Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(11.5967\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −11.5967 | −1.02501 | −0.512506 | − | 0.858684i | \(-0.671283\pi\) | ||||
−0.512506 | + | 0.858684i | \(0.671283\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 6.48306 | 0.0506489 | ||||||||
\(5\) | 401.104 | 1.43503 | 0.717517 | − | 0.696541i | \(-0.245279\pi\) | ||||
0.717517 | + | 0.696541i | \(0.245279\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 213.573 | 0.235344 | 0.117672 | − | 0.993053i | \(-0.462457\pi\) | ||||
0.117672 | + | 0.993053i | \(0.462457\pi\) | |||||||
\(8\) | 1409.19 | 0.973096 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4651.48 | −1.47093 | ||||||||
\(11\) | 4974.14 | 1.12679 | 0.563396 | − | 0.826187i | \(-0.309495\pi\) | ||||
0.563396 | + | 0.826187i | \(0.309495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12649.9 | −1.59693 | −0.798467 | − | 0.602038i | \(-0.794355\pi\) | ||||
−0.798467 | + | 0.602038i | \(0.794355\pi\) | |||||||
\(14\) | −2476.74 | −0.241230 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −17171.8 | −1.04808 | ||||||||
\(17\) | −36937.0 | −1.82344 | −0.911718 | − | 0.410816i | \(-0.865244\pi\) | ||||
−0.911718 | + | 0.410816i | \(0.865244\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −31065.7 | −1.03907 | −0.519533 | − | 0.854451i | \(-0.673894\pi\) | ||||
−0.519533 | + | 0.854451i | \(0.673894\pi\) | |||||||
\(20\) | 2600.38 | 0.0726829 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −57683.5 | −1.15497 | ||||||||
\(23\) | −52594.0 | −0.901341 | −0.450670 | − | 0.892690i | \(-0.648815\pi\) | ||||
−0.450670 | + | 0.892690i | \(0.648815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 82759.6 | 1.05932 | ||||||||
\(26\) | 146697. | 1.63688 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1384.61 | 0.0119199 | ||||||||
\(29\) | 209912. | 1.59825 | 0.799123 | − | 0.601167i | \(-0.205298\pi\) | ||||
0.799123 | + | 0.601167i | \(0.205298\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11865.2 | −0.0715333 | −0.0357667 | − | 0.999360i | \(-0.511387\pi\) | ||||
−0.0357667 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(32\) | 18759.2 | 0.101202 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 428347. | 1.86904 | ||||||||
\(35\) | 85665.0 | 0.337727 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 16919.7 | 0.0549143 | 0.0274572 | − | 0.999623i | \(-0.491259\pi\) | ||||
0.0274572 | + | 0.999623i | \(0.491259\pi\) | |||||||
\(38\) | 360259. | 1.06505 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 565233. | 1.39643 | ||||||||
\(41\) | −801040. | −1.81514 | −0.907571 | − | 0.419898i | \(-0.862066\pi\) | ||||
−0.907571 | + | 0.419898i | \(0.862066\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 720238. | 1.38145 | 0.690727 | − | 0.723115i | \(-0.257290\pi\) | ||||
0.690727 | + | 0.723115i | \(0.257290\pi\) | |||||||
\(44\) | 32247.7 | 0.0570708 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 609916. | 0.923885 | ||||||||
\(47\) | 54403.0 | 0.0764329 | 0.0382164 | − | 0.999269i | \(-0.487832\pi\) | ||||
0.0382164 | + | 0.999269i | \(0.487832\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −777930. | −0.944613 | ||||||||
\(50\) | −959737. | −1.08582 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −82010.4 | −0.0808830 | ||||||||
\(53\) | 295498. | 0.272639 | 0.136320 | − | 0.990665i | \(-0.456473\pi\) | ||||
0.136320 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.99515e6 | 1.61698 | ||||||||
\(56\) | 300965. | 0.229012 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.43428e6 | −1.63822 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.37027e6 | 0.772952 | 0.386476 | − | 0.922300i | \(-0.373692\pi\) | ||||
0.386476 | + | 0.922300i | \(0.373692\pi\) | |||||||
\(62\) | 137597. | 0.0733225 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.98045e6 | 0.944350 | ||||||||
\(65\) | −5.07395e6 | −2.29166 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.05207e6 | 1.23975 | 0.619873 | − | 0.784702i | \(-0.287184\pi\) | ||||
0.619873 | + | 0.784702i | \(0.287184\pi\) | |||||||
\(68\) | −239465. | −0.0923551 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −993430. | −0.346174 | ||||||||
\(71\) | 4.70310e6 | 1.55948 | 0.779740 | − | 0.626104i | \(-0.215351\pi\) | ||||
0.779740 | + | 0.626104i | \(0.215351\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.65576e6 | −1.09989 | −0.549943 | − | 0.835202i | \(-0.685351\pi\) | ||||
−0.549943 | + | 0.835202i | \(0.685351\pi\) | |||||||
\(74\) | −196212. | −0.0562878 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −201401. | −0.0526275 | ||||||||
\(77\) | 1.06234e6 | 0.265184 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.37313e6 | 1.45431 | 0.727157 | − | 0.686471i | \(-0.240841\pi\) | ||||
0.727157 | + | 0.686471i | \(0.240841\pi\) | |||||||
\(80\) | −6.88768e6 | −1.50404 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.28941e6 | 1.86054 | ||||||||
\(83\) | 2.08701e6 | 0.400636 | 0.200318 | − | 0.979731i | \(-0.435802\pi\) | ||||
0.200318 | + | 0.979731i | \(0.435802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.48156e7 | −2.61669 | ||||||||
\(86\) | −8.35238e6 | −1.41601 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.00953e6 | 1.09648 | ||||||||
\(89\) | −1.43644e6 | −0.215984 | −0.107992 | − | 0.994152i | \(-0.534442\pi\) | ||||
−0.107992 | + | 0.994152i | \(0.534442\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70169e6 | −0.375829 | ||||||||
\(92\) | −340970. | −0.0456519 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −630894. | −0.0783446 | ||||||||
\(95\) | −1.24606e7 | −1.49109 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.42693e6 | −0.714994 | −0.357497 | − | 0.933914i | \(-0.616370\pi\) | ||||
−0.357497 | + | 0.933914i | \(0.616370\pi\) | |||||||
\(98\) | 9.02140e6 | 0.968240 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 536536. | 0.0536536 | ||||||||
\(101\) | −1.06724e6 | −0.103071 | −0.0515356 | − | 0.998671i | \(-0.516412\pi\) | ||||
−0.0515356 | + | 0.998671i | \(0.516412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.80605e6 | −0.884227 | −0.442113 | − | 0.896959i | \(-0.645771\pi\) | ||||
−0.442113 | + | 0.896959i | \(0.645771\pi\) | |||||||
\(104\) | −1.78262e7 | −1.55397 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.42679e6 | −0.279459 | ||||||||
\(107\) | 1.96135e7 | 1.54779 | 0.773895 | − | 0.633314i | \(-0.218306\pi\) | ||||
0.773895 | + | 0.633314i | \(0.218306\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.55432e7 | 1.88922 | 0.944610 | − | 0.328194i | \(-0.106440\pi\) | ||||
0.944610 | + | 0.328194i | \(0.106440\pi\) | |||||||
\(110\) | −2.31371e7 | −1.65743 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.66743e6 | −0.246660 | ||||||||
