Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [99,9,Mod(19,99)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(99, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("99.19");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 99 = 3^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 99.k (of order \(10\), degree \(4\), 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: | \(40.3304823961\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 11) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 28.3 | ||
Character | \(\chi\) | \(=\) | 99.28 |
Dual form | 99.9.k.a.46.3 |
$q$-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 \(\left(\mathbb{Z}/99\mathbb{Z}\right)^\times\).
\(n\) | \(46\) | \(56\) |
\(\chi(n)\) | \(e\left(\frac{9}{10}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.67744 | + | 2.16963i | −0.417340 | + | 0.135602i | −0.510157 | − | 0.860081i | \(-0.670413\pi\) |
0.0928173 | + | 0.995683i | \(0.470413\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −167.227 | + | 121.498i | −0.653232 | + | 0.474601i | ||||
\(5\) | 217.294 | − | 668.763i | 0.347671 | − | 1.07002i | −0.612467 | − | 0.790496i | \(-0.709823\pi\) |
0.960138 | − | 0.279525i | \(-0.0901771\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −790.545 | − | 1088.09i | −0.329256 | − | 0.453183i | 0.612009 | − | 0.790851i | \(-0.290362\pi\) |
−0.941265 | + | 0.337668i | \(0.890362\pi\) | |||||||
\(8\) | 1909.53 | − | 2628.24i | 0.466193 | − | 0.641660i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4937.07i | 0.493707i | ||||||||
\(11\) | 14415.0 | + | 2562.63i | 0.984563 | + | 0.175031i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 18414.6 | − | 5983.26i | 0.644746 | − | 0.209491i | 0.0316498 | − | 0.999499i | \(-0.489924\pi\) |
0.613096 | + | 0.790008i | \(0.289924\pi\) | |||||||
\(14\) | 7639.57 | + | 5550.47i | 0.198864 | + | 0.144483i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9303.62 | − | 28633.6i | 0.141962 | − | 0.436914i | ||||
\(17\) | −65096.6 | − | 21151.2i | −0.779404 | − | 0.253244i | −0.107819 | − | 0.994171i | \(-0.534387\pi\) |
−0.671586 | + | 0.740927i | \(0.734387\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −117001. | + | 161038.i | −0.897793 | + | 1.23571i | 0.0733740 | + | 0.997304i | \(0.476623\pi\) |
−0.971167 | + | 0.238401i | \(0.923377\pi\) | |||||||
\(20\) | 44915.7 | + | 138236.i | 0.280723 | + | 0.863977i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −101815. | + | 14163.4i | −0.434632 | + | 0.0604611i | ||||
\(23\) | 350509. | 1.25253 | 0.626265 | − | 0.779610i | \(-0.284583\pi\) | ||||
0.626265 | + | 0.779610i | \(0.284583\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −84005.1 | − | 61033.3i | −0.215053 | − | 0.156245i | ||||
\(26\) | −109981. | + | 79905.7i | −0.240671 | + | 0.174858i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 264402. | + | 85909.3i | 0.430162 | + | 0.139768i | ||||
\(29\) | −224769. | − | 309368.i | −0.317793 | − | 0.437405i | 0.619998 | − | 0.784603i | \(-0.287133\pi\) |
−0.937792 | + | 0.347198i | \(0.887133\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −312538. | − | 961894.i | −0.338420 | − | 1.04155i | −0.965013 | − | 0.262203i | \(-0.915551\pi\) |
0.626592 | − | 0.779347i | \(-0.284449\pi\) | |||||||
\(32\) | 1.04305e6i | 0.994727i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 480569. | 0.359617 | ||||||||
\(35\) | −899456. | + | 292251.i | −0.599388 | + | 0.194753i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −310990. | + | 225947.i | −0.165936 | + | 0.120559i | −0.667654 | − | 0.744472i | \(-0.732701\pi\) |
0.501718 | + | 0.865031i | \(0.332701\pi\) | |||||||
\(38\) | 431875. | − | 1.32917e6i | 0.207121 | − | 0.637452i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.34274e6 | − | 1.84812e6i | −0.524508 | − | 0.721923i | ||||
\(41\) | 1.87467e6 | − | 2.58026e6i | 0.663420 | − | 0.913120i | −0.336168 | − | 0.941802i | \(-0.609131\pi\) |
0.999589 | + | 0.0286824i | \(0.00913114\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 823502.i | 0.240875i | 0.992721 | + | 0.120437i | \(0.0384297\pi\) | ||||
−0.992721 | + | 0.120437i | \(0.961570\pi\) | |||||||
\(44\) | −2.72194e6 | + | 1.32285e6i | −0.726218 | + | 0.352938i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.34050e6 | + | 760476.i | −0.522731 | + | 0.169846i | ||||
\(47\) | −410370. | − | 298151.i | −0.0840978 | − | 0.0611006i | 0.544942 | − | 0.838474i | \(-0.316552\pi\) |
−0.629040 | + | 0.777373i | \(0.716552\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.22244e6 | − | 3.76228e6i | 0.212052 | − | 0.652630i | ||||
\(50\) | 693358. | + | 225286.i | 0.110937 | + | 0.0360457i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.35247e6 | + | 3.23790e6i | −0.321744 | + | 0.442843i | ||||
\(53\) | −2.23998e6 | − | 6.89394e6i | −0.283883 | − | 0.873703i | −0.986731 | − | 0.162363i | \(-0.948089\pi\) |
0.702848 | − | 0.711340i | \(-0.251911\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.84609e6 | − | 9.08337e6i | 0.529591 | − | 0.992650i | ||||
\(56\) | −4.36933e6 | −0.444286 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.17210e6 | + | 1.57812e6i | 0.191941 | + | 0.139453i | ||||
\(59\) | −1.56962e7 | + | 1.14040e7i | −1.29535 | + | 0.941126i | −0.999899 | − | 0.0142328i | \(-0.995469\pi\) |
−0.295450 | + | 0.955358i | \(0.595469\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.18306e7 | − | 7.09320e6i | −1.57669 | − | 0.512298i | −0.615490 | − | 0.788145i | \(-0.711042\pi\) |
−0.961202 | + | 0.275846i | \(0.911042\pi\) | |||||||
\(62\) | 4.17391e6 | + | 5.74489e6i | 0.282472 | + | 0.388790i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 118699. | + | 365318.i | 0.00707500 | + | 0.0217746i | ||||
\(65\) | − | 1.36151e7i | − | 0.762725i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.55334e7 | −1.76335 | −0.881673 | − | 0.471861i | \(-0.843583\pi\) | ||||
−0.881673 | + | 0.471861i | \(0.843583\pi\) | |||||||
\(68\) | 1.34558e7 | − | 4.37204e6i | 0.629322 | − | 0.204479i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.37199e6 | − | 3.90298e6i | 0.223740 | − | 0.162556i | ||||
\(71\) | 9.45943e6 | − | 2.91131e7i | 0.372247 | − | 1.14566i | −0.573070 | − | 0.819506i | \(-0.694248\pi\) |
0.945317 | − | 0.326153i | \(-0.105752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.84406e7 | − | 3.91452e7i | −1.00149 | − | 1.37844i | −0.924405 | − | 0.381411i | \(-0.875438\pi\) |
−0.0770868 | − | 0.997024i | \(-0.524562\pi\) | |||||||
\(74\) | 1.58639e6 | − | 2.18348e6i | 0.0529034 | − | 0.0728153i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.11455e7i | − | 1.23330i | ||||||
\(77\) | −8.60731e6 | − | 1.77107e7i | −0.244853 | − | 0.503817i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.20948e7 | − | 1.36774e7i | 1.08074 | − | 0.351152i | 0.286076 | − | 0.958207i | \(-0.407649\pi\) |
0.794660 | + | 0.607055i | \(0.207649\pi\) | |||||||
\(80\) | −1.71275e7 | − | 1.24438e7i | −0.418151 | − | 0.303804i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.91976e6 | + | 2.12968e7i | −0.153051 | + | 0.471042i | ||||
\(83\) | −3.72684e7 | − | 1.21092e7i | −0.785286 | − | 0.255155i | −0.111191 | − | 0.993799i | \(-0.535466\pi\) |
−0.674096 | + | 0.738644i | \(0.735466\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.82903e7 | + | 3.89382e7i | −0.541952 | + | 0.745934i | ||||
\(86\) | −1.78670e6 | − | 5.49889e6i | −0.0326631 | − | 0.100527i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.42610e7 | − | 3.29926e7i | 0.571307 | − | 0.550156i | ||||
\(89\) | 2.40233e7 | 0.382888 | 0.191444 | − | 0.981503i | \(-0.438683\pi\) | ||||
0.191444 | + | 0.981503i | \(0.438683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.10679e7 | − | 1.53067e7i | −0.307224 | − | 0.223211i | ||||
\(92\) | −5.86148e7 | + | 4.25862e7i | −0.818194 | + | 0.594453i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.38710e6 | + | 1.10054e6i | 0.0433827 | + | 0.0140959i | ||||
\(95\) | 8.22728e7 | + | 1.13239e8i | 1.01009 | + | 1.39028i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.79731e7 | + | 1.16869e8i | 0.428933 | + | 1.32012i | 0.899177 | + | 0.437584i | \(0.144166\pi\) |
−0.470244 | + | 0.882536i | \(0.655834\pi\) | |||||||
\(98\) | 2.77746e7i | 0.301123i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.14634e7 | 0.214634 | ||||||||
\(101\) | −1.72564e6 | + | 560696.i | −0.0165831 | + | 0.00538817i | −0.317297 | − | 0.948326i | \(-0.602775\pi\) |
0.300714 | + | 0.953714i | \(0.402775\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.15046e7 | + | 3.74203e7i | −0.457612 | + | 0.332475i | −0.792594 | − | 0.609750i | \(-0.791270\pi\) |
0.334982 | + | 0.942225i | \(0.391270\pi\) | |||||||
\(104\) | 1.94377e7 | − | 5.98231e7i | 0.166154 | − | 0.511371i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.99146e7 | + | 4.11739e7i | 0.236952 | + | 0.326136i | ||||
\(107\) | −1.37406e7 | + | 1.89124e7i | −0.104827 | + | 0.144282i | −0.858208 | − | 0.513303i | \(-0.828422\pi\) |
0.753381 | + | 0.657585i | \(0.228422\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.51242e8i | 1.07144i | 0.844396 | + | 0.535719i | \(0.179959\pi\) | ||||
