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 | 1.1 | ||
Root | \(-2.08613\) 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 | ||||||||
\(7\) | −2.43807 | −0.921504 | −0.460752 | − | 0.887529i | \(-0.652420\pi\) | ||||
−0.460752 | + | 0.887529i | \(0.652420\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.08613 | 1.23201 | 0.616007 | − | 0.787740i | \(-0.288749\pi\) | ||||
0.616007 | + | 0.787740i | \(0.288749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.79001 | 1.05116 | 0.525580 | − | 0.850744i | \(-0.323848\pi\) | ||||
0.525580 | + | 0.850744i | \(0.323848\pi\) | |||||||
\(14\) | −2.43807 | −0.651601 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.73419 | −0.905674 | −0.452837 | − | 0.891593i | \(-0.649588\pi\) | ||||
−0.452837 | + | 0.891593i | \(0.649588\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.08613 | 0.871166 | ||||||||
\(23\) | −0.351939 | −0.0733844 | −0.0366922 | − | 0.999327i | \(-0.511682\pi\) | ||||
−0.0366922 | + | 0.999327i | \(0.511682\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.79001 | 0.743282 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.43807 | −0.460752 | ||||||||
\(29\) | 6.73419 | 1.25051 | 0.625254 | − | 0.780421i | \(-0.284995\pi\) | ||||
0.625254 | + | 0.780421i | \(0.284995\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.34452 | 1.67833 | 0.839163 | − | 0.543880i | \(-0.183045\pi\) | ||||
0.839163 | + | 0.543880i | \(0.183045\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.73419 | −0.640408 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.17226 | −1.01471 | −0.507357 | − | 0.861736i | \(-0.669377\pi\) | ||||
−0.507357 | + | 0.861736i | \(0.669377\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.05582 | 0.633412 | 0.316706 | − | 0.948524i | \(-0.397423\pi\) | ||||
0.316706 | + | 0.948524i | \(0.397423\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.913870 | 0.139364 | 0.0696819 | − | 0.997569i | \(-0.477802\pi\) | ||||
0.0696819 | + | 0.997569i | \(0.477802\pi\) | |||||||
\(44\) | 4.08613 | 0.616007 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.351939 | −0.0518906 | ||||||||
\(47\) | 5.52420 | 0.805787 | 0.402894 | − | 0.915247i | \(-0.368004\pi\) | ||||
0.402894 | + | 0.915247i | \(0.368004\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.05582 | −0.150831 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.79001 | 0.525580 | ||||||||
\(53\) | −6.96227 | −0.956341 | −0.478171 | − | 0.878267i | \(-0.658700\pi\) | ||||
−0.478171 | + | 0.878267i | \(0.658700\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.43807 | −0.325801 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.73419 | 0.884243 | ||||||||
\(59\) | −14.3068 | −1.86259 | −0.931293 | − | 0.364272i | \(-0.881318\pi\) | ||||
−0.931293 | + | 0.364272i | \(0.881318\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.1345 | −1.68170 | −0.840852 | − | 0.541265i | \(-0.817946\pi\) | ||||
−0.840852 | + | 0.541265i | \(0.817946\pi\) | |||||||
\(62\) | 9.34452 | 1.18676 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.61033 | −0.929750 | −0.464875 | − | 0.885376i | \(-0.653901\pi\) | ||||
−0.464875 | + | 0.885376i | \(0.653901\pi\) | |||||||
\(68\) | −3.73419 | −0.452837 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.73419 | 1.15524 | 0.577618 | − | 0.816307i | \(-0.303982\pi\) | ||||
0.577618 | + | 0.816307i | \(0.303982\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.9926 | 1.40363 | 0.701813 | − | 0.712361i | \(-0.252374\pi\) | ||||
0.701813 | + | 0.712361i | \(0.252374\pi\) | |||||||
\(74\) | −6.17226 | −0.717511 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −9.96227 | −1.13531 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.17226 | −0.356907 | −0.178454 | − | 0.983948i | \(-0.557109\pi\) | ||||
−0.178454 | + | 0.983948i | \(0.557109\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.05582 | 0.447890 | ||||||||
\(83\) | −2.90645 | −0.319024 | −0.159512 | − | 0.987196i | \(-0.550992\pi\) | ||||
−0.159512 | + | 0.987196i | \(0.550992\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.913870 | 0.0985451 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.08613 | 0.435583 | ||||||||
\(89\) | 15.2887 | 1.62060 | 0.810300 | − | 0.586016i | \(-0.199304\pi\) | ||||
0.810300 | + | 0.586016i | \(0.199304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.24030 | −0.968647 | ||||||||
\(92\) | −0.351939 | −0.0366922 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.52420 | 0.569778 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 16.0787 | 1.63255 | 0.816273 | − | 0.577666i | \(-0.196037\pi\) | ||||
0.816273 | + | 0.577666i | \(0.196037\pi\) | |||||||
\(98\) | −1.05582 | −0.106654 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.38225 | 0.635058 | 0.317529 | − | 0.948249i | \(-0.397147\pi\) | ||||
0.317529 | + | 0.948249i | \(0.397147\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.35194 | 0.822941 | 0.411471 | − | 0.911423i | \(-0.365015\pi\) | ||||
0.411471 | + | 0.911423i | \(0.365015\pi\) | |||||||
\(104\) | 3.79001 | 0.371641 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.96227 | −0.676235 | ||||||||
\(107\) | −17.4307 | −1.68508 | −0.842542 | − | 0.538630i | \(-0.818942\pi\) | ||||
−0.842542 | + | 0.538630i | \(0.818942\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.8761 | 1.04175 | 0.520873 | − | 0.853634i | \(-0.325607\pi\) | ||||
0.520873 | + | 0.853634i | \(0.325607\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.43807 | −0.230376 | ||||||||
\(113\) | −1.05582 | −0.0993230 | −0.0496615 | − | 0.998766i | \(-0.515814\pi\) | ||||
−0.0496615 | + | 0.998766i | \(0.515814\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.73419 | 0.625254 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.3068 | −1.31705 | ||||||||
\(119\) | 9.10422 | 0.834582 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.69646 | 0.517860 | ||||||||
