Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,10,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not 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: | \(25.2367559720\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 427x^{4} - 3606x^{3} + 183492x^{2} - 858816x + 4064256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 18.2 | ||
Root | \(-11.1179 - 19.2567i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.10.c.e.30.2 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.68036 | − | 11.5707i | −0.295233 | − | 0.511359i | 0.679806 | − | 0.733392i | \(-0.262064\pi\) |
−0.975039 | + | 0.222033i | \(0.928731\pi\) | |||||||
\(3\) | 81.7073 | − | 141.521i | 0.582392 | − | 1.00873i | −0.412804 | − | 0.910820i | \(-0.635450\pi\) |
0.995195 | − | 0.0979117i | \(-0.0312163\pi\) | |||||||
\(4\) | 166.746 | − | 288.812i | 0.325675 | − | 0.564085i | ||||
\(5\) | 961.094 | + | 1664.66i | 0.687703 | + | 1.19114i | 0.972579 | + | 0.232572i | \(0.0747143\pi\) |
−0.284876 | + | 0.958564i | \(0.591952\pi\) | |||||||
\(6\) | −2183.34 | −0.687765 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −11296.4 | −0.975066 | ||||||||
\(9\) | −3510.66 | − | 6080.64i | −0.178360 | − | 0.308928i | ||||
\(10\) | 12840.9 | − | 22241.1i | 0.406065 | − | 0.703326i | ||||
\(11\) | 45099.9 | − | 78115.4i | 0.928772 | − | 1.60868i | 0.143391 | − | 0.989666i | \(-0.454199\pi\) |
0.785380 | − | 0.619014i | \(-0.212467\pi\) | |||||||
\(12\) | −27248.6 | − | 47196.0i | −0.379341 | − | 0.657037i | ||||
\(13\) | 3199.89 | 0.0310734 | 0.0155367 | − | 0.999879i | \(-0.495054\pi\) | ||||
0.0155367 | + | 0.999879i | \(0.495054\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 314114. | 1.60205 | ||||||||
\(16\) | −9909.84 | − | 17164.3i | −0.0378030 | − | 0.0654768i | ||||
\(17\) | 58247.1 | − | 100887.i | 0.169143 | − | 0.292965i | −0.768976 | − | 0.639278i | \(-0.779233\pi\) |
0.938119 | + | 0.346313i | \(0.112567\pi\) | |||||||
\(18\) | −46904.9 | + | 81241.8i | −0.105316 | + | 0.182412i | ||||
\(19\) | −71224.7 | − | 123365.i | −0.125383 | − | 0.217170i | 0.796499 | − | 0.604639i | \(-0.206683\pi\) |
−0.921883 | + | 0.387469i | \(0.873349\pi\) | |||||||
\(20\) | 641033. | 0.895870 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.20514e6 | −1.09682 | ||||||||
\(23\) | −636955. | − | 1.10324e6i | −0.474606 | − | 0.822043i | 0.524971 | − | 0.851120i | \(-0.324076\pi\) |
−0.999577 | + | 0.0290778i | \(0.990743\pi\) | |||||||
\(24\) | −922996. | + | 1.59868e6i | −0.567870 | + | 0.983580i | ||||
\(25\) | −870842. | + | 1.50834e6i | −0.445871 | + | 0.772272i | ||||
\(26\) | −21376.4 | − | 37025.0i | −0.00917391 | − | 0.0158897i | ||||
\(27\) | 2.06910e6 | 0.749282 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.42931e6 | −0.375262 | −0.187631 | − | 0.982240i | \(-0.560081\pi\) | ||||
−0.187631 | + | 0.982240i | \(0.560081\pi\) | |||||||
\(30\) | −2.09839e6 | − | 3.63452e6i | −0.472978 | − | 0.819222i | ||||
\(31\) | 4.83747e6 | − | 8.37875e6i | 0.940786 | − | 1.62949i | 0.176809 | − | 0.984245i | \(-0.443422\pi\) |
0.763977 | − | 0.645244i | \(-0.223244\pi\) | |||||||
\(32\) | −3.02427e6 | + | 5.23820e6i | −0.509854 | + | 0.883094i | ||||
\(33\) | −7.36999e6 | − | 1.27652e7i | −1.08182 | − | 1.87376i | ||||
\(34\) | −1.55645e6 | −0.199747 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.34155e6 | −0.232349 | ||||||||
\(37\) | 4.33872e6 | + | 7.51488e6i | 0.380587 | + | 0.659196i | 0.991146 | − | 0.132775i | \(-0.0423886\pi\) |
−0.610559 | + | 0.791971i | \(0.709055\pi\) | |||||||
\(38\) | −951614. | + | 1.64824e6i | −0.0740346 | + | 0.128232i | ||||
\(39\) | 261454. | − | 452851.i | 0.0180969 | − | 0.0313448i | ||||
\(40\) | −1.08569e7 | − | 1.88047e7i | −0.670556 | − | 1.16144i | ||||
\(41\) | −1.32544e7 | −0.732541 | −0.366271 | − | 0.930508i | \(-0.619366\pi\) | ||||
−0.366271 | + | 0.930508i | \(0.619366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.97554e7 | −1.32726 | −0.663632 | − | 0.748060i | \(-0.730986\pi\) | ||||
−0.663632 | + | 0.748060i | \(0.730986\pi\) | |||||||
\(44\) | −1.50404e7 | − | 2.60508e7i | −0.604955 | − | 1.04781i | ||||
\(45\) | 6.74815e6 | − | 1.16881e7i | 0.245317 | − | 0.424902i | ||||
\(46\) | −8.51018e6 | + | 1.47401e7i | −0.280239 | + | 0.485388i | ||||
\(47\) | −5.39846e6 | − | 9.35041e6i | −0.161373 | − | 0.279506i | 0.773989 | − | 0.633200i | \(-0.218259\pi\) |
−0.935361 | + | 0.353694i | \(0.884925\pi\) | |||||||
\(48\) | −3.23882e6 | −0.0880647 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.32702e7 | 0.526544 | ||||||||
\(51\) | −9.51843e6 | − | 1.64864e7i | −0.197015 | − | 0.341240i | ||||
\(52\) | 533567. | − | 924164.i | 0.0101198 | − | 0.0175281i | ||||
\(53\) | −3.53700e7 | + | 6.12626e7i | −0.615734 | + | 1.06648i | 0.374521 | + | 0.927218i | \(0.377807\pi\) |
−0.990255 | + | 0.139264i | \(0.955526\pi\) | |||||||
\(54\) | −1.38224e7 | − | 2.39410e7i | −0.221213 | − | 0.383152i | ||||
\(55\) | 1.73381e8 | 2.55488 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.32783e7 | −0.292089 | ||||||||
\(58\) | 9.54828e6 | + | 1.65381e7i | 0.110790 | + | 0.191893i | ||||
\(59\) | 3.20200e6 | − | 5.54603e6i | 0.0344023 | − | 0.0595865i | −0.848312 | − | 0.529497i | \(-0.822381\pi\) |
0.882714 | + | 0.469911i | \(0.155714\pi\) | |||||||
\(60\) | 5.23770e7 | − | 9.07197e7i | 0.521747 | − | 0.903693i | ||||
\(61\) | 8.45948e7 | + | 1.46523e8i | 0.782275 | + | 1.35494i | 0.930613 | + | 0.366004i | \(0.119274\pi\) |
−0.148338 | + | 0.988937i | \(0.547392\pi\) | |||||||
\(62\) | −1.29264e8 | −1.11100 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.06653e7 | 0.526498 | ||||||||
\(65\) | 3.07539e6 | + | 5.32673e6i | 0.0213693 | + | 0.0370127i | ||||
\(66\) | −9.84684e7 | + | 1.70552e8i | −0.638777 | + | 1.10639i | ||||
\(67\) | 5.81380e7 | − | 1.00698e8i | 0.352471 | − | 0.610498i | −0.634210 | − | 0.773160i | \(-0.718675\pi\) |
0.986682 | + | 0.162662i | \(0.0520081\pi\) | |||||||
\(68\) | −1.94249e7 | − | 3.36449e7i | −0.110171 | − | 0.190822i | ||||
\(69\) | −2.08176e8 | −1.10563 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.44496e8 | 0.674826 | 0.337413 | − | 0.941357i | \(-0.390448\pi\) | ||||
0.337413 | + | 0.941357i | \(0.390448\pi\) | |||||||
\(72\) | 3.96577e7 | + | 6.86892e7i | 0.173913 | + | 0.301226i | ||||
\(73\) | 8.00775e7 | − | 1.38698e8i | 0.330033 | − | 0.571634i | −0.652485 | − | 0.757802i | \(-0.726273\pi\) |
0.982518 | + | 0.186168i | \(0.0596068\pi\) | |||||||
\(74\) | 5.79684e7 | − | 1.00404e8i | 0.224724 | − | 0.389233i | ||||
\(75\) | 1.42308e8 | + | 2.46485e8i | 0.519343 | + | 0.899529i | ||||
\(76\) | −4.75056e7 | −0.163337 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.98643e6 | −0.0213712 | ||||||||
\(79\) | 2.44661e8 | + | 4.23766e8i | 0.706713 | + | 1.22406i | 0.966070 | + | 0.258281i | \(0.0831561\pi\) |
−0.259357 | + | 0.965782i | \(0.583511\pi\) | |||||||
\(80\) | 1.90486e7 | − | 3.29931e7i | 0.0519945 | − | 0.0900572i | ||||
\(81\) | 2.38161e8 | − | 4.12507e8i | 0.614735 | − | 1.06475i | ||||
\(82\) | 8.85441e7 | + | 1.53363e8i | 0.216270 | + | 0.374591i | ||||
\(83\) | 8.31590e7 | 0.192335 | 0.0961674 | − | 0.995365i | \(-0.469342\pi\) | ||||
0.0961674 | + | 0.995365i | \(0.469342\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.23924e8 | 0.465281 | ||||||||
\(86\) | 1.98777e8 | + | 3.44291e8i | 0.391852 | + | 0.678708i | ||||
\(87\) | −1.16785e8 | + | 2.02277e8i | −0.218549 | + | 0.378538i | ||||
\(88\) | −5.09466e8 | + | 8.82421e8i | −0.905614 | + | 1.56857i | ||||
\(89\) | 1.04042e6 | + | 1.80205e6i | 0.00175773 | + | 0.00304448i | 0.866903 | − | 0.498477i | \(-0.166107\pi\) |
−0.865145 | + | 0.501521i | \(0.832774\pi\) | |||||||
\(90\) | −1.80320e8 | −0.289703 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −4.24838e8 | −0.618270 | ||||||||
\(93\) | −7.90513e8 | − | 1.36921e9i | −1.09581 | − | 1.89800i | ||||
\(94\) | −7.21274e7 | + | 1.24928e8i | −0.0952851 | + | 0.165039i | ||||
\(95\) | 1.36907e8 | − | 2.37131e8i | 0.172453 | − | 0.298697i | ||||
\(96\) | 4.94210e8 | + | 8.55998e8i | 0.593870 | + | 1.02861i | ||||
\(97\) | 3.15885e8 | 0.362290 | 0.181145 | − | 0.983456i | \(-0.442020\pi\) | ||||
0.181145 | + | 0.983456i | \(0.442020\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.33322e8 | −0.662623 | ||||||||
\(100\) | 2.90418e8 | + | 5.03019e8i | 0.290418 | + | 0.503019i | ||||
\(101\) | −2.87420e8 | + | 4.97827e8i | −0.274835 | + | 0.476028i | −0.970093 | − | 0.242732i | \(-0.921956\pi\) |
0.695259 | + | 0.718760i | \(0.255290\pi\) | |||||||
\(102\) | −1.27173e8 | + | 2.20270e8i | −0.116331 | + | 0.201491i | ||||
\(103\) | −7.59350e8 | − | 1.31523e9i | −0.664775 | − | 1.15142i | −0.979346 | − | 0.202190i | \(-0.935194\pi\) |
0.314571 | − | 0.949234i | \(-0.398139\pi\) | |||||||
\(104\) | −3.61471e7 | −0.0302987 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.45137e8 | 0.727140 | ||||||||
\(107\) | 1.00932e8 | + | 1.74819e8i | 0.0744390 | + | 0.128932i | 0.900842 | − | 0.434147i | \(-0.142950\pi\) |
−0.826403 | + | 0.563079i | \(0.809617\pi\) | |||||||
\(108\) | 3.45014e8 | − | 5.97581e8i | 0.244022 | − | 0.422659i | ||||
\(109\) | 4.36976e8 | − | 7.56865e8i | 0.296509 | − | 0.513569i | −0.678826 | − | 0.734300i | \(-0.737511\pi\) |
0.975335 | + | 0.220730i | \(0.0708441\pi\) | |||||||
\(110\) | −1.15825e9 | − | 2.00615e9i | −0.754284 | − | 1.30646i | ||||
\(111\) | 1.41802e9 | 0.886603 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.52955e9 | 0.882491 | 0.441245 | − | 0.897386i | \(-0.354537\pi\) | ||||
