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: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 570) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.48119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8550.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.35026 | −1.26628 | −0.633140 | − | 0.774037i | \(-0.718234\pi\) | ||||
−0.633140 | + | 0.774037i | \(0.718234\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.962389 | 0.290171 | 0.145086 | − | 0.989419i | \(-0.453654\pi\) | ||||
0.145086 | + | 0.989419i | \(0.453654\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.61213 | −0.447124 | −0.223562 | − | 0.974690i | \(-0.571768\pi\) | ||||
−0.223562 | + | 0.974690i | \(0.571768\pi\) | |||||||
\(14\) | −3.35026 | −0.895395 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.387873 | 0.0940731 | 0.0470365 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470365 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.962389 | 0.205182 | ||||||||
\(23\) | 0.962389 | 0.200672 | 0.100336 | − | 0.994954i | \(-0.468008\pi\) | ||||
0.100336 | + | 0.994954i | \(0.468008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1.61213 | −0.316164 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.35026 | −0.633140 | ||||||||
\(29\) | −6.96239 | −1.29288 | −0.646442 | − | 0.762964i | \(-0.723744\pi\) | ||||
−0.646442 | + | 0.762964i | \(0.723744\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.35026 | 0.601725 | 0.300862 | − | 0.953668i | \(-0.402726\pi\) | ||||
0.300862 | + | 0.953668i | \(0.402726\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.387873 | 0.0665197 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.61213 | −0.265032 | −0.132516 | − | 0.991181i | \(-0.542306\pi\) | ||||
−0.132516 | + | 0.991181i | \(0.542306\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.27504 | 1.44852 | 0.724259 | − | 0.689528i | \(-0.242182\pi\) | ||||
0.724259 | + | 0.689528i | \(0.242182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.18664 | 0.943454 | 0.471727 | − | 0.881745i | \(-0.343631\pi\) | ||||
0.471727 | + | 0.881745i | \(0.343631\pi\) | |||||||
\(44\) | 0.962389 | 0.145086 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.962389 | 0.141896 | ||||||||
\(47\) | −0.962389 | −0.140379 | −0.0701894 | − | 0.997534i | \(-0.522360\pi\) | ||||
−0.0701894 | + | 0.997534i | \(0.522360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22425 | 0.603465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.61213 | −0.223562 | ||||||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.35026 | −0.447698 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.96239 | −0.914206 | ||||||||
\(59\) | −10.3127 | −1.34259 | −0.671296 | − | 0.741189i | \(-0.734262\pi\) | ||||
−0.671296 | + | 0.741189i | \(0.734262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.9248 | 1.52681 | 0.763406 | − | 0.645919i | \(-0.223526\pi\) | ||||
0.763406 | + | 0.645919i | \(0.223526\pi\) | |||||||
\(62\) | 3.35026 | 0.425484 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.22425 | −0.882583 | −0.441292 | − | 0.897364i | \(-0.645480\pi\) | ||||
−0.441292 | + | 0.897364i | \(0.645480\pi\) | |||||||
\(68\) | 0.387873 | 0.0470365 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.22425 | −0.857361 | −0.428681 | − | 0.903456i | \(-0.641021\pi\) | ||||
−0.428681 | + | 0.903456i | \(0.641021\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.22425 | −0.377370 | −0.188685 | − | 0.982038i | \(-0.560423\pi\) | ||||
−0.188685 | + | 0.982038i | \(0.560423\pi\) | |||||||
\(74\) | −1.61213 | −0.187406 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −3.22425 | −0.367438 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.35026 | −0.376934 | −0.188467 | − | 0.982080i | \(-0.560352\pi\) | ||||
−0.188467 | + | 0.982080i | \(0.560352\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.27504 | 1.02426 | ||||||||
\(83\) | −15.0132 | −1.64791 | −0.823955 | − | 0.566655i | \(-0.808237\pi\) | ||||
−0.823955 | + | 0.566655i | \(0.808237\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.18664 | 0.667123 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.962389 | 0.102591 | ||||||||
\(89\) | −4.64974 | −0.492871 | −0.246436 | − | 0.969159i | \(-0.579259\pi\) | ||||
−0.246436 | + | 0.969159i | \(0.579259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.40105 | 0.566184 | ||||||||
\(92\) | 0.962389 | 0.100336 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.962389 | −0.0992628 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.9624 | −1.11306 | −0.556531 | − | 0.830827i | \(-0.687868\pi\) | ||||
−0.556531 | + | 0.830827i | \(0.687868\pi\) | |||||||
\(98\) | 4.22425 | 0.426714 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.72496 | −0.271144 | −0.135572 | − | 0.990768i | \(-0.543287\pi\) | ||||
−0.135572 | + | 0.990768i | \(0.543287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.574515 | 0.0566087 | 0.0283043 | − | 0.999599i | \(-0.490989\pi\) | ||||
0.0283043 | + | 0.999599i | \(0.490989\pi\) | |||||||
\(104\) | −1.61213 | −0.158082 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −10.7005 | −1.03446 | −0.517229 | − | 0.855847i | \(-0.673037\pi\) | ||||
−0.517229 | + | 0.855847i | \(0.673037\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.1260 | 0.969896 | 0.484948 | − | 0.874543i | \(-0.338839\pi\) | ||||
0.484948 | + | 0.874543i | \(0.338839\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.35026 | −0.316570 | ||||||||
\(113\) | −20.5501 | −1.93319 | −0.966594 | − | 0.256311i | \(-0.917493\pi\) | ||||
−0.966594 | + | 0.256311i | \(0.917493\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.96239 | −0.646442 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −10.3127 | −0.949356 | ||||||||
\(119\) | −1.29948 | −0.119123 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.0738 | −0.915801 | ||||||||
