Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.788.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 7x - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.476452\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.476452 | −0.180082 | −0.0900410 | − | 0.995938i | \(-0.528700\pi\) | ||||
−0.0900410 | + | 0.995938i | \(0.528700\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.34364 | −1.00814 | −0.504072 | − | 0.863661i | \(-0.668165\pi\) | ||||
−0.504072 | + | 0.863661i | \(0.668165\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | −0.121268 | − | 0.992620i | \(-0.538696\pi\) | ||||
−0.121268 | + | 0.992620i | \(0.538696\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.77299 | −1.55383 | −0.776916 | − | 0.629605i | \(-0.783217\pi\) | ||||
−0.776916 | + | 0.629605i | \(0.783217\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.476452 | −0.103970 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.77299 | 0.995238 | 0.497619 | − | 0.867396i | \(-0.334208\pi\) | ||||
0.497619 | + | 0.867396i | \(0.334208\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.59308 | 1.41000 | 0.705000 | − | 0.709207i | \(-0.250947\pi\) | ||||
0.705000 | + | 0.709207i | \(0.250947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.93672 | 1.42548 | 0.712739 | − | 0.701430i | \(-0.247455\pi\) | ||||
0.712739 | + | 0.701430i | \(0.247455\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.34364 | −0.582053 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.82009 | −1.28561 | −0.642807 | − | 0.766028i | \(-0.722230\pi\) | ||||
−0.642807 | + | 0.766028i | \(0.722230\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.46027 | 1.47745 | 0.738723 | − | 0.674009i | \(-0.235429\pi\) | ||||
0.738723 | + | 0.674009i | \(0.235429\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.82009 | −0.277561 | −0.138781 | − | 0.990323i | \(-0.544318\pi\) | ||||
−0.138781 | + | 0.990323i | \(0.544318\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.06953 | 1.32293 | 0.661464 | − | 0.749977i | \(-0.269936\pi\) | ||||
0.661464 | + | 0.749977i | \(0.269936\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.77299 | −0.967570 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.50736 | −1.30594 | −0.652968 | − | 0.757385i | \(-0.726477\pi\) | ||||
−0.652968 | + | 0.757385i | \(0.726477\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.77299 | −0.897105 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.16373 | 0.411882 | 0.205941 | − | 0.978564i | \(-0.433974\pi\) | ||||
0.205941 | + | 0.978564i | \(0.433974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.59308 | −1.22827 | −0.614134 | − | 0.789202i | \(-0.710495\pi\) | ||||
−0.614134 | + | 0.789202i | \(0.710495\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.476452 | −0.0600273 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.34364 | 0.164151 | 0.0820757 | − | 0.996626i | \(-0.473845\pi\) | ||||
0.0820757 | + | 0.996626i | \(0.473845\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.77299 | 0.574601 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.86719 | −0.577629 | −0.288814 | − | 0.957385i | \(-0.593261\pi\) | ||||
−0.288814 | + | 0.957385i | \(0.593261\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4132 | 1.68693 | 0.843467 | − | 0.537181i | \(-0.180511\pi\) | ||||
0.843467 | + | 0.537181i | \(0.180511\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.59308 | 0.181549 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.17991 | −0.245259 | −0.122630 | − | 0.992453i | \(-0.539133\pi\) | ||||
−0.122630 | + | 0.992453i | \(0.539133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.16373 | −1.00585 | −0.502925 | − | 0.864330i | \(-0.667743\pi\) | ||||
−0.502925 | + | 0.864330i | \(0.667743\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.59308 | 0.814064 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.5931 | −1.12286 | −0.561432 | − | 0.827523i | \(-0.689749\pi\) | ||||
−0.561432 | + | 0.827523i | \(0.689749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.476452 | 0.0499457 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.93672 | 0.823000 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.04710 | −0.715524 | −0.357762 | − | 0.933813i | \(-0.616460\pi\) | ||||
−0.357762 | + | 0.933813i | \(0.616460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.34364 | −0.336048 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.3661 | −1.82749 | −0.913746 | − | 0.406285i | \(-0.866824\pi\) | ||||
−0.913746 | + | 0.406285i | \(0.866824\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.5545 | 1.33556 | 0.667780 | − | 0.744358i | \(-0.267245\pi\) | ||||
0.667780 | + | 0.744358i | \(0.267245\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.2333 | −1.56933 | −0.784664 | − | 0.619921i | \(-0.787165\pi\) | ||||
−0.784664 | + | 0.619921i | \(0.787165\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.4132 | −1.57210 | −0.786048 | − | 0.618165i | \(-0.787876\pi\) | ||||
−0.786048 | + | 0.618165i | \(0.787876\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.82009 | −0.742250 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.59308 | −0.808369 | −0.404185 | − | 0.914677i | \(-0.632445\pi\) | ||||
