Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,9,Mod(53,84)]
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, 3, 4]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.53");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.p (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: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 65.17 | ||
Character | \(\chi\) | \(=\) | 84.65 |
Dual form | 84.9.p.b.53.17 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 67.5468 | − | 44.7037i | 0.833912 | − | 0.551898i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 737.233 | + | 425.642i | 1.17957 | + | 0.681027i | 0.955916 | − | 0.293641i | \(-0.0948669\pi\) |
0.223658 | + | 0.974668i | \(0.428200\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2359.93 | + | 442.194i | 0.982894 | + | 0.184171i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2564.15 | − | 6039.19i | 0.390817 | − | 0.920468i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5724.94 | − | 3305.29i | 0.391021 | − | 0.225756i | −0.291582 | − | 0.956546i | \(-0.594181\pi\) |
0.682602 | + | 0.730790i | \(0.260848\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 27957.8 | 0.978879 | 0.489440 | − | 0.872037i | \(-0.337201\pi\) | ||||
0.489440 | + | 0.872037i | \(0.337201\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 68825.6 | − | 4206.32i | 1.35952 | − | 0.0830878i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −99130.5 | + | 57233.0i | −1.18689 | + | 0.685253i | −0.957599 | − | 0.288104i | \(-0.906975\pi\) |
−0.229294 | + | 0.973357i | \(0.573642\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −77405.2 | + | 134070.i | −0.593958 | + | 1.02877i | 0.399735 | + | 0.916631i | \(0.369102\pi\) |
−0.993693 | + | 0.112135i | \(0.964231\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 179173. | − | 75628.8i | 0.921290 | − | 0.388875i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 225502. | + | 130194.i | 0.805821 | + | 0.465241i | 0.845503 | − | 0.533971i | \(-0.179301\pi\) |
−0.0396813 | + | 0.999212i | \(0.512634\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 167030. | + | 289304.i | 0.427596 | + | 0.740617i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −96774.1 | − | 522556.i | −0.182098 | − | 0.983280i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 17129.9i | 0.0242194i | 0.999927 | + | 0.0121097i | \(0.00385473\pi\) | ||||
−0.999927 | + | 0.0121097i | \(0.996145\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −405878. | − | 703001.i | −0.439490 | − | 0.761219i | 0.558160 | − | 0.829733i | \(-0.311507\pi\) |
−0.997650 | + | 0.0685146i | \(0.978174\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 238942. | − | 479188.i | 0.201483 | − | 0.404064i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.55160e6 | + | 1.33048e6i | 1.03397 | + | 0.886620i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 247100. | − | 427990.i | 0.131846 | − | 0.228364i | −0.792542 | − | 0.609817i | \(-0.791243\pi\) |
0.924388 | + | 0.381453i | \(0.124576\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.88846e6 | − | 1.24982e6i | 0.816299 | − | 0.540242i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 424820.i | − | 0.150338i | −0.997171 | − | 0.0751691i | \(-0.976050\pi\) | ||
0.997171 | − | 0.0751691i | \(-0.0239496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.54551e6 | −1.32956 | −0.664781 | − | 0.747039i | \(-0.731475\pi\) | ||||
−0.664781 | + | 0.747039i | \(0.731475\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.46091e6 | − | 3.36088e6i | 1.08786 | − | 0.819603i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.85874e6 | + | 1.65049e6i | 0.585845 | + | 0.338238i | 0.763453 | − | 0.645864i | \(-0.223503\pi\) |
−0.177608 | + | 0.984101i | \(0.556836\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.37373e6 | + | 2.08709e6i | 0.932162 | + | 0.362041i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.13742e6 | + | 8.29742e6i | −0.611574 | + | 1.22648i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.31496e7 | − | 7.59194e6i | 1.66652 | − | 0.962164i | 0.697022 | − | 0.717049i | \(-0.254508\pi\) |
0.969494 | − | 0.245114i | \(-0.0788255\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.62749e6 | 0.614984 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 764942. | + | 1.25163e7i | 0.0724651 | + | 1.18570i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.96730e6 | − | 3.44522e6i | 0.492459 | − | 0.284321i | −0.233135 | − | 0.972444i | \(-0.574898\pi\) |
0.725594 | + | 0.688123i | \(0.241565\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.03062e6 | − | 1.78509e6i | 0.0744356 | − | 0.128926i | −0.826405 | − | 0.563076i | \(-0.809618\pi\) |
0.900841 | + | 0.434150i | \(0.142951\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.72171e6 | − | 1.31182e7i | 0.553655 | − | 0.832746i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.06114e7 | + | 1.19000e7i | 1.15466 | + | 0.666643i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.09091e7 | + | 1.88951e7i | 0.541364 | + | 0.937671i | 0.998826 | + | 0.0484413i | \(0.0154254\pi\) |
−0.457462 | + | 0.889229i | \(0.651241\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.10521e7 | − | 1.28661e6i | 0.928749 | − | 0.0567611i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.05615e7i | − | 1.59618i | −0.602541 | − | 0.798088i | \(-0.705845\pi\) | ||
0.602541 | − | 0.798088i | \(-0.294155\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.19692e7 | − | 3.80517e7i | −0.773610 | − | 1.33993i | −0.935572 | − | 0.353135i | \(-0.885116\pi\) |
0.161962 | − | 0.986797i | \(-0.448218\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.42153e7 | + | 1.20747e7i | 0.765322 | + | 0.381620i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.49720e7 | − | 5.26873e6i | 0.425910 | − | 0.149880i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.58177e7 | + | 6.20381e7i | −0.919580 | + | 1.59276i | −0.119526 | + | 0.992831i | \(0.538138\pi\) |
−0.800054 | + | 0.599928i | \(0.795196\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.98970e7 | − | 3.09708e7i | −0.694524 | − | 0.719470i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.39935e7i | 0.505571i | 0.967522 | + | 0.252785i | \(0.0813466\pi\) | ||||
−0.967522 | + | 0.252785i | \(0.918653\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.74431e7 | −1.86670 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 765771. | + | 1.15707e6i | 0.0133666 | + | 0.0201968i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.76023e7 | − | 1.01627e7i | −0.280549 | − | 0.161975i | 0.353123 | − | 0.935577i | \(-0.385120\pi\) |
−0.633672 | + | 0.773602i | \(0.718453\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.59784e7 | + | 1.23628e7i | 0.962135 | + | 0.180281i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.88426e7 | − | 2.93413e7i | −0.786611 | − | 0.392235i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.14131e8 | + | 6.58938e7i | −1.40123 | + | 0.809003i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 271197. | 0.00306336 | 0.00153168 | − | 0.999999i | \(-0.499512\pi\) | ||||
0.00153168 | + | 0.999999i | \(0.499512\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.28170e6 | − | 4.30493e7i | −0.0549836 | − | 0.448152i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.56327e7 | + | 3.78930e7i | −0.630717 | + | 0.364145i | −0.781030 | − | 0.624494i | \(-0.785305\pi\) |
0.150313 | + | 0.988639i | \(0.451972\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.78145e7 | − | 1.17458e8i | 0.602523 | − | 1.04360i | −0.389914 | − | 0.920851i | \(-0.627495\pi\) |
0.992438 | − | 0.122750i | \(-0.0391713\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.64283e8 | + | 2.05076e7i | 1.35156 | + | 0.168717i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.30545e7 | − | 3.64045e7i | −0.481039 | − | 0.277728i | 0.239810 | − | 0.970820i | \(-0.422915\pi\) |
−0.720850 | + | 0.693092i | \(0.756248\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.41755e6 | − | 1.28476e7i | −0.0525478 | − | 0.0910155i | 0.838555 | − | 0.544817i | \(-0.183401\pi\) |
