Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [729,2,Mod(1,729)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(729, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("729.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 729 = 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 729.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: | \(5.82109430735\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\Q(\zeta_{36})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 6x^{4} + 9x^{2} - 3 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.28558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 729.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.28558 | −0.909039 | −0.454519 | − | 0.890737i | \(-0.650189\pi\) | ||||
−0.454519 | + | 0.890737i | \(0.650189\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.347296 | −0.173648 | ||||||||
\(5\) | −0.446476 | −0.199670 | −0.0998350 | − | 0.995004i | \(-0.531831\pi\) | ||||
−0.0998350 | + | 0.995004i | \(0.531831\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.53209 | −1.33500 | −0.667502 | − | 0.744608i | \(-0.732636\pi\) | ||||
−0.667502 | + | 0.744608i | \(0.732636\pi\) | |||||||
\(8\) | 3.01763 | 1.06689 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.573978 | 0.181508 | ||||||||
\(11\) | 2.78006 | 0.838220 | 0.419110 | − | 0.907935i | \(-0.362342\pi\) | ||||
0.419110 | + | 0.907935i | \(0.362342\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.29086 | 0.912720 | 0.456360 | − | 0.889795i | \(-0.349153\pi\) | ||||
0.456360 | + | 0.889795i | \(0.349153\pi\) | |||||||
\(14\) | 4.54077 | 1.21357 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.18479 | −0.796198 | ||||||||
\(17\) | 7.03936 | 1.70730 | 0.853648 | − | 0.520850i | \(-0.174385\pi\) | ||||
0.853648 | + | 0.520850i | \(0.174385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.18479 | −1.18947 | −0.594736 | − | 0.803921i | \(-0.702744\pi\) | ||||
−0.594736 | + | 0.803921i | \(0.702744\pi\) | |||||||
\(20\) | 0.155059 | 0.0346723 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.57398 | −0.761975 | ||||||||
\(23\) | −7.27693 | −1.51734 | −0.758672 | − | 0.651473i | \(-0.774152\pi\) | ||||
−0.758672 | + | 0.651473i | \(0.774152\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80066 | −0.960132 | ||||||||
\(26\) | −4.23065 | −0.829698 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22668 | 0.231821 | ||||||||
\(29\) | −3.61916 | −0.672061 | −0.336031 | − | 0.941851i | \(-0.609085\pi\) | ||||
−0.336031 | + | 0.941851i | \(0.609085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.93582 | −0.347684 | −0.173842 | − | 0.984774i | \(-0.555618\pi\) | ||||
−0.173842 | + | 0.984774i | \(0.555618\pi\) | |||||||
\(32\) | −1.94096 | −0.343117 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.04963 | −1.55200 | ||||||||
\(35\) | 1.57699 | 0.266560 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.22668 | −0.530463 | −0.265232 | − | 0.964185i | \(-0.585448\pi\) | ||||
−0.265232 | + | 0.964185i | \(0.585448\pi\) | |||||||
\(38\) | 6.66544 | 1.08128 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.34730 | −0.213026 | ||||||||
\(41\) | 4.86084 | 0.759135 | 0.379568 | − | 0.925164i | \(-0.376073\pi\) | ||||
0.379568 | + | 0.925164i | \(0.376073\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.75877 | −0.878204 | −0.439102 | − | 0.898437i | \(-0.644703\pi\) | ||||
−0.439102 | + | 0.898437i | \(0.644703\pi\) | |||||||
\(44\) | −0.965505 | −0.145555 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9.35504 | 1.37932 | ||||||||
\(47\) | −3.01763 | −0.440166 | −0.220083 | − | 0.975481i | \(-0.570633\pi\) | ||||
−0.220083 | + | 0.975481i | \(0.570633\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.47565 | 0.782236 | ||||||||
\(50\) | 6.17161 | 0.872797 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.14290 | −0.158492 | ||||||||
\(53\) | −8.77141 | −1.20485 | −0.602423 | − | 0.798177i | \(-0.705798\pi\) | ||||
−0.602423 | + | 0.798177i | \(0.705798\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.24123 | −0.167367 | ||||||||
\(56\) | −10.6585 | −1.42431 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.65270 | 0.610930 | ||||||||
\(59\) | −2.96377 | −0.385851 | −0.192925 | − | 0.981213i | \(-0.561797\pi\) | ||||
−0.192925 | + | 0.981213i | \(0.561797\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.88713 | 1.00984 | 0.504922 | − | 0.863165i | \(-0.331521\pi\) | ||||
0.504922 | + | 0.863165i | \(0.331521\pi\) | |||||||
\(62\) | 2.48865 | 0.316058 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.86484 | 1.10810 | ||||||||
\(65\) | −1.46929 | −0.182243 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.43882 | −1.15313 | −0.576567 | − | 0.817050i | \(-0.695608\pi\) | ||||
−0.576567 | + | 0.817050i | \(0.695608\pi\) | |||||||
\(68\) | −2.44474 | −0.296469 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.02734 | −0.242314 | ||||||||
\(71\) | −5.30731 | −0.629862 | −0.314931 | − | 0.949115i | \(-0.601981\pi\) | ||||
−0.314931 | + | 0.949115i | \(0.601981\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.55438 | −0.181926 | −0.0909631 | − | 0.995854i | \(-0.528995\pi\) | ||||
−0.0909631 | + | 0.995854i | \(0.528995\pi\) | |||||||
\(74\) | 4.14814 | 0.482212 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.80066 | 0.206550 | ||||||||
\(77\) | −9.81942 | −1.11903 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9017 | −1.33904 | −0.669521 | − | 0.742793i | \(-0.733501\pi\) | ||||
−0.669521 | + | 0.742793i | \(0.733501\pi\) | |||||||
\(80\) | 1.42193 | 0.158977 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.24897 | −0.690083 | ||||||||
\(83\) | 16.2573 | 1.78447 | 0.892233 | − | 0.451576i | \(-0.149138\pi\) | ||||
0.892233 | + | 0.451576i | \(0.149138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.14290 | −0.340896 | ||||||||
\(86\) | 7.40333 | 0.798322 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.38919 | 0.894290 | ||||||||
\(89\) | −18.4258 | −1.95313 | −0.976567 | − | 0.215214i | \(-0.930955\pi\) | ||||
−0.976567 | + | 0.215214i | \(0.930955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −11.6236 | −1.21849 | ||||||||
\(92\) | 2.52725 | 0.263484 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.87939 | 0.400128 | ||||||||
\(95\) | 2.31488 | 0.237502 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1138 | 1.02690 | 0.513451 | − | 0.858119i | \(-0.328367\pi\) | ||||
0.513451 | + | 0.858119i | \(0.328367\pi\) | |||||||
\(98\) | −7.03936 | −0.711083 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.66725 | 0.166725 | ||||||||
\(101\) | 2.08077 | 0.207045 | 0.103522 | − | 0.994627i | \(-0.466989\pi\) | ||||
0.103522 | + | 0.994627i | \(0.466989\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.44831 | −0.142706 | −0.0713531 | − | 0.997451i | \(-0.522732\pi\) | ||||
−0.0713531 | + | 0.997451i | \(0.522732\pi\) | |||||||
