Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(61,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.61");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(34.2198032451\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 61.4 | ||
Root | \(-122.377 - 211.963i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.61 |
Dual form | 84.9.m.b.73.4 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 40.5000 | − | 23.3827i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −133.903 | − | 77.3091i | −0.214245 | − | 0.123695i | 0.389037 | − | 0.921222i | \(-0.372808\pi\) |
−0.603283 | + | 0.797527i | \(0.706141\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2234.88 | + | 877.558i | −0.930813 | + | 0.365497i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1093.50 | − | 1894.00i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3950.92 | + | 6843.20i | 0.269853 | + | 0.467400i | 0.968824 | − | 0.247751i | \(-0.0796914\pi\) |
−0.698970 | + | 0.715151i | \(0.746358\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4177.64i | 0.146271i | 0.997322 | + | 0.0731354i | \(0.0233005\pi\) | ||||
−0.997322 | + | 0.0731354i | \(0.976699\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7230.78 | −0.142830 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 110620. | − | 63866.3i | 1.32445 | − | 0.764674i | 0.340019 | − | 0.940419i | \(-0.389567\pi\) |
0.984436 | + | 0.175745i | \(0.0562333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 139247. | + | 80394.4i | 1.06849 | + | 0.616895i | 0.927769 | − | 0.373154i | \(-0.121724\pi\) |
0.140724 | + | 0.990049i | \(0.455057\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −69993.0 | + | 87798.6i | −0.359896 | + | 0.451451i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −16422.4 | + | 28444.4i | −0.0586847 | + | 0.101645i | −0.893875 | − | 0.448316i | \(-0.852024\pi\) |
0.835191 | + | 0.549961i | \(0.185357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −183359. | − | 317587.i | −0.469399 | − | 0.813023i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 102276.i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 659560. | 0.932528 | 0.466264 | − | 0.884646i | \(-0.345600\pi\) | ||||
0.466264 | + | 0.884646i | \(0.345600\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5163.53 | + | 2981.17i | −0.00559114 | + | 0.00322804i | −0.502793 | − | 0.864407i | \(-0.667694\pi\) |
0.497202 | + | 0.867635i | \(0.334361\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 320025. | + | 184766.i | 0.269853 | + | 0.155800i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 367101. | + | 55268.8i | 0.244632 | + | 0.0368305i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 329534. | − | 570770.i | 0.175830 | − | 0.304547i | −0.764618 | − | 0.644484i | \(-0.777072\pi\) |
0.940448 | + | 0.339937i | \(0.110406\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 97684.5 | + | 169195.i | 0.0422248 | + | 0.0731354i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.10208e6i | − | 0.390013i | −0.980802 | − | 0.195007i | \(-0.937527\pi\) | ||
0.980802 | − | 0.195007i | \(-0.0624728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.57153e6 | 1.33717 | 0.668586 | − | 0.743635i | \(-0.266900\pi\) | ||||
0.668586 | + | 0.743635i | \(0.266900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −292847. | + | 169075.i | −0.0714151 | + | 0.0412315i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.35905e6 | − | 784649.i | −0.278512 | − | 0.160799i | 0.354237 | − | 0.935156i | \(-0.384740\pi\) |
−0.632750 | + | 0.774356i | \(0.718074\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.22459e6 | − | 3.92247e6i | 0.732824 | − | 0.680418i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.98673e6 | − | 5.17317e6i | 0.441485 | − | 0.764674i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.31027e6 | + | 7.46560e6i | 0.546262 | + | 0.946153i | 0.998526 | + | 0.0542691i | \(0.0172829\pi\) |
−0.452265 | + | 0.891884i | \(0.649384\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.22177e6i | − | 0.133518i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.51934e6 | 0.712329 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.85511e7 | − | 1.07105e7i | 1.53095 | − | 0.883895i | 0.531634 | − | 0.846974i | \(-0.321578\pi\) |
0.999318 | − | 0.0369211i | \(-0.0117550\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.16597e7 | + | 1.25052e7i | 1.56435 | + | 0.903177i | 0.996808 | + | 0.0798301i | \(0.0254378\pi\) |
0.567539 | + | 0.823346i | \(0.307896\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −781750. | + | 5.19247e6i | −0.0496256 | + | 0.329619i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 322970. | − | 559400.i | 0.0180929 | − | 0.0313379i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.65705e6 | − | 1.67265e7i | −0.479231 | − | 0.830053i | 0.520485 | − | 0.853871i | \(-0.325751\pi\) |
−0.999716 | + | 0.0238177i | \(0.992418\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.53600e6i | 0.0677632i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.50918e6 | 0.374205 | 0.187103 | − | 0.982340i | \(-0.440090\pi\) | ||||
0.187103 | + | 0.982340i | \(0.440090\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.91695e6 | − | 3.99350e6i | 0.243570 | − | 0.140625i | −0.373247 | − | 0.927732i | \(-0.621755\pi\) |
0.616816 | + | 0.787107i | \(0.288422\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.48521e7 | − | 8.57486e6i | −0.469399 | − | 0.271008i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.48351e7 | − | 1.18266e7i | −0.422016 | − | 0.336431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.32777e6 | + | 2.29977e6i | −0.0340891 | + | 0.0590441i | −0.882567 | − | 0.470187i | \(-0.844186\pi\) |
0.848478 | + | 0.529231i | \(0.177520\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.39148e6 | − | 4.14217e6i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.37421e7i | 1.13241i | 0.824266 | + | 0.566203i | \(0.191588\pi\) | ||||
−0.824266 | + | 0.566203i | \(0.808412\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.97498e7 | −0.378344 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.67122e7 | − | 1.54223e7i | 0.466264 | − | 0.269198i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.33121e7 | − | 1.92328e7i | −0.530936 | − | 0.306536i | 0.210461 | − | 0.977602i | \(-0.432503\pi\) |
−0.741398 | + | 0.671066i | \(0.765837\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.66612e6 | − | 9.33654e6i | −0.0534615 | − | 0.136151i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −139415. | + | 241475.i | −0.00186371 | + | 0.00322804i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.24304e7 | − | 2.15302e7i | −0.152613 | − | 0.264334i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.56754e7i | 0.290021i | 0.989430 | + | 0.145011i | \(0.0463216\pi\) | ||||
−0.989430 | + | 0.145011i | \(0.953678\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72813e7 | 0.179902 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.37265e8 | + | 7.92500e7i | −1.31909 | + | 0.761577i | −0.983582 | − | 0.180461i | \(-0.942241\pi\) |
−0.335507 | + | 0.942038i | \(0.608908\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.36862e7 | − | 1.36753e7i | −0.210449 | − | 0.121503i | 0.391071 | − | 0.920361i | \(-0.372105\pi\) |
−0.601520 | + | 0.798858i | \(0.705438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.61599e7 | − | 6.34543e6i | 0.132948 | − | 0.0522040i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.08597e7 | + | 1.40053e8i | −0.616875 | + | 1.06846i | 0.373178 | + | 0.927760i | \(0.378268\pi\) |
−0.990053 | + | 0.140698i | \(0.955065\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.95165e7 | − | 5.11241e7i | −0.209102 | − | 0.362176i | 0.742330 | − | 0.670035i | \(-0.233721\pi\) |
−0.951432 | + | 0.307859i | \(0.900388\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.08216e7i | − | 0.203031i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.64113e8 | −1.00654 | −0.503268 | − | 0.864131i | \(-0.667869\pi\) | ||||