−0.404185 | + | 0.914677i | \(0.632445\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.476452 | 0.0436763 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.179911 | 0.0163555 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.46027 | 0.853004 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.86719 | −0.254422 | −0.127211 | − | 0.991876i | \(-0.540602\pi\) | ||||
−0.127211 | + | 0.991876i | \(0.540602\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.82009 | −0.160250 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.1475 | −1.41082 | −0.705409 | − | 0.708801i | \(-0.749237\pi\) | ||||
−0.705409 | + | 0.708801i | \(0.749237\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.22701 | 0.279817 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.2333 | −1.89952 | −0.949758 | − | 0.312986i | \(-0.898671\pi\) | ||||
−0.949758 | + | 0.312986i | \(0.898671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.28036 | 0.787150 | 0.393575 | − | 0.919293i | \(-0.371238\pi\) | ||||
0.393575 | + | 0.919293i | \(0.371238\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.06953 | 0.763793 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.34364 | 0.279609 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.77299 | −0.558627 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.1391 | −1.81370 | −0.906852 | − | 0.421450i | \(-0.861521\pi\) | ||||
−0.906852 | + | 0.421450i | \(0.861521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.0224 | −1.30389 | −0.651944 | − | 0.758267i | \(-0.726046\pi\) | ||||
−0.651944 | + | 0.758267i | \(0.726046\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.22701 | −0.496969 | −0.248485 | − | 0.968636i | \(-0.579933\pi\) | ||||
−0.248485 | + | 0.968636i | \(0.579933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.50736 | −0.753983 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.27410 | −0.179224 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.6935 | −1.38586 | −0.692932 | − | 0.721003i | \(-0.743681\pi\) | ||||
−0.692932 | + | 0.721003i | \(0.743681\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.179911 | −0.0139219 | −0.00696095 | − | 0.999976i | \(-0.502216\pi\) | ||||
−0.00696095 | + | 0.999976i | \(0.502216\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.77299 | −0.517944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.4603 | 0.947337 | 0.473668 | − | 0.880703i | \(-0.342930\pi\) | ||||
0.473668 | + | 0.880703i | \(0.342930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.16373 | 0.237800 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.55446 | −0.415160 | −0.207580 | − | 0.978218i | \(-0.566559\pi\) | ||||
−0.207580 | + | 0.978218i | \(0.566559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.0063 | 1.78437 | 0.892185 | − | 0.451669i | \(-0.149171\pi\) | ||||
0.892185 | + | 0.451669i | \(0.149171\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.59308 | −0.709141 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.34364 | 0.244511 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.476452 | −0.0346568 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.18617 | 0.230543 | 0.115271 | − | 0.993334i | \(-0.463226\pi\) | ||||
0.115271 | + | 0.993334i | \(0.463226\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.8672 | 1.07016 | 0.535082 | − | 0.844800i | \(-0.320281\pi\) | ||||
0.535082 | + | 0.844800i | \(0.320281\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −23.7259 | −1.69040 | −0.845200 | − | 0.534450i | \(-0.820519\pi\) | ||||
−0.845200 | + | 0.534450i | \(0.820519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.64018 | −0.683374 | −0.341687 | − | 0.939814i | \(-0.610998\pi\) | ||||
−0.341687 | + | 0.939814i | \(0.610998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.34364 | 0.0947729 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.61774 | −0.253916 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.77299 | 0.331746 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.6464 | 1.56649 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.8672 | −0.748128 | −0.374064 | − | 0.927403i | \(-0.622036\pi\) | ||||
−0.374064 | + | 0.927403i | \(0.622036\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.86719 | −0.333494 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.78147 | −0.256703 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.4132 | 0.973952 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | 0.0672673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.2417 | 1.48942 | 0.744708 | − | 0.667390i | \(-0.232589\pi\) | ||||
0.744708 | + | 0.667390i | \(0.232589\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.4827 | −1.55860 | −0.779301 | − | 0.626650i | \(-0.784426\pi\) | ||||
−0.779301 | + | 0.626650i | \(0.784426\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 28.3723 | 1.87490 | 0.937448 | − | 0.348125i | \(-0.113181\pi\) | ||||
0.937448 | + | 0.348125i | \(0.113181\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.59308 | 0.104817 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.5931 | 1.08705 | 0.543524 | − | 0.839393i | \(-0.317089\pi\) | ||||
0.543524 | + | 0.839393i | \(0.317089\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −2.17991 | −0.141600 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0224 | 0.777667 | 0.388833 | − | 0.921308i | \(-0.372878\pi\) | ||||
0.388833 | + | 0.921308i | \(0.372878\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.6935 | −1.52623 | −0.763117 | − | 0.646260i | \(-0.776332\pi\) | ||||
