Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.23 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 86.2630 | 0.953080 | 0.476540 | − | 0.879153i | \(-0.341891\pi\) | ||||
0.476540 | + | 0.879153i | \(0.341891\pi\) | |||||||
\(3\) | −729.000 | −0.577350 | ||||||||
\(4\) | −750.700 | −0.0916382 | ||||||||
\(5\) | −64842.3 | −1.85589 | −0.927947 | − | 0.372713i | \(-0.878428\pi\) | ||||
−0.927947 | + | 0.372713i | \(0.878428\pi\) | |||||||
\(6\) | −62885.7 | −0.550261 | ||||||||
\(7\) | −98287.1 | −0.315761 | −0.157881 | − | 0.987458i | \(-0.550466\pi\) | ||||
−0.157881 | + | 0.987458i | \(0.550466\pi\) | |||||||
\(8\) | −771424. | −1.04042 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −5.59349e6 | −1.76882 | ||||||||
\(11\) | −5.83499e6 | −0.993088 | −0.496544 | − | 0.868011i | \(-0.665398\pi\) | ||||
−0.496544 | + | 0.868011i | \(0.665398\pi\) | |||||||
\(12\) | 547261. | 0.0529074 | ||||||||
\(13\) | 2.22899e6 | 0.128079 | 0.0640393 | − | 0.997947i | \(-0.479602\pi\) | ||||
0.0640393 | + | 0.997947i | \(0.479602\pi\) | |||||||
\(14\) | −8.47853e6 | −0.300946 | ||||||||
\(15\) | 4.72700e7 | 1.07150 | ||||||||
\(16\) | −6.03956e7 | −0.899964 | ||||||||
\(17\) | 9.15906e7 | 0.920308 | 0.460154 | − | 0.887839i | \(-0.347794\pi\) | ||||
0.460154 | + | 0.887839i | \(0.347794\pi\) | |||||||
\(18\) | 4.58437e7 | 0.317693 | ||||||||
\(19\) | 1.28544e8 | 0.626835 | 0.313417 | − | 0.949615i | \(-0.398526\pi\) | ||||
0.313417 | + | 0.949615i | \(0.398526\pi\) | |||||||
\(20\) | 4.86771e7 | 0.170071 | ||||||||
\(21\) | 7.16513e7 | 0.182305 | ||||||||
\(22\) | −5.03344e8 | −0.946493 | ||||||||
\(23\) | 1.09713e9 | 1.54536 | 0.772678 | − | 0.634798i | \(-0.218917\pi\) | ||||
0.772678 | + | 0.634798i | \(0.218917\pi\) | |||||||
\(24\) | 5.62368e8 | 0.600686 | ||||||||
\(25\) | 2.98381e9 | 2.44434 | ||||||||
\(26\) | 1.92279e8 | 0.122069 | ||||||||
\(27\) | −3.87420e8 | −0.192450 | ||||||||
\(28\) | 7.37842e7 | 0.0289358 | ||||||||
\(29\) | 5.10901e8 | 0.159496 | 0.0797480 | − | 0.996815i | \(-0.474588\pi\) | ||||
0.0797480 | + | 0.996815i | \(0.474588\pi\) | |||||||
\(30\) | 4.07765e9 | 1.02123 | ||||||||
\(31\) | −2.94741e9 | −0.596470 | −0.298235 | − | 0.954492i | \(-0.596398\pi\) | ||||
−0.298235 | + | 0.954492i | \(0.596398\pi\) | |||||||
\(32\) | 1.10960e9 | 0.182681 | ||||||||
\(33\) | 4.25371e9 | 0.573360 | ||||||||
\(34\) | 7.90088e9 | 0.877127 | ||||||||
\(35\) | 6.37316e9 | 0.586020 | ||||||||
\(36\) | −3.98953e8 | −0.0305461 | ||||||||
\(37\) | 2.19059e10 | 1.40362 | 0.701811 | − | 0.712363i | \(-0.252375\pi\) | ||||
0.701811 | + | 0.712363i | \(0.252375\pi\) | |||||||
\(38\) | 1.10886e10 | 0.597424 | ||||||||
\(39\) | −1.62494e9 | −0.0739462 | ||||||||
\(40\) | 5.00209e10 | 1.93091 | ||||||||
\(41\) | −5.73033e10 | −1.88401 | −0.942007 | − | 0.335592i | \(-0.891064\pi\) | ||||
−0.942007 | + | 0.335592i | \(0.891064\pi\) | |||||||
\(42\) | 6.18085e9 | 0.173751 | ||||||||
\(43\) | −6.16354e10 | −1.48691 | −0.743456 | − | 0.668785i | \(-0.766815\pi\) | ||||
−0.743456 | + | 0.668785i | \(0.766815\pi\) | |||||||
\(44\) | 4.38033e9 | 0.0910049 | ||||||||
\(45\) | −3.44598e10 | −0.618631 | ||||||||
\(46\) | 9.46420e10 | 1.47285 | ||||||||
\(47\) | −4.57698e10 | −0.619360 | −0.309680 | − | 0.950841i | \(-0.600222\pi\) | ||||
−0.309680 | + | 0.950841i | \(0.600222\pi\) | |||||||
\(48\) | 4.40284e10 | 0.519595 | ||||||||
\(49\) | −8.72287e10 | −0.900295 | ||||||||
\(50\) | 2.57393e11 | 2.32965 | ||||||||
\(51\) | −6.67696e10 | −0.531340 | ||||||||
\(52\) | −1.67331e9 | −0.0117369 | ||||||||
\(53\) | 2.65343e11 | 1.64443 | 0.822214 | − | 0.569179i | \(-0.192739\pi\) | ||||
0.822214 | + | 0.569179i | \(0.192739\pi\) | |||||||
\(54\) | −3.34200e10 | −0.183420 | ||||||||
\(55\) | 3.78354e11 | 1.84307 | ||||||||
\(56\) | 7.58210e10 | 0.328524 | ||||||||
\(57\) | −9.37085e10 | −0.361903 | ||||||||
\(58\) | 4.40718e10 | 0.152012 | ||||||||
\(59\) | −4.21805e10 | −0.130189 | ||||||||
\(60\) | −3.54856e10 | −0.0981904 | ||||||||
\(61\) | 1.54568e11 | 0.384129 | 0.192064 | − | 0.981382i | \(-0.438482\pi\) | ||||
0.192064 | + | 0.981382i | \(0.438482\pi\) | |||||||
\(62\) | −2.54252e11 | −0.568484 | ||||||||
\(63\) | −5.22338e10 | −0.105254 | ||||||||
\(64\) | 5.90478e11 | 1.07407 | ||||||||
\(65\) | −1.44533e11 | −0.237700 | ||||||||
\(66\) | 3.66938e11 | 0.546458 | ||||||||
\(67\) | 2.77636e11 | 0.374964 | 0.187482 | − | 0.982268i | \(-0.439967\pi\) | ||||
0.187482 | + | 0.982268i | \(0.439967\pi\) | |||||||
\(68\) | −6.87571e10 | −0.0843354 | ||||||||
\(69\) | −7.99810e11 | −0.892211 | ||||||||
\(70\) | 5.49767e11 | 0.558524 | ||||||||
\(71\) | 8.61174e11 | 0.797832 | 0.398916 | − | 0.916987i | \(-0.369386\pi\) | ||||
0.398916 | + | 0.916987i | \(0.369386\pi\) | |||||||
\(72\) | −4.09966e11 | −0.346806 | ||||||||
\(73\) | −1.38364e12 | −1.07010 | −0.535050 | − | 0.844820i | \(-0.679707\pi\) | ||||
−0.535050 | + | 0.844820i | \(0.679707\pi\) | |||||||
\(74\) | 1.88967e12 | 1.33776 | ||||||||
\(75\) | −2.17520e12 | −1.41124 | ||||||||
\(76\) | −9.64980e10 | −0.0574420 | ||||||||
\(77\) | 5.73504e11 | 0.313579 | ||||||||
\(78\) | −1.40172e11 | −0.0704767 | ||||||||
\(79\) | 1.78937e12 | 0.828179 | 0.414090 | − | 0.910236i | \(-0.364100\pi\) | ||||
0.414090 | + | 0.910236i | \(0.364100\pi\) | |||||||
\(80\) | 3.91619e12 | 1.67024 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −4.94315e12 | −1.79562 | ||||||||
\(83\) | −3.09290e12 | −1.03839 | −0.519193 | − | 0.854657i | \(-0.673767\pi\) | ||||
−0.519193 | + | 0.854657i | \(0.673767\pi\) | |||||||
\(84\) | −5.37886e10 | −0.0167061 | ||||||||
\(85\) | −5.93894e12 | −1.70799 | ||||||||
\(86\) | −5.31685e12 | −1.41715 | ||||||||
\(87\) | −3.72447e11 | −0.0920850 | ||||||||
\(88\) | 4.50125e12 | 1.03323 | ||||||||
\(89\) | 3.36119e12 | 0.716899 | 0.358449 | − | 0.933549i | \(-0.383306\pi\) | ||||
0.358449 | + | 0.933549i | \(0.383306\pi\) | |||||||
\(90\) | −2.97261e12 | −0.589605 | ||||||||
\(91\) | −2.19081e11 | −0.0404423 | ||||||||
\(92\) | −8.23618e11 | −0.141614 | ||||||||
\(93\) | 2.14866e12 | 0.344372 | ||||||||
\(94\) | −3.94824e12 | −0.590299 | ||||||||
\(95\) | −8.33508e12 | −1.16334 | ||||||||
\(96\) | −8.08901e11 | −0.105471 | ||||||||
\(97\) | 4.52881e12 | 0.552036 | 0.276018 | − | 0.961152i | \(-0.410985\pi\) | ||||
0.276018 | + | 0.961152i | \(0.410985\pi\) | |||||||
\(98\) | −7.52460e12 | −0.858053 | ||||||||
\(99\) | −3.10095e12 | −0.331029 | ||||||||
\(100\) | −2.23995e12 | −0.223995 | ||||||||
\(101\) | 8.28016e12 | 0.776157 | 0.388079 | − | 0.921626i | \(-0.373139\pi\) | ||||
0.388079 | + | 0.921626i | \(0.373139\pi\) | |||||||
\(102\) | −5.75974e12 | −0.506410 | ||||||||
\(103\) | 6.20956e12 | 0.512412 | 0.256206 | − | 0.966622i | \(-0.417527\pi\) | ||||
0.256206 | + | 0.966622i | \(0.417527\pi\) | |||||||
\(104\) | −1.71950e12 | −0.133255 | ||||||||
\(105\) | −4.64603e12 | −0.338339 | ||||||||
\(106\) | 2.28893e13 | 1.56727 | ||||||||
\(107\) | 4.94526e12 | 0.318563 | 0.159281 | − | 0.987233i | \(-0.449082\pi\) | ||||
0.159281 | + | 0.987233i | \(0.449082\pi\) | |||||||
\(108\) | 2.90837e11 | 0.0176358 | ||||||||
\(109\) | 4.50602e12 | 0.257348 | 0.128674 | − | 0.991687i | \(-0.458928\pi\) | ||||
0.128674 | + | 0.991687i | \(0.458928\pi\) | |||||||
\(110\) | 3.26379e13 | 1.75659 | ||||||||
\(111\) | −1.59694e13 | −0.810381 | ||||||||
\(112\) | 5.93610e12 | 0.284174 | ||||||||
\(113\) | 9.61297e12 | 0.434358 | 0.217179 | − | 0.976132i | \(-0.430314\pi\) | ||||
