Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,8,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(2.81146522936\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{10}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 10 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.16228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18.9737 | 1.67705 | 0.838525 | − | 0.544862i | \(-0.183418\pi\) | ||||
0.838525 | + | 0.544862i | \(0.183418\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 232.000 | 1.81250 | ||||||||
\(5\) | −303.579 | −1.08612 | −0.543058 | − | 0.839695i | \(-0.682734\pi\) | ||||
−0.543058 | + | 0.839695i | \(0.682734\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 260.000 | 0.286504 | 0.143252 | − | 0.989686i | \(-0.454244\pi\) | ||||
0.143252 | + | 0.989686i | \(0.454244\pi\) | |||||||
\(8\) | 1973.26 | 1.36260 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5760.00 | −1.82147 | ||||||||
\(11\) | −6071.57 | −1.37539 | −0.687697 | − | 0.725998i | \(-0.741378\pi\) | ||||
−0.687697 | + | 0.725998i | \(0.741378\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6890.00 | 0.869796 | 0.434898 | − | 0.900480i | \(-0.356784\pi\) | ||||
0.434898 | + | 0.900480i | \(0.356784\pi\) | |||||||
\(14\) | 4933.15 | 0.480481 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7744.00 | 0.472656 | ||||||||
\(17\) | 23679.1 | 1.16895 | 0.584473 | − | 0.811413i | \(-0.301301\pi\) | ||||
0.584473 | + | 0.811413i | \(0.301301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 33176.0 | 1.10965 | 0.554826 | − | 0.831967i | \(-0.312785\pi\) | ||||
0.554826 | + | 0.831967i | \(0.312785\pi\) | |||||||
\(20\) | −70430.2 | −1.96859 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −115200. | −2.30660 | ||||||||
\(23\) | 31572.2 | 0.541075 | 0.270537 | − | 0.962709i | \(-0.412799\pi\) | ||||
0.270537 | + | 0.962709i | \(0.412799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14035.0 | 0.179648 | ||||||||
\(26\) | 130729. | 1.45869 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 60320.0 | 0.519288 | ||||||||
\(29\) | −138128. | −1.05169 | −0.525847 | − | 0.850579i | \(-0.676252\pi\) | ||||
−0.525847 | + | 0.850579i | \(0.676252\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1508.00 | 0.00909150 | 0.00454575 | − | 0.999990i | \(-0.498553\pi\) | ||||
0.00454575 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(32\) | −105645. | −0.569935 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 449280. | 1.96038 | ||||||||
\(35\) | −78930.5 | −0.311176 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −380770. | −1.23582 | −0.617912 | − | 0.786247i | \(-0.712021\pi\) | ||||
−0.617912 | + | 0.786247i | \(0.712021\pi\) | |||||||
\(38\) | 629470. | 1.86094 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −599040. | −1.47995 | ||||||||
\(41\) | 88037.8 | 0.199492 | 0.0997461 | − | 0.995013i | \(-0.468197\pi\) | ||||
0.0997461 | + | 0.995013i | \(0.468197\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7640.00 | 0.0146539 | 0.00732696 | − | 0.999973i | \(-0.497668\pi\) | ||||
0.00732696 | + | 0.999973i | \(0.497668\pi\) | |||||||
\(44\) | −1.40860e6 | −2.49290 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 599040. | 0.907410 | ||||||||
\(47\) | 565871. | 0.795014 | 0.397507 | − | 0.917599i | \(-0.369875\pi\) | ||||
0.397507 | + | 0.917599i | \(0.369875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −755943. | −0.917916 | ||||||||
\(50\) | 266295. | 0.301279 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.59848e6 | 1.57651 | ||||||||
\(53\) | 1.03004e6 | 0.950363 | 0.475182 | − | 0.879888i | \(-0.342382\pi\) | ||||
0.475182 | + | 0.879888i | \(0.342382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.84320e6 | 1.49384 | ||||||||
\(56\) | 513048. | 0.390391 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.62080e6 | −1.76375 | ||||||||
\(59\) | −2.70792e6 | −1.71654 | −0.858270 | − | 0.513198i | \(-0.828461\pi\) | ||||
−0.858270 | + | 0.513198i | \(0.828461\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −988858. | −0.557801 | −0.278901 | − | 0.960320i | \(-0.589970\pi\) | ||||
−0.278901 | + | 0.960320i | \(0.589970\pi\) | |||||||
\(62\) | 28612.3 | 0.0152469 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.99571e6 | −1.42847 | ||||||||
\(65\) | −2.09166e6 | −0.944700 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.85736e6 | 1.56685 | 0.783427 | − | 0.621484i | \(-0.213470\pi\) | ||||
0.783427 | + | 0.621484i | \(0.213470\pi\) | |||||||
\(68\) | 5.49356e6 | 2.11872 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.49760e6 | −0.521858 | ||||||||
\(71\) | 4.22581e6 | 1.40122 | 0.700610 | − | 0.713545i | \(-0.252911\pi\) | ||||
0.700610 | + | 0.713545i | \(0.252911\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00473e6 | −0.603151 | −0.301575 | − | 0.953442i | \(-0.597512\pi\) | ||||
−0.301575 | + | 0.953442i | \(0.597512\pi\) | |||||||
\(74\) | −7.22460e6 | −2.07254 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.69683e6 | 2.01124 | ||||||||
\(77\) | −1.57861e6 | −0.394055 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.69968e6 | 0.616053 | 0.308027 | − | 0.951378i | \(-0.400331\pi\) | ||||
0.308027 | + | 0.951378i | \(0.400331\pi\) | |||||||
\(80\) | −2.35091e6 | −0.513360 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.67040e6 | 0.334558 | ||||||||
\(83\) | 2.71156e6 | 0.520531 | 0.260266 | − | 0.965537i | \(-0.416190\pi\) | ||||
0.260266 | + | 0.965537i | \(0.416190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.18848e6 | −1.26961 | ||||||||
\(86\) | 144959. | 0.0245754 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.19808e7 | −1.87412 | ||||||||
\(89\) | 7.74126e6 | 1.16398 | 0.581991 | − | 0.813195i | \(-0.302274\pi\) | ||||
0.581991 | + | 0.813195i | \(0.302274\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.79140e6 | 0.249200 | ||||||||
\(92\) | 7.32475e6 | 0.980698 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.07366e7 | 1.33328 | ||||||||
\(95\) | −1.00715e7 | −1.20521 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.29575e7 | −1.44152 | −0.720759 | − | 0.693186i | \(-0.756206\pi\) | ||||
−0.720759 | + | 0.693186i | \(0.756206\pi\) | |||||||
\(98\) | −1.43430e7 | −1.53939 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.25612e6 | 0.325612 | ||||||||
\(101\) | −5.58433e6 | −0.539320 | −0.269660 | − | 0.962956i | \(-0.586911\pi\) | ||||
−0.269660 | + | 0.962956i | \(0.586911\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.07326e6 | 0.457464 | 0.228732 | − | 0.973489i | \(-0.426542\pi\) | ||||
0.228732 | + | 0.973489i | \(0.426542\pi\) | |||||||
\(104\) | 1.35958e7 | 1.18519 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.95437e7 | 1.59381 | ||||||||
\(107\) | −3.69395e6 | −0.291506 | −0.145753 | − | 0.989321i | \(-0.546560\pi\) | ||||
−0.145753 | + | 0.989321i | \(0.546560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.59383e6 | 0.487692 | 0.243846 | − | 0.969814i | \(-0.421591\pi\) | ||||
0.243846 | + | 0.969814i | \(0.421591\pi\) | |||||||
