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 | 1.6 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −332.840 | −0.919349 | −0.459675 | − | 0.888087i | \(-0.652034\pi\) | ||||
−0.459675 | + | 0.888087i | \(0.652034\pi\) | |||||||
\(3\) | −18225.8 | −1.60382 | −0.801912 | − | 0.597443i | \(-0.796183\pi\) | ||||
−0.801912 | + | 0.597443i | \(0.796183\pi\) | |||||||
\(4\) | −20289.6 | −0.154797 | ||||||||
\(5\) | −318485. | −0.364623 | −0.182312 | − | 0.983241i | \(-0.558358\pi\) | ||||
−0.182312 | + | 0.983241i | \(0.558358\pi\) | |||||||
\(6\) | 6.06628e6 | 1.47447 | ||||||||
\(7\) | 9.82044e6 | 0.643869 | 0.321935 | − | 0.946762i | \(-0.395667\pi\) | ||||
0.321935 | + | 0.946762i | \(0.395667\pi\) | |||||||
\(8\) | 5.03792e7 | 1.06166 | ||||||||
\(9\) | 2.03040e8 | 1.57225 | ||||||||
\(10\) | 1.06005e8 | 0.335216 | ||||||||
\(11\) | 9.36358e6 | 0.0131706 | 0.00658528 | − | 0.999978i | \(-0.497904\pi\) | ||||
0.00658528 | + | 0.999978i | \(0.497904\pi\) | |||||||
\(12\) | 3.69795e8 | 0.248268 | ||||||||
\(13\) | −3.20633e9 | −1.09016 | −0.545080 | − | 0.838384i | \(-0.683501\pi\) | ||||
−0.545080 | + | 0.838384i | \(0.683501\pi\) | |||||||
\(14\) | −3.26863e9 | −0.591940 | ||||||||
\(15\) | 5.80466e9 | 0.584791 | ||||||||
\(16\) | −1.41088e10 | −0.821240 | ||||||||
\(17\) | 8.46481e9 | 0.294307 | 0.147154 | − | 0.989114i | \(-0.452989\pi\) | ||||
0.147154 | + | 0.989114i | \(0.452989\pi\) | |||||||
\(18\) | −6.75799e10 | −1.44544 | ||||||||
\(19\) | −7.69200e10 | −1.03904 | −0.519522 | − | 0.854457i | \(-0.673890\pi\) | ||||
−0.519522 | + | 0.854457i | \(0.673890\pi\) | |||||||
\(20\) | 6.46194e9 | 0.0564427 | ||||||||
\(21\) | −1.78986e11 | −1.03265 | ||||||||
\(22\) | −3.11657e9 | −0.0121083 | ||||||||
\(23\) | 1.60829e11 | 0.428231 | 0.214116 | − | 0.976808i | \(-0.431313\pi\) | ||||
0.214116 | + | 0.976808i | \(0.431313\pi\) | |||||||
\(24\) | −9.18202e11 | −1.70272 | ||||||||
\(25\) | −6.61507e11 | −0.867050 | ||||||||
\(26\) | 1.06720e12 | 1.00224 | ||||||||
\(27\) | −1.34689e12 | −0.917785 | ||||||||
\(28\) | −1.99253e11 | −0.0996692 | ||||||||
\(29\) | 5.00246e11 | 0.185695 | ||||||||
\(30\) | −1.93202e12 | −0.537627 | ||||||||
\(31\) | −4.63610e12 | −0.976289 | −0.488144 | − | 0.872763i | \(-0.662326\pi\) | ||||
−0.488144 | + | 0.872763i | \(0.662326\pi\) | |||||||
\(32\) | −1.90733e12 | −0.306655 | ||||||||
\(33\) | −1.70659e11 | −0.0211232 | ||||||||
\(34\) | −2.81742e12 | −0.270571 | ||||||||
\(35\) | −3.12767e12 | −0.234770 | ||||||||
\(36\) | −4.11961e12 | −0.243380 | ||||||||
\(37\) | 4.51018e12 | 0.211096 | 0.105548 | − | 0.994414i | \(-0.466340\pi\) | ||||
0.105548 | + | 0.994414i | \(0.466340\pi\) | |||||||
\(38\) | 2.56020e13 | 0.955244 | ||||||||
\(39\) | 5.84380e13 | 1.74842 | ||||||||
\(40\) | −1.60450e13 | −0.387107 | ||||||||
\(41\) | −1.95332e13 | −0.382042 | −0.191021 | − | 0.981586i | \(-0.561180\pi\) | ||||
−0.191021 | + | 0.981586i | \(0.561180\pi\) | |||||||
\(42\) | 5.95735e13 | 0.949368 | ||||||||
\(43\) | −2.62720e13 | −0.342776 | −0.171388 | − | 0.985204i | \(-0.554825\pi\) | ||||
−0.171388 | + | 0.985204i | \(0.554825\pi\) | |||||||
\(44\) | −1.89983e11 | −0.00203877 | ||||||||
\(45\) | −6.46654e13 | −0.573278 | ||||||||
\(46\) | −5.35304e13 | −0.393694 | ||||||||
\(47\) | −2.05312e14 | −1.25772 | −0.628859 | − | 0.777519i | \(-0.716478\pi\) | ||||
−0.628859 | + | 0.777519i | \(0.716478\pi\) | |||||||
\(48\) | 2.57145e14 | 1.31712 | ||||||||
\(49\) | −1.36189e14 | −0.585433 | ||||||||
\(50\) | 2.20176e14 | 0.797121 | ||||||||
\(51\) | −1.54278e14 | −0.472017 | ||||||||
\(52\) | 6.50552e13 | 0.168754 | ||||||||
\(53\) | −1.23971e14 | −0.273511 | −0.136755 | − | 0.990605i | \(-0.543667\pi\) | ||||
−0.136755 | + | 0.990605i | \(0.543667\pi\) | |||||||
\(54\) | 4.48300e14 | 0.843765 | ||||||||
\(55\) | −2.98216e12 | −0.00480229 | ||||||||
\(56\) | 4.94746e14 | 0.683571 | ||||||||
\(57\) | 1.40193e15 | 1.66644 | ||||||||
\(58\) | −1.66502e14 | −0.170719 | ||||||||
\(59\) | 6.96656e13 | 0.0617698 | 0.0308849 | − | 0.999523i | \(-0.490167\pi\) | ||||
0.0308849 | + | 0.999523i | \(0.490167\pi\) | |||||||
\(60\) | −1.17774e14 | −0.0905241 | ||||||||
\(61\) | 2.14181e15 | 1.43047 | 0.715233 | − | 0.698886i | \(-0.246320\pi\) | ||||
0.715233 | + | 0.698886i | \(0.246320\pi\) | |||||||
\(62\) | 1.54308e15 | 0.897550 | ||||||||
\(63\) | 1.99395e15 | 1.01232 | ||||||||
\(64\) | 2.48410e15 | 1.10316 | ||||||||
\(65\) | 1.02117e15 | 0.397497 | ||||||||
\(66\) | 5.68021e13 | 0.0194196 | ||||||||
\(67\) | −1.15108e15 | −0.346314 | −0.173157 | − | 0.984894i | \(-0.555397\pi\) | ||||
−0.173157 | + | 0.984894i | \(0.555397\pi\) | |||||||
\(68\) | −1.71748e14 | −0.0455580 | ||||||||
\(69\) | −2.93124e15 | −0.686807 | ||||||||
\(70\) | 1.04101e15 | 0.215835 | ||||||||
\(71\) | −2.06784e14 | −0.0380033 | −0.0190016 | − | 0.999819i | \(-0.506049\pi\) | ||||
−0.0190016 | + | 0.999819i | \(0.506049\pi\) | |||||||
\(72\) | 1.02290e16 | 1.66920 | ||||||||
\(73\) | 2.75508e14 | 0.0399844 | 0.0199922 | − | 0.999800i | \(-0.493636\pi\) | ||||
0.0199922 | + | 0.999800i | \(0.493636\pi\) | |||||||
\(74\) | −1.50117e15 | −0.194071 | ||||||||
\(75\) | 1.20565e16 | 1.39059 | ||||||||
\(76\) | 1.56068e15 | 0.160841 | ||||||||
\(77\) | 9.19545e13 | 0.00848011 | ||||||||
\(78\) | −1.94505e16 | −1.60741 | ||||||||
\(79\) | −1.64938e16 | −1.22318 | −0.611591 | − | 0.791174i | \(-0.709470\pi\) | ||||
−0.611591 | + | 0.791174i | \(0.709470\pi\) | |||||||
\(80\) | 4.49345e15 | 0.299443 | ||||||||
\(81\) | −1.67245e15 | −0.100284 | ||||||||
\(82\) | 6.50144e15 | 0.351230 | ||||||||
\(83\) | 1.11291e16 | 0.542371 | 0.271185 | − | 0.962527i | \(-0.412584\pi\) | ||||
0.271185 | + | 0.962527i | \(0.412584\pi\) | |||||||
\(84\) | 3.63155e15 | 0.159852 | ||||||||
\(85\) | −2.69592e15 | −0.107311 | ||||||||
\(86\) | 8.74436e15 | 0.315131 | ||||||||
\(87\) | −9.11740e15 | −0.297822 | ||||||||
\(88\) | 4.71729e14 | 0.0139827 | ||||||||
\(89\) | −6.18759e16 | −1.66612 | −0.833061 | − | 0.553182i | \(-0.813414\pi\) | ||||
−0.833061 | + | 0.553182i | \(0.813414\pi\) | |||||||
\(90\) | 2.15232e16 | 0.527043 | ||||||||
\(91\) | −3.14876e16 | −0.701920 | ||||||||
\(92\) | −3.26316e15 | −0.0662890 | ||||||||
\(93\) | 8.44967e16 | 1.56579 | ||||||||
\(94\) | 6.83361e16 | 1.15628 | ||||||||
\(95\) | 2.44979e16 | 0.378859 | ||||||||
\(96\) | 3.47626e16 | 0.491821 | ||||||||
\(97\) | 1.57070e15 | 0.0203485 | 0.0101743 | − | 0.999948i | \(-0.496761\pi\) | ||||
0.0101743 | + | 0.999948i | \(0.496761\pi\) | |||||||
\(98\) | 4.53293e16 | 0.538217 | ||||||||
\(99\) | 1.90118e15 | 0.0207074 | ||||||||
\(100\) | 1.34217e16 | 0.134217 | ||||||||
\(101\) | 1.07285e17 | 0.985840 | 0.492920 | − | 0.870075i | \(-0.335930\pi\) | ||||
0.492920 | + | 0.870075i | \(0.335930\pi\) | |||||||
\(102\) | 5.13499e16 | 0.433948 | ||||||||
\(103\) | −3.50328e15 | −0.0272495 | −0.0136248 | − | 0.999907i | \(-0.504337\pi\) | ||||
−0.0136248 | + | 0.999907i | \(0.504337\pi\) | |||||||
\(104\) | −1.61532e17 | −1.15738 | ||||||||
\(105\) | 5.70043e16 | 0.376529 | ||||||||
\(106\) | 4.12624e16 | 0.251452 | ||||||||
\(107\) | −3.49430e17 | −1.96607 | −0.983034 | − | 0.183422i | \(-0.941283\pi\) | ||||
−0.983034 | + | 0.183422i | \(0.941283\pi\) | |||||||
\(108\) | 2.73279e16 | 0.142071 | ||||||||
\(109\) | −2.87690e17 | −1.38293 | −0.691464 | − | 0.722411i | \(-0.743034\pi\) | ||||
−0.691464 | + | 0.722411i | \(0.743034\pi\) | |||||||
\(110\) | 9.92583e14 | 0.00441498 | ||||||||
\(111\) | −8.22018e16 | −0.338560 | ||||||||
