Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,9,Mod(23,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.23");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4434941320\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 23.21 | ||
Character | \(\chi\) | \(=\) | 33.23 |
Dual form | 33.9.b.a.23.6 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 17.8320i | 1.11450i | 0.830346 | + | 0.557249i | \(0.188143\pi\) | ||||
−0.830346 | + | 0.557249i | \(0.811857\pi\) | |||||||
\(3\) | 18.7312 | + | 78.8045i | 0.231249 | + | 0.972895i | ||||
\(4\) | −61.9787 | −0.242104 | ||||||||
\(5\) | 794.590i | 1.27134i | 0.771959 | + | 0.635672i | \(0.219277\pi\) | ||||
−0.771959 | + | 0.635672i | \(0.780723\pi\) | |||||||
\(6\) | −1405.24 | + | 334.014i | −1.08429 | + | 0.257727i | ||||
\(7\) | 2438.07 | 1.01544 | 0.507721 | − | 0.861522i | \(-0.330488\pi\) | ||||
0.507721 | + | 0.861522i | \(0.330488\pi\) | |||||||
\(8\) | 3459.78i | 0.844673i | ||||||||
\(9\) | −5859.29 | + | 2952.20i | −0.893048 | + | 0.449962i | ||||
\(10\) | −14169.1 | −1.41691 | ||||||||
\(11\) | 4414.43i | 0.301511i | ||||||||
\(12\) | −1160.94 | − | 4884.20i | −0.0559865 | − | 0.235542i | ||||
\(13\) | 43779.7 | 1.53285 | 0.766425 | − | 0.642334i | \(-0.222034\pi\) | ||||
0.766425 | + | 0.642334i | \(0.222034\pi\) | |||||||
\(14\) | 43475.6i | 1.13171i | ||||||||
\(15\) | −62617.2 | + | 14883.6i | −1.23688 | + | 0.293997i | ||||
\(16\) | −77561.2 | −1.18349 | ||||||||
\(17\) | − | 149669.i | − | 1.79199i | −0.444066 | − | 0.895994i | \(-0.646464\pi\) | ||
0.444066 | − | 0.895994i | \(-0.353536\pi\) | |||||||
\(18\) | −52643.6 | − | 104483.i | −0.501482 | − | 0.995299i | ||||
\(19\) | −17473.1 | −0.134078 | −0.0670389 | − | 0.997750i | \(-0.521355\pi\) | ||||
−0.0670389 | + | 0.997750i | \(0.521355\pi\) | |||||||
\(20\) | − | 49247.7i | − | 0.307798i | ||||||
\(21\) | 45668.0 | + | 192131.i | 0.234820 | + | 0.987917i | ||||
\(22\) | −78717.9 | −0.336034 | ||||||||
\(23\) | − | 463124.i | − | 1.65495i | −0.561500 | − | 0.827477i | \(-0.689776\pi\) | ||
0.561500 | − | 0.827477i | \(-0.310224\pi\) | |||||||
\(24\) | −272646. | + | 64805.8i | −0.821777 | + | 0.195330i | ||||
\(25\) | −240748. | −0.616315 | ||||||||
\(26\) | 780678.i | 1.70836i | ||||||||
\(27\) | −342398. | − | 406440.i | −0.644282 | − | 0.764788i | ||||
\(28\) | −151109. | −0.245843 | ||||||||
\(29\) | 499557.i | 0.706307i | 0.935565 | + | 0.353153i | \(0.114891\pi\) | ||||
−0.935565 | + | 0.353153i | \(0.885109\pi\) | |||||||
\(30\) | −265404. | − | 1.11659e6i | −0.327659 | − | 1.37850i | ||||
\(31\) | 137455. | 0.148838 | 0.0744189 | − | 0.997227i | \(-0.476290\pi\) | ||||
0.0744189 | + | 0.997227i | \(0.476290\pi\) | |||||||
\(32\) | − | 497364.i | − | 0.474324i | ||||||
\(33\) | −347877. | + | 82687.5i | −0.293339 | + | 0.0697243i | ||||
\(34\) | 2.66889e6 | 1.99717 | ||||||||
\(35\) | 1.93727e6i | 1.29098i | ||||||||
\(36\) | 363151. | − | 182974.i | 0.216211 | − | 0.108938i | ||||
\(37\) | 564033. | 0.300952 | 0.150476 | − | 0.988614i | \(-0.451919\pi\) | ||||
0.150476 | + | 0.988614i | \(0.451919\pi\) | |||||||
\(38\) | − | 311580.i | − | 0.149429i | ||||||
\(39\) | 820046. | + | 3.45004e6i | 0.354470 | + | 1.49130i | ||||
\(40\) | −2.74911e6 | −1.07387 | ||||||||
\(41\) | − | 376771.i | − | 0.133334i | −0.997775 | − | 0.0666672i | \(-0.978763\pi\) | ||
0.997775 | − | 0.0666672i | \(-0.0212366\pi\) | |||||||
\(42\) | −3.42607e6 | + | 814351.i | −1.10103 | + | 0.261706i | ||||
\(43\) | 5.67728e6 | 1.66061 | 0.830303 | − | 0.557312i | \(-0.188167\pi\) | ||||
0.830303 | + | 0.557312i | \(0.188167\pi\) | |||||||
\(44\) | − | 273601.i | − | 0.0729972i | ||||||
\(45\) | −2.34579e6 | − | 4.65573e6i | −0.572057 | − | 1.13537i | ||||
\(46\) | 8.25840e6 | 1.84444 | ||||||||
\(47\) | 9.56433e6i | 1.96003i | 0.198919 | + | 0.980016i | \(0.436257\pi\) | ||||
−0.198919 | + | 0.980016i | \(0.563743\pi\) | |||||||
\(48\) | −1.45281e6 | − | 6.11217e6i | −0.273681 | − | 1.15141i | ||||
\(49\) | 179407. | 0.0311211 | ||||||||
\(50\) | − | 4.29301e6i | − | 0.686882i | ||||||
\(51\) | 1.17946e7 | − | 2.80347e6i | 1.74342 | − | 0.414396i | ||||
\(52\) | −2.71341e6 | −0.371109 | ||||||||
\(53\) | − | 4.43429e6i | − | 0.561980i | −0.959711 | − | 0.280990i | \(-0.909337\pi\) | ||
0.959711 | − | 0.280990i | \(-0.0906628\pi\) | |||||||
\(54\) | 7.24761e6 | − | 6.10563e6i | 0.852354 | − | 0.718051i | ||||
\(55\) | −3.50766e6 | −0.383325 | ||||||||
\(56\) | 8.43520e6i | 0.857716i | ||||||||
\(57\) | −327293. | − | 1.37696e6i | −0.0310054 | − | 0.130443i | ||||
\(58\) | −8.90809e6 | −0.787177 | ||||||||
\(59\) | − | 2.31520e6i | − | 0.191065i | −0.995426 | − | 0.0955323i | \(-0.969545\pi\) | ||
0.995426 | − | 0.0955323i | \(-0.0304553\pi\) | |||||||
\(60\) | 3.88094e6 | − | 922467.i | 0.299455 | − | 0.0711780i | ||||
\(61\) | −2.29915e7 | −1.66054 | −0.830268 | − | 0.557365i | \(-0.811813\pi\) | ||||
−0.830268 | + | 0.557365i | \(0.811813\pi\) | |||||||
\(62\) | 2.45109e6i | 0.165879i | ||||||||
\(63\) | −1.42854e7 | + | 7.19769e6i | −0.906837 | + | 0.456910i | ||||
\(64\) | −1.09867e7 | −0.654857 | ||||||||
\(65\) | 3.47869e7i | 1.94878i | ||||||||
\(66\) | −1.47448e6 | − | 6.20332e6i | −0.0777075 | − | 0.326925i | ||||
\(67\) | 7.17358e6 | 0.355989 | 0.177995 | − | 0.984031i | \(-0.443039\pi\) | ||||
0.177995 | + | 0.984031i | \(0.443039\pi\) | |||||||
\(68\) | 9.27627e6i | 0.433848i | ||||||||
\(69\) | 3.64962e7 | − | 8.67486e6i | 1.61010 | − | 0.382707i | ||||
\(70\) | −3.45453e7 | −1.43879 | ||||||||
\(71\) | 3.78446e6i | 0.148926i | 0.997224 | + | 0.0744630i | \(0.0237243\pi\) | ||||
−0.997224 | + | 0.0744630i | \(0.976276\pi\) | |||||||
\(72\) | −1.02140e7 | − | 2.02718e7i | −0.380071 | − | 0.754333i | ||||
\(73\) | −9.80584e6 | −0.345297 | −0.172649 | − | 0.984983i | \(-0.555233\pi\) | ||||
−0.172649 | + | 0.984983i | \(0.555233\pi\) | |||||||
\(74\) | 1.00578e7i | 0.335410i | ||||||||
\(75\) | −4.50950e6 | − | 1.89720e7i | −0.142522 | − | 0.599610i | ||||
\(76\) | 1.08296e6 | 0.0324608 | ||||||||
\(77\) | 1.07627e7i | 0.306167i | ||||||||
\(78\) | −6.15209e7 | + | 1.46230e7i | −1.66205 | + | 0.395056i | ||||
\(79\) | 1.13989e6 | 0.0292653 | 0.0146327 | − | 0.999893i | \(-0.495342\pi\) | ||||
0.0146327 | + | 0.999893i | \(0.495342\pi\) | |||||||
\(80\) | − | 6.16293e7i | − | 1.50462i | ||||||
\(81\) | 2.56157e7 | − | 3.45956e7i | 0.595068 | − | 0.803675i | ||||
\(82\) | 6.71856e6 | 0.148601 | ||||||||
\(83\) | − | 2.95242e7i | − | 0.622109i | −0.950392 | − | 0.311054i | \(-0.899318\pi\) | ||
0.950392 | − | 0.311054i | \(-0.100682\pi\) | |||||||
\(84\) | −2.83045e6 | − | 1.19080e7i | −0.0568510 | − | 0.239179i | ||||
\(85\) | 1.18925e8 | 2.27823 | ||||||||
\(86\) | 1.01237e8i | 1.85074i | ||||||||
\(87\) | −3.93673e7 | + | 9.35730e6i | −0.687162 | + | 0.163333i | ||||
\(88\) | −1.52729e7 | −0.254678 | ||||||||
\(89\) | − | 5.92978e7i | − | 0.945101i | −0.881303 | − | 0.472551i | \(-0.843333\pi\) | ||
0.881303 | − | 0.472551i | \(-0.156667\pi\) | |||||||
\(90\) | 8.30208e7 | − | 4.18300e7i | 1.26537 | − | 0.637556i | ||||
\(91\) | 1.06738e8 | 1.55652 | ||||||||
\(92\) | 2.87038e7i | 0.400671i | ||||||||
\(93\) | 2.57469e6 | + | 1.08321e7i | 0.0344186 | + | 0.144804i | ||||
\(94\) | −1.70551e8 | −2.18445 | ||||||||
\(95\) | − | 1.38840e7i | − | 0.170459i | ||||||
\(96\) | 3.91945e7 | − | 9.31623e6i | 0.461467 | − | 0.109687i | ||||
\(97\) | 7.89069e7 | 0.891309 | 0.445654 | − | 0.895205i | \(-0.352971\pi\) | ||||
0.445654 | + | 0.895205i | \(0.352971\pi\) | |||||||
\(98\) | 3.19918e6i | 0.0346844i | ||||||||
\(99\) | −1.30323e7 | − | 2.58654e7i | −0.135669 | − | 0.269264i | ||||
\(100\) | 1.49213e7 | 0.149213 | ||||||||
\(101\) | 5.31378e7i | 0.510644i | 0.966856 | + | 0.255322i | \(0.0821815\pi\) | ||||
−0.966856 | + | 0.255322i | \(0.917819\pi\) | |||||||
\(102\) | 4.99914e7 | + | 2.10320e8i | 0.461843 | + | 1.94303i | ||||
\(103\) | −7.34994e6 | −0.0653032 | −0.0326516 | − | 0.999467i | \(-0.510395\pi\) | ||||
−0.0326516 | + | 0.999467i | \(0.510395\pi\) | |||||||
\(104\) | 1.51468e8i | 1.29476i | ||||||||
\(105\) | −1.52665e8 | + | 3.62874e7i | −1.25598 | + | 0.298537i | ||||
\(106\) | 7.90721e7 | 0.626325 | ||||||||
\(107\) | − | 2.06587e7i | − | 0.157604i | −0.996890 | − | 0.0788022i | \(-0.974890\pi\) | ||
0.996890 | − | 0.0788022i | \(-0.0251096\pi\) | |||||||
\(108\) | 2.12214e7 | + | 2.51906e7i | 0.155984 | + | 0.185158i | ||||
\(109\) | 9.90700e7 | 0.701837 | 0.350918 | − | 0.936406i | \(-0.385869\pi\) | ||||
0.350918 | + | 0.936406i | \(0.385869\pi\) | |||||||
\(110\) | − | 6.25484e7i | − | 0.427214i | ||||||
\(111\) | 1.05650e7 | + | 4.44483e7i | 0.0695950 | + | 0.292795i | ||||
\(112\) | −1.89100e8 | −1.20176 | ||||||||
\(113\) | 6.46222e6i | 0.0396340i | 0.999804 | + | 0.0198170i | \(0.00630836\pi\) | ||||
−0.999804 | + | 0.0198170i | \(0.993692\pi\) | |||||||