\(110\) | 3.49723e7 | 2.50524 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.01344e6 | 0.135418 | ||||||||
\(113\) | −4.75161e6 | −0.309789 | −0.154895 | − | 0.987931i | \(-0.549504\pi\) | ||||
−0.154895 | + | 0.987931i | \(0.549504\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.58464e6 | −0.587670 | ||||||||
\(116\) | −3.20458e7 | −1.90620 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.13792e7 | −2.87873 | ||||||||
\(119\) | 6.15658e6 | 0.334907 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.73768e7 | 0.891706 | ||||||||
\(122\) | −1.87623e7 | −0.935461 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 349856. | 0.0164783 | ||||||||
\(125\) | 1.94564e7 | 0.890997 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.95361e7 | 0.846303 | 0.423151 | − | 0.906059i | \(-0.360924\pi\) | ||||
0.423151 | + | 0.906059i | \(0.360924\pi\) | |||||||
\(128\) | −4.33170e7 | −1.82568 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.96864e7 | −1.58431 | ||||||||
\(131\) | 3.72552e7 | 1.44789 | 0.723947 | − | 0.689855i | \(-0.242326\pi\) | ||||
0.723947 | + | 0.689855i | \(0.242326\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.62576e6 | 0.317919 | ||||||||
\(134\) | 7.31883e7 | 2.62769 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.67251e7 | 1.59281 | ||||||||
\(137\) | −2.12171e7 | −0.704960 | −0.352480 | − | 0.935819i | \(-0.614661\pi\) | ||||
−0.352480 | + | 0.935819i | \(0.614661\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.44669e7 | −0.772728 | −0.386364 | − | 0.922346i | \(-0.626269\pi\) | ||||
−0.386364 | + | 0.922346i | \(0.626269\pi\) | |||||||
\(140\) | −1.83119e7 | −0.564007 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.01792e7 | 2.34992 | ||||||||
\(143\) | −4.18331e7 | −1.19631 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.19328e7 | 1.14226 | ||||||||
\(146\) | −3.80371e7 | −1.01151 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.83386e7 | −2.23993 | ||||||||
\(149\) | −1.85320e7 | −0.458954 | −0.229477 | − | 0.973314i | \(-0.573702\pi\) | ||||
−0.229477 | + | 0.973314i | \(0.573702\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12102e7 | −1.21042 | −0.605211 | − | 0.796065i | \(-0.706911\pi\) | ||||
−0.605211 | + | 0.796065i | \(0.706911\pi\) | |||||||
\(152\) | 6.54649e7 | 1.51201 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.99520e7 | −0.660851 | ||||||||
\(155\) | −457797. | −0.00987442 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.63815e6 | 0.198767 | 0.0993836 | − | 0.995049i | \(-0.468313\pi\) | ||||
0.0993836 | + | 0.995049i | \(0.468313\pi\) | |||||||
\(158\) | 5.12229e7 | 1.03315 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.20717e7 | 0.619016 | ||||||||
\(161\) | 8.20877e6 | 0.155020 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.18666e7 | −1.29978 | −0.649891 | − | 0.760027i | \(-0.725185\pi\) | ||||
−0.649891 | + | 0.760027i | \(0.725185\pi\) | |||||||
\(164\) | 2.04248e7 | 0.361579 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.14483e7 | 0.872957 | ||||||||
\(167\) | −8.56578e6 | −0.142318 | −0.0711589 | − | 0.997465i | \(-0.522670\pi\) | ||||
−0.0711589 | + | 0.997465i | \(0.522670\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.52764e7 | −0.243455 | ||||||||
\(170\) | −1.36392e8 | −2.12920 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.77248e6 | 0.0265602 | ||||||||
\(173\) | 4.97065e7 | 0.729880 | 0.364940 | − | 0.931031i | \(-0.381090\pi\) | ||||
0.364940 | + | 0.931031i | \(0.381090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.64910e6 | 0.0514698 | ||||||||
\(176\) | −4.70183e7 | −0.650088 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.46880e8 | 1.95206 | ||||||||
\(179\) | −5.73035e7 | −0.746785 | −0.373393 | − | 0.927673i | \(-0.621806\pi\) | ||||
−0.373393 | + | 0.927673i | \(0.621806\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.15744e7 | 1.02254 | 0.511268 | − | 0.859421i | \(-0.329176\pi\) | ||||
0.511268 | + | 0.859421i | \(0.329176\pi\) | |||||||
\(182\) | 3.39894e7 | 0.417921 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.23002e7 | 0.737270 | ||||||||
\(185\) | 1.15594e8 | 1.34225 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.43770e8 | −1.60776 | ||||||||
\(188\) | 1.31282e8 | 1.44096 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.91094e8 | −2.02120 | ||||||||
\(191\) | 1.60229e8 | 1.66389 | 0.831944 | − | 0.554860i | \(-0.187228\pi\) | ||||
0.831944 | + | 0.554860i | \(0.187228\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00372e7 | 0.601133 | 0.300566 | − | 0.953761i | \(-0.402824\pi\) | ||||
0.300566 | + | 0.953761i | \(0.402824\pi\) | |||||||
\(194\) | −2.45851e8 | −2.41750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.75379e8 | −1.66372 | ||||||||
\(197\) | −1.90188e8 | −1.77236 | −0.886179 | − | 0.463343i | \(-0.846650\pi\) | ||||
−0.886179 | + | 0.463343i | \(0.846650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.94001e8 | 1.74509 | 0.872545 | − | 0.488533i | \(-0.162468\pi\) | ||||
0.872545 | + | 0.488533i | \(0.162468\pi\) | |||||||
\(200\) | 2.76947e7 | 0.244789 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.05955e8 | −0.904466 | ||||||||
\(203\) | −3.59134e7 | −0.301314 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.67264e7 | −0.216672 | ||||||||
\(206\) | 9.62583e7 | 0.767190 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.33562e7 | 0.411115 | ||||||||
\(209\) | −2.01431e8 | −1.52621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.04896e7 | −0.0768727 | −0.0384364 | − | 0.999261i | \(-0.512238\pi\) | ||||
−0.0384364 | + | 0.999261i | \(0.512238\pi\) | |||||||
\(212\) | 2.38970e8 | 1.72253 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.00877e7 | −0.488870 | ||||||||
\(215\) | −2.31934e6 | −0.0159159 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 392080. | 0.00260475 | ||||||||
\(218\) | 1.25109e8 | 0.817884 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.27622e8 | 2.70758 | ||||||||
\(221\) | 1.63149e8 | 1.01675 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.25160e8 | 1.35964 | 0.679820 | − | 0.733379i | \(-0.262058\pi\) | ||||
0.679820 | + | 0.733379i | \(0.262058\pi\) | |||||||
\(224\) | −2.74678e7 | −0.163289 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.01555e7 | −0.519533 | ||||||||
\(227\) | −1.69490e8 | −0.961733 | −0.480867 | − | 0.876794i | \(-0.659678\pi\) | ||||
−0.480867 | + | 0.876794i | \(0.659678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.52595e7 | −0.359103 | −0.179552 | − | 0.983749i | \(-0.557465\pi\) | ||||
−0.179552 | + | 0.983749i | \(0.557465\pi\) | |||||||
\(230\) | −1.81856e8 | −0.985552 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.72563e8 | −1.43304 | ||||||||
\(233\) | 1.86355e8 | 0.965150 | 0.482575 | − | 0.875855i | \(-0.339702\pi\) | ||||
0.482575 | + | 0.875855i | \(0.339702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.71786e8 | −0.863477 | ||||||||
\(236\) | −6.28238e8 | −3.11123 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.16813e8 | 0.561657 | ||||||||
