Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,8,Mod(1,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.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: | \(119.955849786\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{366}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 366 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(19.1311\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.1 |
$q$-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 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 241.049 | 0.862403 | 0.431202 | − | 0.902256i | \(-0.358090\pi\) | ||||
0.431202 | + | 0.902256i | \(0.358090\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1255.25 | −1.38320 | −0.691601 | − | 0.722280i | \(-0.743094\pi\) | ||||
−0.691601 | + | 0.722280i | \(0.743094\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2415.27 | 0.547132 | 0.273566 | − | 0.961853i | \(-0.411797\pi\) | ||||
0.273566 | + | 0.961853i | \(0.411797\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13408.9 | −1.69275 | −0.846375 | − | 0.532588i | \(-0.821220\pi\) | ||||
−0.846375 | + | 0.532588i | \(0.821220\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6508.32 | −0.497909 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25571.4 | 1.26236 | 0.631179 | − | 0.775637i | \(-0.282571\pi\) | ||||
0.631179 | + | 0.775637i | \(0.282571\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38780.3 | 1.29710 | 0.648551 | − | 0.761171i | \(-0.275375\pi\) | ||||
0.648551 | + | 0.761171i | \(0.275375\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 33891.6 | 0.798592 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 49641.1 | 0.850735 | 0.425367 | − | 0.905021i | \(-0.360145\pi\) | ||||
0.425367 | + | 0.905021i | \(0.360145\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20020.4 | −0.256261 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −231355. | −1.76152 | −0.880758 | − | 0.473567i | \(-0.842966\pi\) | ||||
−0.880758 | + | 0.473567i | \(0.842966\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 246856. | 1.48826 | 0.744129 | − | 0.668036i | \(-0.232865\pi\) | ||||
0.744129 | + | 0.668036i | \(0.232865\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −65212.4 | −0.315887 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −302576. | −1.19288 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −297314. | −0.964961 | −0.482480 | − | 0.875907i | \(-0.660264\pi\) | ||||
−0.482480 | + | 0.875907i | \(0.660264\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 362041. | 0.977309 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −616533. | −1.39705 | −0.698526 | − | 0.715585i | \(-0.746160\pi\) | ||||
−0.698526 | + | 0.715585i | \(0.746160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 968744. | 1.85810 | 0.929050 | − | 0.369953i | \(-0.120626\pi\) | ||||
0.929050 | + | 0.369953i | \(0.120626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 175725. | 0.287468 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −359217. | −0.504678 | −0.252339 | − | 0.967639i | \(-0.581200\pi\) | ||||
−0.252339 | + | 0.967639i | \(0.581200\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 752097. | 0.913246 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −690426. | −0.728823 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.39933e6 | 1.29108 | 0.645541 | − | 0.763725i | \(-0.276632\pi\) | ||||
0.645541 | + | 0.763725i | \(0.276632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 582199. | 0.471848 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.04707e6 | −0.748882 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −214279. | −0.135831 | −0.0679153 | − | 0.997691i | \(-0.521635\pi\) | ||||
−0.0679153 | + | 0.997691i | \(0.521635\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.75876e6 | 0.992091 | 0.496046 | − | 0.868296i | \(-0.334785\pi\) | ||||
0.496046 | + | 0.868296i | \(0.334785\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −915074. | −0.461067 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.23221e6 | −1.45983 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.08452e6 | −0.440532 | −0.220266 | − | 0.975440i | \(-0.570693\pi\) | ||||
−0.220266 | + | 0.975440i | \(0.570693\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.34031e6 | −0.491172 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.02995e6 | −0.341517 | −0.170758 | − | 0.985313i | \(-0.554622\pi\) | ||||
−0.170758 | + | 0.985313i | \(0.554622\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 822221. | 0.247376 | 0.123688 | − | 0.992321i | \(-0.460528\pi\) | ||||
0.123688 | + | 0.992321i | \(0.460528\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 540550. | 0.147952 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.03176e6 | −0.756794 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.25755e6 | −0.971550 | −0.485775 | − | 0.874084i | \(-0.661463\pi\) | ||||
−0.485775 | + | 0.874084i | \(0.661463\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.69750e6 | 1.09373 | 0.546866 | − | 0.837220i | \(-0.315821\pi\) | ||||
0.546866 | + | 0.837220i | \(0.315821\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.16395e6 | 1.08866 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.24659e6 | 1.01701 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.57345e6 | −0.988390 | −0.494195 | − | 0.869351i | \(-0.664537\pi\) | ||||
−0.494195 | + | 0.869351i | \(0.664537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.68315e7 | 2.34141 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.66512e6 | −0.859246 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.34796e6 | 1.11862 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.55287e6 | 0.840254 | 0.420127 | − | 0.907465i | \(-0.361985\pi\) | ||||
0.420127 | + | 0.907465i | \(0.361985\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.76073e6 | 0.182377 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.02082e6 | 0.678052 | 0.339026 | − | 0.940777i | \(-0.389902\pi\) | ||||
0.339026 | + | 0.940777i | \(0.389902\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.83883e7 | −1.65810 | −0.829051 | − | 0.559172i | \(-0.811119\pi\) | ||||
−0.829051 | + | 0.559172i | \(0.811119\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.16954e6 | 0.688708 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.41357e7 | −1.11551 | −0.557755 | − | 0.830005i | \(-0.688337\pi\) | ||||
−0.557755 | + | 0.830005i | \(0.688337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.63280e6 | −0.342650 | −0.171325 | − | 0.985215i | \(-0.554805\pi\) | ||||