−0.763117 | + | 0.646260i | \(0.776332\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.77299 | 0.430955 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.16373 | −0.580728 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7406 | 1.18290 | 0.591449 | − | 0.806342i | \(-0.298556\pi\) | ||||
0.591449 | + | 0.806342i | \(0.298556\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.9592 | −1.00334 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.24173 | 0.576484 | 0.288242 | − | 0.957558i | \(-0.406929\pi\) | ||||
0.288242 | + | 0.957558i | \(0.406929\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.72590 | 0.231516 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.59308 | 0.470000 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 17.9143 | 1.10464 | 0.552321 | − | 0.833632i | \(-0.313742\pi\) | ||||
0.552321 | + | 0.833632i | \(0.313742\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.5931 | −0.648286 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.28036 | −0.382920 | −0.191460 | − | 0.981500i | \(-0.561322\pi\) | ||||
−0.191460 | + | 0.981500i | \(0.561322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.2881 | −1.11092 | −0.555461 | − | 0.831543i | \(-0.687458\pi\) | ||||
−0.555461 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.476452 | 0.0288362 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.7645 | −0.766946 | −0.383473 | − | 0.923552i | \(-0.625272\pi\) | ||||
−0.383473 | + | 0.923552i | \(0.625272\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.93672 | 0.475159 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.8263 | −1.60033 | −0.800163 | − | 0.599783i | \(-0.795254\pi\) | ||||
−0.800163 | + | 0.599783i | \(0.795254\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.4518 | 1.27518 | 0.637588 | − | 0.770377i | \(-0.279932\pi\) | ||||
0.637588 | + | 0.770377i | \(0.279932\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.50736 | −0.266061 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.0000 | −0.941176 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.04710 | −0.413108 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.3745 | 0.664508 | 0.332254 | − | 0.943190i | \(-0.392191\pi\) | ||||
0.332254 | + | 0.943190i | \(0.392191\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.34364 | −0.194018 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.77299 | −0.276029 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.867185 | 0.0499837 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −18.3661 | −1.05510 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0857 | 0.803914 | 0.401957 | − | 0.915658i | \(-0.368330\pi\) | ||||
0.401957 | + | 0.915658i | \(0.368330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 13.5545 | 0.771086 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.4518 | −0.989601 | −0.494800 | − | 0.869007i | \(-0.664759\pi\) | ||||
−0.494800 | + | 0.869007i | \(0.664759\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.39844 | 0.361661 | 0.180831 | − | 0.983514i | \(-0.442121\pi\) | ||||
0.180831 | + | 0.983514i | \(0.442121\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.58683 | −0.313788 | −0.156894 | − | 0.987615i | \(-0.550148\pi\) | ||||
−0.156894 | + | 0.987615i | \(0.550148\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −25.3885 | −1.42148 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −16.2333 | −0.906052 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.77299 | 0.376859 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −16.4132 | −0.907650 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.32120 | −0.238235 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.4132 | 0.572360 | 0.286180 | − | 0.958176i | \(-0.407615\pi\) | ||||
0.286180 | + | 0.958176i | \(0.407615\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.82009 | −0.428538 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.3661 | 0.891517 | 0.445758 | − | 0.895153i | \(-0.352934\pi\) | ||||
0.445758 | + | 0.895153i | \(0.352934\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.59308 | −0.466712 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −26.5375 | −1.43709 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.56217 | 0.354324 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.3723 | 1.95257 | 0.976285 | − | 0.216491i | \(-0.0694613\pi\) | ||||
0.976285 | + | 0.216491i | \(0.0694613\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.7259 | −0.948846 | −0.474423 | − | 0.880297i | \(-0.657343\pi\) | ||||
−0.474423 | + | 0.880297i | \(0.657343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19.5375 | −1.03988 | −0.519938 | − | 0.854204i | \(-0.674045\pi\) | ||||
−0.519938 | + | 0.854204i | \(0.674045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.476452 | 0.0252165 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.92825 | −0.312881 | −0.156440 | − | 0.987687i | \(-0.550002\pi\) | ||||
−0.156440 | + | 0.987687i | \(0.550002\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.8734 | 1.41439 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.179911 | 0.00944286 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.2804 | 1.42402 | 0.712012 | − | 0.702168i | \(-0.247784\pi\) | ||||
