Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,26,Mod(1,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.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: | \(63.3594847924\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{106705}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 26676 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{7}\cdot 3\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 2) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-162.829\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.1 |
$q$-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 | ||||||||
\(3\) | 1.37803e6 | 1.49707 | 0.748537 | − | 0.663093i | \(-0.230757\pi\) | ||||
0.748537 | + | 0.663093i | \(0.230757\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 8.78994e8 | 1.61013 | 0.805065 | − | 0.593187i | \(-0.202130\pi\) | ||||
0.805065 | + | 0.593187i | \(0.202130\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.00388e10 | −0.820270 | −0.410135 | − | 0.912025i | \(-0.634518\pi\) | ||||
−0.410135 | + | 0.912025i | \(0.634518\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.05168e12 | 1.24123 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.73599e12 | −0.551061 | −0.275531 | − | 0.961292i | \(-0.588854\pi\) | ||||
−0.275531 | + | 0.961292i | \(0.588854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.07343e13 | −0.127786 | −0.0638928 | − | 0.997957i | \(-0.520352\pi\) | ||||
−0.0638928 | + | 0.997957i | \(0.520352\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.21128e15 | 2.41048 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.97473e15 | 1.23833 | 0.619164 | − | 0.785262i | \(-0.287472\pi\) | ||||
0.619164 | + | 0.785262i | \(0.287472\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.42738e15 | 0.562561 | 0.281281 | − | 0.959626i | \(-0.409241\pi\) | ||||
0.281281 | + | 0.959626i | \(0.409241\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.13944e16 | −1.22800 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.04540e17 | 0.994683 | 0.497341 | − | 0.867555i | \(-0.334310\pi\) | ||||
0.497341 | + | 0.867555i | \(0.334310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.74607e17 | 1.59252 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.81659e17 | 0.361141 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.09182e18 | 1.62270 | 0.811352 | − | 0.584558i | \(-0.198732\pi\) | ||||
0.811352 | + | 0.584558i | \(0.198732\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.26809e18 | 0.973222 | 0.486611 | − | 0.873619i | \(-0.338233\pi\) | ||||
0.486611 | + | 0.873619i | \(0.338233\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.90437e18 | −0.824980 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.64039e19 | −1.32074 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.51028e19 | −1.12637 | −0.563186 | − | 0.826330i | \(-0.690424\pi\) | ||||
−0.563186 | + | 0.826330i | \(0.690424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.47922e19 | −0.191305 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.56724e19 | −0.523769 | −0.261884 | − | 0.965099i | \(-0.584344\pi\) | ||||
−0.261884 | + | 0.965099i | \(0.584344\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.39036e20 | 0.530605 | 0.265302 | − | 0.964165i | \(-0.414528\pi\) | ||||
0.265302 | + | 0.964165i | \(0.414528\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.24421e20 | 1.99854 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.67328e20 | −0.586676 | −0.293338 | − | 0.956009i | \(-0.594766\pi\) | ||||
−0.293338 | + | 0.956009i | \(0.594766\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.38741e20 | −0.327158 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.09927e21 | 1.85387 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.24315e21 | −0.347595 | −0.173797 | − | 0.984781i | \(-0.555604\pi\) | ||||
−0.173797 | + | 0.984781i | \(0.555604\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.04190e21 | −0.887280 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.47909e21 | 0.842196 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.32468e22 | 0.969303 | 0.484652 | − | 0.874707i | \(-0.338946\pi\) | ||||
0.484652 | + | 0.874707i | \(0.338946\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.36984e20 | −0.0114313 | −0.00571565 | − | 0.999984i | \(-0.501819\pi\) | ||||
−0.00571565 | + | 0.999984i | \(0.501819\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.15912e22 | −1.01814 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.43539e21 | −0.205752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.36922e22 | 0.801634 | 0.400817 | − | 0.916158i | \(-0.368726\pi\) | ||||
0.400817 | + | 0.916158i | \(0.368726\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.44059e23 | 1.48911 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.27032e23 | 1.64194 | 0.820971 | − | 0.570970i | \(-0.193433\pi\) | ||||
0.820971 | + | 0.570970i | \(0.193433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.78528e23 | 1.42342 | 0.711710 | − | 0.702473i | \(-0.247921\pi\) | ||||
0.711710 | + | 0.702473i | \(0.247921\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.54024e23 | 2.38412 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.72302e23 | 0.452019 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.36958e23 | −1.21275 | −0.606376 | − | 0.795178i | \(-0.707378\pi\) | ||||
−0.606376 | + | 0.795178i | \(0.707378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.02942e23 | −0.700576 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.19662e24 | −1.22880 | −0.614398 | − | 0.788996i | \(-0.710601\pi\) | ||||
−0.614398 | + | 0.788996i | \(0.710601\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.61477e24 | 1.99387 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.26063e24 | 2.42931 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.22134e24 | −1.38249 | −0.691244 | − | 0.722621i | \(-0.742937\pi\) | ||||
−0.691244 | + | 0.722621i | \(0.742937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.22445e23 | 0.104819 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.88156e24 | 1.45699 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.77063e24 | 0.905797 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.58465e24 | 0.524566 | 0.262283 | − | 0.964991i | \(-0.415525\pi\) | ||||
0.262283 | + | 0.964991i | \(0.415525\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.03243e24 | −0.683994 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.40630e24 | −0.300792 | −0.150396 | − | 0.988626i | \(-0.548055\pi\) | ||||
−0.150396 | + | 0.988626i | \(0.548055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.27075e24 | −0.571583 | −0.285792 | − | 0.958292i | \(-0.592257\pi\) | ||||
