Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3808,2,Mod(1,3808)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3808, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3808.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3808 = 2^{5} \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3808.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: | \(30.4070330897\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.109859312.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 7x^{4} + 15x^{3} + 13x^{2} - 9x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.13809\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3808.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.59220 | −1.49661 | −0.748303 | − | 0.663357i | \(-0.769131\pi\) | ||||
−0.748303 | + | 0.663357i | \(0.769131\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.54237 | −1.58419 | −0.792097 | − | 0.610395i | \(-0.791011\pi\) | ||||
−0.792097 | + | 0.610395i | \(0.791011\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.71950 | 1.23983 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.51681 | −1.36187 | −0.680935 | − | 0.732344i | \(-0.738427\pi\) | ||||
−0.680935 | + | 0.732344i | \(0.738427\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.73108 | 1.03482 | 0.517408 | − | 0.855739i | \(-0.326897\pi\) | ||||
0.517408 | + | 0.855739i | \(0.326897\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.18252 | 2.37092 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.43935 | −0.330209 | −0.165105 | − | 0.986276i | \(-0.552796\pi\) | ||||
−0.165105 | + | 0.986276i | \(0.552796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.59220 | 0.565664 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.43935 | −0.717154 | −0.358577 | − | 0.933500i | \(-0.616738\pi\) | ||||
−0.358577 | + | 0.933500i | \(0.616738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.54836 | 1.50967 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.86508 | −0.358934 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.39551 | −1.00192 | −0.500961 | − | 0.865470i | \(-0.667020\pi\) | ||||
−0.500961 | + | 0.865470i | \(0.667020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.51250 | 1.70850 | 0.854248 | − | 0.519866i | \(-0.174018\pi\) | ||||
0.854248 | + | 0.519866i | \(0.174018\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.7085 | 2.03818 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.54237 | 0.598769 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.46886 | −0.241479 | −0.120740 | − | 0.992684i | \(-0.538527\pi\) | ||||
−0.120740 | + | 0.992684i | \(0.538527\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.67170 | −1.54871 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.4770 | 1.63623 | 0.818116 | − | 0.575054i | \(-0.195019\pi\) | ||||
0.818116 | + | 0.575054i | \(0.195019\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.53439 | 0.386491 | 0.193246 | − | 0.981150i | \(-0.438099\pi\) | ||||
0.193246 | + | 0.981150i | \(0.438099\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13.1758 | −1.96414 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.60860 | −0.818099 | −0.409050 | − | 0.912512i | \(-0.634140\pi\) | ||||
−0.409050 | + | 0.912512i | \(0.634140\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.59220 | 0.362980 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4283 | 1.43244 | 0.716221 | − | 0.697874i | \(-0.245870\pi\) | ||||
0.716221 | + | 0.697874i | \(0.245870\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16.0002 | 2.15747 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.73108 | 0.494194 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.74541 | −0.227232 | −0.113616 | − | 0.993525i | \(-0.536243\pi\) | ||||
−0.113616 | + | 0.993525i | \(0.536243\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.45540 | 0.826529 | 0.413265 | − | 0.910611i | \(-0.364388\pi\) | ||||
0.413265 | + | 0.910611i | \(0.364388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.71950 | −0.468612 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.2169 | −1.63935 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.62100 | 0.686715 | 0.343358 | − | 0.939205i | \(-0.388436\pi\) | ||||
0.343358 | + | 0.939205i | \(0.388436\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.91548 | 1.07330 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.96226 | 1.06362 | 0.531812 | − | 0.846862i | \(-0.321511\pi\) | ||||
0.531812 | + | 0.846862i | \(0.321511\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.8458 | 1.97165 | 0.985825 | − | 0.167775i | \(-0.0536583\pi\) | ||||
0.985825 | + | 0.167775i | \(0.0536583\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −19.5669 | −2.25939 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.51681 | 0.514739 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −14.8075 | −1.66598 | −0.832989 | − | 0.553289i | \(-0.813372\pi\) | ||||
−0.832989 | + | 0.553289i | \(0.813372\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.32384 | −0.702649 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.6314 | −1.27671 | −0.638357 | − | 0.769741i | \(-0.720386\pi\) | ||||
−0.638357 | + | 0.769741i | \(0.720386\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.54237 | 0.384224 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.9862 | 1.49948 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.54632 | 0.269910 | 0.134955 | − | 0.990852i | \(-0.456911\pi\) | ||||
0.134955 | + | 0.990852i | \(0.456911\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.73108 | −0.391123 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −24.6583 | −2.55695 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.09870 | 0.523116 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.8522 | −1.71108 | −0.855540 | − | 0.517737i | \(-0.826775\pi\) | ||||
−0.855540 | + | 0.517737i | \(0.826775\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −16.8003 | −1.68849 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.94062 | 0.989129 | 0.494564 | − | 0.869141i | \(-0.335328\pi\) | ||||
0.494564 | + | 0.869141i | \(0.335328\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.28346 | 0.816193 | 0.408097 | − | 0.912939i | \(-0.366193\pi\) | ||||
0.408097 | + | 0.912939i | \(0.366193\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.18252 | −0.896122 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.2339 | −0.989351 | −0.494675 | − | 0.869078i | \(-0.664713\pi\) | ||||
