Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7803,2,Mod(1,7803)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7803, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("7803.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7803 = 3^{3} \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7803.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: | \(62.3072686972\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.29952.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 8x^{2} + 13 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 459) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.39417\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7803.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.39417 | 1.69293 | 0.846467 | − | 0.532441i | \(-0.178725\pi\) | ||||
0.846467 | + | 0.532441i | \(0.178725\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.73205 | 1.86603 | ||||||||
\(5\) | 1.73205 | 0.774597 | 0.387298 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387298 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.75265 | 0.662441 | 0.331221 | − | 0.943553i | \(-0.392540\pi\) | ||||
0.331221 | + | 0.943553i | \(0.392540\pi\) | |||||||
\(8\) | 4.14682 | 1.46612 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.14682 | 1.31134 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.46410 | 0.683419 | 0.341709 | − | 0.939806i | \(-0.388994\pi\) | ||||
0.341709 | + | 0.939806i | \(0.388994\pi\) | |||||||
\(14\) | 4.19615 | 1.12147 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.46410 | 0.616025 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.19615 | 0.733248 | 0.366624 | − | 0.930369i | \(-0.380514\pi\) | ||||
0.366624 | + | 0.930369i | \(0.380514\pi\) | |||||||
\(20\) | 6.46410 | 1.44542 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.78834 | 1.02088 | ||||||||
\(23\) | −1.53590 | −0.320257 | −0.160128 | − | 0.987096i | \(-0.551191\pi\) | ||||
−0.160128 | + | 0.987096i | \(0.551191\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | −0.400000 | ||||||||
\(26\) | 5.89948 | 1.15698 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.54099 | 1.23613 | ||||||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.57668 | 1.72002 | 0.860011 | − | 0.510275i | \(-0.170456\pi\) | ||||
0.860011 | + | 0.510275i | \(0.170456\pi\) | |||||||
\(32\) | −2.39417 | −0.423233 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.03569 | 0.513125 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0463 | −1.65160 | −0.825801 | − | 0.563962i | \(-0.809277\pi\) | ||||
−0.825801 | + | 0.563962i | \(0.809277\pi\) | |||||||
\(38\) | 7.65213 | 1.24134 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.18251 | 1.13565 | ||||||||
\(41\) | 10.6603 | 1.66485 | 0.832426 | − | 0.554136i | \(-0.186951\pi\) | ||||
0.832426 | + | 0.554136i | \(0.186951\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.73205 | −0.569132 | −0.284566 | − | 0.958656i | \(-0.591850\pi\) | ||||
−0.284566 | + | 0.958656i | \(0.591850\pi\) | |||||||
\(44\) | 7.46410 | 1.12526 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.67720 | −0.542174 | ||||||||
\(47\) | 10.0463 | 1.46540 | 0.732702 | − | 0.680550i | \(-0.238259\pi\) | ||||
0.732702 | + | 0.680550i | \(0.238259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.92820 | −0.561172 | ||||||||
\(50\) | −4.78834 | −0.677174 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.19615 | 1.27528 | ||||||||
\(53\) | −11.3293 | −1.55620 | −0.778102 | − | 0.628138i | \(-0.783817\pi\) | ||||
−0.778102 | + | 0.628138i | \(0.783817\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46410 | 0.467099 | ||||||||
\(56\) | 7.26795 | 0.971221 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.14682 | −0.544505 | ||||||||
\(59\) | −3.03569 | −0.395213 | −0.197606 | − | 0.980281i | \(-0.563317\pi\) | ||||
−0.197606 | + | 0.980281i | \(0.563317\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.54099 | 0.837489 | 0.418744 | − | 0.908104i | \(-0.362470\pi\) | ||||
0.418744 | + | 0.908104i | \(0.362470\pi\) | |||||||
\(62\) | 22.9282 | 2.91188 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.6603 | −1.33253 | ||||||||
\(65\) | 4.26795 | 0.529374 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.73205 | 0.944620 | 0.472310 | − | 0.881432i | \(-0.343420\pi\) | ||||
0.472310 | + | 0.881432i | \(0.343420\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.26795 | 0.868686 | ||||||||
\(71\) | 12.4641 | 1.47922 | 0.739608 | − | 0.673037i | \(-0.235011\pi\) | ||||
0.739608 | + | 0.673037i | \(0.235011\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.03569 | 0.355300 | 0.177650 | − | 0.984094i | \(-0.443150\pi\) | ||||
0.177650 | + | 0.984094i | \(0.443150\pi\) | |||||||
\(74\) | −24.0526 | −2.79605 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 11.9282 | 1.36826 | ||||||||
\(77\) | 3.50531 | 0.399467 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.82403 | 0.880272 | 0.440136 | − | 0.897931i | \(-0.354930\pi\) | ||||
0.440136 | + | 0.897931i | \(0.354930\pi\) | |||||||
\(80\) | 4.26795 | 0.477171 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 25.5225 | 2.81848 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.93516 | −0.963504 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.29365 | 0.884106 | ||||||||
\(89\) | −13.0820 | −1.38669 | −0.693344 | − | 0.720607i | \(-0.743863\pi\) | ||||
−0.693344 | + | 0.720607i | \(0.743863\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.31872 | 0.452725 | ||||||||
\(92\) | −5.73205 | −0.597608 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.0526 | 2.48083 | ||||||||
\(95\) | 5.53590 | 0.567971 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.6124 | −1.28059 | −0.640296 | − | 0.768128i | \(-0.721188\pi\) | ||||
−0.640296 | + | 0.768128i | \(0.721188\pi\) | |||||||
\(98\) | −9.40479 | −0.950027 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.46410 | −0.746410 | ||||||||
\(101\) | 5.25796 | 0.523187 | 0.261593 | − | 0.965178i | \(-0.415752\pi\) | ||||
0.261593 | + | 0.965178i | \(0.415752\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.1962 | −1.69439 | −0.847194 | − | 0.531284i | \(-0.821710\pi\) | ||||
−0.847194 | + | 0.531284i | \(0.821710\pi\) | |||||||
\(104\) | 10.2182 | 1.00198 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −27.1244 | −2.63455 | ||||||||
\(107\) | 3.00000 | 0.290021 | 0.145010 | − | 0.989430i | \(-0.453678\pi\) | ||||
