Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [17,12,Mod(16,17)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("17.16");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 17 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 17.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: | \(13.0618340695\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2012924 x^{14} + 1580196076372 x^{12} + \cdots + 11\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{29}\cdot 3^{4}\cdot 17^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 16.14 | ||
Root | \(37.5132i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 17.16 |
Dual form | 17.12.b.a.16.13 |
$q$-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 \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 61.5054 | 1.35909 | 0.679545 | − | 0.733634i | \(-0.262177\pi\) | ||||
0.679545 | + | 0.733634i | \(0.262177\pi\) | |||||||
\(3\) | 37.5132i | 0.0891287i | 0.999007 | + | 0.0445643i | \(0.0141900\pi\) | ||||
−0.999007 | + | 0.0445643i | \(0.985810\pi\) | |||||||
\(4\) | 1734.91 | 0.847125 | ||||||||
\(5\) | 7015.33i | 1.00395i | 0.864881 | + | 0.501976i | \(0.167394\pi\) | ||||
−0.864881 | + | 0.501976i | \(0.832606\pi\) | |||||||
\(6\) | 2307.27i | 0.121134i | ||||||||
\(7\) | 40939.8i | 0.920675i | 0.887744 | + | 0.460338i | \(0.152272\pi\) | ||||
−0.887744 | + | 0.460338i | \(0.847728\pi\) | |||||||
\(8\) | −19256.6 | −0.207771 | ||||||||
\(9\) | 175740. | 0.992056 | ||||||||
\(10\) | 431481.i | 1.36446i | ||||||||
\(11\) | 436092.i | 0.816429i | 0.912886 | + | 0.408214i | \(0.133848\pi\) | ||||
−0.912886 | + | 0.408214i | \(0.866152\pi\) | |||||||
\(12\) | 65082.1i | 0.0755031i | ||||||||
\(13\) | 954432. | 0.712946 | 0.356473 | − | 0.934306i | \(-0.383979\pi\) | ||||
0.356473 | + | 0.934306i | \(0.383979\pi\) | |||||||
\(14\) | 2.51802e6i | 1.25128i | ||||||||
\(15\) | −263168. | −0.0894810 | ||||||||
\(16\) | −4.73748e6 | −1.12950 | ||||||||
\(17\) | 1.84007e6 | − | 5.55752e6i | 0.314316 | − | 0.949319i | ||||
\(18\) | 1.08089e7 | 1.34829 | ||||||||
\(19\) | −2.78988e6 | −0.258489 | −0.129244 | − | 0.991613i | \(-0.541255\pi\) | ||||
−0.129244 | + | 0.991613i | \(0.541255\pi\) | |||||||
\(20\) | 1.21710e7i | 0.850473i | ||||||||
\(21\) | −1.53578e6 | −0.0820586 | ||||||||
\(22\) | 2.68220e7i | 1.10960i | ||||||||
\(23\) | 4.14357e7i | 1.34237i | 0.741291 | + | 0.671184i | \(0.234214\pi\) | ||||
−0.741291 | + | 0.671184i | \(0.765786\pi\) | |||||||
\(24\) | − | 722376.i | − | 0.0185183i | ||||||
\(25\) | −386743. | −0.00792050 | ||||||||
\(26\) | 5.87027e7 | 0.968957 | ||||||||
\(27\) | 1.32379e7i | 0.177549i | ||||||||
\(28\) | 7.10269e7i | 0.779927i | ||||||||
\(29\) | − | 1.18734e8i | − | 1.07495i | −0.843281 | − | 0.537473i | \(-0.819379\pi\) | ||
0.843281 | − | 0.537473i | \(-0.180621\pi\) | |||||||
\(30\) | −1.61862e7 | −0.121613 | ||||||||
\(31\) | − | 1.77240e8i | − | 1.11192i | −0.831210 | − | 0.555959i | \(-0.812351\pi\) | ||
0.831210 | − | 0.555959i | \(-0.187649\pi\) | |||||||
\(32\) | −2.51943e8 | −1.32733 | ||||||||
\(33\) | −1.63592e7 | −0.0727672 | ||||||||
\(34\) | 1.13174e8 | − | 3.41817e8i | 0.427183 | − | 1.29021i | ||||
\(35\) | −2.87206e8 | −0.924314 | ||||||||
\(36\) | 3.04893e8 | 0.840396 | ||||||||
\(37\) | − | 5.80565e8i | − | 1.37639i | −0.725526 | − | 0.688195i | \(-0.758404\pi\) | ||
0.725526 | − | 0.688195i | \(-0.241596\pi\) | |||||||
\(38\) | −1.71593e8 | −0.351309 | ||||||||
\(39\) | 3.58038e7i | 0.0635439i | ||||||||
\(40\) | − | 1.35091e8i | − | 0.208592i | ||||||
\(41\) | − | 1.07835e8i | − | 0.145361i | −0.997355 | − | 0.0726804i | \(-0.976845\pi\) | ||
0.997355 | − | 0.0726804i | \(-0.0231553\pi\) | |||||||
\(42\) | −9.44590e7 | −0.111525 | ||||||||
\(43\) | −1.42735e7 | −0.0148065 | −0.00740326 | − | 0.999973i | \(-0.502357\pi\) | ||||
−0.00740326 | + | 0.999973i | \(0.502357\pi\) | |||||||
\(44\) | 7.56581e8i | 0.691617i | ||||||||
\(45\) | 1.23287e9i | 0.995977i | ||||||||
\(46\) | 2.54852e9i | 1.82440i | ||||||||
\(47\) | 1.65181e9 | 1.05056 | 0.525281 | − | 0.850929i | \(-0.323960\pi\) | ||||
0.525281 | + | 0.850929i | \(0.323960\pi\) | |||||||
\(48\) | − | 1.77718e8i | − | 0.100671i | ||||||
\(49\) | 3.01260e8 | 0.152357 | ||||||||
\(50\) | −2.37868e7 | −0.0107647 | ||||||||
\(51\) | 2.08480e8 | + | 6.90271e7i | 0.0846115 | + | 0.0280145i | ||||
\(52\) | 1.65586e9 | 0.603954 | ||||||||
\(53\) | −1.69980e9 | −0.558318 | −0.279159 | − | 0.960245i | \(-0.590056\pi\) | ||||
−0.279159 | + | 0.960245i | \(0.590056\pi\) | |||||||
\(54\) | 8.14203e8i | 0.241305i | ||||||||
\(55\) | −3.05933e9 | −0.819656 | ||||||||
\(56\) | − | 7.88360e8i | − | 0.191289i | ||||||
\(57\) | − | 1.04658e8i | − | 0.0230387i | ||||||
\(58\) | − | 7.30279e9i | − | 1.46095i | ||||||
\(59\) | 1.97623e9 | 0.359876 | 0.179938 | − | 0.983678i | \(-0.442410\pi\) | ||||
0.179938 | + | 0.983678i | \(0.442410\pi\) | |||||||
\(60\) | −4.56573e8 | −0.0758016 | ||||||||
\(61\) | 7.84931e9i | 1.18992i | 0.803756 | + | 0.594960i | \(0.202832\pi\) | ||||
−0.803756 | + | 0.594960i | \(0.797168\pi\) | |||||||
\(62\) | − | 1.09012e10i | − | 1.51120i | ||||||
\(63\) | 7.19475e9i | 0.913361i | ||||||||
\(64\) | −5.79350e9 | −0.674452 | ||||||||
\(65\) | 6.69565e9i | 0.715763i | ||||||||
\(66\) | −1.00618e9 | −0.0988972 | ||||||||
\(67\) | 1.92771e10 | 1.74434 | 0.872169 | − | 0.489205i | \(-0.162713\pi\) | ||||
0.872169 | + | 0.489205i | \(0.162713\pi\) | |||||||
\(68\) | 3.19237e9 | − | 9.64181e9i | 0.266265 | − | 0.804192i | ||||
\(69\) | −1.55439e9 | −0.119643 | ||||||||
\(70\) | −1.76647e10 | −1.25623 | ||||||||
\(71\) | − | 4.81174e9i | − | 0.316505i | −0.987399 | − | 0.158253i | \(-0.949414\pi\) | ||
0.987399 | − | 0.158253i | \(-0.0505860\pi\) | |||||||
\(72\) | −3.38415e9 | −0.206120 | ||||||||
\(73\) | 1.24976e10i | 0.705586i | 0.935701 | + | 0.352793i | \(0.114768\pi\) | ||||
−0.935701 | + | 0.352793i | \(0.885232\pi\) | |||||||
\(74\) | − | 3.57079e10i | − | 1.87064i | ||||||
\(75\) | − | 1.45080e7i | − | 0.000705944i | ||||||
\(76\) | −4.84020e9 | −0.218972 | ||||||||
\(77\) | −1.78535e10 | −0.751666 | ||||||||
\(78\) | 2.20213e9i | 0.0863619i | ||||||||
\(79\) | 2.94120e10i | 1.07541i | 0.843132 | + | 0.537706i | \(0.180709\pi\) | ||||
−0.843132 | + | 0.537706i | \(0.819291\pi\) | |||||||
\(80\) | − | 3.32350e10i | − | 1.13397i | ||||||
\(81\) | 3.06352e10 | 0.976231 | ||||||||
\(82\) | − | 6.63241e9i | − | 0.197558i | ||||||
\(83\) | 2.55654e9 | 0.0712399 | 0.0356199 | − | 0.999365i | \(-0.488659\pi\) | ||||
0.0356199 | + | 0.999365i | \(0.488659\pi\) | |||||||
\(84\) | −2.66445e9 | −0.0695139 | ||||||||
\(85\) | 3.89878e10 | + | 1.29087e10i | 0.953071 | + | 0.315558i | ||||
\(86\) | −8.77895e8 | −0.0201234 | ||||||||
\(87\) | 4.45410e9 | 0.0958085 | ||||||||
\(88\) | − | 8.39764e9i | − | 0.169630i | ||||||
\(89\) | −9.01332e10 | −1.71096 | −0.855480 | − | 0.517837i | \(-0.826738\pi\) | ||||
−0.855480 | + | 0.517837i | \(0.826738\pi\) | |||||||
\(90\) | 7.58283e10i | 1.35362i | ||||||||
\(91\) | 3.90742e10i | 0.656391i | ||||||||
\(92\) | 7.18873e10i | 1.13715i | ||||||||
\(93\) | 6.64885e9 | 0.0991038 | ||||||||
\(94\) | 1.01595e11 | 1.42781 | ||||||||
\(95\) | − | 1.95720e10i | − | 0.259510i | ||||||
\(96\) | − | 9.45120e9i | − | 0.118303i | ||||||
\(97\) | 1.01766e10i | 0.120325i | 0.998189 | + | 0.0601626i | \(0.0191619\pi\) | ||||
−0.998189 | + | 0.0601626i | \(0.980838\pi\) | |||||||
\(98\) | 1.85291e10 | 0.207067 | ||||||||
\(99\) | 7.66387e10i | 0.809943i | ||||||||
\(100\) | −6.70965e8 | −0.00670965 | ||||||||
\(101\) | 6.71725e10 | 0.635951 | 0.317976 | − | 0.948099i | \(-0.396997\pi\) | ||||
0.317976 | + | 0.948099i | \(0.396997\pi\) | |||||||
\(102\) | 1.28227e10 | + | 4.24554e9i | 0.114995 | + | 0.0380743i | ||||
\(103\) | −5.26906e10 | −0.447846 | −0.223923 | − | 0.974607i | \(-0.571886\pi\) | ||||
−0.223923 | + | 0.974607i | \(0.571886\pi\) | |||||||
\(104\) | −1.83791e10 | −0.148129 | ||||||||
\(105\) | − | 1.07740e10i | − | 0.0823829i | ||||||
\(106\) | −1.04547e11 | −0.758804 | ||||||||
\(107\) | − | 2.30745e11i | − | 1.59046i | −0.606309 | − | 0.795229i | \(-0.707350\pi\) | ||
