Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.29 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 44.1717i | 1.38037i | 0.723635 | + | 0.690183i | \(0.242470\pi\) | ||||
−0.723635 | + | 0.690183i | \(0.757530\pi\) | |||||||
\(3\) | 389.187i | 1.60159i | 0.598937 | + | 0.800796i | \(0.295590\pi\) | ||||
−0.598937 | + | 0.800796i | \(0.704410\pi\) | |||||||
\(4\) | −927.142 | −0.905412 | ||||||||
\(5\) | − | 5234.98i | − | 1.67519i | −0.546290 | − | 0.837596i | \(-0.683960\pi\) | ||
0.546290 | − | 0.837596i | \(-0.316040\pi\) | |||||||
\(6\) | −17191.1 | −2.21078 | ||||||||
\(7\) | − | 21894.1i | − | 1.30268i | −0.758786 | − | 0.651340i | \(-0.774207\pi\) | ||
0.758786 | − | 0.651340i | \(-0.225793\pi\) | |||||||
\(8\) | 4278.39i | 0.130566i | ||||||||
\(9\) | −92417.4 | −1.56510 | ||||||||
\(10\) | 231238. | 2.31238 | ||||||||
\(11\) | 16244.7 | 0.100867 | 0.0504333 | − | 0.998727i | \(-0.483940\pi\) | ||||
0.0504333 | + | 0.998727i | \(0.483940\pi\) | |||||||
\(12\) | − | 360831.i | − | 1.45010i | ||||||
\(13\) | 326289. | 0.878790 | 0.439395 | − | 0.898294i | \(-0.355193\pi\) | ||||
0.439395 | + | 0.898294i | \(0.355193\pi\) | |||||||
\(14\) | 967102. | 1.79818 | ||||||||
\(15\) | 2.03738e6 | 2.68297 | ||||||||
\(16\) | −1.13838e6 | −1.08564 | ||||||||
\(17\) | 287393. | 0.202410 | 0.101205 | − | 0.994866i | \(-0.467730\pi\) | ||||
0.101205 | + | 0.994866i | \(0.467730\pi\) | |||||||
\(18\) | − | 4.08224e6i | − | 2.16041i | ||||||
\(19\) | − | 139732.i | − | 0.0564324i | −0.999602 | − | 0.0282162i | \(-0.991017\pi\) | ||
0.999602 | − | 0.0282162i | \(-0.00898269\pi\) | |||||||
\(20\) | 4.85357e6i | 1.51674i | ||||||||
\(21\) | 8.52091e6 | 2.08636 | ||||||||
\(22\) | 717555.i | 0.139233i | ||||||||
\(23\) | 1.90806e6 | 0.296450 | 0.148225 | − | 0.988954i | \(-0.452644\pi\) | ||||
0.148225 | + | 0.988954i | \(0.452644\pi\) | |||||||
\(24\) | −1.66509e6 | −0.209114 | ||||||||
\(25\) | −1.76393e7 | −1.80627 | ||||||||
\(26\) | 1.44127e7i | 1.21305i | ||||||||
\(27\) | − | 1.29865e7i | − | 0.905054i | ||||||
\(28\) | 2.02990e7i | 1.17946i | ||||||||
\(29\) | − | 3.83545e7i | − | 1.86994i | −0.354733 | − | 0.934968i | \(-0.615428\pi\) | ||
0.354733 | − | 0.934968i | \(-0.384572\pi\) | |||||||
\(30\) | 8.99948e7i | 3.70349i | ||||||||
\(31\) | 5.40348e7 | 1.88741 | 0.943703 | − | 0.330794i | \(-0.107317\pi\) | ||||
0.943703 | + | 0.330794i | \(0.107317\pi\) | |||||||
\(32\) | − | 4.59030e7i | − | 1.36802i | ||||||
\(33\) | 6.32221e6i | 0.161547i | ||||||||
\(34\) | 1.26946e7i | 0.279399i | ||||||||
\(35\) | −1.14615e8 | −2.18224 | ||||||||
\(36\) | 8.56840e7 | 1.41706 | ||||||||
\(37\) | − | 8.73532e7i | − | 1.25971i | −0.776713 | − | 0.629855i | \(-0.783114\pi\) | ||
0.776713 | − | 0.629855i | \(-0.216886\pi\) | |||||||
\(38\) | 6.17221e6 | 0.0778974 | ||||||||
\(39\) | 1.26987e8i | 1.40746i | ||||||||
\(40\) | 2.23973e7 | 0.218723 | ||||||||
\(41\) | 8.87662e7 | 0.766176 | 0.383088 | − | 0.923712i | \(-0.374861\pi\) | ||||
0.383088 | + | 0.923712i | \(0.374861\pi\) | |||||||
\(42\) | 3.76384e8i | 2.87994i | ||||||||
\(43\) | −6.67162e7 | + | 1.30998e8i | −0.453826 | + | 0.891091i | ||||
\(44\) | −1.50611e7 | −0.0913259 | ||||||||
\(45\) | 4.83803e8i | 2.62184i | ||||||||
\(46\) | 8.42821e7i | 0.409210i | ||||||||
\(47\) | 1.99511e8 | 0.869918 | 0.434959 | − | 0.900450i | \(-0.356763\pi\) | ||||
0.434959 | + | 0.900450i | \(0.356763\pi\) | |||||||
\(48\) | − | 4.43041e8i | − | 1.73875i | ||||||
\(49\) | −1.96878e8 | −0.696976 | ||||||||
\(50\) | − | 7.79160e8i | − | 2.49331i | ||||||
\(51\) | 1.11849e8i | 0.324177i | ||||||||
\(52\) | −3.02516e8 | −0.795667 | ||||||||
\(53\) | −3.58718e8 | −0.857776 | −0.428888 | − | 0.903358i | \(-0.641094\pi\) | ||||
−0.428888 | + | 0.903358i | \(0.641094\pi\) | |||||||
\(54\) | 5.73638e8 | 1.24931 | ||||||||
\(55\) | − | 8.50405e7i | − | 0.168971i | ||||||
\(56\) | 9.36717e7 | 0.170086 | ||||||||
\(57\) | 5.43819e7 | 0.0903817 | ||||||||
\(58\) | 1.69419e9 | 2.58120 | ||||||||
\(59\) | 9.43790e8 | 1.32013 | 0.660063 | − | 0.751211i | \(-0.270530\pi\) | ||||
0.660063 | + | 0.751211i | \(0.270530\pi\) | |||||||
\(60\) | −1.88894e9 | −2.42920 | ||||||||
\(61\) | − | 1.50091e9i | − | 1.77708i | −0.458803 | − | 0.888538i | \(-0.651722\pi\) | ||
0.458803 | − | 0.888538i | \(-0.348278\pi\) | |||||||
\(62\) | 2.38681e9i | 2.60531i | ||||||||
\(63\) | 2.02340e9i | 2.03882i | ||||||||
\(64\) | 8.61918e8 | 0.802723 | ||||||||
\(65\) | − | 1.70811e9i | − | 1.47214i | ||||||
\(66\) | −2.79263e8 | −0.222994 | ||||||||
\(67\) | −1.23620e9 | −0.915616 | −0.457808 | − | 0.889051i | \(-0.651365\pi\) | ||||
−0.457808 | + | 0.889051i | \(0.651365\pi\) | |||||||
\(68\) | −2.66454e8 | −0.183264 | ||||||||
\(69\) | 7.42590e8i | 0.474792i | ||||||||
\(70\) | − | 5.06276e9i | − | 3.01229i | ||||||
\(71\) | 1.85479e9i | 1.02802i | 0.857783 | + | 0.514012i | \(0.171841\pi\) | ||||
−0.857783 | + | 0.514012i | \(0.828159\pi\) | |||||||
\(72\) | − | 3.95398e8i | − | 0.204349i | ||||||
\(73\) | − | 1.84969e9i | − | 0.892247i | −0.894971 | − | 0.446124i | \(-0.852804\pi\) | ||
0.894971 | − | 0.446124i | \(-0.147196\pi\) | |||||||
\(74\) | 3.85854e9 | 1.73886 | ||||||||
\(75\) | − | 6.86500e9i | − | 2.89291i | ||||||
\(76\) | 1.29552e8i | 0.0510946i | ||||||||
\(77\) | − | 3.55663e8i | − | 0.131397i | ||||||
\(78\) | −5.60925e9 | −1.94282 | ||||||||
\(79\) | −8.05333e8 | −0.261722 | −0.130861 | − | 0.991401i | \(-0.541774\pi\) | ||||
−0.130861 | + | 0.991401i | \(0.541774\pi\) | |||||||
\(80\) | 5.95938e9i | 1.81866i | ||||||||
\(81\) | −4.02965e8 | −0.115569 | ||||||||
\(82\) | 3.92096e9i | 1.05760i | ||||||||
\(83\) | −6.35127e9 | −1.61239 | −0.806195 | − | 0.591649i | \(-0.798477\pi\) | ||||
−0.806195 | + | 0.591649i | \(0.798477\pi\) | |||||||
\(84\) | −7.90010e9 | −1.88902 | ||||||||
\(85\) | − | 1.50449e9i | − | 0.339075i | ||||||
\(86\) | −5.78640e9 | − | 2.94697e9i | −1.23003 | − | 0.626446i | ||||
\(87\) | 1.49271e10 | 2.99487 | ||||||||
\(88\) | 6.95010e7i | 0.0131698i | ||||||||
\(89\) | − | 3.36937e9i | − | 0.603390i | −0.953404 | − | 0.301695i | \(-0.902448\pi\) | ||
0.953404 | − | 0.301695i | \(-0.0975525\pi\) | |||||||
\(90\) | −2.13704e10 | −3.61910 | ||||||||
\(91\) | − | 7.14381e9i | − | 1.14478i | ||||||
\(92\) | −1.76904e9 | −0.268410 | ||||||||
\(93\) | 2.10296e10i | 3.02285i | ||||||||
\(94\) | 8.81277e9i | 1.20081i | ||||||||
\(95\) | −7.31495e8 | −0.0945351 | ||||||||
\(96\) | 1.78649e10 | 2.19100 | ||||||||
\(97\) | 1.34193e10 | 1.56269 | 0.781343 | − | 0.624102i | \(-0.214535\pi\) | ||||
0.781343 | + | 0.624102i | \(0.214535\pi\) | |||||||
\(98\) | − | 8.69646e9i | − | 0.962082i | ||||||
\(99\) | −1.50129e9 | −0.157866 | ||||||||
\(100\) | 1.63542e10 | 1.63542 | ||||||||
\(101\) | 1.38886e10 | 1.32145 | 0.660727 | − | 0.750626i | \(-0.270248\pi\) | ||||
0.660727 | + | 0.750626i | \(0.270248\pi\) | |||||||
\(102\) | −4.94058e9 | −0.447484 | ||||||||
\(103\) | 1.78504e9 | 0.153979 | 0.0769894 | − | 0.997032i | \(-0.475469\pi\) | ||||
0.0769894 | + | 0.997032i | \(0.475469\pi\) | |||||||
\(104\) | 1.39599e9i | 0.114740i | ||||||||
\(105\) | − | 4.46068e10i | − | 3.49506i | ||||||
\(106\) | − | 1.58452e10i | − | 1.18404i | ||||||
\(107\) | 1.17048e10 | 0.834537 | 0.417268 | − | 0.908783i | \(-0.362988\pi\) | ||||
0.417268 | + | 0.908783i | \(0.362988\pi\) | |||||||
\(108\) | 1.20404e10i | 0.819447i | ||||||||
\(109\) | −7.22912e9 | −0.469843 | −0.234921 | − | 0.972014i | \(-0.575483\pi\) | ||||
−0.234921 | + | 0.972014i | \(0.575483\pi\) | |||||||
\(110\) | 3.75638e9 | 0.233242 | ||||||||
\(111\) | 3.39967e10 | 2.01754 | ||||||||
\(112\) | 2.49238e10i | 1.41424i | ||||||||
\(113\) | 5.13237e9i | 0.278565i | 0.990253 | + | 0.139282i | \(0.0444795\pi\) | ||||
−0.990253 | + | 0.139282i | \(0.955520\pi\) | |||||||