\(114\) | 2.45539e7 | − | 5.83627e6i | 0.145379 | − | 0.0345554i | ||||
\(115\) | 3.67993e8 | 2.10401 | ||||||||
\(116\) | − | 3.09619e7i | − | 0.171000i | ||||||
\(117\) | −2.56518e8 | + | 1.29247e8i | −1.36891 | + | 0.689724i | ||||
\(118\) | 4.12845e7 | 0.212941 | ||||||||
\(119\) | − | 3.64903e8i | − | 1.81966i | ||||||
\(120\) | −5.14940e7 | − | 2.16642e8i | −0.248331 | − | 1.04476i | ||||
\(121\) | −1.94872e7 | −0.0909091 | ||||||||
\(122\) | − | 4.09984e8i | − | 1.85066i | ||||||
\(123\) | 2.96912e7 | − | 7.05737e6i | 0.129720 | − | 0.0308335i | ||||
\(124\) | −8.51928e6 | −0.0360343 | ||||||||
\(125\) | 1.19091e8i | 0.487795i | ||||||||
\(126\) | −1.28349e8 | − | 2.54736e8i | −0.509225 | − | 1.01067i | ||||
\(127\) | −3.58839e8 | −1.37938 | −0.689692 | − | 0.724103i | \(-0.742254\pi\) | ||||
−0.689692 | + | 0.724103i | \(0.742254\pi\) | |||||||
\(128\) | − | 3.23239e8i | − | 1.20416i | ||||||
\(129\) | 1.06342e8 | + | 4.47395e8i | 0.384014 | + | 1.61560i | ||||
\(130\) | −6.20319e8 | −2.17191 | ||||||||
\(131\) | 1.61346e8i | 0.547865i | 0.961749 | + | 0.273933i | \(0.0883245\pi\) | ||||
−0.961749 | + | 0.273933i | \(0.911675\pi\) | |||||||
\(132\) | 2.15609e7 | − | 5.12486e6i | 0.0710186 | − | 0.0168806i | ||||
\(133\) | −4.26008e7 | −0.136148 | ||||||||
\(134\) | 1.27919e8i | 0.396749i | ||||||||
\(135\) | 3.22953e8 | − | 2.72066e8i | 0.972308 | − | 0.819104i | ||||
\(136\) | 5.17821e8 | 1.51364 | ||||||||
\(137\) | 1.61874e8i | 0.459511i | 0.973248 | + | 0.229756i | \(0.0737927\pi\) | ||||
−0.973248 | + | 0.229756i | \(0.926207\pi\) | |||||||
\(138\) | 1.54690e8 | + | 6.50799e8i | 0.426526 | + | 1.79445i | ||||
\(139\) | −2.22110e8 | −0.594988 | −0.297494 | − | 0.954724i | \(-0.596151\pi\) | ||||
−0.297494 | + | 0.954724i | \(0.596151\pi\) | |||||||
\(140\) | − | 1.20069e8i | − | 0.312551i | ||||||
\(141\) | −7.53712e8 | + | 1.79151e8i | −1.90690 | + | 0.453256i | ||||
\(142\) | −6.74844e7 | −0.165978 | ||||||||
\(143\) | 1.93262e8i | 0.462171i | ||||||||
\(144\) | 4.54453e8 | − | 2.28976e8i | 1.05691 | − | 0.532526i | ||||
\(145\) | −3.96943e8 | −0.897959 | ||||||||
\(146\) | − | 1.74857e8i | − | 0.384833i | ||||||
\(147\) | 3.36050e6 | + | 1.41381e7i | 0.00719673 | + | 0.0302775i | ||||
\(148\) | −3.49580e7 | −0.0728618 | ||||||||
\(149\) | − | 1.98969e8i | − | 0.403683i | −0.979418 | − | 0.201842i | \(-0.935307\pi\) | ||
0.979418 | − | 0.201842i | \(-0.0646926\pi\) | |||||||
\(150\) | 3.38308e8 | − | 8.04132e7i | 0.668263 | − | 0.158841i | ||||
\(151\) | −8.07910e8 | −1.55401 | −0.777007 | − | 0.629492i | \(-0.783263\pi\) | ||||
−0.777007 | + | 0.629492i | \(0.783263\pi\) | |||||||
\(152\) | − | 6.04532e7i | − | 0.113252i | ||||||
\(153\) | 4.41852e8 | + | 8.76951e8i | 0.806327 | + | 1.60033i | ||||
\(154\) | −1.91920e8 | −0.341222 | ||||||||
\(155\) | 1.09220e8i | 0.189224i | ||||||||
\(156\) | −5.08254e7 | − | 2.13829e8i | −0.0858188 | − | 0.361050i | ||||
\(157\) | 7.01708e8 | 1.15494 | 0.577468 | − | 0.816413i | \(-0.304041\pi\) | ||||
0.577468 | + | 0.816413i | \(0.304041\pi\) | |||||||
\(158\) | 2.03264e7i | 0.0326162i | ||||||||
\(159\) | 3.49442e8 | − | 8.30596e7i | 0.546747 | − | 0.129957i | ||||
\(160\) | 3.95201e8 | 0.603028 | ||||||||
\(161\) | − | 1.12913e9i | − | 1.68051i | ||||||
\(162\) | 6.16907e8 | + | 4.56778e8i | 0.895694 | + | 0.663202i | ||||
\(163\) | 2.75803e8 | 0.390705 | 0.195353 | − | 0.980733i | \(-0.437415\pi\) | ||||
0.195353 | + | 0.980733i | \(0.437415\pi\) | |||||||
\(164\) | 2.33518e7i | 0.0322808i | ||||||||
\(165\) | −6.57026e7 | − | 2.76419e8i | −0.0886435 | − | 0.372934i | ||||
\(166\) | 5.26475e8 | 0.693338 | ||||||||
\(167\) | − | 7.99618e7i | − | 0.102806i | −0.998678 | − | 0.0514028i | \(-0.983631\pi\) | ||
0.998678 | − | 0.0514028i | \(-0.0163692\pi\) | |||||||
\(168\) | −6.64731e8 | + | 1.58001e8i | −0.834467 | + | 0.198346i | ||||
\(169\) | 1.10093e9 | 1.34963 | ||||||||
\(170\) | 2.12067e9i | 2.53909i | ||||||||
\(171\) | 1.02380e8 | − | 5.15843e7i | 0.119738 | − | 0.0603299i | ||||
\(172\) | −3.51871e8 | −0.402040 | ||||||||
\(173\) | − | 3.23146e7i | − | 0.0360756i | −0.999837 | − | 0.0180378i | \(-0.994258\pi\) | ||
0.999837 | − | 0.0180378i | \(-0.00574192\pi\) | |||||||
\(174\) | −1.66859e8 | − | 7.01997e8i | −0.182034 | − | 0.765840i | ||||
\(175\) | −5.86962e8 | −0.625832 | ||||||||
\(176\) | − | 3.42388e8i | − | 0.356836i | ||||||
\(177\) | 1.82448e8 | − | 4.33664e7i | 0.185886 | − | 0.0441835i | ||||
\(178\) | 1.05740e9 | 1.05331 | ||||||||
\(179\) | − | 1.32151e9i | − | 1.28723i | −0.765348 | − | 0.643617i | \(-0.777433\pi\) | ||
0.765348 | − | 0.643617i | \(-0.222567\pi\) | |||||||
\(180\) | 1.45389e8 | + | 2.88556e8i | 0.138497 | + | 0.274878i | ||||
\(181\) | −1.43857e9 | −1.34035 | −0.670173 | − | 0.742205i | \(-0.733780\pi\) | ||||
−0.670173 | + | 0.742205i | \(0.733780\pi\) | |||||||
\(182\) | 1.90335e9i | 1.73474i | ||||||||
\(183\) | −4.30658e8 | − | 1.81183e9i | −0.383998 | − | 1.61553i | ||||
\(184\) | 1.60231e9 | 1.39789 | ||||||||
\(185\) | 4.48175e8i | 0.382614i | ||||||||
\(186\) | −1.93157e8 | + | 4.59118e7i | −0.161383 | + | 0.0383595i | ||||
\(187\) | 6.60701e8 | 0.540305 | ||||||||
\(188\) | − | 5.92785e8i | − | 0.474532i | ||||||
\(189\) | −8.34792e8 | − | 9.90930e8i | −0.654231 | − | 0.776597i | ||||
\(190\) | 2.47579e8 | 0.189976 | ||||||||
\(191\) | − | 6.10916e8i | − | 0.459038i | −0.973304 | − | 0.229519i | \(-0.926285\pi\) | ||
0.973304 | − | 0.229519i | \(-0.0737152\pi\) | |||||||
\(192\) | −2.05794e8 | − | 8.65800e8i | −0.151435 | − | 0.637107i | ||||
\(193\) | 3.86706e8 | 0.278709 | 0.139355 | − | 0.990243i | \(-0.455497\pi\) | ||||
0.139355 | + | 0.990243i | \(0.455497\pi\) | |||||||
\(194\) | 1.40706e9i | 0.993361i | ||||||||
\(195\) | −2.74136e9 | + | 6.51600e8i | −1.89596 | + | 0.450654i | ||||
\(196\) | −1.11194e7 | −0.00753455 | ||||||||
\(197\) | 3.67511e8i | 0.244009i | 0.992530 | + | 0.122004i | \(0.0389322\pi\) | ||||
−0.992530 | + | 0.122004i | \(0.961068\pi\) | |||||||
\(198\) | 4.61231e8 | − | 2.32391e8i | 0.300094 | − | 0.151202i | ||||
\(199\) | −1.34145e8 | −0.0855387 | −0.0427693 | − | 0.999085i | \(-0.513618\pi\) | ||||
−0.0427693 | + | 0.999085i | \(0.513618\pi\) | |||||||
\(200\) | − | 8.32935e8i | − | 0.520585i | ||||||
\(201\) | 1.34370e8 | + | 5.65310e8i | 0.0823222 | + | 0.346340i | ||||
\(202\) | −9.47552e8 | −0.569111 | ||||||||
\(203\) | 1.21796e9i | 0.717213i | ||||||||
\(204\) | −7.31012e8 | + | 1.73756e8i | −0.422089 | + | 0.100327i | ||||
\(205\) | 2.99378e8 | 0.169514 | ||||||||
\(206\) | − | 1.31064e8i | − | 0.0727803i | ||||||
\(207\) | 1.36724e9 | + | 2.71357e9i | 0.744667 | + | 1.47795i | ||||
\(208\) | −3.39561e9 | −1.81411 | ||||||||
\(209\) | − | 7.71339e7i | − | 0.0404260i | ||||||
\(210\) | −6.47075e8 | − | 2.72232e9i | −0.332719 | − | 1.39979i | ||||
\(211\) | −3.26060e8 | −0.164501 | −0.0822504 | − | 0.996612i | \(-0.526211\pi\) | ||||
−0.0822504 | + | 0.996612i | \(0.526211\pi\) | |||||||
\(212\) | 2.74832e8i | 0.136058i | ||||||||
\(213\) | −2.98232e8 | + | 7.08875e7i | −0.144889 | + | 0.0344390i | ||||
\(214\) | 3.68386e8 | 0.175650 | ||||||||
\(215\) | 4.51111e9i | 2.11120i | ||||||||
\(216\) | 1.40619e9 | − | 1.18462e9i | 0.645995 | − | 0.544208i | ||||
\(217\) | 3.35125e8 | 0.151136 | ||||||||
\(218\) | 1.76661e9i | 0.782195i | ||||||||
\(219\) | −1.83675e8 | − | 7.72744e8i | −0.0798497 | − | 0.335938i | ||||
\(220\) | 2.17400e8 | 0.0928046 | ||||||||
\(221\) | − | 6.55245e9i | − | 2.74685i | ||||||
\(222\) | −7.92600e8 | + | 1.88395e8i | −0.326319 | + | 0.0775634i | ||||
\(223\) | −3.88094e9 | −1.56934 | −0.784671 | − | 0.619912i | \(-0.787168\pi\) | ||||
−0.784671 | + | 0.619912i | \(0.787168\pi\) | |||||||
\(224\) | − | 1.21261e9i | − | 0.481648i | ||||||
\(225\) | 1.41061e9 | − | 7.10737e8i | 0.550399 | − | 0.277319i | ||||
\(226\) | −1.15234e8 | −0.0441720 | ||||||||
\(227\) | − | 2.76866e9i | − | 1.04272i | −0.853338 | − | 0.521358i | \(-0.825426\pi\) | ||
0.853338 | − | 0.521358i | \(-0.174574\pi\) | |||||||
\(228\) | 2.02852e7 | + | 8.53423e7i | 0.00750654 | + | 0.0315809i | ||||
\(229\) | 4.15714e9 | 1.51165 | 0.755827 | − | 0.654771i | \(-0.227235\pi\) | ||||
0.755827 | + | 0.654771i | \(0.227235\pi\) | |||||||
\(230\) | 6.56204e9i | 2.34492i | ||||||||
\(231\) | −8.48149e8 | + | 2.01598e8i | −0.297868 | + | 0.0708009i | ||||
\(232\) | −1.72836e9 | −0.596598 | ||||||||
\(233\) | 1.25649e9i | 0.426321i | 0.977017 | + | 0.213161i | \(0.0683758\pi\) | ||||
−0.977017 | + | 0.213161i | \(0.931624\pi\) | |||||||
\(234\) | −2.30472e9 | − | 4.57421e9i | −0.768696 | − | 1.52564i | ||||
\(235\) | −7.59972e9 | −2.49187 | ||||||||
\(236\) | 1.43493e8i | 0.0462576i | ||||||||
\(237\) | 2.13515e7 | + | 8.98282e7i | 0.00676759 | + | 0.0284721i | ||||
\(238\) | 6.50694e9 | 2.02801 | ||||||||
\(239\) | 4.11430e9i | 1.26097i | 0.776202 | + | 0.630484i | \(0.217144\pi\) | ||||
