Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [20,11,Mod(11,20)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("20.11");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 20 = 2^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 20.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.7071450535\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + 84 x^{18} - 86 x^{17} - 51565 x^{16} + 188134 x^{15} - 12946328 x^{14} + \cdots + 11\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{94}\cdot 3^{4}\cdot 5^{29} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.13 | ||
Root | \(5.61235 - 15.2006i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 20.11 |
Dual form | 20.11.b.a.11.14 |
$q$-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 \(\left(\mathbb{Z}/20\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(17\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 9.98863 | − | 30.4011i | 0.312145 | − | 0.950035i | ||||
\(3\) | − | 330.781i | − | 1.36124i | −0.732638 | − | 0.680618i | \(-0.761711\pi\) | ||
0.732638 | − | 0.680618i | \(-0.238289\pi\) | |||||||
\(4\) | −824.454 | − | 607.331i | −0.805131 | − | 0.593097i | ||||
\(5\) | 1397.54 | 0.447214 | ||||||||
\(6\) | −10056.1 | − | 3304.05i | −1.29322 | − | 0.424903i | ||||
\(7\) | − | 29449.0i | − | 1.75218i | −0.482144 | − | 0.876092i | \(-0.660142\pi\) | ||
0.482144 | − | 0.876092i | \(-0.339858\pi\) | |||||||
\(8\) | −26698.7 | + | 18997.9i | −0.814780 | + | 0.579770i | ||||
\(9\) | −50366.8 | −0.852965 | ||||||||
\(10\) | 13959.5 | − | 42486.8i | 0.139595 | − | 0.424868i | ||||
\(11\) | 122442.i | 0.760271i | 0.924931 | + | 0.380136i | \(0.124123\pi\) | ||||
−0.924931 | + | 0.380136i | \(0.875877\pi\) | |||||||
\(12\) | −200893. | + | 272713.i | −0.807345 | + | 1.09597i | ||||
\(13\) | 449354. | 1.21024 | 0.605120 | − | 0.796134i | \(-0.293125\pi\) | ||||
0.605120 | + | 0.796134i | \(0.293125\pi\) | |||||||
\(14\) | −895281. | − | 294155.i | −1.66464 | − | 0.546935i | ||||
\(15\) | − | 462280.i | − | 0.608764i | ||||||
\(16\) | 310874. | + | 1.00143e6i | 0.296473 | + | 0.955041i | ||||
\(17\) | −132144. | −0.0930683 | −0.0465342 | − | 0.998917i | \(-0.514818\pi\) | ||||
−0.0465342 | + | 0.998917i | \(0.514818\pi\) | |||||||
\(18\) | −503095. | + | 1.53120e6i | −0.266249 | + | 0.810347i | ||||
\(19\) | 3.03458e6i | 1.22555i | 0.790258 | + | 0.612775i | \(0.209947\pi\) | ||||
−0.790258 | + | 0.612775i | \(0.790053\pi\) | |||||||
\(20\) | −1.15221e6 | − | 848771.i | −0.360066 | − | 0.265241i | ||||
\(21\) | −9.74114e6 | −2.38514 | ||||||||
\(22\) | 3.72238e6 | + | 1.22303e6i | 0.722284 | + | 0.237315i | ||||
\(23\) | − | 4.11212e6i | − | 0.638890i | −0.947605 | − | 0.319445i | \(-0.896503\pi\) | ||
0.947605 | − | 0.319445i | \(-0.103497\pi\) | |||||||
\(24\) | 6.28414e6 | + | 8.83141e6i | 0.789205 | + | 1.10911i | ||||
\(25\) | 1.95312e6 | 0.200000 | ||||||||
\(26\) | 4.48843e6 | − | 1.36609e7i | 0.377770 | − | 1.14977i | ||||
\(27\) | − | 2.87192e6i | − | 0.200149i | ||||||
\(28\) | −1.78853e7 | + | 2.42793e7i | −1.03921 | + | 1.41074i | ||||
\(29\) | −2.05671e7 | −1.00273 | −0.501363 | − | 0.865237i | \(-0.667168\pi\) | ||||
−0.501363 | + | 0.865237i | \(0.667168\pi\) | |||||||
\(30\) | −1.40538e7 | − | 4.61754e6i | −0.578346 | − | 0.190022i | ||||
\(31\) | − | 4.65842e7i | − | 1.62716i | −0.581452 | − | 0.813581i | \(-0.697515\pi\) | ||
0.581452 | − | 0.813581i | \(-0.302485\pi\) | |||||||
\(32\) | 3.35499e7 | + | 552041.i | 0.999865 | + | 0.0164521i | ||||
\(33\) | 4.05016e7 | 1.03491 | ||||||||
\(34\) | −1.31994e6 | + | 4.01731e6i | −0.0290508 | + | 0.0884181i | ||||
\(35\) | − | 4.11562e7i | − | 0.783601i | ||||||
\(36\) | 4.15251e7 | + | 3.05893e7i | 0.686749 | + | 0.505891i | ||||
\(37\) | 7.43988e7 | 1.07290 | 0.536448 | − | 0.843934i | \(-0.319766\pi\) | ||||
0.536448 | + | 0.843934i | \(0.319766\pi\) | |||||||
\(38\) | 9.22546e7 | + | 3.03113e7i | 1.16431 | + | 0.382549i | ||||
\(39\) | − | 1.48637e8i | − | 1.64742i | ||||||
\(40\) | −3.73126e7 | + | 2.65504e7i | −0.364381 | + | 0.259281i | ||||
\(41\) | 1.29152e7 | 0.111476 | 0.0557382 | − | 0.998445i | \(-0.482249\pi\) | ||||
0.0557382 | + | 0.998445i | \(0.482249\pi\) | |||||||
\(42\) | −9.73007e7 | + | 2.96141e8i | −0.744508 | + | 2.26596i | ||||
\(43\) | 4.13136e7i | 0.281029i | 0.990079 | + | 0.140515i | \(0.0448757\pi\) | ||||
−0.990079 | + | 0.140515i | \(0.955124\pi\) | |||||||
\(44\) | 7.43631e7 | − | 1.00948e8i | 0.450914 | − | 0.612118i | ||||
\(45\) | −7.03897e7 | −0.381458 | ||||||||
\(46\) | −1.25013e8 | − | 4.10744e7i | −0.606968 | − | 0.199426i | ||||
\(47\) | − | 1.40161e8i | − | 0.611138i | −0.952170 | − | 0.305569i | \(-0.901153\pi\) | ||
0.952170 | − | 0.305569i | \(-0.0988467\pi\) | |||||||
\(48\) | 3.31255e8 | − | 1.02831e8i | 1.30004 | − | 0.403569i | ||||
\(49\) | −5.84766e8 | −2.07015 | ||||||||
\(50\) | 1.95091e7 | − | 5.93772e7i | 0.0624290 | − | 0.190007i | ||||
\(51\) | 4.37106e7i | 0.126688i | ||||||||
\(52\) | −3.70472e8 | − | 2.72906e8i | −0.974402 | − | 0.717790i | ||||
\(53\) | −7.63529e8 | −1.82577 | −0.912885 | − | 0.408216i | \(-0.866151\pi\) | ||||
−0.912885 | + | 0.408216i | \(0.866151\pi\) | |||||||
\(54\) | −8.73095e7 | − | 2.86865e7i | −0.190148 | − | 0.0624755i | ||||
\(55\) | 1.71118e8i | 0.340004i | ||||||||
\(56\) | 5.59469e8 | + | 7.86249e8i | 1.01586 | + | 1.42764i | ||||
\(57\) | 1.00378e9 | 1.66826 | ||||||||
\(58\) | −2.05437e8 | + | 6.25262e8i | −0.312996 | + | 0.952625i | ||||
\(59\) | 3.73192e8i | 0.522002i | 0.965338 | + | 0.261001i | \(0.0840527\pi\) | ||||
−0.965338 | + | 0.261001i | \(0.915947\pi\) | |||||||
\(60\) | −2.80757e8 | + | 3.81129e8i | −0.361056 | + | 0.490135i | ||||
\(61\) | 1.40526e9 | 1.66383 | 0.831913 | − | 0.554906i | \(-0.187246\pi\) | ||||
0.831913 | + | 0.554906i | \(0.187246\pi\) | |||||||
\(62\) | −1.41621e9 | − | 4.65313e8i | −1.54586 | − | 0.507910i | ||||
\(63\) | 1.48325e9i | 1.49455i | ||||||||
\(64\) | 3.51900e8 | − | 1.01444e9i | 0.327733 | − | 0.944771i | ||||
\(65\) | 6.27991e8 | 0.541236 | ||||||||
\(66\) | 4.04555e8 | − | 1.23129e9i | 0.323041 | − | 0.983199i | ||||
\(67\) | − | 1.39456e9i | − | 1.03291i | −0.856314 | − | 0.516456i | \(-0.827251\pi\) | ||
0.856314 | − | 0.516456i | \(-0.172749\pi\) | |||||||
\(68\) | 1.08946e8 | + | 8.02550e7i | 0.0749322 | + | 0.0551985i | ||||
\(69\) | −1.36021e9 | −0.869681 | ||||||||
\(70\) | −1.25119e9 | − | 4.11094e8i | −0.744448 | − | 0.244597i | ||||
\(71\) | 7.53953e8i | 0.417881i | 0.977928 | + | 0.208941i | \(0.0670015\pi\) | ||||
−0.977928 | + | 0.208941i | \(0.932998\pi\) | |||||||
\(72\) | 1.34473e9 | − | 9.56863e8i | 0.694979 | − | 0.494524i | ||||
\(73\) | 1.69785e8 | 0.0819002 | 0.0409501 | − | 0.999161i | \(-0.486962\pi\) | ||||
0.0409501 | + | 0.999161i | \(0.486962\pi\) | |||||||
\(74\) | 7.43142e8 | − | 2.26181e9i | 0.334899 | − | 1.01929i | ||||
\(75\) | − | 6.46056e8i | − | 0.272247i | ||||||
\(76\) | 1.84300e9 | − | 2.50187e9i | 0.726869 | − | 0.986728i | ||||
\(77\) | 3.60580e9 | 1.33213 | ||||||||
\(78\) | −4.51874e9 | − | 1.48469e9i | −1.56511 | − | 0.514235i | ||||
\(79\) | 3.47862e9i | 1.13050i | 0.824919 | + | 0.565251i | \(0.191221\pi\) | ||||
−0.824919 | + | 0.565251i | \(0.808779\pi\) | |||||||
\(80\) | 4.34460e8 | + | 1.39955e9i | 0.132587 | + | 0.427107i | ||||
\(81\) | −3.92408e9 | −1.12542 | ||||||||
\(82\) | 1.29005e8 | − | 3.92637e8i | 0.0347968 | − | 0.105906i | ||||
\(83\) | 8.27276e8i | 0.210020i | 0.994471 | + | 0.105010i | \(0.0334874\pi\) | ||||
−0.994471 | + | 0.105010i | \(0.966513\pi\) | |||||||
\(84\) | 8.03113e9 | + | 5.91610e9i | 1.92035 | + | 1.41462i | ||||
\(85\) | −1.84676e8 | −0.0416214 | ||||||||
\(86\) | 1.25598e9 | + | 4.12667e8i | 0.266987 | + | 0.0877218i | ||||
\(87\) | 6.80319e9i | 1.36495i | ||||||||
\(88\) | −2.32615e9 | − | 3.26905e9i | −0.440783 | − | 0.619454i | ||||
\(89\) | 6.94167e9 | 1.24312 | 0.621561 | − | 0.783365i | \(-0.286499\pi\) | ||||
0.621561 | + | 0.783365i | \(0.286499\pi\) | |||||||
\(90\) | −7.03097e8 | + | 2.13992e9i | −0.119070 | + | 0.362398i | ||||
\(91\) | − | 1.32330e10i | − | 2.12056i | ||||||
\(92\) | −2.49742e9 | + | 3.39025e9i | −0.378924 | + | 0.514391i | ||||
\(93\) | −1.54092e10 | −2.21495 | ||||||||
\(94\) | −4.26106e9 | − | 1.40002e9i | −0.580602 | − | 0.190764i | ||||
\(95\) | 4.24096e9i | 0.548082i | ||||||||
\(96\) | 1.82605e8 | − | 1.10977e10i | 0.0223952 | − | 1.36105i | ||||
\(97\) | 1.99530e8 | 0.0232354 | 0.0116177 | − | 0.999933i | \(-0.496302\pi\) | ||||
0.0116177 | + | 0.999933i | \(0.496302\pi\) | |||||||
\(98\) | −5.84101e9 | + | 1.77775e10i | −0.646186 | + | 1.96671i | ||||
\(99\) | − | 6.16703e9i | − | 0.648485i | ||||||
\(100\) | −1.61026e9 | − | 1.18619e9i | −0.161026 | − | 0.118619i | ||||
\(101\) | 1.55739e10 | 1.48180 | 0.740900 | − | 0.671615i | \(-0.234399\pi\) | ||||
0.740900 | + | 0.671615i | \(0.234399\pi\) | |||||||
\(102\) | 1.32885e9 | + | 4.36609e8i | 0.120358 | + | 0.0395450i | ||||
\(103\) | 5.68607e9i | 0.490486i | 0.969462 | + | 0.245243i | \(0.0788677\pi\) | ||||
−0.969462 | + | 0.245243i | \(0.921132\pi\) | |||||||
\(104\) | −1.19972e10 | + | 8.53678e9i | −0.986080 | + | 0.701661i | ||||
\(105\) | −1.36137e10 | −1.06667 | ||||||||
\(106\) | −7.62661e9 | + | 2.32121e10i | −0.569905 | + | 1.73454i | ||||
\(107\) | − | 1.17015e10i | − | 0.834300i | −0.908838 | − | 0.417150i | \(-0.863029\pi\) | ||
0.908838 | − | 0.417150i | \(-0.136971\pi\) | |||||||
\(108\) | −1.74421e9 | + | 2.36777e9i | −0.118708 | + | 0.161146i | ||||
\(109\) | 8.01843e9 | 0.521143 | 0.260571 | − | 0.965455i | \(-0.416089\pi\) | ||||
0.260571 | + | 0.965455i | \(0.416089\pi\) | |||||||
\(110\) | 5.20219e9 | + | 1.70924e9i | 0.323015 | + | 0.106130i | ||||
