Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8550,2,Mod(1,8550)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8550, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8550.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8550 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8550.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: | \(68.2720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2850) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.16228 | −1.19523 | −0.597614 | − | 0.801784i | \(-0.703885\pi\) | ||||
−0.597614 | + | 0.801784i | \(0.703885\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16228 | 0.651951 | 0.325976 | − | 0.945378i | \(-0.394307\pi\) | ||||
0.325976 | + | 0.945378i | \(0.394307\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.16228 | −0.322358 | −0.161179 | − | 0.986925i | \(-0.551530\pi\) | ||||
−0.161179 | + | 0.986925i | \(0.551530\pi\) | |||||||
\(14\) | 3.16228 | 0.845154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.16228 | −1.73711 | −0.868554 | − | 0.495595i | \(-0.834950\pi\) | ||||
−0.868554 | + | 0.495595i | \(0.834950\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.16228 | −0.460999 | ||||||||
\(23\) | −7.32456 | −1.52728 | −0.763638 | − | 0.645645i | \(-0.776589\pi\) | ||||
−0.763638 | + | 0.645645i | \(0.776589\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.16228 | 0.227941 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.16228 | −0.597614 | ||||||||
\(29\) | 10.1623 | 1.88709 | 0.943544 | − | 0.331248i | \(-0.107470\pi\) | ||||
0.943544 | + | 0.331248i | \(0.107470\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.32456 | −1.31553 | −0.657764 | − | 0.753224i | \(-0.728498\pi\) | ||||
−0.657764 | + | 0.753224i | \(0.728498\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.16228 | 1.22832 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.0000 | 1.64399 | 0.821995 | − | 0.569495i | \(-0.192861\pi\) | ||||
0.821995 | + | 0.569495i | \(0.192861\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.32456 | −0.987730 | −0.493865 | − | 0.869539i | \(-0.664416\pi\) | ||||
−0.493865 | + | 0.869539i | \(0.664416\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.83772 | −0.432749 | −0.216374 | − | 0.976310i | \(-0.569423\pi\) | ||||
−0.216374 | + | 0.976310i | \(0.569423\pi\) | |||||||
\(44\) | 2.16228 | 0.325976 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.32456 | 1.07995 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.16228 | −0.161179 | ||||||||
\(53\) | −8.16228 | −1.12118 | −0.560588 | − | 0.828095i | \(-0.689425\pi\) | ||||
−0.560588 | + | 0.828095i | \(0.689425\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.16228 | 0.422577 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.1623 | −1.33437 | ||||||||
\(59\) | −11.4868 | −1.49546 | −0.747729 | − | 0.664004i | \(-0.768856\pi\) | ||||
−0.747729 | + | 0.664004i | \(0.768856\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.16228 | 0.276851 | 0.138426 | − | 0.990373i | \(-0.455796\pi\) | ||||
0.138426 | + | 0.990373i | \(0.455796\pi\) | |||||||
\(62\) | 7.32456 | 0.930219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4868 | 1.52551 | 0.762755 | − | 0.646688i | \(-0.223846\pi\) | ||||
0.762755 | + | 0.646688i | \(0.223846\pi\) | |||||||
\(68\) | −7.16228 | −0.868554 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.16228 | 0.612650 | 0.306325 | − | 0.951927i | \(-0.400901\pi\) | ||||
0.306325 | + | 0.951927i | \(0.400901\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.00000 | −0.117041 | −0.0585206 | − | 0.998286i | \(-0.518638\pi\) | ||||
−0.0585206 | + | 0.998286i | \(0.518638\pi\) | |||||||
\(74\) | −10.0000 | −1.16248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −6.83772 | −0.779231 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.32456 | 0.824077 | 0.412038 | − | 0.911166i | \(-0.364817\pi\) | ||||
0.412038 | + | 0.911166i | \(0.364817\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.32456 | 0.698430 | ||||||||
\(83\) | 12.4868 | 1.37061 | 0.685304 | − | 0.728257i | \(-0.259669\pi\) | ||||
0.685304 | + | 0.728257i | \(0.259669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.83772 | 0.305999 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.16228 | −0.230500 | ||||||||
\(89\) | −5.32456 | −0.564402 | −0.282201 | − | 0.959355i | \(-0.591064\pi\) | ||||
−0.282201 | + | 0.959355i | \(0.591064\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.67544 | 0.385291 | ||||||||
\(92\) | −7.32456 | −0.763638 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 19.4868 | 1.97859 | 0.989294 | − | 0.145936i | \(-0.0466193\pi\) | ||||
0.989294 | + | 0.145936i | \(0.0466193\pi\) | |||||||
\(98\) | −3.00000 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.8114 | −1.77230 | −0.886150 | − | 0.463399i | \(-0.846630\pi\) | ||||
−0.886150 | + | 0.463399i | \(0.846630\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.64911 | −0.950755 | −0.475378 | − | 0.879782i | \(-0.657689\pi\) | ||||
−0.475378 | + | 0.879782i | \(0.657689\pi\) | |||||||
\(104\) | 1.16228 | 0.113971 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.16228 | 0.792790 | ||||||||
\(107\) | −19.1623 | −1.85249 | −0.926244 | − | 0.376925i | \(-0.876981\pi\) | ||||
−0.926244 | + | 0.376925i | \(0.876981\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20.3246 | 1.94674 | 0.973370 | − | 0.229241i | \(-0.0736244\pi\) | ||||
0.973370 | + | 0.229241i | \(0.0736244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.16228 | −0.298807 | ||||||||
\(113\) | 15.6491 | 1.47214 | 0.736072 | − | 0.676903i | \(-0.236678\pi\) | ||||
0.736072 | + | 0.676903i | \(0.236678\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.1623 | 0.943544 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.4868 | 1.05745 | ||||||||
