Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,10,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("80.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(41.2028668931\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6049}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1512 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(39.3877\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −109.551 | −0.780853 | −0.390426 | − | 0.920634i | \(-0.627672\pi\) | ||||
−0.390426 | + | 0.920634i | \(0.627672\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 625.000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 9209.37 | 1.44974 | 0.724868 | − | 0.688888i | \(-0.241901\pi\) | ||||
0.724868 | + | 0.688888i | \(0.241901\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7681.66 | −0.390269 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 29861.4 | 0.614955 | 0.307477 | − | 0.951555i | \(-0.400515\pi\) | ||||
0.307477 | + | 0.951555i | \(0.400515\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 16775.2 | 0.162901 | 0.0814505 | − | 0.996677i | \(-0.474045\pi\) | ||||
0.0814505 | + | 0.996677i | \(0.474045\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −68469.1 | −0.349208 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −312472. | −0.907385 | −0.453692 | − | 0.891158i | \(-0.649894\pi\) | ||||
−0.453692 | + | 0.891158i | \(0.649894\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 36401.6 | 0.0640810 | 0.0320405 | − | 0.999487i | \(-0.489799\pi\) | ||||
0.0320405 | + | 0.999487i | \(0.489799\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00889e6 | −1.13203 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −951749. | −0.709165 | −0.354583 | − | 0.935025i | \(-0.615377\pi\) | ||||
−0.354583 | + | 0.935025i | \(0.615377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.99782e6 | 1.08560 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.02575e6 | −0.794404 | −0.397202 | − | 0.917731i | \(-0.630019\pi\) | ||||
−0.397202 | + | 0.917731i | \(0.630019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.43462e6 | 1.83483 | 0.917417 | − | 0.397926i | \(-0.130270\pi\) | ||||
0.917417 | + | 0.397926i | \(0.130270\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.27134e6 | −0.480189 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.75586e6 | 0.648342 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.16984e7 | −1.02617 | −0.513084 | − | 0.858339i | \(-0.671497\pi\) | ||||
−0.513084 | + | 0.858339i | \(0.671497\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.83774e6 | −0.127202 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.49741e7 | 1.93295 | 0.966473 | − | 0.256769i | \(-0.0826578\pi\) | ||||
0.966473 | + | 0.256769i | \(0.0826578\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.26136e7 | 1.00870 | 0.504349 | − | 0.863500i | \(-0.331732\pi\) | ||||
0.504349 | + | 0.863500i | \(0.331732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.80104e6 | −0.174533 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.58030e6 | 0.166808 | 0.0834041 | − | 0.996516i | \(-0.473421\pi\) | ||||
0.0834041 | + | 0.996516i | \(0.473421\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.44590e7 | 1.10173 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.42316e7 | 0.708534 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.54605e7 | 0.965477 | 0.482739 | − | 0.875765i | \(-0.339642\pi\) | ||||
0.482739 | + | 0.875765i | \(0.339642\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.86634e7 | 0.275016 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.98782e6 | −0.0500378 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.51084e7 | −0.914404 | −0.457202 | − | 0.889363i | \(-0.651148\pi\) | ||||
−0.457202 | + | 0.889363i | \(0.651148\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.85791e7 | 0.449226 | 0.224613 | − | 0.974448i | \(-0.427888\pi\) | ||||
0.224613 | + | 0.974448i | \(0.427888\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.07433e7 | −0.565787 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.04845e7 | 0.0728515 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.20748e7 | 0.315712 | 0.157856 | − | 0.987462i | \(-0.449542\pi\) | ||||
0.157856 | + | 0.987462i | \(0.449542\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.04265e8 | 0.553754 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.14674e8 | 0.535551 | 0.267776 | − | 0.963481i | \(-0.413711\pi\) | ||||
0.267776 | + | 0.963481i | \(0.413711\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.47760e8 | 1.84541 | 0.922704 | − | 0.385508i | \(-0.125974\pi\) | ||||
0.922704 | + | 0.385508i | \(0.125974\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.27932e7 | −0.156171 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.75005e8 | 0.891522 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.18141e7 | 0.265208 | 0.132604 | − | 0.991169i | \(-0.457666\pi\) | ||||
0.132604 | + | 0.991169i | \(0.457666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.77215e8 | −0.457422 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.87254e8 | 1.35823 | 0.679117 | − | 0.734030i | \(-0.262363\pi\) | ||||
0.679117 | + | 0.734030i | \(0.262363\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.95295e8 | −0.405795 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.31472e8 | 0.620313 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.81494e8 | −0.813459 | −0.406729 | − | 0.913549i | \(-0.633331\pi\) | ||||
−0.406729 | + | 0.913549i | \(0.633331\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.54489e8 | 0.236163 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.03357e9 | −1.43274 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.27510e7 | 0.0286579 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.37193e9 | 1.57347 | 0.786733 | − | 0.617293i | \(-0.211771\pi\) | ||||
0.786733 | + | 0.617293i | \(0.211771\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.29385e8 | −0.239998 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.23051e9 | −1.17662 | −0.588312 | − | 0.808634i | \(-0.700207\pi\) | ||||
−0.588312 | + | 0.808634i | \(0.700207\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.07913e8 | 0.707289 | 0.353645 | − | 0.935380i | \(-0.384942\pi\) | ||||
0.353645 | + | 0.935380i | \(0.384942\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.30558e8 | −0.506259 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.59875e9 | −1.17911 | −0.589553 | − | 0.807730i | \(-0.700696\pi\) | ||||
−0.589553 | + | 0.807730i | \(0.700696\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.08078e9 | −0.733361 | −0.366680 | − | 0.930347i | \(-0.619506\pi\) | ||||
