Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} + \cdots - 375 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.99250\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.99250 | −0.891073 | −0.445536 | − | 0.895264i | \(-0.646987\pi\) | ||||
−0.445536 | + | 0.895264i | \(0.646987\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.0206178 | −0.00779281 | −0.00389641 | − | 0.999992i | \(-0.501240\pi\) | ||||
−0.00389641 | + | 0.999992i | \(0.501240\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.99250 | −0.630084 | ||||||||
\(11\) | −5.26122 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.30783 | 0.362726 | 0.181363 | − | 0.983416i | \(-0.441949\pi\) | ||||
0.181363 | + | 0.983416i | \(0.441949\pi\) | |||||||
\(14\) | −0.0206178 | −0.00551035 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.05669 | 0.983892 | 0.491946 | − | 0.870626i | \(-0.336286\pi\) | ||||
0.491946 | + | 0.870626i | \(0.336286\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.295188 | 0.0677207 | 0.0338604 | − | 0.999427i | \(-0.489220\pi\) | ||||
0.0338604 | + | 0.999427i | \(0.489220\pi\) | |||||||
\(20\) | −1.99250 | −0.445536 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.26122 | −1.12170 | ||||||||
\(23\) | 1.64920 | 0.343882 | 0.171941 | − | 0.985107i | \(-0.444996\pi\) | ||||
0.171941 | + | 0.985107i | \(0.444996\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.02995 | −0.205990 | ||||||||
\(26\) | 1.30783 | 0.256486 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0206178 | −0.00389641 | ||||||||
\(29\) | 3.96430 | 0.736153 | 0.368076 | − | 0.929796i | \(-0.380016\pi\) | ||||
0.368076 | + | 0.929796i | \(0.380016\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.69374 | 1.56144 | 0.780721 | − | 0.624880i | \(-0.214852\pi\) | ||||
0.780721 | + | 0.624880i | \(0.214852\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.05669 | 0.695717 | ||||||||
\(35\) | 0.0410810 | 0.00694396 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.66851 | −1.42509 | −0.712547 | − | 0.701624i | \(-0.752459\pi\) | ||||
−0.712547 | + | 0.701624i | \(0.752459\pi\) | |||||||
\(38\) | 0.295188 | 0.0478858 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.99250 | −0.315042 | ||||||||
\(41\) | 0.291717 | 0.0455585 | 0.0227793 | − | 0.999741i | \(-0.492749\pi\) | ||||
0.0227793 | + | 0.999741i | \(0.492749\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.389669 | −0.0594240 | −0.0297120 | − | 0.999559i | \(-0.509459\pi\) | ||||
−0.0297120 | + | 0.999559i | \(0.509459\pi\) | |||||||
\(44\) | −5.26122 | −0.793159 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.64920 | 0.243161 | ||||||||
\(47\) | −4.57012 | −0.666621 | −0.333310 | − | 0.942817i | \(-0.608166\pi\) | ||||
−0.333310 | + | 0.942817i | \(0.608166\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.99957 | −0.999939 | ||||||||
\(50\) | −1.02995 | −0.145657 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.30783 | 0.181363 | ||||||||
\(53\) | −7.77757 | −1.06833 | −0.534166 | − | 0.845380i | \(-0.679374\pi\) | ||||
−0.534166 | + | 0.845380i | \(0.679374\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.4830 | 1.41352 | ||||||||
\(56\) | −0.0206178 | −0.00275517 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.96430 | 0.520539 | ||||||||
\(59\) | −12.8606 | −1.67430 | −0.837151 | − | 0.546972i | \(-0.815781\pi\) | ||||
−0.837151 | + | 0.546972i | \(0.815781\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.40709 | 0.948381 | 0.474190 | − | 0.880422i | \(-0.342741\pi\) | ||||
0.474190 | + | 0.880422i | \(0.342741\pi\) | |||||||
\(62\) | 8.69374 | 1.10411 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.60584 | −0.323215 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.96178 | 0.728348 | 0.364174 | − | 0.931331i | \(-0.381351\pi\) | ||||
0.364174 | + | 0.931331i | \(0.381351\pi\) | |||||||
\(68\) | 4.05669 | 0.491946 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0410810 | 0.00491012 | ||||||||
\(71\) | 10.2613 | 1.21779 | 0.608895 | − | 0.793251i | \(-0.291613\pi\) | ||||
0.608895 | + | 0.793251i | \(0.291613\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.21734 | 0.610644 | 0.305322 | − | 0.952249i | \(-0.401236\pi\) | ||||
0.305322 | + | 0.952249i | \(0.401236\pi\) | |||||||
\(74\) | −8.66851 | −1.00769 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.295188 | 0.0338604 | ||||||||
\(77\) | 0.108475 | 0.0123619 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.69527 | 0.640768 | 0.320384 | − | 0.947288i | \(-0.396188\pi\) | ||||
0.320384 | + | 0.947288i | \(0.396188\pi\) | |||||||
\(80\) | −1.99250 | −0.222768 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.291717 | 0.0322147 | ||||||||
\(83\) | −11.8162 | −1.29700 | −0.648499 | − | 0.761215i | \(-0.724603\pi\) | ||||
−0.648499 | + | 0.761215i | \(0.724603\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.08295 | −0.876720 | ||||||||
\(86\) | −0.389669 | −0.0420191 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.26122 | −0.560848 | ||||||||
\(89\) | −11.4015 | −1.20855 | −0.604277 | − | 0.796775i | \(-0.706538\pi\) | ||||
−0.604277 | + | 0.796775i | \(0.706538\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.0269646 | −0.00282665 | ||||||||
\(92\) | 1.64920 | 0.171941 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.57012 | −0.471372 | ||||||||
\(95\) | −0.588161 | −0.0603441 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.168718 | −0.0171308 | −0.00856538 | − | 0.999963i | \(-0.502726\pi\) | ||||
−0.00856538 | + | 0.999963i | \(0.502726\pi\) | |||||||
\(98\) | −6.99957 | −0.707064 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.02995 | −0.102995 | ||||||||
\(101\) | −15.0043 | −1.49298 | −0.746492 | − | 0.665395i | \(-0.768263\pi\) | ||||
−0.746492 | + | 0.665395i | \(0.768263\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19991 | −0.216763 | −0.108382 | − | 0.994109i | \(-0.534567\pi\) | ||||
−0.108382 | + | 0.994109i | \(0.534567\pi\) | |||||||
\(104\) | 1.30783 | 0.128243 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.77757 | −0.755425 | ||||||||
\(107\) | 4.80921 | 0.464924 | 0.232462 | − | 0.972605i | \(-0.425322\pi\) | ||||
0.232462 | + | 0.972605i | \(0.425322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.8433 | −1.23016 | −0.615081 | − | 0.788464i | \(-0.710877\pi\) | ||||
−0.615081 | + | 0.788464i | \(0.710877\pi\) | |||||||
\(110\) | 10.4830 | 0.999513 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.0206178 | −0.00194820 | ||||||||
\(113\) | 3.21231 | 0.302189 | 0.151094 | − | 0.988519i | \(-0.451720\pi\) | ||||
