Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,8,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.6");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.c (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.4325560958\) |
Analytic rank: | \(0\) |
Dimension: | \(50\) |
Relative dimension: | \(25\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.2 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.8.c.a.36.2 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −18.9187 | −1.67219 | −0.836095 | − | 0.548584i | \(-0.815167\pi\) | ||||
−0.836095 | + | 0.548584i | \(0.815167\pi\) | |||||||
\(3\) | 27.7018 | − | 47.9809i | 0.592357 | − | 1.02599i | −0.401557 | − | 0.915834i | \(-0.631531\pi\) |
0.993914 | − | 0.110159i | \(-0.0351358\pi\) | |||||||
\(4\) | 229.916 | 1.79622 | ||||||||
\(5\) | −117.718 | + | 203.893i | −0.421161 | + | 0.729471i | −0.996053 | − | 0.0887574i | \(-0.971710\pi\) |
0.574893 | + | 0.818229i | \(0.305044\pi\) | |||||||
\(6\) | −524.081 | + | 907.736i | −0.990534 | + | 1.71566i | ||||
\(7\) | −543.713 | − | 941.739i | −0.599138 | − | 1.03774i | −0.992949 | − | 0.118545i | \(-0.962177\pi\) |
0.393811 | − | 0.919191i | \(-0.371156\pi\) | |||||||
\(8\) | −1928.13 | −1.33144 | ||||||||
\(9\) | −441.279 | − | 764.318i | −0.201774 | − | 0.349483i | ||||
\(10\) | 2227.07 | − | 3857.40i | 0.704261 | − | 1.21982i | ||||
\(11\) | 2490.92 | 0.564268 | 0.282134 | − | 0.959375i | \(-0.408958\pi\) | ||||
0.282134 | + | 0.959375i | \(0.408958\pi\) | |||||||
\(12\) | 6369.10 | − | 11031.6i | 1.06401 | − | 1.84291i | ||||
\(13\) | −6018.84 | − | 10424.9i | −0.759821 | − | 1.31605i | −0.942942 | − | 0.332958i | \(-0.891953\pi\) |
0.183121 | − | 0.983090i | \(-0.441380\pi\) | |||||||
\(14\) | 10286.3 | + | 17816.5i | 1.00187 | + | 1.73529i | ||||
\(15\) | 6522.00 | + | 11296.4i | 0.498955 | + | 0.864215i | ||||
\(16\) | 7048.28 | 0.430193 | ||||||||
\(17\) | −5537.17 | − | 9590.66i | −0.273349 | − | 0.473454i | 0.696369 | − | 0.717684i | \(-0.254798\pi\) |
−0.969717 | + | 0.244231i | \(0.921465\pi\) | |||||||
\(18\) | 8348.42 | + | 14459.9i | 0.337404 | + | 0.584401i | ||||
\(19\) | −19340.1 | + | 33498.0i | −0.646876 | + | 1.12042i | 0.336989 | + | 0.941509i | \(0.390591\pi\) |
−0.983865 | + | 0.178913i | \(0.942742\pi\) | |||||||
\(20\) | −27065.3 | + | 46878.5i | −0.756498 | + | 1.31029i | ||||
\(21\) | −60247.3 | −1.41961 | ||||||||
\(22\) | −47124.9 | −0.943564 | ||||||||
\(23\) | −19363.3 | + | 33538.2i | −0.331842 | + | 0.574768i | −0.982873 | − | 0.184283i | \(-0.941004\pi\) |
0.651031 | + | 0.759051i | \(0.274337\pi\) | |||||||
\(24\) | −53412.5 | + | 92513.2i | −0.788685 | + | 1.36604i | ||||
\(25\) | 11347.5 | + | 19654.4i | 0.145248 | + | 0.251576i | ||||
\(26\) | 113869. | + | 197226.i | 1.27057 | + | 2.20068i | ||||
\(27\) | 72270.7 | 0.706626 | ||||||||
\(28\) | −125009. | − | 216521.i | −1.07618 | − | 1.86401i | ||||
\(29\) | 13317.4 | + | 23066.4i | 0.101397 | + | 0.175625i | 0.912261 | − | 0.409610i | \(-0.134335\pi\) |
−0.810863 | + | 0.585236i | \(0.801002\pi\) | |||||||
\(30\) | −123388. | − | 213714.i | −0.834348 | − | 1.44513i | ||||
\(31\) | −116985. | + | 202625.i | −0.705287 | + | 1.22159i | 0.261301 | + | 0.965257i | \(0.415848\pi\) |
−0.966588 | + | 0.256335i | \(0.917485\pi\) | |||||||
\(32\) | 113456. | 0.612072 | ||||||||
\(33\) | 69003.0 | − | 119517.i | 0.334248 | − | 0.578935i | ||||
\(34\) | 104756. | + | 181443.i | 0.457091 | + | 0.791705i | ||||
\(35\) | 256019. | 1.00933 | ||||||||
\(36\) | −101457. | − | 175729.i | −0.362431 | − | 0.627748i | ||||
\(37\) | −226356. | + | 392060.i | −0.734660 | + | 1.27247i | 0.220212 | + | 0.975452i | \(0.429325\pi\) |
−0.954872 | + | 0.297016i | \(0.904008\pi\) | |||||||
\(38\) | 365889. | − | 633738.i | 1.08170 | − | 1.87356i | ||||
\(39\) | −666931. | −1.80034 | ||||||||
\(40\) | 226975. | − | 393132.i | 0.560748 | − | 0.971244i | ||||
\(41\) | 173051. | 0.392130 | 0.196065 | − | 0.980591i | \(-0.437184\pi\) | ||||
0.196065 | + | 0.980591i | \(0.437184\pi\) | |||||||
\(42\) | 1.13980e6 | 2.37387 | ||||||||
\(43\) | −485315. | − | 190493.i | −0.930860 | − | 0.365376i | ||||
\(44\) | 572704. | 1.01355 | ||||||||
\(45\) | 207786. | 0.339917 | ||||||||
\(46\) | 366328. | − | 634499.i | 0.554904 | − | 0.961122i | ||||
\(47\) | −283888. | −0.398846 | −0.199423 | − | 0.979914i | \(-0.563907\pi\) | ||||
−0.199423 | + | 0.979914i | \(0.563907\pi\) | |||||||
\(48\) | 195250. | − | 338183.i | 0.254828 | − | 0.441374i | ||||
\(49\) | −179476. | + | 310862.i | −0.217932 | + | 0.377469i | ||||
\(50\) | −214679. | − | 371835.i | −0.242882 | − | 0.420684i | ||||
\(51\) | −613558. | −0.647680 | ||||||||
\(52\) | −1.38383e6 | − | 2.39687e6i | −1.36481 | − | 2.36392i | ||||
\(53\) | −324961. | + | 562849.i | −0.299823 | + | 0.519309i | −0.976095 | − | 0.217343i | \(-0.930261\pi\) |
0.676272 | + | 0.736652i | \(0.263594\pi\) | |||||||
\(54\) | −1.36727e6 | −1.18161 | ||||||||
\(55\) | −293226. | + | 507883.i | −0.237647 | + | 0.411618i | ||||
\(56\) | 1.04835e6 | + | 1.81579e6i | 0.797713 | + | 1.38168i | ||||
\(57\) | 1.07151e6 | + | 1.85591e6i | 0.766363 | + | 1.32738i | ||||
\(58\) | −251948. | − | 436386.i | −0.169556 | − | 0.293679i | ||||
\(59\) | −1.07185e6 | −0.679441 | −0.339720 | − | 0.940526i | \(-0.610332\pi\) | ||||
−0.339720 | + | 0.940526i | \(0.610332\pi\) | |||||||
\(60\) | 1.49951e6 | + | 2.59724e6i | 0.896234 | + | 1.55232i | ||||
\(61\) | 1.25611e6 | + | 2.17565e6i | 0.708555 | + | 1.22725i | 0.965393 | + | 0.260798i | \(0.0839858\pi\) |
−0.256839 | + | 0.966454i | \(0.582681\pi\) | |||||||
\(62\) | 2.21321e6 | − | 3.83339e6i | 1.17937 | − | 2.04274i | ||||
\(63\) | −479859. | + | 831140.i | −0.241781 | + | 0.418776i | ||||
\(64\) | −3.04862e6 | −1.45369 | ||||||||
\(65\) | 2.83410e6 | 1.28003 | ||||||||
\(66\) | −1.30545e6 | + | 2.26110e6i | −0.558927 | + | 0.968090i | ||||
\(67\) | 952192. | − | 1.64924e6i | 0.386779 | − | 0.669921i | −0.605235 | − | 0.796047i | \(-0.706921\pi\) |
0.992014 | + | 0.126126i | \(0.0402544\pi\) | |||||||
\(68\) | −1.27309e6 | − | 2.20505e6i | −0.490995 | − | 0.850428i | ||||
\(69\) | 1.07280e6 | + | 1.85814e6i | 0.393139 | + | 0.680936i | ||||
\(70\) | −4.84354e6 | −1.68780 | ||||||||
\(71\) | 443116. | + | 767500.i | 0.146931 | + | 0.254492i | 0.930092 | − | 0.367327i | \(-0.119727\pi\) |
−0.783161 | + | 0.621819i | \(0.786394\pi\) | |||||||
\(72\) | 850842. | + | 1.47370e6i | 0.268649 | + | 0.465314i | ||||
\(73\) | −1.73038e6 | − | 2.99710e6i | −0.520607 | − | 0.901718i | −0.999713 | − | 0.0239610i | \(-0.992372\pi\) |
0.479106 | − | 0.877757i | \(-0.340961\pi\) | |||||||
\(74\) | 4.28236e6 | − | 7.41727e6i | 1.22849 | − | 2.12781i | ||||
\(75\) | 1.25738e6 | 0.344154 | ||||||||
\(76\) | −4.44660e6 | + | 7.70175e6i | −1.16193 | + | 2.01253i | ||||
\(77\) | −1.35435e6 | − | 2.34580e6i | −0.338074 | − | 0.585562i | ||||
\(78\) | 1.26175e7 | 3.01051 | ||||||||
\(79\) | −2.33820e6 | − | 4.04989e6i | −0.533565 | − | 0.924162i | −0.999231 | − | 0.0392017i | \(-0.987519\pi\) |
0.465666 | − | 0.884961i | \(-0.345815\pi\) | |||||||
\(80\) | −829708. | + | 1.43710e6i | −0.181180 | + | 0.313813i | ||||
\(81\) | 2.96711e6 | − | 5.13918e6i | 0.620348 | − | 1.07448i | ||||
\(82\) | −3.27389e6 | −0.655716 | ||||||||
\(83\) | −2.48910e6 | + | 4.31125e6i | −0.477826 | + | 0.827618i | −0.999677 | − | 0.0254181i | \(-0.991908\pi\) |
0.521851 | + | 0.853037i | \(0.325242\pi\) | |||||||
\(84\) | −1.38519e7 | −2.54994 | ||||||||
\(85\) | 2.60730e6 | 0.460494 | ||||||||
\(86\) | 9.18152e6 | + | 3.60389e6i | 1.55658 | + | 0.610979i | ||||
\(87\) | 1.47566e6 | 0.240254 | ||||||||
\(88\) | −4.80281e6 | −0.751287 | ||||||||
\(89\) | −2.69552e6 | + | 4.66878e6i | −0.405301 | + | 0.702003i | −0.994357 | − | 0.106090i | \(-0.966167\pi\) |
0.589055 | + | 0.808093i | \(0.299500\pi\) | |||||||
\(90\) | −3.93104e6 | −0.568406 | ||||||||
\(91\) | −6.54505e6 | + | 1.13364e7i | −0.910475 | + | 1.57699i | ||||
\(92\) | −4.45194e6 | + | 7.71099e6i | −0.596063 | + | 1.03241i | ||||
\(93\) | 6.48141e6 | + | 1.12261e7i | 0.835563 | + | 1.44724i | ||||
\(94\) | 5.37079e6 | 0.666946 | ||||||||
\(95\) | −4.55335e6 | − | 7.88663e6i | −0.544877 | − | 0.943755i | ||||
\(96\) | 3.14293e6 | − | 5.44372e6i | 0.362565 | − | 0.627981i | ||||
\(97\) | −1.39182e7 | −1.54839 | −0.774195 | − | 0.632947i | \(-0.781845\pi\) | ||||
−0.774195 | + | 0.632947i | \(0.781845\pi\) | |||||||
\(98\) | 3.39545e6 | − | 5.88110e6i | 0.364424 | − | 0.631200i | ||||
\(99\) | −1.09919e6 | − | 1.90386e6i | −0.113855 | − | 0.197202i | ||||
\(100\) | 2.60897e6 | + | 4.51887e6i | 0.260897 | + | 0.451887i | ||||
\(101\) | −2.09191e6 | − | 3.62330e6i | −0.202031 | − | 0.349929i | 0.747151 | − | 0.664654i | \(-0.231421\pi\) |
−0.949183 | + | 0.314725i | \(0.898088\pi\) | |||||||
\(102\) | 1.16077e7 | 1.08304 | ||||||||
\(103\) | −134779. | − | 233445.i | −0.0121533 | − | 0.0210501i | 0.859885 | − | 0.510488i | \(-0.170535\pi\) |
−0.872038 | + | 0.489438i | \(0.837202\pi\) | |||||||
\(104\) | 1.16051e7 | + | 2.01006e7i | 1.01165 | + | 1.75223i | ||||
\(105\) | 7.09219e6 | − | 1.22840e7i | 0.597885 | − | 1.03557i | ||||
\(106\) | 6.14783e6 | − | 1.06484e7i | 0.501362 | − | 0.868384i | ||||
\(107\) | −2.43959e7 | −1.92519 | −0.962597 | − | 0.270939i | \(-0.912666\pi\) | ||||
−0.962597 | + | 0.270939i | \(0.912666\pi\) | |||||||
\(108\) | 1.66162e7 | 1.26926 | ||||||||
\(109\) | 1.11897e7 | − | 1.93811e7i | 0.827608 | − | 1.43346i | −0.0723025 | − | 0.997383i | \(-0.523035\pi\) |
0.899910 | − | 0.436076i | \(-0.143632\pi\) | |||||||
\(110\) | 5.54745e6 | − | 9.60847e6i | 0.397392 | − | 0.688303i | ||||
\(111\) | 1.25409e7 | + | 2.17216e7i | 0.870362 | + | 1.50751i | ||||
\(112\) | −3.83224e6 | − | 6.63763e6i | −0.257745 | − | 0.446427i | ||||
\(113\) | 2.16019e7 | 1.40837 | 0.704187 | − | 0.710014i | \(-0.251312\pi\) | ||||
