Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,26,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(39.5996779952\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 148387471 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(12181.4\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 1.24712e6 | 1.35486 | 0.677428 | − | 0.735589i | \(-0.263095\pi\) | ||||
0.677428 | + | 0.735589i | \(0.263095\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | −2.44141e8 | −0.447214 | ||||||||
\(6\) | −5.10821e9 | −0.958027 | ||||||||
\(7\) | 3.92781e10 | 1.07257 | 0.536284 | − | 0.844038i | \(-0.319828\pi\) | ||||
0.536284 | + | 0.844038i | \(0.319828\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 7.08023e11 | 0.835633 | ||||||||
\(10\) | 1.00000e12 | 0.316228 | ||||||||
\(11\) | −1.50696e13 | −1.44775 | −0.723876 | − | 0.689930i | \(-0.757641\pi\) | ||||
−0.723876 | + | 0.689930i | \(0.757641\pi\) | |||||||
\(12\) | 2.09232e13 | 0.677428 | ||||||||
\(13\) | −1.45379e14 | −1.73065 | −0.865324 | − | 0.501213i | \(-0.832887\pi\) | ||||
−0.865324 | + | 0.501213i | \(0.832887\pi\) | |||||||
\(14\) | −1.60883e14 | −0.758419 | ||||||||
\(15\) | −3.04473e14 | −0.605910 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 1.30302e15 | 0.542426 | 0.271213 | − | 0.962519i | \(-0.412575\pi\) | ||||
0.271213 | + | 0.962519i | \(0.412575\pi\) | |||||||
\(18\) | −2.90006e15 | −0.590882 | ||||||||
\(19\) | −9.75151e15 | −1.01077 | −0.505385 | − | 0.862894i | \(-0.668649\pi\) | ||||
−0.505385 | + | 0.862894i | \(0.668649\pi\) | |||||||
\(20\) | −4.09600e15 | −0.223607 | ||||||||
\(21\) | 4.89845e16 | 1.45317 | ||||||||
\(22\) | 6.17252e16 | 1.02372 | ||||||||
\(23\) | 1.00704e17 | 0.958180 | 0.479090 | − | 0.877766i | \(-0.340967\pi\) | ||||
0.479090 | + | 0.877766i | \(0.340967\pi\) | |||||||
\(24\) | −8.57015e16 | −0.479014 | ||||||||
\(25\) | 5.96046e16 | 0.200000 | ||||||||
\(26\) | 5.95471e17 | 1.22375 | ||||||||
\(27\) | −1.73682e17 | −0.222693 | ||||||||
\(28\) | 6.58976e17 | 0.536284 | ||||||||
\(29\) | −1.41726e18 | −0.743834 | −0.371917 | − | 0.928266i | \(-0.621299\pi\) | ||||
−0.371917 | + | 0.928266i | \(0.621299\pi\) | |||||||
\(30\) | 1.24712e18 | 0.428443 | ||||||||
\(31\) | −3.30375e18 | −0.753332 | −0.376666 | − | 0.926349i | \(-0.622930\pi\) | ||||
−0.376666 | + | 0.926349i | \(0.622930\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | −1.87937e19 | −1.96149 | ||||||||
\(34\) | −5.33718e18 | −0.383553 | ||||||||
\(35\) | −9.58937e18 | −0.479667 | ||||||||
\(36\) | 1.18786e19 | 0.417817 | ||||||||
\(37\) | 6.55066e19 | 1.63593 | 0.817963 | − | 0.575271i | \(-0.195103\pi\) | ||||
0.817963 | + | 0.575271i | \(0.195103\pi\) | |||||||
\(38\) | 3.99422e19 | 0.714722 | ||||||||
\(39\) | −1.81305e20 | −2.34478 | ||||||||
\(40\) | 1.67772e19 | 0.158114 | ||||||||
\(41\) | −9.42027e19 | −0.652026 | −0.326013 | − | 0.945365i | \(-0.605705\pi\) | ||||
−0.326013 | + | 0.945365i | \(0.605705\pi\) | |||||||
\(42\) | −2.00640e20 | −1.02755 | ||||||||
\(43\) | 1.20866e20 | 0.461263 | 0.230632 | − | 0.973041i | \(-0.425921\pi\) | ||||
0.230632 | + | 0.973041i | \(0.425921\pi\) | |||||||
\(44\) | −2.52827e20 | −0.723876 | ||||||||
\(45\) | −1.72857e20 | −0.373707 | ||||||||
\(46\) | −4.12482e20 | −0.677535 | ||||||||
\(47\) | −8.86966e20 | −1.11348 | −0.556742 | − | 0.830686i | \(-0.687949\pi\) | ||||
−0.556742 | + | 0.830686i | \(0.687949\pi\) | |||||||
\(48\) | 3.51033e20 | 0.338714 | ||||||||
\(49\) | 2.01697e20 | 0.150400 | ||||||||
\(50\) | −2.44141e20 | −0.141421 | ||||||||
\(51\) | 1.62503e21 | 0.734909 | ||||||||
\(52\) | −2.43905e21 | −0.865324 | ||||||||
\(53\) | −6.79454e21 | −1.89982 | −0.949908 | − | 0.312530i | \(-0.898824\pi\) | ||||
−0.949908 | + | 0.312530i | \(0.898824\pi\) | |||||||
\(54\) | 7.11400e20 | 0.157468 | ||||||||
\(55\) | 3.67911e21 | 0.647454 | ||||||||
\(56\) | −2.69917e21 | −0.379210 | ||||||||
\(57\) | −1.21613e22 | −1.36945 | ||||||||
\(58\) | 5.80511e21 | 0.525970 | ||||||||
\(59\) | −1.11112e22 | −0.813039 | −0.406520 | − | 0.913642i | \(-0.633258\pi\) | ||||
−0.406520 | + | 0.913642i | \(0.633258\pi\) | |||||||
\(60\) | −5.10821e21 | −0.302955 | ||||||||
\(61\) | −3.14899e22 | −1.51897 | −0.759483 | − | 0.650527i | \(-0.774548\pi\) | ||||
−0.759483 | + | 0.650527i | \(0.774548\pi\) | |||||||
\(62\) | 1.35322e22 | 0.532686 | ||||||||
\(63\) | 2.78098e22 | 0.896273 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 3.54928e22 | 0.773969 | ||||||||
\(66\) | 7.69788e22 | 1.38699 | ||||||||
\(67\) | 4.52478e22 | 0.675558 | 0.337779 | − | 0.941225i | \(-0.390324\pi\) | ||||
0.337779 | + | 0.941225i | \(0.390324\pi\) | |||||||
\(68\) | 2.18611e22 | 0.271213 | ||||||||
\(69\) | 1.25590e23 | 1.29819 | ||||||||
\(70\) | 3.92781e22 | 0.339176 | ||||||||
\(71\) | −3.31126e22 | −0.239477 | −0.119739 | − | 0.992805i | \(-0.538206\pi\) | ||||
−0.119739 | + | 0.992805i | \(0.538206\pi\) | |||||||
\(72\) | −4.86549e22 | −0.295441 | ||||||||
\(73\) | 3.04253e23 | 1.55489 | 0.777445 | − | 0.628952i | \(-0.216516\pi\) | ||||
0.777445 | + | 0.628952i | \(0.216516\pi\) | |||||||
\(74\) | −2.68315e23 | −1.15677 | ||||||||
\(75\) | 7.43342e22 | 0.270971 | ||||||||
\(76\) | −1.63603e23 | −0.505385 | ||||||||
\(77\) | −5.91906e23 | −1.55281 | ||||||||
\(78\) | 7.42625e23 | 1.65801 | ||||||||
\(79\) | −1.45524e23 | −0.277075 | −0.138537 | − | 0.990357i | \(-0.544240\pi\) | ||||
−0.138537 | + | 0.990357i | \(0.544240\pi\) | |||||||
\(80\) | −6.87195e22 | −0.111803 | ||||||||
\(81\) | −8.16501e23 | −1.13735 | ||||||||
\(82\) | 3.85854e23 | 0.461052 | ||||||||
\(83\) | 8.80567e23 | 0.904245 | 0.452122 | − | 0.891956i | \(-0.350667\pi\) | ||||
0.452122 | + | 0.891956i | \(0.350667\pi\) | |||||||
\(84\) | 8.21823e23 | 0.726587 | ||||||||
\(85\) | −3.18121e23 | −0.242580 | ||||||||
\(86\) | −4.95068e23 | −0.326162 | ||||||||
\(87\) | −1.76750e24 | −1.00779 | ||||||||
\(88\) | 1.03558e24 | 0.511858 | ||||||||
\(89\) | −1.79771e23 | −0.0771514 | −0.0385757 | − | 0.999256i | \(-0.512282\pi\) | ||||
−0.0385757 | + | 0.999256i | \(0.512282\pi\) | |||||||
\(90\) | 7.08023e23 | 0.264250 | ||||||||
\(91\) | −5.71019e24 | −1.85624 | ||||||||
\(92\) | 1.68953e24 | 0.479090 | ||||||||
\(93\) | −4.12018e24 | −1.02066 | ||||||||
\(94\) | 3.63301e24 | 0.787352 | ||||||||
\(95\) | 2.38074e24 | 0.452030 | ||||||||
\(96\) | −1.43783e24 | −0.239507 | ||||||||
\(97\) | −7.02806e24 | −1.02846 | −0.514232 | − | 0.857651i | \(-0.671923\pi\) | ||||
−0.514232 | + | 0.857651i | \(0.671923\pi\) | |||||||
\(98\) | −8.26151e23 | −0.106349 | ||||||||
\(99\) | −1.06696e25 | −1.20979 | ||||||||
\(100\) | 1.00000e24 | 0.100000 | ||||||||
\(101\) | −6.59850e24 | −0.582677 | −0.291339 | − | 0.956620i | \(-0.594101\pi\) | ||||
−0.291339 | + | 0.956620i | \(0.594101\pi\) | |||||||
\(102\) | −6.65611e24 | −0.519659 | ||||||||
\(103\) | 2.14556e25 | 1.48278 | 0.741389 | − | 0.671075i | \(-0.234167\pi\) | ||||
0.741389 | + | 0.671075i | \(0.234167\pi\) | |||||||
\(104\) | 9.99035e24 | 0.611877 | ||||||||
\(105\) | −1.19591e25 | −0.649879 | ||||||||
\(106\) | 2.78304e25 | 1.34337 | ||||||||
\(107\) | 2.29745e24 | 0.0986164 | 0.0493082 | − | 0.998784i | \(-0.484298\pi\) | ||||
0.0493082 | + | 0.998784i | \(0.484298\pi\) | |||||||
\(108\) | −2.91389e24 | −0.111347 | ||||||||
\(109\) | 2.46259e25 | 0.838611 | 0.419305 | − | 0.907845i | \(-0.362274\pi\) | ||||
0.419305 | + | 0.907845i | \(0.362274\pi\) | |||||||
\(110\) | −1.50696e25 | −0.457819 | ||||||||
\(111\) | 8.16947e25 | 2.21644 | ||||||||