0.712012 | + | 0.702168i | \(0.247784\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.46027 | 0.492482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.52980 | 0.235176 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.2866 | 1.41285 | 0.706424 | − | 0.707789i | \(-0.250307\pi\) | ||||
0.706424 | + | 0.707789i | \(0.250307\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.59308 | −0.391064 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.4503 | −1.71823 | −0.859114 | − | 0.511784i | \(-0.828985\pi\) | ||||
−0.859114 | + | 0.511784i | \(0.828985\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.86719 | −0.146890 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.60156 | −0.132933 | −0.0664666 | − | 0.997789i | \(-0.521173\pi\) | ||||
−0.0664666 | + | 0.997789i | \(0.521173\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.82009 | −0.0925203 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.781467 | −0.0396219 | −0.0198110 | − | 0.999804i | \(-0.506306\pi\) | ||||
−0.0198110 | + | 0.999804i | \(0.506306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.77299 | −0.241381 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.1475 | −0.814536 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.49889 | 0.326170 | 0.163085 | − | 0.986612i | \(-0.447856\pi\) | ||||
0.163085 | + | 0.986612i | \(0.447856\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.22701 | 0.161552 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0063 | 1.04900 | 0.524501 | − | 0.851410i | \(-0.324252\pi\) | ||||
0.524501 | + | 0.851410i | \(0.324252\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.93672 | −0.395356 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.1475 | 1.29609 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.08572 | −0.399813 | −0.199907 | − | 0.979815i | \(-0.564064\pi\) | ||||
−0.199907 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.2333 | −1.09669 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.50736 | −0.0741725 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.28036 | 0.454461 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.91428 | 0.0935188 | 0.0467594 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467594 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.1089 | −1.32121 | −0.660604 | − | 0.750735i | \(-0.729700\pi\) | ||||
−0.660604 | + | 0.750735i | \(0.729700\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.06953 | 0.440976 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.57064 | 0.221189 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.34364 | 0.161432 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.0386 | −0.628048 | −0.314024 | − | 0.949415i | \(-0.601677\pi\) | ||||
−0.314024 | + | 0.949415i | \(0.601677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.3275 | 1.26522 | 0.632608 | − | 0.774472i | \(-0.281984\pi\) | ||||
0.632608 | + | 0.774472i | \(0.281984\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −32.3275 | −1.54643 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.69353 | 0.367192 | 0.183596 | − | 0.983002i | \(-0.441226\pi\) | ||||
0.183596 | + | 0.983002i | \(0.441226\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.77299 | −0.322523 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −23.7259 | −1.12725 | −0.563626 | − | 0.826030i | \(-0.690594\pi\) | ||||
−0.563626 | + | 0.826030i | \(0.690594\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22.1391 | −1.04714 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.73437 | 0.459393 | 0.229697 | − | 0.973262i | \(-0.426227\pi\) | ||||
0.229697 | + | 0.973262i | \(0.426227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.6317 | −1.48948 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0224 | −0.752800 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.64865 | 0.264233 | 0.132116 | − | 0.991234i | \(-0.457823\pi\) | ||||
0.132116 | + | 0.991234i | \(0.457823\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.4540 | −0.580041 | −0.290021 | − | 0.957020i | \(-0.593662\pi\) | ||||
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.2642 | −0.662912 | −0.331456 | − | 0.943471i | \(-0.607540\pi\) | ||||
−0.331456 | + | 0.943471i | \(0.607540\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.7815 | 0.869103 | 0.434551 | − | 0.900647i | \(-0.356907\pi\) | ||||
0.434551 | + | 0.900647i | \(0.356907\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.640179 | −0.0295607 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.22701 | −0.286925 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.08572 | 0.279822 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.50736 | −0.435312 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.7954 | −0.584638 | −0.292319 | − | 0.956321i | \(-0.594427\pi\) | ||||
−0.292319 | + | 0.956321i | \(0.594427\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.82009 | 0.356565 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.27410 | −0.103475 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.4378 | −0.699555 | −0.349777 | − | 0.936833i | \(-0.613743\pi\) | ||||
−0.349777 | + | 0.936833i | \(0.613743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.6935 | −0.800129 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.3745 | −0.513326 | −0.256663 | − | 0.966501i | \(-0.582623\pi\) | ||||
