Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 16x^{4} + 26x^{3} + 52x^{2} - 48x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(2.85512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.20659 | 1.21198 | 0.605989 | − | 0.795473i | \(-0.292778\pi\) | ||||
0.605989 | + | 0.795473i | \(0.292778\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.11246 | 1.54146 | 0.770732 | − | 0.637160i | \(-0.219891\pi\) | ||||
0.770732 | + | 0.637160i | \(0.219891\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.597792 | 0.165798 | 0.0828988 | − | 0.996558i | \(-0.473582\pi\) | ||||
0.0828988 | + | 0.996558i | \(0.473582\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.98790 | −1.45228 | −0.726140 | − | 0.687547i | \(-0.758688\pi\) | ||||
−0.726140 | + | 0.687547i | \(0.758688\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.11246 | −0.714047 | −0.357023 | − | 0.934095i | \(-0.616208\pi\) | ||||
−0.357023 | + | 0.934095i | \(0.616208\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.64671 | −0.862873 | −0.431436 | − | 0.902143i | \(-0.641993\pi\) | ||||
−0.431436 | + | 0.902143i | \(0.641993\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.39011 | 0.608882 | 0.304441 | − | 0.952531i | \(-0.401530\pi\) | ||||
0.304441 | + | 0.952531i | \(0.401530\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.20659 | −0.542013 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.51188 | −1.07055 | −0.535273 | − | 0.844679i | \(-0.679791\pi\) | ||||
−0.535273 | + | 0.844679i | \(0.679791\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.4767 | −1.79236 | −0.896181 | − | 0.443688i | \(-0.853670\pi\) | ||||
−0.896181 | + | 0.443688i | \(0.853670\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.71025 | −0.565808 | −0.282904 | − | 0.959148i | \(-0.591298\pi\) | ||||
−0.282904 | + | 0.959148i | \(0.591298\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.80717 | 0.263602 | 0.131801 | − | 0.991276i | \(-0.457924\pi\) | ||||
0.131801 | + | 0.991276i | \(0.457924\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.28222 | 0.468889 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.13553 | −1.11750 | −0.558750 | − | 0.829336i | \(-0.688719\pi\) | ||||
−0.558750 | + | 0.829336i | \(0.688719\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.11246 | −0.689364 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.80438 | 0.495288 | 0.247644 | − | 0.968851i | \(-0.420344\pi\) | ||||
0.247644 | + | 0.968851i | \(0.420344\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.07454 | −0.905802 | −0.452901 | − | 0.891561i | \(-0.649611\pi\) | ||||
−0.452901 | + | 0.891561i | \(0.649611\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.597792 | −0.0741470 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.0987010 | 0.0120583 | 0.00602913 | − | 0.999982i | \(-0.498081\pi\) | ||||
0.00602913 | + | 0.999982i | \(0.498081\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.51463 | −1.12918 | −0.564590 | − | 0.825372i | \(-0.690966\pi\) | ||||
−0.564590 | + | 0.825372i | \(0.690966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.41593 | −0.867969 | −0.433985 | − | 0.900920i | \(-0.642893\pi\) | ||||
−0.433985 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.3936 | 1.86822 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.96209 | −0.670787 | −0.335394 | − | 0.942078i | \(-0.608869\pi\) | ||||
−0.335394 | + | 0.942078i | \(0.608869\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.55235 | 0.499685 | 0.249843 | − | 0.968286i | \(-0.419621\pi\) | ||||
0.249843 | + | 0.968286i | \(0.419621\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.98790 | 0.649479 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.9776 | −1.16363 | −0.581813 | − | 0.813323i | \(-0.697656\pi\) | ||||
−0.581813 | + | 0.813323i | \(0.697656\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.91687 | 0.200943 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.11246 | 0.319331 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.4630 | 1.06235 | 0.531176 | − | 0.847261i | \(-0.321750\pi\) | ||||
0.531176 | + | 0.847261i | \(0.321750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4905 | −1.34236 | −0.671178 | − | 0.741296i | \(-0.734211\pi\) | ||||
−0.671178 | + | 0.741296i | \(0.734211\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.2949 | 1.50705 | 0.753525 | − | 0.657419i | \(-0.228352\pi\) | ||||
0.753525 | + | 0.657419i | \(0.228352\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.09761 | −0.782826 | −0.391413 | − | 0.920215i | \(-0.628014\pi\) | ||||
−0.391413 | + | 0.920215i | \(0.628014\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.51010 | −0.240424 | −0.120212 | − | 0.992748i | \(-0.538357\pi\) | ||||
