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 | 1.6 | ||
Root | \(15.1764\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.1764 | 1.34141 | 0.670707 | − | 0.741722i | \(-0.265991\pi\) | ||||
0.670707 | + | 0.741722i | \(0.265991\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 102.322 | 0.799392 | ||||||||
\(5\) | 149.395 | 0.534491 | 0.267246 | − | 0.963628i | \(-0.413886\pi\) | ||||
0.267246 | + | 0.963628i | \(0.413886\pi\) | |||||||
\(6\) | −409.762 | −0.774466 | ||||||||
\(7\) | −45.6786 | −0.0503349 | −0.0251675 | − | 0.999683i | \(-0.508012\pi\) | ||||
−0.0251675 | + | 0.999683i | \(0.508012\pi\) | |||||||
\(8\) | −389.696 | −0.269098 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 2267.27 | 0.716974 | ||||||||
\(11\) | 6854.49 | 1.55275 | 0.776373 | − | 0.630274i | \(-0.217057\pi\) | ||||
0.776373 | + | 0.630274i | \(0.217057\pi\) | |||||||
\(12\) | −2762.70 | −0.461529 | ||||||||
\(13\) | 12280.7 | 1.55032 | 0.775160 | − | 0.631765i | \(-0.217669\pi\) | ||||
0.775160 | + | 0.631765i | \(0.217669\pi\) | |||||||
\(14\) | −693.235 | −0.0675200 | ||||||||
\(15\) | −4033.66 | −0.308589 | ||||||||
\(16\) | −19011.4 | −1.16036 | ||||||||
\(17\) | 7816.83 | 0.385886 | 0.192943 | − | 0.981210i | \(-0.438197\pi\) | ||||
0.192943 | + | 0.981210i | \(0.438197\pi\) | |||||||
\(18\) | 11063.6 | 0.447138 | ||||||||
\(19\) | 17025.7 | 0.569465 | 0.284733 | − | 0.958607i | \(-0.408095\pi\) | ||||
0.284733 | + | 0.958607i | \(0.408095\pi\) | |||||||
\(20\) | 15286.4 | 0.427268 | ||||||||
\(21\) | 1233.32 | 0.0290609 | ||||||||
\(22\) | 104026. | 2.08288 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | 10521.8 | 0.155364 | ||||||||
\(25\) | −55806.2 | −0.714319 | ||||||||
\(26\) | 186376. | 2.07962 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −4673.93 | −0.0402374 | ||||||||
\(29\) | 232578. | 1.77083 | 0.885414 | − | 0.464803i | \(-0.153875\pi\) | ||||
0.885414 | + | 0.464803i | \(0.153875\pi\) | |||||||
\(30\) | −61216.3 | −0.413945 | ||||||||
\(31\) | 317034. | 1.91135 | 0.955676 | − | 0.294422i | \(-0.0951271\pi\) | ||||
0.955676 | + | 0.294422i | \(0.0951271\pi\) | |||||||
\(32\) | −238643. | −1.28743 | ||||||||
\(33\) | −185071. | −0.896478 | ||||||||
\(34\) | 118631. | 0.517633 | ||||||||
\(35\) | −6824.15 | −0.0269036 | ||||||||
\(36\) | 74592.9 | 0.266464 | ||||||||
\(37\) | −180572. | −0.586064 | −0.293032 | − | 0.956103i | \(-0.594664\pi\) | ||||
−0.293032 | + | 0.956103i | \(0.594664\pi\) | |||||||
\(38\) | 258388. | 0.763889 | ||||||||
\(39\) | −331579. | −0.895078 | ||||||||
\(40\) | −58218.5 | −0.143831 | ||||||||
\(41\) | −313962. | −0.711432 | −0.355716 | − | 0.934594i | \(-0.615763\pi\) | ||||
−0.355716 | + | 0.934594i | \(0.615763\pi\) | |||||||
\(42\) | 18717.3 | 0.0389827 | ||||||||
\(43\) | −659855. | −1.26564 | −0.632818 | − | 0.774301i | \(-0.718102\pi\) | ||||
−0.632818 | + | 0.774301i | \(0.718102\pi\) | |||||||
\(44\) | 701366. | 1.24125 | ||||||||
\(45\) | 108909. | 0.178164 | ||||||||
\(46\) | −184651. | −0.279704 | ||||||||
\(47\) | 553964. | 0.778286 | 0.389143 | − | 0.921177i | \(-0.372771\pi\) | ||||
0.389143 | + | 0.921177i | \(0.372771\pi\) | |||||||
\(48\) | 513308. | 0.669937 | ||||||||
\(49\) | −821456. | −0.997466 | ||||||||
\(50\) | −846935. | −0.958198 | ||||||||
\(51\) | −211054. | −0.222792 | ||||||||
\(52\) | 1.25659e6 | 1.23931 | ||||||||
\(53\) | 839775. | 0.774814 | 0.387407 | − | 0.921909i | \(-0.373371\pi\) | ||||
0.387407 | + | 0.921909i | \(0.373371\pi\) | |||||||
\(54\) | −298716. | −0.258155 | ||||||||
\(55\) | 1.02402e6 | 0.829929 | ||||||||
\(56\) | 17800.8 | 0.0135450 | ||||||||
\(57\) | −459694. | −0.328781 | ||||||||
\(58\) | 3.52970e6 | 2.37541 | ||||||||
\(59\) | −166614. | −0.105616 | −0.0528081 | − | 0.998605i | \(-0.516817\pi\) | ||||
−0.0528081 | + | 0.998605i | \(0.516817\pi\) | |||||||
\(60\) | −412733. | −0.246683 | ||||||||
\(61\) | −1.79776e6 | −1.01409 | −0.507045 | − | 0.861920i | \(-0.669262\pi\) | ||||
−0.507045 | + | 0.861920i | \(0.669262\pi\) | |||||||
\(62\) | 4.81143e6 | 2.56391 | ||||||||
\(63\) | −33299.7 | −0.0167783 | ||||||||
\(64\) | −1.18828e6 | −0.566614 | ||||||||
\(65\) | 1.83467e6 | 0.828633 | ||||||||
\(66\) | −2.80871e6 | −1.20255 | ||||||||
\(67\) | −4.71895e6 | −1.91683 | −0.958415 | − | 0.285380i | \(-0.907880\pi\) | ||||
−0.958415 | + | 0.285380i | \(0.907880\pi\) | |||||||
\(68\) | 799835. | 0.308474 | ||||||||
\(69\) | 328509. | 0.120386 | ||||||||
\(70\) | −103566. | −0.0360889 | ||||||||
\(71\) | −1.33587e6 | −0.442954 | −0.221477 | − | 0.975166i | \(-0.571088\pi\) | ||||
−0.221477 | + | 0.975166i | \(0.571088\pi\) | |||||||
\(72\) | −284088. | −0.0896994 | ||||||||
\(73\) | −2.18765e6 | −0.658186 | −0.329093 | − | 0.944298i | \(-0.606743\pi\) | ||||
−0.329093 | + | 0.944298i | \(0.606743\pi\) | |||||||
\(74\) | −2.74043e6 | −0.786155 | ||||||||
\(75\) | 1.50677e6 | 0.412412 | ||||||||
\(76\) | 1.74211e6 | 0.455226 | ||||||||
\(77\) | −313103. | −0.0781574 | ||||||||
\(78\) | −5.03216e6 | −1.20067 | ||||||||
\(79\) | 8.31933e6 | 1.89842 | 0.949212 | − | 0.314636i | \(-0.101882\pi\) | ||||
0.949212 | + | 0.314636i | \(0.101882\pi\) | |||||||
\(80\) | −2.84021e6 | −0.620205 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −4.76480e6 | −0.954324 | ||||||||
\(83\) | −5.82314e6 | −1.11785 | −0.558926 | − | 0.829218i | \(-0.688786\pi\) | ||||
−0.558926 | + | 0.829218i | \(0.688786\pi\) | |||||||
\(84\) | 126196. | 0.0232310 | ||||||||
\(85\) | 1.16779e6 | 0.206253 | ||||||||
\(86\) | −1.00142e7 | −1.69774 | ||||||||
\(87\) | −6.27962e6 | −1.02239 | ||||||||
\(88\) | −2.67116e6 | −0.417841 | ||||||||
\(89\) | −4.66139e6 | −0.700891 | −0.350446 | − | 0.936583i | \(-0.613970\pi\) | ||||
−0.350446 | + | 0.936583i | \(0.613970\pi\) | |||||||
\(90\) | 1.65284e6 | 0.238991 | ||||||||
\(91\) | −560965. | −0.0780353 | ||||||||
\(92\) | −1.24495e6 | −0.166685 | ||||||||
\(93\) | −8.55993e6 | −1.10352 | ||||||||
\(94\) | 8.40716e6 | 1.04400 | ||||||||
\(95\) | 2.54355e6 | 0.304374 | ||||||||
\(96\) | 6.44336e6 | 0.743299 | ||||||||
\(97\) | 9.60089e6 | 1.06810 | 0.534048 | − | 0.845454i | \(-0.320670\pi\) | ||||
0.534048 | + | 0.845454i | \(0.320670\pi\) | |||||||
\(98\) | −1.24667e7 | −1.33802 | ||||||||
\(99\) | 4.99692e6 | 0.517582 | ||||||||
\(100\) | −5.71021e6 | −0.571021 | ||||||||
\(101\) | −1.06823e7 | −1.03167 | −0.515834 | − | 0.856689i | \(-0.672518\pi\) | ||||
−0.515834 | + | 0.856689i | \(0.672518\pi\) | |||||||
\(102\) | −3.20304e6 | −0.298856 | ||||||||
\(103\) | 1.20136e7 | 1.08329 | 0.541643 | − | 0.840608i | \(-0.317802\pi\) | ||||
0.541643 | + | 0.840608i | \(0.317802\pi\) | |||||||
\(104\) | −4.78574e6 | −0.417188 | ||||||||
\(105\) | 184252. | 0.0155328 | ||||||||
\(106\) | 1.27447e7 | 1.03935 | ||||||||
\(107\) | 5.52839e6 | 0.436270 | 0.218135 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218135 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(108\) | −2.01401e6 | −0.153843 | ||||||||
\(109\) | 1.75316e7 | 1.29667 | 0.648334 | − | 0.761356i | \(-0.275466\pi\) | ||||
0.648334 | + | 0.761356i | \(0.275466\pi\) | |||||||
\(110\) | 1.55410e7 | 1.11328 | ||||||||
\(111\) | 4.87545e6 | 0.338364 | ||||||||
\(112\) | 868414. | 0.0584069 | ||||||||
\(113\) | −4.98398e6 | −0.324939 | −0.162469 | − | 0.986714i | \(-0.551946\pi\) | ||||
−0.162469 | + | 0.986714i | \(0.551946\pi\) | |||||||