\(111\) | − | 2.46097e10i | − | 1.46046i | ||||||
\(112\) | 2.94912e10 | − | 9.15491e9i | 1.67341 | − | 0.519474i | ||||
\(113\) | −1.16116e10 | −0.630231 | −0.315116 | − | 0.949053i | \(-0.602043\pi\) | ||||
−0.315116 | + | 0.949053i | \(0.602043\pi\) | |||||||
\(114\) | 1.00264e10 | − | 3.05160e10i | 0.520739 | − | 1.58491i | ||||
\(115\) | − | 5.74686e9i | − | 0.285720i | ||||||
\(116\) | 1.69566e10 | + | 1.24910e10i | 0.807327 | + | 0.594714i | ||||
\(117\) | −2.26325e10 | −1.03229 | ||||||||
\(118\) | 1.13455e10 | + | 3.72768e9i | 0.495920 | + | 0.162940i | ||||
\(119\) | 3.89149e9i | 0.163073i | ||||||||
\(120\) | 8.78235e9 | + | 1.23423e10i | 0.352943 | + | 0.496008i | ||||
\(121\) | 1.09453e10 | 0.421988 | ||||||||
\(122\) | 1.40366e10 | − | 4.27215e10i | 0.519355 | − | 1.58069i | ||||
\(123\) | − | 4.27210e9i | − | 0.151746i | ||||||
\(124\) | −2.82921e10 | + | 3.84066e10i | −0.965064 | + | 1.31008i | ||||
\(125\) | 2.72958e9 | 0.0894427 | ||||||||
\(126\) | 4.50924e10 | + | 1.48156e10i | 1.41988 | + | 0.466517i | ||||
\(127\) | 1.28991e10i | 0.390428i | 0.980761 | + | 0.195214i | \(0.0625401\pi\) | ||||
−0.980761 | + | 0.195214i | \(0.937460\pi\) | |||||||
\(128\) | −2.73251e10 | − | 2.08310e10i | −0.795265 | − | 0.606263i | ||||
\(129\) | 1.36657e10 | 0.382547 | ||||||||
\(130\) | 6.27277e9 | − | 1.90916e10i | 0.168944 | − | 0.514193i | ||||
\(131\) | 2.97636e10i | 0.771488i | 0.922606 | + | 0.385744i | \(0.126055\pi\) | ||||
−0.922606 | + | 0.385744i | \(0.873945\pi\) | |||||||
\(132\) | −3.33917e10 | − | 2.45979e10i | −0.833237 | − | 0.613801i | ||||
\(133\) | 8.93652e10 | 2.14739 | ||||||||
\(134\) | −4.23962e10 | − | 1.39297e10i | −0.981302 | − | 0.322418i | ||||
\(135\) | − | 4.01363e9i | − | 0.0895093i | ||||||
\(136\) | 3.52807e9 | − | 2.51045e9i | 0.0758302 | − | 0.0539582i | ||||
\(137\) | −1.43872e10 | −0.298107 | −0.149053 | − | 0.988829i | \(-0.547623\pi\) | ||||
−0.149053 | + | 0.988829i | \(0.547623\pi\) | |||||||
\(138\) | −1.35866e10 | + | 4.13518e10i | −0.271466 | + | 0.826227i | ||||
\(139\) | − | 4.79542e10i | − | 0.924172i | −0.886835 | − | 0.462086i | \(-0.847101\pi\) | ||
0.886835 | − | 0.462086i | \(-0.152899\pi\) | |||||||
\(140\) | −2.49954e10 | + | 3.39314e10i | −0.464751 | + | 0.630901i | ||||
\(141\) | −4.63627e10 | −0.831904 | ||||||||
\(142\) | 2.29210e10 | + | 7.53096e9i | 0.397001 | + | 0.130439i | ||||
\(143\) | 5.50200e10i | 0.920111i | ||||||||
\(144\) | −1.56577e10 | − | 5.04390e10i | −0.252881 | − | 0.814617i | ||||
\(145\) | −2.87434e10 | −0.448433 | ||||||||
\(146\) | 1.69592e9 | − | 5.16165e9i | 0.0255647 | − | 0.0778080i | ||||
\(147\) | 1.93429e11i | 2.81796i | ||||||||
\(148\) | −6.13384e10 | − | 4.51847e10i | −0.863821 | − | 0.636331i | ||||
\(149\) | −4.81786e10 | −0.656029 | −0.328014 | − | 0.944673i | \(-0.606379\pi\) | ||||
−0.328014 | + | 0.944673i | \(0.606379\pi\) | |||||||
\(150\) | −1.96408e10 | − | 6.45321e9i | −0.258644 | − | 0.0849806i | ||||
\(151\) | − | 1.16695e11i | − | 1.48651i | −0.669009 | − | 0.743254i | \(-0.733281\pi\) | ||
0.669009 | − | 0.743254i | \(-0.266719\pi\) | |||||||
\(152\) | −5.76507e10 | − | 8.10194e10i | −0.710537 | − | 0.998553i | ||||
\(153\) | 6.65565e9 | 0.0793840 | ||||||||
\(154\) | 3.60170e10 | − | 1.09620e11i | 0.415819 | − | 1.26557i | ||||
\(155\) | − | 6.51035e10i | − | 0.727689i | ||||||
\(156\) | −9.02722e10 | + | 1.22545e11i | −0.977082 | + | 1.32639i | ||||
\(157\) | 1.19475e11 | 1.25250 | 0.626251 | − | 0.779621i | \(-0.284588\pi\) | ||||
0.626251 | + | 0.779621i | \(0.284588\pi\) | |||||||
\(158\) | 1.05754e11 | + | 3.47466e10i | 1.07402 | + | 0.352880i | ||||
\(159\) | 2.52561e11i | 2.48531i | ||||||||
\(160\) | 4.68874e10 | + | 7.71501e8i | 0.447153 | + | 0.00735761i | ||||
\(161\) | −1.21098e11 | −1.11945 | ||||||||
\(162\) | −3.91962e10 | + | 1.19296e11i | −0.351293 | + | 1.06918i | ||||
\(163\) | 2.89533e9i | 0.0251629i | 0.999921 | + | 0.0125814i | \(0.00400490\pi\) | ||||
−0.999921 | + | 0.0125814i | \(0.995995\pi\) | |||||||
\(164\) | −1.06480e10 | − | 7.84382e9i | −0.0897531 | − | 0.0661163i | ||||
\(165\) | 5.66027e10 | 0.462825 | ||||||||
\(166\) | 2.51501e10 | + | 8.26336e9i | 0.199526 | + | 0.0655566i | ||||
\(167\) | 3.31302e10i | 0.255060i | 0.991835 | + | 0.127530i | \(0.0407048\pi\) | ||||
−0.991835 | + | 0.127530i | \(0.959295\pi\) | |||||||
\(168\) | 2.60076e11 | − | 1.85061e11i | 1.94336 | − | 1.38283i | ||||
\(169\) | 6.40603e10 | 0.464682 | ||||||||
\(170\) | −1.84467e9 | + | 5.61437e9i | −0.0129919 | + | 0.0395418i | ||||
\(171\) | − | 1.52842e11i | − | 1.04535i | ||||||
\(172\) | 2.50911e10 | − | 3.40612e10i | 0.166677 | − | 0.226265i | ||||
\(173\) | −1.42255e11 | −0.917988 | −0.458994 | − | 0.888439i | \(-0.651790\pi\) | ||||
−0.458994 | + | 0.888439i | \(0.651790\pi\) | |||||||
\(174\) | 2.06824e11 | + | 6.79546e10i | 1.29675 | + | 0.426062i | ||||
\(175\) | − | 5.75175e10i | − | 0.350437i | ||||||
\(176\) | −1.22618e11 | + | 3.80642e10i | −0.726090 | + | 0.225399i | ||||
\(177\) | 1.23445e11 | 0.710569 | ||||||||
\(178\) | 6.93378e10 | − | 2.11034e11i | 0.388034 | − | 1.18101i | ||||
\(179\) | 3.52295e10i | 0.191708i | 0.995395 | + | 0.0958542i | \(0.0305583\pi\) | ||||
−0.995395 | + | 0.0958542i | \(0.969442\pi\) | |||||||
\(180\) | 5.80331e10 | + | 4.27498e10i | 0.307124 | + | 0.226241i | ||||
\(181\) | −8.52774e10 | −0.438977 | −0.219488 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219488 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(182\) | −4.02298e11 | − | 1.32180e11i | −2.01461 | − | 0.661923i | ||||
\(183\) | − | 4.64833e11i | − | 2.26486i | ||||||
\(184\) | 7.81217e10 | + | 1.09788e11i | 0.370410 | + | 0.520555i | ||||
\(185\) | 1.03975e11 | 0.479813 | ||||||||
\(186\) | −1.53916e11 | + | 4.68455e11i | −0.691386 | + | 2.10428i | ||||
\(187\) | − | 1.61800e10i | − | 0.0707571i | ||||||
\(188\) | −8.51244e10 | + | 1.15557e11i | −0.362464 | + | 0.492046i | ||||
\(189\) | −8.45750e10 | −0.350698 | ||||||||
\(190\) | 1.28930e11 | + | 4.23614e10i | 0.520697 | + | 0.171081i | ||||
\(191\) | − | 3.50495e11i | − | 1.37884i | −0.724360 | − | 0.689422i | \(-0.757865\pi\) | ||
0.724360 | − | 0.689422i | \(-0.242135\pi\) | |||||||
\(192\) | −3.35557e11 | − | 1.16402e11i | −1.28606 | − | 0.446122i | ||||
\(193\) | 1.57930e11 | 0.589765 | 0.294883 | − | 0.955533i | \(-0.404719\pi\) | ||||
0.294883 | + | 0.955533i | \(0.404719\pi\) | |||||||
\(194\) | 1.99303e9 | − | 6.06593e9i | 0.00725280 | − | 0.0220744i | ||||
\(195\) | − | 2.07727e11i | − | 0.736750i | ||||||
\(196\) | 4.82113e11 | + | 3.55147e11i | 1.66674 | + | 1.22780i | ||||
\(197\) | 3.95179e11 | 1.33187 | 0.665936 | − | 0.746009i | \(-0.268032\pi\) | ||||
0.665936 | + | 0.746009i | \(0.268032\pi\) | |||||||
\(198\) | −1.87484e11 | − | 6.16002e10i | −0.616083 | − | 0.202421i | ||||
\(199\) | 2.13388e10i | 0.0683763i | 0.999415 | + | 0.0341881i | \(0.0108845\pi\) | ||||
−0.999415 | + | 0.0341881i | \(0.989115\pi\) | |||||||
\(200\) | −5.21459e10 | + | 3.71053e10i | −0.162956 | + | 0.115954i | ||||
\(201\) | −4.61293e11 | −1.40604 | ||||||||
\(202\) | 1.55562e11 | − | 4.73463e11i | 0.462536 | − | 1.40776i | ||||
\(203\) | 6.05679e11i | 1.75696i | ||||||||
\(204\) | 2.65468e10 | − | 3.60374e10i | 0.0751382 | − | 0.102000i | ||||
\(205\) | 1.80496e10 | 0.0498537 | ||||||||
\(206\) | 1.72863e11 | + | 5.67961e10i | 0.465978 | + | 0.153103i | ||||
\(207\) | 2.07114e11i | 0.544951i | ||||||||
\(208\) | 1.39692e11 | + | 4.49998e11i | 0.358803 | + | 1.15583i | ||||
\(209\) | −3.71561e11 | −0.931749 | ||||||||
\(210\) | −1.35982e11 | + | 4.13870e11i | −0.332954 | + | 1.01337i | ||||
\(211\) | 2.89532e11i | 0.692283i | 0.938182 | + | 0.346141i | \(0.112508\pi\) | ||||
−0.938182 | + | 0.346141i | \(0.887492\pi\) | |||||||
\(212\) | 6.29495e11 | + | 4.63715e11i | 1.46998 | + | 1.08286i | ||||
\(213\) | 2.49393e11 | 0.568835 | ||||||||
\(214\) | −3.55738e11 | − | 1.16882e11i | −0.792614 | − | 0.260422i | ||||
\(215\) | 5.77376e10i | 0.125680i | ||||||||
\(216\) | 5.45605e10 | + | 7.66765e10i | 0.116040 | + | 0.163077i | ||||
\(217\) | −1.37186e12 | −2.85109 | ||||||||
\(218\) | 8.00932e10 | − | 2.43769e11i | 0.162672 | − | 0.495104i | ||||
\(219\) | − | 5.61616e10i | − | 0.111486i | ||||||
\(220\) | 1.03926e11 | − | 1.41079e11i | 0.201655 | − | 0.273747i | ||||
\(221\) | −5.93793e10 | −0.112635 | ||||||||
\(222\) | −7.48161e11 | − | 2.45817e11i | −1.38749 | − | 0.455876i | ||||
\(223\) | − | 7.87602e11i | − | 1.42818i | −0.700055 | − | 0.714089i | \(-0.746841\pi\) | ||
0.700055 | − | 0.714089i | \(-0.253159\pi\) | |||||||
\(224\) | 1.62570e10 | − | 9.88009e11i | 0.0288271 | − | 1.75195i | ||||
\(225\) | −9.83726e10 | −0.170593 | ||||||||
\(226\) | −1.15984e11 | + | 3.53005e11i | −0.196723 | + | 0.598741i | ||||
\(227\) | 1.02226e12i | 1.69602i | 0.529982 | + | 0.848009i | \(0.322199\pi\) | ||||
−0.529982 | + | 0.848009i | \(0.677801\pi\) | |||||||
\(228\) | −8.27571e11 | − | 6.09627e11i | −1.34317 | − | 0.989441i | ||||
\(229\) | 1.03140e12 | 1.63775 | 0.818877 | − | 0.573970i | \(-0.194597\pi\) | ||||
0.818877 | + | 0.573970i | \(0.194597\pi\) | |||||||
\(230\) | −1.74711e11 | − | 5.74033e10i | −0.271444 | − | 0.0891862i | ||||
\(231\) | − | 1.19273e12i | − | 1.81335i | ||||||
\(232\) | 5.49115e11 | − | 3.90732e11i | 0.817002 | − | 0.581351i | ||||
\(233\) | 2.15652e11 | 0.314032 | 0.157016 | − | 0.987596i | \(-0.449813\pi\) | ||||
0.157016 | + | 0.987596i | \(0.449813\pi\) | |||||||
\(234\) | −2.26068e11 | + | 6.88053e11i | −0.322225 | + | 0.980714i | ||||
\(235\) | − | 1.95882e11i | − | 0.273309i | ||||||
\(236\) | 2.26651e11 | − | 3.07680e11i | 0.309598 | − | 0.420280i | ||||
