Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,8,Mod(1,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, 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("175.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.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: | \(54.6673794597\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 584x^{3} + 2550x^{2} + 46220x - 155664 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(3.21232\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.21232 | −0.460708 | −0.230354 | − | 0.973107i | \(-0.573988\pi\) | ||||
−0.230354 | + | 0.973107i | \(0.573988\pi\) | |||||||
\(3\) | 60.7456 | 1.29894 | 0.649472 | − | 0.760385i | \(-0.274990\pi\) | ||||
0.649472 | + | 0.760385i | \(0.274990\pi\) | |||||||
\(4\) | −100.832 | −0.787748 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −316.626 | −0.598435 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 1192.74 | 0.823630 | ||||||||
\(9\) | 1503.03 | 0.687258 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7403.54 | 1.67712 | 0.838562 | − | 0.544807i | \(-0.183397\pi\) | ||||
0.838562 | + | 0.544807i | \(0.183397\pi\) | |||||||
\(12\) | −6125.09 | −1.02324 | ||||||||
\(13\) | −3789.85 | −0.478432 | −0.239216 | − | 0.970966i | \(-0.576890\pi\) | ||||
−0.239216 | + | 0.970966i | \(0.576890\pi\) | |||||||
\(14\) | 1787.83 | 0.174131 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6689.50 | 0.408295 | ||||||||
\(17\) | −19226.5 | −0.949137 | −0.474568 | − | 0.880219i | \(-0.657396\pi\) | ||||
−0.474568 | + | 0.880219i | \(0.657396\pi\) | |||||||
\(18\) | −7834.29 | −0.316625 | ||||||||
\(19\) | −16627.4 | −0.556143 | −0.278071 | − | 0.960560i | \(-0.589695\pi\) | ||||
−0.278071 | + | 0.960560i | \(0.589695\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −20835.8 | −0.490955 | ||||||||
\(22\) | −38589.6 | −0.772665 | ||||||||
\(23\) | 31983.7 | 0.548127 | 0.274063 | − | 0.961712i | \(-0.411632\pi\) | ||||
0.274063 | + | 0.961712i | \(0.411632\pi\) | |||||||
\(24\) | 72454.0 | 1.06985 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 19753.9 | 0.220418 | ||||||||
\(27\) | −41548.0 | −0.406235 | ||||||||
\(28\) | 34585.3 | 0.297741 | ||||||||
\(29\) | 45395.3 | 0.345635 | 0.172817 | − | 0.984954i | \(-0.444713\pi\) | ||||
0.172817 | + | 0.984954i | \(0.444713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 92419.3 | 0.557182 | 0.278591 | − | 0.960410i | \(-0.410133\pi\) | ||||
0.278591 | + | 0.960410i | \(0.410133\pi\) | |||||||
\(32\) | −187539. | −1.01173 | ||||||||
\(33\) | 449733. | 2.17849 | ||||||||
\(34\) | 100215. | 0.437275 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −151553. | −0.541386 | ||||||||
\(37\) | 266269. | 0.864201 | 0.432100 | − | 0.901826i | \(-0.357773\pi\) | ||||
0.432100 | + | 0.901826i | \(0.357773\pi\) | |||||||
\(38\) | 86667.2 | 0.256220 | ||||||||
\(39\) | −230217. | −0.621457 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 627735. | 1.42244 | 0.711218 | − | 0.702971i | \(-0.248144\pi\) | ||||
0.711218 | + | 0.702971i | \(0.248144\pi\) | |||||||
\(42\) | 108603. | 0.226187 | ||||||||
\(43\) | 557671. | 1.06964 | 0.534821 | − | 0.844966i | \(-0.320379\pi\) | ||||
0.534821 | + | 0.844966i | \(0.320379\pi\) | |||||||
\(44\) | −746512. | −1.32115 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −166709. | −0.252526 | ||||||||
\(47\) | −412354. | −0.579332 | −0.289666 | − | 0.957128i | \(-0.593544\pi\) | ||||
−0.289666 | + | 0.957128i | \(0.593544\pi\) | |||||||
\(48\) | 406358. | 0.530352 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.16793e6 | −1.23288 | ||||||||
\(52\) | 382137. | 0.376884 | ||||||||
\(53\) | −1.34794e6 | −1.24367 | −0.621835 | − | 0.783148i | \(-0.713613\pi\) | ||||
−0.621835 | + | 0.783148i | \(0.713613\pi\) | |||||||
\(54\) | 216561. | 0.187156 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −409111. | −0.311303 | ||||||||
\(57\) | −1.01004e6 | −0.722399 | ||||||||
\(58\) | −236615. | −0.159237 | ||||||||
\(59\) | 2.79079e6 | 1.76907 | 0.884537 | − | 0.466471i | \(-0.154475\pi\) | ||||
0.884537 | + | 0.466471i | \(0.154475\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.92449e6 | 1.08558 | 0.542789 | − | 0.839869i | \(-0.317368\pi\) | ||||
0.542789 | + | 0.839869i | \(0.317368\pi\) | |||||||
\(62\) | −481719. | −0.256698 | ||||||||
\(63\) | −515540. | −0.259759 | ||||||||
\(64\) | 121257. | 0.0578199 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.34415e6 | −1.00365 | ||||||||
\(67\) | 2.92866e6 | 1.18962 | 0.594808 | − | 0.803868i | \(-0.297228\pi\) | ||||
0.594808 | + | 0.803868i | \(0.297228\pi\) | |||||||
\(68\) | 1.93864e6 | 0.747681 | ||||||||
\(69\) | 1.94287e6 | 0.711986 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.95928e6 | −0.981256 | −0.490628 | − | 0.871369i | \(-0.663233\pi\) | ||||
−0.490628 | + | 0.871369i | \(0.663233\pi\) | |||||||
\(72\) | 1.79273e6 | 0.566046 | ||||||||
\(73\) | −3.95050e6 | −1.18856 | −0.594281 | − | 0.804257i | \(-0.702563\pi\) | ||||
−0.594281 | + | 0.804257i | \(0.702563\pi\) | |||||||
\(74\) | −1.38788e6 | −0.398144 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.67657e6 | 0.438100 | ||||||||
\(77\) | −2.53941e6 | −0.633893 | ||||||||
\(78\) | 1.19996e6 | 0.286311 | ||||||||
\(79\) | 7.19828e6 | 1.64261 | 0.821304 | − | 0.570491i | \(-0.193247\pi\) | ||||
0.821304 | + | 0.570491i | \(0.193247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.81099e6 | −1.21493 | ||||||||
\(82\) | −3.27196e6 | −0.655328 | ||||||||
\(83\) | 7.88355e6 | 1.51338 | 0.756691 | − | 0.653773i | \(-0.226815\pi\) | ||||
0.756691 | + | 0.653773i | \(0.226815\pi\) | |||||||
\(84\) | 2.10091e6 | 0.386749 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −2.90676e6 | −0.492793 | ||||||||
\(87\) | 2.75756e6 | 0.448961 | ||||||||
\(88\) | 8.83053e6 | 1.38133 | ||||||||
\(89\) | 3.37393e6 | 0.507307 | 0.253654 | − | 0.967295i | \(-0.418368\pi\) | ||||
0.253654 | + | 0.967295i | \(0.418368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29992e6 | 0.180830 | ||||||||
\(92\) | −3.22497e6 | −0.431786 | ||||||||
\(93\) | 5.61407e6 | 0.723748 | ||||||||
\(94\) | 2.14932e6 | 0.266903 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.13922e7 | −1.31419 | ||||||||
\(97\) | 9.18493e6 | 1.02182 | 0.510911 | − | 0.859634i | \(-0.329308\pi\) | ||||
0.510911 | + | 0.859634i | \(0.329308\pi\) | |||||||
\(98\) | −613224. | −0.0658155 | ||||||||
\(99\) | 1.11278e7 | 1.15262 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.49820e6 | 0.917311 | 0.458655 | − | 0.888614i | \(-0.348331\pi\) | ||||
0.458655 | + | 0.888614i | \(0.348331\pi\) | |||||||
\(102\) | 6.08760e6 | 0.567996 | ||||||||
\(103\) | 1.40943e7 | 1.27090 | 0.635451 | − | 0.772141i | \(-0.280814\pi\) | ||||
0.635451 | + | 0.772141i | \(0.280814\pi\) | |||||||
\(104\) | −4.52032e6 | −0.394051 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.02590e6 | 0.572969 | ||||||||
\(107\) | 9.75316e6 | 0.769666 | 0.384833 | − | 0.922986i | \(-0.374259\pi\) | ||||
0.384833 | + | 0.922986i | \(0.374259\pi\) | |||||||
\(108\) | 4.18936e6 | 0.320011 | ||||||||
\(109\) | 8.22102e6 | 0.608041 | 0.304021 | − | 0.952665i | \(-0.401671\pi\) | ||||
