Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,15,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.94631745215\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 4349 x^{10} - 33891 x^{9} + 12151288 x^{8} - 474141530 x^{7} + 82897017850 x^{6} + \cdots + 37\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{66}\cdot 3^{6}\cdot 5^{2}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.5 | ||
Root | \(4.85446 - 62.4824i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.15.d.b.3.6 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 27.7089 | − | 124.965i | 0.216476 | − | 0.976288i | ||||
\(3\) | 563.873 | 0.257830 | 0.128915 | − | 0.991656i | \(-0.458851\pi\) | ||||
0.128915 | + | 0.991656i | \(0.458851\pi\) | |||||||
\(4\) | −14848.4 | − | 6925.28i | −0.906276 | − | 0.422686i | ||||
\(5\) | 134561.i | 1.72238i | 0.508283 | + | 0.861190i | \(0.330280\pi\) | ||||
−0.508283 | + | 0.861190i | \(0.669720\pi\) | |||||||
\(6\) | 15624.3 | − | 70464.4i | 0.0558139 | − | 0.251716i | ||||
\(7\) | 255103.i | 0.309762i | 0.987933 | + | 0.154881i | \(0.0494995\pi\) | ||||
−0.987933 | + | 0.154881i | \(0.950501\pi\) | |||||||
\(8\) | −1.27685e6 | + | 1.66364e6i | −0.608850 | + | 0.793285i | ||||
\(9\) | −4.46502e6 | −0.933524 | ||||||||
\(10\) | 1.68154e7 | + | 3.72854e6i | 1.68154 | + | 0.372854i | ||||
\(11\) | 2.74265e7 | 1.40741 | 0.703707 | − | 0.710490i | \(-0.251527\pi\) | ||||
0.703707 | + | 0.710490i | \(0.251527\pi\) | |||||||
\(12\) | −8.37264e6 | − | 3.90498e6i | −0.233665 | − | 0.108981i | ||||
\(13\) | 6.59643e7i | 1.05125i | 0.850717 | + | 0.525624i | \(0.176168\pi\) | ||||
−0.850717 | + | 0.525624i | \(0.823832\pi\) | |||||||
\(14\) | 3.18789e7 | + | 7.06862e6i | 0.302417 | + | 0.0670561i | ||||
\(15\) | 7.58753e7i | 0.444081i | ||||||||
\(16\) | 1.72516e8 | + | 2.05659e8i | 0.642674 | + | 0.766140i | ||||
\(17\) | 1.25101e8 | 0.304871 | 0.152436 | − | 0.988313i | \(-0.451288\pi\) | ||||
0.152436 | + | 0.988313i | \(0.451288\pi\) | |||||||
\(18\) | −1.23721e8 | + | 5.57970e8i | −0.202085 | + | 0.911388i | ||||
\(19\) | −1.21905e9 | −1.36379 | −0.681895 | − | 0.731450i | \(-0.738844\pi\) | ||||
−0.681895 | + | 0.731450i | \(0.738844\pi\) | |||||||
\(20\) | 9.31873e8 | − | 1.99802e9i | 0.728025 | − | 1.56095i | ||||
\(21\) | 1.43846e8i | 0.0798659i | ||||||||
\(22\) | 7.59959e8 | − | 3.42735e9i | 0.304671 | − | 1.37404i | ||||
\(23\) | − | 1.70944e8i | − | 0.0502064i | −0.999685 | − | 0.0251032i | \(-0.992009\pi\) | ||
0.999685 | − | 0.0251032i | \(-0.00799144\pi\) | |||||||
\(24\) | −7.19982e8 | + | 9.38082e8i | −0.156980 | + | 0.204532i | ||||
\(25\) | −1.20031e10 | −1.96659 | ||||||||
\(26\) | 8.24322e9 | + | 1.82780e9i | 1.02632 | + | 0.227570i | ||||
\(27\) | −5.21469e9 | −0.498520 | ||||||||
\(28\) | 1.76666e9 | − | 3.78787e9i | 0.130932 | − | 0.280730i | ||||
\(29\) | 3.68026e9i | 0.213350i | 0.994294 | + | 0.106675i | \(0.0340204\pi\) | ||||
−0.994294 | + | 0.106675i | \(0.965980\pi\) | |||||||
\(30\) | 9.48175e9 | + | 2.10242e9i | 0.433551 | + | 0.0961328i | ||||
\(31\) | 3.83689e10i | 1.39459i | 0.716782 | + | 0.697297i | \(0.245614\pi\) | ||||
−0.716782 | + | 0.697297i | \(0.754386\pi\) | |||||||
\(32\) | 3.04804e10 | − | 1.58599e10i | 0.887097 | − | 0.461584i | ||||
\(33\) | 1.54651e10 | 0.362873 | ||||||||
\(34\) | 3.46640e9 | − | 1.56332e10i | 0.0659973 | − | 0.297642i | ||||
\(35\) | −3.43269e10 | −0.533529 | ||||||||
\(36\) | 6.62985e10 | + | 3.09215e10i | 0.846031 | + | 0.394587i | ||||
\(37\) | − | 6.18516e10i | − | 0.651537i | −0.945450 | − | 0.325768i | \(-0.894377\pi\) | ||
0.945450 | − | 0.325768i | \(-0.105623\pi\) | |||||||
\(38\) | −3.37786e10 | + | 1.52339e11i | −0.295228 | + | 1.33145i | ||||
\(39\) | 3.71955e10i | 0.271043i | ||||||||
\(40\) | −2.23861e11 | − | 1.71814e11i | −1.36634 | − | 1.04867i | ||||
\(41\) | −9.79916e10 | −0.503155 | −0.251578 | − | 0.967837i | \(-0.580949\pi\) | ||||
−0.251578 | + | 0.967837i | \(0.580949\pi\) | |||||||
\(42\) | 1.79756e10 | + | 3.98581e9i | 0.0779721 | + | 0.0172891i | ||||
\(43\) | 3.97454e11 | 1.46220 | 0.731102 | − | 0.682268i | \(-0.239006\pi\) | ||||
0.731102 | + | 0.682268i | \(0.239006\pi\) | |||||||
\(44\) | −4.07241e11 | − | 1.89936e11i | −1.27551 | − | 0.594894i | ||||
\(45\) | − | 6.00817e11i | − | 1.60788i | ||||||
\(46\) | −2.13620e10 | − | 4.73668e9i | −0.0490159 | − | 0.0108685i | ||||
\(47\) | 1.44033e11i | 0.284300i | 0.989845 | + | 0.142150i | \(0.0454015\pi\) | ||||
−0.989845 | + | 0.142150i | \(0.954598\pi\) | |||||||
\(48\) | 9.72774e10 | + | 1.15966e11i | 0.165700 | + | 0.197534i | ||||
\(49\) | 6.13146e11 | 0.904047 | ||||||||
\(50\) | −3.32594e11 | + | 1.49997e12i | −0.425720 | + | 1.91996i | ||||
\(51\) | 7.05409e10 | 0.0786049 | ||||||||
\(52\) | 4.56821e11 | − | 9.79466e11i | 0.444348 | − | 0.952721i | ||||
\(53\) | − | 1.05052e12i | − | 0.894281i | −0.894464 | − | 0.447141i | \(-0.852442\pi\) | ||
0.894464 | − | 0.447141i | \(-0.147558\pi\) | |||||||
\(54\) | −1.44493e11 | + | 6.51653e11i | −0.107918 | + | 0.486699i | ||||
\(55\) | 3.69054e12i | 2.42410i | ||||||||
\(56\) | −4.24399e11 | − | 3.25728e11i | −0.245730 | − | 0.188599i | ||||
\(57\) | −6.87392e11 | −0.351625 | ||||||||
\(58\) | 4.59903e11 | + | 1.01976e11i | 0.208291 | + | 0.0461851i | ||||
\(59\) | 6.74504e11 | 0.271032 | 0.135516 | − | 0.990775i | \(-0.456731\pi\) | ||||
0.135516 | + | 0.990775i | \(0.456731\pi\) | |||||||
\(60\) | 5.25458e11 | − | 1.12663e12i | 0.187707 | − | 0.402460i | ||||
\(61\) | − | 3.05006e12i | − | 0.970509i | −0.874373 | − | 0.485254i | \(-0.838727\pi\) | ||
0.874373 | − | 0.485254i | \(-0.161273\pi\) | |||||||
\(62\) | 4.79477e12 | + | 1.06316e12i | 1.36153 | + | 0.301896i | ||||
\(63\) | − | 1.13904e12i | − | 0.289171i | ||||||
\(64\) | −1.13735e12 | − | 4.24844e12i | −0.258603 | − | 0.965984i | ||||
\(65\) | −8.87621e12 | −1.81065 | ||||||||
\(66\) | 4.28521e11 | − | 1.93259e12i | 0.0785533 | − | 0.354269i | ||||
\(67\) | −3.94665e12 | −0.651186 | −0.325593 | − | 0.945510i | \(-0.605564\pi\) | ||||
−0.325593 | + | 0.945510i | \(0.605564\pi\) | |||||||
\(68\) | −1.85755e12 | − | 8.66357e11i | −0.276298 | − | 0.128865i | ||||
\(69\) | − | 9.63909e10i | − | 0.0129447i | ||||||
\(70\) | −9.51160e11 | + | 4.28965e12i | −0.115496 | + | 0.520878i | ||||
\(71\) | 1.12918e13i | 1.24152i | 0.784000 | + | 0.620761i | \(0.213176\pi\) | ||||
−0.784000 | + | 0.620761i | \(0.786824\pi\) | |||||||
\(72\) | 5.70116e12 | − | 7.42818e12i | 0.568376 | − | 0.740551i | ||||
\(73\) | 1.04132e13 | 0.942596 | 0.471298 | − | 0.881974i | \(-0.343786\pi\) | ||||
0.471298 | + | 0.881974i | \(0.343786\pi\) | |||||||
\(74\) | −7.72928e12 | − | 1.71384e12i | −0.636088 | − | 0.141042i | ||||
\(75\) | −6.76825e12 | −0.507046 | ||||||||
\(76\) | 1.81010e13 | + | 8.44229e12i | 1.23597 | + | 0.576454i | ||||
\(77\) | 6.99658e12i | 0.435964i | ||||||||
\(78\) | 4.64813e12 | + | 1.03065e12i | 0.264616 | + | 0.0586743i | ||||
\(79\) | − | 2.96260e13i | − | 1.54271i | −0.636408 | − | 0.771353i | \(-0.719580\pi\) | ||
0.636408 | − | 0.771353i | \(-0.280420\pi\) | |||||||
\(80\) | −2.76737e13 | + | 2.32140e13i | −1.31958 | + | 1.10693i | ||||
\(81\) | 1.84156e13 | 0.804991 | ||||||||
\(82\) | −2.71524e12 | + | 1.22455e13i | −0.108921 | + | 0.491224i | ||||
\(83\) | 4.21939e13 | 1.55490 | 0.777451 | − | 0.628943i | \(-0.216512\pi\) | ||||
0.777451 | + | 0.628943i | \(0.216512\pi\) | |||||||
\(84\) | 9.96171e11 | − | 2.13588e12i | 0.0337582 | − | 0.0723806i | ||||
\(85\) | 1.68336e13i | 0.525105i | ||||||||
\(86\) | 1.10130e13 | − | 4.96678e13i | 0.316532 | − | 1.42753i | ||||
\(87\) | 2.07520e12i | 0.0550079i | ||||||||
\(88\) | −3.50196e13 | + | 4.56279e13i | −0.856904 | + | 1.11648i | ||||
\(89\) | −2.18657e13 | −0.494349 | −0.247175 | − | 0.968971i | \(-0.579502\pi\) | ||||
−0.247175 | + | 0.968971i | \(0.579502\pi\) | |||||||
\(90\) | −7.50810e13 | − | 1.66480e13i | −1.56976 | − | 0.348068i | ||||
\(91\) | −1.68277e13 | −0.325637 | ||||||||
\(92\) | −1.18384e12 | + | 2.53825e12i | −0.0212215 | + | 0.0455009i | ||||
\(93\) | 2.16352e13i | 0.359568i | ||||||||
\(94\) | 1.79991e13 | + | 3.99100e12i | 0.277559 | + | 0.0615441i | ||||
\(95\) | − | 1.64037e14i | − | 2.34896i | ||||||
\(96\) | 1.71871e13 | − | 8.94297e12i | 0.228720 | − | 0.119010i | ||||
\(97\) | 6.74953e13 | 0.835356 | 0.417678 | − | 0.908595i | \(-0.362844\pi\) | ||||
0.417678 | + | 0.908595i | \(0.362844\pi\) | |||||||
\(98\) | 1.69896e13 | − | 7.66217e13i | 0.195704 | − | 0.882610i | ||||
\(99\) | −1.22460e14 | −1.31386 | ||||||||
\(100\) | 1.78228e14 | + | 8.31251e13i | 1.78228 | + | 0.831251i | ||||
\(101\) | 7.28472e13i | 0.679459i | 0.940523 | + | 0.339729i | \(0.110335\pi\) | ||||
−0.940523 | + | 0.339729i | \(0.889665\pi\) | |||||||
\(102\) | 1.95461e12 | − | 8.81513e12i | 0.0170161 | − | 0.0767410i | ||||
\(103\) | 1.62010e14i | 1.31729i | 0.752453 | + | 0.658646i | \(0.228870\pi\) | ||||
−0.752453 | + | 0.658646i | \(0.771130\pi\) | |||||||
\(104\) | −1.09741e14 | − | 8.42265e13i | −0.833940 | − | 0.640052i | ||||
\(105\) | −1.93560e13 | −0.137559 | ||||||||
\(106\) | −1.31278e14 | − | 2.91088e13i | −0.873076 | − | 0.193590i | ||||
\(107\) | 6.31256e13 | 0.393114 | 0.196557 | − | 0.980492i | \(-0.437024\pi\) | ||||
0.196557 | + | 0.980492i | \(0.437024\pi\) | |||||||
\(108\) | 7.74300e13 | + | 3.61132e13i | 0.451797 | + | 0.210717i | ||||
\(109\) | 1.94913e14i | 1.06624i | 0.846039 | + | 0.533121i | \(0.178981\pi\) | ||||
−0.846039 | + | 0.533121i | \(0.821019\pi\) | |||||||
\(110\) | 4.61188e14 | + | 1.02261e14i | 2.36662 | + | 0.524760i | ||||
\(111\) | − | 3.48765e13i | − | 0.167986i | ||||||