\(113\) | 1.24785e7 | 0.813559 | 0.406780 | − | 0.913526i | \(-0.366652\pi\) | ||||
0.406780 | + | 0.913526i | \(0.366652\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.10957e7 | −1.29345 | ||||||||
\(116\) | 1.36087e6 | 0.0809494 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.38172e6 | −0.133445 | ||||||||
\(119\) | −7.88875e6 | −0.429135 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.25490e6 | 0.269659 | ||||||||
\(122\) | −1.58906e7 | −0.792284 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −76922.7 | −0.00362308 | ||||||||
\(125\) | 1.85896e6 | 0.0851305 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.73455e7 | −0.751403 | −0.375701 | − | 0.926741i | \(-0.622598\pi\) | ||||
−0.375701 | + | 0.926741i | \(0.622598\pi\) | |||||||
\(128\) | −2.53678e7 | −1.06917 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.88410e7 | 2.34897 | ||||||||
\(131\) | 1.36249e7 | 0.529520 | 0.264760 | − | 0.964314i | \(-0.414707\pi\) | ||||
0.264760 | + | 0.964314i | \(0.414707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.63478e6 | −0.244538 | ||||||||
\(134\) | −3.53939e7 | −1.27075 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.20514e7 | −1.77438 | ||||||||
\(137\) | 1.67308e7 | 0.555898 | 0.277949 | − | 0.960596i | \(-0.410345\pi\) | ||||
0.277949 | + | 0.960596i | \(0.410345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.17094e7 | 0.369813 | 0.184907 | − | 0.982756i | \(-0.440802\pi\) | ||||
0.184907 | + | 0.982756i | \(0.440802\pi\) | |||||||
\(140\) | 555371. | 0.0171055 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.45403e7 | −1.59848 | ||||||||
\(143\) | −6.29226e7 | −1.79941 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.41965e7 | 2.29354 | ||||||||
\(146\) | 4.23947e7 | 1.12740 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 109691. | 0.00278135 | ||||||||
\(149\) | −153329. | −0.00379728 | −0.00189864 | − | 0.999998i | \(-0.500604\pi\) | ||||
−0.00189864 | + | 0.999998i | \(0.500604\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.64791e7 | 1.80769 | 0.903843 | − | 0.427863i | \(-0.140734\pi\) | ||||
0.903843 | + | 0.427863i | \(0.140734\pi\) | |||||||
\(152\) | −4.37775e7 | −1.01111 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.23196e7 | −0.271816 | ||||||||
\(155\) | −4.75917e6 | −0.102653 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.86729e6 | −0.141624 | −0.0708119 | − | 0.997490i | \(-0.522559\pi\) | ||||
−0.0708119 | + | 0.997490i | \(0.522559\pi\) | |||||||
\(158\) | −7.39072e7 | −1.49069 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.52439e6 | 0.145228 | ||||||||
\(161\) | −1.12327e7 | −0.212125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.89828e7 | −0.343323 | −0.171662 | − | 0.985156i | \(-0.554914\pi\) | ||||
−0.171662 | + | 0.985156i | \(0.554914\pi\) | |||||||
\(164\) | −5.19319e6 | −0.0919350 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.42024e7 | −0.410657 | ||||||||
\(167\) | 1.70383e7 | 0.283085 | 0.141543 | − | 0.989932i | \(-0.454794\pi\) | ||||
0.141543 | + | 0.989932i | \(0.454794\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.72727e7 | 1.55020 | ||||||||
\(170\) | 1.71812e8 | 2.68214 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.66935e6 | 0.0699692 | ||||||||
\(173\) | 8.07641e6 | 0.118592 | 0.0592962 | − | 0.998240i | \(-0.481114\pi\) | ||||
0.0592962 | + | 0.998240i | \(0.481114\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.76752e7 | 0.249305 | ||||||||
\(176\) | −8.54149e7 | −1.18097 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.66579e7 | 0.221386 | ||||||||
\(179\) | −4.99947e7 | −0.651536 | −0.325768 | − | 0.945450i | \(-0.605623\pi\) | ||||
−0.325768 | + | 0.945450i | \(0.605623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.07416e7 | 0.886747 | 0.443373 | − | 0.896337i | \(-0.353782\pi\) | ||||
0.443373 | + | 0.896337i | \(0.353782\pi\) | |||||||
\(182\) | 3.13306e7 | 0.385229 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −7.41151e7 | −0.877091 | ||||||||
\(185\) | 6.78655e6 | 0.0788039 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.83730e8 | −2.05463 | ||||||||
\(188\) | 352698. | 0.00387124 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.44501e8 | 1.52839 | ||||||||
\(191\) | 1.40226e8 | 1.45617 | 0.728086 | − | 0.685486i | \(-0.240410\pi\) | ||||
0.728086 | + | 0.685486i | \(0.240410\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.81729e7 | −0.582465 | −0.291233 | − | 0.956652i | \(-0.594065\pi\) | ||||
−0.291233 | + | 0.956652i | \(0.594065\pi\) | |||||||
\(194\) | 7.45311e7 | 0.732878 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.04337e6 | −0.0478436 | ||||||||
\(197\) | −6.06171e7 | −0.564889 | −0.282445 | − | 0.959284i | \(-0.591145\pi\) | ||||
−0.282445 | + | 0.959284i | \(0.591145\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 234342. | 0.00210797 | 0.00105398 | − | 0.999999i | \(-0.499665\pi\) | ||||
0.00105398 | + | 0.999999i | \(0.499665\pi\) | |||||||
\(200\) | 1.16624e8 | 1.03082 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.23765e7 | 0.105649 | ||||||||
\(203\) | 4.48314e7 | 0.376137 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.21300e8 | −2.60479 | ||||||||
\(206\) | 1.13718e8 | 0.906343 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.17222e8 | 1.67372 | ||||||||
\(209\) | −1.54525e8 | −1.17081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.04520e8 | −1.49881 | −0.749406 | − | 0.662111i | \(-0.769661\pi\) | ||||
−0.749406 | + | 0.662111i | \(0.769661\pi\) | |||||||
\(212\) | 1.91573e6 | 0.0138089 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.27452e8 | −1.58650 | ||||||||
\(215\) | 2.88891e8 | 1.98243 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.53408e6 | −0.0168349 | ||||||||
\(218\) | −2.96216e8 | −1.93647 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.29347e7 | 0.0818985 | ||||||||
\(221\) | 4.67251e8 | 2.91191 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.44062e8 | 1.47378 | 0.736892 | − | 0.676011i | \(-0.236293\pi\) | ||||
0.736892 | + | 0.676011i | \(0.236293\pi\) | |||||||
\(224\) | 4.00645e6 | 0.0238173 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.44710e8 | −0.833908 | ||||||||
\(227\) | 1.77415e8 | 1.00670 | 0.503350 | − | 0.864083i | \(-0.332101\pi\) | ||||
0.503350 | + | 0.864083i | \(0.332101\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.17580e8 | 1.19728 | 0.598638 | − | 0.801020i | \(-0.295709\pi\) | ||||
0.598638 | + | 0.801020i | \(0.295709\pi\) | |||||||
\(230\) | 2.44640e8 | 1.32581 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.95806e8 | 1.55525 | ||||||||
\(233\) | 3.27814e8 | 1.69778 | 0.848890 | − | 0.528570i | \(-0.177272\pi\) | ||||
0.848890 | + | 0.528570i | \(0.177272\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.18213e7 | 0.109684 | ||||||||