0.704187 | + | 0.710014i | \(0.251312\pi\) | |||||||
\(114\) | −2.02716e7 | − | 3.51114e7i | −1.28150 | − | 2.21963i | ||||
\(115\) | −4.55882e6 | − | 7.89610e6i | −0.279518 | − | 0.484139i | ||||
\(116\) | 3.06189e6 | + | 5.30335e6i | 0.182132 | + | 0.315462i | ||||
\(117\) | −5.31198e6 | + | 9.20062e6i | −0.306624 | + | 0.531088i | ||||
\(118\) | 2.02780e7 | 1.13615 | ||||||||
\(119\) | −6.02126e6 | + | 1.04291e7i | −0.327547 | + | 0.567328i | ||||
\(120\) | −1.25752e7 | − | 2.17809e7i | −0.664326 | − | 1.15065i | ||||
\(121\) | −1.32825e7 | −0.681601 | ||||||||
\(122\) | −2.37639e7 | − | 4.11604e7i | −1.18484 | − | 2.05220i | ||||
\(123\) | 4.79381e6 | − | 8.30313e6i | 0.232281 | − | 0.402322i | ||||
\(124\) | −2.68969e7 | + | 4.65867e7i | −1.26685 | + | 2.19425i | ||||
\(125\) | −2.37366e7 | −1.08701 | ||||||||
\(126\) | 9.07829e6 | − | 1.57241e7i | 0.404303 | − | 0.700274i | ||||
\(127\) | 869527. | 0.0376678 | 0.0188339 | − | 0.999823i | \(-0.494005\pi\) | ||||
0.0188339 | + | 0.999823i | \(0.494005\pi\) | |||||||
\(128\) | 4.31534e7 | 1.81878 | ||||||||
\(129\) | −2.25842e7 | + | 1.80089e7i | −0.926275 | + | 0.738622i | ||||
\(130\) | −5.36175e7 | −2.14045 | ||||||||
\(131\) | 4.13799e7 | 1.60820 | 0.804099 | − | 0.594496i | \(-0.202648\pi\) | ||||
0.804099 | + | 0.594496i | \(0.202648\pi\) | |||||||
\(132\) | 1.58649e7 | − | 2.74789e7i | 0.600384 | − | 1.03990i | ||||
\(133\) | 4.20618e7 | 1.55027 | ||||||||
\(134\) | −1.80142e7 | + | 3.12015e7i | −0.646768 | + | 1.12024i | ||||
\(135\) | −8.50756e6 | + | 1.47355e7i | −0.297603 | + | 0.515463i | ||||
\(136\) | 1.06764e7 | + | 1.84920e7i | 0.363946 | + | 0.630373i | ||||
\(137\) | 5.73787e7 | 1.90646 | 0.953232 | − | 0.302241i | \(-0.0977348\pi\) | ||||
0.953232 | + | 0.302241i | \(0.0977348\pi\) | |||||||
\(138\) | −2.02959e7 | − | 3.51535e7i | −0.657403 | − | 1.13865i | ||||
\(139\) | 1.07042e7 | − | 1.85403e7i | 0.338068 | − | 0.585551i | −0.646001 | − | 0.763336i | \(-0.723560\pi\) |
0.984069 | + | 0.177785i | \(0.0568932\pi\) | |||||||
\(140\) | 5.88630e7 | 1.81299 | ||||||||
\(141\) | −7.86421e6 | + | 1.36212e7i | −0.236259 | + | 0.409213i | ||||
\(142\) | −8.38318e6 | − | 1.45201e7i | −0.245697 | − | 0.425559i | ||||
\(143\) | −1.49925e7 | − | 2.59677e7i | −0.428743 | − | 0.742604i | ||||
\(144\) | −3.11026e6 | − | 5.38713e6i | −0.0868016 | − | 0.150345i | ||||
\(145\) | −6.27079e6 | −0.170818 | ||||||||
\(146\) | 3.27364e7 | + | 5.67011e7i | 0.870555 | + | 1.50785i | ||||
\(147\) | 9.94363e6 | + | 1.72229e7i | 0.258187 | + | 0.447193i | ||||
\(148\) | −5.20430e7 | + | 9.01412e7i | −1.31961 | + | 2.28564i | ||||
\(149\) | −3.32485e7 | + | 5.75881e7i | −0.823418 | + | 1.42620i | 0.0797038 | + | 0.996819i | \(0.474603\pi\) |
−0.903122 | + | 0.429384i | \(0.858731\pi\) | |||||||
\(150\) | −2.37880e7 | −0.575491 | ||||||||
\(151\) | −4.78016e7 | −1.12986 | −0.564928 | − | 0.825140i | \(-0.691096\pi\) | ||||
−0.564928 | + | 0.825140i | \(0.691096\pi\) | |||||||
\(152\) | 3.72901e7 | − | 6.45884e7i | 0.861274 | − | 1.49177i | ||||
\(153\) | −4.88688e6 | + | 8.46432e6i | −0.110309 | + | 0.191061i | ||||
\(154\) | 2.56224e7 | + | 4.43794e7i | 0.565325 | + | 0.979171i | ||||
\(155\) | −2.75426e7 | − | 4.77051e7i | −0.594078 | − | 1.02897i | ||||
\(156\) | −1.53338e8 | −3.23381 | ||||||||
\(157\) | −3.98170e7 | − | 6.89651e7i | −0.821145 | − | 1.42226i | −0.904830 | − | 0.425772i | \(-0.860002\pi\) |
0.0836854 | − | 0.996492i | \(-0.473331\pi\) | |||||||
\(158\) | 4.42357e7 | + | 7.66185e7i | 0.892223 | + | 1.54538i | ||||
\(159\) | 1.80040e7 | + | 3.11838e7i | 0.355205 | + | 0.615233i | ||||
\(160\) | −1.33558e7 | + | 2.31329e7i | −0.257780 | + | 0.446489i | ||||
\(161\) | 4.21123e7 | 0.795277 | ||||||||
\(162\) | −5.61338e7 | + | 9.72265e7i | −1.03734 | + | 1.79673i | ||||
\(163\) | −1.32305e7 | − | 2.29159e7i | −0.239287 | − | 0.414458i | 0.721223 | − | 0.692703i | \(-0.243580\pi\) |
−0.960510 | + | 0.278246i | \(0.910247\pi\) | |||||||
\(164\) | 3.97872e7 | 0.704352 | ||||||||
\(165\) | 1.62458e7 | + | 2.81385e7i | 0.281544 | + | 0.487649i | ||||
\(166\) | 4.70905e7 | − | 8.15632e7i | 0.799016 | − | 1.38394i | ||||
\(167\) | −5.27924e7 | + | 9.14392e7i | −0.877130 | + | 1.51923i | −0.0226540 | + | 0.999743i | \(0.507212\pi\) |
−0.854476 | + | 0.519491i | \(0.826122\pi\) | |||||||
\(168\) | 1.16164e8 | 1.89012 | ||||||||
\(169\) | −4.10786e7 | + | 7.11503e7i | −0.654655 | + | 1.13390i | ||||
\(170\) | −4.93266e7 | −0.770035 | ||||||||
\(171\) | 3.41375e7 | 0.522090 | ||||||||
\(172\) | −1.11582e8 | − | 4.37976e7i | −1.67203 | − | 0.656297i | ||||
\(173\) | 5.36542e7 | 0.787847 | 0.393924 | − | 0.919143i | \(-0.371117\pi\) | ||||
0.393924 | + | 0.919143i | \(0.371117\pi\) | |||||||
\(174\) | −2.79176e7 | −0.401750 | ||||||||
\(175\) | 1.23395e7 | − | 2.13727e7i | 0.174047 | − | 0.301458i | ||||
\(176\) | 1.75567e7 | 0.242744 | ||||||||
\(177\) | −2.96921e7 | + | 5.14283e7i | −0.402472 | + | 0.697101i | ||||
\(178\) | 5.09958e7 | − | 8.83272e7i | 0.677741 | − | 1.17388i | ||||
\(179\) | −2.43678e7 | − | 4.22063e7i | −0.317564 | − | 0.550037i | 0.662415 | − | 0.749137i | \(-0.269532\pi\) |
−0.979979 | + | 0.199100i | \(0.936198\pi\) | |||||||
\(180\) | 4.77734e7 | 0.610566 | ||||||||
\(181\) | −4.11993e6 | − | 7.13593e6i | −0.0516434 | − | 0.0894490i | 0.839048 | − | 0.544057i | \(-0.183113\pi\) |
−0.890691 | + | 0.454608i | \(0.849779\pi\) | |||||||
\(182\) | 1.23824e8 | − | 2.14469e8i | 1.52249 | − | 2.63703i | ||||
\(183\) | 1.39186e8 | 1.67887 | ||||||||
\(184\) | 3.73349e7 | − | 6.46659e7i | 0.441827 | − | 0.765267i | ||||
\(185\) | −5.32924e7 | − | 9.23051e7i | −0.618819 | − | 1.07183i | ||||
\(186\) | −1.22620e8 | − | 2.12384e8i | −1.39722 | − | 2.42006i | ||||
\(187\) | −1.37927e7 | − | 2.38896e7i | −0.154242 | − | 0.267155i | ||||
\(188\) | −6.52706e7 | −0.716415 | ||||||||
\(189\) | −3.92945e7 | − | 6.80602e7i | −0.423366 | − | 0.733291i | ||||
\(190\) | 8.61434e7 | + | 1.49205e8i | 0.911138 | + | 1.57814i | ||||
\(191\) | 5.51977e7 | − | 9.56052e7i | 0.573197 | − | 0.992806i | −0.423038 | − | 0.906112i | \(-0.639036\pi\) |
0.996235 | − | 0.0866944i | \(-0.0276304\pi\) | |||||||
\(192\) | −8.44522e7 | + | 1.46275e8i | −0.861106 | + | 1.49148i | ||||
\(193\) | 9.80664e7 | 0.981905 | 0.490953 | − | 0.871186i | \(-0.336649\pi\) | ||||
0.490953 | + | 0.871186i | \(0.336649\pi\) | |||||||
\(194\) | 2.63313e8 | 2.58920 | ||||||||
\(195\) | 7.85097e7 | − | 1.35983e8i | 0.758232 | − | 1.31330i | ||||
\(196\) | −4.12646e7 | + | 7.14723e7i | −0.391454 | + | 0.678019i | ||||
\(197\) | 2.20507e7 | + | 3.81930e7i | 0.205490 | + | 0.355919i | 0.950289 | − | 0.311370i | \(-0.100788\pi\) |
−0.744799 | + | 0.667289i | \(0.767454\pi\) | |||||||
\(198\) | 2.07953e7 | + | 3.60185e7i | 0.190387 | + | 0.329759i | ||||
\(199\) | −1.15134e8 | −1.03566 | −0.517832 | − | 0.855482i | \(-0.673261\pi\) | ||||
−0.517832 | + | 0.855482i | \(0.673261\pi\) | |||||||
\(200\) | −2.18793e7 | − | 3.78961e7i | −0.193388 | − | 0.334958i | ||||
\(201\) | −5.27549e7 | − | 9.13741e7i | −0.458222 | − | 0.793664i | ||||
\(202\) | 3.95763e7 | + | 6.85481e7i | 0.337835 | + | 0.585148i | ||||
\(203\) | 1.44817e7 | − | 2.50830e7i | 0.121502 | − | 0.210448i | ||||
\(204\) | −1.41067e8 | −1.16338 | ||||||||
\(205\) | −2.03712e7 | + | 3.52839e7i | −0.165150 | + | 0.286047i | ||||
\(206\) | 2.54985e6 | + | 4.41647e6i | 0.0203226 | + | 0.0351998i | ||||
\(207\) | 3.41785e7 | 0.267829 | ||||||||
\(208\) | −4.24225e7 | − | 7.34778e7i | −0.326869 | − | 0.566154i | ||||
\(209\) | −4.81746e7 | + | 8.34409e7i | −0.365011 | + | 0.632218i | ||||
\(210\) | −1.34175e8 | + | 2.32398e8i | −0.999778 | + | 1.73167i | ||||
\(211\) | 3.66018e7 | 0.268234 | 0.134117 | − | 0.990965i | \(-0.457180\pi\) | ||||
0.134117 | + | 0.990965i | \(0.457180\pi\) | |||||||
\(212\) | −7.47138e7 | + | 1.29408e8i | −0.538549 | + | 0.932795i | ||||
\(213\) | 4.91005e7 | 0.348143 | ||||||||
\(214\) | 4.61539e8 | 3.21929 | ||||||||
\(215\) | 9.59707e7 | − | 7.65281e7i | 0.658573 | − | 0.525154i | ||||
\(216\) | −1.39347e8 | −0.940827 | ||||||||
\(217\) | 2.54426e8 | 1.69026 | ||||||||
\(218\) | −2.11694e8 | + | 3.66664e8i | −1.38392 | + | 2.39702i | ||||
\(219\) | −1.91738e8 | −1.23354 | ||||||||
\(220\) | −6.74175e7 | + | 1.16771e8i | −0.426868 | + | 0.739357i | ||||
\(221\) | −6.66547e7 | + | 1.15449e8i | −0.415392 | + | 0.719480i | ||||
\(222\) | −2.37258e8 | − | 4.10943e8i | −1.45541 | − | 2.52085i | ||||
\(223\) | 9.94144e7 | 0.600319 | 0.300160 | − | 0.953889i | \(-0.402960\pi\) | ||||
0.300160 | + | 0.953889i | \(0.402960\pi\) | |||||||
\(224\) | −6.16875e7 | − | 1.06846e8i | −0.366715 | − | 0.635169i | ||||
\(225\) | 1.00148e7 | − | 1.73462e7i | 0.0586144 | − | 0.101523i | ||||
\(226\) | −4.08680e8 | −2.35507 | ||||||||
\(227\) | 5.39425e7 | − | 9.34312e7i | 0.306084 | − | 0.530153i | −0.671418 | − | 0.741079i | \(-0.734314\pi\) |
0.977502 | + | 0.210926i | \(0.0676478\pi\) | |||||||
\(228\) | 2.46358e8 | + | 4.26704e8i | 1.37656 | + | 2.38427i | ||||
\(229\) | −1.34768e8 | − | 2.33426e8i | −0.741590 | − | 1.28447i | −0.951771 | − | 0.306810i | \(-0.900739\pi\) |
0.210181 | − | 0.977663i | \(-0.432595\pi\) | |||||||
\(230\) | 8.62468e7 | + | 1.49384e8i | 0.467407 | + | 0.809573i | ||||
\(231\) | −1.50071e8 | −0.801043 | ||||||||
\(232\) | −2.56776e7 | − | 4.44750e7i | −0.135004 | − | 0.233834i | ||||
\(233\) | 3.49599e7 | + | 6.05524e7i | 0.181061 | + | 0.313607i | 0.942242 | − | 0.334933i | \(-0.108714\pi\) |
−0.761181 | + | 0.648539i | \(0.775380\pi\) | |||||||
\(234\) | 1.00496e8 | − | 1.74064e8i | 0.512734 | − | 0.888081i | ||||
\(235\) | 3.34187e7 | − | 5.78829e7i | 0.167978 | − | 0.290946i | ||||
\(236\) | −2.46436e8 | −1.22043 | ||||||||
\(237\) | −2.59090e8 | −1.26424 | ||||||||
\(238\) | 1.13914e8 | − | 1.97305e8i | 0.547721 | − | 0.948680i | ||||