0.441245 | + | 0.897386i | \(0.354537\pi\) | |||||||
\(114\) | 1.55508e8 | + | 2.69347e8i | 0.0862343 | + | 0.149362i | ||||
\(115\) | 1.22435e9 | − | 2.12063e9i | 0.652777 | − | 1.13064i | ||||
\(116\) | −2.38330e8 | + | 4.12800e8i | −0.122213 | + | 0.211680i | ||||
\(117\) | −1.12337e7 | − | 1.94573e7i | −0.00554226 | − | 0.00959947i | ||||
\(118\) | −8.55621e7 | −0.0406268 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.54834e9 | −1.56210 | ||||||||
\(121\) | −2.88904e9 | − | 5.00396e9i | −1.22523 | − | 2.12217i | ||||
\(122\) | 1.13025e9 | − | 1.95765e9i | 0.461907 | − | 0.800046i | ||||
\(123\) | −1.08298e9 | + | 1.87578e9i | −0.426626 | + | 0.738938i | ||||
\(124\) | −1.61325e9 | − | 2.79424e9i | −0.612781 | − | 1.06137i | ||||
\(125\) | 4.06429e8 | 0.148898 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.71958e8 | −0.297426 | −0.148713 | − | 0.988880i | \(-0.547513\pi\) | ||||
−0.148713 | + | 0.988880i | \(0.547513\pi\) | |||||||
\(128\) | 1.07636e9 | + | 1.86431e9i | 0.354415 | + | 0.613865i | ||||
\(129\) | −2.43123e9 | + | 4.21101e9i | −0.772987 | + | 1.33885i | ||||
\(130\) | 4.10895e7 | − | 7.11690e7i | 0.0126179 | − | 0.0218548i | ||||
\(131\) | 1.12202e9 | + | 1.94339e9i | 0.332874 | + | 0.576554i | 0.983074 | − | 0.183209i | \(-0.0586484\pi\) |
−0.650200 | + | 0.759763i | \(0.725315\pi\) | |||||||
\(132\) | −4.91565e9 | −1.40928 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.55353e9 | −0.416245 | ||||||||
\(135\) | 1.98860e9 | + | 3.44436e9i | 0.515283 | + | 0.892497i | ||||
\(136\) | −6.57981e8 | + | 1.13966e9i | −0.164926 | + | 0.285660i | ||||
\(137\) | −2.08071e9 | + | 3.60389e9i | −0.504624 | + | 0.874035i | 0.495361 | + | 0.868687i | \(0.335036\pi\) |
−0.999986 | + | 0.00534799i | \(0.998298\pi\) | |||||||
\(138\) | 1.39069e9 | + | 2.40874e9i | 0.326418 | + | 0.565372i | ||||
\(139\) | 6.03383e9 | 1.37097 | 0.685483 | − | 0.728089i | \(-0.259591\pi\) | ||||
0.685483 | + | 0.728089i | \(0.259591\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.76438e9 | −0.375928 | ||||||||
\(142\) | −9.65283e8 | − | 1.67192e9i | −0.199231 | − | 0.345078i | ||||
\(143\) | 1.44315e8 | − | 2.49960e8i | 0.0288601 | − | 0.0499872i | ||||
\(144\) | −6.95801e7 | + | 1.20516e8i | −0.0134851 | + | 0.0233569i | ||||
\(145\) | −1.37370e9 | − | 2.37931e9i | −0.258069 | − | 0.446988i | ||||
\(146\) | −2.13979e9 | −0.389747 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.89385e9 | 0.495790 | ||||||||
\(149\) | 2.18916e9 | + | 3.79173e9i | 0.363864 | + | 0.630231i | 0.988593 | − | 0.150611i | \(-0.0481240\pi\) |
−0.624729 | + | 0.780841i | \(0.714791\pi\) | |||||||
\(150\) | 1.90134e9 | − | 3.29322e9i | 0.306655 | − | 0.531141i | ||||
\(151\) | 1.34682e9 | − | 2.33277e9i | 0.210821 | − | 0.365153i | −0.741151 | − | 0.671339i | \(-0.765720\pi\) |
0.951972 | + | 0.306186i | \(0.0990529\pi\) | |||||||
\(152\) | 8.04581e8 | + | 1.39358e9i | 0.122257 | + | 0.211755i | ||||
\(153\) | −8.17943e8 | −0.120673 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.85971e10 | 2.58793 | ||||||||
\(156\) | −8.71925e7 | − | 1.51022e8i | −0.0117874 | − | 0.0204164i | ||||
\(157\) | −6.65221e8 | + | 1.15220e9i | −0.0873810 | + | 0.151348i | −0.906403 | − | 0.422413i | \(-0.861183\pi\) |
0.819022 | + | 0.573762i | \(0.194516\pi\) | |||||||
\(158\) | 3.26885e9 | − | 5.66181e9i | 0.417290 | − | 0.722768i | ||||
\(159\) | 5.77997e9 | + | 1.00112e10i | 0.717197 | + | 1.24222i | ||||
\(160\) | −1.16265e10 | −1.40251 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −6.36401e9 | −0.725961 | ||||||||
\(163\) | 1.78047e9 | + | 3.08387e9i | 0.197556 | + | 0.342177i | 0.947736 | − | 0.319057i | \(-0.103366\pi\) |
−0.750179 | + | 0.661234i | \(0.770033\pi\) | |||||||
\(164\) | −2.21011e9 | + | 3.82802e9i | −0.238570 | + | 0.413216i | ||||
\(165\) | 1.41665e10 | − | 2.45371e10i | 1.48794 | − | 2.57719i | ||||
\(166\) | −5.55532e8 | − | 9.62210e8i | −0.0567836 | − | 0.0983521i | ||||
\(167\) | 1.04285e10 | 1.03752 | 0.518762 | − | 0.854919i | \(-0.326393\pi\) | ||||
0.518762 | + | 0.854919i | \(0.326393\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05943e10 | −0.999034 | ||||||||
\(170\) | −1.49589e9 | − | 2.59096e9i | −0.137366 | − | 0.237926i | ||||
\(171\) | −5.00092e8 | + | 8.66184e8i | −0.0447267 | + | 0.0774690i | ||||
\(172\) | −4.96157e9 | + | 8.59369e9i | −0.432256 | + | 0.748690i | ||||
\(173\) | 1.02358e10 | + | 1.77290e10i | 0.868793 | + | 1.50479i | 0.863231 | + | 0.504808i | \(0.168437\pi\) |
0.00556121 | + | 0.999985i | \(0.498230\pi\) | |||||||
\(174\) | 3.12066e9 | 0.258092 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.78773e9 | −0.140442 | ||||||||
\(177\) | −5.23254e8 | − | 9.06302e8i | −0.0400712 | − | 0.0694054i | ||||
\(178\) | 1.39007e7 | − | 2.40768e7i | 0.00103788 | − | 0.00179766i | ||||
\(179\) | −2.73353e9 | + | 4.73461e9i | −0.199014 | + | 0.344703i | −0.948209 | − | 0.317647i | \(-0.897107\pi\) |
0.749195 | + | 0.662350i | \(0.230441\pi\) | |||||||
\(180\) | −2.25045e9 | − | 3.89789e9i | −0.159787 | − | 0.276760i | ||||
\(181\) | 2.11628e9 | 0.146561 | 0.0732807 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732807 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.76481e10 | 1.82236 | ||||||||
\(184\) | 7.19528e9 | + | 1.24626e10i | 0.462773 | + | 0.801546i | ||||
\(185\) | −8.33984e9 | + | 1.44450e10i | −0.523462 | + | 0.906662i | ||||
\(186\) | −1.05618e10 | + | 1.82936e10i | −0.647040 | + | 1.12071i | ||||
\(187\) | −5.25389e9 | − | 9.10000e9i | −0.314191 | − | 0.544194i | ||||
\(188\) | −3.60068e9 | −0.210220 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.65836e9 | −0.203655 | ||||||||
\(191\) | −8.62104e9 | − | 1.49321e10i | −0.468715 | − | 0.811839i | 0.530645 | − | 0.847594i | \(-0.321950\pi\) |
−0.999361 | + | 0.0357551i | \(0.988616\pi\) | |||||||
\(192\) | 5.77387e9 | − | 1.00006e10i | 0.306628 | − | 0.531095i | ||||
\(193\) | −1.01015e10 | + | 1.74963e10i | −0.524055 | + | 0.907691i | 0.475552 | + | 0.879687i | \(0.342248\pi\) |
−0.999608 | + | 0.0280032i | \(0.991085\pi\) | |||||||
\(194\) | −2.11023e9 | − | 3.65502e9i | −0.106960 | − | 0.185260i | ||||
\(195\) | 1.00513e9 | 0.0497812 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.22592e10 | −1.05296 | −0.526481 | − | 0.850187i | \(-0.676489\pi\) | ||||
−0.526481 | + | 0.850187i | \(0.676489\pi\) | |||||||
\(198\) | 4.23082e9 | + | 7.32800e9i | 0.195628 | + | 0.338838i | ||||
\(199\) | 8.52940e9 | − | 1.47733e10i | 0.385549 | − | 0.667790i | −0.606296 | − | 0.795239i | \(-0.707345\pi\) |
0.991845 | + | 0.127449i | \(0.0406788\pi\) | |||||||
\(200\) | 9.83736e9 | − | 1.70388e10i | 0.434754 | − | 0.753016i | ||||
\(201\) | −9.50060e9 | − | 1.64555e10i | −0.410553 | − | 0.711098i | ||||
\(202\) | 7.68029e9 | 0.324561 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.34862e9 | −0.256651 | ||||||||
\(205\) | −1.27387e10 | − | 2.20641e10i | −0.503771 | − | 0.872557i | ||||
\(206\) | −1.01455e10 | + | 1.75725e10i | −0.392527 | + | 0.679877i | ||||
\(207\) | −4.47227e9 | + | 7.74619e9i | −0.169302 | + | 0.293239i | ||||
\(208\) | −3.17104e7 | − | 5.49239e7i | −0.00117467 | − | 0.00203459i | ||||
\(209\) | −1.28489e10 | −0.465810 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.19873e10 | −1.11098 | −0.555490 | − | 0.831523i | \(-0.687469\pi\) | ||||
−0.555490 | + | 0.831523i | \(0.687469\pi\) | |||||||
\(212\) | 1.17956e10 | + | 2.04305e10i | 0.401058 | + | 0.694653i | ||||
\(213\) | 1.18063e10 | − | 2.04492e10i | 0.393013 | − | 0.680719i | ||||
\(214\) | 1.34852e9 | − | 2.33571e9i | 0.0439537 | − | 0.0761300i | ||||
\(215\) | −2.85977e10 | − | 4.95327e10i | −0.912763 | − | 1.58095i | ||||
\(216\) | −2.33734e10 | −0.730599 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.16766e10 | −0.350157 | ||||||||
\(219\) | −1.30858e10 | − | 2.26653e10i | −0.384417 | − | 0.665830i | ||||
\(220\) | 2.89105e10 | − | 5.00745e10i | 0.832059 | − | 1.44117i | ||||
\(221\) | 1.86384e8 | − | 3.22827e8i | 0.00525586 | − | 0.00910342i | ||||
\(222\) | −9.47289e9 | − | 1.64075e10i | −0.261754 | − | 0.453372i | ||||
\(223\) | 2.30967e10 | 0.625428 | 0.312714 | − | 0.949847i | \(-0.398762\pi\) | ||||
0.312714 | + | 0.949847i | \(0.398762\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.22289e10 | 0.318102 | ||||||||
\(226\) | −1.02179e10 | − | 1.76980e10i | −0.260540 | − | 0.451269i | ||||
\(227\) | −1.15447e10 | + | 1.99960e10i | −0.288580 | + | 0.499836i | −0.973471 | − | 0.228810i | \(-0.926517\pi\) |
0.684891 | + | 0.728646i | \(0.259850\pi\) | |||||||
\(228\) | −3.88156e9 | + | 6.72305e9i | −0.0951260 | + | 0.164763i | ||||
\(229\) | 2.12748e10 | + | 3.68490e10i | 0.511218 | + | 0.885455i | 0.999915 | + | 0.0130017i | \(0.00413870\pi\) |
−0.488698 | + | 0.872453i | \(0.662528\pi\) | |||||||
\(230\) | −3.27164e10 | −0.770885 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.61460e10 | 0.365905 | ||||||||
\(233\) | 6.33397e9 | + | 1.09708e10i | 0.140791 | + | 0.243857i | 0.927795 | − | 0.373091i | \(-0.121702\pi\) |
−0.787004 | + | 0.616948i | \(0.788369\pi\) | |||||||
\(234\) | −1.50090e8 | + | 2.59964e8i | −0.00327252 | + | 0.00566816i | ||||
\(235\) | 1.03769e10 | − | 1.79733e10i | 0.221953 | − | 0.384434i | ||||
\(236\) | −1.06784e9 | − | 1.84955e9i | −0.0224079 | − | 0.0388117i | ||||
\(237\) | 7.99624e10 | 1.64633 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.37875e10 | 1.26458 | 0.632289 | − | 0.774733i | \(-0.282116\pi\) | ||||
0.632289 | + | 0.774733i | \(0.282116\pi\) | |||||||