0.606309 | − | 0.795229i | \(-0.292650\pi\) | |||||||
\(108\) | 2.29666e10i | 0.150406i | ||||||||
\(109\) | − | 2.37657e11i | − | 1.47946i | −0.672901 | − | 0.739732i | \(-0.734952\pi\) | ||
0.672901 | − | 0.739732i | \(-0.265048\pi\) | |||||||
\(110\) | −1.88165e11 | −1.11399 | ||||||||
\(111\) | 2.17789e10 | 0.122676 | ||||||||
\(112\) | − | 1.93952e11i | − | 1.03991i | ||||||
\(113\) | − | 1.18308e11i | − | 0.604062i | −0.953298 | − | 0.302031i | \(-0.902335\pi\) | ||
0.953298 | − | 0.302031i | \(-0.0976646\pi\) | |||||||
\(114\) | − | 6.43700e9i | − | 0.0313117i | ||||||
\(115\) | −2.90685e11 | −1.34767 | ||||||||
\(116\) | − | 2.05993e11i | − | 0.910614i | ||||||
\(117\) | 1.67732e11 | 0.707282 | ||||||||
\(118\) | 1.21549e11 | 0.489103 | ||||||||
\(119\) | 2.27524e11 | + | 7.53322e10i | 0.874014 | + | 0.289383i | ||||
\(120\) | 5.06771e9 | 0.0185915 | ||||||||
\(121\) | 9.51354e10 | 0.333444 | ||||||||
\(122\) | 4.82775e11i | 1.61721i | ||||||||
\(123\) | 4.04523e9 | 0.0129558 | ||||||||
\(124\) | − | 3.07496e11i | − | 0.941934i | ||||||
\(125\) | 3.39832e11i | 0.996001i | ||||||||
\(126\) | 4.42516e11i | 1.24134i | ||||||||
\(127\) | −5.94266e11 | −1.59610 | −0.798050 | − | 0.602591i | \(-0.794135\pi\) | ||||
−0.798050 | + | 0.602591i | \(0.794135\pi\) | |||||||
\(128\) | 1.59648e11 | 0.410686 | ||||||||
\(129\) | − | 5.35444e8i | − | 0.00131969i | ||||||
\(130\) | 4.11819e11i | 0.972787i | ||||||||
\(131\) | 3.66561e11i | 0.830145i | 0.909788 | + | 0.415073i | \(0.136244\pi\) | ||||
−0.909788 | + | 0.415073i | \(0.863756\pi\) | |||||||
\(132\) | −2.83818e10 | −0.0616429 | ||||||||
\(133\) | − | 1.14217e11i | − | 0.237984i | ||||||
\(134\) | 1.18565e12 | 2.37071 | ||||||||
\(135\) | −9.28684e10 | −0.178251 | ||||||||
\(136\) | −3.54335e10 | + | 1.07019e11i | −0.0653056 | + | 0.197241i | ||||
\(137\) | 1.59466e11 | 0.282297 | 0.141148 | − | 0.989988i | \(-0.454921\pi\) | ||||
0.141148 | + | 0.989988i | \(0.454921\pi\) | |||||||
\(138\) | −9.56031e10 | −0.162606 | ||||||||
\(139\) | − | 7.52929e11i | − | 1.23076i | −0.788231 | − | 0.615379i | \(-0.789003\pi\) | ||
0.788231 | − | 0.615379i | \(-0.210997\pi\) | |||||||
\(140\) | −4.98278e11 | −0.783010 | ||||||||
\(141\) | 6.19647e10i | 0.0936352i | ||||||||
\(142\) | − | 2.95948e11i | − | 0.430159i | ||||||
\(143\) | 4.16220e11i | 0.582069i | ||||||||
\(144\) | −8.32564e11 | −1.12053 | ||||||||
\(145\) | 8.32959e11 | 1.07919 | ||||||||
\(146\) | 7.68669e11i | 0.958955i | ||||||||
\(147\) | 1.13012e10i | 0.0135794i | ||||||||
\(148\) | − | 1.00723e12i | − | 1.16597i | ||||||
\(149\) | −1.63907e12 | −1.82840 | −0.914202 | − | 0.405259i | \(-0.867181\pi\) | ||||
−0.914202 | + | 0.405259i | \(0.867181\pi\) | |||||||
\(150\) | − | 8.92319e8i | − | 0.000959441i | ||||||
\(151\) | 1.57160e12 | 1.62917 | 0.814587 | − | 0.580041i | \(-0.196963\pi\) | ||||
0.814587 | + | 0.580041i | \(0.196963\pi\) | |||||||
\(152\) | 5.37236e10 | 0.0537063 | ||||||||
\(153\) | 3.23374e11 | − | 9.76677e11i | 0.311819 | − | 0.941777i | ||||
\(154\) | −1.09809e12 | −1.02158 | ||||||||
\(155\) | 1.24340e12 | 1.11631 | ||||||||
\(156\) | 6.21165e10i | 0.0538296i | ||||||||
\(157\) | −1.24309e12 | −1.04005 | −0.520027 | − | 0.854150i | \(-0.674078\pi\) | ||||
−0.520027 | + | 0.854150i | \(0.674078\pi\) | |||||||
\(158\) | 1.80899e12i | 1.46158i | ||||||||
\(159\) | − | 6.37651e10i | − | 0.0497621i | ||||||
\(160\) | − | 1.76747e12i | − | 1.33257i | ||||||
\(161\) | −1.69637e12 | −1.23588 | ||||||||
\(162\) | 1.88423e12 | 1.32679 | ||||||||
\(163\) | − | 1.76482e12i | − | 1.20135i | −0.799494 | − | 0.600675i | \(-0.794899\pi\) | ||
0.799494 | − | 0.600675i | \(-0.205101\pi\) | |||||||
\(164\) | − | 1.87084e11i | − | 0.123139i | ||||||
\(165\) | − | 1.14765e11i | − | 0.0730548i | ||||||
\(166\) | 1.57241e11 | 0.0968214 | ||||||||
\(167\) | 2.00184e12i | 1.19258i | 0.802768 | + | 0.596292i | \(0.203360\pi\) | ||||
−0.802768 | + | 0.596292i | \(0.796640\pi\) | |||||||
\(168\) | 2.95739e10 | 0.0170494 | ||||||||
\(169\) | −8.81221e11 | −0.491709 | ||||||||
\(170\) | 2.39796e12 | + | 7.93956e11i | 1.29531 | + | 0.428872i | ||||
\(171\) | −4.90293e11 | −0.256435 | ||||||||
\(172\) | −2.47632e10 | −0.0125430 | ||||||||
\(173\) | − | 3.54453e11i | − | 0.173902i | −0.996213 | − | 0.0869511i | \(-0.972288\pi\) | ||
0.996213 | − | 0.0869511i | \(-0.0277124\pi\) | |||||||
\(174\) | 2.73951e11 | 0.130212 | ||||||||
\(175\) | − | 1.58332e10i | − | 0.00729221i | ||||||
\(176\) | − | 2.06598e12i | − | 0.922160i | ||||||
\(177\) | 7.41349e10i | 0.0320752i | ||||||||
\(178\) | −5.54368e12 | −2.32535 | ||||||||
\(179\) | 3.84094e11 | 0.156223 | 0.0781116 | − | 0.996945i | \(-0.475111\pi\) | ||||
0.0781116 | + | 0.996945i | \(0.475111\pi\) | |||||||
\(180\) | 2.13893e12i | 0.843717i | ||||||||
\(181\) | − | 3.59801e12i | − | 1.37667i | −0.725392 | − | 0.688336i | \(-0.758341\pi\) | ||
0.725392 | − | 0.688336i | \(-0.241659\pi\) | |||||||
\(182\) | 2.40328e12i | 0.892095i | ||||||||
\(183\) | −2.94453e11 | −0.106056 | ||||||||
\(184\) | − | 7.97910e11i | − | 0.278905i | ||||||
\(185\) | 4.07285e12 | 1.38183 | ||||||||
\(186\) | 4.08940e11 | 0.134691 | ||||||||
\(187\) | 2.42359e12 | + | 8.02441e11i | 0.775051 | + | 0.256616i | ||||
\(188\) | 2.86574e12 | 0.889957 | ||||||||
\(189\) | −5.41958e11 | −0.163465 | ||||||||
\(190\) | − | 1.20378e12i | − | 0.352698i | ||||||
\(191\) | −5.54417e12 | −1.57817 | −0.789084 | − | 0.614285i | \(-0.789444\pi\) | ||||
−0.789084 | + | 0.614285i | \(0.789444\pi\) | |||||||
\(192\) | − | 2.17333e11i | − | 0.0601130i | ||||||
\(193\) | − | 6.31838e11i | − | 0.169840i | −0.996388 | − | 0.0849202i | \(-0.972936\pi\) | ||
0.996388 | − | 0.0849202i | \(-0.0270635\pi\) | |||||||
\(194\) | 6.25914e11i | 0.163533i | ||||||||
\(195\) | −2.51176e11 | −0.0637951 | ||||||||
\(196\) | 5.22660e11 | 0.129066 | ||||||||
\(197\) | 7.74159e12i | 1.85894i | 0.368895 | + | 0.929471i | \(0.379736\pi\) | ||||
−0.368895 | + | 0.929471i | \(0.620264\pi\) | |||||||
\(198\) | 4.71369e12i | 1.10079i | ||||||||
\(199\) | 1.47357e12i | 0.334718i | 0.985896 | + | 0.167359i | \(0.0535239\pi\) | ||||
−0.985896 | + | 0.167359i | \(0.946476\pi\) | |||||||
\(200\) | 7.44735e9 | 0.00164565 | ||||||||
\(201\) | 7.23147e11i | 0.155471i | ||||||||
\(202\) | 4.13147e12 | 0.864315 | ||||||||
\(203\) | 4.86095e12 | 0.989676 | ||||||||
\(204\) | 3.61695e11 | + | 1.19756e11i | 0.0716765 | + | 0.0237318i | ||||
\(205\) | 7.56496e11 | 0.145935 | ||||||||
\(206\) | −3.24076e12 | −0.608663 | ||||||||
\(207\) | 7.28190e12i | 1.33170i | ||||||||
\(208\) | −4.52160e12 | −0.805275 | ||||||||
\(209\) | − | 1.21665e12i | − | 0.211038i | ||||||
\(210\) | − | 6.62661e11i | − | 0.111966i | ||||||
\(211\) | 1.93592e11i | 0.0318664i | 0.999873 | + | 0.0159332i | \(0.00507191\pi\) | ||||
−0.999873 | + | 0.0159332i | \(0.994928\pi\) | |||||||
\(212\) | −2.94901e12 | −0.472965 | ||||||||
\(213\) | 1.80504e11 | 0.0282097 | ||||||||
\(214\) | − | 1.41921e13i | − | 2.16158i | ||||||
\(215\) | − | 1.00133e11i | − | 0.0148650i | ||||||
\(216\) | − | 2.54917e11i | − | 0.0368895i | ||||||
\(217\) | 7.25617e12 | 1.02372 | ||||||||
\(218\) | − | 1.46172e13i | − | 2.01072i | ||||||
\(219\) | −4.68825e11 | −0.0628880 | ||||||||
\(220\) | −5.30767e12 | −0.694351 | ||||||||
\(221\) | 1.75622e12 | − | 5.30427e12i | 0.224090 | − | 0.676812i | ||||
\(222\) | 1.33952e12 | 0.166727 | ||||||||
\(223\) | −8.10132e12 | −0.983737 | −0.491869 | − | 0.870669i | \(-0.663686\pi\) | ||||
−0.491869 | + | 0.870669i | \(0.663686\pi\) | |||||||
\(224\) | − | 1.03145e13i | − | 1.22204i | ||||||
\(225\) | −6.79661e10 | −0.00785758 | ||||||||
\(226\) | − | 7.27656e12i | − | 0.820975i | ||||||
\(227\) | 1.47294e13i | 1.62197i | 0.585065 | + | 0.810987i | \(0.301069\pi\) | ||||
−0.585065 | + | 0.810987i | \(0.698931\pi\) | |||||||
\(228\) | − | 1.81572e11i | − | 0.0195167i | ||||||
\(229\) | −6.60411e12 | −0.692977 | −0.346489 | − | 0.938054i | \(-0.612626\pi\) | ||||
−0.346489 | + | 0.938054i | \(0.612626\pi\) | |||||||
\(230\) | −1.78787e13 | −1.83161 | ||||||||