\(239\) | 4.26103e7 | 0.201893 | 0.100947 | − | 0.994892i | \(-0.467813\pi\) | ||||
0.100947 | + | 0.994892i | \(0.467813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.56943e8 | −1.18243 | −0.591217 | − | 0.806513i | \(-0.701352\pi\) | ||||
−0.591217 | + | 0.806513i | \(0.701352\pi\) | |||||||
\(242\) | 3.29702e8 | 1.49544 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.29415e8 | −1.01101 | ||||||||
\(245\) | 2.29488e8 | 0.996963 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.28583e8 | 0.965170 | ||||||||
\(248\) | 2.97568e6 | 0.0123881 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.69158e8 | 1.49425 | ||||||||
\(251\) | 2.73968e8 | 1.09356 | 0.546778 | − | 0.837278i | \(-0.315854\pi\) | ||||
0.546778 | + | 0.837278i | \(0.315854\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.91693e8 | −0.744190 | ||||||||
\(254\) | 3.70672e8 | 1.41929 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.38432e8 | −1.63329 | ||||||||
\(257\) | −3.19542e8 | −1.17425 | −0.587127 | − | 0.809495i | \(-0.699741\pi\) | ||||
−0.587127 | + | 0.809495i | \(0.699741\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.90002e7 | −0.354068 | ||||||||
\(260\) | −4.85264e8 | −1.71227 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.06867e8 | 2.42819 | ||||||||
\(263\) | −2.71016e8 | −0.918648 | −0.459324 | − | 0.888269i | \(-0.651908\pi\) | ||||
−0.459324 | + | 0.888269i | \(0.651908\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.12699e8 | −1.03220 | ||||||||
\(266\) | 1.63662e8 | 0.533167 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.94908e8 | 2.83992 | ||||||||
\(269\) | −1.09930e8 | −0.344338 | −0.172169 | − | 0.985067i | \(-0.555077\pi\) | ||||
−0.172169 | + | 0.985067i | \(0.555077\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.35740e8 | 1.32995 | 0.664974 | − | 0.746866i | \(-0.268443\pi\) | ||||
0.664974 | + | 0.746866i | \(0.268443\pi\) | |||||||
\(272\) | 1.83371e8 | 0.552510 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.02566e8 | −1.18225 | ||||||||
\(275\) | −8.52145e7 | −0.247087 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.35120e8 | −0.664676 | −0.332338 | − | 0.943160i | \(-0.607837\pi\) | ||||
−0.332338 | + | 0.943160i | \(0.607837\pi\) | |||||||
\(278\) | −4.64226e8 | −1.29590 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.55750e8 | −0.424010 | ||||||||
\(281\) | 2.13052e8 | 0.572812 | 0.286406 | − | 0.958108i | \(-0.407539\pi\) | ||||
0.286406 | + | 0.958108i | \(0.407539\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.90664e7 | −0.181140 | −0.0905700 | − | 0.995890i | \(-0.528869\pi\) | ||||
−0.0905700 | + | 0.995890i | \(0.528869\pi\) | |||||||
\(284\) | 9.80389e8 | 2.53971 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.93728e8 | −2.00628 | ||||||||
\(287\) | 2.28898e7 | 0.0571552 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.50363e8 | 0.366436 | ||||||||
\(290\) | 7.95619e8 | 1.91563 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.65097e8 | −1.09321 | ||||||||
\(293\) | −6.91892e8 | −1.60695 | −0.803474 | − | 0.595340i | \(-0.797017\pi\) | ||||
−0.803474 | + | 0.595340i | \(0.797017\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.22067e8 | 1.86436 | ||||||||
\(296\) | −7.51359e8 | −1.68394 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.51619e8 | −0.769690 | ||||||||
\(299\) | 2.17532e8 | 0.470625 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.98640e6 | 0.00419840 | ||||||||
\(302\) | −9.71645e8 | −2.02994 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.56915e8 | 0.524483 | ||||||||
\(305\) | 3.00196e8 | 0.605837 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.97049e8 | −1.76942 | −0.884712 | − | 0.466139i | \(-0.845645\pi\) | ||||
−0.884712 | + | 0.466139i | \(0.845645\pi\) | |||||||
\(308\) | −3.66237e8 | −0.714225 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.68608e6 | −0.0165599 | ||||||||
\(311\) | 1.63228e8 | 0.307704 | 0.153852 | − | 0.988094i | \(-0.450832\pi\) | ||||
0.153852 | + | 0.988094i | \(0.450832\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.86242e8 | 1.26495 | 0.632473 | − | 0.774583i | \(-0.282040\pi\) | ||||
0.632473 | + | 0.774583i | \(0.282040\pi\) | |||||||
\(314\) | 1.82871e8 | 0.333343 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.26327e8 | 1.11660 | ||||||||
\(317\) | 5.23972e8 | 0.923849 | 0.461924 | − | 0.886919i | \(-0.347159\pi\) | ||||
0.461924 | + | 0.886919i | \(0.347159\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.38656e8 | 1.44649 | ||||||||
\(320\) | 9.09434e8 | 1.55148 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.55750e8 | 0.259976 | ||||||||
\(323\) | 7.85579e8 | 1.29712 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.67012e7 | 0.156257 | ||||||||
\(326\) | −1.36357e9 | −2.17980 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.73722e8 | 0.271829 | ||||||||
\(329\) | 1.47126e8 | 0.227774 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.72280e8 | −0.867382 | −0.433691 | − | 0.901062i | \(-0.642789\pi\) | ||||
−0.433691 | + | 0.901062i | \(0.642789\pi\) | |||||||
\(332\) | 6.29083e8 | 0.943462 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.62524e8 | −0.238674 | ||||||||
\(335\) | −1.17101e9 | −1.70178 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.56883e8 | −0.792609 | −0.396305 | − | 0.918119i | \(-0.629708\pi\) | ||||
−0.396305 | + | 0.918119i | \(0.629708\pi\) | |||||||
\(338\) | −2.89850e8 | −0.408286 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.66773e9 | −2.30117 | ||||||||
\(341\) | −9.15593e6 | −0.0125044 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.10666e8 | −0.549490 | ||||||||
\(344\) | 1.50757e7 | 0.0199675 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.43114e8 | 1.22405 | ||||||||
\(347\) | −8.89499e8 | −1.14286 | −0.571429 | − | 0.820652i | \(-0.693611\pi\) | ||||
−0.571429 | + | 0.820652i | \(0.693611\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.80706e8 | 0.983102 | 0.491551 | − | 0.870849i | \(-0.336430\pi\) | ||||
0.491551 | + | 0.870849i | \(0.336430\pi\) | |||||||
\(350\) | 6.92368e7 | 0.0863175 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.41434e8 | 0.783885 | ||||||||
\(353\) | −5.40517e8 | −0.654030 | −0.327015 | − | 0.945019i | \(-0.606043\pi\) | ||||
−0.327015 | + | 0.945019i | \(0.606043\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.28287e9 | −1.52189 | ||||||||
\(356\) | 1.79597e9 | 2.10972 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.08726e9 | −1.25240 | ||||||||
\(359\) | −6.93617e7 | −0.0791205 | −0.0395602 | − | 0.999217i | \(-0.512596\pi\) | ||||
−0.0395602 | + | 0.999217i | \(0.512596\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.06775e8 | 0.231325 | ||||||||
\(362\) | 1.54777e9 | 1.71485 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.15605e8 | 0.451675 | ||||||||
\(365\) | 6.08593e8 | 0.655092 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.73436e8 | −0.394353 | −0.197177 | − | 0.980368i | \(-0.563177\pi\) | ||||
−0.197177 | + | 0.980368i | \(0.563177\pi\) | |||||||