−0.366680 | + | 0.930347i | \(0.619506\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.28157e9 | 0.801286 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52041e9 | 0.877217 | 0.438608 | − | 0.898678i | \(-0.355472\pi\) | ||||
0.438608 | + | 0.898678i | \(0.355472\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.94843e8 | −0.317148 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.28862e8 | −0.0635751 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.87768e9 | −1.31547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.46624e9 | −0.621831 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.83144e9 | −1.50935 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.44141e8 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.75891e9 | −1.62327 | −0.811634 | − | 0.584166i | \(-0.801422\pi\) | ||||
−0.811634 | + | 0.584166i | \(0.801422\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.47733e9 | −0.787645 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.43225e9 | 1.01826 | 0.509129 | − | 0.860690i | \(-0.329968\pi\) | ||||
0.509129 | + | 0.860690i | \(0.329968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.35236e8 | 0.0929005 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.87363e9 | 0.485493 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.21292e7 | −0.0126427 | −0.00632133 | − | 0.999980i | \(-0.502012\pi\) | ||||
−0.00632133 | + | 0.999980i | \(0.502012\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.87422e9 | −1.33470 | −0.667350 | − | 0.744744i | \(-0.732571\pi\) | ||||
−0.667350 | + | 0.744744i | \(0.732571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.11325e8 | −0.130253 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.00932e8 | 0.100177 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.89109e9 | −0.355268 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.87051e9 | −0.860292 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.63272e9 | 1.60107 | 0.800535 | − | 0.599285i | \(-0.204549\pi\) | ||||
0.800535 | + | 0.599285i | \(0.204549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.41660e9 | 1.00440 | 0.502202 | − | 0.864750i | \(-0.332523\pi\) | ||||
0.502202 | + | 0.864750i | \(0.332523\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.40031e9 | 0.354124 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.89664e9 | 0.820563 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.12424e10 | 1.47676 | 0.738381 | − | 0.674384i | \(-0.235591\pi\) | ||||
0.738381 | + | 0.674384i | \(0.235591\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.07573e9 | −0.753896 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.76502e9 | −1.02810 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.86388e9 | 0.428726 | 0.214363 | − | 0.976754i | \(-0.431232\pi\) | ||||
0.214363 | + | 0.976754i | \(0.431232\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.04458e9 | −0.214747 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.78459e10 | 1.77547 | 0.887736 | − | 0.460353i | \(-0.152277\pi\) | ||||
0.887736 | + | 0.460353i | \(0.152277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.03231e10 | −0.973463 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.79625e8 | −0.0250088 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.32509e10 | −1.12470 | −0.562351 | − | 0.826899i | \(-0.690103\pi\) | ||||
−0.562351 | + | 0.826899i | \(0.690103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.59741e9 | 0.289947 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.32367e9 | 0.714015 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.98157e9 | 0.435488 | 0.217744 | − | 0.976006i | \(-0.430130\pi\) | ||||
0.217744 | + | 0.976006i | \(0.430130\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.23916e10 | −1.55071 | −0.775355 | − | 0.631525i | \(-0.782429\pi\) | ||||
−0.775355 | + | 0.631525i | \(0.782429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.32187e9 | −0.350780 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.31149e9 | −0.458916 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.33087e9 | −0.558001 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.76080e10 | 1.57383 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.90074e10 | 1.57710 | 0.788549 | − | 0.614972i | \(-0.210833\pi\) | ||||
0.788549 | + | 0.614972i | \(0.210833\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.00528e10 | 1.04032 | 0.520161 | − | 0.854068i | \(-0.325872\pi\) | ||||
0.520161 | + | 0.854068i | \(0.325872\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.14859e9 | −0.0568863 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.23440e10 | 0.583928 | 0.291964 | − | 0.956429i | \(-0.405691\pi\) | ||||
0.291964 | + | 0.956429i | \(0.405691\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.71589e10 | 1.22765 | 0.613823 | − | 0.789443i | \(-0.289631\pi\) | ||||
0.613823 | + | 0.789443i | \(0.289631\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.70483e9 | −0.246525 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.78652e10 | −1.15168 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.18588e10 | 0.864440 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.31101e9 | 0.276765 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.08700e9 | 0.0394069 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.20982e9 | −0.319875 | −0.159937 | − | 0.987127i | \(-0.551129\pi\) | ||||
−0.159937 | + | 0.987127i | \(0.551129\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.25626e10 | −0.418187 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.41335e10 | 0.451104 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.68870e10 | 2.66003 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.90524e10 | −1.44099 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.24180e9 | −0.147814 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.43587e10 | 0.659601 | 0.329801 | − | 0.944051i | \(-0.393018\pi\) | ||||
0.329801 | + | 0.944051i | \(0.393018\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00065e9 | −0.0780537 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.95512e9 | −0.148859 | −0.0744294 | − | 0.997226i | \(-0.523714\pi\) | ||||
−0.0744294 | + | 0.997226i | \(0.523714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.97476e10 | −0.474521 | −0.237260 | − | 0.971446i | \(-0.576249\pi\) | ||||
−0.237260 | + | 0.971446i | \(0.576249\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.01270e10 | −0.696148 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.95653e10 | −1.10173 | −0.550866 | − | 0.834594i | \(-0.685702\pi\) | ||||