0.145010 | + | 0.989430i | \(0.453678\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6124 | −1.20805 | −0.604023 | − | 0.796967i | \(-0.706436\pi\) | ||||
−0.604023 | + | 0.796967i | \(0.706436\pi\) | |||||||
\(110\) | 8.29365 | 0.790768 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.31872 | 0.408080 | ||||||||
\(113\) | 4.53590 | 0.426701 | 0.213351 | − | 0.976976i | \(-0.431562\pi\) | ||||
0.213351 | + | 0.976976i | \(0.431562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.66025 | −0.248070 | ||||||||
\(116\) | −6.46410 | −0.600177 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.26795 | −0.669069 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 15.6603 | 1.41781 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 35.7407 | 3.20961 | ||||||||
\(125\) | −12.1244 | −1.08444 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.92820 | −0.259836 | −0.129918 | − | 0.991525i | \(-0.541471\pi\) | ||||
−0.129918 | + | 0.991525i | \(0.541471\pi\) | |||||||
\(128\) | −20.7341 | −1.83265 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 10.2182 | 0.896195 | ||||||||
\(131\) | 1.00000 | 0.0873704 | 0.0436852 | − | 0.999045i | \(-0.486090\pi\) | ||||
0.0436852 | + | 0.999045i | \(0.486090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.60175 | 0.485733 | ||||||||
\(134\) | 18.5118 | 1.59918 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.0820 | −1.11767 | −0.558835 | − | 0.829279i | \(-0.688751\pi\) | ||||
−0.558835 | + | 0.829279i | \(0.688751\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.01062 | 0.594633 | 0.297316 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297316 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(140\) | 11.3293 | 0.957504 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 29.8412 | 2.50422 | ||||||||
\(143\) | 4.92820 | 0.412117 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | 7.26795 | 0.601500 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −37.4933 | −3.08193 | ||||||||
\(149\) | −11.3293 | −0.928135 | −0.464068 | − | 0.885800i | \(-0.653611\pi\) | ||||
−0.464068 | + | 0.885800i | \(0.653611\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.73205 | −0.140952 | −0.0704761 | − | 0.997513i | \(-0.522452\pi\) | ||||
−0.0704761 | + | 0.997513i | \(0.522452\pi\) | |||||||
\(152\) | 13.2539 | 1.07503 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.39230 | 0.676271 | ||||||||
\(155\) | 16.5873 | 1.33232 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.9282 | 1.82987 | 0.914935 | − | 0.403601i | \(-0.132242\pi\) | ||||
0.914935 | + | 0.403601i | \(0.132242\pi\) | |||||||
\(158\) | 18.7321 | 1.49024 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.14682 | −0.327835 | ||||||||
\(161\) | −2.69190 | −0.212151 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.57668 | −0.750104 | −0.375052 | − | 0.927004i | \(-0.622375\pi\) | ||||
−0.375052 | + | 0.927004i | \(0.622375\pi\) | |||||||
\(164\) | 39.7846 | 3.10666 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.92820 | 0.536120 | 0.268060 | − | 0.963402i | \(-0.413617\pi\) | ||||
0.268060 | + | 0.963402i | \(0.413617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.92820 | −0.532939 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.9282 | −1.06202 | ||||||||
\(173\) | 1.07180 | 0.0814872 | 0.0407436 | − | 0.999170i | \(-0.487027\pi\) | ||||
0.0407436 | + | 0.999170i | \(0.487027\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.50531 | −0.264976 | ||||||||
\(176\) | 4.92820 | 0.371477 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −31.3205 | −2.34757 | ||||||||
\(179\) | 9.57668 | 0.715795 | 0.357897 | − | 0.933761i | \(-0.383494\pi\) | ||||
0.357897 | + | 0.933761i | \(0.383494\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.57668 | 0.711829 | 0.355915 | − | 0.934519i | \(-0.384169\pi\) | ||||
0.355915 | + | 0.934519i | \(0.384169\pi\) | |||||||
\(182\) | 10.3397 | 0.766433 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.36910 | −0.469536 | ||||||||
\(185\) | −17.4007 | −1.27933 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 37.4933 | 2.73448 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.2539 | 0.961538 | ||||||||
\(191\) | 2.56606 | 0.185674 | 0.0928369 | − | 0.995681i | \(-0.470406\pi\) | ||||
0.0928369 | + | 0.995681i | \(0.470406\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.5873 | 1.19398 | 0.596990 | − | 0.802249i | \(-0.296363\pi\) | ||||
0.596990 | + | 0.802249i | \(0.296363\pi\) | |||||||
\(194\) | −30.1962 | −2.16796 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.6603 | −1.04716 | ||||||||
\(197\) | −0.660254 | −0.0470412 | −0.0235206 | − | 0.999723i | \(-0.507488\pi\) | ||||
−0.0235206 | + | 0.999723i | \(0.507488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.6481 | −1.10926 | −0.554631 | − | 0.832097i | \(-0.687140\pi\) | ||||
−0.554631 | + | 0.832097i | \(0.687140\pi\) | |||||||
\(200\) | −8.29365 | −0.586450 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.5885 | 0.885721 | ||||||||
\(203\) | −3.03569 | −0.213063 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 18.4641 | 1.28959 | ||||||||
\(206\) | −41.1705 | −2.86849 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.07180 | 0.421003 | ||||||||
\(209\) | 6.39230 | 0.442165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4113 | −1.68054 | −0.840272 | − | 0.542164i | \(-0.817605\pi\) | ||||
−0.840272 | + | 0.542164i | \(0.817605\pi\) | |||||||
\(212\) | −42.2817 | −2.90392 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.18251 | 0.490986 | ||||||||
\(215\) | −6.46410 | −0.440848 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.7846 | 1.13941 | ||||||||
\(218\) | −30.1962 | −2.04514 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 12.9282 | 0.871619 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.5885 | 1.57960 | 0.789800 | − | 0.613365i | \(-0.210184\pi\) | ||||
0.789800 | + | 0.613365i | \(0.210184\pi\) | |||||||
\(224\) | −4.19615 | −0.280367 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 10.8597 | 0.722377 | ||||||||
\(227\) | 23.7846 | 1.57864 | 0.789320 | − | 0.613982i | \(-0.210433\pi\) | ||||
0.789320 | + | 0.613982i | \(0.210433\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.3923 | 1.01715 | 0.508576 | − | 0.861017i | \(-0.330172\pi\) | ||||
0.508576 | + | 0.861017i | \(0.330172\pi\) | |||||||
\(230\) | −6.36910 | −0.419966 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.18251 | −0.471555 | ||||||||
