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: | \(3\) |
Coefficient field: | 3.3.564.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.51414\) 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 | ||||||||
\(7\) | 0.193252 | 0.0730426 | 0.0365213 | − | 0.999333i | \(-0.488372\pi\) | ||||
0.0365213 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.514137 | −0.155018 | −0.0775091 | − | 0.996992i | \(-0.524697\pi\) | ||||
−0.0775091 | + | 0.996992i | \(0.524697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.12763 | 0.867449 | 0.433725 | − | 0.901046i | \(-0.357199\pi\) | ||||
0.433725 | + | 0.901046i | \(0.357199\pi\) | |||||||
\(14\) | 0.193252 | 0.0516489 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.83502 | 0.687594 | 0.343797 | − | 0.939044i | \(-0.388287\pi\) | ||||
0.343797 | + | 0.939044i | \(0.388287\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.514137 | −0.109614 | ||||||||
\(23\) | −2.32088 | −0.483938 | −0.241969 | − | 0.970284i | \(-0.577793\pi\) | ||||
−0.241969 | + | 0.970284i | \(0.577793\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.12763 | 0.613379 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.193252 | 0.0365213 | ||||||||
\(29\) | 0.164979 | 0.0306358 | 0.0153179 | − | 0.999883i | \(-0.495124\pi\) | ||||
0.0153179 | + | 0.999883i | \(0.495124\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.05655 | −1.62660 | −0.813302 | − | 0.581842i | \(-0.802332\pi\) | ||||
−0.813302 | + | 0.581842i | \(0.802332\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.83502 | 0.486202 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.02827 | 0.497845 | 0.248923 | − | 0.968523i | \(-0.419924\pi\) | ||||
0.248923 | + | 0.968523i | \(0.419924\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.96265 | 1.55591 | 0.777953 | − | 0.628323i | \(-0.216258\pi\) | ||||
0.777953 | + | 0.628323i | \(0.216258\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.51414 | 0.840898 | 0.420449 | − | 0.907316i | \(-0.361873\pi\) | ||||
0.420449 | + | 0.907316i | \(0.361873\pi\) | |||||||
\(44\) | −0.514137 | −0.0775091 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.32088 | −0.342196 | ||||||||
\(47\) | −1.70739 | −0.249048 | −0.124524 | − | 0.992217i | \(-0.539740\pi\) | ||||
−0.124524 | + | 0.992217i | \(0.539740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.96265 | −0.994665 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.12763 | 0.433725 | ||||||||
\(53\) | 2.90064 | 0.398434 | 0.199217 | − | 0.979955i | \(-0.436160\pi\) | ||||
0.199217 | + | 0.979955i | \(0.436160\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.193252 | 0.0258244 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.164979 | 0.0216627 | ||||||||
\(59\) | 13.9572 | 1.81707 | 0.908536 | − | 0.417807i | \(-0.137201\pi\) | ||||
0.908536 | + | 0.417807i | \(0.137201\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.92892 | 0.759120 | 0.379560 | − | 0.925167i | \(-0.376075\pi\) | ||||
0.379560 | + | 0.925167i | \(0.376075\pi\) | |||||||
\(62\) | −9.05655 | −1.15018 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.22153 | 0.515742 | 0.257871 | − | 0.966179i | \(-0.416979\pi\) | ||||
0.257871 | + | 0.966179i | \(0.416979\pi\) | |||||||
\(68\) | 2.83502 | 0.343797 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.16498 | 0.375614 | 0.187807 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187807 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.37743 | −0.980504 | −0.490252 | − | 0.871581i | \(-0.663095\pi\) | ||||
−0.490252 | + | 0.871581i | \(0.663095\pi\) | |||||||
\(74\) | 3.02827 | 0.352030 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −0.0993582 | −0.0113229 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.02827 | 0.678234 | 0.339117 | − | 0.940744i | \(-0.389872\pi\) | ||||
0.339117 | + | 0.940744i | \(0.389872\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.96265 | 1.10019 | ||||||||
\(83\) | 12.8633 | 1.41193 | 0.705965 | − | 0.708247i | \(-0.250514\pi\) | ||||
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.51414 | 0.594605 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.514137 | −0.0548072 | ||||||||
\(89\) | −9.01920 | −0.956033 | −0.478017 | − | 0.878351i | \(-0.658644\pi\) | ||||
−0.478017 | + | 0.878351i | \(0.658644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.604422 | 0.0633607 | ||||||||
\(92\) | −2.32088 | −0.241969 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.70739 | −0.176104 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.89157 | −0.902802 | −0.451401 | − | 0.892321i | \(-0.649076\pi\) | ||||
−0.451401 | + | 0.892321i | \(0.649076\pi\) | |||||||
\(98\) | −6.96265 | −0.703334 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.15591 | −0.214521 | −0.107260 | − | 0.994231i | \(-0.534208\pi\) | ||||
−0.107260 | + | 0.994231i | \(0.534208\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.3209 | 1.01695 | 0.508473 | − | 0.861078i | \(-0.330210\pi\) | ||||
0.508473 | + | 0.861078i | \(0.330210\pi\) | |||||||
\(104\) | 3.12763 | 0.306690 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.90064 | 0.281735 | ||||||||
\(107\) | 5.57068 | 0.538538 | 0.269269 | − | 0.963065i | \(-0.413218\pi\) | ||||
0.269269 | + | 0.963065i | \(0.413218\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.61350 | 0.537675 | 0.268838 | − | 0.963186i | \(-0.413360\pi\) | ||||
0.268838 | + | 0.963186i | \(0.413360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.193252 | 0.0182606 | ||||||||
\(113\) | −6.96265 | −0.654991 | −0.327496 | − | 0.944853i | \(-0.606205\pi\) | ||||
−0.327496 | + | 0.944853i | \(0.606205\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.164979 | 0.0153179 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.9572 | 1.28486 | ||||||||
\(119\) | 0.547875 | 0.0502236 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7357 | −0.975969 | ||||||||