−0.550866 | + | 0.834594i | \(0.685702\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.48769e9 | 0.0745989 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.00583e10 | −0.207089 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.55103e10 | 0.505738 | 0.252869 | − | 0.967501i | \(-0.418626\pi\) | ||||
0.252869 | + | 0.967501i | \(0.418626\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.72387e10 | 0.902031 | 0.451015 | − | 0.892516i | \(-0.351062\pi\) | ||||
0.451015 | + | 0.892516i | \(0.351062\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.95920e10 | −0.728416 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.77868e10 | 0.492711 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.10645e8 | 0.0104389 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.43340e10 | −1.06058 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.60294e10 | −0.572962 | −0.286481 | − | 0.958086i | \(-0.592485\pi\) | ||||
−0.286481 | + | 0.958086i | \(0.592485\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.84206e10 | −0.436104 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.13947e10 | 0.316866 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.80945e10 | −1.11666 | −0.558330 | − | 0.829619i | \(-0.688558\pi\) | ||||
−0.558330 | + | 0.829619i | \(0.688558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.07735e11 | −1.48767 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.32427e10 | 0.310031 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.93335e10 | −0.249178 | −0.124589 | − | 0.992208i | \(-0.539761\pi\) | ||||
−0.124589 | + | 0.992208i | \(0.539761\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.46628e10 | 0.431774 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.27479e10 | 0.635192 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.70381e11 | −1.98398 | −0.991989 | − | 0.126327i | \(-0.959681\pi\) | ||||
−0.991989 | + | 0.126327i | \(0.959681\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.21132e10 | 0.586929 | 0.293465 | − | 0.955970i | \(-0.405192\pi\) | ||||
0.293465 | + | 0.955970i | \(0.405192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.69244e10 | −0.184409 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.16646e10 | 0.122991 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.96913e10 | −0.711245 | −0.355623 | − | 0.934630i | \(-0.615731\pi\) | ||||
−0.355623 | + | 0.934630i | \(0.615731\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.24736e10 | −0.716078 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.23747e11 | −1.18401 | −0.592005 | − | 0.805935i | \(-0.701663\pi\) | ||||
−0.592005 | + | 0.805935i | \(0.701663\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.02892e11 | −0.953544 | −0.476772 | − | 0.879027i | \(-0.658193\pi\) | ||||
−0.476772 | + | 0.879027i | \(0.658193\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.49239e9 | −0.0223776 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.22090e11 | 2.80226 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.09489e10 | −0.176653 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50295e11 | −1.22865 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.52713e10 | −0.358855 | −0.179427 | − | 0.983771i | \(-0.557424\pi\) | ||||
−0.179427 | + | 0.983771i | \(0.557424\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.31927e10 | −0.408934 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.95190e10 | 0.667592 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.59658e10 | −0.115524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.08257e11 | 1.46235 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.34803e11 | 0.918771 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.03619e10 | 0.200900 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.27144e11 | 1.45941 | 0.729707 | − | 0.683760i | \(-0.239657\pi\) | ||||
0.729707 | + | 0.683760i | \(0.239657\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.85074e10 | −0.552289 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.15793e11 | −0.701877 | −0.350939 | − | 0.936398i | \(-0.614137\pi\) | ||||
−0.350939 | + | 0.936398i | \(0.614137\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.00580e11 | 0.592329 | 0.296164 | − | 0.955137i | \(-0.404292\pi\) | ||||
0.296164 | + | 0.955137i | \(0.404292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.42145e10 | −0.253027 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.04758e10 | 0.447609 | 0.223805 | − | 0.974634i | \(-0.428152\pi\) | ||||
0.223805 | + | 0.974634i | \(0.428152\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.03530e10 | −0.488522 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.75144e11 | 0.920709 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.13745e10 | −0.0581461 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.55283e9 | 0.0325802 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.18400e11 | 0.572647 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.13911e10 | 0.241828 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.95335e11 | −1.81025 | −0.905127 | − | 0.425141i | \(-0.860225\pi\) | ||||
−0.905127 | + | 0.425141i | \(0.860225\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.98630e10 | 0.400481 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.25467e10 | 0.141191 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.03418e11 | 1.28146 | 0.640732 | − | 0.767765i | \(-0.278631\pi\) | ||||
0.640732 | + | 0.767765i | \(0.278631\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.66562e11 | −0.684977 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.81731e11 | 1.12834 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.78077e10 | 0.147488 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.51655e10 | 0.247646 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.49981e11 | 0.555332 | 0.277666 | − | 0.960678i | \(-0.410439\pi\) | ||||
0.277666 | + | 0.960678i | \(0.410439\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.12719e11 | −1.48916 | −0.744578 | − | 0.667535i | \(-0.767349\pi\) | ||||
−0.744578 | + | 0.667535i | \(0.767349\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.02891e10 | 0.176845 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.72053e11 | −1.27532 | −0.637659 | − | 0.770319i | \(-0.720097\pi\) | ||||
−0.637659 | + | 0.770319i | \(0.720097\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.16710e10 | 0.239506 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.15251e11 | 1.02719 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.29954e11 | 0.412920 | 0.206460 | − | 0.978455i | \(-0.433806\pi\) | ||||
0.206460 | + | 0.978455i | \(0.433806\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.21363e11 | −0.995894 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.60628e11 | 0.485558 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.79850e11 | 0.825292 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.13597e11 | 1.19009 | 0.595045 | − | 0.803692i | \(-0.297134\pi\) | ||||
