Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18.0234 | 0.398265 | 0.199133 | − | 0.979973i | \(-0.436188\pi\) | ||||
0.199133 | + | 0.979973i | \(0.436188\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −1723.16 | −0.841385 | ||||||||
\(5\) | −3879.65 | −0.555210 | −0.277605 | − | 0.960695i | \(-0.589541\pi\) | ||||
−0.277605 | + | 0.960695i | \(0.589541\pi\) | |||||||
\(6\) | −4379.69 | −0.229938 | ||||||||
\(7\) | 32120.2 | 0.722335 | 0.361167 | − | 0.932501i | \(-0.382378\pi\) | ||||
0.361167 | + | 0.932501i | \(0.382378\pi\) | |||||||
\(8\) | −67969.1 | −0.733359 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −69924.5 | −0.221121 | ||||||||
\(11\) | −362420. | −0.678505 | −0.339252 | − | 0.940695i | \(-0.610174\pi\) | ||||
−0.339252 | + | 0.940695i | \(0.610174\pi\) | |||||||
\(12\) | 418727. | 0.485774 | ||||||||
\(13\) | −286043. | −0.213670 | −0.106835 | − | 0.994277i | \(-0.534072\pi\) | ||||
−0.106835 | + | 0.994277i | \(0.534072\pi\) | |||||||
\(14\) | 578915. | 0.287681 | ||||||||
\(15\) | 942754. | 0.320551 | ||||||||
\(16\) | 2.30399e6 | 0.549314 | ||||||||
\(17\) | 9.02842e6 | 1.54221 | 0.771104 | − | 0.636710i | \(-0.219705\pi\) | ||||
0.771104 | + | 0.636710i | \(0.219705\pi\) | |||||||
\(18\) | 1.06426e6 | 0.132755 | ||||||||
\(19\) | −2.13529e7 | −1.97839 | −0.989194 | − | 0.146615i | \(-0.953162\pi\) | ||||
−0.989194 | + | 0.146615i | \(0.953162\pi\) | |||||||
\(20\) | 6.68524e6 | 0.467145 | ||||||||
\(21\) | −7.80520e6 | −0.417040 | ||||||||
\(22\) | −6.53205e6 | −0.270225 | ||||||||
\(23\) | −5.38940e7 | −1.74597 | −0.872986 | − | 0.487745i | \(-0.837820\pi\) | ||||
−0.872986 | + | 0.487745i | \(0.837820\pi\) | |||||||
\(24\) | 1.65165e7 | 0.423405 | ||||||||
\(25\) | −3.37765e7 | −0.691742 | ||||||||
\(26\) | −5.15548e6 | −0.0850972 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −5.53480e7 | −0.607761 | ||||||||
\(29\) | 1.58491e8 | 1.43488 | 0.717440 | − | 0.696621i | \(-0.245314\pi\) | ||||
0.717440 | + | 0.696621i | \(0.245314\pi\) | |||||||
\(30\) | 1.69917e7 | 0.127664 | ||||||||
\(31\) | −1.44016e8 | −0.903483 | −0.451742 | − | 0.892149i | \(-0.649197\pi\) | ||||
−0.451742 | + | 0.892149i | \(0.649197\pi\) | |||||||
\(32\) | 1.80727e8 | 0.952132 | ||||||||
\(33\) | 8.80681e7 | 0.391735 | ||||||||
\(34\) | 1.62723e8 | 0.614207 | ||||||||
\(35\) | −1.24615e8 | −0.401047 | ||||||||
\(36\) | −1.01751e8 | −0.280462 | ||||||||
\(37\) | −1.68394e8 | −0.399224 | −0.199612 | − | 0.979875i | \(-0.563968\pi\) | ||||
−0.199612 | + | 0.979875i | \(0.563968\pi\) | |||||||
\(38\) | −3.84852e8 | −0.787923 | ||||||||
\(39\) | 6.95085e7 | 0.123362 | ||||||||
\(40\) | 2.63696e8 | 0.407168 | ||||||||
\(41\) | −1.21824e9 | −1.64219 | −0.821093 | − | 0.570795i | \(-0.806635\pi\) | ||||
−0.821093 | + | 0.570795i | \(0.806635\pi\) | |||||||
\(42\) | −1.40676e8 | −0.166092 | ||||||||
\(43\) | −6.48935e8 | −0.673170 | −0.336585 | − | 0.941653i | \(-0.609272\pi\) | ||||
−0.336585 | + | 0.941653i | \(0.609272\pi\) | |||||||
\(44\) | 6.24507e8 | 0.570884 | ||||||||
\(45\) | −2.29089e8 | −0.185070 | ||||||||
\(46\) | −9.71354e8 | −0.695360 | ||||||||
\(47\) | 1.87600e8 | 0.119315 | 0.0596576 | − | 0.998219i | \(-0.480999\pi\) | ||||
0.0596576 | + | 0.998219i | \(0.480999\pi\) | |||||||
\(48\) | −5.59869e8 | −0.317146 | ||||||||
\(49\) | −9.45622e8 | −0.478233 | ||||||||
\(50\) | −6.08767e8 | −0.275497 | ||||||||
\(51\) | −2.19391e9 | −0.890394 | ||||||||
\(52\) | 4.92897e8 | 0.179779 | ||||||||
\(53\) | −2.62856e9 | −0.863376 | −0.431688 | − | 0.902023i | \(-0.642082\pi\) | ||||
−0.431688 | + | 0.902023i | \(0.642082\pi\) | |||||||
\(54\) | −2.58616e8 | −0.0766462 | ||||||||
\(55\) | 1.40606e9 | 0.376712 | ||||||||
\(56\) | −2.18318e9 | −0.529731 | ||||||||
\(57\) | 5.18875e9 | 1.14222 | ||||||||
\(58\) | 2.85655e9 | 0.571462 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | −1.62451e9 | −0.269706 | ||||||||
\(61\) | −3.26106e9 | −0.494361 | −0.247181 | − | 0.968969i | \(-0.579504\pi\) | ||||
−0.247181 | + | 0.968969i | \(0.579504\pi\) | |||||||
\(62\) | −2.59565e9 | −0.359826 | ||||||||
\(63\) | 1.89666e9 | 0.240778 | ||||||||
\(64\) | −1.46126e9 | −0.170113 | ||||||||
\(65\) | 1.10975e9 | 0.118632 | ||||||||
\(66\) | 1.58729e9 | 0.156014 | ||||||||
\(67\) | 1.11768e10 | 1.01136 | 0.505681 | − | 0.862721i | \(-0.331241\pi\) | ||||
0.505681 | + | 0.862721i | \(0.331241\pi\) | |||||||
\(68\) | −1.55574e10 | −1.29759 | ||||||||
\(69\) | 1.30962e10 | 1.00804 | ||||||||
\(70\) | −2.24599e9 | −0.159723 | ||||||||
\(71\) | −1.81403e10 | −1.19323 | −0.596614 | − | 0.802528i | \(-0.703488\pi\) | ||||
−0.596614 | + | 0.802528i | \(0.703488\pi\) | |||||||
\(72\) | −4.01351e9 | −0.244453 | ||||||||
\(73\) | −4.66168e9 | −0.263188 | −0.131594 | − | 0.991304i | \(-0.542010\pi\) | ||||
−0.131594 | + | 0.991304i | \(0.542010\pi\) | |||||||
\(74\) | −3.03503e9 | −0.158997 | ||||||||
\(75\) | 8.20768e9 | 0.399377 | ||||||||
\(76\) | 3.67943e10 | 1.66459 | ||||||||
\(77\) | −1.16410e10 | −0.490107 | ||||||||
\(78\) | 1.25278e9 | 0.0491309 | ||||||||
\(79\) | 3.85674e10 | 1.41017 | 0.705085 | − | 0.709122i | \(-0.250909\pi\) | ||||
0.705085 | + | 0.709122i | \(0.250909\pi\) | |||||||
\(80\) | −8.93866e9 | −0.304984 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −2.19569e10 | −0.654025 | ||||||||
\(83\) | 4.48401e10 | 1.24950 | 0.624751 | − | 0.780824i | \(-0.285201\pi\) | ||||
0.624751 | + | 0.780824i | \(0.285201\pi\) | |||||||
\(84\) | 1.34496e10 | 0.350891 | ||||||||
\(85\) | −3.50271e10 | −0.856249 | ||||||||
\(86\) | −1.16960e10 | −0.268100 | ||||||||
\(87\) | −3.85133e10 | −0.828428 | ||||||||
\(88\) | 2.46334e10 | 0.497588 | ||||||||
\(89\) | 8.91551e10 | 1.69239 | 0.846197 | − | 0.532871i | \(-0.178887\pi\) | ||||
0.846197 | + | 0.532871i | \(0.178887\pi\) | |||||||
\(90\) | −4.12897e9 | −0.0737069 | ||||||||
\(91\) | −9.18775e9 | −0.154341 | ||||||||
\(92\) | 9.28678e10 | 1.46904 | ||||||||
\(93\) | 3.49958e10 | 0.521626 | ||||||||
\(94\) | 3.38120e9 | 0.0475190 | ||||||||
\(95\) | 8.28416e10 | 1.09842 | ||||||||
\(96\) | −4.39165e10 | −0.549713 | ||||||||
\(97\) | −1.14808e11 | −1.35746 | −0.678731 | − | 0.734387i | \(-0.737470\pi\) | ||||
−0.678731 | + | 0.734387i | \(0.737470\pi\) | |||||||
\(98\) | −1.70434e10 | −0.190463 | ||||||||
\(99\) | −2.14006e10 | −0.226168 | ||||||||
\(100\) | 5.82021e10 | 0.582021 | ||||||||
\(101\) | −1.27258e11 | −1.20481 | −0.602404 | − | 0.798192i | \(-0.705790\pi\) | ||||
−0.602404 | + | 0.798192i | \(0.705790\pi\) | |||||||
\(102\) | −3.95417e10 | −0.354613 | ||||||||
\(103\) | 1.39054e11 | 1.18189 | 0.590945 | − | 0.806712i | \(-0.298755\pi\) | ||||
0.590945 | + | 0.806712i | \(0.298755\pi\) | |||||||
\(104\) | 1.94421e10 | 0.156697 | ||||||||
\(105\) | 3.02814e10 | 0.231545 | ||||||||
\(106\) | −4.73756e10 | −0.343853 | ||||||||
\(107\) | −2.97788e10 | −0.205257 | −0.102628 | − | 0.994720i | \(-0.532725\pi\) | ||||
−0.102628 | + | 0.994720i | \(0.532725\pi\) | |||||||
\(108\) | 2.47254e10 | 0.161925 | ||||||||
\(109\) | 1.33959e11 | 0.833924 | 0.416962 | − | 0.908924i | \(-0.363095\pi\) | ||||
0.416962 | + | 0.908924i | \(0.363095\pi\) | |||||||
\(110\) | 2.53421e10 | 0.150031 | ||||||||
\(111\) | 4.09197e10 | 0.230492 | ||||||||
\(112\) | 7.40044e10 | 0.396788 | ||||||||
\(113\) | −1.64153e11 | −0.838140 | −0.419070 | − | 0.907954i | \(-0.637644\pi\) | ||||
−0.419070 | + | 0.907954i | \(0.637644\pi\) | |||||||
\(114\) | 9.35189e10 | 0.454907 | ||||||||
\(115\) | 2.09090e11 | 0.969381 | ||||||||
