Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("69.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(21.5545667584\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 775x^{5} - 474x^{4} + 167184x^{3} - 33920x^{2} - 9348928x + 28965760 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(5.40652\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.40652 | 0.477873 | 0.238937 | − | 0.971035i | \(-0.423201\pi\) | ||||
0.238937 | + | 0.971035i | \(0.423201\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | −98.7695 | −0.771637 | ||||||||
\(5\) | −344.177 | −1.23137 | −0.615683 | − | 0.787994i | \(-0.711120\pi\) | ||||
−0.615683 | + | 0.787994i | \(0.711120\pi\) | |||||||
\(6\) | −145.976 | −0.275900 | ||||||||
\(7\) | 525.740 | 0.579332 | 0.289666 | − | 0.957128i | \(-0.406456\pi\) | ||||
0.289666 | + | 0.957128i | \(0.406456\pi\) | |||||||
\(8\) | −1226.03 | −0.846618 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −1860.80 | −0.588437 | ||||||||
\(11\) | −6690.01 | −1.51549 | −0.757744 | − | 0.652552i | \(-0.773698\pi\) | ||||
−0.757744 | + | 0.652552i | \(0.773698\pi\) | |||||||
\(12\) | 2666.78 | 0.445505 | ||||||||
\(13\) | 3864.31 | 0.487831 | 0.243916 | − | 0.969796i | \(-0.421568\pi\) | ||||
0.243916 | + | 0.969796i | \(0.421568\pi\) | |||||||
\(14\) | 2842.42 | 0.276847 | ||||||||
\(15\) | 9292.78 | 0.710929 | ||||||||
\(16\) | 6013.92 | 0.367061 | ||||||||
\(17\) | 4992.87 | 0.246479 | 0.123239 | − | 0.992377i | \(-0.460672\pi\) | ||||
0.123239 | + | 0.992377i | \(0.460672\pi\) | |||||||
\(18\) | 3941.35 | 0.159291 | ||||||||
\(19\) | 52377.6 | 1.75190 | 0.875948 | − | 0.482405i | \(-0.160237\pi\) | ||||
0.875948 | + | 0.482405i | \(0.160237\pi\) | |||||||
\(20\) | 33994.2 | 0.950167 | ||||||||
\(21\) | −14195.0 | −0.334478 | ||||||||
\(22\) | −36169.7 | −0.724211 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | 33102.9 | 0.488795 | ||||||||
\(25\) | 40332.9 | 0.516261 | ||||||||
\(26\) | 20892.5 | 0.233122 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −51927.1 | −0.447034 | ||||||||
\(29\) | 69355.1 | 0.528062 | 0.264031 | − | 0.964514i | \(-0.414948\pi\) | ||||
0.264031 | + | 0.964514i | \(0.414948\pi\) | |||||||
\(30\) | 50241.6 | 0.339734 | ||||||||
\(31\) | 74305.9 | 0.447979 | 0.223989 | − | 0.974592i | \(-0.428092\pi\) | ||||
0.223989 | + | 0.974592i | \(0.428092\pi\) | |||||||
\(32\) | 189447. | 1.02203 | ||||||||
\(33\) | 180630. | 0.874967 | ||||||||
\(34\) | 26994.1 | 0.117786 | ||||||||
\(35\) | −180948. | −0.713370 | ||||||||
\(36\) | −72003.0 | −0.257212 | ||||||||
\(37\) | −345774. | −1.12224 | −0.561121 | − | 0.827734i | \(-0.689630\pi\) | ||||
−0.561121 | + | 0.827734i | \(0.689630\pi\) | |||||||
\(38\) | 283181. | 0.837185 | ||||||||
\(39\) | −104336. | −0.281650 | ||||||||
\(40\) | 421973. | 1.04250 | ||||||||
\(41\) | 304729. | 0.690510 | 0.345255 | − | 0.938509i | \(-0.387792\pi\) | ||||
0.345255 | + | 0.938509i | \(0.387792\pi\) | |||||||
\(42\) | −76745.4 | −0.159838 | ||||||||
\(43\) | 334242. | 0.641093 | 0.320546 | − | 0.947233i | \(-0.396133\pi\) | ||||
0.320546 | + | 0.947233i | \(0.396133\pi\) | |||||||
\(44\) | 660769. | 1.16941 | ||||||||
\(45\) | −250905. | −0.410455 | ||||||||
\(46\) | −65781.1 | −0.0996435 | ||||||||
\(47\) | −685540. | −0.963141 | −0.481571 | − | 0.876407i | \(-0.659934\pi\) | ||||
−0.481571 | + | 0.876407i | \(0.659934\pi\) | |||||||
\(48\) | −162376. | −0.211923 | ||||||||
\(49\) | −547141. | −0.664374 | ||||||||
\(50\) | 218061. | 0.246707 | ||||||||
\(51\) | −134808. | −0.142305 | ||||||||
\(52\) | −381676. | −0.376429 | ||||||||
\(53\) | 759966. | 0.701179 | 0.350589 | − | 0.936529i | \(-0.385981\pi\) | ||||
0.350589 | + | 0.936529i | \(0.385981\pi\) | |||||||
\(54\) | −106417. | −0.0919668 | ||||||||
\(55\) | 2.30255e6 | 1.86612 | ||||||||
\(56\) | −644575. | −0.490473 | ||||||||
\(57\) | −1.41420e6 | −1.01146 | ||||||||
\(58\) | 374970. | 0.252347 | ||||||||
\(59\) | 893975. | 0.566687 | 0.283343 | − | 0.959019i | \(-0.408556\pi\) | ||||
0.283343 | + | 0.959019i | \(0.408556\pi\) | |||||||
\(60\) | −917844. | −0.548579 | ||||||||
\(61\) | 1.01834e6 | 0.574430 | 0.287215 | − | 0.957866i | \(-0.407271\pi\) | ||||
0.287215 | + | 0.957866i | \(0.407271\pi\) | |||||||
\(62\) | 401736. | 0.214077 | ||||||||
\(63\) | 383264. | 0.193111 | ||||||||
\(64\) | 254466. | 0.121339 | ||||||||
\(65\) | −1.33001e6 | −0.600699 | ||||||||
\(66\) | 976581. | 0.418123 | ||||||||
\(67\) | 1.90825e6 | 0.775128 | 0.387564 | − | 0.921843i | \(-0.373317\pi\) | ||||
0.387564 | + | 0.921843i | \(0.373317\pi\) | |||||||
\(68\) | −493144. | −0.190192 | ||||||||
\(69\) | 328509. | 0.120386 | ||||||||
\(70\) | −978297. | −0.340900 | ||||||||
\(71\) | −3.91381e6 | −1.29776 | −0.648882 | − | 0.760889i | \(-0.724763\pi\) | ||||
−0.648882 | + | 0.760889i | \(0.724763\pi\) | |||||||
\(72\) | −893779. | −0.282206 | ||||||||
\(73\) | 1.34857e6 | 0.405735 | 0.202868 | − | 0.979206i | \(-0.434974\pi\) | ||||
0.202868 | + | 0.979206i | \(0.434974\pi\) | |||||||
\(74\) | −1.86943e6 | −0.536289 | ||||||||
\(75\) | −1.08899e6 | −0.298063 | ||||||||
\(76\) | −5.17332e6 | −1.35183 | ||||||||
\(77\) | −3.51720e6 | −0.877970 | ||||||||
\(78\) | −564096. | −0.134593 | ||||||||
\(79\) | −5.28649e6 | −1.20635 | −0.603174 | − | 0.797609i | \(-0.706098\pi\) | ||||
−0.603174 | + | 0.797609i | \(0.706098\pi\) | |||||||
\(80\) | −2.06985e6 | −0.451986 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.64752e6 | 0.329976 | ||||||||
\(83\) | 4.24345e6 | 0.814603 | 0.407302 | − | 0.913294i | \(-0.366470\pi\) | ||||
0.407302 | + | 0.913294i | \(0.366470\pi\) | |||||||
\(84\) | 1.40203e6 | 0.258095 | ||||||||
\(85\) | −1.71843e6 | −0.303505 | ||||||||
\(86\) | 1.80708e6 | 0.306361 | ||||||||
\(87\) | −1.87259e6 | −0.304877 | ||||||||
\(88\) | 8.20218e6 | 1.28304 | ||||||||
\(89\) | −4.56295e6 | −0.686089 | −0.343045 | − | 0.939319i | \(-0.611458\pi\) | ||||
−0.343045 | + | 0.939319i | \(0.611458\pi\) | |||||||
\(90\) | −1.35652e6 | −0.196146 | ||||||||
\(91\) | 2.03162e6 | 0.282616 | ||||||||
\(92\) | 1.20173e6 | 0.160897 | ||||||||
\(93\) | −2.00626e6 | −0.258641 | ||||||||
\(94\) | −3.70638e6 | −0.460260 | ||||||||
\(95\) | −1.80272e7 | −2.15722 | ||||||||
\(96\) | −5.11506e6 | −0.590067 | ||||||||
\(97\) | 1.25318e7 | 1.39416 | 0.697081 | − | 0.716992i | \(-0.254482\pi\) | ||||
0.697081 | + | 0.716992i | \(0.254482\pi\) | |||||||
\(98\) | −2.95813e6 | −0.317487 | ||||||||
\(99\) | −4.87702e6 | −0.505162 | ||||||||
\(100\) | −3.98366e6 | −0.398366 | ||||||||
\(101\) | 1.24737e7 | 1.20468 | 0.602339 | − | 0.798241i | \(-0.294236\pi\) | ||||
0.602339 | + | 0.798241i | \(0.294236\pi\) | |||||||
\(102\) | −728840. | −0.0680035 | ||||||||
\(103\) | 4.58949e6 | 0.413842 | 0.206921 | − | 0.978358i | \(-0.433656\pi\) | ||||
0.206921 | + | 0.978358i | \(0.433656\pi\) | |||||||
\(104\) | −4.73777e6 | −0.413007 | ||||||||
\(105\) | 4.88559e6 | 0.411864 | ||||||||
\(106\) | 4.10877e6 | 0.335075 | ||||||||
\(107\) | −1.62881e7 | −1.28537 | −0.642684 | − | 0.766131i | \(-0.722179\pi\) | ||||
−0.642684 | + | 0.766131i | \(0.722179\pi\) | |||||||
\(108\) | 1.94408e6 | 0.148502 | ||||||||
\(109\) | 1.09431e7 | 0.809370 | 0.404685 | − | 0.914456i | \(-0.367381\pi\) | ||||
0.404685 | + | 0.914456i | \(0.367381\pi\) | |||||||
\(110\) | 1.24488e7 | 0.891768 | ||||||||
\(111\) | 9.33590e6 | 0.647926 | ||||||||
\(112\) | 3.16176e6 | 0.212650 | ||||||||
