Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,11,Mod(7,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.7");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.f (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: | \(9.53035879011\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} - 49316 x^{17} + 18276332 x^{16} - 230627572 x^{15} + 1992333560 x^{14} - 394917674060 x^{13} + 80687382741790 x^{12} + \cdots + 14\!\cdots\!04 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{34}\cdot 5^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.7 | ||
Root | \(-15.9113 + 15.9113i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.7 |
Dual form | 15.11.f.a.13.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 11.6866 | + | 11.6866i | 0.365206 | + | 0.365206i | 0.865725 | − | 0.500519i | \(-0.166858\pi\) |
−0.500519 | + | 0.865725i | \(0.666858\pi\) | |||||||
\(3\) | 99.2043 | − | 99.2043i | 0.408248 | − | 0.408248i | ||||
\(4\) | − | 750.847i | − | 0.733249i | ||||||
\(5\) | 2257.04 | + | 2161.34i | 0.722253 | + | 0.691629i | ||||
\(6\) | 2318.72 | 0.298189 | ||||||||
\(7\) | −21416.5 | − | 21416.5i | −1.27426 | − | 1.27426i | −0.943831 | − | 0.330427i | \(-0.892807\pi\) |
−0.330427 | − | 0.943831i | \(-0.607193\pi\) | |||||||
\(8\) | 20741.9 | − | 20741.9i | 0.632993 | − | 0.632993i | ||||
\(9\) | − | 19683.0i | − | 0.333333i | ||||||
\(10\) | 1118.39 | + | 51635.8i | 0.0111839 | + | 0.516358i | ||||
\(11\) | 144236. | 0.895590 | 0.447795 | − | 0.894136i | \(-0.352209\pi\) | ||||
0.447795 | + | 0.894136i | \(0.352209\pi\) | |||||||
\(12\) | −74487.3 | − | 74487.3i | −0.299348 | − | 0.299348i | ||||
\(13\) | 314136. | − | 314136.i | 0.846059 | − | 0.846059i | −0.143580 | − | 0.989639i | \(-0.545861\pi\) |
0.989639 | + | 0.143580i | \(0.0458614\pi\) | |||||||
\(14\) | − | 500571.i | − | 0.930734i | ||||||
\(15\) | 438323. | − | 9493.74i | 0.577215 | − | 0.0125020i | ||||
\(16\) | −284063. | −0.270903 | ||||||||
\(17\) | 422713. | + | 422713.i | 0.297715 | + | 0.297715i | 0.840118 | − | 0.542403i | \(-0.182485\pi\) |
−0.542403 | + | 0.840118i | \(0.682485\pi\) | |||||||
\(18\) | 230027. | − | 230027.i | 0.121735 | − | 0.121735i | ||||
\(19\) | − | 1.72877e6i | − | 0.698185i | −0.937088 | − | 0.349092i | \(-0.886490\pi\) | ||
0.937088 | − | 0.349092i | \(-0.113510\pi\) | |||||||
\(20\) | 1.62284e6 | − | 1.69469e6i | 0.507136 | − | 0.529591i | ||||
\(21\) | −4.24921e6 | −1.04043 | ||||||||
\(22\) | 1.68562e6 | + | 1.68562e6i | 0.327075 | + | 0.327075i | ||||
\(23\) | −4.18986e6 | + | 4.18986e6i | −0.650969 | + | 0.650969i | −0.953226 | − | 0.302257i | \(-0.902260\pi\) |
0.302257 | + | 0.953226i | \(0.402260\pi\) | |||||||
\(24\) | − | 4.11538e6i | − | 0.516837i | ||||||
\(25\) | 422834. | + | 9.75647e6i | 0.0432982 | + | 0.999062i | ||||
\(26\) | 7.34235e6 | 0.617972 | ||||||||
\(27\) | −1.95264e6 | − | 1.95264e6i | −0.136083 | − | 0.136083i | ||||
\(28\) | −1.60805e7 | + | 1.60805e7i | −0.934349 | + | 0.934349i | ||||
\(29\) | 2.54576e7i | 1.24116i | 0.784144 | + | 0.620579i | \(0.213102\pi\) | ||||
−0.784144 | + | 0.620579i | \(0.786898\pi\) | |||||||
\(30\) | 5.23345e6 | + | 5.01155e6i | 0.215368 | + | 0.206237i | ||||
\(31\) | −7.20415e6 | −0.251637 | −0.125818 | − | 0.992053i | \(-0.540156\pi\) | ||||
−0.125818 | + | 0.992053i | \(0.540156\pi\) | |||||||
\(32\) | −2.45594e7 | − | 2.45594e7i | −0.731929 | − | 0.731929i | ||||
\(33\) | 1.43088e7 | − | 1.43088e7i | 0.365623 | − | 0.365623i | ||||
\(34\) | 9.88016e6i | 0.217455i | ||||||||
\(35\) | −2.04953e6 | − | 9.46261e7i | −0.0390224 | − | 1.80165i | ||||
\(36\) | −1.47789e7 | −0.244416 | ||||||||
\(37\) | 8.48288e7 | + | 8.48288e7i | 1.22331 | + | 1.22331i | 0.966450 | + | 0.256855i | \(0.0826863\pi\) |
0.256855 | + | 0.966450i | \(0.417314\pi\) | |||||||
\(38\) | 2.02035e7 | − | 2.02035e7i | 0.254981 | − | 0.254981i | ||||
\(39\) | − | 6.23273e7i | − | 0.690804i | ||||||
\(40\) | 9.16457e7 | − | 1.98498e6i | 0.894977 | − | 0.0193845i | ||||
\(41\) | −4.68731e7 | −0.404580 | −0.202290 | − | 0.979326i | \(-0.564838\pi\) | ||||
−0.202290 | + | 0.979326i | \(0.564838\pi\) | |||||||
\(42\) | −4.96588e7 | − | 4.96588e7i | −0.379970 | − | 0.379970i | ||||
\(43\) | 2.34944e7 | − | 2.34944e7i | 0.159817 | − | 0.159817i | −0.622669 | − | 0.782486i | \(-0.713952\pi\) |
0.782486 | + | 0.622669i | \(0.213952\pi\) | |||||||
\(44\) | − | 1.08299e8i | − | 0.656690i | ||||||
\(45\) | 4.25417e7 | − | 4.44253e7i | 0.230543 | − | 0.240751i | ||||
\(46\) | −9.79304e7 | −0.475476 | ||||||||
\(47\) | 3.23645e7 | + | 3.23645e7i | 0.141117 | + | 0.141117i | 0.774136 | − | 0.633019i | \(-0.218185\pi\) |
−0.633019 | + | 0.774136i | \(0.718185\pi\) | |||||||
\(48\) | −2.81803e7 | + | 2.81803e7i | −0.110596 | + | 0.110596i | ||||
\(49\) | 6.34855e8i | 2.24747i | ||||||||
\(50\) | −1.09078e8 | + | 1.18961e8i | −0.349051 | + | 0.380676i | ||||
\(51\) | 8.38700e7 | 0.243084 | ||||||||
\(52\) | −2.35868e8 | − | 2.35868e8i | −0.620372 | − | 0.620372i | ||||
\(53\) | 4.66906e8 | − | 4.66906e8i | 1.11648 | − | 1.11648i | 0.124225 | − | 0.992254i | \(-0.460356\pi\) |
0.992254 | − | 0.124225i | \(-0.0396444\pi\) | |||||||
\(54\) | − | 4.56394e7i | − | 0.0993965i | ||||||
\(55\) | 3.25546e8 | + | 3.11742e8i | 0.646842 | + | 0.619416i | ||||
\(56\) | −8.88437e8 | −1.61319 | ||||||||
\(57\) | −1.71502e8 | − | 1.71502e8i | −0.285033 | − | 0.285033i | ||||
\(58\) | −2.97512e8 | + | 2.97512e8i | −0.453278 | + | 0.453278i | ||||
\(59\) | 1.01716e9i | 1.42275i | 0.702811 | + | 0.711376i | \(0.251928\pi\) | ||||
−0.702811 | + | 0.711376i | \(0.748072\pi\) | |||||||
\(60\) | −7.12835e6 | − | 3.29113e8i | −0.00916712 | − | 0.423242i | ||||
\(61\) | 2.76359e7 | 0.0327208 | 0.0163604 | − | 0.999866i | \(-0.494792\pi\) | ||||
0.0163604 | + | 0.999866i | \(0.494792\pi\) | |||||||
\(62\) | −8.41919e7 | − | 8.41919e7i | −0.0918993 | − | 0.0918993i | ||||
\(63\) | −4.21540e8 | + | 4.21540e8i | −0.424753 | + | 0.424753i | ||||
\(64\) | − | 2.83152e8i | − | 0.263706i | ||||||
\(65\) | 1.38797e9 | − | 3.00624e7i | 1.19623 | − | 0.0259094i | ||||
\(66\) | 3.34442e8 | 0.267055 | ||||||||
\(67\) | −1.06739e9 | − | 1.06739e9i | −0.790590 | − | 0.790590i | 0.191000 | − | 0.981590i | \(-0.438827\pi\) |
−0.981590 | + | 0.191000i | \(0.938827\pi\) | |||||||
\(68\) | 3.17393e8 | − | 3.17393e8i | 0.218300 | − | 0.218300i | ||||
\(69\) | 8.31305e8i | 0.531514i | ||||||||
\(70\) | 1.08190e9 | − | 1.12981e9i | 0.643723 | − | 0.672225i | ||||
\(71\) | 1.17851e9 | 0.653193 | 0.326597 | − | 0.945164i | \(-0.394098\pi\) | ||||
0.326597 | + | 0.945164i | \(0.394098\pi\) | |||||||
\(72\) | −4.08263e8 | − | 4.08263e8i | −0.210998 | − | 0.210998i | ||||
\(73\) | 1.90205e9 | − | 1.90205e9i | 0.917501 | − | 0.917501i | −0.0793462 | − | 0.996847i | \(-0.525283\pi\) |
0.996847 | + | 0.0793462i | \(0.0252833\pi\) | |||||||
\(74\) | 1.98272e9i | 0.893517i | ||||||||
\(75\) | 1.00983e9 | + | 9.25937e8i | 0.425542 | + | 0.390189i | ||||
\(76\) | −1.29805e9 | −0.511943 | ||||||||
\(77\) | −3.08902e9 | − | 3.08902e9i | −1.14121 | − | 1.14121i | ||||
\(78\) | 7.28393e8 | − | 7.28393e8i | 0.252286 | − | 0.252286i | ||||
\(79\) | − | 1.33930e9i | − | 0.435255i | −0.976032 | − | 0.217627i | \(-0.930168\pi\) | ||
0.976032 | − | 0.217627i | \(-0.0698317\pi\) | |||||||
\(80\) | −6.41141e8 | − | 6.13957e8i | −0.195661 | − | 0.187365i | ||||
\(81\) | −3.87420e8 | −0.111111 | ||||||||
\(82\) | −5.47787e8 | − | 5.47787e8i | −0.147755 | − | 0.147755i | ||||
\(83\) | −9.32585e8 | + | 9.32585e8i | −0.236754 | + | 0.236754i | −0.815505 | − | 0.578750i | \(-0.803541\pi\) |
0.578750 | + | 0.815505i | \(0.303541\pi\) | |||||||
\(84\) | 3.19051e9i | 0.762893i | ||||||||
\(85\) | 4.04532e7 | + | 1.86771e9i | 0.00911713 | + | 0.420934i | ||||
\(86\) | 5.49139e8 | 0.116732 | ||||||||
\(87\) | 2.52550e9 | + | 2.52550e9i | 0.506700 | + | 0.506700i | ||||
\(88\) | 2.99172e9 | − | 2.99172e9i | 0.566902 | − | 0.566902i | ||||
\(89\) | 7.88621e9i | 1.41227i | 0.708076 | + | 0.706136i | \(0.249563\pi\) | ||||
−0.708076 | + | 0.706136i | \(0.750437\pi\) | |||||||
\(90\) | 1.01635e9 | − | 2.20133e7i | 0.172119 | − | 0.00372798i | ||||
\(91\) | −1.34554e10 | −2.15620 | ||||||||
\(92\) | 3.14595e9 | + | 3.14595e9i | 0.477323 | + | 0.477323i | ||||
\(93\) | −7.14683e8 | + | 7.14683e8i | −0.102730 | + | 0.102730i | ||||
\(94\) | 7.56461e8i | 0.103074i | ||||||||
\(95\) | 3.73647e9 | − | 3.90191e9i | 0.482885 | − | 0.504266i | ||||
\(96\) | −4.87281e9 | −0.597617 | ||||||||
\(97\) | 2.17281e9 | + | 2.17281e9i | 0.253025 | + | 0.253025i | 0.822210 | − | 0.569184i | \(-0.192741\pi\) |
−0.569184 | + | 0.822210i | \(0.692741\pi\) | |||||||
\(98\) | −7.41929e9 | + | 7.41929e9i | −0.820790 | + | 0.820790i | ||||
\(99\) | − | 2.83899e9i | − | 0.298530i | ||||||
\(100\) | 7.32562e9 | − | 3.17484e8i | 0.732562 | − | 0.0317484i | ||||
\(101\) | 1.31685e9 | 0.125294 | 0.0626469 | − | 0.998036i | \(-0.480046\pi\) | ||||
0.0626469 | + | 0.998036i | \(0.480046\pi\) | |||||||
\(102\) | 9.80154e8 | + | 9.80154e8i | 0.0887756 | + | 0.0887756i | ||||
\(103\) | 2.12255e9 | − | 2.12255e9i | 0.183093 | − | 0.183093i | −0.609609 | − | 0.792702i | \(-0.708674\pi\) |
0.792702 | + | 0.609609i | \(0.208674\pi\) | |||||||
\(104\) | − | 1.30316e10i | − | 1.07110i | ||||||
\(105\) | −9.59064e9 | − | 9.18400e9i | −0.751452 | − | 0.719590i | ||||
\(106\) | 1.09131e10 | 0.815490 | ||||||||
\(107\) | −7.88889e9 | − | 7.88889e9i | −0.562467 | − | 0.562467i | 0.367541 | − | 0.930007i | \(-0.380200\pi\) |
−0.930007 | + | 0.367541i | \(0.880200\pi\) | |||||||
\(108\) | −1.46613e9 | + | 1.46613e9i | −0.0997826 | + | 0.0997826i | ||||
\(109\) | − | 6.94026e8i | − | 0.0451069i | −0.999746 | − | 0.0225535i | \(-0.992820\pi\) | ||
0.999746 | − | 0.0225535i | \(-0.00717960\pi\) | |||||||
\(110\) | 1.61312e8 | + | 7.44772e9i | 0.0100162 | + | 0.462445i | ||||
\(111\) | 1.68308e10 | 0.998824 | ||||||||
\(112\) | 6.08362e9 | + | 6.08362e9i | 0.345201 | + | 0.345201i | ||||