−0.503268 | + | 0.864131i | \(0.667869\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.39802e6 | − | 2.53920e6i | 0.0251458 | − | 0.0145180i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.91245e6 | + | 4.56825e6i | 0.0422248 | + | 0.0243785i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.91176e8 | + | 2.39809e8i | −0.953333 | + | 1.19585i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.59599e7 | − | 1.31566e8i | 0.354358 | − | 0.613767i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.57697e7 | − | 4.46344e7i | −0.112587 | − | 0.195007i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.17099e8i | 0.479638i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.21072e8 | 0.465403 | 0.232702 | − | 0.972548i | \(-0.425243\pi\) | ||||
0.232702 | + | 0.972548i | \(0.425243\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.85147e8 | − | 1.06895e8i | 0.668586 | − | 0.386008i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.54093e7 | + | 3.19906e7i | 0.188147 | + | 0.108627i | 0.591115 | − | 0.806587i | \(-0.298688\pi\) |
−0.402968 | + | 0.915214i | \(0.632021\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.81751e8 | − | 5.74744e7i | −1.22004 | − | 0.183683i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.90686e6 | + | 1.36951e7i | −0.0238050 | + | 0.0412315i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.56859e8 | − | 2.71688e8i | −0.445274 | − | 0.771237i | 0.552797 | − | 0.833316i | \(-0.313560\pi\) |
−0.998071 | + | 0.0620787i | \(0.980227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.04519e8i | 0.547867i | 0.961749 | + | 0.273934i | \(0.0883248\pi\) | ||||
−0.961749 | + | 0.273934i | \(0.911675\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.33888e7 | −0.185675 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.85884e7 | + | 1.65055e7i | −0.0683670 | + | 0.0394717i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.83172e7 | − | 5.09900e7i | −0.199790 | − | 0.115349i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.93777e7 | − | 2.57642e8i | 0.169992 | − | 0.551757i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.34340e8 | + | 5.79093e8i | −0.678333 | + | 1.17491i | 0.297150 | + | 0.954831i | \(0.403964\pi\) |
−0.975483 | + | 0.220076i | \(0.929369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.10149e8 | + | 1.90784e8i | 0.211872 | + | 0.366973i | 0.952300 | − | 0.305162i | \(-0.0987107\pi\) |
−0.740428 | + | 0.672135i | \(0.765377\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 2.79351e8i | − | 0.509783i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 921886. | 0.00159717 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.29270e8 | − | 4.21044e8i | 1.20030 | − | 0.692994i | 0.239678 | − | 0.970852i | \(-0.422958\pi\) |
0.960622 | + | 0.277859i | \(0.0896247\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.49132e8 | + | 2.01571e8i | 0.546262 | + | 0.315384i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.17405e7 | − | 7.79814e7i | 0.0174736 | − | 0.116061i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.08666e8 | − | 8.81036e8i | 0.720581 | − | 1.24808i | −0.240187 | − | 0.970727i | \(-0.577209\pi\) |
0.960767 | − | 0.277355i | \(-0.0894580\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.85683e7 | − | 4.94817e7i | −0.0385432 | − | 0.0667588i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.85051e8i | 1.00933i | 0.863316 | + | 0.504664i | \(0.168383\pi\) | ||||
−0.863316 | + | 0.504664i | \(0.831617\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.98278e8 | 0.978605 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.04533e8 | − | 1.75822e8i | 0.356164 | − | 0.205632i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −4.30544e8 | − | 2.48575e8i | −0.480655 | − | 0.277506i | 0.240035 | − | 0.970764i | \(-0.422841\pi\) |
−0.720689 | + | 0.693258i | \(0.756175\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.88487e8 | + | 5.48862e8i | 0.734080 | + | 0.585208i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.00880e8 | − | 8.67549e8i | 0.510317 | − | 0.883895i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.80361e8 | + | 1.52483e9i | 0.857529 | + | 1.48528i | 0.874279 | + | 0.485424i | \(0.161335\pi\) |
−0.0167496 | + | 0.999860i | \(0.505332\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.40594e9i | − | 1.30994i | −0.755653 | − | 0.654972i | \(-0.772680\pi\) | ||
0.755653 | − | 0.654972i | \(-0.227320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.16962e9 | 1.04290 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.82515e7 | + | 5.09520e7i | −0.0753417 | + | 0.0434985i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.74100e8 | + | 5.04662e8i | 0.714817 | + | 0.412700i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.97530e7 | + | 2.28574e8i | 0.0703399 | + | 0.179135i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.46452e8 | − | 6.00072e8i | 0.260321 | − | 0.450889i | −0.706006 | − | 0.708206i | \(-0.749505\pi\) |
0.966327 | + | 0.257317i | \(0.0828383\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.17803e8 | − | 8.96861e8i | −0.373195 | − | 0.646392i | 0.616860 | − | 0.787073i | \(-0.288404\pi\) |
−0.990055 | + | 0.140680i | \(0.955071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 3.02076e7i | − | 0.0208919i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.58650e9 | −1.05335 | −0.526676 | − | 0.850066i | \(-0.676562\pi\) | ||||
−0.526676 | + | 0.850066i | \(0.676562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.38090e8 | − | 2.52932e8i | 0.279352 | − | 0.161284i | −0.353778 | − | 0.935329i | \(-0.615103\pi\) |
0.633130 | + | 0.774046i | \(0.281770\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.82221e8 | − | 4.51616e8i | −0.479231 | − | 0.276684i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.47404e9 | + | 5.78802e8i | −0.868009 | + | 0.340836i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.52012e7 | + | 1.47573e8i | −0.0482425 | + | 0.0835585i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.59157e7 | + | 6.22079e7i | 0.0195616 | + | 0.0338816i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.27053e9i | 0.665885i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.53493e8 | 0.430596 | 0.215298 | − | 0.976548i | \(-0.430928\pi\) | ||||
0.215298 | + | 0.976548i | \(0.430928\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.85122e8 | − | 2.22350e8i | 0.187103 | − | 0.108024i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.12143e8 | − | 3.53421e8i | −0.286483 | − | 0.165401i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.92373e6 | − | 1.11939e7i | 0.00402446 | − | 0.00504825i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.86758e8 | − | 3.23474e8i | 0.0811899 | − | 0.140625i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.66811e8 | + | 4.62130e8i | 0.111850 | + | 0.193729i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19055e9i | 0.481426i | 0.970596 | + | 0.240713i | \(0.0773812\pi\) | ||||
−0.970596 | + | 0.240713i | \(0.922619\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.02013e8 | −0.312933 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.55248e9 | + | 8.96322e8i | −0.584684 | + | 0.337567i | −0.762993 | − | 0.646407i | \(-0.776271\pi\) |
0.178309 | + | 0.983975i | \(0.442937\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.51985e9 | − | 2.03219e9i | −1.27992 | − | 0.738961i | −0.303085 | − | 0.952964i | \(-0.598016\pi\) |
−0.976833 | + | 0.214003i | \(0.931350\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.77360e8 | − | 1.32091e8i | −0.308127 | − | 0.0463900i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.96945e8 | − | 8.60734e8i | 0.168610 | − | 0.292042i | −0.769321 | − | 0.638862i | \(-0.779405\pi\) |
0.937932 | + | 0.346820i | \(0.112739\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.21321e8 | + | 2.10134e8i | 0.0397800 | + | 0.0689010i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.24188e8i | 0.0393627i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.71719e9 | 0.526291 | 0.263145 | − | 0.964756i | \(-0.415240\pi\) | ||||