\(116\) | −2.73105e11 | −1.20729 | ||||||||
\(117\) | −1.68906e10 | −0.0712233 | ||||||||
\(118\) | −1.28854e10 | −0.0518497 | ||||||||
\(119\) | 2.89994e11 | 1.11399 | ||||||||
\(120\) | −6.40782e10 | −0.235079 | ||||||||
\(121\) | −1.53963e11 | −0.539632 | ||||||||
\(122\) | −5.87754e10 | −0.196887 | ||||||||
\(123\) | 2.96033e11 | 0.948116 | ||||||||
\(124\) | 2.48161e11 | 0.760177 | ||||||||
\(125\) | 3.20477e11 | 0.939272 | ||||||||
\(126\) | 3.41844e10 | 0.0958935 | ||||||||
\(127\) | 2.89349e11 | 0.777143 | 0.388571 | − | 0.921419i | \(-0.372969\pi\) | ||||
0.388571 | + | 0.921419i | \(0.372969\pi\) | |||||||
\(128\) | −3.96465e11 | −1.01988 | ||||||||
\(129\) | 1.57691e11 | 0.388655 | ||||||||
\(130\) | 2.00014e10 | 0.0472468 | ||||||||
\(131\) | 5.85181e11 | 1.32525 | 0.662625 | − | 0.748951i | \(-0.269442\pi\) | ||||
0.662625 | + | 0.748951i | \(0.269442\pi\) | |||||||
\(132\) | −1.51755e11 | −0.329600 | ||||||||
\(133\) | −6.85857e11 | −1.42906 | ||||||||
\(134\) | 2.01444e11 | 0.402790 | ||||||||
\(135\) | 5.56687e10 | 0.106850 | ||||||||
\(136\) | −6.13654e11 | −1.13099 | ||||||||
\(137\) | 2.05345e11 | 0.363514 | 0.181757 | − | 0.983344i | \(-0.441822\pi\) | ||||
0.181757 | + | 0.983344i | \(0.441822\pi\) | |||||||
\(138\) | 2.36039e11 | 0.401466 | ||||||||
\(139\) | 1.85933e11 | 0.303930 | 0.151965 | − | 0.988386i | \(-0.451440\pi\) | ||||
0.151965 | + | 0.988386i | \(0.451440\pi\) | |||||||
\(140\) | 2.14731e11 | 0.337435 | ||||||||
\(141\) | −4.55869e10 | −0.0688866 | ||||||||
\(142\) | −3.26950e11 | −0.475221 | ||||||||
\(143\) | 1.03668e11 | 0.144976 | ||||||||
\(144\) | 1.36048e11 | 0.183105 | ||||||||
\(145\) | −6.14889e11 | −0.796659 | ||||||||
\(146\) | −8.40194e10 | −0.104819 | ||||||||
\(147\) | 2.29786e11 | 0.276108 | ||||||||
\(148\) | 2.90169e11 | 0.335901 | ||||||||
\(149\) | 1.54005e11 | 0.171794 | 0.0858972 | − | 0.996304i | \(-0.472624\pi\) | ||||
0.0858972 | + | 0.996304i | \(0.472624\pi\) | |||||||
\(150\) | 1.47930e11 | 0.159058 | ||||||||
\(151\) | 4.71655e11 | 0.488935 | 0.244467 | − | 0.969658i | \(-0.421387\pi\) | ||||
0.244467 | + | 0.969658i | \(0.421387\pi\) | |||||||
\(152\) | 1.45134e12 | 1.45087 | ||||||||
\(153\) | 5.33119e11 | 0.514069 | ||||||||
\(154\) | −2.09811e11 | −0.195193 | ||||||||
\(155\) | 5.58730e11 | 0.501623 | ||||||||
\(156\) | −1.19774e11 | −0.103795 | ||||||||
\(157\) | −2.47986e11 | −0.207481 | −0.103740 | − | 0.994604i | \(-0.533081\pi\) | ||||
−0.103740 | + | 0.994604i | \(0.533081\pi\) | |||||||
\(158\) | 6.95117e11 | 0.561622 | ||||||||
\(159\) | 6.38739e11 | 0.498470 | ||||||||
\(160\) | −7.01155e11 | −0.528633 | ||||||||
\(161\) | −1.73108e12 | −1.26118 | ||||||||
\(162\) | 6.28438e10 | 0.0442517 | ||||||||
\(163\) | 6.84742e11 | 0.466117 | 0.233059 | − | 0.972463i | \(-0.425127\pi\) | ||||
0.233059 | + | 0.972463i | \(0.425127\pi\) | |||||||
\(164\) | 2.09922e12 | 1.38171 | ||||||||
\(165\) | −3.41673e11 | −0.217495 | ||||||||
\(166\) | 8.08171e11 | 0.497633 | ||||||||
\(167\) | 1.79932e12 | 1.07193 | 0.535967 | − | 0.844239i | \(-0.319947\pi\) | ||||
0.535967 | + | 0.844239i | \(0.319947\pi\) | |||||||
\(168\) | 5.30513e11 | 0.305840 | ||||||||
\(169\) | −1.71034e12 | −0.954345 | ||||||||
\(170\) | −6.31308e11 | −0.341014 | ||||||||
\(171\) | −1.26087e12 | −0.659462 | ||||||||
\(172\) | 1.11822e12 | 0.566395 | ||||||||
\(173\) | 2.05890e11 | 0.101014 | 0.0505070 | − | 0.998724i | \(-0.483916\pi\) | ||||
0.0505070 | + | 0.998724i | \(0.483916\pi\) | |||||||
\(174\) | −6.94141e11 | −0.329934 | ||||||||
\(175\) | −1.08491e12 | −0.499669 | ||||||||
\(176\) | −8.35012e11 | −0.372712 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.60688e12 | 0.674021 | ||||||||
\(179\) | −3.45127e12 | −1.40374 | −0.701872 | − | 0.712304i | \(-0.747652\pi\) | ||||
−0.701872 | + | 0.712304i | \(0.747652\pi\) | |||||||
\(180\) | 3.94757e11 | 0.155715 | ||||||||
\(181\) | −3.37062e12 | −1.28967 | −0.644834 | − | 0.764323i | \(-0.723073\pi\) | ||||
−0.644834 | + | 0.764323i | \(0.723073\pi\) | |||||||
\(182\) | −1.65595e11 | −0.0614687 | ||||||||
\(183\) | 7.92437e11 | 0.285420 | ||||||||
\(184\) | 3.66313e12 | 1.28043 | ||||||||
\(185\) | 6.53308e11 | 0.221653 | ||||||||
\(186\) | 6.30744e11 | 0.207746 | ||||||||
\(187\) | −3.27208e12 | −1.04639 | ||||||||
\(188\) | −3.23265e11 | −0.100390 | ||||||||
\(189\) | −4.60889e11 | −0.139013 | ||||||||
\(190\) | 1.49309e12 | 0.437462 | ||||||||
\(191\) | 2.38809e12 | 0.679778 | 0.339889 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339889 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(192\) | 3.55085e11 | 0.0982146 | ||||||||
\(193\) | 5.57651e12 | 1.49899 | 0.749493 | − | 0.662012i | \(-0.230297\pi\) | ||||
0.749493 | + | 0.662012i | \(0.230297\pi\) | |||||||
\(194\) | −2.06923e12 | −0.540629 | ||||||||
\(195\) | −2.69668e11 | −0.0684920 | ||||||||
\(196\) | 1.62946e12 | 0.402378 | ||||||||
\(197\) | −8.64153e11 | −0.207504 | −0.103752 | − | 0.994603i | \(-0.533085\pi\) | ||||
−0.103752 | + | 0.994603i | \(0.533085\pi\) | |||||||
\(198\) | −3.85711e11 | −0.0900749 | ||||||||
\(199\) | 3.45541e11 | 0.0784889 | 0.0392445 | − | 0.999230i | \(-0.487505\pi\) | ||||
0.0392445 | + | 0.999230i | \(0.487505\pi\) | |||||||
\(200\) | 2.29576e12 | 0.507295 | ||||||||
\(201\) | −2.71596e12 | −0.583910 | ||||||||
\(202\) | −2.29363e12 | −0.479833 | ||||||||
\(203\) | 5.09075e12 | 1.03646 | ||||||||
\(204\) | 3.78044e12 | 0.749164 | ||||||||
\(205\) | 4.72635e12 | 0.911758 | ||||||||
\(206\) | 2.50622e12 | 0.470706 | ||||||||
\(207\) | −3.18239e12 | −0.581991 | ||||||||
\(208\) | −6.59040e11 | −0.117372 | ||||||||
\(209\) | 7.73871e12 | 1.34234 | ||||||||
\(210\) | 5.45775e11 | 0.0922162 | ||||||||
\(211\) | 6.76550e12 | 1.11364 | 0.556822 | − | 0.830632i | \(-0.312021\pi\) | ||||
0.556822 | + | 0.830632i | \(0.312021\pi\) | |||||||
\(212\) | 4.52941e12 | 0.726432 | ||||||||
\(213\) | 4.40809e12 | 0.688911 | ||||||||
\(214\) | −5.36717e11 | −0.0817465 | ||||||||
\(215\) | 2.51764e12 | 0.373751 | ||||||||
\(216\) | 9.75283e11 | 0.141135 | ||||||||
\(217\) | −4.62580e12 | −0.652617 | ||||||||
\(218\) | 2.41440e12 | 0.332123 | ||||||||
\(219\) | 1.13279e12 | 0.151952 | ||||||||
\(220\) | −2.42287e12 | −0.316960 | ||||||||
\(221\) | −2.58252e12 | −0.329523 | ||||||||
\(222\) | 7.37512e11 | 0.0917968 | ||||||||
\(223\) | 3.60649e12 | 0.437933 | 0.218967 | − | 0.975732i | \(-0.429731\pi\) | ||||
0.218967 | + | 0.975732i | \(0.429731\pi\) | |||||||
\(224\) | 5.80496e12 | 0.687758 | ||||||||
\(225\) | −1.99447e12 | −0.230581 | ||||||||
\(226\) | −2.95859e12 | −0.333802 | ||||||||
\(227\) | −2.38826e12 | −0.262990 | −0.131495 | − | 0.991317i | \(-0.541978\pi\) | ||||
−0.131495 | + | 0.991317i | \(0.541978\pi\) | |||||||
\(228\) | −8.94102e12 | −0.961049 | ||||||||
\(229\) | 5.83285e12 | 0.612048 | 0.306024 | − | 0.952024i | \(-0.401001\pi\) | ||||
0.306024 | + | 0.952024i | \(0.401001\pi\) | |||||||
\(230\) | 3.76851e12 | 0.386071 | ||||||||
\(231\) | 2.82876e12 | 0.282964 | ||||||||
\(232\) | −1.07725e13 | −1.05228 | ||||||||
\(233\) | −6.07236e12 | −0.579295 | −0.289648 | − | 0.957133i | \(-0.593538\pi\) | ||||
−0.289648 | + | 0.957133i | \(0.593538\pi\) | |||||||
\(234\) | −3.04426e11 | −0.0283657 | ||||||||
\(235\) | −7.27823e11 | −0.0662449 | ||||||||
\(236\) | 1.23193e12 | 0.109539 | ||||||||
\(237\) | −9.37189e12 | −0.814163 | ||||||||
\(238\) | 5.22669e12 | 0.443663 | ||||||||
\(239\) | −5.24155e12 | −0.434782 | −0.217391 | − | 0.976085i | \(-0.569755\pi\) | ||||
