Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,27,Mod(2,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 27, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 27);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 27 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.c (of order \(4\), degree \(2\), 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: | \(21.4146460365\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2.7 | ||
Character | \(\chi\) | \(=\) | 5.2 |
Dual form | 5.27.c.a.3.7 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 584.877 | + | 584.877i | 0.0713962 | + | 0.0713962i | 0.741903 | − | 0.670507i | \(-0.233923\pi\) |
−0.670507 | + | 0.741903i | \(0.733923\pi\) | |||||||
\(3\) | −2.17135e6 | + | 2.17135e6i | −1.36193 | + | 1.36193i | −0.490464 | + | 0.871462i | \(0.663173\pi\) |
−0.871462 | + | 0.490464i | \(0.836827\pi\) | |||||||
\(4\) | − | 6.64247e7i | − | 0.989805i | ||||||
\(5\) | −1.21727e9 | + | 9.14507e7i | −0.997190 | + | 0.0749164i | ||||
\(6\) | −2.53995e9 | −0.194472 | ||||||||
\(7\) | −4.74948e10 | − | 4.74948e10i | −0.490198 | − | 0.490198i | 0.418171 | − | 0.908368i | \(-0.362671\pi\) |
−0.908368 | + | 0.418171i | \(0.862671\pi\) | |||||||
\(8\) | 7.81007e10 | − | 7.81007e10i | 0.142064 | − | 0.142064i | ||||
\(9\) | − | 6.88765e12i | − | 2.70968i | ||||||
\(10\) | −7.65443e11 | − | 6.58468e11i | −0.0765443 | − | 0.0658468i | ||||
\(11\) | −1.55936e13 | −0.451691 | −0.225845 | − | 0.974163i | \(-0.572514\pi\) | ||||
−0.225845 | + | 0.974163i | \(0.572514\pi\) | |||||||
\(12\) | 1.44231e14 | + | 1.44231e14i | 1.34804 | + | 1.34804i | ||||
\(13\) | −2.89952e14 | + | 2.89952e14i | −0.957332 | + | 0.957332i | −0.999126 | − | 0.0417946i | \(-0.986692\pi\) |
0.0417946 | + | 0.999126i | \(0.486692\pi\) | |||||||
\(14\) | − | 5.55572e13i | − | 0.0699964i | ||||||
\(15\) | 2.44455e15 | − | 2.84170e15i | 1.25607 | − | 1.46013i | ||||
\(16\) | −4.36633e15 | −0.969519 | ||||||||
\(17\) | 1.79130e15 | + | 1.79130e15i | 0.180856 | + | 0.180856i | 0.791729 | − | 0.610873i | \(-0.209181\pi\) |
−0.610873 | + | 0.791729i | \(0.709181\pi\) | |||||||
\(18\) | 4.02843e15 | − | 4.02843e15i | 0.193461 | − | 0.193461i | ||||
\(19\) | 3.35630e16i | 0.798113i | 0.916926 | + | 0.399056i | \(0.130662\pi\) | ||||
−0.916926 | + | 0.399056i | \(0.869338\pi\) | |||||||
\(20\) | 6.07459e15 | + | 8.08570e16i | 0.0741527 | + | 0.987024i | ||||
\(21\) | 2.06255e17 | 1.33523 | ||||||||
\(22\) | −9.12034e15 | − | 9.12034e15i | −0.0322490 | − | 0.0322490i | ||||
\(23\) | 9.60657e16 | − | 9.60657e16i | 0.190593 | − | 0.190593i | −0.605359 | − | 0.795952i | \(-0.706971\pi\) |
0.795952 | + | 0.605359i | \(0.206971\pi\) | |||||||
\(24\) | 3.39168e17i | 0.386962i | ||||||||
\(25\) | 1.47339e18 | − | 2.22641e17i | 0.988775 | − | 0.149412i | ||||
\(26\) | −3.39173e17 | −0.136700 | ||||||||
\(27\) | 9.43621e18 | + | 9.43621e18i | 2.32846 | + | 2.32846i | ||||
\(28\) | −3.15483e18 | + | 3.15483e18i | −0.485200 | + | 0.485200i | ||||
\(29\) | − | 5.76526e18i | − | 0.561882i | −0.959725 | − | 0.280941i | \(-0.909353\pi\) | ||
0.959725 | − | 0.280941i | \(-0.0906465\pi\) | |||||||
\(30\) | 3.09181e18 | − | 2.32280e17i | 0.193926 | − | 0.0145692i | ||||
\(31\) | −2.05949e18 | −0.0843445 | −0.0421722 | − | 0.999110i | \(-0.513428\pi\) | ||||
−0.0421722 | + | 0.999110i | \(0.513428\pi\) | |||||||
\(32\) | −7.79502e18 | − | 7.79502e18i | −0.211284 | − | 0.211284i | ||||
\(33\) | 3.38591e19 | − | 3.38591e19i | 0.615169 | − | 0.615169i | ||||
\(34\) | 2.09538e18i | 0.0258248i | ||||||||
\(35\) | 6.21575e19 | + | 5.34706e19i | 0.525544 | + | 0.452096i | ||||
\(36\) | −4.57510e20 | −2.68206 | ||||||||
\(37\) | 1.41998e20 | + | 1.41998e20i | 0.582990 | + | 0.582990i | 0.935724 | − | 0.352734i | \(-0.114748\pi\) |
−0.352734 | + | 0.935724i | \(0.614748\pi\) | |||||||
\(38\) | −1.96302e19 | + | 1.96302e19i | −0.0569822 | + | 0.0569822i | ||||
\(39\) | − | 1.25917e21i | − | 2.60763i | ||||||
\(40\) | −8.79275e19 | + | 1.02212e20i | −0.131022 | + | 0.152308i | ||||
\(41\) | −1.34542e21 | −1.45435 | −0.727175 | − | 0.686453i | \(-0.759167\pi\) | ||||
−0.727175 | + | 0.686453i | \(0.759167\pi\) | |||||||
\(42\) | 1.20634e20 | + | 1.20634e20i | 0.0953299 | + | 0.0953299i | ||||
\(43\) | 1.49931e21 | − | 1.49931e21i | 0.872571 | − | 0.872571i | −0.120181 | − | 0.992752i | \(-0.538348\pi\) |
0.992752 | + | 0.120181i | \(0.0383476\pi\) | |||||||
\(44\) | 1.03580e21i | 0.447086i | ||||||||
\(45\) | 6.29880e20 | + | 8.38414e21i | 0.203000 | + | 2.70207i | ||||
\(46\) | 1.12373e20 | 0.0272152 | ||||||||
\(47\) | 5.76556e20 | + | 5.76556e20i | 0.105577 | + | 0.105577i | 0.757922 | − | 0.652345i | \(-0.226215\pi\) |
−0.652345 | + | 0.757922i | \(0.726215\pi\) | |||||||
\(48\) | 9.48082e21 | − | 9.48082e21i | 1.32041 | − | 1.32041i | ||||
\(49\) | − | 4.87598e21i | − | 0.519413i | ||||||
\(50\) | 9.91970e20 | + | 7.31535e20i | 0.0812622 | + | 0.0599273i | ||||
\(51\) | −7.77906e21 | −0.492623 | ||||||||
\(52\) | 1.92600e22 | + | 1.92600e22i | 0.947572 | + | 0.947572i | ||||
\(53\) | −1.74562e22 | + | 1.74562e22i | −0.670444 | + | 0.670444i | −0.957818 | − | 0.287374i | \(-0.907218\pi\) |
0.287374 | + | 0.957818i | \(0.407218\pi\) | |||||||
\(54\) | 1.10380e22i | 0.332486i | ||||||||
\(55\) | 1.89817e22 | − | 1.42604e21i | 0.450421 | − | 0.0338391i | ||||
\(56\) | −7.41875e21 | −0.139279 | ||||||||
\(57\) | −7.28770e22 | − | 7.28770e22i | −1.08697 | − | 1.08697i | ||||
\(58\) | 3.37197e21 | − | 3.37197e21i | 0.0401162 | − | 0.0401162i | ||||
\(59\) | − | 7.32328e22i | − | 0.697637i | −0.937190 | − | 0.348819i | \(-0.886583\pi\) | ||
0.937190 | − | 0.348819i | \(-0.113417\pi\) | |||||||
\(60\) | −1.88759e23 | − | 1.62379e23i | −1.44524 | − | 1.24326i | ||||
\(61\) | 1.97728e23 | 1.22118 | 0.610591 | − | 0.791946i | \(-0.290932\pi\) | ||||
0.610591 | + | 0.791946i | \(0.290932\pi\) | |||||||
\(62\) | −1.20455e21 | − | 1.20455e21i | −0.00602187 | − | 0.00602187i | ||||
\(63\) | −3.27127e23 | + | 3.27127e23i | −1.32828 | + | 1.32828i | ||||
\(64\) | 2.83901e23i | 0.939350i | ||||||||
\(65\) | 3.26434e23 | − | 3.79467e23i | 0.882921 | − | 1.02636i | ||||
\(66\) | 3.96069e22 | 0.0878414 | ||||||||
\(67\) | 2.61879e23 | + | 2.61879e23i | 0.477669 | + | 0.477669i | 0.904386 | − | 0.426716i | \(-0.140330\pi\) |
−0.426716 | + | 0.904386i | \(0.640330\pi\) | |||||||
\(68\) | 1.18986e23 | − | 1.18986e23i | 0.179012 | − | 0.179012i | ||||
\(69\) | 4.17185e23i | 0.519147i | ||||||||
\(70\) | 5.08075e21 | + | 6.76283e22i | 0.00524388 | + | 0.0697997i | ||||
\(71\) | 1.02318e24 | 0.878198 | 0.439099 | − | 0.898439i | \(-0.355298\pi\) | ||||
0.439099 | + | 0.898439i | \(0.355298\pi\) | |||||||
\(72\) | −5.37930e23 | − | 5.37930e23i | −0.384949 | − | 0.384949i | ||||
\(73\) | 9.63289e23 | − | 9.63289e23i | 0.576182 | − | 0.576182i | −0.357667 | − | 0.933849i | \(-0.616428\pi\) |
0.933849 | + | 0.357667i | \(0.116428\pi\) | |||||||
\(74\) | 1.66103e23i | 0.0832464i | ||||||||
\(75\) | −2.71581e24 | + | 3.68267e24i | −1.14315 | + | 1.55013i | ||||
\(76\) | 2.22941e24 | 0.789976 | ||||||||
\(77\) | 7.40614e23 | + | 7.40614e23i | 0.221418 | + | 0.221418i | ||||
\(78\) | 7.36462e23 | − | 7.36462e23i | 0.186175 | − | 0.186175i | ||||
\(79\) | − | 4.00738e24i | − | 0.858438i | −0.903201 | − | 0.429219i | \(-0.858789\pi\) | ||
0.903201 | − | 0.429219i | \(-0.141211\pi\) | |||||||
\(80\) | 5.31501e24 | − | 3.99304e23i | 0.966795 | − | 0.0726329i | ||||
\(81\) | −2.34711e25 | −3.63269 | ||||||||
\(82\) | −7.86907e23 | − | 7.86907e23i | −0.103835 | − | 0.103835i | ||||
\(83\) | 4.36215e24 | − | 4.36215e24i | 0.491683 | − | 0.491683i | −0.417153 | − | 0.908836i | \(-0.636972\pi\) |
0.908836 | + | 0.417153i | \(0.136972\pi\) | |||||||
\(84\) | − | 1.37005e25i | − | 1.32161i | ||||||
\(85\) | −2.34431e24 | − | 2.01668e24i | −0.193896 | − | 0.166798i | ||||
\(86\) | 1.75382e24 | 0.124596 | ||||||||
\(87\) | 1.25184e25 | + | 1.25184e25i | 0.765241 | + | 0.765241i | ||||
\(88\) | −1.21787e24 | + | 1.21787e24i | −0.0641692 | + | 0.0641692i | ||||
\(89\) | 3.55980e25i | 1.61941i | 0.586839 | + | 0.809704i | \(0.300372\pi\) | ||||
−0.586839 | + | 0.809704i | \(0.699628\pi\) | |||||||
\(90\) | −4.53529e24 | + | 5.27210e24i | −0.178424 | + | 0.207411i | ||||
\(91\) | 2.75424e25 | 0.938563 | ||||||||
\(92\) | −6.38114e24 | − | 6.38114e24i | −0.188650 | − | 0.188650i | ||||
\(93\) | 4.47186e24 | − | 4.47186e24i | 0.114871 | − | 0.114871i | ||||
\(94\) | 6.74429e23i | 0.0150756i | ||||||||
\(95\) | −3.06936e24 | − | 4.08553e25i | −0.0597917 | − | 0.795870i | ||||
\(96\) | 3.38514e25 | 0.575507 | ||||||||
\(97\) | 1.59614e25 | + | 1.59614e25i | 0.237158 | + | 0.237158i | 0.815672 | − | 0.578514i | \(-0.196367\pi\) |
−0.578514 | + | 0.815672i | \(0.696367\pi\) | |||||||
\(98\) | 2.85185e24 | − | 2.85185e24i | 0.0370841 | − | 0.0370841i | ||||
\(99\) | 1.07403e26i | 1.22394i | ||||||||
\(100\) | −1.47889e25 | − | 9.78695e25i | −0.147889 | − | 0.978695i | ||||
\(101\) | 6.33718e25 | 0.556825 | 0.278412 | − | 0.960462i | \(-0.410192\pi\) | ||||
0.278412 | + | 0.960462i | \(0.410192\pi\) | |||||||
\(102\) | −4.54980e24 | − | 4.54980e24i | −0.0351714 | − | 0.0351714i | ||||
\(103\) | −1.35417e26 | + | 1.35417e26i | −0.922122 | + | 0.922122i | −0.997179 | − | 0.0750575i | \(-0.976086\pi\) |
0.0750575 | + | 0.997179i | \(0.476086\pi\) | |||||||
\(104\) | 4.52909e25i | 0.272006i | ||||||||
\(105\) | −2.51069e26 | + | 1.88622e25i | −1.33147 | + | 0.100030i | ||||
\(106\) | −2.04194e25 | −0.0957342 | ||||||||
\(107\) | −2.65446e26 | − | 2.65446e26i | −1.10151 | − | 1.10151i | −0.994229 | − | 0.107278i | \(-0.965786\pi\) |
−0.107278 | − | 0.994229i | \(-0.534214\pi\) | |||||||
\(108\) | 6.26797e26 | − | 6.26797e26i | 2.30472 | − | 2.30472i | ||||
\(109\) | 8.26937e25i | 0.269729i | 0.990864 | + | 0.134865i | \(0.0430600\pi\) | ||||
−0.990864 | + | 0.134865i | \(0.956940\pi\) | |||||||
\(110\) | 1.19360e25 | + | 1.02679e25i | 0.0345743 | + | 0.0297424i | ||||