\(368\) | 2.44495e8 | 0.255742 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.19324e9 | 2.25102 | ||||||||
\(371\) | 2.67811e8 | 0.272283 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.78207e8 | 0.277579 | 0.138790 | − | 0.990322i | \(-0.455679\pi\) | ||||
0.138790 | + | 0.990322i | \(0.455679\pi\) | |||||||
\(374\) | −2.72784e9 | −2.69630 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.11661e9 | 1.08329 | ||||||||
\(377\) | −9.51704e8 | −0.914760 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.36851e9 | −1.29125 | −0.645626 | − | 0.763654i | \(-0.723404\pi\) | ||||
−0.645626 | + | 0.763654i | \(0.723404\pi\) | |||||||
\(380\) | −2.33659e9 | −2.18444 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.04013e9 | 2.79042 | ||||||||
\(383\) | 2.07950e9 | 1.89131 | 0.945655 | − | 0.325173i | \(-0.105422\pi\) | ||||
0.945655 | + | 0.325173i | \(0.105422\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.79232e8 | 0.427990 | ||||||||
\(386\) | 1.13913e9 | 1.00813 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.00614e9 | −2.61275 | ||||||||
\(389\) | −1.96793e8 | −0.169507 | −0.0847533 | − | 0.996402i | \(-0.527010\pi\) | ||||
−0.0847533 | + | 0.996402i | \(0.527010\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.47602e8 | 0.632487 | ||||||||
\(392\) | −1.49167e9 | −1.25076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.60857e9 | −2.97234 | ||||||||
\(395\) | −8.19566e8 | −0.669105 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.99153e8 | 0.239953 | 0.119977 | − | 0.992777i | \(-0.461718\pi\) | ||||
0.119977 | + | 0.992777i | \(0.461718\pi\) | |||||||
\(398\) | 3.68091e9 | 2.92661 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.08687e8 | 0.0849117 | ||||||||
\(401\) | 8.45142e8 | 0.654522 | 0.327261 | − | 0.944934i | \(-0.393874\pi\) | ||||
0.327261 | + | 0.944934i | \(0.393874\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.03901e7 | 0.00790775 | ||||||||
\(404\) | −1.29556e9 | −0.977517 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.81408e8 | −0.505320 | ||||||||
\(407\) | 2.31187e9 | 1.69974 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.07268e9 | 0.775248 | 0.387624 | − | 0.921818i | \(-0.373296\pi\) | ||||
0.387624 | + | 0.921818i | \(0.373296\pi\) | |||||||
\(410\) | −5.07098e8 | −0.363369 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.17700e9 | 0.829153 | ||||||||
\(413\) | −7.04060e8 | −0.491795 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.23173e8 | −0.565357 | ||||||||
\(416\) | −7.27897e8 | −0.495728 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.82188e9 | −2.55953 | ||||||||
\(419\) | −1.41451e9 | −0.939416 | −0.469708 | − | 0.882822i | \(-0.655641\pi\) | ||||
−0.469708 | + | 0.882822i | \(0.655641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.41562e9 | 0.924613 | 0.462307 | − | 0.886720i | \(-0.347022\pi\) | ||||
0.462307 | + | 0.886720i | \(0.347022\pi\) | |||||||
\(422\) | −1.99027e8 | −0.128919 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.03254e9 | 1.29497 | ||||||||
\(425\) | 3.32337e8 | 0.209999 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.57103e8 | −0.159812 | ||||||||
\(428\) | −8.56995e8 | −0.528354 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.40064e7 | −0.0266917 | ||||||||
\(431\) | −3.27067e9 | −1.96773 | −0.983867 | − | 0.178900i | \(-0.942746\pi\) | ||||
−0.983867 | + | 0.178900i | \(0.942746\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.30708e9 | 0.773741 | 0.386870 | − | 0.922134i | \(-0.373556\pi\) | ||||
0.386870 | + | 0.922134i | \(0.373556\pi\) | |||||||
\(434\) | 7.43919e6 | 0.00436829 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.52977e9 | 0.883941 | ||||||||
\(437\) | 1.04744e9 | 0.600404 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.54539e9 | 1.43591 | 0.717957 | − | 0.696087i | \(-0.245077\pi\) | ||||
0.717957 | + | 0.696087i | \(0.245077\pi\) | |||||||
\(440\) | 3.63712e9 | 2.03551 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.09554e9 | 1.70513 | ||||||||
\(443\) | −2.69926e8 | −0.147514 | −0.0737568 | − | 0.997276i | \(-0.523499\pi\) | ||||
−0.0737568 | + | 0.997276i | \(0.523499\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.35008e9 | −1.26422 | ||||||||
\(446\) | 4.27211e9 | 2.28018 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.78885e8 | −0.409261 | ||||||||
\(449\) | 9.77302e8 | 0.509526 | 0.254763 | − | 0.967004i | \(-0.418003\pi\) | ||||
0.254763 | + | 0.967004i | \(0.418003\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.34528e8 | −0.274380 | ||||||||
\(452\) | −1.10237e9 | −0.561493 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.21585e9 | −1.61288 | ||||||||
\(455\) | −5.43831e8 | −0.270660 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.83182e9 | −1.38790 | −0.693951 | − | 0.720022i | \(-0.744132\pi\) | ||||
−0.693951 | + | 0.720022i | \(0.744132\pi\) | |||||||
\(458\) | −1.23821e9 | −0.602234 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.22364e9 | −1.06515 | ||||||||
\(461\) | −3.52138e9 | −1.67402 | −0.837008 | − | 0.547190i | \(-0.815697\pi\) | ||||
−0.837008 | + | 0.547190i | \(0.815697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.59163e9 | 0.745261 | 0.372631 | − | 0.927980i | \(-0.378456\pi\) | ||||
0.372631 | + | 0.927980i | \(0.378456\pi\) | |||||||
\(464\) | −1.06967e9 | −0.497090 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.53583e9 | 1.61861 | ||||||||
\(467\) | 1.77030e9 | 0.804336 | 0.402168 | − | 0.915566i | \(-0.368257\pi\) | ||||
0.402168 | + | 0.915566i | \(0.368257\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.00291e9 | 0.448909 | ||||||||
\(470\) | −3.25941e9 | −1.44810 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.34344e9 | −2.33896 | ||||||||
\(473\) | −4.63868e7 | −0.0201549 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.65625e8 | 0.199347 | ||||||||
\(476\) | 1.42833e9 | 0.607020 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.08474e8 | 0.338585 | ||||||||
\(479\) | 2.80890e9 | 1.16778 | 0.583892 | − | 0.811831i | \(-0.301529\pi\) | ||||
0.583892 | + | 0.811831i | \(0.301529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.62351e9 | −1.07492 | ||||||||
\(482\) | −4.87515e9 | −1.98300 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.03142e9 | 1.61622 | ||||||||
\(485\) | 3.93362e9 | 1.56565 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.42599e9 | −1.34411 | −0.672054 | − | 0.740502i | \(-0.734588\pi\) | ||||
−0.672054 | + | 0.740502i | \(0.734588\pi\) | |||||||
\(488\) | −1.95128e9 | −0.760062 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.35423e9 | 1.67196 | ||||||||
\(491\) | 1.72132e9 | 0.656259 | 0.328129 | − | 0.944633i | \(-0.393582\pi\) | ||||
0.328129 | + | 0.944633i | \(0.393582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.27076e9 | −1.22937 | ||||||||
\(494\) | 4.33705e9 | 1.61864 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.16780e7 | 0.00429715 | ||||||||
\(497\) | 1.09871e9 | 0.401455 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.16845e9 | 1.50184 | 0.750919 | − | 0.660395i | \(-0.229611\pi\) | ||||