\(113\) | 2.89680e7 | 1.88862 | 0.944308 | − | 0.329063i | \(-0.106733\pi\) | ||||
0.944308 | + | 0.329063i | \(0.106733\pi\) | |||||||
\(114\) | −7.64588e6 | −0.483349 | ||||||||
\(115\) | 4.18760e6 | 0.256757 | ||||||||
\(116\) | −6.85017e6 | −0.407472 | ||||||||
\(117\) | 2.81708e6 | 0.162610 | ||||||||
\(118\) | 4.83329e6 | 0.270805 | ||||||||
\(119\) | 2.62495e6 | 0.142793 | ||||||||
\(120\) | −1.13933e7 | −0.601886 | ||||||||
\(121\) | 2.52690e7 | 1.29670 | ||||||||
\(122\) | 5.50566e6 | 0.274505 | ||||||||
\(123\) | −8.22768e6 | −0.398666 | ||||||||
\(124\) | −7.33916e6 | −0.345677 | ||||||||
\(125\) | 1.30072e7 | 0.595659 | ||||||||
\(126\) | 2.07213e6 | 0.0922825 | ||||||||
\(127\) | 3.95171e7 | 1.71188 | 0.855938 | − | 0.517079i | \(-0.172981\pi\) | ||||
0.855938 | + | 0.517079i | \(0.172981\pi\) | |||||||
\(128\) | −2.28734e7 | −0.964042 | ||||||||
\(129\) | −9.02452e6 | −0.370135 | ||||||||
\(130\) | −7.19070e6 | −0.287058 | ||||||||
\(131\) | −261338. | −0.0101567 | −0.00507835 | − | 0.999987i | \(-0.501616\pi\) | ||||
−0.00507835 | + | 0.999987i | \(0.501616\pi\) | |||||||
\(132\) | −1.78408e7 | −0.675157 | ||||||||
\(133\) | 2.75370e7 | 1.01493 | ||||||||
\(134\) | 1.03170e7 | 0.370413 | ||||||||
\(135\) | 6.77444e6 | 0.236976 | ||||||||
\(136\) | −6.12143e6 | −0.208673 | ||||||||
\(137\) | −3.74106e7 | −1.24300 | −0.621502 | − | 0.783412i | \(-0.713477\pi\) | ||||
−0.621502 | + | 0.783412i | \(0.713477\pi\) | |||||||
\(138\) | 1.77609e6 | 0.0575292 | ||||||||
\(139\) | 3.90753e7 | 1.23410 | 0.617051 | − | 0.786923i | \(-0.288327\pi\) | ||||
0.617051 | + | 0.786923i | \(0.288327\pi\) | |||||||
\(140\) | 1.78721e7 | 0.550462 | ||||||||
\(141\) | 1.85096e7 | 0.556070 | ||||||||
\(142\) | −2.11601e7 | −0.620167 | ||||||||
\(143\) | −2.58522e7 | −0.739302 | ||||||||
\(144\) | 4.38415e6 | 0.122354 | ||||||||
\(145\) | −2.38704e7 | −0.650238 | ||||||||
\(146\) | 7.29106e6 | 0.193890 | ||||||||
\(147\) | 1.47728e7 | 0.383577 | ||||||||
\(148\) | 3.41519e7 | 0.865963 | ||||||||
\(149\) | 2.34345e6 | 0.0580368 | 0.0290184 | − | 0.999579i | \(-0.490762\pi\) | ||||
0.0290184 | + | 0.999579i | \(0.490762\pi\) | |||||||
\(150\) | −5.88764e6 | −0.142437 | ||||||||
\(151\) | 3.81804e7 | 0.902446 | 0.451223 | − | 0.892411i | \(-0.350988\pi\) | ||||
0.451223 | + | 0.892411i | \(0.350988\pi\) | |||||||
\(152\) | −6.42168e7 | −1.48319 | ||||||||
\(153\) | 3.63980e6 | 0.0821595 | ||||||||
\(154\) | −1.90158e7 | −0.419559 | ||||||||
\(155\) | −2.55744e7 | −0.551625 | ||||||||
\(156\) | 1.03052e7 | 0.217331 | ||||||||
\(157\) | 5.74409e7 | 1.18460 | 0.592301 | − | 0.805717i | \(-0.298220\pi\) | ||||
0.592301 | + | 0.805717i | \(0.298220\pi\) | |||||||
\(158\) | −2.85815e7 | −0.576482 | ||||||||
\(159\) | −2.05191e7 | −0.404826 | ||||||||
\(160\) | −6.52032e7 | −1.25849 | ||||||||
\(161\) | −6.39668e6 | −0.120799 | ||||||||
\(162\) | 2.87325e6 | 0.0530970 | ||||||||
\(163\) | −3.34219e7 | −0.604470 | −0.302235 | − | 0.953233i | \(-0.597733\pi\) | ||||
−0.302235 | + | 0.953233i | \(0.597733\pi\) | |||||||
\(164\) | −3.00979e7 | −0.532823 | ||||||||
\(165\) | −6.21688e7 | −1.07740 | ||||||||
\(166\) | 2.29423e7 | 0.389277 | ||||||||
\(167\) | 9.67231e7 | 1.60703 | 0.803513 | − | 0.595288i | \(-0.202962\pi\) | ||||
0.803513 | + | 0.595288i | \(0.202962\pi\) | |||||||
\(168\) | 1.74035e7 | 0.283175 | ||||||||
\(169\) | −4.78157e7 | −0.762020 | ||||||||
\(170\) | −9.29074e6 | −0.145037 | ||||||||
\(171\) | 3.81833e7 | 0.583965 | ||||||||
\(172\) | −3.30129e7 | −0.494691 | ||||||||
\(173\) | −4.48058e7 | −0.657920 | −0.328960 | − | 0.944344i | \(-0.606698\pi\) | ||||
−0.328960 | + | 0.944344i | \(0.606698\pi\) | |||||||
\(174\) | −1.01242e7 | −0.145693 | ||||||||
\(175\) | 2.12046e7 | 0.299087 | ||||||||
\(176\) | −4.02332e7 | −0.556276 | ||||||||
\(177\) | −2.41373e7 | −0.327177 | ||||||||
\(178\) | −2.46697e7 | −0.327864 | ||||||||
\(179\) | 7.17236e7 | 0.934710 | 0.467355 | − | 0.884070i | \(-0.345207\pi\) | ||||
0.467355 | + | 0.884070i | \(0.345207\pi\) | |||||||
\(180\) | 2.47818e7 | 0.316722 | ||||||||
\(181\) | −1.36040e8 | −1.70526 | −0.852629 | − | 0.522516i | \(-0.824993\pi\) | ||||
−0.852629 | + | 0.522516i | \(0.824993\pi\) | |||||||
\(182\) | 1.09840e7 | 0.135055 | ||||||||
\(183\) | −2.74951e7 | −0.331647 | ||||||||
\(184\) | 1.49172e7 | 0.176532 | ||||||||
\(185\) | 1.19008e8 | 1.38189 | ||||||||
\(186\) | −1.08469e7 | −0.123597 | ||||||||
\(187\) | −3.34024e7 | −0.373535 | ||||||||
\(188\) | 6.77104e7 | 0.743196 | ||||||||
\(189\) | −1.03481e7 | −0.111493 | ||||||||
\(190\) | −9.74644e7 | −1.03088 | ||||||||
\(191\) | 6.40998e7 | 0.665641 | 0.332820 | − | 0.942990i | \(-0.392000\pi\) | ||||
0.332820 | + | 0.942990i | \(0.392000\pi\) | |||||||
\(192\) | −6.87058e6 | −0.0700549 | ||||||||
\(193\) | −1.11188e8 | −1.11329 | −0.556645 | − | 0.830751i | \(-0.687912\pi\) | ||||
−0.556645 | + | 0.830751i | \(0.687912\pi\) | |||||||
\(194\) | 6.77536e7 | 0.666233 | ||||||||
\(195\) | 3.59102e7 | 0.346814 | ||||||||
\(196\) | 5.40408e7 | 0.512656 | ||||||||
\(197\) | 1.37510e8 | 1.28145 | 0.640727 | − | 0.767768i | \(-0.278633\pi\) | ||||
0.640727 | + | 0.767768i | \(0.278633\pi\) | |||||||
\(198\) | −2.63677e7 | −0.241404 | ||||||||
\(199\) | −1.77736e8 | −1.59879 | −0.799394 | − | 0.600808i | \(-0.794846\pi\) | ||||
−0.799394 | + | 0.600808i | \(0.794846\pi\) | |||||||
\(200\) | −4.94495e7 | −0.437076 | ||||||||
\(201\) | −5.15228e7 | −0.447521 | ||||||||
\(202\) | 6.74393e7 | 0.575683 | ||||||||
\(203\) | 3.64627e7 | 0.305924 | ||||||||
\(204\) | 1.33149e7 | 0.109807 | ||||||||
\(205\) | −1.04881e8 | −0.850271 | ||||||||
\(206\) | 2.48132e7 | 0.197764 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | 2.32396e7 | 0.179064 | ||||||||
\(209\) | −3.50407e8 | −2.65498 | ||||||||
\(210\) | 2.64140e7 | 0.196819 | ||||||||
\(211\) | 2.06909e8 | 1.51632 | 0.758159 | − | 0.652069i | \(-0.226099\pi\) | ||||
0.758159 | + | 0.652069i | \(0.226099\pi\) | |||||||
\(212\) | −7.50615e7 | −0.541056 | ||||||||
\(213\) | 1.05673e8 | 0.749265 | ||||||||
\(214\) | −8.80621e7 | −0.614244 | ||||||||
\(215\) | −1.15038e8 | −0.789419 | ||||||||
\(216\) | 2.41320e7 | 0.162932 | ||||||||
\(217\) | 3.90655e7 | 0.259528 | ||||||||
\(218\) | 5.91641e7 | 0.386777 | ||||||||
\(219\) | −3.64113e7 | −0.234251 | ||||||||
\(220\) | −2.27422e8 | −1.43997 | ||||||||
\(221\) | 1.92940e7 | 0.120240 | ||||||||
\(222\) | 5.04747e7 | 0.309627 | ||||||||
\(223\) | −1.36885e8 | −0.826585 | −0.413293 | − | 0.910598i | \(-0.635621\pi\) | ||||
−0.413293 | + | 0.910598i | \(0.635621\pi\) | |||||||
\(224\) | 9.95997e7 | 0.592093 | ||||||||
\(225\) | 2.94027e7 | 0.172087 | ||||||||
\(226\) | 1.56616e8 | 0.902519 | ||||||||
\(227\) | 2.59280e8 | 1.47123 | 0.735613 | − | 0.677402i | \(-0.236894\pi\) | ||||
0.735613 | + | 0.677402i | \(0.236894\pi\) | |||||||
\(228\) | 1.39680e8 | 0.780478 | ||||||||
\(229\) | 2.74400e8 | 1.50994 | 0.754971 | − | 0.655758i | \(-0.227651\pi\) | ||||
0.754971 | + | 0.655758i | \(0.227651\pi\) | |||||||
\(230\) | 2.26404e7 | 0.122698 | ||||||||
\(231\) | 9.49645e7 | 0.506896 | ||||||||
\(232\) | −8.50317e7 | −0.447067 | ||||||||
\(233\) | −1.65096e8 | −0.855046 | −0.427523 | − | 0.904004i | \(-0.640614\pi\) | ||||
−0.427523 | + | 0.904004i | \(0.640614\pi\) | |||||||
\(234\) | 1.52306e7 | 0.0777072 | ||||||||
\(235\) | 2.35947e8 | 1.18598 | ||||||||
