Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,22,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(58.6902423003\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.50 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.22.c.b.20.49 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 247.072i | 0.170612i | 0.996355 | + | 0.0853058i | \(0.0271867\pi\) | ||||
−0.996355 | + | 0.0853058i | \(0.972813\pi\) | |||||||
\(3\) | −16209.6 | + | 100983.i | −0.158489 | + | 0.987361i | ||||
\(4\) | 2.03611e6 | 0.970892 | ||||||||
\(5\) | 3.48005e7 | 1.59368 | 0.796839 | − | 0.604192i | \(-0.206504\pi\) | ||||
0.796839 | + | 0.604192i | \(0.206504\pi\) | |||||||
\(6\) | −2.49501e7 | − | 4.00494e6i | −0.168455 | − | 0.0270401i | ||||
\(7\) | 7.14474e8 | − | 2.19256e8i | 0.955998 | − | 0.293374i | ||||
\(8\) | 1.02121e9i | 0.336257i | ||||||||
\(9\) | −9.93485e9 | − | 3.27379e9i | −0.949762 | − | 0.312972i | ||||
\(10\) | 8.59823e9i | 0.271900i | ||||||||
\(11\) | 9.21376e10i | 1.07106i | 0.844516 | + | 0.535530i | \(0.179888\pi\) | ||||
−0.844516 | + | 0.535530i | \(0.820112\pi\) | |||||||
\(12\) | −3.30045e10 | + | 2.05613e11i | −0.153876 | + | 0.958620i | ||||
\(13\) | 1.67572e11i | 0.337130i | 0.985691 | + | 0.168565i | \(0.0539133\pi\) | ||||
−0.985691 | + | 0.168565i | \(0.946087\pi\) | |||||||
\(14\) | 5.41720e10 | + | 1.76527e11i | 0.0500530 | + | 0.163104i | ||||
\(15\) | −5.64102e11 | + | 3.51427e12i | −0.252580 | + | 1.57353i | ||||
\(16\) | 4.01771e12 | 0.913522 | ||||||||
\(17\) | −7.92508e12 | −0.953432 | −0.476716 | − | 0.879057i | \(-0.658173\pi\) | ||||
−0.476716 | + | 0.879057i | \(0.658173\pi\) | |||||||
\(18\) | 8.08863e11 | − | 2.45462e12i | 0.0533966 | − | 0.162041i | ||||
\(19\) | 3.32012e13i | 1.24234i | 0.783675 | + | 0.621171i | \(0.213343\pi\) | ||||
−0.783675 | + | 0.621171i | \(0.786657\pi\) | |||||||
\(20\) | 7.08576e13 | 1.54729 | ||||||||
\(21\) | 1.05598e13 | + | 7.57039e13i | 0.138151 | + | 0.990411i | ||||
\(22\) | −2.27646e13 | −0.182735 | ||||||||
\(23\) | − | 3.78679e14i | − | 1.90603i | −0.302928 | − | 0.953013i | \(-0.597964\pi\) | ||
0.302928 | − | 0.953013i | \(-0.402036\pi\) | |||||||
\(24\) | −1.03125e14 | − | 1.65535e13i | −0.332007 | − | 0.0532930i | ||||
\(25\) | 7.34238e14 | 1.53981 | ||||||||
\(26\) | −4.14025e13 | −0.0575183 | ||||||||
\(27\) | 4.91638e14 | − | 9.50186e14i | 0.459543 | − | 0.888156i | ||||
\(28\) | 1.45475e15 | − | 4.46428e14i | 0.928170 | − | 0.284834i | ||||
\(29\) | 2.17759e15i | 0.961165i | 0.876950 | + | 0.480583i | \(0.159575\pi\) | ||||
−0.876950 | + | 0.480583i | \(0.840425\pi\) | |||||||
\(30\) | −8.68277e14 | − | 1.39374e14i | −0.268463 | − | 0.0430932i | ||||
\(31\) | 3.73514e15i | 0.818482i | 0.912426 | + | 0.409241i | \(0.134206\pi\) | ||||
−0.912426 | + | 0.409241i | \(0.865794\pi\) | |||||||
\(32\) | 3.13430e15i | 0.492115i | ||||||||
\(33\) | −9.30435e15 | − | 1.49351e15i | −1.05752 | − | 0.169751i | ||||
\(34\) | − | 1.95807e15i | − | 0.162667i | ||||||
\(35\) | 2.48640e16 | − | 7.63021e15i | 1.52355 | − | 0.467544i | ||||
\(36\) | −2.02284e16 | − | 6.66579e15i | −0.922116 | − | 0.303862i | ||||
\(37\) | −1.35512e16 | −0.463296 | −0.231648 | − | 0.972800i | \(-0.574412\pi\) | ||||
−0.231648 | + | 0.972800i | \(0.574412\pi\) | |||||||
\(38\) | −8.20309e15 | −0.211958 | ||||||||
\(39\) | −1.69220e16 | − | 2.71628e15i | −0.332869 | − | 0.0534314i | ||||
\(40\) | 3.55387e16i | 0.535885i | ||||||||
\(41\) | 6.54994e16 | 0.762092 | 0.381046 | − | 0.924556i | \(-0.375564\pi\) | ||||
0.381046 | + | 0.924556i | \(0.375564\pi\) | |||||||
\(42\) | −1.87043e16 | + | 2.60904e15i | −0.168976 | + | 0.0235702i | ||||
\(43\) | 4.14672e15 | 0.0292608 | 0.0146304 | − | 0.999893i | \(-0.495343\pi\) | ||||
0.0146304 | + | 0.999893i | \(0.495343\pi\) | |||||||
\(44\) | 1.87602e17i | 1.03988i | ||||||||
\(45\) | −3.45738e17 | − | 1.13930e17i | −1.51362 | − | 0.498776i | ||||
\(46\) | 9.35610e16 | 0.325190 | ||||||||
\(47\) | 4.66357e17 | 1.29327 | 0.646637 | − | 0.762798i | \(-0.276175\pi\) | ||||
0.646637 | + | 0.762798i | \(0.276175\pi\) | |||||||
\(48\) | −6.51255e16 | + | 4.05721e17i | −0.144783 | + | 0.901976i | ||||
\(49\) | 4.62400e17 | − | 3.13305e17i | 0.827863 | − | 0.560930i | ||||
\(50\) | 1.81410e17i | 0.262709i | ||||||||
\(51\) | 1.28462e17 | − | 8.00299e17i | 0.151108 | − | 0.941382i | ||||
\(52\) | 3.41196e17i | 0.327317i | ||||||||
\(53\) | − | 1.25598e18i | − | 0.986476i | −0.869894 | − | 0.493238i | \(-0.835813\pi\) | ||
0.869894 | − | 0.493238i | \(-0.164187\pi\) | |||||||
\(54\) | 2.34764e17 | + | 1.21470e17i | 0.151530 | + | 0.0784034i | ||||
\(55\) | 3.20643e18i | 1.70692i | ||||||||
\(56\) | 2.23907e17 | + | 7.29630e17i | 0.0986491 | + | 0.321461i | ||||
\(57\) | −3.35276e18 | − | 5.38178e17i | −1.22664 | − | 0.196898i | ||||
\(58\) | −5.38023e17 | −0.163986 | ||||||||
\(59\) | −5.49943e17 | −0.140079 | −0.0700393 | − | 0.997544i | \(-0.522312\pi\) | ||||
−0.0700393 | + | 0.997544i | \(0.522312\pi\) | |||||||
\(60\) | −1.14857e18 | + | 7.15542e18i | −0.245228 | + | 1.52773i | ||||
\(61\) | 7.00101e18i | 1.25660i | 0.777971 | + | 0.628301i | \(0.216249\pi\) | ||||
−0.777971 | + | 0.628301i | \(0.783751\pi\) | |||||||
\(62\) | −9.22849e17 | −0.139643 | ||||||||
\(63\) | −7.81599e18 | − | 1.60766e17i | −0.999789 | − | 0.0205645i | ||||
\(64\) | 7.65136e18 | 0.829562 | ||||||||
\(65\) | 5.83161e18i | 0.537277i | ||||||||
\(66\) | 3.69006e17 | − | 2.29884e18i | 0.0289615 | − | 0.180426i | ||||
\(67\) | −1.30709e19 | −0.876032 | −0.438016 | − | 0.898967i | \(-0.644319\pi\) | ||||
−0.438016 | + | 0.898967i | \(0.644319\pi\) | |||||||
\(68\) | −1.61363e19 | −0.925679 | ||||||||
\(69\) | 3.82402e19 | + | 6.13824e18i | 1.88194 | + | 0.302084i | ||||
\(70\) | 1.88521e18 | + | 6.14321e18i | 0.0797684 | + | 0.259936i | ||||
\(71\) | − | 3.38969e19i | − | 1.23580i | −0.786258 | − | 0.617898i | \(-0.787984\pi\) | ||
0.786258 | − | 0.617898i | \(-0.212016\pi\) | |||||||
\(72\) | 3.34324e18 | − | 1.01456e19i | 0.105239 | − | 0.319364i | ||||
\(73\) | 5.69462e19i | 1.55087i | 0.631430 | + | 0.775433i | \(0.282468\pi\) | ||||
−0.631430 | + | 0.775433i | \(0.717532\pi\) | |||||||
\(74\) | − | 3.34811e18i | − | 0.0790436i | ||||||
\(75\) | −1.19017e19 | + | 7.41457e19i | −0.244043 | + | 1.52035i | ||||
\(76\) | 6.76012e19i | 1.20618i | ||||||||
\(77\) | 2.02017e19 | + | 6.58299e19i | 0.314221 | + | 1.02393i | ||||
\(78\) | 6.71118e17 | − | 4.18095e18i | 0.00911602 | − | 0.0567913i | ||||
\(79\) | −5.19511e19 | −0.617320 | −0.308660 | − | 0.951172i | \(-0.599881\pi\) | ||||
−0.308660 | + | 0.951172i | \(0.599881\pi\) | |||||||
\(80\) | 1.39818e20 | 1.45586 | ||||||||
\(81\) | 8.79835e19 | + | 6.50493e19i | 0.804098 | + | 0.594497i | ||||
\(82\) | 1.61831e19i | 0.130022i | ||||||||
\(83\) | −1.77530e20 | −1.25589 | −0.627946 | − | 0.778257i | \(-0.716104\pi\) | ||||
−0.627946 | + | 0.778257i | \(0.716104\pi\) | |||||||
\(84\) | 2.15009e19 | + | 1.54141e20i | 0.134130 | + | 0.961582i | ||||
\(85\) | −2.75797e20 | −1.51946 | ||||||||
\(86\) | 1.02454e18i | 0.00499223i | ||||||||
\(87\) | −2.19900e20 | − | 3.52979e19i | −0.949017 | − | 0.152334i | ||||
\(88\) | −9.40921e19 | −0.360151 | ||||||||
\(89\) | 4.40189e20 | 1.49639 | 0.748194 | − | 0.663480i | \(-0.230921\pi\) | ||||
0.748194 | + | 0.663480i | \(0.230921\pi\) | |||||||
\(90\) | 2.81488e19 | − | 8.54222e19i | 0.0850970 | − | 0.258240i | ||||
\(91\) | 3.67412e19 | + | 1.19726e20i | 0.0989052 | + | 0.322296i | ||||
\(92\) | − | 7.71031e20i | − | 1.85055i | ||||||
\(93\) | −3.77186e20 | − | 6.05451e19i | −0.808137 | − | 0.129720i | ||||
\(94\) | 1.15224e20i | 0.220648i | ||||||||
\(95\) | 1.15542e21i | 1.97989i | ||||||||
\(96\) | −3.16512e20 | − | 5.08058e19i | −0.485895 | − | 0.0779948i | ||||
\(97\) | − | 5.59451e20i | − | 0.770297i | −0.922855 | − | 0.385149i | \(-0.874150\pi\) | ||
0.922855 | − | 0.385149i | \(-0.125850\pi\) | |||||||
\(98\) | 7.74089e19 | + | 1.14246e20i | 0.0957012 | + | 0.141243i | ||||
\(99\) | 3.01639e20 | − | 9.15373e20i | 0.335211 | − | 1.01725i | ||||
\(100\) | 1.49499e21 | 1.49499 | ||||||||
\(101\) | −7.90626e20 | −0.712191 | −0.356095 | − | 0.934450i | \(-0.615892\pi\) | ||||
−0.356095 | + | 0.934450i | \(0.615892\pi\) | |||||||
\(102\) | 1.97732e20 | + | 3.17395e19i | 0.160611 | + | 0.0257809i | ||||
\(103\) | 3.92142e20i | 0.287509i | 0.989613 | + | 0.143755i | \(0.0459176\pi\) | ||||
−0.989613 | + | 0.143755i | \(0.954082\pi\) | |||||||
\(104\) | −1.71127e20 | −0.113362 | ||||||||
\(105\) | 3.67487e20 | + | 2.63453e21i | 0.220168 | + | 1.57840i | ||||
\(106\) | 3.10318e20 | 0.168304 | ||||||||
\(107\) | − | 1.59873e21i | − | 0.785678i | −0.919607 | − | 0.392839i | \(-0.871493\pi\) | ||
0.919607 | − | 0.392839i | \(-0.128507\pi\) | |||||||
\(108\) | 1.00103e21 | − | 1.93468e21i | 0.446166 | − | 0.862303i | ||||
\(109\) | −6.51658e20 | −0.263658 | −0.131829 | − | 0.991272i | \(-0.542085\pi\) | ||||
−0.131829 | + | 0.991272i | \(0.542085\pi\) | |||||||
\(110\) | −7.92221e20 | −0.291221 | ||||||||
\(111\) | 2.19659e20 | − | 1.36844e21i | 0.0734273 | − | 0.457440i | ||||
\(112\) | 2.87055e21 | − | 8.80907e20i | 0.873325 | − | 0.268004i | ||||
\(113\) | − | 6.17950e21i | − | 1.71250i | −0.516565 | − | 0.856248i | \(-0.672789\pi\) | ||
0.516565 | − | 0.856248i | \(-0.327211\pi\) | |||||||