−0.844396 | + | 0.535719i | \(0.820041\pi\) | |||||||
\(110\) | −1.26519e7 | + | 7.11678e7i | −0.0864142 | + | 0.486086i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.85109e7 | + | 1.25129e7i | −0.244744 | + | 0.0795220i | ||||
\(113\) | −1.05791e8 | − | 7.68614e7i | −0.648834 | − | 0.471405i | 0.214040 | − | 0.976825i | \(-0.431338\pi\) |
−0.862874 | + | 0.505420i | \(0.831338\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.61637e7 | − | 2.34408e8i | 0.435469 | − | 1.34023i | ||||
\(116\) | 7.51752e7 | + | 2.44259e7i | 0.415186 | + | 0.134902i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.00680e7 | − | 1.10204e8i | 0.412982 | − | 0.568421i | ||||
\(119\) | 2.84474e7 | + | 8.75521e7i | 0.141858 | + | 0.436595i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.01225e8 | + | 7.38806e7i | 0.938728 | + | 0.344659i | ||||
\(122\) | 1.61162e8 | 0.727485 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.69133e8 | + | 1.22882e8i | 0.715388 | + | 0.519760i | ||||
\(125\) | 1.63150e8 | − | 1.18535e8i | 0.668261 | − | 0.485520i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.18610e8 | − | 1.03523e8i | −1.22474 | − | 0.397942i | −0.375934 | − | 0.926646i | \(-0.622678\pi\) |
−0.848806 | + | 0.528704i | \(0.822678\pi\) | |||||||
\(128\) | −1.58536e8 | − | 2.18206e8i | −0.590591 | − | 0.812879i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.95398e7 | + | 9.09141e7i | 0.103427 | + | 0.318316i | ||||
\(131\) | 3.32594e8i | 1.12935i | 0.825312 | + | 0.564677i | \(0.190999\pi\) | ||||
−0.825312 | + | 0.564677i | \(0.809001\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.67719e8 | 0.855604 | ||||||||
\(134\) | 2.37272e8 | − | 7.70944e7i | 0.735915 | − | 0.239113i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.79894e8 | + | 1.30701e8i | −0.525849 | + | 0.382052i | ||||
\(137\) | −2.38491e7 | + | 7.34000e7i | −0.0677002 | + | 0.208360i | −0.979183 | − | 0.202978i | \(-0.934938\pi\) |
0.911483 | + | 0.411337i | \(0.134938\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.74632e8 | + | 2.40360e8i | 0.467805 | + | 0.643878i | 0.976104 | − | 0.217302i | \(-0.0697256\pi\) |
−0.508299 | + | 0.861180i | \(0.669726\pi\) | |||||||
\(140\) | 1.14906e8 | − | 1.58154e8i | 0.299110 | − | 0.411689i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.14924e8i | 0.528607i | ||||||||
\(143\) | 2.80779e8 | − | 3.90588e7i | 0.671460 | − | 0.0934060i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.55735e8 | + | 8.30934e7i | −0.578520 | + | 0.187973i | ||||
\(146\) | 2.74841e8 | + | 1.99684e8i | 0.604881 | + | 0.439472i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.45539e7 | − | 7.55692e7i | 0.0511769 | − | 0.157506i | ||||
\(149\) | −7.65026e8 | − | 2.48572e8i | −1.55214 | − | 0.504321i | −0.597447 | − | 0.801908i | \(-0.703818\pi\) |
−0.954695 | + | 0.297587i | \(0.903818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.45478e8 | − | 2.00233e8i | 0.279826 | − | 0.385148i | −0.645850 | − | 0.763464i | \(-0.723497\pi\) |
0.925676 | + | 0.378317i | \(0.123497\pi\) | |||||||
\(152\) | 1.99830e8 | + | 6.15014e8i | 0.374358 | + | 1.15216i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.59005e7 | + | 9.95874e7i | 0.170505 | + | 0.177060i | ||||
\(155\) | −7.11192e8 | −1.23214 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.83915e8 | − | 2.06276e8i | −0.467293 | − | 0.339508i | 0.329092 | − | 0.944298i | \(-0.393257\pi\) |
−0.796385 | + | 0.604789i | \(0.793257\pi\) | |||||||
\(158\) | −2.51410e8 | + | 1.82660e8i | −0.403417 | + | 0.293100i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.97551e8 | + | 2.26648e8i | 1.06438 | + | 0.345838i | ||||
\(161\) | −2.77093e8 | − | 3.81386e8i | −0.412404 | − | 0.567625i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.26055e8 | + | 3.87958e8i | 0.178571 | + | 0.549585i | 0.999779 | − | 0.0210449i | \(-0.00669929\pi\) |
−0.821208 | + | 0.570629i | \(0.806699\pi\) | |||||||
\(164\) | 6.59258e8i | 0.911339i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.75130e8 | 0.362331 | ||||||||
\(167\) | 1.01780e9 | − | 3.30703e8i | 1.30857 | − | 0.425179i | 0.430014 | − | 0.902822i | \(-0.358509\pi\) |
0.878554 | + | 0.477643i | \(0.158509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.56642e8 | + | 2.59116e8i | −0.437206 | + | 0.317649i | ||||
\(170\) | 1.04425e8 | − | 3.21387e8i | 0.125028 | − | 0.384798i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.00054e8 | − | 1.37712e8i | −0.114319 | − | 0.157347i | ||||
\(173\) | −2.70031e7 | + | 3.71665e7i | −0.0301459 | + | 0.0414923i | −0.823824 | − | 0.566846i | \(-0.808164\pi\) |
0.793678 | + | 0.608338i | \(0.208164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.39655e8i | 0.148903i | ||||||||
\(176\) | 2.07489e8 | − | 3.88911e8i | 0.216244 | − | 0.405321i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.60414e8 | + | 5.21216e7i | −0.159795 | + | 0.0519204i | ||||
\(179\) | −8.32761e8 | − | 6.05036e8i | −0.811163 | − | 0.589345i | 0.103004 | − | 0.994681i | \(-0.467154\pi\) |
−0.914168 | + | 0.405336i | \(0.867154\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.53006e8 | − | 7.78673e8i | 0.235731 | − | 0.725506i | −0.761293 | − | 0.648409i | \(-0.775435\pi\) |
0.997024 | − | 0.0770970i | \(-0.0245651\pi\) | |||||||
\(182\) | 1.73889e8 | + | 5.65001e7i | 0.158485 | + | 0.0514948i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.69307e8 | − | 9.21223e8i | 0.583921 | − | 0.803699i | ||||
\(185\) | 8.35289e7 | + | 2.57076e8i | 0.0713099 | + | 0.219469i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.84164e8 | − | 4.71713e8i | −0.723047 | − | 0.385755i | ||||
\(188\) | 1.04850e8 | 0.0839338 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.95058e8 | − | 5.77644e8i | −0.610077 | − | 0.443247i | ||||
\(191\) | 5.40048e8 | − | 3.92367e8i | 0.405787 | − | 0.294822i | −0.366107 | − | 0.930573i | \(-0.619310\pi\) |
0.771894 | + | 0.635751i | \(0.219310\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.09726e9 | − | 6.81442e8i | −1.51155 | − | 0.491134i | −0.568192 | − | 0.822896i | \(-0.692357\pi\) |
−0.943363 | + | 0.331762i | \(0.892357\pi\) | |||||||
\(194\) | −5.07126e8 | − | 6.98000e8i | −0.358022 | − | 0.492775i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.52684e8 | + | 7.77681e8i | 0.171219 | + | 0.526959i | ||||
\(197\) | − | 2.23782e8i | − | 0.148580i | −0.997237 | − | 0.0742899i | \(-0.976331\pi\) | ||
0.997237 | − | 0.0742899i | \(-0.0236690\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.49591e9 | 0.953880 | 0.476940 | − | 0.878936i | \(-0.341746\pi\) | ||||
0.476940 | + | 0.878936i | \(0.341746\pi\) | |||||||
\(200\) | −3.20820e8 | + | 1.04241e8i | −0.200512 | + | 0.0651505i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.03064e7 | − | 7.48802e6i | 0.00619014 | − | 0.00449740i | ||||
\(203\) | −1.58931e8 | + | 4.89139e8i | −0.0935889 | + | 0.288037i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.31823e9 | − | 1.81438e9i | −0.746405 | − | 1.02734i | ||||
\(206\) | 2.62731e8 | − | 3.61618e8i | 0.145896 | − | 0.200808i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 5.82942e8i | − | 0.311438i | ||||||
\(209\) | −2.09925e9 | + | 2.02153e9i | −1.10022 | + | 1.05949i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.47026e9 | + | 4.77716e8i | −0.741760 | + | 0.241013i | −0.655432 | − | 0.755254i | \(-0.727513\pi\) |
−0.0863283 | + | 0.996267i | \(0.527513\pi\) | |||||||
\(212\) | 1.21218e9 | + | 8.80703e8i | 0.600102 | + | 0.436000i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.07194e7 | − | 1.56098e8i | 0.0241835 | − | 0.0744292i | ||||
\(215\) | 5.50728e8 | + | 1.78942e8i | 0.257741 | + | 0.0837451i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.99553e8 | + | 1.10049e9i | −0.360585 | + | 0.496303i | ||||
\(218\) | −3.28140e8 | − | 1.00991e9i | −0.145289 | − | 0.447154i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.93210e8 | + | 2.10778e9i | 0.125167 | + | 0.899775i | ||||
\(221\) | −1.32528e9 | −0.555570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.58942e9 | − | 1.15478e9i | −0.642716 | − | 0.466960i | 0.218066 | − | 0.975934i | \(-0.430025\pi\) |
−0.860782 | + | 0.508974i | \(0.830025\pi\) | |||||||
\(224\) | 1.13493e9 | − | 8.24575e8i | 0.450793 | − | 0.327520i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 8.73171e8 | + | 2.83710e8i | 0.334708 | + | 0.108753i | ||||
\(227\) | 3.86822e8 | + | 5.32415e8i | 0.145683 | + | 0.200515i | 0.875622 | − | 0.482997i | \(-0.160452\pi\) |
−0.729939 | + | 0.683512i | \(0.760452\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.66531e7 | + | 1.12807e8i | 0.0133281 | + | 0.0410197i | 0.957499 | − | 0.288435i | \(-0.0931350\pi\) |
−0.944171 | + | 0.329455i | \(0.893135\pi\) | |||||||
\(230\) | 1.73049e9i | 0.618383i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.24230e9 | −0.428818 | ||||||||
\(233\) | 1.79732e7 | − | 5.83985e6i | 0.00609820 | − | 0.00198143i | −0.305966 | − | 0.952042i | \(-0.598979\pi\) |
0.312065 | + | 0.950061i | \(0.398979\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.88564e8 | + | 2.09654e8i | −0.0946173 | + | 0.0687435i | ||||