0.304021 | + | 0.952665i | \(0.401671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.61747e7 | 1.12255 | ||||||||
\(112\) | −2.29450e6 | −0.154321 | ||||||||
\(113\) | −1.63107e7 | −1.06341 | −0.531703 | − | 0.846931i | \(-0.678448\pi\) | ||||
−0.531703 | + | 0.846931i | \(0.678448\pi\) | |||||||
\(114\) | 5.26466e6 | 0.332815 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.57728e6 | −0.272273 | ||||||||
\(117\) | −5.69627e6 | −0.328806 | ||||||||
\(118\) | −1.45465e7 | −0.815027 | ||||||||
\(119\) | 6.59469e6 | 0.358740 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.53252e7 | 1.81274 | ||||||||
\(122\) | −1.00310e7 | −0.500135 | ||||||||
\(123\) | 3.81322e7 | 1.84767 | ||||||||
\(124\) | −9.31880e6 | −0.438919 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.68716e6 | 0.119673 | ||||||||
\(127\) | 2.17950e6 | 0.0944158 | 0.0472079 | − | 0.998885i | \(-0.484968\pi\) | ||||
0.0472079 | + | 0.998885i | \(0.484968\pi\) | |||||||
\(128\) | 2.33730e7 | 0.985097 | ||||||||
\(129\) | 3.38761e7 | 1.38940 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.74218e7 | −1.45437 | −0.727185 | − | 0.686442i | \(-0.759172\pi\) | ||||
−0.727185 | + | 0.686442i | \(0.759172\pi\) | |||||||
\(132\) | −4.53473e7 | −1.71610 | ||||||||
\(133\) | 5.70319e6 | 0.210202 | ||||||||
\(134\) | −1.52651e7 | −0.548066 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.29323e7 | −0.781738 | ||||||||
\(137\) | 4.62620e7 | 1.53710 | 0.768550 | − | 0.639790i | \(-0.220978\pi\) | ||||
0.768550 | + | 0.639790i | \(0.220978\pi\) | |||||||
\(138\) | −1.01268e7 | −0.328018 | ||||||||
\(139\) | 3.79070e7 | 1.19720 | 0.598601 | − | 0.801047i | \(-0.295723\pi\) | ||||
0.598601 | + | 0.801047i | \(0.295723\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.50487e7 | −0.752520 | ||||||||
\(142\) | 1.54247e7 | 0.452073 | ||||||||
\(143\) | −2.80583e7 | −0.802390 | ||||||||
\(144\) | 1.00545e7 | 0.280604 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.05913e7 | 0.547580 | ||||||||
\(147\) | 7.14666e6 | 0.185564 | ||||||||
\(148\) | −2.68484e7 | −0.680772 | ||||||||
\(149\) | −7.04498e7 | −1.74473 | −0.872365 | − | 0.488856i | \(-0.837414\pi\) | ||||
−0.872365 | + | 0.488856i | \(0.837414\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.29486e7 | −1.48788 | −0.743938 | − | 0.668249i | \(-0.767044\pi\) | ||||
−0.743938 | + | 0.668249i | \(0.767044\pi\) | |||||||
\(152\) | −1.98322e7 | −0.458056 | ||||||||
\(153\) | −2.88981e7 | −0.652302 | ||||||||
\(154\) | 1.32362e7 | 0.292040 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.32132e7 | 0.489552 | ||||||||
\(157\) | −8.03559e7 | −1.65718 | −0.828588 | − | 0.559859i | \(-0.810855\pi\) | ||||
−0.828588 | + | 0.559859i | \(0.810855\pi\) | |||||||
\(158\) | −3.75197e7 | −0.756763 | ||||||||
\(159\) | −8.18815e7 | −1.61546 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.09704e7 | −0.207172 | ||||||||
\(162\) | 3.02888e7 | 0.559730 | ||||||||
\(163\) | −4.93485e7 | −0.892518 | −0.446259 | − | 0.894904i | \(-0.647244\pi\) | ||||
−0.446259 | + | 0.894904i | \(0.647244\pi\) | |||||||
\(164\) | −6.32956e7 | −1.12052 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.10916e7 | −0.697227 | ||||||||
\(167\) | 2.78438e7 | 0.462616 | 0.231308 | − | 0.972881i | \(-0.425699\pi\) | ||||
0.231308 | + | 0.972881i | \(0.425699\pi\) | |||||||
\(168\) | −2.48517e7 | −0.404365 | ||||||||
\(169\) | −4.83855e7 | −0.771102 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.49915e7 | −0.382214 | ||||||||
\(172\) | −5.62309e7 | −0.842608 | ||||||||
\(173\) | 3.91017e7 | 0.574162 | 0.287081 | − | 0.957906i | \(-0.407315\pi\) | ||||
0.287081 | + | 0.957906i | \(0.407315\pi\) | |||||||
\(174\) | −1.43733e7 | −0.206840 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.95260e7 | 0.684761 | ||||||||
\(177\) | 1.69529e8 | 2.29793 | ||||||||
\(178\) | −1.75860e7 | −0.233721 | ||||||||
\(179\) | −3.05418e7 | −0.398024 | −0.199012 | − | 0.979997i | \(-0.563773\pi\) | ||||
−0.199012 | + | 0.979997i | \(0.563773\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.42309e7 | 0.679785 | 0.339892 | − | 0.940464i | \(-0.389609\pi\) | ||||
0.339892 | + | 0.940464i | \(0.389609\pi\) | |||||||
\(182\) | −6.77560e6 | −0.0833101 | ||||||||
\(183\) | 1.16904e8 | 1.41011 | ||||||||
\(184\) | 3.81483e7 | 0.451454 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.92623e7 | −0.333437 | ||||||||
\(187\) | −1.42344e8 | −1.59182 | ||||||||
\(188\) | 4.15784e7 | 0.456368 | ||||||||
\(189\) | 1.42510e7 | 0.153542 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.75614e8 | 1.82366 | 0.911828 | − | 0.410573i | \(-0.134671\pi\) | ||||
0.911828 | + | 0.410573i | \(0.134671\pi\) | |||||||
\(192\) | 7.36584e6 | 0.0751049 | ||||||||
\(193\) | −1.10954e8 | −1.11095 | −0.555474 | − | 0.831534i | \(-0.687463\pi\) | ||||
−0.555474 | + | 0.831534i | \(0.687463\pi\) | |||||||
\(194\) | −4.78748e7 | −0.470762 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.18628e7 | −0.112535 | ||||||||
\(197\) | −1.00536e8 | −0.936895 | −0.468448 | − | 0.883491i | \(-0.655187\pi\) | ||||
−0.468448 | + | 0.883491i | \(0.655187\pi\) | |||||||
\(198\) | −5.80015e7 | −0.531020 | ||||||||
\(199\) | 4.14944e7 | 0.373253 | 0.186627 | − | 0.982431i | \(-0.440245\pi\) | ||||
0.186627 | + | 0.982431i | \(0.440245\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.77903e8 | 1.54524 | ||||||||
\(202\) | −4.95076e7 | −0.422613 | ||||||||
\(203\) | −1.55706e7 | −0.130638 | ||||||||
\(204\) | 1.17764e8 | 0.971196 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.34638e7 | −0.585515 | ||||||||
\(207\) | 4.80725e7 | 0.376704 | ||||||||
\(208\) | −2.53522e7 | −0.195341 | ||||||||
\(209\) | −1.23102e8 | −0.932720 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.53393e8 | 1.85698 | 0.928488 | − | 0.371362i | \(-0.121109\pi\) | ||||
0.928488 | + | 0.371362i | \(0.121109\pi\) | |||||||
\(212\) | 1.35915e8 | 0.979699 | ||||||||
\(213\) | −1.79764e8 | −1.27460 | ||||||||
\(214\) | −5.08366e7 | −0.354591 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.95561e7 | −0.334587 | ||||||||
\(217\) | −3.16998e7 | −0.210595 | ||||||||
\(218\) | −4.28506e7 | −0.280130 | ||||||||
\(219\) | −2.39976e8 | −1.54388 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.28656e7 | 0.454098 | ||||||||
\(222\) | −8.43076e7 | −0.517168 | ||||||||
\(223\) | 2.33810e8 | 1.41188 | 0.705938 | − | 0.708274i | \(-0.250526\pi\) | ||||
0.705938 | + | 0.708274i | \(0.250526\pi\) | |||||||
\(224\) | 6.43259e7 | 0.382400 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.50168e7 | 0.489920 | ||||||||
\(227\) | −6.88221e7 | −0.390515 | −0.195257 | − | 0.980752i | \(-0.562554\pi\) | ||||
−0.195257 | + | 0.980752i | \(0.562554\pi\) | |||||||
\(228\) | 1.01844e8 | 0.569068 | ||||||||
\(229\) | 3.13920e7 | 0.172741 | 0.0863703 | − | 0.996263i | \(-0.472473\pi\) | ||||
0.0863703 | + | 0.996263i | \(0.472473\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.54258e8 | −0.823392 | ||||||||
\(232\) | 5.41449e7 | 0.284675 | ||||||||
\(233\) | −7.51549e7 | −0.389235 | −0.194617 | − | 0.980879i | \(-0.562346\pi\) | ||||
−0.194617 | + | 0.980879i | \(0.562346\pi\) | |||||||