−0.171325 | + | 0.985215i | \(0.554805\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.02748e6 | 0.557120 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.05522e7 | 0.687970 | 0.343985 | − | 0.938975i | \(-0.388223\pi\) | ||||
0.343985 | + | 0.938975i | \(0.388223\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19659e7 | 0.733676 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.77512e6 | −0.564250 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.20983e7 | −1.74609 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.36536e7 | −0.700647 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.66464e7 | 0.806588 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.36578e7 | −1.08340 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.59436e6 | 0.415626 | 0.207813 | − | 0.978169i | \(-0.433365\pi\) | ||||
0.207813 | + | 0.978169i | \(0.433365\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.61561e7 | −1.07277 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.51622e7 | −0.977910 | −0.488955 | − | 0.872309i | \(-0.662622\pi\) | ||||
−0.488955 | + | 0.872309i | \(0.662622\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.86788e7 | −1.79415 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.74457e6 | −0.165970 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.08875e7 | −1.35853 | −0.679263 | − | 0.733895i | \(-0.737701\pi\) | ||||
−0.679263 | + | 0.733895i | \(0.737701\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.93884e7 | −1.24399 | −0.621994 | − | 0.783022i | \(-0.713677\pi\) | ||||
−0.621994 | + | 0.783022i | \(0.713677\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.69885e6 | 0.291376 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.23863e7 | −0.926157 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.57680e7 | −1.51914 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.03066e7 | −0.527263 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.70043e6 | 0.0916431 | 0.0458216 | − | 0.998950i | \(-0.485409\pi\) | ||||
0.0458216 | + | 0.998950i | \(0.485409\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24292e7 | −0.293781 | −0.146891 | − | 0.989153i | \(-0.546927\pi\) | ||||
−0.146891 | + | 0.989153i | \(0.546927\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.86415e7 | 0.420786 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.95045e7 | 1.28348 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.82244e7 | −0.582072 | −0.291036 | − | 0.956712i | \(-0.594000\pi\) | ||||
−0.291036 | + | 0.956712i | \(0.594000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.77819e7 | −0.745407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.23118e7 | −1.17674 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.47825e7 | 1.17166 | 0.585830 | − | 0.810434i | \(-0.300769\pi\) | ||||
0.585830 | + | 0.810434i | \(0.300769\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.57194e7 | −0.272422 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.65214e7 | −0.939086 | −0.469543 | − | 0.882910i | \(-0.655581\pi\) | ||||
−0.469543 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.17051e8 | 1.86540 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82709e7 | 0.432367 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.07852e7 | −0.158367 | −0.0791836 | − | 0.996860i | \(-0.525231\pi\) | ||||
−0.0791836 | + | 0.996860i | \(0.525231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.51305e7 | 0.354460 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.78553e6 | 0.0784218 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.53198e6 | 0.0199649 | 0.00998247 | − | 0.999950i | \(-0.496822\pi\) | ||||
0.00998247 | + | 0.999950i | \(0.496822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.26121e8 | −1.58093 | −0.790467 | − | 0.612505i | \(-0.790162\pi\) | ||||
−0.790467 | + | 0.612505i | \(0.790162\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.74865e7 | −0.572784 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.16673e7 | −0.832185 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.17618e7 | 0.690676 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.47070e7 | 0.266197 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.41139e8 | −1.46565 | −0.732826 | − | 0.680417i | \(-0.761799\pi\) | ||||
−0.732826 | + | 0.680417i | \(0.761799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.15274e8 | −1.15420 | −0.577100 | − | 0.816674i | \(-0.695816\pi\) | ||||
−0.577100 | + | 0.816674i | \(0.695816\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.72697e7 | 0.842835 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.22603e7 | 0.300633 | 0.150316 | − | 0.988638i | \(-0.451971\pi\) | ||||
0.150316 | + | 0.988638i | \(0.451971\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.49688e7 | −0.494459 | −0.247230 | − | 0.968957i | \(-0.579520\pi\) | ||||
−0.247230 | + | 0.968957i | \(0.579520\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.92822e7 | 0.254341 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.90408e8 | 2.43653 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.48615e8 | −1.20482 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.61884e7 | 0.283578 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.36651e7 | 0.709686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.55364e7 | −0.406995 | −0.203498 | − | 0.979075i | \(-0.565231\pi\) | ||||
−0.203498 | + | 0.979075i | \(0.565231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.78087e7 | 0.197175 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.33515e8 | 1.60243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.09865e8 | −2.05856 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.22000e7 | −0.142823 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.42885e8 | −2.13686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.26355e8 | −0.763004 | −0.381502 | − | 0.924368i | \(-0.624593\pi\) | ||||
−0.381502 | + | 0.924368i | \(0.624593\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.45949e7 | −0.0854203 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.81110e8 | 1.02767 | 0.513834 | − | 0.857890i | \(-0.328225\pi\) | ||||
0.513834 | + | 0.857890i | \(0.328225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.46997e8 | 0.808880 | 0.404440 | − | 0.914564i | \(-0.367466\pi\) | ||||
0.404440 | + | 0.914564i | \(0.367466\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.18576e7 | 0.436935 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.68176e8 | 0.870998 | 0.435499 | − | 0.900189i | \(-0.356572\pi\) | ||||