\(112\) | −5.24642e13 | + | 4.40094e13i | −0.237321 | + | 0.199076i | ||||
\(113\) | −3.86200e14 | −1.64159 | −0.820793 | − | 0.571226i | \(-0.806468\pi\) | ||||
−0.820793 | + | 0.571226i | \(0.806468\pi\) | |||||||
\(114\) | −1.90469e13 | + | 8.58998e13i | −0.0761184 | + | 0.343288i | ||||
\(115\) | 2.30024e13 | 0.0864746 | ||||||||
\(116\) | 2.54868e13 | − | 5.46460e13i | 0.0901798 | − | 0.193354i | ||||
\(117\) | − | 2.94532e14i | − | 0.981365i | ||||||
\(118\) | 1.86898e13 | − | 8.42892e13i | 0.0586718 | − | 0.264605i | ||||
\(119\) | 3.19135e13i | 0.0944377i | ||||||||
\(120\) | −1.26229e14 | − | 9.68815e13i | −0.352283 | − | 0.270378i | ||||
\(121\) | 3.72465e14 | 0.980816 | ||||||||
\(122\) | −3.81150e14 | − | 8.45138e13i | −0.947496 | − | 0.210092i | ||||
\(123\) | −5.52549e13 | −0.129728 | ||||||||
\(124\) | 2.65716e14 | − | 5.69718e14i | 0.589475 | − | 1.26389i | ||||
\(125\) | − | 7.93858e14i | − | 1.66484i | ||||||
\(126\) | −1.42340e14 | − | 3.15615e13i | −0.282314 | − | 0.0625985i | ||||
\(127\) | 8.40323e14i | 1.57696i | 0.615061 | + | 0.788479i | \(0.289131\pi\) | ||||
−0.615061 | + | 0.788479i | \(0.710869\pi\) | |||||||
\(128\) | −5.62421e14 | + | 2.44091e13i | −0.999060 | + | 0.0433593i | ||||
\(129\) | 2.24114e14 | 0.377000 | ||||||||
\(130\) | −2.45950e14 | + | 1.10921e15i | −0.391962 | + | 1.76771i | ||||
\(131\) | 1.74806e14 | 0.264032 | 0.132016 | − | 0.991248i | \(-0.457855\pi\) | ||||
0.132016 | + | 0.991248i | \(0.457855\pi\) | |||||||
\(132\) | −2.29632e14 | − | 1.07100e14i | −0.328863 | − | 0.153381i | ||||
\(133\) | − | 3.10984e14i | − | 0.422451i | ||||||
\(134\) | −1.09357e14 | + | 4.93193e14i | −0.140966 | + | 0.635745i | ||||
\(135\) | − | 7.01694e14i | − | 0.858640i | ||||||
\(136\) | −1.59735e14 | + | 2.08122e14i | −0.185621 | + | 0.241850i | ||||
\(137\) | 1.71133e13 | 0.0188926 | 0.00944628 | − | 0.999955i | \(-0.496993\pi\) | ||||
0.00944628 | + | 0.999955i | \(0.496993\pi\) | |||||||
\(138\) | −1.20455e13 | − | 2.67089e12i | −0.0126378 | − | 0.00280222i | ||||
\(139\) | 1.32491e15 | 1.32155 | 0.660773 | − | 0.750586i | \(-0.270229\pi\) | ||||
0.660773 | + | 0.750586i | \(0.270229\pi\) | |||||||
\(140\) | 5.09700e14 | + | 2.37723e14i | 0.483524 | + | 0.225515i | ||||
\(141\) | 8.12163e13i | 0.0733009i | ||||||||
\(142\) | 1.41108e15 | + | 3.12883e14i | 1.21208 | + | 0.268760i | ||||
\(143\) | 1.80917e15i | 1.47954i | ||||||||
\(144\) | −7.70288e14 | − | 9.18271e14i | −0.599951 | − | 0.715210i | ||||
\(145\) | −4.95219e14 | −0.367469 | ||||||||
\(146\) | 2.88539e14 | − | 1.30129e15i | 0.204049 | − | 0.920245i | ||||
\(147\) | 3.45737e14 | 0.233090 | ||||||||
\(148\) | −4.28340e14 | + | 9.18400e14i | −0.275395 | + | 0.590472i | ||||
\(149\) | 6.47857e14i | 0.397352i | 0.980065 | + | 0.198676i | \(0.0636641\pi\) | ||||
−0.980065 | + | 0.198676i | \(0.936336\pi\) | |||||||
\(150\) | −1.87541e14 | + | 8.45793e14i | −0.109763 | + | 0.495023i | ||||
\(151\) | − | 1.52015e15i | − | 0.849275i | −0.905363 | − | 0.424638i | \(-0.860401\pi\) | ||
0.905363 | − | 0.424638i | \(-0.139599\pi\) | |||||||
\(152\) | 1.55655e15 | − | 2.02807e15i | 0.830343 | − | 1.08187i | ||||
\(153\) | −5.58576e14 | −0.284605 | ||||||||
\(154\) | 8.74327e14 | + | 1.93868e14i | 0.425627 | + | 0.0943757i | ||||
\(155\) | −5.16296e15 | −2.40202 | ||||||||
\(156\) | 2.57589e14 | − | 5.52295e14i | 0.114566 | − | 0.245640i | ||||
\(157\) | 1.16282e14i | 0.0494555i | 0.999694 | + | 0.0247277i | \(0.00787188\pi\) | ||||
−0.999694 | + | 0.0247277i | \(0.992128\pi\) | |||||||
\(158\) | −3.70221e15 | − | 8.20904e14i | −1.50612 | − | 0.333959i | ||||
\(159\) | − | 5.92362e14i | − | 0.230572i | ||||||
\(160\) | 2.13412e15 | + | 4.10147e15i | 0.795022 | + | 1.52792i | ||||
\(161\) | 4.36083e13 | 0.0155521 | ||||||||
\(162\) | 5.10277e14 | − | 2.30130e15i | 0.174261 | − | 0.785903i | ||||
\(163\) | −5.48073e14 | −0.179277 | −0.0896386 | − | 0.995974i | \(-0.528571\pi\) | ||||
−0.0896386 | + | 0.995974i | \(0.528571\pi\) | |||||||
\(164\) | 1.45502e15 | + | 6.78619e14i | 0.455998 | + | 0.212676i | ||||
\(165\) | 2.08100e15i | 0.625005i | ||||||||
\(166\) | 1.16915e15 | − | 5.27276e15i | 0.336599 | − | 1.51803i | ||||
\(167\) | − | 2.02070e15i | − | 0.557810i | −0.960319 | − | 0.278905i | \(-0.910028\pi\) | ||
0.960319 | − | 0.278905i | \(-0.0899715\pi\) | |||||||
\(168\) | −2.39307e14 | − | 1.83669e14i | −0.0633565 | − | 0.0486264i | ||||
\(169\) | −4.13908e14 | −0.105123 | ||||||||
\(170\) | 2.10361e15 | + | 4.66442e14i | 0.512653 | + | 0.113672i | ||||
\(171\) | 5.44309e15 | 1.27313 | ||||||||
\(172\) | −5.90157e15 | − | 2.75248e15i | −1.32516 | − | 0.618053i | ||||
\(173\) | 5.06047e15i | 1.09111i | 0.838076 | + | 0.545554i | \(0.183681\pi\) | ||||
−0.838076 | + | 0.545554i | \(0.816319\pi\) | |||||||
\(174\) | 2.59327e14 | + | 5.75015e13i | 0.0537035 | + | 0.0119079i | ||||
\(175\) | − | 3.06203e15i | − | 0.609177i | ||||||
\(176\) | 4.73153e15 | + | 5.64052e15i | 0.904508 | + | 1.07828i | ||||
\(177\) | 3.80335e14 | 0.0698800 | ||||||||
\(178\) | −6.05875e14 | + | 2.73245e15i | −0.107015 | + | 0.482627i | ||||
\(179\) | −9.58052e14 | −0.162711 | −0.0813557 | − | 0.996685i | \(-0.525925\pi\) | ||||
−0.0813557 | + | 0.996685i | \(0.525925\pi\) | |||||||
\(180\) | −4.16083e15 | + | 8.92119e15i | −0.679629 | + | 1.45719i | ||||
\(181\) | 1.41227e15i | 0.221906i | 0.993826 | + | 0.110953i | \(0.0353903\pi\) | ||||
−0.993826 | + | 0.110953i | \(0.964610\pi\) | |||||||
\(182\) | −4.66276e14 | + | 2.10287e15i | −0.0704926 | + | 0.317916i | ||||
\(183\) | − | 1.71985e15i | − | 0.250226i | ||||||
\(184\) | 2.84390e14 | + | 2.18270e14i | 0.0398280 | + | 0.0305682i | ||||
\(185\) | 8.32281e15 | 1.12219 | ||||||||
\(186\) | 2.70364e15 | + | 5.99488e14i | 0.351041 | + | 0.0778377i | ||||
\(187\) | 3.43107e15 | 0.429080 | ||||||||
\(188\) | 9.97468e14 | − | 2.13866e15i | 0.120169 | − | 0.257654i | ||||
\(189\) | − | 1.33028e15i | − | 0.154423i | ||||||
\(190\) | −2.04989e16 | − | 4.54529e15i | −2.29327 | − | 0.508494i | ||||
\(191\) | − | 5.35607e15i | − | 0.577581i | −0.957392 | − | 0.288790i | \(-0.906747\pi\) | ||
0.957392 | − | 0.288790i | \(-0.0932530\pi\) | |||||||
\(192\) | −6.41321e14 | − | 2.39558e15i | −0.0666756 | − | 0.249059i | ||||
\(193\) | 3.80935e15 | 0.381900 | 0.190950 | − | 0.981600i | \(-0.438843\pi\) | ||||
0.190950 | + | 0.981600i | \(0.438843\pi\) | |||||||
\(194\) | 1.87022e15 | − | 8.43454e15i | 0.180834 | − | 0.815548i | ||||
\(195\) | −5.00506e15 | −0.466839 | ||||||||
\(196\) | −9.10425e15 | − | 4.24621e15i | −0.819317 | − | 0.382128i | ||||
\(197\) | − | 9.44057e15i | − | 0.819851i | −0.912119 | − | 0.409925i | \(-0.865555\pi\) | ||
0.912119 | − | 0.409925i | \(-0.134445\pi\) | |||||||
\(198\) | −3.39323e15 | + | 1.53032e16i | −0.284418 | + | 1.28270i | ||||
\(199\) | 8.55401e15i | 0.692147i | 0.938207 | + | 0.346074i | \(0.112485\pi\) | ||||
−0.938207 | + | 0.346074i | \(0.887515\pi\) | |||||||
\(200\) | 1.53262e16 | − | 1.99689e16i | 1.19736 | − | 1.56007i | ||||
\(201\) | −2.22541e15 | −0.167895 | ||||||||
\(202\) | 9.10334e15 | + | 2.01852e15i | 0.663347 | + | 0.147086i | ||||
\(203\) | −9.38843e14 | −0.0660877 | ||||||||
\(204\) | −1.04742e15 | − | 4.88515e14i | −0.0712378 | − | 0.0332252i | ||||
\(205\) | − | 1.31858e16i | − | 0.866624i | ||||||
\(206\) | 2.02456e16 | + | 4.48913e15i | 1.28606 | + | 0.285162i | ||||
\(207\) | 7.63268e14i | 0.0468689i | ||||||||
\(208\) | −1.35662e16 | + | 1.13799e16i | −0.805403 | + | 0.675610i | ||||
\(209\) | −3.34344e16 | −1.91942 | ||||||||
\(210\) | −5.36334e14 | + | 2.41882e15i | −0.0297783 | + | 0.134298i | ||||
\(211\) | 4.48478e15 | 0.240859 | 0.120430 | − | 0.992722i | \(-0.461573\pi\) | ||||
0.120430 | + | 0.992722i | \(0.461573\pi\) | |||||||
\(212\) | −7.27516e15 | + | 1.55986e16i | −0.378000 | + | 0.810466i | ||||
\(213\) | 6.36714e15i | 0.320101i | ||||||||
\(214\) | 1.74914e15 | − | 7.88848e15i | 0.0850998 | − | 0.383793i | ||||
\(215\) | 5.34818e16i | 2.51847i | ||||||||
\(216\) | 6.65838e15 | − | 8.67537e15i | 0.303524 | − | 0.395468i | ||||
\(217\) | −9.78801e15 | −0.431993 | ||||||||
\(218\) | 2.43573e16 | + | 5.40083e15i | 1.04096 | + | 0.230816i | ||||
\(219\) | 5.87174e15 | 0.243029 | ||||||||
\(220\) | 2.55580e16 | − | 5.47987e16i | 1.02463 | − | 2.19691i | ||||
\(221\) | 8.25217e15i | 0.320496i | ||||||||
\(222\) | −4.35833e15 | − | 9.66390e14i | −0.164002 | − | 0.0363648i | ||||
\(223\) | − | 1.11919e16i | − | 0.408103i | −0.978960 | − | 0.204051i | \(-0.934589\pi\) | ||
0.978960 | − | 0.204051i | \(-0.0654110\pi\) | |||||||
\(224\) | 4.04590e15 | + | 7.77563e15i | 0.142981 | + | 0.274789i | ||||
\(225\) | 5.35942e16 | 1.83586 | ||||||||
\(226\) | −1.07012e16 | + | 4.82615e16i | −0.355364 | + | 1.60266i | ||||
\(227\) | −1.72654e16 | −0.555897 | −0.277949 | − | 0.960596i | \(-0.589654\pi\) | ||||
−0.277949 | + | 0.960596i | \(0.589654\pi\) | |||||||
\(228\) | 1.02067e16 | + | 4.76038e15i | 0.318670 | + | 0.148627i | ||||
\(229\) | − | 4.57480e16i | − | 1.38524i | −0.721305 | − | 0.692618i | \(-0.756457\pi\) | ||
0.721305 | − | 0.692618i | \(-0.243543\pi\) | |||||||
\(230\) | 6.37372e14 | − | 2.87449e15i | 0.0187197 | − | 0.0844241i | ||||
\(231\) | 3.94519e15i | 0.112404i | ||||||||
\(232\) | −6.12262e15 | − | 4.69914e15i | −0.169247 | − | 0.129898i | ||||
\(233\) | −4.64388e16 | −1.24563 | −0.622816 | − | 0.782369i | \(-0.714011\pi\) | ||||
−0.622816 | + | 0.782369i | \(0.714011\pi\) | |||||||
\(234\) | −3.68061e16 | − | 8.16115e15i | −0.958095 | − | 0.212442i | ||||
\(235\) | −1.93812e16 | −0.489672 | ||||||||
\(236\) | −1.00153e16 | − | 4.67113e15i | −0.245630 | − | 0.114561i | ||||