−0.120212 | + | 0.992748i | \(0.538357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.9075 | −1.40238 | −0.701191 | − | 0.712973i | \(-0.747348\pi\) | ||||
−0.701191 | + | 0.712973i | \(0.747348\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −19.2008 | −1.76013 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.1372 | 1.37611 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.26008 | 0.644228 | 0.322114 | − | 0.946701i | \(-0.395607\pi\) | ||||
0.322114 | + | 0.946701i | \(0.395607\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.66229 | 0.232605 | 0.116303 | − | 0.993214i | \(-0.462896\pi\) | ||||
0.116303 | + | 0.993214i | \(0.462896\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.98038 | −0.865408 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 19.5439 | 1.66975 | 0.834875 | − | 0.550439i | \(-0.185540\pi\) | ||||
0.834875 | + | 0.550439i | \(0.185540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.08664 | −0.0921675 | −0.0460838 | − | 0.998938i | \(-0.514674\pi\) | ||||
−0.0460838 | + | 0.998938i | \(0.514674\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.05619 | 0.255571 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.64671 | 0.385888 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.33223 | −0.191064 | −0.0955320 | − | 0.995426i | \(-0.530455\pi\) | ||||
−0.0955320 | + | 0.995426i | \(0.530455\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.71847 | 0.302605 | 0.151303 | − | 0.988488i | \(-0.451653\pi\) | ||||
0.151303 | + | 0.988488i | \(0.451653\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.39011 | −0.272300 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.97219 | 0.556441 | 0.278221 | − | 0.960517i | \(-0.410255\pi\) | ||||
0.278221 | + | 0.960517i | \(0.410255\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.20659 | −0.252715 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.58464 | −0.750727 | −0.375364 | − | 0.926878i | \(-0.622482\pi\) | ||||
−0.375364 | + | 0.926878i | \(0.622482\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.78479 | 0.679788 | 0.339894 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339894 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6426 | −0.972511 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −20.2193 | −1.53725 | −0.768624 | − | 0.639700i | \(-0.779058\pi\) | ||||
−0.768624 | + | 0.639700i | \(0.779058\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.20659 | 0.242395 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.66502 | 0.498167 | 0.249083 | − | 0.968482i | \(-0.419871\pi\) | ||||
0.249083 | + | 0.968482i | \(0.419871\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.2331 | 1.50392 | 0.751959 | − | 0.659210i | \(-0.229109\pi\) | ||||
0.751959 | + | 0.659210i | \(0.229109\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.51188 | 0.478763 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30.6129 | −2.23864 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.9169 | −1.00699 | −0.503495 | − | 0.863998i | \(-0.667953\pi\) | ||||
−0.503495 | + | 0.863998i | \(0.667953\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.8113 | −1.92992 | −0.964960 | − | 0.262397i | \(-0.915487\pi\) | ||||
−0.964960 | + | 0.262397i | \(0.915487\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.4183 | 1.52599 | 0.762996 | − | 0.646403i | \(-0.223728\pi\) | ||||
0.762996 | + | 0.646403i | \(0.223728\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.1628 | 1.14575 | 0.572876 | − | 0.819642i | \(-0.305828\pi\) | ||||
0.572876 | + | 0.819642i | \(0.305828\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −14.9001 | −1.04578 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.4767 | 0.801569 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.9123 | −1.10068 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.7247 | 1.63327 | 0.816637 | − | 0.577152i | \(-0.195836\pi\) | ||||
0.816637 | + | 0.577152i | \(0.195836\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.71025 | 0.253037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.8707 | 0.737951 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.57952 | −0.240785 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4339 | 1.77014 | 0.885071 | − | 0.465456i | \(-0.154110\pi\) | ||||
0.885071 | + | 0.465456i | \(0.154110\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.4119 | 1.22204 | 0.611021 | − | 0.791614i | \(-0.290759\pi\) | ||||
0.611021 | + | 0.791614i | \(0.290759\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.94703 | 0.525155 | 0.262577 | − | 0.964911i | \(-0.415428\pi\) | ||||
0.262577 | + | 0.964911i | \(0.415428\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.2711 | 0.934928 | 0.467464 | − | 0.884012i | \(-0.345168\pi\) | ||||
0.467464 | + | 0.884012i | \(0.345168\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.80717 | −0.117886 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.53665 | 0.616874 | 0.308437 | − | 0.951245i | \(-0.400194\pi\) | ||||