\(237\) | 1.15066e12 | 1.53888 | ||||||||
\(238\) | 1.18306e11 | + | 3.88707e10i | 0.154925 | + | 0.0509023i | ||||
\(239\) | 1.01800e12i | 1.30545i | 0.757597 | + | 0.652723i | \(0.226373\pi\) | ||||
−0.757597 | + | 0.652723i | \(0.773627\pi\) | |||||||
\(240\) | 4.62942e11 | − | 1.43711e11i | 0.581394 | − | 0.180482i | ||||
\(241\) | 7.81848e11 | 0.961694 | 0.480847 | − | 0.876804i | \(-0.340329\pi\) | ||||
0.480847 | + | 0.876804i | \(0.340329\pi\) | |||||||
\(242\) | 1.09328e11 | − | 3.32749e11i | 0.131721 | − | 0.400903i | ||||
\(243\) | 1.12843e12i | 1.33181i | ||||||||
\(244\) | −1.15857e12 | − | 8.53459e11i | −1.33960 | − | 0.986810i | ||||
\(245\) | −8.17235e11 | −0.925799 | ||||||||
\(246\) | −1.29877e11 | − | 4.26725e10i | −0.144164 | − | 0.0473666i | ||||
\(247\) | 1.36360e12i | 1.48321i | ||||||||
\(248\) | 8.85003e11 | + | 1.24374e12i | 0.943380 | + | 1.32578i | ||||
\(249\) | 2.73647e11 | 0.285887 | ||||||||
\(250\) | 2.72647e10 | − | 8.29821e10i | 0.0279191 | − | 0.0849737i | ||||
\(251\) | − | 6.23828e11i | − | 0.626176i | −0.949724 | − | 0.313088i | \(-0.898637\pi\) | ||
0.949724 | − | 0.313088i | \(-0.101363\pi\) | |||||||
\(252\) | 9.00823e11 | − | 1.22287e12i | 0.886414 | − | 1.20331i | ||||
\(253\) | 5.03498e11 | 0.485730 | ||||||||
\(254\) | 3.92147e11 | + | 1.28844e11i | 0.370920 | + | 0.121870i | ||||
\(255\) | 6.10874e10i | 0.0566566i | ||||||||
\(256\) | −9.06226e11 | + | 6.22639e11i | −0.824208 | + | 0.566287i | ||||
\(257\) | 1.04389e12 | 0.931086 | 0.465543 | − | 0.885025i | \(-0.345859\pi\) | ||||
0.465543 | + | 0.885025i | \(0.345859\pi\) | |||||||
\(258\) | 1.36502e11 | − | 4.15454e11i | 0.119410 | − | 0.363433i | ||||
\(259\) | − | 2.19097e12i | − | 1.87991i | ||||||
\(260\) | −5.17750e11 | − | 3.81398e11i | −0.435766 | − | 0.321005i | ||||
\(261\) | 1.03590e12 | 0.855291 | ||||||||
\(262\) | 9.04847e11 | + | 2.97298e11i | 0.732940 | + | 0.240816i | ||||
\(263\) | 2.25563e12i | 1.79262i | 0.443423 | + | 0.896312i | \(0.353764\pi\) | ||||
−0.443423 | + | 0.896312i | \(0.646236\pi\) | |||||||
\(264\) | −1.08134e12 | + | 7.69445e11i | −0.843223 | + | 0.600009i | ||||
\(265\) | −1.06706e12 | −0.816509 | ||||||||
\(266\) | 8.92637e11 | − | 2.71680e12i | 0.670296 | − | 2.04009i | ||||
\(267\) | − | 2.29617e12i | − | 1.69218i | ||||||
\(268\) | −8.46959e11 | + | 1.14975e12i | −0.612616 | + | 0.831629i | ||||
\(269\) | 4.57791e11 | 0.325017 | 0.162509 | − | 0.986707i | \(-0.448042\pi\) | ||||
0.162509 | + | 0.986707i | \(0.448042\pi\) | |||||||
\(270\) | −1.22019e11 | − | 4.00907e10i | −0.0850369 | − | 0.0279399i | ||||
\(271\) | 7.07347e10i | 0.0483934i | 0.999707 | + | 0.0241967i | \(0.00770280\pi\) | ||||
−0.999707 | + | 0.0241967i | \(0.992297\pi\) | |||||||
\(272\) | −4.10800e10 | − | 1.32333e11i | −0.0275922 | − | 0.0888841i | ||||
\(273\) | −4.37722e12 | −2.88659 | ||||||||
\(274\) | −1.43708e11 | + | 4.37385e11i | −0.0930525 | + | 0.283212i | ||||
\(275\) | 2.39145e11i | 0.152054i | ||||||||
\(276\) | 1.12143e12 | + | 8.26097e11i | 0.700207 | + | 0.515805i | ||||
\(277\) | −2.83728e12 | −1.73982 | −0.869908 | − | 0.493214i | \(-0.835822\pi\) | ||||
−0.869908 | + | 0.493214i | \(0.835822\pi\) | |||||||
\(278\) | −1.45786e12 | − | 4.78997e11i | −0.877995 | − | 0.288475i | ||||
\(279\) | 2.34630e12i | 1.38791i | ||||||||
\(280\) | 7.81881e11 | + | 1.09882e12i | 0.454308 | + | 0.638462i | ||||
\(281\) | −4.75819e11 | −0.271588 | −0.135794 | − | 0.990737i | \(-0.543358\pi\) | ||||
−0.135794 | + | 0.990737i | \(0.543358\pi\) | |||||||
\(282\) | −4.63100e11 | + | 1.40948e12i | −0.259674 | + | 0.790337i | ||||
\(283\) | − | 9.46174e11i | − | 0.521241i | −0.965441 | − | 0.260621i | \(-0.916073\pi\) | ||
0.965441 | − | 0.260621i | \(-0.0839272\pi\) | |||||||
\(284\) | 4.57899e11 | − | 6.21600e11i | 0.247844 | − | 0.336449i | ||||
\(285\) | 1.40283e12 | 0.746070 | ||||||||
\(286\) | 1.67267e12 | + | 5.49574e11i | 0.874137 | + | 0.287208i | ||||
\(287\) | − | 3.80340e11i | − | 0.195327i | ||||||
\(288\) | −1.68980e12 | − | 2.78045e10i | −0.852850 | − | 0.0140331i | ||||
\(289\) | −1.99853e12 | −0.991338 | ||||||||
\(290\) | −2.87107e11 | + | 8.73830e11i | −0.139976 | + | 0.426027i | ||||
\(291\) | − | 6.60006e10i | − | 0.0316288i | ||||||
\(292\) | −1.39980e11 | − | 1.03116e11i | −0.0659404 | − | 0.0485748i | ||||
\(293\) | 2.37212e12 | 1.09849 | 0.549247 | − | 0.835660i | \(-0.314915\pi\) | ||||
0.549247 | + | 0.835660i | \(0.314915\pi\) | |||||||
\(294\) | 5.88046e12 | + | 1.93209e12i | 2.67716 | + | 0.879613i | ||||
\(295\) | 5.21552e11i | 0.233447i | ||||||||
\(296\) | −1.98635e12 | + | 1.41342e12i | −0.874173 | + | 0.622033i | ||||
\(297\) | 3.51645e11 | 0.152167 | ||||||||
\(298\) | −4.81238e11 | + | 1.46468e12i | −0.204776 | + | 0.623250i | ||||
\(299\) | − | 1.84780e12i | − | 0.773211i | ||||||
\(300\) | −3.92370e11 | + | 5.32643e11i | −0.161469 | + | 0.219195i | ||||
\(301\) | 1.21664e12 | 0.492415 | ||||||||
\(302\) | −3.54766e12 | − | 1.16562e12i | −1.41223 | − | 0.464006i | ||||
\(303\) | − | 5.15153e12i | − | 2.01708i | ||||||
\(304\) | −3.03893e12 | + | 9.43372e11i | −1.17045 | + | 0.363342i | ||||
\(305\) | 1.96391e12 | 0.744086 | ||||||||
\(306\) | 6.64808e10 | − | 2.02339e11i | 0.0247793 | − | 0.0754176i | ||||
\(307\) | − | 3.27142e12i | − | 1.19962i | −0.800142 | − | 0.599811i | \(-0.795243\pi\) | ||
0.800142 | − | 0.599811i | \(-0.204757\pi\) | |||||||
\(308\) | −2.97282e12 | − | 2.18992e12i | −1.07254 | − | 0.790085i | ||||
\(309\) | 1.88084e12 | 0.667667 | ||||||||
\(310\) | −1.97922e12 | − | 6.50295e11i | −0.691329 | − | 0.227144i | ||||
\(311\) | 2.94681e12i | 1.01286i | 0.862280 | + | 0.506431i | \(0.169036\pi\) | ||||
−0.862280 | + | 0.506431i | \(0.830964\pi\) | |||||||
\(312\) | 2.82380e12 | + | 3.96843e12i | 0.955127 | + | 1.34229i | ||||
\(313\) | −3.18034e11 | −0.105865 | −0.0529324 | − | 0.998598i | \(-0.516857\pi\) | ||||
−0.0529324 | + | 0.998598i | \(0.516857\pi\) | |||||||
\(314\) | 1.19339e12 | − | 3.63217e12i | 0.390962 | − | 1.18992i | ||||
\(315\) | 2.07290e12i | 0.668384i | ||||||||
\(316\) | 2.11267e12 | − | 2.86796e12i | 0.670497 | − | 0.910202i | ||||
\(317\) | 3.80109e12 | 1.18744 | 0.593720 | − | 0.804672i | \(-0.297659\pi\) | ||||
0.593720 | + | 0.804672i | \(0.297659\pi\) | |||||||
\(318\) | 7.67812e12 | + | 2.52273e12i | 2.36113 | + | 0.775775i | ||||
\(319\) | − | 2.51828e12i | − | 0.762344i | ||||||
\(320\) | 4.91796e11 | − | 1.41772e12i | 0.146567 | − | 0.422514i | ||||
\(321\) | −3.87063e12 | −1.13568 | ||||||||
\(322\) | −1.20960e12 | + | 3.68150e12i | −0.349432 | + | 1.06352i | ||||
\(323\) | − | 4.01001e11i | − | 0.114060i | ||||||
\(324\) | 3.23523e12 | + | 2.38322e12i | 0.906107 | + | 0.667480i | ||||
\(325\) | 8.77644e11 | 0.242048 | ||||||||
\(326\) | 8.80213e10 | + | 2.89204e10i | 0.0239056 | + | 0.00785447i | ||||
\(327\) | − | 2.65234e12i | − | 0.709399i | ||||||
\(328\) | −3.44820e11 | + | 2.45362e11i | −0.0908287 | + | 0.0646307i | ||||
\(329\) | −4.12761e12 | −1.07083 | ||||||||
\(330\) | 5.65383e11 | − | 1.72078e12i | 0.144469 | − | 0.439700i | ||||
\(331\) | 4.34328e12i | 1.09315i | 0.837411 | + | 0.546573i | \(0.184068\pi\) | ||||
−0.837411 | + | 0.546573i | \(0.815932\pi\) | |||||||
\(332\) | 5.02431e11 | − | 6.82051e11i | 0.124562 | − | 0.169093i | ||||
\(333\) | −3.74723e12 | −0.915142 | ||||||||
\(334\) | 1.00719e12 | + | 3.30925e11i | 0.242315 | + | 0.0796155i | ||||
\(335\) | − | 1.94896e12i | − | 0.461932i | ||||||
\(336\) | −3.02827e12 | − | 9.75511e12i | −0.707128 | − | 2.27790i | ||||
\(337\) | 7.56835e11 | 0.174121 | 0.0870606 | − | 0.996203i | \(-0.472253\pi\) | ||||
0.0870606 | + | 0.996203i | \(0.472253\pi\) | |||||||
\(338\) | 6.39875e11 | − | 1.94750e12i | 0.145048 | − | 0.441464i | ||||
\(339\) | 3.84089e12i | 0.857894i | ||||||||
\(340\) | 1.52257e11 | + | 1.12160e11i | 0.0335107 | + | 0.0246855i | ||||
\(341\) | 5.70389e12 | 1.23708 | ||||||||
\(342\) | −4.64657e12 | − | 1.52668e12i | −0.993119 | − | 0.326301i | ||||
\(343\) | 8.90215e12i | 1.87510i | ||||||||
\(344\) | −7.84873e11 | − | 1.10302e12i | −0.162932 | − | 0.228977i | ||||
\(345\) | −1.90095e12 | −0.388933 | ||||||||
\(346\) | −1.42093e12 | + | 4.32471e12i | −0.286545 | + | 0.872120i | ||||
\(347\) | − | 4.88633e11i | − | 0.0971260i | −0.998820 | − | 0.0485630i | \(-0.984536\pi\) | ||
0.998820 | − | 0.0485630i | \(-0.0154642\pi\) | |||||||
\(348\) | 4.13179e12 | − | 5.60892e12i | 0.809547 | − | 1.09896i | ||||
\(349\) | −2.32017e12 | −0.448118 | −0.224059 | − | 0.974576i | \(-0.571931\pi\) | ||||
−0.224059 | + | 0.974576i | \(0.571931\pi\) | |||||||
\(350\) | −1.74860e12 | − | 5.74521e11i | −0.332927 | − | 0.109387i | ||||
\(351\) | − | 1.29051e12i | − | 0.242228i | ||||||
\(352\) | −6.75933e10 | + | 4.10793e12i | −0.0125081 | + | 0.760168i | ||||
\(353\) | 2.85311e12 | 0.520529 | 0.260265 | − | 0.965537i | \(-0.416190\pi\) | ||||
0.260265 | + | 0.965537i | \(0.416190\pi\) | |||||||
\(354\) | 1.23304e12 | − | 3.75286e12i | 0.221800 | − | 0.675065i | ||||
\(355\) | 1.05368e12i | 0.186882i | ||||||||
\(356\) | −5.72309e12 | − | 4.21589e12i | −1.00088 | − | 0.737292i | ||||
\(357\) | 1.28723e12 | 0.221981 | ||||||||
\(358\) | 1.07102e12 | + | 3.51894e11i | 0.182130 | + | 0.0598408i | ||||
\(359\) | 1.59682e12i | 0.267783i | 0.990996 | + | 0.133892i | \(0.0427474\pi\) | ||||
−0.990996 | + | 0.133892i | \(0.957253\pi\) | |||||||
\(360\) | 1.87931e12 | − | 1.33726e12i | 0.310804 | − | 0.221158i | ||||
\(361\) | −3.07761e12 | −0.501971 | ||||||||
\(362\) | −8.51805e11 | + | 2.59253e12i | −0.137024 | + | 0.417043i | ||||
\(363\) | − | 3.62049e12i | − | 0.574425i | ||||||
\(364\) | −8.03681e12 | + | 1.09100e13i | −1.25770 | + | 1.70733i | ||||