0.435499 | + | 0.900189i | \(0.356572\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.65888e7 | −0.435236 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.14954e8 | 0.560925 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.06268e8 | −0.977326 | −0.488663 | − | 0.872473i | \(-0.662515\pi\) | ||||
−0.488663 | + | 0.872473i | \(0.662515\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.39136e8 | −1.56068 | −0.780341 | − | 0.625354i | \(-0.784954\pi\) | ||||
−0.780341 | + | 0.625354i | \(0.784954\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.81292e8 | 0.787586 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.20003e8 | −2.19567 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.53833e8 | −0.631467 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.62781e7 | 0.144806 | 0.0724030 | − | 0.997375i | \(-0.476933\pi\) | ||||
0.0724030 | + | 0.997375i | \(0.476933\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.19897e8 | 0.465464 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.66427e8 | −0.628539 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.14951e8 | −1.89234 | −0.946172 | − | 0.323665i | \(-0.895085\pi\) | ||||
−0.946172 | + | 0.323665i | \(0.895085\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.73202e8 | 1.33474 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.68658e8 | −0.587172 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.03571e7 | −0.306279 | −0.153139 | − | 0.988205i | \(-0.548938\pi\) | ||||
−0.153139 | + | 0.988205i | \(0.548938\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.37307e8 | 1.11343 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.77483e8 | 0.570647 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.05304e8 | −0.956311 | −0.478156 | − | 0.878275i | \(-0.658694\pi\) | ||||
−0.478156 | + | 0.878275i | \(0.658694\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.67428e8 | 0.511019 | 0.255509 | − | 0.966807i | \(-0.417757\pi\) | ||||
0.255509 | + | 0.966807i | \(0.417757\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.54451e8 | −1.35182 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.83547e7 | −0.140208 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.46391e8 | 0.696538 | 0.348269 | − | 0.937395i | \(-0.386770\pi\) | ||||
0.348269 | + | 0.937395i | \(0.386770\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.79958e8 | 0.496086 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.35835e8 | −0.902929 | −0.451465 | − | 0.892289i | \(-0.649098\pi\) | ||||
−0.451465 | + | 0.892289i | \(0.649098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.73786e8 | −0.980325 | −0.490162 | − | 0.871631i | \(-0.663063\pi\) | ||||
−0.490162 | + | 0.871631i | \(0.663063\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.52395e8 | −0.645838 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.73899e8 | 1.93240 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.43555e8 | 0.593547 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.03927e8 | −0.485121 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.15803e8 | −0.965720 | −0.482860 | − | 0.875697i | \(-0.660402\pi\) | ||||
−0.482860 | + | 0.875697i | \(0.660402\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.16517e7 | −0.117141 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.75398e7 | −0.105296 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.65635e8 | −1.44008 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.21601e9 | −2.57013 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.89562e8 | −0.391474 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.23947e8 | 0.855583 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.19257e8 | 0.432484 | 0.216242 | − | 0.976340i | \(-0.430620\pi\) | ||||
0.216242 | + | 0.976340i | \(0.430620\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.96484e8 | 0.957306 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.13624e8 | 0.402707 | 0.201354 | − | 0.979519i | \(-0.435466\pi\) | ||||
0.201354 | + | 0.979519i | \(0.435466\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.19563e8 | 1.51070 | 0.755348 | − | 0.655324i | \(-0.227468\pi\) | ||||
0.755348 | + | 0.655324i | \(0.227468\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.20578e8 | −0.397626 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.31470e8 | 0.760753 | 0.380376 | − | 0.924832i | \(-0.375794\pi\) | ||||
0.380376 | + | 0.924832i | \(0.375794\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.58786e8 | −0.963781 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.81664e8 | 0.644040 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.91666e8 | 1.63741 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.68452e8 | 0.433785 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.25086e8 | 0.197829 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50905e8 | 0.698071 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.22158e7 | 0.124611 | 0.0623056 | − | 0.998057i | \(-0.480155\pi\) | ||||
0.0623056 | + | 0.998057i | \(0.480155\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.16742e8 | −0.321654 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.61424e8 | −0.379916 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.93277e8 | 1.27140 | 0.635699 | − | 0.771937i | \(-0.280712\pi\) | ||||
0.635699 | + | 0.771937i | \(0.280712\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.84910e8 | −0.397199 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.96226e8 | 0.814274 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.96820e7 | 0.119999 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.23080e8 | −0.423588 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.08416e8 | 0.910197 | 0.455099 | − | 0.890441i | \(-0.349604\pi\) | ||||
0.455099 | + | 0.890441i | \(0.349604\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.85138e8 | −0.233134 | −0.116567 | − | 0.993183i | \(-0.537189\pi\) | ||||
−0.116567 | + | 0.993183i | \(0.537189\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.63928e8 | 0.325770 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.62041e9 | −1.96071 | −0.980355 | − | 0.197240i | \(-0.936802\pi\) | ||||
−0.980355 | + | 0.197240i | \(0.936802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.48269e8 | −0.294525 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.66654e8 | 1.00811 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.30456e8 | −0.262880 | −0.131440 | − | 0.991324i | \(-0.541960\pi\) | ||||