−0.217391 | + | 0.976085i | \(0.569755\pi\) | |||||||
\(240\) | 2.17209e12 | 0.176083 | ||||||||
\(241\) | 1.50319e13 | 1.19103 | 0.595513 | − | 0.803346i | \(-0.296949\pi\) | ||||
0.595513 | + | 0.803346i | \(0.296949\pi\) | |||||||
\(242\) | −2.77494e12 | −0.214916 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 5.61931e12 | 0.415948 | ||||||||
\(245\) | 3.66868e12 | 0.265520 | ||||||||
\(246\) | 5.33552e12 | 0.377602 | ||||||||
\(247\) | 6.10784e12 | 0.422722 | ||||||||
\(248\) | 9.78861e12 | 0.662578 | ||||||||
\(249\) | −1.08961e13 | −0.721400 | ||||||||
\(250\) | 5.77609e12 | 0.374079 | ||||||||
\(251\) | 2.00908e13 | 1.27289 | 0.636446 | − | 0.771321i | \(-0.280404\pi\) | ||||
0.636446 | + | 0.771321i | \(0.280404\pi\) | |||||||
\(252\) | −3.26825e12 | −0.202587 | ||||||||
\(253\) | 1.95323e13 | 1.18465 | ||||||||
\(254\) | 5.21505e12 | 0.309509 | ||||||||
\(255\) | 8.51158e12 | 0.494356 | ||||||||
\(256\) | −4.15300e12 | −0.236071 | ||||||||
\(257\) | −1.74585e13 | −0.971349 | −0.485674 | − | 0.874140i | \(-0.661426\pi\) | ||||
−0.485674 | + | 0.874140i | \(0.661426\pi\) | |||||||
\(258\) | 2.84214e12 | 0.154788 | ||||||||
\(259\) | −5.40883e12 | −0.288373 | ||||||||
\(260\) | −1.91227e12 | −0.0998148 | ||||||||
\(261\) | 9.35873e12 | 0.478293 | ||||||||
\(262\) | 1.05470e13 | 0.527801 | ||||||||
\(263\) | −1.19269e13 | −0.584482 | −0.292241 | − | 0.956345i | \(-0.594401\pi\) | ||||
−0.292241 | + | 0.956345i | \(0.594401\pi\) | |||||||
\(264\) | −5.98592e12 | −0.287282 | ||||||||
\(265\) | 1.01979e13 | 0.479355 | ||||||||
\(266\) | −1.23615e13 | −0.569144 | ||||||||
\(267\) | −2.16647e13 | −0.977104 | ||||||||
\(268\) | −1.92594e13 | −0.850944 | ||||||||
\(269\) | −1.82284e13 | −0.789063 | −0.394531 | − | 0.918882i | \(-0.629093\pi\) | ||||
−0.394531 | + | 0.918882i | \(0.629093\pi\) | |||||||
\(270\) | 1.00334e12 | 0.0425547 | ||||||||
\(271\) | 5.45181e12 | 0.226574 | 0.113287 | − | 0.993562i | \(-0.463862\pi\) | ||||
0.113287 | + | 0.993562i | \(0.463862\pi\) | |||||||
\(272\) | 2.08014e13 | 0.847155 | ||||||||
\(273\) | 2.23262e12 | 0.0891089 | ||||||||
\(274\) | 3.70102e12 | 0.144775 | ||||||||
\(275\) | 1.22413e13 | 0.469350 | ||||||||
\(276\) | −2.25669e13 | −0.848148 | ||||||||
\(277\) | −1.60314e13 | −0.590652 | −0.295326 | − | 0.955397i | \(-0.595428\pi\) | ||||
−0.295326 | + | 0.955397i | \(0.595428\pi\) | |||||||
\(278\) | 3.35114e12 | 0.121045 | ||||||||
\(279\) | −8.50397e12 | −0.301161 | ||||||||
\(280\) | 8.46996e12 | 0.294112 | ||||||||
\(281\) | 3.31008e13 | 1.12708 | 0.563538 | − | 0.826090i | \(-0.309440\pi\) | ||||
0.563538 | + | 0.826090i | \(0.309440\pi\) | |||||||
\(282\) | −8.21632e11 | −0.0274351 | ||||||||
\(283\) | 4.22069e13 | 1.38216 | 0.691079 | − | 0.722779i | \(-0.257136\pi\) | ||||
0.691079 | + | 0.722779i | \(0.257136\pi\) | |||||||
\(284\) | 3.12586e13 | 1.00396 | ||||||||
\(285\) | −2.01305e13 | −0.634173 | ||||||||
\(286\) | 1.86845e12 | 0.0577389 | ||||||||
\(287\) | −3.91301e13 | −1.18621 | ||||||||
\(288\) | 1.06717e13 | 0.317377 | ||||||||
\(289\) | 4.72405e13 | 1.37840 | ||||||||
\(290\) | −1.10824e13 | −0.317282 | ||||||||
\(291\) | 2.78983e13 | 0.783730 | ||||||||
\(292\) | 8.03280e12 | 0.221443 | ||||||||
\(293\) | 2.36378e13 | 0.639492 | 0.319746 | − | 0.947503i | \(-0.396402\pi\) | ||||
0.319746 | + | 0.947503i | \(0.396402\pi\) | |||||||
\(294\) | 4.14153e12 | 0.109964 | ||||||||
\(295\) | 2.77365e12 | 0.0722822 | ||||||||
\(296\) | 1.14456e13 | 0.292774 | ||||||||
\(297\) | 5.20034e12 | 0.130578 | ||||||||
\(298\) | 2.77569e12 | 0.0684197 | ||||||||
\(299\) | 1.54160e13 | 0.373062 | ||||||||
\(300\) | −1.41431e13 | −0.336030 | ||||||||
\(301\) | −2.08439e13 | −0.486254 | ||||||||
\(302\) | 8.50083e12 | 0.194726 | ||||||||
\(303\) | 3.09237e13 | 0.695596 | ||||||||
\(304\) | −4.91967e13 | −1.08675 | ||||||||
\(305\) | 1.26518e13 | 0.274474 | ||||||||
\(306\) | 9.60863e12 | 0.204736 | ||||||||
\(307\) | −7.37980e12 | −0.154449 | −0.0772243 | − | 0.997014i | \(-0.524606\pi\) | ||||
−0.0772243 | + | 0.997014i | \(0.524606\pi\) | |||||||
\(308\) | 2.00593e13 | 0.412369 | ||||||||
\(309\) | −3.37900e13 | −0.682365 | ||||||||
\(310\) | 1.00702e13 | 0.199779 | ||||||||
\(311\) | −2.70914e13 | −0.528019 | −0.264010 | − | 0.964520i | \(-0.585045\pi\) | ||||
−0.264010 | + | 0.964520i | \(0.585045\pi\) | |||||||
\(312\) | −4.72443e12 | −0.0904689 | ||||||||
\(313\) | −6.62339e13 | −1.24620 | −0.623098 | − | 0.782144i | \(-0.714126\pi\) | ||||
−0.623098 | + | 0.782144i | \(0.714126\pi\) | |||||||
\(314\) | −4.46955e12 | −0.0826324 | ||||||||
\(315\) | −7.35838e12 | −0.133682 | ||||||||
\(316\) | −6.64577e13 | −1.18650 | ||||||||
\(317\) | −2.57294e13 | −0.451445 | −0.225722 | − | 0.974192i | \(-0.572474\pi\) | ||||
−0.225722 | + | 0.974192i | \(0.572474\pi\) | |||||||
\(318\) | 1.15123e13 | 0.198523 | ||||||||
\(319\) | −5.74403e13 | −0.973572 | ||||||||
\(320\) | 5.66916e12 | 0.0944483 | ||||||||
\(321\) | 7.23626e12 | 0.118505 | ||||||||
\(322\) | −3.12001e13 | −0.502283 | ||||||||
\(323\) | −1.92783e14 | −3.05108 | ||||||||
\(324\) | −6.00827e12 | −0.0934872 | ||||||||
\(325\) | 9.66153e12 | 0.147804 | ||||||||
\(326\) | 1.23414e13 | 0.185638 | ||||||||
\(327\) | −3.25521e13 | −0.481466 | ||||||||
\(328\) | 8.28028e13 | 1.20431 | ||||||||
\(329\) | 6.02575e12 | 0.0861854 | ||||||||
\(330\) | −6.15812e12 | −0.0866207 | ||||||||
\(331\) | −5.48873e13 | −0.759308 | −0.379654 | − | 0.925129i | \(-0.623957\pi\) | ||||
−0.379654 | + | 0.925129i | \(0.623957\pi\) | |||||||
\(332\) | −7.72664e13 | −1.05131 | ||||||||
\(333\) | −9.94348e12 | −0.133075 | ||||||||
\(334\) | 3.24299e13 | 0.426914 | ||||||||
\(335\) | −4.33621e13 | −0.561518 | ||||||||
\(336\) | −1.79831e13 | −0.229086 | ||||||||
\(337\) | −9.79581e13 | −1.22765 | −0.613827 | − | 0.789441i | \(-0.710371\pi\) | ||||
−0.613827 | + | 0.789441i | \(0.710371\pi\) | |||||||
\(338\) | −3.08262e13 | −0.380082 | ||||||||
\(339\) | 3.98891e13 | 0.483901 | ||||||||
\(340\) | 6.03572e13 | 0.720435 | ||||||||
\(341\) | 5.21942e13 | 0.613017 | ||||||||
\(342\) | −2.27251e13 | −0.262641 | ||||||||
\(343\) | −9.38856e13 | −1.06778 | ||||||||
\(344\) | 4.41076e13 | 0.493676 | ||||||||
\(345\) | −5.08088e13 | −0.559673 | ||||||||
\(346\) | 3.71084e12 | 0.0402303 | ||||||||
\(347\) | 7.13794e12 | 0.0761659 | 0.0380829 | − | 0.999275i | \(-0.487875\pi\) | ||||
0.0380829 | + | 0.999275i | \(0.487875\pi\) | |||||||
\(348\) | 6.63644e13 | 0.697027 | ||||||||
\(349\) | −1.62450e14 | −1.67950 | −0.839748 | − | 0.542976i | \(-0.817298\pi\) | ||||
−0.839748 | + | 0.542976i | \(0.817298\pi\) | |||||||
\(350\) | −1.95537e13 | −0.199001 | ||||||||
\(351\) | 4.10441e12 | 0.0411208 | ||||||||
\(352\) | −6.54990e13 | −0.646026 | ||||||||
\(353\) | 1.51005e14 | 1.46632 | 0.733162 | − | 0.680054i | \(-0.238044\pi\) | ||||
0.733162 | + | 0.680054i | \(0.238044\pi\) | |||||||
\(354\) | 3.13115e12 | 0.0299354 | ||||||||
\(355\) | 7.03780e13 | 0.662492 | ||||||||
\(356\) | −1.53628e14 | −1.42395 | ||||||||
\(357\) | −7.04686e13 | −0.643162 | ||||||||
\(358\) | −6.22037e13 | −0.559062 | ||||||||
\(359\) | 2.50228e13 | 0.221471 | 0.110736 | − | 0.993850i | \(-0.464679\pi\) | ||||
0.110736 | + | 0.993850i | \(0.464679\pi\) | |||||||
\(360\) | 1.55710e13 | 0.135723 | ||||||||
\(361\) | 3.39455e14 | 2.91402 | ||||||||
\(362\) | −6.07501e13 | −0.513630 | ||||||||
\(363\) | 3.74131e13 | 0.311556 | ||||||||
\(364\) | 1.58319e13 | 0.129860 | ||||||||