\(104\) | 9.93058 | 0.973774 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2763 | 1.09525 | ||||||||
\(107\) | 2.23583 | 0.216146 | 0.108073 | − | 0.994143i | \(-0.465532\pi\) | ||||
0.108073 | + | 0.994143i | \(0.465532\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.5030 | −1.10179 | −0.550893 | − | 0.834576i | \(-0.685713\pi\) | ||||
−0.550893 | + | 0.834576i | \(0.685713\pi\) | |||||||
\(110\) | 1.59569 | 0.152143 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.2490 | 1.06293 | ||||||||
\(113\) | −1.68815 | −0.158808 | −0.0794039 | − | 0.996843i | \(-0.525302\pi\) | ||||
−0.0794039 | + | 0.996843i | \(0.525302\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.24897 | 0.302968 | ||||||||
\(116\) | 1.25692 | 0.116702 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.81016 | 0.350753 | ||||||||
\(119\) | −24.8637 | −2.27925 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.27126 | −0.297387 | ||||||||
\(122\) | −10.1395 | −0.917987 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.672304 | 0.0603747 | ||||||||
\(125\) | 4.37576 | 0.391379 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.67230 | −0.237129 | −0.118564 | − | 0.992946i | \(-0.537829\pi\) | ||||
−0.118564 | + | 0.992946i | \(0.537829\pi\) | |||||||
\(128\) | −7.51449 | −0.664194 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.88888 | 0.165666 | ||||||||
\(131\) | 2.91987 | 0.255111 | 0.127555 | − | 0.991831i | \(-0.459287\pi\) | ||||
0.127555 | + | 0.991831i | \(0.459287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.3131 | 1.58795 | ||||||||
\(134\) | 12.1343 | 1.04824 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 21.2422 | 1.82150 | ||||||||
\(137\) | 4.65722 | 0.397893 | 0.198947 | − | 0.980010i | \(-0.436248\pi\) | ||||
0.198947 | + | 0.980010i | \(0.436248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00269 | −0.678779 | −0.339390 | − | 0.940646i | \(-0.610220\pi\) | ||||
−0.339390 | + | 0.940646i | \(0.610220\pi\) | |||||||
\(140\) | −0.547683 | −0.0462877 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.82295 | 0.572569 | ||||||||
\(143\) | 9.14879 | 0.765060 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.61587 | 0.134190 | ||||||||
\(146\) | 1.99827 | 0.165378 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.12061 | 0.0921140 | ||||||||
\(149\) | −20.2117 | −1.65581 | −0.827905 | − | 0.560869i | \(-0.810467\pi\) | ||||
−0.827905 | + | 0.560869i | \(0.810467\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.70233 | 0.545428 | 0.272714 | − | 0.962095i | \(-0.412079\pi\) | ||||
0.272714 | + | 0.962095i | \(0.412079\pi\) | |||||||
\(152\) | −15.6458 | −1.26904 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.6236 | 1.01724 | ||||||||
\(155\) | 0.864297 | 0.0694220 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.32501 | 0.424982 | 0.212491 | − | 0.977163i | \(-0.431842\pi\) | ||||
0.212491 | + | 0.977163i | \(0.431842\pi\) | |||||||
\(158\) | 15.3005 | 1.21724 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.866592 | 0.0685101 | ||||||||
\(161\) | 25.7028 | 2.02566 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.81521 | 0.298830 | 0.149415 | − | 0.988775i | \(-0.452261\pi\) | ||||
0.149415 | + | 0.988775i | \(0.452261\pi\) | |||||||
\(164\) | −1.68815 | −0.131822 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −20.8999 | −1.62215 | ||||||||
\(167\) | 9.13538 | 0.706917 | 0.353459 | − | 0.935450i | \(-0.385006\pi\) | ||||
0.353459 | + | 0.935450i | \(0.385006\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.17024 | −0.166942 | ||||||||
\(170\) | 4.04044 | 0.309888 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 6.07386 | 0.461787 | 0.230893 | − | 0.972979i | \(-0.425835\pi\) | ||||
0.230893 | + | 0.972979i | \(0.425835\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.9564 | 1.28178 | ||||||||
\(176\) | −8.85392 | −0.667389 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 23.6878 | 1.77547 | ||||||||
\(179\) | 10.2811 | 0.768449 | 0.384224 | − | 0.923240i | \(-0.374469\pi\) | ||||
0.384224 | + | 0.923240i | \(0.374469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.1411 | −1.72007 | −0.860034 | − | 0.510237i | \(-0.829558\pi\) | ||||
−0.860034 | + | 0.510237i | \(0.829558\pi\) | |||||||
\(182\) | 14.9430 | 1.10765 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −21.9590 | −1.61884 | ||||||||
\(185\) | 1.44063 | 0.105918 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.5699 | 1.43109 | ||||||||
\(188\) | 1.04801 | 0.0764340 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.97596 | −0.215899 | ||||||||
\(191\) | 14.6703 | 1.06151 | 0.530753 | − | 0.847526i | \(-0.321909\pi\) | ||||
0.530753 | + | 0.847526i | \(0.321909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.4415 | 1.68736 | 0.843678 | − | 0.536849i | \(-0.180386\pi\) | ||||
0.843678 | + | 0.536849i | \(0.180386\pi\) | |||||||
\(194\) | −13.0021 | −0.933494 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.90167 | −0.135834 | ||||||||
\(197\) | −9.02768 | −0.643196 | −0.321598 | − | 0.946876i | \(-0.604220\pi\) | ||||
−0.321598 | + | 0.946876i | \(0.604220\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.60401 | 0.184593 | 0.0922966 | − | 0.995732i | \(-0.470579\pi\) | ||||
0.0922966 | + | 0.995732i | \(0.470579\pi\) | |||||||
\(200\) | −14.4866 | −1.02436 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.67499 | −0.188212 | ||||||||
\(203\) | 12.7832 | 0.897205 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.17024 | −0.151576 | ||||||||
\(206\) | 1.86191 | 0.129726 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −10.4807 | −0.726706 | ||||||||
\(209\) | −14.4140 | −0.997040 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.3550 | −1.12593 | −0.562964 | − | 0.826482i | \(-0.690339\pi\) | ||||
−0.562964 | + | 0.826482i | \(0.690339\pi\) | |||||||
\(212\) | 3.04628 | 0.209219 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.87433 | −0.196485 | ||||||||
\(215\) | 2.57115 | 0.175351 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.83750 | 0.464159 | ||||||||
\(218\) | 14.7880 | 1.00157 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.431074 | 0.0290630 | ||||||||
\(221\) | 23.1656 | 1.55828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.70233 | 0.247927 | 0.123963 | − | 0.992287i | \(-0.460439\pi\) | ||||
0.123963 | + | 0.992287i | \(0.460439\pi\) | |||||||
\(224\) | 6.85565 | 0.458062 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.17024 | 0.144363 | ||||||||
\(227\) | −10.5608 | −0.700943 | −0.350472 | − | 0.936573i | \(-0.613979\pi\) | ||||
−0.350472 | + | 0.936573i | \(0.613979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5253 | 0.893776 | 0.446888 | − | 0.894590i | \(-0.352532\pi\) | ||||
0.446888 | + | 0.894590i | \(0.352532\pi\) | |||||||
\(230\) | −4.17680 | −0.275410 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.9213 | −0.717017 | ||||||||