\(236\) | −8.82975e7 | −0.437277 | ||||||||
\(237\) | 1.42735e8 | 0.696486 | ||||||||
\(238\) | 1.41919e7 | 0.0682370 | ||||||||
\(239\) | 3.09433e8 | 1.46613 | 0.733067 | − | 0.680157i | \(-0.238088\pi\) | ||||
0.733067 | + | 0.680157i | \(0.238088\pi\) | |||||||
\(240\) | 5.58861e7 | 0.260954 | ||||||||
\(241\) | 6.69995e6 | 0.0308327 | 0.0154164 | − | 0.999881i | \(-0.495093\pi\) | ||||
0.0154164 | + | 0.999881i | \(0.495093\pi\) | |||||||
\(242\) | 1.36618e8 | 0.619659 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −1.00581e8 | −0.443251 | ||||||||
\(245\) | 1.88313e8 | 0.818087 | ||||||||
\(246\) | −4.44831e7 | −0.190512 | ||||||||
\(247\) | 2.02403e8 | 0.854630 | ||||||||
\(248\) | −9.11015e7 | −0.379267 | ||||||||
\(249\) | −1.14573e8 | −0.470311 | ||||||||
\(250\) | 7.03236e7 | 0.284650 | ||||||||
\(251\) | −3.18373e8 | −1.27080 | −0.635402 | − | 0.772182i | \(-0.719165\pi\) | ||||
−0.635402 | + | 0.772182i | \(0.719165\pi\) | |||||||
\(252\) | −3.78548e7 | −0.149011 | ||||||||
\(253\) | 8.13973e7 | 0.316001 | ||||||||
\(254\) | 2.13650e8 | 0.818060 | ||||||||
\(255\) | 4.63977e7 | 0.175229 | ||||||||
\(256\) | −1.56237e8 | −0.582029 | ||||||||
\(257\) | −2.14248e8 | −0.787320 | −0.393660 | − | 0.919256i | \(-0.628791\pi\) | ||||
−0.393660 | + | 0.919256i | \(0.628791\pi\) | |||||||
\(258\) | −4.87913e7 | −0.176878 | ||||||||
\(259\) | −1.81787e8 | −0.650151 | ||||||||
\(260\) | 1.31364e8 | 0.463521 | ||||||||
\(261\) | 5.05598e7 | 0.176021 | ||||||||
\(262\) | −1.41293e6 | −0.00485362 | ||||||||
\(263\) | −4.13165e6 | −0.0140048 | −0.00700242 | − | 0.999975i | \(-0.502229\pi\) | ||||
−0.00700242 | + | 0.999975i | \(0.502229\pi\) | |||||||
\(264\) | −2.21459e8 | −0.740763 | ||||||||
\(265\) | −2.61563e8 | −0.863407 | ||||||||
\(266\) | 1.48879e8 | 0.485008 | ||||||||
\(267\) | 1.23200e8 | 0.396114 | ||||||||
\(268\) | −1.88477e8 | −0.598118 | ||||||||
\(269\) | −2.07795e8 | −0.650881 | −0.325441 | − | 0.945562i | \(-0.605513\pi\) | ||||
−0.325441 | + | 0.945562i | \(0.605513\pi\) | |||||||
\(270\) | 3.66261e7 | 0.113245 | ||||||||
\(271\) | −1.80493e7 | −0.0550893 | −0.0275447 | − | 0.999621i | \(-0.508769\pi\) | ||||
−0.0275447 | + | 0.999621i | \(0.508769\pi\) | |||||||
\(272\) | 3.00268e7 | 0.0904726 | ||||||||
\(273\) | −5.48537e7 | −0.163169 | ||||||||
\(274\) | −2.02261e8 | −0.593999 | ||||||||
\(275\) | −2.69827e8 | −0.782387 | ||||||||
\(276\) | −3.24467e7 | −0.0928942 | ||||||||
\(277\) | −1.54789e8 | −0.437583 | −0.218791 | − | 0.975772i | \(-0.570211\pi\) | ||||
−0.218791 | + | 0.975772i | \(0.570211\pi\) | |||||||
\(278\) | 2.11262e8 | 0.589744 | ||||||||
\(279\) | 5.41690e7 | 0.149326 | ||||||||
\(280\) | 2.21848e8 | 0.603952 | ||||||||
\(281\) | −4.62346e8 | −1.24307 | −0.621534 | − | 0.783387i | \(-0.713490\pi\) | ||||
−0.621534 | + | 0.783387i | \(0.713490\pi\) | |||||||
\(282\) | 1.00072e8 | 0.265731 | ||||||||
\(283\) | 6.13374e8 | 1.60869 | 0.804346 | − | 0.594162i | \(-0.202516\pi\) | ||||
0.804346 | + | 0.594162i | \(0.202516\pi\) | |||||||
\(284\) | 3.86566e8 | 1.00140 | ||||||||
\(285\) | 4.86734e8 | 1.24547 | ||||||||
\(286\) | −1.39771e8 | −0.353293 | ||||||||
\(287\) | 1.60208e8 | 0.400035 | ||||||||
\(288\) | 1.38107e8 | 0.340676 | ||||||||
\(289\) | −3.85410e8 | −0.939248 | ||||||||
\(290\) | −1.29056e8 | −0.310731 | ||||||||
\(291\) | −3.38359e8 | −0.804920 | ||||||||
\(292\) | −1.33197e8 | −0.313080 | ||||||||
\(293\) | 3.81082e7 | 0.0885078 | 0.0442539 | − | 0.999020i | \(-0.485909\pi\) | ||||
0.0442539 | + | 0.999020i | \(0.485909\pi\) | |||||||
\(294\) | 7.98694e7 | 0.183301 | ||||||||
\(295\) | −3.07686e8 | −0.697799 | ||||||||
\(296\) | 4.23931e8 | 0.950110 | ||||||||
\(297\) | 1.31679e8 | 0.291656 | ||||||||
\(298\) | 1.26699e7 | 0.0277342 | ||||||||
\(299\) | −4.70170e7 | −0.101720 | ||||||||
\(300\) | 1.07559e8 | 0.229997 | ||||||||
\(301\) | 1.75724e8 | 0.371406 | ||||||||
\(302\) | 2.06423e8 | 0.431255 | ||||||||
\(303\) | −3.36790e8 | −0.695521 | ||||||||
\(304\) | 3.14995e8 | 0.643052 | ||||||||
\(305\) | −3.50488e8 | −0.707333 | ||||||||
\(306\) | 1.96787e7 | 0.0392619 | ||||||||
\(307\) | −4.87833e8 | −0.962247 | −0.481124 | − | 0.876653i | \(-0.659771\pi\) | ||||
−0.481124 | + | 0.876653i | \(0.659771\pi\) | |||||||
\(308\) | 3.47393e8 | 0.677474 | ||||||||
\(309\) | −1.23916e8 | −0.238932 | ||||||||
\(310\) | −1.38268e8 | −0.263607 | ||||||||
\(311\) | −8.21826e7 | −0.154924 | −0.0774619 | − | 0.996995i | \(-0.524682\pi\) | ||||
−0.0774619 | + | 0.996995i | \(0.524682\pi\) | |||||||
\(312\) | 1.27920e8 | 0.238450 | ||||||||
\(313\) | 9.13866e7 | 0.168452 | 0.0842262 | − | 0.996447i | \(-0.473158\pi\) | ||||
0.0842262 | + | 0.996447i | \(0.473158\pi\) | |||||||
\(314\) | 3.10556e8 | 0.566090 | ||||||||
\(315\) | −1.31911e8 | −0.237790 | ||||||||
\(316\) | 5.22144e8 | 0.930863 | ||||||||
\(317\) | −6.21150e8 | −1.09519 | −0.547595 | − | 0.836744i | \(-0.684456\pi\) | ||||
−0.547595 | + | 0.836744i | \(0.684456\pi\) | |||||||
\(318\) | −1.10937e8 | −0.193455 | ||||||||
\(319\) | −4.63986e8 | −0.800272 | ||||||||
\(320\) | −8.75813e7 | −0.149412 | ||||||||
\(321\) | 4.39779e8 | 0.742108 | ||||||||
\(322\) | −3.45838e7 | −0.0577267 | ||||||||
\(323\) | 2.61515e8 | 0.431805 | ||||||||
\(324\) | −5.24902e7 | −0.0857374 | ||||||||
\(325\) | 1.55859e8 | 0.251848 | ||||||||
\(326\) | −1.80696e8 | −0.288860 | ||||||||
\(327\) | −2.95463e8 | −0.467290 | ||||||||
\(328\) | −3.73608e8 | −0.584599 | ||||||||
\(329\) | −3.60415e8 | −0.557979 | ||||||||
\(330\) | −3.36117e8 | −0.514863 | ||||||||
\(331\) | 9.48538e8 | 1.43766 | 0.718831 | − | 0.695185i | \(-0.244678\pi\) | ||||
0.718831 | + | 0.695185i | \(0.244678\pi\) | |||||||
\(332\) | −4.19124e8 | −0.628578 | ||||||||
\(333\) | −2.52069e8 | −0.374081 | ||||||||
\(334\) | 5.22936e8 | 0.767955 | ||||||||
\(335\) | −6.56776e8 | −0.954466 | ||||||||
\(336\) | −8.53675e7 | −0.122774 | ||||||||
\(337\) | −6.86971e8 | −0.977763 | −0.488882 | − | 0.872350i | \(-0.662595\pi\) | ||||
−0.488882 | + | 0.872350i | \(0.662595\pi\) | |||||||
\(338\) | −2.58516e8 | −0.364149 | ||||||||
\(339\) | −7.82135e8 | −1.09039 | ||||||||
\(340\) | 1.69729e8 | 0.234196 | ||||||||
\(341\) | −4.97107e8 | −0.678906 | ||||||||
\(342\) | 2.06439e8 | 0.279062 | ||||||||
\(343\) | −7.20623e8 | −0.964226 | ||||||||
\(344\) | −4.09792e8 | −0.542761 | ||||||||
\(345\) | −1.13065e8 | −0.148239 | ||||||||
\(346\) | −2.42243e8 | −0.314402 | ||||||||
\(347\) | 1.20692e8 | 0.155069 | 0.0775345 | − | 0.996990i | \(-0.475295\pi\) | ||||
0.0775345 | + | 0.996990i | \(0.475295\pi\) | |||||||
\(348\) | 1.84955e8 | 0.235254 | ||||||||
\(349\) | −9.54223e8 | −1.20160 | −0.600801 | − | 0.799398i | \(-0.705152\pi\) | ||||
−0.600801 | + | 0.799398i | \(0.705152\pi\) | |||||||
\(350\) | 1.14643e8 | 0.142926 | ||||||||
\(351\) | −7.60611e7 | −0.0938832 | ||||||||
\(352\) | −1.26740e9 | −1.54887 | ||||||||
\(353\) | −3.62096e8 | −0.438139 | −0.219070 | − | 0.975709i | \(-0.570302\pi\) | ||||
−0.219070 | + | 0.975709i | \(0.570302\pi\) | |||||||
\(354\) | −1.30499e8 | −0.156349 | ||||||||
\(355\) | 1.34704e9 | 1.59802 | ||||||||
\(356\) | 4.50681e8 | 0.529412 | ||||||||
\(357\) | −7.08737e7 | −0.0824416 | ||||||||
\(358\) | 3.87775e8 | 0.446673 | ||||||||
\(359\) | 5.77679e8 | 0.658956 | 0.329478 | − | 0.944163i | \(-0.393127\pi\) | ||||
0.329478 | + | 0.944163i | \(0.393127\pi\) | |||||||
\(360\) | 3.07618e8 | 0.347499 | ||||||||