\(231\) | − | 6.69743e11i | − | 0.0669950i | ||||||
\(232\) | 2.28641e12i | 0.223342i | ||||||||
\(233\) | − | 1.89377e13i | − | 1.80663i | −0.428979 | − | 0.903314i | \(-0.641127\pi\) | ||
0.428979 | − | 0.903314i | \(-0.358873\pi\) | |||||||
\(234\) | 1.03164e13 | 0.961260 | ||||||||
\(235\) | 1.15880e13i | 1.05471i | ||||||||
\(236\) | 3.42859e12 | 0.304860 | ||||||||
\(237\) | −1.10334e12 | −0.0958501 | ||||||||
\(238\) | 1.39939e13 | + | 4.63334e12i | 1.18786 | + | 0.393297i | ||||
\(239\) | 8.13918e12 | 0.675138 | 0.337569 | − | 0.941301i | \(-0.390395\pi\) | ||||
0.337569 | + | 0.941301i | \(0.390395\pi\) | |||||||
\(240\) | 1.24675e12 | 0.101069 | ||||||||
\(241\) | 5.41957e12i | 0.429409i | 0.976679 | + | 0.214704i | \(0.0688788\pi\) | ||||
−0.976679 | + | 0.214704i | \(0.931121\pi\) | |||||||
\(242\) | 5.85134e12 | 0.453180 | ||||||||
\(243\) | 3.49428e12i | 0.264560i | ||||||||
\(244\) | 1.36179e13i | 1.00801i | ||||||||
\(245\) | 2.11344e12i | 0.152960i | ||||||||
\(246\) | 2.48803e11 | 0.0176081 | ||||||||
\(247\) | −2.66275e12 | −0.184288 | ||||||||
\(248\) | 3.41304e12i | 0.231024i | ||||||||
\(249\) | 9.59041e10i | 0.00634952i | ||||||||
\(250\) | 2.09015e13i | 1.35365i | ||||||||
\(251\) | 1.61292e13 | 1.02190 | 0.510950 | − | 0.859610i | \(-0.329294\pi\) | ||||
0.510950 | + | 0.859610i | \(0.329294\pi\) | |||||||
\(252\) | 1.24823e13i | 0.773731i | ||||||||
\(253\) | −1.80698e13 | −1.09595 | ||||||||
\(254\) | −3.65505e13 | −2.16924 | ||||||||
\(255\) | −4.84248e11 | + | 1.46256e12i | −0.0281253 | + | 0.0849459i | ||||
\(256\) | 2.16843e13 | 1.23261 | ||||||||
\(257\) | −5.15196e12 | −0.286642 | −0.143321 | − | 0.989676i | \(-0.545778\pi\) | ||||
−0.143321 | + | 0.989676i | \(0.545778\pi\) | |||||||
\(258\) | − | 3.29327e10i | − | 0.00179357i | ||||||
\(259\) | 2.37682e13 | 1.26721 | ||||||||
\(260\) | 1.16164e13i | 0.606341i | ||||||||
\(261\) | − | 2.08663e13i | − | 1.06641i | ||||||
\(262\) | 2.25455e13i | 1.12824i | ||||||||
\(263\) | 1.77857e12 | 0.0871592 | 0.0435796 | − | 0.999050i | \(-0.486124\pi\) | ||||
0.0435796 | + | 0.999050i | \(0.486124\pi\) | |||||||
\(264\) | 3.15023e11 | 0.0151189 | ||||||||
\(265\) | − | 1.19247e13i | − | 0.560525i | ||||||
\(266\) | − | 7.02498e12i | − | 0.323442i | ||||||
\(267\) | − | 3.38119e12i | − | 0.152496i | ||||||
\(268\) | 3.34441e13 | 1.47767 | ||||||||
\(269\) | − | 1.78034e13i | − | 0.770663i | −0.922778 | − | 0.385331i | \(-0.874087\pi\) | ||
0.922778 | − | 0.385331i | \(-0.125913\pi\) | |||||||
\(270\) | −5.71191e12 | −0.242259 | ||||||||
\(271\) | −3.26277e13 | −1.35599 | −0.677993 | − | 0.735069i | \(-0.737150\pi\) | ||||
−0.677993 | + | 0.735069i | \(0.737150\pi\) | |||||||
\(272\) | −8.71732e12 | + | 2.63287e13i | −0.355021 | + | 1.07226i | ||||
\(273\) | −1.46580e12 | −0.0585033 | ||||||||
\(274\) | 9.80804e12 | 0.383667 | ||||||||
\(275\) | − | 1.68656e11i | − | 0.00646652i | ||||||
\(276\) | −2.69672e12 | −0.101353 | ||||||||
\(277\) | − | 2.71764e13i | − | 1.00128i | −0.865657 | − | 0.500638i | \(-0.833099\pi\) | ||
0.865657 | − | 0.500638i | \(-0.166901\pi\) | |||||||
\(278\) | − | 4.63092e13i | − | 1.67271i | ||||||
\(279\) | − | 3.11481e13i | − | 1.10309i | ||||||
\(280\) | 5.53061e12 | 0.192045 | ||||||||
\(281\) | −3.57016e13 | −1.21563 | −0.607817 | − | 0.794077i | \(-0.707954\pi\) | ||||
−0.607817 | + | 0.794077i | \(0.707954\pi\) | |||||||
\(282\) | 3.81116e12i | 0.127259i | ||||||||
\(283\) | − | 1.04843e13i | − | 0.343333i | −0.985155 | − | 0.171666i | \(-0.945085\pi\) | ||
0.985155 | − | 0.171666i | \(-0.0549151\pi\) | |||||||
\(284\) | − | 8.34794e12i | − | 0.268120i | ||||||
\(285\) | 7.34207e11 | 0.0231298 | ||||||||
\(286\) | 2.55998e13i | 0.791085i | ||||||||
\(287\) | 4.41473e12 | 0.133830 | ||||||||
\(288\) | −4.42765e13 | −1.31678 | ||||||||
\(289\) | −2.75002e13 | − | 2.04525e13i | −0.802411 | − | 0.596771i | ||||
\(290\) | 5.12315e13 | 1.46672 | ||||||||
\(291\) | −3.81756e11 | −0.0107244 | ||||||||
\(292\) | 2.16822e13i | 0.597720i | ||||||||
\(293\) | 7.03512e13 | 1.90327 | 0.951633 | − | 0.307238i | \(-0.0994047\pi\) | ||||
0.951633 | + | 0.307238i | \(0.0994047\pi\) | |||||||
\(294\) | 6.95087e11i | 0.0184556i | ||||||||
\(295\) | 1.38639e13i | 0.361298i | ||||||||
\(296\) | 1.11797e13i | 0.285973i | ||||||||
\(297\) | −5.77295e12 | −0.144956 | ||||||||
\(298\) | −1.00811e14 | −2.48497 | ||||||||
\(299\) | 3.95475e13i | 0.957035i | ||||||||
\(300\) | − | 2.51701e10i | − | 0.000598023i | ||||||
\(301\) | − | 5.84353e11i | − | 0.0136320i | ||||||
\(302\) | 9.66616e13 | 2.21419 | ||||||||
\(303\) | 2.51986e12i | 0.0566815i | ||||||||
\(304\) | 1.32170e13 | 0.291964 | ||||||||
\(305\) | −5.50655e13 | −1.19462 | ||||||||
\(306\) | 1.98892e13 | − | 6.00709e13i | 0.423790 | − | 1.27996i | ||||
\(307\) | 3.93815e13 | 0.824197 | 0.412099 | − | 0.911139i | \(-0.364796\pi\) | ||||
0.412099 | + | 0.911139i | \(0.364796\pi\) | |||||||
\(308\) | −3.09743e13 | −0.636755 | ||||||||
\(309\) | − | 1.97659e12i | − | 0.0399159i | ||||||
\(310\) | 7.64757e13 | 1.51717 | ||||||||
\(311\) | 8.38957e13i | 1.63515i | 0.575823 | + | 0.817575i | \(0.304682\pi\) | ||||
−0.575823 | + | 0.817575i | \(0.695318\pi\) | |||||||
\(312\) | − | 6.89459e11i | − | 0.0132026i | ||||||
\(313\) | − | 5.07613e13i | − | 0.955078i | −0.878610 | − | 0.477539i | \(-0.841529\pi\) | ||
0.878610 | − | 0.477539i | \(-0.158471\pi\) | |||||||
\(314\) | −7.64570e13 | −1.41353 | ||||||||
\(315\) | −5.04735e13 | −0.916971 | ||||||||
\(316\) | 5.10272e13i | 0.911009i | ||||||||
\(317\) | − | 7.52575e12i | − | 0.132046i | −0.997818 | − | 0.0660228i | \(-0.978969\pi\) | ||
0.997818 | − | 0.0660228i | \(-0.0210310\pi\) | |||||||
\(318\) | − | 3.92190e12i | − | 0.0676312i | ||||||
\(319\) | 5.17790e13 | 0.877617 | ||||||||
\(320\) | − | 4.06433e13i | − | 0.677118i | ||||||
\(321\) | 8.65600e12 | 0.141755 | ||||||||
\(322\) | −1.04336e14 | −1.67968 | ||||||||
\(323\) | −5.13359e12 | + | 1.55048e13i | −0.0812470 | + | 0.245388i | ||||
\(324\) | 5.31493e13 | 0.826990 | ||||||||
\(325\) | −3.69120e11 | −0.00564689 | ||||||||
\(326\) | − | 1.08546e14i | − | 1.63274i | ||||||
\(327\) | 8.91527e12 | 0.131863 | ||||||||
\(328\) | 2.07653e12i | 0.0302017i | ||||||||
\(329\) | 6.76247e13i | 0.967226i | ||||||||
\(330\) | − | 7.05868e12i | − | 0.0992881i | ||||||
\(331\) | 4.92457e13 | 0.681262 | 0.340631 | − | 0.940197i | \(-0.389359\pi\) | ||||
0.340631 | + | 0.940197i | \(0.389359\pi\) | |||||||
\(332\) | 4.43537e12 | 0.0603491 | ||||||||
\(333\) | − | 1.02028e14i | − | 1.36546i | ||||||
\(334\) | 1.23124e14i | 1.62083i | ||||||||
\(335\) | 1.35235e14i | 1.75123i | ||||||||
\(336\) | 7.27575e12 | 0.0926855 | ||||||||
\(337\) | 1.20199e13i | 0.150638i | 0.997159 | + | 0.0753190i | \(0.0239975\pi\) | ||||
−0.997159 | + | 0.0753190i | \(0.976002\pi\) | |||||||
\(338\) | −5.41998e13 | −0.668276 | ||||||||
\(339\) | 4.43810e12 | 0.0538393 | ||||||||
\(340\) | 6.76405e13 | + | 2.23955e13i | 0.807370 | + | 0.267317i | ||||
\(341\) | 7.72930e13 | 0.907802 | ||||||||
\(342\) | −3.01557e13 | −0.348518 | ||||||||
\(343\) | 9.32849e13i | 1.06095i | ||||||||
\(344\) | 2.74858e11 | 0.00307636 | ||||||||
\(345\) | − | 1.09045e13i | − | 0.120116i | ||||||
\(346\) | − | 2.18008e13i | − | 0.236349i | ||||||
\(347\) | 3.76384e13i | 0.401624i | 0.979630 | + | 0.200812i | \(0.0643580\pi\) | ||||
−0.979630 | + | 0.200812i | \(0.935642\pi\) | |||||||
\(348\) | 7.72747e12 | 0.0811618 | ||||||||
\(349\) | −4.41594e13 | −0.456545 | −0.228273 | − | 0.973597i | \(-0.573308\pi\) | ||||
−0.228273 | + | 0.973597i | \(0.573308\pi\) | |||||||
\(350\) | − | 9.73826e11i | − | 0.00991076i | ||||||
\(351\) | 1.26347e13i | 0.126583i | ||||||||
\(352\) | − | 1.09870e14i | − | 1.08367i | ||||||
\(353\) | 1.03528e14 | 1.00530 | 0.502652 | − | 0.864489i | \(-0.332358\pi\) | ||||
0.502652 | + | 0.864489i | \(0.332358\pi\) | |||||||
\(354\) | 4.55970e12i | 0.0435931i | ||||||||
\(355\) | 3.37559e13 | 0.317756 | ||||||||
\(356\) | −1.56373e14 | −1.44940 | ||||||||
\(357\) | −2.82595e12 | + | 8.53515e12i | −0.0257923 | + | 0.0778997i | ||||
\(358\) | 2.36238e13 | 0.212321 | ||||||||