\(111\) | −6.16656e26 | −1.58798 | ||||||||
\(112\) | 2.07378e26 | + | 2.07378e26i | 0.475256 | + | 0.475256i | ||||
\(113\) | −1.45365e26 | + | 1.45365e26i | −0.296784 | + | 0.296784i | −0.839753 | − | 0.542969i | \(-0.817300\pi\) |
0.542969 | + | 0.839753i | \(0.317300\pi\) | |||||||
\(114\) | − | 8.52482e25i | − | 0.155211i | ||||||
\(115\) | −1.08153e26 | + | 1.25723e26i | −0.175779 | + | 0.204336i | ||||
\(116\) | −3.82956e26 | −0.556154 | ||||||||
\(117\) | 1.99709e27 | + | 1.99709e27i | 2.59406 | + | 2.59406i | ||||
\(118\) | 4.28322e25 | − | 4.28322e25i | 0.0498086 | − | 0.0498086i | ||||
\(119\) | − | 1.70154e26i | − | 0.177310i | ||||||
\(120\) | −3.10172e25 | − | 4.12860e26i | −0.0289898 | − | 0.385875i | ||||
\(121\) | −9.48658e26 | −0.795975 | ||||||||
\(122\) | 1.15647e26 | + | 1.15647e26i | 0.0871876 | + | 0.0871876i | ||||
\(123\) | 2.92138e27 | − | 2.92138e27i | 1.98071 | − | 1.98071i | ||||
\(124\) | 1.36801e26i | 0.0834846i | ||||||||
\(125\) | −1.77316e27 | + | 4.05757e26i | −0.974803 | + | 0.223067i | ||||
\(126\) | −3.82658e26 | −0.189668 | ||||||||
\(127\) | −1.05974e27 | − | 1.05974e27i | −0.473970 | − | 0.473970i | 0.429227 | − | 0.903197i | \(-0.358786\pi\) |
−0.903197 | + | 0.429227i | \(0.858786\pi\) | |||||||
\(128\) | −6.89162e26 | + | 6.89162e26i | −0.278350 | + | 0.278350i | ||||
\(129\) | 6.51104e27i | 2.37675i | ||||||||
\(130\) | 4.12866e26 | − | 3.10176e25i | 0.136315 | − | 0.0102410i | ||||
\(131\) | 2.18379e27 | 0.652655 | 0.326327 | − | 0.945257i | \(-0.394189\pi\) | ||||
0.326327 | + | 0.945257i | \(0.394189\pi\) | |||||||
\(132\) | −2.24908e27 | − | 2.24908e27i | −0.608898 | − | 0.608898i | ||||
\(133\) | 1.59407e27 | − | 1.59407e27i | 0.391233 | − | 0.391233i | ||||
\(134\) | 3.06334e26i | 0.0682075i | ||||||||
\(135\) | −1.23494e28 | − | 1.06235e28i | −2.49635 | − | 2.14748i | ||||
\(136\) | 2.79803e26 | 0.0513863 | ||||||||
\(137\) | 4.23871e27 | + | 4.23871e27i | 0.707728 | + | 0.707728i | 0.966057 | − | 0.258329i | \(-0.0831720\pi\) |
−0.258329 | + | 0.966057i | \(0.583172\pi\) | |||||||
\(138\) | −2.44002e26 | + | 2.44002e26i | −0.0370651 | + | 0.0370651i | ||||
\(139\) | − | 4.44426e27i | − | 0.614621i | −0.951609 | − | 0.307310i | \(-0.900571\pi\) | ||
0.951609 | − | 0.307310i | \(-0.0994290\pi\) | |||||||
\(140\) | 3.55177e27 | − | 4.12879e27i | 0.447487 | − | 0.520186i | ||||
\(141\) | −2.50381e27 | −0.287576 | ||||||||
\(142\) | 5.98434e26 | + | 5.98434e26i | 0.0627000 | + | 0.0627000i | ||||
\(143\) | 4.52139e27 | − | 4.52139e27i | 0.432418 | − | 0.432418i | ||||
\(144\) | 3.00737e28i | 2.62709i | ||||||||
\(145\) | 5.27237e26 | + | 7.01790e27i | 0.0420942 | + | 0.560303i | ||||
\(146\) | 1.12681e27 | 0.0822743 | ||||||||
\(147\) | 1.05874e28 | + | 1.05874e28i | 0.707401 | + | 0.707401i | ||||
\(148\) | 9.43220e27 | − | 9.43220e27i | 0.577046 | − | 0.577046i | ||||
\(149\) | − | 1.09366e28i | − | 0.613003i | −0.951870 | − | 0.306502i | \(-0.900842\pi\) | ||
0.951870 | − | 0.306502i | \(-0.0991585\pi\) | |||||||
\(150\) | −3.74233e27 | + | 5.65496e26i | −0.192290 | + | 0.0290565i | ||||
\(151\) | 6.12606e27 | 0.288723 | 0.144361 | − | 0.989525i | \(-0.453887\pi\) | ||||
0.144361 | + | 0.989525i | \(0.453887\pi\) | |||||||
\(152\) | 2.62130e27 | + | 2.62130e27i | 0.113383 | + | 0.113383i | ||||
\(153\) | 1.23378e28 | − | 1.23378e28i | 0.490061 | − | 0.490061i | ||||
\(154\) | 8.66336e26i | 0.0316167i | ||||||||
\(155\) | 2.50696e27 | − | 1.88341e26i | 0.0841075 | − | 0.00631879i | ||||
\(156\) | −8.36402e28 | −2.58104 | ||||||||
\(157\) | 3.08998e28 | + | 3.08998e28i | 0.877526 | + | 0.877526i | 0.993278 | − | 0.115752i | \(-0.0369277\pi\) |
−0.115752 | + | 0.993278i | \(0.536928\pi\) | |||||||
\(158\) | 2.34383e27 | − | 2.34383e27i | 0.0612891 | − | 0.0612891i | ||||
\(159\) | − | 7.58068e28i | − | 1.82619i | ||||||
\(160\) | 1.02015e28 | + | 8.77580e27i | 0.226519 | + | 0.194862i | ||||
\(161\) | −9.12524e27 | −0.186856 | ||||||||
\(162\) | −1.37277e28 | − | 1.37277e28i | −0.259360 | − | 0.259360i | ||||
\(163\) | 9.56786e27 | − | 9.56786e27i | 0.166869 | − | 0.166869i | −0.618733 | − | 0.785602i | \(-0.712354\pi\) |
0.785602 | + | 0.618733i | \(0.212354\pi\) | |||||||
\(164\) | 8.93693e28i | 1.43952i | ||||||||
\(165\) | −3.81193e28 | + | 4.43122e28i | −0.567354 | + | 0.659527i | ||||
\(166\) | 5.10264e27 | 0.0702085 | ||||||||
\(167\) | −8.26346e28 | − | 8.26346e28i | −1.05159 | − | 1.05159i | −0.998595 | − | 0.0529990i | \(-0.983122\pi\) |
−0.0529990 | − | 0.998595i | \(-0.516878\pi\) | |||||||
\(168\) | 1.61087e28 | − | 1.61087e28i | 0.189688 | − | 0.189688i | ||||
\(169\) | − | 7.64109e28i | − | 0.832968i | ||||||
\(170\) | −1.91624e26 | − | 2.55065e27i | −0.00193470 | − | 0.0257522i | ||||
\(171\) | 2.31170e29 | 2.16263 | ||||||||
\(172\) | −9.95910e28 | − | 9.95910e28i | −0.863675 | − | 0.863675i | ||||
\(173\) | −1.29926e29 | + | 1.29926e29i | −1.04495 | + | 1.04495i | −0.0460131 | + | 0.998941i | \(0.514652\pi\) |
−0.998941 | + | 0.0460131i | \(0.985348\pi\) | |||||||
\(174\) | 1.46435e28i | 0.109271i | ||||||||
\(175\) | −8.05526e28 | − | 5.94040e28i | −0.557936 | − | 0.411454i | ||||
\(176\) | 6.80867e28 | 0.437923 | ||||||||
\(177\) | 1.59014e29 | + | 1.59014e29i | 0.950130 | + | 0.950130i | ||||
\(178\) | −2.08205e28 | + | 2.08205e28i | −0.115619 | + | 0.115619i | ||||
\(179\) | 1.66199e29i | 0.858104i | 0.903280 | + | 0.429052i | \(0.141152\pi\) | ||||
−0.903280 | + | 0.429052i | \(0.858848\pi\) | |||||||
\(180\) | 5.56914e29 | − | 4.18396e28i | 2.67452 | − | 0.200930i | ||||
\(181\) | 8.37582e28 | 0.374288 | 0.187144 | − | 0.982333i | \(-0.440077\pi\) | ||||
0.187144 | + | 0.982333i | \(0.440077\pi\) | |||||||
\(182\) | 1.61089e28 | + | 1.61089e28i | 0.0670098 | + | 0.0670098i | ||||
\(183\) | −4.29336e29 | + | 4.29336e29i | −1.66316 | + | 1.66316i | ||||
\(184\) | − | 1.50056e28i | − | 0.0541529i | ||||||
\(185\) | −1.85837e29 | − | 1.59865e29i | −0.625027 | − | 0.537676i | ||||
\(186\) | 5.23098e27 | 0.0164027 | ||||||||
\(187\) | −2.79328e28 | − | 2.79328e28i | −0.0816908 | − | 0.0816908i | ||||
\(188\) | 3.82976e28 | − | 3.82976e28i | 0.104501 | − | 0.104501i | ||||
\(189\) | − | 8.96341e29i | − | 2.28281i | ||||||
\(190\) | 2.21002e28 | − | 2.56906e28i | 0.0525531 | − | 0.0610909i | ||||
\(191\) | 1.10097e29 | 0.244536 | 0.122268 | − | 0.992497i | \(-0.460983\pi\) | ||||
0.122268 | + | 0.992497i | \(0.460983\pi\) | |||||||
\(192\) | −6.16448e29 | − | 6.16448e29i | −1.27932 | − | 1.27932i | ||||
\(193\) | 1.04789e29 | − | 1.04789e29i | 0.203269 | − | 0.203269i | −0.598130 | − | 0.801399i | \(-0.704089\pi\) |
0.801399 | + | 0.598130i | \(0.204089\pi\) | |||||||
\(194\) | 1.86709e28i | 0.0338644i | ||||||||
\(195\) | 1.15152e29 | + | 1.53276e30i | 0.195354 | + | 2.60030i | ||||
\(196\) | −3.23885e29 | −0.514117 | ||||||||
\(197\) | 1.47531e29 | + | 1.47531e29i | 0.219190 | + | 0.219190i | 0.808157 | − | 0.588967i | \(-0.200465\pi\) |
−0.588967 | + | 0.808157i | \(0.700465\pi\) | |||||||
\(198\) | −6.28177e28 | + | 6.28177e28i | −0.0873845 | + | 0.0873845i | ||||
\(199\) | − | 6.99337e29i | − | 0.911164i | −0.890194 | − | 0.455582i | \(-0.849431\pi\) | ||
0.890194 | − | 0.455582i | \(-0.150569\pi\) | |||||||
\(200\) | 9.76844e28 | − | 1.32461e29i | 0.119244 | − | 0.161696i | ||||
\(201\) | −1.13726e30 | −1.30110 | ||||||||
\(202\) | 3.70647e28 | + | 3.70647e28i | 0.0397551 | + | 0.0397551i | ||||
\(203\) | −2.73820e29 | + | 2.73820e29i | −0.275433 | + | 0.275433i | ||||
\(204\) | 5.16722e29i | 0.487601i | ||||||||
\(205\) | 1.63775e30 | − | 1.23040e29i | 1.45026 | − | 0.108955i | ||||
\(206\) | −1.58404e29 | −0.131672 | ||||||||
\(207\) | −6.61667e29 | − | 6.61667e29i | −0.516446 | − | 0.516446i | ||||
\(208\) | 1.26602e30 | − | 1.26602e30i | 0.928152 | − | 0.928152i | ||||
\(209\) | − | 5.23368e29i | − | 0.360500i | ||||||
\(210\) | −1.57877e29 | − | 1.35813e29i | −0.102204 | − | 0.0879203i | ||||
\(211\) | 2.89924e30 | 1.76446 | 0.882231 | − | 0.470816i | \(-0.156041\pi\) | ||||
0.882231 | + | 0.470816i | \(0.156041\pi\) | |||||||
\(212\) | 1.15952e30 | + | 1.15952e30i | 0.663609 | + | 0.663609i | ||||
\(213\) | −2.22168e30 | + | 2.22168e30i | −1.19604 | + | 1.19604i | ||||
\(214\) | − | 3.10507e29i | − | 0.157287i | ||||||
\(215\) | −1.68795e30 | + | 1.96218e30i | −0.804749 | + | 0.935488i | ||||
\(216\) | 1.47395e30 | 0.661582 | ||||||||
\(217\) | 9.78148e28 | + | 9.78148e28i | 0.0413455 | + | 0.0413455i | ||||
\(218\) | −4.83657e28 | + | 4.83657e28i | −0.0192576 | + | 0.0192576i | ||||
\(219\) | 4.18327e30i | 1.56943i | ||||||||
\(220\) | −9.47246e28 | − | 1.26085e30i | −0.0334941 | − | 0.445829i | ||||
\(221\) | −1.03878e30 | −0.346277 | ||||||||
\(222\) | −3.60668e29 | − | 3.60668e29i | −0.113375 | − | 0.113375i | ||||
\(223\) | 2.69822e30 | − | 2.69822e30i | 0.800045 | − | 0.800045i | −0.183057 | − | 0.983102i | \(-0.558599\pi\) |
0.983102 | + | 0.183057i | \(0.0585994\pi\) | |||||||
\(224\) | 7.40445e29i | 0.207142i | ||||||||
\(225\) | −1.53347e30 | − | 1.01482e31i | −0.404858 | − | 2.67927i | ||||
\(226\) | −1.70041e29 | −0.0423784 | ||||||||
\(227\) | −1.18064e30 | − | 1.18064e30i | −0.277832 | − | 0.277832i | 0.554411 | − | 0.832243i | \(-0.312943\pi\) |
−0.832243 | + | 0.554411i | \(0.812943\pi\) | |||||||
\(228\) | −4.84083e30 | + | 4.84083e30i | −1.07589 | + | 1.07589i | ||||
\(229\) | − | 4.08307e30i | − | 0.857287i | −0.903474 | − | 0.428643i | \(-0.858992\pi\) | ||
0.903474 | − | 0.428643i | \(-0.141008\pi\) | |||||||
\(230\) | −1.36789e29 | + | 1.02766e28i | −0.0271387 | + | 0.00203887i | ||||
\(231\) | −3.21626e30 | −0.603109 | ||||||||
\(232\) | −4.50271e29 | − | 4.50271e29i | −0.0798234 | − | 0.0798234i | ||||
\(233\) | 2.54161e30 | − | 2.54161e30i | 0.426072 | − | 0.426072i | −0.461216 | − | 0.887288i | \(-0.652587\pi\) |
0.887288 | + | 0.461216i | \(0.152587\pi\) | |||||||
\(234\) | 2.33610e30i | 0.370412i | ||||||||
\(235\) | −7.54553e29 | − | 6.49100e29i | −0.113190 | − | 0.0973709i | ||||