\(113\) | 1.71240e10 | − | 1.71240e10i | 0.929422 | − | 0.929422i | −0.0682464 | − | 0.997668i | \(-0.521740\pi\) |
0.997668 | + | 0.0682464i | \(0.0217404\pi\) | |||||||
\(114\) | − | 4.00855e9i | − | 0.208191i | ||||||
\(115\) | −1.85124e10 | + | 4.00965e8i | −0.920394 | + | 0.0199351i | ||||
\(116\) | 1.91147e10 | 0.910077 | ||||||||
\(117\) | −6.18313e9 | − | 6.18313e9i | −0.282020 | − | 0.282020i | ||||
\(118\) | −1.18871e10 | + | 1.18871e10i | −0.519598 | + | 0.519598i | ||||
\(119\) | − | 1.81061e10i | − | 0.758733i | ||||||
\(120\) | 8.89473e9 | − | 9.28857e9i | 0.357459 | − | 0.373287i | ||||
\(121\) | −5.13351e9 | −0.197919 | ||||||||
\(122\) | 3.22969e8 | + | 3.22969e8i | 0.0119498 | + | 0.0119498i | ||||
\(123\) | −4.65002e9 | + | 4.65002e9i | −0.165169 | + | 0.165169i | ||||
\(124\) | 5.40921e9i | 0.184512i | ||||||||
\(125\) | −2.01327e10 | + | 2.29346e10i | −0.659708 | + | 0.751522i | ||||
\(126\) | −9.85274e9 | −0.310245 | ||||||||
\(127\) | 3.71586e10 | + | 3.71586e10i | 1.12471 | + | 1.12471i | 0.991024 | + | 0.133685i | \(0.0426811\pi\) |
0.133685 | + | 0.991024i | \(0.457319\pi\) | |||||||
\(128\) | −2.18398e10 | + | 2.18398e10i | −0.635622 | + | 0.635622i | ||||
\(129\) | − | 4.66149e9i | − | 0.130490i | ||||||
\(130\) | 1.65720e10 | + | 1.58693e10i | 0.446332 | + | 0.427407i | ||||
\(131\) | −5.26963e9 | −0.136592 | −0.0682958 | − | 0.997665i | \(-0.521756\pi\) | ||||
−0.0682958 | + | 0.997665i | \(0.521756\pi\) | |||||||
\(132\) | −1.07437e10 | − | 1.07437e10i | −0.268093 | − | 0.268093i | ||||
\(133\) | −3.70242e10 | + | 3.70242e10i | −0.889668 | + | 0.889668i | ||||
\(134\) | − | 2.49484e10i | − | 0.577456i | ||||||
\(135\) | −1.86865e8 | − | 8.62750e9i | −0.00416735 | − | 0.192405i | ||||
\(136\) | 1.75358e10 | 0.376904 | ||||||||
\(137\) | −1.07552e10 | − | 1.07552e10i | −0.222851 | − | 0.222851i | 0.586847 | − | 0.809698i | \(-0.300369\pi\) |
−0.809698 | + | 0.586847i | \(0.800369\pi\) | |||||||
\(138\) | −9.71512e9 | + | 9.71512e9i | −0.194112 | + | 0.194112i | ||||
\(139\) | − | 6.42485e10i | − | 1.23820i | −0.785314 | − | 0.619098i | \(-0.787498\pi\) | ||
0.785314 | − | 0.619098i | \(-0.212502\pi\) | |||||||
\(140\) | −7.10497e10 | + | 1.53888e9i | −1.32106 | + | 0.0286132i | ||||
\(141\) | 6.42140e9 | 0.115222 | ||||||||
\(142\) | 1.37728e10 | + | 1.37728e10i | 0.238550 | + | 0.238550i | ||||
\(143\) | 4.53096e10 | − | 4.53096e10i | 0.757722 | − | 0.757722i | ||||
\(144\) | 5.59121e9i | 0.0903012i | ||||||||
\(145\) | −5.50225e10 | + | 5.74587e10i | −0.858420 | + | 0.896429i | ||||
\(146\) | 4.44569e10 | 0.670154 | ||||||||
\(147\) | 6.29803e10 | + | 6.29803e10i | 0.917526 | + | 0.917526i | ||||
\(148\) | 6.36935e10 | − | 6.36935e10i | 0.896987 | − | 0.896987i | ||||
\(149\) | 1.12980e11i | 1.53840i | 0.639010 | + | 0.769198i | \(0.279344\pi\) | ||||
−0.639010 | + | 0.769198i | \(0.720656\pi\) | |||||||
\(150\) | 9.80434e8 | + | 2.26225e10i | 0.0129111 | + | 0.297910i | ||||
\(151\) | −8.95064e9 | −0.114017 | −0.0570085 | − | 0.998374i | \(-0.518156\pi\) | ||||
−0.0570085 | + | 0.998374i | \(0.518156\pi\) | |||||||
\(152\) | −3.58581e10 | − | 3.58581e10i | −0.441946 | − | 0.441946i | ||||
\(153\) | 8.32027e9 | − | 8.32027e9i | 0.0992385 | − | 0.0992385i | ||||
\(154\) | − | 7.22002e10i | − | 0.833556i | ||||||
\(155\) | −1.62600e10 | − | 1.55706e10i | −0.181745 | − | 0.174039i | ||||
\(156\) | −4.67982e10 | −0.506532 | ||||||||
\(157\) | −4.35079e10 | − | 4.35079e10i | −0.456110 | − | 0.456110i | 0.441266 | − | 0.897376i | \(-0.354529\pi\) |
−0.897376 | + | 0.441266i | \(0.854529\pi\) | |||||||
\(158\) | 1.56519e10 | − | 1.56519e10i | 0.158958 | − | 0.158958i | ||||
\(159\) | − | 9.26383e10i | − | 0.911601i | ||||||
\(160\) | −2.35031e9 | − | 1.08513e11i | −0.0224143 | − | 1.03486i | ||||
\(161\) | 1.79464e11 | 1.65901 | ||||||||
\(162\) | −4.52763e9 | − | 4.52763e9i | −0.0405784 | − | 0.0405784i | ||||
\(163\) | −1.65838e10 | + | 1.65838e10i | −0.144127 | + | 0.144127i | −0.775489 | − | 0.631361i | \(-0.782496\pi\) |
0.631361 | + | 0.775489i | \(0.282496\pi\) | |||||||
\(164\) | 3.51946e10i | 0.296658i | ||||||||
\(165\) | 6.32217e10 | − | 1.36934e9i | 0.516948 | − | 0.0111967i | ||||
\(166\) | −2.17975e10 | −0.172928 | ||||||||
\(167\) | 5.89827e10 | + | 5.89827e10i | 0.454090 | + | 0.454090i | 0.896710 | − | 0.442619i | \(-0.145951\pi\) |
−0.442619 | + | 0.896710i | \(0.645951\pi\) | |||||||
\(168\) | −8.81368e10 | + | 8.81368e10i | −0.658584 | + | 0.658584i | ||||
\(169\) | − | 5.95040e10i | − | 0.431631i | ||||||
\(170\) | −2.13544e10 | + | 2.22999e10i | −0.150398 | + | 0.157057i | ||||
\(171\) | −3.40275e10 | −0.232728 | ||||||||
\(172\) | −1.76407e10 | − | 1.76407e10i | −0.117185 | − | 0.117185i | ||||
\(173\) | −1.10643e10 | + | 1.10643e10i | −0.0713991 | + | 0.0713991i | −0.741905 | − | 0.670505i | \(-0.766077\pi\) |
0.670505 | + | 0.741905i | \(0.266077\pi\) | |||||||
\(174\) | 5.90290e10i | 0.370100i | ||||||||
\(175\) | 1.99893e11 | − | 2.18005e11i | 1.21789 | − | 1.32824i | ||||
\(176\) | −4.09720e10 | −0.242618 | ||||||||
\(177\) | 1.00907e11 | + | 1.00907e11i | 0.580836 | + | 0.580836i | ||||
\(178\) | −9.21629e10 | + | 9.21629e10i | −0.515770 | + | 0.515770i | ||||
\(179\) | 6.51889e10i | 0.354739i | 0.984144 | + | 0.177369i | \(0.0567587\pi\) | ||||
−0.984144 | + | 0.177369i | \(0.943241\pi\) | |||||||
\(180\) | −3.33566e10 | − | 3.19423e10i | −0.176530 | − | 0.169045i | ||||
\(181\) | −3.30663e11 | −1.70213 | −0.851065 | − | 0.525060i | \(-0.824043\pi\) | ||||
−0.851065 | + | 0.525060i | \(0.824043\pi\) | |||||||
\(182\) | −1.57247e11 | − | 1.57247e11i | −0.787456 | − | 0.787456i | ||||
\(183\) | 2.74160e9 | − | 2.74160e9i | 0.0133582 | − | 0.0133582i | ||||
\(184\) | 1.73812e11i | 0.824118i | ||||||||
\(185\) | 8.11802e9 | + | 3.74806e11i | 0.0374621 | + | 1.72961i | ||||
\(186\) | −1.67044e10 | −0.0750354 | ||||||||
\(187\) | 6.09703e10 | + | 6.09703e10i | 0.266631 | + | 0.266631i | ||||
\(188\) | 2.43008e10 | − | 2.43008e10i | 0.103474 | − | 0.103474i | ||||
\(189\) | 8.36372e10i | 0.346809i | ||||||||
\(190\) | 8.92667e10 | − | 1.93345e9i | 0.360513 | − | 0.00780845i | ||||
\(191\) | −2.55021e11 | −1.00325 | −0.501624 | − | 0.865085i | \(-0.667264\pi\) | ||||
−0.501624 | + | 0.865085i | \(0.667264\pi\) | |||||||
\(192\) | −2.80899e10 | − | 2.80899e10i | −0.107657 | − | 0.107657i | ||||
\(193\) | −5.64731e10 | + | 5.64731e10i | −0.210889 | + | 0.210889i | −0.804645 | − | 0.593756i | \(-0.797645\pi\) |
0.593756 | + | 0.804645i | \(0.297645\pi\) | |||||||
\(194\) | 5.07856e10i | 0.184813i | ||||||||
\(195\) | 1.34710e11 | − | 1.40675e11i | 0.477780 | − | 0.498935i | ||||
\(196\) | 4.76679e11 | 1.64796 | ||||||||
\(197\) | −2.63535e11 | − | 2.63535e11i | −0.888191 | − | 0.888191i | 0.106158 | − | 0.994349i | \(-0.466145\pi\) |
−0.994349 | + | 0.106158i | \(0.966145\pi\) | |||||||
\(198\) | 3.31781e10 | − | 3.31781e10i | 0.109025 | − | 0.109025i | ||||
\(199\) | 3.22945e11i | 1.03482i | 0.855739 | + | 0.517408i | \(0.173103\pi\) | ||||
−0.855739 | + | 0.517408i | \(0.826897\pi\) | |||||||
\(200\) | 2.11138e11 | + | 1.93597e11i | 0.659807 | + | 0.604992i | ||||
\(201\) | −2.11780e11 | −0.645514 | ||||||||
\(202\) | 1.53895e10 | + | 1.53895e10i | 0.0457581 | + | 0.0457581i | ||||
\(203\) | 5.45211e11 | − | 5.45211e11i | 1.58156 | − | 1.58156i | ||||
\(204\) | − | 6.29735e10i | − | 0.178241i | ||||||
\(205\) | −1.05795e11 | − | 1.01309e11i | −0.292209 | − | 0.279820i | ||||
\(206\) | 4.96108e10 | 0.133734 | ||||||||
\(207\) | 8.24691e10 | + | 8.24691e10i | 0.216990 | + | 0.216990i | ||||
\(208\) | −8.92343e10 | + | 8.92343e10i | −0.229200 | + | 0.229200i | ||||
\(209\) | − | 2.49351e11i | − | 0.625287i | ||||||
\(210\) | −4.75229e9 | − | 2.19412e11i | −0.0116361 | − | 0.537233i | ||||
\(211\) | −3.92197e11 | −0.937760 | −0.468880 | − | 0.883262i | \(-0.655342\pi\) | ||||
−0.468880 | + | 0.883262i | \(0.655342\pi\) | |||||||
\(212\) | −3.50575e11 | − | 3.50575e11i | −0.818657 | − | 0.818657i | ||||
\(213\) | 1.16913e11 | − | 1.16913e11i | 0.266665 | − | 0.266665i | ||||
\(214\) | − | 1.84388e11i | − | 0.410832i | ||||||
\(215\) | 1.03807e11 | − | 2.24839e9i | 0.225962 | − | 0.00489417i | ||||
\(216\) | −8.10029e10 | −0.172279 | ||||||||
\(217\) | 1.54287e11 | + | 1.54287e11i | 0.320650 | + | 0.320650i | ||||
\(218\) | 8.11080e9 | − | 8.11080e9i | 0.0164733 | − | 0.0164733i | ||||
\(219\) | − | 3.77382e11i | − | 0.749136i | ||||||
\(220\) | 2.34071e11 | − | 2.44435e11i | 0.454186 | − | 0.474297i | ||||
\(221\) | 2.65579e11 | 0.503770 | ||||||||
\(222\) | 1.96694e11 | + | 1.96694e11i | 0.364777 | + | 0.364777i | ||||
\(223\) | −9.57493e9 | + | 9.57493e9i | −0.0173625 | + | 0.0173625i | −0.715735 | − | 0.698372i | \(-0.753908\pi\) |
0.698372 | + | 0.715735i | \(0.253908\pi\) | |||||||
\(224\) | 1.05195e12i | 1.86533i | ||||||||
\(225\) | 1.92037e11 | − | 8.32264e9i | 0.333021 | − | 0.0144327i | ||||
\(226\) | 4.00242e11 | 0.678861 | ||||||||
\(227\) | −6.38678e11 | − | 6.38678e11i | −1.05963 | − | 1.05963i | −0.998106 | − | 0.0615203i | \(-0.980405\pi\) |
−0.0615203 | − | 0.998106i | \(-0.519595\pi\) | |||||||
\(228\) | −1.28772e11 | + | 1.28772e11i | −0.209000 | + | 0.209000i | ||||
\(229\) | 1.09189e12i | 1.73381i | 0.498471 | + | 0.866907i | \(0.333895\pi\) | ||||
−0.498471 | + | 0.866907i | \(0.666105\pi\) | |||||||
\(230\) | −2.21033e11 | − | 2.11661e11i | −0.343414 | − | 0.328853i | ||||
\(231\) | −6.12888e11 | −0.931797 | ||||||||
\(232\) | 5.28038e11 | + | 5.28038e11i | 0.785644 | + | 0.785644i | ||||
\(233\) | −2.34856e10 | + | 2.34856e10i | −0.0341996 | + | 0.0341996i | −0.724000 | − | 0.689800i | \(-0.757698\pi\) |
0.689800 | + | 0.724000i | \(0.257698\pi\) | |||||||
\(234\) | − | 1.44520e11i | − | 0.205991i | ||||||
\(235\) | 3.09725e9 | + | 1.42999e11i | 0.00432152 | + | 0.199523i | ||||
\(236\) | 7.63732e11 | 1.04323 | ||||||||
\(237\) | −1.32865e11 | − | 1.32865e11i | −0.177692 | − | 0.177692i | ||||
\(238\) | 2.11598e11 | − | 2.11598e11i | 0.277094 | − | 0.277094i | ||||