0.595045 | + | 0.803692i | \(0.297134\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.68659e11 | −0.754368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.10756e11 | 1.39969 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.96023e11 | 1.32682 | 0.663410 | − | 0.748256i | \(-0.269109\pi\) | ||||
0.663410 | + | 0.748256i | \(0.269109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.67458e10 | −0.0698416 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.07576e10 | −0.129409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.86834e11 | −0.465135 | −0.232567 | − | 0.972580i | \(-0.574713\pi\) | ||||
−0.232567 | + | 0.972580i | \(0.574713\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.21341e11 | 1.26753 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.96068e11 | −0.940535 | −0.470267 | − | 0.882524i | \(-0.655843\pi\) | ||||
−0.470267 | + | 0.882524i | \(0.655843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.71878e11 | 0.398701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.73710e11 | −0.393664 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.64849e11 | −1.02929 | −0.514646 | − | 0.857403i | \(-0.672077\pi\) | ||||
−0.514646 | + | 0.857403i | \(0.672077\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.97395e11 | 0.643486 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.76005e11 | −0.795110 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.73838e10 | 0.118605 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.04945e11 | −0.818161 | −0.409080 | − | 0.912498i | \(-0.634150\pi\) | ||||
−0.409080 | + | 0.912498i | \(0.634150\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.67253e10 | −0.0725416 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.10722e11 | −1.75888 | −0.879440 | − | 0.476010i | \(-0.842083\pi\) | ||||
−0.879440 | + | 0.476010i | \(0.842083\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.58268e11 | 0.298896 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.10759e11 | −0.204565 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.49330e11 | −0.631046 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.22611e11 | 1.10017 | 0.550087 | − | 0.835107i | \(-0.314594\pi\) | ||||
0.550087 | + | 0.835107i | \(0.314594\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.71078e9 | 0.00987205 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.83795e11 | −1.32564 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.67034e11 | 0.607421 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.43525e11 | 1.04220 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.77692e11 | 0.915657 | 0.457829 | − | 0.889040i | \(-0.348627\pi\) | ||||
0.457829 | + | 0.889040i | \(0.348627\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.19223e11 | 0.340109 | 0.170054 | − | 0.985435i | \(-0.445606\pi\) | ||||
0.170054 | + | 0.985435i | \(0.445606\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.28660e10 | −0.0651000 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.22060e11 | −0.181477 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.47383e11 | 0.651259 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.48774e10 | −0.0782233 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.43484e11 | −1.03782 | −0.518912 | − | 0.854828i | \(-0.673663\pi\) | ||||
−0.518912 | + | 0.854828i | \(0.673663\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.19028e11 | 0.299436 | 0.149718 | − | 0.988729i | \(-0.452163\pi\) | ||||
0.149718 | + | 0.988729i | \(0.452163\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.07170e11 | 0.277412 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.46452e10 | −0.0454440 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.31553e11 | −1.19706 | −0.598532 | − | 0.801099i | \(-0.704249\pi\) | ||||
−0.598532 | + | 0.801099i | \(0.704249\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.41518e11 | −0.429972 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.53901e11 | −1.17676 | −0.588378 | − | 0.808586i | \(-0.700233\pi\) | ||||
−0.588378 | + | 0.808586i | \(0.700233\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.00934e11 | −0.363790 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.05527e12 | −1.25020 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.16478e11 | 1.06418 | 0.532088 | − | 0.846689i | \(-0.321407\pi\) | ||||
0.532088 | + | 0.846689i | \(0.321407\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04438e12 | 1.18867 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.02943e11 | −0.784292 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.65559e10 | 0.105615 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.25903e11 | 0.885740 | 0.442870 | − | 0.896586i | \(-0.353960\pi\) | ||||
0.442870 | + | 0.896586i | \(0.353960\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −9.36735e11 | −0.985053 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.60225e12 | −1.65225 | −0.826125 | − | 0.563487i | \(-0.809459\pi\) | ||||
−0.826125 | + | 0.563487i | \(0.809459\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.37910e12 | −1.39471 | −0.697353 | − | 0.716728i | \(-0.745639\pi\) | ||||
−0.697353 | + | 0.716728i | \(0.745639\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.45981e11 | −0.640739 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.55852e11 | −0.929961 | −0.464980 | − | 0.885321i | \(-0.653939\pi\) | ||||
−0.464980 | + | 0.885321i | \(0.653939\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.79576e11 | 0.457699 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.23161e12 | −1.15313 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.75274e11 | 0.620304 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.42194e10 | 0.0128162 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.26028e11 | −0.376795 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.16208e12 | −1.00861 | −0.504307 | − | 0.863524i | \(-0.668252\pi\) | ||||
−0.504307 | + | 0.863524i | \(0.668252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.96243e11 | −0.167164 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.60213e11 | 0.802797 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.57453e11 | 0.703676 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.30662e11 | 0.669182 | 0.334591 | − | 0.942364i | \(-0.391402\pi\) | ||||
0.334591 | + | 0.942364i | \(0.391402\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.23291e11 | −0.334772 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.17729e11 | −0.246712 | −0.123356 | − | 0.992362i | \(-0.539366\pi\) | ||||