\(112\) | −1.38555e17 | −0.528771 | ||||||||
\(113\) | −1.91324e17 | −0.677023 | −0.338511 | − | 0.940962i | \(-0.609923\pi\) | ||||
−0.338511 | + | 0.940962i | \(0.609923\pi\) | |||||||
\(114\) | −4.66618e17 | −1.53204 | ||||||||
\(115\) | −5.12217e16 | −0.156143 | ||||||||
\(116\) | −1.01498e16 | −0.0287451 | ||||||||
\(117\) | −6.51015e17 | −1.71400 | ||||||||
\(118\) | −2.31875e16 | −0.0567880 | ||||||||
\(119\) | 8.31281e16 | 0.189495 | ||||||||
\(120\) | 2.92434e17 | 0.620851 | ||||||||
\(121\) | −5.05359e17 | −0.999827 | ||||||||
\(122\) | −7.12881e17 | −1.31510 | ||||||||
\(123\) | 3.56009e17 | 0.612728 | ||||||||
\(124\) | 9.40646e16 | 0.151127 | ||||||||
\(125\) | 4.53665e17 | 0.680770 | ||||||||
\(126\) | −6.63665e17 | −0.930677 | ||||||||
\(127\) | 1.24826e18 | 1.63672 | 0.818359 | − | 0.574708i | \(-0.194884\pi\) | ||||
0.818359 | + | 0.574708i | \(0.194884\pi\) | |||||||
\(128\) | −5.76812e17 | −0.707537 | ||||||||
\(129\) | 4.78828e17 | 0.549753 | ||||||||
\(130\) | −3.39886e17 | −0.365439 | ||||||||
\(131\) | 7.84941e17 | 0.790735 | 0.395368 | − | 0.918523i | \(-0.370617\pi\) | ||||
0.395368 | + | 0.918523i | \(0.370617\pi\) | |||||||
\(132\) | 3.46260e15 | 0.00326982 | ||||||||
\(133\) | −7.55388e17 | −0.669008 | ||||||||
\(134\) | 3.83126e17 | 0.318384 | ||||||||
\(135\) | 4.28965e17 | 0.334646 | ||||||||
\(136\) | 4.26450e17 | 0.312455 | ||||||||
\(137\) | −7.82588e17 | −0.538776 | −0.269388 | − | 0.963032i | \(-0.586821\pi\) | ||||
−0.269388 | + | 0.963032i | \(0.586821\pi\) | |||||||
\(138\) | 9.75635e17 | 0.631415 | ||||||||
\(139\) | 2.40417e18 | 1.46332 | 0.731661 | − | 0.681669i | \(-0.238745\pi\) | ||||
0.731661 | + | 0.681669i | \(0.238745\pi\) | |||||||
\(140\) | 6.34591e16 | 0.0363417 | ||||||||
\(141\) | 3.74199e18 | 2.01716 | ||||||||
\(142\) | 6.88259e16 | 0.0349383 | ||||||||
\(143\) | −3.00227e16 | −0.0143580 | ||||||||
\(144\) | −2.86466e18 | −1.29119 | ||||||||
\(145\) | −1.59321e17 | −0.0677088 | ||||||||
\(146\) | −9.17002e16 | −0.0367596 | ||||||||
\(147\) | 2.48216e18 | 0.938930 | ||||||||
\(148\) | −9.15098e16 | −0.0326771 | ||||||||
\(149\) | 2.84020e18 | 0.957779 | 0.478890 | − | 0.877875i | \(-0.341039\pi\) | ||||
0.478890 | + | 0.877875i | \(0.341039\pi\) | |||||||
\(150\) | −4.01288e18 | −1.27844 | ||||||||
\(151\) | 2.96188e18 | 0.891791 | 0.445895 | − | 0.895085i | \(-0.352885\pi\) | ||||
0.445895 | + | 0.895085i | \(0.352885\pi\) | |||||||
\(152\) | −3.87517e18 | −1.10311 | ||||||||
\(153\) | 1.71870e18 | 0.462724 | ||||||||
\(154\) | −3.06061e16 | −0.00779618 | ||||||||
\(155\) | 1.47653e18 | 0.355978 | ||||||||
\(156\) | −1.18568e18 | −0.270651 | ||||||||
\(157\) | 1.90893e18 | 0.412707 | 0.206354 | − | 0.978478i | \(-0.433840\pi\) | ||||
0.206354 | + | 0.978478i | \(0.433840\pi\) | |||||||
\(158\) | 5.48980e18 | 1.12453 | ||||||||
\(159\) | 2.25947e18 | 0.438663 | ||||||||
\(160\) | 6.07456e17 | 0.111814 | ||||||||
\(161\) | 1.57941e18 | 0.275725 | ||||||||
\(162\) | 5.56658e17 | 0.0921957 | ||||||||
\(163\) | −7.02547e18 | −1.10428 | −0.552142 | − | 0.833750i | \(-0.686189\pi\) | ||||
−0.552142 | + | 0.833750i | \(0.686189\pi\) | |||||||
\(164\) | 3.96322e17 | 0.0591391 | ||||||||
\(165\) | 5.43524e16 | 0.00770202 | ||||||||
\(166\) | −3.70421e18 | −0.498628 | ||||||||
\(167\) | 4.80741e18 | 0.614923 | 0.307462 | − | 0.951560i | \(-0.400520\pi\) | ||||
0.307462 | + | 0.951560i | \(0.400520\pi\) | |||||||
\(168\) | −9.01715e18 | −1.09633 | ||||||||
\(169\) | 1.63015e18 | 0.188447 | ||||||||
\(170\) | 8.97308e17 | 0.0986566 | ||||||||
\(171\) | −1.56179e19 | −1.63363 | ||||||||
\(172\) | 5.33048e17 | 0.0530609 | ||||||||
\(173\) | 1.45503e19 | 1.37874 | 0.689369 | − | 0.724411i | \(-0.257888\pi\) | ||||
0.689369 | + | 0.724411i | \(0.257888\pi\) | |||||||
\(174\) | 3.03464e18 | 0.273803 | ||||||||
\(175\) | −6.49629e18 | −0.558267 | ||||||||
\(176\) | −1.32109e17 | −0.0108162 | ||||||||
\(177\) | −1.26971e18 | −0.0990679 | ||||||||
\(178\) | 2.05948e19 | 1.53175 | ||||||||
\(179\) | 1.08261e19 | 0.767751 | 0.383875 | − | 0.923385i | \(-0.374589\pi\) | ||||
0.383875 | + | 0.923385i | \(0.374589\pi\) | |||||||
\(180\) | 1.31203e18 | 0.0887420 | ||||||||
\(181\) | 1.14959e19 | 0.741777 | 0.370889 | − | 0.928677i | \(-0.379053\pi\) | ||||
0.370889 | + | 0.928677i | \(0.379053\pi\) | |||||||
\(182\) | 1.04803e19 | 0.645309 | ||||||||
\(183\) | −3.90363e19 | −2.29422 | ||||||||
\(184\) | 8.10244e18 | 0.454637 | ||||||||
\(185\) | −1.43643e18 | −0.0769704 | ||||||||
\(186\) | −2.81239e19 | −1.43951 | ||||||||
\(187\) | 7.92609e16 | 0.00387619 | ||||||||
\(188\) | 4.16571e18 | 0.194691 | ||||||||
\(189\) | −1.32271e19 | −0.590933 | ||||||||
\(190\) | −8.15388e18 | −0.348304 | ||||||||
\(191\) | −6.91419e18 | −0.282461 | −0.141230 | − | 0.989977i | \(-0.545106\pi\) | ||||
−0.141230 | + | 0.989977i | \(0.545106\pi\) | |||||||
\(192\) | −4.52748e19 | −1.76928 | ||||||||
\(193\) | 1.71091e19 | 0.639721 | 0.319861 | − | 0.947465i | \(-0.396364\pi\) | ||||
0.319861 | + | 0.947465i | \(0.396364\pi\) | |||||||
\(194\) | −5.22791e17 | −0.0187074 | ||||||||
\(195\) | −1.86117e19 | −0.637516 | ||||||||
\(196\) | 2.76323e18 | 0.0906234 | ||||||||
\(197\) | −1.88385e19 | −0.591675 | −0.295838 | − | 0.955238i | \(-0.595599\pi\) | ||||
−0.295838 | + | 0.955238i | \(0.595599\pi\) | |||||||
\(198\) | −6.32790e17 | −0.0190373 | ||||||||
\(199\) | −2.19879e19 | −0.633773 | −0.316886 | − | 0.948464i | \(-0.602637\pi\) | ||||
−0.316886 | + | 0.948464i | \(0.602637\pi\) | |||||||
\(200\) | −3.33262e19 | −0.920514 | ||||||||
\(201\) | 2.09794e19 | 0.555427 | ||||||||
\(202\) | −3.57087e19 | −0.906331 | ||||||||
\(203\) | 4.91264e18 | 0.119563 | ||||||||
\(204\) | 3.13024e18 | 0.0730670 | ||||||||
\(205\) | 6.22105e18 | 0.139302 | ||||||||
\(206\) | 1.16603e18 | 0.0250518 | ||||||||
\(207\) | 3.26548e19 | 0.673285 | ||||||||
\(208\) | 4.52375e19 | 0.895283 | ||||||||
\(209\) | −7.20246e17 | −0.0136848 | ||||||||
\(210\) | −1.89733e19 | −0.346162 | ||||||||
\(211\) | 8.36965e19 | 1.46658 | 0.733291 | − | 0.679915i | \(-0.237983\pi\) | ||||
0.733291 | + | 0.679915i | \(0.237983\pi\) | |||||||
\(212\) | 2.51532e18 | 0.0423387 | ||||||||
\(213\) | 3.76881e18 | 0.0609505 | ||||||||
\(214\) | 1.16304e20 | 1.80750 | ||||||||
\(215\) | 8.36724e18 | 0.124984 | ||||||||
\(216\) | −6.78553e19 | −0.974377 | ||||||||
\(217\) | −4.55285e19 | −0.628602 | ||||||||
\(218\) | 9.57547e19 | 1.27139 | ||||||||
\(219\) | −5.02137e18 | −0.0641279 | ||||||||
\(220\) | 6.05069e16 | 0.000743382 0 | ||||||||
\(221\) | −2.71410e19 | −0.320842 | ||||||||
\(222\) | 2.73600e19 | 0.311255 | ||||||||
\(223\) | −1.36177e20 | −1.49112 | −0.745558 | − | 0.666440i | \(-0.767817\pi\) | ||||
−0.745558 | + | 0.666440i | \(0.767817\pi\) | |||||||
\(224\) | −1.87308e19 | −0.197446 | ||||||||
\(225\) | −1.34313e20 | −1.36322 | ||||||||
\(226\) | 6.36803e19 | 0.622420 | ||||||||
\(227\) | −1.32204e20 | −1.24459 | −0.622294 | − | 0.782784i | \(-0.713799\pi\) | ||||
−0.622294 | + | 0.782784i | \(0.713799\pi\) | |||||||
\(228\) | −2.84446e19 | −0.257961 | ||||||||
\(229\) | 9.74665e19 | 0.851635 | 0.425818 | − | 0.904809i | \(-0.359986\pi\) | ||||
0.425818 | + | 0.904809i | \(0.359986\pi\) | |||||||
\(230\) | 1.70486e19 | 0.143550 | ||||||||
\(231\) | −1.67595e18 | −0.0136006 | ||||||||
\(232\) | 2.52020e19 | 0.197146 | ||||||||
\(233\) | −1.48581e20 | −1.12057 | −0.560283 | − | 0.828301i | \(-0.689308\pi\) | ||||
−0.560283 | + | 0.828301i | \(0.689308\pi\) | |||||||
\(234\) | 2.16684e20 | 1.57577 | ||||||||