\(233\) | 12.7007 | 0.832050 | 0.416025 | − | 0.909353i | \(-0.363423\pi\) | ||||
0.416025 | + | 0.909353i | \(0.363423\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.34730 | 0.0878879 | ||||||||
\(236\) | 1.02931 | 0.0670022 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 31.9641 | 2.07192 | ||||||||
\(239\) | −5.85154 | −0.378505 | −0.189252 | − | 0.981928i | \(-0.560606\pi\) | ||||
−0.189252 | + | 0.981928i | \(0.560606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.53983 | −0.550099 | −0.275049 | − | 0.961430i | \(-0.588694\pi\) | ||||
−0.275049 | + | 0.961430i | \(0.588694\pi\) | |||||||
\(242\) | 4.20545 | 0.270337 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.73917 | −0.175357 | ||||||||
\(245\) | −2.44474 | −0.156189 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.0624 | −1.08566 | ||||||||
\(248\) | −5.84159 | −0.370941 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.62536 | −0.355779 | ||||||||
\(251\) | −6.75790 | −0.426555 | −0.213277 | − | 0.976992i | \(-0.568414\pi\) | ||||
−0.213277 | + | 0.976992i | \(0.568414\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.2303 | −1.27187 | ||||||||
\(254\) | 3.43545 | 0.215559 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.06923 | −0.504327 | ||||||||
\(257\) | 3.68296 | 0.229737 | 0.114868 | − | 0.993381i | \(-0.463355\pi\) | ||||
0.114868 | + | 0.993381i | \(0.463355\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.3969 | 0.708171 | ||||||||
\(260\) | 0.510278 | 0.0316461 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.75372 | −0.231905 | ||||||||
\(263\) | 3.63786 | 0.224320 | 0.112160 | − | 0.993690i | \(-0.464223\pi\) | ||||
0.112160 | + | 0.993690i | \(0.464223\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.91622 | 0.240572 | ||||||||
\(266\) | −23.5429 | −1.44351 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.27807 | 0.200240 | ||||||||
\(269\) | −7.08672 | −0.432085 | −0.216042 | − | 0.976384i | \(-0.569315\pi\) | ||||
−0.216042 | + | 0.976384i | \(0.569315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.0000 | −1.15417 | −0.577084 | − | 0.816685i | \(-0.695809\pi\) | ||||
−0.577084 | + | 0.816685i | \(0.695809\pi\) | |||||||
\(272\) | −22.4189 | −1.35935 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.98721 | −0.361700 | ||||||||
\(275\) | −13.3461 | −0.804802 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.8922 | −0.834700 | −0.417350 | − | 0.908746i | \(-0.637041\pi\) | ||||
−0.417350 | + | 0.908746i | \(0.637041\pi\) | |||||||
\(278\) | 10.2881 | 0.617037 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.75877 | 0.284391 | ||||||||
\(281\) | 22.1275 | 1.32002 | 0.660008 | − | 0.751259i | \(-0.270553\pi\) | ||||
0.660008 | + | 0.751259i | \(0.270553\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −23.7324 | −1.41074 | −0.705371 | − | 0.708838i | \(-0.749220\pi\) | ||||
−0.705371 | + | 0.708838i | \(0.749220\pi\) | |||||||
\(284\) | 1.84321 | 0.109374 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.7615 | −0.695470 | ||||||||
\(287\) | −17.1689 | −1.01345 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 32.5526 | 1.91486 | ||||||||
\(290\) | −2.07732 | −0.121984 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.539830 | 0.0315911 | ||||||||
\(293\) | 18.6061 | 1.08698 | 0.543489 | − | 0.839416i | \(-0.317103\pi\) | ||||
0.543489 | + | 0.839416i | \(0.317103\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.32325 | 0.0770428 | ||||||||
\(296\) | −9.73692 | −0.565947 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.9837 | 1.50520 | ||||||||
\(299\) | −23.9473 | −1.38491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.3405 | 1.17241 | ||||||||
\(302\) | −8.61635 | −0.495815 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.5125 | 0.947056 | ||||||||
\(305\) | −3.52141 | −0.201635 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.7469 | 1.18409 | 0.592044 | − | 0.805905i | \(-0.298321\pi\) | ||||
0.592044 | + | 0.805905i | \(0.298321\pi\) | |||||||
\(308\) | 3.41025 | 0.194317 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.11112 | −0.0631073 | ||||||||
\(311\) | 20.3855 | 1.15596 | 0.577978 | − | 0.816053i | \(-0.303842\pi\) | ||||
0.577978 | + | 0.816053i | \(0.303842\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.8408 | −1.68670 | −0.843351 | − | 0.537364i | \(-0.819420\pi\) | ||||
−0.843351 | + | 0.537364i | \(0.819420\pi\) | |||||||
\(314\) | −6.84570 | −0.386325 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.13341 | 0.232522 | ||||||||
\(317\) | 4.31661 | 0.242445 | 0.121222 | − | 0.992625i | \(-0.461319\pi\) | ||||
0.121222 | + | 0.992625i | \(0.461319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.0615 | −0.563335 | ||||||||
\(320\) | −3.95793 | −0.221255 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −33.0428 | −1.84140 | ||||||||
\(323\) | −36.4976 | −2.03078 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.7983 | −0.876332 | ||||||||
\(326\) | −4.90474 | −0.271648 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.6682 | 0.809915 | ||||||||
\(329\) | 10.6585 | 0.587623 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.91891 | −0.160438 | −0.0802189 | − | 0.996777i | \(-0.525562\pi\) | ||||
−0.0802189 | + | 0.996777i | \(0.525562\pi\) | |||||||
\(332\) | −5.64608 | −0.309869 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11.7442 | −0.642615 | ||||||||
\(335\) | 4.21420 | 0.230246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.4415 | 0.786679 | 0.393339 | − | 0.919393i | \(-0.371320\pi\) | ||||
0.393339 | + | 0.919393i | \(0.371320\pi\) | |||||||
\(338\) | 2.79001 | 0.151757 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.09152 | 0.0591959 | ||||||||
\(341\) | −5.38170 | −0.291436 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.38413 | 0.290716 | ||||||||
\(344\) | −17.3778 | −0.936949 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.80840 | −0.419782 | ||||||||
\(347\) | −1.45404 | −0.0780571 | −0.0390285 | − | 0.999238i | \(-0.512426\pi\) | ||||
−0.0390285 | + | 0.999238i | \(0.512426\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.5817 | −1.47642 | −0.738208 | − | 0.674573i | \(-0.764328\pi\) | ||||
−0.738208 | + | 0.674573i | \(0.764328\pi\) | |||||||
\(350\) | −21.7987 | −1.16519 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.39599 | −0.287607 | ||||||||
\(353\) | 10.5321 | 0.560568 | 0.280284 | − | 0.959917i | \(-0.409571\pi\) | ||||
0.280284 | + | 0.959917i | \(0.409571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.36959 | 0.125765 | ||||||||
\(356\) | 6.39922 | 0.339158 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.2172 | −0.698550 | ||||||||
\(359\) | 14.7055 | 0.776124 | 0.388062 | − | 0.921633i | \(-0.373145\pi\) | ||||
0.388062 | + | 0.921633i | \(0.373145\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.88207 | 0.414846 | ||||||||