\(114\) | 1.32969e20 | − | 8.28374e20i | 0.0335930 | − | 0.209279i | ||||
\(115\) | − | 1.31782e22i | − | 3.03759i | ||||||
\(116\) | 4.43382e21i | 0.933187i | ||||||||
\(117\) | 5.48598e20 | − | 1.66481e21i | 0.105512 | − | 0.320194i | ||||
\(118\) | − | 1.35876e20i | − | 0.0238990i | ||||||
\(119\) | −5.66226e21 | + | 1.73762e21i | −0.911479 | + | 0.279712i | ||||
\(120\) | −3.58881e21 | − | 5.76069e20i | −0.529112 | − | 0.0849319i | ||||
\(121\) | −1.08909e21 | −0.147169 | ||||||||
\(122\) | −1.72975e21 | −0.214391 | ||||||||
\(123\) | −1.06172e21 | + | 6.61434e21i | −0.120783 | + | 0.752459i | ||||
\(124\) | 7.60514e21i | 0.794657i | ||||||||
\(125\) | 8.95767e21 | 0.860281 | ||||||||
\(126\) | 3.97207e19 | − | 1.93111e21i | 0.00350854 | − | 0.170576i | ||||
\(127\) | 1.92143e21 | 0.156202 | 0.0781008 | − | 0.996945i | \(-0.475114\pi\) | ||||
0.0781008 | + | 0.996945i | \(0.475114\pi\) | |||||||
\(128\) | 8.46355e21i | 0.633648i | ||||||||
\(129\) | −6.72167e19 | + | 4.18749e20i | −0.00463751 | + | 0.0288910i | ||||
\(130\) | −1.44083e21 | −0.0916657 | ||||||||
\(131\) | 3.30217e21 | 0.193843 | 0.0969215 | − | 0.995292i | \(-0.469100\pi\) | ||||
0.0969215 | + | 0.995292i | \(0.469100\pi\) | |||||||
\(132\) | −1.89447e22 | − | 3.04095e21i | −1.02674 | − | 0.164810i | ||||
\(133\) | 7.27956e21 | + | 2.37214e22i | 0.364471 | + | 1.18768i | ||||
\(134\) | − | 3.22946e21i | − | 0.149461i | ||||||
\(135\) | 1.71092e22 | − | 3.30669e22i | 0.732363 | − | 1.41543i | ||||
\(136\) | − | 8.09319e21i | − | 0.320598i | ||||||
\(137\) | − | 1.54231e22i | − | 0.565725i | −0.959160 | − | 0.282863i | \(-0.908716\pi\) | ||
0.959160 | − | 0.282863i | \(-0.0912841\pi\) | |||||||
\(138\) | −1.51659e21 | + | 9.44809e21i | −0.0515391 | + | 0.321080i | ||||
\(139\) | − | 1.70092e22i | − | 0.535830i | −0.963443 | − | 0.267915i | \(-0.913665\pi\) | ||
0.963443 | − | 0.267915i | \(-0.0863347\pi\) | |||||||
\(140\) | 5.06259e22 | − | 1.55359e22i | 1.47920 | − | 0.453934i | ||||
\(141\) | −7.55945e21 | + | 4.70942e22i | −0.204970 | + | 1.27693i | ||||
\(142\) | 8.37497e21 | 0.210841 | ||||||||
\(143\) | −1.54397e22 | −0.361086 | ||||||||
\(144\) | −3.99154e22 | − | 1.31532e22i | −0.867629 | − | 0.285907i | ||||
\(145\) | 7.57814e22i | 1.53179i | ||||||||
\(146\) | −1.40698e22 | −0.264596 | ||||||||
\(147\) | 2.41432e22 | + | 5.17731e22i | 0.422633 | + | 0.906301i | ||||
\(148\) | −2.75916e22 | −0.449810 | ||||||||
\(149\) | 6.09708e22i | 0.926117i | 0.886328 | + | 0.463059i | \(0.153248\pi\) | ||||
−0.886328 | + | 0.463059i | \(0.846752\pi\) | |||||||
\(150\) | −1.83193e22 | − | 2.94058e21i | −0.259389 | − | 0.0416365i | ||||
\(151\) | −1.02653e23 | −1.35554 | −0.677770 | − | 0.735274i | \(-0.737053\pi\) | ||||
−0.677770 | + | 0.735274i | \(0.737053\pi\) | |||||||
\(152\) | −3.39055e22 | −0.417746 | ||||||||
\(153\) | 7.87345e22 | + | 2.59451e22i | 0.905534 | + | 0.298397i | ||||
\(154\) | −1.62647e22 | + | 4.99128e21i | −0.174695 | + | 0.0536098i | ||||
\(155\) | 1.29985e23i | 1.30440i | ||||||||
\(156\) | −3.44550e22 | − | 5.53064e21i | −0.323180 | − | 0.0518761i | ||||
\(157\) | 6.98052e22i | 0.612268i | 0.951988 | + | 0.306134i | \(0.0990355\pi\) | ||||
−0.951988 | + | 0.306134i | \(0.900964\pi\) | |||||||
\(158\) | − | 1.28357e22i | − | 0.105322i | ||||||
\(159\) | 1.26833e23 | + | 2.03589e22i | 0.974007 | + | 0.156346i | ||||
\(160\) | 1.09075e23i | 0.784272i | ||||||||
\(161\) | −8.30276e22 | − | 2.70556e23i | −0.559179 | − | 1.82216i | ||||
\(162\) | −1.60719e22 | + | 2.17383e22i | −0.101428 | + | 0.137188i | ||||
\(163\) | 3.10704e23 | 1.83813 | 0.919066 | − | 0.394103i | \(-0.128945\pi\) | ||||
0.919066 | + | 0.394103i | \(0.128945\pi\) | |||||||
\(164\) | 1.33364e23 | 0.739908 | ||||||||
\(165\) | −3.23796e23 | − | 5.19750e22i | −1.68535 | − | 0.270529i | ||||
\(166\) | − | 4.38627e22i | − | 0.214270i | ||||||
\(167\) | −2.26403e23 | −1.03839 | −0.519194 | − | 0.854656i | \(-0.673768\pi\) | ||||
−0.519194 | + | 0.854656i | \(0.673768\pi\) | |||||||
\(168\) | −7.73098e22 | + | 1.07838e22i | −0.333033 | + | 0.0464542i | ||||
\(169\) | 2.18984e23 | 0.886343 | ||||||||
\(170\) | − | 6.81417e22i | − | 0.259238i | ||||||
\(171\) | 1.08694e23 | − | 3.29849e23i | 0.388818 | − | 1.17993i | ||||
\(172\) | 8.44317e21 | 0.0284091 | ||||||||
\(173\) | 1.54465e23 | 0.489041 | 0.244521 | − | 0.969644i | \(-0.421369\pi\) | ||||
0.244521 | + | 0.969644i | \(0.421369\pi\) | |||||||
\(174\) | 8.72113e21 | − | 5.43312e22i | 0.0259900 | − | 0.161913i | ||||
\(175\) | 5.24594e23 | − | 1.60986e23i | 1.47205 | − | 0.451740i | ||||
\(176\) | 3.70182e23i | 0.978437i | ||||||||
\(177\) | 8.91436e21 | − | 5.55350e22i | 0.0222009 | − | 0.138308i | ||||
\(178\) | 1.08758e23i | 0.255301i | ||||||||
\(179\) | 1.69966e23i | 0.376188i | 0.982151 | + | 0.188094i | \(0.0602310\pi\) | ||||
−0.982151 | + | 0.188094i | \(0.939769\pi\) | |||||||
\(180\) | −7.03959e23 | − | 2.31973e23i | −1.46956 | − | 0.484257i | ||||
\(181\) | − | 2.21194e23i | − | 0.435660i | −0.975987 | − | 0.217830i | \(-0.930102\pi\) | ||
0.975987 | − | 0.217830i | \(-0.0698978\pi\) | |||||||
\(182\) | −2.95810e22 | + | 9.07774e21i | −0.0549874 | + | 0.0168744i | ||||
\(183\) | −7.06984e23 | − | 1.13484e23i | −1.24072 | − | 0.199157i | ||||
\(184\) | 3.86712e23 | 0.640915 | ||||||||
\(185\) | −4.71587e23 | −0.738344 | ||||||||
\(186\) | 1.49590e22 | − | 9.31922e22i | 0.0221318 | − | 0.137878i | ||||
\(187\) | − | 7.30198e23i | − | 1.02118i | ||||||
\(188\) | 9.49552e23 | 1.25563 | ||||||||
\(189\) | 1.42929e23 | − | 7.86677e23i | 0.178760 | − | 0.983893i | ||||
\(190\) | −2.85472e23 | −0.337793 | ||||||||
\(191\) | − | 1.22833e23i | − | 0.137552i | −0.997632 | − | 0.0687758i | \(-0.978091\pi\) | ||
0.997632 | − | 0.0687758i | \(-0.0219093\pi\) | |||||||
\(192\) | −1.24025e23 | + | 7.72658e23i | −0.131476 | + | 0.819077i | ||||
\(193\) | −8.35000e23 | −0.838175 | −0.419087 | − | 0.907946i | \(-0.637650\pi\) | ||||
−0.419087 | + | 0.907946i | \(0.637650\pi\) | |||||||
\(194\) | 1.38225e23 | 0.131422 | ||||||||
\(195\) | −5.88894e23 | − | 9.45280e22i | −0.530486 | − | 0.0851524i | ||||
\(196\) | 9.41495e23 | − | 6.37923e23i | 0.803766 | − | 0.544602i | ||||
\(197\) | − | 1.49542e24i | − | 1.21023i | −0.796138 | − | 0.605115i | \(-0.793127\pi\) | ||
0.796138 | − | 0.605115i | \(-0.206873\pi\) | |||||||
\(198\) | 2.26163e23 | + | 7.45267e22i | 0.173555 | + | 0.0571910i | ||||
\(199\) | 3.32350e23i | 0.241901i | 0.992659 | + | 0.120951i | \(0.0385942\pi\) | ||||
−0.992659 | + | 0.120951i | \(0.961406\pi\) | |||||||
\(200\) | 7.49813e23i | 0.517772i | ||||||||
\(201\) | 2.11874e23 | − | 1.31994e24i | 0.138841 | − | 0.864960i | ||||
\(202\) | − | 1.95342e23i | − | 0.121508i | ||||||
\(203\) | 4.77450e23 | + | 1.55583e24i | 0.281981 | + | 0.918872i | ||||
\(204\) | 2.61563e23 | − | 1.62950e24i | 0.146710 | − | 0.913979i | ||||
\(205\) | 2.27941e24 | 1.21453 | ||||||||
\(206\) | −9.68872e22 | −0.0490525 | ||||||||
\(207\) | −1.23972e24 | + | 3.76212e24i | −0.596532 | + | 1.81027i | ||||
\(208\) | 6.73258e23i | 0.307976i | ||||||||
\(209\) | −3.05908e24 | −1.33062 | ||||||||
\(210\) | −6.50920e23 | + | 9.07958e22i | −0.269293 | + | 0.0375632i | ||||
\(211\) | 2.82664e24 | 1.11251 | 0.556256 | − | 0.831011i | \(-0.312238\pi\) | ||||
0.556256 | + | 0.831011i | \(0.312238\pi\) | |||||||
\(212\) | − | 2.55731e24i | − | 0.957761i | ||||||
\(213\) | 3.42301e24 | + | 5.49455e23i | 1.22018 | + | 0.195860i | ||||
\(214\) | 3.95001e23 | 0.134046 | ||||||||
\(215\) | 1.44308e23 | 0.0466323 | ||||||||
\(216\) | 9.70342e23 | + | 5.02067e23i | 0.298649 | + | 0.154525i | ||||
\(217\) | 8.18951e23 | + | 2.66866e24i | 0.240121 | + | 0.782467i | ||||
\(218\) | − | 1.61006e23i | − | 0.0449832i | ||||||
\(219\) | −5.75060e24 | − | 9.23074e23i | −1.53126 | − | 0.245795i | ||||
\(220\) | 6.52865e24i | 1.65724i | ||||||||
\(221\) | − | 1.32802e24i | − | 0.321431i | ||||||
\(222\) | 3.38103e23 | + | 5.42716e22i | 0.0780446 | + | 0.0125275i | ||||
\(223\) | 4.24179e24i | 0.934004i | 0.884256 | + | 0.467002i | \(0.154666\pi\) | ||||
−0.884256 | + | 0.467002i | \(0.845334\pi\) | |||||||
\(224\) | 6.87214e23 | + | 2.23938e24i | 0.144374 | + | 0.470461i | ||||
\(225\) | −7.29454e24 | − | 2.40374e24i | −1.46245 | − | 0.481916i | ||||
\(226\) | 1.52678e24 | 0.292172 | ||||||||
\(227\) | −3.16057e23 | −0.0577422 | −0.0288711 | − | 0.999583i | \(-0.509191\pi\) | ||||
−0.0288711 | + | 0.999583i | \(0.509191\pi\) | |||||||
\(228\) | −6.82659e24 | − | 1.09579e24i | −1.19093 | − | 0.191166i | ||||
\(229\) | 3.56596e24i | 0.594161i | 0.954853 | + | 0.297080i | \(0.0960129\pi\) | ||||
−0.954853 | + | 0.297080i | \(0.903987\pi\) | |||||||
\(230\) | 3.25597e24 | 0.518249 | ||||||||
\(231\) | −6.97517e24 | + | 9.72956e23i | −1.06079 | + | 0.147968i | ||||
\(232\) | −2.22379e24 | −0.323199 | ||||||||
\(233\) | − | 1.60294e23i | − | 0.0222679i | −0.999938 | − | 0.0111339i | \(-0.996456\pi\) | ||
0.999938 | − | 0.0111339i | \(-0.00354412\pi\) | |||||||
\(234\) | 4.11328e23 | + | 1.35543e23i | 0.0546288 | + | 0.0180016i | ||||
\(235\) | 1.62294e25 | 2.06106 | ||||||||
\(236\) | −1.11974e24 | −0.136001 | ||||||||
\(237\) | 8.42107e23 | − | 5.24619e24i | 0.0978385 | − | 0.609518i | ||||
\(238\) | −4.29317e23 | − | 1.39899e24i | −0.0477222 | − | 0.155509i | ||||
\(239\) | 7.82157e24i | 0.831986i | 0.909368 | + | 0.415993i | \(0.136566\pi\) | ||||