−0.131440 | + | 0.991324i | \(0.541960\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.10043e8 | 0.682472 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.68648e8 | 0.404519 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.98195e8 | 0.213338 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.30643e9 | −1.37960 | −0.689801 | − | 0.723999i | \(-0.742302\pi\) | ||||
−0.689801 | + | 0.723999i | \(0.742302\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.49452e8 | −0.465684 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.75650e9 | −1.78583 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.36011e8 | 0.634576 | 0.317288 | − | 0.948329i | \(-0.397228\pi\) | ||||
0.317288 | + | 0.948329i | \(0.397228\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6.38762e8 | 0.625503 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.10223e9 | 2.98180 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.80291e8 | −0.736240 | −0.368120 | − | 0.929778i | \(-0.619998\pi\) | ||||
−0.368120 | + | 0.929778i | \(0.619998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.59048e8 | −0.239962 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.06788e6 | −0.00279024 | −0.00139512 | − | 0.999999i | \(-0.500444\pi\) | ||||
−0.00139512 | + | 0.999999i | \(0.500444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.30803e8 | −0.652661 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.06214e8 | 0.619367 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.50816e9 | 1.29905 | 0.649524 | − | 0.760341i | \(-0.274968\pi\) | ||||
0.649524 | + | 0.760341i | \(0.274968\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.26939e9 | 1.07393 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.79379e8 | 0.564597 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.02628e9 | −0.837868 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.76390e8 | 0.221694 | 0.110847 | − | 0.993837i | \(-0.464644\pi\) | ||||
0.110847 | + | 0.993837i | \(0.464644\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.31433e9 | 1.03585 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.86311e9 | −1.44289 | −0.721444 | − | 0.692473i | \(-0.756521\pi\) | ||||
−0.721444 | + | 0.692473i | \(0.756521\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.31008e9 | −2.51925 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.28103e8 | 0.0958226 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.18095e8 | −0.527961 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.11458e9 | 0.805524 | 0.402762 | − | 0.915305i | \(-0.368050\pi\) | ||||
0.402762 | + | 0.915305i | \(0.368050\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.10396e9 | 0.784346 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.68973e8 | 0.187881 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.37338e9 | 0.943239 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.06349e9 | 0.718217 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.75638e9 | −1.16646 | −0.583228 | − | 0.812308i | \(-0.698211\pi\) | ||||
−0.583228 | + | 0.812308i | \(0.698211\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.24327e8 | −0.538409 | −0.269204 | − | 0.963083i | \(-0.586761\pi\) | ||||
−0.269204 | + | 0.963083i | \(0.586761\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.61869e8 | −0.168226 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5.11948e8 | −0.323493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.20767e9 | −1.37226 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.74429e8 | 0.534717 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.21141e9 | 1.33045 | 0.665225 | − | 0.746643i | \(-0.268335\pi\) | ||||
0.665225 | + | 0.746643i | \(0.268335\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.91107e8 | −0.527499 | −0.263750 | − | 0.964591i | \(-0.584959\pi\) | ||||
−0.263750 | + | 0.964591i | \(0.584959\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.50573e9 | 0.877074 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.92510e9 | 1.10349 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.22630e8 | −0.0691785 | −0.0345893 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345893 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.48279e8 | 0.304415 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.32516e9 | 1.81719 | 0.908594 | − | 0.417681i | \(-0.137157\pi\) | ||||
0.908594 | + | 0.417681i | \(0.137157\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.58452e9 | −0.852390 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.99115e7 | −0.0529102 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.94013e8 | −0.518239 | −0.259119 | − | 0.965845i | \(-0.583432\pi\) | ||||
−0.259119 | + | 0.965845i | \(0.583432\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.48910e9 | −0.764372 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.35589e8 | 0.169615 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.05722e9 | 2.01924 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.67555e9 | 1.31131 | 0.655657 | − | 0.755059i | \(-0.272392\pi\) | ||||
0.655657 | + | 0.755059i | \(0.272392\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.03321e8 | −0.242941 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.02753e9 | 0.963861 | 0.481931 | − | 0.876209i | \(-0.339936\pi\) | ||||
0.481931 | + | 0.876209i | \(0.339936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.02693e9 | 1.41732 | 0.708661 | − | 0.705549i | \(-0.249300\pi\) | ||||
0.708661 | + | 0.705549i | \(0.249300\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.60662e9 | −0.741017 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.30446e9 | 1.50138 | 0.750690 | − | 0.660654i | \(-0.229721\pi\) | ||||
0.750690 | + | 0.660654i | \(0.229721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.36134e9 | 0.609345 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.62060e8 | 0.336059 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.33978e9 | 1.01663 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.76397e8 | −0.332396 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.02011e9 | 0.430361 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.88113e8 | −0.286079 | −0.143039 | − | 0.989717i | \(-0.545688\pi\) | ||||
−0.143039 | + | 0.989717i | \(0.545688\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.98667e9 | 1.63344 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.68242e9 | 0.679390 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.82061e9 | 0.724638 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.85856e9 | −0.729163 | −0.364581 | − | 0.931172i | \(-0.618788\pi\) | ||||