−0.285792 | + | 0.958292i | \(0.592257\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.63854e25 | −1.97725 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.57986e25 | −0.678142 | −0.339071 | − | 0.940761i | \(-0.610113\pi\) | ||||
−0.339071 | + | 0.940761i | \(0.610113\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.00869e25 | 1.02458 | 0.512290 | − | 0.858813i | \(-0.328797\pi\) | ||||
0.512290 | + | 0.858813i | \(0.328797\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.21530e25 | −1.68626 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.06745e25 | −1.75088 | −0.875439 | − | 0.483329i | \(-0.839428\pi\) | ||||
−0.875439 | + | 0.483329i | \(0.839428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.18901e25 | 1.60157 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.12891e25 | −0.158612 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.93571e25 | −1.01576 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.54455e25 | −0.696332 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.04279e26 | −0.784121 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.55216e26 | 0.954030 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.32973e26 | 0.670221 | 0.335111 | − | 0.942179i | \(-0.391226\pi\) | ||||
0.335111 | + | 0.942179i | \(0.391226\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.91596e26 | 0.794355 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.73908e25 | −0.230520 | −0.115260 | − | 0.993335i | \(-0.536770\pi\) | ||||
−0.115260 | + | 0.993335i | \(0.536770\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.63032e26 | −0.461452 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.47577e26 | 0.581484 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.22963e26 | −0.631170 | −0.315585 | − | 0.948897i | \(-0.602201\pi\) | ||||
−0.315585 | + | 0.948897i | \(0.602201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.21581e25 | 0.150262 | 0.0751309 | − | 0.997174i | \(-0.476063\pi\) | ||||
0.0751309 | + | 0.997174i | \(0.476063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.43992e26 | −0.878298 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.15719e25 | 0.0704177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.71769e27 | 2.61276 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.04599e26 | −0.489779 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −7.12667e26 | −0.487594 | −0.243797 | − | 0.969826i | \(-0.578393\pi\) | ||||
−0.243797 | + | 0.969826i | \(0.578393\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.06161e27 | 1.77312 | 0.886559 | − | 0.462616i | \(-0.153089\pi\) | ||||
0.886559 | + | 0.462616i | \(0.153089\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.12846e27 | 1.53705 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.75162e27 | 1.56701 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.38960e27 | 0.850315 | 0.425157 | − | 0.905119i | \(-0.360219\pi\) | ||||
0.425157 | + | 0.905119i | \(0.360219\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.71309e27 | −0.520375 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.14025e27 | −0.815908 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.63092e27 | −1.47648 | −0.738242 | − | 0.674536i | \(-0.764344\pi\) | ||||
−0.738242 | + | 0.674536i | \(0.764344\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.94790e27 | −1.32832 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.06997e27 | −0.669323 | −0.334662 | − | 0.942338i | \(-0.608622\pi\) | ||||
−0.334662 | + | 0.942338i | \(0.608622\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.94118e27 | −0.983671 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.70787e27 | 0.698269 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.68916e27 | −0.919182 | −0.459591 | − | 0.888131i | \(-0.652004\pi\) | ||||
−0.459591 | + | 0.888131i | \(0.652004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.42566e28 | −1.30629 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.82545e28 | 1.45112 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.31406e27 | 0.298005 | 0.149002 | − | 0.988837i | \(-0.452394\pi\) | ||||
0.149002 | + | 0.988837i | \(0.452394\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.22969e28 | 1.34049 | 0.670243 | − | 0.742142i | \(-0.266190\pi\) | ||||
0.670243 | + | 0.742142i | \(0.266190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.26571e26 | −0.0171135 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.96451e28 | −1.81360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.70630e28 | −0.682394 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.46070e27 | −0.296233 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.91337e28 | 0.587329 | 0.293665 | − | 0.955908i | \(-0.405125\pi\) | ||||
0.293665 | + | 0.955908i | \(0.405125\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.96748e28 | −1.60814 | −0.804071 | − | 0.594533i | \(-0.797337\pi\) | ||||
−0.804071 | + | 0.594533i | \(0.797337\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.30023e28 | −0.308025 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.24204e28 | 1.30166 | 0.650832 | − | 0.759222i | \(-0.274420\pi\) | ||||
0.650832 | + | 0.759222i | \(0.274420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.24229e28 | 0.595921 | 0.297960 | − | 0.954578i | \(-0.403694\pi\) | ||||
0.297960 | + | 0.954578i | \(0.403694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.39895e28 | 1.20011 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.28745e28 | −1.33106 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.65156e28 | −0.843335 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.09943e29 | 1.23463 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.11314e28 | −0.310006 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.82197e28 | −0.337875 | −0.168938 | − | 0.985627i | \(-0.554034\pi\) | ||||
−0.168938 | + | 0.985627i | \(0.554034\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.12857e29 | 2.45811 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.22212e29 | 0.854342 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.28208e29 | −0.798305 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.83820e29 | 2.13097 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.19316e28 | −0.158241 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.11100e29 | −1.37749 | −0.688746 | − | 0.725003i | \(-0.741839\pi\) | ||||
−0.688746 | + | 0.725003i | \(0.741839\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.99135e29 | 1.97668 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.05572e29 | 0.374304 | 0.187152 | − | 0.982331i | \(-0.440074\pi\) | ||||