−0.891103 | + | 0.453801i | \(0.850068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.44192e6 | − | 3.99557e7i | −0.0160857 | − | 0.263201i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.42202e8i | 0.872151i | 0.899910 | + | 0.436076i | \(0.143632\pi\) | ||||
−0.899910 | + | 0.436076i | \(0.856368\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.10832e8 | + | 1.91966e8i | 0.633684 | + | 1.09757i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.16880e7 | − | 1.68842e8i | 0.382563 | − | 0.901027i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.59249e8 | + | 9.12310e7i | −1.29279 | + | 0.454940i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.53295e7 | + | 1.47795e8i | −0.398068 | + | 0.689475i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.89910e7 | − | 2.86952e7i | −0.0829713 | − | 0.125369i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.81536e7i | − | 0.197237i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.99281e8 | −1.53484 | −0.767420 | − | 0.641144i | \(-0.778460\pi\) | ||||
−0.767420 | + | 0.641144i | \(0.778460\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.07035e8 | + | 2.03201e8i | −1.10874 | + | 0.733782i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.81218e8 | − | 1.62361e8i | −0.954900 | − | 0.551311i | −0.0603000 | − | 0.998180i | \(-0.519206\pi\) |
−0.894600 | + | 0.446869i | \(0.852539\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.41956e8 | + | 2.82167e8i | −0.773267 | + | 0.901778i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.51076e8 | − | 4.26437e8i | 0.454843 | − | 1.28386i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.90779e8 | − | 1.67881e8i | 0.825430 | − | 0.476562i | −0.0268553 | − | 0.999639i | \(-0.508549\pi\) |
0.852285 | + | 0.523077i | \(0.175216\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.71007e8 | −1.26173 | −0.630867 | − | 0.775891i | \(-0.717301\pi\) | ||||
−0.630867 | + | 0.775891i | \(0.717301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.66882e8 | − | 1.63107e7i | 0.675215 | − | 0.0412662i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.60056e8 | − | 9.24087e7i | 0.382762 | − | 0.220988i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.29121e6 | + | 1.26287e7i | −0.0164941 | + | 0.0285685i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.56279e8 | − | 9.92493e7i | 0.977151 | − | 0.212549i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.11751e8 | + | 2.37725e8i | 0.835391 | + | 0.482313i | 0.855695 | − | 0.517481i | \(-0.173130\pi\) |
−0.0203042 | + | 0.999794i | \(0.506463\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.70129e8 | − | 6.41082e8i | −0.711943 | − | 1.23312i | −0.964127 | − | 0.265442i | \(-0.914482\pi\) |
0.252184 | − | 0.967679i | \(-0.418851\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.14556e7 | + | 7.45422e8i | 0.166895 | + | 1.36031i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 6.91035e8i | − | 1.19722i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.26987e8 | + | 9.12768e8i | 0.867364 | + | 1.50232i | 0.864681 | + | 0.502322i | \(0.167521\pi\) |
0.00268327 | + | 0.999996i | \(0.499146\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.48827e8 | − | 1.10065e9i | 0.858711 | − | 1.72211i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.74598e8 | + | 4.06963e8i | 0.706353 | + | 0.605692i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.09473e8 | + | 3.62817e8i | −0.296740 | + | 0.513969i | −0.975388 | − | 0.220494i | \(-0.929233\pi\) |
0.678648 | + | 0.734464i | \(0.262566\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.80119e8 | − | 2.51570e8i | 0.512842 | − | 0.339408i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 9.95285e8i | − | 1.27962i | −0.768532 | − | 0.639811i | \(-0.779013\pi\) | ||
0.768532 | − | 0.639811i | \(-0.220987\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.40936e7 | −0.0417951 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.11194e8 | + | 8.11240e8i | 0.714817 | + | 0.948779i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.19011e9 | + | 6.87112e8i | 1.32863 | + | 0.767084i | 0.985088 | − | 0.172053i | \(-0.0550402\pi\) |
0.343541 | + | 0.939138i | \(0.388374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.66250e8 | + | 7.56596e8i | 0.283881 | + | 0.806699i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.49058e8 | − | 4.99474e8i | 0.253751 | − | 0.508886i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.58952e8 | + | 4.38181e8i | −0.739268 | + | 0.426817i | −0.821803 | − | 0.569771i | \(-0.807032\pi\) |
0.0825349 | + | 0.996588i | \(0.473698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.46390e9 | −1.36395 | −0.681974 | − | 0.731377i | \(-0.738878\pi\) | ||||
−0.681974 | + | 0.731377i | \(0.738878\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.01849e7 | − | 1.66650e8i | −0.00908141 | − | 0.148594i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.64341e8 | − | 2.10353e8i | 0.311044 | − | 0.179581i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.78344e8 | + | 6.55311e8i | −0.309400 | + | 0.535897i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.69084e6 | − | 1.27599e9i | 0.00210882 | − | 0.999998i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.04023e9 | + | 1.17793e9i | 1.53301 | + | 0.885086i | 0.999221 | + | 0.0394719i | \(0.0125675\pi\) |
0.533794 | + | 0.845615i | \(0.320766\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.60745e8 | + | 4.51624e8i | 0.187926 | + | 0.325498i | 0.944559 | − | 0.328343i | \(-0.106490\pi\) |
−0.756633 | + | 0.653840i | \(0.773157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.92421e9 | − | 1.17599e8i | 1.33080 | − | 0.0813330i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 4.28916e8i | − | 0.284779i | −0.989811 | − | 0.142389i | \(-0.954521\pi\) | ||
0.989811 | − | 0.142389i | \(-0.0454785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.26328e8 | − | 5.65217e8i | −0.208086 | − | 0.360415i | 0.743026 | − | 0.669263i | \(-0.233390\pi\) |
−0.951111 | + | 0.308848i | \(0.900057\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58156e9 | + | 7.88628e8i | 0.968949 | + | 0.483157i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.57474e6 | + | 4.04254e7i | −0.00446050 | + | 0.0238051i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.80821e8 | − | 3.13191e8i | 0.102384 | − | 0.177335i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.36448e9 | − | 1.02801e9i | 0.743169 | − | 0.559909i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.02339e9i | 0.536359i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.94462e8 | −0.249461 | −0.124731 | − | 0.992191i | \(-0.539807\pi\) | ||||
−0.124731 | + | 0.992191i | \(0.539807\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.81325e9 | − | 2.73980e9i | −0.880926 | − | 1.33107i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.35110e9 | − | 1.93476e9i | −1.56832 | − | 0.905467i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.46980e8 | − | 1.83851e9i | −0.291778 | − | 0.829138i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.18500e9 | − | 1.58817e9i | −1.38463 | − | 0.690431i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.77147e9 | + | 1.60011e9i | −1.16183 | + | 0.670780i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.81279e8 | −0.235053 | −0.117526 | − | 0.993070i | \(-0.537496\pi\) | ||||
−0.117526 | + | 0.993070i | \(0.537496\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.17545e9 | − | 2.66905e8i | 0.848827 | − | 0.104142i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.34115e9 | + | 1.35166e9i | −0.881711 | + | 0.509056i | −0.871222 | − | 0.490889i | \(-0.836672\pi\) |
−0.0104886 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.54279e9 | + | 4.40424e9i | −0.924632 | + | 1.60151i | −0.132479 | + | 0.991186i | \(0.542294\pi\) |
−0.792152 | + | 0.610323i | \(0.791039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.75781e8 | − | 1.02519e9i | 0.272453 | − | 0.360045i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.95404e9 | + | 1.70552e9i | 1.00229 | + | 0.578672i | 0.908925 | − | 0.416960i | \(-0.136904\pi\) |
0.0933650 | + | 0.995632i | \(0.470238\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.40504e9 | + | 2.43360e9i | 0.460698 | + | 0.797952i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.53961e8 | + | 5.79166e9i | 0.112192 | + | 1.83573i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6.19737e9i | − | 1.89940i | −0.313164 | − | 0.949699i | \(-0.601389\pi\) | ||