−0.776202 | + | 0.630484i | \(0.782856\pi\) | |||||||
\(240\) | 4.85667e9 | − | 1.15439e9i | 1.46384 | − | 0.347943i | ||||
\(241\) | 4.78117e9 | 1.41731 | 0.708656 | − | 0.705554i | \(-0.249302\pi\) | ||||
0.708656 | + | 0.705554i | \(0.249302\pi\) | |||||||
\(242\) | − | 3.47494e8i | − | 0.101318i | ||||||
\(243\) | 3.20610e9 | + | 1.37062e9i | 0.919500 | + | 0.393089i | ||||
\(244\) | 1.42498e9 | 0.402023 | ||||||||
\(245\) | 1.42555e8i | 0.0395656i | ||||||||
\(246\) | 1.25847e8 | + | 5.29453e8i | 0.0343638 | + | 0.144573i | ||||
\(247\) | −7.64969e8 | −0.205521 | ||||||||
\(248\) | 4.75564e8i | 0.125719i | ||||||||
\(249\) | 2.32664e9 | − | 5.53024e8i | 0.605246 | − | 0.143862i | ||||
\(250\) | −2.12362e9 | −0.543647 | ||||||||
\(251\) | − | 6.21023e9i | − | 1.56463i | −0.622880 | − | 0.782317i | \(-0.714038\pi\) | ||
0.622880 | − | 0.782317i | \(-0.285962\pi\) | |||||||
\(252\) | 8.85389e8 | − | 4.46104e8i | 0.219549 | − | 0.110620i | ||||
\(253\) | 2.04443e9 | 0.498987 | ||||||||
\(254\) | − | 6.39881e9i | − | 1.53732i | ||||||
\(255\) | 2.22761e9 | + | 9.37184e9i | 0.526840 | + | 2.21648i | ||||
\(256\) | 2.95140e9 | 0.687176 | ||||||||
\(257\) | − | 4.23582e9i | − | 0.970967i | −0.874246 | − | 0.485484i | \(-0.838644\pi\) | ||
0.874246 | − | 0.485484i | \(-0.161356\pi\) | |||||||
\(258\) | −7.97793e9 | + | 1.89629e9i | −1.80058 | + | 0.427983i | ||||
\(259\) | 1.37515e9 | 0.305599 | ||||||||
\(260\) | − | 2.15605e9i | − | 0.471808i | ||||||
\(261\) | −1.47479e9 | − | 2.92705e9i | −0.317811 | − | 0.630766i | ||||
\(262\) | −2.87712e9 | −0.610594 | ||||||||
\(263\) | − | 3.17671e8i | − | 0.0663978i | −0.999449 | − | 0.0331989i | \(-0.989431\pi\) | ||
0.999449 | − | 0.0331989i | \(-0.0105695\pi\) | |||||||
\(264\) | −2.86080e8 | − | 1.20358e9i | −0.0588942 | − | 0.247775i | ||||
\(265\) | 3.52344e9 | 0.714470 | ||||||||
\(266\) | − | 7.59656e8i | − | 0.151737i | ||||||
\(267\) | 4.67293e9 | − | 1.11072e9i | 0.919484 | − | 0.218554i | ||||
\(268\) | −4.44609e8 | −0.0861866 | ||||||||
\(269\) | 8.66604e9i | 1.65505i | 0.561427 | + | 0.827526i | \(0.310252\pi\) | ||||
−0.561427 | + | 0.827526i | \(0.689748\pi\) | |||||||
\(270\) | 4.85147e9 | + | 5.75888e9i | 0.912890 | + | 1.08363i | ||||
\(271\) | 2.09615e8 | 0.0388637 | 0.0194319 | − | 0.999811i | \(-0.493814\pi\) | ||||
0.0194319 | + | 0.999811i | \(0.493814\pi\) | |||||||
\(272\) | 1.16085e10i | 2.12080i | ||||||||
\(273\) | 1.99933e9 | + | 8.41144e9i | 0.359944 | + | 1.51433i | ||||
\(274\) | −2.88654e9 | −0.512124 | ||||||||
\(275\) | − | 1.06277e9i | − | 0.185826i | ||||||
\(276\) | −2.26199e9 | + | 5.37657e8i | −0.389811 | + | 0.0926550i | ||||
\(277\) | 6.26791e9 | 1.06464 | 0.532321 | − | 0.846542i | \(-0.321320\pi\) | ||||
0.532321 | + | 0.846542i | \(0.321320\pi\) | |||||||
\(278\) | − | 3.96065e9i | − | 0.663113i | ||||||
\(279\) | −8.05387e8 | + | 4.05795e8i | −0.132919 | + | 0.0669714i | ||||
\(280\) | −6.70252e9 | −1.09045 | ||||||||
\(281\) | 3.55296e9i | 0.569856i | 0.958549 | + | 0.284928i | \(0.0919698\pi\) | ||||
−0.958549 | + | 0.284928i | \(0.908030\pi\) | |||||||
\(282\) | −3.19462e9 | − | 1.34402e10i | −0.505153 | − | 2.12524i | ||||
\(283\) | −9.44681e9 | −1.47278 | −0.736392 | − | 0.676555i | \(-0.763472\pi\) | ||||
−0.736392 | + | 0.676555i | \(0.763472\pi\) | |||||||
\(284\) | − | 2.34556e8i | − | 0.0360557i | ||||||
\(285\) | 1.09412e9 | − | 2.60064e8i | 0.165839 | − | 0.0394185i | ||||
\(286\) | −3.44625e9 | −0.515089 | ||||||||
\(287\) | − | 9.18596e8i | − | 0.135393i | ||||||
\(288\) | 1.46832e9 | + | 2.91420e9i | 0.213428 | + | 0.423594i | ||||
\(289\) | −1.54250e10 | −2.21122 | ||||||||
\(290\) | − | 7.07827e9i | − | 1.00077i | ||||||
\(291\) | 1.47802e9 | + | 6.21822e9i | 0.206114 | + | 0.867149i | ||||
\(292\) | 6.07753e8 | 0.0835980 | ||||||||
\(293\) | 1.26871e10i | 1.72144i | 0.509080 | + | 0.860719i | \(0.329986\pi\) | ||||
−0.509080 | + | 0.860719i | \(0.670014\pi\) | |||||||
\(294\) | −2.52109e8 | + | 5.99244e7i | −0.0337442 | + | 0.00802074i | ||||
\(295\) | 1.83963e9 | 0.242909 | ||||||||
\(296\) | 1.95143e9i | 0.254206i | ||||||||
\(297\) | 1.79420e9 | − | 1.51149e9i | 0.230592 | − | 0.194258i | ||||
\(298\) | 3.54801e9 | 0.449904 | ||||||||
\(299\) | − | 2.02754e10i | − | 2.53679i | ||||||
\(300\) | 2.79493e8 | + | 1.17586e9i | 0.0345053 | + | 0.145168i | ||||
\(301\) | 1.38416e10 | 1.68625 | ||||||||
\(302\) | − | 1.44066e10i | − | 1.73195i | ||||||
\(303\) | −4.18750e9 | + | 9.95335e8i | −0.496803 | + | 0.118086i | ||||
\(304\) | 1.35524e9 | 0.158680 | ||||||||
\(305\) | − | 1.82688e10i | − | 2.11111i | ||||||
\(306\) | −1.56378e10 | + | 7.87909e9i | −1.78356 | + | 0.898650i | ||||
\(307\) | 2.82965e9 | 0.318551 | 0.159276 | − | 0.987234i | \(-0.449084\pi\) | ||||
0.159276 | + | 0.987234i | \(0.449084\pi\) | |||||||
\(308\) | − | 6.67059e8i | − | 0.0741244i | ||||||
\(309\) | −1.37673e8 | − | 5.79208e8i | −0.0151013 | − | 0.0635331i | ||||
\(310\) | −1.94761e9 | −0.210890 | ||||||||
\(311\) | − | 1.23649e10i | − | 1.32175i | −0.750498 | − | 0.660873i | \(-0.770186\pi\) | ||
0.750498 | − | 0.660873i | \(-0.229814\pi\) | |||||||
\(312\) | −1.19364e10 | + | 2.83718e9i | −1.25966 | + | 0.299411i | ||||
\(313\) | 6.60686e9 | 0.688363 | 0.344182 | − | 0.938903i | \(-0.388156\pi\) | ||||
0.344182 | + | 0.938903i | \(0.388156\pi\) | |||||||
\(314\) | 1.25128e10i | 1.28717i | ||||||||
\(315\) | −5.71921e9 | − | 1.13510e10i | −0.580890 | − | 1.15290i | ||||
\(316\) | −7.06488e7 | −0.00708527 | ||||||||
\(317\) | − | 5.87200e9i | − | 0.581499i | −0.956799 | − | 0.290750i | \(-0.906095\pi\) | ||
0.956799 | − | 0.290750i | \(-0.0939047\pi\) | |||||||
\(318\) | 1.48111e9 | + | 6.23123e9i | 0.144837 | + | 0.609348i | ||||
\(319\) | −2.20526e9 | −0.212960 | ||||||||
\(320\) | − | 8.72991e9i | − | 0.832549i | ||||||
\(321\) | 1.62800e9 | − | 3.86963e8i | 0.153332 | − | 0.0364459i | ||||
\(322\) | 2.01346e10 | 1.87292 | ||||||||
\(323\) | 2.61518e9i | 0.240266i | ||||||||
\(324\) | −1.58763e9 | + | 2.14419e9i | −0.144069 | + | 0.194573i | ||||
\(325\) | −1.05399e10 | −0.944718 | ||||||||
\(326\) | 4.91812e9i | 0.435440i | ||||||||
\(327\) | 1.85570e9 | + | 7.80716e9i | 0.162299 | + | 0.682813i | ||||
\(328\) | 1.30354e9 | 0.112624 | ||||||||
\(329\) | 2.33186e10i | 1.99030i | ||||||||
\(330\) | 4.92910e9 | − | 1.17161e9i | 0.415634 | − | 0.0987930i | ||||
\(331\) | 1.45085e9 | 0.120868 | 0.0604338 | − | 0.998172i | \(-0.480752\pi\) | ||||
0.0604338 | + | 0.998172i | \(0.480752\pi\) | |||||||
\(332\) | 1.82987e9i | 0.150615i | ||||||||
\(333\) | −3.30483e9 | + | 1.66514e9i | −0.268765 | + | 0.135417i | ||||
\(334\) | 1.42588e9 | 0.114577 | ||||||||
\(335\) | 5.70006e9i | 0.452585i | ||||||||
\(336\) | −3.54207e9 | − | 1.49019e10i | −0.277907 | − | 1.16919i | ||||
\(337\) | −1.91392e9 | −0.148390 | −0.0741948 | − | 0.997244i | \(-0.523639\pi\) | ||||
−0.0741948 | + | 0.997244i | \(0.523639\pi\) | |||||||
\(338\) | 1.96318e10i | 1.50415i | ||||||||
\(339\) | −5.09252e8 | + | 1.21045e8i | −0.0385597 | + | 0.00916534i | ||||
\(340\) | −7.37083e9 | −0.551570 | ||||||||
\(341\) | 6.06785e8i | 0.0448763i | ||||||||
\(342\) | 9.19848e8 | + | 1.82564e9i | 0.0672375 | + | 0.133447i | ||||
\(343\) | −1.36176e10 | −0.983840 | ||||||||
\(344\) | 1.96421e10i | 1.40267i | ||||||||
\(345\) | 6.89296e9 | + | 2.89995e10i | 0.486552 | + | 2.04698i | ||||
\(346\) | 5.76232e8 | 0.0402062 | ||||||||
\(347\) | − | 4.93870e9i | − | 0.340639i | −0.985389 | − | 0.170320i | \(-0.945520\pi\) | ||
0.985389 | − | 0.170320i | \(-0.0544800\pi\) | |||||||
\(348\) | 2.43994e9 | − | 5.79954e8i | 0.166365 | − | 0.0395436i | ||||
\(349\) | 2.16559e10 | 1.45973 | 0.729867 | − | 0.683589i | \(-0.239582\pi\) | ||||
0.729867 | + | 0.683589i | \(0.239582\pi\) | |||||||
\(350\) | − | 1.04667e10i | − | 0.697488i | ||||||
\(351\) | −1.49901e10 | − | 1.77938e10i | −0.987588 | − | 1.17230i | ||||
\(352\) | 2.19558e9 | 0.143014 | ||||||||
\(353\) | − | 7.37136e9i | − | 0.474732i | −0.971420 | − | 0.237366i | \(-0.923716\pi\) | ||
0.971420 | − | 0.237366i | \(-0.0762841\pi\) | |||||||
\(354\) | 7.73308e8 | + | 3.25340e9i | 0.0492424 | + | 0.207169i | ||||
\(355\) | −3.00709e9 | −0.189336 | ||||||||
\(356\) | 3.67520e9i | 0.228813i | ||||||||
\(357\) | 2.87560e10 | − | 6.83507e9i | 1.77034 | − | 0.420795i | ||||
\(358\) | 2.35651e10 | 1.43462 | ||||||||
\(359\) | 3.13260e9i | 0.188594i | 0.995544 | + | 0.0942969i | \(0.0300603\pi\) | ||||
−0.995544 | + | 0.0942969i | \(0.969940\pi\) | |||||||
\(360\) | 1.61078e10 | − | 8.11592e9i | 0.959016 | − | 0.483201i | ||||
\(361\) | −1.66783e10 | −0.982023 | ||||||||
\(362\) | − | 2.56525e10i | − | 1.49381i | ||||||
\(363\) | −3.65018e8 | − | 1.53568e9i | −0.0210227 | − | 0.0884450i | ||||
\(364\) | −6.61550e9 | −0.376840 | ||||||||
\(365\) | − | 7.79162e9i | − | 0.438992i | ||||||
\(366\) | 3.23085e10 | − | 7.67948e9i | 1.80050 | − | 0.427964i | ||||