−0.494675 | + | 0.869078i | \(0.664713\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.68155 | −0.448412 | −0.224206 | − | 0.974542i | \(-0.571979\pi\) | ||||
−0.224206 | + | 0.974542i | \(0.571979\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.80758 | 0.361399 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.10023 | 0.573862 | 0.286931 | − | 0.957951i | \(-0.407365\pi\) | ||||
0.286931 | + | 0.957951i | \(0.407365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.1834 | 1.13611 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 13.8777 | 1.28300 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.00000 | 0.0916698 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.40161 | 0.854692 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −27.1585 | −2.44880 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.02723 | −0.807420 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.6546 | 1.30039 | 0.650194 | − | 0.759768i | \(-0.274688\pi\) | ||||
0.650194 | + | 0.759768i | \(0.274688\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.56965 | −0.578426 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.2045 | −1.59053 | −0.795266 | − | 0.606261i | \(-0.792669\pi\) | ||||
−0.795266 | + | 0.606261i | \(0.792669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.43935 | 0.124807 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 6.60679 | 0.568622 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.7465 | −1.43075 | −0.715374 | − | 0.698742i | \(-0.753744\pi\) | ||||
−0.715374 | + | 0.698742i | \(0.753744\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.7185 | 0.909131 | 0.454565 | − | 0.890713i | \(-0.349795\pi\) | ||||
0.454565 | + | 0.890713i | \(0.349795\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 14.5386 | 1.22437 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −16.8526 | −1.40928 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.1129 | 1.58724 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.59220 | −0.213801 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −10.2651 | −0.840951 | −0.420476 | − | 0.907304i | \(-0.638137\pi\) | ||||
−0.420476 | + | 0.907304i | \(0.638137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.32937 | −0.433698 | −0.216849 | − | 0.976205i | \(-0.569578\pi\) | ||||
−0.216849 | + | 0.976205i | \(0.569578\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.71950 | −0.300703 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −33.6968 | −2.70659 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.99488 | −0.398635 | −0.199317 | − | 0.979935i | \(-0.563872\pi\) | ||||
−0.199317 | + | 0.979935i | \(0.563872\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −27.0323 | −2.14380 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.43935 | 0.271059 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3615 | −0.968230 | −0.484115 | − | 0.875005i | \(-0.660858\pi\) | ||||
−0.484115 | + | 0.875005i | \(0.660858\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −41.4757 | −3.22888 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0465 | −0.854803 | −0.427401 | − | 0.904062i | \(-0.640571\pi\) | ||||
−0.427401 | + | 0.904062i | \(0.640571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.920956 | 0.0708428 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.35365 | −0.409404 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.54166 | 0.345296 | 0.172648 | − | 0.984984i | \(-0.444768\pi\) | ||||
0.172648 | + | 0.984984i | \(0.444768\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −7.54836 | −0.570603 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.52444 | 0.340078 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.5026 | 1.08397 | 0.541987 | − | 0.840387i | \(-0.317672\pi\) | ||||
0.541987 | + | 0.840387i | \(0.317672\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.28410 | 0.615753 | 0.307876 | − | 0.951426i | \(-0.400382\pi\) | ||||
0.307876 | + | 0.951426i | \(0.400382\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.7337 | −1.23699 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.20324 | 0.382550 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.51681 | 0.330302 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.86508 | 0.135664 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.46455 | −0.612473 | −0.306236 | − | 0.951955i | \(-0.599070\pi\) | ||||
−0.306236 | + | 0.951955i | \(0.599070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.7456 | −0.989431 | −0.494716 | − | 0.869055i | \(-0.664728\pi\) | ||||
−0.494716 | + | 0.869055i | \(0.664728\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 34.2607 | 2.45346 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.0451 | 1.35690 | 0.678452 | − | 0.734645i | \(-0.262651\pi\) | ||||
0.678452 | + | 0.734645i | \(0.262651\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.6562 | −0.897171 | −0.448585 | − | 0.893740i | \(-0.648072\pi\) | ||||
−0.448585 | + | 0.893740i | \(0.648072\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −14.5708 | −1.02774 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.39551 | 0.378691 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −37.1134 | −2.59211 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.7926 | −0.889150 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.50127 | 0.449702 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7503 | −1.35967 | −0.679835 | − | 0.733365i | \(-0.737948\pi\) | ||||
−0.679835 | + | 0.733365i | \(0.737948\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −23.2320 | −1.59183 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.97775 | −0.612277 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.51250 | −0.645751 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −43.6676 | −2.95079 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.73108 | −0.250980 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.79615 | 0.254209 | 0.127105 | − | 0.991889i | \(-0.459432\pi\) | ||||
0.127105 | + | 0.991889i | \(0.459432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 28.0761 | 1.87174 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.03992 | −0.400884 | −0.200442 | − | 0.979706i | \(-0.564238\pi\) | ||||
−0.200442 | + | 0.979706i | \(0.564238\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.6959 | 0.971131 | 0.485566 | − | 0.874200i | \(-0.338614\pi\) | ||||