\(234\) | 2.96908e7 | 0.151484 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.81401e8 | −1.39358 | ||||||||
\(237\) | 4.37264e8 | 2.13366 | ||||||||
\(238\) | −3.43736e7 | −0.165274 | ||||||||
\(239\) | −1.92365e8 | −0.911453 | −0.455727 | − | 0.890120i | \(-0.650621\pi\) | ||||
−0.455727 | + | 0.890120i | \(0.650621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.32330e7 | 0.0608972 | 0.0304486 | − | 0.999536i | \(-0.490306\pi\) | ||||
0.0304486 | + | 0.999536i | \(0.490306\pi\) | |||||||
\(242\) | −1.84126e8 | −0.835146 | ||||||||
\(243\) | −2.62127e8 | −1.17190 | ||||||||
\(244\) | −1.94050e8 | −0.855162 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.98757e8 | −0.851235 | ||||||||
\(247\) | 6.30154e7 | 0.266077 | ||||||||
\(248\) | 1.10233e8 | 0.458912 | ||||||||
\(249\) | 4.78891e8 | 1.96580 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.72781e8 | 0.689666 | 0.344833 | − | 0.938664i | \(-0.387936\pi\) | ||||
0.344833 | + | 0.938664i | \(0.387936\pi\) | |||||||
\(252\) | 5.19828e7 | 0.204625 | ||||||||
\(253\) | 2.36792e8 | 0.919276 | ||||||||
\(254\) | −1.13603e7 | −0.0434981 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.37348e8 | −0.511662 | ||||||||
\(257\) | −2.03178e8 | −0.746638 | −0.373319 | − | 0.927703i | \(-0.621780\pi\) | ||||
−0.373319 | + | 0.927703i | \(0.621780\pi\) | |||||||
\(258\) | −1.76573e8 | −0.640110 | ||||||||
\(259\) | −9.13303e7 | −0.326637 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.82306e7 | 0.237540 | ||||||||
\(262\) | 1.95054e8 | 0.670040 | ||||||||
\(263\) | −5.23865e6 | −0.0177572 | −0.00887859 | − | 0.999961i | \(-0.502826\pi\) | ||||
−0.00887859 | + | 0.999961i | \(0.502826\pi\) | |||||||
\(264\) | 5.36416e8 | 1.79427 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.97269e7 | −0.0968419 | ||||||||
\(267\) | 2.04951e8 | 0.658964 | ||||||||
\(268\) | −2.95301e8 | −0.937117 | ||||||||
\(269\) | −2.67408e8 | −0.837609 | −0.418805 | − | 0.908076i | \(-0.637551\pi\) | ||||
−0.418805 | + | 0.908076i | \(0.637551\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.64451e8 | −1.72280 | −0.861398 | − | 0.507931i | \(-0.830410\pi\) | ||||
−0.861398 | + | 0.507931i | \(0.830410\pi\) | |||||||
\(272\) | −1.28616e8 | −0.387528 | ||||||||
\(273\) | 7.89645e7 | 0.234889 | ||||||||
\(274\) | −2.41132e8 | −0.708155 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.95903e8 | −0.560866 | ||||||||
\(277\) | −4.66139e8 | −1.31776 | −0.658880 | − | 0.752248i | \(-0.728969\pi\) | ||||
−0.658880 | + | 0.752248i | \(0.728969\pi\) | |||||||
\(278\) | −1.97583e8 | −0.551561 | ||||||||
\(279\) | 1.38909e8 | 0.382928 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.15073e8 | −0.847108 | −0.423554 | − | 0.905871i | \(-0.639218\pi\) | ||||
−0.423554 | + | 0.905871i | \(0.639218\pi\) | |||||||
\(282\) | 1.30562e8 | 0.346692 | ||||||||
\(283\) | 8.18186e7 | 0.214585 | 0.107293 | − | 0.994227i | \(-0.465782\pi\) | ||||
0.107293 | + | 0.994227i | \(0.465782\pi\) | |||||||
\(284\) | 2.98390e8 | 0.772982 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.46249e8 | 0.369668 | ||||||||
\(287\) | −2.15313e8 | −0.537631 | ||||||||
\(288\) | −2.81877e8 | −0.695323 | ||||||||
\(289\) | −4.06806e7 | −0.0991390 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.57945e8 | 1.32729 | ||||||||
\(292\) | 3.98336e8 | 0.936287 | ||||||||
\(293\) | 1.99777e8 | 0.463989 | 0.231995 | − | 0.972717i | \(-0.425475\pi\) | ||||
0.231995 | + | 0.972717i | \(0.425475\pi\) | |||||||
\(294\) | −3.72507e7 | −0.0854907 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.17591e8 | 0.711782 | ||||||||
\(297\) | −3.07602e8 | −0.681306 | ||||||||
\(298\) | 3.67207e8 | 0.803811 | ||||||||
\(299\) | −1.21213e8 | −0.262242 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.91281e8 | −0.404286 | ||||||||
\(302\) | 3.28108e8 | 0.685477 | ||||||||
\(303\) | 5.76974e8 | 1.19154 | ||||||||
\(304\) | −1.11229e8 | −0.227070 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.50626e8 | 0.300521 | ||||||||
\(307\) | 4.82719e7 | 0.0952160 | 0.0476080 | − | 0.998866i | \(-0.484840\pi\) | ||||
0.0476080 | + | 0.998866i | \(0.484840\pi\) | |||||||
\(308\) | 2.56054e8 | 0.499348 | ||||||||
\(309\) | 8.56165e8 | 1.65083 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.27544e8 | 0.428947 | 0.214473 | − | 0.976730i | \(-0.431196\pi\) | ||||
0.214473 | + | 0.976730i | \(0.431196\pi\) | |||||||
\(312\) | −2.74590e8 | −0.511851 | ||||||||
\(313\) | −1.84509e8 | −0.340104 | −0.170052 | − | 0.985435i | \(-0.554394\pi\) | ||||
−0.170052 | + | 0.985435i | \(0.554394\pi\) | |||||||
\(314\) | 4.18840e8 | 0.763475 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.25815e8 | −1.29396 | ||||||||
\(317\) | −1.33207e8 | −0.234865 | −0.117433 | − | 0.993081i | \(-0.537466\pi\) | ||||
−0.117433 | + | 0.993081i | \(0.537466\pi\) | |||||||
\(318\) | 4.26793e8 | 0.744255 | ||||||||
\(319\) | 3.36086e8 | 0.579672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.92462e8 | 0.999754 | ||||||||
\(322\) | 5.71812e7 | 0.0954460 | ||||||||
\(323\) | 3.19686e8 | 0.527856 | ||||||||
\(324\) | 5.85933e8 | 0.957062 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.57220e8 | 0.411191 | ||||||||
\(327\) | 4.99391e8 | 0.789812 | ||||||||
\(328\) | 7.48727e8 | 1.17156 | ||||||||
\(329\) | 1.41437e8 | 0.218967 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.48801e8 | −0.377098 | −0.188549 | − | 0.982064i | \(-0.560378\pi\) | ||||
−0.188549 | + | 0.982064i | \(0.560378\pi\) | |||||||
\(332\) | −7.94912e8 | −1.19216 | ||||||||
\(333\) | 4.00211e8 | 0.593929 | ||||||||
\(334\) | −1.45131e8 | −0.213131 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.39381e8 | −0.200454 | ||||||||
\(337\) | 1.76663e8 | 0.251444 | 0.125722 | − | 0.992065i | \(-0.459875\pi\) | ||||
0.125722 | + | 0.992065i | \(0.459875\pi\) | |||||||
\(338\) | 2.52201e8 | 0.355253 | ||||||||
\(339\) | −9.90807e8 | −1.38131 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.84230e8 | 0.934463 | ||||||||
\(342\) | 1.30264e8 | 0.176089 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 6.65158e8 | 0.880989 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.03811e8 | −0.264521 | ||||||||
\(347\) | 4.82632e8 | 0.620101 | 0.310051 | − | 0.950720i | \(-0.399654\pi\) | ||||
0.310051 | + | 0.950720i | \(0.399654\pi\) | |||||||
\(348\) | −2.78050e8 | −0.353668 | ||||||||
\(349\) | 9.78940e7 | 0.123273 | 0.0616364 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616364 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.57461e8 | 0.194356 | ||||||||
\(352\) | −1.38845e9 | −1.69680 | ||||||||
\(353\) | −1.60663e8 | −0.194404 | −0.0972021 | − | 0.995265i | \(-0.530989\pi\) | ||||
−0.0972021 | + | 0.995265i | \(0.530989\pi\) | |||||||
\(354\) | −8.83637e8 | −1.05867 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.40199e8 | −0.399630 | ||||||||
\(357\) | 4.00599e8 | 0.465984 | ||||||||
\(358\) | 1.59194e8 | 0.183373 | ||||||||
\(359\) | −1.27950e9 | −1.45952 | −0.729761 | − | 0.683702i | \(-0.760369\pi\) | ||||
−0.729761 | + | 0.683702i | \(0.760369\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.17402e8 | −0.690705 | ||||||||