\(236\) | 1.33148e6 | 0.00659393 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.14833e7 | 0.439868 | ||||||||
\(239\) | −2.79462e8 | −1.32413 | −0.662064 | − | 0.749448i | \(-0.730319\pi\) | ||||
−0.662064 | + | 0.749448i | \(0.730319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.83280e8 | 1.76383 | 0.881915 | − | 0.471409i | \(-0.156254\pi\) | ||||
0.881915 | + | 0.471409i | \(0.156254\pi\) | |||||||
\(242\) | −6.09394e7 | −0.276404 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.88356e6 | 0.0391492 | ||||||||
\(245\) | −3.12031e8 | −1.35555 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.92979e8 | 1.65932 | ||||||||
\(248\) | −1.67203e7 | −0.0696088 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.15578e7 | −0.0872598 | ||||||||
\(251\) | 4.23948e8 | 1.69221 | 0.846106 | − | 0.533014i | \(-0.178941\pi\) | ||||
0.846106 | + | 0.533014i | \(0.178941\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.61610e8 | −1.01562 | ||||||||
\(254\) | 2.01150e8 | 0.770196 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.06850e7 | 0.151564 | ||||||||
\(257\) | −1.80864e8 | −0.664638 | −0.332319 | − | 0.943167i | \(-0.607831\pi\) | ||||
−0.332319 | + | 0.943167i | \(0.607831\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.61358e6 | 0.0129237 | ||||||||
\(260\) | −3.28947e7 | −0.116070 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.58003e8 | −0.542764 | ||||||||
\(263\) | −4.23691e8 | −1.43616 | −0.718082 | − | 0.695958i | \(-0.754980\pi\) | ||||
−0.718082 | + | 0.695958i | \(0.754980\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.18525e8 | 0.391247 | ||||||||
\(266\) | 7.69415e7 | 0.250654 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.97868e7 | 0.0627918 | ||||||||
\(269\) | −3.48418e8 | −1.09136 | −0.545679 | − | 0.837994i | \(-0.683728\pi\) | ||||
−0.545679 | + | 0.837994i | \(0.683728\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.26441e8 | −0.385918 | −0.192959 | − | 0.981207i | \(-0.561809\pi\) | ||||
−0.192959 | + | 0.981207i | \(0.561809\pi\) | |||||||
\(272\) | 6.34275e8 | 1.91111 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.94022e8 | −0.569802 | ||||||||
\(275\) | 4.11658e8 | 1.19364 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.22094e8 | −0.627852 | −0.313926 | − | 0.949447i | \(-0.601644\pi\) | ||||
−0.313926 | + | 0.949447i | \(0.601644\pi\) | |||||||
\(278\) | −1.35790e8 | −0.379063 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.20719e8 | 0.328640 | ||||||||
\(281\) | 3.20287e8 | 0.861128 | 0.430564 | − | 0.902560i | \(-0.358315\pi\) | ||||
0.430564 | + | 0.902560i | \(0.358315\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.46262e8 | 0.645870 | 0.322935 | − | 0.946421i | \(-0.395331\pi\) | ||||
0.322935 | + | 0.946421i | \(0.395331\pi\) | |||||||
\(284\) | 3.04905e7 | 0.0789860 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.29694e8 | 1.84442 | ||||||||
\(287\) | −1.71080e8 | −0.427183 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.54005e8 | 2.32492 | ||||||||
\(290\) | −9.76400e8 | −2.35090 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.37005e7 | −0.0557080 | ||||||||
\(293\) | −2.26005e8 | −0.524905 | −0.262453 | − | 0.964945i | \(-0.584531\pi\) | ||||
−0.262453 | + | 0.964945i | \(0.584531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.23784e7 | 0.186826 | ||||||||
\(296\) | 2.38431e7 | 0.0534369 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.77811e6 | 0.00389226 | ||||||||
\(299\) | 6.65312e8 | 1.43938 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.53823e8 | 0.325117 | ||||||||
\(302\) | −8.86903e8 | −1.85290 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.33453e8 | 1.08903 | ||||||||
\(305\) | 5.49622e8 | 1.10921 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.53693e8 | 1.09216 | 0.546078 | − | 0.837734i | \(-0.316120\pi\) | ||||
0.546078 | + | 0.837734i | \(0.316120\pi\) | |||||||
\(308\) | 6.88722e6 | 0.0134313 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5.51906e7 | 0.105220 | ||||||||
\(311\) | −8.72060e8 | −1.64394 | −0.821968 | − | 0.569534i | \(-0.807124\pi\) | ||||
−0.821968 | + | 0.569534i | \(0.807124\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.27729e8 | 0.604102 | 0.302051 | − | 0.953292i | \(-0.402329\pi\) | ||||
0.302051 | + | 0.953292i | \(0.402329\pi\) | |||||||
\(314\) | 7.96378e7 | 0.145166 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.13174e7 | 0.0736594 | ||||||||
\(317\) | −1.07872e9 | −1.90196 | −0.950982 | − | 0.309246i | \(-0.899923\pi\) | ||||
−0.950982 | + | 0.309246i | \(0.899923\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.04413e9 | 1.80089 | ||||||||
\(320\) | 7.94365e8 | 1.35518 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.30262e8 | 0.217431 | ||||||||
\(323\) | 1.14747e9 | 1.89467 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.04690e9 | −1.69167 | ||||||||
\(326\) | 2.20137e8 | 0.351910 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.12882e9 | −1.76631 | ||||||||
\(329\) | 1.16190e7 | 0.0179880 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.91834e8 | 0.290755 | 0.145378 | − | 0.989376i | \(-0.453560\pi\) | ||||
0.145378 | + | 0.989376i | \(0.453560\pi\) | |||||||
\(332\) | 1.35302e7 | 0.0202918 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.97587e8 | −0.290166 | ||||||||
\(335\) | 1.22420e9 | 1.77908 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.73052e8 | 0.673294 | 0.336647 | − | 0.941631i | \(-0.390707\pi\) | ||||
0.336647 | + | 0.941631i | \(0.390707\pi\) | |||||||
\(338\) | −1.12804e9 | −1.58897 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.60504e7 | −0.132533 | ||||||||
\(341\) | −5.90190e7 | −0.0806031 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.42031e8 | −0.457653 | ||||||||
\(344\) | 1.01496e9 | 1.34429 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9.36596e7 | −0.121559 | ||||||||
\(347\) | 2.39433e8 | 0.307631 | 0.153815 | − | 0.988100i | \(-0.450844\pi\) | ||||
0.153815 | + | 0.988100i | \(0.450844\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.55293e8 | 0.321477 | 0.160738 | − | 0.986997i | \(-0.448612\pi\) | ||||
0.160738 | + | 0.986997i | \(0.448612\pi\) | |||||||
\(350\) | −2.04974e8 | −0.255541 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.33108e7 | 0.114034 | ||||||||
\(353\) | −9.16807e8 | −1.10934 | −0.554672 | − | 0.832069i | \(-0.687156\pi\) | ||||
−0.554672 | + | 0.832069i | \(0.687156\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.88643e9 | 2.23791 | ||||||||
\(356\) | −9.31252e6 | −0.0109394 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.79773e8 | 0.667832 | ||||||||
\(359\) | 1.06121e8 | 0.121051 | 0.0605256 | − | 0.998167i | \(-0.480722\pi\) | ||||
0.0605256 | + | 0.998167i | \(0.480722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.12032e7 | 0.0796570 | ||||||||