\(119\) | 22.6491 | 2.07624 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.32456 | −0.574960 | ||||||||
\(122\) | −2.16228 | −0.195763 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.32456 | −0.657764 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.64911 | −0.856220 | −0.428110 | − | 0.903727i | \(-0.640820\pi\) | ||||
−0.428110 | + | 0.903727i | \(0.640820\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.48683 | −0.566757 | −0.283379 | − | 0.959008i | \(-0.591455\pi\) | ||||
−0.283379 | + | 0.959008i | \(0.591455\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.16228 | 0.274204 | ||||||||
\(134\) | −12.4868 | −1.07870 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.16228 | 0.614160 | ||||||||
\(137\) | 10.3246 | 0.882086 | 0.441043 | − | 0.897486i | \(-0.354609\pi\) | ||||
0.441043 | + | 0.897486i | \(0.354609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.51317 | 0.213164 | 0.106582 | − | 0.994304i | \(-0.466009\pi\) | ||||
0.106582 | + | 0.994304i | \(0.466009\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.16228 | −0.433209 | ||||||||
\(143\) | −2.51317 | −0.210162 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.00000 | 0.0827606 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0000 | 0.821995 | ||||||||
\(149\) | 8.64911 | 0.708563 | 0.354281 | − | 0.935139i | \(-0.384726\pi\) | ||||
0.354281 | + | 0.935139i | \(0.384726\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.0000 | −0.813788 | −0.406894 | − | 0.913475i | \(-0.633388\pi\) | ||||
−0.406894 | + | 0.913475i | \(0.633388\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.83772 | 0.550999 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.67544 | 0.452950 | 0.226475 | − | 0.974017i | \(-0.427280\pi\) | ||||
0.226475 | + | 0.974017i | \(0.427280\pi\) | |||||||
\(158\) | −7.32456 | −0.582710 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.1623 | 1.82544 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.64911 | 0.207494 | 0.103747 | − | 0.994604i | \(-0.466917\pi\) | ||||
0.103747 | + | 0.994604i | \(0.466917\pi\) | |||||||
\(164\) | −6.32456 | −0.493865 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −12.4868 | −0.969166 | ||||||||
\(167\) | 22.6491 | 1.75264 | 0.876320 | − | 0.481729i | \(-0.159991\pi\) | ||||
0.876320 | + | 0.481729i | \(0.159991\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6491 | −0.896085 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.83772 | −0.216374 | ||||||||
\(173\) | −4.16228 | −0.316452 | −0.158226 | − | 0.987403i | \(-0.550577\pi\) | ||||
−0.158226 | + | 0.987403i | \(0.550577\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.16228 | 0.162988 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.32456 | 0.399092 | ||||||||
\(179\) | −4.64911 | −0.347491 | −0.173745 | − | 0.984791i | \(-0.555587\pi\) | ||||
−0.173745 | + | 0.984791i | \(0.555587\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.83772 | 0.210926 | 0.105463 | − | 0.994423i | \(-0.466368\pi\) | ||||
0.105463 | + | 0.994423i | \(0.466368\pi\) | |||||||
\(182\) | −3.67544 | −0.272442 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.32456 | 0.539973 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.4868 | −1.13251 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.64911 | 0.264040 | 0.132020 | − | 0.991247i | \(-0.457854\pi\) | ||||
0.132020 | + | 0.991247i | \(0.457854\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.83772 | −0.204264 | −0.102132 | − | 0.994771i | \(-0.532566\pi\) | ||||
−0.102132 | + | 0.994771i | \(0.532566\pi\) | |||||||
\(194\) | −19.4868 | −1.39907 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | 0.214286 | ||||||||
\(197\) | −20.1359 | −1.43463 | −0.717313 | − | 0.696751i | \(-0.754628\pi\) | ||||
−0.717313 | + | 0.696751i | \(0.754628\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.64911 | 0.471343 | 0.235671 | − | 0.971833i | \(-0.424271\pi\) | ||||
0.235671 | + | 0.971833i | \(0.424271\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.8114 | 1.25320 | ||||||||
\(203\) | −32.1359 | −2.25550 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.64911 | 0.672285 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.16228 | −0.0805895 | ||||||||
\(209\) | −2.16228 | −0.149568 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.8114 | 0.881972 | 0.440986 | − | 0.897514i | \(-0.354629\pi\) | ||||
0.440986 | + | 0.897514i | \(0.354629\pi\) | |||||||
\(212\) | −8.16228 | −0.560588 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 19.1623 | 1.30991 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 23.1623 | 1.57236 | ||||||||
\(218\) | −20.3246 | −1.37655 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.32456 | 0.559970 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.350889 | −0.0234973 | −0.0117486 | − | 0.999931i | \(-0.503740\pi\) | ||||
−0.0117486 | + | 0.999931i | \(0.503740\pi\) | |||||||
\(224\) | 3.16228 | 0.211289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.6491 | −1.04096 | ||||||||
\(227\) | 2.00000 | 0.132745 | 0.0663723 | − | 0.997795i | \(-0.478857\pi\) | ||||
0.0663723 | + | 0.997795i | \(0.478857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.83772 | 0.121440 | 0.0607201 | − | 0.998155i | \(-0.480660\pi\) | ||||
0.0607201 | + | 0.998155i | \(0.480660\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.1623 | −0.667186 | ||||||||
\(233\) | −19.8114 | −1.29789 | −0.648944 | − | 0.760837i | \(-0.724789\pi\) | ||||
−0.648944 | + | 0.760837i | \(0.724789\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −11.4868 | −0.747729 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.6491 | −1.46812 | ||||||||
\(239\) | 11.6754 | 0.755222 | 0.377611 | − | 0.925964i | \(-0.376746\pi\) | ||||