0.308437 | + | 0.951245i | \(0.400194\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.05344 | 0.389936 | 0.194968 | − | 0.980810i | \(-0.437540\pi\) | ||||
0.194968 | + | 0.980810i | \(0.437540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.28222 | −0.209694 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.86060 | −0.118387 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.1956 | −0.706659 | −0.353329 | − | 0.935499i | \(-0.614951\pi\) | ||||
−0.353329 | + | 0.935499i | \(0.614951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.11246 | −0.321417 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −13.2002 | −0.823403 | −0.411701 | − | 0.911319i | \(-0.635065\pi\) | ||||
−0.411701 | + | 0.911319i | \(0.635065\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.8809 | −1.29748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.8787 | −1.16411 | −0.582057 | − | 0.813148i | \(-0.697752\pi\) | ||||
−0.582057 | + | 0.813148i | \(0.697752\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.13553 | 0.499761 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −14.8862 | −0.907629 | −0.453815 | − | 0.891096i | \(-0.649937\pi\) | ||||
−0.453815 | + | 0.891096i | \(0.649937\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.5368 | −0.640067 | −0.320033 | − | 0.947406i | \(-0.603694\pi\) | ||||
−0.320033 | + | 0.947406i | \(0.603694\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.11246 | 0.308293 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.0724 | −1.20603 | −0.603016 | − | 0.797729i | \(-0.706035\pi\) | ||||
−0.603016 | + | 0.797729i | \(0.706035\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.2597 | 1.08928 | 0.544642 | − | 0.838669i | \(-0.316666\pi\) | ||||
0.544642 | + | 0.838669i | \(0.316666\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8395 | −0.763232 | −0.381616 | − | 0.924321i | \(-0.624632\pi\) | ||||
−0.381616 | + | 0.924321i | \(0.624632\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −36.8011 | −2.17230 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.8550 | 1.10912 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4701 | 0.845355 | 0.422678 | − | 0.906280i | \(-0.361090\pi\) | ||||
0.422678 | + | 0.906280i | \(0.361090\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.80438 | −0.221500 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.597792 | −0.0345712 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.8973 | −0.685746 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.07454 | 0.405087 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.2424 | −0.698708 | −0.349354 | − | 0.936991i | \(-0.613599\pi\) | ||||
−0.349354 | + | 0.936991i | \(0.613599\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.98585 | 0.396131 | 0.198066 | − | 0.980189i | \(-0.436534\pi\) | ||||
0.198066 | + | 0.980189i | \(0.436534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.99868 | 0.565159 | 0.282579 | − | 0.959244i | \(-0.408810\pi\) | ||||
0.282579 | + | 0.959244i | \(0.408810\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.244471 | 0.0137308 | 0.00686542 | − | 0.999976i | \(-0.497815\pi\) | ||||
0.00686542 | + | 0.999976i | \(0.497815\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.7561 | −1.33009 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 18.6371 | 1.03700 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.597792 | 0.0331595 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.79484 | 0.319480 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.5908 | 0.966880 | 0.483440 | − | 0.875378i | \(-0.339387\pi\) | ||||
0.483440 | + | 0.875378i | \(0.339387\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0987010 | −0.00539261 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.6226 | 1.17786 | 0.588928 | − | 0.808186i | \(-0.299550\pi\) | ||||
0.588928 | + | 0.808186i | \(0.299550\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.3318 | 0.938570 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.9214 | −0.643694 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4205 | −0.827816 | −0.413908 | − | 0.910319i | \(-0.635836\pi\) | ||||
−0.413908 | + | 0.910319i | \(0.635836\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.4998 | −1.47203 | −0.736014 | − | 0.676966i | \(-0.763294\pi\) | ||||
−0.736014 | + | 0.676966i | \(0.763294\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.36248 | 0.232191 | 0.116096 | − | 0.993238i | \(-0.462962\pi\) | ||||
0.116096 | + | 0.993238i | \(0.462962\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.51463 | 0.504984 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −25.5106 | −1.34640 | −0.673199 | − | 0.739462i | \(-0.735080\pi\) | ||||