\(239\) | − | 3.47769e11i | − | 0.445966i | −0.974822 | − | 0.222983i | \(-0.928421\pi\) | ||
0.974822 | − | 0.222983i | \(-0.0715794\pi\) | |||||||
\(240\) | −1.24511e11 | + | 2.69682e9i | −0.156370 | + | 0.00338685i | ||||
\(241\) | −8.60967e11 | −1.05901 | −0.529506 | − | 0.848306i | \(-0.677623\pi\) | ||||
−0.529506 | + | 0.848306i | \(0.677623\pi\) | |||||||
\(242\) | −5.99932e10 | − | 5.99932e10i | −0.0722812 | − | 0.0722812i | ||||
\(243\) | −3.84338e10 | + | 3.84338e10i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 2.07503e10i | − | 0.0239925i | ||||||
\(245\) | −1.37214e12 | + | 1.43289e12i | −1.55442 | + | 1.62324i | ||||
\(246\) | −1.08686e11 | −0.120642 | ||||||||
\(247\) | −5.43070e11 | − | 5.43070e11i | −0.590705 | − | 0.590705i | ||||
\(248\) | −1.49428e11 | + | 1.49428e11i | −0.159284 | + | 0.159284i | ||||
\(249\) | 1.85033e11i | 0.193309i | ||||||||
\(250\) | −5.03310e11 | + | 3.27450e10i | −0.515390 | + | 0.0335308i | ||||
\(251\) | 1.89145e12 | 1.89857 | 0.949286 | − | 0.314414i | \(-0.101808\pi\) | ||||
0.949286 | + | 0.314414i | \(0.101808\pi\) | |||||||
\(252\) | 3.16512e11 | + | 3.16512e11i | 0.311450 | + | 0.311450i | ||||
\(253\) | −6.04327e11 | + | 6.04327e11i | −0.583002 | + | 0.583002i | ||||
\(254\) | 8.68514e11i | 0.821501i | ||||||||
\(255\) | 1.89298e11 | + | 1.81272e11i | 0.175568 | + | 0.168124i | ||||
\(256\) | −8.00413e11 | −0.727972 | ||||||||
\(257\) | 5.56295e11 | + | 5.56295e11i | 0.496181 | + | 0.496181i | 0.910247 | − | 0.414066i | \(-0.135892\pi\) |
−0.414066 | + | 0.910247i | \(0.635892\pi\) | |||||||
\(258\) | 5.44770e10 | − | 5.44770e10i | 0.0476557 | − | 0.0476557i | ||||
\(259\) | − | 3.63347e12i | − | 3.11761i | ||||||
\(260\) | −2.25723e10 | − | 1.04215e12i | −0.0189980 | − | 0.877133i | ||||
\(261\) | 5.01081e11 | 0.413719 | ||||||||
\(262\) | −6.15841e10 | − | 6.15841e10i | −0.0498841 | − | 0.0498841i | ||||
\(263\) | 2.40805e11 | − | 2.40805e11i | 0.191376 | − | 0.191376i | −0.604914 | − | 0.796290i | \(-0.706793\pi\) |
0.796290 | + | 0.604914i | \(0.206793\pi\) | |||||||
\(264\) | − | 5.93584e11i | − | 0.462874i | ||||||
\(265\) | 2.06297e12 | − | 4.46824e10i | 1.57857 | − | 0.0341906i | ||||
\(266\) | −8.65374e11 | −0.649824 | ||||||||
\(267\) | 7.82346e11 | + | 7.82346e11i | 0.576558 | + | 0.576558i | ||||
\(268\) | −8.01450e11 | + | 8.01450e11i | −0.579699 | + | 0.579699i | ||||
\(269\) | − | 1.50352e12i | − | 1.06745i | −0.845657 | − | 0.533727i | \(-0.820791\pi\) | ||
0.845657 | − | 0.533727i | \(-0.179209\pi\) | |||||||
\(270\) | 9.86423e10 | − | 1.03010e11i | 0.0687455 | − | 0.0717894i | ||||
\(271\) | 1.24987e12 | 0.855101 | 0.427550 | − | 0.903991i | \(-0.359377\pi\) | ||||
0.427550 | + | 0.903991i | \(0.359377\pi\) | |||||||
\(272\) | −1.20077e11 | − | 1.20077e11i | −0.0806521 | − | 0.0806521i | ||||
\(273\) | −1.33483e12 | + | 1.33483e12i | −0.880263 | + | 0.880263i | ||||
\(274\) | − | 2.51382e11i | − | 0.162773i | ||||||
\(275\) | 6.09877e10 | + | 1.40723e12i | 0.0387774 | + | 0.894750i | ||||
\(276\) | 6.24183e11 | 0.389732 | ||||||||
\(277\) | 1.80941e12 | + | 1.80941e12i | 1.10953 | + | 1.10953i | 0.993212 | + | 0.116315i | \(0.0371083\pi\) |
0.116315 | + | 0.993212i | \(0.462892\pi\) | |||||||
\(278\) | 7.50846e11 | − | 7.50846e11i | 0.452196 | − | 0.452196i | ||||
\(279\) | 1.41799e11i | 0.0838789i | ||||||||
\(280\) | −2.00524e12 | − | 1.92022e12i | −1.16513 | − | 1.11573i | ||||
\(281\) | −2.89679e12 | −1.65343 | −0.826714 | − | 0.562622i | \(-0.809793\pi\) | ||||
−0.826714 | + | 0.562622i | \(0.809793\pi\) | |||||||
\(282\) | 7.50443e10 | + | 7.50443e10i | 0.0420796 | + | 0.0420796i | ||||
\(283\) | 1.86922e12 | − | 1.86922e12i | 1.02974 | − | 1.02974i | 0.0301957 | − | 0.999544i | \(-0.490387\pi\) |
0.999544 | − | 0.0301957i | \(-0.00961304\pi\) | |||||||
\(284\) | − | 8.84881e11i | − | 0.478953i | ||||||
\(285\) | −1.64125e10 | − | 7.57761e11i | −0.00872874 | − | 0.403003i | ||||
\(286\) | 1.05903e12 | 0.553449 | ||||||||
\(287\) | 1.00386e12 | + | 1.00386e12i | 0.515540 | + | 0.515540i | ||||
\(288\) | −4.83404e11 | + | 4.83404e11i | −0.243976 | + | 0.243976i | ||||
\(289\) | − | 1.65862e12i | − | 0.822731i | ||||||
\(290\) | −1.31452e12 | + | 2.84716e10i | −0.640882 | + | 0.0138810i | ||||
\(291\) | 4.31105e11 | 0.206594 | ||||||||
\(292\) | −1.42815e12 | − | 1.42815e12i | −0.672757 | − | 0.672757i | ||||
\(293\) | 2.31503e11 | − | 2.31503e11i | 0.107206 | − | 0.107206i | −0.651469 | − | 0.758675i | \(-0.725847\pi\) |
0.758675 | + | 0.651469i | \(0.225847\pi\) | |||||||
\(294\) | 1.47205e12i | 0.670172i | ||||||||
\(295\) | −2.19843e12 | + | 2.29577e12i | −0.984017 | + | 1.02759i | ||||
\(296\) | 3.51902e12 | 1.54869 | ||||||||
\(297\) | −2.81640e11 | − | 2.81640e11i | −0.121874 | − | 0.121874i | ||||
\(298\) | −1.32035e12 | + | 1.32035e12i | −0.561832 | + | 0.561832i | ||||
\(299\) | 2.63237e12i | 1.10152i | ||||||||
\(300\) | 6.95237e11 | − | 7.58229e11i | 0.286106 | − | 0.312028i | ||||
\(301\) | −1.00633e12 | −0.407296 | ||||||||
\(302\) | −1.04603e11 | − | 1.04603e11i | −0.0416397 | − | 0.0416397i | ||||
\(303\) | 1.30637e11 | − | 1.30637e11i | 0.0511510 | − | 0.0511510i | ||||
\(304\) | 4.91081e11i | 0.189141i | ||||||||
\(305\) | 6.23752e10 | + | 5.97305e10i | 0.0236327 | + | 0.0226306i | ||||
\(306\) | 1.94471e11 | 0.0724850 | ||||||||
\(307\) | 7.98088e11 | + | 7.98088e11i | 0.292657 | + | 0.292657i | 0.838129 | − | 0.545472i | \(-0.183650\pi\) |
−0.545472 | + | 0.838129i | \(0.683650\pi\) | |||||||
\(308\) | −2.31938e12 | + | 2.31938e12i | −0.836793 | + | 0.836793i | ||||
\(309\) | − | 4.21133e11i | − | 0.149495i | ||||||
\(310\) | −8.05707e9 | − | 3.71992e11i | −0.00281429 | − | 0.129935i | ||||
\(311\) | 6.73547e11 | 0.231508 | 0.115754 | − | 0.993278i | \(-0.463072\pi\) | ||||
0.115754 | + | 0.993278i | \(0.463072\pi\) | |||||||
\(312\) | −1.29279e12 | − | 1.29279e12i | −0.437274 | − | 0.437274i | ||||
\(313\) | −2.59138e11 | + | 2.59138e11i | −0.0862599 | + | 0.0862599i | −0.748920 | − | 0.662660i | \(-0.769427\pi\) |
0.662660 | + | 0.748920i | \(0.269427\pi\) | |||||||
\(314\) | − | 1.01692e12i | − | 0.333148i | ||||||
\(315\) | −1.86253e12 | + | 4.03409e10i | −0.600550 | + | 0.0130075i | ||||
\(316\) | −1.00561e12 | −0.319150 | ||||||||
\(317\) | −7.43982e11 | − | 7.43982e11i | −0.232416 | − | 0.232416i | 0.581284 | − | 0.813700i | \(-0.302550\pi\) |
−0.813700 | + | 0.581284i | \(0.802550\pi\) | |||||||
\(318\) | 1.08263e12 | − | 1.08263e12i | 0.332922 | − | 0.332922i | ||||
\(319\) | 3.67189e12i | 1.11157i | ||||||||
\(320\) | 6.11988e11 | − | 6.39086e11i | 0.182387 | − | 0.190462i | ||||
\(321\) | −1.56522e12 | −0.459252 | ||||||||
\(322\) | 2.09732e12 | + | 2.09732e12i | 0.605879 | + | 0.605879i | ||||
\(323\) | 7.30776e11 | − | 7.30776e11i | 0.207860 | − | 0.207860i | ||||
\(324\) | 2.90894e11i | 0.0814721i | ||||||||
\(325\) | 3.19768e12 | + | 2.93203e12i | 0.881898 | + | 0.808633i | ||||
\(326\) | −3.87617e11 | −0.105272 | ||||||||
\(327\) | −6.88504e10 | − | 6.88504e10i | −0.0184148 | − | 0.0184148i | ||||
\(328\) | −9.72239e11 | + | 9.72239e11i | −0.256097 | + | 0.256097i | ||||
\(329\) | − | 1.38627e12i | − | 0.359639i | ||||||
\(330\) | 7.54849e11 | + | 7.22844e11i | 0.192882 | + | 0.184703i | ||||
\(331\) | −2.55641e12 | −0.643414 | −0.321707 | − | 0.946839i | \(-0.604257\pi\) | ||||
−0.321707 | + | 0.946839i | \(0.604257\pi\) | |||||||
\(332\) | 7.00229e11 | + | 7.00229e11i | 0.173600 | + | 0.173600i | ||||
\(333\) | 1.66969e12 | − | 1.66969e12i | 0.407768 | − | 0.407768i | ||||
\(334\) | 1.37861e12i | 0.331673i | ||||||||
\(335\) | −1.02148e11 | − | 4.71616e12i | −0.0242107 | − | 1.11780i | ||||
\(336\) | 1.20704e12 | 0.281856 | ||||||||
\(337\) | −8.83879e11 | − | 8.83879e11i | −0.203350 | − | 0.203350i | 0.598084 | − | 0.801433i | \(-0.295929\pi\) |
−0.801433 | + | 0.598084i | \(0.795929\pi\) | |||||||
\(338\) | 6.95399e11 | − | 6.95399e11i | 0.157634 | − | 0.157634i | ||||
\(339\) | − | 3.39755e12i | − | 0.758870i | ||||||
\(340\) | 1.40236e12 | − | 3.03742e10i | 0.308650 | − | 0.00668513i | ||||
\(341\) | −1.03909e12 | −0.225363 | ||||||||
\(342\) | −3.97665e11 | − | 3.97665e11i | −0.0849937 | − | 0.0849937i | ||||
\(343\) | 7.54672e12 | − | 7.54672e12i | 1.58960 | − | 1.58960i | ||||
\(344\) | − | 9.74638e11i | − | 0.202326i | ||||||
\(345\) | −1.79673e12 | + | 1.87629e12i | −0.367611 | + | 0.383888i | ||||
\(346\) | −2.58607e11 | −0.0521507 | ||||||||
\(347\) | −4.10042e12 | − | 4.10042e12i | −0.815043 | − | 0.815043i | 0.170342 | − | 0.985385i | \(-0.445513\pi\) |
−0.985385 | + | 0.170342i | \(0.945513\pi\) | |||||||
\(348\) | 1.89626e12 | − | 1.89626e12i | 0.371538 | − | 0.371538i | ||||
\(349\) | − | 1.56174e11i | − | 0.0301635i | −0.999886 | − | 0.0150817i | \(-0.995199\pi\) | ||
0.999886 | − | 0.0150817i | \(-0.00480084\pi\) | |||||||
\(350\) | 4.88380e12 | − | 2.11658e11i | 0.929861 | − | 0.0402991i | ||||
\(351\) | −1.22679e12 | −0.230268 | ||||||||
\(352\) | −3.54235e12 | − | 3.54235e12i | −0.655508 | − | 0.655508i | ||||
\(353\) | −3.67864e12 | + | 3.67864e12i | −0.671141 | + | 0.671141i | −0.957979 | − | 0.286838i | \(-0.907396\pi\) |
0.286838 | + | 0.957979i | \(0.407396\pi\) | |||||||
\(354\) | 2.35851e12i | 0.424250i | ||||||||
\(355\) | 2.65995e12 | + | 2.54716e12i | 0.471771 | + | 0.451768i | ||||
\(356\) | 5.92134e12 | 1.03555 | ||||||||
\(357\) | −1.79620e12 | − | 1.79620e12i | −0.309751 | − | 0.309751i | ||||
\(358\) | −7.61836e11 | + | 7.61836e11i | −0.129553 | + | 0.129553i | ||||
\(359\) | 2.88632e12i | 0.484029i | 0.970273 | + | 0.242015i | \(0.0778082\pi\) | ||||
−0.970273 | + | 0.242015i | \(0.922192\pi\) | |||||||
\(360\) | −3.90703e10 | − | 1.80386e12i | −0.00646152 | − | 0.298326i | ||||
\(361\) | 3.14241e12 | 0.512538 | ||||||||
\(362\) | −3.86432e12 | − | 3.86432e12i | −0.621628 | − | 0.621628i | ||||
\(363\) | −5.09266e11 | + | 5.09266e11i | −0.0808001 | + | 0.0808001i | ||||
\(364\) | 1.01029e13i | 1.58103i | ||||||||
