Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,26,Mod(1,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.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: | \(197.998389976\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{4}\cdot 5^{18} \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(134113.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 1.47469e6 | 1.60209 | 0.801043 | − | 0.598607i | \(-0.204279\pi\) | ||||
0.801043 | + | 0.598607i | \(0.204279\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.04034e9 | −1.13285 | ||||||||
\(7\) | −3.57876e9 | −0.0977254 | −0.0488627 | − | 0.998806i | \(-0.515560\pi\) | ||||
−0.0488627 | + | 0.998806i | \(0.515560\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 1.32743e12 | 1.56668 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.08564e12 | 0.104299 | 0.0521493 | − | 0.998639i | \(-0.483393\pi\) | ||||
0.0521493 | + | 0.998639i | \(0.483393\pi\) | |||||||
\(12\) | 2.47412e13 | 0.801043 | ||||||||
\(13\) | −2.13293e13 | −0.253913 | −0.126956 | − | 0.991908i | \(-0.540521\pi\) | ||||
−0.126956 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(14\) | 1.46586e13 | 0.0691023 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 3.79275e15 | 1.57886 | 0.789428 | − | 0.613844i | \(-0.210377\pi\) | ||||
0.789428 | + | 0.613844i | \(0.210377\pi\) | |||||||
\(18\) | −5.43715e15 | −1.10781 | ||||||||
\(19\) | 6.90611e15 | 0.715836 | 0.357918 | − | 0.933753i | \(-0.383487\pi\) | ||||
0.357918 | + | 0.933753i | \(0.383487\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.27758e15 | −0.156564 | ||||||||
\(22\) | −4.44680e15 | −0.0737503 | ||||||||
\(23\) | 1.56245e17 | 1.48665 | 0.743324 | − | 0.668932i | \(-0.233248\pi\) | ||||
0.743324 | + | 0.668932i | \(0.233248\pi\) | |||||||
\(24\) | −1.01340e17 | −0.566423 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.73648e16 | 0.179544 | ||||||||
\(27\) | 7.08060e17 | 0.907868 | ||||||||
\(28\) | −6.00417e16 | −0.0488627 | ||||||||
\(29\) | 6.08503e17 | 0.319365 | 0.159683 | − | 0.987168i | \(-0.448953\pi\) | ||||
0.159683 | + | 0.987168i | \(0.448953\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.42961e18 | −0.782030 | −0.391015 | − | 0.920384i | \(-0.627876\pi\) | ||||
−0.391015 | + | 0.920384i | \(0.627876\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | 1.60099e18 | 0.167095 | ||||||||
\(34\) | −1.55351e19 | −1.11642 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.22706e19 | 0.783339 | ||||||||
\(37\) | −7.61614e19 | −1.90201 | −0.951006 | − | 0.309173i | \(-0.899948\pi\) | ||||
−0.951006 | + | 0.309173i | \(0.899948\pi\) | |||||||
\(38\) | −2.82874e19 | −0.506172 | ||||||||
\(39\) | −3.14542e19 | −0.406790 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.17158e20 | 1.50306 | 0.751532 | − | 0.659696i | \(-0.229315\pi\) | ||||
0.751532 | + | 0.659696i | \(0.229315\pi\) | |||||||
\(42\) | 2.16169e19 | 0.110708 | ||||||||
\(43\) | −4.70339e20 | −1.79496 | −0.897481 | − | 0.441052i | \(-0.854605\pi\) | ||||
−0.897481 | + | 0.441052i | \(0.854605\pi\) | |||||||
\(44\) | 1.82141e19 | 0.0521493 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.39979e20 | −1.05122 | ||||||||
\(47\) | 6.53190e20 | 0.820004 | 0.410002 | − | 0.912085i | \(-0.365528\pi\) | ||||
0.410002 | + | 0.912085i | \(0.365528\pi\) | |||||||
\(48\) | 4.15089e20 | 0.400521 | ||||||||
\(49\) | −1.32826e21 | −0.990450 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.59313e21 | 2.52946 | ||||||||
\(52\) | −3.57846e20 | −0.126956 | ||||||||
\(53\) | 4.54358e21 | 1.27043 | 0.635214 | − | 0.772336i | \(-0.280912\pi\) | ||||
0.635214 | + | 0.772336i | \(0.280912\pi\) | |||||||
\(54\) | −2.90021e21 | −0.641960 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.45931e20 | 0.0345512 | ||||||||
\(57\) | 1.01844e22 | 1.14683 | ||||||||
\(58\) | −2.49243e21 | −0.225825 | ||||||||
\(59\) | 1.39811e22 | 1.02303 | 0.511517 | − | 0.859273i | \(-0.329084\pi\) | ||||
0.511517 | + | 0.859273i | \(0.329084\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.30120e21 | −0.207475 | −0.103738 | − | 0.994605i | \(-0.533080\pi\) | ||||
−0.103738 | + | 0.994605i | \(0.533080\pi\) | |||||||
\(62\) | 1.40477e22 | 0.552979 | ||||||||
\(63\) | −4.75056e21 | −0.153104 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.55766e21 | −0.118154 | ||||||||
\(67\) | −3.04650e22 | −0.454848 | −0.227424 | − | 0.973796i | \(-0.573030\pi\) | ||||
−0.227424 | + | 0.973796i | \(0.573030\pi\) | |||||||
\(68\) | 6.36317e22 | 0.789428 | ||||||||
\(69\) | 2.30413e23 | 2.38174 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.08644e22 | −0.295540 | −0.147770 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147770 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(72\) | −9.12202e22 | −0.553905 | ||||||||
\(73\) | 1.14063e23 | 0.582918 | 0.291459 | − | 0.956583i | \(-0.405859\pi\) | ||||
0.291459 | + | 0.956583i | \(0.405859\pi\) | |||||||
\(74\) | 3.11957e23 | 1.34493 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.15865e23 | 0.357918 | ||||||||
\(77\) | −3.88526e21 | −0.0101926 | ||||||||
\(78\) | 1.28836e23 | 0.287644 | ||||||||
\(79\) | 6.98160e23 | 1.32928 | 0.664640 | − | 0.747164i | \(-0.268585\pi\) | ||||
0.664640 | + | 0.747164i | \(0.268585\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.05452e22 | −0.112196 | ||||||||
\(82\) | −8.89479e23 | −1.06283 | ||||||||
\(83\) | −1.18110e24 | −1.21286 | −0.606428 | − | 0.795139i | \(-0.707398\pi\) | ||||
−0.606428 | + | 0.795139i | \(0.707398\pi\) | |||||||
\(84\) | −8.85430e22 | −0.0782822 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.92651e24 | 1.26923 | ||||||||
\(87\) | 8.97354e23 | 0.511650 | ||||||||
\(88\) | −7.46049e22 | −0.0368751 | ||||||||
\(89\) | 2.79755e24 | 1.20061 | 0.600307 | − | 0.799770i | \(-0.295045\pi\) | ||||
0.600307 | + | 0.799770i | \(0.295045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.63325e22 | 0.0248137 | ||||||||
\(92\) | 2.62136e24 | 0.743324 | ||||||||
\(93\) | −5.05762e24 | −1.25288 | ||||||||
\(94\) | −2.67546e24 | −0.579831 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.70020e24 | −0.283211 | ||||||||
\(97\) | 1.06166e25 | 1.55360 | 0.776798 | − | 0.629750i | \(-0.216843\pi\) | ||||
0.776798 | + | 0.629750i | \(0.216843\pi\) | |||||||
\(98\) | 5.44056e24 | 0.700354 | ||||||||
\(99\) | 1.44112e24 | 0.163403 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.61024e24 | 0.672019 | 0.336009 | − | 0.941859i | \(-0.390923\pi\) | ||||
0.336009 | + | 0.941859i | \(0.390923\pi\) | |||||||
\(102\) | −2.29095e25 | −1.78860 | ||||||||
\(103\) | 1.50264e25 | 1.03846 | 0.519229 | − | 0.854635i | \(-0.326219\pi\) | ||||
0.519229 | + | 0.854635i | \(0.326219\pi\) | |||||||
\(104\) | 1.46574e24 | 0.0897718 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.86105e25 | −0.898328 | ||||||||
\(107\) | −3.03661e24 | −0.130344 | −0.0651721 | − | 0.997874i | \(-0.520760\pi\) | ||||
−0.0651721 | + | 0.997874i | \(0.520760\pi\) | |||||||
\(108\) | 1.18793e25 | 0.453934 | ||||||||
\(109\) | −3.16922e25 | −1.07925 | −0.539625 | − | 0.841906i | \(-0.681434\pi\) | ||||
−0.539625 | + | 0.841906i | \(0.681434\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.12315e26 | −3.04719 | ||||||||
