Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,8,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.a (trivial) |
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: | yes |
Analytic conductor: | \(170.874608940\) |
Analytic rank: | \(1\) |
Dimension: | \(156\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −20.1873 | −1.78432 | −0.892162 | − | 0.451717i | \(-0.850812\pi\) | ||||
−0.892162 | + | 0.451717i | \(0.850812\pi\) | |||||||
\(3\) | 34.9985 | 0.748385 | 0.374193 | − | 0.927351i | \(-0.377920\pi\) | ||||
0.374193 | + | 0.927351i | \(0.377920\pi\) | |||||||
\(4\) | 279.528 | 2.18381 | ||||||||
\(5\) | −313.532 | −1.12173 | −0.560863 | − | 0.827909i | \(-0.689530\pi\) | ||||
−0.560863 | + | 0.827909i | \(0.689530\pi\) | |||||||
\(6\) | −706.526 | −1.33536 | ||||||||
\(7\) | 1440.96 | 1.58785 | 0.793924 | − | 0.608017i | \(-0.208035\pi\) | ||||
0.793924 | + | 0.608017i | \(0.208035\pi\) | |||||||
\(8\) | −3058.93 | −2.11230 | ||||||||
\(9\) | −962.103 | −0.439919 | ||||||||
\(10\) | 6329.36 | 2.00152 | ||||||||
\(11\) | −893.205 | −0.202338 | −0.101169 | − | 0.994869i | \(-0.532258\pi\) | ||||
−0.101169 | + | 0.994869i | \(0.532258\pi\) | |||||||
\(12\) | 9783.05 | 1.63433 | ||||||||
\(13\) | 10490.3 | 1.32430 | 0.662151 | − | 0.749371i | \(-0.269644\pi\) | ||||
0.662151 | + | 0.749371i | \(0.269644\pi\) | |||||||
\(14\) | −29089.1 | −2.83323 | ||||||||
\(15\) | −10973.1 | −0.839483 | ||||||||
\(16\) | 25972.1 | 1.58521 | ||||||||
\(17\) | −13076.6 | −0.645542 | −0.322771 | − | 0.946477i | \(-0.604614\pi\) | ||||
−0.322771 | + | 0.946477i | \(0.604614\pi\) | |||||||
\(18\) | 19422.3 | 0.784958 | ||||||||
\(19\) | 40332.1 | 1.34900 | 0.674502 | − | 0.738273i | \(-0.264358\pi\) | ||||
0.674502 | + | 0.738273i | \(0.264358\pi\) | |||||||
\(20\) | −87640.7 | −2.44963 | ||||||||
\(21\) | 50431.5 | 1.18832 | ||||||||
\(22\) | 18031.4 | 0.361036 | ||||||||
\(23\) | −90822.6 | −1.55649 | −0.778245 | − | 0.627961i | \(-0.783890\pi\) | ||||
−0.778245 | + | 0.627961i | \(0.783890\pi\) | |||||||
\(24\) | −107058. | −1.58081 | ||||||||
\(25\) | 20177.1 | 0.258267 | ||||||||
\(26\) | −211771. | −2.36298 | ||||||||
\(27\) | −110214. | −1.07761 | ||||||||
\(28\) | 402788. | 3.46755 | ||||||||
\(29\) | 185391. | 1.41155 | 0.705773 | − | 0.708438i | \(-0.250600\pi\) | ||||
0.705773 | + | 0.708438i | \(0.250600\pi\) | |||||||
\(30\) | 221518. | 1.49791 | ||||||||
\(31\) | −43656.9 | −0.263201 | −0.131600 | − | 0.991303i | \(-0.542012\pi\) | ||||
−0.131600 | + | 0.991303i | \(0.542012\pi\) | |||||||
\(32\) | −132764. | −0.716233 | ||||||||
\(33\) | −31260.8 | −0.151427 | ||||||||
\(34\) | 263982. | 1.15186 | ||||||||
\(35\) | −451787. | −1.78113 | ||||||||
\(36\) | −268934. | −0.960699 | ||||||||
\(37\) | −80252.9 | −0.260468 | −0.130234 | − | 0.991483i | \(-0.541573\pi\) | ||||
−0.130234 | + | 0.991483i | \(0.541573\pi\) | |||||||
\(38\) | −814197. | −2.40706 | ||||||||
\(39\) | 367146. | 0.991088 | ||||||||
\(40\) | 959073. | 2.36942 | ||||||||
\(41\) | 69266.3 | 0.156956 | 0.0784781 | − | 0.996916i | \(-0.474994\pi\) | ||||
0.0784781 | + | 0.996916i | \(0.474994\pi\) | |||||||
\(42\) | −1.01808e6 | −2.12035 | ||||||||
\(43\) | −505879. | −0.970301 | −0.485151 | − | 0.874431i | \(-0.661235\pi\) | ||||
−0.485151 | + | 0.874431i | \(0.661235\pi\) | |||||||
\(44\) | −249675. | −0.441867 | ||||||||
\(45\) | 301650. | 0.493468 | ||||||||
\(46\) | 1.83346e6 | 2.77728 | ||||||||
\(47\) | 341684. | 0.480046 | 0.240023 | − | 0.970767i | \(-0.422845\pi\) | ||||
0.240023 | + | 0.970767i | \(0.422845\pi\) | |||||||
\(48\) | 908986. | 1.18635 | ||||||||
\(49\) | 1.25282e6 | 1.52126 | ||||||||
\(50\) | −407322. | −0.460832 | ||||||||
\(51\) | −457663. | −0.483114 | ||||||||
\(52\) | 2.93233e6 | 2.89202 | ||||||||
\(53\) | −524279. | −0.483723 | −0.241861 | − | 0.970311i | \(-0.577758\pi\) | ||||
−0.241861 | + | 0.970311i | \(0.577758\pi\) | |||||||
\(54\) | 2.22492e6 | 1.92281 | ||||||||
\(55\) | 280048. | 0.226967 | ||||||||
\(56\) | −4.40780e6 | −3.35401 | ||||||||
\(57\) | 1.41156e6 | 1.00958 | ||||||||
\(58\) | −3.74254e6 | −2.51865 | ||||||||
\(59\) | 1.46495e6 | 0.928626 | 0.464313 | − | 0.885671i | \(-0.346301\pi\) | ||||
0.464313 | + | 0.885671i | \(0.346301\pi\) | |||||||
\(60\) | −3.06730e6 | −1.83327 | ||||||||
\(61\) | 1.06050e6 | 0.598212 | 0.299106 | − | 0.954220i | \(-0.403312\pi\) | ||||
0.299106 | + | 0.954220i | \(0.403312\pi\) | |||||||
\(62\) | 881315. | 0.469635 | ||||||||
\(63\) | −1.38635e6 | −0.698525 | ||||||||
\(64\) | −644289. | −0.307221 | ||||||||
\(65\) | −3.28905e6 | −1.48550 | ||||||||
\(66\) | 631072. | 0.270194 | ||||||||
\(67\) | −3.43501e6 | −1.39530 | −0.697648 | − | 0.716441i | \(-0.745770\pi\) | ||||
−0.697648 | + | 0.716441i | \(0.745770\pi\) | |||||||
\(68\) | −3.65528e6 | −1.40974 | ||||||||
\(69\) | −3.17866e6 | −1.16485 | ||||||||
\(70\) | 9.12036e6 | 3.17811 | ||||||||
\(71\) | −1.63429e6 | −0.541908 | −0.270954 | − | 0.962592i | \(-0.587339\pi\) | ||||
−0.270954 | + | 0.962592i | \(0.587339\pi\) | |||||||
\(72\) | 2.94301e6 | 0.929240 | ||||||||
\(73\) | −5.51772e6 | −1.66008 | −0.830041 | − | 0.557702i | \(-0.811683\pi\) | ||||
−0.830041 | + | 0.557702i | \(0.811683\pi\) | |||||||
\(74\) | 1.62009e6 | 0.464759 | ||||||||
\(75\) | 706169. | 0.193283 | ||||||||
\(76\) | 1.12739e7 | 2.94597 | ||||||||
\(77\) | −1.28707e6 | −0.321281 | ||||||||
\(78\) | −7.41168e6 | −1.76842 | ||||||||
\(79\) | 3.54074e6 | 0.807978 | 0.403989 | − | 0.914764i | \(-0.367623\pi\) | ||||
0.403989 | + | 0.914764i | \(0.367623\pi\) | |||||||
\(80\) | −8.14308e6 | −1.77817 | ||||||||
\(81\) | −1.75321e6 | −0.366552 | ||||||||
\(82\) | −1.39830e6 | −0.280060 | ||||||||
\(83\) | −7.05178e6 | −1.35371 | −0.676855 | − | 0.736116i | \(-0.736658\pi\) | ||||
−0.676855 | + | 0.736116i | \(0.736658\pi\) | |||||||
\(84\) | 1.40970e7 | 2.59507 | ||||||||
\(85\) | 4.09994e6 | 0.724121 | ||||||||
\(86\) | 1.02123e7 | 1.73133 | ||||||||
\(87\) | 6.48840e6 | 1.05638 | ||||||||
\(88\) | 2.73225e6 | 0.427397 | ||||||||
\(89\) | −1.13603e7 | −1.70814 | −0.854072 | − | 0.520154i | \(-0.825874\pi\) | ||||
−0.854072 | + | 0.520154i | \(0.825874\pi\) | |||||||
\(90\) | −6.08950e6 | −0.880507 | ||||||||
\(91\) | 1.51161e7 | 2.10279 | ||||||||
\(92\) | −2.53874e7 | −3.39908 | ||||||||
\(93\) | −1.52793e6 | −0.196975 | ||||||||
\(94\) | −6.89769e6 | −0.856557 | ||||||||
\(95\) | −1.26454e7 | −1.51321 | ||||||||
\(96\) | −4.64653e6 | −0.536018 | ||||||||
\(97\) | −3.92765e6 | −0.436950 | −0.218475 | − | 0.975843i | \(-0.570108\pi\) | ||||
−0.218475 | + | 0.975843i | \(0.570108\pi\) | |||||||
\(98\) | −2.52911e7 | −2.71442 | ||||||||
\(99\) | 859355. | 0.0890122 | ||||||||
\(100\) | 5.64006e6 | 0.564006 | ||||||||
\(101\) | −1.82904e7 | −1.76644 | −0.883218 | − | 0.468962i | \(-0.844628\pi\) | ||||
−0.883218 | + | 0.468962i | \(0.844628\pi\) | |||||||
\(102\) | 9.23898e6 | 0.862032 | ||||||||
\(103\) | 1.88696e7 | 1.70151 | 0.850753 | − | 0.525566i | \(-0.176146\pi\) | ||||
0.850753 | + | 0.525566i | \(0.176146\pi\) | |||||||
\(104\) | −3.20892e7 | −2.79732 | ||||||||
\(105\) | −1.58119e7 | −1.33297 | ||||||||
\(106\) | 1.05838e7 | 0.863118 | ||||||||
\(107\) | 1.12587e7 | 0.888475 | 0.444237 | − | 0.895909i | \(-0.353475\pi\) | ||||
0.444237 | + | 0.895909i | \(0.353475\pi\) | |||||||
\(108\) | −3.08078e7 | −2.35330 | ||||||||