\(359\) | −7.07192e13 | −0.625918 | −0.312959 | − | 0.949767i | \(-0.601320\pi\) | ||||
−0.312959 | + | 0.949767i | \(0.601320\pi\) | |||||||
\(360\) | − | 2.37409e13i | − | 0.206935i | ||||||
\(361\) | −1.08707e14 | −0.933184 | ||||||||
\(362\) | − | 2.21297e14i | − | 1.87102i | ||||||
\(363\) | 3.56884e12i | 0.0297194i | ||||||||
\(364\) | 6.77904e13i | 0.556046i | ||||||||
\(365\) | −8.76747e13 | −0.708375 | ||||||||
\(366\) | −1.81104e13 | −0.144140 | ||||||||
\(367\) | − | 1.59083e13i | − | 0.124727i | −0.998053 | − | 0.0623636i | \(-0.980136\pi\) | ||
0.998053 | − | 0.0623636i | \(-0.0198639\pi\) | |||||||
\(368\) | − | 1.96301e14i | − | 1.51621i | ||||||
\(369\) | − | 1.89508e13i | − | 0.144206i | ||||||
\(370\) | 2.50502e14 | 1.87803 | ||||||||
\(371\) | − | 6.95896e13i | − | 0.514029i | ||||||
\(372\) | 1.15352e13 | 0.0839533 | ||||||||
\(373\) | −1.58474e13 | −0.113647 | −0.0568237 | − | 0.998384i | \(-0.518097\pi\) | ||||
−0.0568237 | + | 0.998384i | \(0.518097\pi\) | |||||||
\(374\) | 1.49064e14 | + | 4.93545e13i | 1.05336 | + | 0.348765i | ||||
\(375\) | −1.27482e13 | −0.0887722 | ||||||||
\(376\) | −3.18082e13 | −0.218276 | ||||||||
\(377\) | − | 1.13324e14i | − | 0.766378i | ||||||
\(378\) | −3.33333e13 | −0.222164 | ||||||||
\(379\) | 6.78416e12i | 0.0445636i | 0.999752 | + | 0.0222818i | \(0.00709311\pi\) | ||||
−0.999752 | + | 0.0222818i | \(0.992907\pi\) | |||||||
\(380\) | − | 3.39556e13i | − | 0.219838i | ||||||
\(381\) | − | 2.22928e13i | − | 0.142258i | ||||||
\(382\) | −3.40996e14 | −2.14487 | ||||||||
\(383\) | −8.16812e13 | −0.506441 | −0.253221 | − | 0.967409i | \(-0.581490\pi\) | ||||
−0.253221 | + | 0.967409i | \(0.581490\pi\) | |||||||
\(384\) | 5.98892e12i | 0.0366039i | ||||||||
\(385\) | − | 1.25248e14i | − | 0.754637i | ||||||
\(386\) | − | 3.88615e13i | − | 0.230828i | ||||||
\(387\) | −2.50842e12 | −0.0146889 | ||||||||
\(388\) | 1.76555e13i | 0.101931i | ||||||||
\(389\) | 1.02293e14 | 0.582270 | 0.291135 | − | 0.956682i | \(-0.405967\pi\) | ||||
0.291135 | + | 0.956682i | \(0.405967\pi\) | |||||||
\(390\) | −1.54486e13 | −0.0867032 | ||||||||
\(391\) | 2.30280e14 | + | 7.62447e13i | 1.27433 | + | 0.421927i | ||||
\(392\) | −5.80124e12 | −0.0316554 | ||||||||
\(393\) | −1.37509e13 | −0.0739897 | ||||||||
\(394\) | 4.76149e14i | 2.52647i | ||||||||
\(395\) | −2.06335e14 | −1.07966 | ||||||||
\(396\) | 1.32961e14i | 0.686123i | ||||||||
\(397\) | − | 4.33650e13i | − | 0.220694i | −0.993893 | − | 0.110347i | \(-0.964804\pi\) | ||
0.993893 | − | 0.110347i | \(-0.0351963\pi\) | |||||||
\(398\) | 9.06325e13i | 0.454911i | ||||||||
\(399\) | 4.28466e12 | 0.0212112 | ||||||||
\(400\) | 1.83219e12 | 0.00894624 | ||||||||
\(401\) | 1.20106e13i | 0.0578459i | 0.999582 | + | 0.0289229i | \(0.00920774\pi\) | ||||
−0.999582 | + | 0.0289229i | \(0.990792\pi\) | |||||||
\(402\) | 4.44774e13i | 0.211298i | ||||||||
\(403\) | − | 1.69164e14i | − | 0.792737i | ||||||
\(404\) | 1.16538e14 | 0.538730 | ||||||||
\(405\) | 2.14916e14i | 0.980090i | ||||||||
\(406\) | 2.98975e14 | 1.34506 | ||||||||
\(407\) | 2.53180e14 | 1.12372 | ||||||||
\(408\) | −4.01462e12 | − | 1.32923e12i | −0.0175798 | − | 0.00582060i | ||||
\(409\) | 2.37591e14 | 1.02648 | 0.513242 | − | 0.858244i | \(-0.328444\pi\) | ||||
0.513242 | + | 0.858244i | \(0.328444\pi\) | |||||||
\(410\) | 4.65286e13 | 0.198339 | ||||||||
\(411\) | 5.98209e12i | 0.0251607i | ||||||||
\(412\) | −9.14136e13 | −0.379381 | ||||||||
\(413\) | 8.09066e13i | 0.331328i | ||||||||
\(414\) | 4.47876e14i | 1.80991i | ||||||||
\(415\) | 1.79350e13i | 0.0715215i | ||||||||
\(416\) | −2.40463e14 | −0.946312 | ||||||||
\(417\) | 2.82448e13 | 0.109696 | ||||||||
\(418\) | − | 7.48303e13i | − | 0.286819i | ||||||
\(419\) | 4.63527e14i | 1.75347i | 0.480974 | + | 0.876735i | \(0.340283\pi\) | ||||
−0.480974 | + | 0.876735i | \(0.659717\pi\) | |||||||
\(420\) | − | 1.86920e13i | − | 0.0697886i | ||||||
\(421\) | −5.04223e14 | −1.85811 | −0.929055 | − | 0.369942i | \(-0.879378\pi\) | ||||
−0.929055 | + | 0.369942i | \(0.879378\pi\) | |||||||
\(422\) | 1.19069e13i | 0.0433093i | ||||||||
\(423\) | 2.90288e14 | 1.04222 | ||||||||
\(424\) | 3.27324e13 | 0.116002 | ||||||||
\(425\) | −7.11636e11 | + | 2.14933e12i | −0.00248954 | + | 0.00751908i | ||||
\(426\) | 1.11020e13 | 0.0383395 | ||||||||
\(427\) | −3.21349e14 | −1.09553 | ||||||||
\(428\) | − | 4.00323e14i | − | 1.34732i | ||||||
\(429\) | −1.56138e13 | −0.0518791 | ||||||||
\(430\) | − | 6.15872e12i | − | 0.0202029i | ||||||
\(431\) | − | 3.94622e14i | − | 1.27807i | −0.769176 | − | 0.639037i | \(-0.779333\pi\) | ||
0.769176 | − | 0.639037i | \(-0.220667\pi\) | |||||||
\(432\) | − | 6.27144e13i | − | 0.200543i | ||||||
\(433\) | −4.14797e14 | −1.30964 | −0.654820 | − | 0.755785i | \(-0.727256\pi\) | ||||
−0.654820 | + | 0.755785i | \(0.727256\pi\) | |||||||
\(434\) | 4.46294e14 | 1.39132 | ||||||||
\(435\) | 3.12470e13i | 0.0961872i | ||||||||
\(436\) | − | 4.12314e14i | − | 1.25329i | ||||||
\(437\) | − | 1.15601e14i | − | 0.346987i | ||||||
\(438\) | −2.88352e13 | −0.0854704 | ||||||||
\(439\) | − | 3.31859e14i | − | 0.971402i | −0.874125 | − | 0.485701i | \(-0.838564\pi\) | ||
0.874125 | − | 0.485701i | \(-0.161436\pi\) | |||||||
\(440\) | 5.89122e13 | 0.170300 | ||||||||
\(441\) | 5.29434e13 | 0.151147 | ||||||||
\(442\) | 1.08017e14 | − | 3.26241e14i | 0.304558 | − | 0.919849i | ||||
\(443\) | 3.44788e13 | 0.0960135 | 0.0480067 | − | 0.998847i | \(-0.484713\pi\) | ||||
0.0480067 | + | 0.998847i | \(0.484713\pi\) | |||||||
\(444\) | 3.77844e13 | 0.103922 | ||||||||
\(445\) | − | 6.32314e14i | − | 1.71772i | ||||||
\(446\) | −4.98275e14 | −1.33699 | ||||||||
\(447\) | − | 6.14867e13i | − | 0.162963i | ||||||
\(448\) | − | 2.37185e14i | − | 0.620951i | ||||||
\(449\) | 2.93233e14i | 0.758329i | 0.925329 | + | 0.379164i | \(0.123789\pi\) | ||||
−0.925329 | + | 0.379164i | \(0.876211\pi\) | |||||||
\(450\) | −4.18028e12 | −0.0106792 | ||||||||
\(451\) | 4.70258e13 | 0.118677 | ||||||||
\(452\) | − | 2.05254e14i | − | 0.511716i | ||||||
\(453\) | 5.89556e13i | 0.145206i | ||||||||
\(454\) | 9.05939e14i | 2.20441i | ||||||||
\(455\) | −2.74119e14 | −0.658986 | ||||||||
\(456\) | 2.01535e12i | 0.00478678i | ||||||||
\(457\) | 4.64192e14 | 1.08933 | 0.544664 | − | 0.838654i | \(-0.316657\pi\) | ||||
0.544664 | + | 0.838654i | \(0.316657\pi\) | |||||||
\(458\) | −4.06188e14 | −0.941818 | ||||||||
\(459\) | 7.35700e13 | + | 2.43587e13i | 0.168551 | + | 0.0558065i | ||||
\(460\) | −5.04313e14 | −1.14165 | ||||||||
\(461\) | 6.23883e14 | 1.39556 | 0.697779 | − | 0.716313i | \(-0.254172\pi\) | ||||
0.697779 | + | 0.716313i | \(0.254172\pi\) | |||||||
\(462\) | − | 4.11928e13i | − | 0.0910522i | ||||||
\(463\) | 2.75054e14 | 0.600790 | 0.300395 | − | 0.953815i | \(-0.402881\pi\) | ||||
0.300395 | + | 0.953815i | \(0.402881\pi\) | |||||||
\(464\) | 5.62501e14i | 1.21416i | ||||||||
\(465\) | 4.66439e13i | 0.0994955i | ||||||||
\(466\) | − | 1.16477e15i | − | 2.45537i | ||||||
\(467\) | −5.49799e14 | −1.14541 | −0.572705 | − | 0.819761i | \(-0.694106\pi\) | ||||
−0.572705 | + | 0.819761i | \(0.694106\pi\) | |||||||
\(468\) | 2.91000e14 | 0.599156 | ||||||||
\(469\) | 7.89201e14i | 1.60597i | ||||||||
\(470\) | 7.12724e14i | 1.43345i | ||||||||
\(471\) | − | 4.66325e13i | − | 0.0926987i | ||||||
\(472\) | −3.80555e13 | −0.0747716 | ||||||||
\(473\) | − | 6.22454e12i | − | 0.0120885i | ||||||
\(474\) | −6.78612e13 | −0.130269 | ||||||||
\(475\) | 1.07897e12 | 0.00204736 | ||||||||
\(476\) | 3.94734e14 | + | 1.30695e14i | 0.740399 | + | 0.245143i | ||||
\(477\) | −2.98723e14 | −0.553883 | ||||||||
\(478\) | 5.00603e14 | 0.917573 | ||||||||
\(479\) | 8.02043e14i | 1.45329i | 0.687013 | + | 0.726645i | \(0.258922\pi\) | ||||
−0.687013 | + | 0.726645i | \(0.741078\pi\) | |||||||
\(480\) | 6.63033e13 | 0.118770 | ||||||||
\(481\) | − | 5.54109e14i | − | 0.981291i | ||||||
\(482\) | 3.33333e14i | 0.583605i | ||||||||
\(483\) | − | 6.36362e13i | − | 0.110153i | ||||||
\(484\) | 1.65052e14 | 0.282469 | ||||||||
\(485\) | −7.13920e13 | −0.120801 | ||||||||
\(486\) | 2.14917e14i | 0.359560i | ||||||||
