Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(1,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, 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("819.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.199374400.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 8x^{4} + 10x^{2} - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-2.54574\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 819.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.15293 | 1.52235 | 0.761174 | − | 0.648548i | \(-0.224623\pi\) | ||||
0.761174 | + | 0.648548i | \(0.224623\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.63509 | 1.31754 | ||||||||
\(5\) | 4.16251 | 1.86153 | 0.930765 | − | 0.365617i | \(-0.119142\pi\) | ||||
0.930765 | + | 0.365617i | \(0.119142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 1.36730 | 0.483413 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.96157 | 2.83390 | ||||||||
\(11\) | −0.785627 | −0.236875 | −0.118438 | − | 0.992961i | \(-0.537789\pi\) | ||||
−0.118438 | + | 0.992961i | \(0.537789\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | −2.15293 | −0.575394 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.32648 | −0.581621 | ||||||||
\(17\) | 5.87710 | 1.42541 | 0.712704 | − | 0.701465i | \(-0.247470\pi\) | ||||
0.712704 | + | 0.701465i | \(0.247470\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.59666 | −1.97221 | −0.986105 | − | 0.166125i | \(-0.946875\pi\) | ||||
−0.986105 | + | 0.166125i | \(0.946875\pi\) | |||||||
\(20\) | 10.9686 | 2.45265 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.69140 | −0.360607 | ||||||||
\(23\) | 0.928968 | 0.193703 | 0.0968517 | − | 0.995299i | \(-0.469123\pi\) | ||||
0.0968517 | + | 0.995299i | \(0.469123\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.3265 | 2.46530 | ||||||||
\(26\) | 2.15293 | 0.422223 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.63509 | −0.497985 | ||||||||
\(29\) | −5.23482 | −0.972082 | −0.486041 | − | 0.873936i | \(-0.661559\pi\) | ||||
−0.486041 | + | 0.873936i | \(0.661559\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.32648 | −0.956665 | −0.478332 | − | 0.878179i | \(-0.658759\pi\) | ||||
−0.478332 | + | 0.878179i | \(0.658759\pi\) | |||||||
\(32\) | −7.74335 | −1.36884 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.6530 | 2.16997 | ||||||||
\(35\) | −4.16251 | −0.703593 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.27018 | −0.208816 | −0.104408 | − | 0.994535i | \(-0.533295\pi\) | ||||
−0.104408 | + | 0.994535i | \(0.533295\pi\) | |||||||
\(38\) | −18.5080 | −3.00239 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.69140 | 0.899889 | ||||||||
\(41\) | −1.07231 | −0.167467 | −0.0837334 | − | 0.996488i | \(-0.526684\pi\) | ||||
−0.0837334 | + | 0.996488i | \(0.526684\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.59666 | 1.31098 | 0.655489 | − | 0.755204i | \(-0.272462\pi\) | ||||
0.655489 | + | 0.755204i | \(0.272462\pi\) | |||||||
\(44\) | −2.07020 | −0.312094 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | −1.71459 | −0.250099 | −0.125050 | − | 0.992150i | \(-0.539909\pi\) | ||||
−0.125050 | + | 0.992150i | \(0.539909\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 26.5380 | 3.75304 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.63509 | 0.365421 | ||||||||
\(53\) | 6.80607 | 0.934886 | 0.467443 | − | 0.884023i | \(-0.345175\pi\) | ||||
0.467443 | + | 0.884023i | \(0.345175\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.27018 | −0.440951 | ||||||||
\(56\) | −1.36730 | −0.182713 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −11.2702 | −1.47985 | ||||||||
\(59\) | −13.7032 | −1.78400 | −0.892001 | − | 0.452033i | \(-0.850699\pi\) | ||||
−0.892001 | + | 0.452033i | \(0.850699\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0000 | 1.28037 | 0.640184 | − | 0.768221i | \(-0.278858\pi\) | ||||
0.640184 | + | 0.768221i | \(0.278858\pi\) | |||||||
\(62\) | −11.4675 | −1.45638 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.0179 | −1.50223 | ||||||||
\(65\) | 4.16251 | 0.516296 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.729822 | 0.0891620 | 0.0445810 | − | 0.999006i | \(-0.485805\pi\) | ||||
0.0445810 | + | 0.999006i | \(0.485805\pi\) | |||||||
\(68\) | 15.4867 | 1.87804 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −8.96157 | −1.07111 | ||||||||
\(71\) | −7.53939 | −0.894761 | −0.447381 | − | 0.894344i | \(-0.647643\pi\) | ||||
−0.447381 | + | 0.894344i | \(0.647643\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.32648 | −0.857500 | −0.428750 | − | 0.903423i | \(-0.641046\pi\) | ||||
−0.428750 | + | 0.903423i | \(0.641046\pi\) | |||||||
\(74\) | −2.73460 | −0.317891 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.6530 | −2.59847 | ||||||||
\(77\) | 0.785627 | 0.0895305 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0563 | 1.13142 | 0.565711 | − | 0.824603i | \(-0.308602\pi\) | ||||
0.565711 | + | 0.824603i | \(0.308602\pi\) | |||||||
\(80\) | −9.68401 | −1.08271 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.30860 | −0.254943 | ||||||||
\(83\) | 10.0396 | 1.10199 | 0.550995 | − | 0.834508i | \(-0.314248\pi\) | ||||
0.550995 | + | 0.834508i | \(0.314248\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 24.4635 | 2.65344 | ||||||||
\(86\) | 18.5080 | 1.99577 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.07419 | −0.114509 | ||||||||
\(89\) | −16.2034 | −1.71756 | −0.858779 | − | 0.512347i | \(-0.828776\pi\) | ||||
−0.858779 | + | 0.512347i | \(0.828776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 2.44791 | 0.255213 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.69140 | −0.380738 | ||||||||
\(95\) | −35.7837 | −3.67133 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.5967 | −1.07593 | −0.537964 | − | 0.842968i | \(-0.680806\pi\) | ||||
−0.537964 | + | 0.842968i | \(0.680806\pi\) | |||||||
\(98\) | 2.15293 | 0.217478 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 32.4814 | 3.24814 | ||||||||
\(101\) | −11.0596 | −1.10047 | −0.550237 | − | 0.835009i | \(-0.685462\pi\) | ||||
−0.550237 | + | 0.835009i | \(0.685462\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.9231 | 1.37189 | 0.685944 | − | 0.727654i | \(-0.259389\pi\) | ||||
0.685944 | + | 0.727654i | \(0.259389\pi\) | |||||||
\(104\) | 1.36730 | 0.134075 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 14.6530 | 1.42322 | ||||||||
\(107\) | 7.73504 | 0.747775 | 0.373887 | − | 0.927474i | \(-0.378025\pi\) | ||||
0.373887 | + | 0.927474i | \(0.378025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | −7.04045 | −0.671281 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.32648 | 0.219832 | ||||||||
