Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,18,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(53.1344053299\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −65.9873 | −0.182266 | −0.0911330 | − | 0.995839i | \(-0.529049\pi\) | ||||
−0.0911330 | + | 0.995839i | \(0.529049\pi\) | |||||||
\(3\) | 22515.6 | 1.98132 | 0.990658 | − | 0.136372i | \(-0.0435442\pi\) | ||||
0.990658 | + | 0.136372i | \(0.0435442\pi\) | |||||||
\(4\) | −126718. | −0.966779 | ||||||||
\(5\) | 342266. | 0.391849 | 0.195924 | − | 0.980619i | \(-0.437229\pi\) | ||||
0.195924 | + | 0.980619i | \(0.437229\pi\) | |||||||
\(6\) | −1.48575e6 | −0.361126 | ||||||||
\(7\) | 1.63719e7 | 1.07341 | 0.536707 | − | 0.843769i | \(-0.319668\pi\) | ||||
0.536707 | + | 0.843769i | \(0.319668\pi\) | |||||||
\(8\) | 1.70108e7 | 0.358477 | ||||||||
\(9\) | 3.77814e8 | 2.92561 | ||||||||
\(10\) | −2.25852e7 | −0.0714206 | ||||||||
\(11\) | 1.38186e8 | 0.194369 | 0.0971846 | − | 0.995266i | \(-0.469016\pi\) | ||||
0.0971846 | + | 0.995266i | \(0.469016\pi\) | |||||||
\(12\) | −2.85313e9 | −1.91549 | ||||||||
\(13\) | −3.21553e9 | −1.09329 | −0.546644 | − | 0.837365i | \(-0.684095\pi\) | ||||
−0.546644 | + | 0.837365i | \(0.684095\pi\) | |||||||
\(14\) | −1.08034e9 | −0.195647 | ||||||||
\(15\) | 7.70633e9 | 0.776376 | ||||||||
\(16\) | 1.54866e10 | 0.901441 | ||||||||
\(17\) | 3.77540e10 | 1.31264 | 0.656322 | − | 0.754481i | \(-0.272111\pi\) | ||||
0.656322 | + | 0.754481i | \(0.272111\pi\) | |||||||
\(18\) | −2.49309e10 | −0.533239 | ||||||||
\(19\) | −6.09675e10 | −0.823556 | −0.411778 | − | 0.911284i | \(-0.635092\pi\) | ||||
−0.411778 | + | 0.911284i | \(0.635092\pi\) | |||||||
\(20\) | −4.33711e10 | −0.378831 | ||||||||
\(21\) | 3.68625e11 | 2.12677 | ||||||||
\(22\) | −9.11855e9 | −0.0354269 | ||||||||
\(23\) | 2.42040e11 | 0.644468 | 0.322234 | − | 0.946660i | \(-0.395566\pi\) | ||||
0.322234 | + | 0.946660i | \(0.395566\pi\) | |||||||
\(24\) | 3.83010e11 | 0.710256 | ||||||||
\(25\) | −6.45794e11 | −0.846455 | ||||||||
\(26\) | 2.12184e11 | 0.199269 | ||||||||
\(27\) | 5.59905e12 | 3.81524 | ||||||||
\(28\) | −2.07461e12 | −1.03775 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | −5.08520e11 | −0.141507 | ||||||||
\(31\) | −1.83676e12 | −0.386793 | −0.193397 | − | 0.981121i | \(-0.561950\pi\) | ||||
−0.193397 | + | 0.981121i | \(0.561950\pi\) | |||||||
\(32\) | −3.25157e12 | −0.522779 | ||||||||
\(33\) | 3.11136e12 | 0.385107 | ||||||||
\(34\) | −2.49128e12 | −0.239250 | ||||||||
\(35\) | 5.60355e12 | 0.420615 | ||||||||
\(36\) | −4.78757e13 | −2.82842 | ||||||||
\(37\) | 1.75933e13 | 0.823440 | 0.411720 | − | 0.911310i | \(-0.364928\pi\) | ||||
0.411720 | + | 0.911310i | \(0.364928\pi\) | |||||||
\(38\) | 4.02308e12 | 0.150106 | ||||||||
\(39\) | −7.23998e13 | −2.16615 | ||||||||
\(40\) | 5.82223e12 | 0.140469 | ||||||||
\(41\) | 1.19591e13 | 0.233902 | 0.116951 | − | 0.993138i | \(-0.462688\pi\) | ||||
0.116951 | + | 0.993138i | \(0.462688\pi\) | |||||||
\(42\) | −2.43246e13 | −0.387638 | ||||||||
\(43\) | −5.09731e13 | −0.665058 | −0.332529 | − | 0.943093i | \(-0.607902\pi\) | ||||
−0.332529 | + | 0.943093i | \(0.607902\pi\) | |||||||
\(44\) | −1.75107e13 | −0.187912 | ||||||||
\(45\) | 1.29313e14 | 1.14640 | ||||||||
\(46\) | −1.59716e13 | −0.117464 | ||||||||
\(47\) | 5.99637e13 | 0.367330 | 0.183665 | − | 0.982989i | \(-0.441204\pi\) | ||||
0.183665 | + | 0.982989i | \(0.441204\pi\) | |||||||
\(48\) | 3.48692e14 | 1.78604 | ||||||||
\(49\) | 3.54101e13 | 0.152216 | ||||||||
\(50\) | 4.26142e13 | 0.154280 | ||||||||
\(51\) | 8.50055e14 | 2.60076 | ||||||||
\(52\) | 4.07465e14 | 1.05697 | ||||||||
\(53\) | 8.34952e14 | 1.84212 | 0.921058 | − | 0.389426i | \(-0.127327\pi\) | ||||
0.921058 | + | 0.389426i | \(0.127327\pi\) | |||||||
\(54\) | −3.69466e14 | −0.695389 | ||||||||
\(55\) | 4.72965e13 | 0.0761633 | ||||||||
\(56\) | 2.78501e14 | 0.384794 | ||||||||
\(57\) | −1.37272e15 | −1.63172 | ||||||||
\(58\) | −3.30099e13 | −0.0338459 | ||||||||
\(59\) | −9.87609e14 | −0.875675 | −0.437838 | − | 0.899054i | \(-0.644255\pi\) | ||||
−0.437838 | + | 0.899054i | \(0.644255\pi\) | |||||||
\(60\) | −9.76528e14 | −0.750584 | ||||||||
\(61\) | −5.79160e14 | −0.386807 | −0.193404 | − | 0.981119i | \(-0.561953\pi\) | ||||
−0.193404 | + | 0.981119i | \(0.561953\pi\) | |||||||
\(62\) | 1.21203e14 | 0.0704992 | ||||||||
\(63\) | 6.18555e15 | 3.14039 | ||||||||
\(64\) | −1.81530e15 | −0.806156 | ||||||||
\(65\) | −1.10057e15 | −0.428403 | ||||||||
\(66\) | −2.05310e14 | −0.0701919 | ||||||||
\(67\) | 5.24224e15 | 1.57718 | 0.788589 | − | 0.614921i | \(-0.210812\pi\) | ||||
0.788589 | + | 0.614921i | \(0.210812\pi\) | |||||||
\(68\) | −4.78410e15 | −1.26904 | ||||||||
\(69\) | 5.44969e15 | 1.27689 | ||||||||
\(70\) | −3.69763e14 | −0.0766639 | ||||||||
\(71\) | 9.25752e15 | 1.70137 | 0.850685 | − | 0.525676i | \(-0.176187\pi\) | ||||
0.850685 | + | 0.525676i | \(0.176187\pi\) | |||||||
\(72\) | 6.42693e15 | 1.04876 | ||||||||
\(73\) | −1.03766e16 | −1.50595 | −0.752973 | − | 0.658052i | \(-0.771381\pi\) | ||||
−0.752973 | + | 0.658052i | \(0.771381\pi\) | |||||||
\(74\) | −1.16093e15 | −0.150085 | ||||||||
\(75\) | −1.45405e16 | −1.67709 | ||||||||
\(76\) | 7.72566e15 | 0.796196 | ||||||||
\(77\) | 2.26238e15 | 0.208639 | ||||||||
\(78\) | 4.77747e15 | 0.394815 | ||||||||
\(79\) | 1.94267e16 | 1.44068 | 0.720341 | − | 0.693620i | \(-0.243985\pi\) | ||||
0.720341 | + | 0.693620i | \(0.243985\pi\) | |||||||
\(80\) | 5.30054e15 | 0.353228 | ||||||||
\(81\) | 7.72752e16 | 4.63359 | ||||||||
\(82\) | −7.89146e14 | −0.0426324 | ||||||||
\(83\) | −1.07716e16 | −0.524948 | −0.262474 | − | 0.964939i | \(-0.584538\pi\) | ||||
−0.262474 | + | 0.964939i | \(0.584538\pi\) | |||||||
\(84\) | −4.67113e16 | −2.05612 | ||||||||
\(85\) | 1.29219e16 | 0.514358 | ||||||||
\(86\) | 3.36358e15 | 0.121217 | ||||||||
\(87\) | 1.12634e16 | 0.367921 | ||||||||
\(88\) | 2.35067e15 | 0.0696769 | ||||||||
\(89\) | 5.92817e15 | 0.159627 | 0.0798133 | − | 0.996810i | \(-0.474568\pi\) | ||||
0.0798133 | + | 0.996810i | \(0.474568\pi\) | |||||||
\(90\) | −8.53300e15 | −0.208949 | ||||||||
\(91\) | −5.26446e16 | −1.17355 | ||||||||
\(92\) | −3.06708e16 | −0.623058 | ||||||||
\(93\) | −4.13559e16 | −0.766360 | ||||||||
\(94\) | −3.95685e15 | −0.0669518 | ||||||||
\(95\) | −2.08671e16 | −0.322709 | ||||||||
\(96\) | −7.32111e16 | −1.03579 | ||||||||
\(97\) | 7.11503e16 | 0.921758 | 0.460879 | − | 0.887463i | \(-0.347534\pi\) | ||||
0.460879 | + | 0.887463i | \(0.347534\pi\) | |||||||
\(98\) | −2.33662e15 | −0.0277438 | ||||||||
\(99\) | 5.22088e16 | 0.568649 | ||||||||
\(100\) | 8.18335e16 | 0.818335 | ||||||||
\(101\) | −3.90210e16 | −0.358564 | −0.179282 | − | 0.983798i | \(-0.557377\pi\) | ||||
−0.179282 | + | 0.983798i | \(0.557377\pi\) | |||||||
\(102\) | −5.60929e16 | −0.474030 | ||||||||
\(103\) | −1.05247e17 | −0.818642 | −0.409321 | − | 0.912390i | \(-0.634234\pi\) | ||||
−0.409321 | + | 0.912390i | \(0.634234\pi\) | |||||||
\(104\) | −5.46990e16 | −0.391918 | ||||||||
\(105\) | 1.26168e17 | 0.833372 | ||||||||
\(106\) | −5.50963e16 | −0.335755 | ||||||||
\(107\) | 8.88125e16 | 0.499703 | 0.249851 | − | 0.968284i | \(-0.419618\pi\) | ||||
0.249851 | + | 0.968284i | \(0.419618\pi\) | |||||||
\(108\) | −7.09498e17 | −3.68850 | ||||||||
\(109\) | −1.95228e17 | −0.938462 | −0.469231 | − | 0.883076i | \(-0.655469\pi\) | ||||
−0.469231 | + | 0.883076i | \(0.655469\pi\) | |||||||
\(110\) | −3.12097e15 | −0.0138820 | ||||||||