0.750919 | + | 0.660395i | \(0.229611\pi\) | |||||||
\(500\) | 4.51387e9 | 1.61493 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.19817e9 | 1.83395 | ||||||||
\(503\) | −2.73826e9 | −0.959370 | −0.479685 | − | 0.877441i | \(-0.659249\pi\) | ||||
−0.479685 | + | 0.877441i | \(0.659249\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.69528e9 | 0.585764 | ||||||||
\(506\) | −3.63712e9 | −1.24804 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.53238e9 | 1.53392 | ||||||||
\(509\) | −1.76205e9 | −0.592253 | −0.296126 | − | 0.955149i | \(-0.595695\pi\) | ||||
−0.296126 | + | 0.955149i | \(0.595695\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.21230e8 | −0.172805 | ||||||||
\(512\) | −2.77408e9 | −0.913427 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.06288e9 | −1.96928 | ||||||||
\(515\) | −1.54013e9 | −0.496859 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.43572e9 | −1.09346 | ||||||||
\(518\) | −1.87840e9 | −0.593790 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.12739e9 | −1.28725 | ||||||||
\(521\) | −5.30709e9 | −1.64408 | −0.822042 | − | 0.569427i | \(-0.807165\pi\) | ||||
−0.822042 | + | 0.569427i | \(0.807165\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.17075e9 | 1.27485 | 0.637424 | − | 0.770513i | \(-0.280000\pi\) | ||||
0.637424 | + | 0.770513i | \(0.280000\pi\) | |||||||
\(524\) | 8.64320e9 | 2.62431 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.14216e9 | −1.54062 | ||||||||
\(527\) | 3.57081e7 | 0.0106275 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.40802e9 | −0.707238 | ||||||||
\(530\) | −5.93304e9 | −1.73106 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00118e9 | 0.576228 | ||||||||
\(533\) | 6.06581e8 | 0.173517 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.12140e9 | 0.316609 | ||||||||
\(536\) | 7.61158e9 | 2.13500 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.08578e9 | −0.577472 | ||||||||
\(539\) | 4.58976e9 | 1.26249 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.78986e9 | 0.485991 | 0.242996 | − | 0.970027i | \(-0.421870\pi\) | ||||
0.242996 | + | 0.970027i | \(0.421870\pi\) | |||||||
\(542\) | 8.26758e9 | 2.23039 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.50159e9 | −0.666224 | ||||||||
\(545\) | −2.00175e9 | −0.529690 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.59509e9 | 0.677948 | 0.338974 | − | 0.940796i | \(-0.389920\pi\) | ||||
0.338974 | + | 0.940796i | \(0.389920\pi\) | |||||||
\(548\) | −4.92237e9 | −1.27774 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.61683e9 | −0.414377 | ||||||||
\(551\) | −4.58254e9 | −1.16701 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.01918e8 | 0.176501 | ||||||||
\(554\) | −4.46108e9 | −1.11470 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.67631e9 | −1.40057 | ||||||||
\(557\) | 3.59472e9 | 0.881397 | 0.440698 | − | 0.897655i | \(-0.354731\pi\) | ||||
0.440698 | + | 0.897655i | \(0.354731\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.26396e7 | 0.0127459 | ||||||||
\(560\) | −6.11237e8 | −0.147079 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.04237e9 | 0.960636 | ||||||||
\(563\) | −2.58729e9 | −0.611035 | −0.305518 | − | 0.952186i | \(-0.598829\pi\) | ||||
−0.305518 | + | 0.952186i | \(0.598829\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.44249e9 | 0.336467 | ||||||||
\(566\) | −1.31044e9 | −0.303781 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.33864e9 | 1.90931 | ||||||||
\(569\) | 4.24097e9 | 0.965100 | 0.482550 | − | 0.875868i | \(-0.339711\pi\) | ||||
0.482550 | + | 0.875868i | \(0.339711\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.88953e9 | 1.32390 | 0.661949 | − | 0.749549i | \(-0.269730\pi\) | ||||
0.661949 | + | 0.749549i | \(0.269730\pi\) | |||||||
\(572\) | −9.70529e9 | −2.16831 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.34304e8 | 0.0958522 | ||||||||
\(575\) | 4.43116e8 | 0.0972030 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.36032e8 | 0.0944936 | 0.0472468 | − | 0.998883i | \(-0.484955\pi\) | ||||
0.0472468 | + | 0.998883i | \(0.484955\pi\) | |||||||
\(578\) | 2.85293e9 | 0.614531 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.72841e9 | 2.07035 | ||||||||
\(581\) | 7.05007e8 | 0.149134 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.25398e9 | −1.30712 | ||||||||
\(584\) | −3.95586e9 | −0.821856 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.31277e10 | −2.69493 | ||||||||
\(587\) | 5.28188e8 | 0.107784 | 0.0538921 | − | 0.998547i | \(-0.482837\pi\) | ||||
0.0538921 | + | 0.998547i | \(0.482837\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00294e7 | 0.0100884 | ||||||||
\(590\) | 1.55976e10 | 3.12663 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.94868e9 | −0.584120 | ||||||||
\(593\) | 8.24070e9 | 1.62283 | 0.811414 | − | 0.584471i | \(-0.198698\pi\) | ||||
0.811414 | + | 0.584471i | \(0.198698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.86900e9 | −0.363748 | ||||||||
\(596\) | −4.29941e9 | −0.831855 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.12739e9 | 0.789261 | ||||||||
\(599\) | 1.08340e9 | 0.205966 | 0.102983 | − | 0.994683i | \(-0.467161\pi\) | ||||
0.102983 | + | 0.994683i | \(0.467161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.28702e6 | 0.00174508 | 0.000872541 | − | 1.00000i | \(-0.499722\pi\) | ||||
0.000872541 | 1.00000i | \(0.499722\pi\) | ||||||||
\(602\) | 3.76893e7 | 0.00704093 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.18808e10 | −2.19389 | ||||||||
\(605\) | −5.27523e9 | −0.968496 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.72021e9 | −0.675161 | −0.337580 | − | 0.941297i | \(-0.609608\pi\) | ||||
−0.337580 | + | 0.941297i | \(0.609608\pi\) | |||||||
\(608\) | −3.50489e9 | −0.632429 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.69582e9 | 1.01602 | ||||||||
\(611\) | 3.89885e9 | 0.691500 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.10111e9 | 1.42047 | 0.710236 | − | 0.703963i | \(-0.248588\pi\) | ||||
0.710236 | + | 0.703963i | \(0.248588\pi\) | |||||||
\(614\) | −1.70203e10 | −2.96741 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.11501e9 | −0.536941 | ||||||||
\(617\) | −5.74845e9 | −0.985264 | −0.492632 | − | 0.870238i | \(-0.663965\pi\) | ||||
−0.492632 | + | 0.870238i | \(0.663965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.12511e9 | −0.360134 | −0.180067 | − | 0.983654i | \(-0.557632\pi\) | ||||
−0.180067 | + | 0.983654i | \(0.557632\pi\) | |||||||
\(620\) | −1.06209e8 | −0.0178974 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.09704e9 | 0.516036 | ||||||||
\(623\) | 2.01273e9 | 0.333485 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00302e9 | −1.14737 | ||||||||
\(626\) | 1.30205e10 | 2.12138 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.23605e9 | 0.360266 | ||||||||
\(629\) | −9.01630e9 | −1.44461 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.09353e10 | −1.73272 | −0.866362 | − | 0.499417i | \(-0.833548\pi\) | ||||
