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: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{5} - 25534923283x^{3} - 31863478542482x^{2} + 141941149085067124800x + 2515032055818200956928000 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{5}\cdot 5^{12} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(107996.\) 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 | ||||||||
\(3\) | −1.22475e6 | −1.33056 | −0.665278 | − | 0.746595i | \(-0.731687\pi\) | ||||
−0.665278 | + | 0.746595i | \(0.731687\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 5.01659e9 | 0.940846 | ||||||||
\(7\) | 5.40343e10 | 1.47552 | 0.737758 | − | 0.675065i | \(-0.235885\pi\) | ||||
0.737758 | + | 0.675065i | \(0.235885\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 6.52735e11 | 0.770381 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.79977e13 | −1.72905 | −0.864524 | − | 0.502591i | \(-0.832380\pi\) | ||||
−0.864524 | + | 0.502591i | \(0.832380\pi\) | |||||||
\(12\) | −2.05480e13 | −0.665278 | ||||||||
\(13\) | −5.05810e13 | −0.602138 | −0.301069 | − | 0.953602i | \(-0.597343\pi\) | ||||
−0.301069 | + | 0.953602i | \(0.597343\pi\) | |||||||
\(14\) | −2.21324e14 | −1.04335 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | −1.91806e15 | −0.798456 | −0.399228 | − | 0.916852i | \(-0.630722\pi\) | ||||
−0.399228 | + | 0.916852i | \(0.630722\pi\) | |||||||
\(18\) | −2.67360e15 | −0.544742 | ||||||||
\(19\) | −3.52431e15 | −0.365303 | −0.182652 | − | 0.983178i | \(-0.558468\pi\) | ||||
−0.182652 | + | 0.983178i | \(0.558468\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.61787e16 | −1.96326 | ||||||||
\(22\) | 7.37184e16 | 1.22262 | ||||||||
\(23\) | −1.31301e17 | −1.24931 | −0.624653 | − | 0.780902i | \(-0.714760\pi\) | ||||
−0.624653 | + | 0.780902i | \(0.714760\pi\) | |||||||
\(24\) | 8.41645e16 | 0.470423 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.07180e17 | 0.425776 | ||||||||
\(27\) | 2.38280e17 | 0.305521 | ||||||||
\(28\) | 9.06545e17 | 0.737758 | ||||||||
\(29\) | 3.38023e18 | 1.77407 | 0.887037 | − | 0.461699i | \(-0.152760\pi\) | ||||
0.887037 | + | 0.461699i | \(0.152760\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.09603e18 | −0.249920 | −0.124960 | − | 0.992162i | \(-0.539880\pi\) | ||||
−0.124960 | + | 0.992162i | \(0.539880\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | 2.20427e19 | 2.30060 | ||||||||
\(34\) | 7.85638e18 | 0.564594 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.09511e19 | 0.385190 | ||||||||
\(37\) | −4.59139e19 | −1.14663 | −0.573314 | − | 0.819336i | \(-0.694343\pi\) | ||||
−0.573314 | + | 0.819336i | \(0.694343\pi\) | |||||||
\(38\) | 1.44356e19 | 0.258309 | ||||||||
\(39\) | 6.19494e19 | 0.801178 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.75209e19 | −0.328917 | −0.164458 | − | 0.986384i | \(-0.552588\pi\) | ||||
−0.164458 | + | 0.986384i | \(0.552588\pi\) | |||||||
\(42\) | 2.71068e20 | 1.38823 | ||||||||
\(43\) | 1.40138e20 | 0.534810 | 0.267405 | − | 0.963584i | \(-0.413834\pi\) | ||||
0.267405 | + | 0.963584i | \(0.413834\pi\) | |||||||
\(44\) | −3.01950e20 | −0.864524 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.37807e20 | 0.883393 | ||||||||
\(47\) | −9.40719e20 | −1.18096 | −0.590482 | − | 0.807051i | \(-0.701062\pi\) | ||||
−0.590482 | + | 0.807051i | \(0.701062\pi\) | |||||||
\(48\) | −3.44738e20 | −0.332639 | ||||||||
\(49\) | 1.57863e21 | 1.17715 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.34916e21 | 1.06239 | ||||||||
\(52\) | −8.48609e20 | −0.301069 | ||||||||
\(53\) | −4.94559e21 | −1.38283 | −0.691416 | − | 0.722457i | \(-0.743013\pi\) | ||||
−0.691416 | + | 0.722457i | \(0.743013\pi\) | |||||||
\(54\) | −9.75996e20 | −0.216036 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.71321e21 | −0.521674 | ||||||||
\(57\) | 4.31641e21 | 0.486057 | ||||||||
\(58\) | −1.38454e22 | −1.25446 | ||||||||
\(59\) | 8.56554e21 | 0.626765 | 0.313382 | − | 0.949627i | \(-0.398538\pi\) | ||||
0.313382 | + | 0.949627i | \(0.398538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.83544e22 | −1.36772 | −0.683861 | − | 0.729612i | \(-0.739701\pi\) | ||||
−0.683861 | + | 0.729612i | \(0.739701\pi\) | |||||||
\(62\) | 4.48934e21 | 0.176720 | ||||||||
\(63\) | 3.52701e22 | 1.13671 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.02869e22 | −1.62677 | ||||||||
\(67\) | −5.48848e22 | −0.819440 | −0.409720 | − | 0.912211i | \(-0.634374\pi\) | ||||
−0.409720 | + | 0.912211i | \(0.634374\pi\) | |||||||
\(68\) | −3.21797e22 | −0.399228 | ||||||||
\(69\) | 1.60811e23 | 1.66227 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.54981e23 | 1.84408 | 0.922038 | − | 0.387100i | \(-0.126523\pi\) | ||||
0.922038 | + | 0.387100i | \(0.126523\pi\) | |||||||
\(72\) | −4.48556e22 | −0.272371 | ||||||||
\(73\) | −7.34354e22 | −0.375292 | −0.187646 | − | 0.982237i | \(-0.560086\pi\) | ||||
−0.187646 | + | 0.982237i | \(0.560086\pi\) | |||||||
\(74\) | 1.88063e23 | 0.810789 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.91281e22 | −0.182652 | ||||||||
\(77\) | −9.72490e23 | −2.55124 | ||||||||
\(78\) | −2.53745e23 | −0.566519 | ||||||||
\(79\) | 3.27839e22 | 0.0624197 | 0.0312099 | − | 0.999513i | \(-0.490064\pi\) | ||||
0.0312099 | + | 0.999513i | \(0.490064\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.44890e23 | −1.17689 | ||||||||
\(82\) | 1.94646e23 | 0.232579 | ||||||||
\(83\) | −1.62267e24 | −1.66630 | −0.833149 | − | 0.553048i | \(-0.813465\pi\) | ||||
−0.833149 | + | 0.553048i | \(0.813465\pi\) | |||||||
\(84\) | −1.11029e24 | −0.981629 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.74004e23 | −0.378167 | ||||||||
\(87\) | −4.13995e24 | −2.36051 | ||||||||
\(88\) | 1.23679e24 | 0.611311 | ||||||||
\(89\) | 1.92566e24 | 0.826429 | 0.413214 | − | 0.910634i | \(-0.364406\pi\) | ||||
0.413214 | + | 0.910634i | \(0.364406\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.73311e24 | −0.888464 | ||||||||
\(92\) | −2.20286e24 | −0.624653 | ||||||||
\(93\) | 1.34237e24 | 0.332533 | ||||||||
\(94\) | 3.85318e24 | 0.835067 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.41205e24 | 0.235211 | ||||||||
\(97\) | 9.42112e24 | 1.37866 | 0.689328 | − | 0.724450i | \(-0.257906\pi\) | ||||
0.689328 | + | 0.724450i | \(0.257906\pi\) | |||||||
\(98\) | −6.46609e24 | −0.832368 | ||||||||
\(99\) | −1.17477e25 | −1.33203 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.26202e24 | −0.552964 | −0.276482 | − | 0.961019i | \(-0.589169\pi\) | ||||
−0.276482 | + | 0.961019i | \(0.589169\pi\) | |||||||
\(102\) | −9.62214e24 | −0.751224 | ||||||||
\(103\) | −9.51652e24 | −0.657677 | −0.328839 | − | 0.944386i | \(-0.606657\pi\) | ||||
−0.328839 | + | 0.944386i | \(0.606657\pi\) | |||||||
\(104\) | 3.47590e24 | 0.212888 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.02571e25 | 0.977810 | ||||||||
\(107\) | 5.03847e24 | 0.216273 | 0.108136 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108136 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(108\) | 3.99768e24 | 0.152761 | ||||||||
\(109\) | −1.74857e25 | −0.595461 | −0.297730 | − | 0.954650i | \(-0.596230\pi\) | ||||
