Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,9,Mod(6,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.6");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(2.85165027043\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1016x^{2} + 51570 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 6.3 | ||
Root | \(7.32010i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.6 |
Dual form | 7.9.b.b.6.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/7\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.5647 | 1.34779 | 0.673896 | − | 0.738827i | \(-0.264620\pi\) | ||||
0.673896 | + | 0.738827i | \(0.264620\pi\) | |||||||
\(3\) | − | 119.877i | − | 1.47997i | −0.672626 | − | 0.739983i | \(-0.734834\pi\) | ||
0.672626 | − | 0.739983i | \(-0.265166\pi\) | |||||||
\(4\) | 209.035 | 0.816541 | ||||||||
\(5\) | 786.953i | 1.25912i | 0.776950 | + | 0.629562i | \(0.216766\pi\) | ||||
−0.776950 | + | 0.629562i | \(0.783234\pi\) | |||||||
\(6\) | − | 2585.11i | − | 1.99468i | ||||||
\(7\) | 1971.19 | + | 1370.84i | 0.820989 | + | 0.570944i | ||||
\(8\) | −1012.79 | −0.247264 | ||||||||
\(9\) | −7809.55 | −1.19030 | ||||||||
\(10\) | 16970.4i | 1.69704i | ||||||||
\(11\) | −6464.40 | −0.441527 | −0.220764 | − | 0.975327i | \(-0.570855\pi\) | ||||
−0.220764 | + | 0.975327i | \(0.570855\pi\) | |||||||
\(12\) | − | 25058.5i | − | 1.20845i | ||||||
\(13\) | − | 23304.2i | − | 0.815946i | −0.912994 | − | 0.407973i | \(-0.866236\pi\) | ||
0.912994 | − | 0.407973i | \(-0.133764\pi\) | |||||||
\(14\) | 42508.1 | + | 29561.6i | 1.10652 | + | 0.769513i | ||||
\(15\) | 94337.7 | 1.86346 | ||||||||
\(16\) | −75353.4 | −1.14980 | ||||||||
\(17\) | − | 85372.2i | − | 1.02216i | −0.859532 | − | 0.511082i | \(-0.829245\pi\) | ||
0.859532 | − | 0.511082i | \(-0.170755\pi\) | |||||||
\(18\) | −168410. | −1.60427 | ||||||||
\(19\) | 171975.i | 1.31963i | 0.751429 | + | 0.659814i | \(0.229365\pi\) | ||||
−0.751429 | + | 0.659814i | \(0.770635\pi\) | |||||||
\(20\) | 164500.i | 1.02813i | ||||||||
\(21\) | 164332. | − | 236301.i | 0.844978 | − | 1.21504i | ||||
\(22\) | −139403. | −0.595086 | ||||||||
\(23\) | 145847. | 0.521178 | 0.260589 | − | 0.965450i | \(-0.416083\pi\) | ||||
0.260589 | + | 0.965450i | \(0.416083\pi\) | |||||||
\(24\) | 121411.i | 0.365942i | ||||||||
\(25\) | −228670. | −0.585396 | ||||||||
\(26\) | − | 502548.i | − | 1.09972i | ||||||
\(27\) | 149672.i | 0.281634i | ||||||||
\(28\) | 412048. | + | 286552.i | 0.670371 | + | 0.466199i | ||||
\(29\) | −684636. | −0.967983 | −0.483992 | − | 0.875073i | \(-0.660813\pi\) | ||||
−0.483992 | + | 0.875073i | \(0.660813\pi\) | |||||||
\(30\) | 2.03436e6 | 2.51156 | ||||||||
\(31\) | − | 597349.i | − | 0.646817i | −0.946259 | − | 0.323409i | \(-0.895171\pi\) | ||
0.946259 | − | 0.323409i | \(-0.104829\pi\) | |||||||
\(32\) | −1.36570e6 | −1.30243 | ||||||||
\(33\) | 774934.i | 0.653445i | ||||||||
\(34\) | − | 1.84102e6i | − | 1.37766i | ||||||
\(35\) | −1.07878e6 | + | 1.55124e6i | −0.718890 | + | 1.03373i | ||||
\(36\) | −1.63246e6 | −0.971927 | ||||||||
\(37\) | 2.08191e6 | 1.11085 | 0.555423 | − | 0.831568i | \(-0.312556\pi\) | ||||
0.555423 | + | 0.831568i | \(0.312556\pi\) | |||||||
\(38\) | 3.70859e6i | 1.77858i | ||||||||
\(39\) | −2.79365e6 | −1.20757 | ||||||||
\(40\) | − | 797021.i | − | 0.311336i | ||||||
\(41\) | 226141.i | 0.0800282i | 0.999199 | + | 0.0400141i | \(0.0127403\pi\) | ||||
−0.999199 | + | 0.0400141i | \(0.987260\pi\) | |||||||
\(42\) | 3.54377e6 | − | 5.09576e6i | 1.13885 | − | 1.63761i | ||||
\(43\) | 3.79260e6 | 1.10934 | 0.554669 | − | 0.832071i | \(-0.312845\pi\) | ||||
0.554669 | + | 0.832071i | \(0.312845\pi\) | |||||||
\(44\) | −1.35128e6 | −0.360525 | ||||||||
\(45\) | − | 6.14575e6i | − | 1.49873i | ||||||
\(46\) | 3.14514e6 | 0.702440 | ||||||||
\(47\) | − | 105710.i | − | 0.0216633i | −0.999941 | − | 0.0108317i | \(-0.996552\pi\) | ||
0.999941 | − | 0.0108317i | \(-0.00344789\pi\) | |||||||
\(48\) | 9.03316e6i | 1.70167i | ||||||||
\(49\) | 2.00641e6 | + | 5.40437e6i | 0.348046 | + | 0.937478i | ||||
\(50\) | −4.93120e6 | −0.788991 | ||||||||
\(51\) | −1.02342e7 | −1.51277 | ||||||||
\(52\) | − | 4.87139e6i | − | 0.666253i | ||||||
\(53\) | −3.46490e6 | −0.439124 | −0.219562 | − | 0.975599i | \(-0.570463\pi\) | ||||
−0.219562 | + | 0.975599i | \(0.570463\pi\) | |||||||
\(54\) | 3.22763e6i | 0.379584i | ||||||||
\(55\) | − | 5.08718e6i | − | 0.555938i | ||||||
\(56\) | −1.99641e6 | − | 1.38837e6i | −0.203001 | − | 0.141174i | ||||
\(57\) | 2.06159e7 | 1.95300 | ||||||||
\(58\) | −1.47639e7 | −1.30464 | ||||||||
\(59\) | 1.35101e7i | 1.11494i | 0.830198 | + | 0.557468i | \(0.188227\pi\) | ||||
−0.830198 | + | 0.557468i | \(0.811773\pi\) | |||||||
\(60\) | 1.97198e7 | 1.52159 | ||||||||
\(61\) | − | 842042.i | − | 0.0608156i | −0.999538 | − | 0.0304078i | \(-0.990319\pi\) | ||
0.999538 | − | 0.0304078i | \(-0.00968059\pi\) | |||||||
\(62\) | − | 1.28816e7i | − | 0.871775i | ||||||
\(63\) | −1.53941e7 | − | 1.07056e7i | −0.977222 | − | 0.679594i | ||||
\(64\) | −1.01603e7 | −0.605600 | ||||||||
\(65\) | 1.83393e7 | 1.02738 | ||||||||
\(66\) | 1.67112e7i | 0.880707i | ||||||||
\(67\) | 9.62973e6 | 0.477875 | 0.238938 | − | 0.971035i | \(-0.423201\pi\) | ||||
0.238938 | + | 0.971035i | \(0.423201\pi\) | |||||||
\(68\) | − | 1.78457e7i | − | 0.834640i | ||||||
\(69\) | − | 1.74837e7i | − | 0.771326i | ||||||
\(70\) | −2.32636e7 | + | 3.34519e7i | −0.968914 | + | 1.39325i | ||||
\(71\) | −4.99364e6 | −0.196509 | −0.0982547 | − | 0.995161i | \(-0.531326\pi\) | ||||
−0.0982547 | + | 0.995161i | \(0.531326\pi\) | |||||||
\(72\) | 7.90946e6 | 0.294318 | ||||||||
\(73\) | − | 2.22669e7i | − | 0.784095i | −0.919945 | − | 0.392048i | \(-0.871767\pi\) | ||
0.919945 | − | 0.392048i | \(-0.128233\pi\) | |||||||
\(74\) | 4.48956e7 | 1.49719 | ||||||||
\(75\) | 2.74123e7i | 0.866365i | ||||||||
\(76\) | 3.59488e7i | 1.07753i | ||||||||
\(77\) | −1.27426e7 | − | 8.86163e6i | −0.362489 | − | 0.252087i | ||||
\(78\) | −6.02440e7 | −1.62755 | ||||||||
\(79\) | −3.48440e7 | −0.894582 | −0.447291 | − | 0.894389i | \(-0.647611\pi\) | ||||
−0.447291 | + | 0.894389i | \(0.647611\pi\) | |||||||
\(80\) | − | 5.92996e7i | − | 1.44774i | ||||||
\(81\) | −3.32962e7 | −0.773489 | ||||||||
\(82\) | 4.87665e6i | 0.107861i | ||||||||
\(83\) | 8.16858e7i | 1.72121i | 0.509271 | + | 0.860606i | \(0.329915\pi\) | ||||
−0.509271 | + | 0.860606i | \(0.670085\pi\) | |||||||
\(84\) | 3.43511e7 | − | 4.93951e7i | 0.689959 | − | 0.992127i | ||||
\(85\) | 6.71839e7 | 1.28703 | ||||||||
\(86\) | 8.17862e7 | 1.49515 | ||||||||
\(87\) | 8.20723e7i | 1.43258i | ||||||||
\(88\) | 6.54710e6 | 0.109174 | ||||||||
\(89\) | − | 7.05328e7i | − | 1.12417i | −0.827080 | − | 0.562084i | \(-0.810000\pi\) | ||
0.827080 | − | 0.562084i | \(-0.190000\pi\) | |||||||
\(90\) | − | 1.32531e8i | − | 2.01998i | ||||||
\(91\) | 3.19463e7 | − | 4.59372e7i | 0.465859 | − | 0.669882i | ||||
\(92\) | 3.04871e7 | 0.425564 | ||||||||
\(93\) | −7.16086e7 | −0.957267 | ||||||||
\(94\) | − | 2.27960e6i | − | 0.0291977i | ||||||
\(95\) | −1.35336e8 | −1.66158 | ||||||||
\(96\) | 1.63716e8i | 1.92755i | ||||||||
\(97\) | 3.15476e7i | 0.356352i | 0.983999 | + | 0.178176i | \(0.0570197\pi\) | ||||
−0.983999 | + | 0.178176i | \(0.942980\pi\) | |||||||
\(98\) | 4.32677e7 | + | 1.16543e8i | 0.469093 | + | 1.26352i | ||||
\(99\) | 5.04840e7 | 0.525549 | ||||||||
\(100\) | −4.78000e7 | −0.478000 | ||||||||
\(101\) | − | 4.13782e7i | − | 0.397636i | −0.980036 | − | 0.198818i | \(-0.936290\pi\) | ||
0.980036 | − | 0.198818i | \(-0.0637103\pi\) | |||||||
\(102\) | −2.20697e8 | −2.03890 | ||||||||
\(103\) | − | 1.44223e8i | − | 1.28140i | −0.767790 | − | 0.640701i | \(-0.778644\pi\) | ||
0.767790 | − | 0.640701i | \(-0.221356\pi\) | |||||||
\(104\) | 2.36024e7i | 0.201754i | ||||||||
\(105\) | 1.85958e8 | + | 1.29322e8i | 1.52988 | + | 1.06393i | ||||
\(106\) | −7.47193e7 | −0.591847 | ||||||||
\(107\) | −1.97515e6 | −0.0150683 | −0.00753416 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753416 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(108\) | 3.12866e7i | 0.229966i | ||||||||
\(109\) | 2.26352e8 | 1.60353 | 0.801767 | − | 0.597636i | \(-0.203893\pi\) | ||||
0.801767 | + | 0.597636i | \(0.203893\pi\) | |||||||
\(110\) | − | 1.09703e8i | − | 0.749288i | ||||||
\(111\) | − | 2.49573e8i | − | 1.64401i | ||||||