\(112\) | −1.00733e24 | −0.0244314 | ||||||||
\(113\) | −6.24206e25 | −1.35471 | −0.677357 | − | 0.735655i | \(-0.736875\pi\) | ||||
−0.677357 | + | 0.735655i | \(0.736875\pi\) | |||||||
\(114\) | −4.17152e25 | −0.810931 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.02090e25 | 0.159683 | ||||||||
\(117\) | −2.83131e25 | −0.397800 | ||||||||
\(118\) | −5.72664e25 | −0.723394 | ||||||||
\(119\) | −1.35733e25 | −0.154294 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.07168e26 | −0.989122 | ||||||||
\(122\) | 1.76177e25 | 0.146707 | ||||||||
\(123\) | 3.20241e26 | 2.40804 | ||||||||
\(124\) | −5.75393e25 | −0.391015 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.94583e25 | 0.108261 | ||||||||
\(127\) | 1.67435e26 | 0.843917 | 0.421959 | − | 0.906615i | \(-0.361343\pi\) | ||||
0.421959 | + | 0.906615i | \(0.361343\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | −6.93606e26 | −2.87568 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.90057e26 | −0.650118 | −0.325059 | − | 0.945694i | \(-0.605384\pi\) | ||||
−0.325059 | + | 0.945694i | \(0.605384\pi\) | |||||||
\(132\) | 2.68602e25 | 0.0835477 | ||||||||
\(133\) | −2.47153e25 | −0.0699553 | ||||||||
\(134\) | 1.24785e26 | 0.321626 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.60636e26 | −0.558210 | ||||||||
\(137\) | 3.51717e26 | 0.687364 | 0.343682 | − | 0.939086i | \(-0.388326\pi\) | ||||
0.343682 | + | 0.939086i | \(0.388326\pi\) | |||||||
\(138\) | −9.43773e26 | −1.68414 | ||||||||
\(139\) | 3.91803e26 | 0.638827 | 0.319414 | − | 0.947615i | \(-0.396514\pi\) | ||||
0.319414 | + | 0.947615i | \(0.396514\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.63254e26 | 1.31372 | ||||||||
\(142\) | 1.67381e26 | 0.208978 | ||||||||
\(143\) | −2.31560e25 | −0.0264828 | ||||||||
\(144\) | 3.73638e26 | 0.391670 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.67201e26 | −0.412186 | ||||||||
\(147\) | −1.95878e27 | −1.58679 | ||||||||
\(148\) | −1.27778e27 | −0.951006 | ||||||||
\(149\) | 1.80648e27 | 1.23596 | 0.617979 | − | 0.786194i | \(-0.287952\pi\) | ||||
0.617979 | + | 0.786194i | \(0.287952\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.68416e26 | −0.0975373 | −0.0487687 | − | 0.998810i | \(-0.515530\pi\) | ||||
−0.0487687 | + | 0.998810i | \(0.515530\pi\) | |||||||
\(152\) | −4.74584e26 | −0.253086 | ||||||||
\(153\) | 5.03460e27 | 2.47356 | ||||||||
\(154\) | 1.59140e25 | 0.00720728 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.27713e26 | −0.203395 | ||||||||
\(157\) | 1.56946e27 | 0.558475 | 0.279237 | − | 0.960222i | \(-0.409918\pi\) | ||||
0.279237 | + | 0.960222i | \(0.409918\pi\) | |||||||
\(158\) | −2.85967e27 | −0.939943 | ||||||||
\(159\) | 6.70039e27 | 2.03533 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.59164e26 | −0.145283 | ||||||||
\(162\) | 3.29913e26 | 0.0793345 | ||||||||
\(163\) | 5.35307e27 | 1.19195 | 0.595974 | − | 0.803004i | \(-0.296766\pi\) | ||||
0.595974 | + | 0.803004i | \(0.296766\pi\) | |||||||
\(164\) | 3.64331e27 | 0.751532 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.83777e27 | 0.857618 | ||||||||
\(167\) | 1.01057e28 | 1.66192 | 0.830959 | − | 0.556334i | \(-0.187793\pi\) | ||||
0.830959 | + | 0.556334i | \(0.187793\pi\) | |||||||
\(168\) | 3.62672e26 | 0.0553539 | ||||||||
\(169\) | −6.60147e27 | −0.935528 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.16737e27 | 1.12148 | ||||||||
\(172\) | −7.89098e27 | −0.897481 | ||||||||
\(173\) | 8.66506e26 | 0.0916633 | 0.0458316 | − | 0.998949i | \(-0.485406\pi\) | ||||
0.0458316 | + | 0.998949i | \(0.485406\pi\) | |||||||
\(174\) | −3.67556e27 | −0.361791 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.05581e26 | 0.0260747 | ||||||||
\(177\) | 2.06178e28 | 1.63899 | ||||||||
\(178\) | −1.14588e28 | −0.848962 | ||||||||
\(179\) | −2.03208e28 | −1.40371 | −0.701856 | − | 0.712319i | \(-0.747645\pi\) | ||||
−0.701856 | + | 0.712319i | \(0.747645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.11555e27 | −0.367666 | −0.183833 | − | 0.982957i | \(-0.558851\pi\) | ||||
−0.183833 | + | 0.982957i | \(0.558851\pi\) | |||||||
\(182\) | −3.12658e26 | −0.0175460 | ||||||||
\(183\) | −6.34295e27 | −0.332393 | ||||||||
\(184\) | −1.07371e28 | −0.525609 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.07160e28 | 0.885919 | ||||||||
\(187\) | 4.11757e27 | 0.164672 | ||||||||
\(188\) | 1.09587e28 | 0.410002 | ||||||||
\(189\) | −2.53398e27 | −0.0887218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.25038e28 | 0.383819 | 0.191909 | − | 0.981413i | \(-0.438532\pi\) | ||||
0.191909 | + | 0.981413i | \(0.438532\pi\) | |||||||
\(192\) | 6.96404e27 | 0.200261 | ||||||||
\(193\) | 4.00087e28 | 1.07817 | 0.539086 | − | 0.842251i | \(-0.318770\pi\) | ||||
0.539086 | + | 0.842251i | \(0.318770\pi\) | |||||||
\(194\) | −4.34855e28 | −1.09856 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.22845e28 | −0.495225 | ||||||||
\(197\) | −1.19953e28 | −0.250141 | −0.125070 | − | 0.992148i | \(-0.539916\pi\) | ||||
−0.125070 | + | 0.992148i | \(0.539916\pi\) | |||||||
\(198\) | −5.90281e27 | −0.115543 | ||||||||
\(199\) | 3.34370e28 | 0.614559 | 0.307280 | − | 0.951619i | \(-0.400581\pi\) | ||||
0.307280 | + | 0.951619i | \(0.400581\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.49265e28 | −0.728705 | ||||||||
\(202\) | −3.11715e28 | −0.475189 | ||||||||
\(203\) | −2.17769e27 | −0.0312101 | ||||||||
\(204\) | 9.38372e28 | 1.26473 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −6.15480e28 | −0.734301 | ||||||||
\(207\) | 2.07404e29 | 2.32910 | ||||||||
\(208\) | −6.00366e27 | −0.0634782 | ||||||||
\(209\) | 7.49757e27 | 0.0746607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.92258e28 | 0.611980 | 0.305990 | − | 0.952035i | \(-0.401013\pi\) | ||||
0.305990 | + | 0.952035i | \(0.401013\pi\) | |||||||
\(212\) | 7.62287e28 | 0.635214 | ||||||||
\(213\) | −6.02624e28 | −0.473480 | ||||||||
\(214\) | 1.24379e28 | 0.0921672 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.86575e28 | −0.320980 | ||||||||
\(217\) | 1.22738e28 | 0.0764242 | ||||||||
\(218\) | 1.29811e29 | 0.763144 | ||||||||
\(219\) | 1.68207e29 | 0.933885 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.08966e28 | −0.400892 | ||||||||
\(222\) | 4.60040e29 | 2.15469 | ||||||||
\(223\) | 4.37006e29 | 1.93498 | 0.967490 | − | 0.252908i | \(-0.0813869\pi\) | ||||
0.967490 | + | 0.252908i | \(0.0813869\pi\) | |||||||
\(224\) | 4.12603e27 | 0.0172756 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.55675e29 | 0.957927 | ||||||||
\(227\) | −4.51616e28 | −0.160120 | −0.0800600 | − | 0.996790i | \(-0.525511\pi\) | ||||
−0.0800600 | + | 0.996790i | \(0.525511\pi\) | |||||||
\(228\) | 1.70866e29 | 0.573415 | ||||||||
\(229\) | −3.96675e29 | −1.26035 | −0.630175 | − | 0.776454i | \(-0.717017\pi\) | ||||
−0.630175 | + | 0.776454i | \(0.717017\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.72957e27 | −0.0163295 | ||||||||
\(232\) | −4.18160e28 | −0.112913 | ||||||||
\(233\) | −2.52711e29 | −0.646658 | −0.323329 | − | 0.946287i | \(-0.604802\pi\) | ||||
−0.323329 | + | 0.946287i | \(0.604802\pi\) | |||||||