0.313164 | − | 0.949699i | \(-0.398611\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.73668e9 | − | 4.74006e9i | −0.811251 | − | 1.40513i | −0.911989 | − | 0.410215i | \(-0.865454\pi\) |
0.100738 | − | 0.994913i | \(-0.467880\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −3.40396e9 | − | 7.55474e8i | −0.976245 | − | 0.216668i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.07334e9 | + | 3.82596e9i | 0.852994 | + | 1.06188i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.16408e9 | + | 3.74829e9i | −0.581413 | + | 1.00704i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.07260e9 | + | 1.62069e9i | 0.279023 | + | 0.421601i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 3.83957e9i | − | 0.967359i | −0.875245 | − | 0.483679i | \(-0.839300\pi\) | ||
0.875245 | − | 0.483679i | \(-0.160700\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.72131e9 | 0.420124 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.58197e9 | + | 4.35607e9i | −1.55667 | + | 1.03023i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.84207e9 | − | 3.95027e9i | −1.56839 | − | 0.905513i | −0.996357 | − | 0.0852853i | \(-0.972820\pi\) |
−0.572038 | − | 0.820227i | \(-0.693847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.72394e8 | − | 9.00761e8i | 0.171648 | − | 0.200175i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.03451e8 | + | 4.39237e7i | 0.0222932 | + | 0.00946535i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.19117e9 | + | 1.84242e9i | −0.667002 | + | 0.385094i | −0.794940 | − | 0.606688i | \(-0.792498\pi\) |
0.127938 | + | 0.991782i | \(0.459164\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.29258e10 | 2.62104 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.64329e9 | + | 1.00431e8i | −0.323347 | + | 0.0197615i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.92677e9 | + | 2.26712e9i | −0.749941 | + | 0.432978i | −0.825672 | − | 0.564150i | \(-0.809204\pi\) |
0.0757319 | + | 0.997128i | \(0.475871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.65092e9 | − | 6.32358e9i | 0.676901 | − | 1.17243i | −0.299009 | − | 0.954250i | \(-0.596656\pi\) |
0.975909 | − | 0.218176i | \(-0.0700107\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.00929e9 | − | 2.11441e9i | 0.901832 | − | 0.380662i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.91247e9 | + | 1.10416e9i | 0.334398 | + | 0.193065i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.12992e7 | + | 1.58135e8i | 0.0155077 | + | 0.0268602i | 0.873675 | − | 0.486510i | \(-0.161730\pi\) |
−0.858167 | + | 0.513370i | \(0.828397\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.28629e9 | + | 6.48573e8i | −0.872438 | + | 0.107039i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.03022e8i | 0.0806792i | 0.999186 | + | 0.0403396i | \(0.0128440\pi\) | ||||
−0.999186 | + | 0.0403396i | \(0.987156\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.26060e9 | − | 3.91547e9i | −0.352434 | − | 0.610434i | 0.634241 | − | 0.773135i | \(-0.281313\pi\) |
−0.986675 | + | 0.162701i | \(0.947979\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.76352e9 | + | 9.55302e9i | −0.722019 | + | 1.44798i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.87853e8 | − | 1.00254e9i | 0.0276879 | − | 0.147767i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.06336e9 | − | 5.30590e9i | 0.439144 | − | 0.760619i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.83185e7 | − | 1.21235e7i | 0.00255457 | − | 0.00169066i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 4.43372e8i | − | 0.0601586i | −0.999548 | − | 0.0300793i | \(-0.990424\pi\) | ||
0.999548 | − | 0.0300793i | \(-0.00957598\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.86572e9 | 0.774521 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.28123e9 | − | 2.67173e9i | −0.293185 | − | 0.343374i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.30453e9 | + | 3.63992e9i | 0.788802 | + | 0.455415i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.07271e10 | − | 2.01000e9i | −1.30682 | − | 0.244866i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.73932e9 | + | 5.49358e9i | −0.324992 | + | 0.651756i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.51962e9 | − | 8.77352e8i | 0.175604 | − | 0.101385i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.08706e9 | −1.02299 | −0.511493 | − | 0.859287i | \(-0.670908\pi\) | ||||
−0.511493 | + | 0.859287i | \(0.670908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −6.70164e8 | − | 1.09655e10i | −0.0735101 | − | 1.20280i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.38439e9 | − | 7.99278e8i | 0.147985 | − | 0.0854390i | −0.424179 | − | 0.905578i | \(-0.639437\pi\) |
0.572164 | + | 0.820139i | \(0.306104\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.42736e9 | + | 7.66841e9i | −0.461283 | + | 0.798965i | −0.999025 | − | 0.0441441i | \(-0.985944\pi\) |
0.537743 | + | 0.843109i | \(0.319277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.20136e10 | − | 5.95886e9i | 1.22020 | − | 0.605231i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.50897e10 | + | 8.71204e9i | 1.49432 | + | 0.862746i | 0.999979 | − | 0.00652281i | \(-0.00207629\pi\) |
0.494340 | + | 0.869268i | \(0.335410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.66194e7 | + | 9.80676e7i | 0.00546767 | + | 0.00947028i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.88655e9 | + | 3.59760e8i | −0.554422 | + | 0.0338839i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.77205e10i | − | 1.62805i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.66977e9 | + | 8.08829e9i | 0.418565 | + | 0.724975i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.07537e9 | − | 5.36221e8i | −0.0940515 | − | 0.0468978i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.01658e9 | + | 5.15916e9i | 0.513530 | + | 0.440347i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.18605e9 | − | 1.59107e10i | 0.765273 | − | 1.32549i | −0.174828 | − | 0.984599i | \(-0.555937\pi\) |
0.940102 | − | 0.340894i | \(-0.110730\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.95111e9 | − | 2.58972e9i | −0.158674 | − | 0.210608i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.85735e10i | 1.47474i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.78424e10 | 1.38335 | 0.691677 | − | 0.722207i | \(-0.256872\pi\) | ||||
0.691677 | + | 0.722207i | \(0.256872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.35696e9 | + | 9.60529e9i | 0.481338 | + | 0.727297i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.64725e9 | − | 2.68309e9i | −0.343699 | − | 0.198435i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.17587e10 | + | 7.30162e9i | 0.849540 | + | 0.527525i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.60679e10 | + | 8.01211e9i | 1.13418 | + | 0.565550i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.52110e9 | + | 8.78209e8i | −0.104916 | + | 0.0605732i | −0.551540 | − | 0.834149i | \(-0.685960\pi\) |
0.446624 | + | 0.894722i | \(0.352626\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.65106e9 | 0.111291 | 0.0556457 | − | 0.998451i | \(-0.482278\pi\) | ||||
0.0556457 | + | 0.998451i | \(0.482278\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.70559e9 | − | 1.46095e10i | −0.178252 | − | 0.962513i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.15852e9 | + | 4.71032e9i | −0.525427 | + | 0.303356i | −0.739152 | − | 0.673538i | \(-0.764774\pi\) |
0.213725 | + | 0.976894i | \(0.431440\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.72647e10 | − | 2.99033e10i | 1.08704 | − | 1.88281i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.34331e10 | + | 1.77518e10i | −0.826995 | + | 1.09287i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.94388e10 | + | 1.12230e10i | 1.17029 | + | 0.675666i | 0.953748 | − | 0.300608i | \(-0.0971896\pi\) |
0.216540 | + | 0.976274i | \(0.430523\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.49136e9 | − | 6.04721e9i | −0.205573 | − | 0.356062i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.43252e8 | + | 1.37976e10i | 0.0485658 | + | 0.794654i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.74040e10i | − | 2.10740i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.30340e10 | + | 2.25755e10i | 0.718476 | + | 1.24444i | 0.961604 | + | 0.274442i | \(0.0884931\pi\) |