0.151094 | + | 0.988519i | \(0.451720\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.28603 | −0.306424 | ||||||||
\(116\) | 3.96430 | 0.368076 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.8606 | −1.18391 | ||||||||
\(119\) | −0.0836402 | −0.00766729 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.6804 | 1.51640 | ||||||||
\(122\) | 7.40709 | 0.670607 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.69374 | 0.780721 | ||||||||
\(125\) | 12.0147 | 1.07462 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1266 | 1.25354 | 0.626768 | − | 0.779206i | \(-0.284377\pi\) | ||||
0.626768 | + | 0.779206i | \(0.284377\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.60584 | −0.228548 | ||||||||
\(131\) | −17.7947 | −1.55473 | −0.777364 | − | 0.629051i | \(-0.783444\pi\) | ||||
−0.777364 | + | 0.629051i | \(0.783444\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.00608613 | −0.000527735 0 | ||||||||
\(134\) | 5.96178 | 0.515020 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.05669 | 0.347858 | ||||||||
\(137\) | −3.79487 | −0.324217 | −0.162109 | − | 0.986773i | \(-0.551830\pi\) | ||||
−0.162109 | + | 0.986773i | \(0.551830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.1582 | −1.11607 | −0.558034 | − | 0.829818i | \(-0.688444\pi\) | ||||
−0.558034 | + | 0.829818i | \(0.688444\pi\) | |||||||
\(140\) | 0.0410810 | 0.00347198 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.2613 | 0.861108 | ||||||||
\(143\) | −6.88076 | −0.575398 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.89887 | −0.655966 | ||||||||
\(146\) | 5.21734 | 0.431790 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.66851 | −0.712547 | ||||||||
\(149\) | −1.00000 | −0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.5614 | −1.10361 | −0.551806 | − | 0.833972i | \(-0.686061\pi\) | ||||
−0.551806 | + | 0.833972i | \(0.686061\pi\) | |||||||
\(152\) | 0.295188 | 0.0239429 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.108475 | 0.00874116 | ||||||||
\(155\) | −17.3223 | −1.39136 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.9231 | −0.951564 | −0.475782 | − | 0.879563i | \(-0.657835\pi\) | ||||
−0.475782 | + | 0.879563i | \(0.657835\pi\) | |||||||
\(158\) | 5.69527 | 0.453091 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.99250 | −0.157521 | ||||||||
\(161\) | −0.0340029 | −0.00267981 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.75467 | −0.215763 | −0.107881 | − | 0.994164i | \(-0.534407\pi\) | ||||
−0.107881 | + | 0.994164i | \(0.534407\pi\) | |||||||
\(164\) | 0.291717 | 0.0227793 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.8162 | −0.917116 | ||||||||
\(167\) | −21.6245 | −1.67336 | −0.836678 | − | 0.547695i | \(-0.815505\pi\) | ||||
−0.836678 | + | 0.547695i | \(0.815505\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2896 | −0.868430 | ||||||||
\(170\) | −8.08295 | −0.619934 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.389669 | −0.0297120 | ||||||||
\(173\) | −17.8683 | −1.35850 | −0.679252 | − | 0.733905i | \(-0.737696\pi\) | ||||
−0.679252 | + | 0.733905i | \(0.737696\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.0212353 | 0.00160524 | ||||||||
\(176\) | −5.26122 | −0.396579 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −11.4015 | −0.854576 | ||||||||
\(179\) | −14.6929 | −1.09820 | −0.549098 | − | 0.835758i | \(-0.685029\pi\) | ||||
−0.549098 | + | 0.835758i | \(0.685029\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.5258 | 1.52567 | 0.762834 | − | 0.646595i | \(-0.223808\pi\) | ||||
0.762834 | + | 0.646595i | \(0.223808\pi\) | |||||||
\(182\) | −0.0269646 | −0.00199875 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.64920 | 0.121581 | ||||||||
\(185\) | 17.2720 | 1.26986 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.3432 | −1.56077 | ||||||||
\(188\) | −4.57012 | −0.333310 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.588161 | −0.0426697 | ||||||||
\(191\) | −16.1527 | −1.16877 | −0.584384 | − | 0.811477i | \(-0.698664\pi\) | ||||
−0.584384 | + | 0.811477i | \(0.698664\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.667178 | 0.0480245 | 0.0240123 | − | 0.999712i | \(-0.492356\pi\) | ||||
0.0240123 | + | 0.999712i | \(0.492356\pi\) | |||||||
\(194\) | −0.168718 | −0.0121133 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.99957 | −0.499970 | ||||||||
\(197\) | −2.10056 | −0.149659 | −0.0748295 | − | 0.997196i | \(-0.523841\pi\) | ||||
−0.0748295 | + | 0.997196i | \(0.523841\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.4910 | −1.23990 | −0.619951 | − | 0.784641i | \(-0.712848\pi\) | ||||
−0.619951 | + | 0.784641i | \(0.712848\pi\) | |||||||
\(200\) | −1.02995 | −0.0728283 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.0043 | −1.05570 | ||||||||
\(203\) | −0.0817354 | −0.00573670 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.581245 | −0.0405959 | ||||||||
\(206\) | −2.19991 | −0.153275 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.30783 | 0.0906815 | ||||||||
\(209\) | −1.55305 | −0.107427 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.81415 | −0.469105 | −0.234553 | − | 0.972103i | \(-0.575363\pi\) | ||||
−0.234553 | + | 0.972103i | \(0.575363\pi\) | |||||||
\(212\) | −7.77757 | −0.534166 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.80921 | 0.328751 | ||||||||
\(215\) | 0.776416 | 0.0529511 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.179246 | −0.0121680 | ||||||||
\(218\) | −12.8433 | −0.869857 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.4830 | 0.706762 | ||||||||
\(221\) | 5.30545 | 0.356883 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.9915 | −1.33873 | −0.669366 | − | 0.742933i | \(-0.733434\pi\) | ||||
−0.669366 | + | 0.742933i | \(0.733434\pi\) | |||||||
\(224\) | −0.0206178 | −0.00137759 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.21231 | 0.213680 | ||||||||
\(227\) | 13.5705 | 0.900706 | 0.450353 | − | 0.892851i | \(-0.351298\pi\) | ||||
0.450353 | + | 0.892851i | \(0.351298\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.0742 | 1.78912 | 0.894558 | − | 0.446952i | \(-0.147491\pi\) | ||||
0.894558 | + | 0.446952i | \(0.147491\pi\) | |||||||
\(230\) | −3.28603 | −0.216674 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.96430 | 0.260269 | ||||||||
\(233\) | −1.11238 | −0.0728743 | −0.0364371 | − | 0.999336i | \(-0.511601\pi\) | ||||
−0.0364371 | + | 0.999336i | \(0.511601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.10596 | 0.594007 | ||||||||
\(236\) | −12.8606 | −0.837151 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0836402 | −0.00542159 | ||||||||
\(239\) | 21.3359 | 1.38011 | 0.690053 | − | 0.723759i | \(-0.257587\pi\) | ||||