\(236\) | −4.86447e30 | −0.690525 | ||||||||
\(237\) | 8.70143e30 | + | 8.70143e30i | 1.16913 | + | 1.16913i | ||||
\(238\) | 9.95195e28 | − | 9.95195e28i | 0.0126592 | − | 0.0126592i | ||||
\(239\) | 1.11754e31i | 1.34614i | 0.739579 | + | 0.673070i | \(0.235025\pi\) | ||||
−0.739579 | + | 0.673070i | \(0.764975\pi\) | |||||||
\(240\) | −1.06737e31 | + | 1.24078e31i | −1.21778 | + | 1.41562i | ||||
\(241\) | 1.81933e30 | 0.196648 | 0.0983241 | − | 0.995154i | \(-0.468652\pi\) | ||||
0.0983241 | + | 0.995154i | \(0.468652\pi\) | |||||||
\(242\) | −5.54848e29 | − | 5.54848e29i | −0.0568296 | − | 0.0568296i | ||||
\(243\) | 2.69784e31 | − | 2.69784e31i | 2.61900 | − | 2.61900i | ||||
\(244\) | − | 1.31340e31i | − | 1.20873i | ||||||
\(245\) | 4.45911e29 | + | 5.93539e30i | 0.0389125 | + | 0.517953i | ||||
\(246\) | 3.41730e30 | 0.282831 | ||||||||
\(247\) | −9.73166e30 | − | 9.73166e30i | −0.764058 | − | 0.764058i | ||||
\(248\) | −1.60847e29 | + | 1.60847e29i | −0.0119824 | + | 0.0119824i | ||||
\(249\) | 1.89435e31i | 1.33927i | ||||||||
\(250\) | −1.27440e30 | − | 7.99761e29i | −0.0855233 | − | 0.0536710i | ||||
\(251\) | −2.40455e31 | −1.53206 | −0.766029 | − | 0.642805i | \(-0.777770\pi\) | ||||
−0.766029 | + | 0.642805i | \(0.777770\pi\) | |||||||
\(252\) | 2.17293e31 | + | 2.17293e31i | 1.31474 | + | 1.31474i | ||||
\(253\) | −1.49801e30 | + | 1.49801e30i | −0.0860890 | + | 0.0860890i | ||||
\(254\) | − | 1.23964e30i | − | 0.0676793i | ||||||
\(255\) | 9.46924e30 | − | 7.11401e29i | 0.491239 | − | 0.0369056i | ||||
\(256\) | 1.82461e31 | 0.899603 | ||||||||
\(257\) | 2.23633e31 | + | 2.23633e31i | 1.04811 | + | 1.04811i | 0.998783 | + | 0.0493257i | \(0.0157072\pi\) |
0.0493257 | + | 0.998783i | \(0.484293\pi\) | |||||||
\(258\) | −3.80816e30 | + | 3.80816e30i | −0.169691 | + | 0.169691i | ||||
\(259\) | − | 1.34884e31i | − | 0.571560i | ||||||
\(260\) | −2.52060e31 | − | 2.16833e31i | −1.01590 | − | 0.873920i | ||||
\(261\) | −3.97091e31 | −1.52252 | ||||||||
\(262\) | 1.27725e30 | + | 1.27725e30i | 0.0465971 | + | 0.0465971i | ||||
\(263\) | −8.57416e30 | + | 8.57416e30i | −0.297692 | + | 0.297692i | −0.840109 | − | 0.542417i | \(-0.817509\pi\) |
0.542417 | + | 0.840109i | \(0.317509\pi\) | |||||||
\(264\) | − | 5.28885e30i | − | 0.174787i | ||||||
\(265\) | 1.96525e31 | − | 2.28453e31i | 0.618333 | − | 0.718787i | ||||
\(266\) | 1.86467e30 | 0.0558650 | ||||||||
\(267\) | −7.72958e31 | − | 7.72958e31i | −2.20551 | − | 2.20551i | ||||
\(268\) | 1.73952e31 | − | 1.73952e31i | 0.472800 | − | 0.472800i | ||||
\(269\) | 3.97784e31i | 1.03007i | 0.857168 | + | 0.515037i | \(0.172222\pi\) | ||||
−0.857168 | + | 0.515037i | \(0.827778\pi\) | |||||||
\(270\) | −1.00944e30 | − | 1.34363e31i | −0.0249087 | − | 0.331552i | ||||
\(271\) | 5.99004e31 | 1.40873 | 0.704366 | − | 0.709837i | \(-0.251231\pi\) | ||||
0.704366 | + | 0.709837i | \(0.251231\pi\) | |||||||
\(272\) | −7.82139e30 | − | 7.82139e30i | −0.175343 | − | 0.175343i | ||||
\(273\) | −5.98041e31 | + | 5.98041e31i | −1.27825 | + | 1.27825i | ||||
\(274\) | 4.95825e30i | 0.101058i | ||||||||
\(275\) | −2.29754e31 | + | 3.47177e30i | −0.446621 | + | 0.0674879i | ||||
\(276\) | 2.77114e31 | 0.513854 | ||||||||
\(277\) | 3.13521e31 | + | 3.13521e31i | 0.554664 | + | 0.554664i | 0.927783 | − | 0.373120i | \(-0.121712\pi\) |
−0.373120 | + | 0.927783i | \(0.621712\pi\) | |||||||
\(278\) | 2.59935e30 | − | 2.59935e30i | 0.0438816 | − | 0.0438816i | ||||
\(279\) | 1.41850e31i | 0.228547i | ||||||||
\(280\) | 9.03065e30 | − | 6.78450e29i | 0.138888 | − | 0.0104343i | ||||
\(281\) | 6.05769e31 | 0.889457 | 0.444728 | − | 0.895666i | \(-0.353300\pi\) | ||||
0.444728 | + | 0.895666i | \(0.353300\pi\) | |||||||
\(282\) | −1.46442e30 | − | 1.46442e30i | −0.0205318 | − | 0.0205318i | ||||
\(283\) | −2.00009e31 | + | 2.00009e31i | −0.267810 | + | 0.267810i | −0.828217 | − | 0.560407i | \(-0.810645\pi\) |
0.560407 | + | 0.828217i | \(0.310645\pi\) | |||||||
\(284\) | − | 6.79643e31i | − | 0.869245i | ||||||
\(285\) | 9.53759e31 | + | 8.20466e31i | 1.16535 | + | 1.00248i | ||||
\(286\) | 5.28892e30 | 0.0617459 | ||||||||
\(287\) | 6.39005e31 | + | 6.39005e31i | 0.712918 | + | 0.712918i | ||||
\(288\) | −5.36893e31 | + | 5.36893e31i | −0.572513 | + | 0.572513i | ||||
\(289\) | − | 9.16832e31i | − | 0.934583i | ||||||
\(290\) | −3.79624e30 | + | 4.41298e30i | −0.0369981 | + | 0.0430088i | ||||
\(291\) | −6.93155e31 | −0.645984 | ||||||||
\(292\) | −6.39862e31 | − | 6.39862e31i | −0.570307 | − | 0.570307i | ||||
\(293\) | 1.04124e32 | − | 1.04124e32i | 0.887710 | − | 0.887710i | −0.106593 | − | 0.994303i | \(-0.533994\pi\) |
0.994303 | + | 0.106593i | \(0.0339942\pi\) | |||||||
\(294\) | 1.23847e31i | 0.101011i | ||||||||
\(295\) | 6.69720e30 | + | 8.91443e31i | 0.0522645 | + | 0.695677i | ||||
\(296\) | 2.21804e31 | 0.165644 | ||||||||
\(297\) | −1.47144e32 | − | 1.47144e32i | −1.05174 | − | 1.05174i | ||||
\(298\) | 6.39660e30 | − | 6.39660e30i | 0.0437661 | − | 0.0437661i | ||||
\(299\) | 5.57089e31i | 0.364921i | ||||||||
\(300\) | 2.44621e32 | + | 1.80397e32i | 1.53432 | + | 1.13150i | ||||
\(301\) | −1.42418e32 | −0.855464 | ||||||||
\(302\) | 3.58300e30 | + | 3.58300e30i | 0.0206137 | + | 0.0206137i | ||||
\(303\) | −1.37602e32 | + | 1.37602e32i | −0.758353 | + | 0.758353i | ||||
\(304\) | − | 1.46547e32i | − | 0.773786i | ||||||
\(305\) | −2.40689e32 | + | 1.80824e31i | −1.21775 | + | 0.0914865i | ||||
\(306\) | 1.44322e31 | 0.0699769 | ||||||||
\(307\) | 1.27797e32 | + | 1.27797e32i | 0.593910 | + | 0.593910i | 0.938685 | − | 0.344775i | \(-0.112045\pi\) |
−0.344775 | + | 0.938685i | \(0.612045\pi\) | |||||||
\(308\) | 4.91951e31 | − | 4.91951e31i | 0.219160 | − | 0.219160i | ||||
\(309\) | − | 5.88074e32i | − | 2.51172i | ||||||
\(310\) | 1.57642e30 | + | 1.35610e30i | 0.00645609 | + | 0.00555381i | ||||
\(311\) | −1.29479e32 | −0.508528 | −0.254264 | − | 0.967135i | \(-0.581833\pi\) | ||||
−0.254264 | + | 0.967135i | \(0.581833\pi\) | |||||||
\(312\) | −9.83424e31 | − | 9.83424e31i | −0.370451 | − | 0.370451i | ||||
\(313\) | −3.36725e32 | + | 3.36725e32i | −1.21674 | + | 1.21674i | −0.247979 | + | 0.968765i | \(0.579767\pi\) |
−0.968765 | + | 0.247979i | \(0.920233\pi\) | |||||||
\(314\) | 3.61452e31i | 0.125304i | ||||||||
\(315\) | 3.68287e32 | − | 4.28119e32i | 1.22504 | − | 1.42406i | ||||
\(316\) | −2.66189e32 | −0.849686 | ||||||||
\(317\) | 1.47703e32 | + | 1.47703e32i | 0.452501 | + | 0.452501i | 0.896184 | − | 0.443683i | \(-0.146328\pi\) |
−0.443683 | + | 0.896184i | \(0.646328\pi\) | |||||||
\(318\) | 4.43377e31 | − | 4.43377e31i | 0.130383 | − | 0.130383i | ||||
\(319\) | 8.99011e31i | 0.253797i | ||||||||
\(320\) | −2.59630e31 | − | 3.45585e32i | −0.0703727 | − | 0.936710i | ||||
\(321\) | 1.15275e33 | 3.00034 | ||||||||
\(322\) | −5.33715e30 | − | 5.33715e30i | −0.0133408 | − | 0.0133408i | ||||
\(323\) | −6.01213e31 | + | 6.01213e31i | −0.144343 | + | 0.144343i | ||||
\(324\) | 1.55906e33i | 3.59566i | ||||||||
\(325\) | −3.62657e32 | + | 4.91767e32i | −0.803549 | + | 1.08962i | ||||
\(326\) | 1.11920e31 | 0.0238276 | ||||||||
\(327\) | −1.79557e32 | − | 1.79557e32i | −0.367351 | − | 0.367351i | ||||
\(328\) | −1.05079e32 | + | 1.05079e32i | −0.206611 | + | 0.206611i | ||||
\(329\) | − | 5.47668e31i | − | 0.103507i | ||||||
\(330\) | −4.82124e31 | + | 3.62208e30i | −0.0875946 | + | 0.00658076i | ||||
\(331\) | 6.74699e32 | 1.17855 | 0.589273 | − | 0.807934i | \(-0.299414\pi\) | ||||
0.589273 | + | 0.807934i | \(0.299414\pi\) | |||||||
\(332\) | −2.89754e32 | − | 2.89754e32i | −0.486670 | − | 0.486670i | ||||
\(333\) | 9.78034e32 | − | 9.78034e32i | 1.57972 | − | 1.57972i | ||||
\(334\) | − | 9.66622e31i | − | 0.150159i | ||||||
\(335\) | −3.42727e32 | − | 2.94829e32i | −0.512112 | − | 0.440542i | ||||
\(336\) | −9.00579e32 | −1.29453 | ||||||||
\(337\) | 7.95724e31 | + | 7.95724e31i | 0.110046 | + | 0.110046i | 0.759986 | − | 0.649940i | \(-0.225206\pi\) |
−0.649940 | + | 0.759986i | \(0.725206\pi\) | |||||||
\(338\) | 4.46910e31 | − | 4.46910e31i | 0.0594707 | − | 0.0594707i | ||||
\(339\) | − | 6.31276e32i | − | 0.808394i | ||||||
\(340\) | −1.33958e32 | + | 1.55720e32i | −0.165098 | + | 0.191920i | ||||
\(341\) | 3.21148e31 | 0.0380976 | ||||||||
\(342\) | 1.35206e32 | + | 1.35206e32i | 0.154404 | + | 0.154404i | ||||
\(343\) | −6.77439e32 | + | 6.77439e32i | −0.744812 | + | 0.744812i | ||||
\(344\) | − | 2.34194e32i | − | 0.247923i | ||||||
\(345\) | −3.81518e31 | − | 5.07827e32i | −0.0388926 | − | 0.517688i | ||||
\(346\) | −1.51982e32 | −0.149211 | ||||||||
\(347\) | 1.06237e33 | + | 1.06237e33i | 1.00460 | + | 1.00460i | 0.999989 | + | 0.00461146i | \(0.00146788\pi\) |
0.00461146 | + | 0.999989i | \(0.498532\pi\) | |||||||
\(348\) | 8.31531e32 | − | 8.31531e32i | 0.757440 | − | 0.757440i | ||||
\(349\) | 1.25891e33i | 1.10475i | 0.833597 | + | 0.552373i | \(0.186278\pi\) | ||||
−0.833597 | + | 0.552373i | \(0.813722\pi\) | |||||||
\(350\) | −1.23693e31 | − | 8.18574e31i | −0.0104583 | − | 0.0692107i | ||||
\(351\) | −5.47209e33 | −4.45821 | ||||||||
\(352\) | 1.21552e32 | + | 1.21552e32i | 0.0954352 | + | 0.0954352i | ||||
\(353\) | 1.12455e33 | − | 1.12455e33i | 0.850957 | − | 0.850957i | −0.139294 | − | 0.990251i | \(-0.544483\pi\) |
0.990251 | + | 0.139294i | \(0.0444832\pi\) | |||||||
\(354\) | 1.86007e32i | 0.135671i | ||||||||
\(355\) | −1.24549e33 | + | 9.35704e31i | −0.875731 | + | 0.0657915i | ||||
\(356\) | 2.36459e33 | 1.60290 | ||||||||
\(357\) | 3.69465e32 | + | 3.69465e32i | 0.241483 | + | 0.241483i | ||||
\(358\) | −9.72062e31 | + | 9.72062e31i | −0.0612653 | + | 0.0612653i | ||||
\(359\) | − | 2.90240e33i | − | 1.76413i | −0.471130 | − | 0.882064i | \(-0.656154\pi\) | ||
0.471130 | − | 0.882064i | \(-0.343846\pi\) | |||||||
\(360\) | 7.04002e32 | + | 6.05614e32i | 0.412707 | + | 0.355029i | ||||
\(361\) | 6.41977e32 | 0.363016 | ||||||||