\(362\) | −8.20368e8 | −0.908926 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.75152e7 | −0.0190353 | ||||||||
\(365\) | −1.46634e9 | −1.57837 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.13340e9 | 1.19689 | 0.598444 | − | 0.801164i | \(-0.295786\pi\) | ||||
0.598444 | + | 0.801164i | \(0.295786\pi\) | |||||||
\(368\) | 9.03134e8 | 0.944680 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −7.87014e7 | −0.0807749 | ||||||||
\(371\) | 6.31103e7 | 0.0641640 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.48649e8 | 0.347863 | 0.173931 | − | 0.984758i | \(-0.444353\pi\) | ||||
0.173931 | + | 0.984758i | \(0.444353\pi\) | |||||||
\(374\) | 2.13066e9 | 2.10602 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.66643e7 | 0.0743765 | ||||||||
\(377\) | −2.65537e9 | −2.55229 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.97757e8 | −0.186592 | −0.0932962 | − | 0.995638i | \(-0.529740\pi\) | ||||
−0.0932962 | + | 0.995638i | \(0.529740\pi\) | |||||||
\(380\) | −8.07826e7 | −0.0755223 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.62616e9 | −1.49259 | ||||||||
\(383\) | 1.60320e9 | 1.45811 | 0.729056 | − | 0.684454i | \(-0.239959\pi\) | ||||
0.729056 | + | 0.684454i | \(0.239959\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.26110e8 | 0.380547 | ||||||||
\(386\) | 6.74613e8 | 0.597034 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −4.16662e7 | −0.0362137 | ||||||||
\(389\) | 7.74392e8 | 0.667018 | 0.333509 | − | 0.942747i | \(-0.391767\pi\) | ||||
0.333509 | + | 0.942747i | \(0.391767\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.94267e9 | 1.64354 | ||||||||
\(392\) | −1.09625e9 | −0.919199 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.02957e8 | 0.579018 | ||||||||
\(395\) | 2.55629e9 | 2.08699 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.24932e9 | −1.00209 | −0.501044 | − | 0.865422i | \(-0.667050\pi\) | ||||
−0.501044 | + | 0.865422i | \(0.667050\pi\) | |||||||
\(398\) | −2.71759e6 | −0.00216069 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.42113e9 | −1.11026 | ||||||||
\(401\) | 2.10043e9 | 1.62668 | 0.813341 | − | 0.581788i | \(-0.197647\pi\) | ||||
0.813341 | + | 0.581788i | \(0.197647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.50094e8 | 0.114234 | ||||||||
\(404\) | −6.91899e6 | −0.00522045 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.19896e8 | −0.385545 | ||||||||
\(407\) | 8.41607e7 | 0.0618770 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.09675e9 | 1.51535 | 0.757677 | − | 0.652629i | \(-0.226334\pi\) | ||||
0.757677 | + | 0.652629i | \(0.226334\pi\) | |||||||
\(410\) | 3.72602e9 | 2.66994 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.35732e7 | −0.0447851 | ||||||||
\(413\) | 4.38634e7 | 0.0306392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.37107e8 | 0.574927 | ||||||||
\(416\) | −2.37303e8 | −0.161613 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.79198e9 | 1.20009 | ||||||||
\(419\) | 7.54525e8 | 0.501100 | 0.250550 | − | 0.968104i | \(-0.419388\pi\) | ||||
0.250550 | + | 0.968104i | \(0.419388\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.83091e8 | −0.119586 | −0.0597931 | − | 0.998211i | \(-0.519044\pi\) | ||||
−0.0597931 | + | 0.998211i | \(0.519044\pi\) | |||||||
\(422\) | 2.37175e9 | 1.53630 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.16413e8 | 0.265304 | ||||||||
\(425\) | −3.05689e9 | −1.93161 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.92653e8 | 0.181909 | ||||||||
\(428\) | 1.27155e8 | 0.0783938 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.35017e9 | −2.03202 | ||||||||
\(431\) | −2.72495e8 | −0.163941 | −0.0819706 | − | 0.996635i | \(-0.526121\pi\) | ||||
−0.0819706 | + | 0.996635i | \(0.526121\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.06889e8 | −0.536842 | −0.268421 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268421 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(434\) | 2.93869e7 | 0.0172560 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.65598e8 | 0.0956870 | ||||||||
\(437\) | 1.63387e9 | 0.936552 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.54375e7 | −0.0369148 | −0.0184574 | − | 0.999830i | \(-0.505876\pi\) | ||||
−0.0184574 | + | 0.999830i | \(0.505876\pi\) | |||||||
\(440\) | 2.81155e9 | 1.57348 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.41857e9 | −2.98474 | ||||||||
\(443\) | −2.60048e9 | −1.42115 | −0.710575 | − | 0.703621i | \(-0.751565\pi\) | ||||
−0.710575 | + | 0.703621i | \(0.751565\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.76162e8 | −0.309945 | ||||||||
\(446\) | −2.83031e9 | −1.51065 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.22970e8 | 0.222247 | ||||||||
\(449\) | −2.52865e9 | −1.31834 | −0.659168 | − | 0.751996i | \(-0.729091\pi\) | ||||
−0.659168 | + | 0.751996i | \(0.729091\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.98448e9 | −2.04529 | ||||||||
\(452\) | 8.08992e7 | 0.0412059 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.05742e9 | −1.03188 | ||||||||
\(455\) | −1.08366e9 | −0.539327 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.26888e9 | −0.621888 | −0.310944 | − | 0.950428i | \(-0.600645\pi\) | ||||
−0.310944 | + | 0.950428i | \(0.600645\pi\) | |||||||
\(458\) | −2.52320e9 | −1.22722 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.36765e8 | −0.0655121 | ||||||||
\(461\) | −6.17722e8 | −0.293656 | −0.146828 | − | 0.989162i | \(-0.546906\pi\) | ||||
−0.146828 | + | 0.989162i | \(0.546906\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.76885e9 | 0.828241 | 0.414120 | − | 0.910222i | \(-0.364089\pi\) | ||||
0.414120 | + | 0.910222i | \(0.364089\pi\) | |||||||
\(464\) | −3.60456e9 | −1.67510 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.80155e9 | −1.74024 | ||||||||
\(467\) | −2.09197e9 | −0.950489 | −0.475244 | − | 0.879854i | \(-0.657640\pi\) | ||||
−0.475244 | + | 0.879854i | \(0.657640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.51839e8 | 0.291767 | ||||||||
\(470\) | −2.53054e8 | −0.112427 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.89419e8 | 0.126686 | ||||||||
\(473\) | 3.58257e9 | 1.55661 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.57098e9 | −1.10071 | ||||||||
\(476\) | −5.11432e7 | −0.0217352 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.24083e9 | 1.35725 | ||||||||
\(479\) | 7.21973e8 | 0.300156 | 0.150078 | − | 0.988674i | \(-0.452048\pi\) | ||||
0.150078 | + | 0.988674i | \(0.452048\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.14033e8 | −0.0876945 | ||||||||
\(482\) | −4.44478e9 | −1.80795 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.40678e7 | 0.0136580 | ||||||||
\(485\) | −2.57787e9 | −1.02604 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.53074e9 | 0.992878 | 0.496439 | − | 0.868072i | \(-0.334641\pi\) | ||||