\(236\) | 1.23928e9 | − | 3.81411e9i | 0.399504 | − | 1.22955i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.79911e8 | − | 5.22903e8i | −0.118406 | − | 0.162972i | ||||
\(239\) | 7.91860e8 | − | 1.08990e9i | 0.242693 | − | 0.334038i | −0.670243 | − | 0.742142i | \(-0.733810\pi\) |
0.912935 | + | 0.408104i | \(0.133810\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.25935e9i | − | 1.55906i | −0.626363 | − | 0.779531i | \(-0.715457\pi\) | ||
0.626363 | − | 0.779531i | \(-0.284543\pi\) | |||||||
\(242\) | −1.50396e9 | − | 5.67501e7i | −0.438505 | − | 0.0165465i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.51249e9 | − | 1.46620e9i | 1.27308 | − | 0.413650i | ||||
\(245\) | −2.25045e9 | − | 1.63504e9i | −0.624603 | − | 0.453801i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.19099e9 | + | 3.66550e9i | −0.319979 | + | 0.984795i | ||||
\(248\) | −3.12489e9 | − | 1.01534e9i | −0.826090 | − | 0.268413i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.32244e8 | + | 1.14549e9i | −0.213054 | + | 0.293244i | ||||
\(251\) | −1.84918e7 | − | 5.69120e7i | −0.00465892 | − | 0.0143387i | 0.948700 | − | 0.316178i | \(-0.102400\pi\) |
−0.953359 | + | 0.301839i | \(0.902400\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.05259e9 | + | 8.98227e8i | 1.23320 | + | 0.219232i | ||||
\(254\) | 2.35210e9 | 0.565095 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.45248e9 | + | 1.05529e9i | 0.338183 | + | 0.245704i | ||||
\(257\) | −9.77634e8 | + | 7.10292e8i | −0.224101 | + | 0.162819i | −0.694171 | − | 0.719810i | \(-0.744229\pi\) |
0.470070 | + | 0.882629i | \(0.344229\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.91703e8 | + | 1.59764e8i | 0.109271 | + | 0.0355042i | ||||
\(260\) | 1.65421e9 | + | 2.27682e9i | 0.361990 | + | 0.498237i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.21607e8 | − | 2.22088e9i | −0.153142 | − | 0.471324i | ||||
\(263\) | − | 4.22692e8i | − | 0.0883490i | −0.999024 | − | 0.0441745i | \(-0.985934\pi\) | ||
0.999024 | − | 0.0441745i | \(-0.0140658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.09714e9 | −1.03358 | ||||||||
\(266\) | −1.78768e9 | + | 5.80852e8i | −0.357078 | + | 0.116022i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.94216e9 | − | 4.31723e9i | 1.15187 | − | 0.836886i | ||||
\(269\) | 1.37486e9 | − | 4.23137e9i | 0.262572 | − | 0.808112i | −0.729671 | − | 0.683798i | \(-0.760327\pi\) |
0.992243 | − | 0.124314i | \(-0.0396731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.33326e8 | + | 1.14697e9i | 0.154503 | + | 0.212656i | 0.879251 | − | 0.476359i | \(-0.158044\pi\) |
−0.724748 | + | 0.689014i | \(0.758044\pi\) | |||||||
\(272\) | −1.21127e9 | + | 1.66717e9i | −0.221291 | + | 0.304582i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.41868e8i | − | 0.0961371i | ||||||
\(275\) | −1.05453e9 | − | 1.09507e9i | −0.184385 | − | 0.191474i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.22449e9 | + | 1.04770e9i | −0.547700 | + | 0.177958i | −0.569779 | − | 0.821798i | \(-0.692971\pi\) |
0.0220796 | + | 0.999756i | \(0.492971\pi\) | |||||||
\(278\) | −1.68759e9 | − | 1.22610e9i | −0.282545 | − | 0.205281i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.49431e8 | + | 2.92205e9i | −0.154465 | + | 0.475396i | ||||
\(281\) | 8.68202e9 | + | 2.82096e9i | 1.39250 | + | 0.452451i | 0.906758 | − | 0.421651i | \(-0.138549\pi\) |
0.485743 | + | 0.874102i | \(0.338549\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.81537e9 | + | 5.25141e9i | −0.594828 | + | 0.818711i | −0.995223 | − | 0.0976323i | \(-0.968873\pi\) |
0.400394 | + | 0.916343i | \(0.368873\pi\) | |||||||
\(284\) | 1.95531e9 | + | 6.01781e9i | 0.300567 | + | 0.925051i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.79014e9 | + | 8.69999e8i | −0.267561 | + | 0.130033i | ||||
\(287\) | −4.28956e9 | −0.632245 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.85331e9 | − | 1.34651e9i | −0.265678 | − | 0.193027i | ||||
\(290\) | 1.52737e9 | − | 1.10970e9i | 0.215950 | − | 0.156897i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.51211e9 | + | 3.09067e9i | 1.30841 | + | 0.425130i | ||||
\(293\) | 5.45610e9 | + | 7.50968e9i | 0.740307 | + | 1.01895i | 0.998601 | + | 0.0528793i | \(0.0168398\pi\) |
−0.258293 | + | 0.966066i | \(0.583160\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.21585e9 | + | 1.29751e10i | 0.556669 | + | 1.71325i | ||||
\(296\) | 1.24881e9i | 0.162678i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.64773e9 | 0.716157 | ||||||||
\(299\) | 6.45449e9 | − | 2.09719e9i | 0.807564 | − | 0.262393i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.96046e8 | − | 6.51016e8i | 0.109160 | − | 0.0793095i | ||||
\(302\) | −5.36986e8 | + | 1.65267e9i | −0.0645558 | + | 0.198682i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.52257e9 | + | 4.84840e9i | 0.412445 | + | 0.567681i | ||||
\(305\) | −9.48734e9 | + | 1.30582e10i | −1.09634 | + | 1.50898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.17364e9i | − | 0.357276i | −0.983915 | − | 0.178638i | \(-0.942831\pi\) | ||
0.983915 | − | 0.178638i | \(-0.0571691\pi\) | |||||||
\(308\) | 3.59119e9 | + | 1.91595e9i | 0.399058 | + | 0.212902i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.74894e9 | − | 1.54302e9i | 0.514221 | − | 0.167080i | ||||
\(311\) | 1.51260e9 | + | 1.09897e9i | 0.161690 | + | 0.117474i | 0.665688 | − | 0.746230i | \(-0.268138\pi\) |
−0.503998 | + | 0.863705i | \(0.668138\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.41074e8 | − | 1.66526e9i | 0.0563741 | − | 0.173502i | −0.918905 | − | 0.394480i | \(-0.870925\pi\) |
0.975279 | + | 0.220978i | \(0.0709249\pi\) | |||||||
\(314\) | 2.34337e9 | + | 7.61406e8i | 0.241058 | + | 0.0783245i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.37762e9 | + | 7.40166e9i | −0.539314 | + | 0.742303i | ||||
\(317\) | −5.21490e9 | − | 1.60498e10i | −0.516427 | − | 1.58940i | −0.780671 | − | 0.624943i | \(-0.785122\pi\) |
0.264244 | − | 0.964456i | \(-0.414878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.44725e9 | − | 5.03554e9i | −0.236328 | − | 0.486277i | ||||
\(320\) | 2.70104e8 | 0.0257591 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.67774e9 | + | 1.94549e9i | 0.249084 | + | 0.180970i | ||||
\(323\) | 1.10225e10 | − | 8.00834e9i | 1.01268 | − | 0.735754i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.91210e9 | − | 6.21278e8i | −0.171386 | − | 0.0556868i | ||||
\(326\) | −1.68345e9 | − | 2.31707e9i | −0.149049 | − | 0.205149i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −3.20181e9 | − | 9.85414e9i | −0.276630 | − | 0.851380i | ||||
\(329\) | 6.82222e8i | 0.0582294i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.80681e9 | 0.317138 | 0.158569 | − | 0.987348i | \(-0.449312\pi\) | ||||
0.158569 | + | 0.987348i | \(0.449312\pi\) | |||||||
\(332\) | 7.70354e9 | − | 2.50303e9i | 0.634071 | − | 0.206022i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.07879e9 | + | 4.41650e9i | −0.488462 | + | 0.354889i | ||||
\(335\) | −7.72121e9 | + | 2.37634e10i | −0.613064 | + | 1.88682i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.51776e9 | + | 1.31001e10i | 0.737930 | + | 1.01567i | 0.998735 | + | 0.0502817i | \(0.0160119\pi\) |
−0.260805 | + | 0.965391i | \(0.583988\pi\) | |||||||
\(338\) | 1.81927e9 | − | 2.50401e9i | 0.139390 | − | 0.191853i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 9.94874e9i | − | 0.744479i | ||||||
\(341\) | −2.04025e9 | − | 1.46666e10i | −0.150892 | − | 1.08471i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.24340e10 | + | 4.04006e9i | −0.898328 | + | 0.291885i | ||||
\(344\) | 2.16436e9 | + | 1.57250e9i | 0.154560 | + | 0.112294i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.96736e7 | − | 3.06764e8i | 0.00695466 | − | 0.0214042i | ||||
\(347\) | −5.39777e9 | − | 1.75384e9i | −0.372303 | − | 0.120968i | 0.116888 | − | 0.993145i | \(-0.462708\pi\) |
−0.489191 | + | 0.872177i | \(0.662708\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.71903e9 | − | 1.20007e10i | 0.587715 | − | 0.808920i | −0.406800 | − | 0.913517i | \(-0.633355\pi\) |
0.994515 | + | 0.104597i | \(0.0333554\pi\) | |||||||
\(350\) | −3.02999e8 | − | 9.32536e8i | −0.0201915 | − | 0.0621431i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.67295e9 | + | 1.50355e10i | −0.174108 | + | 0.979371i | ||||
\(353\) | 9.89071e9 | 0.636984 | 0.318492 | − | 0.947926i | \(-0.396824\pi\) | ||||
0.318492 | + | 0.947926i | \(0.396824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.74143e10 | − | 1.26522e10i | −1.09646 | − | 0.796625i | ||||
\(356\) | −4.01735e9 | + | 2.91878e9i | −0.250115 | + | 0.181719i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.87341e9 | + | 2.23331e9i | 0.418447 | + | 0.135962i | ||||
\(359\) | −7.63373e9 | − | 1.05069e10i | −0.459578 | − | 0.632555i | 0.514843 | − | 0.857284i | \(-0.327850\pi\) |
−0.974421 | + | 0.224730i | \(0.927850\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.99587e9 | − | 2.15311e10i | −0.411920 | − | 1.26776i | ||||
\(362\) | 5.74847e9i | 0.334748i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.38286e9 | 0.306625 | ||||||||