0.217179 | + | 0.976132i | \(0.430314\pi\) | |||||||
\(114\) | −8.08357e12 | −0.344923 | ||||||||
\(115\) | −7.11406e13 | −2.86802 | ||||||||
\(116\) | −3.83533e11 | −0.0146159 | ||||||||
\(117\) | 1.18458e12 | 0.0426929 | ||||||||
\(118\) | −3.63862e12 | −0.124080 | ||||||||
\(119\) | −9.00218e12 | −0.290598 | ||||||||
\(120\) | −3.64652e13 | −1.11481 | ||||||||
\(121\) | −4.75576e11 | −0.0137757 | ||||||||
\(122\) | 1.33335e13 | 0.366105 | ||||||||
\(123\) | 4.17741e13 | 1.08774 | ||||||||
\(124\) | 2.21262e12 | 0.0546595 | ||||||||
\(125\) | −1.14324e14 | −2.68054 | ||||||||
\(126\) | −4.50584e12 | −0.100315 | ||||||||
\(127\) | −8.14494e13 | −1.72252 | −0.861259 | − | 0.508167i | \(-0.830323\pi\) | ||||
−0.861259 | + | 0.508167i | \(0.830323\pi\) | |||||||
\(128\) | 4.18465e13 | 0.840997 | ||||||||
\(129\) | 4.49322e13 | 0.858469 | ||||||||
\(130\) | −1.24678e13 | −0.226547 | ||||||||
\(131\) | 6.35655e13 | 1.09890 | 0.549450 | − | 0.835527i | \(-0.314837\pi\) | ||||
0.549450 | + | 0.835527i | \(0.314837\pi\) | |||||||
\(132\) | −3.19326e12 | −0.0525417 | ||||||||
\(133\) | −1.26342e13 | −0.197930 | ||||||||
\(134\) | 2.39497e13 | 0.357370 | ||||||||
\(135\) | 2.51212e13 | 0.357167 | ||||||||
\(136\) | −7.06552e13 | −0.957506 | ||||||||
\(137\) | 8.45302e13 | 1.09227 | 0.546133 | − | 0.837699i | \(-0.316099\pi\) | ||||
0.546133 | + | 0.837699i | \(0.316099\pi\) | |||||||
\(138\) | −6.89940e13 | −0.850349 | ||||||||
\(139\) | −1.58702e12 | −0.0186632 | −0.00933159 | − | 0.999956i | \(-0.502970\pi\) | ||||
−0.00933159 | + | 0.999956i | \(0.502970\pi\) | |||||||
\(140\) | −4.78433e12 | −0.0537018 | ||||||||
\(141\) | 3.33662e13 | 0.357587 | ||||||||
\(142\) | 7.42874e13 | 0.760398 | ||||||||
\(143\) | −1.30062e13 | −0.127193 | ||||||||
\(144\) | −3.20967e13 | −0.299988 | ||||||||
\(145\) | −3.31280e13 | −0.296007 | ||||||||
\(146\) | −1.19357e14 | −1.01989 | ||||||||
\(147\) | 6.35897e13 | 0.519785 | ||||||||
\(148\) | −1.64448e13 | −0.128625 | ||||||||
\(149\) | −7.75642e12 | −0.0580698 | −0.0290349 | − | 0.999578i | \(-0.509243\pi\) | ||||
−0.0290349 | + | 0.999578i | \(0.509243\pi\) | |||||||
\(150\) | −1.87639e14 | −1.34503 | ||||||||
\(151\) | −2.79033e14 | −1.91560 | −0.957802 | − | 0.287429i | \(-0.907199\pi\) | ||||
−0.957802 | + | 0.287429i | \(0.907199\pi\) | |||||||
\(152\) | −9.91618e13 | −0.652171 | ||||||||
\(153\) | 4.86750e13 | 0.306769 | ||||||||
\(154\) | 4.94722e13 | 0.298866 | ||||||||
\(155\) | 1.91116e14 | 1.10699 | ||||||||
\(156\) | 1.21984e12 | 0.00677630 | ||||||||
\(157\) | 3.05432e13 | 0.162767 | 0.0813837 | − | 0.996683i | \(-0.474066\pi\) | ||||
0.0813837 | + | 0.996683i | \(0.474066\pi\) | |||||||
\(158\) | 1.54356e14 | 0.789321 | ||||||||
\(159\) | −1.93435e14 | −0.949411 | ||||||||
\(160\) | −7.19492e13 | −0.339036 | ||||||||
\(161\) | −1.07834e14 | −0.487964 | ||||||||
\(162\) | 2.43632e13 | 0.105898 | ||||||||
\(163\) | −8.07722e13 | −0.337320 | −0.168660 | − | 0.985674i | \(-0.553944\pi\) | ||||
−0.168660 | + | 0.985674i | \(0.553944\pi\) | |||||||
\(164\) | 4.30176e13 | 0.172648 | ||||||||
\(165\) | −2.75820e14 | −1.06409 | ||||||||
\(166\) | −2.66803e14 | −0.989665 | ||||||||
\(167\) | −7.80333e13 | −0.278370 | −0.139185 | − | 0.990266i | \(-0.544448\pi\) | ||||
−0.139185 | + | 0.990266i | \(0.544448\pi\) | |||||||
\(168\) | −5.52735e13 | −0.189674 | ||||||||
\(169\) | −2.97907e14 | −0.983596 | ||||||||
\(170\) | −5.12311e14 | −1.62785 | ||||||||
\(171\) | 6.83135e13 | 0.208945 | ||||||||
\(172\) | 4.62697e13 | 0.136258 | ||||||||
\(173\) | 6.55147e14 | 1.85797 | 0.928986 | − | 0.370116i | \(-0.120682\pi\) | ||||
0.928986 | + | 0.370116i | \(0.120682\pi\) | |||||||
\(174\) | −3.21284e13 | −0.0877644 | ||||||||
\(175\) | −2.93270e14 | −0.771829 | ||||||||
\(176\) | 3.52408e14 | 0.893744 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 2.89946e14 | 0.683262 | ||||||||
\(179\) | −5.41032e14 | −1.22936 | −0.614678 | − | 0.788778i | \(-0.710714\pi\) | ||||
−0.614678 | + | 0.788778i | \(0.710714\pi\) | |||||||
\(180\) | 2.58690e13 | 0.0566903 | ||||||||
\(181\) | 2.37050e14 | 0.501106 | 0.250553 | − | 0.968103i | \(-0.419388\pi\) | ||||
0.250553 | + | 0.968103i | \(0.419388\pi\) | |||||||
\(182\) | −1.88986e13 | −0.0385448 | ||||||||
\(183\) | −1.12680e14 | −0.221777 | ||||||||
\(184\) | −8.46355e14 | −1.60782 | ||||||||
\(185\) | −1.42043e15 | −2.60497 | ||||||||
\(186\) | 1.85350e14 | 0.328214 | ||||||||
\(187\) | −5.34431e14 | −0.913947 | ||||||||
\(188\) | 3.43594e13 | 0.0567570 | ||||||||
\(189\) | 3.80784e13 | 0.0607683 | ||||||||
\(190\) | −7.19008e14 | −1.10875 | ||||||||
\(191\) | 1.24471e15 | 1.85503 | 0.927514 | − | 0.373788i | \(-0.121941\pi\) | ||||
0.927514 | + | 0.373788i | \(0.121941\pi\) | |||||||
\(192\) | −4.30459e14 | −0.620117 | ||||||||
\(193\) | 3.55205e13 | 0.0494717 | 0.0247358 | − | 0.999694i | \(-0.492126\pi\) | ||||
0.0247358 | + | 0.999694i | \(0.492126\pi\) | |||||||
\(194\) | 3.90668e14 | 0.526135 | ||||||||
\(195\) | 1.05364e14 | 0.137236 | ||||||||
\(196\) | 6.54826e13 | 0.0825014 | ||||||||
\(197\) | 8.59190e14 | 1.04727 | 0.523635 | − | 0.851943i | \(-0.324576\pi\) | ||||
0.523635 | + | 0.851943i | \(0.324576\pi\) | |||||||
\(198\) | −2.67498e14 | −0.315498 | ||||||||
\(199\) | −7.01662e14 | −0.800909 | −0.400454 | − | 0.916317i | \(-0.631148\pi\) | ||||
−0.400454 | + | 0.916317i | \(0.631148\pi\) | |||||||
\(200\) | −2.30179e15 | −2.54314 | ||||||||
\(201\) | −2.02396e14 | −0.216485 | ||||||||
\(202\) | 7.14271e14 | 0.739740 | ||||||||
\(203\) | −5.02149e13 | −0.0503627 | ||||||||
\(204\) | 5.01240e13 | 0.0486911 | ||||||||
\(205\) | 3.71567e15 | 3.49653 | ||||||||
\(206\) | 5.35655e14 | 0.488370 | ||||||||
\(207\) | 5.83062e14 | 0.515119 | ||||||||
\(208\) | −1.34621e14 | −0.115266 | ||||||||
\(209\) | −7.50053e14 | −0.622502 | ||||||||
\(210\) | −4.00780e14 | −0.322464 | ||||||||
\(211\) | 1.48001e15 | 1.15459 | 0.577296 | − | 0.816535i | \(-0.304108\pi\) | ||||
0.577296 | + | 0.816535i | \(0.304108\pi\) | |||||||
\(212\) | −1.99193e14 | −0.150692 | ||||||||
\(213\) | −6.27796e14 | −0.460629 | ||||||||
\(214\) | 4.26593e14 | 0.303616 | ||||||||
\(215\) | 3.99658e15 | 2.75955 | ||||||||
\(216\) | 2.98865e14 | 0.200229 | ||||||||
\(217\) | 2.89692e14 | 0.188342 | ||||||||
\(218\) | 3.88703e14 | 0.245273 | ||||||||
\(219\) | 1.00867e15 | 0.617823 | ||||||||
\(220\) | −2.84031e14 | −0.168895 | ||||||||
\(221\) | 2.04155e14 | 0.117872 | ||||||||
\(222\) | −1.37757e15 | −0.772358 | ||||||||
\(223\) | 1.85860e15 | 1.01206 | 0.506029 | − | 0.862516i | \(-0.331113\pi\) | ||||
0.506029 | + | 0.862516i | \(0.331113\pi\) | |||||||
\(224\) | −1.09060e14 | −0.0576835 | ||||||||
\(225\) | 1.58572e15 | 0.814780 | ||||||||
\(226\) | 8.29243e14 | 0.413978 | ||||||||
\(227\) | −3.09502e15 | −1.50140 | −0.750698 | − | 0.660645i | \(-0.770283\pi\) | ||||
−0.750698 | + | 0.660645i | \(0.770283\pi\) | |||||||
\(228\) | 7.03470e13 | 0.0331642 | ||||||||
\(229\) | −8.23402e13 | −0.0377295 | −0.0188648 | − | 0.999822i | \(-0.506005\pi\) | ||||
−0.0188648 | + | 0.999822i | \(0.506005\pi\) | |||||||
\(230\) | −6.13680e15 | −2.73345 | ||||||||
\(231\) | −4.18085e14 | −0.181045 | ||||||||
\(232\) | −3.94121e14 | −0.165943 | ||||||||
\(233\) | 2.54213e15 | 1.04084 | 0.520421 | − | 0.853910i | \(-0.325775\pi\) | ||||
0.520421 | + | 0.853910i | \(0.325775\pi\) | |||||||
\(234\) | 1.02185e14 | 0.0406897 | ||||||||
\(235\) | 2.96782e15 | 1.14947 | ||||||||
\(236\) | 3.16649e13 | 0.0119303 | ||||||||
\(237\) | −1.30445e15 | −0.478149 | ||||||||