\(109\) | 1.72287e7 | 1.27427 | 0.637133 | − | 0.770754i | \(-0.280120\pi\) | ||||
0.637133 | + | 0.770754i | \(0.280120\pi\) | |||||||
\(110\) | −5.65342e6 | −0.404983 | ||||||||
\(111\) | −2.80873e6 | −0.194931 | ||||||||
\(112\) | 3.74248e7 | 2.51707 | ||||||||
\(113\) | 1.18251e7 | 0.770955 | 0.385478 | − | 0.922717i | \(-0.374037\pi\) | ||||
0.385478 | + | 0.922717i | \(0.374037\pi\) | |||||||
\(114\) | −2.84957e7 | −1.80141 | ||||||||
\(115\) | 2.84758e7 | 1.74595 | ||||||||
\(116\) | 5.18218e7 | 3.08255 | ||||||||
\(117\) | −1.00928e7 | −0.582586 | ||||||||
\(118\) | −2.95734e7 | −1.65697 | ||||||||
\(119\) | −1.88429e7 | −1.02502 | ||||||||
\(120\) | 3.35661e7 | 1.77324 | ||||||||
\(121\) | −1.86894e7 | −0.959060 | ||||||||
\(122\) | −2.14086e7 | −1.06740 | ||||||||
\(123\) | 2.42422e6 | 0.117464 | ||||||||
\(124\) | −1.22033e7 | −0.574780 | ||||||||
\(125\) | 1.81685e7 | 0.832020 | ||||||||
\(126\) | 2.79867e7 | 1.24639 | ||||||||
\(127\) | −4.54097e6 | −0.196714 | −0.0983570 | − | 0.995151i | \(-0.531359\pi\) | ||||
−0.0983570 | + | 0.995151i | \(0.531359\pi\) | |||||||
\(128\) | 3.00002e7 | 1.26441 | ||||||||
\(129\) | −1.77050e7 | −0.726159 | ||||||||
\(130\) | 6.63970e7 | 2.65062 | ||||||||
\(131\) | 2.84820e7 | 1.10693 | 0.553466 | − | 0.832872i | \(-0.313305\pi\) | ||||
0.553466 | + | 0.832872i | \(0.313305\pi\) | |||||||
\(132\) | −8.73827e6 | −0.330687 | ||||||||
\(133\) | 5.81169e7 | 2.14201 | ||||||||
\(134\) | 6.93436e7 | 2.48966 | ||||||||
\(135\) | 3.45556e7 | 1.20879 | ||||||||
\(136\) | 4.00005e7 | 1.36358 | ||||||||
\(137\) | 2.88141e6 | 0.0957377 | 0.0478688 | − | 0.998854i | \(-0.484757\pi\) | ||||
0.0478688 | + | 0.998854i | \(0.484757\pi\) | |||||||
\(138\) | 6.41685e7 | 2.07848 | ||||||||
\(139\) | 4.54316e7 | 1.43485 | 0.717424 | − | 0.696637i | \(-0.245321\pi\) | ||||
0.717424 | + | 0.696637i | \(0.245321\pi\) | |||||||
\(140\) | −1.26287e8 | −3.88964 | ||||||||
\(141\) | 1.19585e7 | 0.359259 | ||||||||
\(142\) | 3.29919e7 | 0.966938 | ||||||||
\(143\) | −9.37000e6 | −0.267956 | ||||||||
\(144\) | −2.49879e7 | −0.697365 | ||||||||
\(145\) | −5.81259e7 | −1.58337 | ||||||||
\(146\) | 1.11388e8 | 2.96212 | ||||||||
\(147\) | 4.38469e7 | 1.13849 | ||||||||
\(148\) | −2.24329e7 | −0.568813 | ||||||||
\(149\) | −3.84291e7 | −0.951719 | −0.475859 | − | 0.879521i | \(-0.657863\pi\) | ||||
−0.475859 | + | 0.879521i | \(0.657863\pi\) | |||||||
\(150\) | −1.42557e7 | −0.344880 | ||||||||
\(151\) | 3.91346e7 | 0.925000 | 0.462500 | − | 0.886619i | \(-0.346953\pi\) | ||||
0.462500 | + | 0.886619i | \(0.346953\pi\) | |||||||
\(152\) | −1.23373e8 | −2.84950 | ||||||||
\(153\) | 1.25811e7 | 0.283986 | ||||||||
\(154\) | 2.59825e7 | 0.573269 | ||||||||
\(155\) | 1.36878e7 | 0.295239 | ||||||||
\(156\) | 1.02627e8 | 2.16435 | ||||||||
\(157\) | 2.65725e7 | 0.548005 | 0.274002 | − | 0.961729i | \(-0.411652\pi\) | ||||
0.274002 | + | 0.961729i | \(0.411652\pi\) | |||||||
\(158\) | −7.14780e7 | −1.44169 | ||||||||
\(159\) | −1.83490e7 | −0.362011 | ||||||||
\(160\) | 4.16256e7 | 0.803417 | ||||||||
\(161\) | −1.30872e8 | −2.47147 | ||||||||
\(162\) | 3.53925e7 | 0.654047 | ||||||||
\(163\) | −8.26037e7 | −1.49397 | −0.746987 | − | 0.664839i | \(-0.768500\pi\) | ||||
−0.746987 | + | 0.664839i | \(0.768500\pi\) | |||||||
\(164\) | 1.93618e7 | 0.342762 | ||||||||
\(165\) | 9.80127e6 | 0.169859 | ||||||||
\(166\) | 1.42357e8 | 2.41546 | ||||||||
\(167\) | 4.39922e7 | 0.730916 | 0.365458 | − | 0.930828i | \(-0.380912\pi\) | ||||
0.365458 | + | 0.930828i | \(0.380912\pi\) | |||||||
\(168\) | −1.54266e8 | −2.51009 | ||||||||
\(169\) | 4.72982e7 | 0.753774 | ||||||||
\(170\) | −8.27667e7 | −1.29207 | ||||||||
\(171\) | −3.88037e7 | −0.593453 | ||||||||
\(172\) | −1.41407e8 | −2.11895 | ||||||||
\(173\) | 9.93656e7 | 1.45906 | 0.729532 | − | 0.683946i | \(-0.239738\pi\) | ||||
0.729532 | + | 0.683946i | \(0.239738\pi\) | |||||||
\(174\) | −1.30983e8 | −1.88492 | ||||||||
\(175\) | 2.90744e7 | 0.410089 | ||||||||
\(176\) | −2.31984e7 | −0.320748 | ||||||||
\(177\) | 5.12711e7 | 0.694970 | ||||||||
\(178\) | 2.29334e8 | 3.04788 | ||||||||
\(179\) | 9.08490e7 | 1.18395 | 0.591977 | − | 0.805955i | \(-0.298348\pi\) | ||||
0.591977 | + | 0.805955i | \(0.298348\pi\) | |||||||
\(180\) | 8.43194e7 | 1.07764 | ||||||||
\(181\) | −6.48032e7 | −0.812309 | −0.406155 | − | 0.913804i | \(-0.633131\pi\) | ||||
−0.406155 | + | 0.913804i | \(0.633131\pi\) | |||||||
\(182\) | −3.05154e8 | −3.75205 | ||||||||
\(183\) | 3.71159e7 | 0.447693 | ||||||||
\(184\) | 2.77820e8 | 3.28777 | ||||||||
\(185\) | 2.51618e7 | 0.292174 | ||||||||
\(186\) | 3.08447e7 | 0.351468 | ||||||||
\(187\) | 1.16801e7 | 0.130617 | ||||||||
\(188\) | 9.55102e7 | 1.04833 | ||||||||
\(189\) | −1.58814e8 | −1.71109 | ||||||||
\(190\) | 2.55277e8 | 2.70006 | ||||||||
\(191\) | −1.41189e8 | −1.46617 | −0.733085 | − | 0.680136i | \(-0.761920\pi\) | ||||
−0.733085 | + | 0.680136i | \(0.761920\pi\) | |||||||
\(192\) | −2.25492e7 | −0.229920 | ||||||||
\(193\) | 7.55673e6 | 0.0756629 | 0.0378315 | − | 0.999284i | \(-0.487955\pi\) | ||||
0.0378315 | + | 0.999284i | \(0.487955\pi\) | |||||||
\(194\) | 7.92887e7 | 0.779660 | ||||||||
\(195\) | −1.15112e8 | −1.11173 | ||||||||
\(196\) | 3.50198e8 | 3.32214 | ||||||||
\(197\) | 4.96606e7 | 0.462786 | 0.231393 | − | 0.972860i | \(-0.425672\pi\) | ||||
0.231393 | + | 0.972860i | \(0.425672\pi\) | |||||||
\(198\) | −1.73481e7 | −0.158827 | ||||||||
\(199\) | −1.06500e8 | −0.957994 | −0.478997 | − | 0.877817i | \(-0.658999\pi\) | ||||
−0.478997 | + | 0.877817i | \(0.658999\pi\) | |||||||
\(200\) | −6.17205e7 | −0.545537 | ||||||||
\(201\) | −1.20220e8 | −1.04422 | ||||||||
\(202\) | 3.69234e8 | 3.15189 | ||||||||
\(203\) | 2.67141e8 | 2.24132 | ||||||||
\(204\) | −1.27929e8 | −1.05503 | ||||||||
\(205\) | −2.17172e7 | −0.176062 | ||||||||
\(206\) | −3.80927e8 | −3.03604 | ||||||||
\(207\) | 8.73807e7 | 0.684730 | ||||||||
\(208\) | 2.72456e8 | 2.09930 | ||||||||
\(209\) | −3.60248e7 | −0.272954 | ||||||||
\(210\) | 3.19199e8 | 2.37845 | ||||||||
\(211\) | −1.73101e8 | −1.26856 | −0.634280 | − | 0.773103i | \(-0.718704\pi\) | ||||
−0.634280 | + | 0.773103i | \(0.718704\pi\) | |||||||
\(212\) | −1.46550e8 | −1.05636 | ||||||||
\(213\) | −5.71978e7 | −0.405556 | ||||||||
\(214\) | −2.27283e8 | −1.58533 | ||||||||
\(215\) | 1.58609e8 | 1.08841 | ||||||||
\(216\) | 3.37137e8 | 2.27624 | ||||||||
\(217\) | −6.29078e7 | −0.417922 | ||||||||
\(218\) | −3.47801e8 | −2.27370 | ||||||||
\(219\) | −1.93112e8 | −1.24238 | ||||||||
\(220\) | 7.82811e7 | 0.495653 | ||||||||
\(221\) | −1.37178e8 | −0.854892 | ||||||||
\(222\) | 5.67008e7 | 0.347819 | ||||||||
\(223\) | −2.79295e8 | −1.68654 | −0.843270 | − | 0.537491i | \(-0.819372\pi\) | ||||
−0.843270 | + | 0.537491i | \(0.819372\pi\) | |||||||
\(224\) | −1.91307e8 | −1.13727 | ||||||||
\(225\) | −1.94125e7 | −0.113617 | ||||||||
\(226\) | −2.38716e8 | −1.37563 | ||||||||
\(227\) | −5.76230e6 | −0.0326968 | −0.0163484 | − | 0.999866i | \(-0.505204\pi\) | ||||
−0.0163484 | + | 0.999866i | \(0.505204\pi\) | |||||||
\(228\) | 3.94571e8 | 2.20472 | ||||||||
\(229\) | 3.01983e8 | 1.66172 | 0.830860 | − | 0.556481i | \(-0.187849\pi\) | ||||
0.830860 | + | 0.556481i | \(0.187849\pi\) | |||||||
\(230\) | −5.74849e8 | −3.11535 | ||||||||
\(231\) | −4.50456e7 | −0.240442 | ||||||||
\(232\) | −5.67098e8 | −2.98161 | ||||||||