\(365\) | −3.23588e10 | + | 1.05140e10i | −1.82315 | + | 0.592376i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.44759e10 | − | 1.05174e10i | 0.797962 | − | 0.579754i | −0.112353 | − | 0.993668i | \(-0.535839\pi\) |
0.910316 | + | 0.413915i | \(0.135839\pi\) | |||||||
\(368\) | 3.26101e9 | − | 1.00363e10i | 0.177812 | − | 0.547248i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.11552e9 | − | 1.53538e9i | −0.0595210 | − | 0.0819236i | ||||
\(371\) | −5.73043e9 | + | 7.88726e9i | −0.302477 | + | 0.416323i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91399e10i | 0.988789i | 0.869238 | + | 0.494394i | \(0.164610\pi\) | ||||
−0.869238 | + | 0.494394i | \(0.835390\pi\) | |||||||
\(374\) | 6.92739e9 | + | 1.23152e9i | 0.354065 | + | 0.0629442i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.56723e9 | + | 5.09223e8i | −0.0784116 | + | 0.0254775i | ||||
\(377\) | −5.99006e9 | − | 4.35204e9i | −0.296528 | − | 0.215440i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.23013e9 | − | 2.22520e10i | 0.350420 | − | 1.07848i | −0.608197 | − | 0.793786i | \(-0.708107\pi\) |
0.958618 | − | 0.284697i | \(-0.0918929\pi\) | |||||||
\(380\) | −2.75166e10 | − | 8.94067e9i | −1.31965 | − | 0.428781i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.75484e9 | + | 3.79171e9i | −0.129373 | + | 0.178066i | ||||
\(383\) | 1.32385e9 | + | 4.07439e9i | 0.0615239 | + | 0.189351i | 0.977094 | − | 0.212806i | \(-0.0682604\pi\) |
−0.915570 | + | 0.402158i | \(0.868260\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37146e10 | + | 1.90782e9i | −0.624223 | + | 0.0868348i | ||||
\(386\) | 1.54828e10 | 0.697431 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.05495e10 | − | 1.49301e10i | −0.906724 | − | 0.658773i | ||||
\(389\) | 1.96672e10 | − | 1.42891e10i | 0.858903 | − | 0.624029i | −0.0686834 | − | 0.997639i | \(-0.521880\pi\) |
0.927586 | + | 0.373609i | \(0.121880\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.28170e10 | − | 7.41369e9i | −0.976228 | − | 0.317196i | ||||
\(392\) | −7.55389e9 | − | 1.03970e10i | −0.319909 | − | 0.440317i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.85524e8 | + | 1.49429e9i | 0.0201477 | + | 0.0620083i | ||||
\(395\) | − | 3.11234e10i | − | 1.27850i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.11498e9 | 0.366939 | 0.183469 | − | 0.983025i | \(-0.441267\pi\) | ||||
0.183469 | + | 0.983025i | \(0.441267\pi\) | |||||||
\(398\) | −9.98885e9 | + | 3.24558e9i | −0.398092 | + | 0.129348i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.52915e9 | + | 1.83754e9i | −0.0987950 | + | 0.0717788i | ||||
\(401\) | 2.39904e9 | − | 7.38349e9i | 0.0927813 | − | 0.285551i | −0.893888 | − | 0.448291i | \(-0.852033\pi\) |
0.986669 | + | 0.162739i | \(0.0520329\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.15105e10 | − | 1.58429e10i | −0.436390 | − | 0.600639i | ||||
\(404\) | 2.20452e8 | − | 3.03426e8i | 0.00827538 | − | 0.0113901i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 3.61102e9i | − | 0.132900i | ||||||
\(407\) | −5.06194e9 | + | 2.46008e9i | −0.184476 | + | 0.0896542i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.69258e10 | + | 1.19979e10i | −1.31958 | + | 0.428758i | −0.882351 | − | 0.470591i | \(-0.844041\pi\) |
−0.437230 | + | 0.899350i | \(0.644041\pi\) | |||||||
\(410\) | 1.27389e10 | + | 9.25536e9i | 0.450814 | + | 0.327535i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.06650e9 | − | 1.25154e10i | 0.141134 | − | 0.434366i | ||||
\(413\) | 2.48171e10 | + | 8.06357e9i | 0.853004 | + | 0.277158i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.61964e10 | + | 2.22924e10i | −0.546042 | + | 0.751563i | ||||
\(416\) | 6.24082e9 | + | 1.92073e10i | 0.208386 | + | 0.641346i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.63165e9 | − | 1.80533e10i | 0.315497 | − | 0.591359i | ||||
\(419\) | 2.41027e9 | 0.0782005 | 0.0391003 | − | 0.999235i | \(-0.487551\pi\) | ||||
0.0391003 | + | 0.999235i | \(0.487551\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.94463e10 | + | 2.86594e10i | 1.25568 | + | 0.912303i | 0.998537 | − | 0.0540713i | \(-0.0172198\pi\) |
0.257140 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(422\) | 8.78108e9 | − | 6.37983e9i | 0.276884 | − | 0.201168i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.23962e10 | − | 7.27697e9i | −0.692965 | − | 0.225158i | ||||
\(425\) | 4.17752e9 | + | 5.74987e9i | 0.128045 | + | 0.176239i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.54003e9 | + | 2.93612e10i | 0.286971 | + | 0.883207i | ||||
\(428\) | − | 4.83213e9i | − | 0.144000i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.06569e9 | −0.118922 | ||||||||
\(431\) | 6.49011e9 | − | 2.10877e9i | 0.188080 | − | 0.0611110i | −0.213463 | − | 0.976951i | \(-0.568474\pi\) |
0.401543 | + | 0.915840i | \(0.368474\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.53158e10 | − | 1.83930e10i | 0.720177 | − | 0.523239i | −0.166264 | − | 0.986081i | \(-0.553170\pi\) |
0.886441 | + | 0.462842i | \(0.153170\pi\) | |||||||
\(434\) | 2.95131e9 | − | 9.08319e9i | 0.0831870 | − | 0.256023i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.83756e10 | − | 2.52919e10i | −0.508506 | − | 0.699898i | ||||
\(437\) | −4.10100e10 | + | 5.64455e10i | −1.12451 | + | 1.54776i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.21529e9i | 0.0865689i | 0.999063 | + | 0.0432845i | \(0.0137822\pi\) | ||||
−0.999063 | + | 0.0432845i | \(0.986218\pi\) | |||||||
\(440\) | −1.46195e10 | − | 3.00816e10i | −0.390052 | − | 0.802584i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.84948e9 | − | 2.87537e9i | 0.231861 | − | 0.0753363i | ||||
\(443\) | −3.90304e10 | − | 2.83572e10i | −1.01342 | − | 0.736290i | −0.0484937 | − | 0.998823i | \(-0.515442\pi\) |
−0.964923 | + | 0.262533i | \(0.915442\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.22012e9 | − | 1.60659e10i | 0.133119 | − | 0.409699i | ||||
\(446\) | 1.31187e10 | + | 4.26252e9i | 0.331552 | + | 0.107728i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.03662e8 | − | 4.17955e8i | 0.00753839 | − | 0.0103757i | ||||
\(449\) | 9.74677e9 | + | 2.99975e10i | 0.239814 | + | 0.738073i | 0.996446 | + | 0.0842317i | \(0.0268436\pi\) |
−0.756632 | + | 0.653841i | \(0.773156\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.36355e10 | − | 3.23903e10i | 0.813003 | − | 0.782904i | ||||
\(452\) | 2.70296e10 | 0.647569 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.73812e9 | − | 2.71591e9i | −0.0879894 | − | 0.0639280i | ||||
\(455\) | −1.48145e10 | + | 1.07634e10i | −0.345654 | + | 0.251132i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.79138e10 | − | 1.55681e10i | −1.09849 | − | 0.356921i | −0.296968 | − | 0.954887i | \(-0.595976\pi\) |
−0.801521 | + | 0.597966i | \(0.795976\pi\) | |||||||
\(458\) | −4.89497e8 | − | 6.73735e8i | −0.0111247 | − | 0.0153118i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.57434e10 | + | 4.84532e10i | 0.351615 | + | 1.08216i | ||||
\(461\) | 5.01336e10i | 1.11001i | 0.831849 | + | 0.555003i | \(0.187283\pi\) | ||||
−0.831849 | + | 0.555003i | \(0.812717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.36331e10 | 0.514276 | 0.257138 | − | 0.966375i | \(-0.417221\pi\) | ||||
0.257138 | + | 0.966375i | \(0.417221\pi\) | |||||||
\(464\) | −1.09495e10 | + | 3.55771e9i | −0.236223 | + | 0.0767535i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.07345e8 | + | 7.79904e7i | −0.00227634 | + | 0.00165386i | ||||
\(467\) | 2.54200e10 | − | 7.82347e10i | 0.534451 | − | 1.64487i | −0.210380 | − | 0.977620i | \(-0.567470\pi\) |
0.744832 | − | 0.667253i | \(-0.232530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.80907e10 | + | 3.86636e10i | 0.580593 | + | 0.799118i | ||||
\(470\) | 1.47199e9 | − | 2.02603e9i | 0.0301658 | − | 0.0415197i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.30295e10i | 1.26992i | ||||||||
\(473\) | −2.11034e9 | + | 1.18708e10i | −0.0421606 | + | 0.237156i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.96574e10 | − | 6.38707e9i | 0.386146 | − | 0.125466i | ||||
\(476\) | −1.53946e10 | − | 1.11848e10i | −0.299875 | − | 0.217872i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.92291e9 | + | 8.99579e9i | −0.0559892 | + | 0.172317i | ||||
\(479\) | 6.05538e9 | + | 1.96751e9i | 0.115027 | + | 0.0373745i | 0.365965 | − | 0.930629i | \(-0.380739\pi\) |
−0.250938 | + | 0.968003i | \(0.580739\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.37485e9 | + | 6.02146e9i | −0.0817302 | + | 0.112492i | ||||
\(482\) | 1.14108e10 | + | 3.51190e10i | 0.211412 | + | 0.650659i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.26266e10 | + | 1.20935e10i | −0.776783 | + | 0.220379i | ||||
\(485\) | 8.64092e10 | 1.56168 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.79044e10 | + | 2.75391e10i | 0.673866 | + | 0.489592i | 0.871317 | − | 0.490720i | \(-0.163266\pi\) |
−0.197451 | + | 0.980313i | \(0.563266\pi\) | |||||||
\(488\) | −6.03288e10 | + | 4.38314e10i | −1.06376 | + | 0.772870i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.85747e10 | + | 6.03527e9i | 0.322208 | + | 0.104692i | ||||