0.263145 | + | 0.964756i | \(0.415240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.95118e9 | + | 2.28121e9i | −1.17127 | + | 0.676235i | −0.953980 | − | 0.299872i | \(-0.903056\pi\) |
−0.217293 | + | 0.976106i | \(0.569723\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.93710e8 | − | 1.11839e8i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.68929e8 | + | 1.98633e8i | −0.241168 | + | 0.0551300i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.35859e8 | + | 5.81725e8i | −0.0902338 | + | 0.156289i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.25664e9 | + | 2.17656e9i | 0.326898 | + | 0.566203i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.49784e8i | 0.0377373i | 0.999822 | + | 0.0188687i | \(0.00600644\pi\) | ||||
−0.999822 | + | 0.0188687i | \(0.993994\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.59534e8 | −0.0633450 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.99867e8 | + | 4.61804e8i | −0.189172 | + | 0.109219i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.35751e9 | − | 3.67051e9i | −1.45732 | − | 0.841384i | −0.458440 | − | 0.888725i | \(-0.651592\pi\) |
−0.998879 | + | 0.0473414i | \(0.984925\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.35586e8 | + | 1.56479e9i | −0.0523541 | + | 0.347742i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.21228e8 | − | 1.24920e9i | 0.155421 | − | 0.269198i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.40019e9 | + | 4.15725e9i | 0.501675 | + | 0.868926i | 0.999998 | + | 0.00193513i | \(0.000615971\pi\) |
−0.498323 | + | 0.866991i | \(0.666051\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.33289e9i | − | 0.270278i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.79886e9 | −0.353958 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.69474e9 | + | 1.55581e9i | −0.514645 | + | 0.297131i | −0.734741 | − | 0.678348i | \(-0.762696\pi\) |
0.220096 | + | 0.975478i | \(0.429363\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.16838e9 | − | 1.82927e9i | −0.587436 | − | 0.339156i | 0.176647 | − | 0.984274i | \(-0.443475\pi\) |
−0.764083 | + | 0.645118i | \(0.776808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.66791e8 | − | 2.92406e8i | −0.0660341 | − | 0.0526424i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.44888e9 | − | 2.50953e9i | 0.253338 | − | 0.438794i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.24448e9 | + | 9.08370e9i | 0.890806 | + | 1.54292i | 0.838911 | + | 0.544269i | \(0.183193\pi\) |
0.0518958 | + | 0.998653i | \(0.483474\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.30396e7i | 0.00215203i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.88553e9 | 0.302419 | 0.151210 | − | 0.988502i | \(-0.451683\pi\) | ||||
0.151210 | + | 0.988502i | \(0.451683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.50968e9 | − | 8.71616e8i | 0.235364 | − | 0.135887i | −0.377680 | − | 0.925936i | \(-0.623278\pi\) |
0.613044 | + | 0.790049i | \(0.289945\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00687e9 | − | 5.81314e8i | −0.152613 | − | 0.0881113i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.67143e8 | + | 2.46303e9i | 0.142549 | + | 0.363029i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.66994e9 | − | 8.08857e9i | 0.669453 | − | 1.15953i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00359e8 | + | 1.03985e9i | 0.0837219 | + | 0.145011i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 7.68210e9i | − | 1.04234i | −0.853453 | − | 0.521170i | \(-0.825496\pi\) | ||
0.853453 | − | 0.521170i | \(-0.174504\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.31207e9 | −0.437333 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.99894e8 | − | 4.04084e8i | 0.0899511 | − | 0.0519333i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.18831e8 | − | 6.86068e7i | −0.0148677 | − | 0.00858386i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.02168e10 | + | 4.01178e9i | −1.24466 | + | 0.488732i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.70615e9 | + | 6.41925e9i | −0.439696 | + | 0.761577i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.93354e9 | − | 3.34899e9i | −0.223436 | − | 0.387003i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.93846e9i | 1.00626i | 0.864211 | + | 0.503129i | \(0.167818\pi\) | ||||
−0.864211 | + | 0.503129i | \(0.832182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.27906e9 | −0.140299 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.36754e10 | − | 7.89550e9i | 1.46184 | − | 0.843992i | 0.462740 | − | 0.886494i | \(-0.346866\pi\) |
0.999096 | + | 0.0425024i | \(0.0135330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.18174e9 | − | 4.72373e9i | −0.852449 | − | 0.492162i | 0.00902752 | − | 0.999959i | \(-0.497126\pi\) |
−0.861476 | + | 0.507798i | \(0.830460\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.06104e8 | − | 6.34853e8i | 0.0514041 | − | 0.0644808i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.46257e9 | − | 1.46576e10i | 0.838041 | − | 1.45153i | −0.0534897 | − | 0.998568i | \(-0.517034\pi\) |
0.891530 | − | 0.452961i | \(-0.149632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.60587e9 | + | 4.51350e9i | 0.251646 | + | 0.435863i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.56287e9i | 0.712305i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.05380e10 | 1.88689 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.32677e9 | − | 7.66009e8i | 0.118922 | − | 0.0686595i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.39084e9 | − | 1.38035e9i | −0.209102 | − | 0.120725i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.72589e9 | + | 5.60950e8i | 0.318014 | + | 0.0478785i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.02406e10 | − | 1.77372e10i | 0.853123 | − | 1.47765i | −0.0252519 | − | 0.999681i | \(-0.508039\pi\) |
0.878375 | − | 0.477972i | \(-0.158628\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.20691e8 | − | 1.24827e9i | −0.0586101 | − | 0.101516i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.98631e9i | 0.237113i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.14997e10 | 1.66691 | 0.833456 | − | 0.552586i | \(-0.186359\pi\) | ||||
0.833456 | + | 0.552586i | \(0.186359\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.64657e9 | + | 3.83740e9i | −0.503268 | + | 0.290562i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.08014e7 | − | 2.35567e7i | −0.00301757 | − | 0.00174220i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.99925e9 | + | 1.24736e10i | −0.433431 | + | 0.901187i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.18747e8 | − | 2.05675e8i | 0.00838195 | − | 0.0145180i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.58609e9 | + | 1.31395e10i | 0.523239 | + | 0.906277i | 0.999634 | + | 0.0270456i | \(0.00860994\pi\) |
−0.476395 | + | 0.879231i | \(0.658057\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.30313e9i | 0.0878387i | 0.999035 | + | 0.0439194i | \(0.0139845\pi\) | ||||
−0.999035 | + | 0.0439194i | \(0.986016\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.27272e8 | 0.0281498 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.83413e10 | − | 1.05893e10i | 1.18122 | − | 0.681978i | 0.224924 | − | 0.974376i | \(-0.427787\pi\) |
0.956297 | + | 0.292399i | \(0.0944534\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.27331e9 | − | 7.35147e8i | −0.0801717 | − | 0.0462872i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.13523e9 | + | 1.41825e10i | −0.131454 | + | 0.873130i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.50520e10 | − | 2.60708e10i | 0.906184 | − | 1.56956i | 0.0868642 | − | 0.996220i | \(-0.472315\pi\) |
0.819320 | − | 0.573337i | \(-0.194351\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.43472e9 | + | 7.68117e9i | 0.261119 | + | 0.452271i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 7.10458e9i | − | 0.409178i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.23494e9 | −0.0695783 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.68403e9 | + | 3.28168e9i | −0.313323 | + | 0.180897i | −0.648412 | − | 0.761289i | \(-0.724567\pi\) |