0.485566 | + | 0.874200i | \(0.338614\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.7085 | −0.770361 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.77786 | 0.116472 | 0.0582358 | − | 0.998303i | \(-0.481452\pi\) | ||||
0.0582358 | + | 0.998303i | \(0.481452\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.8677 | 1.29603 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 38.3841 | 2.49331 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.74043 | 0.436002 | 0.218001 | − | 0.975949i | \(-0.430046\pi\) | ||||
0.218001 | + | 0.975949i | \(0.430046\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.20167 | 0.592732 | 0.296366 | − | 0.955074i | \(-0.404225\pi\) | ||||
0.296366 | + | 0.955074i | \(0.404225\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.9879 | 1.41052 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.54237 | −0.226314 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.37033 | −0.341706 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.1509 | 1.91074 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.6222 | −0.733588 | −0.366794 | − | 0.930302i | \(-0.619545\pi\) | ||||
−0.366794 | + | 0.930302i | \(0.619545\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.5349 | 0.976671 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.18252 | −0.575032 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 26.0183 | 1.62298 | 0.811490 | − | 0.584367i | \(-0.198657\pi\) | ||||
0.811490 | + | 0.584367i | \(0.198657\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.46886 | 0.0912705 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0686 | −1.24221 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 8.26913 | 0.509897 | 0.254948 | − | 0.966955i | \(-0.417942\pi\) | ||||
0.254948 | + | 0.966955i | \(0.417942\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −36.9410 | −2.26927 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −6.60058 | −0.403949 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.7447 | 0.655113 | 0.327556 | − | 0.944832i | \(-0.393775\pi\) | ||||
0.327556 | + | 0.944832i | \(0.393775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.79067 | −0.533995 | −0.266998 | − | 0.963697i | \(-0.586032\pi\) | ||||
−0.266998 | + | 0.963697i | \(0.586032\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.67170 | 0.585358 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −34.0945 | −2.05598 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2113 | −1.45472 | −0.727359 | − | 0.686257i | \(-0.759252\pi\) | ||||
−0.727359 | + | 0.686257i | \(0.759252\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 35.3817 | 2.11825 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.2067 | −1.14577 | −0.572886 | − | 0.819635i | \(-0.694176\pi\) | ||||
−0.572886 | + | 0.819635i | \(0.694176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.821301 | 0.0488213 | 0.0244106 | − | 0.999702i | \(-0.492229\pi\) | ||||
0.0244106 | + | 0.999702i | \(0.492229\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.2169 | −0.782899 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.4770 | −0.618437 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 43.6842 | 2.56081 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1753 | 0.594448 | 0.297224 | − | 0.954808i | \(-0.403939\pi\) | ||||
0.297224 | + | 0.954808i | \(0.403939\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.18287 | 0.359980 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.42421 | 0.488822 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −12.8325 | −0.742122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.53439 | −0.146080 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.7681 | −1.48034 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.8674 | −1.30938 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.76145 | 0.557115 | 0.278558 | − | 0.960420i | \(-0.410144\pi\) | ||||
0.278558 | + | 0.960420i | \(0.410144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.4724 | −1.22152 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.7977 | 1.63297 | 0.816484 | − | 0.577368i | \(-0.195920\pi\) | ||||
0.816484 | + | 0.577368i | \(0.195920\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −30.0549 | −1.69880 | −0.849401 | − | 0.527748i | \(-0.823037\pi\) | ||||
−0.849401 | + | 0.527748i | \(0.823037\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.1758 | 0.742373 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.7111 | −1.55641 | −0.778204 | − | 0.628011i | \(-0.783869\pi\) | ||||
−0.778204 | + | 0.628011i | \(0.783869\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 24.3705 | 1.36449 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.5284 | 1.48067 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.43935 | 0.0800875 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 28.1635 | 1.56223 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.1355 | 0.671096 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.60860 | 0.309212 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 36.2511 | 1.99254 | 0.996270 | − | 0.0862866i | \(-0.0275001\pi\) | ||||
0.996270 | + | 0.0862866i | \(0.0275001\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.46342 | −0.299393 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.9117 | −1.08789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.5223 | −1.33582 | −0.667908 | − | 0.744244i | \(-0.732810\pi\) | ||||
−0.667908 | + | 0.744244i | \(0.732810\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −15.8130 | −0.858845 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −42.9662 | −2.32675 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −31.5819 | −1.70031 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.53870 | −0.243650 | −0.121825 | − | 0.992552i | \(-0.538875\pi\) | ||||
−0.121825 | + | 0.992552i | \(0.538875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.0234 | 0.750654 | 0.375327 | − | 0.926892i | \(-0.377530\pi\) | ||||
0.375327 | + | 0.926892i | \(0.377530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.95875 | −0.371431 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.5746 | −0.988625 | −0.494313 | − | 0.869284i | \(-0.664580\pi\) | ||||
−0.494313 | + | 0.869284i | \(0.664580\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.7476 | −1.68499 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.59220 | −0.137194 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.2116 | 0.644502 | 0.322251 | − | 0.946654i | \(-0.395561\pi\) | ||||