\(234\) | 1.15971e29 | 0.281287 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.34563e29 | 0.511517 | ||||||||
\(237\) | 1.02957e30 | 2.12962 | ||||||||
\(238\) | 5.55964e28 | 0.109103 | ||||||||
\(239\) | 7.75729e29 | 1.44456 | 0.722281 | − | 0.691600i | \(-0.243094\pi\) | ||||
0.722281 | + | 0.691600i | \(0.243094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.98502e28 | −0.0333082 | −0.0166541 | − | 0.999861i | \(-0.505301\pi\) | ||||
−0.0166541 | + | 0.999861i | \(0.505301\pi\) | |||||||
\(242\) | 4.38962e29 | 0.699415 | ||||||||
\(243\) | −7.18710e29 | −1.08762 | ||||||||
\(244\) | −7.21621e28 | −0.103738 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.31171e30 | −1.70274 | ||||||||
\(247\) | −1.47302e29 | −0.181760 | ||||||||
\(248\) | 2.35681e29 | 0.276489 | ||||||||
\(249\) | −1.74175e30 | −1.94310 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.10004e29 | −0.918590 | −0.459295 | − | 0.888284i | \(-0.651898\pi\) | ||||
−0.459295 | + | 0.888284i | \(0.651898\pi\) | |||||||
\(252\) | −7.97011e28 | −0.0765522 | ||||||||
\(253\) | 1.69626e29 | 0.155055 | ||||||||
\(254\) | −6.85814e29 | −0.596740 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 1.13259e30 | 0.850961 | 0.425480 | − | 0.904968i | \(-0.360105\pi\) | ||||
0.425480 | + | 0.904968i | \(0.360105\pi\) | |||||||
\(258\) | 2.84101e30 | 2.03342 | ||||||||
\(259\) | 2.72563e29 | 0.185875 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.07744e29 | 0.500343 | ||||||||
\(262\) | 7.78473e29 | 0.459703 | ||||||||
\(263\) | 7.83926e29 | 0.441396 | 0.220698 | − | 0.975342i | \(-0.429167\pi\) | ||||
0.220698 | + | 0.975342i | \(0.429167\pi\) | |||||||
\(264\) | −1.10019e29 | −0.0590771 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.01234e29 | 0.0494659 | ||||||||
\(267\) | 4.12553e30 | 1.92349 | ||||||||
\(268\) | −5.11118e29 | −0.227424 | ||||||||
\(269\) | 2.21562e30 | 0.941005 | 0.470502 | − | 0.882399i | \(-0.344073\pi\) | ||||
0.470502 | + | 0.882399i | \(0.344073\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.34900e29 | −0.129658 | −0.0648289 | − | 0.997896i | \(-0.520650\pi\) | ||||
−0.0648289 | + | 0.997896i | \(0.520650\pi\) | |||||||
\(272\) | 1.06756e30 | 0.394714 | ||||||||
\(273\) | 1.12567e29 | 0.0397537 | ||||||||
\(274\) | −1.44063e30 | −0.486040 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.86569e30 | 1.19087 | ||||||||
\(277\) | 3.78301e30 | 1.11388 | 0.556942 | − | 0.830552i | \(-0.311975\pi\) | ||||
0.556942 | + | 0.830552i | \(0.311975\pi\) | |||||||
\(278\) | −1.60483e30 | −0.451719 | ||||||||
\(279\) | −4.55256e30 | −1.22519 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.06047e30 | −0.507151 | −0.253576 | − | 0.967316i | \(-0.581607\pi\) | ||||
−0.253576 | + | 0.967316i | \(0.581607\pi\) | |||||||
\(282\) | −3.94549e30 | −0.928938 | ||||||||
\(283\) | 1.40735e30 | 0.317010 | 0.158505 | − | 0.987358i | \(-0.449333\pi\) | ||||
0.158505 | + | 0.987358i | \(0.449333\pi\) | |||||||
\(284\) | −6.85591e29 | −0.147770 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.48471e28 | 0.0187261 | ||||||||
\(287\) | −7.77157e29 | −0.146888 | ||||||||
\(288\) | −1.53042e30 | −0.276952 | ||||||||
\(289\) | 8.61430e30 | 1.49278 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.56562e31 | 2.48899 | ||||||||
\(292\) | 1.91365e30 | 0.291459 | ||||||||
\(293\) | 3.14320e30 | 0.458698 | 0.229349 | − | 0.973344i | \(-0.426340\pi\) | ||||
0.229349 | + | 0.973344i | \(0.426340\pi\) | |||||||
\(294\) | 8.02315e30 | 1.12203 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.23377e30 | 0.672463 | ||||||||
\(297\) | 7.68701e29 | 0.0946894 | ||||||||
\(298\) | −7.39933e30 | −0.873955 | ||||||||
\(299\) | −3.33260e30 | −0.377479 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.68323e30 | 0.175413 | ||||||||
\(302\) | 6.89831e29 | 0.0689693 | ||||||||
\(303\) | 1.12228e31 | 1.07663 | ||||||||
\(304\) | 1.94390e30 | 0.178959 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.06217e31 | −1.74907 | ||||||||
\(307\) | 6.65869e29 | 0.0542200 | 0.0271100 | − | 0.999632i | \(-0.491370\pi\) | ||||
0.0271100 | + | 0.999632i | \(0.491370\pi\) | |||||||
\(308\) | −6.51839e28 | −0.00509631 | ||||||||
\(309\) | 2.21593e31 | 1.66370 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.30158e31 | −0.901497 | −0.450749 | − | 0.892651i | \(-0.648843\pi\) | ||||
−0.450749 | + | 0.892651i | \(0.648843\pi\) | |||||||
\(312\) | 2.16151e30 | 0.143822 | ||||||||
\(313\) | 1.48840e31 | 0.951514 | 0.475757 | − | 0.879577i | \(-0.342174\pi\) | ||||
0.475757 | + | 0.879577i | \(0.342174\pi\) | |||||||
\(314\) | −6.42849e30 | −0.394901 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.17132e31 | 0.664640 | ||||||||
\(317\) | −4.63362e30 | −0.252743 | −0.126372 | − | 0.991983i | \(-0.540333\pi\) | ||||
−0.126372 | + | 0.991983i | \(0.540333\pi\) | |||||||
\(318\) | −2.74448e31 | −1.43920 | ||||||||
\(319\) | 6.60617e29 | 0.0333093 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.47806e30 | −0.208822 | ||||||||
\(322\) | 2.29034e30 | 0.102731 | ||||||||
\(323\) | 2.61931e31 | 1.13020 | ||||||||
\(324\) | −1.35132e30 | −0.0560980 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.19262e31 | −0.842835 | ||||||||
\(327\) | −4.67363e31 | −1.72905 | ||||||||
\(328\) | −1.49230e31 | −0.531414 | ||||||||
\(329\) | −2.33761e30 | −0.0801352 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.64006e31 | −0.521207 | −0.260604 | − | 0.965446i | \(-0.583922\pi\) | ||||
−0.260604 | + | 0.965446i | \(0.583922\pi\) | |||||||
\(332\) | −1.98155e31 | −0.606428 | ||||||||
\(333\) | −1.01099e32 | −2.97984 | ||||||||
\(334\) | −4.13928e31 | −1.17515 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.48551e30 | −0.0391411 | ||||||||
\(337\) | 8.69817e30 | 0.220828 | 0.110414 | − | 0.993886i | \(-0.464782\pi\) | ||||
0.110414 | + | 0.993886i | \(0.464782\pi\) | |||||||
\(338\) | 2.70396e31 | 0.661518 | ||||||||
\(339\) | −9.20512e31 | −2.17037 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.72333e30 | −0.0815647 | ||||||||
\(342\) | −3.75495e31 | −0.793009 | ||||||||
\(343\) | 9.55290e30 | 0.194518 | ||||||||
\(344\) | 3.23215e31 | 0.634615 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.54921e30 | −0.0648157 | ||||||||
\(347\) | −8.06238e31 | −1.42019 | −0.710093 | − | 0.704108i | \(-0.751347\pi\) | ||||
−0.710093 | + | 0.704108i | \(0.751347\pi\) | |||||||
\(348\) | 1.50551e31 | 0.255825 | ||||||||
\(349\) | −9.75945e31 | −1.59995 | −0.799977 | − | 0.600031i | \(-0.795155\pi\) | ||||
−0.799977 | + | 0.600031i | \(0.795155\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.51024e31 | −0.230519 | ||||||||
\(352\) | −1.25166e30 | −0.0184376 | ||||||||
\(353\) | 1.35792e31 | 0.193060 | 0.0965298 | − | 0.995330i | \(-0.469226\pi\) | ||||
0.0965298 | + | 0.995330i | \(0.469226\pi\) | |||||||
\(354\) | −8.44503e31 | −1.15894 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.69351e31 | 0.600307 | ||||||||
\(357\) | −2.00165e31 | −0.247193 | ||||||||
\(358\) | 8.32340e31 | 0.992574 | ||||||||
\(359\) | 1.23431e32 | 1.42148 | 0.710742 | − | 0.703453i | \(-0.248359\pi\) | ||||
0.710742 | + | 0.703453i | \(0.248359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.53822e31 | −0.487579 | ||||||||