\(111\) | 3.96124e17 | 1.63150 | ||||||||
\(112\) | 2.53546e17 | 0.967619 | ||||||||
\(113\) | 3.31667e17 | 1.17364 | 0.586821 | − | 0.809716i | \(-0.300379\pi\) | ||||
0.586821 | + | 0.809716i | \(0.300379\pi\) | |||||||
\(114\) | 9.05823e16 | 0.297408 | ||||||||
\(115\) | 8.28421e16 | 0.252534 | ||||||||
\(116\) | −6.33901e16 | −0.179526 | ||||||||
\(117\) | −1.21487e18 | −3.19854 | ||||||||
\(118\) | 6.51697e16 | 0.159606 | ||||||||
\(119\) | 6.18106e17 | 1.40901 | ||||||||
\(120\) | 1.31091e17 | 0.278313 | ||||||||
\(121\) | −4.86352e17 | −0.962221 | ||||||||
\(122\) | 3.82172e16 | 0.0705018 | ||||||||
\(123\) | 2.69266e17 | 0.463434 | ||||||||
\(124\) | 2.32750e17 | 0.373944 | ||||||||
\(125\) | −4.82161e17 | −0.723531 | ||||||||
\(126\) | −4.08168e17 | −0.572386 | ||||||||
\(127\) | −9.02041e17 | −1.18276 | −0.591378 | − | 0.806395i | \(-0.701416\pi\) | ||||
−0.591378 | + | 0.806395i | \(0.701416\pi\) | |||||||
\(128\) | 5.45976e17 | 0.669714 | ||||||||
\(129\) | −1.14769e18 | −1.31769 | ||||||||
\(130\) | 7.26234e16 | 0.0780833 | ||||||||
\(131\) | 1.14535e18 | 1.15380 | 0.576902 | − | 0.816814i | \(-0.304262\pi\) | ||||
0.576902 | + | 0.816814i | \(0.304262\pi\) | |||||||
\(132\) | −3.94264e17 | −0.372313 | ||||||||
\(133\) | −9.98157e17 | −0.884015 | ||||||||
\(134\) | −3.45921e17 | −0.287466 | ||||||||
\(135\) | 1.91636e18 | 1.49500 | ||||||||
\(136\) | 6.42227e17 | 0.470553 | ||||||||
\(137\) | −1.40517e18 | −0.967398 | −0.483699 | − | 0.875234i | \(-0.660707\pi\) | ||||
−0.483699 | + | 0.875234i | \(0.660707\pi\) | |||||||
\(138\) | −3.59611e17 | −0.232734 | ||||||||
\(139\) | −3.85585e17 | −0.234690 | −0.117345 | − | 0.993091i | \(-0.537438\pi\) | ||||
−0.117345 | + | 0.993091i | \(0.537438\pi\) | |||||||
\(140\) | −7.10069e17 | −0.406642 | ||||||||
\(141\) | 1.35012e18 | 0.727798 | ||||||||
\(142\) | −6.10879e17 | −0.310102 | ||||||||
\(143\) | −4.44343e17 | −0.212502 | ||||||||
\(144\) | 5.85107e18 | 2.63727 | ||||||||
\(145\) | 1.71217e17 | 0.0727645 | ||||||||
\(146\) | 6.84721e17 | 0.274482 | ||||||||
\(147\) | 7.97281e17 | 0.301588 | ||||||||
\(148\) | −2.22938e18 | −0.796085 | ||||||||
\(149\) | −1.18889e17 | −0.0400921 | −0.0200460 | − | 0.999799i | \(-0.506381\pi\) | ||||
−0.0200460 | + | 0.999799i | \(0.506381\pi\) | |||||||
\(150\) | 9.59486e17 | 0.305677 | ||||||||
\(151\) | −5.97320e18 | −1.79847 | −0.899235 | − | 0.437466i | \(-0.855876\pi\) | ||||
−0.899235 | + | 0.437466i | \(0.855876\pi\) | |||||||
\(152\) | −1.03711e18 | −0.295226 | ||||||||
\(153\) | 1.42640e19 | 3.84029 | ||||||||
\(154\) | −1.49288e17 | −0.0380277 | ||||||||
\(155\) | −6.28661e17 | −0.151564 | ||||||||
\(156\) | 9.17434e18 | 2.09419 | ||||||||
\(157\) | −3.79849e18 | −0.821229 | −0.410614 | − | 0.911809i | \(-0.634686\pi\) | ||||
−0.410614 | + | 0.911809i | \(0.634686\pi\) | |||||||
\(158\) | −1.28191e18 | −0.262587 | ||||||||
\(159\) | 1.87995e19 | 3.64981 | ||||||||
\(160\) | −1.11290e18 | −0.204850 | ||||||||
\(161\) | 3.96267e18 | 0.691780 | ||||||||
\(162\) | −5.09918e18 | −0.844545 | ||||||||
\(163\) | −1.06189e19 | −1.66910 | −0.834552 | − | 0.550929i | \(-0.814274\pi\) | ||||
−0.834552 | + | 0.550929i | \(0.814274\pi\) | |||||||
\(164\) | −1.51542e18 | −0.226132 | ||||||||
\(165\) | 1.06491e18 | 0.150904 | ||||||||
\(166\) | 7.10789e17 | 0.0956802 | ||||||||
\(167\) | 2.59417e17 | 0.0331824 | 0.0165912 | − | 0.999862i | \(-0.494719\pi\) | ||||
0.0165912 | + | 0.999862i | \(0.494719\pi\) | |||||||
\(168\) | 6.27062e18 | 0.762398 | ||||||||
\(169\) | 1.68925e18 | 0.195279 | ||||||||
\(170\) | −8.52681e17 | −0.0937499 | ||||||||
\(171\) | −2.30344e19 | −2.40940 | ||||||||
\(172\) | 6.45920e18 | 0.642964 | ||||||||
\(173\) | −3.94225e18 | −0.373553 | −0.186776 | − | 0.982402i | \(-0.559804\pi\) | ||||
−0.186776 | + | 0.982402i | \(0.559804\pi\) | |||||||
\(174\) | −7.43239e17 | −0.0670595 | ||||||||
\(175\) | −1.05729e19 | −0.908596 | ||||||||
\(176\) | 2.14004e18 | 0.175212 | ||||||||
\(177\) | −2.22366e19 | −1.73499 | ||||||||
\(178\) | −3.91184e17 | −0.0290945 | ||||||||
\(179\) | 1.98644e19 | 1.40872 | 0.704360 | − | 0.709843i | \(-0.251234\pi\) | ||||
0.704360 | + | 0.709843i | \(0.251234\pi\) | |||||||
\(180\) | −1.63862e19 | −1.10831 | ||||||||
\(181\) | −2.32630e19 | −1.50106 | −0.750531 | − | 0.660835i | \(-0.770202\pi\) | ||||
−0.750531 | + | 0.660835i | \(0.770202\pi\) | |||||||
\(182\) | 3.47387e18 | 0.213898 | ||||||||
\(183\) | −1.30402e19 | −0.766388 | ||||||||
\(184\) | 4.11731e18 | 0.231027 | ||||||||
\(185\) | 6.02158e18 | 0.322664 | ||||||||
\(186\) | 2.72897e18 | 0.139681 | ||||||||
\(187\) | 5.21709e18 | 0.255138 | ||||||||
\(188\) | −7.59847e18 | −0.355127 | ||||||||
\(189\) | 9.16673e19 | 4.09533 | ||||||||
\(190\) | 1.37696e18 | 0.0588189 | ||||||||
\(191\) | −3.80256e19 | −1.55343 | −0.776717 | − | 0.629850i | \(-0.783116\pi\) | ||||
−0.776717 | + | 0.629850i | \(0.783116\pi\) | |||||||
\(192\) | −4.08727e19 | −1.59725 | ||||||||
\(193\) | 1.89543e19 | 0.708712 | 0.354356 | − | 0.935111i | \(-0.384700\pi\) | ||||
0.354356 | + | 0.935111i | \(0.384700\pi\) | |||||||
\(194\) | −4.69502e18 | −0.168005 | ||||||||
\(195\) | −2.47800e19 | −0.848802 | ||||||||
\(196\) | −4.48709e18 | −0.147159 | ||||||||
\(197\) | −5.59698e19 | −1.75789 | −0.878943 | − | 0.476926i | \(-0.841751\pi\) | ||||
−0.878943 | + | 0.476926i | \(0.841751\pi\) | |||||||
\(198\) | −3.44512e18 | −0.103645 | ||||||||
\(199\) | 1.86947e19 | 0.538849 | 0.269424 | − | 0.963022i | \(-0.413167\pi\) | ||||
0.269424 | + | 0.963022i | \(0.413167\pi\) | |||||||
\(200\) | −1.09855e19 | −0.303434 | ||||||||
\(201\) | 1.18032e20 | 3.12489 | ||||||||
\(202\) | 2.57489e18 | 0.0653540 | ||||||||
\(203\) | 8.19001e18 | 0.199328 | ||||||||
\(204\) | −1.07717e20 | −2.51436 | ||||||||
\(205\) | 4.09317e18 | 0.0916542 | ||||||||
\(206\) | 6.94498e18 | 0.149211 | ||||||||
\(207\) | 9.14462e19 | 1.88546 | ||||||||
\(208\) | −4.97978e19 | −0.985535 | ||||||||
\(209\) | −8.42489e18 | −0.160074 | ||||||||
\(210\) | −8.32546e18 | −0.151895 | ||||||||
\(211\) | 1.83677e19 | 0.321851 | 0.160926 | − | 0.986967i | \(-0.448552\pi\) | ||||
0.160926 | + | 0.986967i | \(0.448552\pi\) | |||||||
\(212\) | −1.05803e20 | −1.78092 | ||||||||
\(213\) | 2.08439e20 | 3.37095 | ||||||||
\(214\) | −5.86050e18 | −0.0910788 | ||||||||
\(215\) | −1.74464e19 | −0.260602 | ||||||||
\(216\) | 9.52445e19 | 1.36768 | ||||||||
\(217\) | −3.00714e19 | −0.415189 | ||||||||
\(218\) | 1.28826e19 | 0.171050 | ||||||||
\(219\) | −2.33635e20 | −2.98375 | ||||||||
\(220\) | −5.99330e18 | −0.0736331 | ||||||||
\(221\) | −1.21399e20 | −1.43510 | ||||||||
\(222\) | −2.61392e19 | −0.297366 | ||||||||
\(223\) | −8.87499e18 | −0.0971799 | −0.0485900 | − | 0.998819i | \(-0.515473\pi\) | ||||
−0.0485900 | + | 0.998819i | \(0.515473\pi\) | |||||||
\(224\) | −5.32345e19 | −0.561158 | ||||||||
\(225\) | −2.43990e20 | −2.47640 | ||||||||
\(226\) | −2.18858e19 | −0.213915 | ||||||||
\(227\) | −6.49039e19 | −0.611014 | −0.305507 | − | 0.952190i | \(-0.598826\pi\) | ||||
−0.305507 | + | 0.952190i | \(0.598826\pi\) | |||||||
\(228\) | 1.73948e20 | 1.57752 | ||||||||
\(229\) | −8.59117e19 | −0.750673 | −0.375336 | − | 0.926889i | \(-0.622473\pi\) | ||||
−0.375336 | + | 0.926889i | \(0.622473\pi\) | |||||||
\(230\) | −5.46653e18 | −0.0460283 | ||||||||
\(231\) | 5.09390e19 | 0.413379 | ||||||||
\(232\) | 8.50961e18 | 0.0665675 | ||||||||
\(233\) | 1.92886e20 | 1.45471 | 0.727354 | − | 0.686263i | \(-0.240750\pi\) | ||||
0.727354 | + | 0.686263i | \(0.240750\pi\) | |||||||