\(362\) | 4.89882e31 | + | 4.89882e31i | 0.0267227 | + | 0.0267227i | ||||
\(363\) | 2.05987e33 | − | 2.05987e33i | 1.08406 | − | 1.08406i | ||||
\(364\) | − | 1.82950e33i | − | 0.928995i | ||||||
\(365\) | −1.08449e33 | + | 1.26068e33i | −0.531397 | + | 0.617728i | ||||
\(366\) | −5.02218e32 | −0.237486 | ||||||||
\(367\) | 9.90575e32 | + | 9.90575e32i | 0.452094 | + | 0.452094i | 0.896049 | − | 0.443955i | \(-0.146425\pi\) |
−0.443955 | + | 0.896049i | \(0.646425\pi\) | |||||||
\(368\) | −4.19455e32 | + | 4.19455e32i | −0.184784 | + | 0.184784i | ||||
\(369\) | 9.26680e33i | 3.94082i | ||||||||
\(370\) | −1.51903e31 | − | 2.02193e32i | −0.00623653 | − | 0.0830125i | ||||
\(371\) | 1.65815e33 | 0.657300 | ||||||||
\(372\) | −2.97042e32 | − | 2.97042e32i | −0.113700 | − | 0.113700i | ||||
\(373\) | −2.06595e33 | + | 2.06595e33i | −0.763669 | + | 0.763669i | −0.976984 | − | 0.213315i | \(-0.931574\pi\) |
0.213315 | + | 0.976984i | \(0.431574\pi\) | |||||||
\(374\) | − | 3.26745e31i | − | 0.0116648i | ||||||
\(375\) | 2.96910e33 | − | 4.73118e33i | 1.02381 | − | 1.63141i | ||||
\(376\) | 9.00589e31 | 0.0299975 | ||||||||
\(377\) | 1.67165e33 | + | 1.67165e33i | 0.537907 | + | 0.537907i | ||||
\(378\) | 5.24249e32 | − | 5.24249e32i | 0.162984 | − | 0.162984i | ||||
\(379\) | − | 1.23086e33i | − | 0.369742i | −0.982763 | − | 0.184871i | \(-0.940813\pi\) | ||
0.982763 | − | 0.184871i | \(-0.0591867\pi\) | |||||||
\(380\) | −2.71380e33 | + | 2.03881e32i | −0.787756 | + | 0.0591822i | ||||
\(381\) | 4.60213e33 | 1.29102 | ||||||||
\(382\) | 6.43934e31 | + | 6.43934e31i | 0.0174589 | + | 0.0174589i | ||||
\(383\) | −2.72533e33 | + | 2.72533e33i | −0.714225 | + | 0.714225i | −0.967416 | − | 0.253191i | \(-0.918520\pi\) |
0.253191 | + | 0.967416i | \(0.418520\pi\) | |||||||
\(384\) | − | 2.99282e33i | − | 0.758185i | ||||||
\(385\) | −9.69259e32 | − | 8.33799e32i | −0.237383 | − | 0.204208i | ||||
\(386\) | 1.22578e32 | 0.0290252 | ||||||||
\(387\) | −1.03267e34 | − | 1.03267e34i | −2.36439 | − | 2.36439i | ||||
\(388\) | 1.06023e33 | − | 1.06023e33i | 0.234741 | − | 0.234741i | ||||
\(389\) | − | 3.51517e33i | − | 0.752665i | −0.926485 | − | 0.376332i | \(-0.877185\pi\) | ||
0.926485 | − | 0.376332i | \(-0.122815\pi\) | |||||||
\(390\) | −8.29125e32 | + | 9.63825e32i | −0.171704 | + | 0.199599i | ||||
\(391\) | 3.44165e32 | 0.0689395 | ||||||||
\(392\) | −3.80817e32 | − | 3.80817e32i | −0.0737901 | − | 0.0737901i | ||||
\(393\) | −4.74177e33 | + | 4.74177e33i | −0.888867 | + | 0.888867i | ||||
\(394\) | 1.72575e32i | 0.0312987i | ||||||||
\(395\) | 3.66478e32 | + | 4.87808e33i | 0.0643111 | + | 0.856025i | ||||
\(396\) | 7.13422e33 | 1.21146 | ||||||||
\(397\) | 2.77671e33 | + | 2.77671e33i | 0.456303 | + | 0.456303i | 0.897440 | − | 0.441137i | \(-0.145425\pi\) |
−0.441137 | + | 0.897440i | \(0.645425\pi\) | |||||||
\(398\) | 4.09026e32 | − | 4.09026e32i | 0.0650536 | − | 0.0650536i | ||||
\(399\) | 6.92255e33i | 1.06566i | ||||||||
\(400\) | −6.43330e33 | + | 9.72123e32i | −0.958637 | + | 0.144858i | ||||
\(401\) | −9.69690e33 | −1.39880 | −0.699401 | − | 0.714730i | \(-0.746550\pi\) | ||||
−0.699401 | + | 0.714730i | \(0.746550\pi\) | |||||||
\(402\) | −6.65157e32 | − | 6.65157e32i | −0.0928936 | − | 0.0928936i | ||||
\(403\) | 5.97152e32 | − | 5.97152e32i | 0.0807457 | − | 0.0807457i | ||||
\(404\) | − | 4.20945e33i | − | 0.551148i | ||||||
\(405\) | 2.85708e34 | − | 2.14645e33i | 3.62248 | − | 0.272148i | ||||
\(406\) | −3.20302e32 | −0.0393297 | ||||||||
\(407\) | −2.21426e33 | − | 2.21426e33i | −0.263331 | − | 0.263331i | ||||
\(408\) | −6.07551e32 | + | 6.07551e32i | −0.0699843 | + | 0.0699843i | ||||
\(409\) | − | 1.68312e34i | − | 1.87807i | −0.343826 | − | 0.939033i | \(-0.611723\pi\) | ||
0.343826 | − | 0.939033i | \(-0.388277\pi\) | |||||||
\(410\) | 1.02984e33 | + | 8.85918e32i | 0.111322 | + | 0.0957642i | ||||
\(411\) | −1.84074e34 | −1.92774 | ||||||||
\(412\) | 8.99501e33 | + | 8.99501e33i | 0.912721 | + | 0.912721i | ||||
\(413\) | −3.47818e33 | + | 3.47818e33i | −0.341980 | + | 0.341980i | ||||
\(414\) | − | 7.73988e32i | − | 0.0737445i | ||||||
\(415\) | −4.91100e33 | + | 5.70884e33i | −0.453466 | + | 0.527136i | ||||
\(416\) | 4.52036e33 | 0.404538 | ||||||||
\(417\) | 9.65004e33 | + | 9.65004e33i | 0.837068 | + | 0.837068i | ||||
\(418\) | 3.06106e32 | − | 3.06106e32i | 0.0257383 | − | 0.0257383i | ||||
\(419\) | − | 9.88043e33i | − | 0.805366i | −0.915339 | − | 0.402683i | \(-0.868078\pi\) | ||
0.915339 | − | 0.402683i | \(-0.131922\pi\) | |||||||
\(420\) | 1.25292e33 | + | 1.66772e34i | 0.0990105 | + | 1.31790i | ||||
\(421\) | 1.54830e34 | 1.18628 | 0.593141 | − | 0.805098i | \(-0.297888\pi\) | ||||
0.593141 | + | 0.805098i | \(0.297888\pi\) | |||||||
\(422\) | 1.69570e33 | + | 1.69570e33i | 0.125976 | + | 0.125976i | ||||
\(423\) | 3.97112e33 | − | 3.97112e33i | 0.286080 | − | 0.286080i | ||||
\(424\) | 2.72668e33i | 0.190492i | ||||||||
\(425\) | 3.03810e33 | + | 2.24046e33i | 0.205847 | + | 0.151803i | ||||
\(426\) | −2.59882e33 | −0.170785 | ||||||||
\(427\) | −9.39104e33 | − | 9.39104e33i | −0.598620 | − | 0.598620i | ||||
\(428\) | −1.76322e34 | + | 1.76322e34i | −1.09028 | + | 1.09028i | ||||
\(429\) | 1.96350e34i | 1.17784i | ||||||||
\(430\) | −2.13488e33 | + | 1.60388e32i | −0.124246 | + | 0.00933431i | ||||
\(431\) | 2.61174e34 | 1.47477 | 0.737387 | − | 0.675470i | \(-0.236059\pi\) | ||||
0.737387 | + | 0.675470i | \(0.236059\pi\) | |||||||
\(432\) | −4.12016e34 | − | 4.12016e34i | −2.25749 | − | 2.25749i | ||||
\(433\) | 1.79399e34 | − | 1.79399e34i | 0.953844 | − | 0.953844i | −0.0451367 | − | 0.998981i | \(-0.514372\pi\) |
0.998981 | + | 0.0451367i | \(0.0143723\pi\) | |||||||
\(434\) | 1.14419e32i | 0.00590382i | ||||||||
\(435\) | −1.63831e34 | − | 1.40935e34i | −0.820420 | − | 0.705762i | ||||
\(436\) | 5.49291e33 | 0.266979 | ||||||||
\(437\) | 3.22426e33 | + | 3.22426e33i | 0.152115 | + | 0.152115i | ||||
\(438\) | −2.44670e33 | + | 2.44670e33i | −0.112051 | + | 0.112051i | ||||
\(439\) | − | 2.56244e34i | − | 1.13924i | −0.821909 | − | 0.569619i | \(-0.807091\pi\) | ||
0.821909 | − | 0.569619i | \(-0.192909\pi\) | |||||||
\(440\) | 1.37111e33 | − | 1.59386e33i | 0.0591815 | − | 0.0687962i | ||||
\(441\) | −3.35840e34 | −1.40744 | ||||||||
\(442\) | −6.07559e32 | − | 6.07559e32i | −0.0247229 | − | 0.0247229i | ||||
\(443\) | −1.85005e34 | + | 1.85005e34i | −0.731029 | + | 0.731029i | −0.970824 | − | 0.239795i | \(-0.922920\pi\) |
0.239795 | + | 0.970824i | \(0.422920\pi\) | |||||||
\(444\) | 4.09612e34i | 1.57179i | ||||||||
\(445\) | −3.25547e33 | − | 4.33325e34i | −0.121320 | − | 1.61486i | ||||
\(446\) | 3.15626e33 | 0.114240 | ||||||||
\(447\) | 2.37473e34 | + | 2.37473e34i | 0.834865 | + | 0.834865i | ||||
\(448\) | 1.34838e34 | − | 1.34838e34i | 0.460467 | − | 0.460467i | ||||
\(449\) | − | 3.29255e33i | − | 0.109227i | −0.998508 | − | 0.0546134i | \(-0.982607\pi\) | ||
0.998508 | − | 0.0546134i | \(-0.0173926\pi\) | |||||||
\(450\) | 5.03855e33 | − | 6.83234e33i | 0.162384 | − | 0.220195i | ||||
\(451\) | 2.09800e34 | 0.656916 | ||||||||
\(452\) | 9.65582e33 | + | 9.65582e33i | 0.293758 | + | 0.293758i | ||||
\(453\) | −1.33018e34 | + | 1.33018e34i | −0.393219 | + | 0.393219i | ||||
\(454\) | − | 1.38106e33i | − | 0.0396722i | ||||||
\(455\) | −3.35266e34 | + | 2.51877e33i | −0.935926 | + | 0.0703138i | ||||
\(456\) | −1.13835e34 | −0.308840 | ||||||||
\(457\) | 2.99714e34 | + | 2.99714e34i | 0.790308 | + | 0.790308i | 0.981544 | − | 0.191236i | \(-0.0612495\pi\) |
−0.191236 | + | 0.981544i | \(0.561249\pi\) | |||||||
\(458\) | 2.38810e33 | − | 2.38810e33i | 0.0612070 | − | 0.0612070i | ||||
\(459\) | 3.38061e34i | 0.842229i | ||||||||
\(460\) | 8.35115e33 | + | 7.18403e33i | 0.202253 | + | 0.173987i | ||||
\(461\) | 4.28219e34 | 1.00822 | 0.504108 | − | 0.863640i | \(-0.331821\pi\) | ||||
0.504108 | + | 0.863640i | \(0.331821\pi\) | |||||||
\(462\) | −1.88112e33 | − | 1.88112e33i | −0.0430597 | − | 0.0430597i | ||||
\(463\) | −2.59467e33 | + | 2.59467e33i | −0.0577469 | + | 0.0577469i | −0.735390 | − | 0.677644i | \(-0.763001\pi\) |
0.677644 | + | 0.735390i | \(0.263001\pi\) | |||||||
\(464\) | 2.51730e34i | 0.544756i | ||||||||
\(465\) | −5.03452e33 | + | 5.85243e33i | −0.105942 | + | 0.123154i | ||||
\(466\) | 2.97306e33 | 0.0608397 | ||||||||
\(467\) | −7.71974e33 | − | 7.71974e33i | −0.153633 | − | 0.153633i | 0.626106 | − | 0.779738i | \(-0.284648\pi\) |
−0.779738 | + | 0.626106i | \(0.784648\pi\) | |||||||
\(468\) | 1.32656e35 | − | 1.32656e35i | 2.56762 | − | 2.56762i | ||||
\(469\) | − | 2.48757e34i | − | 0.468305i | ||||||
\(470\) | −6.16770e31 | − | 8.20964e32i | −0.00112941 | − | 0.0150332i | ||||
\(471\) | −1.34188e35 | −2.39025 | ||||||||
\(472\) | −5.71954e33 | − | 5.71954e33i | −0.0991095 | − | 0.0991095i | ||||
\(473\) | −2.33796e34 | + | 2.33796e34i | −0.394132 | + | 0.394132i | ||||
\(474\) | 1.01785e34i | 0.166942i | ||||||||
\(475\) | 7.47250e33 | + | 4.94514e34i | 0.119247 | + | 0.789154i | ||||
\(476\) | −1.13025e34 | −0.175502 | ||||||||
\(477\) | 1.20232e35 | + | 1.20232e35i | 1.81669 | + | 1.81669i | ||||
\(478\) | −6.53624e33 | + | 6.53624e33i | −0.0961092 | + | 0.0961092i | ||||
\(479\) | − | 9.13862e34i | − | 1.30773i | −0.756610 | − | 0.653867i | \(-0.773146\pi\) | ||
0.756610 | − | 0.653867i | \(-0.226854\pi\) | |||||||
\(480\) | −4.12064e34 | + | 3.09574e33i | −0.573890 | + | 0.0431149i | ||||
\(481\) | −8.23454e34 | −1.11623 | ||||||||
\(482\) | 1.06408e33 | + | 1.06408e33i | 0.0140399 | + | 0.0140399i | ||||
\(483\) | 1.98141e34 | − | 1.98141e34i | 0.254484 | − | 0.254484i | ||||
\(484\) | 6.30143e34i | 0.787861i | ||||||||
\(485\) | −2.08891e34 | − | 1.79697e34i | −0.254259 | − | 0.218725i | ||||
\(486\) | 3.15581e34 | 0.373973 | ||||||||
\(487\) | −7.26028e33 | − | 7.26028e33i | −0.0837678 | − | 0.0837678i | 0.663981 | − | 0.747749i | \(-0.268865\pi\) |
−0.747749 | + | 0.663981i | \(0.768865\pi\) | |||||||