−0.297730 | + | 0.954650i | \(0.596230\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.62333e25 | 1.52565 | ||||||||
\(112\) | 1.52093e25 | 0.368879 | ||||||||
\(113\) | −4.83834e25 | −1.05006 | −0.525032 | − | 0.851082i | \(-0.675947\pi\) | ||||
−0.525032 | + | 0.851082i | \(0.675947\pi\) | |||||||
\(114\) | −1.76800e25 | −0.343694 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.67109e25 | 0.887037 | ||||||||
\(117\) | −3.30160e25 | −0.463875 | ||||||||
\(118\) | −3.50844e25 | −0.443189 | ||||||||
\(119\) | −1.03641e26 | −1.17813 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.15568e26 | 1.98961 | ||||||||
\(122\) | 1.16140e26 | 0.967126 | ||||||||
\(123\) | 5.82014e25 | 0.437643 | ||||||||
\(124\) | −1.83883e25 | −0.124960 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.44466e26 | −0.803775 | ||||||||
\(127\) | 2.16513e26 | 1.09128 | 0.545640 | − | 0.838019i | \(-0.316286\pi\) | ||||
0.545640 | + | 0.838019i | \(0.316286\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | −1.71634e26 | −0.711594 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.82649e26 | −1.30891 | −0.654454 | − | 0.756102i | \(-0.727102\pi\) | ||||
−0.654454 | + | 0.756102i | \(0.727102\pi\) | |||||||
\(132\) | 3.69815e26 | 1.15030 | ||||||||
\(133\) | −1.90433e26 | −0.539011 | ||||||||
\(134\) | 2.24808e26 | 0.579431 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.31808e26 | 0.282297 | ||||||||
\(137\) | −8.94431e26 | −1.74799 | −0.873996 | − | 0.485933i | \(-0.838480\pi\) | ||||
−0.873996 | + | 0.485933i | \(0.838480\pi\) | |||||||
\(138\) | −6.58682e26 | −1.17540 | ||||||||
\(139\) | −6.14787e26 | −1.00240 | −0.501199 | − | 0.865332i | \(-0.667107\pi\) | ||||
−0.501199 | + | 0.865332i | \(0.667107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.15215e27 | 1.57134 | ||||||||
\(142\) | −1.04440e27 | −1.30396 | ||||||||
\(143\) | 9.10340e26 | 1.04113 | ||||||||
\(144\) | 1.83729e26 | 0.192595 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.00791e26 | 0.265372 | ||||||||
\(147\) | −1.93344e27 | −1.56626 | ||||||||
\(148\) | −7.70307e26 | −0.573314 | ||||||||
\(149\) | −1.52978e27 | −1.04665 | −0.523325 | − | 0.852133i | \(-0.675309\pi\) | ||||
−0.523325 | + | 0.852133i | \(0.675309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.66948e27 | −0.966873 | −0.483436 | − | 0.875379i | \(-0.660612\pi\) | ||||
−0.483436 | + | 0.875379i | \(0.660612\pi\) | |||||||
\(152\) | 2.42189e26 | 0.129154 | ||||||||
\(153\) | −1.25199e27 | −0.615116 | ||||||||
\(154\) | 3.98332e27 | 1.80400 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.03934e27 | 0.400589 | ||||||||
\(157\) | −1.97558e27 | −0.702988 | −0.351494 | − | 0.936190i | \(-0.614326\pi\) | ||||
−0.351494 | + | 0.936190i | \(0.614326\pi\) | |||||||
\(158\) | −1.34283e26 | −0.0441374 | ||||||||
\(159\) | 6.05713e27 | 1.83994 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.09473e27 | −1.84337 | ||||||||
\(162\) | 3.46067e27 | 0.832190 | ||||||||
\(163\) | 4.18722e27 | 0.932353 | 0.466176 | − | 0.884692i | \(-0.345631\pi\) | ||||
0.466176 | + | 0.884692i | \(0.345631\pi\) | |||||||
\(164\) | −7.97268e26 | −0.164458 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.64644e27 | 1.17825 | ||||||||
\(167\) | 1.83560e27 | 0.301871 | 0.150936 | − | 0.988544i | \(-0.451771\pi\) | ||||
0.150936 | + | 0.988544i | \(0.451771\pi\) | |||||||
\(168\) | 4.54777e27 | 0.694116 | ||||||||
\(169\) | −4.49797e27 | −0.637430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.30044e27 | −0.281423 | ||||||||
\(172\) | 2.35112e27 | 0.267405 | ||||||||
\(173\) | 7.54567e27 | 0.798218 | 0.399109 | − | 0.916903i | \(-0.369319\pi\) | ||||
0.399109 | + | 0.916903i | \(0.369319\pi\) | |||||||
\(174\) | 1.69573e28 | 1.66913 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.06589e27 | −0.432262 | ||||||||
\(177\) | −1.04907e28 | −0.833946 | ||||||||
\(178\) | −7.88752e27 | −0.584374 | ||||||||
\(179\) | −2.40551e28 | −1.66167 | −0.830834 | − | 0.556521i | \(-0.812136\pi\) | ||||
−0.830834 | + | 0.556521i | \(0.812136\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.05290e28 | 1.83540 | 0.917699 | − | 0.397277i | \(-0.130045\pi\) | ||||
0.917699 | + | 0.397277i | \(0.130045\pi\) | |||||||
\(182\) | 1.11948e28 | 0.628239 | ||||||||
\(183\) | 3.47272e28 | 1.81983 | ||||||||
\(184\) | 9.02291e27 | 0.441696 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.49834e27 | −0.235136 | ||||||||
\(187\) | 3.45206e28 | 1.38057 | ||||||||
\(188\) | −1.57826e28 | −0.590482 | ||||||||
\(189\) | 1.28753e28 | 0.450801 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.33829e28 | 1.02472 | 0.512362 | − | 0.858769i | \(-0.328770\pi\) | ||||
0.512362 | + | 0.858769i | \(0.328770\pi\) | |||||||
\(192\) | −5.78374e27 | −0.166320 | ||||||||
\(193\) | 2.89791e28 | 0.780942 | 0.390471 | − | 0.920615i | \(-0.372312\pi\) | ||||
0.390471 | + | 0.920615i | \(0.372312\pi\) | |||||||
\(194\) | −3.85889e28 | −0.974857 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.64851e28 | 0.588573 | ||||||||
\(197\) | −5.37586e28 | −1.12104 | −0.560519 | − | 0.828142i | \(-0.689398\pi\) | ||||
−0.560519 | + | 0.828142i | \(0.689398\pi\) | |||||||
\(198\) | 4.81186e28 | 0.941885 | ||||||||
\(199\) | 2.53738e28 | 0.466361 | 0.233180 | − | 0.972434i | \(-0.425087\pi\) | ||||
0.233180 | + | 0.972434i | \(0.425087\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.72204e28 | 1.09031 | ||||||||
\(202\) | 2.56492e28 | 0.391005 | ||||||||
\(203\) | 1.82648e29 | 2.61767 | ||||||||
\(204\) | 3.94123e28 | 0.531196 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.89797e28 | 0.465048 | ||||||||
\(207\) | −8.57045e28 | −0.962442 | ||||||||
\(208\) | −1.42373e28 | −0.150534 | ||||||||
\(209\) | 6.34293e28 | 0.631627 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.53161e28 | −0.665821 | −0.332910 | − | 0.942958i | \(-0.608031\pi\) | ||||
−0.332910 | + | 0.942958i | \(0.608031\pi\) | |||||||
\(212\) | −8.29731e28 | −0.691416 | ||||||||
\(213\) | −3.12289e29 | −2.45365 | ||||||||
\(214\) | −2.06376e28 | −0.152928 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.63745e28 | −0.108018 | ||||||||
\(217\) | −5.92232e28 | −0.368761 | ||||||||
\(218\) | 7.16216e28 | 0.421054 | ||||||||
\(219\) | 8.99404e28 | 0.499348 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.70176e28 | 0.480781 | ||||||||
\(222\) | −2.30331e29 | −1.07880 | ||||||||
\(223\) | −2.07743e29 | −0.919848 | −0.459924 | − | 0.887958i | \(-0.652123\pi\) | ||||
−0.459924 | + | 0.887958i | \(0.652123\pi\) | |||||||
\(224\) | −6.22973e28 | −0.260837 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.98179e29 | 0.742508 | ||||||||
\(227\) | −4.74953e29 | −1.68394 | −0.841971 | − | 0.539523i | \(-0.818605\pi\) | ||||
−0.841971 | + | 0.539523i | \(0.818605\pi\) | |||||||
\(228\) | 7.24174e28 | 0.243028 | ||||||||
\(229\) | 4.47901e29 | 1.42311 | 0.711555 | − | 0.702630i | \(-0.247991\pi\) | ||||
0.711555 | + | 0.702630i | \(0.247991\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.19106e30 | 3.39457 | ||||||||
\(232\) | −2.32288e29 | −0.627230 | ||||||||
\(233\) | −1.19571e29 | −0.305970 | −0.152985 | − | 0.988229i | \(-0.548889\pi\) | ||||
−0.152985 | + | 0.988229i | \(0.548889\pi\) | |||||||