\(235\) | 6.53890e19 | 0.458593 | ||||||||
\(236\) | −1.41349e18 | −0.00956181 | ||||||||
\(237\) | 3.00613e20 | 1.96177 | ||||||||
\(238\) | −2.76684e19 | −0.174212 | ||||||||
\(239\) | 1.89117e19 | 0.114908 | 0.0574538 | − | 0.998348i | \(-0.481702\pi\) | ||||
0.0574538 | + | 0.998348i | \(0.481702\pi\) | |||||||
\(240\) | −8.18968e19 | −0.480254 | ||||||||
\(241\) | −4.04261e19 | −0.228832 | −0.114416 | − | 0.993433i | \(-0.536500\pi\) | ||||
−0.114416 | + | 0.993433i | \(0.536500\pi\) | |||||||
\(242\) | 1.68204e20 | 0.919190 | ||||||||
\(243\) | 2.04420e20 | 1.07862 | ||||||||
\(244\) | −4.34565e19 | −0.221433 | ||||||||
\(245\) | 4.33743e19 | 0.213462 | ||||||||
\(246\) | −1.18494e20 | −0.563311 | ||||||||
\(247\) | 2.46631e20 | 1.13272 | ||||||||
\(248\) | −2.33563e20 | −1.03649 | ||||||||
\(249\) | −2.02837e20 | −0.869866 | ||||||||
\(250\) | −1.50998e20 | −0.625865 | ||||||||
\(251\) | 2.84259e20 | 1.13890 | 0.569452 | − | 0.822025i | \(-0.307156\pi\) | ||||
0.569452 | + | 0.822025i | \(0.307156\pi\) | |||||||
\(252\) | −4.04564e19 | −0.156705 | ||||||||
\(253\) | 1.50594e18 | 0.00564004 | ||||||||
\(254\) | −4.15471e20 | −1.50471 | ||||||||
\(255\) | 4.91353e19 | 0.172108 | ||||||||
\(256\) | −1.33611e20 | −0.452690 | ||||||||
\(257\) | 2.56438e20 | 0.840524 | 0.420262 | − | 0.907403i | \(-0.361938\pi\) | ||||
0.420262 | + | 0.907403i | \(0.361938\pi\) | |||||||
\(258\) | −1.59373e20 | −0.505415 | ||||||||
\(259\) | 4.42920e19 | 0.135918 | ||||||||
\(260\) | −2.07191e19 | −0.0615316 | ||||||||
\(261\) | 1.01570e20 | 0.291959 | ||||||||
\(262\) | −2.61260e20 | −0.726962 | ||||||||
\(263\) | 2.38051e20 | 0.641277 | 0.320639 | − | 0.947202i | \(-0.396103\pi\) | ||||
0.320639 | + | 0.947202i | \(0.396103\pi\) | |||||||
\(264\) | −8.59766e18 | −0.0224257 | ||||||||
\(265\) | 3.94828e19 | 0.0997283 | ||||||||
\(266\) | 2.51423e20 | 0.615052 | ||||||||
\(267\) | 1.12774e21 | 2.67216 | ||||||||
\(268\) | 2.33550e19 | 0.0536085 | ||||||||
\(269\) | 4.64530e20 | 1.03305 | 0.516523 | − | 0.856273i | \(-0.327226\pi\) | ||||
0.516523 | + | 0.856273i | \(0.327226\pi\) | |||||||
\(270\) | −1.42777e20 | −0.307656 | ||||||||
\(271\) | 6.34118e20 | 1.32413 | 0.662066 | − | 0.749446i | \(-0.269680\pi\) | ||||
0.662066 | + | 0.749446i | \(0.269680\pi\) | |||||||
\(272\) | −1.19428e20 | −0.241697 | ||||||||
\(273\) | 5.73887e20 | 1.12576 | ||||||||
\(274\) | 2.60476e20 | 0.495323 | ||||||||
\(275\) | −6.19407e18 | −0.0114195 | ||||||||
\(276\) | 5.94737e19 | 0.106316 | ||||||||
\(277\) | 4.44454e19 | 0.0770458 | 0.0385229 | − | 0.999258i | \(-0.487735\pi\) | ||||
0.0385229 | + | 0.999258i | \(0.487735\pi\) | |||||||
\(278\) | −8.00205e20 | −1.34530 | ||||||||
\(279\) | −9.41315e20 | −1.53497 | ||||||||
\(280\) | −1.57569e20 | −0.249246 | ||||||||
\(281\) | −8.82170e20 | −1.35378 | −0.676891 | − | 0.736083i | \(-0.736673\pi\) | ||||
−0.676891 | + | 0.736083i | \(0.736673\pi\) | |||||||
\(282\) | −1.24548e21 | −1.85447 | ||||||||
\(283\) | 1.15837e21 | 1.67364 | 0.836822 | − | 0.547475i | \(-0.184411\pi\) | ||||
0.836822 | + | 0.547475i | \(0.184411\pi\) | |||||||
\(284\) | 4.19556e18 | 0.00588280 | ||||||||
\(285\) | −4.46494e20 | −0.607623 | ||||||||
\(286\) | 9.99276e18 | 0.0132000 | ||||||||
\(287\) | −1.91825e20 | −0.245985 | ||||||||
\(288\) | −3.87265e20 | −0.482138 | ||||||||
\(289\) | −7.55587e20 | −0.913383 | ||||||||
\(290\) | 5.30284e19 | 0.0622481 | ||||||||
\(291\) | −2.86273e19 | −0.0326354 | ||||||||
\(292\) | −5.58996e18 | −0.00618948 | ||||||||
\(293\) | −1.59557e21 | −1.71609 | −0.858047 | − | 0.513571i | \(-0.828322\pi\) | ||||
−0.858047 | + | 0.513571i | \(0.828322\pi\) | |||||||
\(294\) | −8.26164e20 | −0.863205 | ||||||||
\(295\) | −2.21875e19 | −0.0225227 | ||||||||
\(296\) | 2.27219e20 | 0.224112 | ||||||||
\(297\) | −1.26117e19 | −0.0120877 | ||||||||
\(298\) | −9.45331e20 | −0.880533 | ||||||||
\(299\) | −5.15672e20 | −0.466840 | ||||||||
\(300\) | −2.44622e20 | −0.215260 | ||||||||
\(301\) | −2.58002e20 | −0.220703 | ||||||||
\(302\) | −9.85831e20 | −0.819867 | ||||||||
\(303\) | −1.95535e21 | −1.58111 | ||||||||
\(304\) | 1.08525e21 | 0.853304 | ||||||||
\(305\) | −6.82136e20 | −0.521582 | ||||||||
\(306\) | −5.72051e20 | −0.425405 | ||||||||
\(307\) | 1.77466e21 | 1.28362 | 0.641812 | − | 0.766862i | \(-0.278183\pi\) | ||||
0.641812 | + | 0.766862i | \(0.278183\pi\) | |||||||
\(308\) | −1.86572e18 | −0.00131270 | ||||||||
\(309\) | 6.38502e19 | 0.0437034 | ||||||||
\(310\) | −4.91448e20 | −0.327268 | ||||||||
\(311\) | 1.63898e21 | 1.06197 | 0.530984 | − | 0.847382i | \(-0.321823\pi\) | ||||
0.530984 | + | 0.847382i | \(0.321823\pi\) | |||||||
\(312\) | 2.94406e21 | 1.85623 | ||||||||
\(313\) | −7.94089e19 | −0.0487240 | −0.0243620 | − | 0.999703i | \(-0.507755\pi\) | ||||
−0.0243620 | + | 0.999703i | \(0.507755\pi\) | |||||||
\(314\) | −6.35366e20 | −0.379422 | ||||||||
\(315\) | −6.35043e20 | −0.369116 | ||||||||
\(316\) | 3.34653e20 | 0.189345 | ||||||||
\(317\) | −2.25505e21 | −1.24209 | −0.621044 | − | 0.783776i | \(-0.713291\pi\) | ||||
−0.621044 | + | 0.783776i | \(0.713291\pi\) | |||||||
\(318\) | −7.52041e20 | −0.403284 | ||||||||
\(319\) | 4.68410e18 | 0.00244571 | ||||||||
\(320\) | −7.91151e20 | −0.402239 | ||||||||
\(321\) | 6.36866e21 | 3.15323 | ||||||||
\(322\) | −5.25692e20 | −0.253487 | ||||||||
\(323\) | −6.51113e20 | −0.305798 | ||||||||
\(324\) | 3.39333e19 | 0.0155236 | ||||||||
\(325\) | 2.12101e21 | 0.945222 | ||||||||
\(326\) | 2.33836e21 | 1.01522 | ||||||||
\(327\) | 5.24339e21 | 2.21797 | ||||||||
\(328\) | −9.84068e20 | −0.405600 | ||||||||
\(329\) | −2.01626e21 | −0.809806 | ||||||||
\(330\) | −1.80906e19 | −0.00708085 | ||||||||
\(331\) | 5.11331e21 | 1.95058 | 0.975290 | − | 0.220927i | \(-0.0709084\pi\) | ||||
0.975290 | + | 0.220927i | \(0.0709084\pi\) | |||||||
\(332\) | −2.25805e20 | −0.0839575 | ||||||||
\(333\) | 9.15749e20 | 0.331895 | ||||||||
\(334\) | −1.60010e21 | −0.565329 | ||||||||
\(335\) | 3.66602e20 | 0.126274 | ||||||||
\(336\) | 2.52527e21 | 0.848056 | ||||||||
\(337\) | −1.78584e21 | −0.584773 | −0.292387 | − | 0.956300i | \(-0.594449\pi\) | ||||
−0.292387 | + | 0.956300i | \(0.594449\pi\) | |||||||
\(338\) | −5.42578e20 | −0.173249 | ||||||||
\(339\) | 3.48704e21 | 1.08582 | ||||||||
\(340\) | 5.46991e19 | 0.0166115 | ||||||||
\(341\) | −4.34105e19 | −0.0128583 | ||||||||
\(342\) | 5.19825e21 | 1.50188 | ||||||||
\(343\) | −3.62197e21 | −1.02081 | ||||||||
\(344\) | −1.32356e21 | −0.363913 | ||||||||
\(345\) | 9.33558e20 | 0.250426 | ||||||||
\(346\) | −4.84294e21 | −1.26754 | ||||||||
\(347\) | −4.18884e21 | −1.06978 | −0.534889 | − | 0.844922i | \(-0.679647\pi\) | ||||
−0.534889 | + | 0.844922i | \(0.679647\pi\) | |||||||
\(348\) | 1.84988e20 | 0.0461021 | ||||||||
\(349\) | 2.00753e21 | 0.488254 | 0.244127 | − | 0.969743i | \(-0.421499\pi\) | ||||
0.244127 | + | 0.969743i | \(0.421499\pi\) | |||||||
\(350\) | 2.16222e21 | 0.513242 | ||||||||
\(351\) | 4.31858e21 | 1.00053 | ||||||||
\(352\) | −1.78594e19 | −0.00403882 | ||||||||
\(353\) | −2.68437e21 | −0.592595 | −0.296298 | − | 0.955096i | \(-0.595752\pi\) | ||||
−0.296298 | + | 0.955096i | \(0.595752\pi\) | |||||||
\(354\) | 4.22611e20 | 0.0910780 | ||||||||
\(355\) | 6.58576e19 | 0.0138569 | ||||||||
\(356\) | 1.25544e21 | 0.257911 | ||||||||
\(357\) | −1.51508e21 | −0.303917 | ||||||||
\(358\) | −3.60335e21 | −0.705831 | ||||||||
\(359\) | −9.74174e21 | −1.86352 | −0.931759 | − | 0.363077i | \(-0.881726\pi\) | ||||
−0.931759 | + | 0.363077i | \(0.881726\pi\) | |||||||