\(122\) | −13.1345 | −1.18914 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.34452 | 0.839163 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.64064 | 0.766733 | 0.383367 | − | 0.923596i | \(-0.374765\pi\) | ||||
0.383367 | + | 0.923596i | \(0.374765\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0303126 | −0.00264842 | −0.00132421 | − | 0.999999i | \(-0.500422\pi\) | ||||
−0.00132421 | + | 0.999999i | \(0.500422\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.43807 | −0.211407 | ||||||||
\(134\) | −7.61033 | −0.657432 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.73419 | −0.320204 | ||||||||
\(137\) | 1.46838 | 0.125452 | 0.0627262 | − | 0.998031i | \(-0.480021\pi\) | ||||
0.0627262 | + | 0.998031i | \(0.480021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.6661 | 1.58324 | 0.791621 | − | 0.611012i | \(-0.209237\pi\) | ||||
0.791621 | + | 0.611012i | \(0.209237\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.73419 | 0.816875 | ||||||||
\(143\) | 15.4865 | 1.29504 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 11.9926 | 0.992513 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.17226 | −0.507357 | ||||||||
\(149\) | 14.8761 | 1.21870 | 0.609350 | − | 0.792901i | \(-0.291430\pi\) | ||||
0.609350 | + | 0.792901i | \(0.291430\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5726 | 1.02314 | 0.511572 | − | 0.859241i | \(-0.329063\pi\) | ||||
0.511572 | + | 0.859241i | \(0.329063\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −9.96227 | −0.802783 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.22808 | 0.656672 | 0.328336 | − | 0.944561i | \(-0.393512\pi\) | ||||
0.328336 | + | 0.944561i | \(0.393512\pi\) | |||||||
\(158\) | −3.17226 | −0.252371 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.858052 | 0.0676240 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.40776 | 0.266916 | 0.133458 | − | 0.991054i | \(-0.457392\pi\) | ||||
0.133458 | + | 0.991054i | \(0.457392\pi\) | |||||||
\(164\) | 4.05582 | 0.316706 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.90645 | −0.225584 | ||||||||
\(167\) | −18.4562 | −1.42818 | −0.714090 | − | 0.700054i | \(-0.753159\pi\) | ||||
−0.714090 | + | 0.700054i | \(0.753159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.36417 | 0.104936 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.913870 | 0.0696819 | ||||||||
\(173\) | 25.9549 | 1.97331 | 0.986655 | − | 0.162823i | \(-0.0520598\pi\) | ||||
0.986655 | + | 0.162823i | \(0.0520598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.08613 | 0.308004 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.2887 | 1.14594 | ||||||||
\(179\) | 5.23550 | 0.391319 | 0.195660 | − | 0.980672i | \(-0.437315\pi\) | ||||
0.195660 | + | 0.980672i | \(0.437315\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.2584 | −1.87744 | −0.938721 | − | 0.344679i | \(-0.887988\pi\) | ||||
−0.938721 | + | 0.344679i | \(0.887988\pi\) | |||||||
\(182\) | −9.24030 | −0.684937 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.351939 | −0.0259453 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.2584 | −1.11580 | ||||||||
\(188\) | 5.52420 | 0.402894 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.95160 | 0.285928 | 0.142964 | − | 0.989728i | \(-0.454337\pi\) | ||||
0.142964 | + | 0.989728i | \(0.454337\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.43807 | −0.175496 | −0.0877480 | − | 0.996143i | \(-0.527967\pi\) | ||||
−0.0877480 | + | 0.996143i | \(0.527967\pi\) | |||||||
\(194\) | 16.0787 | 1.15438 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.05582 | −0.0754155 | ||||||||
\(197\) | 13.6029 | 0.969167 | 0.484584 | − | 0.874745i | \(-0.338971\pi\) | ||||
0.484584 | + | 0.874745i | \(0.338971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.81551 | 0.341363 | 0.170681 | − | 0.985326i | \(-0.445403\pi\) | ||||
0.170681 | + | 0.985326i | \(0.445403\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.38225 | 0.449054 | ||||||||
\(203\) | −16.4184 | −1.15235 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.35194 | 0.581907 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.79001 | 0.262790 | ||||||||
\(209\) | 4.08613 | 0.282644 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.4307 | −1.26882 | −0.634409 | − | 0.772997i | \(-0.718757\pi\) | ||||
−0.634409 | + | 0.772997i | \(0.718757\pi\) | |||||||
\(212\) | −6.96227 | −0.478171 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −17.4307 | −1.19153 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.7826 | −1.54658 | ||||||||
\(218\) | 10.8761 | 0.736625 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −14.1526 | −0.952008 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.22808 | −0.484028 | −0.242014 | − | 0.970273i | \(-0.577808\pi\) | ||||
−0.242014 | + | 0.970273i | \(0.577808\pi\) | |||||||
\(224\) | −2.43807 | −0.162900 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.05582 | −0.0702319 | ||||||||
\(227\) | 21.3929 | 1.41990 | 0.709949 | − | 0.704253i | \(-0.248718\pi\) | ||||
0.709949 | + | 0.704253i | \(0.248718\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.96969 | 0.130161 | 0.0650803 | − | 0.997880i | \(-0.479270\pi\) | ||||
0.0650803 | + | 0.997880i | \(0.479270\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.73419 | 0.442121 | ||||||||
\(233\) | 5.08132 | 0.332889 | 0.166444 | − | 0.986051i | \(-0.446771\pi\) | ||||
0.166444 | + | 0.986051i | \(0.446771\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14.3068 | −0.931293 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.10422 | 0.590139 | ||||||||
\(239\) | 15.1648 | 0.980932 | 0.490466 | − | 0.871460i | \(-0.336827\pi\) | ||||
0.490466 | + | 0.871460i | \(0.336827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.79482 | 0.373277 | 0.186638 | − | 0.982429i | \(-0.440241\pi\) | ||||