\(488\) | 1.54427e34 | − | 1.54427e34i | 0.173486 | − | 0.173486i | ||||
\(489\) | 4.15503e34i | 0.454526i | ||||||||
\(490\) | −3.21067e33 | + | 3.73228e33i | −0.0342016 | + | 0.0397581i | ||||
\(491\) | −9.35922e34 | −0.970913 | −0.485456 | − | 0.874261i | \(-0.661346\pi\) | ||||
−0.485456 | + | 0.874261i | \(0.661346\pi\) | |||||||
\(492\) | −1.94052e35 | − | 1.94052e35i | −1.96052 | − | 1.96052i | ||||
\(493\) | 1.03273e34 | − | 1.03273e34i | 0.101619 | − | 0.101619i | ||||
\(494\) | − | 1.13837e34i | − | 0.109102i | ||||||
\(495\) | −9.82209e33 | − | 1.30739e35i | −0.0916931 | − | 1.22050i | ||||
\(496\) | 8.99239e33 | 0.0817736 | ||||||||
\(497\) | −4.85956e34 | − | 4.85956e34i | −0.430491 | − | 0.430491i | ||||
\(498\) | −1.10796e34 | + | 1.10796e34i | −0.0956188 | + | 0.0956188i | ||||
\(499\) | − | 3.71291e34i | − | 0.312182i | −0.987743 | − | 0.156091i | \(-0.950111\pi\) | ||
0.987743 | − | 0.156091i | \(-0.0498893\pi\) | |||||||
\(500\) | 2.69523e34 | + | 1.17781e35i | 0.220793 | + | 0.964865i | ||||
\(501\) | 3.58857e35 | 2.86438 | ||||||||
\(502\) | −1.40637e34 | − | 1.40637e34i | −0.109383 | − | 0.109383i | ||||
\(503\) | 6.29619e34 | − | 6.29619e34i | 0.477193 | − | 0.477193i | −0.427040 | − | 0.904233i | \(-0.640444\pi\) |
0.904233 | + | 0.427040i | \(0.140444\pi\) | |||||||
\(504\) | 5.10977e34i | 0.377403i | ||||||||
\(505\) | −7.71408e34 | + | 5.79540e33i | −0.555260 | + | 0.0417153i | ||||
\(506\) | −1.75230e33 | −0.0122929 | ||||||||
\(507\) | 1.65915e35 | + | 1.65915e35i | 1.13444 | + | 1.13444i | ||||
\(508\) | −7.03929e34 | + | 7.03929e34i | −0.469138 | + | 0.469138i | ||||
\(509\) | 2.89188e35i | 1.87866i | 0.343010 | + | 0.939332i | \(0.388554\pi\) | ||||
−0.343010 | + | 0.939332i | \(0.611446\pi\) | |||||||
\(510\) | 5.95443e33 | + | 5.12226e33i | 0.0377075 | + | 0.0324377i | ||||
\(511\) | −9.15024e34 | −0.564886 | ||||||||
\(512\) | 5.69206e34 | + | 5.69206e34i | 0.342579 | + | 0.342579i | ||||
\(513\) | −3.16708e35 | + | 3.16708e35i | −1.85837 | + | 1.85837i | ||||
\(514\) | 2.61596e34i | 0.149662i | ||||||||
\(515\) | 1.52455e35 | − | 1.77223e35i | 0.850448 | − | 0.988612i | ||||
\(516\) | 4.32494e35 | 2.35252 | ||||||||
\(517\) | −8.99058e33 | − | 8.99058e33i | −0.0476882 | − | 0.0476882i | ||||
\(518\) | 7.88903e33 | − | 7.88903e33i | 0.0408072 | − | 0.0408072i | ||||
\(519\) | − | 5.64230e35i | − | 2.84630i | ||||||
\(520\) | −4.14189e33 | − | 5.51314e34i | −0.0203777 | − | 0.271241i | ||||
\(521\) | −1.51202e35 | −0.725548 | −0.362774 | − | 0.931877i | \(-0.618170\pi\) | ||||
−0.362774 | + | 0.931877i | \(0.618170\pi\) | |||||||
\(522\) | −2.32249e34 | − | 2.32249e34i | −0.108702 | − | 0.108702i | ||||
\(523\) | −1.20055e35 | + | 1.20055e35i | −0.548099 | + | 0.548099i | −0.925891 | − | 0.377792i | \(-0.876684\pi\) |
0.377792 | + | 0.925891i | \(0.376684\pi\) | |||||||
\(524\) | − | 1.45057e35i | − | 0.646001i | ||||||
\(525\) | 3.03895e35 | − | 4.59209e34i | 1.32024 | − | 0.199498i | ||||
\(526\) | −1.00297e34 | −0.0425081 | ||||||||
\(527\) | −3.68915e33 | − | 3.68915e33i | −0.0152542 | − | 0.0152542i | ||||
\(528\) | −1.47840e35 | + | 1.47840e35i | −0.596418 | + | 0.596418i | ||||
\(529\) | 2.35595e35i | 0.927349i | ||||||||
\(530\) | 2.48560e34 | − | 1.86737e33i | 0.0954652 | − | 0.00717207i | ||||
\(531\) | −5.04402e35 | −1.89038 | ||||||||
\(532\) | −1.05885e35 | − | 1.05885e35i | −0.387244 | − | 0.387244i | ||||
\(533\) | 3.90108e35 | − | 3.90108e35i | 1.39229 | − | 1.39229i | ||||
\(534\) | − | 9.04171e34i | − | 0.314930i | ||||||
\(535\) | 3.47396e35 | + | 2.98845e35i | 1.18093 | + | 1.01589i | ||||
\(536\) | 4.09058e34 | 0.135720 | ||||||||
\(537\) | −3.60877e35 | − | 3.60877e35i | −1.16867 | − | 1.16867i | ||||
\(538\) | −2.32655e34 | + | 2.32655e34i | −0.0735433 | + | 0.0735433i | ||||
\(539\) | 7.60340e34i | 0.234614i | ||||||||
\(540\) | −7.05662e35 | + | 8.20304e35i | −2.12558 | + | 2.47091i | ||||
\(541\) | 1.60345e35 | 0.471510 | 0.235755 | − | 0.971812i | \(-0.424244\pi\) | ||||
0.235755 | + | 0.971812i | \(0.424244\pi\) | |||||||
\(542\) | 3.50344e34 | + | 3.50344e34i | 0.100578 | + | 0.100578i | ||||
\(543\) | −1.81868e35 | + | 1.81868e35i | −0.509752 | + | 0.509752i | ||||
\(544\) | − | 2.79264e34i | − | 0.0764239i | ||||||
\(545\) | −7.56240e33 | − | 1.00661e35i | −0.0202072 | − | 0.268971i | ||||
\(546\) | −6.99562e34 | −0.182525 | ||||||||
\(547\) | 3.88776e34 | + | 3.88776e34i | 0.0990522 | + | 0.0990522i | 0.754896 | − | 0.655844i | \(-0.227687\pi\) |
−0.655844 | + | 0.754896i | \(0.727687\pi\) | |||||||
\(548\) | 2.81555e35 | − | 2.81555e35i | 0.700512 | − | 0.700512i | ||||
\(549\) | − | 1.36188e36i | − | 3.30901i | ||||||
\(550\) | −1.54684e34 | − | 1.14072e34i | −0.0367054 | − | 0.0270686i | ||||
\(551\) | 1.93500e35 | 0.448445 | ||||||||
\(552\) | 3.25824e34 | + | 3.25824e34i | 0.0737523 | + | 0.0737523i | ||||
\(553\) | −1.90330e35 | + | 1.90330e35i | −0.420804 | + | 0.420804i | ||||
\(554\) | 3.66743e34i | 0.0792017i | ||||||||
\(555\) | 7.50638e35 | − | 5.63936e34i | 1.58351 | − | 0.118966i | ||||
\(556\) | −2.95209e35 | −0.608355 | ||||||||
\(557\) | −1.15013e35 | − | 1.15013e35i | −0.231541 | − | 0.231541i | 0.581795 | − | 0.813336i | \(-0.302351\pi\) |
−0.813336 | + | 0.581795i | \(0.802351\pi\) | |||||||
\(558\) | −8.29649e33 | + | 8.29649e33i | −0.0163174 | + | 0.0163174i | ||||
\(559\) | 8.69454e35i | 1.67068i | ||||||||
\(560\) | −2.71400e35 | − | 2.33470e35i | −0.509525 | − | 0.438316i | ||||
\(561\) | 1.21304e35 | 0.222513 | ||||||||
\(562\) | 3.54300e34 | + | 3.54300e34i | 0.0635038 | + | 0.0635038i | ||||
\(563\) | −1.31797e35 | + | 1.31797e35i | −0.230832 | + | 0.230832i | −0.813040 | − | 0.582208i | \(-0.802189\pi\) |
0.582208 | + | 0.813040i | \(0.302189\pi\) | |||||||
\(564\) | 1.66315e35i | 0.284644i | ||||||||
\(565\) | 1.63655e35 | − | 1.90242e35i | 0.273716 | − | 0.318184i | ||||
\(566\) | −2.33962e34 | −0.0382412 | ||||||||
\(567\) | 1.11476e36 | + | 1.11476e36i | 1.78074 | + | 1.78074i | ||||
\(568\) | 7.99110e34 | − | 7.99110e34i | 0.124761 | − | 0.124761i | ||||
\(569\) | 7.73690e35i | 1.18061i | 0.807179 | + | 0.590307i | \(0.200993\pi\) | ||||
−0.807179 | + | 0.590307i | \(0.799007\pi\) | |||||||
\(570\) | 7.79601e33 | + | 1.03770e35i | 0.0116278 | + | 0.154775i | ||||
\(571\) | −3.49753e35 | −0.509908 | −0.254954 | − | 0.966953i | \(-0.582060\pi\) | ||||
−0.254954 | + | 0.966953i | \(0.582060\pi\) | |||||||
\(572\) | −3.00332e35 | − | 3.00332e35i | −0.428009 | − | 0.428009i | ||||
\(573\) | −2.39060e35 | + | 2.39060e35i | −0.333040 | + | 0.333040i | ||||
\(574\) | 7.47479e34i | 0.101799i | ||||||||
\(575\) | 1.20154e35 | − | 1.62930e35i | 0.159977 | − | 0.216930i | ||||
\(576\) | 1.95541e36 | 2.54534 | ||||||||
\(577\) | −6.69537e35 | − | 6.69537e35i | −0.852096 | − | 0.852096i | 0.138295 | − | 0.990391i | \(-0.455838\pi\) |
−0.990391 | + | 0.138295i | \(0.955838\pi\) | |||||||
\(578\) | 5.36234e34 | − | 5.36234e34i | 0.0667256 | − | 0.0667256i | ||||
\(579\) | 4.55067e35i | 0.553674i | ||||||||
\(580\) | 4.66162e35 | − | 3.50216e34i | 0.554591 | − | 0.0416650i | ||||
\(581\) | −4.14358e35 | −0.482044 | ||||||||
\(582\) | −4.05411e34 | − | 4.05411e34i | −0.0461208 | − | 0.0461208i | ||||
\(583\) | 2.72204e35 | − | 2.72204e35i | 0.302833 | − | 0.302833i | ||||
\(584\) | − | 1.50467e35i | − | 0.163710i | ||||||
\(585\) | −2.61363e36 | − | 2.24836e36i | −2.78111 | − | 2.39244i | ||||
\(586\) | 1.21799e35 | 0.126758 | ||||||||
\(587\) | 3.03209e34 | + | 3.03209e34i | 0.0308636 | + | 0.0308636i | 0.722370 | − | 0.691507i | \(-0.243053\pi\) |
−0.691507 | + | 0.722370i | \(0.743053\pi\) | |||||||
\(588\) | 7.03268e35 | − | 7.03268e35i | 0.700189 | − | 0.700189i | ||||
\(589\) | − | 6.91226e34i | − | 0.0673164i | ||||||
\(590\) | −4.82215e34 | + | 5.60555e34i | −0.0459372 | + | 0.0534001i | ||||
\(591\) | −6.40681e35 | −0.597042 | ||||||||
\(592\) | −6.20011e35 | − | 6.20011e35i | −0.565220 | − | 0.565220i | ||||
\(593\) | −1.06738e36 | + | 1.06738e36i | −0.951935 | + | 0.951935i | −0.998897 | − | 0.0469616i | \(-0.985046\pi\) |
0.0469616 | + | 0.998897i | \(0.485046\pi\) | |||||||
\(594\) | − | 1.72123e35i | − | 0.150181i | ||||||
\(595\) | 1.55607e34 | + | 2.07124e35i | 0.0132834 | + | 0.176812i | ||||
\(596\) | −7.26464e35 | −0.606754 | ||||||||
\(597\) | 1.51850e36 | + | 1.51850e36i | 1.24094 | + | 1.24094i | ||||
\(598\) | −3.25829e34 | + | 3.25829e34i | −0.0260540 | + | 0.0260540i | ||||
\(599\) | 1.50216e36i | 1.17535i | 0.809096 | + | 0.587676i | \(0.199957\pi\) | ||||
−0.809096 | + | 0.587676i | \(0.800043\pi\) | |||||||
\(600\) | 7.55127e34 | + | 4.99727e35i | 0.0578167 | + | 0.382619i | ||||
\(601\) | −1.91246e36 | −1.43293 | −0.716463 | − | 0.697625i | \(-0.754240\pi\) | ||||
−0.716463 | + | 0.697625i | \(0.754240\pi\) | |||||||
\(602\) | −8.32973e34 | − | 8.32973e34i | −0.0610768 | − | 0.0610768i | ||||
\(603\) | 1.80373e36 | − | 1.80373e36i | 1.29433 | − | 1.29433i | ||||
\(604\) | − | 4.06922e35i | − | 0.285779i | ||||||
\(605\) | 1.15478e36 | − | 8.67554e34i | 0.793739 | − | 0.0596316i | ||||
\(606\) | −1.60961e35 | −0.108287 | ||||||||
\(607\) | 1.04936e36 | + | 1.04936e36i | 0.690990 | + | 0.690990i | 0.962450 | − | 0.271460i | \(-0.0875065\pi\) |
−0.271460 | + | 0.962450i | \(0.587506\pi\) | |||||||
\(608\) | 2.61624e35 | − | 2.61624e35i | 0.168629 | − | 0.168629i | ||||
\(609\) | − | 1.18912e36i | − | 0.750239i | ||||||
\(610\) | −1.51349e35 | − | 1.30197e35i | −0.0934744 | − | 0.0804108i | ||||
\(611\) | −3.34347e35 | −0.202144 | ||||||||
\(612\) | −8.19536e35 | − | 8.19536e35i | −0.485065 | − | 0.485065i | ||||
\(613\) | 1.26683e36 | − | 1.26683e36i | 0.734063 | − | 0.734063i | −0.237359 | − | 0.971422i | \(-0.576282\pi\) |
0.971422 | + | 0.237359i | \(0.0762819\pi\) | |||||||
\(614\) | 1.49491e35i | 0.0848058i | ||||||||
\(615\) | −3.28896e36 | + | 3.82328e36i | −1.82676 | + | 2.12354i | ||||
\(616\) | 1.15685e35 | 0.0629112 | ||||||||