\(114\) | −6.97648e6 | −0.441031 | ||||||||
\(115\) | −1.81769e6 | −0.111449 | ||||||||
\(116\) | 2.37979e7 | 1.41559 | ||||||||
\(117\) | 8.95263e6 | 0.516773 | ||||||||
\(118\) | −2.52860e6 | −0.141675 | ||||||||
\(119\) | −357062. | −0.0194236 | ||||||||
\(120\) | 1.57190e6 | 0.0830407 | ||||||||
\(121\) | 2.74968e7 | 1.41102 | ||||||||
\(122\) | −2.72834e7 | −1.36031 | ||||||||
\(123\) | 8.47697e6 | 0.410745 | ||||||||
\(124\) | 3.24397e7 | 1.52792 | ||||||||
\(125\) | −2.00086e7 | −0.916289 | ||||||||
\(126\) | −505368. | −0.0225067 | ||||||||
\(127\) | 1.56305e7 | 0.677112 | 0.338556 | − | 0.940946i | \(-0.390061\pi\) | ||||
0.338556 | + | 0.940946i | \(0.390061\pi\) | |||||||
\(128\) | 1.25126e7 | 0.527367 | ||||||||
\(129\) | 1.78161e7 | 0.730715 | ||||||||
\(130\) | 2.78437e7 | 1.11154 | ||||||||
\(131\) | 4.19670e7 | 1.63102 | 0.815509 | − | 0.578744i | \(-0.196457\pi\) | ||||
0.815509 | + | 0.578744i | \(0.196457\pi\) | |||||||
\(132\) | −1.89369e7 | −0.716638 | ||||||||
\(133\) | −777710. | −0.0286640 | ||||||||
\(134\) | −7.16165e7 | −2.57126 | ||||||||
\(135\) | −2.94054e6 | −0.102863 | ||||||||
\(136\) | −3.04618e6 | −0.103841 | ||||||||
\(137\) | −3.23047e7 | −1.07336 | −0.536678 | − | 0.843787i | \(-0.680321\pi\) | ||||
−0.536678 | + | 0.843787i | \(0.680321\pi\) | |||||||
\(138\) | 4.98557e6 | 0.161487 | ||||||||
\(139\) | −1.98327e7 | −0.626369 | −0.313184 | − | 0.949692i | \(-0.601396\pi\) | ||||
−0.313184 | + | 0.949692i | \(0.601396\pi\) | |||||||
\(140\) | −698262. | −0.0215065 | ||||||||
\(141\) | −1.49570e7 | −0.449344 | ||||||||
\(142\) | −2.02736e7 | −0.594185 | ||||||||
\(143\) | 8.41779e7 | 2.40725 | ||||||||
\(144\) | −1.38593e7 | −0.386788 | ||||||||
\(145\) | 3.47460e7 | 0.946492 | ||||||||
\(146\) | −3.32006e7 | −0.882900 | ||||||||
\(147\) | 2.21793e7 | 0.575887 | ||||||||
\(148\) | −1.84766e7 | −0.468495 | ||||||||
\(149\) | −3.65263e7 | −0.904595 | −0.452297 | − | 0.891867i | \(-0.649395\pi\) | ||||
−0.452297 | + | 0.891867i | \(0.649395\pi\) | |||||||
\(150\) | 2.28672e7 | 0.553216 | ||||||||
\(151\) | 2.05824e7 | 0.486492 | 0.243246 | − | 0.969965i | \(-0.421788\pi\) | ||||
0.243246 | + | 0.969965i | \(0.421788\pi\) | |||||||
\(152\) | −6.63484e6 | −0.153242 | ||||||||
\(153\) | 5.69847e6 | 0.128629 | ||||||||
\(154\) | −4.75177e6 | −0.104841 | ||||||||
\(155\) | 4.73633e7 | 1.02160 | ||||||||
\(156\) | −3.39279e7 | −0.715518 | ||||||||
\(157\) | −5.88728e7 | −1.21413 | −0.607066 | − | 0.794652i | \(-0.707654\pi\) | ||||
−0.607066 | + | 0.794652i | \(0.707654\pi\) | |||||||
\(158\) | 1.26257e8 | 2.54657 | ||||||||
\(159\) | −2.26739e7 | −0.447339 | ||||||||
\(160\) | −3.56521e7 | −0.688121 | ||||||||
\(161\) | 555771. | 0.0104956 | ||||||||
\(162\) | 8.06535e6 | 0.149046 | ||||||||
\(163\) | −2.85151e7 | −0.515725 | −0.257862 | − | 0.966182i | \(-0.583018\pi\) | ||||
−0.257862 | + | 0.966182i | \(0.583018\pi\) | |||||||
\(164\) | −3.21252e7 | −0.568713 | ||||||||
\(165\) | −2.76487e7 | −0.479160 | ||||||||
\(166\) | −8.83742e7 | −1.49950 | ||||||||
\(167\) | −8.91994e7 | −1.48202 | −0.741010 | − | 0.671494i | \(-0.765653\pi\) | ||||
−0.741010 | + | 0.671494i | \(0.765653\pi\) | |||||||
\(168\) | −480620. | −0.00782023 | ||||||||
\(169\) | 8.80671e7 | 1.40349 | ||||||||
\(170\) | 1.77229e7 | 0.276670 | ||||||||
\(171\) | 1.24117e7 | 0.189822 | ||||||||
\(172\) | −6.75178e7 | −1.01174 | ||||||||
\(173\) | 2.98805e7 | 0.438759 | 0.219379 | − | 0.975640i | \(-0.429597\pi\) | ||||
0.219379 | + | 0.975640i | \(0.429597\pi\) | |||||||
\(174\) | −9.53018e7 | −1.37145 | ||||||||
\(175\) | 2.54915e6 | 0.0359552 | ||||||||
\(176\) | −1.30313e8 | −1.80175 | ||||||||
\(177\) | 4.49859e6 | 0.0609775 | ||||||||
\(178\) | −7.07430e7 | −0.940186 | ||||||||
\(179\) | −4.75128e7 | −0.619191 | −0.309596 | − | 0.950868i | \(-0.600194\pi\) | ||||
−0.309596 | + | 0.950868i | \(0.600194\pi\) | |||||||
\(180\) | 1.11438e7 | 0.142423 | ||||||||
\(181\) | 7.79262e7 | 0.976806 | 0.488403 | − | 0.872618i | \(-0.337580\pi\) | ||||
0.488403 | + | 0.872618i | \(0.337580\pi\) | |||||||
\(182\) | −8.51341e6 | −0.104678 | ||||||||
\(183\) | 4.85394e7 | 0.585485 | ||||||||
\(184\) | 4.74143e6 | 0.0561109 | ||||||||
\(185\) | −2.69766e7 | −0.313246 | ||||||||
\(186\) | −1.29909e8 | −1.48028 | ||||||||
\(187\) | 5.35803e7 | 0.599183 | ||||||||
\(188\) | 5.66828e7 | 0.622156 | ||||||||
\(189\) | 899092. | 0.00968696 | ||||||||
\(190\) | 3.86019e7 | 0.408292 | ||||||||
\(191\) | 6.55466e7 | 0.680665 | 0.340332 | − | 0.940305i | \(-0.389460\pi\) | ||||
0.340332 | + | 0.940305i | \(0.389460\pi\) | |||||||
\(192\) | 3.20834e7 | 0.327135 | ||||||||
\(193\) | 3.05653e7 | 0.306040 | 0.153020 | − | 0.988223i | \(-0.451100\pi\) | ||||
0.153020 | + | 0.988223i | \(0.451100\pi\) | |||||||
\(194\) | 1.45707e8 | 1.43276 | ||||||||
\(195\) | −4.95362e7 | −0.478411 | ||||||||
\(196\) | −8.40532e7 | −0.797367 | ||||||||
\(197\) | −6.62379e7 | −0.617269 | −0.308635 | − | 0.951181i | \(-0.599872\pi\) | ||||
−0.308635 | + | 0.951181i | \(0.599872\pi\) | |||||||
\(198\) | 7.58351e7 | 0.694292 | ||||||||
\(199\) | 3.82627e7 | 0.344184 | 0.172092 | − | 0.985081i | \(-0.444947\pi\) | ||||
0.172092 | + | 0.985081i | \(0.444947\pi\) | |||||||
\(200\) | 2.17474e7 | 0.192222 | ||||||||
\(201\) | 1.27412e8 | 1.10668 | ||||||||
\(202\) | −1.62118e8 | −1.38389 | ||||||||
\(203\) | −1.06239e7 | −0.0891345 | ||||||||
\(204\) | −2.15955e7 | −0.178098 | ||||||||
\(205\) | −4.69043e7 | −0.380254 | ||||||||
\(206\) | 1.82323e8 | 1.45314 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | −2.33473e8 | −1.79894 | ||||||||
\(209\) | 1.16702e8 | 0.884235 | ||||||||
\(210\) | 2.79628e6 | 0.0208359 | ||||||||
\(211\) | −7.26236e7 | −0.532218 | −0.266109 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266109 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(212\) | 8.59276e7 | 0.619380 | ||||||||
\(213\) | 3.60684e7 | 0.255740 | ||||||||
\(214\) | 8.39009e7 | 0.585219 | ||||||||
\(215\) | −9.85789e7 | −0.676471 | ||||||||
\(216\) | 7.67038e6 | 0.0517880 | ||||||||
\(217\) | −1.44817e7 | −0.0962077 | ||||||||
\(218\) | 2.66066e8 | 1.73937 | ||||||||
\(219\) | 5.90666e7 | 0.380004 | ||||||||
\(220\) | 1.04780e8 | 0.663439 | ||||||||
\(221\) | 9.59961e7 | 0.598247 | ||||||||
\(222\) | 7.39917e7 | 0.453887 | ||||||||
\(223\) | 1.65402e8 | 0.998787 | 0.499393 | − | 0.866375i | \(-0.333556\pi\) | ||||
0.499393 | + | 0.866375i | \(0.333556\pi\) | |||||||
\(224\) | 1.09009e7 | 0.0648028 | ||||||||
\(225\) | −4.06827e7 | −0.238106 | ||||||||
\(226\) | −7.56387e7 | −0.435877 | ||||||||
\(227\) | −1.12210e8 | −0.636708 | −0.318354 | − | 0.947972i | \(-0.603130\pi\) | ||||
−0.318354 | + | 0.947972i | \(0.603130\pi\) | |||||||
\(228\) | −4.70369e7 | −0.262825 | ||||||||
\(229\) | −1.99510e8 | −1.09784 | −0.548922 | − | 0.835873i | \(-0.684962\pi\) | ||||
−0.548922 | + | 0.835873i | \(0.684962\pi\) | |||||||
\(230\) | −2.75859e7 | −0.149499 | ||||||||
\(231\) | 8.45379e6 | 0.0451242 | ||||||||
\(232\) | −9.06349e7 | −0.476527 | ||||||||
\(233\) | −1.05157e8 | −0.544618 | −0.272309 | − | 0.962210i | \(-0.587787\pi\) | ||||
−0.272309 | + | 0.962210i | \(0.587787\pi\) | |||||||
\(234\) | 1.35868e8 | 0.693207 | ||||||||
\(235\) | 8.27594e7 | 0.415987 | ||||||||
\(236\) | −1.70484e7 | −0.0844288 | ||||||||
\(237\) | −2.24622e8 | −1.09606 | ||||||||
\(238\) | −5.41890e6 | −0.0260550 | ||||||||