\(122\) | 5.92892 | 0.536779 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −9.05655 | −0.813302 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.6983 | −1.21553 | −0.607765 | − | 0.794117i | \(-0.707934\pi\) | ||||
−0.607765 | + | 0.794117i | \(0.707934\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4768 | 0.915361 | 0.457681 | − | 0.889117i | \(-0.348680\pi\) | ||||
0.457681 | + | 0.889117i | \(0.348680\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.193252 | 0.0167571 | ||||||||
\(134\) | 4.22153 | 0.364684 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.83502 | 0.243101 | ||||||||
\(137\) | −11.6700 | −0.997039 | −0.498520 | − | 0.866878i | \(-0.666123\pi\) | ||||
−0.498520 | + | 0.866878i | \(0.666123\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7411 | 1.08069 | 0.540344 | − | 0.841444i | \(-0.318294\pi\) | ||||
0.540344 | + | 0.841444i | \(0.318294\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.16498 | 0.265599 | ||||||||
\(143\) | −1.60803 | −0.134470 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.37743 | −0.693321 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.02827 | 0.248923 | ||||||||
\(149\) | 9.61350 | 0.787568 | 0.393784 | − | 0.919203i | \(-0.371166\pi\) | ||||
0.393784 | + | 0.919203i | \(0.371166\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.12217 | −0.742352 | −0.371176 | − | 0.928563i | \(-0.621045\pi\) | ||||
−0.371176 | + | 0.928563i | \(0.621045\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0993582 | −0.00800651 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.93438 | 0.393806 | 0.196903 | − | 0.980423i | \(-0.436912\pi\) | ||||
0.196903 | + | 0.980423i | \(0.436912\pi\) | |||||||
\(158\) | 6.02827 | 0.479584 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.448517 | −0.0353481 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.2835 | 0.883795 | 0.441897 | − | 0.897066i | \(-0.354306\pi\) | ||||
0.441897 | + | 0.897066i | \(0.354306\pi\) | |||||||
\(164\) | 9.96265 | 0.777953 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.8633 | 0.998385 | ||||||||
\(167\) | −11.8688 | −0.918432 | −0.459216 | − | 0.888325i | \(-0.651870\pi\) | ||||
−0.459216 | + | 0.888325i | \(0.651870\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.21792 | −0.247532 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.51414 | 0.420449 | ||||||||
\(173\) | −4.27807 | −0.325256 | −0.162628 | − | 0.986687i | \(-0.551997\pi\) | ||||
−0.162628 | + | 0.986687i | \(0.551997\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.514137 | −0.0387545 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.01920 | −0.676018 | ||||||||
\(179\) | 22.3118 | 1.66766 | 0.833832 | − | 0.552019i | \(-0.186142\pi\) | ||||
0.833832 | + | 0.552019i | \(0.186142\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4576 | −0.851636 | −0.425818 | − | 0.904809i | \(-0.640014\pi\) | ||||
−0.425818 | + | 0.904809i | \(0.640014\pi\) | |||||||
\(182\) | 0.604422 | 0.0448028 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.32088 | −0.171098 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.45759 | −0.106589 | ||||||||
\(188\) | −1.70739 | −0.124524 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.4148 | 1.33245 | 0.666223 | − | 0.745752i | \(-0.267910\pi\) | ||||
0.666223 | + | 0.745752i | \(0.267910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.193252 | 0.0139106 | 0.00695531 | − | 0.999976i | \(-0.497786\pi\) | ||||
0.00695531 | + | 0.999976i | \(0.497786\pi\) | |||||||
\(194\) | −8.89157 | −0.638377 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.96265 | −0.497332 | ||||||||
\(197\) | −18.5990 | −1.32512 | −0.662560 | − | 0.749008i | \(-0.730530\pi\) | ||||
−0.662560 | + | 0.749008i | \(0.730530\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.5671 | 1.45796 | 0.728981 | − | 0.684534i | \(-0.239994\pi\) | ||||
0.728981 | + | 0.684534i | \(0.239994\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.15591 | −0.151689 | ||||||||
\(203\) | 0.0318825 | 0.00223771 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.3209 | 0.719090 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.12763 | 0.216862 | ||||||||
\(209\) | −0.514137 | −0.0355636 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.57068 | 0.314659 | 0.157329 | − | 0.987546i | \(-0.449712\pi\) | ||||
0.157329 | + | 0.987546i | \(0.449712\pi\) | |||||||
\(212\) | 2.90064 | 0.199217 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.57068 | 0.380804 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.75020 | −0.118811 | ||||||||
\(218\) | 5.61350 | 0.380194 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.86690 | 0.596453 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.93438 | −0.263466 | −0.131733 | − | 0.991285i | \(-0.542054\pi\) | ||||
−0.131733 | + | 0.991285i | \(0.542054\pi\) | |||||||
\(224\) | 0.193252 | 0.0129122 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.96265 | −0.463149 | ||||||||
\(227\) | −11.4713 | −0.761379 | −0.380689 | − | 0.924703i | \(-0.624313\pi\) | ||||
−0.380689 | + | 0.924703i | \(0.624313\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4768 | 0.824490 | 0.412245 | − | 0.911073i | \(-0.364745\pi\) | ||||
0.412245 | + | 0.911073i | \(0.364745\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.164979 | 0.0108314 | ||||||||
\(233\) | 27.4021 | 1.79517 | 0.897586 | − | 0.440840i | \(-0.145319\pi\) | ||||
0.897586 | + | 0.440840i | \(0.145319\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 13.9572 | 0.908536 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.547875 | 0.0355134 | ||||||||
\(239\) | −14.4057 | −0.931828 | −0.465914 | − | 0.884830i | \(-0.654274\pi\) | ||||
−0.465914 | + | 0.884830i | \(0.654274\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.7886 | −1.40353 | −0.701764 | − | 0.712410i | \(-0.747604\pi\) | ||||