0.496439 | + | 0.868072i | \(0.334641\pi\) | |||||||
\(488\) | 1.93098e9 | 0.752156 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.61852e9 | 1.38946 | ||||||||
\(491\) | −4.02112e9 | −1.53307 | −0.766535 | − | 0.642203i | \(-0.778021\pi\) | ||||
−0.766535 | + | 0.642203i | \(0.778021\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.75351e9 | −2.91430 | ||||||||
\(494\) | −4.55725e9 | −1.70082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.03746e8 | 0.0749729 | ||||||||
\(497\) | 1.00445e9 | 0.367014 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.21528e9 | −0.437849 | −0.218924 | − | 0.975742i | \(-0.570255\pi\) | ||||
−0.218924 | + | 0.975742i | \(0.570255\pi\) | |||||||
\(500\) | 1.20518e7 | 0.00431177 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.91640e9 | −1.73454 | ||||||||
\(503\) | −4.23068e9 | −1.48225 | −0.741126 | − | 0.671366i | \(-0.765708\pi\) | ||||
−0.741126 | + | 0.671366i | \(0.765708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.28075e8 | −0.147911 | ||||||||
\(506\) | 3.03381e9 | 1.04103 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.12452e8 | −0.0380577 | ||||||||
\(509\) | −5.89664e9 | −1.98195 | −0.990974 | − | 0.134052i | \(-0.957201\pi\) | ||||
−0.990974 | + | 0.134052i | \(0.957201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.80771e8 | −0.258851 | ||||||||
\(512\) | 2.77526e9 | 0.913818 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.09742e9 | 0.681262 | ||||||||
\(515\) | −3.93325e9 | −1.26890 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.70608e8 | 0.0861239 | ||||||||
\(518\) | −4.19055e7 | −0.0132470 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.15017e9 | −2.23000 | ||||||||
\(521\) | 3.53847e8 | 0.109618 | 0.0548092 | − | 0.998497i | \(-0.482545\pi\) | ||||
0.0548092 | + | 0.998497i | \(0.482545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.49203e9 | 0.456059 | 0.228029 | − | 0.973654i | \(-0.426772\pi\) | ||||
0.228029 | + | 0.973654i | \(0.426772\pi\) | |||||||
\(524\) | 8.83307e7 | 0.0268196 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.91341e9 | 1.47209 | ||||||||
\(527\) | 4.38264e8 | 0.130436 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.38695e8 | −0.187585 | ||||||||
\(530\) | −1.37450e9 | −0.401033 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.30137e7 | −0.0123856 | ||||||||
\(533\) | 1.01331e10 | 2.89866 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.86706e9 | 2.22113 | ||||||||
\(536\) | 4.30096e9 | 1.20639 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 4.04049e9 | 1.11866 | ||||||||
\(539\) | −3.86953e9 | −1.06438 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.13831e9 | −0.580603 | −0.290302 | − | 0.956935i | \(-0.593756\pi\) | ||||
−0.290302 | + | 0.956935i | \(0.593756\pi\) | |||||||
\(542\) | 1.46630e9 | 0.395571 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.92908e8 | −0.184535 | ||||||||
\(545\) | 1.02455e10 | 2.71110 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.11049e9 | −0.551351 | −0.275676 | − | 0.961251i | \(-0.588902\pi\) | ||||
−0.275676 | + | 0.961251i | \(0.588902\pi\) | |||||||
\(548\) | 1.08467e8 | 0.0281556 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.77387e9 | −1.22349 | ||||||||
\(551\) | −6.52104e9 | −1.66068 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.36113e9 | 0.342264 | ||||||||
\(554\) | 2.57555e9 | 0.643556 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.59126e7 | 0.0187306 | ||||||||
\(557\) | 5.51882e9 | 1.35317 | 0.676586 | − | 0.736364i | \(-0.263459\pi\) | ||||
0.676586 | + | 0.736364i | \(0.263459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.11098e9 | −2.20609 | ||||||||
\(560\) | −1.47102e9 | −0.353966 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.71427e9 | −0.882666 | ||||||||
\(563\) | 3.94126e8 | 0.0930798 | 0.0465399 | − | 0.998916i | \(-0.485181\pi\) | ||||
0.0465399 | + | 0.998916i | \(0.485181\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.00520e9 | 1.16749 | ||||||||
\(566\) | −2.85582e9 | −0.662024 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.62757e9 | 1.51752 | ||||||||
\(569\) | 5.23096e9 | 1.19039 | 0.595194 | − | 0.803582i | \(-0.297075\pi\) | ||||
0.595194 | + | 0.803582i | \(0.297075\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.54290e9 | 0.796401 | 0.398201 | − | 0.917298i | \(-0.369635\pi\) | ||||
0.398201 | + | 0.917298i | \(0.369635\pi\) | |||||||
\(572\) | −4.07931e8 | −0.0911383 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.98397e9 | 0.437867 | ||||||||
\(575\) | −4.35266e9 | −0.954811 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.36264e8 | −0.116215 | −0.0581077 | − | 0.998310i | \(-0.518507\pi\) | ||||
−0.0581077 | + | 0.998310i | \(0.518507\pi\) | |||||||
\(578\) | −1.10633e10 | −2.38307 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.45851e8 | 0.116165 | ||||||||
\(581\) | 4.45728e8 | 0.0942873 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.46985e9 | 0.307208 | ||||||||
\(584\) | −5.15167e9 | −1.07029 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.62090e9 | 0.538034 | ||||||||
\(587\) | 1.65503e9 | 0.337733 | 0.168867 | − | 0.985639i | \(-0.445989\pi\) | ||||
0.168867 | + | 0.985639i | \(0.445989\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.68599e8 | 0.0743278 | ||||||||
\(590\) | −9.55316e8 | −0.191498 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.90541e8 | −0.0575548 | ||||||||
\(593\) | 8.05027e9 | 1.58533 | 0.792664 | − | 0.609659i | \(-0.208693\pi\) | ||||
0.792664 | + | 0.609659i | \(0.208693\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.16421e9 | −0.615823 | ||||||||
\(596\) | −994042. | −0.000192328 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.71541e9 | −1.47538 | ||||||||
\(599\) | 2.91923e7 | 0.00554976 | 0.00277488 | − | 0.999996i | \(-0.499117\pi\) | ||||
0.00277488 | + | 0.999996i | \(0.499117\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.20322e9 | −0.977713 | −0.488856 | − | 0.872364i | \(-0.662586\pi\) | ||||
−0.488856 | + | 0.872364i | \(0.662586\pi\) | |||||||
\(602\) | −1.78384e9 | −0.333249 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.95818e8 | 0.0915574 | ||||||||
\(605\) | 2.10776e9 | 0.386970 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.88385e9 | 1.43080 | 0.715398 | − | 0.698717i | \(-0.246245\pi\) | ||||
0.715398 | + | 0.698717i | \(0.246245\pi\) | |||||||
\(608\) | −5.82766e8 | −0.105155 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.37379e9 | −1.13696 | ||||||||
\(611\) | −6.88195e8 | −0.122058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.27886e9 | −0.574926 | −0.287463 | − | 0.957792i | \(-0.592812\pi\) | ||||
−0.287463 | + | 0.957792i | \(0.592812\pi\) | |||||||
\(614\) | −6.42100e9 | −1.11947 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.49704e9 | 0.258049 | ||||||||