0.187152 | + | 0.982331i | \(0.440074\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.70322e29 | −1.17662 | −0.588310 | − | 0.808635i | \(-0.700207\pi\) | ||||
−0.588310 | + | 0.808635i | \(0.700207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.37438e29 | 0.676706 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.84781e28 | −0.175228 | −0.0876138 | − | 0.996155i | \(-0.527924\pi\) | ||||
−0.0876138 | + | 0.996155i | \(0.527924\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.10778e29 | −0.944625 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.77748e29 | −1.81558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.87773e29 | −0.722111 | −0.361055 | − | 0.932544i | \(-0.617583\pi\) | ||||
−0.361055 | + | 0.932544i | \(0.617583\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.03723e30 | 1.74046 | 0.870230 | − | 0.492646i | \(-0.163970\pi\) | ||||
0.870230 | + | 0.492646i | \(0.163970\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.31717e29 | −1.40996 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.85651e29 | −0.526766 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.82591e28 | −0.0718873 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.64898e30 | −1.83960 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.47990e30 | −1.49386 | −0.746930 | − | 0.664903i | \(-0.768473\pi\) | ||||
−0.746930 | + | 0.664903i | \(0.768473\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.99641e29 | −0.548131 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.60323e30 | 2.98497 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.75384e29 | 0.507442 | 0.253721 | − | 0.967277i | \(-0.418345\pi\) | ||||
0.253721 | + | 0.967277i | \(0.418345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.35483e30 | 0.923929 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.25161e30 | 2.01415 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.42102e30 | −0.800119 | −0.400059 | − | 0.916489i | \(-0.631011\pi\) | ||||
−0.400059 | + | 0.916489i | \(0.631011\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.09272e30 | −0.559673 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.43911e30 | −2.06969 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.90129e30 | −0.807504 | −0.403752 | − | 0.914868i | \(-0.632294\pi\) | ||||
−0.403752 | + | 0.914868i | \(0.632294\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.45800e30 | 0.564471 | 0.282236 | − | 0.959345i | \(-0.408924\pi\) | ||||
0.282236 | + | 0.959345i | \(0.408924\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.44340e29 | 0.156921 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.72234e30 | −0.877575 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.31088e29 | −0.156376 | −0.0781879 | − | 0.996939i | \(-0.524913\pi\) | ||||
−0.0781879 | + | 0.996939i | \(0.524913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.48867e30 | 1.20799 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.64974e30 | −0.898323 | −0.449161 | − | 0.893451i | \(-0.648277\pi\) | ||||
−0.449161 | + | 0.893451i | \(0.648277\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.43965e30 | 0.324285 | 0.162143 | − | 0.986767i | \(-0.448160\pi\) | ||||
0.162143 | + | 0.986767i | \(0.448160\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.57408e30 | 1.35604 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.27311e30 | 0.429632 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.07837e30 | 0.533456 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.93976e30 | 0.785315 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.24504e31 | 1.81692 | 0.908462 | − | 0.417967i | \(-0.137257\pi\) | ||||
0.908462 | + | 0.417967i | \(0.137257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.16438e31 | 1.56070 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.61559e30 | −0.199011 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.12217e30 | −0.127106 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.17647e30 | −0.435239 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.69399e30 | −0.450307 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.08307e29 | −0.0184059 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.27193e31 | −1.84997 | −0.924986 | − | 0.380001i | \(-0.875924\pi\) | ||||
−0.924986 | + | 0.380001i | \(0.875924\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.13974e31 | −0.855703 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.84336e31 | 1.27675 | 0.638374 | − | 0.769726i | \(-0.279607\pi\) | ||||
0.638374 | + | 0.769726i | \(0.279607\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.98693e30 | 0.318808 | 0.159404 | − | 0.987213i | \(-0.449043\pi\) | ||||
0.159404 | + | 0.987213i | \(0.449043\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.77685e31 | −1.63934 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.79478e30 | −0.479716 | −0.239858 | − | 0.970808i | \(-0.577101\pi\) | ||||
−0.239858 | + | 0.970808i | \(0.577101\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.77347e31 | −0.894209 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.17709e31 | −1.01523 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.61450e31 | 0.696635 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −5.09458e30 | −0.203501 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.14606e31 | 1.53387 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.40380e31 | 0.481233 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97122e31 | −1.89764 | −0.948818 | − | 0.315822i | \(-0.897720\pi\) | ||||
−0.948818 | + | 0.315822i | \(0.897720\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.74337e31 | −1.39809 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.71951e31 | 1.29073 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.08428e31 | 0.275275 | 0.137638 | − | 0.990483i | \(-0.456049\pi\) | ||||
0.137638 | + | 0.990483i | \(0.456049\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.11172e32 | −2.62119 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.44817e31 | −0.536305 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5.34633e31 | 1.08863 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.26627e32 | 2.39767 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.20193e30 | −0.126862 | −0.0634308 | − | 0.997986i | \(-0.520204\pi\) | ||||
−0.0634308 | + | 0.997986i | \(0.520204\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.27779e31 | 0.865235 | 0.432618 | − | 0.901577i | \(-0.357590\pi\) | ||||
0.432618 | + | 0.901577i | \(0.357590\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −3.02342e30 | −0.0461487 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.67715e31 | −0.807135 | −0.403567 | − | 0.914950i | \(-0.632230\pi\) | ||||