\(362\) | 2.50493e31 | 0.259979 | ||||||||
\(363\) | −1.58040e32 | −1.58466 | ||||||||
\(364\) | 1.28065e30 | 0.0124069 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.59807e31 | 0.235038 | ||||||||
\(367\) | −1.94163e31 | −0.169762 | −0.0848811 | − | 0.996391i | \(-0.527051\pi\) | ||||
−0.0848811 | + | 0.996391i | \(0.527051\pi\) | |||||||
\(368\) | 4.39791e31 | 0.371662 | ||||||||
\(369\) | 2.88262e32 | 2.35482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.62604e31 | −0.124153 | ||||||||
\(372\) | −8.48527e31 | −0.626439 | ||||||||
\(373\) | −1.75681e32 | −1.25420 | −0.627098 | − | 0.778941i | \(-0.715757\pi\) | ||||
−0.627098 | + | 0.778941i | \(0.715757\pi\) | |||||||
\(374\) | −1.68656e31 | −0.116441 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.48869e31 | −0.289915 | ||||||||
\(377\) | −1.29789e31 | −0.0810909 | ||||||||
\(378\) | 1.03792e31 | 0.0627358 | ||||||||
\(379\) | 2.09100e32 | 1.22283 | 0.611413 | − | 0.791312i | \(-0.290601\pi\) | ||||
0.611413 | + | 0.791312i | \(0.290601\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.46915e32 | 1.35203 | ||||||||
\(382\) | −5.12157e31 | −0.271401 | ||||||||
\(383\) | 1.47981e32 | 0.758966 | 0.379483 | − | 0.925199i | \(-0.376102\pi\) | ||||
0.379483 | + | 0.925199i | \(0.376102\pi\) | |||||||
\(384\) | −2.85247e31 | −0.141606 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.63876e32 | −0.762383 | ||||||||
\(387\) | −6.24342e32 | −2.81213 | ||||||||
\(388\) | 1.78117e32 | 0.776798 | ||||||||
\(389\) | 2.19739e32 | 0.927978 | 0.463989 | − | 0.885841i | \(-0.346418\pi\) | ||||
0.463989 | + | 0.885841i | \(0.346418\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.92598e32 | 2.34720 | ||||||||
\(392\) | 9.12774e31 | 0.350177 | ||||||||
\(393\) | −2.80275e32 | −1.04155 | ||||||||
\(394\) | 4.91329e31 | 0.176876 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.41779e31 | 0.0817013 | ||||||||
\(397\) | 1.95462e32 | 0.640003 | 0.320001 | − | 0.947417i | \(-0.396317\pi\) | ||||
0.320001 | + | 0.947417i | \(0.396317\pi\) | |||||||
\(398\) | −1.36958e32 | −0.434559 | ||||||||
\(399\) | −3.64475e31 | −0.112074 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.71177e32 | −1.36107 | −0.680534 | − | 0.732717i | \(-0.738252\pi\) | ||||
−0.680534 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(402\) | 1.84019e32 | 0.515273 | ||||||||
\(403\) | 7.31511e31 | 0.198567 | ||||||||
\(404\) | 1.27679e32 | 0.336009 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.91980e30 | 0.0220689 | ||||||||
\(407\) | −8.26841e31 | −0.198377 | ||||||||
\(408\) | −3.84357e32 | −0.894300 | ||||||||
\(409\) | −4.32845e32 | −0.976767 | −0.488384 | − | 0.872629i | \(-0.662413\pi\) | ||||
−0.488384 | + | 0.872629i | \(0.662413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.18675e32 | 1.10122 | ||||||||
\(412\) | 2.52101e32 | 0.519229 | ||||||||
\(413\) | −5.00349e31 | −0.0999763 | ||||||||
\(414\) | −8.49528e32 | −1.64692 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.45910e31 | 0.0448859 | ||||||||
\(417\) | 5.77790e32 | 1.02346 | ||||||||
\(418\) | −3.07101e31 | −0.0527931 | ||||||||
\(419\) | 9.61858e31 | 0.160485 | 0.0802427 | − | 0.996775i | \(-0.474430\pi\) | ||||
0.0802427 | + | 0.996775i | \(0.474430\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.59673e31 | 0.0251018 | 0.0125509 | − | 0.999921i | \(-0.496005\pi\) | ||||
0.0125509 | + | 0.999921i | \(0.496005\pi\) | |||||||
\(422\) | −2.83549e32 | −0.432735 | ||||||||
\(423\) | 8.67063e32 | 1.28468 | ||||||||
\(424\) | −3.12233e32 | −0.449164 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.46835e32 | 0.334801 | ||||||||
\(427\) | 1.53930e31 | 0.0202756 | ||||||||
\(428\) | −5.09458e31 | −0.0651721 | ||||||||
\(429\) | −3.41480e31 | −0.0424277 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.11839e32 | −0.834479 | −0.417240 | − | 0.908796i | \(-0.637002\pi\) | ||||
−0.417240 | + | 0.908796i | \(0.637002\pi\) | |||||||
\(432\) | 1.99301e32 | 0.226967 | ||||||||
\(433\) | 9.69753e32 | 1.07291 | 0.536454 | − | 0.843930i | \(-0.319764\pi\) | ||||
0.536454 | + | 0.843930i | \(0.319764\pi\) | |||||||
\(434\) | −5.02733e31 | −0.0540401 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.31708e32 | −0.539625 | ||||||||
\(437\) | 1.07904e33 | 1.06420 | ||||||||
\(438\) | −6.88977e32 | −0.660357 | ||||||||
\(439\) | −6.89367e32 | −0.642161 | −0.321081 | − | 0.947052i | \(-0.604046\pi\) | ||||
−0.321081 | + | 0.947052i | \(0.604046\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.76317e33 | −1.55172 | ||||||||
\(442\) | 3.31353e32 | 0.283473 | ||||||||
\(443\) | 1.47442e33 | 1.22624 | 0.613120 | − | 0.789990i | \(-0.289914\pi\) | ||||
0.613120 | + | 0.789990i | \(0.289914\pi\) | |||||||
\(444\) | −1.88433e33 | −1.52359 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.78998e33 | −1.36824 | ||||||||
\(447\) | 2.66400e33 | 1.98011 | ||||||||
\(448\) | −1.69002e31 | −0.0122157 | ||||||||
\(449\) | 2.43553e33 | 1.71204 | 0.856020 | − | 0.516942i | \(-0.172930\pi\) | ||||
0.856020 | + | 0.516942i | \(0.172930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.35756e32 | 0.156768 | ||||||||
\(452\) | −1.04724e33 | −0.677357 | ||||||||
\(453\) | −2.48361e32 | −0.156263 | ||||||||
\(454\) | 1.84982e32 | 0.113222 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.99866e32 | −0.405466 | ||||||||
\(457\) | 1.75801e33 | 0.990990 | 0.495495 | − | 0.868611i | \(-0.334987\pi\) | ||||
0.495495 | + | 0.868611i | \(0.334987\pi\) | |||||||
\(458\) | 1.62478e33 | 0.891201 | ||||||||
\(459\) | 2.68549e33 | 1.43339 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.02960e33 | 1.02600 | 0.513002 | − | 0.858387i | \(-0.328533\pi\) | ||||
0.513002 | + | 0.858387i | \(0.328533\pi\) | |||||||
\(462\) | 2.34683e31 | 0.0115467 | ||||||||
\(463\) | −5.63047e32 | −0.269639 | −0.134819 | − | 0.990870i | \(-0.543045\pi\) | ||||
−0.134819 | + | 0.990870i | \(0.543045\pi\) | |||||||
\(464\) | 1.71278e32 | 0.0798413 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.03510e33 | 0.457256 | ||||||||
\(467\) | −3.35205e33 | −1.44162 | −0.720808 | − | 0.693134i | \(-0.756229\pi\) | ||||
−0.720808 | + | 0.693134i | \(0.756229\pi\) | |||||||
\(468\) | −4.75016e32 | −0.198900 | ||||||||
\(469\) | 1.09027e32 | 0.0444502 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.31447e33 | 0.894725 | ||||||||
\(472\) | −9.60771e32 | −0.361697 | ||||||||
\(473\) | −5.10621e32 | −0.187212 | ||||||||
\(474\) | −4.21713e33 | −1.50587 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.27723e32 | −0.0771471 | ||||||||
\(477\) | 6.03128e33 | 1.99035 | ||||||||
\(478\) | −3.17739e33 | −1.02146 | ||||||||
\(479\) | 3.28090e33 | 1.02754 | 0.513770 | − | 0.857928i | \(-0.328248\pi\) | ||||
0.513770 | + | 0.857928i | \(0.328248\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.62447e33 | 0.482945 | ||||||||
\(482\) | 8.13063e31 | 0.0235525 | ||||||||
\(483\) | −8.24595e32 | −0.232756 | ||||||||
\(484\) | −1.79799e33 | −0.494561 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.94384e33 | 0.769061 | ||||||||
\(487\) | 2.83575e33 | 0.722032 | 0.361016 | − | 0.932560i | \(-0.382430\pi\) | ||||
0.361016 | + | 0.932560i | \(0.382430\pi\) | |||||||