0.377611 | + | 0.925964i | \(0.376746\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.4868 | 1.89941 | 0.949707 | − | 0.313140i | \(-0.101381\pi\) | ||||
0.949707 | + | 0.313140i | \(0.101381\pi\) | |||||||
\(242\) | 6.32456 | 0.406558 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.16228 | 0.138426 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.16228 | 0.0739540 | ||||||||
\(248\) | 7.32456 | 0.465110 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.6491 | −0.924644 | −0.462322 | − | 0.886712i | \(-0.652984\pi\) | ||||
−0.462322 | + | 0.886712i | \(0.652984\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −15.8377 | −0.995709 | ||||||||
\(254\) | 9.64911 | 0.605439 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 6.67544 | 0.416403 | 0.208201 | − | 0.978086i | \(-0.433239\pi\) | ||||
0.208201 | + | 0.978086i | \(0.433239\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −31.6228 | −1.96494 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.48683 | 0.400758 | ||||||||
\(263\) | 5.97367 | 0.368352 | 0.184176 | − | 0.982893i | \(-0.441038\pi\) | ||||
0.184176 | + | 0.982893i | \(0.441038\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.16228 | −0.193892 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.4868 | 0.762755 | ||||||||
\(269\) | 0.324555 | 0.0197885 | 0.00989424 | − | 0.999951i | \(-0.496851\pi\) | ||||
0.00989424 | + | 0.999951i | \(0.496851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.16228 | 0.313586 | 0.156793 | − | 0.987631i | \(-0.449884\pi\) | ||||
0.156793 | + | 0.987631i | \(0.449884\pi\) | |||||||
\(272\) | −7.16228 | −0.434277 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −10.3246 | −0.623729 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.81139 | −0.409257 | −0.204628 | − | 0.978840i | \(-0.565599\pi\) | ||||
−0.204628 | + | 0.978840i | \(0.565599\pi\) | |||||||
\(278\) | −2.51317 | −0.150730 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.6491 | 1.05286 | 0.526429 | − | 0.850219i | \(-0.323531\pi\) | ||||
0.526429 | + | 0.850219i | \(0.323531\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.649111 | −0.0385856 | −0.0192928 | − | 0.999814i | \(-0.506141\pi\) | ||||
−0.0192928 | + | 0.999814i | \(0.506141\pi\) | |||||||
\(284\) | 5.16228 | 0.306325 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.51317 | 0.148607 | ||||||||
\(287\) | 20.0000 | 1.18056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 34.2982 | 2.01754 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.00000 | −0.0585206 | ||||||||
\(293\) | 2.48683 | 0.145282 | 0.0726412 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726412 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.0000 | −0.581238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.64911 | −0.501030 | ||||||||
\(299\) | 8.51317 | 0.492329 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.97367 | 0.517234 | ||||||||
\(302\) | 10.0000 | 0.575435 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.4868 | 1.85412 | 0.927061 | − | 0.374911i | \(-0.122327\pi\) | ||||
0.927061 | + | 0.374911i | \(0.122327\pi\) | |||||||
\(308\) | −6.83772 | −0.389615 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.0000 | 1.47432 | 0.737162 | − | 0.675716i | \(-0.236165\pi\) | ||||
0.737162 | + | 0.675716i | \(0.236165\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3246 | −1.31838 | −0.659191 | − | 0.751976i | \(-0.729101\pi\) | ||||
−0.659191 | + | 0.751976i | \(0.729101\pi\) | |||||||
\(314\) | −5.67544 | −0.320284 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.32456 | 0.412038 | ||||||||
\(317\) | 2.16228 | 0.121446 | 0.0607228 | − | 0.998155i | \(-0.480659\pi\) | ||||
0.0607228 | + | 0.998155i | \(0.480659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.9737 | 1.23029 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −23.1623 | −1.29078 | ||||||||
\(323\) | 7.16228 | 0.398520 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.64911 | −0.146721 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.32456 | 0.349215 | ||||||||
\(329\) | 18.9737 | 1.04605 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.8114 | −1.91341 | −0.956703 | − | 0.291064i | \(-0.905991\pi\) | ||||
−0.956703 | + | 0.291064i | \(0.905991\pi\) | |||||||
\(332\) | 12.4868 | 0.685304 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −22.6491 | −1.23930 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9737 | 1.90514 | 0.952568 | − | 0.304324i | \(-0.0984306\pi\) | ||||
0.952568 | + | 0.304324i | \(0.0984306\pi\) | |||||||
\(338\) | 11.6491 | 0.633628 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.8377 | −0.857661 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6491 | 0.682988 | ||||||||
\(344\) | 2.83772 | 0.153000 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.16228 | 0.223765 | ||||||||
\(347\) | 20.0000 | 1.07366 | 0.536828 | − | 0.843692i | \(-0.319622\pi\) | ||||
0.536828 | + | 0.843692i | \(0.319622\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.1623 | −1.29338 | −0.646689 | − | 0.762754i | \(-0.723847\pi\) | ||||
−0.646689 | + | 0.762754i | \(0.723847\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.16228 | −0.115250 | ||||||||
\(353\) | 7.81139 | 0.415758 | 0.207879 | − | 0.978155i | \(-0.433344\pi\) | ||||
0.207879 | + | 0.978155i | \(0.433344\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.32456 | −0.282201 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.64911 | 0.245713 | ||||||||
\(359\) | 24.3246 | 1.28380 | 0.641900 | − | 0.766788i | \(-0.278146\pi\) | ||||
0.641900 | + | 0.766788i | \(0.278146\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −2.83772 | −0.149147 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.67544 | 0.192646 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.4868 | 0.599608 | 0.299804 | − | 0.954001i | \(-0.403079\pi\) | ||||