\(365\) | 2.37282e11 | 0.0366269 | ||||||||
\(366\) | −1.41314e13 | − | 4.64305e12i | −2.15170 | − | 0.706965i | ||||
\(367\) | − | 2.96640e11i | − | 0.0445553i | −0.999752 | − | 0.0222777i | \(-0.992908\pi\) | ||
0.999752 | − | 0.0222777i | \(-0.00709178\pi\) | |||||||
\(368\) | 4.11801e12 | − | 1.27835e12i | 0.610167 | − | 0.189413i | ||||
\(369\) | −6.50498e11 | −0.0950855 | ||||||||
\(370\) | 1.03857e12 | − | 3.16097e12i | 0.149771 | − | 0.455839i | ||||
\(371\) | 2.24851e13i | 3.19909i | ||||||||
\(372\) | 1.27041e13 | + | 9.35846e12i | 1.78333 | + | 1.31368i | ||||
\(373\) | 9.87929e12 | 1.36830 | 0.684151 | − | 0.729341i | \(-0.260173\pi\) | ||||
0.684151 | + | 0.729341i | \(0.260173\pi\) | |||||||
\(374\) | −4.91890e11 | − | 1.61616e11i | −0.0672217 | − | 0.0220865i | ||||
\(375\) | − | 9.02890e11i | − | 0.121753i | ||||||
\(376\) | 2.66278e12 | + | 3.74213e12i | 0.354320 | + | 0.497943i | ||||
\(377\) | −9.24190e12 | −1.21354 | ||||||||
\(378\) | −8.44789e11 | + | 2.57117e12i | −0.109468 | + | 0.333175i | ||||
\(379\) | − | 2.68525e12i | − | 0.343391i | −0.985150 | − | 0.171696i | \(-0.945075\pi\) | ||
0.985150 | − | 0.171696i | \(-0.0549246\pi\) | |||||||
\(380\) | 2.57566e12 | − | 3.49647e12i | 0.325066 | − | 0.441278i | ||||
\(381\) | 4.26677e12 | 0.531464 | ||||||||
\(382\) | −1.06554e13 | − | 3.50097e12i | −1.30995 | − | 0.430399i | ||||
\(383\) | − | 2.79218e12i | − | 0.338805i | −0.985547 | − | 0.169403i | \(-0.945816\pi\) | ||
0.985547 | − | 0.169403i | \(-0.0541838\pi\) | |||||||
\(384\) | −6.89050e12 | + | 9.03860e12i | −0.825267 | + | 1.08254i | ||||
\(385\) | 5.03926e12 | 0.595749 | ||||||||
\(386\) | 1.57751e12 | − | 4.80126e12i | 0.184092 | − | 0.560297i | ||||
\(387\) | − | 2.08083e12i | − | 0.239708i | ||||||
\(388\) | −1.64503e11 | − | 1.21181e11i | −0.0187075 | − | 0.0137808i | ||||
\(389\) | 4.54004e12 | 0.509697 | 0.254848 | − | 0.966981i | \(-0.417974\pi\) | ||||
0.254848 | + | 0.966981i | \(0.417974\pi\) | |||||||
\(390\) | −6.31514e12 | − | 2.07491e12i | −0.699938 | − | 0.229973i | ||||
\(391\) | 5.43390e11i | 0.0594604i | ||||||||
\(392\) | 1.56125e13 | − | 1.11093e13i | 1.68672 | − | 1.20021i | ||||
\(393\) | 9.84523e12 | 1.05018 | ||||||||
\(394\) | 3.94730e12 | − | 1.20139e13i | 0.415737 | − | 1.26533i | ||||
\(395\) | 4.86151e12i | 0.505576i | ||||||||
\(396\) | −3.74543e12 | + | 5.08443e12i | −0.384614 | + | 0.522115i | ||||
\(397\) | −1.56339e13 | −1.58532 | −0.792659 | − | 0.609666i | \(-0.791304\pi\) | ||||
−0.792659 | + | 0.609666i | \(0.791304\pi\) | |||||||
\(398\) | 6.48724e11 | + | 2.13146e11i | 0.0649598 | + | 0.0213433i | ||||
\(399\) | − | 2.95603e13i | − | 2.92310i | ||||||
\(400\) | 6.07176e11 | + | 1.95592e12i | 0.0592945 | + | 0.191008i | ||||
\(401\) | −9.95481e12 | −0.960088 | −0.480044 | − | 0.877244i | \(-0.659379\pi\) | ||||
−0.480044 | + | 0.877244i | \(0.659379\pi\) | |||||||
\(402\) | −4.60769e12 | + | 1.40238e13i | −0.438887 | + | 1.33578i | ||||
\(403\) | − | 2.09328e13i | − | 1.96926i | ||||||
\(404\) | −1.28399e13 | − | 9.45850e12i | −1.19304 | − | 0.878851i | ||||
\(405\) | −5.48407e12 | −0.503301 | ||||||||
\(406\) | 1.84133e13 | + | 6.04991e12i | 1.66917 | + | 0.548427i | ||||
\(407\) | 9.10957e12i | 0.815691i | ||||||||
\(408\) | −8.30409e11 | − | 1.16702e12i | −0.0734499 | − | 0.103223i | ||||
\(409\) | −3.95071e12 | −0.345191 | −0.172595 | − | 0.984993i | \(-0.555215\pi\) | ||||
−0.172595 | + | 0.984993i | \(0.555215\pi\) | |||||||
\(410\) | 1.80291e11 | − | 5.48727e11i | 0.0155616 | − | 0.0473628i | ||||
\(411\) | 4.75899e12i | 0.405794i | ||||||||
\(412\) | 3.45333e12 | − | 4.68791e12i | 0.290905 | − | 0.394905i | ||||
\(413\) | 1.09901e13 | 0.914644 | ||||||||
\(414\) | 6.29649e12 | + | 2.06879e12i | 0.517723 | + | 0.170104i | ||||
\(415\) | 1.15615e12i | 0.0939237i | ||||||||
\(416\) | 1.50758e13 | + | 2.48062e11i | 1.21008 | + | 0.0199110i | ||||
\(417\) | −1.58623e13 | −1.25802 | ||||||||
\(418\) | −3.71139e12 | + | 1.12959e13i | −0.290841 | + | 0.885194i | ||||
\(419\) | 1.57517e13i | 1.21971i | 0.792513 | + | 0.609856i | \(0.208773\pi\) | ||||
−0.792513 | + | 0.609856i | \(0.791227\pi\) | |||||||
\(420\) | 1.12238e13 | + | 8.26800e12i | 0.858806 | + | 0.632636i | ||||
\(421\) | 1.89265e12 | 0.143107 | 0.0715534 | − | 0.997437i | \(-0.477204\pi\) | ||||
0.0715534 | + | 0.997437i | \(0.477204\pi\) | |||||||
\(422\) | 8.80208e12 | + | 2.89202e12i | 0.657693 | + | 0.216093i | ||||
\(423\) | 7.05948e12i | 0.521280i | ||||||||
\(424\) | 2.03852e13 | − | 1.45055e13i | 1.48760 | − | 1.05853i | ||||
\(425\) | −2.58093e11 | −0.0186137 | ||||||||
\(426\) | 2.49110e12 | − | 7.58182e12i | 0.177559 | − | 0.540413i | ||||
\(427\) | − | 4.13835e13i | − | 2.91533i | ||||||
\(428\) | −7.10668e12 | + | 9.64735e12i | −0.494821 | + | 0.671721i | ||||
\(429\) | 1.81995e13 | 1.25249 | ||||||||
\(430\) | 1.75529e12 | + | 5.76719e11i | 0.119400 | + | 0.0392304i | ||||
\(431\) | − | 1.61299e13i | − | 1.08454i | −0.840204 | − | 0.542271i | \(-0.817565\pi\) | ||
0.840204 | − | 0.542271i | \(-0.182435\pi\) | |||||||
\(432\) | 2.87604e12 | − | 8.92805e11i | 0.191151 | − | 0.0593387i | ||||
\(433\) | −2.27857e13 | −1.49700 | −0.748501 | − | 0.663134i | \(-0.769226\pi\) | ||||
−0.748501 | + | 0.663134i | \(0.769226\pi\) | |||||||
\(434\) | −1.37030e13 | + | 4.17060e13i | −0.889952 | + | 2.70863i | ||||
\(435\) | 9.50775e12i | 0.610424i | ||||||||
\(436\) | −6.61083e12 | − | 4.86984e12i | −0.419588 | − | 0.309088i | ||||
\(437\) | 1.24786e13 | 0.782991 | ||||||||
\(438\) | −1.70737e12 | − | 5.60977e11i | −0.105915 | − | 0.0347997i | ||||
\(439\) | 7.33847e12i | 0.450073i | 0.974350 | + | 0.225036i | \(0.0722501\pi\) | ||||
−0.974350 | + | 0.225036i | \(0.927750\pi\) | |||||||
\(440\) | −3.25089e12 | − | 4.56864e12i | −0.197124 | − | 0.277028i | ||||
\(441\) | 2.94528e13 | 1.76577 | ||||||||
\(442\) | −5.93118e11 | + | 1.80520e12i | −0.0351584 | + | 0.107007i | ||||
\(443\) | − | 3.68107e11i | − | 0.0215753i | −0.999942 | − | 0.0107876i | \(-0.996566\pi\) | ||
0.999942 | − | 0.0107876i | \(-0.00343388\pi\) | |||||||
\(444\) | −1.49462e13 | + | 2.02896e13i | −0.866197 | + | 1.17587i | ||||
\(445\) | 9.70128e12 | 0.555941 | ||||||||
\(446\) | −2.39440e13 | − | 7.86707e12i | −1.35682 | − | 0.445799i | ||||
\(447\) | 1.59365e13i | 0.893010i | ||||||||
\(448\) | −2.98742e13 | − | 1.03631e13i | −1.65541 | − | 0.574248i | ||||
\(449\) | 1.73670e13 | 0.951687 | 0.475844 | − | 0.879530i | \(-0.342143\pi\) | ||||
0.475844 | + | 0.879530i | \(0.342143\pi\) | |||||||
\(450\) | −9.82608e11 | + | 2.99063e12i | −0.0532497 | + | 0.162069i | ||||
\(451\) | 1.58137e12i | 0.0847522i | ||||||||
\(452\) | 9.57323e12 | + | 7.05209e12i | 0.507419 | + | 0.373788i | ||||
\(453\) | −3.86004e13 | −2.02349 | ||||||||
\(454\) | 3.10777e13 | + | 1.02109e13i | 1.61128 | + | 0.529403i | ||||
\(455\) | − | 1.84937e13i | − | 0.948345i | ||||||
\(456\) | −2.67996e13 | + | 1.90697e13i | −1.35927 | + | 0.967209i | ||||
\(457\) | 1.79800e13 | 0.902005 | 0.451003 | − | 0.892523i | \(-0.351067\pi\) | ||||
0.451003 | + | 0.892523i | \(0.351067\pi\) | |||||||
\(458\) | 1.03022e13 | − | 3.13556e13i | 0.511216 | − | 1.55592i | ||||
\(459\) | 3.79506e11i | 0.0186275i | ||||||||
\(460\) | −3.49025e12 | + | 4.73802e12i | −0.169460 | + | 0.230042i | ||||
\(461\) | −4.09031e13 | −1.96450 | −0.982249 | − | 0.187580i | \(-0.939936\pi\) | ||||
−0.982249 | + | 0.187580i | \(0.939936\pi\) | |||||||
\(462\) | −3.62603e13 | − | 1.19137e13i | −1.72275 | − | 0.566028i | ||||
\(463\) | 1.70952e13i | 0.803469i | 0.915756 | + | 0.401735i | \(0.131593\pi\) | ||||
−0.915756 | + | 0.401735i | \(0.868407\pi\) | |||||||
\(464\) | −6.39377e12 | − | 2.05966e13i | −0.297281 | − | 0.957646i | ||||
\(465\) | −2.15350e13 | −0.990556 | ||||||||
\(466\) | 2.15407e12 | − | 6.55607e12i | 0.0980236 | − | 0.298342i | ||||
\(467\) | 2.45776e13i | 1.10651i | 0.833012 | + | 0.553255i | \(0.186614\pi\) | ||||
−0.833012 | + | 0.553255i | \(0.813386\pi\) | |||||||
\(468\) | 1.86595e13 | + | 1.37454e13i | 0.831131 | + | 0.612250i | ||||
\(469\) | −4.10683e13 | −1.80985 | ||||||||
\(470\) | −5.95502e12 | − | 1.95659e12i | −0.259653 | − | 0.0853121i | ||||
\(471\) | − | 3.95200e13i | − | 1.70495i | ||||||
\(472\) | −7.08987e12 | − | 9.96375e12i | −0.302642 | − | 0.425317i | ||||
\(473\) | −5.05854e12 | −0.213658 | ||||||||
\(474\) | 1.14935e13 | − | 3.49813e13i | 0.480353 | − | 1.46199i | ||||
\(475\) | 5.92692e12i | 0.245110i | ||||||||
\(476\) | 2.36343e12 | − | 3.20836e12i | 0.0967180 | − | 0.131295i | ||||
\(477\) | 3.84565e13 | 1.55732 | ||||||||
\(478\) | 3.09484e13 | + | 1.01684e13i | 1.24022 | + | 0.407488i | ||||
\(479\) | 3.22393e13i | 1.27852i | 0.768990 | + | 0.639261i | \(0.220760\pi\) | ||||
−0.768990 | + | 0.639261i | \(0.779240\pi\) | |||||||
\(480\) | 2.55198e11 | − | 1.55094e13i | 0.0100155 | − | 0.608681i | ||||
\(481\) | 3.34314e13 | 1.29846 | ||||||||
\(482\) | 7.80959e12 | − | 2.37690e13i | 0.300188 | − | 0.913643i | ||||
\(483\) | 4.00567e13i | 1.52384i | ||||||||
\(484\) | −9.02388e12 | − | 6.64741e12i | −0.339756 | − | 0.250280i | ||||
\(485\) | 2.78852e11 | 0.0103912 | ||||||||
\(486\) | 3.43054e13 | + | 1.12714e13i | 1.26526 | + | 0.415717i | ||||
\(487\) | 3.24299e13i | 1.18386i | 0.805990 | + | 0.591930i | \(0.201634\pi\) | ||||
−0.805990 | + | 0.591930i | \(0.798366\pi\) | |||||||
\(488\) | −3.75187e13 | + | 2.66970e13i | −1.35565 | + | 0.964637i | ||||
\(489\) | 9.57720e11 | 0.0342527 | ||||||||
\(490\) | −8.16306e12 | + | 2.48449e13i | −0.288983 | + | 0.879541i | ||||
\(491\) | − | 1.26956e13i | − | 0.444882i | −0.974946 | − | 0.222441i | \(-0.928597\pi\) | ||
0.974946 | − | 0.222441i | \(-0.0714025\pi\) | |||||||