−0.364581 | + | 0.931172i | \(0.618788\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.74913e9 | −0.676458 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.10855e9 | −1.18515 | −0.592574 | − | 0.805516i | \(-0.701888\pi\) | ||||
−0.592574 | + | 0.805516i | \(0.701888\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.91607e9 | −2.22366 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.24423e8 | 0.157283 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.29284e9 | 0.472387 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.95742e6 | −0.00106552 | −0.000532759 | − | 1.00000i | \(-0.500170\pi\) | ||||
−0.000532759 | 1.00000i | \(0.500170\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.52608e9 | 0.542182 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.89330e8 | 0.276548 | 0.138274 | − | 0.990394i | \(-0.455845\pi\) | ||||
0.138274 | + | 0.990394i | \(0.455845\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.69236e9 | 0.584755 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.16038e9 | −1.07699 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 4.84341e8 | 0.162794 | 0.0813971 | − | 0.996682i | \(-0.474062\pi\) | ||||
0.0813971 | + | 0.996682i | \(0.474062\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.03209e9 | −0.342171 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.63313e8 | −0.249627 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.43248e9 | −1.42995 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.67607e8 | −0.276125 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.91199e8 | 0.0914334 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.48726e9 | −1.39011 | −0.695056 | − | 0.718956i | \(-0.744620\pi\) | ||||
−0.695056 | + | 0.718956i | \(0.744620\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.86000e9 | 0.874200 | 0.437100 | − | 0.899413i | \(-0.356006\pi\) | ||||
0.437100 | + | 0.899413i | \(0.356006\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.78523e8 | −0.204648 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.31245e9 | 1.87871 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.40585e8 | −0.276251 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.56209e8 | −0.0452769 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.26705e9 | 2.36486 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.40739e9 | −0.962020 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.13635e7 | −0.0115268 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.81652e9 | 0.499666 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.29923e9 | −0.624297 | −0.312148 | − | 0.950033i | \(-0.601049\pi\) | ||||
−0.312148 | + | 0.950033i | \(0.601049\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.40528e9 | 0.912752 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.11673e9 | −0.295503 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.06117e8 | −0.210592 | −0.105296 | − | 0.994441i | \(-0.533579\pi\) | ||||
−0.105296 | + | 0.994441i | \(0.533579\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.28213e9 | 0.330697 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.97203e9 | −2.28486 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.34427e9 | 1.34385 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.93502e9 | 0.480462 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.67124e9 | −1.39054 | −0.695272 | − | 0.718747i | \(-0.744716\pi\) | ||||
−0.695272 | + | 0.718747i | \(0.744716\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.29898e10 | −3.14530 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.66757e9 | −0.398762 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.83103e9 | 0.668598 | 0.334299 | − | 0.942467i | \(-0.391500\pi\) | ||||
0.334299 | + | 0.942467i | \(0.391500\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.54360e9 | 0.593307 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.67089e8 | −0.153689 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.35162e8 | 0.0307583 | 0.0153792 | − | 0.999882i | \(-0.495104\pi\) | ||||
0.0153792 | + | 0.999882i | \(0.495104\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.87175e9 | −1.54469 | −0.772344 | − | 0.635204i | \(-0.780916\pi\) | ||||
−0.772344 | + | 0.635204i | \(0.780916\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.81076e9 | 0.846194 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.93834e8 | −0.218010 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.78800e9 | 0.604195 | 0.302098 | − | 0.953277i | \(-0.402313\pi\) | ||||
0.302098 | + | 0.953277i | \(0.402313\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.11240e9 | 0.666377 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.15176e9 | −1.51285 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.37976e9 | 0.706392 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.35628e9 | −0.486611 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.87741e9 | 0.791240 | 0.395620 | − | 0.918414i | \(-0.370530\pi\) | ||||
0.395620 | + | 0.918414i | \(0.370530\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.57317e9 | 1.93042 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.71027e8 | −0.173570 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.58123e9 | 0.705245 | 0.352623 | − | 0.935766i | \(-0.385290\pi\) | ||||
0.352623 | + | 0.935766i | \(0.385290\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.73727e9 | −1.50584 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.48416e9 | 0.285476 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.81275e9 | 0.534734 | 0.267367 | − | 0.963595i | \(-0.413846\pi\) | ||||
0.267367 | + | 0.963595i | \(0.413846\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.21845e9 | 1.35639 | 0.678193 | − | 0.734884i | \(-0.262764\pi\) | ||||
0.678193 | + | 0.734884i | \(0.262764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.90619e8 | −0.146844 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.29119e9 | −0.604240 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.43874e9 | −1.71298 | −0.856492 | − | 0.516160i | \(-0.827361\pi\) | ||||
−0.856492 | + | 0.516160i | \(0.827361\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.84100e9 | −1.40673 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.81672e9 | 0.854293 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.64596e9 | −1.16532 | −0.582661 | − | 0.812715i | \(-0.697989\pi\) | ||||
−0.582661 | + | 0.812715i | \(0.697989\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.01259e9 | 0.695604 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.57521e9 | −1.12697 | −0.563484 | − | 0.826127i | \(-0.690539\pi\) | ||||