\(362\) | 29.7497 | 1.56361 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.03684 | 0.211588 | ||||||||
\(365\) | 0.693992 | 0.0363252 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.3628 | −1.11513 | −0.557564 | − | 0.830134i | \(-0.688264\pi\) | ||||
−0.557564 | + | 0.830134i | \(0.688264\pi\) | |||||||
\(368\) | 23.1755 | 1.20811 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.85204 | −0.0962832 | ||||||||
\(371\) | 30.9814 | 1.60847 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.6245 | 1.17145 | 0.585727 | − | 0.810508i | \(-0.300809\pi\) | ||||
0.585727 | + | 0.810508i | \(0.300809\pi\) | |||||||
\(374\) | −25.1585 | −1.30092 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.10607 | −0.469610 | ||||||||
\(377\) | −11.9101 | −0.613404 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.0743 | −0.877047 | −0.438523 | − | 0.898720i | \(-0.644498\pi\) | ||||
−0.438523 | + | 0.898720i | \(0.644498\pi\) | |||||||
\(380\) | −0.803951 | −0.0412418 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.8598 | −0.964951 | ||||||||
\(383\) | −38.9916 | −1.99238 | −0.996188 | − | 0.0872303i | \(-0.972198\pi\) | ||||
−0.996188 | + | 0.0872303i | \(0.972198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.38413 | 0.223436 | ||||||||
\(386\) | −30.1358 | −1.53387 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.51249 | −0.178320 | ||||||||
\(389\) | 10.2120 | 0.517771 | 0.258886 | − | 0.965908i | \(-0.416645\pi\) | ||||
0.258886 | + | 0.965908i | \(0.416645\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −51.2249 | −2.59056 | ||||||||
\(392\) | 16.5235 | 0.834561 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 11.6058 | 0.584690 | ||||||||
\(395\) | 5.31381 | 0.267367 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.14290 | −0.0573607 | −0.0286803 | − | 0.999589i | \(-0.509130\pi\) | ||||
−0.0286803 | + | 0.999589i | \(0.509130\pi\) | |||||||
\(398\) | −3.34765 | −0.167802 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.2891 | 0.764455 | ||||||||
\(401\) | −20.5540 | −1.02642 | −0.513208 | − | 0.858264i | \(-0.671543\pi\) | ||||
−0.513208 | + | 0.858264i | \(0.671543\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.37052 | −0.317338 | ||||||||
\(404\) | −0.722645 | −0.0359530 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.4338 | −0.815594 | ||||||||
\(407\) | −8.97037 | −0.444645 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.12836 | −0.401921 | −0.200961 | − | 0.979599i | \(-0.564406\pi\) | ||||
−0.200961 | + | 0.979599i | \(0.564406\pi\) | |||||||
\(410\) | 2.79001 | 0.137789 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.502993 | 0.0247807 | ||||||||
\(413\) | 10.4683 | 0.515112 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.25847 | −0.356304 | ||||||||
\(416\) | −6.38743 | −0.313170 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 18.5303 | 0.906348 | ||||||||
\(419\) | 35.7784 | 1.74789 | 0.873946 | − | 0.486024i | \(-0.161553\pi\) | ||||
0.873946 | + | 0.486024i | \(0.161553\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.1189 | −0.639374 | −0.319687 | − | 0.947523i | \(-0.603578\pi\) | ||||
−0.319687 | + | 0.947523i | \(0.603578\pi\) | |||||||
\(422\) | 21.0256 | 1.02351 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −26.4688 | −1.28544 | ||||||||
\(425\) | −33.7936 | −1.63923 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.8580 | −1.34814 | ||||||||
\(428\) | −0.776497 | −0.0375334 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.30541 | −0.159401 | ||||||||
\(431\) | 9.48411 | 0.456833 | 0.228417 | − | 0.973563i | \(-0.426645\pi\) | ||||
0.228417 | + | 0.973563i | \(0.426645\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6628 | 0.848820 | 0.424410 | − | 0.905470i | \(-0.360481\pi\) | ||||
0.424410 | + | 0.905470i | \(0.360481\pi\) | |||||||
\(434\) | −8.79012 | −0.421939 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.99495 | 0.191323 | ||||||||
\(437\) | 37.7294 | 1.80484 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.6655 | −0.843128 | −0.421564 | − | 0.906799i | \(-0.638519\pi\) | ||||
−0.421564 | + | 0.906799i | \(0.638519\pi\) | |||||||
\(440\) | −3.74557 | −0.178563 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −29.7811 | −1.41654 | ||||||||
\(443\) | −12.9921 | −0.617274 | −0.308637 | − | 0.951180i | \(-0.599873\pi\) | ||||
−0.308637 | + | 0.951180i | \(0.599873\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.22668 | 0.389982 | ||||||||
\(446\) | −4.75963 | −0.225375 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −31.3114 | −1.47932 | ||||||||
\(449\) | −4.62857 | −0.218436 | −0.109218 | − | 0.994018i | \(-0.534835\pi\) | ||||
−0.109218 | + | 0.994018i | \(0.534835\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5134 | 0.636322 | ||||||||
\(452\) | 0.586289 | 0.0275767 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.5767 | 0.637185 | ||||||||
\(455\) | 5.18966 | 0.243295 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.5672 | 0.962092 | 0.481046 | − | 0.876695i | \(-0.340257\pi\) | ||||
0.481046 | + | 0.876695i | \(0.340257\pi\) | |||||||
\(458\) | −17.3878 | −0.812477 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.12836 | −0.0526098 | ||||||||
\(461\) | −33.5725 | −1.56363 | −0.781813 | − | 0.623513i | \(-0.785705\pi\) | ||||
−0.781813 | + | 0.623513i | \(0.785705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.1310 | 0.610251 | 0.305126 | − | 0.952312i | \(-0.401302\pi\) | ||||
0.305126 | + | 0.952312i | \(0.401302\pi\) | |||||||
\(464\) | 11.5263 | 0.535094 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.3277 | −0.756366 | ||||||||
\(467\) | 23.6307 | 1.09350 | 0.546750 | − | 0.837296i | \(-0.315865\pi\) | ||||
0.546750 | + | 0.837296i | \(0.315865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 33.3387 | 1.53944 | ||||||||
\(470\) | −1.73205 | −0.0798935 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.94356 | −0.411661 | ||||||||
\(473\) | −16.0097 | −0.736128 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.8904 | 1.14205 | ||||||||
\(476\) | 8.63506 | 0.395787 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.52259 | 0.344075 | ||||||||
\(479\) | −5.88019 | −0.268673 | −0.134336 | − | 0.990936i | \(-0.542890\pi\) | ||||
−0.134336 | + | 0.990936i | \(0.542890\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6186 | −0.484164 | ||||||||
\(482\) | 10.9786 | 0.500061 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.13610 | 0.0516407 | ||||||||
\(485\) | −4.51557 | −0.205041 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.7965 | 1.75804 | 0.879020 | − | 0.476786i | \(-0.158198\pi\) | ||||
0.879020 | + | 0.476786i | \(0.158198\pi\) | |||||||
\(488\) | 23.8004 | 1.07739 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.14290 | 0.141982 | ||||||||
\(491\) | −37.5842 | −1.69615 | −0.848077 | − | 0.529873i | \(-0.822239\pi\) | ||||
−0.848077 | + | 0.529873i | \(0.822239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −25.4766 | −1.14741 | ||||||||
