Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,10,Mod(28,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.28");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(14.9360392488\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 28.17 | ||
Character | \(\chi\) | \(=\) | 29.28 |
Dual form | 29.10.b.a.28.6 |
$q$-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 \(\left(\mathbb{Z}/29\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 25.3186i | 1.11894i | 0.828852 | + | 0.559468i | \(0.188995\pi\) | ||||
−0.828852 | + | 0.559468i | \(0.811005\pi\) | |||||||
\(3\) | − | 226.177i | − | 1.61214i | −0.591818 | − | 0.806072i | \(-0.701589\pi\) | ||
0.591818 | − | 0.806072i | \(-0.298411\pi\) | |||||||
\(4\) | −129.033 | −0.252018 | ||||||||
\(5\) | −952.179 | −0.681324 | −0.340662 | − | 0.940186i | \(-0.610651\pi\) | ||||
−0.340662 | + | 0.940186i | \(0.610651\pi\) | |||||||
\(6\) | 5726.51 | 1.80389 | ||||||||
\(7\) | 6455.42 | 1.01621 | 0.508105 | − | 0.861295i | \(-0.330346\pi\) | ||||
0.508105 | + | 0.861295i | \(0.330346\pi\) | |||||||
\(8\) | 9696.20i | 0.836944i | ||||||||
\(9\) | −31473.3 | −1.59901 | ||||||||
\(10\) | − | 24107.9i | − | 0.762357i | ||||||
\(11\) | − | 72133.8i | − | 1.48550i | −0.669571 | − | 0.742748i | \(-0.733522\pi\) | ||
0.669571 | − | 0.742748i | \(-0.266478\pi\) | |||||||
\(12\) | 29184.4i | 0.406289i | ||||||||
\(13\) | −190298. | −1.84795 | −0.923974 | − | 0.382454i | \(-0.875079\pi\) | ||||
−0.923974 | + | 0.382454i | \(0.875079\pi\) | |||||||
\(14\) | 163443.i | 1.13707i | ||||||||
\(15\) | 215361.i | 1.09839i | ||||||||
\(16\) | −311559. | −1.18850 | ||||||||
\(17\) | − | 58686.4i | − | 0.170419i | −0.996363 | − | 0.0852094i | \(-0.972844\pi\) | ||
0.996363 | − | 0.0852094i | \(-0.0271559\pi\) | |||||||
\(18\) | − | 796860.i | − | 1.78919i | ||||||
\(19\) | − | 524361.i | − | 0.923079i | −0.887120 | − | 0.461540i | \(-0.847297\pi\) | ||
0.887120 | − | 0.461540i | \(-0.152703\pi\) | |||||||
\(20\) | 122863. | 0.171706 | ||||||||
\(21\) | − | 1.46007e6i | − | 1.63828i | ||||||
\(22\) | 1.82633e6 | 1.66218 | ||||||||
\(23\) | −1.18194e6 | −0.880682 | −0.440341 | − | 0.897831i | \(-0.645142\pi\) | ||||
−0.440341 | + | 0.897831i | \(0.645142\pi\) | |||||||
\(24\) | 2.19306e6 | 1.34927 | ||||||||
\(25\) | −1.04648e6 | −0.535798 | ||||||||
\(26\) | − | 4.81809e6i | − | 2.06774i | ||||||
\(27\) | 2.66669e6i | 0.965686i | ||||||||
\(28\) | −832964. | −0.256103 | ||||||||
\(29\) | 1.63877e6 | − | 3.43825e6i | 0.430257 | − | 0.902707i | ||||
\(30\) | −5.45266e6 | −1.22903 | ||||||||
\(31\) | 8.71446e6i | 1.69478i | 0.530972 | + | 0.847389i | \(0.321827\pi\) | ||||
