Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,19,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, 19, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.2");
S:= CuspForms(chi, 19);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 19 \) |
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: | \(10.2693068855\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1365649 x^{14} + 735328563216 x^{12} + \cdots + 22\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{39}\cdot 3^{12}\cdot 5^{25} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.8 | ||
Root | \(590.308i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.3 |
Dual form | 5.19.c.a.2.8 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 622.308 | − | 622.308i | 1.21544 | − | 1.21544i | 0.246235 | − | 0.969210i | \(-0.420807\pi\) |
0.969210 | − | 0.246235i | \(-0.0791934\pi\) | |||||||
\(3\) | −24393.6 | − | 24393.6i | −1.23933 | − | 1.23933i | −0.960277 | − | 0.279049i | \(-0.909981\pi\) |
−0.279049 | − | 0.960277i | \(-0.590019\pi\) | |||||||
\(4\) | − | 512390.i | − | 1.95461i | ||||||
\(5\) | 1.93064e6 | − | 295511.i | 0.988488 | − | 0.151301i | ||||
\(6\) | −3.03607e7 | −3.01266 | ||||||||
\(7\) | −3.63215e6 | + | 3.63215e6i | −0.0900080 | + | 0.0900080i | −0.750677 | − | 0.660669i | \(-0.770273\pi\) |
0.660669 | + | 0.750677i | \(0.270273\pi\) | |||||||
\(8\) | −1.55730e8 | − | 1.55730e8i | −1.16028 | − | 1.16028i | ||||
\(9\) | 8.02680e8i | 2.07186i | ||||||||
\(10\) | 1.01755e9 | − | 1.38535e9i | 1.01755 | − | 1.38535i | ||||
\(11\) | 1.61251e9 | 0.683861 | 0.341930 | − | 0.939725i | \(-0.388919\pi\) | ||||
0.341930 | + | 0.939725i | \(0.388919\pi\) | |||||||
\(12\) | −1.24991e10 | + | 1.24991e10i | −2.42240 | + | 2.42240i | ||||
\(13\) | −6.40234e9 | − | 6.40234e9i | −0.603738 | − | 0.603738i | 0.337565 | − | 0.941302i | \(-0.390397\pi\) |
−0.941302 | + | 0.337565i | \(0.890397\pi\) | |||||||
\(14\) | 4.52063e9i | 0.218799i | ||||||||
\(15\) | −5.43039e10 | − | 3.98868e10i | −1.41257 | − | 1.03755i | ||||
\(16\) | −5.95041e10 | −0.865898 | ||||||||
\(17\) | 6.97717e9 | − | 6.97717e9i | 0.0588354 | − | 0.0588354i | −0.677077 | − | 0.735912i | \(-0.736754\pi\) |
0.735912 | + | 0.677077i | \(0.236754\pi\) | |||||||
\(18\) | 4.99514e11 | + | 4.99514e11i | 2.51823 | + | 2.51823i | ||||
\(19\) | − | 1.05230e11i | − | 0.326105i | −0.986617 | − | 0.163052i | \(-0.947866\pi\) | ||
0.986617 | − | 0.163052i | \(-0.0521339\pi\) | |||||||
\(20\) | −1.51417e11 | − | 9.89241e11i | −0.295736 | − | 1.93211i | ||||
\(21\) | 1.77203e11 | 0.223098 | ||||||||
\(22\) | 1.00348e12 | − | 1.00348e12i | 0.831195 | − | 0.831195i | ||||
\(23\) | −1.83599e12 | − | 1.83599e12i | −1.01934 | − | 1.01934i | −0.999809 | − | 0.0195353i | \(-0.993781\pi\) |
−0.0195353 | − | 0.999809i | \(-0.506219\pi\) | |||||||
\(24\) | 7.59765e12i | 2.87593i | ||||||||
\(25\) | 3.64004e12 | − | 1.14105e12i | 0.954216 | − | 0.299119i | ||||
\(26\) | −7.96845e12 | −1.46762 | ||||||||
\(27\) | 1.01297e13 | − | 1.01297e13i | 1.32838 | − | 1.32838i | ||||
\(28\) | 1.86108e12 | + | 1.86108e12i | 0.175931 | + | 0.175931i | ||||
\(29\) | 1.51916e13i | 1.04718i | 0.851971 | + | 0.523590i | \(0.175407\pi\) | ||||
−0.851971 | + | 0.523590i | \(0.824593\pi\) | |||||||
\(30\) | −5.86156e13 | + | 8.97192e12i | −2.97798 | + | 0.455821i | ||||
\(31\) | 2.32707e13 | 0.880145 | 0.440073 | − | 0.897962i | \(-0.354953\pi\) | ||||
0.440073 | + | 0.897962i | \(0.354953\pi\) | |||||||
\(32\) | 3.79385e12 | − | 3.79385e12i | 0.107828 | − | 0.107828i | ||||
\(33\) | −3.93349e13 | − | 3.93349e13i | −0.847526 | − | 0.847526i | ||||
\(34\) | − | 8.68389e12i | − | 0.143022i | ||||||
\(35\) | −5.93903e12 | + | 8.08570e12i | −0.0753534 | + | 0.102590i | ||||
\(36\) | 4.11285e14 | 4.04968 | ||||||||
\(37\) | 1.21070e13 | − | 1.21070e13i | 0.0931584 | − | 0.0931584i | −0.658992 | − | 0.752150i | \(-0.729017\pi\) |
0.752150 | + | 0.658992i | \(0.229017\pi\) | |||||||
\(38\) | −6.54854e13 | − | 6.54854e13i | −0.396362 | − | 0.396362i | ||||
\(39\) | 3.12353e14i | 1.49646i | ||||||||
\(40\) | −3.46679e14 | − | 2.54639e14i | −1.32247 | − | 0.971370i | ||||
\(41\) | −4.41756e14 | −1.34936 | −0.674680 | − | 0.738111i | \(-0.735718\pi\) | ||||
−0.674680 | + | 0.738111i | \(0.735718\pi\) | |||||||
\(42\) | 1.10275e14 | − | 1.10275e14i | 0.271164 | − | 0.271164i | ||||
\(43\) | 1.75004e14 | + | 1.75004e14i | 0.348202 | + | 0.348202i | 0.859440 | − | 0.511237i | \(-0.170813\pi\) |
−0.511237 | + | 0.859440i | \(0.670813\pi\) | |||||||
\(44\) | − | 8.26233e14i | − | 1.33668i | ||||||
\(45\) | 2.37200e14 | + | 1.54969e15i | 0.313475 | + | 2.04800i | ||||
\(46\) | −2.28511e15 | −2.47791 | ||||||||
\(47\) | 1.26772e15 | − | 1.26772e15i | 1.13277 | − | 1.13277i | 0.143060 | − | 0.989714i | \(-0.454306\pi\) |
0.989714 | − | 0.143060i | \(-0.0456941\pi\) | |||||||
\(48\) | 1.45152e15 | + | 1.45152e15i | 1.07313 | + | 1.07313i | ||||
\(49\) | 1.60203e15i | 0.983797i | ||||||||
\(50\) | 1.55514e15 | − | 2.97531e15i | 0.796234 | − | 1.52336i | ||||
\(51\) | −3.40397e14 | −0.145832 | ||||||||
\(52\) | −3.28049e15 | + | 3.28049e15i | −1.18007 | + | 1.18007i | ||||
\(53\) | 1.11472e15 | + | 1.11472e15i | 0.337818 | + | 0.337818i | 0.855546 | − | 0.517727i | \(-0.173222\pi\) |
−0.517727 | + | 0.855546i | \(0.673222\pi\) | |||||||
\(54\) | − | 1.26076e16i | − | 3.22914i | ||||||
\(55\) | 3.11317e15 | − | 4.76513e14i | 0.675988 | − | 0.103469i | ||||
\(56\) | 1.13127e15 | 0.208869 | ||||||||
\(57\) | −2.56694e15 | + | 2.56694e15i | −0.404150 | + | 0.404150i | ||||
\(58\) | 9.45384e15 | + | 9.45384e15i | 1.27279 | + | 1.27279i | ||||
\(59\) | − | 6.28063e15i | − | 0.724995i | −0.931985 | − | 0.362497i | \(-0.881924\pi\) | ||
0.931985 | − | 0.362497i | \(-0.118076\pi\) | |||||||
\(60\) | −2.04376e16 | + | 2.78248e16i | −2.02800 | + | 2.76103i | ||||
\(61\) | 5.12455e15 | 0.438215 | 0.219108 | − | 0.975701i | \(-0.429685\pi\) | ||||
0.219108 | + | 0.975701i | \(0.429685\pi\) | |||||||
\(62\) | 1.44815e16 | − | 1.44815e16i | 1.06977 | − | 1.06977i | ||||
\(63\) | −2.91545e15 | − | 2.91545e15i | −0.186484 | − | 0.186484i | ||||
\(64\) | − | 2.03205e16i | − | 1.12802i | ||||||
\(65\) | −1.42526e16 | − | 1.04686e16i | −0.688134 | − | 0.505441i | ||||
\(66\) | −4.89569e16 | −2.06024 | ||||||||
\(67\) | −3.69810e15 | + | 3.69810e15i | −0.135927 | + | 0.135927i | −0.771797 | − | 0.635870i | \(-0.780642\pi\) |
0.635870 | + | 0.771797i | \(0.280642\pi\) | |||||||
\(68\) | −3.57503e15 | − | 3.57503e15i | −0.115000 | − | 0.115000i | ||||
\(69\) | 8.95732e16i | 2.52660i | ||||||||
\(70\) | 1.33589e15 | + | 8.72770e15i | 0.0331047 | + | 0.216281i | ||||
\(71\) | 8.23007e16 | 1.79506 | 0.897529 | − | 0.440956i | \(-0.145361\pi\) | ||||
0.897529 | + | 0.440956i | \(0.145361\pi\) | |||||||
\(72\) | 1.25001e17 | − | 1.25001e17i | 2.40393 | − | 2.40393i | ||||
\(73\) | 2.68205e16 | + | 2.68205e16i | 0.455577 | + | 0.455577i | 0.897200 | − | 0.441624i | \(-0.145597\pi\) |
−0.441624 | + | 0.897200i | \(0.645597\pi\) | |||||||
\(74\) | − | 1.50686e16i | − | 0.226458i | ||||||
\(75\) | −1.16628e17 | − | 6.09596e16i | −1.55329 | − | 0.811878i | ||||
\(76\) | −5.39188e16 | −0.637408 | ||||||||
\(77\) | −5.85686e15 | + | 5.85686e15i | −0.0615529 | + | 0.0615529i | ||||
\(78\) | 1.94380e17 | + | 1.94380e17i | 1.81886 | + | 1.81886i | ||||
\(79\) | − | 1.50642e17i | − | 1.25691i | −0.777848 | − | 0.628453i | \(-0.783688\pi\) | ||
0.777848 | − | 0.628453i | \(-0.216312\pi\) | |||||||
\(80\) | −1.14881e17 | + | 1.75841e16i | −0.855930 | + | 0.131012i | ||||
\(81\) | −1.83225e17 | −1.22073 | ||||||||
\(82\) | −2.74908e17 | + | 2.74908e17i | −1.64007 | + | 1.64007i | ||||
\(83\) | −6.69322e16 | − | 6.69322e16i | −0.358040 | − | 0.358040i | 0.505050 | − | 0.863090i | \(-0.331474\pi\) |
−0.863090 | + | 0.505050i | \(0.831474\pi\) | |||||||
\(84\) | − | 9.07968e16i | − | 0.436071i | ||||||
\(85\) | 1.14086e16 | − | 1.55322e16i | 0.0492562 | − | 0.0670600i | ||||
\(86\) | 2.17813e17 | 0.846441 | ||||||||
\(87\) | 3.70578e17 | − | 3.70578e17i | 1.29780 | − | 1.29780i | ||||
\(88\) | −2.51116e17 | − | 2.51116e17i | −0.793469 | − | 0.793469i | ||||
\(89\) | 2.86724e17i | 0.818377i | 0.912450 | + | 0.409188i | \(0.134188\pi\) | ||||
−0.912450 | + | 0.409188i | \(0.865812\pi\) | |||||||
\(90\) | 1.11199e18 | + | 8.16770e17i | 2.87025 | + | 2.10823i | ||||
\(91\) | 4.65084e16 | 0.108682 | ||||||||
\(92\) | −9.40745e17 | + | 9.40745e17i | −1.99242 | + | 1.99242i | ||||
\(93\) | −5.67658e17 | − | 5.67658e17i | −1.09079 | − | 1.09079i | ||||
\(94\) | − | 1.57783e18i | − | 2.75365i | ||||||
\(95\) | −3.10966e16 | − | 2.03161e17i | −0.0493401 | − | 0.322350i | ||||
\(96\) | −1.85092e17 | −0.267267 | ||||||||
\(97\) | 8.46795e17 | − | 8.46795e17i | 1.11387 | − | 1.11387i | 0.121243 | − | 0.992623i | \(-0.461312\pi\) |
0.992623 | − | 0.121243i | \(-0.0386880\pi\) | |||||||
\(98\) | 9.96955e17 | + | 9.96955e17i | 1.19575 | + | 1.19575i | ||||
\(99\) | 1.29433e18i | 1.41686i | ||||||||
\(100\) | −5.84662e17 | − | 1.86512e18i | −0.584662 | − | 1.86512i | ||||
\(101\) | −3.70254e17 | −0.338538 | −0.169269 | − | 0.985570i | \(-0.554141\pi\) | ||||
−0.169269 | + | 0.985570i | \(0.554141\pi\) | |||||||
\(102\) | −2.11832e17 | + | 2.11832e17i | −0.177251 | + | 0.177251i | ||||
\(103\) | 1.03050e18 | + | 1.03050e18i | 0.789796 | + | 0.789796i | 0.981461 | − | 0.191664i | \(-0.0613885\pi\) |
−0.191664 | + | 0.981461i | \(0.561388\pi\) | |||||||
\(104\) | 1.99407e18i | 1.40101i | ||||||||
\(105\) | 3.42114e17 | − | 5.23653e16i | 0.220530 | − | 0.0337551i | ||||
\(106\) | 1.38740e18 | 0.821199 | ||||||||
\(107\) | −2.13275e18 | + | 2.13275e18i | −1.16008 | + | 1.16008i | −0.175619 | + | 0.984458i | \(0.556193\pi\) |
−0.984458 | + | 0.175619i | \(0.943807\pi\) | |||||||
\(108\) | −5.19035e18 | − | 5.19035e18i | −2.59647 | − | 2.59647i | ||||
\(109\) | 3.04401e18i | 1.40155i | 0.713384 | + | 0.700774i | \(0.247162\pi\) | ||||