0.186638 | + | 0.982429i | \(0.440241\pi\) | |||||||
\(242\) | 5.69646 | 0.366182 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.1345 | −0.840852 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.79001 | 0.241152 | ||||||||
\(248\) | 9.34452 | 0.593378 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 16.0558 | 1.01343 | 0.506717 | − | 0.862112i | \(-0.330859\pi\) | ||||
0.506717 | + | 0.862112i | \(0.330859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.43807 | −0.0904106 | ||||||||
\(254\) | 8.64064 | 0.542162 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.22808 | 0.201362 | 0.100681 | − | 0.994919i | \(-0.467898\pi\) | ||||
0.100681 | + | 0.994919i | \(0.467898\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 15.0484 | 0.935062 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.0303126 | −0.00187272 | ||||||||
\(263\) | 25.5120 | 1.57314 | 0.786568 | − | 0.617504i | \(-0.211856\pi\) | ||||
0.786568 | + | 0.617504i | \(0.211856\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.43807 | −0.149488 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.61033 | −0.464875 | ||||||||
\(269\) | −18.2691 | −1.11388 | −0.556942 | − | 0.830551i | \(-0.688025\pi\) | ||||
−0.556942 | + | 0.830551i | \(0.688025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0787 | −1.46268 | −0.731339 | − | 0.682014i | \(-0.761104\pi\) | ||||
−0.731339 | + | 0.682014i | \(0.761104\pi\) | |||||||
\(272\) | −3.73419 | −0.226419 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.46838 | 0.0887082 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.49389 | −0.209927 | −0.104964 | − | 0.994476i | \(-0.533473\pi\) | ||||
−0.104964 | + | 0.994476i | \(0.533473\pi\) | |||||||
\(278\) | 18.6661 | 1.11952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.5800 | 1.10839 | 0.554195 | − | 0.832387i | \(-0.313026\pi\) | ||||
0.554195 | + | 0.832387i | \(0.313026\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.64064 | −0.0975261 | −0.0487630 | − | 0.998810i | \(-0.515528\pi\) | ||||
−0.0487630 | + | 0.998810i | \(0.515528\pi\) | |||||||
\(284\) | 9.73419 | 0.577618 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.4865 | 0.915734 | ||||||||
\(287\) | −9.88836 | −0.583692 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.05582 | −0.179754 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 11.9926 | 0.701813 | ||||||||
\(293\) | 15.8384 | 0.925290 | 0.462645 | − | 0.886544i | \(-0.346901\pi\) | ||||
0.462645 | + | 0.886544i | \(0.346901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.17226 | −0.358755 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 14.8761 | 0.861752 | ||||||||
\(299\) | −1.33385 | −0.0771387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.22808 | −0.128424 | ||||||||
\(302\) | 12.5726 | 0.723472 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.32643 | −0.532288 | −0.266144 | − | 0.963933i | \(-0.585750\pi\) | ||||
−0.266144 | + | 0.963933i | \(0.585750\pi\) | |||||||
\(308\) | −9.96227 | −0.567653 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.6965 | 1.11688 | 0.558442 | − | 0.829544i | \(-0.311399\pi\) | ||||
0.558442 | + | 0.829544i | \(0.311399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.94418 | −0.166415 | −0.0832075 | − | 0.996532i | \(-0.526516\pi\) | ||||
−0.0832075 | + | 0.996532i | \(0.526516\pi\) | |||||||
\(314\) | 8.22808 | 0.464337 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.17226 | −0.178454 | ||||||||
\(317\) | −18.7342 | −1.05222 | −0.526108 | − | 0.850417i | \(-0.676349\pi\) | ||||
−0.526108 | + | 0.850417i | \(0.676349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.5168 | 1.54064 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.858052 | 0.0478174 | ||||||||
\(323\) | −3.73419 | −0.207776 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.40776 | 0.188738 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.05582 | 0.223945 | ||||||||
\(329\) | −13.4684 | −0.742536 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8942 | 0.873626 | 0.436813 | − | 0.899552i | \(-0.356107\pi\) | ||||
0.436813 | + | 0.899552i | \(0.356107\pi\) | |||||||
\(332\) | −2.90645 | −0.159512 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.4562 | −1.00988 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.8129 | −1.18822 | −0.594112 | − | 0.804382i | \(-0.702497\pi\) | ||||
−0.594112 | + | 0.804382i | \(0.702497\pi\) | |||||||
\(338\) | 1.36417 | 0.0742008 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 38.1829 | 2.06772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.6406 | 1.06050 | ||||||||
\(344\) | 0.913870 | 0.0492726 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.9549 | 1.39534 | ||||||||
\(347\) | −18.5168 | −0.994033 | −0.497016 | − | 0.867741i | \(-0.665571\pi\) | ||||
−0.497016 | + | 0.867741i | \(0.665571\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.7678 | −1.91460 | −0.957302 | − | 0.289090i | \(-0.906647\pi\) | ||||
−0.957302 | + | 0.289090i | \(0.906647\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.08613 | 0.217791 | ||||||||
\(353\) | 18.5497 | 0.987301 | 0.493651 | − | 0.869660i | \(-0.335662\pi\) | ||||
0.493651 | + | 0.869660i | \(0.335662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.2887 | 0.810300 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.23550 | 0.276705 | ||||||||
\(359\) | −29.0288 | −1.53208 | −0.766040 | − | 0.642793i | \(-0.777775\pi\) | ||||
−0.766040 | + | 0.642793i | \(0.777775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −25.2584 | −1.32755 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.24030 | −0.484324 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.36261 | 0.436525 | 0.218262 | − | 0.975890i | \(-0.429961\pi\) | ||||
0.218262 | + | 0.975890i | \(0.429961\pi\) | |||||||