\(234\) | 1.35234e29 | 0.328009 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.43706e29 | 0.313382 | ||||||||
\(237\) | −4.01522e28 | −0.0830530 | ||||||||
\(238\) | 4.24514e29 | 0.833067 | ||||||||
\(239\) | −1.73647e29 | −0.323365 | −0.161682 | − | 0.986843i | \(-0.551692\pi\) | ||||
−0.161682 | + | 0.986843i | \(0.551692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.54337e29 | 1.09796 | 0.548982 | − | 0.835834i | \(-0.315016\pi\) | ||||
0.548982 | + | 0.835834i | \(0.315016\pi\) | |||||||
\(242\) | −8.82968e29 | −1.40687 | ||||||||
\(243\) | 8.32891e29 | 1.26040 | ||||||||
\(244\) | −4.75708e29 | −0.683861 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.38393e29 | −0.309460 | ||||||||
\(247\) | 1.78263e29 | 0.219963 | ||||||||
\(248\) | 7.53186e28 | 0.0883601 | ||||||||
\(249\) | 1.98737e30 | 2.21711 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.53799e29 | 0.659968 | 0.329984 | − | 0.943987i | \(-0.392957\pi\) | ||||
0.329984 | + | 0.943987i | \(0.392957\pi\) | |||||||
\(252\) | 5.91734e29 | 0.568355 | ||||||||
\(253\) | 2.36310e30 | 2.16011 | ||||||||
\(254\) | −8.86835e29 | −0.771652 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | −1.59934e29 | −0.120165 | −0.0600823 | − | 0.998193i | \(-0.519136\pi\) | ||||
−0.0600823 | + | 0.998193i | \(0.519136\pi\) | |||||||
\(258\) | 7.03014e29 | 0.503173 | ||||||||
\(259\) | −2.48092e30 | −1.69187 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.20640e30 | 1.36671 | ||||||||
\(262\) | 1.56733e30 | 0.925538 | ||||||||
\(263\) | −1.44294e30 | −0.812461 | −0.406231 | − | 0.913771i | \(-0.633157\pi\) | ||||
−0.406231 | + | 0.913771i | \(0.633157\pi\) | |||||||
\(264\) | −1.51476e30 | −0.813384 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 7.80015e29 | 0.381138 | ||||||||
\(267\) | −2.35847e30 | −1.09961 | ||||||||
\(268\) | −9.20814e29 | −0.409720 | ||||||||
\(269\) | 3.68677e30 | 1.56582 | 0.782911 | − | 0.622134i | \(-0.213734\pi\) | ||||
0.782911 | + | 0.622134i | \(0.213734\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.98811e30 | 1.54401 | 0.772007 | − | 0.635613i | \(-0.219253\pi\) | ||||
0.772007 | + | 0.635613i | \(0.219253\pi\) | |||||||
\(272\) | −5.39887e29 | −0.199614 | ||||||||
\(273\) | 3.34739e30 | 1.18215 | ||||||||
\(274\) | 3.66359e30 | 1.23602 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.69796e30 | 0.831136 | ||||||||
\(277\) | 3.61317e30 | 1.06388 | 0.531939 | − | 0.846783i | \(-0.321464\pi\) | ||||
0.531939 | + | 0.846783i | \(0.321464\pi\) | |||||||
\(278\) | 2.51817e30 | 0.708802 | ||||||||
\(279\) | −7.15417e29 | −0.192534 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.28210e29 | 0.0315568 | 0.0157784 | − | 0.999876i | \(-0.494977\pi\) | ||||
0.0157784 | + | 0.999876i | \(0.494977\pi\) | |||||||
\(282\) | −4.71920e30 | −1.11110 | ||||||||
\(283\) | 7.90843e30 | 1.78139 | 0.890697 | − | 0.454598i | \(-0.150217\pi\) | ||||
0.890697 | + | 0.454598i | \(0.150217\pi\) | |||||||
\(284\) | 4.27787e30 | 0.922038 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.72875e30 | −0.736187 | ||||||||
\(287\) | −2.56776e30 | −0.485322 | ||||||||
\(288\) | −7.52552e29 | −0.136185 | ||||||||
\(289\) | −2.09166e30 | −0.362467 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.15386e31 | −1.83438 | ||||||||
\(292\) | −1.23204e30 | −0.187646 | ||||||||
\(293\) | −6.25018e30 | −0.912110 | −0.456055 | − | 0.889952i | \(-0.650738\pi\) | ||||
−0.456055 | + | 0.889952i | \(0.650738\pi\) | |||||||
\(294\) | 7.91937e30 | 1.10751 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.15518e30 | 0.405394 | ||||||||
\(297\) | −4.28849e30 | −0.528261 | ||||||||
\(298\) | 6.26600e30 | 0.740094 | ||||||||
\(299\) | 6.64132e30 | 0.752254 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.57224e30 | 0.789120 | ||||||||
\(302\) | 6.83819e30 | 0.683682 | ||||||||
\(303\) | 7.66943e30 | 0.735750 | ||||||||
\(304\) | −9.92004e29 | −0.0913259 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 5.12814e30 | 0.434952 | ||||||||
\(307\) | −2.00082e31 | −1.62922 | −0.814609 | − | 0.580010i | \(-0.803049\pi\) | ||||
−0.814609 | + | 0.580010i | \(0.803049\pi\) | |||||||
\(308\) | −1.63157e31 | −1.27562 | ||||||||
\(309\) | 1.16554e31 | 0.875077 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.26965e31 | −1.57201 | −0.786003 | − | 0.618223i | \(-0.787853\pi\) | ||||
−0.786003 | + | 0.618223i | \(0.787853\pi\) | |||||||
\(312\) | −4.25713e30 | −0.283259 | ||||||||
\(313\) | −1.47728e31 | −0.944405 | −0.472203 | − | 0.881490i | \(-0.656541\pi\) | ||||
−0.472203 | + | 0.881490i | \(0.656541\pi\) | |||||||
\(314\) | 8.09196e30 | 0.497088 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.50022e29 | 0.0312099 | ||||||||
\(317\) | 2.36061e30 | 0.128761 | 0.0643805 | − | 0.997925i | \(-0.479493\pi\) | ||||
0.0643805 | + | 0.997925i | \(0.479493\pi\) | |||||||
\(318\) | −2.48100e31 | −1.30103 | ||||||||
\(319\) | −6.08362e31 | −3.06746 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.17089e30 | −0.287763 | ||||||||
\(322\) | 2.90600e31 | 1.30346 | ||||||||
\(323\) | 6.75984e30 | 0.291679 | ||||||||
\(324\) | −1.41749e31 | −0.588447 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.71508e31 | −0.659273 | ||||||||
\(327\) | 2.14157e31 | 0.792294 | ||||||||
\(328\) | 3.26561e30 | 0.116290 | ||||||||
\(329\) | −5.08311e31 | −1.74253 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.93789e31 | 0.933653 | 0.466826 | − | 0.884349i | \(-0.345397\pi\) | ||||
0.466826 | + | 0.884349i | \(0.345397\pi\) | |||||||
\(332\) | −2.72238e31 | −0.833149 | ||||||||
\(333\) | −2.99696e31 | −0.883341 | ||||||||
\(334\) | −7.51861e30 | −0.213455 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.86277e31 | −0.490814 | ||||||||
\(337\) | 6.82670e31 | 1.73315 | 0.866577 | − | 0.499044i | \(-0.166315\pi\) | ||||
0.866577 | + | 0.499044i | \(0.166315\pi\) | |||||||
\(338\) | 1.84237e31 | 0.450731 | ||||||||
\(339\) | 5.92578e31 | 1.39717 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.97260e31 | 0.432124 | ||||||||
\(342\) | 9.42260e30 | 0.198996 | ||||||||
\(343\) | 1.28367e31 | 0.261383 | ||||||||
\(344\) | −9.63019e30 | −0.189084 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.09071e31 | −0.564425 | ||||||||
\(347\) | 1.59692e31 | 0.281296 | 0.140648 | − | 0.990060i | \(-0.455081\pi\) | ||||
0.140648 | + | 0.990060i | \(0.455081\pi\) | |||||||
\(348\) | −6.94569e31 | −1.18025 | ||||||||
\(349\) | −4.91783e31 | −0.806225 | −0.403112 | − | 0.915150i | \(-0.632072\pi\) | ||||
−0.403112 | + | 0.915150i | \(0.632072\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.20525e31 | −0.183966 | ||||||||
\(352\) | 2.07499e31 | 0.305656 | ||||||||
\(353\) | 3.19773e30 | 0.0454630 | 0.0227315 | − | 0.999742i | \(-0.492764\pi\) | ||||
0.0227315 | + | 0.999742i | \(0.492764\pi\) | |||||||
\(354\) | 4.29698e31 | 0.589689 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.23073e31 | 0.413214 | ||||||||
\(357\) | 1.26935e32 | 1.56758 | ||||||||
\(358\) | 9.85296e31 | 1.17498 | ||||||||
\(359\) | −3.57527e31 | −0.411745 | −0.205872 | − | 0.978579i | \(-0.566003\pi\) | ||||
−0.205872 | + | 0.978579i | \(0.566003\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.06558e31 | −0.866553 | ||||||||