\(114\) | 2.40214e9i | 0.124760i | ||||||||
\(115\) | − | 9.98863e9i | − | 0.496611i | ||||||
\(116\) | 3.55601e10i | 1.69306i | ||||||||
\(117\) | −3.01548e10 | −1.37539 | ||||||||
\(118\) | 4.16888e10i | 1.82226i | ||||||||
\(119\) | − | 6.29221e9i | − | 0.263675i | ||||||
\(120\) | 8.71672e9i | 0.350306i | ||||||||
\(121\) | −2.56735e10 | −0.989826 | ||||||||
\(122\) | 6.62979e10 | 2.45302 | ||||||||
\(123\) | 3.45467e10i | 1.22710i | ||||||||
\(124\) | −5.00979e10 | −1.70888 | ||||||||
\(125\) | 4.12187e10i | 1.35066i | ||||||||
\(126\) | −8.93771e10 | −2.81432 | ||||||||
\(127\) | −3.96185e9 | −0.119917 | −0.0599583 | − | 0.998201i | \(-0.519097\pi\) | ||||
−0.0599583 | + | 0.998201i | \(0.519097\pi\) | |||||||
\(128\) | − | 8.93230e9i | − | 0.259964i | ||||||
\(129\) | −5.09826e10 | − | 2.59651e10i | −1.42716 | − | 0.726843i | ||||
\(130\) | 7.54503e10 | 2.03210 | ||||||||
\(131\) | − | 2.31997e10i | − | 0.601349i | −0.953727 | − | 0.300674i | \(-0.902788\pi\) | ||
0.953727 | − | 0.300674i | \(-0.0972117\pi\) | |||||||
\(132\) | − | 5.86159e9i | − | 0.146267i | ||||||
\(133\) | −3.05932e9 | −0.0735134 | ||||||||
\(134\) | − | 5.46049e10i | − | 1.26389i | ||||||
\(135\) | −6.79842e10 | −1.51614 | ||||||||
\(136\) | 1.22958e9i | 0.0264278i | ||||||||
\(137\) | 3.32676e10i | 0.689317i | 0.938728 | + | 0.344658i | \(0.112005\pi\) | ||||
−0.938728 | + | 0.344658i | \(0.887995\pi\) | |||||||
\(138\) | −3.28015e10 | −0.655388 | ||||||||
\(139\) | 3.77175e10 | 0.726890 | 0.363445 | − | 0.931616i | \(-0.381600\pi\) | ||||
0.363445 | + | 0.931616i | \(0.381600\pi\) | |||||||
\(140\) | 1.06265e11 | 1.97583 | ||||||||
\(141\) | 7.76472e10i | 1.39325i | ||||||||
\(142\) | −8.19293e10 | −1.41905 | ||||||||
\(143\) | 5.30045e9 | 0.0886406 | ||||||||
\(144\) | 1.05206e11 | 1.69913 | ||||||||
\(145\) | −2.00785e11 | −3.13250 | ||||||||
\(146\) | 8.17041e10 | 1.23163 | ||||||||
\(147\) | − | 7.66225e10i | − | 1.11627i | ||||||
\(148\) | 8.09888e10i | 1.14056i | ||||||||
\(149\) | − | 4.43509e10i | − | 0.603908i | −0.953323 | − | 0.301954i | \(-0.902361\pi\) | ||
0.953323 | − | 0.301954i | \(-0.0976389\pi\) | |||||||
\(150\) | 3.03239e11 | 3.99327 | ||||||||
\(151\) | − | 4.70013e10i | − | 0.598722i | −0.954140 | − | 0.299361i | \(-0.903226\pi\) | ||
0.954140 | − | 0.299361i | \(-0.0967735\pi\) | |||||||
\(152\) | 5.97829e8 | 0.00736816 | ||||||||
\(153\) | −2.65601e10 | −0.316790 | ||||||||
\(154\) | 1.57103e10 | 0.181376 | ||||||||
\(155\) | − | 2.82871e11i | − | 3.16177i | ||||||
\(156\) | − | 1.17735e11i | − | 1.27433i | ||||||
\(157\) | 1.29297e11i | 1.35547i | 0.735308 | + | 0.677733i | \(0.237037\pi\) | ||||
−0.735308 | + | 0.677733i | \(0.762963\pi\) | |||||||
\(158\) | − | 3.55729e10i | − | 0.361272i | ||||||
\(159\) | − | 1.39608e11i | − | 1.37381i | ||||||
\(160\) | −2.40301e11 | −2.29169 | ||||||||
\(161\) | − | 4.17753e10i | − | 0.386180i | ||||||
\(162\) | − | 1.77997e10i | − | 0.159528i | ||||||
\(163\) | 4.46002e10i | 0.387613i | 0.981040 | + | 0.193807i | \(0.0620834\pi\) | ||||
−0.981040 | + | 0.193807i | \(0.937917\pi\) | |||||||
\(164\) | −8.22989e10 | −0.693705 | ||||||||
\(165\) | 3.30966e10 | 0.270623 | ||||||||
\(166\) | − | 2.80547e11i | − | 2.22569i | ||||||
\(167\) | −9.28129e9 | −0.0714539 | −0.0357270 | − | 0.999362i | \(-0.511375\pi\) | ||||
−0.0357270 | + | 0.999362i | \(0.511375\pi\) | |||||||
\(168\) | 3.64558e10i | 0.272408i | ||||||||
\(169\) | −3.13942e10 | −0.227727 | ||||||||
\(170\) | 6.64561e10 | 0.468048 | ||||||||
\(171\) | 1.29137e10i | 0.0883222i | ||||||||
\(172\) | 6.18554e10 | − | 1.21454e11i | 0.410899 | − | 0.806804i | ||||
\(173\) | −8.77693e10 | −0.566386 | −0.283193 | − | 0.959063i | \(-0.591394\pi\) | ||||
−0.283193 | + | 0.959063i | \(0.591394\pi\) | |||||||
\(174\) | 6.59355e11i | 4.13402i | ||||||||
\(175\) | 3.86198e11i | 2.35299i | ||||||||
\(176\) | −1.84926e10 | −0.109505 | ||||||||
\(177\) | 3.67311e11i | 2.11430i | ||||||||
\(178\) | 1.48831e11 | 0.832900 | ||||||||
\(179\) | − | 3.05725e11i | − | 1.66367i | −0.555026 | − | 0.831833i | \(-0.687292\pi\) | ||
0.555026 | − | 0.831833i | \(-0.312708\pi\) | |||||||
\(180\) | − | 4.48554e11i | − | 2.37384i | ||||||
\(181\) | −5.19389e10 | −0.267362 | −0.133681 | − | 0.991024i | \(-0.542680\pi\) | ||||
−0.133681 | + | 0.991024i | \(0.542680\pi\) | |||||||
\(182\) | 3.15555e11 | 1.58022 | ||||||||
\(183\) | 5.84135e11 | 2.84615 | ||||||||
\(184\) | 8.16341e9i | 0.0387064i | ||||||||
\(185\) | −4.57292e11 | −2.11026 | ||||||||
\(186\) | −9.28916e11 | −4.17265 | ||||||||
\(187\) | 4.66860e9 | 0.0204164 | ||||||||
\(188\) | −1.84975e11 | −0.787635 | ||||||||
\(189\) | −2.84329e11 | −1.17900 | ||||||||
\(190\) | − | 3.23114e10i | − | 0.130493i | ||||||
\(191\) | − | 4.65718e11i | − | 1.83213i | −0.401031 | − | 0.916064i | \(-0.631348\pi\) | ||
0.401031 | − | 0.916064i | \(-0.368652\pi\) | |||||||
\(192\) | 3.35447e11i | 1.28564i | ||||||||
\(193\) | −1.21544e11 | −0.453888 | −0.226944 | − | 0.973908i | \(-0.572873\pi\) | ||||
−0.226944 | + | 0.973908i | \(0.572873\pi\) | |||||||
\(194\) | 5.92754e11i | 2.15708i | ||||||||
\(195\) | 6.64775e11 | 2.35777 | ||||||||
\(196\) | 1.82534e11 | 0.631050 | ||||||||
\(197\) | 2.78554e11 | 0.938813 | 0.469406 | − | 0.882982i | \(-0.344468\pi\) | ||||
0.469406 | + | 0.882982i | \(0.344468\pi\) | |||||||
\(198\) | − | 6.63146e10i | − | 0.217913i | ||||||
\(199\) | 4.27701e11i | 1.37049i | 0.728314 | + | 0.685244i | \(0.240304\pi\) | ||||
−0.728314 | + | 0.685244i | \(0.759696\pi\) | |||||||
\(200\) | − | 7.54680e10i | − | 0.235838i | ||||||
\(201\) | − | 4.81111e11i | − | 1.46644i | ||||||
\(202\) | 6.13484e11i | 1.82409i | ||||||||
\(203\) | −8.39740e11 | −2.43593 | ||||||||
\(204\) | − | 1.03700e11i | − | 0.293514i | ||||||
\(205\) | − | 4.64689e11i | − | 1.28349i | ||||||
\(206\) | 7.88481e10i | 0.212547i | ||||||||
\(207\) | −1.76338e11 | −0.463973 | ||||||||
\(208\) | −3.71440e11 | −0.954051 | ||||||||
\(209\) | − | 2.26990e9i | − | 0.00569215i | ||||||
\(210\) | 1.97036e12 | 4.82446 | ||||||||
\(211\) | 1.70602e11i | 0.407917i | 0.978980 | + | 0.203959i | \(0.0653808\pi\) | ||||
−0.978980 | + | 0.203959i | \(0.934619\pi\) | |||||||
\(212\) | 3.32582e11 | 0.776640 | ||||||||
\(213\) | −7.21860e11 | −1.64647 | ||||||||
\(214\) | 5.17022e11i | 1.15197i | ||||||||
\(215\) | 6.85770e11 | + | 3.49258e11i | 1.49275 | + | 0.760245i | ||||
\(216\) | 5.55615e10 | 0.118169 | ||||||||
\(217\) | − | 1.18305e12i | − | 2.45869i | ||||||
\(218\) | − | 3.19323e11i | − | 0.648555i | ||||||
\(219\) | 7.19876e11 | 1.42902 | ||||||||
\(220\) | 7.88446e10i | 0.152988i | ||||||||
\(221\) | 9.37730e10 | 0.177876 | ||||||||
\(222\) | 1.50169e12i | 2.78495i | ||||||||
\(223\) | 5.36910e11i | 0.973593i | 0.873515 | + | 0.486796i | \(0.161835\pi\) | ||||
−0.873515 | + | 0.486796i | \(0.838165\pi\) | |||||||
\(224\) | −1.00501e12 | −1.78209 | ||||||||
\(225\) | 1.63018e12 | 2.82699 | ||||||||
\(226\) | −2.26706e11 | −0.384521 | ||||||||
\(227\) | − | 1.51475e11i | − | 0.251311i | −0.992074 | − | 0.125656i | \(-0.959897\pi\) | ||
0.992074 | − | 0.125656i | \(-0.0401034\pi\) | |||||||
\(228\) | −5.04198e10 | −0.0818327 | ||||||||
\(229\) | −4.10757e11 | −0.652240 | −0.326120 | − | 0.945328i | \(-0.605741\pi\) | ||||
−0.326120 | + | 0.945328i | \(0.605741\pi\) | |||||||
\(230\) | 4.41215e11 | 0.685506 | ||||||||
\(231\) | 1.38419e11 | 0.210444 | ||||||||
\(232\) | 1.64096e11 | 0.244150 | ||||||||
\(233\) | 1.03337e12i | 1.50479i | 0.658712 | + | 0.752395i | \(0.271101\pi\) | ||||
−0.658712 | + | 0.752395i | \(0.728899\pi\) | |||||||
\(234\) | − | 1.33199e12i | − | 1.89855i | ||||||
\(235\) | − | 1.04444e12i | − | 1.45728i | ||||||
\(236\) | −8.75027e11 | −1.19526 | ||||||||
\(237\) | − | 3.13425e11i | − | 0.419171i | ||||||
\(238\) | 2.77938e11 | 0.363968 | ||||||||