\(240\) | −3.11282e9 | − | 5.39156e9i | −0.0605624 | − | 0.104897i | ||||
\(241\) | −1.45802e10 | + | 2.52537e10i | −0.278412 | + | 0.482223i | −0.970990 | − | 0.239119i | \(-0.923141\pi\) |
0.692579 | + | 0.721342i | \(0.256475\pi\) | |||||||
\(242\) | −3.85996e10 | + | 6.68565e10i | −0.723459 | + | 1.25307i | ||||
\(243\) | −1.85559e10 | − | 3.21398e10i | −0.341393 | − | 0.591309i | ||||
\(244\) | 5.64232e10 | 1.01907 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.89388e10 | 0.503816 | ||||||||
\(247\) | −2.27911e8 | − | 3.94753e8i | −0.00389609 | − | 0.00674823i | ||||
\(248\) | −5.46459e10 | + | 9.46494e10i | −0.917328 | + | 1.58886i | ||||
\(249\) | 6.79470e9 | − | 1.17688e10i | 0.112014 | − | 0.194014i | ||||
\(250\) | −2.71509e9 | − | 4.70268e9i | −0.0439597 | − | 0.0761404i | ||||
\(251\) | −6.28939e10 | −1.00018 | −0.500088 | − | 0.865974i | \(-0.666699\pi\) | ||||
−0.500088 | + | 0.865974i | \(0.666699\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.14907e11 | −1.76320 | ||||||||
\(254\) | 5.82500e9 | + | 1.00892e10i | 0.0878100 | + | 0.152091i | ||||
\(255\) | 1.82962e10 | − | 3.16900e10i | 0.270976 | − | 0.469344i | ||||
\(256\) | 3.24712e10 | − | 5.62419e10i | 0.472519 | − | 0.818427i | ||||
\(257\) | 5.72402e10 | + | 9.91429e10i | 0.818469 | + | 1.41763i | 0.906810 | + | 0.421539i | \(0.138510\pi\) |
−0.0883418 | + | 0.996090i | \(0.528157\pi\) | |||||||
\(258\) | 6.49660e10 | 0.912845 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.05123e9 | 0.0278378 | ||||||||
\(261\) | 5.01780e9 | + | 8.69109e9i | 0.0669316 | + | 0.115929i | ||||
\(262\) | 1.49910e10 | − | 2.59651e10i | 0.196551 | − | 0.340436i | ||||
\(263\) | −7.03523e9 | + | 1.21854e10i | −0.0906728 | + | 0.157050i | −0.907794 | − | 0.419415i | \(-0.862235\pi\) |
0.817122 | + | 0.576465i | \(0.195568\pi\) | |||||||
\(264\) | 8.32541e10 | + | 1.44200e11i | 1.05484 | + | 1.82704i | ||||
\(265\) | −1.35975e11 | −1.69377 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.40038e8 | 0.00409475 | ||||||||
\(268\) | −1.93885e10 | − | 3.35819e10i | −0.229582 | − | 0.397648i | ||||
\(269\) | 4.19572e10 | − | 7.26719e10i | 0.488563 | − | 0.846216i | −0.511350 | − | 0.859372i | \(-0.670854\pi\) |
0.999913 | + | 0.0131560i | \(0.00418781\pi\) | |||||||
\(270\) | 2.65692e10 | − | 4.60192e10i | 0.304257 | − | 0.526989i | ||||
\(271\) | 9.92007e9 | + | 1.71821e10i | 0.111726 | + | 0.193514i | 0.916466 | − | 0.400112i | \(-0.131029\pi\) |
−0.804740 | + | 0.593627i | \(0.797696\pi\) | |||||||
\(272\) | −2.30888e9 | −0.0255765 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.55995e10 | 0.595927 | ||||||||
\(275\) | 7.85499e10 | + | 1.36052e11i | 0.828225 | + | 1.43453i | ||||
\(276\) | −3.47123e10 | + | 6.01235e10i | −0.360075 | + | 0.623668i | ||||
\(277\) | 3.58956e10 | − | 6.21729e10i | 0.366338 | − | 0.634516i | −0.622652 | − | 0.782499i | \(-0.713945\pi\) |
0.988990 | + | 0.147983i | \(0.0472781\pi\) | |||||||
\(278\) | −4.03082e10 | − | 6.98158e10i | −0.404754 | − | 0.701055i | ||||
\(279\) | −6.79308e10 | −0.671194 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.02853e11 | 0.984101 | 0.492050 | − | 0.870567i | \(-0.336248\pi\) | ||||
0.492050 | + | 0.870567i | \(0.336248\pi\) | |||||||
\(282\) | 1.17867e10 | + | 2.04151e10i | 0.110986 | + | 0.192234i | ||||
\(283\) | −2.76441e10 | + | 4.78810e10i | −0.256191 | + | 0.443736i | −0.965218 | − | 0.261445i | \(-0.915801\pi\) |
0.709027 | + | 0.705181i | \(0.249134\pi\) | |||||||
\(284\) | 2.40940e10 | − | 4.17320e10i | 0.219774 | − | 0.380660i | ||||
\(285\) | −2.23727e10 | − | 3.87506e10i | −0.200870 | − | 0.347918i | ||||
\(286\) | −3.85630e9 | −0.0340819 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.24688e10 | 0.363750 | ||||||||
\(289\) | 5.25085e10 | + | 9.09474e10i | 0.442781 | + | 0.766920i | ||||
\(290\) | −1.83536e10 | + | 3.17894e10i | −0.152381 | + | 0.263931i | ||||
\(291\) | 2.58101e10 | − | 4.47044e10i | 0.210995 | − | 0.365453i | ||||
\(292\) | −2.67051e10 | − | 4.62546e10i | −0.214967 | − | 0.372334i | ||||
\(293\) | −1.05721e11 | −0.838028 | −0.419014 | − | 0.907980i | \(-0.637624\pi\) | ||||
−0.419014 | + | 0.907980i | \(0.637624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.23097e10 | 0.0946343 | ||||||||
\(296\) | −4.90118e10 | − | 8.48909e10i | −0.371097 | − | 0.642760i | ||||
\(297\) | 9.33164e10 | − | 1.61629e11i | 0.695912 | − | 1.20535i | ||||
\(298\) | 2.92487e10 | − | 5.06603e10i | 0.214849 | − | 0.372130i | ||||
\(299\) | −2.03818e9 | − | 3.53024e9i | −0.0147477 | − | 0.0255437i | ||||
\(300\) | 9.49171e10 | 0.676548 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.59891e10 | −0.248966 | ||||||||
\(303\) | 4.69687e10 | + | 8.13521e10i | 0.320123 | + | 0.554469i | ||||
\(304\) | −1.41165e9 | + | 2.44505e9i | −0.00947974 | + | 0.0164194i | ||||
\(305\) | −1.62607e11 | + | 2.81644e11i | −1.07595 | + | 1.86359i | ||||
\(306\) | 5.46416e9 | + | 9.46420e9i | 0.0356268 | + | 0.0617074i | ||||
\(307\) | 8.10064e10 | 0.520471 | 0.260236 | − | 0.965545i | \(-0.416200\pi\) | ||||
0.260236 | + | 0.965545i | \(0.416200\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.48178e11 | −1.54864 | ||||||||
\(310\) | −1.24235e11 | − | 2.15182e11i | −0.764041 | − | 1.32336i | ||||
\(311\) | −1.59217e11 | + | 2.75772e11i | −0.965091 | + | 1.67159i | −0.255722 | + | 0.966750i | \(0.582313\pi\) |
−0.709369 | + | 0.704837i | \(0.751020\pi\) | |||||||
\(312\) | −2.95348e9 | + | 5.11558e9i | −0.0176457 | + | 0.0305632i | ||||
\(313\) | 6.44379e10 | + | 1.11610e11i | 0.379483 | + | 0.657283i | 0.990987 | − | 0.133958i | \(-0.0427687\pi\) |
−0.611504 | + | 0.791241i | \(0.709435\pi\) | |||||||
\(314\) | 1.77757e10 | 0.103191 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.63185e11 | 0.920635 | ||||||||
\(317\) | 3.72361e10 | + | 6.44948e10i | 0.207108 | + | 0.358722i | 0.950802 | − | 0.309798i | \(-0.100261\pi\) |
−0.743694 | + | 0.668520i | \(0.766928\pi\) | |||||||
\(318\) | 7.72245e10 | − | 1.33757e11i | 0.423480 | − | 0.733490i | ||||
\(319\) | −6.44616e10 | + | 1.11651e11i | −0.348532 | + | 0.603676i | ||||
\(320\) | 6.79160e10 | + | 1.17634e11i | 0.362074 | + | 0.627131i | ||||
\(321\) | 3.29874e10 | 0.173411 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.65945e10 | −0.0848309 | ||||||||
\(324\) | −7.94246e10 | − | 1.37567e11i | −0.400408 | − | 0.693526i | ||||
\(325\) | −2.78660e9 | + | 4.82652e9i | −0.0138548 | + | 0.0239971i | ||||
\(326\) | 2.37884e10 | − | 4.12027e10i | 0.116650 | − | 0.202044i | ||||
\(327\) | −7.14082e10 | − | 1.23683e11i | −0.345369 | − | 0.598197i | ||||
\(328\) | 1.49726e11 | 0.714276 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −3.78550e11 | −1.75715 | ||||||||
\(331\) | −1.41920e11 | − | 2.45813e11i | −0.649857 | − | 1.12559i | −0.983157 | − | 0.182764i | \(-0.941495\pi\) |
0.333300 | − | 0.942821i | \(-0.391838\pi\) | |||||||
\(332\) | 1.38664e10 | − | 2.40173e10i | 0.0626386 | − | 0.108493i | ||||
\(333\) | 3.04635e10 | − | 5.27644e10i | 0.135763 | − | 0.235148i | ||||
\(334\) | −6.96662e10 | − | 1.20665e11i | −0.306311 | − | 0.530547i | ||||
\(335\) | 2.23505e11 | 0.969583 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.61414e9 | −0.0237109 | −0.0118555 | − | 0.999930i | \(-0.503774\pi\) | ||||
−0.0118555 | + | 0.999930i | \(0.503774\pi\) | |||||||
\(338\) | 7.07735e10 | + | 1.22583e11i | 0.294948 | + | 0.510865i | ||||
\(339\) | 1.24975e11 | − | 2.16463e11i | 0.513955 | − | 0.890197i | ||||
\(340\) | 3.73383e10 | − | 6.46719e10i | 0.151530 | − | 0.262458i | ||||
\(341\) | −4.36339e11 | − | 7.55762e11i | −1.74755 | − | 3.02685i | ||||
\(342\) | 1.33632e10 | 0.0528192 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.36128e11 | 1.29417 | ||||||||
\(345\) | −2.00076e11 | − | 3.46542e11i | −0.760343 | − | 1.31695i | ||||
\(346\) | 1.36758e11 | − | 2.36872e11i | 0.512993 | − | 0.888529i | ||||
\(347\) | −1.69923e11 | + | 2.94315e11i | −0.629171 | + | 1.08976i | 0.358547 | + | 0.933512i | \(0.383272\pi\) |
−0.987718 | + | 0.156245i | \(0.950061\pi\) | |||||||
\(348\) | 3.89466e10 | + | 6.74576e10i | 0.142352 | + | 0.246561i | ||||
\(349\) | −3.46718e10 | −0.125101 | −0.0625506 | − | 0.998042i | \(-0.519923\pi\) | ||||
−0.0625506 | + | 0.998042i | \(0.519923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.62089e9 | 0.0232828 | ||||||||
\(352\) | 2.72789e11 | + | 4.72485e11i | 0.947077 | + | 1.64039i | ||||
\(353\) | −1.73450e11 | + | 3.00424e11i | −0.594550 | + | 1.02979i | 0.399060 | + | 0.916925i | \(0.369336\pi\) |
−0.993610 | + | 0.112866i | \(0.963997\pi\) | |||||||
\(354\) | −6.99105e9 | + | 1.21088e10i | −0.0236607 | + | 0.0409815i | ||||
\(355\) | 1.38874e11 | + | 2.40537e11i | 0.464080 | + | 0.803811i | ||||
\(356\) | 6.93939e8 | 0.00228979 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.30438e10 | 0.235023 | ||||||||
\(359\) | 1.25506e11 | + | 2.17382e11i | 0.398785 | + | 0.690715i | 0.993576 | − | 0.113165i | \(-0.0360988\pi\) |
−0.594792 | + | 0.803880i | \(0.702765\pi\) | |||||||
\(360\) | −7.62296e10 | + | 1.32034e11i | −0.239201 | + | 0.414308i | ||||
\(361\) | 1.51198e11 | − | 2.61882e11i | 0.468558 | − | 0.811566i | ||||
\(362\) | −1.41375e10 | − | 2.44869e10i | −0.0432698 | − | 0.0749455i | ||||
\(363\) | −9.44221e11 | −2.85426 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.07848e11 | 0.907859 | ||||||||
\(366\) | −1.84699e11 | − | 3.19908e11i | −0.538022 | − | 0.931881i | ||||
\(367\) | 2.39936e11 | − | 4.15581e11i | 0.690394 | − | 1.19580i | −0.281314 | − | 0.959616i | \(-0.590770\pi\) |
0.971709 | − | 0.236183i | \(-0.0758963\pi\) | |||||||
