Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,20,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(22.8816696556\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 2925852 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1711.01\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 512.000 | 0.707107 | ||||||||
\(3\) | −17348.2 | −0.508866 | −0.254433 | − | 0.967090i | \(-0.581889\pi\) | ||||
−0.254433 | + | 0.967090i | \(0.581889\pi\) | |||||||
\(4\) | 262144. | 0.500000 | ||||||||
\(5\) | 1.95312e6 | 0.447214 | ||||||||
\(6\) | −8.88230e6 | −0.359823 | ||||||||
\(7\) | 5.57963e7 | 0.522606 | 0.261303 | − | 0.965257i | \(-0.415848\pi\) | ||||
0.261303 | + | 0.965257i | \(0.415848\pi\) | |||||||
\(8\) | 1.34218e8 | 0.353553 | ||||||||
\(9\) | −8.61300e8 | −0.741055 | ||||||||
\(10\) | 1.00000e9 | 0.316228 | ||||||||
\(11\) | −5.35830e9 | −0.685167 | −0.342584 | − | 0.939487i | \(-0.611302\pi\) | ||||
−0.342584 | + | 0.939487i | \(0.611302\pi\) | |||||||
\(12\) | −4.54774e9 | −0.254433 | ||||||||
\(13\) | 6.91495e10 | 1.80854 | 0.904268 | − | 0.426965i | \(-0.140417\pi\) | ||||
0.904268 | + | 0.426965i | \(0.140417\pi\) | |||||||
\(14\) | 2.85677e10 | 0.369538 | ||||||||
\(15\) | −3.38833e10 | −0.227572 | ||||||||
\(16\) | 6.87195e10 | 0.250000 | ||||||||
\(17\) | 8.22149e11 | 1.68146 | 0.840728 | − | 0.541457i | \(-0.182127\pi\) | ||||
0.840728 | + | 0.541457i | \(0.182127\pi\) | |||||||
\(18\) | −4.40986e11 | −0.524005 | ||||||||
\(19\) | −3.19849e11 | −0.227397 | −0.113699 | − | 0.993515i | \(-0.536270\pi\) | ||||
−0.113699 | + | 0.993515i | \(0.536270\pi\) | |||||||
\(20\) | 5.12000e11 | 0.223607 | ||||||||
\(21\) | −9.67968e11 | −0.265936 | ||||||||
\(22\) | −2.74345e12 | −0.484486 | ||||||||
\(23\) | 8.01595e12 | 0.927984 | 0.463992 | − | 0.885839i | \(-0.346417\pi\) | ||||
0.463992 | + | 0.885839i | \(0.346417\pi\) | |||||||
\(24\) | −2.32844e12 | −0.179911 | ||||||||
\(25\) | 3.81470e12 | 0.200000 | ||||||||
\(26\) | 3.54046e13 | 1.27883 | ||||||||
\(27\) | 3.51052e13 | 0.885964 | ||||||||
\(28\) | 1.46267e13 | 0.261303 | ||||||||
\(29\) | 2.41111e13 | 0.308629 | 0.154314 | − | 0.988022i | \(-0.450683\pi\) | ||||
0.154314 | + | 0.988022i | \(0.450683\pi\) | |||||||
\(30\) | −1.73482e13 | −0.160918 | ||||||||
\(31\) | 2.07759e14 | 1.41132 | 0.705658 | − | 0.708553i | \(-0.250652\pi\) | ||||
0.705658 | + | 0.708553i | \(0.250652\pi\) | |||||||
\(32\) | 3.51844e13 | 0.176777 | ||||||||
\(33\) | 9.29571e13 | 0.348659 | ||||||||
\(34\) | 4.20940e14 | 1.18897 | ||||||||
\(35\) | 1.08977e14 | 0.233716 | ||||||||
\(36\) | −2.25785e14 | −0.370528 | ||||||||
\(37\) | −2.90774e14 | −0.367823 | −0.183912 | − | 0.982943i | \(-0.558876\pi\) | ||||
−0.183912 | + | 0.982943i | \(0.558876\pi\) | |||||||
\(38\) | −1.63763e14 | −0.160794 | ||||||||
\(39\) | −1.19962e15 | −0.920303 | ||||||||
\(40\) | 2.62144e14 | 0.158114 | ||||||||
\(41\) | 9.57878e14 | 0.456945 | 0.228472 | − | 0.973550i | \(-0.426627\pi\) | ||||
0.228472 | + | 0.973550i | \(0.426627\pi\) | |||||||
\(42\) | −4.95600e14 | −0.188045 | ||||||||
\(43\) | −5.00622e15 | −1.51901 | −0.759503 | − | 0.650503i | \(-0.774558\pi\) | ||||
−0.759503 | + | 0.650503i | \(0.774558\pi\) | |||||||
\(44\) | −1.40465e15 | −0.342584 | ||||||||
\(45\) | −1.68223e15 | −0.331410 | ||||||||
\(46\) | 4.10417e15 | 0.656184 | ||||||||
\(47\) | −3.13847e14 | −0.0409062 | −0.0204531 | − | 0.999791i | \(-0.506511\pi\) | ||||
−0.0204531 | + | 0.999791i | \(0.506511\pi\) | |||||||
\(48\) | −1.19216e15 | −0.127217 | ||||||||
\(49\) | −8.28567e15 | −0.726883 | ||||||||
\(50\) | 1.95312e15 | 0.141421 | ||||||||
\(51\) | −1.42628e16 | −0.855636 | ||||||||
\(52\) | 1.81271e16 | 0.904268 | ||||||||
\(53\) | −1.16717e16 | −0.485861 | −0.242930 | − | 0.970044i | \(-0.578109\pi\) | ||||
−0.242930 | + | 0.970044i | \(0.578109\pi\) | |||||||
\(54\) | 1.79739e16 | 0.626471 | ||||||||
\(55\) | −1.04654e16 | −0.306416 | ||||||||
\(56\) | 7.48886e15 | 0.184769 | ||||||||
\(57\) | 5.54882e15 | 0.115715 | ||||||||
\(58\) | 1.23449e16 | 0.218233 | ||||||||
\(59\) | −2.11995e16 | −0.318590 | −0.159295 | − | 0.987231i | \(-0.550922\pi\) | ||||
−0.159295 | + | 0.987231i | \(0.550922\pi\) | |||||||
\(60\) | −8.88230e15 | −0.113786 | ||||||||
\(61\) | 4.20425e16 | 0.460314 | 0.230157 | − | 0.973153i | \(-0.426076\pi\) | ||||
0.230157 | + | 0.973153i | \(0.426076\pi\) | |||||||
\(62\) | 1.06373e17 | 0.997951 | ||||||||
\(63\) | −4.80574e16 | −0.387280 | ||||||||
\(64\) | 1.80144e16 | 0.125000 | ||||||||
\(65\) | 1.35058e17 | 0.808802 | ||||||||
\(66\) | 4.75940e16 | 0.246539 | ||||||||
\(67\) | 2.45879e17 | 1.10410 | 0.552052 | − | 0.833810i | \(-0.313845\pi\) | ||||
0.552052 | + | 0.833810i | \(0.313845\pi\) | |||||||
\(68\) | 2.15521e17 | 0.840728 | ||||||||
\(69\) | −1.39063e17 | −0.472220 | ||||||||
\(70\) | 5.57963e16 | 0.165262 | ||||||||
\(71\) | −3.98392e17 | −1.03123 | −0.515616 | − | 0.856820i | \(-0.672437\pi\) | ||||
−0.515616 | + | 0.856820i | \(0.672437\pi\) | |||||||
\(72\) | −1.15602e17 | −0.262003 | ||||||||
\(73\) | −5.53484e17 | −1.10037 | −0.550184 | − | 0.835044i | \(-0.685442\pi\) | ||||
−0.550184 | + | 0.835044i | \(0.685442\pi\) | |||||||
\(74\) | −1.48876e17 | −0.260090 | ||||||||
\(75\) | −6.61783e16 | −0.101773 | ||||||||
\(76\) | −8.38464e16 | −0.113699 | ||||||||
\(77\) | −2.98973e17 | −0.358072 | ||||||||
\(78\) | −6.14207e17 | −0.650753 | ||||||||
\(79\) | −1.76148e18 | −1.65356 | −0.826780 | − | 0.562526i | \(-0.809830\pi\) | ||||
−0.826780 | + | 0.562526i | \(0.809830\pi\) | |||||||
\(80\) | 1.34218e17 | 0.111803 | ||||||||
\(81\) | 3.92041e17 | 0.290218 | ||||||||
\(82\) | 4.90433e17 | 0.323109 | ||||||||
\(83\) | 1.89559e18 | 1.11302 | 0.556511 | − | 0.830841i | \(-0.312140\pi\) | ||||
0.556511 | + | 0.830841i | \(0.312140\pi\) | |||||||
\(84\) | −2.53747e17 | −0.132968 | ||||||||
\(85\) | 1.60576e18 | 0.751970 | ||||||||
\(86\) | −2.56318e18 | −1.07410 | ||||||||
\(87\) | −4.18286e17 | −0.157051 | ||||||||
\(88\) | −7.19179e17 | −0.242243 | ||||||||
\(89\) | 4.56180e18 | 1.38016 | 0.690082 | − | 0.723731i | \(-0.257574\pi\) | ||||
0.690082 | + | 0.723731i | \(0.257574\pi\) | |||||||
\(90\) | −8.61300e17 | −0.234342 | ||||||||
\(91\) | 3.85829e18 | 0.945152 | ||||||||
\(92\) | 2.10133e18 | 0.463992 | ||||||||
\(93\) | −3.60426e18 | −0.718171 | ||||||||
\(94\) | −1.60690e17 | −0.0289250 | ||||||||
\(95\) | −6.24705e17 | −0.101695 | ||||||||
\(96\) | −6.10387e17 | −0.0899557 | ||||||||
\(97\) | 1.22283e19 | 1.63318 | 0.816592 | − | 0.577215i | \(-0.195860\pi\) | ||||
0.816592 | + | 0.577215i | \(0.195860\pi\) | |||||||
\(98\) | −4.24226e18 | −0.513984 | ||||||||
\(99\) | 4.61510e18 | 0.507747 | ||||||||
\(100\) | 1.00000e18 | 0.100000 | ||||||||
\(101\) | −1.90414e18 | −0.173239 | −0.0866194 | − | 0.996241i | \(-0.527606\pi\) | ||||
−0.0866194 | + | 0.996241i | \(0.527606\pi\) | |||||||
\(102\) | −7.30257e18 | −0.605026 | ||||||||
\(103\) | 5.63296e17 | 0.0425386 | 0.0212693 | − | 0.999774i | \(-0.493229\pi\) | ||||
0.0212693 | + | 0.999774i | \(0.493229\pi\) | |||||||
\(104\) | 9.28109e18 | 0.639414 | ||||||||
\(105\) | −1.89056e18 | −0.118930 | ||||||||
\(106\) | −5.97589e18 | −0.343556 | ||||||||
\(107\) | −3.13426e19 | −1.64812 | −0.824062 | − | 0.566500i | \(-0.808297\pi\) | ||||
−0.824062 | + | 0.566500i | \(0.808297\pi\) | |||||||
\(108\) | 9.20263e18 | 0.442982 | ||||||||
\(109\) | 1.61520e19 | 0.712319 | 0.356160 | − | 0.934425i | \(-0.384086\pi\) | ||||
0.356160 | + | 0.934425i | \(0.384086\pi\) | |||||||
\(110\) | −5.35830e18 | −0.216669 | ||||||||
\(111\) | 5.04442e18 | 0.187173 | ||||||||