\(112\) | −1.48536e8 | − | 1.03297e8i | −0.943974 | − | 0.656472i | ||||
\(113\) | −1.03426e8 | −0.634329 | −0.317164 | − | 0.948371i | \(-0.602731\pi\) | ||||
−0.317164 | + | 0.948371i | \(0.602731\pi\) | |||||||
\(114\) | 4.44575e8 | 2.63224 | ||||||||
\(115\) | 1.14775e8i | 0.656229i | ||||||||
\(116\) | −1.43113e8 | −0.790398 | ||||||||
\(117\) | 1.81995e8i | 0.971218i | ||||||||
\(118\) | 2.91340e8i | 1.50270i | ||||||||
\(119\) | 1.17031e8 | − | 1.68285e8i | 0.583599 | − | 0.839186i | ||||
\(120\) | −9.55447e7 | −0.460767 | ||||||||
\(121\) | −1.72570e8 | −0.805054 | ||||||||
\(122\) | − | 1.81584e7i | − | 0.0819667i | ||||||
\(123\) | 2.71091e7 | 0.118439 | ||||||||
\(124\) | − | 1.24867e8i | − | 0.528153i | ||||||
\(125\) | 1.27451e8i | 0.522039i | ||||||||
\(126\) | −3.31969e8 | − | 2.30863e8i | −1.31709 | − | 0.915950i | ||||
\(127\) | −7.49190e7 | −0.287990 | −0.143995 | − | 0.989578i | \(-0.545995\pi\) | ||||
−0.143995 | + | 0.989578i | \(0.545995\pi\) | |||||||
\(128\) | 1.30515e8 | 0.486206 | ||||||||
\(129\) | − | 4.54647e8i | − | 1.64178i | ||||||
\(130\) | 3.95481e8 | 1.38469 | ||||||||
\(131\) | 5.60831e8i | 1.90435i | 0.305553 | + | 0.952175i | \(0.401159\pi\) | ||||
−0.305553 | + | 0.952175i | \(0.598841\pi\) | |||||||
\(132\) | 1.61988e8i | 0.533565i | ||||||||
\(133\) | −2.35750e8 | + | 3.38997e8i | −0.753434 | + | 1.08340i | ||||
\(134\) | 2.07662e8 | 0.644076 | ||||||||
\(135\) | −1.17785e8 | −0.354613 | ||||||||
\(136\) | 8.64644e7i | 0.252745i | ||||||||
\(137\) | −2.79251e8 | −0.792706 | −0.396353 | − | 0.918098i | \(-0.629724\pi\) | ||||
−0.396353 | + | 0.918098i | \(0.629724\pi\) | |||||||
\(138\) | − | 3.77031e8i | − | 1.03959i | ||||||
\(139\) | − | 3.08039e8i | − | 0.825175i | −0.910918 | − | 0.412588i | \(-0.864625\pi\) | ||
0.910918 | − | 0.412588i | \(-0.135375\pi\) | |||||||
\(140\) | −2.25503e8 | + | 3.24262e8i | −0.587003 | + | 0.844081i | ||||
\(141\) | −1.26722e7 | −0.0320610 | ||||||||
\(142\) | −1.07686e8 | −0.264854 | ||||||||
\(143\) | 1.50648e8i | 0.360262i | ||||||||
\(144\) | 5.88476e8 | 1.36861 | ||||||||
\(145\) | − | 5.38777e8i | − | 1.21881i | ||||||
\(146\) | − | 4.80179e8i | − | 1.05680i | ||||||
\(147\) | 6.47861e8 | − | 2.40523e8i | 1.38743 | − | 0.515096i | ||||
\(148\) | 4.35190e8 | 0.907052 | ||||||||
\(149\) | −9.31424e8 | −1.88974 | −0.944870 | − | 0.327445i | \(-0.893812\pi\) | ||||
−0.944870 | + | 0.327445i | \(0.893812\pi\) | |||||||
\(150\) | 5.91138e8i | 1.16768i | ||||||||
\(151\) | 9.56551e8 | 1.83993 | 0.919963 | − | 0.392006i | \(-0.128219\pi\) | ||||
0.919963 | + | 0.392006i | \(0.128219\pi\) | |||||||
\(152\) | − | 1.74175e8i | − | 0.326297i | ||||||
\(153\) | 6.66718e8i | 1.21668i | ||||||||
\(154\) | −2.74789e8 | − | 1.91098e8i | −0.488559 | − | 0.339761i | ||||
\(155\) | 4.70086e8 | 0.814424 | ||||||||
\(156\) | −5.83968e8 | −0.986032 | ||||||||
\(157\) | 1.79019e8i | 0.294647i | 0.989088 | + | 0.147323i | \(0.0470658\pi\) | ||||
−0.989088 | + | 0.147323i | \(0.952934\pi\) | |||||||
\(158\) | −7.51400e8 | −1.20571 | ||||||||
\(159\) | 4.15362e8i | 0.649888i | ||||||||
\(160\) | − | 1.07474e9i | − | 1.63992i | ||||||
\(161\) | 2.87493e8 | + | 1.99933e8i | 0.427882 | + | 0.297564i | ||||
\(162\) | −7.18020e8 | −1.04250 | ||||||||
\(163\) | −8.94662e8 | −1.26739 | −0.633693 | − | 0.773585i | \(-0.718462\pi\) | ||||
−0.633693 | + | 0.773585i | \(0.718462\pi\) | |||||||
\(164\) | 4.72712e7i | 0.0653464i | ||||||||
\(165\) | −6.09837e8 | −0.822769 | ||||||||
\(166\) | 1.76153e9i | 2.31983i | ||||||||
\(167\) | − | 7.60480e7i | − | 0.0977736i | −0.998804 | − | 0.0488868i | \(-0.984433\pi\) | ||
0.998804 | − | 0.0488868i | \(-0.0155674\pi\) | |||||||
\(168\) | −1.66434e8 | + | 2.39324e8i | −0.208933 | + | 0.300435i | ||||
\(169\) | 2.72644e8 | 0.334233 | ||||||||
\(170\) | 1.44880e9 | 1.73465 | ||||||||
\(171\) | − | 1.34305e9i | − | 1.57075i | ||||||
\(172\) | 7.92785e8 | 0.905819 | ||||||||
\(173\) | − | 1.27621e9i | − | 1.42474i | −0.701802 | − | 0.712372i | \(-0.747621\pi\) | ||
0.701802 | − | 0.712372i | \(-0.252379\pi\) | |||||||
\(174\) | 1.76986e9i | 1.93082i | ||||||||
\(175\) | −4.50753e8 | − | 3.13469e8i | −0.480603 | − | 0.334228i | ||||
\(176\) | 4.87114e8 | 0.507668 | ||||||||
\(177\) | 1.61955e9 | 1.65007 | ||||||||
\(178\) | − | 1.52102e9i | − | 1.51514i | ||||||
\(179\) | −6.63361e8 | −0.646157 | −0.323078 | − | 0.946372i | \(-0.604718\pi\) | ||||
−0.323078 | + | 0.946372i | \(0.604718\pi\) | |||||||
\(180\) | − | 1.28467e9i | − | 1.22378i | ||||||
\(181\) | 9.11648e8i | 0.849401i | 0.905334 | + | 0.424701i | \(0.139621\pi\) | ||||
−0.905334 | + | 0.424701i | \(0.860379\pi\) | |||||||
\(182\) | 6.88911e8 | − | 9.90619e8i | 0.627881 | − | 0.902862i | ||||
\(183\) | −1.00942e8 | −0.0900049 | ||||||||
\(184\) | −1.47713e8 | −0.128869 | ||||||||
\(185\) | 1.63836e9i | 1.39869i | ||||||||
\(186\) | −1.54421e9 | −1.29020 | ||||||||
\(187\) | 5.51880e8i | 0.451313i | ||||||||
\(188\) | − | 2.20971e7i | − | 0.0176890i | ||||||
\(189\) | −2.05176e8 | + | 2.95033e8i | −0.160798 | + | 0.231219i | ||||
\(190\) | −2.91849e9 | −2.23946 | ||||||||
\(191\) | 1.97881e9 | 1.48686 | 0.743431 | − | 0.668813i | \(-0.233197\pi\) | ||||
0.743431 | + | 0.668813i | \(0.233197\pi\) | |||||||
\(192\) | 1.21799e9i | 0.896267i | ||||||||
\(193\) | −2.76067e8 | −0.198969 | −0.0994846 | − | 0.995039i | \(-0.531719\pi\) | ||||
−0.0994846 | + | 0.995039i | \(0.531719\pi\) | |||||||
\(194\) | 6.80313e8i | 0.480288i | ||||||||
\(195\) | − | 2.19847e9i | − | 1.52048i | ||||||
\(196\) | 4.19410e8 | + | 1.12970e9i | 0.284194 | + | 0.765489i | ||||
\(197\) | 4.93962e8 | 0.327966 | 0.163983 | − | 0.986463i | \(-0.447566\pi\) | ||||
0.163983 | + | 0.986463i | \(0.447566\pi\) | |||||||
\(198\) | 1.08867e9 | 0.708330 | ||||||||
\(199\) | 1.93233e9i | 1.23216i | 0.787682 | + | 0.616082i | \(0.211281\pi\) | ||||
−0.787682 | + | 0.616082i | \(0.788719\pi\) | |||||||
\(200\) | 2.31596e8 | 0.144747 | ||||||||
\(201\) | − | 1.15438e9i | − | 0.707239i | ||||||
\(202\) | − | 8.92307e8i | − | 0.535931i | ||||||
\(203\) | −1.34955e9 | − | 9.38524e8i | −0.794704 | − | 0.552664i | ||||
\(204\) | −2.13930e9 | −1.23524 | ||||||||
\(205\) | −1.77962e8 | −0.100766 | ||||||||
\(206\) | − | 3.11012e9i | − | 1.72706i | ||||||
\(207\) | −1.13900e9 | −0.620358 | ||||||||
\(208\) | 1.75605e9i | 0.938176i | ||||||||
\(209\) | − | 1.11172e9i | − | 0.582652i | ||||||
\(210\) | 4.01012e9 | + | 2.78878e9i | 2.06196 | + | 1.43396i | ||||
\(211\) | 8.33410e8 | 0.420464 | 0.210232 | − | 0.977652i | \(-0.432578\pi\) | ||||
0.210232 | + | 0.977652i | \(0.432578\pi\) | |||||||
\(212\) | −7.24283e8 | −0.358563 | ||||||||
\(213\) | 5.98623e8i | 0.290827i | ||||||||
\(214\) | −4.25934e7 | −0.0203089 | ||||||||
\(215\) | 2.98460e9i | 1.39679i | ||||||||
\(216\) | − | 1.51587e8i | − | 0.0696381i | ||||||
\(217\) | 8.18869e8 | − | 1.17749e9i | 0.369297 | − | 0.531030i | ||||
\(218\) | 4.88120e9 | 2.16123 | ||||||||
\(219\) | −2.66930e9 | −1.16043 | ||||||||
\(220\) | − | 1.06340e9i | − | 0.453946i | ||||||
\(221\) | −1.98953e9 | −0.834031 | ||||||||
\(222\) | − | 5.38196e9i | − | 2.21579i | ||||||
\(223\) | 1.71586e9i | 0.693843i | 0.937894 | + | 0.346921i | \(0.112773\pi\) | ||||
−0.937894 | + | 0.346921i | \(0.887227\pi\) | |||||||
\(224\) | −2.69205e9 | − | 1.87215e9i | −1.06928 | − | 0.743614i | ||||
\(225\) | 1.78581e9 | 0.696795 | ||||||||
\(226\) | −2.23034e9 | −0.854942 | ||||||||
\(227\) | 7.60049e8i | 0.286245i | 0.989705 | + | 0.143123i | \(0.0457143\pi\) | ||||
−0.989705 | + | 0.143123i | \(0.954286\pi\) | |||||||
\(228\) | 4.30944e9 | 1.59471 | ||||||||
\(229\) | − | 3.48407e9i | − | 1.26691i | −0.773781 | − | 0.633453i | \(-0.781637\pi\) | ||
0.773781 | − | 0.633453i | \(-0.218363\pi\) | |||||||
\(230\) | 2.47508e9i | 0.884459i | ||||||||
\(231\) | −1.06231e9 | + | 1.52755e9i | −0.373080 | + | 0.536471i | ||||
\(232\) | 6.93395e8 | 0.239347 | ||||||||
\(233\) | 8.66821e8 | 0.294107 | 0.147054 | − | 0.989129i | \(-0.453021\pi\) | ||||
0.147054 | + | 0.989129i | \(0.453021\pi\) | |||||||
\(234\) | 3.92467e9i | 1.30900i | ||||||||
\(235\) | 8.31890e7 | 0.0272768 | ||||||||
\(236\) | 2.82407e9i | 0.910391i | ||||||||
\(237\) | 4.17701e9i | 1.32395i | ||||||||
\(238\) | 2.52374e9 | − | 3.62901e9i | 0.786569 | − | 1.13105i | ||||
\(239\) | −3.59978e9 | −1.10328 | −0.551638 | − | 0.834084i | \(-0.685997\pi\) | ||||