\(362\) | −2.82669e8 | −0.313182 | ||||||||
\(363\) | 2.14585e9 | 2.35465 | ||||||||
\(364\) | −1.31073e8 | −0.142449 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.09342e8 | −0.649647 | ||||||||
\(367\) | 1.35171e9 | 1.42743 | 0.713713 | − | 0.700439i | \(-0.247012\pi\) | ||||
0.713713 | + | 0.700439i | \(0.247012\pi\) | |||||||
\(368\) | 2.13955e8 | 0.223797 | ||||||||
\(369\) | 9.43507e8 | 0.977581 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.62344e8 | 0.470063 | ||||||||
\(372\) | −5.66077e8 | −0.570131 | ||||||||
\(373\) | −1.65708e9 | −1.65334 | −0.826669 | − | 0.562689i | \(-0.809767\pi\) | ||||
−0.826669 | + | 0.562689i | \(0.809767\pi\) | |||||||
\(374\) | 7.41943e8 | 0.733365 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.91833e8 | −0.477155 | ||||||||
\(377\) | −1.72041e8 | −0.165363 | ||||||||
\(378\) | −7.42806e7 | −0.0707382 | ||||||||
\(379\) | 5.29980e8 | 0.500060 | 0.250030 | − | 0.968238i | \(-0.419559\pi\) | ||||
0.250030 | + | 0.968238i | \(0.419559\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.32395e8 | 0.122641 | ||||||||
\(382\) | −9.15357e8 | −0.840173 | ||||||||
\(383\) | 1.00532e9 | 0.914338 | 0.457169 | − | 0.889380i | \(-0.348864\pi\) | ||||
0.457169 | + | 0.889380i | \(0.348864\pi\) | |||||||
\(384\) | 1.41981e9 | 1.27959 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.78329e8 | 0.511823 | ||||||||
\(387\) | 8.38197e8 | 0.735119 | ||||||||
\(388\) | −9.26133e8 | −0.804938 | ||||||||
\(389\) | 9.23418e7 | 0.0795380 | 0.0397690 | − | 0.999209i | \(-0.487338\pi\) | ||||
0.0397690 | + | 0.999209i | \(0.487338\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.14934e8 | −0.520247 | ||||||||
\(392\) | 1.40325e8 | 0.117661 | ||||||||
\(393\) | −2.27321e9 | −1.88915 | ||||||||
\(394\) | 5.24027e8 | 0.431635 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.12203e9 | −0.907971 | ||||||||
\(397\) | 1.43695e9 | 1.15259 | 0.576294 | − | 0.817242i | \(-0.304498\pi\) | ||||
0.576294 | + | 0.817242i | \(0.304498\pi\) | |||||||
\(398\) | −2.16282e8 | −0.171961 | ||||||||
\(399\) | 3.46444e8 | 0.273041 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.72906e9 | −1.33907 | −0.669536 | − | 0.742780i | \(-0.733507\pi\) | ||||
−0.669536 | + | 0.742780i | \(0.733507\pi\) | |||||||
\(402\) | −9.27288e8 | −0.711907 | ||||||||
\(403\) | −3.50256e8 | −0.266574 | ||||||||
\(404\) | −9.57720e8 | −0.722610 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.11588e7 | 0.0601858 | ||||||||
\(407\) | 1.97133e9 | 1.44937 | ||||||||
\(408\) | −1.39304e9 | −1.01543 | ||||||||
\(409\) | −5.81285e8 | −0.420105 | −0.210052 | − | 0.977690i | \(-0.567363\pi\) | ||||
−0.210052 | + | 0.977690i | \(0.567363\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.81021e9 | 1.99661 | ||||||||
\(412\) | −1.42115e9 | −1.00115 | ||||||||
\(413\) | −9.57243e8 | −0.668647 | ||||||||
\(414\) | −2.50569e8 | −0.173551 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.10745e8 | 0.484047 | ||||||||
\(417\) | 2.30268e9 | 1.55510 | ||||||||
\(418\) | 6.41644e8 | 0.429712 | ||||||||
\(419\) | 2.05004e8 | 0.136149 | 0.0680743 | − | 0.997680i | \(-0.478314\pi\) | ||||
0.0680743 | + | 0.997680i | \(0.478314\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32820e9 | −0.867514 | −0.433757 | − | 0.901030i | \(-0.642812\pi\) | ||||
−0.433757 | + | 0.901030i | \(0.642812\pi\) | |||||||
\(422\) | −1.32077e9 | −0.855524 | ||||||||
\(423\) | −6.19782e8 | −0.398151 | ||||||||
\(424\) | −1.60775e9 | −1.02432 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9.36985e8 | 0.587218 | ||||||||
\(427\) | −6.60100e8 | −0.410310 | ||||||||
\(428\) | −9.83428e8 | −0.606303 | ||||||||
\(429\) | −1.70442e9 | −1.04226 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.71243e9 | 1.03025 | 0.515124 | − | 0.857116i | \(-0.327746\pi\) | ||||
0.515124 | + | 0.857116i | \(0.327746\pi\) | |||||||
\(432\) | −2.77935e8 | −0.165864 | ||||||||
\(433\) | −1.26981e9 | −0.751675 | −0.375838 | − | 0.926686i | \(-0.622645\pi\) | ||||
−0.375838 | + | 0.926686i | \(0.622645\pi\) | |||||||
\(434\) | 1.65230e8 | 0.0970228 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.28940e8 | −0.478983 | ||||||||
\(437\) | −5.31805e8 | −0.304837 | ||||||||
\(438\) | 1.25083e9 | 0.711277 | ||||||||
\(439\) | −7.13810e8 | −0.402677 | −0.201339 | − | 0.979522i | \(-0.564529\pi\) | ||||
−0.201339 | + | 0.979522i | \(0.564529\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.76830e8 | 0.0981797 | ||||||||
\(442\) | −3.79799e8 | −0.209207 | ||||||||
\(443\) | −1.33285e9 | −0.728399 | −0.364199 | − | 0.931321i | \(-0.618657\pi\) | ||||
−0.364199 | + | 0.931321i | \(0.618657\pi\) | |||||||
\(444\) | −1.63092e9 | −0.884286 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.21869e9 | −0.650463 | ||||||||
\(447\) | −4.27952e9 | −2.26631 | ||||||||
\(448\) | −4.15912e7 | −0.0218539 | ||||||||
\(449\) | −8.55950e8 | −0.446258 | −0.223129 | − | 0.974789i | \(-0.571627\pi\) | ||||
−0.223129 | + | 0.974789i | \(0.571627\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.64746e9 | 2.38560 | ||||||||
\(452\) | 1.64464e9 | 0.837696 | ||||||||
\(453\) | −3.82385e9 | −1.93267 | ||||||||
\(454\) | 3.58723e8 | 0.179913 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.20472e9 | −0.594990 | ||||||||
\(457\) | 3.18676e9 | 1.56186 | 0.780931 | − | 0.624618i | \(-0.214745\pi\) | ||||
0.780931 | + | 0.624618i | \(0.214745\pi\) | |||||||
\(458\) | −1.63625e8 | −0.0795830 | ||||||||
\(459\) | 7.98823e8 | 0.385572 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.02974e9 | 1.44030 | 0.720148 | − | 0.693821i | \(-0.244074\pi\) | ||||
0.720148 | + | 0.693821i | \(0.244074\pi\) | |||||||
\(462\) | 8.04044e8 | 0.379344 | ||||||||
\(463\) | 1.53211e9 | 0.717390 | 0.358695 | − | 0.933455i | \(-0.383222\pi\) | ||||
0.358695 | + | 0.933455i | \(0.383222\pi\) | |||||||
\(464\) | 3.03672e8 | 0.141121 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.91731e8 | 0.179324 | ||||||||
\(467\) | 3.47187e9 | 1.57745 | 0.788724 | − | 0.614748i | \(-0.210742\pi\) | ||||
0.788724 | + | 0.614748i | \(0.210742\pi\) | |||||||
\(468\) | 5.74365e8 | 0.259017 | ||||||||
\(469\) | −1.00453e9 | −0.449632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.88127e9 | −2.15258 | ||||||||
\(472\) | 3.32870e9 | 1.45706 | ||||||||
\(473\) | 4.12874e9 | 1.79392 | ||||||||
\(474\) | −2.27916e9 | −0.982993 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.64954e8 | −0.282597 | ||||||||
\(477\) | −2.02600e9 | −0.854722 | ||||||||
\(478\) | 1.00267e9 | 0.419914 | ||||||||
\(479\) | 4.81799e8 | 0.200305 | 0.100152 | − | 0.994972i | \(-0.468067\pi\) | ||||
0.100152 | + | 0.994972i | \(0.468067\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.00912e9 | −0.413462 | ||||||||
\(482\) | −6.89744e7 | −0.0280559 | ||||||||
\(483\) | −6.66404e8 | −0.269105 | ||||||||
\(484\) | −3.56190e9 | −1.42798 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.36629e9 | 0.539903 | ||||||||
\(487\) | −2.95036e9 | −1.15751 | −0.578753 | − | 0.815503i | \(-0.696461\pi\) | ||||
−0.578753 | + | 0.815503i | \(0.696461\pi\) | |||||||
\(488\) | 2.29542e9 | 0.894115 | ||||||||