0.335090 | + | 0.942186i | \(0.391233\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.08734e9 | − | 1.20513e9i | −0.112587 | − | 0.0650022i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.61844e10 | − | 1.29022e10i | −0.854283 | − | 0.681034i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.45827e9 | + | 1.11861e10i | −0.333642 | + | 0.577885i | −0.983223 | − | 0.182407i | \(-0.941611\pi\) |
0.649581 | + | 0.760293i | \(0.274944\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.73809e9 | + | 4.74251e9i | 0.138460 | + | 0.239819i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.75540e9i | 0.136402i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.24358e10 | −1.08739 | −0.543694 | − | 0.839283i | \(-0.682975\pi\) | ||||
−0.543694 | + | 0.839283i | \(0.682975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.90342e9 | − | 2.83099e9i | 0.232702 | − | 0.134350i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.40505e10 | − | 1.38855e10i | −1.11771 | − | 0.645309i | −0.176894 | − | 0.984230i | \(-0.556605\pi\) |
−0.940815 | + | 0.338921i | \(0.889938\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.07217e9 | + | 2.73051e9i | 0.0488003 | + | 0.124280i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.99896e9 | − | 8.65846e9i | 0.222862 | − | 0.386008i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.31848e9 | + | 1.44080e10i | 0.363284 | + | 0.629226i | 0.988499 | − | 0.151226i | \(-0.0483223\pi\) |
−0.625216 | + | 0.780452i | \(0.714989\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.19535e9i | 0.179499i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.99210e9 | 0.125431 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.55587e8 | − | 2.05298e8i | 0.0146069 | − | 0.00843329i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.08327e10 | − | 6.25426e9i | −0.436088 | − | 0.251776i | 0.265849 | − | 0.964015i | \(-0.414348\pi\) |
−0.701937 | + | 0.712239i | \(0.747681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.68048e10 | + | 6.59866e9i | −0.663045 | + | 0.260354i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.27309e8 | + | 1.43294e9i | −0.0319956 | + | 0.0554180i | −0.881580 | − | 0.472035i | \(-0.843520\pi\) |
0.849584 | + | 0.527453i | \(0.176853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.24543e7 | − | 2.15714e7i | −0.000472169 | − | 0.000817821i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.39534e8i | 0.0274877i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.20786e9 | 0.189794 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.00393e10 | − | 5.79619e9i | 0.358765 | − | 0.207133i | −0.309774 | − | 0.950810i | \(-0.600253\pi\) |
0.668539 | + | 0.743677i | \(0.266920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.27056e10 | − | 7.33557e9i | −0.445274 | − | 0.257079i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.20604e10 | + | 4.02163e10i | −1.10197 | + | 1.38230i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.15476e9 | − | 7.19625e9i | 0.140073 | − | 0.242613i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.78221e9 | + | 8.28303e9i | 0.158156 | + | 0.273934i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.35810e10i | 0.765079i | 0.923939 | + | 0.382540i | \(0.124950\pi\) | ||||
−0.923939 | + | 0.382540i | \(0.875050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.62676e9 | 0.274612 | 0.137306 | − | 0.990529i | \(-0.456156\pi\) | ||||
0.137306 | + | 0.990529i | \(0.456156\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.97225e9 | + | 1.71603e9i | −0.0928375 | + | 0.0535997i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.05663e10 | − | 2.34209e10i | −1.24340 | − | 0.717875i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.93809e10 | − | 8.94007e9i | −1.78622 | − | 0.268924i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.71888e8 | + | 1.33695e9i | −0.0227890 | + | 0.0394717i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.28994e10 | − | 2.23424e10i | −0.373818 | − | 0.647472i | 0.616331 | − | 0.787487i | \(-0.288618\pi\) |
−0.990149 | + | 0.140015i | \(0.955285\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.11174e10i | 1.16970i | 0.811142 | + | 0.584849i | \(0.198846\pi\) | ||||
−0.811142 | + | 0.584849i | \(0.801154\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.76913e9 | −0.133193 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.57354e9 | + | 2.64053e9i | −0.125408 | + | 0.0724046i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.33223e10 | − | 1.92386e10i | −0.897174 | − | 0.517983i | −0.0208914 | − | 0.999782i | \(-0.506650\pi\) |
−0.876282 | + | 0.481798i | \(0.839984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.80957e9 | − | 1.22906e10i | −0.0742824 | − | 0.324951i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.20399e9 | − | 1.07456e10i | 0.161085 | − | 0.279008i | −0.774173 | − | 0.632974i | \(-0.781834\pi\) |
0.935258 | + | 0.353966i | \(0.115167\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.97374e9 | + | 5.15067e9i | 0.0758338 | + | 0.131348i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.12710e10i | 0.783271i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.45902e10 | 0.851076 | 0.425538 | − | 0.904941i | \(-0.360085\pi\) | ||||
0.425538 | + | 0.904941i | \(0.360085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.54178e9 | − | 4.35425e9i | 0.182292 | − | 0.105246i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.92208e9 | + | 5.15117e9i | 0.211872 | + | 0.122324i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.30893e8 | + | 1.53362e9i | −0.00538723 | + | 0.0357826i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.64356e9 | + | 4.57878e9i | −0.0606072 | + | 0.104975i | −0.894737 | − | 0.446593i | \(-0.852637\pi\) |
0.834130 | + | 0.551568i | \(0.185970\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.53199e9 | − | 1.13137e10i | −0.147162 | − | 0.254891i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.55209e10i | 0.786466i | 0.919439 | + | 0.393233i | \(0.128643\pi\) | ||||
−0.919439 | + | 0.393233i | \(0.871357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.68452e8 | 0.0123700 | 0.00618500 | − | 0.999981i | \(-0.498031\pi\) | ||||
0.00618500 | + | 0.999981i | \(0.498031\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.73364e7 | − | 2.15562e7i | 0.000798584 | − | 0.000461062i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.20351e9 | + | 6.94848e8i | 0.0253036 | + | 0.0146091i | 0.512598 | − | 0.858628i | \(-0.328683\pi\) |
−0.487295 | + | 0.873238i | \(0.662016\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.62608e10 | + | 2.89071e10i | 0.749456 | + | 0.597466i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.96903e10 | − | 3.41046e10i | 0.400100 | − | 0.692994i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.80617e10 | + | 3.12839e10i | 0.360840 | + | 0.624994i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 5.89641e10i | − | 1.15828i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.88531e10 | 0.364174 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.91139e10 | + | 2.83559e10i | −0.932958 | + | 0.538644i | −0.887746 | − | 0.460334i | \(-0.847730\pi\) |
−0.0452122 | + | 0.998977i | \(0.514396\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.38447e9 | + | 1.37668e9i | 0.0445464 | + | 0.0257189i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.34793e9 | − | 3.43277e9i | −0.0247672 | − | 0.0630749i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.98494e9 | − | 3.43802e9i | 0.0358741 | − | 0.0621357i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.00673e10 | + | 3.47576e10i | 0.356758 | + | 0.617923i | 0.987417 | − | 0.158137i | \(-0.0505487\pi\) |
−0.630659 | + | 0.776060i | \(0.717215\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 4.75759e10i | − | 0.832055i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.70262e8 | −0.0115324 | −0.00576619 | − | 0.999983i | \(-0.501835\pi\) | ||||