\(113\) | 5.23482 | 0.492450 | 0.246225 | − | 0.969213i | \(-0.420810\pi\) | ||||
0.246225 | + | 0.969213i | \(0.420810\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.86684 | 0.360585 | ||||||||
\(116\) | −13.7942 | −1.28076 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −29.5019 | −2.71587 | ||||||||
\(119\) | −5.87710 | −0.538753 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3828 | −0.943890 | ||||||||
\(122\) | 21.5293 | 1.94917 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.0358 | −1.26045 | ||||||||
\(125\) | 30.4966 | 2.72770 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.00000 | 0.354943 | 0.177471 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177471 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(128\) | −10.3869 | −0.918082 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.96157 | 0.785982 | ||||||||
\(131\) | −6.46708 | −0.565032 | −0.282516 | − | 0.959263i | \(-0.591169\pi\) | ||||
−0.282516 | + | 0.959263i | \(0.591169\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.59666 | 0.745425 | ||||||||
\(134\) | 1.57125 | 0.135736 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.03576 | 0.689061 | ||||||||
\(137\) | 3.23354 | 0.276260 | 0.138130 | − | 0.990414i | \(-0.455891\pi\) | ||||
0.138130 | + | 0.990414i | \(0.455891\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.81053 | 0.492843 | 0.246421 | − | 0.969163i | \(-0.420745\pi\) | ||||
0.246421 | + | 0.969163i | \(0.420745\pi\) | |||||||
\(140\) | −10.9686 | −0.927014 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −16.2318 | −1.36214 | ||||||||
\(143\) | −0.785627 | −0.0656974 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7900 | −1.80956 | ||||||||
\(146\) | −15.7734 | −1.30541 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.34703 | −0.275124 | ||||||||
\(149\) | −2.94686 | −0.241416 | −0.120708 | − | 0.992688i | \(-0.538516\pi\) | ||||
−0.120708 | + | 0.992688i | \(0.538516\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.9231 | −1.13305 | −0.566525 | − | 0.824045i | \(-0.691712\pi\) | ||||
−0.566525 | + | 0.824045i | \(0.691712\pi\) | |||||||
\(152\) | −11.7542 | −0.953392 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.69140 | 0.136297 | ||||||||
\(155\) | −22.1715 | −1.78086 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.1933 | −1.53179 | −0.765897 | − | 0.642963i | \(-0.777705\pi\) | ||||
−0.765897 | + | 0.642963i | \(0.777705\pi\) | |||||||
\(158\) | 21.6505 | 1.72242 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −32.2318 | −2.54814 | ||||||||
\(161\) | −0.928968 | −0.0732130 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.5404 | 0.825584 | 0.412792 | − | 0.910825i | \(-0.364554\pi\) | ||||
0.412792 | + | 0.910825i | \(0.364554\pi\) | |||||||
\(164\) | −2.82563 | −0.220645 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 21.6145 | 1.67761 | ||||||||
\(167\) | 2.00128 | 0.154864 | 0.0774318 | − | 0.996998i | \(-0.475328\pi\) | ||||
0.0774318 | + | 0.996998i | \(0.475328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 52.6681 | 4.03946 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.6530 | 1.72727 | ||||||||
\(173\) | −20.9559 | −1.59325 | −0.796623 | − | 0.604476i | \(-0.793383\pi\) | ||||
−0.796623 | + | 0.604476i | \(0.793383\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.3265 | −0.931795 | ||||||||
\(176\) | 1.82775 | 0.137772 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −34.8847 | −2.61472 | ||||||||
\(179\) | 11.1119 | 0.830544 | 0.415272 | − | 0.909697i | \(-0.363686\pi\) | ||||
0.415272 | + | 0.909697i | \(0.363686\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | −2.15293 | −0.159585 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.27018 | 0.0936387 | ||||||||
\(185\) | −5.28713 | −0.388717 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.61721 | −0.337644 | ||||||||
\(188\) | −4.51811 | −0.329517 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −77.0396 | −5.58904 | ||||||||
\(191\) | −5.59042 | −0.404509 | −0.202254 | − | 0.979333i | \(-0.564827\pi\) | ||||
−0.202254 | + | 0.979333i | \(0.564827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.92315 | 0.282394 | 0.141197 | − | 0.989981i | \(-0.454905\pi\) | ||||
0.141197 | + | 0.989981i | \(0.454905\pi\) | |||||||
\(194\) | −22.8138 | −1.63794 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.63509 | 0.188221 | ||||||||
\(197\) | −13.7032 | −0.976311 | −0.488156 | − | 0.872757i | \(-0.662330\pi\) | ||||
−0.488156 | + | 0.872757i | \(0.662330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.45964 | −0.670576 | −0.335288 | − | 0.942116i | \(-0.608834\pi\) | ||||
−0.335288 | + | 0.942116i | \(0.608834\pi\) | |||||||
\(200\) | 16.8540 | 1.19176 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.8105 | −1.67530 | ||||||||
\(203\) | 5.23482 | 0.367412 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.46350 | −0.311745 | ||||||||
\(206\) | 29.9755 | 2.08849 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.32648 | −0.161313 | ||||||||
\(209\) | 6.75377 | 0.467168 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.5967 | −0.867190 | −0.433595 | − | 0.901108i | \(-0.642755\pi\) | ||||
−0.433595 | + | 0.901108i | \(0.642755\pi\) | |||||||
\(212\) | 17.9346 | 1.23175 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.6530 | 1.13837 | ||||||||
\(215\) | 35.7837 | 2.44043 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.32648 | 0.361585 | ||||||||
\(218\) | 21.5293 | 1.45815 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.61721 | −0.580972 | ||||||||
\(221\) | 5.87710 | 0.395337 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5967 | 0.843535 | 0.421767 | − | 0.906704i | \(-0.361410\pi\) | ||||
0.421767 | + | 0.906704i | \(0.361410\pi\) | |||||||
\(224\) | 7.74335 | 0.517374 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.2702 | 0.749681 | ||||||||
\(227\) | 2.94686 | 0.195590 | 0.0977949 | − | 0.995207i | \(-0.468821\pi\) | ||||
0.0977949 | + | 0.995207i | \(0.468821\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.9231 | 0.787904 | 0.393952 | − | 0.919131i | \(-0.371108\pi\) | ||||
0.393952 | + | 0.919131i | \(0.371108\pi\) | |||||||
\(230\) | 8.32502 | 0.548935 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.15756 | −0.469917 | ||||||||
\(233\) | 16.8844 | 1.10613 | 0.553067 | − | 0.833137i | \(-0.313457\pi\) | ||||
0.553067 | + | 0.833137i | \(0.313457\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.13702 | −0.465568 | ||||||||