−0.909368 | + | 0.415993i | \(0.863434\pi\) | |||||||
\(240\) | −2.26640e24 | + | 1.41193e25i | −0.230738 | + | 1.43746i | ||||
\(241\) | − | 1.45971e25i | − | 1.42261i | −0.702882 | − | 0.711306i | \(-0.748104\pi\) | ||
0.702882 | − | 0.711306i | \(-0.251896\pi\) | |||||||
\(242\) | − | 2.69083e23i | − | 0.0251088i | ||||||
\(243\) | −7.99506e24 | + | 7.83043e24i | −0.714424 | + | 0.699713i | ||||
\(244\) | 1.42548e25i | 1.22002i | ||||||||
\(245\) | 1.60917e25 | − | 1.09032e25i | 1.31935 | − | 0.893941i | ||||
\(246\) | −1.63422e24 | − | 2.62321e23i | −0.128378 | − | 0.0206070i | ||||
\(247\) | −5.56361e24 | −0.418831 | ||||||||
\(248\) | −3.81437e24 | −0.275220 | ||||||||
\(249\) | 2.87769e24 | − | 1.79276e25i | 0.199045 | − | 1.24002i | ||||
\(250\) | 2.21319e24i | 0.146774i | ||||||||
\(251\) | −1.07792e25 | −0.685508 | −0.342754 | − | 0.939425i | \(-0.611360\pi\) | ||||
−0.342754 | + | 0.939425i | \(0.611360\pi\) | |||||||
\(252\) | −1.59142e25 | − | 3.27336e23i | −0.970686 | − | 0.0199659i | ||||
\(253\) | 3.48906e25 | 2.04147 | ||||||||
\(254\) | 4.74731e23i | 0.0266498i | ||||||||
\(255\) | 4.47055e24 | − | 2.78508e25i | 0.240818 | − | 1.50026i | ||||
\(256\) | 1.39550e25 | 0.721454 | ||||||||
\(257\) | 2.56886e25 | 1.27480 | 0.637401 | − | 0.770533i | \(-0.280010\pi\) | ||||
0.637401 | + | 0.770533i | \(0.280010\pi\) | |||||||
\(258\) | −1.03461e23 | − | 1.66074e22i | −0.00492913 | − | 0.000791214i | ||||
\(259\) | −9.68194e24 | + | 2.97117e24i | −0.442910 | + | 0.135919i | ||||
\(260\) | 1.18738e25i | 0.521637i | ||||||||
\(261\) | 7.12899e24 | − | 2.16341e25i | 0.300817 | − | 0.912878i | ||||
\(262\) | 8.15873e23i | 0.0330719i | ||||||||
\(263\) | − | 1.48951e25i | − | 0.580105i | −0.957011 | − | 0.290053i | \(-0.906327\pi\) | ||
0.957011 | − | 0.290053i | \(-0.0936728\pi\) | |||||||
\(264\) | 1.52520e24 | − | 9.50172e24i | 0.0570800 | − | 0.355599i | ||||
\(265\) | − | 4.37088e25i | − | 1.57212i | ||||||
\(266\) | −5.86090e24 | + | 1.79858e24i | −0.202631 | + | 0.0621830i | ||||
\(267\) | −7.13529e24 | + | 4.44517e25i | −0.237161 | + | 1.47747i | ||||
\(268\) | −2.66138e25 | −0.850532 | ||||||||
\(269\) | −5.79749e25 | −1.78173 | −0.890863 | − | 0.454273i | \(-0.849899\pi\) | ||||
−0.890863 | + | 0.454273i | \(0.849899\pi\) | |||||||
\(270\) | 8.16992e24 | + | 4.22722e24i | 0.241490 | + | 0.124950i | ||||
\(271\) | − | 2.99675e25i | − | 0.852066i | −0.904708 | − | 0.426033i | \(-0.859911\pi\) | ||
0.904708 | − | 0.426033i | \(-0.140089\pi\) | |||||||
\(272\) | −3.18407e25 | −0.870982 | ||||||||
\(273\) | −1.26859e25 | + | 1.76953e24i | −0.333897 | + | 0.0465748i | ||||
\(274\) | 3.81062e24 | 0.0965193 | ||||||||
\(275\) | 6.76509e25i | 1.64923i | ||||||||
\(276\) | 7.78612e25 | + | 1.24981e25i | 1.82716 | + | 0.293291i | ||||
\(277\) | 1.61099e25 | 0.363962 | 0.181981 | − | 0.983302i | \(-0.441749\pi\) | ||||
0.181981 | + | 0.983302i | \(0.441749\pi\) | |||||||
\(278\) | 4.20249e24 | 0.0914189 | ||||||||
\(279\) | 1.22281e25 | − | 3.71080e25i | 0.256161 | − | 0.777363i | ||||
\(280\) | 7.79207e24 | + | 2.53915e25i | 0.157215 | + | 0.512305i | ||||
\(281\) | − | 3.88973e25i | − | 0.755967i | −0.925812 | − | 0.377983i | \(-0.876618\pi\) | ||
0.925812 | − | 0.377983i | \(-0.123382\pi\) | |||||||
\(282\) | −1.16357e25 | − | 1.86773e24i | −0.217859 | − | 0.0349702i | ||||
\(283\) | − | 6.67261e25i | − | 1.20376i | −0.798588 | − | 0.601878i | \(-0.794419\pi\) | ||
0.798588 | − | 0.601878i | \(-0.205581\pi\) | |||||||
\(284\) | − | 6.90177e25i | − | 1.19982i | ||||||
\(285\) | −1.16678e26 | − | 1.87289e25i | −1.95487 | − | 0.313791i | ||||
\(286\) | − | 3.81473e24i | − | 0.0616056i | ||||||
\(287\) | 4.67976e25 | − | 1.43611e25i | 0.728558 | − | 0.223578i | ||||
\(288\) | 1.02611e25 | − | 3.11388e25i | 0.154018 | − | 0.467392i | ||||
\(289\) | −6.28509e24 | −0.0909671 | ||||||||
\(290\) | −1.87235e25 | −0.261341 | ||||||||
\(291\) | 5.64951e25 | + | 9.06847e24i | 0.760561 | + | 0.122084i | ||||
\(292\) | 1.15948e26i | 1.50572i | ||||||||
\(293\) | 2.91436e25 | 0.365118 | 0.182559 | − | 0.983195i | \(-0.441562\pi\) | ||||
0.182559 | + | 0.983195i | \(0.441562\pi\) | |||||||
\(294\) | −1.27917e25 | + | 5.96512e24i | −0.154626 | + | 0.0721061i | ||||
\(295\) | −1.91383e25 | −0.223240 | ||||||||
\(296\) | − | 1.38386e25i | − | 0.155786i | ||||||
\(297\) | 8.75479e25 | + | 4.52983e25i | 0.951268 | + | 0.492198i | ||||
\(298\) | −1.50642e25 | −0.158006 | ||||||||
\(299\) | 6.34562e25 | 0.642579 | ||||||||
\(300\) | −2.42331e25 | + | 1.50969e26i | −0.236939 | + | 1.47609i | ||||
\(301\) | 2.96272e24 | − | 9.09193e23i | 0.0279732 | − | 0.00858436i | ||||
\(302\) | − | 2.53626e25i | − | 0.231271i | ||||||
\(303\) | 1.28157e25 | − | 7.98399e25i | 0.112874 | − | 0.703189i | ||||
\(304\) | 1.33393e26i | 1.13491i | ||||||||
\(305\) | 2.43639e26i | 2.00262i | ||||||||
\(306\) | −6.41030e24 | + | 1.94531e25i | −0.0509100 | + | 0.154495i | ||||
\(307\) | 1.50702e26i | 1.15655i | 0.815842 | + | 0.578276i | \(0.196274\pi\) | ||||
−0.815842 | + | 0.578276i | \(0.803726\pi\) | |||||||
\(308\) | 4.11328e25 | + | 1.34037e26i | 0.305075 | + | 0.994126i | ||||
\(309\) | −3.95997e25 | − | 6.35646e24i | −0.283875 | − | 0.0455671i | ||||
\(310\) | −3.21156e25 | −0.222545 | ||||||||
\(311\) | −7.43049e25 | −0.497775 | −0.248888 | − | 0.968532i | \(-0.580065\pi\) | ||||
−0.248888 | + | 0.968532i | \(0.580065\pi\) | |||||||
\(312\) | 2.77390e24 | − | 1.72810e25i | 0.0179667 | − | 0.111930i | ||||
\(313\) | − | 2.26853e26i | − | 1.42079i | −0.703803 | − | 0.710395i | \(-0.748516\pi\) | ||
0.703803 | − | 0.710395i | \(-0.251484\pi\) | |||||||
\(314\) | −1.72469e25 | −0.104460 | ||||||||
\(315\) | −2.72000e26 | − | 5.59472e24i | −1.59334 | − | 0.0327731i | ||||
\(316\) | −1.05778e26 | −0.599351 | ||||||||
\(317\) | − | 1.87990e26i | − | 1.03042i | −0.857065 | − | 0.515209i | \(-0.827714\pi\) | ||
0.857065 | − | 0.515209i | \(-0.172286\pi\) | |||||||
\(318\) | −5.03013e24 | + | 3.13369e25i | −0.0266744 | + | 0.166177i | ||||
\(319\) | −2.00638e26 | −1.02947 | ||||||||
\(320\) | 2.66271e26 | 1.32205 | ||||||||
\(321\) | 1.61445e26 | + | 2.59147e25i | 0.775748 | + | 0.124521i | ||||
\(322\) | 6.68469e25 | − | 2.05138e25i | 0.310881 | − | 0.0954024i | ||||
\(323\) | − | 2.63122e26i | − | 1.18449i | ||||||
\(324\) | 1.79144e26 | + | 1.32447e26i | 0.780692 | + | 0.577193i | ||||
\(325\) | 1.23038e26i | 0.519116i | ||||||||
\(326\) | 7.67662e25i | 0.313607i | ||||||||
\(327\) | 1.05631e25 | − | 6.58065e25i | 0.0417869 | − | 0.260326i | ||||
\(328\) | 6.68889e25i | 0.256259i | ||||||||
\(329\) | 3.33200e26 | − | 1.02251e26i | 1.23637 | − | 0.379413i | ||||
\(330\) | 1.28416e25 | − | 8.00010e25i | 0.0461553 | − | 0.287540i | ||||
\(331\) | −4.01134e26 | −1.39667 | −0.698337 | − | 0.715769i | \(-0.746076\pi\) | ||||
−0.698337 | + | 0.715769i | \(0.746076\pi\) | |||||||
\(332\) | −3.61470e26 | −1.21933 | ||||||||
\(333\) | 1.34629e26 | + | 4.43637e25i | 0.440021 | + | 0.144998i | ||||
\(334\) | − | 5.59379e25i | − | 0.177161i | ||||||
\(335\) | −4.54874e26 | −1.39611 | ||||||||
\(336\) | 4.24263e25 | + | 3.04156e26i | 0.126204 | + | 0.904763i | ||||
\(337\) | 9.72732e25 | 0.280465 | 0.140233 | − | 0.990119i | \(-0.455215\pi\) | ||||
0.140233 | + | 0.990119i | \(0.455215\pi\) | |||||||
\(338\) | 5.41048e25i | 0.151221i | ||||||||
\(339\) | 6.24025e26 | + | 1.00167e26i | 1.69085 | + | 0.271412i | ||||
\(340\) | −5.61552e26 | −1.47523 | ||||||||
\(341\) | −3.44147e26 | −0.876643 | ||||||||
\(342\) | 8.14965e25 | + | 2.68552e25i | 0.201310 | + | 0.0663368i | ||||
\(343\) | 2.61678e26 | − | 3.25232e26i | 0.626873 | − | 0.779121i | ||||
\(344\) | 4.23469e24i | 0.00983915i | ||||||||
\(345\) | 1.33078e27 | + | 2.13614e26i | 2.99920 | + | 0.481425i | ||||
\(346\) | 3.81639e25i | 0.0834361i | ||||||||
\(347\) | 1.17581e26i | 0.249390i | 0.992195 | + | 0.124695i | \(0.0397953\pi\) | ||||
−0.992195 | + | 0.124695i | \(0.960205\pi\) | |||||||
\(348\) | −4.47741e26 | − | 7.18704e25i | −0.921392 | − | 0.147900i | ||||
\(349\) | − | 3.71476e26i | − | 0.741761i | −0.928681 | − | 0.370881i | \(-0.879056\pi\) | ||
0.928681 | − | 0.370881i | \(-0.120944\pi\) | |||||||
\(350\) | 3.97751e25 | + | 1.29612e26i | 0.0770721 | + | 0.251150i | ||||
\(351\) | 1.59225e26 | + | 8.23850e25i | 0.299424 | + | 0.154926i | ||||
\(352\) | −2.88787e26 | −0.527084 | ||||||||
\(353\) | −4.02575e26 | −0.713202 | −0.356601 | − | 0.934257i | \(-0.616064\pi\) | ||||
−0.356601 | + | 0.934257i | \(0.616064\pi\) | |||||||
\(354\) | 1.37212e25 | + | 2.20249e24i | 0.0235970 | + | 0.00378773i | ||||
\(355\) | − | 1.17963e27i | − | 1.96946i | ||||||
\(356\) | 8.96272e26 | 1.45283 | ||||||||
\(357\) | −8.36874e25 | − | 5.99959e26i | −0.131718 | − | 0.944290i | ||||
\(358\) | −4.19939e25 | −0.0641821 | ||||||||
\(359\) | − | 8.57792e26i | − | 1.27318i | −0.771202 | − | 0.636591i | \(-0.780344\pi\) | ||
0.771202 | − | 0.636591i | \(-0.219656\pi\) | |||||||
\(360\) | 1.16346e26 | − | 3.53072e26i | 0.167717 | − | 0.508964i | ||||
\(361\) | −3.88111e26 | −0.543414 | ||||||||
\(362\) | 5.46508e25 | 0.0743287 | ||||||||
\(363\) | 1.76537e25 | − | 1.09980e26i | 0.0233247 | − | 0.145309i | ||||
\(364\) | 7.48091e25 | + | 2.43775e26i | 0.0960263 | + | 0.312914i | ||||
\(365\) | 1.98175e27i | 2.47158i | ||||||||