−0.551638 | + | 0.834084i | \(0.685997\pi\) | |||||||
\(240\) | −7.10867e9 | −2.14261 | ||||||||
\(241\) | − | 6.07605e9i | − | 1.80116i | −0.434686 | − | 0.900582i | \(-0.643141\pi\) | ||
0.434686 | − | 0.900582i | \(-0.356859\pi\) | |||||||
\(242\) | −3.72142e9 | −1.08504 | ||||||||
\(243\) | 4.97345e9i | 1.42637i | ||||||||
\(244\) | − | 1.76016e8i | − | 0.0496584i | ||||||
\(245\) | −4.25299e9 | + | 1.57895e9i | −1.18040 | + | 0.438233i | ||||
\(246\) | 5.84599e8 | 0.159631 | ||||||||
\(247\) | 4.00775e9 | 1.07674 | ||||||||
\(248\) | 6.04992e8i | 0.159935i | ||||||||
\(249\) | 9.79227e9 | 2.54733 | ||||||||
\(250\) | 2.74843e9i | 0.703599i | ||||||||
\(251\) | − | 2.42395e9i | − | 0.610701i | −0.952240 | − | 0.305350i | \(-0.901226\pi\) | ||
0.952240 | − | 0.305350i | \(-0.0987736\pi\) | |||||||
\(252\) | −3.21791e9 | − | 2.23784e9i | −0.797942 | − | 0.554916i | ||||
\(253\) | −9.42813e8 | −0.230114 | ||||||||
\(254\) | −1.61560e9 | −0.388150 | ||||||||
\(255\) | − | 8.05382e9i | − | 1.90476i | ||||||
\(256\) | 5.41554e9 | 1.26090 | ||||||||
\(257\) | − | 2.33555e9i | − | 0.535373i | −0.963506 | − | 0.267686i | \(-0.913741\pi\) | ||
0.963506 | − | 0.267686i | \(-0.0862591\pi\) | |||||||
\(258\) | − | 9.80430e9i | − | 2.21278i | ||||||
\(259\) | 4.10384e9 | + | 2.85395e9i | 0.911993 | + | 0.634231i | ||||
\(260\) | 3.83355e9 | 0.838896 | ||||||||
\(261\) | 5.34670e9 | 1.15219 | ||||||||
\(262\) | 1.20941e10i | 2.56667i | ||||||||
\(263\) | 2.69681e9 | 0.563673 | 0.281837 | − | 0.959462i | \(-0.409056\pi\) | ||||
0.281837 | + | 0.959462i | \(0.409056\pi\) | |||||||
\(264\) | − | 7.84848e8i | − | 0.161573i | ||||||
\(265\) | − | 2.72671e9i | − | 0.552912i | ||||||
\(266\) | −5.08387e9 | + | 7.31035e9i | −1.01547 | + | 1.46020i | ||||
\(267\) | −8.45527e9 | −1.66373 | ||||||||
\(268\) | 2.01295e9 | 0.390205 | ||||||||
\(269\) | 4.85295e9i | 0.926823i | 0.886143 | + | 0.463412i | \(0.153375\pi\) | ||||
−0.886143 | + | 0.463412i | \(0.846625\pi\) | |||||||
\(270\) | −2.53999e9 | −0.477944 | ||||||||
\(271\) | − | 8.17058e9i | − | 1.51487i | −0.652909 | − | 0.757436i | \(-0.726452\pi\) | ||
0.652909 | − | 0.757436i | \(-0.273548\pi\) | |||||||
\(272\) | 6.43309e9i | 1.17529i | ||||||||
\(273\) | −5.50682e9 | − | 3.82963e9i | −0.991403 | − | 0.689456i | ||||
\(274\) | −6.02195e9 | −1.06840 | ||||||||
\(275\) | 1.47821e9 | 0.258468 | ||||||||
\(276\) | − | 3.65471e9i | − | 0.629820i | ||||||
\(277\) | −7.55633e9 | −1.28349 | −0.641744 | − | 0.766919i | \(-0.721789\pi\) | ||||
−0.641744 | + | 0.766919i | \(0.721789\pi\) | |||||||
\(278\) | − | 6.64275e9i | − | 1.11216i | ||||||
\(279\) | 4.66503e9i | 0.769905i | ||||||||
\(280\) | 1.09259e9 | − | 1.57108e9i | 0.177756 | − | 0.255604i | ||||
\(281\) | 6.19336e9 | 0.993347 | 0.496673 | − | 0.867938i | \(-0.334555\pi\) | ||||
0.496673 | + | 0.867938i | \(0.334555\pi\) | |||||||
\(282\) | −2.73273e8 | −0.0432115 | ||||||||
\(283\) | 7.64290e9i | 1.19155i | 0.803151 | + | 0.595775i | \(0.203155\pi\) | ||||
−0.803151 | + | 0.595775i | \(0.796845\pi\) | |||||||
\(284\) | −1.04384e9 | −0.160458 | ||||||||
\(285\) | 1.62238e10i | 2.45908i | ||||||||
\(286\) | 3.24867e9i | 0.485558i | ||||||||
\(287\) | −3.10002e8 | + | 4.45767e8i | −0.0456916 | + | 0.0657023i | ||||
\(288\) | 1.06655e10 | 1.55028 | ||||||||
\(289\) | −3.12658e8 | −0.0448207 | ||||||||
\(290\) | − | 1.16185e10i | − | 1.64270i | ||||||
\(291\) | 3.78184e9 | 0.527389 | ||||||||
\(292\) | − | 4.65456e9i | − | 0.640246i | ||||||
\(293\) | − | 9.50343e9i | − | 1.28947i | −0.764408 | − | 0.644733i | \(-0.776969\pi\) | ||
0.764408 | − | 0.644733i | \(-0.223031\pi\) | |||||||
\(294\) | 1.39709e10 | − | 5.18681e9i | 1.86997 | − | 0.694242i | ||||
\(295\) | −1.06318e10 | −1.40384 | ||||||||
\(296\) | −2.10854e9 | −0.274672 | ||||||||
\(297\) | − | 9.67540e8i | − | 0.124349i | ||||||
\(298\) | −2.00858e10 | −2.54698 | ||||||||
\(299\) | − | 3.39885e9i | − | 0.425253i | ||||||
\(300\) | 5.73013e9i | 0.707423i | ||||||||
\(301\) | 7.47596e9 | + | 5.19904e9i | 0.910753 | + | 0.633369i | ||||
\(302\) | 2.06277e10 | 2.47984 | ||||||||
\(303\) | −4.96030e9 | −0.588488 | ||||||||
\(304\) | − | 1.29589e10i | − | 1.51731i | ||||||
\(305\) | 6.62648e8 | 0.0765744 | ||||||||
\(306\) | 1.43776e10i | 1.63983i | ||||||||
\(307\) | 1.40766e9i | 0.158469i | 0.996856 | + | 0.0792343i | \(0.0252475\pi\) | ||||
−0.996856 | + | 0.0792343i | \(0.974752\pi\) | |||||||
\(308\) | −2.66364e9 | − | 1.85239e9i | −0.295987 | − | 0.205840i | ||||
\(309\) | −1.72890e10 | −1.89643 | ||||||||
\(310\) | 1.01372e10 | 1.09767 | ||||||||
\(311\) | − | 2.56247e8i | − | 0.0273916i | −0.999906 | − | 0.0136958i | \(-0.995640\pi\) | ||
0.999906 | − | 0.0136958i | \(-0.00435964\pi\) | |||||||
\(312\) | 2.82939e9 | 0.298589 | ||||||||
\(313\) | 8.27127e9i | 0.861777i | 0.902405 | + | 0.430889i | \(0.141800\pi\) | ||||
−0.902405 | + | 0.430889i | \(0.858200\pi\) | |||||||
\(314\) | 3.86049e9i | 0.397122i | ||||||||
\(315\) | 8.42481e9 | − | 1.21145e10i | 0.855693 | − | 1.23044i | ||||
\(316\) | −7.28361e9 | −0.730463 | ||||||||
\(317\) | −4.96438e9 | −0.491618 | −0.245809 | − | 0.969318i | \(-0.579054\pi\) | ||||
−0.245809 | + | 0.969318i | \(0.579054\pi\) | |||||||
\(318\) | 8.95715e9i | 0.875913i | ||||||||
\(319\) | 4.42576e9 | 0.427391 | ||||||||
\(320\) | − | 7.99567e9i | − | 0.762526i | ||||||
\(321\) | 2.36775e8i | 0.0223006i | ||||||||
\(322\) | 6.19969e9 | + | 4.31148e9i | 0.576695 | + | 0.401054i | ||||
\(323\) | 1.46819e10 | 1.34888 | ||||||||
\(324\) | −6.96005e9 | −0.631585 | ||||||||
\(325\) | 5.32898e9i | 0.477651i | ||||||||
\(326\) | −1.92931e10 | −1.70817 | ||||||||
\(327\) | − | 2.71344e10i | − | 2.37318i | ||||||
\(328\) | − | 2.29034e8i | − | 0.0197881i | ||||||
\(329\) | 1.44911e8 | − | 2.08375e8i | 0.0123686 | − | 0.0177854i | ||||
\(330\) | −1.31509e10 | −1.10892 | ||||||||
\(331\) | 5.89699e9 | 0.491268 | 0.245634 | − | 0.969363i | \(-0.421004\pi\) | ||||
0.245634 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(332\) | 1.70752e10i | 1.40544i | ||||||||
\(333\) | −1.62587e10 | −1.32224 | ||||||||
\(334\) | − | 1.63995e9i | − | 0.131778i | ||||||
\(335\) | 7.57814e9i | 0.601705i | ||||||||
\(336\) | −1.23830e10 | + | 1.78061e10i | −0.971557 | + | 1.39705i | ||||
\(337\) | 6.30457e9 | 0.488806 | 0.244403 | − | 0.969674i | \(-0.421408\pi\) | ||||
0.244403 | + | 0.969674i | \(0.421408\pi\) | |||||||
\(338\) | 5.87947e9 | 0.450476 | ||||||||
\(339\) | 1.23984e10i | 0.938784i | ||||||||
\(340\) | 1.40438e10 | 1.05092 | ||||||||
\(341\) | 3.86150e9i | 0.285587i | ||||||||
\(342\) | − | 2.89624e10i | − | 2.11704i | ||||||
\(343\) | −3.45348e9 | + | 1.34035e10i | −0.249505 | + | 0.968373i | ||||
\(344\) | −3.84112e9 | −0.274299 | ||||||||
\(345\) | 1.37589e10 | 0.971196 | ||||||||
\(346\) | − | 2.75210e10i | − | 1.92026i | ||||||
\(347\) | 1.53411e10 | 1.05813 | 0.529063 | − | 0.848582i | \(-0.322543\pi\) | ||||
0.529063 | + | 0.848582i | \(0.322543\pi\) | |||||||
\(348\) | 1.71559e10i | 1.16976i | ||||||||
\(349\) | − | 7.69217e9i | − | 0.518498i | −0.965810 | − | 0.259249i | \(-0.916525\pi\) | ||
0.965810 | − | 0.259249i | \(-0.0834751\pi\) | |||||||
\(350\) | −9.72034e9 | − | 6.75986e9i | −0.647753 | − | 0.450470i | ||||
\(351\) | 3.48799e9 | 0.229798 | ||||||||
\(352\) | 8.82840e9 | 0.575057 | ||||||||
\(353\) | − | 1.38763e10i | − | 0.893663i | −0.894618 | − | 0.446832i | \(-0.852552\pi\) | ||
0.894618 | − | 0.446832i | \(-0.147448\pi\) | |||||||
\(354\) | 3.49251e10 | 2.22395 | ||||||||
\(355\) | − | 3.92976e9i | − | 0.247430i | ||||||
\(356\) | − | 1.47438e10i | − | 0.917929i | ||||||
\(357\) | −2.01736e10 | − | 1.40294e10i | −1.24197 | − | 0.863706i | ||||
\(358\) | −1.43052e10 | −0.870885 | ||||||||
\(359\) | 7.39469e9 | 0.445186 | 0.222593 | − | 0.974911i | \(-0.428548\pi\) | ||||
0.222593 | + | 0.974911i | \(0.428548\pi\) | |||||||
\(360\) | 6.22437e9i | 0.370583i | ||||||||
\(361\) | −1.25919e10 | −0.741419 | ||||||||
\(362\) | 1.96594e10i | 1.14482i | ||||||||
\(363\) | 2.06873e10i | 1.19145i | ||||||||
\(364\) | 6.67788e9 | − | 9.60245e9i | 0.380393 | − | 0.546987i | ||||
\(365\) | 1.75230e10 | 0.987274 | ||||||||
\(366\) | −2.17677e9 | −0.121308 | ||||||||
\(367\) | − | 4.89461e9i | − | 0.269807i | −0.990859 | − | 0.134904i | \(-0.956928\pi\) | ||
0.990859 | − | 0.134904i | \(-0.0430725\pi\) | |||||||
\(368\) | −1.09901e10 | −0.599252 | ||||||||