\(489\) | −2.99770e9 | −1.15933 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.55876e8 | −0.0594285 | −0.0297143 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297143 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(492\) | −3.84493e9 | −1.45550 | ||||||||
\(493\) | −8.72792e8 | −0.328055 | ||||||||
\(494\) | −3.28456e8 | −0.122584 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.18239e8 | 0.227494 | ||||||||
\(497\) | 1.01503e9 | 0.370880 | ||||||||
\(498\) | −2.49613e9 | −0.905660 | ||||||||
\(499\) | 3.27549e9 | 1.18012 | 0.590058 | − | 0.807361i | \(-0.299105\pi\) | ||||
0.590058 | + | 0.807361i | \(0.299105\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.69139e9 | 0.600913 | ||||||||
\(502\) | −9.00591e8 | −0.317735 | ||||||||
\(503\) | 2.93132e9 | 1.02701 | 0.513506 | − | 0.858086i | \(-0.328346\pi\) | ||||
0.513506 | + | 0.858086i | \(0.328346\pi\) | |||||||
\(504\) | −6.14908e8 | −0.213945 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.23424e9 | −0.423518 | ||||||||
\(507\) | −2.93921e9 | −1.00162 | ||||||||
\(508\) | −2.19763e8 | −0.0743759 | ||||||||
\(509\) | −2.94603e9 | −0.990205 | −0.495103 | − | 0.868834i | \(-0.664870\pi\) | ||||
−0.495103 | + | 0.868834i | \(0.664870\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35502e9 | 0.449234 | ||||||||
\(512\) | −2.27584e9 | −0.749370 | ||||||||
\(513\) | 6.90835e8 | 0.225925 | ||||||||
\(514\) | 1.05903e9 | 0.343982 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.41578e9 | −1.09450 | ||||||||
\(517\) | −3.05288e9 | −0.971611 | ||||||||
\(518\) | 4.76042e8 | 0.150484 | ||||||||
\(519\) | 2.37526e9 | 0.745805 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.63933e9 | 1.43722 | 0.718610 | − | 0.695414i | \(-0.244779\pi\) | ||||
0.718610 | + | 0.695414i | \(0.244779\pi\) | |||||||
\(522\) | −3.55639e8 | −0.109437 | ||||||||
\(523\) | −4.38133e9 | −1.33921 | −0.669607 | − | 0.742716i | \(-0.733537\pi\) | ||||
−0.669607 | + | 0.742716i | \(0.733537\pi\) | |||||||
\(524\) | 3.77330e9 | 1.14568 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.73055e7 | 0.00818088 | ||||||||
\(527\) | −1.77690e9 | −0.528842 | ||||||||
\(528\) | 3.00849e9 | 0.889466 | ||||||||
\(529\) | −2.38187e9 | −0.699557 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.19466e9 | 1.21581 | ||||||||
\(532\) | −5.75063e8 | −0.165586 | ||||||||
\(533\) | −2.37902e9 | −0.680540 | ||||||||
\(534\) | −1.06827e9 | −0.303590 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.49314e9 | 0.979803 | ||||||||
\(537\) | −1.85528e9 | −0.517011 | ||||||||
\(538\) | 1.39382e9 | 0.385894 | ||||||||
\(539\) | 8.71019e8 | 0.239589 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.97296e9 | −1.07876 | −0.539379 | − | 0.842063i | \(-0.681341\pi\) | ||||
−0.539379 | + | 0.842063i | \(0.681341\pi\) | |||||||
\(542\) | 2.94210e9 | 0.793706 | ||||||||
\(543\) | 3.29429e9 | 0.883003 | ||||||||
\(544\) | 3.60572e9 | 0.960275 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.11588e8 | −0.108215 | ||||||||
\(547\) | −2.57944e8 | −0.0673859 | −0.0336930 | − | 0.999432i | \(-0.510727\pi\) | ||||
−0.0336930 | + | 0.999432i | \(0.510727\pi\) | |||||||
\(548\) | −4.66468e9 | −1.21085 | ||||||||
\(549\) | 2.89257e9 | 0.746072 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.54804e8 | −0.192222 | ||||||||
\(552\) | 2.31734e9 | 0.586413 | ||||||||
\(553\) | −2.46901e9 | −0.620847 | ||||||||
\(554\) | 2.42967e9 | 0.607103 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.82223e9 | −0.943094 | ||||||||
\(557\) | 3.66731e9 | 0.899197 | 0.449598 | − | 0.893231i | \(-0.351567\pi\) | ||||
0.449598 | + | 0.893231i | \(0.351567\pi\) | |||||||
\(558\) | −7.24040e8 | −0.176418 | ||||||||
\(559\) | −2.11349e9 | −0.511751 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.64679e9 | −2.06769 | ||||||||
\(562\) | 1.64226e9 | 0.390270 | ||||||||
\(563\) | 4.50414e9 | 1.06373 | 0.531866 | − | 0.846828i | \(-0.321491\pi\) | ||||
0.531866 | + | 0.846828i | \(0.321491\pi\) | |||||||
\(564\) | 2.52570e9 | 0.592796 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.26464e8 | −0.0988611 | ||||||||
\(567\) | 1.99317e9 | 0.459202 | ||||||||
\(568\) | −3.52967e9 | −0.808192 | ||||||||
\(569\) | 2.99694e9 | 0.682000 | 0.341000 | − | 0.940063i | \(-0.389234\pi\) | ||||
0.341000 | + | 0.940063i | \(0.389234\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.03468e9 | 1.80610 | 0.903051 | − | 0.429534i | \(-0.141322\pi\) | ||||
0.903051 | + | 0.429534i | \(0.141322\pi\) | |||||||
\(572\) | 2.82917e9 | 0.632081 | ||||||||
\(573\) | 1.06678e10 | 2.36883 | ||||||||
\(574\) | 1.12228e9 | 0.247691 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.82253e8 | 0.0397372 | ||||||||
\(577\) | 1.52605e9 | 0.330714 | 0.165357 | − | 0.986234i | \(-0.447122\pi\) | ||||
0.165357 | + | 0.986234i | \(0.447122\pi\) | |||||||
\(578\) | 2.12040e8 | 0.0456742 | ||||||||
\(579\) | −6.73999e9 | −1.44306 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.70406e9 | −0.572004 | ||||||||
\(582\) | −2.90819e9 | −0.611493 | ||||||||
\(583\) | −9.97953e9 | −2.08579 | ||||||||
\(584\) | −4.71193e9 | −0.978936 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.04130e9 | −0.213764 | ||||||||
\(587\) | 4.10777e9 | 0.838247 | 0.419124 | − | 0.907929i | \(-0.362337\pi\) | ||||
0.419124 | + | 0.907929i | \(0.362337\pi\) | |||||||
\(588\) | −7.20611e8 | −0.146177 | ||||||||
\(589\) | −1.53669e9 | −0.309873 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.10714e9 | −1.21698 | ||||||||
\(592\) | 1.78121e9 | 0.352849 | ||||||||
\(593\) | −5.07612e9 | −0.999632 | −0.499816 | − | 0.866132i | \(-0.666599\pi\) | ||||
−0.499816 | + | 0.866132i | \(0.666599\pi\) | |||||||
\(594\) | 1.60332e9 | 0.313883 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.10358e9 | 1.37441 | ||||||||
\(597\) | 2.52060e9 | 0.484836 | ||||||||
\(598\) | 6.31803e8 | 0.120817 | ||||||||
\(599\) | 2.86911e9 | 0.545448 | 0.272724 | − | 0.962092i | \(-0.412075\pi\) | ||||
0.272724 | + | 0.962092i | \(0.412075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.37052e9 | −0.257528 | −0.128764 | − | 0.991675i | \(-0.541101\pi\) | ||||
−0.128764 | + | 0.991675i | \(0.541101\pi\) | |||||||
\(602\) | 9.97018e8 | 0.186258 | ||||||||
\(603\) | 4.40187e9 | 0.817573 | ||||||||
\(604\) | 6.34721e9 | 1.17207 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.00737e9 | −0.548951 | ||||||||
\(607\) | −7.35729e9 | −1.33523 | −0.667617 | − | 0.744505i | \(-0.732686\pi\) | ||||
−0.667617 | + | 0.744505i | \(0.732686\pi\) | |||||||
\(608\) | 3.11828e9 | 0.562669 | ||||||||
\(609\) | −9.45844e8 | −0.169691 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.56276e9 | 0.277171 | ||||||||
\(612\) | 2.91384e9 | 0.513849 | ||||||||
\(613\) | −3.55720e9 | −0.623729 | −0.311865 | − | 0.950127i | \(-0.600954\pi\) | ||||
−0.311865 | + | 0.950127i | \(0.600954\pi\) | |||||||
\(614\) | −2.51608e8 | −0.0438668 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.02887e9 | −0.522093 | ||||||||
\(617\) | 1.02547e10 | 1.75761 | 0.878806 | − | 0.477180i | \(-0.158341\pi\) | ||||
0.878806 | + | 0.477180i | \(0.158341\pi\) | |||||||