\(122\) | 11.9248 | 1.07962 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.35026 | 0.300862 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.35026 | 0.119816 | 0.0599082 | − | 0.998204i | \(-0.480919\pi\) | ||||
0.0599082 | + | 0.998204i | \(0.480919\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4387 | −1.08677 | −0.543385 | − | 0.839483i | \(-0.682858\pi\) | ||||
−0.543385 | + | 0.839483i | \(0.682858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.35026 | −0.290505 | ||||||||
\(134\) | −7.22425 | −0.624080 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.387873 | 0.0332598 | ||||||||
\(137\) | 18.1622 | 1.55170 | 0.775851 | − | 0.630916i | \(-0.217321\pi\) | ||||
0.775851 | + | 0.630916i | \(0.217321\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.77575 | 0.744349 | 0.372175 | − | 0.928163i | \(-0.378612\pi\) | ||||
0.372175 | + | 0.928163i | \(0.378612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.22425 | −0.606246 | ||||||||
\(143\) | −1.55149 | −0.129742 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.22425 | −0.266841 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.61213 | −0.132516 | ||||||||
\(149\) | −15.9756 | −1.30877 | −0.654385 | − | 0.756162i | \(-0.727072\pi\) | ||||
−0.654385 | + | 0.756162i | \(0.727072\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.4241 | 1.49933 | 0.749665 | − | 0.661818i | \(-0.230215\pi\) | ||||
0.749665 | + | 0.661818i | \(0.230215\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.22425 | −0.259818 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.7889 | −1.10048 | −0.550238 | − | 0.835008i | \(-0.685463\pi\) | ||||
−0.550238 | + | 0.835008i | \(0.685463\pi\) | |||||||
\(158\) | −3.35026 | −0.266533 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.22425 | −0.254107 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.73813 | −0.292793 | −0.146397 | − | 0.989226i | \(-0.546768\pi\) | ||||
−0.146397 | + | 0.989226i | \(0.546768\pi\) | |||||||
\(164\) | 9.27504 | 0.724259 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0132 | −1.16525 | ||||||||
\(167\) | −15.4763 | −1.19759 | −0.598795 | − | 0.800902i | \(-0.704354\pi\) | ||||
−0.598795 | + | 0.800902i | \(0.704354\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4010 | −0.800081 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.18664 | 0.471727 | ||||||||
\(173\) | 1.47627 | 0.112239 | 0.0561194 | − | 0.998424i | \(-0.482127\pi\) | ||||
0.0561194 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.962389 | 0.0725428 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.64974 | −0.348513 | ||||||||
\(179\) | 14.3127 | 1.06978 | 0.534889 | − | 0.844922i | \(-0.320353\pi\) | ||||
0.534889 | + | 0.844922i | \(0.320353\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.82653 | −0.656071 | −0.328035 | − | 0.944665i | \(-0.606387\pi\) | ||||
−0.328035 | + | 0.944665i | \(0.606387\pi\) | |||||||
\(182\) | 5.40105 | 0.400352 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.962389 | 0.0709482 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.373285 | 0.0272973 | ||||||||
\(188\) | −0.962389 | −0.0701894 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.31265 | −0.167338 | −0.0836688 | − | 0.996494i | \(-0.526664\pi\) | ||||
−0.0836688 | + | 0.996494i | \(0.526664\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.58769 | 0.546174 | 0.273087 | − | 0.961989i | \(-0.411955\pi\) | ||||
0.273087 | + | 0.961989i | \(0.411955\pi\) | |||||||
\(194\) | −10.9624 | −0.787054 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.22425 | 0.301732 | ||||||||
\(197\) | 18.8119 | 1.34030 | 0.670148 | − | 0.742228i | \(-0.266231\pi\) | ||||
0.670148 | + | 0.742228i | \(0.266231\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.40105 | −0.666423 | −0.333211 | − | 0.942852i | \(-0.608132\pi\) | ||||
−0.333211 | + | 0.942852i | \(0.608132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.72496 | −0.191728 | ||||||||
\(203\) | 23.3258 | 1.63715 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.574515 | 0.0400284 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.61213 | −0.111781 | ||||||||
\(209\) | 0.962389 | 0.0665698 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.77575 | 0.328776 | 0.164388 | − | 0.986396i | \(-0.447435\pi\) | ||||
0.164388 | + | 0.986396i | \(0.447435\pi\) | |||||||
\(212\) | −6.00000 | −0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.7005 | −0.731473 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2243 | −0.761952 | ||||||||
\(218\) | 10.1260 | 0.685820 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.625301 | −0.0420623 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.6761 | −1.65243 | −0.826216 | − | 0.563353i | \(-0.809511\pi\) | ||||
−0.826216 | + | 0.563353i | \(0.809511\pi\) | |||||||
\(224\) | −3.35026 | −0.223849 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.5501 | −1.36697 | ||||||||
\(227\) | −15.4763 | −1.02720 | −0.513598 | − | 0.858031i | \(-0.671688\pi\) | ||||
−0.513598 | + | 0.858031i | \(0.671688\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.3258 | 1.40925 | 0.704625 | − | 0.709580i | \(-0.251115\pi\) | ||||
0.704625 | + | 0.709580i | \(0.251115\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.96239 | −0.457103 | ||||||||
\(233\) | 9.01317 | 0.590473 | 0.295236 | − | 0.955424i | \(-0.404602\pi\) | ||||
0.295236 | + | 0.955424i | \(0.404602\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.3127 | −0.671296 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.29948 | −0.0842326 | ||||||||
\(239\) | 0.135857 | 0.00878787 | 0.00439393 | − | 0.999990i | \(-0.498601\pi\) | ||||
0.00439393 | + | 0.999990i | \(0.498601\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −25.8496 | −1.66512 | −0.832558 | − | 0.553938i | \(-0.813125\pi\) | ||||
−0.832558 | + | 0.553938i | \(0.813125\pi\) | |||||||