\(492\) | −2.59458e12 | + | 3.52216e12i | −0.0899999 | + | 0.122175i | ||||
\(493\) | 2.71781e12 | 0.0933221 | ||||||||
\(494\) | 4.14550e13 | + | 1.36205e13i | 1.40910 | + | 0.462976i | ||||
\(495\) | − | 8.61868e12i | − | 0.290011i | ||||||
\(496\) | 4.66510e13 | − | 1.44818e13i | 1.55401 | − | 0.482409i | ||||
\(497\) | 2.22031e13 | 0.732205 | ||||||||
\(498\) | 2.73336e12 | − | 8.31917e12i | 0.0892380 | − | 0.271602i | ||||
\(499\) | − | 1.08543e13i | − | 0.350832i | −0.984494 | − | 0.175416i | \(-0.943873\pi\) | ||
0.984494 | − | 0.175416i | \(-0.0561270\pi\) | |||||||
\(500\) | −2.25041e12 | − | 1.65776e12i | −0.0720131 | − | 0.0530482i | ||||
\(501\) | 1.09588e13 | 0.347196 | ||||||||
\(502\) | −1.89651e13 | − | 6.23119e12i | −0.594889 | − | 0.195458i | ||||
\(503\) | 1.24893e13i | 0.387881i | 0.981013 | + | 0.193940i | \(0.0621269\pi\) | ||||
−0.981013 | + | 0.193940i | \(0.937873\pi\) | |||||||
\(504\) | −2.81786e13 | − | 3.96008e13i | −0.866497 | − | 1.21773i | ||||
\(505\) | 2.17652e13 | 0.662681 | ||||||||
\(506\) | 5.02925e12 | − | 1.53069e13i | 0.151618 | − | 0.461460i | ||||
\(507\) | − | 2.11899e13i | − | 0.632542i | ||||||
\(508\) | 7.83402e12 | − | 1.06347e13i | 0.231561 | − | 0.314345i | ||||
\(509\) | −4.73601e12 | −0.138619 | −0.0693097 | − | 0.997595i | \(-0.522080\pi\) | ||||
−0.0693097 | + | 0.997595i | \(0.522080\pi\) | |||||||
\(510\) | 1.85712e12 | + | 6.10179e11i | 0.0538257 | + | 0.0176851i | ||||
\(511\) | − | 4.99999e12i | − | 0.143504i | ||||||
\(512\) | 9.87695e12 | + | 3.37696e13i | 0.280720 | + | 0.959790i | ||||
\(513\) | 8.71507e12 | 0.245292 | ||||||||
\(514\) | 1.04270e13 | − | 3.17354e13i | 0.290634 | − | 0.884564i | ||||
\(515\) | 7.94653e12i | 0.219352i | ||||||||
\(516\) | −1.12668e13 | − | 8.29963e12i | −0.308001 | − | 0.226887i | ||||
\(517\) | 1.71617e13 | 0.464631 | ||||||||
\(518\) | −6.66078e13 | − | 2.18848e13i | −1.78598 | − | 0.586804i | ||||
\(519\) | 4.70552e13i | 1.24960i | ||||||||
\(520\) | −1.67665e13 | + | 1.19305e13i | −0.440988 | + | 0.313793i | ||||
\(521\) | −3.60036e13 | −0.937902 | −0.468951 | − | 0.883224i | \(-0.655368\pi\) | ||||
−0.468951 | + | 0.883224i | \(0.655368\pi\) | |||||||
\(522\) | 1.03472e13 | − | 3.14924e13i | 0.266975 | − | 0.812556i | ||||
\(523\) | − | 4.44220e13i | − | 1.13525i | −0.823289 | − | 0.567623i | \(-0.807863\pi\) | ||
0.823289 | − | 0.567623i | \(-0.192137\pi\) | |||||||
\(524\) | 1.80764e13 | − | 2.45387e13i | 0.457567 | − | 0.621149i | ||||
\(525\) | −1.90257e13 | −0.477027 | ||||||||
\(526\) | 6.85737e13 | + | 2.25307e13i | 1.70306 | + | 0.559559i | ||||
\(527\) | 6.15581e12i | 0.151437i | ||||||||
\(528\) | 1.25909e13 | + | 4.05596e13i | 0.306822 | + | 0.988381i | ||||
\(529\) | 2.45170e13 | 0.591819 | ||||||||
\(530\) | −1.06585e13 | + | 3.24399e13i | −0.254869 | + | 0.775712i | ||||
\(531\) | − | 1.87965e13i | − | 0.445250i | ||||||
\(532\) | −7.36776e13 | − | 5.42743e13i | −1.72893 | − | 1.27361i | ||||
\(533\) | 5.80350e12 | 0.134913 | ||||||||
\(534\) | −6.98061e13 | − | 2.29356e13i | −1.60763 | − | 0.528207i | ||||
\(535\) | − | 1.63533e13i | − | 0.373110i | ||||||
\(536\) | 2.64937e13 | + | 3.72329e13i | 0.598851 | + | 0.841596i | ||||
\(537\) | 1.16532e13 | 0.260960 | ||||||||
\(538\) | 4.57271e12 | − | 1.39174e13i | 0.101452 | − | 0.308777i | ||||
\(539\) | − | 7.16001e13i | − | 1.57387i | ||||||
\(540\) | −2.43760e12 | + | 3.30905e12i | −0.0530877 | + | 0.0720667i | ||||
\(541\) | −8.68078e12 | −0.187315 | −0.0936575 | − | 0.995604i | \(-0.529856\pi\) | ||||
−0.0936575 | + | 0.995604i | \(0.529856\pi\) | |||||||
\(542\) | 2.15041e12 | + | 7.06543e11i | 0.0459754 | + | 0.0151058i | ||||
\(543\) | 2.82081e13i | 0.597551i | ||||||||
\(544\) | −4.43341e12 | − | 7.29488e10i | −0.0930557 | − | 0.00153117i | ||||
\(545\) | 1.12061e13 | 0.233062 | ||||||||
\(546\) | −4.37224e13 | + | 1.33072e14i | −0.901034 | + | 2.74236i | ||||
\(547\) | 1.93160e13i | 0.394439i | 0.980359 | + | 0.197220i | \(0.0631912\pi\) | ||||
−0.980359 | + | 0.197220i | \(0.936809\pi\) | |||||||
\(548\) | 1.18616e13 | + | 8.73777e12i | 0.240015 | + | 0.176806i | ||||
\(549\) | −7.07784e13 | −1.41919 | ||||||||
\(550\) | 7.27028e12 | + | 2.38874e12i | 0.144457 | + | 0.0474629i | ||||
\(551\) | − | 6.24125e13i | − | 1.22889i | ||||||
\(552\) | 3.63158e13 | − | 2.58411e13i | 0.708599 | − | 0.504215i | ||||
\(553\) | 1.02442e14 | 1.98085 | ||||||||
\(554\) | −2.83406e13 | + | 8.62565e13i | −0.543075 | + | 1.65289i | ||||
\(555\) | − | 3.43931e13i | − | 0.653139i | ||||||
\(556\) | −2.91241e13 | + | 3.95360e13i | −0.548123 | + | 0.744079i | ||||
\(557\) | −9.40071e13 | −1.75341 | −0.876707 | − | 0.481024i | \(-0.840265\pi\) | ||||
−0.876707 | + | 0.481024i | \(0.840265\pi\) | |||||||
\(558\) | 7.13300e13 | + | 2.34363e13i | 1.31856 | + | 0.433230i | ||||
\(559\) | 1.85644e13i | 0.340113i | ||||||||
\(560\) | 4.12152e13 | − | 1.27944e13i | 0.748371 | − | 0.232316i | ||||
\(561\) | −5.35203e12 | −0.0963172 | ||||||||
\(562\) | −4.75278e12 | + | 1.44654e13i | −0.0847747 | + | 0.258018i | ||||
\(563\) | 1.01341e13i | 0.179162i | 0.995980 | + | 0.0895808i | \(0.0285527\pi\) | ||||
−0.995980 | + | 0.0895808i | \(0.971447\pi\) | |||||||
\(564\) | 3.82239e13 | + | 2.81575e13i | 0.669792 | + | 0.493399i | ||||
\(565\) | −1.62277e13 | −0.281848 | ||||||||
\(566\) | −2.87647e13 | − | 9.45099e12i | −0.495197 | − | 0.162703i | ||||
\(567\) | 1.15560e14i | 1.97194i | ||||||||
\(568\) | −1.43235e13 | − | 2.01296e13i | −0.242275 | − | 0.340481i | ||||
\(569\) | −4.06690e13 | −0.681871 | −0.340936 | − | 0.940087i | \(-0.610744\pi\) | ||||
−0.340936 | + | 0.940087i | \(0.610744\pi\) | |||||||
\(570\) | 1.40123e13 | − | 4.26474e13i | 0.232882 | − | 0.708792i | ||||
\(571\) | 8.31022e13i | 1.36909i | 0.728970 | + | 0.684545i | \(0.239999\pi\) | ||||
−0.728970 | + | 0.684545i | \(0.760001\pi\) | |||||||
\(572\) | 3.34153e13 | − | 4.53614e13i | 0.545715 | − | 0.740810i | ||||
\(573\) | −1.15937e14 | −1.87693 | ||||||||
\(574\) | −1.15628e13 | − | 3.79908e12i | −0.185567 | − | 0.0609703i | ||||
\(575\) | − | 8.03148e12i | − | 0.127778i | ||||||
\(576\) | −1.77241e13 | + | 5.10940e13i | −0.279545 | + | 0.805857i | ||||
\(577\) | −4.07454e13 | −0.637089 | −0.318544 | − | 0.947908i | \(-0.603194\pi\) | ||||
−0.318544 | + | 0.947908i | \(0.603194\pi\) | |||||||
\(578\) | −1.99626e13 | + | 6.07576e13i | −0.309441 | + | 0.941806i | ||||
\(579\) | − | 5.22403e13i | − | 0.802810i | ||||||
\(580\) | 2.36976e13 | + | 1.74567e13i | 0.361048 | + | 0.265964i | ||||
\(581\) | 2.43624e13 | 0.367993 | ||||||||
\(582\) | −2.00649e12 | − | 6.59256e11i | −0.0300485 | − | 0.00987278i | ||||
\(583\) | − | 9.34883e13i | − | 1.38808i | ||||||
\(584\) | −4.53304e12 | + | 3.22556e12i | −0.0667307 | + | 0.0474833i | ||||
\(585\) | −3.16299e13 | −0.461656 | ||||||||
\(586\) | 2.36942e13 | − | 7.21149e13i | 0.342889 | − | 1.04361i | ||||
\(587\) | − | 1.26918e14i | − | 1.82109i | −0.413408 | − | 0.910546i | \(-0.635662\pi\) | ||
0.413408 | − | 0.910546i | \(-0.364338\pi\) | |||||||
\(588\) | 1.17476e14 | − | 1.59474e14i | 1.67132 | − | 2.26883i | ||||
\(589\) | 1.41364e14 | 1.99417 | ||||||||
\(590\) | 1.58558e13 | + | 5.20959e12i | 0.221782 | + | 0.0728691i | ||||
\(591\) | − | 1.30718e14i | − | 1.81299i | ||||||
\(592\) | 2.31286e13 | + | 7.45054e13i | 0.318084 | + | 1.02466i | ||||
\(593\) | 1.08224e13 | 0.147588 | 0.0737941 | − | 0.997273i | \(-0.476489\pi\) | ||||
0.0737941 | + | 0.997273i | \(0.476489\pi\) | |||||||
\(594\) | 3.51245e12 | − | 1.06904e13i | 0.0474983 | − | 0.144564i | ||||
\(595\) | 5.43853e12i | 0.0729284i | ||||||||
\(596\) | 3.97211e13 | + | 2.92604e13i | 0.528189 | + | 0.389088i | ||||
\(597\) | 7.05847e12 | 0.0930763 | ||||||||
\(598\) | −5.61750e13 | − | 1.84570e13i | −0.734577 | − | 0.241354i | ||||
\(599\) | 1.11833e14i | 1.45023i | 0.688630 | + | 0.725113i | \(0.258212\pi\) | ||||
−0.688630 | + | 0.725113i | \(0.741788\pi\) | |||||||
\(600\) | 1.22737e13 | + | 1.72489e13i | 0.157841 | + | 0.221822i | ||||
\(601\) | −1.24369e14 | −1.58613 | −0.793067 | − | 0.609134i | \(-0.791517\pi\) | ||||
−0.793067 | + | 0.609134i | \(0.791517\pi\) | |||||||
\(602\) | 1.21526e13 | − | 3.69873e13i | 0.153705 | − | 0.467811i | ||||
\(603\) | 7.02394e13i | 0.881038i | ||||||||
\(604\) | −7.08725e13 | + | 9.62097e13i | −0.881643 | + | 1.19683i | ||||
\(605\) | 1.52965e13 | 0.188719 | ||||||||
\(606\) | −1.56612e14 | − | 5.14568e13i | −1.91630 | − | 0.629622i | ||||
\(607\) | 1.04683e14i | 1.27038i | 0.772355 | + | 0.635192i | \(0.219079\pi\) | ||||
−0.772355 | + | 0.635192i | \(0.780921\pi\) | |||||||
\(608\) | −1.67521e12 | + | 1.01810e14i | −0.0201629 | + | 1.22538i | ||||
\(609\) | 2.00347e14 | 2.39164 | ||||||||
\(610\) | 1.96168e13 | − | 5.97051e13i | 0.232262 | − | 0.706907i | ||||
\(611\) | − | 6.29821e13i | − | 0.739624i | ||||||
\(612\) | −5.48728e12 | − | 4.04218e12i | −0.0639146 | − | 0.0470824i | ||||
\(613\) | 6.83052e13 | 0.789135 | 0.394567 | − | 0.918867i | \(-0.370894\pi\) | ||||
0.394567 | + | 0.918867i | \(0.370894\pi\) | |||||||
\(614\) | −9.94547e13 | − | 3.26770e13i | −1.13968 | − | 0.374456i | ||||
\(615\) | − | 5.97045e12i | − | 0.0678627i | ||||||
\(616\) | −9.62702e13 | + | 6.85027e13i | −1.08540 | + | 0.772332i | ||||
\(617\) | 1.45376e14 | 1.62580 | 0.812899 | − | 0.582405i | \(-0.197888\pi\) | ||||
0.812899 | + | 0.582405i | \(0.197888\pi\) | |||||||
\(618\) | 1.87870e13 | − | 5.71797e13i | 0.208409 | − | 0.634307i | ||||
\(619\) | 8.38798e13i | 0.923005i | 0.887139 | + | 0.461503i | \(0.152690\pi\) | ||||
−0.887139 | + | 0.461503i | \(0.847310\pi\) | |||||||
\(620\) | −3.95394e13 | + | 5.36748e13i | −0.431590 | + | 0.585885i | ||||
\(621\) | −1.18097e13 | −0.127873 | ||||||||