−0.673199 | + | 0.739462i | \(0.735080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.31261 | −0.490137 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.41593 | 0.388168 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.6833 | −0.609865 | −0.304933 | − | 0.952374i | \(-0.598634\pi\) | ||||
−0.304933 | + | 0.952374i | \(0.598634\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.0873 | −1.35439 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.7597 | 1.43734 | 0.718672 | − | 0.695350i | \(-0.244750\pi\) | ||||
0.718672 | + | 0.695350i | \(0.244750\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.77777 | −0.143062 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −33.8557 | −1.73905 | −0.869525 | − | 0.493889i | \(-0.835575\pi\) | ||||
−0.869525 | + | 0.493889i | \(0.835575\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.7690 | −0.959053 | −0.479527 | − | 0.877527i | \(-0.659192\pi\) | ||||
−0.479527 | + | 0.877527i | \(0.659192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.3936 | −0.835493 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −24.8319 | −1.25903 | −0.629513 | − | 0.776990i | \(-0.716745\pi\) | ||||
−0.629513 | + | 0.776990i | \(0.716745\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.98790 | 0.302821 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.96209 | 0.299985 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.27232 | 0.214421 | 0.107211 | − | 0.994236i | \(-0.465808\pi\) | ||||
0.107211 | + | 0.994236i | \(0.465808\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.4425 | −0.970913 | −0.485456 | − | 0.874261i | \(-0.661347\pi\) | ||||
−0.485456 | + | 0.874261i | \(0.661347\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.02658 | 0.100951 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −33.2917 | −1.65021 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.1621 | 0.898058 | 0.449029 | − | 0.893517i | \(-0.351770\pi\) | ||||
0.449029 | + | 0.893517i | \(0.351770\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.1991 | 0.600278 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.55235 | −0.223466 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.91499 | 0.337819 | 0.168910 | − | 0.985632i | \(-0.445975\pi\) | ||||
0.168910 | + | 0.985632i | \(0.445975\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.97855 | 0.340114 | 0.170057 | − | 0.985434i | \(-0.445605\pi\) | ||||
0.170057 | + | 0.985434i | \(0.445605\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.98790 | −0.290456 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.6852 | −1.09781 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.04796 | −0.243151 | −0.121576 | − | 0.992582i | \(-0.538795\pi\) | ||||
−0.121576 | + | 0.992582i | \(0.538795\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1582 | −0.920685 | −0.460342 | − | 0.887741i | \(-0.652273\pi\) | ||||
−0.460342 | + | 0.887741i | \(0.652273\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.11246 | 0.148889 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0192 | −1.05092 | −0.525460 | − | 0.850818i | \(-0.676107\pi\) | ||||
−0.525460 | + | 0.850818i | \(0.676107\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.0174 | −0.665989 | −0.332994 | − | 0.942929i | \(-0.608059\pi\) | ||||
−0.332994 | + | 0.942929i | \(0.608059\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.9776 | 0.520389 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.6121 | −1.06713 | −0.533566 | − | 0.845758i | \(-0.679148\pi\) | ||||
−0.533566 | + | 0.845758i | \(0.679148\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −58.6742 | −2.76286 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.91687 | −0.0898644 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.90826 | −0.0892645 | −0.0446322 | − | 0.999003i | \(-0.514212\pi\) | ||||
−0.0446322 | + | 0.999003i | \(0.514212\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.0302 | −0.932898 | −0.466449 | − | 0.884548i | \(-0.654467\pi\) | ||||
−0.466449 | + | 0.884548i | \(0.654467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.1824 | −0.566166 | −0.283083 | − | 0.959095i | \(-0.591357\pi\) | ||||
−0.283083 | + | 0.959095i | \(0.591357\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.39322 | −0.249568 | −0.124784 | − | 0.992184i | \(-0.539824\pi\) | ||||
−0.124784 | + | 0.992184i | \(0.539824\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.316494 | 0.0146143 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.9685 | −0.872172 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.11246 | −0.142809 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.2098 | 0.877720 | 0.438860 | − | 0.898555i | \(-0.355382\pi\) | ||||