0.690053 | + | 0.723759i | \(0.257587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.94889 | 0.512033 | 0.256016 | − | 0.966672i | \(-0.417590\pi\) | ||||
0.256016 | + | 0.966672i | \(0.417590\pi\) | |||||||
\(242\) | 16.6804 | 1.07226 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 7.40709 | 0.474190 | ||||||||
\(245\) | 13.9466 | 0.891019 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.386054 | 0.0245640 | ||||||||
\(248\) | 8.69374 | 0.552053 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0147 | 0.759874 | ||||||||
\(251\) | −30.3459 | −1.91541 | −0.957707 | − | 0.287745i | \(-0.907094\pi\) | ||||
−0.957707 | + | 0.287745i | \(0.907094\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.67680 | −0.545506 | ||||||||
\(254\) | 14.1266 | 0.886383 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.3203 | 0.706142 | 0.353071 | − | 0.935596i | \(-0.385137\pi\) | ||||
0.353071 | + | 0.935596i | \(0.385137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.178726 | 0.0111055 | ||||||||
\(260\) | −2.60584 | −0.161608 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −17.7947 | −1.09936 | ||||||||
\(263\) | 0.0140866 | 0.000868618 0 | 0.000434309 | − | 1.00000i | \(-0.499862\pi\) | ||||
0.000434309 | 1.00000i | \(0.499862\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.4968 | 0.951961 | ||||||||
\(266\) | −0.00608613 | −0.000373165 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.96178 | 0.364174 | ||||||||
\(269\) | −13.4107 | −0.817663 | −0.408831 | − | 0.912610i | \(-0.634064\pi\) | ||||
−0.408831 | + | 0.912610i | \(0.634064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.1331 | 1.83045 | 0.915227 | − | 0.402938i | \(-0.132011\pi\) | ||||
0.915227 | + | 0.402938i | \(0.132011\pi\) | |||||||
\(272\) | 4.05669 | 0.245973 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.79487 | −0.229256 | ||||||||
\(275\) | 5.41878 | 0.326765 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7209 | −1.12483 | −0.562414 | − | 0.826856i | \(-0.690127\pi\) | ||||
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(278\) | −13.1582 | −0.789179 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.0410810 | 0.00245506 | ||||||||
\(281\) | −7.41800 | −0.442521 | −0.221260 | − | 0.975215i | \(-0.571017\pi\) | ||||
−0.221260 | + | 0.975215i | \(0.571017\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.1335 | −1.25625 | −0.628127 | − | 0.778111i | \(-0.716178\pi\) | ||||
−0.628127 | + | 0.778111i | \(0.716178\pi\) | |||||||
\(284\) | 10.2613 | 0.608895 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.88076 | −0.406868 | ||||||||
\(287\) | −0.00601457 | −0.000355029 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.543249 | −0.0319558 | ||||||||
\(290\) | −7.89887 | −0.463838 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.21734 | 0.305322 | ||||||||
\(293\) | 5.04458 | 0.294707 | 0.147354 | − | 0.989084i | \(-0.452924\pi\) | ||||
0.147354 | + | 0.989084i | \(0.452924\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.6247 | 1.49192 | ||||||||
\(296\) | −8.66851 | −0.503847 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 2.15687 | 0.124735 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.00803414 | 0.000463080 0 | ||||||||
\(302\) | −13.5614 | −0.780372 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.295188 | 0.0169302 | ||||||||
\(305\) | −14.7586 | −0.845076 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.06035 | −0.231736 | −0.115868 | − | 0.993265i | \(-0.536965\pi\) | ||||
−0.115868 | + | 0.993265i | \(0.536965\pi\) | |||||||
\(308\) | 0.108475 | 0.00618094 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.3223 | −0.983839 | ||||||||
\(311\) | 30.1221 | 1.70807 | 0.854033 | − | 0.520219i | \(-0.174150\pi\) | ||||
0.854033 | + | 0.520219i | \(0.174150\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.86146 | 0.331309 | 0.165655 | − | 0.986184i | \(-0.447026\pi\) | ||||
0.165655 | + | 0.986184i | \(0.447026\pi\) | |||||||
\(314\) | −11.9231 | −0.672857 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.69527 | 0.320384 | ||||||||
\(317\) | 13.0792 | 0.734602 | 0.367301 | − | 0.930102i | \(-0.380282\pi\) | ||||
0.367301 | + | 0.930102i | \(0.380282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.8571 | −1.16777 | ||||||||
\(320\) | −1.99250 | −0.111384 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.0340029 | −0.00189491 | ||||||||
\(323\) | 1.19749 | 0.0666299 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.34699 | −0.0747177 | ||||||||
\(326\) | −2.75467 | −0.152567 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.291717 | 0.0161074 | ||||||||
\(329\) | 0.0942260 | 0.00519485 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.3159 | 0.621977 | 0.310988 | − | 0.950414i | \(-0.399340\pi\) | ||||
0.310988 | + | 0.950414i | \(0.399340\pi\) | |||||||
\(332\) | −11.8162 | −0.648499 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −21.6245 | −1.18324 | ||||||||
\(335\) | −11.8788 | −0.649011 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.41103 | 0.185810 | 0.0929052 | − | 0.995675i | \(-0.470385\pi\) | ||||
0.0929052 | + | 0.995675i | \(0.470385\pi\) | |||||||
\(338\) | −11.2896 | −0.614073 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.08295 | −0.438360 | ||||||||
\(341\) | −45.7397 | −2.47694 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.288641 | 0.0155851 | ||||||||
\(344\) | −0.389669 | −0.0210096 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −17.8683 | −0.960608 | ||||||||
\(347\) | −5.91948 | −0.317774 | −0.158887 | − | 0.987297i | \(-0.550791\pi\) | ||||
−0.158887 | + | 0.987297i | \(0.550791\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.2779 | 0.603692 | 0.301846 | − | 0.953357i | \(-0.402397\pi\) | ||||
0.301846 | + | 0.953357i | \(0.402397\pi\) | |||||||
\(350\) | 0.0212353 | 0.00113507 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.26122 | −0.280424 | ||||||||
\(353\) | −14.0935 | −0.750123 | −0.375061 | − | 0.927000i | \(-0.622378\pi\) | ||||
−0.375061 | + | 0.927000i | \(0.622378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4456 | −1.08514 | ||||||||
\(356\) | −11.4015 | −0.604277 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.6929 | −0.776542 | ||||||||
\(359\) | −3.81544 | −0.201371 | −0.100686 | − | 0.994918i | \(-0.532104\pi\) | ||||
−0.100686 | + | 0.994918i | \(0.532104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9129 | −0.995414 | ||||||||
\(362\) | 20.5258 | 1.07881 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.0269646 | −0.00141333 | ||||||||