\(112\) | 3.83429e18 | 0.130651 | ||||||||
\(113\) | −4.99152e19 | −1.56310 | −0.781551 | − | 0.623841i | \(-0.785571\pi\) | ||||
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(114\) | 2.84099e18 | 0.0818228 | ||||||||
\(115\) | 1.56562e19 | 0.415007 | ||||||||
\(116\) | 6.32058e18 | 0.154314 | ||||||||
\(117\) | −5.95585e19 | −1.34023 | ||||||||
\(118\) | −1.08542e19 | −0.225277 | ||||||||
\(119\) | 4.58729e19 | 0.878739 | ||||||||
\(120\) | −4.54774e18 | −0.0804588 | ||||||||
\(121\) | −3.24477e19 | −0.530546 | ||||||||
\(122\) | 2.15257e19 | 0.325491 | ||||||||
\(123\) | −1.66175e19 | −0.232524 | ||||||||
\(124\) | 5.44628e19 | 0.705658 | ||||||||
\(125\) | 7.45058e18 | 0.0894427 | ||||||||
\(126\) | −2.46054e19 | −0.273848 | ||||||||
\(127\) | −5.46401e19 | −0.564126 | −0.282063 | − | 0.959396i | \(-0.591019\pi\) | ||||
−0.282063 | + | 0.959396i | \(0.591019\pi\) | |||||||
\(128\) | 9.22337e18 | 0.0883883 | ||||||||
\(129\) | 8.68491e19 | 0.772971 | ||||||||
\(130\) | 6.91495e19 | 0.571910 | ||||||||
\(131\) | −1.25613e20 | −0.965958 | −0.482979 | − | 0.875632i | \(-0.660445\pi\) | ||||
−0.482979 | + | 0.875632i | \(0.660445\pi\) | |||||||
\(132\) | 2.43682e19 | 0.174329 | ||||||||
\(133\) | −1.78464e19 | −0.118839 | ||||||||
\(134\) | 1.25890e20 | 0.780720 | ||||||||
\(135\) | 6.85649e19 | 0.396215 | ||||||||
\(136\) | 1.10347e20 | 0.594485 | ||||||||
\(137\) | 2.02938e20 | 1.01981 | 0.509904 | − | 0.860231i | \(-0.329681\pi\) | ||||
0.509904 | + | 0.860231i | \(0.329681\pi\) | |||||||
\(138\) | −7.12001e19 | −0.333910 | ||||||||
\(139\) | 3.97467e20 | 1.74045 | 0.870223 | − | 0.492657i | \(-0.163974\pi\) | ||||
0.870223 | + | 0.492657i | \(0.163974\pi\) | |||||||
\(140\) | 2.85677e19 | 0.116858 | ||||||||
\(141\) | 5.44470e18 | 0.0208158 | ||||||||
\(142\) | −2.03977e20 | −0.729191 | ||||||||
\(143\) | −3.70524e20 | −1.23915 | ||||||||
\(144\) | −5.91881e19 | −0.185264 | ||||||||
\(145\) | 4.70920e19 | 0.138023 | ||||||||
\(146\) | −2.83384e20 | −0.778077 | ||||||||
\(147\) | 1.43742e20 | 0.369886 | ||||||||
\(148\) | −7.62246e19 | −0.183912 | ||||||||
\(149\) | 7.30310e19 | 0.165287 | 0.0826433 | − | 0.996579i | \(-0.473664\pi\) | ||||
0.0826433 | + | 0.996579i | \(0.473664\pi\) | |||||||
\(150\) | −3.38833e19 | −0.0719646 | ||||||||
\(151\) | −5.89188e20 | −1.17482 | −0.587412 | − | 0.809288i | \(-0.699853\pi\) | ||||
−0.587412 | + | 0.809288i | \(0.699853\pi\) | |||||||
\(152\) | −4.29294e19 | −0.0803971 | ||||||||
\(153\) | −7.08116e20 | −1.24605 | ||||||||
\(154\) | −1.53074e20 | −0.253195 | ||||||||
\(155\) | 4.05780e20 | 0.631159 | ||||||||
\(156\) | −3.14474e20 | −0.460152 | ||||||||
\(157\) | 4.26722e20 | 0.587623 | 0.293811 | − | 0.955863i | \(-0.405076\pi\) | ||||
0.293811 | + | 0.955863i | \(0.405076\pi\) | |||||||
\(158\) | −9.01876e20 | −1.16924 | ||||||||
\(159\) | 2.02483e20 | 0.247238 | ||||||||
\(160\) | 6.87195e19 | 0.0790569 | ||||||||
\(161\) | 4.47261e20 | 0.484970 | ||||||||
\(162\) | 2.00725e20 | 0.205215 | ||||||||
\(163\) | −1.38073e21 | −1.33146 | −0.665729 | − | 0.746194i | \(-0.731879\pi\) | ||||
−0.665729 | + | 0.746194i | \(0.731879\pi\) | |||||||
\(164\) | 2.51102e20 | 0.228472 | ||||||||
\(165\) | 1.81557e20 | 0.155925 | ||||||||
\(166\) | 9.70544e20 | 0.787025 | ||||||||
\(167\) | 1.82808e19 | 0.0140020 | 0.00700099 | − | 0.999975i | \(-0.497771\pi\) | ||||
0.00700099 | + | 0.999975i | \(0.497771\pi\) | |||||||
\(168\) | −1.29918e20 | −0.0940227 | ||||||||
\(169\) | 3.31974e21 | 2.27081 | ||||||||
\(170\) | 8.22149e20 | 0.531723 | ||||||||
\(171\) | 2.75486e20 | 0.168514 | ||||||||
\(172\) | −1.31235e21 | −0.759503 | ||||||||
\(173\) | 7.10579e20 | 0.389201 | 0.194601 | − | 0.980883i | \(-0.437659\pi\) | ||||
0.194601 | + | 0.980883i | \(0.437659\pi\) | |||||||
\(174\) | −2.14162e20 | −0.111052 | ||||||||
\(175\) | 2.12846e20 | 0.104521 | ||||||||
\(176\) | −3.68220e20 | −0.171292 | ||||||||
\(177\) | 3.67775e20 | 0.162120 | ||||||||
\(178\) | 2.33564e21 | 0.975923 | ||||||||
\(179\) | −1.09003e21 | −0.431851 | −0.215926 | − | 0.976410i | \(-0.569277\pi\) | ||||
−0.215926 | + | 0.976410i | \(0.569277\pi\) | |||||||
\(180\) | −4.40986e20 | −0.165705 | ||||||||
\(181\) | −2.79419e21 | −0.996114 | −0.498057 | − | 0.867144i | \(-0.665953\pi\) | ||||
−0.498057 | + | 0.867144i | \(0.665953\pi\) | |||||||
\(182\) | 1.97544e21 | 0.668323 | ||||||||
\(183\) | −7.29363e20 | −0.234239 | ||||||||
\(184\) | 1.07588e21 | 0.328092 | ||||||||
\(185\) | −5.67918e20 | −0.164495 | ||||||||
\(186\) | −1.84538e21 | −0.507823 | ||||||||
\(187\) | −4.40532e21 | −1.15208 | ||||||||
\(188\) | −8.22732e19 | −0.0204531 | ||||||||
\(189\) | 1.95874e21 | 0.463010 | ||||||||
\(190\) | −3.19849e20 | −0.0719094 | ||||||||
\(191\) | 4.63773e21 | 0.991947 | 0.495974 | − | 0.868338i | \(-0.334811\pi\) | ||||
0.495974 | + | 0.868338i | \(0.334811\pi\) | |||||||
\(192\) | −3.12518e20 | −0.0636083 | ||||||||
\(193\) | −8.23942e20 | −0.159625 | −0.0798127 | − | 0.996810i | \(-0.525432\pi\) | ||||
−0.0798127 | + | 0.996810i | \(0.525432\pi\) | |||||||
\(194\) | 6.26090e21 | 1.15484 | ||||||||
\(195\) | −2.34301e21 | −0.411572 | ||||||||
\(196\) | −2.17204e21 | −0.363442 | ||||||||
\(197\) | −8.41762e20 | −0.134202 | −0.0671012 | − | 0.997746i | \(-0.521375\pi\) | ||||
−0.0671012 | + | 0.997746i | \(0.521375\pi\) | |||||||
\(198\) | 2.36293e21 | 0.359031 | ||||||||
\(199\) | −1.16067e22 | −1.68114 | −0.840571 | − | 0.541701i | \(-0.817780\pi\) | ||||
−0.840571 | + | 0.541701i | \(0.817780\pi\) | |||||||
\(200\) | 5.12000e20 | 0.0707107 | ||||||||
\(201\) | −4.26556e21 | −0.561841 | ||||||||
\(202\) | −9.74918e20 | −0.122498 | ||||||||
\(203\) | 1.34531e21 | 0.161291 | ||||||||
\(204\) | −3.73892e21 | −0.427818 | ||||||||
\(205\) | 1.87086e21 | 0.204352 | ||||||||
\(206\) | 2.88407e20 | 0.0300793 | ||||||||
\(207\) | −6.90414e21 | −0.687688 | ||||||||
\(208\) | 4.75192e21 | 0.452134 | ||||||||
\(209\) | 1.71385e21 | 0.155805 | ||||||||
\(210\) | −9.67968e20 | −0.0840965 | ||||||||
\(211\) | 7.16116e20 | 0.0594703 | 0.0297352 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297352 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(212\) | −3.05966e21 | −0.242930 | ||||||||
\(213\) | 6.91140e21 | 0.524759 | ||||||||
\(214\) | −1.60474e22 | −1.16540 | ||||||||
\(215\) | −9.77777e21 | −0.679320 | ||||||||
\(216\) | 4.71175e21 | 0.313236 | ||||||||
\(217\) | 1.15922e22 | 0.737561 | ||||||||
\(218\) | 8.26983e21 | 0.503686 | ||||||||
\(219\) | 9.60197e21 | 0.559940 | ||||||||
\(220\) | −2.74345e21 | −0.153208 | ||||||||
\(221\) | 5.68512e22 | 3.04098 | ||||||||
\(222\) | 2.58274e21 | 0.132351 | ||||||||
\(223\) | −1.19410e22 | −0.586335 | −0.293168 | − | 0.956061i | \(-0.594709\pi\) | ||||
−0.293168 | + | 0.956061i | \(0.594709\pi\) | |||||||
\(224\) | 1.96316e21 | 0.0923845 | ||||||||
\(225\) | −3.28560e21 | −0.148211 | ||||||||
\(226\) | −2.55566e22 | −1.10528 | ||||||||
\(227\) | 2.69537e22 | 1.11782 | 0.558911 | − | 0.829228i | \(-0.311219\pi\) | ||||
0.558911 | + | 0.829228i | \(0.311219\pi\) | |||||||
\(228\) | 1.45459e21 | 0.0578574 | ||||||||
\(229\) | −4.02051e22 | −1.53406 | −0.767032 | − | 0.641609i | \(-0.778267\pi\) | ||||
−0.767032 | + | 0.641609i | \(0.778267\pi\) | |||||||
\(230\) | 8.01595e21 | 0.293454 | ||||||||
\(231\) | 5.18667e21 | 0.182211 | ||||||||
\(232\) | 3.23614e21 | 0.109117 | ||||||||
\(233\) | 5.19383e22 | 1.68115 | 0.840575 | − | 0.541696i | \(-0.182217\pi\) | ||||
0.840575 | + | 0.541696i | \(0.182217\pi\) | |||||||
\(234\) | −3.04939e22 | −0.947683 | ||||||||
\(235\) | −6.12983e20 | −0.0182938 | ||||||||