\(238\) | −7.76554e14 | −0.276963 | ||||||||
\(239\) | 1.25403e15 | 0.435233 | 0.217616 | − | 0.976034i | \(-0.430172\pi\) | ||||
0.217616 | + | 0.976034i | \(0.430172\pi\) | |||||||
\(240\) | −2.85490e15 | −0.964312 | ||||||||
\(241\) | −3.17662e15 | −1.04437 | −0.522185 | − | 0.852832i | \(-0.674883\pi\) | ||||
−0.522185 | + | 0.852832i | \(0.674883\pi\) | |||||||
\(242\) | −4.10246e13 | −0.0131294 | ||||||||
\(243\) | −2.05891e14 | −0.0641500 | ||||||||
\(244\) | −1.16035e14 | −0.0352009 | ||||||||
\(245\) | 5.65610e15 | 1.67085 | ||||||||
\(246\) | 3.60356e15 | 1.03670 | ||||||||
\(247\) | 2.86523e14 | 0.0802841 | ||||||||
\(248\) | 2.27370e15 | 0.620579 | ||||||||
\(249\) | 2.25473e15 | 0.599513 | ||||||||
\(250\) | −9.86194e15 | −2.55477 | ||||||||
\(251\) | −5.28279e15 | −1.33347 | −0.666736 | − | 0.745294i | \(-0.732309\pi\) | ||||
−0.666736 | + | 0.745294i | \(0.732309\pi\) | |||||||
\(252\) | 3.92119e13 | 0.00964528 | ||||||||
\(253\) | −6.40176e15 | −1.53467 | ||||||||
\(254\) | −7.02607e15 | −1.64170 | ||||||||
\(255\) | 4.32949e15 | 0.986110 | ||||||||
\(256\) | −1.22739e15 | −0.272536 | ||||||||
\(257\) | −4.27042e15 | −0.924497 | −0.462249 | − | 0.886750i | \(-0.652957\pi\) | ||||
−0.462249 | + | 0.886750i | \(0.652957\pi\) | |||||||
\(258\) | 3.87599e15 | 0.818190 | ||||||||
\(259\) | −2.15307e15 | −0.443210 | ||||||||
\(260\) | 1.08501e14 | 0.0217824 | ||||||||
\(261\) | 2.71514e14 | 0.0531653 | ||||||||
\(262\) | 5.48335e15 | 1.04734 | ||||||||
\(263\) | −7.59894e14 | −0.141593 | −0.0707963 | − | 0.997491i | \(-0.522554\pi\) | ||||
−0.0707963 | + | 0.997491i | \(0.522554\pi\) | |||||||
\(264\) | −3.28141e15 | −0.596534 | ||||||||
\(265\) | −1.72054e16 | −3.05188 | ||||||||
\(266\) | −1.08986e15 | −0.188643 | ||||||||
\(267\) | −2.45031e15 | −0.413902 | ||||||||
\(268\) | −2.08421e14 | −0.0343610 | ||||||||
\(269\) | 2.22489e15 | 0.358029 | 0.179015 | − | 0.983846i | \(-0.442709\pi\) | ||||
0.179015 | + | 0.983846i | \(0.442709\pi\) | |||||||
\(270\) | 2.16703e15 | 0.340409 | ||||||||
\(271\) | 1.64080e15 | 0.251626 | 0.125813 | − | 0.992054i | \(-0.459846\pi\) | ||||
0.125813 | + | 0.992054i | \(0.459846\pi\) | |||||||
\(272\) | −5.53167e15 | −0.828244 | ||||||||
\(273\) | 1.59710e14 | 0.0233494 | ||||||||
\(274\) | 7.29182e15 | 1.04102 | ||||||||
\(275\) | −1.74105e16 | −2.42745 | ||||||||
\(276\) | 6.00418e14 | 0.0817607 | ||||||||
\(277\) | −3.74169e15 | −0.497679 | −0.248839 | − | 0.968545i | \(-0.580049\pi\) | ||||
−0.248839 | + | 0.968545i | \(0.580049\pi\) | |||||||
\(278\) | −1.36901e14 | −0.0177875 | ||||||||
\(279\) | −1.56637e15 | −0.198823 | ||||||||
\(280\) | −4.91640e15 | −0.609706 | ||||||||
\(281\) | −1.35510e15 | −0.164202 | −0.0821012 | − | 0.996624i | \(-0.526163\pi\) | ||||
−0.0821012 | + | 0.996624i | \(0.526163\pi\) | |||||||
\(282\) | 2.87827e15 | 0.340810 | ||||||||
\(283\) | 1.51639e16 | 1.75468 | 0.877341 | − | 0.479868i | \(-0.159315\pi\) | ||||
0.877341 | + | 0.479868i | \(0.159315\pi\) | |||||||
\(284\) | −6.46484e14 | −0.0731120 | ||||||||
\(285\) | 6.07627e15 | 0.671654 | ||||||||
\(286\) | −1.12195e15 | −0.121226 | ||||||||
\(287\) | 5.63217e15 | 0.594899 | ||||||||
\(288\) | 5.89689e14 | 0.0608936 | ||||||||
\(289\) | −1.51573e15 | −0.153033 | ||||||||
\(290\) | −2.85772e15 | −0.282119 | ||||||||
\(291\) | −3.30150e15 | −0.318718 | ||||||||
\(292\) | 1.03870e15 | 0.0980621 | ||||||||
\(293\) | −7.97683e15 | −0.736530 | −0.368265 | − | 0.929721i | \(-0.620048\pi\) | ||||
−0.368265 | + | 0.929721i | \(0.620048\pi\) | |||||||
\(294\) | 5.48544e15 | 0.495397 | ||||||||
\(295\) | 2.73508e15 | 0.241617 | ||||||||
\(296\) | −1.68987e16 | −1.46035 | ||||||||
\(297\) | 2.26060e15 | 0.191120 | ||||||||
\(298\) | −6.69091e14 | −0.0553452 | ||||||||
\(299\) | 2.44550e15 | 0.197927 | ||||||||
\(300\) | 1.63292e15 | 0.129324 | ||||||||
\(301\) | 6.05796e15 | 0.469510 | ||||||||
\(302\) | −2.40702e16 | −1.82572 | ||||||||
\(303\) | −6.03624e15 | −0.448115 | ||||||||
\(304\) | −7.76348e15 | −0.564129 | ||||||||
\(305\) | −1.00226e16 | −0.712902 | ||||||||
\(306\) | 4.19885e15 | 0.292376 | ||||||||
\(307\) | −1.70874e16 | −1.16487 | −0.582433 | − | 0.812878i | \(-0.697899\pi\) | ||||
−0.582433 | + | 0.812878i | \(0.697899\pi\) | |||||||
\(308\) | −4.30530e14 | −0.0287358 | ||||||||
\(309\) | −4.52677e15 | −0.295841 | ||||||||
\(310\) | 1.64863e16 | 1.05505 | ||||||||
\(311\) | −3.12441e16 | −1.95806 | −0.979029 | − | 0.203722i | \(-0.934696\pi\) | ||||
−0.979029 | + | 0.203722i | \(0.934696\pi\) | |||||||
\(312\) | 1.25351e15 | 0.0769351 | ||||||||
\(313\) | 2.72138e16 | 1.63588 | 0.817939 | − | 0.575304i | \(-0.195116\pi\) | ||||
0.817939 | + | 0.575304i | \(0.195116\pi\) | |||||||
\(314\) | 2.63475e15 | 0.155130 | ||||||||
\(315\) | 3.38696e15 | 0.195340 | ||||||||
\(316\) | −1.34328e15 | −0.0758929 | ||||||||
\(317\) | −1.58624e16 | −0.877977 | −0.438989 | − | 0.898493i | \(-0.644663\pi\) | ||||
−0.438989 | + | 0.898493i | \(0.644663\pi\) | |||||||
\(318\) | −1.66863e16 | −0.904864 | ||||||||
\(319\) | −2.98110e15 | −0.158394 | ||||||||
\(320\) | −3.82879e16 | −1.99337 | ||||||||
\(321\) | −3.60510e15 | −0.183922 | ||||||||
\(322\) | −9.30208e15 | −0.465069 | ||||||||
\(323\) | 1.17734e16 | 0.576881 | ||||||||
\(324\) | −2.12020e14 | −0.0101820 | ||||||||
\(325\) | 6.65090e15 | 0.313068 | ||||||||
\(326\) | −6.96765e15 | −0.321493 | ||||||||
\(327\) | −3.28489e15 | −0.148580 | ||||||||
\(328\) | 4.42051e16 | 1.96016 | ||||||||
\(329\) | 4.49858e15 | 0.195570 | ||||||||
\(330\) | −2.37931e16 | −1.01417 | ||||||||
\(331\) | −1.38811e16 | −0.580153 | −0.290076 | − | 0.957003i | \(-0.593681\pi\) | ||||
−0.290076 | + | 0.957003i | \(0.593681\pi\) | |||||||
\(332\) | 2.32185e15 | 0.0951559 | ||||||||
\(333\) | 1.16417e16 | 0.467874 | ||||||||
\(334\) | −6.73138e15 | −0.265309 | ||||||||
\(335\) | −1.80025e16 | −0.695893 | ||||||||
\(336\) | −4.32742e15 | −0.164068 | ||||||||
\(337\) | −4.71553e16 | −1.75362 | −0.876811 | − | 0.480835i | \(-0.840334\pi\) | ||||
−0.876811 | + | 0.480835i | \(0.840334\pi\) | |||||||
\(338\) | −2.56983e16 | −0.937446 | ||||||||
\(339\) | −7.00786e15 | −0.250777 | ||||||||
\(340\) | 4.45837e15 | 0.156518 | ||||||||
\(341\) | 1.71981e16 | 0.592348 | ||||||||
\(342\) | 5.89292e15 | 0.199141 | ||||||||
\(343\) | 1.80964e16 | 0.600040 | ||||||||
\(344\) | 4.75470e16 | 1.54701 | ||||||||
\(345\) | 5.18615e16 | 1.65585 | ||||||||
\(346\) | 5.65149e16 | 1.77080 | ||||||||
\(347\) | −4.17216e15 | −0.128298 | −0.0641489 | − | 0.997940i | \(-0.520433\pi\) | ||||
−0.0641489 | + | 0.997940i | \(0.520433\pi\) | |||||||
\(348\) | 2.79596e14 | 0.00843851 | ||||||||
\(349\) | −5.65752e16 | −1.67595 | −0.837975 | − | 0.545709i | \(-0.816261\pi\) | ||||
−0.837975 | + | 0.545709i | \(0.816261\pi\) | |||||||
\(350\) | −2.52984e16 | −0.735615 | ||||||||
\(351\) | −8.63557e14 | −0.0246487 | ||||||||
\(352\) | −6.47452e15 | −0.181418 | ||||||||
\(353\) | 4.63052e16 | 1.27378 | 0.636890 | − | 0.770955i | \(-0.280221\pi\) | ||||
0.636890 | + | 0.770955i | \(0.280221\pi\) | |||||||
\(354\) | 2.65255e15 | 0.0716379 | ||||||||
\(355\) | −5.58405e16 | −1.48069 | ||||||||
\(356\) | −2.52325e15 | −0.0656953 | ||||||||
\(357\) | 6.56259e15 | 0.167777 | ||||||||
\(358\) | −4.66710e16 | −1.17168 | ||||||||
\(359\) | 4.08485e16 | 1.00708 | 0.503538 | − | 0.863973i | \(-0.332031\pi\) | ||||
0.503538 | + | 0.863973i | \(0.332031\pi\) | |||||||
\(360\) | 2.65831e16 | 0.643635 | ||||||||
\(361\) | −2.55295e16 | −0.607078 | ||||||||