0.322251 | + | 0.946654i | \(0.395561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.9283 | −0.890962 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −24.3708 | −1.27914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −59.6740 | −3.12348 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.86036 | 0.149309 | 0.0746547 | − | 0.997209i | \(-0.476215\pi\) | ||||
0.0746547 | + | 0.997209i | \(0.476215\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 38.9691 | 2.02865 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.4283 | −0.541412 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.3536 | 0.691423 | 0.345712 | − | 0.938341i | \(-0.387638\pi\) | ||||
0.345712 | + | 0.938341i | \(0.387638\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 23.4004 | 1.20839 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −20.1311 | −1.03680 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.7199 | 0.602011 | 0.301006 | − | 0.953622i | \(-0.402678\pi\) | ||||
0.301006 | + | 0.953622i | \(0.402678\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −37.9877 | −1.94617 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.30474 | 0.475450 | 0.237725 | − | 0.971333i | \(-0.423598\pi\) | ||||
0.237725 | + | 0.971333i | \(0.423598\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0002 | −0.815446 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.42666 | 0.479184 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.62846 | −0.234672 | −0.117336 | − | 0.993092i | \(-0.537435\pi\) | ||||
−0.117336 | + | 0.993092i | \(0.537435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.43935 | 0.173935 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 47.1896 | 2.38040 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 52.4537 | 2.63923 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50815 | −0.376823 | −0.188412 | − | 0.982090i | \(-0.560334\pi\) | ||||
−0.188412 | + | 0.982090i | \(0.560334\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.73108 | −0.186788 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.40815 | 0.220133 | 0.110066 | − | 0.993924i | \(-0.464894\pi\) | ||||
0.110066 | + | 0.993924i | \(0.464894\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.4919 | 1.76798 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 22.4013 | 1.11313 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.63457 | 0.328863 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.9817 | −0.740799 | −0.370399 | − | 0.928873i | \(-0.620779\pi\) | ||||
−0.370399 | + | 0.928873i | \(0.620779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 43.4102 | 2.14127 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.74541 | 0.0858858 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 41.2027 | 2.02256 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.7845 | −1.36061 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.548311 | 0.0267868 | 0.0133934 | − | 0.999910i | \(-0.495737\pi\) | ||||
0.0133934 | + | 0.999910i | \(0.495737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 35.6285 | 1.73643 | 0.868214 | − | 0.496189i | \(-0.165268\pi\) | ||||
0.868214 | + | 0.496189i | \(0.165268\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.8612 | −1.01431 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.54836 | −0.366149 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.45540 | −0.312399 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43.6853 | 2.10914 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.0338 | 0.964996 | 0.482498 | − | 0.875897i | \(-0.339730\pi\) | ||||
0.482498 | + | 0.875897i | \(0.339730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −35.9905 | −1.72959 | −0.864797 | − | 0.502121i | \(-0.832553\pi\) | ||||
−0.864797 | + | 0.502121i | \(0.832553\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −49.5444 | −2.37547 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.95042 | 0.236811 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.6939 | 1.60812 | 0.804060 | − | 0.594548i | \(-0.202669\pi\) | ||||
0.804060 | + | 0.594548i | \(0.202669\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.71950 | 0.177119 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.8734 | 1.22928 | 0.614642 | − | 0.788806i | \(-0.289301\pi\) | ||||
0.614642 | + | 0.788806i | \(0.289301\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.02002 | −0.427590 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 26.6092 | 1.25857 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.10618 | −0.240975 | −0.120488 | − | 0.992715i | \(-0.538446\pi\) | ||||
−0.120488 | + | 0.992715i | \(0.538446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.3226 | −2.22834 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8148 | 0.649076 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.2169 | 0.619616 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.46562 | −0.208893 | −0.104446 | − | 0.994531i | \(-0.533307\pi\) | ||||
−0.104446 | + | 0.994531i | \(0.533307\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.86508 | 0.0870543 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.1862 | −1.68536 | −0.842679 | − | 0.538416i | \(-0.819023\pi\) | ||||
−0.842679 | + | 0.538416i | \(0.819023\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −34.1567 | −1.58740 | −0.793698 | − | 0.608312i | \(-0.791847\pi\) | ||||
−0.793698 | + | 0.608312i | \(0.791847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 87.3487 | 4.05070 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −28.8993 | −1.33730 | −0.668650 | − | 0.743577i | \(-0.733127\pi\) | ||||
−0.668650 | + | 0.743577i | \(0.733127\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.62100 | −0.259554 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.9477 | 0.596599 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −11.4474 | −0.526351 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.8647 | −0.498508 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 38.7881 | 1.77599 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.51566 | −0.297708 | −0.148854 | − | 0.988859i | \(-0.547558\pi\) | ||||
−0.148854 | + | 0.988859i | \(0.547558\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.48043 | −0.249886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.91548 | −0.405668 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59.6966 | 2.71068 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −31.9526 | −1.44791 | −0.723954 | − | 0.689848i | \(-0.757677\pi\) | ||||