\(239\) | −6.69098e7 | + | 1.15891e8i | −0.317028 | + | 0.549108i | −0.979866 | − | 0.199654i | \(-0.936018\pi\) |
0.662839 | + | 0.748762i | \(0.269352\pi\) | |||||||
\(240\) | 4.59688e7 | + | 7.96204e7i | 0.214647 | + | 0.371779i | ||||
\(241\) | −5.38219e7 | − | 9.32223e7i | −0.247685 | − | 0.429003i | 0.715198 | − | 0.698922i | \(-0.246336\pi\) |
−0.962883 | + | 0.269919i | \(0.913003\pi\) | |||||||
\(242\) | 2.51287e8 | 1.13977 | ||||||||
\(243\) | −8.53604e7 | − | 1.47849e8i | −0.381623 | − | 0.660990i | ||||
\(244\) | 2.88800e8 | + | 5.00217e8i | 1.27272 | + | 2.20442i | ||||
\(245\) | −4.22552e7 | − | 7.31881e7i | −0.183569 | − | 0.317950i | ||||
\(246\) | −9.06926e7 | + | 1.57084e8i | −0.388418 | + | 0.672759i | ||||
\(247\) | 4.65620e8 | 1.96604 | ||||||||
\(248\) | 2.25562e8 | − | 3.90686e8i | 0.939044 | − | 1.62647i | ||||
\(249\) | 1.37905e8 | + | 2.38859e8i | 0.566087 | + | 0.980491i | ||||
\(250\) | 4.49066e8 | 1.81769 | ||||||||
\(251\) | −1.58154e8 | − | 2.73931e8i | −0.631282 | − | 1.09341i | −0.987290 | − | 0.158929i | \(-0.949196\pi\) |
0.356008 | − | 0.934483i | \(-0.384137\pi\) | |||||||
\(252\) | −1.10327e8 | + | 1.91093e8i | −0.434292 | + | 0.752215i | ||||
\(253\) | −4.82325e7 | + | 8.35411e7i | −0.187248 | + | 0.324323i | ||||
\(254\) | −1.64503e7 | −0.0629878 | ||||||||
\(255\) | 7.22268e7 | − | 1.25101e8i | 0.272777 | − | 0.472464i | ||||
\(256\) | −4.26183e8 | −1.58766 | ||||||||
\(257\) | −1.76381e8 | −0.648167 | −0.324083 | − | 0.946029i | \(-0.605056\pi\) | ||||
−0.324083 | + | 0.946029i | \(0.605056\pi\) | |||||||
\(258\) | 4.27262e8 | − | 3.40704e8i | 1.54891 | − | 1.23512i | ||||
\(259\) | 4.92291e8 | 1.76065 | ||||||||
\(260\) | 6.51607e8 | 2.29921 | ||||||||
\(261\) | 1.17534e7 | − | 2.03575e7i | 0.0409187 | − | 0.0708732i | ||||
\(262\) | −7.82852e8 | −2.68921 | ||||||||
\(263\) | −6.59657e7 | + | 1.14256e8i | −0.223601 | + | 0.387288i | −0.955899 | − | 0.293697i | \(-0.905114\pi\) |
0.732298 | + | 0.680984i | \(0.238448\pi\) | |||||||
\(264\) | −1.33046e8 | + | 2.30443e8i | −0.445030 | + | 0.770815i | ||||
\(265\) | −7.65074e7 | − | 1.32515e8i | −0.252547 | − | 0.437425i | ||||
\(266\) | −7.95754e8 | −2.59235 | ||||||||
\(267\) | 1.49342e8 | + | 2.58667e8i | 0.480166 | + | 0.831673i | ||||
\(268\) | 2.18925e8 | − | 3.79189e8i | 0.694741 | − | 1.20333i | ||||
\(269\) | −2.96610e8 | −0.929079 | −0.464539 | − | 0.885552i | \(-0.653780\pi\) | ||||
−0.464539 | + | 0.885552i | \(0.653780\pi\) | |||||||
\(270\) | 1.60952e8 | − | 2.78777e8i | 0.497649 | − | 0.861953i | ||||
\(271\) | 1.26614e8 | + | 2.19302e8i | 0.386446 | + | 0.669344i | 0.991969 | − | 0.126484i | \(-0.0403693\pi\) |
−0.605523 | + | 0.795828i | \(0.707036\pi\) | |||||||
\(272\) | −3.90275e7 | − | 6.75976e7i | −0.117593 | − | 0.203676i | ||||
\(273\) | 3.62619e8 | + | 6.28075e8i | 1.07865 | + | 1.86828i | ||||
\(274\) | −1.08553e9 | −3.18797 | ||||||||
\(275\) | 2.82657e7 | + | 4.89576e7i | 0.0819586 | + | 0.141957i | ||||
\(276\) | 2.46654e8 | + | 4.27217e8i | 0.706164 | + | 1.22311i | ||||
\(277\) | −2.34145e8 | + | 4.05552e8i | −0.661921 | + | 1.14648i | 0.318189 | + | 0.948027i | \(0.396925\pi\) |
−0.980110 | + | 0.198454i | \(0.936408\pi\) | |||||||
\(278\) | −2.02510e8 | + | 3.50758e8i | −0.565315 | + | 0.979154i | ||||
\(279\) | 2.06493e8 | 0.569234 | ||||||||
\(280\) | −4.93637e8 | −1.34386 | ||||||||
\(281\) | 2.63542e8 | − | 4.56469e8i | 0.708563 | − | 1.22727i | −0.256828 | − | 0.966457i | \(-0.582677\pi\) |
0.965390 | − | 0.260809i | \(-0.0839894\pi\) | |||||||
\(282\) | 1.48781e8 | − | 2.57695e8i | 0.395070 | − | 0.684282i | ||||
\(283\) | −1.22768e8 | − | 2.12640e8i | −0.321982 | − | 0.557690i | 0.658915 | − | 0.752218i | \(-0.271016\pi\) |
−0.980897 | + | 0.194528i | \(0.937683\pi\) | |||||||
\(284\) | 1.01880e8 | + | 1.76461e8i | 0.263921 | + | 0.457124i | ||||
\(285\) | −5.04544e8 | −1.29105 | ||||||||
\(286\) | 2.83638e8 | + | 4.91275e8i | 0.716940 | + | 1.24178i | ||||
\(287\) | −9.40899e7 | − | 1.62968e8i | −0.234940 | − | 0.406927i | ||||
\(288\) | −5.00658e7 | − | 8.67165e7i | −0.123500 | − | 0.213908i | ||||
\(289\) | 1.43849e8 | − | 2.49153e8i | 0.350561 | − | 0.607190i | ||||
\(290\) | 1.18635e8 | 0.285641 | ||||||||
\(291\) | −3.85558e8 | + | 6.67806e8i | −0.917200 | + | 1.58864i | ||||
\(292\) | −3.97842e8 | − | 6.89082e8i | −0.935127 | − | 1.61969i | ||||
\(293\) | 1.71068e8 | 0.397313 | 0.198657 | − | 0.980069i | \(-0.436342\pi\) | ||||
0.198657 | + | 0.980069i | \(0.436342\pi\) | |||||||
\(294\) | −1.88120e8 | − | 3.25834e8i | −0.431738 | − | 0.747792i | ||||
\(295\) | 1.26176e8 | − | 2.18543e8i | 0.286154 | − | 0.495633i | ||||
\(296\) | 4.36443e8 | − | 7.55942e8i | 0.978153 | − | 1.69421i | ||||
\(297\) | 1.80021e8 | 0.398726 | ||||||||
\(298\) | 6.29018e8 | − | 1.08949e9i | 1.37691 | − | 2.38488i | ||||
\(299\) | 4.66179e8 | 1.00856 | ||||||||
\(300\) | 2.89093e8 | 0.618177 | ||||||||
\(301\) | 8.44772e7 | + | 5.60614e8i | 0.178549 | + | 1.18490i | ||||
\(302\) | 9.04344e8 | 1.88934 | ||||||||
\(303\) | −2.31799e8 | −0.478699 | ||||||||
\(304\) | −1.36314e8 | + | 2.36103e8i | −0.278281 | + | 0.481997i | ||||
\(305\) | −5.91467e8 | −1.19366 | ||||||||
\(306\) | 9.24533e7 | − | 1.60134e8i | 0.184458 | − | 0.319491i | ||||
\(307\) | 3.08588e7 | − | 5.34490e7i | 0.0608688 | − | 0.105428i | −0.833985 | − | 0.551787i | \(-0.813946\pi\) |
0.894854 | + | 0.446359i | \(0.147280\pi\) | |||||||
\(308\) | −3.11387e8 | − | 5.39337e8i | −0.607257 | − | 1.05180i | ||||
\(309\) | −1.49345e7 | −0.0287963 | ||||||||
\(310\) | 5.21069e8 | + | 9.02518e8i | 0.993412 | + | 1.72064i | ||||
\(311\) | −1.99279e8 | + | 3.45161e8i | −0.375664 | + | 0.650670i | −0.990426 | − | 0.138043i | \(-0.955919\pi\) |
0.614762 | + | 0.788713i | \(0.289252\pi\) | |||||||
\(312\) | 1.28593e9 | 2.39704 | ||||||||
\(313\) | −4.64941e8 | + | 8.05301e8i | −0.857023 | + | 1.48441i | 0.0177333 | + | 0.999843i | \(0.494355\pi\) |
−0.874756 | + | 0.484564i | \(0.838978\pi\) | |||||||
\(314\) | 7.53285e8 | + | 1.30473e9i | 1.37311 | + | 2.37830i | ||||
\(315\) | −1.12976e8 | − | 1.95680e8i | −0.203657 | − | 0.352744i | ||||
\(316\) | −5.37592e8 | − | 9.31136e8i | −0.958402 | − | 1.66000i | ||||
\(317\) | −8.83384e8 | −1.55755 | −0.778776 | − | 0.627303i | \(-0.784159\pi\) | ||||
−0.778776 | + | 0.627303i | \(0.784159\pi\) | |||||||
\(318\) | −3.40612e8 | − | 5.89957e8i | −0.593970 | − | 1.02879i | ||||
\(319\) | 3.31726e7 | + | 5.74567e7i | 0.0572153 | + | 0.0990998i | ||||
\(320\) | 3.58877e8 | − | 6.21593e8i | 0.612238 | − | 1.06043i | ||||
\(321\) | −6.75811e8 | + | 1.17054e9i | −1.14040 | + | 1.97523i | ||||
\(322\) | −7.96710e8 | −1.32986 | ||||||||
\(323\) | 4.28358e8 | 0.707290 | ||||||||
\(324\) | 6.82187e8 | − | 1.18158e9i | 1.11428 | − | 1.93000i | ||||
\(325\) | 1.36597e8 | − | 2.36593e8i | 0.220724 | − | 0.382306i | ||||
\(326\) | 2.50303e8 | + | 4.33538e8i | 0.400134 | + | 0.693052i | ||||
\(327\) | −6.19948e8 | − | 1.07378e9i | −0.980478 | − | 1.69824i | ||||
\(328\) | −3.33663e8 | −0.522095 | ||||||||
\(329\) | 1.54354e8 | + | 2.67348e8i | 0.238963 | + | 0.413897i | ||||
\(330\) | −3.07349e8 | − | 5.32344e8i | −0.470796 | − | 0.815442i | ||||
\(331\) | 4.62069e8 | + | 8.00328e8i | 0.700341 | + | 1.21303i | 0.968347 | + | 0.249608i | \(0.0803019\pi\) |
−0.268006 | + | 0.963417i | \(0.586365\pi\) | |||||||
\(332\) | −5.72286e8 | + | 9.91228e8i | −0.858281 | + | 1.48659i | ||||
\(333\) | 3.99545e8 | 0.592941 | ||||||||
\(334\) | 9.98763e8 | − | 1.72991e9i | 1.46673 | − | 2.54045i | ||||
\(335\) | 2.24180e8 | + | 3.88291e8i | 0.325792 | + | 0.564288i | ||||
\(336\) | −4.24640e8 | −0.610707 | ||||||||
\(337\) | −1.05164e8 | − | 1.82149e8i | −0.149679 | − | 0.259252i | 0.781430 | − | 0.623993i | \(-0.214491\pi\) |
−0.931109 | + | 0.364742i | \(0.881157\pi\) | |||||||
\(338\) | 7.77154e8 | − | 1.34607e9i | 1.09471 | − | 1.89609i | ||||
\(339\) | 5.98413e8 | − | 1.03648e9i | 0.834261 | − | 1.44498i | ||||
\(340\) | 5.99461e8 | 0.827150 | ||||||||
\(341\) | −2.91401e8 | + | 5.04722e8i | −0.397971 | + | 0.689306i | ||||
\(342\) | −6.45837e8 | −0.873035 | ||||||||
\(343\) | −5.05208e8 | −0.675990 | ||||||||
\(344\) | 9.35748e8 | + | 3.67295e8i | 1.23938 | + | 0.486475i | ||||
\(345\) | −5.05150e8 | −0.662298 | ||||||||
\(346\) | −1.01507e9 | −1.31743 | ||||||||
\(347\) | 3.48798e8 | − | 6.04137e8i | 0.448148 | − | 0.776215i | −0.550118 | − | 0.835087i | \(-0.685417\pi\) |
0.998266 | + | 0.0588723i | \(0.0187505\pi\) | |||||||
\(348\) | 3.39280e8 | 0.431549 | ||||||||
\(349\) | −3.72573e8 | + | 6.45315e8i | −0.469161 | + | 0.812611i | −0.999378 | − | 0.0352509i | \(-0.988777\pi\) |
0.530217 | + | 0.847862i | \(0.322110\pi\) | |||||||
\(350\) | −2.33448e8 | + | 4.04343e8i | −0.291039 | + | 0.504095i | ||||
\(351\) | −4.34986e8 | − | 7.53418e8i | −0.536909 | − | 0.929953i | ||||
\(352\) | 2.82610e8 | 0.345373 | ||||||||
\(353\) | 5.43083e8 | + | 9.40647e8i | 0.657135 | + | 1.13819i | 0.981354 | + | 0.192209i | \(0.0615651\pi\) |
−0.324219 | + | 0.945982i | \(0.605102\pi\) | |||||||
\(354\) | 5.61736e8 | − | 9.72956e8i | 0.673009 | − | 1.16569i | ||||
\(355\) | −2.08651e8 | −0.247526 | ||||||||
\(356\) | −6.19745e8 | + | 1.07343e9i | −0.728012 | + | 1.26095i | ||||
\(357\) | 3.33600e8 | + | 5.77812e8i | 0.388049 | + | 0.672121i | ||||
\(358\) | 4.61007e8 | + | 7.98488e8i | 0.531028 | + | 0.919767i | ||||
\(359\) | −7.67315e8 | − | 1.32903e9i | −0.875272 | − | 1.51602i | −0.856473 | − | 0.516193i | \(-0.827349\pi\) |
−0.0187996 | − | 0.999823i | \(-0.505984\pi\) | |||||||
\(360\) | −4.00637e8 | −0.452577 | ||||||||
\(361\) | −3.01142e8 | − | 5.21593e8i | −0.336896 | − | 0.583522i | ||||
\(362\) | 7.79436e7 | + | 1.35002e8i | 0.0863576 | + | 0.149576i | ||||
\(363\) | −3.67949e8 | + | 6.37306e8i | −0.403751 | + | 0.699318i | ||||
\(364\) | −1.50481e9 | + | 2.60641e9i | −1.63541 | + | 2.83262i | ||||