\(236\) | −36.1091 | −2.35050 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.6530 | −0.820170 | ||||||||
\(239\) | 4.21482 | 0.272634 | 0.136317 | − | 0.990665i | \(-0.456473\pi\) | ||||
0.136317 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 21.9795 | 1.41582 | 0.707911 | − | 0.706302i | \(-0.249638\pi\) | ||||
0.707911 | + | 0.706302i | \(0.249638\pi\) | |||||||
\(242\) | −22.3534 | −1.43693 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 26.3509 | 1.68694 | ||||||||
\(245\) | 4.16251 | 0.265933 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.59666 | −0.546993 | ||||||||
\(248\) | −7.28290 | −0.462464 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 65.6568 | 4.15250 | ||||||||
\(251\) | 28.6909 | 1.81096 | 0.905478 | − | 0.424394i | \(-0.139513\pi\) | ||||
0.905478 | + | 0.424394i | \(0.139513\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.729822 | −0.0458835 | ||||||||
\(254\) | 8.61170 | 0.540346 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67352 | 0.104595 | ||||||||
\(257\) | −2.44791 | −0.152697 | −0.0763484 | − | 0.997081i | \(-0.524326\pi\) | ||||
−0.0763484 | + | 0.997081i | \(0.524326\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.27018 | 0.0789250 | ||||||||
\(260\) | 10.9686 | 0.680243 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.9231 | −0.860175 | ||||||||
\(263\) | 17.5790 | 1.08397 | 0.541984 | − | 0.840389i | \(-0.317673\pi\) | ||||
0.541984 | + | 0.840389i | \(0.317673\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.3303 | 1.74032 | ||||||||
\(266\) | 18.5080 | 1.13480 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.92315 | 0.117475 | ||||||||
\(269\) | −16.0601 | −0.979199 | −0.489600 | − | 0.871947i | \(-0.662857\pi\) | ||||
−0.489600 | + | 0.871947i | \(0.662857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.38279 | −0.205490 | −0.102745 | − | 0.994708i | \(-0.532763\pi\) | ||||
−0.102745 | + | 0.994708i | \(0.532763\pi\) | |||||||
\(272\) | −13.6730 | −0.829047 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.96157 | 0.420564 | ||||||||
\(275\) | −9.68401 | −0.583968 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.40334 | 0.0843184 | 0.0421592 | − | 0.999111i | \(-0.486576\pi\) | ||||
0.0421592 | + | 0.999111i | \(0.486576\pi\) | |||||||
\(278\) | 12.5096 | 0.750279 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.69140 | −0.340126 | ||||||||
\(281\) | 30.3532 | 1.81072 | 0.905361 | − | 0.424644i | \(-0.139601\pi\) | ||||
0.905361 | + | 0.424644i | \(0.139601\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | −19.8670 | −1.17889 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.69140 | −0.100014 | ||||||||
\(287\) | 1.07231 | 0.0632965 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.5404 | 1.03179 | ||||||||
\(290\) | −46.9122 | −2.75478 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −19.3059 | −1.12979 | ||||||||
\(293\) | 13.0609 | 0.763026 | 0.381513 | − | 0.924364i | \(-0.375403\pi\) | ||||
0.381513 | + | 0.924364i | \(0.375403\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −57.0396 | −3.32097 | ||||||||
\(296\) | −1.73671 | −0.100944 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.34436 | −0.367519 | ||||||||
\(299\) | 0.928968 | 0.0537236 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.59666 | −0.495503 | ||||||||
\(302\) | −29.9755 | −1.72490 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.0000 | 1.14708 | ||||||||
\(305\) | 41.6251 | 2.38345 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7900 | 1.01533 | 0.507664 | − | 0.861555i | \(-0.330509\pi\) | ||||
0.507664 | + | 0.861555i | \(0.330509\pi\) | |||||||
\(308\) | 2.07020 | 0.117960 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −47.7337 | −2.71109 | ||||||||
\(311\) | 25.5484 | 1.44872 | 0.724359 | − | 0.689423i | \(-0.242136\pi\) | ||||
0.724359 | + | 0.689423i | \(0.242136\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.5404 | 1.16101 | 0.580505 | − | 0.814257i | \(-0.302855\pi\) | ||||
0.580505 | + | 0.814257i | \(0.302855\pi\) | |||||||
\(314\) | −41.3218 | −2.33192 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 26.4993 | 1.49070 | ||||||||
\(317\) | 0.482333 | 0.0270905 | 0.0135453 | − | 0.999908i | \(-0.495688\pi\) | ||||
0.0135453 | + | 0.999908i | \(0.495688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.11261 | 0.230262 | ||||||||
\(320\) | −50.0245 | −2.79646 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | −50.5235 | −2.81120 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.3265 | 0.683750 | ||||||||
\(326\) | 22.6926 | 1.25683 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.46617 | −0.0809556 | ||||||||
\(329\) | 1.71459 | 0.0945287 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6530 | 0.805400 | 0.402700 | − | 0.915332i | \(-0.368072\pi\) | ||||
0.402700 | + | 0.915332i | \(0.368072\pi\) | |||||||
\(332\) | 26.4553 | 1.45192 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4.30860 | 0.235756 | ||||||||
\(335\) | 3.03789 | 0.165978 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0602 | −1.25617 | −0.628084 | − | 0.778146i | \(-0.716160\pi\) | ||||
−0.628084 | + | 0.778146i | \(0.716160\pi\) | |||||||
\(338\) | 2.15293 | 0.117104 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 64.4635 | 3.49602 | ||||||||
\(341\) | 4.18463 | 0.226610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 11.7542 | 0.633744 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −45.1165 | −2.42548 | ||||||||
\(347\) | −14.2021 | −0.762410 | −0.381205 | − | 0.924491i | \(-0.624491\pi\) | ||||
−0.381205 | + | 0.924491i | \(0.624491\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6774 | 1.05331 | 0.526653 | − | 0.850080i | \(-0.323447\pi\) | ||||
0.526653 | + | 0.850080i | \(0.323447\pi\) | |||||||
\(350\) | −26.5380 | −1.41852 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.08338 | 0.324245 | ||||||||
\(353\) | −19.4757 | −1.03659 | −0.518293 | − | 0.855203i | \(-0.673432\pi\) | ||||
−0.518293 | + | 0.855203i | \(0.673432\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.3828 | −1.66563 | ||||||||
\(356\) | −42.6974 | −2.26296 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.9231 | 1.26438 | ||||||||
\(359\) | 22.6182 | 1.19374 | 0.596871 | − | 0.802337i | \(-0.296410\pi\) | ||||
0.596871 | + | 0.802337i | \(0.296410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 54.9026 | 2.88961 | ||||||||
\(362\) | 21.5293 | 1.13155 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.63509 | −0.138116 | ||||||||
\(365\) | −30.4966 | −1.59626 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −15.2702 | −0.797097 | −0.398548 | − | 0.917147i | \(-0.630486\pi\) | ||||