−0.866362 | + | 0.499417i | \(0.833548\pi\) | |||||||
\(632\) | 5.32718e9 | 0.839436 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.94167e9 | 1.54934 | ||||||||
\(635\) | −5.93076e9 | −0.919183 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.20845e9 | −0.798400 | ||||||||
\(638\) | 1.59124e10 | 2.42584 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.31501e10 | 1.98290 | ||||||||
\(641\) | −1.71030e9 | −0.256490 | −0.128245 | − | 0.991743i | \(-0.540934\pi\) | ||||
−0.128245 | + | 0.991743i | \(0.540934\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.49295e9 | 0.963172 | 0.481586 | − | 0.876399i | \(-0.340061\pi\) | ||||
0.481586 | + | 0.876399i | \(0.340061\pi\) | |||||||
\(644\) | 1.90443e9 | 0.280974 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.49053e10 | 2.17534 | ||||||||
\(647\) | 4.41995e9 | 0.641582 | 0.320791 | − | 0.947150i | \(-0.396051\pi\) | ||||
0.320791 | + | 0.947150i | \(0.396051\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.64413e10 | 2.36092 | ||||||||
\(650\) | 1.83478e9 | 0.262051 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.66731e10 | −2.35585 | ||||||||
\(653\) | 2.06198e9 | 0.289793 | 0.144896 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144896 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.13099e10 | −1.57258 | ||||||||
\(656\) | 6.81765e8 | 0.0942912 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.79153e9 | 0.381989 | ||||||||
\(659\) | −5.97125e9 | −0.812767 | −0.406383 | − | 0.913703i | \(-0.633210\pi\) | ||||
−0.406383 | + | 0.913703i | \(0.633210\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.91741e8 | −0.0796942 | −0.0398471 | − | 0.999206i | \(-0.512687\pi\) | ||||
−0.0398471 | + | 0.999206i | \(0.512687\pi\) | |||||||
\(662\) | −1.08582e10 | −1.45464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.35063e9 | 0.709278 | ||||||||
\(665\) | −2.61860e9 | −0.345297 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.36101e9 | −0.569045 | ||||||||
\(668\) | −1.98726e9 | −0.257951 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.22184e10 | −2.85398 | ||||||||
\(671\) | 6.00392e9 | 0.767196 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.50848e9 | 0.317219 | 0.158609 | − | 0.987341i | \(-0.449299\pi\) | ||||
0.158609 | + | 0.987341i | \(0.449299\pi\) | |||||||
\(674\) | −1.05661e10 | −1.32925 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.54413e9 | −0.441262 | ||||||||
\(677\) | 1.17984e10 | 1.46138 | 0.730689 | − | 0.682711i | \(-0.239199\pi\) | ||||
0.730689 | + | 0.682711i | \(0.239199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.36895e9 | −0.413000 | ||||||||
\(680\) | −1.41847e10 | −1.72998 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.73722e8 | −0.0209705 | ||||||||
\(683\) | −5.40513e9 | −0.649133 | −0.324567 | − | 0.945863i | \(-0.605218\pi\) | ||||
−0.324567 | + | 0.945863i | \(0.605218\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.44106e9 | 0.765668 | ||||||||
\(686\) | −7.79185e9 | −0.921523 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.91642e7 | 0.00692627 | ||||||||
\(689\) | 7.09699e9 | 0.826622 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.38617e10 | 1.59825 | 0.799125 | − | 0.601165i | \(-0.205296\pi\) | ||||
0.799125 | + | 0.601165i | \(0.205296\pi\) | |||||||
\(692\) | 1.15319e10 | 1.32291 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.68771e10 | −1.91663 | ||||||||
\(695\) | 7.42762e9 | 0.839272 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.08466e9 | 0.233196 | ||||||||
\(698\) | 1.48129e10 | 1.64871 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8.46591e8 | 0.0932890 | ||||||||
\(701\) | 6.02060e9 | 0.660126 | 0.330063 | − | 0.943959i | \(-0.392930\pi\) | ||||
0.330063 | + | 0.943959i | \(0.392930\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.26324e10 | −1.37133 | ||||||||
\(704\) | 1.81887e10 | 1.96470 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.02556e10 | −1.09684 | ||||||||
\(707\) | −1.45193e9 | −0.154517 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.36497e9 | 0.670710 | 0.335355 | − | 0.942092i | \(-0.391144\pi\) | ||||
0.335355 | + | 0.942092i | \(0.391144\pi\) | |||||||
\(710\) | −2.43407e10 | −2.55228 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.52755e10 | 1.58605 | ||||||||
\(713\) | 4.76108e7 | 0.00491918 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.26996e10 | 1.29933 | ||||||||
\(716\) | −1.32944e10 | −1.35355 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.31604e9 | −0.132689 | ||||||||
\(719\) | −1.25812e10 | −1.26232 | −0.631162 | − | 0.775651i | \(-0.717422\pi\) | ||||
−0.631162 | + | 0.775651i | \(0.717422\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.31905e9 | 0.131065 | ||||||||
\(722\) | 3.92328e9 | 0.387944 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.89253e10 | 1.85335 | ||||||||
\(725\) | −1.93863e9 | −0.188935 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.10511e9 | 0.203191 | 0.101596 | − | 0.994826i | \(-0.467605\pi\) | ||||
0.101596 | + | 0.994826i | \(0.467605\pi\) | |||||||
\(728\) | 3.53490e9 | 0.339561 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.15472e10 | 1.09862 | ||||||||
\(731\) | 1.80909e8 | 0.0171296 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.15189e9 | −0.389388 | −0.194694 | − | 0.980864i | \(-0.562371\pi\) | ||||
−0.194694 | + | 0.980864i | \(0.562371\pi\) | |||||||
\(734\) | −7.08546e9 | −0.661350 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.33545e9 | −0.308378 | ||||||||
\(737\) | −2.34202e10 | −2.15504 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.05151e10 | −0.958429 | −0.479214 | − | 0.877698i | \(-0.659078\pi\) | ||||
−0.479214 | + | 0.877698i | \(0.659078\pi\) | |||||||
\(740\) | 2.68177e10 | 2.43283 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.08136e9 | 0.456632 | ||||||||
\(743\) | 3.59871e9 | 0.321874 | 0.160937 | − | 0.986965i | \(-0.448548\pi\) | ||||
0.160937 | + | 0.986965i | \(0.448548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.62591e9 | 0.498478 | ||||||||
\(746\) | 5.27861e9 | 0.465515 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.33545e10 | −2.91407 | ||||||||
\(749\) | −9.60426e8 | −0.0835175 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.44144e8 | 0.0641087 | 0.0320544 | − | 0.999486i | \(-0.489795\pi\) | ||||
0.0320544 | + | 0.999486i | \(0.489795\pi\) | |||||||
\(752\) | 4.38210e9 | 0.375768 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.80573e10 | −1.53410 | ||||||||
\(755\) | 1.55463e10 | 1.31466 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.80850e9 | 0.821802 | 0.410901 | − | 0.911680i | \(-0.365214\pi\) | ||||
0.410901 | + | 0.911680i | \(0.365214\pi\) | |||||||
\(758\) | −2.59657e10 | −2.16550 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.98738e10 | −1.64222 | ||||||||
\(761\) | 1.73200e10 | 1.42463 | 0.712315 | − | 0.701860i | \(-0.247647\pi\) | ||||
0.712315 | + | 0.701860i | \(0.247647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.71440e9 | 0.139725 | ||||||||
