5692 | 1.03132 | 0.515661 | − | 0.856793i | \(-0.327547\pi\) | ||||
0.515661 | + | 0.856793i | \(0.327547\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.55343i | 0.213636i | 0.994279 | + | 0.106818i | \(0.0340662\pi\) | ||||
−0.994279 | + | 0.106818i | \(0.965934\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 20.6603i | − 0.672790i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.2765 | 0.366438 | 0.183219 | − | 0.983072i | \(-0.441348\pi\) | ||||
0.183219 | + | 0.983072i | \(0.441348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.248711 | 0.00807351 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 59.5728i | − 1.92975i | −0.262703 | − | 0.964877i | \(-0.584614\pi\) | ||||
0.262703 | − | 0.964877i | \(-0.415386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 14.9474i | − 0.483688i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.48477 | −0.112529 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.4974 | −2.53217 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 27.6551i | − 0.890250i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 24.2487i | − 0.779786i | −0.920860 | − | 0.389893i | \(-0.872512\pi\) | ||||
0.920860 | − | 0.389893i | \(-0.127488\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.0368 | −0.514646 | −0.257323 | − | 0.966325i | \(-0.582840\pi\) | ||||
−0.257323 | + | 0.966325i | \(0.582840\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.3205 | −0.362919 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 41.2624i | − 1.32010i | −0.751221 | − | 0.660050i | \(-0.770535\pi\) | ||||
0.751221 | − | 0.660050i | \(-0.229465\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 9.19615i | − 0.293910i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 61.1629 | 1.95079 | 0.975397 | − | 0.220456i | \(-0.0707544\pi\) | ||||
0.975397 | + | 0.220456i | \(0.0707544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 59.5692 | 1.89803 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 9.14162i | − 0.290687i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.8372i | 1.04311i | 0.853219 | + | 0.521554i | \(0.174647\pi\) | ||||
−0.853219 | + | 0.521554i | \(0.825353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 42.3348 | 1.34210 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −15.0718 | −0.477329 | −0.238664 | − | 0.971102i | \(-0.576710\pi\) | ||||
−0.238664 | + | 0.971102i | \(0.576710\pi\) | |||||||
\(998\) | 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 | 6048.2.h.b.2591.4 | yes | 8 | |
3.2 | odd | 2 | inner | 6048.2.h.b.2591.6 | yes | 8 | |
4.3 | odd | 2 | inner | 6048.2.h.b.2591.3 | ✓ | 8 | |
12.11 | even | 2 | inner | 6048.2.h.b.2591.5 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.h.b.2591.3 | ✓ | 8 | 4.3 | odd | 2 | inner | |
6048.2.h.b.2591.4 | yes | 8 | 1.1 | even | 1 | trivial | |
6048.2.h.b.2591.5 | yes | 8 | 12.11 | even | 2 | inner | |
6048.2.h.b.2591.6 | yes | 8 | 3.2 | odd | 2 | inner |