\(368\) | −1.26243e10 | + | 2.18658e10i | −0.0358831 | + | 0.0621514i | ||||
\(369\) | 4.65316e10 | + | 8.05951e10i | 0.130656 | + | 0.226303i | ||||
\(370\) | 2.22853e11 | 0.618173 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.27258e11 | −1.42751 | ||||||||
\(373\) | 9.23970e10 | + | 1.60036e11i | 0.247154 | + | 0.428084i | 0.962735 | − | 0.270446i | \(-0.0871713\pi\) |
−0.715581 | + | 0.698530i | \(0.753838\pi\) | |||||||
\(374\) | −7.01957e10 | + | 1.21583e11i | −0.185519 | + | 0.321328i | ||||
\(375\) | 3.32082e10 | − | 5.75183e10i | 0.0867171 | − | 0.150198i | ||||
\(376\) | 6.09831e10 | + | 1.05626e11i | 0.157349 | + | 0.272536i | ||||
\(377\) | −4.57361e9 | −0.0116607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7.08908e11 | −1.76487 | −0.882437 | − | 0.470431i | \(-0.844098\pi\) | ||||
−0.882437 | + | 0.470431i | \(0.844098\pi\) | |||||||
\(380\) | −4.56574e10 | − | 7.90809e10i | −0.112327 | − | 0.194556i | ||||
\(381\) | −7.12453e10 | + | 1.23401e11i | −0.173218 | + | 0.300023i | ||||
\(382\) | −1.15183e11 | + | 1.99503e11i | −0.276761 | + | 0.479364i | ||||
\(383\) | 6.18945e10 | + | 1.07204e11i | 0.146980 | + | 0.254576i | 0.930110 | − | 0.367282i | \(-0.119711\pi\) |
−0.783130 | + | 0.621858i | \(0.786378\pi\) | |||||||
\(384\) | 3.51785e11 | 0.825633 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.69926e11 | 0.618874 | ||||||||
\(387\) | 1.04461e11 | + | 1.80932e11i | 0.236731 | + | 0.410029i | ||||
\(388\) | 5.26724e10 | − | 9.12313e10i | 0.117989 | − | 0.204362i | ||||
\(389\) | 1.48985e11 | − | 2.58050e11i | 0.329891 | − | 0.571388i | −0.652599 | − | 0.757704i | \(-0.726321\pi\) |
0.982490 | + | 0.186315i | \(0.0596547\pi\) | |||||||
\(390\) | −6.71462e9 | − | 1.16301e10i | −0.0146971 | − | 0.0254561i | ||||
\(391\) | −1.48403e11 | −0.321106 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.66708e11 | 0.775451 | ||||||||
\(394\) | 1.48700e11 | + | 2.57556e11i | 0.310869 | + | 0.538441i | ||||
\(395\) | −4.70285e11 | + | 8.14557e11i | −0.972018 | + | 1.68358i | ||||
\(396\) | −1.05604e11 | + | 1.82911e11i | −0.215800 | + | 0.373776i | ||||
\(397\) | 2.66713e11 | + | 4.61960e11i | 0.538873 | + | 0.933356i | 0.998965 | + | 0.0454846i | \(0.0144832\pi\) |
−0.460092 | + | 0.887871i | \(0.652183\pi\) | |||||||
\(398\) | −2.27918e11 | −0.455307 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.45196e10 | 0.0674212 | ||||||||
\(401\) | −2.07820e11 | − | 3.59954e11i | −0.401363 | − | 0.695181i | 0.592528 | − | 0.805550i | \(-0.298130\pi\) |
−0.993891 | + | 0.110369i | \(0.964797\pi\) | |||||||
\(402\) | −1.26935e11 | + | 2.19858e11i | −0.242418 | + | 0.419879i | ||||
\(403\) | 1.54794e10 | − | 2.68110e10i | 0.0292335 | − | 0.0506338i | ||||
\(404\) | 9.58521e10 | + | 1.66021e11i | 0.179013 | + | 0.310060i | ||||
\(405\) | 9.15581e11 | 1.69102 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.82704e11 | 1.41391 | ||||||||
\(408\) | 1.07524e11 | + | 1.86237e11i | 0.192103 | + | 0.332732i | ||||
\(409\) | 5.39891e11 | − | 9.35118e11i | 0.954006 | − | 1.65239i | 0.217379 | − | 0.976087i | \(-0.430249\pi\) |
0.736627 | − | 0.676299i | \(-0.236417\pi\) | |||||||
\(410\) | −1.70198e11 | + | 2.94792e11i | −0.297460 | + | 0.515215i | ||||
\(411\) | 3.40018e11 | + | 5.88928e11i | 0.587778 | + | 1.01806i | ||||
\(412\) | −5.06473e11 | −0.866002 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.19505e11 | 0.199934 | ||||||||
\(415\) | 7.99237e10 | + | 1.38432e11i | 0.132269 | + | 0.229097i | ||||
\(416\) | −9.67733e9 | + | 1.67616e10i | −0.0158429 | + | 0.0274408i | ||||
\(417\) | 4.93008e11 | − | 8.53914e11i | 0.798439 | − | 1.38294i | ||||
\(418\) | 8.58355e10 | + | 1.48671e11i | 0.137522 | + | 0.238196i | ||||
\(419\) | 2.20998e11 | 0.350289 | 0.175144 | − | 0.984543i | \(-0.443961\pi\) | ||||
0.175144 | + | 0.984543i | \(0.443961\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.47478e11 | 0.539086 | 0.269543 | − | 0.962988i | \(-0.413127\pi\) | ||||
0.269543 | + | 0.962988i | \(0.413127\pi\) | |||||||
\(422\) | 2.13687e11 | + | 3.70116e11i | 0.327998 | + | 0.568109i | ||||
\(423\) | −3.79043e10 | + | 6.56522e10i | −0.0575648 | + | 0.0997052i | ||||
\(424\) | 3.99552e11 | − | 6.92045e11i | 0.600381 | − | 1.03989i | ||||
\(425\) | 1.01448e11 | + | 1.75713e11i | 0.150832 | + | 0.261249i | ||||
\(426\) | −3.15483e11 | −0.464122 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.73196e10 | 0.0969716 | ||||||||
\(429\) | −2.35831e10 | − | 4.08472e10i | −0.0336158 | − | 0.0582243i | ||||
\(430\) | −3.82086e11 | + | 6.61792e11i | −0.538956 | + | 0.933499i | ||||
\(431\) | −6.17869e10 | + | 1.07018e11i | −0.0862479 | + | 0.149386i | −0.905922 | − | 0.423444i | \(-0.860821\pi\) |
0.819674 | + | 0.572830i | \(0.194154\pi\) | |||||||
\(432\) | −2.05045e10 | − | 3.55148e10i | −0.0283251 | − | 0.0490606i | ||||
\(433\) | 7.27679e11 | 0.994820 | 0.497410 | − | 0.867516i | \(-0.334284\pi\) | ||||
0.497410 | + | 0.867516i | \(0.334284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.48964e11 | −0.601188 | ||||||||
\(436\) | −1.45728e11 | − | 2.52408e11i | −0.193131 | − | 0.334513i | ||||
\(437\) | −9.07340e10 | + | 1.57156e11i | −0.119015 | + | 0.206141i | ||||
\(438\) | −1.74836e11 | + | 3.02825e11i | −0.226985 | + | 0.393150i | ||||
\(439\) | −2.92983e11 | − | 5.07461e11i | −0.376489 | − | 0.652097i | 0.614060 | − | 0.789259i | \(-0.289535\pi\) |
−0.990549 | + | 0.137162i | \(0.956202\pi\) | |||||||
\(440\) | −1.95858e12 | −2.49117 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.98045e9 | −0.00620681 | ||||||||
\(443\) | 1.05773e11 | + | 1.83204e11i | 0.130484 | + | 0.226006i | 0.923863 | − | 0.382722i | \(-0.125013\pi\) |
−0.793379 | + | 0.608728i | \(0.791680\pi\) | |||||||
\(444\) | 2.36448e11 | − | 4.09541e11i | 0.288744 | − | 0.500120i | ||||
\(445\) | −1.99988e9 | + | 3.46389e9i | −0.00241759 | + | 0.00418739i | ||||
\(446\) | −1.54294e11 | − | 2.67245e11i | −0.184647 | − | 0.319818i | ||||
\(447\) | 7.15480e11 | 0.847645 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.21048e11 | −1.06948 | −0.534741 | − | 0.845016i | \(-0.679591\pi\) | ||||
−0.534741 | + | 0.845016i | \(0.679591\pi\) | |||||||
\(450\) | −8.16936e10 | − | 1.41497e11i | −0.0939143 | − | 0.162664i | ||||
\(451\) | −5.97772e11 | + | 1.03537e12i | −0.680363 | + | 1.17842i | ||||
\(452\) | 2.55045e11 | − | 4.41751e11i | 0.287405 | − | 0.497800i | ||||
\(453\) | −2.20090e11 | − | 3.81208e11i | −0.245561 | − | 0.425324i | ||||
\(454\) | 3.08491e11 | 0.340794 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.62961e11 | 0.284806 | ||||||||
\(457\) | −4.05592e11 | − | 7.02506e11i | −0.434977 | − | 0.753403i | 0.562316 | − | 0.826922i | \(-0.309910\pi\) |
−0.997294 | + | 0.0735191i | \(0.976577\pi\) | |||||||
\(458\) | 2.84247e11 | − | 4.92330e11i | 0.301857 | − | 0.522831i | ||||
\(459\) | 1.20519e11 | − | 2.08746e11i | 0.126736 | − | 0.219513i | ||||
\(460\) | −4.08309e11 | − | 7.07212e11i | −0.425186 | − | 0.736444i | ||||
\(461\) | 1.90069e11 | 0.196001 | 0.0980004 | − | 0.995186i | \(-0.468755\pi\) | ||||
0.0980004 | + | 0.995186i | \(0.468755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.76945e11 | 0.482341 | 0.241170 | − | 0.970483i | \(-0.422469\pi\) | ||||
0.241170 | + | 0.970483i | \(0.422469\pi\) | |||||||
\(464\) | 1.41642e10 | + | 2.45331e10i | 0.0141860 | + | 0.0245709i | ||||
\(465\) | 1.51952e12 | − | 2.63188e12i | 1.50719 | − | 2.61052i | ||||
\(466\) | 8.46264e10 | − | 1.46577e11i | 0.0831322 | − | 0.143989i | ||||
\(467\) | 5.31958e11 | + | 9.21379e11i | 0.517549 | + | 0.896422i | 0.999792 | + | 0.0203841i | \(0.00648891\pi\) |
−0.482243 | + | 0.876038i | \(0.660178\pi\) | |||||||
\(468\) | −7.49268e9 | −0.00721990 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.77285e11 | −0.262111 | ||||||||
\(471\) | 1.08707e11 | + | 1.88286e11i | 0.101780 | + | 0.176288i | ||||
\(472\) | −3.61710e10 | + | 6.26500e10i | −0.0335445 | + | 0.0581008i | ||||
\(473\) | −1.34196e12 | + | 2.32435e12i | −1.23272 | + | 2.13514i | ||||
\(474\) | −5.34178e11 | − | 9.25223e11i | −0.486053 | − | 0.841868i | ||||
\(475\) | 2.48102e11 | 0.223619 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.96687e11 | 0.439289 | ||||||||
\(478\) | −4.26124e11 | − | 7.38068e11i | −0.373345 | − | 0.646653i | ||||
\(479\) | −4.21707e11 | + | 7.30419e11i | −0.366017 | + | 0.633960i | −0.988939 | − | 0.148324i | \(-0.952612\pi\) |
0.622922 | + | 0.782284i | \(0.285946\pi\) | |||||||
\(480\) | −9.49966e11 | + | 1.64539e12i | −0.816812 | + | 1.41476i | ||||
\(481\) | 1.38834e10 | + | 2.40468e10i | 0.0118261 | + | 0.0204835i | ||||
\(482\) | 3.89605e11 | 0.328785 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.92694e12 | −1.59611 | ||||||||
\(485\) | 3.03595e11 | + | 5.25842e11i | 0.249148 | + | 0.431537i | ||||
\(486\) | −2.47920e11 | + | 4.29411e11i | −0.201581 | + | 0.349148i | ||||
\(487\) | −5.76008e11 | + | 9.97675e11i | −0.464032 | + | 0.803728i | −0.999157 | − | 0.0410453i | \(-0.986931\pi\) |
0.535125 | + | 0.844773i | \(0.320265\pi\) | |||||||
\(488\) | −9.55615e11 | − | 1.65517e12i | −0.762770 | − | 1.32116i | ||||
\(489\) | 5.81910e11 | 0.460220 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.68703e11 | −0.752184 | −0.376092 | − | 0.926582i | \(-0.622732\pi\) | ||||
−0.376092 | + | 0.926582i | \(0.622732\pi\) | |||||||
\(492\) | 3.61164e11 | + | 6.25554e11i | 0.277883 | + | 0.481307i | ||||
\(493\) | −8.32530e10 | + | 1.44198e11i | −0.0634729 | + | 0.109938i | ||||