−0.398548 | + | 0.917147i | \(0.630486\pi\) | |||||||
\(368\) | −2.16123 | −0.112662 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −11.3828 | −0.591763 | ||||||||
\(371\) | −6.80607 | −0.353354 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.9231 | 1.23869 | 0.619347 | − | 0.785118i | \(-0.287398\pi\) | ||||
0.619347 | + | 0.785118i | \(0.287398\pi\) | |||||||
\(374\) | −9.94051 | −0.514011 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.34436 | −0.120901 | ||||||||
\(377\) | −5.23482 | −0.269607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 38.0358 | 1.95377 | 0.976883 | − | 0.213775i | \(-0.0685760\pi\) | ||||
0.976883 | + | 0.213775i | \(0.0685760\pi\) | |||||||
\(380\) | −94.2932 | −4.83714 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −12.0358 | −0.615803 | ||||||||
\(383\) | −8.80735 | −0.450035 | −0.225017 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225017 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.27018 | 0.166664 | ||||||||
\(386\) | 8.44624 | 0.429902 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.9231 | −1.41758 | ||||||||
\(389\) | −17.2234 | −0.873261 | −0.436631 | − | 0.899641i | \(-0.643828\pi\) | ||||
−0.436631 | + | 0.899641i | \(0.643828\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.45964 | 0.276106 | ||||||||
\(392\) | 1.36730 | 0.0690590 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −29.5019 | −1.48629 | ||||||||
\(395\) | 41.8595 | 2.10618 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.7861 | 0.641717 | 0.320859 | − | 0.947127i | \(-0.396029\pi\) | ||||
0.320859 | + | 0.947127i | \(0.396029\pi\) | |||||||
\(398\) | −20.3659 | −1.02085 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −28.6774 | −1.43387 | ||||||||
\(401\) | 0.482333 | 0.0240866 | 0.0120433 | − | 0.999927i | \(-0.496166\pi\) | ||||
0.0120433 | + | 0.999927i | \(0.496166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.32648 | −0.265331 | ||||||||
\(404\) | −29.1431 | −1.44992 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.2702 | 0.559330 | ||||||||
\(407\) | 0.997885 | 0.0494633 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.05631 | −0.200571 | −0.100286 | − | 0.994959i | \(-0.531976\pi\) | ||||
−0.100286 | + | 0.994959i | \(0.531976\pi\) | |||||||
\(410\) | −9.60959 | −0.474584 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 36.6887 | 1.80752 | ||||||||
\(413\) | 13.7032 | 0.674289 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.7900 | 2.05139 | ||||||||
\(416\) | −7.74335 | −0.379649 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.5404 | 0.711192 | ||||||||
\(419\) | −1.46664 | −0.0716500 | −0.0358250 | − | 0.999358i | \(-0.511406\pi\) | ||||
−0.0358250 | + | 0.999358i | \(0.511406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.8105 | −0.965506 | −0.482753 | − | 0.875756i | \(-0.660363\pi\) | ||||
−0.482753 | + | 0.875756i | \(0.660363\pi\) | |||||||
\(422\) | −27.1197 | −1.32017 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 9.30594 | 0.451936 | ||||||||
\(425\) | 72.4440 | 3.51405 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0000 | −0.483934 | ||||||||
\(428\) | 20.3825 | 0.985226 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 77.0396 | 3.71518 | ||||||||
\(431\) | −30.7611 | −1.48171 | −0.740856 | − | 0.671664i | \(-0.765580\pi\) | ||||
−0.740856 | + | 0.671664i | \(0.765580\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1933 | −0.922372 | −0.461186 | − | 0.887303i | \(-0.652576\pi\) | ||||
−0.461186 | + | 0.887303i | \(0.652576\pi\) | |||||||
\(434\) | 11.4675 | 0.550459 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 26.3509 | 1.26198 | ||||||||
\(437\) | −7.98603 | −0.382024 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.18947 | 0.104498 | 0.0522488 | − | 0.998634i | \(-0.483361\pi\) | ||||
0.0522488 | + | 0.998634i | \(0.483361\pi\) | |||||||
\(440\) | −4.47131 | −0.213161 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 12.6530 | 0.601840 | ||||||||
\(443\) | 37.8403 | 1.79785 | 0.898924 | − | 0.438106i | \(-0.144350\pi\) | ||||
0.898924 | + | 0.438106i | \(0.144350\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −67.4468 | −3.19729 | ||||||||
\(446\) | 27.1197 | 1.28415 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.0179 | 0.567791 | ||||||||
\(449\) | −18.7036 | −0.882679 | −0.441339 | − | 0.897340i | \(-0.645496\pi\) | ||||
−0.441339 | + | 0.897340i | \(0.645496\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.842435 | 0.0396687 | ||||||||
\(452\) | 13.7942 | 0.648825 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.34436 | 0.297756 | ||||||||
\(455\) | −4.16251 | −0.195141 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5723 | 0.541327 | 0.270664 | − | 0.962674i | \(-0.412757\pi\) | ||||
0.270664 | + | 0.962674i | \(0.412757\pi\) | |||||||
\(458\) | 25.6696 | 1.19946 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.1895 | 0.475086 | ||||||||
\(461\) | −23.0095 | −1.07166 | −0.535829 | − | 0.844327i | \(-0.680001\pi\) | ||||
−0.535829 | + | 0.844327i | \(0.680001\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.72982 | −0.219813 | −0.109907 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109907 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(464\) | 12.1787 | 0.565383 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 36.3509 | 1.68392 | ||||||||
\(467\) | 5.18251 | 0.239818 | 0.119909 | − | 0.992785i | \(-0.461740\pi\) | ||||
0.119909 | + | 0.992785i | \(0.461740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.729822 | −0.0337001 | ||||||||
\(470\) | −15.3655 | −0.708756 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.7363 | −0.862410 | ||||||||
\(473\) | −6.75377 | −0.310538 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −105.967 | −4.86208 | ||||||||
\(476\) | −15.4867 | −0.709831 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 9.07419 | 0.415044 | ||||||||
\(479\) | −18.0779 | −0.826003 | −0.413001 | − | 0.910730i | \(-0.635520\pi\) | ||||
−0.413001 | + | 0.910730i | \(0.635520\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.27018 | −0.0579151 | ||||||||
\(482\) | 47.3201 | 2.15537 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −27.3596 | −1.24362 | ||||||||
\(485\) | −44.1087 | −2.00287 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.81053 | 0.0820431 | 0.0410215 | − | 0.999158i | \(-0.486939\pi\) | ||||
0.0410215 | + | 0.999158i | \(0.486939\pi\) | |||||||
\(488\) | 13.6730 | 0.618947 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.96157 | 0.404843 | ||||||||