−0.123356 | + | 0.992362i | \(0.539366\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.45462e11 | 0.720830 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.43366e11 | −0.107330 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.05607e12 | 0.776408 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.15696e12 | 1.55736 | 0.778680 | − | 0.627421i | \(-0.215889\pi\) | ||||
0.778680 | + | 0.627421i | \(0.215889\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.95503e12 | −1.38638 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.24185e12 | −0.864996 | −0.432498 | − | 0.901635i | \(-0.642368\pi\) | ||||
−0.432498 | + | 0.901635i | \(0.642368\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.69067e11 | −0.526202 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.13090e12 | 0.760132 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.49436e12 | 1.64713 | 0.823566 | − | 0.567220i | \(-0.191981\pi\) | ||||
0.823566 | + | 0.567220i | \(0.191981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.12359e12 | 2.67536 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.09125e11 | 0.0695660 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.04945e11 | 0.316309 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.66636e11 | 0.102579 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.45164e12 | 0.878227 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.12898e11 | −0.364434 | −0.182217 | − | 0.983258i | \(-0.558327\pi\) | ||||
−0.182217 | + | 0.983258i | \(0.558327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.03989e12 | 1.77664 | 0.888321 | − | 0.459223i | \(-0.151872\pi\) | ||||
0.888321 | + | 0.459223i | \(0.151872\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.94099e11 | −0.226406 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.94806e12 | −1.66490 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.95326e11 | −0.497085 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.53773e11 | 0.356863 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.86700e11 | 0.314879 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.99218e11 | −0.527312 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.55285e11 | −0.340052 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.32761e12 | 0.677517 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.86670e12 | 1.43878 | 0.719390 | − | 0.694606i | \(-0.244421\pi\) | ||||
0.719390 | + | 0.694606i | \(0.244421\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.45301e12 | 1.21088 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.75487e11 | −0.327969 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.44503e12 | −1.16772 | −0.583862 | − | 0.811853i | \(-0.698459\pi\) | ||||
−0.583862 | + | 0.811853i | \(0.698459\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.73168e11 | −0.175319 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.10142e11 | −0.0509062 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.45550e11 | 0.384482 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00978e11 | 0.358346 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.40112e12 | −0.616777 | −0.308389 | − | 0.951260i | \(-0.599790\pi\) | ||||
−0.308389 | + | 0.951260i | \(0.599790\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.79348e11 | 0.164318 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.02220e12 | 0.435716 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.12352e11 | 0.131026 | 0.0655129 | − | 0.997852i | \(-0.479132\pi\) | ||||
0.0655129 | + | 0.997852i | \(0.479132\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.50254e11 | 0.392303 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.63203e12 | −0.663141 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.50839e12 | −0.603266 | −0.301633 | − | 0.953424i | \(-0.597532\pi\) | ||||
−0.301633 | + | 0.953424i | \(0.597532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.77207e12 | 0.697621 | 0.348810 | − | 0.937193i | \(-0.386586\pi\) | ||||
0.348810 | + | 0.937193i | \(0.386586\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.17778e12 | −1.23148 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.71777e11 | −0.141833 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.81248e10 | 0.0218308 | 0.0109154 | − | 0.999940i | \(-0.496525\pi\) | ||||
0.0109154 | + | 0.999940i | \(0.496525\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.19680e12 | −0.812338 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.40824e12 | 1.96908 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.65613e12 | 0.593725 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.05385e10 | −0.0284317 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.72424e11 | 0.233761 | 0.116880 | − | 0.993146i | \(-0.462711\pi\) | ||||
0.116880 | + | 0.993146i | \(0.462711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.43435e11 | 0.117578 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.35230e12 | −0.455962 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.33711e12 | 1.44031 | 0.720153 | − | 0.693816i | \(-0.244072\pi\) | ||||
0.720153 | + | 0.693816i | \(0.244072\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.79855e12 | −0.588295 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.97527e12 | −0.958611 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.37288e11 | 0.107048 | 0.0535242 | − | 0.998567i | \(-0.482955\pi\) | ||||
0.0535242 | + | 0.998567i | \(0.482955\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.13643e11 | −0.0980619 | −0.0490309 | − | 0.998797i | \(-0.515613\pi\) | ||||
−0.0490309 | + | 0.998797i | \(0.515613\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00021e11 | −0.123212 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.16403e11 | −0.278091 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.29060e12 | −0.385872 | −0.192936 | − | 0.981211i | \(-0.561801\pi\) | ||||
−0.192936 | + | 0.981211i | \(0.561801\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.05265e12 | 0.899290 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.36109e10 | 0.0271732 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.58380e12 | 1.02511 | 0.512556 | − | 0.858654i | \(-0.328699\pi\) | ||||
0.512556 | + | 0.858654i | \(0.328699\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.39465e12 | −0.675000 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.46900e12 | −1.51923 | −0.759617 | − | 0.650370i | \(-0.774614\pi\) | ||||
−0.759617 | + | 0.650370i | \(0.774614\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.83483e12 | 1.59743 | 0.798713 | − | 0.601713i | \(-0.205515\pi\) | ||||