−0.713384 | + | 0.700774i | \(0.752838\pi\) | |||||||
\(110\) | 1.64081e18 | − | 2.23389e18i | 0.695865 | − | 0.947387i | ||||
\(111\) | −5.90669e17 | −0.230907 | ||||||||
\(112\) | 2.16127e17 | − | 2.16127e17i | 0.0779377 | − | 0.0779377i | ||||
\(113\) | 1.67873e17 | + | 1.67873e17i | 0.0558823 | + | 0.0558823i | 0.734496 | − | 0.678613i | \(-0.237419\pi\) |
−0.678613 | + | 0.734496i | \(0.737419\pi\) | |||||||
\(114\) | 3.19486e18i | 0.982444i | ||||||||
\(115\) | −4.08720e18 | − | 3.00209e18i | −1.16184 | − | 0.853381i | ||||
\(116\) | 7.78401e18 | 2.04683 | ||||||||
\(117\) | 5.13903e18 | − | 5.13903e18i | 1.25086 | − | 1.25086i | ||||
\(118\) | −3.90848e18 | − | 3.90848e18i | −0.881191 | − | 0.881191i | ||||
\(119\) | 5.06842e16i | 0.0105913i | ||||||||
\(120\) | 2.24519e18 | + | 1.46683e19i | 0.435132 | + | 2.84282i | ||||
\(121\) | −2.95974e18 | −0.532335 | ||||||||
\(122\) | 3.18905e18 | − | 3.18905e18i | 0.532626 | − | 0.532626i | ||||
\(123\) | 1.07760e19 | + | 1.07760e19i | 1.67230 | + | 1.67230i | ||||
\(124\) | − | 1.19237e19i | − | 1.72034i | ||||||
\(125\) | 6.69042e18 | − | 3.27863e18i | 0.897973 | − | 0.440050i | ||||
\(126\) | −3.62861e18 | −0.453321 | ||||||||
\(127\) | −6.42294e18 | + | 6.42294e18i | −0.747310 | + | 0.747310i | −0.973973 | − | 0.226663i | \(-0.927218\pi\) |
0.226663 | + | 0.973973i | \(0.427218\pi\) | |||||||
\(128\) | −1.16511e19 | − | 1.16511e19i | −1.26321 | − | 1.26321i | ||||
\(129\) | − | 8.53797e18i | − | 0.863072i | ||||||
\(130\) | −1.53842e19 | + | 2.35476e18i | −1.45072 | + | 0.222053i | ||||
\(131\) | −1.48921e18 | −0.131073 | −0.0655366 | − | 0.997850i | \(-0.520876\pi\) | ||||
−0.0655366 | + | 0.997850i | \(0.520876\pi\) | |||||||
\(132\) | −2.01548e19 | + | 2.01548e19i | −1.65659 | + | 1.65659i | ||||
\(133\) | 3.82211e17 | + | 3.82211e17i | 0.0293520 | + | 0.0293520i | ||||
\(134\) | 4.60272e18i | 0.330424i | ||||||||
\(135\) | 1.65633e19 | − | 2.25502e19i | 1.11210 | − | 1.51407i | ||||
\(136\) | −2.17311e18 | −0.136531 | ||||||||
\(137\) | −8.39955e18 | + | 8.39955e18i | −0.494050 | + | 0.494050i | −0.909580 | − | 0.415530i | \(-0.863596\pi\) |
0.415530 | + | 0.909580i | \(0.363596\pi\) | |||||||
\(138\) | 5.57421e19 | + | 5.57421e19i | 3.07094 | + | 3.07094i | ||||
\(139\) | − | 8.28997e18i | − | 0.427976i | −0.976836 | − | 0.213988i | \(-0.931355\pi\) | ||
0.976836 | − | 0.213988i | \(-0.0686454\pi\) | |||||||
\(140\) | 4.14303e18 | + | 3.04310e18i | 0.200524 | + | 0.147287i | ||||
\(141\) | −6.18487e19 | −2.80775 | ||||||||
\(142\) | 5.12164e19 | − | 5.12164e19i | 2.18179 | − | 2.18179i | ||||
\(143\) | −1.03238e19 | − | 1.03238e19i | −0.412873 | − | 0.412873i | ||||
\(144\) | − | 4.77627e19i | − | 1.79402i | ||||||
\(145\) | 4.48928e18 | + | 2.93295e19i | 0.158440 | + | 1.03512i | ||||
\(146\) | 3.33812e19 | 1.10746 | ||||||||
\(147\) | 3.90793e19 | − | 3.90793e19i | 1.21925 | − | 1.21925i | ||||
\(148\) | −6.20352e18 | − | 6.20352e18i | −0.182089 | − | 0.182089i | ||||
\(149\) | 5.75268e19i | 1.58926i | 0.607096 | + | 0.794628i | \(0.292334\pi\) | ||||
−0.607096 | + | 0.794628i | \(0.707666\pi\) | |||||||
\(150\) | −1.10514e20 | + | 3.46431e19i | −2.87473 | + | 0.901146i | ||||
\(151\) | −3.67875e19 | −0.901379 | −0.450689 | − | 0.892681i | \(-0.648822\pi\) | ||||
−0.450689 | + | 0.892681i | \(0.648822\pi\) | |||||||
\(152\) | −1.63875e19 | + | 1.63875e19i | −0.378372 | + | 0.378372i | ||||
\(153\) | 5.60043e18 | + | 5.60043e18i | 0.121898 | + | 0.121898i | ||||
\(154\) | 7.28954e18i | 0.149628i | ||||||||
\(155\) | 4.49274e19 | − | 6.87675e18i | 0.870013 | − | 0.133167i | ||||
\(156\) | 1.60046e20 | 2.92499 | ||||||||
\(157\) | 7.10154e18 | − | 7.10154e18i | 0.122534 | − | 0.122534i | −0.643181 | − | 0.765714i | \(-0.722386\pi\) |
0.765714 | + | 0.643181i | \(0.222386\pi\) | |||||||
\(158\) | −9.37458e19 | − | 9.37458e19i | −1.52770 | − | 1.52770i | ||||
\(159\) | − | 5.43842e19i | − | 0.837333i | ||||||
\(160\) | 6.20344e18 | − | 8.44568e18i | 0.0902719 | − | 0.122901i | ||||
\(161\) | 1.33372e19 | 0.183498 | ||||||||
\(162\) | −1.14023e20 | + | 1.14023e20i | −1.48373 | + | 1.48373i | ||||
\(163\) | 3.42433e19 | + | 3.42433e19i | 0.421587 | + | 0.421587i | 0.885750 | − | 0.464163i | \(-0.153645\pi\) |
−0.464163 | + | 0.885750i | \(0.653645\pi\) | |||||||
\(164\) | 2.26351e20i | 2.63747i | ||||||||
\(165\) | −8.75655e19 | − | 6.43177e19i | −0.966001 | − | 0.709537i | ||||
\(166\) | −8.33048e19 | −0.870357 | ||||||||
\(167\) | 4.92075e19 | − | 4.92075e19i | 0.487061 | − | 0.487061i | −0.420317 | − | 0.907377i | \(-0.638081\pi\) |
0.907377 | + | 0.420317i | \(0.138081\pi\) | |||||||
\(168\) | −2.75958e19 | − | 2.75958e19i | −0.258856 | − | 0.258856i | ||||
\(169\) | − | 3.04755e19i | − | 0.271001i | ||||||
\(170\) | −2.56618e18 | − | 1.67655e19i | −0.0216395 | − | 0.141376i | ||||
\(171\) | 8.44659e19 | 0.675642 | ||||||||
\(172\) | 8.96702e19 | − | 8.96702e19i | 0.680600 | − | 0.680600i | ||||
\(173\) | 5.37211e19 | + | 5.37211e19i | 0.387017 | + | 0.387017i | 0.873622 | − | 0.486605i | \(-0.161765\pi\) |
−0.486605 | + | 0.873622i | \(0.661765\pi\) | |||||||
\(174\) | − | 4.61227e20i | − | 3.15480i | ||||||
\(175\) | −9.07671e18 | + | 1.73656e19i | −0.0589639 | + | 0.112810i | ||||
\(176\) | −9.59508e19 | −0.592154 | ||||||||
\(177\) | −1.53207e20 | + | 1.53207e20i | −0.898504 | + | 0.898504i | ||||
\(178\) | 1.78430e20 | + | 1.78430e20i | 0.994692 | + | 0.994692i | ||||
\(179\) | 2.43429e20i | 1.29031i | 0.764051 | + | 0.645156i | \(0.223208\pi\) | ||||
−0.764051 | + | 0.645156i | \(0.776792\pi\) | |||||||
\(180\) | 7.94043e20 | − | 1.21539e20i | 4.00306 | − | 0.612722i | ||||
\(181\) | −4.05960e17 | −0.00194704 | −0.000973522 | − | 1.00000i | \(-0.500310\pi\) | ||||
−0.000973522 | 1.00000i | \(0.500310\pi\) | ||||||||
\(182\) | 2.89426e19 | − | 2.89426e19i | 0.132098 | − | 0.132098i | ||||
\(183\) | −1.25007e20 | − | 1.25007e20i | −0.543091 | − | 0.543091i | ||||
\(184\) | 5.71839e20i | 2.36545i | ||||||||
\(185\) | 1.97966e19 | − | 2.69521e19i | 0.0779909 | − | 0.106181i | ||||
\(186\) | −7.06515e20 | −2.65158 | ||||||||
\(187\) | 1.12507e19 | − | 1.12507e19i | 0.0402352 | − | 0.0402352i | ||||
\(188\) | −6.49568e20 | − | 6.49568e20i | −2.21413 | − | 2.21413i | ||||
\(189\) | 7.35850e19i | 0.239129i | ||||||||
\(190\) | −1.45780e20 | − | 1.07077e20i | −0.451769 | − | 0.331829i | ||||
\(191\) | 3.39662e20 | 1.00403 | 0.502014 | − | 0.864859i | \(-0.332592\pi\) | ||||
0.502014 | + | 0.864859i | \(0.332592\pi\) | |||||||
\(192\) | −4.95692e20 | + | 4.95692e20i | −1.39798 | + | 1.39798i | ||||
\(193\) | −1.07293e20 | − | 1.07293e20i | −0.288772 | − | 0.288772i | 0.547823 | − | 0.836594i | \(-0.315457\pi\) |
−0.836594 | + | 0.547823i | \(0.815457\pi\) | |||||||
\(194\) | − | 1.05393e21i | − | 2.70769i | ||||||
\(195\) | 9.23036e19 | + | 6.03041e20i | 0.226416 | + | 1.47923i | ||||
\(196\) | 8.20863e20 | 1.92294 | ||||||||
\(197\) | −9.25616e19 | + | 9.25616e19i | −0.207126 | + | 0.207126i | −0.803045 | − | 0.595919i | \(-0.796788\pi\) |
0.595919 | + | 0.803045i | \(0.296788\pi\) | |||||||
\(198\) | 8.05470e20 | + | 8.05470e20i | 1.72212 | + | 1.72212i | ||||
\(199\) | 1.74927e20i | 0.357420i | 0.983902 | + | 0.178710i | \(0.0571924\pi\) | ||||
−0.983902 | + | 0.178710i | \(0.942808\pi\) | |||||||
\(200\) | −7.44560e20 | − | 3.89168e20i | −1.45422 | − | 0.760095i | ||||
\(201\) | 1.80420e20 | 0.336916 | ||||||||
\(202\) | −2.30412e20 | + | 2.30412e20i | −0.411474 | + | 0.411474i | ||||
\(203\) | −5.51780e19 | − | 5.51780e19i | −0.0942545 | − | 0.0942545i | ||||
\(204\) | 1.74416e20i | 0.285046i | ||||||||
\(205\) | −8.52871e20 | + | 1.30544e20i | −1.33382 | + | 0.204160i | ||||
\(206\) | 1.28258e21 | 1.91991 | ||||||||
\(207\) | 1.47372e21 | − | 1.47372e21i | 2.11194 | − | 2.11194i | ||||
\(208\) | 3.80965e20 | + | 3.80965e20i | 0.522775 | + | 0.522775i | ||||
\(209\) | − | 1.69684e20i | − | 0.223010i | ||||||
\(210\) | 1.80313e20 | − | 2.45488e20i | 0.227015 | − | 0.309070i | ||||
\(211\) | −3.59108e20 | −0.433194 | −0.216597 | − | 0.976261i | \(-0.569496\pi\) | ||||
−0.216597 | + | 0.976261i | \(0.569496\pi\) | |||||||
\(212\) | 5.71171e20 | − | 5.71171e20i | 0.660304 | − | 0.660304i | ||||
\(213\) | −2.00761e21 | − | 2.00761e21i | −2.22466 | − | 2.22466i | ||||
\(214\) | 2.65446e21i | 2.82002i | ||||||||
\(215\) | 3.89585e20 | + | 2.86154e20i | 0.396877 | + | 0.291510i | ||||
\(216\) | −3.15499e21 | −3.08258 | ||||||||
\(217\) | −8.45226e19 | + | 8.45226e19i | −0.0792201 | + | 0.0792201i | ||||
\(218\) | 1.89431e21 | + | 1.89431e21i | 1.70350 | + | 1.70350i | ||||
\(219\) | − | 1.30850e21i | − | 1.12922i | ||||||
\(220\) | −2.44161e20 | − | 1.59516e21i | −0.202242 | − | 1.32129i | ||||
\(221\) | −8.93403e19 | −0.0710423 | ||||||||
\(222\) | −3.67578e20 | + | 3.67578e20i | −0.280655 | + | 0.280655i | ||||
\(223\) | 1.63575e20 | + | 1.63575e20i | 0.119942 | + | 0.119942i | 0.764530 | − | 0.644588i | \(-0.222971\pi\) |
−0.644588 | + | 0.764530i | \(0.722971\pi\) | |||||||
\(224\) | 2.75596e19i | 0.0194107i | ||||||||
\(225\) | 9.15897e20 | + | 2.92179e21i | 0.619732 | + | 1.97700i | ||||
\(226\) | 2.08937e20 | 0.135844 | ||||||||
\(227\) | 2.23800e19 | − | 2.23800e19i | 0.0139839 | − | 0.0139839i | −0.700080 | − | 0.714064i | \(-0.746852\pi\) |
0.714064 | + | 0.700080i | \(0.246852\pi\) | |||||||
\(228\) | 1.31528e21 | + | 1.31528e21i | 0.789956 | + | 0.789956i | ||||
\(229\) | − | 3.12885e20i | − | 0.180661i | −0.995912 | − | 0.0903307i | \(-0.971208\pi\) | ||
0.995912 | − | 0.0903307i | \(-0.0287924\pi\) | |||||||
\(230\) | −4.41172e21 | + | 6.75274e20i | −2.44939 | + | 0.374912i | ||||
\(231\) | 2.85741e20 | 0.152568 | ||||||||
\(232\) | 2.36579e21 | − | 2.36579e21i | 1.21502 | − | 1.21502i | ||||
\(233\) | 1.70610e21 | + | 1.70610e21i | 0.842949 | + | 0.842949i | 0.989241 | − | 0.146292i | \(-0.0467340\pi\) |
−0.146292 | + | 0.989241i | \(0.546734\pi\) | |||||||
\(234\) | − | 6.39611e21i | − | 3.04070i | ||||||