\(233\) | 5.33975 | 0.349818 | 0.174909 | − | 0.984585i | \(-0.444037\pi\) | ||||
0.174909 | + | 0.984585i | \(0.444037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.4007 | 1.13510 | ||||||||
\(236\) | −11.3293 | −0.737477 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.6837 | −1.20855 | −0.604275 | − | 0.796776i | \(-0.706537\pi\) | ||||
−0.604275 | + | 0.796776i | \(0.706537\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50531 | 0.225797 | 0.112898 | − | 0.993607i | \(-0.463987\pi\) | ||||
0.112898 | + | 0.993607i | \(0.463987\pi\) | |||||||
\(242\) | −16.7592 | −1.07732 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.4113 | 1.56277 | ||||||||
\(245\) | −6.80385 | −0.434682 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.87564 | 0.501115 | ||||||||
\(248\) | 39.7128 | 2.52177 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −29.0278 | −1.83588 | ||||||||
\(251\) | 16.5873 | 1.04698 | 0.523490 | − | 0.852032i | \(-0.324630\pi\) | ||||
0.523490 | + | 0.852032i | \(0.324630\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.07180 | −0.193122 | ||||||||
\(254\) | −7.01062 | −0.439885 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −28.3205 | −1.77003 | ||||||||
\(257\) | 20.9060 | 1.30408 | 0.652041 | − | 0.758184i | \(-0.273913\pi\) | ||||
0.652041 | + | 0.758184i | \(0.273913\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −17.6077 | −1.09409 | ||||||||
\(260\) | 15.9282 | 0.987825 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.39417 | 0.147912 | ||||||||
\(263\) | −6.07137 | −0.374377 | −0.187188 | − | 0.982324i | \(-0.559937\pi\) | ||||
−0.187188 | + | 0.982324i | \(0.559937\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.6230 | −1.20543 | ||||||||
\(266\) | 13.4115 | 0.822314 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 28.8564 | 1.76269 | ||||||||
\(269\) | 17.3205 | 1.05605 | 0.528025 | − | 0.849229i | \(-0.322933\pi\) | ||||
0.528025 | + | 0.849229i | \(0.322933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −31.3205 | −1.89214 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −23.1283 | −1.38964 | −0.694822 | − | 0.719182i | \(-0.744517\pi\) | ||||
−0.694822 | + | 0.719182i | \(0.744517\pi\) | |||||||
\(278\) | 16.7846 | 1.00667 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.5885 | 0.752304 | ||||||||
\(281\) | −1.75265 | −0.104555 | −0.0522773 | − | 0.998633i | \(-0.516648\pi\) | ||||
−0.0522773 | + | 0.998633i | \(0.516648\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.9060 | 1.24273 | 0.621367 | − | 0.783520i | \(-0.286578\pi\) | ||||
0.621367 | + | 0.783520i | \(0.286578\pi\) | |||||||
\(284\) | 46.5167 | 2.76026 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 11.7990 | 0.697687 | ||||||||
\(287\) | 18.6837 | 1.10287 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −7.18251 | −0.421772 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.3293 | 0.662999 | ||||||||
\(293\) | −12.2686 | −0.716738 | −0.358369 | − | 0.933580i | \(-0.616667\pi\) | ||||
−0.358369 | + | 0.933580i | \(0.616667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.25796 | −0.306130 | ||||||||
\(296\) | −41.6603 | −2.42145 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −27.1244 | −1.57127 | ||||||||
\(299\) | −3.78461 | −0.218870 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.54099 | −0.377017 | ||||||||
\(302\) | −4.14682 | −0.238623 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.87564 | 0.451699 | ||||||||
\(305\) | 11.3293 | 0.648716 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.58846 | −0.547242 | −0.273621 | − | 0.961838i | \(-0.588221\pi\) | ||||
−0.273621 | + | 0.961838i | \(0.588221\pi\) | |||||||
\(308\) | 13.0820 | 0.745416 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 39.7128 | 2.25554 | ||||||||
\(311\) | −21.7128 | −1.23122 | −0.615610 | − | 0.788051i | \(-0.711090\pi\) | ||||
−0.615610 | + | 0.788051i | \(0.711090\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.6481 | −0.884480 | −0.442240 | − | 0.896897i | \(-0.645816\pi\) | ||||
−0.442240 | + | 0.896897i | \(0.645816\pi\) | |||||||
\(314\) | 54.8940 | 3.09785 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 29.1997 | 1.64261 | ||||||||
\(317\) | −19.5885 | −1.10020 | −0.550099 | − | 0.835100i | \(-0.685410\pi\) | ||||
−0.550099 | + | 0.835100i | \(0.685410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.46410 | −0.193952 | ||||||||
\(320\) | −18.4641 | −1.03217 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.44486 | −0.359158 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.92820 | −0.273368 | ||||||||
\(326\) | −22.9282 | −1.26988 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 44.2062 | 2.44088 | ||||||||
\(329\) | 17.6077 | 0.970744 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.12436 | 0.116765 | 0.0583826 | − | 0.998294i | \(-0.481406\pi\) | ||||
0.0583826 | + | 0.998294i | \(0.481406\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.5873 | 0.907617 | ||||||||
\(335\) | 13.3923 | 0.731700 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.1997 | 1.59061 | 0.795304 | − | 0.606211i | \(-0.207311\pi\) | ||||
0.795304 | + | 0.606211i | \(0.207311\pi\) | |||||||
\(338\) | −16.5873 | −0.902230 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.1534 | 1.03721 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.1534 | −1.03418 | ||||||||
\(344\) | −15.4762 | −0.834419 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.56606 | 0.137952 | ||||||||
\(347\) | −26.8564 | −1.44173 | −0.720864 | − | 0.693077i | \(-0.756255\pi\) | ||||
−0.720864 | + | 0.693077i | \(0.756255\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −31.2487 | −1.67271 | −0.836353 | − | 0.548192i | \(-0.815316\pi\) | ||||
−0.836353 | + | 0.548192i | \(0.815316\pi\) | |||||||
\(350\) | −8.39230 | −0.448588 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.78834 | −0.255219 | ||||||||
\(353\) | 6.07137 | 0.323147 | 0.161573 | − | 0.986861i | \(-0.448343\pi\) | ||||
0.161573 | + | 0.986861i | \(0.448343\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.5885 | 1.14580 | ||||||||
\(356\) | −48.8226 | −2.58760 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.9282 | 1.21179 | ||||||||
\(359\) | −18.6837 | −0.986090 | −0.493045 | − | 0.870004i | \(-0.664116\pi\) | ||||
−0.493045 | + | 0.870004i | \(0.664116\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.78461 | −0.462348 | ||||||||