\(362\) | 2.04487e16 | 0.477594 | ||||||||
\(363\) | 3.46695e14 | 0.00795343 | ||||||||
\(364\) | 1.64464e14 | 0.00370606 | ||||||||
\(365\) | 8.97183e16 | 1.98599 | ||||||||
\(366\) | −9.72014e15 | −0.211371 | ||||||||
\(367\) | 8.38920e16 | 1.79222 | 0.896110 | − | 0.443832i | \(-0.146381\pi\) | ||||
0.896110 | + | 0.443832i | \(0.146381\pi\) | |||||||
\(368\) | −6.62620e16 | −1.39076 | ||||||||
\(369\) | −3.04533e16 | −0.628005 | ||||||||
\(370\) | −1.22530e17 | −2.48275 | ||||||||
\(371\) | −2.60798e16 | −0.519247 | ||||||||
\(372\) | −1.61300e15 | −0.0315577 | ||||||||
\(373\) | 5.71890e16 | 1.09953 | 0.549763 | − | 0.835321i | \(-0.314718\pi\) | ||||
0.549763 | + | 0.835321i | \(0.314718\pi\) | |||||||
\(374\) | −4.61016e16 | −0.871065 | ||||||||
\(375\) | 8.33423e16 | 1.54761 | ||||||||
\(376\) | 3.53079e16 | 0.644393 | ||||||||
\(377\) | 1.13879e15 | 0.0204280 | ||||||||
\(378\) | 3.28476e15 | 0.0579171 | ||||||||
\(379\) | −5.17150e16 | −0.896318 | −0.448159 | − | 0.893954i | \(-0.647920\pi\) | ||||
−0.448159 | + | 0.893954i | \(0.647920\pi\) | |||||||
\(380\) | 6.25715e15 | 0.106606 | ||||||||
\(381\) | 5.93766e16 | 0.994496 | ||||||||
\(382\) | 1.07372e17 | 1.76799 | ||||||||
\(383\) | −5.94733e16 | −0.962787 | −0.481394 | − | 0.876505i | \(-0.659869\pi\) | ||||
−0.481394 | + | 0.876505i | \(0.659869\pi\) | |||||||
\(384\) | −3.05061e16 | −0.485550 | ||||||||
\(385\) | −3.71873e16 | −0.581969 | ||||||||
\(386\) | 3.06410e15 | 0.0471504 | ||||||||
\(387\) | −3.27556e16 | −0.495637 | ||||||||
\(388\) | −3.39978e15 | −0.0505876 | ||||||||
\(389\) | −7.67585e15 | −0.112319 | −0.0561596 | − | 0.998422i | \(-0.517886\pi\) | ||||
−0.0561596 | + | 0.998422i | \(0.517886\pi\) | |||||||
\(390\) | 9.08905e15 | 0.130797 | ||||||||
\(391\) | 1.00487e17 | 1.42220 | ||||||||
\(392\) | 6.72903e16 | 0.936683 | ||||||||
\(393\) | −4.63393e16 | −0.634450 | ||||||||
\(394\) | 7.41163e16 | 0.998132 | ||||||||
\(395\) | −1.16027e17 | −1.53701 | ||||||||
\(396\) | 2.32789e15 | 0.0303350 | ||||||||
\(397\) | 6.18010e16 | 0.792241 | 0.396121 | − | 0.918199i | \(-0.370356\pi\) | ||||
0.396121 | + | 0.918199i | \(0.370356\pi\) | |||||||
\(398\) | −6.05275e16 | −0.763330 | ||||||||
\(399\) | 9.21033e15 | 0.114275 | ||||||||
\(400\) | −1.80209e17 | −2.19982 | ||||||||
\(401\) | 5.53128e16 | 0.664335 | 0.332167 | − | 0.943220i | \(-0.392220\pi\) | ||||
0.332167 | + | 0.943220i | \(0.392220\pi\) | |||||||
\(402\) | −1.74593e16 | −0.206328 | ||||||||
\(403\) | −6.56974e15 | −0.0763951 | ||||||||
\(404\) | −6.21592e15 | −0.0711257 | ||||||||
\(405\) | −1.83134e16 | −0.206210 | ||||||||
\(406\) | −4.33169e15 | −0.0479997 | ||||||||
\(407\) | −1.27821e17 | −1.39392 | ||||||||
\(408\) | 5.15076e16 | 0.552816 | ||||||||
\(409\) | −4.58801e16 | −0.484645 | −0.242322 | − | 0.970196i | \(-0.577909\pi\) | ||||
−0.242322 | + | 0.970196i | \(0.577909\pi\) | |||||||
\(410\) | 3.20525e17 | 3.33247 | ||||||||
\(411\) | −6.16225e16 | −0.630620 | ||||||||
\(412\) | −4.66152e15 | −0.0469565 | ||||||||
\(413\) | 4.14580e15 | 0.0411086 | ||||||||
\(414\) | 5.02966e16 | 0.490949 | ||||||||
\(415\) | 2.00551e17 | 1.92713 | ||||||||
\(416\) | 2.47330e15 | 0.0233975 | ||||||||
\(417\) | 1.15694e15 | 0.0107752 | ||||||||
\(418\) | −6.47018e16 | −0.593294 | ||||||||
\(419\) | 7.97031e16 | 0.719588 | 0.359794 | − | 0.933032i | \(-0.382847\pi\) | ||||
0.359794 | + | 0.933032i | \(0.382847\pi\) | |||||||
\(420\) | 3.48778e15 | 0.0310048 | ||||||||
\(421\) | −6.83289e16 | −0.598096 | −0.299048 | − | 0.954238i | \(-0.596669\pi\) | ||||
−0.299048 | + | 0.954238i | \(0.596669\pi\) | |||||||
\(422\) | 1.27670e17 | 1.10042 | ||||||||
\(423\) | −2.43239e16 | −0.206453 | ||||||||
\(424\) | −2.04692e17 | −1.71089 | ||||||||
\(425\) | 2.73290e17 | 2.24955 | ||||||||
\(426\) | −5.41555e16 | −0.439016 | ||||||||
\(427\) | −1.51921e16 | −0.121293 | ||||||||
\(428\) | −3.71241e15 | −0.0291925 | ||||||||
\(429\) | 9.48149e15 | 0.0734351 | ||||||||
\(430\) | 3.44757e17 | 2.63007 | ||||||||
\(431\) | −2.57213e16 | −0.193281 | −0.0966407 | − | 0.995319i | \(-0.530810\pi\) | ||||
−0.0966407 | + | 0.995319i | \(0.530810\pi\) | |||||||
\(432\) | 2.33985e16 | 0.173198 | ||||||||
\(433\) | 5.45317e16 | 0.397629 | 0.198814 | − | 0.980037i | \(-0.436291\pi\) | ||||
0.198814 | + | 0.980037i | \(0.436291\pi\) | |||||||
\(434\) | 2.49897e16 | 0.179505 | ||||||||
\(435\) | 2.41503e16 | 0.170900 | ||||||||
\(436\) | −3.38267e15 | −0.0235829 | ||||||||
\(437\) | 1.41030e17 | 0.968683 | ||||||||
\(438\) | 8.70112e16 | 0.588835 | ||||||||
\(439\) | −2.08605e17 | −1.39093 | −0.695466 | − | 0.718559i | \(-0.744802\pi\) | ||||
−0.695466 | + | 0.718559i | \(0.744802\pi\) | |||||||
\(440\) | −2.91871e17 | −1.91756 | ||||||||
\(441\) | −4.63569e16 | −0.300098 | ||||||||
\(442\) | 1.76110e16 | 0.112341 | ||||||||
\(443\) | 3.67195e16 | 0.230819 | 0.115410 | − | 0.993318i | \(-0.463182\pi\) | ||||
0.115410 | + | 0.993318i | \(0.463182\pi\) | |||||||
\(444\) | 1.19882e16 | 0.0742619 | ||||||||
\(445\) | −2.17947e17 | −1.33049 | ||||||||
\(446\) | 1.60329e17 | 0.964573 | ||||||||
\(447\) | 5.65443e15 | 0.0335266 | ||||||||
\(448\) | −5.80364e16 | −0.339151 | ||||||||
\(449\) | 1.05036e17 | 0.604973 | 0.302487 | − | 0.953154i | \(-0.402183\pi\) | ||||
0.302487 | + | 0.953154i | \(0.402183\pi\) | |||||||
\(450\) | 1.36789e17 | 0.776551 | ||||||||
\(451\) | 3.34364e17 | 1.87099 | ||||||||
\(452\) | −7.21646e15 | −0.0398038 | ||||||||
\(453\) | 2.03415e17 | 1.10597 | ||||||||
\(454\) | −2.66986e17 | −1.43095 | ||||||||
\(455\) | 1.42057e16 | 0.0750566 | ||||||||
\(456\) | 7.22890e16 | 0.376531 | ||||||||
\(457\) | 3.14990e17 | 1.61749 | 0.808746 | − | 0.588159i | \(-0.200147\pi\) | ||||
0.808746 | + | 0.588159i | \(0.200147\pi\) | |||||||
\(458\) | −7.10291e15 | −0.0359592 | ||||||||
\(459\) | −3.54841e16 | −0.177113 | ||||||||
\(460\) | 5.34053e16 | 0.262820 | ||||||||
\(461\) | −9.87682e16 | −0.479249 | −0.239624 | − | 0.970866i | \(-0.577024\pi\) | ||||
−0.239624 | + | 0.970866i | \(0.577024\pi\) | |||||||
\(462\) | −3.60652e16 | −0.172550 | ||||||||
\(463\) | 3.25645e17 | 1.53627 | 0.768135 | − | 0.640288i | \(-0.221185\pi\) | ||||
0.768135 | + | 0.640288i | \(0.221185\pi\) | |||||||
\(464\) | −3.08561e16 | −0.143541 | ||||||||
\(465\) | −1.39324e17 | −0.639118 | ||||||||
\(466\) | 2.19292e17 | 0.992006 | ||||||||
\(467\) | 1.64843e17 | 0.735377 | 0.367688 | − | 0.929949i | \(-0.380149\pi\) | ||||
0.367688 | + | 0.929949i | \(0.380149\pi\) | |||||||
\(468\) | −8.89263e14 | −0.00391230 | ||||||||
\(469\) | −2.72880e16 | −0.118399 | ||||||||
\(470\) | 2.56013e17 | 1.09553 | ||||||||
\(471\) | −2.22660e16 | −0.0939738 | ||||||||
\(472\) | 3.25391e16 | 0.135451 | ||||||||
\(473\) | 3.59642e17 | 1.47664 | ||||||||
\(474\) | −1.12526e17 | −0.455715 | ||||||||
\(475\) | 3.83551e17 | 1.53220 | ||||||||
\(476\) | 6.75794e15 | 0.0266299 | ||||||||
\(477\) | 1.41014e17 | 0.548142 | ||||||||
\(478\) | 1.08176e17 | 0.414811 | ||||||||
\(479\) | −2.98017e17 | −1.12735 | −0.563677 | − | 0.825996i | \(-0.690614\pi\) | ||||
−0.563677 | + | 0.825996i | \(0.690614\pi\) | |||||||
\(480\) | 5.24509e16 | 0.195743 | ||||||||
\(481\) | 4.88281e16 | 0.179774 | ||||||||
\(482\) | −2.74025e17 | −0.995368 | ||||||||
\(483\) | 7.86110e16 | 0.281726 | ||||||||
\(484\) | 3.57015e14 | 0.00126238 | ||||||||
\(485\) | −2.93658e17 | −1.02452 | ||||||||
\(486\) | −1.77608e16 | −0.0611401 | ||||||||
\(487\) | 2.75750e17 | 0.936651 | 0.468326 | − | 0.883556i | \(-0.344857\pi\) | ||||