\(617\) | −1.20684e9 | −0.206848 | −0.103424 | − | 0.994637i | \(-0.532980\pi\) | ||||
−0.103424 | + | 0.994637i | \(0.532980\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.26264e9 | −0.722372 | −0.361186 | − | 0.932494i | \(-0.617628\pi\) | ||||
−0.361186 | + | 0.932494i | \(0.617628\pi\) | |||||||
\(620\) | −3.08540e7 | −0.00519925 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.01130e10 | 1.68505 | ||||||||
\(623\) | −3.06784e8 | −0.0508306 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.71996e9 | −0.937158 | ||||||||
\(626\) | −3.80057e9 | −0.619211 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.45210e7 | −0.00717310 | ||||||||
\(629\) | −6.24962e8 | −0.100133 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.40983e9 | −0.540294 | −0.270147 | − | 0.962819i | \(-0.587072\pi\) | ||||
−0.270147 | + | 0.962819i | \(0.587072\pi\) | |||||||
\(632\) | 8.98098e9 | 1.41519 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.25096e10 | 1.94954 | ||||||||
\(635\) | −6.95733e9 | −1.07829 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.84077e9 | 1.50849 | ||||||||
\(638\) | −1.21084e10 | −1.84593 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.01751e10 | −1.53430 | ||||||||
\(641\) | 7.05809e9 | 1.05848 | 0.529242 | − | 0.848471i | \(-0.322476\pi\) | ||||
0.529242 | + | 0.848471i | \(0.322476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.53642e9 | 1.41464 | 0.707322 | − | 0.706892i | \(-0.249903\pi\) | ||||
0.707322 | + | 0.706892i | \(0.249903\pi\) | |||||||
\(644\) | −7.28220e7 | −0.0107439 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.33069e10 | −1.94206 | ||||||||
\(647\) | −1.17077e10 | −1.69945 | −0.849723 | − | 0.527230i | \(-0.823231\pi\) | ||||
−0.849723 | + | 0.527230i | \(0.823231\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.02158e9 | 0.146696 | ||||||||
\(650\) | 1.21406e10 | 1.73398 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.23066e8 | −0.0173889 | ||||||||
\(653\) | 1.32050e9 | 0.185584 | 0.0927921 | − | 0.995686i | \(-0.470421\pi\) | ||||
0.0927921 | + | 0.995686i | \(0.470421\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.46499e9 | 0.759879 | ||||||||
\(656\) | 1.37553e10 | 1.90242 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.34742e8 | −0.0184379 | ||||||||
\(659\) | 2.98482e9 | 0.406275 | 0.203137 | − | 0.979150i | \(-0.434886\pi\) | ||||
0.203137 | + | 0.979150i | \(0.434886\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.22973e10 | −1.65617 | −0.828087 | − | 0.560600i | \(-0.810571\pi\) | ||||
−0.828087 | + | 0.560600i | \(0.810571\pi\) | |||||||
\(662\) | −2.22464e9 | −0.298027 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.94100e9 | 0.389858 | ||||||||
\(665\) | −2.66124e9 | −0.350920 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.10401e10 | −1.44056 | ||||||||
\(668\) | 1.10460e8 | 0.0143380 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.41966e10 | −1.82358 | ||||||||
\(671\) | 6.81592e9 | 0.870955 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.89633e9 | −0.998557 | −0.499278 | − | 0.866442i | \(-0.666401\pi\) | ||||
−0.499278 | + | 0.866442i | \(0.666401\pi\) | |||||||
\(674\) | −5.48584e9 | −0.690134 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.30625e8 | 0.0785159 | ||||||||
\(677\) | 1.34037e9 | 0.166021 | 0.0830106 | − | 0.996549i | \(-0.473546\pi\) | ||||
0.0830106 | + | 0.996549i | \(0.473546\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.37262e9 | −0.168270 | ||||||||
\(680\) | −2.08780e10 | −2.54629 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.84425e8 | 0.0826191 | ||||||||
\(683\) | 6.85009e9 | 0.822667 | 0.411333 | − | 0.911485i | \(-0.365063\pi\) | ||||
0.411333 | + | 0.911485i | \(0.365063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.71080e9 | 0.797732 | ||||||||
\(686\) | 3.96643e9 | 0.469100 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.23678e10 | −1.44788 | ||||||||
\(689\) | −3.73803e9 | −0.435387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.48604e10 | 1.71340 | 0.856698 | − | 0.515818i | \(-0.172512\pi\) | ||||
0.856698 | + | 0.515818i | \(0.172512\pi\) | |||||||
\(692\) | 5.23599e7 | 0.00600658 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.77662e9 | −0.315325 | ||||||||
\(695\) | 4.69668e9 | 0.530694 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.95880e10 | 3.30980 | ||||||||
\(698\) | −2.96055e9 | −0.329518 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.14589e8 | 0.0126270 | ||||||||
\(701\) | 1.54673e10 | 1.69590 | 0.847952 | − | 0.530073i | \(-0.177836\pi\) | ||||
0.847952 | + | 0.530073i | \(0.177836\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.25620e8 | −0.0570596 | ||||||||
\(704\) | 9.85102e9 | 1.06409 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.06319e10 | 1.13709 | ||||||||
\(707\) | −2.27934e8 | −0.0242572 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.09686e9 | 0.220957 | 0.110478 | − | 0.993879i | \(-0.464762\pi\) | ||||
0.110478 | + | 0.993879i | \(0.464762\pi\) | |||||||
\(710\) | −2.18764e10 | −2.29388 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.02422e9 | −0.210173 | ||||||||
\(713\) | 6.24037e8 | 0.0644759 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.52385e10 | −2.58222 | ||||||||
\(716\) | −3.24119e8 | −0.0329996 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.23065e9 | −0.124079 | ||||||||
\(719\) | 1.96050e10 | 1.96705 | 0.983527 | − | 0.180761i | \(-0.0578561\pi\) | ||||
0.983527 | + | 0.180761i | \(0.0578561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.09431e9 | −0.208097 | ||||||||
\(722\) | −8.25721e8 | −0.0816494 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.58622e8 | 0.0449128 | ||||||||
\(725\) | 1.73722e10 | 1.69306 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.11617e10 | −1.07735 | −0.538677 | − | 0.842513i | \(-0.681075\pi\) | ||||
−0.538677 | + | 0.842513i | \(0.681075\pi\) | |||||||
\(728\) | −3.80720e9 | −0.365717 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.70047e10 | 1.61785 | ||||||||
\(731\) | −2.66035e10 | −2.51899 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.37783e10 | 1.29221 | 0.646103 | − | 0.763250i | \(-0.276397\pi\) | ||||
0.646103 | + | 0.763250i | \(0.276397\pi\) | |||||||
\(734\) | −1.31437e10 | −1.22683 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.86621e8 | −0.0912175 | ||||||||
\(737\) | 1.51814e10 | 1.39694 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.03220e9 | 0.276377 | 0.138189 | − | 0.990406i | \(-0.455872\pi\) | ||||
0.138189 | + | 0.990406i | \(0.455872\pi\) | |||||||
\(740\) | 4.39976e7 | 0.00399133 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.31870e8 | −0.0657689 | ||||||||
\(743\) | 1.93427e9 | 0.173004 | 0.0865020 | − | 0.996252i | \(-0.472431\pi\) | ||||