\(365\) | 8.14785e8 | 0.877037 | ||||||||
\(366\) | −2.63322e9 | −2.80739 | ||||||||
\(367\) | 4.13364e8 | − | 7.15967e8i | 0.436517 | − | 0.756070i | −0.560901 | − | 0.827883i | \(-0.689545\pi\) |
0.997418 | + | 0.0718130i | \(0.0228785\pi\) | |||||||
\(368\) | −1.36478e8 | + | 2.36387e8i | −0.142756 | + | 0.247261i | ||||
\(369\) | −7.63637e7 | − | 1.32266e8i | −0.0791215 | − | 0.137042i | ||||
\(370\) | 1.00822e9 | + | 1.74629e9i | 1.03478 | + | 1.79230i | ||||
\(371\) | 7.06742e8 | 0.718542 | ||||||||
\(372\) | 1.49018e9 | + | 2.58107e9i | 1.50086 | + | 2.59956i | ||||
\(373\) | −4.79786e6 | − | 8.31013e6i | −0.00478703 | − | 0.00829138i | 0.863622 | − | 0.504140i | \(-0.168190\pi\) |
−0.868409 | + | 0.495849i | \(0.834857\pi\) | |||||||
\(374\) | 2.60939e8 | + | 4.51959e8i | 0.257922 | + | 0.446734i | ||||
\(375\) | −6.57547e8 | + | 1.13891e9i | −0.643899 | + | 1.11527i | ||||
\(376\) | 5.47372e8 | 0.531037 | ||||||||
\(377\) | 1.60311e8 | − | 2.77666e8i | 0.154088 | − | 0.266888i | ||||
\(378\) | 7.43401e8 | + | 1.28761e9i | 0.707949 | + | 1.22620i | ||||
\(379\) | −1.05009e9 | −0.990805 | −0.495402 | − | 0.868664i | \(-0.664979\pi\) | ||||
−0.495402 | + | 0.868664i | \(0.664979\pi\) | |||||||
\(380\) | −1.04689e9 | − | 1.81327e9i | −0.978720 | − | 1.69519i | ||||
\(381\) | 2.40875e7 | − | 4.17207e7i | 0.0223128 | − | 0.0386469i | ||||
\(382\) | −1.04427e9 | + | 1.80872e9i | −0.958495 | + | 1.66016i | ||||
\(383\) | −1.63075e9 | −1.48318 | −0.741588 | − | 0.670855i | \(-0.765927\pi\) | ||||
−0.741588 | + | 0.670855i | \(0.765927\pi\) | |||||||
\(384\) | 1.19543e9 | − | 2.07054e9i | 1.07737 | − | 1.86606i | ||||
\(385\) | 6.37723e8 | 0.569534 | ||||||||
\(386\) | −1.85529e9 | −1.64193 | ||||||||
\(387\) | 6.85619e7 | + | 4.54996e8i | 0.0601305 | + | 0.399043i | ||||
\(388\) | −3.20001e9 | −2.78125 | ||||||||
\(389\) | 1.00079e9 | 0.862028 | 0.431014 | − | 0.902345i | \(-0.358156\pi\) | ||||
0.431014 | + | 0.902345i | \(0.358156\pi\) | |||||||
\(390\) | −1.48530e9 | + | 2.57262e9i | −1.26791 | + | 2.19608i | ||||
\(391\) | 4.28872e8 | 0.362835 | ||||||||
\(392\) | 3.46053e8 | − | 5.99381e8i | 0.290162 | − | 0.502576i | ||||
\(393\) | 1.14630e9 | − | 1.98544e9i | 0.952627 | − | 1.65000i | ||||
\(394\) | −4.17170e8 | − | 7.22560e8i | −0.343619 | − | 0.595165i | ||||
\(395\) | 1.10099e9 | 0.898867 | ||||||||
\(396\) | −2.52722e8 | − | 4.37728e8i | −0.204508 | − | 0.354218i | ||||
\(397\) | 1.58473e8 | − | 2.74483e8i | 0.127113 | − | 0.220165i | −0.795444 | − | 0.606027i | \(-0.792762\pi\) |
0.922557 | + | 0.385861i | \(0.126096\pi\) | |||||||
\(398\) | 2.17819e9 | 1.73183 | ||||||||
\(399\) | 1.16519e9 | − | 2.01817e9i | 0.918314 | − | 1.59057i | ||||
\(400\) | 7.99801e7 | + | 1.38530e8i | 0.0624845 | + | 0.108226i | ||||
\(401\) | −2.21170e8 | − | 3.83077e8i | −0.171285 | − | 0.296675i | 0.767584 | − | 0.640948i | \(-0.221459\pi\) |
−0.938869 | + | 0.344273i | \(0.888125\pi\) | |||||||
\(402\) | 9.98052e8 | + | 1.72868e9i | 0.766235 | + | 1.32716i | ||||
\(403\) | 2.81647e9 | 2.14357 | ||||||||
\(404\) | −4.80966e8 | − | 8.33057e8i | −0.362893 | − | 0.628550i | ||||
\(405\) | 6.98564e8 | + | 1.20995e9i | 0.522533 | + | 0.905053i | ||||
\(406\) | −2.73975e8 | + | 4.74538e8i | −0.203175 | + | 0.351909i | ||||
\(407\) | −5.63835e8 | + | 9.76592e8i | −0.414545 | + | 0.718013i | ||||
\(408\) | 1.18302e9 | 0.862344 | ||||||||
\(409\) | −1.74407e8 | −0.126047 | −0.0630235 | − | 0.998012i | \(-0.520074\pi\) | ||||
−0.0630235 | + | 0.998012i | \(0.520074\pi\) | |||||||
\(410\) | 3.85396e8 | − | 6.67525e8i | 0.276162 | − | 0.478326i | ||||
\(411\) | 1.58949e9 | − | 2.75308e9i | 1.12931 | − | 1.95602i | ||||
\(412\) | −3.09880e7 | − | 5.36728e7i | −0.0218300 | − | 0.0378106i | ||||
\(413\) | 5.82778e8 | + | 1.00940e9i | 0.407079 | + | 0.705081i | ||||
\(414\) | −6.46612e8 | −0.447860 | ||||||||
\(415\) | −5.86024e8 | − | 1.01502e9i | −0.402483 | − | 0.697120i | ||||
\(416\) | −6.82873e8 | − | 1.18277e9i | −0.465065 | − | 0.805516i | ||||
\(417\) | −5.93054e8 | − | 1.02720e9i | −0.400514 | − | 0.693711i | ||||
\(418\) | 9.11400e8 | − | 1.57859e9i | 0.610369 | − | 1.05719i | ||||
\(419\) | −2.44919e8 | −0.162657 | −0.0813285 | − | 0.996687i | \(-0.525916\pi\) | ||||
−0.0813285 | + | 0.996687i | \(0.525916\pi\) | |||||||
\(420\) | 1.63061e9 | − | 2.82430e9i | 1.07393 | − | 1.86011i | ||||
\(421\) | 6.25354e8 | + | 1.08315e9i | 0.408450 | + | 0.707456i | 0.994716 | − | 0.102663i | \(-0.0327362\pi\) |
−0.586266 | + | 0.810118i | \(0.699403\pi\) | |||||||
\(422\) | −6.92458e8 | −0.448539 | ||||||||
\(423\) | 1.25274e8 | + | 2.16981e8i | 0.0804766 | + | 0.139390i | ||||
\(424\) | 6.26565e8 | − | 1.08524e9i | 0.399196 | − | 0.691427i | ||||
\(425\) | 1.25666e8 | − | 2.17660e8i | 0.0794065 | − | 0.137536i | ||||
\(426\) | −9.28916e8 | −0.582161 | ||||||||
\(427\) | 1.36593e9 | − | 2.36586e9i | 0.849044 | − | 1.47059i | ||||
\(428\) | −5.60903e9 | −3.45807 | ||||||||
\(429\) | −1.66127e9 | −1.01588 | ||||||||
\(430\) | −1.81564e9 | + | 1.44781e9i | −1.10126 | + | 0.878157i | ||||
\(431\) | −1.16838e9 | −0.702932 | −0.351466 | − | 0.936201i | \(-0.614317\pi\) | ||||
−0.351466 | + | 0.936201i | \(0.614317\pi\) | |||||||
\(432\) | 5.09384e8 | 0.303985 | ||||||||
\(433\) | 3.48623e8 | − | 6.03833e8i | 0.206371 | − | 0.357445i | −0.744198 | − | 0.667959i | \(-0.767168\pi\) |
0.950569 | + | 0.310514i | \(0.100501\pi\) | |||||||
\(434\) | −4.81340e9 | −2.82643 | ||||||||
\(435\) | −1.73712e8 | + | 3.00878e8i | −0.101185 | + | 0.175258i | ||||
\(436\) | 2.57269e9 | − | 4.45603e9i | 1.48657 | − | 2.57481i | ||||
\(437\) | −7.48976e8 | − | 1.29726e9i | −0.429322 | − | 0.743607i | ||||
\(438\) | 3.62743e9 | 2.06272 | ||||||||
\(439\) | 1.90865e7 | + | 3.30589e7i | 0.0107672 | + | 0.0186493i | 0.871359 | − | 0.490646i | \(-0.163239\pi\) |
−0.860592 | + | 0.509296i | \(0.829906\pi\) | |||||||
\(440\) | 5.65377e8 | − | 9.79261e8i | 0.316412 | − | 0.548042i | ||||
\(441\) | 3.16797e8 | 0.175892 | ||||||||
\(442\) | 1.26102e9 | − | 2.18415e9i | 0.694614 | − | 1.20311i | ||||
\(443\) | 3.80898e8 | + | 6.59735e8i | 0.208159 | + | 0.360542i | 0.951135 | − | 0.308776i | \(-0.0999194\pi\) |
−0.742975 | + | 0.669319i | \(0.766586\pi\) | |||||||
\(444\) | 2.88337e9 | + | 4.99414e9i | 1.56336 | + | 2.70783i | ||||
\(445\) | −6.34623e8 | − | 1.09920e9i | −0.341394 | − | 0.591312i | ||||
\(446\) | −1.88079e9 | −1.00385 | ||||||||
\(447\) | 1.84209e9 | + | 3.19059e9i | 0.975515 | + | 1.68964i | ||||
\(448\) | 1.65757e9 | + | 2.87100e9i | 0.870963 | + | 1.50855i | ||||
\(449\) | −9.46214e8 | + | 1.63889e9i | −0.493318 | + | 0.854452i | −0.999970 | − | 0.00769823i | \(-0.997550\pi\) |
0.506652 | + | 0.862151i | \(0.330883\pi\) | |||||||
\(450\) | −1.89467e8 | + | 3.28167e8i | −0.0980144 | + | 0.169766i | ||||
\(451\) | 4.31055e8 | 0.221266 | ||||||||
\(452\) | 4.96664e9 | 2.52975 | ||||||||
\(453\) | −1.32419e9 | + | 2.29357e9i | −0.669278 | + | 1.15922i | ||||
\(454\) | −1.02052e9 | + | 1.76760e9i | −0.511831 | + | 0.886517i | ||||
\(455\) | −1.54094e9 | − | 2.66898e9i | −0.766912 | − | 1.32833i | ||||
\(456\) | −2.06601e9 | − | 3.57843e9i | −1.02036 | − | 1.76732i | ||||
\(457\) | 2.03413e9 | 0.996946 | 0.498473 | − | 0.866905i | \(-0.333894\pi\) | ||||
0.498473 | + | 0.866905i | \(0.333894\pi\) | |||||||
\(458\) | 2.54964e9 | + | 4.41611e9i | 1.24008 | + | 2.14788i | ||||
\(459\) | −4.00175e8 | − | 6.93124e8i | −0.193155 | − | 0.334554i | ||||
\(460\) | −1.04815e9 | − | 1.81544e9i | −0.502076 | − | 0.869622i | ||||
\(461\) | 1.14056e8 | − | 1.97551e8i | 0.0542209 | − | 0.0939133i | −0.837641 | − | 0.546221i | \(-0.816066\pi\) |
0.891862 | + | 0.452308i | \(0.149399\pi\) | |||||||
\(462\) | 2.83915e9 | 1.33950 | ||||||||
\(463\) | 6.83061e8 | − | 1.18310e9i | 0.319835 | − | 0.553971i | −0.660618 | − | 0.750722i | \(-0.729706\pi\) |
0.980453 | + | 0.196751i | \(0.0630391\pi\) | |||||||
\(464\) | 9.38648e7 | + | 1.62579e8i | 0.0436204 | + | 0.0755528i | ||||
\(465\) | −3.05191e9 | −1.40762 | ||||||||
\(466\) | −6.61396e8 | − | 1.14557e9i | −0.302769 | − | 0.524410i | ||||
\(467\) | −1.62878e9 | + | 2.82112e9i | −0.740035 | + | 1.28178i | 0.212444 | + | 0.977173i | \(0.431858\pi\) |
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(468\) | −1.22131e9 | + | 2.11537e9i | −0.550765 | + | 0.953952i | ||||
\(469\) | −2.07088e9 | −0.926935 | ||||||||
\(470\) | −6.32238e8 | + | 1.09507e9i | −0.280891 | + | 0.486518i | ||||
\(471\) | −4.41201e9 | −1.94564 | ||||||||
\(472\) | 2.06666e9 | 0.904632 | ||||||||
\(473\) | −1.20888e9 | − | 4.74504e8i | −0.525255 | − | 0.206170i | ||||
\(474\) | 4.90164e9 | 2.11406 | ||||||||
\(475\) | −8.77845e8 | −0.375829 | ||||||||
\(476\) | −1.38439e9 | + | 2.39783e9i | −0.588347 | + | 1.01905i | ||||
\(477\) | 5.73594e8 | 0.241986 | ||||||||
\(478\) | 1.26585e9 | − | 2.19251e9i | 0.530131 | − | 0.918214i | ||||
\(479\) | −1.81722e9 | + | 3.14751e9i | −0.755497 | + | 1.30856i | 0.189630 | + | 0.981856i | \(0.439271\pi\) |
−0.945127 | + | 0.326703i | \(0.894062\pi\) | |||||||
\(480\) | 7.39959e8 | + | 1.28165e9i | 0.305396 | + | 0.528962i | ||||
\(481\) | 5.44961e9 | 2.23284 | ||||||||
\(482\) | 1.01824e9 | + | 1.76364e9i | 0.414176 | + | 0.717375i | ||||
\(483\) | 1.16659e9 | − | 2.02059e9i | 0.471088 | − | 0.815949i | ||||
\(484\) | −3.05386e9 | −1.22431 | ||||||||
\(485\) | 1.63842e9 | − | 2.83782e9i | 0.652121 | − | 1.12951i | ||||
\(486\) | 1.61491e9 | + | 2.79710e9i | 0.638146 | + | 1.10530i | ||||
\(487\) | −5.72522e8 | − | 9.91637e8i | −0.224616 | − | 0.389046i | 0.731588 | − | 0.681747i | \(-0.238779\pi\) |
−0.956204 | + | 0.292700i | \(0.905446\pi\) | |||||||
\(488\) | −2.42194e9 | − | 4.19492e9i | −0.943395 | − | 1.63401i | ||||
\(489\) | −1.46603e9 | −0.566974 | ||||||||
\(490\) | 7.99412e8 | + | 1.38462e9i | 0.306962 | + | 0.531673i | ||||