\(365\) | −10.3955 | −0.544128 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4625 | −0.859337 | −0.429669 | − | 0.902987i | \(-0.641370\pi\) | ||||
−0.429669 | + | 0.902987i | \(0.641370\pi\) | |||||||
\(368\) | 1.64920 | 0.0859704 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 17.2720 | 0.897928 | ||||||||
\(371\) | 0.160357 | 0.00832531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 20.1014 | 1.04081 | 0.520406 | − | 0.853919i | \(-0.325781\pi\) | ||||
0.520406 | + | 0.853919i | \(0.325781\pi\) | |||||||
\(374\) | −21.3432 | −1.10363 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.57012 | −0.235686 | ||||||||
\(377\) | 5.18462 | 0.267022 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.0507386 | −0.00260627 | −0.00130313 | − | 0.999999i | \(-0.500415\pi\) | ||||
−0.00130313 | + | 0.999999i | \(0.500415\pi\) | |||||||
\(380\) | −0.588161 | −0.0301720 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.1527 | −0.826444 | ||||||||
\(383\) | 24.2127 | 1.23721 | 0.618605 | − | 0.785702i | \(-0.287698\pi\) | ||||
0.618605 | + | 0.785702i | \(0.287698\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.216136 | −0.0110153 | ||||||||
\(386\) | 0.667178 | 0.0339585 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.168718 | −0.00856538 | ||||||||
\(389\) | 16.8468 | 0.854168 | 0.427084 | − | 0.904212i | \(-0.359541\pi\) | ||||
0.427084 | + | 0.904212i | \(0.359541\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.69029 | 0.338343 | ||||||||
\(392\) | −6.99957 | −0.353532 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.10056 | −0.105825 | ||||||||
\(395\) | −11.3478 | −0.570971 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 25.7132 | 1.29051 | 0.645254 | − | 0.763968i | \(-0.276752\pi\) | ||||
0.645254 | + | 0.763968i | \(0.276752\pi\) | |||||||
\(398\) | −17.4910 | −0.876743 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.02995 | −0.0514974 | ||||||||
\(401\) | 18.5979 | 0.928733 | 0.464366 | − | 0.885643i | \(-0.346282\pi\) | ||||
0.464366 | + | 0.885643i | \(0.346282\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3699 | 0.566375 | ||||||||
\(404\) | −15.0043 | −0.746492 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0817354 | −0.00405646 | ||||||||
\(407\) | 45.6069 | 2.26065 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 36.7789 | 1.81860 | 0.909300 | − | 0.416142i | \(-0.136618\pi\) | ||||
0.909300 | + | 0.416142i | \(0.136618\pi\) | |||||||
\(410\) | −0.581245 | −0.0287057 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.19991 | −0.108382 | ||||||||
\(413\) | 0.265157 | 0.0130475 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 23.5438 | 1.15572 | ||||||||
\(416\) | 1.30783 | 0.0641215 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.55305 | −0.0759620 | ||||||||
\(419\) | −9.76046 | −0.476830 | −0.238415 | − | 0.971163i | \(-0.576628\pi\) | ||||
−0.238415 | + | 0.971163i | \(0.576628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −32.0064 | −1.55990 | −0.779949 | − | 0.625843i | \(-0.784755\pi\) | ||||
−0.779949 | + | 0.625843i | \(0.784755\pi\) | |||||||
\(422\) | −6.81415 | −0.331707 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −7.77757 | −0.377712 | ||||||||
\(425\) | −4.17818 | −0.202672 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.152718 | −0.00739055 | ||||||||
\(428\) | 4.80921 | 0.232462 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.776416 | 0.0374421 | ||||||||
\(431\) | −33.5502 | −1.61605 | −0.808027 | − | 0.589145i | \(-0.799465\pi\) | ||||
−0.808027 | + | 0.589145i | \(0.799465\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.8412 | 1.72242 | 0.861208 | − | 0.508253i | \(-0.169708\pi\) | ||||
0.861208 | + | 0.508253i | \(0.169708\pi\) | |||||||
\(434\) | −0.179246 | −0.00860409 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8433 | −0.615081 | ||||||||
\(437\) | 0.486823 | 0.0232879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.89036 | −0.233404 | −0.116702 | − | 0.993167i | \(-0.537232\pi\) | ||||
−0.116702 | + | 0.993167i | \(0.537232\pi\) | |||||||
\(440\) | 10.4830 | 0.499756 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.30545 | 0.252355 | ||||||||
\(443\) | 6.82947 | 0.324478 | 0.162239 | − | 0.986752i | \(-0.448128\pi\) | ||||
0.162239 | + | 0.986752i | \(0.448128\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.7174 | 1.07691 | ||||||||
\(446\) | −19.9915 | −0.946627 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.0206178 | −0.000974101 0 | ||||||||
\(449\) | −29.7864 | −1.40571 | −0.702854 | − | 0.711334i | \(-0.748091\pi\) | ||||
−0.702854 | + | 0.711334i | \(0.748091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.53479 | −0.0722703 | ||||||||
\(452\) | 3.21231 | 0.151094 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.5705 | 0.636895 | ||||||||
\(455\) | 0.0537269 | 0.00251875 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.05153 | 0.189522 | 0.0947612 | − | 0.995500i | \(-0.469791\pi\) | ||||
0.0947612 | + | 0.995500i | \(0.469791\pi\) | |||||||
\(458\) | 27.0742 | 1.26510 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.28603 | −0.153212 | ||||||||
\(461\) | −39.8347 | −1.85529 | −0.927643 | − | 0.373468i | \(-0.878168\pi\) | ||||
−0.927643 | + | 0.373468i | \(0.878168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.9167 | −1.06503 | −0.532515 | − | 0.846421i | \(-0.678753\pi\) | ||||
−0.532515 | + | 0.846421i | \(0.678753\pi\) | |||||||
\(464\) | 3.96430 | 0.184038 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.11238 | −0.0515299 | ||||||||
\(467\) | −1.53647 | −0.0710993 | −0.0355496 | − | 0.999368i | \(-0.511318\pi\) | ||||
−0.0355496 | + | 0.999368i | \(0.511318\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.122919 | −0.00567588 | ||||||||
\(470\) | 9.10596 | 0.420027 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.8606 | −0.591955 | ||||||||
\(473\) | 2.05014 | 0.0942654 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.304028 | −0.0139498 | ||||||||
\(476\) | −0.0836402 | −0.00383364 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 21.3359 | 0.975882 | ||||||||
\(479\) | −22.1043 | −1.00997 | −0.504985 | − | 0.863128i | \(-0.668502\pi\) | ||||
−0.504985 | + | 0.863128i | \(0.668502\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.3369 | −0.516918 | ||||||||
\(482\) | 7.94889 | 0.362062 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 16.6804 | 0.758202 | ||||||||
\(485\) | 0.336171 | 0.0152648 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.8299 | −1.57829 | −0.789147 | − | 0.614204i | \(-0.789477\pi\) | ||||
−0.789147 | + | 0.614204i | \(0.789477\pi\) | |||||||
\(488\) | 7.40709 | 0.335303 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 13.9466 | 0.630045 | ||||||||