\(488\) | 2.95576e32 | 0.0733536 | ||||||||
\(489\) | 7.89413e33 | 1.90960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.18264e33 | −1.42120 | −0.710600 | − | 0.703596i | \(-0.751576\pi\) | ||||
−0.710600 | + | 0.703596i | \(0.751576\pi\) | |||||||
\(492\) | 5.37276e33 | 1.20402 | ||||||||
\(493\) | 2.30790e33 | 0.504231 | ||||||||
\(494\) | 6.03351e32 | 0.128524 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.65349e32 | −0.195507 | ||||||||
\(497\) | 1.46244e32 | 0.0288817 | ||||||||
\(498\) | 7.13422e33 | 1.37398 | ||||||||
\(499\) | −2.73531e33 | −0.513748 | −0.256874 | − | 0.966445i | \(-0.582693\pi\) | ||||
−0.256874 | + | 0.966445i | \(0.582693\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.49028e34 | 2.66253 | ||||||||
\(502\) | 3.72738e33 | 0.649542 | ||||||||
\(503\) | −1.17377e33 | −0.199519 | −0.0997597 | − | 0.995012i | \(-0.531807\pi\) | ||||
−0.0997597 | + | 0.995012i | \(0.531807\pi\) | |||||||
\(504\) | 3.26456e32 | 0.0541306 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −6.94790e32 | −0.109641 | ||||||||
\(507\) | −9.73514e33 | −1.49880 | ||||||||
\(508\) | 2.80909e33 | 0.421959 | ||||||||
\(509\) | −4.20998e33 | −0.617031 | −0.308516 | − | 0.951219i | \(-0.599832\pi\) | ||||
−0.308516 | + | 0.951219i | \(0.599832\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.08203e32 | −0.0569659 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | 4.88994e33 | 0.649885 | ||||||||
\(514\) | −4.63910e33 | −0.601720 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.16368e34 | −1.43784 | ||||||||
\(517\) | 7.09131e32 | 0.0855253 | ||||||||
\(518\) | −1.11642e33 | −0.131433 | ||||||||
\(519\) | 1.27783e33 | 0.146852 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.42619e34 | −1.56208 | −0.781042 | − | 0.624478i | \(-0.785312\pi\) | ||||
−0.781042 | + | 0.624478i | \(0.785312\pi\) | |||||||
\(522\) | −3.30852e33 | −0.353796 | ||||||||
\(523\) | −1.07993e34 | −1.12752 | −0.563760 | − | 0.825939i | \(-0.690646\pi\) | ||||
−0.563760 | + | 0.825939i | \(0.690646\pi\) | |||||||
\(524\) | −3.18863e33 | −0.325059 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.21096e33 | −0.312114 | ||||||||
\(527\) | −1.30076e34 | −1.23471 | ||||||||
\(528\) | 4.50639e32 | 0.0417738 | ||||||||
\(529\) | 1.33667e34 | 1.21012 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.85589e34 | 1.60276 | ||||||||
\(532\) | −4.14654e32 | −0.0349777 | ||||||||
\(533\) | −4.63183e33 | −0.381647 | ||||||||
\(534\) | −1.68982e34 | −1.36011 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.09354e33 | 0.160813 | ||||||||
\(537\) | −2.99669e34 | −2.24887 | ||||||||
\(538\) | −9.07518e33 | −0.665391 | ||||||||
\(539\) | −1.44202e33 | −0.103303 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.36097e32 | −0.0640258 | −0.0320129 | − | 0.999487i | \(-0.510192\pi\) | ||||
−0.0320129 | + | 0.999487i | \(0.510192\pi\) | |||||||
\(542\) | 1.37175e33 | 0.0916819 | ||||||||
\(543\) | −9.01856e33 | −0.589033 | ||||||||
\(544\) | −4.37274e33 | −0.279105 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.61074e32 | −0.0281101 | ||||||||
\(547\) | 1.05246e34 | 0.627137 | 0.313568 | − | 0.949566i | \(-0.398475\pi\) | ||||
0.313568 | + | 0.949566i | \(0.398475\pi\) | |||||||
\(548\) | 5.90084e33 | 0.343682 | ||||||||
\(549\) | −5.70954e33 | −0.325047 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.20238e33 | 0.228613 | ||||||||
\(552\) | −1.58339e34 | −0.842071 | ||||||||
\(553\) | −2.49855e33 | −0.129904 | ||||||||
\(554\) | −1.54952e34 | −0.787635 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.57337e33 | 0.319414 | ||||||||
\(557\) | 9.65307e33 | 0.458644 | 0.229322 | − | 0.973351i | \(-0.426349\pi\) | ||||
0.229322 | + | 0.973351i | \(0.426349\pi\) | |||||||
\(558\) | 1.86473e34 | 0.866340 | ||||||||
\(559\) | 1.00320e34 | 0.455764 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.07215e33 | 0.263819 | ||||||||
\(562\) | 8.43969e33 | 0.358610 | ||||||||
\(563\) | −4.08658e34 | −1.69826 | −0.849132 | − | 0.528180i | \(-0.822875\pi\) | ||||
−0.849132 | + | 0.528180i | \(0.822875\pi\) | |||||||
\(564\) | 1.61607e34 | 0.656859 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.76452e33 | −0.224160 | ||||||||
\(567\) | 2.88252e32 | 0.0109644 | ||||||||
\(568\) | 2.80818e33 | 0.104489 | ||||||||
\(569\) | 8.49519e33 | 0.309221 | 0.154611 | − | 0.987975i | \(-0.450588\pi\) | ||||
0.154611 | + | 0.987975i | \(0.450588\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.91693e34 | −1.01619 | −0.508095 | − | 0.861301i | \(-0.669650\pi\) | ||||
−0.508095 | + | 0.861301i | \(0.669650\pi\) | |||||||
\(572\) | −3.88494e32 | −0.0132414 | ||||||||
\(573\) | 1.84393e34 | 0.614910 | ||||||||
\(574\) | 3.18324e33 | 0.103865 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.26861e33 | 0.195835 | ||||||||
\(577\) | −5.12659e33 | −0.156722 | −0.0783611 | − | 0.996925i | \(-0.524969\pi\) | ||||
−0.0783611 | + | 0.996925i | \(0.524969\pi\) | |||||||
\(578\) | −3.52842e34 | −1.05556 | ||||||||
\(579\) | 5.90005e34 | 1.72732 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.22686e33 | 0.118527 | ||||||||
\(582\) | −6.41278e34 | −1.75998 | ||||||||
\(583\) | 4.93271e33 | 0.132504 | ||||||||
\(584\) | −7.83833e33 | −0.206093 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.28746e34 | −0.324349 | ||||||||
\(587\) | −6.37641e34 | −1.57253 | −0.786266 | − | 0.617888i | \(-0.787989\pi\) | ||||
−0.786266 | + | 0.617888i | \(0.787989\pi\) | |||||||
\(588\) | −3.28628e34 | −0.793393 | ||||||||
\(589\) | −2.36852e34 | −0.559805 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.76894e34 | −0.400747 | ||||||||
\(592\) | −2.14375e34 | −0.475503 | ||||||||
\(593\) | 7.56532e34 | 1.64302 | 0.821511 | − | 0.570192i | \(-0.193131\pi\) | ||||
0.821511 | + | 0.570192i | \(0.193131\pi\) | |||||||
\(594\) | −3.14860e33 | −0.0669556 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.03076e34 | 0.617979 | ||||||||
\(597\) | 4.93093e34 | 0.984577 | ||||||||
\(598\) | 1.36503e34 | 0.266918 | ||||||||
\(599\) | 6.58590e34 | 1.26119 | 0.630594 | − | 0.776113i | \(-0.282811\pi\) | ||||
0.630594 | + | 0.776113i | \(0.282811\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.63692e34 | −0.668041 | −0.334020 | − | 0.942566i | \(-0.608405\pi\) | ||||
−0.334020 | + | 0.942566i | \(0.608405\pi\) | |||||||
\(602\) | −6.89452e33 | −0.124036 | ||||||||
\(603\) | −4.04401e34 | −0.712601 | ||||||||
\(604\) | −2.82555e33 | −0.0487687 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −4.59684e34 | −0.761293 | ||||||||
\(607\) | −1.13535e35 | −1.84193 | −0.920963 | − | 0.389650i | \(-0.872596\pi\) | ||||
−0.920963 | + | 0.389650i | \(0.872596\pi\) | |||||||
\(608\) | −7.96220e33 | −0.126543 | ||||||||
\(609\) | −3.21142e33 | −0.0500012 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.39321e34 | −0.208210 | ||||||||
\(612\) | 8.44666e34 | 1.23678 | ||||||||
\(613\) | 8.49768e34 | 1.21911 | 0.609557 | − | 0.792742i | \(-0.291347\pi\) | ||||
0.609557 | + | 0.792742i | \(0.291347\pi\) | |||||||
\(614\) | −2.72740e33 | −0.0383393 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.66993e32 | 0.00360364 | ||||||||