0.438860 | + | 0.898555i | \(0.355382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.89275 | −0.177494 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −10.4630 | −0.475099 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.6289 | −0.753526 | −0.376763 | − | 0.926310i | \(-0.622963\pi\) | ||||
−0.376763 | + | 0.926310i | \(0.622963\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 40.5038 | 1.82791 | 0.913956 | − | 0.405814i | \(-0.133012\pi\) | ||||
0.913956 | + | 0.405814i | \(0.133012\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.8241 | 1.25313 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.5095 | −1.36854 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.0798 | −1.21226 | −0.606129 | − | 0.795366i | \(-0.707279\pi\) | ||||
−0.606129 | + | 0.795366i | \(0.707279\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11.7892 | 0.525656 | 0.262828 | − | 0.964843i | \(-0.415345\pi\) | ||||
0.262828 | + | 0.964843i | \(0.415345\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.4905 | 0.600320 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.2798 | −1.38645 | −0.693227 | − | 0.720719i | \(-0.743812\pi\) | ||||
−0.693227 | + | 0.720719i | \(0.743812\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −23.7799 | −1.05196 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −15.2949 | −0.673973 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.23906 | 0.406333 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.7282 | −0.995740 | −0.497870 | − | 0.867252i | \(-0.665884\pi\) | ||||
−0.497870 | + | 0.867252i | \(0.665884\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.44196 | −0.369141 | −0.184571 | − | 0.982819i | \(-0.559089\pi\) | ||||
−0.184571 | + | 0.982819i | \(0.559089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −20.2997 | −0.884267 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.86069 | −0.297169 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.09761 | 0.350090 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 16.7802 | 0.722775 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.3987 | 1.73687 | 0.868437 | − | 0.495799i | \(-0.165125\pi\) | ||||
0.868437 | + | 0.495799i | \(0.165125\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.51010 | 0.107521 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.7337 | 1.61337 | 0.806687 | − | 0.590978i | \(-0.201258\pi\) | ||||
0.806687 | + | 0.590978i | \(0.201258\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.4627 | 0.616132 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.1180 | −0.812979 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.0703 | −1.65546 | −0.827732 | − | 0.561124i | \(-0.810369\pi\) | ||||
−0.827732 | + | 0.561124i | \(0.810369\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.21796 | −0.0938096 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.5551 | −1.24560 | −0.622800 | − | 0.782381i | \(-0.714005\pi\) | ||||
−0.622800 | + | 0.782381i | \(0.714005\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.9075 | 0.627164 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.2322 | 0.638568 | 0.319284 | − | 0.947659i | \(-0.396558\pi\) | ||||
0.319284 | + | 0.947659i | \(0.396558\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.389436 | 0.0162974 | 0.00814869 | − | 0.999967i | \(-0.497406\pi\) | ||||
0.00814869 | + | 0.999967i | \(0.497406\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.1490 | 1.75469 | 0.877343 | − | 0.479863i | \(-0.159314\pi\) | ||||
0.877343 | + | 0.479863i | \(0.159314\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.5975 | 0.605607 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −41.5925 | −1.72259 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.46664 | 0.390730 | 0.195365 | − | 0.980731i | \(-0.437411\pi\) | ||||
0.195365 | + | 0.980731i | \(0.437411\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.5516 | −0.434770 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.9855 | 1.51881 | 0.759407 | − | 0.650616i | \(-0.225489\pi\) | ||||
0.759407 | + | 0.650616i | \(0.225489\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 19.2008 | 0.787154 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.5153 | 0.511360 | 0.255680 | − | 0.966762i | \(-0.417701\pi\) | ||||
0.255680 | + | 0.966762i | \(0.417701\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.92898 | 0.241848 | 0.120924 | − | 0.992662i | \(-0.461414\pi\) | ||||
0.120924 | + | 0.992662i | \(0.461414\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.1372 | −0.615416 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.7076 | 1.32756 | 0.663781 | − | 0.747927i | \(-0.268951\pi\) | ||||
0.663781 | + | 0.747927i | \(0.268951\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.08031 | 0.0437046 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.6704 | 0.915651 | 0.457825 | − | 0.889042i | \(-0.348629\pi\) | ||||