\(237\) | − | 1.67053e16i | − | 0.397755i | ||||||
\(238\) | 3.98806e15 | + | 8.84288e14i | 0.0921984 | + | 0.0204435i | ||||
\(239\) | − | 1.43569e16i | − | 0.322311i | −0.986929 | − | 0.161156i | \(-0.948478\pi\) | ||
0.986929 | − | 0.161156i | \(-0.0515221\pi\) | |||||||
\(240\) | −1.56045e16 | + | 1.30897e16i | −0.340228 | + | 0.285399i | ||||
\(241\) | 3.11942e16 | 0.660624 | 0.330312 | − | 0.943872i | \(-0.392846\pi\) | ||||
0.330312 | + | 0.943872i | \(0.392846\pi\) | |||||||
\(242\) | 1.03206e16 | − | 4.65450e16i | 0.212323 | − | 0.957558i | ||||
\(243\) | 3.53258e16 | 0.706070 | ||||||||
\(244\) | −2.11225e16 | + | 4.52886e16i | −0.410220 | + | 0.879549i | ||||
\(245\) | 8.25055e16i | 1.55711i | ||||||||
\(246\) | −1.53105e15 | + | 6.90491e15i | −0.0280830 | + | 0.126652i | ||||
\(247\) | − | 8.04140e16i | − | 1.43368i | ||||||
\(248\) | −6.38321e16 | − | 4.89914e16i | −1.10631 | − | 0.849098i | ||||
\(249\) | 2.37920e16 | 0.400900 | ||||||||
\(250\) | −9.92043e16 | − | 2.19969e16i | −1.62536 | − | 0.360398i | ||||
\(251\) | 5.26304e16 | 0.838534 | 0.419267 | − | 0.907863i | \(-0.362287\pi\) | ||||
0.419267 | + | 0.907863i | \(0.362287\pi\) | |||||||
\(252\) | −7.88816e15 | + | 1.69129e16i | −0.122228 | + | 0.262068i | ||||
\(253\) | − | 4.68841e15i | − | 0.0706613i | ||||||
\(254\) | 1.05011e17 | + | 2.32844e16i | 1.53957 | + | 0.341374i | ||||
\(255\) | 9.49205e15i | 0.135387i | ||||||||
\(256\) | −1.25338e16 | + | 7.09592e16i | −0.173941 | + | 0.984756i | ||||
\(257\) | −4.88092e16 | −0.659128 | −0.329564 | − | 0.944133i | \(-0.606902\pi\) | ||||
−0.329564 | + | 0.944133i | \(0.606902\pi\) | |||||||
\(258\) | 6.20996e15 | − | 2.80064e16i | 0.0816113 | − | 0.368060i | ||||
\(259\) | 1.57785e16 | 0.201822 | ||||||||
\(260\) | 1.31798e17 | + | 6.14703e16i | 1.64095 | + | 0.765335i | ||||
\(261\) | − | 1.64324e16i | − | 0.199167i | ||||||
\(262\) | 4.84368e15 | − | 2.18446e16i | 0.0571566 | − | 0.257771i | ||||
\(263\) | − | 9.75867e16i | − | 1.12124i | −0.828072 | − | 0.560622i | \(-0.810562\pi\) | ||
0.828072 | − | 0.560622i | \(-0.189438\pi\) | |||||||
\(264\) | −1.97466e16 | + | 2.57283e16i | −0.220935 | + | 0.287862i | ||||
\(265\) | 1.41359e17 | 1.54029 | ||||||||
\(266\) | −3.88620e16 | − | 8.61702e15i | −0.412434 | − | 0.0914504i | ||||
\(267\) | −1.23295e16 | −0.127458 | ||||||||
\(268\) | 5.86016e16 | + | 2.73317e16i | 0.590155 | + | 0.275247i | ||||
\(269\) | 1.30574e17i | 1.28112i | 0.767908 | + | 0.640561i | \(0.221298\pi\) | ||||
−0.767908 | + | 0.640561i | \(0.778702\pi\) | |||||||
\(270\) | −8.76871e16 | − | 1.94432e16i | −0.838280 | − | 0.185875i | ||||
\(271\) | 1.62419e17i | 1.51305i | 0.653967 | + | 0.756523i | \(0.273104\pi\) | ||||
−0.653967 | + | 0.756523i | \(0.726896\pi\) | |||||||
\(272\) | 2.15819e16 | + | 2.57281e16i | 0.195933 | + | 0.233574i | ||||
\(273\) | −9.48867e15 | −0.0839589 | ||||||||
\(274\) | 4.74192e14 | − | 2.13857e15i | 0.00408979 | − | 0.0184446i | ||||
\(275\) | −3.29204e17 | −2.76781 | ||||||||
\(276\) | −6.67534e14 | + | 1.43125e15i | −0.00547154 | + | 0.0117315i | ||||
\(277\) | 1.39285e17i | 1.11313i | 0.830803 | + | 0.556567i | \(0.187882\pi\) | ||||
−0.830803 | + | 0.556567i | \(0.812118\pi\) | |||||||
\(278\) | 3.67118e16 | − | 1.65567e17i | 0.286083 | − | 1.29021i | ||||
\(279\) | − | 1.71318e17i | − | 1.30189i | ||||||
\(280\) | 4.38303e16 | − | 5.71075e16i | 0.324839 | − | 0.423240i | ||||
\(281\) | −1.43583e17 | −1.03791 | −0.518953 | − | 0.854803i | \(-0.673678\pi\) | ||||
−0.518953 | + | 0.854803i | \(0.673678\pi\) | |||||||
\(282\) | 1.01492e16 | + | 2.25042e15i | 0.0715628 | + | 0.0158679i | ||||
\(283\) | 1.74150e17 | 1.19789 | 0.598946 | − | 0.800789i | \(-0.295586\pi\) | ||||
0.598946 | + | 0.800789i | \(0.295586\pi\) | |||||||
\(284\) | 7.81989e16 | − | 1.67665e17i | 0.524774 | − | 1.12516i | ||||
\(285\) | − | 9.24961e16i | − | 0.605633i | ||||||
\(286\) | 2.26083e17 | + | 5.01302e16i | 1.44446 | + | 0.320285i | ||||
\(287\) | − | 2.49979e16i | − | 0.155859i | ||||||
\(288\) | −1.36096e17 | + | 7.08147e16i | −0.828126 | + | 0.430899i | ||||
\(289\) | −1.52728e17 | −0.907053 | ||||||||
\(290\) | −1.37220e16 | + | 6.18849e16i | −0.0795482 | + | 0.358756i | ||||
\(291\) | 3.80588e16 | 0.215379 | ||||||||
\(292\) | −1.54620e17 | − | 7.21146e16i | −0.854252 | − | 0.398422i | ||||
\(293\) | − | 2.46698e17i | − | 1.33074i | −0.746515 | − | 0.665368i | \(-0.768275\pi\) | ||
0.746515 | − | 0.665368i | \(-0.231725\pi\) | |||||||
\(294\) | 9.57999e15 | − | 4.32049e16i | 0.0504584 | − | 0.227563i | ||||
\(295\) | 9.07618e16i | 0.466820i | ||||||||
\(296\) | 1.02899e17 | + | 7.89753e16i | 0.516855 | + | 0.396688i | ||||
\(297\) | −1.43021e17 | −0.701624 | ||||||||
\(298\) | 8.09594e16 | + | 1.79514e16i | 0.387930 | + | 0.0860171i | ||||
\(299\) | 1.12762e16 | 0.0527794 | ||||||||
\(300\) | 1.00498e17 | + | 4.68720e16i | 0.459524 | + | 0.214321i | ||||
\(301\) | 1.01392e17i | 0.452936i | ||||||||
\(302\) | −1.89966e17 | − | 4.21218e16i | −0.829137 | − | 0.183848i | ||||
\(303\) | 4.10766e16i | 0.175185i | ||||||||
\(304\) | −2.10307e17 | − | 2.50709e17i | −0.876472 | − | 1.04485i | ||||
\(305\) | 4.10419e17 | 1.67158 | ||||||||
\(306\) | −1.54775e16 | + | 6.98024e16i | −0.0616101 | + | 0.277856i | ||||
\(307\) | 9.06833e16 | 0.352824 | 0.176412 | − | 0.984316i | \(-0.443551\pi\) | ||||
0.176412 | + | 0.984316i | \(0.443551\pi\) | |||||||
\(308\) | 4.84533e16 | − | 1.03888e17i | 0.184276 | − | 0.395104i | ||||
\(309\) | 9.13533e16i | 0.339637i | ||||||||
\(310\) | −1.43060e17 | + | 6.45188e17i | −0.519980 | + | 2.34506i | ||||
\(311\) | 4.09285e17i | 1.45446i | 0.686392 | + | 0.727231i | \(0.259193\pi\) | ||||
−0.686392 | + | 0.727231i | \(0.740807\pi\) | |||||||
\(312\) | −6.18799e16 | − | 4.74931e16i | −0.215014 | − | 0.165024i | ||||
\(313\) | 1.83768e17 | 0.624396 | 0.312198 | − | 0.950017i | \(-0.398935\pi\) | ||||
0.312198 | + | 0.950017i | \(0.398935\pi\) | |||||||
\(314\) | 1.45311e16 | + | 3.22204e15i | 0.0482828 | + | 0.0107059i | ||||
\(315\) | 1.53270e17 | 0.498062 | ||||||||
\(316\) | −2.05168e17 | + | 4.39899e17i | −0.652080 | + | 1.39812i | ||||
\(317\) | − | 4.43833e17i | − | 1.37976i | −0.723922 | − | 0.689882i | \(-0.757662\pi\) | ||
0.723922 | − | 0.689882i | \(-0.242338\pi\) | |||||||
\(318\) | −7.40244e16 | − | 1.64137e16i | −0.225105 | − | 0.0499133i | ||||
\(319\) | 1.00937e17i | 0.300271i | ||||||||
\(320\) | 5.71674e17 | − | 1.53043e17i | 1.66379 | − | 0.445413i | ||||
\(321\) | 3.55948e16 | 0.101357 | ||||||||
\(322\) | 1.20834e15 | − | 5.44951e15i | 0.00336665 | − | 0.0151833i | ||||
\(323\) | −1.52504e17 | −0.415781 | ||||||||
\(324\) | −2.73443e17 | − | 1.27533e17i | −0.729544 | − | 0.340258i | ||||
\(325\) | − | 7.91778e17i | − | 2.06738i | ||||||
\(326\) | −1.51865e16 | + | 6.84898e16i | −0.0388092 | + | 0.175026i | ||||
\(327\) | 1.09906e17i | 0.274909i | ||||||||
\(328\) | 1.25121e17 | − | 1.63023e17i | 0.306346 | − | 0.399146i | ||||
\(329\) | −3.67432e16 | −0.0880654 | ||||||||
\(330\) | 2.60051e17 | + | 5.76622e16i | 0.610185 | + | 0.135299i | ||||
\(331\) | 5.54550e17 | 1.27393 | 0.636964 | − | 0.770894i | \(-0.280190\pi\) | ||||
0.636964 | + | 0.770894i | \(0.280190\pi\) | |||||||
\(332\) | −6.26513e17 | − | 2.92205e17i | −1.40917 | − | 0.657235i | ||||
\(333\) | 2.76168e17i | 0.608225i | ||||||||
\(334\) | −2.52516e17 | − | 5.59914e16i | −0.544583 | − | 0.120752i | ||||
\(335\) | − | 5.31065e17i | − | 1.12159i | ||||||
\(336\) | −2.95832e16 | + | 2.48157e16i | −0.0611885 | + | 0.0513277i | ||||
\(337\) | −7.14833e17 | −1.44809 | −0.724045 | − | 0.689753i | \(-0.757719\pi\) | ||||
−0.724045 | + | 0.689753i | \(0.757719\pi\) | |||||||
\(338\) | −1.14690e16 | + | 5.17240e16i | −0.0227566 | + | 0.102630i | ||||
\(339\) | −2.17768e17 | −0.423249 | ||||||||
\(340\) | 1.16578e17 | − | 2.49953e17i | 0.221954 | − | 0.475890i | ||||
\(341\) | 1.05233e18i | 1.96277i | ||||||||
\(342\) | 1.50822e17 | − | 6.80195e17i | 0.275602 | − | 1.24294i | ||||
\(343\) | 3.29432e17i | 0.589802i | ||||||||
\(344\) | −5.07490e17 | + | 6.61221e17i | −0.890263 | + | 1.15995i | ||||
\(345\) | 1.29704e16 | 0.0222957 | ||||||||
\(346\) | 6.32381e17 | + | 1.40220e17i | 1.06524 | + | 0.236199i | ||||
\(347\) | −1.75858e16 | −0.0290306 | −0.0145153 | − | 0.999895i | \(-0.504621\pi\) | ||||
−0.0145153 | + | 0.999895i | \(0.504621\pi\) | |||||||
\(348\) | 1.43713e16 | − | 3.08134e16i | 0.0232510 | − | 0.0498523i | ||||
\(349\) | − | 5.58810e17i | − | 0.886106i | −0.896495 | − | 0.443053i | \(-0.853895\pi\) | ||
0.896495 | − | 0.443053i | \(-0.146105\pi\) | |||||||
\(350\) | −3.82646e17 | − | 8.48456e16i | −0.594732 | − | 0.131872i | ||||
\(351\) | − | 3.43983e17i | − | 0.524068i | ||||||
\(352\) | 8.35972e17 | − | 4.34982e17i | 1.24851 | − | 0.649640i | ||||
\(353\) | −1.29351e17 | −0.189386 | −0.0946930 | − | 0.995507i | \(-0.530187\pi\) | ||||
−0.0946930 | + | 0.995507i | \(0.530187\pi\) | |||||||
\(354\) | 1.05387e16 | − | 4.75285e16i | 0.0151273 | − | 0.0682230i | ||||
\(355\) | −1.51943e18 | −2.13837 | ||||||||
\(356\) | 3.24672e17 | + | 1.51426e17i | 0.448017 | + | 0.208954i | ||||
\(357\) | 1.79952e16i | 0.0243488i | ||||||||
\(358\) | −2.65466e16 | + | 1.19723e17i | −0.0352231 | + | 0.158853i | ||||
\(359\) | 2.42896e15i | 0.00316053i | 0.999999 | + | 0.00158026i | \(0.000503014\pi\) | ||||
−0.999999 | + | 0.00158026i | \(0.999497\pi\) | |||||||
\(360\) | 9.99543e17 | + | 7.67153e17i | 1.27551 | + | 0.978959i | ||||
\(361\) | 6.87084e17 | 0.859923 | ||||||||
\(362\) | 1.76485e17 | + | 3.91326e16i | 0.216644 | + | 0.0480373i | ||||
\(363\) | 2.10023e17 | 0.252883 | ||||||||