\(622\) | 8.95863e13 | + | 2.94346e13i | 0.962254 | + | 0.316160i | ||||
\(623\) | − | 2.04425e14i | − | 2.17818i | ||||||
\(624\) | 1.48851e14 | − | 4.62075e13i | 1.57336 | − | 0.488416i | ||||
\(625\) | 3.81470e12 | 0.0400000 | ||||||||
\(626\) | −3.17672e12 | + | 9.66858e12i | −0.0330451 | + | 0.100575i | ||||
\(627\) | 1.22905e14i | 1.26833i | ||||||||
\(628\) | −9.85017e13 | − | 7.25609e13i | −1.00843 | − | 0.742855i | ||||
\(629\) | −9.83133e12 | −0.0998525 | ||||||||
\(630\) | 6.30185e13 | + | 2.07055e13i | 0.634988 | + | 0.208633i | ||||
\(631\) | − | 8.77540e13i | − | 0.877244i | −0.898672 | − | 0.438622i | \(-0.855467\pi\) | ||
0.898672 | − | 0.438622i | \(-0.144533\pi\) | |||||||
\(632\) | −6.60865e13 | − | 9.28746e13i | −0.655431 | − | 0.921110i | ||||
\(633\) | 9.57714e13 | 0.942361 | ||||||||
\(634\) | 3.79677e13 | − | 1.15557e14i | 0.370653 | − | 1.12811i | ||||
\(635\) | 1.80270e13i | 0.174605i | ||||||||
\(636\) | 1.53388e14 | − | 2.08225e14i | 1.47403 | − | 2.00100i | ||||
\(637\) | −2.62767e14 | −2.50538 | ||||||||
\(638\) | −7.65586e13 | − | 2.51542e13i | −0.724253 | − | 0.237962i | ||||
\(639\) | − | 3.79742e13i | − | 0.356438i | ||||||
\(640\) | −3.81880e13 | − | 2.91122e13i | −0.355653 | − | 0.271129i | ||||
\(641\) | −7.91930e12 | −0.0731807 | −0.0365903 | − | 0.999330i | \(-0.511650\pi\) | ||||
−0.0365903 | + | 0.999330i | \(0.511650\pi\) | |||||||
\(642\) | −3.86623e13 | + | 1.17671e14i | −0.354497 | + | 1.07894i | ||||
\(643\) | 6.97979e13i | 0.635020i | 0.948255 | + | 0.317510i | \(0.102847\pi\) | ||||
−0.948255 | + | 0.317510i | \(0.897153\pi\) | |||||||
\(644\) | 9.98394e13 | + | 7.35463e13i | 0.901307 | + | 0.663944i | ||||
\(645\) | 1.90985e13 | 0.171080 | ||||||||
\(646\) | −1.21909e13 | − | 4.00545e12i | −0.108361 | − | 0.0356032i | ||||
\(647\) | − | 3.64847e13i | − | 0.321803i | −0.986970 | − | 0.160901i | \(-0.948560\pi\) | ||
0.986970 | − | 0.160901i | \(-0.0514401\pi\) | |||||||
\(648\) | 1.04768e14 | − | 7.45494e13i | 0.916966 | − | 0.652483i | ||||
\(649\) | −4.56946e13 | −0.396863 | ||||||||
\(650\) | 8.76647e12 | − | 2.66813e13i | 0.0755541 | − | 0.229954i | ||||
\(651\) | 4.53784e14i | 3.88100i | ||||||||
\(652\) | 1.75843e12 | − | 2.38707e12i | 0.0149240 | − | 0.0202594i | ||||
\(653\) | 1.18590e14 | 0.998811 | 0.499406 | − | 0.866368i | \(-0.333552\pi\) | ||||
0.499406 | + | 0.866368i | \(0.333552\pi\) | |||||||
\(654\) | −8.06341e13 | − | 2.64933e13i | −0.673953 | − | 0.221435i | ||||
\(655\) | 4.15959e13i | 0.345020i | ||||||||
\(656\) | 4.01501e12 | + | 1.29337e13i | 0.0330497 | + | 0.106465i | ||||
\(657\) | −8.55152e12 | −0.0698581 | ||||||||
\(658\) | −4.12292e13 | + | 1.25484e14i | −0.334253 | + | 1.01732i | ||||
\(659\) | − | 8.68704e13i | − | 0.698948i | −0.936946 | − | 0.349474i | \(-0.886360\pi\) | ||
0.936946 | − | 0.349474i | \(-0.113640\pi\) | |||||||
\(660\) | −4.66663e13 | − | 3.43766e13i | −0.372635 | − | 0.274500i | ||||
\(661\) | −1.41387e14 | −1.12048 | −0.560238 | − | 0.828332i | \(-0.689290\pi\) | ||||
−0.560238 | + | 0.828332i | \(0.689290\pi\) | |||||||
\(662\) | 1.32041e14 | + | 4.33835e13i | 1.03853 | + | 0.341220i | ||||
\(663\) | 1.96415e13i | 0.153323i | ||||||||
\(664\) | −1.57165e13 | − | 2.20872e13i | −0.121763 | − | 0.171120i | ||||
\(665\) | 1.24892e14 | 0.960341 | ||||||||
\(666\) | −3.74297e13 | + | 1.13920e14i | −0.285657 | + | 0.869417i | ||||
\(667\) | 8.45743e13i | 0.640633i | ||||||||
\(668\) | 2.01210e13 | − | 2.73143e13i | 0.151275 | − | 0.205356i | ||||
\(669\) | −2.60523e14 | −1.94409 | ||||||||
\(670\) | −5.92504e13 | − | 1.94674e13i | −0.438851 | − | 0.144190i | ||||
\(671\) | 1.72064e14i | 1.26496i | ||||||||
\(672\) | −3.26814e14 | − | 5.37751e12i | −2.38481 | − | 0.0392406i | ||||
\(673\) | −8.61618e13 | −0.624079 | −0.312039 | − | 0.950069i | \(-0.601012\pi\) | ||||
−0.312039 | + | 0.950069i | \(0.601012\pi\) | |||||||
\(674\) | 7.55975e12 | − | 2.30086e13i | 0.0543510 | − | 0.165421i | ||||
\(675\) | − | 5.60922e12i | − | 0.0400298i | ||||||
\(676\) | −5.28148e13 | − | 3.89058e13i | −0.374130 | − | 0.275601i | ||||
\(677\) | 1.26787e14 | 0.891520 | 0.445760 | − | 0.895152i | \(-0.352933\pi\) | ||||
0.445760 | + | 0.895152i | \(0.352933\pi\) | |||||||
\(678\) | 1.16767e14 | + | 3.83653e13i | 0.815029 | + | 0.267787i | ||||
\(679\) | − | 5.87595e12i | − | 0.0407126i | ||||||
\(680\) | 4.93062e12 | − | 3.50847e12i | 0.0339123 | − | 0.0241309i | ||||
\(681\) | 3.38142e14 | 2.30868 | ||||||||
\(682\) | 5.69740e13 | − | 1.73404e14i | 0.386149 | − | 1.17527i | ||||
\(683\) | 1.04109e14i | 0.700461i | 0.936664 | + | 0.350230i | \(0.113897\pi\) | ||||
−0.936664 | + | 0.350230i | \(0.886103\pi\) | |||||||
\(684\) | −9.28257e13 | + | 1.26011e14i | −0.619994 | + | 0.841645i | ||||
\(685\) | −2.01067e13 | −0.133317 | ||||||||
\(686\) | 2.70635e14 | + | 8.89203e13i | 1.78141 | + | 0.585302i | ||||
\(687\) | − | 3.41166e14i | − | 2.22937i | ||||||
\(688\) | −4.13729e13 | + | 1.28433e13i | −0.268394 | + | 0.0833174i | ||||
\(689\) | −3.43095e14 | −2.20962 | ||||||||
\(690\) | −1.89879e13 | + | 5.77909e13i | −0.121403 | + | 0.369500i | ||||
\(691\) | − | 3.73752e13i | − | 0.237243i | −0.992940 | − | 0.118621i | \(-0.962153\pi\) | ||
0.992940 | − | 0.118621i | \(-0.0378475\pi\) | |||||||
\(692\) | 1.17283e14 | + | 8.63959e13i | 0.739101 | + | 0.544456i | ||||
\(693\) | −1.81613e14 | −1.13626 | ||||||||
\(694\) | −1.48550e13 | − | 4.88078e12i | −0.0922730 | − | 0.0303174i | ||||
\(695\) | − | 6.70180e13i | − | 0.413302i | ||||||
\(696\) | −1.29246e14 | − | 1.81636e14i | −0.791357 | − | 1.11213i | ||||
\(697\) | −1.70667e12 | −0.0103749 | ||||||||
\(698\) | −2.31753e13 | + | 7.05357e13i | −0.139878 | + | 0.425727i | ||||
\(699\) | − | 7.13336e13i | − | 0.427472i | ||||||
\(700\) | −3.49322e13 | + | 4.74206e13i | −0.207843 | + | 0.282148i | ||||
\(701\) | −1.57586e13 | −0.0930950 | −0.0465475 | − | 0.998916i | \(-0.514822\pi\) | ||||
−0.0465475 | + | 0.998916i | \(0.514822\pi\) | |||||||
\(702\) | −3.92328e13 | − | 1.28904e13i | −0.230125 | − | 0.0756103i | ||||
\(703\) | 2.25769e14i | 1.31489i | ||||||||
\(704\) | 1.24210e14 | + | 4.30875e13i | 0.718282 | + | 0.249166i | ||||
\(705\) | −6.47938e13 | −0.372039 | ||||||||
\(706\) | 2.84987e13 | − | 8.67377e13i | 0.162481 | − | 0.494521i | ||||
\(707\) | − | 4.58634e14i | − | 2.59639i | ||||||
\(708\) | −1.01775e14 | − | 7.49718e13i | −0.572101 | − | 0.421436i | ||||
\(709\) | 2.52712e14 | 1.41057 | 0.705285 | − | 0.708924i | \(-0.250819\pi\) | ||||
0.705285 | + | 0.708924i | \(0.250819\pi\) | |||||||
\(710\) | 3.20331e13 | + | 1.05248e13i | 0.177544 | + | 0.0583343i | ||||
\(711\) | − | 1.75207e14i | − | 0.964278i | ||||||
\(712\) | −1.85334e14 | + | 1.31877e14i | −1.01287 | + | 0.720726i | ||||
\(713\) | −1.91560e14 | −1.03958 | ||||||||
\(714\) | 1.28577e13 | − | 3.91332e13i | 0.0692901 | − | 0.210889i | ||||
\(715\) | 7.68927e13i | 0.411486i | ||||||||
\(716\) | 2.13960e13 | − | 2.90451e13i | 0.113702 | − | 0.154350i | ||||
\(717\) | 3.36735e14 | 1.77702 | ||||||||
\(718\) | 4.85450e13 | + | 1.59500e13i | 0.254403 | + | 0.0835871i | ||||
\(719\) | − | 1.11740e13i | − | 0.0581517i | −0.999577 | − | 0.0290759i | \(-0.990744\pi\) | ||
0.999577 | − | 0.0290759i | \(-0.00925644\pi\) | |||||||
\(720\) | −2.18823e13 | − | 7.04906e13i | −0.113092 | − | 0.364308i | ||||
\(721\) | 1.67449e14 | 0.859421 | ||||||||
\(722\) | −3.07412e13 | + | 9.35629e13i | −0.156688 | + | 0.476889i | ||||
\(723\) | − | 2.58620e14i | − | 1.30909i | ||||||
\(724\) | 7.03074e13 | + | 5.17916e13i | 0.353434 | + | 0.260356i | ||||
\(725\) | −4.01701e13 | −0.200545 | ||||||||
\(726\) | −1.10067e14 | − | 3.61637e13i | −0.545724 | − | 0.179304i | ||||
\(727\) | − | 1.13819e14i | − | 0.560455i | −0.959934 | − | 0.280228i | \(-0.909590\pi\) | ||
0.959934 | − | 0.280228i | \(-0.0904100\pi\) | |||||||
\(728\) | 2.51399e14 | + | 3.53304e14i | 1.22944 | + | 1.72779i | ||||
\(729\) | 1.41548e14 | 0.687490 | ||||||||
\(730\) | 2.37012e12 | − | 7.21363e12i | 0.0114329 | − | 0.0347968i | ||||
\(731\) | − | 5.45934e12i | − | 0.0261549i | ||||||
\(732\) | −2.82308e14 | + | 3.83234e14i | −1.34328 | + | 1.82351i | ||||
\(733\) | 3.18416e12 | 0.0150479 | 0.00752393 | − | 0.999972i | \(-0.497605\pi\) | ||||
0.00752393 | + | 0.999972i | \(0.497605\pi\) | |||||||
\(734\) | −9.01819e12 | − | 2.96303e12i | −0.0423291 | − | 0.0139077i | ||||
\(735\) | 2.70325e14i | 1.26023i | ||||||||
\(736\) | 2.27006e12 | − | 1.37961e14i | 0.0105111 | − | 0.638804i | ||||
\(737\) | 1.70753e14 | 0.785293 | ||||||||
\(738\) | −6.49759e12 | + | 1.97759e13i | −0.0296804 | + | 0.0903345i | ||||
\(739\) | − | 1.84171e14i | − | 0.835599i | −0.908539 | − | 0.417800i | \(-0.862801\pi\) | ||
0.908539 | − | 0.417800i | \(-0.137199\pi\) | |||||||
\(740\) | −8.57230e13 | − | 6.31475e13i | −0.386313 | − | 0.284576i | ||||
\(741\) | 4.51052e14 | 2.01900 | ||||||||
\(742\) | 6.83573e14 | + | 2.24596e14i | 3.03924 | + | 0.998578i | ||||
\(743\) | 2.17569e14i | 0.960844i | 0.877037 | + | 0.480422i | \(0.159517\pi\) | ||||
−0.877037 | + | 0.480422i | \(0.840483\pi\) | |||||||
\(744\) | 4.11405e14 | − | 2.92742e14i | 1.80470 | − | 1.28416i | ||||
\(745\) | −6.73316e13 | −0.293385 | ||||||||
\(746\) | 9.86807e13 | − | 3.00341e14i | 0.427108 | − | 1.29993i | ||||
\(747\) | − | 4.16672e13i | − | 0.179140i | ||||||
\(748\) | −9.82661e12 | + | 1.33397e13i | −0.0419658 | + | 0.0569688i | ||||
\(749\) | −3.44597e14 | −1.46185 | ||||||||
\(750\) | −2.74489e13 | − | 9.01864e12i | −0.115669 | − | 0.0380045i | ||||
\(751\) | 2.81405e14i | 1.17797i | 0.808146 | + | 0.588983i | \(0.200471\pi\) | ||||
−0.808146 | + | 0.588983i | \(0.799529\pi\) | |||||||