0.457825 | + | 0.889042i | \(0.348629\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.19087 | −0.249235 | −0.124618 | − | 0.992205i | \(-0.539770\pi\) | ||||
−0.124618 | + | 0.992205i | \(0.539770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.30848 | −0.374139 | −0.187070 | − | 0.982347i | \(-0.559899\pi\) | ||||
−0.187070 | + | 0.982347i | \(0.559899\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −35.2008 | −1.41029 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 38.9925 | 1.55473 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.1998 | −1.32166 | −0.660832 | − | 0.750534i | \(-0.729797\pi\) | ||||
−0.660832 | + | 0.750534i | \(0.729797\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.26008 | −0.288107 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.96209 | 0.0777407 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.4347 | 1.71557 | 0.857784 | − | 0.514011i | \(-0.171841\pi\) | ||||
0.857784 | + | 0.514011i | \(0.171841\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.13171 | 0.162939 | 0.0814694 | − | 0.996676i | \(-0.474039\pi\) | ||||
0.0814694 | + | 0.996676i | \(0.474039\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.95836 | 0.0769912 | 0.0384956 | − | 0.999259i | \(-0.487743\pi\) | ||||
0.0384956 | + | 0.999259i | \(0.487743\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.4497 | 0.763469 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.0317 | −1.21436 | −0.607181 | − | 0.794563i | \(-0.707700\pi\) | ||||
−0.607181 | + | 0.794563i | \(0.707700\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.66229 | −0.104024 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.1084 | −1.40658 | −0.703292 | − | 0.710901i | \(-0.748287\pi\) | ||||
−0.703292 | + | 0.710901i | \(0.748287\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −35.9247 | −1.39731 | −0.698654 | − | 0.715459i | \(-0.746217\pi\) | ||||
−0.698654 | + | 0.715459i | \(0.746217\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.98038 | 0.387022 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.64671 | 0.179921 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36.1683 | −1.39626 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.1463 | 1.23915 | 0.619574 | − | 0.784938i | \(-0.287305\pi\) | ||||
0.619574 | + | 0.784938i | \(0.287305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.1407 | −0.658769 | −0.329385 | − | 0.944196i | \(-0.606841\pi\) | ||||
−0.329385 | + | 0.944196i | \(0.606841\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 33.5504 | 1.28755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.8878 | 1.14362 | 0.571812 | − | 0.820385i | \(-0.306241\pi\) | ||||
0.571812 | + | 0.820385i | \(0.306241\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.5439 | −0.746735 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.86335 | −0.185279 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.9726 | 0.759794 | 0.379897 | − | 0.925029i | \(-0.375959\pi\) | ||||
0.379897 | + | 0.925029i | \(0.375959\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.08664 | 0.0412186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 68.7215 | 2.60301 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.92969 | −0.261731 | −0.130865 | − | 0.991400i | \(-0.541776\pi\) | ||||
−0.130865 | + | 0.991400i | \(0.541776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.2680 | 0.764420 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −43.2585 | −1.62690 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.9233 | −0.635567 | −0.317784 | − | 0.948163i | \(-0.602939\pi\) | ||||
−0.317784 | + | 0.948163i | \(0.602939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.39011 | −0.126961 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.05619 | −0.114295 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 45.0448 | 1.67989 | 0.839944 | − | 0.542672i | \(-0.182587\pi\) | ||||
0.839944 | + | 0.542672i | \(0.182587\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 49.0445 | 1.82651 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.64671 | −0.172575 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.0659 | 1.44887 | 0.724437 | − | 0.689341i | \(-0.242100\pi\) | ||||
0.724437 | + | 0.689341i | \(0.242100\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 22.2166 | 0.821711 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.3959 | 0.383980 | 0.191990 | − | 0.981397i | \(-0.438506\pi\) | ||||
0.191990 | + | 0.981397i | \(0.438506\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.504605 | 0.0185874 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.2681 | −1.33414 | −0.667072 | − | 0.744993i | \(-0.732453\pi\) | ||||
−0.667072 | + | 0.744993i | \(0.732453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 36.4179 | 1.33604 | 0.668021 | − | 0.744142i | \(-0.267141\pi\) | ||||