−0.243128 | + | 0.969994i | \(0.578174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.56557e9 | − | 1.08930e9i | −0.138381 | − | 0.0587547i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.43893e10 | − | 1.21017e10i | 1.81521 | − | 0.638782i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.96157e9 | − | 8.59369e9i | 0.256321 | − | 0.443961i | −0.708933 | − | 0.705276i | \(-0.750823\pi\) |
0.965253 | + | 0.261316i | \(0.0841563\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.15265e9 | − | 3.25263e9i | −0.108855 | − | 0.164478i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.78914e8i | 0.0237078i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.22862e10 | −1.08014 | −0.540069 | − | 0.841621i | \(-0.681602\pi\) | ||||
−0.540069 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.69701e10 | + | 1.78493e10i | −1.27992 | + | 0.847076i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.89715e10 | − | 1.09532e10i | −0.881671 | − | 0.509033i | −0.0104621 | − | 0.999945i | \(-0.503330\pi\) |
−0.871209 | + | 0.490912i | \(0.836664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.32805e10 | + | 2.48844e9i | 0.604464 | + | 0.113262i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.16554e10 | + | 2.74512e10i | −0.519616 | + | 1.22382i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.97181e9 | − | 4.60253e9i | 0.348144 | − | 0.201001i | −0.315724 | − | 0.948851i | \(-0.602247\pi\) |
0.663867 | + | 0.747850i | \(0.268914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.98055e10 | −1.27523 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.62535e10 | + | 1.60450e9i | −1.10057 | + | 0.0672621i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5.28120e10 | + | 3.04910e10i | −2.16942 | + | 1.25252i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.56436e9 | − | 9.63775e9i | 0.224002 | − | 0.387984i | −0.732017 | − | 0.681286i | \(-0.761421\pi\) |
0.956020 | + | 0.293302i | \(0.0947543\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.72942e9 | + | 2.98758e10i | −0.147146 | + | 1.17877i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.38739e10 | − | 8.01009e9i | −0.536563 | − | 0.309785i | 0.207122 | − | 0.978315i | \(-0.433590\pi\) |
−0.743685 | + | 0.668531i | \(0.766924\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.13474e10 | − | 1.96544e10i | −0.430207 | − | 0.745141i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.85857e9 | − | 3.55581e10i | −0.329263 | − | 1.32166i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.26696e9i | − | 0.119060i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.45257e9 | − | 1.11762e10i | −0.230589 | − | 0.399392i | 0.727392 | − | 0.686222i | \(-0.240732\pi\) |
−0.957982 | + | 0.286829i | \(0.907399\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.21363e10 | − | 2.43387e10i | 0.425322 | − | 0.852964i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.56059e10 | − | 5.49178e9i | 0.536398 | − | 0.188761i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.02127e10 | + | 1.76888e10i | −0.344307 | + | 0.596358i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.18150e10 | + | 2.10558e10i | −1.05217 | + | 0.696348i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.16778e10i | 0.703331i | 0.936126 | + | 0.351665i | \(0.114385\pi\) | ||||
−0.936126 | + | 0.351665i | \(0.885615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.47352e10 | 0.469059 | 0.234530 | − | 0.972109i | \(-0.424645\pi\) | ||||
0.234530 | + | 0.972109i | \(0.424645\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.72979e10 | − | 1.30323e10i | 0.540295 | − | 0.407062i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.31155e10 | − | 1.91192e10i | −1.01502 | − | 0.586023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.22155e9 | − | 3.75695e9i | 0.0969067 | − | 0.113012i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.68030e9 | − | 1.33970e10i | 0.197227 | − | 0.395530i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.75141e10 | + | 1.01118e10i | −0.507550 | + | 0.293034i | −0.731826 | − | 0.681492i | \(-0.761332\pi\) |
0.224276 | + | 0.974526i | \(0.427998\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.65884e10 | 1.60981 | 0.804907 | − | 0.593401i | \(-0.202215\pi\) | ||||
0.804907 | + | 0.593401i | \(0.202215\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.20539e7 | + | 1.17898e9i | 0.00201234 | + | 0.0329267i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.49100e10 | + | 2.01553e10i | −0.957248 | + | 0.552668i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.27059e9 | + | 1.60571e10i | −0.249603 | + | 0.432325i | −0.963416 | − | 0.268012i | \(-0.913633\pi\) |
0.713813 | + | 0.700336i | \(0.246967\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.63834e10 | − | 2.71014e10i | 0.697552 | − | 0.716534i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.71616e10 | − | 9.90825e9i | −0.445598 | − | 0.257266i | 0.260372 | − | 0.965509i | \(-0.416155\pi\) |
−0.705969 | + | 0.708243i | \(0.749488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.65132e9 | − | 1.49845e10i | −0.220619 | − | 0.382123i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.84397e10 | − | 2.34927e9i | 0.962829 | − | 0.0588440i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5.08034e10i | − | 1.24999i | −0.780627 | − | 0.624997i | \(-0.785100\pi\) | ||
0.780627 | − | 0.624997i | \(-0.214900\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.40415e9 | − | 2.43207e9i | −0.0339397 | − | 0.0587854i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.36598e10 | − | 2.67569e10i | −1.27425 | − | 0.635394i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.33793e10 | + | 3.71974e10i | 1.01213 | + | 0.867895i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.78637e10 | + | 4.82613e10i | −0.638813 | + | 1.10646i | 0.346881 | + | 0.937909i | \(0.387241\pi\) |
−0.985694 | + | 0.168547i | \(0.946092\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.95007e10 | + | 4.62625e10i | 0.889926 | + | 1.04227i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.67468e10i | 1.47784i | 0.673794 | + | 0.738919i | \(0.264664\pi\) | ||||
−0.673794 | + | 0.738919i | \(0.735336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.05204e10 | −0.881759 | −0.440879 | − | 0.897566i | \(-0.645333\pi\) | ||||
−0.440879 | + | 0.897566i | \(0.645333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.08918e10 | − | 4.66772e10i | −0.660742 | − | 0.998374i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.46885e10 | + | 1.42539e10i | 0.519072 | + | 0.299686i | 0.736555 | − | 0.676378i | \(-0.236451\pi\) |
−0.217483 | + | 0.976064i | \(0.569785\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.73894e10 | + | 4.94151e10i | 0.359413 | + | 1.02133i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.64005e10 | + | 3.80963e10i | 1.55243 | + | 0.774104i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.60227e10 | + | 1.50242e10i | −0.519886 | + | 0.300156i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.17158e10 | −1.01590 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.21315e10 | − | 9.88799e10i | −0.234338 | − | 1.91001i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.66737e10 | + | 3.84941e10i | −1.26652 | + | 0.731227i | −0.974328 | − | 0.225133i | \(-0.927718\pi\) |
−0.292193 | + | 0.956359i | \(0.594385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.90838e9 | − | 1.19657e10i | 0.129061 | − | 0.223541i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.02503e10 | + | 6.27279e9i | 0.923316 | + | 0.115258i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.99935e8 | + | 1.15433e8i | 0.00361346 | + | 0.00208623i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.55719e10 | + | 4.42919e10i | 0.454619 | + | 0.787423i | 0.998666 | − | 0.0516314i | \(-0.0164421\pi\) |
−0.544047 | + | 0.839055i | \(0.683109\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.07007e9 | + | 3.38714e10i | 0.0362034 | + | 0.592375i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 3.21356e10i | − | 0.552918i | −0.961026 | − | 0.276459i | \(-0.910839\pi\) | ||