\(360\) | −3.25779e21 | −0.608628 | ||||||||
\(361\) | 4.36301e20 | 0.0796113 | ||||||||
\(362\) | −3.82628e21 | −0.681952 | ||||||||
\(363\) | 9.21059e21 | 1.60354 | ||||||||
\(364\) | 6.38871e20 | 0.108655 | ||||||||
\(365\) | −8.77454e19 | −0.0145792 | ||||||||
\(366\) | 1.29928e22 | 2.10919 | ||||||||
\(367\) | 3.91305e21 | 0.620660 | 0.310330 | − | 0.950629i | \(-0.399560\pi\) | ||||
0.310330 | + | 0.950629i | \(0.399560\pi\) | |||||||
\(368\) | −2.26911e21 | −0.351681 | ||||||||
\(369\) | −3.96604e21 | −0.600665 | ||||||||
\(370\) | 4.78100e20 | 0.0707627 | ||||||||
\(371\) | −1.21745e21 | −0.176105 | ||||||||
\(372\) | −1.71440e21 | −0.242381 | ||||||||
\(373\) | 2.02358e20 | 0.0279638 | 0.0139819 | − | 0.999902i | \(-0.495549\pi\) | ||||
0.0139819 | + | 0.999902i | \(0.495549\pi\) | |||||||
\(374\) | −2.63812e19 | −0.00356357 | ||||||||
\(375\) | −8.26842e21 | −1.09183 | ||||||||
\(376\) | −1.03435e22 | −1.33527 | ||||||||
\(377\) | −1.60396e21 | −0.202437 | ||||||||
\(378\) | 4.40250e21 | 0.543274 | ||||||||
\(379\) | 1.06563e21 | 0.128579 | 0.0642897 | − | 0.997931i | \(-0.479522\pi\) | ||||
0.0642897 | + | 0.997931i | \(0.479522\pi\) | |||||||
\(380\) | −4.97052e20 | −0.0586464 | ||||||||
\(381\) | −2.27506e22 | −2.62501 | ||||||||
\(382\) | 2.30132e21 | 0.259680 | ||||||||
\(383\) | 8.39158e21 | 0.926092 | 0.463046 | − | 0.886334i | \(-0.346756\pi\) | ||||
0.463046 | + | 0.886334i | \(0.346756\pi\) | |||||||
\(384\) | 1.05129e22 | 1.13476 | ||||||||
\(385\) | −2.92861e19 | −0.00309205 | ||||||||
\(386\) | −5.69460e21 | −0.588127 | ||||||||
\(387\) | −5.33427e21 | −0.538930 | ||||||||
\(388\) | −3.18688e19 | −0.00314990 | ||||||||
\(389\) | 1.40638e22 | 1.35997 | 0.679985 | − | 0.733226i | \(-0.261986\pi\) | ||||
0.679985 | + | 0.733226i | \(0.261986\pi\) | |||||||
\(390\) | 6.19470e21 | 0.586099 | ||||||||
\(391\) | 1.36139e21 | 0.126032 | ||||||||
\(392\) | −6.86111e21 | −0.621531 | ||||||||
\(393\) | −1.43062e22 | −1.26820 | ||||||||
\(394\) | 6.27020e21 | 0.543956 | ||||||||
\(395\) | 5.25304e21 | 0.446001 | ||||||||
\(396\) | −3.85743e19 | −0.00320545 | ||||||||
\(397\) | −7.22062e21 | −0.587293 | −0.293647 | − | 0.955914i | \(-0.594869\pi\) | ||||
−0.293647 | + | 0.955914i | \(0.594869\pi\) | |||||||
\(398\) | 7.31846e21 | 0.582658 | ||||||||
\(399\) | 1.37676e22 | 1.07297 | ||||||||
\(400\) | 9.33307e21 | 0.712056 | ||||||||
\(401\) | −5.40980e21 | −0.404067 | −0.202034 | − | 0.979379i | \(-0.564755\pi\) | ||||
−0.202034 | + | 0.979379i | \(0.564755\pi\) | |||||||
\(402\) | −6.98278e21 | −0.510631 | ||||||||
\(403\) | 1.48649e22 | 1.06431 | ||||||||
\(404\) | −2.17677e21 | −0.152605 | ||||||||
\(405\) | 5.32650e20 | 0.0365658 | ||||||||
\(406\) | −1.63512e21 | −0.109921 | ||||||||
\(407\) | 4.22315e19 | 0.00278025 | ||||||||
\(408\) | −7.77240e21 | −0.501122 | ||||||||
\(409\) | −2.89928e21 | −0.183080 | −0.0915402 | − | 0.995801i | \(-0.529179\pi\) | ||||
−0.0915402 | + | 0.995801i | \(0.529179\pi\) | |||||||
\(410\) | −2.07061e21 | −0.128067 | ||||||||
\(411\) | 1.42633e22 | 0.864101 | ||||||||
\(412\) | 7.10802e19 | 0.00421816 | ||||||||
\(413\) | 6.84147e20 | 0.0397717 | ||||||||
\(414\) | −1.08688e22 | −0.618984 | ||||||||
\(415\) | −3.54445e21 | −0.197761 | ||||||||
\(416\) | 6.11552e21 | 0.334303 | ||||||||
\(417\) | −4.38180e22 | −2.34691 | ||||||||
\(418\) | 2.39727e20 | 0.0125811 | ||||||||
\(419\) | −1.52164e21 | −0.0782513 | −0.0391257 | − | 0.999234i | \(-0.512457\pi\) | ||||
−0.0391257 | + | 0.999234i | \(0.512457\pi\) | |||||||
\(420\) | −1.15659e21 | −0.0582857 | ||||||||
\(421\) | −1.72305e22 | −0.850944 | −0.425472 | − | 0.904971i | \(-0.639892\pi\) | ||||
−0.425472 | + | 0.904971i | \(0.639892\pi\) | |||||||
\(422\) | −2.78575e22 | −1.34830 | ||||||||
\(423\) | −4.16867e22 | −1.97745 | ||||||||
\(424\) | −6.24554e21 | −0.290376 | ||||||||
\(425\) | −5.59952e21 | −0.255179 | ||||||||
\(426\) | −1.25441e21 | −0.0560348 | ||||||||
\(427\) | 2.10335e22 | 0.921034 | ||||||||
\(428\) | 7.08980e21 | 0.304342 | ||||||||
\(429\) | 5.47189e20 | 0.0230277 | ||||||||
\(430\) | −2.78495e21 | −0.114904 | ||||||||
\(431\) | 1.14752e22 | 0.464198 | 0.232099 | − | 0.972692i | \(-0.425441\pi\) | ||||
0.232099 | + | 0.972692i | \(0.425441\pi\) | |||||||
\(432\) | 1.90030e22 | 0.753722 | ||||||||
\(433\) | 2.22821e22 | 0.866579 | 0.433289 | − | 0.901255i | \(-0.357353\pi\) | ||||
0.433289 | + | 0.901255i | \(0.357353\pi\) | |||||||
\(434\) | 1.51537e22 | 0.577905 | ||||||||
\(435\) | 2.90376e21 | 0.108593 | ||||||||
\(436\) | 5.83712e21 | 0.214074 | ||||||||
\(437\) | −1.23710e22 | −0.444951 | ||||||||
\(438\) | 1.67131e21 | 0.0589559 | ||||||||
\(439\) | 8.42409e21 | 0.291457 | 0.145729 | − | 0.989325i | \(-0.453447\pi\) | ||||
0.145729 | + | 0.989325i | \(0.453447\pi\) | |||||||
\(440\) | −1.50239e20 | −0.00509841 | ||||||||
\(441\) | −2.76520e22 | −0.920445 | ||||||||
\(442\) | 9.03360e21 | 0.294966 | ||||||||
\(443\) | 2.61533e22 | 0.837712 | 0.418856 | − | 0.908053i | \(-0.362431\pi\) | ||||
0.418856 | + | 0.908053i | \(0.362431\pi\) | |||||||
\(444\) | 1.66784e21 | 0.0524082 | ||||||||
\(445\) | 1.97066e22 | 0.607507 | ||||||||
\(446\) | 4.53251e22 | 1.37086 | ||||||||
\(447\) | −5.17649e22 | −1.53611 | ||||||||
\(448\) | 2.43950e22 | 0.710293 | ||||||||
\(449\) | −2.97454e22 | −0.849819 | −0.424909 | − | 0.905236i | \(-0.639694\pi\) | ||||
−0.424909 | + | 0.905236i | \(0.639694\pi\) | |||||||
\(450\) | 4.47046e22 | 1.25327 | ||||||||
\(451\) | −1.82901e20 | −0.00503171 | ||||||||
\(452\) | 3.88189e21 | 0.104801 | ||||||||
\(453\) | −5.39826e22 | −1.43027 | ||||||||
\(454\) | 4.40028e22 | 1.14421 | ||||||||
\(455\) | 1.00283e22 | 0.255936 | ||||||||
\(456\) | 7.06281e22 | 1.76920 | ||||||||
\(457\) | 6.40802e22 | 1.57557 | 0.787783 | − | 0.615953i | \(-0.211229\pi\) | ||||
0.787783 | + | 0.615953i | \(0.211229\pi\) | |||||||
\(458\) | −3.24407e22 | −0.782950 | ||||||||
\(459\) | −1.14012e22 | −0.270111 | ||||||||
\(460\) | 1.03927e21 | 0.0241705 | ||||||||
\(461\) | −5.46473e21 | −0.124770 | −0.0623851 | − | 0.998052i | \(-0.519871\pi\) | ||||
−0.0623851 | + | 0.998052i | \(0.519871\pi\) | |||||||
\(462\) | 5.57822e20 | 0.0125037 | ||||||||
\(463\) | 5.22777e22 | 1.15048 | 0.575239 | − | 0.817986i | \(-0.304909\pi\) | ||||
0.575239 | + | 0.817986i | \(0.304909\pi\) | |||||||
\(464\) | −7.05788e21 | −0.152501 | ||||||||
\(465\) | −2.69110e22 | −0.570925 | ||||||||
\(466\) | 4.94536e22 | 1.03019 | ||||||||
\(467\) | 9.48870e21 | 0.194095 | 0.0970473 | − | 0.995280i | \(-0.469060\pi\) | ||||
0.0970473 | + | 0.995280i | \(0.469060\pi\) | |||||||
\(468\) | 1.32088e22 | 0.265323 | ||||||||
\(469\) | −1.13041e22 | −0.222981 | ||||||||
\(470\) | −2.17641e22 | −0.421607 | ||||||||
\(471\) | −3.47917e22 | −0.661909 | ||||||||
\(472\) | 3.50970e21 | 0.0655787 | ||||||||
\(473\) | −2.46000e20 | −0.00451456 | ||||||||
\(474\) | −1.00056e23 | −1.80355 | ||||||||
\(475\) | 5.08831e22 | 0.900902 | ||||||||
\(476\) | −1.68664e21 | −0.0293334 | ||||||||
\(477\) | −2.51711e22 | −0.430027 | ||||||||
\(478\) | −6.29458e21 | −0.105640 | ||||||||
\(479\) | 2.56708e22 | 0.423240 | 0.211620 | − | 0.977352i | \(-0.432126\pi\) | ||||
0.211620 | + | 0.977352i | \(0.432126\pi\) | |||||||
\(480\) | −1.10714e22 | −0.179329 | ||||||||
\(481\) | −1.44611e22 | −0.230128 | ||||||||
\(482\) | 1.34554e22 | 0.210377 | ||||||||
\(483\) | −2.87861e22 | −0.442214 | ||||||||
\(484\) | 1.02535e22 | 0.154771 | ||||||||
\(485\) | −5.00244e20 | −0.00741954 | ||||||||
\(486\) | −6.80390e22 | −0.991630 | ||||||||