\(618\) | −4.46260e9 | −0.760552 | ||||||||
\(619\) | 1.10323e10 | 1.86961 | 0.934804 | − | 0.355164i | \(-0.115575\pi\) | ||||
0.934804 | + | 0.355164i | \(0.115575\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.32886e9 | −0.222668 | ||||||||
\(622\) | −1.18603e9 | −0.197619 | ||||||||
\(623\) | −1.15726e9 | −0.191744 | ||||||||
\(624\) | −1.54004e9 | −0.253738 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 9.61719e8 | 0.156689 | ||||||||
\(627\) | −7.47788e9 | −1.21155 | ||||||||
\(628\) | 8.10242e9 | 1.30544 | ||||||||
\(629\) | −5.11942e9 | −0.820245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.48622e9 | −1.50311 | −0.751554 | − | 0.659671i | \(-0.770696\pi\) | ||||
−0.751554 | + | 0.659671i | \(0.770696\pi\) | |||||||
\(632\) | 8.58570e9 | 1.35290 | ||||||||
\(633\) | 1.53925e10 | 2.41211 | ||||||||
\(634\) | 6.94317e8 | 0.108204 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 8.25626e9 | 1.27257 | ||||||||
\(637\) | −4.45872e8 | −0.0683475 | ||||||||
\(638\) | −1.75179e9 | −0.267060 | ||||||||
\(639\) | −4.44790e9 | −0.674376 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.00094e9 | −0.899945 | −0.449972 | − | 0.893042i | \(-0.648566\pi\) | ||||
−0.449972 | + | 0.893042i | \(0.648566\pi\) | |||||||
\(642\) | −3.08810e9 | −0.460595 | ||||||||
\(643\) | 1.05337e10 | 1.56258 | 0.781292 | − | 0.624165i | \(-0.214561\pi\) | ||||
0.781292 | + | 0.624165i | \(0.214561\pi\) | |||||||
\(644\) | 1.10616e9 | 0.163200 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.66631e9 | −0.243188 | ||||||||
\(647\) | −4.76649e9 | −0.691884 | −0.345942 | − | 0.938256i | \(-0.612441\pi\) | ||||
−0.345942 | + | 0.938256i | \(0.612441\pi\) | |||||||
\(648\) | −6.93103e9 | −1.00066 | ||||||||
\(649\) | 2.06618e10 | 2.96695 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.92563e9 | −0.273551 | ||||||||
\(652\) | 4.97589e9 | 0.703079 | ||||||||
\(653\) | 6.45834e9 | 0.907663 | 0.453831 | − | 0.891088i | \(-0.350057\pi\) | ||||
0.453831 | + | 0.891088i | \(0.350057\pi\) | |||||||
\(654\) | −2.60299e9 | −0.363873 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.19923e9 | 0.580773 | ||||||||
\(657\) | −5.93773e9 | −0.816849 | ||||||||
\(658\) | −7.37217e8 | −0.100880 | ||||||||
\(659\) | −3.10819e9 | −0.423067 | −0.211533 | − | 0.977371i | \(-0.567846\pi\) | ||||
−0.211533 | + | 0.977371i | \(0.567846\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.37479e9 | −0.723863 | −0.361931 | − | 0.932205i | \(-0.617883\pi\) | ||||
−0.361931 | + | 0.932205i | \(0.617883\pi\) | |||||||
\(662\) | 1.29683e9 | 0.173732 | ||||||||
\(663\) | 4.42627e9 | 0.589848 | ||||||||
\(664\) | 9.40305e9 | 1.24647 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.08603e9 | −0.273628 | ||||||||
\(667\) | 1.45191e9 | 0.189452 | ||||||||
\(668\) | −2.80754e9 | −0.364425 | ||||||||
\(669\) | 1.42029e10 | 1.83395 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.42480e10 | 1.82065 | ||||||||
\(672\) | 3.90752e9 | 0.496716 | ||||||||
\(673\) | 2.18575e9 | 0.276406 | 0.138203 | − | 0.990404i | \(-0.455867\pi\) | ||||
0.138203 | + | 0.990404i | \(0.455867\pi\) | |||||||
\(674\) | −9.20825e8 | −0.115842 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.87880e9 | 0.607434 | ||||||||
\(677\) | −4.11027e9 | −0.509108 | −0.254554 | − | 0.967059i | \(-0.581929\pi\) | ||||
−0.254554 | + | 0.967059i | \(0.581929\pi\) | |||||||
\(678\) | 5.16440e9 | 0.636379 | ||||||||
\(679\) | −3.15043e9 | −0.386212 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.18065e9 | −0.507257 | ||||||||
\(682\) | −3.56643e9 | −0.430515 | ||||||||
\(683\) | 5.78846e8 | 0.0695169 | 0.0347585 | − | 0.999396i | \(-0.488934\pi\) | ||||
0.0347585 | + | 0.999396i | \(0.488934\pi\) | |||||||
\(684\) | 2.51994e9 | 0.301088 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.10336e8 | 0.0248759 | ||||||||
\(687\) | 1.90693e9 | 0.224380 | ||||||||
\(688\) | 3.73054e9 | 0.436729 | ||||||||
\(689\) | 5.10850e9 | 0.595012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.15960e9 | −0.133701 | −0.0668506 | − | 0.997763i | \(-0.521295\pi\) | ||||
−0.0668506 | + | 0.997763i | \(0.521295\pi\) | |||||||
\(692\) | −3.94269e9 | −0.452295 | ||||||||
\(693\) | −3.81682e9 | −0.435648 | ||||||||
\(694\) | −2.51563e9 | −0.285686 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.28907e9 | 0.369777 | ||||||||
\(697\) | −1.20691e10 | −1.35009 | ||||||||
\(698\) | −5.10255e8 | −0.0567928 | ||||||||
\(699\) | −4.56533e9 | −0.505594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.18229e10 | 1.29632 | 0.648159 | − | 0.761505i | \(-0.275539\pi\) | ||||
0.648159 | + | 0.761505i | \(0.275539\pi\) | |||||||
\(702\) | −8.20736e8 | −0.0895414 | ||||||||
\(703\) | −4.42736e9 | −0.480619 | ||||||||
\(704\) | 8.97732e8 | 0.0969711 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.37429e8 | 0.0895636 | ||||||||
\(707\) | −3.25788e9 | −0.346711 | ||||||||
\(708\) | −1.70939e10 | −1.81019 | ||||||||
\(709\) | −1.23818e10 | −1.30473 | −0.652365 | − | 0.757905i | \(-0.726223\pi\) | ||||
−0.652365 | + | 0.757905i | \(0.726223\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.08193e10 | 1.12890 | ||||||||
\(712\) | 4.02423e9 | 0.417833 | ||||||||
\(713\) | 2.95591e9 | 0.305406 | ||||||||
\(714\) | −2.08805e9 | −0.214682 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.07958e9 | 0.313542 | ||||||||
\(717\) | −1.16854e10 | −1.18393 | ||||||||
\(718\) | 6.66918e9 | 0.672414 | ||||||||
\(719\) | −1.25293e10 | −1.25712 | −0.628559 | − | 0.777762i | \(-0.716355\pi\) | ||||
−0.628559 | + | 0.777762i | \(0.716355\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.83433e9 | −0.480356 | ||||||||
\(722\) | 3.21809e9 | 0.318214 | ||||||||
\(723\) | 8.03845e8 | 0.0791022 | ||||||||
\(724\) | −5.46819e9 | −0.535499 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.11849e10 | −1.08481 | ||||||||
\(727\) | −5.51212e9 | −0.532045 | −0.266022 | − | 0.963967i | \(-0.585710\pi\) | ||||
−0.266022 | + | 0.963967i | \(0.585710\pi\) | |||||||
\(728\) | 1.55047e9 | 0.148937 | ||||||||
\(729\) | −3.21443e9 | −0.307297 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.07220e10 | −1.01524 | ||||||||
\(732\) | −1.17877e10 | −1.11081 | ||||||||
\(733\) | −1.21406e10 | −1.13861 | −0.569307 | − | 0.822125i | \(-0.692789\pi\) | ||||
−0.569307 | + | 0.822125i | \(0.692789\pi\) | |||||||
\(734\) | −7.04556e9 | −0.657627 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.99819e9 | −0.554559 | ||||||||
\(737\) | 2.16824e10 | 1.99513 | ||||||||
\(738\) | −4.91786e9 | −0.450380 | ||||||||
\(739\) | −9.03077e9 | −0.823132 | −0.411566 | − | 0.911380i | \(-0.635018\pi\) | ||||
−0.411566 | + | 0.911380i | \(0.635018\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.82791e9 | 0.345619 | ||||||||
\(742\) | −2.40988e9 | −0.216562 | ||||||||
\(743\) | −1.08266e10 | −0.968348 | −0.484174 | − | 0.874972i | \(-0.660880\pi\) | ||||
−0.484174 | + | 0.874972i | \(0.660880\pi\) | |||||||
\(744\) | 6.69615e9 | 0.596101 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.63721e9 | 0.761706 | ||||||||
\(747\) | 1.18492e10 | 1.04008 | ||||||||
\(748\) | 1.43528e10 | 1.25395 | ||||||||