\(491\) | 9.48836 | 0.428204 | 0.214102 | − | 0.976811i | \(-0.431318\pi\) | ||||
0.214102 | + | 0.976811i | \(0.431318\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −30.7656 | −1.38561 | ||||||||
\(494\) | −18.5080 | −0.832713 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.3920 | 0.556416 | ||||||||
\(497\) | 7.53939 | 0.338188 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −38.3866 | −1.71842 | −0.859211 | − | 0.511621i | \(-0.829045\pi\) | ||||
−0.859211 | + | 0.511621i | \(0.829045\pi\) | |||||||
\(500\) | 80.3611 | 3.59386 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 61.7694 | 2.75691 | ||||||||
\(503\) | −2.85582 | −0.127335 | −0.0636674 | − | 0.997971i | \(-0.520280\pi\) | ||||
−0.0636674 | + | 0.997971i | \(0.520280\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −46.0358 | −2.04856 | ||||||||
\(506\) | −1.57125 | −0.0698507 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 10.5404 | 0.467653 | ||||||||
\(509\) | −26.6730 | −1.18226 | −0.591131 | − | 0.806576i | \(-0.701318\pi\) | ||||
−0.591131 | + | 0.806576i | \(0.701318\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.32648 | 0.324105 | ||||||||
\(512\) | 24.3768 | 1.07731 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.27018 | −0.232458 | ||||||||
\(515\) | 57.9552 | 2.55381 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.34703 | 0.0592424 | ||||||||
\(518\) | 2.73460 | 0.120151 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.69140 | 0.249584 | ||||||||
\(521\) | −0.0166098 | −0.000727689 0 | −0.000363845 | − | 1.00000i | \(-0.500116\pi\) | ||||
−0.000363845 | 1.00000i | \(0.500116\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.7298 | −0.731544 | −0.365772 | − | 0.930704i | \(-0.619195\pi\) | ||||
−0.365772 | + | 0.930704i | \(0.619195\pi\) | |||||||
\(524\) | −17.0413 | −0.744454 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37.8463 | 1.65018 | ||||||||
\(527\) | −31.3043 | −1.36364 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.1370 | −0.962479 | ||||||||
\(530\) | 60.9931 | 2.64937 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22.6530 | 0.982131 | ||||||||
\(533\) | −1.07231 | −0.0464469 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 32.1972 | 1.39201 | ||||||||
\(536\) | 0.997885 | 0.0431021 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −34.5761 | −1.49068 | ||||||||
\(539\) | −0.785627 | −0.0338393 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.2702 | 1.43040 | 0.715198 | − | 0.698922i | \(-0.246336\pi\) | ||||
0.715198 | + | 0.698922i | \(0.246336\pi\) | |||||||
\(542\) | −7.28290 | −0.312827 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −45.5085 | −1.95116 | ||||||||
\(545\) | 41.6251 | 1.78302 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.6774 | 1.26891 | 0.634456 | − | 0.772959i | \(-0.281224\pi\) | ||||
0.634456 | + | 0.772959i | \(0.281224\pi\) | |||||||
\(548\) | 8.52067 | 0.363985 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −20.8490 | −0.889003 | ||||||||
\(551\) | 45.0020 | 1.91715 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0563 | −0.427638 | ||||||||
\(554\) | 3.02128 | 0.128362 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.3113 | 0.649343 | ||||||||
\(557\) | 30.4578 | 1.29054 | 0.645270 | − | 0.763955i | \(-0.276745\pi\) | ||||
0.645270 | + | 0.763955i | \(0.276745\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.59666 | 0.363600 | ||||||||
\(560\) | 9.68401 | 0.409224 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 65.3482 | 2.75655 | ||||||||
\(563\) | −9.18507 | −0.387105 | −0.193552 | − | 0.981090i | \(-0.562001\pi\) | ||||
−0.193552 | + | 0.981090i | \(0.562001\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.7900 | 0.916712 | ||||||||
\(566\) | −8.61170 | −0.361977 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −10.3086 | −0.432539 | ||||||||
\(569\) | −33.6391 | −1.41022 | −0.705112 | − | 0.709096i | \(-0.749103\pi\) | ||||
−0.705112 | + | 0.709096i | \(0.749103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.0563 | 0.588238 | 0.294119 | − | 0.955769i | \(-0.404974\pi\) | ||||
0.294119 | + | 0.955769i | \(0.404974\pi\) | |||||||
\(572\) | −2.07020 | −0.0865592 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.30860 | 0.0963593 | ||||||||
\(575\) | 11.4509 | 0.477536 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.9231 | −1.32898 | −0.664489 | − | 0.747298i | \(-0.731351\pi\) | ||||
−0.664489 | + | 0.747298i | \(0.731351\pi\) | |||||||
\(578\) | 37.7631 | 1.57074 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −57.4186 | −2.38418 | ||||||||
\(581\) | −10.0396 | −0.416513 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.34703 | −0.221451 | ||||||||
\(584\) | −10.0175 | −0.414527 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 28.1191 | 1.16159 | ||||||||
\(587\) | −4.75249 | −0.196156 | −0.0980781 | − | 0.995179i | \(-0.531269\pi\) | ||||
−0.0980781 | + | 0.995179i | \(0.531269\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 45.7900 | 1.88674 | ||||||||
\(590\) | −122.802 | −5.05568 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.95505 | 0.121452 | ||||||||
\(593\) | 12.8788 | 0.528870 | 0.264435 | − | 0.964404i | \(-0.414815\pi\) | ||||
0.264435 | + | 0.964404i | \(0.414815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.4635 | −1.00291 | ||||||||
\(596\) | −7.76523 | −0.318076 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.00000 | 0.0817861 | ||||||||
\(599\) | −27.9440 | −1.14176 | −0.570881 | − | 0.821033i | \(-0.693398\pi\) | ||||
−0.570881 | + | 0.821033i | \(0.693398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.6211 | −0.555615 | −0.277807 | − | 0.960637i | \(-0.589608\pi\) | ||||
−0.277807 | + | 0.960637i | \(0.589608\pi\) | |||||||
\(602\) | −18.5080 | −0.754329 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −36.6887 | −1.49284 | ||||||||
\(605\) | −43.2185 | −1.75708 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1165 | 0.775914 | 0.387957 | − | 0.921678i | \(-0.373181\pi\) | ||||
0.387957 | + | 0.921678i | \(0.373181\pi\) | |||||||
\(608\) | 66.5669 | 2.69965 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 89.6157 | 3.62843 | ||||||||
\(611\) | −1.71459 | −0.0693651 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.11261 | −0.246886 | −0.123443 | − | 0.992352i | \(-0.539394\pi\) | ||||
−0.123443 | + | 0.992352i | \(0.539394\pi\) | |||||||
\(614\) | 38.3005 | 1.54568 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.07419 | 0.0432802 | ||||||||
\(617\) | −7.80947 | −0.314397 | −0.157199 | − | 0.987567i | \(-0.550246\pi\) | ||||