\(764\) | 3.71731e10 | 3.01580 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.94557e10 | 3.17182 | ||||||||
\(767\) | −1.86576e10 | −1.49304 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.35092e10 | −1.86421 | −0.932107 | − | 0.362183i | \(-0.882032\pi\) | ||||
−0.932107 | + | 0.362183i | \(0.882032\pi\) | |||||||
\(770\) | 9.09279e9 | 0.717760 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.39286e10 | 1.08955 | ||||||||
\(773\) | −1.71140e10 | −1.33268 | −0.666338 | − | 0.745650i | \(-0.732139\pi\) | ||||
−0.666338 | + | 0.745650i | \(0.732139\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.11648e7 | 0.00163327 | ||||||||
\(776\) | −2.55685e10 | −1.96422 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.73389e9 | −0.284271 | ||||||||
\(779\) | 2.92074e9 | 0.221367 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.56573e10 | −1.92723 | ||||||||
\(782\) | 1.41847e10 | 1.06071 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.85402e9 | −0.433859 | ||||||||
\(785\) | −2.92594e9 | −0.215884 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03332e10 | 0.755654 | 0.377827 | − | 0.925876i | \(-0.376671\pi\) | ||||
0.377827 | + | 0.925876i | \(0.376671\pi\) | |||||||
\(788\) | −4.41236e10 | −3.21240 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.55502e10 | −1.12212 | ||||||||
\(791\) | −1.23542e9 | −0.0887558 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.81323e9 | −0.485173 | ||||||||
\(794\) | 5.67603e9 | 0.402414 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.50082e10 | 3.16298 | ||||||||
\(797\) | 2.96320e9 | 0.207328 | 0.103664 | − | 0.994612i | \(-0.466943\pi\) | ||||
0.103664 | + | 0.994612i | \(0.466943\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.33993e10 | 0.929328 | ||||||||
\(800\) | −1.48273e9 | −0.102388 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.60354e10 | 1.09767 | ||||||||
\(803\) | 1.21719e10 | 0.829569 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.49201e9 | −0.168370 | ||||||||
\(806\) | 1.97139e8 | 0.0132617 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.10193e10 | −0.734879 | ||||||||
\(809\) | 2.47434e10 | 1.64301 | 0.821504 | − | 0.570203i | \(-0.193136\pi\) | ||||
0.821504 | + | 0.570203i | \(0.193136\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.30066e8 | 0.0151454 | 0.00757269 | − | 0.999971i | \(-0.497590\pi\) | ||||
0.00757269 | + | 0.999971i | \(0.497590\pi\) | |||||||
\(812\) | −8.33190e9 | −0.546132 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.38647e10 | 2.85056 | ||||||||
\(815\) | 2.18172e10 | 1.41171 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.53465e8 | 0.0162607 | ||||||||
\(818\) | 2.03528e10 | 1.30013 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.20052e9 | −0.392717 | ||||||||
\(821\) | 3.04369e9 | 0.191955 | 0.0959774 | − | 0.995384i | \(-0.469402\pi\) | ||||
0.0959774 | + | 0.995384i | \(0.469402\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.37505e9 | −0.148516 | −0.0742582 | − | 0.997239i | \(-0.523659\pi\) | ||||
−0.0742582 | + | 0.997239i | \(0.523659\pi\) | |||||||
\(824\) | 1.00109e10 | 0.623342 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.33586e10 | −0.824766 | ||||||||
\(827\) | −5.58209e9 | −0.343184 | −0.171592 | − | 0.985168i | \(-0.554891\pi\) | ||||
−0.171592 | + | 0.985168i | \(0.554891\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.06578e10 | −1.25934 | −0.629670 | − | 0.776863i | \(-0.716810\pi\) | ||||
−0.629670 | + | 0.776863i | \(0.716810\pi\) | |||||||
\(830\) | −1.56186e10 | −0.948133 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.06405e10 | −1.24247 | ||||||||
\(833\) | −1.79001e10 | −1.07299 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.60039e9 | 0.154574 | ||||||||
\(836\) | −4.67319e10 | −2.76625 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.68385e10 | −1.57545 | ||||||||
\(839\) | −7.55935e9 | −0.441894 | −0.220947 | − | 0.975286i | \(-0.570915\pi\) | ||||
−0.220947 | + | 0.975286i | \(0.570915\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.82955e9 | 0.106061 | ||||||||
\(842\) | 2.68595e10 | 1.55062 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.43360e9 | −0.139332 | ||||||||
\(845\) | 4.63759e9 | 0.264420 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.51798e9 | 0.255477 | ||||||||
\(848\) | 7.97665e9 | 0.449195 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.30564e9 | 0.352179 | ||||||||
\(851\) | −1.20217e10 | −0.668673 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.47919e10 | 1.36769 | 0.683846 | − | 0.729626i | \(-0.260306\pi\) | ||||
0.683846 | + | 0.729626i | \(0.260306\pi\) | |||||||
\(854\) | −4.87819e9 | −0.268013 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.28912e9 | −0.397207 | ||||||||
\(857\) | −2.93883e9 | −0.159493 | −0.0797464 | − | 0.996815i | \(-0.525411\pi\) | ||||
−0.0797464 | + | 0.996815i | \(0.525411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.08095e10 | 1.12017 | 0.560086 | − | 0.828435i | \(-0.310768\pi\) | ||||
0.560086 | + | 0.828435i | \(0.310768\pi\) | |||||||
\(860\) | −5.38087e8 | −0.0288475 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.20566e10 | −3.29999 | ||||||||
\(863\) | −2.36529e10 | −1.25270 | −0.626350 | − | 0.779542i | \(-0.715452\pi\) | ||||
−0.626350 | + | 0.779542i | \(0.715452\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.50898e10 | −0.792734 | ||||||||
\(866\) | 2.48001e10 | 1.29760 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.09626e7 | 0.00472110 | ||||||||
\(869\) | −1.63913e10 | −0.847315 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.65772e10 | 1.36284 | ||||||||
\(872\) | 1.30114e10 | 0.664530 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.98738e10 | 1.00691 | ||||||||
\(875\) | 5.05865e9 | 0.255274 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.67295e10 | −0.837501 | −0.418751 | − | 0.908101i | \(-0.637532\pi\) | ||||
−0.418751 | + | 0.908101i | \(0.637532\pi\) | |||||||
\(878\) | 4.82954e10 | 2.40810 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.42737e10 | 0.706071 | ||||||||
\(881\) | 2.71046e10 | 1.33545 | 0.667724 | − | 0.744409i | \(-0.267269\pi\) | ||||
0.667724 | + | 0.744409i | \(0.267269\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.22708e10 | −0.599805 | −0.299903 | − | 0.953970i | \(-0.596954\pi\) | ||||
−0.299903 | + | 0.953970i | \(0.596954\pi\) | |||||||
\(884\) | 3.78506e10 | 1.84285 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.12149e9 | −0.247388 | ||||||||
\(887\) | −3.38351e10 | −1.62793 | −0.813963 | − | 0.580917i | \(-0.802694\pi\) | ||||
−0.813963 | + | 0.580917i | \(0.802694\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.07940e9 | 0.242469 | ||||||||
\(890\) | −4.45896e10 | −2.12016 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.22371e10 | 2.46435 | ||||||||
\(893\) | 1.87733e10 | 0.882188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.73961e10 | 0.811095 | ||||||||
\(896\) | −1.12624e10 | −0.523063 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.85430e10 | 0.854501 | ||||||||