−0.403567 | + | 0.914950i | \(0.632230\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.99560e32 | 2.64374 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.23137e32 | −1.52067 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.18925e31 | −0.252125 | −0.126062 | − | 0.992022i | \(-0.540234\pi\) | ||||
−0.126062 | + | 0.992022i | \(0.540234\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.36201e31 | −0.683525 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.03966e32 | −1.04246 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.44824e32 | 2.29189 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.00500e32 | −0.878699 | −0.439349 | − | 0.898316i | \(-0.644791\pi\) | ||||
−0.439349 | + | 0.898316i | \(0.644791\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.95833e31 | −0.650118 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.73425e31 | 0.285122 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.31052e31 | 0.450510 | 0.225255 | − | 0.974300i | \(-0.427678\pi\) | ||||
0.225255 | + | 0.974300i | \(0.427678\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.13893e32 | 1.42825 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.31886e31 | −0.207358 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.85755e31 | 0.517993 | 0.258996 | − | 0.965878i | \(-0.416608\pi\) | ||||
0.258996 | + | 0.965878i | \(0.416608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.83241e32 | 1.00337 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.08315e31 | −0.465856 | −0.232928 | − | 0.972494i | \(-0.574831\pi\) | ||||
−0.232928 | + | 0.972494i | \(0.574831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.51453e32 | 0.727809 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.46221e32 | 0.658603 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.13043e31 | 0.301124 | 0.150562 | − | 0.988601i | \(-0.451892\pi\) | ||||
0.150562 | + | 0.988601i | \(0.451892\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.10978e32 | 1.23174 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.28666e31 | −0.345106 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.59883e32 | −1.95269 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.99427e31 | 0.0980413 | 0.0490206 | − | 0.998798i | \(-0.484390\pi\) | ||||
0.0490206 | + | 0.998798i | \(0.484390\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.24663e32 | −0.690828 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.00588e32 | −1.44603 | −0.723013 | − | 0.690835i | \(-0.757243\pi\) | ||||
−0.723013 | + | 0.690835i | \(0.757243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.58150e31 | −0.124364 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.42083e32 | −1.12802 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.58709e32 | 0.620700 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.78379e32 | −0.628195 | −0.314097 | − | 0.949391i | \(-0.601702\pi\) | ||||
−0.314097 | + | 0.949391i | \(0.601702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.45054e32 | −0.944908 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.97916e32 | −0.795090 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.05182e33 | −1.97852 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.26997e32 | 0.224953 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.36828e32 | 1.06254 | 0.531272 | − | 0.847201i | \(-0.321714\pi\) | ||||
0.531272 | + | 0.847201i | \(0.321714\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.92275e32 | −0.616686 | −0.308343 | − | 0.951275i | \(-0.599775\pi\) | ||||
−0.308343 | + | 0.951275i | \(0.599775\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.91480e32 | −0.728201 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.41183e33 | 1.97206 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.11870e30 | 0.00937675 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.48480e31 | 0.105421 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.44178e32 | −0.286247 | −0.143124 | − | 0.989705i | \(-0.545715\pi\) | ||||
−0.143124 | + | 0.989705i | \(0.545715\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.12872e32 | 1.00998 | 0.504988 | − | 0.863126i | \(-0.331497\pi\) | ||||
0.504988 | + | 0.863126i | \(0.331497\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.74506e33 | 3.91150 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.67378e32 | 0.559570 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.07601e32 | −0.565995 | −0.282997 | − | 0.959121i | \(-0.591329\pi\) | ||||
−0.282997 | + | 0.959121i | \(0.591329\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.61416e32 | −0.406078 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.06289e32 | −0.753737 | −0.376869 | − | 0.926267i | \(-0.622999\pi\) | ||||
−0.376869 | + | 0.926267i | \(0.622999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.83154e33 | −2.22598 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.82078e32 | −0.729965 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.21579e33 | −0.854630 | −0.427315 | − | 0.904103i | \(-0.640540\pi\) | ||||
−0.427315 | + | 0.904103i | \(0.640540\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.34056e32 | 0.288629 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.21899e33 | 2.65449 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.83428e32 | 0.168772 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.59530e32 | −0.315407 | −0.157703 | − | 0.987487i | \(-0.550409\pi\) | ||||
−0.157703 | + | 0.987487i | \(0.550409\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.37859e32 | 0.447211 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.78592e32 | −0.191386 | −0.0956930 | − | 0.995411i | \(-0.530507\pi\) | ||||
−0.0956930 | + | 0.995411i | \(0.530507\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.77039e33 | −1.32672 | −0.663359 | − | 0.748301i | \(-0.730870\pi\) | ||||
−0.663359 | + | 0.748301i | \(0.730870\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 5.16985e33 | 2.34594 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.31922e33 | 0.997428 | 0.498714 | − | 0.866767i | \(-0.333806\pi\) | ||||
0.498714 | + | 0.866767i | \(0.333806\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.61285e33 | −0.657556 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.29294e33 | 1.27298 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.97508e32 | −0.292396 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.57587e33 | 0.895889 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.30739e33 | −0.431446 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.24376e33 | −0.702720 | −0.351360 | − | 0.936240i | \(-0.614281\pi\) | ||||