\(233\) | 4.30976e7 | 0.223207 | 0.111603 | − | 0.993753i | \(-0.464401\pi\) | ||||
0.111603 | + | 0.993753i | \(0.464401\pi\) | |||||||
\(234\) | 2.03746e8 | 1.03952 | ||||||||
\(235\) | −1.07129e8 | −0.538480 | ||||||||
\(236\) | 4.09494e8 | 2.02794 | ||||||||
\(237\) | 1.23921e8 | 0.604679 | ||||||||
\(238\) | 3.80387e8 | 1.82897 | ||||||||
\(239\) | 1.34579e8 | 0.637652 | 0.318826 | − | 0.947813i | \(-0.396711\pi\) | ||||
0.318826 | + | 0.947813i | \(0.396711\pi\) | |||||||
\(240\) | −2.84996e8 | −1.33076 | ||||||||
\(241\) | −1.58485e8 | −0.729336 | −0.364668 | − | 0.931138i | \(-0.618817\pi\) | ||||
−0.364668 | + | 0.931138i | \(0.618817\pi\) | |||||||
\(242\) | 3.77288e8 | 1.71127 | ||||||||
\(243\) | 1.79678e8 | 0.803292 | ||||||||
\(244\) | 2.96438e8 | 1.30638 | ||||||||
\(245\) | −3.92799e8 | −1.70643 | ||||||||
\(246\) | −4.89384e7 | −0.209593 | ||||||||
\(247\) | 4.23097e8 | 1.78649 | ||||||||
\(248\) | 1.33543e8 | 0.555958 | ||||||||
\(249\) | −2.46802e8 | −1.01310 | ||||||||
\(250\) | −3.66773e8 | −1.48459 | ||||||||
\(251\) | 2.38896e8 | 0.953564 | 0.476782 | − | 0.879021i | \(-0.341803\pi\) | ||||
0.476782 | + | 0.879021i | \(0.341803\pi\) | |||||||
\(252\) | −3.87524e8 | −1.52544 | ||||||||
\(253\) | 8.11231e7 | 0.314936 | ||||||||
\(254\) | 9.16699e7 | 0.351001 | ||||||||
\(255\) | 1.43492e8 | 0.541921 | ||||||||
\(256\) | −5.23155e8 | −1.94890 | ||||||||
\(257\) | −1.21568e8 | −0.446739 | −0.223370 | − | 0.974734i | \(-0.571706\pi\) | ||||
−0.223370 | + | 0.974734i | \(0.571706\pi\) | |||||||
\(258\) | 3.57416e8 | 1.29570 | ||||||||
\(259\) | −1.15641e8 | −0.413584 | ||||||||
\(260\) | −9.19379e8 | −3.24405 | ||||||||
\(261\) | −1.78365e8 | −0.620966 | ||||||||
\(262\) | −5.74975e8 | −1.97513 | ||||||||
\(263\) | −4.45794e8 | −1.51108 | −0.755542 | − | 0.655100i | \(-0.772627\pi\) | ||||
−0.755542 | + | 0.655100i | \(0.772627\pi\) | |||||||
\(264\) | 9.56248e7 | 0.319858 | ||||||||
\(265\) | 1.64378e8 | 0.542604 | ||||||||
\(266\) | −1.17322e9 | −3.82204 | ||||||||
\(267\) | −3.97594e8 | −1.27835 | ||||||||
\(268\) | −9.60180e8 | −3.04706 | ||||||||
\(269\) | 4.13312e8 | 1.29463 | 0.647314 | − | 0.762224i | \(-0.275892\pi\) | ||||
0.647314 | + | 0.762224i | \(0.275892\pi\) | |||||||
\(270\) | −6.97584e8 | −2.15687 | ||||||||
\(271\) | 4.45149e8 | 1.35867 | 0.679334 | − | 0.733830i | \(-0.262269\pi\) | ||||
0.679334 | + | 0.733830i | \(0.262269\pi\) | |||||||
\(272\) | −3.39628e8 | −1.02332 | ||||||||
\(273\) | 5.29042e8 | 1.57370 | ||||||||
\(274\) | −5.81679e7 | −0.170827 | ||||||||
\(275\) | −1.80223e7 | −0.0522572 | ||||||||
\(276\) | −8.88522e8 | −2.54382 | ||||||||
\(277\) | −4.55821e7 | −0.128859 | −0.0644296 | − | 0.997922i | \(-0.520523\pi\) | ||||
−0.0644296 | + | 0.997922i | \(0.520523\pi\) | |||||||
\(278\) | −9.17141e8 | −2.56023 | ||||||||
\(279\) | 4.20024e7 | 0.115787 | ||||||||
\(280\) | 1.38198e9 | 3.76227 | ||||||||
\(281\) | −6.46666e8 | −1.73863 | −0.869317 | − | 0.494255i | \(-0.835441\pi\) | ||||
−0.869317 | + | 0.494255i | \(0.835441\pi\) | |||||||
\(282\) | −2.41409e8 | −0.641035 | ||||||||
\(283\) | −1.71067e8 | −0.448656 | −0.224328 | − | 0.974514i | \(-0.572019\pi\) | ||||
−0.224328 | + | 0.974514i | \(0.572019\pi\) | |||||||
\(284\) | −4.56829e8 | −1.18342 | ||||||||
\(285\) | −4.42570e8 | −1.13247 | ||||||||
\(286\) | 1.89155e8 | 0.478120 | ||||||||
\(287\) | 9.98099e7 | 0.249222 | ||||||||
\(288\) | 1.27732e8 | 0.315085 | ||||||||
\(289\) | −2.39341e8 | −0.583276 | ||||||||
\(290\) | 1.17341e9 | 2.82524 | ||||||||
\(291\) | −1.37462e8 | −0.327007 | ||||||||
\(292\) | −1.54235e9 | −3.62530 | ||||||||
\(293\) | −7.86048e8 | −1.82563 | −0.912814 | − | 0.408376i | \(-0.866095\pi\) | ||||
−0.912814 | + | 0.408376i | \(0.866095\pi\) | |||||||
\(294\) | −8.85152e8 | −2.03143 | ||||||||
\(295\) | −4.59308e8 | −1.04166 | ||||||||
\(296\) | 2.45488e8 | 0.550186 | ||||||||
\(297\) | 9.84436e7 | 0.218042 | ||||||||
\(298\) | 7.75781e8 | 1.69817 | ||||||||
\(299\) | −9.52757e8 | −2.06126 | ||||||||
\(300\) | 1.97394e8 | 0.422094 | ||||||||
\(301\) | −7.28951e8 | −1.54069 | ||||||||
\(302\) | −7.90023e8 | −1.65050 | ||||||||
\(303\) | −6.40137e8 | −1.32198 | ||||||||
\(304\) | 1.04751e9 | 2.13846 | ||||||||
\(305\) | −3.32500e8 | −0.671030 | ||||||||
\(306\) | −2.53978e8 | −0.506723 | ||||||||
\(307\) | −6.05296e8 | −1.19394 | −0.596971 | − | 0.802263i | \(-0.703629\pi\) | ||||
−0.596971 | + | 0.802263i | \(0.703629\pi\) | |||||||
\(308\) | −3.59772e8 | −0.701617 | ||||||||
\(309\) | 6.60410e8 | 1.27338 | ||||||||
\(310\) | −2.76320e8 | −0.526801 | ||||||||
\(311\) | −2.15847e8 | −0.406898 | −0.203449 | − | 0.979086i | \(-0.565215\pi\) | ||||
−0.203449 | + | 0.979086i | \(0.565215\pi\) | |||||||
\(312\) | −1.12307e9 | −2.09347 | ||||||||
\(313\) | −1.22640e8 | −0.226062 | −0.113031 | − | 0.993591i | \(-0.536056\pi\) | ||||
−0.113031 | + | 0.993591i | \(0.536056\pi\) | |||||||
\(314\) | −5.36428e8 | −0.977817 | ||||||||
\(315\) | 4.34665e8 | 0.783552 | ||||||||
\(316\) | 9.89735e8 | 1.76447 | ||||||||
\(317\) | 3.18524e8 | 0.561610 | 0.280805 | − | 0.959765i | \(-0.409399\pi\) | ||||
0.280805 | + | 0.959765i | \(0.409399\pi\) | |||||||
\(318\) | 3.70417e8 | 0.645945 | ||||||||
\(319\) | −1.65592e8 | −0.285609 | ||||||||
\(320\) | 2.02005e8 | 0.344617 | ||||||||
\(321\) | 3.94038e8 | 0.664922 | ||||||||
\(322\) | 2.64195e9 | 4.40990 | ||||||||
\(323\) | −5.27408e8 | −0.870839 | ||||||||
\(324\) | −4.90069e8 | −0.800479 | ||||||||
\(325\) | 2.11664e8 | 0.342024 | ||||||||
\(326\) | 1.66755e9 | 2.66573 | ||||||||
\(327\) | 6.02979e8 | 0.953642 | ||||||||
\(328\) | −2.11881e8 | −0.331538 | ||||||||
\(329\) | 4.92354e8 | 0.762240 | ||||||||
\(330\) | −1.97861e8 | −0.303083 | ||||||||
\(331\) | −8.17220e8 | −1.23863 | −0.619314 | − | 0.785143i | \(-0.712589\pi\) | ||||
−0.619314 | + | 0.785143i | \(0.712589\pi\) | |||||||
\(332\) | −1.97117e9 | −2.95624 | ||||||||
\(333\) | 7.72116e7 | 0.114585 | ||||||||
\(334\) | −8.88083e8 | −1.30419 | ||||||||
\(335\) | 1.07698e9 | 1.56514 | ||||||||
\(336\) | 1.30981e9 | 1.88374 | ||||||||
\(337\) | −8.51210e8 | −1.21152 | −0.605762 | − | 0.795646i | \(-0.707132\pi\) | ||||
−0.605762 | + | 0.795646i | \(0.707132\pi\) | |||||||
\(338\) | −9.54823e8 | −1.34498 | ||||||||
\(339\) | 4.13860e8 | 0.576972 | ||||||||
\(340\) | 1.14605e9 | 1.58134 | ||||||||
\(341\) | 3.89945e7 | 0.0532554 | ||||||||
\(342\) | 7.83341e8 | 1.05891 | ||||||||
\(343\) | 6.18574e8 | 0.827680 | ||||||||
\(344\) | 1.54745e9 | 2.04956 | ||||||||
\(345\) | 9.96609e8 | 1.30665 | ||||||||
\(346\) | −2.00592e9 | −2.60344 | ||||||||
\(347\) | 1.05847e8 | 0.135996 | 0.0679979 | − | 0.997685i | \(-0.478339\pi\) | ||||
0.0679979 | + | 0.997685i | \(0.478339\pi\) | |||||||
\(348\) | 1.81369e9 | 2.30693 | ||||||||
\(349\) | −5.35227e8 | −0.673983 | −0.336991 | − | 0.941508i | \(-0.609409\pi\) | ||||
−0.336991 | + | 0.941508i | \(0.609409\pi\) | |||||||
\(350\) | −5.86934e8 | −0.731731 | ||||||||
\(351\) | −1.15618e9 | −1.42709 | ||||||||
\(352\) | 1.18585e8 | 0.144921 | ||||||||
\(353\) | 1.15795e9 | 1.40113 | 0.700564 | − | 0.713590i | \(-0.252932\pi\) | ||||
0.700564 | + | 0.713590i | \(0.252932\pi\) | |||||||
\(354\) | −1.03503e9 | −1.24005 | ||||||||
\(355\) | 5.12402e8 | 0.607871 | ||||||||
\(356\) | −3.17552e9 | −3.73026 | ||||||||
\(357\) | −6.59473e8 | −0.767112 | ||||||||
\(358\) | −1.83400e9 | −2.11256 | ||||||||