\(361\) | 1.84955e9 | 2.06914 | ||||||||
\(362\) | −7.35501e8 | −0.814898 | ||||||||
\(363\) | −6.82264e8 | −0.748651 | ||||||||
\(364\) | −2.00662e8 | −0.218077 | ||||||||
\(365\) | −4.64146e8 | −0.499608 | ||||||||
\(366\) | −1.48653e8 | −0.158485 | ||||||||
\(367\) | 8.05566e8 | 0.850687 | 0.425343 | − | 0.905032i | \(-0.360153\pi\) | ||||
0.425343 | + | 0.905032i | \(0.360153\pi\) | |||||||
\(368\) | −7.31714e7 | −0.0765374 | ||||||||
\(369\) | 2.22147e8 | 0.230170 | ||||||||
\(370\) | 6.43417e8 | 0.660368 | ||||||||
\(371\) | 3.99545e8 | 0.406215 | ||||||||
\(372\) | 1.98157e8 | 0.199577 | ||||||||
\(373\) | 1.53686e9 | 1.53340 | 0.766698 | − | 0.642008i | \(-0.221898\pi\) | ||||
0.766698 | + | 0.642008i | \(0.221898\pi\) | |||||||
\(374\) | −1.80591e8 | −0.178503 | ||||||||
\(375\) | −3.51194e8 | −0.343904 | ||||||||
\(376\) | 8.40495e8 | 0.815413 | ||||||||
\(377\) | 2.68009e8 | 0.257605 | ||||||||
\(378\) | −5.59474e7 | −0.0532793 | ||||||||
\(379\) | 1.48201e9 | 1.39835 | 0.699173 | − | 0.714953i | \(-0.253552\pi\) | ||||
0.699173 | + | 0.714953i | \(0.253552\pi\) | |||||||
\(380\) | 1.78054e9 | 1.66459 | ||||||||
\(381\) | −1.06696e9 | −0.988352 | ||||||||
\(382\) | 3.46557e8 | 0.318092 | ||||||||
\(383\) | −8.66673e8 | −0.788242 | −0.394121 | − | 0.919059i | \(-0.628951\pi\) | ||||
−0.394121 | + | 0.919059i | \(0.628951\pi\) | |||||||
\(384\) | 6.17582e8 | 0.556590 | ||||||||
\(385\) | 1.21054e9 | 1.08110 | ||||||||
\(386\) | −6.01141e8 | −0.532011 | ||||||||
\(387\) | 2.43662e8 | 0.213698 | ||||||||
\(388\) | −1.23776e9 | −1.07579 | ||||||||
\(389\) | −1.38485e9 | −1.19283 | −0.596417 | − | 0.802674i | \(-0.703410\pi\) | ||||
−0.596417 | + | 0.802674i | \(0.703410\pi\) | |||||||
\(390\) | 1.94149e8 | 0.165733 | ||||||||
\(391\) | −6.07483e7 | −0.0513944 | ||||||||
\(392\) | 6.70813e8 | 0.562471 | ||||||||
\(393\) | 7.05612e6 | 0.00586397 | ||||||||
\(394\) | 7.43452e8 | 0.612373 | ||||||||
\(395\) | 1.81949e9 | 1.48546 | ||||||||
\(396\) | 4.81701e8 | 0.389802 | ||||||||
\(397\) | −9.97021e8 | −0.799719 | −0.399859 | − | 0.916576i | \(-0.630941\pi\) | ||||
−0.399859 | + | 0.916576i | \(0.630941\pi\) | |||||||
\(398\) | −9.60936e8 | −0.764018 | ||||||||
\(399\) | −7.43499e8 | −0.585970 | ||||||||
\(400\) | 2.42559e8 | 0.189499 | ||||||||
\(401\) | 2.19367e9 | 1.69889 | 0.849445 | − | 0.527677i | \(-0.176937\pi\) | ||||
0.849445 | + | 0.527677i | \(0.176937\pi\) | |||||||
\(402\) | −2.78559e8 | −0.213858 | ||||||||
\(403\) | 2.87141e8 | 0.218538 | ||||||||
\(404\) | −1.23202e9 | −0.929573 | ||||||||
\(405\) | −1.82910e8 | −0.136818 | ||||||||
\(406\) | 1.97136e8 | 0.146193 | ||||||||
\(407\) | 2.31323e9 | 1.70074 | ||||||||
\(408\) | 1.65279e8 | 0.120478 | ||||||||
\(409\) | 3.18875e8 | 0.230456 | 0.115228 | − | 0.993339i | \(-0.463240\pi\) | ||||
0.115228 | + | 0.993339i | \(0.463240\pi\) | |||||||
\(410\) | −5.67040e8 | −0.406322 | ||||||||
\(411\) | 1.01009e9 | 0.717649 | ||||||||
\(412\) | −4.53302e8 | −0.319336 | ||||||||
\(413\) | 4.69998e8 | 0.328300 | ||||||||
\(414\) | −4.79544e7 | −0.0332145 | ||||||||
\(415\) | −1.46050e9 | −1.00307 | ||||||||
\(416\) | 7.32080e8 | 0.498577 | ||||||||
\(417\) | −1.05503e9 | −0.712509 | ||||||||
\(418\) | −1.89448e9 | −1.26874 | ||||||||
\(419\) | −7.98056e8 | −0.530010 | −0.265005 | − | 0.964247i | \(-0.585374\pi\) | ||||
−0.265005 | + | 0.964247i | \(0.585374\pi\) | |||||||
\(420\) | −4.82547e8 | −0.317810 | ||||||||
\(421\) | 2.70591e9 | 1.76737 | 0.883684 | − | 0.468085i | \(-0.155056\pi\) | ||||
0.883684 | + | 0.468085i | \(0.155056\pi\) | |||||||
\(422\) | 1.11866e9 | 0.724608 | ||||||||
\(423\) | −4.99758e8 | −0.321047 | ||||||||
\(424\) | −9.31745e8 | −0.593631 | ||||||||
\(425\) | 2.01377e8 | 0.127247 | ||||||||
\(426\) | 5.71323e8 | 0.358054 | ||||||||
\(427\) | 5.35380e8 | 0.332786 | ||||||||
\(428\) | 1.60877e9 | 0.991838 | ||||||||
\(429\) | 6.98010e8 | 0.426836 | ||||||||
\(430\) | −6.21957e8 | −0.377243 | ||||||||
\(431\) | 4.37854e8 | 0.263426 | 0.131713 | − | 0.991288i | \(-0.457952\pi\) | ||||
0.131713 | + | 0.991288i | \(0.457952\pi\) | |||||||
\(432\) | −1.18372e8 | −0.0706409 | ||||||||
\(433\) | −8.64340e8 | −0.511655 | −0.255827 | − | 0.966722i | \(-0.582348\pi\) | ||||
−0.255827 | + | 0.966722i | \(0.582348\pi\) | |||||||
\(434\) | 2.11209e8 | 0.124022 | ||||||||
\(435\) | 6.44502e8 | 0.375415 | ||||||||
\(436\) | −1.08084e9 | −0.624540 | ||||||||
\(437\) | −6.37279e8 | −0.365296 | ||||||||
\(438\) | −1.96858e8 | −0.111942 | ||||||||
\(439\) | 1.19683e8 | 0.0675160 | 0.0337580 | − | 0.999430i | \(-0.489252\pi\) | ||||
0.0337580 | + | 0.999430i | \(0.489252\pi\) | |||||||
\(440\) | −2.82300e9 | −1.57989 | ||||||||
\(441\) | −3.98866e8 | −0.221458 | ||||||||
\(442\) | 1.04313e8 | 0.0574595 | ||||||||
\(443\) | 2.73826e9 | 1.49645 | 0.748225 | − | 0.663445i | \(-0.230906\pi\) | ||||
0.748225 | + | 0.663445i | \(0.230906\pi\) | |||||||
\(444\) | −9.22102e8 | −0.499964 | ||||||||
\(445\) | 1.57046e9 | 0.844827 | ||||||||
\(446\) | −7.40069e8 | −0.395003 | ||||||||
\(447\) | −6.32731e7 | −0.0335076 | ||||||||
\(448\) | 1.33783e8 | 0.0702954 | ||||||||
\(449\) | −1.10118e9 | −0.574111 | −0.287055 | − | 0.957914i | \(-0.592676\pi\) | ||||
−0.287055 | + | 0.957914i | \(0.592676\pi\) | |||||||
\(450\) | 1.58966e8 | 0.0822358 | ||||||||
\(451\) | −2.03864e9 | −1.04646 | ||||||||
\(452\) | −2.86115e9 | −1.45733 | ||||||||
\(453\) | −1.03087e9 | −0.521028 | ||||||||
\(454\) | 1.40181e9 | 0.703060 | ||||||||
\(455\) | −6.99237e8 | −0.348004 | ||||||||
\(456\) | 1.73385e9 | 0.856319 | ||||||||
\(457\) | 1.98372e9 | 0.972239 | 0.486119 | − | 0.873892i | \(-0.338412\pi\) | ||||
0.486119 | + | 0.873892i | \(0.338412\pi\) | |||||||
\(458\) | 1.48355e9 | 0.721561 | ||||||||
\(459\) | −9.82747e7 | −0.0474348 | ||||||||
\(460\) | −4.13608e8 | −0.198124 | ||||||||
\(461\) | −7.95089e8 | −0.377975 | −0.188987 | − | 0.981980i | \(-0.560520\pi\) | ||||
−0.188987 | + | 0.981980i | \(0.560520\pi\) | |||||||
\(462\) | 5.13427e8 | 0.242232 | ||||||||
\(463\) | −7.69252e8 | −0.360193 | −0.180097 | − | 0.983649i | \(-0.557641\pi\) | ||||
−0.180097 | + | 0.983649i | \(0.557641\pi\) | |||||||
\(464\) | 4.17096e8 | 0.193831 | ||||||||
\(465\) | 6.90508e8 | 0.318481 | ||||||||
\(466\) | −8.92592e8 | −0.408604 | ||||||||
\(467\) | −2.36312e9 | −1.07368 | −0.536841 | − | 0.843683i | \(-0.680383\pi\) | ||||
−0.536841 | + | 0.843683i | \(0.680383\pi\) | |||||||
\(468\) | −2.78242e8 | −0.125476 | ||||||||
\(469\) | 1.00324e9 | 0.449057 | ||||||||
\(470\) | 1.27565e9 | 0.566748 | ||||||||
\(471\) | −1.55091e9 | −0.683931 | ||||||||
\(472\) | −1.09604e9 | −0.479767 | ||||||||
\(473\) | −2.23608e9 | −0.971568 | ||||||||
\(474\) | 7.71701e8 | 0.332832 | ||||||||
\(475\) | 2.11254e9 | 0.904436 | ||||||||
\(476\) | −2.59265e8 | −0.110184 | ||||||||
\(477\) | 5.54015e8 | 0.233726 | ||||||||
\(478\) | 1.67295e9 | 0.700626 | ||||||||
\(479\) | −3.11846e9 | −1.29648 | −0.648240 | − | 0.761436i | \(-0.724495\pi\) | ||||
−0.648240 | + | 0.761436i | \(0.724495\pi\) | |||||||
\(480\) | 1.76049e9 | 0.726589 | ||||||||
\(481\) | −1.33618e9 | −0.547465 | ||||||||
\(482\) | 3.62234e7 | 0.0147341 | ||||||||
\(483\) | 1.72710e8 | 0.0697434 | ||||||||
\(484\) | −2.49581e9 | −1.00058 | ||||||||
\(485\) | −4.31317e9 | −1.71672 | ||||||||
\(486\) | −7.75777e7 | −0.0306556 | ||||||||
\(487\) | −3.77527e9 | −1.48114 | −0.740570 | − | 0.671979i | \(-0.765444\pi\) | ||||