\(491\) | −3.52475e8 | − | 6.10505e8i | −0.134383 | − | 0.232758i | 0.790979 | − | 0.611844i | \(-0.209572\pi\) |
−0.925361 | + | 0.379086i | \(0.876238\pi\) | |||||||
\(492\) | 1.10218e9 | − | 1.90903e9i | 0.417228 | − | 0.722660i | ||||
\(493\) | 1.47482e8 | − | 2.55446e8i | 0.0554336 | − | 0.0960139i | ||||
\(494\) | −8.80891e9 | −3.28759 | ||||||||
\(495\) | 5.17578e8 | 0.191804 | ||||||||
\(496\) | −8.24545e8 | + | 1.42815e9i | −0.303409 | + | 0.525520i | ||||
\(497\) | 4.81856e8 | − | 8.34600e8i | 0.176064 | − | 0.304952i | ||||
\(498\) | −2.60899e9 | − | 4.51890e9i | −0.946605 | − | 1.63957i | ||||
\(499\) | 1.65292e9 | + | 2.86293e9i | 0.595524 | + | 1.03148i | 0.993473 | + | 0.114070i | \(0.0363887\pi\) |
−0.397949 | + | 0.917407i | \(0.630278\pi\) | |||||||
\(500\) | −5.45744e9 | −1.95251 | ||||||||
\(501\) | 2.92489e9 | + | 5.06606e9i | 1.03915 | + | 1.79986i | ||||
\(502\) | 2.99207e9 | + | 5.18242e9i | 1.05562 | + | 1.82839i | ||||
\(503\) | −1.53437e9 | − | 2.65760e9i | −0.537578 | − | 0.931113i | −0.999034 | − | 0.0439496i | \(-0.986006\pi\) |
0.461455 | − | 0.887163i | \(-0.347327\pi\) | |||||||
\(504\) | 9.25228e8 | − | 1.60254e9i | 0.321915 | − | 0.557574i | ||||
\(505\) | 9.85023e8 | 0.340351 | ||||||||
\(506\) | 9.12494e8 | − | 1.58049e9i | 0.313115 | − | 0.542331i | ||||
\(507\) | 2.27590e9 | + | 3.94198e9i | 0.775579 | + | 1.34334i | ||||
\(508\) | 1.99919e8 | 0.0676597 | ||||||||
\(509\) | −7.64750e8 | − | 1.32459e9i | −0.257044 | − | 0.445213i | 0.708405 | − | 0.705806i | \(-0.249415\pi\) |
−0.965449 | + | 0.260593i | \(0.916082\pi\) | |||||||
\(510\) | −1.36644e9 | + | 2.36674e9i | −0.456135 | + | 0.790050i | ||||
\(511\) | −1.88166e9 | + | 3.25912e9i | −0.623831 | + | 1.08051i | ||||
\(512\) | 2.53918e9 | 0.836083 | ||||||||
\(513\) | −1.39772e9 | + | 2.42093e9i | −0.457099 | + | 0.791719i | ||||
\(514\) | 3.33690e9 | 1.08386 | ||||||||
\(515\) | 6.34638e7 | 0.0204739 | ||||||||
\(516\) | −5.19247e9 | + | 4.14053e9i | −1.66380 | + | 1.32673i | ||||
\(517\) | −7.07143e8 | −0.225056 | ||||||||
\(518\) | −9.31350e9 | −2.94414 | ||||||||
\(519\) | 1.48632e9 | − | 2.57438e9i | 0.466687 | − | 0.808325i | ||||
\(520\) | −5.46450e9 | −1.70427 | ||||||||
\(521\) | 5.68038e8 | − | 9.83871e8i | 0.175973 | − | 0.304794i | −0.764525 | − | 0.644594i | \(-0.777026\pi\) |
0.940497 | + | 0.339801i | \(0.110360\pi\) | |||||||
\(522\) | −2.22359e8 | + | 3.85137e8i | −0.0684238 | + | 0.118514i | ||||
\(523\) | −2.18215e9 | − | 3.77959e9i | −0.667003 | − | 1.15528i | −0.978738 | − | 0.205115i | \(-0.934243\pi\) |
0.311735 | − | 0.950169i | \(-0.399090\pi\) | |||||||
\(524\) | 9.51391e9 | 2.88868 | ||||||||
\(525\) | −6.83655e8 | − | 1.18413e9i | −0.206196 | − | 0.357141i | ||||
\(526\) | 1.24798e9 | − | 2.16157e9i | 0.373903 | − | 0.647619i | ||||
\(527\) | 2.59107e9 | 0.771156 | ||||||||
\(528\) | 4.86352e8 | − | 8.42387e8i | 0.143791 | − | 0.249054i | ||||
\(529\) | 9.52538e8 | + | 1.64984e9i | 0.279761 | + | 0.484560i | ||||
\(530\) | 1.44742e9 | + | 2.50700e9i | 0.422308 | + | 0.731458i | ||||
\(531\) | 4.72985e8 | + | 8.19234e8i | 0.137093 | + | 0.237453i | ||||
\(532\) | 9.67071e9 | 2.78463 | ||||||||
\(533\) | −1.04156e9 | − | 1.80404e9i | −0.297948 | − | 0.516061i | ||||
\(534\) | −2.82535e9 | − | 4.89365e9i | −0.802930 | − | 1.39072i | ||||
\(535\) | 2.87184e9 | − | 4.97417e9i | 0.810815 | − | 1.40437i | ||||
\(536\) | −1.83595e9 | + | 3.17995e9i | −0.514971 | + | 0.891956i | ||||
\(537\) | −2.70013e9 | −0.752445 | ||||||||
\(538\) | 5.61147e9 | 1.55360 | ||||||||
\(539\) | −4.47061e8 | + | 7.74333e8i | −0.122972 | + | 0.212994i | ||||
\(540\) | −1.95603e9 | + | 3.38794e9i | −0.534561 | + | 0.925886i | ||||
\(541\) | 1.56933e9 | + | 2.71817e9i | 0.426113 | + | 0.738050i | 0.996524 | − | 0.0833102i | \(-0.0265492\pi\) |
−0.570411 | + | 0.821360i | \(0.693216\pi\) | |||||||
\(542\) | −2.39537e9 | − | 4.14890e9i | −0.646211 | − | 1.11927i | ||||
\(543\) | −4.56518e8 | −0.122365 | ||||||||
\(544\) | −6.28225e8 | − | 1.08812e9i | −0.167309 | − | 0.289788i | ||||
\(545\) | 2.63445e9 | + | 4.56300e9i | 0.697111 | + | 1.20743i | ||||
\(546\) | −6.86027e9 | − | 1.18823e10i | −1.80371 | − | 3.12412i | ||||
\(547\) | 6.45511e8 | − | 1.11806e9i | 0.168635 | − | 0.292085i | −0.769305 | − | 0.638882i | \(-0.779397\pi\) |
0.937940 | + | 0.346797i | \(0.112731\pi\) | |||||||
\(548\) | 1.31923e10 | 3.42443 | ||||||||
\(549\) | 1.10859e9 | − | 1.92014e9i | 0.285936 | − | 0.495255i | ||||
\(550\) | −5.34749e8 | − | 9.26213e8i | −0.137050 | − | 0.237378i | ||||
\(551\) | −1.03024e9 | −0.262366 | ||||||||
\(552\) | −2.06849e9 | − | 3.58272e9i | −0.523439 | − | 0.906622i | ||||
\(553\) | −2.54262e9 | + | 4.40395e9i | −0.639358 | + | 1.10740i | ||||
\(554\) | 4.42972e9 | − | 7.67250e9i | 1.10686 | − | 1.91714i | ||||
\(555\) | −5.90518e9 | −1.46625 | ||||||||
\(556\) | 2.46108e9 | − | 4.26272e9i | 0.607246 | − | 1.05178i | ||||
\(557\) | 8.97173e8 | 0.219980 | 0.109990 | − | 0.993933i | \(-0.464918\pi\) | ||||
0.109990 | + | 0.993933i | \(0.464918\pi\) | |||||||
\(558\) | −3.90657e9 | −0.951867 | ||||||||
\(559\) | 9.35152e8 | + | 6.20593e9i | 0.226434 | + | 1.50268i | ||||
\(560\) | 1.80449e9 | 0.434207 | ||||||||
\(561\) | −1.52833e9 | −0.365465 | ||||||||
\(562\) | −4.98587e9 | + | 8.63579e9i | −1.18485 | + | 2.05222i | ||||
\(563\) | 6.10272e9 | 1.44126 | 0.720632 | − | 0.693317i | \(-0.243852\pi\) | ||||
0.720632 | + | 0.693317i | \(0.243852\pi\) | |||||||
\(564\) | −1.80811e9 | + | 3.13174e9i | −0.424374 | + | 0.735037i | ||||
\(565\) | −2.54294e9 | + | 4.40449e9i | −0.593152 | + | 1.02737i | ||||
\(566\) | 2.32261e9 | + | 4.02287e9i | 0.538416 | + | 0.932564i | ||||
\(567\) | −6.45302e9 | −1.48670 | ||||||||
\(568\) | −8.54384e8 | − | 1.47984e9i | −0.195629 | − | 0.338840i | ||||
\(569\) | 1.67478e8 | − | 2.90081e8i | 0.0381123 | − | 0.0660124i | −0.846340 | − | 0.532643i | \(-0.821199\pi\) |
0.884452 | + | 0.466631i | \(0.154532\pi\) | |||||||
\(570\) | 9.54531e9 | 2.15888 | ||||||||
\(571\) | 2.94391e9 | − | 5.09901e9i | 0.661757 | − | 1.14620i | −0.318397 | − | 0.947958i | \(-0.603144\pi\) |
0.980154 | − | 0.198239i | \(-0.0635223\pi\) | |||||||
\(572\) | −3.44701e9 | − | 5.97040e9i | −0.770117 | − | 1.33388i | ||||
\(573\) | −3.05815e9 | − | 5.29687e9i | −0.679075 | − | 1.17619i | ||||
\(574\) | 1.78006e9 | + | 3.08315e9i | 0.392864 | + | 0.680460i | ||||
\(575\) | −8.78898e8 | −0.192797 | ||||||||
\(576\) | 1.34529e9 | + | 2.33011e9i | 0.293317 | + | 0.508040i | ||||
\(577\) | 1.61918e9 | + | 2.80449e9i | 0.350896 | + | 0.607770i | 0.986407 | − | 0.164322i | \(-0.0525437\pi\) |
−0.635511 | + | 0.772092i | \(0.719210\pi\) | |||||||
\(578\) | −2.72143e9 | + | 4.71365e9i | −0.586205 | + | 1.01534i | ||||
\(579\) | 2.71662e9 | − | 4.70532e9i | 0.581639 | − | 1.00743i | ||||
\(580\) | −1.44176e9 | −0.306828 | ||||||||
\(581\) | 5.41343e9 | 1.14513 | ||||||||
\(582\) | 7.29425e9 | − | 1.26340e10i | 1.53373 | − | 2.65651i | ||||
\(583\) | −8.09452e8 | + | 1.40201e9i | −0.169181 | + | 0.293030i | ||||
\(584\) | 3.33638e9 | + | 5.77878e9i | 0.693155 | + | 1.20058i | ||||
\(585\) | −1.25063e9 | − | 2.16616e9i | −0.258276 | − | 0.447347i | ||||
\(586\) | −3.23639e9 | −0.664383 | ||||||||
\(587\) | 2.84289e9 | + | 4.92403e9i | 0.580132 | + | 1.00482i | 0.995463 | + | 0.0951477i | \(0.0303323\pi\) |
−0.415331 | + | 0.909670i | \(0.636334\pi\) | |||||||
\(588\) | 2.28620e9 | + | 3.95982e9i | 0.463761 | + | 0.803258i | ||||
\(589\) | −4.52502e9 | − | 7.83756e9i | −0.912466 | − | 1.58044i | ||||
\(590\) | −2.38708e9 | + | 4.13455e9i | −0.478503 | + | 0.828792i | ||||
\(591\) | 2.44338e9 | 0.486894 | ||||||||
\(592\) | −1.59542e9 | + | 2.76335e9i | −0.316045 | + | 0.547406i | ||||
\(593\) | 2.54390e9 | + | 4.40616e9i | 0.500966 | + | 0.867698i | 0.999999 | + | 0.00111551i | \(0.000355077\pi\) |
−0.499034 | + | 0.866583i | \(0.666312\pi\) | |||||||
\(594\) | −3.40575e9 | −0.666747 | ||||||||
\(595\) | −1.41762e9 | − | 2.45539e9i | −0.275900 | − | 0.477872i | ||||
\(596\) | −7.64438e9 | + | 1.32405e10i | −1.47904 | + | 2.56178i | ||||
\(597\) | −3.18943e9 | + | 5.52425e9i | −0.613483 | + | 1.06258i | ||||
\(598\) | −8.81948e9 | −1.68651 | ||||||||
\(599\) | 2.67747e9 | − | 4.63751e9i | 0.509015 | − | 0.881640i | −0.490930 | − | 0.871199i | \(-0.663343\pi\) |
0.999945 | − | 0.0104413i | \(-0.00332362\pi\) | |||||||
\(600\) | −2.42439e9 | −0.458219 | ||||||||
\(601\) | −9.02767e9 | −1.69635 | −0.848174 | − | 0.529717i | \(-0.822298\pi\) | ||||
−0.848174 | + | 0.529717i | \(0.822298\pi\) | |||||||
\(602\) | −1.59820e9 | − | 1.06061e10i | −0.298567 | − | 1.98138i | ||||
\(603\) | −1.68073e9 | −0.312167 | ||||||||
\(604\) | −1.09904e10 | −2.02947 | ||||||||
\(605\) | 1.56359e9 | − | 2.70821e9i | 0.287064 | − | 0.497209i | ||||
\(606\) | 4.38533e9 | 0.800476 | ||||||||
\(607\) | 8.87250e8 | − | 1.53676e9i | 0.161022 | − | 0.278898i | −0.774213 | − | 0.632925i | \(-0.781854\pi\) |
0.935236 | + | 0.354026i | \(0.115188\pi\) | |||||||
\(608\) | −2.19425e9 | + | 3.80055e9i | −0.395934 | + | 0.685778i | ||||
\(609\) | −8.02338e8 | − | 1.38969e9i | −0.143945 | − | 0.249320i | ||||
\(610\) | 1.11898e10 | 1.99603 | ||||||||
\(611\) | 1.70868e9 | + | 2.95952e9i | 0.303051 | + | 0.524900i | ||||
\(612\) | −1.12357e9 | + | 1.94609e9i | −0.198140 | + | 0.343188i | ||||
\(613\) | −1.73810e9 | −0.304764 | −0.152382 | − | 0.988322i | \(-0.548694\pi\) | ||||
−0.152382 | + | 0.988322i | \(0.548694\pi\) | |||||||
\(614\) | −5.83808e8 | + | 1.01118e9i | −0.101784 | + | 0.176296i | ||||
\(615\) | 1.12864e9 | + | 1.95485e9i | 0.195655 | + | 0.338884i | ||||
\(616\) | 2.61135e9 | + | 4.52299e9i | 0.450124 | + | 0.779638i | ||||
\(617\) | −4.04456e9 | − | 7.00538e9i | −0.693223 | − | 1.20070i | −0.970776 | − | 0.239987i | \(-0.922857\pi\) |
0.277553 | − | 0.960710i | \(-0.410477\pi\) | |||||||
\(618\) | 2.82542e8 | 0.0481529 | ||||||||