\(365\) | 8.40396e12 | − | 1.82024e11i | 1.29724 | − | 0.0280972i | ||||
\(366\) | 6.40798e10 | 0.00975699 | ||||||||
\(367\) | −1.30889e12 | − | 1.30889e12i | −0.196596 | − | 0.196596i | 0.601943 | − | 0.798539i | \(-0.294393\pi\) |
−0.798539 | + | 0.601943i | \(0.794393\pi\) | |||||||
\(368\) | 1.19018e12 | − | 1.19018e12i | 0.176350 | − | 0.176350i | ||||
\(369\) | 9.22604e11i | 0.134860i | ||||||||
\(370\) | −4.28533e12 | + | 4.47508e12i | −0.617982 | + | 0.645345i | ||||
\(371\) | −1.99990e13 | −2.84537 | ||||||||
\(372\) | 5.36617e11 | + | 5.36617e11i | 0.0753269 | + | 0.0753269i | ||||
\(373\) | −3.21248e12 | + | 3.21248e12i | −0.444934 | + | 0.444934i | −0.893666 | − | 0.448732i | \(-0.851876\pi\) |
0.448732 | + | 0.893666i | \(0.351876\pi\) | |||||||
\(374\) | 1.42507e12i | 0.194750i | ||||||||
\(375\) | 2.77963e11 | + | 4.27247e12i | 0.0374827 | + | 0.576132i | ||||
\(376\) | 1.34260e12 | 0.178652 | ||||||||
\(377\) | 7.99713e12 | + | 7.99713e12i | 1.05009 | + | 1.05009i | ||||
\(378\) | −9.77434e11 | + | 9.77434e11i | −0.126657 | + | 0.126657i | ||||
\(379\) | 2.67708e12i | 0.342346i | 0.985241 | + | 0.171173i | \(0.0547557\pi\) | ||||
−0.985241 | + | 0.171173i | \(0.945244\pi\) | |||||||
\(380\) | −2.92974e12 | − | 2.80552e12i | −0.369752 | − | 0.354075i | ||||
\(381\) | 7.37258e12 | 0.918321 | ||||||||
\(382\) | −2.98032e12 | − | 2.98032e12i | −0.366393 | − | 0.366393i | ||||
\(383\) | −5.35266e12 | + | 5.35266e12i | −0.649495 | + | 0.649495i | −0.952871 | − | 0.303376i | \(-0.901886\pi\) |
0.303376 | + | 0.952871i | \(0.401886\pi\) | |||||||
\(384\) | 4.33320e12i | 0.518983i | ||||||||
\(385\) | −2.95615e11 | − | 1.36485e13i | −0.0349481 | − | 1.61354i | ||||
\(386\) | −1.31996e12 | −0.154036 | ||||||||
\(387\) | −4.62440e11 | − | 4.62440e11i | −0.0532722 | − | 0.0532722i | ||||
\(388\) | 1.63145e12 | − | 1.63145e12i | 0.185531 | − | 0.185531i | ||||
\(389\) | − | 4.78950e12i | − | 0.537703i | −0.963182 | − | 0.268851i | \(-0.913356\pi\) | ||
0.963182 | − | 0.268851i | \(-0.0866440\pi\) | |||||||
\(390\) | 3.21832e12 | − | 6.97064e10i | 0.356702 | − | 0.00772591i | ||||
\(391\) | −3.54222e12 | −0.387607 | ||||||||
\(392\) | 1.31681e13 | + | 1.31681e13i | 1.42263 | + | 1.42263i | ||||
\(393\) | −5.22771e11 | + | 5.22771e11i | −0.0557633 | + | 0.0557633i | ||||
\(394\) | − | 6.15964e12i | − | 0.648746i | ||||||
\(395\) | 2.89469e12 | − | 3.02286e12i | 0.301035 | − | 0.314364i | ||||
\(396\) | −2.13165e12 | −0.218897 | ||||||||
\(397\) | −7.44312e12 | − | 7.44312e12i | −0.754748 | − | 0.754748i | 0.220613 | − | 0.975361i | \(-0.429194\pi\) |
−0.975361 | + | 0.220613i | \(0.929194\pi\) | |||||||
\(398\) | −3.77413e12 | + | 3.77413e12i | −0.377921 | + | 0.377921i | ||||
\(399\) | 7.34593e12i | 0.726411i | ||||||||
\(400\) | −1.20111e11 | − | 2.77145e12i | −0.0117296 | − | 0.270649i | ||||
\(401\) | −8.09887e12 | −0.781092 | −0.390546 | − | 0.920583i | \(-0.627714\pi\) | ||||
−0.390546 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(402\) | −2.47499e12 | − | 2.47499e12i | −0.235745 | − | 0.235745i | ||||
\(403\) | −2.26308e12 | + | 2.26308e12i | −0.212900 | + | 0.212900i | ||||
\(404\) | − | 9.88753e11i | − | 0.0918716i | ||||||
\(405\) | −8.74424e11 | − | 8.37348e11i | −0.0802503 | − | 0.0768477i | ||||
\(406\) | 1.27433e13 | 1.15519 | ||||||||
\(407\) | 1.22353e13 | + | 1.22353e13i | 1.09558 | + | 1.09558i | ||||
\(408\) | 1.73962e12 | − | 1.73962e12i | 0.153870 | − | 0.153870i | ||||
\(409\) | − | 5.40623e12i | − | 0.472366i | −0.971709 | − | 0.236183i | \(-0.924104\pi\) | ||
0.971709 | − | 0.236183i | \(-0.0758964\pi\) | |||||||
\(410\) | −5.24226e10 | − | 2.42033e12i | −0.00452480 | − | 0.208908i | ||||
\(411\) | −2.13392e12 | −0.181957 | ||||||||
\(412\) | −1.59371e12 | − | 1.59371e12i | −0.134253 | − | 0.134253i | ||||
\(413\) | 2.17840e13 | − | 2.17840e13i | 1.81295 | − | 1.81295i | ||||
\(414\) | 1.92756e12i | 0.158492i | ||||||||
\(415\) | −4.12052e12 | + | 8.92474e10i | −0.334743 | + | 0.00725028i | ||||
\(416\) | −1.54300e13 | −1.23851 | ||||||||
\(417\) | −6.37373e12 | − | 6.37373e12i | −0.505491 | − | 0.505491i | ||||
\(418\) | 2.91406e12 | − | 2.91406e12i | 0.228359 | − | 0.228359i | ||||
\(419\) | 1.12531e12i | 0.0871371i | 0.999050 | + | 0.0435686i | \(0.0138727\pi\) | ||||
−0.999050 | + | 0.0435686i | \(0.986127\pi\) | |||||||
\(420\) | −6.89578e12 | + | 7.20111e12i | −0.527639 | + | 0.551001i | ||||
\(421\) | 9.96777e12 | 0.753681 | 0.376841 | − | 0.926278i | \(-0.377010\pi\) | ||||
0.376841 | + | 0.926278i | \(0.377010\pi\) | |||||||
\(422\) | −4.58345e12 | − | 4.58345e12i | −0.342476 | − | 0.342476i | ||||
\(423\) | 6.37030e11 | − | 6.37030e11i | 0.0470390 | − | 0.0470390i | ||||
\(424\) | − | 1.93691e13i | − | 1.41345i | ||||||
\(425\) | −3.94545e12 | + | 4.30293e12i | −0.284546 | + | 0.310327i | ||||
\(426\) | 2.73264e12 | 0.194775 | ||||||||
\(427\) | −5.91862e11 | − | 5.91862e11i | −0.0416947 | − | 0.0416947i | ||||
\(428\) | −5.92335e12 | + | 5.92335e12i | −0.412428 | + | 0.412428i | ||||
\(429\) | − | 8.98981e12i | − | 0.618677i | ||||||
\(430\) | 1.23943e12 | + | 1.18688e12i | 0.0843101 | + | 0.0807353i | ||||
\(431\) | 2.30725e13 | 1.55134 | 0.775672 | − | 0.631137i | \(-0.217411\pi\) | ||||
0.775672 | + | 0.631137i | \(0.217411\pi\) | |||||||
\(432\) | 5.54672e11 | + | 5.54672e11i | 0.0368653 | + | 0.0368653i | ||||
\(433\) | 2.90034e12 | − | 2.90034e12i | 0.190550 | − | 0.190550i | −0.605384 | − | 0.795934i | \(-0.706980\pi\) |
0.795934 | + | 0.605384i | \(0.206980\pi\) | |||||||
\(434\) | 3.60619e12i | 0.234207i | ||||||||
\(435\) | 2.41688e11 | + | 1.11586e13i | 0.0155170 | + | 0.716414i | ||||
\(436\) | −5.21108e11 | −0.0330746 | ||||||||
\(437\) | 7.24333e12 | + | 7.24333e12i | 0.454497 | + | 0.454497i | ||||
\(438\) | 4.41031e12 | − | 4.41031e12i | 0.273589 | − | 0.273589i | ||||
\(439\) | 1.89524e13i | 1.16236i | 0.813775 | + | 0.581180i | \(0.197409\pi\) | ||||
−0.813775 | + | 0.581180i | \(0.802591\pi\) | |||||||
\(440\) | 1.32186e13 | − | 2.86305e11i | 0.801533 | − | 0.0173606i | ||||
\(441\) | 1.24958e13 | 0.749157 | ||||||||
\(442\) | 3.10371e12 | + | 3.10371e12i | 0.183980 | + | 0.183980i | ||||
\(443\) | −2.22224e13 | + | 2.22224e13i | −1.30248 | + | 1.30248i | −0.375771 | + | 0.926713i | \(0.622622\pi\) |
−0.926713 | + | 0.375771i | \(0.877378\pi\) | |||||||
\(444\) | − | 1.26373e13i | − | 0.732387i | ||||||
\(445\) | −1.70448e13 | + | 1.77995e13i | −0.976769 | + | 1.02002i | ||||
\(446\) | −2.23797e11 | −0.0126817 | ||||||||
\(447\) | 1.12081e13 | + | 1.12081e13i | 0.628048 | + | 0.628048i | ||||
\(448\) | −6.06412e12 | + | 6.06412e12i | −0.336030 | + | 0.336030i | ||||
\(449\) | − | 3.18162e13i | − | 1.74348i | −0.489972 | − | 0.871738i | \(-0.662993\pi\) | ||
0.489972 | − | 0.871738i | \(-0.337007\pi\) | |||||||
\(450\) | 2.34152e12 | + | 2.14699e12i | 0.126892 | + | 0.116350i | ||||
\(451\) | −6.76078e12 | −0.362338 | ||||||||
\(452\) | −1.28575e13 | − | 1.28575e13i | −0.681498 | − | 0.681498i | ||||
\(453\) | −8.87943e11 | + | 8.87943e11i | −0.0465472 | + | 0.0465472i | ||||
\(454\) | − | 1.49279e13i | − | 0.773964i | ||||||
\(455\) | −3.03693e13 | − | 2.90816e13i | −1.55732 | − | 1.49129i | ||||
\(456\) | −7.11456e12 | −0.360847 | ||||||||
\(457\) | 3.99239e11 | + | 3.99239e11i | 0.0200287 | + | 0.0200287i | 0.717050 | − | 0.697022i | \(-0.245492\pi\) |
−0.697022 | + | 0.717050i | \(0.745492\pi\) | |||||||
\(458\) | −1.27605e13 | + | 1.27605e13i | −0.633199 | + | 0.633199i | ||||
\(459\) | − | 1.65081e12i | − | 0.0810279i | ||||||
\(460\) | 3.01063e11 | + | 1.39000e13i | 0.0146174 | + | 0.674878i | ||||
\(461\) | 2.83811e12 | 0.136309 | 0.0681546 | − | 0.997675i | \(-0.478289\pi\) | ||||
0.0681546 | + | 0.997675i | \(0.478289\pi\) | |||||||
\(462\) | −7.16257e12 | − | 7.16257e12i | −0.340298 | − | 0.340298i | ||||
\(463\) | −7.39172e12 | + | 7.39172e12i | −0.347409 | + | 0.347409i | −0.859143 | − | 0.511735i | \(-0.829003\pi\) |
0.511735 | + | 0.859143i | \(0.329003\pi\) | |||||||
\(464\) | − | 7.23155e12i | − | 0.336234i | ||||||
\(465\) | −3.15774e12 | + | 6.83943e10i | −0.145248 | + | 0.00314598i | ||||
\(466\) | −5.48932e11 | −0.0249798 | ||||||||
\(467\) | 2.41845e13 | + | 2.41845e13i | 1.08881 | + | 1.08881i | 0.995651 | + | 0.0931594i | \(0.0296966\pi\) |
0.0931594 | + | 0.995651i | \(0.470303\pi\) | |||||||
\(468\) | −4.64259e12 | + | 4.64259e12i | −0.206791 | + | 0.206791i | ||||
\(469\) | 4.57197e13i | 2.01483i | ||||||||
\(470\) | −1.63497e12 | + | 1.70736e12i | −0.0712887 | + | 0.0744452i | ||||
\(471\) | −8.63234e12 | −0.372412 | ||||||||
\(472\) | 2.10978e13 | + | 2.10978e13i | 0.900592 | + | 0.900592i | ||||
\(473\) | 3.38873e12 | − | 3.38873e12i | 0.143130 | − | 0.143130i | ||||
\(474\) | − | 3.10547e12i | − | 0.129788i | ||||||
\(475\) | 1.68667e13 | − | 7.30985e11i | 0.697530 | − | 0.0302301i | ||||
\(476\) | −1.35949e13 | −0.556340 | ||||||||
\(477\) | −9.19012e12 | − | 9.19012e12i | −0.372160 | − | 0.372160i | ||||
\(478\) | 4.06423e12 | − | 4.06423e12i | 0.162869 | − | 0.162869i | ||||
\(479\) | 7.36494e12i | 0.292073i | 0.989279 | + | 0.146037i | \(0.0466517\pi\) | ||||
−0.989279 | + | 0.146037i | \(0.953348\pi\) | |||||||
\(480\) | −1.09981e13 | − | 1.05318e13i | −0.431631 | − | 0.413329i | ||||
\(481\) | 5.32955e13 | 2.06998 | ||||||||
\(482\) | −1.00618e13 | − | 1.00618e13i | −0.386758 | − | 0.386758i | ||||
\(483\) | 1.78036e13 | − | 1.78036e13i | 0.677287 | − | 0.677287i | ||||
\(484\) | 3.85448e12i | 0.145124i | ||||||||
\(485\) | 2.07936e11 | + | 9.60032e12i | 0.00774856 | + | 0.357748i | ||||
\(486\) | −8.98320e11 | −0.0331322 | ||||||||
\(487\) | −2.49057e13 | − | 2.49057e13i | −0.909187 | − | 0.909187i | 0.0870194 | − | 0.996207i | \(-0.472266\pi\) |
−0.996207 | + | 0.0870194i | \(0.972266\pi\) | |||||||
\(488\) | 5.73220e11 | − | 5.73220e11i | 0.0207120 | − | 0.0207120i | ||||
\(489\) | 3.29037e12i | 0.117680i | ||||||||
\(490\) | −3.27812e13 | + | 7.10018e11i | −1.16050 | + | 0.0251356i | ||||