−0.563484 | + | 0.826127i | \(0.690539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.34093e9 | 0.905107 | 0.452553 | − | 0.891737i | \(-0.350513\pi\) | ||||
0.452553 | + | 0.891737i | \(0.350513\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.77086e8 | −0.163724 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.25129e9 | 1.36714 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.13861e9 | −0.678070 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.52896e9 | −0.409737 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.60273e9 | −1.21813 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.30915e9 | −0.365889 | −0.182945 | − | 0.983123i | \(-0.558563\pi\) | ||||
−0.182945 | + | 0.983123i | \(0.558563\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.49948e9 | 0.234979 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.31271e9 | 0.358437 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00848e10 | −1.54590 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.50834e8 | −0.113839 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.73538e9 | 0.710152 | 0.355076 | − | 0.934837i | \(-0.384455\pi\) | ||||
0.355076 | + | 0.934837i | \(0.384455\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.22576e8 | −0.0626854 | −0.0313427 | − | 0.999509i | \(-0.509978\pi\) | ||||
−0.0313427 | + | 0.999509i | \(0.509978\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.30490e9 | −0.925165 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.01310e9 | 1.01799 | 0.508997 | − | 0.860769i | \(-0.330017\pi\) | ||||
0.508997 | + | 0.860769i | \(0.330017\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.17543e8 | −0.0743173 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.36636e9 | 1.18851 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.04168e10 | −1.46399 | −0.731995 | − | 0.681310i | \(-0.761410\pi\) | ||||
−0.731995 | + | 0.681310i | \(0.761410\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.06532e9 | −0.843353 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.99399e8 | 0.0824588 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.07019e10 | 1.45667 | 0.728337 | − | 0.685219i | \(-0.240294\pi\) | ||||
0.728337 | + | 0.685219i | \(0.240294\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.65225e9 | −1.03059 | −0.515293 | − | 0.857014i | \(-0.672317\pi\) | ||||
−0.515293 | + | 0.857014i | \(0.672317\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.25789e9 | 1.23371 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.17340e10 | −1.54728 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.14847e10 | −1.49858 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.41159e9 | 0.440520 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.24788e9 | 0.542805 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.47157e9 | −0.439009 | −0.219505 | − | 0.975611i | \(-0.570444\pi\) | ||||
−0.219505 | + | 0.975611i | \(0.570444\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.94061e8 | 0.0493174 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.01392e10 | 1.25587 | 0.627936 | − | 0.778265i | \(-0.283900\pi\) | ||||
0.627936 | + | 0.778265i | \(0.283900\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.48070e9 | −1.16224 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.88998e9 | −0.593324 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.29238e9 | 0.755689 | 0.377844 | − | 0.925869i | \(-0.376665\pi\) | ||||
0.377844 | + | 0.925869i | \(0.376665\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.85588e9 | −1.17160 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.96892e9 | −0.467007 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.87635e10 | −2.18548 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.09543e10 | 1.26303 | 0.631514 | − | 0.775365i | \(-0.282434\pi\) | ||||
0.631514 | + | 0.775365i | \(0.282434\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.21015e9 | −0.252265 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.49453e9 | −1.07282 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.57656e10 | −1.76358 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.54074e9 | −0.502871 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.41208e10 | 1.54827 | 0.774137 | − | 0.633018i | \(-0.218184\pi\) | ||||
0.774137 | + | 0.633018i | \(0.218184\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.15299e10 | −1.25165 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.33790e9 | 0.251283 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.81285e9 | −0.937883 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.66122e10 | −1.75052 | −0.875258 | − | 0.483656i | \(-0.839309\pi\) | ||||
−0.875258 | + | 0.483656i | \(0.839309\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.10376e9 | −0.323850 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.22542e10 | 1.26611 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.80668e9 | −0.798721 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5.56924e9 | 0.564259 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.53237e10 | −1.53749 | −0.768747 | − | 0.639553i | \(-0.779119\pi\) | ||||
−0.768747 | + | 0.639553i | \(0.779119\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.30818e10 | 2.29349 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.15667e9 | 0.901060 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.63182e9 | 0.451407 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.65903e9 | 0.353180 | 0.176590 | − | 0.984285i | \(-0.443493\pi\) | ||||
0.176590 | + | 0.984285i | \(0.443493\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.47721e10 | 2.34559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.09932e9 | 0.478243 | 0.239121 | − | 0.970990i | \(-0.423141\pi\) | ||||
0.239121 | + | 0.970990i | \(0.423141\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.89489e9 | −0.454713 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.61942e9 | −0.241029 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.78005e9 | −0.162247 | −0.0811236 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811236 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.40401e10 | 1.26767 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.36627e9 | −0.301084 | −0.150542 | − | 0.988604i | \(-0.548102\pi\) | ||||
−0.150542 | + | 0.988604i | \(0.548102\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.91984e8 | 0.0790333 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.15348e9 | 0.364578 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.77438e10 | 1.54298 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.21469e10 | 1.90798 | 0.953989 | − | 0.299842i | \(-0.0969341\pi\) | ||||