\(112\) | 1.10558e25 | 0.268142 | ||||||||
\(113\) | −4.71863e25 | −1.02408 | −0.512042 | − | 0.858960i | \(-0.671111\pi\) | ||||
−0.512042 | + | 0.858960i | \(0.671111\pi\) | |||||||
\(114\) | 4.98128e25 | 0.968345 | ||||||||
\(115\) | −2.45858e25 | −0.428511 | ||||||||
\(116\) | −2.37777e25 | −0.371917 | ||||||||
\(117\) | −1.02931e26 | −1.44619 | ||||||||
\(118\) | 4.55116e25 | 0.574906 | ||||||||
\(119\) | 5.11802e25 | 0.581789 | ||||||||
\(120\) | 2.09232e25 | 0.214221 | ||||||||
\(121\) | 1.18747e26 | 1.09599 | ||||||||
\(122\) | 1.28982e26 | 1.07407 | ||||||||
\(123\) | −1.17482e26 | −0.883401 | ||||||||
\(124\) | −5.54278e25 | −0.376666 | ||||||||
\(125\) | −1.45519e25 | −0.0894427 | ||||||||
\(126\) | −1.13909e26 | −0.633761 | ||||||||
\(127\) | −1.28089e26 | −0.645605 | −0.322802 | − | 0.946466i | \(-0.604625\pi\) | ||||
−0.322802 | + | 0.946466i | \(0.604625\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 1.50735e26 | 0.624945 | ||||||||
\(130\) | −1.45379e26 | −0.547279 | ||||||||
\(131\) | 1.65371e26 | 0.565675 | 0.282838 | − | 0.959168i | \(-0.408724\pi\) | ||||
0.282838 | + | 0.959168i | \(0.408724\pi\) | |||||||
\(132\) | −3.15305e26 | −0.980747 | ||||||||
\(133\) | −3.83020e26 | −1.08412 | ||||||||
\(134\) | −1.85335e26 | −0.477692 | ||||||||
\(135\) | 4.24027e25 | 0.0995914 | ||||||||
\(136\) | −8.95431e25 | −0.191777 | ||||||||
\(137\) | −3.20644e26 | −0.626637 | −0.313319 | − | 0.949648i | \(-0.601441\pi\) | ||||
−0.313319 | + | 0.949648i | \(0.601441\pi\) | |||||||
\(138\) | −5.14415e26 | −0.917962 | ||||||||
\(139\) | 5.33177e26 | 0.869333 | 0.434666 | − | 0.900592i | \(-0.356866\pi\) | ||||
0.434666 | + | 0.900592i | \(0.356866\pi\) | |||||||
\(140\) | −1.60883e26 | −0.239833 | ||||||||
\(141\) | −1.10615e27 | −1.50861 | ||||||||
\(142\) | 1.35629e26 | 0.169336 | ||||||||
\(143\) | 2.19080e27 | 2.50555 | ||||||||
\(144\) | 1.99291e26 | 0.208908 | ||||||||
\(145\) | 3.46012e26 | 0.332653 | ||||||||
\(146\) | −1.24622e27 | −1.09947 | ||||||||
\(147\) | 2.51541e26 | 0.203771 | ||||||||
\(148\) | 1.09902e27 | 0.817963 | ||||||||
\(149\) | 5.79851e26 | 0.396724 | 0.198362 | − | 0.980129i | \(-0.436438\pi\) | ||||
0.198362 | + | 0.980129i | \(0.436438\pi\) | |||||||
\(150\) | −3.04473e26 | −0.191605 | ||||||||
\(151\) | 2.88738e27 | 1.67222 | 0.836109 | − | 0.548564i | \(-0.184825\pi\) | ||||
0.836109 | + | 0.548564i | \(0.184825\pi\) | |||||||
\(152\) | 6.70119e26 | 0.357361 | ||||||||
\(153\) | 9.22570e26 | 0.453269 | ||||||||
\(154\) | 2.42445e27 | 1.09800 | ||||||||
\(155\) | 8.06580e26 | 0.336900 | ||||||||
\(156\) | −3.04179e27 | −1.17239 | ||||||||
\(157\) | −4.99584e27 | −1.77772 | −0.888859 | − | 0.458181i | \(-0.848501\pi\) | ||||
−0.888859 | + | 0.458181i | \(0.848501\pi\) | |||||||
\(158\) | 5.96067e26 | 0.195921 | ||||||||
\(159\) | −8.47361e27 | −2.57398 | ||||||||
\(160\) | 2.81475e26 | 0.0790569 | ||||||||
\(161\) | 3.95544e27 | 1.02771 | ||||||||
\(162\) | 3.34439e27 | 0.804228 | ||||||||
\(163\) | 9.78636e25 | 0.0217909 | 0.0108955 | − | 0.999941i | \(-0.496532\pi\) | ||||
0.0108955 | + | 0.999941i | \(0.496532\pi\) | |||||||
\(164\) | −1.58046e27 | −0.326013 | ||||||||
\(165\) | 4.58830e27 | 0.877207 | ||||||||
\(166\) | −3.60680e27 | −0.639398 | ||||||||
\(167\) | 8.79974e27 | 1.44715 | 0.723576 | − | 0.690245i | \(-0.242497\pi\) | ||||
0.723576 | + | 0.690245i | \(0.242497\pi\) | |||||||
\(168\) | −3.36619e27 | −0.513774 | ||||||||
\(169\) | 1.40786e28 | 1.99514 | ||||||||
\(170\) | 1.30302e27 | 0.171530 | ||||||||
\(171\) | −6.90429e27 | −0.844632 | ||||||||
\(172\) | 2.02780e27 | 0.230632 | ||||||||
\(173\) | −1.48916e28 | −1.57530 | −0.787651 | − | 0.616122i | \(-0.788703\pi\) | ||||
−0.787651 | + | 0.616122i | \(0.788703\pi\) | |||||||
\(174\) | 7.23968e27 | 0.712613 | ||||||||
\(175\) | 2.34115e27 | 0.214513 | ||||||||
\(176\) | −4.24173e27 | −0.361938 | ||||||||
\(177\) | −1.38570e28 | −1.10155 | ||||||||
\(178\) | 7.36341e26 | 0.0545543 | ||||||||
\(179\) | −1.83964e28 | −1.27078 | −0.635390 | − | 0.772191i | \(-0.719161\pi\) | ||||
−0.635390 | + | 0.772191i | \(0.719161\pi\) | |||||||
\(180\) | −2.90006e27 | −0.186853 | ||||||||
\(181\) | 1.98192e28 | 1.19153 | 0.595764 | − | 0.803160i | \(-0.296849\pi\) | ||||
0.595764 | + | 0.803160i | \(0.296849\pi\) | |||||||
\(182\) | 2.33889e28 | 1.31256 | ||||||||
\(183\) | −3.92717e28 | −2.05798 | ||||||||
\(184\) | −6.92030e27 | −0.338768 | ||||||||
\(185\) | −1.59928e28 | −0.731608 | ||||||||
\(186\) | 1.68763e28 | 0.721713 | ||||||||
\(187\) | −1.96361e28 | −0.785299 | ||||||||
\(188\) | −1.48808e28 | −0.556742 | ||||||||
\(189\) | −6.82188e27 | −0.238853 | ||||||||
\(190\) | −9.75151e27 | −0.319633 | ||||||||
\(191\) | −3.54565e28 | −1.08837 | −0.544187 | − | 0.838964i | \(-0.683162\pi\) | ||||
−0.544187 | + | 0.838964i | \(0.683162\pi\) | |||||||
\(192\) | 5.88936e27 | 0.169357 | ||||||||
\(193\) | −1.29750e28 | −0.349657 | −0.174829 | − | 0.984599i | \(-0.555937\pi\) | ||||
−0.174829 | + | 0.984599i | \(0.555937\pi\) | |||||||
\(194\) | 2.87869e28 | 0.727234 | ||||||||
\(195\) | 4.42639e28 | 1.04862 | ||||||||
\(196\) | 3.38392e27 | 0.0752001 | ||||||||
\(197\) | 6.04380e28 | 1.26032 | 0.630162 | − | 0.776463i | \(-0.282988\pi\) | ||||
0.630162 | + | 0.776463i | \(0.282988\pi\) | |||||||
\(198\) | 4.37029e28 | 0.855451 | ||||||||
\(199\) | 5.51931e28 | 1.01443 | 0.507215 | − | 0.861820i | \(-0.330675\pi\) | ||||
0.507215 | + | 0.861820i | \(0.330675\pi\) | |||||||
\(200\) | −4.09600e27 | −0.0707107 | ||||||||
\(201\) | 5.64295e28 | 0.915283 | ||||||||
\(202\) | 2.70275e28 | 0.412015 | ||||||||
\(203\) | −5.56674e28 | −0.797812 | ||||||||
\(204\) | 2.72634e28 | 0.367455 | ||||||||
\(205\) | 2.29987e28 | 0.291595 | ||||||||
\(206\) | −8.78823e28 | −1.04848 | ||||||||
\(207\) | 7.13004e28 | 0.800687 | ||||||||
\(208\) | −4.09205e28 | −0.432662 | ||||||||
\(209\) | 1.46952e29 | 1.46334 | ||||||||
\(210\) | 4.89845e28 | 0.459534 | ||||||||
\(211\) | −7.38048e28 | −0.652460 | −0.326230 | − | 0.945290i | \(-0.605778\pi\) | ||||
−0.326230 | + | 0.945290i | \(0.605778\pi\) | |||||||
\(212\) | −1.13993e29 | −0.949908 | ||||||||
\(213\) | −4.12955e28 | −0.324457 | ||||||||
\(214\) | −9.41036e27 | −0.0697323 | ||||||||
\(215\) | −2.95083e28 | −0.206283 | ||||||||
\(216\) | 1.19353e28 | 0.0787339 | ||||||||
\(217\) | −1.29765e29 | −0.807999 | ||||||||
\(218\) | −1.00868e29 | −0.592987 | ||||||||
\(219\) | 3.79441e29 | 2.10665 | ||||||||
\(220\) | 6.17252e28 | 0.323727 | ||||||||
\(221\) | −1.89432e29 | −0.938749 | ||||||||
\(222\) | −3.34621e29 | −1.56726 | ||||||||
\(223\) | 3.22437e29 | 1.42769 | 0.713846 | − | 0.700303i | \(-0.246952\pi\) | ||||
0.713846 | + | 0.700303i | \(0.246952\pi\) | |||||||
\(224\) | −4.52845e28 | −0.189605 | ||||||||
\(225\) | 4.22014e28 | 0.167127 | ||||||||
\(226\) | 1.93275e29 | 0.724137 | ||||||||
\(227\) | −4.50494e29 | −1.59722 | −0.798611 | − | 0.601847i | \(-0.794432\pi\) | ||||
−0.798611 | + | 0.601847i | \(0.794432\pi\) | |||||||
\(228\) | −2.04033e29 | −0.684723 | ||||||||
\(229\) | −3.03906e28 | −0.0965596 | −0.0482798 | − | 0.998834i | \(-0.515374\pi\) | ||||
−0.0482798 | + | 0.998834i | \(0.515374\pi\) | |||||||
\(230\) | 1.00704e29 | 0.303003 | ||||||||
\(231\) | −7.38178e29 | −2.10383 | ||||||||
\(232\) | 9.73937e28 | 0.262985 | ||||||||
\(233\) | −1.03711e29 | −0.265386 | −0.132693 | − | 0.991157i | \(-0.542362\pi\) | ||||
−0.132693 | + | 0.991157i | \(0.542362\pi\) | |||||||
\(234\) | 4.21607e29 | 1.02261 | ||||||||
\(235\) | 2.16544e29 | 0.497965 | ||||||||