\(235\) | 2.07289e21 | − | 2.82214e21i | 0.948343 | − | 1.29112i | ||||
\(236\) | −3.21813e21 | −1.41708 | ||||||||
\(237\) | −3.67471e21 | + | 3.67471e21i | −1.55772 | + | 1.55772i | ||||
\(238\) | 3.15411e19 | + | 3.15411e19i | 0.0128732 | + | 0.0128732i | ||||
\(239\) | − | 1.00998e21i | − | 0.396946i | −0.980106 | − | 0.198473i | \(-0.936402\pi\) | ||
0.980106 | − | 0.198473i | \(-0.0635981\pi\) | |||||||
\(240\) | 3.23130e21 | + | 2.37342e21i | 1.22314 | + | 0.898409i | ||||
\(241\) | −2.26889e21 | −0.827295 | −0.413648 | − | 0.910437i | \(-0.635745\pi\) | ||||
−0.413648 | + | 0.910437i | \(0.635745\pi\) | |||||||
\(242\) | −1.84187e21 | + | 1.84187e21i | −0.647023 | + | 0.647023i | ||||
\(243\) | 5.45088e20 | + | 5.45088e20i | 0.184506 | + | 0.184506i | ||||
\(244\) | − | 2.62577e21i | − | 0.856541i | ||||||
\(245\) | 4.73417e20 | + | 3.09294e21i | 0.148850 | + | 0.972471i | ||||
\(246\) | 1.34120e22 | 4.06517 | ||||||||
\(247\) | −6.73718e20 | + | 6.73718e20i | −0.196882 | + | 0.196882i | ||||
\(248\) | −3.62395e21 | − | 3.62395e21i | −1.02121 | − | 1.02121i | ||||
\(249\) | 3.26544e21i | 0.887457i | ||||||||
\(250\) | 2.12319e21 | − | 6.20382e21i | 0.556580 | − | 1.62629i | ||||
\(251\) | 4.80359e21 | 1.21479 | 0.607396 | − | 0.794399i | \(-0.292214\pi\) | ||||
0.607396 | + | 0.794399i | \(0.292214\pi\) | |||||||
\(252\) | −1.49385e21 | + | 1.49385e21i | −0.364503 | + | 0.364503i | ||||
\(253\) | −2.96056e21 | − | 2.96056e21i | −0.697090 | − | 0.697090i | ||||
\(254\) | 7.99410e21i | 1.81663i | ||||||||
\(255\) | −6.57184e20 | + | 1.00591e20i | −0.144154 | + | 0.0220647i | ||||
\(256\) | −9.17422e21 | −1.94272 | ||||||||
\(257\) | 5.42937e21 | − | 5.42937e21i | 1.11007 | − | 1.11007i | 0.116932 | − | 0.993140i | \(-0.462694\pi\) |
0.993140 | − | 0.116932i | \(-0.0373058\pi\) | |||||||
\(258\) | −5.31324e21 | − | 5.31324e21i | −1.04902 | − | 1.04902i | ||||
\(259\) | 8.79490e19i | 0.0167700i | ||||||||
\(260\) | −5.36403e21 | + | 7.30287e21i | −0.987941 | + | 1.34504i | ||||
\(261\) | −1.21940e22 | −2.16960 | ||||||||
\(262\) | −9.26746e20 | + | 9.26746e20i | −0.159312 | + | 0.159312i | ||||
\(263\) | 4.37793e21 | + | 4.37793e21i | 0.727222 | + | 0.727222i | 0.970066 | − | 0.242843i | \(-0.0780800\pi\) |
−0.242843 | + | 0.970066i | \(0.578080\pi\) | |||||||
\(264\) | 1.22513e22i | 1.96673i | ||||||||
\(265\) | 2.48153e21 | + | 1.82271e21i | 0.385041 | + | 0.282817i | ||||
\(266\) | 4.75705e20 | 0.0713515 | ||||||||
\(267\) | 6.99423e21 | − | 6.99423e21i | 1.01424 | − | 1.01424i | ||||
\(268\) | 1.89487e21 | + | 1.89487e21i | 0.265685 | + | 0.265685i | ||||
\(269\) | − | 3.81640e21i | − | 0.517468i | −0.965949 | − | 0.258734i | \(-0.916695\pi\) | ||
0.965949 | − | 0.258734i | \(-0.0833053\pi\) | |||||||
\(270\) | −3.72567e21 | − | 2.43407e22i | −0.488574 | − | 3.19197i | ||||
\(271\) | −9.97918e21 | −1.26582 | −0.632909 | − | 0.774226i | \(-0.718139\pi\) | ||||
−0.632909 | + | 0.774226i | \(0.718139\pi\) | |||||||
\(272\) | −4.15170e20 | + | 4.15170e20i | −0.0509455 | + | 0.0509455i | ||||
\(273\) | −1.13451e21 | − | 1.13451e21i | −0.134693 | − | 0.134693i | ||||
\(274\) | 1.04542e22i | 1.20098i | ||||||||
\(275\) | 5.86960e21 | − | 1.83995e21i | 0.652551 | − | 0.204556i | ||||
\(276\) | 4.58964e22 | 4.93852 | ||||||||
\(277\) | 7.85415e21 | − | 7.85415e21i | 0.818053 | − | 0.818053i | −0.167773 | − | 0.985826i | \(-0.553657\pi\) |
0.985826 | + | 0.167773i | \(0.0536575\pi\) | |||||||
\(278\) | −5.15891e21 | − | 5.15891e21i | −0.520181 | − | 0.520181i | ||||
\(279\) | 1.86789e22i | 1.82353i | ||||||||
\(280\) | 2.18407e21 | − | 3.34302e20i | 0.206464 | − | 0.0316021i | ||||
\(281\) | 1.61885e22 | 1.48201 | 0.741004 | − | 0.671500i | \(-0.234350\pi\) | ||||
0.741004 | + | 0.671500i | \(0.234350\pi\) | |||||||
\(282\) | −3.84889e22 | + | 3.84889e22i | −3.41267 | + | 3.41267i | ||||
\(283\) | −3.88499e21 | − | 3.88499e21i | −0.333666 | − | 0.333666i | 0.520311 | − | 0.853977i | \(-0.325816\pi\) |
−0.853977 | + | 0.520311i | \(0.825816\pi\) | |||||||
\(284\) | − | 4.21700e22i | − | 3.50864i | ||||||
\(285\) | −4.19728e21 | + | 5.71440e21i | −0.338349 | + | 0.460646i | ||||
\(286\) | −1.28492e22 | −1.00365 | ||||||||
\(287\) | 1.60452e21 | − | 1.60452e21i | 0.121453 | − | 0.121453i | ||||
\(288\) | 3.04525e21 | + | 3.04525e21i | 0.223404 | + | 0.223404i | ||||
\(289\) | 1.39657e22i | 0.993077i | ||||||||
\(290\) | 2.10457e22 | + | 1.54582e22i | 1.45071 | + | 1.06556i | ||||
\(291\) | −4.13129e22 | −2.76089 | ||||||||
\(292\) | 1.37426e22 | − | 1.37426e22i | 0.890476 | − | 0.890476i | ||||
\(293\) | −2.09887e22 | − | 2.09887e22i | −1.31879 | − | 1.31879i | −0.914733 | − | 0.404059i | \(-0.867599\pi\) |
−0.404059 | − | 0.914733i | \(-0.632401\pi\) | |||||||
\(294\) | − | 4.86387e22i | − | 2.96385i | ||||||
\(295\) | −1.85599e21 | − | 1.21256e22i | −0.109693 | − | 0.716648i | ||||
\(296\) | −3.77086e21 | −0.216179 | ||||||||
\(297\) | 1.63342e22 | − | 1.63342e22i | 0.908426 | − | 0.908426i | ||||
\(298\) | 3.57994e22 | + | 3.57994e22i | 1.93165 | + | 1.93165i | ||||
\(299\) | 2.35093e22i | 1.23083i | ||||||||
\(300\) | −3.12351e22 | + | 5.97592e22i | −1.58691 | + | 3.03608i | ||||
\(301\) | −1.27128e21 | −0.0626819 | ||||||||
\(302\) | −2.28931e22 | + | 2.28931e22i | −1.09558 | + | 1.09558i | ||||
\(303\) | 9.03184e21 | + | 9.03184e21i | 0.419559 | + | 0.419559i | ||||
\(304\) | 6.26161e21i | 0.282373i | ||||||||
\(305\) | 9.89367e21 | − | 1.51436e21i | 0.433170 | − | 0.0663026i | ||||
\(306\) | 6.97038e21 | 0.296322 | ||||||||
\(307\) | −1.15443e21 | + | 1.15443e21i | −0.0476567 | + | 0.0476567i | −0.730534 | − | 0.682877i | \(-0.760729\pi\) |
0.682877 | + | 0.730534i | \(0.260729\pi\) | |||||||
\(308\) | 3.00100e21 | + | 3.00100e21i | 0.120312 | + | 0.120312i | ||||
\(309\) | − | 5.02755e22i | − | 1.95763i | ||||||
\(310\) | 2.36792e22 | − | 3.22381e22i | 0.895595 | − | 1.21931i | ||||
\(311\) | −1.39389e22 | −0.512134 | −0.256067 | − | 0.966659i | \(-0.582427\pi\) | ||||
−0.256067 | + | 0.966659i | \(0.582427\pi\) | |||||||
\(312\) | 4.86427e22 | − | 4.86427e22i | 1.73631 | − | 1.73631i | ||||
\(313\) | 2.27399e22 | + | 2.27399e22i | 0.788660 | + | 0.788660i | 0.981274 | − | 0.192615i | \(-0.0616967\pi\) |
−0.192615 | + | 0.981274i | \(0.561697\pi\) | |||||||
\(314\) | − | 8.83868e21i | − | 0.297866i | ||||||
\(315\) | −6.49023e21 | − | 4.76714e21i | −0.212552 | − | 0.156121i | ||||
\(316\) | −7.71875e22 | −2.45676 | ||||||||
\(317\) | −3.57070e22 | + | 3.57070e22i | −1.10464 | + | 1.10464i | −0.110796 | + | 0.993843i | \(0.535340\pi\) |
−0.993843 | + | 0.110796i | \(0.964660\pi\) | |||||||
\(318\) | −3.38437e22 | − | 3.38437e22i | −1.01773 | − | 1.01773i | ||||
\(319\) | 2.44965e22i | 0.716125i | ||||||||
\(320\) | −6.00493e21 | − | 3.92316e22i | −0.170670 | − | 1.11503i | ||||
\(321\) | 1.04051e23 | 2.87543 | ||||||||
\(322\) | 8.29985e21 | − | 8.29985e21i | 0.223032 | − | 0.223032i | ||||
\(323\) | −7.34207e20 | − | 7.34207e20i | −0.0191865 | − | 0.0191865i | ||||
\(324\) | 9.38829e22i | 2.38606i | ||||||||
\(325\) | −3.06102e22 | − | 1.59994e22i | −0.756686 | − | 0.395506i | ||||
\(326\) | 4.26197e22 | 1.02483 | ||||||||
\(327\) | 7.42545e22 | − | 7.42545e22i | 1.73697 | − | 1.73697i | ||||
\(328\) | 6.87946e22 | + | 6.87946e22i | 1.56563 | + | 1.56563i | ||||
\(329\) | 9.20910e21i | 0.203917i | ||||||||
\(330\) | −9.45181e22 | + | 1.44673e22i | −2.03652 | + | 0.311718i | ||||
\(331\) | −6.14668e22 | −1.28881 | −0.644405 | − | 0.764685i | \(-0.722895\pi\) | ||||
−0.644405 | + | 0.764685i | \(0.722895\pi\) | |||||||
\(332\) | −3.42954e22 | + | 3.42954e22i | −0.699830 | + | 0.699830i | ||||
\(333\) | 9.71806e21 | + | 9.71806e21i | 0.193011 | + | 0.193011i | ||||
\(334\) | − | 6.12444e22i | − | 1.18399i | ||||||
\(335\) | −6.04688e21 | + | 8.23253e21i | −0.113796 | + | 0.154928i | ||||
\(336\) | −1.05443e22 | −0.193180 | ||||||||
\(337\) | −3.53317e22 | + | 3.53317e22i | −0.630225 | + | 0.630225i | −0.948124 | − | 0.317899i | \(-0.897023\pi\) |
0.317899 | + | 0.948124i | \(0.397023\pi\) | |||||||
\(338\) | −1.89652e22 | − | 1.89652e22i | −0.329387 | − | 0.329387i | ||||
\(339\) | − | 8.19006e21i | − | 0.138513i | ||||||
\(340\) | −7.95855e21 | − | 5.84564e21i | −0.131076 | − | 0.0962768i | ||||
\(341\) | 3.75242e22 | 0.601897 | ||||||||
\(342\) | 5.25638e22 | − | 5.25638e22i | 0.821206 | − | 0.821206i | ||||
\(343\) | −1.17334e22 | − | 1.17334e22i | −0.178558 | − | 0.178558i | ||||
\(344\) | − | 5.45067e22i | − | 0.808024i | ||||||
\(345\) | 2.64699e22 | + | 1.72934e23i | 0.382278 | + | 2.49751i | ||||
\(346\) | 6.68621e22 | 0.940795 | ||||||||
\(347\) | −5.68349e22 | + | 5.68349e22i | −0.779202 | + | 0.779202i | −0.979695 | − | 0.200493i | \(-0.935746\pi\) |
0.200493 | + | 0.979695i | \(0.435746\pi\) | |||||||
\(348\) | −1.89880e23 | − | 1.89880e23i | −2.53669 | − | 2.53669i | ||||
\(349\) | 2.48541e22i | 0.323571i | 0.986826 | + | 0.161785i | \(0.0517252\pi\) | ||||
−0.986826 | + | 0.161785i | \(0.948275\pi\) | |||||||
\(350\) | 5.15826e21 | + | 1.64553e22i | 0.0654471 | + | 0.208782i | ||||
\(351\) | −1.29707e23 | −1.60399 | ||||||||
\(352\) | 6.11761e21 | − | 6.11761e21i | 0.0737391 | − | 0.0737391i | ||||
\(353\) | −1.12896e23 | − | 1.12896e23i | −1.32649 | − | 1.32649i | −0.908409 | − | 0.418082i | \(-0.862702\pi\) |
−0.418082 | − | 0.908409i | \(-0.637298\pi\) | |||||||
\(354\) | 1.90684e23i | 2.18417i | ||||||||
\(355\) | 1.58893e23 | − | 2.43207e22i | 1.77439 | − | 0.271595i | ||||
\(356\) | 1.46914e23 | 1.59961 | ||||||||
\(357\) | 1.23637e21 | − | 1.23637e21i | 0.0131261 | − | 0.0131261i | ||||
\(358\) | 1.51488e23 | + | 1.51488e23i | 1.56830 | + | 1.56830i | ||||
\(359\) | − | 2.18161e22i | − | 0.220255i | −0.993917 | − | 0.110128i | \(-0.964874\pi\) | ||
0.993917 | − | 0.110128i | \(-0.0351260\pi\) | |||||||
\(360\) | 2.04393e23 | − | 2.78272e23i | 2.01254 | − | 2.73998i | ||||
\(361\) | 9.30540e22 | 0.893656 | ||||||||