\(239\) | −6.49764e11 | −0.833232 | −0.416616 | − | 0.909082i | \(-0.636784\pi\) | ||||
−0.416616 | + | 0.909082i | \(0.636784\pi\) | |||||||
\(240\) | −2.31931e12 | −2.91275 | ||||||||
\(241\) | 9.03941e11i | 1.11187i | 0.831225 | + | 0.555936i | \(0.187640\pi\) | ||||
−0.831225 | + | 0.555936i | \(0.812360\pi\) | |||||||
\(242\) | − | 1.13404e12i | − | 1.36632i | ||||||
\(243\) | − | 9.23671e11i | − | 1.09015i | ||||||
\(244\) | 1.39156e12i | 1.60899i | ||||||||
\(245\) | 1.03065e12i | 1.16757i | ||||||||
\(246\) | −1.52599e12 | −1.69385 | ||||||||
\(247\) | − | 4.55930e10i | − | 0.0495923i | ||||||
\(248\) | 2.31182e11i | 0.246431i | ||||||||
\(249\) | − | 2.47183e12i | − | 2.58239i | ||||||
\(250\) | −1.82070e12 | −1.86440 | ||||||||
\(251\) | 1.76657e12 | 1.77322 | 0.886611 | − | 0.462516i | \(-0.153053\pi\) | ||||
0.886611 | + | 0.462516i | \(0.153053\pi\) | |||||||
\(252\) | − | 1.87598e12i | − | 1.84597i | ||||||
\(253\) | 3.09957e10 | 0.0299019 | ||||||||
\(254\) | − | 1.75002e11i | − | 0.165529i | ||||||
\(255\) | 5.85529e11 | 0.543060 | ||||||||
\(256\) | 1.27716e12 | 1.16157 | ||||||||
\(257\) | − | 8.68522e11i | − | 0.774667i | −0.921940 | − | 0.387333i | \(-0.873396\pi\) | ||
0.921940 | − | 0.387333i | \(-0.126604\pi\) | |||||||
\(258\) | 1.14692e12 | − | 2.25199e12i | 1.00331 | − | 1.97001i | ||||
\(259\) | −1.91252e12 | −1.64100 | ||||||||
\(260\) | 1.58366e12i | 1.33290i | ||||||||
\(261\) | 3.54462e12i | 2.92663i | ||||||||
\(262\) | 1.02477e12 | 0.830082 | ||||||||
\(263\) | − | 2.81196e11i | − | 0.223476i | −0.993738 | − | 0.111738i | \(-0.964358\pi\) | ||
0.993738 | − | 0.111738i | \(-0.0356417\pi\) | |||||||
\(264\) | −2.70489e10 | −0.0210926 | ||||||||
\(265\) | 1.87788e12i | 1.43694i | ||||||||
\(266\) | − | 1.35135e11i | − | 0.101475i | ||||||
\(267\) | 1.31131e12 | 0.966385 | ||||||||
\(268\) | 1.14613e12 | 0.829010 | ||||||||
\(269\) | 1.95784e12 | 1.39000 | 0.695002 | − | 0.719008i | \(-0.255403\pi\) | ||||
0.695002 | + | 0.719008i | \(0.255403\pi\) | |||||||
\(270\) | − | 3.00298e12i | − | 2.09283i | ||||||
\(271\) | −9.57099e11 | −0.654803 | −0.327401 | − | 0.944885i | \(-0.606173\pi\) | ||||
−0.327401 | + | 0.944885i | \(0.606173\pi\) | |||||||
\(272\) | −3.27161e11 | −0.219744 | ||||||||
\(273\) | 2.78028e12 | 1.83348 | ||||||||
\(274\) | −1.46949e12 | −0.951510 | ||||||||
\(275\) | −2.86545e11 | −0.182192 | ||||||||
\(276\) | − | 6.88487e11i | − | 0.429883i | ||||||
\(277\) | 1.00767e12i | 0.617900i | 0.951078 | + | 0.308950i | \(0.0999775\pi\) | ||||
−0.951078 | + | 0.308950i | \(0.900022\pi\) | |||||||
\(278\) | 1.66605e12i | 1.00337i | ||||||||
\(279\) | −4.99376e12 | −2.95397 | ||||||||
\(280\) | − | 4.90369e11i | − | 0.284927i | ||||||
\(281\) | −1.64012e12 | −0.936147 | −0.468073 | − | 0.883690i | \(-0.655052\pi\) | ||||
−0.468073 | + | 0.883690i | \(0.655052\pi\) | |||||||
\(282\) | −3.42981e12 | −1.92320 | ||||||||
\(283\) | −3.07182e12 | −1.69225 | −0.846124 | − | 0.532986i | \(-0.821070\pi\) | ||||
−0.846124 | + | 0.532986i | \(0.821070\pi\) | |||||||
\(284\) | − | 1.71965e12i | − | 0.930785i | ||||||
\(285\) | − | 2.84688e11i | − | 0.151407i | ||||||
\(286\) | 2.34130e11i | 0.122357i | ||||||||
\(287\) | − | 1.94346e12i | − | 0.998082i | ||||||
\(288\) | 4.24224e12i | 2.14108i | ||||||||
\(289\) | −1.93340e12 | −0.959030 | ||||||||
\(290\) | − | 8.86902e12i | − | 4.32400i | ||||||
\(291\) | 5.22262e12i | 2.50278i | ||||||||
\(292\) | 1.71493e12i | 0.807852i | ||||||||
\(293\) | 2.79147e12 | 1.29269 | 0.646346 | − | 0.763045i | \(-0.276296\pi\) | ||||
0.646346 | + | 0.763045i | \(0.276296\pi\) | |||||||
\(294\) | 3.38455e12 | 1.54086 | ||||||||
\(295\) | − | 4.94072e12i | − | 2.21146i | ||||||
\(296\) | 3.73731e11 | 0.164475 | ||||||||
\(297\) | − | 2.10962e11i | − | 0.0912898i | ||||||
\(298\) | 1.95905e12 | 0.833614 | ||||||||
\(299\) | 6.22577e11 | 0.260518 | ||||||||
\(300\) | 6.36483e12i | 2.61927i | ||||||||
\(301\) | 2.86809e12 | + | 1.46069e12i | 1.16081 | + | 0.591190i | ||||
\(302\) | 2.07613e12 | 0.826456 | ||||||||
\(303\) | 5.40526e12i | 2.11643i | ||||||||
\(304\) | 1.59068e11i | 0.0612653i | ||||||||
\(305\) | −7.85724e12 | −2.97694 | ||||||||
\(306\) | − | 1.17320e12i | − | 0.437287i | ||||||
\(307\) | 4.91023e11 | 0.180057 | 0.0900284 | − | 0.995939i | \(-0.471304\pi\) | ||||
0.0900284 | + | 0.995939i | \(0.471304\pi\) | |||||||
\(308\) | 3.29750e11i | 0.118968i | ||||||||
\(309\) | 6.94713e11i | 0.246611i | ||||||||
\(310\) | 1.24949e13 | 4.36440 | ||||||||
\(311\) | −1.24650e12 | −0.428439 | −0.214220 | − | 0.976785i | \(-0.568721\pi\) | ||||
−0.214220 | + | 0.976785i | \(0.568721\pi\) | |||||||
\(312\) | −5.43301e11 | −0.183767 | ||||||||
\(313\) | − | 5.02951e12i | − | 1.67419i | −0.547060 | − | 0.837093i | \(-0.684253\pi\) | ||
0.547060 | − | 0.837093i | \(-0.315747\pi\) | |||||||
\(314\) | −5.71125e12 | −1.87104 | ||||||||
\(315\) | 1.05924e13 | 3.41542 | ||||||||
\(316\) | 7.46658e11 | 0.236966 | ||||||||
\(317\) | −2.31349e12 | −0.722723 | −0.361362 | − | 0.932426i | \(-0.617688\pi\) | ||||
−0.361362 | + | 0.932426i | \(0.617688\pi\) | |||||||
\(318\) | 6.16674e12 | 1.89636 | ||||||||
\(319\) | − | 6.23057e11i | − | 0.188614i | ||||||
\(320\) | − | 4.51212e12i | − | 1.34472i | ||||||
\(321\) | 4.55536e12i | 1.33659i | ||||||||
\(322\) | 1.84529e12 | 0.533070 | ||||||||
\(323\) | − | 4.01580e10i | − | 0.0114225i | ||||||
\(324\) | 3.73606e11 | 0.104638 | ||||||||
\(325\) | −5.75552e12 | −1.58733 | ||||||||
\(326\) | −1.97007e12 | −0.535048 | ||||||||
\(327\) | − | 2.81348e12i | − | 0.752497i | ||||||
\(328\) | 3.79777e11i | 0.100037i | ||||||||
\(329\) | − | 4.36813e12i | − | 1.13323i | ||||||
\(330\) | 1.46194e12i | 0.373558i | ||||||||
\(331\) | 5.06669e12i | 1.27522i | 0.770361 | + | 0.637608i | \(0.220076\pi\) | ||||
−0.770361 | + | 0.637608i | \(0.779924\pi\) | |||||||
\(332\) | 5.88853e12 | 1.45988 | ||||||||
\(333\) | 8.07296e12i | 1.97157i | ||||||||
\(334\) | − | 4.09971e11i | − | 0.0986326i | ||||||
\(335\) | 6.47146e12i | 1.53383i | ||||||||
\(336\) | −9.70001e12 | −2.26504 | ||||||||
\(337\) | 2.41861e12 | 0.556437 | 0.278218 | − | 0.960518i | \(-0.410256\pi\) | ||||
0.278218 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(338\) | − | 1.38673e12i | − | 0.314347i | ||||||
\(339\) | −1.99745e12 | −0.446147 | ||||||||
\(340\) | 1.39488e12i | 0.307002i | ||||||||
\(341\) | 8.77778e11 | 0.190376 | ||||||||
\(342\) | −5.70420e11 | −0.121917 | ||||||||
\(343\) | − | 1.87407e12i | − | 0.394743i | ||||||
\(344\) | −5.60460e11 | − | 2.85438e11i | −0.116346 | − | 0.0592542i | ||||
\(345\) | 3.88744e12 | 0.795369 | ||||||||
\(346\) | − | 3.87692e12i | − | 0.781820i | ||||||
\(347\) | 1.55356e12i | 0.308803i | 0.988008 | + | 0.154402i | \(0.0493449\pi\) | ||||
−0.988008 | + | 0.154402i | \(0.950655\pi\) | |||||||
\(348\) | −1.38395e13 | −2.71159 | ||||||||
\(349\) | 5.81530e12i | 1.12317i | 0.827419 | + | 0.561585i | \(0.189808\pi\) | ||||
−0.827419 | + | 0.561585i | \(0.810192\pi\) | |||||||
\(350\) | −1.70591e13 | −3.24799 | ||||||||
\(351\) | − | 4.23736e12i | − | 0.795353i | ||||||
\(352\) | − | 7.45679e11i | − | 0.137987i | ||||||
\(353\) | 8.34462e12 | 1.52241 | 0.761207 | − | 0.648509i | \(-0.224607\pi\) | ||||
0.761207 | + | 0.648509i | \(0.224607\pi\) | |||||||
\(354\) | −1.62247e13 | −2.91851 | ||||||||
\(355\) | 9.70978e12 | 1.72214 | ||||||||
\(356\) | 3.12388e12i | 0.546317i | ||||||||
\(357\) | 2.44885e12 | 0.422300 | ||||||||
\(358\) | 1.35044e13 | 2.29647 | ||||||||
\(359\) | 5.63916e12 | 0.945675 | 0.472838 | − | 0.881150i | \(-0.343230\pi\) | ||||
0.472838 | + | 0.881150i | \(0.343230\pi\) | |||||||
\(360\) | −2.06990e12 | −0.342323 | ||||||||
\(361\) | 6.11154e12 | 0.996815 | ||||||||
\(362\) | − | 2.29423e12i | − | 0.369058i | ||||||
\(363\) | − | 9.99180e12i | − | 1.58530i | ||||||