\(236\) | −1.86415e29 | −0.406520 | ||||||||
\(237\) | −1.81486e29 | −0.375396 | ||||||||
\(238\) | −2.09634e29 | −0.411387 | ||||||||
\(239\) | 8.96475e29 | 1.66942 | 0.834708 | − | 0.550693i | \(-0.185636\pi\) | ||||
0.834708 | + | 0.550693i | \(0.185636\pi\) | |||||||
\(240\) | −8.57015e28 | −0.151477 | ||||||||
\(241\) | 1.66839e29 | 0.279952 | 0.139976 | − | 0.990155i | \(-0.455297\pi\) | ||||
0.139976 | + | 0.990155i | \(0.455297\pi\) | |||||||
\(242\) | −4.86387e29 | −0.774979 | ||||||||
\(243\) | −8.71118e29 | −1.31825 | ||||||||
\(244\) | −5.28312e29 | −0.759483 | ||||||||
\(245\) | −4.92425e28 | −0.0672610 | ||||||||
\(246\) | 4.81207e29 | 0.624659 | ||||||||
\(247\) | 1.41766e30 | 1.74929 | ||||||||
\(248\) | 2.27032e29 | 0.266343 | ||||||||
\(249\) | 1.09817e30 | 1.22512 | ||||||||
\(250\) | 5.96046e28 | 0.0632456 | ||||||||
\(251\) | −1.77969e28 | −0.0179648 | −0.00898241 | − | 0.999960i | \(-0.502859\pi\) | ||||
−0.00898241 | + | 0.999960i | \(0.502859\pi\) | |||||||
\(252\) | 4.66570e29 | 0.448136 | ||||||||
\(253\) | −1.51757e30 | −1.38721 | ||||||||
\(254\) | 5.24654e29 | 0.456512 | ||||||||
\(255\) | −3.96735e29 | −0.328661 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 1.02153e30 | 0.767515 | 0.383758 | − | 0.923434i | \(-0.374630\pi\) | ||||
0.383758 | + | 0.923434i | \(0.374630\pi\) | |||||||
\(258\) | −6.17409e29 | −0.441903 | ||||||||
\(259\) | 2.57297e30 | 1.75464 | ||||||||
\(260\) | 5.95471e29 | 0.386985 | ||||||||
\(261\) | −1.00346e30 | −0.621572 | ||||||||
\(262\) | −6.77358e29 | −0.399993 | ||||||||
\(263\) | −2.39313e30 | −1.34747 | −0.673735 | − | 0.738973i | \(-0.735311\pi\) | ||||
−0.673735 | + | 0.738973i | \(0.735311\pi\) | |||||||
\(264\) | 1.29149e30 | 0.693493 | ||||||||
\(265\) | 1.65882e30 | 0.849624 | ||||||||
\(266\) | 1.56885e30 | 0.766587 | ||||||||
\(267\) | −2.24196e29 | −0.104529 | ||||||||
\(268\) | 7.59132e29 | 0.337779 | ||||||||
\(269\) | 7.43966e29 | 0.315973 | 0.157986 | − | 0.987441i | \(-0.449500\pi\) | ||||
0.157986 | + | 0.987441i | \(0.449500\pi\) | |||||||
\(270\) | −1.73682e29 | −0.0704217 | ||||||||
\(271\) | −2.89456e30 | −1.12064 | −0.560319 | − | 0.828277i | \(-0.689322\pi\) | ||||
−0.560319 | + | 0.828277i | \(0.689322\pi\) | |||||||
\(272\) | 3.66768e29 | 0.135607 | ||||||||
\(273\) | −7.12130e30 | −2.51493 | ||||||||
\(274\) | 1.31336e30 | 0.443099 | ||||||||
\(275\) | −8.98220e29 | −0.289550 | ||||||||
\(276\) | 2.10704e30 | 0.649097 | ||||||||
\(277\) | −2.46028e30 | −0.724415 | −0.362208 | − | 0.932097i | \(-0.617977\pi\) | ||||
−0.362208 | + | 0.932097i | \(0.617977\pi\) | |||||||
\(278\) | −2.18389e30 | −0.614711 | ||||||||
\(279\) | −2.33913e30 | −0.629509 | ||||||||
\(280\) | 6.58976e29 | 0.169588 | ||||||||
\(281\) | 5.42013e30 | 1.33408 | 0.667038 | − | 0.745024i | \(-0.267562\pi\) | ||||
0.667038 | + | 0.745024i | \(0.267562\pi\) | |||||||
\(282\) | 4.53081e30 | 1.06675 | ||||||||
\(283\) | 6.30761e30 | 1.42080 | 0.710402 | − | 0.703796i | \(-0.248513\pi\) | ||||
0.710402 | + | 0.703796i | \(0.248513\pi\) | |||||||
\(284\) | −5.55538e29 | −0.119739 | ||||||||
\(285\) | 2.96907e30 | 0.612435 | ||||||||
\(286\) | −8.97353e30 | −1.77169 | ||||||||
\(287\) | −3.70010e30 | −0.699342 | ||||||||
\(288\) | −8.16294e29 | −0.147720 | ||||||||
\(289\) | −4.07276e30 | −0.705774 | ||||||||
\(290\) | −1.41726e30 | −0.235221 | ||||||||
\(291\) | −8.76484e30 | −1.39342 | ||||||||
\(292\) | 5.10452e30 | 0.777445 | ||||||||
\(293\) | 9.79285e30 | 1.42910 | 0.714552 | − | 0.699582i | \(-0.246631\pi\) | ||||
0.714552 | + | 0.699582i | \(0.246631\pi\) | |||||||
\(294\) | −1.03031e30 | −0.144088 | ||||||||
\(295\) | 2.71270e30 | 0.363602 | ||||||||
\(296\) | −4.50158e30 | −0.578387 | ||||||||
\(297\) | 2.61732e30 | 0.322404 | ||||||||
\(298\) | −2.37507e30 | −0.280526 | ||||||||
\(299\) | −1.46402e31 | −1.65827 | ||||||||
\(300\) | 1.24712e30 | 0.135486 | ||||||||
\(301\) | 4.74739e30 | 0.494736 | ||||||||
\(302\) | −1.18267e31 | −1.18244 | ||||||||
\(303\) | −8.22913e30 | −0.789444 | ||||||||
\(304\) | −2.74481e30 | −0.252692 | ||||||||
\(305\) | 7.68796e30 | 0.679302 | ||||||||
\(306\) | −3.77885e30 | −0.320510 | ||||||||
\(307\) | −5.75594e30 | −0.468691 | −0.234345 | − | 0.972153i | \(-0.575295\pi\) | ||||
−0.234345 | + | 0.972153i | \(0.575295\pi\) | |||||||
\(308\) | −9.93053e30 | −0.776406 | ||||||||
\(309\) | 2.67578e31 | 2.00895 | ||||||||
\(310\) | −3.30375e30 | −0.238224 | ||||||||
\(311\) | 1.84953e31 | 1.28102 | 0.640510 | − | 0.767950i | \(-0.278723\pi\) | ||||
0.640510 | + | 0.767950i | \(0.278723\pi\) | |||||||
\(312\) | 1.24592e31 | 0.829004 | ||||||||
\(313\) | 2.39300e31 | 1.52982 | 0.764908 | − | 0.644140i | \(-0.222784\pi\) | ||||
0.764908 | + | 0.644140i | \(0.222784\pi\) | |||||||
\(314\) | 2.04630e31 | 1.25704 | ||||||||
\(315\) | −6.78949e30 | −0.400825 | ||||||||
\(316\) | −2.44149e30 | −0.138537 | ||||||||
\(317\) | −2.04161e30 | −0.111360 | −0.0556802 | − | 0.998449i | \(-0.517733\pi\) | ||||
−0.0556802 | + | 0.998449i | \(0.517733\pi\) | |||||||
\(318\) | 3.47079e31 | 1.82008 | ||||||||
\(319\) | 2.13577e31 | 1.07689 | ||||||||
\(320\) | −1.15292e30 | −0.0559017 | ||||||||
\(321\) | 2.86520e30 | 0.133611 | ||||||||
\(322\) | −1.62015e31 | −0.726702 | ||||||||
\(323\) | −1.27064e31 | −0.548268 | ||||||||
\(324\) | −1.36986e31 | −0.568675 | ||||||||
\(325\) | −8.66525e30 | −0.346130 | ||||||||
\(326\) | −4.00849e29 | −0.0154085 | ||||||||
\(327\) | 3.07114e31 | 1.13620 | ||||||||
\(328\) | 6.47356e30 | 0.230526 | ||||||||
\(329\) | −3.48383e31 | −1.19429 | ||||||||
\(330\) | −1.87937e31 | −0.620279 | ||||||||
\(331\) | −1.75414e31 | −0.557459 | −0.278730 | − | 0.960370i | \(-0.589913\pi\) | ||||
−0.278730 | + | 0.960370i | \(0.589913\pi\) | |||||||
\(332\) | 1.47735e31 | 0.452122 | ||||||||
\(333\) | 4.63802e31 | 1.36703 | ||||||||
\(334\) | −3.60437e31 | −1.02329 | ||||||||
\(335\) | −1.10468e31 | −0.302119 | ||||||||
\(336\) | 1.37879e31 | 0.363293 | ||||||||
\(337\) | −7.33154e31 | −1.86132 | −0.930661 | − | 0.365882i | \(-0.880768\pi\) | ||||
−0.930661 | + | 0.365882i | \(0.880768\pi\) | |||||||
\(338\) | −5.76658e31 | −1.41078 | ||||||||
\(339\) | −5.88471e31 | −1.38749 | ||||||||
\(340\) | −5.33718e30 | −0.121290 | ||||||||
\(341\) | 4.97863e31 | 1.09064 | ||||||||
\(342\) | 2.82800e31 | 0.597245 | ||||||||
\(343\) | −4.47523e31 | −0.911253 | ||||||||
\(344\) | −8.30586e30 | −0.163081 | ||||||||
\(345\) | −3.06615e31 | −0.580570 | ||||||||
\(346\) | 6.09958e31 | 1.11391 | ||||||||
\(347\) | −1.54701e31 | −0.272505 | −0.136253 | − | 0.990674i | \(-0.543506\pi\) | ||||
−0.136253 | + | 0.990674i | \(0.543506\pi\) | |||||||
\(348\) | −2.96537e31 | −0.503894 | ||||||||
\(349\) | −1.14544e31 | −0.187782 | −0.0938910 | − | 0.995582i | \(-0.529931\pi\) | ||||
−0.0938910 | + | 0.995582i | \(0.529931\pi\) | |||||||
\(350\) | −9.58937e30 | −0.151684 | ||||||||
\(351\) | 2.52496e31 | 0.385403 | ||||||||
\(352\) | 1.73741e31 | 0.255929 | ||||||||
\(353\) | 3.77306e31 | 0.536427 | 0.268213 | − | 0.963360i | \(-0.413567\pi\) | ||||
0.268213 | + | 0.963360i | \(0.413567\pi\) | |||||||
\(354\) | 5.67584e31 | 0.778914 | ||||||||
\(355\) | 8.08414e30 | 0.107098 | ||||||||
\(356\) | −3.01605e30 | −0.0385757 | ||||||||
\(357\) | 6.38279e31 | 0.788239 | ||||||||
\(358\) | 7.53518e31 | 0.898578 | ||||||||
\(359\) | −1.13693e32 | −1.30934 | −0.654671 | − | 0.755914i | \(-0.727193\pi\) | ||||
−0.654671 | + | 0.755914i | \(0.727193\pi\) | |||||||
\(360\) | 1.18786e31 | 0.132125 | ||||||||
\(361\) | 2.01551e30 | 0.0216544 | ||||||||