\(365\) | 1.80857e13 | 0.146125 | ||||||||
\(366\) | 1.42824e13 | 0.113673 | ||||||||
\(367\) | 1.47297e14 | 1.15487 | 0.577433 | − | 0.816438i | \(-0.304055\pi\) | ||||
0.577433 | + | 0.816438i | \(0.304055\pi\) | |||||||
\(368\) | −1.24171e14 | −0.959086 | ||||||||
\(369\) | −7.19359e13 | −0.547395 | ||||||||
\(370\) | 1.17748e13 | 0.0882766 | ||||||||
\(371\) | −8.44296e13 | −0.623646 | ||||||||
\(372\) | −6.03032e13 | −0.438888 | ||||||||
\(373\) | −7.52002e13 | −0.539288 | −0.269644 | − | 0.962960i | \(-0.586906\pi\) | ||||
−0.269644 | + | 0.962960i | \(0.586906\pi\) | |||||||
\(374\) | −5.89741e13 | −0.416743 | ||||||||
\(375\) | −7.78758e13 | −0.542289 | ||||||||
\(376\) | −1.27510e13 | −0.0875009 | ||||||||
\(377\) | −4.53352e13 | −0.306590 | ||||||||
\(378\) | −8.30680e12 | −0.0553642 | ||||||||
\(379\) | 1.75453e14 | 1.15251 | 0.576257 | − | 0.817269i | \(-0.304513\pi\) | ||||
0.576257 | + | 0.817269i | \(0.304513\pi\) | |||||||
\(380\) | −1.42749e14 | −0.924194 | ||||||||
\(381\) | −7.03117e13 | −0.448684 | ||||||||
\(382\) | 4.30416e13 | 0.270732 | ||||||||
\(383\) | −2.55697e14 | −1.58537 | −0.792687 | − | 0.609629i | \(-0.791319\pi\) | ||||
−0.792687 | + | 0.609629i | \(0.791319\pi\) | |||||||
\(384\) | 9.63409e13 | 0.588829 | ||||||||
\(385\) | 4.51630e13 | 0.272112 | ||||||||
\(386\) | 1.00508e14 | 0.596994 | ||||||||
\(387\) | −3.83190e13 | −0.224390 | ||||||||
\(388\) | 1.97832e14 | 1.14215 | ||||||||
\(389\) | 2.60045e14 | 1.48022 | 0.740108 | − | 0.672488i | \(-0.234774\pi\) | ||||
0.740108 | + | 0.672488i | \(0.234774\pi\) | |||||||
\(390\) | −4.86035e12 | −0.0272780 | ||||||||
\(391\) | −4.86578e14 | −2.69265 | ||||||||
\(392\) | 6.42731e13 | 0.350716 | ||||||||
\(393\) | −1.42199e14 | −0.765134 | ||||||||
\(394\) | −1.55750e13 | −0.0826415 | ||||||||
\(395\) | −1.49628e14 | −0.782941 | ||||||||
\(396\) | 3.68765e13 | 0.190295 | ||||||||
\(397\) | −1.25874e14 | −0.640602 | −0.320301 | − | 0.947316i | \(-0.603784\pi\) | ||||
−0.320301 | + | 0.947316i | \(0.603784\pi\) | |||||||
\(398\) | 6.22784e12 | 0.0312594 | ||||||||
\(399\) | 1.66663e14 | 0.825067 | ||||||||
\(400\) | −7.78206e13 | −0.379983 | ||||||||
\(401\) | −3.18523e13 | −0.153407 | −0.0767037 | − | 0.997054i | \(-0.524440\pi\) | ||||
−0.0767037 | + | 0.997054i | \(0.524440\pi\) | |||||||
\(402\) | −4.89510e13 | −0.232551 | ||||||||
\(403\) | 4.11947e13 | 0.193047 | ||||||||
\(404\) | 2.19285e14 | 1.01371 | ||||||||
\(405\) | −1.35275e13 | −0.0616900 | ||||||||
\(406\) | 9.17528e13 | 0.412787 | ||||||||
\(407\) | 6.10293e13 | 0.270875 | ||||||||
\(408\) | 1.49118e14 | 0.652979 | ||||||||
\(409\) | −2.50325e14 | −1.08150 | −0.540749 | − | 0.841184i | \(-0.681859\pi\) | ||||
−0.540749 | + | 0.841184i | \(0.681859\pi\) | |||||||
\(410\) | 8.51849e13 | 0.363121 | ||||||||
\(411\) | −4.98988e13 | −0.209875 | ||||||||
\(412\) | −2.39611e14 | −0.994425 | ||||||||
\(413\) | −2.29635e13 | −0.0940399 | ||||||||
\(414\) | −5.73575e13 | −0.231787 | ||||||||
\(415\) | −1.73964e14 | −0.693735 | ||||||||
\(416\) | −5.16956e13 | −0.203442 | ||||||||
\(417\) | −4.51816e13 | −0.175474 | ||||||||
\(418\) | 1.39478e14 | 0.534609 | ||||||||
\(419\) | 2.94744e13 | 0.111498 | 0.0557491 | − | 0.998445i | \(-0.482245\pi\) | ||||
0.0557491 | + | 0.998445i | \(0.482245\pi\) | |||||||
\(420\) | −5.21796e13 | −0.194818 | ||||||||
\(421\) | 4.40544e14 | 1.62344 | 0.811722 | − | 0.584044i | \(-0.198530\pi\) | ||||
0.811722 | + | 0.584044i | \(0.198530\pi\) | |||||||
\(422\) | 1.21937e14 | 0.443525 | ||||||||
\(423\) | 1.10776e13 | 0.0397717 | ||||||||
\(424\) | 1.78661e14 | 0.633165 | ||||||||
\(425\) | −3.04948e14 | −1.06681 | ||||||||
\(426\) | 7.94489e13 | 0.274369 | ||||||||
\(427\) | −1.04746e14 | −0.357094 | ||||||||
\(428\) | 5.13136e13 | 0.172700 | ||||||||
\(429\) | −2.51913e13 | −0.0837019 | ||||||||
\(430\) | 4.53765e13 | 0.148852 | ||||||||
\(431\) | −1.08455e14 | −0.351256 | −0.175628 | − | 0.984457i | \(-0.556196\pi\) | ||||
−0.175628 | + | 0.984457i | \(0.556196\pi\) | |||||||
\(432\) | −3.30597e13 | −0.105715 | ||||||||
\(433\) | −2.49683e14 | −0.788326 | −0.394163 | − | 0.919041i | \(-0.628965\pi\) | ||||
−0.394163 | + | 0.919041i | \(0.628965\pi\) | |||||||
\(434\) | −8.33728e13 | −0.259915 | ||||||||
\(435\) | 1.49418e14 | 0.459951 | ||||||||
\(436\) | −2.30833e14 | −0.701651 | ||||||||
\(437\) | 1.15079e15 | 3.45421 | ||||||||
\(438\) | 2.04167e13 | 0.0605171 | ||||||||
\(439\) | 5.41840e14 | 1.58605 | 0.793024 | − | 0.609190i | \(-0.208505\pi\) | ||||
0.793024 | + | 0.609190i | \(0.208505\pi\) | |||||||
\(440\) | −9.55689e13 | −0.276266 | ||||||||
\(441\) | −5.58381e13 | −0.159411 | ||||||||
\(442\) | −4.65458e13 | −0.131238 | ||||||||
\(443\) | −3.54094e14 | −0.986048 | −0.493024 | − | 0.870016i | \(-0.664109\pi\) | ||||
−0.493024 | + | 0.870016i | \(0.664109\pi\) | |||||||
\(444\) | −7.05110e13 | −0.193932 | ||||||||
\(445\) | −3.45890e14 | −0.939633 | ||||||||
\(446\) | 6.50013e13 | 0.174413 | ||||||||
\(447\) | −3.74231e13 | −0.0991856 | ||||||||
\(448\) | −4.69358e13 | −0.122878 | ||||||||
\(449\) | −4.79011e14 | −1.23877 | −0.619385 | − | 0.785087i | \(-0.712618\pi\) | ||||
−0.619385 | + | 0.785087i | \(0.712618\pi\) | |||||||
\(450\) | −3.59471e13 | −0.0918322 | ||||||||
\(451\) | 4.41515e14 | 1.11423 | ||||||||
\(452\) | 2.82861e14 | 0.705199 | ||||||||
\(453\) | −1.14612e14 | −0.282287 | ||||||||
\(454\) | −4.30446e13 | −0.104740 | ||||||||
\(455\) | 3.56452e13 | 0.0856917 | ||||||||
\(456\) | −3.52675e14 | −0.837659 | ||||||||
\(457\) | 1.22388e14 | 0.287210 | 0.143605 | − | 0.989635i | \(-0.454131\pi\) | ||||
0.143605 | + | 0.989635i | \(0.454131\pi\) | |||||||
\(458\) | 1.05128e14 | 0.243757 | ||||||||
\(459\) | −1.29548e14 | −0.296798 | ||||||||
\(460\) | −3.60294e14 | −0.815623 | ||||||||
\(461\) | −8.45619e14 | −1.89156 | −0.945779 | − | 0.324812i | \(-0.894699\pi\) | ||||
−0.945779 | + | 0.324812i | \(0.894699\pi\) | |||||||
\(462\) | 5.09840e13 | 0.112695 | ||||||||
\(463\) | 7.32000e14 | 1.59888 | 0.799439 | − | 0.600747i | \(-0.205130\pi\) | ||||
0.799439 | + | 0.600747i | \(0.205130\pi\) | |||||||
\(464\) | 3.65161e14 | 0.788199 | ||||||||
\(465\) | −1.35771e14 | −0.289612 | ||||||||
\(466\) | −1.09445e14 | −0.230713 | ||||||||
\(467\) | −1.14805e14 | −0.239175 | −0.119588 | − | 0.992824i | \(-0.538157\pi\) | ||||
−0.119588 | + | 0.992824i | \(0.538157\pi\) | |||||||
\(468\) | 2.91051e13 | 0.0599262 | ||||||||
\(469\) | 3.59001e14 | 0.730541 | ||||||||
\(470\) | −1.31179e13 | −0.0263830 | ||||||||
\(471\) | 6.02605e13 | 0.119789 | ||||||||
\(472\) | 4.85928e13 | 0.0954753 | ||||||||
\(473\) | 2.35187e14 | 0.456749 | ||||||||
\(474\) | −1.68913e14 | −0.324253 | ||||||||
\(475\) | 7.21224e14 | 1.36853 | ||||||||
\(476\) | −4.99706e14 | −0.937294 | ||||||||
\(477\) | −1.55214e14 | −0.287792 | ||||||||
\(478\) | −9.44707e13 | −0.173158 | ||||||||
\(479\) | 9.95247e14 | 1.80337 | 0.901686 | − | 0.432391i | \(-0.142330\pi\) | ||||
0.901686 | + | 0.432391i | \(0.142330\pi\) | |||||||
\(480\) | 1.70381e14 | 0.305206 | ||||||||
\(481\) | 4.81679e13 | 0.0853020 | ||||||||
\(482\) | 2.70927e14 | 0.474344 | ||||||||
\(483\) | 4.20653e14 | 0.728141 | ||||||||
\(484\) | 2.65303e14 | 0.454038 | ||||||||
\(485\) | 4.45414e14 | 0.753676 | ||||||||
\(486\) | −1.52710e13 | −0.0255487 | ||||||||
\(487\) | −5.98697e13 | −0.0990371 | −0.0495186 | − | 0.998773i | \(-0.515769\pi\) | ||||
−0.0495186 | + | 0.998773i | \(0.515769\pi\) | |||||||