\(487\) | −1.28868e23 | −1.84565 | −0.922825 | − | 0.385219i | \(-0.874126\pi\) | ||||
−0.922825 | + | 0.385219i | \(0.874126\pi\) | |||||||
\(488\) | 1.07903e23 | 1.51867 | ||||||||
\(489\) | 1.28045e23 | 1.77108 | ||||||||
\(490\) | −1.44367e22 | −0.196246 | ||||||||
\(491\) | 1.27346e23 | 1.70134 | 0.850670 | − | 0.525700i | \(-0.176196\pi\) | ||||
0.850670 | + | 0.525700i | \(0.176196\pi\) | |||||||
\(492\) | −7.22329e21 | −0.0948487 | ||||||||
\(493\) | 4.23449e21 | 0.0546515 | ||||||||
\(494\) | −8.20887e22 | −1.04137 | ||||||||
\(495\) | −6.05499e20 | −0.00755039 | ||||||||
\(496\) | 6.54098e22 | 0.801768 | ||||||||
\(497\) | −2.03071e21 | −0.0244691 | ||||||||
\(498\) | 6.75122e22 | 0.799711 | ||||||||
\(499\) | −6.05712e22 | −0.705362 | −0.352681 | − | 0.935744i | \(-0.614730\pi\) | ||||
−0.352681 | + | 0.935744i | \(0.614730\pi\) | |||||||
\(500\) | −9.20468e21 | −0.105381 | ||||||||
\(501\) | −8.76189e22 | −0.986228 | ||||||||
\(502\) | −9.46126e22 | −1.04705 | ||||||||
\(503\) | −8.97254e21 | −0.0976309 | −0.0488155 | − | 0.998808i | \(-0.515545\pi\) | ||||
−0.0488155 | + | 0.998808i | \(0.515545\pi\) | |||||||
\(504\) | 1.00453e23 | 1.07474 | ||||||||
\(505\) | −3.41686e22 | −0.359460 | ||||||||
\(506\) | −5.01236e20 | −0.00518516 | ||||||||
\(507\) | −2.97108e22 | −0.302236 | ||||||||
\(508\) | −2.53267e22 | −0.253360 | ||||||||
\(509\) | 1.76507e22 | 0.173644 | 0.0868220 | − | 0.996224i | \(-0.472329\pi\) | ||||
0.0868220 | + | 0.996224i | \(0.472329\pi\) | |||||||
\(510\) | −1.63542e22 | −0.158228 | ||||||||
\(511\) | 2.70561e21 | 0.0257447 | ||||||||
\(512\) | 1.20075e23 | 1.12372 | ||||||||
\(513\) | 1.03603e23 | 0.953618 | ||||||||
\(514\) | −8.53526e22 | −0.772735 | ||||||||
\(515\) | 1.11574e21 | 0.00993581 | ||||||||
\(516\) | −9.71524e21 | −0.0851003 | ||||||||
\(517\) | −1.92246e21 | −0.0165648 | ||||||||
\(518\) | −1.47421e22 | −0.124956 | ||||||||
\(519\) | −2.65192e23 | −2.21125 | ||||||||
\(520\) | 5.14457e22 | 0.422008 | ||||||||
\(521\) | 7.01454e22 | 0.566081 | 0.283041 | − | 0.959108i | \(-0.408657\pi\) | ||||
0.283041 | + | 0.959108i | \(0.408657\pi\) | |||||||
\(522\) | −3.38066e22 | −0.268412 | ||||||||
\(523\) | 3.66650e22 | 0.286410 | 0.143205 | − | 0.989693i | \(-0.454259\pi\) | ||||
0.143205 | + | 0.989693i | \(0.454259\pi\) | |||||||
\(524\) | −1.59261e22 | −0.122404 | ||||||||
\(525\) | 1.18400e23 | 0.895361 | ||||||||
\(526\) | −7.92328e22 | −0.589557 | ||||||||
\(527\) | −3.92437e22 | −0.287329 | ||||||||
\(528\) | 2.40779e21 | 0.0173473 | ||||||||
\(529\) | −1.15184e23 | −0.816618 | ||||||||
\(530\) | −1.31415e22 | −0.0916851 | ||||||||
\(531\) | 1.41449e22 | 0.0971175 | ||||||||
\(532\) | 1.53265e22 | 0.103561 | ||||||||
\(533\) | 6.26300e22 | 0.416487 | ||||||||
\(534\) | −3.75357e23 | −2.45665 | ||||||||
\(535\) | 1.11288e23 | 0.716874 | ||||||||
\(536\) | −5.79905e22 | −0.367668 | ||||||||
\(537\) | −1.97314e23 | −1.23134 | ||||||||
\(538\) | −1.54614e23 | −0.949729 | ||||||||
\(539\) | −1.27522e21 | −0.00771047 | ||||||||
\(540\) | −8.70354e21 | −0.0518023 | ||||||||
\(541\) | 3.22978e23 | 1.89233 | 0.946165 | − | 0.323686i | \(-0.104922\pi\) | ||||
0.946165 | + | 0.323686i | \(0.104922\pi\) | |||||||
\(542\) | −2.11060e23 | −1.21734 | ||||||||
\(543\) | −2.09521e23 | −1.18968 | ||||||||
\(544\) | −1.61452e22 | −0.0902509 | ||||||||
\(545\) | 9.16251e22 | 0.504248 | ||||||||
\(546\) | −1.91013e23 | −1.03496 | ||||||||
\(547\) | 1.61822e23 | 0.863267 | 0.431633 | − | 0.902049i | \(-0.357937\pi\) | ||||
0.431633 | + | 0.902049i | \(0.357937\pi\) | |||||||
\(548\) | 1.58784e22 | 0.0834011 | ||||||||
\(549\) | 4.34874e23 | 2.24905 | ||||||||
\(550\) | 2.06163e21 | 0.0104985 | ||||||||
\(551\) | −3.84790e22 | −0.192946 | ||||||||
\(552\) | −1.47674e23 | −0.729157 | ||||||||
\(553\) | −1.61977e23 | −0.787569 | ||||||||
\(554\) | −1.47932e22 | −0.0708319 | ||||||||
\(555\) | 2.61801e22 | 0.123447 | ||||||||
\(556\) | −4.87797e22 | −0.226518 | ||||||||
\(557\) | −1.97039e23 | −0.901121 | −0.450561 | − | 0.892746i | \(-0.648776\pi\) | ||||
−0.450561 | + | 0.892746i | \(0.648776\pi\) | |||||||
\(558\) | 3.13307e23 | 1.41117 | ||||||||
\(559\) | 8.42367e22 | 0.373681 | ||||||||
\(560\) | 4.41276e22 | 0.192802 | ||||||||
\(561\) | −1.44459e21 | −0.00621672 | ||||||||
\(562\) | 2.93621e23 | 1.24460 | ||||||||
\(563\) | −4.24181e23 | −1.77104 | −0.885522 | − | 0.464597i | \(-0.846199\pi\) | ||||
−0.885522 | + | 0.464597i | \(0.846199\pi\) | |||||||
\(564\) | −7.59234e22 | −0.312251 | ||||||||
\(565\) | 6.09340e22 | 0.246858 | ||||||||
\(566\) | −3.85552e23 | −1.53866 | ||||||||
\(567\) | −1.64242e22 | −0.0645696 | ||||||||
\(568\) | −1.04176e22 | −0.0403466 | ||||||||
\(569\) | 3.39173e23 | 1.29410 | 0.647049 | − | 0.762449i | \(-0.276003\pi\) | ||||
0.647049 | + | 0.762449i | \(0.276003\pi\) | |||||||
\(570\) | 1.48611e23 | 0.558618 | ||||||||
\(571\) | 6.84513e22 | 0.253498 | 0.126749 | − | 0.991935i | \(-0.459546\pi\) | ||||
0.126749 | + | 0.991935i | \(0.459546\pi\) | |||||||
\(572\) | 6.09149e20 | 0.00222258 | ||||||||
\(573\) | 1.26017e23 | 0.453017 | ||||||||
\(574\) | 6.38470e22 | 0.226146 | ||||||||
\(575\) | −1.06390e23 | −0.371298 | ||||||||
\(576\) | 5.04373e23 | 1.73445 | ||||||||
\(577\) | −1.80057e23 | −0.610121 | −0.305061 | − | 0.952333i | \(-0.598677\pi\) | ||||
−0.305061 | + | 0.952333i | \(0.598677\pi\) | |||||||
\(578\) | 2.51490e23 | 0.839718 | ||||||||
\(579\) | −3.11828e23 | −1.02600 | ||||||||
\(580\) | 3.23256e21 | 0.0104812 | ||||||||
\(581\) | 1.09293e23 | 0.349216 | ||||||||
\(582\) | 9.52829e21 | 0.0300033 | ||||||||
\(583\) | −1.16081e21 | −0.00360229 | ||||||||
\(584\) | 1.38799e22 | 0.0424499 | ||||||||
\(585\) | 2.07339e23 | 0.624965 | ||||||||
\(586\) | 5.31069e23 | 1.57769 | ||||||||
\(587\) | 8.40746e22 | 0.246173 | 0.123087 | − | 0.992396i | \(-0.460721\pi\) | ||||
0.123087 | + | 0.992396i | \(0.460721\pi\) | |||||||
\(588\) | −5.03621e22 | −0.145344 | ||||||||
\(589\) | 3.56609e23 | 1.01441 | ||||||||
\(590\) | 7.38488e21 | 0.0207062 | ||||||||
\(591\) | 3.43347e23 | 0.948942 | ||||||||
\(592\) | −6.36333e22 | −0.173360 | ||||||||
\(593\) | −3.81961e23 | −1.02578 | −0.512890 | − | 0.858455i | \(-0.671425\pi\) | ||||
−0.512890 | + | 0.858455i | \(0.671425\pi\) | |||||||
\(594\) | 4.19769e21 | 0.0111128 | ||||||||
\(595\) | −2.64751e22 | −0.0690944 | ||||||||
\(596\) | −5.76265e22 | −0.148262 | ||||||||
\(597\) | 4.00748e23 | 1.01646 | ||||||||
\(598\) | 1.71636e23 | 0.429189 | ||||||||
\(599\) | −3.18627e23 | −0.785514 | −0.392757 | − | 0.919642i | \(-0.628479\pi\) | ||||
−0.392757 | + | 0.919642i | \(0.628479\pi\) | |||||||
\(600\) | 6.07397e23 | 1.47634 | ||||||||
\(601\) | 5.82853e23 | 1.39677 | 0.698387 | − | 0.715720i | \(-0.253901\pi\) | ||||
0.698387 | + | 0.715720i | \(0.253901\pi\) | |||||||
\(602\) | 8.58735e22 | 0.202903 | ||||||||
\(603\) | −2.33716e23 | −0.544492 | ||||||||
\(604\) | −6.00953e22 | −0.138047 | ||||||||
\(605\) | 1.60950e23 | 0.364560 | ||||||||
\(606\) | 6.50820e23 | 1.45359 | ||||||||
\(607\) | 6.70463e23 | 1.47663 | 0.738313 | − | 0.674458i | \(-0.235623\pi\) | ||||
0.738313 | + | 0.674458i | \(0.235623\pi\) | |||||||
\(608\) | 1.46712e23 | 0.318628 | ||||||||
\(609\) | −8.95369e22 | −0.191759 | ||||||||
\(610\) | 2.27042e23 | 0.479515 | ||||||||
\(611\) | 6.58300e23 | 1.37111 | ||||||||
\(612\) | −3.48717e22 | −0.0716285 | ||||||||
\(613\) | −9.15701e23 | −1.85498 | −0.927491 | − | 0.373845i | \(-0.878039\pi\) | ||||
−0.927491 | + | 0.373845i | \(0.878039\pi\) | |||||||