\(487\) | − | 1.07735e15i | − | 1.78216i | −0.453843 | − | 0.891082i | \(-0.649947\pi\) | ||
0.453843 | − | 0.891082i | \(-0.350053\pi\) | |||||||
\(488\) | − | 1.51151e14i | − | 0.247230i | ||||||
\(489\) | 6.62042e13 | 0.107075 | ||||||||
\(490\) | 1.29988e14i | 0.207886i | ||||||||
\(491\) | 5.30247e14 | 0.838552 | 0.419276 | − | 0.907859i | \(-0.362284\pi\) | ||||
0.419276 | + | 0.907859i | \(0.362284\pi\) | |||||||
\(492\) | 7.01811e12 | 0.0109752 | ||||||||
\(493\) | −6.59867e14 | − | 2.18480e14i | −1.02047 | − | 0.337872i | ||||
\(494\) | −1.63774e14 | −0.250464 | ||||||||
\(495\) | −5.37646e14 | −0.813144 | ||||||||
\(496\) | 8.39672e14i | 1.25592i | ||||||||
\(497\) | 1.96991e14 | 0.291398 | ||||||||
\(498\) | 5.89862e12i | 0.00862956i | ||||||||
\(499\) | − | 4.36944e14i | − | 0.632227i | −0.948721 | − | 0.316113i | \(-0.897622\pi\) | ||
0.948721 | − | 0.316113i | \(-0.102378\pi\) | |||||||
\(500\) | 5.89579e14i | 0.843737i | ||||||||
\(501\) | −7.50955e13 | −0.106293 | ||||||||
\(502\) | 9.92035e14 | 1.38885 | ||||||||
\(503\) | − | 4.09919e14i | − | 0.567642i | −0.958877 | − | 0.283821i | \(-0.908398\pi\) | ||
0.958877 | − | 0.283821i | \(-0.0916022\pi\) | |||||||
\(504\) | − | 1.38546e14i | − | 0.189770i | ||||||
\(505\) | 4.71237e14i | 0.638465i | ||||||||
\(506\) | −1.11139e15 | −1.48949 | ||||||||
\(507\) | − | 3.30574e13i | − | 0.0438253i | ||||||
\(508\) | −1.03100e15 | −1.35210 | ||||||||
\(509\) | 1.07378e15 | 1.39305 | 0.696524 | − | 0.717533i | \(-0.254729\pi\) | ||||
0.696524 | + | 0.717533i | \(0.254729\pi\) | |||||||
\(510\) | −2.97838e13 | + | 8.99553e13i | −0.0382248 | + | 0.115449i | ||||
\(511\) | −5.11648e14 | −0.649616 | ||||||||
\(512\) | 1.00674e15 | 1.26454 | ||||||||
\(513\) | − | 3.69323e13i | − | 0.0458945i | ||||||
\(514\) | −3.16873e14 | −0.389573 | ||||||||
\(515\) | − | 3.69642e14i | − | 0.449616i | ||||||
\(516\) | − | 9.28948e11i | − | 0.00111794i | ||||||
\(517\) | 7.20341e14i | 0.857709i | ||||||||
\(518\) | 1.46187e15 | 1.72225 | ||||||||
\(519\) | 1.32967e13 | 0.0154997 | ||||||||
\(520\) | − | 1.28935e14i | − | 0.148715i | ||||||
\(521\) | 1.25271e15i | 1.42970i | 0.699278 | + | 0.714849i | \(0.253505\pi\) | ||||
−0.699278 | + | 0.714849i | \(0.746495\pi\) | |||||||
\(522\) | − | 1.28339e15i | − | 1.44934i | ||||||
\(523\) | −4.63073e14 | −0.517476 | −0.258738 | − | 0.965948i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965948i | \(0.583307\pi\) | |||||||
\(524\) | 6.35951e14i | 0.703237i | ||||||||
\(525\) | 5.93954e11 | 0.000649945 | ||||||||
\(526\) | 1.09391e14 | 0.118457 | ||||||||
\(527\) | −9.85016e14 | − | 3.26135e14i | −1.05556 | − | 0.349493i | ||||
\(528\) | 7.75015e13 | 0.0821909 | ||||||||
\(529\) | −7.64106e14 | −0.801951 | ||||||||
\(530\) | − | 7.33433e14i | − | 0.761803i | ||||||
\(531\) | 3.47303e14 | 0.357017 | ||||||||
\(532\) | − | 1.98157e14i | − | 0.201602i | ||||||
\(533\) | − | 1.02921e14i | − | 0.103634i | ||||||
\(534\) | − | 2.07961e14i | − | 0.207255i | ||||||
\(535\) | 1.61876e15 | 1.59674 | ||||||||
\(536\) | −3.71211e14 | −0.362422 | ||||||||
\(537\) | 1.44086e13i | 0.0139240i | ||||||||
\(538\) | − | 1.09500e15i | − | 1.04740i | ||||||
\(539\) | 1.31377e14i | 0.124389i | ||||||||
\(540\) | −1.61118e14 | −0.151001 | ||||||||
\(541\) | 3.93255e14i | 0.364829i | 0.983222 | + | 0.182415i | \(0.0583913\pi\) | ||||
−0.983222 | + | 0.182415i | \(0.941609\pi\) | |||||||
\(542\) | −2.00678e15 | −1.84291 | ||||||||
\(543\) | 1.34973e14 | 0.122701 | ||||||||
\(544\) | −4.63594e14 | + | 1.40018e15i | −0.417200 | + | 1.26006i | ||||
\(545\) | 1.66724e15 | 1.48531 | ||||||||
\(546\) | −9.01546e13 | −0.0795112 | ||||||||
\(547\) | − | 1.15470e15i | − | 1.00818i | −0.863652 | − | 0.504089i | \(-0.831828\pi\) | ||
0.863652 | − | 0.504089i | \(-0.168172\pi\) | |||||||
\(548\) | 2.76660e14 | 0.239141 | ||||||||
\(549\) | 1.37944e15i | 1.18047i | ||||||||
\(550\) | − | 1.03732e13i | − | 0.00878859i | ||||||
\(551\) | 3.31254e14i | 0.277861i | ||||||||
\(552\) | 2.99322e13 | 0.0248584 | ||||||||
\(553\) | −1.20412e15 | −0.990105 | ||||||||
\(554\) | − | 1.67150e15i | − | 1.36082i | ||||||
\(555\) | 1.52786e14i | 0.123161i | ||||||||
\(556\) | − | 1.30627e15i | − | 1.04261i | ||||||
\(557\) | 6.77959e14 | 0.535796 | 0.267898 | − | 0.963447i | \(-0.413671\pi\) | ||||
0.267898 | + | 0.963447i | \(0.413671\pi\) | |||||||
\(558\) | − | 1.91578e15i | − | 1.49919i | ||||||
\(559\) | −1.36230e13 | −0.0105562 | ||||||||
\(560\) | 1.36063e15 | 1.04402 | ||||||||
\(561\) | −3.01022e13 | + | 9.09167e13i | −0.0228719 | + | 0.0690793i | ||||
\(562\) | −2.19584e15 | −1.65215 | ||||||||
\(563\) | −1.64475e15 | −1.22547 | −0.612735 | − | 0.790289i | \(-0.709931\pi\) | ||||
−0.612735 | + | 0.790289i | \(0.709931\pi\) | |||||||
\(564\) | 1.07503e14i | 0.0793207i | ||||||||
\(565\) | 8.29968e14 | 0.606450 | ||||||||
\(566\) | − | 6.44843e14i | − | 0.466620i | ||||||
\(567\) | 1.25420e15i | 0.898792i | ||||||||
\(568\) | 9.26576e13i | 0.0657605i | ||||||||
\(569\) | 6.00657e14 | 0.422191 | 0.211096 | − | 0.977465i | \(-0.432297\pi\) | ||||
0.211096 | + | 0.977465i | \(0.432297\pi\) | |||||||
\(570\) | 4.51577e13 | 0.0314355 | ||||||||
\(571\) | − | 6.83687e14i | − | 0.471367i | −0.971830 | − | 0.235683i | \(-0.924267\pi\) | ||
0.971830 | − | 0.235683i | \(-0.0757328\pi\) | |||||||
\(572\) | 7.22105e14i | 0.493086i | ||||||||
\(573\) | − | 2.07980e14i | − | 0.140660i | ||||||
\(574\) | 2.71530e14 | 0.181887 | ||||||||
\(575\) | − | 1.60250e13i | − | 0.0106322i | ||||||
\(576\) | −1.01815e15 | −0.669095 | ||||||||
\(577\) | 2.27361e15 | 1.47995 | 0.739977 | − | 0.672632i | \(-0.234836\pi\) | ||||
0.739977 | + | 0.672632i | \(0.234836\pi\) | |||||||
\(578\) | −1.69141e15 | − | 1.25794e15i | −1.09055 | − | 0.811066i | ||||
\(579\) | 2.37023e13 | 0.0151376 | ||||||||
\(580\) | 1.44511e15 | 0.914213 | ||||||||
\(581\) | 1.04664e14i | 0.0655888i | ||||||||
\(582\) | −2.34800e13 | −0.0145755 | ||||||||
\(583\) | − | 7.41271e14i | − | 0.455827i | ||||||
\(584\) | − | 2.40661e14i | − | 0.146600i | ||||||
\(585\) | 1.17669e15i | 0.710078i | ||||||||
\(586\) | 4.32698e15 | 2.58671 | ||||||||
\(587\) | −1.59694e15 | −0.945755 | −0.472877 | − | 0.881128i | \(-0.656785\pi\) | ||||
−0.472877 | + | 0.881128i | \(0.656785\pi\) | |||||||
\(588\) | 1.96067e13i | 0.0115035i | ||||||||
\(589\) | 4.94479e14i | 0.287418i | ||||||||
\(590\) | 8.52707e14i | 0.491036i | ||||||||
\(591\) | −2.90412e14 | −0.165685 | ||||||||
\(592\) | 2.75042e15i | 1.55464i | ||||||||
\(593\) | −2.87894e15 | −1.61225 | −0.806123 | − | 0.591748i | \(-0.798438\pi\) | ||||
−0.806123 | + | 0.591748i | \(0.798438\pi\) | |||||||
\(594\) | −3.55068e14 | −0.197009 | ||||||||
\(595\) | −5.28480e14 | + | 1.59615e15i | −0.290526 | + | 0.877468i | ||||
\(596\) | −2.84364e15 | −1.54889 | ||||||||
\(597\) | −5.52783e13 | −0.0298330 | ||||||||
\(598\) | 2.43239e15i | 1.30070i | ||||||||
\(599\) | 4.13434e14 | 0.219058 | 0.109529 | − | 0.993984i | \(-0.465066\pi\) | ||||
0.109529 | + | 0.993984i | \(0.465066\pi\) | |||||||
\(600\) | 2.79374e11i | 0.000146674i | ||||||||
\(601\) | 2.17849e15i | 1.13330i | 0.823958 | + | 0.566652i | \(0.191761\pi\) | ||||
−0.823958 | + | 0.566652i | \(0.808239\pi\) | |||||||
\(602\) | − | 3.59408e13i | − | 0.0185271i | ||||||
\(603\) | 3.38776e15 | 1.73048 | ||||||||
\(604\) | 2.72658e15 | 1.38011 | ||||||||
\(605\) | 6.67407e14i | 0.334762i | ||||||||
\(606\) | 1.54985e14i | 0.0770352i | ||||||||
\(607\) | 3.25356e15i | 1.60258i | 0.598273 | + | 0.801292i | \(0.295854\pi\) | ||||
−0.598273 | + | 0.801292i | \(0.704146\pi\) | |||||||
\(608\) | 7.02892e14 | 0.343099 | ||||||||
\(609\) | 1.82350e14i | 0.0882085i | ||||||||
\(610\) | −3.38683e15 | −1.62360 | ||||||||
\(611\) | 1.57654e15 | 0.748993 | ||||||||
\(612\) | 5.61026e14 | − | 1.69445e15i | 0.264150 | − | 0.797803i | ||||
\(613\) | 1.72107e15 | 0.803095 | 0.401547 | − | 0.915838i | \(-0.368472\pi\) | ||||
0.401547 | + | 0.915838i | \(0.368472\pi\) | |||||||
\(614\) | 2.42217e15 | 1.12016 | ||||||||
\(615\) | 2.83786e13i | 0.0130070i | ||||||||