\(494\) | 21.9350 | 0.986904 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.16519 | 0.276825 | ||||||||
\(497\) | 18.7459 | 0.840868 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.7520 | 1.51095 | 0.755473 | − | 0.655180i | \(-0.227407\pi\) | ||||
0.755473 | + | 0.655180i | \(0.227407\pi\) | |||||||
\(500\) | −1.51968 | −0.0679623 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.68779 | 0.387755 | ||||||||
\(503\) | −18.7119 | −0.834324 | −0.417162 | − | 0.908832i | \(-0.636975\pi\) | ||||
−0.417162 | + | 0.908832i | \(0.636975\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.929015 | −0.0413406 | ||||||||
\(506\) | 26.0076 | 1.15618 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.928081 | 0.0411770 | ||||||||
\(509\) | 21.7682 | 0.964858 | 0.482429 | − | 0.875935i | \(-0.339755\pi\) | ||||
0.482429 | + | 0.875935i | \(0.339755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.49020 | 0.242872 | ||||||||
\(512\) | 25.4026 | 1.12265 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.73473 | −0.208840 | ||||||||
\(515\) | 0.646635 | 0.0284942 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.38919 | −0.368956 | ||||||||
\(518\) | −14.6516 | −0.643755 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.43376 | −0.194433 | ||||||||
\(521\) | −6.47643 | −0.283738 | −0.141869 | − | 0.989885i | \(-0.545311\pi\) | ||||
−0.141869 | + | 0.989885i | \(0.545311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.8726 | −0.475425 | −0.237712 | − | 0.971336i | \(-0.576398\pi\) | ||||
−0.237712 | + | 0.971336i | \(0.576398\pi\) | |||||||
\(524\) | −1.01406 | −0.0442995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.67675 | −0.203916 | ||||||||
\(527\) | −13.6270 | −0.593599 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 29.9537 | 1.30233 | ||||||||
\(530\) | −5.03460 | −0.218689 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.36009 | −0.275745 | ||||||||
\(533\) | 15.9963 | 0.692878 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.998245 | −0.0431579 | ||||||||
\(536\) | −28.4828 | −1.23027 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.11051 | 0.392782 | ||||||||
\(539\) | 15.2226 | 0.655686 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.6459 | 1.05961 | 0.529805 | − | 0.848120i | \(-0.322265\pi\) | ||||
0.529805 | + | 0.848120i | \(0.322265\pi\) | |||||||
\(542\) | 24.4259 | 1.04918 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −13.6631 | −0.585802 | ||||||||
\(545\) | 5.13581 | 0.219994 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.9273 | 1.32235 | 0.661177 | − | 0.750230i | \(-0.270057\pi\) | ||||
0.661177 | + | 0.750230i | \(0.270057\pi\) | |||||||
\(548\) | −1.61744 | −0.0690934 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.1575 | 0.731596 | ||||||||
\(551\) | 18.7646 | 0.799399 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.0378 | 1.78763 | ||||||||
\(554\) | 17.8594 | 0.758775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.77930 | 0.117869 | ||||||||
\(557\) | 23.3627 | 0.989908 | 0.494954 | − | 0.868919i | \(-0.335185\pi\) | ||||
0.494954 | + | 0.868919i | \(0.335185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −18.9513 | −0.801555 | ||||||||
\(560\) | −5.02239 | −0.212235 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.4466 | −1.19995 | ||||||||
\(563\) | 33.6877 | 1.41977 | 0.709884 | − | 0.704319i | \(-0.248747\pi\) | ||||
0.709884 | + | 0.704319i | \(0.248747\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.753718 | 0.0317092 | ||||||||
\(566\) | 30.5097 | 1.28242 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −16.0155 | −0.671995 | ||||||||
\(569\) | −30.7959 | −1.29103 | −0.645515 | − | 0.763748i | \(-0.723357\pi\) | ||||
−0.645515 | + | 0.763748i | \(0.723357\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.8753 | −1.25024 | −0.625120 | − | 0.780528i | \(-0.714950\pi\) | ||||
−0.625120 | + | 0.780528i | \(0.714950\pi\) | |||||||
\(572\) | −3.17734 | −0.132851 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 22.0719 | 0.921264 | ||||||||
\(575\) | 34.9340 | 1.45685 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.80747 | 0.200137 | 0.100069 | − | 0.994981i | \(-0.468094\pi\) | ||||
0.100069 | + | 0.994981i | \(0.468094\pi\) | |||||||
\(578\) | −41.8488 | −1.74068 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.561185 | −0.0233019 | ||||||||
\(581\) | −57.4221 | −2.38227 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −24.3851 | −1.00993 | ||||||||
\(584\) | −4.69053 | −0.194096 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.9195 | −0.988106 | ||||||||
\(587\) | 7.93761 | 0.327620 | 0.163810 | − | 0.986492i | \(-0.447622\pi\) | ||||
0.163810 | + | 0.986492i | \(0.447622\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.0368 | 0.413561 | ||||||||
\(590\) | −1.70114 | −0.0700349 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.2763 | 0.422354 | ||||||||
\(593\) | 36.2753 | 1.48965 | 0.744824 | − | 0.667261i | \(-0.232533\pi\) | ||||
0.744824 | + | 0.667261i | \(0.232533\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.1010 | 0.455097 | ||||||||
\(596\) | 7.01946 | 0.287528 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30.7861 | 1.25894 | ||||||||
\(599\) | 33.6450 | 1.37470 | 0.687349 | − | 0.726327i | \(-0.258774\pi\) | ||||
0.687349 | + | 0.726327i | \(0.258774\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.97771 | −0.121463 | −0.0607317 | − | 0.998154i | \(-0.519343\pi\) | ||||
−0.0607317 | + | 0.998154i | \(0.519343\pi\) | |||||||
\(602\) | −26.1492 | −1.06576 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.32770 | −0.0947126 | ||||||||
\(605\) | 1.46054 | 0.0593793 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.6486 | −0.635156 | −0.317578 | − | 0.948232i | \(-0.602870\pi\) | ||||
−0.317578 | + | 0.948232i | \(0.602870\pi\) | |||||||
\(608\) | 10.0635 | 0.408128 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.52704 | 0.183294 | ||||||||
\(611\) | −9.93058 | −0.401748 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.06687 | −0.0430903 | −0.0215452 | − | 0.999768i | \(-0.506859\pi\) | ||||
−0.0215452 | + | 0.999768i | \(0.506859\pi\) | |||||||
\(614\) | −26.6717 | −1.07638 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −29.6313 | −1.19388 | ||||||||
\(617\) | −13.0700 | −0.526177 | −0.263088 | − | 0.964772i | \(-0.584741\pi\) | ||||
−0.263088 | + | 0.964772i | \(0.584741\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.5175 | 0.824670 | 0.412335 | − | 0.911032i | \(-0.364713\pi\) | ||||
0.412335 | + | 0.911032i | \(0.364713\pi\) | |||||||
\(620\) | −0.300167 | −0.0120550 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −26.2071 | −1.05081 | ||||||||
\(623\) | 65.0817 | 2.60744 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 22.0496 | 0.881985 | ||||||||
\(626\) | 38.3626 | 1.53328 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.84936 | −0.0737973 | ||||||||