0.961026 | − | 0.276459i | \(-0.0891610\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.80396e8 | − | 1.69810e9i | −0.0165964 | − | 0.0287458i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.44297e10 | − | 3.39855e10i | 0.240346 | − | 0.566073i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.79360e10 | − | 9.57223e10i | 0.293969 | − | 1.56887i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.38782e10 | + | 4.13582e10i | −0.385123 | + | 0.667052i | −0.991786 | − | 0.127907i | \(-0.959174\pi\) |
0.606663 | + | 0.794959i | \(0.292508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.44930e10 | − | 6.72284e10i | −0.706221 | − | 1.06709i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.19041e9i | 0.0654613i | 0.999464 | + | 0.0327306i | \(0.0104203\pi\) | ||||
−0.999464 | + | 0.0327306i | \(0.989580\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.45155e10 | −0.991970 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.30291e9 | + | 1.52411e9i | −0.0348534 | + | 0.0230666i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.97316e10 | + | 3.44860e10i | 0.889883 | + | 0.513774i | 0.873904 | − | 0.486098i | \(-0.161580\pi\) |
0.0159785 | + | 0.999872i | \(0.494914\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.50194e10 | − | 9.95140e10i | −0.513601 | − | 1.45949i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.75497e10 | + | 2.74740e10i | 1.11972 | + | 0.396692i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.99903e10 | − | 5.77294e10i | 1.42144 | − | 0.820669i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18214e10 | 0.305437 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.11105e11 | − | 6.79025e9i | 1.53131 | − | 0.0935871i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.71114e10 | − | 4.45203e10i | 1.04657 | − | 0.604237i | 0.124882 | − | 0.992172i | \(-0.460145\pi\) |
0.921687 | + | 0.387935i | \(0.126811\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.08198e10 | + | 5.33814e10i | −0.411929 | + | 0.713483i | −0.995101 | − | 0.0988666i | \(-0.968478\pi\) |
0.583171 | + | 0.812349i | \(0.301812\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.18070e10 | + | 3.92033e10i | 0.681948 | + | 0.516042i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.04698e10 | + | 4.64593e10i | 1.04325 | + | 0.602323i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.25477e9 | − | 9.10153e9i | −0.0671014 | − | 0.116223i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.50530e9 | − | 4.48717e10i | −0.0692473 | − | 0.564410i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.18770e10i | − | 0.147163i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.09906e10 | − | 5.36772e10i | −0.378281 | − | 0.655202i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.16765e10 | + | 6.35257e10i | −0.380925 | + | 0.763928i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.76627e10 | − | 5.81328e9i | 0.446228 | − | 0.0688758i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.06098e10 | − | 7.03382e10i | 0.474069 | − | 0.821111i | −0.525490 | − | 0.850800i | \(-0.676118\pi\) |
0.999559 | + | 0.0296882i | \(0.00945144\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.88819e10 | + | 6.54419e10i | −1.13741 | + | 0.752760i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.26289e10i | − | 0.143146i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.62204e10 | 0.963076 | 0.481538 | − | 0.876425i | \(-0.340078\pi\) | ||||
0.481538 | + | 0.876425i | \(0.340078\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8.13784e9 | − | 1.08014e10i | −0.0895817 | − | 0.118902i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.29660e9 | − | 1.32594e9i | −0.0249161 | − | 0.0143853i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.11960e11 | + | 1.30567e11i | −1.19719 | + | 1.39615i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.52066e10 | − | 3.04961e10i | 0.160272 | − | 0.321419i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.48180e10 | − | 1.43287e10i | 0.257838 | − | 0.148863i | −0.365510 | − | 0.930807i | \(-0.619105\pi\) |
0.623348 | + | 0.781945i | \(0.285772\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.27082e11 | −1.30148 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.73891e9 | + | 6.11776e10i | 0.0377480 | + | 0.617648i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.03960e11 | − | 6.00214e10i | 1.03475 | − | 0.597410i | 0.116405 | − | 0.993202i | \(-0.462863\pi\) |
0.918340 | + | 0.395791i | \(0.129530\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.05271e10 | + | 1.04836e11i | −0.593959 | + | 1.02877i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.68596e10 | − | 8.63092e10i | −0.550138 | − | 0.835074i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.69153e11 | − | 9.76605e10i | −1.61373 | − | 0.931687i | −0.988496 | − | 0.151248i | \(-0.951671\pi\) |
−0.625233 | − | 0.780438i | \(-0.714996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.06566e10 | + | 1.05060e11i | 0.570603 | + | 0.988313i | 0.996504 | + | 0.0835434i | \(0.0266237\pi\) |
−0.425901 | + | 0.904770i | \(0.640043\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.90469e11 | − | 1.16407e10i | 1.76688 | − | 0.107984i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.69847e10i | 0.795740i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.93010e10 | + | 1.71994e11i | 0.895881 | + | 1.55171i | 0.832710 | + | 0.553709i | \(0.186788\pi\) |
0.0631706 | + | 0.998003i | \(0.479879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.78018e10 | + | 1.88495e10i | 0.336355 | + | 0.167720i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.06098e10 | + | 5.66230e10i | −0.0931113 | + | 0.496923i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.01871e10 | − | 8.69267e10i | 0.434428 | − | 0.752452i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.24717e11 | − | 9.39628e10i | 1.06489 | − | 0.802292i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.82000e10i | − | 0.405971i | −0.979182 | − | 0.202985i | \(-0.934936\pi\) | ||
0.979182 | − | 0.202985i | \(-0.0650644\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.25668e11 | 1.04415 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.91742e10 | − | 2.89719e10i | −0.157169 | − | 0.237480i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.84197e10 | − | 1.06346e10i | −0.148958 | − | 0.0860010i | 0.423669 | − | 0.905817i | \(-0.360742\pi\) |
−0.572627 | + | 0.819816i | \(0.694075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.29959e11 | − | 4.30887e10i | −1.83477 | − | 0.343792i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.73097e10 | − | 2.35905e10i | −0.372437 | − | 0.185712i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.52238e10 | + | 3.18835e10i | −0.428962 | + | 0.247661i | −0.698904 | − | 0.715215i | \(-0.746329\pi\) |
0.269942 | + | 0.962876i | \(0.412995\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.10722e10 | −0.544756 | −0.272378 | − | 0.962190i | \(-0.587810\pi\) | ||||
−0.272378 | + | 0.962190i | \(0.587810\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.42084e11 | − | 1.74322e10i | 1.07467 | − | 0.131851i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.25816e11 | + | 7.26396e10i | −0.939102 | + | 0.542191i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.65702e9 | + | 2.87004e9i | −0.0122060 | + | 0.0211414i | −0.872064 | − | 0.489392i | \(-0.837219\pi\) |
0.859858 | + | 0.510533i | \(0.170552\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.29551e9 | + | 3.06922e9i | 0.00941832 | + | 0.0223131i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.99239e10 | + | 4.61441e10i | 0.573471 | + | 0.331094i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.59650e10 | − | 4.49727e10i | −0.183885 | − | 0.318498i | 0.759315 | − | 0.650723i | \(-0.225534\pi\) |
−0.943200 | + | 0.332225i | \(0.892201\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.78693e9 | − | 2.92385e10i | −0.0124913 | − | 0.204387i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.76641e11i | 1.21885i | 0.792843 | + | 0.609426i | \(0.208600\pi\) | ||||