−0.00576619 | + | 0.999983i | \(0.501835\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.29603e10 | − | 4.21237e10i | 1.23509 | − | 0.713080i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.31403e9 | − | 1.33601e9i | −0.0385432 | − | 0.0222529i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.12519e10 | + | 8.34486e9i | −0.348315 | + | 0.136771i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.56562e10 | − | 7.90788e10i | 0.736372 | − | 1.27543i | −0.217747 | − | 0.976005i | \(-0.569871\pi\) |
0.954119 | − | 0.299428i | \(-0.0967959\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.83566e10 | + | 3.17946e10i | 0.291368 | + | 0.504664i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.38153e10i | 0.684468i | 0.939615 | + | 0.342234i | \(0.111184\pi\) | ||||
−0.939615 | + | 0.342234i | \(0.888816\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.45070e10 | 0.376812 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.23303e10 | − | 1.86659e10i | 0.489302 | − | 0.282499i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.28346e10 | − | 3.05041e10i | −0.787132 | − | 0.454451i | 0.0518199 | − | 0.998656i | \(-0.483498\pi\) |
−0.838952 | + | 0.544206i | \(0.816831\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.19540e10 | + | 1.49950e10i | −0.175320 | + | 0.219920i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.22240e9 | − | 1.42416e10i | 0.118721 | − | 0.205632i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.11444e9 | + | 3.66232e9i | 0.0300585 | + | 0.0520628i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.24004e10i | − | 0.173569i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.32494e10 | −0.320436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.04455e10 | + | 5.22187e10i | −1.22754 | + | 0.708721i | −0.966515 | − | 0.256611i | \(-0.917394\pi\) |
−0.261026 | + | 0.965332i | \(0.584061\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.17123e10 | − | 3.56296e10i | −0.824831 | − | 0.476216i | 0.0272488 | − | 0.999629i | \(-0.491325\pi\) |
−0.852079 | + | 0.523413i | \(0.824659\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.07176e10 | + | 6.13022e9i | 0.535975 | + | 0.0806935i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.80792e8 | + | 6.59552e8i | −0.00493680 | + | 0.00855079i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.86161e10 | + | 6.68851e10i | 0.493112 | + | 0.854095i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 4.68476e10i | − | 0.589264i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.60411e9 | 0.0570476 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.16548e10 | − | 1.25024e10i | 0.264325 | − | 0.152608i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.13093e10 | + | 4.11704e10i | 0.857529 | + | 0.495095i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.35333e10 | + | 1.34123e10i | 0.515782 | + | 0.158909i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.99851e10 | − | 1.03897e11i | 0.700251 | − | 1.21287i | −0.268127 | − | 0.963384i | \(-0.586405\pi\) |
0.968378 | − | 0.249487i | \(-0.0802621\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.28747e10 | − | 5.69406e10i | −0.378148 | − | 0.654972i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.12759e9i | 0.103459i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.67882e10 | 0.857720 | 0.428860 | − | 0.903371i | \(-0.358915\pi\) | ||||
0.428860 | + | 0.903371i | \(0.358915\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.73698e10 | − | 2.73490e10i | 0.521449 | − | 0.301059i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.18418e10 | + | 5.30249e10i | 0.996400 | + | 0.575272i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.49234e8 | − | 6.30492e9i | 0.0101502 | − | 0.0674185i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.38279e9 | + | 4.12711e9i | −0.0251139 | + | 0.0434985i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.00412e9 | − | 1.03994e10i | −0.0623775 | − | 0.108041i | 0.833150 | − | 0.553047i | \(-0.186535\pi\) |
−0.895528 | + | 0.445006i | \(0.853202\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.90982e10i | 0.195589i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.72014e10 | 0.476545 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.79826e10 | − | 4.50233e10i | 0.776183 | − | 0.448129i | −0.0588931 | − | 0.998264i | \(-0.518757\pi\) |
0.835076 | + | 0.550135i | \(0.185424\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.19753e10 | + | 1.26874e10i | 0.215645 | + | 0.124503i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.97968e9 | + | 7.15860e9i | 0.0868818 | + | 0.0692621i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.50444e10 | + | 9.53398e10i | −0.525127 | + | 0.909547i | 0.474445 | + | 0.880285i | \(0.342649\pi\) |
−0.999572 | + | 0.0292615i | \(0.990684\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.27688e9 | + | 3.94367e9i | 0.0214188 | + | 0.0370985i | 0.876536 | − | 0.481336i | \(-0.159848\pi\) |
−0.855117 | + | 0.518435i | \(0.826515\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 3.24039e10i | − | 0.300593i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.20448e10 | 0.110186 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.58023e10 | − | 1.48969e10i | 0.232785 | − | 0.134398i | −0.379071 | − | 0.925367i | \(-0.623757\pi\) |
0.611856 | + | 0.790969i | \(0.290423\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.19420e10 | − | 2.42153e10i | −0.373195 | − | 0.215464i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.71618e10 | − | 1.20107e11i | −0.413891 | − | 1.05406i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.40591e10 | + | 5.89920e10i | −0.294821 | + | 0.510645i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.06335e8 | − | 1.22341e9i | −0.00603097 | − | 0.0104460i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.87063e10i | 0.410235i | 0.978737 | + | 0.205118i | \(0.0657577\pi\) | ||||
−0.978737 | + | 0.205118i | \(0.934242\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.58676e8 | −0.00796546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.42531e10 | + | 3.70965e10i | −0.526676 | + | 0.304077i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.48606e11 | − | 8.57978e10i | −1.20176 | − | 0.693837i | −0.240815 | − | 0.970571i | \(-0.577415\pi\) |
−0.960947 | + | 0.276734i | \(0.910748\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.41385e10 | − | 1.73316e10i | 0.352168 | − | 0.138284i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.18284e10 | − | 2.04875e10i | 0.0931173 | − | 0.161284i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.22733e11 | + | 2.12580e11i | 0.953355 | + | 1.65126i | 0.738087 | + | 0.674705i | \(0.235729\pi\) |
0.215268 | + | 0.976555i | \(0.430937\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.97408e10i | − | 0.534551i | −0.963620 | − | 0.267275i | \(-0.913877\pi\) | ||
0.963620 | − | 0.267275i | \(-0.0861233\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.22399e10 | −0.319488 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.03426e10 | + | 1.17448e10i | −0.151839 | + | 0.0876644i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.32636e10 | + | 4.80723e10i | 0.613339 | + | 0.354111i | 0.774271 | − | 0.632854i | \(-0.218117\pi\) |
−0.160932 | + | 0.986965i | \(0.551450\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.61646e10 | + | 5.79084e10i | −0.335614 | + | 0.420991i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.27798e9 | − | 5.67763e9i | 0.0235202 | − | 0.0407383i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.64299e10 | − | 9.77394e10i | −0.399638 | − | 0.692194i | 0.594043 | − | 0.804433i | \(-0.297531\pi\) |
−0.993681 | + | 0.112239i | \(0.964198\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.96893e9i | 0.0557057i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.66934e11 | −1.15187 | −0.575936 | − | 0.817495i | \(-0.695362\pi\) | ||||
−0.575936 | + | 0.817495i | \(0.695362\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.13512e11 | + | 1.23271e11i | −1.45432 | + | 0.839650i | −0.998722 | − | 0.0505371i | \(-0.983907\pi\) |