\(362\) | −1.25047e32 | −1.29782 | ||||||||
\(363\) | −2.64018e32 | −2.64729 | ||||||||
\(364\) | −4.58540e31 | −0.444232 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.42243e32 | −1.28682 | ||||||||
\(367\) | 2.22256e32 | 1.94325 | 0.971623 | − | 0.236536i | \(-0.0760122\pi\) | ||||
0.971623 | + | 0.236536i | \(0.0760122\pi\) | |||||||
\(368\) | −3.69578e31 | −0.312327 | ||||||||
\(369\) | −3.10185e31 | −0.253391 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.67231e32 | −2.04039 | ||||||||
\(372\) | 2.25212e31 | 0.166266 | ||||||||
\(373\) | −2.11651e32 | −1.51099 | −0.755493 | − | 0.655157i | \(-0.772603\pi\) | ||||
−0.755493 | + | 0.655157i | \(0.772603\pi\) | |||||||
\(374\) | −1.41396e32 | −0.976210 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.46457e31 | 0.417534 | ||||||||
\(377\) | −1.70976e32 | −1.06824 | ||||||||
\(378\) | −5.27373e31 | −0.318765 | ||||||||
\(379\) | 1.57098e32 | 0.918713 | 0.459357 | − | 0.888252i | \(-0.348080\pi\) | ||||
0.459357 | + | 0.888252i | \(0.348080\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.65175e32 | −1.45201 | ||||||||
\(382\) | −1.36736e32 | −0.724590 | ||||||||
\(383\) | 2.04365e32 | 1.04815 | 0.524073 | − | 0.851673i | \(-0.324412\pi\) | ||||
0.524073 | + | 0.851673i | \(0.324412\pi\) | |||||||
\(384\) | 2.36902e31 | 0.117606 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.18699e32 | −0.552210 | ||||||||
\(387\) | 9.14728e31 | 0.412007 | ||||||||
\(388\) | 1.58060e32 | 0.689328 | ||||||||
\(389\) | 1.78110e32 | 0.752174 | 0.376087 | − | 0.926584i | \(-0.377269\pi\) | ||||
0.376087 | + | 0.926584i | \(0.377269\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.51843e32 | 0.997516 | ||||||||
\(392\) | −1.08483e32 | −0.416184 | ||||||||
\(393\) | 4.68651e32 | 1.74158 | ||||||||
\(394\) | 2.20195e32 | 0.792694 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.97094e32 | −0.666013 | ||||||||
\(397\) | −1.81768e32 | −0.595163 | −0.297581 | − | 0.954696i | \(-0.596180\pi\) | ||||
−0.297581 | + | 0.954696i | \(0.596180\pi\) | |||||||
\(398\) | −1.03931e32 | −0.329767 | ||||||||
\(399\) | 2.33234e32 | 0.717185 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.87592e32 | −0.541889 | −0.270945 | − | 0.962595i | \(-0.587336\pi\) | ||||
−0.270945 | + | 0.962595i | \(0.587336\pi\) | |||||||
\(402\) | −2.75335e32 | −0.770966 | ||||||||
\(403\) | 5.54383e31 | 0.150486 | ||||||||
\(404\) | −1.05059e32 | −0.276482 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.48128e32 | −1.85097 | ||||||||
\(407\) | 8.26342e32 | 1.98258 | ||||||||
\(408\) | −1.61433e32 | −0.375612 | ||||||||
\(409\) | −3.48178e32 | −0.785706 | −0.392853 | − | 0.919601i | \(-0.628512\pi\) | ||||
−0.392853 | + | 0.919601i | \(0.628512\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.09546e33 | 2.32580 | ||||||||
\(412\) | −1.59661e32 | −0.328839 | ||||||||
\(413\) | 4.62833e32 | 0.924801 | ||||||||
\(414\) | 3.51046e32 | 0.680549 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.83160e31 | 0.106444 | ||||||||
\(417\) | 7.52964e32 | 1.33375 | ||||||||
\(418\) | −2.59806e32 | −0.446628 | ||||||||
\(419\) | −8.02659e32 | −1.33923 | −0.669616 | − | 0.742708i | \(-0.733541\pi\) | ||||
−0.669616 | + | 0.742708i | \(0.733541\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.26783e32 | 0.670936 | 0.335468 | − | 0.942052i | \(-0.391106\pi\) | ||||
0.335468 | + | 0.942052i | \(0.391106\pi\) | |||||||
\(422\) | 3.08495e32 | 0.470806 | ||||||||
\(423\) | −6.14040e32 | −0.909792 | ||||||||
\(424\) | 3.39858e32 | 0.488905 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.27914e33 | 1.73499 | ||||||||
\(427\) | −1.53211e33 | −2.01810 | ||||||||
\(428\) | 8.45315e31 | 0.108136 | ||||||||
\(429\) | −1.11494e33 | −1.38528 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.47631e32 | 0.759210 | 0.379605 | − | 0.925149i | \(-0.376060\pi\) | ||||
0.379605 | + | 0.925149i | \(0.376060\pi\) | |||||||
\(432\) | 6.70700e31 | 0.0763803 | ||||||||
\(433\) | 5.41225e32 | 0.598796 | 0.299398 | − | 0.954128i | \(-0.403214\pi\) | ||||
0.299398 | + | 0.954128i | \(0.403214\pi\) | |||||||
\(434\) | 2.42578e32 | 0.260753 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.93362e32 | −0.297730 | ||||||||
\(437\) | 4.62744e32 | 0.456376 | ||||||||
\(438\) | −3.68396e32 | −0.353092 | ||||||||
\(439\) | −4.19028e32 | −0.390334 | −0.195167 | − | 0.980770i | \(-0.562525\pi\) | ||||
−0.195167 | + | 0.980770i | \(0.562525\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.03043e33 | 0.906851 | ||||||||
\(442\) | −3.97384e32 | −0.339963 | ||||||||
\(443\) | 5.75377e32 | 0.478527 | 0.239263 | − | 0.970955i | \(-0.423094\pi\) | ||||
0.239263 | + | 0.970955i | \(0.423094\pi\) | |||||||
\(444\) | 9.43437e32 | 0.762827 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.50916e32 | 0.650431 | ||||||||
\(447\) | 1.87361e33 | 1.39263 | ||||||||
\(448\) | 2.55170e32 | 0.184439 | ||||||||
\(449\) | 8.31503e32 | 0.584500 | 0.292250 | − | 0.956342i | \(-0.405596\pi\) | ||||
0.292250 | + | 0.956342i | \(0.405596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.55264e32 | 0.568714 | ||||||||
\(452\) | −8.11739e32 | −0.525032 | ||||||||
\(453\) | 2.04470e33 | 1.28648 | ||||||||
\(454\) | 1.94541e33 | 1.19073 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.96622e32 | −0.171847 | ||||||||
\(457\) | −1.74441e33 | −0.983322 | −0.491661 | − | 0.870787i | \(-0.663610\pi\) | ||||
−0.491661 | + | 0.870787i | \(0.663610\pi\) | |||||||
\(458\) | −1.83460e33 | −1.00629 | ||||||||
\(459\) | −4.57037e32 | −0.243945 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.31968e33 | 0.667126 | 0.333563 | − | 0.942728i | \(-0.391749\pi\) | ||||
0.333563 | + | 0.942728i | \(0.391749\pi\) | |||||||
\(462\) | −4.87859e33 | −2.40032 | ||||||||
\(463\) | 1.40349e33 | 0.672121 | 0.336061 | − | 0.941840i | \(-0.390905\pi\) | ||||
0.336061 | + | 0.941840i | \(0.390905\pi\) | |||||||
\(464\) | 9.51451e32 | 0.443518 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.89765e32 | 0.216353 | ||||||||
\(467\) | −7.68890e32 | −0.330676 | −0.165338 | − | 0.986237i | \(-0.552872\pi\) | ||||
−0.165338 | + | 0.986237i | \(0.552872\pi\) | |||||||
\(468\) | −5.53917e32 | −0.231938 | ||||||||
\(469\) | −2.96566e33 | −1.20910 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.41960e33 | 0.935366 | ||||||||
\(472\) | −5.88619e32 | −0.221595 | ||||||||
\(473\) | −2.52215e33 | −0.924712 | ||||||||
\(474\) | 1.64463e32 | 0.0587273 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.73881e33 | −0.589067 | ||||||||
\(477\) | −3.22816e33 | −1.06531 | ||||||||
\(478\) | 7.11256e32 | 0.228653 | ||||||||
\(479\) | 2.68490e33 | 0.840879 | 0.420440 | − | 0.907321i | \(-0.361876\pi\) | ||||
0.420440 | + | 0.907321i | \(0.361876\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.32237e33 | 0.690428 | ||||||||
\(482\) | −2.68016e33 | −0.776378 | ||||||||
\(483\) | 8.68931e33 | 2.45271 | ||||||||
\(484\) | 3.61664e33 | 0.994805 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −3.41152e33 | −0.891240 | ||||||||
\(487\) | −4.59053e33 | −1.16883 | −0.584415 | − | 0.811455i | \(-0.698676\pi\) | ||||