\(359\) | 2.73189e8 | 0.311626 | 0.155813 | − | 0.987787i | \(-0.450200\pi\) | ||||
0.155813 | + | 0.987787i | \(0.450200\pi\) | |||||||
\(360\) | −9.22727e8 | −1.04235 | ||||||||
\(361\) | 7.32807e8 | 0.819813 | ||||||||
\(362\) | 1.30820e9 | 1.44942 | ||||||||
\(363\) | −6.54100e8 | −0.717746 | ||||||||
\(364\) | 4.22537e9 | 4.59209 | ||||||||
\(365\) | 1.72998e9 | 1.86216 | ||||||||
\(366\) | −7.49270e8 | −0.798830 | ||||||||
\(367\) | 8.77227e8 | 0.926362 | 0.463181 | − | 0.886264i | \(-0.346708\pi\) | ||||
0.463181 | + | 0.886264i | \(0.346708\pi\) | |||||||
\(368\) | −2.35885e9 | −2.46737 | ||||||||
\(369\) | −6.66413e7 | −0.0690480 | ||||||||
\(370\) | −5.07950e8 | −0.521332 | ||||||||
\(371\) | −7.55465e8 | −0.768078 | ||||||||
\(372\) | −4.27097e8 | −0.430157 | ||||||||
\(373\) | −3.96814e8 | −0.395919 | −0.197959 | − | 0.980210i | \(-0.563431\pi\) | ||||
−0.197959 | + | 0.980210i | \(0.563431\pi\) | |||||||
\(374\) | −2.35790e8 | −0.233064 | ||||||||
\(375\) | 6.35871e8 | 0.622672 | ||||||||
\(376\) | −1.04519e9 | −1.01400 | ||||||||
\(377\) | 1.94481e9 | 1.86931 | ||||||||
\(378\) | 3.20603e9 | 3.05313 | ||||||||
\(379\) | 6.97685e7 | 0.0658298 | 0.0329149 | − | 0.999458i | \(-0.489521\pi\) | ||||
0.0329149 | + | 0.999458i | \(0.489521\pi\) | |||||||
\(380\) | −3.53474e9 | −3.30457 | ||||||||
\(381\) | −1.58927e8 | −0.147218 | ||||||||
\(382\) | 2.85023e9 | 2.61612 | ||||||||
\(383\) | −1.78953e9 | −1.62759 | −0.813793 | − | 0.581155i | \(-0.802601\pi\) | ||||
−0.813793 | + | 0.581155i | \(0.802601\pi\) | |||||||
\(384\) | 1.04996e9 | 0.946269 | ||||||||
\(385\) | 4.03538e8 | 0.360389 | ||||||||
\(386\) | −1.52550e8 | −0.135007 | ||||||||
\(387\) | 4.86707e8 | 0.426854 | ||||||||
\(388\) | −1.09789e9 | −0.954215 | ||||||||
\(389\) | −6.69935e8 | −0.577044 | −0.288522 | − | 0.957473i | \(-0.593164\pi\) | ||||
−0.288522 | + | 0.957473i | \(0.593164\pi\) | |||||||
\(390\) | 2.32380e9 | 1.98368 | ||||||||
\(391\) | 1.18765e9 | 1.00478 | ||||||||
\(392\) | −3.83230e9 | −3.21335 | ||||||||
\(393\) | 9.96829e8 | 0.828412 | ||||||||
\(394\) | −1.00251e9 | −0.825759 | ||||||||
\(395\) | −1.11013e9 | −0.906329 | ||||||||
\(396\) | 2.40213e8 | 0.194386 | ||||||||
\(397\) | 3.64916e8 | 0.292703 | 0.146351 | − | 0.989233i | \(-0.453247\pi\) | ||||
0.146351 | + | 0.989233i | \(0.453247\pi\) | |||||||
\(398\) | 2.14994e9 | 1.70937 | ||||||||
\(399\) | 2.03401e9 | 1.60305 | ||||||||
\(400\) | 5.24042e8 | 0.409408 | ||||||||
\(401\) | 5.75325e6 | 0.00445562 | 0.00222781 | − | 0.999998i | \(-0.499291\pi\) | ||||
0.00222781 | + | 0.999998i | \(0.499291\pi\) | |||||||
\(402\) | 2.42692e9 | 1.86322 | ||||||||
\(403\) | −4.57974e8 | −0.348557 | ||||||||
\(404\) | −5.11267e9 | −3.85756 | ||||||||
\(405\) | 5.49686e8 | 0.411170 | ||||||||
\(406\) | −5.39285e9 | −3.99924 | ||||||||
\(407\) | 7.16823e7 | 0.0527025 | ||||||||
\(408\) | 1.39996e9 | 1.02048 | ||||||||
\(409\) | −2.70795e9 | −1.95708 | −0.978541 | − | 0.206054i | \(-0.933938\pi\) | ||||
−0.978541 | + | 0.206054i | \(0.933938\pi\) | |||||||
\(410\) | 4.38411e8 | 0.314151 | ||||||||
\(411\) | 1.00845e8 | 0.0716487 | ||||||||
\(412\) | 5.27459e9 | 3.71576 | ||||||||
\(413\) | 2.11093e9 | 1.47452 | ||||||||
\(414\) | −1.76398e9 | −1.22178 | ||||||||
\(415\) | 2.21096e9 | 1.51849 | ||||||||
\(416\) | −1.39273e9 | −0.948508 | ||||||||
\(417\) | 1.59004e9 | 1.07382 | ||||||||
\(418\) | 7.27244e8 | 0.487039 | ||||||||
\(419\) | −1.91901e9 | −1.27447 | −0.637234 | − | 0.770670i | \(-0.719922\pi\) | ||||
−0.637234 | + | 0.770670i | \(0.719922\pi\) | |||||||
\(420\) | −4.41985e9 | −2.91095 | ||||||||
\(421\) | 1.43923e9 | 0.940029 | 0.470015 | − | 0.882659i | \(-0.344249\pi\) | ||||
0.470015 | + | 0.882659i | \(0.344249\pi\) | |||||||
\(422\) | 3.49445e9 | 2.26352 | ||||||||
\(423\) | −3.28736e8 | −0.211181 | ||||||||
\(424\) | 1.60373e9 | 1.02177 | ||||||||
\(425\) | −2.63849e8 | −0.166722 | ||||||||
\(426\) | 1.15467e9 | 0.723643 | ||||||||
\(427\) | 1.52814e9 | 0.949870 | ||||||||
\(428\) | 3.14712e9 | 1.94026 | ||||||||
\(429\) | −3.27936e8 | −0.200534 | ||||||||
\(430\) | −3.20189e9 | −1.94208 | ||||||||
\(431\) | 5.52326e8 | 0.332296 | 0.166148 | − | 0.986101i | \(-0.446867\pi\) | ||||
0.166148 | + | 0.986101i | \(0.446867\pi\) | |||||||
\(432\) | −2.86249e9 | −1.70825 | ||||||||
\(433\) | −2.10681e9 | −1.24715 | −0.623573 | − | 0.781765i | \(-0.714320\pi\) | ||||
−0.623573 | + | 0.781765i | \(0.714320\pi\) | |||||||
\(434\) | 1.26994e9 | 0.745708 | ||||||||
\(435\) | −2.03432e9 | −1.18497 | ||||||||
\(436\) | 4.81590e9 | 2.78275 | ||||||||
\(437\) | −3.66307e9 | −2.09971 | ||||||||
\(438\) | 3.89841e9 | 2.21681 | ||||||||
\(439\) | −5.02898e8 | −0.283697 | −0.141848 | − | 0.989888i | \(-0.545305\pi\) | ||||
−0.141848 | + | 0.989888i | \(0.545305\pi\) | |||||||
\(440\) | −8.56648e8 | −0.479422 | ||||||||
\(441\) | −1.20534e9 | −0.669231 | ||||||||
\(442\) | 2.76925e9 | 1.52540 | ||||||||
\(443\) | −5.97939e7 | −0.0326771 | −0.0163386 | − | 0.999867i | \(-0.505201\pi\) | ||||
−0.0163386 | + | 0.999867i | \(0.505201\pi\) | |||||||
\(444\) | −7.85118e8 | −0.425691 | ||||||||
\(445\) | 3.56181e9 | 1.91607 | ||||||||
\(446\) | 5.63822e9 | 3.00933 | ||||||||
\(447\) | −1.34496e9 | −0.712253 | ||||||||
\(448\) | −9.28395e8 | −0.487820 | ||||||||
\(449\) | −1.06534e9 | −0.555426 | −0.277713 | − | 0.960664i | \(-0.589576\pi\) | ||||
−0.277713 | + | 0.960664i | \(0.589576\pi\) | |||||||
\(450\) | 3.91886e8 | 0.202729 | ||||||||
\(451\) | −6.18689e7 | −0.0317581 | ||||||||
\(452\) | 3.30543e9 | 1.68362 | ||||||||
\(453\) | 1.36965e9 | 0.692257 | ||||||||
\(454\) | 1.16325e8 | 0.0583416 | ||||||||
\(455\) | −4.73938e9 | −2.35875 | ||||||||
\(456\) | −4.31788e9 | −2.13252 | ||||||||
\(457\) | 4.31135e8 | 0.211303 | 0.105652 | − | 0.994403i | \(-0.466307\pi\) | ||||
0.105652 | + | 0.994403i | \(0.466307\pi\) | |||||||
\(458\) | −6.09622e9 | −2.96505 | ||||||||
\(459\) | 1.44123e9 | 0.695645 | ||||||||
\(460\) | 7.95976e9 | 3.81283 | ||||||||
\(461\) | −1.10900e8 | −0.0527202 | −0.0263601 | − | 0.999653i | \(-0.508392\pi\) | ||||
−0.0263601 | + | 0.999653i | \(0.508392\pi\) | |||||||
\(462\) | 9.09350e8 | 0.429027 | ||||||||
\(463\) | −3.05318e9 | −1.42961 | −0.714807 | − | 0.699322i | \(-0.753485\pi\) | ||||
−0.714807 | + | 0.699322i | \(0.753485\pi\) | |||||||
\(464\) | 4.81499e9 | 2.23760 | ||||||||
\(465\) | 4.79053e8 | 0.220952 | ||||||||
\(466\) | −8.70024e8 | −0.398273 | ||||||||
\(467\) | 1.24433e9 | 0.565360 | 0.282680 | − | 0.959214i | \(-0.408776\pi\) | ||||
0.282680 | + | 0.959214i | \(0.408776\pi\) | |||||||
\(468\) | −2.82121e9 | −1.27226 | ||||||||
\(469\) | −4.94971e9 | −2.21552 | ||||||||
\(470\) | 2.16264e9 | 0.960821 | ||||||||
\(471\) | 9.30000e8 | 0.410119 | ||||||||
\(472\) | −4.48118e9 | −1.96153 | ||||||||
\(473\) | 4.51853e8 | 0.196328 | ||||||||
\(474\) | −2.50163e9 | −1.07894 | ||||||||
\(475\) | 8.13786e8 | 0.348404 | ||||||||
\(476\) | −5.26711e9 | −2.23845 | ||||||||
\(477\) | 5.04410e8 | 0.212799 | ||||||||
\(478\) | −2.71678e9 | −1.13778 | ||||||||
\(479\) | 6.52185e8 | 0.271142 | 0.135571 | − | 0.990768i | \(-0.456713\pi\) | ||||
0.135571 | + | 0.990768i | \(0.456713\pi\) | |||||||
\(480\) | 1.45684e9 | 0.601265 | ||||||||
\(481\) | −8.41878e8 | −0.344938 | ||||||||
\(482\) | 3.19938e9 | 1.30137 | ||||||||
\(483\) | −4.58032e9 | −1.84961 | ||||||||
\(484\) | −5.22419e9 | −2.09440 | ||||||||
\(485\) | 1.23144e9 | 0.490138 | ||||||||