\(494\) | −3.04506e9 | + | 5.27419e9i | −0.00230051 | + | 0.00398460i | ||||
\(495\) | −6.08682e11 | − | 1.05427e12i | −0.455688 | − | 0.789274i | ||||
\(496\) | −1.91754e11 | −0.142258 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.81564e11 | −0.132281 | ||||||||
\(499\) | −1.31410e12 | − | 2.27609e12i | −0.948805 | − | 1.64338i | −0.747948 | − | 0.663758i | \(-0.768961\pi\) |
−0.200857 | − | 0.979621i | \(-0.564373\pi\) | |||||||
\(500\) | 6.77702e10 | − | 1.17381e11i | 0.0484924 | − | 0.0839913i | ||||
\(501\) | 8.52085e11 | − | 1.47585e12i | 0.604245 | − | 1.04658i | ||||
\(502\) | 4.20154e11 | + | 7.27728e11i | 0.295285 | + | 0.511449i | ||||
\(503\) | −3.95070e11 | −0.275181 | −0.137590 | − | 0.990489i | \(-0.543936\pi\) | ||||
−0.137590 | + | 0.990489i | \(0.543936\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.10495e12 | −0.756019 | ||||||||
\(506\) | 7.67618e11 | + | 1.32955e12i | 0.520556 | + | 0.901630i | ||||
\(507\) | −8.65628e11 | + | 1.49931e12i | −0.581829 | + | 1.00776i | ||||
\(508\) | −1.45395e11 | + | 2.51832e11i | −0.0968641 | + | 0.167774i | ||||
\(509\) | 3.32078e11 | + | 5.75177e11i | 0.219286 | + | 0.379814i | 0.954590 | − | 0.297923i | \(-0.0962939\pi\) |
−0.735304 | + | 0.677737i | \(0.762961\pi\) | |||||||
\(510\) | −4.88901e11 | −0.320004 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.34512e11 | 0.150817 | ||||||||
\(513\) | −1.47371e11 | − | 2.55255e11i | −0.0939474 | − | 0.162722i | ||||
\(514\) | 7.64770e11 | − | 1.32462e12i | 0.483278 | − | 0.837062i | ||||
\(515\) | 1.45961e12 | − | 2.52813e12i | 0.914336 | − | 1.58368i | ||||
\(516\) | 8.10793e11 | + | 1.40433e12i | 0.503485 | + | 0.872061i | ||||
\(517\) | −9.73882e11 | −0.599513 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.34537e12 | 2.02391 | ||||||||
\(520\) | −3.47408e10 | − | 6.01728e10i | −0.0208365 | − | 0.0360898i | ||||
\(521\) | 2.61383e11 | − | 4.52729e11i | 0.155420 | − | 0.269196i | −0.777792 | − | 0.628522i | \(-0.783660\pi\) |
0.933212 | + | 0.359326i | \(0.116993\pi\) | |||||||
\(522\) | 6.70415e10 | − | 1.16119e11i | 0.0395209 | − | 0.0684522i | ||||
\(523\) | −1.54568e12 | − | 2.67719e12i | −0.903360 | − | 1.56467i | −0.823103 | − | 0.567892i | \(-0.807759\pi\) |
−0.0802570 | − | 0.996774i | \(-0.525574\pi\) | |||||||
\(524\) | 7.48366e11 | 0.433634 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.87991e11 | 0.107078 | ||||||||
\(527\) | −5.63538e11 | − | 9.76076e11i | −0.318255 | − | 0.551234i | ||||
\(528\) | −1.46071e11 | + | 2.53002e11i | −0.0817920 | + | 0.141668i | ||||
\(529\) | 8.91523e10 | − | 1.54416e11i | 0.0494974 | − | 0.0857319i | ||||
\(530\) | 9.08365e11 | + | 1.57334e12i | 0.500057 | + | 0.866124i | ||||
\(531\) | −4.49645e10 | −0.0245440 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.24125e10 | −0.0227626 | ||||||||
\(534\) | −2.27158e9 | − | 3.93449e9i | −0.00120891 | − | 0.00209389i | ||||
\(535\) | −1.94010e11 | + | 3.36035e11i | −0.102384 | + | 0.177334i | ||||
\(536\) | −6.56749e11 | + | 1.13752e12i | −0.343683 | + | 0.595276i | ||||
\(537\) | 4.46698e11 | + | 7.73704e11i | 0.231809 | + | 0.401504i | ||||
\(538\) | −1.12116e12 | −0.576960 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.32636e12 | 0.671259 | ||||||||
\(541\) | 7.37449e11 | + | 1.27730e12i | 0.370121 | + | 0.641069i | 0.989584 | − | 0.143957i | \(-0.0459827\pi\) |
−0.619462 | + | 0.785026i | \(0.712649\pi\) | |||||||
\(542\) | 1.32539e11 | − | 2.29565e11i | 0.0659702 | − | 0.114264i | ||||
\(543\) | 1.72916e11 | − | 2.99499e11i | 0.0853561 | − | 0.147841i | ||||
\(544\) | 3.52311e11 | + | 6.10220e11i | 0.172477 | + | 0.298739i | ||||
\(545\) | 1.67990e12 | 0.815642 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.12294e12 | 1.01390 | 0.506949 | − | 0.861976i | \(-0.330773\pi\) | ||||
0.506949 | + | 0.861976i | \(0.330773\pi\) | |||||||
\(548\) | 6.93897e11 | + | 1.20186e12i | 0.328687 | + | 0.569302i | ||||
\(549\) | 5.93967e11 | − | 1.02878e12i | 0.279053 | − | 0.483334i | ||||
\(550\) | 1.04948e12 | − | 1.81776e12i | 0.489039 | − | 0.847040i | ||||
\(551\) | 1.01802e11 | + | 1.76326e11i | 0.0470515 | + | 0.0814957i | ||||
\(552\) | 2.35163e12 | 1.07806 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.59181e11 | −0.432620 | ||||||||
\(555\) | 1.36285e12 | + | 2.36053e12i | 0.609719 | + | 1.05606i | ||||
\(556\) | 1.00611e12 | − | 1.74264e12i | 0.446489 | − | 0.773341i | ||||
\(557\) | 1.76428e12 | − | 3.05583e12i | 0.776641 | − | 1.34518i | −0.157227 | − | 0.987563i | \(-0.550255\pi\) |
0.933868 | − | 0.357619i | \(-0.116411\pi\) | |||||||
\(558\) | 4.53803e11 | + | 7.86009e11i | 0.198159 | + | 0.343221i | ||||
\(559\) | −9.52137e10 | −0.0412426 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.71712e12 | −0.731928 | ||||||||
\(562\) | −6.87097e11 | − | 1.19009e12i | −0.290539 | − | 0.503228i | ||||
\(563\) | −1.67640e12 | + | 2.90361e12i | −0.703218 | + | 1.21801i | 0.264113 | + | 0.964492i | \(0.414921\pi\) |
−0.967331 | + | 0.253517i | \(0.918413\pi\) | |||||||
\(564\) | −2.94202e11 | + | 5.09572e11i | −0.122430 | + | 0.212056i | ||||
\(565\) | 1.47004e12 | + | 2.54618e12i | 0.606892 | + | 1.05117i | ||||
\(566\) | 7.38691e11 | 0.302544 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.63228e12 | −0.658000 | ||||||||
\(569\) | −1.49682e12 | − | 2.59257e12i | −0.598637 | − | 1.03687i | −0.993022 | − | 0.117925i | \(-0.962376\pi\) |
0.394385 | − | 0.918945i | \(-0.370958\pi\) | |||||||
\(570\) | −2.98915e11 | + | 5.17736e11i | −0.118607 | + | 0.205434i | ||||
\(571\) | −2.33634e12 | + | 4.04665e12i | −0.919756 | + | 1.59306i | −0.119971 | + | 0.992777i | \(0.538280\pi\) |
−0.799785 | + | 0.600287i | \(0.795053\pi\) | |||||||
\(572\) | −4.81276e10 | − | 8.33595e10i | −0.0187980 | − | 0.0325592i | ||||
\(573\) | −2.81761e12 | −1.09190 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.21875e12 | 0.846453 | ||||||||
\(576\) | −2.48082e11 | − | 4.29690e11i | −0.0939061 | − | 0.162650i | ||||
\(577\) | −1.81399e12 | + | 3.14193e12i | −0.681310 | + | 1.18006i | 0.293271 | + | 0.956029i | \(0.405256\pi\) |
−0.974581 | + | 0.224034i | \(0.928077\pi\) | |||||||
\(578\) | 7.01551e11 | − | 1.21512e12i | 0.261447 | − | 0.452840i | ||||
\(579\) | 1.65073e12 | + | 2.85915e12i | 0.610411 | + | 1.05726i | ||||
\(580\) | −9.16232e11 | −0.336186 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −6.89683e11 | −0.249170 | ||||||||
\(583\) | 3.19037e12 | + | 5.52588e12i | 1.14375 | + | 1.98104i | ||||
\(584\) | −9.04585e11 | + | 1.56679e12i | −0.321804 | + | 0.557381i | ||||
\(585\) | 2.15933e10 | − | 3.74007e10i | 0.00762286 | − | 0.0132032i | ||||
\(586\) | 7.06258e11 | + | 1.22327e12i | 0.247414 | + | 0.428533i | ||||
\(587\) | −3.97200e12 | −1.38082 | −0.690411 | − | 0.723417i | \(-0.742570\pi\) | ||||
−0.690411 | + | 0.723417i | \(0.742570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.37819e12 | −0.471835 | ||||||||
\(590\) | −8.22332e10 | − | 1.42432e11i | −0.0279392 | − | 0.0483921i | ||||
\(591\) | −1.81874e12 | + | 3.15015e12i | −0.613236 | + | 1.06216i | ||||
\(592\) | 8.59921e10 | − | 1.48943e11i | 0.0287747 | − | 0.0498392i | ||||
\(593\) | 1.33718e12 | + | 2.31606e12i | 0.444061 | + | 0.769137i | 0.997986 | − | 0.0634297i | \(-0.0202039\pi\) |
−0.553925 | + | 0.832567i | \(0.686871\pi\) | |||||||
\(594\) | −2.49355e12 | −0.821825 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.46013e12 | 0.474005 | ||||||||
\(597\) | −1.39383e12 | − | 2.41418e12i | −0.449081 | − | 0.777831i | ||||
\(598\) | −2.72316e10 | + | 4.71665e10i | −0.00870799 | + | 0.0150827i | ||||
\(599\) | −2.42261e12 | + | 4.19608e12i | −0.768887 | + | 1.33175i | 0.169279 | + | 0.985568i | \(0.445856\pi\) |
−0.938167 | + | 0.346184i | \(0.887477\pi\) | |||||||
\(600\) | −1.60757e12 | − | 2.78439e12i | −0.506394 | − | 0.877100i | ||||
\(601\) | 4.64764e12 | 1.45311 | 0.726553 | − | 0.687110i | \(-0.241121\pi\) | ||||
0.726553 | + | 0.687110i | \(0.241121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −8.16411e11 | −0.251467 | ||||||||
\(604\) | −4.49153e11 | − | 7.77956e11i | −0.137318 | − | 0.237842i | ||||
\(605\) | 5.55327e12 | − | 9.61855e12i | 1.68519 | − | 2.91884i | ||||
\(606\) | 6.27536e11 | − | 1.08692e12i | 0.189022 | − | 0.327395i | ||||
\(607\) | −3.26224e12 | − | 5.65036e12i | −0.975363 | − | 1.68938i | −0.678731 | − | 0.734387i | \(-0.737470\pi\) |
−0.296633 | − | 0.954992i | \(-0.595864\pi\) | |||||||
\(608\) | 8.61613e11 | 0.255709 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.34510e12 | 1.27062 | ||||||||
\(611\) | −1.72745e10 | − | 2.99203e10i | −0.00501440 | − | 0.00868520i | ||||
\(612\) | −1.36388e11 | + | 2.36232e11i | −0.0393003 | + | 0.0680701i | ||||
\(613\) | 4.77268e11 | − | 8.26652e11i | 0.136518 | − | 0.236456i | −0.789658 | − | 0.613547i | \(-0.789742\pi\) |
0.926176 | + | 0.377091i | \(0.123075\pi\) | |||||||
\(614\) | −5.41152e11 | − | 9.37303e11i | −0.153660 | − | 0.266148i | ||||
\(615\) | −4.16338e12 | −1.17357 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.50764e12 | −1.25218 | −0.626088 | − | 0.779752i | \(-0.715345\pi\) | ||||
−0.626088 | + | 0.779752i | \(0.715345\pi\) | |||||||
\(618\) | 1.65792e12 | + | 2.87160e12i | 0.457209 | + | 0.791909i | ||||
\(619\) | 1.82173e12 | − | 3.15533e12i | 0.498742 | − | 0.863847i | −0.501257 | − | 0.865298i | \(-0.667129\pi\) |
0.999999 | + | 0.00145199i | \(0.000462184\pi\) | |||||||
\(620\) | 3.10098e12 | − | 5.37105e12i | 0.842822 | − | 1.45981i | ||||
\(621\) | −1.31793e12 | − | 2.28272e12i | −0.355614 | − | 0.615942i | ||||