\(488\) | 2.21651e14 | 0.362545 | ||||||||
\(489\) | −1.66392e14 | −0.269113 | ||||||||
\(490\) | 6.61222e13 | 0.105747 | ||||||||
\(491\) | −5.55539e13 | −0.0878550 | −0.0439275 | − | 0.999035i | \(-0.513987\pi\) | ||||
−0.0439275 | + | 0.999035i | \(0.513987\pi\) | |||||||
\(492\) | −5.10111e14 | −0.797731 | ||||||||
\(493\) | 1.43092e15 | 2.21288 | ||||||||
\(494\) | 1.10084e14 | 0.168355 | ||||||||
\(495\) | 8.30266e13 | 0.125571 | ||||||||
\(496\) | −3.31810e14 | −0.496296 | ||||||||
\(497\) | −5.82669e14 | −0.861910 | ||||||||
\(498\) | −1.96386e14 | −0.287308 | ||||||||
\(499\) | 1.10932e14 | 0.160510 | 0.0802550 | − | 0.996774i | \(-0.474427\pi\) | ||||
0.0802550 | + | 0.996774i | \(0.474427\pi\) | |||||||
\(500\) | −5.52231e14 | −0.790289 | ||||||||
\(501\) | −4.37235e14 | −0.618881 | ||||||||
\(502\) | 3.62105e14 | 0.506949 | ||||||||
\(503\) | −6.51056e14 | −0.901560 | −0.450780 | − | 0.892635i | \(-0.648854\pi\) | ||||
−0.450780 | + | 0.892635i | \(0.648854\pi\) | |||||||
\(504\) | −1.28915e14 | −0.176577 | ||||||||
\(505\) | 4.93716e14 | 0.668921 | ||||||||
\(506\) | 3.52039e14 | 0.471805 | ||||||||
\(507\) | 4.15613e14 | 0.550991 | ||||||||
\(508\) | −4.98593e14 | −0.653876 | ||||||||
\(509\) | −2.39761e13 | −0.0311050 | −0.0155525 | − | 0.999879i | \(-0.504951\pi\) | ||||
−0.0155525 | + | 0.999879i | \(0.504951\pi\) | |||||||
\(510\) | 1.53408e14 | 0.196885 | ||||||||
\(511\) | −1.49734e14 | −0.190110 | ||||||||
\(512\) | 7.37109e14 | 0.925863 | ||||||||
\(513\) | 3.06390e14 | 0.380741 | ||||||||
\(514\) | −3.14662e14 | −0.386854 | ||||||||
\(515\) | −5.39479e14 | −0.656197 | ||||||||
\(516\) | −2.71727e14 | −0.327008 | ||||||||
\(517\) | −6.79902e13 | −0.0809559 | ||||||||
\(518\) | −9.74856e13 | −0.114849 | ||||||||
\(519\) | −5.00312e13 | −0.0583204 | ||||||||
\(520\) | −7.54285e13 | −0.0869996 | ||||||||
\(521\) | −2.07535e14 | −0.236856 | −0.118428 | − | 0.992963i | \(-0.537785\pi\) | ||||
−0.118428 | + | 0.992963i | \(0.537785\pi\) | |||||||
\(522\) | 1.68676e14 | 0.190487 | ||||||||
\(523\) | 2.09577e14 | 0.234199 | 0.117099 | − | 0.993120i | \(-0.462640\pi\) | ||||
0.117099 | + | 0.993120i | \(0.462640\pi\) | |||||||
\(524\) | −1.00836e15 | −1.11505 | ||||||||
\(525\) | 2.63632e14 | 0.288484 | ||||||||
\(526\) | −2.14964e14 | −0.232779 | ||||||||
\(527\) | −1.30023e15 | −1.39336 | ||||||||
\(528\) | 2.02908e14 | 0.215185 | ||||||||
\(529\) | 1.95176e15 | 2.04842 | ||||||||
\(530\) | 1.83801e14 | 0.190910 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | 1.18184e15 | 1.20239 | ||||||||
\(533\) | 3.48470e14 | 0.350885 | ||||||||
\(534\) | −3.90472e14 | −0.389146 | ||||||||
\(535\) | 1.15531e14 | 0.113960 | ||||||||
\(536\) | −7.59678e14 | −0.741691 | ||||||||
\(537\) | 8.38659e14 | 0.810451 | ||||||||
\(538\) | −3.28538e14 | −0.314256 | ||||||||
\(539\) | 3.42713e14 | 0.324483 | ||||||||
\(540\) | −9.59259e13 | −0.0899021 | ||||||||
\(541\) | −4.31551e12 | −0.00400357 | −0.00200178 | − | 0.999998i | \(-0.500637\pi\) | ||||
−0.00200178 | + | 0.999998i | \(0.500637\pi\) | |||||||
\(542\) | 9.82602e13 | 0.0902364 | ||||||||
\(543\) | 8.19061e14 | 0.744590 | ||||||||
\(544\) | 1.63168e15 | 1.46838 | ||||||||
\(545\) | −5.19714e14 | −0.463003 | ||||||||
\(546\) | 4.02395e13 | 0.0354890 | ||||||||
\(547\) | 1.27963e15 | 1.11726 | 0.558630 | − | 0.829417i | \(-0.311327\pi\) | ||||
0.558630 | + | 0.829417i | \(0.311327\pi\) | |||||||
\(548\) | −3.53841e14 | −0.305855 | ||||||||
\(549\) | −1.92562e14 | −0.164787 | ||||||||
\(550\) | 2.20630e14 | 0.186926 | ||||||||
\(551\) | −3.38423e15 | −2.83875 | ||||||||
\(552\) | −8.90141e14 | −0.739254 | ||||||||
\(553\) | 1.23879e15 | 1.01862 | ||||||||
\(554\) | −2.88940e14 | −0.235236 | ||||||||
\(555\) | −1.58754e14 | −0.127971 | ||||||||
\(556\) | −3.20391e14 | −0.255722 | ||||||||
\(557\) | −2.47444e14 | −0.195557 | −0.0977785 | − | 0.995208i | \(-0.531174\pi\) | ||||
−0.0977785 | + | 0.995208i | \(0.531174\pi\) | |||||||
\(558\) | −1.53271e14 | −0.119942 | ||||||||
\(559\) | 1.85624e14 | 0.143836 | ||||||||
\(560\) | −2.87111e14 | −0.220301 | ||||||||
\(561\) | 7.95116e14 | 0.604136 | ||||||||
\(562\) | 5.96589e14 | 0.448875 | ||||||||
\(563\) | −7.22104e14 | −0.538027 | −0.269013 | − | 0.963136i | \(-0.586698\pi\) | ||||
−0.269013 | + | 0.963136i | \(0.586698\pi\) | |||||||
\(564\) | 7.85533e13 | 0.0579602 | ||||||||
\(565\) | 6.36855e14 | 0.465344 | ||||||||
\(566\) | 7.60712e14 | 0.550465 | ||||||||
\(567\) | 1.11996e14 | 0.0802594 | ||||||||
\(568\) | 1.23298e15 | 0.875065 | ||||||||
\(569\) | 9.44684e14 | 0.664002 | 0.332001 | − | 0.943279i | \(-0.392276\pi\) | ||||
0.332001 | + | 0.943279i | \(0.392276\pi\) | |||||||
\(570\) | −3.62821e14 | −0.252569 | ||||||||
\(571\) | −9.77473e13 | −0.0673916 | −0.0336958 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336958 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(572\) | −1.78636e14 | −0.121981 | ||||||||
\(573\) | −5.80306e14 | −0.392470 | ||||||||
\(574\) | −7.05258e14 | −0.472425 | ||||||||
\(575\) | 1.82035e15 | 1.20776 | ||||||||
\(576\) | −8.62858e13 | −0.0567042 | ||||||||
\(577\) | 1.50543e14 | 0.0979924 | 0.0489962 | − | 0.998799i | \(-0.484398\pi\) | ||||
0.0489962 | + | 0.998799i | \(0.484398\pi\) | |||||||
\(578\) | 8.51436e14 | 0.548970 | ||||||||
\(579\) | −1.35509e15 | −0.865440 | ||||||||
\(580\) | 1.05955e15 | 0.670297 | ||||||||
\(581\) | 1.44027e15 | 0.902558 | ||||||||
\(582\) | 5.02823e14 | 0.312132 | ||||||||
\(583\) | 9.52642e14 | 0.585805 | ||||||||
\(584\) | 3.16850e14 | 0.193012 | ||||||||
\(585\) | 6.55294e13 | 0.0395439 | ||||||||
\(586\) | 4.26034e14 | 0.254687 | ||||||||
\(587\) | −6.10101e14 | −0.361320 | −0.180660 | − | 0.983546i | \(-0.557823\pi\) | ||||
−0.180660 | + | 0.983546i | \(0.557823\pi\) | |||||||
\(588\) | −3.95958e14 | −0.232313 | ||||||||
\(589\) | 3.07514e15 | 1.78744 | ||||||||
\(590\) | 4.99907e13 | 0.0287875 | ||||||||
\(591\) | 2.09989e14 | 0.119802 | ||||||||
\(592\) | −3.87977e14 | −0.219299 | ||||||||
\(593\) | −7.60782e13 | −0.0426049 | −0.0213024 | − | 0.999773i | \(-0.506781\pi\) | ||||
−0.0213024 | + | 0.999773i | \(0.506781\pi\) | |||||||
\(594\) | 9.37278e13 | 0.0520048 | ||||||||
\(595\) | −1.12508e15 | −0.618498 | ||||||||
\(596\) | −2.65374e14 | −0.144545 | ||||||||
\(597\) | −8.39666e13 | −0.0453156 | ||||||||
\(598\) | 2.77849e14 | 0.148577 | ||||||||
\(599\) | 3.07445e15 | 1.62899 | 0.814497 | − | 0.580168i | \(-0.197013\pi\) | ||||
0.814497 | + | 0.580168i | \(0.197013\pi\) | |||||||
\(600\) | −5.57869e14 | −0.292887 | ||||||||
\(601\) | 2.51066e15 | 1.30611 | 0.653053 | − | 0.757312i | \(-0.273488\pi\) | ||||
0.653053 | + | 0.757312i | \(0.273488\pi\) | |||||||
\(602\) | −3.75678e14 | −0.193658 | ||||||||
\(603\) | 6.59979e14 | 0.337121 | ||||||||
\(604\) | −8.12735e14 | −0.411382 | ||||||||
\(605\) | 5.97323e14 | 0.299609 | ||||||||
\(606\) | 5.57351e14 | 0.277032 | ||||||||
\(607\) | 3.18922e15 | 1.57089 | 0.785446 | − | 0.618931i | \(-0.212434\pi\) | ||||
0.785446 | + | 0.618931i | \(0.212434\pi\) | |||||||
\(608\) | −3.85903e15 | −1.88369 | ||||||||
\(609\) | −1.23705e15 | −0.598402 | ||||||||
\(610\) | 2.28028e14 | 0.109314 | ||||||||
\(611\) | −5.36618e13 | −0.0254940 | ||||||||
\(612\) | −9.18648e14 | −0.432530 | ||||||||
\(613\) | 1.38627e15 | 0.646868 | 0.323434 | − | 0.946251i | \(-0.395163\pi\) | ||||
0.323434 | + | 0.946251i | \(0.395163\pi\) | |||||||
\(614\) | −1.33009e14 | −0.0615115 | ||||||||
\(615\) | −1.14850e15 | −0.526403 | ||||||||