\(236\) | −5.55733e21 | −0.159295 | ||||||||
\(237\) | 3.05585e22 | 0.841440 | ||||||||
\(238\) | 2.34869e22 | 0.621362 | ||||||||
\(239\) | −5.71264e22 | −1.45230 | −0.726151 | − | 0.687535i | \(-0.758693\pi\) | ||||
−0.726151 | + | 0.687535i | \(0.758693\pi\) | |||||||
\(240\) | −2.32844e21 | −0.0568930 | ||||||||
\(241\) | 2.38712e22 | 0.560675 | 0.280338 | − | 0.959901i | \(-0.409554\pi\) | ||||
0.280338 | + | 0.959901i | \(0.409554\pi\) | |||||||
\(242\) | −1.66132e22 | −0.375153 | ||||||||
\(243\) | −4.76027e22 | −1.03365 | ||||||||
\(244\) | 1.10212e22 | 0.230157 | ||||||||
\(245\) | −1.61829e22 | −0.325072 | ||||||||
\(246\) | −8.50816e21 | −0.164419 | ||||||||
\(247\) | −2.21174e22 | −0.411257 | ||||||||
\(248\) | 2.78850e22 | 0.498975 | ||||||||
\(249\) | −3.28852e22 | −0.566379 | ||||||||
\(250\) | 3.81470e21 | 0.0632456 | ||||||||
\(251\) | −9.12101e22 | −1.45594 | −0.727968 | − | 0.685611i | \(-0.759535\pi\) | ||||
−0.727968 | + | 0.685611i | \(0.759535\pi\) | |||||||
\(252\) | −1.25979e22 | −0.193640 | ||||||||
\(253\) | −4.29519e22 | −0.635825 | ||||||||
\(254\) | −2.79757e22 | −0.398897 | ||||||||
\(255\) | −2.78571e22 | −0.382652 | ||||||||
\(256\) | 4.72237e21 | 0.0625000 | ||||||||
\(257\) | 9.15373e22 | 1.16744 | 0.583718 | − | 0.811956i | \(-0.301597\pi\) | ||||
0.583718 | + | 0.811956i | \(0.301597\pi\) | |||||||
\(258\) | 4.44668e22 | 0.546573 | ||||||||
\(259\) | −1.62241e22 | −0.192226 | ||||||||
\(260\) | 3.54046e22 | 0.404401 | ||||||||
\(261\) | −2.07669e22 | −0.228711 | ||||||||
\(262\) | −6.43140e22 | −0.683036 | ||||||||
\(263\) | 5.82421e22 | 0.596565 | 0.298282 | − | 0.954478i | \(-0.403586\pi\) | ||||
0.298282 | + | 0.954478i | \(0.403586\pi\) | |||||||
\(264\) | 1.24765e22 | 0.123269 | ||||||||
\(265\) | −2.27962e22 | −0.217284 | ||||||||
\(266\) | −9.13735e21 | −0.0840320 | ||||||||
\(267\) | −7.91391e22 | −0.702319 | ||||||||
\(268\) | 6.44556e22 | 0.552052 | ||||||||
\(269\) | 2.11389e23 | 1.74758 | 0.873788 | − | 0.486307i | \(-0.161656\pi\) | ||||
0.873788 | + | 0.486307i | \(0.161656\pi\) | |||||||
\(270\) | 3.51052e22 | 0.280166 | ||||||||
\(271\) | 1.73503e23 | 1.33690 | 0.668451 | − | 0.743757i | \(-0.266958\pi\) | ||||
0.668451 | + | 0.743757i | \(0.266958\pi\) | |||||||
\(272\) | 5.64976e22 | 0.420364 | ||||||||
\(273\) | −6.69345e22 | −0.480956 | ||||||||
\(274\) | 1.03904e23 | 0.721113 | ||||||||
\(275\) | −2.04403e22 | −0.137033 | ||||||||
\(276\) | −3.64545e22 | −0.236110 | ||||||||
\(277\) | −8.04324e22 | −0.503354 | −0.251677 | − | 0.967811i | \(-0.580982\pi\) | ||||
−0.251677 | + | 0.967811i | \(0.580982\pi\) | |||||||
\(278\) | 2.03503e23 | 1.23068 | ||||||||
\(279\) | −1.78943e23 | −1.04586 | ||||||||
\(280\) | 1.46267e22 | 0.0826312 | ||||||||
\(281\) | 3.28300e23 | 1.79292 | 0.896459 | − | 0.443127i | \(-0.146131\pi\) | ||||
0.896459 | + | 0.443127i | \(0.146131\pi\) | |||||||
\(282\) | 2.78769e21 | 0.0147190 | ||||||||
\(283\) | −3.19635e23 | −1.63186 | −0.815930 | − | 0.578151i | \(-0.803775\pi\) | ||||
−0.815930 | + | 0.578151i | \(0.803775\pi\) | |||||||
\(284\) | −1.04436e23 | −0.515616 | ||||||||
\(285\) | 1.08375e22 | 0.0517493 | ||||||||
\(286\) | −1.89708e23 | −0.876212 | ||||||||
\(287\) | 5.34461e22 | 0.238802 | ||||||||
\(288\) | −3.03043e22 | −0.131001 | ||||||||
\(289\) | 4.36856e23 | 1.82730 | ||||||||
\(290\) | 2.41111e22 | 0.0975970 | ||||||||
\(291\) | −2.12140e23 | −0.831073 | ||||||||
\(292\) | −1.45092e23 | −0.550184 | ||||||||
\(293\) | −4.15387e23 | −1.52479 | −0.762396 | − | 0.647110i | \(-0.775977\pi\) | ||||
−0.762396 | + | 0.647110i | \(0.775977\pi\) | |||||||
\(294\) | 7.35958e22 | 0.261549 | ||||||||
\(295\) | −4.14053e22 | −0.142478 | ||||||||
\(296\) | −3.90270e22 | −0.130045 | ||||||||
\(297\) | −1.88104e23 | −0.607034 | ||||||||
\(298\) | 3.73919e22 | 0.116875 | ||||||||
\(299\) | 5.54299e23 | 1.67829 | ||||||||
\(300\) | −1.73482e22 | −0.0508866 | ||||||||
\(301\) | −2.79329e23 | −0.793842 | ||||||||
\(302\) | −3.01664e23 | −0.830726 | ||||||||
\(303\) | 3.30334e22 | 0.0881553 | ||||||||
\(304\) | −2.19798e22 | −0.0568494 | ||||||||
\(305\) | 8.21142e22 | 0.205859 | ||||||||
\(306\) | −3.62556e23 | −0.881092 | ||||||||
\(307\) | 4.98091e23 | 1.17353 | 0.586765 | − | 0.809757i | \(-0.300401\pi\) | ||||
0.586765 | + | 0.809757i | \(0.300401\pi\) | |||||||
\(308\) | −7.83741e22 | −0.179036 | ||||||||
\(309\) | −9.77219e21 | −0.0216464 | ||||||||
\(310\) | 2.07759e23 | 0.446297 | ||||||||
\(311\) | 4.96675e23 | 1.03478 | 0.517390 | − | 0.855750i | \(-0.326904\pi\) | ||||
0.517390 | + | 0.855750i | \(0.326904\pi\) | |||||||
\(312\) | −1.61011e23 | −0.325376 | ||||||||
\(313\) | −8.89041e23 | −1.74281 | −0.871406 | − | 0.490562i | \(-0.836792\pi\) | ||||
−0.871406 | + | 0.490562i | \(0.836792\pi\) | |||||||
\(314\) | 2.18482e23 | 0.415512 | ||||||||
\(315\) | −9.38620e22 | −0.173197 | ||||||||
\(316\) | −4.61761e23 | −0.826780 | ||||||||
\(317\) | 2.61249e23 | 0.453934 | 0.226967 | − | 0.973902i | \(-0.427119\pi\) | ||||
0.226967 | + | 0.973902i | \(0.427119\pi\) | |||||||
\(318\) | 1.03671e23 | 0.174824 | ||||||||
\(319\) | −1.29195e23 | −0.211462 | ||||||||
\(320\) | 3.51844e22 | 0.0559017 | ||||||||
\(321\) | 5.43740e23 | 0.838674 | ||||||||
\(322\) | 2.28997e23 | 0.342926 | ||||||||
\(323\) | −2.62963e23 | −0.382359 | ||||||||
\(324\) | 1.02771e23 | 0.145109 | ||||||||
\(325\) | 2.63784e23 | 0.361707 | ||||||||
\(326\) | −7.06935e23 | −0.941483 | ||||||||
\(327\) | −2.80209e23 | −0.362475 | ||||||||
\(328\) | 1.28564e23 | 0.161554 | ||||||||
\(329\) | −1.75115e22 | −0.0213778 | ||||||||
\(330\) | 9.29571e22 | 0.110256 | ||||||||
\(331\) | 9.76825e22 | 0.112577 | 0.0562887 | − | 0.998415i | \(-0.482073\pi\) | ||||
0.0562887 | + | 0.998415i | \(0.482073\pi\) | |||||||
\(332\) | 4.96918e23 | 0.556511 | ||||||||
\(333\) | 2.50443e23 | 0.272577 | ||||||||
\(334\) | 9.35979e21 | 0.00990090 | ||||||||
\(335\) | 4.80232e23 | 0.493770 | ||||||||
\(336\) | −6.65183e22 | −0.0664841 | ||||||||
\(337\) | 3.88676e23 | 0.377662 | 0.188831 | − | 0.982010i | \(-0.439530\pi\) | ||||
0.188831 | + | 0.982010i | \(0.439530\pi\) | |||||||
\(338\) | 1.69970e24 | 1.60570 | ||||||||
\(339\) | 8.65941e23 | 0.795410 | ||||||||
\(340\) | 4.20940e23 | 0.375985 | ||||||||
\(341\) | −1.11324e24 | −0.966987 | ||||||||
\(342\) | 1.41049e23 | 0.119157 | ||||||||
\(343\) | −1.09833e24 | −0.902479 | ||||||||
\(344\) | −6.71924e23 | −0.537050 | ||||||||
\(345\) | −2.71607e23 | −0.211183 | ||||||||
\(346\) | 3.63816e23 | 0.275207 | ||||||||
\(347\) | 6.38185e23 | 0.469696 | 0.234848 | − | 0.972032i | \(-0.424541\pi\) | ||||
0.234848 | + | 0.972032i | \(0.424541\pi\) | |||||||
\(348\) | −1.09651e23 | −0.0785254 | ||||||||
\(349\) | −7.25583e23 | −0.505645 | −0.252822 | − | 0.967513i | \(-0.581359\pi\) | ||||
−0.252822 | + | 0.967513i | \(0.581359\pi\) | |||||||
\(350\) | 1.08977e23 | 0.0739076 | ||||||||
\(351\) | 2.42751e24 | 1.60230 | ||||||||
\(352\) | −1.88528e23 | −0.121122 | ||||||||
\(353\) | −8.60947e23 | −0.538415 | −0.269207 | − | 0.963082i | \(-0.586762\pi\) | ||||
−0.269207 | + | 0.963082i | \(0.586762\pi\) | |||||||
\(354\) | 1.88301e23 | 0.114636 | ||||||||
\(355\) | −7.78109e23 | −0.461181 | ||||||||
\(356\) | 1.19585e24 | 0.690082 | ||||||||
\(357\) | −7.95814e23 | −0.447160 | ||||||||
\(358\) | −5.58095e23 | −0.305365 | ||||||||
\(359\) | −1.95940e24 | −1.04406 | −0.522030 | − | 0.852927i | \(-0.674825\pi\) | ||||
−0.522030 | + | 0.852927i | \(0.674825\pi\) | |||||||
\(360\) | −2.25785e23 | −0.117171 | ||||||||
\(361\) | −1.87612e24 | −0.948290 | ||||||||