0.668021 | + | 0.744142i | \(0.267141\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.33223 | 0.0854464 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.9657 | −0.948767 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.5873 | 1.04317 | 0.521583 | − | 0.853201i | \(-0.325342\pi\) | ||||
0.521583 | + | 0.853201i | \(0.325342\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.71847 | −0.135329 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.4091 | −0.669091 | −0.334546 | − | 0.942380i | \(-0.608583\pi\) | ||||
−0.334546 | + | 0.942380i | \(0.608583\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.3926 | 0.702981 | 0.351490 | − | 0.936191i | \(-0.385675\pi\) | ||||
0.351490 | + | 0.936191i | \(0.385675\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.04886 | −0.291388 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.27423 | 0.0821176 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.205159 | 0.00739823 | 0.00369912 | − | 0.999993i | \(-0.498823\pi\) | ||||
0.00369912 | + | 0.999993i | \(0.498823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.1930 | −1.01403 | −0.507015 | − | 0.861937i | \(-0.669251\pi\) | ||||
−0.507015 | + | 0.861937i | \(0.669251\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.39011 | 0.121776 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 35.7208 | 1.27983 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −48.6431 | −1.74059 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.97219 | −0.248848 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25.3346 | 0.903081 | 0.451541 | − | 0.892251i | \(-0.350875\pi\) | ||||
0.451541 | + | 0.892251i | \(0.350875\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −47.8023 | −1.69966 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.22910 | −0.150180 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.56341 | −0.232488 | −0.116244 | − | 0.993221i | \(-0.537085\pi\) | ||||
−0.116244 | + | 0.993221i | \(0.537085\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.8211 | −0.382824 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −37.9136 | −1.33794 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.20659 | 0.113017 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 13.0910 | 0.460254 | 0.230127 | − | 0.973161i | \(-0.426086\pi\) | ||||
0.230127 | + | 0.973161i | \(0.426086\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.0233 | 1.26495 | 0.632475 | − | 0.774581i | \(-0.282039\pi\) | ||||
0.632475 | + | 0.774581i | \(0.282039\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.58464 | 0.335735 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.5480 | 0.404013 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4828 | 0.400753 | 0.200376 | − | 0.979719i | \(-0.435784\pi\) | ||||
0.200376 | + | 0.979719i | \(0.435784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −55.5316 | −1.93571 | −0.967855 | − | 0.251509i | \(-0.919073\pi\) | ||||
−0.967855 | + | 0.251509i | \(0.919073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.3188 | −0.880420 | −0.440210 | − | 0.897895i | \(-0.645096\pi\) | ||||
−0.440210 | + | 0.897895i | \(0.645096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.70766 | 0.163504 | 0.0817519 | − | 0.996653i | \(-0.473948\pi\) | ||||
0.0817519 | + | 0.996653i | \(0.473948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −19.6536 | −0.680958 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.78479 | −0.304010 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19.9612 | 0.689138 | 0.344569 | − | 0.938761i | \(-0.388025\pi\) | ||||
0.344569 | + | 0.938761i | \(0.388025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.40806 | −0.255450 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.6426 | 0.434920 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 48.5389 | 1.66782 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.51188 | 0.223224 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.6148 | −0.842795 | −0.421398 | − | 0.906876i | \(-0.638460\pi\) | ||||
−0.421398 | + | 0.906876i | \(0.638460\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 22.4111 | 0.765548 | 0.382774 | − | 0.923842i | \(-0.374969\pi\) | ||||
0.382774 | + | 0.923842i | \(0.374969\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.46831 | 0.220696 | 0.110348 | − | 0.993893i | \(-0.464803\pi\) | ||||
0.110348 | + | 0.993893i | \(0.464803\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.58867 | 0.0540789 | 0.0270395 | − | 0.999634i | \(-0.491392\pi\) | ||||
0.0270395 | + | 0.999634i | \(0.491392\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.2193 | 0.687478 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −30.4809 | −1.03399 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.0590027 | 0.00199923 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.20659 | −0.108403 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.7991 | −0.601032 | −0.300516 | − | 0.953777i | \(-0.597159\pi\) | ||||