0.468326 | + | 0.883556i | \(0.344857\pi\) | |||||||
\(488\) | −1.19238e17 | −0.399655 | ||||||||
\(489\) | 5.88829e16 | 0.194752 | ||||||||
\(490\) | 4.87912e17 | 1.59246 | ||||||||
\(491\) | 8.70439e16 | 0.280355 | 0.140178 | − | 0.990126i | \(-0.455233\pi\) | ||||
0.140178 | + | 0.990126i | \(0.455233\pi\) | |||||||
\(492\) | −3.13598e16 | −0.0996783 | ||||||||
\(493\) | 4.67937e16 | 0.146785 | ||||||||
\(494\) | 2.47164e16 | 0.0765172 | ||||||||
\(495\) | 2.01073e17 | 0.614355 | ||||||||
\(496\) | 1.78010e17 | 0.536802 | ||||||||
\(497\) | −8.46423e16 | −0.251925 | ||||||||
\(498\) | 1.94499e17 | 0.571384 | ||||||||
\(499\) | −5.00052e17 | −1.44998 | −0.724989 | − | 0.688760i | \(-0.758155\pi\) | ||||
−0.724989 | + | 0.688760i | \(0.758155\pi\) | |||||||
\(500\) | 8.58232e16 | 0.245640 | ||||||||
\(501\) | 5.68863e16 | 0.160717 | ||||||||
\(502\) | −4.55709e17 | −1.27091 | ||||||||
\(503\) | −2.80829e17 | −0.773124 | −0.386562 | − | 0.922263i | \(-0.626338\pi\) | ||||
−0.386562 | + | 0.922263i | \(0.626338\pi\) | |||||||
\(504\) | 4.02944e16 | 0.109508 | ||||||||
\(505\) | −5.36904e17 | −1.44047 | ||||||||
\(506\) | −5.52235e17 | −1.46267 | ||||||||
\(507\) | 2.17174e17 | 0.567879 | ||||||||
\(508\) | 6.11441e16 | 0.157848 | ||||||||
\(509\) | 1.73337e17 | 0.441801 | 0.220900 | − | 0.975296i | \(-0.429100\pi\) | ||||
0.220900 | + | 0.975296i | \(0.429100\pi\) | |||||||
\(510\) | 3.73475e17 | 0.939842 | ||||||||
\(511\) | 1.35994e17 | 0.337896 | ||||||||
\(512\) | −4.48685e17 | −1.10075 | ||||||||
\(513\) | −4.98005e16 | −0.120634 | ||||||||
\(514\) | −3.68379e17 | −0.881120 | ||||||||
\(515\) | −4.02642e17 | −0.950982 | ||||||||
\(516\) | −3.37306e16 | −0.0786686 | ||||||||
\(517\) | 2.67066e17 | 0.615079 | ||||||||
\(518\) | −1.85730e17 | −0.422414 | ||||||||
\(519\) | −4.77602e17 | −1.07270 | ||||||||
\(520\) | 1.11496e17 | 0.247308 | ||||||||
\(521\) | −5.14922e17 | −1.12797 | −0.563983 | − | 0.825786i | \(-0.690732\pi\) | ||||
−0.563983 | + | 0.825786i | \(0.690732\pi\) | |||||||
\(522\) | 2.34216e16 | 0.0506708 | ||||||||
\(523\) | −1.42777e15 | −0.00305069 | −0.00152534 | − | 0.999999i | \(-0.500486\pi\) | ||||
−0.00152534 | + | 0.999999i | \(0.500486\pi\) | |||||||
\(524\) | −4.77187e16 | −0.100701 | ||||||||
\(525\) | 2.13794e17 | 0.445616 | ||||||||
\(526\) | −6.55507e16 | −0.134949 | ||||||||
\(527\) | −2.69955e17 | −0.548936 | ||||||||
\(528\) | −2.56905e17 | −0.516003 | ||||||||
\(529\) | 6.99665e17 | 1.38812 | ||||||||
\(530\) | −1.48419e18 | −2.90869 | ||||||||
\(531\) | −2.24165e16 | −0.0433963 | ||||||||
\(532\) | 9.48450e15 | 0.0181380 | ||||||||
\(533\) | −1.27729e17 | −0.241302 | ||||||||
\(534\) | −2.11371e17 | −0.394481 | ||||||||
\(535\) | −3.20662e17 | −0.591219 | ||||||||
\(536\) | −2.14175e17 | −0.390119 | ||||||||
\(537\) | 3.94412e17 | 0.709770 | ||||||||
\(538\) | 1.91925e17 | 0.341230 | ||||||||
\(539\) | 5.08979e17 | 0.894072 | ||||||||
\(540\) | −1.88585e16 | −0.0327301 | ||||||||
\(541\) | 5.48273e17 | 0.940188 | 0.470094 | − | 0.882616i | \(-0.344220\pi\) | ||||
0.470094 | + | 0.882616i | \(0.344220\pi\) | |||||||
\(542\) | 1.41541e17 | 0.239820 | ||||||||
\(543\) | −1.72810e17 | −0.289314 | ||||||||
\(544\) | 1.01629e17 | 0.168123 | ||||||||
\(545\) | −2.92180e17 | −0.477611 | ||||||||
\(546\) | 1.37771e16 | 0.0222538 | ||||||||
\(547\) | 9.28212e17 | 1.48159 | 0.740797 | − | 0.671729i | \(-0.234448\pi\) | ||||
0.740797 | + | 0.671729i | \(0.234448\pi\) | |||||||
\(548\) | −6.34568e16 | −0.100093 | ||||||||
\(549\) | 8.21440e16 | 0.128043 | ||||||||
\(550\) | −1.50188e18 | −2.31355 | ||||||||
\(551\) | 6.56732e16 | 0.0999776 | ||||||||
\(552\) | 6.16993e17 | 0.928274 | ||||||||
\(553\) | −1.75872e17 | −0.261507 | ||||||||
\(554\) | −3.22769e17 | −0.474328 | ||||||||
\(555\) | 1.03549e18 | 1.50398 | ||||||||
\(556\) | 1.19138e15 | 0.00171026 | ||||||||
\(557\) | 6.05578e16 | 0.0859234 | 0.0429617 | − | 0.999077i | \(-0.486321\pi\) | ||||
0.0429617 | + | 0.999077i | \(0.486321\pi\) | |||||||
\(558\) | −1.35120e17 | −0.189495 | ||||||||
\(559\) | −1.37385e17 | −0.190442 | ||||||||
\(560\) | −3.84910e17 | −0.527397 | ||||||||
\(561\) | 3.89600e17 | 0.527667 | ||||||||
\(562\) | −1.16895e17 | −0.156498 | ||||||||
\(563\) | 1.22604e18 | 1.62256 | 0.811280 | − | 0.584658i | \(-0.198771\pi\) | ||||
0.811280 | + | 0.584658i | \(0.198771\pi\) | |||||||
\(564\) | −2.50480e16 | −0.0327687 | ||||||||
\(565\) | −6.23327e17 | −0.806122 | ||||||||
\(566\) | 1.30808e18 | 1.67235 | ||||||||
\(567\) | −2.77592e16 | −0.0350846 | ||||||||
\(568\) | −6.64330e17 | −0.830080 | ||||||||
\(569\) | 5.61647e17 | 0.693799 | 0.346899 | − | 0.937902i | \(-0.387235\pi\) | ||||
0.346899 | + | 0.937902i | \(0.387235\pi\) | |||||||
\(570\) | 5.24157e17 | 0.640140 | ||||||||
\(571\) | −6.81412e17 | −0.822764 | −0.411382 | − | 0.911463i | \(-0.634954\pi\) | ||||
−0.411382 | + | 0.911463i | \(0.634954\pi\) | |||||||
\(572\) | 9.76373e15 | 0.0116558 | ||||||||
\(573\) | −9.07392e17 | −1.07100 | ||||||||
\(574\) | 4.85848e17 | 0.566987 | ||||||||
\(575\) | 3.27364e18 | 3.77738 | ||||||||
\(576\) | 3.13804e17 | 0.358025 | ||||||||
\(577\) | −9.59858e17 | −1.08284 | −0.541420 | − | 0.840752i | \(-0.682113\pi\) | ||||
−0.541420 | + | 0.840752i | \(0.682113\pi\) | |||||||
\(578\) | −1.30752e17 | −0.145853 | ||||||||
\(579\) | −2.58944e16 | −0.0285625 | ||||||||
\(580\) | 2.48692e16 | 0.0271256 | ||||||||
\(581\) | 3.03993e17 | 0.327882 | ||||||||
\(582\) | −2.84797e17 | −0.303764 | ||||||||
\(583\) | −1.54828e18 | −1.63306 | ||||||||
\(584\) | 1.06737e18 | 1.11335 | ||||||||
\(585\) | −7.68107e16 | −0.0792335 | ||||||||
\(586\) | −6.88105e17 | −0.701972 | ||||||||
\(587\) | 1.17241e17 | 0.118286 | 0.0591430 | − | 0.998250i | \(-0.481163\pi\) | ||||
0.0591430 | + | 0.998250i | \(0.481163\pi\) | |||||||
\(588\) | −4.77368e16 | −0.0476322 | ||||||||
\(589\) | −3.78871e17 | −0.373888 | ||||||||
\(590\) | 2.35936e17 | 0.230280 | ||||||||
\(591\) | −6.26349e17 | −0.604642 | ||||||||
\(592\) | −1.32302e18 | −1.26321 | ||||||||
\(593\) | −2.03990e17 | −0.192643 | −0.0963213 | − | 0.995350i | \(-0.530708\pi\) | ||||
−0.0963213 | + | 0.995350i | \(0.530708\pi\) | |||||||
\(594\) | 1.95006e17 | 0.182153 | ||||||||
\(595\) | 5.83721e17 | 0.539319 | ||||||||
\(596\) | 5.82274e15 | 0.00532141 | ||||||||
\(597\) | 5.11512e17 | 0.462405 | ||||||||
\(598\) | 2.10956e17 | 0.188640 | ||||||||
\(599\) | −1.55751e18 | −1.37771 | −0.688854 | − | 0.724900i | \(-0.741886\pi\) | ||||
−0.688854 | + | 0.724900i | \(0.741886\pi\) | |||||||
\(600\) | 1.67800e18 | 1.46828 | ||||||||
\(601\) | −1.59055e18 | −1.37677 | −0.688387 | − | 0.725343i | \(-0.741681\pi\) | ||||
−0.688387 | + | 0.725343i | \(0.741681\pi\) | |||||||
\(602\) | 5.22578e17 | 0.447480 | ||||||||
\(603\) | 1.47547e17 | 0.124988 | ||||||||
\(604\) | 2.09470e17 | 0.175543 | ||||||||
\(605\) | 3.08374e16 | 0.0255663 | ||||||||
\(606\) | −5.20704e17 | −0.427089 | ||||||||
\(607\) | 4.42280e17 | 0.358898 | 0.179449 | − | 0.983767i | \(-0.442569\pi\) | ||||
0.179449 | + | 0.983767i | \(0.442569\pi\) | |||||||
\(608\) | 1.42633e17 | 0.114511 | ||||||||
\(609\) | 3.66067e16 | 0.0290769 | ||||||||
\(610\) | −8.64576e17 | −0.679453 | ||||||||
\(611\) | −1.02021e17 | −0.0793268 | ||||||||
\(612\) | −3.65404e16 | −0.0281118 | ||||||||
\(613\) | 1.50989e18 | 1.14935 | 0.574676 | − | 0.818381i | \(-0.305128\pi\) | ||||
0.574676 | + | 0.818381i | \(0.305128\pi\) | |||||||
\(614\) | −1.47401e18 | −1.11021 | ||||||||