−0.351360 | + | 0.936240i | \(0.614281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.84147e32 | 0.143934 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −4.32737e33 | −1.22148 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.15089e33 | 0.844620 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.71393e32 | −0.0945632 | −0.0472816 | − | 0.998882i | \(-0.515056\pi\) | ||||
−0.0472816 | + | 0.998882i | \(0.515056\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.13761e33 | −2.21041 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.65508e33 | 0.610323 | 0.305161 | − | 0.952301i | \(-0.401290\pi\) | ||||
0.305161 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.19732e33 | 2.00944 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.30247e33 | −1.10132 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.81976e33 | −1.34684 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.39117e33 | 0.449111 | 0.224556 | − | 0.974461i | \(-0.427907\pi\) | ||||
0.224556 | + | 0.974461i | \(0.427907\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.60855e33 | −1.00203 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.34146e33 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.99412e33 | −0.484314 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.56517e33 | −1.47263 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.62528e32 | −0.0531337 | −0.0265668 | − | 0.999647i | \(-0.508457\pi\) | ||||
−0.0265668 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.36664e33 | −1.16759 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.52867e33 | 0.203164 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.26994e33 | −0.920323 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.68059e33 | 0.323295 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.19739e34 | −1.37608 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.23573e33 | 0.902050 | 0.451025 | − | 0.892511i | \(-0.351058\pi\) | ||||
0.451025 | + | 0.892511i | \(0.351058\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.20443e34 | 1.25750 | 0.628752 | − | 0.777606i | \(-0.283566\pi\) | ||||
0.628752 | + | 0.777606i | \(0.283566\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.96461e34 | −1.95562 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.26964e34 | 1.20517 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.17149e32 | −0.0106057 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.39314e34 | 1.20313 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.12291e32 | 0.0669301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.38868e34 | −1.09190 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.94490e33 | 0.446135 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.51661e33 | 0.180284 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.30366e34 | 0.891657 | 0.445829 | − | 0.895118i | \(-0.352909\pi\) | ||||
0.445829 | + | 0.895118i | \(0.352909\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.07258e34 | 2.00681 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.64462e34 | 1.64971 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.78334e34 | 1.06266 | 0.531328 | − | 0.847166i | \(-0.321693\pi\) | ||||
0.531328 | + | 0.847166i | \(0.321693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.49231e32 | −0.0141889 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.67805e34 | 0.912871 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.91334e34 | 0.994784 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5.46321e34 | −2.71510 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.73339e33 | 0.414947 | 0.207474 | − | 0.978241i | \(-0.433476\pi\) | ||||
0.207474 | + | 0.978241i | \(0.433476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.49245e33 | −0.0678037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.35134e34 | −1.02160 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.82416e34 | −1.58921 | −0.794606 | − | 0.607126i | \(-0.792322\pi\) | ||||
−0.794606 | + | 0.607126i | \(0.792322\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.09124e34 | −2.81914 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.51078e34 | 0.574661 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3.49591e34 | 1.27250 | 0.636248 | − | 0.771484i | \(-0.280485\pi\) | ||||
0.636248 | + | 0.771484i | \(0.280485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.60524e34 | 1.25598 | 0.627989 | − | 0.778222i | \(-0.283878\pi\) | ||||
0.627989 | + | 0.778222i | \(0.283878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.63668e34 | 0.879276 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.96155e34 | 1.58405 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.45926e34 | −1.36322 | −0.681609 | − | 0.731717i | \(-0.738719\pi\) | ||||
−0.681609 | + | 0.731717i | \(0.738719\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.22337e34 | −2.40751 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.59450e34 | 1.00794 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.13067e33 | 0.191546 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.92303e33 | −0.255385 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.50958e34 | 0.618905 | 0.309452 | − | 0.950915i | \(-0.399854\pi\) | ||||
0.309452 | + | 0.950915i | \(0.399854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.31645e34 | 0.547497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.60173e34 | 1.94869 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.88078e33 | −0.106000 | −0.0530000 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0530000 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.85444e34 | −1.63551 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.46798e34 | 0.892138 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.61838e34 | −0.884412 | −0.442206 | − | 0.896914i | \(-0.645804\pi\) | ||||
−0.442206 | + | 0.896914i | \(0.645804\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.07405e34 | −0.564651 | −0.282325 | − | 0.959319i | \(-0.591106\pi\) | ||||
−0.282325 | + | 0.959319i | \(0.591106\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.64671e34 | 0.995013 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −6.63161e34 | −1.12118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.03737e35 | −1.68297 | −0.841484 | − | 0.540282i | \(-0.818318\pi\) | ||||
−0.841484 | + | 0.540282i | \(0.818318\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.27984e35 | −1.99269 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.01644e33 | 0.0749688 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.85744e34 | 0.409941 | 0.204970 | − | 0.978768i | \(-0.434290\pi\) | ||||