\(622\) | 4.25452e12 | 1.13971 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.03639e10 | −0.00273647 | ||||||||
\(625\) | 2.09148e12 | + | 3.62255e12i | 0.548269 | + | 0.949630i | ||||
\(626\) | 8.60937e11 | − | 1.49119e12i | 0.224072 | − | 0.388104i | ||||
\(627\) | −1.04985e12 | + | 1.81840e12i | −0.271284 | + | 0.469877i | ||||
\(628\) | 2.21845e11 | + | 3.84247e11i | 0.0569156 | + | 0.0985807i | ||||
\(629\) | 1.01087e12 | 0.257495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.61498e12 | 0.907766 | 0.453883 | − | 0.891061i | \(-0.350038\pi\) | ||||
0.453883 | + | 0.891061i | \(0.350038\pi\) | |||||||
\(632\) | −2.76378e12 | − | 4.78701e12i | −0.689092 | − | 1.19354i | ||||
\(633\) | −2.61359e12 | + | 4.52687e12i | −0.647025 | + | 1.12068i | ||||
\(634\) | 4.97501e11 | − | 8.61698e11i | 0.122290 | − | 0.211813i | ||||
\(635\) | −8.38034e11 | − | 1.45152e12i | −0.204541 | − | 0.354275i | ||||
\(636\) | 3.85513e12 | 0.934292 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.72251e12 | 0.411593 | ||||||||
\(639\) | −5.07275e11 | − | 8.78626e11i | −0.120362 | − | 0.208473i | ||||
\(640\) | −2.06896e12 | + | 3.58355e12i | −0.487465 | + | 0.844313i | ||||
\(641\) | 1.33152e12 | − | 2.30626e12i | 0.311521 | − | 0.539570i | −0.667171 | − | 0.744905i | \(-0.732495\pi\) |
0.978692 | + | 0.205335i | \(0.0658283\pi\) | |||||||
\(642\) | −2.20368e11 | − | 3.81688e11i | −0.0511965 | − | 0.0886750i | ||||
\(643\) | −4.09899e12 | −0.945644 | −0.472822 | − | 0.881158i | \(-0.656765\pi\) | ||||
−0.472822 | + | 0.881158i | \(0.656765\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.34656e12 | −2.12634 | ||||||||
\(646\) | 1.10858e11 | + | 1.92011e11i | 0.0250449 | + | 0.0433790i | ||||
\(647\) | 3.05663e12 | − | 5.29423e12i | 0.685761 | − | 1.18777i | −0.287436 | − | 0.957800i | \(-0.592803\pi\) |
0.973197 | − | 0.229973i | \(-0.0738639\pi\) | |||||||
\(648\) | −2.69036e12 | + | 4.65983e12i | −0.599408 | + | 1.03820i | ||||
\(649\) | −2.88820e11 | − | 5.00251e11i | −0.0639037 | − | 0.110685i | ||||
\(650\) | 7.44619e10 | 0.0163615 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.18754e12 | 0.257356 | ||||||||
\(653\) | −3.83135e12 | − | 6.63609e12i | −0.824598 | − | 1.42825i | −0.902226 | − | 0.431264i | \(-0.858068\pi\) |
0.0776274 | − | 0.996982i | \(-0.475266\pi\) | |||||||
\(654\) | −9.54066e11 | + | 1.65249e12i | −0.203929 | + | 0.353215i | ||||
\(655\) | −2.15673e12 | + | 3.73557e12i | −0.457836 | + | 0.792996i | ||||
\(656\) | 1.31349e11 | + | 2.27503e11i | 0.0276923 | + | 0.0479644i | ||||
\(657\) | −1.12450e12 | −0.235459 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.20110e9 | −0.00169390 | −0.000846950 | − | 1.00000i | \(-0.500270\pi\) | ||||
−0.000846950 | 1.00000i | \(0.500270\pi\) | ||||||||
\(660\) | −4.72440e12 | − | 8.18291e12i | −0.969168 | − | 1.67865i | ||||
\(661\) | 1.60461e12 | − | 2.77927e12i | 0.326936 | − | 0.566270i | −0.654966 | − | 0.755658i | \(-0.727317\pi\) |
0.981902 | + | 0.189388i | \(0.0606504\pi\) | |||||||
\(662\) | −1.89615e12 | + | 3.28424e12i | −0.383719 | + | 0.664620i | ||||
\(663\) | −3.04579e10 | − | 5.27546e10i | −0.00612194 | − | 0.0106035i | ||||
\(664\) | −9.39395e11 | −0.187539 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.14030e11 | −0.160327 | ||||||||
\(667\) | 9.10404e11 | + | 1.57687e12i | 0.178102 | + | 0.308481i | ||||
\(668\) | 1.73891e12 | − | 3.01188e12i | 0.337895 | − | 0.585252i | ||||
\(669\) | 1.88717e12 | − | 3.26867e12i | 0.364244 | − | 0.630889i | ||||
\(670\) | −1.49309e12 | − | 2.58611e12i | −0.286253 | − | 0.495805i | ||||
\(671\) | 1.52609e13 | 2.90622 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.91229e12 | −0.923031 | −0.461515 | − | 0.887132i | \(-0.652694\pi\) | ||||
−0.461515 | + | 0.887132i | \(0.652694\pi\) | |||||||
\(674\) | 3.75045e10 | + | 6.49596e10i | 0.00700025 | + | 0.0121248i | ||||
\(675\) | −1.80186e12 | + | 3.12092e12i | −0.334083 | + | 0.578649i | ||||
\(676\) | −1.76655e12 | + | 3.05975e12i | −0.325360 | + | 0.563541i | ||||
\(677\) | −1.55955e12 | − | 2.70122e12i | −0.285332 | − | 0.494209i | 0.687358 | − | 0.726319i | \(-0.258770\pi\) |
−0.972690 | + | 0.232110i | \(0.925437\pi\) | |||||||
\(678\) | −3.33952e12 | −0.606946 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.52953e12 | −0.453680 | ||||||||
\(681\) | 1.88657e12 | + | 3.26764e12i | 0.336133 | + | 0.582200i | ||||
\(682\) | −5.82981e12 | + | 1.00975e13i | −1.03187 | + | 1.78725i | ||||
\(683\) | −1.45903e12 | + | 2.52712e12i | −0.256550 | + | 0.444357i | −0.965315 | − | 0.261087i | \(-0.915919\pi\) |
0.708766 | + | 0.705444i | \(0.249252\pi\) | |||||||
\(684\) | 1.66776e11 | + | 2.88865e11i | 0.0291327 | + | 0.0504594i | ||||
\(685\) | −7.99902e12 | −1.38813 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.95322e12 | 1.19092 | ||||||||
\(688\) | 2.94871e11 | + | 5.10731e11i | 0.0501746 | + | 0.0869049i | ||||
\(689\) | −1.13180e11 | + | 1.96033e11i | −0.0191330 | + | 0.0331393i | ||||
\(690\) | −2.67316e12 | + | 4.63006e12i | −0.448957 | + | 0.777616i | ||||
\(691\) | 2.37348e12 | + | 4.11100e12i | 0.396037 | + | 0.685955i | 0.993233 | − | 0.116140i | \(-0.0370520\pi\) |
−0.597196 | + | 0.802095i | \(0.703719\pi\) | |||||||
\(692\) | 6.82712e12 | 1.13178 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 4.54058e12 | 0.743009 | ||||||||
\(695\) | 5.79908e12 | + | 1.00443e13i | 0.942817 | + | 1.63301i | ||||
\(696\) | 1.31924e12 | − | 2.28500e12i | 0.213100 | − | 0.369100i | ||||
\(697\) | −7.72030e11 | + | 1.33719e12i | −0.123904 | + | 0.214609i | ||||
\(698\) | 2.31620e11 | + | 4.01177e11i | 0.0369340 | + | 0.0639716i | ||||
\(699\) | 2.07013e12 | 0.327981 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.24423e11 | −0.0351023 | −0.0175512 | − | 0.999846i | \(-0.505587\pi\) | ||||
−0.0175512 | + | 0.999846i | \(0.505587\pi\) | |||||||
\(702\) | −4.42300e10 | − | 7.66085e10i | −0.00687384 | − | 0.0119058i | ||||
\(703\) | 6.18048e11 | − | 1.07049e12i | 0.0954385 | − | 0.165304i | ||||
\(704\) | 3.18700e12 | − | 5.52005e12i | 0.488996 | − | 0.846966i | ||||
\(705\) | −1.69573e12 | − | 2.93709e12i | −0.258527 | − | 0.447782i | ||||
\(706\) | 4.63484e12 | 0.702123 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.49001e11 | −0.0522007 | ||||||||
\(709\) | −2.12731e12 | − | 3.68462e12i | −0.316172 | − | 0.547626i | 0.663514 | − | 0.748164i | \(-0.269064\pi\) |
−0.979686 | + | 0.200538i | \(0.935731\pi\) | |||||||
\(710\) | 1.85546e12 | − | 3.21374e12i | 0.274024 | − | 0.474623i | ||||
\(711\) | 1.71784e12 | − | 2.97539e12i | 0.252099 | − | 0.436648i | ||||
\(712\) | −1.17529e10 | − | 2.03567e10i | −0.00171390 | − | 0.00296857i | ||||
\(713\) | −1.23250e13 | −1.78601 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.54800e11 | 0.0793888 | ||||||||
\(716\) | 9.11606e11 | + | 1.57895e12i | 0.129628 | + | 0.224522i | ||||
\(717\) | 5.21191e12 | − | 9.02729e12i | 0.736479 | − | 1.27562i | ||||
\(718\) | 1.67685e12 | − | 2.90438e12i | 0.235469 | − | 0.407844i | ||||
\(719\) | −2.14465e12 | − | 3.71465e12i | −0.299280 | − | 0.518368i | 0.676692 | − | 0.736267i | \(-0.263413\pi\) |
−0.975971 | + | 0.217899i | \(0.930080\pi\) | |||||||
\(720\) | −2.67492e11 | −0.0370950 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.04023e12 | −0.553335 | ||||||||
\(723\) | 2.38262e12 | + | 4.12682e12i | 0.324289 | + | 0.561685i | ||||
\(724\) | 3.52880e11 | − | 6.11207e11i | 0.0477314 | − | 0.0826732i | ||||
\(725\) | 1.24470e12 | − | 2.15588e12i | 0.167318 | − | 0.289804i | ||||
\(726\) | 6.30774e12 | + | 1.09253e13i | 0.842673 | + | 1.45955i | ||||
\(727\) | −1.28935e13 | −1.71185 | −0.855926 | − | 0.517098i | \(-0.827012\pi\) | ||||
−0.855926 | + | 0.517098i | \(0.827012\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.31084e12 | 0.434174 | ||||||||
\(730\) | −2.05654e12 | − | 3.56203e12i | −0.268030 | − | 0.464242i | ||||
\(731\) | −1.73316e12 | + | 3.00193e12i | −0.224497 | + | 0.388841i | ||||
\(732\) | 4.61019e12 | − | 7.98508e12i | 0.593497 | − | 1.02797i | ||||
\(733\) | 1.35724e12 | + | 2.35080e12i | 0.173655 | + | 0.300780i | 0.939695 | − | 0.342013i | \(-0.111109\pi\) |
−0.766040 | + | 0.642793i | \(0.777775\pi\) | |||||||
\(734\) | −6.41143e12 | −0.815309 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.70531e12 | 0.967921 | ||||||||
\(737\) | −5.24405e12 | − | 9.08295e12i | −0.654731 | − | 1.13403i | ||||
\(738\) | 6.21696e11 | − | 1.07681e12i | 0.0771480 | − | 0.133624i | ||||
\(739\) | 4.81290e12 | − | 8.33618e12i | 0.593617 | − | 1.02818i | −0.400123 | − | 0.916461i | \(-0.631033\pi\) |
0.993740 | − | 0.111714i | \(-0.0356340\pi\) | |||||||
\(740\) | 2.78126e12 | + | 4.81729e12i | 0.340957 | + | 0.590554i | ||||
\(741\) | −7.44880e10 | −0.00907620 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.24362e13 | −1.49706 | −0.748529 | − | 0.663103i | \(-0.769239\pi\) | ||||
−0.748529 | + | 0.663103i | \(0.769239\pi\) | |||||||
\(744\) | 8.92993e12 | + | 1.54671e13i | 1.06849 | + | 1.85068i | ||||
\(745\) | −4.20797e12 | + | 7.28842e12i | −0.500460 | + | 0.866823i | ||||
\(746\) | 1.23449e12 | − | 2.13820e12i | 0.145936 | − | 0.252769i | ||||
\(747\) | −2.91943e11 | − | 5.05660e11i | −0.0343048 | − | 0.0594177i | ||||
\(748\) | −3.50425e12 | −0.409296 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8.87371e11 | −0.102407 | ||||||||
\(751\) | −2.13480e12 | − | 3.69758e12i | −0.244893 | − | 0.424168i | 0.717208 | − | 0.696859i | \(-0.245420\pi\) |
−0.962102 | + | 0.272691i | \(0.912086\pi\) | |||||||
\(752\) | −1.06996e11 | + | 1.85322e11i | −0.0122008 | + | 0.0211323i | ||||