\(615\) | −2.70873e18 | −2.01872 | ||||||||
\(616\) | −4.42415e17 | −0.326253 | ||||||||
\(617\) | −1.64765e18 | −1.20229 | −0.601147 | − | 0.799138i | \(-0.705290\pi\) | ||||
−0.601147 | + | 0.799138i | \(0.705290\pi\) | |||||||
\(618\) | −3.90493e17 | −0.281960 | ||||||||
\(619\) | −2.47368e18 | −1.76748 | −0.883741 | − | 0.467976i | \(-0.844983\pi\) | ||||
−0.883741 | + | 0.467976i | \(0.844983\pi\) | |||||||
\(620\) | −1.43471e17 | −0.101442 | ||||||||
\(621\) | −4.25052e17 | −0.297404 | ||||||||
\(622\) | −2.69521e18 | −1.86619 | ||||||||
\(623\) | −3.30361e17 | −0.226369 | ||||||||
\(624\) | 9.81389e16 | 0.0665490 | ||||||||
\(625\) | 3.77068e18 | 2.53046 | ||||||||
\(626\) | 2.34754e18 | 1.55912 | ||||||||
\(627\) | 5.46788e17 | 0.359402 | ||||||||
\(628\) | −2.29288e16 | −0.0149157 | ||||||||
\(629\) | 2.00638e18 | 1.29176 | ||||||||
\(630\) | 2.92169e17 | 0.186175 | ||||||||
\(631\) | 7.80619e16 | 0.0492321 | 0.0246160 | − | 0.999697i | \(-0.492164\pi\) | ||||
0.0246160 | + | 0.999697i | \(0.492164\pi\) | |||||||
\(632\) | −1.38036e18 | −0.861653 | ||||||||
\(633\) | −1.07893e18 | −0.666604 | ||||||||
\(634\) | −1.36834e18 | −0.836783 | ||||||||
\(635\) | 5.28136e18 | 3.19681 | ||||||||
\(636\) | 1.45212e17 | 0.0870023 | ||||||||
\(637\) | −1.94432e17 | −0.115309 | ||||||||
\(638\) | −2.57159e17 | −0.150962 | ||||||||
\(639\) | 4.57663e17 | 0.265944 | ||||||||
\(640\) | −2.71342e18 | −1.56080 | ||||||||
\(641\) | −1.70759e18 | −0.972316 | −0.486158 | − | 0.873871i | \(-0.661602\pi\) | ||||
−0.486158 | + | 0.873871i | \(0.661602\pi\) | |||||||
\(642\) | −3.10986e17 | −0.175293 | ||||||||
\(643\) | −1.28298e18 | −0.715894 | −0.357947 | − | 0.933742i | \(-0.616523\pi\) | ||||
−0.357947 | + | 0.933742i | \(0.616523\pi\) | |||||||
\(644\) | 8.09510e16 | 0.0447161 | ||||||||
\(645\) | −2.91351e18 | −1.59323 | ||||||||
\(646\) | 1.01561e18 | 0.549814 | ||||||||
\(647\) | 1.34776e18 | 0.722331 | 0.361165 | − | 0.932502i | \(-0.382379\pi\) | ||||
0.361165 | + | 0.932502i | \(0.382379\pi\) | |||||||
\(648\) | −2.17873e17 | −0.115602 | ||||||||
\(649\) | 2.46123e17 | 0.129289 | ||||||||
\(650\) | 5.73726e17 | 0.298379 | ||||||||
\(651\) | −2.11185e17 | −0.108740 | ||||||||
\(652\) | 6.06357e16 | 0.0309114 | ||||||||
\(653\) | −1.20789e18 | −0.609664 | −0.304832 | − | 0.952406i | \(-0.598600\pi\) | ||||
−0.304832 | + | 0.952406i | \(0.598600\pi\) | |||||||
\(654\) | −2.83364e17 | −0.141609 | ||||||||
\(655\) | −4.12173e18 | −2.03944 | ||||||||
\(656\) | 3.46086e18 | 1.69555 | ||||||||
\(657\) | −7.35323e17 | −0.356700 | ||||||||
\(658\) | 3.88061e17 | 0.186394 | ||||||||
\(659\) | 4.86997e17 | 0.231617 | 0.115809 | − | 0.993272i | \(-0.463054\pi\) | ||||
0.115809 | + | 0.993272i | \(0.463054\pi\) | |||||||
\(660\) | 2.07058e17 | 0.0975118 | ||||||||
\(661\) | −4.01281e18 | −1.87128 | −0.935640 | − | 0.352956i | \(-0.885177\pi\) | ||||
−0.935640 | + | 0.352956i | \(0.885177\pi\) | |||||||
\(662\) | −1.19743e18 | −0.552932 | ||||||||
\(663\) | −1.48829e17 | −0.0680533 | ||||||||
\(664\) | 2.38594e18 | 1.08036 | ||||||||
\(665\) | 8.19230e17 | 0.367338 | ||||||||
\(666\) | 1.00425e18 | 0.445921 | ||||||||
\(667\) | 5.60526e17 | 0.246478 | ||||||||
\(668\) | 5.85796e16 | 0.0255094 | ||||||||
\(669\) | −1.35492e18 | −0.584312 | ||||||||
\(670\) | −1.55295e18 | −0.663241 | ||||||||
\(671\) | −9.01905e17 | −0.381474 | ||||||||
\(672\) | 7.95045e16 | 0.0333036 | ||||||||
\(673\) | −3.60435e18 | −1.49530 | −0.747652 | − | 0.664091i | \(-0.768819\pi\) | ||||
−0.747652 | + | 0.664091i | \(0.768819\pi\) | |||||||
\(674\) | −4.06776e18 | −1.67134 | ||||||||
\(675\) | −1.15599e18 | −0.470414 | ||||||||
\(676\) | 2.23639e17 | 0.0901350 | ||||||||
\(677\) | 3.19700e18 | 1.27619 | 0.638097 | − | 0.769956i | \(-0.279722\pi\) | ||||
0.638097 | + | 0.769956i | \(0.279722\pi\) | |||||||
\(678\) | −6.04518e17 | −0.239010 | ||||||||
\(679\) | −4.45123e17 | −0.174312 | ||||||||
\(680\) | 4.58144e18 | 1.77703 | ||||||||
\(681\) | 2.25627e18 | 0.866832 | ||||||||
\(682\) | 1.48356e18 | 0.564555 | ||||||||
\(683\) | 2.15760e18 | 0.813271 | 0.406636 | − | 0.913590i | \(-0.366702\pi\) | ||||
0.406636 | + | 0.913590i | \(0.366702\pi\) | |||||||
\(684\) | −5.12830e16 | −0.0191473 | ||||||||
\(685\) | −5.48113e18 | −2.02713 | ||||||||
\(686\) | 1.56105e18 | 0.571886 | ||||||||
\(687\) | 6.00260e16 | 0.0217831 | ||||||||
\(688\) | 3.72251e18 | 1.33817 | ||||||||
\(689\) | 5.91448e17 | 0.210616 | ||||||||
\(690\) | 4.47373e18 | 1.57816 | ||||||||
\(691\) | −1.49915e18 | −0.523888 | −0.261944 | − | 0.965083i | \(-0.584364\pi\) | ||||
−0.261944 | + | 0.965083i | \(0.584364\pi\) | |||||||
\(692\) | −4.91819e17 | −0.170261 | ||||||||
\(693\) | 3.04784e17 | 0.104526 | ||||||||
\(694\) | −3.59903e17 | −0.122278 | ||||||||
\(695\) | 1.02906e17 | 0.0346369 | ||||||||
\(696\) | 2.87314e17 | 0.0958070 | ||||||||
\(697\) | −5.24844e18 | −1.73387 | ||||||||
\(698\) | −4.88035e18 | −1.59731 | ||||||||
\(699\) | −1.85322e18 | −0.600931 | ||||||||
\(700\) | 2.20158e17 | 0.0707290 | ||||||||
\(701\) | 3.69368e18 | 1.17569 | 0.587844 | − | 0.808974i | \(-0.299977\pi\) | ||||
0.587844 | + | 0.808974i | \(0.299977\pi\) | |||||||
\(702\) | −7.44930e16 | −0.0234922 | ||||||||
\(703\) | 2.81587e18 | 0.879839 | ||||||||
\(704\) | −3.44544e18 | −1.06665 | ||||||||
\(705\) | −2.16354e18 | −0.663644 | ||||||||
\(706\) | 3.99442e18 | 1.21401 | ||||||||
\(707\) | −8.13833e17 | −0.245081 | ||||||||
\(708\) | −2.30837e16 | −0.00688795 | ||||||||
\(709\) | −2.41023e18 | −0.712620 | −0.356310 | − | 0.934368i | \(-0.615965\pi\) | ||||
−0.356310 | + | 0.934368i | \(0.615965\pi\) | |||||||
\(710\) | −4.81696e18 | −1.41122 | ||||||||
\(711\) | 9.50945e17 | 0.276060 | ||||||||
\(712\) | −2.59290e18 | −0.745875 | ||||||||
\(713\) | −3.23370e18 | −0.921759 | ||||||||
\(714\) | 5.66108e17 | 0.159905 | ||||||||
\(715\) | 8.43348e17 | 0.236057 | ||||||||
\(716\) | 4.06153e17 | 0.112656 | ||||||||
\(717\) | −9.14187e17 | −0.251282 | ||||||||
\(718\) | 3.52371e18 | 0.959825 | ||||||||
\(719\) | 6.00754e18 | 1.62166 | 0.810828 | − | 0.585285i | \(-0.199017\pi\) | ||||
0.810828 | + | 0.585285i | \(0.199017\pi\) | |||||||
\(720\) | 2.08122e18 | 0.556746 | ||||||||
\(721\) | −6.10320e17 | −0.161800 | ||||||||
\(722\) | −2.20225e18 | −0.578594 | ||||||||
\(723\) | 2.31575e18 | 0.602967 | ||||||||
\(724\) | −1.77954e17 | −0.0459205 | ||||||||
\(725\) | 1.52443e18 | 0.389862 | ||||||||
\(726\) | 2.99069e16 | 0.00758025 | ||||||||
\(727\) | −4.22863e18 | −1.06225 | −0.531124 | − | 0.847294i | \(-0.678230\pi\) | ||||
−0.531124 | + | 0.847294i | \(0.678230\pi\) | |||||||
\(728\) | 1.69004e17 | 0.0420769 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 7.73937e18 | 1.89281 | ||||||||
\(731\) | −5.64523e18 | −1.36842 | ||||||||
\(732\) | 8.45892e16 | 0.0203232 | ||||||||
\(733\) | 4.95380e17 | 0.117968 | 0.0589838 | − | 0.998259i | \(-0.481214\pi\) | ||||
0.0589838 | + | 0.998259i | \(0.481214\pi\) | |||||||
\(734\) | 7.23677e18 | 1.70813 | ||||||||
\(735\) | −4.12330e18 | −0.964666 | ||||||||
\(736\) | 1.21738e18 | 0.282307 | ||||||||
\(737\) | −1.62000e18 | −0.372372 | ||||||||
\(738\) | −2.62699e18 | −0.598539 | ||||||||
\(739\) | 4.95738e18 | 1.11960 | 0.559800 | − | 0.828627i | \(-0.310878\pi\) | ||||
0.559800 | + | 0.828627i | \(0.310878\pi\) | |||||||
\(740\) | 1.06632e18 | 0.238715 | ||||||||
\(741\) | −2.08876e17 | −0.0463521 | ||||||||
\(742\) | −2.24972e18 | −0.494884 | ||||||||
\(743\) | −1.06107e18 | −0.231376 | −0.115688 | − | 0.993286i | \(-0.536907\pi\) | ||||