\(242\) | −10.0738 | −0.647569 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.9248 | 0.763406 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.61213 | −0.102577 | ||||||||
\(248\) | 3.35026 | 0.212742 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.1114 | 0.638227 | 0.319114 | − | 0.947716i | \(-0.396615\pi\) | ||||
0.319114 | + | 0.947716i | \(0.396615\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.926192 | 0.0582292 | ||||||||
\(254\) | 1.35026 | 0.0847230 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −26.9986 | −1.68413 | −0.842063 | − | 0.539380i | \(-0.818659\pi\) | ||||
−0.842063 | + | 0.539380i | \(0.818659\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.40105 | 0.335605 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −12.4387 | −0.768463 | ||||||||
\(263\) | −15.0376 | −0.927259 | −0.463629 | − | 0.886029i | \(-0.653453\pi\) | ||||
−0.463629 | + | 0.886029i | \(0.653453\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.35026 | −0.205418 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.22425 | −0.441292 | ||||||||
\(269\) | 4.51388 | 0.275216 | 0.137608 | − | 0.990487i | \(-0.456059\pi\) | ||||
0.137608 | + | 0.990487i | \(0.456059\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8496 | 0.962792 | 0.481396 | − | 0.876503i | \(-0.340130\pi\) | ||||
0.481396 | + | 0.876503i | \(0.340130\pi\) | |||||||
\(272\) | 0.387873 | 0.0235183 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 18.1622 | 1.09722 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.3127 | 0.619627 | 0.309814 | − | 0.950797i | \(-0.399733\pi\) | ||||
0.309814 | + | 0.950797i | \(0.399733\pi\) | |||||||
\(278\) | 8.77575 | 0.526334 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.3488 | −1.45253 | −0.726265 | − | 0.687415i | \(-0.758746\pi\) | ||||
−0.726265 | + | 0.687415i | \(0.758746\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2882 | 1.56267 | 0.781336 | − | 0.624111i | \(-0.214539\pi\) | ||||
0.781336 | + | 0.624111i | \(0.214539\pi\) | |||||||
\(284\) | −7.22425 | −0.428681 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.55149 | −0.0917417 | ||||||||
\(287\) | −31.0738 | −1.83423 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8496 | −0.991150 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.22425 | −0.188685 | ||||||||
\(293\) | 13.0738 | 0.763780 | 0.381890 | − | 0.924208i | \(-0.375273\pi\) | ||||
0.381890 | + | 0.924208i | \(0.375273\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.61213 | −0.0937030 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −15.9756 | −0.925439 | ||||||||
\(299\) | −1.55149 | −0.0897251 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.7269 | −1.19468 | ||||||||
\(302\) | 18.4241 | 1.06019 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.07381 | −0.403724 | −0.201862 | − | 0.979414i | \(-0.564699\pi\) | ||||
−0.201862 | + | 0.979414i | \(0.564699\pi\) | |||||||
\(308\) | −3.22425 | −0.183719 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.3127 | −1.49205 | −0.746027 | − | 0.665916i | \(-0.768041\pi\) | ||||
−0.746027 | + | 0.665916i | \(0.768041\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.7005 | −1.05702 | −0.528508 | − | 0.848928i | \(-0.677248\pi\) | ||||
−0.528508 | + | 0.848928i | \(0.677248\pi\) | |||||||
\(314\) | −13.7889 | −0.778154 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.35026 | −0.188467 | ||||||||
\(317\) | −26.4749 | −1.48698 | −0.743488 | − | 0.668749i | \(-0.766830\pi\) | ||||
−0.743488 | + | 0.668749i | \(0.766830\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.70052 | −0.375157 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.22425 | −0.179681 | ||||||||
\(323\) | 0.387873 | 0.0215818 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.73813 | −0.207036 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.27504 | 0.512128 | ||||||||
\(329\) | 3.22425 | 0.177759 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −30.7005 | −1.68745 | −0.843727 | − | 0.536773i | \(-0.819643\pi\) | ||||
−0.843727 | + | 0.536773i | \(0.819643\pi\) | |||||||
\(332\) | −15.0132 | −0.823955 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.4763 | −0.846824 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.81194 | 0.371070 | 0.185535 | − | 0.982638i | \(-0.440598\pi\) | ||||
0.185535 | + | 0.982638i | \(0.440598\pi\) | |||||||
\(338\) | −10.4010 | −0.565742 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.22425 | 0.174603 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.29948 | 0.502125 | ||||||||
\(344\) | 6.18664 | 0.333561 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.47627 | 0.0793648 | ||||||||
\(347\) | −18.3879 | −0.987113 | −0.493556 | − | 0.869714i | \(-0.664303\pi\) | ||||
−0.493556 | + | 0.869714i | \(0.664303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.1490 | 1.66737 | 0.833685 | − | 0.552241i | \(-0.186227\pi\) | ||||
0.833685 | + | 0.552241i | \(0.186227\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.962389 | 0.0512955 | ||||||||
\(353\) | −7.61213 | −0.405153 | −0.202576 | − | 0.979266i | \(-0.564931\pi\) | ||||
−0.202576 | + | 0.979266i | \(0.564931\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.64974 | −0.246436 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.3127 | 0.756447 | ||||||||
\(359\) | 35.3112 | 1.86366 | 0.931828 | − | 0.362901i | \(-0.118214\pi\) | ||||
0.931828 | + | 0.362901i | \(0.118214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −8.82653 | −0.463912 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.40105 | 0.283092 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.9756 | 1.66911 | 0.834555 | − | 0.550924i | \(-0.185725\pi\) | ||||
0.834555 | + | 0.550924i | \(0.185725\pi\) | |||||||
\(368\) | 0.962389 | 0.0501680 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.1016 | 1.04362 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.4894 | 1.37157 | 0.685786 | − | 0.727804i | \(-0.259459\pi\) | ||||