0.798713 | + | 0.601713i | \(0.205515\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.85317e12 | −0.769866 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.43426e12 | −1.17930 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.19082e11 | −0.0307710 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.65542e12 | 0.931129 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.43138e12 | −1.11277 | −0.556387 | − | 0.830923i | \(-0.687813\pi\) | ||||
−0.556387 | + | 0.830923i | \(0.687813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.00894e12 | 0.249775 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.97432e12 | −0.725948 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.45810e11 | 0.179474 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.80883e11 | −0.209009 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.38785e12 | 0.558659 | 0.279329 | − | 0.960195i | \(-0.409888\pi\) | ||||
0.279329 | + | 0.960195i | \(0.409888\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.42772e12 | 0.329378 | 0.164689 | − | 0.986346i | \(-0.447338\pi\) | ||||
0.164689 | + | 0.986346i | \(0.447338\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.54833e12 | −0.352246 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.43250e12 | 0.994443 | 0.497221 | − | 0.867624i | \(-0.334354\pi\) | ||||
0.497221 | + | 0.867624i | \(0.334354\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.54146e12 | −0.562317 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.51852e12 | −2.07709 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.61930e11 | −0.142463 | −0.0712316 | − | 0.997460i | \(-0.522693\pi\) | ||||
−0.0712316 | + | 0.997460i | \(0.522693\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.14516e12 | 0.455379 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.43954e12 | −0.720205 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.94755e12 | −1.64153 | −0.820765 | − | 0.571266i | \(-0.806452\pi\) | ||||
−0.820765 | + | 0.571266i | \(0.806452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.06071e11 | 0.164235 | 0.0821177 | − | 0.996623i | \(-0.473832\pi\) | ||||
0.0821177 | + | 0.996623i | \(0.473832\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.74242e11 | 0.115421 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.09522e11 | 0.0415464 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.87975e12 | 0.563364 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.66851e12 | −0.515052 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.45064e12 | 0.276254 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.67873e12 | −0.691241 | −0.345621 | − | 0.938374i | \(-0.612332\pi\) | ||||
−0.345621 | + | 0.938374i | \(0.612332\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.17102e12 | 0.217119 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.60384e12 | −1.39118 | −0.695591 | − | 0.718438i | \(-0.744857\pi\) | ||||
−0.695591 | + | 0.718438i | \(0.744857\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.26346e13 | 2.28111 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.52388e11 | 0.116237 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.89820e12 | 1.21295 | 0.606475 | − | 0.795103i | \(-0.292583\pi\) | ||||
0.606475 | + | 0.795103i | \(0.292583\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.25807e10 | −0.00565397 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.16336e12 | 0.370531 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.30362e11 | 0.157277 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.45838e12 | −0.743920 | −0.371960 | − | 0.928249i | \(-0.621314\pi\) | ||||
−0.371960 | + | 0.928249i | \(0.621314\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.11249e12 | −0.347933 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.67139e12 | −0.596896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.09285e13 | −1.75393 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.42991e12 | 0.860291 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.34128e12 | −0.366203 | −0.183102 | − | 0.983094i | \(-0.558614\pi\) | ||||
−0.183102 | + | 0.983094i | \(0.558614\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.25840e11 | −0.0657578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.82078e11 | −0.0582507 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.13322e13 | −1.70579 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.10575e12 | 0.758841 | 0.379421 | − | 0.925224i | \(-0.376123\pi\) | ||||
0.379421 | + | 0.925224i | \(0.376123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.05284e11 | −0.103503 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.97940e12 | −1.30120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.13083e11 | 0.0448004 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.79467e12 | −0.394907 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.39438e12 | 0.194581 | 0.0972907 | − | 0.995256i | \(-0.468982\pi\) | ||||
0.0972907 | + | 0.995256i | \(0.468982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.44037e12 | 1.02538 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.17503e12 | −0.704353 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.18193e12 | −0.158881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.87221e12 | 0.381339 | 0.190669 | − | 0.981654i | \(-0.438934\pi\) | ||||
0.190669 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 7.82545e12 | 1.02621 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.06612e12 | −0.915278 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.91043e12 | 0.500330 | 0.250165 | − | 0.968203i | \(-0.419515\pi\) | ||||
0.250165 | + | 0.968203i | \(0.419515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.04407e12 | −0.384734 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.55503e12 | 0.194149 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.00098e12 | 0.123460 | 0.0617298 | − | 0.998093i | \(-0.480338\pi\) | ||||
0.0617298 | + | 0.998093i | \(0.480338\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.68966e10 | −0.00815121 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.19147e12 | 0.624943 | 0.312472 | − | 0.949927i | \(-0.398843\pi\) | ||||
0.312472 | + | 0.949927i | \(0.398843\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.02045e12 | 0.716021 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.51108e12 | −0.530076 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.47235e13 | −1.70939 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.48763e13 | 1.70654 | 0.853268 | − | 0.521473i | \(-0.174617\pi\) | ||||
0.853268 | + | 0.521473i | \(0.174617\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.94705e12 | 0.447399 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.01038e12 | 0.449183 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.03576e13 | 1.14637 | 0.573187 | − | 0.819425i | \(-0.305707\pi\) | ||||