\(616\) | 3.43798e14 | 0.156174 | ||||||||
\(617\) | − | 4.72457e14i | − | 0.212713i | −0.994328 | − | 0.106357i | \(-0.966082\pi\) | ||
0.994328 | − | 0.106357i | \(-0.0339185\pi\) | |||||||
\(618\) | − | 1.21571e14i | − | 0.0542493i | ||||||
\(619\) | − | 3.90001e15i | − | 1.72491i | −0.506131 | − | 0.862456i | \(-0.668925\pi\) | ||
0.506131 | − | 0.862456i | \(-0.331075\pi\) | |||||||
\(620\) | 2.15719e15 | 0.945657 | ||||||||
\(621\) | −5.48522e14 | −0.238336 | ||||||||
\(622\) | 5.16003e15i | 2.22231i | ||||||||
\(623\) | − | 3.69003e15i | − | 1.57524i | ||||||
\(624\) | − | 1.69620e14i | − | 0.0717731i | ||||||
\(625\) | −2.40292e15 | −1.00786 | ||||||||
\(626\) | − | 3.12209e15i | − | 1.29804i | ||||||
\(627\) | 4.56403e13 | 0.0188095 | ||||||||
\(628\) | −2.15666e15 | −0.881056 | ||||||||
\(629\) | −3.22650e15 | − | 1.06828e15i | −1.30663 | − | 0.432621i | ||||
\(630\) | −3.10439e15 | −1.24625 | ||||||||
\(631\) | −2.31182e15 | −0.920011 | −0.460006 | − | 0.887916i | \(-0.652153\pi\) | ||||
−0.460006 | + | 0.887916i | \(0.652153\pi\) | |||||||
\(632\) | − | 5.66374e14i | − | 0.223439i | ||||||
\(633\) | −7.26225e12 | −0.00284021 | ||||||||
\(634\) | − | 4.62874e14i | − | 0.179462i | ||||||
\(635\) | − | 4.16897e15i | − | 1.60241i | ||||||
\(636\) | − | 1.10627e14i | − | 0.0421548i | ||||||
\(637\) | 2.87532e14 | 0.108622 | ||||||||
\(638\) | 3.18469e15 | 1.19276 | ||||||||
\(639\) | − | 8.45613e14i | − | 0.313991i | ||||||
\(640\) | 1.11999e15i | 0.412309i | ||||||||
\(641\) | − | 3.34975e15i | − | 1.22263i | −0.791389 | − | 0.611313i | \(-0.790642\pi\) | ||
0.791389 | − | 0.611313i | \(-0.209358\pi\) | |||||||
\(642\) | 5.32391e14 | 0.192658 | ||||||||
\(643\) | − | 3.23818e15i | − | 1.16182i | −0.813966 | − | 0.580912i | \(-0.802696\pi\) | ||
0.813966 | − | 0.580912i | \(-0.197304\pi\) | |||||||
\(644\) | −2.94305e15 | −1.04695 | ||||||||
\(645\) | 3.75631e12 | 0.00132490 | ||||||||
\(646\) | −3.15743e14 | + | 9.53631e14i | −0.110422 | + | 0.333504i | ||||
\(647\) | 1.93334e15 | 0.670401 | 0.335201 | − | 0.942147i | \(-0.391196\pi\) | ||||
0.335201 | + | 0.942147i | \(0.391196\pi\) | |||||||
\(648\) | −5.89929e14 | −0.202832 | ||||||||
\(649\) | 8.61820e14i | 0.293813i | ||||||||
\(650\) | −2.27029e13 | −0.00767462 | ||||||||
\(651\) | 2.72202e14i | 0.0912424i | ||||||||
\(652\) | − | 3.06181e15i | − | 1.01769i | ||||||
\(653\) | − | 3.67243e15i | − | 1.21041i | −0.796071 | − | 0.605203i | \(-0.793092\pi\) | ||
0.796071 | − | 0.605203i | \(-0.206908\pi\) | |||||||
\(654\) | 5.48337e14 | 0.179213 | ||||||||
\(655\) | −2.57155e15 | −0.833426 | ||||||||
\(656\) | 5.10865e14i | 0.164186i | ||||||||
\(657\) | 2.19632e15i | 0.699981i | ||||||||
\(658\) | 4.15928e15i | 1.31455i | ||||||||
\(659\) | −3.41018e15 | −1.06883 | −0.534414 | − | 0.845223i | \(-0.679468\pi\) | ||||
−0.534414 | + | 0.845223i | \(0.679468\pi\) | |||||||
\(660\) | − | 1.99108e14i | − | 0.0618866i | ||||||
\(661\) | 3.62601e15 | 1.11769 | 0.558845 | − | 0.829272i | \(-0.311245\pi\) | ||||
0.558845 | + | 0.829272i | \(0.311245\pi\) | |||||||
\(662\) | 3.02888e15 | 0.925897 | ||||||||
\(663\) | 1.98980e14 | + | 6.58816e13i | 0.0603234 | + | 0.0199728i | ||||
\(664\) | −4.92302e13 | −0.0148016 | ||||||||
\(665\) | 8.01272e14 | 0.238925 | ||||||||
\(666\) | − | 6.27529e15i | − | 1.85578i | ||||||
\(667\) | 4.91983e15 | 1.44297 | ||||||||
\(668\) | 3.47302e15i | 1.01027i | ||||||||
\(669\) | − | 3.03907e14i | − | 0.0876792i | ||||||
\(670\) | 8.31770e15i | 2.38008i | ||||||||
\(671\) | −3.42302e15 | −0.971484 | ||||||||
\(672\) | 3.86930e14 | 0.108919 | ||||||||
\(673\) | − | 2.54005e15i | − | 0.709184i | −0.935021 | − | 0.354592i | \(-0.884620\pi\) | ||
0.935021 | − | 0.354592i | \(-0.115380\pi\) | |||||||
\(674\) | 7.39286e14i | 0.204731i | ||||||||
\(675\) | − | 5.11967e12i | − | 0.00140628i | ||||||
\(676\) | −1.52884e15 | −0.416539 | ||||||||
\(677\) | 5.36364e15i | 1.44951i | 0.689005 | + | 0.724757i | \(0.258048\pi\) | ||||
−0.689005 | + | 0.724757i | \(0.741952\pi\) | |||||||
\(678\) | 2.72967e14 | 0.0731724 | ||||||||
\(679\) | −4.16627e14 | −0.110780 | ||||||||
\(680\) | −7.50773e14 | − | 2.48578e14i | −0.198020 | − | 0.0655637i | ||||
\(681\) | −5.52548e14 | −0.144564 | ||||||||
\(682\) | 4.75394e15 | 1.23378 | ||||||||
\(683\) | 1.42743e15i | 0.367486i | 0.982974 | + | 0.183743i | \(0.0588214\pi\) | ||||
−0.982974 | + | 0.183743i | \(0.941179\pi\) | |||||||
\(684\) | −8.50616e14 | −0.217233 | ||||||||
\(685\) | 1.11871e15i | 0.283412i | ||||||||
\(686\) | 5.73752e15i | 1.44192i | ||||||||
\(687\) | − | 2.47741e14i | − | 0.0617641i | ||||||
\(688\) | 6.76203e13 | 0.0167240 | ||||||||
\(689\) | −1.62235e15 | −0.398050 | ||||||||
\(690\) | − | 6.70687e14i | − | 0.163249i | ||||||
\(691\) | − | 1.20192e15i | − | 0.290233i | −0.989415 | − | 0.145117i | \(-0.953644\pi\) | ||
0.989415 | − | 0.145117i | \(-0.0463558\pi\) | |||||||
\(692\) | − | 6.14945e14i | − | 0.147317i | ||||||
\(693\) | −3.13757e15 | −0.745695 | ||||||||
\(694\) | 2.31497e15i | 0.545843i | ||||||||
\(695\) | 5.28205e15 | 1.23562 | ||||||||
\(696\) | −8.57707e13 | −0.0199062 | ||||||||
\(697\) | −5.99293e14 | − | 1.98424e14i | −0.137994 | − | 0.0456892i | ||||
\(698\) | −2.71604e15 | −0.620486 | ||||||||
\(699\) | 7.10413e14 | 0.161022 | ||||||||
\(700\) | − | 2.74692e13i | − | 0.00617741i | ||||||
\(701\) | −1.33740e15 | −0.298409 | −0.149205 | − | 0.988806i | \(-0.547671\pi\) | ||||
−0.149205 | + | 0.988806i | \(0.547671\pi\) | |||||||
\(702\) | 7.77101e14i | 0.172038i | ||||||||
\(703\) | 1.61971e15i | 0.355781i | ||||||||
\(704\) | − | 2.52650e15i | − | 0.550642i | ||||||
\(705\) | −4.34703e14 | −0.0940053 | ||||||||
\(706\) | 6.36753e15 | 1.36630 | ||||||||
\(707\) | 2.75003e15i | 0.585504i | ||||||||
\(708\) | 1.28618e14i | 0.0271717i | ||||||||
\(709\) | − | 6.70214e15i | − | 1.40494i | −0.711711 | − | 0.702472i | \(-0.752079\pi\) | ||
0.711711 | − | 0.702472i | \(-0.247921\pi\) | |||||||
\(710\) | 2.07617e15 | 0.431859 | ||||||||
\(711\) | 5.16885e15i | 1.06687i | ||||||||
\(712\) | 1.73566e15 | 0.355487 | ||||||||
\(713\) | 7.34407e15 | 1.49260 | ||||||||
\(714\) | −1.73811e14 | + | 5.24957e14i | −0.0350540 | + | 0.105873i | ||||
\(715\) | −2.91992e15 | −0.584370 | ||||||||
\(716\) | 6.66369e14 | 0.132341 | ||||||||
\(717\) | 3.05327e14i | 0.0601741i | ||||||||
\(718\) | −4.34961e15 | −0.850679 | ||||||||
\(719\) | 5.55050e15i | 1.07727i | 0.842540 | + | 0.538633i | \(0.181059\pi\) | ||||
−0.842540 | + | 0.538633i | \(0.818941\pi\) | |||||||
\(720\) | − | 5.84071e15i | − | 1.12496i | ||||||
\(721\) | − | 2.15714e15i | − | 0.412320i | ||||||
\(722\) | −6.68605e15 | −1.26828 | ||||||||
\(723\) | −2.03306e14 | −0.0382726 | ||||||||
\(724\) | − | 6.24224e15i | − | 1.16621i | ||||||
\(725\) | 4.59196e13i | 0.00851411i | ||||||||
\(726\) | 2.19503e14i | 0.0403914i | ||||||||
\(727\) | −7.21071e15 | −1.31686 | −0.658428 | − | 0.752643i | \(-0.728778\pi\) | ||||
−0.658428 | + | 0.752643i | \(0.728778\pi\) | |||||||
\(728\) | − | 7.52436e14i | − | 0.136379i | ||||||
\(729\) | 5.29585e15 | 0.952652 | ||||||||
\(730\) | −5.39246e15 | −0.962746 | ||||||||
\(731\) | −2.62642e13 | + | 7.93251e13i | −0.00465392 | + | 0.0140561i | ||||
\(732\) | −5.10850e14 | −0.0898426 | ||||||||
\(733\) | −1.98314e15 | −0.346163 | −0.173082 | − | 0.984907i | \(-0.555372\pi\) | ||||
−0.173082 | + | 0.984907i | \(0.555372\pi\) | |||||||
\(734\) | − | 9.78448e14i | − | 0.169516i | ||||||
\(735\) | −7.92820e13 | −0.0136331 | ||||||||
\(736\) | − | 1.04394e16i | − | 1.78176i | ||||||
\(737\) | 8.40660e15i | 1.42413i | ||||||||
\(738\) | − | 1.16558e15i | − | 0.195989i | ||||||
\(739\) | −2.59631e15 | −0.433323 | −0.216662 | − | 0.976247i | \(-0.569517\pi\) | ||||
−0.216662 | + | 0.976247i | \(0.569517\pi\) | |||||||
\(740\) | 7.06605e15 | 1.17058 | ||||||||
\(741\) | − | 9.98885e13i | − | 0.0164254i | ||||||
\(742\) | − | 4.28014e15i | − | 0.698612i | ||||||
\(743\) | 1.13755e15i | 0.184304i | 0.995745 | + | 0.0921518i | \(0.0293745\pi\) | ||||
−0.995745 | + | 0.0921518i | \(0.970625\pi\) | |||||||
\(744\) | −1.28034e14 | −0.0205909 | ||||||||