0.685786 | + | 0.727804i | \(0.259459\pi\) | |||||||
\(374\) | 0.373285 | 0.0193021 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.962389 | −0.0496314 | ||||||||
\(377\) | 11.2243 | 0.578078 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3258 | −0.992701 | −0.496350 | − | 0.868122i | \(-0.665327\pi\) | ||||
−0.496350 | + | 0.868122i | \(0.665327\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.31265 | −0.118325 | ||||||||
\(383\) | −3.37470 | −0.172439 | −0.0862195 | − | 0.996276i | \(-0.527479\pi\) | ||||
−0.0862195 | + | 0.996276i | \(0.527479\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.58769 | 0.386203 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10.9624 | −0.556531 | ||||||||
\(389\) | 11.3503 | 0.575481 | 0.287741 | − | 0.957708i | \(-0.407096\pi\) | ||||
0.287741 | + | 0.957708i | \(0.407096\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.373285 | 0.0188778 | ||||||||
\(392\) | 4.22425 | 0.213357 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8119 | 0.947732 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.8364 | −0.945371 | −0.472685 | − | 0.881231i | \(-0.656715\pi\) | ||||
−0.472685 | + | 0.881231i | \(0.656715\pi\) | |||||||
\(398\) | −9.40105 | −0.471232 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.12601 | 0.206043 | 0.103022 | − | 0.994679i | \(-0.467149\pi\) | ||||
0.103022 | + | 0.994679i | \(0.467149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.40105 | −0.269045 | ||||||||
\(404\) | −2.72496 | −0.135572 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.3258 | 1.15764 | ||||||||
\(407\) | −1.55149 | −0.0769046 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.52373 | 0.124790 | 0.0623952 | − | 0.998052i | \(-0.480126\pi\) | ||||
0.0623952 | + | 0.998052i | \(0.480126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.574515 | 0.0283043 | ||||||||
\(413\) | 34.5501 | 1.70010 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.61213 | −0.0790410 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.962389 | 0.0470720 | ||||||||
\(419\) | −7.51247 | −0.367008 | −0.183504 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183504 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.67750 | 0.179230 | 0.0896152 | − | 0.995976i | \(-0.471436\pi\) | ||||
0.0896152 | + | 0.995976i | \(0.471436\pi\) | |||||||
\(422\) | 4.77575 | 0.232480 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −39.9511 | −1.93337 | ||||||||
\(428\) | −10.7005 | −0.517229 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.3272 | 0.497446 | 0.248723 | − | 0.968575i | \(-0.419989\pi\) | ||||
0.248723 | + | 0.968575i | \(0.419989\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 31.5877 | 1.51801 | 0.759004 | − | 0.651086i | \(-0.225686\pi\) | ||||
0.759004 | + | 0.651086i | \(0.225686\pi\) | |||||||
\(434\) | −11.2243 | −0.538781 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.1260 | 0.484948 | ||||||||
\(437\) | 0.962389 | 0.0460373 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −38.1524 | −1.82091 | −0.910456 | − | 0.413605i | \(-0.864269\pi\) | ||||
−0.910456 | + | 0.413605i | \(0.864269\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.625301 | −0.0297425 | ||||||||
\(443\) | −16.3127 | −0.775037 | −0.387519 | − | 0.921862i | \(-0.626668\pi\) | ||||
−0.387519 | + | 0.921862i | \(0.626668\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.6761 | −1.16845 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.35026 | −0.158285 | ||||||||
\(449\) | 37.5271 | 1.77101 | 0.885506 | − | 0.464629i | \(-0.153812\pi\) | ||||
0.885506 | + | 0.464629i | \(0.153812\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.92619 | 0.420318 | ||||||||
\(452\) | −20.5501 | −0.966594 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.4763 | −0.726337 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.00000 | −0.374224 | −0.187112 | − | 0.982339i | \(-0.559913\pi\) | ||||
−0.187112 | + | 0.982339i | \(0.559913\pi\) | |||||||
\(458\) | 21.3258 | 0.996490 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.3780 | −0.576502 | −0.288251 | − | 0.957555i | \(-0.593074\pi\) | ||||
−0.288251 | + | 0.957555i | \(0.593074\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 32.4504 | 1.50810 | 0.754049 | − | 0.656818i | \(-0.228098\pi\) | ||||
0.754049 | + | 0.656818i | \(0.228098\pi\) | |||||||
\(464\) | −6.96239 | −0.323221 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.01317 | 0.417527 | ||||||||
\(467\) | −7.53690 | −0.348766 | −0.174383 | − | 0.984678i | \(-0.555793\pi\) | ||||
−0.174383 | + | 0.984678i | \(0.555793\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.2031 | 1.11760 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.3127 | −0.474678 | ||||||||
\(473\) | 5.95395 | 0.273763 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.29948 | −0.0595614 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0.135857 | 0.00621396 | ||||||||
\(479\) | −15.2097 | −0.694947 | −0.347474 | − | 0.937690i | \(-0.612960\pi\) | ||||
−0.347474 | + | 0.937690i | \(0.612960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.59895 | 0.118502 | ||||||||
\(482\) | −25.8496 | −1.17741 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.0738 | −0.457900 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.19982 | −0.0543689 | −0.0271844 | − | 0.999630i | \(-0.508654\pi\) | ||||
−0.0271844 | + | 0.999630i | \(0.508654\pi\) | |||||||
\(488\) | 11.9248 | 0.539809 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.11283 | 0.230739 | 0.115369 | − | 0.993323i | \(-0.463195\pi\) | ||||
0.115369 | + | 0.993323i | \(0.463195\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.70052 | −0.121625 | ||||||||
\(494\) | −1.61213 | −0.0725330 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.35026 | 0.150431 | ||||||||