\(369\) | − | 1.76606e9i | − | 0.0952574i | ||||||
\(370\) | 3.53307e10i | 1.88515i | ||||||||
\(371\) | −6.82999e9 | − | 4.74981e9i | −0.360516 | − | 0.250715i | ||||
\(372\) | −1.49687e10 | −0.781648 | ||||||||
\(373\) | −3.07017e10 | −1.58609 | −0.793043 | − | 0.609165i | \(-0.791505\pi\) | ||||
−0.793043 | + | 0.609165i | \(0.791505\pi\) | |||||||
\(374\) | 1.19011e10i | 0.608276i | ||||||||
\(375\) | 1.52785e10 | 0.772599 | ||||||||
\(376\) | 1.07063e8i | 0.00535657i | ||||||||
\(377\) | 1.59549e10i | 0.789822i | ||||||||
\(378\) | −4.42455e9 | + | 6.36228e9i | −0.216721 | + | 0.311635i | ||||
\(379\) | −1.58224e10 | −0.766859 | −0.383430 | − | 0.923570i | \(-0.625257\pi\) | ||||
−0.383430 | + | 0.923570i | \(0.625257\pi\) | |||||||
\(380\) | −2.82900e10 | −1.35675 | ||||||||
\(381\) | 8.98108e9i | 0.426215i | ||||||||
\(382\) | 4.26723e10 | 2.00398 | ||||||||
\(383\) | − | 1.55165e10i | − | 0.721104i | −0.932739 | − | 0.360552i | \(-0.882588\pi\) | ||
0.932739 | − | 0.360552i | \(-0.117412\pi\) | |||||||
\(384\) | − | 1.56458e10i | − | 0.719568i | ||||||
\(385\) | 6.97369e9 | − | 1.00278e10i | 0.317409 | − | 0.456419i | ||||
\(386\) | −5.95330e9 | −0.268169 | ||||||||
\(387\) | −2.96185e10 | −1.32044 | ||||||||
\(388\) | 6.59454e9i | 0.290976i | ||||||||
\(389\) | −1.17629e10 | −0.513710 | −0.256855 | − | 0.966450i | \(-0.582686\pi\) | ||||
−0.256855 | + | 0.966450i | \(0.582686\pi\) | |||||||
\(390\) | − | 4.74092e10i | − | 2.04929i | ||||||
\(391\) | − | 1.24513e10i | − | 0.532730i | ||||||
\(392\) | −2.03208e9 | − | 5.47351e9i | −0.0860592 | − | 0.231805i | ||||
\(393\) | 6.72309e10 | 2.81837 | ||||||||
\(394\) | 1.06521e10 | 0.442030 | ||||||||
\(395\) | − | 2.74206e10i | − | 1.12639i | ||||||
\(396\) | 1.05529e10 | 0.429132 | ||||||||
\(397\) | 4.43659e10i | 1.78602i | 0.450033 | + | 0.893012i | \(0.351412\pi\) | ||||
−0.450033 | + | 0.893012i | \(0.648588\pi\) | |||||||
\(398\) | 4.16700e10i | 1.66070i | ||||||||
\(399\) | 4.06380e10 | + | 2.82611e10i | 1.60340 | + | 1.11506i | ||||
\(400\) | 1.72311e10 | 0.673089 | ||||||||
\(401\) | 1.00671e10 | 0.389337 | 0.194668 | − | 0.980869i | \(-0.437637\pi\) | ||||
0.194668 | + | 0.980869i | \(0.437637\pi\) | |||||||
\(402\) | − | 2.48939e10i | − | 0.953211i | ||||||
\(403\) | −1.39208e10 | −0.527768 | ||||||||
\(404\) | − | 8.64947e9i | − | 0.324686i | ||||||
\(405\) | − | 2.62025e10i | − | 0.973919i | ||||||
\(406\) | −2.91026e10 | − | 2.02390e10i | −1.07109 | − | 0.744876i | ||||
\(407\) | −1.34583e10 | −0.490469 | ||||||||
\(408\) | 1.03651e10 | 0.374053 | ||||||||
\(409\) | 3.34366e8i | 0.0119489i | 0.999982 | + | 0.00597447i | \(0.00190174\pi\) | ||||
−0.999982 | + | 0.00597447i | \(0.998098\pi\) | |||||||
\(410\) | −3.83769e9 | −0.135811 | ||||||||
\(411\) | 3.34758e10i | 1.17318i | ||||||||
\(412\) | − | 3.01476e10i | − | 1.04632i | ||||||
\(413\) | −1.85201e10 | + | 2.66310e10i | −0.636566 | + | 0.915350i | ||||
\(414\) | −2.45621e10 | −0.836112 | ||||||||
\(415\) | −6.42829e10 | −2.16722 | ||||||||
\(416\) | 3.18265e10i | 1.06271i | ||||||||
\(417\) | −3.69268e10 | −1.22123 | ||||||||
\(418\) | − | 2.39738e10i | − | 0.785293i | ||||||
\(419\) | − | 5.14322e10i | − | 1.66870i | −0.551232 | − | 0.834352i | \(-0.685842\pi\) | ||
0.551232 | − | 0.834352i | \(-0.314158\pi\) | |||||||
\(420\) | 3.88717e10 | + | 2.70327e10i | 1.24921 | + | 0.868745i | ||||
\(421\) | 5.97070e10 | 1.90063 | 0.950313 | − | 0.311297i | \(-0.100763\pi\) | ||||
0.950313 | + | 0.311297i | \(0.100763\pi\) | |||||||
\(422\) | 1.79722e10 | 0.566698 | ||||||||
\(423\) | 8.25548e8i | 0.0257858i | ||||||||
\(424\) | 3.50923e9 | 0.108580 | ||||||||
\(425\) | 1.95221e10i | 0.598371i | ||||||||
\(426\) | 1.29091e10i | 0.391974i | ||||||||
\(427\) | 1.15430e9 | − | 1.65983e9i | 0.0347223 | − | 0.0499289i | ||||
\(428\) | −4.12874e8 | −0.0123039 | ||||||||
\(429\) | 1.80592e10 | 0.533175 | ||||||||
\(430\) | 6.43619e10i | 1.88259i | ||||||||
\(431\) | −2.34704e10 | −0.680160 | −0.340080 | − | 0.940396i | \(-0.610454\pi\) | ||||
−0.340080 | + | 0.940396i | \(0.610454\pi\) | |||||||
\(432\) | − | 1.12783e10i | − | 0.323824i | ||||||
\(433\) | − | 2.35962e10i | − | 0.671260i | −0.941994 | − | 0.335630i | \(-0.891051\pi\) | ||
0.941994 | − | 0.335630i | \(-0.108949\pi\) | |||||||
\(434\) | 1.76586e10 | − | 2.53922e10i | 0.497735 | − | 0.715718i | ||||
\(435\) | −6.45870e10 | −1.80380 | ||||||||
\(436\) | 4.73154e10 | 1.30935 | ||||||||
\(437\) | 2.50821e10i | 0.687762i | ||||||||
\(438\) | −5.75625e10 | −1.56402 | ||||||||
\(439\) | − | 9.78599e9i | − | 0.263479i | −0.991284 | − | 0.131740i | \(-0.957944\pi\) | ||
0.991284 | − | 0.131740i | \(-0.0420563\pi\) | |||||||
\(440\) | 5.15226e9i | 0.137463i | ||||||||
\(441\) | −1.56692e10 | − | 4.22057e10i | −0.414278 | − | 1.11588i | ||||
\(442\) | −4.29036e10 | −1.12410 | ||||||||
\(443\) | 5.27088e10 | 1.36857 | 0.684287 | − | 0.729213i | \(-0.260113\pi\) | ||||
0.684287 | + | 0.729213i | \(0.260113\pi\) | |||||||
\(444\) | − | 5.21694e10i | − | 1.34241i | ||||||
\(445\) | 5.55060e10 | 1.41547 | ||||||||
\(446\) | 3.70018e10i | 0.935155i | ||||||||
\(447\) | 1.11656e11i | 2.79675i | ||||||||
\(448\) | −2.00279e10 | − | 1.39281e10i | −0.497191 | − | 0.345764i | ||||
\(449\) | −4.29146e10 | −1.05589 | −0.527946 | − | 0.849278i | \(-0.677038\pi\) | ||||
−0.527946 | + | 0.849278i | \(0.677038\pi\) | |||||||
\(450\) | 3.85104e10 | 0.939135 | ||||||||
\(451\) | − | 1.46186e9i | − | 0.0353346i | ||||||
\(452\) | −2.16195e10 | −0.517955 | ||||||||
\(453\) | − | 1.14669e11i | − | 2.72303i | ||||||
\(454\) | 1.63902e10i | 0.385799i | ||||||||
\(455\) | 3.61504e10 | + | 2.51402e10i | 0.843466 | + | 0.586575i | ||||
\(456\) | −2.08797e10 | −0.482908 | ||||||||
\(457\) | 1.49031e10 | 0.341675 | 0.170837 | − | 0.985299i | \(-0.445353\pi\) | ||||
0.170837 | + | 0.985299i | \(0.445353\pi\) | |||||||
\(458\) | − | 7.51327e10i | − | 1.70752i | ||||||
\(459\) | 1.27778e10 | 0.287877 | ||||||||
\(460\) | 2.39919e10i | 0.535838i | ||||||||
\(461\) | − | 1.30027e10i | − | 0.287891i | −0.989586 | − | 0.143946i | \(-0.954021\pi\) | ||
0.989586 | − | 0.143946i | \(-0.0459791\pi\) | |||||||
\(462\) | −2.29083e10 | + | 3.29410e10i | −0.502834 | + | 0.723051i | ||||
\(463\) | 4.41828e10 | 0.961455 | 0.480728 | − | 0.876870i | \(-0.340373\pi\) | ||||
0.480728 | + | 0.876870i | \(0.340373\pi\) | |||||||
\(464\) | 5.15897e10 | 1.11299 | ||||||||
\(465\) | − | 5.63526e10i | − | 1.20532i | ||||||
\(466\) | 1.86927e10 | 0.396395 | ||||||||
\(467\) | 4.47136e10i | 0.940097i | 0.882641 | + | 0.470048i | \(0.155764\pi\) | ||||
−0.882641 | + | 0.470048i | \(0.844236\pi\) | |||||||
\(468\) | 3.80433e10i | 0.793040i | ||||||||
\(469\) | 1.89821e10 | + | 1.32008e10i | 0.392330 | + | 0.272840i | ||||
\(470\) | 1.79394e9 | 0.0367635 | ||||||||
\(471\) | 2.14603e10 | 0.436067 | ||||||||
\(472\) | − | 1.36829e10i | − | 0.275684i | ||||||
\(473\) | −2.45169e10 | −0.489802 | ||||||||
\(474\) | 9.00757e10i | 1.78441i | ||||||||
\(475\) | − | 3.93256e10i | − | 0.772505i | ||||||
\(476\) | 2.44636e10 | − | 3.51774e10i | 0.476533 | − | 0.685230i | ||||
\(477\) | 2.70593e10 | 0.522688 | ||||||||
\(478\) | −7.76280e10 | −1.48699 | ||||||||
\(479\) | 1.63389e10i | 0.310371i | 0.987885 | + | 0.155185i | \(0.0495975\pi\) | ||||
−0.987885 | + | 0.155185i | \(0.950402\pi\) | |||||||
\(480\) | −1.28837e11 | −2.42703 | ||||||||
\(481\) | − | 4.85172e10i | − | 0.906390i | ||||||
\(482\) | − | 1.31028e11i | − | 2.42759i | ||||||
\(483\) | 2.39674e10 | − | 3.44639e10i | 0.440384 | − | 0.633250i | ||||
\(484\) | −3.60732e10 | −0.657360 | ||||||||
\(485\) | −2.48265e10 | −0.448692 | ||||||||
\(486\) | 1.07251e11i | 1.92245i | ||||||||
\(487\) | 2.29878e10 | 0.408678 | 0.204339 | − | 0.978900i | \(-0.434496\pi\) | ||||
0.204339 | + | 0.978900i | \(0.434496\pi\) | |||||||
\(488\) | 8.52815e8i | 0.0150375i | ||||||||
\(489\) | 1.07250e11i | 1.87569i | ||||||||
\(490\) | −9.17142e10 | + | 3.40496e10i | −1.59093 | + | 0.590647i | ||||
\(491\) | −8.49647e10 | −1.46188 | −0.730942 | − | 0.682440i | \(-0.760919\pi\) | ||||
−0.730942 | + | 0.682440i | \(0.760919\pi\) | |||||||
\(492\) | 5.66674e9 | 0.0967104 | ||||||||
\(493\) | 5.84489e10i | 0.989438i | ||||||||
\(494\) | 8.64258e10 | 1.45123 | ||||||||
\(495\) | 3.97285e10i | 0.661732i | ||||||||
\(496\) | 4.50123e10i | 0.743712i | ||||||||
\(497\) | −9.84343e9 | − | 6.84546e9i | −0.161332 | − | 0.112196i | ||||