\(364\) | 6.62333e12i | 1.03650i | ||||||||
\(365\) | −9.68310e12 | −1.49469 | ||||||||
\(366\) | 2.58023e13i | 3.92873i | ||||||||
\(367\) | −3.17914e12 | −0.477506 | −0.238753 | − | 0.971080i | \(-0.576739\pi\) | ||||
−0.238753 | + | 0.971080i | \(0.576739\pi\) | |||||||
\(368\) | −2.17209e12 | −0.321839 | ||||||||
\(369\) | −8.20354e12 | −1.19914 | ||||||||
\(370\) | − | 2.01994e13i | − | 2.91293i | ||||||
\(371\) | 7.85382e12i | 1.11741i | ||||||||
\(372\) | − | 1.94975e13i | − | 2.73693i | ||||||
\(373\) | 3.17793e12i | 0.440149i | 0.975483 | + | 0.220075i | \(0.0706301\pi\) | ||||
−0.975483 | + | 0.220075i | \(0.929370\pi\) | |||||||
\(374\) | 2.06220e11i | 0.0281821i | ||||||||
\(375\) | −1.60418e13 | −2.16320 | ||||||||
\(376\) | 8.53588e11i | 0.113582i | ||||||||
\(377\) | − | 1.25146e13i | − | 1.64328i | ||||||
\(378\) | − | 1.25593e13i | − | 1.62745i | ||||||
\(379\) | 4.13270e12 | 0.528491 | 0.264246 | − | 0.964455i | \(-0.414877\pi\) | ||||
0.264246 | + | 0.964455i | \(0.414877\pi\) | |||||||
\(380\) | 6.78199e11 | 0.0855932 | ||||||||
\(381\) | − | 1.54190e12i | − | 0.192057i | ||||||
\(382\) | 2.05716e13 | 2.52901 | ||||||||
\(383\) | − | 8.82149e12i | − | 1.07040i | −0.844724 | − | 0.535202i | \(-0.820235\pi\) | ||
0.844724 | − | 0.535202i | \(-0.179765\pi\) | |||||||
\(384\) | 3.47633e12 | 0.416356 | ||||||||
\(385\) | −1.86189e12 | −0.220115 | ||||||||
\(386\) | − | 5.36883e12i | − | 0.626532i | ||||||
\(387\) | 6.16574e12 | − | 1.21065e13i | 0.710281 | − | 1.39464i | ||||
\(388\) | −1.24416e13 | −1.41487 | ||||||||
\(389\) | − | 9.50961e12i | − | 1.06762i | −0.845606 | − | 0.533808i | \(-0.820761\pi\) | ||
0.845606 | − | 0.533808i | \(-0.179239\pi\) | |||||||
\(390\) | 2.93643e13i | 3.25459i | ||||||||
\(391\) | 5.48361e11 | 0.0600044 | ||||||||
\(392\) | − | 8.42323e11i | − | 0.0910014i | ||||||
\(393\) | 9.02903e12 | 0.963115 | ||||||||
\(394\) | 1.23042e13i | 1.29591i | ||||||||
\(395\) | 4.21590e12i | 0.438434i | ||||||||
\(396\) | 1.39191e12 | 0.142934 | ||||||||
\(397\) | −1.98113e12 | −0.200891 | −0.100446 | − | 0.994943i | \(-0.532027\pi\) | ||||
−0.100446 | + | 0.994943i | \(0.532027\pi\) | |||||||
\(398\) | −1.88923e13 | −1.89177 | ||||||||
\(399\) | − | 1.19065e12i | − | 0.117738i | ||||||
\(400\) | 2.00802e13 | 1.96096 | ||||||||
\(401\) | 6.65423e12 | 0.641765 | 0.320883 | − | 0.947119i | \(-0.396021\pi\) | ||||
0.320883 | + | 0.947119i | \(0.396021\pi\) | |||||||
\(402\) | 2.12515e13 | 2.02423 | ||||||||
\(403\) | 1.76310e13 | 1.65863 | ||||||||
\(404\) | −1.28767e13 | −1.19646 | ||||||||
\(405\) | 2.10951e12i | 0.193601i | ||||||||
\(406\) | − | 3.70928e13i | − | 3.36247i | ||||||
\(407\) | − | 1.41902e12i | − | 0.127063i | ||||||
\(408\) | −4.78535e11 | −0.0423266 | ||||||||
\(409\) | 2.33376e12i | 0.203911i | 0.994789 | + | 0.101955i | \(0.0325099\pi\) | ||||
−0.994789 | + | 0.101955i | \(0.967490\pi\) | |||||||
\(410\) | 2.05261e13 | 1.77169 | ||||||||
\(411\) | −1.29473e13 | −1.10400 | ||||||||
\(412\) | −1.65498e12 | −0.139414 | ||||||||
\(413\) | − | 2.06635e13i | − | 1.71970i | ||||||
\(414\) | − | 7.78914e12i | − | 0.640453i | ||||||
\(415\) | 3.32488e13i | 2.70106i | ||||||||
\(416\) | − | 1.49776e13i | − | 1.20220i | ||||||
\(417\) | 1.46791e13i | 1.16418i | ||||||||
\(418\) | 1.00266e11 | 0.00785725 | ||||||||
\(419\) | − | 5.16084e12i | − | 0.399623i | −0.979834 | − | 0.199811i | \(-0.935967\pi\) | ||
0.979834 | − | 0.199811i | \(-0.0640329\pi\) | |||||||
\(420\) | 4.13568e13i | 3.16447i | ||||||||
\(421\) | 1.86467e13i | 1.40991i | 0.709251 | + | 0.704956i | \(0.249033\pi\) | ||||
−0.709251 | + | 0.704956i | \(0.750967\pi\) | |||||||
\(422\) | −7.53579e12 | −0.563075 | ||||||||
\(423\) | −1.84383e13 | −1.36151 | ||||||||
\(424\) | − | 1.53474e12i | − | 0.111996i | ||||||
\(425\) | −5.06942e12 | −0.365606 | ||||||||
\(426\) | − | 3.18858e13i | − | 2.27274i | ||||||
\(427\) | −3.28612e13 | −2.31496 | ||||||||
\(428\) | −1.08520e13 | −0.755600 | ||||||||
\(429\) | 2.06287e12i | 0.141966i | ||||||||
\(430\) | −1.54273e13 | + | 3.02917e13i | −1.04942 | + | 2.06054i | ||||
\(431\) | 6.14696e12 | 0.413308 | 0.206654 | − | 0.978414i | \(-0.433743\pi\) | ||||
0.206654 | + | 0.978414i | \(0.433743\pi\) | |||||||
\(432\) | 1.47836e13i | 0.982564i | ||||||||
\(433\) | − | 3.26476e12i | − | 0.214492i | −0.994233 | − | 0.107246i | \(-0.965797\pi\) | ||
0.994233 | − | 0.107246i | \(-0.0342033\pi\) | |||||||
\(434\) | 5.22572e13 | 3.39389 | ||||||||
\(435\) | − | 7.81429e13i | − | 5.01699i | ||||||
\(436\) | 6.70242e12 | 0.425401 | ||||||||
\(437\) | − | 2.66617e11i | − | 0.0167294i | ||||||
\(438\) | 3.17982e13i | 1.97257i | ||||||||
\(439\) | −1.89155e13 | −1.16010 | −0.580049 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580049 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(440\) | 3.63836e11 | 0.0220619 | ||||||||
\(441\) | 1.81950e13 | 1.09083 | ||||||||
\(442\) | 4.14211e12i | 0.245533i | ||||||||
\(443\) | −1.44922e13 | −0.849405 | −0.424703 | − | 0.905333i | \(-0.639621\pi\) | ||||
−0.424703 | + | 0.905333i | \(0.639621\pi\) | |||||||
\(444\) | −3.15198e13 | −1.82671 | ||||||||
\(445\) | −1.76386e13 | −1.01079 | ||||||||
\(446\) | −2.37163e13 | −1.34391 | ||||||||
\(447\) | 1.72608e13 | 0.967214 | ||||||||
\(448\) | − | 1.88710e13i | − | 1.04569i | ||||||
\(449\) | 3.15308e13i | 1.72784i | 0.503629 | + | 0.863920i | \(0.331998\pi\) | ||||
−0.503629 | + | 0.863920i | \(0.668002\pi\) | |||||||
\(450\) | 7.20080e13i | 3.90228i | ||||||||
\(451\) | 1.44198e12 | 0.0772816 | ||||||||
\(452\) | − | 4.75844e12i | − | 0.252216i | ||||||
\(453\) | 1.82923e13 | 0.958909 | ||||||||
\(454\) | 6.69092e12 | 0.346902 | ||||||||
\(455\) | −3.73977e13 | −1.91773 | ||||||||
\(456\) | 2.32667e11i | 0.0118008i | ||||||||
\(457\) | 3.13837e12i | 0.157443i | 0.996897 | + | 0.0787214i | \(0.0250838\pi\) | ||||
−0.996897 | + | 0.0787214i | \(0.974916\pi\) | |||||||
\(458\) | − | 1.81438e13i | − | 0.900331i | ||||||
\(459\) | − | 3.73223e12i | − | 0.183192i | ||||||
\(460\) | 9.26087e12i | 0.449638i | ||||||||
\(461\) | −1.70711e13 | −0.819895 | −0.409947 | − | 0.912109i | \(-0.634453\pi\) | ||||
−0.409947 | + | 0.912109i | \(0.634453\pi\) | |||||||
\(462\) | 6.11423e12i | 0.290490i | ||||||||
\(463\) | 1.76507e13i | 0.829576i | 0.909918 | + | 0.414788i | \(0.136144\pi\) | ||||
−0.909918 | + | 0.414788i | \(0.863856\pi\) | |||||||
\(464\) | 4.36619e13i | 2.03008i | ||||||||
\(465\) | 1.10090e14 | 5.06386 | ||||||||
\(466\) | −4.56457e13 | −2.07716 | ||||||||
\(467\) | 3.03925e13i | 1.36830i | 0.729340 | + | 0.684152i | \(0.239827\pi\) | ||||
−0.729340 | + | 0.684152i | \(0.760173\pi\) | |||||||
\(468\) | 2.79577e13 | 1.24530 | ||||||||
\(469\) | 2.70655e13i | 1.19276i | ||||||||
\(470\) | 4.61346e13 | 2.01158 | ||||||||
\(471\) | −5.03205e13 | −2.17090 | ||||||||
\(472\) | 4.03790e12i | 0.172364i | ||||||||
\(473\) | −1.08378e12 | + | 2.12802e12i | −0.0457759 | + | 0.0898813i | ||||
\(474\) | 1.38445e13 | 0.578610 | ||||||||
\(475\) | 2.46479e12i | 0.101932i | ||||||||
\(476\) | 5.83378e12i | 0.238734i | ||||||||
\(477\) | 3.31518e13 | 1.34250 | ||||||||
\(478\) | − | 2.87012e13i | − | 1.15017i | ||||||
\(479\) | 4.42392e13 | 1.75440 | 0.877201 | − | 0.480123i | \(-0.159408\pi\) | ||||
0.877201 | + | 0.480123i | \(0.159408\pi\) | |||||||
\(480\) | − | 9.35221e13i | − | 3.67035i | ||||||
\(481\) | − | 2.85024e13i | − | 1.10702i | ||||||
\(482\) | −3.99286e13 | −1.53479 | ||||||||
\(483\) | 1.62584e13 | 0.618503 | ||||||||
\(484\) | 2.38030e13 | 0.896200 | ||||||||
\(485\) | − | 7.02498e13i | − | 2.61780i | ||||||
\(486\) | 4.08001e13 | 1.50481 | ||||||||
\(487\) | −1.57076e13 | −0.573411 | −0.286705 | − | 0.958019i | \(-0.592560\pi\) | ||||
−0.286705 | + | 0.958019i | \(0.592560\pi\) | |||||||
\(488\) | 6.42149e12 | 0.232026 | ||||||||