\(362\) | −2.52632e20 | + | 2.52632e20i | −0.00236653 | + | 0.00236653i | ||||
\(363\) | 7.21988e22 | + | 7.21988e22i | 0.659736 | + | 0.659736i | ||||
\(364\) | − | 2.38305e22i | − | 0.212432i | ||||||
\(365\) | 5.97065e22 | + | 4.38550e22i | 0.519261 | + | 0.381403i | ||||
\(366\) | −1.55585e23 | −1.32020 | ||||||||
\(367\) | −8.39097e22 | + | 8.39097e22i | −0.694733 | + | 0.694733i | −0.963269 | − | 0.268537i | \(-0.913460\pi\) |
0.268537 | + | 0.963269i | \(0.413460\pi\) | |||||||
\(368\) | 1.09249e23 | + | 1.09249e23i | 0.882648 | + | 0.882648i | ||||
\(369\) | − | 3.54588e23i | − | 2.79568i | ||||||
\(370\) | −4.45293e21 | − | 2.90920e22i | −0.0342634 | − | 0.223851i | ||||
\(371\) | −8.09765e21 | −0.0608126 | ||||||||
\(372\) | −2.90862e23 | + | 2.90862e23i | −2.13207 | + | 2.13207i | ||||
\(373\) | −5.06563e22 | − | 5.06563e22i | −0.362455 | − | 0.362455i | 0.502261 | − | 0.864716i | \(-0.332502\pi\) |
−0.864716 | + | 0.502261i | \(0.832502\pi\) | |||||||
\(374\) | − | 1.40028e22i | − | 0.0978074i | ||||||
\(375\) | −2.43182e23 | − | 8.32261e22i | −1.65825 | − | 0.567516i | ||||
\(376\) | −3.94845e23 | −2.62867 | ||||||||
\(377\) | 9.72616e22 | − | 9.72616e22i | 0.632222 | − | 0.632222i | ||||
\(378\) | 4.57925e22 | + | 4.57925e22i | 0.290649 | + | 0.290649i | ||||
\(379\) | 1.14751e23i | 0.711218i | 0.934635 | + | 0.355609i | \(0.115727\pi\) | ||||
−0.934635 | + | 0.355609i | \(0.884273\pi\) | |||||||
\(380\) | −1.04098e23 | + | 1.59336e22i | −0.630070 | + | 0.0964408i | ||||
\(381\) | 3.13358e23 | 1.85232 | ||||||||
\(382\) | 2.11374e23 | − | 2.11374e23i | 1.22034 | − | 1.22034i | ||||
\(383\) | 6.33293e22 | + | 6.33293e22i | 0.357121 | + | 0.357121i | 0.862751 | − | 0.505629i | \(-0.168740\pi\) |
−0.505629 | + | 0.862751i | \(0.668740\pi\) | |||||||
\(384\) | 5.68425e23i | 3.13106i | ||||||||
\(385\) | −9.57673e21 | + | 1.30383e22i | −0.0515312 | + | 0.0701573i | ||||
\(386\) | −1.33538e23 | −0.701972 | ||||||||
\(387\) | −1.40472e23 | + | 1.40472e23i | −0.721425 | + | 0.721425i | ||||
\(388\) | −4.33890e23 | − | 4.33890e23i | −2.17718 | − | 2.17718i | ||||
\(389\) | − | 2.75999e23i | − | 1.35320i | −0.736352 | − | 0.676598i | \(-0.763453\pi\) | ||
0.736352 | − | 0.676598i | \(-0.236547\pi\) | |||||||
\(390\) | 4.32718e23 | + | 3.17836e23i | 2.07312 | + | 1.52272i | ||||
\(391\) | −2.56201e22 | −0.119947 | ||||||||
\(392\) | 2.49484e23 | − | 2.49484e23i | 1.14148 | − | 1.14148i | ||||
\(393\) | 3.63272e22 | + | 3.63272e22i | 0.162442 | + | 0.162442i | ||||
\(394\) | 1.15204e23i | 0.503501i | ||||||||
\(395\) | −4.45164e22 | − | 2.90836e23i | −0.190172 | − | 1.24244i | ||||
\(396\) | 6.63200e23 | 2.76941 | ||||||||
\(397\) | −3.96269e22 | + | 3.96269e22i | −0.161762 | + | 0.161762i | −0.783347 | − | 0.621585i | \(-0.786489\pi\) |
0.621585 | + | 0.783347i | \(0.286489\pi\) | |||||||
\(398\) | 1.08858e23 | + | 1.08858e23i | 0.434424 | + | 0.434424i | ||||
\(399\) | − | 1.86470e22i | − | 0.0727534i | ||||||
\(400\) | −2.16597e23 | + | 6.78971e22i | −0.826254 | + | 0.259007i | ||||
\(401\) | −1.66355e23 | −0.620494 | −0.310247 | − | 0.950656i | \(-0.600412\pi\) | ||||
−0.310247 | + | 0.950656i | \(0.600412\pi\) | |||||||
\(402\) | 1.12277e23 | − | 1.12277e23i | 0.409502 | − | 0.409502i | ||||
\(403\) | −1.48987e23 | − | 1.48987e23i | −0.531377 | − | 0.531377i | ||||
\(404\) | 1.89714e23i | 0.661711i | ||||||||
\(405\) | −3.53742e23 | + | 5.41451e22i | −1.20668 | + | 0.184699i | ||||
\(406\) | −6.86754e22 | −0.229122 | ||||||||
\(407\) | 1.95227e22 | − | 1.95227e22i | 0.0637074 | − | 0.0637074i | ||||
\(408\) | 5.30100e22 | + | 5.30100e22i | 0.169206 | + | 0.169206i | ||||
\(409\) | 4.47799e23i | 1.39821i | 0.715018 | + | 0.699107i | \(0.246419\pi\) | ||||
−0.715018 | + | 0.699107i | \(0.753581\pi\) | |||||||
\(410\) | −4.49510e23 | + | 6.11987e23i | −1.37305 | + | 1.86934i | ||||
\(411\) | 4.09791e23 | 1.22458 | ||||||||
\(412\) | 5.28020e23 | − | 5.28020e23i | 1.54375 | − | 1.54375i | ||||
\(413\) | 2.28121e22 | + | 2.28121e22i | 0.0652553 | + | 0.0652553i | ||||
\(414\) | − | 1.83421e24i | − | 5.13388i | ||||||
\(415\) | −1.49001e23 | − | 1.09443e23i | −0.408091 | − | 0.299746i | ||||
\(416\) | −4.85790e22 | −0.130199 | ||||||||
\(417\) | −2.02223e23 | + | 2.02223e23i | −0.530402 | + | 0.530402i | ||||
\(418\) | −1.05596e23 | − | 1.05596e23i | −0.271057 | − | 0.271057i | ||||
\(419\) | 5.93809e23i | 1.49183i | 0.666039 | + | 0.745917i | \(0.267988\pi\) | ||||
−0.666039 | + | 0.745917i | \(0.732012\pi\) | |||||||
\(420\) | −2.68314e22 | − | 1.75296e23i | −0.0659782 | − | 0.431051i | ||||
\(421\) | 4.76273e23 | 1.14635 | 0.573175 | − | 0.819433i | \(-0.305711\pi\) | ||||
0.573175 | + | 0.819433i | \(0.305711\pi\) | |||||||
\(422\) | −2.23476e23 | + | 2.23476e23i | −0.526524 | + | 0.526524i | ||||
\(423\) | 1.01757e24 | + | 1.01757e24i | 2.34694 | + | 2.34694i | ||||
\(424\) | − | 3.47191e23i | − | 0.783927i | ||||||
\(425\) | 1.74359e22 | − | 3.33585e22i | 0.0385429 | − | 0.0737405i | ||||
\(426\) | −2.49871e24 | −5.40790 | ||||||||
\(427\) | −1.86131e22 | + | 1.86131e22i | −0.0394429 | + | 0.0394429i | ||||
\(428\) | 1.09280e24 | + | 1.09280e24i | 2.26750 | + | 2.26750i | ||||
\(429\) | 5.03671e23i | 1.02337i | ||||||||
\(430\) | 4.20518e23 | − | 6.43659e22i | 0.836697 | − | 0.128068i | ||||
\(431\) | −7.59177e22 | −0.147927 | −0.0739636 | − | 0.997261i | \(-0.523565\pi\) | ||||
−0.0739636 | + | 0.997261i | \(0.523565\pi\) | |||||||
\(432\) | −6.02757e23 | + | 6.02757e23i | −1.15024 | + | 1.15024i | ||||
\(433\) | −5.82274e23 | − | 5.82274e23i | −1.08827 | − | 1.08827i | −0.995707 | − | 0.0925632i | \(-0.970494\pi\) |
−0.0925632 | − | 0.995707i | \(-0.529506\pi\) | |||||||
\(434\) | 1.05198e23i | 0.192575i | ||||||||
\(435\) | 6.05943e23 | − | 8.24963e23i | 1.08650 | − | 1.47921i | ||||
\(436\) | 1.55972e24 | 2.73948 | ||||||||
\(437\) | −1.93202e23 | + | 1.93202e23i | −0.332413 | + | 0.332413i | ||||
\(438\) | −8.14290e23 | − | 8.14290e23i | −1.37250 | − | 1.37250i | ||||
\(439\) | − | 7.39853e23i | − | 1.22170i | −0.791746 | − | 0.610850i | \(-0.790828\pi\) | ||
0.791746 | − | 0.610850i | \(-0.209172\pi\) | |||||||
\(440\) | −5.59022e23 | − | 4.10607e23i | −0.904388 | − | 0.664281i | ||||
\(441\) | −1.28592e24 | −2.03829 | ||||||||
\(442\) | −5.55972e22 | + | 5.55972e22i | −0.0863480 | + | 0.0863480i | ||||
\(443\) | −5.19135e23 | − | 5.19135e23i | −0.790035 | − | 0.790035i | 0.191464 | − | 0.981500i | \(-0.438676\pi\) |
−0.981500 | + | 0.191464i | \(0.938676\pi\) | |||||||
\(444\) | 3.02653e23i | 0.451334i | ||||||||
\(445\) | 8.47299e22 | + | 5.53560e23i | 0.123822 | + | 0.808955i | ||||
\(446\) | 2.03587e23 | 0.291566 | ||||||||
\(447\) | 1.40329e24 | − | 1.40329e24i | 1.96961 | − | 1.96961i | ||||
\(448\) | 7.38071e22 | + | 7.38071e22i | 0.101530 | + | 0.101530i | ||||
\(449\) | − | 2.01668e23i | − | 0.271907i | −0.990715 | − | 0.135954i | \(-0.956590\pi\) | ||
0.990715 | − | 0.135954i | \(-0.0434098\pi\) | |||||||
\(450\) | 2.38822e24 | + | 1.24828e24i | 3.15618 | + | 1.64968i | ||||
\(451\) | −7.12335e23 | −0.922774 | ||||||||
\(452\) | 8.60163e22 | − | 8.60163e22i | 0.109228 | − | 0.109228i | ||||
\(453\) | 8.97380e23 | + | 8.97380e23i | 1.11710 | + | 1.11710i | ||||
\(454\) | − | 2.78545e22i | − | 0.0339933i | ||||||
\(455\) | 8.97911e22 | − | 1.37437e22i | 0.107431 | − | 0.0164438i | ||||
\(456\) | 7.99500e23 | 0.937853 | ||||||||
\(457\) | −8.60567e23 | + | 8.60567e23i | −0.989780 | + | 0.989780i | −0.999948 | − | 0.0101681i | \(-0.996763\pi\) |
0.0101681 | + | 0.999948i | \(0.496763\pi\) | |||||||
\(458\) | −1.94711e23 | − | 1.94711e23i | −0.219584 | − | 0.219584i | ||||
\(459\) | − | 1.41353e23i | − | 0.156311i | ||||||
\(460\) | −1.53824e24 | + | 2.09424e24i | −1.66803 | + | 2.27094i | ||||
\(461\) | 9.16818e23 | 0.974933 | 0.487466 | − | 0.873142i | \(-0.337921\pi\) | ||||
0.487466 | + | 0.873142i | \(0.337921\pi\) | |||||||
\(462\) | 1.77819e23 | − | 1.77819e23i | 0.185438 | − | 0.185438i | ||||
\(463\) | 3.64839e23 | + | 3.64839e23i | 0.373140 | + | 0.373140i | 0.868620 | − | 0.495480i | \(-0.165008\pi\) |
−0.495480 | + | 0.868620i | \(0.665008\pi\) | |||||||
\(464\) | − | 9.03961e23i | − | 0.906750i | ||||||
\(465\) | −1.26369e24 | − | 9.28193e23i | −1.24327 | − | 0.913192i | ||||
\(466\) | 2.12344e24 | 2.04912 | ||||||||
\(467\) | 3.81305e23 | − | 3.81305e23i | 0.360928 | − | 0.360928i | −0.503227 | − | 0.864154i | \(-0.667854\pi\) |
0.864154 | + | 0.503227i | \(0.167854\pi\) | |||||||
\(468\) | −2.63319e24 | − | 2.63319e24i | −2.44494 | − | 2.44494i | ||||
\(469\) | − | 2.68641e22i | − | 0.0244690i | ||||||
\(470\) | −4.66265e23 | − | 3.04621e24i | −0.416631 | − | 2.72195i | ||||
\(471\) | −3.46465e23 | −0.303718 | ||||||||
\(472\) | −9.78082e23 | + | 9.78082e23i | −0.841196 | + | 0.841196i | ||||
\(473\) | 2.82195e23 | + | 2.82195e23i | 0.238122 | + | 0.238122i | ||||
\(474\) | 4.57360e24i | 3.78663i | ||||||||
\(475\) | −1.20073e23 | − | 3.83042e23i | −0.0975442 | − | 0.311174i | ||||
\(476\) | 2.59701e22 | 0.0207019 | ||||||||
\(477\) | −8.94763e23 | + | 8.94763e23i | −0.699911 | + | 0.699911i | ||||
\(478\) | −6.28517e23 | − | 6.28517e23i | −0.482465 | − | 0.482465i | ||||
\(479\) | 3.41833e23i | 0.257510i | 0.991676 | + | 0.128755i | \(0.0410981\pi\) | ||||
−0.991676 | + | 0.128755i | \(0.958902\pi\) | |||||||
\(480\) | −3.57345e23 | + | 5.46966e22i | −0.264190 | + | 0.0404379i | ||||
\(481\) | −1.55027e23 | −0.112487 | ||||||||
\(482\) | −1.41195e24 | + | 1.41195e24i | −1.00553 | + | 1.00553i | ||||
\(483\) | −3.25343e23 | − | 3.25343e23i | −0.227414 | − | 0.227414i | ||||
\(484\) | 1.51654e24i | 1.04051i | ||||||||
\(485\) | 1.38462e24 | − | 1.88509e24i | 0.932513 | − | 1.26957i | ||||
\(486\) | 6.78425e23 | 0.448513 | ||||||||
\(487\) | −1.56878e24 | + | 1.56878e24i | −1.01813 | + | 1.01813i | −0.0182958 | + | 0.999833i | \(0.505824\pi\) |
−0.999833 | + | 0.0182958i | \(0.994176\pi\) | |||||||