0.204970 | + | 0.978768i | \(0.434290\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.16606e34 | −1.26254 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.36336e34 | 0.709370 | 0.354685 | − | 0.934986i | \(-0.384588\pi\) | ||||
0.354685 | + | 0.934986i | \(0.384588\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.60909e34 | −0.839477 | −0.419738 | − | 0.907645i | \(-0.637878\pi\) | ||||
−0.419738 | + | 0.907645i | \(0.637878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.94447e34 | 0.359221 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.67651e34 | 1.13401 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.00979e33 | −0.0564053 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.29000e34 | −0.464102 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.34168e35 | −1.39482 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.62816e34 | −0.862087 | −0.431043 | − | 0.902331i | \(-0.641854\pi\) | ||||
−0.431043 | + | 0.902331i | \(0.641854\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.26679e34 | −0.505824 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.16883e35 | 1.07914 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.70958e33 | 0.0418061 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.38765e35 | 2.03803 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.77093e35 | 1.45370 | 0.726850 | − | 0.686796i | \(-0.240983\pi\) | ||||
0.726850 | + | 0.686796i | \(0.240983\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.98617e34 | 0.630524 | 0.315262 | − | 0.949005i | \(-0.397908\pi\) | ||||
0.315262 | + | 0.949005i | \(0.397908\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.68412e35 | 1.27901 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.16671e35 | 1.58306 | 0.791530 | − | 0.611130i | \(-0.209285\pi\) | ||||
0.791530 | + | 0.611130i | \(0.209285\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59833e34 | −0.534145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.76675e35 | −1.19512 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.41184e35 | 1.57013 | 0.785063 | − | 0.619416i | \(-0.212631\pi\) | ||||
0.785063 | + | 0.619416i | \(0.212631\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.92361e34 | −0.371168 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.92923e35 | 1.76679 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.18788e35 | −1.27045 | −0.635223 | − | 0.772329i | \(-0.719092\pi\) | ||||
−0.635223 | + | 0.772329i | \(0.719092\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.90411e34 | −0.497820 | −0.248910 | − | 0.968527i | \(-0.580072\pi\) | ||||
−0.248910 | + | 0.968527i | \(0.580072\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −4.40028e34 | −0.236898 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.43304e35 | −0.742998 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.23219e35 | 1.61408 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.28705e35 | −2.06221 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.35934e33 | 0.00629934 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.39665e35 | 1.07008 | 0.535040 | − | 0.844827i | \(-0.320297\pi\) | ||||
0.535040 | + | 0.844827i | \(0.320297\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.33678e35 | 0.575124 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.79216e34 | −0.157227 | −0.0786137 | − | 0.996905i | \(-0.525049\pi\) | ||||
−0.0786137 | + | 0.996905i | \(0.525049\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.07679e35 | −0.430286 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.45481e35 | 0.560361 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3.21208e35 | 1.19269 | 0.596345 | − | 0.802729i | \(-0.296619\pi\) | ||||
0.596345 | + | 0.802729i | \(0.296619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.83883e35 | −1.01627 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.10316e35 | −1.76149 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.33443e34 | 0.0444177 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.34540e34 | −0.267899 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.81207e35 | 0.561060 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.10064e34 | 0.241941 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.25105e35 | −0.648597 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.43649e34 | −0.262329 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.50008e35 | 0.402383 | 0.201191 | − | 0.979552i | \(-0.435519\pi\) | ||||
0.201191 | + | 0.979552i | \(0.435519\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.44790e35 | −0.633653 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.66066e35 | −1.41417 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.02321e35 | 0.246730 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.12042e35 | −0.493564 | −0.246782 | − | 0.969071i | \(-0.579373\pi\) | ||||
−0.246782 | + | 0.969071i | \(0.579373\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.69877e35 | −1.50531 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.46186e35 | 0.968048 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.41213e34 | 0.113382 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.34363e35 | −1.08105 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.27911e35 | −0.640686 | −0.320343 | − | 0.947302i | \(-0.603798\pi\) | ||||
−0.320343 | + | 0.947302i | \(0.603798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48443e35 | 0.468853 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.42934e36 | 2.60560 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.46740e36 | 2.58419 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.40795e35 | −0.409701 | −0.204850 | − | 0.978793i | \(-0.565671\pi\) | ||||
−0.204850 | + | 0.978793i | \(0.565671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.57797e35 | −1.41023 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.13594e35 | 0.657063 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.39196e35 | −0.520776 | −0.260388 | − | 0.965504i | \(-0.583850\pi\) | ||||
−0.260388 | + | 0.965504i | \(0.583850\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.31439e35 | −0.788608 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.07978e35 | −0.441749 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.23366e36 | −1.71057 | −0.855284 | − | 0.518159i | \(-0.826617\pi\) | ||||
−0.855284 | + | 0.518159i | \(0.826617\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.02829e34 | −0.107621 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.24478e35 | 0.809389 | 0.404694 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404694 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.26430e35 | −0.785090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.25846e36 | −1.52522 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.74570e35 | 0.556259 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.41291e35 | 0.500294 | 0.250147 | − | 0.968208i | \(-0.419521\pi\) | ||||