\(497\) | 24.2031 | 1.08566 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 14.2981 | 0.640069 | 0.320035 | − | 0.947406i | \(-0.396305\pi\) | ||||
0.320035 | + | 0.947406i | \(0.396305\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.1114 | 0.451295 | ||||||||
\(503\) | −11.5125 | −0.513316 | −0.256658 | − | 0.966502i | \(-0.582621\pi\) | ||||
−0.256658 | + | 0.966502i | \(0.582621\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.926192 | 0.0411742 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.35026 | 0.0599082 | ||||||||
\(509\) | 31.9610 | 1.41665 | 0.708323 | − | 0.705889i | \(-0.249452\pi\) | ||||
0.708323 | + | 0.705889i | \(0.249452\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8021 | 0.477857 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −26.9986 | −1.19086 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.926192 | −0.0407339 | ||||||||
\(518\) | 5.40105 | 0.237308 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.2750 | 1.45781 | 0.728903 | − | 0.684617i | \(-0.240031\pi\) | ||||
0.728903 | + | 0.684617i | \(0.240031\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.29948 | −0.406638 | −0.203319 | − | 0.979113i | \(-0.565173\pi\) | ||||
−0.203319 | + | 0.979113i | \(0.565173\pi\) | |||||||
\(524\) | −12.4387 | −0.543385 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0376 | −0.655671 | ||||||||
\(527\) | 1.29948 | 0.0566061 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0738 | −0.959731 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.35026 | −0.145252 | ||||||||
\(533\) | −14.9525 | −0.647666 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.22425 | −0.312040 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.51388 | 0.194607 | ||||||||
\(539\) | 4.06537 | 0.175108 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.5501 | 1.22746 | 0.613732 | − | 0.789515i | \(-0.289668\pi\) | ||||
0.613732 | + | 0.789515i | \(0.289668\pi\) | |||||||
\(542\) | 15.8496 | 0.680797 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.387873 | 0.0166299 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.4749 | −1.21750 | −0.608748 | − | 0.793363i | \(-0.708328\pi\) | ||||
−0.608748 | + | 0.793363i | \(0.708328\pi\) | |||||||
\(548\) | 18.1622 | 0.775851 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.96239 | −0.296608 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.2243 | 0.477304 | ||||||||
\(554\) | 10.3127 | 0.438143 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.77575 | 0.372175 | ||||||||
\(557\) | 4.88717 | 0.207076 | 0.103538 | − | 0.994626i | \(-0.466984\pi\) | ||||
0.103538 | + | 0.994626i | \(0.466984\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.97365 | −0.421841 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −24.3488 | −1.02709 | ||||||||
\(563\) | −30.8021 | −1.29815 | −0.649077 | − | 0.760723i | \(-0.724845\pi\) | ||||
−0.649077 | + | 0.760723i | \(0.724845\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.2882 | 1.10498 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.22425 | −0.303123 | ||||||||
\(569\) | 24.1260 | 1.01141 | 0.505707 | − | 0.862705i | \(-0.331232\pi\) | ||||
0.505707 | + | 0.862705i | \(0.331232\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.67276 | −0.237398 | −0.118699 | − | 0.992930i | \(-0.537872\pi\) | ||||
−0.118699 | + | 0.992930i | \(0.537872\pi\) | |||||||
\(572\) | −1.55149 | −0.0648712 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −31.0738 | −1.29700 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.0000 | −1.33218 | −0.666089 | − | 0.745873i | \(-0.732033\pi\) | ||||
−0.666089 | + | 0.745873i | \(0.732033\pi\) | |||||||
\(578\) | −16.8496 | −0.700849 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.2981 | 2.08672 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.77433 | −0.239148 | ||||||||
\(584\) | −3.22425 | −0.133421 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.0738 | 0.540074 | ||||||||
\(587\) | 13.6121 | 0.561833 | 0.280916 | − | 0.959732i | \(-0.409362\pi\) | ||||
0.280916 | + | 0.959732i | \(0.409362\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.35026 | 0.138045 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.61213 | −0.0662580 | ||||||||
\(593\) | −23.4617 | −0.963456 | −0.481728 | − | 0.876321i | \(-0.659991\pi\) | ||||
−0.481728 | + | 0.876321i | \(0.659991\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.9756 | −0.654385 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.55149 | −0.0634452 | ||||||||
\(599\) | −10.0263 | −0.409665 | −0.204833 | − | 0.978797i | \(-0.565665\pi\) | ||||
−0.204833 | + | 0.978797i | \(0.565665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.7743 | 0.480285 | 0.240143 | − | 0.970738i | \(-0.422806\pi\) | ||||
0.240143 | + | 0.970738i | \(0.422806\pi\) | |||||||
\(602\) | −20.7269 | −0.844764 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.4241 | 0.749665 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.4993 | 1.56264 | 0.781319 | − | 0.624132i | \(-0.214547\pi\) | ||||
0.781319 | + | 0.624132i | \(0.214547\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.55149 | 0.0627667 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.61213 | −0.307451 | −0.153725 | − | 0.988114i | \(-0.549127\pi\) | ||||
−0.153725 | + | 0.988114i | \(0.549127\pi\) | |||||||
\(614\) | −7.07381 | −0.285476 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.22425 | −0.129909 | ||||||||
\(617\) | 29.5369 | 1.18911 | 0.594555 | − | 0.804055i | \(-0.297328\pi\) | ||||
0.594555 | + | 0.804055i | \(0.297328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.5501 | −0.906364 | −0.453182 | − | 0.891418i | \(-0.649711\pi\) | ||||
−0.453182 | + | 0.891418i | \(0.649711\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.3127 | −1.05504 | ||||||||
\(623\) | 15.5778 | 0.624113 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.7005 | −0.747423 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −13.7889 | −0.550238 | ||||||||