−0.256663 | + | 0.966501i | \(0.582623\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.59308 | −0.341975 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.31898 | 0.104020 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 43.7075 | 1.95662 | 0.978308 | − | 0.207155i | \(-0.0664205\pi\) | ||||
0.978308 | + | 0.207155i | \(0.0664205\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.179911 | −0.00803781 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5846 | −0.471944 | −0.235972 | − | 0.971760i | \(-0.575827\pi\) | ||||
−0.235972 | + | 0.971760i | \(0.575827\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.05335 | 0.179662 | 0.0898308 | − | 0.995957i | \(-0.471367\pi\) | ||||
0.0898308 | + | 0.995957i | \(0.471367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.86719 | −0.303786 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.77299 | −0.299035 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.3252 | −1.33370 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12.4603 | 0.546945 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.1862 | 0.840561 | 0.420281 | − | 0.907394i | \(-0.361932\pi\) | ||||
0.420281 | + | 0.907394i | \(0.361932\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.2333 | 1.75928 | 0.879639 | − | 0.475642i | \(-0.157784\pi\) | ||||
0.879639 | + | 0.475642i | \(0.157784\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.93672 | −0.345729 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.218533 | −0.00950146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.16373 | 0.137294 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.46027 | −0.409770 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.55446 | −0.239693 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 22.6464 | 0.975451 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.7708 | 1.88185 | 0.940926 | − | 0.338611i | \(-0.109957\pi\) | ||||
0.940926 | + | 0.338611i | \(0.109957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.0063 | 1.03021 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.72590 | −0.0737940 | −0.0368970 | − | 0.999319i | \(-0.511747\pi\) | ||||
−0.0368970 | + | 0.999319i | \(0.511747\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.59308 | −0.409423 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −51.4279 | −2.19090 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.03862 | 0.0441667 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.6016 | −0.703430 | −0.351715 | − | 0.936107i | \(-0.614401\pi\) | ||||
−0.351715 | + | 0.936107i | \(0.614401\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.82009 | 0.0769816 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.34364 | 0.141168 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.1453 | 1.14404 | 0.572020 | − | 0.820240i | \(-0.306160\pi\) | ||||
0.572020 | + | 0.820240i | \(0.306160\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.476452 | −0.0200091 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.0232 | −1.00710 | −0.503552 | − | 0.863965i | \(-0.667974\pi\) | ||||
−0.503552 | + | 0.863965i | \(0.667974\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.9592 | 1.58854 | 0.794271 | − | 0.607564i | \(-0.207853\pi\) | ||||
0.794271 | + | 0.607564i | \(0.207853\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.18617 | 0.133104 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −39.7020 | −1.65282 | −0.826408 | − | 0.563072i | \(-0.809619\pi\) | ||||
−0.826408 | + | 0.563072i | \(0.809619\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.8672 | 0.617859 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.36608 | 0.181135 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 31.7892 | 1.31657 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 32.6070 | 1.34584 | 0.672918 | − | 0.739717i | \(-0.265040\pi\) | ||||
0.672918 | + | 0.739717i | \(0.265040\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −53.7554 | −2.21495 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.7259 | −0.975953 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.454013 | 0.0186441 | 0.00932204 | − | 0.999957i | \(-0.497033\pi\) | ||||
0.00932204 | + | 0.999957i | \(0.497033\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −9.64018 | −0.394546 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.31898 | −0.339904 | −0.169952 | − | 0.985452i | \(-0.554361\pi\) | ||||
−0.169952 | + | 0.985452i | \(0.554361\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.3337 | 1.48208 | 0.741041 | − | 0.671459i | \(-0.234332\pi\) | ||||
0.741041 | + | 0.671459i | \(0.234332\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.34364 | 0.0547171 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.9654 | −1.41920 | −0.709601 | − | 0.704604i | \(-0.751125\pi\) | ||||
−0.709601 | + | 0.704604i | \(0.751125\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.61774 | −0.146598 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.06953 | −0.366914 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.3745 | −0.620972 | −0.310486 | − | 0.950578i | \(-0.600492\pi\) | ||||
−0.310486 | + | 0.950578i | \(0.600492\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.8734 | 0.478007 | 0.239003 | − | 0.971019i | \(-0.423179\pi\) | ||||
0.239003 | + | 0.971019i | \(0.423179\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.1946 | 0.530337 | 0.265169 | − | 0.964202i | \(-0.414572\pi\) | ||||