−0.455595 | + | 0.890187i | \(0.650573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.90918e9 | + | 1.67961e9i | 0.0195616 | + | 0.0112939i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.13266e10 | + | 1.37496e10i | 0.606240 | + | 0.0912723i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.25718e10 | + | 1.08378e11i | −0.410071 | + | 0.710263i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.97084e10 | + | 5.14564e10i | 0.192224 | + | 0.332942i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 8.41846e10i | − | 0.537811i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.85012e11 | −1.79782 | −0.898910 | − | 0.438133i | \(-0.855640\pi\) | ||||
−0.898910 | + | 0.438133i | \(0.855640\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.45665e10 | − | 1.99570e10i | 0.215298 | − | 0.124302i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.62120e10 | − | 9.35998e9i | −0.0997104 | − | 0.0575679i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.63867e10 | + | 1.76488e10i | 0.0995254 | + | 0.107191i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.03983e10 | − | 1.80104e10i | 0.0623675 | − | 0.108024i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.12062e11 | − | 1.94098e11i | −0.663785 | − | 1.14971i | −0.979613 | − | 0.200893i | \(-0.935616\pi\) |
0.315828 | − | 0.948816i | \(-0.397718\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.37170e11i | − | 1.38745i | −0.720241 | − | 0.693724i | \(-0.755969\pi\) | ||
0.720241 | − | 0.693724i | \(-0.244031\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.30557e10 | −0.190989 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.95163e11 | + | 1.12678e11i | −1.11373 | + | 0.643014i | −0.939794 | − | 0.341742i | \(-0.888983\pi\) |
−0.173940 | + | 0.984756i | \(0.555650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.46588e11 | + | 8.46326e10i | 0.826265 | + | 0.477044i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.96689e7 | − | 6.62012e8i | 0.000554927 | − | 0.00368589i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9.06390e10 | + | 1.56991e11i | −0.498497 | + | 0.863422i | −0.999998 | − | 0.00173469i | \(-0.999448\pi\) |
0.501502 | + | 0.865157i | \(0.332781\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.94632e9 | − | 8.56729e9i | −0.0268731 | − | 0.0465455i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.74676e10i | − | 0.0937501i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00364e11 | 1.06238 | 0.531189 | − | 0.847253i | \(-0.321745\pi\) | ||||
0.531189 | + | 0.847253i | \(0.321745\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.46518e10 | + | 4.88737e10i | −0.443435 | + | 0.256017i | −0.705054 | − | 0.709154i | \(-0.749077\pi\) |
0.261618 | + | 0.965171i | \(0.415744\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.16117e10 | + | 1.24775e10i | 0.111850 | + | 0.0645764i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.66745e10 | + | 3.72089e10i | 0.238667 | + | 0.190266i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.08315e10 | + | 1.87608e10i | −0.0547251 | + | 0.0947867i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.78383e10 | + | 4.82174e10i | 0.138976 | + | 0.240713i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.97629e11i | 0.974901i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.14833e11 | −1.04723 | −0.523614 | − | 0.851956i | \(-0.675416\pi\) | ||||
−0.523614 | + | 0.851956i | \(0.675416\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.24815e10 | + | 1.87532e10i | −0.156466 | + | 0.0903359i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.10418e11 | − | 1.21485e11i | −1.00168 | − | 0.578320i | −0.0929348 | − | 0.995672i | \(-0.529625\pi\) |
−0.908745 | + | 0.417352i | \(0.862958\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.25316e10 | − | 5.73814e10i | −0.106002 | − | 0.269955i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.19168e10 | + | 7.26021e10i | −0.194895 | + | 0.337567i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.78386e11 | − | 3.08973e11i | −0.819742 | − | 1.41984i | −0.905872 | − | 0.423552i | \(-0.860783\pi\) |
0.0861296 | − | 0.996284i | \(-0.472550\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.85065e10i | 0.220312i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.90072e11 | −0.853278 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.11886e10 | + | 1.80068e10i | −0.138395 | + | 0.0799022i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.06169e11 | + | 1.76767e11i | 1.34291 | + | 0.775332i | 0.987234 | − | 0.159275i | \(-0.0509158\pi\) |
0.355680 | + | 0.934608i | \(0.384249\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.86217e10 | + | 1.51654e10i | −0.167455 | + | 0.0657537i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.58112e10 | − | 2.73858e10i | 0.0677682 | − | 0.117378i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.03861e10 | − | 1.21912e11i | −0.298233 | − | 0.516555i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 4.64796e10i | − | 0.194695i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.14132e11 | 1.30089 | 0.650445 | − | 0.759553i | \(-0.274582\pi\) | ||||
0.650445 | + | 0.759553i | \(0.274582\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.17734e10 | − | 5.29854e10i | 0.375747 | − | 0.216938i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9.82701e9 | + | 5.67362e9i | 0.0397800 | + | 0.0229670i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.37224e11 | − | 2.97572e11i | 0.949471 | − | 1.19101i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.40578e11 | + | 2.43487e11i | −0.556328 | + | 0.963589i | 0.441471 | + | 0.897276i | \(0.354457\pi\) |
−0.997799 | + | 0.0663130i | \(0.978876\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.90384e9 | + | 5.02960e9i | 0.0113630 | + | 0.0196814i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.95831e8i | − | 0.000757747i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.10412e9 | 0.0195297 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.95460e10 | − | 4.01524e10i | 0.263145 | − | 0.151927i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.14076e11 | + | 2.39067e11i | 1.54940 | + | 0.894548i | 0.998187 | + | 0.0601845i | \(0.0191689\pi\) |
0.551215 | + | 0.834363i | \(0.314164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.49367e10 | + | 9.77652e9i | 0.240298 | + | 0.0361779i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.06682e11 | + | 1.84778e11i | −0.390424 | + | 0.676235i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.20936e11 | − | 2.09468e11i | −0.437728 | − | 0.758167i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.00817e11i | 1.79284i | 0.443206 | + | 0.896420i | \(0.353841\pi\) | ||||
−0.443206 | + | 0.896420i | \(0.646159\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.05701e11 | − | 2.91967e11i | 1.77102 | − | 1.02250i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.44252e10 | − | 4.87429e10i | −0.292453 | − | 0.168848i | 0.346594 | − | 0.938015i | \(-0.387338\pi\) |
−0.639048 | + | 0.769167i | \(0.720671\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.05471e10 | + | 2.83626e10i | −0.104669 | + | 0.0971843i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.63085e10 | − | 1.32170e11i | 0.258644 | − | 0.447985i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.10837e11 | − | 1.91976e11i | −0.371628 | − | 0.643678i | 0.618188 | − | 0.786030i | \(-0.287867\pi\) |
−0.989816 | + | 0.142352i | \(0.954534\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.14131e10i | 0.104193i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.62831e11 | 0.862426 | 0.431213 | − | 0.902250i | \(-0.358086\pi\) | ||||
0.431213 | + | 0.902250i | \(0.358086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.95384e10 | − | 5.16950e10i | 0.290659 | − | 0.167812i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.01787e11 | + | 5.87670e10i | 0.326898 | + | 0.188734i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.78071e10 | − | 3.83961e11i | 0.183677 | − | 1.22000i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.37391e11 | + | 2.37969e11i | −0.431917 | + | 0.748102i | −0.997038 | − | 0.0769059i | \(-0.975496\pi\) |