\(234\) | 8.01662e19 | 0.582984 | ||||||||
\(235\) | 2.05235e19 | 0.143938 | ||||||||
\(236\) | 1.25148e20 | 0.846584 | ||||||||
\(237\) | 4.37404e20 | 2.85445 | ||||||||
\(238\) | −4.07872e19 | −0.256814 | ||||||||
\(239\) | 6.89822e18 | 0.0419136 | 0.0209568 | − | 0.999780i | \(-0.493329\pi\) | ||||
0.0209568 | + | 0.999780i | \(0.493329\pi\) | |||||||
\(240\) | 1.19345e20 | 0.699857 | ||||||||
\(241\) | −2.63569e20 | −1.49193 | −0.745966 | − | 0.665983i | \(-0.768012\pi\) | ||||
−0.745966 | + | 0.665983i | \(0.768012\pi\) | |||||||
\(242\) | 3.20930e19 | 0.175380 | ||||||||
\(243\) | 1.01684e21 | 5.36536 | ||||||||
\(244\) | 7.33898e19 | 0.373957 | ||||||||
\(245\) | 1.21197e19 | 0.0596457 | ||||||||
\(246\) | −1.77681e19 | −0.0844682 | ||||||||
\(247\) | 1.96043e20 | 0.900384 | ||||||||
\(248\) | −3.12449e19 | −0.138656 | ||||||||
\(249\) | −2.42529e20 | −1.04009 | ||||||||
\(250\) | 3.18165e19 | 0.131875 | ||||||||
\(251\) | −1.94638e20 | −0.779831 | −0.389916 | − | 0.920851i | \(-0.627496\pi\) | ||||
−0.389916 | + | 0.920851i | \(0.627496\pi\) | |||||||
\(252\) | −7.83818e20 | −3.03606 | ||||||||
\(253\) | 3.34467e19 | 0.125265 | ||||||||
\(254\) | 5.95233e19 | 0.215576 | ||||||||
\(255\) | 2.90945e20 | 1.01911 | ||||||||
\(256\) | 2.01908e20 | 0.684090 | ||||||||
\(257\) | −2.59950e20 | −0.852035 | −0.426018 | − | 0.904715i | \(-0.640084\pi\) | ||||
−0.426018 | + | 0.904715i | \(0.640084\pi\) | |||||||
\(258\) | 7.57332e19 | 0.240170 | ||||||||
\(259\) | 2.88036e20 | 0.883892 | ||||||||
\(260\) | 1.39461e20 | 0.414171 | ||||||||
\(261\) | 1.89000e20 | 0.543272 | ||||||||
\(262\) | −7.55785e19 | −0.210299 | ||||||||
\(263\) | −6.08855e20 | −1.64017 | −0.820087 | − | 0.572239i | \(-0.806075\pi\) | ||||
−0.820087 | + | 0.572239i | \(0.806075\pi\) | |||||||
\(264\) | 5.29268e19 | 0.138052 | ||||||||
\(265\) | 2.85775e20 | 0.721830 | ||||||||
\(266\) | 6.58657e19 | 0.161126 | ||||||||
\(267\) | 1.33476e20 | 0.316271 | ||||||||
\(268\) | −6.64284e20 | −1.52478 | ||||||||
\(269\) | 2.10139e20 | 0.467319 | 0.233659 | − | 0.972319i | \(-0.424930\pi\) | ||||
0.233659 | + | 0.972319i | \(0.424930\pi\) | |||||||
\(270\) | −1.26456e20 | −0.272487 | ||||||||
\(271\) | −5.03341e20 | −1.05105 | −0.525525 | − | 0.850778i | \(-0.676131\pi\) | ||||
−0.525525 | + | 0.850778i | \(0.676131\pi\) | |||||||
\(272\) | 5.84683e20 | 1.18327 | ||||||||
\(273\) | −1.18533e21 | −2.32517 | ||||||||
\(274\) | 9.27236e19 | 0.176324 | ||||||||
\(275\) | −8.92399e19 | −0.164525 | ||||||||
\(276\) | −6.90572e20 | −1.23447 | ||||||||
\(277\) | 4.95306e20 | 0.858609 | 0.429304 | − | 0.903160i | \(-0.358759\pi\) | ||||
0.429304 | + | 0.903160i | \(0.358759\pi\) | |||||||
\(278\) | 2.54437e19 | 0.0427760 | ||||||||
\(279\) | −6.93955e20 | −1.13161 | ||||||||
\(280\) | 9.53212e19 | 0.150781 | ||||||||
\(281\) | −9.17961e19 | −0.140871 | −0.0704353 | − | 0.997516i | \(-0.522439\pi\) | ||||
−0.0704353 | + | 0.997516i | \(0.522439\pi\) | |||||||
\(282\) | −8.90909e19 | −0.132653 | ||||||||
\(283\) | −2.56229e20 | −0.370205 | −0.185103 | − | 0.982719i | \(-0.559262\pi\) | ||||
−0.185103 | + | 0.982719i | \(0.559262\pi\) | |||||||
\(284\) | −1.17309e21 | −1.64485 | ||||||||
\(285\) | −4.69836e20 | −0.639388 | ||||||||
\(286\) | 2.93210e19 | 0.0387318 | ||||||||
\(287\) | 1.95793e20 | 0.251074 | ||||||||
\(288\) | −1.22849e21 | −1.52945 | ||||||||
\(289\) | 5.98124e20 | 0.723036 | ||||||||
\(290\) | −1.12982e19 | −0.0132625 | ||||||||
\(291\) | 1.60199e21 | 1.82629 | ||||||||
\(292\) | 1.31489e21 | 1.45592 | ||||||||
\(293\) | 1.42832e21 | 1.53621 | 0.768105 | − | 0.640324i | \(-0.221200\pi\) | ||||
0.768105 | + | 0.640324i | \(0.221200\pi\) | |||||||
\(294\) | −5.26104e19 | −0.0549692 | ||||||||
\(295\) | −3.38025e20 | −0.343132 | ||||||||
\(296\) | 2.99277e20 | 0.295184 | ||||||||
\(297\) | 7.73713e20 | 0.741566 | ||||||||
\(298\) | 7.84517e18 | 0.00730742 | ||||||||
\(299\) | −7.78289e20 | −0.704589 | ||||||||
\(300\) | 1.84253e21 | 1.62138 | ||||||||
\(301\) | −8.34529e20 | −0.713882 | ||||||||
\(302\) | 3.94156e20 | 0.327800 | ||||||||
\(303\) | −8.78582e20 | −0.710428 | ||||||||
\(304\) | −9.44182e20 | −0.742387 | ||||||||
\(305\) | −1.98226e20 | −0.151570 | ||||||||
\(306\) | −9.41242e20 | −0.699953 | ||||||||
\(307\) | 1.09544e21 | 0.792342 | 0.396171 | − | 0.918177i | \(-0.370339\pi\) | ||||
0.396171 | + | 0.918177i | \(0.370339\pi\) | |||||||
\(308\) | −2.86684e20 | −0.201707 | ||||||||
\(309\) | −2.36971e21 | −1.62199 | ||||||||
\(310\) | 4.14837e19 | 0.0276250 | ||||||||
\(311\) | −8.72677e20 | −0.565445 | −0.282723 | − | 0.959202i | \(-0.591238\pi\) | ||||
−0.282723 | + | 0.959202i | \(0.591238\pi\) | |||||||
\(312\) | −1.23158e21 | −0.776514 | ||||||||
\(313\) | 2.31722e21 | 1.42181 | 0.710903 | − | 0.703290i | \(-0.248286\pi\) | ||||
0.710903 | + | 0.703290i | \(0.248286\pi\) | |||||||
\(314\) | 2.50652e20 | 0.149682 | ||||||||
\(315\) | 2.11710e21 | 1.23056 | ||||||||
\(316\) | −2.46170e21 | −1.39282 | ||||||||
\(317\) | 2.00368e21 | 1.10363 | 0.551816 | − | 0.833966i | \(-0.313935\pi\) | ||||
0.551816 | + | 0.833966i | \(0.313935\pi\) | |||||||
\(318\) | −1.24053e21 | −0.665236 | ||||||||
\(319\) | 6.91273e19 | 0.0360935 | ||||||||
\(320\) | −6.21316e20 | −0.315891 | ||||||||
\(321\) | 1.99967e21 | 0.990069 | ||||||||
\(322\) | −2.61486e20 | −0.126088 | ||||||||
\(323\) | −2.30177e21 | −1.08104 | ||||||||
\(324\) | −9.79213e21 | −4.47966 | ||||||||
\(325\) | 2.07657e21 | 0.925419 | ||||||||
\(326\) | 7.00710e20 | 0.304221 | ||||||||
\(327\) | −4.39568e21 | −1.85939 | ||||||||
\(328\) | 2.03434e20 | 0.0838485 | ||||||||
\(329\) | 9.81723e20 | 0.394297 | ||||||||
\(330\) | −7.02706e19 | −0.0275046 | ||||||||
\(331\) | 1.98894e20 | 0.0758725 | 0.0379362 | − | 0.999280i | \(-0.487922\pi\) | ||||
0.0379362 | + | 0.999280i | \(0.487922\pi\) | |||||||
\(332\) | 1.36495e21 | 0.507509 | ||||||||
\(333\) | 6.64699e21 | 2.40907 | ||||||||
\(334\) | −1.71182e19 | −0.00604803 | ||||||||
\(335\) | 1.79424e21 | 0.618015 | ||||||||
\(336\) | 5.70876e21 | 1.91716 | ||||||||
\(337\) | 5.06276e21 | 1.65780 | 0.828901 | − | 0.559395i | \(-0.188966\pi\) | ||||
0.828901 | + | 0.559395i | \(0.188966\pi\) | |||||||
\(338\) | −1.11469e20 | −0.0355927 | ||||||||
\(339\) | 7.46770e21 | 2.32536 | ||||||||
\(340\) | −1.63743e21 | −0.497270 | ||||||||
\(341\) | −2.53816e20 | −0.0751807 | ||||||||
\(342\) | 1.51998e21 | 0.439152 | ||||||||
\(343\) | −3.22888e21 | −0.910023 | ||||||||
\(344\) | −8.67096e20 | −0.238408 | ||||||||
\(345\) | 1.86524e21 | 0.500349 | ||||||||
\(346\) | 2.60138e20 | 0.0680859 | ||||||||
\(347\) | −3.81221e20 | −0.0973589 | −0.0486795 | − | 0.998814i | \(-0.515501\pi\) | ||||
−0.0486795 | + | 0.998814i | \(0.515501\pi\) | |||||||
\(348\) | −1.42727e21 | −0.355698 | ||||||||
\(349\) | 6.19750e21 | 1.50730 | 0.753652 | − | 0.657274i | \(-0.228291\pi\) | ||||
0.753652 | + | 0.657274i | \(0.228291\pi\) | |||||||
\(350\) | 6.97677e20 | 0.165606 | ||||||||
\(351\) | −1.80039e22 | −4.17116 | ||||||||
\(352\) | −4.49323e20 | −0.101612 | ||||||||
\(353\) | 7.56185e21 | 1.66933 | 0.834667 | − | 0.550755i | \(-0.185660\pi\) | ||||
0.834667 | + | 0.550755i | \(0.185660\pi\) | |||||||
\(354\) | 1.46734e21 | 0.316229 | ||||||||
\(355\) | 3.16853e21 | 0.666679 | ||||||||
\(356\) | −7.51203e20 | −0.154324 | ||||||||
\(357\) | 1.39171e22 | 2.79169 | ||||||||
\(358\) | −1.31080e21 | −0.256762 | ||||||||
\(359\) | −6.32890e21 | −1.21067 | −0.605334 | − | 0.795971i | \(-0.706961\pi\) | ||||
−0.605334 | + | 0.795971i | \(0.706961\pi\) | |||||||