\(239\) | −2.54683e8 | −1.20672 | −0.603360 | − | 0.797469i | \(-0.706172\pi\) | ||||
−0.603360 | + | 0.797469i | \(0.706172\pi\) | |||||||
\(240\) | 7.66856e7 | 0.358075 | ||||||||
\(241\) | −2.61663e8 | −1.20416 | −0.602079 | − | 0.798437i | \(-0.705661\pi\) | ||||
−0.602079 | + | 0.798437i | \(0.705661\pi\) | |||||||
\(242\) | 4.17302e8 | 1.89276 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | −1.83950e8 | −0.810655 | ||||||||
\(245\) | −1.22721e8 | −0.533137 | ||||||||
\(246\) | 1.28650e8 | 0.550979 | ||||||||
\(247\) | 2.09087e8 | 0.882854 | ||||||||
\(248\) | −1.23547e8 | −0.514341 | ||||||||
\(249\) | 1.57225e8 | 0.645392 | ||||||||
\(250\) | −3.03658e8 | −1.22912 | ||||||||
\(251\) | 1.15081e8 | 0.459351 | 0.229675 | − | 0.973267i | \(-0.426234\pi\) | ||||
0.229675 | + | 0.973267i | \(0.426234\pi\) | |||||||
\(252\) | −3.40730e6 | −0.0134125 | ||||||||
\(253\) | −8.33985e7 | −0.323770 | ||||||||
\(254\) | 2.37215e8 | 0.908288 | ||||||||
\(255\) | −3.15304e7 | −0.119080 | ||||||||
\(256\) | 3.41995e8 | 1.27403 | ||||||||
\(257\) | −4.61638e8 | −1.69643 | −0.848215 | − | 0.529652i | \(-0.822323\pi\) | ||||
−0.848215 | + | 0.529652i | \(0.822323\pi\) | |||||||
\(258\) | 2.70383e8 | 0.980192 | ||||||||
\(259\) | 8.24829e6 | 0.0294995 | ||||||||
\(260\) | 1.87728e8 | 0.662402 | ||||||||
\(261\) | 1.69550e8 | 0.590276 | ||||||||
\(262\) | 6.36907e8 | 2.18787 | ||||||||
\(263\) | 2.86469e8 | 0.971030 | 0.485515 | − | 0.874228i | \(-0.338632\pi\) | ||||
0.485515 | + | 0.874228i | \(0.338632\pi\) | |||||||
\(264\) | 7.21214e7 | 0.241241 | ||||||||
\(265\) | 1.25458e8 | 0.414131 | ||||||||
\(266\) | −1.18028e7 | −0.0384503 | ||||||||
\(267\) | 1.25858e8 | 0.404660 | ||||||||
\(268\) | −4.82853e8 | −1.53230 | ||||||||
\(269\) | −2.73894e8 | −0.857926 | −0.428963 | − | 0.903322i | \(-0.641121\pi\) | ||||
−0.428963 | + | 0.903322i | \(0.641121\pi\) | |||||||
\(270\) | −4.46267e7 | −0.137982 | ||||||||
\(271\) | −3.00122e8 | −0.916020 | −0.458010 | − | 0.888947i | \(-0.651438\pi\) | ||||
−0.458010 | + | 0.888947i | \(0.651438\pi\) | |||||||
\(272\) | −1.48609e8 | −0.447769 | ||||||||
\(273\) | 1.51461e7 | 0.0450537 | ||||||||
\(274\) | −4.90268e8 | −1.43981 | ||||||||
\(275\) | −3.82523e8 | −1.10916 | ||||||||
\(276\) | 3.36138e7 | 0.0962355 | ||||||||
\(277\) | 4.92991e8 | 1.39367 | 0.696835 | − | 0.717231i | \(-0.254591\pi\) | ||||
0.696835 | + | 0.717231i | \(0.254591\pi\) | |||||||
\(278\) | −3.00988e8 | −0.840220 | ||||||||
\(279\) | 2.31118e8 | 0.637117 | ||||||||
\(280\) | 2.65934e6 | 0.00723971 | ||||||||
\(281\) | 2.30293e8 | 0.619168 | 0.309584 | − | 0.950872i | \(-0.399810\pi\) | ||||
0.309584 | + | 0.950872i | \(0.399810\pi\) | |||||||
\(282\) | −2.26993e8 | −0.602756 | ||||||||
\(283\) | 2.26945e8 | 0.595208 | 0.297604 | − | 0.954689i | \(-0.403812\pi\) | ||||
0.297604 | + | 0.954689i | \(0.403812\pi\) | |||||||
\(284\) | −1.36689e8 | −0.354094 | ||||||||
\(285\) | −6.86759e7 | −0.175731 | ||||||||
\(286\) | 1.27751e9 | 3.22912 | ||||||||
\(287\) | 1.43413e7 | 0.0358099 | ||||||||
\(288\) | −1.73971e8 | −0.429144 | ||||||||
\(289\) | −3.49236e8 | −0.851092 | ||||||||
\(290\) | 5.27319e8 | 1.26964 | ||||||||
\(291\) | −2.59224e8 | −0.616665 | ||||||||
\(292\) | −2.23846e8 | −0.526149 | ||||||||
\(293\) | 2.13906e7 | 0.0496805 | 0.0248403 | − | 0.999691i | \(-0.492092\pi\) | ||||
0.0248403 | + | 0.999691i | \(0.492092\pi\) | |||||||
\(294\) | 3.36602e8 | 0.772504 | ||||||||
\(295\) | −2.48913e7 | −0.0564509 | ||||||||
\(296\) | 7.03683e7 | 0.157709 | ||||||||
\(297\) | −1.34917e8 | −0.298826 | ||||||||
\(298\) | −5.54337e8 | −1.21344 | ||||||||
\(299\) | −1.49419e8 | −0.323264 | ||||||||
\(300\) | 1.54176e8 | 0.329679 | ||||||||
\(301\) | 3.01412e7 | 0.0637057 | ||||||||
\(302\) | 3.12366e8 | 0.652588 | ||||||||
\(303\) | 2.88422e8 | 0.595634 | ||||||||
\(304\) | −3.23682e8 | −0.660787 | ||||||||
\(305\) | −2.68576e8 | −0.542022 | ||||||||
\(306\) | 8.64820e7 | 0.172544 | ||||||||
\(307\) | −6.56081e8 | −1.29412 | −0.647058 | − | 0.762441i | \(-0.724001\pi\) | ||||
−0.647058 | + | 0.762441i | \(0.724001\pi\) | |||||||
\(308\) | −3.20374e7 | −0.0624784 | ||||||||
\(309\) | −3.24368e8 | −0.625436 | ||||||||
\(310\) | 7.18803e8 | 1.37039 | ||||||||
\(311\) | −2.04155e8 | −0.384856 | −0.192428 | − | 0.981311i | \(-0.561636\pi\) | ||||
−0.192428 | + | 0.981311i | \(0.561636\pi\) | |||||||
\(312\) | 1.29215e8 | 0.240864 | ||||||||
\(313\) | −3.33636e7 | −0.0614989 | −0.0307494 | − | 0.999527i | \(-0.509789\pi\) | ||||
−0.0307494 | + | 0.999527i | \(0.509789\pi\) | |||||||
\(314\) | −8.93475e8 | −1.62865 | ||||||||
\(315\) | −4.97480e6 | −0.00896786 | ||||||||
\(316\) | 8.51252e8 | 1.51759 | ||||||||
\(317\) | −7.39942e8 | −1.30464 | −0.652319 | − | 0.757945i | \(-0.726204\pi\) | ||||
−0.652319 | + | 0.757945i | \(0.726204\pi\) | |||||||
\(318\) | −3.44108e8 | −0.600067 | ||||||||
\(319\) | 1.59421e9 | 2.74965 | ||||||||
\(320\) | −1.77522e8 | −0.302850 | ||||||||
\(321\) | −1.49266e8 | −0.251881 | ||||||||
\(322\) | 8.43459e6 | 0.0140789 | ||||||||
\(323\) | 1.33087e8 | 0.219749 | ||||||||
\(324\) | 5.43782e7 | 0.0888214 | ||||||||
\(325\) | −6.85339e8 | −1.10742 | ||||||||
\(326\) | −4.32756e8 | −0.691801 | ||||||||
\(327\) | −4.73353e8 | −0.748631 | ||||||||
\(328\) | 1.22350e8 | 0.191445 | ||||||||
\(329\) | −2.53043e7 | −0.0391750 | ||||||||
\(330\) | −4.19606e8 | −0.642752 | ||||||||
\(331\) | 4.38506e8 | 0.664626 | 0.332313 | − | 0.943169i | \(-0.392171\pi\) | ||||
0.332313 | + | 0.943169i | \(0.392171\pi\) | |||||||
\(332\) | −5.95837e8 | −0.893602 | ||||||||
\(333\) | −1.31637e8 | −0.195355 | ||||||||
\(334\) | −1.35372e9 | −1.98800 | ||||||||
\(335\) | −7.04987e8 | −1.02453 | ||||||||
\(336\) | −2.34472e7 | −0.0337212 | ||||||||
\(337\) | −5.92928e8 | −0.843912 | −0.421956 | − | 0.906616i | \(-0.638656\pi\) | ||||
−0.421956 | + | 0.906616i | \(0.638656\pi\) | |||||||
\(338\) | 1.33654e9 | 1.88267 | ||||||||
\(339\) | 1.34567e8 | 0.187603 | ||||||||
\(340\) | 1.19491e8 | 0.164877 | ||||||||
\(341\) | 2.17311e9 | 2.96784 | ||||||||
\(342\) | 1.88365e8 | 0.254630 | ||||||||
\(343\) | 7.51413e7 | 0.100542 | ||||||||
\(344\) | 2.57143e8 | 0.340580 | ||||||||
\(345\) | 4.90776e7 | 0.0643452 | ||||||||
\(346\) | 4.53477e8 | 0.588557 | ||||||||
\(347\) | −4.47661e8 | −0.575170 | −0.287585 | − | 0.957755i | \(-0.592852\pi\) | ||||
−0.287585 | + | 0.957755i | \(0.592852\pi\) | |||||||
\(348\) | −6.42544e8 | −0.817289 | ||||||||
\(349\) | −2.47824e8 | −0.312071 | −0.156036 | − | 0.987751i | \(-0.549871\pi\) | ||||
−0.156036 | + | 0.987751i | \(0.549871\pi\) | |||||||
\(350\) | 3.86868e7 | 0.0482308 | ||||||||
\(351\) | −2.41721e8 | −0.298359 | ||||||||
\(352\) | −1.63578e9 | −1.99905 | ||||||||
\(353\) | −2.71331e8 | −0.328313 | −0.164156 | − | 0.986434i | \(-0.552490\pi\) | ||||
−0.164156 | + | 0.986434i | \(0.552490\pi\) | |||||||
\(354\) | 6.82723e7 | 0.0817962 | ||||||||
\(355\) | −1.99571e8 | −0.236755 | ||||||||
\(356\) | −4.76964e8 | −0.560287 | ||||||||
\(357\) | 9.64066e6 | 0.0112142 | ||||||||
\(358\) | −7.21071e8 | −0.830592 | ||||||||
\(359\) | −1.44169e9 | −1.64453 | −0.822266 | − | 0.569103i | \(-0.807291\pi\) | ||||
−0.822266 | + | 0.569103i | \(0.807291\pi\) | |||||||
\(360\) | −4.24413e7 | −0.0479435 | ||||||||
\(361\) | −6.03997e8 | −0.675709 | ||||||||
\(362\) | 1.18264e9 | 1.31030 | ||||||||
\(363\) | −7.42414e8 | −0.814653 | ||||||||