\(368\) | −0.351939 | −0.0183461 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.9745 | 0.881272 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33.1223 | −1.71501 | −0.857504 | − | 0.514477i | \(-0.827986\pi\) | ||||
−0.857504 | + | 0.514477i | \(0.827986\pi\) | |||||||
\(374\) | −15.2584 | −0.788993 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.52420 | 0.284889 | ||||||||
\(377\) | 25.5226 | 1.31448 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 37.1090 | 1.90616 | 0.953081 | − | 0.302715i | \(-0.0978929\pi\) | ||||
0.953081 | + | 0.302715i | \(0.0978929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.95160 | 0.202181 | ||||||||
\(383\) | −17.5981 | −0.899221 | −0.449611 | − | 0.893225i | \(-0.648437\pi\) | ||||
−0.449611 | + | 0.893225i | \(0.648437\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.43807 | −0.124094 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 16.0787 | 0.816273 | ||||||||
\(389\) | 8.87614 | 0.450038 | 0.225019 | − | 0.974354i | \(-0.427756\pi\) | ||||
0.225019 | + | 0.974354i | \(0.427756\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.31421 | 0.0664624 | ||||||||
\(392\) | −1.05582 | −0.0533268 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 13.6029 | 0.685305 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −37.1952 | −1.86677 | −0.933386 | − | 0.358875i | \(-0.883160\pi\) | ||||
−0.933386 | + | 0.358875i | \(0.883160\pi\) | |||||||
\(398\) | 4.81551 | 0.241380 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1116 | 0.854514 | 0.427257 | − | 0.904130i | \(-0.359480\pi\) | ||||
0.427257 | + | 0.904130i | \(0.359480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.4158 | 1.76419 | ||||||||
\(404\) | 6.38225 | 0.317529 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.4184 | −0.814833 | ||||||||
\(407\) | −25.2207 | −1.25014 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −16.2691 | −0.804453 | −0.402227 | − | 0.915540i | \(-0.631764\pi\) | ||||
−0.402227 | + | 0.915540i | \(0.631764\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.35194 | 0.411471 | ||||||||
\(413\) | 34.8809 | 1.71638 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.79001 | 0.185820 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.08613 | 0.199859 | ||||||||
\(419\) | −3.12386 | −0.152611 | −0.0763053 | − | 0.997085i | \(-0.524312\pi\) | ||||
−0.0763053 | + | 0.997085i | \(0.524312\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.8639 | −0.578212 | −0.289106 | − | 0.957297i | \(-0.593358\pi\) | ||||
−0.289106 | + | 0.957297i | \(0.593358\pi\) | |||||||
\(422\) | −18.4307 | −0.897190 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.96227 | −0.338118 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 32.0229 | 1.54970 | ||||||||
\(428\) | −17.4307 | −0.842542 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.69165 | 0.274157 | 0.137079 | − | 0.990560i | \(-0.456229\pi\) | ||||
0.137079 | + | 0.990560i | \(0.456229\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.36261 | 0.401881 | 0.200941 | − | 0.979603i | \(-0.435600\pi\) | ||||
0.200941 | + | 0.979603i | \(0.435600\pi\) | |||||||
\(434\) | −22.7826 | −1.09360 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.8761 | 0.520873 | ||||||||
\(437\) | −0.351939 | −0.0168355 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.9368 | 0.665165 | 0.332583 | − | 0.943074i | \(-0.392080\pi\) | ||||
0.332583 | + | 0.943074i | \(0.392080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.1526 | −0.673171 | ||||||||
\(443\) | 32.7194 | 1.55454 | 0.777272 | − | 0.629165i | \(-0.216603\pi\) | ||||
0.777272 | + | 0.629165i | \(0.216603\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.22808 | −0.342259 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.43807 | −0.115188 | ||||||||
\(449\) | 32.0288 | 1.51153 | 0.755765 | − | 0.654843i | \(-0.227265\pi\) | ||||
0.755765 | + | 0.654843i | \(0.227265\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.5726 | 0.780373 | ||||||||
\(452\) | −1.05582 | −0.0496615 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.3929 | 1.00402 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.70869 | 0.220263 | 0.110132 | − | 0.993917i | \(-0.464873\pi\) | ||||
0.110132 | + | 0.993917i | \(0.464873\pi\) | |||||||
\(458\) | 1.96969 | 0.0920374 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −30.2084 | −1.40695 | −0.703474 | − | 0.710721i | \(-0.748369\pi\) | ||||
−0.703474 | + | 0.710721i | \(0.748369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.82774 | 0.270838 | 0.135419 | − | 0.990788i | \(-0.456762\pi\) | ||||
0.135419 | + | 0.990788i | \(0.456762\pi\) | |||||||
\(464\) | 6.73419 | 0.312627 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.08132 | 0.235388 | ||||||||
\(467\) | 17.0591 | 0.789399 | 0.394700 | − | 0.918810i | \(-0.370849\pi\) | ||||
0.394700 | + | 0.918810i | \(0.370849\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.5545 | 0.856768 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.3068 | −0.658523 | ||||||||
\(473\) | 3.73419 | 0.171698 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.10422 | 0.417291 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.1648 | 0.693624 | ||||||||
\(479\) | 4.94418 | 0.225905 | 0.112953 | − | 0.993600i | \(-0.463969\pi\) | ||||
0.112953 | + | 0.993600i | \(0.463969\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −23.3929 | −1.06663 | ||||||||
\(482\) | 5.79482 | 0.263947 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.69646 | 0.258930 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.9097 | 0.811566 | 0.405783 | − | 0.913969i | \(-0.366999\pi\) | ||||
0.405783 | + | 0.913969i | \(0.366999\pi\) | |||||||
\(488\) | −13.1345 | −0.594572 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.9852 | 1.17269 | 0.586347 | − | 0.810060i | \(-0.300566\pi\) | ||||
0.586347 | + | 0.810060i | \(0.300566\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.1468 | −1.13255 | ||||||||