−0.584415 | + | 0.811455i | \(0.698676\pi\) | |||||||
\(488\) | 1.94850e33 | 0.483563 | ||||||||
\(489\) | −5.12831e33 | −1.24055 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.15180e33 | 1.18424 | 0.592120 | − | 0.805849i | \(-0.298291\pi\) | ||||
0.592120 | + | 0.805849i | \(0.298291\pi\) | |||||||
\(492\) | 9.76458e32 | 0.218821 | ||||||||
\(493\) | −6.48350e33 | −1.41652 | ||||||||
\(494\) | −7.30166e32 | −0.155537 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.08505e32 | −0.0624800 | ||||||||
\(497\) | 1.37777e34 | 2.72096 | ||||||||
\(498\) | −8.14026e33 | −1.56773 | ||||||||
\(499\) | 7.46002e33 | 1.40115 | 0.700573 | − | 0.713581i | \(-0.252928\pi\) | ||||
0.700573 | + | 0.713581i | \(0.252928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.24816e33 | −0.401657 | ||||||||
\(502\) | −2.67796e33 | −0.466668 | ||||||||
\(503\) | 2.55159e33 | 0.433722 | 0.216861 | − | 0.976203i | \(-0.430418\pi\) | ||||
0.216861 | + | 0.976203i | \(0.430418\pi\) | |||||||
\(504\) | −2.42374e33 | −0.401887 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −9.67927e33 | −1.52743 | ||||||||
\(507\) | 5.50891e33 | 0.848137 | ||||||||
\(508\) | 3.63248e33 | 0.545640 | ||||||||
\(509\) | 8.95543e33 | 1.31254 | 0.656272 | − | 0.754524i | \(-0.272132\pi\) | ||||
0.656272 | + | 0.754524i | \(0.272132\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.96803e33 | −0.553750 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | −8.39773e32 | −0.111608 | ||||||||
\(514\) | 6.55089e32 | 0.0849692 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.87954e33 | −0.355797 | ||||||||
\(517\) | 1.69307e34 | 2.04194 | ||||||||
\(518\) | 1.01619e34 | 1.19633 | ||||||||
\(519\) | −9.24159e33 | −1.06207 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.35519e33 | 0.915134 | 0.457567 | − | 0.889175i | \(-0.348721\pi\) | ||||
0.457567 | + | 0.889175i | \(0.348721\pi\) | |||||||
\(522\) | −9.03740e33 | −0.966412 | ||||||||
\(523\) | 1.81744e34 | 1.89753 | 0.948765 | − | 0.315981i | \(-0.102334\pi\) | ||||
0.948765 | + | 0.315981i | \(0.102334\pi\) | |||||||
\(524\) | −6.41978e33 | −0.654454 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.91030e33 | 0.574497 | ||||||||
\(527\) | 2.10225e33 | 0.199550 | ||||||||
\(528\) | 6.20447e33 | 0.575149 | ||||||||
\(529\) | 6.19409e33 | 0.560766 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.59103e33 | 0.482848 | ||||||||
\(532\) | −3.19494e33 | −0.269505 | ||||||||
\(533\) | 2.40366e33 | 0.198053 | ||||||||
\(534\) | 9.66028e33 | 0.777542 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.77165e33 | 0.289716 | ||||||||
\(537\) | 2.94616e34 | 2.21094 | ||||||||
\(538\) | −1.51010e34 | −1.10720 | ||||||||
\(539\) | −2.84117e34 | −2.03534 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.80008e33 | −0.465102 | −0.232551 | − | 0.972584i | \(-0.574707\pi\) | ||||
−0.232551 | + | 0.972584i | \(0.574707\pi\) | |||||||
\(542\) | −1.63353e34 | −1.09178 | ||||||||
\(543\) | −3.73905e34 | −2.44210 | ||||||||
\(544\) | 2.21138e33 | 0.141148 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.37109e34 | −0.835907 | ||||||||
\(547\) | 2.41615e34 | 1.43973 | 0.719866 | − | 0.694113i | \(-0.244203\pi\) | ||||
0.719866 | + | 0.694113i | \(0.244203\pi\) | |||||||
\(548\) | −1.50061e34 | −0.873996 | ||||||||
\(549\) | −1.85079e34 | −1.05367 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.19130e34 | −0.648075 | ||||||||
\(552\) | −1.10509e34 | −0.587702 | ||||||||
\(553\) | 1.77145e33 | 0.0921013 | ||||||||
\(554\) | −1.47996e34 | −0.752275 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.03144e34 | −0.501199 | ||||||||
\(557\) | 1.04132e33 | 0.0494762 | 0.0247381 | − | 0.999694i | \(-0.492125\pi\) | ||||
0.0247381 | + | 0.999694i | \(0.492125\pi\) | |||||||
\(558\) | 2.93035e33 | 0.136142 | ||||||||
\(559\) | −7.08831e33 | −0.322029 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.22793e34 | −1.83693 | ||||||||
\(562\) | −5.25148e32 | −0.0223140 | ||||||||
\(563\) | −3.05082e34 | −1.26783 | −0.633915 | − | 0.773403i | \(-0.718553\pi\) | ||||
−0.633915 | + | 0.773403i | \(0.718553\pi\) | |||||||
\(564\) | 1.93299e34 | 0.785670 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.23929e34 | −1.25964 | ||||||||
\(567\) | −4.56530e34 | −1.73653 | ||||||||
\(568\) | −1.75222e34 | −0.651979 | ||||||||
\(569\) | 1.30060e34 | 0.473413 | 0.236707 | − | 0.971581i | \(-0.423932\pi\) | ||||
0.236707 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50202e34 | 0.871646 | 0.435823 | − | 0.900032i | \(-0.356457\pi\) | ||||
0.435823 | + | 0.900032i | \(0.356457\pi\) | |||||||
\(572\) | 1.52730e34 | 0.520563 | ||||||||
\(573\) | −4.08859e34 | −1.36345 | ||||||||
\(574\) | 1.05175e34 | 0.343175 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.08245e33 | 0.0962976 | ||||||||
\(577\) | −6.21101e33 | −0.189874 | −0.0949368 | − | 0.995483i | \(-0.530265\pi\) | ||||
−0.0949368 | + | 0.995483i | \(0.530265\pi\) | |||||||
\(578\) | 8.56746e33 | 0.256303 | ||||||||
\(579\) | −3.54923e34 | −1.03909 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.76796e34 | −2.45865 | ||||||||
\(582\) | 4.72619e34 | 1.29710 | ||||||||
\(583\) | 8.90089e34 | 2.39098 | ||||||||
\(584\) | 5.04644e33 | 0.132686 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.56007e34 | 0.644959 | ||||||||
\(587\) | −2.21731e34 | −0.546827 | −0.273413 | − | 0.961897i | \(-0.588153\pi\) | ||||
−0.273413 | + | 0.961897i | \(0.588153\pi\) | |||||||
\(588\) | −3.24377e34 | −0.783130 | ||||||||
\(589\) | 3.86275e33 | 0.0912967 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.58411e34 | 1.49160 | ||||||||
\(592\) | −1.29236e34 | −0.286657 | ||||||||
\(593\) | −4.72404e34 | −1.02596 | −0.512980 | − | 0.858401i | \(-0.671458\pi\) | ||||
−0.512980 | + | 0.858401i | \(0.671458\pi\) | |||||||
\(594\) | 1.75656e34 | 0.373537 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.56655e34 | −0.523325 | ||||||||
\(597\) | −3.10767e34 | −0.620519 | ||||||||
\(598\) | −2.72029e34 | −0.531924 | ||||||||
\(599\) | 9.34743e34 | 1.79002 | 0.895008 | − | 0.446050i | \(-0.147170\pi\) | ||||
0.895008 | + | 0.446050i | \(0.147170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.28681e34 | 0.236365 | 0.118183 | − | 0.992992i | \(-0.462293\pi\) | ||||
0.118183 | + | 0.992992i | \(0.462293\pi\) | |||||||
\(602\) | −3.10159e34 | −0.557992 | ||||||||
\(603\) | −3.58252e34 | −0.631281 | ||||||||
\(604\) | −2.80092e34 | −0.483436 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.14140e34 | −0.520254 | ||||||||
\(607\) | 6.95915e34 | 1.12901 | 0.564505 | − | 0.825430i | \(-0.309067\pi\) | ||||
0.564505 | + | 0.825430i | \(0.309067\pi\) | |||||||
\(608\) | 4.06325e33 | 0.0645771 | ||||||||
\(609\) | −2.23699e35 | −3.48296 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.75825e34 | 0.711103 | ||||||||
\(612\) | −2.10048e34 | −0.307558 | ||||||||
\(613\) | 1.91426e34 | 0.274628 | 0.137314 | − | 0.990528i | \(-0.456153\pi\) | ||||
0.137314 | + | 0.990528i | \(0.456153\pi\) | |||||||
\(614\) | 8.19538e34 | 1.15203 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.68290e34 | 0.901999 | ||||||||
\(617\) | 1.16629e35 | 1.54255 | 0.771277 | − | 0.636499i | \(-0.219618\pi\) | ||||