0.573187 | + | 0.819425i | \(0.305707\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.11349e12 | 0.340533 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.88282e11 | 0.0311592 | 0.0155796 | − | 0.999879i | \(-0.495041\pi\) | ||||
0.0155796 | + | 0.999879i | \(0.495041\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.95330e12 | −1.06318 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.50019e12 | 0.158369 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.42771e12 | −0.148957 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.28801e13 | 1.32816 | 0.664081 | − | 0.747661i | \(-0.268823\pi\) | ||||
0.664081 | + | 0.747661i | \(0.268823\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.55530e12 | 0.871948 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.40486e12 | 0.947425 | 0.473712 | − | 0.880680i | \(-0.342914\pi\) | ||||
0.473712 | + | 0.880680i | \(0.342914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.68540e12 | 0.366967 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.18024e13 | 1.16165 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.27311e12 | 0.123865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.42431e12 | 0.329340 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.07063e12 | −0.862401 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.02650e12 | 0.660428 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.24747e12 | −0.766363 | −0.383181 | − | 0.923673i | \(-0.625172\pi\) | ||||
−0.383181 | + | 0.923673i | \(0.625172\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.11800e12 | 0.194572 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.40020e13 | 1.27173 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.14926e11 | 0.0731794 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.79733e12 | −0.337152 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.35880e12 | 0.294864 | 0.147432 | − | 0.989072i | \(-0.452899\pi\) | ||||
0.147432 | + | 0.989072i | \(0.452899\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.74369e12 | −0.151359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.69867e12 | 0.317468 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.33707e13 | 1.13484 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.47813e12 | −0.459781 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.86654e13 | 1.54919 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.87559e12 | −0.564341 | −0.282171 | − | 0.959364i | \(-0.591054\pi\) | ||||
−0.282171 | + | 0.959364i | \(0.591054\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.11160e13 | −1.71402 | −0.857012 | − | 0.515296i | \(-0.827682\pi\) | ||||
−0.857012 | + | 0.515296i | \(0.827682\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.70903e12 | −0.458305 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.41493e12 | 0.191732 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.23171e11 | 0.0646384 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.18674e12 | −0.0921672 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.67955e12 | −0.282651 | −0.141325 | − | 0.989963i | \(-0.545136\pi\) | ||||
−0.141325 | + | 0.989963i | \(0.545136\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.15696e12 | −0.467807 | −0.233904 | − | 0.972260i | \(-0.575150\pi\) | ||||
−0.233904 | + | 0.972260i | \(0.575150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.27787e12 | −0.0960378 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.99295e12 | −0.296838 | −0.148419 | − | 0.988925i | \(-0.547418\pi\) | ||||
−0.148419 | + | 0.988925i | \(0.547418\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.16163e12 | 0.0854229 | 0.0427114 | − | 0.999087i | \(-0.486400\pi\) | ||||
0.0427114 | + | 0.999087i | \(0.486400\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.63472e12 | 0.555378 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.38922e13 | −0.999697 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.11537e13 | 0.794015 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.82833e13 | 1.99189 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.05218e13 | −0.733099 | −0.366550 | − | 0.930398i | \(-0.619461\pi\) | ||||
−0.366550 | + | 0.930398i | \(0.619461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.35201e12 | −0.368922 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.35565e13 | 0.924537 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.45193e12 | −0.435346 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.35032e13 | −0.901490 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.12718e13 | 0.744578 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.11339e13 | 0.727722 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.18899e13 | 0.768967 | 0.384484 | − | 0.923132i | \(-0.374380\pi\) | ||||
0.384484 | + | 0.923132i | \(0.374380\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.74765e11 | −0.0111843 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.57517e12 | −0.163077 | −0.0815385 | − | 0.996670i | \(-0.525983\pi\) | ||||
−0.0815385 | + | 0.996670i | \(0.525983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.61942e13 | −1.01482 | −0.507411 | − | 0.861704i | \(-0.669398\pi\) | ||||
−0.507411 | + | 0.861704i | \(0.669398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.52852e13 | −2.18815 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.94014e12 | 0.303173 | 0.151586 | − | 0.988444i | \(-0.451562\pi\) | ||||
0.151586 | + | 0.988444i | \(0.451562\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.28180e12 | −0.502982 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.29496e12 | 0.137940 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.74170e12 | 0.163091 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.73567e11 | 0.0514298 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.05387e13 | −0.614075 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.24838e12 | 0.129668 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.68472e12 | −0.495744 | −0.247872 | − | 0.968793i | \(-0.579731\pi\) | ||||
−0.247872 | + | 0.968793i | \(0.579731\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.95950e12 | 0.280213 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.02139e13 | −0.571214 | −0.285607 | − | 0.958347i | \(-0.592195\pi\) | ||||
−0.285607 | + | 0.958347i | \(0.592195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.58719e12 | −0.198578 | −0.0992891 | − | 0.995059i | \(-0.531657\pi\) | ||||