−0.740570 | + | 0.671979i | \(0.765444\pi\) | |||||||
\(488\) | −1.24852e9 | −0.486323 | ||||||||
\(489\) | 9.02391e8 | 0.348991 | ||||||||
\(490\) | 1.01812e9 | 0.390942 | ||||||||
\(491\) | 1.21830e9 | 0.464482 | 0.232241 | − | 0.972658i | \(-0.425394\pi\) | ||||
0.232241 | + | 0.972658i | \(0.425394\pi\) | |||||||
\(492\) | 8.12644e8 | 0.307626 | ||||||||
\(493\) | 3.46281e8 | 0.130156 | ||||||||
\(494\) | 1.09430e9 | 0.408405 | ||||||||
\(495\) | 1.67856e9 | 0.622039 | ||||||||
\(496\) | 4.46870e8 | 0.164435 | ||||||||
\(497\) | −2.05765e9 | −0.751837 | ||||||||
\(498\) | −6.19443e8 | −0.224749 | ||||||||
\(499\) | −4.76230e9 | −1.71579 | −0.857897 | − | 0.513822i | \(-0.828229\pi\) | ||||
−0.857897 | + | 0.513822i | \(0.828229\pi\) | |||||||
\(500\) | −1.28471e9 | −0.459633 | ||||||||
\(501\) | −2.61152e9 | −0.927817 | ||||||||
\(502\) | −1.72129e9 | −0.607283 | ||||||||
\(503\) | 4.21755e9 | 1.47765 | 0.738826 | − | 0.673896i | \(-0.235380\pi\) | ||||
0.738826 | + | 0.673896i | \(0.235380\pi\) | |||||||
\(504\) | −4.69895e8 | −0.163491 | ||||||||
\(505\) | −4.29316e9 | −1.48340 | ||||||||
\(506\) | 4.40076e8 | 0.151008 | ||||||||
\(507\) | 1.29102e9 | 0.439953 | ||||||||
\(508\) | −3.90309e9 | −1.32095 | ||||||||
\(509\) | 1.94818e9 | 0.654813 | 0.327407 | − | 0.944884i | \(-0.393825\pi\) | ||||
0.327407 | + | 0.944884i | \(0.393825\pi\) | |||||||
\(510\) | 2.50850e8 | 0.0837372 | ||||||||
\(511\) | 7.08995e8 | 0.235055 | ||||||||
\(512\) | 2.08310e9 | 0.685906 | ||||||||
\(513\) | −1.03095e9 | −0.337153 | ||||||||
\(514\) | −1.15834e9 | −0.376239 | ||||||||
\(515\) | −1.57960e9 | −0.509591 | ||||||||
\(516\) | 8.91348e8 | 0.285610 | ||||||||
\(517\) | 4.58627e9 | 1.45963 | ||||||||
\(518\) | −9.82836e8 | −0.310690 | ||||||||
\(519\) | 1.20976e9 | 0.379850 | ||||||||
\(520\) | 1.63063e9 | 0.508563 | ||||||||
\(521\) | 4.07821e9 | 1.26339 | 0.631695 | − | 0.775217i | \(-0.282359\pi\) | ||||
0.631695 | + | 0.775217i | \(0.282359\pi\) | |||||||
\(522\) | 2.73353e8 | 0.0841157 | ||||||||
\(523\) | 6.06342e9 | 1.85337 | 0.926684 | − | 0.375841i | \(-0.122646\pi\) | ||||
0.926684 | + | 0.375841i | \(0.122646\pi\) | |||||||
\(524\) | 2.58122e7 | 0.00783729 | ||||||||
\(525\) | −5.72524e8 | −0.172678 | ||||||||
\(526\) | −2.23378e7 | −0.00669254 | ||||||||
\(527\) | 3.71000e8 | 0.110417 | ||||||||
\(528\) | 1.08630e9 | 0.321166 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | −1.41415e9 | −0.412599 | ||||||||
\(531\) | 6.51707e8 | 0.188896 | ||||||||
\(532\) | −2.71982e9 | −0.783158 | ||||||||
\(533\) | 1.17757e9 | 0.336853 | ||||||||
\(534\) | 6.66081e8 | 0.189292 | ||||||||
\(535\) | 5.60600e9 | 1.58276 | ||||||||
\(536\) | −2.33958e9 | −0.656238 | ||||||||
\(537\) | −1.93654e9 | −0.539655 | ||||||||
\(538\) | −1.12345e9 | −0.311039 | ||||||||
\(539\) | 3.66038e9 | 1.00685 | ||||||||
\(540\) | −6.69108e8 | −0.182860 | ||||||||
\(541\) | −6.00472e9 | −1.63043 | −0.815215 | − | 0.579159i | \(-0.803381\pi\) | ||||
−0.815215 | + | 0.579159i | \(0.803381\pi\) | |||||||
\(542\) | −9.75838e7 | −0.0263257 | ||||||||
\(543\) | 3.67307e9 | 0.984532 | ||||||||
\(544\) | 9.45884e8 | 0.251908 | ||||||||
\(545\) | −3.76636e9 | −0.996631 | ||||||||
\(546\) | −2.96568e8 | −0.0779740 | ||||||||
\(547\) | 5.57969e9 | 1.45765 | 0.728827 | − | 0.684698i | \(-0.240066\pi\) | ||||
0.728827 | + | 0.684698i | \(0.240066\pi\) | |||||||
\(548\) | 3.69503e9 | 0.959148 | ||||||||
\(549\) | 7.42368e8 | 0.191477 | ||||||||
\(550\) | −1.45883e9 | −0.373882 | ||||||||
\(551\) | 3.63266e9 | 0.925111 | ||||||||
\(552\) | −4.02763e8 | −0.101921 | ||||||||
\(553\) | −2.77932e9 | −0.698877 | ||||||||
\(554\) | −8.36868e8 | −0.209109 | ||||||||
\(555\) | −3.21320e9 | −0.797834 | ||||||||
\(556\) | −3.85945e9 | −0.952278 | ||||||||
\(557\) | 3.59539e9 | 0.881562 | 0.440781 | − | 0.897615i | \(-0.354702\pi\) | ||||
0.440781 | + | 0.897615i | \(0.354702\pi\) | |||||||
\(558\) | 2.92866e8 | 0.0713590 | ||||||||
\(559\) | 1.29161e9 | 0.312745 | ||||||||
\(560\) | −1.08820e9 | −0.261850 | ||||||||
\(561\) | 9.01864e8 | 0.215661 | ||||||||
\(562\) | −2.49968e9 | −0.594029 | ||||||||
\(563\) | −9.98324e8 | −0.235772 | −0.117886 | − | 0.993027i | \(-0.537612\pi\) | ||||
−0.117886 | + | 0.993027i | \(0.537612\pi\) | |||||||
\(564\) | −1.82818e9 | −0.429084 | ||||||||
\(565\) | −9.97012e9 | −2.32558 | ||||||||
\(566\) | 3.31622e9 | 0.768751 | ||||||||
\(567\) | 2.79400e8 | 0.0643702 | ||||||||
\(568\) | 4.79847e9 | 1.09871 | ||||||||
\(569\) | 3.60988e9 | 0.821486 | 0.410743 | − | 0.911751i | \(-0.365269\pi\) | ||||
0.410743 | + | 0.911751i | \(0.365269\pi\) | |||||||
\(570\) | 2.63154e9 | 0.595179 | ||||||||
\(571\) | 3.06436e9 | 0.688832 | 0.344416 | − | 0.938817i | \(-0.388077\pi\) | ||||
0.344416 | + | 0.938817i | \(0.388077\pi\) | |||||||
\(572\) | 2.55341e9 | 0.570473 | ||||||||
\(573\) | −1.73069e9 | −0.384308 | ||||||||
\(574\) | 8.66168e8 | 0.191166 | ||||||||
\(575\) | −4.90730e8 | −0.107648 | ||||||||
\(576\) | 1.85506e8 | 0.0404462 | ||||||||
\(577\) | −1.25398e9 | −0.271753 | −0.135876 | − | 0.990726i | \(-0.543385\pi\) | ||||
−0.135876 | + | 0.990726i | \(0.543385\pi\) | |||||||
\(578\) | −2.08373e9 | −0.448842 | ||||||||
\(579\) | 3.00208e9 | 0.642758 | ||||||||
\(580\) | 2.35767e9 | 0.501748 | ||||||||
\(581\) | 2.23095e9 | 0.471926 | ||||||||
\(582\) | −1.82935e9 | −0.384650 | ||||||||
\(583\) | −5.08418e9 | −1.06263 | ||||||||
\(584\) | −1.65339e9 | −0.343503 | ||||||||
\(585\) | −9.69574e8 | −0.200233 | ||||||||
\(586\) | 2.06033e8 | 0.0422955 | ||||||||
\(587\) | 6.31504e9 | 1.28867 | 0.644336 | − | 0.764742i | \(-0.277134\pi\) | ||||
0.644336 | + | 0.764742i | \(0.277134\pi\) | |||||||
\(588\) | −1.45910e9 | −0.295982 | ||||||||
\(589\) | 3.89197e9 | 0.784812 | ||||||||
\(590\) | −1.66351e9 | −0.333459 | ||||||||
\(591\) | −3.71278e9 | −0.739848 | ||||||||
\(592\) | −2.07946e9 | −0.411931 | ||||||||
\(593\) | 4.12267e9 | 0.811872 | 0.405936 | − | 0.913902i | \(-0.366946\pi\) | ||||
0.405936 | + | 0.913902i | \(0.366946\pi\) | |||||||
\(594\) | 7.11927e8 | 0.139374 | ||||||||
\(595\) | −9.03448e8 | −0.175830 | ||||||||
\(596\) | −2.31461e8 | −0.0447833 | ||||||||
\(597\) | 4.79888e9 | 0.923060 | ||||||||
\(598\) | −2.54198e8 | −0.0486092 | ||||||||
\(599\) | 8.48783e9 | 1.61363 | 0.806813 | − | 0.590808i | \(-0.201191\pi\) | ||||
0.806813 | + | 0.590808i | \(0.201191\pi\) | |||||||
\(600\) | 1.33514e9 | 0.252346 | ||||||||
\(601\) | −1.68246e9 | −0.316144 | −0.158072 | − | 0.987428i | \(-0.550528\pi\) | ||||
−0.158072 | + | 0.987428i | \(0.550528\pi\) | |||||||
\(602\) | 9.50056e8 | 0.177485 | ||||||||
\(603\) | 1.39111e9 | 0.258376 | ||||||||
\(604\) | −3.77106e9 | −0.696361 | ||||||||
\(605\) | −8.69702e9 | −1.59671 | ||||||||
\(606\) | −1.82086e9 | −0.332371 | ||||||||
\(607\) | −2.99741e9 | −0.543984 | −0.271992 | − | 0.962299i | \(-0.587682\pi\) | ||||
−0.271992 | + | 0.962299i | \(0.587682\pi\) | |||||||
\(608\) | 9.92278e9 | 1.79048 | ||||||||
\(609\) | −9.84493e8 | −0.176625 | ||||||||
\(610\) | −1.89492e9 | −0.338016 | ||||||||
\(611\) | −2.64914e9 | −0.469851 | ||||||||
\(612\) | −3.59502e8 | −0.0633973 | ||||||||
\(613\) | 3.01310e9 | 0.528325 | 0.264163 | − | 0.964478i | \(-0.414904\pi\) | ||||
0.264163 | + | 0.964478i | \(0.414904\pi\) | |||||||
\(614\) | −2.63748e9 | −0.459832 | ||||||||
\(615\) | 2.83178e9 | 0.490904 | ||||||||