\(753\) | −5.13889e12 | + | 8.90081e12i | −0.582494 | + | 1.00891i | ||||
\(754\) | 3.05534e10 | + | 5.29200e10i | 0.00344262 | + | 0.00596278i | ||||
\(755\) | 5.17770e12 | 0.579930 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.76840e12 | 1.08116 | 0.540582 | − | 0.841291i | \(-0.318204\pi\) | ||||
0.540582 | + | 0.841291i | \(0.318204\pi\) | |||||||
\(758\) | 4.73576e12 | + | 8.20258e12i | 0.521049 | + | 0.902484i | ||||
\(759\) | −9.38871e12 | + | 1.62617e13i | −1.02688 | + | 1.77860i | ||||
\(760\) | −1.54656e12 | + | 2.67872e12i | −0.168153 | + | 0.291250i | ||||
\(761\) | 6.16679e12 | + | 1.06812e13i | 0.666543 | + | 1.15449i | 0.978864 | + | 0.204510i | \(0.0655601\pi\) |
−0.312321 | + | 0.949977i | \(0.601107\pi\) | |||||||
\(762\) | 1.90378e12 | 0.204559 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.75008e12 | −0.610595 | ||||||||
\(765\) | −7.86121e11 | − | 1.36160e12i | −0.0829875 | − | 0.143739i | ||||
\(766\) | 8.26955e11 | − | 1.43233e12i | 0.0867865 | − | 0.150319i | ||||
\(767\) | 1.02460e10 | − | 1.77467e10i | 0.00106900 | − | 0.00185156i | ||||
\(768\) | −5.30627e12 | − | 9.19074e12i | −0.550382 | − | 0.953290i | ||||
\(769\) | 1.68919e13 | 1.74185 | 0.870926 | − | 0.491415i | \(-0.163520\pi\) | ||||
0.870926 | + | 0.491415i | \(0.163520\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.87078e13 | 1.90668 | ||||||||
\(772\) | 3.36875e12 | + | 5.83485e12i | 0.341343 | + | 0.591224i | ||||
\(773\) | 7.35930e12 | − | 1.27467e13i | 0.741359 | − | 1.28407i | −0.210518 | − | 0.977590i | \(-0.567515\pi\) |
0.951877 | − | 0.306481i | \(-0.0991517\pi\) | |||||||
\(774\) | 1.39567e12 | − | 2.41738e12i | 0.139781 | − | 0.242108i | ||||
\(775\) | 8.42535e12 | + | 1.45931e13i | 0.838939 | + | 1.45308i | ||||
\(776\) | −3.56835e12 | −0.353257 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.98111e12 | −0.389579 | ||||||||
\(779\) | 9.44040e11 | + | 1.63512e12i | 0.0918484 | + | 0.159086i | ||||
\(780\) | 1.67601e11 | − | 2.90293e11i | 0.0162125 | − | 0.0280809i | ||||
\(781\) | 6.51674e12 | − | 1.12873e13i | 0.626760 | − | 1.08558i | ||||
\(782\) | 9.91388e11 | + | 1.71713e12i | 0.0948010 | + | 0.164200i | ||||
\(783\) | −2.95738e12 | −0.281177 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.55736e12 | −0.240369 | ||||||||
\(786\) | −2.44974e12 | − | 4.24308e12i | −0.228939 | − | 0.396534i | ||||
\(787\) | −9.12328e12 | + | 1.58020e13i | −0.847744 | + | 1.46834i | 0.0354729 | + | 0.999371i | \(0.488706\pi\) |
−0.883217 | + | 0.468965i | \(0.844627\pi\) | |||||||
\(788\) | −3.71163e12 | + | 6.42873e12i | −0.342923 | + | 0.593960i | ||||
\(789\) | 1.14966e12 | + | 1.99127e12i | 0.105614 | + | 0.182929i | ||||
\(790\) | 1.25667e13 | 1.14789 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 7.15424e12 | 0.646101 | ||||||||
\(793\) | 2.70694e11 | + | 4.68855e11i | 0.0243080 | + | 0.0421027i | ||||
\(794\) | 3.56348e12 | − | 6.17212e12i | 0.318186 | − | 0.551115i | ||||
\(795\) | −1.11102e13 | + | 1.92434e13i | −0.986437 | + | 1.70856i | ||||
\(796\) | −2.84448e12 | − | 4.92678e12i | −0.251127 | − | 0.434965i | ||||
\(797\) | 1.21558e13 | 1.06714 | 0.533568 | − | 0.845757i | \(-0.320851\pi\) | ||||
0.533568 | + | 0.845757i | \(0.320851\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.25778e12 | −0.109180 | ||||||||
\(800\) | −5.26733e12 | − | 9.12328e12i | −0.454659 | − | 0.787492i | ||||
\(801\) | 7.30510e9 | − | 1.26528e10i | 0.000627017 | − | 0.00108603i | ||||
\(802\) | −2.77662e12 | + | 4.80925e12i | −0.236991 | + | 0.410481i | ||||
\(803\) | −7.22298e12 | − | 1.25106e13i | −0.613051 | − | 1.06184i | ||||
\(804\) | −6.33673e12 | −0.534827 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.13631e11 | −0.0345227 | ||||||||
\(807\) | −6.85641e12 | − | 1.18757e13i | −0.569070 | − | 0.985659i | ||||
\(808\) | 3.24681e12 | − | 5.62364e12i | 0.267982 | − | 0.464158i | ||||
\(809\) | 1.30946e12 | − | 2.26806e12i | 0.107479 | − | 0.186160i | −0.807269 | − | 0.590184i | \(-0.799055\pi\) |
0.914749 | + | 0.404024i | \(0.132389\pi\) | |||||||
\(810\) | −6.11641e12 | − | 1.05939e13i | −0.499246 | − | 0.864719i | ||||
\(811\) | −1.16994e13 | −0.949662 | −0.474831 | − | 0.880077i | \(-0.657491\pi\) | ||||
−0.474831 | + | 0.880077i | \(0.657491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.24217e12 | 0.260272 | ||||||||
\(814\) | −5.22875e12 | − | 9.05646e12i | −0.417434 | − | 0.723017i | ||||
\(815\) | −3.42240e12 | + | 5.92777e12i | −0.271720 | + | 0.470633i | ||||
\(816\) | −1.88652e11 | + | 3.26755e11i | −0.0148955 | + | 0.0257998i | ||||
\(817\) | 2.11932e12 | + | 3.67077e12i | 0.166417 | + | 0.288242i | ||||
\(818\) | −1.44267e13 | −1.12662 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.49649e12 | −0.656262 | ||||||||
\(821\) | −2.58836e12 | − | 4.48318e12i | −0.198830 | − | 0.344383i | 0.749320 | − | 0.662209i | \(-0.230381\pi\) |
−0.948149 | + | 0.317826i | \(0.897047\pi\) | |||||||
\(822\) | 4.54288e12 | − | 7.86850e12i | 0.347063 | − | 0.601131i | ||||
\(823\) | 3.92009e12 | − | 6.78979e12i | 0.297849 | − | 0.515890i | −0.677795 | − | 0.735251i | \(-0.737064\pi\) |
0.975644 | + | 0.219362i | \(0.0703974\pi\) | |||||||
\(824\) | 8.57790e12 | + | 1.48574e13i | 0.648200 | + | 1.12271i | ||||
\(825\) | 2.56724e13 | 1.92941 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.43263e13 | −1.06502 | −0.532512 | − | 0.846422i | \(-0.678752\pi\) | ||||
−0.532512 | + | 0.846422i | \(0.678752\pi\) | |||||||
\(828\) | 1.49146e12 | + | 2.58329e12i | 0.110275 | + | 0.191001i | ||||
\(829\) | 2.47773e12 | − | 4.29155e12i | 0.182204 | − | 0.315587i | −0.760427 | − | 0.649424i | \(-0.775010\pi\) |
0.942631 | + | 0.333837i | \(0.108343\pi\) | |||||||
\(830\) | 1.06784e12 | − | 1.84955e12i | 0.0781005 | − | 0.135274i | ||||
\(831\) | −5.86586e12 | − | 1.01600e13i | −0.426704 | − | 0.739073i | ||||
\(832\) | 2.26121e11 | 0.0163601 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.31739e13 | −0.942902 | ||||||||
\(835\) | 1.00228e13 | + | 1.73600e13i | 0.713508 | + | 1.23583i | ||||
\(836\) | −2.14250e12 | + | 3.71092e12i | −0.151703 | + | 0.262757i | ||||
\(837\) | 1.00092e13 | − | 1.73365e13i | 0.704914 | − | 1.22095i | ||||
\(838\) | −1.47635e12 | − | 2.55711e12i | −0.103417 | − | 0.179123i | ||||
\(839\) | −7.38235e12 | −0.514358 | −0.257179 | − | 0.966364i | \(-0.582793\pi\) | ||||
−0.257179 | + | 0.966364i | \(0.582793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.24642e13 | −0.859179 | ||||||||
\(842\) | −2.32128e12 | − | 4.02058e12i | −0.159156 | − | 0.275666i | ||||
\(843\) | 8.40386e12 | − | 1.45559e13i | 0.573132 | − | 0.992694i | ||||
\(844\) | −5.33373e12 | + | 9.23830e12i | −0.361818 | + | 0.626687i | ||||
\(845\) | −1.01821e13 | − | 1.76359e13i | −0.687039 | − | 1.18999i | ||||
\(846\) | 1.01286e12 | 0.0679802 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.40204e12 | 0.0931065 | ||||||||
\(849\) | 4.51745e12 | + | 7.82446e12i | 0.298407 | + | 0.516856i | ||||
\(850\) | 1.35542e12 | − | 2.34766e12i | 0.0890613 | − | 0.154259i | ||||
\(851\) | 5.52714e12 | − | 9.57329e12i | 0.361258 | − | 0.625717i | ||||
\(852\) | −3.93731e12 | − | 6.81962e12i | −0.255989 | − | 0.443386i | ||||
\(853\) | −2.13356e13 | −1.37985 | −0.689927 | − | 0.723879i | \(-0.742357\pi\) | ||||
−0.689927 | + | 0.723879i | \(0.742357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.92254e12 | −0.123035 | ||||||||
\(856\) | −1.14016e12 | − | 1.97482e12i | −0.0725829 | − | 0.125717i | ||||
\(857\) | 8.25038e12 | − | 1.42901e13i | 0.522468 | − | 0.904942i | −0.477190 | − | 0.878800i | \(-0.658345\pi\) |
0.999658 | − | 0.0261416i | \(-0.00832208\pi\) | |||||||
\(858\) | −3.15088e11 | + | 5.45748e11i | −0.0198490 | + | 0.0343795i | ||||
\(859\) | −9.74083e12 | − | 1.68716e13i | −0.610417 | − | 1.05727i | −0.991170 | − | 0.132597i | \(-0.957669\pi\) |
0.380753 | − | 0.924677i | \(-0.375665\pi\) | |||||||
\(860\) | −1.90742e13 | −1.18906 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.65103e12 | 0.101853 | ||||||||
\(863\) | −8.05297e12 | − | 1.39482e13i | −0.494205 | − | 0.855989i | 0.505772 | − | 0.862667i | \(-0.331208\pi\) |
−0.999978 | + | 0.00667822i | \(0.997874\pi\) | |||||||
\(864\) | −6.25754e12 | + | 1.08384e13i | −0.382025 | + | 0.661686i | ||||
\(865\) | −1.96752e13 | + | 3.40785e13i | −1.19494 | + | 2.06970i | ||||
\(866\) | −4.86116e12 | − | 8.41978e12i | −0.293704 | − | 0.508710i | ||||
\(867\) | 1.71613e13 | 1.03149 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.41368e13 | 2.62550 | ||||||||
\(870\) | 2.99924e12 | + | 5.19484e12i | 0.177491 | + | 0.307423i | ||||
\(871\) | 1.86035e11 | − | 3.22222e11i | 0.0109525 | − | 0.0189703i | ||||
\(872\) | −4.93624e12 | + | 8.54983e12i | −0.289116 | + | 0.500764i | ||||
\(873\) | −1.10896e12 | − | 1.92078e12i | −0.0646180 | − | 0.111922i | ||||
\(874\) | 2.42454e12 | 0.140549 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.72801e12 | −0.500780 | ||||||||
\(877\) | 9.24594e12 | + | 1.60144e13i | 0.527780 | + | 0.914142i | 0.999476 | + | 0.0323804i | \(0.0103088\pi\) |
−0.471696 | + | 0.881761i | \(0.656358\pi\) | |||||||
\(878\) | −3.91446e12 | + | 6.78005e12i | −0.222304 | + | 0.385041i | ||||
\(879\) | −8.63821e12 | + | 1.49618e13i | −0.488061 | + | 0.845346i | ||||
\(880\) | −1.71818e12 | − | 2.97598e12i | −0.0965821 | − | 0.167285i | ||||
\(881\) | 2.83078e13 | 1.58312 | 0.791562 | − | 0.611089i | \(-0.209268\pi\) | ||||
0.791562 | + | 0.611089i | \(0.209268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.32328e12 | −0.405399 | −0.202700 | − | 0.979241i | \(-0.564971\pi\) | ||||