−0.157199 | + | 0.987567i | \(0.550246\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4635 | 0.822498 | 0.411249 | − | 0.911523i | \(-0.365093\pi\) | ||||
0.411249 | + | 0.911523i | \(0.365093\pi\) | |||||||
\(620\) | −58.4240 | −2.34636 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 55.0039 | 2.20545 | ||||||||
\(623\) | 16.2034 | 0.649176 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 65.3098 | 2.61239 | ||||||||
\(626\) | 44.2219 | 1.76746 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −50.5761 | −2.01821 | ||||||||
\(629\) | −7.46497 | −0.297648 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 22.2740 | 0.886715 | 0.443358 | − | 0.896345i | \(-0.353787\pi\) | ||||
0.443358 | + | 0.896345i | \(0.353787\pi\) | |||||||
\(632\) | 13.7500 | 0.546945 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.03843 | 0.0412412 | ||||||||
\(635\) | 16.6500 | 0.660737 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.00000 | 0.0396214 | ||||||||
\(638\) | 8.85415 | 0.350539 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −43.2356 | −1.70904 | ||||||||
\(641\) | 3.76818 | 0.148834 | 0.0744171 | − | 0.997227i | \(-0.476290\pi\) | ||||
0.0744171 | + | 0.997227i | \(0.476290\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.4596 | −1.16177 | −0.580887 | − | 0.813984i | \(-0.697294\pi\) | ||||
−0.580887 | + | 0.813984i | \(0.697294\pi\) | |||||||
\(644\) | −2.44791 | −0.0964613 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −108.773 | −4.27963 | ||||||||
\(647\) | −1.85794 | −0.0730430 | −0.0365215 | − | 0.999333i | \(-0.511628\pi\) | ||||
−0.0365215 | + | 0.999333i | \(0.511628\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.7656 | 0.422586 | ||||||||
\(650\) | 26.5380 | 1.04091 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 27.7748 | 1.08774 | ||||||||
\(653\) | −42.9097 | −1.67918 | −0.839592 | − | 0.543217i | \(-0.817206\pi\) | ||||
−0.839592 | + | 0.543217i | \(0.817206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.9193 | −1.05182 | ||||||||
\(656\) | 2.49471 | 0.0974022 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.69140 | 0.143906 | ||||||||
\(659\) | −11.1119 | −0.432859 | −0.216430 | − | 0.976298i | \(-0.569441\pi\) | ||||
−0.216430 | + | 0.976298i | \(0.569441\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.9026 | 1.39645 | 0.698225 | − | 0.715879i | \(-0.253974\pi\) | ||||
0.698225 | + | 0.715879i | \(0.253974\pi\) | |||||||
\(662\) | 31.5468 | 1.22610 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.7272 | 0.532717 | ||||||||
\(665\) | 35.7837 | 1.38763 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.86298 | −0.188295 | ||||||||
\(668\) | 5.27355 | 0.204040 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.54036 | 0.252676 | ||||||||
\(671\) | −7.85627 | −0.303288 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.05631 | 0.156359 | 0.0781796 | − | 0.996939i | \(-0.475089\pi\) | ||||
0.0781796 | + | 0.996939i | \(0.475089\pi\) | |||||||
\(674\) | −49.6468 | −1.91232 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.63509 | 0.101350 | ||||||||
\(677\) | −41.0351 | −1.57711 | −0.788554 | − | 0.614966i | \(-0.789170\pi\) | ||||
−0.788554 | + | 0.614966i | \(0.789170\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 10.5967 | 0.406663 | ||||||||
\(680\) | 33.4489 | 1.28271 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.00919 | 0.344980 | ||||||||
\(683\) | −33.3745 | −1.27704 | −0.638520 | − | 0.769605i | \(-0.720453\pi\) | ||||
−0.638520 | + | 0.769605i | \(0.720453\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.4596 | 0.514267 | ||||||||
\(686\) | −2.15293 | −0.0821991 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −20.0000 | −0.762493 | ||||||||
\(689\) | 6.80607 | 0.259291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.8668 | −0.907937 | −0.453969 | − | 0.891018i | \(-0.649992\pi\) | ||||
−0.453969 | + | 0.891018i | \(0.649992\pi\) | |||||||
\(692\) | −55.2206 | −2.09917 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.5761 | −1.16065 | ||||||||
\(695\) | 24.1864 | 0.917442 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.30208 | −0.238708 | ||||||||
\(698\) | 42.3639 | 1.60350 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −32.4814 | −1.22768 | ||||||||
\(701\) | 22.2762 | 0.841359 | 0.420679 | − | 0.907209i | \(-0.361792\pi\) | ||||
0.420679 | + | 0.907209i | \(0.361792\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.9193 | 0.411829 | ||||||||
\(704\) | 9.44157 | 0.355842 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −41.9297 | −1.57804 | ||||||||
\(707\) | 11.0596 | 0.415940 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24.3866 | −0.915860 | −0.457930 | − | 0.888988i | \(-0.651409\pi\) | ||||
−0.457930 | + | 0.888988i | \(0.651409\pi\) | |||||||
\(710\) | −67.5648 | −2.53566 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22.1549 | −0.830290 | ||||||||
\(713\) | −4.94814 | −0.185309 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.27018 | −0.122298 | ||||||||
\(716\) | 29.2809 | 1.09428 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 48.6953 | 1.81729 | ||||||||
\(719\) | 20.6526 | 0.770212 | 0.385106 | − | 0.922872i | \(-0.374165\pi\) | ||||
0.385106 | + | 0.922872i | \(0.374165\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.9231 | −0.518525 | ||||||||
\(722\) | 118.201 | 4.39899 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 26.3509 | 0.979323 | ||||||||
\(725\) | −64.5269 | −2.39647 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.1933 | −1.08272 | −0.541360 | − | 0.840791i | \(-0.682090\pi\) | ||||
−0.541360 | + | 0.840791i | \(0.682090\pi\) | |||||||
\(728\) | −1.36730 | −0.0506755 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −65.6568 | −2.43007 | ||||||||
\(731\) | 50.5235 | 1.86868 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.78613 | −0.176780 | −0.0883899 | − | 0.996086i | \(-0.528172\pi\) | ||||
−0.0883899 | + | 0.996086i | \(0.528172\pi\) | |||||||
\(734\) | −32.8756 | −1.21346 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.19332 | −0.265149 | ||||||||
\(737\) | −0.573368 | −0.0211203 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.5761 | −1.63976 | −0.819879 | − | 0.572536i | \(-0.805960\pi\) | ||||
−0.819879 | + | 0.572536i | \(0.805960\pi\) | |||||||
\(740\) | −13.9320 | −0.512152 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.6530 | −0.537927 | ||||||||
\(743\) | 5.39477 | 0.197915 | 0.0989575 | − | 0.995092i | \(-0.468449\pi\) | ||||
0.0989575 | + | 0.995092i | \(0.468449\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.2663 | −0.449403 | ||||||||