\(360\) | 2.19972e21 | 0.410957 | ||||||||
\(361\) | −1.76335e21 | −0.321756 | ||||||||
\(362\) | 1.53507e21 | 0.273592 | ||||||||
\(363\) | −1.09505e22 | −1.90646 | ||||||||
\(364\) | 6.67100e21 | 1.13456 | ||||||||
\(365\) | −3.55154e21 | −0.590102 | ||||||||
\(366\) | 8.60485e20 | 0.139686 | ||||||||
\(367\) | 2.22304e21 | 0.352603 | 0.176301 | − | 0.984336i | \(-0.443587\pi\) | ||||
0.176301 | + | 0.984336i | \(0.443587\pi\) | |||||||
\(368\) | 3.74839e21 | 0.580950 | ||||||||
\(369\) | 4.51830e21 | 0.684307 | ||||||||
\(370\) | −3.97348e20 | −0.0588106 | ||||||||
\(371\) | 1.36698e22 | 1.97735 | ||||||||
\(372\) | 5.24053e21 | 0.740900 | ||||||||
\(373\) | −1.03913e22 | −1.43597 | −0.717985 | − | 0.696059i | \(-0.754935\pi\) | ||||
−0.717985 | + | 0.696059i | \(0.754935\pi\) | |||||||
\(374\) | −3.44262e20 | −0.0465029 | ||||||||
\(375\) | −1.08562e22 | −1.43354 | ||||||||
\(376\) | 1.02003e21 | 0.131679 | ||||||||
\(377\) | −1.60856e21 | −0.203019 | ||||||||
\(378\) | −6.04888e21 | −0.746439 | ||||||||
\(379\) | −9.65759e21 | −1.16529 | −0.582647 | − | 0.812725i | \(-0.697983\pi\) | ||||
−0.582647 | + | 0.812725i | \(0.697983\pi\) | |||||||
\(380\) | 2.64423e21 | 0.311988 | ||||||||
\(381\) | −2.03100e22 | −2.34341 | ||||||||
\(382\) | 2.50921e21 | 0.283138 | ||||||||
\(383\) | −1.49999e22 | −1.65539 | −0.827693 | − | 0.561182i | \(-0.810347\pi\) | ||||
−0.827693 | + | 0.561182i | \(0.810347\pi\) | |||||||
\(384\) | 1.22930e22 | 1.32691 | ||||||||
\(385\) | 7.74335e20 | 0.0817547 | ||||||||
\(386\) | −1.25074e21 | −0.129174 | ||||||||
\(387\) | −1.92584e22 | −1.94570 | ||||||||
\(388\) | −9.01600e21 | −0.891137 | ||||||||
\(389\) | 2.53264e21 | 0.244908 | 0.122454 | − | 0.992474i | \(-0.460924\pi\) | ||||
0.122454 | + | 0.992474i | \(0.460924\pi\) | |||||||
\(390\) | 1.63516e21 | 0.154708 | ||||||||
\(391\) | 9.13799e21 | 0.845957 | ||||||||
\(392\) | 6.02356e20 | 0.0545659 | ||||||||
\(393\) | 2.57883e22 | 2.28605 | ||||||||
\(394\) | 3.69330e21 | 0.320403 | ||||||||
\(395\) | 6.64909e21 | 0.564530 | ||||||||
\(396\) | −6.61577e21 | −0.549758 | ||||||||
\(397\) | −6.77939e21 | −0.551406 | −0.275703 | − | 0.961243i | \(-0.588911\pi\) | ||||
−0.275703 | + | 0.961243i | \(0.588911\pi\) | |||||||
\(398\) | −1.23361e21 | −0.0982138 | ||||||||
\(399\) | −2.24741e22 | −1.75151 | ||||||||
\(400\) | −1.00012e22 | −0.763029 | ||||||||
\(401\) | −1.41959e22 | −1.06032 | −0.530159 | − | 0.847898i | \(-0.677868\pi\) | ||||
−0.530159 | + | 0.847898i | \(0.677868\pi\) | |||||||
\(402\) | −7.78863e21 | −0.569560 | ||||||||
\(403\) | 5.90618e21 | 0.422877 | ||||||||
\(404\) | 4.94465e21 | 0.346652 | ||||||||
\(405\) | 2.64486e22 | 1.81566 | ||||||||
\(406\) | −5.40437e20 | −0.0363307 | ||||||||
\(407\) | 2.43115e21 | 0.160052 | ||||||||
\(408\) | 1.44602e22 | 0.932313 | ||||||||
\(409\) | 9.66139e20 | 0.0610087 | 0.0305043 | − | 0.999535i | \(-0.490289\pi\) | ||||
0.0305043 | + | 0.999535i | \(0.490289\pi\) | |||||||
\(410\) | −2.70098e20 | −0.0167054 | ||||||||
\(411\) | −3.16384e22 | −1.91672 | ||||||||
\(412\) | 1.33367e22 | 0.791446 | ||||||||
\(413\) | −1.61691e22 | −0.939961 | ||||||||
\(414\) | −6.03429e21 | −0.343655 | ||||||||
\(415\) | −3.68675e21 | −0.205700 | ||||||||
\(416\) | 1.04555e22 | 0.571548 | ||||||||
\(417\) | −8.68169e21 | −0.464995 | ||||||||
\(418\) | 5.55935e20 | 0.0291760 | ||||||||
\(419\) | 7.73948e21 | 0.398009 | 0.199004 | − | 0.979999i | \(-0.436229\pi\) | ||||
0.199004 | + | 0.979999i | \(0.436229\pi\) | |||||||
\(420\) | −1.59877e22 | −0.805687 | ||||||||
\(421\) | 1.25042e22 | 0.617532 | 0.308766 | − | 0.951138i | \(-0.400084\pi\) | ||||
0.308766 | + | 0.951138i | \(0.400084\pi\) | |||||||
\(422\) | −1.21204e21 | −0.0586625 | ||||||||
\(423\) | 2.26551e22 | 1.07467 | ||||||||
\(424\) | 1.42032e22 | 0.660356 | ||||||||
\(425\) | −2.43813e22 | −1.11109 | ||||||||
\(426\) | −1.37543e22 | −0.614409 | ||||||||
\(427\) | −9.48197e21 | −0.415204 | ||||||||
\(428\) | −1.12541e22 | −0.483102 | ||||||||
\(429\) | −1.00047e22 | −0.421033 | ||||||||
\(430\) | 1.15124e21 | 0.0474989 | ||||||||
\(431\) | 9.32674e21 | 0.377288 | 0.188644 | − | 0.982046i | \(-0.439591\pi\) | ||||
0.188644 | + | 0.982046i | \(0.439591\pi\) | |||||||
\(432\) | 8.67104e22 | 3.43922 | ||||||||
\(433\) | 2.93512e22 | 1.14151 | 0.570753 | − | 0.821121i | \(-0.306651\pi\) | ||||
0.570753 | + | 0.821121i | \(0.306651\pi\) | |||||||
\(434\) | 1.98433e21 | 0.0756748 | ||||||||
\(435\) | 3.85506e21 | 0.144169 | ||||||||
\(436\) | 2.47388e22 | 0.907285 | ||||||||
\(437\) | −1.47566e22 | −0.530755 | ||||||||
\(438\) | 1.54169e22 | 0.543836 | ||||||||
\(439\) | 4.39578e21 | 0.152086 | 0.0760428 | − | 0.997105i | \(-0.475771\pi\) | ||||
0.0760428 | + | 0.997105i | \(0.475771\pi\) | |||||||
\(440\) | 8.04553e20 | 0.0273028 | ||||||||
\(441\) | 1.33784e22 | 0.445325 | ||||||||
\(442\) | 8.01081e21 | 0.261570 | ||||||||
\(443\) | −3.38423e21 | −0.108400 | −0.0541999 | − | 0.998530i | \(-0.517261\pi\) | ||||
−0.0541999 | + | 0.998530i | \(0.517261\pi\) | |||||||
\(444\) | −5.01959e22 | −1.57730 | ||||||||
\(445\) | 2.02901e21 | 0.0625495 | ||||||||
\(446\) | 5.85637e20 | 0.0177126 | ||||||||
\(447\) | −2.67686e21 | −0.0794350 | ||||||||
\(448\) | −2.97200e22 | −0.865339 | ||||||||
\(449\) | −3.94737e22 | −1.12775 | −0.563876 | − | 0.825859i | \(-0.690691\pi\) | ||||
−0.563876 | + | 0.825859i | \(0.690691\pi\) | |||||||
\(450\) | 1.61002e22 | 0.451363 | ||||||||
\(451\) | 1.65258e21 | 0.0454634 | ||||||||
\(452\) | −4.20281e22 | −1.13465 | ||||||||
\(453\) | −1.34491e23 | −3.56334 | ||||||||
\(454\) | 4.28283e21 | 0.111367 | ||||||||
\(455\) | −1.80184e22 | −0.459854 | ||||||||
\(456\) | −2.33512e22 | −0.584935 | ||||||||
\(457\) | 9.39007e21 | 0.230877 | 0.115439 | − | 0.993315i | \(-0.463173\pi\) | ||||
0.115439 | + | 0.993315i | \(0.463173\pi\) | |||||||
\(458\) | 5.66908e21 | 0.136822 | ||||||||
\(459\) | 2.11386e23 | 5.00806 | ||||||||
\(460\) | −1.04976e22 | −0.244144 | ||||||||
\(461\) | 1.66822e22 | 0.380888 | 0.190444 | − | 0.981698i | \(-0.439007\pi\) | ||||
0.190444 | + | 0.981698i | \(0.439007\pi\) | |||||||
\(462\) | −3.36132e21 | −0.0753449 | ||||||||
\(463\) | −3.15330e22 | −0.693948 | −0.346974 | − | 0.937875i | \(-0.612791\pi\) | ||||
−0.346974 | + | 0.937875i | \(0.612791\pi\) | |||||||
\(464\) | 7.74714e21 | 0.167393 | ||||||||
\(465\) | −1.41547e22 | −0.300297 | ||||||||
\(466\) | −1.27280e22 | −0.265144 | ||||||||
\(467\) | −5.13437e22 | −1.05025 | −0.525126 | − | 0.851024i | \(-0.675982\pi\) | ||||
−0.525126 | + | 0.851024i | \(0.675982\pi\) | |||||||
\(468\) | 1.53946e23 | 3.09228 | ||||||||
\(469\) | 8.58256e22 | 1.69296 | ||||||||
\(470\) | −1.35429e21 | −0.0262350 | ||||||||
\(471\) | −8.55255e22 | −1.62711 | ||||||||
\(472\) | −1.68001e22 | −0.313909 | ||||||||
\(473\) | −7.04380e21 | −0.129267 | ||||||||
\(474\) | −2.88631e22 | −0.520268 | ||||||||
\(475\) | 3.93724e22 | 0.697102 | ||||||||
\(476\) | −7.83250e22 | −1.36220 | ||||||||
\(477\) | 3.15457e23 | 5.38931 | ||||||||
\(478\) | −4.55195e20 | −0.00763942 | ||||||||
\(479\) | 3.32260e22 | 0.547805 | 0.273902 | − | 0.961758i | \(-0.411686\pi\) | ||||
0.273902 | + | 0.961758i | \(0.411686\pi\) | |||||||
\(480\) | −2.50577e22 | −0.405873 | ||||||||
\(481\) | −5.65718e22 | −0.900258 | ||||||||
\(482\) | 1.73922e22 | 0.271929 | ||||||||
\(483\) | 8.92221e22 | 1.37063 | ||||||||
\(484\) | 6.16293e22 | 0.930255 | ||||||||
\(485\) | 2.43523e22 | 0.361190 | ||||||||
\(486\) | −6.70984e22 | −0.977922 | ||||||||