\(491\) | 12.6656 | 0.571589 | 0.285795 | − | 0.958291i | \(-0.407743\pi\) | ||||
0.285795 | + | 0.958291i | \(0.407743\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0820 | 0.724295 | ||||||||
\(494\) | 0.386054 | 0.0173694 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.69374 | 0.390360 | ||||||||
\(497\) | −0.211566 | −0.00949001 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.1306 | 0.766872 | 0.383436 | − | 0.923567i | \(-0.374741\pi\) | ||||
0.383436 | + | 0.923567i | \(0.374741\pi\) | |||||||
\(500\) | 12.0147 | 0.537312 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −30.3459 | −1.35440 | ||||||||
\(503\) | −8.08515 | −0.360499 | −0.180250 | − | 0.983621i | \(-0.557691\pi\) | ||||
−0.180250 | + | 0.983621i | \(0.557691\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29.8960 | 1.33036 | ||||||||
\(506\) | −8.67680 | −0.385731 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.1266 | 0.626768 | ||||||||
\(509\) | 27.1112 | 1.20168 | 0.600842 | − | 0.799368i | \(-0.294832\pi\) | ||||
0.600842 | + | 0.799368i | \(0.294832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.107570 | −0.00475863 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 11.3203 | 0.499318 | ||||||||
\(515\) | 4.38331 | 0.193152 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0444 | 1.05747 | ||||||||
\(518\) | 0.178726 | 0.00785277 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.60584 | −0.114274 | ||||||||
\(521\) | 4.65077 | 0.203754 | 0.101877 | − | 0.994797i | \(-0.467515\pi\) | ||||
0.101877 | + | 0.994797i | \(0.467515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11.6457 | −0.509232 | −0.254616 | − | 0.967042i | \(-0.581949\pi\) | ||||
−0.254616 | + | 0.967042i | \(0.581949\pi\) | |||||||
\(524\) | −17.7947 | −0.777364 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0140866 | 0.000614206 0 | ||||||||
\(527\) | 35.2678 | 1.53629 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.2801 | −0.881745 | ||||||||
\(530\) | 15.4968 | 0.673138 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.00608613 | −0.000263867 0 | ||||||||
\(533\) | 0.381515 | 0.0165252 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.58235 | −0.414281 | ||||||||
\(536\) | 5.96178 | 0.257510 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.4107 | −0.578175 | ||||||||
\(539\) | 36.8263 | 1.58622 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.80776 | −0.378675 | −0.189338 | − | 0.981912i | \(-0.560634\pi\) | ||||
−0.189338 | + | 0.981912i | \(0.560634\pi\) | |||||||
\(542\) | 30.1331 | 1.29433 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.05669 | 0.173929 | ||||||||
\(545\) | 25.5902 | 1.09616 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6940 | −0.970325 | −0.485162 | − | 0.874424i | \(-0.661239\pi\) | ||||
−0.485162 | + | 0.874424i | \(0.661239\pi\) | |||||||
\(548\) | −3.79487 | −0.162109 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.41878 | 0.231058 | ||||||||
\(551\) | 1.17021 | 0.0498528 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.117424 | −0.00499338 | ||||||||
\(554\) | −18.7209 | −0.795373 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.1582 | −0.558034 | ||||||||
\(557\) | 20.2130 | 0.856454 | 0.428227 | − | 0.903671i | \(-0.359138\pi\) | ||||
0.428227 | + | 0.903671i | \(0.359138\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.509620 | −0.0215546 | ||||||||
\(560\) | 0.0410810 | 0.00173599 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.41800 | −0.312909 | ||||||||
\(563\) | −3.95448 | −0.166662 | −0.0833308 | − | 0.996522i | \(-0.526556\pi\) | ||||
−0.0833308 | + | 0.996522i | \(0.526556\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.40052 | −0.269272 | ||||||||
\(566\) | −21.1335 | −0.888305 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.2613 | 0.430554 | ||||||||
\(569\) | 17.7277 | 0.743182 | 0.371591 | − | 0.928396i | \(-0.378812\pi\) | ||||
0.371591 | + | 0.928396i | \(0.378812\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.10744 | −0.171891 | −0.0859455 | − | 0.996300i | \(-0.527391\pi\) | ||||
−0.0859455 | + | 0.996300i | \(0.527391\pi\) | |||||||
\(572\) | −6.88076 | −0.287699 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.00601457 | −0.000251043 0 | ||||||||
\(575\) | −1.69859 | −0.0708361 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −38.2521 | −1.59245 | −0.796227 | − | 0.604998i | \(-0.793174\pi\) | ||||
−0.796227 | + | 0.604998i | \(0.793174\pi\) | |||||||
\(578\) | −0.543249 | −0.0225962 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.89887 | −0.327983 | ||||||||
\(581\) | 0.243625 | 0.0101073 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.9195 | 1.69471 | ||||||||
\(584\) | 5.21734 | 0.215895 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.04458 | 0.208390 | ||||||||
\(587\) | −26.6533 | −1.10010 | −0.550050 | − | 0.835131i | \(-0.685391\pi\) | ||||
−0.550050 | + | 0.835131i | \(0.685391\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.56629 | 0.105742 | ||||||||
\(590\) | 25.6247 | 1.05495 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.66851 | −0.356274 | ||||||||
\(593\) | 32.6922 | 1.34251 | 0.671254 | − | 0.741228i | \(-0.265756\pi\) | ||||
0.671254 | + | 0.741228i | \(0.265756\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.166653 | 0.00683211 | ||||||||
\(596\) | −1.00000 | −0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.15687 | 0.0882008 | ||||||||
\(599\) | 39.6511 | 1.62010 | 0.810050 | − | 0.586361i | \(-0.199440\pi\) | ||||
0.810050 | + | 0.586361i | \(0.199440\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.2768 | −0.908688 | −0.454344 | − | 0.890826i | \(-0.650126\pi\) | ||||
−0.454344 | + | 0.890826i | \(0.650126\pi\) | |||||||
\(602\) | 0.00803414 | 0.000327447 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.5614 | −0.551806 | ||||||||
\(605\) | −33.2358 | −1.35123 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.442899 | −0.0179767 | −0.00898836 | − | 0.999960i | \(-0.502861\pi\) | ||||
−0.00898836 | + | 0.999960i | \(0.502861\pi\) | |||||||
\(608\) | 0.295188 | 0.0119714 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.7586 | −0.597559 | ||||||||
\(611\) | −5.97693 | −0.241801 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.1291 | 0.934177 | 0.467089 | − | 0.884211i | \(-0.345303\pi\) | ||||
0.467089 | + | 0.884211i | \(0.345303\pi\) | |||||||
\(614\) | −4.06035 | −0.163862 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.108475 | 0.00437058 | ||||||||
\(617\) | −18.6553 | −0.751033 | −0.375517 | − | 0.926816i | \(-0.622535\pi\) | ||||