0.299804 | + | 0.954001i | \(0.403079\pi\) | |||||||
\(368\) | −7.32456 | −0.381819 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.8114 | 1.34006 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.1359 | 1.45682 | 0.728412 | − | 0.685139i | \(-0.240259\pi\) | ||||
0.728412 | + | 0.685139i | \(0.240259\pi\) | |||||||
\(374\) | 15.4868 | 0.800805 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −11.8114 | −0.608317 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9737 | −0.769146 | −0.384573 | − | 0.923095i | \(-0.625651\pi\) | ||||
−0.384573 | + | 0.923095i | \(0.625651\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −3.64911 | −0.186705 | ||||||||
\(383\) | −15.4868 | −0.791340 | −0.395670 | − | 0.918393i | \(-0.629488\pi\) | ||||
−0.395670 | + | 0.918393i | \(0.629488\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.83772 | 0.144436 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.4868 | 0.989294 | ||||||||
\(389\) | 9.35089 | 0.474109 | 0.237054 | − | 0.971496i | \(-0.423818\pi\) | ||||
0.237054 | + | 0.971496i | \(0.423818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 52.4605 | 2.65304 | ||||||||
\(392\) | −3.00000 | −0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20.1359 | 1.01443 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.1359 | −1.36191 | −0.680957 | − | 0.732323i | \(-0.738436\pi\) | ||||
−0.680957 | + | 0.732323i | \(0.738436\pi\) | |||||||
\(398\) | −6.64911 | −0.333290 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.6491 | 0.581729 | 0.290864 | − | 0.956764i | \(-0.406057\pi\) | ||||
0.290864 | + | 0.956764i | \(0.406057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.51317 | 0.424071 | ||||||||
\(404\) | −17.8114 | −0.886150 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 32.1359 | 1.59488 | ||||||||
\(407\) | 21.6228 | 1.07180 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −20.3246 | −1.00498 | −0.502492 | − | 0.864582i | \(-0.667583\pi\) | ||||
−0.502492 | + | 0.864582i | \(0.667583\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −9.64911 | −0.475378 | ||||||||
\(413\) | 36.3246 | 1.78741 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.16228 | 0.0569854 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.16228 | 0.105760 | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.64911 | −0.324058 | −0.162029 | − | 0.986786i | \(-0.551804\pi\) | ||||
−0.162029 | + | 0.986786i | \(0.551804\pi\) | |||||||
\(422\) | −12.8114 | −0.623649 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.16228 | 0.396395 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.83772 | −0.330901 | ||||||||
\(428\) | −19.1623 | −0.926244 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3246 | −0.593653 | −0.296826 | − | 0.954931i | \(-0.595928\pi\) | ||||
−0.296826 | + | 0.954931i | \(0.595928\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.1359 | −0.775444 | −0.387722 | − | 0.921776i | \(-0.626738\pi\) | ||||
−0.387722 | + | 0.921776i | \(0.626738\pi\) | |||||||
\(434\) | −23.1623 | −1.11182 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 20.3246 | 0.973370 | ||||||||
\(437\) | 7.32456 | 0.350381 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.6491 | −0.555982 | −0.277991 | − | 0.960584i | \(-0.589668\pi\) | ||||
−0.277991 | + | 0.960584i | \(0.589668\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −8.32456 | −0.395959 | ||||||||
\(443\) | 18.1623 | 0.862916 | 0.431458 | − | 0.902133i | \(-0.357999\pi\) | ||||
0.431458 | + | 0.902133i | \(0.357999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.350889 | 0.0166151 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.16228 | −0.149404 | ||||||||
\(449\) | 11.0000 | 0.519122 | 0.259561 | − | 0.965727i | \(-0.416422\pi\) | ||||
0.259561 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.6754 | −0.643952 | ||||||||
\(452\) | 15.6491 | 0.736072 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.00000 | −0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.3246 | 1.04430 | 0.522149 | − | 0.852854i | \(-0.325130\pi\) | ||||
0.522149 | + | 0.852854i | \(0.325130\pi\) | |||||||
\(458\) | −1.83772 | −0.0858711 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.3246 | −1.59520 | −0.797599 | − | 0.603188i | \(-0.793897\pi\) | ||||
−0.797599 | + | 0.603188i | \(0.793897\pi\) | |||||||
\(464\) | 10.1623 | 0.471772 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 19.8114 | 0.917745 | ||||||||
\(467\) | −7.13594 | −0.330212 | −0.165106 | − | 0.986276i | \(-0.552797\pi\) | ||||
−0.165106 | + | 0.986276i | \(0.552797\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −39.4868 | −1.82333 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 11.4868 | 0.528724 | ||||||||
\(473\) | −6.13594 | −0.282131 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.6491 | 1.03812 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.6754 | −0.534022 | ||||||||
\(479\) | 2.02633 | 0.0925856 | 0.0462928 | − | 0.998928i | \(-0.485259\pi\) | ||||
0.0462928 | + | 0.998928i | \(0.485259\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.6228 | −0.529953 | ||||||||
\(482\) | −29.4868 | −1.34309 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.32456 | −0.287480 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.35089 | −0.151843 | −0.0759216 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759216 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(488\) | −2.16228 | −0.0978817 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −72.7851 | −3.27807 | ||||||||
\(494\) | −1.16228 | −0.0522933 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.32456 | −0.328882 | ||||||||