\(617\) | 1.49456e35 | 1.97674 | 0.988368 | − | 0.152079i | \(-0.0485967\pi\) | ||||
0.988368 | + | 0.152079i | \(0.0485967\pi\) | |||||||
\(618\) | −9.07644e34 | −1.17641 | ||||||||
\(619\) | −5.75885e34 | −0.731481 | −0.365740 | − | 0.930717i | \(-0.619184\pi\) | ||||
−0.365740 | + | 0.930717i | \(0.619184\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.10631e35 | 1.34968 | ||||||||
\(622\) | 5.33125e34 | 0.637455 | ||||||||
\(623\) | −1.00118e34 | −0.117330 | ||||||||
\(624\) | −8.85356e33 | −0.101698 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6.09648e34 | −0.672822 | ||||||||
\(627\) | 1.10566e34 | 0.119613 | ||||||||
\(628\) | 2.63311e34 | 0.279237 | ||||||||
\(629\) | −2.88861e35 | −3.00300 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.54832e34 | 0.354532 | 0.177266 | − | 0.984163i | \(-0.443275\pi\) | ||||
0.177266 | + | 0.984163i | \(0.443275\pi\) | |||||||
\(632\) | −4.79772e34 | −0.469972 | ||||||||
\(633\) | 1.02087e35 | 0.980445 | ||||||||
\(634\) | 1.89793e34 | 0.178716 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.12414e35 | 1.01767 | ||||||||
\(637\) | 2.83309e34 | 0.251488 | ||||||||
\(638\) | −2.70589e33 | −0.0235533 | ||||||||
\(639\) | −5.42446e34 | −0.463016 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.20958e35 | 0.992909 | 0.496454 | − | 0.868063i | \(-0.334635\pi\) | ||||
0.496454 | + | 0.868063i | \(0.334635\pi\) | |||||||
\(642\) | 1.83421e34 | 0.147660 | ||||||||
\(643\) | 4.32278e34 | 0.341292 | 0.170646 | − | 0.985332i | \(-0.445415\pi\) | ||||
0.170646 | + | 0.985332i | \(0.445415\pi\) | |||||||
\(644\) | −9.38121e33 | −0.0726416 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.07287e35 | −0.799173 | ||||||||
\(647\) | 4.93254e34 | 0.360385 | 0.180193 | − | 0.983631i | \(-0.442328\pi\) | ||||
0.180193 | + | 0.983631i | \(0.442328\pi\) | |||||||
\(648\) | 5.53503e33 | 0.0396673 | ||||||||
\(649\) | 1.51784e34 | 0.106701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.81000e34 | 0.122438 | ||||||||
\(652\) | 8.98095e34 | 0.595974 | ||||||||
\(653\) | −2.81796e35 | −1.83451 | −0.917255 | − | 0.398301i | \(-0.869600\pi\) | ||||
−0.917255 | + | 0.398301i | \(0.869600\pi\) | |||||||
\(654\) | 1.91432e35 | 1.22262 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.11245e34 | 0.375766 | ||||||||
\(657\) | 1.51410e35 | 0.913246 | ||||||||
\(658\) | 9.57486e33 | 0.0566642 | ||||||||
\(659\) | −1.27642e35 | −0.741185 | −0.370592 | − | 0.928796i | \(-0.620845\pi\) | ||||
−0.370592 | + | 0.928796i | \(0.620845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.04753e35 | −1.70384 | −0.851921 | − | 0.523671i | \(-0.824562\pi\) | ||||
−0.851921 | + | 0.523671i | \(0.824562\pi\) | |||||||
\(662\) | 6.71770e34 | 0.368549 | ||||||||
\(663\) | −1.19298e35 | −0.642263 | ||||||||
\(664\) | 8.11643e34 | 0.428809 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.14101e35 | 2.10707 | ||||||||
\(667\) | 9.50755e34 | 0.474783 | ||||||||
\(668\) | 1.69545e35 | 0.830959 | ||||||||
\(669\) | 6.44450e35 | 3.10001 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.66957e33 | −0.0216394 | ||||||||
\(672\) | 6.08463e33 | 0.0276770 | ||||||||
\(673\) | 2.27652e35 | 1.01644 | 0.508221 | − | 0.861227i | \(-0.330303\pi\) | ||||
0.508221 | + | 0.861227i | \(0.330303\pi\) | |||||||
\(674\) | −3.56277e34 | −0.156149 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.10754e35 | −0.467764 | ||||||||
\(677\) | 1.12736e35 | 0.467416 | 0.233708 | − | 0.972307i | \(-0.424914\pi\) | ||||
0.233708 | + | 0.972307i | \(0.424914\pi\) | |||||||
\(678\) | 3.77042e35 | 1.53468 | ||||||||
\(679\) | −3.79942e34 | −0.151826 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.65994e34 | −0.256526 | ||||||||
\(682\) | 1.52508e34 | 0.0576749 | ||||||||
\(683\) | 1.62407e35 | 0.603039 | 0.301520 | − | 0.953460i | \(-0.402506\pi\) | ||||
0.301520 | + | 0.953460i | \(0.402506\pi\) | |||||||
\(684\) | 1.53803e35 | 0.560742 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −3.91287e34 | −0.137545 | ||||||||
\(687\) | −5.84973e35 | −2.01919 | ||||||||
\(688\) | −1.32389e35 | −0.448741 | ||||||||
\(689\) | −9.69114e34 | −0.322578 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.17749e35 | −0.699006 | −0.349503 | − | 0.936935i | \(-0.613649\pi\) | ||||
−0.349503 | + | 0.936935i | \(0.613649\pi\) | |||||||
\(692\) | 1.45376e34 | 0.0458316 | ||||||||
\(693\) | −5.15741e33 | −0.0159686 | ||||||||
\(694\) | 3.30235e35 | 1.00422 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −6.16657e34 | −0.180896 | ||||||||
\(697\) | 8.23625e35 | 2.37312 | ||||||||
\(698\) | 3.99747e35 | 1.13134 | ||||||||
\(699\) | −3.72671e35 | −1.03600 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.31197e35 | −0.351923 | −0.175961 | − | 0.984397i | \(-0.556303\pi\) | ||||
−0.175961 | + | 0.984397i | \(0.556303\pi\) | |||||||
\(702\) | 6.18595e34 | 0.163002 | ||||||||
\(703\) | −5.25979e35 | −1.36153 | ||||||||
\(704\) | 5.12681e33 | 0.0130373 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.56205e34 | −0.136514 | ||||||||
\(707\) | −2.72353e34 | −0.0656733 | ||||||||
\(708\) | 3.45908e35 | 0.819493 | ||||||||
\(709\) | 1.07011e35 | 0.249088 | 0.124544 | − | 0.992214i | \(-0.460253\pi\) | ||||
0.124544 | + | 0.992214i | \(0.460253\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.26759e35 | 2.08256 | ||||||||
\(712\) | −1.92246e35 | −0.424481 | ||||||||
\(713\) | −5.35859e35 | −1.16260 | ||||||||
\(714\) | 8.19876e34 | 0.174792 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.40927e35 | −0.701856 | ||||||||
\(717\) | 1.14396e36 | 2.31431 | ||||||||
\(718\) | −5.05572e35 | −1.00514 | ||||||||
\(719\) | −7.33489e35 | −1.43312 | −0.716560 | − | 0.697526i | \(-0.754284\pi\) | ||||
−0.716560 | + | 0.697526i | \(0.754284\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.37759e34 | −0.101484 | ||||||||
\(722\) | 1.85885e35 | 0.344771 | ||||||||
\(723\) | −2.92729e34 | −0.0533626 | ||||||||
\(724\) | −1.02602e35 | −0.183833 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.47334e35 | 1.12052 | ||||||||
\(727\) | −1.00868e36 | −1.71622 | −0.858111 | − | 0.513465i | \(-0.828362\pi\) | ||||
−0.858111 | + | 0.513465i | \(0.828362\pi\) | |||||||
\(728\) | −5.24553e33 | −0.00877298 | ||||||||
\(729\) | −9.91632e35 | −1.63026 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.78388e36 | −2.83399 | ||||||||
\(732\) | −1.06417e35 | −0.166197 | ||||||||
\(733\) | 1.19811e36 | 1.83948 | 0.919741 | − | 0.392525i | \(-0.128398\pi\) | ||||
0.919741 | + | 0.392525i | \(0.128398\pi\) | |||||||
\(734\) | 7.95292e34 | 0.120040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.80138e35 | −0.262805 | ||||||||
\(737\) | −3.30741e34 | −0.0474400 | ||||||||
\(738\) | −1.18072e36 | −1.66511 | ||||||||
\(739\) | −7.47298e35 | −1.03619 | −0.518094 | − | 0.855324i | \(-0.673358\pi\) | ||||
−0.518094 | + | 0.855324i | \(0.673358\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.17226e35 | −0.291195 | ||||||||
\(742\) | 6.66026e34 | 0.0877895 | ||||||||
\(743\) | 1.09617e36 | 1.42075 | 0.710376 | − | 0.703822i | \(-0.248525\pi\) | ||||
0.710376 | + | 0.703822i | \(0.248525\pi\) | |||||||
\(744\) | 3.47557e35 | 0.442960 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.19590e35 | 0.886850 | ||||||||