\(367\) | 2.33114e10 | 1.28500 | 0.642500 | − | 0.766285i | \(-0.277897\pi\) | ||||
0.642500 | + | 0.766285i | \(0.277897\pi\) | |||||||
\(368\) | 3.59204e10i | 1.95862i | ||||||||
\(369\) | 1.11230e9 | + | 2.20761e9i | 0.0599954 | + | 0.119074i | ||||
\(370\) | −7.99183e9 | −0.426422 | ||||||||
\(371\) | − | 1.08111e10i | − | 0.570658i | ||||||
\(372\) | −1.59576e8 | − | 6.71357e8i | −0.00833291 | − | 0.0350576i | ||||
\(373\) | −8.44159e9 | −0.436103 | −0.218051 | − | 0.975937i | \(-0.569970\pi\) | ||||
−0.218051 | + | 0.975937i | \(0.569970\pi\) | |||||||
\(374\) | 1.17816e10i | 0.602168i | ||||||||
\(375\) | −9.38488e9 | + | 2.23071e9i | −0.474573 | + | 0.112802i | ||||
\(376\) | −3.30905e10 | −1.65559 | ||||||||
\(377\) | 2.18705e10i | 1.08266i | ||||||||
\(378\) | 1.76702e10 | − | 1.48860e10i | 0.865515 | − | 0.729139i | ||||
\(379\) | 1.94801e10 | 0.944136 | 0.472068 | − | 0.881562i | \(-0.343508\pi\) | ||||
0.472068 | + | 0.881562i | \(0.343508\pi\) | |||||||
\(380\) | 8.60512e8i | 0.0412688i | ||||||||
\(381\) | −6.72149e9 | − | 2.82781e10i | −0.318982 | − | 1.34200i | ||||
\(382\) | 1.08938e10 | 0.511596 | ||||||||
\(383\) | − | 1.04727e10i | − | 0.486701i | −0.969938 | − | 0.243351i | \(-0.921753\pi\) | ||
0.969938 | − | 0.243351i | \(-0.0782466\pi\) | |||||||
\(384\) | 2.54727e10 | − | 6.05466e9i | 1.17152 | − | 0.278461i | ||||
\(385\) | −8.55194e9 | −0.389244 | ||||||||
\(386\) | 6.89572e9i | 0.310621i | ||||||||
\(387\) | −3.32648e10 | + | 1.67605e10i | −1.48300 | + | 0.747210i | ||||
\(388\) | −4.89055e9 | −0.215790 | ||||||||
\(389\) | − | 2.50214e10i | − | 1.09273i | −0.837546 | − | 0.546366i | \(-0.816011\pi\) | ||
0.837546 | − | 0.546366i | \(-0.183989\pi\) | |||||||
\(390\) | −1.16193e10 | − | 4.88839e10i | −0.502252 | − | 2.11304i | ||||
\(391\) | −6.93151e10 | −2.96566 | ||||||||
\(392\) | 6.20708e8i | 0.0262871i | ||||||||
\(393\) | −1.27148e10 | + | 3.02221e9i | −0.533015 | + | 0.126693i | ||||
\(394\) | −6.55343e9 | −0.271947 | ||||||||
\(395\) | 9.05743e8i | 0.0372063i | ||||||||
\(396\) | 8.07724e8 | + | 1.60310e9i | 0.0328460 | + | 0.0651900i | ||||
\(397\) | 3.10148e10 | 1.24855 | 0.624276 | − | 0.781204i | \(-0.285394\pi\) | ||||
0.624276 | + | 0.781204i | \(0.285394\pi\) | |||||||
\(398\) | − | 2.39207e9i | − | 0.0953326i | ||||||
\(399\) | −7.97964e8 | − | 3.35714e9i | −0.0314841 | − | 0.132458i | ||||
\(400\) | 1.86727e10 | 0.729403 | ||||||||
\(401\) | 2.65629e10i | 1.02730i | 0.858000 | + | 0.513650i | \(0.171707\pi\) | ||||
−0.858000 | + | 0.513650i | \(0.828293\pi\) | |||||||
\(402\) | −1.00806e10 | + | 2.39608e9i | −0.385995 | + | 0.0917479i | ||||
\(403\) | 6.01773e9 | 0.228146 | ||||||||
\(404\) | − | 3.29341e9i | − | 0.123629i | ||||||
\(405\) | 2.74893e10 | + | 2.03540e10i | 1.02175 | + | 0.756536i | ||||
\(406\) | −2.17186e10 | −0.799332 | ||||||||
\(407\) | 2.48988e9i | 0.0907405i | ||||||||
\(408\) | 9.69939e9 | + | 4.08066e10i | 0.350029 | + | 1.47262i | ||||
\(409\) | 2.09301e10 | 0.747959 | 0.373979 | − | 0.927437i | \(-0.377993\pi\) | ||||
0.373979 | + | 0.927437i | \(0.377993\pi\) | |||||||
\(410\) | 5.33850e9i | 0.188923i | ||||||||
\(411\) | −1.27564e10 | + | 3.03210e9i | −0.447056 | + | 0.106262i | ||||
\(412\) | 4.55540e8 | 0.0158102 | ||||||||
\(413\) | − | 5.64462e9i | − | 0.194015i | ||||||
\(414\) | −4.83883e10 | + | 2.43805e10i | −1.64717 | + | 0.829929i | ||||
\(415\) | 2.34597e10 | 0.790914 | ||||||||
\(416\) | − | 2.17745e10i | − | 0.727067i | ||||||
\(417\) | −4.16038e9 | − | 1.75032e10i | −0.137591 | − | 0.578861i | ||||
\(418\) | 1.37545e9 | 0.0450546 | ||||||||
\(419\) | 3.60119e10i | 1.16839i | 0.811612 | + | 0.584197i | \(0.198591\pi\) | ||||
−0.811612 | + | 0.584197i | \(0.801409\pi\) | |||||||
\(420\) | 9.46201e9 | − | 2.24904e9i | 0.304079 | − | 0.0722771i | ||||
\(421\) | −3.14094e10 | −0.999843 | −0.499922 | − | 0.866071i | \(-0.666638\pi\) | ||||
−0.499922 | + | 0.866071i | \(0.666638\pi\) | |||||||
\(422\) | − | 5.81430e9i | − | 0.183336i | ||||||
\(423\) | −2.82358e10 | − | 5.60401e10i | −0.881940 | − | 1.75040i | ||||
\(424\) | 1.53417e10 | 0.474689 | ||||||||
\(425\) | 3.60324e10i | 1.10443i | ||||||||
\(426\) | −1.26406e9 | − | 5.31807e9i | −0.0383822 | − | 0.161479i | ||||
\(427\) | −5.60550e10 | −1.68618 | ||||||||
\(428\) | 1.28040e9i | 0.0381567i | ||||||||
\(429\) | −1.52299e10 | + | 3.62003e9i | −0.449644 | + | 0.106877i | ||||
\(430\) | −8.04420e10 | −2.35293 | ||||||||
\(431\) | 4.33885e10i | 1.25738i | 0.777657 | + | 0.628689i | \(0.216408\pi\) | ||||
−0.777657 | + | 0.628689i | \(0.783592\pi\) | |||||||
\(432\) | 2.65568e10 | + | 3.15239e10i | 0.762502 | + | 0.905118i | ||||
\(433\) | −4.18298e10 | −1.18996 | −0.594982 | − | 0.803739i | \(-0.702841\pi\) | ||||
−0.594982 | + | 0.803739i | \(0.702841\pi\) | |||||||
\(434\) | 5.97594e9i | 0.168441i | ||||||||
\(435\) | −7.43522e9 | − | 3.12809e10i | −0.207652 | − | 0.873619i | ||||
\(436\) | −6.14023e9 | −0.169918 | ||||||||
\(437\) | 8.09223e9i | 0.221892i | ||||||||
\(438\) | 1.37795e10 | − | 3.27528e9i | 0.374402 | − | 0.0889923i | ||||
\(439\) | 4.51585e10 | 1.21585 | 0.607927 | − | 0.793993i | \(-0.292002\pi\) | ||||
0.607927 | + | 0.793993i | \(0.292002\pi\) | |||||||
\(440\) | − | 1.21357e10i | − | 0.323784i | ||||||
\(441\) | −1.05120e9 | + | 5.29645e8i | −0.0277926 | + | 0.0140033i | ||||
\(442\) | 1.16843e11 | 3.06135 | ||||||||
\(443\) | − | 3.75532e10i | − | 0.975061i | −0.873106 | − | 0.487531i | \(-0.837898\pi\) | ||
0.873106 | − | 0.487531i | \(-0.162102\pi\) | |||||||
\(444\) | −6.54805e8 | − | 2.75485e9i | −0.0168492 | − | 0.0708869i | ||||
\(445\) | 4.71174e10 | 1.20155 | ||||||||
\(446\) | − | 6.92048e10i | − | 1.74903i | ||||||
\(447\) | 1.56797e10 | − | 3.72693e9i | 0.392741 | − | 0.0933514i | ||||
\(448\) | −2.67864e10 | −0.664969 | ||||||||
\(449\) | − | 5.20394e10i | − | 1.28040i | −0.768206 | − | 0.640202i | \(-0.778851\pi\) | ||
0.768206 | − | 0.640202i | \(-0.221149\pi\) | |||||||
\(450\) | 1.26738e10 | + | 2.51540e10i | 0.309071 | + | 0.613418i | ||||
\(451\) | 1.66323e9 | 0.0402018 | ||||||||
\(452\) | − | 4.00520e8i | − | 0.00959557i | ||||||
\(453\) | −1.51331e10 | − | 6.36669e10i | −0.359365 | − | 1.51189i | ||||
\(454\) | 4.93706e10 | 1.16210 | ||||||||
\(455\) | 8.48131e10i | 1.97887i | ||||||||
\(456\) | 4.76398e9 | − | 1.13236e9i | 0.110182 | − | 0.0261894i | ||||
\(457\) | 6.83028e10 | 1.56594 | 0.782968 | − | 0.622062i | \(-0.213705\pi\) | ||||
0.782968 | + | 0.622062i | \(0.213705\pi\) | |||||||
\(458\) | 7.41299e10i | 1.68474i | ||||||||
\(459\) | −6.08313e10 | + | 5.12463e10i | −1.37049 | + | 1.15455i | ||||
\(460\) | −2.28078e10 | −0.509391 | ||||||||
\(461\) | − | 1.04289e10i | − | 0.230906i | −0.993313 | − | 0.115453i | \(-0.963168\pi\) | ||
0.993313 | − | 0.115453i | \(-0.0368320\pi\) | |||||||
\(462\) | −3.59489e9 | − | 1.51242e10i | −0.0789074 | − | 0.331973i | ||||
\(463\) | 4.32260e10 | 0.940636 | 0.470318 | − | 0.882497i | \(-0.344139\pi\) | ||||
0.470318 | + | 0.882497i | \(0.344139\pi\) | |||||||
\(464\) | − | 3.87463e10i | − | 0.835907i | ||||||
\(465\) | −8.60705e9 | + | 2.04583e9i | −0.184095 | + | 0.0437579i | ||||
\(466\) | −2.24058e10 | −0.475134 | ||||||||
\(467\) | − | 4.19215e10i | − | 0.881392i | −0.897656 | − | 0.440696i | \(-0.854732\pi\) | ||
0.897656 | − | 0.440696i | \(-0.145268\pi\) | |||||||
\(468\) | 1.58986e10 | − | 8.01054e9i | 0.331418 | − | 0.166985i | ||||
\(469\) | 1.74897e10 | 0.361486 | ||||||||
\(470\) | − | 1.35518e11i | − | 2.77719i | ||||||
\(471\) | 1.31438e10 | + | 5.52977e10i | 0.267078 | + | 1.12363i | ||||
\(472\) | 8.01007e9 | 0.161387 | ||||||||
\(473\) | 2.50620e10i | 0.500692i | ||||||||
\(474\) | −1.60181e9 | + | 3.80738e8i | −0.0317321 | + | 0.00754246i | ||||
\(475\) | 4.20663e9 | 0.0826341 | ||||||||
\(476\) | 2.26162e10i | 0.440547i | ||||||||
\(477\) | 1.30909e10 | + | 2.59818e10i | 0.252870 | + | 0.501875i | ||||
\(478\) | −7.33660e10 | −1.40535 | ||||||||
\(479\) | − | 6.93538e10i | − | 1.31743i | −0.752392 | − | 0.658716i | \(-0.771100\pi\) | ||
0.752392 | − | 0.658716i | \(-0.228900\pi\) | |||||||
\(480\) | 7.40258e9 | + | 3.11436e10i | 0.139450 | + | 0.586683i | ||||
\(481\) | 2.46932e10 | 0.461314 | ||||||||
\(482\) | 8.52576e10i | 1.57959i | ||||||||
\(483\) | 8.89805e10 | − | 2.11500e10i | 1.63496 | − | 0.388616i | ||||
\(484\) | 1.20779e9 | 0.0220095 | ||||||||
\(485\) | 6.26986e10i | 1.13316i | ||||||||
\(486\) | −2.44408e10 | + | 5.71710e10i | −0.438097 | + | 1.02478i | ||||
\(487\) | −8.34846e10 | −1.48419 | −0.742096 | − | 0.670293i | \(-0.766168\pi\) | ||||
−0.742096 | + | 0.670293i | \(0.766168\pi\) | |||||||
\(488\) | − | 7.95456e10i | − | 1.40261i | ||||||
\(489\) | 5.16613e9 | + | 2.17345e10i | 0.0903503 | + | 0.380115i | ||||
\(490\) | −2.54203e9 | −0.0440958 | ||||||||
\(491\) | 6.29706e10i | 1.08346i | 0.840554 | + | 0.541728i | \(0.182230\pi\) | ||||