\(619\) | 4.68061e9 | + | 8.10705e9i | 0.793204 | + | 1.37387i | 0.923973 | + | 0.382457i | \(0.124922\pi\) |
−0.130770 | + | 0.991413i | \(0.541745\pi\) | |||||||
\(620\) | −6.33249e9 | − | 1.09682e10i | −1.06710 | − | 1.84826i | ||||
\(621\) | −1.39940e9 | + | 2.42383e9i | −0.234488 | + | 0.406146i | ||||
\(622\) | 3.77009e9 | − | 6.52999e9i | 0.628183 | − | 1.08804i | ||||
\(623\) | 5.86237e9 | 0.971326 | ||||||||
\(624\) | −4.70071e9 | −0.774493 | ||||||||
\(625\) | 1.90771e9 | − | 3.30424e9i | 0.312559 | − | 0.541367i | ||||
\(626\) | 8.79606e9 | − | 1.52352e10i | 1.43311 | − | 2.48221i | ||||
\(627\) | 2.66905e9 | + | 4.62293e9i | 0.432434 | + | 0.748998i | ||||
\(628\) | −9.15459e9 | − | 1.58562e10i | −1.47496 | − | 2.55470i | ||||
\(629\) | 5.01349e9 | 0.803273 | ||||||||
\(630\) | 2.13736e9 | + | 3.70201e9i | 0.340553 | + | 0.589855i | ||||
\(631\) | −8.71589e8 | − | 1.50964e9i | −0.138105 | − | 0.239205i | 0.788674 | − | 0.614811i | \(-0.210768\pi\) |
−0.926779 | + | 0.375606i | \(0.877434\pi\) | |||||||
\(632\) | 4.50835e9 | + | 7.80869e9i | 0.710408 | + | 1.23046i | ||||
\(633\) | 1.01394e9 | − | 1.75619e9i | 0.158890 | − | 0.275206i | ||||
\(634\) | 1.67125e10 | 2.60452 | ||||||||
\(635\) | −1.02359e8 | + | 1.77291e8i | −0.0158642 | + | 0.0274776i | ||||
\(636\) | 4.13942e9 | + | 7.16968e9i | 0.638027 | + | 1.10510i | ||||
\(637\) | 4.32096e9 | 0.662357 | ||||||||
\(638\) | −6.27582e8 | − | 1.08700e9i | −0.0956749 | − | 0.165714i | ||||
\(639\) | 3.91076e8 | − | 6.77364e8i | 0.0592937 | − | 0.102700i | ||||
\(640\) | −5.07993e9 | + | 8.79870e9i | −0.765999 | + | 1.32675i | ||||
\(641\) | 1.04777e10 | 1.57131 | 0.785657 | − | 0.618662i | \(-0.212325\pi\) | ||||
0.785657 | + | 0.618662i | \(0.212325\pi\) | |||||||
\(642\) | 1.27855e10 | − | 2.21451e10i | 1.90697 | − | 3.30297i | ||||
\(643\) | 1.68033e9 | 0.249262 | 0.124631 | − | 0.992203i | \(-0.460225\pi\) | ||||
0.124631 | + | 0.992203i | \(0.460225\pi\) | |||||||
\(644\) | 9.68232e9 | 1.42850 | ||||||||
\(645\) | −1.01333e9 | − | 6.72473e9i | −0.148693 | − | 0.986769i | ||||
\(646\) | −8.10396e9 | −1.18272 | ||||||||
\(647\) | −1.12182e10 | −1.62838 | −0.814192 | − | 0.580596i | \(-0.802819\pi\) | ||||
−0.814192 | + | 0.580596i | \(0.802819\pi\) | |||||||
\(648\) | −5.72095e9 | + | 9.90898e9i | −0.825954 | + | 1.43059i | ||||
\(649\) | −2.66989e9 | −0.383387 | ||||||||
\(650\) | −2.58424e9 | + | 4.47604e9i | −0.369093 | + | 0.639288i | ||||
\(651\) | 7.04806e9 | − | 1.22076e10i | 1.00123 | − | 1.73419i | ||||
\(652\) | −3.04191e9 | − | 5.26874e9i | −0.429813 | − | 0.744458i | ||||
\(653\) | −7.17214e8 | −0.100798 | −0.0503991 | − | 0.998729i | \(-0.516049\pi\) | ||||
−0.0503991 | + | 0.998729i | \(0.516049\pi\) | |||||||
\(654\) | 1.17286e10 | + | 2.03145e10i | 1.63955 | + | 2.83978i | ||||
\(655\) | −4.87115e9 | + | 8.43708e9i | −0.677309 | + | 1.17313i | ||||
\(656\) | 1.21971e9 | 0.168691 | ||||||||
\(657\) | −1.52716e9 | + | 2.64511e9i | −0.210090 | + | 0.363886i | ||||
\(658\) | −2.92017e9 | − | 5.05788e9i | −0.399592 | − | 0.692114i | ||||
\(659\) | −3.00543e9 | − | 5.20556e9i | −0.409079 | − | 0.708546i | 0.585707 | − | 0.810523i | \(-0.300817\pi\) |
−0.994787 | + | 0.101976i | \(0.967483\pi\) | |||||||
\(660\) | 3.73517e9 | + | 6.46951e9i | 0.505716 | + | 0.875926i | ||||
\(661\) | −3.34765e9 | −0.450853 | −0.225427 | − | 0.974260i | \(-0.572378\pi\) | ||||
−0.225427 | + | 0.974260i | \(0.572378\pi\) | |||||||
\(662\) | −8.74174e9 | − | 1.51411e10i | −1.17110 | − | 2.02841i | ||||
\(663\) | 3.69291e9 | + | 6.39631e9i | 0.492121 | + | 0.852378i | ||||
\(664\) | 4.79930e9 | − | 8.31263e9i | 0.636194 | − | 1.10192i | ||||
\(665\) | −4.95143e9 | + | 8.57613e9i | −0.652913 | + | 1.13088i | ||||
\(666\) | −7.55887e9 | −0.991510 | ||||||||
\(667\) | −1.03148e9 | −0.134592 | ||||||||
\(668\) | −1.21378e10 | + | 2.10234e10i | −1.57552 | + | 2.72888i | ||||
\(669\) | 2.75396e9 | − | 4.76999e9i | 0.355603 | − | 0.615923i | ||||
\(670\) | −4.24119e9 | − | 7.34596e9i | −0.544786 | − | 0.943598i | ||||
\(671\) | 3.12887e9 | + | 5.41936e9i | 0.399815 | + | 0.692500i | ||||
\(672\) | −6.83542e9 | −0.868906 | ||||||||
\(673\) | −7.22545e9 | − | 1.25149e10i | −0.913718 | − | 1.58261i | −0.808767 | − | 0.588129i | \(-0.799865\pi\) |
−0.104951 | − | 0.994477i | \(-0.533469\pi\) | |||||||
\(674\) | 1.98956e9 | + | 3.44601e9i | 0.250292 | + | 0.433518i | ||||
\(675\) | 8.20090e8 | + | 1.42044e9i | 0.102636 | + | 0.177770i | ||||
\(676\) | −9.44466e9 | + | 1.63586e10i | −1.17591 | + | 2.03673i | ||||
\(677\) | −1.04059e10 | −1.28890 | −0.644451 | − | 0.764645i | \(-0.722914\pi\) | ||||
−0.644451 | + | 0.764645i | \(0.722914\pi\) | |||||||
\(678\) | −1.13212e10 | + | 1.96089e10i | −1.39504 | + | 2.41629i | ||||
\(679\) | 7.56748e9 | + | 1.31073e10i | 0.927699 | + | 1.60682i | ||||
\(680\) | −5.02720e9 | −0.613119 | ||||||||
\(681\) | −2.98861e9 | − | 5.17642e9i | −0.362622 | − | 0.628080i | ||||
\(682\) | 5.51293e9 | − | 9.54867e9i | 0.665483 | − | 1.15265i | ||||
\(683\) | −3.83705e9 | + | 6.64597e9i | −0.460813 | + | 0.798152i | −0.999002 | − | 0.0446725i | \(-0.985776\pi\) |
0.538188 | + | 0.842825i | \(0.319109\pi\) | |||||||
\(684\) | 7.84878e9 | 0.937790 | ||||||||
\(685\) | −6.75450e9 | + | 1.16991e10i | −0.802927 | + | 1.39071i | ||||
\(686\) | 9.55786e9 | 1.13039 | ||||||||
\(687\) | −1.49333e10 | −1.75715 | ||||||||
\(688\) | −3.42064e9 | − | 1.34265e9i | −0.400449 | − | 0.157182i | ||||
\(689\) | 7.82355e9 | 0.911248 | ||||||||
\(690\) | 9.55676e9 | 1.10749 | ||||||||
\(691\) | −6.99312e9 | + | 1.21124e10i | −0.806302 | + | 1.39656i | 0.109106 | + | 0.994030i | \(0.465201\pi\) |
−0.915408 | + | 0.402526i | \(0.868132\pi\) | |||||||
\(692\) | 1.23360e10 | 1.41515 | ||||||||
\(693\) | −1.19529e9 | + | 2.07030e9i | −0.136429 | + | 0.236302i | ||||
\(694\) | −6.59881e9 | + | 1.14295e10i | −0.749389 | + | 1.29798i | ||||
\(695\) | 2.52016e9 | + | 4.36505e9i | 0.284762 | + | 0.493222i | ||||
\(696\) | −2.84527e9 | −0.319883 | ||||||||
\(697\) | −9.58211e8 | − | 1.65967e9i | −0.107188 | − | 0.185655i | ||||
\(698\) | 7.04858e9 | − | 1.22085e10i | 0.784527 | − | 1.35884i | ||||
\(699\) | 3.87381e9 | 0.429011 | ||||||||
\(700\) | 2.83706e9 | − | 4.91394e9i | 0.312627 | − | 0.541485i | ||||
\(701\) | 2.69404e9 | + | 4.66621e9i | 0.295387 | + | 0.511625i | 0.975075 | − | 0.221876i | \(-0.0712182\pi\) |
−0.679688 | + | 0.733501i | \(0.737885\pi\) | |||||||
\(702\) | 8.22936e9 | + | 1.42537e10i | 0.897814 | + | 1.55506i | ||||
\(703\) | −8.75550e9 | − | 1.51650e10i | −0.950467 | − | 1.64626i | ||||
\(704\) | −7.59386e9 | −0.820273 | ||||||||
\(705\) | −1.85152e9 | − | 3.20692e9i | −0.199006 | − | 0.344688i | ||||
\(706\) | −1.02744e10 | − | 1.77958e10i | −1.09885 | − | 1.90327i | ||||
\(707\) | −2.27480e9 | + | 3.94007e9i | −0.242089 | + | 0.419311i | ||||
\(708\) | −6.82671e9 | + | 1.18242e10i | −0.722928 | + | 1.25215i | ||||
\(709\) | 1.09193e10 | 1.15062 | 0.575312 | − | 0.817934i | \(-0.304880\pi\) | ||||
0.575312 | + | 0.817934i | \(0.304880\pi\) | |||||||
\(710\) | 3.94740e9 | 0.413911 | ||||||||
\(711\) | −2.06360e9 | + | 3.57426e9i | −0.215319 | + | 0.372943i | ||||
\(712\) | 5.19731e9 | − | 9.00200e9i | 0.539633 | − | 0.934672i | ||||
\(713\) | −4.53045e9 | − | 7.84696e9i | −0.468088 | − | 0.810753i | ||||
\(714\) | −6.31127e9 | − | 1.09314e10i | −0.648893 | − | 1.12391i | ||||
\(715\) | 7.05953e9 | 0.722278 | ||||||||
\(716\) | −5.60257e9 | − | 9.70393e9i | −0.570416 | − | 0.987989i | ||||
\(717\) | 3.70705e9 | + | 6.42079e9i | 0.375587 | + | 0.650536i | ||||
\(718\) | 1.45166e10 | + | 2.51435e10i | 1.46362 | + | 2.53507i | ||||
\(719\) | 5.97913e9 | − | 1.03562e10i | 0.599911 | − | 1.03908i | −0.392923 | − | 0.919571i | \(-0.628536\pi\) |
0.992834 | − | 0.119505i | \(-0.0381306\pi\) | |||||||
\(720\) | 1.46453e9 | 0.146230 | ||||||||
\(721\) | −1.46563e8 | + | 2.53854e8i | −0.0145630 | + | 0.0252238i | ||||
\(722\) | 5.69721e9 | + | 9.86786e9i | 0.563355 | + | 0.975759i | ||||
\(723\) | −5.96386e9 | −0.586872 | ||||||||
\(724\) | −9.47239e8 | − | 1.64067e9i | −0.0927630 | − | 0.160670i | ||||
\(725\) | −3.02238e8 | + | 5.23491e8i | −0.0294555 | + | 0.0510184i | ||||
\(726\) | 6.96110e9 | − | 1.20570e10i | 0.675149 | − | 1.16939i | ||||
\(727\) | 5.10228e9 | 0.492486 | 0.246243 | − | 0.969208i | \(-0.420804\pi\) | ||||
0.246243 | + | 0.969208i | \(0.420804\pi\) | |||||||
\(728\) | 1.26197e10 | − | 2.18579e10i | 1.21224 | − | 2.09966i | ||||
\(729\) | 3.51958e9 | 0.336469 | ||||||||
\(730\) | −1.54147e10 | −1.46657 | ||||||||
\(731\) | 8.60315e8 | + | 5.70929e9i | 0.0814604 | + | 0.540594i | ||||
\(732\) | 3.20012e10 | 3.01562 | ||||||||
\(733\) | −4.76850e9 | −0.447217 | −0.223608 | − | 0.974679i | \(-0.571784\pi\) | ||||
−0.223608 | + | 0.974679i | \(0.571784\pi\) | |||||||
\(734\) | −7.82030e9 | + | 1.35452e10i | −0.729940 | + | 1.26429i | ||||
\(735\) | −4.68218e9 | −0.434953 | ||||||||
\(736\) | −2.19688e9 | + | 3.80511e9i | −0.203111 | + | 0.351799i | ||||
\(737\) | 2.37183e9 | − | 4.10814e9i | 0.218247 | − | 0.378015i | ||||
\(738\) | 1.44470e9 | + | 2.50229e9i | 0.132306 | + | 0.229161i | ||||
\(739\) | −4.39990e9 | −0.401040 | −0.200520 | − | 0.979690i | \(-0.564263\pi\) | ||||
−0.200520 | + | 0.979690i | \(0.564263\pi\) | |||||||
\(740\) | −1.22528e10 | − | 2.12225e10i | −1.11154 | − | 1.92524i | ||||
\(741\) | 1.28985e10 | − | 2.23409e10i | 1.16460 | − | 2.01714i | ||||
\(742\) | −1.33706e10 | −1.20154 | ||||||||
\(743\) | 5.05034e9 | − | 8.74744e9i | 0.451710 | − | 0.782384i | −0.546783 | − | 0.837275i | \(-0.684148\pi\) |
0.998492 | + | 0.0548902i | \(0.0174809\pi\) | |||||||
\(744\) | −1.24970e10 | − | 2.16454e10i | −1.11250 | − | 1.92690i | ||||
\(745\) | −7.82790e9 | − | 1.35583e10i | −0.693583 | − | 1.20132i | ||||
\(746\) | 9.07691e7 | + | 1.57217e8i | 0.00800483 | + | 0.0138648i | ||||