\(487\) | 2.03886e21 | 0.0292005 | 0.0146003 | − | 0.999893i | \(-0.495352\pi\) | ||||
0.0146003 | + | 0.999893i | \(0.495352\pi\) | |||||||
\(488\) | −9.85200e21 | −0.138661 | ||||||||
\(489\) | −2.39091e23 | −3.30702 | ||||||||
\(490\) | −7.99744e20 | −0.0108714 | ||||||||
\(491\) | −5.86767e22 | −0.783922 | −0.391961 | − | 0.919982i | \(-0.628203\pi\) | ||||
−0.391961 | + | 0.919982i | \(0.628203\pi\) | |||||||
\(492\) | −3.41207e22 | −0.448038 | ||||||||
\(493\) | 1.88863e22 | 0.243752 | ||||||||
\(494\) | −1.29364e22 | −0.164109 | ||||||||
\(495\) | 1.78693e22 | 0.222824 | ||||||||
\(496\) | −2.84453e22 | −0.348671 | ||||||||
\(497\) | 1.51564e23 | 1.82627 | ||||||||
\(498\) | 1.60039e22 | 0.189573 | ||||||||
\(499\) | −6.29044e22 | −0.732532 | −0.366266 | − | 0.930510i | \(-0.619364\pi\) | ||||
−0.366266 | + | 0.930510i | \(0.619364\pi\) | |||||||
\(500\) | 6.10983e22 | 0.699494 | ||||||||
\(501\) | 5.84094e21 | 0.0657449 | ||||||||
\(502\) | 1.28436e22 | 0.142137 | ||||||||
\(503\) | −5.80357e22 | −0.631491 | −0.315746 | − | 0.948844i | \(-0.602255\pi\) | ||||
−0.315746 | + | 0.948844i | \(0.602255\pi\) | |||||||
\(504\) | 1.05221e23 | 1.12576 | ||||||||
\(505\) | −1.33555e22 | −0.140503 | ||||||||
\(506\) | −2.20706e21 | −0.0228315 | ||||||||
\(507\) | 3.80344e22 | 0.386909 | ||||||||
\(508\) | 1.14305e23 | 1.14346 | ||||||||
\(509\) | 7.27184e22 | 0.715391 | 0.357695 | − | 0.933838i | \(-0.383563\pi\) | ||||
0.357695 | + | 0.933838i | \(0.383563\pi\) | |||||||
\(510\) | −1.91987e22 | −0.185748 | ||||||||
\(511\) | −1.69884e23 | −1.61650 | ||||||||
\(512\) | −8.48856e22 | −0.794400 | ||||||||
\(513\) | −3.41360e23 | −3.14206 | ||||||||
\(514\) | 1.71534e22 | 0.155297 | ||||||||
\(515\) | −3.60225e22 | −0.320784 | ||||||||
\(516\) | 1.45433e23 | 1.27391 | ||||||||
\(517\) | 8.28618e21 | 0.0713978 | ||||||||
\(518\) | −1.90067e22 | −0.161103 | ||||||||
\(519\) | −8.87622e22 | −0.740126 | ||||||||
\(520\) | −1.87216e22 | −0.153573 | ||||||||
\(521\) | 6.46306e22 | 0.521576 | 0.260788 | − | 0.965396i | \(-0.416018\pi\) | ||||
0.260788 | + | 0.965396i | \(0.416018\pi\) | |||||||
\(522\) | −1.24716e22 | −0.0990200 | ||||||||
\(523\) | −6.52155e21 | −0.0509433 | −0.0254716 | − | 0.999676i | \(-0.508109\pi\) | ||||
−0.0254716 | + | 0.999676i | \(0.508109\pi\) | |||||||
\(524\) | −1.45136e23 | −1.11547 | ||||||||
\(525\) | −2.38056e23 | −1.80021 | ||||||||
\(526\) | 4.01767e22 | 0.298948 | ||||||||
\(527\) | −6.93452e22 | −0.507722 | ||||||||
\(528\) | 4.81845e22 | 0.347151 | ||||||||
\(529\) | −8.24665e22 | −0.584661 | ||||||||
\(530\) | −1.88576e22 | −0.131565 | ||||||||
\(531\) | −3.73132e23 | −2.56188 | ||||||||
\(532\) | 1.26484e23 | 0.854648 | ||||||||
\(533\) | −3.84548e22 | −0.255722 | ||||||||
\(534\) | −8.80775e21 | −0.0576454 | ||||||||
\(535\) | 3.03975e22 | 0.195808 | ||||||||
\(536\) | 8.91749e22 | 0.565382 | ||||||||
\(537\) | 4.47260e23 | 2.79112 | ||||||||
\(538\) | −1.38665e22 | −0.0851763 | ||||||||
\(539\) | 4.89320e21 | 0.0295861 | ||||||||
\(540\) | −2.42837e23 | −1.44533 | ||||||||
\(541\) | −1.77640e23 | −1.04079 | −0.520396 | − | 0.853925i | \(-0.674216\pi\) | ||||
−0.520396 | + | 0.853925i | \(0.674216\pi\) | |||||||
\(542\) | 3.32141e22 | 0.191570 | ||||||||
\(543\) | −5.23782e23 | −2.97408 | ||||||||
\(544\) | −1.22760e23 | −0.686223 | ||||||||
\(545\) | −6.68198e22 | −0.367735 | ||||||||
\(546\) | 7.82165e22 | 0.423800 | ||||||||
\(547\) | 2.55242e23 | 1.36163 | 0.680817 | − | 0.732454i | \(-0.261625\pi\) | ||||
0.680817 | + | 0.732454i | \(0.261625\pi\) | |||||||
\(548\) | 1.78060e23 | 0.935260 | ||||||||
\(549\) | −2.18815e23 | −1.13165 | ||||||||
\(550\) | 5.88870e21 | 0.0299873 | ||||||||
\(551\) | −3.04988e22 | −0.152930 | ||||||||
\(552\) | 9.27039e22 | 0.457737 | ||||||||
\(553\) | 3.18053e23 | 1.54645 | ||||||||
\(554\) | −3.26839e22 | −0.156495 | ||||||||
\(555\) | 1.35580e23 | 0.639299 | ||||||||
\(556\) | 4.88604e22 | 0.226893 | ||||||||
\(557\) | 4.34159e22 | 0.198554 | 0.0992772 | − | 0.995060i | \(-0.468347\pi\) | ||||
0.0992772 | + | 0.995060i | \(0.468347\pi\) | |||||||
\(558\) | 4.57922e22 | 0.206253 | ||||||||
\(559\) | 1.63906e23 | 0.727100 | ||||||||
\(560\) | 8.67802e22 | 0.379160 | ||||||||
\(561\) | 1.17466e23 | 0.505508 | ||||||||
\(562\) | 6.05738e21 | 0.0256759 | ||||||||
\(563\) | 3.78966e23 | 1.58226 | 0.791132 | − | 0.611645i | \(-0.209492\pi\) | ||||
0.791132 | + | 0.611645i | \(0.209492\pi\) | |||||||
\(564\) | −1.71084e23 | −0.703619 | ||||||||
\(565\) | 1.13518e23 | 0.459890 | ||||||||
\(566\) | 1.69078e22 | 0.0674758 | ||||||||
\(567\) | 1.26515e24 | 4.97376 | ||||||||
\(568\) | 1.57478e23 | 0.609902 | ||||||||
\(569\) | −6.99505e22 | −0.266893 | −0.133446 | − | 0.991056i | \(-0.542604\pi\) | ||||
−0.133446 | + | 0.991056i | \(0.542604\pi\) | |||||||
\(570\) | 3.10032e22 | 0.116539 | ||||||||
\(571\) | 2.29202e23 | 0.848813 | 0.424406 | − | 0.905472i | \(-0.360483\pi\) | ||||
0.424406 | + | 0.905472i | \(0.360483\pi\) | |||||||
\(572\) | 5.63061e22 | 0.205442 | ||||||||
\(573\) | −8.56171e23 | −3.07784 | ||||||||
\(574\) | −1.29199e22 | −0.0457622 | ||||||||
\(575\) | −1.56308e23 | −0.545513 | ||||||||
\(576\) | −6.85846e23 | −2.35850 | ||||||||
\(577\) | 4.59513e23 | 1.55705 | 0.778527 | − | 0.627612i | \(-0.215967\pi\) | ||||
0.778527 | + | 0.627612i | \(0.215967\pi\) | |||||||
\(578\) | −3.94686e22 | −0.131785 | ||||||||
\(579\) | 4.26768e23 | 1.40418 | ||||||||
\(580\) | −2.16962e22 | −0.0703472 | ||||||||
\(581\) | −1.76352e23 | −0.563486 | ||||||||
\(582\) | −1.05711e23 | −0.332871 | ||||||||
\(583\) | 1.15379e23 | 0.358051 | ||||||||
\(584\) | −1.76514e23 | −0.539846 | ||||||||
\(585\) | −4.15809e23 | −1.25334 | ||||||||
\(586\) | −9.42510e22 | −0.279999 | ||||||||
\(587\) | 4.56546e23 | 1.33678 | 0.668391 | − | 0.743810i | \(-0.266983\pi\) | ||||
0.668391 | + | 0.743810i | \(0.266983\pi\) | |||||||
\(588\) | −1.01030e23 | −0.291569 | ||||||||
\(589\) | 1.11983e23 | 0.318546 | ||||||||
\(590\) | 2.23053e22 | 0.0625413 | ||||||||
\(591\) | −1.26020e24 | −3.48293 | ||||||||
\(592\) | 2.72461e23 | 0.742283 | ||||||||
\(593\) | −4.07180e23 | −1.09351 | −0.546754 | − | 0.837294i | \(-0.684137\pi\) | ||||
−0.546754 | + | 0.837294i | \(0.684137\pi\) | |||||||
\(594\) | −5.10552e22 | −0.135162 | ||||||||
\(595\) | 2.11557e23 | 0.552119 | ||||||||
\(596\) | 1.50653e22 | 0.0387602 | ||||||||
\(597\) | 4.20923e23 | 1.06763 | ||||||||
\(598\) | 5.13572e22 | 0.128423 | ||||||||
\(599\) | −1.39283e23 | −0.343376 | −0.171688 | − | 0.985151i | \(-0.554922\pi\) | ||||
−0.171688 | + | 0.985151i | \(0.554922\pi\) | |||||||
\(600\) | −2.47345e23 | −0.601199 | ||||||||
\(601\) | −1.16683e23 | −0.279623 | −0.139812 | − | 0.990178i | \(-0.544650\pi\) | ||||
−0.139812 | + | 0.990178i | \(0.544650\pi\) | |||||||
\(602\) | 5.50684e22 | 0.130116 | ||||||||
\(603\) | 1.98059e24 | 4.61421 | ||||||||
\(604\) | 7.56911e23 | 1.73872 | ||||||||
\(605\) | −1.66461e23 | −0.377045 | ||||||||
\(606\) | 5.79753e22 | 0.129487 | ||||||||
\(607\) | −4.55704e23 | −1.00364 | −0.501821 | − | 0.864972i | \(-0.667336\pi\) | ||||
−0.501821 | + | 0.864972i | \(0.667336\pi\) | |||||||
\(608\) | 1.98240e23 | 0.430537 | ||||||||
\(609\) | 1.84403e23 | 0.394931 | ||||||||
\(610\) | 1.30804e22 | 0.0276260 | ||||||||
\(611\) | −1.92815e23 | −0.401598 | ||||||||
\(612\) | −1.80750e24 | −3.71271 | ||||||||
\(613\) | −1.48674e23 | −0.301176 | −0.150588 | − | 0.988597i | \(-0.548117\pi\) | ||||
−0.150588 | + | 0.988597i | \(0.548117\pi\) | |||||||