\(364\) | 2.49864e17 | + | 1.16536e17i | 0.295117 | + | 0.137642i | ||||
\(365\) | 1.40121e18i | 1.62351i | ||||||||
\(366\) | −2.14920e17 | − | 4.76551e16i | −0.244293 | − | 0.0541679i | ||||
\(367\) | − | 1.14501e17i | − | 0.127687i | −0.997960 | − | 0.0638433i | \(-0.979664\pi\) | ||
0.997960 | − | 0.0638433i | \(-0.0203358\pi\) | |||||||
\(368\) | 3.51562e16 | − | 2.94907e16i | 0.0384652 | − | 0.0322664i | ||||
\(369\) | 4.37534e17 | 0.469707 | ||||||||
\(370\) | 2.30616e17 | − | 1.04006e18i | 0.242928 | − | 1.09558i | ||||
\(371\) | 2.67991e17 | 0.277015 | ||||||||
\(372\) | 1.49830e17 | − | 3.21249e17i | 0.151984 | − | 0.325868i | ||||
\(373\) | 9.66529e17i | 0.962173i | 0.876673 | + | 0.481086i | \(0.159758\pi\) | ||||
−0.876673 | + | 0.481086i | \(0.840242\pi\) | |||||||
\(374\) | 9.50713e16 | − | 4.28764e17i | 0.0928856 | − | 0.418906i | ||||
\(375\) | − | 4.47635e17i | − | 0.429245i | ||||||
\(376\) | −2.39619e17 | − | 1.83909e17i | −0.225531 | − | 0.173096i | ||||
\(377\) | −2.42765e17 | −0.224283 | ||||||||
\(378\) | −1.66238e17 | − | 3.68607e16i | −0.150761 | − | 0.0334288i | ||||
\(379\) | 1.09131e18 | 0.971568 | 0.485784 | − | 0.874079i | \(-0.338534\pi\) | ||||
0.485784 | + | 0.874079i | \(0.338534\pi\) | |||||||
\(380\) | −1.13600e18 | + | 2.43569e18i | −0.992874 | + | 2.12881i | ||||
\(381\) | 4.73836e17i | 0.406587i | ||||||||
\(382\) | −6.69320e17 | − | 1.48411e17i | −0.563885 | − | 0.125032i | ||||
\(383\) | − | 1.30961e18i | − | 1.08330i | −0.840604 | − | 0.541651i | \(-0.817799\pi\) | ||
0.840604 | − | 0.541651i | \(-0.182201\pi\) | |||||||
\(384\) | −3.17134e17 | + | 1.37636e16i | −0.257587 | + | 0.0111793i | ||||
\(385\) | −9.41466e17 | −0.750896 | ||||||||
\(386\) | 1.05553e17 | − | 4.76035e17i | 0.0826722 | − | 0.372845i | ||||
\(387\) | −1.77464e18 | −1.36500 | ||||||||
\(388\) | −1.00220e18 | − | 4.67424e17i | −0.757063 | − | 0.353093i | ||||
\(389\) | − | 1.94220e18i | − | 1.44095i | −0.693483 | − | 0.720473i | \(-0.743925\pi\) | ||
0.693483 | − | 0.720473i | \(-0.256075\pi\) | |||||||
\(390\) | −1.38685e17 | + | 6.25457e17i | −0.101059 | + | 0.455769i | ||||
\(391\) | − | 2.13852e16i | − | 0.0153065i | ||||||
\(392\) | −7.82896e17 | + | 1.02005e18i | −0.550429 | + | 0.717167i | ||||
\(393\) | 9.85683e16 | 0.0680753 | ||||||||
\(394\) | −1.17974e18 | − | 2.61588e17i | −0.800410 | − | 0.177478i | ||||
\(395\) | 3.98650e18 | 2.65713 | ||||||||
\(396\) | 1.81834e18 | + | 8.48069e17i | 1.19072 | + | 0.555348i | ||||
\(397\) | − | 1.86396e18i | − | 1.19923i | −0.800287 | − | 0.599617i | \(-0.795320\pi\) | ||
0.800287 | − | 0.599617i | \(-0.204680\pi\) | |||||||
\(398\) | 1.06895e18 | + | 2.37022e17i | 0.675735 | + | 0.149833i | ||||
\(399\) | − | 1.75355e17i | − | 0.108920i | ||||||
\(400\) | −2.07074e18 | − | 2.46855e18i | −1.26388 | − | 1.50669i | ||||
\(401\) | 2.23064e18 | 1.33789 | 0.668944 | − | 0.743313i | \(-0.266747\pi\) | ||||
0.668944 | + | 0.743313i | \(0.266747\pi\) | |||||||
\(402\) | −6.16637e16 | + | 2.78098e17i | −0.0363452 | + | 0.163914i | ||||
\(403\) | −2.53098e18 | −1.46606 | ||||||||
\(404\) | 5.04487e17 | − | 1.08167e18i | 0.287197 | − | 0.615777i | ||||
\(405\) | 2.47802e18i | 1.38650i | ||||||||
\(406\) | −2.60143e16 | + | 1.17322e17i | −0.0143064 | + | 0.0645206i | ||||
\(407\) | − | 1.69638e18i | − | 0.916982i | ||||||
\(408\) | −9.00702e16 | + | 1.17355e17i | −0.0478586 | + | 0.0623561i | ||||
\(409\) | 6.70663e16 | 0.0350301 | 0.0175150 | − | 0.999847i | \(-0.494425\pi\) | ||||
0.0175150 | + | 0.999847i | \(0.494425\pi\) | |||||||
\(410\) | −1.64777e18 | − | 3.65365e17i | −0.846075 | − | 0.187603i | ||||
\(411\) | 9.64976e15 | 0.00487106 | ||||||||
\(412\) | 1.12197e18 | − | 2.40560e18i | 0.556800 | − | 1.19383i | ||||
\(413\) | 1.72068e17i | 0.0839554i | ||||||||
\(414\) | 9.53817e16 | + | 2.11493e16i | 0.0457576 | + | 0.0101460i | ||||
\(415\) | 5.67765e18i | 2.67813i | ||||||||
\(416\) | 1.04619e18 | + | 2.01062e18i | 0.485239 | + | 0.932559i | ||||
\(417\) | 7.47080e17 | 0.340734 | ||||||||
\(418\) | −9.26431e17 | + | 4.17812e18i | −0.415508 | + | 1.87390i | ||||
\(419\) | −5.79500e17 | −0.255597 | −0.127798 | − | 0.991800i | \(-0.540791\pi\) | ||||
−0.127798 | + | 0.991800i | \(0.540791\pi\) | |||||||
\(420\) | 2.87406e17 | + | 1.34046e17i | 0.124667 | + | 0.0581444i | ||||
\(421\) | − | 3.63547e18i | − | 1.55091i | −0.631403 | − | 0.775455i | \(-0.717521\pi\) | ||
0.631403 | − | 0.775455i | \(-0.282479\pi\) | |||||||
\(422\) | 1.24268e17 | − | 5.60440e17i | 0.0521403 | − | 0.235148i | ||||
\(423\) | − | 6.43109e17i | − | 0.265401i | ||||||
\(424\) | 1.74769e18 | + | 1.34136e18i | 0.709420 | + | 0.544483i | ||||
\(425\) | −1.50160e18 | −0.599558 | ||||||||
\(426\) | 7.95669e17 | + | 1.76427e17i | 0.312511 | + | 0.0692942i | ||||
\(427\) | 7.78078e17 | 0.300627 | ||||||||
\(428\) | −9.37316e17 | − | 4.37163e17i | −0.356270 | − | 0.166164i | ||||
\(429\) | 1.02014e18i | 0.381470i | ||||||||
\(430\) | 6.68335e18 | + | 1.48192e18i | 2.45875 | + | 0.545189i | ||||
\(431\) | 2.49117e18i | 0.901700i | 0.892600 | + | 0.450850i | \(0.148879\pi\) | ||||
−0.892600 | + | 0.450850i | \(0.851121\pi\) | |||||||
\(432\) | −8.99620e17 | − | 1.07245e18i | −0.320385 | − | 0.381936i | ||||
\(433\) | −3.97819e18 | −1.39402 | −0.697012 | − | 0.717059i | \(-0.745488\pi\) | ||||
−0.697012 | + | 0.717059i | \(0.745488\pi\) | |||||||
\(434\) | −2.71215e17 | + | 1.22316e18i | −0.0935160 | + | 0.421749i | ||||
\(435\) | −2.79241e17 | −0.0947444 | ||||||||
\(436\) | 1.34983e18 | − | 2.89416e18i | 0.450685 | − | 0.966310i | ||||
\(437\) | 2.08390e17i | 0.0684710i | ||||||||
\(438\) | 1.62700e17 | − | 7.33762e17i | 0.0526099 | − | 0.237266i | ||||
\(439\) | 1.23400e18i | 0.392702i | 0.980534 | + | 0.196351i | \(0.0629091\pi\) | ||||
−0.980534 | + | 0.196351i | \(0.937091\pi\) | |||||||
\(440\) | −6.13973e18 | − | 4.71227e18i | −1.92301 | − | 1.47591i | ||||
\(441\) | −2.73771e18 | −0.843950 | ||||||||
\(442\) | 1.03123e18 | + | 2.28659e17i | 0.312896 | + | 0.0693796i | ||||
\(443\) | 2.18329e18 | 0.652058 | 0.326029 | − | 0.945360i | \(-0.394289\pi\) | ||||
0.326029 | + | 0.945360i | \(0.394289\pi\) | |||||||
\(444\) | −2.41529e17 | + | 5.17861e17i | −0.0710051 | + | 0.152241i | ||||
\(445\) | − | 2.94227e18i | − | 0.851457i | ||||||
\(446\) | −1.39859e18 | − | 3.10115e17i | −0.398426 | − | 0.0883444i | ||||
\(447\) | 3.65309e17i | 0.102449i | ||||||||
\(448\) | 1.08379e18 | − | 2.90141e17i | 0.299225 | − | 0.0801056i | ||||
\(449\) | 3.10058e18 | 0.842787 | 0.421394 | − | 0.906878i | \(-0.361541\pi\) | ||||
0.421394 | + | 0.906878i | \(0.361541\pi\) | |||||||
\(450\) | 1.48504e18 | − | 6.69739e18i | 0.397420 | − | 1.79233i | ||||
\(451\) | −2.68757e18 | −0.708148 | ||||||||
\(452\) | 5.73447e18 | + | 2.67455e18i | 1.48773 | + | 0.693875i | ||||
\(453\) | − | 8.57173e17i | − | 0.218968i | ||||||
\(454\) | −4.78404e17 | + | 2.15756e18i | −0.120338 | + | 0.542716i | ||||
\(455\) | − | 2.26435e18i | − | 0.560871i | ||||||
\(456\) | 8.77697e17 | − | 1.14357e18i | 0.214087 | − | 0.278939i | ||||
\(457\) | −6.86767e17 | −0.164967 | −0.0824833 | − | 0.996592i | \(-0.526285\pi\) | ||||
−0.0824833 | + | 0.996592i | \(0.526285\pi\) | |||||||
\(458\) | −5.71689e18 | − | 1.26763e18i | −1.35239 | − | 0.299870i | ||||
\(459\) | −6.52361e17 | −0.151984 | ||||||||
\(460\) | −3.41550e17 | − | 1.59298e17i | −0.0783699 | − | 0.0365516i | ||||
\(461\) | − | 3.51449e17i | − | 0.0794248i | −0.999211 | − | 0.0397124i | \(-0.987356\pi\) | ||
0.999211 | − | 0.0397124i | \(-0.0126442\pi\) | |||||||
\(462\) | 4.93010e17 | + | 1.09317e17i | 0.109739 | + | 0.0243329i | ||||
\(463\) | 1.68282e18i | 0.368952i | 0.982837 | + | 0.184476i | \(0.0590589\pi\) | ||||
−0.982837 | + | 0.184476i | \(0.940941\pi\) | |||||||
\(464\) | −7.56878e17 | + | 6.34904e17i | −0.163456 | + | 0.137114i | ||||
\(465\) | −2.91125e18 | −0.619312 | ||||||||
\(466\) | −1.28677e18 | + | 5.80322e18i | −0.269649 | + | 1.21609i | ||||
\(467\) | −9.11832e18 | −1.88233 | −0.941166 | − | 0.337943i | \(-0.890269\pi\) | ||||
−0.941166 | + | 0.337943i | \(0.890269\pi\) | |||||||
\(468\) | −2.03971e18 | + | 4.37333e18i | −0.414809 | + | 0.889388i | ||||
\(469\) | − | 1.00680e18i | − | 0.201713i | ||||||
\(470\) | −5.37032e17 | + | 2.42197e18i | −0.106002 | + | 0.478061i | ||||
\(471\) | 6.55682e16i | 0.0127511i | ||||||||
\(472\) | −8.61240e17 | + | 1.12213e18i | −0.165018 | + | 0.215006i | ||||
\(473\) | 1.09008e19 | 2.05793 | ||||||||
\(474\) | −2.08758e18 | − | 4.62886e17i | −0.388324 | − | 0.0861044i | ||||
\(475\) | 1.46325e19 | 2.68202 | ||||||||
\(476\) | 2.21010e17 | − | 4.73865e17i | 0.0399175 | − | 0.0855867i | ||||
\(477\) | 4.69060e18i | 0.834833i | ||||||||
\(478\) | −1.79411e18 | − | 3.97814e17i | −0.314668 | − | 0.0697726i | ||||
\(479\) | − | 1.06874e19i | − | 1.84724i | −0.383305 | − | 0.923622i | \(-0.625214\pi\) | ||
0.383305 | − | 0.923622i | \(-0.374786\pi\) | |||||||
\(480\) | 1.20337e18 | + | 2.31271e18i | 0.204980 | + | 0.393942i | ||||
\(481\) | 4.08000e18 | 0.684927 | ||||||||
\(482\) | 8.64357e17 | − | 3.89818e18i | 0.143009 | − | 0.644959i | ||||
\(483\) | 2.45896e16 | 0.00400978 | ||||||||
\(484\) | −5.53051e18 | − | 2.57942e18i | −0.888890 | − | 0.414577i | ||||
\(485\) | 9.08223e18i | 1.43880i | ||||||||
\(486\) | 9.78839e17 | − | 4.41448e18i | 0.152847 | − | 0.689328i | ||||
\(487\) | 8.34573e18i | 1.28458i | 0.766461 | + | 0.642291i | \(0.222016\pi\) | ||||
−0.766461 | + | 0.642291i | \(0.777984\pi\) | |||||||
\(488\) | 5.07420e18 | + | 3.89447e18i | 0.769890 | + | 0.590894i | ||||
\(489\) | −3.09044e17 | −0.0462230 | ||||||||