\(364\) | −5.73992e7 | −0.0623808 | ||||||||
\(365\) | −3.26824e8 | −0.351795 | ||||||||
\(366\) | 7.36652e8 | 0.785378 | ||||||||
\(367\) | −1.37060e8 | −0.144737 | −0.0723687 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723687 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(368\) | 2.31312e8 | 0.241953 | ||||||||
\(369\) | −2.28878e8 | −0.237144 | ||||||||
\(370\) | −4.09406e8 | −0.420193 | ||||||||
\(371\) | −3.83597e7 | −0.0390002 | ||||||||
\(372\) | −8.75871e8 | −0.882144 | ||||||||
\(373\) | 1.58651e9 | 1.58293 | 0.791466 | − | 0.611214i | \(-0.209318\pi\) | ||||
0.791466 | + | 0.611214i | \(0.209318\pi\) | |||||||
\(374\) | 8.13155e8 | 0.803753 | ||||||||
\(375\) | 5.40233e8 | 0.529019 | ||||||||
\(376\) | −2.15877e8 | −0.209435 | ||||||||
\(377\) | 2.85623e9 | 2.74535 | ||||||||
\(378\) | 1.36449e7 | 0.0129942 | ||||||||
\(379\) | 1.33727e9 | 1.26177 | 0.630886 | − | 0.775876i | \(-0.282692\pi\) | ||||
0.630886 | + | 0.775876i | \(0.282692\pi\) | |||||||
\(380\) | 2.60262e8 | 0.243314 | ||||||||
\(381\) | −4.22024e8 | −0.390931 | ||||||||
\(382\) | 9.94759e8 | 0.913054 | ||||||||
\(383\) | 3.13397e8 | 0.285036 | 0.142518 | − | 0.989792i | \(-0.454480\pi\) | ||||
0.142518 | + | 0.989792i | \(0.454480\pi\) | |||||||
\(384\) | −3.37840e8 | −0.304475 | ||||||||
\(385\) | −4.67760e7 | −0.0417744 | ||||||||
\(386\) | 4.63870e8 | 0.410526 | ||||||||
\(387\) | −4.81034e8 | −0.421879 | ||||||||
\(388\) | 9.82384e8 | 0.853828 | ||||||||
\(389\) | −1.89508e9 | −1.63231 | −0.816156 | − | 0.577832i | \(-0.803899\pi\) | ||||
−0.816156 | + | 0.577832i | \(0.803899\pi\) | |||||||
\(390\) | −7.51779e8 | −0.641748 | ||||||||
\(391\) | −9.51073e7 | −0.0804628 | ||||||||
\(392\) | 3.20118e8 | 0.268416 | ||||||||
\(393\) | −1.13311e9 | −0.941669 | ||||||||
\(394\) | −1.00525e9 | −0.828014 | ||||||||
\(395\) | 1.24286e9 | 1.01469 | ||||||||
\(396\) | 5.11296e8 | 0.413751 | ||||||||
\(397\) | 1.22322e9 | 0.981159 | 0.490580 | − | 0.871396i | \(-0.336785\pi\) | ||||
0.490580 | + | 0.871396i | \(0.336785\pi\) | |||||||
\(398\) | 5.80689e8 | 0.461693 | ||||||||
\(399\) | 2.09982e7 | 0.0165492 | ||||||||
\(400\) | 1.06095e9 | 0.828870 | ||||||||
\(401\) | 1.76123e9 | 1.36399 | 0.681994 | − | 0.731358i | \(-0.261113\pi\) | ||||
0.681994 | + | 0.731358i | \(0.261113\pi\) | |||||||
\(402\) | 1.93365e9 | 1.48452 | ||||||||
\(403\) | 3.89340e9 | 2.96321 | ||||||||
\(404\) | −1.09304e9 | −0.824707 | ||||||||
\(405\) | 7.93946e7 | 0.0593879 | ||||||||
\(406\) | −1.61232e8 | −0.119566 | ||||||||
\(407\) | −1.23773e9 | −0.910009 | ||||||||
\(408\) | 8.22470e7 | 0.0599528 | ||||||||
\(409\) | 1.17048e7 | 0.00845928 | 0.00422964 | − | 0.999991i | \(-0.498654\pi\) | ||||
0.00422964 | + | 0.999991i | \(0.498654\pi\) | |||||||
\(410\) | −7.11836e8 | −0.510078 | ||||||||
\(411\) | 8.72227e8 | 0.619702 | ||||||||
\(412\) | 1.22926e9 | 0.865971 | ||||||||
\(413\) | 7.61071e6 | 0.00531619 | ||||||||
\(414\) | −1.34610e8 | −0.0932347 | ||||||||
\(415\) | −8.69947e8 | −0.597482 | ||||||||
\(416\) | −2.93070e9 | −1.99593 | ||||||||
\(417\) | 5.35483e8 | 0.361634 | ||||||||
\(418\) | 1.77112e9 | 1.18613 | ||||||||
\(419\) | 2.29028e9 | 1.52103 | 0.760517 | − | 0.649318i | \(-0.224946\pi\) | ||||
0.760517 | + | 0.649318i | \(0.224946\pi\) | |||||||
\(420\) | 1.88531e7 | 0.0124168 | ||||||||
\(421\) | 1.64294e9 | 1.07308 | 0.536542 | − | 0.843874i | \(-0.319730\pi\) | ||||
0.536542 | + | 0.843874i | \(0.319730\pi\) | |||||||
\(422\) | −1.10216e9 | −0.713924 | ||||||||
\(423\) | 4.03840e8 | 0.259429 | ||||||||
\(424\) | −3.27257e8 | −0.208501 | ||||||||
\(425\) | −4.36227e8 | −0.275646 | ||||||||
\(426\) | 5.47387e8 | 0.343053 | ||||||||
\(427\) | 8.21190e7 | 0.0510441 | ||||||||
\(428\) | 5.65677e8 | 0.348751 | ||||||||
\(429\) | −2.27280e9 | −1.38983 | ||||||||
\(430\) | −1.49607e9 | −0.907428 | ||||||||
\(431\) | 1.72851e9 | 1.03992 | 0.519962 | − | 0.854189i | \(-0.325946\pi\) | ||||
0.519962 | + | 0.854189i | \(0.325946\pi\) | |||||||
\(432\) | 3.74202e8 | 0.223312 | ||||||||
\(433\) | 6.64910e8 | 0.393600 | 0.196800 | − | 0.980444i | \(-0.436945\pi\) | ||||
0.196800 | + | 0.980444i | \(0.436945\pi\) | |||||||
\(434\) | −2.19779e8 | −0.129054 | ||||||||
\(435\) | −9.38143e8 | −0.546458 | ||||||||
\(436\) | 1.79387e9 | 1.03655 | ||||||||
\(437\) | −2.07152e8 | −0.118742 | ||||||||
\(438\) | 8.96417e8 | 0.509742 | ||||||||
\(439\) | −2.39908e9 | −1.35338 | −0.676688 | − | 0.736270i | \(-0.736585\pi\) | ||||
−0.676688 | + | 0.736270i | \(0.736585\pi\) | |||||||
\(440\) | −3.99058e8 | −0.223332 | ||||||||
\(441\) | −5.98842e8 | −0.332489 | ||||||||
\(442\) | 1.45687e9 | 0.802497 | ||||||||
\(443\) | 1.19429e9 | 0.652675 | 0.326338 | − | 0.945253i | \(-0.394185\pi\) | ||||
0.326338 | + | 0.945253i | \(0.394185\pi\) | |||||||
\(444\) | 4.98867e8 | 0.270486 | ||||||||
\(445\) | −6.96388e8 | −0.374620 | ||||||||
\(446\) | 2.51020e9 | 1.33979 | ||||||||
\(447\) | 9.86211e8 | 0.522268 | ||||||||
\(448\) | 5.42788e7 | 0.0285205 | ||||||||
\(449\) | −3.02443e9 | −1.57681 | −0.788407 | − | 0.615154i | \(-0.789094\pi\) | ||||
−0.788407 | + | 0.615154i | \(0.789094\pi\) | |||||||
\(450\) | −6.17416e8 | −0.319399 | ||||||||
\(451\) | −2.15205e9 | −1.10467 | ||||||||
\(452\) | −5.09971e8 | −0.259753 | ||||||||
\(453\) | −5.55724e8 | −0.280877 | ||||||||
\(454\) | −1.70294e9 | −0.854089 | ||||||||
\(455\) | −8.38053e7 | −0.0417092 | ||||||||
\(456\) | 1.79141e8 | 0.0884744 | ||||||||
\(457\) | −2.48857e9 | −1.21967 | −0.609836 | − | 0.792528i | \(-0.708765\pi\) | ||||
−0.609836 | + | 0.792528i | \(0.708765\pi\) | |||||||
\(458\) | −3.02784e9 | −1.47266 | ||||||||
\(459\) | −1.53859e8 | −0.0742638 | ||||||||
\(460\) | −1.85990e8 | −0.0890916 | ||||||||
\(461\) | −2.04628e9 | −0.972776 | −0.486388 | − | 0.873743i | \(-0.661686\pi\) | ||||
−0.486388 | + | 0.873743i | \(0.661686\pi\) | |||||||
\(462\) | 1.28298e8 | 0.0605302 | ||||||||
\(463\) | 1.21358e9 | 0.568246 | 0.284123 | − | 0.958788i | \(-0.408298\pi\) | ||||
0.284123 | + | 0.958788i | \(0.408298\pi\) | |||||||
\(464\) | −4.42164e9 | −2.05481 | ||||||||
\(465\) | −1.27881e9 | −0.589821 | ||||||||
\(466\) | −1.59590e9 | −0.730558 | ||||||||
\(467\) | −1.28395e9 | −0.583364 | −0.291682 | − | 0.956515i | \(-0.594215\pi\) | ||||
−0.291682 | + | 0.956515i | \(0.594215\pi\) | |||||||
\(468\) | 9.16053e8 | 0.413105 | ||||||||
\(469\) | 2.15555e8 | 0.0964835 | ||||||||
\(470\) | 1.25599e9 | 0.558011 | ||||||||
\(471\) | 1.58956e9 | 0.700979 | ||||||||
\(472\) | 6.49289e7 | 0.0284211 | ||||||||
\(473\) | −4.52297e9 | −1.96521 | ||||||||
\(474\) | −3.40894e9 | −1.47027 | ||||||||
\(475\) | −9.50139e8 | −0.406780 | ||||||||
\(476\) | −3.65353e7 | −0.0155270 | ||||||||
\(477\) | 6.12196e8 | 0.258271 | ||||||||
\(478\) | −3.86516e9 | −1.61871 | ||||||||
\(479\) | 2.62181e9 | 1.09000 | 0.545001 | − | 0.838435i | \(-0.316529\pi\) | ||||
0.545001 | + | 0.838435i | \(0.316529\pi\) | |||||||
\(480\) | 9.62605e8 | 0.397287 | ||||||||
\(481\) | −2.21755e9 | −0.908587 | ||||||||
\(482\) | −3.97110e9 | −1.61527 | ||||||||
\(483\) | −1.50058e7 | −0.00605961 | ||||||||
\(484\) | 2.81353e9 | 1.12796 | ||||||||
\(485\) | 1.43432e9 | 0.570888 | ||||||||
\(486\) | −2.17764e8 | −0.0860518 | ||||||||
\(487\) | 4.30189e9 | 1.68775 | 0.843875 | − | 0.536540i | \(-0.180269\pi\) | ||||
0.843875 | + | 0.536540i | \(0.180269\pi\) | |||||||
\(488\) | 7.00578e8 | 0.272890 | ||||||||