\(362\) | −8.11795e31 | −0.842537 | ||||||||
\(363\) | 1.48092e32 | 1.48490 | ||||||||
\(364\) | −9.58011e31 | −0.928118 | ||||||||
\(365\) | −7.42806e31 | −0.695368 | ||||||||
\(366\) | 1.60857e32 | 1.45521 | ||||||||
\(367\) | −7.28071e31 | −0.636572 | −0.318286 | − | 0.947995i | \(-0.603107\pi\) | ||||
−0.318286 | + | 0.947995i | \(0.603107\pi\) | |||||||
\(368\) | 2.83455e31 | 0.239545 | ||||||||
\(369\) | −6.66976e31 | −0.544855 | ||||||||
\(370\) | 6.55066e31 | 0.517325 | ||||||||
\(371\) | −2.66876e32 | −2.03768 | ||||||||
\(372\) | −6.91251e31 | −0.510328 | ||||||||
\(373\) | 1.71061e32 | 1.22121 | 0.610604 | − | 0.791936i | \(-0.290927\pi\) | ||||
0.610604 | + | 0.791936i | \(0.290927\pi\) | |||||||
\(374\) | 8.04294e31 | 0.555290 | ||||||||
\(375\) | −1.81480e31 | −0.121182 | ||||||||
\(376\) | 6.09518e31 | 0.393676 | ||||||||
\(377\) | 2.06040e32 | 1.28731 | ||||||||
\(378\) | 2.79424e31 | 0.168895 | ||||||||
\(379\) | 2.81613e31 | 0.164688 | 0.0823441 | − | 0.996604i | \(-0.473759\pi\) | ||||
0.0823441 | + | 0.996604i | \(0.473759\pi\) | |||||||
\(380\) | 3.99422e31 | 0.226015 | ||||||||
\(381\) | −1.59743e32 | −0.874701 | ||||||||
\(382\) | 1.45230e32 | 0.769597 | ||||||||
\(383\) | 9.78501e31 | 0.501853 | 0.250926 | − | 0.968006i | \(-0.419265\pi\) | ||||
0.250926 | + | 0.968006i | \(0.419265\pi\) | |||||||
\(384\) | −2.41228e31 | −0.119753 | ||||||||
\(385\) | 1.44508e32 | 0.694438 | ||||||||
\(386\) | 5.31458e31 | 0.247245 | ||||||||
\(387\) | 8.55760e31 | 0.385447 | ||||||||
\(388\) | −1.17911e32 | −0.514232 | ||||||||
\(389\) | −1.33194e32 | −0.562489 | −0.281244 | − | 0.959636i | \(-0.590747\pi\) | ||||
−0.281244 | + | 0.959636i | \(0.590747\pi\) | |||||||
\(390\) | −1.81305e32 | −0.741484 | ||||||||
\(391\) | 1.31219e32 | 0.519742 | ||||||||
\(392\) | −1.38605e31 | −0.0531745 | ||||||||
\(393\) | 2.06237e32 | 0.766408 | ||||||||
\(394\) | −2.47554e32 | −0.891184 | ||||||||
\(395\) | 3.55284e31 | 0.123912 | ||||||||
\(396\) | −1.79007e32 | −0.604895 | ||||||||
\(397\) | 5.53789e32 | 1.81327 | 0.906637 | − | 0.421912i | \(-0.138641\pi\) | ||||
0.906637 | + | 0.421912i | \(0.138641\pi\) | |||||||
\(398\) | −2.26071e32 | −0.717310 | ||||||||
\(399\) | −4.77673e32 | −1.46882 | ||||||||
\(400\) | 1.67772e31 | 0.0500000 | ||||||||
\(401\) | −1.52543e32 | −0.440643 | −0.220321 | − | 0.975427i | \(-0.570711\pi\) | ||||
−0.220321 | + | 0.975427i | \(0.570711\pi\) | |||||||
\(402\) | −2.31135e32 | −0.647203 | ||||||||
\(403\) | 4.80295e32 | 1.30375 | ||||||||
\(404\) | −1.10704e32 | −0.291339 | ||||||||
\(405\) | 1.99341e32 | 0.508639 | ||||||||
\(406\) | 2.28014e32 | 0.564138 | ||||||||
\(407\) | −9.87161e32 | −2.36841 | ||||||||
\(408\) | −1.11671e32 | −0.259830 | ||||||||
\(409\) | 6.35123e32 | 1.43323 | 0.716616 | − | 0.697468i | \(-0.245690\pi\) | ||||
0.716616 | + | 0.697468i | \(0.245690\pi\) | |||||||
\(410\) | −9.42027e31 | −0.206189 | ||||||||
\(411\) | −3.99882e32 | −0.849003 | ||||||||
\(412\) | 3.59966e32 | 0.741389 | ||||||||
\(413\) | −4.36427e32 | −0.872039 | ||||||||
\(414\) | −2.92046e32 | −0.566171 | ||||||||
\(415\) | −2.14982e32 | −0.404391 | ||||||||
\(416\) | 1.67610e32 | 0.305938 | ||||||||
\(417\) | 6.64936e32 | 1.17782 | ||||||||
\(418\) | −6.01914e32 | −1.03474 | ||||||||
\(419\) | −7.80832e32 | −1.30281 | −0.651406 | − | 0.758729i | \(-0.725821\pi\) | ||||
−0.651406 | + | 0.758729i | \(0.725821\pi\) | |||||||
\(420\) | −2.00640e32 | −0.324939 | ||||||||
\(421\) | 3.57315e32 | 0.561726 | 0.280863 | − | 0.959748i | \(-0.409379\pi\) | ||||
0.280863 | + | 0.959748i | \(0.409379\pi\) | |||||||
\(422\) | 3.02305e32 | 0.461359 | ||||||||
\(423\) | −6.27992e32 | −0.930464 | ||||||||
\(424\) | 4.66917e32 | 0.671686 | ||||||||
\(425\) | 7.76662e31 | 0.108485 | ||||||||
\(426\) | 1.69146e32 | 0.229426 | ||||||||
\(427\) | −1.23686e33 | −1.62919 | ||||||||
\(428\) | 3.85448e31 | 0.0493082 | ||||||||
\(429\) | 2.73220e33 | 3.39466 | ||||||||
\(430\) | 1.20866e32 | 0.145864 | ||||||||
\(431\) | 9.85346e31 | 0.115511 | 0.0577554 | − | 0.998331i | \(-0.481606\pi\) | ||||
0.0577554 | + | 0.998331i | \(0.481606\pi\) | |||||||
\(432\) | −4.88870e31 | −0.0556733 | ||||||||
\(433\) | −5.52126e32 | −0.610857 | −0.305429 | − | 0.952215i | \(-0.598800\pi\) | ||||
−0.305429 | + | 0.952215i | \(0.598800\pi\) | |||||||
\(434\) | 5.31517e32 | 0.571342 | ||||||||
\(435\) | 4.31519e32 | 0.450696 | ||||||||
\(436\) | 4.13153e32 | 0.419305 | ||||||||
\(437\) | −9.82012e32 | −0.968498 | ||||||||
\(438\) | −1.55419e33 | −1.48963 | ||||||||
\(439\) | 1.02785e33 | 0.957470 | 0.478735 | − | 0.877959i | \(-0.341095\pi\) | ||||
0.478735 | + | 0.877959i | \(0.341095\pi\) | |||||||
\(440\) | −2.52827e32 | −0.228910 | ||||||||
\(441\) | 1.42806e32 | 0.125679 | ||||||||
\(442\) | 7.75913e32 | 0.663796 | ||||||||
\(443\) | −8.34580e32 | −0.694099 | −0.347050 | − | 0.937847i | \(-0.612816\pi\) | ||||
−0.347050 | + | 0.937847i | \(0.612816\pi\) | |||||||
\(444\) | 1.37061e33 | 1.10822 | ||||||||
\(445\) | 4.38893e31 | 0.0345032 | ||||||||
\(446\) | −1.32070e33 | −1.00953 | ||||||||
\(447\) | 7.23145e32 | 0.537503 | ||||||||
\(448\) | 1.85485e32 | 0.134071 | ||||||||
\(449\) | −2.21599e33 | −1.55772 | −0.778859 | − | 0.627199i | \(-0.784201\pi\) | ||||
−0.778859 | + | 0.627199i | \(0.784201\pi\) | |||||||
\(450\) | −1.72857e32 | −0.118176 | ||||||||
\(451\) | 1.41960e33 | 0.943972 | ||||||||
\(452\) | −7.91655e32 | −0.512042 | ||||||||
\(453\) | 3.60092e33 | 2.26561 | ||||||||
\(454\) | 1.84522e33 | 1.12941 | ||||||||
\(455\) | 1.39409e33 | 0.830134 | ||||||||
\(456\) | 8.35719e32 | 0.484172 | ||||||||
\(457\) | −1.41006e33 | −0.794847 | −0.397424 | − | 0.917635i | \(-0.630096\pi\) | ||||
−0.397424 | + | 0.917635i | \(0.630096\pi\) | |||||||
\(458\) | 1.24480e32 | 0.0682780 | ||||||||
\(459\) | −2.26311e32 | −0.120795 | ||||||||
\(460\) | −4.12482e32 | −0.214255 | ||||||||
\(461\) | −1.02806e33 | −0.519704 | −0.259852 | − | 0.965648i | \(-0.583674\pi\) | ||||
−0.259852 | + | 0.965648i | \(0.583674\pi\) | |||||||
\(462\) | 3.02358e33 | 1.48764 | ||||||||
\(463\) | −5.11786e31 | −0.0245090 | −0.0122545 | − | 0.999925i | \(-0.503901\pi\) | ||||
−0.0122545 | + | 0.999925i | \(0.503901\pi\) | |||||||
\(464\) | −3.98924e32 | −0.185958 | ||||||||
\(465\) | 1.00590e33 | 0.456451 | ||||||||
\(466\) | 4.24802e32 | 0.187656 | ||||||||
\(467\) | −1.60375e33 | −0.689723 | −0.344861 | − | 0.938654i | \(-0.612074\pi\) | ||||
−0.344861 | + | 0.938654i | \(0.612074\pi\) | |||||||
\(468\) | −1.72690e33 | −0.723094 | ||||||||
\(469\) | 1.77725e33 | 0.724581 | ||||||||
\(470\) | −8.86966e32 | −0.352114 | ||||||||
\(471\) | −6.23042e33 | −2.40855 | ||||||||
\(472\) | 7.63557e32 | 0.287453 | ||||||||
\(473\) | −1.82141e33 | −0.667795 | ||||||||
\(474\) | 7.43368e32 | 0.265445 | ||||||||
\(475\) | −5.81235e32 | −0.202154 | ||||||||
\(476\) | 8.58662e32 | 0.290894 | ||||||||
\(477\) | −4.81069e33 | −1.58755 | ||||||||
\(478\) | −3.67196e33 | −1.18046 | ||||||||
\(479\) | 2.94257e33 | 0.921580 | 0.460790 | − | 0.887509i | \(-0.347566\pi\) | ||||
0.460790 | + | 0.887509i | \(0.347566\pi\) | |||||||
\(480\) | 3.51033e32 | 0.107111 | ||||||||
\(481\) | −9.52326e33 | −2.83121 | ||||||||
\(482\) | −6.83371e32 | −0.197956 | ||||||||
\(483\) | 4.93291e33 | 1.39240 | ||||||||
\(484\) | 1.99224e33 | 0.547993 | ||||||||
\(485\) | 1.71584e33 | 0.459943 | ||||||||
\(486\) | 3.56810e33 | 0.932145 | ||||||||
\(487\) | −7.02175e32 | −0.178786 | −0.0893929 | − | 0.995996i | \(-0.528493\pi\) | ||||
−0.0893929 | + | 0.995996i | \(0.528493\pi\) | |||||||