\(494\) | 3.79001 | 0.170521 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.34452 | 0.419581 | ||||||||
\(497\) | −23.7326 | −1.06455 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.54229 | 0.158575 | 0.0792873 | − | 0.996852i | \(-0.474736\pi\) | ||||
0.0792873 | + | 0.996852i | \(0.474736\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.0558 | 0.716606 | ||||||||
\(503\) | 7.16003 | 0.319250 | 0.159625 | − | 0.987178i | \(-0.448971\pi\) | ||||
0.159625 | + | 0.987178i | \(0.448971\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.43807 | −0.0639300 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.64064 | 0.383367 | ||||||||
\(509\) | 15.9597 | 0.707399 | 0.353700 | − | 0.935359i | \(-0.384923\pi\) | ||||
0.353700 | + | 0.935359i | \(0.384923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.2387 | −1.29345 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.22808 | 0.142384 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5726 | 0.992742 | ||||||||
\(518\) | 15.0484 | 0.661189 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.62842 | −0.246585 | −0.123293 | − | 0.992370i | \(-0.539345\pi\) | ||||
−0.123293 | + | 0.992370i | \(0.539345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.0213 | −1.48765 | −0.743825 | − | 0.668375i | \(-0.766990\pi\) | ||||
−0.743825 | + | 0.668375i | \(0.766990\pi\) | |||||||
\(524\) | −0.0303126 | −0.00132421 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.5120 | 1.11237 | ||||||||
\(527\) | −34.8942 | −1.52002 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.8761 | −0.994615 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.43807 | −0.105704 | ||||||||
\(533\) | 15.3716 | 0.665817 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.61033 | −0.328716 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.2691 | −0.787635 | ||||||||
\(539\) | −4.31421 | −0.185826 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 27.7071 | 1.19122 | 0.595611 | − | 0.803273i | \(-0.296910\pi\) | ||||
0.595611 | + | 0.803273i | \(0.296910\pi\) | |||||||
\(542\) | −24.0787 | −1.03427 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.73419 | −0.160102 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −45.8236 | −1.95927 | −0.979637 | − | 0.200776i | \(-0.935654\pi\) | ||||
−0.979637 | + | 0.200776i | \(0.935654\pi\) | |||||||
\(548\) | 1.46838 | 0.0627262 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.73419 | 0.286886 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.73419 | 0.328891 | ||||||||
\(554\) | −3.49389 | −0.148441 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.6661 | 0.791621 | ||||||||
\(557\) | −10.4184 | −0.441443 | −0.220721 | − | 0.975337i | \(-0.570841\pi\) | ||||
−0.220721 | + | 0.975337i | \(0.570841\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.46357 | 0.146494 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.5800 | 0.783751 | ||||||||
\(563\) | −0.899033 | −0.0378897 | −0.0189449 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189449 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.64064 | −0.0689613 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.73419 | 0.408438 | ||||||||
\(569\) | −34.6136 | −1.45108 | −0.725538 | − | 0.688182i | \(-0.758409\pi\) | ||||
−0.725538 | + | 0.688182i | \(0.758409\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8990 | 0.623505 | 0.311753 | − | 0.950163i | \(-0.399084\pi\) | ||||
0.311753 | + | 0.950163i | \(0.399084\pi\) | |||||||
\(572\) | 15.4865 | 0.647522 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.88836 | −0.412732 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.1116 | −0.878889 | −0.439444 | − | 0.898270i | \(-0.644825\pi\) | ||||
−0.439444 | + | 0.898270i | \(0.644825\pi\) | |||||||
\(578\) | −3.05582 | −0.127105 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.08613 | 0.293982 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.4487 | −1.17823 | ||||||||
\(584\) | 11.9926 | 0.496257 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.8384 | 0.654279 | ||||||||
\(587\) | −13.6858 | −0.564873 | −0.282437 | − | 0.959286i | \(-0.591143\pi\) | ||||
−0.282437 | + | 0.959286i | \(0.591143\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.34452 | 0.385034 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.17226 | −0.253678 | ||||||||
\(593\) | −42.7252 | −1.75451 | −0.877257 | − | 0.480021i | \(-0.840629\pi\) | ||||
−0.877257 | + | 0.480021i | \(0.840629\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.8761 | 0.609350 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.33385 | −0.0545453 | ||||||||
\(599\) | 24.5497 | 1.00307 | 0.501537 | − | 0.865136i | \(-0.332768\pi\) | ||||
0.501537 | + | 0.865136i | \(0.332768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.1755 | −1.14930 | −0.574652 | − | 0.818398i | \(-0.694862\pi\) | ||||
−0.574652 | + | 0.818398i | \(0.694862\pi\) | |||||||
\(602\) | −2.22808 | −0.0908097 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.5726 | 0.511572 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.3855 | 0.624478 | 0.312239 | − | 0.950004i | \(-0.398921\pi\) | ||||
0.312239 | + | 0.950004i | \(0.398921\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.9368 | 0.847011 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.3929 | 0.702493 | 0.351247 | − | 0.936283i | \(-0.385758\pi\) | ||||
0.351247 | + | 0.936283i | \(0.385758\pi\) | |||||||
\(614\) | −9.32643 | −0.376384 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.96227 | −0.401391 | ||||||||
\(617\) | 6.76450 | 0.272329 | 0.136164 | − | 0.990686i | \(-0.456522\pi\) | ||||
0.136164 | + | 0.990686i | \(0.456522\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.1223 | 1.00975 | 0.504875 | − | 0.863192i | \(-0.331538\pi\) | ||||
0.504875 | + | 0.863192i | \(0.331538\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 19.6965 | 0.789756 | ||||||||