\(362\) | 22.9282 | 1.20508 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 16.1177 | 0.844796 | ||||||||
\(365\) | 5.25796 | 0.275214 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.8453 | −1.14031 | −0.570157 | − | 0.821536i | \(-0.693118\pi\) | ||||
−0.570157 | + | 0.821536i | \(0.693118\pi\) | |||||||
\(368\) | −3.78461 | −0.197286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −41.6603 | −2.16581 | ||||||||
\(371\) | −19.8564 | −1.03089 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.2487 | 1.51444 | 0.757220 | − | 0.653159i | \(-0.226557\pi\) | ||||
0.757220 | + | 0.653159i | \(0.226557\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 41.6603 | 2.14846 | ||||||||
\(377\) | −4.26795 | −0.219811 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.69190 | 0.138274 | 0.0691368 | − | 0.997607i | \(-0.477976\pi\) | ||||
0.0691368 | + | 0.997607i | \(0.477976\pi\) | |||||||
\(380\) | 20.6603 | 1.05985 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.14359 | 0.314334 | ||||||||
\(383\) | −15.6481 | −0.799578 | −0.399789 | − | 0.916607i | \(-0.630917\pi\) | ||||
−0.399789 | + | 0.916607i | \(0.630917\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.07137 | 0.309426 | ||||||||
\(386\) | 39.7128 | 2.02133 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −47.0700 | −2.38962 | ||||||||
\(389\) | 16.5873 | 0.841009 | 0.420505 | − | 0.907290i | \(-0.361853\pi\) | ||||
0.420505 | + | 0.907290i | \(0.361853\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −16.2896 | −0.822747 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.58076 | −0.0796376 | ||||||||
\(395\) | 13.5516 | 0.681856 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.0820 | −0.656566 | −0.328283 | − | 0.944579i | \(-0.606470\pi\) | ||||
−0.328283 | + | 0.944579i | \(0.606470\pi\) | |||||||
\(398\) | −37.4641 | −1.87791 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.92820 | −0.246410 | ||||||||
\(401\) | 25.0526 | 1.25107 | 0.625533 | − | 0.780198i | \(-0.284882\pi\) | ||||
0.625533 | + | 0.780198i | \(0.284882\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.5979 | 1.17550 | ||||||||
\(404\) | 19.6230 | 0.976280 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.26795 | −0.360702 | ||||||||
\(407\) | −20.0926 | −0.995953 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −17.9282 | −0.886493 | −0.443246 | − | 0.896400i | \(-0.646173\pi\) | ||||
−0.443246 | + | 0.896400i | \(0.646173\pi\) | |||||||
\(410\) | 44.2062 | 2.18319 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −64.1769 | −3.16177 | ||||||||
\(413\) | −5.32051 | −0.261805 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.89948 | −0.289246 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.3043 | 0.748556 | ||||||||
\(419\) | −19.9282 | −0.973556 | −0.486778 | − | 0.873526i | \(-0.661828\pi\) | ||||
−0.486778 | + | 0.873526i | \(0.661828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.00000 | −0.194948 | −0.0974740 | − | 0.995238i | \(-0.531076\pi\) | ||||
−0.0974740 | + | 0.995238i | \(0.531076\pi\) | |||||||
\(422\) | −58.4449 | −2.84505 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −46.9808 | −2.28159 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.4641 | 0.554787 | ||||||||
\(428\) | 11.1962 | 0.541186 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.4762 | −0.746327 | ||||||||
\(431\) | 6.60770 | 0.318281 | 0.159141 | − | 0.987256i | \(-0.449128\pi\) | ||||
0.159141 | + | 0.987256i | \(0.449128\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.0000 | 0.816968 | 0.408484 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408484 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(434\) | 40.1852 | 1.92895 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −47.0700 | −2.25424 | ||||||||
\(437\) | −4.90897 | −0.234828 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.9166 | 1.33239 | 0.666194 | − | 0.745778i | \(-0.267922\pi\) | ||||
0.666194 | + | 0.745778i | \(0.267922\pi\) | |||||||
\(440\) | 14.3650 | 0.684826 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.7050 | 1.55386 | 0.776930 | − | 0.629587i | \(-0.216776\pi\) | ||||
0.776930 | + | 0.629587i | \(0.216776\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.6587 | −1.07412 | ||||||||
\(446\) | 56.4748 | 2.67416 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −18.6837 | −0.882724 | ||||||||
\(449\) | −26.9282 | −1.27082 | −0.635410 | − | 0.772175i | \(-0.719169\pi\) | ||||
−0.635410 | + | 0.772175i | \(0.719169\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 21.3205 | 1.00394 | ||||||||
\(452\) | 16.9282 | 0.796236 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 56.9444 | 2.67253 | ||||||||
\(455\) | 7.48024 | 0.350679 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.8564 | 0.835287 | 0.417644 | − | 0.908611i | \(-0.362856\pi\) | ||||
0.417644 | + | 0.908611i | \(0.362856\pi\) | |||||||
\(458\) | 36.8518 | 1.72197 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −9.92820 | −0.462905 | ||||||||
\(461\) | −20.0926 | −0.935806 | −0.467903 | − | 0.883780i | \(-0.654990\pi\) | ||||
−0.467903 | + | 0.883780i | \(0.654990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.32051 | −0.433161 | −0.216580 | − | 0.976265i | \(-0.569490\pi\) | ||||
−0.216580 | + | 0.976265i | \(0.569490\pi\) | |||||||
\(464\) | −4.26795 | −0.198135 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.7843 | 0.592219 | ||||||||
\(467\) | 29.1997 | 1.35120 | 0.675600 | − | 0.737269i | \(-0.263885\pi\) | ||||
0.675600 | + | 0.737269i | \(0.263885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5516 | 0.625755 | ||||||||
\(470\) | 41.6603 | 1.92164 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.5885 | −0.579431 | ||||||||
\(473\) | −7.46410 | −0.343200 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.39230 | −0.293299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −44.7321 | −2.04600 | ||||||||
\(479\) | −22.1769 | −1.01329 | −0.506645 | − | 0.862155i | \(-0.669114\pi\) | ||||
−0.506645 | + | 0.862155i | \(0.669114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.7551 | −1.12874 | ||||||||
\(482\) | 8.39230 | 0.382259 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.1244 | −1.18747 | ||||||||
\(485\) | −21.8453 | −0.991942 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −36.6799 | −1.66213 | −0.831063 | − | 0.556179i | \(-0.812267\pi\) | ||||
−0.831063 | + | 0.556179i | \(0.812267\pi\) | |||||||
\(488\) | 27.1244 | 1.22786 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.2896 | −0.735888 | ||||||||