0.771277 | + | 0.636499i | \(0.219618\pi\) | |||||||
\(618\) | −4.77405e34 | −0.618773 | ||||||||
\(619\) | −7.21348e33 | −0.0916246 | −0.0458123 | − | 0.998950i | \(-0.514588\pi\) | ||||
−0.0458123 | + | 0.998950i | \(0.514588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.12864e34 | −0.381689 | ||||||||
\(622\) | 9.29649e34 | 1.11158 | ||||||||
\(623\) | 1.04052e35 | 1.21941 | ||||||||
\(624\) | 1.74372e34 | 0.200295 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.05093e34 | 0.667795 | ||||||||
\(627\) | −7.76853e34 | −0.840416 | ||||||||
\(628\) | −3.31447e34 | −0.351494 | ||||||||
\(629\) | 8.80657e34 | 0.915533 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50645e34 | 0.350349 | 0.175174 | − | 0.984537i | \(-0.443951\pi\) | ||||
0.175174 | + | 0.984537i | \(0.443951\pi\) | |||||||
\(632\) | −2.25289e33 | −0.0220687 | ||||||||
\(633\) | 9.22438e34 | 0.885912 | ||||||||
\(634\) | −9.66908e33 | −0.0910478 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.01622e35 | 0.919968 | ||||||||
\(637\) | −7.98490e34 | −0.708804 | ||||||||
\(638\) | 2.49185e35 | 2.16902 | ||||||||
\(639\) | 1.66435e35 | 1.42064 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.17260e35 | −0.962551 | −0.481276 | − | 0.876569i | \(-0.659826\pi\) | ||||
−0.481276 | + | 0.876569i | \(0.659826\pi\) | |||||||
\(642\) | 2.52760e34 | 0.203479 | ||||||||
\(643\) | 1.79181e35 | 1.41467 | 0.707336 | − | 0.706877i | \(-0.249897\pi\) | ||||
0.707336 | + | 0.706877i | \(0.249897\pi\) | |||||||
\(644\) | −1.19030e35 | −0.921685 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.76883e34 | −0.206248 | ||||||||
\(647\) | 1.07946e35 | 0.788686 | 0.394343 | − | 0.918963i | \(-0.370972\pi\) | ||||
0.394343 | + | 0.918963i | \(0.370972\pi\) | |||||||
\(648\) | 5.80604e34 | 0.416095 | ||||||||
\(649\) | −1.54160e35 | −1.08371 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.25338e34 | 0.490657 | ||||||||
\(652\) | 7.02498e34 | 0.466176 | ||||||||
\(653\) | −1.14134e35 | −0.743017 | −0.371508 | − | 0.928430i | \(-0.621159\pi\) | ||||
−0.371508 | + | 0.928430i | \(0.621159\pi\) | |||||||
\(654\) | −8.77189e34 | −0.560236 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.33759e34 | −0.0822292 | ||||||||
\(657\) | −4.79339e34 | −0.289118 | ||||||||
\(658\) | 2.08204e35 | 1.23216 | ||||||||
\(659\) | 2.00321e35 | 1.16321 | 0.581605 | − | 0.813471i | \(-0.302425\pi\) | ||||
0.581605 | + | 0.813471i | \(0.302425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.41113e35 | −1.34804 | −0.674019 | − | 0.738714i | \(-0.735433\pi\) | ||||
−0.674019 | + | 0.738714i | \(0.735433\pi\) | |||||||
\(662\) | −1.20336e35 | −0.660192 | ||||||||
\(663\) | −1.18823e35 | −0.639706 | ||||||||
\(664\) | 1.11509e35 | 0.589126 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.22756e35 | 0.624616 | ||||||||
\(667\) | −4.43827e35 | −2.21636 | ||||||||
\(668\) | 3.07962e34 | 0.150936 | ||||||||
\(669\) | 2.54434e35 | 1.22391 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.10313e35 | 2.36486 | ||||||||
\(672\) | 7.62989e34 | 0.347058 | ||||||||
\(673\) | 4.10824e34 | 0.183429 | 0.0917145 | − | 0.995785i | \(-0.470765\pi\) | ||||
0.0917145 | + | 0.995785i | \(0.470765\pi\) | |||||||
\(674\) | −2.79622e35 | −1.22552 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.54634e34 | −0.318715 | ||||||||
\(677\) | −2.21198e35 | −0.917111 | −0.458556 | − | 0.888666i | \(-0.651633\pi\) | ||||
−0.458556 | + | 0.888666i | \(0.651633\pi\) | |||||||
\(678\) | −2.42720e35 | −0.987949 | ||||||||
\(679\) | 5.09063e35 | 2.03423 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.81700e35 | 2.24058 | ||||||||
\(682\) | −8.07975e34 | −0.305558 | ||||||||
\(683\) | 1.93443e35 | 0.718280 | 0.359140 | − | 0.933284i | \(-0.383070\pi\) | ||||
0.359140 | + | 0.933284i | \(0.383070\pi\) | |||||||
\(684\) | −3.85950e34 | −0.140711 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.25791e34 | −0.184825 | ||||||||
\(687\) | −5.48569e35 | −1.89353 | ||||||||
\(688\) | 3.94452e34 | 0.133702 | ||||||||
\(689\) | 2.50153e35 | 0.832655 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.57151e33 | −0.00504479 | −0.00252239 | − | 0.999997i | \(-0.500803\pi\) | ||||
−0.00252239 | + | 0.999997i | \(0.500803\pi\) | |||||||
\(692\) | 1.26595e35 | 0.399109 | ||||||||
\(693\) | −6.34778e35 | −1.96543 | ||||||||
\(694\) | −6.54097e34 | −0.198907 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.84496e35 | 0.834565 | ||||||||
\(697\) | 9.11480e34 | 0.262626 | ||||||||
\(698\) | 2.01435e35 | 0.570087 | ||||||||
\(699\) | 1.46446e35 | 0.407110 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.76280e35 | −1.27758 | −0.638789 | − | 0.769382i | \(-0.720564\pi\) | ||||
−0.638789 | + | 0.769382i | \(0.720564\pi\) | |||||||
\(702\) | 4.93669e34 | 0.130083 | ||||||||
\(703\) | 1.61815e35 | 0.418867 | ||||||||
\(704\) | −8.49915e34 | −0.216131 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.30979e34 | −0.0321472 | ||||||||
\(707\) | −3.38363e35 | −0.815907 | ||||||||
\(708\) | −1.76004e35 | −0.416973 | ||||||||
\(709\) | −2.73484e35 | −0.636580 | −0.318290 | − | 0.947993i | \(-0.603109\pi\) | ||||
−0.318290 | + | 0.947993i | \(0.603109\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.13992e34 | 0.0480870 | ||||||||
\(712\) | −1.32331e35 | −0.292187 | ||||||||
\(713\) | 1.43909e35 | 0.312227 | ||||||||
\(714\) | −5.19925e35 | −1.10844 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.03577e35 | −0.830834 | ||||||||
\(717\) | 2.12674e35 | 0.430255 | ||||||||
\(718\) | 1.46443e35 | 0.291148 | ||||||||
\(719\) | −1.61873e35 | −0.316274 | −0.158137 | − | 0.987417i | \(-0.550549\pi\) | ||||
−0.158137 | + | 0.987417i | \(0.550549\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.14218e35 | −0.970413 | ||||||||
\(722\) | 3.30366e35 | 0.612746 | ||||||||
\(723\) | −8.01402e35 | −1.46090 | ||||||||
\(724\) | 5.12191e35 | 0.917699 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.08142e36 | 1.87192 | ||||||||
\(727\) | 3.12165e35 | 0.531134 | 0.265567 | − | 0.964092i | \(-0.414441\pi\) | ||||
0.265567 | + | 0.964092i | \(0.414441\pi\) | |||||||
\(728\) | 1.87818e35 | 0.314119 | ||||||||
\(729\) | −3.04221e35 | −0.500144 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.68793e35 | −0.427022 | ||||||||
\(732\) | 5.82626e35 | 0.909916 | ||||||||
\(733\) | −2.02938e35 | −0.311576 | −0.155788 | − | 0.987791i | \(-0.549792\pi\) | ||||
−0.155788 | + | 0.987791i | \(0.549792\pi\) | |||||||
\(734\) | −9.10360e35 | −1.37408 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.51379e35 | 0.220848 | ||||||||
\(737\) | 9.87798e35 | 1.41685 | ||||||||
\(738\) | 1.27052e35 | 0.179175 | ||||||||
\(739\) | 6.40360e34 | 0.0887910 | 0.0443955 | − | 0.999014i | \(-0.485864\pi\) | ||||
0.0443955 | + | 0.999014i | \(0.485864\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.18329e35 | −0.292673 | ||||||||
\(742\) | 1.09458e36 | 1.44277 | ||||||||
\(743\) | 9.29648e35 | 1.20492 | 0.602460 | − | 0.798149i | \(-0.294187\pi\) | ||||
0.602460 | + | 0.798149i | \(0.294187\pi\) | |||||||
\(744\) | −9.22468e34 | −0.117568 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 8.66924e35 | 1.06843 | ||||||||