0.265169 | + | 0.964202i | \(0.414572\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.77299 | 0.191534 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.04710 | 0.202208 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 22.6464 | 0.904411 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.82009 | 0.311807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.63392 | −0.104855 | −0.0524274 | − | 0.998625i | \(-0.516696\pi\) | ||||
−0.0524274 | + | 0.998625i | \(0.516696\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.8672 | −0.431932 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.77299 | 0.268356 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.86719 | −0.192543 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.4687 | −0.729471 | −0.364736 | − | 0.931111i | \(-0.618841\pi\) | ||||
−0.364736 | + | 0.931111i | \(0.618841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.5074 | 1.43971 | 0.719855 | − | 0.694125i | \(-0.244208\pi\) | ||||
0.719855 | + | 0.694125i | \(0.244208\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.40692 | 0.0553116 | 0.0276558 | − | 0.999618i | \(-0.491196\pi\) | ||||
0.0276558 | + | 0.999618i | \(0.491196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.5784 | −0.415237 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.78147 | −0.148207 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.7469 | 1.51628 | 0.758141 | − | 0.652090i | \(-0.226108\pi\) | ||||
0.758141 | + | 0.652090i | \(0.226108\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.4132 | 0.562311 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.0857 | 1.09406 | 0.547032 | − | 0.837112i | \(-0.315758\pi\) | ||||
0.547032 | + | 0.837112i | \(0.315758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −45.2071 | −1.75835 | −0.879177 | − | 0.476495i | \(-0.841907\pi\) | ||||
−0.879177 | + | 0.476495i | \(0.841907\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.00000 | 0.0388368 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.2417 | 1.40329 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 22.2417 | 0.859915 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 32.0758 | 1.23827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 21.2741 | 0.820056 | 0.410028 | − | 0.912073i | \(-0.365519\pi\) | ||||
0.410028 | + | 0.912073i | \(0.365519\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.5460 | −0.751213 | −0.375607 | − | 0.926779i | \(-0.622566\pi\) | ||||
−0.375607 | + | 0.926779i | \(0.622566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.35760 | 0.128853 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.4827 | −0.899859 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −7.79765 | −0.298369 | −0.149184 | − | 0.988809i | \(-0.547665\pi\) | ||||
−0.149184 | + | 0.988809i | \(0.547665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.3723 | 1.08247 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.50736 | 0.362202 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.7267 | −0.788479 | −0.394240 | − | 0.919008i | \(-0.628992\pi\) | ||||
−0.394240 | + | 0.919008i | \(0.628992\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.59308 | 0.0605162 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.46027 | −0.358333 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.5931 | 0.627608 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −32.7792 | −1.23806 | −0.619028 | − | 0.785369i | \(-0.712473\pi\) | ||||
−0.619028 | + | 0.785369i | \(0.712473\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.9654 | 1.99763 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.75055 | 0.329098 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.08572 | 0.153442 | 0.0767212 | − | 0.997053i | \(-0.475555\pi\) | ||||
0.0767212 | + | 0.997053i | \(0.475555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.17991 | −0.0817530 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.8819 | 1.41869 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0224 | 0.448986 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 30.0857 | 1.12201 | 0.561004 | − | 0.827813i | \(-0.310415\pi\) | ||||
0.561004 | + | 0.827813i | \(0.310415\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.45805 | −0.240510 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.6935 | −0.881172 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −18.9121 | −0.701410 | −0.350705 | − | 0.936486i | \(-0.614058\pi\) | ||||
−0.350705 | + | 0.936486i | \(0.614058\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.82009 | 0.0673184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −30.3893 | −1.12245 | −0.561227 | − | 0.827662i | \(-0.689670\pi\) | ||||
−0.561227 | + | 0.827662i | \(0.689670\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.49264 | −0.165488 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.60927 | −0.206340 | −0.103170 | − | 0.994664i | \(-0.532899\pi\) | ||||
−0.103170 | + | 0.994664i | \(0.532899\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.77299 | 0.248812 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.51507 | −0.349074 | −0.174537 | − | 0.984651i | \(-0.555843\pi\) | ||||