−0.701764 | + | 0.712410i | \(0.747604\pi\) | |||||||
\(242\) | −10.7357 | −0.690115 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.92892 | 0.379560 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.12763 | 0.199006 | ||||||||
\(248\) | −9.05655 | −0.575091 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9627 | 1.38627 | 0.693135 | − | 0.720808i | \(-0.256229\pi\) | ||||
0.693135 | + | 0.720808i | \(0.256229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.19325 | 0.0750191 | ||||||||
\(254\) | −13.6983 | −0.859509 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −0.0656204 | −0.00409329 | −0.00204664 | − | 0.999998i | \(-0.500651\pi\) | ||||
−0.00204664 | + | 0.999998i | \(0.500651\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.585221 | 0.0363639 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.4768 | 0.647258 | ||||||||
\(263\) | 24.8314 | 1.53117 | 0.765585 | − | 0.643334i | \(-0.222450\pi\) | ||||
0.765585 | + | 0.643334i | \(0.222450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.193252 | 0.0118491 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.22153 | 0.257871 | ||||||||
\(269\) | 19.8578 | 1.21075 | 0.605377 | − | 0.795939i | \(-0.293022\pi\) | ||||
0.605377 | + | 0.795939i | \(0.293022\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.891569 | 0.0541590 | 0.0270795 | − | 0.999633i | \(-0.491379\pi\) | ||||
0.0270795 | + | 0.999633i | \(0.491379\pi\) | |||||||
\(272\) | 2.83502 | 0.171898 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −11.6700 | −0.705013 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.76940 | −0.406734 | −0.203367 | − | 0.979103i | \(-0.565188\pi\) | ||||
−0.203367 | + | 0.979103i | \(0.565188\pi\) | |||||||
\(278\) | 12.7411 | 0.764162 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.2553 | 1.02936 | 0.514681 | − | 0.857382i | \(-0.327910\pi\) | ||||
0.514681 | + | 0.857382i | \(0.327910\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.6983 | 1.23039 | 0.615194 | − | 0.788376i | \(-0.289078\pi\) | ||||
0.615194 | + | 0.788376i | \(0.289078\pi\) | |||||||
\(284\) | 3.16498 | 0.187807 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.60803 | −0.0950849 | ||||||||
\(287\) | 1.92531 | 0.113647 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.96265 | −0.527215 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.37743 | −0.490252 | ||||||||
\(293\) | 0.712853 | 0.0416453 | 0.0208227 | − | 0.999783i | \(-0.493371\pi\) | ||||
0.0208227 | + | 0.999783i | \(0.493371\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.02827 | 0.176015 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.61350 | 0.556895 | ||||||||
\(299\) | −7.25887 | −0.419791 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.06562 | 0.0614213 | ||||||||
\(302\) | −9.12217 | −0.524922 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.11856 | 0.292132 | 0.146066 | − | 0.989275i | \(-0.453339\pi\) | ||||
0.146066 | + | 0.989275i | \(0.453339\pi\) | |||||||
\(308\) | −0.0993582 | −0.00566146 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.26434 | 0.185104 | 0.0925518 | − | 0.995708i | \(-0.470498\pi\) | ||||
0.0925518 | + | 0.995708i | \(0.470498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.96265 | 0.167459 | 0.0837295 | − | 0.996489i | \(-0.473317\pi\) | ||||
0.0837295 | + | 0.996489i | \(0.473317\pi\) | |||||||
\(314\) | 4.93438 | 0.278463 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.02827 | 0.339117 | ||||||||
\(317\) | −12.1650 | −0.683253 | −0.341627 | − | 0.939836i | \(-0.610978\pi\) | ||||
−0.341627 | + | 0.939836i | \(0.610978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0848216 | −0.00474910 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.448517 | −0.0249949 | ||||||||
\(323\) | 2.83502 | 0.157745 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.2835 | 0.624937 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.96265 | 0.550096 | ||||||||
\(329\) | −0.329957 | −0.0181911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.67551 | 0.366919 | 0.183460 | − | 0.983027i | \(-0.441270\pi\) | ||||
0.183460 | + | 0.983027i | \(0.441270\pi\) | |||||||
\(332\) | 12.8633 | 0.705965 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.8688 | −0.649430 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.72659 | 0.529841 | 0.264921 | − | 0.964270i | \(-0.414654\pi\) | ||||
0.264921 | + | 0.964270i | \(0.414654\pi\) | |||||||
\(338\) | −3.21792 | −0.175032 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.65631 | 0.252153 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.69832 | −0.145695 | ||||||||
\(344\) | 5.51414 | 0.297302 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.27807 | −0.229991 | ||||||||
\(347\) | 9.08482 | 0.487699 | 0.243849 | − | 0.969813i | \(-0.421590\pi\) | ||||
0.243849 | + | 0.969813i | \(0.421590\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0047 | 1.39200 | 0.695999 | − | 0.718043i | \(-0.254962\pi\) | ||||
0.695999 | + | 0.718043i | \(0.254962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.514137 | −0.0274036 | ||||||||
\(353\) | 27.7321 | 1.47603 | 0.738014 | − | 0.674785i | \(-0.235764\pi\) | ||||
0.738014 | + | 0.674785i | \(0.235764\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.01920 | −0.478017 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.3118 | 1.17922 | ||||||||
\(359\) | −0.746591 | −0.0394036 | −0.0197018 | − | 0.999806i | \(-0.506272\pi\) | ||||
−0.0197018 | + | 0.999806i | \(0.506272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −11.4576 | −0.602198 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.604422 | 0.0316803 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9945 | −0.730509 | −0.365254 | − | 0.930908i | \(-0.619018\pi\) | ||||
−0.365254 | + | 0.930908i | \(0.619018\pi\) | |||||||