\(491\) | 4.75289e13 | 1.66552 | 0.832760 | − | 0.553634i | \(-0.186759\pi\) | ||||
0.832760 | + | 0.553634i | \(0.186759\pi\) | |||||||
\(492\) | 3.49145e12 | + | 3.49145e12i | 0.121110 | + | 0.121110i | ||||
\(493\) | −1.07612e13 | + | 1.07612e13i | −0.369512 | + | 0.369512i | ||||
\(494\) | − | 1.26933e13i | − | 0.431458i | ||||||
\(495\) | 6.13603e12 | − | 6.40771e12i | 0.206472 | − | 0.215614i | ||||
\(496\) | 2.04643e12 | 0.0681693 | ||||||||
\(497\) | −2.52395e13 | − | 2.52395e13i | −0.832337 | − | 0.832337i | ||||
\(498\) | −2.16240e12 | + | 2.16240e12i | −0.0705977 | + | 0.0705977i | ||||
\(499\) | − | 5.13275e13i | − | 1.65900i | −0.558504 | − | 0.829502i | \(-0.688624\pi\) | ||
0.558504 | − | 0.829502i | \(-0.311376\pi\) | |||||||
\(500\) | 1.72204e13 | + | 1.51166e13i | 0.551053 | + | 0.483731i | ||||
\(501\) | 1.17027e13 | 0.370763 | ||||||||
\(502\) | 2.21046e13 | + | 2.21046e13i | 0.693370 | + | 0.693370i | ||||
\(503\) | 3.56079e12 | − | 3.56079e12i | 0.110588 | − | 0.110588i | −0.649648 | − | 0.760235i | \(-0.725084\pi\) |
0.760235 | + | 0.649648i | \(0.225084\pi\) | |||||||
\(504\) | 1.74871e13i | 0.537731i | ||||||||
\(505\) | 2.97218e12 | + | 2.84616e12i | 0.0904938 | + | 0.0866569i | ||||
\(506\) | −1.41251e13 | −0.425831 | ||||||||
\(507\) | −5.90306e12 | − | 5.90306e12i | −0.176213 | − | 0.176213i | ||||
\(508\) | 2.79004e13 | − | 2.79004e13i | 0.824692 | − | 0.824692i | ||||
\(509\) | − | 1.90323e13i | − | 0.557062i | −0.960427 | − | 0.278531i | \(-0.910153\pi\) | ||
0.960427 | − | 0.278531i | \(-0.0898474\pi\) | |||||||
\(510\) | 9.37997e10 | + | 4.33070e12i | 0.00271863 | + | 0.125518i | ||||
\(511\) | −8.14702e13 | −2.33827 | ||||||||
\(512\) | 1.30098e13 | + | 1.30098e13i | 0.369762 | + | 0.369762i | ||||
\(513\) | −3.37567e12 | + | 3.37567e12i | −0.0950109 | + | 0.0950109i | ||||
\(514\) | 1.30024e13i | 0.362416i | ||||||||
\(515\) | 9.37825e12 | − | 2.03126e11i | 0.258872 | − | 0.00560698i | ||||
\(516\) | −3.50007e12 | −0.0956815 | ||||||||
\(517\) | 4.66811e12 | + | 4.66811e12i | 0.126383 | + | 0.126383i | ||||
\(518\) | 4.24628e13 | − | 4.24628e13i | 1.13857 | − | 1.13857i | ||||
\(519\) | 2.19525e12i | 0.0582971i | ||||||||
\(520\) | 2.81656e13 | − | 2.94127e13i | 0.740803 | − | 0.773604i | ||||
\(521\) | −3.57848e13 | −0.932201 | −0.466101 | − | 0.884732i | \(-0.654342\pi\) | ||||
−0.466101 | + | 0.884732i | \(0.654342\pi\) | |||||||
\(522\) | 5.85593e12 | + | 5.85593e12i | 0.151093 | + | 0.151093i | ||||
\(523\) | −1.06389e13 | + | 1.06389e13i | −0.271886 | + | 0.271886i | −0.829859 | − | 0.557973i | \(-0.811579\pi\) |
0.557973 | + | 0.829859i | \(0.311579\pi\) | |||||||
\(524\) | 3.95669e12i | 0.100156i | ||||||||
\(525\) | −1.79671e12 | − | 4.14573e13i | −0.0450487 | − | 1.03945i | ||||
\(526\) | 5.62839e12 | 0.139783 | ||||||||
\(527\) | −3.04529e12 | − | 3.04529e12i | −0.0749162 | − | 0.0749162i | ||||
\(528\) | −4.06460e12 | + | 4.06460e12i | −0.0990485 | + | 0.0990485i | ||||
\(529\) | 6.31662e12i | 0.152478i | ||||||||
\(530\) | 2.46313e13 | + | 2.35869e13i | 0.588990 | + | 0.564016i | ||||
\(531\) | 2.00208e13 | 0.474251 | ||||||||
\(532\) | 2.77995e13 | + | 2.77995e13i | 0.652348 | + | 0.652348i | ||||
\(533\) | −1.47245e13 | + | 1.47245e13i | −0.342299 | + | 0.342299i | ||||
\(534\) | 1.82859e13i | 0.421125i | ||||||||
\(535\) | −7.54958e11 | − | 3.48561e13i | −0.0172248 | − | 0.795262i | ||||
\(536\) | −4.42796e13 | −1.00088 | ||||||||
\(537\) | 6.46702e12 | + | 6.46702e12i | 0.144821 | + | 0.144821i | ||||
\(538\) | 1.75711e13 | − | 1.75711e13i | 0.389841 | − | 0.389841i | ||||
\(539\) | 9.15687e13i | 2.01281i | ||||||||
\(540\) | −6.47794e12 | + | 1.40307e11i | −0.141081 | + | 0.00305571i | ||||
\(541\) | −3.25694e13 | −0.702788 | −0.351394 | − | 0.936228i | \(-0.614292\pi\) | ||||
−0.351394 | + | 0.936228i | \(0.614292\pi\) | |||||||
\(542\) | 1.46067e13 | + | 1.46067e13i | 0.312288 | + | 0.312288i | ||||
\(543\) | −3.28032e13 | + | 3.28032e13i | −0.694892 | + | 0.694892i | ||||
\(544\) | − | 2.07632e13i | − | 0.435813i | ||||||
\(545\) | 1.50003e12 | − | 1.56644e12i | 0.0311973 | − | 0.0325786i | ||||
\(546\) | −3.11992e13 | −0.642955 | ||||||||
\(547\) | −3.15535e13 | − | 3.15535e13i | −0.644334 | − | 0.644334i | 0.307284 | − | 0.951618i | \(-0.400580\pi\) |
−0.951618 | + | 0.307284i | \(0.900580\pi\) | |||||||
\(548\) | −8.07548e12 | + | 8.07548e12i | −0.163405 | + | 0.163405i | ||||
\(549\) | − | 5.43956e11i | − | 0.0109069i | ||||||
\(550\) | −1.57330e13 | + | 1.71585e13i | −0.312606 | + | 0.340930i | ||||
\(551\) | 4.40104e13 | 0.866557 | ||||||||
\(552\) | 1.72429e13 | + | 1.72429e13i | 0.336445 | + | 0.336445i | ||||
\(553\) | −2.86831e13 | + | 2.86831e13i | −0.554627 | + | 0.554627i | ||||
\(554\) | 4.22917e13i | 0.810412i | ||||||||
\(555\) | 3.79877e13 | + | 3.63770e13i | 0.721404 | + | 0.690816i | ||||
\(556\) | −4.82408e13 | −0.907906 | ||||||||
\(557\) | −4.73202e13 | − | 4.73202e13i | −0.882614 | − | 0.882614i | 0.111186 | − | 0.993800i | \(-0.464535\pi\) |
−0.993800 | + | 0.111186i | \(0.964535\pi\) | |||||||
\(558\) | −1.65715e12 | + | 1.65715e12i | −0.0306331 | + | 0.0306331i | ||||
\(559\) | − | 1.47609e13i | − | 0.270429i | ||||||
\(560\) | 5.82196e11 | + | 2.68798e13i | 0.0105713 | + | 0.488074i | ||||
\(561\) | 1.20970e13 | 0.217703 | ||||||||
\(562\) | −3.38536e13 | − | 3.38536e13i | −0.603842 | − | 0.603842i | ||||
\(563\) | −2.29376e13 | + | 2.29376e13i | −0.405515 | + | 0.405515i | −0.880171 | − | 0.474656i | \(-0.842572\pi\) |
0.474656 | + | 0.880171i | \(0.342572\pi\) | |||||||
\(564\) | − | 4.82149e12i | − | 0.0844862i | ||||||
\(565\) | 7.56604e13 | − | 1.63875e12i | 1.31409 | − | 0.0284623i | ||||
\(566\) | 4.36895e13 | 0.752134 | ||||||||
\(567\) | 8.29718e12 | + | 8.29718e12i | 0.141584 | + | 0.141584i | ||||
\(568\) | 2.44446e13 | − | 2.44446e13i | 0.413467 | − | 0.413467i | ||||
\(569\) | 5.10806e13i | 0.856435i | 0.903676 | + | 0.428218i | \(0.140858\pi\) | ||||
−0.903676 | + | 0.428218i | \(0.859142\pi\) | |||||||
\(570\) | 8.66383e12 | − | 9.04745e12i | 0.143991 | − | 0.150367i | ||||
\(571\) | 2.22964e13 | 0.367328 | 0.183664 | − | 0.982989i | \(-0.441204\pi\) | ||||
0.183664 | + | 0.982989i | \(0.441204\pi\) | |||||||
\(572\) | −3.40206e13 | − | 3.40206e13i | −0.555599 | − | 0.555599i | ||||
\(573\) | −2.52992e13 | + | 2.52992e13i | −0.409575 | + | 0.409575i | ||||
\(574\) | 2.34633e13i | 0.376557i | ||||||||
\(575\) | −4.26499e13 | − | 3.91066e13i | −0.678545 | − | 0.622173i | ||||
\(576\) | −5.57328e12 | −0.0879020 | ||||||||
\(577\) | −2.57967e13 | − | 2.57967e13i | −0.403353 | − | 0.403353i | 0.476060 | − | 0.879413i | \(-0.342065\pi\) |
−0.879413 | + | 0.476060i | \(0.842065\pi\) | |||||||
\(578\) | 1.93836e13 | − | 1.93836e13i | 0.300466 | − | 0.300466i | ||||
\(579\) | 1.12047e13i | 0.172191i | ||||||||
\(580\) | 4.31427e13 | + | 4.13135e13i | 0.657306 | + | 0.629436i | ||||
\(581\) | 3.99454e13 | 0.603373 | ||||||||
\(582\) | 5.03815e12 | + | 5.03815e12i | 0.0754495 | + | 0.0754495i | ||||
\(583\) | 6.73445e13 | − | 6.73445e13i | 0.999907 | − | 0.999907i | ||||
\(584\) | − | 7.89041e13i | − | 1.16154i | ||||||
\(585\) | −5.91719e11 | − | 2.73194e13i | −0.00863647 | − | 0.398742i | ||||
\(586\) | 5.41096e12 | 0.0783044 | ||||||||
\(587\) | −7.23929e13 | − | 7.23929e13i | −1.03874 | − | 1.03874i | −0.999219 | − | 0.0395181i | \(-0.987418\pi\) |
−0.0395181 | − | 0.999219i | \(-0.512582\pi\) | |||||||
\(588\) | 4.72886e13 | − | 4.72886e13i | 0.672775 | − | 0.672775i | ||||
\(589\) | 1.24543e13i | 0.175689i | ||||||||
\(590\) | −5.25219e13 | + | 1.13759e12i | −0.734650 | + | 0.0159120i | ||||
\(591\) | −5.22876e13 | −0.725205 | ||||||||
\(592\) | −2.40967e13 | − | 2.40967e13i | −0.331398 | − | 0.331398i | ||||
\(593\) | 6.41987e13 | − | 6.41987e13i | 0.875494 | − | 0.875494i | −0.117571 | − | 0.993064i | \(-0.537511\pi\) |
0.993064 | + | 0.117571i | \(0.0375107\pi\) | |||||||
\(594\) | − | 6.58283e12i | − | 0.0890185i | ||||||
\(595\) | 3.91334e13 | − | 4.08661e13i | 0.524762 | − | 0.547997i | ||||
\(596\) | 8.48304e13 | 1.12803 | ||||||||
\(597\) | 3.20375e13 | + | 3.20375e13i | 0.422462 | + | 0.422462i | ||||
\(598\) | −3.07634e13 | + | 3.07634e13i | −0.402281 | + | 0.402281i | ||||
\(599\) | 8.75969e13i | 1.13594i | 0.823050 | + | 0.567969i | \(0.192271\pi\) | ||||
−0.823050 | + | 0.567969i | \(0.807729\pi\) | |||||||
\(600\) | 4.01515e13 | − | 1.74012e12i | 0.516352 | − | 0.0223781i | ||||
\(601\) | −2.02581e13 | −0.258361 | −0.129180 | − | 0.991621i | \(-0.541235\pi\) | ||||
−0.129180 | + | 0.991621i | \(0.541235\pi\) | |||||||
\(602\) | −1.17606e13 | − | 1.17606e13i | −0.148747 | − | 0.148747i | ||||
\(603\) | −2.10095e13 | + | 2.10095e13i | −0.263530 | + | 0.263530i | ||||
\(604\) | 6.72057e12i | 0.0836029i | ||||||||
\(605\) | −1.15865e13 | − | 1.10953e13i | −0.142948 | − | 0.136887i | ||||
\(606\) | 3.05341e12 | 0.0373613 | ||||||||
\(607\) | 8.06656e13 | + | 8.06656e13i | 0.978915 | + | 0.978915i | 0.999782 | − | 0.0208669i | \(-0.00664263\pi\) |
−0.0208669 | + | 0.999782i | \(0.506643\pi\) | |||||||
\(608\) | −4.24577e13 | + | 4.24577e13i | −0.511021 | + | 0.511021i | ||||
\(609\) | − | 1.08175e14i | − | 1.29133i | ||||||
\(610\) | 3.09078e10 | + | 1.42700e12i | 0.000365947 | + | 0.0168956i | ||||
\(611\) | 2.03337e13 | 0.238787 | ||||||||
\(612\) | −6.24725e12 | − | 6.24725e12i | −0.0727665 | − | 0.0727665i | ||||
\(613\) | −7.64703e13 | + | 7.64703e13i | −0.883467 | + | 0.883467i | −0.993885 | − | 0.110418i | \(-0.964781\pi\) |
0.110418 | + | 0.993885i | \(0.464781\pi\) | |||||||
\(614\) | 1.86539e13i | 0.213760i | ||||||||
\(615\) | −2.05456e13 | + | 4.45002e11i | −0.233530 | + | 0.00505808i | ||||
\(616\) | −1.28144e14 | −1.44476 | ||||||||
\(617\) | 6.75222e13 | + | 6.75222e13i | 0.755128 | + | 0.755128i | 0.975431 | − | 0.220303i | \(-0.0707047\pi\) |
−0.220303 | + | 0.975431i | \(0.570705\pi\) | |||||||
\(618\) | 4.92161e12 | − | 4.92161e12i | 0.0545965 | − | 0.0545965i | ||||