\(617\) | 1.65895e35 | + | 1.65895e35i | 0.0883338 | + | 0.0883338i | 0.749893 | − | 0.661559i | \(-0.230105\pi\) |
−0.661559 | + | 0.749893i | \(0.730105\pi\) | |||||||
\(618\) | 3.43951e35 | − | 3.43951e35i | 0.179327 | − | 0.179327i | ||||
\(619\) | − | 2.32624e36i | − | 1.18762i | −0.804607 | − | 0.593808i | \(-0.797624\pi\) | ||
0.804607 | − | 0.593808i | \(-0.202376\pi\) | |||||||
\(620\) | −1.25105e34 | − | 1.66524e35i | −0.00625437 | − | 0.0832500i | ||||
\(621\) | 1.81299e36 | 0.887575 | ||||||||
\(622\) | −7.57294e34 | − | 7.57294e34i | −0.0363069 | − | 0.0363069i | ||||
\(623\) | 1.69072e36 | − | 1.69072e36i | 0.793830 | − | 0.793830i | ||||
\(624\) | 5.49796e36i | 2.52815i | ||||||||
\(625\) | 2.12131e36 | − | 6.56074e35i | 0.955352 | − | 0.295469i | ||||
\(626\) | −3.93886e35 | −0.173742 | ||||||||
\(627\) | 1.13641e36 | + | 1.13641e36i | 0.490974 | + | 0.490974i | ||||
\(628\) | 2.05251e36 | − | 2.05251e36i | 0.868580 | − | 0.868580i | ||||
\(629\) | 5.08723e35i | 0.210874i | ||||||||
\(630\) | 4.65800e35 | − | 3.49944e34i | 0.189135 | − | 0.0142093i | ||||
\(631\) | 2.11178e36 | 0.839976 | 0.419988 | − | 0.907530i | \(-0.362034\pi\) | ||||
0.419988 | + | 0.907530i | \(0.362034\pi\) | |||||||
\(632\) | −3.12980e35 | − | 3.12980e35i | −0.121953 | − | 0.121953i | ||||
\(633\) | −6.29526e36 | + | 6.29526e36i | −2.40307 | + | 2.40307i | ||||
\(634\) | 1.72776e35i | 0.0646136i | ||||||||
\(635\) | 1.38691e36 | + | 1.19308e36i | 0.508146 | + | 0.437130i | ||||
\(636\) | −5.03545e36 | −1.80757 | ||||||||
\(637\) | 1.41380e36 | + | 1.41380e36i | 0.497250 | + | 0.497250i | ||||
\(638\) | −5.25811e34 | + | 5.25811e34i | −0.0181201 | + | 0.0181201i | ||||
\(639\) | − | 7.04729e36i | − | 2.37964i | ||||||
\(640\) | 7.75874e35 | − | 9.01923e35i | 0.256715 | − | 0.298421i | ||||
\(641\) | 8.23577e35 | 0.267024 | 0.133512 | − | 0.991047i | \(-0.457375\pi\) | ||||
0.133512 | + | 0.991047i | \(0.457375\pi\) | |||||||
\(642\) | 6.74219e35 | + | 6.74219e35i | 0.214213 | + | 0.214213i | ||||
\(643\) | 7.37575e34 | − | 7.37575e34i | 0.0229648 | − | 0.0229648i | −0.695531 | − | 0.718496i | \(-0.744831\pi\) |
0.718496 | + | 0.695531i | \(0.244831\pi\) | |||||||
\(644\) | 6.06141e35i | 0.184951i | ||||||||
\(645\) | −5.95439e35 | − | 7.92571e36i | −0.178058 | − | 2.37007i | ||||
\(646\) | −7.03272e34 | −0.0206111 | ||||||||
\(647\) | −2.25014e36 | − | 2.25014e36i | −0.646329 | − | 0.646329i | 0.305775 | − | 0.952104i | \(-0.401085\pi\) |
−0.952104 | + | 0.305775i | \(0.901085\pi\) | |||||||
\(648\) | −1.83311e36 | + | 1.83311e36i | −0.516076 | + | 0.516076i | ||||
\(649\) | 1.14196e36i | 0.315116i | ||||||||
\(650\) | −4.99733e35 | + | 7.55137e34i | −0.135165 | + | 0.0204245i | ||||
\(651\) | −4.24780e35 | −0.112619 | ||||||||
\(652\) | −6.35542e35 | − | 6.35542e35i | −0.165168 | − | 0.165168i | ||||
\(653\) | −4.31573e36 | + | 4.31573e36i | −1.09947 | + | 1.09947i | −0.104995 | + | 0.994473i | \(0.533483\pi\) |
−0.994473 | + | 0.104995i | \(0.966517\pi\) | |||||||
\(654\) | − | 2.10038e35i | − | 0.0524549i | ||||||
\(655\) | −2.65827e36 | + | 1.99709e35i | −0.650821 | + | 0.0488946i | ||||
\(656\) | 5.87456e36 | 1.41002 | ||||||||
\(657\) | −6.63479e36 | − | 6.63479e36i | −1.56127 | − | 1.56127i | ||||
\(658\) | 3.20319e34 | − | 3.20319e34i | 0.00739002 | − | 0.00739002i | ||||
\(659\) | − | 3.38273e36i | − | 0.765168i | −0.923921 | − | 0.382584i | \(-0.875034\pi\) | ||
0.923921 | − | 0.382584i | \(-0.124966\pi\) | |||||||
\(660\) | 2.94343e36 | + | 2.53207e36i | 0.652803 | + | 0.561570i | ||||
\(661\) | 8.18651e36 | 1.78025 | 0.890123 | − | 0.455721i | \(-0.150619\pi\) | ||||
0.890123 | + | 0.455721i | \(0.150619\pi\) | |||||||
\(662\) | 3.94616e35 | + | 3.94616e35i | 0.0841436 | + | 0.0841436i | ||||
\(663\) | 2.25555e36 | − | 2.25555e36i | 0.471604 | − | 0.471604i | ||||
\(664\) | − | 6.81374e35i | − | 0.139701i | ||||||
\(665\) | −1.79464e36 | + | 2.08619e36i | −0.360824 | + | 0.419443i | ||||
\(666\) | 1.14406e36 | 0.225571 | ||||||||
\(667\) | −5.53844e35 | − | 5.53844e35i | −0.107091 | − | 0.107091i | ||||
\(668\) | −5.48898e36 | + | 5.48898e36i | −1.04087 | + | 1.04087i | ||||
\(669\) | 1.17176e37i | 2.17920i | ||||||||
\(670\) | −2.80144e34 | − | 3.72892e35i | −0.00510986 | − | 0.0680158i | ||||
\(671\) | −3.08329e36 | −0.551596 | ||||||||
\(672\) | −1.60776e36 | − | 1.60776e36i | −0.282112 | − | 0.282112i | ||||
\(673\) | 3.37485e36 | − | 3.37485e36i | 0.580843 | − | 0.580843i | −0.354292 | − | 0.935135i | \(-0.615278\pi\) |
0.935135 | + | 0.354292i | \(0.115278\pi\) | |||||||
\(674\) | 9.30801e34i | 0.0157137i | ||||||||
\(675\) | 1.60041e37 | + | 1.18023e37i | 2.65022 | + | 1.95442i | ||||
\(676\) | −5.07557e36 | −0.824476 | ||||||||
\(677\) | −2.01599e36 | − | 2.01599e36i | −0.321244 | − | 0.321244i | 0.528000 | − | 0.849244i | \(-0.322942\pi\) |
−0.849244 | + | 0.528000i | \(0.822942\pi\) | |||||||
\(678\) | 3.69219e35 | − | 3.69219e35i | 0.0577162 | − | 0.0577162i | ||||
\(679\) | − | 1.51617e36i | − | 0.232509i | ||||||
\(680\) | −3.40597e35 | + | 2.55882e34i | −0.0512419 | + | 0.00384968i | ||||
\(681\) | 5.12717e36 | 0.756772 | ||||||||
\(682\) | 1.87832e34 | + | 1.87832e34i | 0.00272002 | + | 0.00272002i | ||||
\(683\) | 3.31684e36 | − | 3.31684e36i | 0.471255 | − | 0.471255i | −0.431066 | − | 0.902320i | \(-0.641862\pi\) |
0.902320 | + | 0.431066i | \(0.141862\pi\) | |||||||
\(684\) | − | 1.53554e37i | − | 2.14058i | ||||||
\(685\) | −5.54730e36 | − | 4.77203e36i | −0.758759 | − | 0.652718i | ||||
\(686\) | −7.92438e35 | −0.106353 | ||||||||
\(687\) | 8.86578e36 | + | 8.86578e36i | 1.16756 | + | 1.16756i | ||||
\(688\) | −6.54646e36 | + | 6.54646e36i | −0.845974 | + | 0.845974i | ||||
\(689\) | − | 1.01229e37i | − | 1.28367i | ||||||
\(690\) | 2.74703e35 | − | 3.19331e35i | 0.0341841 | − | 0.0397377i | ||||
\(691\) | −9.98786e36 | −1.21971 | −0.609857 | − | 0.792512i | \(-0.708773\pi\) | ||||
−0.609857 | + | 0.792512i | \(0.708773\pi\) | |||||||
\(692\) | 8.63030e36 | + | 8.63030e36i | 1.03430 | + | 1.03430i | ||||
\(693\) | 5.10109e36 | − | 5.10109e36i | 0.599972 | − | 0.599972i | ||||
\(694\) | 1.24271e36i | 0.143449i | ||||||||
\(695\) | 4.06431e35 | + | 5.40988e36i | 0.0460452 | + | 0.612894i | ||||
\(696\) | 1.95539e36 | 0.217427 | ||||||||
\(697\) | −2.41005e36 | − | 2.41005e36i | −0.263027 | − | 0.263027i | ||||
\(698\) | −7.36305e35 | + | 7.36305e35i | −0.0788747 | + | 0.0788747i | ||||
\(699\) | 1.10375e37i | 1.16056i | ||||||||
\(700\) | −3.94589e36 | + | 5.35068e36i | −0.407259 | + | 0.552248i | ||||
\(701\) | −1.70246e36 | −0.172481 | −0.0862406 | − | 0.996274i | \(-0.527485\pi\) | ||||
−0.0862406 | + | 0.996274i | \(0.527485\pi\) | |||||||
\(702\) | −3.20050e36 | − | 3.20050e36i | −0.318299 | − | 0.318299i | ||||
\(703\) | −4.76589e36 | + | 4.76589e36i | −0.465291 | + | 0.465291i | ||||
\(704\) | − | 4.42704e36i | − | 0.424296i | ||||||
\(705\) | 3.04782e36 | − | 2.28975e35i | 0.286768 | − | 0.0215442i | ||||
\(706\) | 1.31545e36 | 0.121510 | ||||||||
\(707\) | −3.00983e36 | − | 3.00983e36i | −0.272954 | − | 0.272954i | ||||
\(708\) | 1.05625e37 | − | 1.05625e37i | 0.940444 | − | 0.940444i | ||||
\(709\) | 1.99265e36i | 0.174193i | 0.996200 | + | 0.0870963i | \(0.0277588\pi\) | ||||
−0.996200 | + | 0.0870963i | \(0.972241\pi\) | |||||||
\(710\) | −7.83184e35 | − | 6.73730e35i | −0.0672211 | − | 0.0578265i | ||||
\(711\) | −2.76014e37 | −2.32609 | ||||||||
\(712\) | 2.78023e36 | + | 2.78023e36i | 0.230060 | + | 0.230060i | ||||
\(713\) | −1.97846e35 | + | 1.97846e35i | −0.0160755 | + | 0.0160755i | ||||
\(714\) | 4.32183e35i | 0.0344819i | ||||||||
\(715\) | −5.09028e36 | + | 5.91725e36i | −0.398807 | + | 0.463598i | ||||
\(716\) | 1.10397e37 | 0.849356 | ||||||||
\(717\) | −2.42657e37 | − | 2.42657e37i | −1.83334 | − | 1.83334i | ||||
\(718\) | 1.69755e36 | − | 1.69755e36i | 0.125952 | − | 0.125952i | ||||
\(719\) | − | 9.34472e36i | − | 0.680912i | −0.940261 | − | 0.340456i | \(-0.889419\pi\) | ||
0.940261 | − | 0.340456i | \(-0.110581\pi\) | |||||||
\(720\) | −2.75026e36 | − | 3.66079e37i | −0.196812 | − | 2.61971i | ||||
\(721\) | 1.28632e37 | 0.904044 | ||||||||
\(722\) | 3.75478e35 | + | 3.75478e35i | 0.0259180 | + | 0.0259180i | ||||
\(723\) | −3.95040e36 | + | 3.95040e36i | −0.267820 | + | 0.267820i | ||||
\(724\) | − | 5.56361e36i | − | 0.370472i | ||||||
\(725\) | −1.28358e36 | − | 8.49448e36i | −0.0839518 | − | 0.555575i | ||||
\(726\) | 2.40954e36 | 0.154795 | ||||||||
\(727\) | 2.09778e37 | + | 2.09778e37i | 1.32377 | + | 1.32377i | 0.910697 | + | 0.413075i | \(0.135545\pi\) |
0.413075 | + | 0.910697i | \(0.364455\pi\) | |||||||
\(728\) | 2.15108e36 | − | 2.15108e36i | 0.133336 | − | 0.133336i | ||||
\(729\) | 5.74987e37i | 3.50106i | ||||||||
\(730\) | −1.37164e36 | + | 1.03048e35i | −0.0820431 | + | 0.00616370i | ||||
\(731\) | 5.37141e36 | 0.315618 | ||||||||
\(732\) | 2.85185e37 | + | 2.85185e37i | 1.64620 | + | 1.64620i | ||||
\(733\) | −1.48463e37 | + | 1.48463e37i | −0.841913 | + | 0.841913i | −0.989108 | − | 0.147194i | \(-0.952976\pi\) |
0.147194 | + | 0.989108i | \(0.452976\pi\) | |||||||
\(734\) | 1.15873e36i | 0.0645555i | ||||||||
\(735\) | −1.38560e37 | − | 1.19196e37i | −0.758409 | − | 0.652417i | ||||
\(736\) | −1.49767e36 | −0.0805386 | ||||||||
\(737\) | −4.08363e36 | − | 4.08363e36i | −0.215759 | − | 0.215759i | ||||
\(738\) | −5.41994e36 | + | 5.41994e36i | −0.281360 | + | 0.281360i | ||||
\(739\) | − | 5.46072e36i | − | 0.278530i | −0.990255 | − | 0.139265i | \(-0.955526\pi\) | ||
0.990255 | − | 0.139265i | \(-0.0444740\pi\) | |||||||
\(740\) | −1.06190e37 | + | 1.23441e37i | −0.532194 | + | 0.618655i | ||||
\(741\) | 4.22617e37 | 2.08118 | ||||||||
\(742\) | 9.69816e35 | + | 9.69816e35i | 0.0469287 | + | 0.0469287i | ||||
\(743\) | 2.68229e37 | − | 2.68229e37i | 1.27541 | − | 1.27541i | 0.332206 | − | 0.943207i | \(-0.392207\pi\) |
0.943207 | − | 0.332206i | \(-0.107793\pi\) | |||||||
\(744\) | − | 6.98512e35i | − | 0.0326381i | ||||||