\(488\) | −7.98047e23 | − | 7.98047e23i | −0.508452 | − | 0.508452i | ||||
\(489\) | − | 1.67064e24i | − | 1.04497i | ||||||
\(490\) | 2.21937e24 | + | 1.63015e24i | 1.36290 | + | 1.00107i | ||||
\(491\) | 2.14063e24 | 1.29065 | 0.645324 | − | 0.763909i | \(-0.276723\pi\) | ||||
0.645324 | + | 0.763909i | \(0.276723\pi\) | |||||||
\(492\) | 5.52153e24 | − | 5.52153e24i | 3.26869 | − | 3.26869i | ||||
\(493\) | 1.05994e23 | + | 1.05994e23i | 0.0616112 | + | 0.0616112i | ||||
\(494\) | 8.38520e23i | 0.478598i | ||||||||
\(495\) | 3.82488e23 | + | 2.49888e24i | 0.214373 | + | 1.40055i | ||||
\(496\) | −1.38470e24 | −0.762116 | ||||||||
\(497\) | −2.98928e23 | + | 2.98928e23i | −0.161569 | + | 0.161569i | ||||
\(498\) | 2.03211e24 | + | 2.03211e24i | 1.07866 | + | 1.07866i | ||||
\(499\) | − | 7.01278e23i | − | 0.365582i | −0.983152 | − | 0.182791i | \(-0.941487\pi\) | ||
0.983152 | − | 0.182791i | \(-0.0585132\pi\) | |||||||
\(500\) | −1.67994e24 | − | 3.42811e24i | −0.860127 | − | 1.75519i | ||||
\(501\) | −2.40070e24 | −1.20725 | ||||||||
\(502\) | 2.98931e24 | − | 2.98931e24i | 1.47651 | − | 1.47651i | ||||
\(503\) | 4.92485e23 | + | 4.92485e23i | 0.238936 | + | 0.238936i | 0.816409 | − | 0.577473i | \(-0.195961\pi\) |
−0.577473 | + | 0.816409i | \(0.695961\pi\) | |||||||
\(504\) | 9.08046e23i | 0.432746i | ||||||||
\(505\) | −7.14827e23 | + | 1.09414e23i | −0.334641 | + | 0.0512213i | ||||
\(506\) | −3.68475e24 | −1.69455 | ||||||||
\(507\) | −7.43410e23 | + | 7.43410e23i | −0.335859 | + | 0.335859i | ||||
\(508\) | 3.29105e24 | + | 3.29105e24i | 1.46070 | + | 1.46070i | ||||
\(509\) | − | 3.49695e23i | − | 0.152486i | −0.997089 | − | 0.0762428i | \(-0.975708\pi\) | ||
0.997089 | − | 0.0762428i | \(-0.0242924\pi\) | |||||||
\(510\) | −3.46372e23 | + | 4.71569e23i | −0.148392 | + | 0.202029i | ||||
\(511\) | −1.94832e23 | −0.0820111 | ||||||||
\(512\) | −2.65493e24 | + | 2.65493e24i | −1.09805 | + | 1.09805i | ||||
\(513\) | −1.06595e24 | − | 1.06595e24i | −0.433191 | − | 0.433191i | ||||
\(514\) | − | 6.75747e24i | − | 2.69846i | ||||||
\(515\) | 2.29406e24 | + | 1.68501e24i | 0.900201 | + | 0.661206i | ||||
\(516\) | −4.37477e24 | −1.68697 | ||||||||
\(517\) | 2.04421e24 | − | 2.04421e24i | 0.774659 | − | 0.774659i | ||||
\(518\) | 5.47313e22 | + | 5.47313e22i | 0.0203830 | + | 0.0203830i | ||||
\(519\) | − | 2.62091e24i | − | 0.959280i | ||||||
\(520\) | 5.89270e23 | + | 3.84984e24i | 0.211975 | + | 1.38488i | ||||
\(521\) | 1.20747e24 | 0.426911 | 0.213456 | − | 0.976953i | \(-0.431528\pi\) | ||||
0.213456 | + | 0.976953i | \(0.431528\pi\) | |||||||
\(522\) | −7.58840e24 | + | 7.58840e24i | −2.63704 | + | 2.63704i | ||||
\(523\) | −3.92939e24 | − | 3.92939e24i | −1.34218 | − | 1.34218i | −0.893888 | − | 0.448290i | \(-0.852033\pi\) |
−0.448290 | − | 0.893888i | \(-0.647967\pi\) | |||||||
\(524\) | 7.63055e23i | 0.256197i | ||||||||
\(525\) | 6.45025e23 | − | 2.02197e23i | 0.212884 | − | 0.0667330i | ||||
\(526\) | 5.44884e24 | 1.76780 | ||||||||
\(527\) | 1.62364e23 | − | 1.62364e23i | 0.0517837 | − | 0.0517837i | ||||
\(528\) | 2.34059e24 | + | 2.34059e24i | 0.733871 | + | 0.733871i | ||||
\(529\) | 3.49760e24i | 1.07813i | ||||||||
\(530\) | 2.67857e24 | − | 4.09991e23i | 0.811745 | − | 0.124249i | ||||
\(531\) | 5.04133e24 | 1.50208 | ||||||||
\(532\) | 1.95841e23 | − | 1.95841e23i | 0.0573718 | − | 0.0573718i | ||||
\(533\) | 2.82827e24 | + | 2.82827e24i | 0.814659 | + | 0.814659i | ||||
\(534\) | − | 8.70513e24i | − | 2.46549i | ||||||
\(535\) | −3.48733e24 | + | 4.74783e24i | −0.971200 | + | 1.32224i | ||||
\(536\) | 1.15181e24 | 0.315427 | ||||||||
\(537\) | 5.93812e24 | − | 5.93812e24i | 1.59912 | − | 1.59912i | ||||
\(538\) | −2.37497e24 | − | 2.37497e24i | −0.628954 | − | 0.628954i | ||||
\(539\) | 2.58328e24i | 0.672780i | ||||||||
\(540\) | −1.15545e25 | − | 8.48689e24i | −2.95942 | − | 2.17373i | ||||
\(541\) | −4.59430e24 | −1.15729 | −0.578647 | − | 0.815578i | \(-0.696419\pi\) | ||||
−0.578647 | + | 0.815578i | \(0.696419\pi\) | |||||||
\(542\) | −6.21012e24 | + | 6.21012e24i | −1.53853 | + | 1.53853i | ||||
\(543\) | 9.90284e21 | + | 9.90284e21i | 0.00241302 | + | 0.00241302i | ||||
\(544\) | − | 5.29406e22i | − | 0.0126882i | ||||||
\(545\) | 8.99538e23 | + | 5.87689e24i | 0.212056 | + | 1.38541i | ||||
\(546\) | −1.41203e24 | −0.327424 | ||||||||
\(547\) | −3.41070e24 | + | 3.41070e24i | −0.777961 | + | 0.777961i | −0.979484 | − | 0.201523i | \(-0.935411\pi\) |
0.201523 | + | 0.979484i | \(0.435411\pi\) | |||||||
\(548\) | 4.30384e24 | + | 4.30384e24i | 0.965676 | + | 0.965676i | ||||
\(549\) | 4.11337e24i | 0.907919i | ||||||||
\(550\) | 2.50768e24 | − | 4.79771e24i | 0.544513 | − | 1.04177i | ||||
\(551\) | 1.59861e24 | 0.341490 | ||||||||
\(552\) | 1.39492e25 | − | 1.39492e25i | 2.93156 | − | 2.93156i | ||||
\(553\) | 5.47154e23 | + | 5.47154e23i | 0.113132 | + | 0.113132i | ||||
\(554\) | − | 9.77540e24i | − | 1.98860i | ||||||
\(555\) | −1.14037e24 | + | 1.74549e23i | −0.228249 | + | 0.0349366i | ||||
\(556\) | −4.24770e24 | −0.836528 | ||||||||
\(557\) | 2.60790e24 | − | 2.60790e24i | 0.505351 | − | 0.505351i | −0.407745 | − | 0.913096i | \(-0.633685\pi\) |
0.913096 | + | 0.407745i | \(0.133685\pi\) | |||||||
\(558\) | 1.16240e25 | + | 1.16240e25i | 2.21641 | + | 2.21641i | ||||
\(559\) | − | 2.24087e24i | − | 0.420446i | ||||||
\(560\) | 3.53396e23 | − | 4.81132e23i | 0.0652484 | − | 0.0888326i | ||||
\(561\) | −5.48893e23 | −0.0997291 | ||||||||
\(562\) | 1.00743e25 | − | 1.00743e25i | 1.80130 | − | 1.80130i | ||||
\(563\) | −7.31957e24 | − | 7.31957e24i | −1.28798 | − | 1.28798i | −0.936011 | − | 0.351971i | \(-0.885511\pi\) |
−0.351971 | − | 0.936011i | \(-0.614489\pi\) | |||||||
\(564\) | 3.16907e25i | 5.48807i | ||||||||
\(565\) | 3.73710e23 | + | 2.74494e23i | 0.0636940 | + | 0.0467839i | ||||
\(566\) | −4.83532e24 | −0.811106 | ||||||||
\(567\) | 6.65501e23 | − | 6.65501e23i | 0.109876 | − | 0.109876i | ||||
\(568\) | −1.28167e25 | − | 1.28167e25i | −2.08277 | − | 2.08277i | ||||
\(569\) | 3.09833e24i | 0.495584i | 0.968813 | + | 0.247792i | \(0.0797049\pi\) | ||||
−0.968813 | + | 0.247792i | \(0.920295\pi\) | |||||||
\(570\) | 9.44114e23 | + | 6.16812e24i | 0.148645 | + | 0.971134i | ||||
\(571\) | 1.26522e24 | 0.196083 | 0.0980415 | − | 0.995182i | \(-0.468742\pi\) | ||||
0.0980415 | + | 0.995182i | \(0.468742\pi\) | |||||||
\(572\) | −5.28982e24 | + | 5.28982e24i | −0.807006 | + | 0.807006i | ||||
\(573\) | −8.28558e24 | − | 8.28558e24i | −1.24432 | − | 1.24432i | ||||
\(574\) | − | 1.99701e24i | − | 0.295239i | ||||||
\(575\) | −8.77806e24 | − | 4.58814e24i | −1.27758 | − | 0.667769i | ||||
\(576\) | 1.63109e25 | 2.33709 | ||||||||
\(577\) | −1.27729e24 | + | 1.27729e24i | −0.180180 | + | 0.180180i | −0.791434 | − | 0.611254i | \(-0.790665\pi\) |
0.611254 | + | 0.791434i | \(0.290665\pi\) | |||||||
\(578\) | 8.69098e24 | + | 8.69098e24i | 1.20703 | + | 1.20703i | ||||
\(579\) | 5.23452e24i | 0.715764i | ||||||||
\(580\) | 1.50281e25 | − | 2.30026e24i | 2.02327 | − | 0.309688i | ||||
\(581\) | 4.86215e23 | 0.0644530 | ||||||||
\(582\) | −2.57093e25 | + | 2.57093e25i | −3.35570 | + | 3.35570i | ||||
\(583\) | 1.79749e24 | + | 1.79749e24i | 0.231021 | + | 0.231021i | ||||
\(584\) | − | 8.35352e24i | − | 1.05719i | ||||||
\(585\) | 8.40297e24 | − | 1.14402e25i | 1.04720 | − | 1.42571i | ||||
\(586\) | −2.61228e25 | −3.20584 | ||||||||
\(587\) | 1.46830e22 | − | 1.46830e22i | 0.00177448 | − | 0.00177448i | −0.706219 | − | 0.707993i | \(-0.749601\pi\) |
0.707993 | + | 0.706219i | \(0.249601\pi\) | |||||||
\(588\) | −2.00239e25 | − | 2.00239e25i | −2.38315 | − | 2.38315i | ||||
\(589\) | − | 2.44878e24i | − | 0.287020i | ||||||
\(590\) | −8.70087e24 | − | 6.39087e24i | −1.00437 | − | 0.737721i | ||||
\(591\) | 4.51583e24 | 0.513393 | ||||||||
\(592\) | −7.20417e23 | + | 7.20417e23i | −0.0806657 | + | 0.0806657i | ||||
\(593\) | 1.24863e25 | + | 1.24863e25i | 1.37702 | + | 1.37702i | 0.849613 | + | 0.527407i | \(0.176836\pi\) |
0.527407 | + | 0.849613i | \(0.323164\pi\) | |||||||
\(594\) | − | 2.03298e25i | − | 2.20828i | ||||||
\(595\) | 1.49777e22 | + | 9.78529e22i | 0.00160248 | + | 0.0104694i | ||||
\(596\) | 2.94762e25 | 3.10638 | ||||||||
\(597\) | 4.26710e24 | − | 4.26710e24i | 0.442960 | − | 0.442960i | ||||
\(598\) | 1.46300e25 | + | 1.46300e25i | 1.49601 | + | 1.49601i | ||||
\(599\) | − | 1.93289e25i | − | 1.94700i | −0.228693 | − | 0.973499i | \(-0.573445\pi\) | ||
0.228693 | − | 0.973499i | \(-0.426555\pi\) | |||||||
\(600\) | 8.66929e24 | + | 2.76558e25i | 0.860245 | + | 2.74426i | ||||
\(601\) | 2.12695e24 | 0.207916 | 0.103958 | − | 0.994582i | \(-0.466849\pi\) | ||||
0.103958 | + | 0.994582i | \(0.466849\pi\) | |||||||
\(602\) | −7.91127e23 | + | 7.91127e23i | −0.0761865 | + | 0.0761865i | ||||
\(603\) | −2.96839e24 | − | 2.96839e24i | −0.281621 | − | 0.281621i | ||||
\(604\) | 1.88495e25i | 1.76185i | ||||||||
\(605\) | −5.71419e24 | + | 8.74634e23i | −0.526206 | + | 0.0805430i | ||||
\(606\) | 1.12412e25 | 1.01990 | ||||||||
\(607\) | −2.97673e24 | + | 2.97673e24i | −0.266098 | + | 0.266098i | −0.827526 | − | 0.561428i | \(-0.810252\pi\) |
0.561428 | + | 0.827526i | \(0.310252\pi\) | |||||||
\(608\) | −3.99227e23 | − | 3.99227e23i | −0.0351631 | − | 0.0351631i | ||||
\(609\) | 2.69199e24i | 0.233624i | ||||||||
\(610\) | 5.21451e24 | − | 7.09930e24i | 0.445908 | − | 0.607082i | ||||
\(611\) | −1.62328e25 | −1.36780 | ||||||||
\(612\) | 2.86960e24 | − | 2.86960e24i | 0.238264 | − | 0.238264i | ||||
\(613\) | 4.60147e24 | + | 4.60147e24i | 0.376489 | + | 0.376489i | 0.869834 | − | 0.493345i | \(-0.164226\pi\) |
−0.493345 | + | 0.869834i | \(0.664226\pi\) | |||||||
\(614\) | 1.43683e24i | 0.115848i | ||||||||
\(615\) | 2.39891e25 | + | 1.76202e25i | 1.90606 | + | 1.40002i | ||||
\(616\) | 1.82418e24 | 0.142837 | ||||||||
\(617\) | 9.13299e24 | − | 9.13299e24i | 0.704768 | − | 0.704768i | −0.260662 | − | 0.965430i | \(-0.583941\pi\) |