−0.840554 | + | 0.541728i | \(0.817770\pi\) | |||||||
\(492\) | −1.84022e9 | + | 4.37407e8i | −0.0314058 | + | 0.00746492i | ||||
\(493\) | 7.47681e10 | 1.26569 | ||||||||
\(494\) | − | 1.36409e10i | − | 0.229053i | ||||||
\(495\) | 2.05524e10 | − | 1.03553e10i | 0.342327 | − | 0.172482i | ||||
\(496\) | −1.06612e10 | −0.176148 | ||||||||
\(497\) | 9.22680e9i | 0.151226i | ||||||||
\(498\) | 9.86150e9 | + | 4.14886e10i | 0.160334 | + | 0.674545i | ||||
\(499\) | 1.47251e10 | 0.237497 | 0.118748 | − | 0.992924i | \(-0.462112\pi\) | ||||
0.118748 | + | 0.992924i | \(0.462112\pi\) | |||||||
\(500\) | − | 7.38109e9i | − | 0.118097i | ||||||
\(501\) | 6.30135e9 | − | 1.49778e9i | 0.100019 | − | 0.0237737i | ||||
\(502\) | 1.10741e11 | 1.74378 | ||||||||
\(503\) | − | 7.62579e10i | − | 1.19128i | −0.803253 | − | 0.595638i | \(-0.796899\pi\) | ||
0.803253 | − | 0.595638i | \(-0.203101\pi\) | |||||||
\(504\) | −2.49024e10 | − | 4.94242e10i | −0.385940 | − | 0.765981i | ||||
\(505\) | −4.22228e10 | −0.649204 | ||||||||
\(506\) | 3.64561e10i | 0.556120i | ||||||||
\(507\) | 2.06218e10 | + | 8.67583e10i | 0.312100 | + | 1.31304i | ||||
\(508\) | 2.22404e10 | 0.333955 | ||||||||
\(509\) | − | 2.49715e10i | − | 0.372025i | −0.982547 | − | 0.186013i | \(-0.940443\pi\) | ||
0.982547 | − | 0.186013i | \(-0.0595566\pi\) | |||||||
\(510\) | −1.67118e11 | + | 3.97227e10i | −2.47026 | + | 0.587162i | ||||
\(511\) | −2.39074e10 | −0.350629 | ||||||||
\(512\) | − | 3.01200e10i | − | 0.438304i | ||||||
\(513\) | 5.98277e9 | + | 7.10178e9i | 0.0863839 | + | 0.102541i | ||||
\(514\) | 7.55329e10 | 1.08214 | ||||||||
\(515\) | − | 5.84018e9i | − | 0.0830228i | ||||||
\(516\) | −6.59096e9 | − | 2.77290e10i | −0.0929715 | − | 0.391143i | ||||
\(517\) | −4.22210e10 | −0.590972 | ||||||||
\(518\) | 2.45217e10i | 0.340590i | ||||||||
\(519\) | 2.54653e9 | − | 6.05290e8i | 0.0350978 | − | 0.00834246i | ||||
\(520\) | −1.20355e11 | −1.64608 | ||||||||
\(521\) | − | 1.00175e11i | − | 1.35959i | −0.733403 | − | 0.679794i | \(-0.762069\pi\) | ||
0.733403 | − | 0.679794i | \(-0.237931\pi\) | |||||||
\(522\) | 5.21950e10 | − | 2.62985e10i | 0.702987 | − | 0.354200i | ||||
\(523\) | 3.81458e10 | 0.509847 | 0.254924 | − | 0.966961i | \(-0.417950\pi\) | ||||
0.254924 | + | 0.966961i | \(0.417950\pi\) | |||||||
\(524\) | − | 1.00000e10i | − | 0.132641i | ||||||
\(525\) | −1.09945e10 | − | 4.62552e10i | −0.144723 | − | 0.608868i | ||||
\(526\) | 5.66469e9 | 0.0740002 | ||||||||
\(527\) | − | 2.05727e10i | − | 0.266716i | ||||||
\(528\) | 2.69817e10 | − | 6.41334e9i | 0.347163 | − | 0.0825180i | ||||
\(529\) | −1.36173e11 | −1.73887 | ||||||||
\(530\) | 6.28299e10i | 0.796275i | ||||||||
\(531\) | 6.83493e9 | + | 1.35654e10i | 0.0859718 | + | 0.170630i | ||||
\(532\) | 2.64034e9 | 0.0329620 | ||||||||
\(533\) | − | 1.64949e10i | − | 0.204381i | ||||||
\(534\) | 1.98063e10 | + | 8.33275e10i | 0.243578 | + | 1.02476i | ||||
\(535\) | 1.64152e10 | 0.200369 | ||||||||
\(536\) | 2.48190e10i | 0.300694i | ||||||||
\(537\) | 1.04141e11 | − | 2.47534e10i | 1.25234 | − | 0.297672i | ||||
\(538\) | −1.54532e11 | −1.84455 | ||||||||
\(539\) | 7.91979e8i | 0.00938336i | ||||||||
\(540\) | −2.00162e10 | + | 1.68623e10i | −0.235400 | + | 0.198309i | ||||
\(541\) | −6.93777e10 | −0.809899 | −0.404950 | − | 0.914339i | \(-0.632711\pi\) | ||||
−0.404950 | + | 0.914339i | \(0.632711\pi\) | |||||||
\(542\) | 3.73784e9i | 0.0433135i | ||||||||
\(543\) | −2.69461e10 | − | 1.13366e11i | −0.309954 | − | 1.30402i | ||||
\(544\) | −7.44399e10 | −0.849983 | ||||||||
\(545\) | 7.87200e10i | 0.892276i | ||||||||
\(546\) | −1.49993e11 | + | 3.56520e10i | −1.68771 | + | 0.401156i | ||||
\(547\) | −1.12694e11 | −1.25878 | −0.629392 | − | 0.777088i | \(-0.716696\pi\) | ||||
−0.629392 | + | 0.777088i | \(0.716696\pi\) | |||||||
\(548\) | − | 1.00328e10i | − | 0.111250i | ||||||
\(549\) | 1.34714e11 | − | 6.78756e10i | 1.48294 | − | 0.747178i | ||||
\(550\) | 1.89512e10 | 0.207103 | ||||||||
\(551\) | − | 8.72884e9i | − | 0.0947000i | ||||||
\(552\) | 3.00131e10 | + | 1.26269e11i | 0.323262 | + | 1.36000i | ||||
\(553\) | 2.77913e9 | 0.0297172 | ||||||||
\(554\) | 1.11769e11i | 1.18654i | ||||||||
\(555\) | −3.53182e10 | + | 8.39485e9i | −0.372243 | + | 0.0884791i | ||||
\(556\) | 1.37661e10 | 0.144049 | ||||||||
\(557\) | − | 5.32134e10i | − | 0.552841i | −0.961037 | − | 0.276421i | \(-0.910852\pi\) | ||
0.961037 | − | 0.276421i | \(-0.0891483\pi\) | |||||||
\(558\) | −7.23611e9 | − | 1.43616e10i | −0.0746395 | − | 0.148138i | ||||
\(559\) | 2.48550e11 | 2.54546 | ||||||||
\(560\) | − | 1.50257e11i | − | 1.52786i | ||||||
\(561\) | 1.23757e10 | + | 5.20662e10i | 0.124945 | + | 0.525660i | ||||
\(562\) | −6.33563e10 | −0.635103 | ||||||||
\(563\) | − | 5.66387e10i | − | 0.563741i | −0.959453 | − | 0.281870i | \(-0.909045\pi\) | ||
0.959453 | − | 0.281870i | \(-0.0909548\pi\) | |||||||
\(564\) | 4.67141e10 | − | 1.11036e10i | 0.461670 | − | 0.109735i | ||||
\(565\) | −5.13482e9 | −0.0503885 | ||||||||
\(566\) | − | 1.68455e11i | − | 1.64141i | ||||||
\(567\) | 6.24530e10 | − | 8.43466e10i | 0.604257 | − | 0.816085i | ||||
\(568\) | −1.30934e10 | −0.125794 | ||||||||
\(569\) | 1.44297e11i | 1.37660i | 0.725426 | + | 0.688301i | \(0.241643\pi\) | ||||
−0.725426 | + | 0.688301i | \(0.758357\pi\) | |||||||
\(570\) | 4.63744e9 | + | 1.95103e10i | 0.0439318 | + | 0.184827i | ||||
\(571\) | −1.10870e11 | −1.04297 | −0.521484 | − | 0.853261i | \(-0.674621\pi\) | ||||
−0.521484 | + | 0.853261i | \(0.674621\pi\) | |||||||
\(572\) | − | 1.19782e10i | − | 0.111894i | ||||||
\(573\) | 4.81429e10 | − | 1.14432e10i | 0.446595 | − | 0.106152i | ||||
\(574\) | 1.63804e10 | 0.150895 | ||||||||
\(575\) | 1.11496e11i | 1.01997i | ||||||||
\(576\) | 6.43741e10 | − | 3.24349e10i | 0.584819 | − | 0.294661i | ||||
\(577\) | 2.43968e10 | 0.220105 | 0.110053 | − | 0.993926i | \(-0.464898\pi\) | ||||
0.110053 | + | 0.993926i | \(0.464898\pi\) | |||||||
\(578\) | − | 2.75057e11i | − | 2.46440i | ||||||
\(579\) | 7.24345e9 | + | 3.04741e10i | 0.0644513 | + | 0.271155i | ||||
\(580\) | 2.46020e10 | 0.217400 | ||||||||
\(581\) | − | 7.19823e10i | − | 0.631715i | ||||||
\(582\) | −1.10883e11 | + | 2.63560e10i | −0.966436 | + | 0.229714i | ||||
\(583\) | 1.95749e10 | 0.169443 | ||||||||
\(584\) | − | 3.39260e10i | − | 0.291663i | ||||||
\(585\) | −1.02698e11 | − | 2.03826e11i | −0.876877 | − | 1.74035i | ||||
\(586\) | −2.26236e11 | −1.91854 | ||||||||
\(587\) | 1.61206e11i | 1.35778i | 0.734241 | + | 0.678889i | \(0.237538\pi\) | ||||
−0.734241 | + | 0.678889i | \(0.762462\pi\) | |||||||
\(588\) | −2.08280e8 | − | 8.76259e8i | −0.00174236 | − | 0.00733032i | ||||
\(589\) | −2.40177e9 | −0.0199558 | ||||||||
\(590\) | 3.28043e10i | 0.270721i | ||||||||
\(591\) | −2.89615e10 | + | 6.88391e9i | −0.237395 | + | 0.0564268i | ||||
\(592\) | −4.37471e10 | −0.356174 | ||||||||
\(593\) | 1.80683e11i | 1.46116i | 0.682825 | + | 0.730582i | \(0.260751\pi\) | ||||
−0.682825 | + | 0.730582i | \(0.739249\pi\) | |||||||
\(594\) | 2.69529e10 | + | 3.19941e10i | 0.216501 | + | 0.256994i | ||||
\(595\) | 2.89949e11 | 2.31341 | ||||||||
\(596\) | 1.23319e10i | 0.0977335i | ||||||||
\(597\) | −2.51270e9 | − | 1.05712e10i | −0.0197808 | − | 0.0832201i | ||||
\(598\) | 3.61550e11 | 2.82725 | ||||||||
\(599\) | − | 7.23626e9i | − | 0.0562091i | −0.999605 | − | 0.0281046i | \(-0.991053\pi\) | ||
0.999605 | − | 0.0281046i | \(-0.00894714\pi\) | |||||||
\(600\) | 6.56390e10 | − | 1.56019e10i | 0.506474 | − | 0.120385i | ||||
\(601\) | 8.49524e10 | 0.651145 | 0.325572 | − | 0.945517i | \(-0.394443\pi\) | ||||
0.325572 | + | 0.945517i | \(0.394443\pi\) | |||||||
\(602\) | 2.46824e11i | 1.87932i | ||||||||
\(603\) | −4.20321e10 | + | 2.11779e10i | −0.317915 | + | 0.160182i | ||||
\(604\) | 5.00732e10 | 0.376234 | ||||||||
\(605\) | − | 1.54843e10i | − | 0.115577i | ||||||
\(606\) | −1.77488e10 | − | 7.46713e10i | −0.131607 | − | 0.553685i | ||||
\(607\) | −1.64821e11 | −1.21411 | −0.607056 | − | 0.794659i | \(-0.707650\pi\) | ||||
−0.607056 | + | 0.794659i | \(0.707650\pi\) | |||||||
\(608\) | 8.69052e9i | 0.0635962i | ||||||||
\(609\) | −9.59805e10 | + | 2.28138e10i | −0.697773 | + | 0.165855i | ||||
\(610\) | 3.25769e11 | 2.35283 | ||||||||
\(611\) | 4.18724e11i | 3.00443i | ||||||||
\(612\) | −2.73854e10 | − | 5.43523e10i | −0.195215 | − | 0.387447i | ||||
\(613\) | 1.48468e11 | 1.05145 | 0.525726 | − | 0.850654i | \(-0.323794\pi\) | ||||
0.525726 | + | 0.850654i | \(0.323794\pi\) | |||||||
\(614\) | 5.04582e10i | 0.355024i | ||||||||
\(615\) | 5.60771e9 | + | 2.35924e10i | 0.0391999 | + | 0.164919i | ||||
\(616\) | −3.72366e10 | −0.258611 | ||||||||
\(617\) | 2.48259e11i | 1.71303i | 0.516126 | + | 0.856513i | \(0.327374\pi\) | ||||
−0.516126 | + | 0.856513i | \(0.672626\pi\) | |||||||
\(618\) | 1.03284e10 | − | 2.45498e9i | 0.0708075 | − | 0.0168304i | ||||