\(491\) | −31.2961 | −1.41237 | −0.706187 | − | 0.708026i | \(-0.749586\pi\) | ||||
−0.706187 | + | 0.708026i | \(0.749586\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 18.8556 | 0.848355 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 23.5979 | 1.05958 | ||||||||
\(497\) | 21.8453 | 0.979894 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.3293 | −0.507171 | −0.253585 | − | 0.967313i | \(-0.581610\pi\) | ||||
−0.253585 | + | 0.967313i | \(0.581610\pi\) | |||||||
\(500\) | −45.2487 | −2.02358 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 39.7128 | 1.77247 | ||||||||
\(503\) | 38.3205 | 1.70863 | 0.854314 | − | 0.519758i | \(-0.173978\pi\) | ||||
0.854314 | + | 0.519758i | \(0.173978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.10706 | 0.405259 | ||||||||
\(506\) | −7.35440 | −0.326943 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.9282 | −0.484861 | ||||||||
\(509\) | 10.5159 | 0.466110 | 0.233055 | − | 0.972464i | \(-0.425128\pi\) | ||||
0.233055 | + | 0.972464i | \(0.425128\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.32051 | 0.235365 | ||||||||
\(512\) | −26.3359 | −1.16389 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 50.0526 | 2.20772 | ||||||||
\(515\) | −29.7846 | −1.31247 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.0926 | 0.883672 | ||||||||
\(518\) | −42.1558 | −1.85222 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.6984 | 0.776128 | ||||||||
\(521\) | −13.6077 | −0.596164 | −0.298082 | − | 0.954540i | \(-0.596347\pi\) | ||||
−0.298082 | + | 0.954540i | \(0.596347\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.92820 | 0.302949 | 0.151475 | − | 0.988461i | \(-0.451598\pi\) | ||||
0.151475 | + | 0.988461i | \(0.451598\pi\) | |||||||
\(524\) | 3.73205 | 0.163035 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.5359 | −0.633795 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6410 | −0.897435 | ||||||||
\(530\) | −46.9808 | −2.04071 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 20.9060 | 0.906391 | ||||||||
\(533\) | 26.2679 | 1.13779 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.19615 | 0.224649 | ||||||||
\(536\) | 32.0635 | 1.38493 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 41.4682 | 1.78782 | ||||||||
\(539\) | −7.85641 | −0.338399 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.1534 | 0.823467 | 0.411734 | − | 0.911304i | \(-0.364923\pi\) | ||||
0.411734 | + | 0.911304i | \(0.364923\pi\) | |||||||
\(542\) | −28.7300 | −1.23406 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.8453 | −0.935748 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −39.2460 | −1.67804 | −0.839018 | − | 0.544103i | \(-0.816870\pi\) | ||||
−0.839018 | + | 0.544103i | \(0.816870\pi\) | |||||||
\(548\) | −48.8226 | −2.08560 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.57668 | −0.408351 | ||||||||
\(551\) | −5.53590 | −0.235837 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7128 | 0.583128 | ||||||||
\(554\) | −55.3731 | −2.35258 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 26.1640 | 1.10960 | ||||||||
\(557\) | 0.813410 | 0.0344653 | 0.0172326 | − | 0.999852i | \(-0.494514\pi\) | ||||
0.0172326 | + | 0.999852i | \(0.494514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.19615 | −0.388956 | ||||||||
\(560\) | 7.48024 | 0.316098 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.19615 | −0.177004 | ||||||||
\(563\) | 5.60175 | 0.236086 | 0.118043 | − | 0.993009i | \(-0.462338\pi\) | ||||
0.118043 | + | 0.993009i | \(0.462338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.85641 | 0.330522 | ||||||||
\(566\) | 50.0526 | 2.10387 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 51.6864 | 2.16871 | ||||||||
\(569\) | −37.4933 | −1.57180 | −0.785901 | − | 0.618353i | \(-0.787800\pi\) | ||||
−0.785901 | + | 0.618353i | \(0.787800\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.3400 | 0.767503 | 0.383752 | − | 0.923436i | \(-0.374632\pi\) | ||||
0.383752 | + | 0.923436i | \(0.374632\pi\) | |||||||
\(572\) | 18.3923 | 0.769021 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 44.7321 | 1.86708 | ||||||||
\(575\) | 3.07180 | 0.128103 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1436 | −0.422283 | −0.211142 | − | 0.977455i | \(-0.567718\pi\) | ||||
−0.211142 | + | 0.977455i | \(0.567718\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.1962 | −0.464895 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6587 | −0.938426 | ||||||||
\(584\) | 12.5885 | 0.520914 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −29.3731 | −1.21339 | ||||||||
\(587\) | 36.2103 | 1.49456 | 0.747279 | − | 0.664510i | \(-0.231360\pi\) | ||||
0.747279 | + | 0.664510i | \(0.231360\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.6085 | 1.26120 | ||||||||
\(590\) | −12.5885 | −0.518259 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.7551 | −1.01743 | ||||||||
\(593\) | 25.2247 | 1.03586 | 0.517928 | − | 0.855424i | \(-0.326704\pi\) | ||||
0.517928 | + | 0.855424i | \(0.326704\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −42.2817 | −1.73192 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.06100 | −0.370532 | ||||||||
\(599\) | −18.6837 | −0.763397 | −0.381698 | − | 0.924287i | \(-0.624661\pi\) | ||||
−0.381698 | + | 0.924287i | \(0.624661\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.6336 | −1.08641 | −0.543204 | − | 0.839601i | \(-0.682789\pi\) | ||||
−0.543204 | + | 0.839601i | \(0.682789\pi\) | |||||||
\(602\) | −15.6603 | −0.638264 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.46410 | −0.263021 | ||||||||
\(605\) | −12.1244 | −0.492925 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.939245 | −0.0381228 | −0.0190614 | − | 0.999818i | \(-0.506068\pi\) | ||||
−0.0190614 | + | 0.999818i | \(0.506068\pi\) | |||||||
\(608\) | −7.65213 | −0.310335 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 27.1244 | 1.09823 | ||||||||
\(611\) | 24.7551 | 1.00148 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 40.1769 | 1.62273 | 0.811365 | − | 0.584540i | \(-0.198725\pi\) | ||||
0.811365 | + | 0.584540i | \(0.198725\pi\) | |||||||
\(614\) | −22.9564 | −0.926445 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.5359 | 0.585668 | ||||||||
\(617\) | 4.51666 | 0.181834 | 0.0909170 | − | 0.995858i | \(-0.471020\pi\) | ||||
0.0909170 | + | 0.995858i | \(0.471020\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −39.2460 | −1.57743 | −0.788714 | − | 0.614760i | \(-0.789253\pi\) | ||||