\(489\) | −1.73578e13 | −0.620798 | ||||||||
\(490\) | −4.55258e13 | −1.61167 | ||||||||
\(491\) | 1.54818e13i | 0.542519i | 0.962506 | + | 0.271260i | \(0.0874402\pi\) | ||||
−0.962506 | + | 0.271260i | \(0.912560\pi\) | |||||||
\(492\) | − | 3.20296e13i | − | 1.11103i | ||||||
\(493\) | − | 1.10228e13i | − | 0.378493i | ||||||
\(494\) | 2.01392e12 | 0.0684555 | ||||||||
\(495\) | 7.85922e12i | 0.264456i | ||||||||
\(496\) | −6.15120e13 | −2.04905 | ||||||||
\(497\) | 4.06091e13 | 1.33919 | ||||||||
\(498\) | 1.09185e14 | 3.56465 | ||||||||
\(499\) | − | 2.61506e13i | − | 0.845237i | −0.906308 | − | 0.422618i | \(-0.861111\pi\) | ||
0.906308 | − | 0.422618i | \(-0.138889\pi\) | |||||||
\(500\) | − | 3.82156e13i | − | 1.22290i | ||||||
\(501\) | − | 3.61216e12i | − | 0.114440i | ||||||
\(502\) | 7.80326e13i | 2.44770i | ||||||||
\(503\) | 9.51220e12i | 0.295421i | 0.989031 | + | 0.147710i | \(0.0471904\pi\) | ||||
−0.989031 | + | 0.147710i | \(0.952810\pi\) | |||||||
\(504\) | −8.65690e12 | −0.266201 | ||||||||
\(505\) | − | 7.27065e13i | − | 2.21369i | ||||||
\(506\) | 1.36914e12i | 0.0412756i | ||||||||
\(507\) | − | 1.22182e13i | − | 0.364726i | ||||||
\(508\) | 3.67320e12 | 0.108574 | ||||||||
\(509\) | −3.68569e13 | −1.07877 | −0.539387 | − | 0.842058i | \(-0.681344\pi\) | ||||
−0.539387 | + | 0.842058i | \(0.681344\pi\) | |||||||
\(510\) | 2.58638e13i | 0.749621i | ||||||||
\(511\) | −4.04974e13 | −1.16231 | ||||||||
\(512\) | 4.72676e13i | 1.34343i | ||||||||
\(513\) | −1.81464e12 | −0.0510744 | ||||||||
\(514\) | 3.83641e13 | 1.06932 | ||||||||
\(515\) | − | 9.34462e12i | − | 0.257944i | ||||||
\(516\) | 4.72681e13 | + | 2.40733e13i | 1.29217 | + | 0.658093i | ||||
\(517\) | 3.24100e12 | 0.0877457 | ||||||||
\(518\) | − | 8.44795e13i | − | 2.26518i | ||||||
\(519\) | − | 3.41587e13i | − | 0.907119i | ||||||
\(520\) | 7.30798e12 | 0.192212 | ||||||||
\(521\) | 3.11431e13i | 0.811285i | 0.914032 | + | 0.405643i | \(0.132952\pi\) | ||||
−0.914032 | + | 0.405643i | \(0.867048\pi\) | |||||||
\(522\) | −1.56572e14 | −4.03982 | ||||||||
\(523\) | 6.70568e13i | 1.71370i | 0.515568 | + | 0.856849i | \(0.327581\pi\) | ||||
−0.515568 | + | 0.856849i | \(0.672419\pi\) | |||||||
\(524\) | 2.15094e13i | 0.544468i | ||||||||
\(525\) | −1.50303e14 | −3.76853 | ||||||||
\(526\) | 1.24209e13 | 0.308479 | ||||||||
\(527\) | 1.55292e13 | 0.382029 | ||||||||
\(528\) | − | 7.19706e12i | − | 0.175382i | ||||||
\(529\) | −3.77858e13 | −0.912117 | ||||||||
\(530\) | −8.29492e13 | −1.98350 | ||||||||
\(531\) | −8.72226e13 | −2.06612 | ||||||||
\(532\) | 2.83642e12 | 0.0665599 | ||||||||
\(533\) | 2.89634e13 | 0.673308 | ||||||||
\(534\) | 5.79230e13i | 1.33397i | ||||||||
\(535\) | − | 6.12744e13i | − | 1.39801i | ||||||
\(536\) | − | 5.28893e12i | − | 0.119548i | ||||||
\(537\) | 1.18984e14 | 2.66451 | ||||||||
\(538\) | 8.64812e13i | 1.91872i | ||||||||
\(539\) | −3.19823e12 | −0.0703016 | ||||||||
\(540\) | 6.30310e13 | 1.37273 | ||||||||
\(541\) | −7.26190e12 | −0.156698 | −0.0783491 | − | 0.996926i | \(-0.524965\pi\) | ||||
−0.0783491 | + | 0.996926i | \(0.524965\pi\) | |||||||
\(542\) | − | 4.22767e13i | − | 0.903868i | ||||||
\(543\) | − | 2.02139e13i | − | 0.428205i | ||||||
\(544\) | − | 1.31922e13i | − | 0.276900i | ||||||
\(545\) | 3.78442e13i | 0.787077i | ||||||||
\(546\) | 1.22810e14i | 2.53087i | ||||||||
\(547\) | −2.42391e12 | −0.0494971 | −0.0247485 | − | 0.999694i | \(-0.507879\pi\) | ||||
−0.0247485 | + | 0.999694i | \(0.507879\pi\) | |||||||
\(548\) | − | 3.08438e13i | − | 0.624116i | ||||||
\(549\) | 1.38710e14i | 2.78130i | ||||||||
\(550\) | − | 1.26572e13i | − | 0.251492i | ||||||
\(551\) | −5.35936e12 | −0.105525 | ||||||||
\(552\) | −3.17709e12 | −0.0619918 | ||||||||
\(553\) | 1.76321e13i | 0.340940i | ||||||||
\(554\) | −4.45104e13 | −0.852928 | ||||||||
\(555\) | − | 1.77972e14i | − | 3.37977i | ||||||
\(556\) | −3.49695e13 | −0.658135 | ||||||||
\(557\) | −7.15510e13 | −1.33457 | −0.667283 | − | 0.744805i | \(-0.732543\pi\) | ||||
−0.667283 | + | 0.744805i | \(0.732543\pi\) | |||||||
\(558\) | − | 2.20583e14i | − | 4.07756i | ||||||
\(559\) | −2.17687e13 | + | 4.27431e13i | −0.398818 | + | 0.783082i | ||||
\(560\) | 1.30475e14 | 2.36913 | ||||||||
\(561\) | 1.81696e12i | 0.0326987i | ||||||||
\(562\) | − | 7.24469e13i | − | 1.29223i | ||||||
\(563\) | 7.78919e13 | 1.37705 | 0.688526 | − | 0.725212i | \(-0.258258\pi\) | ||||
0.688526 | + | 0.725212i | \(0.258258\pi\) | |||||||
\(564\) | − | 7.19900e13i | − | 1.26147i | ||||||
\(565\) | 2.68678e13 | 0.466649 | ||||||||
\(566\) | − | 1.35688e14i | − | 2.33592i | ||||||
\(567\) | 8.82257e12i | 0.150550i | ||||||||
\(568\) | −7.93552e12 | −0.134225 | ||||||||
\(569\) | −5.62609e13 | −0.943289 | −0.471645 | − | 0.881789i | \(-0.656340\pi\) | ||||
−0.471645 | + | 0.881789i | \(0.656340\pi\) | |||||||
\(570\) | 1.25752e13 | 0.208997 | ||||||||
\(571\) | 9.80201e12i | 0.161486i | 0.996735 | + | 0.0807430i | \(0.0257293\pi\) | ||||
−0.996735 | + | 0.0807430i | \(0.974271\pi\) | |||||||
\(572\) | −4.91427e12 | −0.0802563 | ||||||||
\(573\) | 1.81251e14 | 2.93432 | ||||||||
\(574\) | 8.58460e13 | 1.37772 | ||||||||
\(575\) | −3.36569e13 | −0.535469 | ||||||||
\(576\) | −7.96562e13 | −1.25634 | ||||||||
\(577\) | 8.14357e13i | 1.27331i | 0.771147 | + | 0.636657i | \(0.219683\pi\) | ||||
−0.771147 | + | 0.636657i | \(0.780317\pi\) | |||||||
\(578\) | − | 8.54016e13i | − | 1.32381i | ||||||
\(579\) | − | 4.73035e13i | − | 0.726943i | ||||||
\(580\) | 1.86156e14 | 2.83620 | ||||||||
\(581\) | 1.39056e14i | 2.10043i | ||||||||
\(582\) | −2.30692e14 | −3.45476 | ||||||||
\(583\) | −5.82725e12 | −0.0865209 | ||||||||
\(584\) | 7.91371e12 | 0.116497 | ||||||||
\(585\) | 1.57859e14i | 2.30405i | ||||||||
\(586\) | 1.23304e14i | 1.78439i | ||||||||
\(587\) | − | 7.99336e13i | − | 1.14693i | −0.819228 | − | 0.573467i | \(-0.805598\pi\) | ||
0.819228 | − | 0.573467i | \(-0.194402\pi\) | |||||||
\(588\) | 7.10399e13i | 1.01069i | ||||||||
\(589\) | − | 7.55041e12i | − | 0.106511i | ||||||
\(590\) | 2.18240e14 | 3.05263 | ||||||||
\(591\) | 1.08410e14i | 1.50360i | ||||||||
\(592\) | 9.94409e13i | 1.36759i | ||||||||
\(593\) | 3.00724e13i | 0.410105i | 0.978751 | + | 0.205052i | \(0.0657365\pi\) | ||||
−0.978751 | + | 0.205052i | \(0.934264\pi\) | |||||||
\(594\) | 9.31856e12 | 0.126013 | ||||||||
\(595\) | −3.29396e13 | −0.441706 | ||||||||
\(596\) | 4.11195e13i | 0.546785i | ||||||||
\(597\) | −1.66456e14 | −2.19496 | ||||||||
\(598\) | 2.75003e13i | 0.359610i | ||||||||
\(599\) | 8.26667e13 | 1.07200 | 0.536002 | − | 0.844217i | \(-0.319934\pi\) | ||||
0.536002 | + | 0.844217i | \(0.319934\pi\) | |||||||
\(600\) | 2.93712e13 | 0.377715 | ||||||||
\(601\) | − | 1.17845e13i | − | 0.150293i | −0.997172 | − | 0.0751466i | \(-0.976058\pi\) | ||
0.997172 | − | 0.0751466i | \(-0.0239425\pi\) | |||||||
\(602\) | −6.45214e13 | + | 1.26688e14i | −0.816058 | + | 1.60234i | ||||
\(603\) | 1.14246e14 | 1.43303 | ||||||||
\(604\) | 4.35769e13i | 0.542090i | ||||||||
\(605\) | 1.34400e14i | 1.65815i | ||||||||
\(606\) | −2.38760e14 | −2.92145 | ||||||||
\(607\) | 1.83173e13i | 0.222289i | 0.993804 | + | 0.111145i | \(0.0354517\pi\) | ||||
−0.993804 | + | 0.111145i | \(0.964548\pi\) | |||||||
\(608\) | −6.41413e12 | −0.0772005 | ||||||||
\(609\) | − | 3.26816e14i | − | 3.90136i | ||||||
\(610\) | − | 3.47068e14i | − | 4.10927i | ||||||
\(611\) | 6.50983e13 | 0.764476 | ||||||||
\(612\) | 2.46250e13 | 0.286826 | ||||||||
\(613\) | 3.12591e13 | 0.361138 | 0.180569 | − | 0.983562i | \(-0.442206\pi\) | ||||
0.180569 | + | 0.983562i | \(0.442206\pi\) | |||||||
\(614\) | 2.16893e13i | 0.248545i | ||||||||
\(615\) | 1.80851e14 | 2.05563 | ||||||||
\(616\) | 1.52167e12 | 0.0171560 | ||||||||