\(619\) | −7.36993e10 | −0.501997 | −0.250998 | − | 0.967988i | \(-0.580759\pi\) | ||||
−0.250998 | + | 0.967988i | \(0.580759\pi\) | |||||||
\(620\) | − | 6.76933e9i | − | 0.0458120i | ||||||
\(621\) | −1.88232e11 | + | 1.58573e11i | −1.26569 | + | 1.06626i | ||||
\(622\) | 2.20490e11 | 1.47308 | ||||||||
\(623\) | − | 1.44572e11i | − | 0.959695i | ||||||
\(624\) | −6.36037e10 | − | 2.67589e11i | −0.419512 | − | 1.76494i | ||||
\(625\) | −1.88670e11 | −1.23647 | ||||||||
\(626\) | 1.17813e11i | 0.767179i | ||||||||
\(627\) | 6.07850e9 | − | 1.44481e9i | 0.0393302 | − | 0.00934847i | ||||
\(628\) | −4.34910e10 | −0.279615 | ||||||||
\(629\) | − | 8.44180e10i | − | 0.539303i | ||||||
\(630\) | 2.02411e11 | − | 1.01985e11i | 1.28491 | − | 0.647400i | ||||
\(631\) | −1.48945e11 | −0.939522 | −0.469761 | − | 0.882794i | \(-0.655660\pi\) | ||||
−0.469761 | + | 0.882794i | \(0.655660\pi\) | |||||||
\(632\) | 3.94376e9i | 0.0247196i | ||||||||
\(633\) | −6.10750e9 | − | 2.56950e10i | −0.0380407 | − | 0.160042i | ||||
\(634\) | 1.04709e11 | 0.648079 | ||||||||
\(635\) | − | 2.85130e11i | − | 1.75367i | ||||||
\(636\) | −2.16580e10 | + | 5.14792e9i | −0.132370 | + | 0.0314633i | ||||
\(637\) | 7.85438e9 | 0.0477039 | ||||||||
\(638\) | − | 3.93241e10i | − | 0.237343i | ||||||
\(639\) | −1.11725e10 | − | 2.21742e10i | −0.0670111 | − | 0.132998i | ||||
\(640\) | 2.56843e11 | 1.53090 | ||||||||
\(641\) | − | 6.16541e10i | − | 0.365199i | −0.983187 | − | 0.182600i | \(-0.941549\pi\) | ||
0.983187 | − | 0.182600i | \(-0.0584512\pi\) | |||||||
\(642\) | 6.90030e9 | + | 2.90304e10i | 0.0406189 | + | 0.170889i | ||||
\(643\) | −1.57651e10 | −0.0922260 | −0.0461130 | − | 0.998936i | \(-0.514683\pi\) | ||||
−0.0461130 | + | 0.998936i | \(0.514683\pi\) | |||||||
\(644\) | 6.99821e10i | 0.406858i | ||||||||
\(645\) | −3.55496e11 | + | 8.44985e10i | −2.05398 | + | 0.488214i | ||||
\(646\) | −4.66338e10 | −0.267776 | ||||||||
\(647\) | 8.01644e10i | 0.457472i | 0.973489 | + | 0.228736i | \(0.0734592\pi\) | ||||
−0.973489 | + | 0.228736i | \(0.926541\pi\) | |||||||
\(648\) | 1.19693e11 | + | 8.86247e10i | 0.678843 | + | 0.502638i | ||||
\(649\) | 1.02203e10 | 0.0576081 | ||||||||
\(650\) | − | 1.87947e11i | − | 1.05289i | ||||||
\(651\) | 6.27730e9 | + | 2.64094e10i | 0.0349501 | + | 0.147040i | ||||
\(652\) | −1.70939e10 | −0.0945915 | ||||||||
\(653\) | − | 2.16243e10i | − | 0.118929i | −0.998230 | − | 0.0594647i | \(-0.981061\pi\) | ||
0.998230 | − | 0.0594647i | \(-0.0189394\pi\) | |||||||
\(654\) | −1.39217e11 | + | 3.30907e10i | −0.760993 | + | 0.180882i | ||||
\(655\) | −1.28204e11 | −0.696525 | ||||||||
\(656\) | 2.92228e10i | 0.157800i | ||||||||
\(657\) | 5.74552e10 | − | 2.89488e10i | 0.308367 | − | 0.155371i | ||||
\(658\) | −4.15815e11 | −2.21818 | ||||||||
\(659\) | − | 2.62619e11i | − | 1.39246i | −0.717817 | − | 0.696232i | \(-0.754858\pi\) | ||
0.717817 | − | 0.696232i | \(-0.245142\pi\) | |||||||
\(660\) | 4.07217e9 | + | 1.71321e10i | 0.0214610 | + | 0.0902891i | ||||
\(661\) | −1.30141e11 | −0.681726 | −0.340863 | − | 0.940113i | \(-0.610719\pi\) | ||||
−0.340863 | + | 0.940113i | \(0.610719\pi\) | |||||||
\(662\) | 2.58715e10i | 0.134707i | ||||||||
\(663\) | 5.16362e11 | − | 1.22735e11i | 2.67239 | − | 0.635207i | ||||
\(664\) | 1.02147e11 | 0.525478 | ||||||||
\(665\) | − | 3.38502e10i | − | 0.173091i | ||||||
\(666\) | −2.96927e10 | − | 5.89316e10i | −0.150922 | − | 0.299537i | ||||
\(667\) | 2.31357e11 | 1.16890 | ||||||||
\(668\) | 4.95593e9i | 0.0248897i | ||||||||
\(669\) | −7.26947e10 | − | 3.05836e11i | −0.362909 | − | 1.52680i | ||||
\(670\) | −1.01643e11 | −0.504404 | ||||||||
\(671\) | − | 1.01494e11i | − | 0.500670i | ||||||
\(672\) | 9.55592e10 | − | 2.27137e10i | 0.468593 | − | 0.111381i | ||||
\(673\) | −8.82678e10 | −0.430271 | −0.215135 | − | 0.976584i | \(-0.569019\pi\) | ||||
−0.215135 | + | 0.976584i | \(0.569019\pi\) | |||||||
\(674\) | − | 3.41289e10i | − | 0.165380i | ||||||
\(675\) | 8.24317e10 | + | 9.78495e10i | 0.397081 | + | 0.471350i | ||||
\(676\) | −6.82343e10 | −0.326750 | ||||||||
\(677\) | 1.16064e11i | 0.552512i | 0.961084 | + | 0.276256i | \(0.0890938\pi\) | ||||
−0.961084 | + | 0.276256i | \(0.910906\pi\) | |||||||
\(678\) | −2.15847e9 | − | 9.08096e9i | −0.0102147 | − | 0.0429747i | ||||
\(679\) | 1.92381e11 | 0.905072 | ||||||||
\(680\) | 4.11455e11i | 1.92436i | ||||||||
\(681\) | 2.18183e11 | − | 5.18603e10i | 1.01445 | − | 0.241127i | ||||
\(682\) | −1.08202e10 | −0.0500145 | ||||||||
\(683\) | − | 8.64283e9i | − | 0.0397167i | −0.999803 | − | 0.0198584i | \(-0.993678\pi\) | ||
0.999803 | − | 0.0198584i | \(-0.00632153\pi\) | |||||||
\(684\) | −6.34539e9 | + | 3.19713e9i | −0.0289890 | + | 0.0146061i | ||||
\(685\) | −1.28624e11 | −0.584197 | ||||||||
\(686\) | − | 2.42829e11i | − | 1.09649i | ||||||
\(687\) | 7.78682e10 | + | 3.27601e11i | 0.349569 | + | 1.47068i | ||||
\(688\) | −4.40337e11 | −1.96531 | ||||||||
\(689\) | − | 1.94132e11i | − | 0.861430i | ||||||
\(690\) | −5.17118e11 | + | 1.22915e11i | −2.28136 | + | 0.542261i | ||||
\(691\) | −4.32510e11 | −1.89707 | −0.948537 | − | 0.316666i | \(-0.897437\pi\) | ||||
−0.948537 | + | 0.316666i | \(0.897437\pi\) | |||||||
\(692\) | 2.00281e9i | 0.00873406i | ||||||||
\(693\) | −3.17737e10 | − | 6.30618e10i | −0.137764 | − | 0.273422i | ||||
\(694\) | 8.80667e10 | 0.379641 | ||||||||
\(695\) | − | 1.76486e11i | − | 0.756435i | ||||||
\(696\) | −3.23742e10 | − | 1.36202e11i | −0.137963 | − | 0.580427i | ||||
\(697\) | −5.63908e10 | −0.238934 | ||||||||
\(698\) | 3.86166e11i | 1.62687i | ||||||||
\(699\) | −9.90174e10 | + | 2.35356e10i | −0.414766 | + | 0.0985865i | ||||
\(700\) | 3.63791e10 | 0.151517 | ||||||||
\(701\) | 2.44947e11i | 1.01438i | 0.861834 | + | 0.507190i | \(0.169316\pi\) | ||||
−0.861834 | + | 0.507190i | \(0.830684\pi\) | |||||||
\(702\) | 3.17298e11 | − | 2.67303e11i | 1.30653 | − | 1.10066i | ||||
\(703\) | −9.85543e9 | −0.0403510 | ||||||||
\(704\) | − | 4.84999e10i | − | 0.197447i | ||||||
\(705\) | −1.42352e11 | − | 5.98892e11i | −0.576244 | − | 2.42433i | ||||
\(706\) | 1.31446e11 | 0.529088 | ||||||||
\(707\) | 1.29554e11i | 0.518529i | ||||||||
\(708\) | −1.13079e10 | + | 2.68779e9i | −0.0450037 | + | 0.0106970i | ||||
\(709\) | −1.67637e11 | −0.663416 | −0.331708 | − | 0.943382i | \(-0.607625\pi\) | ||||
−0.331708 | + | 0.943382i | \(0.607625\pi\) | |||||||
\(710\) | − | 5.36224e10i | − | 0.211015i | ||||||
\(711\) | −6.67893e9 | + | 3.36518e9i | −0.0261353 | + | 0.0131683i | ||||
\(712\) | 2.05157e11 | 0.798301 | ||||||||
\(713\) | − | 6.36586e10i | − | 0.246320i | ||||||
\(714\) | 1.21883e11 | + | 5.12776e11i | 0.468975 | + | 1.97304i | ||||
\(715\) | −1.53564e11 | −0.587579 | ||||||||
\(716\) | 8.19053e10i | 0.311645i | ||||||||
\(717\) | −3.24225e11 | + | 7.70657e10i | −1.22679 | + | 0.291598i | ||||
\(718\) | −5.58604e10 | −0.210187 | ||||||||
\(719\) | 4.47281e11i | 1.67365i | 0.547469 | + | 0.836826i | \(0.315592\pi\) | ||||
−0.547469 | + | 0.836826i | \(0.684408\pi\) | |||||||
\(720\) | 1.81942e11 | + | 3.61104e11i | 0.677023 | + | 1.34370i | ||||
\(721\) | −1.79197e10 | −0.0663116 | ||||||||
\(722\) | − | 2.97406e11i | − | 1.09446i | ||||||
\(723\) | 8.95569e10 | + | 3.76777e11i | 0.327753 | + | 1.37890i | ||||
\(724\) | 8.91608e10 | 0.324504 | ||||||||
\(725\) | − | 1.20267e11i | − | 0.435308i | ||||||
\(726\) | 2.73841e10 | − | 6.50898e9i | 0.0985717 | − | 0.0234297i | ||||
\(727\) | 3.23809e11 | 1.15918 | 0.579590 | − | 0.814908i | \(-0.303213\pi\) | ||||
0.579590 | + | 0.814908i | \(0.303213\pi\) | |||||||
\(728\) | 3.69291e11i | 1.31475i | ||||||||
\(729\) | −4.79566e10 | + | 2.78328e11i | −0.169800 | + | 0.985478i | ||||
\(730\) | 1.38940e11 | 0.489255 | ||||||||
\(731\) | − | 8.49711e11i | − | 2.97579i | ||||||
\(732\) | 2.66917e10 | + | 1.12295e11i | 0.0929675 | + | 0.391126i | ||||
\(733\) | −4.15223e11 | −1.43835 | −0.719177 | − | 0.694827i | \(-0.755481\pi\) | ||||
−0.719177 | + | 0.694827i | \(0.755481\pi\) | |||||||
\(734\) | 4.15687e11i | 1.43213i | ||||||||
\(735\) | −1.12340e10 | + | 2.67022e9i | −0.0384932 | + | 0.00914952i | ||||
\(736\) | −2.30341e11 | −0.784984 | ||||||||
\(737\) | 3.16673e10i | 0.107335i | ||||||||
\(738\) | −3.93660e10 | + | 1.98346e10i | −0.132708 | + | 0.0668647i | ||||
\(739\) | 3.26651e11 | 1.09523 | 0.547617 | − | 0.836729i | \(-0.315535\pi\) | ||||
0.547617 | + | 0.836729i | \(0.315535\pi\) | |||||||
\(740\) | − | 2.77773e10i | − | 0.0926324i | ||||||
\(741\) | −1.43288e10 | − | 6.02830e10i | −0.0475266 | − | 0.199950i | ||||
\(742\) | 1.92784e11 | 0.635996 | ||||||||
\(743\) | − | 4.93833e10i | − | 0.162041i | −0.996712 | − | 0.0810205i | \(-0.974182\pi\) | ||
0.996712 | − | 0.0810205i | \(-0.0258179\pi\) | |||||||
\(744\) | −3.74765e10 | + | 8.90787e9i | −0.122312 | + | 0.0290725i | ||||
\(745\) | 1.58099e11 | 0.513220 | ||||||||