\(491\) | 2.89700e10 | + | 3.98738e10i | 0.498451 | + | 0.686059i | 0.981919 | − | 0.189303i | \(-0.0606229\pi\) |
−0.483468 | + | 0.875362i | \(0.660623\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.08822e9 | + | 2.48930e10i | 0.136919 | + | 0.421395i | ||||
\(494\) | − | 2.70602e10i | − | 0.454384i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.04502e10 | −0.503110 | ||||||||
\(497\) | −3.91558e10 | + | 1.27225e10i | −0.641758 | + | 0.208520i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.57714e10 | − | 5.50511e10i | 1.22209 | − | 0.887900i | 0.225817 | − | 0.974170i | \(-0.427495\pi\) |
0.996272 | + | 0.0862699i | \(0.0274947\pi\) | |||||||
\(500\) | −1.28813e10 | + | 3.96447e10i | −0.206101 | + | 0.634315i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.46956e8 | + | 3.39906e8i | 0.00388870 | + | 0.00535234i | ||||
\(503\) | 6.84195e10 | − | 9.41713e10i | 1.06883 | − | 1.47112i | 0.197571 | − | 0.980289i | \(-0.436695\pi\) |
0.871257 | − | 0.490827i | \(-0.163305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.27588e9i | 0.0196176i | ||||||||
\(506\) | −3.56872e10 | + | 4.96440e9i | −0.544390 | + | 0.0757294i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.58581e10 | − | 2.13986e10i | 0.988904 | − | 0.321314i | ||||
\(509\) | −4.75110e10 | − | 3.45187e10i | −0.707820 | − | 0.514261i | 0.174650 | − | 0.984631i | \(-0.444121\pi\) |
−0.882470 | + | 0.470369i | \(0.844121\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.01099e10 | + | 6.18920e10i | −0.294935 | + | 0.907718i | ||||
\(512\) | 5.36797e10 | + | 1.74416e10i | 0.781142 | + | 0.253808i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.98701e9 | − | 6.86404e9i | 0.0714477 | − | 0.0983393i | ||||
\(515\) | 1.38337e10 | + | 4.25756e10i | 0.196656 | + | 0.605246i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.15143e9 | − | 5.34948e9i | −0.0721050 | − | 0.0748771i | ||||
\(518\) | −3.62994e9 | −0.0504174 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −3.57838e10 | − | 2.59985e10i | −0.489410 | − | 0.355577i | ||||
\(521\) | 3.03557e10 | − | 2.20547e10i | 0.411993 | − | 0.299330i | −0.362415 | − | 0.932017i | \(-0.618048\pi\) |
0.774408 | + | 0.632687i | \(0.218048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.75238e10 | + | 2.19398e10i | 0.902506 | + | 0.293242i | 0.723271 | − | 0.690564i | \(-0.242638\pi\) |
0.179235 | + | 0.983806i | \(0.442638\pi\) | |||||||
\(524\) | −4.04095e10 | − | 5.56189e10i | −0.535992 | − | 0.737730i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.17086e8 | + | 2.82250e9i | 0.0119803 | + | 0.0368715i | ||||
\(527\) | 6.92266e10i | 0.897492i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.45459e10 | 0.568833 | ||||||||
\(530\) | 3.40359e10 | − | 1.10589e10i | 0.431353 | − | 0.140155i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.47700e10 | + | 3.25273e10i | −0.558909 | + | 0.406071i | ||||
\(533\) | 1.90829e10 | − | 5.87310e10i | 0.236447 | − | 0.727710i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.66214e9 | + | 1.32988e10i | 0.117939 | + | 0.162329i | ||||
\(536\) | −6.78520e10 | + | 9.33903e10i | −0.822060 | + | 1.13147i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.12376e10i | 0.372863i | ||||||||
\(539\) | 2.72628e10 | − | 5.11006e10i | 0.323009 | − | 0.605439i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.70889e9 | − | 3.15461e9i | 0.113339 | − | 0.0368262i | −0.251798 | − | 0.967780i | \(-0.581022\pi\) |
0.365138 | + | 0.930954i | \(0.381022\pi\) | |||||||
\(542\) | −8.05299e9 | − | 5.85084e9i | −0.0933169 | − | 0.0677987i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.20617e10 | − | 6.78988e10i | 0.251909 | − | 0.775295i | ||||
\(545\) | 1.01145e11 | + | 3.28641e10i | 1.14646 | + | 0.372508i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.31776e10 | + | 8.69564e10i | −0.705689 | + | 0.971298i | 0.294190 | + | 0.955747i | \(0.404950\pi\) |
−0.999879 | + | 0.0155510i | \(0.995050\pi\) | |||||||
\(548\) | −4.92972e9 | − | 1.51721e10i | −0.0546638 | − | 0.168238i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.41742e9 | + | 5.02431e9i | 0.102916 | + | 0.0549068i | ||||
\(551\) | 7.61185e10 | 0.825817 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.81601e10 | − | 3.49903e10i | −0.514976 | − | 0.374152i | ||||
\(554\) | 1.92582e10 | − | 1.39919e10i | 0.204445 | − | 0.148538i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.84066e10 | − | 1.89774e10i | −0.611171 | − | 0.198581i | ||||
\(557\) | −7.15576e10 | − | 9.84906e10i | −0.743422 | − | 1.02323i | −0.998415 | − | 0.0562891i | \(-0.982073\pi\) |
0.254993 | − | 0.966943i | \(-0.417927\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.92723e9 | + | 1.51645e10i | 0.0504610 | + | 0.155303i | ||||
\(560\) | 2.84737e10i | 0.289528i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.40941e10 | −0.642499 | ||||||||
\(563\) | −2.42499e9 | + | 7.87927e8i | −0.0241366 | + | 0.00784246i | −0.321060 | − | 0.947059i | \(-0.604039\pi\) |
0.296924 | + | 0.954901i | \(0.404039\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.43898e10 | + | 5.40473e10i | −0.729994 | + | 0.530372i | ||||
\(566\) | 1.40833e10 | − | 4.33439e10i | 0.137227 | − | 0.422340i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.84532e10 | − | 8.04539e10i | −0.561584 | − | 0.772955i | ||||
\(569\) | −1.18370e11 | + | 1.62922e11i | −1.12926 | + | 1.55429i | −0.339779 | + | 0.940505i | \(0.610352\pi\) |
−0.789476 | + | 0.613781i | \(0.789648\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.60852e10i | 0.151315i | 0.997134 | + | 0.0756575i | \(0.0241056\pi\) | ||||
−0.997134 | + | 0.0756575i | \(0.975894\pi\) | |||||||
\(572\) | −4.22084e10 | + | 4.06457e10i | −0.394289 | + | 0.379692i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.86433e10 | − | 9.30677e9i | 0.263861 | − | 0.0857337i | ||||
\(575\) | −2.94446e10 | − | 2.13927e10i | −0.269360 | − | 0.195702i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.08362e10 | − | 9.49040e10i | 0.278200 | − | 0.856212i | −0.710155 | − | 0.704046i | \(-0.751375\pi\) |
0.988355 | − | 0.152166i | \(-0.0486249\pi\) | |||||||
\(578\) | 1.52968e10 | + | 4.97022e9i | 0.137053 | + | 0.0445312i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.26703e10 | − | 4.49668e10i | 0.288696 | − | 0.397356i | ||||
\(581\) | 1.62864e10 | + | 5.01243e10i | 0.142929 | + | 0.439890i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.46226e10 | − | 1.05116e11i | −0.126576 | − | 0.909904i | ||||
\(584\) | −1.57191e11 | −1.35138 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.27260e10 | − | 3.83077e10i | −0.447131 | − | 0.324859i | ||||
\(587\) | 1.26068e10 | − | 9.15934e9i | 0.106182 | − | 0.0771457i | −0.533427 | − | 0.845846i | \(-0.679096\pi\) |
0.639609 | + | 0.768700i | \(0.279096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.91469e11 | + | 6.22121e10i | 1.59088 | + | 0.516909i | ||||
\(590\) | −5.63022e10 | − | 7.74933e10i | −0.464640 | − | 0.639523i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.57635e9 | + | 1.10069e10i | 0.0291175 | + | 0.0896143i | ||||
\(593\) | − | 5.77849e10i | − | 0.467300i | −0.972321 | − | 0.233650i | \(-0.924933\pi\) | ||
0.972321 | − | 0.233650i | \(-0.0750670\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47330e10 | 0.516486 | ||||||||
\(596\) | 1.58134e11 | − | 5.13810e10i | 1.25326 | − | 0.407209i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.85493e10 | + | 2.80077e10i | −0.301448 | + | 0.219014i | ||||
\(599\) | −4.81704e10 | + | 1.48253e11i | −0.374173 | + | 1.15159i | 0.569861 | + | 0.821741i | \(0.306997\pi\) |
−0.944035 | + | 0.329846i | \(0.893003\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.24924e10 | − | 1.71943e10i | −0.0957518 | − | 0.131791i | 0.758453 | − | 0.651728i | \(-0.225956\pi\) |
−0.854205 | + | 0.519937i | \(0.825956\pi\) | |||||||
\(602\) | −4.57083e9 | + | 6.29120e9i | −0.0348024 | + | 0.0479014i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 5.11596e10i | 0.384397i | ||||||||
\(605\) | 9.31336e10 | − | 1.18518e11i | 0.695160 | − | 0.884631i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.54030e10 | − | 8.25395e9i | 0.187125 | − | 0.0608005i | −0.213956 | − | 0.976843i | \(-0.568635\pi\) |
0.401080 | + | 0.916043i | \(0.368635\pi\) | |||||||
\(608\) | −1.67971e11 | − | 1.22038e11i | −1.22919 | − | 0.893059i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3.50196e10 | − | 1.07779e11i | 0.252925 | − | 0.778424i | ||||
\(611\) | −9.34072e9 | − | 3.03498e9i | −0.0670217 | − | 0.0217767i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.46051e10 | + | 1.16449e11i | −0.599176 | + | 0.824696i | −0.995633 | − | 0.0933581i | \(-0.970240\pi\) |
0.396456 | + | 0.918054i | \(0.370240\pi\) | |||||||
\(614\) | 6.88562e9 | + | 2.11918e10i | 0.0484473 | + | 0.149106i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.29838e10 | − | 1.11970e10i | −0.437428 | − | 0.0777640i | ||||
\(617\) | 1.08135e11 | 0.746152 | 0.373076 | − | 0.927801i | \(-0.378303\pi\) | ||||