\(486\) | −3.62722e9 | −1.43333 | ||||||||
\(487\) | −1.97337e8 | −0.0774207 | −0.0387103 | − | 0.999250i | \(-0.512325\pi\) | ||||
−0.0387103 | + | 0.999250i | \(0.512325\pi\) | |||||||
\(488\) | −3.24399e9 | −1.26360 | ||||||||
\(489\) | −2.89101e9 | −1.11807 | ||||||||
\(490\) | 7.92957e9 | 3.04483 | ||||||||
\(491\) | −3.67817e9 | −1.40232 | −0.701160 | − | 0.713004i | \(-0.747334\pi\) | ||||
−0.701160 | + | 0.713004i | \(0.747334\pi\) | |||||||
\(492\) | 6.77635e8 | 0.256518 | ||||||||
\(493\) | −2.42429e9 | −0.911212 | ||||||||
\(494\) | −8.54118e9 | −3.18767 | ||||||||
\(495\) | −2.69435e8 | −0.0998472 | ||||||||
\(496\) | −1.13386e9 | −0.417229 | ||||||||
\(497\) | −2.35495e9 | −0.860467 | ||||||||
\(498\) | 4.98227e9 | 1.80769 | ||||||||
\(499\) | 1.32419e9 | 0.477088 | 0.238544 | − | 0.971132i | \(-0.423330\pi\) | ||||
0.238544 | + | 0.971132i | \(0.423330\pi\) | |||||||
\(500\) | 5.07859e9 | 1.81697 | ||||||||
\(501\) | 1.53966e9 | 0.547007 | ||||||||
\(502\) | −4.82266e9 | −1.70147 | ||||||||
\(503\) | 6.74501e8 | 0.236317 | 0.118158 | − | 0.992995i | \(-0.462301\pi\) | ||||
0.118158 | + | 0.992995i | \(0.462301\pi\) | |||||||
\(504\) | 4.24076e9 | 1.47549 | ||||||||
\(505\) | 5.73462e9 | 1.98146 | ||||||||
\(506\) | −1.63766e9 | −0.561948 | ||||||||
\(507\) | 1.65537e9 | 0.564113 | ||||||||
\(508\) | −1.26932e9 | −0.429586 | ||||||||
\(509\) | 5.04001e9 | 1.69402 | 0.847011 | − | 0.531576i | \(-0.178400\pi\) | ||||
0.847011 | + | 0.531576i | \(0.178400\pi\) | |||||||
\(510\) | −2.89671e9 | −0.966963 | ||||||||
\(511\) | −7.95081e9 | −2.63596 | ||||||||
\(512\) | 6.72106e9 | 2.21306 | ||||||||
\(513\) | −4.44516e9 | −1.45371 | ||||||||
\(514\) | 2.45414e9 | 0.797127 | ||||||||
\(515\) | −5.91623e9 | −1.90862 | ||||||||
\(516\) | −4.94904e9 | −1.58579 | ||||||||
\(517\) | −3.05194e8 | −0.0971313 | ||||||||
\(518\) | 2.33449e9 | 0.737967 | ||||||||
\(519\) | 3.47765e9 | 1.09194 | ||||||||
\(520\) | 1.00610e10 | 3.13782 | ||||||||
\(521\) | −5.26761e9 | −1.63185 | −0.815927 | − | 0.578155i | \(-0.803773\pi\) | ||||
−0.815927 | + | 0.578155i | \(0.803773\pi\) | |||||||
\(522\) | 3.60071e9 | 1.10800 | ||||||||
\(523\) | −8.68988e8 | −0.265618 | −0.132809 | − | 0.991142i | \(-0.542400\pi\) | ||||
−0.132809 | + | 0.991142i | \(0.542400\pi\) | |||||||
\(524\) | 7.96151e9 | 2.41733 | ||||||||
\(525\) | 1.01756e9 | 0.306905 | ||||||||
\(526\) | 8.99937e9 | 2.69626 | ||||||||
\(527\) | 5.70885e8 | 0.169907 | ||||||||
\(528\) | −8.11910e8 | −0.240043 | ||||||||
\(529\) | 4.84391e9 | 1.42266 | ||||||||
\(530\) | −3.31835e9 | −0.968181 | ||||||||
\(531\) | −1.40943e9 | −0.408520 | ||||||||
\(532\) | 1.62453e10 | 4.67775 | ||||||||
\(533\) | 7.26625e8 | 0.207857 | ||||||||
\(534\) | 8.02635e9 | 2.28099 | ||||||||
\(535\) | −3.52996e9 | −0.996625 | ||||||||
\(536\) | 1.05075e10 | 2.94728 | ||||||||
\(537\) | 3.17958e9 | 0.886054 | ||||||||
\(538\) | −8.34365e9 | −2.31003 | ||||||||
\(539\) | −1.11903e9 | −0.307808 | ||||||||
\(540\) | 9.65923e9 | 2.63976 | ||||||||
\(541\) | 5.32013e9 | 1.44455 | 0.722273 | − | 0.691608i | \(-0.243097\pi\) | ||||
0.722273 | + | 0.691608i | \(0.243097\pi\) | |||||||
\(542\) | −8.98636e9 | −2.42430 | ||||||||
\(543\) | −2.26802e9 | −0.607921 | ||||||||
\(544\) | 1.73610e9 | 0.462358 | ||||||||
\(545\) | −5.40174e9 | −1.42938 | ||||||||
\(546\) | −1.06799e10 | −2.80798 | ||||||||
\(547\) | 1.63667e8 | 0.0427569 | ||||||||
\(548\) | 8.05433e8 | 0.209073 | ||||||||
\(549\) | −1.02031e9 | −0.263165 | ||||||||
\(550\) | 3.63822e8 | 0.0932436 | ||||||||
\(551\) | 7.47720e9 | 1.90418 | ||||||||
\(552\) | 9.72330e9 | 2.46052 | ||||||||
\(553\) | 5.10207e9 | 1.28295 | ||||||||
\(554\) | 9.20180e8 | 0.229926 | ||||||||
\(555\) | 8.80627e8 | 0.218659 | ||||||||
\(556\) | 1.26994e10 | 3.13343 | ||||||||
\(557\) | −6.55254e9 | −1.60663 | −0.803316 | − | 0.595554i | \(-0.796933\pi\) | ||||
−0.803316 | + | 0.595554i | \(0.796933\pi\) | |||||||
\(558\) | −8.47916e8 | −0.206601 | ||||||||
\(559\) | −5.30682e9 | −1.28497 | ||||||||
\(560\) | −1.17339e10 | −2.82347 | ||||||||
\(561\) | 4.08786e8 | 0.0977522 | ||||||||
\(562\) | 1.30545e10 | 3.10229 | ||||||||
\(563\) | −2.00044e9 | −0.472440 | −0.236220 | − | 0.971700i | \(-0.575909\pi\) | ||||
−0.236220 | + | 0.971700i | \(0.575909\pi\) | |||||||
\(564\) | 3.34272e9 | 0.784554 | ||||||||
\(565\) | −3.70753e9 | −0.864800 | ||||||||
\(566\) | 3.45338e9 | 0.800547 | ||||||||
\(567\) | −2.52630e9 | −0.582028 | ||||||||
\(568\) | 4.99919e9 | 1.14467 | ||||||||
\(569\) | −8.17447e9 | −1.86023 | −0.930115 | − | 0.367268i | \(-0.880293\pi\) | ||||
−0.930115 | + | 0.367268i | \(0.880293\pi\) | |||||||
\(570\) | 8.93430e9 | 2.02068 | ||||||||
\(571\) | −8.10920e9 | −1.82285 | −0.911426 | − | 0.411464i | \(-0.865018\pi\) | ||||
−0.911426 | + | 0.411464i | \(0.865018\pi\) | |||||||
\(572\) | −2.61917e9 | −0.585164 | ||||||||
\(573\) | −4.94141e9 | −1.09726 | ||||||||
\(574\) | −2.01489e9 | −0.444693 | ||||||||
\(575\) | −1.83254e9 | −0.401990 | ||||||||
\(576\) | 6.19873e8 | 0.135152 | ||||||||
\(577\) | −6.89467e9 | −1.49416 | −0.747081 | − | 0.664733i | \(-0.768545\pi\) | ||||
−0.747081 | + | 0.664733i | \(0.768545\pi\) | |||||||
\(578\) | 4.83164e9 | 1.04075 | ||||||||
\(579\) | 2.64474e8 | 0.0566250 | ||||||||
\(580\) | −1.62478e10 | −3.45777 | ||||||||
\(581\) | −1.01613e10 | −2.14949 | ||||||||
\(582\) | 2.77499e9 | 0.583486 | ||||||||
\(583\) | 4.68288e8 | 0.0978753 | ||||||||
\(584\) | 1.68783e10 | 3.50659 | ||||||||
\(585\) | 3.16440e9 | 0.653501 | ||||||||
\(586\) | 1.58682e10 | 3.25751 | ||||||||
\(587\) | −2.85927e9 | −0.583474 | −0.291737 | − | 0.956499i | \(-0.594233\pi\) | ||||
−0.291737 | + | 0.956499i | \(0.594233\pi\) | |||||||
\(588\) | 1.22564e10 | 2.48624 | ||||||||
\(589\) | −1.76077e9 | −0.355059 | ||||||||
\(590\) | 9.27220e9 | 1.85866 | ||||||||
\(591\) | 1.73805e9 | 0.346342 | ||||||||
\(592\) | −2.08434e9 | −0.412897 | ||||||||
\(593\) | 4.00405e9 | 0.788512 | 0.394256 | − | 0.919001i | \(-0.371002\pi\) | ||||
0.394256 | + | 0.919001i | \(0.371002\pi\) | |||||||
\(594\) | −1.98731e9 | −0.389057 | ||||||||
\(595\) | 5.90784e9 | 1.14979 | ||||||||
\(596\) | −1.07420e10 | −2.07837 | ||||||||
\(597\) | −3.72733e9 | −0.716948 | ||||||||
\(598\) | 1.92336e10 | 3.67796 | ||||||||
\(599\) | 4.04548e9 | 0.769088 | 0.384544 | − | 0.923107i | \(-0.374359\pi\) | ||||
0.384544 | + | 0.923107i | \(0.374359\pi\) | |||||||
\(600\) | −2.16013e9 | −0.408272 | ||||||||
\(601\) | −7.25054e9 | −1.36242 | −0.681208 | − | 0.732090i | \(-0.738545\pi\) | ||||
−0.681208 | + | 0.732090i | \(0.738545\pi\) | |||||||
\(602\) | 1.47156e10 | 2.74909 | ||||||||
\(603\) | 3.30483e9 | 0.613817 | ||||||||
\(604\) | 1.09392e10 | 2.02002 | ||||||||
\(605\) | 5.85971e9 | 1.07580 | ||||||||
\(606\) | 1.29226e10 | 2.35883 | ||||||||
\(607\) | 1.51128e9 | 0.274274 | 0.137137 | − | 0.990552i | \(-0.456210\pi\) | ||||
0.137137 | + | 0.990552i | \(0.456210\pi\) | |||||||
\(608\) | −5.35464e9 | −0.966201 | ||||||||
\(609\) | 9.34953e9 | 1.67737 | ||||||||
\(610\) | 6.71228e9 | 1.19733 | ||||||||
\(611\) | 3.58438e9 | 0.635725 | ||||||||
\(612\) | 3.51675e9 | 0.620172 | ||||||||
\(613\) | −6.33593e9 | −1.11096 | −0.555480 | − | 0.831530i | \(-0.687466\pi\) | ||||
−0.555480 | + | 0.831530i | \(0.687466\pi\) | |||||||
\(614\) | 1.22193e10 | 2.13038 | ||||||||
\(615\) | −7.60069e8 | −0.131762 | ||||||||