\(497\) | −16.3246 | −0.732256 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.8114 | 1.15548 | 0.577738 | − | 0.816222i | \(-0.303935\pi\) | ||||
0.577738 | + | 0.816222i | \(0.303935\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 14.6491 | 0.653822 | ||||||||
\(503\) | −21.2982 | −0.949641 | −0.474820 | − | 0.880083i | \(-0.657487\pi\) | ||||
−0.474820 | + | 0.880083i | \(0.657487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 15.8377 | 0.704073 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.64911 | −0.428110 | ||||||||
\(509\) | 14.8114 | 0.656503 | 0.328252 | − | 0.944590i | \(-0.393541\pi\) | ||||
0.328252 | + | 0.944590i | \(0.393541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.16228 | 0.139891 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.67544 | −0.294441 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.9737 | −0.570581 | ||||||||
\(518\) | 31.6228 | 1.38943 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.9737 | 0.787441 | 0.393720 | − | 0.919230i | \(-0.371188\pi\) | ||||
0.393720 | + | 0.919230i | \(0.371188\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.64911 | 0.378199 | 0.189100 | − | 0.981958i | \(-0.439443\pi\) | ||||
0.189100 | + | 0.981958i | \(0.439443\pi\) | |||||||
\(524\) | −6.48683 | −0.283379 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.97367 | −0.260464 | ||||||||
\(527\) | 52.4605 | 2.28522 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.6491 | 1.33257 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.16228 | 0.137102 | ||||||||
\(533\) | 7.35089 | 0.318402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.4868 | −0.539349 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.324555 | −0.0139926 | ||||||||
\(539\) | 6.48683 | 0.279408 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.16228 | 0.264937 | 0.132469 | − | 0.991187i | \(-0.457710\pi\) | ||||
0.132469 | + | 0.991187i | \(0.457710\pi\) | |||||||
\(542\) | −5.16228 | −0.221739 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.16228 | 0.307080 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.8114 | 0.633289 | 0.316645 | − | 0.948544i | \(-0.397444\pi\) | ||||
0.316645 | + | 0.948544i | \(0.397444\pi\) | |||||||
\(548\) | 10.3246 | 0.441043 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.1623 | −0.432928 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −23.1623 | −0.984960 | ||||||||
\(554\) | 6.81139 | 0.289388 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.51317 | 0.106582 | ||||||||
\(557\) | 29.1623 | 1.23565 | 0.617823 | − | 0.786317i | \(-0.288015\pi\) | ||||
0.617823 | + | 0.786317i | \(0.288015\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.29822 | 0.139500 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.6491 | −0.744483 | ||||||||
\(563\) | −24.8377 | −1.04679 | −0.523393 | − | 0.852092i | \(-0.675334\pi\) | ||||
−0.523393 | + | 0.852092i | \(0.675334\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.649111 | 0.0272842 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.16228 | −0.216604 | ||||||||
\(569\) | −22.0000 | −0.922288 | −0.461144 | − | 0.887325i | \(-0.652561\pi\) | ||||
−0.461144 | + | 0.887325i | \(0.652561\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.8114 | 0.661686 | 0.330843 | − | 0.943686i | \(-0.392667\pi\) | ||||
0.330843 | + | 0.943686i | \(0.392667\pi\) | |||||||
\(572\) | −2.51317 | −0.105081 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −20.0000 | −0.834784 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −29.3246 | −1.22080 | −0.610399 | − | 0.792094i | \(-0.708991\pi\) | ||||
−0.610399 | + | 0.792094i | \(0.708991\pi\) | |||||||
\(578\) | −34.2982 | −1.42662 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.4868 | −1.63819 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.6491 | −0.730951 | ||||||||
\(584\) | 1.00000 | 0.0413803 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.48683 | −0.102730 | ||||||||
\(587\) | −12.8114 | −0.528783 | −0.264391 | − | 0.964415i | \(-0.585171\pi\) | ||||
−0.264391 | + | 0.964415i | \(0.585171\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.32456 | 0.301803 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.0000 | 0.410997 | ||||||||
\(593\) | −10.3246 | −0.423979 | −0.211989 | − | 0.977272i | \(-0.567994\pi\) | ||||
−0.211989 | + | 0.977272i | \(0.567994\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 8.64911 | 0.354281 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −8.51317 | −0.348129 | ||||||||
\(599\) | 35.8114 | 1.46321 | 0.731607 | − | 0.681727i | \(-0.238771\pi\) | ||||
0.731607 | + | 0.681727i | \(0.238771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.1886 | 0.578766 | 0.289383 | − | 0.957213i | \(-0.406550\pi\) | ||||
0.289383 | + | 0.957213i | \(0.406550\pi\) | |||||||
\(602\) | −8.97367 | −0.365739 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.9737 | 1.62248 | 0.811241 | − | 0.584713i | \(-0.198793\pi\) | ||||
0.811241 | + | 0.584713i | \(0.198793\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.97367 | 0.282124 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.2982 | 0.941006 | 0.470503 | − | 0.882398i | \(-0.344072\pi\) | ||||
0.470503 | + | 0.882398i | \(0.344072\pi\) | |||||||
\(614\) | −32.4868 | −1.31106 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.83772 | 0.275500 | ||||||||
\(617\) | 24.3246 | 0.979270 | 0.489635 | − | 0.871928i | \(-0.337130\pi\) | ||||
0.489635 | + | 0.871928i | \(0.337130\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.1623 | 0.689810 | 0.344905 | − | 0.938638i | \(-0.387911\pi\) | ||||
0.344905 | + | 0.938638i | \(0.387911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.0000 | −1.04251 | ||||||||