\(489\) | 7.69907e8 | 0.297754 | ||||||||
\(490\) | −1.86246e9 | −0.715158 | ||||||||
\(491\) | 2.28666e8 | 0.0871798 | 0.0435899 | − | 0.999050i | \(-0.486121\pi\) | ||||
0.0435899 | + | 0.999050i | \(0.486121\pi\) | |||||||
\(492\) | 8.67382e8 | 0.328347 | ||||||||
\(493\) | 1.81803e9 | 0.683338 | ||||||||
\(494\) | 3.17319e9 | 1.18427 | ||||||||
\(495\) | 7.46514e8 | 0.276643 | ||||||||
\(496\) | −6.02727e9 | −2.21786 | ||||||||
\(497\) | 6.10205e7 | 0.0222961 | ||||||||
\(498\) | 2.38610e9 | 0.865738 | ||||||||
\(499\) | 1.73024e9 | 0.623382 | 0.311691 | − | 0.950184i | \(-0.399105\pi\) | ||||
0.311691 | + | 0.950184i | \(0.399105\pi\) | |||||||
\(500\) | −2.04733e9 | −0.732474 | ||||||||
\(501\) | 2.40838e9 | 0.855645 | ||||||||
\(502\) | 1.74651e9 | 0.616180 | ||||||||
\(503\) | 8.27541e8 | 0.289936 | 0.144968 | − | 0.989436i | \(-0.453692\pi\) | ||||
0.144968 | + | 0.989436i | \(0.453692\pi\) | |||||||
\(504\) | 1.29768e7 | 0.00451501 | ||||||||
\(505\) | −1.59588e9 | −0.551417 | ||||||||
\(506\) | −1.26569e9 | −0.434310 | ||||||||
\(507\) | −2.37781e9 | −0.810307 | ||||||||
\(508\) | 1.59935e9 | 0.541278 | ||||||||
\(509\) | −1.63228e9 | −0.548632 | −0.274316 | − | 0.961640i | \(-0.588451\pi\) | ||||
−0.274316 | + | 0.961640i | \(0.588451\pi\) | |||||||
\(510\) | −4.78518e8 | −0.159736 | ||||||||
\(511\) | 9.99289e7 | 0.0331297 | ||||||||
\(512\) | 3.58863e9 | 1.18164 | ||||||||
\(513\) | −3.35117e8 | −0.109594 | ||||||||
\(514\) | −7.00600e9 | −2.27562 | ||||||||
\(515\) | 1.79477e9 | 0.579007 | ||||||||
\(516\) | 1.82298e9 | 0.584128 | ||||||||
\(517\) | 3.79714e9 | 1.20848 | ||||||||
\(518\) | 1.25179e8 | 0.0395710 | ||||||||
\(519\) | −8.06772e8 | −0.253318 | ||||||||
\(520\) | −7.14965e8 | −0.222984 | ||||||||
\(521\) | 1.95096e7 | 0.00604389 | 0.00302195 | − | 0.999995i | \(-0.499038\pi\) | ||||
0.00302195 | + | 0.999995i | \(0.499038\pi\) | |||||||
\(522\) | 2.57315e9 | 0.791805 | ||||||||
\(523\) | −2.79054e9 | −0.852966 | −0.426483 | − | 0.904496i | \(-0.640248\pi\) | ||||
−0.426483 | + | 0.904496i | \(0.640248\pi\) | |||||||
\(524\) | 4.29416e9 | 1.30382 | ||||||||
\(525\) | −6.88270e7 | −0.0207587 | ||||||||
\(526\) | 4.34756e9 | 1.30255 | ||||||||
\(527\) | 2.47820e9 | 0.737564 | ||||||||
\(528\) | 3.51846e9 | 1.04024 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 1.90400e9 | 0.555521 | ||||||||
\(531\) | −1.21462e8 | −0.0352054 | ||||||||
\(532\) | −7.95770e7 | −0.0229138 | ||||||||
\(533\) | −3.85567e9 | −1.10295 | ||||||||
\(534\) | 1.91006e9 | 0.542816 | ||||||||
\(535\) | 8.25913e8 | 0.233183 | ||||||||
\(536\) | 1.83895e9 | 0.515815 | ||||||||
\(537\) | 1.28284e9 | 0.357490 | ||||||||
\(538\) | −4.15672e9 | −1.15083 | ||||||||
\(539\) | −5.63066e9 | −1.54881 | ||||||||
\(540\) | −3.00882e8 | −0.0822278 | ||||||||
\(541\) | 2.92896e9 | 0.795285 | 0.397643 | − | 0.917540i | \(-0.369828\pi\) | ||||
0.397643 | + | 0.917540i | \(0.369828\pi\) | |||||||
\(542\) | −4.55476e9 | −1.22876 | ||||||||
\(543\) | −2.10401e9 | −0.563959 | ||||||||
\(544\) | −1.86543e9 | −0.496802 | ||||||||
\(545\) | 2.61913e9 | 0.693058 | ||||||||
\(546\) | 2.29862e8 | 0.0604357 | ||||||||
\(547\) | 3.11875e9 | 0.814751 | 0.407376 | − | 0.913261i | \(-0.366444\pi\) | ||||
0.407376 | + | 0.913261i | \(0.366444\pi\) | |||||||
\(548\) | −3.30549e9 | −0.858032 | ||||||||
\(549\) | −1.31056e9 | −0.338030 | ||||||||
\(550\) | −5.80531e9 | −1.48784 | ||||||||
\(551\) | 3.95981e9 | 1.00843 | ||||||||
\(552\) | −1.28019e8 | −0.0323956 | ||||||||
\(553\) | −3.80015e8 | −0.0955571 | ||||||||
\(554\) | 7.48182e9 | 1.86949 | ||||||||
\(555\) | 7.28367e8 | 0.180853 | ||||||||
\(556\) | −2.02933e9 | −0.500714 | ||||||||
\(557\) | 4.07990e9 | 1.00036 | 0.500180 | − | 0.865921i | \(-0.333267\pi\) | ||||
0.500180 | + | 0.865921i | \(0.333267\pi\) | |||||||
\(558\) | 3.50753e9 | 0.854638 | ||||||||
\(559\) | −8.10348e9 | −1.96214 | ||||||||
\(560\) | 1.29737e8 | 0.0312180 | ||||||||
\(561\) | −1.44667e9 | −0.345939 | ||||||||
\(562\) | 3.49501e9 | 0.830561 | ||||||||
\(563\) | 6.90942e9 | 1.63178 | 0.815891 | − | 0.578205i | \(-0.196247\pi\) | ||||
0.815891 | + | 0.578205i | \(0.196247\pi\) | |||||||
\(564\) | −1.53044e9 | −0.359202 | ||||||||
\(565\) | −7.44581e8 | −0.173677 | ||||||||
\(566\) | 3.44421e9 | 0.798421 | ||||||||
\(567\) | −2.42755e7 | −0.00559277 | ||||||||
\(568\) | 5.20581e8 | 0.119198 | ||||||||
\(569\) | −1.15725e9 | −0.263350 | −0.131675 | − | 0.991293i | \(-0.542036\pi\) | ||||
−0.131675 | + | 0.991293i | \(0.542036\pi\) | |||||||
\(570\) | −1.04225e9 | −0.235727 | ||||||||
\(571\) | −4.86086e9 | −1.09266 | −0.546332 | − | 0.837569i | \(-0.683976\pi\) | ||||
−0.546332 | + | 0.837569i | \(0.683976\pi\) | |||||||
\(572\) | 8.61327e9 | 1.92434 | ||||||||
\(573\) | −1.76976e9 | −0.392982 | ||||||||
\(574\) | 2.17649e8 | 0.0480359 | ||||||||
\(575\) | 6.78994e8 | 0.148946 | ||||||||
\(576\) | −8.66253e8 | −0.188871 | ||||||||
\(577\) | −5.87427e9 | −1.27303 | −0.636514 | − | 0.771265i | \(-0.719624\pi\) | ||||
−0.636514 | + | 0.771265i | \(0.719624\pi\) | |||||||
\(578\) | −5.30013e9 | −1.14167 | ||||||||
\(579\) | −8.25263e8 | −0.176692 | ||||||||
\(580\) | 3.55529e9 | 0.756619 | ||||||||
\(581\) | 2.65993e8 | 0.0562670 | ||||||||
\(582\) | −3.93408e9 | −0.827204 | ||||||||
\(583\) | 5.75622e9 | 1.20309 | ||||||||
\(584\) | 8.52519e8 | 0.177117 | ||||||||
\(585\) | 1.33748e9 | 0.276211 | ||||||||
\(586\) | 3.24632e8 | 0.0666422 | ||||||||
\(587\) | −4.42899e9 | −0.903797 | −0.451899 | − | 0.892069i | \(-0.649253\pi\) | ||||
−0.451899 | + | 0.892069i | \(0.649253\pi\) | |||||||
\(588\) | 2.26944e9 | 0.460360 | ||||||||
\(589\) | 5.39773e9 | 1.08845 | ||||||||
\(590\) | −3.77760e8 | −0.0757241 | ||||||||
\(591\) | 1.78842e9 | 0.356381 | ||||||||
\(592\) | 3.43293e9 | 0.680048 | ||||||||
\(593\) | −4.19380e9 | −0.825878 | −0.412939 | − | 0.910759i | \(-0.635498\pi\) | ||||
−0.412939 | + | 0.910759i | \(0.635498\pi\) | |||||||
\(594\) | −2.04755e9 | −0.400850 | ||||||||
\(595\) | −5.33432e7 | −0.0103817 | ||||||||
\(596\) | −3.73745e9 | −0.723126 | ||||||||
\(597\) | −1.03309e9 | −0.198714 | ||||||||
\(598\) | −2.26764e9 | −0.433631 | ||||||||
\(599\) | 8.36071e9 | 1.58946 | 0.794729 | − | 0.606964i | \(-0.207613\pi\) | ||||
0.794729 | + | 0.606964i | \(0.207613\pi\) | |||||||
\(600\) | −5.87181e8 | −0.110979 | ||||||||
\(601\) | −6.82190e8 | −0.128187 | −0.0640936 | − | 0.997944i | \(-0.520416\pi\) | ||||
−0.0640936 | + | 0.997944i | \(0.520416\pi\) | |||||||
\(602\) | 4.57435e8 | 0.0854557 | ||||||||
\(603\) | −3.44011e9 | −0.638943 | ||||||||
\(604\) | 2.10603e9 | 0.388898 | ||||||||
\(605\) | 4.10788e9 | 0.754178 | ||||||||
\(606\) | 4.37720e9 | 0.798991 | ||||||||
\(607\) | 7.75495e9 | 1.40740 | 0.703702 | − | 0.710495i | \(-0.251529\pi\) | ||||
0.703702 | + | 0.710495i | \(0.251529\pi\) | |||||||
\(608\) | −4.06306e9 | −0.733147 | ||||||||
\(609\) | 2.86844e8 | 0.0514619 | ||||||||
\(610\) | −4.07600e9 | −0.727076 | ||||||||
\(611\) | 6.80307e9 | 1.20659 | ||||||||
\(612\) | 5.83080e8 | 0.102825 | ||||||||
\(613\) | −2.87474e9 | −0.504065 | −0.252032 | − | 0.967719i | \(-0.581099\pi\) | ||||
−0.252032 | + | 0.967719i | \(0.581099\pi\) | |||||||
\(614\) | −9.95693e9 | −1.73595 | ||||||||
\(615\) | 1.26642e9 | 0.219540 | ||||||||
\(616\) | 1.22015e8 | 0.0210320 | ||||||||
\(617\) | 1.19191e9 | 0.204290 | 0.102145 | − | 0.994770i | \(-0.467429\pi\) | ||||