\(747\) | −1.05917e36 | −1.28369 | ||||||||
\(748\) | 5.79160e35 | 0.690285 | ||||||||
\(749\) | 2.72250e35 | 0.319113 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.56197e35 | 0.403823 | 0.201912 | − | 0.979404i | \(-0.435285\pi\) | ||||
0.201912 | + | 0.979404i | \(0.435285\pi\) | |||||||
\(752\) | −2.64789e35 | −0.295241 | ||||||||
\(753\) | −8.00743e35 | −0.878124 | ||||||||
\(754\) | 7.00316e35 | 0.755357 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.16012e35 | 0.225401 | ||||||||
\(757\) | −1.75236e36 | −1.79856 | −0.899278 | − | 0.437378i | \(-0.855907\pi\) | ||||
−0.899278 | + | 0.437378i | \(0.855907\pi\) | |||||||
\(758\) | −6.43473e35 | −0.649629 | ||||||||
\(759\) | −2.89422e36 | −2.87415 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.03372e36 | −0.993332 | −0.496666 | − | 0.867942i | \(-0.665443\pi\) | ||||
−0.496666 | + | 0.867942i | \(0.665443\pi\) | |||||||
\(762\) | 1.08616e36 | 1.02673 | ||||||||
\(763\) | −9.44830e35 | −0.878611 | ||||||||
\(764\) | 5.60072e35 | 0.512362 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.37079e35 | −0.741151 | ||||||||
\(767\) | −4.33254e35 | −0.377399 | ||||||||
\(768\) | −9.70351e34 | −0.0831598 | ||||||||
\(769\) | 1.96647e35 | 0.165809 | 0.0829044 | − | 0.996558i | \(-0.473580\pi\) | ||||
0.0829044 | + | 0.996558i | \(0.473580\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.95880e35 | 0.159886 | ||||||||
\(772\) | 4.86189e35 | 0.390471 | ||||||||
\(773\) | 3.07830e35 | 0.243258 | 0.121629 | − | 0.992576i | \(-0.461188\pi\) | ||||
0.121629 | + | 0.992576i | \(0.461188\pi\) | |||||||
\(774\) | −3.74672e35 | −0.291333 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.47414e35 | −0.487428 | ||||||||
\(777\) | 3.03852e36 | 2.25113 | ||||||||
\(778\) | −7.29538e35 | −0.531867 | ||||||||
\(779\) | 1.67478e35 | 0.120155 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.58906e36 | −3.18850 | ||||||||
\(782\) | −1.03155e36 | −0.705351 | ||||||||
\(783\) | 8.05443e35 | 0.542017 | ||||||||
\(784\) | 4.44346e35 | 0.294287 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.91959e36 | −1.23148 | ||||||||
\(787\) | 2.22687e36 | 1.40608 | 0.703042 | − | 0.711148i | \(-0.251825\pi\) | ||||
0.703042 | + | 0.711148i | \(0.251825\pi\) | |||||||
\(788\) | −9.01920e35 | −0.560519 | ||||||||
\(789\) | 1.76725e36 | 1.08103 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.61436e36 | −1.54939 | ||||||||
\(792\) | 8.07296e35 | 0.470942 | ||||||||
\(793\) | 1.43420e36 | 0.823557 | ||||||||
\(794\) | 7.44521e35 | 0.420844 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.25702e35 | 0.233180 | ||||||||
\(797\) | −9.40522e35 | −0.507154 | −0.253577 | − | 0.967315i | \(-0.581607\pi\) | ||||
−0.253577 | + | 0.967315i | \(0.581607\pi\) | |||||||
\(798\) | −9.55327e35 | −0.507126 | ||||||||
\(799\) | 1.80436e36 | 0.942948 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.25695e36 | 0.636665 | ||||||||
\(802\) | 7.68378e35 | 0.383174 | ||||||||
\(803\) | 1.32167e36 | 0.648899 | ||||||||
\(804\) | 1.12777e36 | 0.545156 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.27075e35 | −0.106410 | ||||||||
\(807\) | −4.51539e36 | −2.08341 | ||||||||
\(808\) | 4.30322e35 | 0.195502 | ||||||||
\(809\) | 2.23971e36 | 1.00193 | 0.500963 | − | 0.865468i | \(-0.332979\pi\) | ||||
0.500963 | + | 0.865468i | \(0.332979\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.70491e35 | −0.117325 | −0.0586627 | − | 0.998278i | \(-0.518684\pi\) | ||||
−0.0586627 | + | 0.998278i | \(0.518684\pi\) | |||||||
\(812\) | 3.06433e36 | 1.30884 | ||||||||
\(813\) | −4.88446e36 | −2.05440 | ||||||||
\(814\) | −3.38470e36 | −1.40189 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.61228e35 | 0.265598 | ||||||||
\(817\) | −4.93888e35 | −0.195368 | ||||||||
\(818\) | 1.42614e36 | 0.555578 | ||||||||
\(819\) | −1.78400e36 | −0.684455 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.72543e35 | 0.324711 | 0.162356 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162356 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(822\) | −4.48700e36 | −1.64459 | ||||||||
\(823\) | −5.40468e35 | −0.195107 | −0.0975534 | − | 0.995230i | \(-0.531102\pi\) | ||||
−0.0975534 | + | 0.995230i | \(0.531102\pi\) | |||||||
\(824\) | 6.53970e35 | 0.232524 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.89576e36 | −0.653933 | ||||||||
\(827\) | 9.59407e35 | 0.325975 | 0.162987 | − | 0.986628i | \(-0.447887\pi\) | ||||
0.162987 | + | 0.986628i | \(0.447887\pi\) | |||||||
\(828\) | −1.43788e36 | −0.481221 | ||||||||
\(829\) | −2.44895e36 | −0.807326 | −0.403663 | − | 0.914908i | \(-0.632263\pi\) | ||||
−0.403663 | + | 0.914908i | \(0.632263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.42525e36 | −1.41555 | ||||||||
\(832\) | −2.38862e35 | −0.0752672 | ||||||||
\(833\) | −3.02792e36 | −0.939900 | ||||||||
\(834\) | −3.08414e36 | −0.943101 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.06417e36 | 0.315814 | ||||||||
\(837\) | −2.61162e35 | −0.0763559 | ||||||||
\(838\) | 3.28769e36 | 0.946980 | ||||||||
\(839\) | 5.26267e36 | 1.49342 | 0.746709 | − | 0.665151i | \(-0.231633\pi\) | ||||
0.746709 | + | 0.665151i | \(0.231633\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.79561e36 | 2.14734 | ||||||||
\(842\) | −1.74810e36 | −0.474423 | ||||||||
\(843\) | −1.57026e35 | −0.0419881 | ||||||||
\(844\) | −1.26359e36 | −0.332910 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.51511e36 | 0.643320 | ||||||||
\(847\) | 1.16481e37 | 2.93570 | ||||||||
\(848\) | −1.39206e36 | −0.345708 | ||||||||
\(849\) | −9.68588e36 | −2.37024 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.02852e36 | 1.43249 | ||||||||
\(852\) | −5.23934e36 | −1.22682 | ||||||||
\(853\) | 2.08360e36 | 0.480786 | 0.240393 | − | 0.970676i | \(-0.422724\pi\) | ||||
0.240393 | + | 0.970676i | \(0.422724\pi\) | |||||||
\(854\) | 6.27553e36 | 1.42701 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.46241e35 | −0.0764639 | ||||||||
\(857\) | −4.78596e36 | −1.04162 | −0.520810 | − | 0.853673i | \(-0.674370\pi\) | ||||
−0.520810 | + | 0.853673i | \(0.674370\pi\) | |||||||
\(858\) | 4.56681e36 | 0.979538 | ||||||||
\(859\) | −4.96565e36 | −1.04969 | −0.524846 | − | 0.851197i | \(-0.675877\pi\) | ||||
−0.524846 | + | 0.851197i | \(0.675877\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.14487e36 | 0.645749 | ||||||||
\(862\) | −2.65270e36 | −0.536843 | ||||||||
\(863\) | 3.87006e36 | 0.771939 | 0.385969 | − | 0.922512i | \(-0.373867\pi\) | ||||
0.385969 | + | 0.922512i | \(0.373867\pi\) | |||||||
\(864\) | −2.74719e35 | −0.0540090 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.21686e36 | −0.423413 | ||||||||
\(867\) | 2.56178e36 | 0.482284 | ||||||||
\(868\) | −9.93600e35 | −0.184381 | ||||||||
\(869\) | −5.90033e35 | −0.107927 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.77613e36 | 0.493416 | ||||||||
\(872\) | 1.20161e36 | 0.210527 | ||||||||
\(873\) | 6.14949e36 | 1.06209 | ||||||||
\(874\) | −1.89540e36 | −0.322706 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.50895e36 | 0.249674 | ||||||||
\(877\) | 9.31488e36 | 1.51944 | 0.759718 | − | 0.650253i | \(-0.225337\pi\) | ||||