\(747\) | 4.39356e9 | 0.385651 | ||||||||
\(748\) | −3.17116e9 | − | 5.49261e9i | −0.277053 | − | 0.479869i | ||||
\(749\) | 1.32644e10 | + | 2.29746e10i | 1.15346 | + | 1.99784i | ||||
\(750\) | 1.24399e10 | − | 2.15466e10i | 1.07672 | − | 1.86494i | ||||
\(751\) | −7.39038e9 | + | 1.28005e10i | −0.636688 | + | 1.10278i | 0.349467 | + | 0.936949i | \(0.386363\pi\) |
−0.986155 | + | 0.165827i | \(0.946971\pi\) | |||||||
\(752\) | −2.00092e9 | −0.171580 | ||||||||
\(753\) | −1.75246e10 | −1.49578 | ||||||||
\(754\) | −3.03287e9 | + | 5.25308e9i | −0.257664 | + | 0.446287i | ||||
\(755\) | 5.62711e9 | − | 9.74644e9i | 0.475851 | − | 0.824198i | ||||
\(756\) | −9.03446e9 | − | 1.56481e10i | −0.760459 | − | 1.31715i | ||||
\(757\) | 2.20369e9 | + | 3.81690e9i | 0.184635 | + | 0.319797i | 0.943454 | − | 0.331505i | \(-0.107556\pi\) |
−0.758818 | + | 0.651302i | \(0.774223\pi\) | |||||||
\(758\) | 1.98663e10 | 1.65681 | ||||||||
\(759\) | 2.67225e9 | + | 4.62848e9i | 0.221836 | + | 0.384230i | ||||
\(760\) | 8.77943e9 | + | 1.52064e10i | 0.725469 | + | 1.25655i | ||||
\(761\) | 6.44206e9 | + | 1.11580e10i | 0.529881 | + | 0.917781i | 0.999392 | + | 0.0348543i | \(0.0110967\pi\) |
−0.469512 | + | 0.882926i | \(0.655570\pi\) | |||||||
\(762\) | −4.55703e8 | + | 7.89301e8i | −0.0373112 | + | 0.0646250i | ||||
\(763\) | −2.43359e10 | −1.98340 | ||||||||
\(764\) | 1.26909e10 | − | 2.19812e10i | 1.02959 | − | 1.78330i | ||||
\(765\) | −1.15055e9 | − | 1.99281e9i | −0.0929157 | − | 0.160935i | ||||
\(766\) | 3.08517e10 | 2.48015 | ||||||||
\(767\) | 6.45129e9 | + | 1.11740e10i | 0.516253 | + | 0.894177i | ||||
\(768\) | −1.18060e10 | + | 2.04487e10i | −0.940459 | + | 1.62892i | ||||
\(769\) | 3.25669e9 | − | 5.64075e9i | 0.258246 | − | 0.447296i | −0.707526 | − | 0.706688i | \(-0.750189\pi\) |
0.965772 | + | 0.259392i | \(0.0835220\pi\) | |||||||
\(770\) | −1.20649e10 | −0.952370 | ||||||||
\(771\) | −4.88608e9 | + | 8.46294e9i | −0.383946 | + | 0.665014i | ||||
\(772\) | 2.25471e10 | 1.76372 | ||||||||
\(773\) | 1.50111e10 | 1.16892 | 0.584459 | − | 0.811423i | \(-0.301307\pi\) | ||||
0.584459 | + | 0.811423i | \(0.301307\pi\) | |||||||
\(774\) | −1.29710e9 | − | 8.60793e9i | −0.100550 | − | 0.667275i | ||||
\(775\) | −5.30995e9 | −0.409765 | ||||||||
\(776\) | 2.68359e10 | 2.06158 | ||||||||
\(777\) | 1.36374e10 | − | 2.36206e10i | 1.04293 | − | 1.80641i | ||||
\(778\) | −1.89337e10 | −1.44148 | ||||||||
\(779\) | −3.34681e9 | + | 5.79685e9i | −0.253659 | + | 0.439350i | ||||
\(780\) | 1.80507e10 | − | 3.12647e10i | 1.36195 | − | 2.35897i | ||||
\(781\) | 1.10377e9 | + | 1.91178e9i | 0.0829085 | + | 0.143602i | ||||
\(782\) | −8.11369e9 | −0.606729 | ||||||||
\(783\) | 9.62459e8 | + | 1.66703e9i | 0.0716500 | + | 0.124101i | ||||
\(784\) | −1.26500e9 | + | 2.19104e9i | −0.0937527 | + | 0.162384i | ||||
\(785\) | 1.87487e10 | 1.38334 | ||||||||
\(786\) | −2.16864e10 | + | 3.75620e10i | −1.59297 | + | 2.75911i | ||||
\(787\) | −1.62601e9 | − | 2.81633e9i | −0.118908 | − | 0.205955i | 0.800427 | − | 0.599430i | \(-0.204606\pi\) |
−0.919335 | + | 0.393475i | \(0.871273\pi\) | |||||||
\(788\) | 5.06982e9 | + | 8.78119e9i | 0.369106 | + | 0.639310i | ||||
\(789\) | 3.65474e9 | + | 6.33019e9i | 0.264903 | + | 0.458825i | ||||
\(790\) | −2.08294e10 | −1.50308 | ||||||||
\(791\) | −1.17453e10 | − | 2.03434e10i | −0.843810 | − | 1.46152i | ||||
\(792\) | 2.11938e9 | + | 3.67087e9i | 0.151590 | + | 0.262562i | ||||
\(793\) | 1.51207e10 | − | 2.61897e10i | 1.07675 | − | 1.86498i | ||||
\(794\) | −2.99810e9 | + | 5.19286e9i | −0.212556 | + | 0.368159i | ||||
\(795\) | −8.47757e9 | −0.598393 | ||||||||
\(796\) | −2.64713e10 | −1.86028 | ||||||||
\(797\) | 5.17951e9 | − | 8.97117e9i | 0.362397 | − | 0.627690i | −0.625958 | − | 0.779857i | \(-0.715292\pi\) |
0.988355 | + | 0.152167i | \(0.0486252\pi\) | |||||||
\(798\) | −2.20438e10 | + | 3.81810e10i | −1.53560 | + | 2.65973i | ||||
\(799\) | 1.57194e9 | + | 2.72268e9i | 0.109024 | + | 0.188835i | ||||
\(800\) | 1.28744e9 | + | 2.22991e9i | 0.0889020 | + | 0.153983i | ||||
\(801\) | 4.75792e9 | 0.327117 | ||||||||
\(802\) | 4.18424e9 | + | 7.24731e9i | 0.286422 | + | 0.496097i | ||||
\(803\) | −4.31023e9 | − | 7.46553e9i | −0.293762 | − | 0.508811i | ||||
\(804\) | −1.21292e10 | − | 2.10084e10i | −0.823069 | − | 1.42560i | ||||
\(805\) | −4.95738e9 | + | 8.58643e9i | −0.334939 | + | 0.580132i | ||||
\(806\) | −5.32838e10 | −3.58445 | ||||||||
\(807\) | −8.21663e9 | + | 1.42316e10i | −0.550346 | + | 0.953228i | ||||
\(808\) | 4.03347e9 | + | 6.98618e9i | 0.268992 | + | 0.465908i | ||||
\(809\) | 5.36821e9 | 0.356459 | 0.178229 | − | 0.983989i | \(-0.442963\pi\) | ||||
0.178229 | + | 0.983989i | \(0.442963\pi\) | |||||||
\(810\) | −1.32159e10 | − | 2.28906e10i | −0.873774 | − | 1.51342i | ||||
\(811\) | −3.84900e9 | + | 6.66666e9i | −0.253381 | + | 0.438870i | −0.964455 | − | 0.264248i | \(-0.914876\pi\) |
0.711073 | + | 0.703118i | \(0.248209\pi\) | |||||||
\(812\) | 3.32958e9 | − | 5.76700e9i | 0.218245 | − | 0.378011i | ||||
\(813\) | 1.40297e10 | 0.915656 | ||||||||
\(814\) | 1.06670e10 | − | 1.84758e10i | 0.693199 | − | 1.20066i | ||||
\(815\) | 6.22987e9 | 0.403113 | ||||||||
\(816\) | −4.32453e9 | −0.278627 | ||||||||
\(817\) | 1.57672e10 | − | 1.25729e10i | 1.01153 | − | 0.806602i | ||||
\(818\) | 3.29955e9 | 0.210775 | ||||||||
\(819\) | 1.15528e10 | 0.734840 | ||||||||
\(820\) | −4.68367e9 | + | 8.11235e9i | −0.296645 | + | 0.513805i | ||||
\(821\) | −2.94840e8 | −0.0185946 | −0.00929728 | − | 0.999957i | \(-0.502959\pi\) | ||||
−0.00929728 | + | 0.999957i | \(0.502959\pi\) | |||||||
\(822\) | −3.00711e10 | + | 5.20847e10i | −1.88842 | + | 3.27083i | ||||
\(823\) | −4.05261e8 | + | 7.01933e8i | −0.0253417 | + | 0.0438931i | −0.878418 | − | 0.477893i | \(-0.841401\pi\) |
0.853076 | + | 0.521786i | \(0.174734\pi\) | |||||||
\(824\) | 2.59872e8 | + | 4.50111e8i | 0.0161813 | + | 0.0280268i | ||||
\(825\) | 3.13204e9 | 0.194195 | ||||||||
\(826\) | −1.10254e10 | − | 1.90965e10i | −0.680713 | − | 1.17903i | ||||
\(827\) | −4.90634e9 | + | 8.49802e9i | −0.301639 | + | 0.522455i | −0.976507 | − | 0.215484i | \(-0.930867\pi\) |
0.674868 | + | 0.737938i | \(0.264201\pi\) | |||||||
\(828\) | 7.85820e9 | 0.481080 | ||||||||
\(829\) | −9.84555e8 | + | 1.70530e9i | −0.0600205 | + | 0.103958i | −0.894474 | − | 0.447119i | \(-0.852450\pi\) |
0.834454 | + | 0.551078i | \(0.185783\pi\) | |||||||
\(830\) | 1.10868e10 | + | 1.92029e10i | 0.673028 | + | 1.16572i | ||||
\(831\) | 1.29725e10 | + | 2.24690e10i | 0.784188 | + | 1.35825i | ||||
\(832\) | 1.83491e10 | + | 3.17816e10i | 1.10455 | + | 1.91313i | ||||
\(833\) | 3.97516e9 | 0.238285 | ||||||||
\(834\) | 1.12198e10 | + | 1.94333e10i | 0.669736 | + | 1.16002i | ||||
\(835\) | −1.24292e10 | − | 2.15281e10i | −0.738825 | − | 1.27968i | ||||
\(836\) | −1.10761e10 | + | 1.91844e10i | −0.655642 | + | 1.13560i | ||||
\(837\) | −8.45462e9 | + | 1.46438e10i | −0.498374 | + | 0.863208i | ||||
\(838\) | 4.63354e9 | 0.271993 | ||||||||
\(839\) | 7.45062e9 | 0.435537 | 0.217769 | − | 0.976000i | \(-0.430122\pi\) | ||||
0.217769 | + | 0.976000i | \(0.430122\pi\) | |||||||
\(840\) | −1.36746e10 | + | 2.36852e10i | −0.796046 | + | 1.37879i | ||||
\(841\) | 8.27023e9 | − | 1.43245e10i | 0.479437 | − | 0.830409i | ||||
\(842\) | −1.18309e10 | − | 2.04917e10i | −0.683006 | − | 1.18300i | ||||
\(843\) | −1.46012e10 | − | 2.52900e10i | −0.839444 | − | 1.45396i | ||||
\(844\) | 8.41536e9 | 0.481808 | ||||||||
\(845\) | −9.67139e9 | − | 1.67513e10i | −0.551430 | − | 0.955105i | ||||
\(846\) | −2.37002e9 | − | 4.10499e9i | −0.134572 | − | 0.233086i | ||||
\(847\) | 7.22186e9 | + | 1.25086e10i | 0.408373 | + | 0.707323i | ||||
\(848\) | −2.29041e9 | + | 3.96711e9i | −0.128982 | + | 0.223403i | ||||
\(849\) | −1.36036e10 | −0.762914 | ||||||||
\(850\) | −2.37743e9 | + | 4.11783e9i | −0.132783 | + | 0.229987i | ||||
\(851\) | −8.76601e9 | − | 1.51832e10i | −0.487583 | − | 0.844518i | ||||
\(852\) | 1.12890e10 | 0.625341 | ||||||||
\(853\) | 5.40950e9 | + | 9.36954e9i | 0.298425 | + | 0.516888i | 0.975776 | − | 0.218772i | \(-0.0702052\pi\) |
−0.677350 | + | 0.735660i | \(0.736872\pi\) | |||||||
\(854\) | −2.58415e10 | + | 4.47589e10i | −1.41976 | + | 2.45910i | ||||
\(855\) | −4.01860e9 | + | 6.96042e9i | −0.219884 | + | 0.380850i | ||||
\(856\) | 4.70384e10 | 2.56327 | ||||||||
\(857\) | −4.09913e9 | + | 7.09991e9i | −0.222464 | + | 0.385318i | −0.955556 | − | 0.294811i | \(-0.904743\pi\) |
0.733092 | + | 0.680130i | \(0.238077\pi\) | |||||||
\(858\) | 3.14291e10 | 1.69874 | ||||||||
\(859\) | −1.63064e10 | −0.877772 | −0.438886 | − | 0.898543i | \(-0.644627\pi\) | ||||
−0.438886 | + | 0.898543i | \(0.644627\pi\) | |||||||
\(860\) | 2.20652e10 | − | 1.75951e10i | 1.18294 | − | 0.943293i | ||||
\(861\) | −1.04258e10 | −0.556673 | ||||||||
\(862\) | 2.21042e10 | 1.17544 | ||||||||
\(863\) | 1.25401e10 | − | 2.17201e10i | 0.664146 | − | 1.15033i | −0.315371 | − | 0.948969i | \(-0.602129\pi\) |
0.979516 | − | 0.201365i | \(-0.0645379\pi\) | |||||||
\(864\) | 8.19955e9 | 0.432506 | ||||||||
\(865\) | −6.31606e9 | + | 1.09397e10i | −0.331810 | + | 0.574712i | ||||
\(866\) | −6.59549e9 | + | 1.14237e10i | −0.345092 | + | 0.597716i | ||||
\(867\) | −7.96974e9 | − | 1.38040e10i | −0.415315 | − | 0.719346i | ||||
\(868\) | 5.84967e10 | 3.03607 | ||||||||
\(869\) | −5.82428e9 | − | 1.00880e10i | −0.301074 | − | 0.521475i | ||||
\(870\) | 3.28641e9 | − | 5.69222e9i | 0.169201 | − | 0.293065i | ||||
\(871\) | −2.29244e10 | −1.17553 | ||||||||
\(872\) | −2.15751e10 | + | 3.73691e10i | −1.10191 | + | 1.90856i | ||||
\(873\) | 6.14179e9 | + | 1.06379e10i | 0.312425 | + | 0.541135i | ||||
\(874\) | 1.41696e10 | + | 2.45425e10i | 0.717908 | + | 1.24345i | ||||
\(875\) | 1.29059e10 | + | 2.23537e10i | 0.651269 | + | 1.12803i | ||||