0.565122 | + | 0.825008i | \(0.308829\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.50236e9 | + | 6.06626e9i | 0.0108938 | + | 0.0188687i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.40622e10i | − | 0.104830i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.73327e11 | 0.527817 | 0.263909 | − | 0.964548i | \(-0.414988\pi\) | ||||
0.263909 | + | 0.964548i | \(0.414988\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.05111e10 | + | 6.06861e9i | −0.0316725 | + | 0.0182861i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.50804e11 | + | 2.02537e11i | 1.04599 | + | 0.603901i | 0.921523 | − | 0.388323i | \(-0.126946\pi\) |
0.124464 | + | 0.992224i | \(0.460279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.10830e11 | + | 8.83538e10i | 0.327009 | + | 0.260692i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.15964e10 | + | 3.74061e10i | −0.0630574 | + | 0.109219i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.47446e10 | + | 7.74999e10i | 0.129288 | + | 0.223934i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 6.69043e11i | − | 1.91315i | −0.291488 | − | 0.956574i | \(-0.594150\pi\) | ||
0.291488 | − | 0.956574i | \(-0.405850\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.43306e11 | −0.971546 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.11009e10 | + | 4.10502e10i | −0.199140 | + | 0.114973i | −0.596254 | − | 0.802796i | \(-0.703345\pi\) |
0.397115 | + | 0.917769i | \(0.370012\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.89356e9 | + | 1.09325e9i | 0.00524895 | + | 0.00303048i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.70477e10 | + | 6.88826e10i | 0.0742073 | + | 0.188984i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.86014e10 | − | 1.53462e11i | 0.240597 | − | 0.416727i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.75701e10 | + | 6.50732e10i | 0.100981 | + | 0.174903i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6.74570e10i | − | 0.179465i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.30202e11 | −0.342878 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.30594e11 | − | 7.53983e10i | 0.340427 | − | 0.196545i | −0.320034 | − | 0.947406i | \(-0.603694\pi\) |
0.660461 | + | 0.750861i | \(0.270361\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.94415e11 | + | 1.12246e11i | 0.501675 | + | 0.289642i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.66773e11 | − | 1.44019e11i | 0.936896 | − | 0.367885i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.22424e10 | + | 9.04865e10i | −0.132108 | + | 0.228819i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.11666e10 | − | 5.39821e10i | −0.0780227 | − | 0.135139i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.07975e11i | − | 0.515439i | −0.966220 | − | 0.257720i | \(-0.917029\pi\) | ||
0.966220 | − | 0.257720i | \(-0.0829711\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.00451e11 | −0.491836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.28537e10 | + | 4.20621e10i | −0.176979 | + | 0.102179i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.46567e10 | + | 3.15561e10i | 0.131456 | + | 0.0758963i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.60077e9 | + | 9.53433e9i | −0.0180998 | + | 0.0227042i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.27580e10 | + | 1.26021e11i | −0.171548 | + | 0.297131i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.44290e11 | − | 5.96328e11i | −0.803768 | − | 1.39217i | −0.917120 | − | 0.398612i | \(-0.869492\pi\) |
0.113352 | − | 0.993555i | \(-0.463841\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.52097e10i | − | 0.0351591i | −0.999845 | − | 0.0175795i | \(-0.994404\pi\) | ||
0.999845 | − | 0.0175795i | \(-0.00559603\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.71093e11 | −0.391624 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.36224e11 | + | 7.86491e10i | −0.308762 | + | 0.178264i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.36572e11 | + | 3.67525e11i | 1.42876 | + | 0.824895i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.16923e10 | − | 3.26587e9i | −0.0482136 | − | 0.00725878i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.67890e11 | + | 6.37204e11i | −0.809740 | + | 1.40251i | 0.103305 | + | 0.994650i | \(0.467058\pi\) |
−0.913044 | + | 0.407860i | \(0.866275\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.71200e10 | − | 1.68217e11i | −0.211694 | − | 0.366665i | 0.740551 | − | 0.672001i | \(-0.234565\pi\) |
−0.952245 | + | 0.305335i | \(0.901231\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.35514e11i | − | 0.292529i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.50782e11 | 1.17749 | 0.588746 | − | 0.808318i | \(-0.299622\pi\) | ||||
0.588746 | + | 0.808318i | \(0.299622\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −9.83589e10 | + | 5.67875e10i | −0.208255 | + | 0.120236i | −0.600500 | − | 0.799625i | \(-0.705032\pi\) |
0.392245 | + | 0.919861i | \(0.371698\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.24803e11 | + | 2.45260e11i | 0.890806 | + | 0.514307i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.16808e11 | − | 7.03712e11i | 0.450294 | − | 1.46155i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.06916e10 | − | 1.05121e11i | 0.124848 | − | 0.216244i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.04901e8 | + | 5.28105e8i | 0.000621237 | + | 0.00107601i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.71368e11i | 1.15310i | 0.817061 | + | 0.576551i | \(0.195602\pi\) | ||||
−0.817061 | + | 0.576551i | \(0.804398\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.52276e10 | −0.130391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.63641e10 | − | 4.40888e10i | 0.151210 | − | 0.0873008i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.06892e11 | − | 6.17142e10i | −0.209662 | − | 0.121048i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.43042e10 | + | 3.60694e11i | −0.105511 | + | 0.700819i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.07614e10 | − | 7.06009e10i | 0.0784546 | − | 0.135887i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.08235e10 | + | 1.87468e10i | 0.0206371 | + | 0.0357445i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.61864e11i | − | 0.305742i | −0.988246 | − | 0.152871i | \(-0.951148\pi\) | ||
0.988246 | − | 0.152871i | \(-0.0488519\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.43707e10 | −0.101742 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.38704e11 | + | 8.00810e10i | −0.257138 | + | 0.148459i | −0.623028 | − | 0.782199i | \(-0.714098\pi\) |
0.365890 | + | 0.930658i | \(0.380765\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.45231e11 | − | 1.41584e11i | −0.450405 | − | 0.260042i | 0.257596 | − | 0.966253i | \(-0.417070\pi\) |
−0.708001 | + | 0.706211i | \(0.750403\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.67615e10 | + | 7.71382e10i | 0.176072 | + | 0.140364i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.89609e11 | + | 6.74823e11i | −0.702402 | + | 1.21660i | 0.265219 | + | 0.964188i | \(0.414556\pi\) |
−0.967621 | + | 0.252408i | \(0.918778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.84342e10 | + | 6.65700e10i | 0.0686520 | + | 0.118909i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 4.36783e11i | − | 0.773018i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.09837e10 | −0.0367963 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.98774e10 | − | 4.03437e10i | 0.121413 | − | 0.0700976i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.86291e10 | + | 2.80760e10i | 0.0837219 | + | 0.0483369i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.02761e11 | − | 2.61703e11i | −0.175306 | − | 0.446453i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.57632e10 | + | 6.19436e10i | −0.0604557 | + | 0.104712i | −0.894669 | − | 0.446729i | \(-0.852589\pi\) |
