Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,10,Mod(1,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.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: | \(8.75560921479\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-34.1532\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 34.1532 | 1.50937 | 0.754685 | − | 0.656087i | \(-0.227790\pi\) | ||||
0.754685 | + | 0.656087i | \(0.227790\pi\) | |||||||
\(3\) | 169.801 | 1.21031 | 0.605154 | − | 0.796109i | \(-0.293112\pi\) | ||||
0.605154 | + | 0.796109i | \(0.293112\pi\) | |||||||
\(4\) | 654.438 | 1.27820 | ||||||||
\(5\) | 195.287 | 0.139736 | 0.0698679 | − | 0.997556i | \(-0.477742\pi\) | ||||
0.0698679 | + | 0.997556i | \(0.477742\pi\) | |||||||
\(6\) | 5799.26 | 1.82680 | ||||||||
\(7\) | −356.628 | −0.0561402 | −0.0280701 | − | 0.999606i | \(-0.508936\pi\) | ||||
−0.0280701 | + | 0.999606i | \(0.508936\pi\) | |||||||
\(8\) | 4864.71 | 0.419906 | ||||||||
\(9\) | 9149.54 | 0.464845 | ||||||||
\(10\) | 6669.66 | 0.210913 | ||||||||
\(11\) | −21467.8 | −0.442101 | −0.221050 | − | 0.975262i | \(-0.570949\pi\) | ||||
−0.221050 | + | 0.975262i | \(0.570949\pi\) | |||||||
\(12\) | 111125. | 1.54701 | ||||||||
\(13\) | −6206.76 | −0.0602726 | −0.0301363 | − | 0.999546i | \(-0.509594\pi\) | ||||
−0.0301363 | + | 0.999546i | \(0.509594\pi\) | |||||||
\(14\) | −12180.0 | −0.0847364 | ||||||||
\(15\) | 33160.0 | 0.169123 | ||||||||
\(16\) | −168927. | −0.644406 | ||||||||
\(17\) | 83521.0 | 0.242536 | ||||||||
\(18\) | 312486. | 0.701623 | ||||||||
\(19\) | 907187. | 1.59700 | 0.798501 | − | 0.601993i | \(-0.205627\pi\) | ||||
0.798501 | + | 0.601993i | \(0.205627\pi\) | |||||||
\(20\) | 127803. | 0.178610 | ||||||||
\(21\) | −60556.0 | −0.0679470 | ||||||||
\(22\) | −733194. | −0.667294 | ||||||||
\(23\) | −1.23486e6 | −0.920115 | −0.460058 | − | 0.887889i | \(-0.652171\pi\) | ||||
−0.460058 | + | 0.887889i | \(0.652171\pi\) | |||||||
\(24\) | 826035. | 0.508216 | ||||||||
\(25\) | −1.91499e6 | −0.980474 | ||||||||
\(26\) | −211980. | −0.0909737 | ||||||||
\(27\) | −1.78860e6 | −0.647702 | ||||||||
\(28\) | −233391. | −0.0717584 | ||||||||
\(29\) | −3.01596e6 | −0.791835 | −0.395917 | − | 0.918286i | \(-0.629573\pi\) | ||||
−0.395917 | + | 0.918286i | \(0.629573\pi\) | |||||||
\(30\) | 1.13252e6 | 0.255270 | ||||||||
\(31\) | −334277. | −0.0650099 | −0.0325049 | − | 0.999472i | \(-0.510348\pi\) | ||||
−0.0325049 | + | 0.999472i | \(0.510348\pi\) | |||||||
\(32\) | −8.26012e6 | −1.39255 | ||||||||
\(33\) | −3.64527e6 | −0.535078 | ||||||||
\(34\) | 2.85251e6 | 0.366076 | ||||||||
\(35\) | −69644.7 | −0.00784481 | ||||||||
\(36\) | 5.98781e6 | 0.594165 | ||||||||
\(37\) | 2.06102e7 | 1.80790 | 0.903949 | − | 0.427640i | \(-0.140655\pi\) | ||||
0.903949 | + | 0.427640i | \(0.140655\pi\) | |||||||
\(38\) | 3.09833e7 | 2.41047 | ||||||||
\(39\) | −1.05392e6 | −0.0729484 | ||||||||
\(40\) | 950014. | 0.0586759 | ||||||||
\(41\) | 1.47571e7 | 0.815593 | 0.407796 | − | 0.913073i | \(-0.366297\pi\) | ||||
0.407796 | + | 0.913073i | \(0.366297\pi\) | |||||||
\(42\) | −2.06818e6 | −0.102557 | ||||||||
\(43\) | −7.75953e6 | −0.346120 | −0.173060 | − | 0.984911i | \(-0.555366\pi\) | ||||
−0.173060 | + | 0.984911i | \(0.555366\pi\) | |||||||
\(44\) | −1.40494e7 | −0.565093 | ||||||||
\(45\) | 1.78679e6 | 0.0649555 | ||||||||
\(46\) | −4.21744e7 | −1.38880 | ||||||||
\(47\) | 3.19993e7 | 0.956534 | 0.478267 | − | 0.878214i | \(-0.341265\pi\) | ||||
0.478267 | + | 0.878214i | \(0.341265\pi\) | |||||||
\(48\) | −2.86841e7 | −0.779929 | ||||||||
\(49\) | −4.02264e7 | −0.996848 | ||||||||
\(50\) | −6.54029e7 | −1.47990 | ||||||||
\(51\) | 1.41820e7 | 0.293543 | ||||||||
\(52\) | −4.06194e6 | −0.0770404 | ||||||||
\(53\) | 9.46750e7 | 1.64814 | 0.824070 | − | 0.566488i | \(-0.191698\pi\) | ||||
0.824070 | + | 0.566488i | \(0.191698\pi\) | |||||||
\(54\) | −6.10862e7 | −0.977623 | ||||||||
\(55\) | −4.19238e6 | −0.0617773 | ||||||||
\(56\) | −1.73489e6 | −0.0235736 | ||||||||
\(57\) | 1.54042e8 | 1.93286 | ||||||||
\(58\) | −1.03005e8 | −1.19517 | ||||||||
\(59\) | 6.01771e7 | 0.646542 | 0.323271 | − | 0.946306i | \(-0.395217\pi\) | ||||
0.323271 | + | 0.946306i | \(0.395217\pi\) | |||||||
\(60\) | 2.17012e7 | 0.216173 | ||||||||
\(61\) | 6.05254e7 | 0.559698 | 0.279849 | − | 0.960044i | \(-0.409716\pi\) | ||||
0.279849 | + | 0.960044i | \(0.409716\pi\) | |||||||
\(62\) | −1.14166e7 | −0.0981240 | ||||||||
\(63\) | −3.26298e6 | −0.0260965 | ||||||||
\(64\) | −1.95619e8 | −1.45747 | ||||||||
\(65\) | −1.21210e6 | −0.00842224 | ||||||||
\(66\) | −1.24497e8 | −0.807631 | ||||||||
\(67\) | −1.26316e8 | −0.765813 | −0.382907 | − | 0.923787i | \(-0.625077\pi\) | ||||
−0.382907 | + | 0.923787i | \(0.625077\pi\) | |||||||
\(68\) | 5.46593e7 | 0.310009 | ||||||||
\(69\) | −2.09681e8 | −1.11362 | ||||||||
\(70\) | −2.37859e6 | −0.0118407 | ||||||||
\(71\) | 3.33917e7 | 0.155947 | 0.0779734 | − | 0.996955i | \(-0.475155\pi\) | ||||
0.0779734 | + | 0.996955i | \(0.475155\pi\) | |||||||
\(72\) | 4.45099e7 | 0.195191 | ||||||||
\(73\) | 2.85706e8 | 1.17752 | 0.588758 | − | 0.808309i | \(-0.299617\pi\) | ||||
0.588758 | + | 0.808309i | \(0.299617\pi\) | |||||||
\(74\) | 7.03903e8 | 2.72879 | ||||||||
\(75\) | −3.25168e8 | −1.18668 | ||||||||
\(76\) | 5.93698e8 | 2.04129 | ||||||||
\(77\) | 7.65603e6 | 0.0248196 | ||||||||
\(78\) | −3.59946e7 | −0.110106 | ||||||||
\(79\) | −7.60575e7 | −0.219695 | −0.109848 | − | 0.993948i | \(-0.535036\pi\) | ||||
−0.109848 | + | 0.993948i | \(0.535036\pi\) | |||||||
\(80\) | −3.29892e7 | −0.0900466 | ||||||||
\(81\) | −4.83797e8 | −1.24876 | ||||||||
\(82\) | 5.04001e8 | 1.23103 | ||||||||
\(83\) | −1.73620e7 | −0.0401558 | −0.0200779 | − | 0.999798i | \(-0.506391\pi\) | ||||
−0.0200779 | + | 0.999798i | \(0.506391\pi\) | |||||||
\(84\) | −3.96301e7 | −0.0868498 | ||||||||
\(85\) | 1.63105e7 | 0.0338909 | ||||||||
\(86\) | −2.65012e8 | −0.522424 | ||||||||
\(87\) | −5.12115e8 | −0.958364 | ||||||||
\(88\) | −1.04435e8 | −0.185641 | ||||||||
\(89\) | 3.96876e8 | 0.670501 | 0.335251 | − | 0.942129i | \(-0.391179\pi\) | ||||
0.335251 | + | 0.942129i | \(0.391179\pi\) | |||||||
\(90\) | 6.10244e7 | 0.0980419 | ||||||||
\(91\) | 2.21350e6 | 0.00338372 | ||||||||
\(92\) | −8.08139e8 | −1.17609 | ||||||||
\(93\) | −5.67608e7 | −0.0786819 | ||||||||
\(94\) | 1.09288e9 | 1.44376 | ||||||||
\(95\) | 1.77162e8 | 0.223159 | ||||||||
\(96\) | −1.40258e9 | −1.68542 | ||||||||
\(97\) | 1.13120e9 | 1.29737 | 0.648687 | − | 0.761055i | \(-0.275318\pi\) | ||||
0.648687 | + | 0.761055i | \(0.275318\pi\) | |||||||
\(98\) | −1.37386e9 | −1.50461 | ||||||||
\(99\) | −1.96421e8 | −0.205508 | ||||||||
\(100\) | −1.25324e9 | −1.25324 | ||||||||
\(101\) | −1.58638e9 | −1.51692 | −0.758458 | − | 0.651722i | \(-0.774047\pi\) | ||||
−0.758458 | + | 0.651722i | \(0.774047\pi\) | |||||||
\(102\) | 4.84360e8 | 0.443065 | ||||||||
\(103\) | −9.77937e8 | −0.856137 | −0.428068 | − | 0.903746i | \(-0.640806\pi\) | ||||
−0.428068 | + | 0.903746i | \(0.640806\pi\) | |||||||
\(104\) | −3.01941e7 | −0.0253088 | ||||||||
\(105\) | −1.18258e7 | −0.00949463 | ||||||||
\(106\) | 3.23345e9 | 2.48765 | ||||||||
\(107\) | −1.71253e8 | −0.126302 | −0.0631511 | − | 0.998004i | \(-0.520115\pi\) | ||||
−0.0631511 | + | 0.998004i | \(0.520115\pi\) | |||||||
\(108\) | −1.17053e9 | −0.827893 | ||||||||
\(109\) | 1.66962e9 | 1.13292 | 0.566461 | − | 0.824089i | \(-0.308312\pi\) | ||||
0.566461 | + | 0.824089i | \(0.308312\pi\) | |||||||
\(110\) | −1.43183e8 | −0.0932449 | ||||||||