−0.788714 | + | 0.614760i | \(0.789253\pi\) | |||||||
\(620\) | 61.9046 | 2.48615 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −51.9842 | −2.08438 | ||||||||
\(623\) | −22.9282 | −0.918599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −37.4641 | −1.49737 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 85.5692 | 3.41458 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0526 | 0.599233 | 0.299616 | − | 0.954060i | \(-0.403141\pi\) | ||||
0.299616 | + | 0.954060i | \(0.403141\pi\) | |||||||
\(632\) | 32.4449 | 1.29059 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −46.8981 | −1.86256 | ||||||||
\(635\) | −5.07180 | −0.201268 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.67949 | −0.383515 | ||||||||
\(638\) | −8.29365 | −0.328349 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −35.9126 | −1.41957 | ||||||||
\(641\) | 19.1962 | 0.758202 | 0.379101 | − | 0.925355i | \(-0.376233\pi\) | ||||
0.379101 | + | 0.925355i | \(0.376233\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.3901 | −0.409745 | −0.204873 | − | 0.978789i | \(-0.565678\pi\) | ||||
−0.204873 | + | 0.978789i | \(0.565678\pi\) | |||||||
\(644\) | −10.0463 | −0.395880 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.6837 | 0.734534 | 0.367267 | − | 0.930116i | \(-0.380294\pi\) | ||||
0.367267 | + | 0.930116i | \(0.380294\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.07137 | −0.238322 | ||||||||
\(650\) | −11.7990 | −0.462793 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −35.7407 | −1.39971 | ||||||||
\(653\) | 44.2487 | 1.73159 | 0.865793 | − | 0.500402i | \(-0.166815\pi\) | ||||
0.865793 | + | 0.500402i | \(0.166815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.73205 | 0.0676768 | ||||||||
\(656\) | 26.2679 | 1.02559 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 42.1558 | 1.64340 | ||||||||
\(659\) | −46.2566 | −1.80190 | −0.900950 | − | 0.433922i | \(-0.857129\pi\) | ||||
−0.900950 | + | 0.433922i | \(0.857129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4641 | −0.484797 | −0.242399 | − | 0.970177i | \(-0.577934\pi\) | ||||
−0.242399 | + | 0.970177i | \(0.577934\pi\) | |||||||
\(662\) | 5.08607 | 0.197676 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.70252 | 0.376247 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.66025 | 0.103005 | ||||||||
\(668\) | 25.8564 | 1.00041 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 32.0635 | 1.23872 | ||||||||
\(671\) | 13.0820 | 0.505025 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.7908 | −1.07126 | −0.535628 | − | 0.844454i | \(-0.679925\pi\) | ||||
−0.535628 | + | 0.844454i | \(0.679925\pi\) | |||||||
\(674\) | 69.9090 | 2.69279 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −25.8564 | −0.994477 | ||||||||
\(677\) | 34.5167 | 1.32658 | 0.663292 | − | 0.748361i | \(-0.269159\pi\) | ||||
0.663292 | + | 0.748361i | \(0.269159\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.1051 | −0.848317 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 45.8564 | 1.75593 | ||||||||
\(683\) | 38.7846 | 1.48405 | 0.742026 | − | 0.670371i | \(-0.233865\pi\) | ||||
0.742026 | + | 0.670371i | \(0.233865\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −22.6587 | −0.865743 | ||||||||
\(686\) | −45.8564 | −1.75081 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.19615 | −0.350600 | ||||||||
\(689\) | −27.9166 | −1.06354 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.6481 | −0.595280 | −0.297640 | − | 0.954678i | \(-0.596200\pi\) | ||||
−0.297640 | + | 0.954678i | \(0.596200\pi\) | |||||||
\(692\) | 4.00000 | 0.152057 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −64.2988 | −2.44075 | ||||||||
\(695\) | 12.1427 | 0.460601 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −74.8147 | −2.83178 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −13.0820 | −0.494453 | ||||||||
\(701\) | 17.5265 | 0.661968 | 0.330984 | − | 0.943636i | \(-0.392619\pi\) | ||||
0.330984 | + | 0.943636i | \(0.392619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32.1095 | −1.21103 | ||||||||
\(704\) | −21.3205 | −0.803547 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.5359 | 0.547066 | ||||||||
\(707\) | 9.21539 | 0.346580 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.7194 | 0.815690 | 0.407845 | − | 0.913051i | \(-0.366280\pi\) | ||||
0.407845 | + | 0.913051i | \(0.366280\pi\) | |||||||
\(710\) | 51.6864 | 1.93976 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −54.2487 | −2.03306 | ||||||||
\(713\) | −14.7088 | −0.550849 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.53590 | 0.319225 | ||||||||
\(716\) | 35.7407 | 1.33569 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −44.7321 | −1.66939 | ||||||||
\(719\) | −22.6077 | −0.843125 | −0.421562 | − | 0.906799i | \(-0.638518\pi\) | ||||
−0.421562 | + | 0.906799i | \(0.638518\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.1389 | −1.12243 | ||||||||
\(722\) | −21.0319 | −0.782724 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 35.7407 | 1.32829 | ||||||||
\(725\) | 3.46410 | 0.128654 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.8038 | 0.549044 | 0.274522 | − | 0.961581i | \(-0.411480\pi\) | ||||
0.274522 | + | 0.961581i | \(0.411480\pi\) | |||||||
\(728\) | 17.9090 | 0.663750 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.5885 | 0.465920 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.5359 | −0.943190 | −0.471595 | − | 0.881815i | \(-0.656322\pi\) | ||||
−0.471595 | + | 0.881815i | \(0.656322\pi\) | |||||||
\(734\) | −52.3013 | −1.93048 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.67720 | 0.135543 | ||||||||
\(737\) | 15.4641 | 0.569628 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.19615 | 0.117572 | 0.0587862 | − | 0.998271i | \(-0.481277\pi\) | ||||
0.0587862 | + | 0.998271i | \(0.481277\pi\) | |||||||
\(740\) | −64.9403 | −2.38725 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −47.5396 | −1.74523 | ||||||||
\(743\) | 28.6410 | 1.05074 | 0.525368 | − | 0.850875i | \(-0.323927\pi\) | ||||
0.525368 | + | 0.850875i | \(0.323927\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −19.6230 | −0.718930 | ||||||||
\(746\) | 70.0264 | 2.56385 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.25796 | 0.192122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.50531 | −0.127911 | −0.0639553 | − | 0.997953i | \(-0.520371\pi\) | ||||