\(368\) | −2.32088 | −0.120984 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.560556 | 0.0291026 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.6099 | −1.06714 | −0.533570 | − | 0.845756i | \(-0.679150\pi\) | ||||
−0.533570 | + | 0.845756i | \(0.679150\pi\) | |||||||
\(374\) | −1.45759 | −0.0753701 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.70739 | −0.0880519 | ||||||||
\(377\) | 0.515992 | 0.0265750 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.63164 | 0.0838117 | 0.0419059 | − | 0.999122i | \(-0.486657\pi\) | ||||
0.0419059 | + | 0.999122i | \(0.486657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 18.4148 | 0.942182 | ||||||||
\(383\) | −12.3173 | −0.629383 | −0.314692 | − | 0.949194i | \(-0.601901\pi\) | ||||
−0.314692 | + | 0.949194i | \(0.601901\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.193252 | 0.00983629 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −8.89157 | −0.451401 | ||||||||
\(389\) | 3.61350 | 0.183211 | 0.0916057 | − | 0.995795i | \(-0.470800\pi\) | ||||
0.0916057 | + | 0.995795i | \(0.470800\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.57976 | −0.332753 | ||||||||
\(392\) | −6.96265 | −0.351667 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.5990 | −0.937002 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.88250 | 0.144668 | 0.0723342 | − | 0.997380i | \(-0.476955\pi\) | ||||
0.0723342 | + | 0.997380i | \(0.476955\pi\) | |||||||
\(398\) | 20.5671 | 1.03093 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.9253 | 1.44446 | 0.722230 | − | 0.691652i | \(-0.243117\pi\) | ||||
0.722230 | + | 0.691652i | \(0.243117\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −28.3255 | −1.41100 | ||||||||
\(404\) | −2.15591 | −0.107260 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.0318825 | 0.00158230 | ||||||||
\(407\) | −1.55695 | −0.0771750 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.8578 | 1.08080 | 0.540400 | − | 0.841408i | \(-0.318273\pi\) | ||||
0.540400 | + | 0.841408i | \(0.318273\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.3209 | 0.508473 | ||||||||
\(413\) | 2.69726 | 0.132724 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.12763 | 0.153345 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.514137 | −0.0251473 | ||||||||
\(419\) | −8.38650 | −0.409708 | −0.204854 | − | 0.978793i | \(-0.565672\pi\) | ||||
−0.204854 | + | 0.978793i | \(0.565672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1523 | −0.641004 | −0.320502 | − | 0.947248i | \(-0.603852\pi\) | ||||
−0.320502 | + | 0.947248i | \(0.603852\pi\) | |||||||
\(422\) | 4.57068 | 0.222497 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.90064 | 0.140868 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.14578 | 0.0554481 | ||||||||
\(428\) | 5.57068 | 0.269269 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.1806 | 0.779391 | 0.389695 | − | 0.920944i | \(-0.372580\pi\) | ||||
0.389695 | + | 0.920944i | \(0.372580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9945 | −0.672534 | −0.336267 | − | 0.941767i | \(-0.609165\pi\) | ||||
−0.336267 | + | 0.941767i | \(0.609165\pi\) | |||||||
\(434\) | −1.75020 | −0.0840123 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.61350 | 0.268838 | ||||||||
\(437\) | −2.32088 | −0.111023 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.3401 | −0.588960 | −0.294480 | − | 0.955658i | \(-0.595146\pi\) | ||||
−0.294480 | + | 0.955658i | \(0.595146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.86690 | 0.421756 | ||||||||
\(443\) | −14.5899 | −0.693186 | −0.346593 | − | 0.938016i | \(-0.612662\pi\) | ||||
−0.346593 | + | 0.938016i | \(0.612662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.93438 | −0.186298 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.193252 | 0.00913032 | ||||||||
\(449\) | 3.74659 | 0.176813 | 0.0884063 | − | 0.996084i | \(-0.471823\pi\) | ||||
0.0884063 | + | 0.996084i | \(0.471823\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.12217 | −0.241193 | ||||||||
\(452\) | −6.96265 | −0.327496 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.4713 | −0.538376 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.2745 | −0.854843 | −0.427422 | − | 0.904052i | \(-0.640578\pi\) | ||||
−0.427422 | + | 0.904052i | \(0.640578\pi\) | |||||||
\(458\) | 12.4768 | 0.583002 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.0957 | −0.609930 | −0.304965 | − | 0.952364i | \(-0.598645\pi\) | ||||
−0.304965 | + | 0.952364i | \(0.598645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.0283 | 0.698423 | 0.349212 | − | 0.937044i | \(-0.386449\pi\) | ||||
0.349212 | + | 0.937044i | \(0.386449\pi\) | |||||||
\(464\) | 0.164979 | 0.00765894 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 27.4021 | 1.26938 | ||||||||
\(467\) | −21.7302 | −1.00555 | −0.502777 | − | 0.864416i | \(-0.667688\pi\) | ||||
−0.502777 | + | 0.864416i | \(0.667688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.815820 | 0.0376711 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 13.9572 | 0.642432 | ||||||||
\(473\) | −2.83502 | −0.130354 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0.547875 | 0.0251118 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.4057 | −0.658902 | ||||||||
\(479\) | −0.962653 | −0.0439848 | −0.0219924 | − | 0.999758i | \(-0.507001\pi\) | ||||
−0.0219924 | + | 0.999758i | \(0.507001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.47133 | 0.431855 | ||||||||
\(482\) | −21.7886 | −0.992444 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.7357 | −0.487985 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −42.5561 | −1.92840 | −0.964202 | − | 0.265170i | \(-0.914572\pi\) | ||||
−0.964202 | + | 0.265170i | \(0.914572\pi\) | |||||||
\(488\) | 5.92892 | 0.268389 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7549 | −0.665878 | −0.332939 | − | 0.942948i | \(-0.608040\pi\) | ||||