\(488\) | 2.16397e33 | 0.537035 | ||||||||
\(489\) | 1.22048e32 | 0.0295236 | ||||||||
\(490\) | 2.01697e32 | 0.0475607 | ||||||||
\(491\) | −5.67432e33 | −1.30435 | −0.652176 | − | 0.758067i | \(-0.726144\pi\) | ||||
−0.652176 | + | 0.758067i | \(0.726144\pi\) | |||||||
\(492\) | −1.97102e33 | −0.441701 | ||||||||
\(493\) | −1.84673e33 | −0.403475 | ||||||||
\(494\) | −5.80674e33 | −1.23693 | ||||||||
\(495\) | 2.60489e33 | 0.541034 | ||||||||
\(496\) | −9.29924e32 | −0.188333 | ||||||||
\(497\) | −1.30060e33 | −0.256856 | ||||||||
\(498\) | −4.49812e33 | −0.866291 | ||||||||
\(499\) | 2.29378e33 | 0.430818 | 0.215409 | − | 0.976524i | \(-0.430891\pi\) | ||||
0.215409 | + | 0.976524i | \(0.430891\pi\) | |||||||
\(500\) | −2.44141e32 | −0.0447214 | ||||||||
\(501\) | 1.09743e34 | 1.96068 | ||||||||
\(502\) | 7.28961e31 | 0.0127031 | ||||||||
\(503\) | 5.06724e32 | 0.0861334 | 0.0430667 | − | 0.999072i | \(-0.486287\pi\) | ||||
0.0430667 | + | 0.999072i | \(0.486287\pi\) | |||||||
\(504\) | −1.91107e33 | −0.316880 | ||||||||
\(505\) | 1.61096e33 | 0.260581 | ||||||||
\(506\) | 6.21595e33 | 0.980903 | ||||||||
\(507\) | 1.75577e34 | 2.70313 | ||||||||
\(508\) | −2.14898e33 | −0.322802 | ||||||||
\(509\) | 5.67895e33 | 0.832330 | 0.416165 | − | 0.909289i | \(-0.363374\pi\) | ||||
0.416165 | + | 0.909289i | \(0.363374\pi\) | |||||||
\(510\) | 1.62503e33 | 0.232399 | ||||||||
\(511\) | 1.19505e34 | 1.66772 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 1.69366e33 | 0.225091 | ||||||||
\(514\) | −4.18419e33 | −0.542715 | ||||||||
\(515\) | −5.23819e33 | −0.663119 | ||||||||
\(516\) | 2.52891e33 | 0.312473 | ||||||||
\(517\) | 1.33663e34 | 1.61205 | ||||||||
\(518\) | −1.05389e34 | −1.24072 | ||||||||
\(519\) | −1.85716e34 | −2.13431 | ||||||||
\(520\) | −2.43905e33 | −0.273640 | ||||||||
\(521\) | −9.13970e33 | −1.00106 | −0.500530 | − | 0.865719i | \(-0.666862\pi\) | ||||
−0.500530 | + | 0.865719i | \(0.666862\pi\) | |||||||
\(522\) | 4.11015e33 | 0.439518 | ||||||||
\(523\) | 3.76955e33 | 0.393566 | 0.196783 | − | 0.980447i | \(-0.436950\pi\) | ||||
0.196783 | + | 0.980447i | \(0.436950\pi\) | |||||||
\(524\) | 2.77446e33 | 0.282838 | ||||||||
\(525\) | 2.91970e33 | 0.290635 | ||||||||
\(526\) | 9.80226e33 | 0.952806 | ||||||||
\(527\) | −4.30487e33 | −0.408627 | ||||||||
\(528\) | −5.28995e33 | −0.490374 | ||||||||
\(529\) | −9.04558e32 | −0.0818918 | ||||||||
\(530\) | −6.79454e33 | −0.600775 | ||||||||
\(531\) | −7.86699e33 | −0.679403 | ||||||||
\(532\) | −6.42602e33 | −0.542059 | ||||||||
\(533\) | 1.36951e34 | 1.12843 | ||||||||
\(534\) | 9.18306e32 | 0.0739132 | ||||||||
\(535\) | −5.60901e32 | −0.0441026 | ||||||||
\(536\) | −3.10941e33 | −0.238846 | ||||||||
\(537\) | −2.29426e34 | −1.72172 | ||||||||
\(538\) | −3.04729e33 | −0.223427 | ||||||||
\(539\) | −3.03950e33 | −0.217742 | ||||||||
\(540\) | 7.11400e32 | 0.0497957 | ||||||||
\(541\) | −1.11229e34 | −0.760770 | −0.380385 | − | 0.924828i | \(-0.624209\pi\) | ||||
−0.380385 | + | 0.924828i | \(0.624209\pi\) | |||||||
\(542\) | 1.18561e34 | 0.792411 | ||||||||
\(543\) | 2.47170e34 | 1.61435 | ||||||||
\(544\) | −1.50228e33 | −0.0958883 | ||||||||
\(545\) | −6.01217e33 | −0.375038 | ||||||||
\(546\) | 2.91689e34 | 1.77833 | ||||||||
\(547\) | 1.75655e34 | 1.04669 | 0.523346 | − | 0.852120i | \(-0.324683\pi\) | ||||
0.523346 | + | 0.852120i | \(0.324683\pi\) | |||||||
\(548\) | −5.37952e33 | −0.313319 | ||||||||
\(549\) | −2.22955e34 | −1.26930 | ||||||||
\(550\) | 3.67911e33 | 0.204743 | ||||||||
\(551\) | 1.38205e34 | 0.751844 | ||||||||
\(552\) | −8.63045e33 | −0.458981 | ||||||||
\(553\) | −5.71591e33 | −0.297181 | ||||||||
\(554\) | 1.00773e34 | 0.512239 | ||||||||
\(555\) | −1.99450e34 | −0.991223 | ||||||||
\(556\) | 8.94522e33 | 0.434666 | ||||||||
\(557\) | 3.64954e33 | 0.173400 | 0.0866999 | − | 0.996234i | \(-0.472368\pi\) | ||||
0.0866999 | + | 0.996234i | \(0.472368\pi\) | |||||||
\(558\) | 9.58108e33 | 0.445130 | ||||||||
\(559\) | −1.75714e34 | −0.798285 | ||||||||
\(560\) | −2.69917e33 | −0.119917 | ||||||||
\(561\) | −2.44886e34 | −1.06397 | ||||||||
\(562\) | −2.22008e34 | −0.943334 | ||||||||
\(563\) | 4.06393e34 | 1.68885 | 0.844426 | − | 0.535672i | \(-0.179942\pi\) | ||||
0.844426 | + | 0.535672i | \(0.179942\pi\) | |||||||
\(564\) | −1.85582e34 | −0.754305 | ||||||||
\(565\) | 1.15201e34 | 0.457984 | ||||||||
\(566\) | −2.58360e34 | −1.00466 | ||||||||
\(567\) | −3.20706e34 | −1.21988 | ||||||||
\(568\) | 2.27548e33 | 0.0846680 | ||||||||
\(569\) | 1.05009e34 | 0.382228 | 0.191114 | − | 0.981568i | \(-0.438790\pi\) | ||||
0.191114 | + | 0.981568i | \(0.438790\pi\) | |||||||
\(570\) | −1.21613e34 | −0.433057 | ||||||||
\(571\) | −3.85212e34 | −1.34199 | −0.670994 | − | 0.741463i | \(-0.734132\pi\) | ||||
−0.670994 | + | 0.741463i | \(0.734132\pi\) | |||||||
\(572\) | 3.67556e34 | 1.25277 | ||||||||
\(573\) | −4.42185e34 | −1.47459 | ||||||||
\(574\) | 1.51556e34 | 0.494509 | ||||||||
\(575\) | 6.00240e33 | 0.191636 | ||||||||
\(576\) | 3.34354e33 | 0.104454 | ||||||||
\(577\) | −5.52922e34 | −1.69031 | −0.845154 | − | 0.534522i | \(-0.820492\pi\) | ||||
−0.845154 | + | 0.534522i | \(0.820492\pi\) | |||||||
\(578\) | 1.66820e34 | 0.499057 | ||||||||
\(579\) | −1.61814e34 | −0.473735 | ||||||||
\(580\) | 5.80511e33 | 0.166326 | ||||||||
\(581\) | 3.45869e34 | 0.969863 | ||||||||
\(582\) | 3.59008e34 | 0.985296 | ||||||||
\(583\) | 1.02391e35 | 2.75046 | ||||||||
\(584\) | −2.09081e34 | −0.549736 | ||||||||
\(585\) | 2.51297e34 | 0.646755 | ||||||||
\(586\) | −4.01115e34 | −1.01053 | ||||||||
\(587\) | −3.59799e34 | −0.887326 | −0.443663 | − | 0.896194i | \(-0.646321\pi\) | ||||
−0.443663 | + | 0.896194i | \(0.646321\pi\) | |||||||
\(588\) | 4.22015e33 | 0.101885 | ||||||||
\(589\) | 3.22166e34 | 0.761445 | ||||||||
\(590\) | −1.11112e34 | −0.257106 | ||||||||
\(591\) | 7.53735e34 | 1.70756 | ||||||||
\(592\) | 1.84385e34 | 0.408981 | ||||||||
\(593\) | 6.31486e33 | 0.137145 | 0.0685725 | − | 0.997646i | \(-0.478156\pi\) | ||||
0.0685725 | + | 0.997646i | \(0.478156\pi\) | |||||||
\(594\) | −1.07205e34 | −0.227974 | ||||||||
\(595\) | −1.24952e34 | −0.260184 | ||||||||
\(596\) | 9.72829e33 | 0.198362 | ||||||||
\(597\) | 6.88325e34 | 1.37440 | ||||||||
\(598\) | 5.99661e34 | 1.17258 | ||||||||
\(599\) | −5.02848e34 | −0.962945 | −0.481472 | − | 0.876461i | \(-0.659898\pi\) | ||||
−0.481472 | + | 0.876461i | \(0.659898\pi\) | |||||||
\(600\) | −5.10821e33 | −0.0958027 | ||||||||
\(601\) | −4.57441e34 | −0.840241 | −0.420120 | − | 0.907468i | \(-0.638012\pi\) | ||||
−0.420120 | + | 0.907468i | \(0.638012\pi\) | |||||||
\(602\) | −1.94453e34 | −0.349831 | ||||||||
\(603\) | 3.20365e34 | 0.564519 | ||||||||
\(604\) | 4.84423e34 | 0.836109 | ||||||||
\(605\) | −2.89909e34 | −0.490140 | ||||||||
\(606\) | 3.37065e34 | 0.558221 | ||||||||
\(607\) | −2.94626e34 | −0.477983 | −0.238991 | − | 0.971022i | \(-0.576817\pi\) | ||||
−0.238991 | + | 0.971022i | \(0.576817\pi\) | |||||||
\(608\) | 1.12427e34 | 0.178680 | ||||||||
\(609\) | −6.94240e34 | −1.08092 | ||||||||
\(610\) | −3.14899e34 | −0.480339 | ||||||||
\(611\) | 1.28946e35 | 1.92705 | ||||||||
\(612\) | 1.54782e34 | 0.226635 | ||||||||
\(613\) | −1.15985e35 | −1.66398 | −0.831989 | − | 0.554792i | \(-0.812798\pi\) | ||||
−0.831989 | + | 0.554792i | \(0.812798\pi\) | |||||||
\(614\) | 2.35763e34 | 0.331414 | ||||||||
\(615\) | 2.86822e34 | 0.395069 | ||||||||
\(616\) | 4.06755e34 | 0.549002 | ||||||||