−0.0639553 | + | 0.997953i | \(0.520371\pi\) | |||||||
\(752\) | 24.7551 | 0.902726 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10.2182 | −0.372125 | ||||||||
\(755\) | −3.00000 | −0.109181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.1769 | −1.38756 | −0.693782 | − | 0.720185i | \(-0.744057\pi\) | ||||
−0.693782 | + | 0.720185i | \(0.744057\pi\) | |||||||
\(758\) | 6.44486 | 0.234088 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.9564 | 0.832716 | ||||||||
\(761\) | −44.5039 | −1.61327 | −0.806633 | − | 0.591052i | \(-0.798713\pi\) | ||||
−0.806633 | + | 0.591052i | \(0.798713\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.1051 | −0.800259 | ||||||||
\(764\) | 9.57668 | 0.346472 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −37.4641 | −1.35363 | ||||||||
\(767\) | −7.48024 | −0.270096 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0718 | −0.868051 | −0.434026 | − | 0.900901i | \(-0.642907\pi\) | ||||
−0.434026 | + | 0.900901i | \(0.642907\pi\) | |||||||
\(770\) | 14.5359 | 0.523837 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 61.9046 | 2.22800 | ||||||||
\(773\) | 22.6587 | 0.814976 | 0.407488 | − | 0.913211i | \(-0.366405\pi\) | ||||
0.407488 | + | 0.913211i | \(0.366405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −19.1534 | −0.688009 | ||||||||
\(776\) | −52.3013 | −1.87751 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 39.7128 | 1.42377 | ||||||||
\(779\) | 34.0718 | 1.22075 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.9282 | 0.892001 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.67949 | −0.345696 | ||||||||
\(785\) | 39.7128 | 1.41741 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −40.8728 | −1.45696 | −0.728479 | − | 0.685068i | \(-0.759772\pi\) | ||||
−0.728479 | + | 0.685068i | \(0.759772\pi\) | |||||||
\(788\) | −2.46410 | −0.0877800 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 32.4449 | 1.15434 | ||||||||
\(791\) | 7.94986 | 0.282665 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1177 | 0.572355 | ||||||||
\(794\) | −31.3205 | −1.11152 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −58.3993 | −2.06991 | ||||||||
\(797\) | 9.70252 | 0.343681 | 0.171840 | − | 0.985125i | \(-0.445029\pi\) | ||||
0.171840 | + | 0.985125i | \(0.445029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.78834 | 0.169293 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 59.9801 | 2.11797 | ||||||||
\(803\) | 6.07137 | 0.214254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.66251 | −0.164332 | ||||||||
\(806\) | 56.4974 | 1.99004 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 21.8038 | 0.767057 | ||||||||
\(809\) | −1.87564 | −0.0659441 | −0.0329721 | − | 0.999456i | \(-0.510497\pi\) | ||||
−0.0329721 | + | 0.999456i | \(0.510497\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.69190 | −0.0945254 | −0.0472627 | − | 0.998882i | \(-0.515050\pi\) | ||||
−0.0472627 | + | 0.998882i | \(0.515050\pi\) | |||||||
\(812\) | −11.3293 | −0.397582 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −48.1051 | −1.68608 | ||||||||
\(815\) | −16.5873 | −0.581028 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.9282 | −0.417315 | ||||||||
\(818\) | −42.9232 | −1.50077 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 68.9090 | 2.40641 | ||||||||
\(821\) | 35.4641 | 1.23771 | 0.618853 | − | 0.785507i | \(-0.287598\pi\) | ||||
0.618853 | + | 0.785507i | \(0.287598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.1640 | −0.912019 | −0.456009 | − | 0.889975i | \(-0.650722\pi\) | ||||
−0.456009 | + | 0.889975i | \(0.650722\pi\) | |||||||
\(824\) | −71.3094 | −2.48418 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.7382 | −0.443219 | ||||||||
\(827\) | 0.215390 | 0.00748985 | 0.00374493 | − | 0.999993i | \(-0.498808\pi\) | ||||
0.00374493 | + | 0.999993i | \(0.498808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.3205 | −0.566835 | −0.283417 | − | 0.958997i | \(-0.591468\pi\) | ||||
−0.283417 | + | 0.958997i | \(0.591468\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −26.2679 | −0.910677 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.0000 | 0.415277 | ||||||||
\(836\) | 23.8564 | 0.825091 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −47.7115 | −1.64817 | ||||||||
\(839\) | −20.4641 | −0.706499 | −0.353250 | − | 0.935529i | \(-0.614923\pi\) | ||||
−0.353250 | + | 0.935529i | \(0.614923\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | −9.57668 | −0.330034 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −91.1043 | −3.13594 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.2686 | −0.421553 | ||||||||
\(848\) | −27.9166 | −0.958661 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.4301 | 0.528937 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.1427 | −0.415760 | −0.207880 | − | 0.978154i | \(-0.566656\pi\) | ||||
−0.207880 | + | 0.978154i | \(0.566656\pi\) | |||||||
\(854\) | 27.4470 | 0.939217 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.4405 | 0.425207 | ||||||||
\(857\) | 31.4641 | 1.07479 | 0.537397 | − | 0.843330i | \(-0.319408\pi\) | ||||
0.537397 | + | 0.843330i | \(0.319408\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −57.8564 | −1.97404 | −0.987018 | − | 0.160612i | \(-0.948653\pi\) | ||||
−0.987018 | + | 0.160612i | \(0.948653\pi\) | |||||||
\(860\) | −24.1244 | −0.822634 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.8199 | 0.538830 | ||||||||
\(863\) | −16.5873 | −0.564638 | −0.282319 | − | 0.959321i | \(-0.591104\pi\) | ||||
−0.282319 | + | 0.959321i | \(0.591104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.85641 | 0.0631197 | ||||||||
\(866\) | 40.7009 | 1.38307 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 62.6410 | 2.12617 | ||||||||
\(869\) | 15.6481 | 0.530824 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.0526 | 0.645571 | ||||||||
\(872\) | −52.3013 | −1.77114 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.7529 | −0.397548 | ||||||||
\(875\) | −21.2498 | −0.718374 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.3781 | −1.49854 | −0.749271 | − | 0.662264i | \(-0.769596\pi\) | ||||
−0.749271 | + | 0.662264i | \(0.769596\pi\) | |||||||
\(878\) | 66.8372 | 2.25565 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.53590 | 0.287745 | ||||||||
\(881\) | −7.98076 | −0.268879 | −0.134439 | − | 0.990922i | \(-0.542923\pi\) | ||||