\(366\) | 2.80386e25 | − | 1.74676e26i | 0.0339786 | − | 0.211681i | ||||
\(367\) | − | 1.01208e27i | − | 1.19185i | −0.803039 | − | 0.595927i | \(-0.796785\pi\) | ||
0.803039 | − | 0.595927i | \(-0.203215\pi\) | |||||||
\(368\) | − | 1.52142e27i | − | 1.74120i | ||||||
\(369\) | −6.50727e26 | − | 2.14432e26i | −0.723806 | − | 0.238513i | ||||
\(370\) | − | 1.16516e26i | − | 0.125970i | ||||||
\(371\) | −2.75381e26 | − | 8.97365e26i | −0.289406 | − | 0.943069i | ||||
\(372\) | −7.67992e26 | − | 1.23276e26i | −0.784613 | − | 0.125944i | ||||
\(373\) | −8.85286e25 | −0.0879308 | −0.0439654 | − | 0.999033i | \(-0.513999\pi\) | ||||
−0.0439654 | + | 0.999033i | \(0.513999\pi\) | |||||||
\(374\) | 1.80411e26 | 0.174226 | ||||||||
\(375\) | −1.45200e26 | + | 9.04574e26i | −0.136345 | + | 0.849407i | ||||
\(376\) | 4.76250e26i | 0.434873i | ||||||||
\(377\) | −3.64905e26 | −0.324038 | ||||||||
\(378\) | 1.94366e26 | + | 3.53137e25i | 0.167864 | + | 0.0304985i | ||||
\(379\) | −1.60854e26 | −0.135120 | −0.0675601 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675601 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(380\) | 2.35256e27i | 1.92226i | ||||||||
\(381\) | −3.11456e25 | + | 1.94032e26i | −0.0247562 | + | 0.154227i | ||||
\(382\) | 3.03487e25 | 0.0234679 | ||||||||
\(383\) | 2.47683e27 | 1.86341 | 0.931705 | − | 0.363216i | \(-0.118321\pi\) | ||||
0.931705 | + | 0.363216i | \(0.118321\pi\) | |||||||
\(384\) | −8.54676e26 | − | 1.37191e26i | −0.625639 | − | 0.100426i | ||||
\(385\) | 7.03030e26 | + | 2.29091e27i | 0.500767 | + | 1.63182i | ||||
\(386\) | − | 2.06305e26i | − | 0.143002i | ||||||
\(387\) | −4.11971e25 | − | 1.35755e25i | −0.0277908 | − | 0.00915780i | ||||
\(388\) | − | 1.13910e27i | − | 0.747875i | ||||||
\(389\) | 1.99655e26i | 0.127588i | 0.997963 | + | 0.0637940i | \(0.0203201\pi\) | ||||
−0.997963 | + | 0.0637940i | \(0.979680\pi\) | |||||||
\(390\) | 2.33552e25 | − | 1.45499e26i | 0.0145280 | − | 0.0905071i | ||||
\(391\) | 3.00106e27i | 1.81727i | ||||||||
\(392\) | 3.19951e26 | + | 4.72209e26i | 0.188617 | + | 0.278375i | ||||
\(393\) | −5.35268e25 | + | 3.33463e26i | −0.0307220 | + | 0.191393i | ||||
\(394\) | 3.69477e26 | 0.206479 | ||||||||
\(395\) | −1.80793e27 | −0.983810 | ||||||||
\(396\) | 6.14170e26 | − | 1.86380e27i | 0.325454 | − | 0.987642i | ||||
\(397\) | − | 1.03765e26i | − | 0.0535487i | −0.999642 | − | 0.0267743i | \(-0.991476\pi\) | ||
0.999642 | − | 0.0267743i | \(-0.00852355\pi\) | |||||||
\(398\) | −8.21143e25 | −0.0412712 | ||||||||
\(399\) | −2.51346e27 | + | 3.50599e26i | −1.23043 | + | 0.171631i | ||||
\(400\) | 2.94996e27 | 1.40665 | ||||||||
\(401\) | − | 2.10386e27i | − | 0.977240i | −0.872497 | − | 0.488620i | \(-0.837500\pi\) | ||
0.872497 | − | 0.488620i | \(-0.162500\pi\) | |||||||
\(402\) | 3.26121e26 | + | 5.23482e25i | 0.147572 | + | 0.0236880i | ||||
\(403\) | −6.25906e26 | −0.275935 | ||||||||
\(404\) | −1.60980e27 | −0.691460 | ||||||||
\(405\) | 3.06187e27 | + | 2.26375e27i | 1.28147 | + | 0.947437i | ||||
\(406\) | −3.84403e26 | + | 1.17965e26i | −0.156770 | + | 0.0481092i | ||||
\(407\) | − | 1.24857e27i | − | 0.496217i | ||||||
\(408\) | 8.17276e26 | + | 1.31187e26i | 0.316546 | + | 0.0508113i | ||||
\(409\) | − | 1.90621e26i | − | 0.0719576i | −0.999353 | − | 0.0359788i | \(-0.988545\pi\) | ||
0.999353 | − | 0.0359788i | \(-0.0114549\pi\) | |||||||
\(410\) | 5.63180e26i | 0.207213i | ||||||||
\(411\) | 1.55747e27 | + | 2.50002e26i | 0.558575 | + | 0.0896612i | ||||
\(412\) | 7.98442e26i | 0.279140i | ||||||||
\(413\) | −3.92920e26 | + | 1.20578e26i | −0.133915 | + | 0.0410954i | ||||
\(414\) | −9.29515e26 | − | 3.06299e26i | −0.308854 | − | 0.101775i | ||||
\(415\) | −6.17814e27 | −2.00149 | ||||||||
\(416\) | −5.25223e26 | −0.165907 | ||||||||
\(417\) | 1.71764e27 | + | 2.75712e26i | 0.529058 | + | 0.0849232i | ||||
\(418\) | − | 7.55813e26i | − | 0.227020i | ||||||
\(419\) | 2.23604e27 | 0.654988 | 0.327494 | − | 0.944853i | \(-0.393796\pi\) | ||||
0.327494 | + | 0.944853i | \(0.393796\pi\) | |||||||
\(420\) | 7.48243e26 | + | 5.36419e27i | 0.213759 | + | 1.53245i | ||||
\(421\) | 9.55945e26 | 0.266361 | 0.133181 | − | 0.991092i | \(-0.457481\pi\) | ||||
0.133181 | + | 0.991092i | \(0.457481\pi\) | |||||||
\(422\) | 6.98383e26i | 0.189807i | ||||||||
\(423\) | −4.63318e27 | − | 1.52676e27i | −1.22830 | − | 0.404758i | ||||
\(424\) | 1.28262e27 | 0.331709 | ||||||||
\(425\) | −5.81889e27 | −1.46810 | ||||||||
\(426\) | −1.35755e26 | + | 8.45731e26i | −0.0334160 | + | 0.208176i | ||||
\(427\) | 1.53501e27 | + | 5.00204e27i | 0.368654 | + | 1.20131i | ||||
\(428\) | − | 3.25518e27i | − | 0.762809i | ||||||
\(429\) | 2.50272e26 | − | 1.55915e27i | 0.0572282 | − | 0.356523i | ||||
\(430\) | 3.56545e25i | 0.00795601i | ||||||||
\(431\) | 8.11612e27i | 1.76741i | 0.468044 | + | 0.883705i | \(0.344959\pi\) | ||||
−0.468044 | + | 0.883705i | \(0.655041\pi\) | |||||||
\(432\) | 1.97526e27 | − | 3.81757e27i | 0.419803 | − | 0.811350i | ||||
\(433\) | 2.10911e27i | 0.437499i | 0.975781 | + | 0.218749i | \(0.0701977\pi\) | ||||
−0.975781 | + | 0.218749i | \(0.929802\pi\) | |||||||
\(434\) | −6.59351e26 | + | 2.02340e26i | −0.133498 | + | 0.0409675i | ||||
\(435\) | −7.65264e27 | − | 1.22839e27i | −1.51243 | − | 0.242771i | ||||
\(436\) | −1.32685e27 | −0.255984 | ||||||||
\(437\) | 1.25726e28 | 2.36794 | ||||||||
\(438\) | 2.28066e26 | − | 1.42081e27i | 0.0419355 | − | 0.261252i | ||||
\(439\) | − | 7.48107e27i | − | 1.34303i | −0.740991 | − | 0.671515i | \(-0.765644\pi\) | ||
0.740991 | − | 0.671515i | \(-0.234356\pi\) | |||||||
\(440\) | −3.27445e27 | −0.573965 | ||||||||
\(441\) | −5.61957e27 | + | 1.59884e27i | −0.961829 | + | 0.273652i | ||||
\(442\) | 3.28118e26 | 0.0548398 | ||||||||
\(443\) | 1.77997e27i | 0.290518i | 0.989394 | + | 0.145259i | \(0.0464016\pi\) | ||||
−0.989394 | + | 0.145259i | \(0.953598\pi\) | |||||||
\(444\) | 4.47249e26 | − | 2.78629e27i | 0.0712899 | − | 0.444125i | ||||
\(445\) | 1.53188e28 | 2.38476 | ||||||||
\(446\) | −1.04803e27 | −0.159352 | ||||||||
\(447\) | −6.15702e27 | − | 9.88312e26i | −0.914412 | − | 0.146779i | ||||
\(448\) | 5.46669e27 | − | 1.67760e27i | 0.793059 | − | 0.243372i | ||||
\(449\) | − | 6.70454e27i | − | 0.950128i | −0.879951 | − | 0.475064i | \(-0.842425\pi\) | ||
0.879951 | − | 0.475064i | \(-0.157575\pi\) | |||||||
\(450\) | 5.93898e26 | − | 1.80228e27i | 0.0822205 | − | 0.249511i | ||||
\(451\) | 6.03496e27i | 0.816246i | ||||||||
\(452\) | − | 1.25821e28i | − | 1.66265i | ||||||
\(453\) | 1.66396e27 | − | 1.03662e28i | 0.214838 | − | 1.33841i | ||||
\(454\) | − | 7.80888e25i | − | 0.00985150i | ||||||
\(455\) | 1.27861e27 | + | 4.16653e27i | 0.157623 | + | 0.513635i | ||||
\(456\) | 5.49595e26 | − | 3.42389e27i | 0.0662082 | − | 0.412466i | ||||
\(457\) | 4.82928e27 | 0.568542 | 0.284271 | − | 0.958744i | \(-0.408249\pi\) | ||||
0.284271 | + | 0.958744i | \(0.408249\pi\) | |||||||
\(458\) | −8.81049e26 | −0.101371 | ||||||||
\(459\) | −3.89627e27 | + | 7.53030e27i | −0.438143 | + | 0.846796i | ||||
\(460\) | − | 2.68323e28i | − | 2.94917i | ||||||
\(461\) | 1.23732e28 | 1.32930 | 0.664648 | − | 0.747157i | \(-0.268582\pi\) | ||||
0.664648 | + | 0.747157i | \(0.268582\pi\) | |||||||
\(462\) | −2.40390e26 | − | 1.72337e27i | −0.0252451 | − | 0.180983i | ||||
\(463\) | 1.82176e28 | 1.87022 | 0.935108 | − | 0.354364i | \(-0.115302\pi\) | ||||
0.935108 | + | 0.354364i | \(0.115302\pi\) | |||||||
\(464\) | 8.74895e27i | 0.878046i | ||||||||
\(465\) | −1.31263e28 | − | 2.10700e27i | −1.28791 | − | 0.206732i | ||||
\(466\) | 3.96041e25 | 0.00379916 | ||||||||
\(467\) | −8.95927e27 | −0.840321 | −0.420161 | − | 0.907450i | \(-0.638026\pi\) | ||||
−0.420161 | + | 0.907450i | \(0.638026\pi\) | |||||||
\(468\) | 1.11700e27 | − | 3.38973e27i | 0.102441 | − | 0.310873i | ||||
\(469\) | −9.33882e27 | + | 2.86587e27i | −0.837485 | + | 0.257005i | ||||
\(470\) | 4.00984e27i | 0.351641i | ||||||||
\(471\) | −7.04915e27 | − | 1.13151e27i | −0.604529 | − | 0.0970377i | ||||
\(472\) | − | 5.61609e26i | − | 0.0471024i | ||||||
\(473\) | 3.82069e26i | 0.0313401i | ||||||||
\(474\) | 1.29619e27 | + | 2.08061e26i | 0.103991 | + | 0.0166924i | ||||
\(475\) | 2.43776e28i | 1.91297i | ||||||||
\(476\) | −1.15290e28 | + | 3.53798e27i | −0.884947 | + | 0.271570i | ||||
\(477\) | −4.11182e27 | + | 1.24780e28i | −0.308739 | + | 0.936918i | ||||
\(478\) | −1.93249e27 | −0.141947 | ||||||||
\(479\) | −3.71334e27 | −0.266834 | −0.133417 | − | 0.991060i | \(-0.542595\pi\) | ||||
−0.133417 | + | 0.991060i | \(0.542595\pi\) | |||||||
\(480\) | −1.10148e28 | − | 1.76807e27i | −0.774360 | − | 0.124298i | ||||
\(481\) | − | 2.27080e27i | − | 0.156191i | ||||||
\(482\) | 3.60653e27 | 0.242714 | ||||||||
\(483\) | 2.86675e28 | − | 3.99878e27i | 1.88775 | − | 0.263319i | ||||
\(484\) | −2.21750e27 | −0.142885 | ||||||||
\(485\) | − | 1.94692e28i | − | 1.22761i | ||||||
\(486\) | −1.93468e27 | − | 1.97536e27i | −0.119379 | − | 0.121889i | ||||
\(487\) | −1.08522e28 | −0.655334 | −0.327667 | − | 0.944793i | \(-0.606262\pi\) | ||||
−0.327667 | + | 0.944793i | \(0.606262\pi\) | |||||||
\(488\) | −7.14952e27 | −0.422541 | ||||||||
\(489\) | −5.03638e27 | + | 3.13759e28i | −0.291324 | + | 1.81490i | ||||
\(490\) | 2.69387e27 | + | 3.97582e27i | 0.152517 | + | 0.225096i | ||||