\(362\) | −1.43062e24 | −0.704359 | ||||||||
\(363\) | 5.62911e23 | 0.269977 | ||||||||
\(364\) | 1.01143e24 | 0.472576 | ||||||||
\(365\) | −1.08102e24 | −0.492099 | ||||||||
\(366\) | −3.73434e23 | −0.165632 | ||||||||
\(367\) | −1.70386e24 | −0.736387 | −0.368193 | − | 0.929749i | \(-0.620024\pi\) | ||||
−0.368193 | + | 0.929749i | \(0.620024\pi\) | |||||||
\(368\) | 5.50852e23 | 0.231996 | ||||||||
\(369\) | −8.25020e23 | −0.338621 | ||||||||
\(370\) | −2.90774e23 | −0.116316 | ||||||||
\(371\) | −6.51236e23 | −0.253914 | ||||||||
\(372\) | −9.44834e23 | −0.359085 | ||||||||
\(373\) | −5.66530e22 | −0.0209889 | −0.0104944 | − | 0.999945i | \(-0.503341\pi\) | ||||
−0.0104944 | + | 0.999945i | \(0.503341\pi\) | |||||||
\(374\) | −2.25552e24 | −0.814643 | ||||||||
\(375\) | −1.29255e23 | −0.0455144 | ||||||||
\(376\) | −4.21239e22 | −0.0144625 | ||||||||
\(377\) | 1.66727e24 | 0.558166 | ||||||||
\(378\) | 1.00288e24 | 0.327397 | ||||||||
\(379\) | 2.57014e23 | 0.0818247 | 0.0409123 | − | 0.999163i | \(-0.486974\pi\) | ||||
0.0409123 | + | 0.999163i | \(0.486974\pi\) | |||||||
\(380\) | −1.63763e23 | −0.0508476 | ||||||||
\(381\) | 9.47909e23 | 0.287065 | ||||||||
\(382\) | 2.37452e24 | 0.701413 | ||||||||
\(383\) | 4.38632e24 | 1.26390 | 0.631949 | − | 0.775010i | \(-0.282255\pi\) | ||||
0.631949 | + | 0.775010i | \(0.282255\pi\) | |||||||
\(384\) | −1.60009e23 | −0.0449778 | ||||||||
\(385\) | −5.83933e23 | −0.160135 | ||||||||
\(386\) | −4.21858e23 | −0.112872 | ||||||||
\(387\) | 4.31186e24 | 1.12567 | ||||||||
\(388\) | 3.20558e24 | 0.816592 | ||||||||
\(389\) | −1.37553e24 | −0.341939 | −0.170970 | − | 0.985276i | \(-0.554690\pi\) | ||||
−0.170970 | + | 0.985276i | \(0.554690\pi\) | |||||||
\(390\) | −1.19962e24 | −0.291025 | ||||||||
\(391\) | 6.59030e24 | 1.56037 | ||||||||
\(392\) | −1.11208e24 | −0.256992 | ||||||||
\(393\) | 2.17917e24 | 0.491544 | ||||||||
\(394\) | −4.30982e23 | −0.0948954 | ||||||||
\(395\) | −3.44039e24 | −0.739494 | ||||||||
\(396\) | 1.20982e24 | 0.253873 | ||||||||
\(397\) | −4.17970e24 | −0.856319 | −0.428160 | − | 0.903703i | \(-0.640838\pi\) | ||||
−0.428160 | + | 0.903703i | \(0.640838\pi\) | |||||||
\(398\) | −5.94263e24 | −1.18875 | ||||||||
\(399\) | 3.09603e23 | 0.0604733 | ||||||||
\(400\) | 2.62144e23 | 0.0500000 | ||||||||
\(401\) | 3.45018e23 | 0.0642644 | 0.0321322 | − | 0.999484i | \(-0.489770\pi\) | ||||
0.0321322 | + | 0.999484i | \(0.489770\pi\) | |||||||
\(402\) | −2.18397e24 | −0.397282 | ||||||||
\(403\) | 1.43664e25 | 2.55242 | ||||||||
\(404\) | −4.99158e23 | −0.0866194 | ||||||||
\(405\) | 7.65706e23 | 0.129789 | ||||||||
\(406\) | 6.88799e23 | 0.114050 | ||||||||
\(407\) | 1.55805e24 | 0.252020 | ||||||||
\(408\) | −1.91433e24 | −0.302513 | ||||||||
\(409\) | 1.82296e24 | 0.281452 | 0.140726 | − | 0.990049i | \(-0.455056\pi\) | ||||
0.140726 | + | 0.990049i | \(0.455056\pi\) | |||||||
\(410\) | 9.57878e23 | 0.144499 | ||||||||
\(411\) | −3.52062e24 | −0.518946 | ||||||||
\(412\) | 1.47665e23 | 0.0212693 | ||||||||
\(413\) | −1.18286e24 | −0.166497 | ||||||||
\(414\) | −3.53492e24 | −0.486269 | ||||||||
\(415\) | 3.70233e24 | 0.497758 | ||||||||
\(416\) | 2.43298e24 | 0.319707 | ||||||||
\(417\) | −6.89536e24 | −0.885655 | ||||||||
\(418\) | 8.77489e23 | 0.110171 | ||||||||
\(419\) | −1.44355e25 | −1.77174 | −0.885869 | − | 0.463935i | \(-0.846437\pi\) | ||||
−0.885869 | + | 0.463935i | \(0.846437\pi\) | |||||||
\(420\) | −4.95600e23 | −0.0594652 | ||||||||
\(421\) | −4.71956e24 | −0.553632 | −0.276816 | − | 0.960923i | \(-0.589279\pi\) | ||||
−0.276816 | + | 0.960923i | \(0.589279\pi\) | |||||||
\(422\) | 3.66652e23 | 0.0420519 | ||||||||
\(423\) | 2.70317e23 | 0.0303137 | ||||||||
\(424\) | −1.56654e24 | −0.171778 | ||||||||
\(425\) | 3.13625e24 | 0.336291 | ||||||||
\(426\) | 3.53864e24 | 0.371061 | ||||||||
\(427\) | 2.34581e24 | 0.240563 | ||||||||
\(428\) | −8.21629e24 | −0.824062 | ||||||||
\(429\) | 6.42794e24 | 0.630562 | ||||||||
\(430\) | −5.00622e24 | −0.480352 | ||||||||
\(431\) | −1.44126e25 | −1.35272 | −0.676361 | − | 0.736570i | \(-0.736444\pi\) | ||||
−0.676361 | + | 0.736570i | \(0.736444\pi\) | |||||||
\(432\) | 2.41241e24 | 0.221491 | ||||||||
\(433\) | −1.38601e25 | −1.24489 | −0.622447 | − | 0.782662i | \(-0.713862\pi\) | ||||
−0.622447 | + | 0.782662i | \(0.713862\pi\) | |||||||
\(434\) | 5.93520e24 | 0.521535 | ||||||||
\(435\) | −8.16964e23 | −0.0702352 | ||||||||
\(436\) | 4.23415e24 | 0.356160 | ||||||||
\(437\) | −2.56389e24 | −0.211021 | ||||||||
\(438\) | 4.91621e24 | 0.395937 | ||||||||
\(439\) | −1.25797e25 | −0.991418 | −0.495709 | − | 0.868489i | \(-0.665092\pi\) | ||||
−0.495709 | + | 0.868489i | \(0.665092\pi\) | |||||||
\(440\) | −1.40465e24 | −0.108334 | ||||||||
\(441\) | 7.13644e24 | 0.538661 | ||||||||
\(442\) | 2.91078e25 | 2.15029 | ||||||||
\(443\) | 2.28568e24 | 0.165264 | 0.0826322 | − | 0.996580i | \(-0.473667\pi\) | ||||
0.0826322 | + | 0.996580i | \(0.473667\pi\) | |||||||
\(444\) | 1.32236e24 | 0.0935864 | ||||||||
\(445\) | 8.90976e24 | 0.617228 | ||||||||
\(446\) | −6.11381e24 | −0.414601 | ||||||||
\(447\) | −1.26696e24 | −0.0841088 | ||||||||
\(448\) | 1.00514e24 | 0.0653257 | ||||||||
\(449\) | −4.27635e24 | −0.272103 | −0.136051 | − | 0.990702i | \(-0.543441\pi\) | ||||
−0.136051 | + | 0.990702i | \(0.543441\pi\) | |||||||
\(450\) | −1.68223e24 | −0.104801 | ||||||||
\(451\) | −5.13260e24 | −0.313083 | ||||||||
\(452\) | −1.30850e25 | −0.781551 | ||||||||
\(453\) | 1.02214e25 | 0.597828 | ||||||||
\(454\) | 1.38003e25 | 0.790420 | ||||||||
\(455\) | 7.53572e24 | 0.422685 | ||||||||
\(456\) | 7.44749e23 | 0.0409114 | ||||||||
\(457\) | 1.82618e25 | 0.982515 | 0.491257 | − | 0.871014i | \(-0.336537\pi\) | ||||
0.491257 | + | 0.871014i | \(0.336537\pi\) | |||||||
\(458\) | −2.05850e25 | −1.08475 | ||||||||
\(459\) | 2.88617e25 | 1.48971 | ||||||||
\(460\) | 4.10417e24 | 0.207504 | ||||||||
\(461\) | −7.90654e24 | −0.391587 | −0.195793 | − | 0.980645i | \(-0.562728\pi\) | ||||
−0.195793 | + | 0.980645i | \(0.562728\pi\) | |||||||
\(462\) | 2.65557e24 | 0.128843 | ||||||||
\(463\) | −2.91664e25 | −1.38632 | −0.693160 | − | 0.720784i | \(-0.743782\pi\) | ||||
−0.693160 | + | 0.720784i | \(0.743782\pi\) | |||||||
\(464\) | 1.65690e24 | 0.0771572 | ||||||||
\(465\) | −7.03956e24 | −0.321176 | ||||||||
\(466\) | 2.65924e25 | 1.18875 | ||||||||
\(467\) | −2.90132e25 | −1.27082 | −0.635411 | − | 0.772174i | \(-0.719169\pi\) | ||||
−0.635411 | + | 0.772174i | \(0.719169\pi\) | |||||||
\(468\) | −1.56129e25 | −0.670113 | ||||||||
\(469\) | 1.37191e25 | 0.577011 | ||||||||
\(470\) | −3.13847e23 | −0.0129357 | ||||||||
\(471\) | −7.40288e24 | −0.299021 | ||||||||
\(472\) | −2.84535e24 | −0.112639 | ||||||||
\(473\) | 2.68248e25 | 1.04077 | ||||||||
\(474\) | 1.56460e25 | 0.594988 | ||||||||
\(475\) | −1.22013e24 | −0.0454795 | ||||||||
\(476\) | 1.20253e25 | 0.439369 | ||||||||
\(477\) | 1.00528e25 | 0.360050 | ||||||||
\(478\) | −2.92487e25 | −1.02693 | ||||||||
\(479\) | 4.33547e25 | 1.49228 | 0.746138 | − | 0.665792i | \(-0.231906\pi\) | ||||
0.746138 | + | 0.665792i | \(0.231906\pi\) | |||||||
\(480\) | −1.19216e24 | −0.0402294 | ||||||||
\(481\) | −2.01069e25 | −0.665222 | ||||||||
\(482\) | 1.22220e25 | 0.396457 | ||||||||
\(483\) | −7.75919e24 | −0.246785 | ||||||||
\(484\) | −8.50597e24 | −0.265273 | ||||||||
\(485\) | 2.38834e25 | 0.730382 | ||||||||
\(486\) | −2.43726e25 | −0.730898 | ||||||||
\(487\) | −2.20894e25 | −0.649619 | −0.324809 | − | 0.945780i | \(-0.605300\pi\) | ||||
−0.324809 | + | 0.945780i | \(0.605300\pi\) | |||||||