0.373076 | + | 0.927801i | \(0.378303\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.38033e11 | − | 1.00287e11i | −0.940197 | − | 0.683093i | 0.00827096 | − | 0.999966i | \(-0.497367\pi\) |
−0.948468 | + | 0.316873i | \(0.897367\pi\) | |||||||
\(620\) | 1.18931e11 | − | 8.64083e10i | 0.804873 | − | 0.584775i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.24846e10 | − | 4.05650e9i | −0.0834093 | − | 0.0271013i | ||||
\(623\) | −1.89915e10 | − | 2.61395e10i | −0.126068 | − | 0.173518i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.63545e10 | − | 1.73441e11i | −0.369325 | − | 1.13666i | ||||
\(626\) | 1.22936e10i | 0.0800536i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.25405e10 | 0.466382 | ||||||||
\(629\) | 2.50234e10 | − | 8.13061e9i | 0.159862 | − | 0.0519422i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.61104e11 | − | 1.17049e11i | 1.01622 | − | 0.738328i | 0.0507169 | − | 0.998713i | \(-0.483849\pi\) |
0.965505 | + | 0.260385i | \(0.0838494\pi\) | |||||||
\(632\) | 4.44336e10 | − | 1.36752e11i | 0.278511 | − | 0.857170i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.96443e10 | + | 9.58572e10i | 0.431051 | + | 0.593291i | ||||
\(635\) | −1.38464e11 | + | 1.90580e11i | −0.851613 | + | 1.17214i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 7.65950e10i | − | 0.465203i | ||||||
\(638\) | 2.72666e10 | + | 2.83149e10i | 0.164569 | + | 0.170896i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.80377e11 | + | 5.86080e10i | −1.07513 | + | 0.349331i | ||||
\(641\) | −2.29444e10 | − | 1.66701e10i | −0.135908 | − | 0.0987428i | 0.517754 | − | 0.855529i | \(-0.326768\pi\) |
−0.653662 | + | 0.756787i | \(0.726768\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.16155e10 | + | 1.89633e11i | −0.360451 | + | 1.10935i | 0.592330 | + | 0.805695i | \(0.298208\pi\) |
−0.952781 | + | 0.303658i | \(0.901792\pi\) | |||||||
\(644\) | 9.26753e10 | + | 3.01120e10i | 0.538791 | + | 0.175064i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.62272e10 | + | 7.73900e10i | −0.322861 | + | 0.444381i | ||||
\(647\) | 8.63286e9 | + | 2.65692e10i | 0.0492649 | + | 0.151622i | 0.972663 | − | 0.232223i | \(-0.0745998\pi\) |
−0.923398 | + | 0.383845i | \(0.874600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.55485e11 | + | 1.24164e11i | −1.44008 | + | 0.699871i | ||||
\(650\) | 1.41158e10 | 0.0790776 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.82160e10 | − | 4.95618e10i | −0.377482 | − | 0.274256i | ||||
\(653\) | −1.56085e11 | + | 1.13402e11i | −0.858435 | + | 0.623689i | −0.927459 | − | 0.373926i | \(-0.878011\pi\) |
0.0690241 | + | 0.997615i | \(0.478011\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.22427e11 | + | 7.22709e10i | 1.20843 | + | 0.392643i | ||||
\(656\) | −5.64408e10 | − | 7.76842e10i | −0.304774 | − | 0.419486i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.48017e9 | − | 4.55550e9i | −0.00789602 | − | 0.0243014i | ||||
\(659\) | 2.89730e11i | 1.53621i | 0.640322 | + | 0.768107i | \(0.278801\pi\) | ||||
−0.640322 | + | 0.768107i | \(0.721199\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.56337e10 | −0.291428 | −0.145714 | − | 0.989327i | \(-0.546548\pi\) | ||||
−0.145714 | + | 0.989327i | \(0.546548\pi\) | |||||||
\(662\) | −2.54197e10 | + | 8.25936e9i | −0.132354 | + | 0.0430046i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.02991e11 | + | 7.48273e10i | −0.529818 | + | 0.384935i | ||||
\(665\) | 5.81739e10 | − | 1.79041e11i | 0.297469 | − | 0.915515i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.87837e10 | − | 1.08437e11i | −0.398046 | − | 0.547863i | ||||
\(668\) | −1.30024e11 | + | 1.78963e11i | −0.653008 | + | 0.898789i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 1.75431e11i | − | 0.870577i | ||||||
\(671\) | −2.96511e11 | − | 1.58192e11i | −1.46268 | − | 0.780360i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.64290e11 | − | 5.33811e10i | 0.800851 | − | 0.260212i | 0.120133 | − | 0.992758i | \(-0.461668\pi\) |
0.680718 | + | 0.732546i | \(0.261668\pi\) | |||||||
\(674\) | −9.19765e10 | − | 6.68249e10i | −0.445695 | − | 0.323816i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.81584e10 | − | 8.66626e10i | 0.134841 | − | 0.414997i | ||||
\(677\) | −6.96950e10 | − | 2.26453e10i | −0.331778 | − | 0.107801i | 0.138391 | − | 0.990378i | \(-0.455807\pi\) |
−0.470169 | + | 0.882577i | \(0.655807\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.71450e10 | − | 1.33709e11i | 0.457027 | − | 0.629043i | ||||
\(680\) | 4.83179e10 | + | 1.48707e11i | 0.225981 | + | 0.695498i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.54448e10 | + | 9.35087e10i | 0.210061 | + | 0.432230i | ||||
\(683\) | 3.37571e11 | 1.55125 | 0.775625 | − | 0.631194i | \(-0.217435\pi\) | ||||
0.775625 | + | 0.631194i | \(0.217435\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.39049e10 | + | 3.18988e10i | 0.199412 | + | 0.144881i | ||||
\(686\) | 7.42619e10 | − | 5.39545e10i | 0.335328 | − | 0.243630i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.35798e10 | + | 7.66155e9i | 0.105241 | + | 0.0341950i | ||||
\(689\) | −8.24964e10 | − | 1.13547e11i | −0.366065 | − | 0.503845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.88802e10 | − | 2.42768e11i | −0.345984 | − | 1.06483i | −0.961055 | − | 0.276357i | \(-0.910873\pi\) |
0.615071 | − | 0.788471i | \(-0.289127\pi\) | |||||||
\(692\) | − | 9.49608e9i | − | 0.0414114i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 3.98484e10 | 0.171780 | ||||||||
\(695\) | 1.98691e11 | − | 6.45586e10i | 0.851606 | − | 0.276703i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.76610e11 | + | 1.28315e11i | −0.748314 | + | 0.543682i | ||||
\(698\) | −3.21837e10 | + | 9.90511e10i | −0.135586 | + | 0.417290i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.69678e10 | − | 2.33541e10i | −0.0706695 | − | 0.0972683i | ||||
\(701\) | 2.78124e10 | − | 3.82805e10i | 0.115177 | − | 0.158528i | −0.747536 | − | 0.664221i | \(-0.768763\pi\) |
0.862713 | + | 0.505693i | \(0.168763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 7.65174e10i | − | 0.313285i | ||||||
\(704\) | 7.74867e8 | + | 5.57023e9i | 0.00315455 | + | 0.0226768i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.60446e10 | + | 2.14592e10i | −0.265839 | + | 0.0863763i | ||||
\(707\) | 1.97429e9 | + | 1.43440e9i | 0.00790192 | + | 0.00574108i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.02491e11 | + | 3.15434e11i | −0.405601 | + | 1.24831i | 0.514791 | + | 0.857315i | \(0.327869\pi\) |
−0.920392 | + | 0.390996i | \(0.872131\pi\) | |||||||
\(710\) | 1.43734e11 | + | 4.67019e10i | 0.565620 | + | 0.183781i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.58731e10 | − | 6.31389e10i | 0.178500 | − | 0.245684i | ||||
\(713\) | −1.09548e11 | − | 3.37153e11i | −0.423882 | − | 1.30457i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.48906e10 | − | 1.96262e11i | 0.133501 | − | 0.750951i | ||||
\(716\) | 2.12771e11 | 0.809582 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.37699e10 | + | 5.35970e10i | 0.277576 | + | 0.201671i | ||||
\(719\) | 3.14538e11 | − | 2.28525e11i | 1.17695 | − | 0.855103i | 0.185124 | − | 0.982715i | \(-0.440731\pi\) |
0.991824 | + | 0.127612i | \(0.0407312\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.14334e10 | + | 2.64593e10i | 0.301343 | + | 0.0979124i | ||||
\(722\) | 9.34289e10 | + | 1.28594e11i | 0.343821 | + | 0.473229i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.22975e10 | + | 1.60955e11i | 0.190339 | + | 0.585802i | ||||
\(725\) | 3.97069e10i | 0.143719i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.54660e11 | 1.26962 | 0.634812 | − | 0.772667i | \(-0.281078\pi\) | ||||
0.634812 | + | 0.772667i | \(0.281078\pi\) | |||||||
\(728\) | −8.04594e10 | + | 2.61429e10i | −0.286452 | + | 0.0930738i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.93262e11 | − | 1.40413e11i | 0.680544 | − | 0.494444i | ||||
\(731\) | 1.74180e10 | − | 5.36072e10i | 0.0610000 | − | 0.187739i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.31226e11 | − | 4.55894e11i | −1.14738 | − | 1.57924i | −0.749786 | − | 0.661680i | \(-0.769844\pi\) |
−0.397599 | − | 0.917559i | \(-0.630156\pi\) | |||||||
\(734\) | −7.38433e10 | + | 1.01637e11i | −0.254406 | + | 0.350159i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.65598e11i | 1.24593i | ||||||||
\(737\) | −5.12213e11 | − | 9.10591e10i | −1.73613 | − | 0.308641i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.78819e11 | + | 5.81018e10i | −0.599565 | + | 0.194810i | −0.593046 | − | 0.805168i | \(-0.702075\pi\) |
−0.00651835 | + | 0.999979i | \(0.502075\pi\) | |||||||
\(740\) | −4.52025e10 | − | 3.28415e10i | −0.150742 | − | 0.109521i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.11521e10 | − | 6.50996e10i | 0.0697813 | − | 0.214765i | ||||
\(743\) | 3.87281e11 | + | 1.25835e11i | 1.27078 | + | 0.412902i | 0.865325 | − | 0.501211i | \(-0.167112\pi\) |
0.405458 | + | 0.914114i | \(0.367112\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.32472e11 | + | 4.57608e11i | −1.07927 | + | 1.48549i | ||||
\(746\) | −4.15264e10 | − | 1.27805e11i | −0.134082 | − | 0.412661i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.05169e11 | − | 2.85408e10i | 0.655397 | − | 0.0911715i | ||||