\(617\) | −5.88912e34 | −0.778907 | −0.389454 | − | 0.921046i | \(-0.627336\pi\) | ||||
−0.389454 | + | 0.921046i | \(0.627336\pi\) | |||||||
\(618\) | −1.09600e35 | −1.42054 | ||||||||
\(619\) | 6.29583e34 | 0.799687 | 0.399844 | − | 0.916583i | \(-0.369064\pi\) | ||||
0.399844 | + | 0.916583i | \(0.369064\pi\) | |||||||
\(620\) | 1.35322e34 | 0.168450 | ||||||||
\(621\) | −1.74904e34 | −0.213380 | ||||||||
\(622\) | −7.57566e34 | −0.905817 | ||||||||
\(623\) | −7.06104e33 | −0.0827501 | ||||||||
\(624\) | −5.10328e34 | −0.586195 | ||||||||
\(625\) | 3.55271e33 | 0.0400000 | ||||||||
\(626\) | −9.80174e34 | −1.08174 | ||||||||
\(627\) | 1.83267e35 | 1.98262 | ||||||||
\(628\) | −8.38163e34 | −0.888859 | ||||||||
\(629\) | 8.53566e34 | 0.887369 | ||||||||
\(630\) | 2.78098e34 | 0.283426 | ||||||||
\(631\) | −5.00486e33 | −0.0500063 | −0.0250032 | − | 0.999687i | \(-0.507960\pi\) | ||||
−0.0250032 | + | 0.999687i | \(0.507960\pi\) | |||||||
\(632\) | 1.00003e34 | 0.0979607 | ||||||||
\(633\) | −9.20436e34 | −0.883989 | ||||||||
\(634\) | 8.36242e33 | 0.0787438 | ||||||||
\(635\) | 3.12718e34 | 0.288723 | ||||||||
\(636\) | −1.42164e35 | −1.28699 | ||||||||
\(637\) | −2.93225e34 | −0.260290 | ||||||||
\(638\) | −8.74810e34 | −0.761474 | ||||||||
\(639\) | −2.34445e34 | −0.200115 | ||||||||
\(640\) | 4.72237e33 | 0.0395285 | ||||||||
\(641\) | 2.47946e34 | 0.203532 | 0.101766 | − | 0.994808i | \(-0.467551\pi\) | ||||
0.101766 | + | 0.994808i | \(0.467551\pi\) | |||||||
\(642\) | −1.17359e34 | −0.0944772 | ||||||||
\(643\) | −1.87298e35 | −1.47875 | −0.739376 | − | 0.673293i | \(-0.764879\pi\) | ||||
−0.739376 | + | 0.673293i | \(0.764879\pi\) | |||||||
\(644\) | 6.63613e34 | 0.513856 | ||||||||
\(645\) | −3.68005e34 | −0.279484 | ||||||||
\(646\) | 5.20456e34 | 0.387684 | ||||||||
\(647\) | 1.37605e35 | 1.00538 | 0.502692 | − | 0.864465i | \(-0.332343\pi\) | ||||
0.502692 | + | 0.864465i | \(0.332343\pi\) | |||||||
\(648\) | 5.61096e34 | 0.402114 | ||||||||
\(649\) | 1.67442e35 | 1.17708 | ||||||||
\(650\) | 3.54928e34 | 0.244751 | ||||||||
\(651\) | −1.61833e35 | −1.09472 | ||||||||
\(652\) | 1.64188e33 | 0.0108955 | ||||||||
\(653\) | −1.43663e35 | −0.935256 | −0.467628 | − | 0.883925i | \(-0.654891\pi\) | ||||
−0.467628 | + | 0.883925i | \(0.654891\pi\) | |||||||
\(654\) | −1.25794e35 | −0.803412 | ||||||||
\(655\) | −4.03737e34 | −0.252978 | ||||||||
\(656\) | −2.65157e34 | −0.163007 | ||||||||
\(657\) | 2.15418e35 | 1.29932 | ||||||||
\(658\) | 1.42698e35 | 0.844488 | ||||||||
\(659\) | −1.67433e35 | −0.972238 | −0.486119 | − | 0.873893i | \(-0.661588\pi\) | ||||
−0.486119 | + | 0.873893i | \(0.661588\pi\) | |||||||
\(660\) | 7.69788e34 | 0.438604 | ||||||||
\(661\) | −8.14435e34 | −0.455342 | −0.227671 | − | 0.973738i | \(-0.573111\pi\) | ||||
−0.227671 | + | 0.973738i | \(0.573111\pi\) | |||||||
\(662\) | 7.18494e34 | 0.394183 | ||||||||
\(663\) | −2.36244e35 | −1.27187 | ||||||||
\(664\) | −6.05121e34 | −0.319699 | ||||||||
\(665\) | 9.35109e34 | 0.484832 | ||||||||
\(666\) | −1.89973e35 | −0.966639 | ||||||||
\(667\) | −1.42724e35 | −0.712726 | ||||||||
\(668\) | 1.47635e35 | 0.723576 | ||||||||
\(669\) | 4.02118e35 | 1.93432 | ||||||||
\(670\) | 4.52478e34 | 0.213630 | ||||||||
\(671\) | 4.74541e35 | 2.19909 | ||||||||
\(672\) | −5.64753e34 | −0.256887 | ||||||||
\(673\) | 2.14831e35 | 0.959198 | 0.479599 | − | 0.877488i | \(-0.340782\pi\) | ||||
0.479599 | + | 0.877488i | \(0.340782\pi\) | |||||||
\(674\) | 3.00300e35 | 1.31615 | ||||||||
\(675\) | −1.03522e34 | −0.0445386 | ||||||||
\(676\) | 2.36199e35 | 0.997572 | ||||||||
\(677\) | −1.65762e35 | −0.687268 | −0.343634 | − | 0.939104i | \(-0.611658\pi\) | ||||
−0.343634 | + | 0.939104i | \(0.611658\pi\) | |||||||
\(678\) | 2.41038e35 | 0.981100 | ||||||||
\(679\) | −2.76049e35 | −1.10310 | ||||||||
\(680\) | 2.18611e34 | 0.0857651 | ||||||||
\(681\) | −5.61820e35 | −2.16401 | ||||||||
\(682\) | −2.03925e35 | −0.771197 | ||||||||
\(683\) | 4.25978e35 | 1.58172 | 0.790858 | − | 0.612000i | \(-0.209635\pi\) | ||||
0.790858 | + | 0.612000i | \(0.209635\pi\) | |||||||
\(684\) | −1.15835e35 | −0.422316 | ||||||||
\(685\) | 7.82823e34 | 0.280241 | ||||||||
\(686\) | 1.83305e35 | 0.644353 | ||||||||
\(687\) | −3.79007e34 | −0.130824 | ||||||||
\(688\) | 3.40208e34 | 0.115316 | ||||||||
\(689\) | 9.87781e35 | 3.28791 | ||||||||
\(690\) | 1.25590e35 | 0.410525 | ||||||||
\(691\) | −3.56127e35 | −1.14322 | −0.571609 | − | 0.820526i | \(-0.693681\pi\) | ||||
−0.571609 | + | 0.820526i | \(0.693681\pi\) | |||||||
\(692\) | −2.49839e35 | −0.787651 | ||||||||
\(693\) | −4.19083e35 | −1.29758 | ||||||||
\(694\) | 6.33656e34 | 0.192690 | ||||||||
\(695\) | −1.30170e35 | −0.388777 | ||||||||
\(696\) | 1.21462e35 | 0.356307 | ||||||||
\(697\) | −1.22748e35 | −0.353676 | ||||||||
\(698\) | 4.69172e34 | 0.132782 | ||||||||
\(699\) | −1.29341e35 | −0.359559 | ||||||||
\(700\) | 3.92781e34 | 0.107257 | ||||||||
\(701\) | −6.93164e34 | −0.185935 | −0.0929674 | − | 0.995669i | \(-0.529635\pi\) | ||||
−0.0929674 | + | 0.995669i | \(0.529635\pi\) | |||||||
\(702\) | −1.03422e35 | −0.272521 | ||||||||
\(703\) | −6.38788e35 | −1.65354 | ||||||||
\(704\) | −7.11643e34 | −0.180969 | ||||||||
\(705\) | 2.70057e35 | 0.674671 | ||||||||
\(706\) | −1.54545e35 | −0.379311 | ||||||||
\(707\) | −2.59176e35 | −0.624961 | ||||||||
\(708\) | −2.32482e35 | −0.550775 | ||||||||
\(709\) | −1.75968e34 | −0.0409596 | −0.0204798 | − | 0.999790i | \(-0.506519\pi\) | ||||
−0.0204798 | + | 0.999790i | \(0.506519\pi\) | |||||||
\(710\) | −3.31126e34 | −0.0757294 | ||||||||
\(711\) | −1.03034e35 | −0.231533 | ||||||||
\(712\) | 1.23538e34 | 0.0272771 | ||||||||
\(713\) | −3.32700e35 | −0.721827 | ||||||||
\(714\) | −2.61439e35 | −0.557369 | ||||||||
\(715\) | −5.34864e35 | −1.12052 | ||||||||
\(716\) | −3.08641e35 | −0.635390 | ||||||||
\(717\) | 1.11801e36 | 2.26182 | ||||||||
\(718\) | 4.65687e35 | 0.925845 | ||||||||
\(719\) | −3.47246e35 | −0.678462 | −0.339231 | − | 0.940703i | \(-0.610167\pi\) | ||||
−0.339231 | + | 0.940703i | \(0.610167\pi\) | |||||||
\(720\) | −4.86549e34 | −0.0934266 | ||||||||
\(721\) | 8.42736e35 | 1.59038 | ||||||||
\(722\) | −8.25554e33 | −0.0153120 | ||||||||
\(723\) | 2.08068e35 | 0.379294 | ||||||||
\(724\) | 3.32511e35 | 0.595764 | ||||||||
\(725\) | −8.44755e34 | −0.148767 | ||||||||
\(726\) | −6.06584e35 | −1.04998 | ||||||||
\(727\) | −4.86443e35 | −0.827660 | −0.413830 | − | 0.910354i | \(-0.635809\pi\) | ||||
−0.413830 | + | 0.910354i | \(0.635809\pi\) | |||||||
\(728\) | 3.92401e35 | 0.656279 | ||||||||
\(729\) | −3.94577e35 | −0.648691 | ||||||||
\(730\) | 3.04253e35 | 0.491699 | ||||||||
\(731\) | 1.57491e35 | 0.250201 | ||||||||
\(732\) | −6.58869e35 | −1.02899 | ||||||||
\(733\) | −1.02677e36 | −1.57643 | −0.788216 | − | 0.615398i | \(-0.788995\pi\) | ||||
−0.788216 | + | 0.615398i | \(0.788995\pi\) | |||||||
\(734\) | 2.98218e35 | 0.450125 | ||||||||
\(735\) | −6.14113e34 | −0.0911290 | ||||||||
\(736\) | −1.16103e35 | −0.169384 | ||||||||
\(737\) | −6.81868e35 | −0.978040 | ||||||||
\(738\) | 2.73194e35 | 0.385271 | ||||||||
\(739\) | 5.26186e35 | 0.729599 | 0.364799 | − | 0.931086i | \(-0.381138\pi\) | ||||
0.364799 | + | 0.931086i | \(0.381138\pi\) | |||||||
\(740\) | −2.68315e35 | −0.365804 | ||||||||
\(741\) | 1.76800e36 | 2.37003 | ||||||||
\(742\) | 1.09313e36 | 1.44086 | ||||||||
\(743\) | 6.09530e35 | 0.790014 | 0.395007 | − | 0.918678i | \(-0.370742\pi\) | ||||
0.395007 | + | 0.918678i | \(0.370742\pi\) | |||||||
\(744\) | 2.83137e35 | 0.360856 | ||||||||