0.102145 | + | 0.994770i | \(0.467429\pi\) | |||||||
\(618\) | −4.92272e9 | −0.838968 | ||||||||
\(619\) | −1.27744e9 | −0.216483 | −0.108242 | − | 0.994125i | \(-0.534522\pi\) | ||||
−0.108242 | + | 0.994125i | \(0.534522\pi\) | |||||||
\(620\) | 4.84632e9 | 0.816659 | ||||||||
\(621\) | 2.39483e8 | 0.0401286 | ||||||||
\(622\) | −3.09833e9 | −0.516251 | ||||||||
\(623\) | 2.12926e8 | 0.0352793 | ||||||||
\(624\) | 6.30378e9 | 1.03862 | ||||||||
\(625\) | 1.37067e9 | 0.224571 | ||||||||
\(626\) | −5.06338e8 | −0.0824955 | ||||||||
\(627\) | −3.15096e9 | −0.510513 | ||||||||
\(628\) | −6.02399e9 | −0.970567 | ||||||||
\(629\) | −1.41150e9 | −0.226154 | ||||||||
\(630\) | −7.54994e7 | −0.0120296 | ||||||||
\(631\) | 1.09977e10 | 1.74261 | 0.871306 | − | 0.490739i | \(-0.163273\pi\) | ||||
0.871306 | + | 0.490739i | \(0.163273\pi\) | |||||||
\(632\) | −3.24201e9 | −0.510863 | ||||||||
\(633\) | 1.96084e9 | 0.307276 | ||||||||
\(634\) | −1.12296e10 | −1.75006 | ||||||||
\(635\) | 2.33512e9 | 0.361911 | ||||||||
\(636\) | −2.32005e9 | −0.357599 | ||||||||
\(637\) | −1.00881e10 | −1.54639 | ||||||||
\(638\) | 2.41943e10 | 3.68842 | ||||||||
\(639\) | −9.73846e8 | −0.147651 | ||||||||
\(640\) | 1.86932e9 | 0.281873 | ||||||||
\(641\) | 2.50921e9 | 0.376300 | 0.188150 | − | 0.982140i | \(-0.439751\pi\) | ||||
0.188150 | + | 0.982140i | \(0.439751\pi\) | |||||||
\(642\) | −2.26532e9 | −0.337876 | ||||||||
\(643\) | 4.00837e9 | 0.594606 | 0.297303 | − | 0.954783i | \(-0.403913\pi\) | ||||
0.297303 | + | 0.954783i | \(0.403913\pi\) | |||||||
\(644\) | 5.68678e7 | 0.00839007 | ||||||||
\(645\) | 2.66163e9 | 0.390561 | ||||||||
\(646\) | 2.01978e9 | 0.294774 | ||||||||
\(647\) | −1.09131e10 | −1.58410 | −0.792052 | − | 0.610454i | \(-0.790987\pi\) | ||||
−0.792052 | + | 0.610454i | \(0.790987\pi\) | |||||||
\(648\) | −2.07100e8 | −0.0298998 | ||||||||
\(649\) | −1.14206e9 | −0.163995 | ||||||||
\(650\) | −1.04010e10 | −1.48551 | ||||||||
\(651\) | 3.91005e8 | 0.0555456 | ||||||||
\(652\) | −2.91773e9 | −0.412267 | ||||||||
\(653\) | −6.66520e9 | −0.936735 | −0.468368 | − | 0.883534i | \(-0.655158\pi\) | ||||
−0.468368 | + | 0.883534i | \(0.655158\pi\) | |||||||
\(654\) | −7.18378e9 | −1.00422 | ||||||||
\(655\) | 6.26966e9 | 0.871765 | ||||||||
\(656\) | 5.96885e9 | 0.825520 | ||||||||
\(657\) | −1.59480e9 | −0.219395 | ||||||||
\(658\) | −3.84027e8 | −0.0525499 | ||||||||
\(659\) | 2.60764e9 | 0.354935 | 0.177468 | − | 0.984127i | \(-0.443209\pi\) | ||||
0.177468 | + | 0.984127i | \(0.443209\pi\) | |||||||
\(660\) | −2.82907e9 | −0.383037 | ||||||||
\(661\) | 4.72170e9 | 0.635906 | 0.317953 | − | 0.948106i | \(-0.397005\pi\) | ||||
0.317953 | + | 0.948106i | \(0.397005\pi\) | |||||||
\(662\) | 6.65492e9 | 0.891538 | ||||||||
\(663\) | −2.59190e9 | −0.345398 | ||||||||
\(664\) | 2.26925e9 | 0.300812 | ||||||||
\(665\) | −1.16186e8 | −0.0153207 | ||||||||
\(666\) | −1.99777e9 | −0.262052 | ||||||||
\(667\) | −2.82978e9 | −0.369243 | ||||||||
\(668\) | −9.12708e9 | −1.18472 | ||||||||
\(669\) | −4.46584e9 | −0.576650 | ||||||||
\(670\) | −1.06991e10 | −1.37432 | ||||||||
\(671\) | −1.23227e10 | −1.57462 | ||||||||
\(672\) | −2.94324e8 | −0.0374139 | ||||||||
\(673\) | 4.41241e8 | 0.0557986 | 0.0278993 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0278993 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(674\) | −8.99849e9 | −1.13204 | ||||||||
\(675\) | 1.09843e9 | 0.137471 | ||||||||
\(676\) | 9.01122e9 | 1.12194 | ||||||||
\(677\) | −7.16818e8 | −0.0887868 | −0.0443934 | − | 0.999014i | \(-0.514136\pi\) | ||||
−0.0443934 | + | 0.999014i | \(0.514136\pi\) | |||||||
\(678\) | 2.04224e9 | 0.251654 | ||||||||
\(679\) | −4.38555e8 | −0.0537625 | ||||||||
\(680\) | −4.55084e8 | −0.0555023 | ||||||||
\(681\) | 3.02966e9 | 0.367603 | ||||||||
\(682\) | 3.29799e10 | 3.98111 | ||||||||
\(683\) | 1.46026e10 | 1.75370 | 0.876852 | − | 0.480761i | \(-0.159639\pi\) | ||||
0.876852 | + | 0.480761i | \(0.159639\pi\) | |||||||
\(684\) | 1.27000e9 | 0.151742 | ||||||||
\(685\) | −4.82616e9 | −0.573699 | ||||||||
\(686\) | 1.14037e9 | 0.134869 | ||||||||
\(687\) | 5.38677e9 | 0.633841 | ||||||||
\(688\) | 1.25448e10 | 1.46860 | ||||||||
\(689\) | 1.03130e10 | 1.20121 | ||||||||
\(690\) | 7.44819e8 | 0.0863136 | ||||||||
\(691\) | −1.63420e10 | −1.88422 | −0.942111 | − | 0.335301i | \(-0.891162\pi\) | ||||
−0.942111 | + | 0.335301i | \(0.891162\pi\) | |||||||
\(692\) | 3.05743e9 | 0.350740 | ||||||||
\(693\) | −2.28252e8 | −0.0260525 | ||||||||
\(694\) | −6.79388e9 | −0.771542 | ||||||||
\(695\) | −2.96290e9 | −0.334789 | ||||||||
\(696\) | 2.44714e9 | 0.275123 | ||||||||
\(697\) | −2.45418e9 | −0.274532 | ||||||||
\(698\) | −3.76106e9 | −0.418617 | ||||||||
\(699\) | 2.83923e9 | 0.314435 | ||||||||
\(700\) | 2.60834e8 | 0.0287423 | ||||||||
\(701\) | −1.33002e10 | −1.45829 | −0.729147 | − | 0.684357i | \(-0.760083\pi\) | ||||
−0.729147 | + | 0.684357i | \(0.760083\pi\) | |||||||
\(702\) | −3.66845e9 | −0.400223 | ||||||||
\(703\) | −3.07437e9 | −0.333743 | ||||||||
\(704\) | −8.14502e9 | −0.879808 | ||||||||
\(705\) | −2.23450e9 | −0.240170 | ||||||||
\(706\) | −4.11782e9 | −0.440404 | ||||||||
\(707\) | 4.87952e8 | 0.0519289 | ||||||||
\(708\) | 4.60306e8 | 0.0487450 | ||||||||
\(709\) | −5.40175e9 | −0.569211 | −0.284605 | − | 0.958645i | \(-0.591863\pi\) | ||||
−0.284605 | + | 0.958645i | \(0.591863\pi\) | |||||||
\(710\) | −3.02877e9 | −0.317587 | ||||||||
\(711\) | 6.06479e9 | 0.632808 | ||||||||
\(712\) | 1.81653e9 | 0.188609 | ||||||||
\(713\) | −3.85736e9 | −0.398544 | ||||||||
\(714\) | 1.46310e8 | 0.0150429 | ||||||||
\(715\) | 1.25757e10 | 1.28666 | ||||||||
\(716\) | −4.86161e9 | −0.494976 | ||||||||
\(717\) | 6.87643e9 | 0.696700 | ||||||||
\(718\) | −2.18797e10 | −2.20600 | ||||||||
\(719\) | 8.57269e9 | 0.860134 | 0.430067 | − | 0.902797i | \(-0.358490\pi\) | ||||
0.430067 | + | 0.902797i | \(0.358490\pi\) | |||||||
\(720\) | −2.07051e9 | −0.206735 | ||||||||
\(721\) | −5.48765e8 | −0.0545272 | ||||||||
\(722\) | −9.16649e9 | −0.906406 | ||||||||
\(723\) | 7.06491e9 | 0.695221 | ||||||||
\(724\) | 7.97358e9 | 0.780851 | ||||||||
\(725\) | −1.29793e10 | −1.26494 | ||||||||
\(726\) | −1.12671e10 | −1.09279 | ||||||||
\(727\) | 1.61791e10 | 1.56165 | 0.780827 | − | 0.624747i | \(-0.214798\pi\) | ||||
0.780827 | + | 0.624747i | \(0.214798\pi\) | |||||||
\(728\) | 2.18606e8 | 0.0209992 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −4.96000e9 | −0.471902 | ||||||||
\(731\) | −5.15797e9 | −0.488392 | ||||||||
\(732\) | 4.96666e9 | 0.468032 | ||||||||
\(733\) | −1.43824e10 | −1.34886 | −0.674431 | − | 0.738338i | \(-0.735611\pi\) | ||||
−0.674431 | + | 0.738338i | \(0.735611\pi\) | |||||||
\(734\) | −2.08008e9 | −0.194153 | ||||||||
\(735\) | 3.31348e9 | 0.307807 | ||||||||
\(736\) | 2.90357e9 | 0.268448 | ||||||||
\(737\) | −3.23460e10 | −2.97635 | ||||||||
\(738\) | −3.47354e9 | −0.318108 | ||||||||
\(739\) | 1.15738e10 | 1.05492 | 0.527461 | − | 0.849579i | \(-0.323144\pi\) | ||||
0.527461 | + | 0.849579i | \(0.323144\pi\) | |||||||
\(740\) | −2.76030e9 | −0.250407 | ||||||||
\(741\) | −5.64536e9 | −0.509716 | ||||||||
\(742\) | −5.82161e8 | −0.0523154 | ||||||||
\(743\) | −1.91780e10 | −1.71531 | −0.857656 | − | 0.514223i | \(-0.828080\pi\) | ||||
−0.857656 | + | 0.514223i | \(0.828080\pi\) | |||||||
\(744\) | 3.33577e9 | 0.296955 | ||||||||