0.953989 | + | 0.299842i | \(0.0969341\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.79509e8 | −0.0836038 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.99605e9 | −0.253358 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.43073e10 | −1.19873 | −0.599365 | − | 0.800476i | \(-0.704580\pi\) | ||||
−0.599365 | + | 0.800476i | \(0.704580\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.23722e9 | −0.268736 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.23905e10 | −1.01916 | −0.509579 | − | 0.860424i | \(-0.670199\pi\) | ||||
−0.509579 | + | 0.860424i | \(0.670199\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.81530e9 | 0.473954 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.49352e9 | 0.362887 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.87325e9 | 0.229927 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.76200e10 | −1.39722 | −0.698608 | − | 0.715505i | \(-0.746197\pi\) | ||||
−0.698608 | + | 0.715505i | \(0.746197\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.39037e10 | 1.09255 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.38497e9 | −0.730811 | −0.365405 | − | 0.930849i | \(-0.619070\pi\) | ||||
−0.365405 | + | 0.930849i | \(0.619070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.94216e9 | −0.381382 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.00765e10 | −0.770610 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.39093e10 | −1.81212 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.48761e9 | −0.186855 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.55377e9 | 0.339004 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.80347e9 | −0.501980 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.16968e10 | 1.58666 | 0.793330 | − | 0.608791i | \(-0.208345\pi\) | ||||
0.793330 | + | 0.608791i | \(0.208345\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.43964e9 | 0.176830 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.32456e10 | −0.951600 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.35831e10 | −1.67936 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.10728e9 | −0.642841 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.39497e9 | 0.447439 | 0.223720 | − | 0.974654i | \(-0.428180\pi\) | ||||
0.223720 | + | 0.974654i | \(0.428180\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.18566e9 | −0.637084 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.79204e9 | −0.329463 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.98589e9 | 0.135348 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.50202e10 | −1.01482 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.24320e9 | 0.552126 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.80487e9 | −0.319052 | −0.159526 | − | 0.987194i | \(-0.550997\pi\) | ||||
−0.159526 | + | 0.987194i | \(0.550997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.20422e10 | −0.792745 | −0.396372 | − | 0.918090i | \(-0.629731\pi\) | ||||
−0.396372 | + | 0.918090i | \(0.629731\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.52057e9 | −0.295037 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.56158e10 | 1.01044 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.75682e10 | 2.41015 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.22702e10 | 0.780471 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.71353e10 | −1.71133 | −0.855666 | − | 0.517528i | \(-0.826852\pi\) | ||||
−0.855666 | + | 0.517528i | \(0.826852\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.01740e10 | −1.26152 | −0.630758 | − | 0.775980i | \(-0.717256\pi\) | ||||
−0.630758 | + | 0.775980i | \(0.717256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.30558e9 | 0.0809494 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.66064e10 | 1.63575 | 0.817875 | − | 0.575396i | \(-0.195152\pi\) | ||||
0.817875 | + | 0.575396i | \(0.195152\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.75290e9 | 0.533594 | 0.266797 | − | 0.963753i | \(-0.414035\pi\) | ||||
0.266797 | + | 0.963753i | \(0.414035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.65255e9 | −0.402147 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.92321e10 | 1.15284 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.36244e10 | −0.809871 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.85887e9 | −0.286415 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.75179e9 | −0.102404 | −0.0512018 | − | 0.998688i | \(-0.516305\pi\) | ||||
−0.0512018 | + | 0.998688i | \(0.516305\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.62754e10 | 2.10294 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.06754e9 | 0.521306 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.82151e10 | 1.60873 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.71386e10 | 0.969135 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.00922e10 | 0.565991 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.47590e10 | −0.820926 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.65193e9 | 0.311799 | 0.155900 | − | 0.987773i | \(-0.450172\pi\) | ||||
0.155900 | + | 0.987773i | \(0.450172\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.81466e9 | 0.372875 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.32497e9 | −0.397533 | −0.198766 | − | 0.980047i | \(-0.563694\pi\) | ||||
−0.198766 | + | 0.980047i | \(0.563694\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.93541e10 | −1.04183 | −0.520914 | − | 0.853609i | \(-0.674409\pi\) | ||||
−0.520914 | + | 0.853609i | \(0.674409\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.08953e10 | −1.11567 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.55088e10 | −0.821371 | −0.410685 | − | 0.911777i | \(-0.634711\pi\) | ||||
−0.410685 | + | 0.911777i | \(0.634711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.59975e9 | −0.136576 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −6.57599e9 | −0.342685 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.02832e10 | −0.531566 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.45423e10 | 0.745711 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.50604e9 | 0.280085 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.96964e10 | 1.49856 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.13613e10 | −1.06937 | −0.534686 | − | 0.845051i | \(-0.679570\pi\) | ||||