\(616\) | 7.91228e14 | 0.359425 | ||||||||
\(617\) | 1.52685e15 | 0.687429 | 0.343715 | − | 0.939074i | \(-0.388315\pi\) | ||||
0.343715 | + | 0.939074i | \(0.388315\pi\) | |||||||
\(618\) | −6.09011e14 | −0.271762 | ||||||||
\(619\) | −4.10703e15 | −1.81648 | −0.908238 | − | 0.418455i | \(-0.862572\pi\) | ||||
−0.908238 | + | 0.418455i | \(0.862572\pi\) | |||||||
\(620\) | −9.62778e14 | −0.422058 | ||||||||
\(621\) | 7.73320e14 | 0.336013 | ||||||||
\(622\) | −4.88280e14 | −0.210292 | ||||||||
\(623\) | 2.86368e15 | 1.22247 | ||||||||
\(624\) | 1.60147e14 | 0.0677646 | ||||||||
\(625\) | 4.05905e14 | 0.170249 | ||||||||
\(626\) | −1.19376e15 | −0.496316 | ||||||||
\(627\) | −1.88051e15 | −0.775003 | ||||||||
\(628\) | 4.27318e14 | 0.174571 | ||||||||
\(629\) | −1.52033e15 | −0.615686 | ||||||||
\(630\) | −1.32623e14 | −0.0532410 | ||||||||
\(631\) | −4.75010e14 | −0.189035 | −0.0945173 | − | 0.995523i | \(-0.530131\pi\) | ||||
−0.0945173 | + | 0.995523i | \(0.530131\pi\) | |||||||
\(632\) | −2.62140e15 | −1.03416 | ||||||||
\(633\) | −1.64402e15 | −0.642963 | ||||||||
\(634\) | −4.63732e14 | −0.179795 | ||||||||
\(635\) | −1.12257e15 | −0.431477 | ||||||||
\(636\) | −1.10065e15 | −0.419406 | ||||||||
\(637\) | 2.70489e14 | 0.102184 | ||||||||
\(638\) | −1.03527e15 | −0.387740 | ||||||||
\(639\) | −1.07117e15 | −0.397743 | ||||||||
\(640\) | 1.53814e15 | 0.566248 | ||||||||
\(641\) | 3.96744e15 | 1.44808 | 0.724038 | − | 0.689760i | \(-0.242284\pi\) | ||||
0.724038 | + | 0.689760i | \(0.242284\pi\) | |||||||
\(642\) | 1.30422e14 | 0.0471964 | ||||||||
\(643\) | 5.00082e15 | 1.79424 | 0.897120 | − | 0.441787i | \(-0.145655\pi\) | ||||
0.897120 | + | 0.441787i | \(0.145655\pi\) | |||||||
\(644\) | 2.98293e15 | 1.06113 | ||||||||
\(645\) | −6.11786e14 | −0.215785 | ||||||||
\(646\) | −3.47460e15 | −1.21514 | ||||||||
\(647\) | −5.11962e14 | −0.177527 | −0.0887634 | − | 0.996053i | \(-0.528292\pi\) | ||||
−0.0887634 | + | 0.996053i | \(0.528292\pi\) | |||||||
\(648\) | −2.36994e14 | −0.0814844 | ||||||||
\(649\) | 2.59103e14 | 0.0883338 | ||||||||
\(650\) | 1.74134e14 | 0.0588653 | ||||||||
\(651\) | 1.12407e15 | 0.376789 | ||||||||
\(652\) | −1.17992e15 | −0.392184 | ||||||||
\(653\) | −5.33380e15 | −1.75798 | −0.878990 | − | 0.476840i | \(-0.841782\pi\) | ||||
−0.878990 | + | 0.476840i | \(0.841782\pi\) | |||||||
\(654\) | −5.86700e14 | −0.191751 | ||||||||
\(655\) | −2.27030e15 | −0.735792 | ||||||||
\(656\) | −2.80681e15 | −0.902075 | ||||||||
\(657\) | −2.75267e14 | −0.0877294 | ||||||||
\(658\) | 1.08605e14 | 0.0343247 | ||||||||
\(659\) | −3.31774e15 | −1.03985 | −0.519927 | − | 0.854211i | \(-0.674041\pi\) | ||||
−0.519927 | + | 0.854211i | \(0.674041\pi\) | |||||||
\(660\) | 5.88757e14 | 0.182997 | ||||||||
\(661\) | −2.53460e15 | −0.781270 | −0.390635 | − | 0.920546i | \(-0.627745\pi\) | ||||
−0.390635 | + | 0.920546i | \(0.627745\pi\) | |||||||
\(662\) | −9.89257e14 | −0.302406 | ||||||||
\(663\) | 6.27552e14 | 0.190250 | ||||||||
\(664\) | −3.04774e15 | −0.916333 | ||||||||
\(665\) | 2.66088e15 | 0.793427 | ||||||||
\(666\) | −1.79215e14 | −0.0529989 | ||||||||
\(667\) | −8.54171e15 | −2.50526 | ||||||||
\(668\) | −3.10051e15 | −0.901909 | ||||||||
\(669\) | −8.76377e14 | −0.252841 | ||||||||
\(670\) | −7.81533e14 | −0.223633 | ||||||||
\(671\) | 1.18187e15 | 0.335426 | ||||||||
\(672\) | −1.41061e15 | −0.397077 | ||||||||
\(673\) | 5.86295e15 | 1.63694 | 0.818471 | − | 0.574548i | \(-0.194822\pi\) | ||||
0.818471 | + | 0.574548i | \(0.194822\pi\) | |||||||
\(674\) | −1.76554e15 | −0.488932 | ||||||||
\(675\) | 4.84655e14 | 0.133126 | ||||||||
\(676\) | 2.94718e15 | 0.802972 | ||||||||
\(677\) | −1.87975e13 | −0.00507999 | −0.00254000 | − | 0.999997i | \(-0.500809\pi\) | ||||
−0.00254000 | + | 0.999997i | \(0.500809\pi\) | |||||||
\(678\) | 7.18938e14 | 0.192721 | ||||||||
\(679\) | −3.68765e15 | −0.980541 | ||||||||
\(680\) | 2.38076e15 | 0.627938 | ||||||||
\(681\) | 5.80347e14 | 0.151837 | ||||||||
\(682\) | 9.40717e14 | 0.244143 | ||||||||
\(683\) | −6.07603e15 | −1.56425 | −0.782125 | − | 0.623121i | \(-0.785864\pi\) | ||||
−0.782125 | + | 0.623121i | \(0.785864\pi\) | |||||||
\(684\) | 2.17267e15 | 0.554862 | ||||||||
\(685\) | −7.96665e14 | −0.201826 | ||||||||
\(686\) | −1.69214e15 | −0.425259 | ||||||||
\(687\) | −1.41738e15 | −0.353366 | ||||||||
\(688\) | −1.49514e15 | −0.369781 | ||||||||
\(689\) | 7.51881e14 | 0.184477 | ||||||||
\(690\) | −9.15749e14 | −0.222898 | ||||||||
\(691\) | 1.75688e15 | 0.424242 | 0.212121 | − | 0.977243i | \(-0.431963\pi\) | ||||
0.212121 | + | 0.977243i | \(0.431963\pi\) | |||||||
\(692\) | −3.54780e14 | −0.0849916 | ||||||||
\(693\) | −6.87389e14 | −0.163369 | ||||||||
\(694\) | 1.28650e14 | 0.0303342 | ||||||||
\(695\) | −7.21352e14 | −0.168745 | ||||||||
\(696\) | 2.61772e15 | 0.607535 | ||||||||
\(697\) | −1.09988e16 | −2.53259 | ||||||||
\(698\) | −2.92790e15 | −0.668885 | ||||||||
\(699\) | 1.47558e15 | 0.334456 | ||||||||
\(700\) | 1.86946e15 | 0.420414 | ||||||||
\(701\) | −3.30315e15 | −0.737020 | −0.368510 | − | 0.929624i | \(-0.620132\pi\) | ||||
−0.368510 | + | 0.929624i | \(0.620132\pi\) | |||||||
\(702\) | 7.39755e13 | 0.0163770 | ||||||||
\(703\) | 3.59569e15 | 0.789819 | ||||||||
\(704\) | 5.29589e14 | 0.115422 | ||||||||
\(705\) | 1.76861e14 | 0.0382465 | ||||||||
\(706\) | 2.72162e15 | 0.583986 | ||||||||
\(707\) | −4.08755e15 | −0.870274 | ||||||||
\(708\) | −2.99358e14 | −0.0632424 | ||||||||
\(709\) | 4.88990e15 | 1.02505 | 0.512526 | − | 0.858672i | \(-0.328710\pi\) | ||||
0.512526 | + | 0.858672i | \(0.328710\pi\) | |||||||
\(710\) | 1.26845e15 | 0.263848 | ||||||||
\(711\) | 2.27737e15 | 0.470057 | ||||||||
\(712\) | −6.05980e15 | −1.24113 | ||||||||
\(713\) | 7.76158e15 | 1.57746 | ||||||||
\(714\) | −1.27009e15 | −0.256149 | ||||||||
\(715\) | −4.02195e14 | −0.0804921 | ||||||||
\(716\) | 5.94708e15 | 1.18109 | ||||||||
\(717\) | 1.27370e15 | 0.251021 | ||||||||
\(718\) | 4.50997e14 | 0.0882042 | ||||||||
\(719\) | 7.32137e15 | 1.42097 | 0.710483 | − | 0.703715i | \(-0.248477\pi\) | ||||
0.710483 | + | 0.703715i | \(0.248477\pi\) | |||||||
\(720\) | −5.27819e14 | −0.101661 | ||||||||
\(721\) | 4.46642e15 | 0.853720 | ||||||||
\(722\) | 6.11813e15 | 1.16055 | ||||||||
\(723\) | −3.65276e15 | −0.687639 | ||||||||
\(724\) | 5.80811e15 | 1.08511 | ||||||||
\(725\) | −5.35326e15 | −0.992566 | ||||||||
\(726\) | 6.74311e14 | 0.124082 | ||||||||
\(727\) | 8.09516e15 | 1.47838 | 0.739190 | − | 0.673497i | \(-0.235209\pi\) | ||||
0.739190 | + | 0.673497i | \(0.235209\pi\) | |||||||
\(728\) | 6.24483e14 | 0.113187 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 3.25966e14 | 0.0581964 | ||||||||
\(731\) | −5.85886e15 | −1.03817 | ||||||||
\(732\) | −1.36549e15 | −0.240148 | ||||||||
\(733\) | −3.29018e15 | −0.574313 | −0.287156 | − | 0.957884i | \(-0.592710\pi\) | ||||
−0.287156 | + | 0.957884i | \(0.592710\pi\) | |||||||
\(734\) | 2.65480e15 | 0.459942 | ||||||||
\(735\) | −8.91490e14 | −0.153298 | ||||||||
\(736\) | −9.74008e15 | −1.66240 | ||||||||
\(737\) | −4.05070e15 | −0.686213 | ||||||||
\(738\) | −1.29653e15 | −0.218008 | ||||||||
\(739\) | 2.17098e15 | 0.362336 | 0.181168 | − | 0.983452i | \(-0.442012\pi\) | ||||
0.181168 | + | 0.983452i | \(0.442012\pi\) | |||||||
\(740\) | −1.12575e15 | −0.186495 | ||||||||
\(741\) | −1.48421e15 | −0.244058 | ||||||||
\(742\) | −1.52171e15 | −0.248377 | ||||||||
\(743\) | 4.01946e15 | 0.651222 | 0.325611 | − | 0.945504i | \(-0.394430\pi\) | ||||