\(752\) | 1.40362e14 | − | 4.35725e13i | 0.583662 | − | 0.181186i | ||||
\(753\) | −2.06350e14 | −0.852374 | ||||||||
\(754\) | −9.23139e13 | + | 2.80964e14i | −0.378800 | + | 1.15291i | ||||
\(755\) | − | 1.63086e14i | − | 0.664787i | ||||||
\(756\) | 6.97282e13 | + | 5.13650e13i | 0.282358 | + | 0.207998i | ||||
\(757\) | −8.77891e13 | −0.353152 | −0.176576 | − | 0.984287i | \(-0.556502\pi\) | ||||
−0.176576 | + | 0.984287i | \(0.556502\pi\) | |||||||
\(758\) | −8.16347e13 | − | 2.68220e13i | −0.326234 | − | 0.107188i | ||||
\(759\) | − | 1.66547e14i | − | 0.661193i | ||||||
\(760\) | −8.05693e13 | − | 1.13228e14i | −0.317762 | − | 0.446566i | ||||
\(761\) | −3.64374e14 | −1.42766 | −0.713829 | − | 0.700320i | \(-0.753041\pi\) | ||||
−0.713829 | + | 0.700320i | \(0.753041\pi\) | |||||||
\(762\) | 4.26192e13 | − | 1.29714e14i | 0.165894 | − | 0.504909i | ||||
\(763\) | − | 2.36134e14i | − | 0.913138i | ||||||
\(764\) | −2.12867e14 | + | 2.88967e14i | −0.817788 | + | 1.11015i | ||||
\(765\) | 9.30155e12 | 0.0355016 | ||||||||
\(766\) | −8.48855e13 | − | 2.78901e13i | −0.321877 | − | 0.105756i | ||||
\(767\) | 1.67695e14i | 0.631748i | ||||||||
\(768\) | 2.05957e14 | + | 2.99762e14i | 0.770851 | + | 1.12194i | ||||
\(769\) | −2.27454e14 | −0.845790 | −0.422895 | − | 0.906179i | \(-0.638986\pi\) | ||||
−0.422895 | + | 0.906179i | \(0.638986\pi\) | |||||||
\(770\) | 5.03353e13 | − | 1.53199e14i | 0.185960 | − | 0.565982i | ||||
\(771\) | − | 3.45299e14i | − | 1.26743i | ||||||
\(772\) | −1.30206e14 | − | 9.59161e13i | −0.474839 | − | 0.349788i | ||||
\(773\) | −2.31980e14 | −0.840531 | −0.420265 | − | 0.907401i | \(-0.638063\pi\) | ||||
−0.420265 | + | 0.907401i | \(0.638063\pi\) | |||||||
\(774\) | −6.32596e13 | − | 2.07847e13i | −0.227731 | − | 0.0748236i | ||||
\(775\) | − | 9.09848e13i | − | 0.325432i | ||||||
\(776\) | −5.32719e12 | + | 3.79065e12i | −0.0189317 | + | 0.0134712i | ||||
\(777\) | −7.24729e14 | −2.55900 | ||||||||
\(778\) | 4.53488e13 | − | 1.38022e14i | 0.159099 | − | 0.484230i | ||||
\(779\) | 3.91923e13i | 0.136620i | ||||||||
\(780\) | −1.26159e14 | + | 1.71262e14i | −0.436964 | + | 0.593181i | ||||
\(781\) | −9.23159e13 | −0.317703 | ||||||||
\(782\) | 1.65197e13 | + | 5.42773e12i | 0.0564895 | + | 0.0185603i | ||||
\(783\) | 5.90670e13i | 0.200695i | ||||||||
\(784\) | −1.81788e14 | − | 5.85604e14i | −0.613742 | − | 1.97708i | ||||
\(785\) | 1.66971e14 | 0.560136 | ||||||||
\(786\) | 9.83404e13 | − | 2.99306e14i | 0.327808 | − | 0.997705i | ||||
\(787\) | 4.63128e14i | 1.53401i | 0.641644 | + | 0.767003i | \(0.278253\pi\) | ||||
−0.641644 | + | 0.767003i | \(0.721747\pi\) | |||||||
\(788\) | −3.25807e14 | − | 2.40004e14i | −1.07233 | − | 0.789929i | ||||
\(789\) | 7.46119e14 | 2.44019 | ||||||||
\(790\) | 1.47795e14 | + | 4.85599e13i | 0.480314 | + | 0.157813i | ||||
\(791\) | 3.41950e14i | 1.10428i | ||||||||
\(792\) | 1.17161e14 | + | 1.64652e14i | 0.375972 | + | 0.528372i | ||||
\(793\) | 6.31459e14 | 2.01363 | ||||||||
\(794\) | −1.56162e14 | + | 4.75289e14i | −0.494849 | + | 1.50611i | ||||
\(795\) | 3.52964e14i | 1.11146i | ||||||||
\(796\) | 1.29597e13 | − | 1.75929e13i | 0.0405537 | − | 0.0550519i | ||||
\(797\) | 5.47068e13 | 0.170118 | 0.0850588 | − | 0.996376i | \(-0.472892\pi\) | ||||
0.0850588 | + | 0.996376i | \(0.472892\pi\) | |||||||
\(798\) | −8.98665e14 | − | 2.95267e14i | −2.77705 | − | 0.912431i | ||||
\(799\) | 1.85215e13i | 0.0568776i | ||||||||
\(800\) | 6.55271e13 | + | 1.07821e12i | 0.199973 | + | 0.00329042i | ||||
\(801\) | −3.49629e14 | −1.06034 | ||||||||
\(802\) | −9.94350e13 | + | 3.02637e14i | −0.299687 | + | 0.912117i | ||||
\(803\) | 2.07889e13i | 0.0622664i | ||||||||
\(804\) | 3.80315e14 | + | 2.80158e14i | 1.13204 | + | 0.833916i | ||||
\(805\) | −1.69239e14 | −0.500635 | ||||||||
\(806\) | −6.36380e14 | − | 2.09090e14i | −1.87086 | − | 0.614693i | ||||
\(807\) | − | 1.51428e14i | − | 0.442425i | ||||||
\(808\) | −4.15802e14 | + | 2.95871e14i | −1.20734 | + | 0.859104i | ||||
\(809\) | 3.59793e14 | 1.03827 | 0.519135 | − | 0.854692i | \(-0.326254\pi\) | ||||
0.519135 | + | 0.854692i | \(0.326254\pi\) | |||||||
\(810\) | −5.47784e13 | + | 1.66722e14i | −0.157103 | + | 0.478153i | ||||
\(811\) | 4.03312e13i | 0.114957i | 0.998347 | + | 0.0574787i | \(0.0183061\pi\) | ||||
−0.998347 | + | 0.0574787i | \(0.981694\pi\) | |||||||
\(812\) | 3.67848e14 | − | 4.99355e14i | 1.04205 | − | 1.41459i | ||||
\(813\) | 2.33977e13 | 0.0658749 | ||||||||
\(814\) | 2.76941e14 | + | 9.09921e13i | 0.774935 | + | 0.254614i | ||||
\(815\) | 4.04635e12i | 0.0112532i | ||||||||
\(816\) | −4.37732e13 | + | 1.35885e13i | −0.120992 | + | 0.0375595i | ||||
\(817\) | −1.25370e14 | −0.344415 | ||||||||
\(818\) | −3.94622e13 | + | 1.20106e14i | −0.107749 | + | 0.327943i | ||||
\(819\) | 6.66503e14i | 1.80877i | ||||||||
\(820\) | −1.48811e13 | − | 1.09621e13i | −0.0401388 | − | 0.0295681i | ||||
\(821\) | 6.29121e14 | 1.68662 | 0.843312 | − | 0.537424i | \(-0.180602\pi\) | ||||
0.843312 | + | 0.537424i | \(0.180602\pi\) | |||||||
\(822\) | 1.44679e14 | + | 4.75358e13i | 0.385518 | + | 0.126667i | ||||
\(823\) | − | 3.91664e13i | − | 0.103732i | −0.998654 | − | 0.0518662i | \(-0.983483\pi\) | ||
0.998654 | − | 0.0518662i | \(-0.0165169\pi\) | |||||||
\(824\) | −1.08024e14 | − | 1.51811e14i | −0.284369 | − | 0.399638i | ||||
\(825\) | 7.91046e13 | 0.206982 | ||||||||
\(826\) | 1.09776e14 | − | 3.34112e14i | 0.285502 | − | 0.868944i | ||||
\(827\) | − | 5.12246e14i | − | 1.32419i | −0.749419 | − | 0.662096i | \(-0.769667\pi\) | ||
0.749419 | − | 0.662096i | \(-0.230333\pi\) | |||||||
\(828\) | 1.25787e14 | − | 1.70756e14i | 0.323209 | − | 0.438757i | ||||
\(829\) | 2.87121e14 | 0.733317 | 0.366658 | − | 0.930356i | \(-0.380502\pi\) | ||||
0.366658 | + | 0.930356i | \(0.380502\pi\) | |||||||
\(830\) | 3.51483e13 | + | 1.15484e13i | 0.0892307 | + | 0.0293178i | ||||
\(831\) | 9.38517e14i | 2.36830i | ||||||||
\(832\) | 1.58128e14 | − | 4.55842e14i | 0.396635 | − | 1.14340i | ||||
\(833\) | 7.72731e13 | 0.192665 | ||||||||
\(834\) | −1.58443e14 | + | 4.82232e14i | −0.392683 | + | 1.19516i | ||||
\(835\) | 4.63008e13i | 0.114066i | ||||||||
\(836\) | 3.06335e14 | + | 2.25661e14i | 0.750181 | + | 0.552618i | ||||
\(837\) | −1.33786e14 | −0.325675 | ||||||||
\(838\) | 4.78869e14 | + | 1.57338e14i | 1.15877 | + | 0.380727i | ||||
\(839\) | − | 2.95325e14i | − | 0.710379i | −0.934794 | − | 0.355190i | \(-0.884416\pi\) | ||
0.934794 | − | 0.355190i | \(-0.115584\pi\) | |||||||
\(840\) | 3.63467e14 | − | 2.58631e14i | 0.869098 | − | 0.618421i | ||||
\(841\) | 2.29764e12 | 0.00546136 | ||||||||
\(842\) | 1.89050e13 | − | 5.75387e13i | 0.0446700 | − | 0.135956i | ||||
\(843\) | 1.57392e14i | 0.369695i | ||||||||
\(844\) | 1.75841e14 | − | 2.38706e14i | 0.410591 | − | 0.557379i | ||||
\(845\) | 8.95270e13 | 0.207812 | ||||||||
\(846\) | 2.14616e14 | + | 7.05145e13i | 0.495234 | + | 0.162715i | ||||
\(847\) | − | 3.22327e14i | − | 0.739401i | ||||||
\(848\) | −2.37361e14 | − | 7.64623e14i | −0.541291 | − | 1.74369i | ||||
\(849\) | −3.12976e14 | −0.709533 | ||||||||
\(850\) | −2.57800e12 | + | 7.84632e12i | −0.00581016 | + | 0.0176836i | ||||
\(851\) | − | 3.05937e14i | − | 0.685462i | ||||||
\(852\) | −2.05613e14 | − | 1.51464e14i | −0.457987 | − | 0.337374i | ||||
\(853\) | −1.08283e14 | −0.239780 | −0.119890 | − | 0.992787i | \(-0.538254\pi\) | ||||
−0.119890 | + | 0.992787i | \(0.538254\pi\) | |||||||
\(854\) | −1.25810e15 | − | 4.13364e14i | −2.76966 | − | 0.910005i | ||||
\(855\) | − | 2.13603e14i | − | 0.467495i | ||||||
\(856\) | 2.22304e14 | + | 3.12415e14i | 0.483702 | + | 0.679771i | ||||
\(857\) | −3.60461e14 | −0.779748 | −0.389874 | − | 0.920868i | \(-0.627481\pi\) | ||||
−0.389874 | + | 0.920868i | \(0.627481\pi\) | |||||||
\(858\) | 1.81788e14 | − | 5.53286e14i | 0.390958 | − | 1.18991i | ||||
\(859\) | − | 6.06012e13i | − | 0.129573i | −0.997899 | − | 0.0647866i | \(-0.979363\pi\) | ||
0.997899 | − | 0.0647866i | \(-0.0206367\pi\) | |||||||
\(860\) | 3.50658e13 | − | 4.76020e13i | 0.0745404 | − | 0.101189i | ||||
\(861\) | −1.25809e14 | −0.265886 | ||||||||
\(862\) | −4.90368e14 | − | 1.61116e14i | −1.03035 | − | 0.338534i | ||||
\(863\) | − | 1.17507e13i | − | 0.0245476i | −0.999925 | − | 0.0122738i | \(-0.996093\pi\) | ||
0.999925 | − | 0.0122738i | \(-0.00390698\pi\) | |||||||
\(864\) | 1.58542e12 | − | 9.63525e13i | 0.00329287 | − | 0.200122i | ||||
\(865\) | −1.98807e14 | −0.410537 | ||||||||
\(866\) | −2.27598e14 | + | 6.92709e14i | −0.467281 | + | 1.42220i | ||||
\(867\) | 6.61075e14i | 1.34945i | ||||||||
\(868\) | 1.13103e15 | + | 8.33172e14i | 2.29550 | + | 1.69097i | ||||
\(869\) | −4.25930e14 | −0.859487 | ||||||||
\(870\) | 2.89046e14 | + | 9.49694e13i | 0.579924 | + | 0.190541i | ||||
\(871\) | − | 6.26651e14i | − | 1.25007i | ||||||
\(872\) | −2.14082e14 | + | 1.52333e14i | −0.424617 | + | 0.302143i | ||||
\(873\) | −1.00497e13 | −0.0198190 | ||||||||
\(874\) | 1.24644e14 | − | 3.79362e14i | 0.244407 | − | 0.743869i | ||||
\(875\) | − | 8.03831e13i | − | 0.156720i | ||||||
\(876\) | −3.41087e13 | + | 4.63027e13i | −0.0661217 | + | 0.0897605i | ||||
\(877\) | 6.85003e14 | 1.32037 | 0.660183 | − | 0.751104i | \(-0.270479\pi\) | ||||
0.660183 | + | 0.751104i | \(0.270479\pi\) | |||||||
\(878\) | 2.23098e14 | + | 7.33013e13i | 0.427585 | + | 0.140488i | ||||
\(879\) | − | 7.84650e14i | − | 1.49531i | ||||||
\(880\) | −1.71364e14 | + | 5.31963e13i | −0.324717 | + | 0.100802i | ||||
\(881\) | −2.09299e14 | −0.394355 | −0.197177 | − | 0.980368i | \(-0.563177\pi\) | ||||
−0.197177 | + | 0.980368i | \(0.563177\pi\) | |||||||
\(882\) | 2.94193e14 | − | 8.95396e14i | 0.551175 | − | 1.67754i | ||||