−0.332939 | + | 0.942948i | \(0.608040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.467718 | 0.0210649 | ||||||||
\(494\) | 3.12763 | 0.140719 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.05655 | −0.406651 | ||||||||
\(497\) | 0.611640 | 0.0274358 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.64538 | −0.342254 | −0.171127 | − | 0.985249i | \(-0.554741\pi\) | ||||
−0.171127 | + | 0.985249i | \(0.554741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.9627 | 0.980241 | ||||||||
\(503\) | 4.51053 | 0.201115 | 0.100557 | − | 0.994931i | \(-0.467937\pi\) | ||||
0.100557 | + | 0.994931i | \(0.467937\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.19325 | 0.0530465 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −13.6983 | −0.607765 | ||||||||
\(509\) | −41.1943 | −1.82591 | −0.912953 | − | 0.408065i | \(-0.866204\pi\) | ||||
−0.912953 | + | 0.408065i | \(0.866204\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.61896 | −0.0716185 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.0656204 | −0.00289439 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.877832 | 0.0386070 | ||||||||
\(518\) | 0.585221 | 0.0257131 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.1595 | 0.445096 | 0.222548 | − | 0.974922i | \(-0.428563\pi\) | ||||
0.222548 | + | 0.974922i | \(0.428563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.6308 | 0.639762 | 0.319881 | − | 0.947458i | \(-0.396357\pi\) | ||||
0.319881 | + | 0.947458i | \(0.396357\pi\) | |||||||
\(524\) | 10.4768 | 0.457681 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.8314 | 1.08270 | ||||||||
\(527\) | −25.6755 | −1.11844 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.6135 | −0.765804 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.193252 | 0.00837856 | ||||||||
\(533\) | 31.1595 | 1.34967 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.22153 | 0.182342 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.8578 | 0.856132 | ||||||||
\(539\) | 3.57976 | 0.154191 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.0511 | −0.561110 | −0.280555 | − | 0.959838i | \(-0.590518\pi\) | ||||
−0.280555 | + | 0.959838i | \(0.590518\pi\) | |||||||
\(542\) | 0.891569 | 0.0382962 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.83502 | 0.121551 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10.0420 | 0.429365 | 0.214683 | − | 0.976684i | \(-0.431128\pi\) | ||||
0.214683 | + | 0.976684i | \(0.431128\pi\) | |||||||
\(548\) | −11.6700 | −0.498520 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.164979 | 0.00702832 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.16498 | 0.0495399 | ||||||||
\(554\) | −6.76940 | −0.287604 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.7411 | 0.540344 | ||||||||
\(557\) | 6.03188 | 0.255579 | 0.127790 | − | 0.991801i | \(-0.459212\pi\) | ||||
0.127790 | + | 0.991801i | \(0.459212\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.2462 | 0.729436 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17.2553 | 0.727869 | ||||||||
\(563\) | 35.2407 | 1.48522 | 0.742610 | − | 0.669724i | \(-0.233588\pi\) | ||||
0.742610 | + | 0.669724i | \(0.233588\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 20.6983 | 0.870015 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.16498 | 0.132800 | ||||||||
\(569\) | 21.9144 | 0.918699 | 0.459349 | − | 0.888256i | \(-0.348083\pi\) | ||||
0.459349 | + | 0.888256i | \(0.348083\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.2407 | −0.888897 | −0.444448 | − | 0.895804i | \(-0.646600\pi\) | ||||
−0.444448 | + | 0.895804i | \(0.646600\pi\) | |||||||
\(572\) | −1.60803 | −0.0672352 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.92531 | 0.0803608 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.9253 | −1.37070 | −0.685349 | − | 0.728215i | \(-0.740350\pi\) | ||||
−0.685349 | + | 0.728215i | \(0.740350\pi\) | |||||||
\(578\) | −8.96265 | −0.372797 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.48586 | 0.103131 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.49133 | −0.0617645 | ||||||||
\(584\) | −8.37743 | −0.346661 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.712853 | 0.0294477 | ||||||||
\(587\) | −21.5798 | −0.890692 | −0.445346 | − | 0.895359i | \(-0.646919\pi\) | ||||
−0.445346 | + | 0.895359i | \(0.646919\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.05655 | −0.373169 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.02827 | 0.124461 | ||||||||
\(593\) | 1.98907 | 0.0816814 | 0.0408407 | − | 0.999166i | \(-0.486996\pi\) | ||||
0.0408407 | + | 0.999166i | \(0.486996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.61350 | 0.393784 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.25887 | −0.296837 | ||||||||
\(599\) | 33.7321 | 1.37825 | 0.689127 | − | 0.724640i | \(-0.257994\pi\) | ||||
0.689127 | + | 0.724640i | \(0.257994\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.7211 | 1.04919 | 0.524593 | − | 0.851353i | \(-0.324217\pi\) | ||||
0.524593 | + | 0.851353i | \(0.324217\pi\) | |||||||
\(602\) | 1.06562 | 0.0434314 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.12217 | −0.371176 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.8488 | −1.53623 | −0.768117 | − | 0.640310i | \(-0.778806\pi\) | ||||
−0.768117 | + | 0.640310i | \(0.778806\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.34009 | −0.216037 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.4713 | −0.624881 | −0.312440 | − | 0.949937i | \(-0.601146\pi\) | ||||
−0.312440 | + | 0.949937i | \(0.601146\pi\) | |||||||
\(614\) | 5.11856 | 0.206568 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0993582 | −0.00400326 | ||||||||
\(617\) | −10.3118 | −0.415138 | −0.207569 | − | 0.978220i | \(-0.566555\pi\) | ||||
−0.207569 | + | 0.978220i | \(0.566555\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6099 | 0.506834 | 0.253417 | − | 0.967357i | \(-0.418446\pi\) | ||||