\(623\) | 16.8377 | 0.674589 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.3246 | 0.932237 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 5.67544 | 0.226475 | ||||||||
\(629\) | −71.6228 | −2.85579 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.29822 | −0.210919 | −0.105459 | − | 0.994424i | \(-0.533631\pi\) | ||||
−0.105459 | + | 0.994424i | \(0.533631\pi\) | |||||||
\(632\) | −7.32456 | −0.291355 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.16228 | −0.0858750 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.48683 | −0.138153 | ||||||||
\(638\) | −21.9737 | −0.869946 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2982 | −0.525248 | −0.262624 | − | 0.964898i | \(-0.584588\pi\) | ||||
−0.262624 | + | 0.964898i | \(0.584588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.6491 | −0.735449 | −0.367725 | − | 0.929935i | \(-0.619863\pi\) | ||||
−0.367725 | + | 0.929935i | \(0.619863\pi\) | |||||||
\(644\) | 23.1623 | 0.912722 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.16228 | −0.281796 | ||||||||
\(647\) | 9.00000 | 0.353827 | 0.176913 | − | 0.984226i | \(-0.443389\pi\) | ||||
0.176913 | + | 0.984226i | \(0.443389\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.8377 | −0.974966 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.64911 | 0.103747 | ||||||||
\(653\) | 30.9737 | 1.21209 | 0.606047 | − | 0.795429i | \(-0.292754\pi\) | ||||
0.606047 | + | 0.795429i | \(0.292754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.32456 | −0.246932 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −18.9737 | −0.739671 | ||||||||
\(659\) | 18.1886 | 0.708528 | 0.354264 | − | 0.935146i | \(-0.384731\pi\) | ||||
0.354264 | + | 0.935146i | \(0.384731\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.2982 | −0.517241 | −0.258620 | − | 0.965979i | \(-0.583268\pi\) | ||||
−0.258620 | + | 0.965979i | \(0.583268\pi\) | |||||||
\(662\) | 34.8114 | 1.35298 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.4868 | −0.484583 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −74.4342 | −2.88210 | ||||||||
\(668\) | 22.6491 | 0.876320 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.67544 | 0.180494 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.4605 | 0.942883 | 0.471441 | − | 0.881897i | \(-0.343734\pi\) | ||||
0.471441 | + | 0.881897i | \(0.343734\pi\) | |||||||
\(674\) | −34.9737 | −1.34714 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.6491 | −0.448043 | ||||||||
\(677\) | 0.486833 | 0.0187105 | 0.00935526 | − | 0.999956i | \(-0.497022\pi\) | ||||
0.00935526 | + | 0.999956i | \(0.497022\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −61.6228 | −2.36487 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.8377 | 0.606458 | ||||||||
\(683\) | −45.1096 | −1.72607 | −0.863036 | − | 0.505143i | \(-0.831440\pi\) | ||||
−0.863036 | + | 0.505143i | \(0.831440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −12.6491 | −0.482945 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.83772 | −0.108187 | ||||||||
\(689\) | 9.48683 | 0.361420 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.48683 | −0.208729 | −0.104364 | − | 0.994539i | \(-0.533281\pi\) | ||||
−0.104364 | + | 0.994539i | \(0.533281\pi\) | |||||||
\(692\) | −4.16228 | −0.158226 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 45.2982 | 1.71579 | ||||||||
\(698\) | 24.1623 | 0.914556 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.97367 | −0.263392 | −0.131696 | − | 0.991290i | \(-0.542042\pi\) | ||||
−0.131696 | + | 0.991290i | \(0.542042\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.0000 | −0.377157 | ||||||||
\(704\) | 2.16228 | 0.0814939 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.81139 | −0.293985 | ||||||||
\(707\) | 56.3246 | 2.11830 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.4868 | 1.59563 | 0.797813 | − | 0.602905i | \(-0.205990\pi\) | ||||
0.797813 | + | 0.602905i | \(0.205990\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.32456 | 0.199546 | ||||||||
\(713\) | 53.6491 | 2.00917 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.64911 | −0.173745 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.3246 | −0.907784 | ||||||||
\(719\) | −6.67544 | −0.248952 | −0.124476 | − | 0.992223i | \(-0.539725\pi\) | ||||
−0.124476 | + | 0.992223i | \(0.539725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.5132 | 1.13637 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.83772 | 0.105463 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.6228 | 0.505241 | 0.252620 | − | 0.967565i | \(-0.418708\pi\) | ||||
0.252620 | + | 0.967565i | \(0.418708\pi\) | |||||||
\(728\) | −3.67544 | −0.136221 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.3246 | 0.751731 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.5132 | 1.16397 | 0.581983 | − | 0.813201i | \(-0.302277\pi\) | ||||
0.581983 | + | 0.813201i | \(0.302277\pi\) | |||||||
\(734\) | −11.4868 | −0.423987 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.32456 | 0.269987 | ||||||||
\(737\) | 27.0000 | 0.994558 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.32456 | −0.232653 | −0.116326 | − | 0.993211i | \(-0.537112\pi\) | ||||
−0.116326 | + | 0.993211i | \(0.537112\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −25.8114 | −0.947566 | ||||||||
\(743\) | 20.6491 | 0.757542 | 0.378771 | − | 0.925490i | \(-0.376347\pi\) | ||||
0.378771 | + | 0.925490i | \(0.376347\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −28.1359 | −1.03013 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.4868 | −0.566255 | ||||||||
\(749\) | 60.5964 | 2.21415 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.0000 | −0.948753 | −0.474377 | − | 0.880322i | \(-0.657327\pi\) | ||||