−0.134439 | + | 0.990922i | \(0.542923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.48334 | −0.117224 | −0.0586119 | − | 0.998281i | \(-0.518667\pi\) | ||||
−0.0586119 | + | 0.998281i | \(0.518667\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 78.3013 | 2.63058 | ||||||||
\(887\) | 26.0000 | 0.872995 | 0.436497 | − | 0.899706i | \(-0.356219\pi\) | ||||
0.436497 | + | 0.899706i | \(0.356219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.13213 | −0.172126 | ||||||||
\(890\) | −54.2487 | −1.81842 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 88.0333 | 2.94757 | ||||||||
\(893\) | 32.1095 | 1.07450 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 16.5873 | 0.554452 | ||||||||
\(896\) | −36.3397 | −1.21403 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −64.4707 | −2.15142 | ||||||||
\(899\) | −16.5873 | −0.553217 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 51.0449 | 1.69961 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 18.8096 | 0.625597 | ||||||||
\(905\) | 16.5873 | 0.551380 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.2686 | 0.407371 | 0.203686 | − | 0.979036i | \(-0.434708\pi\) | ||||
0.203686 | + | 0.979036i | \(0.434708\pi\) | |||||||
\(908\) | 88.7654 | 2.94578 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 17.9090 | 0.593676 | ||||||||
\(911\) | 41.2487 | 1.36663 | 0.683315 | − | 0.730123i | \(-0.260537\pi\) | ||||
0.683315 | + | 0.730123i | \(0.260537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 42.7513 | 1.41409 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 57.4449 | 1.89803 | ||||||||
\(917\) | 1.75265 | 0.0578777 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.9808 | −0.461183 | −0.230591 | − | 0.973051i | \(-0.574066\pi\) | ||||
−0.230591 | + | 0.973051i | \(0.574066\pi\) | |||||||
\(920\) | −11.0316 | −0.363701 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −48.1051 | −1.58426 | ||||||||
\(923\) | 30.7128 | 1.01092 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0926 | 0.660641 | ||||||||
\(926\) | −22.3149 | −0.733313 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.14682 | 0.136126 | ||||||||
\(929\) | 6.12436 | 0.200934 | 0.100467 | − | 0.994940i | \(-0.467966\pi\) | ||||
0.100467 | + | 0.994940i | \(0.467966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.5551 | −0.411478 | ||||||||
\(932\) | 19.9282 | 0.652770 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 69.9090 | 2.28749 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.1436 | −0.494720 | −0.247360 | − | 0.968924i | \(-0.579563\pi\) | ||||
−0.247360 | + | 0.968924i | \(0.579563\pi\) | |||||||
\(938\) | 32.4449 | 1.05936 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 64.9403 | 2.11812 | ||||||||
\(941\) | −10.3923 | −0.338779 | −0.169390 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169390 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.3731 | −0.533180 | ||||||||
\(944\) | −7.48024 | −0.243461 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.8703 | −0.581015 | ||||||||
\(947\) | −26.7846 | −0.870383 | −0.435191 | − | 0.900338i | \(-0.643319\pi\) | ||||
−0.435191 | + | 0.900338i | \(0.643319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.48024 | 0.242819 | ||||||||
\(950\) | −15.3043 | −0.496536 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.44455 | −0.143973 | −0.0719866 | − | 0.997406i | \(-0.522934\pi\) | ||||
−0.0719866 | + | 0.997406i | \(0.522934\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.44455 | 0.143822 | ||||||||
\(956\) | −69.7287 | −2.25519 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −53.0953 | −1.71543 | ||||||||
\(959\) | −22.9282 | −0.740390 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 60.7128 | 1.95848 | ||||||||
\(962\) | −59.2679 | −1.91088 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.0820 | 0.421342 | ||||||||
\(965\) | 28.7300 | 0.924853 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.58846 | −0.115397 | −0.0576985 | − | 0.998334i | \(-0.518376\pi\) | ||||
−0.0576985 | + | 0.998334i | \(0.518376\pi\) | |||||||
\(968\) | −29.0278 | −0.932988 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −52.3013 | −1.67929 | ||||||||
\(971\) | 13.5516 | 0.434892 | 0.217446 | − | 0.976072i | \(-0.430227\pi\) | ||||
0.217446 | + | 0.976072i | \(0.430227\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.2872 | 0.393909 | ||||||||
\(974\) | −87.8179 | −2.81387 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.1177 | 0.515914 | ||||||||
\(977\) | 7.82403 | 0.250313 | 0.125156 | − | 0.992137i | \(-0.460057\pi\) | ||||
0.125156 | + | 0.992137i | \(0.460057\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −26.1640 | −0.836204 | ||||||||
\(980\) | −25.3923 | −0.811127 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −74.9282 | −2.39106 | ||||||||
\(983\) | 12.3205 | 0.392963 | 0.196482 | − | 0.980508i | \(-0.437048\pi\) | ||||
0.196482 | + | 0.980508i | \(0.437048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.14359 | −0.0364379 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 29.3923 | 0.935094 | ||||||||
\(989\) | 5.73205 | 0.182269 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −46.1307 | −1.46539 | −0.732696 | − | 0.680556i | \(-0.761738\pi\) | ||||
−0.732696 | + | 0.680556i | \(0.761738\pi\) | |||||||
\(992\) | −22.9282 | −0.727971 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 52.3013 | 1.65890 | ||||||||
\(995\) | −27.1032 | −0.859230 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.1640 | −0.828622 | −0.414311 | − | 0.910135i | \(-0.635977\pi\) | ||||
−0.414311 | + | 0.910135i | \(0.635977\pi\) | |||||||
\(998\) | −27.1244 | −0.858606 | ||||||||
\(999\) | 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 | 7803.2.a.bi.1.4 | 4 | ||
3.2 | odd | 2 | 7803.2.a.bh.1.1 | 4 | |||
17.4 | even | 4 | 459.2.d.b.271.1 | ✓ | 8 | ||
17.13 | even | 4 | 459.2.d.b.271.2 | yes | 8 | ||
17.16 | even | 2 | 7803.2.a.bh.1.4 | 4 | |||
51.38 | odd | 4 | 459.2.d.b.271.8 | yes | 8 | ||
51.47 | odd | 4 | 459.2.d.b.271.7 | yes | 8 | ||
51.50 | odd | 2 | inner | 7803.2.a.bi.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
459.2.d.b.271.1 | ✓ | 8 | 17.4 | even | 4 | ||
459.2.d.b.271.2 | yes | 8 | 17.13 | even | 4 | ||
459.2.d.b.271.7 | yes | 8 | 51.47 | odd | 4 | ||
459.2.d.b.271.8 | yes | 8 | 51.38 | odd | 4 | ||
7803.2.a.bh.1.1 | 4 | 3.2 | odd | 2 | |||
7803.2.a.bh.1.4 | 4 | 17.16 | even | 2 | |||
7803.2.a.bi.1.1 | 4 | 51.50 | odd | 2 | inner | ||
7803.2.a.bi.1.4 | 4 | 1.1 | even | 1 | trivial |