\(490\) | 1.03103e19 | + | 2.28614e18i | 1.52019 | + | 0.337077i | ||||
\(491\) | 3.83730e18 | 0.557770 | 0.278885 | − | 0.960324i | \(-0.410035\pi\) | ||||
0.278885 | + | 0.960324i | \(0.410035\pi\) | |||||||
\(492\) | 8.20448e17 | + | 3.82655e17i | 0.117570 | + | 0.0548343i | ||||
\(493\) | 4.60402e17i | 0.0650442i | ||||||||
\(494\) | −1.00489e19 | − | 2.22818e18i | −1.39969 | − | 0.310358i | ||||
\(495\) | − | 1.64783e19i | − | 2.26296i | ||||||
\(496\) | −7.89092e18 | + | 6.61927e18i | −1.06845 | + | 0.896269i | ||||
\(497\) | −2.88057e18 | −0.384577 | ||||||||
\(498\) | 6.59251e17 | − | 2.97317e18i | 0.0867852 | − | 0.391394i | ||||
\(499\) | −2.22902e17 | −0.0289341 | −0.0144671 | − | 0.999895i | \(-0.504605\pi\) | ||||
−0.0144671 | + | 0.999895i | \(0.504605\pi\) | |||||||
\(500\) | −5.49769e18 | + | 1.17875e19i | −0.703704 | + | 1.50881i | ||||
\(501\) | − | 1.13942e18i | − | 0.143820i | ||||||
\(502\) | 1.45833e18 | − | 6.57695e18i | 0.181522 | − | 0.818650i | ||||
\(503\) | − | 2.66300e18i | − | 0.326885i | −0.986553 | − | 0.163443i | \(-0.947740\pi\) | ||
0.986553 | − | 0.163443i | \(-0.0522599\pi\) | |||||||
\(504\) | 1.89495e18 | + | 1.45438e18i | 0.229395 | + | 0.176062i | ||||
\(505\) | −9.80238e18 | −1.17029 | ||||||||
\(506\) | −5.85886e17 | − | 1.29911e17i | −0.0689858 | − | 0.0152965i | ||||
\(507\) | −2.33392e17 | −0.0271038 | ||||||||
\(508\) | 5.81947e18 | − | 1.24775e19i | 0.666558 | − | 1.42916i | ||||
\(509\) | 2.62685e18i | 0.296764i | 0.988930 | + | 0.148382i | \(0.0474065\pi\) | ||||
−0.988930 | + | 0.148382i | \(0.952593\pi\) | |||||||
\(510\) | 1.18617e18 | + | 2.63014e17i | 0.132177 | + | 0.0293081i | ||||
\(511\) | 2.65644e18i | 0.291981i | ||||||||
\(512\) | 8.52010e18 | + | 3.53248e18i | 0.923751 | + | 0.382993i | ||||
\(513\) | 6.35699e18 | 0.679876 | ||||||||
\(514\) | −1.35245e18 | + | 6.09943e18i | −0.142685 | + | 0.643499i | ||||
\(515\) | −2.18003e19 | −2.26888 | ||||||||
\(516\) | −3.32774e18 | − | 1.55205e18i | −0.341666 | − | 0.159352i | ||||
\(517\) | 3.95032e18i | 0.400128i | ||||||||
\(518\) | 4.37206e17 | − | 1.97176e18i | 0.0436895 | − | 0.197036i | ||||
\(519\) | 2.85346e18i | 0.281320i | ||||||||
\(520\) | 1.13336e19 | − | 1.47668e19i | 1.10241 | − | 1.43636i | ||||
\(521\) | −7.32584e18 | −0.703062 | −0.351531 | − | 0.936176i | \(-0.614339\pi\) | ||||
−0.351531 | + | 0.936176i | \(0.614339\pi\) | |||||||
\(522\) | −2.05347e18 | − | 4.55324e17i | −0.194444 | − | 0.0431149i | ||||
\(523\) | −3.21486e18 | −0.300366 | −0.150183 | − | 0.988658i | \(-0.547986\pi\) | ||||
−0.150183 | + | 0.988658i | \(0.547986\pi\) | |||||||
\(524\) | −2.59559e18 | − | 1.21058e18i | −0.239286 | − | 0.111603i | ||||
\(525\) | − | 1.72660e18i | − | 0.157064i | ||||||
\(526\) | −1.21949e19 | − | 2.70402e18i | −1.09466 | − | 0.242723i | ||||
\(527\) | 4.79997e18i | 0.425172i | ||||||||
\(528\) | 2.66798e18 | + | 3.18054e18i | 0.233209 | + | 0.278012i | ||||
\(529\) | 1.15636e19 | 0.997479 | ||||||||
\(530\) | 3.91691e18 | − | 1.76649e19i | 0.333436 | − | 1.50377i | ||||
\(531\) | −3.01167e18 | −0.253015 | ||||||||
\(532\) | −2.15365e18 | + | 4.61762e18i | −0.178564 | + | 0.382857i | ||||
\(533\) | − | 6.46394e18i | − | 0.528941i | ||||||
\(534\) | −3.41637e17 | + | 1.54075e18i | −0.0275915 | + | 0.124436i | ||||
\(535\) | 8.49424e18i | 0.677093i | ||||||||
\(536\) | 5.03929e18 | − | 6.56581e18i | 0.396475 | − | 0.516576i | ||||
\(537\) | −5.40220e17 | −0.0419518 | ||||||||
\(538\) | 1.63171e19 | + | 3.61806e18i | 1.25074 | + | 0.277332i | ||||
\(539\) | 1.68165e19 | 1.27237 | ||||||||
\(540\) | −4.85943e18 | + | 1.04191e19i | −0.362935 | + | 0.778166i | ||||
\(541\) | − | 1.13830e19i | − | 0.839220i | −0.907704 | − | 0.419610i | \(-0.862167\pi\) | ||
0.907704 | − | 0.419610i | \(-0.137833\pi\) | |||||||
\(542\) | 2.02967e19 | + | 4.50046e18i | 1.47717 | + | 0.327538i | ||||
\(543\) | 7.96343e17i | 0.0572139i | ||||||||
\(544\) | 3.81312e18 | − | 1.98408e18i | 0.270450 | − | 0.140724i | ||||
\(545\) | −2.62277e19 | −1.83647 | ||||||||
\(546\) | −2.62921e17 | + | 1.18575e18i | −0.0181751 | + | 0.0819681i | ||||
\(547\) | 2.28532e18 | 0.155968 | 0.0779841 | − | 0.996955i | \(-0.475152\pi\) | ||||
0.0779841 | + | 0.996955i | \(0.475152\pi\) | |||||||
\(548\) | −2.54106e17 | − | 1.18515e17i | −0.0171219 | − | 0.00798562i | ||||
\(549\) | 1.36186e19i | 0.905993i | ||||||||
\(550\) | −9.12189e18 | + | 4.11390e19i | −0.599165 | + | 2.70218i | ||||
\(551\) | − | 4.48643e18i | − | 0.290964i | ||||||
\(552\) | 1.60360e17 | + | 1.23077e17i | 0.0102688 | + | 0.00788139i | ||||
\(553\) | 7.55767e18 | 0.477872 | ||||||||
\(554\) | 1.74058e19 | + | 3.85945e18i | 1.08674 | + | 0.240966i | ||||
\(555\) | 4.69301e18 | 0.289335 | ||||||||
\(556\) | −1.96728e19 | − | 9.17536e18i | −1.19769 | − | 0.558598i | ||||
\(557\) | 1.37134e19i | 0.824440i | 0.911084 | + | 0.412220i | \(0.135247\pi\) | ||||
−0.911084 | + | 0.412220i | \(0.864753\pi\) | |||||||
\(558\) | −2.14087e19 | − | 4.74703e18i | −1.27102 | − | 0.281827i | ||||
\(559\) | 2.62178e19i | 1.53714i | ||||||||
\(560\) | −5.92195e18 | − | 7.05963e18i | −0.342885 | − | 0.408758i | ||||
\(561\) | 1.93469e18 | 0.110630 | ||||||||
\(562\) | −3.97852e18 | + | 1.79428e19i | −0.224682 | + | 1.01329i | ||||
\(563\) | 2.14062e19 | 1.19393 | 0.596967 | − | 0.802266i | \(-0.296372\pi\) | ||||
0.596967 | + | 0.802266i | \(0.296372\pi\) | |||||||
\(564\) | 5.62446e17 | − | 1.20593e18i | 0.0309833 | − | 0.0664309i | ||||
\(565\) | − | 5.19675e19i | − | 2.82743i | ||||||
\(566\) | 4.82550e18 | − | 2.17626e19i | 0.259315 | − | 1.16949i | ||||
\(567\) | 4.69787e18i | 0.249356i | ||||||||
\(568\) | −1.87855e19 | − | 1.44179e19i | −0.984882 | − | 0.755901i | ||||
\(569\) | 1.41821e19 | 0.734440 | 0.367220 | − | 0.930134i | \(-0.380310\pi\) | ||||
0.367220 | + | 0.930134i | \(0.380310\pi\) | |||||||
\(570\) | −1.15588e19 | − | 2.56297e18i | −0.591272 | − | 0.131105i | ||||
\(571\) | −1.28761e19 | −0.650628 | −0.325314 | − | 0.945606i | \(-0.605470\pi\) | ||||
−0.325314 | + | 0.945606i | \(0.605470\pi\) | |||||||
\(572\) | 1.25290e19 | − | 2.68633e19i | 0.625381 | − | 1.34087i | ||||
\(573\) | − | 3.02015e18i | − | 0.148917i | ||||||
\(574\) | −3.12386e18 | − | 6.92665e17i | −0.152163 | − | 0.0337396i | ||||
\(575\) | 2.05187e18i | 0.0987356i | ||||||||
\(576\) | 5.07829e18 | + | 1.89694e19i | 0.241413 | + | 0.901769i | ||||
\(577\) | −7.59706e18 | −0.356792 | −0.178396 | − | 0.983959i | \(-0.557091\pi\) | ||||
−0.178396 | + | 0.983959i | \(0.557091\pi\) | |||||||
\(578\) | −4.23192e18 | + | 1.90856e19i | −0.196355 | + | 0.885545i | ||||
\(579\) | 2.14799e18 | 0.0984652 | ||||||||
\(580\) | 7.35322e18 | + | 3.42953e18i | 0.333029 | + | 0.155324i | ||||
\(581\) | 1.07638e19i | 0.481650i | ||||||||
\(582\) | 1.05457e18 | − | 4.75601e18i | 0.0466245 | − | 0.210272i | ||||
\(583\) | − | 2.88122e19i | − | 1.25862i | ||||||
\(584\) | −1.32961e19 | + | 1.73239e19i | −0.573899 | + | 0.747747i | ||||
\(585\) | 3.96324e19 | 1.69028 | ||||||||
\(586\) | −3.08286e19 | − | 6.83573e18i | −1.29918 | − | 0.288072i | ||||
\(587\) | −1.31679e19 | −0.548339 | −0.274170 | − | 0.961681i | \(-0.588403\pi\) | ||||
−0.274170 | + | 0.961681i | \(0.588403\pi\) | |||||||
\(588\) | −5.13365e18 | − | 2.39432e18i | −0.211244 | − | 0.0985239i | ||||
\(589\) | − | 4.67738e19i | − | 1.90193i | ||||||
\(590\) | 1.13420e19 | + | 2.51491e18i | 0.455750 | + | 0.101055i | ||||
\(591\) | − | 5.32329e18i | − | 0.211382i | ||||||
\(592\) | 1.27204e19 | − | 1.06704e19i | 0.499169 | − | 0.418726i | ||||
\(593\) | −7.19403e18 | −0.278990 | −0.139495 | − | 0.990223i | \(-0.544548\pi\) | ||||
−0.139495 | + | 0.990223i | \(0.544548\pi\) | |||||||
\(594\) | −3.96295e18 | + | 1.78726e19i | −0.151885 | + | 0.684987i | ||||
\(595\) | −4.29431e18 | −0.162658 | ||||||||
\(596\) | 4.48659e18 | − | 9.61966e18i | 0.167955 | − | 0.360111i | ||||
\(597\) | 4.82338e18i | 0.178456i | ||||||||
\(598\) | 3.12452e17 | − | 1.40913e18i | 0.0114255 | − | 0.0515279i | ||||
\(599\) | 5.20533e18i | 0.188131i | 0.995566 | + | 0.0940656i | \(0.0299863\pi\) | ||||
−0.995566 | + | 0.0940656i | \(0.970014\pi\) | |||||||
\(600\) | 8.64204e18 | − | 1.12599e19i | 0.308715 | − | 0.402232i | ||||
\(601\) | −2.93182e19 | −1.03518 | −0.517591 | − | 0.855628i | \(-0.673171\pi\) | ||||
−0.517591 | + | 0.855628i | \(0.673171\pi\) | |||||||
\(602\) | 1.26704e19 | + | 2.80945e18i | 0.442196 | + | 0.0980497i | ||||
\(603\) | 1.76219e19 | 0.607898 | ||||||||
\(604\) | −1.05275e19 | + | 2.25719e19i | −0.358977 | + | 0.769678i | ||||
\(605\) | 5.01192e19i | 1.68934i | ||||||||
\(606\) | 5.13313e18 | + | 1.13819e18i | 0.171031 | + | 0.0379232i | ||||
\(607\) | 3.86424e19i | 1.27275i | 0.771380 | + | 0.636375i | \(0.219567\pi\) | ||||
−0.771380 | + | 0.636375i | \(0.780433\pi\) | |||||||
\(608\) | −3.71572e19 | + | 1.93341e19i | −1.20981 | + | 0.629503i | ||||
\(609\) | −5.29389e17 | −0.0170394 | ||||||||
\(610\) | 1.13723e19 | − | 5.12879e19i | 0.361858 | − | 1.63195i | ||||
\(611\) | −9.50102e18 | −0.298870 | ||||||||
\(612\) | 8.29398e18 | + | 3.86830e18i | 0.257931 | + | 0.120298i | ||||
\(613\) | 4.72455e19i | 1.45257i | 0.687393 | + | 0.726286i | \(0.258755\pi\) | ||||
−0.687393 | + | 0.726286i | \(0.741245\pi\) | |||||||
\(614\) | 2.51274e18 | − | 1.13322e19i | 0.0763780 | − | 0.344458i | ||||
\(615\) | − | 7.43515e18i | − | 0.223441i | ||||||
\(616\) | −1.16398e19 | − | 8.93359e18i | −0.345844 | − | 0.265437i | ||||
\(617\) | −5.23267e19 | −1.53719 | −0.768594 | − | 0.639736i | \(-0.779044\pi\) | ||||
−0.768594 | + | 0.639736i | \(0.779044\pi\) | |||||||