\(616\) | 4.31221e9 | 0.743306 | ||||||||
\(617\) | −1.05608e9 | −0.181008 | −0.0905040 | − | 0.995896i | \(-0.528848\pi\) | ||||
−0.0905040 | + | 0.995896i | \(0.528848\pi\) | |||||||
\(618\) | −6.69956e8 | −0.114179 | ||||||||
\(619\) | 5.70924e9 | 0.967522 | 0.483761 | − | 0.875200i | \(-0.339270\pi\) | ||||
0.483761 | + | 0.875200i | \(0.339270\pi\) | |||||||
\(620\) | 2.52597e9 | 0.425654 | ||||||||
\(621\) | 2.39483e8 | 0.0401286 | ||||||||
\(622\) | −4.44322e8 | −0.0740340 | ||||||||
\(623\) | −2.39892e9 | −0.397474 | ||||||||
\(624\) | −6.27470e8 | −0.103382 | ||||||||
\(625\) | −7.62778e9 | −1.24974 | ||||||||
\(626\) | 4.94083e8 | 0.0804989 | ||||||||
\(627\) | 9.46099e9 | 1.53285 | ||||||||
\(628\) | −5.67341e9 | −0.914083 | ||||||||
\(629\) | −1.72641e9 | −0.276609 | ||||||||
\(630\) | −7.13178e8 | −0.113633 | ||||||||
\(631\) | 1.21714e10 | 1.92858 | 0.964288 | − | 0.264856i | \(-0.0853244\pi\) | ||||
0.964288 | + | 0.264856i | \(0.0853244\pi\) | |||||||
\(632\) | 6.48142e9 | 1.02132 | ||||||||
\(633\) | −5.58654e9 | −0.875447 | ||||||||
\(634\) | −3.35826e9 | −0.523362 | ||||||||
\(635\) | −1.36009e10 | −2.10794 | ||||||||
\(636\) | 2.02666e9 | 0.312379 | ||||||||
\(637\) | −2.11432e9 | −0.324103 | ||||||||
\(638\) | −2.50855e9 | −0.382429 | ||||||||
\(639\) | −2.85317e9 | −0.432588 | ||||||||
\(640\) | 7.87250e9 | 1.18709 | ||||||||
\(641\) | −3.46116e9 | −0.519062 | −0.259531 | − | 0.965735i | \(-0.583568\pi\) | ||||
−0.259531 | + | 0.965735i | \(0.583568\pi\) | |||||||
\(642\) | 2.37768e9 | 0.354634 | ||||||||
\(643\) | 2.11373e9 | 0.313553 | 0.156777 | − | 0.987634i | \(-0.449890\pi\) | ||||
0.156777 | + | 0.987634i | \(0.449890\pi\) | |||||||
\(644\) | 6.31797e8 | 0.0932131 | ||||||||
\(645\) | 3.10603e9 | 0.455772 | ||||||||
\(646\) | 1.41389e9 | 0.206348 | ||||||||
\(647\) | 8.83366e9 | 1.28226 | 0.641130 | − | 0.767433i | \(-0.278466\pi\) | ||||
0.641130 | + | 0.767433i | \(0.278466\pi\) | |||||||
\(648\) | −6.51565e8 | −0.0940687 | ||||||||
\(649\) | −5.98070e9 | −0.858807 | ||||||||
\(650\) | 8.42653e8 | 0.120352 | ||||||||
\(651\) | −1.05477e9 | −0.149839 | ||||||||
\(652\) | 3.30107e9 | 0.466431 | ||||||||
\(653\) | −5.02955e9 | −0.706859 | −0.353430 | − | 0.935461i | \(-0.614985\pi\) | ||||
−0.353430 | + | 0.935461i | \(0.614985\pi\) | |||||||
\(654\) | −1.59743e9 | −0.223306 | ||||||||
\(655\) | 8.99465e7 | 0.0125066 | ||||||||
\(656\) | 1.83262e9 | 0.253459 | ||||||||
\(657\) | 9.83105e8 | 0.135245 | ||||||||
\(658\) | −1.94859e9 | −0.266643 | ||||||||
\(659\) | 3.65728e9 | 0.497805 | 0.248902 | − | 0.968529i | \(-0.419930\pi\) | ||||
0.248902 | + | 0.968529i | \(0.419930\pi\) | |||||||
\(660\) | 6.14038e9 | 0.831365 | ||||||||
\(661\) | 8.02439e9 | 1.08070 | 0.540352 | − | 0.841439i | \(-0.318291\pi\) | ||||
0.540352 | + | 0.841439i | \(0.318291\pi\) | |||||||
\(662\) | 5.12829e9 | 0.687020 | ||||||||
\(663\) | −5.20938e8 | −0.0694206 | ||||||||
\(664\) | −5.20262e9 | −0.689658 | ||||||||
\(665\) | −9.47761e9 | −1.24975 | ||||||||
\(666\) | −1.36282e9 | −0.178763 | ||||||||
\(667\) | −8.43843e8 | −0.110109 | ||||||||
\(668\) | −9.55330e9 | −1.24004 | ||||||||
\(669\) | 3.69588e9 | 0.477229 | ||||||||
\(670\) | −3.55087e9 | −0.456114 | ||||||||
\(671\) | −6.81268e9 | −0.870541 | ||||||||
\(672\) | −2.68919e9 | −0.341845 | ||||||||
\(673\) | −6.32514e9 | −0.799867 | −0.399933 | − | 0.916544i | \(-0.630967\pi\) | ||||
−0.399933 | + | 0.916544i | \(0.630967\pi\) | |||||||
\(674\) | −3.71412e9 | −0.467247 | ||||||||
\(675\) | −7.93872e8 | −0.0993545 | ||||||||
\(676\) | 4.72273e9 | 0.588003 | ||||||||
\(677\) | −7.59623e9 | −0.940888 | −0.470444 | − | 0.882430i | \(-0.655906\pi\) | ||||
−0.470444 | + | 0.882430i | \(0.655906\pi\) | |||||||
\(678\) | −4.22863e9 | −0.521070 | ||||||||
\(679\) | 6.58848e9 | 0.807683 | ||||||||
\(680\) | 2.10686e9 | 0.256953 | ||||||||
\(681\) | −7.00057e9 | −0.849412 | ||||||||
\(682\) | −2.68762e9 | −0.324431 | ||||||||
\(683\) | −1.36892e10 | −1.64402 | −0.822008 | − | 0.569476i | \(-0.807146\pi\) | ||||
−0.822008 | + | 0.569476i | \(0.807146\pi\) | |||||||
\(684\) | −3.77135e9 | −0.450609 | ||||||||
\(685\) | 1.28759e10 | 1.53059 | ||||||||
\(686\) | −3.89606e9 | −0.460778 | ||||||||
\(687\) | −7.40881e9 | −0.871766 | ||||||||
\(688\) | 2.01010e9 | 0.235320 | ||||||||
\(689\) | 2.93674e9 | 0.342057 | ||||||||
\(690\) | −6.11290e8 | −0.0708395 | ||||||||
\(691\) | 7.98642e9 | 0.920829 | 0.460414 | − | 0.887704i | \(-0.347701\pi\) | ||||
0.460414 | + | 0.887704i | \(0.347701\pi\) | |||||||
\(692\) | 4.42545e9 | 0.507675 | ||||||||
\(693\) | −2.56404e9 | −0.292657 | ||||||||
\(694\) | 6.52523e8 | 0.0741033 | ||||||||
\(695\) | −1.34488e10 | −1.51963 | ||||||||
\(696\) | 2.29586e9 | 0.258114 | ||||||||
\(697\) | 1.52147e9 | 0.170196 | ||||||||
\(698\) | −5.15903e9 | −0.574214 | ||||||||
\(699\) | 4.45758e9 | 0.493661 | ||||||||
\(700\) | −2.09437e9 | −0.230786 | ||||||||
\(701\) | 1.29422e10 | 1.41904 | 0.709520 | − | 0.704685i | \(-0.248912\pi\) | ||||
0.709520 | + | 0.704685i | \(0.248912\pi\) | |||||||
\(702\) | −4.11226e8 | −0.0448643 | ||||||||
\(703\) | −1.81108e10 | −1.96605 | ||||||||
\(704\) | −1.70238e9 | −0.183887 | ||||||||
\(705\) | −6.37057e9 | −0.684725 | ||||||||
\(706\) | −1.95768e9 | −0.209375 | ||||||||
\(707\) | 6.55792e9 | 0.697908 | ||||||||
\(708\) | 2.38403e9 | 0.252462 | ||||||||
\(709\) | −1.36942e9 | −0.144303 | −0.0721513 | − | 0.997394i | \(-0.522986\pi\) | ||||
−0.0721513 | + | 0.997394i | \(0.522986\pi\) | |||||||
\(710\) | 7.28283e9 | 0.763652 | ||||||||
\(711\) | −3.85385e9 | −0.402116 | ||||||||
\(712\) | 5.59433e9 | 0.580856 | ||||||||
\(713\) | −9.04080e8 | −0.0934100 | ||||||||
\(714\) | −3.83180e8 | −0.0393966 | ||||||||
\(715\) | 8.89775e9 | 0.910351 | ||||||||
\(716\) | −7.08411e9 | −0.721257 | ||||||||
\(717\) | −8.35468e9 | −0.846473 | ||||||||
\(718\) | 3.12323e9 | 0.314897 | ||||||||
\(719\) | 1.52783e10 | 1.53294 | 0.766470 | − | 0.642280i | \(-0.222012\pi\) | ||||
0.766470 | + | 0.642280i | \(0.222012\pi\) | |||||||
\(720\) | −1.50892e9 | −0.150662 | ||||||||
\(721\) | 2.41288e9 | 0.239752 | ||||||||
\(722\) | 9.99961e9 | 0.988787 | ||||||||
\(723\) | −1.80899e8 | −0.0178013 | ||||||||
\(724\) | 1.34366e10 | 1.31584 | ||||||||
\(725\) | 2.79729e9 | 0.272618 | ||||||||
\(726\) | −3.68867e9 | −0.357760 | ||||||||
\(727\) | 4.60649e9 | 0.444631 | 0.222315 | − | 0.974975i | \(-0.428639\pi\) | ||||
0.222315 | + | 0.974975i | \(0.428639\pi\) | |||||||
\(728\) | −2.49083e9 | −0.239268 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −2.50941e9 | −0.238749 | ||||||||
\(731\) | 1.66883e9 | 0.158016 | ||||||||
\(732\) | 2.71568e9 | 0.255911 | ||||||||
\(733\) | −1.57570e10 | −1.47778 | −0.738888 | − | 0.673829i | \(-0.764649\pi\) | ||||
−0.738888 | + | 0.673829i | \(0.764649\pi\) | |||||||
\(734\) | 4.35531e9 | 0.406521 | ||||||||
\(735\) | −5.08446e9 | −0.472323 | ||||||||
\(736\) | −2.30500e9 | −0.213107 | ||||||||
\(737\) | −1.27662e10 | −1.17470 | ||||||||
\(738\) | 1.20104e9 | 0.109992 | ||||||||
\(739\) | −1.35450e10 | −1.23459 | −0.617296 | − | 0.786731i | \(-0.711772\pi\) | ||||
−0.617296 | + | 0.786731i | \(0.711772\pi\) | |||||||
\(740\) | −1.17543e10 | −1.06632 | ||||||||
\(741\) | −5.46489e9 | −0.493421 | ||||||||
\(742\) | 2.16015e9 | 0.194120 | ||||||||
\(743\) | −1.32438e10 | −1.18455 | −0.592273 | − | 0.805738i | \(-0.701769\pi\) | ||||