\(488\) | 5.64284e24 | 0.162746 | ||||||||
\(489\) | 2.39533e25 | 0.677534 | ||||||||
\(490\) | −8.28567e24 | −0.229861 | ||||||||
\(491\) | −1.76617e25 | −0.480573 | −0.240286 | − | 0.970702i | \(-0.577241\pi\) | ||||
−0.240286 | + | 0.970702i | \(0.577241\pi\) | |||||||
\(492\) | −4.35618e24 | −0.116262 | ||||||||
\(493\) | 1.98229e25 | 0.518946 | ||||||||
\(494\) | −1.13241e25 | −0.290802 | ||||||||
\(495\) | 9.01388e24 | 0.227071 | ||||||||
\(496\) | 1.42771e25 | 0.352829 | ||||||||
\(497\) | −2.22288e25 | −0.538928 | ||||||||
\(498\) | −1.68372e25 | −0.400490 | ||||||||
\(499\) | −4.52317e25 | −1.05557 | −0.527786 | − | 0.849377i | \(-0.676978\pi\) | ||||
−0.527786 | + | 0.849377i | \(0.676978\pi\) | |||||||
\(500\) | 1.95313e24 | 0.0447214 | ||||||||
\(501\) | −3.17140e23 | −0.00712514 | ||||||||
\(502\) | −4.66996e25 | −1.02950 | ||||||||
\(503\) | 1.28554e25 | 0.278092 | 0.139046 | − | 0.990286i | \(-0.455596\pi\) | ||||
0.139046 | + | 0.990286i | \(0.455596\pi\) | |||||||
\(504\) | −6.45015e24 | −0.136924 | ||||||||
\(505\) | −3.71902e24 | −0.0774747 | ||||||||
\(506\) | −2.19914e25 | −0.449596 | ||||||||
\(507\) | −5.75916e25 | −1.15554 | ||||||||
\(508\) | −1.43236e25 | −0.282063 | ||||||||
\(509\) | 4.19437e25 | 0.810677 | 0.405338 | − | 0.914167i | \(-0.367154\pi\) | ||||
0.405338 | + | 0.914167i | \(0.367154\pi\) | |||||||
\(510\) | −1.42628e25 | −0.270576 | ||||||||
\(511\) | −3.08824e25 | −0.575058 | ||||||||
\(512\) | 2.41785e24 | 0.0441942 | ||||||||
\(513\) | −1.12284e25 | −0.201466 | ||||||||
\(514\) | 4.68671e25 | 0.825502 | ||||||||
\(515\) | 1.10019e24 | 0.0190238 | ||||||||
\(516\) | 2.27670e25 | 0.386486 | ||||||||
\(517\) | 1.68169e24 | 0.0280276 | ||||||||
\(518\) | −8.30674e24 | −0.135925 | ||||||||
\(519\) | −1.23273e25 | −0.198051 | ||||||||
\(520\) | 1.81271e25 | 0.285955 | ||||||||
\(521\) | 3.05094e25 | 0.472581 | 0.236290 | − | 0.971682i | \(-0.424068\pi\) | ||||
0.236290 | + | 0.971682i | \(0.424068\pi\) | |||||||
\(522\) | −1.06327e25 | −0.161723 | ||||||||
\(523\) | 6.76475e23 | 0.0101038 | 0.00505191 | − | 0.999987i | \(-0.498392\pi\) | ||||
0.00505191 | + | 0.999987i | \(0.498392\pi\) | |||||||
\(524\) | −3.29288e25 | −0.482979 | ||||||||
\(525\) | −3.69251e24 | −0.0531873 | ||||||||
\(526\) | 2.98200e25 | 0.421835 | ||||||||
\(527\) | 1.70809e26 | 2.37306 | ||||||||
\(528\) | 6.38797e24 | 0.0871646 | ||||||||
\(529\) | −1.03600e25 | −0.138845 | ||||||||
\(530\) | −1.16717e25 | −0.153643 | ||||||||
\(531\) | 1.82592e25 | 0.236093 | ||||||||
\(532\) | −4.67832e24 | −0.0594196 | ||||||||
\(533\) | 6.62368e25 | 0.826401 | ||||||||
\(534\) | −4.05192e25 | −0.496614 | ||||||||
\(535\) | −6.12161e25 | −0.737063 | ||||||||
\(536\) | 3.30013e25 | 0.390360 | ||||||||
\(537\) | 1.89101e25 | 0.219755 | ||||||||
\(538\) | 1.08231e26 | 1.23572 | ||||||||
\(539\) | 4.43971e25 | 0.498037 | ||||||||
\(540\) | 1.79739e25 | 0.198108 | ||||||||
\(541\) | −5.91055e25 | −0.640109 | −0.320055 | − | 0.947399i | \(-0.603701\pi\) | ||||
−0.320055 | + | 0.947399i | \(0.603701\pi\) | |||||||
\(542\) | 8.88336e25 | 0.945332 | ||||||||
\(543\) | 4.84742e25 | 0.506889 | ||||||||
\(544\) | 2.89268e25 | 0.297242 | ||||||||
\(545\) | 3.15469e25 | 0.318559 | ||||||||
\(546\) | −3.42705e25 | −0.340087 | ||||||||
\(547\) | −8.46391e25 | −0.825452 | −0.412726 | − | 0.910855i | \(-0.635423\pi\) | ||||
−0.412726 | + | 0.910855i | \(0.635423\pi\) | |||||||
\(548\) | 5.31990e25 | 0.509904 | ||||||||
\(549\) | −3.62112e25 | −0.341118 | ||||||||
\(550\) | −1.04654e25 | −0.0968973 | ||||||||
\(551\) | −7.71191e24 | −0.0701814 | ||||||||
\(552\) | −1.86647e25 | −0.166955 | ||||||||
\(553\) | −9.82840e25 | −0.864159 | ||||||||
\(554\) | −4.11814e25 | −0.355925 | ||||||||
\(555\) | 9.85238e24 | 0.0837062 | ||||||||
\(556\) | 1.04194e26 | 0.870223 | ||||||||
\(557\) | 4.71567e25 | 0.387185 | 0.193593 | − | 0.981082i | \(-0.437986\pi\) | ||||
0.193593 | + | 0.981082i | \(0.437986\pi\) | |||||||
\(558\) | −9.16188e25 | −0.739536 | ||||||||
\(559\) | −3.46178e26 | −2.74718 | ||||||||
\(560\) | 7.48886e24 | 0.0584291 | ||||||||
\(561\) | 7.64246e25 | 0.586254 | ||||||||
\(562\) | 1.68089e26 | 1.26778 | ||||||||
\(563\) | −5.00520e25 | −0.371186 | −0.185593 | − | 0.982627i | \(-0.559421\pi\) | ||||
−0.185593 | + | 0.982627i | \(0.559421\pi\) | |||||||
\(564\) | 1.42730e24 | 0.0104079 | ||||||||
\(565\) | −9.74906e25 | −0.699041 | ||||||||
\(566\) | −1.63653e26 | −1.15390 | ||||||||
\(567\) | 2.18745e25 | 0.151670 | ||||||||
\(568\) | −5.34713e25 | −0.364595 | ||||||||
\(569\) | −2.44961e26 | −1.64259 | −0.821296 | − | 0.570502i | \(-0.806749\pi\) | ||||
−0.821296 | + | 0.570502i | \(0.806749\pi\) | |||||||
\(570\) | 5.54882e24 | 0.0365923 | ||||||||
\(571\) | 2.66645e26 | 1.72938 | 0.864690 | − | 0.502306i | \(-0.167515\pi\) | ||||
0.864690 | + | 0.502306i | \(0.167515\pi\) | |||||||
\(572\) | −9.71306e25 | −0.619575 | ||||||||
\(573\) | −8.04565e25 | −0.504768 | ||||||||
\(574\) | 2.73644e25 | 0.168858 | ||||||||
\(575\) | 3.05784e25 | 0.185597 | ||||||||
\(576\) | −1.55158e25 | −0.0926319 | ||||||||
\(577\) | −1.31556e25 | −0.0772576 | −0.0386288 | − | 0.999254i | \(-0.512299\pi\) | ||||
−0.0386288 | + | 0.999254i | \(0.512299\pi\) | |||||||
\(578\) | 2.23670e26 | 1.29209 | ||||||||
\(579\) | 1.42939e25 | 0.0812280 | ||||||||
\(580\) | 1.23449e25 | 0.0690115 | ||||||||
\(581\) | 1.05767e26 | 0.581671 | ||||||||
\(582\) | −1.08616e26 | −0.587657 | ||||||||
\(583\) | 6.25403e25 | 0.332896 | ||||||||
\(584\) | −7.42873e25 | −0.389039 | ||||||||
\(585\) | −1.16325e26 | −0.599367 | ||||||||
\(586\) | −2.12678e26 | −1.07819 | ||||||||
\(587\) | −1.54368e26 | −0.770009 | −0.385005 | − | 0.922915i | \(-0.625800\pi\) | ||||
−0.385005 | + | 0.922915i | \(0.625800\pi\) | |||||||
\(588\) | 3.76810e25 | 0.184943 | ||||||||
\(589\) | −6.64515e25 | −0.320929 | ||||||||
\(590\) | −2.11995e25 | −0.100747 | ||||||||
\(591\) | 1.46031e25 | 0.0682911 | ||||||||
\(592\) | −1.99818e25 | −0.0919558 | ||||||||
\(593\) | 4.05526e26 | 1.83654 | 0.918268 | − | 0.395959i | \(-0.129588\pi\) | ||||
0.918268 | + | 0.395959i | \(0.129588\pi\) | |||||||
\(594\) | −9.63095e25 | −0.429238 | ||||||||
\(595\) | 8.95954e25 | 0.392984 | ||||||||
\(596\) | 1.91446e25 | 0.0826433 | ||||||||
\(597\) | 2.01356e26 | 0.855476 | ||||||||
\(598\) | 2.83801e26 | 1.18673 | ||||||||
\(599\) | 4.12101e26 | 1.69609 | 0.848045 | − | 0.529925i | \(-0.177780\pi\) | ||||
0.848045 | + | 0.529925i | \(0.177780\pi\) | |||||||
\(600\) | −8.88230e24 | −0.0359823 | ||||||||
\(601\) | −2.12493e25 | −0.0847300 | −0.0423650 | − | 0.999102i | \(-0.513489\pi\) | ||||
−0.0423650 | + | 0.999102i | \(0.513489\pi\) | |||||||
\(602\) | −1.43016e26 | −0.561331 | ||||||||
\(603\) | −2.11775e26 | −0.818202 | ||||||||
\(604\) | −1.54452e26 | −0.587412 | ||||||||
\(605\) | −6.33744e25 | −0.237267 | ||||||||
\(606\) | 1.69131e25 | 0.0623352 | ||||||||
\(607\) | 2.90231e26 | 1.05305 | 0.526527 | − | 0.850158i | \(-0.323494\pi\) | ||||
0.526527 | + | 0.850158i | \(0.323494\pi\) | |||||||
\(608\) | −1.12537e25 | −0.0401986 | ||||||||
\(609\) | −2.33388e25 | −0.0820756 | ||||||||
\(610\) | 4.20425e25 | 0.145564 | ||||||||
\(611\) | −2.17024e25 | −0.0739803 | ||||||||
\(612\) | −1.85628e26 | −0.623026 | ||||||||
\(613\) | −4.17018e26 | −1.37810 | −0.689049 | − | 0.724715i | \(-0.741972\pi\) | ||||
−0.689049 | + | 0.724715i | \(0.741972\pi\) | |||||||
\(614\) | 2.55023e26 | 0.829811 | ||||||||
\(615\) | −3.24561e25 | −0.103988 | ||||||||
\(616\) | −4.01275e25 | −0.126598 | ||||||||
\(617\) | −1.23091e26 | −0.382400 | −0.191200 | − | 0.981551i | \(-0.561238\pi\) | ||||