\(111\) | 3.49964e9 | 2.18811 | ||||||||
\(112\) | 6.02441e7 | 0.0361771 | ||||||||
\(113\) | −2.55660e9 | −1.47506 | −0.737531 | − | 0.675313i | \(-0.764008\pi\) | ||||
−0.737531 | + | 0.675313i | \(0.764008\pi\) | |||||||
\(114\) | 5.26101e9 | 2.91741 | ||||||||
\(115\) | −2.41152e8 | −0.128573 | ||||||||
\(116\) | −1.97376e9 | −1.01212 | ||||||||
\(117\) | −5.67890e7 | −0.0280174 | ||||||||
\(118\) | 2.05524e9 | 0.975872 | ||||||||
\(119\) | −2.97859e7 | −0.0136160 | ||||||||
\(120\) | 1.61314e8 | 0.0710159 | ||||||||
\(121\) | −1.89708e9 | −0.804547 | ||||||||
\(122\) | 2.06713e9 | 0.844792 | ||||||||
\(123\) | 2.50578e9 | 0.987118 | ||||||||
\(124\) | −2.18764e8 | −0.0830956 | ||||||||
\(125\) | −7.55391e8 | −0.276743 | ||||||||
\(126\) | −1.11441e8 | −0.0393893 | ||||||||
\(127\) | −1.57297e9 | −0.536542 | −0.268271 | − | 0.963344i | \(-0.586452\pi\) | ||||
−0.268271 | + | 0.963344i | \(0.586452\pi\) | |||||||
\(128\) | −2.45181e9 | −0.807313 | ||||||||
\(129\) | −1.31758e9 | −0.418912 | ||||||||
\(130\) | −4.13970e7 | −0.0127123 | ||||||||
\(131\) | 1.54185e9 | 0.457426 | 0.228713 | − | 0.973494i | \(-0.426548\pi\) | ||||
0.228713 | + | 0.973494i | \(0.426548\pi\) | |||||||
\(132\) | −2.38560e9 | −0.683936 | ||||||||
\(133\) | −3.23528e8 | −0.0896561 | ||||||||
\(134\) | −4.31410e9 | −1.15590 | ||||||||
\(135\) | −3.49289e8 | −0.0905072 | ||||||||
\(136\) | 4.06306e8 | 0.101842 | ||||||||
\(137\) | −7.48495e9 | −1.81529 | −0.907646 | − | 0.419736i | \(-0.862123\pi\) | ||||
−0.907646 | + | 0.419736i | \(0.862123\pi\) | |||||||
\(138\) | −7.16127e9 | −1.68087 | ||||||||
\(139\) | 4.97076e9 | 1.12942 | 0.564711 | − | 0.825289i | \(-0.308988\pi\) | ||||
0.564711 | + | 0.825289i | \(0.308988\pi\) | |||||||
\(140\) | −4.55782e7 | −0.0100272 | ||||||||
\(141\) | 5.43353e9 | 1.15770 | ||||||||
\(142\) | 1.14043e9 | 0.235382 | ||||||||
\(143\) | 1.33246e8 | 0.0266465 | ||||||||
\(144\) | −1.54561e9 | −0.299549 | ||||||||
\(145\) | −5.88977e8 | −0.110648 | ||||||||
\(146\) | 9.75777e9 | 1.77731 | ||||||||
\(147\) | −6.83051e9 | −1.20649 | ||||||||
\(148\) | 1.34881e10 | 2.31085 | ||||||||
\(149\) | −2.17167e9 | −0.360957 | −0.180479 | − | 0.983579i | \(-0.557765\pi\) | ||||
−0.180479 | + | 0.983579i | \(0.557765\pi\) | |||||||
\(150\) | −1.11055e10 | −1.79113 | ||||||||
\(151\) | 5.05353e9 | 0.791040 | 0.395520 | − | 0.918457i | \(-0.370564\pi\) | ||||
0.395520 | + | 0.918457i | \(0.370564\pi\) | |||||||
\(152\) | 4.41320e9 | 0.670591 | ||||||||
\(153\) | 7.64179e8 | 0.112741 | ||||||||
\(154\) | 2.61478e8 | 0.0374620 | ||||||||
\(155\) | −6.52799e7 | −0.00908421 | ||||||||
\(156\) | −6.89723e8 | −0.0932426 | ||||||||
\(157\) | −1.14585e10 | −1.50515 | −0.752577 | − | 0.658504i | \(-0.771190\pi\) | ||||
−0.752577 | + | 0.658504i | \(0.771190\pi\) | |||||||
\(158\) | −2.59760e9 | −0.331601 | ||||||||
\(159\) | 1.60760e10 | 1.99476 | ||||||||
\(160\) | −1.61309e9 | −0.194590 | ||||||||
\(161\) | 4.40386e8 | 0.0516555 | ||||||||
\(162\) | −1.65232e10 | −1.88485 | ||||||||
\(163\) | 1.58612e10 | 1.75992 | 0.879960 | − | 0.475048i | \(-0.157569\pi\) | ||||
0.879960 | + | 0.475048i | \(0.157569\pi\) | |||||||
\(164\) | 9.65760e9 | 1.04249 | ||||||||
\(165\) | −7.11873e8 | −0.0747696 | ||||||||
\(166\) | −5.92966e8 | −0.0606099 | ||||||||
\(167\) | −7.94993e9 | −0.790932 | −0.395466 | − | 0.918481i | \(-0.629417\pi\) | ||||
−0.395466 | + | 0.918481i | \(0.629417\pi\) | |||||||
\(168\) | −2.94587e8 | −0.0285313 | ||||||||
\(169\) | −1.05660e10 | −0.996367 | ||||||||
\(170\) | 5.57057e8 | 0.0511540 | ||||||||
\(171\) | 8.30035e9 | 0.742359 | ||||||||
\(172\) | −5.07813e9 | −0.442411 | ||||||||
\(173\) | 4.82389e9 | 0.409440 | 0.204720 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204720 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(174\) | −1.74903e10 | −1.44653 | ||||||||
\(175\) | 6.82938e8 | 0.0550440 | ||||||||
\(176\) | 3.62650e9 | 0.284892 | ||||||||
\(177\) | 1.02182e10 | 0.782515 | ||||||||
\(178\) | 1.35546e10 | 1.01203 | ||||||||
\(179\) | −6.50866e9 | −0.473863 | −0.236932 | − | 0.971526i | \(-0.576142\pi\) | ||||
−0.236932 | + | 0.971526i | \(0.576142\pi\) | |||||||
\(180\) | 1.16934e9 | 0.0830261 | ||||||||
\(181\) | 9.87513e9 | 0.683895 | 0.341947 | − | 0.939719i | \(-0.388914\pi\) | ||||
0.341947 | + | 0.939719i | \(0.388914\pi\) | |||||||
\(182\) | 7.55982e7 | 0.00510728 | ||||||||
\(183\) | 1.02773e10 | 0.677407 | ||||||||
\(184\) | −6.00724e9 | −0.386362 | ||||||||
\(185\) | 4.02490e9 | 0.252628 | ||||||||
\(186\) | −1.93856e9 | −0.118760 | ||||||||
\(187\) | −1.79301e9 | −0.107225 | ||||||||
\(188\) | 2.09416e10 | 1.22264 | ||||||||
\(189\) | 6.37864e8 | 0.0363622 | ||||||||
\(190\) | 6.05063e9 | 0.336829 | ||||||||
\(191\) | 1.73272e10 | 0.942060 | 0.471030 | − | 0.882117i | \(-0.343882\pi\) | ||||
0.471030 | + | 0.882117i | \(0.343882\pi\) | |||||||
\(192\) | −3.32163e10 | −1.76399 | ||||||||
\(193\) | −5.92773e9 | −0.307525 | −0.153763 | − | 0.988108i | \(-0.549139\pi\) | ||||
−0.153763 | + | 0.988108i | \(0.549139\pi\) | |||||||
\(194\) | 3.86339e10 | 1.95822 | ||||||||
\(195\) | −2.05816e8 | −0.0101935 | ||||||||
\(196\) | −2.63257e10 | −1.27417 | ||||||||
\(197\) | −1.61285e10 | −0.762948 | −0.381474 | − | 0.924380i | \(-0.624583\pi\) | ||||
−0.381474 | + | 0.924380i | \(0.624583\pi\) | |||||||
\(198\) | −6.70839e9 | −0.310188 | ||||||||
\(199\) | −4.38224e10 | −1.98088 | −0.990438 | − | 0.137958i | \(-0.955946\pi\) | ||||
−0.990438 | + | 0.137958i | \(0.955946\pi\) | |||||||
\(200\) | −9.31586e9 | −0.411707 | ||||||||
\(201\) | −2.14487e10 | −0.926870 | ||||||||
\(202\) | −5.41800e10 | −2.28959 | ||||||||
\(203\) | 1.07558e9 | 0.0444538 | ||||||||
\(204\) | 9.28123e9 | 0.375206 | ||||||||
\(205\) | 2.88186e9 | 0.113968 | ||||||||
\(206\) | −3.33996e10 | −1.29223 | ||||||||
\(207\) | −1.12984e10 | −0.427711 | ||||||||
\(208\) | 1.04849e9 | 0.0388400 | ||||||||
\(209\) | −1.94753e10 | −0.706036 | ||||||||
\(210\) | −4.03888e8 | −0.0143309 | ||||||||
\(211\) | 4.85013e10 | 1.68454 | 0.842272 | − | 0.539053i | \(-0.181218\pi\) | ||||
0.842272 | + | 0.539053i | \(0.181218\pi\) | |||||||
\(212\) | 6.19589e10 | 2.10665 | ||||||||
\(213\) | 5.66997e9 | 0.188744 | ||||||||
\(214\) | −5.84883e9 | −0.190637 | ||||||||
\(215\) | −1.51533e9 | −0.0483654 | ||||||||
\(216\) | −8.70100e9 | −0.271974 | ||||||||
\(217\) | 1.19213e8 | 0.00364967 | ||||||||
\(218\) | 5.70230e10 | 1.71000 | ||||||||
\(219\) | 4.85133e10 | 1.42516 | ||||||||
\(220\) | −2.74366e9 | −0.0789637 | ||||||||
\(221\) | −5.18395e8 | −0.0146182 | ||||||||
\(222\) | 1.19524e11 | 3.30267 | ||||||||
\(223\) | −1.32607e9 | −0.0359082 | −0.0179541 | − | 0.999839i | \(-0.505715\pi\) | ||||
−0.0179541 | + | 0.999839i | \(0.505715\pi\) | |||||||
\(224\) | 2.94579e9 | 0.0781783 | ||||||||
\(225\) | −1.75213e10 | −0.455768 | ||||||||
\(226\) | −8.73161e10 | −2.22642 | ||||||||
\(227\) | −6.30032e10 | −1.57487 | −0.787437 | − | 0.616395i | \(-0.788593\pi\) | ||||
−0.787437 | + | 0.616395i | \(0.788593\pi\) | |||||||
\(228\) | 1.00811e11 | 2.47059 | ||||||||
\(229\) | 3.36520e10 | 0.808632 | 0.404316 | − | 0.914619i | \(-0.367510\pi\) | ||||
0.404316 | + | 0.914619i | \(0.367510\pi\) | |||||||
\(230\) | −8.23610e9 | −0.194064 | ||||||||
\(231\) | 1.30001e9 | 0.0300394 | ||||||||
\(232\) | −1.46718e10 | −0.332496 | ||||||||
\(233\) | −3.25593e10 | −0.723724 | −0.361862 | − | 0.932232i | \(-0.617859\pi\) | ||||
−0.361862 | + | 0.932232i | \(0.617859\pi\) | |||||||
\(234\) | −1.93952e9 | −0.0422887 | ||||||||
\(235\) | 6.24905e9 | 0.133662 | ||||||||