\(745\) | −5.45685e9 | −0.483498 | ||||||||
\(746\) | 2.40775e10 | 2.12337 | ||||||||
\(747\) | −4.24507e9 | −0.372617 | ||||||||
\(748\) | 5.48246e9 | 0.478983 | ||||||||
\(749\) | −2.52529e8 | −0.0219596 | ||||||||
\(750\) | 8.19878e9 | 0.709634 | ||||||||
\(751\) | 1.46703e10 | 1.26386 | 0.631929 | − | 0.775026i | \(-0.282263\pi\) | ||||
0.631929 | + | 0.775026i | \(0.282263\pi\) | |||||||
\(752\) | −1.05316e10 | −0.903095 | ||||||||
\(753\) | −3.10718e9 | −0.265206 | ||||||||
\(754\) | 4.33471e10 | 3.68265 | ||||||||
\(755\) | 3.07490e9 | 0.260026 | ||||||||
\(756\) | 9.19970e7 | 0.00774368 | ||||||||
\(757\) | 4.15177e9 | 0.347855 | 0.173927 | − | 0.984758i | \(-0.444354\pi\) | ||||
0.173927 | + | 0.984758i | \(0.444354\pi\) | |||||||
\(758\) | 2.02949e10 | 1.69256 | ||||||||
\(759\) | 2.25176e9 | 0.186929 | ||||||||
\(760\) | −9.91211e8 | −0.0819066 | ||||||||
\(761\) | −1.08914e10 | −0.895857 | −0.447929 | − | 0.894069i | \(-0.647838\pi\) | ||||
−0.447929 | + | 0.894069i | \(0.647838\pi\) | |||||||
\(762\) | −6.40480e9 | −0.524400 | ||||||||
\(763\) | −8.00819e8 | −0.0652677 | ||||||||
\(764\) | 6.70687e9 | 0.544118 | ||||||||
\(765\) | 8.51322e8 | 0.0687509 | ||||||||
\(766\) | 4.75623e9 | 0.382351 | ||||||||
\(767\) | −2.04614e9 | −0.163739 | ||||||||
\(768\) | −9.23387e9 | −0.735562 | ||||||||
\(769\) | 1.94850e10 | 1.54511 | 0.772554 | − | 0.634949i | \(-0.218979\pi\) | ||||
0.772554 | + | 0.634949i | \(0.218979\pi\) | |||||||
\(770\) | −7.09890e8 | −0.0560368 | ||||||||
\(771\) | 1.24642e10 | 0.979435 | ||||||||
\(772\) | 3.12751e9 | 0.244646 | ||||||||
\(773\) | −1.02798e10 | −0.800492 | −0.400246 | − | 0.916408i | \(-0.631075\pi\) | ||||
−0.400246 | + | 0.916408i | \(0.631075\pi\) | |||||||
\(774\) | −7.30035e9 | −0.565914 | ||||||||
\(775\) | −1.76925e10 | −1.36531 | ||||||||
\(776\) | −3.74143e9 | −0.287423 | ||||||||
\(777\) | −2.22704e8 | −0.0170315 | ||||||||
\(778\) | −2.87604e10 | −2.18961 | ||||||||
\(779\) | −5.34542e9 | −0.405136 | ||||||||
\(780\) | −5.06865e9 | −0.382438 | ||||||||
\(781\) | −9.15667e9 | −0.687795 | ||||||||
\(782\) | −1.44338e9 | −0.107934 | ||||||||
\(783\) | −4.57784e9 | −0.340796 | ||||||||
\(784\) | 1.56170e10 | 1.15742 | ||||||||
\(785\) | −8.79529e9 | −0.648943 | ||||||||
\(786\) | −1.71965e10 | −1.26317 | ||||||||
\(787\) | −8.67563e9 | −0.634438 | −0.317219 | − | 0.948352i | \(-0.602749\pi\) | ||||
−0.317219 | + | 0.948352i | \(0.602749\pi\) | |||||||
\(788\) | −6.77761e9 | −0.493440 | ||||||||
\(789\) | −7.73467e9 | −0.560625 | ||||||||
\(790\) | 1.88622e10 | 1.36112 | ||||||||
\(791\) | 2.27661e8 | 0.0163558 | ||||||||
\(792\) | −1.94728e9 | −0.139280 | ||||||||
\(793\) | −2.20777e10 | −1.57216 | ||||||||
\(794\) | 1.85641e10 | 1.31614 | ||||||||
\(795\) | −3.38737e9 | −0.239099 | ||||||||
\(796\) | 3.91513e9 | 0.275138 | ||||||||
\(797\) | 6.59704e9 | 0.461578 | 0.230789 | − | 0.973004i | \(-0.425869\pi\) | ||||
0.230789 | + | 0.973004i | \(0.425869\pi\) | |||||||
\(798\) | 3.18676e8 | 0.0221993 | ||||||||
\(799\) | 4.33024e9 | 0.300330 | ||||||||
\(800\) | 1.33178e10 | 0.919637 | ||||||||
\(801\) | −3.39816e9 | −0.233630 | ||||||||
\(802\) | 2.67291e10 | 1.82967 | ||||||||
\(803\) | −1.49952e10 | −1.02200 | ||||||||
\(804\) | 1.30370e10 | 0.884673 | ||||||||
\(805\) | 8.30294e7 | 0.00560979 | ||||||||
\(806\) | 5.90877e10 | 3.97489 | ||||||||
\(807\) | 7.39514e9 | 0.495324 | ||||||||
\(808\) | 4.16285e9 | 0.277620 | ||||||||
\(809\) | −1.17222e10 | −0.778374 | −0.389187 | − | 0.921159i | \(-0.627244\pi\) | ||||
−0.389187 | + | 0.921159i | \(0.627244\pi\) | |||||||
\(810\) | 1.20492e9 | 0.0796638 | ||||||||
\(811\) | 3.14796e9 | 0.207232 | 0.103616 | − | 0.994617i | \(-0.466959\pi\) | ||||
0.103616 | + | 0.994617i | \(0.466959\pi\) | |||||||
\(812\) | −1.08706e9 | −0.0712535 | ||||||||
\(813\) | 8.10329e9 | 0.528865 | ||||||||
\(814\) | −1.87843e10 | −1.22070 | ||||||||
\(815\) | −4.26001e9 | −0.275650 | ||||||||
\(816\) | 4.01244e9 | 0.258519 | ||||||||
\(817\) | −1.12345e10 | −0.720736 | ||||||||
\(818\) | 1.77637e8 | 0.0113474 | ||||||||
\(819\) | −4.08944e8 | −0.0260118 | ||||||||
\(820\) | −4.79935e9 | −0.303972 | ||||||||
\(821\) | 1.04194e10 | 0.657113 | 0.328556 | − | 0.944484i | \(-0.393438\pi\) | ||||
0.328556 | + | 0.944484i | \(0.393438\pi\) | |||||||
\(822\) | 1.32372e10 | 0.831277 | ||||||||
\(823\) | −1.05440e10 | −0.659334 | −0.329667 | − | 0.944097i | \(-0.606936\pi\) | ||||
−0.329667 | + | 0.944097i | \(0.606936\pi\) | |||||||
\(824\) | −4.68165e9 | −0.291510 | ||||||||
\(825\) | 1.03281e10 | 0.640372 | ||||||||
\(826\) | 1.15503e8 | 0.00713121 | ||||||||
\(827\) | 2.77244e10 | 1.70448 | 0.852241 | − | 0.523149i | \(-0.175243\pi\) | ||||
0.852241 | + | 0.523149i | \(0.175243\pi\) | |||||||
\(828\) | −9.07572e8 | −0.0555616 | ||||||||
\(829\) | 3.00153e10 | 1.82979 | 0.914896 | − | 0.403691i | \(-0.132273\pi\) | ||||
0.914896 | + | 0.403691i | \(0.132273\pi\) | |||||||
\(830\) | −1.32026e10 | −0.801471 | ||||||||
\(831\) | −1.33108e10 | −0.804636 | ||||||||
\(832\) | −1.45929e10 | −0.878433 | ||||||||
\(833\) | −6.42118e9 | −0.384909 | ||||||||
\(834\) | 8.12669e9 | 0.485101 | ||||||||
\(835\) | −1.33259e10 | −0.792127 | ||||||||
\(836\) | 1.19412e10 | 0.706851 | ||||||||
\(837\) | −6.24019e9 | −0.367840 | ||||||||
\(838\) | 3.47581e10 | 2.04034 | ||||||||
\(839\) | −1.61747e10 | −0.945516 | −0.472758 | − | 0.881192i | \(-0.656741\pi\) | ||||
−0.472758 | + | 0.881192i | \(0.656741\pi\) | |||||||
\(840\) | −7.18022e7 | −0.00417985 | ||||||||
\(841\) | 3.68429e10 | 2.13583 | ||||||||
\(842\) | 2.49338e10 | 1.43945 | ||||||||
\(843\) | −6.21791e9 | −0.357477 | ||||||||
\(844\) | −7.43101e9 | −0.425451 | ||||||||
\(845\) | 1.31568e10 | 0.750155 | ||||||||
\(846\) | 6.12882e9 | 0.348001 | ||||||||
\(847\) | −1.25602e9 | −0.0710236 | ||||||||
\(848\) | −1.59653e10 | −0.899066 | ||||||||
\(849\) | −6.12752e9 | −0.343644 | ||||||||
\(850\) | −6.62035e9 | −0.369755 | ||||||||
\(851\) | 2.19702e9 | 0.122203 | ||||||||
\(852\) | 3.69060e9 | 0.204436 | ||||||||
\(853\) | 1.01140e10 | 0.557958 | 0.278979 | − | 0.960297i | \(-0.410004\pi\) | ||||
0.278979 | + | 0.960297i | \(0.410004\pi\) | |||||||
\(854\) | 1.24627e9 | 0.0684713 | ||||||||
\(855\) | 1.85425e9 | 0.101458 | ||||||||
\(856\) | −2.15439e9 | −0.117399 | ||||||||
\(857\) | 2.45418e10 | 1.33190 | 0.665952 | − | 0.745995i | \(-0.268026\pi\) | ||||
0.665952 | + | 0.745995i | \(0.268026\pi\) | |||||||
\(858\) | −3.44929e10 | −1.86434 | ||||||||
\(859\) | −7.47642e9 | −0.402455 | −0.201228 | − | 0.979545i | \(-0.564493\pi\) | ||||
−0.201228 | + | 0.979545i | \(0.564493\pi\) | |||||||
\(860\) | −1.00868e10 | −0.540766 | ||||||||
\(861\) | −3.87216e8 | −0.0206748 | ||||||||
\(862\) | 2.62325e10 | 1.39497 | ||||||||
\(863\) | 1.37132e10 | 0.726276 | 0.363138 | − | 0.931735i | \(-0.381705\pi\) | ||||
0.363138 | + | 0.931735i | \(0.381705\pi\) | |||||||
\(864\) | 4.69721e9 | 0.247766 | ||||||||
\(865\) | 4.46399e9 | 0.234513 | ||||||||
\(866\) | 1.00909e10 | 0.527981 | ||||||||
\(867\) | 9.42937e9 | 0.491378 | ||||||||
\(868\) | −1.48180e9 | −0.0769077 | ||||||||
\(869\) | 5.70247e10 | 2.94777 | ||||||||
\(870\) | −1.42376e10 | −0.733026 | ||||||||
\(871\) | −5.79520e10 | −2.97170 | ||||||||
\(872\) | −6.83199e9 | −0.348931 | ||||||||
\(873\) | 6.99905e9 | 0.356032 | ||||||||
\(874\) | −3.14381e9 | −0.159282 | ||||||||