\(623\) | −37.2749 | −1.49339 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.94418 | −0.117673 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.22808 | 0.328336 | ||||||||
\(629\) | 23.0484 | 0.919000 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.9368 | 0.674242 | 0.337121 | − | 0.941461i | \(-0.390547\pi\) | ||||
0.337121 | + | 0.941461i | \(0.390547\pi\) | |||||||
\(632\) | −3.17226 | −0.126186 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.7342 | −0.744030 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.00156 | −0.158547 | ||||||||
\(638\) | 27.5168 | 1.08940 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.0532 | −0.515571 | −0.257785 | − | 0.966202i | \(-0.582993\pi\) | ||||
−0.257785 | + | 0.966202i | \(0.582993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.51678 | 0.0992522 | 0.0496261 | − | 0.998768i | \(-0.484197\pi\) | ||||
0.0496261 | + | 0.998768i | \(0.484197\pi\) | |||||||
\(644\) | 0.858052 | 0.0338120 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.73419 | −0.146920 | ||||||||
\(647\) | 28.5094 | 1.12082 | 0.560409 | − | 0.828216i | \(-0.310644\pi\) | ||||
0.560409 | + | 0.828216i | \(0.310644\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −58.4594 | −2.29473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.40776 | 0.133458 | ||||||||
\(653\) | 3.18449 | 0.124619 | 0.0623093 | − | 0.998057i | \(-0.480153\pi\) | ||||
0.0623093 | + | 0.998057i | \(0.480153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.05582 | 0.158353 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.4684 | −0.525052 | ||||||||
\(659\) | −25.9984 | −1.01276 | −0.506378 | − | 0.862312i | \(-0.669016\pi\) | ||||
−0.506378 | + | 0.862312i | \(0.669016\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.65287 | −0.103185 | −0.0515923 | − | 0.998668i | \(-0.516430\pi\) | ||||
−0.0515923 | + | 0.998668i | \(0.516430\pi\) | |||||||
\(662\) | 15.8942 | 0.617747 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.90645 | −0.112792 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.37003 | −0.0917678 | ||||||||
\(668\) | −18.4562 | −0.714090 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −53.6694 | −2.07188 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.27803 | −0.280548 | −0.140274 | − | 0.990113i | \(-0.544798\pi\) | ||||
−0.140274 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(674\) | −21.8129 | −0.840202 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.36417 | 0.0524679 | ||||||||
\(677\) | −46.9984 | −1.80630 | −0.903148 | − | 0.429328i | \(-0.858750\pi\) | ||||
−0.903148 | + | 0.429328i | \(0.858750\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −39.2010 | −1.50440 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 38.1829 | 1.46210 | ||||||||
\(683\) | −2.03773 | −0.0779716 | −0.0389858 | − | 0.999240i | \(-0.512413\pi\) | ||||
−0.0389858 | + | 0.999240i | \(0.512413\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 19.6406 | 0.749883 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.913870 | 0.0348410 | ||||||||
\(689\) | −26.3871 | −1.00527 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −46.6513 | −1.77470 | −0.887350 | − | 0.461097i | \(-0.847456\pi\) | ||||
−0.887350 | + | 0.461097i | \(0.847456\pi\) | |||||||
\(692\) | 25.9549 | 0.986655 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.5168 | −0.702887 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.1452 | −0.573665 | ||||||||
\(698\) | −35.7678 | −1.35383 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 46.3052 | 1.74892 | 0.874462 | − | 0.485094i | \(-0.161214\pi\) | ||||
0.874462 | + | 0.485094i | \(0.161214\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.17226 | −0.232791 | ||||||||
\(704\) | 4.08613 | 0.154002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 18.5497 | 0.698127 | ||||||||
\(707\) | −15.5604 | −0.585208 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.2026 | 0.383166 | 0.191583 | − | 0.981476i | \(-0.438638\pi\) | ||||
0.191583 | + | 0.981476i | \(0.438638\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.2887 | 0.572968 | ||||||||
\(713\) | −3.28870 | −0.123163 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.23550 | 0.195660 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −29.0288 | −1.08334 | ||||||||
\(719\) | 7.83997 | 0.292381 | 0.146191 | − | 0.989256i | \(-0.453299\pi\) | ||||
0.146191 | + | 0.989256i | \(0.453299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.3626 | −0.758343 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.2584 | −0.938721 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.3419 | −1.08823 | −0.544116 | − | 0.839010i | \(-0.683135\pi\) | ||||
−0.544116 | + | 0.839010i | \(0.683135\pi\) | |||||||
\(728\) | −9.24030 | −0.342468 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.41256 | −0.126218 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.1903 | −1.29979 | −0.649893 | − | 0.760026i | \(-0.725186\pi\) | ||||
−0.649893 | + | 0.760026i | \(0.725186\pi\) | |||||||
\(734\) | 8.36261 | 0.308669 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.351939 | −0.0129727 | ||||||||
\(737\) | −31.0968 | −1.14547 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.5168 | −0.386866 | −0.193433 | − | 0.981113i | \(-0.561962\pi\) | ||||
−0.193433 | + | 0.981113i | \(0.561962\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 16.9745 | 0.623153 | ||||||||
\(743\) | −13.9852 | −0.513066 | −0.256533 | − | 0.966535i | \(-0.582580\pi\) | ||||
−0.256533 | + | 0.966535i | \(0.582580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −33.1223 | −1.21269 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.2584 | −0.557902 | ||||||||
\(749\) | 42.4971 | 1.55281 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.9681 | −1.42197 | −0.710984 | − | 0.703209i | \(-0.751750\pi\) | ||||