\(236\) | 3.93822e10 | 0.826410 | ||||||||
\(237\) | −1.29147e10 | −0.265899 | ||||||||
\(238\) | −1.01728e9 | −0.0205516 | ||||||||
\(239\) | 4.25086e10 | 0.842725 | 0.421363 | − | 0.906892i | \(-0.361552\pi\) | ||||
0.421363 | + | 0.906892i | \(0.361552\pi\) | |||||||
\(240\) | −5.60162e9 | −0.108984 | ||||||||
\(241\) | −6.46314e10 | −1.23415 | −0.617074 | − | 0.786905i | \(-0.711682\pi\) | ||||
−0.617074 | + | 0.786905i | \(0.711682\pi\) | |||||||
\(242\) | −6.47913e10 | −1.21436 | ||||||||
\(243\) | −4.69445e10 | −0.863687 | ||||||||
\(244\) | 3.96102e10 | 0.715406 | ||||||||
\(245\) | −7.85569e9 | −0.139295 | ||||||||
\(246\) | 8.55801e10 | 1.48993 | ||||||||
\(247\) | −5.63069e9 | −0.0962555 | ||||||||
\(248\) | −1.62616e9 | −0.0272980 | ||||||||
\(249\) | −2.94809e9 | −0.0486008 | ||||||||
\(250\) | −2.57990e10 | −0.417708 | ||||||||
\(251\) | −1.00795e11 | −1.60290 | −0.801452 | − | 0.598060i | \(-0.795939\pi\) | ||||
−0.801452 | + | 0.598060i | \(0.795939\pi\) | |||||||
\(252\) | −2.13542e9 | −0.0333565 | ||||||||
\(253\) | 2.65098e10 | 0.406784 | ||||||||
\(254\) | −5.37219e10 | −0.809840 | ||||||||
\(255\) | 2.76956e9 | 0.0410185 | ||||||||
\(256\) | 1.64197e10 | 0.238938 | ||||||||
\(257\) | −7.98430e10 | −1.14166 | −0.570831 | − | 0.821067i | \(-0.693379\pi\) | ||||
−0.570831 | + | 0.821067i | \(0.693379\pi\) | |||||||
\(258\) | −4.49995e10 | −0.632294 | ||||||||
\(259\) | −7.35017e9 | −0.101496 | ||||||||
\(260\) | −7.93243e8 | −0.0107653 | ||||||||
\(261\) | −2.75947e10 | −0.368080 | ||||||||
\(262\) | 5.26590e10 | 0.690425 | ||||||||
\(263\) | 9.26392e10 | 1.19397 | 0.596986 | − | 0.802252i | \(-0.296365\pi\) | ||||
0.596986 | + | 0.802252i | \(0.296365\pi\) | |||||||
\(264\) | −1.77332e10 | −0.224682 | ||||||||
\(265\) | 1.84888e10 | 0.230304 | ||||||||
\(266\) | −1.10495e10 | −0.135324 | ||||||||
\(267\) | 6.73901e10 | 0.811513 | ||||||||
\(268\) | −8.26662e10 | −0.978862 | ||||||||
\(269\) | −6.38400e10 | −0.743375 | −0.371687 | − | 0.928358i | \(-0.621221\pi\) | ||||
−0.371687 | + | 0.928358i | \(0.621221\pi\) | |||||||
\(270\) | −1.19293e10 | −0.136609 | ||||||||
\(271\) | 1.39281e11 | 1.56866 | 0.784331 | − | 0.620343i | \(-0.213007\pi\) | ||||
0.784331 | + | 0.620343i | \(0.213007\pi\) | |||||||
\(272\) | −1.41090e10 | −0.156291 | ||||||||
\(273\) | 3.75856e8 | 0.00409534 | ||||||||
\(274\) | −2.55635e11 | −2.73995 | ||||||||
\(275\) | 4.11106e10 | 0.433468 | ||||||||
\(276\) | −1.37223e11 | −1.42343 | ||||||||
\(277\) | 1.33421e11 | 1.36165 | 0.680826 | − | 0.732445i | \(-0.261621\pi\) | ||||
0.680826 | + | 0.732445i | \(0.261621\pi\) | |||||||
\(278\) | 1.69767e11 | 1.70472 | ||||||||
\(279\) | −3.05848e9 | −0.0302195 | ||||||||
\(280\) | −3.38802e8 | −0.00329408 | ||||||||
\(281\) | −1.22205e11 | −1.16926 | −0.584629 | − | 0.811301i | \(-0.698760\pi\) | ||||
−0.584629 | + | 0.811301i | \(0.698760\pi\) | |||||||
\(282\) | 1.85572e11 | 1.74740 | ||||||||
\(283\) | 1.48138e11 | 1.37286 | 0.686430 | − | 0.727196i | \(-0.259177\pi\) | ||||
0.686430 | + | 0.727196i | \(0.259177\pi\) | |||||||
\(284\) | 2.18528e10 | 0.199331 | ||||||||
\(285\) | 3.00823e10 | 0.270090 | ||||||||
\(286\) | 4.55076e9 | 0.0402195 | ||||||||
\(287\) | −5.26279e9 | −0.0457876 | ||||||||
\(288\) | −7.55764e10 | −0.647321 | ||||||||
\(289\) | 6.97576e9 | 0.0588235 | ||||||||
\(290\) | −2.01154e10 | −0.167008 | ||||||||
\(291\) | 1.92079e11 | 1.57022 | ||||||||
\(292\) | 1.86977e11 | 1.50510 | ||||||||
\(293\) | 1.17196e11 | 0.928986 | 0.464493 | − | 0.885577i | \(-0.346237\pi\) | ||||
0.464493 | + | 0.885577i | \(0.346237\pi\) | |||||||
\(294\) | −2.33283e11 | −1.82105 | ||||||||
\(295\) | 1.17518e10 | 0.0903452 | ||||||||
\(296\) | 1.00263e11 | 0.759147 | ||||||||
\(297\) | 3.83973e10 | 0.286350 | ||||||||
\(298\) | −7.41694e10 | −0.544818 | ||||||||
\(299\) | 7.66448e9 | 0.0554577 | ||||||||
\(300\) | −2.12802e11 | −1.51681 | ||||||||
\(301\) | 2.76726e9 | 0.0194313 | ||||||||
\(302\) | 1.72594e11 | 1.19397 | ||||||||
\(303\) | −2.69370e11 | −1.83594 | ||||||||
\(304\) | −1.53248e11 | −1.02912 | ||||||||
\(305\) | 1.18198e10 | 0.0782099 | ||||||||
\(306\) | 2.60991e10 | 0.170169 | ||||||||
\(307\) | −4.33130e10 | −0.278288 | −0.139144 | − | 0.990272i | \(-0.544435\pi\) | ||||
−0.139144 | + | 0.990272i | \(0.544435\pi\) | |||||||
\(308\) | 5.01040e9 | 0.0317244 | ||||||||
\(309\) | −1.66055e11 | −1.03619 | ||||||||
\(310\) | −2.22952e9 | −0.0137114 | ||||||||
\(311\) | 1.79166e11 | 1.08601 | 0.543006 | − | 0.839729i | \(-0.317286\pi\) | ||||
0.543006 | + | 0.839729i | \(0.317286\pi\) | |||||||
\(312\) | −5.12700e9 | −0.0306315 | ||||||||
\(313\) | −6.30182e10 | −0.371122 | −0.185561 | − | 0.982633i | \(-0.559410\pi\) | ||||
−0.185561 | + | 0.982633i | \(0.559410\pi\) | |||||||
\(314\) | −3.91346e11 | −2.27184 | ||||||||
\(315\) | −6.37218e8 | −0.00364662 | ||||||||
\(316\) | −4.97749e10 | −0.280814 | ||||||||
\(317\) | 4.25331e10 | 0.236570 | 0.118285 | − | 0.992980i | \(-0.462260\pi\) | ||||
0.118285 | + | 0.992980i | \(0.462260\pi\) | |||||||
\(318\) | 5.49045e11 | 3.01083 | ||||||||
\(319\) | 6.47461e10 | 0.350071 | ||||||||
\(320\) | −3.82017e10 | −0.203661 | ||||||||
\(321\) | −2.90790e10 | −0.152865 | ||||||||
\(322\) | 1.50406e10 | 0.0779673 | ||||||||
\(323\) | 7.57692e10 | 0.387330 | ||||||||
\(324\) | −3.16615e11 | −1.59617 | ||||||||
\(325\) | 1.18859e10 | 0.0590957 | ||||||||
\(326\) | 5.41711e11 | 2.65637 | ||||||||
\(327\) | 2.83505e11 | 1.37118 | ||||||||
\(328\) | 7.17890e10 | 0.342472 | ||||||||
\(329\) | −1.14119e10 | −0.0537001 | ||||||||
\(330\) | −2.43127e10 | −0.112855 | ||||||||
\(331\) | −1.36038e11 | −0.622921 | −0.311461 | − | 0.950259i | \(-0.600818\pi\) | ||||
−0.311461 | + | 0.950259i | \(0.600818\pi\) | |||||||
\(332\) | −1.13623e10 | −0.0513271 | ||||||||
\(333\) | 1.88574e11 | 0.840393 | ||||||||
\(334\) | −2.71515e11 | −1.19381 | ||||||||
\(335\) | −2.46679e10 | −0.107012 | ||||||||
\(336\) | 1.02295e10 | 0.0437854 | ||||||||
\(337\) | −4.52614e11 | −1.91158 | −0.955792 | − | 0.294042i | \(-0.904999\pi\) | ||||
−0.955792 | + | 0.294042i | \(0.904999\pi\) | |||||||
\(338\) | −3.60861e11 | −1.50389 | ||||||||
\(339\) | −4.34115e11 | −1.78528 | ||||||||
\(340\) | 1.06742e10 | 0.0433194 | ||||||||
\(341\) | 7.17621e9 | 0.0287409 | ||||||||
\(342\) | 2.83483e11 | 1.12049 | ||||||||
\(343\) | 2.87371e10 | 0.112104 | ||||||||
\(344\) | −3.77479e10 | −0.145338 | ||||||||
\(345\) | −4.09479e10 | −0.155613 | ||||||||
\(346\) | 1.64751e11 | 0.617996 | ||||||||
\(347\) | −2.00653e11 | −0.742955 | −0.371478 | − | 0.928442i | \(-0.621149\pi\) | ||||
−0.371478 | + | 0.928442i | \(0.621149\pi\) | |||||||
\(348\) | −3.35147e11 | −1.22498 | ||||||||
\(349\) | 1.48945e11 | 0.537416 | 0.268708 | − | 0.963222i | \(-0.413403\pi\) | ||||
0.268708 | + | 0.963222i | \(0.413403\pi\) | |||||||
\(350\) | 2.33245e10 | 0.0830819 | ||||||||
\(351\) | 1.11014e10 | 0.0390387 | ||||||||
\(352\) | 1.77327e11 | 0.615649 | ||||||||
\(353\) | −3.46998e11 | −1.18944 | −0.594718 | − | 0.803934i | \(-0.702736\pi\) | ||||
−0.594718 | + | 0.803934i | \(0.702736\pi\) | |||||||
\(354\) | 3.48982e11 | 1.18111 | ||||||||
\(355\) | 6.52097e9 | 0.0217914 | ||||||||
\(356\) | 2.59731e11 | 0.857034 | ||||||||
\(357\) | −5.05769e9 | −0.0164796 | ||||||||
\(358\) | −2.22291e11 | −0.715235 | ||||||||
\(359\) | −5.87619e11 | −1.86711 | −0.933556 | − | 0.358431i | \(-0.883312\pi\) | ||||
−0.933556 | + | 0.358431i | \(0.883312\pi\) | |||||||
\(360\) | 8.69219e9 | 0.0272752 | ||||||||
\(361\) | 5.00300e11 | 1.55042 | ||||||||
\(362\) | 3.37267e11 | 1.03225 | ||||||||