−0.0992891 | + | 0.995059i | \(0.531657\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.82730e12 | 0.319317 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.72905e13 | 1.48032 | 0.740160 | − | 0.672431i | \(-0.234750\pi\) | ||||
0.740160 | + | 0.672431i | \(0.234750\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.38266e13 | −2.35331 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.29187e12 | −0.281294 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.03132e11 | 0.0106892 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.73848e12 | 0.194756 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.74907e12 | 0.0902070 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.85468e13 | −1.45760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.73299e13 | −0.876059 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.28147e13 | −1.14188 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.39947e13 | −0.693499 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.79849e13 | 0.882418 | 0.441209 | − | 0.897404i | \(-0.354550\pi\) | ||||
0.441209 | + | 0.897404i | \(0.354550\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9.45233e12 | 0.459200 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.80978e13 | 0.870549 | 0.435275 | − | 0.900298i | \(-0.356651\pi\) | ||||
0.435275 | + | 0.900298i | \(0.356651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.75362e13 | 0.835252 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.32617e12 | −0.156873 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.16089e13 | 1.47621 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.09898e13 | −1.43317 | −0.716586 | − | 0.697498i | \(-0.754296\pi\) | ||||
−0.716586 | + | 0.697498i | \(0.754296\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.48838e13 | −1.13959 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.92368e12 | 0.0872418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.56968e12 | −0.205233 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.20611e12 | −0.276033 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.53410e13 | −1.11623 | −0.558113 | − | 0.829765i | \(-0.688475\pi\) | ||||
−0.558113 | + | 0.829765i | \(0.688475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.61838e12 | 0.0706002 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.26852e13 | 0.548063 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.83179e12 | −0.249545 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.05858e12 | 0.299150 | 0.149575 | − | 0.988750i | \(-0.452209\pi\) | ||||
0.149575 | + | 0.988750i | \(0.452209\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.10186e13 | −0.462522 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.06352e12 | 0.168947 | 0.0844733 | − | 0.996426i | \(-0.473079\pi\) | ||||
0.0844733 | + | 0.996426i | \(0.473079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.32866e13 | −1.37078 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.72550e13 | 0.703837 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.96392e12 | −0.160158 | −0.0800792 | − | 0.996789i | \(-0.525517\pi\) | ||||
−0.0800792 | + | 0.996789i | \(0.525517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.51128e12 | 0.300619 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.81618e12 | −0.349517 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.82636e12 | −0.0717246 | −0.0358623 | − | 0.999357i | \(-0.511418\pi\) | ||||
−0.0358623 | + | 0.999357i | \(0.511418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.81296e13 | 0.705299 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.89823e12 | 0.381464 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.80077e11 | −0.0183285 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.25725e13 | 2.36662 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.22810e13 | 0.460168 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.25330e13 | 0.465246 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.71062e13 | −0.629122 | −0.314561 | − | 0.949237i | \(-0.601857\pi\) | ||||
−0.314561 | + | 0.949237i | \(0.601857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.24608e12 | 0.0454036 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.43910e12 | 0.232455 | 0.116227 | − | 0.993223i | \(-0.462920\pi\) | ||||
0.116227 | + | 0.993223i | \(0.462920\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.40979e13 | −1.93496 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −7.17866e11 | −0.0254403 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.72264e13 | 0.604880 | 0.302440 | − | 0.953168i | \(-0.402199\pi\) | ||||
0.302440 | + | 0.953168i | \(0.402199\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.43781e13 | −0.500240 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.30217e12 | 0.286208 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.22407e13 | −0.418134 | −0.209067 | − | 0.977901i | \(-0.567043\pi\) | ||||
−0.209067 | + | 0.977901i | \(0.567043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.71502e12 | 0.261140 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.62992e12 | −0.188832 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.15225e13 | −0.715334 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.74736e13 | 0.904867 | 0.452434 | − | 0.891798i | \(-0.350556\pi\) | ||||
0.452434 | + | 0.891798i | \(0.350556\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.33092e13 | 1.41354 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.69743e13 | 0.549020 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.32279e13 | 0.423996 | 0.211998 | − | 0.977270i | \(-0.432003\pi\) | ||||
0.211998 | + | 0.977270i | \(0.432003\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.50696e13 | −1.11400 |
(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 | 80.10.a.h.1.1 | 2 | ||
4.3 | odd | 2 | 40.10.a.b.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 400.10.c.o.49.3 | 4 | |||
5.3 | odd | 4 | 400.10.c.o.49.2 | 4 | |||
5.4 | even | 2 | 400.10.a.o.1.2 | 2 | |||
8.3 | odd | 2 | 320.10.a.p.1.1 | 2 | |||
8.5 | even | 2 | 320.10.a.o.1.2 | 2 | |||
12.11 | even | 2 | 360.10.a.a.1.1 | 2 | |||
20.3 | even | 4 | 200.10.c.e.49.3 | 4 | |||
20.7 | even | 4 | 200.10.c.e.49.2 | 4 | |||
20.19 | odd | 2 | 200.10.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.10.a.b.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
80.10.a.h.1.1 | 2 | 1.1 | even | 1 | trivial | ||
200.10.a.d.1.1 | 2 | 20.19 | odd | 2 | |||
200.10.c.e.49.2 | 4 | 20.7 | even | 4 | |||
200.10.c.e.49.3 | 4 | 20.3 | even | 4 | |||
320.10.a.o.1.2 | 2 | 8.5 | even | 2 | |||
320.10.a.p.1.1 | 2 | 8.3 | odd | 2 | |||
360.10.a.a.1.1 | 2 | 12.11 | even | 2 | |||
400.10.a.o.1.2 | 2 | 5.4 | even | 2 | |||
400.10.c.o.49.2 | 4 | 5.3 | odd | 4 | |||
400.10.c.o.49.3 | 4 | 5.2 | odd | 4 |