0.0865020 | + | 0.996252i | \(0.472431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.15009e7 | −0.00544923 | ||||||||
\(746\) | −4.04318e9 | −0.356563 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.19113e9 | −0.104065 | ||||||||
\(749\) | 4.18891e9 | 0.364263 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.54431e9 | 0.477647 | 0.238824 | − | 0.971063i | \(-0.423238\pi\) | ||||
0.238824 | + | 0.971063i | \(0.423238\pi\) | |||||||
\(752\) | −9.34197e8 | −0.0801081 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.07935e10 | 2.61613 | ||||||||
\(755\) | 3.06761e10 | 2.59409 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.76557e10 | 1.47927 | 0.739637 | − | 0.673006i | \(-0.234997\pi\) | ||||
0.739637 | + | 0.673006i | \(0.234997\pi\) | |||||||
\(758\) | 2.29332e9 | 0.191259 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.75593e10 | −1.45098 | ||||||||
\(761\) | −2.32983e9 | −0.191636 | −0.0958180 | − | 0.995399i | \(-0.530547\pi\) | ||||
−0.0958180 | + | 0.995399i | \(0.530547\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.45534e9 | 0.444617 | ||||||||
\(764\) | 9.09095e8 | 0.0737535 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.85918e10 | −1.49458 | ||||||||
\(767\) | −2.59803e9 | −0.207903 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.88822e9 | 0.704811 | 0.352405 | − | 0.935847i | \(-0.385364\pi\) | ||||
0.352405 | + | 0.935847i | \(0.385364\pi\) | |||||||
\(770\) | −4.94146e9 | −0.390066 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3.77138e8 | −0.0295012 | ||||||||
\(773\) | 1.51855e9 | 0.118250 | 0.0591251 | − | 0.998251i | \(-0.481169\pi\) | ||||
0.0591251 | + | 0.998251i | \(0.481169\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.81957e8 | −0.0757769 | ||||||||
\(776\) | −9.05679e9 | −0.695758 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.98038e9 | −0.683701 | ||||||||
\(779\) | 2.48848e10 | 1.88605 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.33939e10 | 1.75721 | ||||||||
\(782\) | −2.25285e10 | −1.68464 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.33585e10 | 0.990034 | ||||||||
\(785\) | −2.75450e9 | −0.203235 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.14294e9 | 0.376097 | 0.188048 | − | 0.982160i | \(-0.439784\pi\) | ||||
0.188048 | + | 0.982160i | \(0.439784\pi\) | |||||||
\(788\) | −3.92984e8 | −0.0286110 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.96445e10 | −2.13919 | ||||||||
\(791\) | 2.66508e9 | 0.191466 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.73339e10 | −1.23435 | ||||||||
\(794\) | 1.44879e10 | 1.02715 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.51925e6 | 0.000106766 0 | ||||||||
\(797\) | −2.31164e10 | −1.61739 | −0.808697 | − | 0.588225i | \(-0.799827\pi\) | ||||
−0.808697 | + | 0.588225i | \(0.799827\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.00948e9 | −0.139371 | ||||||||
\(800\) | 1.55250e9 | 0.107206 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.43580e10 | −1.66737 | ||||||||
\(803\) | −1.81843e10 | −1.23934 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.50547e9 | −0.304407 | ||||||||
\(806\) | −1.74059e9 | −0.117091 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.50395e9 | −0.100298 | ||||||||
\(809\) | −2.29952e10 | −1.52692 | −0.763462 | − | 0.645853i | \(-0.776502\pi\) | ||||
−0.763462 | + | 0.645853i | \(0.776502\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.76002e9 | −0.181694 | −0.0908468 | − | 0.995865i | \(-0.528957\pi\) | ||||
−0.0908468 | + | 0.995865i | \(0.528957\pi\) | |||||||
\(812\) | 2.90645e8 | 0.0190510 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.75985e8 | −0.0634246 | ||||||||
\(815\) | −7.61407e9 | −0.492680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.23747e10 | −1.43542 | ||||||||
\(818\) | −2.43153e10 | −1.55326 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.08301e9 | −0.131930 | ||||||||
\(821\) | −5.67826e9 | −0.358108 | −0.179054 | − | 0.983839i | \(-0.557304\pi\) | ||||
−0.179054 | + | 0.983839i | \(0.557304\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.56662e7 | −0.00160495 | −0.000802475 | − | 1.00000i | \(-0.500255\pi\) | ||||
−0.000802475 | 1.00000i | \(0.500255\pi\) | ||||||||
\(824\) | −1.38186e10 | −0.860437 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.08670e8 | −0.0314055 | ||||||||
\(827\) | 2.08817e10 | 1.28380 | 0.641899 | − | 0.766789i | \(-0.278147\pi\) | ||||
0.641899 | + | 0.766789i | \(0.278147\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.54198e10 | −1.54964 | −0.774821 | − | 0.632180i | \(-0.782160\pi\) | ||||
−0.774821 | + | 0.632180i | \(0.782160\pi\) | |||||||
\(830\) | −9.70767e9 | −0.589307 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.50525e10 | −1.50807 | ||||||||
\(833\) | 2.87344e10 | 1.72244 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.83412e9 | 0.406237 | ||||||||
\(836\) | −1.00179e9 | −0.0593003 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.74999e9 | −0.513634 | ||||||||
\(839\) | 3.56300e9 | 0.208281 | 0.104140 | − | 0.994563i | \(-0.466791\pi\) | ||||
0.104140 | + | 0.994563i | \(0.466791\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.68130e10 | 1.55439 | ||||||||
\(842\) | 2.12325e9 | 0.122577 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.32592e9 | −0.0759132 | ||||||||
\(845\) | 3.90165e10 | 2.22459 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.12230e9 | 0.0634627 | ||||||||
\(848\) | −5.07423e9 | −0.285749 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.54498e10 | 1.97992 | ||||||||
\(851\) | −8.89873e8 | −0.0494965 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.29229e10 | 1.26458 | 0.632291 | − | 0.774731i | \(-0.282115\pi\) | ||||
0.632291 | + | 0.774731i | \(0.282115\pi\) | |||||||
\(854\) | −3.39380e9 | −0.186459 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.76392e10 | 1.50615 | ||||||||
\(857\) | 1.48684e10 | 0.806924 | 0.403462 | − | 0.914996i | \(-0.367807\pi\) | ||||
0.403462 | + | 0.914996i | \(0.367807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.17432e10 | −1.17043 | −0.585217 | − | 0.810877i | \(-0.698991\pi\) | ||||
−0.585217 | + | 0.810877i | \(0.698991\pi\) | |||||||
\(860\) | 1.87290e9 | 0.100408 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.16004e9 | 0.168042 | ||||||||
\(863\) | 1.50753e10 | 0.798414 | 0.399207 | − | 0.916861i | \(-0.369285\pi\) | ||||
0.399207 | + | 0.916861i | \(0.369285\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.23948e9 | 0.170184 | ||||||||
\(866\) | 1.05169e10 | 0.550269 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.64286e7 | −0.000852671 0 | ||||||||
\(869\) | 3.17009e10 | 1.63871 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.86085e10 | −1.97979 | ||||||||
\(872\) | 3.59953e10 | 1.83839 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.89474e10 | −0.959977 | ||||||||