\(363\) | −3.22127e11 | −0.973750 | ||||||||
\(364\) | 1.44860e9 | 0.00432507 | ||||||||
\(365\) | 5.57947e10 | 0.164541 | ||||||||
\(366\) | 3.51003e11 | 1.02246 | ||||||||
\(367\) | −8.17833e10 | −0.235325 | −0.117662 | − | 0.993054i | \(-0.537540\pi\) | ||||
−0.117662 | + | 0.993054i | \(0.537540\pi\) | |||||||
\(368\) | 2.08601e11 | 0.592928 | ||||||||
\(369\) | 1.35021e11 | 0.379124 | ||||||||
\(370\) | 1.37463e11 | 0.381310 | ||||||||
\(371\) | −3.37638e10 | −0.0925269 | ||||||||
\(372\) | −3.71464e10 | −0.100571 | ||||||||
\(373\) | 3.70187e11 | 0.990218 | 0.495109 | − | 0.868831i | \(-0.335128\pi\) | ||||
0.495109 | + | 0.868831i | \(0.335128\pi\) | |||||||
\(374\) | −6.12371e10 | −0.161842 | ||||||||
\(375\) | −1.28267e11 | −0.334945 | ||||||||
\(376\) | 1.55668e11 | 0.401655 | ||||||||
\(377\) | 1.87193e10 | 0.0477259 | ||||||||
\(378\) | 2.17851e10 | 0.0548840 | ||||||||
\(379\) | 5.17440e11 | 1.28820 | 0.644100 | − | 0.764941i | \(-0.277232\pi\) | ||||
0.644100 | + | 0.764941i | \(0.277232\pi\) | |||||||
\(380\) | 1.15941e11 | 0.285241 | ||||||||
\(381\) | −2.67092e11 | −0.649380 | ||||||||
\(382\) | 5.91779e11 | 1.42192 | ||||||||
\(383\) | 2.03437e11 | 0.483099 | 0.241549 | − | 0.970389i | \(-0.422344\pi\) | ||||
0.241549 | + | 0.970389i | \(0.422344\pi\) | |||||||
\(384\) | −4.16321e11 | −0.977098 | ||||||||
\(385\) | 1.49512e9 | 0.00346819 | ||||||||
\(386\) | −2.02451e11 | −0.464170 | ||||||||
\(387\) | −7.09961e10 | −0.160892 | ||||||||
\(388\) | 7.40298e11 | 1.65830 | ||||||||
\(389\) | 7.76405e11 | 1.71916 | 0.859578 | − | 0.511005i | \(-0.170727\pi\) | ||||
0.859578 | + | 0.511005i | \(0.170727\pi\) | |||||||
\(390\) | −7.02927e9 | −0.0153858 | ||||||||
\(391\) | −1.03137e11 | −0.223161 | ||||||||
\(392\) | −1.95690e11 | −0.418583 | ||||||||
\(393\) | 2.61808e11 | 0.553626 | ||||||||
\(394\) | −5.50838e11 | −1.15157 | ||||||||
\(395\) | −1.48530e10 | −0.0306993 | ||||||||
\(396\) | −1.28545e11 | −0.262681 | ||||||||
\(397\) | 4.33956e11 | 0.876776 | 0.438388 | − | 0.898786i | \(-0.355550\pi\) | ||||
0.438388 | + | 0.898786i | \(0.355550\pi\) | |||||||
\(398\) | −1.49667e12 | −2.98988 | ||||||||
\(399\) | −5.49356e10 | −0.108511 | ||||||||
\(400\) | 3.23493e11 | 0.631823 | ||||||||
\(401\) | 3.07899e11 | 0.594645 | 0.297323 | − | 0.954777i | \(-0.403906\pi\) | ||||
0.297323 | + | 0.954777i | \(0.403906\pi\) | |||||||
\(402\) | −7.32541e11 | −1.39899 | ||||||||
\(403\) | 2.07478e9 | 0.00391831 | ||||||||
\(404\) | −1.03819e12 | −1.93892 | ||||||||
\(405\) | −9.44791e10 | −0.174497 | ||||||||
\(406\) | 3.67343e10 | 0.0670973 | ||||||||
\(407\) | −4.42456e11 | −0.799273 | ||||||||
\(408\) | 6.89913e10 | 0.123260 | ||||||||
\(409\) | −5.32344e11 | −0.940671 | −0.470335 | − | 0.882488i | \(-0.655867\pi\) | ||||
−0.470335 | + | 0.882488i | \(0.655867\pi\) | |||||||
\(410\) | 9.84248e10 | 0.172019 | ||||||||
\(411\) | −1.27096e12 | −2.19706 | ||||||||
\(412\) | −6.39999e11 | −1.09431 | ||||||||
\(413\) | −2.14608e10 | −0.0362970 | ||||||||
\(414\) | −3.85876e11 | −0.645574 | ||||||||
\(415\) | −3.39057e9 | −0.00561120 | ||||||||
\(416\) | 5.12686e10 | 0.0839328 | ||||||||
\(417\) | 8.44042e11 | 1.36695 | ||||||||
\(418\) | −6.65144e11 | −1.06567 | ||||||||
\(419\) | −1.78965e11 | −0.283665 | −0.141833 | − | 0.989891i | \(-0.545299\pi\) | ||||
−0.141833 | + | 0.989891i | \(0.545299\pi\) | |||||||
\(420\) | −7.73924e9 | −0.0121360 | ||||||||
\(421\) | 1.88185e11 | 0.291954 | 0.145977 | − | 0.989288i | \(-0.453367\pi\) | ||||
0.145977 | + | 0.989288i | \(0.453367\pi\) | |||||||
\(422\) | 1.65647e12 | 2.54260 | ||||||||
\(423\) | 2.92779e11 | 0.444640 | ||||||||
\(424\) | 4.60567e11 | 0.692064 | ||||||||
\(425\) | −1.59942e11 | −0.237800 | ||||||||
\(426\) | 1.93647e11 | 0.284884 | ||||||||
\(427\) | −2.15851e10 | −0.0314216 | ||||||||
\(428\) | −1.12074e11 | −0.161439 | ||||||||
\(429\) | 2.26253e10 | 0.0322505 | ||||||||
\(430\) | −5.17534e10 | −0.0730014 | ||||||||
\(431\) | −6.39015e11 | −0.891997 | −0.445998 | − | 0.895034i | \(-0.647151\pi\) | ||||
−0.445998 | + | 0.895034i | \(0.647151\pi\) | |||||||
\(432\) | 3.02142e11 | 0.417383 | ||||||||
\(433\) | 3.97400e11 | 0.543291 | 0.271645 | − | 0.962397i | \(-0.412432\pi\) | ||||
0.271645 | + | 0.962397i | \(0.412432\pi\) | |||||||
\(434\) | 4.07149e9 | 0.00550870 | ||||||||
\(435\) | −1.00009e11 | −0.133918 | ||||||||
\(436\) | 1.09267e12 | 1.44810 | ||||||||
\(437\) | −1.12025e12 | −1.46943 | ||||||||
\(438\) | 1.65688e12 | 2.15109 | ||||||||
\(439\) | −1.41931e11 | −0.182384 | −0.0911918 | − | 0.995833i | \(-0.529068\pi\) | ||||
−0.0911918 | + | 0.995833i | \(0.529068\pi\) | |||||||
\(440\) | −2.03947e10 | −0.0259407 | ||||||||
\(441\) | −3.68053e11 | −0.463380 | ||||||||
\(442\) | −1.77048e10 | −0.0220644 | ||||||||
\(443\) | 1.16614e12 | 1.43858 | 0.719289 | − | 0.694711i | \(-0.244468\pi\) | ||||
0.719289 | + | 0.694711i | \(0.244468\pi\) | |||||||
\(444\) | 2.29030e12 | 2.79685 | ||||||||
\(445\) | 7.75046e10 | 0.0936931 | ||||||||
\(446\) | −4.52893e10 | −0.0541987 | ||||||||
\(447\) | −3.68753e11 | −0.436870 | ||||||||
\(448\) | 6.97631e10 | 0.0818229 | ||||||||
\(449\) | 9.04654e11 | 1.05045 | 0.525223 | − | 0.850964i | \(-0.323982\pi\) | ||||
0.525223 | + | 0.850964i | \(0.323982\pi\) | |||||||
\(450\) | −5.98407e11 | −0.687923 | ||||||||
\(451\) | −3.16803e11 | −0.360574 | ||||||||
\(452\) | −1.67314e12 | −1.88542 | ||||||||
\(453\) | 8.58097e11 | 0.957402 | ||||||||
\(454\) | −2.15176e12 | −2.37707 | ||||||||
\(455\) | 4.32268e8 | 0.000472827 0 | ||||||||
\(456\) | 7.49368e11 | 0.811621 | ||||||||
\(457\) | −2.89019e10 | −0.0309959 | −0.0154979 | − | 0.999880i | \(-0.504933\pi\) | ||||
−0.0154979 | + | 0.999880i | \(0.504933\pi\) | |||||||
\(458\) | 1.14932e12 | 1.22052 | ||||||||
\(459\) | −1.49385e11 | −0.157091 | ||||||||
\(460\) | −1.57819e11 | −0.164342 | ||||||||
\(461\) | −3.33362e11 | −0.343765 | −0.171883 | − | 0.985117i | \(-0.554985\pi\) | ||||
−0.171883 | + | 0.985117i | \(0.554985\pi\) | |||||||
\(462\) | 4.43993e10 | 0.0453406 | ||||||||
\(463\) | 9.65145e11 | 0.976064 | 0.488032 | − | 0.872826i | \(-0.337715\pi\) | ||||
0.488032 | + | 0.872826i | \(0.337715\pi\) | |||||||
\(464\) | 5.09477e11 | 0.510263 | ||||||||
\(465\) | −1.10846e10 | −0.0109947 | ||||||||
\(466\) | −1.11200e12 | −1.09237 | ||||||||
\(467\) | −7.21341e11 | −0.701802 | −0.350901 | − | 0.936413i | \(-0.614125\pi\) | ||||
−0.350901 | + | 0.936413i | \(0.614125\pi\) | |||||||
\(468\) | −3.71649e10 | −0.0358118 | ||||||||
\(469\) | 4.50479e10 | 0.0429929 | ||||||||
\(470\) | 2.13425e11 | 0.201746 | ||||||||
\(471\) | −1.94568e12 | −1.82170 | ||||||||
\(472\) | 2.92744e11 | 0.271487 | ||||||||
\(473\) | 1.66580e11 | 0.153020 | ||||||||
\(474\) | −4.41077e11 | −0.401340 | ||||||||
\(475\) | −1.73725e12 | −1.56582 | ||||||||
\(476\) | −1.94930e10 | −0.0174040 | ||||||||
\(477\) | 8.66233e11 | 0.766129 | ||||||||
\(478\) | 1.45180e12 | 1.27198 | ||||||||
\(479\) | 1.57016e12 | 1.36281 | 0.681403 | − | 0.731909i | \(-0.261370\pi\) | ||||
0.681403 | + | 0.731909i | \(0.261370\pi\) | |||||||
\(480\) | −2.73906e11 | −0.235513 | ||||||||
\(481\) | −1.27922e11 | −0.108967 | ||||||||
\(482\) | −2.20737e12 | −1.86279 | ||||||||
\(483\) | 7.47781e10 | 0.0625191 | ||||||||
\(484\) | −1.24152e12 | −1.02837 | ||||||||
\(485\) | 2.20908e11 | 0.181290 | ||||||||
\(486\) | −1.60330e12 | −1.30362 | ||||||||
\(487\) | 1.48730e12 | 1.19817 | 0.599084 | − | 0.800686i | \(-0.295532\pi\) | ||||
0.599084 | + | 0.800686i | \(0.295532\pi\) | |||||||
\(488\) | 2.94439e11 | 0.235021 | ||||||||