\(616\) | 3.93707e9 | 0.678641 | ||||||||
\(617\) | 1.06446e9 | 0.182445 | 0.0912224 | − | 0.995831i | \(-0.470923\pi\) | ||||
0.0912224 | + | 0.995831i | \(0.470923\pi\) | |||||||
\(618\) | −1.33319e10 | −2.27213 | ||||||||
\(619\) | 9.54226e9 | 1.61709 | 0.808544 | − | 0.588435i | \(-0.200256\pi\) | ||||
0.808544 | + | 0.588435i | \(0.200256\pi\) | |||||||
\(620\) | 3.82612e9 | 0.644745 | ||||||||
\(621\) | 1.00099e10 | 1.67730 | ||||||||
\(622\) | 4.35738e9 | 0.726038 | ||||||||
\(623\) | −1.63697e10 | −2.71227 | ||||||||
\(624\) | 9.53554e9 | 1.57108 | ||||||||
\(625\) | −7.27274e9 | −1.19157 | ||||||||
\(626\) | 2.47577e9 | 0.403367 | ||||||||
\(627\) | −1.26082e9 | −0.204275 | ||||||||
\(628\) | 7.42776e9 | 1.19674 | ||||||||
\(629\) | 1.04944e9 | 0.168143 | ||||||||
\(630\) | −8.77472e9 | −1.39811 | ||||||||
\(631\) | −9.18516e9 | −1.45540 | −0.727702 | − | 0.685893i | \(-0.759412\pi\) | ||||
−0.727702 | + | 0.685893i | \(0.759412\pi\) | |||||||
\(632\) | −1.08309e10 | −1.70669 | ||||||||
\(633\) | −6.05828e9 | −0.949373 | ||||||||
\(634\) | −6.43014e9 | −1.00209 | ||||||||
\(635\) | 1.42374e9 | 0.220659 | ||||||||
\(636\) | −5.12905e9 | −0.790563 | ||||||||
\(637\) | 1.31425e10 | 2.01461 | ||||||||
\(638\) | 3.34285e9 | 0.509618 | ||||||||
\(639\) | 1.57236e9 | 0.238396 | ||||||||
\(640\) | −9.40602e9 | −1.41833 | ||||||||
\(641\) | −8.43980e9 | −1.26570 | −0.632848 | − | 0.774276i | \(-0.718114\pi\) | ||||
−0.632848 | + | 0.774276i | \(0.718114\pi\) | |||||||
\(642\) | −7.95457e9 | −1.18644 | ||||||||
\(643\) | −4.30752e9 | −0.638983 | −0.319491 | − | 0.947589i | \(-0.603512\pi\) | ||||
−0.319491 | + | 0.947589i | \(0.603512\pi\) | |||||||
\(644\) | −3.65822e10 | −5.39721 | ||||||||
\(645\) | 5.55108e9 | 0.814551 | ||||||||
\(646\) | 1.06469e10 | 1.55386 | ||||||||
\(647\) | −2.03241e9 | −0.295016 | −0.147508 | − | 0.989061i | \(-0.547125\pi\) | ||||
−0.147508 | + | 0.989061i | \(0.547125\pi\) | |||||||
\(648\) | 5.36294e9 | 0.774267 | ||||||||
\(649\) | −1.30850e9 | −0.187896 | ||||||||
\(650\) | −4.27293e9 | −0.610280 | ||||||||
\(651\) | −2.20168e9 | −0.312767 | ||||||||
\(652\) | −2.30900e10 | −3.26255 | ||||||||
\(653\) | 4.80229e9 | 0.674920 | 0.337460 | − | 0.941340i | \(-0.390432\pi\) | ||||
0.337460 | + | 0.941340i | \(0.390432\pi\) | |||||||
\(654\) | −1.21725e10 | −1.70160 | ||||||||
\(655\) | −8.93001e9 | −1.24167 | ||||||||
\(656\) | 1.79899e9 | 0.248809 | ||||||||
\(657\) | 5.30862e9 | 0.730302 | ||||||||
\(658\) | −9.93930e9 | −1.36008 | ||||||||
\(659\) | 2.92321e9 | 0.397888 | 0.198944 | − | 0.980011i | \(-0.436249\pi\) | ||||
0.198944 | + | 0.980011i | \(0.436249\pi\) | |||||||
\(660\) | 2.73972e9 | 0.370939 | ||||||||
\(661\) | −1.05017e10 | −1.41434 | −0.707169 | − | 0.707044i | \(-0.750028\pi\) | ||||
−0.707169 | + | 0.707044i | \(0.750028\pi\) | |||||||
\(662\) | 1.64975e10 | 2.21011 | ||||||||
\(663\) | −4.80102e9 | −0.639789 | ||||||||
\(664\) | 2.15709e10 | 2.85944 | ||||||||
\(665\) | −1.82215e10 | −2.40275 | ||||||||
\(666\) | −1.55869e9 | −0.204457 | ||||||||
\(667\) | −1.68377e10 | −2.19706 | ||||||||
\(668\) | 1.22970e10 | 1.59618 | ||||||||
\(669\) | −9.77492e9 | −1.26218 | ||||||||
\(670\) | −2.17414e10 | −2.79271 | ||||||||
\(671\) | −9.47242e8 | −0.121041 | ||||||||
\(672\) | −6.69547e9 | −0.851115 | ||||||||
\(673\) | 1.54011e9 | 0.194760 | 0.0973801 | − | 0.995247i | \(-0.468954\pi\) | ||||
0.0973801 | + | 0.995247i | \(0.468954\pi\) | |||||||
\(674\) | 1.71836e10 | 2.16175 | ||||||||
\(675\) | −2.22380e9 | −0.278312 | ||||||||
\(676\) | 1.32211e10 | 1.64610 | ||||||||
\(677\) | −2.05812e9 | −0.254924 | −0.127462 | − | 0.991843i | \(-0.540683\pi\) | ||||
−0.127462 | + | 0.991843i | \(0.540683\pi\) | |||||||
\(678\) | −8.35472e9 | −1.02950 | ||||||||
\(679\) | −5.65958e9 | −0.693810 | ||||||||
\(680\) | −1.25414e10 | −1.52956 | ||||||||
\(681\) | −2.01672e8 | −0.0244698 | ||||||||
\(682\) | −7.87195e8 | −0.0950248 | ||||||||
\(683\) | −1.30589e10 | −1.56832 | −0.784158 | − | 0.620562i | \(-0.786905\pi\) | ||||
−0.784158 | + | 0.620562i | \(0.786905\pi\) | |||||||
\(684\) | −1.08467e10 | −1.29599 | ||||||||
\(685\) | −9.03413e8 | −0.107391 | ||||||||
\(686\) | −1.24873e10 | −1.47685 | ||||||||
\(687\) | 1.05690e10 | 1.24361 | ||||||||
\(688\) | −1.31387e10 | −1.53813 | ||||||||
\(689\) | −5.49985e9 | −0.640595 | ||||||||
\(690\) | −2.01189e10 | −2.33148 | ||||||||
\(691\) | −2.65141e8 | −0.0305706 | −0.0152853 | − | 0.999883i | \(-0.504866\pi\) | ||||
−0.0152853 | + | 0.999883i | \(0.504866\pi\) | |||||||
\(692\) | 2.77754e10 | 3.18632 | ||||||||
\(693\) | 1.23830e9 | 0.141338 | ||||||||
\(694\) | −2.13677e9 | −0.242661 | ||||||||
\(695\) | −1.42442e10 | −1.60950 | ||||||||
\(696\) | −1.98476e10 | −2.23139 | ||||||||
\(697\) | −9.05769e8 | −0.101322 | ||||||||
\(698\) | 1.08048e10 | 1.20260 | ||||||||
\(699\) | 1.50835e9 | 0.167045 | ||||||||
\(700\) | 8.12710e9 | 0.895556 | ||||||||
\(701\) | 5.87882e9 | 0.644580 | 0.322290 | − | 0.946641i | \(-0.395547\pi\) | ||||
0.322290 | + | 0.946641i | \(0.395547\pi\) | |||||||
\(702\) | 2.33401e10 | 2.54638 | ||||||||
\(703\) | −3.23677e9 | −0.351373 | ||||||||
\(704\) | 5.75482e8 | 0.0621623 | ||||||||
\(705\) | −3.74935e9 | −0.402990 | ||||||||
\(706\) | −2.33759e10 | −2.50006 | ||||||||
\(707\) | −2.63557e10 | −2.80483 | ||||||||
\(708\) | 1.43317e10 | 1.51768 | ||||||||
\(709\) | 8.43565e9 | 0.888908 | 0.444454 | − | 0.895802i | \(-0.353398\pi\) | ||||
0.444454 | + | 0.895802i | \(0.353398\pi\) | |||||||
\(710\) | −1.03440e10 | −1.08464 | ||||||||
\(711\) | −3.40656e9 | −0.355445 | ||||||||
\(712\) | 3.47504e10 | 3.60811 | ||||||||
\(713\) | 3.96503e9 | 0.409669 | ||||||||
\(714\) | 1.33130e10 | 1.36878 | ||||||||
\(715\) | 2.93779e9 | 0.300573 | ||||||||
\(716\) | 2.53948e10 | 2.58553 | ||||||||
\(717\) | 4.71006e9 | 0.477209 | ||||||||
\(718\) | −5.51496e9 | −0.556041 | ||||||||
\(719\) | 2.77509e8 | 0.0278437 | 0.0139218 | − | 0.999903i | \(-0.495568\pi\) | ||||
0.0139218 | + | 0.999903i | \(0.495568\pi\) | |||||||
\(720\) | 7.83448e9 | 0.782252 | ||||||||
\(721\) | 2.71904e10 | 2.70173 | ||||||||
\(722\) | −1.47934e10 | −1.46281 | ||||||||
\(723\) | −5.54673e9 | −0.545824 | ||||||||
\(724\) | −1.81143e10 | −1.77393 | ||||||||
\(725\) | 3.74065e9 | 0.364556 | ||||||||
\(726\) | 1.32045e10 | 1.28069 | ||||||||
\(727\) | 4.44199e9 | 0.428753 | 0.214376 | − | 0.976751i | \(-0.431228\pi\) | ||||
0.214376 | + | 0.976751i | \(0.431228\pi\) | |||||||
\(728\) | −4.62392e10 | −4.44171 | ||||||||
\(729\) | 1.01227e10 | 0.967724 | ||||||||
\(730\) | −3.49236e10 | −3.32269 | ||||||||
\(731\) | 6.61518e9 | 0.626370 | ||||||||
\(732\) | 1.03749e10 | 0.977677 | ||||||||
\(733\) | 2.19158e8 | 0.0205539 | 0.0102769 | − | 0.999947i | \(-0.496729\pi\) | ||||
0.0102769 | + | 0.999947i | \(0.496729\pi\) | |||||||
\(734\) | −1.77089e10 | −1.65293 | ||||||||
\(735\) | −1.37474e10 | −1.27707 | ||||||||
\(736\) | 1.20579e10 | 1.11481 | ||||||||
\(737\) | 3.06817e9 | 0.282321 | ||||||||
\(738\) | 1.34531e9 | 0.123204 | ||||||||
\(739\) | −5.72237e9 | −0.521580 | −0.260790 | − | 0.965396i | \(-0.583983\pi\) | ||||
−0.260790 | + | 0.965396i | \(0.583983\pi\) | |||||||
\(740\) | 7.03342e9 | 0.638052 | ||||||||
\(741\) | 1.48078e10 | 1.33698 | ||||||||
\(742\) | 1.52508e10 | 1.37050 | ||||||||
\(743\) | 1.28569e9 | 0.114994 | 0.0574971 | − | 0.998346i | \(-0.481688\pi\) | ||||