\(746\) | 51.5048 | 1.88572 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.1668 | −0.444861 | ||||||||
\(749\) | −7.73504 | −0.282632 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −45.7900 | −1.67090 | −0.835450 | − | 0.549566i | \(-0.814793\pi\) | ||||
−0.835450 | + | 0.549566i | \(0.814793\pi\) | |||||||
\(752\) | 3.98898 | 0.145463 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.2702 | −0.410436 | ||||||||
\(755\) | −57.9552 | −2.10921 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.2535 | 1.75380 | 0.876901 | − | 0.480670i | \(-0.159607\pi\) | ||||
0.876901 | + | 0.480670i | \(0.159607\pi\) | |||||||
\(758\) | 81.8882 | 2.97431 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −48.9270 | −1.77477 | ||||||||
\(761\) | 30.4221 | 1.10280 | 0.551401 | − | 0.834240i | \(-0.314094\pi\) | ||||
0.551401 | + | 0.834240i | \(0.314094\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | −0.362024 | ||||||||
\(764\) | −14.7313 | −0.532958 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.9616 | −0.685109 | ||||||||
\(767\) | −13.7032 | −0.494793 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 45.2496 | 1.63174 | 0.815872 | − | 0.578233i | \(-0.196258\pi\) | ||||
0.815872 | + | 0.578233i | \(0.196258\pi\) | |||||||
\(770\) | 7.04045 | 0.253720 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.3378 | 0.372067 | ||||||||
\(773\) | 24.1894 | 0.870033 | 0.435017 | − | 0.900422i | \(-0.356742\pi\) | ||||
0.435017 | + | 0.900422i | \(0.356742\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −65.6568 | −2.35846 | ||||||||
\(776\) | −14.4888 | −0.520118 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −37.0807 | −1.32941 | ||||||||
\(779\) | 9.21829 | 0.330280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.92315 | 0.211947 | ||||||||
\(782\) | 11.7542 | 0.420330 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.32648 | −0.0830887 | ||||||||
\(785\) | −79.8924 | −2.85148 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −17.0602 | −0.608129 | −0.304065 | − | 0.952651i | \(-0.598344\pi\) | ||||
−0.304065 | + | 0.952651i | \(0.598344\pi\) | |||||||
\(788\) | −36.1091 | −1.28633 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 90.1203 | 3.20634 | ||||||||
\(791\) | −5.23482 | −0.186129 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 27.5276 | 0.976917 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.9270 | −0.883514 | ||||||||
\(797\) | −44.7510 | −1.58516 | −0.792581 | − | 0.609767i | \(-0.791263\pi\) | ||||
−0.792581 | + | 0.609767i | \(0.791263\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0769 | −0.356493 | ||||||||
\(800\) | −95.4482 | −3.37460 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.03843 | 0.0366681 | ||||||||
\(803\) | 5.75588 | 0.203121 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.86684 | −0.136288 | ||||||||
\(806\) | −11.4675 | −0.403926 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.1218 | −0.531983 | ||||||||
\(809\) | −32.4591 | −1.14120 | −0.570601 | − | 0.821228i | \(-0.693290\pi\) | ||||
−0.570601 | + | 0.821228i | \(0.693290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.4635 | 0.718571 | 0.359285 | − | 0.933228i | \(-0.383020\pi\) | ||||
0.359285 | + | 0.933228i | \(0.383020\pi\) | |||||||
\(812\) | 13.7942 | 0.484082 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.14837 | 0.0753004 | ||||||||
\(815\) | 43.8743 | 1.53685 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −73.9026 | −2.58552 | ||||||||
\(818\) | −8.73293 | −0.305340 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.7617 | −0.410737 | ||||||||
\(821\) | 30.9266 | 1.07935 | 0.539673 | − | 0.841875i | \(-0.318548\pi\) | ||||
0.539673 | + | 0.841875i | \(0.318548\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8463 | 0.412936 | 0.206468 | − | 0.978453i | \(-0.433803\pi\) | ||||
0.206468 | + | 0.978453i | \(0.433803\pi\) | |||||||
\(824\) | 19.0371 | 0.663189 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 29.5019 | 1.02650 | ||||||||
\(827\) | −55.1296 | −1.91704 | −0.958522 | − | 0.285019i | \(-0.908000\pi\) | ||||
−0.958522 | + | 0.285019i | \(0.908000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0000 | −0.625166 | −0.312583 | − | 0.949890i | \(-0.601194\pi\) | ||||
−0.312583 | + | 0.949890i | \(0.601194\pi\) | |||||||
\(830\) | 89.9707 | 3.12293 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.0179 | −0.416645 | ||||||||
\(833\) | 5.87710 | 0.203630 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.33034 | 0.288283 | ||||||||
\(836\) | 17.7968 | 0.615514 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.15756 | −0.109076 | ||||||||
\(839\) | −14.2765 | −0.492881 | −0.246441 | − | 0.969158i | \(-0.579261\pi\) | ||||
−0.246441 | + | 0.969158i | \(0.579261\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.59666 | −0.0550573 | ||||||||
\(842\) | −42.6506 | −1.46984 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −33.1933 | −1.14256 | ||||||||
\(845\) | 4.16251 | 0.143195 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.3828 | 0.356757 | ||||||||
\(848\) | −15.8342 | −0.543749 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 155.967 | 5.34961 | ||||||||
\(851\) | −1.17996 | −0.0404483 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.6735 | 0.570890 | 0.285445 | − | 0.958395i | \(-0.407859\pi\) | ||||
0.285445 | + | 0.958395i | \(0.407859\pi\) | |||||||
\(854\) | −21.5293 | −0.736716 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.5761 | 0.361484 | ||||||||
\(857\) | −56.1139 | −1.91681 | −0.958407 | − | 0.285404i | \(-0.907872\pi\) | ||||
−0.958407 | + | 0.285404i | \(0.907872\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −43.9589 | −1.49986 | −0.749929 | − | 0.661518i | \(-0.769913\pi\) | ||||
−0.749929 | + | 0.661518i | \(0.769913\pi\) | |||||||
\(860\) | 94.2932 | 3.21537 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −66.2264 | −2.25568 | ||||||||
\(863\) | 14.3978 | 0.490106 | 0.245053 | − | 0.969510i | \(-0.421195\pi\) | ||||
0.245053 | + | 0.969510i | \(0.421195\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −87.2291 | −2.96588 | ||||||||
\(866\) | −41.3218 | −1.40417 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.0358 | 0.476405 | ||||||||
\(869\) | −7.90050 | −0.268006 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.729822 | 0.0247291 | ||||||||
\(872\) | 13.6730 | 0.463026 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.1933 | −0.581573 | ||||||||
\(875\) | −30.4966 | −1.03097 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 39.1933 | 1.32346 | 0.661732 | − | 0.749740i | \(-0.269822\pi\) | ||||