\(491\) | 1.43543e28i | 0.795472i | 0.917500 | + | 0.397736i | \(0.130204\pi\) | ||||
−0.917500 | + | 0.397736i | \(0.869796\pi\) | |||||||
\(492\) | −2.16178e27 | + | 1.34675e28i | −0.117267 | + | 0.730556i | ||||
\(493\) | − | 1.72576e28i | − | 0.916406i | ||||||
\(494\) | − | 1.37461e27i | − | 0.0714574i | ||||||
\(495\) | 1.04972e28 | − | 3.18555e28i | 0.534219 | − | 1.62117i | ||||
\(496\) | 1.50067e28i | 0.747701i | ||||||||
\(497\) | −7.43209e27 | − | 2.42184e28i | −0.362551 | − | 1.18142i | ||||
\(498\) | 4.42940e27 | + | 7.10997e26i | 0.211561 | + | 0.0339594i | ||||
\(499\) | 1.12880e28 | 0.527912 | 0.263956 | − | 0.964535i | \(-0.414973\pi\) | ||||
0.263956 | + | 0.964535i | \(0.414973\pi\) | |||||||
\(500\) | 1.82388e28 | 0.835239 | ||||||||
\(501\) | 3.66991e27 | − | 2.28629e28i | 0.164573 | − | 1.02526i | ||||
\(502\) | − | 2.66324e27i | − | 0.116956i | ||||||
\(503\) | −1.02864e28 | −0.442386 | −0.221193 | − | 0.975230i | \(-0.570995\pi\) | ||||
−0.221193 | + | 0.975230i | \(0.570995\pi\) | |||||||
\(504\) | 1.64176e26 | − | 7.98179e27i | 0.00691495 | − | 0.336186i | ||||
\(505\) | −2.75142e28 | −1.13500 | ||||||||
\(506\) | 8.62049e27i | 0.348298i | ||||||||
\(507\) | −3.54964e27 | + | 2.21137e28i | −0.140476 | + | 0.875141i | ||||
\(508\) | 3.91224e27 | 0.151655 | ||||||||
\(509\) | −8.65416e27 | −0.328616 | −0.164308 | − | 0.986409i | \(-0.552539\pi\) | ||||
−0.164308 | + | 0.986409i | \(0.552539\pi\) | |||||||
\(510\) | 6.88116e27 | + | 1.10455e27i | 0.255962 | + | 0.0410864i | ||||
\(511\) | 1.24858e28 | + | 4.06865e28i | 0.454984 | + | 1.48262i | ||||
\(512\) | 2.11972e28i | 0.756736i | ||||||||
\(513\) | 3.15473e28 | + | 1.63230e28i | 1.10339 | + | 0.570909i | ||||
\(514\) | 6.34693e27i | 0.217496i | ||||||||
\(515\) | 1.36467e28i | 0.458197i | ||||||||
\(516\) | −1.36860e26 | + | 8.52618e26i | −0.00450252 | + | 0.0280500i | ||||
\(517\) | 4.29690e28i | 1.38517i | ||||||||
\(518\) | −7.34093e26 | − | 2.39214e27i | −0.0231894 | − | 0.0755655i | ||||
\(519\) | −2.50381e27 | + | 1.55983e28i | −0.0775076 | + | 0.482860i | ||||
\(520\) | −5.95531e27 | −0.180663 | ||||||||
\(521\) | 4.59585e28 | 1.36637 | 0.683187 | − | 0.730244i | \(-0.260593\pi\) | ||||
0.683187 | + | 0.730244i | \(0.260593\pi\) | |||||||
\(522\) | 5.34518e27 | + | 1.76138e27i | 0.155748 | + | 0.0513230i | ||||
\(523\) | − | 5.26887e28i | − | 1.50470i | −0.658764 | − | 0.752349i | \(-0.728921\pi\) | ||
0.658764 | − | 0.752349i | \(-0.271079\pi\) | |||||||
\(524\) | 6.72356e27 | 0.188201 | ||||||||
\(525\) | 7.75342e27 | + | 5.55847e28i | 0.212726 | + | 1.52504i | ||||
\(526\) | 3.68015e27 | 0.0989728 | ||||||||
\(527\) | − | 2.96013e28i | − | 0.780367i | ||||||
\(528\) | −3.73822e28 | − | 6.00051e27i | −0.966070 | − | 0.155071i | ||||
\(529\) | −1.03926e29 | −2.63294 | ||||||||
\(530\) | 1.07992e28 | 0.268223 | ||||||||
\(531\) | 5.46360e27 | + | 1.80040e27i | 0.133041 | + | 0.0438406i | ||||
\(532\) | 1.48220e28 | + | 4.82993e28i | 0.353862 | + | 1.15310i | ||||
\(533\) | 1.09759e28i | 0.256924i | ||||||||
\(534\) | −1.09828e28 | − | 1.76293e27i | −0.252074 | − | 0.0404624i | ||||
\(535\) | − | 5.56365e28i | − | 1.25212i | ||||||
\(536\) | − | 1.33482e28i | − | 0.294572i | ||||||
\(537\) | −1.71637e28 | − | 2.75508e27i | −0.371433 | − | 0.0596217i | ||||
\(538\) | − | 1.43240e28i | − | 0.303983i | ||||||
\(539\) | 2.88672e28 | + | 4.26044e28i | 0.600789 | + | 0.886691i | ||||
\(540\) | 3.48363e28 | − | 6.73279e28i | 0.711045 | − | 1.37423i | ||||
\(541\) | 2.60992e28 | 0.522464 | 0.261232 | − | 0.965276i | \(-0.415871\pi\) | ||||
0.261232 | + | 0.965276i | \(0.415871\pi\) | |||||||
\(542\) | 7.40413e27 | 0.145372 | ||||||||
\(543\) | 2.23368e28 | + | 3.58546e27i | 0.430153 | + | 0.0690473i | ||||
\(544\) | − | 2.48396e28i | − | 0.469198i | ||||||
\(545\) | −2.26780e28 | −0.420186 | ||||||||
\(546\) | −4.37203e26 | − | 3.13433e27i | −0.00794621 | − | 0.0569668i | ||||
\(547\) | −8.15351e28 | −1.45371 | −0.726855 | − | 0.686791i | \(-0.759019\pi\) | ||||
−0.726855 | + | 0.686791i | \(0.759019\pi\) | |||||||
\(548\) | − | 3.14031e28i | − | 0.549258i | ||||||
\(549\) | 2.29199e28 | − | 6.95540e28i | 0.393280 | − | 1.19347i | ||||
\(550\) | −1.67147e28 | −0.281377 | ||||||||
\(551\) | −7.22988e28 | −1.19410 | ||||||||
\(552\) | −6.26845e27 | + | 3.90514e28i | −0.101578 | + | 0.632814i | ||||
\(553\) | −3.71177e28 | + | 1.13906e28i | −0.590157 | + | 0.181106i | ||||
\(554\) | 3.98031e27i | 0.0620961i | ||||||||
\(555\) | 7.64424e27 | − | 4.76224e28i | 0.117019 | − | 0.729012i | ||||
\(556\) | − | 3.46325e28i | − | 0.520233i | ||||||
\(557\) | 8.12529e28i | 1.19773i | 0.800850 | + | 0.598865i | \(0.204382\pi\) | ||||
−0.800850 | + | 0.598865i | \(0.795618\pi\) | |||||||
\(558\) | 9.16836e27 | + | 3.02122e27i | 0.132627 | + | 0.0437041i | ||||
\(559\) | 6.94876e26i | 0.00986469i | ||||||||
\(560\) | 9.98966e28 | − | 3.06560e28i | 1.39180 | − | 0.427112i | ||||
\(561\) | 7.37377e28 | + | 1.18362e28i | 1.00828 | + | 0.161846i | ||||
\(562\) | 9.61043e27 | 0.128977 | ||||||||
\(563\) | −1.36835e29 | −1.80243 | −0.901215 | − | 0.433372i | \(-0.857324\pi\) | ||||
−0.901215 | + | 0.433372i | \(0.857324\pi\) | |||||||
\(564\) | −1.53919e28 | + | 9.58888e28i | −0.199003 | + | 1.23976i | ||||
\(565\) | − | 2.15050e29i | − | 2.72917i | ||||||
\(566\) | 1.64862e28 | 0.205375 | ||||||||
\(567\) | 7.71244e28 | + | 2.71851e28i | 0.943126 | + | 0.332437i | ||||
\(568\) | 3.46159e28 | 0.415545 | ||||||||
\(569\) | 9.33152e28i | 1.09970i | 0.835264 | + | 0.549849i | \(0.185315\pi\) | ||||
−0.835264 | + | 0.549849i | \(0.814685\pi\) | |||||||
\(570\) | 4.62738e27 | − | 2.88278e28i | 0.0535364 | − | 0.333523i | ||||
\(571\) | 1.49938e29 | 1.70307 | 0.851536 | − | 0.524296i | \(-0.175671\pi\) | ||||
0.851536 | + | 0.524296i | \(0.175671\pi\) | |||||||
\(572\) | −3.14369e28 | −0.350576 | ||||||||
\(573\) | 1.24041e28 | + | 1.99108e27i | 0.135813 | + | 0.0218004i | ||||
\(574\) | 3.54824e27 | + | 1.15624e28i | 0.0381450 | + | 0.124300i | ||||
\(575\) | − | 2.78041e29i | − | 2.93492i | ||||||
\(576\) | −7.60151e28 | − | 2.50490e28i | −0.787887 | − | 0.259629i | ||||
\(577\) | − | 6.52072e28i | − | 0.663666i | −0.943338 | − | 0.331833i | \(-0.892333\pi\) | ||
0.943338 | − | 0.331833i | \(-0.107667\pi\) | |||||||
\(578\) | − | 1.55287e27i | − | 0.0155200i | ||||||
\(579\) | 1.35350e28 | − | 8.43209e28i | 0.132841 | − | 0.827581i | ||||
\(580\) | 1.54299e29i | 1.48720i | ||||||||
\(581\) | −1.26841e29 | + | 3.89245e28i | −1.20063 | + | 0.368446i | ||||
\(582\) | −2.24057e27 | + | 1.39584e28i | −0.0208289 | + | 0.129761i | ||||
\(583\) | 1.15723e29 | 1.05657 | ||||||||
\(584\) | −5.81542e28 | −0.521490 | ||||||||
\(585\) | 1.90915e28 | − | 5.79361e28i | 0.168152 | − | 0.510285i | ||||
\(586\) | 7.20057e27i | 0.0622934i | ||||||||
\(587\) | 8.71061e28 | 0.740199 | 0.370099 | − | 0.928992i | \(-0.379324\pi\) | ||||
0.370099 | + | 0.928992i | \(0.379324\pi\) | |||||||
\(588\) | 4.91582e28 | + | 1.05416e29i | 0.410331 | + | 0.879920i | ||||
\(589\) | −1.24011e29 | −1.01683 | ||||||||
\(590\) | − | 4.72854e27i | − | 0.0380874i | ||||||
\(591\) | 1.51012e29 | + | 2.42402e28i | 1.19493 | + | 0.191808i | ||||
\(592\) | −5.44447e28 | −0.423231 | ||||||||
\(593\) | 2.35881e29 | 1.80143 | 0.900716 | − | 0.434408i | \(-0.143042\pi\) | ||||
0.900716 | + | 0.434408i | \(0.143042\pi\) | |||||||
\(594\) | −1.11920e28 | + | 2.16306e28i | −0.0839747 | + | 0.162297i | ||||
\(595\) | −1.97049e29 | + | 6.04700e28i | −1.45260 | + | 0.445771i | ||||
\(596\) | 1.24143e29i | 0.899160i | ||||||||
\(597\) | −3.35617e28 | − | 5.38725e27i | −0.238844 | − | 0.0383387i | ||||
\(598\) | 1.56783e28i | 0.109631i | ||||||||
\(599\) | − | 1.72970e29i | − | 1.18848i | −0.804290 | − | 0.594238i | \(-0.797454\pi\) | ||
0.804290 | − | 0.594238i | \(-0.202546\pi\) | |||||||
\(600\) | −7.57185e28 | − | 1.21542e28i | −0.511227 | − | 0.0820611i | ||||
\(601\) | 2.72534e28i | 0.180817i | 0.995905 | + | 0.0904084i | \(0.0288172\pi\) | ||||
−0.995905 | + | 0.0904084i | \(0.971183\pi\) | |||||||
\(602\) | 2.24636e26 | + | 7.32006e26i | 0.00146459 | + | 0.00477256i | ||||
\(603\) | 1.29857e29 | + | 4.27914e28i | 0.832023 | + | 0.274173i | ||||
\(604\) | −2.09012e29 | −1.31608 | ||||||||
\(605\) | −3.79008e28 | −0.234540 | ||||||||
\(606\) | 1.97262e28 | + | 3.16641e27i | 0.119972 | + | 0.0192577i | ||||
\(607\) | − | 2.01615e29i | − | 1.20515i | −0.798061 | − | 0.602576i | \(-0.794141\pi\) | ||
0.798061 | − | 0.602576i | \(-0.205859\pi\) | |||||||
\(608\) | −1.04063e29 | −0.611375 | ||||||||
\(609\) | −1.64852e29 | + | 2.29950e28i | −0.951949 | + | 0.132786i | ||||
\(610\) | −6.01963e28 | −0.341670 | ||||||||
\(611\) | 7.81486e28i | 0.436002i | ||||||||
\(612\) | 1.60312e29 | + | 5.28269e28i | 0.879176 | + | 0.289711i | ||||
\(613\) | 1.72405e29 | 0.929428 | 0.464714 | − | 0.885461i | \(-0.346157\pi\) | ||||
0.464714 | + | 0.885461i | \(0.346157\pi\) | |||||||
\(614\) | −3.72342e28 | −0.197321 | ||||||||
\(615\) | −3.69484e28 | + | 2.30182e29i | −0.192489 | + | 1.19918i | ||||
\(616\) | −6.72264e28 | + | 2.06302e28i | −0.344304 | + | 0.105659i | ||||
\(617\) | 2.50226e29i | 1.25991i | 0.776633 | + | 0.629954i | \(0.216926\pi\) | ||||
−0.776633 | + | 0.629954i | \(0.783074\pi\) | |||||||
\(618\) | 1.57050e27 | − | 9.78398e27i | 0.00777427 | − | 0.0484325i | ||||