−0.474377 | + | 0.880322i | \(0.657327\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.8114 | 0.430145 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.1359 | −1.78588 | −0.892938 | − | 0.450179i | \(-0.851360\pi\) | ||||
−0.892938 | + | 0.450179i | \(0.851360\pi\) | |||||||
\(758\) | 14.9737 | 0.543868 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.5132 | 0.743602 | 0.371801 | − | 0.928313i | \(-0.378740\pi\) | ||||
0.371801 | + | 0.928313i | \(0.378740\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −64.2719 | −2.32680 | ||||||||
\(764\) | 3.64911 | 0.132020 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.4868 | 0.559562 | ||||||||
\(767\) | 13.3509 | 0.482073 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 47.3246 | 1.70657 | 0.853284 | − | 0.521447i | \(-0.174608\pi\) | ||||
0.853284 | + | 0.521447i | \(0.174608\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.83772 | −0.102132 | ||||||||
\(773\) | 28.9737 | 1.04211 | 0.521055 | − | 0.853523i | \(-0.325539\pi\) | ||||
0.521055 | + | 0.853523i | \(0.325539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.4868 | −0.699537 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9.35089 | −0.335246 | ||||||||
\(779\) | 6.32456 | 0.226601 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.1623 | 0.399418 | ||||||||
\(782\) | −52.4605 | −1.87598 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5132 | 0.552985 | 0.276492 | − | 0.961016i | \(-0.410828\pi\) | ||||
0.276492 | + | 0.961016i | \(0.410828\pi\) | |||||||
\(788\) | −20.1359 | −0.717313 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −49.4868 | −1.75955 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.51317 | −0.0892452 | ||||||||
\(794\) | 27.1359 | 0.963019 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.64911 | 0.235671 | ||||||||
\(797\) | 15.6228 | 0.553387 | 0.276694 | − | 0.960958i | \(-0.410761\pi\) | ||||
0.276694 | + | 0.960958i | \(0.410761\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.9737 | 1.52030 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −11.6491 | −0.411344 | ||||||||
\(803\) | −2.16228 | −0.0763051 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.51317 | −0.299864 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.8114 | 0.626602 | ||||||||
\(809\) | 16.8377 | 0.591983 | 0.295991 | − | 0.955191i | \(-0.404350\pi\) | ||||
0.295991 | + | 0.955191i | \(0.404350\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.8114 | 1.50331 | 0.751656 | − | 0.659556i | \(-0.229256\pi\) | ||||
0.751656 | + | 0.659556i | \(0.229256\pi\) | |||||||
\(812\) | −32.1359 | −1.12775 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.6228 | −0.757878 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.83772 | 0.0992793 | ||||||||
\(818\) | 20.3246 | 0.710631 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.1623 | −1.50637 | −0.753187 | − | 0.657807i | \(-0.771484\pi\) | ||||
−0.753187 | + | 0.657807i | \(0.771484\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.2982 | 0.812125 | 0.406062 | − | 0.913845i | \(-0.366902\pi\) | ||||
0.406062 | + | 0.913845i | \(0.366902\pi\) | |||||||
\(824\) | 9.64911 | 0.336143 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36.3246 | −1.26389 | ||||||||
\(827\) | 1.16228 | 0.0404164 | 0.0202082 | − | 0.999796i | \(-0.493567\pi\) | ||||
0.0202082 | + | 0.999796i | \(0.493567\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.7851 | 1.62491 | 0.812456 | − | 0.583022i | \(-0.198130\pi\) | ||||
0.812456 | + | 0.583022i | \(0.198130\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.16228 | −0.0402947 | ||||||||
\(833\) | −21.4868 | −0.744475 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.16228 | −0.0747839 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.00000 | 0.276355 | ||||||||
\(839\) | 19.1623 | 0.661555 | 0.330778 | − | 0.943709i | \(-0.392689\pi\) | ||||
0.330778 | + | 0.943709i | \(0.392689\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 74.2719 | 2.56110 | ||||||||
\(842\) | 6.64911 | 0.229143 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.8114 | 0.440986 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.0000 | 0.687208 | ||||||||
\(848\) | −8.16228 | −0.280294 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −73.2456 | −2.51083 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.6754 | 0.673674 | 0.336837 | − | 0.941563i | \(-0.390643\pi\) | ||||
0.336837 | + | 0.941563i | \(0.390643\pi\) | |||||||
\(854\) | 6.83772 | 0.233982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1623 | 0.654953 | ||||||||
\(857\) | −38.3246 | −1.30914 | −0.654571 | − | 0.756001i | \(-0.727151\pi\) | ||||
−0.654571 | + | 0.756001i | \(0.727151\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.6491 | −1.04573 | −0.522867 | − | 0.852414i | \(-0.675138\pi\) | ||||
−0.522867 | + | 0.852414i | \(0.675138\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.3246 | 0.419776 | ||||||||
\(863\) | −17.0263 | −0.579583 | −0.289792 | − | 0.957090i | \(-0.593586\pi\) | ||||
−0.289792 | + | 0.957090i | \(0.593586\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 16.1359 | 0.548322 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.1623 | 0.786179 | ||||||||
\(869\) | 15.8377 | 0.537258 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.5132 | −0.491760 | ||||||||
\(872\) | −20.3246 | −0.688276 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.32456 | −0.247757 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.6228 | −0.595079 | −0.297539 | − | 0.954710i | \(-0.596166\pi\) | ||||
−0.297539 | + | 0.954710i | \(0.596166\pi\) | |||||||
\(878\) | 11.6491 | 0.393138 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.67544 | −0.0564472 | −0.0282236 | − | 0.999602i | \(-0.508985\pi\) | ||||
−0.0282236 | + | 0.999602i | \(0.508985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.5132 | −0.353796 | −0.176898 | − | 0.984229i | \(-0.556606\pi\) | ||||