\(749\) | 3.14410e10 | 0.0999008 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.03886e11 | + | 2.20786e11i | 0.955325 | + | 0.694085i | 0.952060 | − | 0.305910i | \(-0.0989607\pi\) |
0.00326502 | + | 0.999995i | \(0.498961\pi\) | |||||||
\(752\) | −1.23551e10 | + | 8.97648e9i | −0.0386344 | + | 0.0280695i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.94406e10 | + | 1.60642e10i | 0.152967 | + | 0.0497020i | ||||
\(755\) | −1.02297e11 | − | 1.40800e11i | −0.314829 | − | 0.433325i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.23949e11 | + | 3.81476e11i | 0.377450 | + | 1.16167i | 0.941811 | + | 0.336144i | \(0.109123\pi\) |
−0.564360 | + | 0.825529i | \(0.690877\pi\) | |||||||
\(758\) | 1.64273e11i | 0.497611i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.54721e11 | 1.36298 | ||||||||
\(761\) | −5.36336e11 | + | 1.74266e11i | −1.59918 | + | 0.519607i | −0.966906 | − | 0.255134i | \(-0.917880\pi\) |
−0.632279 | + | 0.774741i | \(0.717880\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.64565e11 | − | 1.19564e11i | 0.485557 | − | 0.352778i | ||||
\(764\) | −4.26390e10 | + | 1.31229e11i | −0.125151 | + | 0.385174i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.76799e10 | − | 2.43342e10i | −0.0513527 | − | 0.0706810i | ||||
\(767\) | −2.20806e11 | + | 3.03914e11i | −0.638013 | + | 0.878150i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.98817e11i | 1.14043i | 0.821495 | + | 0.570215i | \(0.193140\pi\) | ||||
−0.821495 | + | 0.570215i | \(0.806860\pi\) | |||||||
\(770\) | 8.74390e10 | − | 4.24949e10i | 0.248738 | − | 0.120885i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.33514e11 | − | 1.40857e11i | 1.22049 | − | 0.396561i | ||||
\(773\) | 1.15593e11 | + | 8.39832e10i | 0.323753 | + | 0.235220i | 0.737775 | − | 0.675047i | \(-0.235877\pi\) |
−0.414022 | + | 0.910267i | \(0.635877\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.24527e10 | + | 9.98792e10i | −0.0899589 | + | 0.276865i | ||||
\(776\) | 3.79671e11 | + | 1.23363e11i | 1.04703 | + | 0.340202i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.00324e11 | + | 1.38085e11i | −0.273835 | + | 0.376901i | ||||
\(779\) | 1.96182e11 | + | 6.03787e11i | 0.532733 | + | 1.63958i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.10964e11 | − | 3.95424e11i | 0.567027 | − | 1.06282i | ||||
\(782\) | 1.68444e11 | 0.450431 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −9.63545e10 | − | 7.00056e10i | −0.255040 | − | 0.185297i | ||||
\(785\) | −1.99643e11 | + | 1.45049e11i | −0.525745 | + | 0.381976i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.52231e11 | + | 8.19548e10i | 0.657505 | + | 0.213636i | 0.618721 | − | 0.785611i | \(-0.287651\pi\) |
0.0387847 | + | 0.999248i | \(0.487651\pi\) | |||||||
\(788\) | 2.71890e10 | + | 3.74225e10i | 0.0705161 | + | 0.0970571i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.75264e10 | + | 2.07825e11i | 0.173366 | + | 0.533567i | ||||
\(791\) | 1.75872e11i | 0.449253i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.44442e11 | −1.12389 | ||||||||
\(794\) | −6.08647e10 | + | 1.97761e10i | −0.153138 | + | 0.0497576i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.50157e11 | + | 1.81750e11i | −0.623105 | + | 0.452712i | ||||
\(797\) | 1.33254e11 | − | 4.10115e11i | 0.330254 | − | 1.01642i | −0.638759 | − | 0.769407i | \(-0.720552\pi\) |
0.969013 | − | 0.247010i | \(-0.0794482\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.04075e10 | + | 2.80885e10i | 0.0500728 | + | 0.0689193i | ||||
\(800\) | 6.36606e10 | − | 8.76212e10i | 0.155421 | − | 0.213919i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.45078e10i | 0.131753i | ||||||||
\(803\) | −3.09656e11 | − | 6.37160e11i | −0.744763 | − | 1.53245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.15268e11 | + | 1.02437e11i | −0.750752 | + | 0.243934i | ||||
\(806\) | 1.11234e11 | + | 8.08162e10i | 0.263571 | + | 0.191495i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.82152e9 | + | 5.60607e9i | −0.00427355 | + | 0.0131526i | ||||
\(809\) | 6.52104e10 | + | 2.11881e10i | 0.152238 | + | 0.0494651i | 0.384145 | − | 0.923273i | \(-0.374496\pi\) |
−0.231907 | + | 0.972738i | \(0.574496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.07499e11 | + | 1.47960e11i | −0.248498 | + | 0.342028i | −0.914984 | − | 0.403489i | \(-0.867797\pi\) |
0.666487 | + | 0.745517i | \(0.267797\pi\) | |||||||
\(812\) | −3.28517e10 | − | 1.01107e11i | −0.0755674 | − | 0.232572i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.84633e10 | − | 2.74095e10i | 0.0648317 | − | 0.0624315i | ||||
\(815\) | 2.86843e11 | 0.650151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.32616e11 | − | 9.63508e10i | −0.297650 | − | 0.216256i | ||||
\(818\) | 2.20538e11 | − | 1.60231e11i | 0.492573 | − | 0.357876i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.40887e11 | + | 1.43253e11i | 0.975152 | + | 0.316846i | ||||
\(821\) | 5.13013e11 | + | 7.06101e11i | 1.12916 | + | 1.55416i | 0.789655 | + | 0.613551i | \(0.210260\pi\) |
0.339505 | + | 0.940604i | \(0.389740\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.38003e10 | + | 7.32498e10i | 0.0518780 | + | 0.159664i | 0.973639 | − | 0.228094i | \(-0.0732495\pi\) |
−0.921761 | + | 0.387758i | \(0.873249\pi\) | |||||||
\(824\) | 2.06822e11i | 0.448629i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.83210e11 | −0.393575 | ||||||||
\(827\) | 2.40691e10 | − | 7.82051e9i | 0.0514561 | − | 0.0167191i | −0.283176 | − | 0.959068i | \(-0.591388\pi\) |
0.334632 | + | 0.942349i | \(0.391388\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.42821e10 | + | 3.21728e10i | −0.0937584 | + | 0.0681195i | −0.633677 | − | 0.773598i | \(-0.718455\pi\) |
0.539918 | + | 0.841717i | \(0.318455\pi\) | |||||||
\(830\) | 5.97841e10 | − | 1.83997e11i | 0.125972 | − | 0.387702i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.37158e9 | + | 6.01696e9i | 0.00912316 | + | 0.0125570i | ||||
\(833\) | −1.59153e11 | + | 2.19056e11i | −0.330549 | + | 0.454962i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 7.52526e11i | − | 1.54802i | ||||||
\(836\) | 1.05441e11 | − | 5.93111e11i | 0.215865 | − | 1.21426i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.60944e10 | + | 5.22940e9i | −0.0326362 | + | 0.0106041i | ||||
\(839\) | −4.12964e11 | − | 3.00036e11i | −0.833421 | − | 0.605516i | 0.0871039 | − | 0.996199i | \(-0.472239\pi\) |
−0.920525 | + | 0.390683i | \(0.872239\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.09397e11 | − | 3.36690e11i | 0.218686 | − | 0.673048i | ||||
\(842\) | −3.25581e11 | − | 1.05788e11i | −0.647754 | − | 0.210468i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.87826e11 | − | 2.58520e11i | 0.370157 | − | 0.509477i | ||||
\(845\) | 9.57908e10 | + | 2.94814e11i | 0.187887 | + | 0.578257i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.86882e10 | − | 2.77357e11i | −0.152889 | − | 0.538896i | ||||
\(848\) | −2.18238e11 | −0.422033 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4.03702e10 | − | 2.93307e10i | −0.0773367 | − | 0.0561884i | ||||
\(851\) | −1.09005e11 | + | 7.91967e10i | −0.207839 | + | 0.151004i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.49438e11 | − | 2.43507e11i | −1.41560 | − | 0.459955i | −0.501397 | − | 0.865217i | \(-0.667180\pi\) |
−0.914201 | + | 0.405262i | \(0.867180\pi\) | |||||||
\(854\) | −1.27406e11 | − | 1.75359e11i | −0.239529 | − | 0.329683i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.34681e10 | + | 7.22274e10i | 0.0437102 | + | 0.134526i | ||||
\(857\) | 1.32237e11i | 0.245150i | 0.992459 | + | 0.122575i | \(0.0391151\pi\) | ||||
−0.992459 | + | 0.122575i | \(0.960885\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.70268e11 | 0.680055 | 0.340027 | − | 0.940416i | \(-0.389564\pi\) | ||||
0.340027 | + | 0.940416i | \(0.389564\pi\) | |||||||
\(860\) | −1.13838e11 | + | 3.69882e10i | −0.208110 | + | 0.0676191i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.87621e10 | + | 2.81623e10i | −0.0702066 | + | 0.0510081i | ||||
\(863\) | 1.58241e11 | − | 4.87017e11i | 0.285284 | − | 0.878013i | −0.701030 | − | 0.713132i | \(-0.747276\pi\) |
0.986313 | − | 0.164881i | \(-0.0527240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.89880e10 | + | 2.61347e10i | 0.0339168 | + | 0.0466824i | ||||
\(866\) | −1.29138e11 | + | 1.77744e11i | −0.229606 | + | 0.316026i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 2.81176e11i | − | 0.495336i | ||||||
\(869\) | 6.41846e11 | − | 8.92863e10i | 1.12552 | − | 0.156569i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.54333e11 | + | 2.12606e11i | −1.13691 | + | 0.369404i | ||||
\(872\) | 3.97501e11 | + | 2.88801e11i | 0.687499 | + | 0.499497i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.51376e11 | − | 4.65888e11i | 0.259425 | − | 0.798428i | ||||
\(875\) | −2.57954e11 | − | 8.38144e10i | −0.440059 | − | 0.142984i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.70663e10 | + | 1.06073e11i | −0.130277 | + | 0.179310i | −0.869172 | − | 0.494510i | \(-0.835348\pi\) |