\(749\) | −3.34533e9 | −0.290906 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.06510e10 | 0.917598 | 0.458799 | − | 0.888540i | \(-0.348280\pi\) | ||||
0.458799 | + | 0.888540i | \(0.348280\pi\) | |||||||
\(752\) | −2.75844e9 | −0.236538 | ||||||||
\(753\) | 1.04957e10 | 0.895838 | ||||||||
\(754\) | 8.96734e8 | 0.0761840 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.43695e9 | −0.120953 | ||||||||
\(757\) | 3.90535e9 | 0.327208 | 0.163604 | − | 0.986526i | \(-0.447688\pi\) | ||||
0.163604 | + | 0.986526i | \(0.447688\pi\) | |||||||
\(758\) | −2.76243e9 | −0.230382 | ||||||||
\(759\) | 1.43841e10 | 1.19409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.33048e9 | −0.602957 | −0.301478 | − | 0.953473i | \(-0.597480\pi\) | ||||
−0.301478 | + | 0.953473i | \(0.597480\pi\) | |||||||
\(762\) | −6.90087e8 | −0.0565017 | ||||||||
\(763\) | −2.81981e9 | −0.229818 | ||||||||
\(764\) | −1.77075e10 | −1.43658 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.24002e9 | −0.421243 | ||||||||
\(767\) | −1.05767e10 | −0.846382 | ||||||||
\(768\) | −8.34331e9 | −0.664621 | ||||||||
\(769\) | 5.64716e9 | 0.447804 | 0.223902 | − | 0.974612i | \(-0.428120\pi\) | ||||
0.223902 | + | 0.974612i | \(0.428120\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.23422e10 | −0.969842 | ||||||||
\(772\) | 1.11877e10 | 0.875146 | ||||||||
\(773\) | 5.49066e9 | 0.427559 | 0.213780 | − | 0.976882i | \(-0.431423\pi\) | ||||
0.213780 | + | 0.976882i | \(0.431423\pi\) | |||||||
\(774\) | −4.36895e9 | −0.338676 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.09553e10 | 0.841603 | ||||||||
\(777\) | −5.54792e9 | −0.424284 | ||||||||
\(778\) | −4.81315e8 | −0.0366438 | ||||||||
\(779\) | −1.04376e10 | −0.791078 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.19092e10 | −1.64569 | ||||||||
\(782\) | 3.20523e9 | 0.239682 | ||||||||
\(783\) | −1.88608e9 | −0.140409 | ||||||||
\(784\) | 7.87013e8 | 0.0583278 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.18487e10 | 0.870345 | ||||||||
\(787\) | 8.20098e9 | 0.599728 | 0.299864 | − | 0.953982i | \(-0.403059\pi\) | ||||
0.299864 | + | 0.953982i | \(0.403059\pi\) | |||||||
\(788\) | 1.01372e10 | 0.738037 | ||||||||
\(789\) | −3.18225e8 | −0.0230656 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.59459e9 | 0.401930 | ||||||||
\(792\) | 1.32726e10 | 0.949330 | ||||||||
\(793\) | −7.29353e9 | −0.519376 | ||||||||
\(794\) | −7.48983e9 | −0.531007 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.18395e9 | −0.294030 | ||||||||
\(797\) | 1.68355e10 | 1.17793 | 0.588967 | − | 0.808157i | \(-0.299535\pi\) | ||||
0.588967 | + | 0.808157i | \(0.299535\pi\) | |||||||
\(798\) | −1.80578e9 | −0.125792 | ||||||||
\(799\) | 7.92812e9 | 0.549866 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.07113e9 | 0.348651 | ||||||||
\(802\) | 9.01240e9 | 0.616922 | ||||||||
\(803\) | −2.92477e10 | −1.99337 | ||||||||
\(804\) | −1.79383e10 | −1.21726 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.82564e9 | 0.122813 | ||||||||
\(807\) | −1.62439e10 | −1.08801 | ||||||||
\(808\) | 1.13289e10 | 0.755525 | ||||||||
\(809\) | −2.21360e10 | −1.46987 | −0.734937 | − | 0.678136i | \(-0.762788\pi\) | ||||
−0.734937 | + | 0.678136i | \(0.762788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.33276e10 | 1.53567 | 0.767835 | − | 0.640648i | \(-0.221334\pi\) | ||||
0.767835 | + | 0.640648i | \(0.221334\pi\) | |||||||
\(812\) | 1.57001e9 | 0.102910 | ||||||||
\(813\) | −3.42879e10 | −2.23782 | ||||||||
\(814\) | −1.02752e10 | −0.667737 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −7.81284e9 | −0.503377 | ||||||||
\(817\) | −9.27260e9 | −0.594873 | ||||||||
\(818\) | 3.02984e9 | 0.193546 | ||||||||
\(819\) | 1.95382e9 | 0.124277 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.93627e9 | 0.122114 | 0.0610570 | − | 0.998134i | \(-0.480553\pi\) | ||||
0.0610570 | + | 0.998134i | \(0.480553\pi\) | |||||||
\(822\) | −1.46477e10 | −0.919854 | ||||||||
\(823\) | −3.03967e8 | −0.0190076 | −0.00950380 | − | 0.999955i | \(-0.503025\pi\) | ||||
−0.00950380 | + | 0.999955i | \(0.503025\pi\) | |||||||
\(824\) | 1.68108e10 | 1.04675 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.98945e9 | 0.308051 | ||||||||
\(827\) | −1.45016e10 | −0.891551 | −0.445776 | − | 0.895145i | \(-0.647072\pi\) | ||||
−0.445776 | + | 0.895145i | \(0.647072\pi\) | |||||||
\(828\) | −4.84723e9 | −0.296748 | ||||||||
\(829\) | 2.11779e9 | 0.129104 | 0.0645522 | − | 0.997914i | \(-0.479438\pi\) | ||||
0.0645522 | + | 0.997914i | \(0.479438\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.83159e10 | −1.71170 | ||||||||
\(832\) | −4.59547e8 | −0.0276629 | ||||||||
\(833\) | −2.26198e9 | −0.135591 | ||||||||
\(834\) | −1.20023e10 | −0.716447 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.24125e10 | 0.734748 | ||||||||
\(837\) | −3.83984e9 | −0.226347 | ||||||||
\(838\) | −1.06855e9 | −0.0627248 | ||||||||
\(839\) | 6.30920e9 | 0.368814 | 0.184407 | − | 0.982850i | \(-0.440964\pi\) | ||||
0.184407 | + | 0.982850i | \(0.440964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.51891e10 | −0.880537 | ||||||||
\(842\) | 6.92301e9 | 0.399671 | ||||||||
\(843\) | −1.91393e10 | −1.10035 | ||||||||
\(844\) | −2.55501e10 | −1.46283 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.23050e9 | 0.183431 | ||||||||
\(847\) | −1.21166e10 | −0.685152 | ||||||||
\(848\) | −9.01705e9 | −0.507784 | ||||||||
\(849\) | 4.97012e9 | 0.278734 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.51626e9 | 0.473691 | ||||||||
\(852\) | 1.81259e10 | 1.00406 | ||||||||
\(853\) | −1.88042e10 | −1.03737 | −0.518685 | − | 0.854965i | \(-0.673578\pi\) | ||||
−0.518685 | + | 0.854965i | \(0.673578\pi\) | |||||||
\(854\) | 3.44065e9 | 0.189033 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.16330e10 | 0.633920 | ||||||||
\(857\) | 6.55066e9 | 0.355510 | 0.177755 | − | 0.984075i | \(-0.443116\pi\) | ||||
0.177755 | + | 0.984075i | \(0.443116\pi\) | |||||||
\(858\) | 8.88399e9 | 0.480178 | ||||||||
\(859\) | −9.36968e9 | −0.504369 | −0.252185 | − | 0.967679i | \(-0.581149\pi\) | ||||
−0.252185 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.30793e10 | −0.698352 | ||||||||
\(862\) | −8.92571e9 | −0.474643 | ||||||||
\(863\) | −3.09680e10 | −1.64012 | −0.820060 | − | 0.572277i | \(-0.806060\pi\) | ||||
−0.820060 | + | 0.572277i | \(0.806060\pi\) | |||||||
\(864\) | 7.79187e9 | 0.411002 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.61864e9 | 0.346303 | ||||||||
\(867\) | −2.47117e9 | −0.128776 | ||||||||
\(868\) | 3.19635e9 | 0.165896 | ||||||||
\(869\) | 5.32927e10 | 2.75486 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.10992e10 | −0.569151 | ||||||||
\(872\) | 9.80557e9 | 0.500801 | ||||||||
\(873\) | 1.38053e10 | 0.702255 | ||||||||
\(874\) | 2.77194e9 | 0.140441 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.41972e10 | 1.21619 | ||||||||
\(877\) | −1.81420e10 | −0.908211 | −0.454105 | − | 0.890948i | \(-0.650041\pi\) | ||||
−0.454105 | + | 0.890948i | \(0.650041\pi\) | |||||||
\(878\) | 3.72061e9 | 0.185517 | ||||||||
\(879\) | 1.21356e10 | 0.602697 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.30036e10 | 1.13339 | 0.566695 | − | 0.823928i | \(-0.308222\pi\) | ||||