−0.534686 | + | 0.845051i | \(0.679570\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.12267e10 | 0.557559 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.16334e9 | 0.205129 | 0.102564 | − | 0.994726i | \(-0.467295\pi\) | ||||
0.102564 | + | 0.994726i | \(0.467295\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.68226e10 | −0.822301 | −0.411151 | − | 0.911567i | \(-0.634873\pi\) | ||||
−0.411151 | + | 0.911567i | \(0.634873\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.39460e9 | 0.0676312 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.68120e9 | −0.129002 | −0.0645010 | − | 0.997918i | \(-0.520546\pi\) | ||||
−0.0645010 | + | 0.997918i | \(0.520546\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.20433e10 | −0.574895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.28358e9 | 0.0607924 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.39305e10 | −0.654618 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.69283e8 | 0.0172178 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.79721e10 | 0.831431 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.71115e10 | −2.62159 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.57827e10 | 1.62981 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.28323e10 | 1.48386 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −3.04014e10 | −1.36340 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.89904e9 | 0.129011 | 0.0645057 | − | 0.997917i | \(-0.479453\pi\) | ||||
0.0645057 | + | 0.997917i | \(0.479453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.11818e9 | 0.226017 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.65643e10 | 0.725868 | 0.362934 | − | 0.931815i | \(-0.381775\pi\) | ||||
0.362934 | + | 0.931815i | \(0.381775\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.37610e10 | 0.598416 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.14466e10 | −0.493971 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.15847e10 | 1.35265 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.44040e9 | −0.273721 | −0.136861 | − | 0.990590i | \(-0.543701\pi\) | ||||
−0.136861 | + | 0.990590i | \(0.543701\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5.91995e9 | −0.249695 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.38106e10 | 0.578103 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.95234e9 | 0.247282 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.34051e10 | −0.552701 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.45986e10 | 1.41580 | 0.707902 | − | 0.706311i | \(-0.249642\pi\) | ||||
0.707902 | + | 0.706311i | \(0.249642\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.91666e10 | 1.18457 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.76786e9 | −0.232503 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.48876e10 | 0.595641 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.81853e10 | −1.51638 | −0.758190 | − | 0.652034i | \(-0.773916\pi\) | ||||
−0.758190 | + | 0.652034i | \(0.773916\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.21282e10 | −0.872201 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.28907e9 | −0.246049 | −0.123025 | − | 0.992404i | \(-0.539259\pi\) | ||||
−0.123025 | + | 0.992404i | \(0.539259\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.06054e10 | −1.18852 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.95560e9 | 0.229569 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.30506e10 | −0.881977 | −0.440988 | − | 0.897513i | \(-0.645372\pi\) | ||||
−0.440988 | + | 0.897513i | \(0.645372\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.10251e10 | −0.418746 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.16497e10 | −0.439221 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.46553e10 | 0.548493 | 0.274246 | − | 0.961659i | \(-0.411572\pi\) | ||||
0.274246 | + | 0.961659i | \(0.411572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.40214e10 | −1.26398 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.50872e10 | 0.556439 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.13238e10 | 1.87912 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.34254e10 | 1.21491 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.03049e10 | −0.371837 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.77867e10 | −0.995385 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.23044e9 | −0.0793226 | −0.0396613 | − | 0.999213i | \(-0.512628\pi\) | ||||
−0.0396613 | + | 0.999213i | \(0.512628\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.67750e10 | −0.945357 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.25778e10 | −1.14197 | −0.570984 | − | 0.820961i | \(-0.693438\pi\) | ||||
−0.570984 | + | 0.820961i | \(0.693438\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.94421e10 | 1.72069 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.24820e9 | −0.250446 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.10973e10 | −1.06682 | −0.533411 | − | 0.845856i | \(-0.679090\pi\) | ||||
−0.533411 | + | 0.845856i | \(0.679090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.58767e10 | −0.540780 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.37731e9 | −0.114217 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.12824e9 | 0.105042 | 0.0525210 | − | 0.998620i | \(-0.483274\pi\) | ||||
0.0525210 | + | 0.998620i | \(0.483274\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.77630e9 | 0.259266 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.21744e10 | −0.403031 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.80895e10 | 1.58075 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.75891e10 | −1.55328 | −0.776639 | − | 0.629946i | \(-0.783077\pi\) | ||||
−0.776639 | + | 0.629946i | \(0.783077\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.21983e9 | −0.0719444 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.32502e10 | −0.426423 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.10819e10 | 0.354144 | 0.177072 | − | 0.984198i | \(-0.443338\pi\) | ||||
0.177072 | + | 0.984198i | \(0.443338\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.85204e9 | 0.185707 |
(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 | 384.8.a.f.1.2 | yes | 2 | |
4.3 | odd | 2 | 384.8.a.h.1.2 | yes | 2 | ||
8.3 | odd | 2 | 384.8.a.e.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 384.8.a.g.1.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.8.a.e.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
384.8.a.f.1.2 | yes | 2 | 1.1 | even | 1 | trivial | |
384.8.a.g.1.1 | yes | 2 | 8.5 | even | 2 | ||
384.8.a.h.1.2 | yes | 2 | 4.3 | odd | 2 |