\(746\) | − | 1.50530e11i | − | 0.486035i | ||||||
\(747\) | 8.71615e10 | + | 1.72991e11i | 0.279925 | + | 0.555573i | ||||
\(748\) | −4.09494e10 | −0.130810 | ||||||||
\(749\) | − | 5.03675e10i | − | 0.160038i | ||||||
\(750\) | −3.97779e10 | − | 1.67351e11i | −0.125718 | − | 0.528911i | ||||
\(751\) | 2.95780e11 | 0.929841 | 0.464921 | − | 0.885352i | \(-0.346083\pi\) | ||||
0.464921 | + | 0.885352i | \(0.346083\pi\) | |||||||
\(752\) | − | 7.41821e11i | − | 2.31968i | ||||||
\(753\) | 4.89394e11 | − | 1.16325e11i | 1.52222 | − | 0.361821i | ||||
\(754\) | −3.89993e11 | −1.20662 | ||||||||
\(755\) | − | 6.41957e11i | − | 1.97569i | ||||||
\(756\) | 5.17393e10 | + | 6.14166e10i | 0.158392 | + | 0.188018i | ||||
\(757\) | 5.65447e11 | 1.72190 | 0.860951 | − | 0.508688i | \(-0.169869\pi\) | ||||
0.860951 | + | 0.508688i | \(0.169869\pi\) | |||||||
\(758\) | 3.47369e11i | 1.05224i | ||||||||
\(759\) | 3.82945e10 | + | 1.61110e11i | 0.115390 | + | 0.485462i | ||||
\(760\) | 4.80355e10 | 0.143982 | ||||||||
\(761\) | 1.88062e11i | 0.560742i | 0.959892 | + | 0.280371i | \(0.0904574\pi\) | ||||
−0.959892 | + | 0.280371i | \(0.909543\pi\) | |||||||
\(762\) | 5.04255e11 | − | 1.19857e11i | 1.49565 | − | 0.355504i | ||||
\(763\) | 2.41540e11 | 0.712674 | ||||||||
\(764\) | 3.78638e10i | 0.111135i | ||||||||
\(765\) | −6.96817e11 | + | 3.51091e11i | −2.03457 | + | 1.02512i | ||||
\(766\) | 1.86748e11 | 0.542427 | ||||||||
\(767\) | − | 1.01359e11i | − | 0.292873i | ||||||
\(768\) | 5.52832e10 | + | 2.32583e11i | 0.158909 | + | 0.668550i | ||||
\(769\) | −2.59993e11 | −0.743457 | −0.371728 | − | 0.928342i | \(-0.621235\pi\) | ||||
−0.371728 | + | 0.928342i | \(0.621235\pi\) | |||||||
\(770\) | − | 1.52498e11i | − | 0.433811i | ||||||
\(771\) | 3.33801e11 | − | 7.93419e10i | 0.944649 | − | 0.224535i | ||||
\(772\) | −2.39675e10 | −0.0674767 | ||||||||
\(773\) | − | 5.17513e11i | − | 1.44945i | −0.689038 | − | 0.724725i | \(-0.741967\pi\) | ||
0.689038 | − | 0.724725i | \(-0.258033\pi\) | |||||||
\(774\) | −2.98872e11 | − | 5.93177e11i | −0.832764 | − | 1.65280i | ||||
\(775\) | −3.30920e10 | −0.0917310 | ||||||||
\(776\) | 2.73001e11i | 0.752864i | ||||||||
\(777\) | 2.57583e10 | + | 1.08368e11i | 0.0706696 | + | 0.297316i | ||||
\(778\) | 4.46181e11 | 1.21785 | ||||||||
\(779\) | 6.58337e9i | 0.0178772i | ||||||||
\(780\) | 1.69906e11 | − | 4.03853e10i | 0.459019 | − | 0.109105i | ||||
\(781\) | −1.67062e10 | −0.0449029 | ||||||||
\(782\) | − | 1.23602e12i | − | 3.30522i | ||||||
\(783\) | 2.03040e11 | − | 1.71047e11i | 0.540175 | − | 0.455061i | ||||
\(784\) | −1.39150e10 | −0.0368315 | ||||||||
\(785\) | 5.57570e11i | 1.46832i | ||||||||
\(786\) | −5.38919e10 | − | 2.26730e11i | −0.141199 | − | 0.594044i | ||||
\(787\) | −2.70083e11 | −0.704043 | −0.352021 | − | 0.935992i | \(-0.614506\pi\) | ||||
−0.352021 | + | 0.935992i | \(0.614506\pi\) | |||||||
\(788\) | − | 2.27778e10i | − | 0.0590755i | ||||||
\(789\) | 2.50339e10 | − | 5.95035e9i | 0.0645981 | − | 0.0153544i | ||||
\(790\) | −1.61512e10 | −0.0414663 | ||||||||
\(791\) | 1.57554e10i | 0.0402460i | ||||||||
\(792\) | 8.94885e10 | − | 4.50888e10i | 0.227440 | − | 0.114596i | ||||
\(793\) | −1.00656e12 | −2.54535 | ||||||||
\(794\) | 5.53055e11i | 1.39151i | ||||||||
\(795\) | 6.59983e10 | + | 2.77663e11i | 0.165221 | + | 0.695104i | ||||
\(796\) | 8.31414e9 | 0.0207093 | ||||||||
\(797\) | 5.71162e11i | 1.41555i | 0.706437 | + | 0.707776i | \(0.250301\pi\) | ||||
−0.706437 | + | 0.707776i | \(0.749699\pi\) | |||||||
\(798\) | 5.98643e10 | − | 1.42293e10i | 0.147624 | − | 0.0350890i | ||||
\(799\) | 1.43148e12 | 3.51235 | ||||||||
\(800\) | 1.19740e11i | 0.292333i | ||||||||
\(801\) | 1.75059e11 | + | 3.47443e11i | 0.425260 | + | 0.844021i | ||||
\(802\) | −4.73668e11 | −1.14492 | ||||||||
\(803\) | − | 4.32872e10i | − | 0.104111i | ||||||
\(804\) | −8.32806e9 | − | 3.50372e10i | −0.0199306 | − | 0.0838504i | ||||
\(805\) | 8.97196e11 | 2.13650 | ||||||||
\(806\) | 1.07308e11i | 0.254268i | ||||||||
\(807\) | −6.82923e11 | + | 1.62325e11i | −1.61019 | + | 0.382730i | ||||
\(808\) | −1.83845e11 | −0.431327 | ||||||||
\(809\) | 7.77063e10i | 0.181410i | 0.995878 | + | 0.0907051i | \(0.0289121\pi\) | ||||
−0.995878 | + | 0.0907051i | \(0.971088\pi\) | |||||||
\(810\) | −3.62952e11 | + | 4.90188e11i | −0.843157 | + | 1.13874i | ||||
\(811\) | −4.20722e11 | −0.972550 | −0.486275 | − | 0.873806i | \(-0.661645\pi\) | ||||
−0.486275 | + | 0.873806i | \(0.661645\pi\) | |||||||
\(812\) | − | 7.54875e10i | − | 0.173640i | ||||||
\(813\) | 3.92633e9 | + | 1.65186e10i | 0.00898721 | + | 0.0378103i | ||||
\(814\) | −4.43995e10 | −0.101130 | ||||||||
\(815\) | 2.19151e11i | 0.496721i | ||||||||
\(816\) | −9.14800e11 | + | 2.17441e11i | −2.06331 | + | 0.490433i | ||||
\(817\) | −9.92000e10 | −0.222650 | ||||||||
\(818\) | 3.73224e11i | 0.833598i | ||||||||
\(819\) | −6.25409e11 | + | 3.15113e11i | −1.39004 | + | 0.700375i | ||||
\(820\) | −1.85551e10 | −0.0410400 | ||||||||
\(821\) | − | 1.94681e11i | − | 0.428501i | −0.976779 | − | 0.214250i | \(-0.931269\pi\) | ||
0.976779 | − | 0.214250i | \(-0.0687309\pi\) | |||||||
\(822\) | −5.40683e10 | − | 2.27472e11i | −0.118428 | − | 0.498243i | ||||
\(823\) | −3.96058e11 | −0.863294 | −0.431647 | − | 0.902043i | \(-0.642067\pi\) | ||||
−0.431647 | + | 0.902043i | \(0.642067\pi\) | |||||||
\(824\) | − | 2.54292e10i | − | 0.0551598i | ||||||
\(825\) | 8.37506e10 | − | 1.99069e10i | 0.180789 | − | 0.0429721i | ||||
\(826\) | 1.00655e11 | 0.216229 | ||||||||
\(827\) | − | 3.83915e11i | − | 0.820753i | −0.911916 | − | 0.410377i | \(-0.865397\pi\) | ||
0.911916 | − | 0.410377i | \(-0.134603\pi\) | |||||||
\(828\) | −8.47395e10 | − | 1.68184e11i | −0.180287 | − | 0.357819i | ||||
\(829\) | 4.77482e11 | 1.01097 | 0.505486 | − | 0.862835i | \(-0.331313\pi\) | ||||
0.505486 | + | 0.862835i | \(0.331313\pi\) | |||||||
\(830\) | 4.18332e11i | 0.881471i | ||||||||
\(831\) | 1.17405e11 | + | 4.93939e11i | 0.246198 | + | 1.03578i | ||||
\(832\) | −4.80994e11 | −1.00380 | ||||||||
\(833\) | − | 2.68516e10i | − | 0.0557686i | ||||||
\(834\) | 3.12117e11 | − | 7.41877e10i | 0.645139 | − | 0.153344i | ||||
\(835\) | 6.35369e10 | 0.130701 | ||||||||
\(836\) | 4.78066e9i | 0.00978730i | ||||||||
\(837\) | −4.70643e10 | − | 5.58671e10i | −0.0958936 | − | 0.113829i | ||||
\(838\) | −6.42162e11 | −1.30217 | ||||||||
\(839\) | − | 2.03578e11i | − | 0.410850i | −0.978673 | − | 0.205425i | \(-0.934142\pi\) | ||
0.978673 | − | 0.205425i | \(-0.0658577\pi\) | |||||||
\(840\) | −1.25546e11 | − | 5.28189e11i | −0.252166 | − | 1.06089i | ||||
\(841\) | 2.50689e11 | 0.501131 | ||||||||
\(842\) | − | 5.60092e11i | − | 1.11432i | ||||||
\(843\) | −2.79989e11 | + | 6.65512e10i | −0.554410 | + | 0.131779i | ||||
\(844\) | 2.02088e10 | 0.0398264 | ||||||||
\(845\) | 8.74789e11i | 1.71584i | ||||||||
\(846\) | 9.99305e11 | − | 5.03500e11i | 1.95082 | − | 0.982920i | ||||
\(847\) | −4.75112e10 | −0.0923128 | ||||||||
\(848\) | 3.43929e11i | 0.665097i | ||||||||
\(849\) | −1.76950e11 | − | 7.44450e11i | −0.340580 | − | 1.43286i | ||||
\(850\) | −6.42529e11 | −1.23088 | ||||||||
\(851\) | − | 2.61217e11i | − | 0.498062i | ||||||
\(852\) | 1.84841e10 | − | 4.39351e9i | 0.0350783 | − | 0.00833784i | ||||
\(853\) | 9.38595e11 | 1.77289 | 0.886445 | − | 0.462833i | \(-0.153167\pi\) | ||||
0.886445 | + | 0.462833i | \(0.153167\pi\) | |||||||
\(854\) | − | 9.99571e11i | − | 1.87924i | ||||||
\(855\) | 4.09883e10 | + | 8.13502e10i | 0.0767001 | + | 0.152228i | ||||
\(856\) | 7.14746e10 | 0.133124 | ||||||||
\(857\) | 1.35992e11i | 0.252110i | 0.992023 | + | 0.126055i | \(0.0402316\pi\) | ||||
−0.992023 | + | 0.126055i | \(0.959768\pi\) | |||||||
\(858\) | −6.45523e10 | − | 2.71580e11i | −0.119114 | − | 0.501127i | ||||
\(859\) | 1.34551e11 | 0.247123 | 0.123562 | − | 0.992337i | \(-0.460568\pi\) | ||||
0.123562 | + | 0.992337i | \(0.460568\pi\) | |||||||
\(860\) | − | 2.79593e11i | − | 0.511131i | ||||||
\(861\) | 7.23894e10 | − | 1.72064e10i | 0.131723 | − | 0.0313096i | ||||
\(862\) | −7.73702e11 | −1.40134 | ||||||||
\(863\) | 8.12673e11i | 1.46512i | 0.680703 | + | 0.732560i | \(0.261674\pi\) | ||||
−0.680703 | + | 0.732560i | \(0.738326\pi\) | |||||||
\(864\) | −2.02149e11 | + | 1.70297e11i | −0.362757 | + | 0.305598i | ||||
\(865\) | 2.56768e10 | 0.0458645 | ||||||||
\(866\) | − | 7.45907e11i | − | 1.32621i | ||||||
\(867\) | −2.88928e11 | − | 1.21556e12i | −0.511344 | − | 2.15129i | ||||
\(868\) | −2.07706e10 | −0.0365907 | ||||||||
\(869\) | 5.03195e9i | 0.00882383i | ||||||||
\(870\) | 5.57800e11 | − | 1.32585e11i | 0.973646 | − | 0.231428i | ||||
\(871\) | 3.14057e11 | 0.545678 | ||||||||
\(872\) | 3.42760e11i | 0.592822i | ||||||||
\(873\) | −4.62338e11 | + | 2.32949e11i | −0.795981 | + | 0.401055i | ||||
\(874\) | −1.44300e11 | −0.247298 | ||||||||
\(875\) | 2.90352e11i | 0.495328i | ||||||||