\(629\) | −22.7138 | −0.905658 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.3122 | −0.410523 | −0.205261 | − | 0.978707i | \(-0.565804\pi\) | ||||
−0.205261 | + | 0.978707i | \(0.565804\pi\) | |||||||
\(632\) | −35.9148 | −1.42861 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.54933 | −0.220392 | ||||||||
\(635\) | 1.19312 | 0.0473475 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.0196 | 0.713963 | ||||||||
\(638\) | 12.9348 | 0.512094 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.35504 | 0.132619 | ||||||||
\(641\) | 3.50616 | 0.138485 | 0.0692426 | − | 0.997600i | \(-0.477942\pi\) | ||||
0.0692426 | + | 0.997600i | \(0.477942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.5517 | 1.24428 | 0.622139 | − | 0.782907i | \(-0.286264\pi\) | ||||
0.622139 | + | 0.782907i | \(0.286264\pi\) | |||||||
\(644\) | −8.92647 | −0.351752 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 46.9205 | 1.84606 | ||||||||
\(647\) | −3.04628 | −0.119762 | −0.0598808 | − | 0.998206i | \(-0.519072\pi\) | ||||
−0.0598808 | + | 0.998206i | \(0.519072\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.23947 | −0.323428 | ||||||||
\(650\) | 20.3099 | 0.796620 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.32501 | −0.0518913 | ||||||||
\(653\) | −30.7374 | −1.20285 | −0.601423 | − | 0.798931i | \(-0.705399\pi\) | ||||
−0.601423 | + | 0.798931i | \(0.705399\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.30365 | −0.0509379 | ||||||||
\(656\) | −15.4808 | −0.604422 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −13.7023 | −0.534173 | ||||||||
\(659\) | −33.1839 | −1.29266 | −0.646331 | − | 0.763057i | \(-0.723698\pi\) | ||||
−0.646331 | + | 0.763057i | \(0.723698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.9077 | −0.579841 | −0.289920 | − | 0.957051i | \(-0.593629\pi\) | ||||
−0.289920 | + | 0.957051i | \(0.593629\pi\) | |||||||
\(662\) | 3.75248 | 0.145844 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 49.0583 | 1.90383 | ||||||||
\(665\) | −8.17637 | −0.317066 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 26.3364 | 1.01975 | ||||||||
\(668\) | −3.17269 | −0.122755 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.41767 | −0.209303 | ||||||||
\(671\) | 21.9267 | 0.846471 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.88888 | 0.265547 | 0.132773 | − | 0.991146i | \(-0.457612\pi\) | ||||
0.132773 | + | 0.991146i | \(0.457612\pi\) | |||||||
\(674\) | −18.5656 | −0.715122 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.753718 | 0.0289892 | ||||||||
\(677\) | −13.1892 | −0.506903 | −0.253452 | − | 0.967348i | \(-0.581566\pi\) | ||||
−0.253452 | + | 0.967348i | \(0.581566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −35.7229 | −1.37092 | ||||||||
\(680\) | −9.48411 | −0.363699 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.91859 | 0.264926 | ||||||||
\(683\) | −3.37814 | −0.129261 | −0.0646305 | − | 0.997909i | \(-0.520587\pi\) | ||||
−0.0646305 | + | 0.997909i | \(0.520587\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.07934 | −0.0794473 | ||||||||
\(686\) | −6.92171 | −0.264272 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 18.3405 | 0.699225 | ||||||||
\(689\) | −28.8655 | −1.09969 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4151 | 0.890752 | 0.445376 | − | 0.895344i | \(-0.353070\pi\) | ||||
0.445376 | + | 0.895344i | \(0.353070\pi\) | |||||||
\(692\) | −2.10943 | −0.0801884 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.86928 | 0.0709569 | ||||||||
\(695\) | 3.57300 | 0.135532 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.2172 | 1.29607 | ||||||||
\(698\) | 35.4584 | 1.34212 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5.88888 | −0.222579 | ||||||||
\(701\) | 45.5001 | 1.71852 | 0.859258 | − | 0.511543i | \(-0.170926\pi\) | ||||
0.859258 | + | 0.511543i | \(0.170926\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.7297 | 0.630972 | ||||||||
\(704\) | 24.6448 | 0.928836 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.5398 | −0.509578 | ||||||||
\(707\) | −7.34948 | −0.276406 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.6168 | 1.45028 | 0.725142 | − | 0.688599i | \(-0.241774\pi\) | ||||
0.725142 | + | 0.688599i | \(0.241774\pi\) | |||||||
\(710\) | −3.04628 | −0.114325 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −55.6023 | −2.08378 | ||||||||
\(713\) | 14.0868 | 0.527556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.08471 | −0.152760 | ||||||||
\(716\) | −3.57060 | −0.133440 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.9050 | −0.705527 | ||||||||
\(719\) | −49.3182 | −1.83926 | −0.919630 | − | 0.392786i | \(-0.871511\pi\) | ||||
−0.919630 | + | 0.392786i | \(0.871511\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.11556 | 0.190513 | ||||||||
\(722\) | −10.1330 | −0.377111 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.03684 | 0.298687 | ||||||||
\(725\) | 17.3744 | 0.645268 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.2945 | −1.19774 | −0.598868 | − | 0.800848i | \(-0.704383\pi\) | ||||
−0.598868 | + | 0.800848i | \(0.704383\pi\) | |||||||
\(728\) | −35.0757 | −1.29999 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.892178 | −0.0330210 | ||||||||
\(731\) | −40.5381 | −1.49935 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.4662 | 1.45772 | 0.728858 | − | 0.684665i | \(-0.240051\pi\) | ||||
0.728858 | + | 0.684665i | \(0.240051\pi\) | |||||||
\(734\) | 27.4635 | 1.01369 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.1242 | 0.520626 | ||||||||
\(737\) | −26.2405 | −0.966581 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.3090 | 1.29886 | 0.649432 | − | 0.760420i | \(-0.275007\pi\) | ||||
0.649432 | + | 0.760420i | \(0.275007\pi\) | |||||||
\(740\) | −0.500327 | −0.0183924 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −39.8289 | −1.46217 | ||||||||
\(743\) | −47.4106 | −1.73933 | −0.869663 | − | 0.493646i | \(-0.835664\pi\) | ||||
−0.869663 | + | 0.493646i | \(0.835664\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.02404 | 0.330615 | ||||||||
\(746\) | −29.0855 | −1.06490 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.79654 | −0.248506 | ||||||||
\(749\) | −7.89716 | −0.288556 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.92808 | −0.325790 | −0.162895 | − | 0.986643i | \(-0.552083\pi\) | ||||
−0.162895 | + | 0.986643i | \(0.552083\pi\) | |||||||
\(752\) | 9.61051 | 0.350459 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 15.3114 | 0.557608 | ||||||||
\(755\) | −2.99243 | −0.108906 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.63816 | −0.132231 | −0.0661155 | − | 0.997812i | \(-0.521061\pi\) | ||||
−0.0661155 | + | 0.997812i | \(0.521061\pi\) | |||||||
\(758\) | 21.9503 | 0.797270 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.98545 | 0.253389 | ||||||||