−0.530972 | + | 0.847389i | \(0.678173\pi\) | |||||||
\(32\) | − | 2.92381e6i | − | 0.492917i | ||||||
\(33\) | −1.63150e7 | −2.39483 | ||||||||
\(34\) | 1.48586e6 | 0.190688 | ||||||||
\(35\) | −6.14672e6 | −0.692368 | ||||||||
\(36\) | 4.06110e6 | 0.402979 | ||||||||
\(37\) | − | 5.56889e6i | − | 0.488496i | −0.969713 | − | 0.244248i | \(-0.921459\pi\) | ||
0.969713 | − | 0.244248i | \(-0.0785410\pi\) | |||||||
\(38\) | 1.32761e7 | 1.03287 | ||||||||
\(39\) | 4.30412e7i | 2.97916i | ||||||||
\(40\) | − | 9.23251e6i | − | 0.570230i | ||||||
\(41\) | − | 4.38228e6i | − | 0.242199i | −0.992640 | − | 0.121100i | \(-0.961358\pi\) | ||
0.992640 | − | 0.121100i | \(-0.0386420\pi\) | |||||||
\(42\) | 3.69670e7 | 1.83313 | ||||||||
\(43\) | − | 3.96210e6i | − | 0.176733i | −0.996088 | − | 0.0883664i | \(-0.971835\pi\) | ||
0.996088 | − | 0.0883664i | \(-0.0281646\pi\) | |||||||
\(44\) | 9.30765e6i | 0.374372i | ||||||||
\(45\) | 2.99682e7 | 1.08944 | ||||||||
\(46\) | − | 2.99250e7i | − | 0.985426i | ||||||
\(47\) | − | 1.62041e7i | − | 0.484377i | −0.970229 | − | 0.242189i | \(-0.922135\pi\) | ||
0.970229 | − | 0.242189i | \(-0.0778653\pi\) | |||||||
\(48\) | 7.04677e7i | 1.91604i | ||||||||
\(49\) | 1.31888e6 | 0.0326832 | ||||||||
\(50\) | − | 2.64955e7i | − | 0.599524i | ||||||
\(51\) | −1.32735e7 | −0.274739 | ||||||||
\(52\) | 2.45548e7 | 0.465716 | ||||||||
\(53\) | 2.97542e6 | 0.0517973 | 0.0258986 | − | 0.999665i | \(-0.491755\pi\) | ||||
0.0258986 | + | 0.999665i | \(0.491755\pi\) | |||||||
\(54\) | −6.75170e7 | −1.08054 | ||||||||
\(55\) | 6.86842e7i | 1.01210i | ||||||||
\(56\) | 6.25930e7i | 0.850511i | ||||||||
\(57\) | −1.18599e8 | −1.48814 | ||||||||
\(58\) | 8.70518e7 | + | 4.14915e7i | 1.01007 | + | 0.481430i | ||||
\(59\) | 1.66853e8 | 1.79267 | 0.896333 | − | 0.443382i | \(-0.146222\pi\) | ||||
0.896333 | + | 0.443382i | \(0.146222\pi\) | |||||||
\(60\) | − | 2.77888e7i | − | 0.276814i | ||||||
\(61\) | − | 1.63294e8i | − | 1.51003i | −0.655706 | − | 0.755016i | \(-0.727629\pi\) | ||
0.655706 | − | 0.755016i | \(-0.272371\pi\) | |||||||
\(62\) | −2.20638e8 | −1.89635 | ||||||||
\(63\) | −2.03173e8 | −1.62493 | ||||||||
\(64\) | −8.54916e7 | −0.636962 | ||||||||
\(65\) | 1.81198e8 | 1.25905 | ||||||||
\(66\) | − | 4.13074e8i | − | 2.67967i | ||||||
\(67\) | −1.87780e7 | −0.113845 | −0.0569223 | − | 0.998379i | \(-0.518129\pi\) | ||||
−0.0569223 | + | 0.998379i | \(0.518129\pi\) | |||||||
\(68\) | 7.57249e6i | 0.0429486i | ||||||||
\(69\) | 2.67327e8i | 1.41979i | ||||||||
\(70\) | − | 1.55626e8i | − | 0.774715i | ||||||
\(71\) | 2.59765e8 | 1.21316 | 0.606581 | − | 0.795022i | \(-0.292541\pi\) | ||||
0.606581 | + | 0.795022i | \(0.292541\pi\) | |||||||