−0.710984 | + | 0.703209i | \(0.751750\pi\) | |||||||
\(752\) | 5.52420 | 0.201447 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.5226 | 0.929480 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.5619 | −1.18348 | −0.591742 | − | 0.806128i | \(-0.701559\pi\) | ||||
−0.591742 | + | 0.806128i | \(0.701559\pi\) | |||||||
\(758\) | 37.1090 | 1.34786 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.5955 | 0.964086 | 0.482043 | − | 0.876148i | \(-0.339895\pi\) | ||||
0.482043 | + | 0.876148i | \(0.339895\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.5168 | −0.959972 | ||||||||
\(764\) | 3.95160 | 0.142964 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −17.5981 | −0.635845 | ||||||||
\(767\) | −54.2229 | −1.95787 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.64545 | 0.167519 | 0.0837596 | − | 0.996486i | \(-0.473307\pi\) | ||||
0.0837596 | + | 0.996486i | \(0.473307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.43807 | −0.0877480 | ||||||||
\(773\) | 18.0820 | 0.650363 | 0.325181 | − | 0.945652i | \(-0.394575\pi\) | ||||
0.325181 | + | 0.945652i | \(0.394575\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16.0787 | 0.577192 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.87614 | 0.318225 | ||||||||
\(779\) | 4.05582 | 0.145315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.7752 | 1.42327 | ||||||||
\(782\) | 1.31421 | 0.0469960 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.05582 | −0.0377078 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.07871 | −0.323621 | −0.161811 | − | 0.986822i | \(-0.551733\pi\) | ||||
−0.161811 | + | 0.986822i | \(0.551733\pi\) | |||||||
\(788\) | 13.6029 | 0.484584 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.57416 | 0.0915265 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.7800 | −1.76774 | ||||||||
\(794\) | −37.1952 | −1.32001 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.81551 | 0.170681 | ||||||||
\(797\) | −5.64545 | −0.199972 | −0.0999860 | − | 0.994989i | \(-0.531880\pi\) | ||||
−0.0999860 | + | 0.994989i | \(0.531880\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.6284 | −0.729781 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.1116 | 0.604233 | ||||||||
\(803\) | 49.0032 | 1.72929 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 35.4158 | 1.24747 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.38225 | 0.224527 | ||||||||
\(809\) | −33.7555 | −1.18678 | −0.593391 | − | 0.804915i | \(-0.702211\pi\) | ||||
−0.593391 | + | 0.804915i | \(0.702211\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.3823 | −0.469914 | −0.234957 | − | 0.972006i | \(-0.575495\pi\) | ||||
−0.234957 | + | 0.972006i | \(0.575495\pi\) | |||||||
\(812\) | −16.4184 | −0.576174 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25.2207 | −0.883984 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.913870 | 0.0319723 | ||||||||
\(818\) | −16.2691 | −0.568834 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.1829 | 1.43729 | 0.718647 | − | 0.695375i | \(-0.244762\pi\) | ||||
0.718647 | + | 0.695375i | \(0.244762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | −0.139431 | −0.0697156 | − | 0.997567i | \(-0.522209\pi\) | ||||
−0.0697156 | + | 0.997567i | \(0.522209\pi\) | |||||||
\(824\) | 8.35194 | 0.290954 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.8809 | 1.21366 | ||||||||
\(827\) | 40.7268 | 1.41621 | 0.708104 | − | 0.706108i | \(-0.249551\pi\) | ||||
0.708104 | + | 0.706108i | \(0.249551\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.9016 | 0.830138 | 0.415069 | − | 0.909790i | \(-0.363757\pi\) | ||||
0.415069 | + | 0.909790i | \(0.363757\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.79001 | 0.131395 | ||||||||
\(833\) | 3.94262 | 0.136604 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.08613 | 0.141322 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.12386 | −0.107912 | ||||||||
\(839\) | 22.0639 | 0.761730 | 0.380865 | − | 0.924631i | \(-0.375626\pi\) | ||||
0.380865 | + | 0.924631i | \(0.375626\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.3493 | 0.563770 | ||||||||
\(842\) | −11.8639 | −0.408857 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.4307 | −0.634409 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −13.8884 | −0.477210 | ||||||||
\(848\) | −6.96227 | −0.239085 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.17226 | 0.0744641 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.7793 | −0.711471 | −0.355736 | − | 0.934587i | \(-0.615770\pi\) | ||||
−0.355736 | + | 0.934587i | \(0.615770\pi\) | |||||||
\(854\) | 32.0229 | 1.09580 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.4307 | −0.595767 | ||||||||
\(857\) | 13.9655 | 0.477053 | 0.238527 | − | 0.971136i | \(-0.423336\pi\) | ||||
0.238527 | + | 0.971136i | \(0.423336\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −21.0484 | −0.718162 | −0.359081 | − | 0.933306i | \(-0.616910\pi\) | ||||
−0.359081 | + | 0.933306i | \(0.616910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.69165 | 0.193858 | ||||||||
\(863\) | −57.2058 | −1.94731 | −0.973654 | − | 0.228029i | \(-0.926772\pi\) | ||||
−0.973654 | + | 0.228029i | \(0.926772\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.36261 | 0.284173 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −22.7826 | −0.773291 | ||||||||
\(869\) | −12.9623 | −0.439715 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.8432 | −0.977315 | ||||||||
\(872\) | 10.8761 | 0.368313 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.351939 | −0.0119045 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.47099 | −0.0834395 | −0.0417197 | − | 0.999129i | \(-0.513284\pi\) | ||||
−0.0417197 | + | 0.999129i | \(0.513284\pi\) | |||||||
\(878\) | 13.9368 | 0.470343 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −13.9245 | −0.469130 | −0.234565 | − | 0.972100i | \(-0.575367\pi\) | ||||