\(875\) | 3.97024e8 | 0.0200350 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.29162e10 | −0.646598 | −0.323299 | − | 0.946297i | \(-0.604792\pi\) | ||||
−0.323299 | + | 0.946297i | \(0.604792\pi\) | |||||||
\(878\) | 7.58858e8 | 0.0378381 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −3.42603e10 | −1.69473 | ||||||||
\(881\) | 2.47400e10 | 1.21895 | 0.609473 | − | 0.792807i | \(-0.291381\pi\) | ||||
0.609473 | + | 0.792807i | \(0.291381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.21032e10 | 1.08042 | 0.540211 | − | 0.841530i | \(-0.318345\pi\) | ||||
0.540211 | + | 0.841530i | \(0.318345\pi\) | |||||||
\(884\) | 3.02922e9 | 0.147485 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.01569e10 | 1.45670 | ||||||||
\(887\) | 8.79294e9 | 0.423060 | 0.211530 | − | 0.977372i | \(-0.432155\pi\) | ||||
0.211530 | + | 0.977372i | \(0.432155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.70452e9 | −0.176838 | ||||||||
\(890\) | 6.68156e9 | 0.317697 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.58227e9 | 0.0746455 | ||||||||
\(893\) | −1.69006e9 | −0.0794188 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.00531e10 | −0.934976 | ||||||||
\(896\) | −5.41787e9 | −0.251623 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.93239e10 | 1.35131 | ||||||||
\(899\) | −2.49064e9 | −0.114328 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09148e10 | −0.497141 | ||||||||
\(902\) | 4.62068e10 | 2.09644 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.75847e10 | 0.791671 | ||||||||
\(905\) | 2.83747e10 | 1.27251 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.78075e8 | −0.0301753 | −0.0150877 | − | 0.999886i | \(-0.504803\pi\) | ||||
−0.0150877 | + | 0.999886i | \(0.504803\pi\) | |||||||
\(908\) | 1.15019e9 | 0.0509882 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.25668e10 | 0.552817 | ||||||||
\(911\) | −1.87905e10 | −0.823424 | −0.411712 | − | 0.911314i | \(-0.635069\pi\) | ||||
−0.411712 | + | 0.911314i | \(0.635069\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.03811e10 | 0.451434 | ||||||||
\(914\) | 1.47148e10 | 0.637443 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.41058e9 | 0.0606407 | ||||||||
\(917\) | 2.90990e9 | 0.124619 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.67497e10 | 1.56189 | 0.780943 | − | 0.624603i | \(-0.214739\pi\) | ||||
0.780943 | + | 0.624603i | \(0.214739\pi\) | |||||||
\(920\) | −2.97279e10 | −1.25866 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.16352e9 | 0.301001 | ||||||||
\(923\) | −5.94939e10 | −2.49039 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.40026e9 | 0.0581720 | ||||||||
\(926\) | −2.05128e10 | −0.848957 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.93777e9 | 0.161746 | ||||||||
\(929\) | −5.36643e9 | −0.219599 | −0.109800 | − | 0.993954i | \(-0.535021\pi\) | ||||
−0.109800 | + | 0.993954i | \(0.535021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.41669e10 | 0.981515 | ||||||||
\(932\) | 2.12524e9 | 0.0859907 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.42599e10 | 0.974262 | ||||||||
\(935\) | −7.36948e10 | −2.94847 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.19515e10 | −0.871717 | −0.435859 | − | 0.900015i | \(-0.643555\pi\) | ||||
−0.435859 | + | 0.900015i | \(0.643555\pi\) | |||||||
\(938\) | −7.55918e9 | −0.299064 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.41469e8 | 0.00555537 | ||||||||
\(941\) | −2.82488e10 | −1.10519 | −0.552595 | − | 0.833450i | \(-0.686362\pi\) | ||||
−0.552595 | + | 0.833450i | \(0.686362\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.21299e10 | 1.63606 | ||||||||
\(944\) | −3.52673e9 | −0.136449 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.15459e10 | −1.59554 | ||||||||
\(947\) | −2.51489e10 | −0.962264 | −0.481132 | − | 0.876648i | \(-0.659774\pi\) | ||||
−0.481132 | + | 0.876648i | \(0.659774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.62452e10 | 1.75645 | ||||||||
\(950\) | 2.98149e10 | 1.12824 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.11168e10 | −0.417589 | ||||||||
\(953\) | 4.09484e10 | 1.53254 | 0.766269 | − | 0.642519i | \(-0.222111\pi\) | ||||
0.766269 | + | 0.642519i | \(0.222111\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.62453e10 | 2.08966 | ||||||||
\(956\) | −1.81177e9 | −0.0670656 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.37249e9 | −0.307663 | ||||||||
\(959\) | 3.57325e9 | 0.130827 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.73718e10 | −0.994883 | ||||||||
\(962\) | 2.48207e9 | 0.0898879 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.48483e9 | 0.0893360 | ||||||||
\(965\) | −2.33334e10 | −0.835858 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.25463e10 | −1.86874 | −0.934372 | − | 0.356299i | \(-0.884038\pi\) | ||||
−0.934372 | + | 0.356299i | \(0.884038\pi\) | |||||||
\(968\) | 7.40517e9 | 0.262404 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.98947e10 | 1.05170 | ||||||||
\(971\) | 2.49973e9 | 0.0876246 | 0.0438123 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438123 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.50081e9 | 0.0870332 | ||||||||
\(974\) | −2.93482e10 | −1.01771 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.35300e10 | −0.810118 | ||||||||
\(977\) | 2.71796e10 | 0.932420 | 0.466210 | − | 0.884674i | \(-0.345619\pi\) | ||||
0.466210 | + | 0.884674i | \(0.345619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.14505e9 | −0.243369 | ||||||||
\(980\) | −2.02292e9 | −0.0686573 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.66316e10 | 1.57141 | ||||||||
\(983\) | −3.97905e9 | −0.133611 | −0.0668055 | − | 0.997766i | \(-0.521281\pi\) | ||||
−0.0668055 | + | 0.997766i | \(0.521281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.43138e10 | −0.810635 | ||||||||
\(986\) | 8.99150e10 | 2.98719 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.54771e9 | 0.0840427 | ||||||||
\(989\) | −3.78802e10 | −1.24516 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.12813e9 | −0.0694610 | −0.0347305 | − | 0.999397i | \(-0.511057\pi\) | ||||
−0.0347305 | + | 0.999397i | \(0.511057\pi\) | |||||||
\(992\) | −2.22581e8 | −0.00723931 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.16483e10 | −0.376194 | ||||||||
\(995\) | 9.39956e7 | 0.00302501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.59834e8 | −0.00510784 | −0.00255392 | − | 0.999997i | \(-0.500813\pi\) | ||||
−0.00255392 | + | 0.999997i | \(0.500813\pi\) | |||||||
\(998\) | 1.40932e10 | 0.448800 | ||||||||
\(999\) | 0 | 0 |
(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 | 531.8.a.c.1.5 | 17 | ||
3.2 | odd | 2 | 177.8.a.c.1.13 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.13 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.c.1.5 | 17 | 1.1 | even | 1 | trivial |