0.965430 | + | 0.260662i | \(0.0839408\pi\) | |||||||
\(618\) | −3.12869e25 | − | 3.12869e25i | −2.37939 | − | 2.37939i | ||||
\(619\) | − | 2.29659e24i | − | 0.172135i | −0.996289 | − | 0.0860673i | \(-0.972570\pi\) | ||
0.996289 | − | 0.0860673i | \(-0.0274300\pi\) | |||||||
\(620\) | −3.52358e24 | − | 2.30203e25i | −0.260291 | − | 1.70054i | ||||
\(621\) | −3.71961e25 | −2.70815 | ||||||||
\(622\) | −8.67426e24 | + | 8.67426e24i | −0.622470 | + | 0.622470i | ||||
\(623\) | −1.04142e24 | − | 1.04142e24i | −0.0736604 | − | 0.0736604i | ||||
\(624\) | − | 1.85863e25i | − | 1.29578i | ||||||
\(625\) | 1.19479e25 | − | 8.30694e24i | 0.821055 | − | 0.570849i | ||||
\(626\) | 2.83024e25 | 1.91715 | ||||||||
\(627\) | −4.13921e24 | + | 4.13921e24i | −0.276382 | + | 0.276382i | ||||
\(628\) | −3.63876e24 | − | 3.63876e24i | −0.239506 | − | 0.239506i | ||||
\(629\) | − | 1.68945e23i | − | 0.0109620i | ||||||
\(630\) | −7.00555e24 | + | 1.07229e24i | −0.448102 | + | 0.0685881i | ||||
\(631\) | −1.44627e25 | −0.911979 | −0.455990 | − | 0.889985i | \(-0.650715\pi\) | ||||
−0.455990 | + | 0.889985i | \(0.650715\pi\) | |||||||
\(632\) | −2.34595e25 | + | 2.34595e25i | −1.45836 | + | 1.45836i | ||||
\(633\) | 8.75995e24 | + | 8.75995e24i | 0.536869 | + | 0.536869i | ||||
\(634\) | 4.44415e25i | 2.68526i | ||||||||
\(635\) | −1.05023e25 | + | 1.42984e25i | −0.625637 | + | 0.851775i | ||||
\(636\) | −2.78659e25 | −1.63666 | ||||||||
\(637\) | 1.02567e25 | − | 1.02567e25i | 0.593956 | − | 0.593956i | ||||
\(638\) | 1.52444e25 | + | 1.52444e25i | 0.870410 | + | 0.870410i | ||||
\(639\) | 6.60611e25i | 3.71910i | ||||||||
\(640\) | −2.59371e25 | − | 1.90510e25i | −1.43980 | − | 1.05754i | ||||
\(641\) | 9.26904e24 | 0.507356 | 0.253678 | − | 0.967289i | \(-0.418360\pi\) | ||||
0.253678 | + | 0.967289i | \(0.418360\pi\) | |||||||
\(642\) | 6.47519e25 | − | 6.47519e25i | 3.49492 | − | 3.49492i | ||||
\(643\) | 2.64464e24 | + | 2.64464e24i | 0.140756 | + | 0.140756i | 0.773974 | − | 0.633218i | \(-0.218266\pi\) |
−0.633218 | + | 0.773974i | \(0.718266\pi\) | |||||||
\(644\) | − | 6.83385e24i | − | 0.358668i | ||||||
\(645\) | −2.52306e24 | − | 1.64837e25i | −0.130584 | − | 0.853136i | ||||
\(646\) | −9.13805e23 | −0.0466403 | ||||||||
\(647\) | −3.44868e24 | + | 3.44868e24i | −0.173586 | + | 0.173586i | −0.788553 | − | 0.614967i | \(-0.789169\pi\) |
0.614967 | + | 0.788553i | \(0.289169\pi\) | |||||||
\(648\) | 2.85337e25 | + | 2.85337e25i | 1.41639 | + | 1.41639i | ||||
\(649\) | − | 1.01276e25i | − | 0.495795i | ||||||
\(650\) | −2.90055e25 | + | 9.09240e24i | −1.40043 | + | 0.438994i | ||||
\(651\) | 4.12363e24 | 0.196359 | ||||||||
\(652\) | 1.75459e25 | − | 1.75459e25i | 0.824039 | − | 0.824039i | ||||
\(653\) | −5.78972e24 | − | 5.78972e24i | −0.268188 | − | 0.268188i | 0.560182 | − | 0.828370i | \(-0.310731\pi\) |
−0.828370 | + | 0.560182i | \(0.810731\pi\) | |||||||
\(654\) | − | 9.24184e25i | − | 4.22239i | ||||||
\(655\) | −2.87512e24 | + | 4.40077e23i | −0.129564 | + | 0.0198316i | ||||
\(656\) | 2.62863e25 | 1.16841 | ||||||||
\(657\) | −2.15283e25 | + | 2.15283e25i | −0.943890 | + | 0.943890i | ||||
\(658\) | 5.73089e24 | + | 5.73089e24i | 0.247850 | + | 0.247850i | ||||
\(659\) | − | 3.06925e25i | − | 1.30938i | −0.755900 | − | 0.654688i | \(-0.772800\pi\) | ||
0.755900 | − | 0.654688i | \(-0.227200\pi\) | |||||||
\(660\) | −3.29558e25 | + | 4.48677e25i | −1.38687 | + | 1.88816i | ||||
\(661\) | 2.86757e25 | 1.19042 | 0.595211 | − | 0.803570i | \(-0.297069\pi\) | ||||
0.595211 | + | 0.803570i | \(0.297069\pi\) | |||||||
\(662\) | −3.82513e25 | + | 3.82513e25i | −1.56648 | + | 1.56648i | ||||
\(663\) | 2.17934e24 | + | 2.17934e24i | 0.0880446 | + | 0.0880446i | ||||
\(664\) | 2.08467e25i | 0.830854i | ||||||||
\(665\) | 8.50858e23 | + | 6.24964e23i | 0.0334551 | + | 0.0245731i | ||||
\(666\) | 1.20953e25 | 0.469188 | ||||||||
\(667\) | 2.78917e25 | − | 2.78917e25i | 1.06744 | − | 1.06744i | ||||
\(668\) | −2.52134e25 | − | 2.52134e25i | −0.952015 | − | 0.952015i | ||||
\(669\) | − | 7.98036e24i | − | 0.297295i | ||||||
\(670\) | 1.36015e24 | + | 8.88619e24i | 0.0499936 | + | 0.326620i | ||||
\(671\) | 8.26338e24 | 0.299678 | ||||||||
\(672\) | 6.72280e23 | − | 6.72280e23i | 0.0240562 | − | 0.0240562i | ||||
\(673\) | 2.21113e25 | + | 2.21113e25i | 0.780691 | + | 0.780691i | 0.979947 | − | 0.199256i | \(-0.0638525\pi\) |
−0.199256 | + | 0.979947i | \(0.563853\pi\) | |||||||
\(674\) | 4.39744e25i | 1.53201i | ||||||||
\(675\) | 2.53140e25 | − | 4.84310e25i | 0.870216 | − | 1.66490i | ||||
\(676\) | −1.56154e25 | −0.529702 | ||||||||
\(677\) | −2.71432e25 | + | 2.71432e25i | −0.908580 | + | 0.908580i | −0.996158 | − | 0.0875781i | \(-0.972087\pi\) |
0.0875781 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(678\) | −5.09674e24 | − | 5.09674e24i | −0.168355 | − | 0.168355i | ||||
\(679\) | 6.15137e24i | 0.200514i | ||||||||
\(680\) | −4.19549e24 | + | 6.42177e23i | −0.134959 | + | 0.0206573i | ||||
\(681\) | −1.09186e24 | −0.0346611 | ||||||||
\(682\) | 2.33516e25 | − | 2.33516e25i | 0.731572 | − | 0.731572i | ||||
\(683\) | −1.67180e25 | − | 1.67180e25i | −0.516888 | − | 0.516888i | 0.399740 | − | 0.916628i | \(-0.369100\pi\) |
−0.916628 | + | 0.399740i | \(0.869100\pi\) | |||||||
\(684\) | − | 4.32795e25i | − | 1.32062i | ||||||
\(685\) | −1.37343e25 | + | 1.86987e25i | −0.413612 | + | 0.563113i | ||||
\(686\) | −1.46036e25 | −0.434054 | ||||||||
\(687\) | −7.63241e24 | + | 7.63241e24i | −0.223898 | + | 0.223898i | ||||
\(688\) | −1.04134e25 | − | 1.04134e25i | −0.301508 | − | 0.301508i | ||||
\(689\) | − | 1.42736e25i | − | 0.407907i | ||||||
\(690\) | 1.24090e26 | + | 9.11456e25i | 3.50023 | + | 2.57095i | ||||
\(691\) | −2.42360e24 | −0.0674774 | −0.0337387 | − | 0.999431i | \(-0.510741\pi\) | ||||
−0.0337387 | + | 0.999431i | \(0.510741\pi\) | |||||||
\(692\) | 2.75261e25 | − | 2.75261e25i | 0.756468 | − | 0.756468i | ||||
\(693\) | −4.70118e24 | − | 4.70118e24i | −0.127529 | − | 0.127529i | ||||
\(694\) | 7.07377e25i | 1.89415i | ||||||||
\(695\) | −2.44977e24 | − | 1.60049e25i | −0.0647534 | − | 0.423049i | ||||
\(696\) | −1.15420e26 | −3.01161 | ||||||||
\(697\) | −3.08220e24 | + | 3.08220e24i | −0.0793901 | + | 0.0793901i | ||||
\(698\) | 1.54669e25 | + | 1.54669e25i | 0.393282 | + | 0.393282i | ||||
\(699\) | − | 8.32360e25i | − | 2.08938i | ||||||
\(700\) | 8.89797e24 | + | 4.65082e24i | 0.220500 | + | 0.115252i | ||||
\(701\) | −7.79904e24 | −0.190800 | −0.0954002 | − | 0.995439i | \(-0.530413\pi\) | ||||
−0.0954002 | + | 0.995439i | \(0.530413\pi\) | |||||||
\(702\) | −8.07179e25 | + | 8.07179e25i | −1.94956 | + | 1.94956i | ||||
\(703\) | −1.27402e24 | − | 1.27402e24i | −0.0303794 | − | 0.0303794i | ||||
\(704\) | − | 3.27670e25i | − | 0.771405i | ||||||
\(705\) | −1.19408e26 | + | 1.82770e25i | −2.77543 | + | 0.424817i | ||||
\(706\) | −1.40512e26 | −3.22455 | ||||||||
\(707\) | 1.34482e24 | − | 1.34482e24i | 0.0304711 | − | 0.0304711i | ||||
\(708\) | 7.85019e25 | + | 7.85019e25i | 1.75623 | + | 1.75623i | ||||
\(709\) | − | 9.63065e23i | − | 0.0212735i | −0.999943 | − | 0.0106368i | \(-0.996614\pi\) | ||
0.999943 | − | 0.0106368i | \(-0.00338585\pi\) | |||||||
\(710\) | 8.37454e25 | − | 1.14015e26i | 1.82657 | − | 2.48678i | ||||
\(711\) | 1.20917e26 | 2.60413 | ||||||||
\(712\) | 4.46515e25 | − | 4.46515e25i | 0.949545 | − | 0.949545i | ||||
\(713\) | −4.27249e25 | − | 4.27249e25i | −0.897171 | − | 0.897171i | ||||
\(714\) | − | 1.53881e24i | − | 0.0319081i | ||||||
\(715\) | −2.29824e25 | − | 1.68808e25i | −0.470588 | − | 0.345651i | ||||
\(716\) | 1.24731e26 | 2.52206 | ||||||||
\(717\) | −2.46371e25 | + | 2.46371e25i | −0.491945 | + | 0.491945i | ||||
\(718\) | −1.35763e25 | − | 1.35763e25i | −0.267708 | − | 0.267708i | ||||
\(719\) | 8.14469e25i | 1.58604i | 0.609194 | + | 0.793021i | \(0.291493\pi\) | ||||
−0.609194 | + | 0.793021i | \(0.708507\pi\) | |||||||
\(720\) | −1.41144e25 | − | 9.22126e25i | −0.271437 | − | 1.77336i | ||||
\(721\) | −7.48589e24 | −0.142176 | ||||||||
\(722\) | 5.79082e25 | − | 5.79082e25i | 1.08619 | − | 1.08619i | ||||
\(723\) | 5.53466e25 | + | 5.53466e25i | 1.02529 | + | 1.02529i | ||||
\(724\) | 2.08010e23i | 0.00380572i | ||||||||
\(725\) | 1.73343e25 | + | 5.52980e25i | 0.313232 | + | 0.999235i | ||||
\(726\) | 8.98597e25 | 1.60375 | ||||||||
\(727\) | −2.64975e25 | + | 2.64975e25i | −0.467085 | + | 0.467085i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(728\) | −7.24276e24 | − | 7.24276e24i | −0.126102 | − | 0.126102i | ||||
\(729\) | 4.43919e25i | 0.763407i | ||||||||
\(730\) | 6.44472e25 | − | 9.86452e24i | 1.09471 | − | 0.167560i | ||||
\(731\) | 2.44206e24 | 0.0409732 | ||||||||
\(732\) | −6.40521e25 | + | 6.40521e25i | −1.06153 | + | 1.06153i | ||||
\(733\) | 8.48127e24 | + | 8.48127e24i | 0.138843 | + | 0.138843i | 0.773112 | − | 0.634269i | \(-0.218699\pi\) |
−0.634269 | + | 0.773112i | \(0.718699\pi\) | |||||||
\(734\) | 1.04435e26i | 1.68882i | ||||||||
\(735\) | 6.38997e25 | − | 8.69965e25i | 1.02074 | − | 1.38968i | ||||
\(736\) | −1.39310e25 | −0.219827 | ||||||||
\(737\) | −5.96322e24 | + | 5.96322e24i | −0.0929551 | + | 0.0929551i | ||||
\(738\) | −2.20663e26 | − | 2.20663e26i | −3.39799 | − | 3.39799i | ||||
\(739\) | − | 6.86829e25i | − | 1.04484i | −0.852689 | − | 0.522419i | \(-0.825030\pi\) | ||
0.852689 | − | 0.522419i | \(-0.174970\pi\) | |||||||
\(740\) | −1.38100e25 | − | 1.01436e25i | −0.207543 | − | 0.152442i | ||||
\(741\) | 3.28689e25 | 0.488001 | ||||||||
\(742\) | −5.03923e24 | + | 5.03923e24i | −0.0739144 | + | 0.0739144i | ||||
\(743\) | −2.29148e25 | − | 2.29148e25i | −0.332060 | − | 0.332060i | 0.521308 | − | 0.853369i | \(-0.325444\pi\) |
−0.853369 | + | 0.521308i | \(0.825444\pi\) | |||||||
\(744\) | 1.76803e26i | 2.53123i | ||||||||
\(745\) | 1.69998e25 | + | 1.11064e26i | 0.240457 | + | 1.57096i | ||||
\(746\) | −6.30476e25 | −0.881088 | ||||||||