0.738896 | + | 0.673820i | \(0.235348\pi\) | |||||||
\(878\) | −6.97599e9 | − | 2.14699e10i | −0.0117389 | − | 0.0361287i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.15003e11 | − | 2.23269e11i | −0.358521 | − | 0.372304i | ||||
\(881\) | −1.82199e11 | −0.302443 | −0.151221 | − | 0.988500i | \(-0.548321\pi\) | ||||
−0.151221 | + | 0.988500i | \(0.548321\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.07332e11 | − | 7.79809e10i | −0.176557 | − | 0.128276i | 0.495997 | − | 0.868324i | \(-0.334803\pi\) |
−0.672554 | + | 0.740048i | \(0.734803\pi\) | |||||||
\(884\) | 2.21623e11 | − | 1.61019e11i | 0.362916 | − | 0.263674i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.22148e11 | + | 1.04672e11i | 0.522781 | + | 0.169862i | ||||
\(887\) | −5.41297e11 | − | 7.45031e11i | −0.874462 | − | 1.20359i | −0.977924 | − | 0.208960i | \(-0.932992\pi\) |
0.103462 | − | 0.994633i | \(-0.467008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.39233e11 | + | 4.28516e11i | 0.222913 | + | 0.686056i | ||||
\(890\) | 1.18605e11i | 0.189035i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.06098e11 | 0.641463 | ||||||||
\(893\) | 9.60277e10 | − | 3.12013e10i | 0.151005 | − | 0.0490644i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.85580e11 | + | 4.25449e11i | −0.912629 | + | 0.663064i | ||||
\(896\) | −1.12098e11 | + | 3.45003e11i | −0.173927 | + | 0.535291i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.30167e11 | − | 1.79159e11i | −0.200168 | − | 0.275508i | ||||
\(899\) | −2.27330e11 | + | 3.12893e11i | −0.348032 | + | 0.479025i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.96150e11i | 0.752860i | ||||||||
\(902\) | −1.54324e11 | + | 2.89261e11i | −0.233135 | + | 0.436982i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.04020e11 | + | 1.31274e11i | −0.604964 | + | 0.196565i | ||||
\(905\) | −4.65771e11 | − | 3.38402e11i | −0.694349 | − | 0.504474i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.00690e11 | − | 3.09892e11i | 0.148784 | − | 0.457911i | −0.848694 | − | 0.528885i | \(-0.822610\pi\) |
0.997478 | + | 0.0709731i | \(0.0226105\pi\) | |||||||
\(908\) | −1.29375e11 | − | 4.20363e10i | −0.190329 | − | 0.0618417i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.55704e10 | − | 1.04014e11i | 0.110201 | − | 0.151679i | ||||
\(911\) | −1.01820e11 | − | 3.13368e11i | −0.147828 | − | 0.454969i | 0.849536 | − | 0.527531i | \(-0.176882\pi\) |
−0.997364 | + | 0.0725627i | \(0.976882\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.06191e11 | − | 2.70060e11i | −0.728504 | − | 0.388666i | ||||
\(914\) | 3.53719e11 | 0.506843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.98352e10 | − | 1.44111e10i | −0.0281743 | − | 0.0204699i | ||||
\(917\) | 3.61893e11 | − | 2.62931e11i | 0.511803 | − | 0.371847i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.21241e12 | − | 3.93934e11i | −1.69975 | − | 0.552283i | −0.711177 | − | 0.703013i | \(-0.751838\pi\) |
−0.988575 | + | 0.150730i | \(0.951838\pi\) | |||||||
\(920\) | −4.70643e11 | − | 6.47785e11i | −0.656962 | − | 0.904231i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.08771e11 | − | 3.34764e11i | −0.150519 | − | 0.463249i | ||||
\(923\) | − | 5.92704e11i | − | 0.816641i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.99150e10 | 0.0545217 | ||||||||
\(926\) | −1.57808e11 | + | 5.12750e10i | −0.214628 | + | 0.0697368i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.22686e11 | − | 2.34445e11i | 0.435099 | − | 0.316118i | ||||
\(929\) | −1.67960e11 | + | 5.16929e11i | −0.225499 | + | 0.694014i | 0.772742 | + | 0.634720i | \(0.218885\pi\) |
−0.998241 | + | 0.0592934i | \(0.981115\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.62845e11 | + | 6.37051e11i | 0.616079 | + | 0.847961i | ||||
\(932\) | −2.29608e9 | + | 3.16029e9i | −0.00304316 | + | 0.00418855i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.77560e11i | 0.758943i | ||||||||
\(935\) | −5.07588e11 | + | 4.88796e11i | −0.664148 | + | 0.639560i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.04197e11 | − | 2.28807e11i | 0.913557 | − | 0.296833i | 0.185736 | − | 0.982600i | \(-0.440533\pi\) |
0.727821 | + | 0.685767i | \(0.240533\pi\) | |||||||
\(938\) | −2.71460e11 | − | 1.97227e11i | −0.350667 | − | 0.254774i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.27833e10 | − | 7.01198e10i | 0.0291813 | − | 0.0898109i | ||||
\(941\) | 1.85400e11 | + | 6.02401e10i | 0.236456 | + | 0.0768293i | 0.424848 | − | 0.905265i | \(-0.360327\pi\) |
−0.188392 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.57088e11 | − | 9.04405e11i | 0.830954 | − | 1.14371i | ||||
\(944\) | 1.80505e11 | + | 5.55537e11i | 0.227301 | + | 0.699560i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.16636e10 | − | 8.38450e10i | −0.0145635 | − | 0.104692i | ||||
\(947\) | 3.03034e11 | 0.376783 | 0.188392 | − | 0.982094i | \(-0.439673\pi\) | ||||
0.188392 | + | 0.982094i | \(0.439673\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.57938e11 | − | 5.50674e11i | −0.934477 | − | 0.678938i | ||||
\(950\) | −1.17403e11 | + | 8.52986e10i | −0.144141 | + | 0.104724i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.84429e11 | + | 9.24165e10i | 0.346279 | + | 0.112513i | ||||
\(953\) | −2.21859e11 | − | 3.05362e11i | −0.268970 | − | 0.370206i | 0.653071 | − | 0.757296i | \(-0.273480\pi\) |
−0.922042 | + | 0.387090i | \(0.873480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.45052e11 | − | 4.46423e11i | −0.174385 | − | 0.536702i | ||||
\(956\) | 2.78471e11i | 0.333387i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.47032e10 | −0.0530734 | ||||||||
\(959\) | 9.87197e10 | − | 3.20760e10i | 0.116716 | − | 0.0379232i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.37556e11 | + | 9.99401e10i | −0.161282 | + | 0.117178i | ||||
\(962\) | 1.61484e10 | − | 4.96997e10i | 0.0188551 | − | 0.0580302i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 6.39000e11 | + | 8.79507e11i | 0.739933 | + | 1.01843i | ||||
\(965\) | −9.11447e11 | + | 1.25450e12i | −1.05105 | + | 1.44664i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.05058e10i | 0.103507i | 0.998660 | + | 0.0517536i | \(0.0164810\pi\) | ||||
−0.998660 | + | 0.0517536i | \(0.983519\pi\) | |||||||
\(968\) | 5.78420e11 | − | 3.87789e11i | 0.658782 | − | 0.441667i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.76992e11 | + | 1.87476e11i | −0.651753 | + | 0.211767i | ||||
\(971\) | −6.31302e11 | − | 4.58668e11i | −0.710167 | − | 0.515966i | 0.173061 | − | 0.984911i | \(-0.444634\pi\) |
−0.883228 | + | 0.468945i | \(0.844634\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.23480e11 | − | 3.80031e11i | 0.137767 | − | 0.424002i | ||||
\(974\) | −3.12854e11 | − | 1.01652e11i | −0.347621 | − | 0.112949i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.06207e11 | + | 5.59097e11i | −0.447660 | + | 0.616152i | ||||
\(977\) | −1.03690e11 | − | 3.19126e11i | −0.113805 | − | 0.350255i | 0.877891 | − | 0.478860i | \(-0.158950\pi\) |
−0.991696 | + | 0.128605i | \(0.958950\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.46295e11 | + | 6.15629e10i | 0.376978 | + | 0.0670175i | ||||
\(980\) | 5.74991e11 | 0.623385 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.79957e11 | − | 2.03400e11i | −0.301054 | − | 0.218729i | ||||
\(983\) | 8.23027e11 | − | 5.97964e11i | 0.881455 | − | 0.640415i | −0.0521809 | − | 0.998638i | \(-0.516617\pi\) |
0.933636 | + | 0.358223i | \(0.116617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.49657e11 | − | 4.86265e10i | −0.158983 | − | 0.0516569i | ||||
\(986\) | −1.08017e11 | − | 1.48673e11i | −0.114284 | − | 0.157298i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.46184e11 | − | 7.57676e11i | −0.258364 | − | 0.795163i | ||||
\(989\) | 2.88645e11i | 0.301703i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.14619e11 | 0.948299 | 0.474150 | − | 0.880444i | \(-0.342756\pi\) | ||||
0.474150 | + | 0.880444i | \(0.342756\pi\) | |||||||
\(992\) | 1.00330e12 | − | 3.25992e11i | 1.03606 | − | 0.336636i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.33858e11 | − | 1.69907e11i | 0.239555 | − | 0.174047i | ||||
\(995\) | 3.25053e11 | − | 1.00041e12i | 0.331636 | − | 1.02067i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.76915e11 | − | 1.06933e12i | −0.786308 | − | 1.08226i | −0.994558 | − | 0.104185i | \(-0.966777\pi\) |
0.208250 | − | 0.978076i | \(-0.433223\pi\) | |||||||
\(998\) | −3.86518e11 | + | 5.31996e11i | −0.389626 | + | 0.536274i | ||||
\(999\) | 0 | 0 |
(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 | 99.9.k.a.28.3 | 28 | ||
3.2 | odd | 2 | 11.9.d.a.6.5 | yes | 28 | ||
11.2 | odd | 10 | inner | 99.9.k.a.46.3 | 28 | ||
33.2 | even | 10 | 11.9.d.a.2.5 | ✓ | 28 | ||
33.8 | even | 10 | 121.9.b.b.120.17 | 28 | |||
33.14 | odd | 10 | 121.9.b.b.120.12 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.9.d.a.2.5 | ✓ | 28 | 33.2 | even | 10 | ||
11.9.d.a.6.5 | yes | 28 | 3.2 | odd | 2 | ||
99.9.k.a.28.3 | 28 | 1.1 | even | 1 | trivial | ||
99.9.k.a.46.3 | 28 | 11.2 | odd | 10 | inner | ||
121.9.b.b.120.12 | 28 | 33.14 | odd | 10 | |||
121.9.b.b.120.17 | 28 | 33.8 | even | 10 |