−0.234565 | + | 0.972100i | \(0.575367\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.3823 | 0.484001 | 0.242001 | − | 0.970276i | \(-0.422196\pi\) | ||||
0.242001 | + | 0.970276i | \(0.422196\pi\) | |||||||
\(884\) | −14.1526 | −0.476004 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.7194 | 1.09923 | ||||||||
\(887\) | 24.7645 | 0.831511 | 0.415755 | − | 0.909477i | \(-0.363517\pi\) | ||||
0.415755 | + | 0.909477i | \(0.363517\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.0665 | −0.706547 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.22808 | −0.242014 | ||||||||
\(893\) | 5.52420 | 0.184860 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.43807 | −0.0814502 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 32.0288 | 1.06881 | ||||||||
\(899\) | 62.9278 | 2.09876 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.9984 | 0.866134 | ||||||||
\(902\) | 16.5726 | 0.551807 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.05582 | −0.0351160 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.16745 | −0.138378 | −0.0691890 | − | 0.997604i | \(-0.522041\pi\) | ||||
−0.0691890 | + | 0.997604i | \(0.522041\pi\) | |||||||
\(908\) | 21.3929 | 0.709949 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.4535 | −0.909577 | −0.454788 | − | 0.890600i | \(-0.650285\pi\) | ||||
−0.454788 | + | 0.890600i | \(0.650285\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.8761 | −0.393043 | ||||||||
\(914\) | 4.70869 | 0.155749 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.96969 | 0.0650803 | ||||||||
\(917\) | 0.0739042 | 0.00244053 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.0303 | 0.759700 | 0.379850 | − | 0.925048i | \(-0.375976\pi\) | ||||
0.379850 | + | 0.925048i | \(0.375976\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −30.2084 | −0.994862 | ||||||||
\(923\) | 36.8927 | 1.21434 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.82774 | 0.191511 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.73419 | 0.221061 | ||||||||
\(929\) | −38.1116 | −1.25040 | −0.625201 | − | 0.780464i | \(-0.714983\pi\) | ||||
−0.625201 | + | 0.780464i | \(0.714983\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.05582 | −0.0346030 | ||||||||
\(932\) | 5.08132 | 0.166444 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.0591 | 0.558190 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.7401 | −1.46159 | −0.730797 | − | 0.682595i | \(-0.760851\pi\) | ||||
−0.730797 | + | 0.682595i | \(0.760851\pi\) | |||||||
\(938\) | 18.5545 | 0.605826 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.7268 | −0.447480 | −0.223740 | − | 0.974649i | \(-0.571827\pi\) | ||||
−0.223740 | + | 0.974649i | \(0.571827\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.42740 | −0.0464826 | ||||||||
\(944\) | −14.3068 | −0.465646 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.73419 | 0.121409 | ||||||||
\(947\) | 29.5652 | 0.960739 | 0.480370 | − | 0.877066i | \(-0.340503\pi\) | ||||
0.480370 | + | 0.877066i | \(0.340503\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.4520 | 1.47543 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 9.10422 | 0.295069 | ||||||||
\(953\) | −35.6284 | −1.15412 | −0.577059 | − | 0.816703i | \(-0.695800\pi\) | ||||
−0.577059 | + | 0.816703i | \(0.695800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.1648 | 0.490466 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.94418 | 0.159739 | ||||||||
\(959\) | −3.58002 | −0.115605 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 56.3201 | 1.81678 | ||||||||
\(962\) | −23.3929 | −0.754218 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.79482 | 0.186638 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.9581 | 1.70302 | 0.851509 | − | 0.524340i | \(-0.175688\pi\) | ||||
0.851509 | + | 0.524340i | \(0.175688\pi\) | |||||||
\(968\) | 5.69646 | 0.183091 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.5423 | 0.819691 | 0.409845 | − | 0.912155i | \(-0.365583\pi\) | ||||
0.409845 | + | 0.912155i | \(0.365583\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −45.5094 | −1.45896 | ||||||||
\(974\) | 17.9097 | 0.573864 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.1345 | −0.420426 | ||||||||
\(977\) | 12.6629 | 0.405122 | 0.202561 | − | 0.979270i | \(-0.435074\pi\) | ||||
0.202561 | + | 0.979270i | \(0.435074\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 62.4716 | 1.99660 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 25.9852 | 0.829220 | ||||||||
\(983\) | 8.26581 | 0.263638 | 0.131819 | − | 0.991274i | \(-0.457918\pi\) | ||||
0.131819 | + | 0.991274i | \(0.457918\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25.1468 | −0.800836 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.79001 | 0.120576 | ||||||||
\(989\) | −0.321627 | −0.0102271 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −44.9655 | −1.42838 | −0.714188 | − | 0.699954i | \(-0.753204\pi\) | ||||
−0.714188 | + | 0.699954i | \(0.753204\pi\) | |||||||
\(992\) | 9.34452 | 0.296689 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23.7326 | −0.752753 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.4939 | −0.680718 | −0.340359 | − | 0.940296i | \(-0.610549\pi\) | ||||
−0.340359 | + | 0.940296i | \(0.610549\pi\) | |||||||
\(998\) | 3.54229 | 0.112129 | ||||||||
\(999\) | 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.1.1 | yes | 3 | |
3.2 | odd | 2 | 8550.2.a.cg.1.1 | yes | 3 | ||
5.4 | even | 2 | 8550.2.a.cd.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 8550.2.a.cn.1.3 | yes | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8550.2.a.cd.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
8550.2.a.cg.1.1 | yes | 3 | 3.2 | odd | 2 | ||
8550.2.a.cn.1.3 | yes | 3 | 15.14 | odd | 2 | ||
8550.2.a.cs.1.1 | yes | 3 | 1.1 | even | 1 | trivial |