\(619\) | − | 8.43752e13i | − | 0.928456i | −0.885716 | − | 0.464228i | \(-0.846332\pi\) | ||
0.885716 | − | 0.464228i | \(-0.153668\pi\) | |||||||
\(620\) | −1.16912e13 | + | 1.22088e13i | −0.127614 | + | 0.133265i | ||||
\(621\) | 1.63626e13 | 0.177171 | ||||||||
\(622\) | 7.87147e12 | + | 7.87147e12i | 0.0845481 | + | 0.0845481i | ||||
\(623\) | 1.68895e14 | − | 1.68895e14i | 1.79960 | − | 1.79960i | ||||
\(624\) | 1.77049e13i | 0.187141i | ||||||||
\(625\) | −9.50099e13 | + | 8.25073e12i | −0.996251 | + | 0.0865152i | ||||
\(626\) | −6.05687e12 | −0.0630052 | ||||||||
\(627\) | −2.47367e13 | − | 2.47367e13i | −0.255272 | − | 0.255272i | ||||
\(628\) | −3.26678e13 | + | 3.26678e13i | −0.334442 | + | 0.334442i | ||||
\(629\) | 7.17165e13i | 0.728394i | ||||||||
\(630\) | −2.22380e13 | − | 2.12951e13i | −0.224075 | − | 0.214574i | ||||
\(631\) | 1.38987e14 | 1.38940 | 0.694698 | − | 0.719301i | \(-0.255538\pi\) | ||||
0.694698 | + | 0.719301i | \(0.255538\pi\) | |||||||
\(632\) | −2.77797e13 | − | 2.77797e13i | −0.275513 | − | 0.275513i | ||||
\(633\) | −3.89076e13 | + | 3.89076e13i | −0.382839 | + | 0.382839i | ||||
\(634\) | − | 1.73892e13i | − | 0.169760i | ||||||
\(635\) | 3.55603e12 | + | 1.64181e14i | 0.0344427 | + | 1.59021i | ||||
\(636\) | −6.95572e13 | −0.668431 | ||||||||
\(637\) | 1.99431e14 | + | 1.99431e14i | 1.90149 | + | 1.90149i | ||||
\(638\) | −4.29118e13 | + | 4.29118e13i | −0.405951 | + | 0.405951i | ||||
\(639\) | − | 2.31966e13i | − | 0.217731i | ||||||
\(640\) | −9.64965e13 | + | 2.09004e12i | −0.898694 | + | 0.0194650i | ||||
\(641\) | −1.18929e14 | −1.09900 | −0.549500 | − | 0.835494i | \(-0.685182\pi\) | ||||
−0.549500 | + | 0.835494i | \(0.685182\pi\) | |||||||
\(642\) | −1.82921e13 | − | 1.82921e13i | −0.167722 | − | 0.167722i | ||||
\(643\) | −3.02629e13 | + | 3.02629e13i | −0.275331 | + | 0.275331i | −0.831242 | − | 0.555911i | \(-0.812370\pi\) |
0.555911 | + | 0.831242i | \(0.312370\pi\) | |||||||
\(644\) | − | 1.34750e14i | − | 1.21647i | ||||||
\(645\) | 1.00751e13 | − | 1.05212e13i | 0.0902506 | − | 0.0942466i | ||||
\(646\) | 1.70806e13 | 0.151824 | ||||||||
\(647\) | −1.05612e14 | − | 1.05612e14i | −0.931521 | − | 0.931521i | 0.0662803 | − | 0.997801i | \(-0.478887\pi\) |
−0.997801 | + | 0.0662803i | \(0.978887\pi\) | |||||||
\(648\) | −8.03584e12 | + | 8.03584e12i | −0.0703326 | + | 0.0703326i | ||||
\(649\) | 1.46711e14i | 1.27420i | ||||||||
\(650\) | 3.10460e12 | + | 7.16354e13i | 0.0267571 | + | 0.617392i | ||||
\(651\) | 3.06120e13 | 0.261810 | ||||||||
\(652\) | 1.24519e13 | + | 1.24519e13i | 0.105681 | + | 0.105681i | ||||
\(653\) | −6.91878e12 | + | 6.91878e12i | −0.0582725 | + | 0.0582725i | −0.735643 | − | 0.677370i | \(-0.763120\pi\) |
0.677370 | + | 0.735643i | \(0.263120\pi\) | |||||||
\(654\) | − | 1.60925e12i | − | 0.0134504i | ||||||
\(655\) | −1.18938e13 | − | 1.13895e13i | −0.0986537 | − | 0.0944707i | ||||
\(656\) | 1.33149e13 | 0.109602 | ||||||||
\(657\) | −3.74380e13 | − | 3.74380e13i | −0.305834 | − | 0.305834i | ||||
\(658\) | 1.62007e13 | − | 1.62007e13i | 0.131342 | − | 0.131342i | ||||
\(659\) | − | 1.02130e14i | − | 0.821723i | −0.911698 | − | 0.410862i | \(-0.865228\pi\) | ||
0.911698 | − | 0.410862i | \(-0.134772\pi\) | |||||||
\(660\) | −1.02816e12 | − | 4.74699e13i | −0.00820998 | − | 0.379052i | ||||
\(661\) | 1.82173e14 | 1.44370 | 0.721850 | − | 0.692049i | \(-0.243292\pi\) | ||||
0.721850 | + | 0.692049i | \(0.243292\pi\) | |||||||
\(662\) | −2.98757e13 | − | 2.98757e13i | −0.234979 | − | 0.234979i | ||||
\(663\) | 2.63466e13 | − | 2.63466e13i | 0.205663 | − | 0.205663i | ||||
\(664\) | 3.86872e13i | 0.299728i | ||||||||
\(665\) | −1.63587e14 | + | 3.54318e12i | −1.25789 | + | 0.0272449i | ||||
\(666\) | 3.90259e13 | 0.297839 | ||||||||
\(667\) | −1.06664e14 | − | 1.06664e14i | −0.807955 | − | 0.807955i | ||||
\(668\) | 4.42870e13 | − | 4.42870e13i | 0.332961 | − | 0.332961i | ||||
\(669\) | 1.89975e12i | 0.0141764i | ||||||||
\(670\) | 5.39220e13 | − | 5.63096e13i | 0.399386 | − | 0.417069i | ||||
\(671\) | 3.98607e12 | 0.0293044 | ||||||||
\(672\) | 1.04358e14 | + | 1.04358e14i | 0.761519 | + | 0.761519i | ||||
\(673\) | −1.51317e14 | + | 1.51317e14i | −1.09601 | + | 1.09601i | −0.101133 | + | 0.994873i | \(0.532247\pi\) |
−0.994873 | + | 0.101133i | \(0.967753\pi\) | |||||||
\(674\) | − | 2.06591e13i | − | 0.148529i | ||||||
\(675\) | 1.82252e13 | − | 1.98765e13i | 0.130063 | − | 0.141847i | ||||
\(676\) | −4.46784e13 | −0.316493 | ||||||||
\(677\) | 1.99536e14 | + | 1.99536e14i | 1.40307 | + | 1.40307i | 0.790134 | + | 0.612934i | \(0.210011\pi\) |
0.612934 | + | 0.790134i | \(0.289989\pi\) | |||||||
\(678\) | 3.97058e13 | − | 3.97058e13i | 0.277144 | − | 0.277144i | ||||
\(679\) | − | 9.30680e13i | − | 0.644840i | ||||||
\(680\) | 3.95789e13 | + | 3.79008e13i | 0.272220 | + | 0.260677i | ||||
\(681\) | −1.26719e14 | −0.865181 | ||||||||
\(682\) | −1.21435e13 | − | 1.21435e13i | −0.0823040 | − | 0.0823040i | ||||
\(683\) | −1.46891e14 | + | 1.46891e14i | −0.988304 | + | 0.988304i | −0.999932 | − | 0.0116281i | \(-0.996299\pi\) |
0.0116281 | + | 0.999932i | \(0.496299\pi\) | |||||||
\(684\) | 2.55494e13i | 0.170648i | ||||||||
\(685\) | −1.02926e12 | − | 4.75204e13i | −0.00682450 | − | 0.315085i | ||||
\(686\) | 1.76391e14 | 1.16106 | ||||||||
\(687\) | 1.08320e14 | + | 1.08320e14i | 0.707826 | + | 0.707826i | ||||
\(688\) | −6.67389e12 | + | 6.67389e12i | −0.0432949 | + | 0.0432949i | ||||
\(689\) | − | 2.93344e14i | − | 1.88921i | ||||||
\(690\) | −4.29251e13 | + | 9.29726e11i | −0.274452 | + | 0.00594442i | ||||
\(691\) | 7.64083e13 | 0.485009 | 0.242505 | − | 0.970150i | \(-0.422031\pi\) | ||||
0.242505 | + | 0.970150i | \(0.422031\pi\) | |||||||
\(692\) | 8.30758e12 | + | 8.30758e12i | 0.0523533 | + | 0.0523533i | ||||
\(693\) | −6.08011e13 | + | 6.08011e13i | −0.380404 | + | 0.380404i | ||||
\(694\) | − | 9.58398e13i | − | 0.595317i | ||||||
\(695\) | 1.38863e14 | − | 1.45012e14i | 0.856372 | − | 0.894290i | ||||
\(696\) | 1.04767e14 | 0.641475 | ||||||||
\(697\) | −1.98139e13 | − | 1.98139e13i | −0.120450 | − | 0.120450i | ||||
\(698\) | 1.82514e12 | − | 1.82514e12i | 0.0110159 | − | 0.0110159i | ||||
\(699\) | 4.65974e12i | 0.0279239i | ||||||||
\(700\) | −1.63688e14 | − | 1.50089e14i | −0.973928 | − | 0.893017i | ||||
\(701\) | −3.54204e13 | −0.209249 | −0.104625 | − | 0.994512i | \(-0.533364\pi\) | ||||
−0.104625 | + | 0.994512i | \(0.533364\pi\) | |||||||
\(702\) | −1.43370e13 | − | 1.43370e13i | −0.0840953 | − | 0.0840953i | ||||
\(703\) | 1.46650e14 | − | 1.46650e14i | 0.854093 | − | 0.854093i | ||||
\(704\) | − | 4.08406e13i | − | 0.236172i | ||||||
\(705\) | 1.44934e13 | + | 1.38788e13i | 0.0832191 | + | 0.0796906i | ||||
\(706\) | −8.59816e13 | −0.490210 | ||||||||
\(707\) | −2.82023e13 | − | 2.82023e13i | −0.159657 | − | 0.159657i | ||||
\(708\) | 7.57655e13 | − | 7.57655e13i | 0.425898 | − | 0.425898i | ||||
\(709\) | − | 2.21716e14i | − | 1.23756i | −0.785565 | − | 0.618780i | \(-0.787627\pi\) | ||
0.785565 | − | 0.618780i | \(-0.212373\pi\) | |||||||
\(710\) | 1.31804e12 | + | 6.08534e13i | 0.00730527 | + | 0.337282i | ||||
\(711\) | −2.63615e13 | −0.145085 | ||||||||
\(712\) | 1.63575e14 | + | 1.63575e14i | 0.893958 | + | 0.893958i | ||||
\(713\) | 3.01844e13 | − | 3.01844e13i | 0.163808 | − | 0.163808i | ||||
\(714\) | − | 4.19829e13i | − | 0.226246i | ||||||
\(715\) | 2.00195e14 | − | 4.33607e12i | 1.07133 | − | 0.0232042i | ||||
\(716\) | 4.89469e13 | 0.260112 | ||||||||
\(717\) | −3.45002e13 | − | 3.45002e13i | −0.182065 | − | 0.182065i | ||||
\(718\) | −3.37312e13 | + | 3.37312e13i | −0.176770 | + | 0.176770i | ||||
\(719\) | 2.91623e14i | 1.51767i | 0.651284 | + | 0.758834i | \(0.274231\pi\) | ||||
−0.651284 | + | 0.758834i | \(0.725769\pi\) | |||||||
\(720\) | −1.20845e13 | + | 1.26196e13i | −0.0624549 | + | 0.0652203i | ||||
\(721\) | −9.09152e13 | −0.466616 | ||||||||
\(722\) | 3.67240e13 | + | 3.67240e13i | 0.187182 | + | 0.187182i | ||||
\(723\) | −8.54116e13 | + | 8.54116e13i | −0.432340 | + | 0.432340i | ||||
\(724\) | 2.48277e14i | 1.24809i | ||||||||
\(725\) | −2.48376e14 | + | 1.07643e13i | −1.23999 | + | 0.0537399i | ||||
\(726\) | −1.19032e13 | −0.0590173 | ||||||||
\(727\) | −2.17241e14 | − | 2.17241e14i | −1.06972 | − | 1.06972i | −0.997380 | − | 0.0723409i | \(-0.976953\pi\) |
−0.0723409 | − | 0.997380i | \(-0.523047\pi\) | |||||||
\(728\) | −2.79090e14 | + | 2.79090e14i | −1.36486 | + | 1.36486i | ||||
\(729\) | 7.62560e12i | 0.0370370i | ||||||||
\(730\) | 1.00341e14 | + | 9.60864e13i | 0.484020 | + | 0.463498i | ||||
\(731\) | 1.98628e13 | 0.0951598 | ||||||||
\(732\) | −2.05852e12 | − | 2.05852e12i | −0.00979489 | − | 0.00979489i | ||||
\(733\) | 1.47497e14 | − | 1.47497e14i | 0.697051 | − | 0.697051i | −0.266723 | − | 0.963773i | \(-0.585941\pi\) |
0.963773 | + | 0.266723i | \(0.0859408\pi\) | |||||||
\(734\) | − | 3.05930e13i | − | 0.143596i | ||||||
\(735\) | 6.02715e12 | + | 2.78271e14i | 0.0280980 | + | 1.29727i | ||||
\(736\) | 2.05801e14 | 0.952926 | ||||||||
\(737\) | −1.53956e14 | − | 1.53956e14i | −0.708044 | − | 0.708044i | ||||
\(738\) | −1.07821e13 | + | 1.07821e13i | −0.0492517 | + | 0.0492517i | ||||
\(739\) | − | 2.87168e14i | − | 1.30291i | −0.758689 | − | 0.651453i | \(-0.774160\pi\) | ||
0.758689 | − | 0.651453i | \(-0.225840\pi\) | |||||||
\(740\) | 2.81422e14 | − | 6.09539e12i | 1.26823 | − | 0.0274690i | ||||
\(741\) | −1.07750e14 | −0.482309 | ||||||||
\(742\) | −2.33720e14 | − | 2.33720e14i | −1.03914 | − | 1.03914i | ||||
\(743\) | 1.11836e14 | − | 1.11836e14i | 0.493899 | − | 0.493899i | −0.415633 | − | 0.909532i | \(-0.636440\pi\) |
0.909532 | + | 0.415633i | \(0.136440\pi\) | |||||||
\(744\) | 2.96478e13i | 0.130055i | ||||||||
\(745\) | −2.44187e14 | + | 2.54999e14i | −1.06400 | + | 1.11111i | ||||
\(746\) | −7.50858e13 | −0.324985 | ||||||||
\(747\) | 1.83561e13 | + | 1.83561e13i | 0.0789181 | + | 0.0789181i | ||||