\(498\) | 2.11167e11 | 3.43328 | ||||||||
\(499\) | −1.03838e11 | −1.67477 | −0.837384 | − | 0.546615i | \(-0.815916\pi\) | ||||
−0.837384 | + | 0.546615i | \(0.815916\pi\) | |||||||
\(500\) | 2.66416e10i | 0.426266i | ||||||||
\(501\) | −9.11642e9 | −0.144702 | ||||||||
\(502\) | − | 5.22716e10i | − | 0.823097i | ||||||
\(503\) | − | 4.42486e10i | − | 0.691238i | −0.938375 | − | 0.345619i | \(-0.887669\pi\) | ||
0.938375 | − | 0.345619i | \(-0.112331\pi\) | |||||||
\(504\) | 1.55911e10 | + | 1.08426e10i | 0.241632 | + | 0.168039i | ||||
\(505\) | 3.25627e10 | 0.500674 | ||||||||
\(506\) | −2.03314e10 | −0.310146 | ||||||||
\(507\) | − | 3.26838e10i | − | 0.494653i | ||||||
\(508\) | −1.56607e10 | −0.235156 | ||||||||
\(509\) | − | 6.37566e10i | − | 0.949847i | −0.880027 | − | 0.474924i | \(-0.842476\pi\) | ||
0.880027 | − | 0.474924i | \(-0.157524\pi\) | |||||||
\(510\) | − | 1.73678e11i | − | 2.56723i | ||||||
\(511\) | 3.05243e10 | − | 4.38925e10i | 0.447675 | − | 0.643734i | ||||
\(512\) | 8.33725e10 | 1.21323 | ||||||||
\(513\) | −2.57399e10 | −0.371653 | ||||||||
\(514\) | − | 5.03653e10i | − | 0.721571i | ||||||
\(515\) | 1.13497e11 | 1.61345 | ||||||||
\(516\) | − | 9.50369e10i | − | 1.34058i | ||||||
\(517\) | 6.83353e8i | 0.00956495i | ||||||||
\(518\) | 8.84979e10 | + | 6.15445e10i | 1.22918 | + | 0.854811i | ||||
\(519\) | −1.52988e11 | −2.10857 | ||||||||
\(520\) | −1.85740e10 | −0.254034 | ||||||||
\(521\) | 8.73971e10i | 1.18617i | 0.805141 | + | 0.593084i | \(0.202090\pi\) | ||||
−0.805141 | + | 0.593084i | \(0.797910\pi\) | |||||||
\(522\) | 1.15300e11 | 1.55291 | ||||||||
\(523\) | 1.17667e11i | 1.57271i | 0.617777 | + | 0.786353i | \(0.288033\pi\) | ||||
−0.617777 | + | 0.786353i | \(0.711967\pi\) | |||||||
\(524\) | 1.17233e11i | 1.55498i | ||||||||
\(525\) | −3.75778e10 | + | 5.40351e10i | −0.494646 | + | 0.711277i | ||||
\(526\) | 5.81558e10 | 0.759714 | ||||||||
\(527\) | −5.09970e10 | −0.661154 | ||||||||
\(528\) | − | 5.83939e10i | − | 0.751332i | ||||||
\(529\) | −5.70396e10 | −0.728373 | ||||||||
\(530\) | − | 5.88006e10i | − | 0.745210i | ||||||
\(531\) | − | 1.05508e11i | − | 1.32711i | ||||||
\(532\) | −4.92799e10 | + | 7.08620e10i | −0.615210 | + | 0.884641i | ||||
\(533\) | 5.27003e9 | 0.0652987 | ||||||||
\(534\) | −1.82335e11 | −2.24236 | ||||||||
\(535\) | − | 1.55435e9i | − | 0.0189729i | ||||||
\(536\) | −9.75293e9 | −0.118161 | ||||||||
\(537\) | 7.95219e10i | 0.956290i | ||||||||
\(538\) | 1.04652e11i | 1.24916i | ||||||||
\(539\) | −1.29703e10 | − | 3.49360e10i | −0.153672 | − | 0.413922i | ||||
\(540\) | −2.46211e10 | −0.289556 | ||||||||
\(541\) | 1.17278e11 | 1.36907 | 0.684536 | − | 0.728979i | \(-0.260005\pi\) | ||||
0.684536 | + | 0.728979i | \(0.260005\pi\) | |||||||
\(542\) | − | 1.76196e11i | − | 2.04173i | ||||||
\(543\) | 1.09286e11 | 1.25708 | ||||||||
\(544\) | 1.16592e11i | 1.33130i | ||||||||
\(545\) | 1.78128e11i | 2.01905i | ||||||||
\(546\) | −1.18753e11 | − | 8.25847e10i | −1.33620 | − | 0.929242i | ||||
\(547\) | 1.38303e8 | 0.00154484 | 0.000772421 | − | 1.00000i | \(-0.499754\pi\) | ||||
0.000772421 | 1.00000i | \(0.499754\pi\) | ||||||||
\(548\) | −5.83731e10 | −0.647278 | ||||||||
\(549\) | 6.57597e9i | 0.0723886i | ||||||||
\(550\) | 3.18772e10 | 0.348361 | ||||||||
\(551\) | − | 1.17740e11i | − | 1.27738i | ||||||
\(552\) | 1.77074e10i | 0.190721i | ||||||||
\(553\) | −6.86844e10 | − | 4.77655e10i | −0.734442 | − | 0.510756i | ||||
\(554\) | −1.62950e11 | −1.72987 | ||||||||
\(555\) | 1.96402e11 | 2.07002 | ||||||||
\(556\) | − | 6.43908e10i | − | 0.673790i | ||||||
\(557\) | −8.27119e10 | −0.859304 | −0.429652 | − | 0.902994i | \(-0.641364\pi\) | ||||
−0.429652 | + | 0.902994i | \(0.641364\pi\) | |||||||
\(558\) | 1.00600e11i | 1.03767i | ||||||||
\(559\) | − | 8.83837e10i | − | 0.905159i | ||||||
\(560\) | 8.12901e10 | − | 1.16891e11i | 0.826581 | − | 1.18858i | ||||
\(561\) | 6.61578e10 | 0.667928 | ||||||||
\(562\) | 1.33558e11 | 1.33882 | ||||||||
\(563\) | 9.86261e10i | 0.981653i | 0.871257 | + | 0.490827i | \(0.163305\pi\) | ||||
−0.871257 | + | 0.490827i | \(0.836695\pi\) | |||||||
\(564\) | −2.64894e9 | −0.0261791 | ||||||||
\(565\) | − | 8.13911e10i | − | 0.798699i | ||||||
\(566\) | 1.64816e11i | 1.60596i | ||||||||
\(567\) | −6.56332e10 | − | 4.56436e10i | −0.635026 | − | 0.441619i | ||||
\(568\) | 5.05752e9 | 0.0485897 | ||||||||
\(569\) | −9.45296e9 | −0.0901818 | −0.0450909 | − | 0.998983i | \(-0.514358\pi\) | ||||
−0.0450909 | + | 0.998983i | \(0.514358\pi\) | |||||||
\(570\) | 3.49860e11i | 3.31432i | ||||||||
\(571\) | 9.06450e10 | 0.852706 | 0.426353 | − | 0.904557i | \(-0.359798\pi\) | ||||
0.426353 | + | 0.904557i | \(0.359798\pi\) | |||||||
\(572\) | 3.14906e10i | 0.294169i | ||||||||
\(573\) | − | 2.37214e11i | − | 2.20050i | ||||||
\(574\) | −6.68509e9 | + | 9.61282e9i | −0.0615828 | + | 0.0885530i | ||||
\(575\) | −3.33509e10 | −0.305096 | ||||||||
\(576\) | 7.93472e10 | 0.720845 | ||||||||
\(577\) | − | 2.11680e11i | − | 1.90975i | −0.297011 | − | 0.954874i | \(-0.595990\pi\) | ||
0.297011 | − | 0.954874i | \(-0.404010\pi\) | |||||||
\(578\) | −6.74237e9 | −0.0604089 | ||||||||
\(579\) | 3.30942e10i | 0.294468i | ||||||||
\(580\) | − | 1.12623e11i | − | 0.995210i | ||||||
\(581\) | −1.11978e11 | + | 1.61019e11i | −0.982716 | + | 1.41310i | ||||
\(582\) | 8.15541e10 | 0.710810 | ||||||||
\(583\) | 2.23985e10 | 0.193885 | ||||||||
\(584\) | 2.25518e10i | 0.193879i | ||||||||
\(585\) | −1.43222e11 | −1.22289 | ||||||||
\(586\) | − | 2.04938e11i | − | 1.73793i | ||||||
\(587\) | 3.78420e10i | 0.318729i | 0.987220 | + | 0.159365i | \(0.0509445\pi\) | ||||
−0.987220 | + | 0.159365i | \(0.949055\pi\) | |||||||
\(588\) | 1.35425e11 | − | 5.02777e10i | 1.13290 | − | 0.420597i | ||||
\(589\) | 1.02729e11 | 0.853559 | ||||||||
\(590\) | −2.29271e11 | −1.89209 | ||||||||
\(591\) | − | 5.92148e10i | − | 0.485378i | ||||||
\(592\) | −1.56879e11 | −1.27725 | ||||||||
\(593\) | 9.79198e10i | 0.791866i | 0.918279 | + | 0.395933i | \(0.129579\pi\) | ||||
−0.918279 | + | 0.395933i | \(0.870421\pi\) | |||||||
\(594\) | − | 2.08647e10i | − | 0.167597i | ||||||
\(595\) | 1.32433e11 | + | 9.20982e10i | 1.05664 | + | 0.734824i | ||||
\(596\) | −1.94700e11 | −1.54305 | ||||||||
\(597\) | 2.31642e11 | 1.82356 | ||||||||
\(598\) | − | 7.32951e10i | − | 0.573153i | ||||||
\(599\) | 1.26460e11 | 0.982305 | 0.491152 | − | 0.871074i | \(-0.336576\pi\) | ||||
0.491152 | + | 0.871074i | \(0.336576\pi\) | |||||||
\(600\) | − | 2.77631e10i | − | 0.214221i | ||||||
\(601\) | 2.23530e11i | 1.71332i | 0.515883 | + | 0.856659i | \(0.327464\pi\) | ||||
−0.515883 | + | 0.856659i | \(0.672536\pi\) | |||||||
\(602\) | 1.61216e11 | + | 1.12115e11i | 1.22751 | + | 0.853650i | ||||
\(603\) | −7.52038e10 | −0.568814 | ||||||||
\(604\) | 1.99952e11 | 1.50237 | ||||||||
\(605\) | − | 1.35805e11i | − | 1.01366i | ||||||
\(606\) | −1.06967e11 | −0.793159 | ||||||||
\(607\) | 4.50465e9i | 0.0331823i | 0.999862 | + | 0.0165911i | \(0.00528136\pi\) | ||||
−0.999862 | + | 0.0165911i | \(0.994719\pi\) | |||||||
\(608\) | − | 2.34866e11i | − | 1.71872i | ||||||
\(609\) | −1.12508e11 | + | 1.61780e11i | −0.817924 | + | 1.17613i | ||||
\(610\) | 1.42898e10 | 0.103206 | ||||||||
\(611\) | −2.46349e9 | −0.0176761 | ||||||||
\(612\) | 1.39367e11i | 0.993470i | ||||||||
\(613\) | −2.46267e11 | −1.74407 | −0.872037 | − | 0.489440i | \(-0.837201\pi\) | ||||
−0.872037 | + | 0.489440i | \(0.837201\pi\) | |||||||
\(614\) | 3.03556e10i | 0.213583i | ||||||||
\(615\) | 2.13336e10i | 0.149130i | ||||||||
\(616\) | 1.29056e10 | + | 8.97501e9i | 0.0896305 | + | 0.0623321i | ||||
\(617\) | −1.54701e11 | −1.06746 | −0.533730 | − | 0.845655i | \(-0.679210\pi\) | ||||
−0.533730 | + | 0.845655i | \(0.679210\pi\) | |||||||
\(618\) | −3.72832e11 | −2.55599 | ||||||||
\(619\) | 1.53782e11i | 1.04748i | 0.851879 | + | 0.523738i | \(0.175463\pi\) | ||||
−0.851879 | + | 0.523738i | \(0.824537\pi\) | |||||||
\(620\) | 9.82642e10 | 0.665011 | ||||||||
\(621\) | 2.18292e10i | 0.146782i | ||||||||
\(622\) | − | 5.52588e9i | − | 0.0369181i | ||||||
\(623\) | 9.66889e10 | − | 1.39034e11i | 0.641837 | − | 0.922929i | ||||
\(624\) | 2.10511e11 | 1.38847 | ||||||||
\(625\) | −1.89622e11 | −1.24271 | ||||||||
\(626\) | 1.78367e11i | 1.16150i | ||||||||
\(627\) | −1.33269e11 | −0.862304 | ||||||||