−0.723954 | + | 0.689848i | \(0.757677\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 32.0435 | 1.44906 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.3657 | −0.964220 | −0.482110 | − | 0.876111i | \(-0.660130\pi\) | ||||
−0.482110 | + | 0.876111i | \(0.660130\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.39551 | 0.243002 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 59.5127 | 2.67490 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.96226 | −0.402012 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 23.7954 | 1.06523 | 0.532613 | − | 0.846359i | \(-0.321210\pi\) | ||||
0.532613 | + | 0.846359i | \(0.321210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28.6347 | 1.27930 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.3116 | 0.771884 | 0.385942 | − | 0.922523i | \(-0.373876\pi\) | ||||
0.385942 | + | 0.922523i | \(0.373876\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −35.2133 | −1.56697 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.38730 | −0.106024 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.9619 | 1.37236 | 0.686181 | − | 0.727431i | \(-0.259286\pi\) | ||||
0.686181 | + | 0.727431i | \(0.259286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.8458 | −0.745214 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.68450 | 0.118523 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −29.3430 | −1.29301 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.3330 | 1.11415 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.7729 | −0.516773 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.6504 | −1.34282 | −0.671410 | − | 0.741086i | \(-0.734311\pi\) | ||||
−0.671410 | + | 0.741086i | \(0.734311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.5317 | −1.24760 | −0.623802 | − | 0.781582i | \(-0.714413\pi\) | ||||
−0.623802 | + | 0.781582i | \(0.714413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 19.5669 | 0.853968 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −9.51250 | −0.414371 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.1709 | −0.485690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.49203 | −0.281730 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.0905 | 1.69320 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 36.2523 | 1.56732 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −37.5936 | −1.62228 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.51681 | −0.194553 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.9235 | 1.80243 | 0.901217 | − | 0.433369i | \(-0.142675\pi\) | ||||
0.901217 | + | 0.433369i | \(0.142675\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −21.4740 | −0.921540 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 16.5838 | 0.710371 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.79915 | −0.0769260 | −0.0384630 | − | 0.999260i | \(-0.512246\pi\) | ||||
−0.0384630 | + | 0.999260i | \(0.512246\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.0108 | 1.02476 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.76603 | 0.330844 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.8075 | 0.629681 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13.4878 | −0.572527 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.9829 | 1.05856 | 0.529281 | − | 0.848447i | \(-0.322462\pi\) | ||||
0.529281 | + | 0.848447i | \(0.322462\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.45602 | 0.399947 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.7085 | −0.494332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.5109 | 1.49661 | 0.748303 | − | 0.663357i | \(-0.230869\pi\) | ||||
0.748303 | + | 0.663357i | \(0.230869\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −21.6093 | −0.909109 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.32384 | 0.265576 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.43122 | 0.143844 | 0.0719221 | − | 0.997410i | \(-0.477087\pi\) | ||||
0.0719221 | + | 0.997410i | \(0.477087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.6591 | −0.571618 | −0.285809 | − | 0.958287i | \(-0.592262\pi\) | ||||
−0.285809 | + | 0.958287i | \(0.592262\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.9418 | 0.916631 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −25.9615 | −1.08267 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.3265 | −0.471530 | −0.235765 | − | 0.971810i | \(-0.575759\pi\) | ||||
−0.235765 | + | 0.971810i | \(0.575759\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 35.6314 | 1.48079 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6314 | 0.482552 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −47.1028 | −1.95080 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −49.1600 | −2.03252 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.2746 | 1.41466 | 0.707332 | − | 0.706882i | \(-0.249899\pi\) | ||||
0.707332 | + | 0.706882i | \(0.249899\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.6918 | −0.564161 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −49.3686 | −2.03075 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.4883 | 1.04668 | 0.523340 | − | 0.852124i | \(-0.324686\pi\) | ||||
0.523340 | + | 0.852124i | \(0.324686\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.54237 | −0.145223 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.8073 | 1.34271 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.2250 | 1.48012 | 0.740058 | − | 0.672544i | \(-0.234798\pi\) | ||||
0.740058 | + | 0.672544i | \(0.234798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −29.6118 | −1.20789 | −0.603946 | − | 0.797025i | \(-0.706406\pi\) | ||||
−0.603946 | + | 0.797025i | \(0.706406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.9073 | 0.851411 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −33.3039 | −1.35400 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.44392 | −0.302139 | −0.151070 | − | 0.988523i | \(-0.548272\pi\) | ||||
−0.151070 | + | 0.988523i | \(0.548272\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.9862 | −0.566751 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.9262 | −0.846581 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.1924 | −1.78492 | −0.892458 | − | 0.451131i | \(-0.851021\pi\) | ||||
−0.892458 | + | 0.451131i | \(0.851021\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 96.2052 | 3.87937 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.2256 | 0.492185 | 0.246092 | − | 0.969246i | \(-0.420853\pi\) | ||||