\(618\) | 1.14159e19 | + | 2.53130e18i | 0.331583 | + | 0.0735232i | ||||
\(619\) | 4.21857e19 | 1.21152 | 0.605761 | − | 0.795647i | \(-0.292869\pi\) | ||||
0.605761 | + | 0.795647i | \(0.292869\pi\) | |||||||
\(620\) | 7.66618e19 | + | 3.57549e19i | 2.17689 | + | 1.01530i | ||||
\(621\) | 8.91421e17i | 0.0250289i | ||||||||
\(622\) | 5.11462e19 | + | 1.13408e19i | 1.41997 | + | 0.314856i | ||||
\(623\) | − | 5.57800e18i | − | 0.153131i | ||||||
\(624\) | −7.64959e18 | + | 6.41683e18i | −0.207657 | + | 0.174192i | ||||
\(625\) | 3.35610e19 | 0.900896 | ||||||||
\(626\) | 5.09202e18 | − | 2.29646e19i | 0.135167 | − | 0.609591i | ||||
\(627\) | −1.88528e19 | −0.494883 | ||||||||
\(628\) | 8.05284e17 | − | 1.72660e18i | 0.0209041 | − | 0.0448203i | ||||
\(629\) | − | 7.73767e18i | − | 0.198635i | ||||||
\(630\) | 4.24694e18 | − | 1.91534e19i | 0.107818 | − | 0.486252i | ||||
\(631\) | − | 6.71976e19i | − | 1.68713i | −0.537028 | − | 0.843565i | \(-0.680453\pi\) | ||
0.537028 | − | 0.843565i | \(-0.319547\pi\) | |||||||
\(632\) | 4.92870e19 | + | 3.78280e19i | 1.22381 | + | 0.939276i | ||||
\(633\) | 2.52885e18 | 0.0621007 | ||||||||
\(634\) | −5.54636e19 | − | 1.22981e19i | −1.34705 | − | 0.298686i | ||||
\(635\) | −1.13075e20 | −2.71612 | ||||||||
\(636\) | −4.10227e18 | + | 8.79564e18i | −0.0974596 | + | 0.208962i | ||||
\(637\) | 4.04457e19i | 0.950378i | ||||||||
\(638\) | 1.26135e19 | + | 2.79684e18i | 0.293151 | + | 0.0650015i | ||||
\(639\) | − | 5.04180e19i | − | 1.15899i | ||||||
\(640\) | −3.28451e18 | − | 7.56798e19i | −0.0746811 | − | 1.72076i | ||||
\(641\) | 3.21170e19 | 0.722318 | 0.361159 | − | 0.932504i | \(-0.382381\pi\) | ||||
0.361159 | + | 0.932504i | \(0.382381\pi\) | |||||||
\(642\) | 9.86295e17 | − | 4.44810e18i | 0.0219413 | − | 0.0989532i | ||||
\(643\) | 3.22678e18 | 0.0710056 | 0.0355028 | − | 0.999370i | \(-0.488697\pi\) | ||||
0.0355028 | + | 0.999370i | \(0.488697\pi\) | |||||||
\(644\) | −6.47515e17 | − | 3.02000e17i | −0.0140945 | − | 0.00657364i | ||||
\(645\) | 3.01570e19i | 0.649337i | ||||||||
\(646\) | −4.22573e18 | + | 1.90577e19i | −0.0900065 | + | 0.405922i | ||||
\(647\) | 2.86365e19i | 0.603378i | 0.953406 | + | 0.301689i | \(0.0975504\pi\) | ||||
−0.953406 | + | 0.301689i | \(0.902450\pi\) | |||||||
\(648\) | −2.35140e19 | + | 3.06369e19i | −0.490119 | + | 0.638587i | ||||
\(649\) | 1.84993e19 | 0.381454 | ||||||||
\(650\) | −9.89444e19 | − | 2.19393e19i | −2.01836 | − | 0.447537i | ||||
\(651\) | −5.51920e18 | −0.111381 | ||||||||
\(652\) | 8.13802e18 | + | 3.79556e18i | 0.162475 | + | 0.0757779i | ||||
\(653\) | − | 3.11703e19i | − | 0.615670i | −0.951440 | − | 0.307835i | \(-0.900395\pi\) | ||
0.951440 | − | 0.307835i | \(-0.0996045\pi\) | |||||||
\(654\) | 1.37344e19 | + | 3.04539e18i | 0.268390 | + | 0.0595111i | ||||
\(655\) | 2.35220e19i | 0.454764i | ||||||||
\(656\) | −1.69052e19 | − | 2.01529e19i | −0.323364 | − | 0.385487i | ||||
\(657\) | −4.64952e19 | −0.879936 | ||||||||
\(658\) | −1.01811e18 | + | 4.59161e18i | −0.0190640 | + | 0.0859772i | ||||
\(659\) | 6.59463e19 | 1.22178 | 0.610889 | − | 0.791716i | \(-0.290812\pi\) | ||||
0.610889 | + | 0.791716i | \(0.290812\pi\) | |||||||
\(660\) | 1.44115e19 | − | 3.08995e19i | 0.264181 | − | 0.566428i | ||||
\(661\) | − | 1.57169e19i | − | 0.285073i | −0.989790 | − | 0.142536i | \(-0.954474\pi\) | ||
0.989790 | − | 0.142536i | \(-0.0455258\pi\) | |||||||
\(662\) | 1.53660e19 | − | 6.92993e19i | 0.275775 | − | 1.24372i | ||||
\(663\) | 4.65318e18i | 0.0826333i | ||||||||
\(664\) | −5.38753e19 | + | 7.01955e19i | −0.946702 | + | 1.23348i | ||||
\(665\) | 4.18463e19 | 0.727621 | ||||||||
\(666\) | 3.45114e19 | + | 7.65233e18i | 0.593803 | + | 0.131666i | ||||
\(667\) | 6.29118e17 | 0.0107115 | ||||||||
\(668\) | −1.39939e19 | + | 3.00042e19i | −0.235778 | + | 0.505530i | ||||
\(669\) | − | 6.31081e18i | − | 0.105221i | ||||||
\(670\) | −6.63645e19 | − | 1.47152e19i | −1.09499 | − | 0.242797i | ||||
\(671\) | − | 8.36525e19i | − | 1.36591i | ||||||
\(672\) | 2.28138e18 | + | 4.38447e18i | 0.0368648 | + | 0.0708488i | ||||
\(673\) | −2.19558e19 | −0.351111 | −0.175555 | − | 0.984470i | \(-0.556172\pi\) | ||||
−0.175555 | + | 0.984470i | \(0.556172\pi\) | |||||||
\(674\) | −1.98072e19 | + | 8.93290e19i | −0.313476 | + | 1.41375i | ||||
\(675\) | 6.25926e19 | 0.980385 | ||||||||
\(676\) | 6.14589e18 | + | 2.86643e18i | 0.0952704 | + | 0.0444339i | ||||
\(677\) | − | 1.76460e19i | − | 0.270724i | −0.990796 | − | 0.135362i | \(-0.956780\pi\) | ||
0.990796 | − | 0.135362i | \(-0.0432197\pi\) | |||||||
\(678\) | −6.03412e18 | + | 2.72134e19i | −0.0916233 | + | 0.413213i | ||||
\(679\) | 1.72182e19i | 0.258762i | ||||||||
\(680\) | −2.80051e19 | − | 2.14941e19i | −0.416558 | − | 0.319710i | ||||
\(681\) | −9.73547e18 | −0.143327 | ||||||||
\(682\) | 1.31504e20 | + | 2.91588e19i | 1.91623 | + | 0.424893i | ||||
\(683\) | −6.08395e18 | −0.0877487 | −0.0438744 | − | 0.999037i | \(-0.513970\pi\) | ||||
−0.0438744 | + | 0.999037i | \(0.513970\pi\) | |||||||
\(684\) | −8.08214e19 | − | 3.76949e19i | −1.15381 | − | 0.538134i | ||||
\(685\) | 2.30279e18i | 0.0325402i | ||||||||
\(686\) | 4.11674e19 | + | 9.12819e18i | 0.575817 | + | 0.127678i | ||||
\(687\) | − | 2.57961e19i | − | 0.357155i | ||||||
\(688\) | 6.85674e19 | + | 8.17401e19i | 0.939720 | + | 1.12025i | ||||
\(689\) | 6.92969e19 | 0.940112 | ||||||||
\(690\) | 3.59397e17 | − | 1.62085e18i | 0.00482648 | − | 0.0217670i | ||||
\(691\) | 1.16139e20 | 1.54394 | 0.771972 | − | 0.635656i | \(-0.219270\pi\) | ||||
0.771972 | + | 0.635656i | \(0.219270\pi\) | |||||||
\(692\) | 3.50452e19 | − | 7.51400e19i | 0.461196 | − | 0.988846i | ||||
\(693\) | − | 3.12398e19i | − | 0.406983i | ||||||
\(694\) | −4.87285e17 | + | 2.19761e18i | −0.00628444 | + | 0.0283423i | ||||
\(695\) | 1.78281e20i | 2.27620i | ||||||||
\(696\) | −3.45238e18 | − | 2.64972e18i | −0.0436369 | − | 0.0334915i | ||||
\(697\) | −1.22588e19 | −0.153398 | ||||||||
\(698\) | −6.98316e19 | − | 1.54840e19i | −0.865095 | − | 0.191821i | ||||
\(699\) | −2.61856e19 | −0.321161 | ||||||||
\(700\) | −2.12054e19 | + | 4.54664e19i | −0.257490 | + | 0.552082i | ||||
\(701\) | − | 6.77920e19i | − | 0.814990i | −0.913207 | − | 0.407495i | \(-0.866402\pi\) | ||
0.913207 | − | 0.407495i | \(-0.133598\pi\) | |||||||
\(702\) | −4.29858e19 | − | 9.53141e18i | −0.511641 | − | 0.113448i | ||||
\(703\) | 7.54004e19i | 0.888559i | ||||||||
\(704\) | −3.11936e19 | − | 1.16520e20i | −0.363962 | − | 1.35954i | ||||
\(705\) | −1.09285e19 | −0.126252 | ||||||||
\(706\) | −3.58419e18 | + | 1.61644e19i | −0.0409975 | + | 0.184895i | ||||
\(707\) | −1.85835e19 | −0.210471 | ||||||||
\(708\) | −5.64737e18 | − | 2.63392e18i | −0.0633306 | − | 0.0295373i | ||||
\(709\) | − | 3.66386e19i | − | 0.406832i | −0.979092 | − | 0.203416i | \(-0.934796\pi\) | ||
0.979092 | − | 0.203416i | \(-0.0652044\pi\) | |||||||
\(710\) | −4.21019e19 | + | 1.89876e20i | −0.462906 | + | 2.08767i | ||||
\(711\) | 1.32280e20i | 1.44015i | ||||||||
\(712\) | 2.79193e19 | − | 3.63767e19i | 0.300984 | − | 0.392160i | ||||
\(713\) | 6.55894e18 | 0.0700176 | ||||||||
\(714\) | 2.24876e18 | + | 4.98627e17i | 0.0237715 | + | 0.00527094i | ||||
\(715\) | −2.43444e20 | −2.54833 | ||||||||
\(716\) | 1.42256e19 | + | 6.63478e18i | 0.147462 | + | 0.0687758i | ||||
\(717\) | − | 8.09547e18i | − | 0.0831013i | ||||||
\(718\) | 3.03535e17 | + | 6.73039e16i | 0.00308558 | + | 0.000684178i | ||||
\(719\) | − | 1.35760e20i | − | 1.36669i | −0.730095 | − | 0.683346i | \(-0.760524\pi\) | ||
0.730095 | − | 0.683346i | \(-0.239476\pi\) | |||||||
\(720\) | 1.23563e20 | − | 1.03651e20i | 1.23186 | − | 1.03334i | ||||
\(721\) | −4.13292e19 | −0.408047 | ||||||||
\(722\) | 1.90384e19 | − | 8.58614e19i | 0.186153 | − | 0.839532i | ||||
\(723\) | 1.75896e19 | 0.170328 | ||||||||
\(724\) | 9.78039e18 | − | 2.09700e19i | 0.0937964 | − | 0.201108i | ||||
\(725\) | − | 4.41746e19i | − | 0.419572i | ||||||
\(726\) | 5.81951e18 | − | 2.62455e19i | 0.0547431 | − | 0.246887i | ||||
\(727\) | − | 9.85861e19i | − | 0.918491i | −0.888309 | − | 0.459245i | \(-0.848120\pi\) | ||
0.888309 | − | 0.459245i | \(-0.151880\pi\) | |||||||
\(728\) | 2.14864e19 | − | 2.79952e19i | 0.198264 | − | 0.258323i | ||||
\(729\) | −6.81620e19 | −0.622945 | ||||||||
\(730\) | 1.75103e20 | + | 3.88261e19i | 1.58501 | + | 0.351450i | ||||
\(731\) | 4.97218e19 | 0.445784 | ||||||||
\(732\) | −1.19104e19 | + | 2.55370e19i | −0.105767 | + | 0.226774i | ||||
\(733\) | 3.09174e19i | 0.271941i | 0.990713 | + | 0.135971i | \(0.0434153\pi\) | ||||
−0.990713 | + | 0.135971i | \(0.956585\pi\) | |||||||
\(734\) | −1.43086e19 | − | 3.17269e18i | −0.124659 | − | 0.0276411i | ||||
\(735\) | 4.65226e19i | 0.401470i | ||||||||
\(736\) | −2.71116e18 | − | 5.21045e18i | −0.0231745 | − | 0.0445380i | ||||
\(737\) | −1.08243e20 | −0.916489 | ||||||||
\(738\) | 1.21236e19 | − | 5.46764e19i | 0.101680 | − | 0.458570i | ||||
\(739\) | 1.25024e20 | 1.03868 | 0.519340 | − | 0.854568i | \(-0.326178\pi\) | ||||
0.519340 | + | 0.854568i | \(0.326178\pi\) | |||||||
\(740\) | −1.23581e20 | − | 5.76378e19i | −1.01702 | − | 0.474335i | ||||
\(741\) | − | 4.53433e19i | − | 0.369646i | ||||||
\(742\) | 7.42574e18 | − | 3.34895e19i | 0.0599670 | − | 0.270446i | ||||
\(743\) | − | 1.92617e19i | − | 0.154089i | −0.997028 | − | 0.0770446i | \(-0.975452\pi\) | ||
0.997028 | − | 0.0770446i | \(-0.0245484\pi\) | |||||||
\(744\) | −3.59932e19 | − | 2.76249e19i | −0.285240 | − | 0.218923i | ||||
\(745\) | −8.71763e19 | −0.684391 | ||||||||
\(746\) | 1.20782e20 | + | 2.67815e19i | 0.939358 | + | 0.208287i | ||||