\(614\) | −7.22851e22 | −0.144417 | ||||||||
\(615\) | 9.21604e22 | 0.181596 | ||||||||
\(616\) | 3.84850e22 | 0.0747921 | ||||||||
\(617\) | −9.12127e23 | −1.74836 | −0.874181 | − | 0.485600i | \(-0.838601\pi\) | ||||
−0.874181 | + | 0.485600i | \(0.838601\pi\) | |||||||
\(618\) | 1.56371e23 | 0.295633 | ||||||||
\(619\) | 2.35729e23 | 0.439584 | 0.219792 | − | 0.975547i | \(-0.429462\pi\) | ||||
0.219792 | + | 0.975547i | \(0.429462\pi\) | |||||||
\(620\) | 7.96625e22 | 0.146529 | ||||||||
\(621\) | 1.35520e24 | 2.45880 | ||||||||
\(622\) | 5.75856e22 | 0.103061 | ||||||||
\(623\) | 9.70556e22 | 0.171345 | ||||||||
\(624\) | −1.12123e24 | −1.95266 | ||||||||
\(625\) | 3.27674e23 | 0.562940 | ||||||||
\(626\) | −1.52907e23 | −0.259147 | ||||||||
\(627\) | −1.89692e23 | −0.317157 | ||||||||
\(628\) | 4.81336e23 | 0.793947 | ||||||||
\(629\) | 6.64217e23 | 1.08088 | ||||||||
\(630\) | −1.39702e23 | −0.224289 | ||||||||
\(631\) | 1.22019e23 | 0.193276 | 0.0966381 | − | 0.995320i | \(-0.469191\pi\) | ||||
0.0966381 | + | 0.995320i | \(0.469191\pi\) | |||||||
\(632\) | 3.30464e23 | 0.516451 | ||||||||
\(633\) | 4.13561e23 | 0.637688 | ||||||||
\(634\) | −1.32217e23 | −0.201154 | ||||||||
\(635\) | −3.08738e23 | −0.463461 | ||||||||
\(636\) | −2.38223e24 | −3.52856 | ||||||||
\(637\) | −1.13862e23 | −0.166416 | ||||||||
\(638\) | −4.56152e21 | −0.00657861 | ||||||||
\(639\) | 3.49762e24 | 4.97755 | ||||||||
\(640\) | 1.86869e23 | 0.262426 | ||||||||
\(641\) | −8.85231e23 | −1.22677 | −0.613385 | − | 0.789784i | \(-0.710193\pi\) | ||||
−0.613385 | + | 0.789784i | \(0.710193\pi\) | |||||||
\(642\) | −1.31953e23 | −0.180456 | ||||||||
\(643\) | 2.08225e23 | 0.281021 | 0.140511 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140511 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(644\) | −5.02141e23 | −0.668799 | ||||||||
\(645\) | −3.92816e23 | −0.516335 | ||||||||
\(646\) | 1.51887e23 | 0.197036 | ||||||||
\(647\) | 1.36987e24 | 1.75386 | 0.876928 | − | 0.480622i | \(-0.159589\pi\) | ||||
0.876928 | + | 0.480622i | \(0.159589\pi\) | |||||||
\(648\) | 1.31452e24 | 1.66103 | ||||||||
\(649\) | −1.36474e23 | −0.170204 | ||||||||
\(650\) | −1.37027e23 | −0.168672 | ||||||||
\(651\) | −6.77077e23 | −0.822621 | ||||||||
\(652\) | 1.34560e24 | 1.61366 | ||||||||
\(653\) | −6.01921e22 | −0.0712488 | −0.0356244 | − | 0.999365i | \(-0.511342\pi\) | ||||
−0.0356244 | + | 0.999365i | \(0.511342\pi\) | |||||||
\(654\) | 2.90059e23 | 0.338903 | ||||||||
\(655\) | 3.92014e23 | 0.452116 | ||||||||
\(656\) | 1.85206e23 | 0.210849 | ||||||||
\(657\) | −3.92041e24 | −4.40581 | ||||||||
\(658\) | −6.47813e22 | −0.0718670 | ||||||||
\(659\) | −9.41383e23 | −1.03096 | −0.515478 | − | 0.856903i | \(-0.672386\pi\) | ||||
−0.515478 | + | 0.856903i | \(0.672386\pi\) | |||||||
\(660\) | −1.34943e23 | −0.145890 | ||||||||
\(661\) | 9.26012e23 | 0.988335 | 0.494168 | − | 0.869367i | \(-0.335473\pi\) | ||||
0.494168 | + | 0.869367i | \(0.335473\pi\) | |||||||
\(662\) | −1.31245e22 | −0.0138290 | ||||||||
\(663\) | −2.73338e24 | −2.84338 | ||||||||
\(664\) | −1.83234e23 | −0.188182 | ||||||||
\(665\) | −3.41635e23 | −0.346400 | ||||||||
\(666\) | −4.38617e23 | −0.439091 | ||||||||
\(667\) | 1.21080e23 | 0.119675 | ||||||||
\(668\) | −3.28727e22 | −0.0320801 | ||||||||
\(669\) | −1.99826e23 | −0.192544 | ||||||||
\(670\) | −1.18397e23 | −0.112643 | ||||||||
\(671\) | −8.00320e22 | −0.0751835 | ||||||||
\(672\) | −1.19861e24 | −1.11183 | ||||||||
\(673\) | 2.41956e23 | 0.221619 | 0.110810 | − | 0.993842i | \(-0.464656\pi\) | ||||
0.110810 | + | 0.993842i | \(0.464656\pi\) | |||||||
\(674\) | −3.34078e23 | −0.302161 | ||||||||
\(675\) | −3.61583e24 | −3.22943 | ||||||||
\(676\) | −2.14057e23 | −0.188792 | ||||||||
\(677\) | 8.03744e23 | 0.700026 | 0.350013 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350013 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(678\) | −4.92774e23 | −0.423833 | ||||||||
\(679\) | 1.16487e24 | 0.989428 | ||||||||
\(680\) | 2.19812e23 | 0.184385 | ||||||||
\(681\) | −1.46135e24 | −1.21061 | ||||||||
\(682\) | 1.67486e22 | 0.0137029 | ||||||||
\(683\) | 1.66430e24 | 1.34480 | 0.672398 | − | 0.740190i | \(-0.265265\pi\) | ||||
0.672398 | + | 0.740190i | \(0.265265\pi\) | |||||||
\(684\) | 2.91886e24 | 2.32936 | ||||||||
\(685\) | −4.80943e23 | −0.379074 | ||||||||
\(686\) | 2.13065e23 | 0.165866 | ||||||||
\(687\) | −1.93436e24 | −1.48732 | ||||||||
\(688\) | −7.89403e23 | −0.599511 | ||||||||
\(689\) | −2.68482e24 | −2.01396 | ||||||||
\(690\) | −1.23082e23 | −0.0911966 | ||||||||
\(691\) | 1.12823e24 | 0.825724 | 0.412862 | − | 0.910794i | \(-0.364529\pi\) | ||||
0.412862 | + | 0.910794i | \(0.364529\pi\) | |||||||
\(692\) | 4.99552e23 | 0.361143 | ||||||||
\(693\) | 8.54759e23 | 0.610395 | ||||||||
\(694\) | 2.51557e22 | 0.0177452 | ||||||||
\(695\) | −1.31973e23 | −0.0919629 | ||||||||
\(696\) | 1.91599e23 | 0.131891 | ||||||||
\(697\) | 4.51502e23 | 0.307030 | ||||||||
\(698\) | −4.08957e23 | −0.274730 | ||||||||
\(699\) | 4.34295e24 | 2.88223 | ||||||||
\(700\) | 1.33977e24 | 0.878411 | ||||||||
\(701\) | −1.63857e24 | −1.06136 | −0.530679 | − | 0.847573i | \(-0.678063\pi\) | ||||
−0.530679 | + | 0.847573i | \(0.678063\pi\) | |||||||
\(702\) | 1.18803e24 | 0.760260 | ||||||||
\(703\) | −1.07262e24 | −0.678149 | ||||||||
\(704\) | −2.50850e23 | −0.156692 | ||||||||
\(705\) | 4.62100e23 | 0.285186 | ||||||||
\(706\) | −4.98986e23 | −0.304263 | ||||||||
\(707\) | −6.38849e23 | −0.384887 | ||||||||
\(708\) | 2.81778e24 | 1.67735 | ||||||||
\(709\) | −7.20175e22 | −0.0423590 | −0.0211795 | − | 0.999776i | \(-0.506742\pi\) | ||||
−0.0211795 | + | 0.999776i | \(0.506742\pi\) | |||||||
\(710\) | −2.09083e23 | −0.121513 | ||||||||
\(711\) | 7.33967e24 | 4.21488 | ||||||||
\(712\) | 1.00843e23 | 0.0572224 | ||||||||
\(713\) | −4.44571e23 | −0.249276 | ||||||||
\(714\) | −9.18349e23 | −0.508831 | ||||||||
\(715\) | −1.52083e23 | −0.0832685 | ||||||||
\(716\) | −2.51717e24 | −1.36192 | ||||||||
\(717\) | 1.55318e23 | 0.0830441 | ||||||||
\(718\) | 4.17627e23 | 0.220664 | ||||||||
\(719\) | −1.27896e24 | −0.667821 | −0.333910 | − | 0.942605i | \(-0.608368\pi\) | ||||
−0.333910 | + | 0.942605i | \(0.608368\pi\) | |||||||
\(720\) | 2.00262e24 | 1.03341 | ||||||||
\(721\) | −1.72310e24 | −0.878741 | ||||||||
\(722\) | 1.16359e23 | 0.0586452 | ||||||||
\(723\) | −5.93442e24 | −2.95599 | ||||||||
\(724\) | 2.94784e24 | 1.45120 | ||||||||
\(725\) | −3.23056e23 | −0.157183 | ||||||||
\(726\) | 7.22595e23 | 0.347483 | ||||||||
\(727\) | −7.38880e23 | −0.351181 | −0.175591 | − | 0.984463i | \(-0.556184\pi\) | ||||
−0.175591 | + | 0.984463i | \(0.556184\pi\) | |||||||
\(728\) | −8.95528e23 | −0.420690 | ||||||||
\(729\) | 1.29154e25 | 5.99688 | ||||||||
\(730\) | 2.34357e23 | 0.107556 | ||||||||
\(731\) | −1.92444e24 | −0.872985 | ||||||||
\(732\) | 1.65242e24 | 0.740927 | ||||||||
\(733\) | 3.18090e24 | 1.40983 | 0.704915 | − | 0.709292i | \(-0.250985\pi\) | ||||
0.704915 | + | 0.709292i | \(0.250985\pi\) | |||||||
\(734\) | −1.46692e23 | −0.0642675 | ||||||||
\(735\) | 2.72882e23 | 0.118177 | ||||||||
\(736\) | −7.87011e23 | −0.336914 | ||||||||
\(737\) | 7.24406e23 | 0.306555 | ||||||||
\(738\) | −2.98150e23 | −0.124726 | ||||||||
\(739\) | −1.82222e23 | −0.0753570 | −0.0376785 | − | 0.999290i | \(-0.511996\pi\) | ||||
−0.0376785 | + | 0.999290i | \(0.511996\pi\) | |||||||
\(740\) | −7.63040e23 | −0.311945 | ||||||||
\(741\) | 4.41404e24 | 1.78394 | ||||||||
\(742\) | −9.02033e23 | −0.360404 | ||||||||