\(72\) | − | 3.05171e8i | − | 1.33828i | ||||||
\(73\) | 3.06047e8i | 1.26135i | 0.776048 | + | 0.630674i | \(0.217221\pi\) | ||||
−0.776048 | + | 0.630674i | \(0.782779\pi\) | |||||||
\(74\) | 1.40997e8 | 0.546595 | ||||||||
\(75\) | 2.36690e8i | 0.863784i | ||||||||
\(76\) | 6.76600e7i | 0.232633i | ||||||||
\(77\) | − | 4.65654e8i | − | 1.50958i | ||||||
\(78\) | −1.08974e9 | −3.33349 | ||||||||
\(79\) | 3.09114e7i | 0.0892889i | 0.999003 | + | 0.0446444i | \(0.0142155\pi\) | ||||
−0.999003 | + | 0.0446444i | \(0.985785\pi\) | |||||||
\(80\) | 2.96660e8 | 0.809756 | ||||||||
\(81\) | −1.63426e7 | −0.0421830 | ||||||||
\(82\) | 1.10953e8 | 0.271005 | ||||||||
\(83\) | 7.54219e8 | 1.74440 | 0.872200 | − | 0.489149i | \(-0.162693\pi\) | ||||
0.872200 | + | 0.489149i | \(0.162693\pi\) | |||||||
\(84\) | 1.88398e8i | 0.412875i | ||||||||
\(85\) | 5.58799e7i | 0.116110i | ||||||||
\(86\) | 1.00315e8 | 0.197753 | ||||||||
\(87\) | −7.77655e8 | − | 3.70653e8i | −1.45529 | − | 0.693635i | ||||
\(88\) | 6.99423e8 | 1.24328 | ||||||||
\(89\) | − | 3.38602e8i | − | 0.572050i | −0.958222 | − | 0.286025i | \(-0.907666\pi\) | ||
0.958222 | − | 0.286025i | \(-0.0923341\pi\) | |||||||
\(90\) | 7.58753e8i | 1.21902i | ||||||||
\(91\) | −1.22846e9 | −1.87790 | ||||||||
\(92\) | 1.52509e8 | 0.221948 | ||||||||
\(93\) | 1.97101e9 | 2.73223 | ||||||||
\(94\) | 4.10265e8 | 0.541987 | ||||||||
\(95\) | 4.99285e8i | 0.628916i | ||||||||
\(96\) | −6.61299e8 | −0.794653 | ||||||||
\(97\) | 3.80361e8i | 0.436238i | 0.975922 | + | 0.218119i | \(0.0699920\pi\) | ||||
−0.975922 | + | 0.218119i | \(0.930008\pi\) | |||||||
\(98\) | 3.33924e7i | 0.0365704i | ||||||||
\(99\) | 2.27028e9i | 2.37532i | ||||||||
\(100\) | 1.35031e8 | 0.135031 | ||||||||
\(101\) | 3.31125e8i | 0.316625i | 0.987389 | + | 0.158313i | \(0.0506054\pi\) | ||||
−0.987389 | + | 0.158313i | \(0.949395\pi\) | |||||||
\(102\) | − | 3.36068e8i | − | 0.307416i | ||||||
\(103\) | 9.76301e7 | 0.0854705 | 0.0427353 | − | 0.999086i | \(-0.486393\pi\) | ||||
0.0427353 | + | 0.999086i | \(0.486393\pi\) | |||||||
\(104\) | − | 1.84517e9i | − | 1.54663i | ||||||
\(105\) | 1.39025e9i | 1.11620i | ||||||||
\(106\) | 7.53336e7i | 0.0579578i | ||||||||
\(107\) | −1.13163e9 | −0.834598 | −0.417299 | − | 0.908769i | \(-0.637023\pi\) | ||||
−0.417299 | + | 0.908769i | \(0.637023\pi\) | |||||||
\(108\) | − | 3.44092e8i | − | 0.243370i | ||||||
\(109\) | 4.83988e8 | 0.328409 | 0.164205 | − | 0.986426i | \(-0.447494\pi\) | ||||
0.164205 | + | 0.986426i | \(0.447494\pi\) | |||||||
\(110\) | −1.73899e9 | −1.13248 | ||||||||
\(111\) | −1.25956e9 | −0.787525 | ||||||||
\(112\) | −2.01125e9 | −1.20777 | ||||||||