\(745\) | 1.00016e36 | + | 1.33129e37i | 0.0459240 | + | 0.611281i | ||||
\(746\) | −2.41666e36 | −0.109046 | ||||||||
\(747\) | −3.00449e37 | − | 3.00449e37i | −1.33230 | − | 1.33230i | ||||
\(748\) | −1.85543e36 | + | 1.85543e36i | −0.0808579 | + | 0.0808579i | ||||
\(749\) | 2.52146e37i | 1.07991i | ||||||||
\(750\) | 4.50372e36 | − | 1.03060e36i | 0.189572 | − | 0.0433805i | ||||
\(751\) | −4.40539e36 | −0.182249 | −0.0911245 | − | 0.995840i | \(-0.529046\pi\) | ||||
−0.0911245 | + | 0.995840i | \(0.529046\pi\) | |||||||
\(752\) | −2.51743e36 | − | 2.51743e36i | −0.102359 | − | 0.102359i | ||||
\(753\) | 5.22112e37 | − | 5.22112e37i | 2.08655 | − | 2.08655i | ||||
\(754\) | 1.95542e36i | 0.0768090i | ||||||||
\(755\) | −7.45709e36 | + | 5.60233e35i | −0.287911 | + | 0.0216301i | ||||
\(756\) | −5.95392e37 | −2.25954 | ||||||||
\(757\) | 8.92923e36 | + | 8.92923e36i | 0.333095 | + | 0.333095i | 0.853761 | − | 0.520666i | \(-0.174316\pi\) |
−0.520666 | + | 0.853761i | \(0.674316\pi\) | |||||||
\(758\) | 7.19902e35 | − | 7.19902e35i | 0.0263982 | − | 0.0263982i | ||||
\(759\) | − | 6.50540e36i | − | 0.234494i | ||||||
\(760\) | −3.43055e36 | − | 2.95111e36i | −0.121559 | − | 0.104571i | ||||
\(761\) | 2.83232e37 | 0.986600 | 0.493300 | − | 0.869859i | \(-0.335790\pi\) | ||||
0.493300 | + | 0.869859i | \(0.335790\pi\) | |||||||
\(762\) | 2.69168e36 | + | 2.69168e36i | 0.0921741 | + | 0.0921741i | ||||
\(763\) | 3.92752e36 | − | 3.92752e36i | 0.132221 | − | 0.132221i | ||||
\(764\) | − | 7.31318e36i | − | 0.242043i | ||||||
\(765\) | −1.38902e37 | + | 1.61468e37i | −0.451970 | + | 0.525397i | ||||
\(766\) | −3.18797e36 | −0.101986 | ||||||||
\(767\) | 2.12340e37 | + | 2.12340e37i | 0.667870 | + | 0.667870i | ||||
\(768\) | −3.96187e37 | + | 3.96187e37i | −1.22519 | + | 1.22519i | ||||
\(769\) | − | 2.43349e37i | − | 0.739923i | −0.929047 | − | 0.369962i | \(-0.879371\pi\) | ||
0.929047 | − | 0.369962i | \(-0.120629\pi\) | |||||||
\(770\) | −7.92271e34 | − | 1.05457e36i | −0.00236861 | − | 0.0315279i | ||||
\(771\) | −9.71173e37 | −2.85489 | ||||||||
\(772\) | −6.96058e36 | − | 6.96058e36i | −0.201197 | − | 0.201197i | ||||
\(773\) | −2.28771e37 | + | 2.28771e37i | −0.650230 | + | 0.650230i | −0.953048 | − | 0.302818i | \(-0.902073\pi\) |
0.302818 | + | 0.953048i | \(0.402073\pi\) | |||||||
\(774\) | − | 1.20797e37i | − | 0.337616i | ||||||
\(775\) | −3.03442e36 | + | 4.58526e35i | −0.0833977 | + | 0.0126021i | ||||
\(776\) | 2.49319e36 | 0.0673835 | ||||||||
\(777\) | 2.92879e37 | + | 2.92879e37i | 0.778422 | + | 0.778422i | ||||
\(778\) | 2.05594e36 | − | 2.05594e36i | 0.0537374 | − | 0.0537374i | ||||
\(779\) | − | 4.51565e37i | − | 1.16073i | ||||||
\(780\) | 1.01813e38 | − | 7.64896e36i | 2.57379 | − | 0.193363i | ||||
\(781\) | −1.59550e37 | −0.396674 | ||||||||
\(782\) | 2.01294e35 | + | 2.01294e35i | 0.00492202 | + | 0.00492202i | ||||
\(783\) | 5.44022e37 | − | 5.44022e37i | 1.30832 | − | 1.30832i | ||||
\(784\) | 2.12901e37i | 0.503581i | ||||||||
\(785\) | −4.04393e37 | − | 3.47877e37i | −0.940801 | − | 0.809319i | ||||
\(786\) | −5.54670e36 | −0.126923 | ||||||||
\(787\) | −3.51698e37 | − | 3.51698e37i | −0.791586 | − | 0.791586i | 0.190166 | − | 0.981752i | \(-0.439097\pi\) |
−0.981752 | + | 0.190166i | \(0.939097\pi\) | |||||||
\(788\) | 9.79968e36 | − | 9.79968e36i | 0.216956 | − | 0.216956i | ||||
\(789\) | − | 3.72350e37i | − | 0.810868i | ||||||
\(790\) | −2.63873e36 | + | 3.06742e36i | −0.0565253 | + | 0.0657085i | ||||
\(791\) | 1.38081e37 | 0.290965 | ||||||||
\(792\) | 8.38827e36 | + | 8.38827e36i | 0.173878 | + | 0.173878i | ||||
\(793\) | −5.73316e37 | + | 5.73316e37i | −1.16908 | + | 1.16908i | ||||
\(794\) | 3.24807e36i | 0.0651566i | ||||||||
\(795\) | 6.93259e36 | + | 9.22776e37i | 0.136812 | + | 1.82106i | ||||
\(796\) | −4.64532e37 | −0.901875 | ||||||||
\(797\) | −1.57853e36 | − | 1.57853e36i | −0.0301506 | − | 0.0301506i | 0.691871 | − | 0.722021i | \(-0.256787\pi\) |
−0.722021 | + | 0.691871i | \(0.756787\pi\) | |||||||
\(798\) | −4.04884e36 | + | 4.04884e36i | −0.0760840 | + | 0.0760840i | ||||
\(799\) | 2.06557e36i | 0.0381884i | ||||||||
\(800\) | −1.32206e37 | − | 9.74961e36i | −0.240481 | − | 0.177344i | ||||
\(801\) | 2.45187e38 | 4.38808 | ||||||||
\(802\) | −5.67150e36 | − | 5.67150e36i | −0.0998690 | − | 0.0998690i | ||||
\(803\) | −1.50211e37 | + | 1.50211e37i | −0.260256 | + | 0.260256i | ||||
\(804\) | 7.55421e37i | 1.28784i | ||||||||
\(805\) | 1.11079e37 | − | 8.34510e35i | 0.186331 | − | 0.0139986i | ||||
\(806\) | 6.98521e35 | 0.0115299 | ||||||||
\(807\) | −8.63729e37 | − | 8.63729e37i | −1.40288 | − | 1.40288i | ||||
\(808\) | 4.94939e36 | − | 4.94939e36i | 0.0791050 | − | 0.0791050i | ||||
\(809\) | 8.05592e37i | 1.26702i | 0.773734 | + | 0.633511i | \(0.218387\pi\) | ||||
−0.773734 | + | 0.633511i | \(0.781613\pi\) | |||||||
\(810\) | 1.79658e37 | + | 1.54550e37i | 0.278062 | + | 0.239201i | ||||
\(811\) | 1.27337e38 | 1.93948 | 0.969739 | − | 0.244143i | \(-0.0785068\pi\) | ||||
0.969739 | + | 0.244143i | \(0.0785068\pi\) | |||||||
\(812\) | 1.81884e37 | + | 1.81884e37i | 0.272625 | + | 0.272625i | ||||
\(813\) | −1.30065e38 | + | 1.30065e38i | −1.91859 | + | 1.91859i | ||||
\(814\) | − | 2.59015e36i | − | 0.0376016i | ||||||
\(815\) | −1.07717e37 | + | 1.25217e37i | −0.153899 | + | 0.178901i | ||||
\(816\) | 3.39659e37 | 0.477608 | ||||||||
\(817\) | 5.03213e37 | + | 5.03213e37i | 0.696410 | + | 0.696410i | ||||
\(818\) | 9.84416e36 | − | 9.84416e36i | 0.134087 | − | 0.134087i | ||||
\(819\) | − | 1.89702e38i | − | 2.54321i | ||||||
\(820\) | −8.17289e36 | − | 1.08787e38i | −0.107844 | − | 1.43548i | ||||
\(821\) | −1.02720e38 | −1.33412 | −0.667061 | − | 0.745003i | \(-0.732448\pi\) | ||||
−0.667061 | + | 0.745003i | \(0.732448\pi\) | |||||||
\(822\) | −1.07661e37 | − | 1.07661e37i | −0.137634 | − | 0.137634i | ||||
\(823\) | 4.91705e37 | − | 4.91705e37i | 0.618738 | − | 0.618738i | −0.326469 | − | 0.945208i | \(-0.605859\pi\) |
0.945208 | + | 0.326469i | \(0.105859\pi\) | |||||||
\(824\) | 2.11523e37i | 0.262001i | ||||||||
\(825\) | 4.23493e37 | − | 5.74261e37i | 0.516350 | − | 0.700177i | ||||
\(826\) | −4.06861e36 | −0.0488321 | ||||||||
\(827\) | −5.51949e37 | − | 5.51949e37i | −0.652119 | − | 0.652119i | 0.301384 | − | 0.953503i | \(-0.402552\pi\) |
−0.953503 | + | 0.301384i | \(0.902552\pi\) | |||||||
\(828\) | −4.39510e37 | + | 4.39510e37i | −0.511181 | + | 0.511181i | ||||
\(829\) | − | 2.06117e36i | − | 0.0235996i | −0.999930 | − | 0.0117998i | \(-0.996244\pi\) | ||
0.999930 | − | 0.0117998i | \(-0.00375609\pi\) | |||||||
\(830\) | −6.21131e36 | + | 4.66640e35i | −0.0700112 | + | 0.00525977i | ||||
\(831\) | −1.36153e38 | −1.51082 | ||||||||
\(832\) | −8.23176e37 | − | 8.23176e37i | −0.899269 | − | 0.899269i | ||||
\(833\) | 8.73432e36 | − | 8.73432e36i | 0.0939386 | − | 0.0939386i | ||||
\(834\) | 1.12882e37i | 0.119527i | ||||||||
\(835\) | 1.08146e38 | + | 9.30319e37i | 1.12742 | + | 0.969857i | ||||
\(836\) | −3.47646e37 | −0.356825 | ||||||||
\(837\) | −1.94337e37 | − | 1.94337e37i | −0.196393 | − | 0.196393i | ||||
\(838\) | 5.77884e36 | − | 5.77884e36i | 0.0575000 | − | 0.0575000i | ||||
\(839\) | 9.33800e37i | 0.914847i | 0.889249 | + | 0.457424i | \(0.151228\pi\) | ||||
−0.889249 | + | 0.457424i | \(0.848772\pi\) | |||||||
\(840\) | −1.81355e37 | + | 2.10818e37i | −0.174944 | + | 0.203366i | ||||
\(841\) | 7.20423e37 | 0.684289 | ||||||||
\(842\) | 9.05566e36 | + | 9.05566e36i | 0.0846960 | + | 0.0846960i | ||||
\(843\) | −1.31534e38 | + | 1.31534e38i | −1.21137 | + | 1.21137i | ||||
\(844\) | − | 1.92581e38i | − | 1.74647i | ||||||
\(845\) | 6.98783e36 | + | 9.30129e37i | 0.0624029 | + | 0.830627i | ||||
\(846\) | 4.64523e36 | 0.0408500 | ||||||||
\(847\) | 4.50563e37 | + | 4.50563e37i | 0.390185 | + | 0.390185i | ||||
\(848\) | 7.62193e37 | − | 7.62193e37i | 0.650008 | − | 0.650008i | ||||
\(849\) | − | 8.68580e37i | − | 0.729474i | ||||||
\(850\) | 4.66517e35 | + | 3.08731e36i | 0.00385853 | + | 0.0255349i | ||||
\(851\) | 2.72824e37 | 0.222227 | ||||||||
\(852\) | 1.47574e38 | + | 1.47574e38i | 1.18385 | + | 1.18385i | ||||
\(853\) | 1.28609e38 | − | 1.28609e38i | 1.01610 | − | 1.01610i | 0.0162296 | − | 0.999868i | \(-0.494834\pi\) |
0.999868 | − | 0.0162296i | \(-0.00516628\pi\) | |||||||
\(854\) | − | 1.09852e37i | − | 0.0854783i | ||||||
\(855\) | −2.81397e38 | + | 2.11407e37i | −2.15655 | + | 0.162017i | ||||
\(856\) | −4.14631e37 | −0.312970 | ||||||||
\(857\) | −7.53926e37 | − | 7.53926e37i | −0.560503 | − | 0.560503i | 0.368947 | − | 0.929450i | \(-0.379718\pi\) |
−0.929450 | + | 0.368947i | \(0.879718\pi\) | |||||||
\(858\) | −1.14841e37 | + | 1.14841e37i | −0.0840934 | + | 0.0840934i | ||||
\(859\) | 1.12492e38i | 0.811357i | 0.914016 | + | 0.405678i | \(0.132965\pi\) | ||||
−0.914016 | + | 0.405678i | \(0.867035\pi\) | |||||||
\(860\) | 1.30337e38 | + | 1.12122e38i | 0.925951 | + | 0.796544i | ||||
\(861\) | −2.77501e38 | −1.94188 | ||||||||
\(862\) | 1.52755e37 | + | 1.52755e37i | 0.105293 | + | 0.105293i | ||||
\(863\) | 7.22473e37 | − | 7.22473e37i | 0.490547 | − | 0.490547i | −0.417931 | − | 0.908479i | \(-0.637245\pi\) |
0.908479 | + | 0.417931i | \(0.137245\pi\) | |||||||
\(864\) | − | 1.47111e38i | − | 0.983934i | ||||||
\(865\) | 1.46274e38 | − | 1.70037e38i | 0.963733 | − | 1.12030i | ||||
\(866\) | 2.09853e37 | 0.136202 | ||||||||
\(867\) | 1.99076e38 | + | 1.99076e38i | 1.27283 | + | 1.27283i | ||||
\(868\) | 6.49732e36 | − | 6.49732e36i | 0.0409240 | − | 0.0409240i | ||||
\(869\) | 6.24895e37i | 0.387748i | ||||||||
\(870\) | −1.33915e36 | − | 1.78251e37i | −0.00818616 | − | 0.108964i | ||||
\(871\) | −1.51864e38 | −0.914576 | ||||||||
\(872\) | 6.45844e36 | + | 6.45844e36i | 0.0383189 | + | 0.0383189i | ||||
\(873\) | 1.09936e38 | − | 1.09936e38i | 0.642624 | − | 0.642624i | ||||
\(874\) | 3.77159e36i | 0.0217208i | ||||||||
\(875\) | 1.03487e38 | + | 6.49443e37i | 0.587193 | + | 0.368499i | ||||