\(489\) | 2.69326e12 | 2.13004 | ||||||||
\(490\) | −2.68297e11 | −0.210248 | ||||||||
\(491\) | 9.71236e11 | 0.754150 | 0.377075 | − | 0.926183i | \(-0.376930\pi\) | ||||
0.377075 | + | 0.926183i | \(0.376930\pi\) | |||||||
\(492\) | 1.63987e12 | 1.26173 | ||||||||
\(493\) | −2.51896e11 | −0.192048 | ||||||||
\(494\) | −1.92306e11 | −0.145285 | ||||||||
\(495\) | −3.83584e10 | −0.0287169 | ||||||||
\(496\) | 5.64685e10 | 0.0418927 | ||||||||
\(497\) | −1.19084e10 | −0.00875489 | ||||||||
\(498\) | −1.00687e11 | −0.0733567 | ||||||||
\(499\) | 1.21621e12 | 0.878127 | 0.439064 | − | 0.898456i | \(-0.355310\pi\) | ||||
0.439064 | + | 0.898456i | \(0.355310\pi\) | |||||||
\(500\) | −4.94357e11 | −0.353733 | ||||||||
\(501\) | −1.34991e12 | −0.957272 | ||||||||
\(502\) | −3.44247e12 | −2.41938 | ||||||||
\(503\) | 2.43415e12 | 1.69548 | 0.847739 | − | 0.530414i | \(-0.177964\pi\) | ||||
0.847739 | + | 0.530414i | \(0.177964\pi\) | |||||||
\(504\) | −1.58735e10 | −0.0109581 | ||||||||
\(505\) | −3.09799e11 | −0.211968 | ||||||||
\(506\) | 9.05392e11 | 0.613987 | ||||||||
\(507\) | −1.79412e12 | −1.20591 | ||||||||
\(508\) | −1.02941e12 | −0.685807 | ||||||||
\(509\) | −2.50151e12 | −1.65186 | −0.825930 | − | 0.563773i | \(-0.809349\pi\) | ||||
−0.825930 | + | 0.563773i | \(0.809349\pi\) | |||||||
\(510\) | 9.45891e10 | 0.0619120 | ||||||||
\(511\) | −1.01891e11 | −0.0661060 | ||||||||
\(512\) | 1.81611e12 | 1.16796 | ||||||||
\(513\) | −1.62259e12 | −1.03438 | ||||||||
\(514\) | −2.72689e12 | −1.72319 | ||||||||
\(515\) | −1.90978e11 | −0.119633 | ||||||||
\(516\) | −8.62274e11 | −0.535453 | ||||||||
\(517\) | −6.86956e11 | −0.422884 | ||||||||
\(518\) | −2.51031e11 | −0.153195 | ||||||||
\(519\) | 8.19103e11 | 0.495548 | ||||||||
\(520\) | −5.89651e9 | −0.00353655 | ||||||||
\(521\) | 2.28180e12 | 1.35678 | 0.678388 | − | 0.734704i | \(-0.262679\pi\) | ||||
0.678388 | + | 0.734704i | \(0.262679\pi\) | |||||||
\(522\) | −9.42445e11 | −0.555570 | ||||||||
\(523\) | 1.67259e12 | 0.977537 | 0.488768 | − | 0.872414i | \(-0.337446\pi\) | ||||
0.488768 | + | 0.872414i | \(0.337446\pi\) | |||||||
\(524\) | 1.00904e12 | 0.584682 | ||||||||
\(525\) | 1.15964e11 | 0.0666202 | ||||||||
\(526\) | 3.16392e12 | 1.80215 | ||||||||
\(527\) | −2.79192e10 | −0.0157672 | ||||||||
\(528\) | 6.15785e11 | 0.344807 | ||||||||
\(529\) | −2.76274e11 | −0.153388 | ||||||||
\(530\) | 6.31450e11 | 0.347614 | ||||||||
\(531\) | 5.50593e11 | 0.300542 | ||||||||
\(532\) | −2.11729e11 | −0.114598 | ||||||||
\(533\) | −9.15937e10 | −0.0491579 | ||||||||
\(534\) | 2.30158e12 | 1.22487 | ||||||||
\(535\) | −3.34434e10 | −0.0176489 | ||||||||
\(536\) | −6.14492e11 | −0.321570 | ||||||||
\(537\) | −1.10518e12 | −0.573520 | ||||||||
\(538\) | −2.18034e12 | −1.12203 | ||||||||
\(539\) | 8.63574e11 | 0.440707 | ||||||||
\(540\) | −2.28588e11 | −0.115686 | ||||||||
\(541\) | −8.84734e11 | −0.444043 | −0.222021 | − | 0.975042i | \(-0.571265\pi\) | ||||
−0.222021 | + | 0.975042i | \(0.571265\pi\) | |||||||
\(542\) | 4.75688e12 | 2.36769 | ||||||||
\(543\) | 1.67681e12 | 0.827723 | ||||||||
\(544\) | −6.89894e11 | −0.337744 | ||||||||
\(545\) | 3.26056e11 | 0.158310 | ||||||||
\(546\) | 1.28367e10 | 0.00618138 | ||||||||
\(547\) | −2.72146e12 | −1.29975 | −0.649874 | − | 0.760042i | \(-0.725178\pi\) | ||||
−0.649874 | + | 0.760042i | \(0.725178\pi\) | |||||||
\(548\) | −4.89844e12 | −2.32031 | ||||||||
\(549\) | 5.53780e11 | 0.260173 | ||||||||
\(550\) | 1.40406e12 | 0.654264 | ||||||||
\(551\) | −2.73604e12 | −1.26456 | ||||||||
\(552\) | −1.02004e12 | −0.467617 | ||||||||
\(553\) | 2.71242e10 | 0.0123337 | ||||||||
\(554\) | 4.55676e12 | 2.05524 | ||||||||
\(555\) | 6.83433e11 | 0.305758 | ||||||||
\(556\) | 3.25305e12 | 1.44363 | ||||||||
\(557\) | −2.68557e12 | −1.18219 | −0.591096 | − | 0.806601i | \(-0.701305\pi\) | ||||
−0.591096 | + | 0.806601i | \(0.701305\pi\) | |||||||
\(558\) | −1.04457e11 | −0.0456124 | ||||||||
\(559\) | 4.81615e10 | 0.0208616 | ||||||||
\(560\) | 1.17649e10 | 0.00505524 | ||||||||
\(561\) | −3.04457e11 | −0.129775 | ||||||||
\(562\) | −4.17369e12 | −1.76484 | ||||||||
\(563\) | −2.81923e12 | −1.18261 | −0.591307 | − | 0.806446i | \(-0.701388\pi\) | ||||
−0.591307 | + | 0.806446i | \(0.701388\pi\) | |||||||
\(564\) | 3.55591e12 | 1.47977 | ||||||||
\(565\) | −4.99271e11 | −0.206119 | ||||||||
\(566\) | 5.05936e12 | 2.07215 | ||||||||
\(567\) | 1.72535e11 | 0.0701059 | ||||||||
\(568\) | 1.62441e11 | 0.0654830 | ||||||||
\(569\) | 3.57453e11 | 0.142960 | 0.0714799 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714799 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(570\) | 1.02741e12 | 0.407667 | ||||||||
\(571\) | −3.25953e11 | −0.128319 | −0.0641596 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641596 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(572\) | 8.72010e10 | 0.0340596 | ||||||||
\(573\) | 2.94219e12 | 1.14018 | ||||||||
\(574\) | −1.79741e11 | −0.0691104 | ||||||||
\(575\) | 2.36474e12 | 0.902149 | ||||||||
\(576\) | −1.78982e12 | −0.677499 | ||||||||
\(577\) | −2.50107e11 | −0.0939365 | −0.0469683 | − | 0.998896i | \(-0.514956\pi\) | ||||
−0.0469683 | + | 0.998896i | \(0.514956\pi\) | |||||||
\(578\) | 2.38244e11 | 0.0887865 | ||||||||
\(579\) | −1.00654e12 | −0.372200 | ||||||||
\(580\) | −3.85449e11 | −0.141430 | ||||||||
\(581\) | 6.19177e9 | 0.00225435 | ||||||||
\(582\) | 6.56010e12 | 2.37005 | ||||||||
\(583\) | −2.03247e12 | −0.728643 | ||||||||
\(584\) | 1.38988e12 | 0.494446 | ||||||||
\(585\) | −1.10901e10 | −0.00391504 | ||||||||
\(586\) | 4.00262e12 | 1.40218 | ||||||||
\(587\) | 9.14514e10 | 0.0317921 | 0.0158960 | − | 0.999874i | \(-0.494940\pi\) | ||||
0.0158960 | + | 0.999874i | \(0.494940\pi\) | |||||||
\(588\) | −4.47014e12 | −1.54214 | ||||||||
\(589\) | −3.03252e11 | −0.103821 | ||||||||
\(590\) | 4.01361e11 | 0.136364 | ||||||||
\(591\) | −2.73864e12 | −0.923402 | ||||||||
\(592\) | −3.48162e12 | −1.16502 | ||||||||
\(593\) | −2.60815e12 | −0.866138 | −0.433069 | − | 0.901361i | \(-0.642569\pi\) | ||||
−0.433069 | + | 0.901361i | \(0.642569\pi\) | |||||||
\(594\) | 1.31139e12 | 0.432208 | ||||||||
\(595\) | −5.81680e9 | −0.00190264 | ||||||||
\(596\) | −1.42122e12 | −0.461376 | ||||||||
\(597\) | −7.44111e12 | −2.39747 | ||||||||
\(598\) | 2.61766e11 | 0.0837063 | ||||||||
\(599\) | 1.25671e12 | 0.398853 | 0.199427 | − | 0.979913i | \(-0.436092\pi\) | ||||
0.199427 | + | 0.979913i | \(0.436092\pi\) | |||||||
\(600\) | −1.58185e12 | −0.498292 | ||||||||
\(601\) | −9.01991e11 | −0.282012 | −0.141006 | − | 0.990009i | \(-0.545034\pi\) | ||||
−0.141006 | + | 0.990009i | \(0.545034\pi\) | |||||||
\(602\) | 9.45108e10 | 0.0293290 | ||||||||
\(603\) | −1.15574e12 | −0.355984 | ||||||||
\(604\) | 3.30722e12 | 1.01111 | ||||||||
\(605\) | −3.70475e11 | −0.112424 | ||||||||
\(606\) | −9.19984e12 | −2.77111 | ||||||||
\(607\) | 4.29234e12 | 1.28335 | 0.641675 | − | 0.766977i | \(-0.278240\pi\) | ||||
0.641675 | + | 0.766977i | \(0.278240\pi\) | |||||||
\(608\) | −7.49348e12 | −2.22391 | ||||||||
\(609\) | 1.82634e11 | 0.0538028 | ||||||||
\(610\) | 4.03684e11 | 0.118048 | ||||||||
\(611\) | −1.98612e11 | −0.0576528 | ||||||||
\(612\) | 5.00108e11 | 0.144106 | ||||||||
\(613\) | 3.09808e12 | 0.886178 | 0.443089 | − | 0.896478i | \(-0.353883\pi\) | ||||
0.443089 | + | 0.896478i | \(0.353883\pi\) | |||||||
\(614\) | −1.47927e12 | −0.420040 | ||||||||
\(615\) | 4.89345e11 | 0.137936 | ||||||||
\(616\) | 3.72444e10 | 0.0104219 | ||||||||