0.253417 | + | 0.967357i | \(0.418446\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.26434 | 0.130888 | ||||||||
\(623\) | −1.74298 | −0.0698311 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.96265 | 0.118411 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.93438 | 0.196903 | ||||||||
\(629\) | 8.58522 | 0.342315 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.34009 | −0.371823 | −0.185911 | − | 0.982566i | \(-0.559524\pi\) | ||||
−0.185911 | + | 0.982566i | \(0.559524\pi\) | |||||||
\(632\) | 6.02827 | 0.239792 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −12.1650 | −0.483133 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −21.7766 | −0.862821 | ||||||||
\(638\) | −0.0848216 | −0.00335812 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.3310 | 1.11901 | 0.559504 | − | 0.828828i | \(-0.310992\pi\) | ||||
0.559504 | + | 0.828828i | \(0.310992\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.0848 | −0.989249 | −0.494624 | − | 0.869107i | \(-0.664694\pi\) | ||||
−0.494624 | + | 0.869107i | \(0.664694\pi\) | |||||||
\(644\) | −0.448517 | −0.0176740 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.83502 | 0.111542 | ||||||||
\(647\) | −19.4623 | −0.765140 | −0.382570 | − | 0.923926i | \(-0.624961\pi\) | ||||
−0.382570 | + | 0.923926i | \(0.624961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.17591 | −0.281679 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.2835 | 0.441897 | ||||||||
\(653\) | −12.5671 | −0.491788 | −0.245894 | − | 0.969297i | \(-0.579081\pi\) | ||||
−0.245894 | + | 0.969297i | \(0.579081\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.96265 | 0.388976 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.329957 | −0.0128631 | ||||||||
\(659\) | −8.22338 | −0.320337 | −0.160169 | − | 0.987090i | \(-0.551204\pi\) | ||||
−0.160169 | + | 0.987090i | \(0.551204\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 26.2371 | 1.02051 | 0.510253 | − | 0.860024i | \(-0.329552\pi\) | ||||
0.510253 | + | 0.860024i | \(0.329552\pi\) | |||||||
\(662\) | 6.67551 | 0.259451 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.8633 | 0.499193 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.382896 | −0.0148258 | ||||||||
\(668\) | −11.8688 | −0.459216 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.04827 | −0.117677 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.29622 | −0.281249 | −0.140624 | − | 0.990063i | \(-0.544911\pi\) | ||||
−0.140624 | + | 0.990063i | \(0.544911\pi\) | |||||||
\(674\) | 9.72659 | 0.374654 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.21792 | −0.123766 | ||||||||
\(677\) | −29.2234 | −1.12315 | −0.561573 | − | 0.827427i | \(-0.689804\pi\) | ||||
−0.561573 | + | 0.827427i | \(0.689804\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.71832 | −0.0659430 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.65631 | 0.178299 | ||||||||
\(683\) | −11.9006 | −0.455365 | −0.227683 | − | 0.973735i | \(-0.573115\pi\) | ||||
−0.227683 | + | 0.973735i | \(0.573115\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.69832 | −0.103022 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.51414 | 0.210224 | ||||||||
\(689\) | 9.07214 | 0.345621 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0137372 | 0.000522589 0 | 0.000261294 | − | 1.00000i | \(-0.499917\pi\) | ||||
0.000261294 | 1.00000i | \(0.499917\pi\) | ||||||||
\(692\) | −4.27807 | −0.162628 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.08482 | 0.344855 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 28.2443 | 1.06983 | ||||||||
\(698\) | 26.0047 | 0.984291 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.266192 | 0.0100539 | 0.00502697 | − | 0.999987i | \(-0.498400\pi\) | ||||
0.00502697 | + | 0.999987i | \(0.498400\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.02827 | 0.114214 | ||||||||
\(704\) | −0.514137 | −0.0193773 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.7321 | 1.04371 | ||||||||
\(707\) | −0.416634 | −0.0156691 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.50506 | −0.356970 | −0.178485 | − | 0.983943i | \(-0.557120\pi\) | ||||
−0.178485 | + | 0.983943i | \(0.557120\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.01920 | −0.338009 | ||||||||
\(713\) | 21.0192 | 0.787175 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 22.3118 | 0.833832 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.746591 | −0.0278625 | ||||||||
\(719\) | 10.4895 | 0.391191 | 0.195596 | − | 0.980685i | \(-0.437336\pi\) | ||||
0.195596 | + | 0.980685i | \(0.437336\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.99454 | 0.0742804 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.4576 | −0.425818 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 36.3502 | 1.34815 | 0.674077 | − | 0.738661i | \(-0.264541\pi\) | ||||
0.674077 | + | 0.738661i | \(0.264541\pi\) | |||||||
\(728\) | 0.604422 | 0.0224014 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.6327 | 0.578196 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0337 | −0.813835 | −0.406917 | − | 0.913465i | \(-0.633396\pi\) | ||||
−0.406917 | + | 0.913465i | \(0.633396\pi\) | |||||||
\(734\) | −13.9945 | −0.516548 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.32088 | −0.0855489 | ||||||||
\(737\) | −2.17044 | −0.0799493 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.0848 | 0.628475 | 0.314238 | − | 0.949344i | \(-0.398251\pi\) | ||||
0.314238 | + | 0.949344i | \(0.398251\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.560556 | 0.0205787 | ||||||||
\(743\) | 26.7549 | 0.981541 | 0.490770 | − | 0.871289i | \(-0.336715\pi\) | ||||
0.490770 | + | 0.871289i | \(0.336715\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −20.6099 | −0.754582 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.45759 | −0.0532947 | ||||||||