0.661732 | + | 0.749740i | \(0.269822\pi\) | |||||||
\(878\) | 4.71376 | 0.159082 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.60802 | 0.256466 | ||||||||
\(881\) | 16.1647 | 0.544602 | 0.272301 | − | 0.962212i | \(-0.412215\pi\) | ||||
0.272301 | + | 0.962212i | \(0.412215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −18.3866 | −0.618760 | −0.309380 | − | 0.950938i | \(-0.600121\pi\) | ||||
−0.309380 | + | 0.950938i | \(0.600121\pi\) | |||||||
\(884\) | 15.4867 | 0.520874 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 81.4674 | 2.73695 | ||||||||
\(887\) | 41.3384 | 1.38801 | 0.694004 | − | 0.719971i | \(-0.255845\pi\) | ||||
0.694004 | + | 0.719971i | \(0.255845\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | −145.208 | −4.86738 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 33.1933 | 1.11139 | ||||||||
\(893\) | 14.7398 | 0.493248 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.2535 | 1.54608 | ||||||||
\(896\) | 10.3869 | 0.347002 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −40.2675 | −1.34374 | ||||||||
\(899\) | 27.8832 | 0.929956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.0000 | 1.33259 | ||||||||
\(902\) | 1.81370 | 0.0603896 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.15756 | 0.238057 | ||||||||
\(905\) | 41.6251 | 1.38366 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 41.6363 | 1.38251 | 0.691255 | − | 0.722611i | \(-0.257058\pi\) | ||||
0.691255 | + | 0.722611i | \(0.257058\pi\) | |||||||
\(908\) | 7.76523 | 0.257698 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.96157 | −0.297073 | ||||||||
\(911\) | −4.93153 | −0.163389 | −0.0816944 | − | 0.996657i | \(-0.526033\pi\) | ||||
−0.0816944 | + | 0.996657i | \(0.526033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.88739 | −0.261034 | ||||||||
\(914\) | 24.9142 | 0.824089 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 31.4186 | 1.03810 | ||||||||
\(917\) | 6.46708 | 0.213562 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.38665 | −0.210676 | −0.105338 | − | 0.994436i | \(-0.533592\pi\) | ||||
−0.105338 | + | 0.994436i | \(0.533592\pi\) | |||||||
\(920\) | 5.28713 | 0.174311 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −49.5377 | −1.63144 | ||||||||
\(923\) | −7.53939 | −0.248162 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.6568 | −0.514793 | ||||||||
\(926\) | −10.1830 | −0.334633 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 40.5350 | 1.33063 | ||||||||
\(929\) | −36.7514 | −1.20577 | −0.602887 | − | 0.797827i | \(-0.705983\pi\) | ||||
−0.602887 | + | 0.797827i | \(0.705983\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.59666 | −0.281744 | ||||||||
\(932\) | 44.4919 | 1.45738 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11.1576 | 0.365087 | ||||||||
\(935\) | −19.2192 | −0.628534 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.27404 | −0.270301 | −0.135150 | − | 0.990825i | \(-0.543152\pi\) | ||||
−0.135150 | + | 0.990825i | \(0.543152\pi\) | |||||||
\(938\) | −1.57125 | −0.0513032 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −18.8067 | −0.613406 | ||||||||
\(941\) | −56.5439 | −1.84328 | −0.921640 | − | 0.388047i | \(-0.873150\pi\) | ||||
−0.921640 | + | 0.388047i | \(0.873150\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.996143 | −0.0324389 | ||||||||
\(944\) | 31.8802 | 1.03761 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.5404 | −0.472748 | ||||||||
\(947\) | −10.9686 | −0.356431 | −0.178216 | − | 0.983991i | \(-0.557032\pi\) | ||||
−0.178216 | + | 0.983991i | \(0.557032\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.32648 | −0.237828 | ||||||||
\(950\) | −228.138 | −7.40178 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8.03576 | −0.260440 | ||||||||
\(953\) | 11.4152 | 0.369775 | 0.184888 | − | 0.982760i | \(-0.440808\pi\) | ||||
0.184888 | + | 0.982760i | \(0.440808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.2702 | −0.753005 | ||||||||
\(956\) | 11.1064 | 0.359207 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −38.9205 | −1.25746 | ||||||||
\(959\) | −3.23354 | −0.104416 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.62856 | −0.0847924 | ||||||||
\(962\) | −2.73460 | −0.0881670 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 57.9178 | 1.86541 | ||||||||
\(965\) | 16.3301 | 0.525686 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.65297 | −0.0853137 | −0.0426569 | − | 0.999090i | \(-0.513582\pi\) | ||||
−0.0426569 | + | 0.999090i | \(0.513582\pi\) | |||||||
\(968\) | −14.1964 | −0.456289 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −94.9628 | −3.04907 | ||||||||
\(971\) | −39.4805 | −1.26699 | −0.633494 | − | 0.773747i | \(-0.718380\pi\) | ||||
−0.633494 | + | 0.773747i | \(0.718380\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.81053 | −0.186277 | ||||||||
\(974\) | 3.89794 | 0.124898 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.2648 | −0.744689 | ||||||||
\(977\) | 16.4544 | 0.526423 | 0.263211 | − | 0.964738i | \(-0.415218\pi\) | ||||
0.263211 | + | 0.964738i | \(0.415218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.7298 | 0.406847 | ||||||||
\(980\) | 10.9686 | 0.350379 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 20.4277 | 0.651875 | ||||||||
\(983\) | 19.6492 | 0.626712 | 0.313356 | − | 0.949636i | \(-0.398547\pi\) | ||||
0.313356 | + | 0.949636i | \(0.398547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −57.0396 | −1.81743 | ||||||||
\(986\) | −66.2360 | −2.10938 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.6530 | −0.720687 | ||||||||
\(989\) | 7.98603 | 0.253941 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.5404 | −0.716018 | −0.358009 | − | 0.933718i | \(-0.616544\pi\) | ||||
−0.358009 | + | 0.933718i | \(0.616544\pi\) | |||||||
\(992\) | 41.2448 | 1.30952 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 16.2318 | 0.514840 | ||||||||
\(995\) | −39.3759 | −1.24830 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.42774 | 0.266909 | 0.133455 | − | 0.991055i | \(-0.457393\pi\) | ||||
0.133455 | + | 0.991055i | \(0.457393\pi\) | |||||||
\(998\) | −82.6436 | −2.61604 | ||||||||
\(999\) | 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 | 819.2.a.m.1.5 | yes | 6 | |
3.2 | odd | 2 | inner | 819.2.a.m.1.2 | ✓ | 6 | |
7.6 | odd | 2 | 5733.2.a.bv.1.5 | 6 | |||
21.20 | even | 2 | 5733.2.a.bv.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
819.2.a.m.1.2 | ✓ | 6 | 3.2 | odd | 2 | inner | |
819.2.a.m.1.5 | yes | 6 | 1.1 | even | 1 | trivial | |
5733.2.a.bv.1.2 | 6 | 21.20 | even | 2 | |||
5733.2.a.bv.1.5 | 6 | 7.6 | odd | 2 |