\(617\) | −5.75834e13 | −0.643979 | −0.321990 | − | 0.946743i | \(-0.604352\pi\) | ||||
−0.321990 | + | 0.946743i | \(0.604352\pi\) | |||||||
\(618\) | −3.06867e13 | −0.340414 | ||||||||
\(619\) | 2.57630e13 | 0.283494 | 0.141747 | − | 0.989903i | \(-0.454728\pi\) | ||||
0.141747 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(620\) | 2.62262e14i | 2.86270i | ||||||||
\(621\) | − | 2.47790e13i | − | 0.268304i | ||||||
\(622\) | − | 5.50600e13i | − | 0.591404i | ||||||
\(623\) | −7.37694e13 | −0.786025 | ||||||||
\(624\) | − | 1.44559e14i | − | 1.52800i | ||||||
\(625\) | 4.35199e13 | 0.456339 | ||||||||
\(626\) | 2.22162e14 | 2.31099 | ||||||||
\(627\) | 8.83417e11 | 0.00911650 | ||||||||
\(628\) | − | 1.19876e14i | − | 1.22726i | ||||||
\(629\) | − | 2.51047e13i | − | 0.254977i | ||||||
\(630\) | 4.67887e14i | 4.71453i | ||||||||
\(631\) | − | 7.65352e13i | − | 0.765094i | −0.923936 | − | 0.382547i | \(-0.875047\pi\) | ||
0.923936 | − | 0.382547i | \(-0.124953\pi\) | |||||||
\(632\) | − | 3.44553e12i | − | 0.0341720i | ||||||
\(633\) | −6.63961e13 | −0.653317 | ||||||||
\(634\) | − | 1.02191e14i | − | 0.997623i | ||||||
\(635\) | 2.07402e13i | 0.200883i | ||||||||
\(636\) | 1.29437e14i | 1.24386i | ||||||||
\(637\) | −6.42392e13 | −0.612496 | ||||||||
\(638\) | 2.75215e13 | 0.260357 | ||||||||
\(639\) | − | 1.71415e14i | − | 1.60896i | ||||||
\(640\) | −4.67604e13 | −0.435490 | ||||||||
\(641\) | 7.91033e13i | 0.730978i | 0.930816 | + | 0.365489i | \(0.119098\pi\) | ||||
−0.930816 | + | 0.365489i | \(0.880902\pi\) | |||||||
\(642\) | −2.01218e14 | −1.84498 | ||||||||
\(643\) | −7.07860e13 | −0.644010 | −0.322005 | − | 0.946738i | \(-0.604357\pi\) | ||||
−0.322005 | + | 0.946738i | \(0.604357\pi\) | |||||||
\(644\) | 3.87316e13i | 0.349652i | ||||||||
\(645\) | −1.35926e14 | + | 2.66893e14i | −1.21760 | + | 2.39077i | ||||
\(646\) | 1.77385e12 | 0.0157672 | ||||||||
\(647\) | 5.00521e12i | 0.0441470i | 0.999756 | + | 0.0220735i | \(0.00702678\pi\) | ||||
−0.999756 | + | 0.0220735i | \(0.992973\pi\) | |||||||
\(648\) | − | 1.72404e12i | − | 0.0150894i | ||||||
\(649\) | 1.53316e13 | 0.133157 | ||||||||
\(650\) | − | 2.54231e14i | − | 2.19110i | ||||||
\(651\) | 4.60426e14 | 3.93781 | ||||||||
\(652\) | − | 4.13507e13i | − | 0.350950i | ||||||
\(653\) | − | 4.06276e13i | − | 0.342181i | −0.985255 | − | 0.171090i | \(-0.945271\pi\) | ||
0.985255 | − | 0.171090i | \(-0.0547290\pi\) | |||||||
\(654\) | 1.24276e14 | 1.03872 | ||||||||
\(655\) | −1.21450e14 | −1.00737 | ||||||||
\(656\) | −1.01049e14 | −0.831792 | ||||||||
\(657\) | 1.70944e14i | 1.39645i | ||||||||
\(658\) | 1.92948e14 | 1.56427 | ||||||||
\(659\) | 1.05908e14 | 0.852123 | 0.426062 | − | 0.904694i | \(-0.359901\pi\) | ||||
0.426062 | + | 0.904694i | \(0.359901\pi\) | |||||||
\(660\) | −3.06853e13 | −0.245025 | ||||||||
\(661\) | 4.93221e13 | 0.390872 | 0.195436 | − | 0.980716i | \(-0.437388\pi\) | ||||
0.195436 | + | 0.980716i | \(0.437388\pi\) | |||||||
\(662\) | −2.23804e14 | −1.76027 | ||||||||
\(663\) | 3.64952e13i | 0.284884i | ||||||||
\(664\) | − | 2.71732e13i | − | 0.210524i | ||||||
\(665\) | 1.60155e13i | 0.123149i | ||||||||
\(666\) | −3.56597e14 | −2.72149 | ||||||||
\(667\) | − | 7.31826e13i | − | 0.554343i | ||||||
\(668\) | 8.60508e12 | 0.0646952 | ||||||||
\(669\) | −2.08958e14 | −1.55930 | ||||||||
\(670\) | −2.85856e14 | −2.11725 | ||||||||
\(671\) | − | 2.43818e13i | − | 0.179248i | ||||||
\(672\) | − | 3.91136e14i | − | 2.85418i | ||||||
\(673\) | 2.16473e14i | 1.56794i | 0.620801 | + | 0.783968i | \(0.286807\pi\) | ||||
−0.620801 | + | 0.783968i | \(0.713193\pi\) | |||||||
\(674\) | 1.06834e14i | 0.768087i | ||||||||
\(675\) | 2.29074e14i | 1.63477i | ||||||||
\(676\) | 2.91068e13 | 0.206187 | ||||||||
\(677\) | − | 1.92061e14i | − | 1.35050i | −0.737588 | − | 0.675251i | \(-0.764036\pi\) | ||
0.737588 | − | 0.675251i | \(-0.235964\pi\) | |||||||
\(678\) | − | 8.82309e13i | − | 0.615846i | ||||||
\(679\) | − | 2.93804e14i | − | 2.03568i | ||||||
\(680\) | 6.43681e12 | 0.0442717 | ||||||||
\(681\) | 5.89521e13 | 0.402498 | ||||||||
\(682\) | 3.87730e13i | 0.262789i | ||||||||
\(683\) | 1.63569e14 | 1.10052 | 0.550260 | − | 0.834994i | \(-0.314529\pi\) | ||||
0.550260 | + | 0.834994i | \(0.314529\pi\) | |||||||
\(684\) | − | 1.19728e13i | − | 0.0799679i | ||||||
\(685\) | 1.74155e14 | 1.15474 | ||||||||
\(686\) | 8.27809e13 | 0.544891 | ||||||||
\(687\) | − | 1.59861e14i | − | 1.04462i | ||||||
\(688\) | 7.59482e13 | − | 1.49125e14i | 0.492692 | − | 0.967405i | ||||
\(689\) | −1.17046e14 | −0.753805 | ||||||||
\(690\) | 1.71715e14i | 1.09790i | ||||||||
\(691\) | 5.58274e13i | 0.354370i | 0.984178 | + | 0.177185i | \(0.0566991\pi\) | ||||
−0.984178 | + | 0.177185i | \(0.943301\pi\) | |||||||
\(692\) | 8.13746e13 | 0.512812 | ||||||||
\(693\) | 3.28695e13i | 0.205649i | ||||||||
\(694\) | −6.86236e13 | −0.426262 | ||||||||
\(695\) | − | 1.97450e14i | − | 1.21768i | ||||||
\(696\) | 6.38639e13i | 0.391029i | ||||||||
\(697\) | 2.55108e13 | 0.155081 | ||||||||
\(698\) | −2.56872e14 | −1.55039 | ||||||||
\(699\) | −4.02174e14 | −2.41006 | ||||||||
\(700\) | − | 3.58061e14i | − | 2.13043i | ||||||
\(701\) | −8.36705e13 | −0.494290 | −0.247145 | − | 0.968978i | \(-0.579492\pi\) | ||||
−0.247145 | + | 0.968978i | \(0.579492\pi\) | |||||||
\(702\) | 1.87172e14 | 1.09788 | ||||||||
\(703\) | −1.22061e13 | −0.0710884 | ||||||||
\(704\) | 1.40016e13 | 0.0809680 | ||||||||
\(705\) | 4.06481e14 | 2.33397 | ||||||||
\(706\) | 3.68596e14i | 2.10149i | ||||||||
\(707\) | − | 3.04079e14i | − | 1.72143i | ||||||
\(708\) | − | 3.40549e14i | − | 1.91431i | ||||||
\(709\) | 1.75974e14 | 0.982241 | 0.491120 | − | 0.871092i | \(-0.336587\pi\) | ||||
0.491120 | + | 0.871092i | \(0.336587\pi\) | |||||||
\(710\) | 4.28898e14i | 2.37718i | ||||||||
\(711\) | 7.44267e13 | 0.409620 | ||||||||
\(712\) | 1.44155e13 | 0.0787823 | ||||||||
\(713\) | 1.03101e14 | 0.559522 | ||||||||
\(714\) | 1.08170e14i | 0.582928i | ||||||||
\(715\) | − | 2.77477e13i | − | 0.148490i | ||||||
\(716\) | 2.83451e14i | 1.50630i | ||||||||
\(717\) | − | 2.52880e14i | − | 1.33450i | ||||||
\(718\) | 2.49091e14i | 1.30538i | ||||||||
\(719\) | −1.71319e14 | −0.891583 | −0.445792 | − | 0.895137i | \(-0.647078\pi\) | ||||
−0.445792 | + | 0.895137i | \(0.647078\pi\) | |||||||
\(720\) | − | 5.50750e14i | − | 2.84637i | ||||||
\(721\) | − | 3.90818e13i | − | 0.200585i | ||||||
\(722\) | 2.69957e14i | 1.37597i | ||||||||
\(723\) | −3.51802e14 | −1.78077 | ||||||||
\(724\) | 4.81547e13 | 0.242073 | ||||||||
\(725\) | 6.76549e14i | 3.37761i | ||||||||
\(726\) | 4.41355e14 | 2.18829 | ||||||||
\(727\) | 2.33883e14i | 1.15167i | 0.817567 | + | 0.575833i | \(0.195322\pi\) | ||||
−0.817567 | + | 0.575833i | \(0.804678\pi\) | |||||||
\(728\) | 3.05640e13 | 0.149470 | ||||||||
\(729\) | 3.35686e14 | 1.63040 | ||||||||
\(730\) | − | 4.27719e14i | − | 2.06321i | ||||||
\(731\) | −1.91737e13 | + | 3.76478e13i | −0.0918586 | + | 0.180365i | ||||
\(732\) | −5.41576e14 | −2.57694 | ||||||||
\(733\) | 1.03433e14i | 0.488809i | 0.969673 | + | 0.244405i | \(0.0785925\pi\) | ||||
−0.969673 | + | 0.244405i | \(0.921407\pi\) | |||||||
\(734\) | − | 1.40428e14i | − | 0.659133i | ||||||
\(735\) | −4.01117e14 | −1.86997 | ||||||||
\(736\) | − | 8.75855e13i | − | 0.405549i | ||||||
\(737\) | −2.00816e13 | −0.0923551 | ||||||||
\(738\) | − | 3.62365e14i | − | 1.65525i | ||||||
\(739\) | − | 1.10575e14i | − | 0.501690i | −0.968027 | − | 0.250845i | \(-0.919292\pi\) | ||
0.968027 | − | 0.250845i | \(-0.0807084\pi\) | |||||||
\(740\) | 4.23975e14 | 1.91065 | ||||||||
\(741\) | 1.77442e13 | 0.0794266 | ||||||||
\(742\) | −3.46917e14 | −1.54243 | ||||||||
\(743\) | − | 6.99827e13i | − | 0.309063i | −0.987988 | − | 0.154531i | \(-0.950613\pi\) | ||
0.987988 | − | 0.154531i | \(-0.0493867\pi\) | |||||||