−0.174537 | + | 0.984651i | \(0.555843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −9.16373 | −0.335283 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.73437 | 0.282608 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.5221 | −1.15026 | −0.575129 | − | 0.818063i | \(-0.695048\pi\) | ||||
−0.575129 | + | 0.818063i | \(0.695048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18.7406 | 0.682946 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.5607 | 0.929020 | 0.464510 | − | 0.885568i | \(-0.346230\pi\) | ||||
0.464510 | + | 0.885568i | \(0.346230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.9592 | −0.579281 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 10.4132 | 0.377477 | 0.188739 | − | 0.982027i | \(-0.439560\pi\) | ||||
0.188739 | + | 0.982027i | \(0.439560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.82009 | 0.283106 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.16373 | −0.114236 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.95290 | −0.106484 | −0.0532422 | − | 0.998582i | \(-0.516956\pi\) | ||||
−0.0532422 | + | 0.998582i | \(0.516956\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.24173 | 0.332833 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.0471 | −0.397336 | −0.198668 | − | 0.980067i | \(-0.563662\pi\) | ||||
−0.198668 | + | 0.980067i | \(0.563662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.72590 | 0.133666 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −64.0743 | −2.29570 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.2741 | 0.582333 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.59308 | 0.271355 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.1553 | 0.540226 | 0.270113 | − | 0.962829i | \(-0.412939\pi\) | ||||
0.270113 | + | 0.962829i | \(0.412939\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.9143 | 0.637765 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.09419 | 0.145573 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.59308 | 0.340660 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.7962 | −1.37423 | −0.687116 | − | 0.726548i | \(-0.741124\pi\) | ||||
−0.687116 | + | 0.726548i | \(0.741124\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.06953 | −0.320857 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.5931 | −0.374288 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.1924 | −1.70067 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.28036 | −0.221079 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −50.1391 | −1.76280 | −0.881398 | − | 0.472375i | \(-0.843397\pi\) | ||||
−0.881398 | + | 0.472375i | \(0.843397\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.5684 | −0.616911 | −0.308455 | − | 0.951239i | \(-0.599812\pi\) | ||||
−0.308455 | + | 0.951239i | \(0.599812\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.2881 | −0.641391 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.3275 | 0.431283 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.476452 | 0.0166486 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.19464 | 0.0416932 | 0.0208466 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208466 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.2458 | −1.54231 | −0.771155 | − | 0.636647i | \(-0.780321\pi\) | ||||
−0.771155 | + | 0.636647i | \(0.780321\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.84475 | 0.238015 | 0.119008 | − | 0.992893i | \(-0.462029\pi\) | ||||
0.119008 | + | 0.992893i | \(0.462029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.04488 | 0.0362901 | 0.0181451 | − | 0.999835i | \(-0.494224\pi\) | ||||
0.0181451 | + | 0.999835i | \(0.494224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.7645 | −0.442796 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.77299 | 0.234670 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.93672 | 0.274333 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.2417 | 1.32025 | 0.660126 | − | 0.751155i | \(-0.270503\pi\) | ||||
0.660126 | + | 0.751155i | \(0.270503\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.6549 | 0.988100 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −26.8263 | −0.923948 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.0857188 | −0.00294533 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.4518 | 0.736224 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −37.3252 | −1.27949 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.9978 | −1.54069 | −0.770347 | − | 0.637624i | \(-0.779917\pi\) | ||||
−0.770347 | + | 0.637624i | \(0.779917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12.3723 | −0.422631 | −0.211315 | − | 0.977418i | \(-0.567775\pi\) | ||||
−0.211315 | + | 0.977418i | \(0.567775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.4750 | −0.766837 | −0.383418 | − | 0.923575i | \(-0.625253\pi\) | ||||
−0.383418 | + | 0.923575i | \(0.625253\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50736 | −0.153611 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.1251 | −0.412743 | −0.206372 | − | 0.978474i | \(-0.566166\pi\) | ||||
−0.206372 | + | 0.978474i | \(0.566166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.28883 | 0.247257 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.34364 | −0.0455274 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.04710 | −0.238508 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.0449 | 0.879473 | 0.439737 | − | 0.898127i | \(-0.355072\pi\) | ||||