\(745\) | −1.41565e35 | −0.177420 | ||||||||
\(746\) | −7.00664e35 | −0.863525 | ||||||||
\(747\) | 6.23461e35 | 0.755617 | ||||||||
\(748\) | −3.29439e35 | −0.392649 | ||||||||
\(749\) | 9.02394e34 | 0.105773 | ||||||||
\(750\) | 7.43342e34 | 0.0856886 | ||||||||
\(751\) | 1.00495e36 | 1.13932 | 0.569660 | − | 0.821881i | \(-0.307075\pi\) | ||||
0.569660 | + | 0.821881i | \(0.307075\pi\) | |||||||
\(752\) | −2.49659e35 | −0.278371 | ||||||||
\(753\) | −2.21949e34 | −0.0243397 | ||||||||
\(754\) | −8.43940e35 | −0.910269 | ||||||||
\(755\) | −7.04928e35 | −0.747838 | ||||||||
\(756\) | −1.14452e35 | −0.119427 | ||||||||
\(757\) | −8.28193e35 | −0.850028 | −0.425014 | − | 0.905187i | \(-0.639731\pi\) | ||||
−0.425014 | + | 0.905187i | \(0.639731\pi\) | |||||||
\(758\) | −1.15349e35 | −0.116452 | ||||||||
\(759\) | −1.89259e36 | −1.87946 | ||||||||
\(760\) | −1.63603e35 | −0.159817 | ||||||||
\(761\) | −1.30553e35 | −0.125452 | −0.0627261 | − | 0.998031i | \(-0.519979\pi\) | ||||
−0.0627261 | + | 0.998031i | \(0.519979\pi\) | |||||||
\(762\) | 6.54308e35 | 0.618507 | ||||||||
\(763\) | 9.67256e35 | 0.899466 | ||||||||
\(764\) | −5.94861e35 | −0.544187 | ||||||||
\(765\) | −2.25237e35 | −0.202708 | ||||||||
\(766\) | −4.00794e35 | −0.354864 | ||||||||
\(767\) | 1.61533e36 | 1.40709 | ||||||||
\(768\) | 9.88071e34 | 0.0846785 | ||||||||
\(769\) | −7.86348e34 | −0.0663033 | −0.0331517 | − | 0.999450i | \(-0.510554\pi\) | ||||
−0.0331517 | + | 0.999450i | \(0.510554\pi\) | |||||||
\(770\) | −5.91906e35 | −0.491042 | ||||||||
\(771\) | 1.27397e36 | 1.03987 | ||||||||
\(772\) | −2.17685e35 | −0.174829 | ||||||||
\(773\) | 3.60085e35 | 0.284552 | 0.142276 | − | 0.989827i | \(-0.454558\pi\) | ||||
0.142276 | + | 0.989827i | \(0.454558\pi\) | |||||||
\(774\) | −3.50519e35 | −0.272552 | ||||||||
\(775\) | −1.96919e35 | −0.150666 | ||||||||
\(776\) | 4.82965e35 | 0.363617 | ||||||||
\(777\) | 3.20881e36 | 2.37728 | ||||||||
\(778\) | 5.45562e35 | 0.397740 | ||||||||
\(779\) | 9.18619e35 | 0.659048 | ||||||||
\(780\) | 7.42625e35 | 0.524308 | ||||||||
\(781\) | 4.98996e35 | 0.346704 | ||||||||
\(782\) | −5.37473e35 | −0.367513 | ||||||||
\(783\) | 2.46153e35 | 0.165647 | ||||||||
\(784\) | 5.67727e34 | 0.0376001 | ||||||||
\(785\) | 1.21969e36 | 0.795020 | ||||||||
\(786\) | −8.44747e35 | −0.541932 | ||||||||
\(787\) | −1.70122e36 | −1.07418 | −0.537089 | − | 0.843526i | \(-0.680476\pi\) | ||||
−0.537089 | + | 0.843526i | \(0.680476\pi\) | |||||||
\(788\) | 1.01398e36 | 0.630162 | ||||||||
\(789\) | −2.98452e36 | −1.82563 | ||||||||
\(790\) | −1.45524e35 | −0.0876187 | ||||||||
\(791\) | −1.85339e36 | −1.09840 | ||||||||
\(792\) | 7.33212e35 | 0.427725 | ||||||||
\(793\) | 4.57796e36 | 2.62880 | ||||||||
\(794\) | −2.26832e36 | −1.28218 | ||||||||
\(795\) | 2.06875e36 | 1.15112 | ||||||||
\(796\) | 9.25987e35 | 0.507215 | ||||||||
\(797\) | −3.28276e36 | −1.77015 | −0.885075 | − | 0.465449i | \(-0.845893\pi\) | ||||
−0.885075 | + | 0.465449i | \(0.845893\pi\) | |||||||
\(798\) | 1.95655e36 | 1.03861 | ||||||||
\(799\) | −1.15574e36 | −0.603983 | ||||||||
\(800\) | −6.87195e34 | −0.0353553 | ||||||||
\(801\) | −1.27282e35 | −0.0644703 | ||||||||
\(802\) | 6.24815e35 | 0.311581 | ||||||||
\(803\) | −4.58498e36 | −2.25109 | ||||||||
\(804\) | 9.46730e35 | 0.457642 | ||||||||
\(805\) | −9.65684e35 | −0.459607 | ||||||||
\(806\) | −1.96729e36 | −0.921892 | ||||||||
\(807\) | 9.27816e35 | 0.428098 | ||||||||
\(808\) | 4.53446e35 | 0.206008 | ||||||||
\(809\) | −1.22121e36 | −0.546303 | −0.273152 | − | 0.961971i | \(-0.588066\pi\) | ||||
−0.273152 | + | 0.961971i | \(0.588066\pi\) | |||||||
\(810\) | −8.16501e35 | −0.359662 | ||||||||
\(811\) | −2.29432e36 | −0.995160 | −0.497580 | − | 0.867418i | \(-0.665778\pi\) | ||||
−0.497580 | + | 0.867418i | \(0.665778\pi\) | |||||||
\(812\) | −9.33944e35 | −0.398906 | ||||||||
\(813\) | −3.60986e36 | −1.51830 | ||||||||
\(814\) | 4.04341e36 | 1.67472 | ||||||||
\(815\) | −2.38925e34 | −0.00974521 | ||||||||
\(816\) | 4.57405e35 | 0.183727 | ||||||||
\(817\) | −1.17863e36 | −0.466231 | ||||||||
\(818\) | −2.60147e36 | −1.01345 | ||||||||
\(819\) | −4.04295e36 | −1.55113 | ||||||||
\(820\) | 3.85854e35 | 0.145798 | ||||||||
\(821\) | 1.68233e36 | 0.626067 | 0.313033 | − | 0.949742i | \(-0.398655\pi\) | ||||
0.313033 | + | 0.949742i | \(0.398655\pi\) | |||||||
\(822\) | 1.63792e36 | 0.600336 | ||||||||
\(823\) | 3.28620e36 | 1.18630 | 0.593152 | − | 0.805091i | \(-0.297883\pi\) | ||||
0.593152 | + | 0.805091i | \(0.297883\pi\) | |||||||
\(824\) | −1.47442e36 | −0.524241 | ||||||||
\(825\) | −1.12019e36 | −0.392299 | ||||||||
\(826\) | 1.78761e36 | 0.616625 | ||||||||
\(827\) | −1.84899e36 | −0.628225 | −0.314112 | − | 0.949386i | \(-0.601707\pi\) | ||||
−0.314112 | + | 0.949386i | \(0.601707\pi\) | |||||||
\(828\) | 1.19622e36 | 0.400343 | ||||||||
\(829\) | 6.47231e35 | 0.213367 | 0.106684 | − | 0.994293i | \(-0.465977\pi\) | ||||
0.106684 | + | 0.994293i | \(0.465977\pi\) | |||||||
\(830\) | 8.80567e35 | 0.285947 | ||||||||
\(831\) | −3.06827e36 | −0.981478 | ||||||||
\(832\) | −6.86531e35 | −0.216331 | ||||||||
\(833\) | 2.62816e35 | 0.0815811 | ||||||||
\(834\) | −2.72358e36 | −0.832845 | ||||||||
\(835\) | −2.14837e36 | −0.647186 | ||||||||
\(836\) | 2.46544e36 | 0.731672 | ||||||||
\(837\) | 5.73801e35 | 0.167762 | ||||||||
\(838\) | 3.19829e36 | 0.921228 | ||||||||
\(839\) | 3.82378e36 | 1.08510 | 0.542549 | − | 0.840024i | \(-0.317459\pi\) | ||||
0.542549 | + | 0.840024i | \(0.317459\pi\) | |||||||
\(840\) | 8.21823e35 | 0.229767 | ||||||||
\(841\) | −1.62172e36 | −0.446711 | ||||||||
\(842\) | −1.46356e36 | −0.397200 | ||||||||
\(843\) | 6.75956e36 | 1.80748 | ||||||||
\(844\) | −1.23824e36 | −0.326230 | ||||||||
\(845\) | −3.43715e36 | −0.892255 | ||||||||
\(846\) | 2.57226e36 | 0.657937 | ||||||||
\(847\) | 4.66415e36 | 1.17552 | ||||||||
\(848\) | −1.91249e36 | −0.474954 | ||||||||
\(849\) | 7.86635e36 | 1.92499 | ||||||||
\(850\) | −3.18121e35 | −0.0767107 | ||||||||
\(851\) | 6.59675e36 | 1.56751 | ||||||||
\(852\) | −6.92823e35 | −0.162229 | ||||||||
\(853\) | 2.67006e36 | 0.616110 | 0.308055 | − | 0.951369i | \(-0.400322\pi\) | ||||
0.308055 | + | 0.951369i | \(0.400322\pi\) | |||||||
\(854\) | 5.06618e36 | 1.15201 | ||||||||
\(855\) | 1.68562e36 | 0.377731 | ||||||||
\(856\) | −1.57880e35 | −0.0348661 | ||||||||
\(857\) | 5.29681e36 | 1.15280 | 0.576400 | − | 0.817167i | \(-0.304457\pi\) | ||||
0.576400 | + | 0.817167i | \(0.304457\pi\) | |||||||
\(858\) | −1.11911e37 | −2.40039 | ||||||||
\(859\) | 9.48590e35 | 0.200523 | 0.100261 | − | 0.994961i | \(-0.468032\pi\) | ||||
0.100261 | + | 0.994961i | \(0.468032\pi\) | |||||||
\(860\) | −4.95068e35 | −0.103142 | ||||||||
\(861\) | −4.61447e36 | −0.947507 | ||||||||
\(862\) | −4.03598e35 | −0.0816785 | ||||||||
\(863\) | −6.15179e36 | −1.22706 | −0.613532 | − | 0.789670i | \(-0.710252\pi\) | ||||
−0.613532 | + | 0.789670i | \(0.710252\pi\) | |||||||
\(864\) | 2.00241e35 | 0.0393669 | ||||||||
\(865\) | 3.63563e36 | 0.704496 | ||||||||
\(866\) | 2.26151e36 | 0.431941 | ||||||||
\(867\) | −5.07922e36 | −0.956221 | ||||||||
\(868\) | −2.17709e36 | −0.403999 | ||||||||
\(869\) | 2.19300e36 | 0.401135 | ||||||||
\(870\) | −1.76750e36 | −0.318690 | ||||||||
\(871\) | −6.57807e36 | −1.16915 | ||||||||
\(872\) | −1.69228e36 | −0.296494 | ||||||||
\(873\) | −4.97603e36 | −0.859418 | ||||||||
\(874\) | 4.02232e36 | 0.684832 | ||||||||
\(875\) | −5.71571e35 | −0.0959333 | ||||||||
\(876\) | 6.36596e36 | 1.05332 | ||||||||