\(747\) | 5.37251e25 | − | 5.37251e25i | 0.741808 | − | 0.741808i | ||||
\(748\) | −5.76476e24 | − | 5.76476e24i | −0.0786443 | − | 0.0786443i | ||||
\(749\) | − | 1.54929e25i | − | 0.208832i | ||||||
\(750\) | −2.03126e26 | + | 9.95415e25i | −2.70529 | + | 1.32572i | ||||
\(751\) | 4.53369e25 | 0.596612 | 0.298306 | − | 0.954470i | \(-0.403578\pi\) | ||||
0.298306 | + | 0.954470i | \(0.403578\pi\) | |||||||
\(752\) | −7.54346e25 | + | 7.54346e25i | −0.980867 | + | 0.980867i | ||||
\(753\) | −1.17177e26 | − | 1.17177e26i | −1.50552 | − | 1.50552i | ||||
\(754\) | − | 1.21053e26i | − | 1.53686i | ||||||
\(755\) | −7.10233e25 | + | 1.08711e25i | −0.891002 | + | 0.136380i | ||||
\(756\) | 3.77042e25 | 0.467405 | ||||||||
\(757\) | 2.83630e25 | − | 2.83630e25i | 0.347447 | − | 0.347447i | −0.511711 | − | 0.859158i | \(-0.670988\pi\) |
0.859158 | + | 0.511711i | \(0.170988\pi\) | |||||||
\(758\) | 7.14103e25 | + | 7.14103e25i | 0.864446 | + | 0.864446i | ||||
\(759\) | 1.44438e26i | 1.72784i | ||||||||
\(760\) | −2.67956e25 | + | 3.64810e25i | −0.316768 | + | 0.431265i | ||||
\(761\) | 1.14310e26 | 1.33543 | 0.667715 | − | 0.744417i | \(-0.267273\pi\) | ||||
0.667715 | + | 0.744417i | \(0.267273\pi\) | |||||||
\(762\) | 1.95005e26 | − | 1.95005e26i | 2.25139 | − | 2.25139i | ||||
\(763\) | −1.10563e25 | − | 1.10563e25i | −0.126150 | − | 0.126150i | ||||
\(764\) | − | 1.74039e26i | − | 1.96249i | ||||||
\(765\) | 1.24674e25 | + | 9.15742e24i | 0.138939 | + | 0.102052i | ||||
\(766\) | 7.88207e25 | 0.868123 | ||||||||
\(767\) | −4.02107e25 | + | 4.02107e25i | −0.437707 | + | 0.437707i | ||||
\(768\) | 2.23793e26 | + | 2.23793e26i | 2.40766 | + | 2.40766i | ||||
\(769\) | − | 1.51660e26i | − | 1.61263i | −0.591488 | − | 0.806314i | \(-0.701459\pi\) | ||
0.591488 | − | 0.806314i | \(-0.298541\pi\) | |||||||
\(770\) | 2.15414e24 | + | 1.40735e25i | 0.0226390 | + | 0.147906i | ||||
\(771\) | −2.64884e26 | −2.75148 | ||||||||
\(772\) | −5.49757e25 | + | 5.49757e25i | −0.564437 | + | 0.564437i | ||||
\(773\) | 8.28025e25 | + | 8.28025e25i | 0.840288 | + | 0.840288i | 0.988896 | − | 0.148608i | \(-0.0474794\pi\) |
−0.148608 | + | 0.988896i | \(0.547479\pi\) | |||||||
\(774\) | 1.74834e26i | 1.75370i | ||||||||
\(775\) | 8.47064e25 | − | 2.65530e25i | 0.839849 | − | 0.263268i | ||||
\(776\) | −2.63743e26 | −2.58479 | ||||||||
\(777\) | 2.14540e24 | − | 2.14540e24i | 0.0207835 | − | 0.0207835i | ||||
\(778\) | −1.71756e26 | − | 1.71756e26i | −1.64474 | − | 1.64474i | ||||
\(779\) | 4.64859e25i | 0.440032i | ||||||||
\(780\) | 3.08992e26 | − | 4.72954e25i | 2.89132 | − | 0.442556i | ||||
\(781\) | 1.32710e26 | 1.22757 | ||||||||
\(782\) | −1.59436e25 | + | 1.59436e25i | −0.145789 | + | 0.145789i | ||||
\(783\) | 1.53886e26 | + | 1.53886e26i | 1.39105 | + | 1.39105i | ||||
\(784\) | − | 9.53272e25i | − | 0.851868i | ||||||
\(785\) | 1.16119e25 | − | 1.58091e25i | 0.102583 | − | 0.139663i | ||||
\(786\) | 4.52134e25 | 0.394879 | ||||||||
\(787\) | −1.19064e26 | + | 1.19064e26i | −1.02804 | + | 1.02804i | −0.0284429 | + | 0.999595i | \(0.509055\pi\) |
−0.999595 | + | 0.0284429i | \(0.990945\pi\) | |||||||
\(788\) | 4.74276e25 | + | 4.74276e25i | 0.404851 | + | 0.404851i | ||||
\(789\) | − | 2.13587e26i | − | 1.80253i | ||||||
\(790\) | −2.08692e26 | − | 1.53286e26i | −1.74126 | − | 1.27897i | ||||
\(791\) | −1.21948e24 | −0.0100597 | ||||||||
\(792\) | 2.01566e26 | − | 2.01566e26i | 1.64395 | − | 1.64395i | ||||
\(793\) | −3.28091e25 | − | 3.28091e25i | −0.264567 | − | 0.264567i | ||||
\(794\) | 4.93202e25i | 0.393225i | ||||||||
\(795\) | −1.60711e25 | − | 1.04996e26i | −0.126690 | − | 0.827694i | ||||
\(796\) | 8.96308e25 | 0.698618 | ||||||||
\(797\) | −8.58745e25 | + | 8.58745e25i | −0.661819 | + | 0.661819i | −0.955809 | − | 0.293989i | \(-0.905017\pi\) |
0.293989 | + | 0.955809i | \(0.405017\pi\) | |||||||
\(798\) | −1.16042e25 | − | 1.16042e25i | −0.0884278 | − | 0.0884278i | ||||
\(799\) | − | 1.76902e25i | − | 0.133294i | ||||||
\(800\) | 9.48081e24 | − | 1.81388e25i | 0.0706376 | − | 0.135144i | ||||
\(801\) | −2.30147e26 | −1.69556 | ||||||||
\(802\) | −1.03524e26 | + | 1.03524e26i | −0.754176 | + | 0.754176i | ||||
\(803\) | 4.32483e25 | + | 4.32483e25i | 0.311551 | + | 0.311551i | ||||
\(804\) | − | 9.24456e25i | − | 0.658540i | ||||||
\(805\) | 2.57493e25 | − | 3.94129e24i | 0.181386 | − | 0.0277636i | ||||
\(806\) | −1.85431e26 | −1.29172 | ||||||||
\(807\) | −9.30959e25 | + | 9.30959e25i | −0.641311 | + | 0.641311i | ||||
\(808\) | 5.76597e25 | + | 5.76597e25i | 0.392798 | + | 0.392798i | ||||
\(809\) | − | 8.56511e25i | − | 0.577027i | −0.957476 | − | 0.288514i | \(-0.906839\pi\) | ||
0.957476 | − | 0.288514i | \(-0.0931610\pi\) | |||||||
\(810\) | −1.86442e26 | + | 2.53831e26i | −1.24216 | + | 1.69114i | ||||
\(811\) | 1.16592e26 | 0.768210 | 0.384105 | − | 0.923289i | \(-0.374510\pi\) | ||||
0.384105 | + | 0.923289i | \(0.374510\pi\) | |||||||
\(812\) | −2.82727e25 | + | 2.82727e25i | −0.184231 | + | 0.184231i | ||||
\(813\) | 2.43429e26 | + | 2.43429e26i | 1.56876 | + | 1.56876i | ||||
\(814\) | − | 2.42982e25i | − | 0.154866i | ||||||
\(815\) | 7.62307e25 | + | 5.59922e25i | 0.480520 | + | 0.352947i | ||||
\(816\) | 2.02550e25 | 0.126276 | ||||||||
\(817\) | 1.84156e25 | − | 1.84156e25i | 0.113550 | − | 0.113550i | ||||
\(818\) | 2.78669e26 | + | 2.78669e26i | 1.69945 | + | 1.69945i | ||||
\(819\) | 3.73314e25i | 0.225174i | ||||||||
\(820\) | 6.68892e25 | + | 4.37003e26i | 0.399054 | + | 2.60711i | ||||
\(821\) | 6.74408e25 | 0.397955 | 0.198978 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198978 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(822\) | 2.55016e26 | − | 2.55016e26i | 1.48841 | − | 1.48841i | ||||
\(823\) | −1.15147e26 | − | 1.15147e26i | −0.664746 | − | 0.664746i | 0.291749 | − | 0.956495i | \(-0.405763\pi\) |
−0.956495 | + | 0.291749i | \(0.905763\pi\) | |||||||
\(824\) | − | 3.20961e26i | − | 1.83277i | ||||||
\(825\) | −1.88064e26 | − | 9.82978e25i | −1.06223 | − | 0.555211i | ||||
\(826\) | 2.83924e25 | 0.158628 | ||||||||
\(827\) | 1.86919e26 | − | 1.86919e26i | 1.03301 | − | 1.03301i | 0.0335706 | − | 0.999436i | \(-0.489312\pi\) |
0.999436 | − | 0.0335706i | \(-0.0106879\pi\) | |||||||
\(828\) | −7.55117e26 | − | 7.55117e26i | −4.12802 | − | 4.12802i | ||||
\(829\) | 2.04538e26i | 1.10607i | 0.833157 | + | 0.553036i | \(0.186531\pi\) | ||||
−0.833157 | + | 0.553036i | \(0.813469\pi\) | |||||||
\(830\) | −1.60832e26 | + | 2.46175e25i | −0.860337 | + | 0.131686i | ||||
\(831\) | −3.83183e26 | −2.02767 | ||||||||
\(832\) | −1.30099e26 | + | 1.30099e26i | −0.681026 | + | 0.681026i | ||||
\(833\) | 1.11776e25 | + | 1.11776e25i | 0.0578821 | + | 0.0578821i | ||||
\(834\) | 2.51689e26i | 1.28935i | ||||||||
\(835\) | 8.04606e25 | − | 1.09543e26i | 0.407761 | − | 0.555147i | ||||
\(836\) | −8.69444e25 | −0.435898 | ||||||||
\(837\) | 2.35725e26 | − | 2.35725e26i | 1.16917 | − | 1.16917i | ||||
\(838\) | 3.69532e26 | + | 3.69532e26i | 1.81324 | + | 1.81324i | ||||
\(839\) | 1.70699e26i | 0.828656i | 0.910128 | + | 0.414328i | \(0.135983\pi\) | ||||
−0.910128 | + | 0.414328i | \(0.864017\pi\) | |||||||
\(840\) | −6.14323e25 | − | 4.51226e25i | −0.295042 | − | 0.216711i | ||||
\(841\) | −2.03268e25 | −0.0965841 | ||||||||
\(842\) | 2.96389e26 | − | 2.96389e26i | 1.39333 | − | 1.39333i | ||||
\(843\) | −3.94897e26 | − | 3.94897e26i | −1.83669 | − | 1.83669i | ||||
\(844\) | 1.84003e26i | 0.846727i | ||||||||
\(845\) | −9.00585e24 | − | 5.88373e25i | −0.0410029 | − | 0.267881i | ||||
\(846\) | 1.26649e27 | 5.70516 | ||||||||
\(847\) | 1.07502e25 | − | 1.07502e25i | 0.0479143 | − | 0.0479143i | ||||
\(848\) | −6.63304e25 | − | 6.63304e25i | −0.292516 | − | 0.292516i | ||||
\(849\) | 1.89538e26i | 0.827042i | ||||||||
\(850\) | −9.90875e24 | − | 3.16097e25i | −0.0427808 | − | 0.136474i | ||||
\(851\) | −4.44569e25 | −0.189921 | ||||||||
\(852\) | −1.02868e27 | + | 1.02868e27i | −4.34835 | + | 4.34835i | ||||
\(853\) | −2.02406e26 | − | 2.02406e26i | −0.846607 | − | 0.846607i | 0.143101 | − | 0.989708i | \(-0.454293\pi\) |
−0.989708 | + | 0.143101i | \(0.954293\pi\) | |||||||
\(854\) | 2.31662e25i | 0.0958812i | ||||||||
\(855\) | 1.63073e26 | − | 2.49606e25i | 0.667864 | − | 0.102226i | ||||
\(856\) | 6.64268e26 | 2.69203 | ||||||||
\(857\) | 5.60488e25 | − | 5.60488e25i | 0.224770 | − | 0.224770i | −0.585733 | − | 0.810504i | \(-0.699193\pi\) |
0.810504 | + | 0.585733i | \(0.199193\pi\) | |||||||
\(858\) | 3.13439e26 | + | 3.13439e26i | 1.24385 | + | 1.24385i | ||||
\(859\) | − | 2.06187e26i | − | 0.809698i | −0.914384 | − | 0.404849i | \(-0.867324\pi\) | ||
0.914384 | − | 0.404849i | \(-0.132676\pi\) | |||||||
\(860\) | 1.46622e26 | − | 1.99619e26i | 0.569789 | − | 0.775741i | ||||
\(861\) | −7.82803e25 | −0.301040 | ||||||||
\(862\) | −4.72442e25 | + | 4.72442e25i | −0.179797 | + | 0.179797i | ||||
\(863\) | −1.11113e26 | − | 1.11113e26i | −0.418472 | − | 0.418472i | 0.466205 | − | 0.884677i | \(-0.345621\pi\) |
−0.884677 | + | 0.466205i | \(0.845621\pi\) | |||||||
\(864\) | − | 7.68610e25i | − | 0.286472i | ||||||
\(865\) | 1.19591e26 | + | 8.78409e25i | 0.441117 | + | 0.324005i | ||||
\(866\) | −7.24708e26 | −2.64546 | ||||||||
\(867\) | 3.40675e26 | − | 3.40675e26i | 1.23075 | − | 1.23075i | ||||
\(868\) | 4.33085e25 | + | 4.33085e25i | 0.154845 | + | 0.154845i | ||||
\(869\) | − | 2.42912e26i | − | 0.859548i | ||||||
\(870\) | −1.36298e26 | − | 8.90464e26i | −0.477326 | − | 3.11848i | ||||
\(871\) | 4.73530e25 | 0.164129 | ||||||||
\(872\) | 4.74044e26 | − | 4.74044e26i | 1.62619 | − | 1.62619i | ||||
\(873\) | 6.79705e26 | + | 6.79705e26i | 2.30777 | + | 2.30777i | ||||
\(874\) | 2.40462e26i | 0.808059i | ||||||||
\(875\) | −1.23921e25 | + | 3.62090e25i | −0.0412167 | + | 0.120433i | ||||
\(876\) | −6.70463e26 | −2.20718 | ||||||||
\(877\) | −9.62236e25 | + | 9.62236e25i | −0.313535 | + | 0.313535i | −0.846277 | − | 0.532743i | \(-0.821161\pi\) |