\(617\) | −2.97483e12 | −0.826378 | −0.413189 | − | 0.910645i | \(-0.635585\pi\) | ||||
−0.413189 | + | 0.910645i | \(0.635585\pi\) | |||||||
\(618\) | −5.67131e12 | −1.56399 | ||||||||
\(619\) | −3.10484e10 | −0.00850025 | −0.00425012 | − | 0.999991i | \(-0.501353\pi\) | ||||
−0.00425012 | + | 0.999991i | \(0.501353\pi\) | |||||||
\(620\) | −4.27217e10 | −0.0116114 | ||||||||
\(621\) | 2.20867e12 | 0.595961 | ||||||||
\(622\) | 6.11910e12 | 1.63920 | ||||||||
\(623\) | −1.41537e11 | −0.0376421 | ||||||||
\(624\) | 1.78035e11 | 0.0470083 | ||||||||
\(625\) | 3.59269e12 | 0.941803 | ||||||||
\(626\) | −2.15227e12 | −0.560160 | ||||||||
\(627\) | −3.30694e12 | −0.854521 | ||||||||
\(628\) | −7.49891e12 | −1.92389 | ||||||||
\(629\) | 1.72138e12 | 0.438480 | ||||||||
\(630\) | −2.17630e10 | −0.00550410 | ||||||||
\(631\) | 5.20764e12 | 1.30770 | 0.653851 | − | 0.756623i | \(-0.273152\pi\) | ||||
0.653851 | + | 0.756623i | \(0.273152\pi\) | |||||||
\(632\) | −3.69998e11 | −0.0922513 | ||||||||
\(633\) | 8.23559e12 | 2.03882 | ||||||||
\(634\) | 1.45264e12 | 0.357072 | ||||||||
\(635\) | −3.07180e11 | −0.0749741 | ||||||||
\(636\) | 1.05207e13 | 2.54970 | ||||||||
\(637\) | 2.49676e11 | 0.0600826 | ||||||||
\(638\) | 2.21128e12 | 0.528386 | ||||||||
\(639\) | 3.05519e11 | 0.0724911 | ||||||||
\(640\) | −4.78806e11 | −0.112811 | ||||||||
\(641\) | 2.80533e12 | 0.656330 | 0.328165 | − | 0.944620i | \(-0.393570\pi\) | ||||
0.328165 | + | 0.944620i | \(0.393570\pi\) | |||||||
\(642\) | −9.93139e11 | −0.230729 | ||||||||
\(643\) | 2.80520e12 | 0.647164 | 0.323582 | − | 0.946200i | \(-0.395113\pi\) | ||||
0.323582 | + | 0.946200i | \(0.395113\pi\) | |||||||
\(644\) | 2.88205e11 | 0.0660260 | ||||||||
\(645\) | −2.57306e11 | −0.0585371 | ||||||||
\(646\) | 2.58776e12 | 0.584624 | ||||||||
\(647\) | 4.72530e12 | 1.06013 | 0.530066 | − | 0.847956i | \(-0.322167\pi\) | ||||
0.530066 | + | 0.847956i | \(0.322167\pi\) | |||||||
\(648\) | −2.35353e12 | −0.524364 | ||||||||
\(649\) | −1.29187e12 | −0.285837 | ||||||||
\(650\) | 4.05940e11 | 0.0891973 | ||||||||
\(651\) | 2.02425e10 | 0.00441722 | ||||||||
\(652\) | 1.03802e13 | 2.24953 | ||||||||
\(653\) | −7.04467e12 | −1.51618 | −0.758091 | − | 0.652149i | \(-0.773868\pi\) | ||||
−0.758091 | + | 0.652149i | \(0.773868\pi\) | |||||||
\(654\) | 9.68258e12 | 2.06962 | ||||||||
\(655\) | 3.01103e11 | 0.0639188 | ||||||||
\(656\) | −2.49287e12 | −0.525572 | ||||||||
\(657\) | 2.61408e12 | 0.547362 | ||||||||
\(658\) | −3.89751e11 | −0.0810533 | ||||||||
\(659\) | −2.93823e12 | −0.606879 | −0.303439 | − | 0.952851i | \(-0.598135\pi\) | ||||
−0.303439 | + | 0.952851i | \(0.598135\pi\) | |||||||
\(660\) | −4.65877e11 | −0.0955704 | ||||||||
\(661\) | −7.72453e11 | −0.157386 | −0.0786929 | − | 0.996899i | \(-0.525075\pi\) | ||||
−0.0786929 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(662\) | −4.64611e12 | −0.940219 | ||||||||
\(663\) | −8.80242e10 | −0.0176926 | ||||||||
\(664\) | −8.44610e10 | −0.0168616 | ||||||||
\(665\) | −6.31808e10 | −0.0125282 | ||||||||
\(666\) | 6.44039e12 | 1.26846 | ||||||||
\(667\) | 3.72429e12 | 0.728580 | ||||||||
\(668\) | −5.20274e12 | −1.01097 | ||||||||
\(669\) | −2.25168e11 | −0.0434599 | ||||||||
\(670\) | −8.42487e11 | −0.161520 | ||||||||
\(671\) | −1.29935e12 | −0.247443 | ||||||||
\(672\) | 5.00200e11 | 0.0946198 | ||||||||
\(673\) | 2.83634e12 | 0.532954 | 0.266477 | − | 0.963841i | \(-0.414140\pi\) | ||||
0.266477 | + | 0.963841i | \(0.414140\pi\) | |||||||
\(674\) | −1.54582e13 | −2.88529 | ||||||||
\(675\) | 3.42514e12 | 0.635055 | ||||||||
\(676\) | −6.91478e12 | −1.27356 | ||||||||
\(677\) | −2.65986e12 | −0.486642 | −0.243321 | − | 0.969946i | \(-0.578237\pi\) | ||||
−0.243321 | + | 0.969946i | \(0.578237\pi\) | |||||||
\(678\) | −1.48264e13 | −2.69465 | ||||||||
\(679\) | −4.03416e11 | −0.0728349 | ||||||||
\(680\) | 7.93461e10 | 0.0142310 | ||||||||
\(681\) | −1.06980e13 | −1.90608 | ||||||||
\(682\) | 2.45090e11 | 0.0433807 | ||||||||
\(683\) | −2.44022e12 | −0.429078 | −0.214539 | − | 0.976715i | \(-0.568825\pi\) | ||||
−0.214539 | + | 0.976715i | \(0.568825\pi\) | |||||||
\(684\) | 5.43206e12 | 0.948882 | ||||||||
\(685\) | −1.46171e12 | −0.253661 | ||||||||
\(686\) | 9.81463e11 | 0.169206 | ||||||||
\(687\) | 5.71415e12 | 0.978693 | ||||||||
\(688\) | 1.31079e12 | 0.223042 | ||||||||
\(689\) | −5.87625e11 | −0.0993376 | ||||||||
\(690\) | −1.39850e12 | −0.234878 | ||||||||
\(691\) | 5.13446e12 | 0.856730 | 0.428365 | − | 0.903606i | \(-0.359090\pi\) | ||||
0.428365 | + | 0.903606i | \(0.359090\pi\) | |||||||
\(692\) | 3.15694e12 | 0.523345 | ||||||||
\(693\) | 7.00492e10 | 0.0115373 | ||||||||
\(694\) | −6.85293e12 | −1.12139 | ||||||||
\(695\) | 9.70724e11 | 0.157821 | ||||||||
\(696\) | −2.49129e12 | −0.402423 | ||||||||
\(697\) | 1.23253e12 | 0.197810 | ||||||||
\(698\) | 5.08693e12 | 0.811159 | ||||||||
\(699\) | −5.52861e12 | −0.875929 | ||||||||
\(700\) | 4.46941e11 | 0.0703573 | ||||||||
\(701\) | −4.00510e12 | −0.626444 | −0.313222 | − | 0.949680i | \(-0.601408\pi\) | ||||
−0.313222 | + | 0.949680i | \(0.601408\pi\) | |||||||
\(702\) | 3.79147e11 | 0.0589238 | ||||||||
\(703\) | 1.86973e13 | 2.88722 | ||||||||
\(704\) | 4.19951e12 | 0.644350 | ||||||||
\(705\) | 1.06110e12 | 0.161772 | ||||||||
\(706\) | −1.18511e13 | −1.79530 | ||||||||
\(707\) | 5.65748e11 | 0.0851600 | ||||||||
\(708\) | 6.68715e12 | 1.00021 | ||||||||
\(709\) | −7.18171e12 | −1.06738 | −0.533691 | − | 0.845680i | \(-0.679195\pi\) | ||||
−0.533691 | + | 0.845680i | \(0.679195\pi\) | |||||||
\(710\) | 2.22712e11 | 0.0328912 | ||||||||
\(711\) | −6.95892e11 | −0.102124 | ||||||||
\(712\) | 1.93069e12 | 0.281548 | ||||||||
\(713\) | 4.12785e11 | 0.0598166 | ||||||||
\(714\) | −1.72736e11 | −0.0248738 | ||||||||
\(715\) | 2.60211e10 | 0.00372348 | ||||||||
\(716\) | −4.25951e12 | −0.605691 | ||||||||
\(717\) | 7.21802e12 | 1.01996 | ||||||||
\(718\) | −2.00690e13 | −2.81816 | ||||||||
\(719\) | 2.19372e10 | 0.00306127 | 0.00153063 | − | 0.999999i | \(-0.499513\pi\) | ||||
0.00153063 | + | 0.999999i | \(0.499513\pi\) | |||||||
\(720\) | −3.01836e11 | −0.0418577 | ||||||||
\(721\) | 3.48760e11 | 0.0480637 | ||||||||
\(722\) | 1.70868e13 | 2.34015 | ||||||||
\(723\) | −1.09745e13 | −1.49370 | ||||||||
\(724\) | 6.46266e12 | 0.874154 | ||||||||
\(725\) | 5.77553e12 | 0.776373 | ||||||||
\(726\) | −1.10017e13 | −1.46975 | ||||||||
\(727\) | 3.47360e11 | 0.0461185 | 0.0230593 | − | 0.999734i | \(-0.492659\pi\) | ||||
0.0230593 | + | 0.999734i | \(0.492659\pi\) | |||||||
\(728\) | 1.07681e10 | 0.00142084 | ||||||||
\(729\) | 1.55133e12 | 0.203437 | ||||||||
\(730\) | 1.90556e12 | 0.248354 | ||||||||
\(731\) | −6.48083e11 | −0.0839465 | ||||||||
\(732\) | 6.72586e12 | 0.865861 | ||||||||
\(733\) | 3.58285e11 | 0.0458417 | 0.0229208 | − | 0.999737i | \(-0.492703\pi\) | ||||
0.0229208 | + | 0.999737i | \(0.492703\pi\) | |||||||
\(734\) | −2.79316e12 | −0.355192 | ||||||||
\(735\) | −1.33391e12 | −0.168590 | ||||||||
\(736\) | 1.02001e13 | 1.28131 | ||||||||
\(737\) | 2.71174e12 | 0.338566 | ||||||||
\(738\) | 4.61138e12 | 0.572239 | ||||||||
\(739\) | −2.16274e12 | −0.266750 | −0.133375 | − | 0.991066i | \(-0.542581\pi\) | ||||
−0.133375 | + | 0.991066i | \(0.542581\pi\) | |||||||
\(740\) | 2.63405e12 | 0.322909 | ||||||||
\(741\) | −9.56100e11 | −0.116499 | ||||||||
\(742\) | −1.15314e12 | −0.139657 | ||||||||
\(743\) | 6.42105e12 | 0.772959 | 0.386479 | − | 0.922298i | \(-0.373691\pi\) | ||||
0.386479 | + | 0.922298i | \(0.373691\pi\) | |||||||
\(744\) | −2.76125e11 | −0.0330390 | ||||||||