−0.375517 | + | 0.926816i | \(0.622535\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.4442 | −0.701142 | −0.350571 | − | 0.936536i | \(-0.614012\pi\) | ||||
−0.350571 | + | 0.936536i | \(0.614012\pi\) | |||||||
\(620\) | −17.3223 | −0.695679 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 30.1221 | 1.20778 | ||||||||
\(623\) | 0.235074 | 0.00941803 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.7895 | −0.751579 | ||||||||
\(626\) | 5.86146 | 0.234271 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.9231 | −0.475782 | ||||||||
\(629\) | −35.1655 | −1.40214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.4513 | 1.49091 | 0.745456 | − | 0.666555i | \(-0.232232\pi\) | ||||
0.745456 | + | 0.666555i | \(0.232232\pi\) | |||||||
\(632\) | 5.69527 | 0.226546 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.0792 | 0.519442 | ||||||||
\(635\) | −28.1473 | −1.11699 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.15423 | −0.362704 | ||||||||
\(638\) | −20.8571 | −0.825740 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.99250 | −0.0787604 | ||||||||
\(641\) | 5.73239 | 0.226416 | 0.113208 | − | 0.993571i | \(-0.463887\pi\) | ||||
0.113208 | + | 0.993571i | \(0.463887\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.32139 | −0.209855 | −0.104928 | − | 0.994480i | \(-0.533461\pi\) | ||||
−0.104928 | + | 0.994480i | \(0.533461\pi\) | |||||||
\(644\) | −0.0340029 | −0.00133990 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.19749 | 0.0471144 | ||||||||
\(647\) | −27.7330 | −1.09030 | −0.545148 | − | 0.838340i | \(-0.683526\pi\) | ||||
−0.545148 | + | 0.838340i | \(0.683526\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 67.6622 | 2.65598 | ||||||||
\(650\) | −1.34699 | −0.0528334 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.75467 | −0.107881 | ||||||||
\(653\) | −10.3642 | −0.405584 | −0.202792 | − | 0.979222i | \(-0.565002\pi\) | ||||
−0.202792 | + | 0.979222i | \(0.565002\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 35.4559 | 1.38538 | ||||||||
\(656\) | 0.291717 | 0.0113896 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.0942260 | 0.00367331 | ||||||||
\(659\) | 36.1988 | 1.41011 | 0.705053 | − | 0.709155i | \(-0.250923\pi\) | ||||
0.705053 | + | 0.709155i | \(0.250923\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.6839 | 1.69911 | 0.849553 | − | 0.527503i | \(-0.176872\pi\) | ||||
0.849553 | + | 0.527503i | \(0.176872\pi\) | |||||||
\(662\) | 11.3159 | 0.439804 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.8162 | −0.458558 | ||||||||
\(665\) | 0.0121266 | 0.000470250 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.53793 | 0.253150 | ||||||||
\(668\) | −21.6245 | −0.836678 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −11.8788 | −0.458920 | ||||||||
\(671\) | −38.9703 | −1.50443 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.3949 | −1.55711 | −0.778555 | − | 0.627576i | \(-0.784047\pi\) | ||||
−0.778555 | + | 0.627576i | \(0.784047\pi\) | |||||||
\(674\) | 3.41103 | 0.131388 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.2896 | −0.434215 | ||||||||
\(677\) | −14.3060 | −0.549823 | −0.274912 | − | 0.961469i | \(-0.588649\pi\) | ||||
−0.274912 | + | 0.961469i | \(0.588649\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.00347861 | 0.000133497 0 | ||||||||
\(680\) | −8.08295 | −0.309967 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −45.7397 | −1.75146 | ||||||||
\(683\) | 2.76087 | 0.105642 | 0.0528209 | − | 0.998604i | \(-0.483179\pi\) | ||||
0.0528209 | + | 0.998604i | \(0.483179\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.56127 | 0.288901 | ||||||||
\(686\) | 0.288641 | 0.0110204 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.389669 | −0.0148560 | ||||||||
\(689\) | −10.1717 | −0.387512 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.81589 | 0.0690797 | 0.0345399 | − | 0.999403i | \(-0.489003\pi\) | ||||
0.0345399 | + | 0.999403i | \(0.489003\pi\) | |||||||
\(692\) | −17.8683 | −0.679252 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5.91948 | −0.224700 | ||||||||
\(695\) | 26.2178 | 0.994497 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.18340 | 0.0448247 | ||||||||
\(698\) | 11.2779 | 0.426875 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.0212353 | 0.000802619 0 | ||||||||
\(701\) | 44.8307 | 1.69323 | 0.846617 | − | 0.532203i | \(-0.178636\pi\) | ||||
0.846617 | + | 0.532203i | \(0.178636\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.55884 | −0.0965084 | ||||||||
\(704\) | −5.26122 | −0.198290 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0935 | −0.530417 | ||||||||
\(707\) | 0.309356 | 0.0116345 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.6903 | 0.739485 | 0.369742 | − | 0.929134i | \(-0.379446\pi\) | ||||
0.369742 | + | 0.929134i | \(0.379446\pi\) | |||||||
\(710\) | −20.4456 | −0.767310 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.4015 | −0.427288 | ||||||||
\(713\) | 14.3377 | 0.536951 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.7099 | 0.512722 | ||||||||
\(716\) | −14.6929 | −0.549098 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.81544 | −0.142391 | ||||||||
\(719\) | −38.2650 | −1.42704 | −0.713522 | − | 0.700632i | \(-0.752901\pi\) | ||||
−0.713522 | + | 0.700632i | \(0.752901\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.0453573 | 0.00168920 | ||||||||
\(722\) | −18.9129 | −0.703864 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 20.5258 | 0.762834 | ||||||||
\(725\) | −4.08303 | −0.151640 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.4811 | −1.01922 | −0.509610 | − | 0.860406i | \(-0.670210\pi\) | ||||
−0.509610 | + | 0.860406i | \(0.670210\pi\) | |||||||
\(728\) | −0.0269646 | −0.000999373 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.3955 | −0.384756 | ||||||||
\(731\) | −1.58077 | −0.0584668 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 10.4364 | 0.385477 | 0.192738 | − | 0.981250i | \(-0.438263\pi\) | ||||
0.192738 | + | 0.981250i | \(0.438263\pi\) | |||||||
\(734\) | −16.4625 | −0.607643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.64920 | 0.0607903 | ||||||||
\(737\) | −31.3663 | −1.15539 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.0604 | 0.995432 | 0.497716 | − | 0.867340i | \(-0.334172\pi\) | ||||
0.497716 | + | 0.867340i | \(0.334172\pi\) | |||||||
\(740\) | 17.2720 | 0.634931 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.160357 | 0.00588688 | ||||||||
\(743\) | 8.47771 | 0.311017 | 0.155508 | − | 0.987835i | \(-0.450298\pi\) | ||||
0.155508 | + | 0.987835i | \(0.450298\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.99250 | 0.0729995 | ||||||||