−0.592273 | + | 0.805738i | \(0.701769\pi\) | |||||||
\(744\) | 2.45974e9 | 0.218970 | ||||||||
\(745\) | −8.06561e8 | −0.0714645 | ||||||||
\(746\) | 8.30908e9 | 0.732769 | ||||||||
\(747\) | 3.09348e9 | 0.271534 | ||||||||
\(748\) | 3.29914e9 | 0.288234 | ||||||||
\(749\) | −8.56331e9 | −0.744656 | ||||||||
\(750\) | −1.89874e9 | −0.164343 | ||||||||
\(751\) | 1.68901e10 | 1.45510 | 0.727548 | − | 0.686057i | \(-0.240660\pi\) | ||||
0.727548 | + | 0.686057i | \(0.240660\pi\) | |||||||
\(752\) | −4.12278e9 | −0.353531 | ||||||||
\(753\) | 8.59607e9 | 0.733698 | ||||||||
\(754\) | 1.44900e9 | 0.123103 | ||||||||
\(755\) | −1.31408e10 | −1.11124 | ||||||||
\(756\) | 1.02208e9 | 0.0860318 | ||||||||
\(757\) | −1.85508e10 | −1.55427 | −0.777134 | − | 0.629335i | \(-0.783327\pi\) | ||||
−0.777134 | + | 0.629335i | \(0.783327\pi\) | |||||||
\(758\) | 8.01253e9 | 0.668232 | ||||||||
\(759\) | −2.19773e9 | −0.182443 | ||||||||
\(760\) | 2.21019e10 | 1.82635 | ||||||||
\(761\) | 7.79417e9 | 0.641097 | 0.320548 | − | 0.947232i | \(-0.396133\pi\) | ||||
0.320548 | + | 0.947232i | \(0.396133\pi\) | |||||||
\(762\) | −5.76855e9 | −0.472307 | ||||||||
\(763\) | 5.75322e9 | 0.468894 | ||||||||
\(764\) | −6.33111e9 | −0.513633 | ||||||||
\(765\) | −1.25274e9 | −0.101168 | ||||||||
\(766\) | −4.68569e9 | −0.376680 | ||||||||
\(767\) | 3.45459e9 | 0.276448 | ||||||||
\(768\) | 4.21840e9 | 0.336035 | ||||||||
\(769\) | −3.68753e9 | −0.292411 | −0.146205 | − | 0.989254i | \(-0.546706\pi\) | ||||
−0.146205 | + | 0.989254i | \(0.546706\pi\) | |||||||
\(770\) | 6.54481e9 | 0.516630 | ||||||||
\(771\) | 5.78470e9 | 0.454559 | ||||||||
\(772\) | 1.09820e10 | 0.859055 | ||||||||
\(773\) | −9.90277e8 | −0.0771132 | −0.0385566 | − | 0.999256i | \(-0.512276\pi\) | ||||
−0.0385566 | + | 0.999256i | \(0.512276\pi\) | |||||||
\(774\) | 1.31736e9 | 0.102120 | ||||||||
\(775\) | 2.99697e9 | 0.231274 | ||||||||
\(776\) | −1.53644e10 | −1.18032 | ||||||||
\(777\) | 4.90825e9 | 0.375365 | ||||||||
\(778\) | −7.48724e9 | −0.570024 | ||||||||
\(779\) | 1.59610e10 | 1.20970 | ||||||||
\(780\) | −3.54683e9 | −0.267614 | ||||||||
\(781\) | 2.61834e10 | 1.96675 | ||||||||
\(782\) | −3.28437e8 | −0.0245600 | ||||||||
\(783\) | −1.36512e9 | −0.101626 | ||||||||
\(784\) | −3.29046e9 | −0.243866 | ||||||||
\(785\) | −1.97699e10 | −1.45868 | ||||||||
\(786\) | 3.81491e7 | 0.00280224 | ||||||||
\(787\) | −3.85492e9 | −0.281905 | −0.140953 | − | 0.990016i | \(-0.545017\pi\) | ||||
−0.140953 | + | 0.990016i | \(0.545017\pi\) | |||||||
\(788\) | −1.35818e10 | −0.988818 | ||||||||
\(789\) | 1.11555e8 | 0.00808570 | ||||||||
\(790\) | 9.83711e9 | 0.709860 | ||||||||
\(791\) | 1.52296e10 | 1.09414 | ||||||||
\(792\) | 5.97939e9 | 0.427680 | ||||||||
\(793\) | 3.93517e9 | 0.280225 | ||||||||
\(794\) | −5.39041e9 | −0.382164 | ||||||||
\(795\) | 7.06220e9 | 0.498489 | ||||||||
\(796\) | 1.75549e10 | 1.23368 | ||||||||
\(797\) | 2.68172e8 | 0.0187633 | 0.00938164 | − | 0.999956i | \(-0.497014\pi\) | ||||
0.00938164 | + | 0.999956i | \(0.497014\pi\) | |||||||
\(798\) | −4.01974e9 | −0.280020 | ||||||||
\(799\) | −3.42281e9 | −0.237394 | ||||||||
\(800\) | 7.64094e9 | 0.527633 | ||||||||
\(801\) | −3.32639e9 | −0.228696 | ||||||||
\(802\) | 1.18601e10 | 0.811854 | ||||||||
\(803\) | −9.02192e9 | −0.614886 | ||||||||
\(804\) | 5.08888e9 | 0.345323 | ||||||||
\(805\) | 2.20159e9 | 0.148748 | ||||||||
\(806\) | 1.55243e9 | 0.104434 | ||||||||
\(807\) | 5.61046e9 | 0.375786 | ||||||||
\(808\) | −1.52932e10 | −1.01990 | ||||||||
\(809\) | 1.50724e10 | 1.00083 | 0.500416 | − | 0.865785i | \(-0.333180\pi\) | ||||
0.500416 | + | 0.865785i | \(0.333180\pi\) | |||||||
\(810\) | −9.88906e8 | −0.0653819 | ||||||||
\(811\) | −2.54700e10 | −1.67670 | −0.838352 | − | 0.545130i | \(-0.816480\pi\) | ||||
−0.838352 | + | 0.545130i | \(0.816480\pi\) | |||||||
\(812\) | −3.60141e9 | −0.236062 | ||||||||
\(813\) | 4.87331e8 | 0.0318058 | ||||||||
\(814\) | 1.25065e10 | 0.812740 | ||||||||
\(815\) | 1.15031e10 | 0.744323 | ||||||||
\(816\) | −8.10722e8 | −0.0522344 | ||||||||
\(817\) | 1.75068e10 | 1.12313 | ||||||||
\(818\) | 1.72400e9 | 0.110129 | ||||||||
\(819\) | 1.48105e9 | 0.0942055 | ||||||||
\(820\) | 1.03590e10 | 0.656100 | ||||||||
\(821\) | −8.54784e9 | −0.539083 | −0.269541 | − | 0.962989i | \(-0.586872\pi\) | ||||
−0.269541 | + | 0.962989i | \(0.586872\pi\) | |||||||
\(822\) | 5.46105e9 | 0.342945 | ||||||||
\(823\) | 9.89326e8 | 0.0618643 | 0.0309321 | − | 0.999521i | \(-0.490152\pi\) | ||||
0.0309321 | + | 0.999521i | \(0.490152\pi\) | |||||||
\(824\) | −5.62688e9 | −0.350366 | ||||||||
\(825\) | 7.28534e9 | 0.451711 | ||||||||
\(826\) | 2.54105e9 | 0.156886 | ||||||||
\(827\) | 2.72623e10 | 1.67608 | 0.838038 | − | 0.545612i | \(-0.183703\pi\) | ||||
0.838038 | + | 0.545612i | \(0.183703\pi\) | |||||||
\(828\) | 8.76060e8 | 0.0536325 | ||||||||
\(829\) | −1.87927e10 | −1.14564 | −0.572821 | − | 0.819681i | \(-0.694151\pi\) | ||||
−0.572821 | + | 0.819681i | \(0.694151\pi\) | |||||||
\(830\) | −7.89622e9 | −0.479342 | ||||||||
\(831\) | 4.17929e9 | 0.252638 | ||||||||
\(832\) | 9.83334e8 | 0.0591928 | ||||||||
\(833\) | −2.73180e9 | −0.163754 | ||||||||
\(834\) | −5.70406e9 | −0.340489 | ||||||||
\(835\) | −3.32899e10 | −1.97884 | ||||||||
\(836\) | 3.46095e10 | 2.04868 | ||||||||
\(837\) | −1.46256e9 | −0.0862135 | ||||||||
\(838\) | −4.31471e9 | −0.253278 | ||||||||
\(839\) | −1.42627e10 | −0.833749 | −0.416874 | − | 0.908964i | \(-0.636875\pi\) | ||||
−0.416874 | + | 0.908964i | \(0.636875\pi\) | |||||||
\(840\) | −5.98989e9 | −0.348692 | ||||||||
\(841\) | −1.24398e10 | −0.721150 | ||||||||
\(842\) | 1.46296e10 | 0.844578 | ||||||||
\(843\) | 1.24833e10 | 0.717686 | ||||||||
\(844\) | −2.04363e10 | −1.17005 | ||||||||
\(845\) | 1.64571e10 | 0.938326 | ||||||||
\(846\) | −2.70195e9 | −0.153420 | ||||||||
\(847\) | 1.32849e10 | 0.751221 | ||||||||
\(848\) | 4.57038e9 | 0.257375 | ||||||||
\(849\) | −1.65611e10 | −0.928778 | ||||||||
\(850\) | 1.08875e9 | 0.0608081 | ||||||||
\(851\) | 4.20703e9 | 0.234004 | ||||||||
\(852\) | −1.04373e10 | −0.578160 | ||||||||
\(853\) | 1.24913e10 | 0.689108 | 0.344554 | − | 0.938766i | \(-0.388030\pi\) | ||||
0.344554 | + | 0.938766i | \(0.388030\pi\) | |||||||
\(854\) | 2.89454e9 | 0.159029 | ||||||||
\(855\) | −1.31418e10 | −0.719075 | ||||||||
\(856\) | 1.99698e10 | 1.08822 | ||||||||
\(857\) | −1.94250e10 | −1.05421 | −0.527106 | − | 0.849800i | \(-0.676723\pi\) | ||||
−0.527106 | + | 0.849800i | \(0.676723\pi\) | |||||||
\(858\) | 3.77381e9 | 0.203974 | ||||||||
\(859\) | −3.37547e10 | −1.81701 | −0.908506 | − | 0.417873i | \(-0.862776\pi\) | ||||
−0.908506 | + | 0.417873i | \(0.862776\pi\) | |||||||
\(860\) | 1.13623e10 | 0.609145 | ||||||||
\(861\) | −4.32562e9 | −0.230960 | ||||||||
\(862\) | 2.36727e9 | 0.125884 | ||||||||
\(863\) | −1.20894e10 | −0.640278 | −0.320139 | − | 0.947371i | \(-0.603730\pi\) | ||||
−0.320139 | + | 0.947371i | \(0.603730\pi\) | |||||||
\(864\) | −3.72888e9 | −0.196689 | ||||||||
\(865\) | 1.54211e10 | 0.810140 | ||||||||
\(866\) | −4.67307e9 | −0.244506 | ||||||||
\(867\) | 1.04061e10 | 0.542275 | ||||||||
\(868\) | −3.85849e9 | −0.200262 | ||||||||
\(869\) | 3.53667e10 | 1.82821 | ||||||||
\(870\) | 3.48451e9 | 0.179401 | ||||||||
\(871\) | 7.37407e9 | 0.378132 | ||||||||
\(872\) | −1.34166e10 | −0.685228 | ||||||||
\(873\) | 9.13570e9 | 0.464721 | ||||||||