0.246092 | + | 0.969246i | \(0.420853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.5860 | 0.907807 | 0.453903 | − | 0.891051i | \(-0.350031\pi\) | ||||
0.453903 | + | 0.891051i | \(0.350031\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.41465 | 0.257411 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.54632 | −0.102016 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.76404 | −0.230562 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.8526 | −0.673028 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.46886 | 0.0585673 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.9781 | 1.71093 | 0.855466 | − | 0.517859i | \(-0.173271\pi\) | ||||
0.855466 | + | 0.517859i | \(0.173271\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 51.1968 | 2.03489 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −51.9121 | −2.06007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.73108 | 0.147831 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 33.3351 | 1.31872 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0.431882 | 0.0170583 | 0.00852915 | − | 0.999964i | \(-0.497285\pi\) | ||||
0.00852915 | + | 0.999964i | \(0.497285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.8009 | 1.29354 | 0.646771 | − | 0.762685i | \(-0.276119\pi\) | ||||
0.646771 | + | 0.762685i | \(0.276119\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 23.2721 | 0.916339 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.8690 | −1.33153 | −0.665764 | − | 0.746163i | \(-0.731894\pi\) | ||||
−0.665764 | + | 0.746163i | \(0.731894\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.88367 | 0.309461 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.6583 | 0.966435 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.6324 | −0.807408 | −0.403704 | − | 0.914890i | \(-0.632277\pi\) | ||||
−0.403704 | + | 0.914890i | \(0.632277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 64.4869 | 2.51971 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 62.6578 | 2.44452 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.0024 | −0.506501 | −0.253251 | − | 0.967401i | \(-0.581500\pi\) | ||||
−0.253251 | + | 0.967401i | \(0.581500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13.4954 | −0.524911 | −0.262456 | − | 0.964944i | \(-0.584532\pi\) | ||||
−0.262456 | + | 0.964944i | \(0.584532\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.67170 | 0.375618 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.09870 | −0.197719 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 18.5571 | 0.718532 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.84039 | −0.380451 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −29.1578 | −1.12563 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.5966 | 0.716848 | 0.358424 | − | 0.933559i | \(-0.383314\pi\) | ||||
0.358424 | + | 0.933559i | \(0.383314\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −14.0783 | −0.541873 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.5433 | 1.63507 | 0.817536 | − | 0.575877i | \(-0.195339\pi\) | ||||
0.817536 | + | 0.575877i | \(0.195339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.8522 | 0.646727 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.6567 | 0.599965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.1730 | −0.733634 | −0.366817 | − | 0.930293i | \(-0.619552\pi\) | ||||
−0.366817 | + | 0.930293i | \(0.619552\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 59.3222 | 2.26658 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −38.0947 | −1.45340 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.9089 | 1.48231 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.5445 | −0.667423 | −0.333711 | − | 0.942675i | \(-0.608301\pi\) | ||||
−0.333711 | + | 0.942675i | \(0.608301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 16.8003 | 0.638190 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −37.9688 | −1.44024 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.4770 | −0.396844 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.60857 | −0.174312 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.9866 | −0.943731 | −0.471865 | − | 0.881671i | \(-0.656419\pi\) | ||||
−0.471865 | + | 0.881671i | \(0.656419\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.11420 | 0.0797386 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −51.5011 | −1.93964 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.94062 | −0.373856 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.26419 | −0.197701 | −0.0988504 | − | 0.995102i | \(-0.531517\pi\) | ||||
−0.0988504 | + | 0.995102i | \(0.531517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −55.0766 | −2.06553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −32.7168 | −1.22525 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 59.6981 | 2.23258 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.4725 | −0.652524 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.34650 | −0.311272 | −0.155636 | − | 0.987814i | \(-0.549743\pi\) | ||||
−0.155636 | + | 0.987814i | \(0.549743\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.28346 | −0.308492 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −23.8526 | −0.887086 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −40.7273 | −1.51257 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.8333 | 0.995192 | 0.497596 | − | 0.867409i | \(-0.334216\pi\) | ||||
0.497596 | + | 0.867409i | \(0.334216\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.0254 | −1.40835 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.53439 | −0.0937379 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.6937 | −1.28144 | −0.640721 | − | 0.767774i | \(-0.721365\pi\) | ||||
−0.640721 | + | 0.767774i | \(0.721365\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.18252 | 0.338702 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.3890 | −0.935217 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.0430 | 0.774079 | 0.387039 | − | 0.922063i | \(-0.373498\pi\) | ||||
0.387039 | + | 0.922063i | \(0.373498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.9210 | 0.511399 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.3303 | −1.40620 | −0.703101 | − | 0.711090i | \(-0.748202\pi\) | ||||