\(748\) | 4.57794e13 | − | 4.57794e13i | 0.195507 | − | 0.195507i | ||||
\(749\) | 3.37904e14i | 1.43346i | ||||||||
\(750\) | −4.66821e13 | + | 5.31790e13i | −0.196718 | + | 0.224096i | ||||
\(751\) | −3.88625e14 | −1.62679 | −0.813395 | − | 0.581712i | \(-0.802383\pi\) | ||||
−0.813395 | + | 0.581712i | \(0.802383\pi\) | |||||||
\(752\) | −9.19355e12 | − | 9.19355e12i | −0.0382291 | − | 0.0382291i | ||||
\(753\) | 1.87640e14 | − | 1.87640e14i | 0.775089 | − | 0.775089i | ||||
\(754\) | 1.86918e14i | 0.767000i | ||||||||
\(755\) | −2.02020e13 | − | 1.93454e13i | −0.0823491 | − | 0.0788575i | ||||
\(756\) | 6.27988e13 | 0.254298 | ||||||||
\(757\) | 1.45441e14 | + | 1.45441e14i | 0.585071 | + | 0.585071i | 0.936293 | − | 0.351221i | \(-0.114233\pi\) |
−0.351221 | + | 0.936293i | \(0.614233\pi\) | |||||||
\(758\) | −3.12859e13 | + | 3.12859e13i | −0.125027 | + | 0.125027i | ||||
\(759\) | 1.19904e14i | 0.476019i | ||||||||
\(760\) | −3.43158e12 | − | 1.58435e14i | −0.0135340 | − | 0.624859i | ||||
\(761\) | −5.67180e13 | −0.222227 | −0.111114 | − | 0.993808i | \(-0.535442\pi\) | ||||
−0.111114 | + | 0.993808i | \(0.535442\pi\) | |||||||
\(762\) | 8.61603e13 | + | 8.61603e13i | 0.335376 | + | 0.335376i | ||||
\(763\) | −1.48636e13 | + | 1.48636e13i | −0.0574779 | + | 0.0574779i | ||||
\(764\) | 1.91482e14i | 0.735631i | ||||||||
\(765\) | 3.67621e13 | − | 7.96240e11i | 0.140311 | − | 0.00303904i | ||||
\(766\) | −1.25109e14 | −0.474399 | ||||||||
\(767\) | 3.19526e14 | + | 3.19526e14i | 1.20373 | + | 1.20373i | ||||
\(768\) | −7.94045e13 | + | 7.94045e13i | −0.297193 | + | 0.297193i | ||||
\(769\) | 4.01367e14i | 1.49248i | 0.665674 | + | 0.746242i | \(0.268144\pi\) | ||||
−0.665674 | + | 0.746242i | \(0.731856\pi\) | |||||||
\(770\) | 1.56049e14 | − | 1.62959e14i | 0.576511 | − | 0.602038i | ||||
\(771\) | 1.10374e14 | 0.405130 | ||||||||
\(772\) | 4.24026e13 | + | 4.24026e13i | 0.154635 | + | 0.154635i | ||||
\(773\) | 3.05262e14 | − | 3.05262e14i | 1.10605 | − | 1.10605i | 0.112387 | − | 0.993665i | \(-0.464150\pi\) |
0.993665 | − | 0.112387i | \(-0.0358496\pi\) | |||||||
\(774\) | − | 1.08087e13i | − | 0.0389107i | ||||||
\(775\) | −3.04616e12 | − | 7.02870e13i | −0.0108954 | − | 0.251401i | ||||
\(776\) | 9.01367e13 | 0.320327 | ||||||||
\(777\) | −3.60456e14 | − | 3.60456e14i | −1.27276 | − | 1.27276i | ||||
\(778\) | 5.59729e13 | − | 5.59729e13i | 0.196372 | − | 0.196372i | ||||
\(779\) | 8.10331e13i | 0.282472i | ||||||||
\(780\) | −1.05625e14 | − | 1.01147e14i | −0.365844 | − | 0.350332i | ||||
\(781\) | 1.69983e14 | 0.584993 | ||||||||
\(782\) | −4.13965e13 | − | 4.13965e13i | −0.141556 | − | 0.141556i | ||||
\(783\) | 4.97094e13 | − | 4.97094e13i | 0.168900 | − | 0.168900i | ||||
\(784\) | − | 1.80339e14i | − | 0.608848i | ||||||
\(785\) | −4.16366e12 | − | 1.92234e14i | −0.0139678 | − | 0.644886i | ||||
\(786\) | −1.22188e13 | −0.0407302 | ||||||||
\(787\) | −1.73114e14 | − | 1.73114e14i | −0.573403 | − | 0.573403i | 0.359675 | − | 0.933078i | \(-0.382888\pi\) |
−0.933078 | + | 0.359675i | \(0.882888\pi\) | |||||||
\(788\) | −1.97874e14 | + | 1.97874e14i | −0.651266 | + | 0.651266i | ||||
\(789\) | − | 4.77779e13i | − | 0.156258i | ||||||
\(790\) | 6.91560e13 | − | 1.49787e12i | 0.224747 | − | 0.00486786i | ||||
\(791\) | −7.33471e14 | −2.36865 | ||||||||
\(792\) | −5.88861e13 | − | 5.88861e13i | −0.188967 | − | 0.188967i | ||||
\(793\) | 8.68141e12 | − | 8.68141e12i | 0.0276837 | − | 0.0276837i | ||||
\(794\) | − | 1.73969e14i | − | 0.551277i | ||||||
\(795\) | 2.00223e14 | − | 2.09088e14i | 0.630490 | − | 0.658407i | ||||
\(796\) | 2.42482e14 | 0.758778 | ||||||||
\(797\) | 1.54981e14 | + | 1.54981e14i | 0.481932 | + | 0.481932i | 0.905748 | − | 0.423816i | \(-0.139310\pi\) |
−0.423816 | + | 0.905748i | \(0.639310\pi\) | |||||||
\(798\) | −8.58489e13 | + | 8.58489e13i | −0.265290 | + | 0.265290i | ||||
\(799\) | 2.73618e13i | 0.0840255i | ||||||||
\(800\) | 2.29229e14 | − | 2.49998e14i | 0.699551 | − | 0.762933i | ||||
\(801\) | 1.55224e14 | 0.470757 | ||||||||
\(802\) | −9.46481e13 | − | 9.46481e13i | −0.285260 | − | 0.285260i | ||||
\(803\) | 2.74343e14 | − | 2.74343e14i | 0.821704 | − | 0.821704i | ||||
\(804\) | 1.59015e14i | 0.473322i | ||||||||
\(805\) | 4.05058e14 | + | 3.87883e14i | 1.19822 | + | 1.14742i | ||||
\(806\) | −5.28954e13 | −0.155504 | ||||||||
\(807\) | −1.49156e14 | − | 1.49156e14i | −0.435786 | − | 0.435786i | ||||
\(808\) | 2.73140e13 | − | 2.73140e13i | 0.0793101 | − | 0.0793101i | ||||
\(809\) | − | 5.41509e14i | − | 1.56265i | −0.624122 | − | 0.781327i | \(-0.714543\pi\) | ||
0.624122 | − | 0.781327i | \(-0.285457\pi\) | |||||||
\(810\) | −4.33289e11 | − | 2.00048e13i | −0.00124266 | − | 0.0573731i | ||||
\(811\) | 7.42708e13 | 0.211696 | 0.105848 | − | 0.994382i | \(-0.466244\pi\) | ||||
0.105848 | + | 0.994382i | \(0.466244\pi\) | |||||||
\(812\) | −4.09370e14 | − | 4.09370e14i | −1.15967 | − | 1.15967i | ||||
\(813\) | 1.23992e14 | − | 1.23992e14i | 0.349093 | − | 0.349093i | ||||
\(814\) | 2.85979e14i | 0.800224i | ||||||||
\(815\) | −7.32736e13 | + | 1.58705e12i | −0.203779 | + | 0.00441371i | ||||
\(816\) | −2.38244e13 | −0.0658522 | ||||||||
\(817\) | −4.06165e13 | − | 4.06165e13i | −0.111582 | − | 0.111582i | ||||
\(818\) | 6.31805e13 | − | 6.31805e13i | 0.172511 | − | 0.172511i | ||||
\(819\) | 2.64842e14i | 0.718732i | ||||||||
\(820\) | −7.60675e13 | + | 7.94356e13i | −0.205177 | + | 0.214262i | ||||
\(821\) | 5.08324e13 | 0.136278 | 0.0681389 | − | 0.997676i | \(-0.478294\pi\) | ||||
0.0681389 | + | 0.997676i | \(0.478294\pi\) | |||||||
\(822\) | −2.49382e13 | − | 2.49382e13i | −0.0664517 | − | 0.0664517i | ||||
\(823\) | −1.56162e14 | + | 1.56162e14i | −0.413597 | + | 0.413597i | −0.882990 | − | 0.469393i | \(-0.844473\pi\) |
0.469393 | + | 0.882990i | \(0.344473\pi\) | |||||||
\(824\) | − | 8.80516e13i | − | 0.231794i | ||||||
\(825\) | 1.45654e14 | + | 1.33553e14i | 0.381111 | + | 0.349449i | ||||
\(826\) | 5.09161e14 | 1.32420 | ||||||||
\(827\) | 3.83051e14 | + | 3.83051e14i | 0.990215 | + | 0.990215i | 0.999953 | − | 0.00973769i | \(-0.00309965\pi\) |
−0.00973769 | + | 0.999953i | \(0.503100\pi\) | |||||||
\(828\) | 6.19217e13 | − | 6.19217e13i | 0.159108 | − | 0.159108i | ||||
\(829\) | 1.71588e14i | 0.438242i | 0.975698 | + | 0.219121i | \(0.0703190\pi\) | ||||
−0.975698 | + | 0.219121i | \(0.929681\pi\) | |||||||
\(830\) | −4.91978e13 | − | 4.71118e13i | −0.124898 | − | 0.119602i | ||||
\(831\) | 3.59003e14 | 0.905926 | ||||||||
\(832\) | −8.89482e13 | − | 8.89482e13i | −0.223111 | − | 0.223111i | ||||
\(833\) | −2.68362e14 | + | 2.68362e14i | −0.669107 | + | 0.669107i | ||||
\(834\) | − | 1.48974e14i | − | 0.369217i | ||||||
\(835\) | 5.64457e12 | + | 2.60608e14i | 0.0139059 | + | 0.642030i | ||||
\(836\) | −1.87224e14 | −0.458491 | ||||||||
\(837\) | 1.40671e13 | + | 1.40671e13i | 0.0342434 | + | 0.0342434i | ||||
\(838\) | −1.31511e13 | + | 1.31511e13i | −0.0318230 | + | 0.0318230i | ||||
\(839\) | 2.36405e14i | 0.568653i | 0.958728 | + | 0.284326i | \(0.0917699\pi\) | ||||
−0.958728 | + | 0.284326i | \(0.908230\pi\) | |||||||
\(840\) | −3.89422e14 | + | 8.43459e12i | −0.931159 | + | 0.0201682i | ||||
\(841\) | −2.27380e14 | −0.540471 | ||||||||
\(842\) | 1.16489e14 | + | 1.16489e14i | 0.275249 | + | 0.275249i | ||||
\(843\) | −2.87374e14 | + | 2.87374e14i | −0.675009 | + | 0.675009i | ||||
\(844\) | 2.94480e14i | 0.687612i | ||||||||
\(845\) | 1.28608e14 | − | 1.34303e14i | 0.298529 | − | 0.311747i | ||||
\(846\) | 1.48894e13 | 0.0343579 | ||||||||
\(847\) | 1.09942e14 | + | 1.09942e14i | 0.252200 | + | 0.252200i | ||||
\(848\) | −1.32631e14 | + | 1.32631e14i | −0.302458 | + | 0.302458i | ||||
\(849\) | − | 3.70869e14i | − | 0.840779i | ||||||
\(850\) | −9.63954e13 | + | 4.17767e12i | −0.217251 | + | 0.00941541i | ||||
\(851\) | −7.10842e14 | −1.59267 | ||||||||
\(852\) | −8.77841e13 | − | 8.77841e13i | −0.195532 | − | 0.195532i | ||||
\(853\) | 1.64973e14 | − | 1.64973e14i | 0.365314 | − | 0.365314i | −0.500451 | − | 0.865765i | \(-0.666832\pi\) |
0.865765 | + | 0.500451i | \(0.166832\pi\) | |||||||
\(854\) | − | 1.38337e13i | − | 0.0304543i | ||||||
\(855\) | −7.68013e13 | − | 7.35450e13i | −0.168089 | − | 0.160962i | ||||
\(856\) | −3.27261e14 | −0.712075 | ||||||||
\(857\) | −1.16143e13 | − | 1.16143e13i | −0.0251239 | − | 0.0251239i | 0.694433 | − | 0.719557i | \(-0.255655\pi\) |
−0.719557 | + | 0.694433i | \(0.755655\pi\) | |||||||
\(858\) | 1.05060e14 | − | 1.05060e14i | 0.225945 | − | 0.225945i | ||||
\(859\) | 1.65139e14i | 0.353089i | 0.984293 | + | 0.176545i | \(0.0564920\pi\) | ||||
−0.984293 | + | 0.176545i | \(0.943508\pi\) | |||||||
\(860\) | −1.68820e12 | − | 7.79434e13i | −0.00358865 | − | 0.165686i | ||||
\(861\) | 1.99174e14 | 0.420937 | ||||||||
\(862\) | 2.69639e14 | + | 2.69639e14i | 0.566560 | + | 0.566560i | ||||
\(863\) | −3.69915e14 | + | 3.69915e14i | −0.772766 | + | 0.772766i | −0.978589 | − | 0.205823i | \(-0.934013\pi\) |
0.205823 | + | 0.978589i | \(0.434013\pi\) | |||||||
\(864\) | 9.59115e13i | 0.199206i | ||||||||
\(865\) | −4.88862e13 | + | 1.05884e12i | −0.100950 | + | 0.00218650i | ||||
\(866\) | 6.77902e13 | 0.139180 | ||||||||
\(867\) | −1.64542e14 | − | 1.64542e14i | −0.335879 | − | 0.335879i | ||||
\(868\) | 1.15846e14 | − | 1.15846e14i | 0.235117 | − | 0.235117i | ||||
\(869\) | − | 1.93175e14i | − | 0.389809i | ||||||
\(870\) | −1.27582e14 | + | 1.33231e14i | −0.255972 | + | 0.267306i | ||||
\(871\) | −6.70614e14 | −1.33777 | ||||||||
\(872\) | −1.43954e13 | − | 1.43954e13i | −0.0285524 | − | 0.0285524i | ||||
\(873\) | 4.27675e13 | − | 4.27675e13i | 0.0843418 | − | 0.0843418i | ||||
\(874\) | 1.69300e14i | 0.331970i | ||||||||
\(875\) | 9.22350e14 | − | 6.00073e13i | 1.79827 | − | 0.116994i | ||||
\(876\) | −2.83356e14 | −0.549304 | ||||||||
\(877\) | 2.06439e14 | + | 2.06439e14i | 0.397918 | + | 0.397918i | 0.877498 | − | 0.479580i | \(-0.159211\pi\) |