−0.191200 | + | 0.981551i | \(0.561238\pi\) | |||||||
\(618\) | −5.00336e24 | −0.0153063 | ||||||||
\(619\) | 5.61407e26 | 1.69128 | 0.845642 | − | 0.533750i | \(-0.179218\pi\) | ||||
0.845642 | + | 0.533750i | \(0.179218\pi\) | |||||||
\(620\) | 1.06373e26 | 0.315580 | ||||||||
\(621\) | 2.81402e26 | 0.822161 | ||||||||
\(622\) | 2.54297e26 | 0.731700 | ||||||||
\(623\) | 2.54531e26 | 0.721282 | ||||||||
\(624\) | −8.24375e25 | −0.230076 | ||||||||
\(625\) | 1.45519e25 | 0.0400000 | ||||||||
\(626\) | −4.55189e26 | −1.23235 | ||||||||
\(627\) | −2.97322e25 | −0.0792840 | ||||||||
\(628\) | 1.11863e26 | 0.293811 | ||||||||
\(629\) | −2.39059e26 | −0.618478 | ||||||||
\(630\) | −4.80574e25 | −0.122469 | ||||||||
\(631\) | 2.24570e25 | 0.0563732 | 0.0281866 | − | 0.999603i | \(-0.491027\pi\) | ||||
0.0281866 | + | 0.999603i | \(0.491027\pi\) | |||||||
\(632\) | −2.36421e26 | −0.584621 | ||||||||
\(633\) | −1.24234e25 | −0.0302624 | ||||||||
\(634\) | 1.33760e26 | 0.320980 | ||||||||
\(635\) | −1.06719e26 | −0.252285 | ||||||||
\(636\) | 5.30797e25 | 0.123619 | ||||||||
\(637\) | −5.72950e26 | −1.31460 | ||||||||
\(638\) | −6.61476e25 | −0.149526 | ||||||||
\(639\) | 3.43135e26 | 0.764199 | ||||||||
\(640\) | 1.80144e25 | 0.0395285 | ||||||||
\(641\) | 3.71414e25 | 0.0802985 | 0.0401492 | − | 0.999194i | \(-0.487217\pi\) | ||||
0.0401492 | + | 0.999194i | \(0.487217\pi\) | |||||||
\(642\) | 2.78395e26 | 0.593032 | ||||||||
\(643\) | −3.15707e26 | −0.662643 | −0.331321 | − | 0.943518i | \(-0.607494\pi\) | ||||
−0.331321 | + | 0.943518i | \(0.607494\pi\) | |||||||
\(644\) | 1.17247e26 | 0.242485 | ||||||||
\(645\) | 1.69627e26 | 0.345683 | ||||||||
\(646\) | −1.34637e26 | −0.270368 | ||||||||
\(647\) | −1.43071e25 | −0.0283114 | −0.0141557 | − | 0.999900i | \(-0.504506\pi\) | ||||
−0.0141557 | + | 0.999900i | \(0.504506\pi\) | |||||||
\(648\) | 5.26189e25 | 0.102608 | ||||||||
\(649\) | 1.13593e26 | 0.218287 | ||||||||
\(650\) | 1.35058e26 | 0.255766 | ||||||||
\(651\) | −2.01104e26 | −0.375320 | ||||||||
\(652\) | −3.61951e26 | −0.665729 | ||||||||
\(653\) | −8.73760e26 | −1.58386 | −0.791930 | − | 0.610612i | \(-0.790924\pi\) | ||||
−0.791930 | + | 0.610612i | \(0.790924\pi\) | |||||||
\(654\) | −1.43467e26 | −0.256309 | ||||||||
\(655\) | −2.45339e26 | −0.431990 | ||||||||
\(656\) | 6.58249e25 | 0.114236 | ||||||||
\(657\) | 4.76715e26 | 0.815433 | ||||||||
\(658\) | −8.96591e24 | −0.0151164 | ||||||||
\(659\) | 5.24673e25 | 0.0871922 | 0.0435961 | − | 0.999049i | \(-0.486119\pi\) | ||||
0.0435961 | + | 0.999049i | \(0.486119\pi\) | |||||||
\(660\) | 4.75940e25 | 0.0779624 | ||||||||
\(661\) | −2.51792e26 | −0.406563 | −0.203281 | − | 0.979120i | \(-0.565161\pi\) | ||||
−0.203281 | + | 0.979120i | \(0.565161\pi\) | |||||||
\(662\) | 5.00134e25 | 0.0796042 | ||||||||
\(663\) | −9.86268e26 | −1.54745 | ||||||||
\(664\) | 2.54422e26 | 0.393512 | ||||||||
\(665\) | −3.48562e25 | −0.0531465 | ||||||||
\(666\) | 1.28227e26 | 0.192741 | ||||||||
\(667\) | 1.93274e26 | 0.286403 | ||||||||
\(668\) | 4.79221e24 | 0.00700099 | ||||||||
\(669\) | 2.07156e26 | 0.298366 | ||||||||
\(670\) | 2.45879e26 | 0.349148 | ||||||||
\(671\) | −2.25276e26 | −0.315392 | ||||||||
\(672\) | −3.40574e25 | −0.0470114 | ||||||||
\(673\) | −7.15963e26 | −0.974423 | −0.487212 | − | 0.873284i | \(-0.661986\pi\) | ||||
−0.487212 | + | 0.873284i | \(0.661986\pi\) | |||||||
\(674\) | 1.99002e26 | 0.267047 | ||||||||
\(675\) | 1.33916e26 | 0.177193 | ||||||||
\(676\) | 8.70249e26 | 1.13540 | ||||||||
\(677\) | −4.37826e26 | −0.563260 | −0.281630 | − | 0.959523i | \(-0.590875\pi\) | ||||
−0.281630 | + | 0.959523i | \(0.590875\pi\) | |||||||
\(678\) | 4.43362e26 | 0.562440 | ||||||||
\(679\) | 6.82295e26 | 0.853512 | ||||||||
\(680\) | 2.15521e26 | 0.265862 | ||||||||
\(681\) | −4.67599e26 | −0.568822 | ||||||||
\(682\) | −5.69977e26 | −0.683763 | ||||||||
\(683\) | 4.02600e26 | 0.476296 | 0.238148 | − | 0.971229i | \(-0.423460\pi\) | ||||
0.238148 | + | 0.971229i | \(0.423460\pi\) | |||||||
\(684\) | 7.22169e25 | 0.0842570 | ||||||||
\(685\) | 3.96364e26 | 0.456072 | ||||||||
\(686\) | −5.62343e26 | −0.638149 | ||||||||
\(687\) | 6.97487e26 | 0.780633 | ||||||||
\(688\) | −3.44025e26 | −0.379752 | ||||||||
\(689\) | −8.07090e26 | −0.878697 | ||||||||
\(690\) | −1.39063e26 | −0.149329 | ||||||||
\(691\) | 5.80847e26 | 0.615206 | 0.307603 | − | 0.951515i | \(-0.400473\pi\) | ||||
0.307603 | + | 0.951515i | \(0.400473\pi\) | |||||||
\(692\) | 1.86274e26 | 0.194601 | ||||||||
\(693\) | 2.57506e26 | 0.265351 | ||||||||
\(694\) | 3.26751e26 | 0.332125 | ||||||||
\(695\) | 7.76303e26 | 0.778351 | ||||||||
\(696\) | −5.61413e25 | −0.0555258 | ||||||||
\(697\) | 7.87518e26 | 0.768332 | ||||||||
\(698\) | −3.71498e26 | −0.357545 | ||||||||
\(699\) | −9.01038e26 | −0.855480 | ||||||||
\(700\) | 5.57963e25 | 0.0522606 | ||||||||
\(701\) | −6.65373e26 | −0.614814 | −0.307407 | − | 0.951578i | \(-0.599461\pi\) | ||||
−0.307407 | + | 0.951578i | \(0.599461\pi\) | |||||||
\(702\) | 1.24289e27 | 1.13300 | ||||||||
\(703\) | 9.30037e25 | 0.0836420 | ||||||||
\(704\) | −9.65266e25 | −0.0856459 | ||||||||
\(705\) | 1.06342e25 | 0.00930910 | ||||||||
\(706\) | −4.40805e26 | −0.380717 | ||||||||
\(707\) | −1.06244e26 | −0.0905356 | ||||||||
\(708\) | 9.64099e25 | 0.0810599 | ||||||||
\(709\) | 2.09393e27 | 1.73709 | 0.868546 | − | 0.495608i | \(-0.165055\pi\) | ||||
0.868546 | + | 0.495608i | \(0.165055\pi\) | |||||||
\(710\) | −3.98392e26 | −0.326104 | ||||||||
\(711\) | 1.51716e27 | 1.22538 | ||||||||
\(712\) | 6.12274e26 | 0.487962 | ||||||||
\(713\) | 1.66539e27 | 1.30968 | ||||||||
\(714\) | −4.07457e26 | −0.316190 | ||||||||
\(715\) | −7.23680e26 | −0.554165 | ||||||||
\(716\) | −2.85744e26 | −0.215926 | ||||||||
\(717\) | 9.91043e26 | 0.739028 | ||||||||
\(718\) | −1.00321e27 | −0.738262 | ||||||||
\(719\) | 9.61307e25 | 0.0698132 | 0.0349066 | − | 0.999391i | \(-0.488887\pi\) | ||||
0.0349066 | + | 0.999391i | \(0.488887\pi\) | |||||||
\(720\) | −1.15602e26 | −0.0828525 | ||||||||
\(721\) | 3.14298e25 | 0.0222309 | ||||||||
\(722\) | −9.60572e26 | −0.670543 | ||||||||
\(723\) | −4.14123e26 | −0.285309 | ||||||||
\(724\) | −7.32479e26 | −0.498057 | ||||||||
\(725\) | 9.19766e25 | 0.0617257 | ||||||||
\(726\) | 2.88210e26 | 0.190902 | ||||||||
\(727\) | −2.28716e27 | −1.49527 | −0.747637 | − | 0.664108i | \(-0.768811\pi\) | ||||
−0.747637 | + | 0.664108i | \(0.768811\pi\) | |||||||
\(728\) | 5.17851e26 | 0.334162 | ||||||||
\(729\) | 3.70169e26 | 0.235770 | ||||||||
\(730\) | −5.53484e26 | −0.347967 | ||||||||
\(731\) | −4.11586e27 | −2.55414 | ||||||||
\(732\) | −1.91198e26 | −0.117119 | ||||||||
\(733\) | 9.50008e26 | 0.574433 | 0.287217 | − | 0.957866i | \(-0.407270\pi\) | ||||
0.287217 | + | 0.957866i | \(0.407270\pi\) | |||||||
\(734\) | −8.72376e26 | −0.520704 | ||||||||
\(735\) | 2.80746e26 | 0.165418 | ||||||||
\(736\) | 2.82036e26 | 0.164046 | ||||||||
\(737\) | −1.31749e27 | −0.756496 | ||||||||
\(738\) | −4.22410e26 | −0.239441 | ||||||||
\(739\) | −2.92022e27 | −1.63415 | −0.817077 | − | 0.576529i | \(-0.804407\pi\) | ||||
−0.817077 | + | 0.576529i | \(0.804407\pi\) | |||||||
\(740\) | −1.48876e26 | −0.0822477 | ||||||||
\(741\) | 3.83698e26 | 0.209275 | ||||||||
\(742\) | −3.33433e26 | −0.179544 | ||||||||
\(743\) | 2.06362e27 | 1.09707 | 0.548536 | − | 0.836127i | \(-0.315185\pi\) | ||||
0.548536 | + | 0.836127i | \(0.315185\pi\) | |||||||
\(744\) | −4.83755e26 | −0.253912 | ||||||||
\(745\) | 1.42639e26 | 0.0739185 | ||||||||
\(746\) | −2.90063e25 | −0.0148414 | ||||||||