0.325611 | + | 0.945504i | \(0.394430\pi\) | |||||||
\(744\) | −2.37863e15 | −0.382539 | ||||||||
\(745\) | −5.97483e14 | −0.0953820 | ||||||||
\(746\) | −1.35537e15 | −0.214780 | ||||||||
\(747\) | 2.64776e15 | 0.416500 | ||||||||
\(748\) | 5.63831e15 | 0.880421 | ||||||||
\(749\) | −9.56501e14 | −0.148264 | ||||||||
\(750\) | −1.40359e15 | −0.215975 | ||||||||
\(751\) | 1.10261e16 | 1.68423 | 0.842116 | − | 0.539296i | \(-0.181310\pi\) | ||||
0.842116 | + | 0.539296i | \(0.181310\pi\) | |||||||
\(752\) | 4.32229e14 | 0.0655414 | ||||||||
\(753\) | −4.88206e15 | −0.734905 | ||||||||
\(754\) | −8.17096e14 | −0.122104 | ||||||||
\(755\) | −1.82985e15 | −0.271461 | ||||||||
\(756\) | 7.94184e14 | 0.116964 | ||||||||
\(757\) | −1.19658e16 | −1.74949 | −0.874747 | − | 0.484579i | \(-0.838973\pi\) | ||||
−0.874747 | + | 0.484579i | \(0.838973\pi\) | |||||||
\(758\) | 3.16227e15 | 0.459006 | ||||||||
\(759\) | −4.74635e15 | −0.683958 | ||||||||
\(760\) | −5.63067e15 | −0.805537 | ||||||||
\(761\) | 4.06587e15 | 0.577481 | 0.288740 | − | 0.957407i | \(-0.406764\pi\) | ||||
0.288740 | + | 0.957407i | \(0.406764\pi\) | |||||||
\(762\) | −1.26726e15 | −0.178695 | ||||||||
\(763\) | 4.30279e15 | 0.602372 | ||||||||
\(764\) | −4.11505e15 | −0.571955 | ||||||||
\(765\) | −2.06831e15 | −0.285416 | ||||||||
\(766\) | −4.60853e15 | −0.631399 | ||||||||
\(767\) | 2.04499e14 | 0.0278174 | ||||||||
\(768\) | 1.00918e15 | 0.136295 | ||||||||
\(769\) | −1.12489e16 | −1.50839 | −0.754195 | − | 0.656650i | \(-0.771973\pi\) | ||||
−0.754195 | + | 0.656650i | \(0.771973\pi\) | |||||||
\(770\) | 8.13991e14 | 0.108373 | ||||||||
\(771\) | 4.24242e15 | 0.560808 | ||||||||
\(772\) | −9.60921e15 | −1.26122 | ||||||||
\(773\) | −1.25407e16 | −1.63431 | −0.817156 | − | 0.576417i | \(-0.804451\pi\) | ||||
−0.817156 | + | 0.576417i | \(0.804451\pi\) | |||||||
\(774\) | −6.90639e14 | −0.0893667 | ||||||||
\(775\) | 4.86434e15 | 0.624977 | ||||||||
\(776\) | 7.80340e15 | 0.995507 | ||||||||
\(777\) | 1.31435e15 | 0.166492 | ||||||||
\(778\) | 4.68689e15 | 0.589518 | ||||||||
\(779\) | 2.60129e16 | 3.24888 | ||||||||
\(780\) | 4.64681e14 | 0.0576281 | ||||||||
\(781\) | 6.57441e15 | 0.809611 | ||||||||
\(782\) | −8.76980e15 | −1.07239 | ||||||||
\(783\) | −2.27417e15 | −0.276143 | ||||||||
\(784\) | −2.17870e15 | −0.262700 | ||||||||
\(785\) | 9.62097e14 | 0.115196 | ||||||||
\(786\) | −2.56291e15 | −0.304726 | ||||||||
\(787\) | 1.32562e16 | 1.56516 | 0.782579 | − | 0.622551i | \(-0.213904\pi\) | ||||
0.782579 | + | 0.622551i | \(0.213904\pi\) | |||||||
\(788\) | 1.48907e15 | 0.174591 | ||||||||
\(789\) | 2.89824e15 | 0.337451 | ||||||||
\(790\) | −2.69681e15 | −0.311818 | ||||||||
\(791\) | −5.27261e15 | −0.605418 | ||||||||
\(792\) | 1.45458e15 | 0.165863 | ||||||||
\(793\) | 9.32804e14 | 0.105630 | ||||||||
\(794\) | −2.26868e15 | −0.255130 | ||||||||
\(795\) | −2.47808e15 | −0.276756 | ||||||||
\(796\) | −5.95422e14 | −0.0660394 | ||||||||
\(797\) | 1.25975e15 | 0.138759 | 0.0693797 | − | 0.997590i | \(-0.477898\pi\) | ||||
0.0693797 | + | 0.997590i | \(0.477898\pi\) | |||||||
\(798\) | 3.00384e15 | 0.328595 | ||||||||
\(799\) | 1.69374e15 | 0.184009 | ||||||||
\(800\) | −6.10430e15 | −0.658629 | ||||||||
\(801\) | 5.26452e15 | 0.564131 | ||||||||
\(802\) | −5.74087e14 | −0.0610968 | ||||||||
\(803\) | 1.68949e15 | 0.178574 | ||||||||
\(804\) | 4.68003e15 | 0.491293 | ||||||||
\(805\) | 6.71600e15 | 0.700218 | ||||||||
\(806\) | 7.42469e14 | 0.0768839 | ||||||||
\(807\) | 4.42951e15 | 0.455566 | ||||||||
\(808\) | 8.64962e15 | 0.883557 | ||||||||
\(809\) | 2.69532e15 | 0.273460 | 0.136730 | − | 0.990608i | \(-0.456341\pi\) | ||||
0.136730 | + | 0.990608i | \(0.456341\pi\) | |||||||
\(810\) | −2.43812e14 | −0.0245690 | ||||||||
\(811\) | −7.63973e15 | −0.764651 | −0.382326 | − | 0.924028i | \(-0.624877\pi\) | ||||
−0.382326 | + | 0.924028i | \(0.624877\pi\) | |||||||
\(812\) | −8.77216e15 | −0.872064 | ||||||||
\(813\) | −1.32479e15 | −0.130812 | ||||||||
\(814\) | 1.09996e15 | 0.107880 | ||||||||
\(815\) | −2.65656e15 | −0.258793 | ||||||||
\(816\) | −5.05473e15 | −0.489105 | ||||||||
\(817\) | 1.38566e16 | 1.33179 | ||||||||
\(818\) | −4.51171e15 | −0.430723 | ||||||||
\(819\) | −5.42528e14 | −0.0514470 | ||||||||
\(820\) | −8.14423e15 | −0.767139 | ||||||||
\(821\) | 2.91872e15 | 0.273089 | 0.136545 | − | 0.990634i | \(-0.456400\pi\) | ||||
0.136545 | + | 0.990634i | \(0.456400\pi\) | |||||||
\(822\) | −8.99347e14 | −0.0835857 | ||||||||
\(823\) | −6.18239e15 | −0.570765 | −0.285382 | − | 0.958414i | \(-0.592121\pi\) | ||||
−0.285382 | + | 0.958414i | \(0.592121\pi\) | |||||||
\(824\) | −9.45135e15 | −0.866750 | ||||||||
\(825\) | −2.97463e15 | −0.270979 | ||||||||
\(826\) | −4.13880e14 | −0.0374528 | ||||||||
\(827\) | −5.31928e15 | −0.478160 | −0.239080 | − | 0.971000i | \(-0.576846\pi\) | ||||
−0.239080 | + | 0.971000i | \(0.576846\pi\) | |||||||
\(828\) | 5.48375e15 | 0.489678 | ||||||||
\(829\) | −7.02110e15 | −0.622809 | −0.311405 | − | 0.950277i | \(-0.600799\pi\) | ||||
−0.311405 | + | 0.950277i | \(0.600799\pi\) | |||||||
\(830\) | −3.13542e15 | −0.276291 | ||||||||
\(831\) | 3.89562e15 | 0.341013 | ||||||||
\(832\) | 4.17983e14 | 0.0363480 | ||||||||
\(833\) | −8.53748e15 | −0.737534 | ||||||||
\(834\) | −8.14327e14 | −0.0698852 | ||||||||
\(835\) | −6.98073e15 | −0.595148 | ||||||||
\(836\) | −1.33350e16 | −1.12943 | ||||||||
\(837\) | 2.06647e15 | 0.173875 | ||||||||
\(838\) | 5.31229e14 | 0.0444058 | ||||||||
\(839\) | −1.16618e16 | −0.968443 | −0.484222 | − | 0.874945i | \(-0.660897\pi\) | ||||
−0.484222 | + | 0.874945i | \(0.660897\pi\) | |||||||
\(840\) | −2.05820e15 | −0.169806 | ||||||||
\(841\) | 1.29189e16 | 1.05888 | ||||||||
\(842\) | 7.94010e15 | 0.646561 | ||||||||
\(843\) | −8.04348e15 | −0.650718 | ||||||||
\(844\) | −1.16580e16 | −0.937003 | ||||||||
\(845\) | 6.63551e15 | 0.529862 | ||||||||
\(846\) | 1.99657e14 | 0.0158397 | ||||||||
\(847\) | −4.94532e15 | −0.389795 | ||||||||
\(848\) | −6.05616e15 | −0.474264 | ||||||||
\(849\) | −1.02563e16 | −0.797989 | ||||||||
\(850\) | −5.49621e15 | −0.424873 | ||||||||
\(851\) | 9.07541e15 | 0.697033 | ||||||||
\(852\) | −7.59583e15 | −0.579639 | ||||||||
\(853\) | −8.18494e15 | −0.620577 | −0.310289 | − | 0.950642i | \(-0.600426\pi\) | ||||
−0.310289 | + | 0.950642i | \(0.600426\pi\) | |||||||
\(854\) | −1.88788e15 | −0.142218 | ||||||||
\(855\) | 4.89171e15 | 0.366140 | ||||||||
\(856\) | 2.02404e15 | 0.150527 | ||||||||
\(857\) | 1.48309e16 | 1.09590 | 0.547952 | − | 0.836510i | \(-0.315408\pi\) | ||||
0.547952 | + | 0.836510i | \(0.315408\pi\) | |||||||
\(858\) | −4.54033e14 | −0.0333355 | ||||||||
\(859\) | 1.84576e16 | 1.34652 | 0.673262 | − | 0.739404i | \(-0.264893\pi\) | ||||
0.673262 | + | 0.739404i | \(0.264893\pi\) | |||||||
\(860\) | −4.33829e15 | −0.314468 | ||||||||
\(861\) | 9.50862e15 | 0.684857 | ||||||||
\(862\) | −1.95473e15 | −0.139893 | ||||||||
\(863\) | 1.57578e16 | 1.12056 | 0.560281 | − | 0.828303i | \(-0.310693\pi\) | ||||
0.560281 | + | 0.828303i | \(0.310693\pi\) | |||||||
\(864\) | −2.59323e15 | −0.183238 | ||||||||
\(865\) | −7.98780e14 | −0.0560840 | ||||||||
\(866\) | −4.50014e15 | −0.313963 | ||||||||
\(867\) | −1.14794e16 | −0.795822 | ||||||||
\(868\) | 7.97098e15 | 0.549102 | ||||||||
\(869\) | −1.39776e16 | −0.956807 | ||||||||
\(870\) | 2.69302e15 | 0.183183 | ||||||||
\(871\) | −3.19705e15 | −0.216097 | ||||||||
\(872\) | −9.10509e15 | −0.611566 | ||||||||