\(743\) | −2.52156e24 | −0.996010 | −0.498005 | − | 0.867174i | \(-0.665934\pi\) | ||||
−0.498005 | + | 0.867174i | \(0.665934\pi\) | |||||||
\(744\) | −7.03499e23 | −0.274722 | ||||||||
\(745\) | −4.06916e22 | −0.0157100 | ||||||||
\(746\) | 6.85694e23 | 0.261728 | ||||||||
\(747\) | −4.06966e24 | −1.53579 | ||||||||
\(748\) | −6.61098e23 | −0.246662 | ||||||||
\(749\) | 1.45403e24 | 0.536388 | ||||||||
\(750\) | 7.16369e23 | 0.261286 | ||||||||
\(751\) | −1.63527e24 | −0.589724 | −0.294862 | − | 0.955540i | \(-0.595274\pi\) | ||||
−0.294862 | + | 0.955540i | \(0.595274\pi\) | |||||||
\(752\) | 9.28637e23 | 0.331127 | ||||||||
\(753\) | −4.38240e24 | −1.54509 | ||||||||
\(754\) | 1.06145e23 | 0.0370034 | ||||||||
\(755\) | −2.04442e24 | −0.704728 | ||||||||
\(756\) | −1.16159e25 | −3.95928 | ||||||||
\(757\) | −1.57529e24 | −0.530941 | −0.265471 | − | 0.964119i | \(-0.585527\pi\) | ||||
−0.265471 | + | 0.964119i | \(0.585527\pi\) | |||||||
\(758\) | 6.37278e23 | 0.212393 | ||||||||
\(759\) | 7.53074e23 | 0.248189 | ||||||||
\(760\) | −3.54967e23 | −0.115684 | ||||||||
\(761\) | −5.40935e24 | −1.74331 | −0.871656 | − | 0.490118i | \(-0.836954\pi\) | ||||
−0.871656 | + | 0.490118i | \(0.836954\pi\) | |||||||
\(762\) | 1.34020e24 | 0.427124 | ||||||||
\(763\) | −3.19626e24 | −1.00736 | ||||||||
\(764\) | 4.81852e24 | 1.50183 | ||||||||
\(765\) | 4.88207e24 | 1.50481 | ||||||||
\(766\) | 9.89804e23 | 0.301720 | ||||||||
\(767\) | 3.17569e24 | 0.957365 | ||||||||
\(768\) | 4.54608e24 | 1.35540 | ||||||||
\(769\) | 1.04343e24 | 0.307673 | 0.153837 | − | 0.988096i | \(-0.450837\pi\) | ||||
0.153837 | + | 0.988096i | \(0.450837\pi\) | |||||||
\(770\) | −5.10963e22 | −0.0149011 | ||||||||
\(771\) | −5.85293e24 | −1.68815 | ||||||||
\(772\) | −2.40184e24 | −0.685168 | ||||||||
\(773\) | −3.76662e24 | −1.06274 | −0.531369 | − | 0.847140i | \(-0.678322\pi\) | ||||
−0.531369 | + | 0.847140i | \(0.678322\pi\) | |||||||
\(774\) | 1.27081e24 | 0.354635 | ||||||||
\(775\) | 1.18617e24 | 0.327403 | ||||||||
\(776\) | 1.21033e24 | 0.330429 | ||||||||
\(777\) | 6.48532e24 | 1.75127 | ||||||||
\(778\) | −1.67122e23 | −0.0446383 | ||||||||
\(779\) | −7.29114e23 | −0.192631 | ||||||||
\(780\) | 3.14006e24 | 0.820604 | ||||||||
\(781\) | 1.27926e24 | 0.330694 | ||||||||
\(782\) | −6.02991e23 | −0.154189 | ||||||||
\(783\) | 2.80090e24 | 0.708473 | ||||||||
\(784\) | 5.48383e23 | 0.137214 | ||||||||
\(785\) | −1.30009e24 | −0.321797 | ||||||||
\(786\) | −1.70170e24 | −0.416669 | ||||||||
\(787\) | 1.71201e22 | 0.00414687 | 0.00207343 | − | 0.999998i | \(-0.499340\pi\) | ||||
0.00207343 | + | 0.999998i | \(0.499340\pi\) | |||||||
\(788\) | 7.09236e24 | 1.69949 | ||||||||
\(789\) | −1.37088e25 | −3.24970 | ||||||||
\(790\) | −4.38755e23 | −0.102894 | ||||||||
\(791\) | 5.43004e24 | 1.25980 | ||||||||
\(792\) | 8.88115e23 | 0.203847 | ||||||||
\(793\) | 1.86231e24 | 0.422892 | ||||||||
\(794\) | 4.47354e23 | 0.100502 | ||||||||
\(795\) | 6.43442e24 | 1.43017 | ||||||||
\(796\) | −2.36895e24 | −0.520948 | ||||||||
\(797\) | 1.29137e24 | 0.280968 | 0.140484 | − | 0.990083i | \(-0.455134\pi\) | ||||
0.140484 | + | 0.990083i | \(0.455134\pi\) | |||||||
\(798\) | 1.48301e24 | 0.319241 | ||||||||
\(799\) | 2.26387e24 | 0.482174 | ||||||||
\(800\) | 2.09984e24 | 0.442509 | ||||||||
\(801\) | 2.23974e24 | 0.467005 | ||||||||
\(802\) | 9.36750e23 | 0.193260 | ||||||||
\(803\) | −1.43390e24 | −0.292709 | ||||||||
\(804\) | −1.49568e25 | −3.02108 | ||||||||
\(805\) | 1.35629e24 | 0.271073 | ||||||||
\(806\) | −3.89733e23 | −0.0770760 | ||||||||
\(807\) | 4.73143e24 | 0.925906 | ||||||||
\(808\) | −6.63780e23 | −0.128537 | ||||||||
\(809\) | −8.56357e24 | −1.64094 | −0.820469 | − | 0.571691i | \(-0.806288\pi\) | ||||
−0.820469 | + | 0.571691i | \(0.806288\pi\) | |||||||
\(810\) | −1.74527e24 | −0.330934 | ||||||||
\(811\) | 4.33814e24 | 0.814003 | 0.407001 | − | 0.913428i | \(-0.366574\pi\) | ||||
0.407001 | + | 0.913428i | \(0.366574\pi\) | |||||||
\(812\) | −1.03782e24 | −0.192706 | ||||||||
\(813\) | −1.13330e25 | −2.08246 | ||||||||
\(814\) | −1.60425e23 | −0.0291719 | ||||||||
\(815\) | −3.63447e24 | −0.654036 | ||||||||
\(816\) | 1.31645e25 | 2.34443 | ||||||||
\(817\) | 3.10771e24 | 0.547712 | ||||||||
\(818\) | −6.37529e22 | −0.0111198 | ||||||||
\(819\) | −1.98898e25 | −3.43335 | ||||||||
\(820\) | −5.18678e23 | −0.0886094 | ||||||||
\(821\) | −2.76330e23 | −0.0467209 | −0.0233604 | − | 0.999727i | \(-0.507437\pi\) | ||||
−0.0233604 | + | 0.999727i | \(0.507437\pi\) | |||||||
\(822\) | 2.08773e24 | 0.349353 | ||||||||
\(823\) | 2.64106e23 | 0.0437401 | 0.0218700 | − | 0.999761i | \(-0.493038\pi\) | ||||
0.0218700 | + | 0.999761i | \(0.493038\pi\) | |||||||
\(824\) | −1.79034e24 | −0.293464 | ||||||||
\(825\) | −2.00929e24 | −0.325976 | ||||||||
\(826\) | 1.06695e24 | 0.171323 | ||||||||
\(827\) | 2.49849e24 | 0.397082 | 0.198541 | − | 0.980093i | \(-0.436380\pi\) | ||||
0.198541 | + | 0.980093i | \(0.436380\pi\) | |||||||
\(828\) | −1.15879e25 | −1.82283 | ||||||||
\(829\) | −8.02963e24 | −1.25021 | −0.625104 | − | 0.780542i | \(-0.714943\pi\) | ||||
−0.625104 | + | 0.780542i | \(0.714943\pi\) | |||||||
\(830\) | 2.43279e23 | 0.0374921 | ||||||||
\(831\) | 1.11521e25 | 1.70117 | ||||||||
\(832\) | 5.83717e24 | 0.881361 | ||||||||
\(833\) | 1.33687e24 | 0.199806 | ||||||||
\(834\) | 5.72882e23 | 0.0847527 | ||||||||
\(835\) | 8.87895e22 | 0.0130025 | ||||||||
\(836\) | 1.06758e24 | 0.154756 | ||||||||
\(837\) | −1.02841e25 | −1.47571 | ||||||||
\(838\) | −5.10708e23 | −0.0725435 | ||||||||
\(839\) | 8.05504e24 | 1.13264 | 0.566319 | − | 0.824186i | \(-0.308367\pi\) | ||||
0.566319 | + | 0.824186i | \(0.308367\pi\) | |||||||
\(840\) | 2.14622e24 | 0.298744 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | −8.25121e23 | −0.112555 | ||||||||
\(843\) | −2.06685e24 | −0.279109 | ||||||||
\(844\) | −2.32752e24 | −0.311159 | ||||||||
\(845\) | 5.78171e23 | 0.0765198 | ||||||||
\(846\) | −1.49495e24 | −0.195875 | ||||||||
\(847\) | −7.96252e24 | −1.03286 | ||||||||
\(848\) | 1.29306e25 | 1.66056 | ||||||||
\(849\) | −5.76915e24 | −0.733494 | ||||||||
\(850\) | 1.60886e24 | 0.202515 | ||||||||
\(851\) | 4.25828e24 | 0.530681 | ||||||||
\(852\) | −2.64129e25 | −3.25897 | ||||||||
\(853\) | 1.35706e25 | 1.65780 | 0.828898 | − | 0.559399i | \(-0.188968\pi\) | ||||
0.828898 | + | 0.559399i | \(0.188968\pi\) | |||||||
\(854\) | 6.25690e23 | 0.0756776 | ||||||||
\(855\) | −7.88387e24 | −0.944121 | ||||||||
\(856\) | 1.51078e24 | 0.179132 | ||||||||
\(857\) | 1.63694e25 | 1.92174 | 0.960871 | − | 0.276995i | \(-0.0893386\pi\) | ||||
0.960871 | + | 0.276995i | \(0.0893386\pi\) | |||||||
\(858\) | 6.60181e23 | 0.0767399 | ||||||||
\(859\) | −1.24343e25 | −1.43113 | −0.715565 | − | 0.698546i | \(-0.753831\pi\) | ||||
−0.715565 | + | 0.698546i | \(0.753831\pi\) | |||||||
\(860\) | 2.21076e24 | 0.251945 | ||||||||
\(861\) | 4.40841e24 | 0.497456 | ||||||||
\(862\) | −6.15446e23 | −0.0687667 | ||||||||
\(863\) | −1.29499e25 | −1.43276 | −0.716381 | − | 0.697709i | \(-0.754203\pi\) | ||||
−0.716381 | + | 0.697709i | \(0.754203\pi\) | |||||||
\(864\) | −1.82057e25 | −1.99453 | ||||||||
\(865\) | −1.34930e24 | −0.146376 | ||||||||
\(866\) | −1.93681e24 | −0.208058 | ||||||||
\(867\) | 1.34671e25 | 1.43256 | ||||||||
\(868\) | 3.81058e24 | 0.401396 | ||||||||
\(869\) | 2.68450e24 | 0.280025 | ||||||||
\(870\) | −2.54385e23 | −0.0262772 | ||||||||
\(871\) | −1.68566e25 | −1.72431 | ||||||||
\(872\) | −3.32099e24 | −0.336417 | ||||||||