\(876\) | 1.13839e10 | + | 4.78937e10i | 0.0193320 | + | 0.0813320i | ||||
\(877\) | −3.79776e10 | −0.0641991 | −0.0320996 | − | 0.999485i | \(-0.510219\pi\) | ||||
−0.0320996 | + | 0.999485i | \(0.510219\pi\) | |||||||
\(878\) | 8.05264e11i | 1.35507i | ||||||||
\(879\) | −9.99799e11 | + | 2.37644e11i | −1.67478 | + | 0.398081i | ||||
\(880\) | 2.72058e11 | 0.453661 | ||||||||
\(881\) | − | 8.59369e11i | − | 1.42651i | −0.700903 | − | 0.713257i | \(-0.747219\pi\) | ||
0.700903 | − | 0.713257i | \(-0.252781\pi\) | |||||||
\(882\) | −9.44462e9 | − | 1.87449e10i | −0.0156067 | − | 0.0309748i | ||||
\(883\) | −7.29170e11 | −1.19946 | −0.599731 | − | 0.800202i | \(-0.704726\pi\) | ||||
−0.599731 | + | 0.800202i | \(0.704726\pi\) | |||||||
\(884\) | 4.06112e11i | 0.665024i | ||||||||
\(885\) | 3.44585e10 | + | 1.44971e11i | 0.0561725 | + | 0.236325i | ||||
\(886\) | 6.69647e11 | 1.08670 | ||||||||
\(887\) | − | 4.01669e10i | − | 0.0648894i | −0.999474 | − | 0.0324447i | \(-0.989671\pi\) | ||
0.999474 | − | 0.0324447i | \(-0.0103293\pi\) | |||||||
\(888\) | −1.53781e11 | + | 3.65526e10i | −0.247316 | + | 0.0587850i | ||||
\(889\) | −8.74877e11 | −1.40068 | ||||||||
\(890\) | 8.40196e11i | 1.33912i | ||||||||
\(891\) | 1.52720e11 | + | 1.13079e11i | 0.242317 | + | 0.179420i | ||||
\(892\) | 2.40536e11 | 0.379945 | ||||||||
\(893\) | − | 1.67119e11i | − | 0.262797i | ||||||
\(894\) | 6.64584e10 | + | 2.79599e11i | 0.104040 | + | 0.437709i | ||||
\(895\) | 1.05006e12 | 1.63652 | ||||||||
\(896\) | − | 7.88082e11i | − | 1.22275i | ||||||
\(897\) | 1.59779e12 | − | 3.79783e11i | 2.46803 | − | 0.586632i | ||||
\(898\) | 9.27965e11 | 1.42701 | ||||||||
\(899\) | 6.86666e10i | 0.105125i | ||||||||
\(900\) | −8.74279e10 | + | 4.40506e10i | −0.133254 | + | 0.0671400i | ||||
\(901\) | −6.63674e11 | −1.00706 | ||||||||
\(902\) | 2.96586e10i | 0.0448048i | ||||||||
\(903\) | 2.59270e11 | + | 1.09078e12i | 0.389944 | + | 1.64054i | ||||
\(904\) | −2.23579e10 | −0.0334778 | ||||||||
\(905\) | − | 1.14307e12i | − | 1.70404i | ||||||
\(906\) | 1.13531e12 | − | 2.69853e11i | 1.68500 | − | 0.400511i | ||||
\(907\) | −5.89931e11 | −0.871710 | −0.435855 | − | 0.900017i | \(-0.643554\pi\) | ||||
−0.435855 | + | 0.900017i | \(0.643554\pi\) | |||||||
\(908\) | 1.71598e11i | 0.252446i | ||||||||
\(909\) | −1.56874e11 | − | 3.11350e11i | −0.229771 | − | 0.456029i | ||||
\(910\) | −1.51238e12 | −2.20545 | ||||||||
\(911\) | − | 6.83544e11i | − | 0.992414i | −0.868204 | − | 0.496207i | \(-0.834726\pi\) | ||
0.868204 | − | 0.496207i | \(-0.165274\pi\) | |||||||
\(912\) | 2.53852e10 | + | 1.06799e11i | 0.0366945 | + | 0.154379i | ||||
\(913\) | 1.30333e11 | 0.187573 | ||||||||
\(914\) | 1.21797e12i | 1.74523i | ||||||||
\(915\) | 1.43966e12 | − | 3.42197e11i | 2.05389 | − | 0.488193i | ||||
\(916\) | −2.57654e11 | −0.365978 | ||||||||
\(917\) | 3.93374e11i | 0.556325i | ||||||||
\(918\) | −9.13821e11 | − | 1.08474e12i | −1.28674 | − | 1.52741i | ||||
\(919\) | −1.13461e11 | −0.159068 | −0.0795341 | − | 0.996832i | \(-0.525343\pi\) | ||||
−0.0795341 | + | 0.996832i | \(0.525343\pi\) | |||||||
\(920\) | 1.27318e12i | 1.77720i | ||||||||
\(921\) | 5.30027e10 | + | 2.22989e11i | 0.0736647 | + | 0.309917i | ||||
\(922\) | 1.85968e11 | 0.257345 | ||||||||
\(923\) | 1.65683e11i | 0.228281i | ||||||||
\(924\) | 5.25672e10 | − | 1.24948e10i | 0.0721152 | − | 0.0171412i | ||||
\(925\) | −1.35790e11 | −0.185481 | ||||||||
\(926\) | 7.70805e11i | 1.04834i | ||||||||
\(927\) | 4.30654e10 | − | 2.16985e10i | 0.0583189 | − | 0.0293840i | ||||
\(928\) | 2.48462e11 | 0.335018 | ||||||||
\(929\) | − | 1.07038e12i | − | 1.43706i | −0.695497 | − | 0.718529i | \(-0.744816\pi\) | ||
0.695497 | − | 0.718529i | \(-0.255184\pi\) | |||||||
\(930\) | −3.64811e10 | − | 1.53480e11i | −0.0487681 | − | 0.205174i | ||||
\(931\) | −3.13480e9 | −0.00417264 | ||||||||
\(932\) | − | 7.78759e10i | − | 0.103214i | ||||||
\(933\) | 9.74407e11 | − | 2.31609e11i | 1.28592 | − | 0.305653i | ||||
\(934\) | 7.47542e11 | 0.982309 | ||||||||
\(935\) | 5.24987e11i | 0.686913i | ||||||||
\(936\) | −4.47165e11 | − | 8.87495e11i | −0.582591 | − | 1.15628i | ||||
\(937\) | 1.71227e11 | 0.222133 | 0.111067 | − | 0.993813i | \(-0.464573\pi\) | ||||
0.111067 | + | 0.993813i | \(0.464573\pi\) | |||||||
\(938\) | 3.11876e11i | 0.402875i | ||||||||
\(939\) | 1.23754e11 | + | 5.20650e11i | 0.159183 | + | 0.669705i | ||||
\(940\) | 4.71021e11 | 0.603294 | ||||||||
\(941\) | 1.43674e12i | 1.83240i | 0.400721 | + | 0.916200i | \(0.368760\pi\) | ||||
−0.400721 | + | 0.916200i | \(0.631240\pi\) | |||||||
\(942\) | −9.86067e11 | + | 2.34380e11i | −1.25228 | + | 0.297658i | ||||
\(943\) | −1.74492e11 | −0.220662 | ||||||||
\(944\) | 1.79569e11i | 0.226123i | ||||||||
\(945\) | 7.87383e11 | − | 6.63317e11i | 0.987322 | − | 0.831753i | ||||
\(946\) | −4.46904e11 | −0.558020 | ||||||||
\(947\) | 5.25277e11i | 0.653113i | 0.945178 | + | 0.326557i | \(0.105888\pi\) | ||||
−0.945178 | + | 0.326557i | \(0.894112\pi\) | |||||||
\(948\) | −1.32334e9 | − | 5.56744e9i | −0.00163846 | − | 0.00689322i | ||||
\(949\) | −4.29297e11 | −0.529289 | ||||||||
\(950\) | 7.50124e10i | 0.0920955i | ||||||||
\(951\) | 4.62740e11 | − | 1.09990e11i | 0.565737 | − | 0.134471i | ||||
\(952\) | 1.26249e12 | 1.53702 | ||||||||
\(953\) | 2.67354e11i | 0.324127i | 0.986780 | + | 0.162064i | \(0.0518150\pi\) | ||||
−0.986780 | + | 0.162064i | \(0.948185\pi\) | |||||||
\(954\) | −4.63306e11 | + | 2.33437e11i | −0.559338 | + | 0.281823i | ||||
\(955\) | 4.85428e11 | 0.583595 | ||||||||
\(956\) | − | 2.54999e11i | − | 0.305286i | ||||||
\(957\) | −4.13071e10 | − | 1.73784e11i | −0.0492467 | − | 0.207187i | ||||
\(958\) | 1.23671e12 | 1.46827 | ||||||||
\(959\) | 3.94662e11i | 0.466607i | ||||||||
\(960\) | 6.87956e11 | − | 1.63522e11i | 0.809982 | − | 0.192526i | ||||
\(961\) | −8.33997e11 | −0.977847 | ||||||||
\(962\) | 4.40328e11i | 0.514133i | ||||||||
\(963\) | 6.09887e10 | + | 1.21045e11i | 0.0709160 | + | 0.140748i | ||||
\(964\) | −2.96331e11 | −0.343138 | ||||||||
\(965\) | 3.07272e11i | 0.354335i | ||||||||
\(966\) | 3.77145e11 | + | 1.58670e12i | 0.433112 | + | 1.82216i | ||||
\(967\) | 9.71724e10 | 0.111131 | 0.0555657 | − | 0.998455i | \(-0.482304\pi\) | ||||
0.0555657 | + | 0.998455i | \(0.482304\pi\) | |||||||
\(968\) | − | 6.74213e10i | − | 0.0767884i | ||||||
\(969\) | −2.06088e11 | + | 4.89855e10i | −0.233753 | + | 0.0555613i | ||||
\(970\) | −1.11804e12 | −1.26290 | ||||||||
\(971\) | − | 5.20921e11i | − | 0.585997i | −0.956113 | − | 0.292998i | \(-0.905347\pi\) | ||
0.956113 | − | 0.292998i | \(-0.0946531\pi\) | |||||||
\(972\) | −1.98710e11 | − | 8.49491e10i | −0.222615 | − | 0.0951686i | ||||
\(973\) | −5.41520e11 | −0.604176 | ||||||||
\(974\) | − | 1.48869e12i | − | 1.65413i | ||||||
\(975\) | −1.97424e11 | − | 8.30590e11i | −0.218465 | − | 0.919111i | ||||
\(976\) | 1.78325e12 | 1.96523 | ||||||||
\(977\) | − | 1.52575e12i | − | 1.67458i | −0.546758 | − | 0.837290i | \(-0.684138\pi\) | ||
0.546758 | − | 0.837290i | \(-0.315862\pi\) | |||||||
\(978\) | −3.87569e11 | + | 9.21222e10i | −0.423637 | + | 0.100695i | ||||
\(979\) | 2.61766e11 | 0.284959 | ||||||||
\(980\) | − | 8.83537e9i | − | 0.00957901i | ||||||
\(981\) | −5.80479e11 | + | 2.92475e11i | −0.626774 | + | 0.315800i | ||||
\(982\) | −1.12289e12 | −1.20751 | ||||||||
\(983\) | − | 6.63916e11i | − | 0.711048i | −0.934667 | − | 0.355524i | \(-0.884302\pi\) | ||
0.934667 | − | 0.355524i | \(-0.115698\pi\) | |||||||
\(984\) | 2.44169e10 | + | 1.02725e11i | 0.0260442 | + | 0.109571i | ||||
\(985\) | −2.92020e11 | −0.310219 | ||||||||
\(986\) | 1.33326e12i | 1.41061i | ||||||||
\(987\) | −1.83761e12 | + | 4.36784e11i | −1.93635 | + | 0.460255i | ||||
\(988\) | 4.74118e10 | 0.0497575 | ||||||||
\(989\) | − | 2.62929e12i | − | 2.74823i | ||||||
\(990\) | 1.84656e11 | + | 3.66489e11i | 0.192230 | + | 0.381523i | ||||
\(991\) | −4.78852e11 | −0.496485 | −0.248243 | − | 0.968698i | \(-0.579853\pi\) | ||||
−0.248243 | + | 0.968698i | \(0.579853\pi\) | |||||||
\(992\) | − | 6.83652e10i | − | 0.0705973i | ||||||
\(993\) | 2.71761e10 | + | 1.14333e11i | 0.0279505 | + | 0.117591i | ||||
\(994\) | −1.64532e11 | −0.168541 | ||||||||
\(995\) | − | 1.06590e11i | − | 0.108749i | ||||||
\(996\) | −1.44202e11 | + | 3.42757e10i | −0.146533 | + | 0.0348297i | ||||
\(997\) | −2.53062e11 | −0.256122 | −0.128061 | − | 0.991766i | \(-0.540875\pi\) | ||||
−0.128061 | + | 0.991766i | \(0.540875\pi\) | |||||||
\(998\) | 2.62578e11i | 0.264689i | ||||||||
\(999\) | −1.93124e11 | − | 2.29245e11i | −0.193898 | − | 0.230164i |
(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 | 33.9.b.a.23.21 | yes | 26 | |
3.2 | odd | 2 | inner | 33.9.b.a.23.6 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.9.b.a.23.6 | ✓ | 26 | 3.2 | odd | 2 | inner | |
33.9.b.a.23.21 | yes | 26 | 1.1 | even | 1 | trivial |