\(761\) | −6.68880 | −0.242469 | −0.121234 | − | 0.992624i | \(-0.538685\pi\) | ||||
−0.121234 | + | 0.992624i | \(0.538685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 40.6296 | 1.47089 | ||||||||
\(764\) | −5.09494 | −0.184329 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 50.1266 | 1.81115 | ||||||||
\(767\) | −9.75337 | −0.352174 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.4712 | −0.774272 | −0.387136 | − | 0.922023i | \(-0.626536\pi\) | ||||
−0.387136 | + | 0.922023i | \(0.626536\pi\) | |||||||
\(770\) | −5.63613 | −0.203112 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.14115 | −0.293006 | ||||||||
\(773\) | −10.2442 | −0.368457 | −0.184228 | − | 0.982883i | \(-0.558979\pi\) | ||||
−0.184228 | + | 0.982883i | \(0.558979\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.29322 | 0.333822 | ||||||||
\(776\) | 30.5197 | 1.09559 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.1284 | −0.470674 | ||||||||
\(779\) | −25.2024 | −0.902971 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7547 | −0.527963 | ||||||||
\(782\) | 65.8535 | 2.35492 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.4388 | −0.622815 | ||||||||
\(785\) | −2.37749 | −0.0848561 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.947682 | 0.0337812 | 0.0168906 | − | 0.999857i | \(-0.494623\pi\) | ||||
0.0168906 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(788\) | 3.13528 | 0.111690 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.83130 | −0.243047 | ||||||||
\(791\) | 5.96270 | 0.212009 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.9554 | 0.921704 | ||||||||
\(794\) | 1.46929 | 0.0521431 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.904362 | −0.0320543 | ||||||||
\(797\) | 7.01071 | 0.248332 | 0.124166 | − | 0.992261i | \(-0.460374\pi\) | ||||
0.124166 | + | 0.992261i | \(0.460374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −21.2422 | −0.751494 | ||||||||
\(800\) | 9.31790 | 0.329437 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 26.4237 | 0.933052 | ||||||||
\(803\) | −4.32127 | −0.152494 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.4757 | −0.404464 | ||||||||
\(806\) | 8.18978 | 0.288473 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.27900 | 0.220894 | ||||||||
\(809\) | −45.1028 | −1.58573 | −0.792866 | − | 0.609396i | \(-0.791412\pi\) | ||||
−0.792866 | + | 0.609396i | \(0.791412\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.07285 | 0.283476 | 0.141738 | − | 0.989904i | \(-0.454731\pi\) | ||||
0.141738 | + | 0.989904i | \(0.454731\pi\) | |||||||
\(812\) | −4.43956 | −0.155798 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.5321 | 0.404200 | ||||||||
\(815\) | −1.70340 | −0.0596674 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.8580 | 1.04460 | ||||||||
\(818\) | 10.4496 | 0.365362 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.753718 | 0.0263210 | ||||||||
\(821\) | 6.26936 | 0.218802 | 0.109401 | − | 0.993998i | \(-0.465107\pi\) | ||||
0.109401 | + | 0.993998i | \(0.465107\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.7929 | −0.689938 | −0.344969 | − | 0.938614i | \(-0.612111\pi\) | ||||
−0.344969 | + | 0.938614i | \(0.612111\pi\) | |||||||
\(824\) | −4.37046 | −0.152252 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −13.4578 | −0.468257 | ||||||||
\(827\) | −41.8003 | −1.45354 | −0.726769 | − | 0.686882i | \(-0.758979\pi\) | ||||
−0.726769 | + | 0.686882i | \(0.758979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7279 | 1.17142 | 0.585710 | − | 0.810521i | \(-0.300816\pi\) | ||||
0.585710 | + | 0.810521i | \(0.300816\pi\) | |||||||
\(830\) | 9.33130 | 0.323894 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 29.1729 | 1.01139 | ||||||||
\(833\) | 38.5451 | 1.33551 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.07873 | −0.141150 | ||||||||
\(836\) | 5.00594 | 0.173134 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −45.9959 | −1.58890 | ||||||||
\(839\) | 29.2868 | 1.01109 | 0.505546 | − | 0.862800i | \(-0.331291\pi\) | ||||
0.505546 | + | 0.862800i | \(0.331291\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.9017 | −0.548334 | ||||||||
\(842\) | 16.8653 | 0.581216 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.68004 | 0.195515 | ||||||||
\(845\) | 0.968961 | 0.0333333 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.5544 | 0.397013 | ||||||||
\(848\) | 27.9351 | 0.959296 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 43.4442 | 1.49012 | ||||||||
\(851\) | 23.4803 | 0.804895 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.5981 | 1.28734 | 0.643668 | − | 0.765305i | \(-0.277412\pi\) | ||||
0.643668 | + | 0.765305i | \(0.277412\pi\) | |||||||
\(854\) | 35.8136 | 1.22552 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.74691 | 0.230605 | ||||||||
\(857\) | 29.0100 | 0.990961 | 0.495481 | − | 0.868619i | \(-0.334992\pi\) | ||||
0.495481 | + | 0.868619i | \(0.334992\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.8675 | −0.848469 | −0.424235 | − | 0.905552i | \(-0.639457\pi\) | ||||
−0.424235 | + | 0.905552i | \(0.639457\pi\) | |||||||
\(860\) | −0.892951 | −0.0304494 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.1925 | −0.415279 | ||||||||
\(863\) | −42.4018 | −1.44337 | −0.721687 | − | 0.692219i | \(-0.756633\pi\) | ||||
−0.721687 | + | 0.692219i | \(0.756633\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.71183 | −0.0922050 | ||||||||
\(866\) | −22.7069 | −0.771611 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.37464 | −0.0806004 | ||||||||
\(869\) | −33.0874 | −1.12241 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.0618 | −1.05249 | ||||||||
\(872\) | −34.7117 | −1.17549 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −48.5039 | −1.64067 | ||||||||
\(875\) | −15.4556 | −0.522493 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.0547 | 0.407058 | 0.203529 | − | 0.979069i | \(-0.434759\pi\) | ||||
0.203529 | + | 0.979069i | \(0.434759\pi\) | |||||||
\(878\) | 22.7103 | 0.766436 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.95306 | 0.133258 | ||||||||
\(881\) | 14.7827 | 0.498041 | 0.249020 | − | 0.968498i | \(-0.419891\pi\) | ||||
0.249020 | + | 0.968498i | \(0.419891\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.8462 | −0.869793 | −0.434896 | − | 0.900480i | \(-0.643215\pi\) | ||||
−0.434896 | + | 0.900480i | \(0.643215\pi\) | |||||||
\(884\) | −8.04531 | −0.270593 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.7023 | 0.561126 | ||||||||
\(887\) | −45.8560 | −1.53969 | −0.769846 | − | 0.638229i | \(-0.779667\pi\) | ||||
−0.769846 | + | 0.638229i | \(0.779667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.43882 | 0.316568 | ||||||||
\(890\) | −10.5760 | −0.354509 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.28581 | −0.0430520 | ||||||||
\(893\) | 15.6458 | 0.523566 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.59028 | −0.153436 | ||||||||