\(747\) | −1.56782e36 | −1.90015 | ||||||||
\(748\) | 6.90814e34 | 0.0823362 | ||||||||
\(749\) | 1.08673e34 | 0.0127379 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.75595e34 | −0.0539186 | −0.0269593 | − | 0.999637i | \(-0.508582\pi\) | ||||
−0.0269593 | + | 0.999637i | \(0.508582\pi\) | |||||||
\(752\) | 1.83857e35 | 0.205001 | ||||||||
\(753\) | −1.34198e36 | −1.47166 | ||||||||
\(754\) | 5.31617e34 | 0.0573399 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.25131e34 | −0.0443609 | ||||||||
\(757\) | −1.35534e36 | −1.39107 | −0.695537 | − | 0.718490i | \(-0.744834\pi\) | ||||
−0.695537 | + | 0.718490i | \(0.744834\pi\) | |||||||
\(758\) | −8.56475e35 | −0.864669 | ||||||||
\(759\) | 2.50147e35 | 0.248412 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4.04146e35 | −0.388356 | −0.194178 | − | 0.980966i | \(-0.562204\pi\) | ||||
−0.194178 | + | 0.980966i | \(0.562204\pi\) | |||||||
\(762\) | −1.01136e36 | −0.956028 | ||||||||
\(763\) | 1.13419e35 | 0.105470 | ||||||||
\(764\) | 2.09779e35 | 0.191909 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.06132e35 | −0.536670 | ||||||||
\(767\) | −2.98206e35 | −0.259761 | ||||||||
\(768\) | 1.16837e35 | 0.100130 | ||||||||
\(769\) | −1.59517e36 | −1.34502 | −0.672509 | − | 0.740089i | \(-0.734783\pi\) | ||||
−0.672509 | + | 0.740089i | \(0.734783\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.67023e36 | 1.36331 | ||||||||
\(772\) | 6.71234e35 | 0.539086 | ||||||||
\(773\) | 5.09562e35 | 0.402674 | 0.201337 | − | 0.979522i | \(-0.435471\pi\) | ||||
0.201337 | + | 0.979522i | \(0.435471\pi\) | |||||||
\(774\) | 2.55730e36 | 1.98848 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.29566e35 | −0.549279 | ||||||||
\(777\) | 4.01947e35 | 0.297787 | ||||||||
\(778\) | −9.00052e35 | −0.656180 | ||||||||
\(779\) | 1.49972e36 | 1.07595 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.43642e34 | −0.0308244 | ||||||||
\(782\) | −2.42728e36 | −1.65972 | ||||||||
\(783\) | 4.30856e35 | 0.289941 | ||||||||
\(784\) | −3.73872e35 | −0.247612 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.14801e36 | 0.736484 | ||||||||
\(787\) | −1.58597e36 | −1.00141 | −0.500703 | − | 0.865619i | \(-0.666925\pi\) | ||||
−0.500703 | + | 0.865619i | \(0.666925\pi\) | |||||||
\(788\) | −2.01248e35 | −0.125070 | ||||||||
\(789\) | 1.15605e36 | 0.707154 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.23389e35 | 0.132390 | ||||||||
\(792\) | −9.90327e34 | −0.0577715 | ||||||||
\(793\) | 9.17416e34 | 0.0526807 | ||||||||
\(794\) | −8.00614e35 | −0.452550 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5.60980e35 | 0.307280 | ||||||||
\(797\) | 1.54676e36 | 0.834053 | 0.417027 | − | 0.908894i | \(-0.363072\pi\) | ||||
0.417027 | + | 0.908894i | \(0.363072\pi\) | |||||||
\(798\) | 1.49289e35 | 0.0792486 | ||||||||
\(799\) | 2.47738e36 | 1.29467 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.71355e36 | 1.88098 | ||||||||
\(802\) | 1.92994e36 | 0.962420 | ||||||||
\(803\) | 1.23831e35 | 0.0607976 | ||||||||
\(804\) | −7.53742e35 | −0.364353 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.99627e35 | −0.140408 | ||||||||
\(807\) | 3.26736e36 | 1.50757 | ||||||||
\(808\) | −5.22972e35 | −0.237594 | ||||||||
\(809\) | 6.21020e35 | 0.277811 | 0.138905 | − | 0.990306i | \(-0.455642\pi\) | ||||
0.138905 | + | 0.990306i | \(0.455642\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.69897e35 | 0.203818 | 0.101909 | − | 0.994794i | \(-0.467505\pi\) | ||||
0.101909 | + | 0.994794i | \(0.467505\pi\) | |||||||
\(812\) | −3.65355e34 | −0.0156050 | ||||||||
\(813\) | −4.93874e35 | −0.207723 | ||||||||
\(814\) | 3.38674e35 | 0.140274 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.57433e36 | 0.632365 | ||||||||
\(817\) | −3.24821e36 | −1.28490 | ||||||||
\(818\) | 1.77293e36 | 0.690679 | ||||||||
\(819\) | 1.01326e35 | 0.0388752 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.77384e36 | −1.40441 | −0.702205 | − | 0.711975i | \(-0.747801\pi\) | ||||
−0.702205 | + | 0.711975i | \(0.747801\pi\) | |||||||
\(822\) | −2.12449e36 | −0.778677 | ||||||||
\(823\) | −1.31964e36 | −0.476385 | −0.238192 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238192 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(824\) | −1.03260e36 | −0.367150 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.04943e35 | 0.0706939 | ||||||||
\(827\) | −2.35273e36 | −0.799380 | −0.399690 | − | 0.916650i | \(-0.630882\pi\) | ||||
−0.399690 | + | 0.916650i | \(0.630882\pi\) | |||||||
\(828\) | 3.47966e36 | 1.16455 | ||||||||
\(829\) | −1.44960e36 | −0.477878 | −0.238939 | − | 0.971035i | \(-0.576800\pi\) | ||||
−0.238939 | + | 0.971035i | \(0.576800\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.57877e36 | 1.78454 | ||||||||
\(832\) | −1.00725e35 | −0.0317391 | ||||||||
\(833\) | −5.03776e36 | −1.56378 | ||||||||
\(834\) | −2.36663e36 | −0.723692 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.25788e35 | 0.0373304 | ||||||||
\(837\) | −2.42837e36 | −0.709980 | ||||||||
\(838\) | −3.93977e35 | −0.113480 | ||||||||
\(839\) | −6.60849e35 | −0.187533 | −0.0937665 | − | 0.995594i | \(-0.529891\pi\) | ||||
−0.0937665 | + | 0.995594i | \(0.529891\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.26009e36 | −0.898006 | ||||||||
\(842\) | −6.54019e34 | −0.0177496 | ||||||||
\(843\) | −3.03856e36 | −0.812500 | ||||||||
\(844\) | 1.16142e36 | 0.305990 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.55149e36 | −0.908408 | ||||||||
\(847\) | 3.83530e35 | 0.0966623 | ||||||||
\(848\) | 1.27890e36 | 0.317607 | ||||||||
\(849\) | 2.07541e36 | 0.507877 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.18998e37 | −2.82762 | ||||||||
\(852\) | −1.01104e36 | −0.236740 | ||||||||
\(853\) | −5.07169e35 | −0.117028 | −0.0585140 | − | 0.998287i | \(-0.518636\pi\) | ||||
−0.0585140 | + | 0.998287i | \(0.518636\pi\) | |||||||
\(854\) | −6.30496e34 | −0.0143370 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.08674e35 | 0.0460836 | ||||||||
\(857\) | 2.45792e36 | 0.534943 | 0.267471 | − | 0.963566i | \(-0.413812\pi\) | ||||
0.267471 | + | 0.963566i | \(0.413812\pi\) | |||||||
\(858\) | 1.39870e35 | 0.0300009 | ||||||||
\(859\) | −7.15238e36 | −1.51194 | −0.755972 | − | 0.654603i | \(-0.772836\pi\) | ||||
−0.755972 | + | 0.654603i | \(0.772836\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.14607e36 | −0.235327 | ||||||||
\(862\) | 2.91569e36 | 0.590066 | ||||||||
\(863\) | −2.16205e36 | −0.431252 | −0.215626 | − | 0.976476i | \(-0.569179\pi\) | ||||
−0.215626 | + | 0.976476i | \(0.569179\pi\) | |||||||
\(864\) | −8.16337e35 | −0.160490 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.97211e36 | −0.758660 | ||||||||
\(867\) | 1.27034e37 | 2.39157 | ||||||||
\(868\) | 2.05919e35 | 0.0382121 | ||||||||
\(869\) | 7.57953e35 | 0.138642 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.49797e35 | 0.115492 | ||||||||
\(872\) | 2.17787e36 | 0.381572 | ||||||||
\(873\) | 1.40928e37 | 2.43399 | ||||||||
\(874\) | −4.41977e36 | −0.752500 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.82205e36 | 0.466943 | ||||||||
\(877\) | −6.84625e36 | −1.11676 | −0.558378 | − | 0.829587i | \(-0.688576\pi\) | ||||