\(628\) | 3.74212e10i | 0.240591i | ||||||||
\(629\) | − | 1.77737e11i | − | 1.13547i | ||||||
\(630\) | 1.81678e11 | − | 2.61244e11i | 1.15330 | − | 1.65838i | ||||
\(631\) | 1.06917e10 | 0.0674419 | 0.0337210 | − | 0.999431i | \(-0.489264\pi\) | ||||
0.0337210 | + | 0.999431i | \(0.489264\pi\) | |||||||
\(632\) | 3.52898e10 | 0.221198 | ||||||||
\(633\) | − | 9.99068e10i | − | 0.622272i | ||||||
\(634\) | −1.07055e11 | −0.662599 | ||||||||
\(635\) | − | 5.89578e10i | − | 0.362615i | ||||||
\(636\) | 8.68251e10i | 0.530660i | ||||||||
\(637\) | 1.25945e11 | − | 4.67579e10i | 0.764931 | − | 0.283986i | ||||
\(638\) | 9.54400e10 | 0.576033 | ||||||||
\(639\) | 3.89980e10 | 0.233905 | ||||||||
\(640\) | 1.02709e11i | 0.612194i | ||||||||
\(641\) | 2.37351e11 | 1.40592 | 0.702958 | − | 0.711232i | \(-0.251862\pi\) | ||||
0.702958 | + | 0.711232i | \(0.251862\pi\) | |||||||
\(642\) | 5.10598e9i | 0.0300565i | ||||||||
\(643\) | 1.62640e11i | 0.951444i | 0.879596 | + | 0.475722i | \(0.157813\pi\) | ||||
−0.879596 | + | 0.475722i | \(0.842187\pi\) | |||||||
\(644\) | 6.00960e10 | + | 4.17928e10i | 0.349383 | + | 0.242973i | ||||
\(645\) | 3.57786e11 | 2.06721 | ||||||||
\(646\) | 3.16610e11 | 1.81801 | ||||||||
\(647\) | − | 8.80528e10i | − | 0.502488i | −0.967924 | − | 0.251244i | \(-0.919160\pi\) | ||
0.967924 | − | 0.251244i | \(-0.0808397\pi\) | |||||||
\(648\) | 3.37221e10 | 0.191256 | ||||||||
\(649\) | − | 8.73345e10i | − | 0.492274i | ||||||
\(650\) | 1.14918e11i | 0.643774i | ||||||||
\(651\) | −1.41154e11 | − | 9.81637e10i | −0.785906 | − | 0.546546i | ||||
\(652\) | −1.87015e11 | −1.03487 | ||||||||
\(653\) | −6.57014e9 | −0.0361345 | −0.0180673 | − | 0.999837i | \(-0.505751\pi\) | ||||
−0.0180673 | + | 0.999837i | \(0.505751\pi\) | |||||||
\(654\) | − | 5.85145e11i | − | 3.19855i | ||||||
\(655\) | −4.41348e11 | −2.39782 | ||||||||
\(656\) | − | 1.70405e10i | − | 0.0920166i | ||||||
\(657\) | 1.73895e11i | 0.933307i | ||||||||
\(658\) | 3.12496e9 | − | 4.49354e9i | 0.0166702 | − | 0.0239710i | ||||
\(659\) | 1.71539e11 | 0.909537 | 0.454769 | − | 0.890610i | \(-0.349722\pi\) | ||||
0.454769 | + | 0.890610i | \(0.349722\pi\) | |||||||
\(660\) | −1.27477e11 | −0.671825 | ||||||||
\(661\) | 1.92585e11i | 1.00883i | 0.863462 | + | 0.504415i | \(0.168292\pi\) | ||||
−0.863462 | + | 0.504415i | \(0.831708\pi\) | |||||||
\(662\) | 1.27167e11 | 0.662127 | ||||||||
\(663\) | 2.38500e11i | 1.23434i | ||||||||
\(664\) | − | 8.27309e10i | − | 0.425594i | ||||||
\(665\) | −2.66775e11 | − | 1.85524e11i | −1.36414 | − | 0.948667i | ||||
\(666\) | −3.50614e11 | −1.78210 | ||||||||
\(667\) | −9.98522e10 | −0.504492 | ||||||||
\(668\) | − | 1.58967e10i | − | 0.0798362i | ||||||
\(669\) | 2.05692e11 | 1.02686 | ||||||||
\(670\) | 1.63420e11i | 0.810973i | ||||||||
\(671\) | 5.44330e9i | 0.0268517i | ||||||||
\(672\) | −2.24428e11 | + | 3.22716e11i | −1.10052 | + | 1.58250i | ||||
\(673\) | −1.00806e9 | −0.00491391 | −0.00245695 | − | 0.999997i | \(-0.500782\pi\) | ||||
−0.00245695 | + | 0.999997i | \(0.500782\pi\) | |||||||
\(674\) | 1.35956e11 | 0.658808 | ||||||||
\(675\) | − | 3.42256e10i | − | 0.164868i | ||||||
\(676\) | 5.69920e10 | 0.272915 | ||||||||
\(677\) | 9.47240e10i | 0.450926i | 0.974252 | + | 0.225463i | \(0.0723895\pi\) | ||||
−0.974252 | + | 0.225463i | \(0.927610\pi\) | |||||||
\(678\) | 2.67367e11i | 1.26529i | ||||||||
\(679\) | −4.32466e10 | + | 6.21865e10i | −0.203457 | + | 0.292561i | ||||
\(680\) | −6.80435e10 | −0.318237 | ||||||||
\(681\) | 9.11125e10 | 0.423633 | ||||||||
\(682\) | 8.32720e10i | 0.384912i | ||||||||
\(683\) | 2.01827e11 | 0.927462 | 0.463731 | − | 0.885976i | \(-0.346510\pi\) | ||||
0.463731 | + | 0.885976i | \(0.346510\pi\) | |||||||
\(684\) | − | 2.80744e11i | − | 1.28258i | ||||||
\(685\) | − | 2.19757e11i | − | 0.998117i | ||||||
\(686\) | −7.44730e10 | + | 2.89043e11i | −0.336281 | + | 1.30517i | ||||
\(687\) | −4.17660e11 | −1.87498 | ||||||||
\(688\) | −2.85786e11 | −1.27552 | ||||||||
\(689\) | 8.07468e10i | 0.358301i | ||||||||
\(690\) | 2.96706e11 | 1.30897 | ||||||||
\(691\) | − | 2.13281e11i | − | 0.935490i | −0.883863 | − | 0.467745i | \(-0.845067\pi\) | ||
0.883863 | − | 0.467745i | \(-0.154933\pi\) | |||||||
\(692\) | − | 2.66771e11i | − | 1.16336i | ||||||
\(693\) | 9.95138e10 | + | 6.92053e10i | 0.431470 | + | 0.300059i | ||||
\(694\) | 3.30825e11 | 1.42613 | ||||||||
\(695\) | 2.42412e11 | 1.03900 | ||||||||
\(696\) | − | 8.31223e10i | − | 0.354226i | ||||||
\(697\) | 1.93061e10 | 0.0818020 | ||||||||
\(698\) | − | 1.65879e11i | − | 0.698827i | ||||||
\(699\) | − | 1.03912e11i | − | 0.435269i | ||||||
\(700\) | −9.42230e10 | − | 6.55260e10i | −0.392433 | − | 0.272911i | ||||
\(701\) | −1.79932e11 | −0.745136 | −0.372568 | − | 0.928005i | \(-0.621523\pi\) | ||||
−0.372568 | + | 0.928005i | \(0.621523\pi\) | |||||||
\(702\) | 7.52174e10 | 0.309720 | ||||||||
\(703\) | 3.58036e11i | 1.46590i | ||||||||
\(704\) | 6.56801e10 | 0.267389 | ||||||||
\(705\) | − | 9.97246e9i | − | 0.0403688i | ||||||
\(706\) | − | 2.99237e11i | − | 1.20447i | ||||||
\(707\) | 5.67228e10 | − | 8.15645e10i | 0.227028 | − | 0.326455i | ||||
\(708\) | 3.38542e11 | 1.34735 | ||||||||
\(709\) | 1.40192e11 | 0.554802 | 0.277401 | − | 0.960754i | \(-0.410527\pi\) | ||||
0.277401 | + | 0.960754i | \(0.410527\pi\) | |||||||
\(710\) | − | 8.47439e10i | − | 0.333484i | ||||||
\(711\) | 2.72116e11 | 1.06482 | ||||||||
\(712\) | 7.14352e10i | 0.277966i | ||||||||
\(713\) | − | 8.71217e10i | − | 0.337107i | ||||||
\(714\) | −4.35036e11 | − | 3.02539e11i | −1.67391 | − | 1.16410i | ||||
\(715\) | −1.18553e11 | −0.453615 | ||||||||
\(716\) | −1.38665e11 | −0.527614 | ||||||||
\(717\) | 4.31531e11i | 1.63281i | ||||||||
\(718\) | 1.59464e11 | 0.600018 | ||||||||
\(719\) | − | 1.02803e11i | − | 0.384670i | −0.981329 | − | 0.192335i | \(-0.938394\pi\) | ||
0.981329 | − | 0.192335i | \(-0.0616061\pi\) | |||||||
\(720\) | 4.63103e11i | 1.72325i | ||||||||
\(721\) | 1.97706e11 | − | 2.84292e11i | 0.731609 | − | 1.05202i | ||||
\(722\) | −2.71541e11 | −0.999278 | ||||||||
\(723\) | −7.28380e11 | −2.66566 | ||||||||
\(724\) | 1.90566e11i | 0.693571i | ||||||||
\(725\) | 1.56556e11 | 0.566653 | ||||||||
\(726\) | 4.46114e11i | 1.60583i | ||||||||
\(727\) | − | 3.57100e10i | − | 0.127836i | −0.997955 | − | 0.0639179i | \(-0.979640\pi\) | ||
0.997955 | − | 0.0639179i | \(-0.0203596\pi\) | |||||||
\(728\) | −3.23550e10 | + | 4.65249e10i | −0.115190 | + | 0.165638i | ||||
\(729\) | 3.77747e11 | 1.33749 | ||||||||
\(730\) | 3.77878e11 | 1.33064 | ||||||||
\(731\) | − | 3.23783e11i | − | 1.13393i | ||||||
\(732\) | −2.11003e10 | −0.0734927 | ||||||||
\(733\) | − | 1.48153e10i | − | 0.0513209i | −0.999671 | − | 0.0256604i | \(-0.991831\pi\) | ||
0.999671 | − | 0.0256604i | \(-0.00816886\pi\) | |||||||
\(734\) | − | 1.05551e11i | − | 0.363644i | ||||||
\(735\) | 1.89281e11 | + | 5.09836e11i | 0.648570 | + | 1.74695i | ||||
\(736\) | −1.99183e11 | −0.678798 | ||||||||
\(737\) | −6.22504e10 | −0.210995 | ||||||||
\(738\) | − | 3.80844e10i | − | 0.128387i | ||||||
\(739\) | −5.42526e10 | −0.181904 | −0.0909522 | − | 0.995855i | \(-0.528991\pi\) | ||||
−0.0909522 | + | 0.995855i | \(0.528991\pi\) | |||||||
\(740\) | 3.42474e11i | 1.14209i | ||||||||
\(741\) | − | 4.80438e11i | − | 1.59355i | ||||||
\(742\) | −1.47286e11 | − | 1.02428e11i | −0.485900 | − | 0.337912i | ||||
\(743\) | 1.08455e11 | 0.355872 | 0.177936 | − | 0.984042i | \(-0.443058\pi\) | ||||
0.177936 | + | 0.984042i | \(0.443058\pi\) | |||||||
\(744\) | 7.25247e10 | 0.236698 | ||||||||
\(745\) | − | 7.32987e11i | − | 2.37942i | ||||||
\(746\) | −6.62071e11 | −2.13771 | ||||||||
\(747\) | − | 6.37929e11i | − | 2.04876i | ||||||
\(748\) | 1.15362e11i | 0.368516i | ||||||||
\(749\) | −3.89340e9 | − | 2.70761e9i | −0.0123709 | − | 0.00860316i | ||||
\(750\) | 3.29475e11 | 1.04130 | ||||||||
\(751\) | −2.03007e11 | −0.638191 | −0.319095 | − | 0.947723i | \(-0.603379\pi\) | ||||
−0.319095 | + | 0.947723i | \(0.603379\pi\) | |||||||
\(752\) | 7.96562e9i | 0.0249085i | ||||||||
\(753\) | −2.90576e11 | −0.903816 | ||||||||
\(754\) | 3.44062e11i | 1.06451i | ||||||||
\(755\) | 7.52761e11i | 2.31670i | ||||||||
\(756\) | −4.28889e10 | + | 6.16721e10i | −0.131298 | + | 0.188800i | ||||
\(757\) | 3.33771e11 | 1.01640 | 0.508201 | − | 0.861239i | \(-0.330311\pi\) | ||||
0.508201 | + | 0.861239i | \(0.330311\pi\) | |||||||