\(873\) | −6.77929e15 | −0.452487 | ||||||||
\(874\) | 2.07412e16 | 1.37569 | ||||||||
\(875\) | 1.02938e16 | 0.678469 | ||||||||
\(876\) | −1.95197e15 | −0.127850 | ||||||||
\(877\) | −1.76366e16 | −1.14794 | −0.573968 | − | 0.818878i | \(-0.694597\pi\) | ||||
−0.573968 | + | 0.818878i | \(0.694597\pi\) | |||||||
\(878\) | 9.76582e15 | 0.631668 | ||||||||
\(879\) | −5.74398e15 | −0.369211 | ||||||||
\(880\) | 3.23955e15 | 0.206933 | ||||||||
\(881\) | 2.32278e16 | 1.47449 | 0.737243 | − | 0.675628i | \(-0.236127\pi\) | ||||
0.737243 | + | 0.675628i | \(0.236127\pi\) | |||||||
\(882\) | −1.00639e15 | −0.0634878 | ||||||||
\(883\) | 2.21922e16 | 1.39128 | 0.695642 | − | 0.718389i | \(-0.255120\pi\) | ||||
0.695642 | + | 0.718389i | \(0.255120\pi\) | |||||||
\(884\) | 4.45008e15 | 0.277256 | ||||||||
\(885\) | −6.73998e14 | −0.0417321 | ||||||||
\(886\) | −6.38199e15 | −0.392709 | ||||||||
\(887\) | 1.93898e16 | 1.18575 | 0.592875 | − | 0.805295i | \(-0.297993\pi\) | ||||
0.592875 | + | 0.805295i | \(0.297993\pi\) | |||||||
\(888\) | −2.78127e15 | −0.169033 | ||||||||
\(889\) | 9.29392e15 | 0.561357 | ||||||||
\(890\) | −6.23413e15 | −0.374223 | ||||||||
\(891\) | −1.26368e15 | −0.0753894 | ||||||||
\(892\) | −6.21454e15 | −0.368470 | ||||||||
\(893\) | −4.00581e15 | −0.236052 | ||||||||
\(894\) | −6.74492e14 | −0.0395021 | ||||||||
\(895\) | 1.33897e16 | 0.779372 | ||||||||
\(896\) | −1.27345e16 | −0.736696 | ||||||||
\(897\) | −3.74609e15 | −0.215387 | ||||||||
\(898\) | −8.63342e15 | −0.493359 | ||||||||
\(899\) | −2.28252e16 | −1.29639 | ||||||||
\(900\) | 3.43678e15 | 0.194007 | ||||||||
\(901\) | −2.37317e16 | −1.33151 | ||||||||
\(902\) | 7.95762e15 | 0.443759 | ||||||||
\(903\) | 5.06507e15 | 0.280739 | ||||||||
\(904\) | 1.11573e16 | 0.614658 | ||||||||
\(905\) | 1.30768e16 | 0.716036 | ||||||||
\(906\) | −2.06570e15 | −0.112425 | ||||||||
\(907\) | −2.54420e16 | −1.37629 | −0.688146 | − | 0.725572i | \(-0.741575\pi\) | ||||
−0.688146 | + | 0.725572i | \(0.741575\pi\) | |||||||
\(908\) | 4.11534e15 | 0.221276 | ||||||||
\(909\) | −7.51446e15 | −0.401603 | ||||||||
\(910\) | 6.42449e14 | 0.0341280 | ||||||||
\(911\) | −9.76594e15 | −0.515659 | −0.257830 | − | 0.966190i | \(-0.583007\pi\) | ||||
−0.257830 | + | 0.966190i | \(0.583007\pi\) | |||||||
\(912\) | 1.19548e16 | 0.627438 | ||||||||
\(913\) | −1.62509e16 | −0.847792 | ||||||||
\(914\) | 2.20585e15 | 0.114386 | ||||||||
\(915\) | −3.07438e15 | −0.158468 | ||||||||
\(916\) | −1.00509e16 | −0.514968 | ||||||||
\(917\) | 1.87961e16 | 0.957274 | ||||||||
\(918\) | −2.33490e15 | −0.118204 | ||||||||
\(919\) | 3.66644e16 | 1.84505 | 0.922527 | − | 0.385933i | \(-0.126121\pi\) | ||||
0.922527 | + | 0.385933i | \(0.126121\pi\) | |||||||
\(920\) | −1.42117e16 | −0.710905 | ||||||||
\(921\) | 1.79329e15 | 0.0891709 | ||||||||
\(922\) | −1.52409e16 | −0.753341 | ||||||||
\(923\) | 5.18891e15 | 0.254957 | ||||||||
\(924\) | −4.87440e15 | −0.238081 | ||||||||
\(925\) | 5.68774e15 | 0.276160 | ||||||||
\(926\) | 1.31931e16 | 0.636778 | ||||||||
\(927\) | 8.21097e15 | 0.393964 | ||||||||
\(928\) | 2.86435e16 | 1.36619 | ||||||||
\(929\) | 1.21481e16 | 0.576001 | 0.288001 | − | 0.957630i | \(-0.407009\pi\) | ||||
0.288001 | + | 0.957630i | \(0.407009\pi\) | |||||||
\(930\) | −2.44706e15 | −0.115342 | ||||||||
\(931\) | 2.01917e16 | 0.946130 | ||||||||
\(932\) | 1.04636e16 | 0.487410 | ||||||||
\(933\) | 6.58321e15 | 0.304852 | ||||||||
\(934\) | −2.06917e15 | −0.0952552 | ||||||||
\(935\) | 1.26945e16 | 0.580969 | ||||||||
\(936\) | 1.14804e15 | 0.0522322 | ||||||||
\(937\) | −1.51708e16 | −0.686183 | −0.343091 | − | 0.939302i | \(-0.611474\pi\) | ||||
−0.343091 | + | 0.939302i | \(0.611474\pi\) | |||||||
\(938\) | 6.47042e15 | 0.290949 | ||||||||
\(939\) | 1.60948e16 | 0.719491 | ||||||||
\(940\) | 1.25415e15 | 0.0557375 | ||||||||
\(941\) | −3.17507e16 | −1.40285 | −0.701423 | − | 0.712745i | \(-0.747451\pi\) | ||||
−0.701423 | + | 0.712745i | \(0.747451\pi\) | |||||||
\(942\) | 1.08610e15 | 0.0477079 | ||||||||
\(943\) | 6.56559e16 | 2.86721 | ||||||||
\(944\) | −1.64718e15 | −0.0715145 | ||||||||
\(945\) | 1.78809e15 | 0.0771816 | ||||||||
\(946\) | 4.23888e15 | 0.181907 | ||||||||
\(947\) | 2.85074e16 | 1.21628 | 0.608138 | − | 0.793831i | \(-0.291917\pi\) | ||||
0.608138 | + | 0.793831i | \(0.291917\pi\) | |||||||
\(948\) | 1.61492e16 | 0.685024 | ||||||||
\(949\) | 1.33344e15 | 0.0562354 | ||||||||
\(950\) | 1.29989e16 | 0.545039 | ||||||||
\(951\) | 6.25225e15 | 0.260642 | ||||||||
\(952\) | −1.97107e16 | −0.816955 | ||||||||
\(953\) | −7.54001e15 | −0.310714 | −0.155357 | − | 0.987858i | \(-0.549653\pi\) | ||||
−0.155357 | + | 0.987858i | \(0.549653\pi\) | |||||||
\(954\) | −2.79748e15 | −0.114618 | ||||||||
\(955\) | −9.26495e15 | −0.377420 | ||||||||
\(956\) | 9.03201e15 | 0.365819 | ||||||||
\(957\) | 1.39580e16 | 0.562092 | ||||||||
\(958\) | 1.79378e16 | 0.718220 | ||||||||
\(959\) | 6.59571e15 | 0.262578 | ||||||||
\(960\) | −1.37761e15 | −0.0545297 | ||||||||
\(961\) | −4.66800e15 | −0.183718 | ||||||||
\(962\) | 8.68149e14 | 0.0339728 | ||||||||
\(963\) | −1.75841e15 | −0.0684188 | ||||||||
\(964\) | −2.59024e16 | −1.00211 | ||||||||
\(965\) | −2.16349e16 | −0.832252 | ||||||||
\(966\) | 7.58161e15 | 0.289993 | ||||||||
\(967\) | 4.65003e16 | 1.76852 | 0.884260 | − | 0.466995i | \(-0.154663\pi\) | ||||
0.884260 | + | 0.466995i | \(0.154663\pi\) | |||||||
\(968\) | 1.04647e16 | 0.395744 | ||||||||
\(969\) | 4.68462e16 | 1.76154 | ||||||||
\(970\) | 8.02789e15 | 0.300163 | ||||||||
\(971\) | 2.80464e15 | 0.104273 | 0.0521365 | − | 0.998640i | \(-0.483397\pi\) | ||||
0.0521365 | + | 0.998640i | \(0.483397\pi\) | |||||||
\(972\) | 1.46001e15 | 0.0539749 | ||||||||
\(973\) | 5.97218e15 | 0.219539 | ||||||||
\(974\) | −1.07906e15 | −0.0394430 | ||||||||
\(975\) | −2.34775e15 | −0.0853349 | ||||||||
\(976\) | −7.51344e15 | −0.271559 | ||||||||
\(977\) | 3.02212e16 | 1.08615 | 0.543077 | − | 0.839683i | \(-0.317259\pi\) | ||||
0.543077 | + | 0.839683i | \(0.317259\pi\) | |||||||
\(978\) | −2.99896e15 | −0.107178 | ||||||||
\(979\) | −3.23116e16 | −1.14830 | ||||||||
\(980\) | −6.32171e15 | −0.223404 | ||||||||
\(981\) | 7.91015e15 | 0.277975 | ||||||||
\(982\) | −1.00127e15 | −0.0349896 | ||||||||
\(983\) | −6.55268e15 | −0.227706 | −0.113853 | − | 0.993498i | \(-0.536319\pi\) | ||||
−0.113853 | + | 0.993498i | \(0.536319\pi\) | |||||||
\(984\) | −2.01211e16 | −0.695310 | ||||||||
\(985\) | 3.35261e15 | 0.115208 | ||||||||
\(986\) | 2.57901e16 | 0.881313 | ||||||||
\(987\) | −1.46426e15 | −0.0497592 | ||||||||
\(988\) | −1.05248e16 | −0.355672 | ||||||||
\(989\) | 3.49737e16 | 1.17534 | ||||||||
\(990\) | 1.49642e15 | 0.0500105 | ||||||||
\(991\) | −4.07952e16 | −1.35583 | −0.677913 | − | 0.735143i | \(-0.737115\pi\) | ||||
−0.677913 | + | 0.735143i | \(0.737115\pi\) | |||||||
\(992\) | −2.60274e16 | −0.860235 | ||||||||
\(993\) | 1.33376e16 | 0.438387 | ||||||||
\(994\) | −1.05017e16 | −0.343269 | ||||||||
\(995\) | −1.34058e15 | −0.0435778 | ||||||||
\(996\) | 1.87757e16 | 0.606975 | ||||||||
\(997\) | −1.46734e16 | −0.471746 | −0.235873 | − | 0.971784i | \(-0.575795\pi\) | ||||
−0.235873 | + | 0.971784i | \(0.575795\pi\) | |||||||
\(998\) | 1.99937e15 | 0.0639255 | ||||||||
\(999\) | 2.41626e15 | 0.0768306 |
(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 | 177.12.a.c.1.17 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.17 | ✓ | 27 | 1.1 | even | 1 | trivial |