\(877\) | 7.20268e35 | 0.117490 | 0.0587448 | − | 0.998273i | \(-0.481290\pi\) | ||||
0.0587448 | + | 0.998273i | \(0.481290\pi\) | |||||||
\(878\) | −4.21009e36 | −0.677034 | ||||||||
\(879\) | 1.22129e37 | 1.93623 | ||||||||
\(880\) | 1.03558e36 | 0.161864 | ||||||||
\(881\) | −6.22632e36 | −0.959472 | −0.479736 | − | 0.877413i | \(-0.659268\pi\) | ||||
−0.479736 | + | 0.877413i | \(0.659268\pi\) | |||||||
\(882\) | −5.84934e35 | −0.0888688 | ||||||||
\(883\) | −7.42861e36 | −1.11275 | −0.556376 | − | 0.830930i | \(-0.687809\pi\) | ||||
−0.556376 | + | 0.830930i | \(0.687809\pi\) | |||||||
\(884\) | −3.17814e36 | −0.469375 | ||||||||
\(885\) | 3.38307e36 | 0.492628 | ||||||||
\(886\) | 3.41844e36 | 0.490802 | ||||||||
\(887\) | 2.96498e36 | 0.419736 | 0.209868 | − | 0.977730i | \(-0.432697\pi\) | ||||
0.209868 | + | 0.977730i | \(0.432697\pi\) | |||||||
\(888\) | −5.61401e36 | −0.783631 | ||||||||
\(889\) | −5.03110e36 | −0.692455 | ||||||||
\(890\) | −1.79771e35 | −0.0243974 | ||||||||
\(891\) | 1.23044e37 | 1.64660 | ||||||||
\(892\) | 5.40960e36 | 0.713846 | ||||||||
\(893\) | 8.64926e36 | 1.12547 | ||||||||
\(894\) | −2.96200e36 | −0.380072 | ||||||||
\(895\) | 4.49132e36 | 0.568310 | ||||||||
\(896\) | −7.59748e35 | −0.0948024 | ||||||||
\(897\) | −1.82580e37 | −2.24672 | ||||||||
\(898\) | 9.07670e36 | 1.10147 | ||||||||
\(899\) | 4.68229e36 | 0.560354 | ||||||||
\(900\) | 7.08023e35 | 0.0835633 | ||||||||
\(901\) | −8.85344e36 | −1.03051 | ||||||||
\(902\) | −5.81468e36 | −0.667489 | ||||||||
\(903\) | 5.92057e36 | 0.670296 | ||||||||
\(904\) | 3.24262e36 | 0.362068 | ||||||||
\(905\) | −4.83868e36 | −0.532867 | ||||||||
\(906\) | −1.47494e37 | −1.60203 | ||||||||
\(907\) | −7.50976e36 | −0.804516 | −0.402258 | − | 0.915526i | \(-0.631775\pi\) | ||||
−0.402258 | + | 0.915526i | \(0.631775\pi\) | |||||||
\(908\) | −7.55803e36 | −0.798611 | ||||||||
\(909\) | −4.67189e36 | −0.486905 | ||||||||
\(910\) | −5.71019e36 | −0.586994 | ||||||||
\(911\) | −9.29828e36 | −0.942807 | −0.471404 | − | 0.881918i | \(-0.656252\pi\) | ||||
−0.471404 | + | 0.881918i | \(0.656252\pi\) | |||||||
\(912\) | −3.42311e36 | −0.342362 | ||||||||
\(913\) | −1.32698e37 | −1.30912 | ||||||||
\(914\) | 5.77559e36 | 0.562042 | ||||||||
\(915\) | 9.58781e36 | 0.920356 | ||||||||
\(916\) | −5.09869e35 | −0.0482798 | ||||||||
\(917\) | 6.49544e36 | 0.606725 | ||||||||
\(918\) | 9.26971e35 | 0.0854147 | ||||||||
\(919\) | 7.54098e36 | 0.685463 | 0.342731 | − | 0.939433i | \(-0.388648\pi\) | ||||
0.342731 | + | 0.939433i | \(0.388648\pi\) | |||||||
\(920\) | 1.68953e36 | 0.151502 | ||||||||
\(921\) | −7.17835e36 | −0.635008 | ||||||||
\(922\) | 4.21093e36 | 0.367486 | ||||||||
\(923\) | 4.81387e36 | 0.414451 | ||||||||
\(924\) | −1.23846e37 | −1.05192 | ||||||||
\(925\) | 3.90450e36 | 0.327185 | ||||||||
\(926\) | 2.09627e35 | 0.0173305 | ||||||||
\(927\) | 1.51911e37 | 1.23906 | ||||||||
\(928\) | 1.63399e36 | 0.131492 | ||||||||
\(929\) | −7.02005e36 | −0.557370 | −0.278685 | − | 0.960383i | \(-0.589899\pi\) | ||||
−0.278685 | + | 0.960383i | \(0.589899\pi\) | |||||||
\(930\) | −4.12018e36 | −0.322760 | ||||||||
\(931\) | −1.96685e36 | −0.152020 | ||||||||
\(932\) | −1.73999e36 | −0.132693 | ||||||||
\(933\) | 2.30658e37 | 1.73560 | ||||||||
\(934\) | 6.56894e36 | 0.487708 | ||||||||
\(935\) | 4.79397e36 | 0.351196 | ||||||||
\(936\) | 7.07339e36 | 0.511304 | ||||||||
\(937\) | −1.69888e37 | −1.21176 | −0.605881 | − | 0.795555i | \(-0.707179\pi\) | ||||
−0.605881 | + | 0.795555i | \(0.707179\pi\) | |||||||
\(938\) | −7.27960e36 | −0.512356 | ||||||||
\(939\) | 2.98437e37 | 2.07268 | ||||||||
\(940\) | 3.63301e36 | 0.248982 | ||||||||
\(941\) | −1.18390e36 | −0.0800651 | −0.0400325 | − | 0.999198i | \(-0.512746\pi\) | ||||
−0.0400325 | + | 0.999198i | \(0.512746\pi\) | |||||||
\(942\) | 2.55198e37 | 1.70310 | ||||||||
\(943\) | −9.48655e36 | −0.624758 | ||||||||
\(944\) | −3.12753e36 | −0.203260 | ||||||||
\(945\) | 1.66550e36 | 0.106818 | ||||||||
\(946\) | 7.46049e36 | 0.472202 | ||||||||
\(947\) | −3.22631e36 | −0.201526 | −0.100763 | − | 0.994910i | \(-0.532128\pi\) | ||||
−0.100763 | + | 0.994910i | \(0.532128\pi\) | |||||||
\(948\) | −3.04484e36 | −0.187698 | ||||||||
\(949\) | −4.42319e37 | −2.69097 | ||||||||
\(950\) | 2.38074e36 | 0.142944 | ||||||||
\(951\) | −2.54613e36 | −0.150877 | ||||||||
\(952\) | −3.51708e36 | −0.205693 | ||||||||
\(953\) | 1.29808e37 | 0.749271 | 0.374635 | − | 0.927172i | \(-0.377768\pi\) | ||||
0.374635 | + | 0.927172i | \(0.377768\pi\) | |||||||
\(954\) | 1.97046e37 | 1.12257 | ||||||||
\(955\) | 8.65636e36 | 0.486736 | ||||||||
\(956\) | 1.50404e37 | 0.834708 | ||||||||
\(957\) | 2.66356e37 | 1.45903 | ||||||||
\(958\) | −1.20528e37 | −0.651656 | ||||||||
\(959\) | −1.25943e37 | −0.672110 | ||||||||
\(960\) | −1.43783e36 | −0.0757387 | ||||||||
\(961\) | −8.31801e36 | −0.432491 | ||||||||
\(962\) | 3.90073e37 | 2.00197 | ||||||||
\(963\) | 1.62665e36 | 0.0824071 | ||||||||
\(964\) | 2.79909e36 | 0.139976 | ||||||||
\(965\) | 3.16773e36 | 0.156371 | ||||||||
\(966\) | −2.02052e37 | −0.984576 | ||||||||
\(967\) | −2.88610e37 | −1.38829 | −0.694146 | − | 0.719834i | \(-0.744218\pi\) | ||||
−0.694146 | + | 0.719834i | \(0.744218\pi\) | |||||||
\(968\) | −8.16022e36 | −0.387490 | ||||||||
\(969\) | −1.58465e37 | −0.742824 | ||||||||
\(970\) | −7.02806e36 | −0.325229 | ||||||||
\(971\) | 1.13134e36 | 0.0516836 | 0.0258418 | − | 0.999666i | \(-0.491773\pi\) | ||||
0.0258418 | + | 0.999666i | \(0.491773\pi\) | |||||||
\(972\) | −1.46149e37 | −0.659126 | ||||||||
\(973\) | 2.09421e37 | 0.932418 | ||||||||
\(974\) | 2.87611e36 | 0.126421 | ||||||||
\(975\) | −1.08066e37 | −0.468956 | ||||||||
\(976\) | −8.86361e36 | −0.379741 | ||||||||
\(977\) | 1.01024e37 | 0.427311 | 0.213655 | − | 0.976909i | \(-0.431463\pi\) | ||||
0.213655 | + | 0.976909i | \(0.431463\pi\) | |||||||
\(978\) | −4.99908e35 | −0.0208763 | ||||||||
\(979\) | 2.70908e36 | 0.111696 | ||||||||
\(980\) | −8.26151e35 | −0.0336305 | ||||||||
\(981\) | 1.74357e37 | 0.700771 | ||||||||
\(982\) | 2.32420e37 | 0.922316 | ||||||||
\(983\) | −3.32494e37 | −1.30276 | −0.651380 | − | 0.758752i | \(-0.725810\pi\) | ||||
−0.651380 | + | 0.758752i | \(0.725810\pi\) | |||||||
\(984\) | 8.07331e36 | 0.312330 | ||||||||
\(985\) | −1.47554e37 | −0.563634 | ||||||||
\(986\) | 7.56420e36 | 0.285300 | ||||||||
\(987\) | −4.34476e37 | −1.61808 | ||||||||
\(988\) | 2.37844e37 | 0.874643 | ||||||||
\(989\) | 1.21717e37 | 0.441973 | ||||||||
\(990\) | −1.06696e37 | −0.382569 | ||||||||
\(991\) | 2.31893e37 | 0.821044 | 0.410522 | − | 0.911851i | \(-0.365347\pi\) | ||||
0.410522 | + | 0.911851i | \(0.365347\pi\) | |||||||
\(992\) | 3.80897e36 | 0.133172 | ||||||||
\(993\) | −2.18762e37 | −0.755277 | ||||||||
\(994\) | 5.32726e36 | 0.181624 | ||||||||
\(995\) | −1.34749e37 | −0.453666 | ||||||||
\(996\) | 1.84243e37 | 0.612561 | ||||||||
\(997\) | 6.52365e36 | 0.214191 | 0.107096 | − | 0.994249i | \(-0.465845\pi\) | ||||
0.107096 | + | 0.994249i | \(0.465845\pi\) | |||||||
\(998\) | −9.39530e36 | −0.304634 | ||||||||
\(999\) | −1.13773e37 | −0.364309 |
(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 | 10.26.a.c.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 50.26.b.c.49.1 | 4 | |||
5.3 | odd | 4 | 50.26.b.c.49.4 | 4 | |||
5.4 | even | 2 | 50.26.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.26.a.e.1.1 | 2 | 5.4 | even | 2 | |||
50.26.b.c.49.1 | 4 | 5.2 | odd | 4 | |||
50.26.b.c.49.4 | 4 | 5.3 | odd | 4 |