\(747\) | −1.63267e27 | −0.824810 | ||||||||
\(748\) | −1.15483e27 | −0.576039 | ||||||||
\(749\) | −1.74880e27 | −0.861319 | ||||||||
\(750\) | −6.61783e25 | −0.0321835 | ||||||||
\(751\) | 2.97915e27 | 1.43058 | 0.715291 | − | 0.698827i | \(-0.246294\pi\) | ||||
0.715291 | + | 0.698827i | \(0.246294\pi\) | |||||||
\(752\) | −2.15674e25 | −0.0102265 | ||||||||
\(753\) | 1.58233e27 | 0.740877 | ||||||||
\(754\) | 8.53643e26 | 0.394683 | ||||||||
\(755\) | −1.15076e27 | −0.525397 | ||||||||
\(756\) | 5.13473e26 | 0.231505 | ||||||||
\(757\) | 2.29450e27 | 1.02159 | 0.510796 | − | 0.859702i | \(-0.329351\pi\) | ||||
0.510796 | + | 0.859702i | \(0.329351\pi\) | |||||||
\(758\) | 1.31591e26 | 0.0578588 | ||||||||
\(759\) | 7.45140e26 | 0.323550 | ||||||||
\(760\) | −8.38464e25 | −0.0359547 | ||||||||
\(761\) | 2.78541e27 | 1.17960 | 0.589801 | − | 0.807548i | \(-0.299206\pi\) | ||||
0.589801 | + | 0.807548i | \(0.299206\pi\) | |||||||
\(762\) | 4.85330e26 | 0.202985 | ||||||||
\(763\) | 9.01223e26 | 0.372262 | ||||||||
\(764\) | 1.21575e27 | 0.495974 | ||||||||
\(765\) | −1.38304e27 | −0.557251 | ||||||||
\(766\) | 2.24580e27 | 0.893710 | ||||||||
\(767\) | −1.46594e27 | −0.576182 | ||||||||
\(768\) | −8.19248e25 | −0.0318041 | ||||||||
\(769\) | −2.23371e27 | −0.856498 | −0.428249 | − | 0.903661i | \(-0.640869\pi\) | ||||
−0.428249 | + | 0.903661i | \(0.640869\pi\) | |||||||
\(770\) | −2.98973e26 | −0.113232 | ||||||||
\(771\) | −1.58801e27 | −0.594069 | ||||||||
\(772\) | −2.15991e26 | −0.0798127 | ||||||||
\(773\) | 9.13265e26 | 0.333343 | 0.166672 | − | 0.986012i | \(-0.446698\pi\) | ||||
0.166672 | + | 0.986012i | \(0.446698\pi\) | |||||||
\(774\) | 2.20767e27 | 0.795967 | ||||||||
\(775\) | 7.92538e26 | 0.282263 | ||||||||
\(776\) | 1.64126e27 | 0.577418 | ||||||||
\(777\) | 2.81460e26 | 0.0978176 | ||||||||
\(778\) | −7.04272e26 | −0.241788 | ||||||||
\(779\) | −3.06376e26 | −0.103908 | ||||||||
\(780\) | −6.14207e26 | −0.205786 | ||||||||
\(781\) | 2.13470e27 | 0.706566 | ||||||||
\(782\) | 3.37424e27 | 1.10334 | ||||||||
\(783\) | 8.46426e26 | 0.273434 | ||||||||
\(784\) | −5.69387e26 | −0.181721 | ||||||||
\(785\) | 8.33442e26 | 0.262793 | ||||||||
\(786\) | 1.11574e27 | 0.347574 | ||||||||
\(787\) | 5.64471e26 | 0.173733 | 0.0868664 | − | 0.996220i | \(-0.472315\pi\) | ||||
0.0868664 | + | 0.996220i | \(0.472315\pi\) | |||||||
\(788\) | −2.20663e26 | −0.0671012 | ||||||||
\(789\) | −1.01040e27 | −0.303572 | ||||||||
\(790\) | −1.76148e27 | −0.522901 | ||||||||
\(791\) | −2.78508e27 | −0.816887 | ||||||||
\(792\) | 6.19429e26 | 0.179516 | ||||||||
\(793\) | 2.90722e27 | 0.832496 | ||||||||
\(794\) | −2.14001e27 | −0.605509 | ||||||||
\(795\) | 3.95474e26 | 0.110568 | ||||||||
\(796\) | −3.04263e27 | −0.840571 | ||||||||
\(797\) | −1.25075e27 | −0.341441 | −0.170721 | − | 0.985319i | \(-0.554610\pi\) | ||||
−0.170721 | + | 0.985319i | \(0.554610\pi\) | |||||||
\(798\) | 1.58517e26 | 0.0427610 | ||||||||
\(799\) | −2.58029e26 | −0.0687820 | ||||||||
\(800\) | 1.34218e26 | 0.0353553 | ||||||||
\(801\) | −3.92907e27 | −1.02278 | ||||||||
\(802\) | 1.76649e26 | 0.0454418 | ||||||||
\(803\) | 2.96573e27 | 0.753936 | ||||||||
\(804\) | −1.11819e27 | −0.280921 | ||||||||
\(805\) | 8.73556e26 | 0.216885 | ||||||||
\(806\) | 7.35562e27 | 1.80483 | ||||||||
\(807\) | −3.66723e27 | −0.889283 | ||||||||
\(808\) | −2.55569e26 | −0.0612491 | ||||||||
\(809\) | −2.25667e26 | −0.0534510 | −0.0267255 | − | 0.999643i | \(-0.508508\pi\) | ||||
−0.0267255 | + | 0.999643i | \(0.508508\pi\) | |||||||
\(810\) | 3.92041e26 | 0.0917750 | ||||||||
\(811\) | −1.12861e27 | −0.261123 | −0.130561 | − | 0.991440i | \(-0.541678\pi\) | ||||
−0.130561 | + | 0.991440i | \(0.541678\pi\) | |||||||
\(812\) | 3.52665e26 | 0.0806456 | ||||||||
\(813\) | −3.00998e27 | −0.680304 | ||||||||
\(814\) | 7.97724e26 | 0.178205 | ||||||||
\(815\) | −2.69674e27 | −0.595446 | ||||||||
\(816\) | −9.80135e26 | −0.213909 | ||||||||
\(817\) | 1.60123e27 | 0.345418 | ||||||||
\(818\) | 9.33354e26 | 0.199017 | ||||||||
\(819\) | −3.32314e27 | −0.700409 | ||||||||
\(820\) | 4.90433e26 | 0.102176 | ||||||||
\(821\) | −4.62062e27 | −0.951569 | −0.475784 | − | 0.879562i | \(-0.657836\pi\) | ||||
−0.475784 | + | 0.879562i | \(0.657836\pi\) | |||||||
\(822\) | −1.80256e27 | −0.366950 | ||||||||
\(823\) | 5.30846e27 | 1.06824 | 0.534121 | − | 0.845408i | \(-0.320643\pi\) | ||||
0.534121 | + | 0.845408i | \(0.320643\pi\) | |||||||
\(824\) | 7.56043e25 | 0.0150397 | ||||||||
\(825\) | 3.54603e26 | 0.0697317 | ||||||||
\(826\) | −6.05622e26 | −0.117731 | ||||||||
\(827\) | 2.89805e27 | 0.556933 | 0.278467 | − | 0.960446i | \(-0.410174\pi\) | ||||
0.278467 | + | 0.960446i | \(0.410174\pi\) | |||||||
\(828\) | −1.80988e27 | −0.343844 | ||||||||
\(829\) | −1.57547e27 | −0.295898 | −0.147949 | − | 0.988995i | \(-0.547267\pi\) | ||||
−0.147949 | + | 0.988995i | \(0.547267\pi\) | |||||||
\(830\) | 1.89559e27 | 0.351968 | ||||||||
\(831\) | 1.39536e27 | 0.256140 | ||||||||
\(832\) | 1.24569e27 | 0.226067 | ||||||||
\(833\) | −6.81205e27 | −1.22222 | ||||||||
\(834\) | −3.53042e27 | −0.626252 | ||||||||
\(835\) | 3.57048e25 | 0.00626188 | ||||||||
\(836\) | 4.49275e26 | 0.0779026 | ||||||||
\(837\) | 7.29343e27 | 1.25037 | ||||||||
\(838\) | −7.39099e27 | −1.25281 | ||||||||
\(839\) | 4.31895e27 | 0.723836 | 0.361918 | − | 0.932210i | \(-0.382122\pi\) | ||||
0.361918 | + | 0.932210i | \(0.382122\pi\) | |||||||
\(840\) | −2.53747e26 | −0.0420482 | ||||||||
\(841\) | −5.52192e27 | −0.904748 | ||||||||
\(842\) | −2.41641e27 | −0.391477 | ||||||||
\(843\) | −5.69542e27 | −0.912355 | ||||||||
\(844\) | 1.87726e26 | 0.0297352 | ||||||||
\(845\) | 6.48386e27 | 1.01553 | ||||||||
\(846\) | 1.38402e26 | 0.0214351 | ||||||||
\(847\) | −1.81046e27 | −0.277266 | ||||||||
\(848\) | −8.02071e26 | −0.121465 | ||||||||
\(849\) | 5.54510e27 | 0.830398 | ||||||||
\(850\) | 1.60576e27 | 0.237794 | ||||||||
\(851\) | −2.33083e27 | −0.341334 | ||||||||
\(852\) | 1.81178e27 | 0.262379 | ||||||||
\(853\) | 4.26621e26 | 0.0610979 | 0.0305490 | − | 0.999533i | \(-0.490274\pi\) | ||||
0.0305490 | + | 0.999533i | \(0.490274\pi\) | |||||||
\(854\) | 1.20106e27 | 0.170104 | ||||||||
\(855\) | 5.38058e26 | 0.0753618 | ||||||||
\(856\) | −4.20674e27 | −0.582700 | ||||||||
\(857\) | 4.56728e27 | 0.625662 | 0.312831 | − | 0.949809i | \(-0.398723\pi\) | ||||
0.312831 | + | 0.949809i | \(0.398723\pi\) | |||||||
\(858\) | 3.29111e27 | 0.445874 | ||||||||
\(859\) | 1.40555e27 | 0.188326 | 0.0941631 | − | 0.995557i | \(-0.469982\pi\) | ||||
0.0941631 | + | 0.995557i | \(0.469982\pi\) | |||||||
\(860\) | −2.56318e27 | −0.339660 | ||||||||
\(861\) | −9.27195e26 | −0.121518 | ||||||||
\(862\) | −7.37926e27 | −0.956519 | ||||||||
\(863\) | 8.51803e27 | 1.09204 | 0.546018 | − | 0.837774i | \(-0.316143\pi\) | ||||
0.546018 | + | 0.837774i | \(0.316143\pi\) | |||||||
\(864\) | 1.23516e27 | 0.156618 | ||||||||
\(865\) | 1.38785e27 | 0.174056 | ||||||||
\(866\) | −7.09639e27 | −0.880274 | ||||||||
\(867\) | −7.57868e27 | −0.929849 | ||||||||
\(868\) | 3.03882e27 | 0.368781 | ||||||||
\(869\) | 9.43853e27 | 1.13296 | ||||||||
\(870\) | −4.18286e26 | −0.0496638 | ||||||||
\(871\) | 1.70024e28 | 1.99681 | ||||||||
\(872\) | 2.16789e27 | 0.251843 | ||||||||
\(873\) | −1.05322e28 | −1.21028 | ||||||||
\(874\) | −1.31271e27 | −0.149215 | ||||||||
\(875\) | 4.15715e26 | 0.0467433 | ||||||||
\(876\) | 2.51710e27 | 0.279970 | ||||||||
\(877\) | −7.77367e27 | −0.855322 | −0.427661 | − | 0.903939i | \(-0.640662\pi\) | ||||
−0.427661 | + | 0.903939i | \(0.640662\pi\) | |||||||