\(745\) | −4.24099e11 | −0.0504387 | ||||||||
\(746\) | 1.26430e13 | 1.49461 | ||||||||
\(747\) | −1.58854e11 | −0.0186662 | ||||||||
\(748\) | −1.17342e12 | −0.137055 | ||||||||
\(749\) | 6.10736e10 | 0.00709064 | ||||||||
\(750\) | −4.38071e12 | −0.505555 | ||||||||
\(751\) | −1.15069e13 | −1.32002 | −0.660010 | − | 0.751257i | \(-0.729448\pi\) | ||||
−0.660010 | + | 0.751257i | \(0.729448\pi\) | |||||||
\(752\) | −5.40555e12 | −0.616396 | ||||||||
\(753\) | −1.71151e13 | −1.94001 | ||||||||
\(754\) | 6.39325e11 | 0.0720361 | ||||||||
\(755\) | 9.86888e11 | 0.110537 | ||||||||
\(756\) | 4.17442e11 | 0.0464781 | ||||||||
\(757\) | −7.80850e12 | −0.864243 | −0.432122 | − | 0.901815i | \(-0.642235\pi\) | ||||
−0.432122 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(758\) | 1.76722e13 | 1.94437 | ||||||||
\(759\) | 4.50140e12 | 0.492333 | ||||||||
\(760\) | 8.61840e11 | 0.0937056 | ||||||||
\(761\) | −6.58284e12 | −0.711512 | −0.355756 | − | 0.934579i | \(-0.615777\pi\) | ||||
−0.355756 | + | 0.934579i | \(0.615777\pi\) | |||||||
\(762\) | −9.12205e12 | −0.980156 | ||||||||
\(763\) | −5.95435e11 | −0.0636025 | ||||||||
\(764\) | 1.13396e13 | 1.20414 | ||||||||
\(765\) | 1.49234e11 | 0.0157540 | ||||||||
\(766\) | 6.94803e12 | 0.729175 | ||||||||
\(767\) | −3.73505e11 | −0.0389688 | ||||||||
\(768\) | 2.78808e12 | 0.289188 | ||||||||
\(769\) | −1.27459e13 | −1.31433 | −0.657163 | − | 0.753748i | \(-0.728244\pi\) | ||||
−0.657163 | + | 0.753748i | \(0.728244\pi\) | |||||||
\(770\) | 5.10631e10 | 0.00523479 | ||||||||
\(771\) | −1.35575e13 | −1.38176 | ||||||||
\(772\) | −3.87933e12 | −0.393079 | ||||||||
\(773\) | −1.07389e13 | −1.08181 | −0.540907 | − | 0.841083i | \(-0.681919\pi\) | ||||
−0.540907 | + | 0.841083i | \(0.681919\pi\) | |||||||
\(774\) | −2.42474e12 | −0.242846 | ||||||||
\(775\) | 6.40137e11 | 0.0637405 | ||||||||
\(776\) | 5.50294e12 | 0.544775 | ||||||||
\(777\) | −1.24807e12 | −0.122841 | ||||||||
\(778\) | 2.65167e13 | 2.59484 | ||||||||
\(779\) | 1.33874e13 | 1.30250 | ||||||||
\(780\) | −1.34694e11 | −0.0130293 | ||||||||
\(781\) | −7.16848e11 | −0.0689442 | ||||||||
\(782\) | −3.52244e12 | −0.336832 | ||||||||
\(783\) | 5.39434e12 | 0.512873 | ||||||||
\(784\) | 6.79533e12 | 0.642375 | ||||||||
\(785\) | −2.23770e12 | −0.210324 | ||||||||
\(786\) | 8.94158e12 | 0.835627 | ||||||||
\(787\) | 3.76105e12 | 0.349481 | 0.174740 | − | 0.984615i | \(-0.444091\pi\) | ||||
0.174740 | + | 0.984615i | \(0.444091\pi\) | |||||||
\(788\) | −1.05551e13 | −0.975200 | ||||||||
\(789\) | 1.57303e13 | 1.44507 | ||||||||
\(790\) | −5.07278e11 | −0.0463366 | ||||||||
\(791\) | 9.11756e11 | 0.0828103 | ||||||||
\(792\) | −9.55531e11 | −0.0862942 | ||||||||
\(793\) | −3.75667e11 | −0.0337344 | ||||||||
\(794\) | 1.48210e13 | 1.32338 | ||||||||
\(795\) | 3.13942e12 | 0.278739 | ||||||||
\(796\) | −2.86790e13 | −2.53195 | ||||||||
\(797\) | 2.18200e13 | 1.91555 | 0.957773 | − | 0.287524i | \(-0.0928322\pi\) | ||||
0.957773 | + | 0.287524i | \(0.0928322\pi\) | |||||||
\(798\) | −1.87622e12 | −0.163784 | ||||||||
\(799\) | 2.67262e12 | 0.231994 | ||||||||
\(800\) | 1.58180e13 | 1.36536 | ||||||||
\(801\) | 3.63123e12 | 0.311679 | ||||||||
\(802\) | 1.05157e13 | 0.897540 | ||||||||
\(803\) | −6.13349e12 | −0.520581 | ||||||||
\(804\) | −1.40368e13 | −1.18472 | ||||||||
\(805\) | 8.60015e10 | 0.00721813 | ||||||||
\(806\) | 7.08602e10 | 0.00591418 | ||||||||
\(807\) | −1.08401e13 | −0.899712 | ||||||||
\(808\) | −7.71729e12 | −0.636962 | ||||||||
\(809\) | −1.90714e13 | −1.56536 | −0.782681 | − | 0.622423i | \(-0.786148\pi\) | ||||
−0.782681 | + | 0.622423i | \(0.786148\pi\) | |||||||
\(810\) | −3.22676e12 | −0.263381 | ||||||||
\(811\) | −1.86624e13 | −1.51486 | −0.757430 | − | 0.652916i | \(-0.773546\pi\) | ||||
−0.757430 | + | 0.652916i | \(0.773546\pi\) | |||||||
\(812\) | 7.03898e11 | 0.0568208 | ||||||||
\(813\) | 2.36501e13 | 1.89856 | ||||||||
\(814\) | −1.51113e13 | −1.20640 | ||||||||
\(815\) | 3.09749e12 | 0.245924 | ||||||||
\(816\) | −2.39572e12 | −0.189161 | ||||||||
\(817\) | −7.03934e12 | −0.552755 | ||||||||
\(818\) | −1.81812e13 | −1.41982 | ||||||||
\(819\) | 2.02526e10 | 0.00157290 | ||||||||
\(820\) | 1.88600e12 | 0.145673 | ||||||||
\(821\) | −4.79906e12 | −0.368648 | −0.184324 | − | 0.982866i | \(-0.559010\pi\) | ||||
−0.184324 | + | 0.982866i | \(0.559010\pi\) | |||||||
\(822\) | −4.34072e13 | −3.31618 | ||||||||
\(823\) | 2.14502e13 | 1.62979 | 0.814895 | − | 0.579609i | \(-0.196795\pi\) | ||||
0.814895 | + | 0.579609i | \(0.196795\pi\) | |||||||
\(824\) | −4.75738e12 | −0.359497 | ||||||||
\(825\) | 6.98065e12 | 0.524630 | ||||||||
\(826\) | −7.32955e11 | −0.0547857 | ||||||||
\(827\) | −1.32157e13 | −0.982463 | −0.491231 | − | 0.871029i | \(-0.663453\pi\) | ||||
−0.491231 | + | 0.871029i | \(0.663453\pi\) | |||||||
\(828\) | −7.39411e12 | −0.546700 | ||||||||
\(829\) | −7.78893e12 | −0.572773 | −0.286386 | − | 0.958114i | \(-0.592454\pi\) | ||||
−0.286386 | + | 0.958114i | \(0.592454\pi\) | |||||||
\(830\) | −1.15799e11 | −0.00846938 | ||||||||
\(831\) | 2.26551e13 | 1.64802 | ||||||||
\(832\) | 1.21416e12 | 0.0878456 | ||||||||
\(833\) | −3.35975e12 | −0.241771 | ||||||||
\(834\) | 2.88267e13 | 2.06323 | ||||||||
\(835\) | −1.55252e12 | −0.110522 | ||||||||
\(836\) | −1.27454e13 | −0.902454 | ||||||||
\(837\) | 5.97887e11 | 0.0421070 | ||||||||
\(838\) | −6.11223e12 | −0.428156 | ||||||||
\(839\) | −9.65976e12 | −0.673035 | −0.336517 | − | 0.941677i | \(-0.609249\pi\) | ||||
−0.336517 | + | 0.941677i | \(0.609249\pi\) | |||||||
\(840\) | −5.75290e10 | −0.00398685 | ||||||||
\(841\) | −5.41113e12 | −0.372997 | ||||||||
\(842\) | 6.42710e12 | 0.440667 | ||||||||
\(843\) | −2.07506e13 | −1.41516 | ||||||||
\(844\) | 3.17411e13 | 2.15318 | ||||||||
\(845\) | −2.06340e12 | −0.139228 | ||||||||
\(846\) | 9.99934e12 | 0.671127 | ||||||||
\(847\) | 6.76552e11 | 0.0451675 | ||||||||
\(848\) | −1.59932e13 | −1.06207 | ||||||||
\(849\) | 2.51540e13 | 1.66158 | ||||||||
\(850\) | −5.46251e12 | −0.358928 | ||||||||
\(851\) | −2.54507e13 | −1.66348 | ||||||||
\(852\) | 3.71064e12 | 0.241252 | ||||||||
\(853\) | 2.43508e13 | 1.57486 | 0.787430 | − | 0.616404i | \(-0.211411\pi\) | ||||
0.787430 | + | 0.616404i | \(0.211411\pi\) | |||||||
\(854\) | −7.37198e11 | −0.0474268 | ||||||||
\(855\) | 1.62095e12 | 0.103734 | ||||||||
\(856\) | −8.33096e11 | −0.0530351 | ||||||||
\(857\) | 2.45424e13 | 1.55419 | 0.777095 | − | 0.629383i | \(-0.216692\pi\) | ||||
0.777095 | + | 0.629383i | \(0.216692\pi\) | |||||||
\(858\) | 7.72726e11 | 0.0486780 | ||||||||
\(859\) | −2.12084e13 | −1.32904 | −0.664521 | − | 0.747270i | \(-0.731364\pi\) | ||||
−0.664521 | + | 0.747270i | \(0.731364\pi\) | |||||||
\(860\) | −9.91692e11 | −0.0618207 | ||||||||
\(861\) | −8.93630e11 | −0.0554170 | ||||||||
\(862\) | −2.18244e13 | −1.34635 | ||||||||
\(863\) | 1.64190e13 | 1.00762 | 0.503811 | − | 0.863814i | \(-0.331931\pi\) | ||||
0.503811 | + | 0.863814i | \(0.331931\pi\) | |||||||
\(864\) | 1.47740e13 | 0.901960 | ||||||||
\(865\) | 9.42042e11 | 0.0572134 | ||||||||
\(866\) | 1.35725e13 | 0.820027 | ||||||||
\(867\) | 1.18449e12 | 0.0711946 | ||||||||
\(868\) | 7.80173e10 | 0.00466500 | ||||||||
\(869\) | 1.63279e12 | 0.0971273 | ||||||||
\(870\) | −3.41563e12 | −0.202132 | ||||||||
\(871\) | 7.84015e11 | 0.0461575 | ||||||||
\(872\) | 8.12224e12 | 0.475720 | ||||||||
\(873\) | 1.03499e13 | 0.603078 | ||||||||
\(874\) | −3.82600e13 | −2.21791 | ||||||||
\(875\) | 2.69394e11 | 0.0155364 | ||||||||
\(876\) | 3.17490e13 | 1.82163 | ||||||||