\(619\) | 1.67096e29i | 0.813233i | 0.913599 | + | 0.406616i | \(0.133291\pi\) | ||||
−0.913599 | + | 0.406616i | \(0.866709\pi\) | |||||||
\(620\) | 2.64663e29i | 1.26643i | ||||||||
\(621\) | −3.59816e29 | − | 1.86173e29i | −1.69285 | − | 0.875901i | ||||
\(622\) | − | 1.83587e28i | − | 0.0849263i | ||||||
\(623\) | 3.14503e29 | − | 9.65140e28i | 1.43054 | − | 0.439001i | ||||
\(624\) | −6.79878e28 | − | 1.09132e28i | −0.304083 | − | 0.0488108i | ||||
\(625\) | −3.83803e28 | −0.168798 | ||||||||
\(626\) | 5.60492e28 | 0.242403 | ||||||||
\(627\) | 4.95865e28 | − | 3.08916e29i | 0.210889 | − | 1.31380i | ||||
\(628\) | 1.42131e29i | 0.594446i | ||||||||
\(629\) | 1.07394e29 | 0.441721 | ||||||||
\(630\) | 1.38230e27 | − | 6.72037e28i | 0.00559148 | − | 0.271843i | ||||
\(631\) | 1.18588e27 | 0.00471774 | 0.00235887 | − | 0.999997i | \(-0.499249\pi\) | ||||
0.00235887 | + | 0.999997i | \(0.499249\pi\) | |||||||
\(632\) | − | 5.30532e28i | − | 0.207578i | ||||||
\(633\) | −4.58187e28 | + | 2.85443e29i | −0.176321 | + | 1.09845i | ||||
\(634\) | 4.64472e28 | 0.175801 | ||||||||
\(635\) | 6.68667e28 | 0.248935 | ||||||||
\(636\) | 2.58245e29 | + | 4.14530e28i | 0.945656 | + | 0.151795i | ||||
\(637\) | 5.25013e28 | + | 7.74855e28i | 0.189106 | + | 0.279098i | ||||
\(638\) | − | 4.95721e28i | − | 0.175639i | ||||||
\(639\) | −1.10971e29 | + | 3.36760e29i | −0.386769 | + | 1.17371i | ||||
\(640\) | 2.94536e29i | 1.00983i | ||||||||
\(641\) | − | 3.71900e29i | − | 1.25434i | −0.778881 | − | 0.627172i | \(-0.784212\pi\) | ||
0.778881 | − | 0.627172i | \(-0.215788\pi\) | |||||||
\(642\) | −6.40281e27 | + | 3.98885e28i | −0.0212448 | + | 0.132352i | ||||
\(643\) | 3.90743e29i | 1.27549i | 0.770249 | + | 0.637743i | \(0.220132\pi\) | ||||
−0.770249 | + | 0.637743i | \(0.779868\pi\) | |||||||
\(644\) | −1.69053e29 | − | 5.50882e29i | −0.542902 | − | 1.76912i | ||||
\(645\) | −2.33917e27 | + | 1.45727e28i | −0.00739070 | + | 0.0460429i | ||||
\(646\) | 6.50101e28 | 0.202088 | ||||||||
\(647\) | −3.08437e29 | −0.943347 | −0.471673 | − | 0.881773i | \(-0.656350\pi\) | ||||
−0.471673 | + | 0.881773i | \(0.656350\pi\) | |||||||
\(648\) | −6.64292e28 | + | 8.98499e28i | −0.199904 | + | 0.270384i | ||||
\(649\) | − | 5.06704e28i | − | 0.150033i | ||||||
\(650\) | −3.03993e28 | −0.0885672 | ||||||||
\(651\) | −2.82764e29 | + | 3.94424e28i | −0.810633 | + | 0.113074i | ||||
\(652\) | 6.32626e29 | 1.78463 | ||||||||
\(653\) | − | 8.04579e28i | − | 0.223347i | −0.993745 | − | 0.111674i | \(-0.964379\pi\) | ||
0.993745 | − | 0.111674i | \(-0.0356211\pi\) | |||||||
\(654\) | 1.62589e28 | + | 2.60985e27i | 0.0444146 | + | 0.00712934i | ||||
\(655\) | 1.14917e29 | 0.308923 | ||||||||
\(656\) | 2.63158e29 | 0.696188 | ||||||||
\(657\) | 1.86430e29 | − | 5.65752e29i | 0.485377 | − | 1.47295i | ||||
\(658\) | 2.52635e28 | + | 8.23243e28i | 0.0647323 | + | 0.210939i | ||||
\(659\) | 5.58260e29i | 1.40780i | 0.710301 | + | 0.703898i | \(0.248559\pi\) | ||||
−0.710301 | + | 0.703898i | \(0.751441\pi\) | |||||||
\(660\) | −6.59283e29 | − | 1.05827e29i | −1.63629 | − | 0.262654i | ||||
\(661\) | − | 2.91146e29i | − | 0.711207i | −0.934637 | − | 0.355603i | \(-0.884275\pi\) | ||
0.934637 | − | 0.355603i | \(-0.115725\pi\) | |||||||
\(662\) | − | 9.91090e28i | − | 0.238289i | ||||||
\(663\) | 1.34108e29 | + | 2.15267e28i | 0.317368 | + | 0.0509432i | ||||
\(664\) | − | 1.81296e29i | − | 0.422302i | ||||||
\(665\) | 2.53332e29 | + | 8.25517e29i | 0.580849 | + | 1.89277i | ||||
\(666\) | −1.09610e28 | + | 3.32630e28i | −0.0247384 | + | 0.0750727i | ||||
\(667\) | 8.24609e29 | 1.83201 | ||||||||
\(668\) | −4.60981e29 | −1.00816 | ||||||||
\(669\) | −4.28350e29 | − | 6.87578e28i | −0.922199 | − | 0.148029i | ||||
\(670\) | − | 1.12387e29i | − | 0.238193i | ||||||
\(671\) | −6.45056e29 | −1.34589 | ||||||||
\(672\) | −2.37279e29 | + | 3.30977e28i | −0.487396 | + | 0.0679861i | ||||
\(673\) | −2.98874e29 | −0.604408 | −0.302204 | − | 0.953243i | \(-0.597722\pi\) | ||||
−0.302204 | + | 0.953243i | \(0.597722\pi\) | |||||||
\(674\) | 2.40335e28i | 0.0478506i | ||||||||
\(675\) | 3.60979e29 | − | 6.97663e29i | 0.707608 | − | 1.36759i | ||||
\(676\) | 4.45875e29 | 0.860543 | ||||||||
\(677\) | −2.07189e29 | −0.393719 | −0.196859 | − | 0.980432i | \(-0.563074\pi\) | ||||
−0.196859 | + | 0.980432i | \(0.563074\pi\) | |||||||
\(678\) | −2.47485e28 | + | 1.54179e29i | −0.0463060 | + | 0.288479i | ||||
\(679\) | −1.22663e29 | − | 3.99713e29i | −0.225985 | − | 0.736403i | ||||
\(680\) | − | 2.81647e29i | − | 0.510930i | ||||||
\(681\) | 5.12315e27 | − | 3.19164e28i | 0.00915151 | − | 0.0570124i | ||||
\(682\) | − | 8.50291e28i | − | 0.149565i | ||||||
\(683\) | 5.00451e28i | 0.0866851i | 0.999060 | + | 0.0433426i | \(0.0138007\pi\) | ||||
−0.999060 | + | 0.0433426i | \(0.986199\pi\) | |||||||
\(684\) | 2.21312e29 | − | 6.71608e29i | 0.377500 | − | 1.14558i | ||||
\(685\) | − | 5.36731e29i | − | 0.901584i | ||||||
\(686\) | 8.03558e28 | + | 6.46534e28i | 0.132927 | + | 0.106952i | ||||
\(687\) | −3.60102e29 | − | 5.78028e28i | −0.586651 | − | 0.0941679i | ||||
\(688\) | 1.66603e28 | 0.0267304 | ||||||||
\(689\) | 2.10468e29 | 0.332571 | ||||||||
\(690\) | −5.27780e28 | + | 3.28798e29i | −0.0821367 | + | 0.511698i | ||||
\(691\) | 4.80820e29i | 0.736993i | 0.929629 | + | 0.368496i | \(0.120127\pi\) | ||||
−0.929629 | + | 0.368496i | \(0.879873\pi\) | |||||||
\(692\) | 3.14507e29 | 0.474806 | ||||||||
\(693\) | 1.48126e28 | − | 7.20146e29i | 0.0220258 | − | 1.07083i | ||||
\(694\) | −2.90511e28 | −0.0425489 | ||||||||
\(695\) | − | 5.91927e29i | − | 0.853941i | ||||||
\(696\) | 3.60467e28 | − | 2.24565e29i | 0.0512234 | − | 0.319114i | ||||
\(697\) | −5.19088e29 | −0.726603 | ||||||||
\(698\) | 9.17814e28 | 0.126553 | ||||||||
\(699\) | 1.61869e28 | + | 2.59829e27i | 0.0219864 | + | 0.00352921i | ||||
\(700\) | 1.06813e30 | − | 3.27785e29i | 1.42920 | − | 0.438590i | ||||
\(701\) | − | 1.10836e30i | − | 1.46097i | −0.682931 | − | 0.730483i | \(-0.739295\pi\) | ||
0.682931 | − | 0.730483i | \(-0.260705\pi\) | |||||||
\(702\) | −2.03550e28 | + | 3.93401e28i | −0.0264321 | + | 0.0510852i | ||||
\(703\) | − | 4.49915e29i | − | 0.575572i | ||||||
\(704\) | 7.04978e29i | 0.888510i | ||||||||
\(705\) | −2.63073e29 | + | 1.63890e30i | −0.326656 | + | 2.03501i | ||||
\(706\) | − | 9.94650e28i | − | 0.121681i | ||||||
\(707\) | −5.64881e29 | + | 1.73349e29i | −0.680853 | + | 0.208938i | ||||
\(708\) | 1.81506e28 | − | 1.13075e29i | 0.0215547 | − | 0.134282i | ||||
\(709\) | 3.69654e29 | 0.432523 | 0.216262 | − | 0.976335i | \(-0.430614\pi\) | ||||
0.216262 | + | 0.976335i | \(0.430614\pi\) | |||||||
\(710\) | 2.91453e29 | 0.336013 | ||||||||
\(711\) | 5.16127e29 | + | 1.70077e29i | 0.586308 | + | 0.193204i | ||||
\(712\) | 4.49527e29i | 0.503171i | ||||||||
\(713\) | 1.41442e30 | 1.56005 | ||||||||
\(714\) | 1.48233e29 | − | 2.06768e28i | 0.161107 | − | 0.0224725i | ||||
\(715\) | −5.37310e29 | −0.575455 | ||||||||
\(716\) | 3.46069e29i | 0.365238i | ||||||||
\(717\) | −7.89847e29 | − | 1.26785e29i | −0.821471 | − | 0.131861i | ||||
\(718\) | 2.11936e29 | 0.217220 | ||||||||
\(719\) | −5.12329e28 | −0.0517482 | −0.0258741 | − | 0.999665i | \(-0.508237\pi\) | ||||
−0.0258741 | + | 0.999665i | \(0.508237\pi\) | |||||||
\(720\) | −1.38908e30 | − | 4.57737e29i | −1.38272 | − | 0.455643i | ||||
\(721\) | 8.59793e28 | + | 2.80175e29i | 0.0843478 | + | 0.274858i | ||||
\(722\) | − | 9.58914e28i | − | 0.0927127i | ||||||
\(723\) | 1.47406e30 | + | 2.36613e29i | 1.40463 | + | 0.225468i | ||||
\(724\) | − | 4.50374e29i | − | 0.422979i | ||||||
\(725\) | 1.59887e30i | 1.48001i | ||||||||
\(726\) | 2.71729e28 | + | 4.36173e27i | 0.0247914 | + | 0.00397946i | ||||
\(727\) | − | 3.90953e29i | − | 0.351571i | −0.984428 | − | 0.175785i | \(-0.943753\pi\) | ||
0.984428 | − | 0.175785i | \(-0.0562465\pi\) | |||||||
\(728\) | −1.22266e29 | + | 3.75206e28i | −0.108374 | + | 0.0332576i | ||||
\(729\) | −6.61145e29 | − | 9.34295e29i | −0.577641 | − | 0.816291i | ||||
\(730\) | −4.89636e29 | −0.421681 | ||||||||
\(731\) | −3.28631e28 | −0.0278982 | ||||||||
\(732\) | −1.43950e30 | − | 2.31065e29i | −1.20460 | − | 0.193360i | ||||
\(733\) | 2.37201e30i | 1.95670i | 0.206956 | + | 0.978350i | \(0.433644\pi\) | ||||
−0.206956 | + | 0.978350i | \(0.566356\pi\) | |||||||
\(734\) | 2.50058e29 | 0.203344 | ||||||||
\(735\) | 8.40196e29 | + | 1.80173e30i | 0.673541 | + | 1.44435i | ||||
\(736\) | 1.18690e30 | 0.937984 | ||||||||
\(737\) | − | 1.20432e30i | − | 0.938283i | ||||||
\(738\) | 5.29801e28 | − | 1.60777e29i | 0.0406931 | − | 0.123490i | ||||
\(739\) | −2.08219e30 | −1.57671 | −0.788357 | − | 0.615217i | \(-0.789068\pi\) | ||||
−0.788357 | + | 0.615217i | \(0.789068\pi\) | |||||||
\(740\) | −9.60202e29 | −0.716852 | ||||||||
\(741\) | 9.01839e28 | − | 5.61831e29i | 0.0663801 | − | 0.413537i | ||||
\(742\) | 2.21714e29 | − | 6.80390e28i | 0.160899 | − | 0.0493761i | ||||
\(743\) | 3.31867e29i | 0.237455i | 0.992927 | + | 0.118728i | \(0.0378815\pi\) | ||||
−0.992927 | + | 0.118728i | \(0.962118\pi\) | |||||||
\(744\) | 6.18294e28 | − | 3.85187e29i | 0.0436194 | − | 0.271742i | ||||
\(745\) | 2.12181e30i | 1.47593i | ||||||||
\(746\) | − | 2.18730e28i | − | 0.0150020i | ||||||
\(747\) | 1.76373e30 | + | 5.81197e29i | 1.19280 | + | 0.393058i | ||||