0.532743 | + | 0.846277i | \(0.321161\pi\) | |||||||
\(878\) | −4.60416e26 | − | 4.60416e26i | −1.48491 | − | 1.48491i | ||||
\(879\) | 1.02398e27i | 3.26883i | ||||||||
\(880\) | −1.85246e26 | + | 2.83545e25i | −0.585337 | + | 0.0895937i | ||||
\(881\) | 2.48703e25 | 0.0777853 | 0.0388926 | − | 0.999243i | \(-0.487617\pi\) | ||||
0.0388926 | + | 0.999243i | \(0.487617\pi\) | |||||||
\(882\) | −8.00235e26 | + | 8.00235e26i | −2.47742 | + | 2.47742i | ||||
\(883\) | −9.50646e25 | − | 9.50646e25i | −0.291321 | − | 0.291321i | 0.546281 | − | 0.837602i | \(-0.316043\pi\) |
−0.837602 | + | 0.546281i | \(0.816043\pi\) | |||||||
\(884\) | 4.57771e25i | 0.138860i | ||||||||
\(885\) | −2.50514e26 | + | 3.41063e26i | −0.752215 | + | 1.02411i | ||||
\(886\) | −6.46123e26 | −1.92049 | ||||||||
\(887\) | −3.62956e25 | + | 3.62956e25i | −0.106793 | + | 0.106793i | −0.758484 | − | 0.651691i | \(-0.774060\pi\) |
0.651691 | + | 0.758484i | \(0.274060\pi\) | |||||||
\(888\) | 9.19849e25 | + | 9.19849e25i | 0.267917 | + | 0.267917i | ||||
\(889\) | − | 4.66581e25i | − | 0.134528i | ||||||
\(890\) | 3.97213e26 | + | 2.91757e26i | 1.13374 | + | 0.832742i | ||||
\(891\) | −2.95452e26 | −0.834811 | ||||||||
\(892\) | 8.38139e25 | − | 8.38139e25i | 0.234440 | − | 0.234440i | ||||
\(893\) | −1.33402e26 | − | 1.33402e26i | −0.369403 | − | 0.369403i | ||||
\(894\) | − | 1.74656e27i | − | 4.78790i | ||||||
\(895\) | 7.19359e25 | + | 4.69974e26i | 0.195226 | + | 1.27546i | ||||
\(896\) | 8.46369e25 | 0.227398 | ||||||||
\(897\) | 5.73478e26 | − | 5.73478e26i | 1.52540 | − | 1.52540i | ||||
\(898\) | −1.25500e26 | − | 1.25500e26i | −0.330488 | − | 0.330488i | ||||
\(899\) | 3.53519e26i | 0.921670i | ||||||||
\(900\) | 1.49710e27 | − | 4.69297e26i | 3.86427 | − | 1.21134i | ||||
\(901\) | 1.55552e25 | 0.0397513 | ||||||||
\(902\) | −4.43291e26 | + | 4.43291e26i | −1.12158 | + | 1.12158i | ||||
\(903\) | 3.10111e25 | + | 3.10111e25i | 0.0776833 | + | 0.0776833i | ||||
\(904\) | − | 5.22857e25i | − | 0.129678i | ||||||
\(905\) | −7.83762e23 | + | 1.19965e23i | −0.00192463 | + | 0.000294591i | ||||
\(906\) | 1.11689e27 | 2.71555 | ||||||||
\(907\) | −4.91588e26 | + | 4.91588e26i | −1.18341 | + | 1.18341i | −0.204557 | + | 0.978855i | \(0.565575\pi\) |
−0.978855 | + | 0.204557i | \(0.934425\pi\) | |||||||
\(908\) | −1.14673e25 | − | 1.14673e25i | −0.0273331 | − | 0.0273331i | ||||
\(909\) | − | 2.97195e26i | − | 0.701402i | ||||||
\(910\) | 4.73248e25 | − | 6.44305e25i | 0.110590 | − | 0.150563i | ||||
\(911\) | 6.05377e26 | 1.40075 | 0.700374 | − | 0.713776i | \(-0.253016\pi\) | ||||
0.700374 | + | 0.713776i | \(0.253016\pi\) | |||||||
\(912\) | 1.52744e26 | − | 1.52744e26i | 0.349953 | − | 0.349953i | ||||
\(913\) | −1.07929e26 | − | 1.07929e26i | −0.244850 | − | 0.244850i | ||||
\(914\) | 1.07107e27i | 2.40605i | ||||||||
\(915\) | −2.78283e26 | − | 2.04402e26i | −0.619010 | − | 0.454669i | ||||
\(916\) | −1.60319e26 | −0.353123 | ||||||||
\(917\) | 5.40902e24 | − | 5.40902e24i | 0.0117976 | − | 0.0117976i | ||||
\(918\) | −8.79651e25 | − | 8.79651e25i | −0.189988 | − | 0.189988i | ||||
\(919\) | − | 5.64170e26i | − | 1.20662i | −0.797507 | − | 0.603310i | \(-0.793848\pi\) | ||
0.797507 | − | 0.603310i | \(-0.206152\pi\) | |||||||
\(920\) | 1.68985e26 | + | 1.10402e27i | 0.357896 | + | 2.33822i | ||||
\(921\) | 5.63217e25 | 0.118124 | ||||||||
\(922\) | 5.70543e26 | − | 5.70543e26i | 1.18498 | − | 1.18498i | ||||
\(923\) | −5.26917e26 | − | 5.26917e26i | −1.08374 | − | 1.08374i | ||||
\(924\) | − | 1.46411e26i | − | 0.298212i | ||||||
\(925\) | 3.02554e25 | − | 5.78848e25i | 0.0610277 | − | 0.116759i | ||||
\(926\) | 4.54084e26 | 0.907062 | ||||||||
\(927\) | −8.27165e26 | + | 8.27165e26i | −1.63634 | + | 1.63634i | ||||
\(928\) | 5.76346e25 | + | 5.76346e25i | 0.112915 | + | 0.112915i | ||||
\(929\) | 4.57944e26i | 0.888527i | 0.895896 | + | 0.444263i | \(0.146535\pi\) | ||||
−0.895896 | + | 0.444263i | \(0.853465\pi\) | |||||||
\(930\) | −1.36403e27 | + | 2.08783e26i | −2.62106 | + | 0.401188i | ||||
\(931\) | 1.68581e26 | 0.320821 | ||||||||
\(932\) | 8.74189e26 | − | 8.74189e26i | 1.64764 | − | 1.64764i | ||||
\(933\) | 3.40019e26 | + | 3.40019e26i | 0.634701 | + | 0.634701i | ||||
\(934\) | − | 4.74578e26i | − | 0.877375i | ||||||
\(935\) | 1.83964e25 | − | 2.50458e25i | 0.0336844 | − | 0.0458597i | ||||
\(936\) | −1.60060e27 | −2.90269 | ||||||||
\(937\) | 3.46364e26 | − | 3.46364e26i | 0.622123 | − | 0.622123i | −0.323951 | − | 0.946074i | \(-0.605011\pi\) |
0.946074 | + | 0.323951i | \(0.105011\pi\) | |||||||
\(938\) | −1.67177e25 | − | 1.67177e25i | −0.0297407 | − | 0.0297407i | ||||
\(939\) | − | 1.10942e27i | − | 1.95481i | ||||||
\(940\) | −1.44604e27 | − | 1.06213e27i | −2.52365 | − | 1.85364i | ||||
\(941\) | −8.65957e26 | −1.49689 | −0.748445 | − | 0.663197i | \(-0.769199\pi\) | ||||
−0.748445 | + | 0.663197i | \(0.769199\pi\) | |||||||
\(942\) | −2.15608e26 | + | 2.15608e26i | −0.369153 | + | 0.369153i | ||||
\(943\) | 8.11061e26 | + | 8.11061e26i | 1.37546 | + | 1.37546i | ||||
\(944\) | 3.73723e26i | 0.627771i | ||||||||
\(945\) | 2.17452e25 | + | 1.42066e26i | 0.0361806 | + | 0.236376i | ||||
\(946\) | 3.51224e26 | 0.578848 | ||||||||
\(947\) | −3.88078e26 | + | 3.88078e26i | −0.633532 | + | 0.633532i | −0.948952 | − | 0.315420i | \(-0.897855\pi\) |
0.315420 | + | 0.948952i | \(0.397855\pi\) | |||||||
\(948\) | 1.88289e27 | + | 1.88289e27i | 3.04473 | + | 3.04473i | ||||
\(949\) | − | 3.43428e26i | − | 0.550098i | ||||||
\(950\) | −3.13092e26 | − | 1.63648e26i | −0.496775 | − | 0.259655i | ||||
\(951\) | 1.74205e27 | 2.73802 | ||||||||
\(952\) | 7.89305e24 | − | 7.89305e24i | 0.0122889 | − | 0.0122889i | ||||
\(953\) | −6.18013e26 | − | 6.18013e26i | −0.953150 | − | 0.953150i | 0.0458004 | − | 0.998951i | \(-0.485416\pi\) |
−0.998951 | + | 0.0458004i | \(0.985416\pi\) | |||||||
\(954\) | 1.11364e27i | 1.70141i | ||||||||
\(955\) | 6.55764e26 | − | 1.00374e26i | 0.992470 | − | 0.151911i | ||||
\(956\) | −5.17503e26 | −0.775875 | ||||||||
\(957\) | 5.97560e26 | − | 5.97560e26i | 0.887512 | − | 0.887512i | ||||
\(958\) | 2.12725e26 | + | 2.12725e26i | 0.312990 | + | 0.312990i | ||||
\(959\) | − | 6.10168e25i | − | 0.0889368i | ||||||
\(960\) | −8.10520e26 | + | 1.10348e27i | −1.17037 | + | 1.59340i | ||||
\(961\) | −1.57528e26 | −0.225344 | ||||||||
\(962\) | −9.64742e25 | + | 9.64742e25i | −0.136721 | + | 0.136721i | ||||
\(963\) | −1.71192e27 | − | 1.71192e27i | −2.40351 | − | 2.40351i | ||||
\(964\) | 1.16256e27i | 1.61704i | ||||||||
\(965\) | −2.38850e26 | − | 1.75437e26i | −0.329139 | − | 0.241756i | ||||
\(966\) | −4.04927e26 | −0.552819 | ||||||||
\(967\) | 3.76289e26 | − | 3.76289e26i | 0.508959 | − | 0.508959i | −0.405248 | − | 0.914207i | \(-0.632815\pi\) |
0.914207 | + | 0.405248i | \(0.132815\pi\) | |||||||
\(968\) | 4.60920e26 | + | 4.60920e26i | 0.617657 | + | 0.617657i | ||||
\(969\) | 3.58200e25i | 0.0475566i | ||||||||
\(970\) | −3.11449e26 | − | 2.03477e27i | −0.409677 | − | 2.67651i | ||||
\(971\) | 1.00379e27 | 1.30818 | 0.654091 | − | 0.756416i | \(-0.273051\pi\) | ||||
0.654091 | + | 0.756416i | \(0.273051\pi\) | |||||||
\(972\) | 2.79298e26 | − | 2.79298e26i | 0.360638 | − | 0.360638i | ||||
\(973\) | 3.01104e25 | + | 3.01104e25i | 0.0385213 | + | 0.0385213i | ||||
\(974\) | 1.95253e27i | 2.47496i | ||||||||
\(975\) | 3.56410e26 | + | 1.13698e27i | 0.447619 | + | 1.42794i | ||||
\(976\) | −3.04932e26 | −0.379450 | ||||||||
\(977\) | 4.67844e25 | − | 4.67844e25i | 0.0576833 | − | 0.0576833i | −0.677677 | − | 0.735360i | \(-0.737013\pi\) |
0.735360 | + | 0.677677i | \(0.237013\pi\) | |||||||
\(978\) | −1.03965e27 | − | 1.03965e27i | −1.27010 | − | 1.27010i | ||||
\(979\) | 4.62344e26i | 0.559656i | ||||||||
\(980\) | 1.58479e27 | − | 2.42574e26i | 1.90080 | − | 0.290944i | ||||
\(981\) | −2.44337e27 | −2.90381 | ||||||||
\(982\) | 1.33213e27 | − | 1.33213e27i | 1.56871 | − | 1.56871i | ||||
\(983\) | 5.61130e25 | + | 5.61130e25i | 0.0654759 | + | 0.0654759i | 0.739086 | − | 0.673611i | \(-0.235257\pi\) |
−0.673611 | + | 0.739086i | \(0.735257\pi\) | |||||||
\(984\) | − | 3.35630e27i | − | 3.88066i | ||||||
\(985\) | −1.51350e26 | + | 2.06056e26i | −0.173403 | + | 0.236080i | ||||
\(986\) | 1.31922e26 | 0.149770 | ||||||||
\(987\) | 2.24644e26 | − | 2.24644e26i | 0.252720 | − | 0.252720i | ||||
\(988\) | 3.45206e26 | + | 3.45206e26i | 0.384828 | + | 0.384828i | ||||
\(989\) | − | 6.42612e26i | − | 0.709876i | ||||||
\(990\) | 1.79310e27 | + | 1.31705e27i | 1.96285 | + | 1.44173i | ||||
\(991\) | −1.08001e27 | −1.17156 | −0.585782 | − | 0.810469i | \(-0.699213\pi\) | ||||
−0.585782 | + | 0.810469i | \(0.699213\pi\) | |||||||
\(992\) | 8.82856e25 | − | 8.82856e25i | 0.0949041 | − | 0.0949041i | ||||
\(993\) | 1.49940e27 | + | 1.49940e27i | 1.59725 | + | 1.59725i | ||||
\(994\) | 3.72051e26i | 0.392757i | ||||||||
\(995\) | 5.16928e25 | + | 3.37721e26i | 0.0540782 | + | 0.353305i | ||||
\(996\) | 1.67318e27 | 1.73464 | ||||||||
\(997\) | −1.19573e27 | + | 1.19573e27i | −1.22851 | + | 1.22851i | −0.263976 | + | 0.964529i | \(0.585034\pi\) |
−0.964529 | + | 0.263976i | \(0.914966\pi\) | |||||||
\(998\) | −4.36411e26 | − | 4.36411e26i | −0.444345 | − | 0.444345i | ||||
\(999\) | − | 2.45281e26i | − | 0.247499i |
(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 | 5.19.c.a.3.8 | yes | 16 | |
3.2 | odd | 2 | 45.19.g.a.28.1 | 16 | |||
5.2 | odd | 4 | inner | 5.19.c.a.2.8 | ✓ | 16 | |
5.3 | odd | 4 | 25.19.c.b.7.1 | 16 | |||
5.4 | even | 2 | 25.19.c.b.18.1 | 16 | |||
15.2 | even | 4 | 45.19.g.a.37.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.19.c.a.2.8 | ✓ | 16 | 5.2 | odd | 4 | inner | |
5.19.c.a.3.8 | yes | 16 | 1.1 | even | 1 | trivial | |
25.19.c.b.7.1 | 16 | 5.3 | odd | 4 | |||
25.19.c.b.18.1 | 16 | 5.4 | even | 2 | |||
45.19.g.a.28.1 | 16 | 3.2 | odd | 2 | |||
45.19.g.a.37.1 | 16 | 15.2 | even | 4 |