\(878\) | −6.44080e27 | −0.701038 | ||||||||
\(879\) | 7.20624e27 | 0.775916 | ||||||||
\(880\) | −7.19179e26 | −0.0766040 | ||||||||
\(881\) | 9.90182e27 | 1.04338 | 0.521692 | − | 0.853134i | \(-0.325301\pi\) | ||||
0.521692 | + | 0.853134i | \(0.325301\pi\) | |||||||
\(882\) | 3.65386e27 | 0.380891 | ||||||||
\(883\) | −1.01292e28 | −1.04460 | −0.522298 | − | 0.852763i | \(-0.674925\pi\) | ||||
−0.522298 | + | 0.852763i | \(0.674925\pi\) | |||||||
\(884\) | 1.49032e28 | 1.52049 | ||||||||
\(885\) | 7.18310e26 | 0.0725021 | ||||||||
\(886\) | 1.17027e27 | 0.116860 | ||||||||
\(887\) | 1.94019e28 | 1.91677 | 0.958384 | − | 0.285483i | \(-0.0921539\pi\) | ||||
0.958384 | + | 0.285483i | \(0.0921539\pi\) | |||||||
\(888\) | 6.77050e26 | 0.0661756 | ||||||||
\(889\) | −3.04871e27 | −0.294815 | ||||||||
\(890\) | 4.56180e27 | 0.436446 | ||||||||
\(891\) | −2.10068e27 | −0.198848 | ||||||||
\(892\) | −3.13027e27 | −0.293168 | ||||||||
\(893\) | 1.00384e26 | 0.00930196 | ||||||||
\(894\) | −6.48684e26 | −0.0594739 | ||||||||
\(895\) | −2.12896e27 | −0.193130 | ||||||||
\(896\) | 5.14630e26 | 0.0461923 | ||||||||
\(897\) | −9.61612e27 | −0.854027 | ||||||||
\(898\) | −2.18949e27 | −0.192406 | ||||||||
\(899\) | 5.00930e27 | 0.435572 | ||||||||
\(900\) | −8.61300e26 | −0.0741055 | ||||||||
\(901\) | −9.59584e27 | −0.816954 | ||||||||
\(902\) | −2.62789e27 | −0.221383 | ||||||||
\(903\) | 4.84586e27 | 0.403959 | ||||||||
\(904\) | −6.69950e27 | −0.552640 | ||||||||
\(905\) | −5.45740e27 | −0.445476 | ||||||||
\(906\) | 5.23334e27 | 0.422728 | ||||||||
\(907\) | −1.39346e28 | −1.11385 | −0.556924 | − | 0.830563i | \(-0.688019\pi\) | ||||
−0.556924 | + | 0.830563i | \(0.688019\pi\) | |||||||
\(908\) | 7.06575e27 | 0.558911 | ||||||||
\(909\) | 1.64003e27 | 0.128379 | ||||||||
\(910\) | 3.85829e27 | 0.298883 | ||||||||
\(911\) | −6.06821e27 | −0.465196 | −0.232598 | − | 0.972573i | \(-0.574723\pi\) | ||||
−0.232598 | + | 0.972573i | \(0.574723\pi\) | |||||||
\(912\) | 3.81312e26 | 0.0289287 | ||||||||
\(913\) | −1.01572e28 | −0.762606 | ||||||||
\(914\) | 9.35003e27 | 0.694743 | ||||||||
\(915\) | −1.42454e27 | −0.104755 | ||||||||
\(916\) | −1.05395e28 | −0.767032 | ||||||||
\(917\) | −7.00876e27 | −0.504815 | ||||||||
\(918\) | 1.47772e28 | 1.05338 | ||||||||
\(919\) | 2.20624e28 | 1.55652 | 0.778260 | − | 0.627942i | \(-0.216102\pi\) | ||||
0.778260 | + | 0.627942i | \(0.216102\pi\) | |||||||
\(920\) | 2.10133e27 | 0.146727 | ||||||||
\(921\) | −8.64101e27 | −0.597170 | ||||||||
\(922\) | −4.04815e27 | −0.276893 | ||||||||
\(923\) | −2.75486e28 | −1.86502 | ||||||||
\(924\) | 1.35965e27 | 0.0911055 | ||||||||
\(925\) | −1.10921e27 | −0.0735646 | ||||||||
\(926\) | −1.49332e28 | −0.980276 | ||||||||
\(927\) | −4.85167e26 | −0.0315234 | ||||||||
\(928\) | 8.48334e26 | 0.0545584 | ||||||||
\(929\) | −2.55096e28 | −1.62388 | −0.811940 | − | 0.583740i | \(-0.801589\pi\) | ||||
−0.811940 | + | 0.583740i | \(0.801589\pi\) | |||||||
\(930\) | −3.60426e27 | −0.227106 | ||||||||
\(931\) | 2.65016e27 | 0.165291 | ||||||||
\(932\) | 1.36153e28 | 0.840575 | ||||||||
\(933\) | −8.61643e27 | −0.526565 | ||||||||
\(934\) | −1.48547e28 | −0.898607 | ||||||||
\(935\) | −8.60414e27 | −0.515225 | ||||||||
\(936\) | −7.99380e27 | −0.473841 | ||||||||
\(937\) | 1.82517e28 | 1.07097 | 0.535485 | − | 0.844545i | \(-0.320129\pi\) | ||||
0.535485 | + | 0.844545i | \(0.320129\pi\) | |||||||
\(938\) | 7.02419e27 | 0.408009 | ||||||||
\(939\) | 1.54233e28 | 0.886859 | ||||||||
\(940\) | −1.60690e26 | −0.00914690 | ||||||||
\(941\) | 2.32888e28 | 1.31234 | 0.656169 | − | 0.754614i | \(-0.272176\pi\) | ||||
0.656169 | + | 0.754614i | \(0.272176\pi\) | |||||||
\(942\) | −3.79028e27 | −0.211440 | ||||||||
\(943\) | 7.67830e27 | 0.424037 | ||||||||
\(944\) | −1.45682e27 | −0.0796475 | ||||||||
\(945\) | 3.82567e27 | 0.207064 | ||||||||
\(946\) | 1.37343e28 | 0.735938 | ||||||||
\(947\) | −2.16819e28 | −1.15020 | −0.575098 | − | 0.818084i | \(-0.695036\pi\) | ||||
−0.575098 | + | 0.818084i | \(0.695036\pi\) | |||||||
\(948\) | 8.01074e27 | 0.420720 | ||||||||
\(949\) | −3.82731e28 | −1.99005 | ||||||||
\(950\) | −6.24705e26 | −0.0321589 | ||||||||
\(951\) | −4.53222e27 | −0.230992 | ||||||||
\(952\) | 6.15695e27 | 0.310681 | ||||||||
\(953\) | −4.92023e27 | −0.245812 | −0.122906 | − | 0.992418i | \(-0.539221\pi\) | ||||
−0.122906 | + | 0.992418i | \(0.539221\pi\) | |||||||
\(954\) | 5.14703e27 | 0.254594 | ||||||||
\(955\) | 9.05807e27 | 0.443612 | ||||||||
\(956\) | −1.49754e28 | −0.726151 | ||||||||
\(957\) | 2.24130e27 | 0.107606 | ||||||||
\(958\) | 2.21976e28 | 1.05520 | ||||||||
\(959\) | 1.13232e28 | 0.532957 | ||||||||
\(960\) | −6.10387e26 | −0.0284465 | ||||||||
\(961\) | 2.14932e28 | 0.991811 | ||||||||
\(962\) | −1.02947e28 | −0.470383 | ||||||||
\(963\) | 2.69954e28 | 1.22135 | ||||||||
\(964\) | 6.25768e27 | 0.280338 | ||||||||
\(965\) | −1.60926e27 | −0.0713866 | ||||||||
\(966\) | −3.97270e27 | −0.174503 | ||||||||
\(967\) | 1.22764e28 | 0.533972 | 0.266986 | − | 0.963700i | \(-0.413972\pi\) | ||||
0.266986 | + | 0.963700i | \(0.413972\pi\) | |||||||
\(968\) | −4.35506e27 | −0.187576 | ||||||||
\(969\) | 4.56195e27 | 0.194569 | ||||||||
\(970\) | 1.22283e28 | 0.516458 | ||||||||
\(971\) | 2.18467e28 | 0.913698 | 0.456849 | − | 0.889544i | \(-0.348978\pi\) | ||||
0.456849 | + | 0.889544i | \(0.348978\pi\) | |||||||
\(972\) | −1.24788e28 | −0.516823 | ||||||||
\(973\) | 2.21772e28 | 0.909567 | ||||||||
\(974\) | −1.13098e28 | −0.459350 | ||||||||
\(975\) | −4.57620e27 | −0.184061 | ||||||||
\(976\) | 2.88914e27 | 0.115079 | ||||||||
\(977\) | 3.53418e28 | 1.39409 | 0.697043 | − | 0.717029i | \(-0.254499\pi\) | ||||
0.697043 | + | 0.717029i | \(0.254499\pi\) | |||||||
\(978\) | 1.22641e28 | 0.479089 | ||||||||
\(979\) | −2.44435e28 | −0.945643 | ||||||||
\(980\) | −4.24226e27 | −0.162536 | ||||||||
\(981\) | −1.39117e28 | −0.527868 | ||||||||
\(982\) | −9.04281e27 | −0.339816 | ||||||||
\(983\) | 2.24443e28 | 0.835309 | 0.417655 | − | 0.908606i | \(-0.362852\pi\) | ||||
0.417655 | + | 0.908606i | \(0.362852\pi\) | |||||||
\(984\) | −2.23036e27 | −0.0822095 | ||||||||
\(985\) | −1.64407e27 | −0.0600171 | ||||||||
\(986\) | 1.01493e28 | 0.366950 | ||||||||
\(987\) | 3.03794e26 | 0.0108784 | ||||||||
\(988\) | −5.79794e27 | −0.205628 | ||||||||
\(989\) | −4.01296e28 | −1.40961 | ||||||||
\(990\) | 4.61510e27 | 0.160564 | ||||||||
\(991\) | 3.80736e28 | 1.31197 | 0.655986 | − | 0.754773i | \(-0.272253\pi\) | ||||
0.655986 | + | 0.754773i | \(0.272253\pi\) | |||||||
\(992\) | 7.30987e27 | 0.249488 | ||||||||
\(993\) | −1.69462e27 | −0.0572868 | ||||||||
\(994\) | −1.13811e28 | −0.381079 | ||||||||
\(995\) | −2.26693e28 | −0.751830 | ||||||||
\(996\) | −8.62066e27 | −0.283189 | ||||||||
\(997\) | 4.84284e28 | 1.57578 | 0.787892 | − | 0.615814i | \(-0.211173\pi\) | ||||
0.787892 | + | 0.615814i | \(0.211173\pi\) | |||||||
\(998\) | −2.31586e28 | −0.746402 | ||||||||
\(999\) | −1.02077e28 | −0.325878 |
(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 | 10.20.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 90.20.a.g.1.2 | 2 | |||
4.3 | odd | 2 | 80.20.a.d.1.2 | 2 | |||
5.2 | odd | 4 | 50.20.b.f.49.4 | 4 | |||
5.3 | odd | 4 | 50.20.b.f.49.1 | 4 | |||
5.4 | even | 2 | 50.20.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.20.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.20.a.f.1.2 | 2 | 5.4 | even | 2 | |||
50.20.b.f.49.1 | 4 | 5.3 | odd | 4 | |||
50.20.b.f.49.4 | 4 | 5.2 | odd | 4 | |||
80.20.a.d.1.2 | 2 | 4.3 | odd | 2 | |||
90.20.a.g.1.2 | 2 | 3.2 | odd | 2 |