−0.202700 | + | 0.979241i | \(0.564971\pi\) | |||||||
\(884\) | −6.21574e10 | − | 1.07660e11i | −0.00342340 | − | 0.00592951i | ||||
\(885\) | 1.00579e12 | − | 1.74208e12i | 0.0551142 | − | 0.0954606i | ||||
\(886\) | 1.41321e12 | − | 2.44774e12i | 0.0770466 | − | 0.133449i | ||||
\(887\) | 7.56860e12 | + | 1.31092e13i | 0.410544 | + | 0.711083i | 0.994949 | − | 0.100379i | \(-0.0320056\pi\) |
−0.584406 | + | 0.811462i | \(0.698672\pi\) | |||||||
\(888\) | −1.60185e13 | −0.864496 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.34396e10 | 0.00285501 | ||||||||
\(891\) | −2.14821e13 | − | 3.72081e13i | −1.14190 | − | 1.97782i | ||||
\(892\) | 3.85126e12 | − | 6.67059e12i | 0.203686 | − | 0.352795i | ||||
\(893\) | −7.69008e11 | + | 1.33196e12i | −0.0404669 | + | 0.0700907i | ||||
\(894\) | −4.77967e12 | − | 8.27863e12i | −0.250253 | − | 0.433451i | ||||
\(895\) | −1.05087e13 | −0.547451 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.66138e11 | −0.0343556 | ||||||||
\(898\) | 6.15293e12 | + | 1.06572e13i | 0.315747 | + | 0.546889i | ||||
\(899\) | −6.91423e12 | + | 1.19758e13i | −0.353041 | + | 0.611485i | ||||
\(900\) | 2.03912e12 | − | 3.53186e12i | 0.103598 | − | 0.179437i | ||||
\(901\) | 4.12040e12 | + | 7.13674e12i | 0.208294 | + | 0.360776i | ||||
\(902\) | 1.59733e13 | 0.803463 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.72783e13 | −0.860487 | ||||||||
\(905\) | 2.03395e12 | + | 3.52290e12i | 0.100791 | + | 0.174575i | ||||
\(906\) | −2.94057e12 | + | 5.09321e12i | −0.144995 | + | 0.251139i | ||||
\(907\) | 1.12169e13 | − | 1.94282e13i | 0.550349 | − | 0.953233i | −0.447900 | − | 0.894084i | \(-0.647828\pi\) |
0.998249 | − | 0.0591491i | \(-0.0188387\pi\) | |||||||
\(908\) | 3.85006e12 | + | 6.66849e12i | 0.187967 | + | 0.325568i | ||||
\(909\) | 4.03614e12 | 0.196078 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.34178e12 | −0.305055 | −0.152528 | − | 0.988299i | \(-0.548741\pi\) | ||||
−0.152528 | + | 0.988299i | \(0.548741\pi\) | |||||||
\(912\) | 2.30684e11 | + | 3.99557e11i | 0.0110418 | + | 0.0191250i | ||||
\(913\) | 3.75047e12 | − | 6.49600e12i | 0.178635 | − | 0.309405i | ||||
\(914\) | −5.41901e12 | + | 9.38600e12i | −0.256839 | + | 0.444859i | ||||
\(915\) | 2.65724e13 | + | 4.60247e13i | 1.25324 | + | 2.17068i | ||||
\(916\) | 1.41899e13 | 0.665963 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.22045e12 | −0.149667 | ||||||||
\(919\) | −4.52236e12 | − | 7.83295e12i | −0.209144 | − | 0.362248i | 0.742301 | − | 0.670066i | \(-0.233734\pi\) |
−0.951445 | + | 0.307819i | \(0.900401\pi\) | |||||||
\(920\) | −1.38307e13 | + | 2.39555e13i | −0.636500 | + | 1.10245i | ||||
\(921\) | 6.61882e12 | − | 1.14641e13i | 0.303118 | − | 0.525016i | ||||
\(922\) | −1.26973e12 | − | 2.19924e12i | −0.0578659 | − | 0.100227i | ||||
\(923\) | 4.62369e11 | 0.0209692 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.51134e13 | −0.678771 | ||||||||
\(926\) | −3.18617e12 | − | 5.51860e12i | −0.142403 | − | 0.246649i | ||||
\(927\) | −5.33164e12 | + | 9.23467e12i | −0.237138 | + | 0.410736i | ||||
\(928\) | 4.32261e12 | − | 7.48698e12i | 0.191329 | − | 0.331391i | ||||
\(929\) | 4.25320e12 | + | 7.36677e12i | 0.187346 | + | 0.324494i | 0.944365 | − | 0.328900i | \(-0.106678\pi\) |
−0.757018 | + | 0.653394i | \(0.773345\pi\) | |||||||
\(930\) | −4.06037e13 | −1.77988 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 4.22464e12 | 0.183408 | ||||||||
\(933\) | 2.60184e13 | + | 4.50652e13i | 1.12412 | + | 1.94704i | ||||
\(934\) | 7.10735e12 | − | 1.23103e13i | 0.305595 | − | 0.529307i | ||||
\(935\) | 1.00990e13 | − | 1.74919e13i | 0.432140 | − | 0.748488i | ||||
\(936\) | 1.26900e11 | + | 2.19797e11i | 0.00540407 | + | 0.00936012i | ||||
\(937\) | 3.00276e13 | 1.27260 | 0.636300 | − | 0.771442i | \(-0.280464\pi\) | ||||
0.636300 | + | 0.771442i | \(0.280464\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.10602e13 | 0.884030 | ||||||||
\(940\) | −3.46059e12 | − | 5.99392e12i | −0.144569 | − | 0.250401i | ||||
\(941\) | −1.57991e13 | + | 2.73649e13i | −0.656870 | + | 1.13773i | 0.324552 | + | 0.945868i | \(0.394787\pi\) |
−0.981422 | + | 0.191864i | \(0.938547\pi\) | |||||||
\(942\) | 1.45240e12 | − | 2.51563e12i | 0.0600976 | − | 0.104092i | ||||
\(943\) | 8.44245e12 | + | 1.46227e13i | 0.347669 | + | 0.602180i | ||||
\(944\) | −1.26925e11 | −0.00520205 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.58592e13 | 1.45576 | ||||||||
\(947\) | 4.42442e12 | + | 7.66332e12i | 0.178765 | + | 0.309630i | 0.941458 | − | 0.337131i | \(-0.109457\pi\) |
−0.762693 | + | 0.646761i | \(0.776123\pi\) | |||||||
\(948\) | 1.33334e13 | − | 2.30941e13i | 0.536170 | − | 0.928673i | ||||
\(949\) | 2.56239e11 | − | 4.43819e11i | 0.0102553 | − | 0.0177626i | ||||
\(950\) | −1.65741e12 | − | 2.87072e12i | −0.0660198 | − | 0.114350i | ||||
\(951\) | 1.21698e13 | 0.482473 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.90260e12 | −0.192534 | −0.0962672 | − | 0.995356i | \(-0.530690\pi\) | ||||
−0.0962672 | + | 0.995356i | \(0.530690\pi\) | |||||||
\(954\) | −3.31805e12 | − | 5.74704e12i | −0.129693 | − | 0.224634i | ||||
\(955\) | 1.65713e13 | − | 2.87023e13i | 0.644674 | − | 1.11661i | ||||
\(956\) | 1.06363e13 | − | 1.84226e13i | 0.411841 | − | 0.713329i | ||||
\(957\) | 1.05340e13 | + | 1.82454e13i | 0.405965 | + | 0.703151i | ||||
\(958\) | 1.12686e13 | 0.432241 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.21969e13 | 0.843476 | ||||||||
\(961\) | −3.35824e13 | − | 5.81665e13i | −1.27016 | − | 2.19998i | ||||
\(962\) | 1.85492e11 | − | 3.21282e11i | 0.00698294 | − | 0.0120948i | ||||
\(963\) | 7.08673e11 | − | 1.22746e12i | 0.0265539 | − | 0.0459926i | ||||
\(964\) | 4.86237e12 | + | 8.42188e12i | 0.181343 | + | 0.314096i | ||||
\(965\) | −3.88339e13 | −1.44158 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55633e13 | 0.572378 | 0.286189 | − | 0.958173i | \(-0.407612\pi\) | ||||
0.286189 | + | 0.958173i | \(0.407612\pi\) | |||||||
\(968\) | 3.26356e13 | + | 5.65266e13i | 1.19468 | + | 2.06925i | ||||
\(969\) | −1.35590e12 | + | 2.34848e12i | −0.0494048 | + | 0.0855716i | ||||
\(970\) | 4.05625e12 | − | 7.02564e12i | 0.147113 | − | 0.254808i | ||||
\(971\) | −1.24598e13 | − | 2.15811e13i | −0.449806 | − | 0.779087i | 0.548567 | − | 0.836107i | \(-0.315174\pi\) |
−0.998373 | + | 0.0570194i | \(0.981840\pi\) | |||||||
\(972\) | −1.23765e13 | −0.444732 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.53918e13 | 0.547991 | ||||||||
\(975\) | 4.55370e11 | + | 7.88724e11i | 0.0161378 | + | 0.0279515i | ||||
\(976\) | 1.67664e12 | − | 2.90403e12i | 0.0591448 | − | 0.102442i | ||||
\(977\) | −2.23949e12 | + | 3.87891e12i | −0.0786364 | + | 0.136202i | −0.902662 | − | 0.430351i | \(-0.858390\pi\) |
0.824025 | + | 0.566553i | \(0.191723\pi\) | |||||||
\(978\) | −3.88737e12 | − | 6.73312e12i | −0.135872 | − | 0.235338i | ||||
\(979\) | 1.87691e11 | 0.00653012 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.13629e12 | −0.211542 | ||||||||
\(982\) | 6.47129e12 | + | 1.12086e13i | 0.222070 | + | 0.384636i | ||||
\(983\) | −7.16166e12 | + | 1.24044e13i | −0.244637 | + | 0.423724i | −0.962030 | − | 0.272945i | \(-0.912002\pi\) |
0.717392 | + | 0.696669i | \(0.245336\pi\) | |||||||
\(984\) | 1.22337e13 | − | 2.11895e13i | 0.415988 | − | 0.720513i | ||||
\(985\) | −2.13932e13 | − | 3.70542e13i | −0.724125 | − | 1.25422i | ||||
\(986\) | 2.22464e12 | 0.0749572 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.52013e11 | −0.00507543 | ||||||||
\(989\) | 1.89528e13 | + | 3.28273e13i | 0.629928 | + | 1.09107i | ||||
\(990\) | −8.13244e12 | + | 1.40858e13i | −0.269068 | + | 0.466040i | ||||
\(991\) | 1.14287e13 | − | 1.97951e13i | 0.376415 | − | 0.651969i | −0.614123 | − | 0.789210i | \(-0.710490\pi\) |
0.990538 | + | 0.137241i | \(0.0438235\pi\) | |||||||
\(992\) | 2.92597e13 | + | 5.06793e13i | 0.959328 | + | 1.66160i | ||||
\(993\) | −4.63836e13 | −1.51388 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.27902e13 | 1.06057 | ||||||||
\(996\) | −2.26597e12 | − | 3.92478e12i | −0.0729604 | − | 0.126371i | ||||
\(997\) | −1.33566e13 | + | 2.31343e13i | −0.428121 | + | 0.741528i | −0.996706 | − | 0.0810966i | \(-0.974158\pi\) |
0.568585 | + | 0.822625i | \(0.307491\pi\) | |||||||
\(998\) | −1.75574e13 | + | 3.04103e13i | −0.560237 | + | 0.970359i | ||||
\(999\) | 8.97726e12 | + | 1.55491e13i | 0.285167 | + | 0.493924i |
(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 | 49.10.c.e.18.2 | 6 | ||
7.2 | even | 3 | inner | 49.10.c.e.30.2 | 6 | ||
7.3 | odd | 6 | 7.10.a.b.1.2 | ✓ | 3 | ||
7.4 | even | 3 | 49.10.a.c.1.2 | 3 | |||
7.5 | odd | 6 | 49.10.c.d.30.2 | 6 | |||
7.6 | odd | 2 | 49.10.c.d.18.2 | 6 | |||
21.17 | even | 6 | 63.10.a.e.1.2 | 3 | |||
28.3 | even | 6 | 112.10.a.h.1.1 | 3 | |||
35.3 | even | 12 | 175.10.b.d.99.3 | 6 | |||
35.17 | even | 12 | 175.10.b.d.99.4 | 6 | |||
35.24 | odd | 6 | 175.10.a.d.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.a.b.1.2 | ✓ | 3 | 7.3 | odd | 6 | ||
49.10.a.c.1.2 | 3 | 7.4 | even | 3 | |||
49.10.c.d.18.2 | 6 | 7.6 | odd | 2 | |||
49.10.c.d.30.2 | 6 | 7.5 | odd | 6 | |||
49.10.c.e.18.2 | 6 | 1.1 | even | 1 | trivial | ||
49.10.c.e.30.2 | 6 | 7.2 | even | 3 | inner | ||
63.10.a.e.1.2 | 3 | 21.17 | even | 6 | |||
112.10.a.h.1.1 | 3 | 28.3 | even | 6 | |||
175.10.a.d.1.2 | 3 | 35.24 | odd | 6 | |||
175.10.b.d.99.3 | 6 | 35.3 | even | 12 | |||
175.10.b.d.99.4 | 6 | 35.17 | even | 12 |