\(747\) | −1.88396e20 | −1.45154 | ||||||||
\(748\) | −5.09461e19 | − | 2.37612e19i | −0.388866 | − | 0.181366i | ||||
\(749\) | 1.61035e19i | 0.121772i | ||||||||
\(750\) | −5.59387e19 | − | 1.24035e19i | −0.419067 | − | 0.0929213i | ||||
\(751\) | 1.79528e20i | 1.33246i | 0.745748 | + | 0.666228i | \(0.232092\pi\) | ||||
−0.745748 | + | 0.666228i | \(0.767908\pi\) | |||||||
\(752\) | −2.96217e19 | + | 2.48480e19i | −0.217814 | + | 0.182712i | ||||
\(753\) | 2.96769e19 | 0.216199 | ||||||||
\(754\) | −6.72676e18 | + | 3.03371e19i | −0.0485520 | + | 0.218965i | ||||
\(755\) | 2.04553e20 | 1.46277 | ||||||||
\(756\) | −9.21258e18 | + | 1.97526e19i | −0.0652723 | + | 0.139950i | ||||
\(757\) | 2.69501e20i | 1.89186i | 0.324365 | + | 0.945932i | \(0.394849\pi\) | ||||
−0.324365 | + | 0.945932i | \(0.605151\pi\) | |||||||
\(758\) | 3.02390e19 | − | 1.36375e20i | 0.210321 | − | 0.948530i | ||||
\(759\) | − | 2.64367e18i | − | 0.0182186i | ||||||
\(760\) | 2.72898e20 | + | 2.09451e20i | 1.86340 | + | 1.43017i | ||||
\(761\) | 6.63474e19 | 0.448881 | 0.224440 | − | 0.974488i | \(-0.427945\pi\) | ||||
0.224440 | + | 0.974488i | \(0.427945\pi\) | |||||||
\(762\) | 5.92128e19 | + | 1.31295e19i | 0.396946 | + | 0.0880162i | ||||
\(763\) | −4.97229e19 | −0.330282 | ||||||||
\(764\) | −3.70923e19 | + | 7.95292e19i | −0.244135 | + | 0.523448i | ||||
\(765\) | − | 7.51625e19i | − | 0.490198i | ||||||
\(766\) | −1.63655e20 | − | 3.62878e19i | −1.05761 | − | 0.234509i | ||||
\(767\) | 4.44931e19i | 0.284922i | ||||||||
\(768\) | −7.06747e18 | + | 4.00120e19i | −0.0448472 | + | 0.253899i | ||||
\(769\) | 2.96170e20 | 1.86233 | 0.931164 | − | 0.364601i | \(-0.118794\pi\) | ||||
0.931164 | + | 0.364601i | \(0.118794\pi\) | |||||||
\(770\) | −2.60870e19 | + | 1.17650e20i | −0.162551 | + | 0.733091i | ||||
\(771\) | −2.75222e19 | −0.169943 | ||||||||
\(772\) | −5.65629e19 | − | 2.63808e19i | −0.346107 | − | 0.161424i | ||||
\(773\) | − | 1.18393e20i | − | 0.717912i | −0.933355 | − | 0.358956i | \(-0.883133\pi\) | ||
0.933355 | − | 0.358956i | \(-0.116867\pi\) | |||||||
\(774\) | −4.91734e19 | + | 2.21768e20i | −0.295490 | + | 1.33264i | ||||
\(775\) | − | 4.60547e20i | − | 2.74260i | ||||||
\(776\) | −8.61814e19 | + | 1.12288e20i | −0.508606 | + | 0.662675i | ||||
\(777\) | 8.89708e18 | 0.0520356 | ||||||||
\(778\) | −2.42707e20 | − | 5.38164e19i | −1.40678 | − | 0.311930i | ||||
\(779\) | 1.19457e20 | 0.686198 | ||||||||
\(780\) | 7.43173e19 | + | 3.46615e19i | 0.423085 | + | 0.197326i | ||||
\(781\) | 3.09695e20i | 1.74734i | ||||||||
\(782\) | −2.67240e18 | − | 5.92561e17i | −0.0149436 | − | 0.00331349i | ||||
\(783\) | − | 1.91914e19i | − | 0.106359i | ||||||
\(784\) | 1.05778e20 | + | 1.26099e20i | 0.581007 | + | 0.692627i | ||||
\(785\) | −1.56470e19 | −0.0851811 | ||||||||
\(786\) | 2.73122e18 | − | 1.23176e19i | 0.0147367 | − | 0.0664611i | ||||
\(787\) | −2.30289e20 | −1.23154 | −0.615771 | − | 0.787925i | \(-0.711155\pi\) | ||||
−0.615771 | + | 0.787925i | \(0.711155\pi\) | |||||||
\(788\) | −6.53786e19 | + | 1.40178e20i | −0.346539 | + | 0.743011i | ||||
\(789\) | − | 5.50266e19i | − | 0.289090i | ||||||
\(790\) | 1.10462e20 | − | 4.98172e20i | 0.575204 | − | 2.59412i | ||||
\(791\) | − | 9.85208e19i | − | 0.508502i | ||||||
\(792\) | 1.56363e20 | − | 2.03729e20i | 0.799941 | − | 1.04226i | ||||
\(793\) | 2.01195e20 | 1.02025 | ||||||||
\(794\) | −2.32930e20 | − | 5.16484e19i | −1.17080 | − | 0.259605i | ||||
\(795\) | 7.97087e19 | 0.397133 | ||||||||
\(796\) | 5.92390e19 | − | 1.27014e20i | 0.292561 | − | 0.627277i | ||||
\(797\) | − | 1.44037e20i | − | 0.705126i | −0.935788 | − | 0.352563i | \(-0.885310\pi\) | ||
0.935788 | − | 0.352563i | \(-0.114690\pi\) | |||||||
\(798\) | −2.19133e19 | − | 4.85891e18i | −0.106338 | − | 0.0235786i | ||||
\(799\) | 1.80186e19i | 0.0866749i | ||||||||
\(800\) | −3.65860e20 | + | 1.90368e20i | −1.74456 | + | 0.907747i | ||||
\(801\) | 9.76308e19 | 0.461487 | ||||||||
\(802\) | 6.18087e19 | − | 2.78752e20i | 0.289620 | − | 1.30616i | ||||
\(803\) | 2.85599e20 | 1.32662 | ||||||||
\(804\) | 3.30439e19 | + | 1.54116e19i | 0.152159 | + | 0.0709668i | ||||
\(805\) | 5.86798e18i | 0.0267866i | ||||||||
\(806\) | −7.01307e19 | + | 3.16283e20i | −0.317368 | + | 1.43130i | ||||
\(807\) | 7.36271e19i | 0.330311i | ||||||||
\(808\) | −1.21191e20 | − | 9.30150e19i | −0.539005 | − | 0.413688i | ||||
\(809\) | −1.06423e20 | −0.469240 | −0.234620 | − | 0.972087i | \(-0.575385\pi\) | ||||
−0.234620 | + | 0.972087i | \(0.575385\pi\) | |||||||
\(810\) | 3.09666e20 | + | 6.86633e19i | 1.35362 | + | 0.300144i | ||||
\(811\) | −2.26102e20 | −0.979847 | −0.489924 | − | 0.871765i | \(-0.662975\pi\) | ||||
−0.489924 | + | 0.871765i | \(0.662975\pi\) | |||||||
\(812\) | 1.39403e19 | + | 6.50175e18i | 0.0598937 | + | 0.0279343i | ||||
\(813\) | 9.15839e19i | 0.390108i | ||||||||
\(814\) | −2.11987e20 | − | 4.70047e19i | −0.895239 | − | 0.198505i | ||||
\(815\) | − | 7.37492e19i | − | 0.308783i | ||||||
\(816\) | 1.21695e19 | + | 1.45074e19i | 0.0505173 | + | 0.0602224i | ||||
\(817\) | −4.84518e20 | −1.99414 | ||||||||
\(818\) | 1.85833e18 | − | 8.38093e18i | 0.00758317 | − | 0.0341995i | ||||
\(819\) | 7.51358e19 | 0.303990 | ||||||||
\(820\) | −9.13157e19 | + | 1.95789e20i | −0.366310 | + | 0.785401i | ||||
\(821\) | 4.51973e20i | 1.79767i | 0.438285 | + | 0.898836i | \(0.355586\pi\) | ||||
−0.438285 | + | 0.898836i | \(0.644414\pi\) | |||||||
\(822\) | 2.67384e17 | − | 1.20588e18i | 0.00105447 | − | 0.00475556i | ||||
\(823\) | − | 4.91151e20i | − | 1.92051i | −0.279126 | − | 0.960254i | \(-0.590045\pi\) | ||
0.279126 | − | 0.960254i | \(-0.409955\pi\) | |||||||
\(824\) | −2.69527e20 | − | 2.06863e20i | −1.04499 | − | 0.802033i | ||||
\(825\) | −1.85630e20 | −0.713624 | ||||||||
\(826\) | 2.15024e19 | + | 4.76781e18i | 0.0819647 | + | 0.0181743i | ||||
\(827\) | −3.46772e20 | −1.31071 | −0.655353 | − | 0.755323i | \(-0.727480\pi\) | ||||
−0.655353 | + | 0.755323i | \(0.727480\pi\) | |||||||
\(828\) | 5.28585e18 | − | 1.13333e19i | 0.0198108 | − | 0.0424762i | ||||
\(829\) | − | 1.60205e20i | − | 0.595378i | −0.954663 | − | 0.297689i | \(-0.903784\pi\) | ||
0.954663 | − | 0.297689i | \(-0.0962159\pi\) | |||||||
\(830\) | 7.09507e20 | + | 1.57322e20i | 2.61463 | + | 0.579751i | ||||
\(831\) | 7.85393e19i | 0.286999i | ||||||||
\(832\) | 2.80245e20 | − | 7.50245e19i | 1.01549 | − | 0.271856i | ||||
\(833\) | 7.67049e19 | 0.275618 | ||||||||
\(834\) | 2.07008e19 | − | 9.33588e19i | 0.0737606 | − | 0.332654i | ||||
\(835\) | 2.71907e20 | 0.960761 | ||||||||
\(836\) | 4.96448e20 | + | 2.31543e20i | 1.73952 | + | 0.811310i | ||||
\(837\) | − | 2.00082e20i | − | 0.695232i | ||||||
\(838\) | −1.60573e19 | + | 7.24171e19i | −0.0553305 | + | 0.249536i | ||||
\(839\) | 5.65312e20i | 1.93177i | 0.258980 | + | 0.965883i | \(0.416614\pi\) | ||||
−0.258980 | + | 0.965883i | \(0.583386\pi\) | |||||||
\(840\) | 2.47147e19 | − | 3.22014e19i | 0.0837531 | − | 0.109124i | ||||
\(841\) | 2.84014e20 | 0.954482 | ||||||||
\(842\) | −4.54307e20 | − | 1.00735e20i | −1.51413 | − | 0.335735i | ||||
\(843\) | −8.09624e19 | −0.267603 | ||||||||
\(844\) | −6.65919e19 | − | 3.10584e19i | −0.218285 | − | 0.101808i | ||||
\(845\) | − | 5.56959e19i | − | 0.181062i | ||||||
\(846\) | −8.03660e19 | − | 1.78199e19i | −0.259108 | − | 0.0574529i | ||||
\(847\) | 9.50167e19i | 0.303820i | ||||||||
\(848\) | 2.16050e20 | − | 1.81232e20i | 0.685145 | − | 0.574731i | ||||
\(849\) | 9.81984e19 | 0.308852 | ||||||||
\(850\) | −4.16077e19 | + | 1.87647e20i | −0.129790 | + | 0.585341i | ||||
\(851\) | −1.05732e19 | −0.0327114 | ||||||||
\(852\) | 4.40943e19 | − | 9.45421e19i | 0.135302 | − | 0.290100i | ||||
\(853\) | 1.53192e20i | 0.466222i | 0.972450 | + | 0.233111i | \(0.0748905\pi\) | ||||
−0.972450 | + | 0.233111i | \(0.925109\pi\) | |||||||
\(854\) | 2.15597e19 | − | 9.72324e19i | 0.0650785 | − | 0.293499i | ||||
\(855\) | 7.32428e20i | 2.19281i | ||||||||
\(856\) | −8.06020e19 | + | 1.05018e20i | −0.239348 | + | 0.311852i | ||||
\(857\) | 3.70285e20 | 1.09061 | 0.545307 | − | 0.838237i | \(-0.316413\pi\) | ||||
0.545307 | + | 0.838237i | \(0.316413\pi\) | |||||||
\(858\) | 1.27482e20 | + | 2.82671e19i | 0.372424 | + | 0.0825790i | ||||
\(859\) | −2.92531e20 | −0.847656 | −0.423828 | − | 0.905743i | \(-0.639314\pi\) | ||||
−0.423828 | + | 0.905743i | \(0.639314\pi\) | |||||||
\(860\) | 3.70377e20 | − | 7.94121e20i | 1.06452 | − | 2.28243i | ||||
\(861\) | − | 1.40957e19i | − | 0.0401849i | ||||||
\(862\) | 3.11308e20 | + | 6.90275e19i | 0.880318 | + | 0.195196i | ||||
\(863\) | 4.09540e19i | 0.114874i | 0.998349 | + | 0.0574368i | \(0.0182928\pi\) | ||||
−0.998349 | + | 0.0574368i | \(0.981707\pi\) | |||||||
\(864\) | −1.58946e20 | + | 8.27045e19i | −0.442235 | + | 0.230109i | ||||
\(865\) | −6.80941e20 | −1.87930 | ||||||||
\(866\) | −1.10231e20 | + | 4.97134e20i | −0.301773 | + | 1.36097i | ||||
\(867\) | −8.61191e19 | −0.233865 | ||||||||
\(868\) | 1.45337e20 | + | 6.77848e19i | 0.391505 | + | 0.182597i | ||||
\(869\) | − | 8.12538e20i | − | 2.17123i | ||||||
\(870\) | −7.73745e18 | + | 3.48953e19i | −0.0205099 | + | 0.0924979i | ||||
\(871\) | − | 2.60338e20i | − | 0.684558i | ||||||
\(872\) | −3.24265e20 | − | 2.48875e20i | −0.845834 | − | 0.649181i | ||||
\(873\) | −3.01368e20 | −0.779824 | ||||||||
\(874\) | 2.60414e19 | + | 5.77426e18i | 0.0668475 | + | 0.0148223i | ||||
\(875\) | 2.02515e20 | 0.515705 | ||||||||
\(876\) | −8.71862e19 | − | 4.06635e19i | −0.220251 | − | 0.102725i | ||||
\(877\) | − | 6.10720e19i | − | 0.153054i | −0.997068 | − | 0.0765270i | \(-0.975617\pi\) | ||