\(629\) | −0.625301 | −0.0249324 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −37.9248 | −1.50976 | −0.754881 | − | 0.655862i | \(-0.772305\pi\) | ||||
−0.754881 | + | 0.655862i | \(0.772305\pi\) | |||||||
\(632\) | −3.35026 | −0.133266 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −26.4749 | −1.05145 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.81003 | −0.269823 | ||||||||
\(638\) | −6.70052 | −0.265276 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.67609 | −0.263690 | −0.131845 | − | 0.991270i | \(-0.542090\pi\) | ||||
−0.131845 | + | 0.991270i | \(0.542090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.2605 | −0.996175 | −0.498087 | − | 0.867127i | \(-0.665964\pi\) | ||||
−0.498087 | + | 0.867127i | \(0.665964\pi\) | |||||||
\(644\) | −3.22425 | −0.127053 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.387873 | 0.0152607 | ||||||||
\(647\) | 16.9135 | 0.664939 | 0.332469 | − | 0.943114i | \(-0.392118\pi\) | ||||
0.332469 | + | 0.943114i | \(0.392118\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.92478 | −0.389582 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.73813 | −0.146397 | ||||||||
\(653\) | 24.1114 | 0.943553 | 0.471776 | − | 0.881718i | \(-0.343613\pi\) | ||||
0.471776 | + | 0.881718i | \(0.343613\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.27504 | 0.362129 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.22425 | 0.125694 | ||||||||
\(659\) | 20.3879 | 0.794199 | 0.397099 | − | 0.917776i | \(-0.370017\pi\) | ||||
0.397099 | + | 0.917776i | \(0.370017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6023 | 0.684649 | 0.342325 | − | 0.939582i | \(-0.388786\pi\) | ||||
0.342325 | + | 0.939582i | \(0.388786\pi\) | |||||||
\(662\) | −30.7005 | −1.19321 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0132 | −0.582624 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.70052 | −0.259445 | ||||||||
\(668\) | −15.4763 | −0.598795 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.4763 | 0.443036 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −44.3634 | −1.71008 | −0.855042 | − | 0.518558i | \(-0.826469\pi\) | ||||
−0.855042 | + | 0.518558i | \(0.826469\pi\) | |||||||
\(674\) | 6.81194 | 0.262386 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.4010 | −0.400040 | ||||||||
\(677\) | 8.70052 | 0.334388 | 0.167194 | − | 0.985924i | \(-0.446529\pi\) | ||||
0.167194 | + | 0.985924i | \(0.446529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.7269 | 1.40945 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.22425 | 0.123463 | ||||||||
\(683\) | −37.8759 | −1.44928 | −0.724641 | − | 0.689127i | \(-0.757994\pi\) | ||||
−0.724641 | + | 0.689127i | \(0.757994\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.29948 | 0.355056 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.18664 | 0.235864 | ||||||||
\(689\) | 9.67276 | 0.368503 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.775746 | −0.0295108 | −0.0147554 | − | 0.999891i | \(-0.504697\pi\) | ||||
−0.0147554 | + | 0.999891i | \(0.504697\pi\) | |||||||
\(692\) | 1.47627 | 0.0561194 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.3879 | −0.697994 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.59754 | 0.136266 | ||||||||
\(698\) | 31.1490 | 1.17901 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −42.3752 | −1.60049 | −0.800245 | − | 0.599674i | \(-0.795297\pi\) | ||||
−0.800245 | + | 0.599674i | \(0.795297\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.61213 | −0.0608025 | ||||||||
\(704\) | 0.962389 | 0.0362714 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.61213 | −0.286486 | ||||||||
\(707\) | 9.12933 | 0.343344 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.2784 | 1.36246 | 0.681231 | − | 0.732068i | \(-0.261445\pi\) | ||||
0.681231 | + | 0.732068i | \(0.261445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.64974 | −0.174256 | ||||||||
\(713\) | 3.22425 | 0.120749 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.3127 | 0.534889 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 35.3112 | 1.31780 | ||||||||
\(719\) | 42.5355 | 1.58631 | 0.793153 | − | 0.609022i | \(-0.208438\pi\) | ||||
0.793153 | + | 0.609022i | \(0.208438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.92478 | −0.0716824 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.82653 | −0.328035 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.378024 | 0.0140201 | 0.00701007 | − | 0.999975i | \(-0.497769\pi\) | ||||
0.00701007 | + | 0.999975i | \(0.497769\pi\) | |||||||
\(728\) | 5.40105 | 0.200176 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.39963 | 0.0887536 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −26.0118 | −0.960766 | −0.480383 | − | 0.877059i | \(-0.659502\pi\) | ||||
−0.480383 | + | 0.877059i | \(0.659502\pi\) | |||||||
\(734\) | 31.9756 | 1.18024 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.962389 | 0.0354741 | ||||||||
\(737\) | −6.95254 | −0.256100 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.8773 | −1.65084 | −0.825419 | − | 0.564520i | \(-0.809061\pi\) | ||||
−0.825419 | + | 0.564520i | \(0.809061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20.1016 | 0.737952 | ||||||||
\(743\) | −4.67418 | −0.171479 | −0.0857394 | − | 0.996318i | \(-0.527325\pi\) | ||||
−0.0857394 | + | 0.996318i | \(0.527325\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.4894 | 0.969847 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.373285 | 0.0136486 | ||||||||
\(749\) | 35.8496 | 1.30991 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.57452 | −0.239907 | −0.119954 | − | 0.992779i | \(-0.538275\pi\) | ||||
−0.119954 | + | 0.992779i | \(0.538275\pi\) | |||||||
\(752\) | −0.962389 | −0.0350947 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 11.2243 | 0.408763 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5633 | 0.565656 | 0.282828 | − | 0.959171i | \(-0.408727\pi\) | ||||