−0.792843 | + | 0.609426i | \(0.791400\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.33248e10 | − | 2.30792e10i | −0.0907607 | − | 0.157202i | 0.817071 | − | 0.576537i | \(-0.195597\pi\) |
−0.907831 | + | 0.419335i | \(0.862263\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.62106e10 | − | 1.30437e11i | 0.310724 | − | 0.877068i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3.70462e10 | − | 3.17668e10i | −0.245919 | − | 0.210873i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.57421e10 | − | 1.48510e11i | 0.561920 | − | 0.973273i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.57493e10 | + | 6.91266e10i | 0.296015 | + | 0.447276i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.65692e10i | 0.361391i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.36815e10 | 0.275537 | 0.137768 | − | 0.990464i | \(-0.456007\pi\) | ||||
0.137768 | + | 0.990464i | \(0.456007\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3.33994e10 | + | 2.21043e10i | −0.208029 | + | 0.137677i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.94363e11 | − | 1.69951e11i | −1.81046 | − | 1.04527i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.50238e11 | + | 5.83505e10i | 0.912474 | + | 0.354394i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.44959e11 | − | 1.04006e11i | −1.46923 | − | 0.623813i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.82752e10 | + | 5.67392e10i | −0.582119 | + | 0.336086i | −0.761975 | − | 0.647606i | \(-0.775770\pi\) |
0.179856 | + | 0.983693i | \(0.442437\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.06840e11 | −0.625017 | −0.312509 | − | 0.949915i | \(-0.601169\pi\) | ||||
−0.312509 | + | 0.949915i | \(0.601169\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.12847e11 | + | 1.91199e10i | −1.80756 | + | 0.110470i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.63667e11 | + | 9.44929e10i | −0.933991 | + | 0.539240i | −0.888072 | − | 0.459705i | \(-0.847955\pi\) |
−0.0459197 | + | 0.998945i | \(0.514622\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.27749e10 | − | 3.94473e10i | 0.128374 | − | 0.222351i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.25890e11 | − | 9.52631e10i | −0.700917 | − | 0.530397i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.67148e11 | + | 9.65027e10i | 0.919279 | + | 0.530746i | 0.883405 | − | 0.468610i | \(-0.155245\pi\) |
0.0358742 | + | 0.999356i | \(0.488578\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.38215e11 | − | 2.39396e11i | −0.750916 | − | 1.30062i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.86134e11 | + | 3.51057e10i | −1.53571 | + | 0.188415i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 2.01067e11i | − | 1.06610i | −0.846083 | − | 0.533051i | \(-0.821045\pi\) | ||
0.846083 | − | 0.533051i | \(-0.178955\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.75229e10 | + | 3.03506e10i | 0.0917912 | + | 0.158987i | 0.908265 | − | 0.418396i | \(-0.137407\pi\) |
−0.816474 | + | 0.577383i | \(0.804074\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.15673e11 | + | 2.31977e11i | −0.598657 | + | 1.20058i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.98480e11 | + | 1.05037e11i | −1.52626 | + | 0.537098i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.23020e9 | + | 3.86283e9i | −0.0112679 | + | 0.0195165i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.92635e10 | + | 2.59853e10i | −0.196013 | + | 0.129725i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.36260e10i | − | 0.0672171i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00983e9 | 0.00979714 | 0.00489857 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489857 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.35013e11 | − | 1.15279e11i | 0.650370 | − | 0.555311i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.07359e11 | + | 1.19719e11i | 0.987117 | + | 0.569912i | 0.904411 | − | 0.426662i | \(-0.140311\pi\) |
0.0827056 | + | 0.996574i | \(0.473644\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.40006e8 | + | 1.19922e8i | 0.00301096 | + | 0.000564181i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.77129e10 | + | 1.95959e11i | −0.454322 | + | 0.911122i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.23598e10 | + | 2.44564e10i | −0.194657 | + | 0.112385i | −0.594161 | − | 0.804346i | \(-0.702516\pi\) |
0.399504 | + | 0.916732i | \(0.369182\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.85829e11 | 1.29821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.51286e10 | + | 4.11165e11i | 0.112809 | + | 1.84582i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.67634e11 | − | 2.12254e11i | 1.63132 | − | 0.941842i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.06906e10 | − | 1.85167e10i | 0.0468913 | − | 0.0812180i | −0.841627 | − | 0.540059i | \(-0.818402\pi\) |
0.888518 | + | 0.458841i | \(0.151735\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.57169e9 | − | 1.03929e11i | 0.0284934 | − | 0.450612i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.47242e11 | − | 2.00480e11i | −1.48831 | − | 0.859275i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.43137e10 | + | 4.21126e10i | 0.103020 | + | 0.178435i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.75779e11 | − | 1.68544e10i | 1.15519 | − | 0.0706002i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23088e11i | 0.509732i | 0.966976 | + | 0.254866i | \(0.0820314\pi\) | ||||
−0.966976 | + | 0.254866i | \(0.917969\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.82537e10 | + | 6.62574e10i | 0.156622 | + | 0.271277i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.03697e11 | + | 1.01571e11i | 0.824570 | + | 0.411163i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.71645e11 | + | 6.04025e10i | −0.686993 | + | 0.241756i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.18701e10 | − | 7.25211e10i | 0.165699 | − | 0.286998i | −0.771205 | − | 0.636587i | \(-0.780345\pi\) |
0.936903 | + | 0.349589i | \(0.113679\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.82818e11 | + | 3.75385e11i | 1.10670 | + | 1.46892i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.11371e11i | − | 0.817875i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.57332e11 | 0.601995 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.77046e11 | − | 4.18613e11i | −1.04827 | − | 1.58393i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.23400e11 | + | 1.28980e11i | 0.835924 | + | 0.482621i | 0.855877 | − | 0.517180i | \(-0.173018\pi\) |
−0.0199527 | + | 0.999801i | \(0.506352\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.11977e11 | − | 2.47206e11i | 0.784418 | − | 0.914782i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.96752e11 | − | 1.97837e11i | −1.45200 | − | 0.724025i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.95574e9 | + | 2.86120e9i | −0.0179373 | + | 0.0103561i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.25752e10 | 0.331403 | 0.165702 | − | 0.986176i | \(-0.447011\pi\) | ||||
0.165702 | + | 0.986176i | \(0.447011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.63699e11 | + | 1.01140e11i | −0.933681 | + | 0.358106i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.50598e11 | − | 2.60153e11i | 1.57805 | − | 0.911086i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.60331e11 | − | 2.77702e11i | 0.555396 | − | 0.961973i | −0.442477 | − | 0.896780i | \(-0.645900\pi\) |
0.997873 | − | 0.0651935i | \(-0.0207665\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.78629e11 | + | 1.21042e11i | 1.29737 | + | 0.414749i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.24908e11 | + | 7.21156e10i | 0.423370 | + | 0.244433i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.36210e9 | + | 1.27515e10i | 0.0246845 | + | 0.0427547i | 0.878104 | − | 0.478470i | \(-0.158809\pi\) |
−0.853419 | + | 0.521225i | \(0.825475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.13861e10 | + | 3.49928e11i | 0.0709346 | + | 1.16066i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.44534e11i | 0.802387i | 0.915993 | + | 0.401194i | \(0.131405\pi\) | ||||