\(873\) | 2.68816e25 | 2.69671 | ||||||||
\(874\) | 9.73748e23 | 0.0967385 | ||||||||
\(875\) | −7.89391e24 | −0.776647 | ||||||||
\(876\) | 2.96057e25 | 2.88463 | ||||||||
\(877\) | −5.42683e24 | −0.523660 | −0.261830 | − | 0.965114i | \(-0.584326\pi\) | ||||
−0.261830 | + | 0.965114i | \(0.584326\pi\) | |||||||
\(878\) | −2.90066e23 | −0.0277200 | ||||||||
\(879\) | 3.21595e25 | 3.04372 | ||||||||
\(880\) | 7.32463e23 | 0.0686568 | ||||||||
\(881\) | −6.05842e24 | −0.562425 | −0.281212 | − | 0.959646i | \(-0.590737\pi\) | ||||
−0.281212 | + | 0.959646i | \(0.590737\pi\) | |||||||
\(882\) | −8.82806e23 | −0.0811676 | ||||||||
\(883\) | −1.01581e24 | −0.0925011 | −0.0462506 | − | 0.998930i | \(-0.514727\pi\) | ||||
−0.0462506 | + | 0.998930i | \(0.514727\pi\) | |||||||
\(884\) | 1.53834e25 | 1.38742 | ||||||||
\(885\) | −7.61084e24 | −0.679853 | ||||||||
\(886\) | 2.23316e23 | 0.0197576 | ||||||||
\(887\) | 1.08483e25 | 0.950624 | 0.475312 | − | 0.879817i | \(-0.342335\pi\) | ||||
0.475312 | + | 0.879817i | \(0.342335\pi\) | |||||||
\(888\) | 6.73840e24 | 0.584853 | ||||||||
\(889\) | −1.47682e25 | −1.26959 | ||||||||
\(890\) | −1.33889e23 | −0.0114006 | ||||||||
\(891\) | 1.06784e25 | 0.900627 | ||||||||
\(892\) | 1.12462e24 | 0.0939515 | ||||||||
\(893\) | −3.65584e24 | −0.302517 | ||||||||
\(894\) | 1.76639e23 | 0.0144783 | ||||||||
\(895\) | 6.79890e24 | 0.552005 | ||||||||
\(896\) | 8.93870e24 | 0.718879 | ||||||||
\(897\) | −1.75237e25 | −1.39601 | ||||||||
\(898\) | 2.60476e24 | 0.205551 | ||||||||
\(899\) | −9.18835e23 | −0.0718257 | ||||||||
\(900\) | 3.09178e25 | 2.39413 | ||||||||
\(901\) | 3.15228e25 | 2.41804 | ||||||||
\(902\) | −1.09049e23 | −0.00828643 | ||||||||
\(903\) | −1.87900e25 | −1.41443 | ||||||||
\(904\) | 5.64194e24 | 0.420724 | ||||||||
\(905\) | −7.96214e24 | −0.588189 | ||||||||
\(906\) | 8.87467e24 | 0.649475 | ||||||||
\(907\) | −1.59876e24 | −0.115910 | −0.0579552 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579552 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(908\) | 8.22447e24 | 0.590715 | ||||||||
\(909\) | −1.47427e25 | −1.04902 | ||||||||
\(910\) | 1.18899e24 | 0.0838157 | ||||||||
\(911\) | 1.21604e25 | 0.849263 | 0.424631 | − | 0.905366i | \(-0.360404\pi\) | ||||
0.424631 | + | 0.905366i | \(0.360404\pi\) | |||||||
\(912\) | −2.12589e25 | −1.47090 | ||||||||
\(913\) | −1.48849e24 | −0.102034 | ||||||||
\(914\) | −6.19625e23 | −0.0420810 | ||||||||
\(915\) | −4.46320e24 | −0.300308 | ||||||||
\(916\) | 1.08865e25 | 0.725735 | ||||||||
\(917\) | 1.87516e25 | 1.23851 | ||||||||
\(918\) | −1.39488e25 | −0.912798 | ||||||||
\(919\) | 7.39958e24 | 0.479761 | 0.239881 | − | 0.970802i | \(-0.422892\pi\) | ||||
0.239881 | + | 0.970802i | \(0.422892\pi\) | |||||||
\(920\) | 1.40921e24 | 0.0905275 | ||||||||
\(921\) | 2.46645e25 | 1.56988 | ||||||||
\(922\) | −1.10082e24 | −0.0694228 | ||||||||
\(923\) | −2.97679e25 | −1.86009 | ||||||||
\(924\) | −6.45487e24 | −0.399646 | ||||||||
\(925\) | −1.13616e25 | −0.697005 | ||||||||
\(926\) | 2.08078e24 | 0.126483 | ||||||||
\(927\) | −3.97638e25 | −2.39503 | ||||||||
\(928\) | −1.62658e24 | −0.0970776 | ||||||||
\(929\) | 1.08328e25 | 0.640627 | 0.320314 | − | 0.947312i | \(-0.396212\pi\) | ||||
0.320314 | + | 0.947312i | \(0.396212\pi\) | |||||||
\(930\) | 9.34031e23 | 0.0547339 | ||||||||
\(931\) | −2.15887e24 | −0.125358 | ||||||||
\(932\) | −2.44421e25 | −1.40638 | ||||||||
\(933\) | −1.96489e25 | −1.12033 | ||||||||
\(934\) | 3.38803e24 | 0.191425 | ||||||||
\(935\) | 1.78563e24 | 0.0999754 | ||||||||
\(936\) | −2.06660e25 | −1.14660 | ||||||||
\(937\) | 1.79869e24 | 0.0988940 | 0.0494470 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494470 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(938\) | −5.66340e24 | −0.308570 | ||||||||
\(939\) | 5.21737e25 | 2.81705 | ||||||||
\(940\) | −2.60069e24 | −0.139156 | ||||||||
\(941\) | −2.05865e25 | −1.09162 | −0.545808 | − | 0.837910i | \(-0.683777\pi\) | ||||
−0.545808 | + | 0.837910i | \(0.683777\pi\) | |||||||
\(942\) | 5.64359e24 | 0.296567 | ||||||||
\(943\) | 2.89457e24 | 0.150742 | ||||||||
\(944\) | −1.52947e25 | −0.789369 | ||||||||
\(945\) | 3.13746e25 | 1.60475 | ||||||||
\(946\) | 4.64801e23 | 0.0235609 | ||||||||
\(947\) | 2.13339e25 | 1.07176 | 0.535878 | − | 0.844295i | \(-0.319981\pi\) | ||||
0.535878 | + | 0.844295i | \(0.319981\pi\) | |||||||
\(948\) | −5.54268e25 | −2.75962 | ||||||||
\(949\) | 3.33662e25 | 1.64643 | ||||||||
\(950\) | −2.59808e24 | −0.127058 | ||||||||
\(951\) | 4.51141e25 | 2.18664 | ||||||||
\(952\) | 1.05145e25 | 0.505097 | ||||||||
\(953\) | 4.12328e24 | 0.196315 | 0.0981574 | − | 0.995171i | \(-0.468705\pi\) | ||||
0.0981574 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(954\) | −2.08161e25 | −0.982288 | ||||||||
\(955\) | −1.30149e25 | −0.608711 | ||||||||
\(956\) | −8.74127e23 | −0.0405212 | ||||||||
\(957\) | 1.55644e24 | 0.0715126 | ||||||||
\(958\) | −2.19249e24 | −0.0998461 | ||||||||
\(959\) | −2.30054e25 | −1.03842 | ||||||||
\(960\) | −1.39893e25 | −0.625880 | ||||||||
\(961\) | −1.91764e25 | −0.850391 | ||||||||
\(962\) | 3.73302e24 | 0.164086 | ||||||||
\(963\) | 3.35546e25 | 1.46194 | ||||||||
\(964\) | 3.33988e25 | 1.44237 | ||||||||
\(965\) | 6.48740e24 | 0.277708 | ||||||||
\(966\) | −5.88753e24 | −0.249820 | ||||||||
\(967\) | −4.17524e25 | −1.75613 | −0.878065 | − | 0.478542i | \(-0.841165\pi\) | ||||
−0.878065 | + | 0.478542i | \(0.841165\pi\) | |||||||
\(968\) | −8.27325e24 | −0.344934 | ||||||||
\(969\) | −5.18258e25 | −2.14187 | ||||||||
\(970\) | −1.60694e24 | −0.0658326 | ||||||||
\(971\) | 3.87541e24 | 0.157382 | 0.0786909 | − | 0.996899i | \(-0.474926\pi\) | ||||
0.0786909 | + | 0.996899i | \(0.474926\pi\) | |||||||
\(972\) | −1.28851e26 | −5.18712 | ||||||||
\(973\) | −6.31278e24 | −0.251919 | ||||||||
\(974\) | −1.34539e23 | −0.00532226 | ||||||||
\(975\) | 4.67553e25 | 1.83355 | ||||||||
\(976\) | −8.96924e24 | −0.348684 | ||||||||
\(977\) | 3.59633e25 | 1.38598 | 0.692988 | − | 0.720949i | \(-0.256294\pi\) | ||||
0.692988 | + | 0.720949i | \(0.256294\pi\) | |||||||
\(978\) | 1.57769e25 | 0.602757 | ||||||||
\(979\) | 8.19192e23 | 0.0310265 | ||||||||
\(980\) | −1.53578e24 | −0.0576642 | ||||||||
\(981\) | −7.37598e25 | −2.74557 | ||||||||
\(982\) | 3.87192e24 | 0.142882 | ||||||||
\(983\) | 4.11968e25 | 1.50716 | 0.753578 | − | 0.657358i | \(-0.228326\pi\) | ||||
0.753578 | + | 0.657358i | \(0.228326\pi\) | |||||||
\(984\) | 4.58044e24 | 0.166130 | ||||||||
\(985\) | −1.91565e25 | −0.688825 | ||||||||
\(986\) | −1.24626e24 | −0.0444277 | ||||||||
\(987\) | 2.21041e25 | 0.781228 | ||||||||
\(988\) | −2.48421e25 | −0.870472 | ||||||||
\(989\) | −1.23376e25 | −0.428608 | ||||||||
\(990\) | −1.17914e24 | −0.0406133 | ||||||||
\(991\) | −1.12200e24 | −0.0383149 | −0.0191574 | − | 0.999816i | \(-0.506098\pi\) | ||||
−0.0191574 | + | 0.999816i | \(0.506098\pi\) | |||||||
\(992\) | 5.97236e24 | 0.202207 | ||||||||
\(993\) | 4.47823e24 | 0.150327 | ||||||||
\(994\) | −1.00013e25 | −0.332867 | ||||||||
\(995\) | 6.39855e24 | 0.211147 | ||||||||
\(996\) | 3.07328e25 | 1.00554 | ||||||||
\(997\) | −3.90220e25 | −1.26590 | −0.632952 | − | 0.774191i | \(-0.718157\pi\) | ||||
−0.632952 | + | 0.774191i | \(0.718157\pi\) | |||||||
\(998\) | 4.15089e24 | 0.133516 | ||||||||
\(999\) | 9.85056e25 | 3.14163 |
(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 | 29.18.a.b.1.9 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.9 | ✓ | 21 | 1.1 | even | 1 | trivial |