\(748\) | − | 1.48676e30i | − | 0.991458i | ||||||
\(749\) | −3.50530e29 | − | 1.14225e30i | −0.230498 | − | 0.751107i | ||||
\(750\) | −2.23495e29 | − | 3.58749e28i | −0.144919 | − | 0.0232620i | ||||
\(751\) | −1.43488e30 | −0.917481 | −0.458740 | − | 0.888570i | \(-0.651699\pi\) | ||||
−0.458740 | + | 0.888570i | \(0.651699\pi\) | |||||||
\(752\) | 1.87369e30 | 1.18144 | ||||||||
\(753\) | 1.74727e29 | − | 1.08852e30i | 0.108645 | − | 0.676844i | ||||
\(754\) | − | 9.01578e28i | − | 0.0552846i | ||||||
\(755\) | −3.57236e30 | −2.16029 | ||||||||
\(756\) | 2.91018e29 | − | 1.60176e30i | 0.173557 | − | 0.955253i | ||||
\(757\) | 2.39650e29 | 0.140952 | 0.0704758 | − | 0.997513i | \(-0.477548\pi\) | ||||
0.0704758 | + | 0.997513i | \(0.477548\pi\) | |||||||
\(758\) | − | 3.97426e28i | − | 0.0230531i | ||||||
\(759\) | −5.65562e29 | + | 3.52336e30i | −0.323550 | + | 2.01567i | ||||
\(760\) | −1.17993e30 | −0.665753 | ||||||||
\(761\) | 1.91913e30 | 1.06799 | 0.533994 | − | 0.845488i | \(-0.320690\pi\) | ||||
0.533994 | + | 0.845488i | \(0.320690\pi\) | |||||||
\(762\) | −4.79399e28 | − | 7.69521e27i | −0.0263130 | − | 0.00422370i | ||||
\(763\) | −4.65592e29 | + | 1.42880e29i | −0.252057 | + | 0.0773505i | ||||
\(764\) | − | 2.50102e29i | − | 0.133548i | ||||||
\(765\) | 2.74000e30 | + | 9.02901e29i | 1.44313 | + | 0.475549i | ||||
\(766\) | 6.11955e29i | 0.317919i | ||||||||
\(767\) | − | 9.21553e28i | − | 0.0472247i | ||||||
\(768\) | −2.26204e29 | + | 1.40922e30i | −0.114343 | + | 0.712335i | ||||
\(769\) | − | 3.84840e29i | − | 0.191890i | −0.995387 | − | 0.0959452i | \(-0.969413\pi\) | ||
0.995387 | − | 0.0959452i | \(-0.0305874\pi\) | |||||||
\(770\) | −5.66021e29 | + | 1.73699e29i | −0.278407 | + | 0.0854367i | ||||
\(771\) | −4.16402e29 | + | 2.59412e30i | −0.202042 | + | 1.25869i | ||||
\(772\) | −1.70015e30 | −0.813777 | ||||||||
\(773\) | 8.12135e29 | 0.383481 | 0.191740 | − | 0.981446i | \(-0.438587\pi\) | ||||
0.191740 | + | 0.981446i | \(0.438587\pi\) | |||||||
\(774\) | 3.35413e27 | − | 1.01786e28i | 0.00156243 | − | 0.00474144i | ||||
\(775\) | 2.74248e30i | 1.26030i | ||||||||
\(776\) | 5.71318e29 | 0.259018 | ||||||||
\(777\) | −1.43098e29 | − | 1.02588e30i | −0.0640047 | − | 0.458853i | ||||
\(778\) | −4.93292e28 | −0.0217680 | ||||||||
\(779\) | 2.17466e30i | 0.946778i | ||||||||
\(780\) | −1.19905e30 | − | 1.92469e29i | −0.515044 | − | 0.0826738i | ||||
\(781\) | 3.12318e30 | 1.32361 | ||||||||
\(782\) | −7.41478e29 | −0.310047 | ||||||||
\(783\) | 2.06912e30 | + | 1.07059e30i | 0.853664 | + | 0.441696i | ||||
\(784\) | 1.85779e30 | − | 1.25877e30i | 0.756272 | − | 0.512422i | ||||
\(785\) | 2.42926e30i | 0.975757i | ||||||||
\(786\) | −8.23894e28 | − | 1.32250e28i | −0.0326539 | − | 0.00524153i | ||||
\(787\) | − | 1.17516e29i | − | 0.0459580i | −0.999736 | − | 0.0229790i | \(-0.992685\pi\) | ||
0.999736 | − | 0.0229790i | \(-0.00731508\pi\) | |||||||
\(788\) | − | 3.04484e30i | − | 1.17500i | ||||||
\(789\) | 1.50415e30 | + | 2.41443e29i | 0.572773 | + | 0.0919403i | ||||
\(790\) | − | 4.46688e29i | − | 0.167849i | ||||||
\(791\) | −1.35489e30 | − | 4.41509e30i | −0.502402 | − | 1.63714i | ||||
\(792\) | 9.34791e29 | + | 3.08038e29i | 0.342058 | + | 0.112717i | ||||
\(793\) | −1.17318e30 | −0.423638 | ||||||||
\(794\) | 2.56373e28 | 0.00913603 | ||||||||
\(795\) | 4.41385e30 | + | 7.08502e29i | 1.55225 | + | 0.249164i | ||||
\(796\) | 6.76699e29i | 0.234860i | ||||||||
\(797\) | 1.58304e30 | 0.542223 | 0.271112 | − | 0.962548i | \(-0.412609\pi\) | ||||
0.271112 | + | 0.962548i | \(0.412609\pi\) | |||||||
\(798\) | −8.66232e28 | − | 6.21006e29i | −0.0292822 | − | 0.209926i | ||||
\(799\) | −3.69591e30 | −1.23305 | ||||||||
\(800\) | 2.30132e30i | 0.757762i | ||||||||
\(801\) | −4.37321e30 | − | 1.44109e30i | −1.42121 | − | 0.468327i | ||||
\(802\) | 5.19806e29 | 0.166729 | ||||||||
\(803\) | −5.24688e30 | −1.66107 | ||||||||
\(804\) | 4.31398e29 | − | 2.68754e30i | 0.134800 | − | 0.839782i | ||||
\(805\) | −2.88940e30 | − | 9.41549e30i | −0.891151 | − | 2.90393i | ||||
\(806\) | − | 1.54644e29i | − | 0.0470777i | ||||||
\(807\) | 9.39749e29 | − | 5.85449e30i | 0.282384 | − | 1.75921i | ||||
\(808\) | − | 8.07397e29i | − | 0.239479i | ||||||
\(809\) | − | 1.05288e30i | − | 0.308262i | −0.988050 | − | 0.154131i | \(-0.950742\pi\) | ||
0.988050 | − | 0.154131i | \(-0.0492578\pi\) | |||||||
\(810\) | −5.59309e29 | + | 7.56503e29i | −0.161644 | + | 0.218634i | ||||
\(811\) | − | 4.54432e30i | − | 1.29643i | −0.761456 | − | 0.648216i | \(-0.775515\pi\) | ||
0.761456 | − | 0.648216i | \(-0.224485\pi\) | |||||||
\(812\) | 9.72140e29 | + | 3.16784e30i | 0.273773 | + | 0.892125i | ||||
\(813\) | 3.02621e30 | + | 4.85761e29i | 0.841296 | + | 0.135043i | ||||
\(814\) | 3.08487e29 | 0.0846605 | ||||||||
\(815\) | 1.08126e31 | 2.92939 | ||||||||
\(816\) | 5.16125e29 | − | 3.21537e30i | 0.138041 | − | 0.859973i | ||||
\(817\) | 1.37676e29i | 0.0363519i | ||||||||
\(818\) | 4.70972e28 | 0.0122768 | ||||||||
\(819\) | 2.69399e28 | − | 1.30974e30i | 0.00693290 | − | 0.337059i | ||||
\(820\) | 4.64113e30 | 1.17918 | ||||||||
\(821\) | − | 2.51589e30i | − | 0.631085i | −0.948911 | − | 0.315542i | \(-0.897814\pi\) | ||
0.948911 | − | 0.315542i | \(-0.102186\pi\) | |||||||
\(822\) | −6.17686e28 | + | 3.84808e29i | −0.0152973 | + | 0.0952994i | ||||
\(823\) | −7.08678e30 | −1.73281 | −0.866404 | − | 0.499343i | \(-0.833575\pi\) | ||||
−0.866404 | + | 0.499343i | \(0.833575\pi\) | |||||||
\(824\) | −4.00460e29 | −0.0966771 | ||||||||
\(825\) | −6.83160e30 | − | 1.09659e30i | −1.62838 | − | 0.261384i | ||||
\(826\) | −2.97915e28 | − | 9.70796e28i | −0.00701136 | − | 0.0228474i | ||||
\(827\) | 4.19827e30i | 0.975579i | 0.872961 | + | 0.487789i | \(0.162197\pi\) | ||||
−0.872961 | + | 0.487789i | \(0.837803\pi\) | |||||||
\(828\) | −2.52420e30 | + | 7.66008e30i | −0.579168 | + | 1.75758i | ||||
\(829\) | 4.30255e30i | 0.974773i | 0.873186 | + | 0.487387i | \(0.162050\pi\) | ||||
−0.873186 | + | 0.487387i | \(0.837950\pi\) | |||||||
\(830\) | − | 1.52645e30i | − | 0.341477i | ||||||
\(831\) | −2.61135e29 | + | 1.62683e30i | −0.0576839 | + | 0.359361i | ||||
\(832\) | 1.28216e30i | 0.279670i | ||||||||
\(833\) | −3.66455e30 | + | 2.48297e30i | −0.789312 | + | 0.534809i | ||||
\(834\) | −6.81206e28 | + | 4.24381e29i | −0.0144889 | + | 0.0902635i | ||||
\(835\) | −7.87895e30 | −1.65486 | ||||||||
\(836\) | −6.22862e30 | −1.29189 | ||||||||
\(837\) | 3.54908e30 | + | 1.83634e30i | 0.726939 | + | 0.376127i | ||||
\(838\) | 5.52464e29i | 0.111749i | ||||||||
\(839\) | −1.19493e30 | −0.238694 | −0.119347 | − | 0.992853i | \(-0.538080\pi\) | ||||
−0.119347 | + | 0.992853i | \(0.538080\pi\) | |||||||
\(840\) | −2.69042e30 | + | 3.75282e29i | −0.530747 | + | 0.0740331i | ||||
\(841\) | 3.90927e29 | 0.0761618 | ||||||||
\(842\) | 2.36187e29i | 0.0454443i | ||||||||
\(843\) | 3.92797e30 | + | 6.30509e29i | 0.746412 | + | 0.119812i | ||||
\(844\) | 5.75534e30 | 1.08013 | ||||||||
\(845\) | 7.62075e30 | 1.41255 | ||||||||
\(846\) | 3.77219e29 | − | 1.14473e30i | 0.0690565 | − | 0.209563i | ||||
\(847\) | −7.78125e29 | + | 2.38789e29i | −0.140693 | + | 0.0431756i | ||||
\(848\) | − | 5.04617e30i | − | 0.901168i | ||||||
\(849\) | 6.73822e30 | + | 1.08160e30i | 1.18854 | + | 0.190782i | ||||
\(850\) | − | 1.43769e30i | − | 0.250476i | ||||||
\(851\) | 5.13154e30i | 0.883054i | ||||||||
\(852\) | 6.96962e30 | + | 1.11875e30i | 1.18466 | + | 0.190159i | ||||
\(853\) | − | 1.04905e31i | − | 1.76130i | −0.473768 | − | 0.880650i | \(-0.657106\pi\) | ||
0.473768 | − | 0.880650i | \(-0.342894\pi\) | |||||||
\(854\) | −1.23586e30 | + | 3.79259e29i | −0.204957 | + | 0.0628967i | ||||
\(855\) | 3.78260e30 | − | 1.14789e31i | 0.619650 | − | 1.88043i | ||||
\(856\) | 1.63264e30 | 0.264190 | ||||||||
\(857\) | −8.27982e30 | −1.32350 | −0.661748 | − | 0.749727i | \(-0.730185\pi\) | ||||
−0.661748 | + | 0.749727i | \(0.730185\pi\) | |||||||
\(858\) | 3.85223e29 | + | 6.18352e28i | 0.0608269 | + | 0.00976380i | ||||
\(859\) | 3.26719e30i | 0.509620i | 0.966991 | + | 0.254810i | \(0.0820129\pi\) | ||||
−0.966991 | + | 0.254810i | \(0.917987\pi\) | |||||||
\(860\) | 2.93827e29 | 0.0452749 | ||||||||
\(861\) | 6.91662e29 | + | 4.95856e30i | 0.105284 | + | 0.754784i | ||||
\(862\) | −2.00527e30 | −0.301541 | ||||||||
\(863\) | − | 3.79827e30i | − | 0.564251i | −0.959377 | − | 0.282126i | \(-0.908960\pi\) | ||
0.959377 | − | 0.282126i | \(-0.0910395\pi\) | |||||||
\(864\) | 2.97817e30 | + | 1.54094e30i | 0.437074 | + | 0.226148i | ||||
\(865\) | 5.37545e30 | 0.779374 | ||||||||
\(866\) | −5.21103e29 | −0.0746424 | ||||||||
\(867\) | 1.01879e29 | − | 6.34689e29i | 0.0144173 | − | 0.0898173i | ||||
\(868\) | 1.66747e30 | + | 5.43368e30i | 0.233132 | + | 0.759690i | ||||
\(869\) | − | 4.78665e30i | − | 0.661187i | ||||||
\(870\) | 3.03500e29 | − | 1.89075e30i | 0.0414196 | − | 0.258038i | ||||
\(871\) | − | 2.19032e30i | − | 0.295337i | ||||||
\(872\) | − | 6.65482e29i | − | 0.0886570i | ||||||
\(873\) | −1.83153e30 | + | 5.55806e30i | −0.241081 | + | 0.731600i | ||||
\(874\) | 3.10634e30i | 0.403998i | ||||||||
\(875\) | 6.40002e30 | − | 1.96402e30i | 0.822426 | − | 0.252384i | ||||
\(876\) | −1.17088e31 | − | 1.87948e30i | −1.48669 | − | 0.238641i | ||||