\(614\) | −5.90676e23 | −1.18010 | ||||||||
\(615\) | −1.13384e23 | −0.223415 | ||||||||
\(616\) | 4.63259e21 | 0.00900301 | ||||||||
\(617\) | −9.04813e23 | −1.73434 | −0.867171 | − | 0.498010i | \(-0.834064\pi\) | ||||
−0.867171 | + | 0.498010i | \(0.834064\pi\) | |||||||
\(618\) | −2.12519e22 | −0.0401787 | ||||||||
\(619\) | −6.78753e23 | −1.26573 | −0.632865 | − | 0.774262i | \(-0.718121\pi\) | ||||
−0.632865 | + | 0.774262i | \(0.718121\pi\) | |||||||
\(620\) | −2.99582e22 | −0.0551044 | ||||||||
\(621\) | −2.16620e23 | −0.393024 | ||||||||
\(622\) | −5.45519e23 | −0.976319 | ||||||||
\(623\) | −6.07649e23 | −1.07276 | ||||||||
\(624\) | −8.24491e23 | −1.43588 | ||||||||
\(625\) | 3.60204e23 | 0.618825 | ||||||||
\(626\) | 2.64305e22 | 0.0447943 | ||||||||
\(627\) | 1.31271e22 | 0.0219480 | ||||||||
\(628\) | −3.87313e22 | −0.0638860 | ||||||||
\(629\) | 3.81778e22 | 0.0621270 | ||||||||
\(630\) | 2.11368e23 | 0.339347 | ||||||||
\(631\) | 9.88826e23 | 1.56628 | 0.783141 | − | 0.621844i | \(-0.213616\pi\) | ||||
0.783141 | + | 0.621844i | \(0.213616\pi\) | |||||||
\(632\) | −8.30945e23 | −1.29861 | ||||||||
\(633\) | −1.52544e24 | −2.35214 | ||||||||
\(634\) | 7.50571e23 | 1.14191 | ||||||||
\(635\) | −3.97553e23 | −0.596785 | ||||||||
\(636\) | −4.58437e22 | −0.0679038 | ||||||||
\(637\) | 4.36669e23 | 0.638215 | ||||||||
\(638\) | −1.55905e21 | −0.00224846 | ||||||||
\(639\) | −4.19855e22 | −0.0597506 | ||||||||
\(640\) | 1.83706e23 | 0.257985 | ||||||||
\(641\) | 7.46475e23 | 1.03448 | 0.517240 | − | 0.855840i | \(-0.326959\pi\) | ||||
0.517240 | + | 0.855840i | \(0.326959\pi\) | |||||||
\(642\) | −2.11974e24 | −2.89892 | ||||||||
\(643\) | −1.60985e23 | −0.217266 | −0.108633 | − | 0.994082i | \(-0.534647\pi\) | ||||
−0.108633 | + | 0.994082i | \(0.534647\pi\) | |||||||
\(644\) | −3.20457e22 | −0.0426815 | ||||||||
\(645\) | −1.52500e23 | −0.200453 | ||||||||
\(646\) | 2.16716e23 | 0.281135 | ||||||||
\(647\) | 1.47953e23 | 0.189425 | 0.0947124 | − | 0.995505i | \(-0.469807\pi\) | ||||
0.0947124 | + | 0.995505i | \(0.469807\pi\) | |||||||
\(648\) | −8.42566e22 | −0.106467 | ||||||||
\(649\) | 6.52320e20 | 0.000813543 0 | ||||||||
\(650\) | −7.05957e23 | −0.868989 | ||||||||
\(651\) | 8.29795e23 | 1.00817 | ||||||||
\(652\) | 1.42544e23 | 0.170940 | ||||||||
\(653\) | −8.40989e23 | −0.995470 | −0.497735 | − | 0.867329i | \(-0.665835\pi\) | ||||
−0.497735 | + | 0.867329i | \(0.665835\pi\) | |||||||
\(654\) | −1.74521e24 | −2.03909 | ||||||||
\(655\) | −2.49992e23 | −0.288320 | ||||||||
\(656\) | 2.75591e23 | 0.313749 | ||||||||
\(657\) | 5.59393e22 | 0.0628654 | ||||||||
\(658\) | 6.71091e23 | 0.744494 | ||||||||
\(659\) | 1.54714e24 | 1.69435 | 0.847175 | − | 0.531314i | \(-0.178302\pi\) | ||||
0.847175 | + | 0.531314i | \(0.178302\pi\) | |||||||
\(660\) | −1.10279e21 | −0.00119225 | ||||||||
\(661\) | −2.20956e23 | −0.235827 | −0.117914 | − | 0.993024i | \(-0.537621\pi\) | ||||
−0.117914 | + | 0.993024i | \(0.537621\pi\) | |||||||
\(662\) | −1.70191e24 | −1.79326 | ||||||||
\(663\) | 4.94667e23 | 0.514574 | ||||||||
\(664\) | 5.60675e23 | 0.575814 | ||||||||
\(665\) | 2.40580e23 | 0.243936 | ||||||||
\(666\) | −3.04798e23 | −0.305127 | ||||||||
\(667\) | 8.04542e22 | 0.0795205 | ||||||||
\(668\) | −9.75404e22 | −0.0951885 | ||||||||
\(669\) | 2.48193e24 | 2.39149 | ||||||||
\(670\) | −1.22020e23 | −0.116090 | ||||||||
\(671\) | 2.00550e22 | 0.0188400 | ||||||||
\(672\) | 3.41384e23 | 0.316668 | ||||||||
\(673\) | 1.15979e24 | 1.06231 | 0.531157 | − | 0.847273i | \(-0.321757\pi\) | ||||
0.531157 | + | 0.847273i | \(0.321757\pi\) | |||||||
\(674\) | 5.94398e23 | 0.537611 | ||||||||
\(675\) | 8.90978e23 | 0.795765 | ||||||||
\(676\) | −3.30750e22 | −0.0291711 | ||||||||
\(677\) | −1.91800e24 | −1.67050 | −0.835248 | − | 0.549873i | \(-0.814676\pi\) | ||||
−0.835248 | + | 0.549873i | \(0.814676\pi\) | |||||||
\(678\) | −1.16063e24 | −0.998252 | ||||||||
\(679\) | 1.54249e22 | 0.0131018 | ||||||||
\(680\) | −1.35818e23 | −0.113928 | ||||||||
\(681\) | 2.40953e24 | 1.99610 | ||||||||
\(682\) | 1.44487e22 | 0.0118212 | ||||||||
\(683\) | −2.26629e24 | −1.83121 | −0.915607 | − | 0.402075i | \(-0.868289\pi\) | ||||
−0.915607 | + | 0.402075i | \(0.868289\pi\) | |||||||
\(684\) | 3.16880e23 | 0.252882 | ||||||||
\(685\) | 2.49243e23 | 0.196450 | ||||||||
\(686\) | 1.20554e24 | 0.938482 | ||||||||
\(687\) | −1.77641e24 | −1.36587 | ||||||||
\(688\) | 3.70666e23 | 0.281502 | ||||||||
\(689\) | 3.97491e23 | 0.298170 | ||||||||
\(690\) | −3.10725e23 | −0.230229 | ||||||||
\(691\) | −6.33975e23 | −0.463990 | −0.231995 | − | 0.972717i | \(-0.574525\pi\) | ||||
−0.231995 | + | 0.972717i | \(0.574525\pi\) | |||||||
\(692\) | −2.95221e23 | −0.213425 | ||||||||
\(693\) | 1.86705e22 | 0.0133328 | ||||||||
\(694\) | 1.39421e24 | 0.983499 | ||||||||
\(695\) | −7.65694e23 | −0.533561 | ||||||||
\(696\) | −4.59327e23 | −0.316187 | ||||||||
\(697\) | −1.65345e23 | −0.112438 | ||||||||
\(698\) | −6.68185e23 | −0.448876 | ||||||||
\(699\) | 2.70801e24 | 1.79719 | ||||||||
\(700\) | 1.31807e23 | 0.0864182 | ||||||||
\(701\) | 1.23966e24 | 0.802971 | 0.401485 | − | 0.915865i | \(-0.368494\pi\) | ||||
0.401485 | + | 0.915865i | \(0.368494\pi\) | |||||||
\(702\) | −1.43740e24 | −0.919838 | ||||||||
\(703\) | −3.46923e23 | −0.219338 | ||||||||
\(704\) | 2.32601e22 | 0.0145293 | ||||||||
\(705\) | −1.19177e24 | −0.735502 | ||||||||
\(706\) | 8.93467e23 | 0.544802 | ||||||||
\(707\) | 1.05358e24 | 0.634752 | ||||||||
\(708\) | 2.57620e22 | 0.0153354 | ||||||||
\(709\) | 1.92953e24 | 1.13490 | 0.567450 | − | 0.823408i | \(-0.307930\pi\) | ||||
0.567450 | + | 0.823408i | \(0.307930\pi\) | |||||||
\(710\) | −2.19201e22 | −0.0127393 | ||||||||
\(711\) | −3.34891e24 | −1.92315 | ||||||||
\(712\) | −3.11726e24 | −1.76886 | ||||||||
\(713\) | −7.45620e23 | −0.418077 | ||||||||
\(714\) | 5.04278e23 | 0.279406 | ||||||||
\(715\) | 9.56180e21 | 0.00523526 | ||||||||
\(716\) | −2.19657e23 | −0.118846 | ||||||||
\(717\) | −3.44682e23 | −0.184292 | ||||||||
\(718\) | 3.24244e24 | 1.71322 | ||||||||
\(719\) | 1.24227e24 | 0.648664 | 0.324332 | − | 0.945943i | \(-0.394861\pi\) | ||||
0.324332 | + | 0.945943i | \(0.394861\pi\) | |||||||
\(720\) | 9.12351e23 | 0.470799 | ||||||||
\(721\) | −3.44038e22 | −0.0175451 | ||||||||
\(722\) | −1.45218e23 | −0.0731905 | ||||||||
\(723\) | 7.36799e23 | 0.367006 | ||||||||
\(724\) | −2.33246e23 | −0.114825 | ||||||||
\(725\) | −3.30916e23 | −0.161007 | ||||||||
\(726\) | −3.06565e24 | −1.47422 | ||||||||
\(727\) | 2.83536e24 | 1.34761 | 0.673807 | − | 0.738907i | \(-0.264658\pi\) | ||||
0.673807 | + | 0.738907i | \(0.264658\pi\) | |||||||
\(728\) | −1.58632e24 | −0.745202 | ||||||||
\(729\) | −3.50974e24 | −1.62964 | ||||||||
\(730\) | 2.92052e22 | 0.0134034 | ||||||||
\(731\) | −2.22387e23 | −0.100882 | ||||||||
\(732\) | 7.92031e23 | 0.355139 | ||||||||
\(733\) | 3.76886e24 | 1.67042 | 0.835210 | − | 0.549931i | \(-0.185346\pi\) | ||||
0.835210 | + | 0.549931i | \(0.185346\pi\) | |||||||
\(734\) | −1.30242e24 | −0.570603 | ||||||||
\(735\) | −7.90533e23 | −0.342356 | ||||||||
\(736\) | −3.06754e23 | −0.131319 | ||||||||
\(737\) | −1.07782e22 | −0.00456115 | ||||||||
\(738\) | 1.32006e24 | 0.552221 | ||||||||
\(739\) | −1.80876e24 | −0.748001 | −0.374000 | − | 0.927429i | \(-0.622014\pi\) | ||||
−0.374000 | + | 0.927429i | \(0.622014\pi\) | |||||||
\(740\) | 2.91445e22 | 0.0119148 | ||||||||
\(741\) | −4.49505e24 | −1.81669 | ||||||||
\(742\) | 4.05215e23 | 0.161902 | ||||||||