\(746\) | 20.1014 | 0.735965 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −21.3432 | −0.780383 | ||||||||
\(749\) | −0.0991556 | −0.00362307 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.633305 | 0.0231096 | 0.0115548 | − | 0.999933i | \(-0.496322\pi\) | ||||
0.0115548 | + | 0.999933i | \(0.496322\pi\) | |||||||
\(752\) | −4.57012 | −0.166655 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.18462 | 0.188813 | ||||||||
\(755\) | 27.0211 | 0.983399 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7917 | −0.610304 | −0.305152 | − | 0.952304i | \(-0.598707\pi\) | ||||
−0.305152 | + | 0.952304i | \(0.598707\pi\) | |||||||
\(758\) | −0.0507386 | −0.00184291 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.588161 | −0.0213348 | ||||||||
\(761\) | −15.9360 | −0.577681 | −0.288841 | − | 0.957377i | \(-0.593270\pi\) | ||||
−0.288841 | + | 0.957377i | \(0.593270\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.264801 | 0.00958643 | ||||||||
\(764\) | −16.1527 | −0.584384 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.2127 | 0.874840 | ||||||||
\(767\) | −16.8194 | −0.607313 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.2867 | 0.587315 | 0.293657 | − | 0.955911i | \(-0.405127\pi\) | ||||
0.293657 | + | 0.955911i | \(0.405127\pi\) | |||||||
\(770\) | −0.216136 | −0.00778901 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.667178 | 0.0240123 | ||||||||
\(773\) | −47.5479 | −1.71018 | −0.855090 | − | 0.518480i | \(-0.826498\pi\) | ||||
−0.855090 | + | 0.518480i | \(0.826498\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.95410 | −0.321641 | ||||||||
\(776\) | −0.168718 | −0.00605664 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 16.8468 | 0.603988 | ||||||||
\(779\) | 0.0861112 | 0.00308525 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −53.9869 | −1.93180 | ||||||||
\(782\) | 6.69029 | 0.239244 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.99957 | −0.249985 | ||||||||
\(785\) | 23.7567 | 0.847912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 49.1312 | 1.75134 | 0.875668 | − | 0.482913i | \(-0.160421\pi\) | ||||
0.875668 | + | 0.482913i | \(0.160421\pi\) | |||||||
\(788\) | −2.10056 | −0.0748295 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −11.3478 | −0.403737 | ||||||||
\(791\) | −0.0662309 | −0.00235490 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.68719 | 0.344002 | ||||||||
\(794\) | 25.7132 | 0.912527 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.4910 | −0.619951 | ||||||||
\(797\) | −41.7653 | −1.47940 | −0.739701 | − | 0.672936i | \(-0.765033\pi\) | ||||
−0.739701 | + | 0.672936i | \(0.765033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.5396 | −0.655883 | ||||||||
\(800\) | −1.02995 | −0.0364142 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.5979 | 0.656713 | ||||||||
\(803\) | −27.4496 | −0.968675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.0677508 | 0.00238790 | ||||||||
\(806\) | 11.3699 | 0.400488 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −15.0043 | −0.527849 | ||||||||
\(809\) | −33.4974 | −1.17771 | −0.588853 | − | 0.808240i | \(-0.700420\pi\) | ||||
−0.588853 | + | 0.808240i | \(0.700420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.2531 | 0.851641 | 0.425821 | − | 0.904808i | \(-0.359985\pi\) | ||||
0.425821 | + | 0.904808i | \(0.359985\pi\) | |||||||
\(812\) | −0.0817354 | −0.00286835 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 45.6069 | 1.59852 | ||||||||
\(815\) | 5.48869 | 0.192260 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.115026 | −0.00402424 | ||||||||
\(818\) | 36.7789 | 1.28594 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.581245 | −0.0202980 | ||||||||
\(821\) | −32.0387 | −1.11816 | −0.559080 | − | 0.829114i | \(-0.688846\pi\) | ||||
−0.559080 | + | 0.829114i | \(0.688846\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 19.6719 | 0.685718 | 0.342859 | − | 0.939387i | \(-0.388605\pi\) | ||||
0.342859 | + | 0.939387i | \(0.388605\pi\) | |||||||
\(824\) | −2.19991 | −0.0766374 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.265157 | 0.00922599 | ||||||||
\(827\) | −31.4913 | −1.09506 | −0.547529 | − | 0.836786i | \(-0.684432\pi\) | ||||
−0.547529 | + | 0.836786i | \(0.684432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.9019 | 0.413371 | 0.206686 | − | 0.978407i | \(-0.433732\pi\) | ||||
0.206686 | + | 0.978407i | \(0.433732\pi\) | |||||||
\(830\) | 23.5438 | 0.817217 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.30783 | 0.0453407 | ||||||||
\(833\) | −28.3951 | −0.983833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 43.0868 | 1.49108 | ||||||||
\(836\) | −1.55305 | −0.0537133 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.76046 | −0.337170 | ||||||||
\(839\) | −12.7598 | −0.440517 | −0.220258 | − | 0.975442i | \(-0.570690\pi\) | ||||
−0.220258 | + | 0.975442i | \(0.570690\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.2843 | −0.458079 | ||||||||
\(842\) | −32.0064 | −1.10301 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.81415 | −0.234553 | ||||||||
\(845\) | 22.4945 | 0.773834 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.343915 | −0.0118170 | ||||||||
\(848\) | −7.77757 | −0.267083 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.17818 | −0.143310 | ||||||||
\(851\) | −14.2961 | −0.490064 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.8050 | 1.12322 | 0.561612 | − | 0.827401i | \(-0.310182\pi\) | ||||
0.561612 | + | 0.827401i | \(0.310182\pi\) | |||||||
\(854\) | −0.152718 | −0.00522591 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.80921 | 0.164375 | ||||||||
\(857\) | 7.56418 | 0.258388 | 0.129194 | − | 0.991619i | \(-0.458761\pi\) | ||||
0.129194 | + | 0.991619i | \(0.458761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.5155 | −1.79181 | −0.895904 | − | 0.444249i | \(-0.853471\pi\) | ||||
−0.895904 | + | 0.444249i | \(0.853471\pi\) | |||||||
\(860\) | 0.776416 | 0.0264756 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.5502 | −1.14272 | ||||||||
\(863\) | −35.4413 | −1.20644 | −0.603218 | − | 0.797576i | \(-0.706115\pi\) | ||||
−0.603218 | + | 0.797576i | \(0.706115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 35.6026 | 1.21053 | ||||||||
\(866\) | 35.8412 | 1.21793 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.179246 | −0.00608401 | ||||||||
\(869\) | −29.9641 | −1.01646 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.79698 | 0.264191 | ||||||||
\(872\) | −12.8433 | −0.434928 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.486823 | 0.0164670 | ||||||||