0.834213 | + | 0.551442i | \(0.185922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.79628e11 | − | 3.11125e11i | −0.300898 | − | 0.521170i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.68861e11i | 1.44227i | 0.692795 | + | 0.721135i | \(0.256379\pi\) | ||||
−0.692795 | + | 0.721135i | \(0.743621\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.82118e11 | −1.45105 | −0.725527 | − | 0.688194i | \(-0.758404\pi\) | ||||
−0.725527 | + | 0.688194i | \(0.758404\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.34139e11 | + | 7.74451e10i | −0.218666 | + | 0.126247i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.26589e11 | − | 4.19496e11i | −1.17380 | − | 0.677694i | −0.219229 | − | 0.975674i | \(-0.570354\pi\) |
−0.954572 | + | 0.297979i | \(0.903687\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.70582e11 | + | 1.06248e11i | −0.433203 | + | 0.170103i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.88971e10 | − | 3.27308e10i | 0.0299837 | − | 0.0519333i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.26163e11 | − | 2.18520e11i | −0.198392 | − | 0.343626i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.72240e11i | − | 0.424287i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.41685e9 | −0.00991179 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.40566e9 | + | 1.96626e9i | −0.00521389 | + | 0.00301024i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.53601e11 | + | 5.50562e11i | 1.44700 | + | 0.835424i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.19975e11 | + | 4.01374e11i | −0.481244 | + | 0.603668i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.08692e11 | + | 1.88260e11i | −0.162033 | + | 0.280649i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.38453e11 | − | 7.59423e11i | −0.647879 | − | 1.12216i | −0.983628 | − | 0.180208i | \(-0.942323\pi\) |
0.335749 | − | 0.941951i | \(-0.391011\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3.46639e11i | 0.507718i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.09312e10 | 0.0158706 | 0.00793529 | − | 0.999969i | \(-0.497474\pi\) | ||||
0.00793529 | + | 0.999969i | \(0.497474\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.67768e11 | + | 2.12331e11i | −0.529287 | + | 0.305584i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.56617e11 | − | 9.04227e10i | −0.223436 | − | 0.129001i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.51907e11 | − | 2.28702e10i | −0.214832 | − | 0.0323440i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.27143e11 | + | 5.66628e11i | −0.458643 | + | 0.794394i | −0.998890 | − | 0.0471134i | \(-0.984998\pi\) |
0.540246 | + | 0.841507i | \(0.318331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.09005e11 | + | 3.62008e11i | 0.290482 | + | 0.503129i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.97260e10i | 0.0547353i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.41692e11 | −0.330138 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.18018e10 | + | 2.99078e10i | −0.0701497 | + | 0.0405009i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.55844e11 | − | 8.99765e10i | −0.209231 | − | 0.120800i | 0.391723 | − | 0.920083i | \(-0.371879\pi\) |
−0.600954 | + | 0.799283i | \(0.705213\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.03606e11 | − | 2.06560e11i | 1.20276 | − | 0.274947i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.69236e11 | − | 6.39536e11i | 0.487279 | − | 0.843992i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.80300e10 | − | 1.35152e11i | −0.102097 | − | 0.176838i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.66845e11i | − | 0.994831i | −0.867512 | − | 0.497415i | \(-0.834282\pi\) | ||
0.867512 | − | 0.497415i | \(-0.165718\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.41814e11 | −0.568299 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.22218e12 | + | 7.05627e11i | −1.55875 | + | 0.899946i | −0.561376 | + | 0.827561i | \(0.689728\pi\) |
−0.997377 | + | 0.0723858i | \(0.976939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.13481e10 | + | 1.80988e10i | 0.0396428 | + | 0.0228878i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.65266e9 | − | 3.75456e10i | 0.00708804 | − | 0.0470795i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.03071e10 | − | 1.78523e10i | 0.0128155 | − | 0.0221971i | −0.859547 | − | 0.511057i | \(-0.829254\pi\) |
0.872362 | + | 0.488860i | \(0.162587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.66834e10 | + | 2.88966e10i | 0.0205694 | + | 0.0356272i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 7.91510e11i | − | 0.967686i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.06006e10 | 0.0249752 | 0.0124876 | − | 0.999922i | \(-0.496025\pi\) | ||||
0.0124876 | + | 0.999922i | \(0.496025\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.27821e10 | + | 5.35677e10i | −0.111545 | + | 0.0644006i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.11075e11 | + | 1.21864e11i | 0.251646 | + | 0.145288i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.88983e11 | + | 4.69537e11i | 0.696351 | + | 0.555131i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.26428e11 | + | 7.38595e11i | −0.499979 | + | 0.865989i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.76840e11 | + | 3.06296e11i | 0.205625 | + | 0.356153i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.60124e11i | 0.184649i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.50116e12 | −1.71681 | −0.858405 | − | 0.512973i | \(-0.828544\pi\) | ||||
−0.858405 | + | 0.512973i | \(0.828544\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.31788e11 | − | 4.80233e11i | 0.943447 | − | 0.544699i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.65121e11 | − | 3.84008e11i | −0.748210 | − | 0.431979i | 0.0768368 | − | 0.997044i | \(-0.475518\pi\) |
−0.825047 | + | 0.565064i | \(0.808851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.79478e11 | − | 4.57076e11i | −0.200244 | − | 0.509962i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.58227e10 | − | 6.20467e10i | 0.0396406 | − | 0.0686595i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.61187e11 | + | 9.72004e11i | 0.615927 | + | 1.06682i | 0.990221 | + | 0.139507i | \(0.0445516\pi\) |
−0.374294 | + | 0.927310i | \(0.622115\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.03949e11i | − | 0.330879i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.29105e11 | −0.139402 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.27850e12 | + | 7.38145e11i | −1.36927 | + | 0.790546i | −0.990834 | − | 0.135083i | \(-0.956870\pi\) |
−0.378432 | + | 0.925629i | \(0.623537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.12437e11 | + | 1.22651e11i | 0.225676 | + | 0.130294i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.64015e11 | − | 6.44029e10i | 0.172829 | − | 0.0678636i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.50753e10 | + | 1.30034e11i | −0.0784715 | + | 0.135917i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.05075e11 | + | 1.22123e12i | 0.731039 | + | 1.26620i | 0.956439 | + | 0.291931i | \(0.0942978\pi\) |
−0.225400 | + | 0.974266i | \(0.572369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.57807e11i | − | 0.985102i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.82157e10 | −0.0797998 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.23084e11 | − | 5.32943e11i | 0.934244 | − | 0.539386i | 0.0460928 | − | 0.998937i | \(-0.485323\pi\) |
0.888151 | + | 0.459551i | \(0.151990\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.83760e10 | − | 3.37034e10i | −0.0586101 | − | 0.0338386i |
(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 | 84.9.m.b.61.4 | ✓ | 12 | |
3.2 | odd | 2 | 252.9.z.d.145.3 | 12 | |||
7.3 | odd | 6 | inner | 84.9.m.b.73.4 | yes | 12 | |
21.17 | even | 6 | 252.9.z.d.73.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
84.9.m.b.73.4 | yes | 12 | 7.3 | odd | 6 | inner | |
252.9.z.d.73.3 | 12 | 21.17 | even | 6 | |||
252.9.z.d.145.3 | 12 | 3.2 | odd | 2 |