−0.176898 | + | 0.984229i | \(0.556606\pi\) | |||||||
\(884\) | 8.32456 | 0.279985 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −18.1623 | −0.610174 | ||||||||
\(887\) | −34.3246 | −1.15251 | −0.576253 | − | 0.817271i | \(-0.695486\pi\) | ||||
−0.576253 | + | 0.817271i | \(0.695486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.5132 | 1.02338 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.350889 | −0.0117486 | ||||||||
\(893\) | 6.00000 | 0.200782 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.16228 | 0.105644 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.0000 | −0.367075 | ||||||||
\(899\) | −74.4342 | −2.48252 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.4605 | 1.94760 | ||||||||
\(902\) | 13.6754 | 0.455343 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.6491 | −0.520482 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −13.3509 | −0.443309 | −0.221655 | − | 0.975125i | \(-0.571146\pi\) | ||||
−0.221655 | + | 0.975125i | \(0.571146\pi\) | |||||||
\(908\) | 2.00000 | 0.0663723 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 44.9737 | 1.49004 | 0.745022 | − | 0.667040i | \(-0.232439\pi\) | ||||
0.745022 | + | 0.667040i | \(0.232439\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 27.0000 | 0.893570 | ||||||||
\(914\) | −22.3246 | −0.738431 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.83772 | 0.0607201 | ||||||||
\(917\) | 20.5132 | 0.677404 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.1623 | −0.830027 | −0.415013 | − | 0.909815i | \(-0.636223\pi\) | ||||
−0.415013 | + | 0.909815i | \(0.636223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.0000 | 0.395199 | ||||||||
\(923\) | −6.00000 | −0.197492 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 34.3246 | 1.12797 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10.1623 | −0.333593 | ||||||||
\(929\) | −13.2982 | −0.436300 | −0.218150 | − | 0.975915i | \(-0.570002\pi\) | ||||
−0.218150 | + | 0.975915i | \(0.570002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.00000 | −0.0983210 | ||||||||
\(932\) | −19.8114 | −0.648944 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.13594 | 0.233495 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.35089 | −0.0441316 | −0.0220658 | − | 0.999757i | \(-0.507024\pi\) | ||||
−0.0220658 | + | 0.999757i | \(0.507024\pi\) | |||||||
\(938\) | 39.4868 | 1.28929 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.18861 | −0.0387476 | −0.0193738 | − | 0.999812i | \(-0.506167\pi\) | ||||
−0.0193738 | + | 0.999812i | \(0.506167\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.3246 | 1.50854 | ||||||||
\(944\) | −11.4868 | −0.373865 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.13594 | 0.199497 | ||||||||
\(947\) | 48.0000 | 1.55979 | 0.779895 | − | 0.625910i | \(-0.215272\pi\) | ||||
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.16228 | 0.0377291 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −22.6491 | −0.734062 | ||||||||
\(953\) | 53.3246 | 1.72735 | 0.863676 | − | 0.504048i | \(-0.168156\pi\) | ||||
0.863676 | + | 0.504048i | \(0.168156\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.6754 | 0.377611 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.02633 | −0.0654679 | ||||||||
\(959\) | −32.6491 | −1.05429 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.6491 | 0.730616 | ||||||||
\(962\) | 11.6228 | 0.374733 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 29.4868 | 0.949707 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.6754 | 0.375457 | 0.187728 | − | 0.982221i | \(-0.439887\pi\) | ||||
0.187728 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(968\) | 6.32456 | 0.203279 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −31.4868 | −1.01046 | −0.505230 | − | 0.862985i | \(-0.668592\pi\) | ||||
−0.505230 | + | 0.862985i | \(0.668592\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.94733 | −0.254780 | ||||||||
\(974\) | 3.35089 | 0.107369 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.16228 | 0.0692128 | ||||||||
\(977\) | −21.9473 | −0.702157 | −0.351079 | − | 0.936346i | \(-0.614185\pi\) | ||||
−0.351079 | + | 0.936346i | \(0.614185\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.5132 | −0.367962 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.13594 | −0.259496 | −0.129748 | − | 0.991547i | \(-0.541417\pi\) | ||||
−0.129748 | + | 0.991547i | \(0.541417\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 72.7851 | 2.31795 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.16228 | 0.0369770 | ||||||||
\(989\) | 20.7851 | 0.660926 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.2982 | −0.835391 | −0.417695 | − | 0.908587i | \(-0.637162\pi\) | ||||
−0.417695 | + | 0.908587i | \(0.637162\pi\) | |||||||
\(992\) | 7.32456 | 0.232555 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.3246 | 0.517783 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.4868 | 1.02887 | 0.514434 | − | 0.857530i | \(-0.328002\pi\) | ||||
0.514434 | + | 0.857530i | \(0.328002\pi\) | |||||||
\(998\) | −25.8114 | −0.817045 | ||||||||
\(999\) | 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 | 8550.2.a.bq.1.1 | 2 | ||
3.2 | odd | 2 | 2850.2.a.bg.1.1 | yes | 2 | ||
5.4 | even | 2 | 8550.2.a.ca.1.2 | 2 | |||
15.2 | even | 4 | 2850.2.d.v.799.3 | 4 | |||
15.8 | even | 4 | 2850.2.d.v.799.2 | 4 | |||
15.14 | odd | 2 | 2850.2.a.bf.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bf.1.2 | ✓ | 2 | 15.14 | odd | 2 | ||
2850.2.a.bg.1.1 | yes | 2 | 3.2 | odd | 2 | ||
2850.2.d.v.799.2 | 4 | 15.8 | even | 4 | |||
2850.2.d.v.799.3 | 4 | 15.2 | even | 4 | |||
8550.2.a.bq.1.1 | 2 | 1.1 | even | 1 | trivial | ||
8550.2.a.ca.1.2 | 2 | 5.4 | even | 2 |