0.0574971 | + | 0.998346i | \(0.481688\pi\) | |||||||
\(744\) | 4.67382e9 | 0.416071 | ||||||||
\(745\) | 1.20488e10 | 1.06757 | ||||||||
\(746\) | 8.01061e9 | 0.706447 | ||||||||
\(747\) | 6.78455e9 | 0.595523 | ||||||||
\(748\) | 3.26491e9 | 0.285243 | ||||||||
\(749\) | 1.62233e10 | 1.41076 | ||||||||
\(750\) | −1.28365e10 | −1.11105 | ||||||||
\(751\) | 1.10781e10 | 0.954389 | 0.477195 | − | 0.878798i | \(-0.341654\pi\) | ||||
0.477195 | + | 0.878798i | \(0.341654\pi\) | |||||||
\(752\) | 8.87427e9 | 0.760975 | ||||||||
\(753\) | 8.36099e9 | 0.713634 | ||||||||
\(754\) | −3.92604e10 | −3.33546 | ||||||||
\(755\) | −1.22699e10 | −1.03760 | ||||||||
\(756\) | −4.43929e10 | −3.73669 | ||||||||
\(757\) | 1.55439e10 | 1.30234 | 0.651172 | − | 0.758930i | \(-0.274278\pi\) | ||||
0.651172 | + | 0.758930i | \(0.274278\pi\) | |||||||
\(758\) | −1.40844e9 | −0.117462 | ||||||||
\(759\) | 2.83919e9 | 0.235694 | ||||||||
\(760\) | 3.86814e10 | 3.19635 | ||||||||
\(761\) | −4.93995e7 | −0.00406328 | −0.00203164 | − | 0.999998i | \(-0.500647\pi\) | ||||
−0.00203164 | + | 0.999998i | \(0.500647\pi\) | |||||||
\(762\) | 3.20831e9 | 0.262684 | ||||||||
\(763\) | 2.48259e10 | 2.02334 | ||||||||
\(764\) | −3.94663e10 | −3.20184 | ||||||||
\(765\) | −3.94456e9 | −0.318555 | ||||||||
\(766\) | 3.61259e10 | 2.90414 | ||||||||
\(767\) | 1.53678e10 | 1.22978 | ||||||||
\(768\) | −1.83096e10 | −1.45853 | ||||||||
\(769\) | −1.42651e10 | −1.13118 | −0.565590 | − | 0.824687i | \(-0.691352\pi\) | ||||
−0.565590 | + | 0.824687i | \(0.691352\pi\) | |||||||
\(770\) | −8.14634e9 | −0.643051 | ||||||||
\(771\) | −4.25471e9 | −0.334333 | ||||||||
\(772\) | 2.11231e9 | 0.165233 | ||||||||
\(773\) | 1.33979e10 | 1.04329 | 0.521647 | − | 0.853161i | \(-0.325318\pi\) | ||||
0.521647 | + | 0.853161i | \(0.325318\pi\) | |||||||
\(774\) | −9.82531e9 | −0.761646 | ||||||||
\(775\) | −8.80870e8 | −0.0679761 | ||||||||
\(776\) | 1.20144e10 | 0.922968 | ||||||||
\(777\) | −4.04727e9 | −0.309520 | ||||||||
\(778\) | 1.35242e10 | 1.02963 | ||||||||
\(779\) | 2.79365e9 | 0.211734 | ||||||||
\(780\) | −3.21769e10 | −2.42780 | ||||||||
\(781\) | 1.45976e9 | 0.109648 | ||||||||
\(782\) | −2.39755e10 | −1.79285 | ||||||||
\(783\) | −2.04327e10 | −1.52110 | ||||||||
\(784\) | 3.25384e10 | 2.41152 | ||||||||
\(785\) | −8.33133e9 | −0.614711 | ||||||||
\(786\) | −2.01233e10 | −1.47816 | ||||||||
\(787\) | −1.07376e10 | −0.785227 | −0.392614 | − | 0.919703i | \(-0.628429\pi\) | ||||
−0.392614 | + | 0.919703i | \(0.628429\pi\) | |||||||
\(788\) | 1.38815e10 | 1.01064 | ||||||||
\(789\) | −1.56021e10 | −1.13087 | ||||||||
\(790\) | 2.24106e10 | 1.61718 | ||||||||
\(791\) | 1.70394e10 | 1.22416 | ||||||||
\(792\) | −2.62871e9 | −0.188020 | ||||||||
\(793\) | 1.11250e10 | 0.792213 | ||||||||
\(794\) | −7.36668e9 | −0.522276 | ||||||||
\(795\) | 5.75299e9 | 0.406077 | ||||||||
\(796\) | −2.97696e10 | −2.09207 | ||||||||
\(797\) | 2.14499e10 | 1.50079 | 0.750397 | − | 0.660987i | \(-0.229862\pi\) | ||||
0.750397 | + | 0.660987i | \(0.229862\pi\) | |||||||
\(798\) | −4.10611e10 | −2.86036 | ||||||||
\(799\) | −4.46808e9 | −0.309890 | ||||||||
\(800\) | −2.67879e9 | −0.184979 | ||||||||
\(801\) | 1.09298e10 | 0.751446 | ||||||||
\(802\) | −1.16143e8 | −0.00795026 | ||||||||
\(803\) | 4.92845e9 | 0.335897 | ||||||||
\(804\) | −3.36049e10 | −2.28037 | ||||||||
\(805\) | 4.10324e10 | 2.77231 | ||||||||
\(806\) | 9.24527e9 | 0.621938 | ||||||||
\(807\) | 1.44653e10 | 0.968881 | ||||||||
\(808\) | 5.59491e10 | 3.73124 | ||||||||
\(809\) | 3.44487e9 | 0.228745 | 0.114373 | − | 0.993438i | \(-0.463514\pi\) | ||||
0.114373 | + | 0.993438i | \(0.463514\pi\) | |||||||
\(810\) | −1.10967e10 | −0.733661 | ||||||||
\(811\) | 1.37994e10 | 0.908421 | 0.454210 | − | 0.890894i | \(-0.349921\pi\) | ||||
0.454210 | + | 0.890894i | \(0.349921\pi\) | |||||||
\(812\) | 7.46732e10 | 4.89461 | ||||||||
\(813\) | 1.55796e10 | 1.01681 | ||||||||
\(814\) | −1.44707e9 | −0.0940383 | ||||||||
\(815\) | 2.58989e10 | 1.67583 | ||||||||
\(816\) | −1.18865e10 | −0.765839 | ||||||||
\(817\) | −2.04031e10 | −1.30894 | ||||||||
\(818\) | 5.46662e10 | 3.49207 | ||||||||
\(819\) | −1.45433e10 | −0.925057 | ||||||||
\(820\) | −6.07055e9 | −0.384485 | ||||||||
\(821\) | 4.91296e9 | 0.309844 | 0.154922 | − | 0.987927i | \(-0.450487\pi\) | ||||
0.154922 | + | 0.987927i | \(0.450487\pi\) | |||||||
\(822\) | −2.03579e9 | −0.127844 | ||||||||
\(823\) | −1.69039e10 | −1.05703 | −0.528516 | − | 0.848923i | \(-0.677251\pi\) | ||||
−0.528516 | + | 0.848923i | \(0.677251\pi\) | |||||||
\(824\) | −5.77210e10 | −3.59409 | ||||||||
\(825\) | −6.30754e8 | −0.0391085 | ||||||||
\(826\) | −4.26141e10 | −2.63101 | ||||||||
\(827\) | 7.46121e9 | 0.458712 | 0.229356 | − | 0.973343i | \(-0.426338\pi\) | ||||
0.229356 | + | 0.973343i | \(0.426338\pi\) | |||||||
\(828\) | 2.44253e10 | 1.49532 | ||||||||
\(829\) | 2.06299e10 | 1.25764 | 0.628821 | − | 0.777550i | \(-0.283538\pi\) | ||||
0.628821 | + | 0.777550i | \(0.283538\pi\) | |||||||
\(830\) | −4.46333e10 | −2.70948 | ||||||||
\(831\) | −1.59531e9 | −0.0964363 | ||||||||
\(832\) | −6.75879e9 | −0.406853 | ||||||||
\(833\) | −1.63827e10 | −0.982037 | ||||||||
\(834\) | −3.20986e10 | −1.91604 | ||||||||
\(835\) | −1.37929e10 | −0.819887 | ||||||||
\(836\) | −1.00699e10 | −0.596080 | ||||||||
\(837\) | 4.81160e9 | 0.283629 | ||||||||
\(838\) | 3.87397e10 | 2.27406 | ||||||||
\(839\) | −1.91337e10 | −1.11849 | −0.559246 | − | 0.829002i | \(-0.688909\pi\) | ||||
−0.559246 | + | 0.829002i | \(0.688909\pi\) | |||||||
\(840\) | 4.83674e10 | 2.81563 | ||||||||
\(841\) | 1.71199e10 | 0.992463 | ||||||||
\(842\) | −2.90541e10 | −1.67732 | ||||||||
\(843\) | −2.26324e10 | −1.30117 | ||||||||
\(844\) | −4.83865e10 | −2.77029 | ||||||||
\(845\) | −1.48295e10 | −0.845527 | ||||||||
\(846\) | 6.63629e9 | 0.376816 | ||||||||
\(847\) | −2.69306e10 | −1.52284 | ||||||||
\(848\) | −1.36166e10 | −0.766803 | ||||||||
\(849\) | −5.98709e9 | −0.335767 | ||||||||
\(850\) | 5.32640e9 | 0.297486 | ||||||||
\(851\) | 7.28878e9 | 0.405416 | ||||||||
\(852\) | −1.59884e10 | −0.885656 | ||||||||
\(853\) | 2.25524e10 | 1.24414 | 0.622072 | − | 0.782960i | \(-0.286291\pi\) | ||||
0.622072 | + | 0.782960i | \(0.286291\pi\) | |||||||
\(854\) | −3.08489e10 | −1.69487 | ||||||||
\(855\) | 1.21662e10 | 0.665691 | ||||||||
\(856\) | −3.44396e10 | −1.87672 | ||||||||
\(857\) | −3.11415e10 | −1.69008 | −0.845039 | − | 0.534705i | \(-0.820423\pi\) | ||||
−0.845039 | + | 0.534705i | \(0.820423\pi\) | |||||||
\(858\) | 6.62015e9 | 0.357818 | ||||||||
\(859\) | −4.11638e9 | −0.221585 | −0.110792 | − | 0.993844i | \(-0.535339\pi\) | ||||
−0.110792 | + | 0.993844i | \(0.535339\pi\) | |||||||
\(860\) | 4.43356e10 | 2.37688 | ||||||||
\(861\) | 3.49320e9 | 0.186514 | ||||||||
\(862\) | −1.11500e10 | −0.592923 | ||||||||
\(863\) | −2.25000e10 | −1.19164 | −0.595821 | − | 0.803117i | \(-0.703173\pi\) | ||||
−0.595821 | + | 0.803117i | \(0.703173\pi\) | |||||||
\(864\) | 1.46324e10 | 0.771823 | ||||||||
\(865\) | −3.11543e10 | −1.63667 | ||||||||
\(866\) | 4.25308e10 | 2.22531 | ||||||||
\(867\) | −8.37656e9 | −0.436515 | ||||||||
\(868\) | −1.75845e10 | −0.912662 | ||||||||
\(869\) | −3.16261e9 | −0.163484 | ||||||||
\(870\) | 4.10675e10 | 2.11437 | ||||||||
\(871\) | −3.60343e10 | −1.84779 | ||||||||
\(872\) | −5.27014e10 | −2.69163 | ||||||||
\(873\) | 3.77880e9 | 0.192223 | ||||||||