−0.558378 | + | 0.829587i | \(0.688576\pi\) | |||||||
\(878\) | 2.82365e36 | 0.454077 | ||||||||
\(879\) | 4.63526e36 | 0.734874 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.59663e36 | 0.400139 | 0.200069 | − | 0.979782i | \(-0.435883\pi\) | ||||
0.200069 | + | 0.979782i | \(0.435883\pi\) | |||||||
\(882\) | 7.22196e36 | 1.09723 | ||||||||
\(883\) | −1.13962e36 | −0.170707 | −0.0853533 | − | 0.996351i | \(-0.527202\pi\) | ||||
−0.0853533 | + | 0.996351i | \(0.527202\pi\) | |||||||
\(884\) | −1.35722e36 | −0.200446 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −6.03924e36 | −0.867083 | ||||||||
\(887\) | 2.38557e36 | 0.337713 | 0.168856 | − | 0.985641i | \(-0.445993\pi\) | ||||
0.168856 | + | 0.985641i | \(0.445993\pi\) | |||||||
\(888\) | 7.71820e36 | 1.07734 | ||||||||
\(889\) | −5.99211e35 | −0.0824722 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −8.74434e34 | −0.0117019 | ||||||||
\(892\) | 7.33175e36 | 0.967490 | ||||||||
\(893\) | 4.51100e36 | 0.586988 | ||||||||
\(894\) | −1.09117e37 | −1.40015 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.92234e34 | 0.00863779 | ||||||||
\(897\) | −4.91456e36 | −0.604754 | ||||||||
\(898\) | −9.97593e36 | −1.21060 | ||||||||
\(899\) | −2.08693e36 | −0.249753 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.72327e37 | 2.00582 | ||||||||
\(902\) | −9.65657e35 | −0.110851 | ||||||||
\(903\) | 2.48225e36 | 0.281027 | ||||||||
\(904\) | 4.28951e36 | 0.478964 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.01729e36 | 0.110495 | ||||||||
\(907\) | 1.67063e37 | 1.78974 | 0.894870 | − | 0.446326i | \(-0.147268\pi\) | ||||
0.894870 | + | 0.446326i | \(0.147268\pi\) | |||||||
\(908\) | −7.57685e35 | −0.0800600 | ||||||||
\(909\) | 1.01021e37 | 1.05284 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.13215e37 | 1.14795 | 0.573976 | − | 0.818872i | \(-0.305400\pi\) | ||||
0.573976 | + | 0.818872i | \(0.305400\pi\) | |||||||
\(912\) | 2.86665e36 | 0.286708 | ||||||||
\(913\) | −1.28225e36 | −0.126499 | ||||||||
\(914\) | −7.20082e36 | −0.700736 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.65510e36 | −0.630175 | ||||||||
\(917\) | 6.80169e35 | 0.0635331 | ||||||||
\(918\) | −1.09998e37 | −1.01356 | ||||||||
\(919\) | 1.76508e37 | 1.60443 | 0.802215 | − | 0.597035i | \(-0.203655\pi\) | ||||
0.802215 | + | 0.597035i | \(0.203655\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.81953e35 | 0.0868651 | ||||||||
\(922\) | −8.31325e36 | −0.725495 | ||||||||
\(923\) | 8.71609e35 | 0.0750413 | ||||||||
\(924\) | −9.61262e34 | −0.00816473 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.30624e36 | 0.190663 | ||||||||
\(927\) | 1.99465e37 | 1.62693 | ||||||||
\(928\) | −7.01556e35 | −0.0564563 | ||||||||
\(929\) | 2.88984e36 | 0.229445 | 0.114722 | − | 0.993398i | \(-0.463402\pi\) | ||||
0.114722 | + | 0.993398i | \(0.463402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.17311e36 | −0.708999 | ||||||||
\(932\) | −4.23978e36 | −0.323329 | ||||||||
\(933\) | −1.91942e37 | −1.44428 | ||||||||
\(934\) | 1.37300e37 | 1.01938 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.94566e36 | 0.140644 | ||||||||
\(937\) | −1.29200e37 | −0.921545 | −0.460772 | − | 0.887518i | \(-0.652428\pi\) | ||||
−0.460772 | + | 0.887518i | \(0.652428\pi\) | |||||||
\(938\) | −4.46575e35 | −0.0314310 | ||||||||
\(939\) | 2.19493e37 | 1.52441 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.06414e37 | 1.39595 | 0.697973 | − | 0.716124i | \(-0.254086\pi\) | ||||
0.697973 | + | 0.716124i | \(0.254086\pi\) | |||||||
\(942\) | −9.48005e36 | −0.632666 | ||||||||
\(943\) | 3.39299e37 | 2.23453 | ||||||||
\(944\) | 3.93532e36 | 0.255758 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.09150e36 | 0.132379 | ||||||||
\(947\) | −2.09426e36 | −0.130815 | −0.0654073 | − | 0.997859i | \(-0.520835\pi\) | ||||
−0.0654073 | + | 0.997859i | \(0.520835\pi\) | |||||||
\(948\) | 1.72734e37 | 1.06481 | ||||||||
\(949\) | −2.43288e36 | −0.148010 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.83316e36 | −0.404916 | ||||||||
\(952\) | 9.32753e35 | 0.0545513 | ||||||||
\(953\) | 1.70726e37 | 0.985461 | 0.492731 | − | 0.870182i | \(-0.335999\pi\) | ||||
0.492731 | + | 0.870182i | \(0.335999\pi\) | |||||||
\(954\) | −2.47041e37 | −1.40739 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.30146e37 | 0.722281 | ||||||||
\(957\) | 9.74207e35 | 0.0533644 | ||||||||
\(958\) | −1.34386e37 | −0.726581 | ||||||||
\(959\) | −1.25871e36 | −0.0671729 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.47058e36 | −0.388429 | ||||||||
\(962\) | −6.65382e36 | −0.341494 | ||||||||
\(963\) | −4.03088e36 | −0.204207 | ||||||||
\(964\) | −3.33031e35 | −0.0166541 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.37754e36 | 0.164584 | ||||||||
\(967\) | 1.41585e37 | 0.681063 | 0.340532 | − | 0.940233i | \(-0.389393\pi\) | ||||
0.340532 | + | 0.940233i | \(0.389393\pi\) | |||||||
\(968\) | 7.36456e36 | 0.349707 | ||||||||
\(969\) | 3.86268e37 | 1.81068 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.45645e37 | −0.665357 | −0.332678 | − | 0.943040i | \(-0.607952\pi\) | ||||
−0.332678 | + | 0.943040i | \(0.607952\pi\) | |||||||
\(972\) | −1.20580e37 | −0.543808 | ||||||||
\(973\) | −1.40217e36 | −0.0624296 | ||||||||
\(974\) | −1.16153e37 | −0.510554 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.21068e36 | −0.0518688 | ||||||||
\(977\) | −2.61043e36 | −0.110415 | −0.0552077 | − | 0.998475i | \(-0.517582\pi\) | ||||
−0.0552077 | + | 0.998475i | \(0.517582\pi\) | |||||||
\(978\) | −3.23343e37 | −1.35029 | ||||||||
\(979\) | 3.03714e36 | 0.125222 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.20692e37 | −1.69084 | ||||||||
\(982\) | 2.53241e37 | 1.00494 | ||||||||
\(983\) | −4.36771e37 | −1.71133 | −0.855667 | − | 0.517527i | \(-0.826853\pi\) | ||||
−0.855667 | + | 0.517527i | \(0.826853\pi\) | |||||||
\(984\) | −2.20068e37 | −0.851370 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.45314e36 | −0.356545 | ||||||||
\(987\) | −3.44726e36 | −0.128384 | ||||||||
\(988\) | −2.47133e36 | −0.0908800 | ||||||||
\(989\) | −7.34881e37 | −2.66848 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.30135e37 | 1.87701 | 0.938503 | − | 0.345271i | \(-0.112213\pi\) | ||||
0.938503 | + | 0.345271i | \(0.112213\pi\) | |||||||
\(992\) | 3.95407e36 | 0.138245 | ||||||||
\(993\) | −2.41859e37 | −0.835019 | ||||||||
\(994\) | −5.99015e35 | −0.0204225 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.92218e37 | −0.971549 | ||||||||
\(997\) | −4.76523e37 | −1.56457 | −0.782284 | − | 0.622921i | \(-0.785946\pi\) | ||||
−0.782284 | + | 0.622921i | \(0.785946\pi\) | |||||||
\(998\) | 1.12038e37 | 0.363275 | ||||||||
\(999\) | −5.39268e37 | −1.72678 |
(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 | 50.26.a.k.1.6 | 6 | ||
5.2 | odd | 4 | 10.26.b.a.9.1 | ✓ | 12 | ||
5.3 | odd | 4 | 10.26.b.a.9.12 | yes | 12 | ||
5.4 | even | 2 | 50.26.a.l.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.b.a.9.1 | ✓ | 12 | 5.2 | odd | 4 | ||
10.26.b.a.9.12 | yes | 12 | 5.3 | odd | 4 | ||
50.26.a.k.1.6 | 6 | 1.1 | even | 1 | trivial | ||
50.26.a.l.1.1 | 6 | 5.4 | even | 2 |