\(749\) | 1.07655 | 0.0393362 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.7002 | −1.15676 | −0.578378 | − | 0.815769i | \(-0.696314\pi\) | ||||
−0.578378 | + | 0.815769i | \(0.696314\pi\) | |||||||
\(752\) | −1.70739 | −0.0622621 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.515992 | 0.0187913 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.1933 | −1.27912 | −0.639560 | − | 0.768741i | \(-0.720884\pi\) | ||||
−0.639560 | + | 0.768741i | \(0.720884\pi\) | |||||||
\(758\) | 1.63164 | 0.0592638 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.9764 | −0.941643 | −0.470822 | − | 0.882228i | \(-0.656042\pi\) | ||||
−0.470822 | + | 0.882228i | \(0.656042\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.08482 | 0.0392732 | ||||||||
\(764\) | 18.4148 | 0.666223 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.3173 | −0.445041 | ||||||||
\(767\) | 43.6530 | 1.57622 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.6146 | −1.60884 | −0.804421 | − | 0.594060i | \(-0.797524\pi\) | ||||
−0.804421 | + | 0.594060i | \(0.797524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.193252 | 0.00695531 | ||||||||
\(773\) | −51.5844 | −1.85536 | −0.927681 | − | 0.373373i | \(-0.878201\pi\) | ||||
−0.927681 | + | 0.373373i | \(0.878201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.89157 | −0.319189 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.61350 | 0.129550 | ||||||||
\(779\) | 9.96265 | 0.356949 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.62723 | −0.0582270 | ||||||||
\(782\) | −6.57976 | −0.235292 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.96265 | −0.248666 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.8916 | 0.566473 | 0.283237 | − | 0.959050i | \(-0.408592\pi\) | ||||
0.283237 | + | 0.959050i | \(0.408592\pi\) | |||||||
\(788\) | −18.5990 | −0.662560 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.34555 | −0.0478422 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.5435 | 0.658498 | ||||||||
\(794\) | 2.88250 | 0.102296 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.5671 | 0.728981 | ||||||||
\(797\) | 43.6146 | 1.54491 | 0.772453 | − | 0.635072i | \(-0.219029\pi\) | ||||
0.772453 | + | 0.635072i | \(0.219029\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.84049 | −0.171244 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.9253 | 1.02139 | ||||||||
\(803\) | 4.30715 | 0.151996 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.3255 | −0.997725 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.15591 | −0.0758445 | ||||||||
\(809\) | 21.4659 | 0.754700 | 0.377350 | − | 0.926071i | \(-0.376835\pi\) | ||||
0.377350 | + | 0.926071i | \(0.376835\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.84409 | −0.170099 | −0.0850496 | − | 0.996377i | \(-0.527105\pi\) | ||||
−0.0850496 | + | 0.996377i | \(0.527105\pi\) | |||||||
\(812\) | 0.0318825 | 0.00111886 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.55695 | −0.0545710 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.51414 | 0.192915 | ||||||||
\(818\) | 21.8578 | 0.764241 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.65631 | 0.267207 | 0.133603 | − | 0.991035i | \(-0.457345\pi\) | ||||
0.133603 | + | 0.991035i | \(0.457345\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 10.3209 | 0.359545 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.69726 | 0.0938497 | ||||||||
\(827\) | 13.7875 | 0.479440 | 0.239720 | − | 0.970842i | \(-0.422944\pi\) | ||||
0.239720 | + | 0.970842i | \(0.422944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.0529 | 1.21744 | 0.608719 | − | 0.793386i | \(-0.291684\pi\) | ||||
0.608719 | + | 0.793386i | \(0.291684\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.12763 | 0.108431 | ||||||||
\(833\) | −19.7393 | −0.683925 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.514137 | −0.0177818 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.38650 | −0.289707 | ||||||||
\(839\) | −43.6464 | −1.50684 | −0.753421 | − | 0.657538i | \(-0.771598\pi\) | ||||
−0.753421 | + | 0.657538i | \(0.771598\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9728 | −0.999061 | ||||||||
\(842\) | −13.1523 | −0.453258 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.57068 | 0.157329 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.07469 | −0.0712873 | ||||||||
\(848\) | 2.90064 | 0.0996084 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.02827 | −0.240926 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.4431 | −1.52170 | −0.760851 | − | 0.648927i | \(-0.775218\pi\) | ||||
−0.760851 | + | 0.648927i | \(0.775218\pi\) | |||||||
\(854\) | 1.14578 | 0.0392077 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.57068 | 0.190402 | ||||||||
\(857\) | −40.5935 | −1.38665 | −0.693324 | − | 0.720626i | \(-0.743854\pi\) | ||||
−0.693324 | + | 0.720626i | \(0.743854\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.58522 | −0.224685 | −0.112342 | − | 0.993670i | \(-0.535835\pi\) | ||||
−0.112342 | + | 0.993670i | \(0.535835\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.1806 | 0.551112 | ||||||||
\(863\) | 7.19792 | 0.245020 | 0.122510 | − | 0.992467i | \(-0.460906\pi\) | ||||
0.122510 | + | 0.992467i | \(0.460906\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.9945 | −0.475554 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.75020 | −0.0594057 | ||||||||
\(869\) | −3.09936 | −0.105139 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.2034 | 0.447379 | ||||||||
\(872\) | 5.61350 | 0.190097 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.32088 | −0.0785051 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.6236 | −1.23669 | −0.618346 | − | 0.785906i | \(-0.712197\pi\) | ||||
−0.618346 | + | 0.785906i | \(0.712197\pi\) | |||||||
\(878\) | −12.3401 | −0.416458 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.80128 | 0.195450 | 0.0977251 | − | 0.995213i | \(-0.468843\pi\) | ||||