\(874\) | 7.39474e10 | 3.74656 | ||||||||
\(875\) | 2.61801e10 | 1.32112 | ||||||||
\(876\) | −5.39801e10 | −2.71312 | ||||||||
\(877\) | 3.89462e10 | 1.94969 | 0.974846 | − | 0.222879i | \(-0.0715453\pi\) | ||||
0.974846 | + | 0.222879i | \(0.0715453\pi\) | |||||||
\(878\) | 1.01522e10 | 0.506207 | ||||||||
\(879\) | −2.75105e10 | −1.36627 | ||||||||
\(880\) | 7.27344e9 | 0.359791 | ||||||||
\(881\) | 2.20801e10 | 1.08789 | 0.543945 | − | 0.839121i | \(-0.316930\pi\) | ||||
0.543945 | + | 0.839121i | \(0.316930\pi\) | |||||||
\(882\) | 2.43327e10 | 1.19412 | ||||||||
\(883\) | 1.12408e10 | 0.549457 | 0.274728 | − | 0.961522i | \(-0.411412\pi\) | ||||
0.274728 | + | 0.961522i | \(0.411412\pi\) | |||||||
\(884\) | −3.83450e10 | −1.86692 | ||||||||
\(885\) | −1.60751e10 | −0.779565 | ||||||||
\(886\) | 1.20708e9 | 0.0583066 | ||||||||
\(887\) | −1.64151e10 | −0.789788 | −0.394894 | − | 0.918727i | \(-0.629219\pi\) | ||||
−0.394894 | + | 0.918727i | \(0.629219\pi\) | |||||||
\(888\) | 8.59173e9 | 0.411751 | ||||||||
\(889\) | −6.54335e9 | −0.312352 | ||||||||
\(890\) | −7.19034e10 | −3.41889 | ||||||||
\(891\) | 1.56597e9 | 0.0741672 | ||||||||
\(892\) | −7.80707e10 | −3.68308 | ||||||||
\(893\) | 1.37809e10 | 0.647584 | ||||||||
\(894\) | 2.71512e10 | 1.27089 | ||||||||
\(895\) | −2.84841e10 | −1.32807 | ||||||||
\(896\) | 4.32291e10 | 2.00770 | ||||||||
\(897\) | −3.33451e10 | −1.54262 | ||||||||
\(898\) | 2.15064e10 | 0.991059 | ||||||||
\(899\) | −8.09358e9 | −0.371520 | ||||||||
\(900\) | −5.42632e9 | −0.248117 | ||||||||
\(901\) | 6.85580e9 | 0.312264 | ||||||||
\(902\) | 1.24897e9 | 0.0566667 | ||||||||
\(903\) | −2.55122e10 | −1.15303 | ||||||||
\(904\) | −3.61721e10 | −1.62849 | ||||||||
\(905\) | 2.03179e10 | 0.911188 | ||||||||
\(906\) | −2.76496e10 | −1.23521 | ||||||||
\(907\) | −1.54682e10 | −0.688357 | −0.344178 | − | 0.938904i | \(-0.611842\pi\) | ||||
−0.344178 | + | 0.938904i | \(0.611842\pi\) | |||||||
\(908\) | −1.61072e9 | −0.0714035 | ||||||||
\(909\) | 1.75972e10 | 0.777089 | ||||||||
\(910\) | 9.56754e10 | 4.20877 | ||||||||
\(911\) | 1.93795e10 | 0.849237 | 0.424618 | − | 0.905372i | \(-0.360408\pi\) | ||||
0.424618 | + | 0.905372i | \(0.360408\pi\) | |||||||
\(912\) | 3.66613e10 | 1.60039 | ||||||||
\(913\) | 6.29869e9 | 0.273906 | ||||||||
\(914\) | −8.70346e9 | −0.377034 | ||||||||
\(915\) | −1.16370e10 | −0.502189 | ||||||||
\(916\) | 8.44125e10 | 3.62888 | ||||||||
\(917\) | 4.10414e10 | 1.75764 | ||||||||
\(918\) | −2.90945e10 | −1.24126 | ||||||||
\(919\) | −3.48975e10 | −1.48317 | −0.741583 | − | 0.670861i | \(-0.765925\pi\) | ||||
−0.741583 | + | 0.670861i | \(0.765925\pi\) | |||||||
\(920\) | −8.71054e10 | −3.68797 | ||||||||
\(921\) | −2.11845e10 | −0.893529 | ||||||||
\(922\) | 2.23877e9 | 0.0940699 | ||||||||
\(923\) | −1.71442e10 | −0.717649 | ||||||||
\(924\) | −1.25915e10 | −0.525080 | ||||||||
\(925\) | −1.61927e9 | −0.0672704 | ||||||||
\(926\) | 6.16355e10 | 2.55089 | ||||||||
\(927\) | −1.81546e10 | −0.748525 | ||||||||
\(928\) | −2.46132e10 | −1.01100 | ||||||||
\(929\) | 3.05212e10 | 1.24896 | 0.624478 | − | 0.781042i | \(-0.285312\pi\) | ||||
0.624478 | + | 0.781042i | \(0.285312\pi\) | |||||||
\(930\) | −9.67080e9 | −0.394250 | ||||||||
\(931\) | 5.05290e10 | 2.05219 | ||||||||
\(932\) | 1.20470e10 | 0.487440 | ||||||||
\(933\) | −7.55434e9 | −0.304517 | ||||||||
\(934\) | −2.51196e10 | −1.00879 | ||||||||
\(935\) | −3.66208e9 | −0.146517 | ||||||||
\(936\) | 3.08731e10 | 1.23059 | ||||||||
\(937\) | −9.96636e8 | −0.0395775 | −0.0197887 | − | 0.999804i | \(-0.506299\pi\) | ||||
−0.0197887 | + | 0.999804i | \(0.506299\pi\) | |||||||
\(938\) | 9.99213e10 | 3.95320 | ||||||||
\(939\) | −4.29222e9 | −0.169181 | ||||||||
\(940\) | −2.99455e10 | −1.17594 | ||||||||
\(941\) | −1.05816e10 | −0.413989 | −0.206994 | − | 0.978342i | \(-0.566368\pi\) | ||||
−0.206994 | + | 0.978342i | \(0.566368\pi\) | |||||||
\(942\) | −1.87742e10 | −0.731784 | ||||||||
\(943\) | −6.29094e9 | −0.244301 | ||||||||
\(944\) | 3.80478e10 | 1.47207 | ||||||||
\(945\) | 4.97932e10 | 1.91937 | ||||||||
\(946\) | −9.12170e9 | −0.350313 | ||||||||
\(947\) | −1.60623e10 | −0.614588 | −0.307294 | − | 0.951615i | \(-0.599423\pi\) | ||||
−0.307294 | + | 0.951615i | \(0.599423\pi\) | |||||||
\(948\) | 3.46392e10 | 1.32050 | ||||||||
\(949\) | −5.78826e10 | −2.19845 | ||||||||
\(950\) | −1.64281e10 | −0.621664 | ||||||||
\(951\) | 1.11479e10 | 0.420301 | ||||||||
\(952\) | 5.76392e10 | 2.16515 | ||||||||
\(953\) | −9.37744e9 | −0.350961 | −0.175481 | − | 0.984483i | \(-0.556148\pi\) | ||||
−0.175481 | + | 0.984483i | \(0.556148\pi\) | |||||||
\(954\) | −1.01827e10 | −0.379702 | ||||||||
\(955\) | 4.42673e10 | 1.64464 | ||||||||
\(956\) | 3.76184e10 | 1.39251 | ||||||||
\(957\) | −5.79547e9 | −0.213746 | ||||||||
\(958\) | −1.31659e10 | −0.483805 | ||||||||
\(959\) | 4.15200e9 | 0.152017 | ||||||||
\(960\) | 7.06988e9 | 0.257907 | ||||||||
\(961\) | −2.56067e10 | −0.930725 | ||||||||
\(962\) | 1.69953e10 | 0.615482 | ||||||||
\(963\) | −1.08320e10 | −0.390857 | ||||||||
\(964\) | −4.43008e10 | −1.59273 | ||||||||
\(965\) | −2.36927e9 | −0.0848730 | ||||||||
\(966\) | 9.24643e10 | 3.30030 | ||||||||
\(967\) | 3.72823e10 | 1.32590 | 0.662949 | − | 0.748665i | \(-0.269305\pi\) | ||||
0.662949 | + | 0.748665i | \(0.269305\pi\) | |||||||
\(968\) | 5.71695e10 | 2.02582 | ||||||||
\(969\) | −1.84585e10 | −0.651723 | ||||||||
\(970\) | −2.48595e10 | −0.874564 | ||||||||
\(971\) | 3.77401e10 | 1.32293 | 0.661463 | − | 0.749977i | \(-0.269936\pi\) | ||||
0.661463 | + | 0.749977i | \(0.269936\pi\) | |||||||
\(972\) | 5.02250e10 | 1.75424 | ||||||||
\(973\) | 6.54651e10 | 2.27832 | ||||||||
\(974\) | 3.98370e9 | 0.138144 | ||||||||
\(975\) | 7.40794e9 | 0.255965 | ||||||||
\(976\) | 2.75434e10 | 0.948294 | ||||||||
\(977\) | 1.12330e9 | 0.0385360 | 0.0192680 | − | 0.999814i | \(-0.493866\pi\) | ||||
0.0192680 | + | 0.999814i | \(0.493866\pi\) | |||||||
\(978\) | 5.83617e10 | 1.99500 | ||||||||
\(979\) | 1.01471e10 | 0.345622 | ||||||||
\(980\) | −1.09798e11 | −3.72653 | ||||||||
\(981\) | −1.65758e10 | −0.560574 | ||||||||
\(982\) | 7.42524e10 | 2.50219 | ||||||||
\(983\) | −2.01354e10 | −0.676119 | −0.338060 | − | 0.941125i | \(-0.609771\pi\) | ||||
−0.338060 | + | 0.941125i | \(0.609771\pi\) | |||||||
\(984\) | −7.41552e9 | −0.248118 | ||||||||
\(985\) | −1.55702e10 | −0.519118 | ||||||||
\(986\) | 4.89398e10 | 1.62590 | ||||||||
\(987\) | 1.72317e10 | 0.570449 | ||||||||
\(988\) | 1.18267e11 | 3.90135 | ||||||||
\(989\) | 4.59452e10 | 1.51026 | ||||||||
\(990\) | 5.43917e9 | 0.178160 | ||||||||
\(991\) | −1.41141e10 | −0.460676 | −0.230338 | − | 0.973111i | \(-0.573983\pi\) | ||||
−0.230338 | + | 0.973111i | \(0.573983\pi\) | |||||||
\(992\) | 5.79605e9 | 0.188513 | ||||||||
\(993\) | −2.86015e10 | −0.926971 | ||||||||
\(994\) | 4.75401e10 | 1.53535 | ||||||||
\(995\) | 3.33910e10 | 1.07461 | ||||||||
\(996\) | −6.89880e10 | −2.21241 | ||||||||
\(997\) | 2.51409e10 | 0.803430 | 0.401715 | − | 0.915765i | \(-0.368414\pi\) | ||||
0.401715 | + | 0.915765i | \(0.368414\pi\) | |||||||
\(998\) | −2.67318e10 | −0.851279 | ||||||||
\(999\) | 8.84499e9 | 0.280684 |
(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 | 547.8.a.a.1.12 | ✓ | 156 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.8.a.a.1.12 | ✓ | 156 | 1.1 | even | 1 | trivial |