\(877\) | 7.74986e12 | 0.442380 | 0.221190 | − | 0.975231i | \(-0.429006\pi\) | ||||
0.221190 | + | 0.975231i | \(0.429006\pi\) | |||||||
\(878\) | −4.84738e12 | −0.275285 | ||||||||
\(879\) | 1.99001e13 | 1.12436 | ||||||||
\(880\) | 7.08207e11 | 0.0398096 | ||||||||
\(881\) | 1.47006e12 | 0.0822135 | 0.0411068 | − | 0.999155i | \(-0.486912\pi\) | ||||
0.0411068 | + | 0.999155i | \(0.486912\pi\) | |||||||
\(882\) | −1.25702e13 | −0.699412 | ||||||||
\(883\) | −2.27229e13 | −1.25788 | −0.628941 | − | 0.777453i | \(-0.716511\pi\) | ||||
−0.628941 | + | 0.777453i | \(0.716511\pi\) | |||||||
\(884\) | −3.39257e11 | −0.0186850 | ||||||||
\(885\) | 1.99547e12 | 0.109345 | ||||||||
\(886\) | 3.98273e13 | 2.17135 | ||||||||
\(887\) | −2.54193e13 | −1.37882 | −0.689411 | − | 0.724371i | \(-0.742130\pi\) | ||||
−0.689411 | + | 0.724371i | \(0.742130\pi\) | |||||||
\(888\) | 1.70247e13 | 0.918802 | ||||||||
\(889\) | 5.60965e11 | 0.0301216 | ||||||||
\(890\) | 2.64703e12 | 0.141418 | ||||||||
\(891\) | 1.03861e13 | 0.552079 | ||||||||
\(892\) | −8.67828e11 | −0.0458978 | ||||||||
\(893\) | 2.90294e13 | 1.52759 | ||||||||
\(894\) | −1.25941e13 | −0.659398 | ||||||||
\(895\) | −1.27106e12 | −0.0662157 | ||||||||
\(896\) | 8.74385e11 | 0.0453228 | ||||||||
\(897\) | 1.30144e12 | 0.0671209 | ||||||||
\(898\) | 3.08968e13 | 1.58551 | ||||||||
\(899\) | 1.00817e12 | 0.0514771 | ||||||||
\(900\) | −1.14666e13 | −0.582563 | ||||||||
\(901\) | 7.90735e12 | 0.399733 | ||||||||
\(902\) | −1.08198e13 | −0.544240 | ||||||||
\(903\) | 4.69886e11 | 0.0235178 | ||||||||
\(904\) | −1.24371e13 | −0.619387 | ||||||||
\(905\) | 1.92848e12 | 0.0955646 | ||||||||
\(906\) | 2.93067e13 | 1.44508 | ||||||||
\(907\) | 2.33059e13 | 1.14349 | 0.571745 | − | 0.820431i | \(-0.306267\pi\) | ||||
0.571745 | + | 0.820431i | \(0.306267\pi\) | |||||||
\(908\) | −4.12317e13 | −2.01300 | ||||||||
\(909\) | −1.45147e13 | −0.705131 | ||||||||
\(910\) | 1.47633e10 | 0.000713671 0 | ||||||||
\(911\) | −6.19635e12 | −0.298060 | −0.149030 | − | 0.988833i | \(-0.547615\pi\) | ||||
−0.149030 | + | 0.988833i | \(0.547615\pi\) | |||||||
\(912\) | −2.60218e13 | −1.24555 | ||||||||
\(913\) | 3.72724e11 | 0.0177529 | ||||||||
\(914\) | −9.87092e11 | −0.0467842 | ||||||||
\(915\) | 2.00702e12 | 0.0946580 | ||||||||
\(916\) | 2.20231e13 | 1.03359 | ||||||||
\(917\) | −5.49866e11 | −0.0256800 | ||||||||
\(918\) | −5.10198e12 | −0.237108 | ||||||||
\(919\) | −2.57602e13 | −1.19132 | −0.595661 | − | 0.803236i | \(-0.703110\pi\) | ||||
−0.595661 | + | 0.803236i | \(0.703110\pi\) | |||||||
\(920\) | −1.17313e12 | −0.0539886 | ||||||||
\(921\) | −7.35460e12 | −0.336815 | ||||||||
\(922\) | −1.13854e13 | −0.518869 | ||||||||
\(923\) | −2.07255e11 | −0.00939932 | ||||||||
\(924\) | 8.50773e11 | 0.0383963 | ||||||||
\(925\) | −3.94682e13 | −1.77260 | ||||||||
\(926\) | 3.29628e13 | 1.47324 | ||||||||
\(927\) | −8.94768e12 | −0.397971 | ||||||||
\(928\) | 2.49122e13 | 1.10267 | ||||||||
\(929\) | 1.87578e13 | 0.826251 | 0.413126 | − | 0.910674i | \(-0.364437\pi\) | ||||
0.413126 | + | 0.910674i | \(0.364437\pi\) | |||||||
\(930\) | −3.78575e11 | −0.0165951 | ||||||||
\(931\) | −3.64929e13 | −1.59197 | ||||||||
\(932\) | −2.13080e13 | −0.925064 | ||||||||
\(933\) | 3.04227e13 | 1.31441 | ||||||||
\(934\) | −2.46361e13 | −1.05928 | ||||||||
\(935\) | −3.50152e11 | −0.0149832 | ||||||||
\(936\) | −2.76262e11 | −0.0117647 | ||||||||
\(937\) | 5.64054e12 | 0.239052 | 0.119526 | − | 0.992831i | \(-0.461863\pi\) | ||||
0.119526 | + | 0.992831i | \(0.461863\pi\) | |||||||
\(938\) | 1.53853e12 | 0.0648923 | ||||||||
\(939\) | −1.07006e13 | −0.449172 | ||||||||
\(940\) | 4.08962e12 | 0.170847 | ||||||||
\(941\) | 2.26889e13 | 0.943321 | 0.471660 | − | 0.881780i | \(-0.343655\pi\) | ||||
0.471660 | + | 0.881780i | \(0.343655\pi\) | |||||||
\(942\) | −6.64511e13 | −2.74962 | ||||||||
\(943\) | −1.82229e13 | −0.750439 | ||||||||
\(944\) | −1.01655e13 | −0.416636 | ||||||||
\(945\) | 1.24566e11 | 0.00508110 | ||||||||
\(946\) | 5.68924e12 | 0.230964 | ||||||||
\(947\) | −1.49881e13 | −0.605582 | −0.302791 | − | 0.953057i | \(-0.597918\pi\) | ||||
−0.302791 | + | 0.953057i | \(0.597918\pi\) | |||||||
\(948\) | −8.45186e12 | −0.339871 | ||||||||
\(949\) | −1.77331e12 | −0.0709719 | ||||||||
\(950\) | −5.93326e13 | −2.36340 | ||||||||
\(951\) | 7.22218e12 | 0.286323 | ||||||||
\(952\) | −1.44900e11 | −0.00571744 | ||||||||
\(953\) | −4.04272e13 | −1.58765 | −0.793827 | − | 0.608143i | \(-0.791915\pi\) | ||||
−0.793827 | + | 0.608143i | \(0.791915\pi\) | |||||||
\(954\) | 2.95846e13 | 1.15637 | ||||||||
\(955\) | 3.38377e12 | 0.131640 | ||||||||
\(956\) | 2.78192e13 | 1.07717 | ||||||||
\(957\) | 1.09940e13 | 0.423693 | ||||||||
\(958\) | 5.36259e13 | 2.05698 | ||||||||
\(959\) | 2.66934e12 | 0.101911 | ||||||||
\(960\) | −6.48671e12 | −0.246493 | ||||||||
\(961\) | −2.63279e13 | −0.995774 | ||||||||
\(962\) | −4.36895e12 | −0.164471 | ||||||||
\(963\) | −1.56689e12 | −0.0587109 | ||||||||
\(964\) | −4.22973e13 | −1.57749 | ||||||||
\(965\) | −1.15761e12 | −0.0429723 | ||||||||
\(966\) | 2.55391e12 | 0.0943644 | ||||||||
\(967\) | −7.15269e12 | −0.263057 | −0.131529 | − | 0.991312i | \(-0.541989\pi\) | ||||
−0.131529 | + | 0.991312i | \(0.541989\pi\) | |||||||
\(968\) | −9.22875e12 | −0.337834 | ||||||||
\(969\) | 1.28657e13 | 0.468788 | ||||||||
\(970\) | 7.54470e12 | 0.273633 | ||||||||
\(971\) | 2.34500e13 | 0.846556 | 0.423278 | − | 0.906000i | \(-0.360879\pi\) | ||||
0.423278 | + | 0.906000i | \(0.360879\pi\) | |||||||
\(972\) | −3.07223e13 | −1.10396 | ||||||||
\(973\) | −1.77271e12 | −0.0634060 | ||||||||
\(974\) | 5.07959e13 | 1.80848 | ||||||||
\(975\) | 2.01824e12 | 0.0715240 | ||||||||
\(976\) | −1.02244e13 | −0.360673 | ||||||||
\(977\) | 3.75171e13 | 1.31736 | 0.658678 | − | 0.752425i | \(-0.271116\pi\) | ||||
0.658678 | + | 0.752425i | \(0.271116\pi\) | |||||||
\(978\) | 9.19834e13 | 3.21503 | ||||||||
\(979\) | −8.52006e12 | −0.296429 | ||||||||
\(980\) | −5.14106e12 | −0.178047 | ||||||||
\(981\) | 1.52763e13 | 0.526633 | ||||||||
\(982\) | 3.31708e13 | 1.13829 | ||||||||
\(983\) | 5.31777e13 | 1.81651 | 0.908256 | − | 0.418414i | \(-0.137414\pi\) | ||||
0.908256 | + | 0.418414i | \(0.137414\pi\) | |||||||
\(984\) | 1.21899e13 | 0.414497 | ||||||||
\(985\) | −3.14968e12 | −0.106611 | ||||||||
\(986\) | −8.60304e12 | −0.289872 | ||||||||
\(987\) | −1.93775e12 | −0.0649936 | ||||||||
\(988\) | −3.68494e12 | −0.123034 | ||||||||
\(989\) | 9.58193e12 | 0.318471 | ||||||||
\(990\) | −1.31006e12 | −0.0433444 | ||||||||
\(991\) | 3.41823e13 | 1.12582 | 0.562912 | − | 0.826517i | \(-0.309681\pi\) | ||||
0.562912 | + | 0.826517i | \(0.309681\pi\) | |||||||
\(992\) | 2.76117e12 | 0.0905297 | ||||||||
\(993\) | −2.30994e13 | −0.753926 | ||||||||
\(994\) | −4.06711e11 | −0.0132144 | ||||||||
\(995\) | −8.55794e12 | −0.276799 | ||||||||
\(996\) | −1.92934e12 | −0.0621216 | ||||||||
\(997\) | 4.83269e13 | 1.54903 | 0.774517 | − | 0.632553i | \(-0.217993\pi\) | ||||
0.774517 | + | 0.632553i | \(0.217993\pi\) | |||||||
\(998\) | 4.15375e13 | 1.32542 | ||||||||
\(999\) | −3.68633e13 | −1.17098 |
(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 | 17.10.a.b.1.6 | ✓ | 7 | |
3.2 | odd | 2 | 153.10.a.f.1.2 | 7 | |||
4.3 | odd | 2 | 272.10.a.g.1.2 | 7 | |||
17.16 | even | 2 | 289.10.a.b.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.b.1.6 | ✓ | 7 | 1.1 | even | 1 | trivial | |
153.10.a.f.1.2 | 7 | 3.2 | odd | 2 | |||
272.10.a.g.1.2 | 7 | 4.3 | odd | 2 | |||
289.10.a.b.1.6 | 7 | 17.16 | even | 2 |