\(875\) | −0.247716 | −0.00837434 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.4135 | 1.22960 | 0.614799 | − | 0.788684i | \(-0.289237\pi\) | ||||
0.614799 | + | 0.788684i | \(0.289237\pi\) | |||||||
\(878\) | −4.89036 | −0.165042 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.4830 | 0.353381 | ||||||||
\(881\) | 56.1916 | 1.89314 | 0.946572 | − | 0.322492i | \(-0.104521\pi\) | ||||
0.946572 | + | 0.322492i | \(0.104521\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.3628 | 0.887180 | 0.443590 | − | 0.896230i | \(-0.353705\pi\) | ||||
0.443590 | + | 0.896230i | \(0.353705\pi\) | |||||||
\(884\) | 5.30545 | 0.178442 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.82947 | 0.229440 | ||||||||
\(887\) | 51.2228 | 1.71989 | 0.859947 | − | 0.510383i | \(-0.170496\pi\) | ||||
0.859947 | + | 0.510383i | \(0.170496\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.291261 | −0.00976857 | ||||||||
\(890\) | 22.7174 | 0.761489 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −19.9915 | −0.669366 | ||||||||
\(893\) | −1.34904 | −0.0451440 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.2755 | 0.978573 | ||||||||
\(896\) | −0.0206178 | −0.000688794 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −29.7864 | −0.993986 | ||||||||
\(899\) | 34.4646 | 1.14946 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.5512 | −1.05112 | ||||||||
\(902\) | −1.53479 | −0.0511028 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.21231 | 0.106840 | ||||||||
\(905\) | −40.8975 | −1.35948 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.8286 | −0.425966 | −0.212983 | − | 0.977056i | \(-0.568318\pi\) | ||||
−0.212983 | + | 0.977056i | \(0.568318\pi\) | |||||||
\(908\) | 13.5705 | 0.450353 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.0537269 | 0.00178103 | ||||||||
\(911\) | −8.07943 | −0.267683 | −0.133842 | − | 0.991003i | \(-0.542731\pi\) | ||||
−0.133842 | + | 0.991003i | \(0.542731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 62.1677 | 2.05745 | ||||||||
\(914\) | 4.05153 | 0.134013 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 27.0742 | 0.894558 | ||||||||
\(917\) | 0.366888 | 0.0121157 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −39.1276 | −1.29070 | −0.645350 | − | 0.763887i | \(-0.723288\pi\) | ||||
−0.645350 | + | 0.763887i | \(0.723288\pi\) | |||||||
\(920\) | −3.28603 | −0.108337 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −39.8347 | −1.31189 | ||||||||
\(923\) | 13.4200 | 0.441724 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.92811 | 0.293555 | ||||||||
\(926\) | −22.9167 | −0.753090 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.96430 | 0.130135 | ||||||||
\(929\) | −27.9350 | −0.916518 | −0.458259 | − | 0.888819i | \(-0.651527\pi\) | ||||
−0.458259 | + | 0.888819i | \(0.651527\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.06619 | −0.0677166 | ||||||||
\(932\) | −1.11238 | −0.0364371 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.53647 | −0.0502748 | ||||||||
\(935\) | 42.5262 | 1.39076 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.7977 | −0.450751 | −0.225375 | − | 0.974272i | \(-0.572361\pi\) | ||||
−0.225375 | + | 0.974272i | \(0.572361\pi\) | |||||||
\(938\) | −0.122919 | −0.00401345 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 9.10596 | 0.297004 | ||||||||
\(941\) | −40.3166 | −1.31428 | −0.657142 | − | 0.753767i | \(-0.728235\pi\) | ||||
−0.657142 | + | 0.753767i | \(0.728235\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.481099 | 0.0156667 | ||||||||
\(944\) | −12.8606 | −0.418576 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.05014 | 0.0666557 | ||||||||
\(947\) | −5.20950 | −0.169286 | −0.0846431 | − | 0.996411i | \(-0.526975\pi\) | ||||
−0.0846431 | + | 0.996411i | \(0.526975\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.82338 | 0.221496 | ||||||||
\(950\) | −0.304028 | −0.00986397 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.0836402 | −0.00271080 | ||||||||
\(953\) | −13.5440 | −0.438733 | −0.219367 | − | 0.975642i | \(-0.570399\pi\) | ||||
−0.219367 | + | 0.975642i | \(0.570399\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.1843 | 1.04146 | ||||||||
\(956\) | 21.3359 | 0.690053 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.1043 | −0.714157 | ||||||||
\(959\) | 0.0782419 | 0.00252656 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 44.5811 | 1.43810 | ||||||||
\(962\) | −11.3369 | −0.365517 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.94889 | 0.256016 | ||||||||
\(965\) | −1.32935 | −0.0427933 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.4315 | −0.946452 | −0.473226 | − | 0.880941i | \(-0.656911\pi\) | ||||
−0.473226 | + | 0.880941i | \(0.656911\pi\) | |||||||
\(968\) | 16.6804 | 0.536130 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.336171 | 0.0107938 | ||||||||
\(971\) | 37.1081 | 1.19086 | 0.595428 | − | 0.803409i | \(-0.296983\pi\) | ||||
0.595428 | + | 0.803409i | \(0.296983\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.271294 | 0.00869730 | ||||||||
\(974\) | −34.8299 | −1.11602 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.40709 | 0.237095 | ||||||||
\(977\) | 44.0988 | 1.41084 | 0.705422 | − | 0.708787i | \(-0.250757\pi\) | ||||
0.705422 | + | 0.708787i | \(0.250757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59.9856 | 1.91715 | ||||||||
\(980\) | 13.9466 | 0.445509 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.6656 | 0.404175 | ||||||||
\(983\) | 57.9838 | 1.84940 | 0.924699 | − | 0.380700i | \(-0.124317\pi\) | ||||
0.924699 | + | 0.380700i | \(0.124317\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.18537 | 0.133357 | ||||||||
\(986\) | 16.0820 | 0.512154 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.386054 | 0.0122820 | ||||||||
\(989\) | −0.642642 | −0.0204348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.591718 | −0.0187965 | −0.00939827 | − | 0.999956i | \(-0.502992\pi\) | ||||
−0.00939827 | + | 0.999956i | \(0.502992\pi\) | |||||||
\(992\) | 8.69374 | 0.276027 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.211566 | −0.00671045 | ||||||||
\(995\) | 34.8507 | 1.10484 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.30402 | 0.294661 | 0.147331 | − | 0.989087i | \(-0.452932\pi\) | ||||
0.147331 | + | 0.989087i | \(0.452932\pi\) | |||||||
\(998\) | 17.1306 | 0.542260 | ||||||||
\(999\) | 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 | 8046.2.a.m.1.3 | yes | 12 | |
3.2 | odd | 2 | 8046.2.a.l.1.10 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.10 | ✓ | 12 | 3.2 | odd | 2 | ||
8046.2.a.m.1.3 | yes | 12 | 1.1 | even | 1 | trivial |