\(113\) | − | 1.33348e9i | − | 0.769369i | −0.923048 | − | 0.384684i | \(-0.874310\pi\) | ||
0.923048 | − | 0.384684i | \(-0.125690\pi\) | |||||||
\(114\) | − | 3.00276e9i | − | 1.66513i | ||||||
\(115\) | 1.12541e9 | 0.600029 | ||||||||
\(116\) | −2.11456e8 | + | 4.43649e8i | −0.108432 | + | 0.227498i | ||||
\(117\) | 5.98931e9 | 2.95488 | ||||||||
\(118\) | 4.22448e9i | 2.00588i | ||||||||
\(119\) | − | 3.78846e8i | − | 0.173181i | ||||||
\(120\) | −2.08819e9 | −0.919292 | ||||||||
\(121\) | −2.84533e9 | −1.20670 | ||||||||
\(122\) | 4.13438e9 | 1.68963 | ||||||||
\(123\) | −9.91172e8 | −0.390460 | ||||||||
\(124\) | − | 1.12445e9i | − | 0.427115i | ||||||
\(125\) | 2.85616e9 | 1.04638 | ||||||||
\(126\) | − | 5.14407e9i | − | 1.81819i | ||||||
\(127\) | − | 2.57244e9i | − | 0.877464i | −0.898618 | − | 0.438732i | \(-0.855428\pi\) | ||
0.898618 | − | 0.438732i | \(-0.144572\pi\) | |||||||
\(128\) | − | 3.66152e9i | − | 1.20564i | ||||||
\(129\) | −8.96137e8 | −0.284919 | ||||||||
\(130\) | 4.58769e9i | 1.40880i | ||||||||
\(131\) | − | 3.86788e8i | − | 0.114750i | −0.998353 | − | 0.0573749i | \(-0.981727\pi\) | ||
0.998353 | − | 0.0573749i | \(-0.0182730\pi\) | |||||||
\(132\) | 2.10518e9 | 0.603541 | ||||||||
\(133\) | − | 3.38497e9i | − | 0.938043i | ||||||
\(134\) | − | 4.75433e8i | − | 0.127385i | ||||||
\(135\) | − | 2.53917e9i | − | 0.657944i | ||||||
\(136\) | 5.69035e8 | 0.142631 | ||||||||
\(137\) | − | 3.34670e9i | − | 0.811660i | −0.913949 | − | 0.405830i | \(-0.866983\pi\) | ||
0.913949 | − | 0.405830i | \(-0.133017\pi\) | |||||||
\(138\) | −6.76837e9 | −1.58865 | ||||||||
\(139\) | −6.78753e9 | −1.54222 | −0.771108 | − | 0.636705i | \(-0.780297\pi\) | ||||
−0.771108 | + | 0.636705i | \(0.780297\pi\) | |||||||
\(140\) | 7.93130e8 | 0.174489 | ||||||||
\(141\) | −3.66500e9 | −0.780886 | ||||||||
\(142\) | 6.57691e9i | 1.35745i | ||||||||
\(143\) | 1.37269e10i | 2.74512i | ||||||||
\(144\) | 9.80579e9 | 1.90043 | ||||||||
\(145\) | −1.56040e9 | + | 3.27383e9i | −0.293144 | + | 0.615035i | ||||
\(146\) | −7.74868e9 | −1.41137 | ||||||||
\(147\) | − | 2.98302e8i | − | 0.0526900i | ||||||
\(148\) | 7.18571e8i | 0.123110i | ||||||||
\(149\) | −4.45493e9 | −0.740461 | −0.370231 | − | 0.928940i | \(-0.620721\pi\) | ||||
−0.370231 | + | 0.928940i | \(0.620721\pi\) | |||||||
\(150\) | −5.99268e9 | −0.966519 | ||||||||
\(151\) | 2.47387e9 | 0.387240 | 0.193620 | − | 0.981077i | \(-0.437977\pi\) | ||||
0.193620 | + | 0.981077i | \(0.437977\pi\) | |||||||
\(152\) | 5.08431e9 | 0.772566 | ||||||||
\(153\) | 1.84705e9i | 0.272501i | ||||||||
\(154\) | 1.17897e10 | 1.68912 | ||||||||