−0.300516 | + | 0.953777i | \(0.597159\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.56857 | 0.153919 | 0.0769595 | − | 0.997034i | \(-0.475479\pi\) | ||||
0.0769595 | + | 0.997034i | \(0.475479\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.86016 | 0.298168 | 0.149084 | − | 0.988825i | \(-0.452367\pi\) | ||||
0.149084 | + | 0.988825i | \(0.452367\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.0417 | −1.51235 | −0.756176 | − | 0.654368i | \(-0.772935\pi\) | ||||
−0.756176 | + | 0.654368i | \(0.772935\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2801 | 0.780790 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.62473 | −0.188224 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.66502 | −0.222787 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.7529 | −0.525388 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.7148 | 1.62292 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −20.2331 | −0.672572 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.8393 | −1.52207 | −0.761035 | − | 0.648711i | \(-0.775308\pi\) | ||||
−0.761035 | + | 0.648711i | \(0.775308\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0322 | 1.59138 | 0.795689 | − | 0.605705i | \(-0.207109\pi\) | ||||
0.795689 | + | 0.605705i | \(0.207109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.2737 | 0.770247 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.53687 | 0.281912 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.0155 | −0.825187 | −0.412593 | − | 0.910915i | \(-0.635377\pi\) | ||||
−0.412593 | + | 0.910915i | \(0.635377\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.68777 | −0.187215 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.51188 | −0.214109 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −53.0509 | −1.74054 | −0.870272 | − | 0.492572i | \(-0.836057\pi\) | ||||
−0.870272 | + | 0.492572i | \(0.836057\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.2158 | −0.334809 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.6129 | 1.00115 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.2729 | 1.28299 | 0.641494 | − | 0.767128i | \(-0.278315\pi\) | ||||
0.641494 | + | 0.767128i | \(0.278315\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.6157 | −0.378661 | −0.189331 | − | 0.981913i | \(-0.560632\pi\) | ||||
−0.189331 | + | 0.981913i | \(0.560632\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.4767 | 0.373733 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.4740 | −0.600323 | −0.300161 | − | 0.953888i | \(-0.597041\pi\) | ||||
−0.300161 | + | 0.953888i | \(0.597041\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.43318 | −0.143907 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29.4785 | 0.954903 | 0.477451 | − | 0.878658i | \(-0.341561\pi\) | ||||
0.477451 | + | 0.878658i | \(0.341561\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.9169 | 0.450339 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 62.6694 | 2.02370 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.5071 | −0.629263 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.8113 | 0.863086 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.25644 | 0.297667 | 0.148834 | − | 0.988862i | \(-0.452448\pi\) | ||||
0.148834 | + | 0.988862i | \(0.452448\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.2356 | −0.874031 | −0.437015 | − | 0.899454i | \(-0.643964\pi\) | ||||
−0.437015 | + | 0.899454i | \(0.643964\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.48441 | −0.111705 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.2495 | 1.06374 | 0.531872 | − | 0.846825i | \(-0.321489\pi\) | ||||
0.531872 | + | 0.846825i | \(0.321489\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −56.1227 | −1.79369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5093 | 0.398983 | 0.199492 | − | 0.979900i | \(-0.436071\pi\) | ||||
0.199492 | + | 0.979900i | \(0.436071\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.4183 | −0.682444 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.71025 | 0.117979 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27.8833 | −0.885743 | −0.442871 | − | 0.896585i | \(-0.646040\pi\) | ||||
−0.442871 | + | 0.896585i | \(0.646040\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.1628 | −0.512396 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.3248 | 1.40378 | 0.701890 | − | 0.712285i | \(-0.252340\pi\) | ||||
0.701890 | + | 0.712285i | \(0.252340\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8280.2.a.bt.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 8280.2.a.bu.1.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8280.2.a.bt.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8280.2.a.bu.1.6 | yes | 6 | 3.2 | odd | 2 |