\(745\) | − | 1.14986e16i | − | 1.83563i | ||||||
\(746\) | −9.74700e14 | −0.154457 | ||||||||
\(747\) | 4.49286e14 | 0.0706740 | ||||||||
\(748\) | 4.20472e15 | + | 1.39217e15i | 0.656565 | + | 0.217386i | ||||
\(749\) | 9.44667e15 | 1.46430 | ||||||||
\(750\) | −7.84083e14 | −0.120649 | ||||||||
\(751\) | 1.21818e16i | 1.86077i | 0.366586 | + | 0.930384i | \(0.380527\pi\) | ||||
−0.366586 | + | 0.930384i | \(0.619473\pi\) | |||||||
\(752\) | −7.82542e15 | −1.18661 | ||||||||
\(753\) | 6.05060e14i | 0.0910806i | ||||||||
\(754\) | − | 6.97001e15i | − | 1.04158i | ||||||
\(755\) | 1.10253e16i | 1.63561i | ||||||||
\(756\) | −9.40249e14 | −0.138476 | ||||||||
\(757\) | −1.32645e15 | −0.193938 | −0.0969689 | − | 0.995287i | \(-0.530915\pi\) | ||||
−0.0969689 | + | 0.995287i | \(0.530915\pi\) | |||||||
\(758\) | 4.17263e14i | 0.0605660i | ||||||||
\(759\) | − | 6.77855e14i | − | 0.0976804i | ||||||
\(760\) | 3.76889e14i | 0.0539186i | ||||||||
\(761\) | 3.04705e15 | 0.432777 | 0.216389 | − | 0.976307i | \(-0.430572\pi\) | ||||
0.216389 | + | 0.976307i | \(0.430572\pi\) | |||||||
\(762\) | − | 1.37113e15i | − | 0.193342i | ||||||
\(763\) | 9.72962e15 | 1.36211 | ||||||||
\(764\) | −9.61865e15 | −1.33691 | ||||||||
\(765\) | 6.85171e15 | + | 2.26858e15i | 0.945500 | + | 0.313051i | ||||
\(766\) | −5.02383e15 | −0.688299 | ||||||||
\(767\) | 1.88618e15 | 0.256572 | ||||||||
\(768\) | 8.13449e14i | 0.109861i | ||||||||
\(769\) | −5.94860e15 | −0.797664 | −0.398832 | − | 0.917024i | \(-0.630584\pi\) | ||||
−0.398832 | + | 0.917024i | \(0.630584\pi\) | |||||||
\(770\) | − | 7.70345e15i | − | 1.02562i | ||||||
\(771\) | − | 1.93267e14i | − | 0.0255481i | ||||||
\(772\) | − | 1.09618e15i | − | 0.143876i | ||||||
\(773\) | −1.28250e16 | −1.67136 | −0.835679 | − | 0.549218i | \(-0.814926\pi\) | ||||
−0.835679 | + | 0.549218i | \(0.814926\pi\) | |||||||
\(774\) | −1.54281e14 | −0.0199635 | ||||||||
\(775\) | 6.85464e13i | 0.00880695i | ||||||||
\(776\) | − | 1.95966e14i | − | 0.0250001i | ||||||
\(777\) | 8.91622e14i | 0.112945i | ||||||||
\(778\) | 6.29159e15 | 0.791357 | ||||||||
\(779\) | 3.00846e14i | 0.0375741i | ||||||||
\(780\) | −4.35768e14 | −0.0540424 | ||||||||
\(781\) | 2.09836e15 | 0.258404 | ||||||||
\(782\) | 1.41634e16 | + | 4.68946e15i | 1.73193 | + | 0.573437i | ||||
\(783\) | 1.57179e15 | 0.190856 | ||||||||
\(784\) | −1.42722e15 | −0.172088 | ||||||||
\(785\) | − | 8.72072e15i | − | 1.04417i | ||||||
\(786\) | −8.45753e14 | −0.100559 | ||||||||
\(787\) | − | 1.44859e16i | − | 1.71035i | −0.518337 | − | 0.855177i | \(-0.673449\pi\) | ||
0.518337 | − | 0.855177i | \(-0.326551\pi\) | |||||||
\(788\) | 1.34310e16i | 1.57476i | ||||||||
\(789\) | 6.67197e13i | 0.00776839i | ||||||||
\(790\) | −1.26907e16 | −1.46736 | ||||||||
\(791\) | 4.84349e15 | 0.556145 | ||||||||
\(792\) | − | 1.47580e15i | − | 0.168282i | ||||||
\(793\) | 7.49163e15i | 0.848348i | ||||||||
\(794\) | − | 2.66718e15i | − | 0.299944i | ||||||
\(795\) | 4.47333e14 | 0.0499588 | ||||||||
\(796\) | 2.55651e15i | 0.283548i | ||||||||
\(797\) | −7.71817e15 | −0.850146 | −0.425073 | − | 0.905159i | \(-0.639752\pi\) | ||||
−0.425073 | + | 0.905159i | \(0.639752\pi\) | |||||||
\(798\) | 2.63529e14 | 0.0288279 | ||||||||
\(799\) | 3.03945e15 | − | 9.17996e15i | 0.330208 | − | 0.997318i | ||||
\(800\) | 9.74373e13 | 0.0105131 | ||||||||
\(801\) | −1.58400e16 | −1.69737 | ||||||||
\(802\) | 7.38719e14i | 0.0786177i | ||||||||
\(803\) | −5.45010e15 | −0.576061 | ||||||||
\(804\) | 1.25460e15i | 0.131703i | ||||||||
\(805\) | − | 1.19006e16i | − | 1.24077i | ||||||
\(806\) | − | 1.04045e16i | − | 1.07740i | ||||||
\(807\) | 6.67861e14 | 0.0686882 | ||||||||
\(808\) | −1.29351e15 | −0.132132 | ||||||||
\(809\) | 1.64116e15i | 0.166508i | 0.996528 | + | 0.0832540i | \(0.0265313\pi\) | ||||
−0.996528 | + | 0.0832540i | \(0.973469\pi\) | |||||||
\(810\) | 1.32185e16i | 1.33203i | ||||||||
\(811\) | 9.52939e15i | 0.953784i | 0.878962 | + | 0.476892i | \(0.158237\pi\) | ||||
−0.878962 | + | 0.476892i | \(0.841763\pi\) | |||||||
\(812\) | 8.43332e15 | 0.838379 | ||||||||
\(813\) | − | 1.22397e15i | − | 0.120857i | ||||||
\(814\) | 1.55719e16 | 1.52724 | ||||||||
\(815\) | 1.23808e16 | 1.20610 | ||||||||
\(816\) | −9.87673e14 | − | 3.27015e14i | −0.0955690 | − | 0.0316425i | ||||
\(817\) | 3.98213e13 | 0.00382731 | ||||||||
\(818\) | 1.46131e16 | 1.39508 | ||||||||
\(819\) | 6.86690e15i | 0.651177i | ||||||||
\(820\) | 1.31245e15 | 0.123625 | ||||||||
\(821\) | 1.50797e16i | 1.41093i | 0.708746 | + | 0.705464i | \(0.249261\pi\) | ||||
−0.708746 | + | 0.705464i | \(0.750739\pi\) | |||||||
\(822\) | 3.67931e14i | 0.0341957i | ||||||||
\(823\) | 1.05599e16i | 0.974902i | 0.873150 | + | 0.487451i | \(0.162073\pi\) | ||||
−0.873150 | + | 0.487451i | \(0.837927\pi\) | |||||||
\(824\) | 1.01464e15 | 0.0930492 | ||||||||
\(825\) | 6.32681e12 | 0.000576353 | ||||||||
\(826\) | 4.97619e15i | 0.450305i | ||||||||
\(827\) | − | 1.10007e16i | − | 0.988871i | −0.869214 | − | 0.494435i | \(-0.835375\pi\) | ||
0.869214 | − | 0.494435i | \(-0.164625\pi\) | |||||||
\(828\) | 1.26335e16i | 1.12812i | ||||||||
\(829\) | −3.29931e15 | −0.292667 | −0.146334 | − | 0.989235i | \(-0.546747\pi\) | ||||
−0.146334 | + | 0.989235i | \(0.546747\pi\) | |||||||
\(830\) | 1.10310e15i | 0.0972041i | ||||||||
\(831\) | 1.01948e15 | 0.0892424 | ||||||||
\(832\) | −5.52950e15 | −0.480848 | ||||||||
\(833\) | 5.54341e14 | − | 1.67426e15i | 0.0478883 | − | 0.144636i | ||||
\(834\) | 1.73721e15 | 0.149086 | ||||||||
\(835\) | −1.40436e16 | −1.19730 | ||||||||
\(836\) | − | 2.11077e15i | − | 0.178775i | ||||||
\(837\) | 2.34629e15 | 0.197420 | ||||||||
\(838\) | 2.85094e16i | 2.38312i | ||||||||
\(839\) | 7.12405e15i | 0.591611i | 0.955248 | + | 0.295806i | \(0.0955881\pi\) | ||||
−0.955248 | + | 0.295806i | \(0.904412\pi\) | |||||||
\(840\) | 2.07471e14i | 0.0171167i | ||||||||
\(841\) | −1.89729e15 | −0.155509 | ||||||||
\(842\) | −3.10125e16 | −2.52534 | ||||||||
\(843\) | − | 1.33928e15i | − | 0.108348i | ||||||
\(844\) | 3.35865e14i | 0.0269949i | ||||||||
\(845\) | − | 6.18205e15i | − | 0.493652i | ||||||
\(846\) | 1.78543e16 | 1.41647 | ||||||||
\(847\) | 3.89482e15i | 0.306993i | ||||||||
\(848\) | 8.05279e15 | 0.630622 | ||||||||
\(849\) | 3.93301e14 | 0.0306008 | ||||||||
\(850\) | −4.37694e13 | + | 1.32196e14i | −0.00338351 | + | 0.0102191i | ||||
\(851\) | 2.40561e16 | 1.84762 | ||||||||
\(852\) | 3.13158e14 | 0.0238971 | ||||||||
\(853\) | − | 2.31162e16i | − | 1.75266i | −0.481713 | − | 0.876329i | \(-0.659985\pi\) | ||
0.481713 | − | 0.876329i | \(-0.340015\pi\) | |||||||
\(854\) | −1.97647e16 | −1.48892 | ||||||||
\(855\) | − | 3.43957e15i | − | 0.257449i | ||||||
\(856\) | 4.44337e15i | 0.330451i | ||||||||
\(857\) | − | 2.55454e16i | − | 1.88764i | −0.330466 | − | 0.943818i | \(-0.607206\pi\) | ||
0.330466 | − | 0.943818i | \(-0.392794\pi\) | |||||||
\(858\) | −9.60330e14 | −0.0705083 | ||||||||
\(859\) | −8.70194e14 | −0.0634825 | −0.0317412 | − | 0.999496i | \(-0.510105\pi\) | ||||
−0.0317412 | + | 0.999496i | \(0.510105\pi\) | |||||||
\(860\) | − | 1.73722e14i | − | 0.0125925i | ||||||
\(861\) | 1.65611e14i | 0.0119281i | ||||||||
\(862\) | − | 2.42714e16i | − | 1.73702i | ||||||
\(863\) | 7.24118e15 | 0.514932 | 0.257466 | − | 0.966287i | \(-0.417112\pi\) | ||||
0.257466 | + | 0.966287i | \(0.417112\pi\) | |||||||
\(864\) | − | 3.33520e15i | − | 0.235666i | ||||||
\(865\) | 2.48661e15 | 0.174590 | ||||||||
\(866\) | −2.55122e16 | −1.77992 | ||||||||
\(867\) | 7.67239e14 | − | 1.03162e15i | 0.0531894 | − | 0.0715179i | ||||
\(868\) | 1.25888e16 | 0.867215 | ||||||||
\(869\) | −1.28263e16 | −0.877998 | ||||||||
\(870\) | 1.92186e15i | 0.130727i | ||||||||
\(871\) | 1.83987e16 | 1.24362 | ||||||||
\(872\) | 4.57646e15i | 0.307389i | ||||||||
\(873\) | 1.78843e15i | 0.119369i | ||||||||
\(874\) | − | 7.11007e15i | − | 0.471586i | ||||||
\(875\) | −1.39127e16 | −0.916993 | ||||||||
\(876\) | −8.13369e14 | −0.0532740 | ||||||||
\(877\) | − | 4.70621e15i | − | 0.306319i | −0.988202 | − | 0.153159i | \(-0.951055\pi\) | ||