\(743\) | 2.01400e24 | 0.795526 | 0.397763 | − | 0.917488i | \(-0.369787\pi\) | ||||
0.397763 | + | 0.917488i | \(0.369787\pi\) | |||||||
\(744\) | 4.25687e24 | 1.66234 | ||||||||
\(745\) | −9.04561e23 | −0.349229 | ||||||||
\(746\) | −6.73529e22 | −0.0257085 | ||||||||
\(747\) | 2.25966e24 | 0.852741 | ||||||||
\(748\) | −1.60817e21 | −0.000600024 0 | ||||||||
\(749\) | −3.43156e24 | −1.26589 | ||||||||
\(750\) | 2.75206e24 | 1.00378 | ||||||||
\(751\) | 4.23140e24 | 1.52596 | 0.762982 | − | 0.646420i | \(-0.223734\pi\) | ||||
0.762982 | + | 0.646420i | \(0.223734\pi\) | |||||||
\(752\) | 2.89671e24 | 1.03289 | ||||||||
\(753\) | −5.18085e24 | −1.82660 | ||||||||
\(754\) | 5.33861e23 | 0.186111 | ||||||||
\(755\) | −9.43314e23 | −0.325168 | ||||||||
\(756\) | 2.68372e23 | 0.0914749 | ||||||||
\(757\) | 2.90411e24 | 0.978809 | 0.489404 | − | 0.872057i | \(-0.337214\pi\) | ||||
0.489404 | + | 0.872057i | \(0.337214\pi\) | |||||||
\(758\) | −3.54683e23 | −0.118209 | ||||||||
\(759\) | −2.74469e22 | −0.00904562 | ||||||||
\(760\) | 1.23418e24 | 0.402221 | ||||||||
\(761\) | 2.36377e23 | 0.0761792 | 0.0380896 | − | 0.999274i | \(-0.487873\pi\) | ||||
0.0380896 | + | 0.999274i | \(0.487873\pi\) | |||||||
\(762\) | 7.57230e24 | 2.41330 | ||||||||
\(763\) | −2.82524e24 | −0.890425 | ||||||||
\(764\) | 1.40286e23 | 0.0437241 | ||||||||
\(765\) | −5.47380e23 | −0.168720 | ||||||||
\(766\) | −2.79305e24 | −0.851402 | ||||||||
\(767\) | −2.23371e23 | −0.0673390 | ||||||||
\(768\) | 2.43516e24 | 0.726035 | ||||||||
\(769\) | 6.49820e24 | 1.91610 | 0.958052 | − | 0.286594i | \(-0.0925230\pi\) | ||||
0.958052 | + | 0.286594i | \(0.0925230\pi\) | |||||||
\(770\) | 9.74760e21 | 0.00284267 | ||||||||
\(771\) | −4.67378e24 | −1.34805 | ||||||||
\(772\) | −3.47137e23 | −0.0990271 | ||||||||
\(773\) | 4.42844e24 | 1.24947 | 0.624734 | − | 0.780837i | \(-0.285207\pi\) | ||||
0.624734 | + | 0.780837i | \(0.285207\pi\) | |||||||
\(774\) | 1.77546e24 | 0.495464 | ||||||||
\(775\) | 3.06681e24 | 0.846491 | ||||||||
\(776\) | 7.91305e22 | 0.0216032 | ||||||||
\(777\) | −8.07258e23 | −0.217989 | ||||||||
\(778\) | −4.68098e24 | −1.25029 | ||||||||
\(779\) | 1.50250e24 | 0.396959 | ||||||||
\(780\) | 3.77623e23 | 0.0986857 | ||||||||
\(781\) | −1.93624e21 | −0.000500524 0 | ||||||||
\(782\) | −4.53124e23 | −0.115867 | ||||||||
\(783\) | −6.73778e23 | −0.170428 | ||||||||
\(784\) | 1.92147e24 | 0.480781 | ||||||||
\(785\) | −6.07965e23 | −0.150483 | ||||||||
\(786\) | 4.76167e24 | 1.16592 | ||||||||
\(787\) | 5.90703e24 | 1.43082 | 0.715408 | − | 0.698707i | \(-0.246241\pi\) | ||||
0.715408 | + | 0.698707i | \(0.246241\pi\) | |||||||
\(788\) | 3.82225e23 | 0.0915897 | ||||||||
\(789\) | −4.33867e24 | −1.02849 | ||||||||
\(790\) | −1.74842e24 | −0.410030 | ||||||||
\(791\) | −1.87889e24 | −0.435914 | ||||||||
\(792\) | 9.57801e22 | 0.0219842 | ||||||||
\(793\) | −6.86736e24 | −1.55944 | ||||||||
\(794\) | 2.40331e24 | 0.539927 | ||||||||
\(795\) | −7.19607e23 | −0.159947 | ||||||||
\(796\) | 4.46127e23 | 0.0981063 | ||||||||
\(797\) | −3.76240e24 | −0.818595 | −0.409297 | − | 0.912401i | \(-0.634226\pi\) | ||||
−0.409297 | + | 0.912401i | \(0.634226\pi\) | |||||||
\(798\) | −4.58240e24 | −0.986434 | ||||||||
\(799\) | −1.73793e24 | −0.370156 | ||||||||
\(800\) | 1.26171e24 | 0.265885 | ||||||||
\(801\) | −1.25633e25 | −2.61956 | ||||||||
\(802\) | 1.80060e24 | 0.371479 | ||||||||
\(803\) | 2.57974e21 | 0.000526617 0 | ||||||||
\(804\) | −4.25664e23 | −0.0859786 | ||||||||
\(805\) | −5.03020e23 | −0.100536 | ||||||||
\(806\) | −4.94762e24 | −0.978472 | ||||||||
\(807\) | −8.46644e24 | −1.65682 | ||||||||
\(808\) | 5.40492e24 | 1.04663 | ||||||||
\(809\) | −2.21471e24 | −0.424379 | −0.212190 | − | 0.977229i | \(-0.568059\pi\) | ||||
−0.212190 | + | 0.977229i | \(0.568059\pi\) | |||||||
\(810\) | −1.77287e23 | −0.0336167 | ||||||||
\(811\) | −2.92354e24 | −0.548569 | −0.274284 | − | 0.961649i | \(-0.588441\pi\) | ||||
−0.274284 | + | 0.961649i | \(0.588441\pi\) | |||||||
\(812\) | −9.96755e22 | −0.0185081 | ||||||||
\(813\) | −1.15573e25 | −2.12367 | ||||||||
\(814\) | −1.40563e22 | −0.00255602 | ||||||||
\(815\) | 2.23751e24 | 0.402648 | ||||||||
\(816\) | 2.17668e24 | 0.387639 | ||||||||
\(817\) | 2.02084e24 | 0.356160 | ||||||||
\(818\) | 9.64996e23 | 0.168315 | ||||||||
\(819\) | −6.39325e24 | −1.10359 | ||||||||
\(820\) | −1.26223e23 | −0.0215635 | ||||||||
\(821\) | −6.60841e24 | −1.11733 | −0.558663 | − | 0.829395i | \(-0.688686\pi\) | ||||
−0.558663 | + | 0.829395i | \(0.688686\pi\) | |||||||
\(822\) | −4.74740e24 | −0.794411 | ||||||||
\(823\) | −9.19312e23 | −0.152252 | −0.0761262 | − | 0.997098i | \(-0.524255\pi\) | ||||
−0.0761262 | + | 0.997098i | \(0.524255\pi\) | |||||||
\(824\) | −1.76493e23 | −0.0289298 | ||||||||
\(825\) | 1.12892e23 | 0.0183149 | ||||||||
\(826\) | −2.27711e23 | −0.0365641 | ||||||||
\(827\) | 7.10161e24 | 1.12865 | 0.564326 | − | 0.825552i | \(-0.309136\pi\) | ||||
0.564326 | + | 0.825552i | \(0.309136\pi\) | |||||||
\(828\) | −6.62553e23 | −0.104223 | ||||||||
\(829\) | 5.68184e23 | 0.0884659 | 0.0442329 | − | 0.999021i | \(-0.485916\pi\) | ||||
0.0442329 | + | 0.999021i | \(0.485916\pi\) | |||||||
\(830\) | 1.17974e24 | 0.181811 | ||||||||
\(831\) | −8.10054e23 | −0.123568 | ||||||||
\(832\) | −7.96486e24 | −1.20262 | ||||||||
\(833\) | −1.15282e24 | −0.172297 | ||||||||
\(834\) | 1.45844e25 | 2.15763 | ||||||||
\(835\) | −1.53109e24 | −0.224215 | ||||||||
\(836\) | 1.46135e22 | 0.00211837 | ||||||||
\(837\) | 6.24433e24 | 0.896023 | ||||||||
\(838\) | 5.06461e23 | 0.0719403 | ||||||||
\(839\) | 1.11695e25 | 1.57057 | 0.785286 | − | 0.619133i | \(-0.212516\pi\) | ||||
0.785286 | + | 0.619133i | \(0.212516\pi\) | |||||||
\(840\) | 2.87183e24 | 0.399746 | ||||||||
\(841\) | 2.50246e23 | 0.0344828 | ||||||||
\(842\) | 5.73501e24 | 0.782315 | ||||||||
\(843\) | 1.60783e25 | 2.17123 | ||||||||
\(844\) | −1.69817e24 | −0.227023 | ||||||||
\(845\) | −5.19178e23 | −0.0687122 | ||||||||
\(846\) | 1.38750e25 | 1.81796 | ||||||||
\(847\) | −4.96285e24 | −0.643757 | ||||||||
\(848\) | 1.74908e24 | 0.224618 | ||||||||
\(849\) | −2.11123e25 | −2.68423 | ||||||||
\(850\) | 1.86374e24 | 0.234599 | ||||||||
\(851\) | 7.25369e23 | 0.0903978 | ||||||||
\(852\) | −7.64676e22 | −0.00943498 | ||||||||
\(853\) | −8.02812e24 | −0.980725 | −0.490362 | − | 0.871519i | \(-0.663136\pi\) | ||||
−0.490362 | + | 0.871519i | \(0.663136\pi\) | |||||||
\(854\) | −7.00080e24 | −0.846751 | ||||||||
\(855\) | 4.97406e24 | 0.595661 | ||||||||
\(856\) | −1.76040e25 | −2.08730 | ||||||||
\(857\) | 3.15264e24 | 0.370115 | 0.185058 | − | 0.982728i | \(-0.440753\pi\) | ||||
0.185058 | + | 0.982728i | \(0.440753\pi\) | |||||||
\(858\) | −1.82126e23 | −0.0211705 | ||||||||
\(859\) | −2.60602e24 | −0.299941 | −0.149970 | − | 0.988691i | \(-0.547918\pi\) | ||||
−0.149970 | + | 0.988691i | \(0.547918\pi\) | |||||||
\(860\) | −1.69768e23 | −0.0193472 | ||||||||
\(861\) | 3.49617e24 | 0.394517 | ||||||||
\(862\) | −3.81940e24 | −0.426760 | ||||||||
\(863\) | 3.85035e24 | 0.425999 | 0.213000 | − | 0.977052i | \(-0.431677\pi\) | ||||
0.213000 | + | 0.977052i | \(0.431677\pi\) | |||||||
\(864\) | 2.56896e24 | 0.281444 | ||||||||
\(865\) | −4.63407e24 | −0.502720 | ||||||||
\(866\) | −7.41636e24 | −0.796688 | ||||||||
\(867\) | 1.37712e25 | 1.46490 | ||||||||
\(868\) | 9.23756e23 | 0.0973059 | ||||||||
\(869\) | −1.54441e23 | −0.0161100 | ||||||||
\(870\) | −9.66487e23 | −0.0998349 | ||||||||
\(871\) | 3.69075e24 | 0.377538 | ||||||||