\(876\) | 2.77873e38 | 1.55343 | ||||||||
\(877\) | 1.27333e38 | + | 1.27333e38i | 0.701370 | + | 0.701370i | 0.964705 | − | 0.263334i | \(-0.0848222\pi\) |
−0.263334 | + | 0.964705i | \(0.584822\pi\) | |||||||
\(878\) | 1.49871e37 | − | 1.49871e37i | 0.0813372 | − | 0.0813372i | ||||
\(879\) | 4.52178e38i | 2.41799i | ||||||||
\(880\) | −8.28801e37 | + | 6.22658e36i | −0.436692 | + | 0.0328076i | ||||
\(881\) | −7.87063e37 | −0.408623 | −0.204312 | − | 0.978906i | \(-0.565496\pi\) | ||||
−0.204312 | + | 0.978906i | \(0.565496\pi\) | |||||||
\(882\) | −1.96425e37 | − | 1.96425e37i | −0.100486 | − | 0.100486i | ||||
\(883\) | −9.98733e36 | + | 9.98733e36i | −0.0503454 | + | 0.0503454i | −0.731831 | − | 0.681486i | \(-0.761334\pi\) |
0.681486 | + | 0.731831i | \(0.261334\pi\) | |||||||
\(884\) | 6.90007e37i | 0.342747i | ||||||||
\(885\) | −2.08105e38 | − | 1.79022e38i | −1.01864 | − | 0.876280i | ||||
\(886\) | −2.16410e37 | −0.104385 | ||||||||
\(887\) | −1.82710e38 | − | 1.82710e38i | −0.868472 | − | 0.868472i | 0.123832 | − | 0.992303i | \(-0.460482\pi\) |
−0.992303 | + | 0.123832i | \(0.960482\pi\) | |||||||
\(888\) | −4.81613e37 | + | 4.81613e37i | −0.225595 | + | 0.225595i | ||||
\(889\) | 1.00664e38i | 0.464678i | ||||||||
\(890\) | 2.34402e37 | − | 2.72483e37i | 0.106633 | − | 0.123956i | ||||
\(891\) | 3.65999e38 | 1.64085 | ||||||||
\(892\) | −1.79229e38 | − | 1.79229e38i | −0.791889 | − | 0.791889i | ||||
\(893\) | −1.93510e37 | + | 1.93510e37i | −0.0842624 | + | 0.0842624i | ||||
\(894\) | 2.77785e37i | 0.119212i | ||||||||
\(895\) | −1.51990e37 | − | 2.02310e38i | −0.0642861 | − | 0.855692i | ||||
\(896\) | 6.54632e37 | 0.272893 | ||||||||
\(897\) | −1.20963e38 | − | 1.20963e38i | −0.496995 | − | 0.496995i | ||||
\(898\) | 1.92573e36 | − | 1.92573e36i | 0.00779838 | − | 0.00779838i | ||||
\(899\) | 1.18735e37i | 0.0473917i | ||||||||
\(900\) | −6.74090e38 | + | 1.01860e38i | −2.65195 | + | 0.400731i | ||||
\(901\) | −6.25384e37 | −0.242507 | ||||||||
\(902\) | 1.22707e37 | + | 1.22707e37i | 0.0469013 | + | 0.0469013i | ||||
\(903\) | 3.09240e38 | − | 3.09240e38i | 1.16508 | − | 1.16508i | ||||
\(904\) | 2.27062e37i | 0.0843248i | ||||||||
\(905\) | −1.01957e38 | + | 7.65974e36i | −0.373236 | + | 0.0280403i | ||||
\(906\) | −1.55599e37 | −0.0561486 | ||||||||
\(907\) | −1.23099e38 | − | 1.23099e38i | −0.437886 | − | 0.437886i | 0.453414 | − | 0.891300i | \(-0.350206\pi\) |
−0.891300 | + | 0.453414i | \(0.850206\pi\) | |||||||
\(908\) | −7.84237e37 | + | 7.84237e37i | −0.274999 | + | 0.274999i | ||||
\(909\) | − | 4.36483e38i | − | 1.50882i | ||||||
\(910\) | −2.10821e37 | − | 1.81358e37i | −0.0718416 | − | 0.0618014i | ||||
\(911\) | 1.59759e38 | 0.536693 | 0.268346 | − | 0.963323i | \(-0.413523\pi\) | ||||
0.268346 | + | 0.963323i | \(0.413523\pi\) | |||||||
\(912\) | 3.18205e38 | + | 3.18205e38i | 1.05384 | + | 1.05384i | ||||
\(913\) | −6.80215e37 | + | 6.80215e37i | −0.222089 | + | 0.222089i | ||||
\(914\) | 3.50592e37i | 0.112850i | ||||||||
\(915\) | 4.83356e38 | − | 5.61882e38i | 1.53389 | − | 1.78308i | ||||
\(916\) | −2.71217e38 | −0.848547 | ||||||||
\(917\) | −1.03718e38 | − | 1.03718e38i | −0.319930 | − | 0.319930i | ||||
\(918\) | −1.97724e37 | + | 1.97724e37i | −0.0601319 | + | 0.0601319i | ||||
\(919\) | 5.38324e38i | 1.61414i | 0.590453 | + | 0.807072i | \(0.298949\pi\) | ||||
−0.590453 | + | 0.807072i | \(0.701051\pi\) | |||||||
\(920\) | 1.37227e36 | + | 1.82659e37i | 0.00405694 | + | 0.0540008i | ||||
\(921\) | −5.54983e38 | −1.61772 | ||||||||
\(922\) | 2.50456e37 | + | 2.50456e37i | 0.0719828 | + | 0.0719828i | ||||
\(923\) | −2.96672e38 | + | 2.96672e38i | −0.840727 | + | 0.840727i | ||||
\(924\) | 2.13639e38i | 0.596960i | ||||||||
\(925\) | 2.40834e38 | + | 1.77604e38i | 0.663551 | + | 0.489340i | ||||
\(926\) | −3.03512e36 | −0.00824582 | ||||||||
\(927\) | 9.32702e38 | + | 9.32702e38i | 2.49866 | + | 2.49866i | ||||
\(928\) | −4.49403e37 | + | 4.49403e37i | −0.118717 | + | 0.118717i | ||||
\(929\) | − | 1.50101e38i | − | 0.391003i | −0.980703 | − | 0.195501i | \(-0.937367\pi\) | ||
0.980703 | − | 0.195501i | \(-0.0626334\pi\) | |||||||
\(930\) | −6.36753e36 | + | 4.78377e35i | −0.0163566 | + | 0.00122883i | ||||
\(931\) | 1.63652e38 | 0.414550 | ||||||||
\(932\) | −1.68826e38 | − | 1.68826e38i | −0.421728 | − | 0.421728i | ||||
\(933\) | 2.81144e38 | − | 2.81144e38i | 0.692577 | − | 0.692577i | ||||
\(934\) | − | 9.03020e36i | − | 0.0219375i | ||||||
\(935\) | 3.65563e37 | + | 3.14473e37i | 0.0875812 | + | 0.0753412i | ||||
\(936\) | 3.11948e38 | 0.737048 | ||||||||
\(937\) | 3.00601e37 | + | 3.00601e37i | 0.0700447 | + | 0.0700447i | 0.741261 | − | 0.671217i | \(-0.234228\pi\) |
−0.671217 | + | 0.741261i | \(0.734228\pi\) | |||||||
\(938\) | 1.45492e37 | − | 1.45492e37i | 0.0334352 | − | 0.0334352i | ||||
\(939\) | − | 1.46230e39i | − | 3.31423i | ||||||
\(940\) | −4.31162e37 | + | 5.01209e37i | −0.0963782 | + | 0.112036i | ||||
\(941\) | −1.25674e38 | −0.277064 | −0.138532 | − | 0.990358i | \(-0.544238\pi\) | ||||
−0.138532 | + | 0.990358i | \(0.544238\pi\) | |||||||
\(942\) | −7.84838e37 | − | 7.84838e37i | −0.170655 | − | 0.170655i | ||||
\(943\) | −1.29249e38 | + | 1.29249e38i | −0.277189 | + | 0.277189i | ||||
\(944\) | 3.19759e38i | 0.676373i | ||||||||
\(945\) | 8.19710e37 | + | 1.09109e39i | 0.171020 | + | 2.27639i | ||||
\(946\) | −2.73484e37 | −0.0562790 | ||||||||
\(947\) | −4.87143e38 | − | 4.87143e38i | −0.988796 | − | 0.988796i | 0.0111424 | − | 0.999938i | \(-0.496453\pi\) |
−0.999938 | + | 0.0111424i | \(0.996453\pi\) | |||||||
\(948\) | 5.77990e38 | − | 5.77990e38i | 1.15721 | − | 1.15721i | ||||
\(949\) | 5.58615e38i | 1.10319i | ||||||||
\(950\) | −2.45525e37 | + | 3.32935e37i | −0.0478287 | + | 0.0648564i | ||||
\(951\) | −6.41430e38 | −1.23254 | ||||||||
\(952\) | −1.32892e37 | − | 1.32892e37i | −0.0251894 | − | 0.0251894i | ||||
\(953\) | 6.26048e38 | − | 6.26048e38i | 1.17058 | − | 1.17058i | 0.188505 | − | 0.982072i | \(-0.439636\pi\) |
0.982072 | − | 0.188505i | \(-0.0603640\pi\) | |||||||
\(954\) | 1.40642e38i | 0.259409i | ||||||||
\(955\) | −1.34018e38 | + | 1.00685e37i | −0.243849 | + | 0.0183198i | ||||
\(956\) | 7.42322e38 | 1.33242 | ||||||||
\(957\) | −1.95207e38 | − | 1.95207e38i | −0.345652 | − | 0.345652i | ||||
\(958\) | 5.34497e37 | − | 5.34497e37i | 0.0933671 | − | 0.0933671i | ||||
\(959\) | − | 4.02633e38i | − | 0.693853i | ||||||
\(960\) | 8.06760e38 | + | 6.94011e38i | 1.37157 | + | 1.17989i | ||||
\(961\) | −5.91975e38 | −0.992886 | ||||||||
\(962\) | −4.81619e37 | − | 4.81619e37i | −0.0796944 | − | 0.0796944i | ||||
\(963\) | −1.82830e39 | + | 1.82830e39i | −2.98473 | + | 2.98473i | ||||
\(964\) | − | 1.20848e38i | − | 0.194643i | ||||||
\(965\) | −1.17974e38 | + | 1.37140e38i | −0.187470 | + | 0.217926i | ||||
\(966\) | 2.31776e37 | 0.0363384 | ||||||||
\(967\) | 8.30973e38 | + | 8.30973e38i | 1.28541 | + | 1.28541i | 0.937543 | + | 0.347870i | \(0.113095\pi\) |
0.347870 | + | 0.937543i | \(0.386905\pi\) | |||||||
\(968\) | −7.40909e37 | + | 7.40909e37i | −0.113080 | + | 0.113080i | ||||
\(969\) | − | 2.61089e38i | − | 0.393169i | ||||||
\(970\) | −1.70747e36 | − | 2.27276e37i | −0.00253700 | − | 0.0337692i | ||||
\(971\) | 1.20931e39 | 1.77291 | 0.886454 | − | 0.462817i | \(-0.153161\pi\) | ||||
0.886454 | + | 0.462817i | \(0.153161\pi\) | |||||||
\(972\) | −1.79203e39 | − | 1.79203e39i | −2.59230 | − | 2.59230i | ||||
\(973\) | −2.11079e38 | + | 2.11079e38i | −0.301286 | + | 0.301286i | ||||
\(974\) | − | 8.49275e36i | − | 0.0119614i | ||||||
\(975\) | −2.80344e38 | − | 1.85525e39i | −0.389610 | − | 2.57836i | ||||
\(976\) | −8.63345e38 | −1.18396 | ||||||||
\(977\) | −4.57714e37 | − | 4.57714e37i | −0.0619391 | − | 0.0619391i | 0.675459 | − | 0.737398i | \(-0.263946\pi\) |
−0.737398 | + | 0.675459i | \(0.763946\pi\) | |||||||
\(978\) | −2.43018e37 | + | 2.43018e37i | −0.0324514 | + | 0.0324514i | ||||
\(979\) | − | 5.55101e38i | − | 0.731471i | ||||||
\(980\) | 3.94257e38 | − | 2.96195e37i | 0.512673 | − | 0.0385158i | ||||
\(981\) | 5.69565e38 | 0.730881 | ||||||||
\(982\) | −5.47399e37 | − | 5.47399e37i | −0.0693194 | − | 0.0693194i | ||||
\(983\) | 6.64842e38 | − | 6.64842e38i | 0.830850 | − | 0.830850i | −0.156783 | − | 0.987633i | \(-0.550112\pi\) |
0.987633 | + | 0.156783i | \(0.0501125\pi\) | |||||||
\(984\) | − | 4.56324e38i | − | 0.562778i | ||||||
\(985\) | −1.93077e38 | − | 1.66093e38i | −0.234995 | − | 0.202153i | ||||
\(986\) | 1.20804e37 | 0.0145105 | ||||||||
\(987\) | 1.18918e38 | + | 1.18918e38i | 0.140969 | + | 0.140969i | ||||
\(988\) | −6.46423e38 | + | 6.46423e38i | −0.756269 | + | 0.756269i | ||||
\(989\) | − | 2.88064e38i | − | 0.332612i | ||||||
\(990\) | 7.07215e37 | − | 8.22109e37i | 0.0805924 | − | 0.0936854i | ||||
\(991\) | 9.14286e38 | 1.02831 | 0.514156 | − | 0.857697i | \(-0.328105\pi\) | ||||
0.514156 | + | 0.857697i | \(0.328105\pi\) | |||||||
\(992\) | 1.60537e37 | + | 1.60537e37i | 0.0178207 | + | 0.0178207i | ||||
\(993\) | −1.46501e39 | + | 1.46501e39i | −1.60509 | + | 1.60509i | ||||
\(994\) | − | 5.68449e37i | − | 0.0614708i | ||||||
\(995\) | 6.39549e37 | + | 8.51284e38i | 0.0682611 | + | 0.908603i | ||||
\(996\) | 1.25832e39 | 1.32562 | ||||||||
\(997\) | 1.59901e38 | + | 1.59901e38i | 0.166270 | + | 0.166270i | 0.785338 | − | 0.619068i | \(-0.212489\pi\) |
−0.619068 | + | 0.785338i | \(0.712489\pi\) | |||||||
\(998\) | 2.17160e37 | − | 2.17160e37i | 0.0222886 | − | 0.0222886i | ||||
\(999\) | 2.67985e39i | 2.71493i |
(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 | 5.27.c.a.2.7 | ✓ | 24 | |
5.2 | odd | 4 | 25.27.c.b.18.6 | 24 | |||
5.3 | odd | 4 | inner | 5.27.c.a.3.7 | yes | 24 | |
5.4 | even | 2 | 25.27.c.b.7.6 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.27.c.a.2.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
5.27.c.a.3.7 | yes | 24 | 5.3 | odd | 4 | inner | |
25.27.c.b.7.6 | 24 | 5.4 | even | 2 | |||
25.27.c.b.18.6 | 24 | 5.2 | odd | 4 |