−0.915993 | + | 0.401194i | \(0.868595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.02371e11 | + | 3.50517e11i | 0.656936 | + | 1.13785i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.44902e11 | + | 6.15231e10i | 0.465362 | + | 0.197586i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.32706e11 | − | 1.13794e11i | −0.421662 | − | 0.361571i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.11817e10 | + | 1.57931e11i | −0.286647 | + | 0.496488i | −0.973007 | − | 0.230774i | \(-0.925874\pi\) |
0.686360 | + | 0.727262i | \(0.259208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.71643e11 | − | 2.59351e11i | −0.533883 | − | 0.806692i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 6.30170e11i | − | 1.93941i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.11403e11 | −0.339246 | −0.169623 | − | 0.985509i | \(-0.554255\pi\) | ||||
−0.169623 | + | 0.985509i | \(0.554255\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.16269e11 | − | 7.69491e10i | 0.350346 | − | 0.231866i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.50095e11 | + | 2.59863e11i | 1.34204 | + | 0.774828i | 0.987107 | − | 0.160063i | \(-0.0511698\pi\) |
0.354935 | + | 0.934891i | \(0.384503\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.18238e10 | − | 3.35994e10i | −0.0348866 | − | 0.0991364i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.49859e11 | + | 5.88478e11i | −0.729540 | + | 1.71824i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.66832e11 | − | 9.63207e10i | 0.482058 | − | 0.278316i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.18834e11 | −0.339809 | −0.169904 | − | 0.985461i | \(-0.554346\pi\) | ||||
−0.169904 | + | 0.985461i | \(0.554346\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.38752e11 | + | 3.90378e10i | −1.80765 | + | 0.110476i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.80476e11 | − | 3.35138e11i | 1.62580 | − | 0.938654i | 0.640467 | − | 0.767986i | \(-0.278741\pi\) |
0.985329 | − | 0.170668i | \(-0.0545925\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.35587e11 | − | 2.34844e11i | 0.375848 | − | 0.650987i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.19054e10 | − | 9.53724e10i | 0.0326633 | − | 0.261661i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.69555e10 | + | 3.28833e10i | 0.154663 | + | 0.0892946i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.34068e11 | − | 2.32212e11i | −0.360346 | − | 0.624138i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.95133e9 | − | 1.65773e9i | 0.0238144 | − | 0.00441029i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.97231e11i | 2.36279i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.40529e10 | − | 1.45584e11i | −0.219106 | − | 0.379503i | 0.735429 | − | 0.677602i | \(-0.236981\pi\) |
−0.954535 | + | 0.298099i | \(0.903647\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.33190e11 | + | 2.67107e11i | −0.343688 | + | 0.689251i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.28808e10 | + | 3.35587e11i | −0.160625 | + | 0.857232i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.88139e10 | − | 4.99072e10i | 0.0728634 | − | 0.126203i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.73096e11 | − | 5.77831e11i | 2.18571 | − | 1.44655i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.40452e11i | − | 1.33944i | −0.742613 | − | 0.669721i | \(-0.766414\pi\) | ||
0.742613 | − | 0.669721i | \(-0.233586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.77851e11 | −0.927114 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.06509e11 | + | 8.02448e10i | −0.258736 | + | 0.194934i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.51544e11 | − | 1.45229e11i | −0.604995 | − | 0.349294i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.76669e11 | + | 5.02035e11i | 0.420703 | + | 1.19550i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.63892e11 | + | 3.28679e11i | −0.386424 | + | 0.774956i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.00440e11 | − | 5.79890e10i | 0.234484 | − | 0.135379i | −0.378155 | − | 0.925742i | \(-0.623441\pi\) |
0.612639 | + | 0.790363i | \(0.290108\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.67234e11 | −0.386581 | −0.193291 | − | 0.981142i | \(-0.561916\pi\) | ||||
−0.193291 | + | 0.981142i | \(0.561916\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.60795e10 | − | 5.90347e11i | −0.0825844 | − | 1.35128i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.08860e11 | + | 1.78321e11i | −0.700054 | + | 0.404176i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.51846e11 | − | 6.09415e11i | 0.789704 | − | 1.36781i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.43840e11 | − | 3.66756e11i | 0.541962 | − | 0.815158i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.33030e10 | + | 4.23215e10i | 0.161343 | + | 0.0931511i | 0.578497 | − | 0.815684i | \(-0.303639\pi\) |
−0.417155 | + | 0.908835i | \(0.636973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.94981e11 | − | 3.37717e11i | −0.425003 | − | 0.736127i | 0.571417 | − | 0.820660i | \(-0.306394\pi\) |
−0.996421 | + | 0.0845322i | \(0.973060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.78541e11 | − | 1.09117e10i | 0.385410 | − | 0.0235546i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.78023e9i | 0.0123573i | 0.999981 | + | 0.00617865i | \(0.00196674\pi\) | ||||
−0.999981 | + | 0.00617865i | \(0.998033\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.50699e11 | + | 4.34223e11i | 0.530803 | + | 0.919378i | 0.999354 | + | 0.0359417i | \(0.0114431\pi\) |
−0.468551 | + | 0.883437i | \(0.655224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.32362e10 | + | 6.60009e9i | 0.0277561 | + | 0.0138403i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.52151e11 | + | 1.00660e11i | −1.35447 | + | 0.209063i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.23635e11 | − | 7.33757e11i | 0.871457 | − | 1.50941i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.28079e11 | + | 2.80126e11i | −0.668461 | + | 0.570758i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.71109e11i | 1.75802i | 0.476799 | + | 0.879012i | \(0.341797\pi\) | ||||
−0.476799 | + | 0.879012i | \(0.658203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.99953e11 | 0.999413 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.24870e10 | + | 3.39775e10i | 0.0445267 | + | 0.0672793i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.51349e10 | − | 1.45116e10i | −0.0493004 | − | 0.0284636i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.66726e11 | + | 3.11054e11i | −0.518240 | + | 0.604368i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.27733e11 | − | 1.63421e11i | −0.630796 | − | 0.314540i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.11443e11 | − | 6.43417e10i | 0.212488 | − | 0.122680i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.38766e10 | −0.177321 | −0.0886607 | − | 0.996062i | \(-0.528259\pi\) | ||||
−0.0886607 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.05295e11 | + | 8.58223e11i | 0.197035 | + | 1.60596i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.94371e11 | − | 2.85425e11i | 0.916494 | − | 0.529138i | 0.0339790 | − | 0.999423i | \(-0.489182\pi\) |
0.882515 | + | 0.470285i | \(0.155849\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.81322e11 | − | 3.14059e11i | 0.333026 | − | 0.576818i | −0.650078 | − | 0.759868i | \(-0.725264\pi\) |
0.983104 | + | 0.183050i | \(0.0585970\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.21286e10 | − | 7.61164e10i | −0.0584628 | − | 0.138505i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.17513e11 | − | 3.56521e11i | −1.11328 | − | 0.642750i | −0.173600 | − | 0.984816i | \(-0.555540\pi\) |
−0.939676 | + | 0.342066i | \(0.888873\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.84927e11 | + | 1.01312e12i | 1.04481 | + | 1.80966i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.02731e10 | − | 4.95340e11i | −0.0535772 | − | 0.876652i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.73552e11i | 0.830403i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.04994e11 | + | 5.28265e11i | 0.529931 | + | 0.917867i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.95390e8 | − | 1.63781e9i | 0.00119721 | − | 0.00281972i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.12932e10 | − | 1.13639e11i | 0.0363253 | − | 0.193863i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.99463e11 | − | 6.91889e11i | 0.675270 | − | 1.16960i | −0.301119 | − | 0.953586i | \(-0.597360\pi\) |