\(896\) | 26.5419 | 0.886701 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.95037 | 0.198566 | ||||||||
\(899\) | 7.00605 | 0.233665 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −61.7452 | −2.05703 | ||||||||
\(902\) | −17.3725 | −0.578442 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.09421 | −0.169431 | ||||||||
\(905\) | 10.3320 | 0.343446 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7000 | −0.388491 | −0.194246 | − | 0.980953i | \(-0.562226\pi\) | ||||
−0.194246 | + | 0.980953i | \(0.562226\pi\) | |||||||
\(908\) | 3.66772 | 0.121717 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.67169 | −0.221165 | ||||||||
\(911\) | −28.6753 | −0.950054 | −0.475027 | − | 0.879971i | \(-0.657562\pi\) | ||||
−0.475027 | + | 0.879971i | \(0.657562\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.1962 | 1.49577 | ||||||||
\(914\) | −26.4406 | −0.874579 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.69728 | −0.155203 | ||||||||
\(917\) | −10.3133 | −0.340574 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.33511 | 0.143002 | 0.0715011 | − | 0.997441i | \(-0.477221\pi\) | ||||
0.0715011 | + | 0.997441i | \(0.477221\pi\) | |||||||
\(920\) | 9.80418 | 0.323234 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 43.1599 | 1.42140 | ||||||||
\(923\) | −17.4656 | −0.574888 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 15.4902 | 0.509315 | ||||||||
\(926\) | −16.8809 | −0.554742 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.02465 | 0.230596 | ||||||||
\(929\) | 12.8909 | 0.422937 | 0.211468 | − | 0.977385i | \(-0.432175\pi\) | ||||
0.211468 | + | 0.977385i | \(0.432175\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.3901 | −0.930449 | ||||||||
\(932\) | −4.41090 | −0.144484 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −30.3791 | −0.994034 | ||||||||
\(935\) | −8.73746 | −0.285746 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.2080 | −1.73823 | −0.869115 | − | 0.494610i | \(-0.835311\pi\) | ||||
−0.869115 | + | 0.494610i | \(0.835311\pi\) | |||||||
\(938\) | −42.8595 | −1.39941 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.467911 | −0.0152616 | ||||||||
\(941\) | −33.4075 | −1.08905 | −0.544526 | − | 0.838744i | \(-0.683290\pi\) | ||||
−0.544526 | + | 0.838744i | \(0.683290\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −35.3719 | −1.15187 | ||||||||
\(944\) | 9.43901 | 0.307214 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 20.5817 | 0.669169 | ||||||||
\(947\) | −15.5048 | −0.503837 | −0.251918 | − | 0.967748i | \(-0.581061\pi\) | ||||
−0.251918 | + | 0.967748i | \(0.581061\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.11524 | −0.166048 | ||||||||
\(950\) | −31.9985 | −1.03817 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −75.0292 | −2.43171 | ||||||||
\(953\) | 22.5049 | 0.729004 | 0.364502 | − | 0.931203i | \(-0.381239\pi\) | ||||
0.364502 | + | 0.931203i | \(0.381239\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.54993 | −0.211951 | ||||||||
\(956\) | 2.03222 | 0.0657266 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.55943 | 0.244234 | ||||||||
\(959\) | −16.4497 | −0.531189 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2526 | −0.879116 | ||||||||
\(962\) | 13.6510 | 0.440124 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.96585 | 0.0955237 | ||||||||
\(965\) | −10.4661 | −0.336914 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −41.8084 | −1.34447 | −0.672234 | − | 0.740339i | \(-0.734665\pi\) | ||||
−0.672234 | + | 0.740339i | \(0.734665\pi\) | |||||||
\(968\) | −9.87144 | −0.317280 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.80510 | 0.186391 | ||||||||
\(971\) | 35.8662 | 1.15100 | 0.575501 | − | 0.817801i | \(-0.304807\pi\) | ||||
0.575501 | + | 0.817801i | \(0.304807\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 28.2662 | 0.906173 | ||||||||
\(974\) | −49.8759 | −1.59813 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.1189 | −0.804035 | ||||||||
\(977\) | 14.0501 | 0.449502 | 0.224751 | − | 0.974416i | \(-0.427843\pi\) | ||||
0.224751 | + | 0.974416i | \(0.427843\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −51.2249 | −1.63716 | ||||||||
\(980\) | 0.849051 | 0.0271219 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 48.3174 | 1.54187 | ||||||||
\(983\) | −17.6891 | −0.564196 | −0.282098 | − | 0.959386i | \(-0.591030\pi\) | ||||
−0.282098 | + | 0.959386i | \(0.591030\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.03064 | 0.128427 | ||||||||
\(986\) | 32.7521 | 1.04304 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.92572 | 0.188522 | ||||||||
\(989\) | 41.9062 | 1.33254 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.8958 | 1.04497 | 0.522485 | − | 0.852649i | \(-0.325005\pi\) | ||||
0.522485 | + | 0.852649i | \(0.325005\pi\) | |||||||
\(992\) | 3.75736 | 0.119296 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −24.0993 | −0.764382 | ||||||||
\(995\) | −1.16263 | −0.0368577 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.0068 | 0.633622 | 0.316811 | − | 0.948489i | \(-0.397388\pi\) | ||||
0.316811 | + | 0.948489i | \(0.397388\pi\) | |||||||
\(998\) | −43.3907 | −1.37351 | ||||||||
\(999\) | 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 | 729.2.a.c.1.2 | ✓ | 6 | |
3.2 | odd | 2 | inner | 729.2.a.c.1.5 | yes | 6 | |
9.2 | odd | 6 | 729.2.c.c.244.2 | 12 | |||
9.4 | even | 3 | 729.2.c.c.487.5 | 12 | |||
9.5 | odd | 6 | 729.2.c.c.487.2 | 12 | |||
9.7 | even | 3 | 729.2.c.c.244.5 | 12 | |||
27.2 | odd | 18 | 729.2.e.q.568.1 | 12 | |||
27.4 | even | 9 | 729.2.e.m.406.1 | 12 | |||
27.5 | odd | 18 | 729.2.e.r.649.2 | 12 | |||
27.7 | even | 9 | 729.2.e.m.325.1 | 12 | |||
27.11 | odd | 18 | 729.2.e.r.82.2 | 12 | |||
27.13 | even | 9 | 729.2.e.q.163.2 | 12 | |||
27.14 | odd | 18 | 729.2.e.q.163.1 | 12 | |||
27.16 | even | 9 | 729.2.e.r.82.1 | 12 | |||
27.20 | odd | 18 | 729.2.e.m.325.2 | 12 | |||
27.22 | even | 9 | 729.2.e.r.649.1 | 12 | |||
27.23 | odd | 18 | 729.2.e.m.406.2 | 12 | |||
27.25 | even | 9 | 729.2.e.q.568.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
729.2.a.c.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
729.2.a.c.1.5 | yes | 6 | 3.2 | odd | 2 | inner | |
729.2.c.c.244.2 | 12 | 9.2 | odd | 6 | |||
729.2.c.c.244.5 | 12 | 9.7 | even | 3 | |||
729.2.c.c.487.2 | 12 | 9.5 | odd | 6 | |||
729.2.c.c.487.5 | 12 | 9.4 | even | 3 | |||
729.2.e.m.325.1 | 12 | 27.7 | even | 9 | |||
729.2.e.m.325.2 | 12 | 27.20 | odd | 18 | |||
729.2.e.m.406.1 | 12 | 27.4 | even | 9 | |||
729.2.e.m.406.2 | 12 | 27.23 | odd | 18 | |||
729.2.e.q.163.1 | 12 | 27.14 | odd | 18 | |||
729.2.e.q.163.2 | 12 | 27.13 | even | 9 | |||
729.2.e.q.568.1 | 12 | 27.2 | odd | 18 | |||
729.2.e.q.568.2 | 12 | 27.25 | even | 9 | |||
729.2.e.r.82.1 | 12 | 27.16 | even | 9 | |||
729.2.e.r.82.2 | 12 | 27.11 | odd | 18 | |||
729.2.e.r.649.1 | 12 | 27.22 | even | 9 | |||
729.2.e.r.649.2 | 12 | 27.5 | odd | 18 |