0.282828 | + | 0.959171i | \(0.408727\pi\) | |||||||
\(758\) | −19.3258 | −0.701946 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8759 | 0.865501 | 0.432750 | − | 0.901514i | \(-0.357543\pi\) | ||||
0.432750 | + | 0.901514i | \(0.357543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.9248 | −1.22816 | ||||||||
\(764\) | −2.31265 | −0.0836688 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.37470 | −0.121933 | ||||||||
\(767\) | 16.6253 | 0.600305 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.4749 | 1.09895 | 0.549476 | − | 0.835510i | \(-0.314827\pi\) | ||||
0.549476 | + | 0.835510i | \(0.314827\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.58769 | 0.273087 | ||||||||
\(773\) | 16.3272 | 0.587250 | 0.293625 | − | 0.955921i | \(-0.405138\pi\) | ||||
0.293625 | + | 0.955921i | \(0.405138\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −10.9624 | −0.393527 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.3503 | 0.406927 | ||||||||
\(779\) | 9.27504 | 0.332313 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.95254 | −0.248781 | ||||||||
\(782\) | 0.373285 | 0.0133486 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.22425 | 0.150866 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.9525 | −1.10334 | −0.551669 | − | 0.834063i | \(-0.686009\pi\) | ||||
−0.551669 | + | 0.834063i | \(0.686009\pi\) | |||||||
\(788\) | 18.8119 | 0.670148 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 68.8481 | 2.44796 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.2243 | −0.682673 | ||||||||
\(794\) | −18.8364 | −0.668478 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.40105 | −0.333211 | ||||||||
\(797\) | 14.8773 | 0.526982 | 0.263491 | − | 0.964662i | \(-0.415126\pi\) | ||||
0.263491 | + | 0.964662i | \(0.415126\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.373285 | −0.0132059 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.12601 | 0.145694 | ||||||||
\(803\) | −3.10299 | −0.109502 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.40105 | −0.190244 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.72496 | −0.0958638 | ||||||||
\(809\) | −25.4471 | −0.894672 | −0.447336 | − | 0.894366i | \(-0.647627\pi\) | ||||
−0.447336 | + | 0.894366i | \(0.647627\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −53.3522 | −1.87345 | −0.936724 | − | 0.350069i | \(-0.886158\pi\) | ||||
−0.936724 | + | 0.350069i | \(0.886158\pi\) | |||||||
\(812\) | 23.3258 | 0.818576 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.55149 | −0.0543798 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.18664 | 0.216443 | ||||||||
\(818\) | 2.52373 | 0.0882402 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.9756 | 0.976354 | 0.488177 | − | 0.872745i | \(-0.337662\pi\) | ||||
0.488177 | + | 0.872745i | \(0.337662\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.87399 | 0.274470 | 0.137235 | − | 0.990539i | \(-0.456178\pi\) | ||||
0.137235 | + | 0.990539i | \(0.456178\pi\) | |||||||
\(824\) | 0.574515 | 0.0200142 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 34.5501 | 1.20215 | ||||||||
\(827\) | 40.1016 | 1.39447 | 0.697234 | − | 0.716843i | \(-0.254414\pi\) | ||||
0.697234 | + | 0.716843i | \(0.254414\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 47.2262 | 1.64023 | 0.820116 | − | 0.572197i | \(-0.193909\pi\) | ||||
0.820116 | + | 0.572197i | \(0.193909\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.61213 | −0.0558904 | ||||||||
\(833\) | 1.63847 | 0.0567698 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.962389 | 0.0332849 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −7.51247 | −0.259514 | ||||||||
\(839\) | 3.89843 | 0.134589 | 0.0672944 | − | 0.997733i | \(-0.478563\pi\) | ||||
0.0672944 | + | 0.997733i | \(0.478563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.4749 | 0.671547 | ||||||||
\(842\) | 3.67750 | 0.126735 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.77575 | 0.164388 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 33.7499 | 1.15966 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.55149 | −0.0531845 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.1900 | −1.20488 | −0.602441 | − | 0.798164i | \(-0.705805\pi\) | ||||
−0.602441 | + | 0.798164i | \(0.705805\pi\) | |||||||
\(854\) | −39.9511 | −1.36710 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.7005 | −0.365736 | ||||||||
\(857\) | −12.1768 | −0.415951 | −0.207976 | − | 0.978134i | \(-0.566687\pi\) | ||||
−0.207976 | + | 0.978134i | \(0.566687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.3522 | 1.95683 | 0.978415 | − | 0.206648i | \(-0.0662554\pi\) | ||||
0.978415 | + | 0.206648i | \(0.0662554\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.3272 | 0.351747 | ||||||||
\(863\) | 14.0752 | 0.479126 | 0.239563 | − | 0.970881i | \(-0.422996\pi\) | ||||
0.239563 | + | 0.970881i | \(0.422996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 31.5877 | 1.07339 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.2243 | −0.380976 | ||||||||
\(869\) | −3.22425 | −0.109375 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.6464 | 0.394624 | ||||||||
\(872\) | 10.1260 | 0.342910 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.962389 | 0.0325533 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.8627 | 0.636949 | 0.318475 | − | 0.947931i | \(-0.396829\pi\) | ||||
0.318475 | + | 0.947931i | \(0.396829\pi\) | |||||||
\(878\) | −38.1524 | −1.28758 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.1490 | 0.645147 | 0.322574 | − | 0.946544i | \(-0.395452\pi\) | ||||
0.322574 | + | 0.946544i | \(0.395452\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.9135 | 1.44415 | 0.722077 | − | 0.691812i | \(-0.243187\pi\) | ||||
0.722077 | + | 0.691812i | \(0.243187\pi\) | |||||||