−0.115688 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(744\) | −1.65753e18 | −0.358291 | ||||||||
\(745\) | 5.02943e17 | 0.107771 | ||||||||
\(746\) | 4.93330e18 | 1.04794 | ||||||||
\(747\) | −1.64370e18 | −0.346129 | ||||||||
\(748\) | 4.01197e17 | 0.0837525 | ||||||||
\(749\) | −4.86056e17 | −0.100590 | ||||||||
\(750\) | 7.18935e18 | 1.47500 | ||||||||
\(751\) | −3.62932e18 | −0.738186 | −0.369093 | − | 0.929392i | \(-0.620332\pi\) | ||||
−0.369093 | + | 0.929392i | \(0.620332\pi\) | |||||||
\(752\) | 2.76429e18 | 0.557402 | ||||||||
\(753\) | 3.85115e18 | 0.769880 | ||||||||
\(754\) | 9.82357e16 | 0.0194695 | ||||||||
\(755\) | 1.80931e19 | 3.55516 | ||||||||
\(756\) | −2.85855e16 | −0.00556870 | ||||||||
\(757\) | −5.58460e18 | −1.07862 | −0.539310 | − | 0.842107i | \(-0.681315\pi\) | ||||
−0.539310 | + | 0.842107i | \(0.681315\pi\) | |||||||
\(758\) | −4.46109e18 | −0.854262 | ||||||||
\(759\) | 4.66689e18 | 0.886045 | ||||||||
\(760\) | 6.42988e18 | 1.21036 | ||||||||
\(761\) | 3.82032e18 | 0.713017 | 0.356508 | − | 0.934292i | \(-0.383967\pi\) | ||||
0.356508 | + | 0.934292i | \(0.383967\pi\) | |||||||
\(762\) | 5.12200e18 | 0.947834 | ||||||||
\(763\) | −4.42884e17 | −0.0812606 | ||||||||
\(764\) | −9.34403e17 | −0.169992 | ||||||||
\(765\) | −3.15620e18 | −0.569331 | ||||||||
\(766\) | −5.13035e18 | −0.917613 | ||||||||
\(767\) | −9.40201e16 | −0.0166744 | ||||||||
\(768\) | 8.94768e17 | 0.157348 | ||||||||
\(769\) | −9.68265e18 | −1.68839 | −0.844196 | − | 0.536035i | \(-0.819921\pi\) | ||||
−0.844196 | + | 0.536035i | \(0.819921\pi\) | |||||||
\(770\) | −3.20789e18 | −0.554663 | ||||||||
\(771\) | 3.11314e18 | 0.533759 | ||||||||
\(772\) | −2.66652e16 | −0.00453350 | ||||||||
\(773\) | 6.59375e18 | 1.11164 | 0.555822 | − | 0.831301i | \(-0.312404\pi\) | ||||
0.555822 | + | 0.831301i | \(0.312404\pi\) | |||||||
\(774\) | −2.82559e18 | −0.472382 | ||||||||
\(775\) | −8.79451e18 | −1.45798 | ||||||||
\(776\) | −3.49363e18 | −0.574349 | ||||||||
\(777\) | 1.56959e18 | 0.255887 | ||||||||
\(778\) | −6.62142e17 | −0.107049 | ||||||||
\(779\) | −7.36599e18 | −1.18097 | ||||||||
\(780\) | −7.90972e16 | −0.0125761 | ||||||||
\(781\) | −5.02494e18 | −0.792318 | ||||||||
\(782\) | 8.66832e18 | 1.35547 | ||||||||
\(783\) | −1.97933e17 | −0.0306950 | ||||||||
\(784\) | 5.26823e18 | 0.810233 | ||||||||
\(785\) | −1.98049e18 | −0.302079 | ||||||||
\(786\) | −3.99736e18 | −0.604682 | ||||||||
\(787\) | −6.49044e18 | −0.973730 | −0.486865 | − | 0.873477i | \(-0.661860\pi\) | ||||
−0.486865 | + | 0.873477i | \(0.661860\pi\) | |||||||
\(788\) | −6.44994e17 | −0.0959700 | ||||||||
\(789\) | 5.53963e17 | 0.0817485 | ||||||||
\(790\) | −1.00088e19 | −1.46490 | ||||||||
\(791\) | −9.44831e17 | −0.137154 | ||||||||
\(792\) | 2.39215e18 | 0.344409 | ||||||||
\(793\) | 3.44532e17 | 0.0491987 | ||||||||
\(794\) | 5.33114e18 | 0.755069 | ||||||||
\(795\) | 1.25428e19 | 1.76201 | ||||||||
\(796\) | 5.26738e17 | 0.0733939 | ||||||||
\(797\) | 4.26258e18 | 0.589106 | 0.294553 | − | 0.955635i | \(-0.404829\pi\) | ||||
0.294553 | + | 0.955635i | \(0.404829\pi\) | |||||||
\(798\) | 7.94511e17 | 0.108913 | ||||||||
\(799\) | −4.19209e18 | −0.570002 | ||||||||
\(800\) | 3.31085e18 | 0.446534 | ||||||||
\(801\) | 1.78627e18 | 0.238966 | ||||||||
\(802\) | 4.77144e18 | 0.633164 | ||||||||
\(803\) | 8.07353e18 | 1.06270 | ||||||||
\(804\) | 1.51939e17 | 0.0198383 | ||||||||
\(805\) | 6.99220e18 | 0.905609 | ||||||||
\(806\) | −5.66726e17 | −0.0728107 | ||||||||
\(807\) | −1.62194e18 | −0.206708 | ||||||||
\(808\) | −6.38751e18 | −0.807529 | ||||||||
\(809\) | −1.36312e19 | −1.70950 | −0.854749 | − | 0.519042i | \(-0.826289\pi\) | ||||
−0.854749 | + | 0.519042i | \(0.826289\pi\) | |||||||
\(810\) | −1.57977e18 | −0.196535 | ||||||||
\(811\) | 3.01246e18 | 0.371780 | 0.185890 | − | 0.982571i | \(-0.440483\pi\) | ||||
0.185890 | + | 0.982571i | \(0.440483\pi\) | |||||||
\(812\) | 3.76964e16 | 0.00461515 | ||||||||
\(813\) | −1.19615e18 | −0.145277 | ||||||||
\(814\) | −1.10262e19 | −1.32852 | ||||||||
\(815\) | 5.23745e18 | 0.626030 | ||||||||
\(816\) | 4.03259e18 | 0.478187 | ||||||||
\(817\) | −7.92286e18 | −0.932048 | ||||||||
\(818\) | −3.95776e18 | −0.461905 | ||||||||
\(819\) | −1.16429e17 | −0.0134808 | ||||||||
\(820\) | −2.78936e18 | −0.320416 | ||||||||
\(821\) | −1.37107e19 | −1.56254 | −0.781268 | − | 0.624195i | \(-0.785427\pi\) | ||||
−0.781268 | + | 0.624195i | \(0.785427\pi\) | |||||||
\(822\) | −5.31574e18 | −0.601031 | ||||||||
\(823\) | −3.22340e18 | −0.361589 | −0.180795 | − | 0.983521i | \(-0.557867\pi\) | ||||
−0.180795 | + | 0.983521i | \(0.557867\pi\) | |||||||
\(824\) | −4.79021e18 | −0.533123 | ||||||||
\(825\) | 1.26923e19 | 1.40149 | ||||||||
\(826\) | 3.57629e17 | 0.0391798 | ||||||||
\(827\) | 8.24057e16 | 0.00895718 | 0.00447859 | − | 0.999990i | \(-0.498574\pi\) | ||||
0.00447859 | + | 0.999990i | \(0.498574\pi\) | |||||||
\(828\) | −4.37705e17 | −0.0472046 | ||||||||
\(829\) | 9.63103e18 | 1.03055 | 0.515274 | − | 0.857026i | \(-0.327690\pi\) | ||||
0.515274 | + | 0.857026i | \(0.327690\pi\) | |||||||
\(830\) | 1.73001e19 | 1.83671 | ||||||||
\(831\) | 2.72769e18 | 0.287335 | ||||||||
\(832\) | 1.31617e18 | 0.137566 | ||||||||
\(833\) | −7.98933e18 | −0.828548 | ||||||||
\(834\) | 9.98007e16 | 0.0102696 | ||||||||
\(835\) | 5.05985e18 | 0.516626 | ||||||||
\(836\) | 5.63065e17 | 0.0570450 | ||||||||
\(837\) | 1.14189e18 | 0.114791 | ||||||||
\(838\) | 6.87542e18 | 0.685825 | ||||||||
\(839\) | −1.75314e18 | −0.173526 | −0.0867628 | − | 0.996229i | \(-0.527652\pi\) | ||||
−0.0867628 | + | 0.996229i | \(0.527652\pi\) | |||||||
\(840\) | 3.58406e18 | 0.352014 | ||||||||
\(841\) | −9.99961e18 | −0.974561 | ||||||||
\(842\) | −5.89425e18 | −0.570033 | ||||||||
\(843\) | 9.87866e17 | 0.0948023 | ||||||||
\(844\) | −1.11104e18 | −0.105805 | ||||||||
\(845\) | 1.93169e19 | 1.82545 | ||||||||
\(846\) | −2.09826e18 | −0.196766 | ||||||||
\(847\) | 4.67430e16 | 0.00434985 | ||||||||
\(848\) | −1.60256e19 | −1.47993 | ||||||||
\(849\) | −1.10545e19 | −1.01307 | ||||||||
\(850\) | 2.35748e19 | 2.14400 | ||||||||
\(851\) | 2.40337e19 | 2.16909 | ||||||||
\(852\) | 4.71287e17 | 0.0422112 | ||||||||
\(853\) | −1.37778e19 | −1.22465 | −0.612326 | − | 0.790605i | \(-0.709766\pi\) | ||||
−0.612326 | + | 0.790605i | \(0.709766\pi\) | |||||||
\(854\) | −1.31051e18 | −0.115602 | ||||||||
\(855\) | −4.42960e18 | −0.387780 | ||||||||
\(856\) | −3.81490e18 | −0.331439 | ||||||||
\(857\) | −1.39335e19 | −1.20139 | −0.600695 | − | 0.799479i | \(-0.705109\pi\) | ||||
−0.600695 | + | 0.799479i | \(0.705109\pi\) | |||||||
\(858\) | 8.17901e17 | 0.0699896 | ||||||||
\(859\) | 1.73655e19 | 1.47480 | 0.737400 | − | 0.675457i | \(-0.236054\pi\) | ||||
0.737400 | + | 0.675457i | \(0.236054\pi\) | |||||||
\(860\) | −3.00023e18 | −0.252880 | ||||||||
\(861\) | −4.10585e18 | −0.343465 | ||||||||
\(862\) | −2.21879e18 | −0.184213 | ||||||||
\(863\) | −1.12262e19 | −0.925041 | −0.462520 | − | 0.886609i | \(-0.653055\pi\) | ||||
−0.462520 | + | 0.886609i | \(0.653055\pi\) | |||||||
\(864\) | −4.29883e17 | −0.0351569 | ||||||||
\(865\) | −4.24812e19 | −3.44820 | ||||||||
\(866\) | 4.70407e18 | 0.378972 | ||||||||
\(867\) | 1.10497e18 | 0.0883539 | ||||||||
\(868\) | −2.17472e17 | −0.0172594 | ||||||||
\(869\) | −1.04410e19 | −0.822455 | ||||||||
\(870\) | 2.08327e18 | 0.162881 | ||||||||
\(871\) | 6.18848e17 | 0.0480248 | ||||||||