−0.703101 | + | 0.711090i | \(0.748202\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 36.3628 | 1.33223 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −43.2630 | −1.58291 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10.2339 | 0.373939 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.07533 | 0.294673 | 0.147336 | − | 0.989086i | \(-0.452930\pi\) | ||||
0.147336 | + | 0.989086i | \(0.452930\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 30.1271 | 1.09789 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.8786 | 0.687063 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.7790 | −1.70021 | −0.850106 | − | 0.526612i | \(-0.823462\pi\) | ||||
−0.850106 | + | 0.526612i | \(0.823462\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −40.2696 | −1.46169 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.34259 | 0.0849187 | 0.0424593 | − | 0.999098i | \(-0.486481\pi\) | ||||
0.0424593 | + | 0.999098i | \(0.486481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.68155 | 0.169484 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.1758 | 0.476373 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.51225 | −0.235144 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.736412 | −0.0265557 | −0.0132778 | − | 0.999912i | \(-0.504227\pi\) | ||||
−0.0132778 | + | 0.999912i | \(0.504227\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −67.4447 | −2.42896 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.0224 | −0.792092 | −0.396046 | − | 0.918231i | \(-0.629618\pi\) | ||||
−0.396046 | + | 0.918231i | \(0.629618\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 71.8038 | 2.57927 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.80758 | −0.136596 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0801 | −0.540299 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −40.4809 | −1.44852 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.0630 | 0.359624 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.6937 | 0.631515 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.8151 | 0.741977 | 0.370988 | − | 0.928637i | \(-0.379019\pi\) | ||||
0.370988 | + | 0.928637i | \(0.379019\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −21.4352 | −0.763115 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.10023 | −0.216899 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24.0856 | 0.855305 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 95.7584 | 3.39620 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −50.1164 | −1.77522 | −0.887608 | − | 0.460600i | \(-0.847634\pi\) | ||||
−0.887608 | + | 0.460600i | \(0.847634\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.60860 | 0.198418 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.47104 | 0.334643 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −76.0893 | −2.68513 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.1834 | −0.429410 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.8523 | −0.980446 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4099 | 0.365991 | 0.182995 | − | 0.983114i | \(-0.441421\pi\) | ||||
0.182995 | + | 0.983114i | \(0.441421\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.8637 | −0.592164 | −0.296082 | − | 0.955163i | \(-0.595680\pi\) | ||||
−0.296082 | + | 0.955163i | \(0.595680\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.7872 | 0.799181 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 43.7891 | 1.53386 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.64788 | −0.127623 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −13.8777 | −0.484927 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.7195 | 0.374113 | 0.187057 | − | 0.982349i | \(-0.440105\pi\) | ||||
0.187057 | + | 0.982349i | \(0.440105\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.7974 | −1.28268 | −0.641338 | − | 0.767259i | \(-0.721620\pi\) | ||||
−0.641338 | + | 0.767259i | \(0.721620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 88.3799 | 3.07699 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.32892 | −0.220078 | −0.110039 | − | 0.993927i | \(-0.535098\pi\) | ||||
−0.110039 | + | 0.993927i | \(0.535098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.9253 | 1.17828 | 0.589138 | − | 0.808033i | \(-0.299467\pi\) | ||||
0.589138 | + | 0.808033i | \(0.299467\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 62.7606 | 2.17714 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.00000 | −0.0346479 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 39.1307 | 1.35417 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.7415 | −0.613238 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.6470 | 1.36877 | 0.684383 | − | 0.729123i | \(-0.260072\pi\) | ||||
0.684383 | + | 0.729123i | \(0.260072\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.111553 | 0.00384666 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 49.7875 | 1.71477 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.26236 | −0.112229 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.40161 | −0.323043 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.12898 | −0.0730663 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.05192 | 0.173178 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.8928 | 1.60558 | 0.802789 | − | 0.596263i | \(-0.203348\pi\) | ||||
0.802789 | + | 0.596263i | \(0.203348\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.9646 | 0.648576 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −43.6201 | −1.49003 | −0.745016 | − | 0.667046i | \(-0.767558\pi\) | ||||
−0.745016 | + | 0.667046i | \(0.767558\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −56.7054 | −1.93476 | −0.967381 | − | 0.253326i | \(-0.918475\pi\) | ||||
−0.967381 | + | 0.253326i | \(0.918475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 27.1585 | 0.925558 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −13.5523 | −0.461326 | −0.230663 | − | 0.973034i | \(-0.574089\pi\) | ||||
−0.230663 | + | 0.973034i | \(0.574089\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16.0882 | −0.547016 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.59220 | −0.0880357 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.8829 | 2.26885 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.9724 | 0.710623 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −62.6816 | −2.12145 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.02723 | 0.305176 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −41.6525 | −1.40651 | −0.703253 | − | 0.710940i | \(-0.748270\pi\) | ||||