−0.479580 | + | 0.877498i | \(0.659211\pi\) | |||||||
\(878\) | −2.21488e14 | + | 2.21488e14i | −0.424501 | + | 0.424501i | ||||
\(879\) | − | 4.59322e13i | − | 0.0875331i | ||||||
\(880\) | −9.24754e13 | − | 8.85544e13i | −0.175232 | − | 0.167802i | ||||
\(881\) | 6.72129e14 | 1.26641 | 0.633203 | − | 0.773986i | \(-0.281740\pi\) | ||||
0.633203 | + | 0.773986i | \(0.281740\pi\) | |||||||
\(882\) | 1.46034e14 | + | 1.46034e14i | 0.273597 | + | 0.273597i | ||||
\(883\) | −2.04026e14 | + | 2.04026e14i | −0.380086 | + | 0.380086i | −0.871133 | − | 0.491047i | \(-0.836614\pi\) |
0.491047 | + | 0.871133i | \(0.336614\pi\) | |||||||
\(884\) | − | 1.99409e14i | − | 0.369389i | ||||||
\(885\) | 9.65666e12 | + | 4.45844e14i | 0.0177873 | + | 0.821234i | ||||
\(886\) | −5.19408e14 | −0.951350 | ||||||||
\(887\) | 7.02000e14 | + | 7.02000e14i | 1.27855 | + | 1.27855i | 0.941478 | + | 0.337075i | \(0.109438\pi\) |
0.337075 | + | 0.941478i | \(0.390562\pi\) | |||||||
\(888\) | 3.49102e14 | − | 3.49102e14i | 0.632249 | − | 0.632249i | ||||
\(889\) | − | 1.59161e15i | − | 2.86634i | ||||||
\(890\) | −4.07211e14 | + | 8.81989e12i | −0.729238 | + | 0.0157948i | ||||
\(891\) | −5.58798e13 | −0.0995100 | ||||||||
\(892\) | 7.18931e12 | + | 7.18931e12i | 0.0127310 | + | 0.0127310i | ||||
\(893\) | 5.59509e13 | − | 5.59509e13i | 0.0985258 | − | 0.0985258i | ||||
\(894\) | 2.61968e14i | 0.458734i | ||||||||
\(895\) | −1.40895e14 | + | 1.47134e14i | −0.245348 | + | 0.256211i | ||||
\(896\) | 9.35462e14 | 1.61989 | ||||||||
\(897\) | 2.61143e14 | + | 2.61143e14i | 0.449692 | + | 0.449692i | ||||
\(898\) | 3.71822e14 | − | 3.71822e14i | 0.636728 | − | 0.636728i | ||||
\(899\) | − | 1.83400e14i | − | 0.312321i | ||||||
\(900\) | −6.24903e12 | − | 1.44190e14i | −0.0105828 | − | 0.244187i | ||||
\(901\) | 3.94735e14 | 0.664786 | ||||||||
\(902\) | −7.90105e13 | − | 7.90105e13i | −0.132328 | − | 0.132328i | ||||
\(903\) | −9.98327e13 | + | 9.98327e13i | −0.166278 | + | 0.166278i | ||||
\(904\) | − | 7.10369e14i | − | 1.17664i | ||||||
\(905\) | −7.46320e14 | − | 7.14676e14i | −1.22937 | − | 1.17724i | ||||
\(906\) | −2.07540e13 | −0.0339987 | ||||||||
\(907\) | −5.77421e14 | − | 5.77421e14i | −0.940711 | − | 0.940711i | 0.0576270 | − | 0.998338i | \(-0.481647\pi\) |
−0.998338 | + | 0.0576270i | \(0.981647\pi\) | |||||||
\(908\) | −4.79550e14 | + | 4.79550e14i | −0.776970 | + | 0.776970i | ||||
\(909\) | − | 2.59196e13i | − | 0.0417646i | ||||||
\(910\) | −1.50484e13 | − | 6.94778e14i | −0.0241148 | − | 1.11337i | ||||
\(911\) | −9.22325e13 | −0.146991 | −0.0734957 | − | 0.997296i | \(-0.523416\pi\) | ||||
−0.0734957 | + | 0.997296i | \(0.523416\pi\) | |||||||
\(912\) | 4.87173e13 | + | 4.87173e13i | 0.0772163 | + | 0.0772163i | ||||
\(913\) | −1.34512e14 | + | 1.34512e14i | −0.212035 | + | 0.212035i | ||||
\(914\) | 9.33149e12i | 0.0146292i | ||||||||
\(915\) | 1.21134e13 | − | 2.62368e11i | 0.0188869 | − | 0.000409077i | ||||
\(916\) | 8.19844e14 | 1.27132 | ||||||||
\(917\) | 1.12857e14 | + | 1.12857e14i | 0.174053 | + | 0.174053i | ||||
\(918\) | 1.92924e13 | − | 1.92924e13i | 0.0295919 | − | 0.0295919i | ||||
\(919\) | 1.90596e14i | 0.290761i | 0.989376 | + | 0.145381i | \(0.0464407\pi\) | ||||
−0.989376 | + | 0.145381i | \(0.953559\pi\) | |||||||
\(920\) | −3.75666e14 | + | 3.92300e14i | −0.569984 | + | 0.595222i | ||||
\(921\) | 1.58348e14 | 0.238953 | ||||||||
\(922\) | 3.31679e13 | + | 3.31679e13i | 0.0497809 | + | 0.0497809i | ||||
\(923\) | 3.70212e14 | − | 3.70212e14i | 0.552640 | − | 0.552640i | ||||
\(924\) | 4.60185e14i | 0.683239i | ||||||||
\(925\) | −7.91761e14 | + | 8.63498e14i | −1.16919 | + | 1.27512i | ||||
\(926\) | −1.72768e14 | −0.253751 | ||||||||
\(927\) | −4.17782e13 | − | 4.17782e13i | −0.0610311 | − | 0.0610311i | ||||
\(928\) | 6.25224e14 | − | 6.25224e14i | 0.908438 | − | 0.908438i | ||||
\(929\) | 1.08880e14i | 0.157351i | 0.996900 | + | 0.0786753i | \(0.0250690\pi\) | ||||
−0.996900 | + | 0.0786753i | \(0.974931\pi\) | |||||||
\(930\) | −3.77025e13 | − | 3.61039e13i | −0.0541946 | − | 0.0518967i | ||||
\(931\) | 1.09752e15 | 1.56915 | ||||||||
\(932\) | 1.76341e13 | + | 1.76341e13i | 0.0250768 | + | 0.0250768i | ||||
\(933\) | 6.68188e13 | − | 6.68188e13i | 0.0945127 | − | 0.0945127i | ||||
\(934\) | 5.65268e14i | 0.795280i | ||||||||
\(935\) | 5.83479e12 | + | 2.69390e14i | 0.00816521 | + | 0.376985i | ||||
\(936\) | −2.56500e14 | −0.357033 | ||||||||
\(937\) | 1.75741e14 | + | 1.75741e14i | 0.243318 | + | 0.243318i | 0.818221 | − | 0.574903i | \(-0.194960\pi\) |
−0.574903 | + | 0.818221i | \(0.694960\pi\) | |||||||
\(938\) | −5.34307e14 | + | 5.34307e14i | −0.735829 | + | 0.735829i | ||||
\(939\) | 5.14151e13i | 0.0704309i | ||||||||
\(940\) | 1.07370e14 | − | 2.32556e12i | 0.146300 | − | 0.00316875i | ||||
\(941\) | 1.07510e15 | 1.45713 | 0.728566 | − | 0.684975i | \(-0.240187\pi\) | ||||
0.728566 | + | 0.684975i | \(0.240187\pi\) | |||||||
\(942\) | −1.00883e14 | − | 1.00883e14i | −0.136007 | − | 0.136007i | ||||
\(943\) | 1.96392e14 | − | 1.96392e14i | 0.263369 | − | 0.263369i | ||||
\(944\) | − | 2.88937e14i | − | 0.385429i | ||||||
\(945\) | −1.80769e14 | + | 1.88773e14i | −0.239863 | + | 0.250484i | ||||
\(946\) | 7.92054e13 | 0.104544 | ||||||||
\(947\) | −7.06380e14 | − | 7.06380e14i | −0.927445 | − | 0.927445i | 0.0700948 | − | 0.997540i | \(-0.477670\pi\) |
−0.997540 | + | 0.0700948i | \(0.977670\pi\) | |||||||
\(948\) | −9.97610e13 | + | 9.97610e13i | −0.130292 | + | 0.130292i | ||||
\(949\) | − | 1.19500e15i | − | 1.55252i | ||||||
\(950\) | 2.05657e14 | + | 1.88572e14i | 0.265782 | + | 0.243702i | ||||
\(951\) | −1.47613e14 | −0.189767 | ||||||||
\(952\) | −3.75554e14 | − | 3.75554e14i | −0.480273 | − | 0.480273i | ||||
\(953\) | 4.13424e14 | − | 4.13424e14i | 0.525934 | − | 0.525934i | −0.393423 | − | 0.919357i | \(-0.628709\pi\) |
0.919357 | + | 0.393423i | \(0.128709\pi\) | |||||||
\(954\) | − | 2.14802e14i | − | 0.271830i | ||||||
\(955\) | −5.75592e14 | − | 5.51187e14i | −0.724599 | − | 0.693876i | ||||
\(956\) | −2.61121e14 | −0.327004 | ||||||||
\(957\) | 3.64267e14 | + | 3.64267e14i | 0.453796 | + | 0.453796i | ||||
\(958\) | −8.60710e13 | + | 8.60710e13i | −0.106667 | + | 0.106667i | ||||
\(959\) | 4.60675e14i | 0.567939i | ||||||||
\(960\) | −2.68817e12 | − | 1.24112e14i | −0.00329686 | − | 0.152215i | ||||
\(961\) | −7.67729e14 | −0.936679 | ||||||||
\(962\) | 6.22843e14 | + | 6.22843e14i | 0.755968 | + | 0.755968i | ||||
\(963\) | −1.55277e14 | + | 1.55277e14i | −0.187489 | + | 0.187489i | ||||
\(964\) | 6.46454e14i | 0.776520i | ||||||||
\(965\) | −2.49520e14 | + | 5.40441e12i | −0.298173 | + | 0.00645820i | ||||
\(966\) | 4.16127e14 | 0.494698 | ||||||||
\(967\) | −1.66726e14 | − | 1.66726e14i | −0.197183 | − | 0.197183i | 0.601608 | − | 0.798791i | \(-0.294527\pi\) |
−0.798791 | + | 0.601608i | \(0.794527\pi\) | |||||||
\(968\) | −1.06479e14 | + | 1.06479e14i | −0.125281 | + | 0.125281i | ||||
\(969\) | − | 1.44992e14i | − | 0.169717i | ||||||
\(970\) | −1.09765e14 | + | 1.14625e14i | −0.127822 | + | 0.133482i | ||||
\(971\) | −1.34411e15 | −1.55718 | −0.778589 | − | 0.627534i | \(-0.784064\pi\) | ||||
−0.778589 | + | 0.627534i | \(0.784064\pi\) | |||||||
\(972\) | 2.88579e13 | + | 2.88579e13i | 0.0332609 | + | 0.0332609i | ||||
\(973\) | −1.37598e15 | + | 1.37598e15i | −1.57778 | + | 1.57778i | ||||
\(974\) | − | 5.82125e14i | − | 0.664081i | ||||||
\(975\) | 6.08094e14 | − | 2.63541e13i | 0.690156 | − | 0.0299106i | ||||
\(976\) | −7.85032e12 | −0.00886417 | ||||||||
\(977\) | −5.60729e13 | − | 5.60729e13i | −0.0629912 | − | 0.0629912i | 0.674909 | − | 0.737901i | \(-0.264183\pi\) |
−0.737901 | + | 0.674909i | \(0.764183\pi\) | |||||||
\(978\) | −3.84533e13 | + | 3.84533e13i | −0.0429773 | + | 0.0429773i | ||||
\(979\) | 1.13747e15i | 1.26482i | ||||||||
\(980\) | 1.07588e15 | + | 1.03027e15i | 1.19024 | + | 1.13977i | ||||
\(981\) | −1.36605e13 | −0.0150356 | ||||||||
\(982\) | 5.55450e14 | + | 5.55450e14i | 0.608258 | + | 0.608258i | ||||
\(983\) | 3.59073e14 | − | 3.59073e14i | 0.391215 | − | 0.391215i | −0.483905 | − | 0.875120i | \(-0.660782\pi\) |
0.875120 | + | 0.483905i | \(0.160782\pi\) | |||||||
\(984\) | 1.92901e14i | 0.209102i | ||||||||
\(985\) | −2.52200e13 | − | 1.16440e15i | −0.0271997 | − | 1.25580i | ||||
\(986\) | −2.51525e14 | −0.269896 | ||||||||
\(987\) | −1.37524e14 | − | 1.37524e14i | −0.146822 | − | 0.146822i | ||||
\(988\) | −4.07762e14 | + | 4.07762e14i | −0.433134 | + | 0.433134i | ||||
\(989\) | 1.96877e14i | 0.208072i | ||||||||
\(990\) | 1.46594e14 | − | 3.17511e12i | 0.154148 | − | 0.00333874i | ||||
\(991\) | 3.64343e14 | 0.381190 | 0.190595 | − | 0.981669i | \(-0.438958\pi\) | ||||
0.190595 | + | 0.981669i | \(0.438958\pi\) | |||||||
\(992\) | 1.76930e14 | + | 1.76930e14i | 0.184180 | + | 0.184180i | ||||
\(993\) | −2.53607e14 | + | 2.53607e14i | −0.262673 | + | 0.262673i | ||||
\(994\) | − | 5.89928e14i | − | 0.607949i | ||||||
\(995\) | −6.97994e14 | + | 7.28900e14i | −0.715709 | + | 0.747399i | ||||
\(996\) | 1.38931e14 | 0.141744 | ||||||||
\(997\) | 3.19212e14 | + | 3.19212e14i | 0.324043 | + | 0.324043i | 0.850316 | − | 0.526273i | \(-0.176411\pi\) |
−0.526273 | + | 0.850316i | \(0.676411\pi\) | |||||||
\(998\) | 5.99844e14 | − | 5.99844e14i | 0.605878 | − | 0.605878i | ||||
\(999\) | − | 3.31280e14i | − | 0.332941i |
(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 | 15.11.f.a.7.7 | ✓ | 20 | |
3.2 | odd | 2 | 45.11.g.c.37.4 | 20 | |||
5.2 | odd | 4 | 75.11.f.d.43.4 | 20 | |||
5.3 | odd | 4 | inner | 15.11.f.a.13.7 | yes | 20 | |
5.4 | even | 2 | 75.11.f.d.7.4 | 20 | |||
15.8 | even | 4 | 45.11.g.c.28.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.11.f.a.7.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
15.11.f.a.13.7 | yes | 20 | 5.3 | odd | 4 | inner | |
45.11.g.c.28.4 | 20 | 15.8 | even | 4 | |||
45.11.g.c.37.4 | 20 | 3.2 | odd | 2 | |||
75.11.f.d.7.4 | 20 | 5.4 | even | 2 | |||
75.11.f.d.43.4 | 20 | 5.2 | odd | 4 |