\(872\) | −1.44936e25 | −1.46820 | ||||||||
\(873\) | 3.18915e23 | 0.0319929 | ||||||||
\(874\) | 4.11756e24 | 0.409065 | ||||||||
\(875\) | 4.45519e24 | 0.438327 | ||||||||
\(876\) | 1.01882e23 | 0.00992683 | ||||||||
\(877\) | −1.23091e25 | −1.18776 | −0.593879 | − | 0.804554i | \(-0.702404\pi\) | ||||
−0.593879 | + | 0.804554i | \(0.702404\pi\) | |||||||
\(878\) | −2.80387e24 | −0.267951 | ||||||||
\(879\) | 2.90806e25 | 2.75231 | ||||||||
\(880\) | 4.20747e22 | 0.00394383 | ||||||||
\(881\) | 6.75609e24 | 0.627191 | 0.313596 | − | 0.949557i | \(-0.398466\pi\) | ||||
0.313596 | + | 0.949557i | \(0.398466\pi\) | |||||||
\(882\) | 9.20368e24 | 0.846210 | ||||||||
\(883\) | −7.82807e24 | −0.712834 | −0.356417 | − | 0.934327i | \(-0.616002\pi\) | ||||
−0.356417 | + | 0.934327i | \(0.616002\pi\) | |||||||
\(884\) | 5.50679e23 | 0.0496655 | ||||||||
\(885\) | 4.04385e23 | 0.0361225 | ||||||||
\(886\) | −8.70486e24 | −0.770150 | ||||||||
\(887\) | 1.67016e25 | 1.46355 | 0.731776 | − | 0.681545i | \(-0.238692\pi\) | ||||
0.731776 | + | 0.681545i | \(0.238692\pi\) | |||||||
\(888\) | −4.14126e24 | −0.359437 | ||||||||
\(889\) | 1.22585e25 | 1.05383 | ||||||||
\(890\) | −6.55913e24 | −0.558511 | ||||||||
\(891\) | −1.56601e22 | −0.00132079 | ||||||||
\(892\) | 2.76297e24 | 0.230821 | ||||||||
\(893\) | 1.57926e25 | 1.30682 | ||||||||
\(894\) | 1.72294e25 | 1.41222 | ||||||||
\(895\) | −3.44795e24 | −0.279940 | ||||||||
\(896\) | −5.66454e24 | −0.455561 | ||||||||
\(897\) | 9.39854e24 | 0.748729 | ||||||||
\(898\) | 9.90046e24 | 0.781280 | ||||||||
\(899\) | −2.31919e24 | −0.181292 | ||||||||
\(900\) | 2.72515e24 | 0.211023 | ||||||||
\(901\) | −1.04939e24 | −0.0804962 | ||||||||
\(902\) | 6.08767e22 | 0.00462590 | ||||||||
\(903\) | 4.70231e24 | 0.353969 | ||||||||
\(904\) | −9.63876e24 | −0.718769 | ||||||||
\(905\) | −3.66126e24 | −0.270469 | ||||||||
\(906\) | 1.79676e25 | 1.31492 | ||||||||
\(907\) | −1.60753e25 | −1.16546 | −0.582729 | − | 0.812667i | \(-0.698015\pi\) | ||||
−0.582729 | + | 0.812667i | \(0.698015\pi\) | |||||||
\(908\) | 2.68237e24 | 0.192659 | ||||||||
\(909\) | 2.17831e25 | 1.54999 | ||||||||
\(910\) | −3.33783e24 | −0.235295 | ||||||||
\(911\) | 5.48262e24 | 0.382897 | 0.191449 | − | 0.981503i | \(-0.438681\pi\) | ||||
0.191449 | + | 0.981503i | \(0.438681\pi\) | |||||||
\(912\) | −1.97796e25 | −1.36855 | ||||||||
\(913\) | 1.04208e23 | 0.00714332 | ||||||||
\(914\) | −2.13285e25 | −1.44849 | ||||||||
\(915\) | 1.24325e25 | 0.836525 | ||||||||
\(916\) | −1.97756e24 | −0.131831 | ||||||||
\(917\) | 7.70847e24 | 0.509130 | ||||||||
\(918\) | 3.79477e24 | 0.248326 | ||||||||
\(919\) | 3.41215e24 | 0.221231 | 0.110616 | − | 0.993863i | \(-0.464718\pi\) | ||||
0.110616 | + | 0.993863i | \(0.464718\pi\) | |||||||
\(920\) | −2.58051e24 | −0.165771 | ||||||||
\(921\) | −3.23446e25 | −2.05871 | ||||||||
\(922\) | 1.81888e24 | 0.114707 | ||||||||
\(923\) | 6.63018e23 | 0.0414296 | ||||||||
\(924\) | 3.40043e22 | 0.00210534 | ||||||||
\(925\) | −2.98352e24 | −0.183031 | ||||||||
\(926\) | −1.74001e25 | −1.05769 | ||||||||
\(927\) | −7.11308e23 | −0.0428430 | ||||||||
\(928\) | −9.54134e23 | −0.0569445 | ||||||||
\(929\) | 1.88183e25 | 1.11287 | 0.556437 | − | 0.830890i | \(-0.312168\pi\) | ||||
0.556437 | + | 0.830890i | \(0.312168\pi\) | |||||||
\(930\) | 8.95704e24 | 0.524879 | ||||||||
\(931\) | 1.04757e25 | 0.608290 | ||||||||
\(932\) | 3.01465e24 | 0.173461 | ||||||||
\(933\) | −2.98718e25 | −1.70321 | ||||||||
\(934\) | −3.15822e24 | −0.178441 | ||||||||
\(935\) | −2.52434e22 | −0.00141335 | ||||||||
\(936\) | −3.27976e25 | −1.81969 | ||||||||
\(937\) | 4.65832e24 | 0.256120 | 0.128060 | − | 0.991766i | \(-0.459125\pi\) | ||||
0.128060 | + | 0.991766i | \(0.459125\pi\) | |||||||
\(938\) | 3.76246e24 | 0.204997 | ||||||||
\(939\) | 1.44729e24 | 0.0781446 | ||||||||
\(940\) | −1.32672e24 | −0.0709890 | ||||||||
\(941\) | 6.56604e24 | 0.348170 | 0.174085 | − | 0.984731i | \(-0.444303\pi\) | ||||
0.174085 | + | 0.984731i | \(0.444303\pi\) | |||||||
\(942\) | 1.15801e25 | 0.608525 | ||||||||
\(943\) | −3.14151e24 | −0.163602 | ||||||||
\(944\) | −9.82899e23 | −0.0507279 | ||||||||
\(945\) | 4.21263e24 | 0.215468 | ||||||||
\(946\) | 8.18785e22 | 0.00415045 | ||||||||
\(947\) | 2.19819e25 | 1.10431 | 0.552153 | − | 0.833742i | \(-0.313806\pi\) | ||||
0.552153 | + | 0.833742i | \(0.313806\pi\) | |||||||
\(948\) | −6.09933e24 | −0.303676 | ||||||||
\(949\) | −8.83371e23 | −0.0435894 | ||||||||
\(950\) | −1.69359e25 | −0.828244 | ||||||||
\(951\) | 4.11001e25 | 1.99209 | ||||||||
\(952\) | 4.18793e24 | 0.201180 | ||||||||
\(953\) | 3.19472e25 | 1.52105 | 0.760525 | − | 0.649308i | \(-0.224942\pi\) | ||||
0.760525 | + | 0.649308i | \(0.224942\pi\) | |||||||
\(954\) | 8.37793e24 | 0.395344 | ||||||||
\(955\) | 2.20207e24 | 0.102992 | ||||||||
\(956\) | −3.83711e23 | −0.0177874 | ||||||||
\(957\) | −8.53715e22 | −0.00392249 | ||||||||
\(958\) | −8.54426e24 | −0.389106 | ||||||||
\(959\) | −7.68536e24 | −0.346901 | ||||||||
\(960\) | 1.44194e25 | 0.645120 | ||||||||
\(961\) | −1.05671e24 | −0.0468607 | ||||||||
\(962\) | 4.81325e24 | 0.211568 | ||||||||
\(963\) | −7.09485e25 | −3.09115 | ||||||||
\(964\) | 8.20230e23 | 0.0354226 | ||||||||
\(965\) | −5.44901e24 | −0.233257 | ||||||||
\(966\) | 9.58116e24 | 0.406549 | ||||||||
\(967\) | −1.36577e25 | −0.574449 | −0.287224 | − | 0.957863i | \(-0.592733\pi\) | ||||
−0.287224 | + | 0.957863i | \(0.592733\pi\) | |||||||
\(968\) | −2.54596e25 | −1.06148 | ||||||||
\(969\) | 1.18671e25 | 0.490446 | ||||||||
\(970\) | 1.66501e23 | 0.00682115 | ||||||||
\(971\) | −1.64712e25 | −0.668903 | −0.334451 | − | 0.942413i | \(-0.608551\pi\) | ||||
−0.334451 | + | 0.942413i | \(0.608551\pi\) | |||||||
\(972\) | −4.14759e24 | −0.166968 | ||||||||
\(973\) | 2.36100e25 | 0.942188 | ||||||||
\(974\) | 4.28925e25 | 1.69680 | ||||||||
\(975\) | −3.86571e25 | −1.51597 | ||||||||
\(976\) | −3.02184e25 | −1.17476 | ||||||||
\(977\) | −9.34255e24 | −0.360049 | −0.180024 | − | 0.983662i | \(-0.557618\pi\) | ||||
−0.180024 | + | 0.983662i | \(0.557618\pi\) | |||||||
\(978\) | −4.26185e25 | −1.62824 | ||||||||
\(979\) | −5.79380e23 | −0.0219437 | ||||||||
\(980\) | −8.80048e23 | −0.0330434 | ||||||||
\(981\) | −5.84127e25 | −2.17431 | ||||||||
\(982\) | −4.23857e25 | −1.56413 | ||||||||
\(983\) | 1.14875e25 | 0.420262 | 0.210131 | − | 0.977673i | \(-0.432611\pi\) | ||||
0.210131 | + | 0.977673i | \(0.432611\pi\) | |||||||
\(984\) | 1.79355e25 | 0.650510 | ||||||||
\(985\) | 5.99978e24 | 0.215738 | ||||||||
\(986\) | −1.40941e24 | −0.0502438 | ||||||||
\(987\) | 3.67480e25 | 1.29879 | ||||||||
\(988\) | −5.00405e24 | −0.175343 | ||||||||
\(989\) | −4.22530e24 | −0.146788 | ||||||||
\(990\) | 2.01534e23 | 0.00694145 | ||||||||
\(991\) | −5.37183e25 | −1.83441 | −0.917204 | − | 0.398418i | \(-0.869559\pi\) | ||||
−0.917204 | + | 0.398418i | \(0.869559\pi\) | |||||||
\(992\) | 8.84256e24 | 0.299384 | ||||||||
\(993\) | −9.31942e25 | −3.12839 | ||||||||
\(994\) | 6.75901e23 | 0.0224957 | ||||||||
\(995\) | 7.00284e24 | 0.231088 | ||||||||
\(996\) | 4.11548e24 | 0.134653 | ||||||||
\(997\) | 3.11554e25 | 1.01071 | 0.505353 | − | 0.862913i | \(-0.331362\pi\) | ||||
0.505353 | + | 0.862913i | \(0.331362\pi\) | |||||||
\(998\) | 2.01605e25 | 0.648473 | ||||||||
\(999\) | −6.07473e24 | −0.193741 |
(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.1.6 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.18.a.b.1.6 | ✓ | 21 | 1.1 | even | 1 | trivial |