\(874\) | −3.44546e9 | −0.174565 | ||||||||
\(875\) | 6.83839e9 | 0.345085 | ||||||||
\(876\) | 3.59633e9 | 0.180757 | ||||||||
\(877\) | −3.99637e9 | −0.200063 | −0.100032 | − | 0.994984i | \(-0.531894\pi\) | ||||
−0.100032 | + | 0.994984i | \(0.531894\pi\) | |||||||
\(878\) | 6.47069e8 | 0.0322641 | ||||||||
\(879\) | −1.02892e9 | −0.0511000 | ||||||||
\(880\) | 1.38473e10 | 0.684979 | ||||||||
\(881\) | 1.00727e10 | 0.496286 | 0.248143 | − | 0.968723i | \(-0.420180\pi\) | ||||
0.248143 | + | 0.968723i | \(0.420180\pi\) | |||||||
\(882\) | −2.15647e9 | −0.105829 | ||||||||
\(883\) | −1.22925e10 | −0.600868 | −0.300434 | − | 0.953803i | \(-0.597131\pi\) | ||||
−0.300434 | + | 0.953803i | \(0.597131\pi\) | |||||||
\(884\) | −1.90566e9 | −0.0927817 | ||||||||
\(885\) | 8.30751e9 | 0.402874 | ||||||||
\(886\) | 1.48045e10 | 0.715114 | ||||||||
\(887\) | −2.39436e10 | −1.15201 | −0.576005 | − | 0.817446i | \(-0.695389\pi\) | ||||
−0.576005 | + | 0.817446i | \(0.695389\pi\) | |||||||
\(888\) | −1.14461e10 | −0.548546 | ||||||||
\(889\) | 2.07757e10 | 0.991744 | ||||||||
\(890\) | 8.49074e9 | 0.403720 | ||||||||
\(891\) | −3.55534e9 | −0.168387 | ||||||||
\(892\) | 1.35200e10 | 0.637824 | ||||||||
\(893\) | −3.59070e10 | −1.68732 | ||||||||
\(894\) | −3.42087e8 | −0.0160124 | ||||||||
\(895\) | −2.46856e10 | −1.15097 | ||||||||
\(896\) | −1.20255e10 | −0.558501 | ||||||||
\(897\) | 1.26946e9 | 0.0587280 | ||||||||
\(898\) | −5.95354e9 | −0.274352 | ||||||||
\(899\) | 5.15349e9 | 0.236561 | ||||||||
\(900\) | −2.90409e9 | −0.132789 | ||||||||
\(901\) | 3.79442e9 | 0.172826 | ||||||||
\(902\) | −1.10219e10 | −0.500075 | ||||||||
\(903\) | −4.74455e9 | −0.214431 | ||||||||
\(904\) | −3.55157e10 | −1.59894 | ||||||||
\(905\) | 4.68217e10 | 2.09980 | ||||||||
\(906\) | −5.57343e9 | −0.248985 | ||||||||
\(907\) | 3.93573e10 | 1.75146 | 0.875729 | − | 0.482804i | \(-0.160382\pi\) | ||||
0.875729 | + | 0.482804i | \(0.160382\pi\) | |||||||
\(908\) | −2.56090e10 | −1.13525 | ||||||||
\(909\) | 9.09333e9 | 0.401559 | ||||||||
\(910\) | −3.78044e9 | −0.166302 | ||||||||
\(911\) | 1.01487e10 | 0.444730 | 0.222365 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(912\) | −8.50487e9 | −0.371266 | ||||||||
\(913\) | −2.83887e10 | −1.23452 | ||||||||
\(914\) | 1.07250e10 | 0.464607 | ||||||||
\(915\) | 9.46319e9 | 0.408379 | ||||||||
\(916\) | −2.71024e10 | −1.16513 | ||||||||
\(917\) | −1.37396e8 | −0.00588410 | ||||||||
\(918\) | −5.31324e8 | −0.0226678 | ||||||||
\(919\) | 7.75386e9 | 0.329544 | 0.164772 | − | 0.986332i | \(-0.447311\pi\) | ||||
0.164772 | + | 0.986332i | \(0.447311\pi\) | |||||||
\(920\) | −5.13414e9 | −0.217376 | ||||||||
\(921\) | 1.31715e10 | 0.555554 | ||||||||
\(922\) | −4.29867e9 | −0.180624 | ||||||||
\(923\) | −1.51242e10 | −0.633090 | ||||||||
\(924\) | −9.37960e9 | −0.391140 | ||||||||
\(925\) | −1.39461e10 | −0.579370 | ||||||||
\(926\) | −4.15898e9 | −0.172127 | ||||||||
\(927\) | 3.34574e9 | 0.137947 | ||||||||
\(928\) | 1.31391e10 | 0.539694 | ||||||||
\(929\) | 8.63007e9 | 0.353150 | 0.176575 | − | 0.984287i | \(-0.443498\pi\) | ||||
0.176575 | + | 0.984287i | \(0.443498\pi\) | |||||||
\(930\) | 3.73325e9 | 0.152194 | ||||||||
\(931\) | −2.86579e10 | −1.16391 | ||||||||
\(932\) | 1.63064e10 | 0.659785 | ||||||||
\(933\) | 2.21893e9 | 0.0894454 | ||||||||
\(934\) | −1.27762e10 | −0.513084 | ||||||||
\(935\) | 1.14963e10 | 0.459958 | ||||||||
\(936\) | −3.45384e9 | −0.137669 | ||||||||
\(937\) | −1.83344e10 | −0.728076 | −0.364038 | − | 0.931384i | \(-0.618602\pi\) | ||||
−0.364038 | + | 0.931384i | \(0.618602\pi\) | |||||||
\(938\) | 5.42406e9 | 0.214592 | ||||||||
\(939\) | −2.46744e9 | −0.0972561 | ||||||||
\(940\) | −2.33044e10 | −0.915145 | ||||||||
\(941\) | −1.16186e10 | −0.454559 | −0.227279 | − | 0.973830i | \(-0.572983\pi\) | ||||
−0.227279 | + | 0.973830i | \(0.572983\pi\) | |||||||
\(942\) | −8.38500e9 | −0.326832 | ||||||||
\(943\) | −3.70764e9 | −0.143981 | ||||||||
\(944\) | 5.37629e9 | 0.208008 | ||||||||
\(945\) | 3.56159e9 | 0.137288 | ||||||||
\(946\) | −1.20894e10 | −0.464286 | ||||||||
\(947\) | −3.46540e10 | −1.32595 | −0.662977 | − | 0.748640i | \(-0.730707\pi\) | ||||
−0.662977 | + | 0.748640i | \(0.730707\pi\) | |||||||
\(948\) | −1.40979e10 | −0.537434 | ||||||||
\(949\) | 5.21128e9 | 0.197930 | ||||||||
\(950\) | 1.14215e10 | 0.432206 | ||||||||
\(951\) | 1.67711e10 | 0.632308 | ||||||||
\(952\) | −3.21828e9 | −0.120891 | ||||||||
\(953\) | 2.12304e10 | 0.794571 | 0.397285 | − | 0.917695i | \(-0.369952\pi\) | ||||
0.397285 | + | 0.917695i | \(0.369952\pi\) | |||||||
\(954\) | 2.99530e9 | 0.111692 | ||||||||
\(955\) | −2.20617e10 | −0.819647 | ||||||||
\(956\) | −3.05625e10 | −1.13132 | ||||||||
\(957\) | 1.25276e10 | 0.462037 | ||||||||
\(958\) | −1.68600e10 | −0.619554 | ||||||||
\(959\) | −1.96682e10 | −0.720113 | ||||||||
\(960\) | 2.36469e9 | 0.0862632 | ||||||||
\(961\) | −2.19913e10 | −0.799315 | ||||||||
\(962\) | −7.22407e9 | −0.261619 | ||||||||
\(963\) | −1.18740e10 | −0.428456 | ||||||||
\(964\) | −6.61751e8 | −0.0237917 | ||||||||
\(965\) | 3.82684e10 | 1.37087 | ||||||||
\(966\) | 9.33761e8 | 0.0333285 | ||||||||
\(967\) | −7.36471e9 | −0.261917 | −0.130958 | − | 0.991388i | \(-0.541805\pi\) | ||||
−0.130958 | + | 0.991388i | \(0.541805\pi\) | |||||||
\(968\) | −3.09807e10 | −1.09781 | ||||||||
\(969\) | −7.06090e9 | −0.249303 | ||||||||
\(970\) | −2.33192e10 | −0.820376 | ||||||||
\(971\) | 2.52233e10 | 0.884167 | 0.442084 | − | 0.896974i | \(-0.354239\pi\) | ||||
0.442084 | + | 0.896974i | \(0.354239\pi\) | |||||||
\(972\) | 1.41723e9 | 0.0495005 | ||||||||
\(973\) | 2.05435e10 | 0.714955 | ||||||||
\(974\) | −2.04111e10 | −0.707798 | ||||||||
\(975\) | −4.20818e9 | −0.145405 | ||||||||
\(976\) | 6.12420e9 | 0.210851 | ||||||||
\(977\) | −1.66661e10 | −0.571745 | −0.285872 | − | 0.958268i | \(-0.592283\pi\) | ||||
−0.285872 | + | 0.958268i | \(0.592283\pi\) | |||||||
\(978\) | 4.87880e9 | 0.166773 | ||||||||
\(979\) | 3.05262e10 | 1.03976 | ||||||||
\(980\) | −1.85996e10 | −0.631267 | ||||||||
\(981\) | 7.97751e9 | 0.269790 | ||||||||
\(982\) | 6.58677e9 | 0.221964 | ||||||||
\(983\) | 1.86831e10 | 0.627354 | 0.313677 | − | 0.949530i | \(-0.398439\pi\) | ||||
0.313677 | + | 0.949530i | \(0.398439\pi\) | |||||||
\(984\) | 1.00874e10 | 0.337518 | ||||||||
\(985\) | −4.73279e10 | −1.57794 | ||||||||
\(986\) | 1.87218e9 | 0.0621981 | ||||||||
\(987\) | 9.73122e9 | 0.322149 | ||||||||
\(988\) | −1.99913e10 | −0.659464 | ||||||||
\(989\) | −4.06672e9 | −0.133677 | ||||||||
\(990\) | 9.07515e9 | 0.297256 | ||||||||
\(991\) | 3.89119e10 | 1.27006 | 0.635031 | − | 0.772487i | \(-0.280987\pi\) | ||||
0.635031 | + | 0.772487i | \(0.280987\pi\) | |||||||
\(992\) | 1.40770e10 | 0.457846 | ||||||||
\(993\) | −2.56105e10 | −0.830034 | ||||||||
\(994\) | −1.11247e10 | −0.359283 | ||||||||
\(995\) | 6.11728e10 | 1.96869 | ||||||||
\(996\) | 1.13163e10 | 0.362910 | ||||||||
\(997\) | −4.49037e10 | −1.43499 | −0.717496 | − | 0.696563i | \(-0.754712\pi\) | ||||
−0.717496 | + | 0.696563i | \(0.754712\pi\) | |||||||
\(998\) | −2.57475e10 | −0.819932 | ||||||||
\(999\) | 6.80587e9 | 0.215975 |
(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 | 69.8.a.c.1.5 | ✓ | 7 | |
3.2 | odd | 2 | 207.8.a.d.1.3 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.c.1.5 | ✓ | 7 | 1.1 | even | 1 | trivial | |
207.8.a.d.1.3 | 7 | 3.2 | odd | 2 |