0.988202 | − | 0.153159i | \(-0.0489448\pi\) | |||||||
\(878\) | − | 2.04111e16i | − | 1.32022i | ||||||
\(879\) | 2.63910e15i | 0.169636i | ||||||||
\(880\) | 1.44935e16 | 0.925805 | ||||||||
\(881\) | 6.34030e15i | 0.402478i | 0.979542 | + | 0.201239i | \(0.0644968\pi\) | ||||
−0.979542 | + | 0.201239i | \(0.935503\pi\) | |||||||
\(882\) | 3.25630e15 | 0.205422 | ||||||||
\(883\) | −2.54085e16 | −1.59292 | −0.796461 | − | 0.604690i | \(-0.793297\pi\) | ||||
−0.796461 | + | 0.604690i | \(0.793297\pi\) | |||||||
\(884\) | 3.04690e15 | − | 9.20245e15i | 0.189832 | − | 0.573345i | ||||
\(885\) | −5.20081e14 | −0.0322020 | ||||||||
\(886\) | 2.12063e15 | 0.130491 | ||||||||
\(887\) | 4.30148e15i | 0.263050i | 0.991313 | + | 0.131525i | \(0.0419874\pi\) | ||||
−0.991313 | + | 0.131525i | \(0.958013\pi\) | |||||||
\(888\) | −4.19386e14 | −0.0254884 | ||||||||
\(889\) | − | 2.43291e16i | − | 1.46949i | ||||||
\(890\) | − | 3.88907e16i | − | 2.33454i | ||||||
\(891\) | 1.33598e16i | 0.797023i | ||||||||
\(892\) | −1.40551e16 | −0.833348 | ||||||||
\(893\) | −4.60835e15 | −0.271558 | ||||||||
\(894\) | − | 3.78176e15i | − | 0.221482i | ||||||
\(895\) | 2.69455e15i | 0.156841i | ||||||||
\(896\) | 6.53597e15i | 0.378108i | ||||||||
\(897\) | −1.48356e15 | −0.0852993 | ||||||||
\(898\) | 1.80354e16i | 1.03064i | ||||||||
\(899\) | −2.10445e16 | −1.19525 | ||||||||
\(900\) | −1.17915e14 | −0.00665635 | ||||||||
\(901\) | −3.12776e15 | + | 9.44669e15i | −0.175488 | + | 0.530022i | ||||
\(902\) | 2.89234e15 | 0.161292 | ||||||||
\(903\) | 2.19209e13 | 0.00121500 | ||||||||
\(904\) | 2.27820e15i | 0.125506i | ||||||||
\(905\) | 2.52413e16 | 1.38211 | ||||||||
\(906\) | 3.62609e15i | 0.197348i | ||||||||
\(907\) | − | 8.06988e15i | − | 0.436543i | −0.975888 | − | 0.218272i | \(-0.929958\pi\) | ||
0.975888 | − | 0.218272i | \(-0.0700419\pi\) | |||||||
\(908\) | 2.55543e16i | 1.37401i | ||||||||
\(909\) | 1.18049e16 | 0.630899 | ||||||||
\(910\) | −1.68598e16 | −0.895621 | ||||||||
\(911\) | 2.04923e16i | 1.08203i | 0.841013 | + | 0.541016i | \(0.181960\pi\) | ||||
−0.841013 | + | 0.541016i | \(0.818040\pi\) | |||||||
\(912\) | 4.95813e14i | 0.0260224i | ||||||||
\(913\) | 1.11489e15i | 0.0581623i | ||||||||
\(914\) | 2.85503e16 | 1.48049 | ||||||||
\(915\) | − | 2.06568e15i | − | 0.106475i | ||||||
\(916\) | −1.14575e16 | −0.587038 | ||||||||
\(917\) | −1.50069e16 | −0.764294 | ||||||||
\(918\) | 4.52495e15 | + | 1.49819e15i | 0.229076 | + | 0.0758461i | ||||
\(919\) | 1.55836e16 | 0.784210 | 0.392105 | − | 0.919921i | \(-0.371747\pi\) | ||||
0.392105 | + | 0.919921i | \(0.371747\pi\) | |||||||
\(920\) | 5.59760e15 | 0.280007 | ||||||||
\(921\) | 1.47733e15i | 0.0734596i | ||||||||
\(922\) | 3.83721e16 | 1.89669 | ||||||||
\(923\) | − | 4.59247e15i | − | 0.225651i | ||||||
\(924\) | − | 1.16195e15i | − | 0.0567531i | ||||||
\(925\) | 2.24529e14i | 0.0109017i | ||||||||
\(926\) | 1.69173e16 | 0.816528 | ||||||||
\(927\) | −9.25984e15 | −0.444288 | ||||||||
\(928\) | 2.99143e16i | 1.42680i | ||||||||
\(929\) | 2.26357e16i | 1.07327i | 0.843816 | + | 0.536633i | \(0.180304\pi\) | ||||
−0.843816 | + | 0.536633i | \(0.819696\pi\) | |||||||
\(930\) | 2.86885e15i | 0.135223i | ||||||||
\(931\) | −8.40481e14 | −0.0393826 | ||||||||
\(932\) | − | 3.28552e16i | − | 1.53044i | ||||||
\(933\) | −3.14720e15 | −0.145739 | ||||||||
\(934\) | −3.38156e16 | −1.55672 | ||||||||
\(935\) | −5.62939e15 | + | 1.70023e16i | −0.257631 | + | 0.778114i | ||||
\(936\) | −3.22994e15 | −0.146952 | ||||||||
\(937\) | 2.85278e16 | 1.29033 | 0.645164 | − | 0.764044i | \(-0.276789\pi\) | ||||
0.645164 | + | 0.764044i | \(0.276789\pi\) | |||||||
\(938\) | 4.85401e16i | 2.18266i | ||||||||
\(939\) | 1.90422e15 | 0.0851249 | ||||||||
\(940\) | 2.01041e16i | 0.893475i | ||||||||
\(941\) | − | 1.88306e15i | − | 0.0831995i | −0.999134 | − | 0.0415997i | \(-0.986755\pi\) | ||
0.999134 | − | 0.0415997i | \(-0.0132454\pi\) | |||||||
\(942\) | − | 2.86815e15i | − | 0.125986i | ||||||
\(943\) | 4.46820e15 | 0.195128 | ||||||||
\(944\) | −9.36238e15 | −0.406481 | ||||||||
\(945\) | − | 3.80201e15i | − | 0.164111i | ||||||
\(946\) | − | 3.82843e14i | − | 0.0164293i | ||||||
\(947\) | 1.78705e16i | 0.762451i | 0.924482 | + | 0.381226i | \(0.124498\pi\) | ||||
−0.924482 | + | 0.381226i | \(0.875502\pi\) | |||||||
\(948\) | −1.91419e15 | −0.0811970 | ||||||||
\(949\) | 1.19281e16i | 0.503045i | ||||||||
\(950\) | 6.63624e13 | 0.00278254 | ||||||||
\(951\) | 2.82315e14 | 0.0117691 | ||||||||
\(952\) | −4.38133e15 | − | 1.45064e15i | −0.181594 | − | 0.0601252i | ||||
\(953\) | 1.70042e15 | 0.0700721 | 0.0350361 | − | 0.999386i | \(-0.488845\pi\) | ||||
0.0350361 | + | 0.999386i | \(0.488845\pi\) | |||||||
\(954\) | −1.83731e16 | −0.752776 | ||||||||
\(955\) | − | 3.88942e16i | − | 1.58441i | ||||||
\(956\) | 1.41208e16 | 0.571926 | ||||||||
\(957\) | 1.94240e15i | 0.0782208i | ||||||||
\(958\) | 4.93300e16i | 1.97515i | ||||||||
\(959\) | 6.52852e15i | 0.259904i | ||||||||
\(960\) | 1.52466e15 | 0.0603506 | ||||||||
\(961\) | −6.00559e15 | −0.236362 | ||||||||
\(962\) | − | 3.40807e16i | − | 1.33366i | ||||||
\(963\) | − | 4.05511e16i | − | 1.57782i | ||||||
\(964\) | 9.40248e15i | 0.363763i | ||||||||
\(965\) | 4.43256e15 | 0.170512 | ||||||||
\(966\) | − | 3.91397e15i | − | 0.149707i | ||||||
\(967\) | −2.07223e16 | −0.788121 | −0.394060 | − | 0.919085i | \(-0.628930\pi\) | ||||
−0.394060 | + | 0.919085i | \(0.628930\pi\) | |||||||
\(968\) | −1.83198e15 | −0.0692799 | ||||||||
\(969\) | −5.81636e14 | − | 1.92578e14i | −0.0218711 | − | 0.00724144i | ||||
\(970\) | −4.39099e15 | −0.164179 | ||||||||
\(971\) | 7.81060e15 | 0.290388 | 0.145194 | − | 0.989403i | \(-0.453619\pi\) | ||||
0.145194 | + | 0.989403i | \(0.453619\pi\) | |||||||
\(972\) | 6.06227e15i | 0.224115i | ||||||||
\(973\) | 3.08248e16 | 1.13313 | ||||||||
\(974\) | − | 6.62628e16i | − | 2.42212i | ||||||
\(975\) | − | 1.38469e13i | − | 0.000503299i | ||||||
\(976\) | − | 3.71860e16i | − | 1.34402i | ||||||
\(977\) | 1.83369e16 | 0.659031 | 0.329516 | − | 0.944150i | \(-0.393115\pi\) | ||||
0.329516 | + | 0.944150i | \(0.393115\pi\) | |||||||
\(978\) | 4.07191e15 | 0.145524 | ||||||||
\(979\) | − | 3.93064e16i | − | 1.39688i | ||||||
\(980\) | 3.66663e15i | 0.129576i | ||||||||
\(981\) | − | 4.17657e16i | − | 1.46771i | ||||||
\(982\) | 3.26131e16 | 1.13967 | ||||||||
\(983\) | − | 2.01380e15i | − | 0.0699797i | −0.999388 | − | 0.0349898i | \(-0.988860\pi\) | ||
0.999388 | − | 0.0349898i | \(-0.0111399\pi\) | |||||||
\(984\) | −7.78972e13 | −0.00269184 | ||||||||
\(985\) | −5.43098e16 | −1.86629 | ||||||||
\(986\) | −4.05854e16 | − | 1.34377e16i | −1.38691 | − | 0.459199i | ||||
\(987\) | −2.53682e15 | −0.0862076 | ||||||||
\(988\) | −4.61964e15 | −0.156115 | ||||||||
\(989\) | − | 5.91431e14i | − | 0.0198758i | ||||||
\(990\) | −3.30681e16 | −1.10514 | ||||||||
\(991\) | 3.19132e16i | 1.06063i | 0.847800 | + | 0.530317i | \(0.177927\pi\) | ||||
−0.847800 | + | 0.530317i | \(0.822073\pi\) | |||||||
\(992\) | 4.46545e16i | 1.47588i | ||||||||
\(993\) | 1.84736e15i | 0.0607200i | ||||||||
\(994\) | 1.21160e16 | 0.396037 | ||||||||
\(995\) | −1.03376e16 | −0.336041 | ||||||||
\(996\) | 1.66385e14i | 0.00537884i | ||||||||
\(997\) | 4.30322e16i | 1.38347i | 0.722150 | + | 0.691736i | \(0.243154\pi\) | ||||
−0.722150 | + | 0.691736i | \(0.756846\pi\) | |||||||
\(998\) | − | 2.68744e16i | − | 0.859253i | ||||||
\(999\) | 7.68547e15 | 0.244377 |
(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 | 17.12.b.a.16.14 | yes | 16 | |
3.2 | odd | 2 | 153.12.d.b.118.3 | 16 | |||
4.3 | odd | 2 | 272.12.b.c.33.8 | 16 | |||
17.16 | even | 2 | inner | 17.12.b.a.16.13 | ✓ | 16 | |
51.50 | odd | 2 | 153.12.d.b.118.4 | 16 | |||
68.67 | odd | 2 | 272.12.b.c.33.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.12.b.a.16.13 | ✓ | 16 | 17.16 | even | 2 | inner | |
17.12.b.a.16.14 | yes | 16 | 1.1 | even | 1 | trivial | |
153.12.d.b.118.3 | 16 | 3.2 | odd | 2 | |||
153.12.d.b.118.4 | 16 | 51.50 | odd | 2 | |||
272.12.b.c.33.8 | 16 | 4.3 | odd | 2 | |||
272.12.b.c.33.9 | 16 | 68.67 | odd | 2 |