0.439737 | + | 0.898127i | \(0.355072\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.3745 | 0.383654 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.4132 | −0.451901 | −0.225951 | − | 0.974139i | \(-0.572549\pi\) | ||||
−0.225951 | + | 0.974139i | \(0.572549\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.5158 | 0.959634 | 0.479817 | − | 0.877369i | \(-0.340703\pi\) | ||||
0.479817 | + | 0.877369i | \(0.340703\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −30.6464 | −1.02901 | −0.514503 | − | 0.857488i | \(-0.672024\pi\) | ||||
−0.514503 | + | 0.857488i | \(0.672024\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.36608 | 0.0458167 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.34364 | −0.112016 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −61.4279 | −2.05561 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.77299 | −0.159366 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 60.2642 | 2.00992 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.50736 | 0.316736 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.867185 | 0.0288581 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.9978 | 1.22849 | 0.614246 | − | 0.789115i | \(-0.289460\pi\) | ||||
0.614246 | + | 0.789115i | \(0.289460\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.3661 | −0.609164 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.3337 | 1.17066 | 0.585329 | − | 0.810796i | \(-0.300965\pi\) | ||||
0.585329 | + | 0.810796i | \(0.300965\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 30.6402 | 1.01404 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.69353 | 0.254063 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.6851 | −1.17714 | −0.588571 | − | 0.808446i | \(-0.700309\pi\) | ||||
−0.588571 | + | 0.808446i | \(0.700309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0857 | 0.464140 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.86719 | 0.160205 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.5545 | 0.445187 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −48.2009 | −1.58142 | −0.790710 | − | 0.612191i | \(-0.790288\pi\) | ||||
−0.790710 | + | 0.612191i | \(0.790288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.8734 | 1.50344 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −17.4518 | −0.571346 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36.1538 | −1.18109 | −0.590547 | − | 0.807004i | \(-0.701088\pi\) | ||||
−0.590547 | + | 0.807004i | \(0.701088\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.39844 | 0.208805 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.66629 | −0.217315 | −0.108657 | − | 0.994079i | \(-0.534655\pi\) | ||||
−0.108657 | + | 0.994079i | \(0.534655\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.1538 | 1.47041 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.3760 | 0.499653 | 0.249827 | − | 0.968291i | \(-0.419626\pi\) | ||||
0.249827 | + | 0.968291i | \(0.419626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.4132 | −0.467871 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.58683 | −0.181165 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.10266 | −0.230078 | −0.115039 | − | 0.993361i | \(-0.536699\pi\) | ||||
−0.115039 | + | 0.993361i | \(0.536699\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −25.3885 | −0.820694 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.5931 | 0.342068 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.9915 | 1.03198 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.2333 | −0.523110 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8573 | 0.927987 | 0.463993 | − | 0.885839i | \(-0.346416\pi\) | ||||
0.463993 | + | 0.885839i | \(0.346416\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.77299 | 0.217580 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.5909 | −0.821250 | −0.410625 | − | 0.911804i | \(-0.634689\pi\) | ||||
−0.410625 | + | 0.911804i | \(0.634689\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.42165 | −0.141751 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −31.6402 | −1.01226 | −0.506129 | − | 0.862457i | \(-0.668924\pi\) | ||||
−0.506129 | + | 0.862457i | \(0.668924\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.4194 | 1.13201 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −16.4132 | −0.524032 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.12289 | 0.163395 | 0.0816973 | − | 0.996657i | \(-0.473966\pi\) | ||||
0.0816973 | + | 0.996657i | \(0.473966\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.32120 | −0.137545 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.68727 | −0.276239 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.3359 | −0.836588 | −0.418294 | − | 0.908312i | \(-0.637372\pi\) | ||||
−0.418294 | + | 0.908312i | \(0.637372\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.4132 | 0.330452 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.0766 | 1.33258 | 0.666289 | − | 0.745694i | \(-0.267882\pi\) | ||||
0.666289 | + | 0.745694i | \(0.267882\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.82009 | −0.247417 |
(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 | 7800.2.a.br.1.2 | yes | 3 | |
5.4 | even | 2 | 7800.2.a.bg.1.2 | ✓ | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7800.2.a.bg.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
7800.2.a.br.1.2 | yes | 3 | 1.1 | even | 1 | trivial |