0.250147 | + | 0.968208i | \(0.419521\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.03934e36 | −2.23642 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.69113e36 | 2.85495 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.83266e35 | 0.188098 | 0.0940489 | − | 0.995568i | \(-0.470019\pi\) | ||||
0.0940489 | + | 0.995568i | \(0.470019\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.26323e35 | −0.820593 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.88027e36 | 1.80681 | 0.903406 | − | 0.428787i | \(-0.141059\pi\) | ||||
0.903406 | + | 0.428787i | \(0.141059\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.03772e35 | −0.840431 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.74990e36 | 2.47485 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.42195e35 | −0.123863 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28453e36 | 1.08309 | 0.541546 | − | 0.840671i | \(-0.317839\pi\) | ||||
0.541546 | + | 0.840671i | \(0.317839\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.30700e35 | 0.759679 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.04808e36 | −0.828226 | −0.414113 | − | 0.910225i | \(-0.635908\pi\) | ||||
−0.414113 | + | 0.910225i | \(0.635908\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.02566e36 | 1.54987 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.86700e36 | 1.38319 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.10703e35 | −0.294652 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30225e36 | −0.904811 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.70840e35 | 0.586025 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.10044e36 | 1.36912 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.93146e35 | 0.563947 | 0.281974 | − | 0.959422i | \(-0.409011\pi\) | ||||
0.281974 | + | 0.959422i | \(0.409011\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.95822e36 | −1.19784 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.42336e36 | 1.43619 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.54386e33 | 0.00146076 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.50580e36 | −0.837872 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.02840e36 | −0.554540 | −0.277270 | − | 0.960792i | \(-0.589430\pi\) | ||||
−0.277270 | + | 0.960792i | \(0.589430\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.39017e36 | −0.726498 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.38782e36 | −1.71599 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.59763e36 | −0.784392 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.76026e36 | −1.31372 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.62004e36 | −1.20889 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.33897e36 | 0.598981 | 0.299490 | − | 0.954099i | \(-0.403183\pi\) | ||||
0.299490 | + | 0.954099i | \(0.403183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.29485e36 | −0.561643 | −0.280821 | − | 0.959760i | \(-0.590607\pi\) | ||||
−0.280821 | + | 0.959760i | \(0.590607\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.00917e36 | 0.845055 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.82854e36 | −2.37733 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.54600e35 | 0.298498 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.39110e35 | 0.130104 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.91664e34 | 0.0145755 | 0.00728777 | − | 0.999973i | \(-0.497680\pi\) | ||||
0.00728777 | + | 0.999973i | \(0.497680\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.40400e36 | 1.22883 | 0.614414 | − | 0.788984i | \(-0.289392\pi\) | ||||
0.614414 | + | 0.788984i | \(0.289392\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.75147e36 | −1.31379 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.02186e36 | 1.70626 | 0.853132 | − | 0.521696i | \(-0.174700\pi\) | ||||
0.853132 | + | 0.521696i | \(0.174700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.20485e35 | 0.270482 | 0.135241 | − | 0.990813i | \(-0.456819\pi\) | ||||
0.135241 | + | 0.990813i | \(0.456819\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.31856e35 | −0.234106 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.30513e36 | −0.405128 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.57748e36 | −1.07770 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.20215e36 | 0.351471 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.38664e36 | 1.52860 | 0.764300 | − | 0.644861i | \(-0.223085\pi\) | ||||
0.764300 | + | 0.644861i | \(0.223085\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.92900e36 | 1.63317 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.02945e36 | −1.34486 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.10126e36 | −1.58384 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.26629e36 | 0.571180 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.98389e36 | 0.485479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.71505e36 | −1.12038 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.55369e35 | 0.220449 | 0.110225 | − | 0.993907i | \(-0.464843\pi\) | ||||
0.110225 | + | 0.993907i | \(0.464843\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.01718e36 | 1.12430 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.39118e36 | −1.17334 | −0.586669 | − | 0.809827i | \(-0.699561\pi\) | ||||
−0.586669 | + | 0.809827i | \(0.699561\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.48992e36 | −1.16052 | −0.580258 | − | 0.814432i | \(-0.697048\pi\) | ||||
−0.580258 | + | 0.814432i | \(0.697048\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.13241e36 | 0.643190 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.89510e36 | 0.577469 | 0.288735 | − | 0.957409i | \(-0.406766\pi\) | ||||
0.288735 | + | 0.957409i | \(0.406766\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.63772e36 | −1.48000 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.24209e36 | 0.798623 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.65359e36 | 0.668301 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.76349e35 | −0.102437 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.76991e36 | 0.651108 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.66251e36 | −0.782562 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.04429e36 | 0.333463 | 0.166731 | − | 0.986002i | \(-0.446679\pi\) | ||||