0.566695 | + | 0.823928i | \(0.308222\pi\) | |||||||
\(882\) | −9.21696e8 | −0.0452322 | ||||||||
\(883\) | 3.55911e10 | 1.73972 | 0.869860 | − | 0.493299i | \(-0.164209\pi\) | ||||
0.869860 | + | 0.493299i | \(0.164209\pi\) | |||||||
\(884\) | −7.34716e9 | −0.357715 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.94725e9 | 0.335579 | ||||||||
\(887\) | 1.65876e10 | 0.798087 | 0.399043 | − | 0.916932i | \(-0.369342\pi\) | ||||
0.399043 | + | 0.916932i | \(0.369342\pi\) | |||||||
\(888\) | 1.92923e10 | 0.924565 | ||||||||
\(889\) | −7.47570e8 | −0.0356858 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.30219e10 | −2.03760 | ||||||||
\(892\) | −2.35755e10 | −1.11220 | ||||||||
\(893\) | 6.85637e9 | 0.322191 | ||||||||
\(894\) | 2.23062e10 | 1.04411 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.01693e9 | −0.372332 | ||||||||
\(897\) | −7.36319e9 | −0.340637 | ||||||||
\(898\) | 4.46148e9 | 0.205595 | ||||||||
\(899\) | 4.19540e9 | 0.192581 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.59162e10 | 1.18041 | ||||||||
\(902\) | −2.42241e10 | −1.09907 | ||||||||
\(903\) | −1.16195e10 | −0.525146 | ||||||||
\(904\) | −1.94545e10 | −0.875854 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.99311e10 | 0.890396 | ||||||||
\(907\) | 1.96890e10 | 0.876189 | 0.438095 | − | 0.898929i | \(-0.355653\pi\) | ||||
0.438095 | + | 0.898929i | \(0.355653\pi\) | |||||||
\(908\) | 6.93946e9 | 0.307627 | ||||||||
\(909\) | 1.42761e10 | 0.630429 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.72050e10 | 0.753946 | 0.376973 | − | 0.926224i | \(-0.376965\pi\) | ||||
0.376973 | + | 0.926224i | \(0.376965\pi\) | |||||||
\(912\) | −6.75667e9 | −0.294952 | ||||||||
\(913\) | 5.83662e10 | 2.53813 | ||||||||
\(914\) | −1.66104e10 | −0.719563 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.16531e9 | −0.136076 | ||||||||
\(917\) | 1.28357e10 | 0.549700 | ||||||||
\(918\) | −4.16372e9 | −0.177636 | ||||||||
\(919\) | −5.20001e9 | −0.221004 | −0.110502 | − | 0.993876i | \(-0.535246\pi\) | ||||
−0.110502 | + | 0.993876i | \(0.535246\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.93231e9 | 0.123680 | ||||||||
\(922\) | −1.57920e10 | −0.663556 | ||||||||
\(923\) | 1.12152e10 | 0.469465 | ||||||||
\(924\) | 1.55541e10 | 0.648625 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.98582e9 | −0.330507 | ||||||||
\(927\) | 2.11841e10 | 0.873437 | ||||||||
\(928\) | −8.51338e9 | −0.349691 | ||||||||
\(929\) | −4.68926e10 | −1.91888 | −0.959442 | − | 0.281905i | \(-0.909034\pi\) | ||||
−0.959442 | + | 0.281905i | \(0.909034\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.95620e9 | −0.0794490 | ||||||||
\(932\) | 7.57800e9 | 0.306619 | ||||||||
\(933\) | 1.38223e10 | 0.557178 | ||||||||
\(934\) | −1.80965e10 | −0.726743 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.79420e9 | −0.270815 | ||||||||
\(937\) | −1.78840e10 | −0.710194 | −0.355097 | − | 0.934829i | \(-0.615552\pi\) | ||||
−0.355097 | + | 0.934829i | \(0.615552\pi\) | |||||||
\(938\) | 5.23593e9 | 0.207149 | ||||||||
\(939\) | −1.12081e10 | −0.441776 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.81758e9 | 0.188480 | 0.0942400 | − | 0.995550i | \(-0.469958\pi\) | ||||
0.0942400 | + | 0.995550i | \(0.469958\pi\) | |||||||
\(942\) | 2.54427e10 | 0.991712 | ||||||||
\(943\) | 2.00773e10 | 0.779675 | ||||||||
\(944\) | 1.86690e10 | 0.722303 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.15203e10 | −0.826474 | ||||||||
\(947\) | 1.97403e10 | 0.755317 | 0.377659 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377659 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(948\) | −4.40901e10 | −1.68078 | ||||||||
\(949\) | 1.49718e10 | 0.568647 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.09174e9 | −0.305077 | ||||||||
\(952\) | 7.86577e9 | 0.295469 | ||||||||
\(953\) | 2.22133e10 | 0.831358 | 0.415679 | − | 0.909511i | \(-0.363544\pi\) | ||||
0.415679 | + | 0.909511i | \(0.363544\pi\) | |||||||
\(954\) | 1.05602e10 | 0.393778 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.93965e10 | 0.717995 | ||||||||
\(957\) | 2.04157e10 | 0.752962 | ||||||||
\(958\) | −2.51129e9 | −0.0922822 | ||||||||
\(959\) | −1.58679e10 | −0.580969 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.89713e10 | −0.689549 | ||||||||
\(962\) | 5.25986e9 | 0.190485 | ||||||||
\(963\) | 1.46593e10 | 0.528959 | ||||||||
\(964\) | −1.33430e9 | −0.0479717 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.47351e9 | 0.123979 | ||||||||
\(967\) | 2.25674e10 | 0.802579 | 0.401290 | − | 0.915951i | \(-0.368562\pi\) | ||||
0.401290 | + | 0.915951i | \(0.368562\pi\) | |||||||
\(968\) | 4.21340e10 | 1.49303 | ||||||||
\(969\) | 1.94196e10 | 0.685656 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.95033e9 | 0.0683659 | 0.0341830 | − | 0.999416i | \(-0.489117\pi\) | ||||
0.0341830 | + | 0.999416i | \(0.489117\pi\) | |||||||
\(972\) | 2.64307e10 | 0.923160 | ||||||||
\(973\) | −1.30021e10 | −0.452500 | ||||||||
\(974\) | 1.53782e10 | 0.533273 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.28739e10 | 0.443236 | ||||||||
\(977\) | −7.74628e9 | −0.265743 | −0.132872 | − | 0.991133i | \(-0.542420\pi\) | ||||
−0.132872 | + | 0.991133i | \(0.542420\pi\) | |||||||
\(978\) | 1.56250e10 | 0.534114 | ||||||||
\(979\) | 2.49790e10 | 0.850817 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.23565e10 | 0.417881 | ||||||||
\(982\) | 8.12477e8 | 0.0273792 | ||||||||
\(983\) | −4.84148e10 | −1.62570 | −0.812851 | − | 0.582472i | \(-0.802085\pi\) | ||||
−0.812851 | + | 0.582472i | \(0.802085\pi\) | |||||||
\(984\) | 4.54819e10 | 1.52179 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.54927e9 | 0.151138 | ||||||||
\(987\) | 8.59170e9 | 0.284426 | ||||||||
\(988\) | −6.35395e9 | −0.209601 | ||||||||
\(989\) | 1.78363e10 | 0.586299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.01522e10 | −1.63694 | −0.818468 | − | 0.574552i | \(-0.805176\pi\) | ||||
−0.818468 | + | 0.574552i | \(0.805176\pi\) | |||||||
\(992\) | −1.73322e10 | −0.563720 | ||||||||
\(993\) | −1.51136e10 | −0.489830 | ||||||||
\(994\) | −5.29068e9 | −0.170867 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.82874e10 | −1.54855 | ||||||||
\(997\) | −4.44770e10 | −1.42136 | −0.710678 | − | 0.703517i | \(-0.751612\pi\) | ||||
−0.710678 | + | 0.703517i | \(0.751612\pi\) | |||||||
\(998\) | −1.70729e10 | −0.543689 | ||||||||
\(999\) | −1.10629e10 | −0.351068 |
(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 | 175.8.a.f.1.3 | 5 | ||
5.2 | odd | 4 | 175.8.b.f.99.5 | 10 | |||
5.3 | odd | 4 | 175.8.b.f.99.6 | 10 | |||
5.4 | even | 2 | 35.8.a.d.1.3 | ✓ | 5 | ||
15.14 | odd | 2 | 315.8.a.m.1.3 | 5 | |||
20.19 | odd | 2 | 560.8.a.s.1.5 | 5 | |||
35.34 | odd | 2 | 245.8.a.f.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.8.a.d.1.3 | ✓ | 5 | 5.4 | even | 2 | ||
175.8.a.f.1.3 | 5 | 1.1 | even | 1 | trivial | ||
175.8.b.f.99.5 | 10 | 5.2 | odd | 4 | |||
175.8.b.f.99.6 | 10 | 5.3 | odd | 4 | |||
245.8.a.f.1.3 | 5 | 35.34 | odd | 2 | |||
315.8.a.m.1.3 | 5 | 15.14 | odd | 2 | |||
560.8.a.s.1.5 | 5 | 20.19 | odd | 2 |