0.759718 | + | 0.650253i | \(0.225337\pi\) | |||||||
\(878\) | 1.71634e36 | 0.276008 | ||||||||
\(879\) | 7.65493e36 | 1.21361 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.30000e36 | 0.508528 | 0.254264 | − | 0.967135i | \(-0.418167\pi\) | ||||
0.254264 | + | 0.967135i | \(0.418167\pi\) | |||||||
\(882\) | −4.22064e36 | −0.641241 | ||||||||
\(883\) | −6.02750e36 | −0.902876 | −0.451438 | − | 0.892302i | \(-0.649089\pi\) | ||||
−0.451438 | + | 0.892302i | \(0.649089\pi\) | |||||||
\(884\) | 1.62768e36 | 0.240390 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.35675e36 | −0.338369 | ||||||||
\(887\) | 3.09975e36 | 0.438814 | 0.219407 | − | 0.975633i | \(-0.429588\pi\) | ||||
0.219407 | + | 0.975633i | \(0.429588\pi\) | |||||||
\(888\) | −3.86432e36 | −0.539400 | ||||||||
\(889\) | 1.16991e37 | 1.61020 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.52060e37 | 2.03491 | ||||||||
\(892\) | −3.48535e36 | −0.459924 | ||||||||
\(893\) | 3.31538e36 | 0.431410 | ||||||||
\(894\) | −7.67431e36 | −0.984737 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.04517e36 | −0.130418 | ||||||||
\(897\) | −8.13399e36 | −1.00092 | ||||||||
\(898\) | −3.40583e36 | −0.413304 | ||||||||
\(899\) | −3.70483e36 | −0.443377 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.48594e36 | 1.10413 | ||||||||
\(902\) | −3.50316e36 | −0.402141 | ||||||||
\(903\) | −9.27413e36 | −1.04997 | ||||||||
\(904\) | 3.32488e36 | 0.371254 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.37510e36 | −0.909678 | ||||||||
\(907\) | −1.94270e36 | −0.208120 | −0.104060 | − | 0.994571i | \(-0.533183\pi\) | ||||
−0.104060 | + | 0.994571i | \(0.533183\pi\) | |||||||
\(908\) | −7.96838e36 | −0.841971 | ||||||||
\(909\) | −4.08744e36 | −0.425993 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.71377e37 | −1.73769 | −0.868845 | − | 0.495085i | \(-0.835137\pi\) | ||||
−0.868845 | + | 0.495085i | \(0.835137\pi\) | |||||||
\(912\) | 1.21496e36 | 0.121514 | ||||||||
\(913\) | 2.92042e37 | 2.88111 | ||||||||
\(914\) | 7.14510e36 | 0.695314 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.51453e36 | 0.711555 | ||||||||
\(917\) | −2.06762e37 | −1.93132 | ||||||||
\(918\) | 1.87202e36 | 0.172495 | ||||||||
\(919\) | −8.92079e35 | −0.0810886 | −0.0405443 | − | 0.999178i | \(-0.512909\pi\) | ||||
−0.0405443 | + | 0.999178i | \(0.512909\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.45052e37 | 2.16777 | ||||||||
\(922\) | −5.40542e36 | −0.471729 | ||||||||
\(923\) | −1.28972e37 | −1.11039 | ||||||||
\(924\) | 1.99827e37 | 1.69728 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.74870e36 | −0.475261 | ||||||||
\(927\) | −6.21177e36 | −0.506662 | ||||||||
\(928\) | −3.89714e36 | −0.313615 | ||||||||
\(929\) | −1.38002e36 | −0.109569 | −0.0547846 | − | 0.998498i | \(-0.517447\pi\) | ||||
−0.0547846 | + | 0.998498i | \(0.517447\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.56359e36 | −0.430016 | ||||||||
\(932\) | −2.00608e36 | −0.152985 | ||||||||
\(933\) | 2.77976e37 | 2.09164 | ||||||||
\(934\) | 3.14937e36 | 0.233823 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.26884e36 | 0.164005 | ||||||||
\(937\) | −1.08251e37 | −0.772126 | −0.386063 | − | 0.922472i | \(-0.626165\pi\) | ||||
−0.386063 | + | 0.922472i | \(0.626165\pi\) | |||||||
\(938\) | 1.21473e37 | 0.854960 | ||||||||
\(939\) | 1.80930e37 | 1.25658 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.75055e36 | −0.524158 | −0.262079 | − | 0.965046i | \(-0.584408\pi\) | ||||
−0.262079 | + | 0.965046i | \(0.584408\pi\) | |||||||
\(942\) | −9.91066e36 | −0.661403 | ||||||||
\(943\) | 6.23952e36 | 0.410918 | ||||||||
\(944\) | 2.41098e36 | 0.156691 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.03307e37 | 0.653870 | ||||||||
\(947\) | −5.61736e36 | −0.350879 | −0.175440 | − | 0.984490i | \(-0.556135\pi\) | ||||
−0.175440 | + | 0.984490i | \(0.556135\pi\) | |||||||
\(948\) | −6.73642e35 | −0.0415265 | ||||||||
\(949\) | 3.71444e36 | 0.225978 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.89117e36 | −0.171324 | ||||||||
\(952\) | 7.12216e36 | 0.416534 | ||||||||
\(953\) | 8.09802e36 | 0.467431 | 0.233715 | − | 0.972305i | \(-0.424912\pi\) | ||||
0.233715 | + | 0.972305i | \(0.424912\pi\) | |||||||
\(954\) | 1.32225e37 | 0.753286 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.91331e36 | −0.161682 | ||||||||
\(957\) | 7.45095e37 | 4.08143 | ||||||||
\(958\) | −1.09973e37 | −0.594591 | ||||||||
\(959\) | −4.83299e37 | −2.57919 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.80315e37 | −0.937540 | ||||||||
\(962\) | −9.51244e36 | −0.488206 | ||||||||
\(963\) | 3.28878e36 | 0.166612 | ||||||||
\(964\) | 1.09779e37 | 0.548982 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.55914e37 | −1.73433 | ||||||||
\(967\) | 8.79417e36 | 0.423023 | 0.211511 | − | 0.977376i | \(-0.432161\pi\) | ||||
0.211511 | + | 0.977376i | \(0.432161\pi\) | |||||||
\(968\) | −1.48137e37 | −0.703433 | ||||||||
\(969\) | −8.27915e36 | −0.388095 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.66027e37 | −0.758472 | −0.379236 | − | 0.925300i | \(-0.623813\pi\) | ||||
−0.379236 | + | 0.925300i | \(0.623813\pi\) | |||||||
\(972\) | 1.39736e37 | 0.630202 | ||||||||
\(973\) | −3.32196e37 | −1.47905 | ||||||||
\(974\) | 1.88028e37 | 0.826487 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.98106e36 | −0.341931 | ||||||||
\(977\) | −2.34433e37 | −0.991601 | −0.495801 | − | 0.868436i | \(-0.665125\pi\) | ||||
−0.495801 | + | 0.868436i | \(0.665125\pi\) | |||||||
\(978\) | 2.10056e37 | 0.877200 | ||||||||
\(979\) | −3.46574e37 | −1.42894 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.14136e37 | −0.458732 | ||||||||
\(982\) | −2.11018e37 | −0.837385 | ||||||||
\(983\) | 3.99283e37 | 1.56445 | 0.782225 | − | 0.622996i | \(-0.214085\pi\) | ||||
0.782225 | + | 0.622996i | \(0.214085\pi\) | |||||||
\(984\) | −3.99957e36 | −0.154730 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.65564e37 | 1.00163 | ||||||||
\(987\) | 6.22556e37 | 2.31854 | ||||||||
\(988\) | 2.99076e36 | 0.109981 | ||||||||
\(989\) | −1.84002e37 | −0.668141 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.11236e37 | 0.747907 | 0.373954 | − | 0.927447i | \(-0.378002\pi\) | ||||
0.373954 | + | 0.927447i | \(0.378002\pi\) | |||||||
\(992\) | 1.26364e36 | 0.0441800 | ||||||||
\(993\) | −3.59819e37 | −1.24228 | ||||||||
\(994\) | −5.64335e37 | −1.92401 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 3.33425e37 | 1.10855 | ||||||||
\(997\) | −2.11846e37 | −0.695555 | −0.347777 | − | 0.937577i | \(-0.613064\pi\) | ||||
−0.347777 | + | 0.937577i | \(0.613064\pi\) | |||||||
\(998\) | −3.05562e37 | −0.990760 | ||||||||
\(999\) | −1.09404e37 | −0.350319 |
(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.i.1.2 | ✓ | 5 | |
5.2 | odd | 4 | 50.26.b.h.49.4 | 10 | |||
5.3 | odd | 4 | 50.26.b.h.49.7 | 10 | |||
5.4 | even | 2 | 50.26.a.j.1.4 | yes | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
50.26.a.i.1.2 | ✓ | 5 | 1.1 | even | 1 | trivial | |
50.26.a.j.1.4 | yes | 5 | 5.4 | even | 2 | ||
50.26.b.h.49.4 | 10 | 5.2 | odd | 4 | |||
50.26.b.h.49.7 | 10 | 5.3 | odd | 4 |