\(758\) | −3.41205e11 | −1.03357 | ||||||||
\(759\) | 1.13022e11i | 0.340561i | ||||||||
\(760\) | 1.37068e11 | 0.410848 | ||||||||
\(761\) | 4.17513e11i | 1.24489i | 0.782663 | + | 0.622445i | \(0.213861\pi\) | ||||
−0.782663 | + | 0.622445i | \(0.786139\pi\) | |||||||
\(762\) | 1.93674e11i | 0.574449i | ||||||||
\(763\) | 4.46184e11 | + | 3.10292e11i | 1.31648 | + | 0.915529i | ||||
\(764\) | 4.13639e11 | 1.21408 | ||||||||
\(765\) | −5.24676e11 | −1.53195 | ||||||||
\(766\) | − | 3.34607e11i | − | 0.971897i | ||||||
\(767\) | 3.14842e11 | 0.909727 | ||||||||
\(768\) | − | 6.49200e11i | − | 1.86609i | ||||||
\(769\) | 6.52921e11i | 1.86705i | 0.358514 | + | 0.933524i | \(0.383283\pi\) | ||||
−0.358514 | + | 0.933524i | \(0.616717\pi\) | |||||||
\(770\) | 1.50385e11 | − | 2.16246e11i | 0.427801 | − | 0.615157i | ||||
\(771\) | −2.79979e11 | −0.792333 | ||||||||
\(772\) | −5.77076e10 | −0.162467 | ||||||||
\(773\) | 3.46148e11i | 0.969492i | 0.874655 | + | 0.484746i | \(0.161088\pi\) | ||||
−0.874655 | + | 0.484746i | \(0.838912\pi\) | |||||||
\(774\) | −6.38713e11 | −1.77968 | ||||||||
\(775\) | 1.36596e11i | 0.378644i | ||||||||
\(776\) | − | 3.19512e10i | − | 0.0881131i | ||||||
\(777\) | 3.42124e11 | − | 4.91957e11i | 0.938640 | − | 1.34972i | ||||
\(778\) | −2.53664e11 | −0.692374 | ||||||||
\(779\) | −3.88906e10 | −0.105608 | ||||||||
\(780\) | − | 4.59556e11i | − | 1.24154i | ||||||
\(781\) | 3.22808e10 | 0.0867642 | ||||||||
\(782\) | − | 2.68508e11i | − | 0.718009i | ||||||
\(783\) | − | 1.02471e11i | − | 0.272617i | ||||||
\(784\) | −1.51190e11 | − | 4.07238e11i | −0.400184 | − | 1.07791i | ||||
\(785\) | −1.40880e11 | −0.370997 | ||||||||
\(786\) | 1.44981e12 | 3.79858 | ||||||||
\(787\) | − | 7.39780e10i | − | 0.192843i | −0.995341 | − | 0.0964214i | \(-0.969260\pi\) | ||
0.995341 | − | 0.0964214i | \(-0.0307396\pi\) | |||||||
\(788\) | 1.03255e11 | 0.267798 | ||||||||
\(789\) | − | 3.23286e11i | − | 0.834217i | ||||||
\(790\) | − | 5.91316e11i | − | 1.51814i | ||||||
\(791\) | −2.03872e11 | − | 1.41780e11i | −0.520777 | − | 0.362166i | ||||
\(792\) | −5.11299e10 | −0.129949 | ||||||||
\(793\) | −1.96231e10 | −0.0496222 | ||||||||
\(794\) | 9.56736e11i | 2.40719i | ||||||||
\(795\) | −3.26871e11 | −0.818290 | ||||||||
\(796\) | 4.03923e11i | 1.00611i | ||||||||
\(797\) | − | 4.59000e11i | − | 1.13757i | −0.822485 | − | 0.568786i | \(-0.807413\pi\) | ||
0.822485 | − | 0.568786i | \(-0.192587\pi\) | |||||||
\(798\) | 8.76344e11 | + | 6.09440e11i | 2.16104 | + | 1.50286i | ||||
\(799\) | −9.02471e9 | −0.0221435 | ||||||||
\(800\) | 3.12294e11 | 0.762436 | ||||||||
\(801\) | 5.50829e11i | 1.33809i | ||||||||
\(802\) | 2.17093e11 | 0.524744 | ||||||||
\(803\) | 1.43942e11i | 0.346199i | ||||||||
\(804\) | − | 2.41306e11i | − | 0.577490i | ||||||
\(805\) | −1.57338e11 | + | 2.26243e11i | −0.374670 | + | 0.538757i | ||||
\(806\) | −3.00197e11 | −0.711321 | ||||||||
\(807\) | 5.81758e11 | 1.37167 | ||||||||
\(808\) | 4.19076e10i | 0.0983212i | ||||||||
\(809\) | −7.57430e11 | −1.76827 | −0.884135 | − | 0.467232i | \(-0.845251\pi\) | ||||
−0.884135 | + | 0.467232i | \(0.845251\pi\) | |||||||
\(810\) | − | 5.65048e11i | − | 1.31264i | ||||||
\(811\) | − | 2.03985e11i | − | 0.471535i | −0.971809 | − | 0.235768i | \(-0.924240\pi\) | ||
0.971809 | − | 0.235768i | \(-0.0757605\pi\) | |||||||
\(812\) | −2.82103e11 | − | 1.96184e11i | −0.648908 | − | 0.451273i | ||||
\(813\) | −9.79467e11 | −2.24196 | ||||||||
\(814\) | −2.90223e11 | −0.661050 | ||||||||
\(815\) | − | 7.04057e11i | − | 1.59580i | ||||||
\(816\) | 7.71181e11 | 1.73938 | ||||||||
\(817\) | 6.52234e11i | 1.46391i | ||||||||
\(818\) | 7.21050e9i | 0.0161047i | ||||||||
\(819\) | −2.49486e11 | + | 3.58748e11i | −0.554511 | + | 0.797360i | ||||
\(820\) | −3.72002e10 | −0.0822792 | ||||||||
\(821\) | −2.87113e11 | −0.631947 | −0.315974 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315974 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(822\) | 7.21895e11i | 1.58120i | ||||||||
\(823\) | 6.04082e10 | 0.131673 | 0.0658365 | − | 0.997830i | \(-0.479028\pi\) | ||||
0.0658365 | + | 0.997830i | \(0.479028\pi\) | |||||||
\(824\) | 1.46068e11i | 0.316845i | ||||||||
\(825\) | − | 1.77204e11i | − | 0.382524i | ||||||
\(826\) | −3.99380e11 | + | 5.74289e11i | −0.857958 | + | 1.23370i | ||||
\(827\) | 7.83324e11 | 1.67463 | 0.837316 | − | 0.546720i | \(-0.184124\pi\) | ||||
0.837316 | + | 0.546720i | \(0.184124\pi\) | |||||||
\(828\) | −2.38090e11 | −0.506548 | ||||||||
\(829\) | − | 3.39080e11i | − | 0.717934i | −0.933350 | − | 0.358967i | \(-0.883129\pi\) | ||
0.933350 | − | 0.358967i | \(-0.116871\pi\) | |||||||
\(830\) | −1.38624e12 | −2.92096 | ||||||||
\(831\) | 9.05832e11i | 1.89952i | ||||||||
\(832\) | 2.36778e11i | 0.494137i | ||||||||
\(833\) | 4.61383e11 | − | 1.71292e11i | 0.958256 | − | 0.355760i | ||||
\(834\) | −7.96315e11 | −1.64596 | ||||||||
\(835\) | 5.98462e10 | 0.123109 | ||||||||
\(836\) | − | 2.32387e11i | − | 0.475759i | ||||||
\(837\) | 8.94066e10 | 0.182166 | ||||||||
\(838\) | − | 1.10912e12i | − | 2.24906i | ||||||
\(839\) | − | 1.06306e11i | − | 0.214541i | −0.994230 | − | 0.107271i | \(-0.965789\pi\) | ||
0.994230 | − | 0.107271i | \(-0.0342111\pi\) | |||||||
\(840\) | −1.88337e11 | − | 1.30976e11i | −0.378285 | − | 0.263072i | ||||
\(841\) | −3.15198e10 | −0.0630085 | ||||||||
\(842\) | 1.28756e12 | 2.56165 | ||||||||
\(843\) | − | 7.42442e11i | − | 1.47012i | ||||||
\(844\) | 1.74211e11 | 0.343326 | ||||||||
\(845\) | 2.14558e11i | 0.420841i | ||||||||
\(846\) | 1.78027e10i | 0.0347539i | ||||||||
\(847\) | −3.40170e11 | − | 2.36566e11i | −0.660940 | − | 0.459641i | ||||
\(848\) | 2.61092e11 | 0.504905 | ||||||||
\(849\) | 9.16209e11 | 1.76345 | ||||||||
\(850\) | 4.20987e11i | 0.806479i | ||||||||
\(851\) | 3.03640e11 | 0.578949 | ||||||||
\(852\) | 1.25133e11i | 0.237472i | ||||||||
\(853\) | 2.60548e11i | 0.492142i | 0.969252 | + | 0.246071i | \(0.0791397\pi\) | ||||
−0.969252 | + | 0.246071i | \(0.920860\pi\) | |||||||
\(854\) | 2.48921e10 | − | 3.57937e10i | 0.0467984 | − | 0.0672937i | ||||
\(855\) | 1.05692e12 | 1.97777 | ||||||||
\(856\) | 2.00042e9 | 0.00372585 | ||||||||
\(857\) | 3.51886e10i | 0.0652347i | 0.999468 | + | 0.0326174i | \(0.0103843\pi\) | ||||
−0.999468 | + | 0.0326174i | \(0.989616\pi\) | |||||||
\(858\) | 3.89441e11 | 0.718609 | ||||||||
\(859\) | − | 7.91386e11i | − | 1.45350i | −0.686901 | − | 0.726751i | \(-0.741029\pi\) | ||
0.686901 | − | 0.726751i | \(-0.258971\pi\) | |||||||
\(860\) | 6.23885e11i | 1.14054i | ||||||||
\(861\) | 5.34373e10 | + | 3.71622e10i | 0.0972371 | + | 0.0676221i | ||||
\(862\) | −5.06131e11 | −0.916714 | ||||||||
\(863\) | −3.72768e11 | −0.672041 | −0.336020 | − | 0.941855i | \(-0.609081\pi\) | ||||
−0.336020 | + | 0.941855i | \(0.609081\pi\) | |||||||
\(864\) | − | 2.04406e11i | − | 0.366809i | ||||||
\(865\) | 1.00432e12 | 1.79393 | ||||||||
\(866\) | − | 5.08844e11i | − | 0.904718i | ||||||
\(867\) | 3.74806e10i | 0.0663331i | ||||||||
\(868\) | 1.71172e11 | − | 2.46137e11i | 0.301546 | − | 0.433608i | ||||
\(869\) | 2.25246e11 | 0.394982 | ||||||||
\(870\) | −1.39280e12 | −2.43115 | ||||||||
\(871\) | − | 2.24413e11i | − | 0.389920i | ||||||
\(872\) | −2.29248e11 | −0.396497 | ||||||||
\(873\) | − | 2.46372e11i | − | 0.424165i | ||||||
\(874\) | 5.40887e11i | 0.926959i | ||||||||
\(875\) | −1.74714e11 | + | 2.51230e11i | −0.298055 | + | 0.428588i | ||||
\(876\) | −5.57975e11 | −0.947542 | ||||||||
\(877\) | −5.73691e11 | −0.969795 | −0.484897 | − | 0.874571i | \(-0.661143\pi\) | ||||
−0.484897 | + | 0.874571i | \(0.661143\pi\) | |||||||
\(878\) | − | 2.11031e11i | − | 0.355115i | ||||||
\(879\) | −1.13924e12 | −1.90837 | ||||||||
\(880\) | 3.83336e11i | 0.639218i | ||||||||
\(881\) | − | 3.87231e10i | − | 0.0642786i | −0.999483 | − | 0.0321393i | \(-0.989768\pi\) | ||
0.999483 | − | 0.0321393i | \(-0.0102320\pi\) | |||||||
\(882\) | −3.37901e11 | − | 9.10151e11i | −0.558361 | − | 1.50397i | ||||
\(883\) | 2.98959e11 | 0.491778 | 0.245889 | − | 0.969298i | \(-0.420920\pi\) | ||||
0.245889 | + | 0.969298i | \(0.420920\pi\) | |||||||
\(884\) | −4.15881e11 | −0.681021 | ||||||||
\(885\) | 1.27451e12i | 2.07764i | ||||||||
\(886\) | 1.13665e12 | 1.84455 | ||||||||
\(887\) | − | 6.35990e11i | − | 1.02744i | −0.857958 | − | 0.513719i | \(-0.828267\pi\) | ||