0.166731 | + | 0.986002i | \(0.446679\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.71570e37 | 2.72007 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.76163e36 | −0.271466 | −0.135733 | − | 0.990745i | \(-0.543339\pi\) | ||||
−0.135733 | + | 0.990745i | \(0.543339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.25672e37 | −1.88248 | −0.941240 | − | 0.337738i | \(-0.890338\pi\) | ||||
−0.941240 | + | 0.337738i | \(0.890338\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.60456e37 | 2.33649 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −8.81003e36 | −1.24719 | −0.623595 | − | 0.781748i | \(-0.714328\pi\) | ||||
−0.623595 | + | 0.781748i | \(0.714328\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.99436e36 | −0.549762 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.88487e36 | 0.386060 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.53636e36 | −0.330041 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.79203e36 | 0.479826 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.54638e36 | −0.190288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.31962e37 | 1.57925 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.69802e36 | −0.430436 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.75530e36 | −0.651585 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.95988e37 | 2.15835 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.59523e37 | 1.70896 | 0.854482 | − | 0.519481i | \(-0.173875\pi\) | ||||
0.854482 | + | 0.519481i | \(0.173875\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.58234e36 | −0.373352 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.71775e36 | 0.174172 | 0.0870862 | − | 0.996201i | \(-0.472244\pi\) | ||||
0.0870862 | + | 0.996201i | \(0.472244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.86379e36 | 0.677142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.87054e35 | −0.0275550 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.02434e36 | 0.189089 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.70373e35 | 0.0700256 | 0.0350128 | − | 0.999387i | \(-0.488853\pi\) | ||||
0.0350128 | + | 0.999387i | \(0.488853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.13079e37 | −2.76955 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.43703e36 | −0.209817 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.14061e37 | −1.79377 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.69819e36 | −0.709467 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.66420e37 | 1.32132 | 0.660662 | − | 0.750684i | \(-0.270276\pi\) | ||||
0.660662 | + | 0.750684i | \(0.270276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.38121e36 | −0.184046 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.54021e37 | 1.91139 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.49983e37 | −1.09874 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.66427e36 | 0.689325 | 0.344663 | − | 0.938727i | \(-0.387993\pi\) | ||||
0.344663 | + | 0.938727i | \(0.387993\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.87214e36 | 0.477279 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.33808e37 | −0.904923 | −0.452461 | − | 0.891784i | \(-0.649454\pi\) | ||||
−0.452461 | + | 0.891784i | \(0.649454\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.91080e36 | −0.520984 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.43690e36 | −0.476974 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.63078e37 | −1.64328 | −0.821638 | − | 0.570010i | \(-0.806939\pi\) | ||||
−0.821638 | + | 0.570010i | \(0.806939\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.98981e36 | −0.181893 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.21195e37 | −0.718170 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9.10378e36 | −0.525485 | −0.262742 | − | 0.964866i | \(-0.584627\pi\) | ||||
−0.262742 | + | 0.964866i | \(0.584627\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.68184e37 | 0.945677 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.44389e37 | −1.33870 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.70142e36 | 0.517729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.01623e36 | −0.0528386 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.66151e37 | −0.841731 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.24538e37 | −2.58932 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.34794e36 | 0.0648394 | 0.0324197 | − | 0.999474i | \(-0.489679\pi\) | ||||
0.0324197 | + | 0.999474i | \(0.489679\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.22483e37 | 1.04291 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.82504e36 | −0.174741 | −0.0873707 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873707 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.76831e36 | −0.123255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.02049e36 | −0.304656 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.16914e37 | 0.494522 | 0.247261 | − | 0.968949i | \(-0.420470\pi\) | ||||
0.247261 | + | 0.968949i | \(0.420470\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.84776e37 | 0.761835 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.16418e37 | 1.27174 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.38138e37 | −0.541244 | −0.270622 | − | 0.962686i | \(-0.587229\pi\) | ||||
−0.270622 | + | 0.962686i | \(0.587229\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.48672e37 | 2.09585 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.93447e37 | 0.720441 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.45348e37 | 0.527784 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.79186e37 | 1.34255 | 0.671276 | − | 0.741207i | \(-0.265746\pi\) | ||||
0.671276 | + | 0.741207i | \(0.265746\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.22853e37 | −2.84090 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.84995e37 | 0.959510 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.34619e37 | 1.75531 | 0.877657 | − | 0.479289i | \(-0.159106\pi\) | ||||
0.877657 | + | 0.479289i | \(0.159106\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.27036e37 | −0.406779 |
(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 | 16.26.a.c.1.2 | 2 | ||
4.3 | odd | 2 | 2.26.a.b.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 18.26.a.e.1.1 | 2 | |||
20.3 | even | 4 | 50.26.b.e.49.1 | 4 | |||
20.7 | even | 4 | 50.26.b.e.49.4 | 4 | |||
20.19 | odd | 2 | 50.26.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.26.a.b.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
16.26.a.c.1.2 | 2 | 1.1 | even | 1 | trivial | ||
18.26.a.e.1.1 | 2 | 12.11 | even | 2 | |||
50.26.a.c.1.2 | 2 | 20.19 | odd | 2 | |||
50.26.b.e.49.1 | 4 | 20.3 | even | 4 | |||
50.26.b.e.49.4 | 4 | 20.7 | even | 4 |