\(884\) | −0.625301 | −0.0210311 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.3127 | −0.548034 | ||||||||
\(887\) | −22.7005 | −0.762209 | −0.381104 | − | 0.924532i | \(-0.624456\pi\) | ||||
−0.381104 | + | 0.924532i | \(0.624456\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.52373 | −0.151721 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.6761 | −0.826216 | ||||||||
\(893\) | −0.962389 | −0.0322051 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.35026 | −0.111924 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.5271 | 1.25229 | ||||||||
\(899\) | −23.3258 | −0.777960 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.32724 | −0.0775316 | ||||||||
\(902\) | 8.92619 | 0.297210 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −20.5501 | −0.683485 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.5501 | 0.483127 | 0.241564 | − | 0.970385i | \(-0.422340\pi\) | ||||
0.241564 | + | 0.970385i | \(0.422340\pi\) | |||||||
\(908\) | −15.4763 | −0.513598 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.998585 | 0.0330846 | 0.0165423 | − | 0.999863i | \(-0.494734\pi\) | ||||
0.0165423 | + | 0.999863i | \(0.494734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.4485 | −0.478176 | ||||||||
\(914\) | −8.00000 | −0.264616 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 21.3258 | 0.704625 | ||||||||
\(917\) | 41.6728 | 1.37616 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33.7743 | −1.11411 | −0.557056 | − | 0.830475i | \(-0.688069\pi\) | ||||
−0.557056 | + | 0.830475i | \(0.688069\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −12.3780 | −0.407649 | ||||||||
\(923\) | 11.6464 | 0.383346 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 32.4504 | 1.06639 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.96239 | −0.228552 | ||||||||
\(929\) | −14.8773 | −0.488109 | −0.244054 | − | 0.969762i | \(-0.578478\pi\) | ||||
−0.244054 | + | 0.969762i | \(0.578478\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.22425 | 0.138444 | ||||||||
\(932\) | 9.01317 | 0.295236 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.53690 | −0.246615 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22.2981 | 0.728446 | 0.364223 | − | 0.931312i | \(-0.381335\pi\) | ||||
0.364223 | + | 0.931312i | \(0.381335\pi\) | |||||||
\(938\) | 24.2031 | 0.790261 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.3634 | 1.18541 | 0.592707 | − | 0.805418i | \(-0.298059\pi\) | ||||
0.592707 | + | 0.805418i | \(0.298059\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.92619 | 0.290677 | ||||||||
\(944\) | −10.3127 | −0.335648 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.95395 | 0.193580 | ||||||||
\(947\) | −50.3390 | −1.63580 | −0.817899 | − | 0.575362i | \(-0.804861\pi\) | ||||
−0.817899 | + | 0.575362i | \(0.804861\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.19791 | 0.168731 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.29948 | −0.0421163 | ||||||||
\(953\) | 16.3272 | 0.528891 | 0.264446 | − | 0.964401i | \(-0.414811\pi\) | ||||
0.264446 | + | 0.964401i | \(0.414811\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.135857 | 0.00439393 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −15.2097 | −0.491402 | ||||||||
\(959\) | −60.8481 | −1.96489 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.7757 | −0.637927 | ||||||||
\(962\) | 2.59895 | 0.0837936 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −25.8496 | −0.832558 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.276454 | 0.00889015 | 0.00444507 | − | 0.999990i | \(-0.498585\pi\) | ||||
0.00444507 | + | 0.999990i | \(0.498585\pi\) | |||||||
\(968\) | −10.0738 | −0.323784 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.9102 | −1.21660 | −0.608298 | − | 0.793709i | \(-0.708147\pi\) | ||||
−0.608298 | + | 0.793709i | \(0.708147\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.4010 | −0.942554 | ||||||||
\(974\) | −1.19982 | −0.0384446 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.9248 | 0.381703 | ||||||||
\(977\) | −28.3996 | −0.908585 | −0.454292 | − | 0.890853i | \(-0.650108\pi\) | ||||
−0.454292 | + | 0.890853i | \(0.650108\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.47486 | −0.143017 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.11283 | 0.163157 | ||||||||
\(983\) | 0.926192 | 0.0295409 | 0.0147705 | − | 0.999891i | \(-0.495298\pi\) | ||||
0.0147705 | + | 0.999891i | \(0.495298\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.70052 | −0.0860022 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.61213 | −0.0512886 | ||||||||
\(989\) | 5.95395 | 0.189325 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.5256 | 0.969679 | 0.484839 | − | 0.874603i | \(-0.338878\pi\) | ||||
0.484839 | + | 0.874603i | \(0.338878\pi\) | |||||||
\(992\) | 3.35026 | 0.106371 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.2031 | 0.767677 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.0132 | 0.665494 | 0.332747 | − | 0.943016i | \(-0.392025\pi\) | ||||
0.332747 | + | 0.943016i | \(0.392025\pi\) | |||||||
\(998\) | 14.2981 | 0.452597 | ||||||||
\(999\) | 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.cq.1.1 | 3 | ||
3.2 | odd | 2 | 2850.2.a.bl.1.1 | 3 | |||
5.2 | odd | 4 | 1710.2.d.f.1369.6 | 6 | |||
5.3 | odd | 4 | 1710.2.d.f.1369.3 | 6 | |||
5.4 | even | 2 | 8550.2.a.ce.1.3 | 3 | |||
15.2 | even | 4 | 570.2.d.c.229.1 | ✓ | 6 | ||
15.8 | even | 4 | 570.2.d.c.229.4 | yes | 6 | ||
15.14 | odd | 2 | 2850.2.a.bm.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.c.229.1 | ✓ | 6 | 15.2 | even | 4 | ||
570.2.d.c.229.4 | yes | 6 | 15.8 | even | 4 | ||
1710.2.d.f.1369.3 | 6 | 5.3 | odd | 4 | |||
1710.2.d.f.1369.6 | 6 | 5.2 | odd | 4 | |||
2850.2.a.bl.1.1 | 3 | 3.2 | odd | 2 | |||
2850.2.a.bm.1.3 | 3 | 15.14 | odd | 2 | |||
8550.2.a.ce.1.3 | 3 | 5.4 | even | 2 | |||
8550.2.a.cq.1.1 | 3 | 1.1 | even | 1 | trivial |