0.997068 | − | 0.0765270i | \(-0.0243831\pi\) | |||||||
\(878\) | 1.54206e20 | + | 3.41927e19i | 0.383390 | + | 0.0850104i | ||||
\(879\) | − | 1.39106e20i | − | 0.343103i | ||||||
\(880\) | −7.58993e20 | + | 6.36679e20i | −1.85720 | + | 1.55791i | ||||
\(881\) | 2.77950e20 | 0.674739 | 0.337370 | − | 0.941372i | \(-0.390463\pi\) | ||||
0.337370 | + | 0.941372i | \(0.390463\pi\) | |||||||
\(882\) | −7.58589e19 | + | 3.42117e20i | −0.182695 | + | 0.823938i | ||||
\(883\) | 9.11825e19 | 0.217864 | 0.108932 | − | 0.994049i | \(-0.465257\pi\) | ||||
0.108932 | + | 0.994049i | \(0.465257\pi\) | |||||||
\(884\) | 5.71486e19 | − | 1.22532e20i | 0.135469 | − | 0.290458i | ||||
\(885\) | 5.11782e19i | 0.120360i | ||||||||
\(886\) | 6.04967e19 | − | 2.72835e20i | 0.141155 | − | 0.636596i | ||||
\(887\) | 2.20272e20i | 0.509909i | 0.966953 | + | 0.254955i | \(0.0820606\pi\) | ||||
−0.966953 | + | 0.254955i | \(0.917939\pi\) | |||||||
\(888\) | 5.80219e19 | + | 4.45321e19i | 0.133260 | + | 0.102278i | ||||
\(889\) | −2.14369e20 | −0.488482 | ||||||||
\(890\) | −3.67681e20 | − | 8.15272e19i | −0.831267 | − | 0.184320i | ||||
\(891\) | 5.05076e20 | 1.13296 | ||||||||
\(892\) | −7.75070e19 | + | 1.66182e20i | −0.172499 | + | 0.369854i | ||||
\(893\) | − | 1.75584e20i | − | 0.387725i | ||||||
\(894\) | 4.56508e19 | + | 1.01223e19i | 0.100020 | + | 0.0221778i | ||||
\(895\) | − | 1.28916e20i | − | 0.280251i | ||||||
\(896\) | −6.22683e18 | − | 1.43475e20i | −0.0134311 | − | 0.309471i | ||||
\(897\) | 6.35835e18 | 0.0136081 | ||||||||
\(898\) | 8.59136e19 | − | 3.87463e20i | 0.182443 | − | 0.822803i | ||||
\(899\) | −1.41207e20 | −0.297536 | ||||||||
\(900\) | −7.95789e20 | − | 3.71155e20i | −1.66380 | − | 0.775992i | ||||
\(901\) | − | 1.31421e20i | − | 0.272641i | ||||||
\(902\) | −7.44696e19 | + | 3.35852e20i | −0.153297 | + | 0.691356i | ||||
\(903\) | 5.71721e19i | 0.116780i | ||||||||
\(904\) | 4.93120e20 | − | 6.42498e20i | 0.999480 | − | 1.30225i | ||||
\(905\) | −1.90037e20 | −0.382206 | ||||||||
\(906\) | −1.07117e20 | − | 2.37514e19i | −0.213776 | − | 0.0474014i | ||||
\(907\) | 8.15128e20 | 1.61427 | 0.807133 | − | 0.590370i | \(-0.201018\pi\) | ||||
0.807133 | + | 0.590370i | \(0.201018\pi\) | |||||||
\(908\) | 2.56363e20 | + | 1.19567e20i | 0.503796 | + | 0.234970i | ||||
\(909\) | − | 3.25264e20i | − | 0.634291i | ||||||
\(910\) | −2.82964e20 | − | 6.27426e19i | −0.547572 | − | 0.121415i | ||||
\(911\) | − | 1.19167e20i | − | 0.228837i | −0.993433 | − | 0.114419i | \(-0.963500\pi\) | ||
0.993433 | − | 0.114419i | \(-0.0365005\pi\) | |||||||
\(912\) | −1.18586e20 | − | 1.41368e20i | −0.225980 | − | 0.269394i | ||||
\(913\) | 1.15723e21 | 2.18839 | ||||||||
\(914\) | −1.90296e19 | + | 8.58217e19i | −0.0357113 | + | 0.161055i | ||||
\(915\) | 2.31424e20 | 0.430984 | ||||||||
\(916\) | −3.16818e20 | + | 6.79286e20i | −0.585519 | + | 1.25541i | ||||
\(917\) | 4.45934e19i | 0.0817872i | ||||||||
\(918\) | −1.80762e19 | + | 8.15222e19i | −0.0329010 | + | 0.148381i | ||||
\(919\) | 8.12236e19i | 0.146715i | 0.997306 | + | 0.0733573i | \(0.0233714\pi\) | ||||
−0.997306 | + | 0.0733573i | \(0.976629\pi\) | |||||||
\(920\) | −2.93706e19 | + | 3.82677e19i | −0.0526500 | + | 0.0685990i | ||||
\(921\) | 5.11339e19 | 0.0909686 | ||||||||
\(922\) | −4.39188e19 | − | 9.73828e18i | −0.0775415 | − | 0.0171936i | ||||
\(923\) | −7.44855e20 | −1.30515 | ||||||||
\(924\) | 2.73215e19 | − | 5.85798e19i | 0.0475118 | − | 0.101870i | ||||
\(925\) | 7.42413e20i | 1.28131i | ||||||||
\(926\) | 2.10293e20 | + | 4.66291e19i | 0.360204 | + | 0.0798693i | ||||
\(927\) | − | 7.23378e20i | − | 1.22972i | ||||||
\(928\) | 5.83685e19 | + | 1.12176e20i | 0.0984787 | + | 0.189262i | ||||
\(929\) | −1.20529e20 | −0.201829 | −0.100914 | − | 0.994895i | \(-0.532177\pi\) | ||||
−0.100914 | + | 0.994895i | \(0.532177\pi\) | |||||||
\(930\) | −8.06677e19 | + | 3.63805e20i | −0.134066 | + | 0.604627i | ||||
\(931\) | −7.47457e20 | −1.23293 | ||||||||
\(932\) | 6.89543e20 | + | 3.21602e20i | 1.12889 | + | 0.526511i | ||||
\(933\) | 2.30785e20i | 0.375004i | ||||||||
\(934\) | −2.52659e20 | + | 1.13947e21i | −0.407480 | + | 1.83770i | ||||
\(935\) | 4.61688e20i | 0.739040i | ||||||||
\(936\) | 4.89994e20 | + | 3.76073e20i | 0.778503 | + | 0.597504i | ||||
\(937\) | 4.42991e20 | 0.698582 | 0.349291 | − | 0.937014i | \(-0.386422\pi\) | ||||
0.349291 | + | 0.937014i | \(0.386422\pi\) | |||||||
\(938\) | −1.25815e20 | − | 2.78974e19i | −0.196930 | − | 0.0436660i | ||||
\(939\) | 1.03622e20 | 0.160988 | ||||||||
\(940\) | 2.87780e20 | + | 1.34220e20i | 0.443779 | + | 0.206978i | ||||
\(941\) | 2.08946e20i | 0.319820i | 0.987132 | + | 0.159910i | \(0.0511205\pi\) | ||||
−0.987132 | + | 0.159910i | \(0.948880\pi\) | |||||||
\(942\) | 8.19372e18 | + | 1.81682e18i | 0.0124487 | + | 0.00276030i | ||||
\(943\) | 1.67511e19i | 0.0252616i | ||||||||
\(944\) | 1.16363e20 | + | 1.38718e20i | 0.174185 | + | 0.207648i | ||||
\(945\) | 1.79004e20 | 0.265975 | ||||||||
\(946\) | 3.02049e20 | − | 1.36222e21i | 0.445492 | − | 2.00913i | ||||
\(947\) | −6.47470e20 | −0.947916 | −0.473958 | − | 0.880547i | \(-0.657175\pi\) | ||||
−0.473958 | + | 0.880547i | \(0.657175\pi\) | |||||||
\(948\) | −1.15689e20 | + | 2.48048e20i | −0.168125 | + | 0.360476i | ||||
\(949\) | 6.86901e20i | 0.990902i | ||||||||
\(950\) | 4.05450e20 | − | 1.82854e21i | 0.580593 | − | 2.61842i | ||||
\(951\) | − | 2.50266e20i | − | 0.355744i | ||||||
\(952\) | −5.30925e19 | − | 4.07488e19i | −0.0749161 | − | 0.0574984i | ||||
\(953\) | −8.53603e20 | −1.19565 | −0.597827 | − | 0.801625i | \(-0.703969\pi\) | ||||
−0.597827 | + | 0.801625i | \(0.703969\pi\) | |||||||
\(954\) | 5.86160e20 | + | 1.29971e20i | 0.815037 | + | 0.180721i | ||||
\(955\) | 7.20718e20 | 0.994813 | ||||||||
\(956\) | −9.94255e19 | + | 2.13177e20i | −0.136236 | + | 0.292103i | ||||
\(957\) | 5.69155e19i | 0.0774189i | ||||||||
\(958\) | −1.33555e21 | − | 2.96137e20i | −1.80344 | − | 0.399884i | ||||
\(959\) | 4.36566e18i | 0.00585221i | ||||||||
\(960\) | 3.22352e20 | − | 8.62968e19i | 0.428975 | − | 0.114841i | ||||
\(961\) | −7.15230e20 | −0.944892 | ||||||||
\(962\) | 1.13052e20 | − | 5.09856e20i | 0.148270 | − | 0.668686i | ||||
\(963\) | −2.81857e20 | −0.366982 | ||||||||
\(964\) | −4.63185e20 | − | 2.16029e20i | −0.598708 | − | 0.279236i | ||||
\(965\) | 5.12590e20i | 0.657778i | ||||||||
\(966\) | 6.81350e17 | − | 3.07283e18i | 0.000868022 | − | 0.00391470i | ||||
\(967\) | − | 6.67218e20i | − | 0.843884i | −0.906623 | − | 0.421942i | \(-0.861349\pi\) | ||
0.906623 | − | 0.421942i | \(-0.138651\pi\) | |||||||
\(968\) | −4.75582e20 | + | 6.19647e20i | −0.597170 | + | 0.778067i | ||||
\(969\) | −8.59931e19 | −0.107201 | ||||||||
\(970\) | 1.13496e21 | + | 2.51659e20i | 1.40468 | + | 0.311466i | ||||
\(971\) | 5.51310e20 | 0.677425 | 0.338712 | − | 0.940890i | \(-0.390009\pi\) | ||||
0.338712 | + | 0.940890i | \(0.390009\pi\) | |||||||
\(972\) | −5.24532e20 | − | 2.44641e20i | −0.639895 | − | 0.298446i | ||||
\(973\) | 3.37988e20i | 0.409365i | ||||||||
\(974\) | 1.04292e21 | + | 2.31251e20i | 1.25412 | + | 0.278081i | ||||
\(975\) | − | 4.46462e20i | − | 0.533031i | ||||||
\(976\) | 6.27273e20 | − | 5.26185e20i | 0.743546 | − | 0.623720i | ||||
\(977\) | −1.40490e21 | −1.65342 | −0.826708 | − | 0.562631i | \(-0.809789\pi\) | ||||
−0.826708 | + | 0.562631i | \(0.809789\pi\) | |||||||
\(978\) | −8.56326e18 | + | 3.86196e19i | −0.0100062 | + | 0.0451269i | ||||
\(979\) | −5.99701e20 | −0.695754 | ||||||||
\(980\) | 5.71374e20 | − | 1.22508e21i | 0.658169 | − | 1.41117i | ||||
\(981\) | − | 8.70291e20i | − | 0.995362i | ||||||
\(982\) | 1.06327e20 | − | 4.79528e20i | 0.120744 | − | 0.544544i | ||||
\(983\) | − | 9.71215e20i | − | 1.09507i | −0.836784 | − | 0.547534i | \(-0.815567\pi\) | ||
0.836784 | − | 0.547534i | \(-0.184433\pi\) | |||||||
\(984\) | 7.05522e19 | − | 9.19242e19i | 0.0789851 | − | 0.102912i | ||||
\(985\) | 1.27033e21 | 1.41209 | ||||||||
\(986\) | 5.75341e19 | + | 1.27572e19i | 0.0635019 | + | 0.0140805i | ||||
\(987\) | −2.07185e19 | −0.0227059 | ||||||||
\(988\) | −5.56889e20 | + | 1.19402e21i | −0.605997 | + | 1.29931i | ||||
\(989\) | − | 6.79425e19i | − | 0.0734121i | ||||||
\(990\) | −2.05921e21 | − | 4.56596e20i | −2.20930 | − | 0.489876i | ||||
\(991\) | 4.26102e20i | 0.453940i | 0.973902 | + | 0.226970i | \(0.0728819\pi\) | ||||
−0.973902 | + | 0.226970i | \(0.927118\pi\) | |||||||
\(992\) | 6.08527e20 | + | 1.16950e21i | 0.643722 | + | 1.23714i | ||||
\(993\) | 3.12696e20 | 0.328456 | ||||||||
\(994\) | −7.98174e19 | + | 3.59970e20i | −0.0832516 | + | 0.375458i | ||||
\(995\) | −1.15104e21 | −1.19214 | ||||||||
\(996\) | −3.53274e20 | − | 1.64766e20i | −0.363326 | − | 0.169455i | ||||
\(997\) | 4.66331e20i | 0.476243i | 0.971235 | + | 0.238121i | \(0.0765316\pi\) | ||||
−0.971235 | + | 0.238121i | \(0.923468\pi\) | |||||||
\(998\) | −6.17637e18 | + | 2.78549e19i | −0.00626354 | + | 0.0282480i | ||||
\(999\) | 3.22537e20i | 0.324804i |
(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 | 8.15.d.b.3.5 | ✓ | 12 | |
3.2 | odd | 2 | 72.15.b.b.19.8 | 12 | |||
4.3 | odd | 2 | 32.15.d.b.15.6 | 12 | |||
8.3 | odd | 2 | inner | 8.15.d.b.3.6 | yes | 12 | |
8.5 | even | 2 | 32.15.d.b.15.5 | 12 | |||
24.11 | even | 2 | 72.15.b.b.19.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.15.d.b.3.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8.15.d.b.3.6 | yes | 12 | 8.3 | odd | 2 | inner | |
32.15.d.b.15.5 | 12 | 8.5 | even | 2 | |||
32.15.d.b.15.6 | 12 | 4.3 | odd | 2 | |||
72.15.b.b.19.7 | 12 | 24.11 | even | 2 | |||
72.15.b.b.19.8 | 12 | 3.2 | odd | 2 |