−0.703253 | + | 0.710940i | \(0.748270\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −26.3764 | −0.889655 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.7683 | 0.564937 | 0.282469 | − | 0.959277i | \(-0.408847\pi\) | ||||
0.282469 | + | 0.959277i | \(0.408847\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.06620 | −0.0695331 | −0.0347665 | − | 0.999395i | \(-0.511069\pi\) | ||||
−0.0347665 | + | 0.999395i | \(0.511069\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0272 | −0.538749 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.6135 | 1.16221 | 0.581104 | − | 0.813829i | \(-0.302621\pi\) | ||||
0.581104 | + | 0.813829i | \(0.302621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.6546 | −0.491501 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.5636 | 0.956916 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.07274 | 0.270144 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −51.3735 | −1.71723 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 33.2644 | 1.11066 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −51.3248 | −1.71178 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.4283 | −0.347418 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.56965 | 0.218624 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −29.3453 | −0.975472 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0657 | −0.467043 | −0.233522 | − | 0.972352i | \(-0.575025\pi\) | ||||
−0.233522 | + | 0.972352i | \(0.575025\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.9741 | 1.22635 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.9222 | 1.05763 | 0.528814 | − | 0.848738i | \(-0.322637\pi\) | ||||
0.528814 | + | 0.848738i | \(0.322637\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.5369 | 1.73872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 59.2768 | 1.95963 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.2045 | 0.601164 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.8206 | −0.521874 | −0.260937 | − | 0.965356i | \(-0.584031\pi\) | ||||
−0.260937 | + | 0.965356i | \(0.584031\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.3036 | −0.833783 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 33.4389 | 1.10065 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.0875 | −0.364554 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30.8103 | 1.01194 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −34.0082 | −1.11577 | −0.557887 | − | 0.829917i | \(-0.688388\pi\) | ||||
−0.557887 | + | 0.829917i | \(0.688388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.43935 | −0.0471728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −74.6494 | −2.44391 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −16.0002 | −0.523263 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.0018 | 0.947449 | 0.473725 | − | 0.880673i | \(-0.342909\pi\) | ||||
0.473725 | + | 0.880673i | \(0.342909\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 77.9082 | 2.54244 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.82875 | −0.222611 | −0.111305 | − | 0.993786i | \(-0.535503\pi\) | ||||
−0.111305 | + | 0.993786i | \(0.535503\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −36.0340 | −1.17343 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.60679 | −0.214919 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.6225 | 0.767628 | 0.383814 | − | 0.923410i | \(-0.374610\pi\) | ||||
0.383814 | + | 0.923410i | \(0.374610\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 62.8530 | 2.04029 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 71.8326 | 2.32933 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.7506 | 0.380639 | 0.190319 | − | 0.981722i | \(-0.439048\pi\) | ||||
0.190319 | + | 0.981722i | \(0.439048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.9845 | 0.970276 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −63.1733 | −2.04210 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 16.7465 | 0.540772 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 59.4876 | 1.91896 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −38.0650 | −1.22663 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 48.6920 | 1.56745 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.4946 | 0.723376 | 0.361688 | − | 0.932299i | \(-0.382200\pi\) | ||||
0.361688 | + | 0.932299i | \(0.382200\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.73108 | −0.119860 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.1947 | −0.776445 | −0.388223 | − | 0.921566i | \(-0.626911\pi\) | ||||
−0.388223 | + | 0.921566i | \(0.626911\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.7185 | −0.343619 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −73.0055 | −2.33805 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45.3568 | −1.45109 | −0.725547 | − | 0.688173i | \(-0.758413\pi\) | ||||
−0.725547 | + | 0.688173i | \(0.758413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.5013 | −0.367582 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −17.4130 | −0.555955 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.89307 | 0.156065 | 0.0780323 | − | 0.996951i | \(-0.475136\pi\) | ||||
0.0780323 | + | 0.996951i | \(0.475136\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −67.4646 | −2.14960 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.5386 | −0.462769 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.71666 | −0.277174 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.0697 | −0.319875 | −0.159938 | − | 0.987127i | \(-0.551129\pi\) | ||||
−0.159938 | + | 0.987127i | \(0.551129\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −93.9701 | −2.98205 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.8327 | 1.42129 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.8627 | 0.502377 | 0.251188 | − | 0.967938i | \(-0.419179\pi\) | ||||
0.251188 | + | 0.967938i | \(0.419179\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.73954 | 0.0866751 |
(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 | 3808.2.a.h.1.2 | ✓ | 6 | |
4.3 | odd | 2 | 3808.2.a.p.1.5 | yes | 6 | ||
8.3 | odd | 2 | 7616.2.a.bu.1.2 | 6 | |||
8.5 | even | 2 | 7616.2.a.cc.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3808.2.a.h.1.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
3808.2.a.p.1.5 | yes | 6 | 4.3 | odd | 2 | ||
7616.2.a.bu.1.2 | 6 | 8.3 | odd | 2 | |||
7616.2.a.cc.1.5 | 6 | 8.5 | even | 2 |