\(899\) | −2.08297e8 | −0.00956148 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.43905e10 | 1.11092 | ||||||||
\(902\) | −1.01420e10 | −0.460149 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.37617e9 | −0.422120 | ||||||||
\(905\) | −2.47643e10 | −1.11059 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.42470e9 | 0.241407 | 0.120704 | − | 0.992689i | \(-0.461485\pi\) | ||||
0.120704 | + | 0.992689i | \(0.461485\pi\) | |||||||
\(908\) | −3.93218e10 | −1.74314 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.03185e10 | −0.453910 | ||||||||
\(911\) | 3.91181e10 | 1.71421 | 0.857104 | − | 0.515144i | \(-0.172262\pi\) | ||||
0.857104 | + | 0.515144i | \(0.172262\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.64635e10 | −0.715935 | ||||||||
\(914\) | −5.37300e10 | −2.32758 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.51402e10 | −0.650875 | ||||||||
\(917\) | 9.68634e9 | 0.414827 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.11381e10 | −0.473375 | −0.236688 | − | 0.971586i | \(-0.576062\pi\) | ||||
−0.236688 | + | 0.971586i | \(0.576062\pi\) | |||||||
\(920\) | −1.89130e10 | −0.800761 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.68135e10 | −2.80741 | ||||||||
\(923\) | 2.91159e10 | 1.21878 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.34411e9 | −0.222013 | ||||||||
\(926\) | 3.01990e10 | 1.24984 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.45926e10 | 0.599398 | ||||||||
\(929\) | −4.22587e10 | −1.72926 | −0.864631 | − | 0.502408i | \(-0.832448\pi\) | ||||
−0.864631 | + | 0.502408i | \(0.832448\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.50792e10 | −1.01857 | ||||||||
\(932\) | 4.32343e10 | 1.74933 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.35891e10 | 1.34891 | ||||||||
\(935\) | 4.36454e10 | 1.74621 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.74502e10 | 1.48719 | 0.743594 | − | 0.668631i | \(-0.233120\pi\) | ||||
0.743594 | + | 0.668631i | \(0.233120\pi\) | |||||||
\(938\) | 1.90289e10 | 0.752844 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.98544e10 | −1.56505 | ||||||||
\(941\) | 1.04380e10 | 0.408369 | 0.204185 | − | 0.978932i | \(-0.434546\pi\) | ||||
0.204185 | + | 0.978932i | \(0.434546\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.77955e9 | 0.107940 | ||||||||
\(944\) | −2.09701e10 | −0.811334 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.80128e8 | −0.0338008 | ||||||||
\(947\) | −9.12893e9 | −0.349297 | −0.174649 | − | 0.984631i | \(-0.555879\pi\) | ||||
−0.174649 | + | 0.984631i | \(0.555879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.38126e10 | −0.524618 | ||||||||
\(950\) | 8.83462e9 | 0.334314 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.21485e10 | 0.456346 | ||||||||
\(953\) | 1.00452e10 | 0.375954 | 0.187977 | − | 0.982173i | \(-0.439807\pi\) | ||||
0.187977 | + | 0.982173i | \(0.439807\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.86420e10 | −1.80717 | ||||||||
\(956\) | 9.88559e9 | 0.365932 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 5.32952e10 | 1.95843 | ||||||||
\(959\) | −5.51645e9 | −0.201974 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.75103e10 | −0.999917 | ||||||||
\(962\) | −4.97775e10 | −1.80269 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.96107e10 | −2.14316 | ||||||||
\(965\) | −1.82260e10 | −0.652900 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.17355e10 | 1.12863 | 0.564316 | − | 0.825559i | \(-0.309140\pi\) | ||||
0.564316 | + | 0.825559i | \(0.309140\pi\) | |||||||
\(968\) | 3.42890e10 | 1.21504 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.46351e10 | 2.62568 | ||||||||
\(971\) | −3.26126e10 | −1.14319 | −0.571594 | − | 0.820537i | \(-0.693675\pi\) | ||||
−0.571594 | + | 0.820537i | \(0.693675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.36138e9 | −0.221389 | ||||||||
\(974\) | −6.50035e10 | −2.25414 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.65772e9 | −0.263648 | ||||||||
\(977\) | 3.72925e10 | 1.27935 | 0.639676 | − | 0.768644i | \(-0.279068\pi\) | ||||
0.639676 | + | 0.768644i | \(0.279068\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.70016e10 | −1.60093 | ||||||||
\(980\) | 5.32413e10 | 1.80700 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.26597e10 | 1.10058 | ||||||||
\(983\) | −9.42117e9 | −0.316350 | −0.158175 | − | 0.987411i | \(-0.550561\pi\) | ||||
−0.158175 | + | 0.987411i | \(0.550561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.77370e10 | 1.92499 | ||||||||
\(986\) | −6.20583e10 | −2.06172 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.30312e10 | 1.74937 | ||||||||
\(989\) | 2.41211e8 | 0.00792886 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.16481e9 | 0.0380188 | 0.0190094 | − | 0.999819i | \(-0.493949\pi\) | ||||
0.0190094 | + | 0.999819i | \(0.493949\pi\) | |||||||
\(992\) | −1.59313e8 | −0.00518157 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.08466e10 | 0.673260 | ||||||||
\(995\) | −5.88945e10 | −1.89537 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.18933e10 | 0.699645 | 0.349822 | − | 0.936816i | \(-0.386242\pi\) | ||||
0.349822 | + | 0.936816i | \(0.386242\pi\) | |||||||
\(998\) | 7.90908e10 | 2.51866 | ||||||||
\(999\) | 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 | 9.8.a.b.1.2 | yes | 2 | |
3.2 | odd | 2 | inner | 9.8.a.b.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 144.8.a.m.1.1 | 2 | |||
5.2 | odd | 4 | 225.8.b.k.199.4 | 4 | |||
5.3 | odd | 4 | 225.8.b.k.199.1 | 4 | |||
5.4 | even | 2 | 225.8.a.q.1.1 | 2 | |||
7.6 | odd | 2 | 441.8.a.k.1.2 | 2 | |||
8.3 | odd | 2 | 576.8.a.bi.1.2 | 2 | |||
8.5 | even | 2 | 576.8.a.bj.1.2 | 2 | |||
9.2 | odd | 6 | 81.8.c.f.28.2 | 4 | |||
9.4 | even | 3 | 81.8.c.f.55.1 | 4 | |||
9.5 | odd | 6 | 81.8.c.f.55.2 | 4 | |||
9.7 | even | 3 | 81.8.c.f.28.1 | 4 | |||
12.11 | even | 2 | 144.8.a.m.1.2 | 2 | |||
15.2 | even | 4 | 225.8.b.k.199.2 | 4 | |||
15.8 | even | 4 | 225.8.b.k.199.3 | 4 | |||
15.14 | odd | 2 | 225.8.a.q.1.2 | 2 | |||
21.20 | even | 2 | 441.8.a.k.1.1 | 2 | |||
24.5 | odd | 2 | 576.8.a.bj.1.1 | 2 | |||
24.11 | even | 2 | 576.8.a.bi.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.8.a.b.1.1 | ✓ | 2 | 3.2 | odd | 2 | inner | |
9.8.a.b.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
81.8.c.f.28.1 | 4 | 9.7 | even | 3 | |||
81.8.c.f.28.2 | 4 | 9.2 | odd | 6 | |||
81.8.c.f.55.1 | 4 | 9.4 | even | 3 | |||
81.8.c.f.55.2 | 4 | 9.5 | odd | 6 | |||
144.8.a.m.1.1 | 2 | 4.3 | odd | 2 | |||
144.8.a.m.1.2 | 2 | 12.11 | even | 2 | |||
225.8.a.q.1.1 | 2 | 5.4 | even | 2 | |||
225.8.a.q.1.2 | 2 | 15.14 | odd | 2 | |||
225.8.b.k.199.1 | 4 | 5.3 | odd | 4 | |||
225.8.b.k.199.2 | 4 | 15.2 | even | 4 | |||
225.8.b.k.199.3 | 4 | 15.8 | even | 4 | |||
225.8.b.k.199.4 | 4 | 5.2 | odd | 4 | |||
441.8.a.k.1.1 | 2 | 21.20 | even | 2 | |||
441.8.a.k.1.2 | 2 | 7.6 | odd | 2 | |||
576.8.a.bi.1.1 | 2 | 24.11 | even | 2 | |||
576.8.a.bi.1.2 | 2 | 8.3 | odd | 2 | |||
576.8.a.bj.1.1 | 2 | 24.5 | odd | 2 | |||
576.8.a.bj.1.2 | 2 | 8.5 | even | 2 |