\(883\) | − | 6.25256e14i | − | 1.16481i | −0.812899 | − | 0.582404i | \(-0.802112\pi\) | ||
0.812899 | − | 0.582404i | \(-0.197888\pi\) | |||||||
\(884\) | 4.89555e13 | + | 3.60629e13i | 0.0906860 | + | 0.0668035i | ||||
\(885\) | 1.72519e14 | 0.317776 | ||||||||
\(886\) | −1.11909e13 | − | 3.67689e12i | −0.0204972 | − | 0.00673460i | ||||
\(887\) | 7.59597e14i | 1.38346i | 0.722158 | + | 0.691728i | \(0.243150\pi\) | ||||
−0.722158 | + | 0.691728i | \(0.756850\pi\) | |||||||
\(888\) | 4.67532e14 | + | 6.57046e14i | 0.846734 | + | 1.18996i | ||||
\(889\) | 3.79865e14 | 0.684101 | ||||||||
\(890\) | 9.69025e13 | − | 2.94930e14i | 0.173534 | − | 0.528164i | ||||
\(891\) | − | 4.80474e14i | − | 0.855621i | ||||||
\(892\) | −4.78335e14 | + | 6.49342e14i | −0.847048 | + | 1.14987i | ||||
\(893\) | 4.25331e14 | 0.748980 | ||||||||
\(894\) | 4.84488e14 | + | 1.59184e14i | 0.848391 | + | 0.278749i | ||||
\(895\) | 4.92347e13i | 0.0857346i | ||||||||
\(896\) | −6.13452e14 | + | 8.04695e14i | −1.06228 | + | 1.39345i | ||||
\(897\) | −6.11215e14 | −1.05252 | ||||||||
\(898\) | 1.73473e14 | − | 5.27977e14i | 0.297064 | − | 0.904136i | ||||
\(899\) | 9.58102e14i | 1.63160i | ||||||||
\(900\) | 8.11037e13 | + | 5.97447e13i | 0.137350 | + | 0.101178i | ||||
\(901\) | 1.00896e14 | 0.169921 | ||||||||
\(902\) | 4.80754e13 | + | 1.57957e13i | 0.0805175 | + | 0.0264550i | ||||
\(903\) | − | 4.02442e14i | − | 0.670293i | ||||||
\(904\) | 3.10015e14 | − | 2.20596e14i | 0.513500 | − | 0.365389i | ||||
\(905\) | −1.19179e14 | −0.196316 | ||||||||
\(906\) | −3.85566e14 | + | 1.17350e15i | −0.631622 | + | 1.92239i | ||||
\(907\) | 6.72197e13i | 0.109512i | 0.998500 | + | 0.0547558i | \(0.0174380\pi\) | ||||
−0.998500 | + | 0.0547558i | \(0.982562\pi\) | |||||||
\(908\) | 6.20848e14 | − | 8.42804e14i | 1.00590 | − | 1.36552i | ||||
\(909\) | −7.84405e14 | −1.26392 | ||||||||
\(910\) | −5.62228e14 | − | 1.84727e14i | −0.900960 | − | 0.296021i | ||||
\(911\) | 9.95355e14i | 1.58630i | 0.609025 | + | 0.793151i | \(0.291561\pi\) | ||||
−0.609025 | + | 0.793151i | \(0.708439\pi\) | |||||||
\(912\) | 3.12049e14 | + | 1.00522e15i | 0.494594 | + | 1.59326i | ||||
\(913\) | −1.01294e14 | −0.159672 | ||||||||
\(914\) | 1.79596e14 | − | 5.46612e14i | 0.281556 | − | 0.856936i | ||||
\(915\) | − | 6.49624e14i | − | 1.01288i | ||||||
\(916\) | −8.50340e14 | − | 6.26399e14i | −1.31861 | − | 0.971346i | ||||
\(917\) | 8.76508e14 | 1.35179 | ||||||||
\(918\) | 1.15374e13 | + | 3.79075e12i | 0.0176968 | + | 0.00581448i | ||||
\(919\) | − | 3.20262e14i | − | 0.488572i | −0.969703 | − | 0.244286i | \(-0.921447\pi\) | ||
0.969703 | − | 0.244286i | \(-0.0785535\pi\) | |||||||
\(920\) | 1.09178e14 | + | 1.53434e14i | 0.165652 | + | 0.232799i | ||||
\(921\) | −1.08212e15 | −1.63297 | ||||||||
\(922\) | −4.08566e14 | + | 1.24350e15i | −0.613208 | + | 1.86634i | ||||
\(923\) | 3.38792e14i | 0.505736i | ||||||||
\(924\) | −7.24381e14 | + | 9.83351e14i | −1.07549 | + | 1.45999i | ||||
\(925\) | 1.45310e14 | 0.214579 | ||||||||
\(926\) | 5.19713e14 | + | 1.70758e14i | 0.763324 | + | 0.250799i | ||||
\(927\) | − | 2.86389e14i | − | 0.418367i | ||||||
\(928\) | −6.90023e14 | − | 1.13539e13i | −1.00259 | − | 0.0164970i | ||||
\(929\) | −6.44525e14 | −0.931454 | −0.465727 | − | 0.884929i | \(-0.654207\pi\) | ||||
−0.465727 | + | 0.884929i | \(0.654207\pi\) | |||||||
\(930\) | −2.15105e14 | + | 6.54686e14i | −0.309197 | + | 0.941063i | ||||
\(931\) | − | 1.77452e15i | − | 2.53707i | ||||||
\(932\) | −1.77795e14 | − | 1.30972e14i | −0.252837 | − | 0.186252i | ||||
\(933\) | 9.74748e14 | 1.37875 | ||||||||
\(934\) | 7.47186e14 | + | 2.45497e14i | 1.05122 | + | 0.345391i | ||||
\(935\) | − | 2.26122e13i | − | 0.0316436i | ||||||
\(936\) | 6.04258e14 | − | 4.29970e14i | 0.841092 | − | 0.598493i | ||||
\(937\) | 1.17565e15 | 1.62772 | 0.813860 | − | 0.581061i | \(-0.197362\pi\) | ||||
0.813860 | + | 0.581061i | \(0.197362\pi\) | |||||||
\(938\) | −4.10217e14 | + | 1.24852e15i | −0.564936 | + | 1.71942i | ||||
\(939\) | 1.05199e14i | 0.144107i | ||||||||
\(940\) | −1.18965e14 | + | 1.61495e14i | −0.162099 | + | 0.220050i | ||||
\(941\) | −1.07542e14 | −0.145757 | −0.0728787 | − | 0.997341i | \(-0.523219\pi\) | ||||
−0.0728787 | + | 0.997341i | \(0.523219\pi\) | |||||||
\(942\) | −1.20145e15 | − | 3.94751e14i | −1.61976 | − | 0.532192i | ||||
\(943\) | − | 5.31089e13i | − | 0.0712212i | ||||||
\(944\) | −3.73727e14 | + | 1.16016e14i | −0.498534 | + | 0.154759i | ||||
\(945\) | −1.18197e14 | −0.156837 | ||||||||
\(946\) | −5.05279e13 | + | 1.53785e14i | −0.0666923 | + | 0.202983i | ||||
\(947\) | 9.03973e14i | 1.18688i | 0.804880 | + | 0.593438i | \(0.202230\pi\) | ||||
−0.804880 | + | 0.593438i | \(0.797770\pi\) | |||||||
\(948\) | −9.48665e14 | − | 6.98831e14i | −1.23900 | − | 0.912705i | ||||
\(949\) | 7.62935e13 | 0.0991190 | ||||||||
\(950\) | 1.80185e14 | + | 5.92018e13i | 0.232863 | + | 0.0765098i | ||||
\(951\) | − | 1.25733e15i | − | 1.61639i | ||||||
\(952\) | −7.39303e13 | − | 1.03898e14i | −0.0945448 | − | 0.132868i | ||||
\(953\) | −6.08081e13 | −0.0773565 | −0.0386783 | − | 0.999252i | \(-0.512315\pi\) | ||||
−0.0386783 | + | 0.999252i | \(0.512315\pi\) | |||||||
\(954\) | 3.84128e14 | − | 1.16912e15i | 0.486109 | − | 1.47951i | ||||
\(955\) | − | 4.89832e14i | − | 0.616638i | ||||||
\(956\) | 6.18264e14 | − | 8.39296e14i | 0.774256 | − | 1.05106i | ||||
\(957\) | −8.32999e14 | −1.03773 | ||||||||
\(958\) | 9.80111e14 | + | 3.22027e14i | 1.21464 | + | 0.399084i | ||||
\(959\) | 4.23687e14i | 0.522338i | ||||||||
\(960\) | −4.68955e14 | − | 1.62676e14i | −0.575142 | − | 0.199512i | ||||
\(961\) | −1.35046e15 | −1.64765 | ||||||||
\(962\) | 3.33934e14 | − | 1.01635e15i | 0.405308 | − | 1.23358i | ||||
\(963\) | 5.89366e14i | 0.711629i | ||||||||
\(964\) | −6.44598e14 | − | 4.74841e14i | −0.774290 | − | 0.570378i | ||||
\(965\) | 2.20714e14 | 0.263751 | ||||||||
\(966\) | 1.21777e15 | + | 4.00112e14i | 1.44770 | + | 0.475659i | ||||
\(967\) | − | 2.41545e13i | − | 0.0285671i | −0.999898 | − | 0.0142836i | \(-0.995453\pi\) | ||
0.999898 | − | 0.0142836i | \(-0.00454675\pi\) | |||||||
\(968\) | −2.92225e14 | + | 2.07938e14i | −0.343827 | + | 0.244656i | ||||
\(969\) | −1.32643e14 | −0.155262 | ||||||||
\(970\) | 2.78535e12 | − | 8.47740e12i | 0.00324355 | − | 0.00987197i | ||||
\(971\) | 4.34211e14i | 0.503042i | 0.967852 | + | 0.251521i | \(0.0809308\pi\) | ||||
−0.967852 | + | 0.251521i | \(0.919069\pi\) | |||||||
\(972\) | 6.85328e14 | − | 9.30335e14i | 0.789891 | − | 1.07228i | ||||
\(973\) | −1.41220e15 | −1.61932 | ||||||||
\(974\) | 9.85903e14 | + | 3.23930e14i | 1.12471 | + | 0.369536i | ||||
\(975\) | − | 2.90308e14i | − | 0.329485i | ||||||
\(976\) | 4.36859e14 | + | 1.40728e15i | 0.493279 | + | 1.58902i | ||||
\(977\) | 8.83322e14 | 0.992308 | 0.496154 | − | 0.868235i | \(-0.334745\pi\) | ||||
0.496154 | + | 0.868235i | \(0.334745\pi\) | |||||||
\(978\) | 9.56631e12 | − | 2.91157e13i | 0.0106918 | − | 0.0325412i | ||||
\(979\) | 8.49955e14i | 0.945110i | ||||||||
\(980\) | 6.73773e14 | + | 4.96332e14i | 0.745390 | + | 0.549088i | ||||
\(981\) | −4.03862e14 | −0.444517 | ||||||||
\(982\) | −3.85960e14 | − | 1.26812e14i | −0.422654 | − | 0.138868i | ||||
\(983\) | 9.46697e14i | 1.03144i | 0.856758 | + | 0.515719i | \(0.172475\pi\) | ||||
−0.856758 | + | 0.515719i | \(0.827525\pi\) | |||||||
\(984\) | 8.11611e13 | + | 1.14060e14i | 0.0879776 | + | 0.123639i | ||||
\(985\) | 5.52279e14 | 0.595632 | ||||||||
\(986\) | 2.71472e13 | − | 8.26244e13i | 0.0291300 | − | 0.0886592i | ||||
\(987\) | 1.36533e15i | 1.45765i | ||||||||
\(988\) | 8.28157e14 | − | 1.12423e15i | 0.879686 | − | 1.19418i | ||||
\(989\) | 1.69887e14 | 0.179547 | ||||||||
\(990\) | −2.62017e14 | − | 8.60889e13i | −0.275521 | − | 0.0905255i | ||||
\(991\) | 6.43587e14i | 0.673347i | 0.941621 | + | 0.336674i | \(0.109302\pi\) | ||||
−0.941621 | + | 0.336674i | \(0.890698\pi\) | |||||||
\(992\) | 2.57164e13 | − | 1.56290e15i | 0.0267702 | − | 1.62694i | ||||
\(993\) | 1.43667e15 | 1.48803 | ||||||||
\(994\) | 2.21779e14 | − | 6.75000e14i | 0.228554 | − | 0.695620i | ||||
\(995\) | 2.98219e13i | 0.0305788i | ||||||||
\(996\) | −2.25609e14 | − | 1.66194e14i | −0.230176 | − | 0.169558i | ||||
\(997\) | 3.34658e14 | 0.339723 | 0.169862 | − | 0.985468i | \(-0.445668\pi\) | ||||
0.169862 | + | 0.985468i | \(0.445668\pi\) | |||||||
\(998\) | −3.29983e14 | − | 1.08420e14i | −0.333303 | − | 0.109510i | ||||
\(999\) | − | 2.13667e14i | − | 0.214739i |
(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 | 20.11.b.a.11.13 | ✓ | 20 | |
3.2 | odd | 2 | 180.11.c.a.91.8 | 20 | |||
4.3 | odd | 2 | inner | 20.11.b.a.11.14 | yes | 20 | |
5.2 | odd | 4 | 100.11.d.c.99.36 | 40 | |||
5.3 | odd | 4 | 100.11.d.c.99.5 | 40 | |||
5.4 | even | 2 | 100.11.b.e.51.8 | 20 | |||
8.3 | odd | 2 | 320.11.b.d.191.3 | 20 | |||
8.5 | even | 2 | 320.11.b.d.191.18 | 20 | |||
12.11 | even | 2 | 180.11.c.a.91.7 | 20 | |||
20.3 | even | 4 | 100.11.d.c.99.35 | 40 | |||
20.7 | even | 4 | 100.11.d.c.99.6 | 40 | |||
20.19 | odd | 2 | 100.11.b.e.51.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
20.11.b.a.11.13 | ✓ | 20 | 1.1 | even | 1 | trivial | |
20.11.b.a.11.14 | yes | 20 | 4.3 | odd | 2 | inner | |
100.11.b.e.51.7 | 20 | 20.19 | odd | 2 | |||
100.11.b.e.51.8 | 20 | 5.4 | even | 2 | |||
100.11.d.c.99.5 | 40 | 5.3 | odd | 4 | |||
100.11.d.c.99.6 | 40 | 20.7 | even | 4 | |||
100.11.d.c.99.35 | 40 | 20.3 | even | 4 | |||
100.11.d.c.99.36 | 40 | 5.2 | odd | 4 | |||
180.11.c.a.91.7 | 20 | 12.11 | even | 2 | |||
180.11.c.a.91.8 | 20 | 3.2 | odd | 2 | |||
320.11.b.d.191.3 | 20 | 8.3 | odd | 2 | |||
320.11.b.d.191.18 | 20 | 8.5 | even | 2 |