\(744\) | −8.99730e13 | −0.394682 | ||||||||
\(745\) | −2.32176e14 | −1.01166 | ||||||||
\(746\) | −1.40375e14 | −0.607567 | ||||||||
\(747\) | 5.86968e14 | 2.52355 | ||||||||
\(748\) | −4.32845e12 | −0.0184852 | ||||||||
\(749\) | − | 2.56267e14i | − | 1.08713i | ||||||
\(750\) | − | 7.08594e14i | − | 2.98601i | ||||||
\(751\) | − | 2.78846e14i | − | 1.16725i | −0.812023 | − | 0.583626i | \(-0.801633\pi\) | ||
0.812023 | − | 0.583626i | \(-0.198367\pi\) | |||||||
\(752\) | −2.27119e14 | −0.944419 | ||||||||
\(753\) | 6.87527e14i | 2.83998i | ||||||||
\(754\) | 5.52794e14 | 2.26833 | ||||||||
\(755\) | −2.46051e14 | −1.00297 | ||||||||
\(756\) | 2.63613e14 | 1.06748 | ||||||||
\(757\) | 2.25706e14i | 0.907955i | 0.891013 | + | 0.453977i | \(0.149995\pi\) | ||||
−0.891013 | + | 0.453977i | \(0.850005\pi\) | |||||||
\(758\) | 1.82548e14i | 0.729511i | ||||||||
\(759\) | 1.20631e13i | 0.0478907i | ||||||||
\(760\) | − | 3.12962e12i | − | 0.0123431i | ||||||
\(761\) | 9.98414e13i | 0.391190i | 0.980685 | + | 0.195595i | \(0.0626638\pi\) | ||||
−0.980685 | + | 0.195595i | \(0.937336\pi\) | |||||||
\(762\) | 6.81084e13 | 0.265110 | ||||||||
\(763\) | 1.58275e14i | 0.612055i | ||||||||
\(764\) | 4.31786e14i | 1.65883i | ||||||||
\(765\) | 1.39041e14i | 0.530685i | ||||||||
\(766\) | 3.89660e14 | 1.47755 | ||||||||
\(767\) | 3.07948e14 | 1.16011 | ||||||||
\(768\) | 4.97053e14i | 1.86036i | ||||||||
\(769\) | −2.32066e14 | −0.862940 | −0.431470 | − | 0.902127i | \(-0.642005\pi\) | ||||
−0.431470 | + | 0.902127i | \(0.642005\pi\) | |||||||
\(770\) | − | 8.22428e13i | − | 0.303840i | ||||||
\(771\) | 3.38017e14 | 1.24070 | ||||||||
\(772\) | 1.12689e14 | 0.410956 | ||||||||
\(773\) | − | 8.76719e13i | − | 0.317660i | −0.987306 | − | 0.158830i | \(-0.949228\pi\) | ||
0.987306 | − | 0.158830i | \(-0.0507722\pi\) | |||||||
\(774\) | 5.34764e14 | + | 2.72351e14i | 1.92512 | + | 0.980448i | ||||
\(775\) | −9.53139e14 | −3.40916 | ||||||||
\(776\) | 5.74131e13i | 0.204034i | ||||||||
\(777\) | − | 7.44329e14i | − | 2.62821i | ||||||
\(778\) | 4.20056e14 | 1.47370 | ||||||||
\(779\) | − | 1.24035e13i | − | 0.0432372i | ||||||
\(780\) | −6.16341e14 | −2.13476 | ||||||||
\(781\) | 3.01305e13i | 0.103693i | ||||||||
\(782\) | 2.42221e13i | 0.0828280i | ||||||||
\(783\) | −4.98092e14 | −1.69239 | ||||||||
\(784\) | 2.24122e14 | 0.756666 | ||||||||
\(785\) | 6.76864e14 | 2.27067 | ||||||||
\(786\) | 3.98828e14i | 1.32945i | ||||||||
\(787\) | −3.41632e14 | −1.13158 | −0.565789 | − | 0.824550i | \(-0.691428\pi\) | ||||
−0.565789 | + | 0.824550i | \(0.691428\pi\) | |||||||
\(788\) | −2.58260e14 | −0.850012 | ||||||||
\(789\) | 1.09438e14 | 0.357917 | ||||||||
\(790\) | −1.86223e14 | −0.605200 | ||||||||
\(791\) | 1.12369e14 | 0.362881 | ||||||||
\(792\) | − | 6.42311e12i | − | 0.0206120i | ||||||
\(793\) | − | 4.89731e14i | − | 1.56168i | ||||||
\(794\) | − | 8.75101e13i | − | 0.277304i | ||||||
\(795\) | −7.30846e14 | −2.30139 | ||||||||
\(796\) | − | 3.96540e14i | − | 1.24086i | ||||||
\(797\) | 1.20344e14 | 0.374226 | 0.187113 | − | 0.982338i | \(-0.440087\pi\) | ||||
0.187113 | + | 0.982338i | \(0.440087\pi\) | |||||||
\(798\) | 5.25929e13 | 0.162522 | ||||||||
\(799\) | 5.73381e13 | 0.176080 | ||||||||
\(800\) | 8.09699e14i | 2.47101i | ||||||||
\(801\) | 3.11388e14i | 0.944364i | ||||||||
\(802\) | 2.93929e14i | 0.885871i | ||||||||
\(803\) | − | 3.00477e13i | − | 0.0899980i | ||||||
\(804\) | 4.46059e14i | 1.32774i | ||||||||
\(805\) | −2.18692e14 | −0.646926 | ||||||||
\(806\) | 7.78790e14i | 2.28952i | ||||||||
\(807\) | 7.61966e14i | 2.22622i | ||||||||
\(808\) | 5.94209e13i | 0.172537i | ||||||||
\(809\) | −4.37310e13 | −0.126196 | −0.0630982 | − | 0.998007i | \(-0.520098\pi\) | ||||
−0.0630982 | + | 0.998007i | \(0.520098\pi\) | |||||||
\(810\) | −9.31808e13 | −0.267240 | ||||||||
\(811\) | − | 4.31250e14i | − | 1.22921i | −0.788836 | − | 0.614604i | \(-0.789316\pi\) | ||
0.788836 | − | 0.614604i | \(-0.210684\pi\) | |||||||
\(812\) | 7.78558e14 | 2.20552 | ||||||||
\(813\) | − | 3.72490e14i | − | 1.04873i | ||||||
\(814\) | 6.26808e13 | 0.175393 | ||||||||
\(815\) | 2.33481e14 | 0.649327 | ||||||||
\(816\) | − | 1.27327e14i | − | 0.351940i | ||||||
\(817\) | 1.83046e13 | + | 9.32240e12i | 0.0502864 | + | 0.0256105i | ||||
\(818\) | −1.03086e14 | −0.281471 | ||||||||
\(819\) | 6.60213e14i | 1.79170i | ||||||||
\(820\) | 4.30833e14i | 1.16209i | ||||||||
\(821\) | −1.52394e14 | −0.408556 | −0.204278 | − | 0.978913i | \(-0.565485\pi\) | ||||
−0.204278 | + | 0.978913i | \(0.565485\pi\) | |||||||
\(822\) | − | 5.71906e14i | − | 1.52393i | ||||||
\(823\) | 3.56707e14 | 0.944742 | 0.472371 | − | 0.881400i | \(-0.343398\pi\) | ||||
0.472371 | + | 0.881400i | \(0.343398\pi\) | |||||||
\(824\) | 7.63708e12i | 0.0201044i | ||||||||
\(825\) | − | 1.11520e14i | − | 0.291798i | ||||||
\(826\) | 9.12741e14 | 2.37382 | ||||||||
\(827\) | −2.45422e14 | −0.634433 | −0.317216 | − | 0.948353i | \(-0.602748\pi\) | ||||
−0.317216 | + | 0.948353i | \(0.602748\pi\) | |||||||
\(828\) | 1.63490e14 | 0.420087 | ||||||||
\(829\) | − | 3.39102e14i | − | 0.866080i | −0.901375 | − | 0.433040i | \(-0.857441\pi\) | ||
0.901375 | − | 0.433040i | \(-0.142559\pi\) | |||||||
\(830\) | −1.46866e15 | −3.72846 | ||||||||
\(831\) | −3.92170e14 | −0.989623 | ||||||||
\(832\) | 2.81234e14 | 0.705426 | ||||||||
\(833\) | −5.65814e13 | −0.141075 | ||||||||
\(834\) | −6.48403e14 | −1.60700 | ||||||||
\(835\) | 4.85873e13i | 0.119699i | ||||||||
\(836\) | 2.10452e12i | 0.00515374i | ||||||||
\(837\) | − | 7.01725e14i | − | 1.70820i | ||||||
\(838\) | 2.27963e14 | 0.551626 | ||||||||
\(839\) | − | 2.23442e14i | − | 0.537470i | −0.963214 | − | 0.268735i | \(-0.913394\pi\) | ||
0.963214 | − | 0.268735i | \(-0.0866056\pi\) | |||||||
\(840\) | 1.90845e14 | 0.456336 | ||||||||
\(841\) | −1.05036e15 | −2.49666 | ||||||||
\(842\) | −8.23658e14 | −1.94619 | ||||||||
\(843\) | − | 6.38313e14i | − | 1.49933i | ||||||
\(844\) | − | 1.58172e14i | − | 0.369333i | ||||||
\(845\) | 1.64348e14i | 0.381487i | ||||||||
\(846\) | − | 8.14453e14i | − | 1.87938i | ||||||
\(847\) | 5.62100e14i | 1.28943i | ||||||||
\(848\) | 4.08356e14 | 0.931236 | ||||||||
\(849\) | − | 1.19551e15i | − | 2.71029i | ||||||
\(850\) | − | 2.23925e14i | − | 0.504670i | ||||||
\(851\) | − | 1.66675e14i | − | 0.373441i | ||||||
\(852\) | 6.69267e14 | 1.49074 | ||||||||
\(853\) | 8.56693e14 | 1.89706 | 0.948528 | − | 0.316693i | \(-0.102572\pi\) | ||||
0.948528 | + | 0.316693i | \(0.102572\pi\) | |||||||
\(854\) | − | 1.45154e15i | − | 3.19550i | ||||||
\(855\) | 6.76028e13 | 0.147957 | ||||||||
\(856\) | 5.00777e13i | 0.108962i | ||||||||
\(857\) | −2.03304e13 | −0.0439786 | −0.0219893 | − | 0.999758i | \(-0.507000\pi\) | ||||
−0.0219893 | + | 0.999758i | \(0.507000\pi\) | |||||||
\(858\) | −9.11204e13 | −0.195965 | ||||||||
\(859\) | 8.96916e14i | 1.91772i | 0.283875 | + | 0.958861i | \(0.408380\pi\) | ||||
−0.283875 | + | 0.958861i | \(0.591620\pi\) | |||||||
\(860\) | −6.35807e14 | − | 3.23811e14i | −1.35155 | − | 0.688335i | ||||
\(861\) | 7.56370e14 | 1.59852 | ||||||||
\(862\) | 2.71522e14i | 0.570517i | ||||||||
\(863\) | − | 5.40883e13i | − | 0.112992i | −0.998403 | − | 0.0564962i | \(-0.982007\pi\) | ||
0.998403 | − | 0.0564962i | \(-0.0179929\pi\) | |||||||
\(864\) | −5.96121e14 | −1.23813 | ||||||||
\(865\) | 4.59470e14i | 0.948805i | ||||||||
\(866\) | 1.44210e14 | 0.296078 | ||||||||
\(867\) | − | 7.52454e14i | − | 1.53598i | ||||||
\(868\) | 1.09685e15i | 2.22612i | ||||||||
\(869\) | −1.30824e13 | −0.0263990 | ||||||||
\(870\) | 3.45171e15 | 6.92528 | ||||||||
\(871\) | −4.03357e14 | −0.804635 | ||||||||
\(872\) | − | 3.09290e13i | − | 0.0613456i | ||||||
\(873\) | −1.24018e15 | −2.44575 | ||||||||
\(874\) | 1.17769e13 | 0.0230927 | ||||||||