0.0977251 | + | 0.995213i | \(0.468843\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.84409 | 0.196669 | 0.0983347 | − | 0.995153i | \(-0.468648\pi\) | ||||
0.0983347 | + | 0.995153i | \(0.468648\pi\) | |||||||
\(884\) | 8.86690 | 0.298226 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.5899 | −0.490157 | ||||||||
\(887\) | 7.68819 | 0.258144 | 0.129072 | − | 0.991635i | \(-0.458800\pi\) | ||||
0.129072 | + | 0.991635i | \(0.458800\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.64723 | −0.0887853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.93438 | −0.131733 | ||||||||
\(893\) | −1.70739 | −0.0571356 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.193252 | 0.00645611 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.74659 | 0.125025 | ||||||||
\(899\) | −1.49414 | −0.0498322 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.22338 | 0.273961 | ||||||||
\(902\) | −5.12217 | −0.170550 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.96265 | −0.231574 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.8880 | −0.726778 | −0.363389 | − | 0.931638i | \(-0.618380\pi\) | ||||
−0.363389 | + | 0.931638i | \(0.618380\pi\) | |||||||
\(908\) | −11.4713 | −0.380689 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.4249 | 0.875496 | 0.437748 | − | 0.899098i | \(-0.355776\pi\) | ||||
0.437748 | + | 0.899098i | \(0.355776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.61350 | −0.218875 | ||||||||
\(914\) | −18.2745 | −0.604466 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.4768 | 0.412245 | ||||||||
\(917\) | 2.02467 | 0.0668603 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.5232 | 0.413103 | 0.206551 | − | 0.978436i | \(-0.433776\pi\) | ||||
0.206551 | + | 0.978436i | \(0.433776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −13.0957 | −0.431286 | ||||||||
\(923\) | 9.89889 | 0.325826 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.0283 | 0.493860 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.164979 | 0.00541569 | ||||||||
\(929\) | −49.9253 | −1.63800 | −0.818998 | − | 0.573796i | \(-0.805470\pi\) | ||||
−0.818998 | + | 0.573796i | \(0.805470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.96265 | −0.228192 | ||||||||
\(932\) | 27.4021 | 0.897586 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.7302 | −0.711034 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40.7658 | −1.33176 | −0.665880 | − | 0.746059i | \(-0.731944\pi\) | ||||
−0.665880 | + | 0.746059i | \(0.731944\pi\) | |||||||
\(938\) | 0.815820 | 0.0266375 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13.2125 | 0.430714 | 0.215357 | − | 0.976535i | \(-0.430909\pi\) | ||||
0.215357 | + | 0.976535i | \(0.430909\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −23.1222 | −0.752961 | ||||||||
\(944\) | 13.9572 | 0.454268 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.83502 | −0.0921745 | ||||||||
\(947\) | −12.4996 | −0.406182 | −0.203091 | − | 0.979160i | \(-0.565099\pi\) | ||||
−0.203091 | + | 0.979160i | \(0.565099\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −26.2015 | −0.850538 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.547875 | 0.0177567 | ||||||||
\(953\) | −19.8405 | −0.642696 | −0.321348 | − | 0.946961i | \(-0.604136\pi\) | ||||
−0.321348 | + | 0.946961i | \(0.604136\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.4057 | −0.465914 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.962653 | −0.0311019 | ||||||||
\(959\) | −2.25526 | −0.0728263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 51.0211 | 1.64584 | ||||||||
\(962\) | 9.47133 | 0.305368 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.7886 | −0.701764 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −21.9709 | −0.706537 | −0.353269 | − | 0.935522i | \(-0.614930\pi\) | ||||
−0.353269 | + | 0.935522i | \(0.614930\pi\) | |||||||
\(968\) | −10.7357 | −0.345057 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3546 | 0.460662 | 0.230331 | − | 0.973112i | \(-0.426019\pi\) | ||||
0.230331 | + | 0.973112i | \(0.426019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.46225 | 0.0789362 | ||||||||
\(974\) | −42.5561 | −1.36359 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.92892 | 0.189780 | ||||||||
\(977\) | 51.4340 | 1.64552 | 0.822759 | − | 0.568390i | \(-0.192433\pi\) | ||||
0.822759 | + | 0.568390i | \(0.192433\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.63710 | 0.148202 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −14.7549 | −0.470847 | ||||||||
\(983\) | 14.8350 | 0.473164 | 0.236582 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236582 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.467718 | 0.0148952 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.12763 | 0.0995032 | ||||||||
\(989\) | −12.7977 | −0.406942 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.59349 | 0.304747 | 0.152374 | − | 0.988323i | \(-0.451308\pi\) | ||||
0.152374 | + | 0.988323i | \(0.451308\pi\) | |||||||
\(992\) | −9.05655 | −0.287546 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.611640 | 0.0194000 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.7694 | −0.784455 | −0.392227 | − | 0.919868i | \(-0.628295\pi\) | ||||
−0.392227 | + | 0.919868i | \(0.628295\pi\) | |||||||
\(998\) | −7.64538 | −0.242010 | ||||||||
\(999\) | 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.cs.1.2 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.cg.1.2 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cd.1.2 | ✓ | 3 | ||
15.14 | odd | 2 | 8550.2.a.cn.1.2 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8550.2.a.cd.1.2 | ✓ | 3 | 5.4 | even | 2 | ||
8550.2.a.cg.1.2 | yes | 3 | 3.2 | odd | 2 | ||
8550.2.a.cn.1.2 | yes | 3 | 15.14 | odd | 2 | ||
8550.2.a.cs.1.2 | yes | 3 | 1.1 | even | 1 | trivial |