\(872\) | −3.47605e18 | −0.267750 | ||||||||
\(873\) | 2.40679e18 | 0.184012 | ||||||||
\(874\) | 1.21656e19 | 0.923232 | ||||||||
\(875\) | 1.12366e19 | 0.846412 | ||||||||
\(876\) | −7.57212e17 | −0.0566162 | ||||||||
\(877\) | −1.89263e19 | −1.40465 | −0.702327 | − | 0.711855i | \(-0.747855\pi\) | ||||
−0.702327 | + | 0.711855i | \(0.747855\pi\) | |||||||
\(878\) | −1.79949e19 | −1.32567 | ||||||||
\(879\) | 5.81511e18 | 0.425236 | ||||||||
\(880\) | −2.28509e19 | −1.65869 | ||||||||
\(881\) | −2.96071e18 | −0.213330 | −0.106665 | − | 0.994295i | \(-0.534017\pi\) | ||||
−0.106665 | + | 0.994295i | \(0.534017\pi\) | |||||||
\(882\) | −3.99888e18 | −0.286018 | ||||||||
\(883\) | −8.98458e18 | −0.637901 | −0.318950 | − | 0.947771i | \(-0.603330\pi\) | ||||
−0.318950 | + | 0.947771i | \(0.603330\pi\) | |||||||
\(884\) | −1.53259e17 | −0.0108016 | ||||||||
\(885\) | −1.99387e18 | −0.139498 | ||||||||
\(886\) | 3.16753e18 | 0.219989 | ||||||||
\(887\) | −1.21271e19 | −0.836088 | −0.418044 | − | 0.908427i | \(-0.637284\pi\) | ||||
−0.418044 | + | 0.908427i | \(0.637284\pi\) | |||||||
\(888\) | 1.23192e19 | 0.843136 | ||||||||
\(889\) | 8.00542e18 | 0.543905 | ||||||||
\(890\) | −1.88008e19 | −1.26806 | ||||||||
\(891\) | −1.64797e18 | −0.110343 | ||||||||
\(892\) | −1.39526e18 | −0.0927432 | ||||||||
\(893\) | −5.88343e18 | −0.388236 | ||||||||
\(894\) | 4.87768e17 | 0.0319536 | ||||||||
\(895\) | 3.50817e19 | 2.28156 | ||||||||
\(896\) | −4.11297e18 | −0.265555 | ||||||||
\(897\) | −1.78277e18 | −0.114273 | ||||||||
\(898\) | 9.06070e18 | 0.576588 | ||||||||
\(899\) | −1.50583e18 | −0.0951346 | ||||||||
\(900\) | −1.19040e18 | −0.0746650 | ||||||||
\(901\) | 2.43029e19 | 1.51338 | ||||||||
\(902\) | 2.88432e19 | 1.78321 | ||||||||
\(903\) | −4.41626e18 | −0.271072 | ||||||||
\(904\) | −7.41568e18 | −0.451914 | ||||||||
\(905\) | −1.53709e19 | −0.929999 | ||||||||
\(906\) | 1.75472e19 | 1.05408 | ||||||||
\(907\) | 1.40064e19 | 0.835370 | 0.417685 | − | 0.908592i | \(-0.362842\pi\) | ||||
0.417685 | + | 0.908592i | \(0.362842\pi\) | |||||||
\(908\) | 2.32343e18 | 0.137585 | ||||||||
\(909\) | 4.40042e18 | 0.258719 | ||||||||
\(910\) | 1.22543e18 | 0.0715350 | ||||||||
\(911\) | 5.73642e18 | 0.332485 | 0.166242 | − | 0.986085i | \(-0.446837\pi\) | ||||
0.166242 | + | 0.986085i | \(0.446837\pi\) | |||||||
\(912\) | 5.65958e18 | 0.325700 | ||||||||
\(913\) | 1.80471e19 | 1.03121 | ||||||||
\(914\) | 2.71720e19 | 1.54160 | ||||||||
\(915\) | 7.30645e18 | 0.411594 | ||||||||
\(916\) | 6.18128e16 | 0.00345747 | ||||||||
\(917\) | −6.24767e18 | −0.346990 | ||||||||
\(918\) | −3.06096e18 | −0.168803 | ||||||||
\(919\) | 1.21399e19 | 0.664761 | 0.332381 | − | 0.943145i | \(-0.392148\pi\) | ||||
0.332381 | + | 0.943145i | \(0.392148\pi\) | |||||||
\(920\) | 5.48795e19 | 2.98394 | ||||||||
\(921\) | 1.24567e19 | 0.672536 | ||||||||
\(922\) | −8.52004e18 | −0.456763 | ||||||||
\(923\) | 1.91955e18 | 0.102185 | ||||||||
\(924\) | 3.13856e17 | 0.0165906 | ||||||||
\(925\) | 6.53632e19 | 3.43093 | ||||||||
\(926\) | 2.80911e19 | 1.46419 | ||||||||
\(927\) | 3.30002e18 | 0.170804 | ||||||||
\(928\) | 5.66897e17 | 0.0291368 | ||||||||
\(929\) | 7.09575e18 | 0.362157 | 0.181078 | − | 0.983469i | \(-0.442041\pi\) | ||||
0.181078 | + | 0.983469i | \(0.442041\pi\) | |||||||
\(930\) | −1.20185e19 | −0.609131 | ||||||||
\(931\) | −1.12127e19 | −0.564336 | ||||||||
\(932\) | −1.90838e18 | −0.0953810 | ||||||||
\(933\) | 2.27769e19 | 1.13049 | ||||||||
\(934\) | 1.42198e19 | 0.700873 | ||||||||
\(935\) | 3.46537e19 | 1.69619 | ||||||||
\(936\) | −9.13812e17 | −0.0444185 | ||||||||
\(937\) | 3.72483e19 | 1.79804 | 0.899021 | − | 0.437906i | \(-0.144280\pi\) | ||||
0.899021 | + | 0.437906i | \(0.144280\pi\) | |||||||
\(938\) | −2.35394e18 | −0.112844 | ||||||||
\(939\) | −1.98389e19 | −0.944475 | ||||||||
\(940\) | −2.22794e18 | −0.105335 | ||||||||
\(941\) | 2.16721e19 | 1.01758 | 0.508791 | − | 0.860890i | \(-0.330093\pi\) | ||||
0.508791 | + | 0.860890i | \(0.330093\pi\) | |||||||
\(942\) | −1.92073e18 | −0.0895645 | ||||||||
\(943\) | −6.28693e19 | −2.91147 | ||||||||
\(944\) | 2.54752e18 | 0.117165 | ||||||||
\(945\) | −2.46909e18 | −0.112780 | ||||||||
\(946\) | 3.10238e19 | 1.40735 | ||||||||
\(947\) | −2.96624e19 | −1.33639 | −0.668193 | − | 0.743988i | \(-0.732932\pi\) | ||||
−0.668193 | + | 0.743988i | \(0.732932\pi\) | |||||||
\(948\) | 9.79252e17 | 0.0438168 | ||||||||
\(949\) | −3.08412e18 | −0.137057 | ||||||||
\(950\) | 3.30863e19 | 1.46031 | ||||||||
\(951\) | 1.15637e19 | 0.506901 | ||||||||
\(952\) | 6.94449e18 | 0.302343 | ||||||||
\(953\) | −3.45780e17 | −0.0149519 | −0.00747595 | − | 0.999972i | \(-0.502380\pi\) | ||||
−0.00747595 | + | 0.999972i | \(0.502380\pi\) | |||||||
\(954\) | 1.21643e19 | 0.522424 | ||||||||
\(955\) | −8.07097e19 | −3.44274 | ||||||||
\(956\) | −9.41400e17 | −0.0398839 | ||||||||
\(957\) | 2.17322e18 | 0.0914485 | ||||||||
\(958\) | −2.57078e19 | −1.07446 | ||||||||
\(959\) | −8.30822e18 | −0.344895 | ||||||||
\(960\) | 2.79119e19 | 1.15087 | ||||||||
\(961\) | −1.57303e19 | −0.644223 | ||||||||
\(962\) | 4.21206e18 | 0.171339 | ||||||||
\(963\) | 2.62812e18 | 0.106188 | ||||||||
\(964\) | 2.38469e18 | 0.0957042 | ||||||||
\(965\) | −2.30323e18 | −0.0918141 | ||||||||
\(966\) | 6.78122e18 | 0.268507 | ||||||||
\(967\) | 3.66584e19 | 1.44179 | 0.720894 | − | 0.693045i | \(-0.243731\pi\) | ||||
0.720894 | + | 0.693045i | \(0.243731\pi\) | |||||||
\(968\) | 3.66871e17 | 0.0143325 | ||||||||
\(969\) | −8.58282e18 | −0.333062 | ||||||||
\(970\) | −2.53318e19 | −0.976450 | ||||||||
\(971\) | 5.54985e18 | 0.212499 | 0.106249 | − | 0.994340i | \(-0.466116\pi\) | ||||
0.106249 | + | 0.994340i | \(0.466116\pi\) | |||||||
\(972\) | 1.54563e17 | 0.00587860 | ||||||||
\(973\) | 1.55983e17 | 0.00589311 | ||||||||
\(974\) | 2.37870e19 | 0.892704 | ||||||||
\(975\) | −4.84851e18 | −0.180750 | ||||||||
\(976\) | −9.33524e18 | −0.345702 | ||||||||
\(977\) | 3.38833e18 | 0.124644 | 0.0623220 | − | 0.998056i | \(-0.480149\pi\) | ||||
0.0623220 | + | 0.998056i | \(0.480149\pi\) | |||||||
\(978\) | 5.07942e18 | 0.185614 | ||||||||
\(979\) | −1.96125e19 | −0.711944 | ||||||||
\(980\) | −4.24604e18 | −0.153114 | ||||||||
\(981\) | 2.39468e18 | 0.0857827 | ||||||||
\(982\) | 7.50867e18 | 0.267201 | ||||||||
\(983\) | 1.69848e19 | 0.600431 | 0.300216 | − | 0.953871i | \(-0.402941\pi\) | ||||
0.300216 | + | 0.953871i | \(0.402941\pi\) | |||||||
\(984\) | −3.22255e19 | −1.13170 | ||||||||
\(985\) | −5.57118e19 | −1.94362 | ||||||||
\(986\) | 4.03657e18 | 0.139898 | ||||||||
\(987\) | −3.27946e18 | −0.112912 | ||||||||
\(988\) | −2.15093e17 | −0.00735710 | ||||||||
\(989\) | −6.76223e19 | −2.29781 | ||||||||
\(990\) | 1.73451e19 | 0.585530 | ||||||||
\(991\) | −2.34108e19 | −0.785124 | −0.392562 | − | 0.919725i | \(-0.628411\pi\) | ||||
−0.392562 | + | 0.919725i | \(0.628411\pi\) | |||||||
\(992\) | −3.27045e18 | −0.108964 | ||||||||
\(993\) | 1.01193e19 | 0.334951 | ||||||||
\(994\) | −7.30149e18 | −0.240104 | ||||||||
\(995\) | 4.54974e19 | 1.48640 | ||||||||
\(996\) | −1.69263e18 | −0.0549383 | ||||||||
\(997\) | 4.83103e19 | 1.55784 | 0.778918 | − | 0.627126i | \(-0.215769\pi\) | ||||
0.778918 | + | 0.627126i | \(0.215769\pi\) | |||||||
\(998\) | −4.31359e19 | −1.38195 | ||||||||
\(999\) | −8.48680e18 | −0.270127 |
(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 | 177.14.a.b.1.23 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.b.1.23 | ✓ | 31 | 1.1 | even | 1 | trivial |