\(876\) | −4.40837e10 | −2.21572 | ||||||||
\(877\) | −1.03573e9 | − | 1.79394e9i | −0.0518501 | − | 0.0898070i | 0.838935 | − | 0.544231i | \(-0.183178\pi\) |
−0.890786 | + | 0.454424i | \(0.849845\pi\) | |||||||
\(878\) | −3.61092e8 | − | 6.25430e8i | −0.0180048 | − | 0.0311851i | ||||
\(879\) | 4.73890e9 | − | 8.20801e9i | 0.235351 | − | 0.407640i | ||||
\(880\) | −2.06674e9 | + | 3.57970e9i | −0.102234 | + | 0.177075i | ||||
\(881\) | 2.36331e9 | 0.116441 | 0.0582205 | − | 0.998304i | \(-0.481457\pi\) | ||||
0.0582205 | + | 0.998304i | \(0.481457\pi\) | |||||||
\(882\) | −5.99338e9 | −0.294125 | ||||||||
\(883\) | 7.20532e9 | − | 1.24800e10i | 0.352201 | − | 0.610030i | −0.634434 | − | 0.772977i | \(-0.718767\pi\) |
0.986635 | + | 0.162947i | \(0.0521000\pi\) | |||||||
\(884\) | −1.53250e10 | + | 2.65437e10i | −0.746136 | + | 1.29235i | ||||
\(885\) | −6.99060e9 | − | 1.21081e10i | −0.339010 | − | 0.587183i | ||||
\(886\) | −7.20609e9 | − | 1.24813e10i | −0.348082 | − | 0.602896i | ||||
\(887\) | −2.24383e10 | −1.07959 | −0.539793 | − | 0.841798i | \(-0.681498\pi\) | ||||
−0.539793 | + | 0.841798i | \(0.681498\pi\) | |||||||
\(888\) | −2.41805e10 | − | 4.18819e10i | −1.15883 | − | 2.00715i | ||||
\(889\) | −4.72773e8 | − | 8.18868e8i | −0.0225682 | − | 0.0390893i | ||||
\(890\) | 1.20062e10 | + | 2.07954e10i | 0.570876 | + | 0.988786i | ||||
\(891\) | 7.39083e9 | − | 1.28013e10i | 0.350043 | − | 0.606292i | ||||
\(892\) | 2.28570e10 | 1.07831 | ||||||||
\(893\) | 5.49042e9 | − | 9.50969e9i | 0.258003 | − | 0.446875i | ||||
\(894\) | −3.48499e10 | − | 6.03618e10i | −1.63125 | − | 2.82540i | ||||
\(895\) | 1.14741e10 | 0.534982 | ||||||||
\(896\) | −2.34631e10 | − | 4.06393e10i | −1.08970 | − | 1.88742i | ||||
\(897\) | 1.29140e10 | − | 2.23677e10i | 0.597430 | − | 1.03478i | ||||
\(898\) | 1.79011e10 | − | 3.10057e10i | 0.824922 | − | 1.42881i | ||||
\(899\) | −6.23177e9 | −0.286057 | ||||||||
\(900\) | 2.30257e9 | − | 3.98817e9i | 0.105284 | − | 0.182358i | ||||
\(901\) | 7.19745e9 | 0.327825 | ||||||||
\(902\) | −8.15500e9 | −0.369999 | ||||||||
\(903\) | 2.92389e10 | + | 1.14767e10i | 1.32146 | + | 0.518693i | ||||
\(904\) | −4.16512e10 | −1.87516 | ||||||||
\(905\) | 1.93996e9 | 0.0870006 | ||||||||
\(906\) | 2.50519e10 | − | 4.33912e10i | 1.11916 | − | 1.93844i | ||||
\(907\) | −3.94390e10 | −1.75509 | −0.877546 | − | 0.479492i | \(-0.840821\pi\) | ||||
−0.877546 | + | 0.479492i | \(0.840821\pi\) | |||||||
\(908\) | 1.24023e10 | − | 2.14814e10i | 0.549795 | − | 0.952273i | ||||
\(909\) | −1.84624e9 | + | 3.19778e9i | −0.0815293 | + | 0.141213i | ||||
\(910\) | 2.91525e10 | + | 5.04937e10i | 1.28242 | + | 2.22122i | ||||
\(911\) | 3.82698e10 | 1.67704 | 0.838518 | − | 0.544874i | \(-0.183422\pi\) | ||||
0.838518 | + | 0.544874i | \(0.183422\pi\) | |||||||
\(912\) | 7.55230e9 | + | 1.30810e10i | 0.329684 | + | 0.571029i | ||||
\(913\) | −6.20016e9 | + | 1.07390e10i | −0.269622 | + | 0.466999i | ||||
\(914\) | −3.84830e10 | −1.66708 | ||||||||
\(915\) | −1.63847e10 | + | 2.83791e10i | −0.707074 | + | 1.22469i | ||||
\(916\) | −3.09855e10 | − | 5.36684e10i | −1.33206 | − | 2.30720i | ||||
\(917\) | −2.24988e10 | − | 3.89690e10i | −0.963532 | − | 1.66889i | ||||
\(918\) | 7.57079e9 | + | 1.31130e10i | 0.322992 | + | 0.559439i | ||||
\(919\) | 1.66849e10 | 0.709119 | 0.354559 | − | 0.935033i | \(-0.384631\pi\) | ||||
0.354559 | + | 0.935033i | \(0.384631\pi\) | |||||||
\(920\) | 8.78997e9 | + | 1.52247e10i | 0.372160 | + | 0.644600i | ||||
\(921\) | −1.70969e9 | − | 2.96127e9i | −0.0721121 | − | 0.124902i | ||||
\(922\) | −2.15780e9 | + | 3.73741e9i | −0.0906676 | + | 0.157041i | ||||
\(923\) | 5.33409e9 | − | 9.23892e9i | 0.223283 | − | 0.386737i | ||||
\(924\) | −3.45039e10 | −1.43885 | ||||||||
\(925\) | −1.02743e10 | −0.426831 | ||||||||
\(926\) | −1.29226e10 | + | 2.23826e10i | −0.534825 | + | 0.926345i | ||||
\(927\) | −1.18951e8 | + | 2.06029e8i | −0.00490442 | + | 0.00849471i | ||||
\(928\) | 1.51094e9 | + | 2.61702e9i | 0.0620625 | + | 0.107495i | ||||
\(929\) | 2.27509e9 | + | 3.94058e9i | 0.0930988 | + | 0.161252i | 0.908814 | − | 0.417202i | \(-0.136989\pi\) |
−0.815715 | + | 0.578454i | \(0.803656\pi\) | |||||||
\(930\) | 5.77382e10 | 2.35382 | ||||||||
\(931\) | −6.94217e9 | − | 1.20242e10i | −0.281950 | − | 0.488351i | ||||
\(932\) | 8.03786e9 | + | 1.39220e10i | 0.325226 | + | 0.563308i | ||||
\(933\) | 1.10408e10 | + | 1.91232e10i | 0.445055 | + | 0.770858i | ||||
\(934\) | 3.08143e10 | − | 5.33719e10i | 1.23748 | − | 2.14338i | ||||
\(935\) | 6.49457e9 | 0.259842 | ||||||||
\(936\) | 1.02422e10 | − | 1.77399e10i | 0.408250 | − | 0.707110i | ||||
\(937\) | 8.60844e9 | + | 1.49103e10i | 0.341850 | + | 0.592102i | 0.984776 | − | 0.173826i | \(-0.0556131\pi\) |
−0.642926 | + | 0.765928i | \(0.722280\pi\) | |||||||
\(938\) | 3.91783e10 | 1.55001 | ||||||||
\(939\) | 2.57594e10 | + | 4.46166e10i | 1.01533 | + | 1.75860i | ||||
\(940\) | 7.68352e9 | − | 1.33082e10i | 0.301726 | − | 0.522604i | ||||
\(941\) | 9.76777e9 | − | 1.69183e10i | 0.382148 | − | 0.661900i | −0.609221 | − | 0.793000i | \(-0.708518\pi\) |
0.991369 | + | 0.131101i | \(0.0418511\pi\) | |||||||
\(942\) | 8.34694e10 | 3.25349 | ||||||||
\(943\) | −3.35083e9 | + | 5.80381e9i | −0.130125 | + | 0.225384i | ||||
\(944\) | −7.55469e9 | −0.292290 | ||||||||
\(945\) | 1.85027e10 | 0.713220 | ||||||||
\(946\) | 2.28705e10 | + | 8.97699e9i | 0.878326 | + | 0.344756i | ||||
\(947\) | −1.20563e10 | −0.461307 | −0.230654 | − | 0.973036i | \(-0.574086\pi\) | ||||
−0.230654 | + | 0.973036i | \(0.574086\pi\) | |||||||
\(948\) | −5.95690e10 | −2.27086 | ||||||||
\(949\) | −2.08297e10 | + | 3.60781e10i | −0.791137 | + | 1.37029i | ||||
\(950\) | 1.66077e10 | 0.628457 | ||||||||
\(951\) | −2.44713e10 | + | 4.23856e10i | −0.922626 | + | 1.59804i | ||||
\(952\) | 1.16098e10 | − | 2.01087e10i | 0.436108 | − | 0.755360i | ||||
\(953\) | 5.24759e9 | + | 9.08910e9i | 0.196397 | + | 0.340170i | 0.947358 | − | 0.320177i | \(-0.103743\pi\) |
−0.750961 | + | 0.660347i | \(0.770409\pi\) | |||||||
\(954\) | −1.08516e10 | −0.404647 | ||||||||
\(955\) | 1.29955e10 | + | 2.25089e10i | 0.482816 | + | 0.836262i | ||||
\(956\) | −1.53837e10 | + | 2.66453e10i | −0.569453 | + | 0.986321i | ||||
\(957\) | 3.67576e9 | 0.135568 | ||||||||
\(958\) | 3.43794e10 | − | 5.95468e10i | 1.26333 | − | 2.18816i | ||||
\(959\) | −3.11975e10 | − | 5.40357e10i | −1.14223 | − | 1.97841i | ||||
\(960\) | −1.98831e10 | − | 3.44385e10i | −0.725327 | − | 1.25630i | ||||
\(961\) | −1.36149e10 | − | 2.35816e10i | −0.494859 | − | 0.857121i | ||||
\(962\) | −1.03099e11 | −3.73373 | ||||||||
\(963\) | 1.07654e10 | + | 1.86463e10i | 0.388454 | + | 0.672821i | ||||
\(964\) | −1.23745e10 | − | 2.14333e10i | −0.444897 | − | 0.770584i | ||||
\(965\) | −1.15442e10 | + | 1.99951e10i | −0.413540 | + | 0.716272i | ||||
\(966\) | −2.20703e10 | + | 3.82269e10i | −0.787749 | + | 1.36442i | ||||
\(967\) | −6.98872e9 | −0.248545 | −0.124272 | − | 0.992248i | \(-0.539660\pi\) | ||||
−0.124272 | + | 0.992248i | \(0.539660\pi\) | |||||||
\(968\) | 2.56103e10 | 0.907509 | ||||||||
\(969\) | 1.18663e10 | − | 2.05530e10i | 0.418968 | − | 0.725674i | ||||
\(970\) | −3.09967e10 | + | 5.36878e10i | −1.09047 | + | 1.88875i | ||||
\(971\) | 2.28430e10 | + | 3.95652e10i | 0.800729 | + | 1.38690i | 0.919137 | + | 0.393939i | \(0.128888\pi\) |
−0.118408 | + | 0.992965i | \(0.537779\pi\) | |||||||
\(972\) | −1.96258e10 | − | 3.39928e10i | −0.685479 | − | 1.18729i | ||||
\(973\) | −2.32802e10 | −0.810198 | ||||||||
\(974\) | 1.08314e10 | + | 1.87605e10i | 0.375601 | + | 0.650560i | ||||
\(975\) | −7.56798e9 | − | 1.31081e10i | −0.261495 | − | 0.452923i | ||||
\(976\) | 8.85341e9 | + | 1.53346e10i | 0.304815 | + | 0.527955i | ||||
\(977\) | −2.66397e10 | + | 4.61413e10i | −0.913899 | + | 1.58292i | −0.105394 | + | 0.994431i | \(0.533610\pi\) |
−0.808505 | + | 0.588489i | \(0.799723\pi\) | |||||||
\(978\) | 2.77354e10 | 0.948088 | ||||||||
\(979\) | −6.71434e9 | + | 1.16296e10i | −0.228699 | + | 0.396118i | ||||
\(980\) | −9.71516e9 | − | 1.68271e10i | −0.329730 | − | 0.571109i | ||||
\(981\) | −1.97511e10 | −0.667958 | ||||||||
\(982\) | 6.66837e9 | + | 1.15500e10i | 0.224714 | + | 0.389215i | ||||
\(983\) | 4.37986e9 | − | 7.58613e9i | 0.147070 | − | 0.254732i | −0.783074 | − | 0.621929i | \(-0.786349\pi\) |
0.930143 | + | 0.367197i | \(0.119683\pi\) | |||||||
\(984\) | −9.24307e9 | + | 1.60095e10i | −0.309267 | + | 0.535666i | ||||
\(985\) | −1.03831e10 | −0.346177 | ||||||||
\(986\) | −2.79016e9 | + | 4.83269e9i | −0.0926956 | + | 0.160554i | ||||
\(987\) | 1.71035e10 | 0.566207 | ||||||||
\(988\) | 1.07054e11 | 3.53144 | ||||||||
\(989\) | 1.57861e10 | − | 1.25880e10i | 0.518906 | − | 0.413781i | ||||
\(990\) | −9.79190e9 | −0.320733 | ||||||||
\(991\) | 3.54374e10 | 1.15666 | 0.578328 | − | 0.815804i | \(-0.303705\pi\) | ||||
0.578328 | + | 0.815804i | \(0.303705\pi\) | |||||||
\(992\) | −1.32727e10 | + | 2.29890e10i | −0.431686 | + | 0.747702i | ||||
\(993\) | 5.12006e10 | 1.65941 | ||||||||
\(994\) | −9.11609e9 | + | 1.57895e10i | −0.294412 | + | 0.509937i | ||||
\(995\) | 1.35534e10 | − | 2.34751e10i | 0.436181 | − | 0.755488i | ||||
\(996\) | 3.17067e10 | + | 5.49176e10i | 1.01682 | + | 1.76118i | ||||
\(997\) | −4.63855e10 | −1.48234 | −0.741172 | − | 0.671315i | \(-0.765730\pi\) | ||||
−0.741172 | + | 0.671315i | \(0.765730\pi\) | |||||||
\(998\) | −3.12710e10 | − | 5.41629e10i | −0.995829 | − | 1.72483i | ||||
\(999\) | −1.63589e10 | + | 2.83345e10i | −0.519129 | + | 0.899159i |
(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 | 43.8.c.a.6.2 | ✓ | 50 | |
43.36 | even | 3 | inner | 43.8.c.a.36.2 | yes | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.8.c.a.6.2 | ✓ | 50 | 1.1 | even | 1 | trivial | |
43.8.c.a.36.2 | yes | 50 | 43.36 | even | 3 | inner |