0.857958 | − | 0.513719i | \(-0.171733\pi\) | |||||||
\(888\) | 2.52766e11i | 0.406506i | ||||||||
\(889\) | −1.47680e11 | − | 1.02702e11i | −0.236437 | − | 0.164426i | ||||
\(890\) | 1.19697e12 | 1.90775 | ||||||||
\(891\) | 2.15240e11 | 0.341516 | ||||||||
\(892\) | 3.58673e11i | 0.566551i | ||||||||
\(893\) | 1.81795e10 | 0.0285876 | ||||||||
\(894\) | 2.40783e12i | 3.76944i | ||||||||
\(895\) | − | 5.22034e11i | − | 0.813592i | ||||||
\(896\) | 2.57270e11 | + | 1.78915e11i | 0.399170 | + | 0.277596i | ||||
\(897\) | −4.07445e11 | −0.629360 | ||||||||
\(898\) | −9.25438e11 | −1.42312 | ||||||||
\(899\) | 4.08967e11i | 0.626108i | ||||||||
\(900\) | 3.73296e11 | 0.568962 | ||||||||
\(901\) | 2.95806e11i | 0.448857i | ||||||||
\(902\) | − | 3.15246e10i | − | 0.0476237i | ||||||
\(903\) | 6.23246e11 | − | 8.96197e11i | 0.937365 | − | 1.34788i | ||||
\(904\) | 1.04749e11 | 0.156847 | ||||||||
\(905\) | −7.17424e11 | −1.06950 | ||||||||
\(906\) | − | 2.47279e12i | − | 3.67007i | ||||||
\(907\) | 1.36448e11 | 0.201622 | 0.100811 | − | 0.994906i | \(-0.467856\pi\) | ||||
0.100811 | + | 0.994906i | \(0.467856\pi\) | |||||||
\(908\) | 1.58876e11i | 0.233731i | ||||||||
\(909\) | 3.23145e11i | 0.473306i | ||||||||
\(910\) | 7.79571e11 | + | 5.42140e11i | 1.13682 | + | 0.790581i | ||||
\(911\) | −6.11198e10 | −0.0887378 | −0.0443689 | − | 0.999015i | \(-0.514128\pi\) | ||||
−0.0443689 | + | 0.999015i | \(0.514128\pi\) | |||||||
\(912\) | −1.55348e12 | −2.24557 | ||||||||
\(913\) | − | 5.28050e11i | − | 0.759962i | ||||||
\(914\) | 3.21381e11 | 0.460506 | ||||||||
\(915\) | − | 7.94364e10i | − | 0.113327i | ||||||
\(916\) | − | 7.28290e11i | − | 1.03448i | ||||||
\(917\) | −7.68808e11 | + | 1.10551e12i | −1.08728 | + | 1.56345i | ||||
\(918\) | 2.75550e11 | 0.387998 | ||||||||
\(919\) | 6.87678e10 | 0.0964102 | 0.0482051 | − | 0.998837i | \(-0.484650\pi\) | ||||
0.0482051 | + | 0.998837i | \(0.484650\pi\) | |||||||
\(920\) | − | 1.16243e11i | − | 0.162262i | ||||||
\(921\) | 1.68746e11 | 0.234528 | ||||||||
\(922\) | − | 2.80398e11i | − | 0.388018i | ||||||
\(923\) | 1.16373e11i | 0.160341i | ||||||||
\(924\) | −2.22059e11 | + | 3.19310e11i | −0.304636 | + | 0.438051i | ||||
\(925\) | −4.76070e11 | −0.650285 | ||||||||
\(926\) | 9.52787e11 | 1.29584 | ||||||||
\(927\) | 1.12632e12i | 1.52525i | ||||||||
\(928\) | 9.35004e11 | 1.26073 | ||||||||
\(929\) | − | 1.07921e12i | − | 1.44891i | −0.689322 | − | 0.724455i | \(-0.742092\pi\) | ||
0.689322 | − | 0.724455i | \(-0.257908\pi\) | |||||||
\(930\) | − | 1.21522e12i | − | 1.62452i | ||||||
\(931\) | −9.29418e11 | + | 3.45054e11i | −1.23712 | + | 0.459291i | ||||
\(932\) | 1.81196e11 | 0.240151 | ||||||||
\(933\) | −3.07182e10 | −0.0405386 | ||||||||
\(934\) | 9.64234e11i | 1.26705i | ||||||||
\(935\) | −4.34304e11 | −0.568260 | ||||||||
\(936\) | − | 1.84324e11i | − | 0.240147i | ||||||
\(937\) | 1.93591e11i | 0.251146i | 0.992084 | + | 0.125573i | \(0.0400769\pi\) | ||||
−0.992084 | + | 0.125573i | \(0.959923\pi\) | |||||||
\(938\) | 4.09342e11 | + | 2.84670e11i | 0.528780 | + | 0.367732i | ||||
\(939\) | 9.91537e11 | 1.27540 | ||||||||
\(940\) | 1.73894e10 | 0.0222727 | ||||||||
\(941\) | − | 7.55658e10i | − | 0.0963755i | −0.998838 | − | 0.0481878i | \(-0.984655\pi\) | ||
0.998838 | − | 0.0481878i | \(-0.0153446\pi\) | |||||||
\(942\) | 4.62785e11 | 0.587727 | ||||||||
\(943\) | 3.29820e10i | 0.0417090i | ||||||||
\(944\) | − | 1.01803e12i | − | 1.28196i | ||||||
\(945\) | −2.32177e11 | − | 1.61464e11i | −0.291133 | − | 0.202464i | ||||
\(946\) | −5.28698e11 | −0.660151 | ||||||||
\(947\) | 1.06768e12 | 1.32752 | 0.663760 | − | 0.747945i | \(-0.268960\pi\) | ||||
0.663760 | + | 0.747945i | \(0.268960\pi\) | |||||||
\(948\) | 8.73139e11i | 1.08106i | ||||||||
\(949\) | −5.18914e11 | −0.639779 | ||||||||
\(950\) | − | 8.48044e11i | − | 1.04118i | ||||||
\(951\) | 5.95116e11i | 0.727578i | ||||||||
\(952\) | −1.18529e11 | + | 1.70438e11i | −0.144303 | + | 0.207501i | ||||
\(953\) | 1.13047e12 | 1.37052 | 0.685261 | − | 0.728298i | \(-0.259688\pi\) | ||||
0.685261 | + | 0.728298i | \(0.259688\pi\) | |||||||
\(954\) | 5.83524e11 | 0.704475 | ||||||||
\(955\) | 1.55723e12i | 1.87214i | ||||||||
\(956\) | −7.52478e11 | −0.900870 | ||||||||
\(957\) | − | 5.30548e11i | − | 0.632524i | ||||||
\(958\) | 3.52343e11i | 0.418315i | ||||||||
\(959\) | −5.50458e11 | − | 3.82807e11i | −0.650803 | − | 0.452591i | ||||
\(960\) | −9.58498e11 | −1.12851 | ||||||||
\(961\) | 4.96065e11 | 0.581627 | ||||||||
\(962\) | − | 1.04626e12i | − | 1.22163i | ||||||
\(963\) | 1.54250e10 | 0.0179358 | ||||||||
\(964\) | − | 1.27010e12i | − | 1.47072i | ||||||
\(965\) | − | 2.17252e11i | − | 0.250527i | ||||||
\(966\) | 5.16848e11 | − | 7.43201e11i | 0.593546 | − | 0.853489i | ||||
\(967\) | −8.33084e11 | −0.952758 | −0.476379 | − | 0.879240i | \(-0.658051\pi\) | ||||
−0.476379 | + | 0.879240i | \(0.658051\pi\) | |||||||
\(968\) | 1.74778e11 | 0.199061 | ||||||||
\(969\) | − | 1.76003e12i | − | 1.99629i | ||||||
\(970\) | −5.35375e11 | −0.604743 | ||||||||
\(971\) | 6.95976e11i | 0.782920i | 0.920195 | + | 0.391460i | \(0.128030\pi\) | ||||
−0.920195 | + | 0.391460i | \(0.871970\pi\) | |||||||
\(972\) | 1.03962e12i | 1.16469i | ||||||||
\(973\) | 4.22271e11 | − | 6.07204e11i | 0.471129 | − | 0.677460i | ||||
\(974\) | 4.95724e11 | 0.550813 | ||||||||
\(975\) | 6.38823e11 | 0.706907 | ||||||||
\(976\) | 6.34508e10i | 0.0699258i | ||||||||
\(977\) | 1.06229e12 | 1.16591 | 0.582955 | − | 0.812504i | \(-0.301896\pi\) | ||||
0.582955 | + | 0.812504i | \(0.301896\pi\) | |||||||
\(978\) | 2.31280e12i | 2.52803i | ||||||||
\(979\) | 4.55952e11i | 0.496350i | ||||||||
\(980\) | −8.89021e11 | + | 3.30056e11i | −0.963846 | + | 0.357835i | ||||
\(981\) | −1.76771e12 | −1.90868 | ||||||||
\(982\) | −1.83224e12 | −1.97031 | ||||||||
\(983\) | 2.85163e11i | 0.305407i | 0.988272 | + | 0.152704i | \(0.0487980\pi\) | ||||
−0.988272 | + | 0.152704i | \(0.951202\pi\) | |||||||
\(984\) | −2.74559e10 | −0.0292857 | ||||||||
\(985\) | 3.88725e11i | 0.412950i | ||||||||
\(986\) | 1.26043e12i | 1.33356i | ||||||||
\(987\) | −2.49795e10 | − | 1.73716e10i | −0.0263217 | − | 0.0183050i | ||||
\(988\) | 8.37758e11 | 0.879207 | ||||||||
\(989\) | 5.53140e11 | 0.578162 | ||||||||
\(990\) | 8.56732e11i | 0.891876i | ||||||||
\(991\) | −8.83520e11 | −0.916056 | −0.458028 | − | 0.888938i | \(-0.651444\pi\) | ||||
−0.458028 | + | 0.888938i | \(0.651444\pi\) | |||||||
\(992\) | 8.15797e11i | 0.842433i | ||||||||
\(993\) | − | 7.06915e11i | − | 0.727060i | ||||||
\(994\) | −2.12270e11 | − | 1.47620e11i | −0.217442 | − | 0.151217i | ||||
\(995\) | −1.52065e12 | −1.55145 | ||||||||
\(996\) | 2.04692e12 | 2.08000 | ||||||||
\(997\) | − | 1.05207e12i | − | 1.06479i | −0.846495 | − | 0.532396i | \(-0.821292\pi\) | ||
0.846495 | − | 0.532396i | \(-0.178708\pi\) | |||||||
\(998\) | −2.23923e12 | −2.25724 | ||||||||
\(999\) | 3.11603e11i | 0.312853i |
(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 | 7.9.b.b.6.3 | ✓ | 4 | |
3.2 | odd | 2 | 63.9.d.c.55.1 | 4 | |||
4.3 | odd | 2 | 112.9.c.b.97.4 | 4 | |||
5.2 | odd | 4 | 175.9.c.c.174.7 | 8 | |||
5.3 | odd | 4 | 175.9.c.c.174.2 | 8 | |||
5.4 | even | 2 | 175.9.d.e.76.2 | 4 | |||
7.2 | even | 3 | 49.9.d.b.31.2 | 8 | |||
7.3 | odd | 6 | 49.9.d.b.19.2 | 8 | |||
7.4 | even | 3 | 49.9.d.b.19.1 | 8 | |||
7.5 | odd | 6 | 49.9.d.b.31.1 | 8 | |||
7.6 | odd | 2 | inner | 7.9.b.b.6.4 | yes | 4 | |
21.20 | even | 2 | 63.9.d.c.55.2 | 4 | |||
28.27 | even | 2 | 112.9.c.b.97.1 | 4 | |||
35.13 | even | 4 | 175.9.c.c.174.1 | 8 | |||
35.27 | even | 4 | 175.9.c.c.174.8 | 8 | |||
35.34 | odd | 2 | 175.9.d.e.76.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.9.b.b.6.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
7.9.b.b.6.4 | yes | 4 | 7.6 | odd | 2 | inner | |
49.9.d.b.19.1 | 8 | 7.4 | even | 3 | |||
49.9.d.b.19.2 | 8 | 7.3 | odd | 6 | |||
49.9.d.b.31.1 | 8 | 7.5 | odd | 6 | |||
49.9.d.b.31.2 | 8 | 7.2 | even | 3 | |||
63.9.d.c.55.1 | 4 | 3.2 | odd | 2 | |||
63.9.d.c.55.2 | 4 | 21.20 | even | 2 | |||
112.9.c.b.97.1 | 4 | 28.27 | even | 2 | |||
112.9.c.b.97.4 | 4 | 4.3 | odd | 2 | |||
175.9.c.c.174.1 | 8 | 35.13 | even | 4 | |||
175.9.c.c.174.2 | 8 | 5.3 | odd | 4 | |||
175.9.c.c.174.7 | 8 | 5.2 | odd | 4 | |||
175.9.c.c.174.8 | 8 | 35.27 | even | 4 | |||
175.9.d.e.76.1 | 4 | 35.34 | odd | 2 | |||
175.9.d.e.76.2 | 4 | 5.4 | even | 2 |