0.976390 | − | 0.216016i | \(-0.0693064\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.98204e10 | − | 2.99484e10i | −0.0332014 | − | 0.0501670i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.69821e10i | − | 0.127787i | −0.997957 | − | 0.0638934i | \(-0.979648\pi\) | ||
0.997957 | − | 0.0638934i | \(-0.0203518\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.26548e11 | 0.208168 | 0.104084 | − | 0.994569i | \(-0.466809\pi\) | ||||
0.104084 | + | 0.994569i | \(0.466809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.96211e11 | − | 2.62220e11i | 0.645882 | − | 0.427457i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.27221e11 | − | 7.34509e10i | −0.205524 | − | 0.118659i | 0.393705 | − | 0.919237i | \(-0.371193\pi\) |
−0.599230 | + | 0.800577i | \(0.704526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.42274e11 | − | 1.76559e11i | −1.50859 | − | 0.282673i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.73526e11 | − | 7.84877e10i | −0.433998 | − | 0.124535i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.42562e11 | + | 2.55513e11i | −0.695935 | + | 0.401798i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.46033e11 | −1.16270 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.88569e11 | − | 3.59708e10i | 0.909134 | − | 0.0555623i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.20423e10 | − | 6.95265e9i | 0.0184362 | − | 0.0106442i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.69019e11 | + | 1.50518e12i | −1.31865 | + | 2.28397i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.14434e11 | + | 3.43771e11i | −1.22491 | + | 0.517034i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.07924e12 | − | 6.23098e11i | −1.60888 | − | 0.928885i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.68384e11 | − | 6.38059e11i | −0.544341 | − | 0.942827i | −0.998648 | − | 0.0519816i | \(-0.983446\pi\) |
0.454307 | − | 0.890845i | \(-0.349887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.05512e10 | + | 4.93532e11i | 0.0886885 | + | 0.722869i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.34089e11i | 0.920612i | 0.887760 | + | 0.460306i | \(0.152260\pi\) | ||||
−0.887760 | + | 0.460306i | \(0.847740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.93057e10 | + | 1.37361e11i | 0.114136 | + | 0.197689i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.34245e10 | − | 1.27195e11i | 0.0904842 | − | 0.181462i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.91859e11 | − | 5.07514e11i | −0.837030 | − | 0.717745i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.08020e11 | − | 3.60301e11i | 0.291637 | − | 0.505131i | −0.682560 | − | 0.730830i | \(-0.739133\pi\) |
0.974197 | + | 0.225699i | \(0.0724666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.13802e11 | + | 4.06226e11i | −0.853081 | + | 0.564584i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.13401e12i | − | 1.56246i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.65092e11 | 0.225507 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.35466e11 | − | 7.10726e11i | −0.725125 | − | 0.962461i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.30922e11 | + | 1.91058e11i | 0.444287 | + | 0.256509i | 0.705414 | − | 0.708795i | \(-0.250761\pi\) |
−0.261128 | + | 0.965304i | \(0.584094\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.95771e11 | + | 5.58903e11i | −0.926121 | + | 0.743940i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 5.77805e10 | − | 1.15876e11i | 0.0762526 | − | 0.152921i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.57856e11 | + | 3.22078e11i | −0.729920 | + | 0.421420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.02637e12 | −1.33151 | −0.665754 | − | 0.746171i | \(-0.731890\pi\) | ||||
−0.665754 | + | 0.746171i | \(0.731890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.37525e10 | + | 7.15896e11i | 0.0562782 | + | 0.920847i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −6.43853e11 | + | 3.71729e11i | −0.821161 | + | 0.474098i | −0.850817 | − | 0.525462i | \(-0.823892\pi\) |
0.0296554 | + | 0.999560i | \(0.490559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.53088e10 | − | 9.57976e10i | 0.0699435 | − | 0.121146i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.45097e11 | − | 9.39555e11i | 0.683513 | − | 1.17813i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.10236e12 | + | 6.36445e11i | 1.37064 | + | 0.791337i | 0.991008 | − | 0.133803i | \(-0.0427189\pi\) |
0.379627 | + | 0.925140i | \(0.376052\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.14209e11 | − | 1.06384e12i | −0.757271 | − | 1.31163i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.40872e12 | − | 8.60950e10i | 1.72228 | − | 0.105258i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.33087e12i | − | 1.61348i | −0.590904 | − | 0.806742i | \(-0.701229\pi\) | ||
0.590904 | − | 0.806742i | \(-0.298771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.00275e12 | + | 1.73682e12i | 1.20554 | + | 2.08805i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.20845e9 | + | 4.09306e9i | 0.00978618 | + | 0.00487978i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.60453e11 | − | 2.67607e11i | 0.899079 | − | 0.316390i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.69716e10 | − | 1.67960e11i | 0.113698 | − | 0.196930i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.81535e11 | + | 2.87451e11i | −0.443639 | + | 0.334241i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.43936e11i | 0.511931i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.91088e10 | 0.0218538 | 0.0109269 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109269 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.92174e11 | − | 1.19697e12i | −0.898516 | − | 1.35765i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.06433e11 | + | 4.07859e11i | 0.794683 | + | 0.458810i | 0.841609 | − | 0.540088i | \(-0.181609\pi\) |
−0.0469256 | + | 0.998898i | \(0.514942\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.11154e12 | − | 2.08276e11i | −1.24015 | − | 0.232374i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6.77005e11 | + | 3.37582e11i | 0.749158 | + | 0.373560i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.55698e11 | − | 3.78567e11i | 0.719657 | − | 0.415494i | −0.0949697 | − | 0.995480i | \(-0.530275\pi\) |
0.814626 | + | 0.579986i | \(0.196942\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.34362e11 | −0.146267 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.66087e10 | + | 1.18529e10i | −0.104313 | + | 0.0127982i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.45625e11 | + | 2.57281e11i | −0.477260 | + | 0.275546i | −0.719274 | − | 0.694727i | \(-0.755525\pi\) |
0.242014 | + | 0.970273i | \(0.422192\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.82565e11 | − | 3.16211e11i | 0.193942 | − | 0.335917i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.37034e11 | + | 7.95215e10i | 0.671265 | + | 0.0837946i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.02502e12 | − | 5.91796e11i | −1.07139 | − | 0.618567i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.18738e11 | + | 2.05661e11i | 0.123111 | + | 0.213234i | 0.920993 | − | 0.389579i | \(-0.127380\pi\) |
−0.797882 | + | 0.602814i | \(0.794046\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −9.07793e10 | − | 1.48537e12i | −0.0933662 | − | 1.52770i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 5.55596e11i | − | 0.566848i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.37631e11 | − | 5.84795e11i | −0.341713 | − | 0.591865i | 0.643038 | − | 0.765835i | \(-0.277674\pi\) |
−0.984751 | + | 0.173970i | \(0.944341\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.47562e11 | − | 8.77053e10i | −0.248554 | − | 0.0880570i |
(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.p.b.65.17 | yes | 40 | |
3.2 | odd | 2 | inner | 84.9.p.b.65.3 | yes | 40 | |
7.4 | even | 3 | inner | 84.9.p.b.53.3 | ✓ | 40 | |
21.11 | odd | 6 | inner | 84.9.p.b.53.17 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.p.b.53.3 | ✓ | 40 | 7.4 | even | 3 | inner | |
84.9.p.b.53.17 | yes | 40 | 21.11 | odd | 6 | inner | |
84.9.p.b.65.3 | yes | 40 | 3.2 | odd | 2 | inner | |
84.9.p.b.65.17 | yes | 40 | 1.1 | even | 1 | trivial |