\(877\) | −2.66342e30 | −0.334151 | −0.167076 | − | 0.985944i | \(-0.553432\pi\) | ||||
−0.167076 | + | 0.985944i | \(0.553432\pi\) | |||||||
\(878\) | 1.84836e30 | 0.229137 | ||||||||
\(879\) | −4.72406e29 | + | 2.94301e30i | −0.0578671 | + | 0.360503i | ||||
\(880\) | 1.28825e31i | 1.55931i | ||||||||
\(881\) | 4.93472e29 | 0.0590222 | 0.0295111 | − | 0.999564i | \(-0.490605\pi\) | ||||
0.0295111 | + | 0.999564i | \(0.490605\pi\) | |||||||
\(882\) | −3.95028e29 | − | 1.38844e30i | −0.0466883 | − | 0.164099i | ||||
\(883\) | −2.54602e30 | −0.297355 | −0.148677 | − | 0.988886i | \(-0.547502\pi\) | ||||
−0.148677 | + | 0.988886i | \(0.547502\pi\) | |||||||
\(884\) | − | 2.70400e30i | − | 0.312074i | ||||||
\(885\) | 3.10224e29 | − | 1.93265e30i | 0.0353811 | − | 0.220418i | ||||
\(886\) | −4.39781e29 | −0.0495658 | ||||||||
\(887\) | −3.68852e30 | −0.410823 | −0.205411 | − | 0.978676i | \(-0.565853\pi\) | ||||
−0.205411 | + | 0.978676i | \(0.565853\pi\) | |||||||
\(888\) | 1.39747e30 | + | 2.24318e29i | 0.153817 | + | 0.0246904i | ||||
\(889\) | 1.37281e30 | − | 4.21284e29i | 0.149328 | − | 0.0458255i | ||||
\(890\) | 3.78485e30i | 0.406868i | ||||||||
\(891\) | −5.99349e30 | + | 8.10659e30i | −0.636742 | + | 0.861237i | ||||
\(892\) | 8.63675e30i | 0.906816i | ||||||||
\(893\) | 1.54836e31i | 1.60669i | ||||||||
\(894\) | 2.44184e29 | − | 1.52123e30i | 0.0250423 | − | 0.156009i | ||||
\(895\) | 5.91490e30i | 0.599523i | ||||||||
\(896\) | 1.85568e30 | + | 6.04698e30i | 0.185896 | + | 0.605766i | ||||
\(897\) | −1.02860e30 | + | 6.40801e30i | −0.101842 | + | 0.634457i | ||||
\(898\) | 1.65650e30 | 0.162103 | ||||||||
\(899\) | −8.13362e30 | −0.786696 | ||||||||
\(900\) | −1.48525e31 | − | 4.89428e30i | −1.41988 | − | 0.467889i | ||||
\(901\) | 9.95374e30i | 0.940538i | ||||||||
\(902\) | −1.49107e30 | −0.139261 | ||||||||
\(903\) | 4.37886e28 | + | 3.13923e29i | 0.00404240 | + | 0.0289802i | ||||
\(904\) | 6.31059e30 | 0.575839 | ||||||||
\(905\) | − | 7.69765e30i | − | 0.694301i | ||||||
\(906\) | 2.56120e30 | + | 4.11118e29i | 0.228348 | + | 0.0366539i | ||||
\(907\) | 1.14185e31 | 1.00631 | 0.503156 | − | 0.864196i | \(-0.332172\pi\) | ||||
0.503156 | + | 0.864196i | \(0.332172\pi\) | |||||||
\(908\) | −6.43525e29 | −0.0560614 | ||||||||
\(909\) | 7.85475e30 | + | 2.58834e30i | 0.676412 | + | 0.222896i | ||||
\(910\) | −1.02943e30 | + | 3.15910e29i | −0.0876322 | + | 0.0268923i | ||||
\(911\) | − | 6.68124e30i | − | 0.562230i | −0.959674 | − | 0.281115i | \(-0.909296\pi\) | ||
0.959674 | − | 0.281115i | \(-0.0907043\pi\) | |||||||
\(912\) | −1.34704e31 | − | 2.16225e30i | −1.12056 | − | 0.179870i | ||||
\(913\) | − | 1.63572e31i | − | 1.34513i | ||||||
\(914\) | 1.19318e30i | 0.0969998i | ||||||||
\(915\) | −2.46034e31 | − | 3.94928e30i | −1.97731 | − | 0.317393i | ||||
\(916\) | 7.26068e30i | 0.576866i | ||||||||
\(917\) | 2.35931e30 | − | 7.24019e29i | 0.185313 | − | 0.0568685i | ||||
\(918\) | −1.86053e30 | − | 9.62659e29i | −0.144473 | − | 0.0747523i | ||||
\(919\) | 1.57690e31 | 1.21057 | 0.605287 | − | 0.796007i | \(-0.293058\pi\) | ||||
0.605287 | + | 0.796007i | \(0.293058\pi\) | |||||||
\(920\) | 1.34578e31 | 1.02141 | ||||||||
\(921\) | −1.52183e31 | − | 2.44281e30i | −1.14193 | − | 0.183301i | ||||
\(922\) | 3.05707e30i | 0.226793i | ||||||||
\(923\) | 5.68018e30 | 0.416624 | ||||||||
\(924\) | −1.42022e31 | + | 1.98104e30i | −1.02991 | + | 0.143661i | ||||
\(925\) | −9.94977e30 | −0.713387 | ||||||||
\(926\) | 4.50107e30i | 0.319081i | ||||||||
\(927\) | 1.28379e30 | − | 3.89587e30i | 0.0899823 | − | 0.273066i | ||||
\(928\) | −6.82524e30 | −0.473003 | ||||||||
\(929\) | 2.75773e31 | 1.88967 | 0.944837 | − | 0.327542i | \(-0.106220\pi\) | ||||
0.944837 | + | 0.327542i | \(0.106220\pi\) | |||||||
\(930\) | 5.20581e29 | − | 3.24313e30i | 0.0352710 | − | 0.219732i | ||||
\(931\) | 1.04021e31 | + | 1.53522e31i | 0.696867 | + | 1.02849i | ||||
\(932\) | − | 3.26375e29i | − | 0.0216197i | ||||||
\(933\) | 1.20445e30 | − | 7.50355e30i | 0.0788919 | − | 0.491484i | ||||
\(934\) | − | 2.21359e30i | − | 0.143369i | ||||||
\(935\) | − | 2.54112e31i | − | 1.62744i | ||||||
\(936\) | 1.70012e30 | + | 5.60235e29i | 0.107667 | + | 0.0354792i | ||||
\(937\) | − | 1.35211e31i | − | 0.846734i | −0.905958 | − | 0.423367i | \(-0.860848\pi\) | ||
0.905958 | − | 0.423367i | \(-0.139152\pi\) | |||||||
\(938\) | −7.08077e29 | − | 2.30736e30i | −0.0438481 | − | 0.142885i | ||||
\(939\) | 2.29084e31 | + | 3.67720e30i | 1.40283 | + | 0.225180i | ||||
\(940\) | 3.30449e31 | 2.00107 | ||||||||
\(941\) | −2.76551e31 | −1.65609 | −0.828045 | − | 0.560661i | \(-0.810547\pi\) | ||||
−0.828045 | + | 0.560661i | \(0.810547\pi\) | |||||||
\(942\) | 2.79566e29 | − | 1.74165e30i | 0.0165558 | − | 0.103140i | ||||
\(943\) | − | 2.48033e31i | − | 1.45257i | ||||||
\(944\) | −2.20951e30 | −0.127965 | ||||||||
\(945\) | 4.97399e30 | − | 2.73768e31i | 0.284886 | − | 1.56801i | ||||
\(946\) | −9.43986e28 | −0.00534698 | ||||||||
\(947\) | 1.41750e31i | 0.794049i | 0.917808 | + | 0.397025i | \(0.129957\pi\) | ||||
−0.917808 | + | 0.397025i | \(0.870043\pi\) | |||||||
\(948\) | 1.71462e30 | − | 1.06818e31i | 0.0949906 | − | 0.591776i | ||||
\(949\) | −9.54261e30 | −0.522844 | ||||||||
\(950\) | −6.02302e30 | −0.326375 | ||||||||
\(951\) | 1.89839e31 | + | 3.04725e30i | 1.01739 | + | 0.163310i | ||||
\(952\) | −1.77448e30 | − | 5.78237e30i | −0.0940552 | − | 0.306491i | ||||
\(953\) | 1.97217e31i | 1.03388i | 0.856022 | + | 0.516939i | \(0.172929\pi\) | ||||
−0.856022 | + | 0.516939i | \(0.827071\pi\) | |||||||
\(954\) | −3.08296e30 | − | 1.01592e30i | −0.159849 | − | 0.0526745i | ||||
\(955\) | − | 4.27466e30i | − | 0.219213i | ||||||
\(956\) | 1.59256e31i | 0.807769i | ||||||||
\(957\) | 3.25227e30 | − | 2.02611e31i | 0.163159 | − | 1.01645i | ||||
\(958\) | − | 9.17463e29i | − | 0.0455251i | ||||||
\(959\) | −3.38160e30 | − | 1.10194e31i | −0.165969 | − | 0.540832i | ||||
\(960\) | −4.31615e30 | + | 2.68889e31i | −0.209531 | + | 1.30534i | ||||
\(961\) | 6.87425e30 | 0.330088 | ||||||||
\(962\) | 5.61052e29 | 0.0266480 | ||||||||
\(963\) | −5.23390e30 | + | 1.58831e31i | −0.245895 | + | 0.746208i | ||||
\(964\) | − | 2.97212e31i | − | 1.38120i | ||||||
\(965\) | −2.90584e31 | −1.33578 | ||||||||
\(966\) | 9.87987e29 | + | 7.08293e30i | 0.0449254 | + | 0.322072i | ||||
\(967\) | −7.32432e29 | −0.0329450 | −0.0164725 | − | 0.999864i | \(-0.505244\pi\) | ||||
−0.0164725 | + | 0.999864i | \(0.505244\pi\) | |||||||
\(968\) | − | 1.11219e30i | − | 0.0494867i | ||||||
\(969\) | 2.65709e31 | + | 4.26510e30i | 1.16952 | + | 0.187728i | ||||
\(970\) | 4.81029e30 | 0.209444 | ||||||||
\(971\) | 1.27667e31 | 0.549893 | 0.274947 | − | 0.961460i | \(-0.411340\pi\) | ||||
0.274947 | + | 0.961460i | \(0.411340\pi\) | |||||||
\(972\) | −1.62788e31 | + | 1.59436e31i | −0.693628 | + | 0.679346i | ||||
\(973\) | −3.72936e30 | − | 1.21526e31i | −0.157199 | − | 0.512253i | ||||
\(974\) | − | 2.68127e30i | − | 0.111808i | ||||||
\(975\) | −1.24248e31 | − | 1.99440e30i | −0.512555 | − | 0.0822741i | ||||
\(976\) | 2.81281e31i | 1.14793i | ||||||||
\(977\) | − | 2.34907e31i | − | 0.948426i | −0.880410 | − | 0.474213i | \(-0.842733\pi\) | ||
0.880410 | − | 0.474213i | \(-0.157267\pi\) | |||||||
\(978\) | −7.75210e30 | − | 1.24435e30i | −0.309643 | − | 0.0497032i | ||||
\(979\) | 4.05580e31i | 1.60272i | ||||||||
\(980\) | 3.27645e31 | − | 2.22000e31i | 1.28094 | − | 0.867920i | ||||
\(981\) | 6.47412e30 | + | 2.13339e30i | 0.250413 | + | 0.0825176i | ||||
\(982\) | −3.54654e30 | −0.135717 | ||||||||
\(983\) | −2.67503e31 | −1.01278 | −0.506392 | − | 0.862304i | \(-0.669021\pi\) | ||||
−0.506392 | + | 0.862304i | \(0.669021\pi\) | |||||||
\(984\) | −6.75465e30 | − | 1.08424e30i | −0.253020 | − | 0.0406142i | ||||
\(985\) | − | 5.20414e31i | − | 1.92872i | ||||||
\(986\) | 4.26387e30 | 0.156350 | ||||||||
\(987\) | 4.92464e30 | + | 3.53050e31i | 0.178667 | + | 1.28087i | ||||
\(988\) | −1.13281e31 | −0.406639 | ||||||||
\(989\) | − | 1.57028e30i | − | 0.0557718i | ||||||
\(990\) | 7.87059e30 | + | 2.59357e30i | 0.276591 | + | 0.0911440i | ||||
\(991\) | −3.65554e31 | −1.27110 | −0.635548 | − | 0.772062i | \(-0.719226\pi\) | ||||
−0.635548 | + | 0.772062i | \(0.719226\pi\) | |||||||
\(992\) | −1.17071e31 | −0.402787 | ||||||||
\(993\) | 6.50222e30 | − | 4.05078e31i | 0.221358 | − | 1.37902i | ||||
\(994\) | 5.98370e30 | − | 1.83626e30i | 0.201564 | − | 0.0618554i | ||||
\(995\) | 1.15659e31i | 0.385512i | ||||||||
\(996\) | 5.85929e30 | − | 3.65024e31i | 0.193251 | − | 1.20392i | ||||
\(997\) | − | 5.76581e29i | − | 0.0188175i | −0.999956 | − | 0.00940874i | \(-0.997005\pi\) | ||
0.999956 | − | 0.00940874i | \(-0.00299494\pi\) | |||||||
\(998\) | 2.78895e30i | 0.0900680i | ||||||||
\(999\) | −6.66226e30 | + | 1.28761e31i | −0.212904 | + | 0.411479i |
(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 | 21.22.c.b.20.50 | yes | 52 | |
3.2 | odd | 2 | inner | 21.22.c.b.20.3 | ✓ | 52 | |
7.6 | odd | 2 | inner | 21.22.c.b.20.4 | yes | 52 | |
21.20 | even | 2 | inner | 21.22.c.b.20.49 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.22.c.b.20.3 | ✓ | 52 | 3.2 | odd | 2 | inner | |
21.22.c.b.20.4 | yes | 52 | 7.6 | odd | 2 | inner | |
21.22.c.b.20.49 | yes | 52 | 21.20 | even | 2 | inner | |
21.22.c.b.20.50 | yes | 52 | 1.1 | even | 1 | trivial |