\(875\) | 9.13966e8 | 0.0461213 | ||||||||
\(876\) | 6.04383e9 | 0.303772 | ||||||||
\(877\) | −1.47072e10 | −0.736260 | −0.368130 | − | 0.929774i | \(-0.620002\pi\) | ||||
−0.368130 | + | 0.929774i | \(0.620002\pi\) | |||||||
\(878\) | −3.64093e10 | −1.81544 | ||||||||
\(879\) | −5.77546e8 | −0.0286831 | ||||||||
\(880\) | −1.94682e10 | −0.963020 | ||||||||
\(881\) | −9.76304e9 | −0.481027 | −0.240513 | − | 0.970646i | \(-0.577316\pi\) | ||||
−0.240513 | + | 0.970646i | \(0.577316\pi\) | |||||||
\(882\) | −9.08824e9 | −0.446005 | ||||||||
\(883\) | 2.10864e10 | 1.03072 | 0.515358 | − | 0.856975i | \(-0.327659\pi\) | ||||
0.515358 | + | 0.856975i | \(0.327659\pi\) | |||||||
\(884\) | 9.82253e9 | 0.478234 | ||||||||
\(885\) | 6.72066e8 | 0.0325920 | ||||||||
\(886\) | 1.81250e10 | 0.875508 | ||||||||
\(887\) | −1.84126e10 | −0.885897 | −0.442948 | − | 0.896547i | \(-0.646068\pi\) | ||||
−0.442948 | + | 0.896547i | \(0.646068\pi\) | |||||||
\(888\) | −1.89994e9 | −0.0910532 | ||||||||
\(889\) | −7.13981e8 | −0.0340824 | ||||||||
\(890\) | −1.05686e10 | −0.502521 | ||||||||
\(891\) | 3.64275e9 | 0.172527 | ||||||||
\(892\) | 1.69243e10 | 0.798422 | ||||||||
\(893\) | 9.43162e9 | 0.443207 | ||||||||
\(894\) | 1.49671e10 | 0.700578 | ||||||||
\(895\) | −7.09816e9 | −0.330952 | ||||||||
\(896\) | −5.71558e8 | −0.0265450 | ||||||||
\(897\) | 4.03432e9 | 0.186637 | ||||||||
\(898\) | −4.58998e10 | −2.11516 | ||||||||
\(899\) | 7.37354e10 | 3.38467 | ||||||||
\(900\) | −4.16274e9 | −0.190340 | ||||||||
\(901\) | 6.56437e9 | 0.298990 | ||||||||
\(902\) | −3.26602e10 | −1.48182 | ||||||||
\(903\) | −8.13813e8 | −0.0367805 | ||||||||
\(904\) | 1.94224e9 | 0.0874404 | ||||||||
\(905\) | 1.16418e10 | 0.522094 | ||||||||
\(906\) | −8.43387e9 | −0.376772 | ||||||||
\(907\) | −2.49645e10 | −1.11096 | −0.555480 | − | 0.831530i | \(-0.687465\pi\) | ||||
−0.555480 | + | 0.831530i | \(0.687465\pi\) | |||||||
\(908\) | −1.14815e10 | −0.508979 | ||||||||
\(909\) | −7.78739e9 | −0.343889 | ||||||||
\(910\) | −1.27186e9 | −0.0559493 | ||||||||
\(911\) | 2.05743e10 | 0.901594 | 0.450797 | − | 0.892627i | \(-0.351140\pi\) | ||||
0.450797 | + | 0.892627i | \(0.351140\pi\) | |||||||
\(912\) | 8.73943e9 | 0.381506 | ||||||||
\(913\) | −3.99146e10 | −1.73574 | ||||||||
\(914\) | −3.77674e10 | −1.63608 | ||||||||
\(915\) | 7.25154e9 | 0.312937 | ||||||||
\(916\) | −2.04143e10 | −0.877608 | ||||||||
\(917\) | −1.91699e9 | −0.0820972 | ||||||||
\(918\) | −2.33502e9 | −0.0996186 | ||||||||
\(919\) | −2.63487e10 | −1.11984 | −0.559918 | − | 0.828548i | \(-0.689167\pi\) | ||||
−0.559918 | + | 0.828548i | \(0.689167\pi\) | |||||||
\(920\) | 7.08345e8 | 0.0299908 | ||||||||
\(921\) | 1.77142e10 | 0.747158 | ||||||||
\(922\) | −3.10552e10 | −1.30489 | ||||||||
\(923\) | −1.64054e10 | −0.686720 | ||||||||
\(924\) | 8.65010e8 | 0.0360719 | ||||||||
\(925\) | 1.00770e10 | 0.418637 | ||||||||
\(926\) | 1.84178e10 | 0.762254 | ||||||||
\(927\) | 8.75792e9 | 0.361095 | ||||||||
\(928\) | −5.55032e10 | −2.27982 | ||||||||
\(929\) | −4.62120e10 | −1.89104 | −0.945518 | − | 0.325571i | \(-0.894443\pi\) | ||||
−0.945518 | + | 0.325571i | \(0.894443\pi\) | |||||||
\(930\) | −1.94077e10 | −0.791195 | ||||||||
\(931\) | −1.39859e10 | −0.568022 | ||||||||
\(932\) | −1.07599e10 | −0.435363 | ||||||||
\(933\) | 5.51217e9 | 0.222196 | ||||||||
\(934\) | −1.94857e10 | −0.782533 | ||||||||
\(935\) | 8.00463e9 | 0.320258 | ||||||||
\(936\) | −3.48880e9 | −0.139063 | ||||||||
\(937\) | −6.52016e9 | −0.258922 | −0.129461 | − | 0.991584i | \(-0.541325\pi\) | ||||
−0.129461 | + | 0.991584i | \(0.541325\pi\) | |||||||
\(938\) | 3.27134e9 | 0.129424 | ||||||||
\(939\) | 9.00816e8 | 0.0355064 | ||||||||
\(940\) | 8.46812e9 | 0.332537 | ||||||||
\(941\) | 6.12084e9 | 0.239468 | 0.119734 | − | 0.992806i | \(-0.461796\pi\) | ||||
0.119734 | + | 0.992806i | \(0.461796\pi\) | |||||||
\(942\) | 2.41238e10 | 0.940303 | ||||||||
\(943\) | 3.81997e9 | 0.148344 | ||||||||
\(944\) | 3.16758e9 | 0.122553 | ||||||||
\(945\) | 1.34320e8 | 0.00517760 | ||||||||
\(946\) | −6.86422e10 | −2.63616 | ||||||||
\(947\) | 6.84254e9 | 0.261814 | 0.130907 | − | 0.991395i | \(-0.458211\pi\) | ||||
0.130907 | + | 0.991395i | \(0.458211\pi\) | |||||||
\(948\) | −2.29838e10 | −0.876179 | ||||||||
\(949\) | −2.68659e10 | −1.02040 | ||||||||
\(950\) | −1.44197e10 | −0.545660 | ||||||||
\(951\) | 1.99784e10 | 0.753233 | ||||||||
\(952\) | 1.39145e8 | 0.00522684 | ||||||||
\(953\) | 3.05467e10 | 1.14324 | 0.571622 | − | 0.820517i | \(-0.306314\pi\) | ||||
0.571622 | + | 0.820517i | \(0.306314\pi\) | |||||||
\(954\) | 9.29091e9 | 0.346449 | ||||||||
\(955\) | 9.79232e9 | 0.363809 | ||||||||
\(956\) | −2.60597e10 | −0.964643 | ||||||||
\(957\) | −4.30436e10 | −1.58751 | ||||||||
\(958\) | 3.97896e10 | 1.46214 | ||||||||
\(959\) | 1.47563e9 | 0.0540273 | ||||||||
\(960\) | 4.79310e9 | 0.174851 | ||||||||
\(961\) | 7.29982e10 | 2.65326 | ||||||||
\(962\) | −3.36544e10 | −1.21879 | ||||||||
\(963\) | 4.03020e9 | 0.145423 | ||||||||
\(964\) | −2.67740e10 | −0.962594 | ||||||||
\(965\) | 4.56630e9 | 0.163576 | ||||||||
\(966\) | −2.27734e8 | −0.00812845 | ||||||||
\(967\) | −1.72169e10 | −0.612296 | −0.306148 | − | 0.951984i | \(-0.599040\pi\) | ||||
−0.306148 | + | 0.951984i | \(0.599040\pi\) | |||||||
\(968\) | −1.07154e10 | −0.379703 | ||||||||
\(969\) | −3.59335e9 | −0.126872 | ||||||||
\(970\) | 2.17678e10 | 0.765797 | ||||||||
\(971\) | −1.63286e10 | −0.572377 | −0.286188 | − | 0.958173i | \(-0.592388\pi\) | ||||
−0.286188 | + | 0.958173i | \(0.592388\pi\) | |||||||
\(972\) | −1.46821e9 | −0.0512810 | ||||||||
\(973\) | 9.05930e8 | 0.0315282 | ||||||||
\(974\) | 6.52871e10 | 2.26397 | ||||||||
\(975\) | 1.85042e10 | 0.639371 | ||||||||
\(976\) | 3.41779e10 | 1.17671 | ||||||||
\(977\) | 3.33959e9 | 0.114568 | 0.0572838 | − | 0.998358i | \(-0.481756\pi\) | ||||
0.0572838 | + | 0.998358i | \(0.481756\pi\) | |||||||
\(978\) | 1.16844e10 | 0.399411 | ||||||||
\(979\) | −3.19514e10 | −1.08831 | ||||||||
\(980\) | −1.25571e10 | −0.426186 | ||||||||
\(981\) | 1.27805e10 | 0.432223 | ||||||||
\(982\) | 3.47032e9 | 0.116944 | ||||||||
\(983\) | −1.18002e10 | −0.396233 | −0.198116 | − | 0.980178i | \(-0.563482\pi\) | ||||
−0.198116 | + | 0.980178i | \(0.563482\pi\) | |||||||
\(984\) | −3.30344e9 | −0.110531 | ||||||||
\(985\) | −9.89560e9 | −0.329925 | ||||||||
\(986\) | 2.75910e10 | 0.916640 | ||||||||
\(987\) | 6.83216e8 | 0.0226177 | ||||||||
\(988\) | 2.13943e10 | 0.705746 | ||||||||
\(989\) | 8.02845e9 | 0.263903 | ||||||||
\(990\) | 1.13294e10 | 0.371093 | ||||||||
\(991\) | 2.60974e10 | 0.851803 | 0.425901 | − | 0.904770i | \(-0.359957\pi\) | ||||
0.425901 | + | 0.904770i | \(0.359957\pi\) | |||||||
\(992\) | −7.56581e10 | −2.46073 | ||||||||
\(993\) | −1.18396e10 | −0.383722 | ||||||||
\(994\) | 9.26069e8 | 0.0299083 | ||||||||
\(995\) | 5.71625e9 | 0.183963 | ||||||||
\(996\) | 1.60876e10 | 0.515921 | ||||||||
\(997\) | 1.94933e10 | 0.622949 | 0.311474 | − | 0.950255i | \(-0.399177\pi\) | ||||
0.311474 | + | 0.950255i | \(0.399177\pi\) | |||||||
\(998\) | 2.62587e10 | 0.836213 | ||||||||
\(999\) | 3.55420e9 | 0.112788 |
(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.1.6 | ✓ | 7 | |
3.2 | odd | 2 | 207.8.a.d.1.2 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.c.1.6 | ✓ | 7 | 1.1 | even | 1 | trivial | |
207.8.a.d.1.2 | 7 | 3.2 | odd | 2 |