\(875\) | 9.02449e14 | 1.75947 | ||||||||
\(876\) | −6.67427e14 | −1.29385 | ||||||||
\(877\) | 9.25212e14 | 1.78338 | 0.891688 | − | 0.452650i | \(-0.149521\pi\) | ||||
0.891688 | + | 0.452650i | \(0.149521\pi\) | |||||||
\(878\) | − | 8.35530e14i | − | 1.60136i | ||||||
\(879\) | 1.08640e15i | 2.07036i | ||||||||
\(880\) | 9.68081e13i | 0.183442i | ||||||||
\(881\) | 6.38962e14 | 1.20391 | 0.601957 | − | 0.798528i | \(-0.294388\pi\) | ||||
0.601957 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(882\) | 8.03704e14i | 1.50575i | ||||||||
\(883\) | 3.36107e14 | 0.626144 | 0.313072 | − | 0.949729i | \(-0.398642\pi\) | ||||
0.313072 | + | 0.949729i | \(0.398642\pi\) | |||||||
\(884\) | −8.69408e13 | −0.161051 | ||||||||
\(885\) | 1.92286e15 | 3.54186 | ||||||||
\(886\) | − | 6.40144e14i | − | 1.17249i | ||||||
\(887\) | 4.56881e14i | 0.832118i | 0.909338 | + | 0.416059i | \(0.136589\pi\) | ||||
−0.909338 | + | 0.416059i | \(0.863411\pi\) | |||||||
\(888\) | 1.45451e14i | 0.263422i | ||||||||
\(889\) | 8.67413e13i | 0.156213i | ||||||||
\(890\) | − | 7.79126e14i | − | 1.39527i | ||||||
\(891\) | −6.54603e12 | −0.0116571 | ||||||||
\(892\) | − | 4.97792e14i | − | 0.881503i | ||||||
\(893\) | − | 2.78782e13i | − | 0.0490916i | ||||||
\(894\) | 7.62438e14i | 1.33511i | ||||||||
\(895\) | −1.60046e15 | −2.78696 | ||||||||
\(896\) | −1.95565e14 | −0.338650 | ||||||||
\(897\) | 2.42299e14i | 0.417243i | ||||||||
\(898\) | −1.39277e15 | −2.38505 | ||||||||
\(899\) | − | 2.07248e15i | − | 3.52933i | ||||||
\(900\) | −1.51141e15 | −2.55959 | ||||||||
\(901\) | −1.03093e14 | −0.173622 | ||||||||
\(902\) | 6.36947e13i | 0.106677i | ||||||||
\(903\) | −5.68483e14 | + | 1.11622e15i | −0.946844 | + | 1.85914i | ||||
\(904\) | −2.19583e13 | −0.0363711 | ||||||||
\(905\) | 2.71899e14i | 0.447883i | ||||||||
\(906\) | 8.08002e14i | 1.32365i | ||||||||
\(907\) | 1.38257e14 | 0.225242 | 0.112621 | − | 0.993638i | \(-0.464075\pi\) | ||||
0.112621 | + | 0.993638i | \(0.464075\pi\) | |||||||
\(908\) | 1.40439e14i | 0.227540i | ||||||||
\(909\) | −1.28355e15 | −2.06820 | ||||||||
\(910\) | − | 1.65192e15i | − | 2.64717i | ||||||
\(911\) | 2.12223e13i | 0.0338221i | 0.999857 | + | 0.0169111i | \(0.00538321\pi\) | ||||
−0.999857 | + | 0.0169111i | \(0.994617\pi\) | |||||||
\(912\) | −6.19072e13 | −0.0981221 | ||||||||
\(913\) | −1.03174e14 | −0.162636 | ||||||||
\(914\) | −1.38627e14 | −0.217329 | ||||||||
\(915\) | − | 3.05793e15i | − | 4.76785i | ||||||
\(916\) | 3.80830e14 | 0.590546 | ||||||||
\(917\) | −5.07938e14 | −0.783365 | ||||||||
\(918\) | 1.64859e14 | 0.252872 | ||||||||
\(919\) | −2.66977e14 | −0.407283 | −0.203642 | − | 0.979046i | \(-0.565278\pi\) | ||||
−0.203642 | + | 0.979046i | \(0.565278\pi\) | |||||||
\(920\) | 4.27352e13 | 0.0648406 | ||||||||
\(921\) | 1.91100e14i | 0.288378i | ||||||||
\(922\) | − | 7.54062e14i | − | 1.13176i | ||||||
\(923\) | 6.05197e14i | 0.903417i | ||||||||
\(924\) | −1.28334e14 | −0.190539 | ||||||||
\(925\) | 1.54085e15i | 2.27537i | ||||||||
\(926\) | −7.79660e14 | −1.14512 | ||||||||
\(927\) | −1.64968e14 | −0.240992 | ||||||||
\(928\) | −1.76059e15 | −2.55810 | ||||||||
\(929\) | 3.15131e14i | 0.455421i | 0.973729 | + | 0.227710i | \(0.0731240\pi\) | ||||
−0.973729 | + | 0.227710i | \(0.926876\pi\) | |||||||
\(930\) | 4.86285e15i | 6.98998i | ||||||||
\(931\) | 2.75103e13i | 0.0393320i | ||||||||
\(932\) | − | 9.58080e14i | − | 1.36245i | ||||||
\(933\) | − | 4.85120e14i | − | 0.686185i | ||||||
\(934\) | −1.34249e15 | −1.88876 | ||||||||
\(935\) | − | 2.44400e13i | − | 0.0342013i | ||||||
\(936\) | − | 1.29014e14i | − | 0.179580i | ||||||
\(937\) | − | 8.58525e14i | − | 1.18865i | −0.804224 | − | 0.594326i | \(-0.797419\pi\) | ||
0.804224 | − | 0.594326i | \(-0.202581\pi\) | |||||||
\(938\) | −1.19553e15 | −1.64644 | ||||||||
\(939\) | 1.95742e15 | 2.68136 | ||||||||
\(940\) | 9.68342e14i | 1.31944i | ||||||||
\(941\) | 1.09478e15 | 1.48381 | 0.741906 | − | 0.670504i | \(-0.233922\pi\) | ||||
0.741906 | + | 0.670504i | \(0.233922\pi\) | |||||||
\(942\) | − | 2.22274e15i | − | 2.99664i | ||||||
\(943\) | 1.69371e14 | 0.227133 | ||||||||
\(944\) | −1.07439e15 | −1.43318 | ||||||||
\(945\) | 1.48846e15i | 1.97505i | ||||||||
\(946\) | −9.39982e13 | − | 4.78725e13i | −0.124069 | − | 0.0631875i | ||||
\(947\) | 1.16773e15 | 1.53317 | 0.766587 | − | 0.642140i | \(-0.221953\pi\) | ||||
0.766587 | + | 0.642140i | \(0.221953\pi\) | |||||||
\(948\) | 2.90589e14i | 0.379523i | ||||||||
\(949\) | − | 6.03534e14i | − | 0.784098i | ||||||
\(950\) | −1.08874e14 | −0.140704 | ||||||||
\(951\) | − | 9.00381e14i | − | 1.15751i | ||||||
\(952\) | 2.69206e13 | 0.0344270 | ||||||||
\(953\) | 1.06155e15i | 1.35044i | 0.737615 | + | 0.675222i | \(0.235952\pi\) | ||||
−0.737615 | + | 0.675222i | \(0.764048\pi\) | |||||||
\(954\) | 1.46437e15i | 1.85314i | ||||||||
\(955\) | −2.43802e15 | −3.06917 | ||||||||
\(956\) | 6.02423e14 | 0.754419 | ||||||||
\(957\) | 2.42485e14 | 0.302083 | ||||||||
\(958\) | 1.95412e15i | 2.42172i | ||||||||
\(959\) | 7.28366e14 | 0.897960 | ||||||||
\(960\) | 1.75606e15 | 2.15369 | ||||||||
\(961\) | 2.10013e15 | 2.56230 | ||||||||
\(962\) | 1.25900e15 | 1.52809 | ||||||||
\(963\) | −1.08173e15 | −1.30613 | ||||||||
\(964\) | − | 8.38082e14i | − | 1.00670i | ||||||
\(965\) | 6.36282e14i | 0.760350i | ||||||||
\(966\) | 7.18161e14i | 0.853761i | ||||||||
\(967\) | 3.84023e14 | 0.454176 | 0.227088 | − | 0.973874i | \(-0.427079\pi\) | ||||
0.227088 | + | 0.973874i | \(0.427079\pi\) | |||||||
\(968\) | − | 1.09841e14i | − | 0.129238i | ||||||
\(969\) | 1.56290e13 | 0.0182941 | ||||||||
\(970\) | 3.10305e15 | 3.61352 | ||||||||
\(971\) | 9.65918e14 | 1.11904 | 0.559518 | − | 0.828818i | \(-0.310986\pi\) | ||||
0.559518 | + | 0.828818i | \(0.310986\pi\) | |||||||
\(972\) | 8.56374e14i | 0.987034i | ||||||||
\(973\) | − | 8.25792e14i | − | 0.946905i | ||||||
\(974\) | − | 6.93833e14i | − | 0.791517i | ||||||
\(975\) | − | 2.23997e15i | − | 2.54226i | ||||||
\(976\) | 1.70860e15i | 1.92927i | ||||||||
\(977\) | −4.53688e13 | −0.0509664 | −0.0254832 | − | 0.999675i | \(-0.508112\pi\) | ||||
−0.0254832 | + | 0.999675i | \(0.508112\pi\) | |||||||
\(978\) | − | 7.66724e14i | − | 0.856929i | ||||||
\(979\) | − | 5.47343e13i | − | 0.0608619i | ||||||
\(980\) | − | 9.55562e14i | − | 1.05713i | ||||||
\(981\) | 6.68096e14 | 0.735350 | ||||||||
\(982\) | −6.83860e14 | −0.748876 | ||||||||
\(983\) | 4.33875e14i | 0.472712i | 0.971666 | + | 0.236356i | \(0.0759532\pi\) | ||||
−0.971666 | + | 0.236356i | \(0.924047\pi\) | |||||||
\(984\) | −1.47804e14 | −0.160218 | ||||||||
\(985\) | − | 1.45823e15i | − | 1.57269i | ||||||
\(986\) | 4.86896e14 | 0.522459 | ||||||||
\(987\) | 1.70002e15 | 1.81496 | ||||||||
\(988\) | 4.22712e13i | 0.0449014i | ||||||||
\(989\) | −1.27298e14 | + | 2.49951e14i | −0.134537 | + | 0.264164i | ||||
\(990\) | −3.47155e14 | −0.365046 | ||||||||
\(991\) | − | 5.53585e14i | − | 0.579183i | −0.957150 | − | 0.289591i | \(-0.906481\pi\) | ||
0.957150 | − | 0.289591i | \(-0.0935194\pi\) | |||||||
\(992\) | − | 2.48036e15i | − | 2.58200i | ||||||
\(993\) | −1.97189e15 | −2.04238 | ||||||||
\(994\) | 1.79377e15i | 1.84857i | ||||||||
\(995\) | 2.23900e15 | 2.29583 | ||||||||
\(996\) | 2.29174e15i | 2.33813i | ||||||||
\(997\) | 1.16710e14i | 0.118476i | 0.998244 | + | 0.0592381i | \(0.0188671\pi\) | ||||
−0.998244 | + | 0.0592381i | \(0.981133\pi\) | |||||||
\(998\) | 1.15512e15 | 1.16674 | ||||||||
\(999\) | −1.13442e15 | −1.14011 |
(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 | 43.11.b.b.42.29 | yes | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.6 | ✓ | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.6 | ✓ | 34 | 43.42 | odd | 2 | inner | |
43.11.b.b.42.29 | yes | 34 | 1.1 | even | 1 | trivial |