\(155\) | − | 8.29772e9i | − | 1.15469i | ||||||
\(156\) | − | 5.55374e9i | − | 0.750802i | ||||||
\(157\) | 8.03709e9i | 1.05572i | 0.849330 | + | 0.527862i | \(0.177006\pi\) | ||||
−0.849330 | + | 0.527862i | \(0.822994\pi\) | |||||||
\(158\) | −7.82635e8 | −0.0999085 | ||||||||
\(159\) | − | 6.72973e8i | − | 0.0835046i | ||||||
\(160\) | 2.78399e9i | 0.335836i | ||||||||
\(161\) | −7.62990e9 | −0.894958 | ||||||||
\(162\) | − | 4.13772e8i | − | 0.0472001i | ||||||
\(163\) | − | 8.10587e9i | − | 0.899405i | −0.893178 | − | 0.449703i | \(-0.851530\pi\) | ||
0.893178 | − | 0.449703i | \(-0.148470\pi\) | |||||||
\(164\) | 5.65459e8i | 0.0610385i | ||||||||
\(165\) | 1.55348e10 | 1.63166 | ||||||||
\(166\) | 1.90958e10i | 1.95187i | ||||||||
\(167\) | 3.68360e9 | 0.366479 | 0.183239 | − | 0.983068i | \(-0.441342\pi\) | ||||
0.183239 | + | 0.983068i | \(0.441342\pi\) | |||||||
\(168\) | 1.41571e10 | 1.37115 | ||||||||
\(169\) | 2.56090e10 | 2.41491 | ||||||||
\(170\) | −1.41480e9 | −0.129920 | ||||||||
\(171\) | 1.65033e10i | 1.47601i | ||||||||
\(172\) | 5.11242e8i | 0.0445398i | ||||||||
\(173\) | −1.10024e9 | −0.0933860 | −0.0466930 | − | 0.998909i | \(-0.514868\pi\) | ||||
−0.0466930 | + | 0.998909i | \(0.514868\pi\) | |||||||
\(174\) | 9.38444e9 | − | 1.96892e10i | 0.776134 | − | 1.62838i | ||||
\(175\) | −6.75548e9 | −0.544484 | ||||||||
\(176\) | 2.24740e10i | 1.76552i | ||||||||
\(177\) | − | 3.77383e10i | − | 2.89003i | ||||||
\(178\) | 8.57293e9 | 0.640088 | ||||||||
\(179\) | −1.64418e10 | −1.19704 | −0.598522 | − | 0.801107i | \(-0.704245\pi\) | ||||
−0.598522 | + | 0.801107i | \(0.704245\pi\) | |||||||
\(180\) | −3.86689e9 | −0.274559 | ||||||||
\(181\) | −1.66762e10 | −1.15490 | −0.577449 | − | 0.816427i | \(-0.695952\pi\) | ||||
−0.577449 | + | 0.816427i | \(0.695952\pi\) | |||||||
\(182\) | − | 3.11028e10i | − | 2.10126i | ||||||
\(183\) | −3.69335e10 | −2.43439 | ||||||||
\(184\) | − | 1.14603e10i | − | 0.737081i | ||||||
\(185\) | 5.30258e9i | 0.332824i | ||||||||
\(186\) | 4.99034e10i | 3.05719i | ||||||||
\(187\) | −4.23327e9 | −0.253156 | ||||||||
\(188\) | 2.09086e9i | 0.122072i | ||||||||
\(189\) | 1.72146e10i | 0.981340i | ||||||||
\(190\) | −1.26412e10 | −0.703717 | ||||||||
\(191\) | − | 1.60750e10i | − | 0.873980i | −0.899466 | − | 0.436990i | \(-0.856045\pi\) | ||
0.899466 | − | 0.436990i | \(-0.143955\pi\) | |||||||
\(192\) | 1.93363e10i | 1.02687i | ||||||||
\(193\) | 7.70364e9i | 0.399658i | 0.979831 | + | 0.199829i | \(0.0640386\pi\) | ||||
−0.979831 | + | 0.199829i | \(0.935961\pi\) | |||||||
\(194\) | −9.63022e9 | −0.488122 | ||||||||
\(195\) | − | 4.09829e10i | − | 2.02977i | ||||||
\(196\) | −1.70180e8 | −0.00823675 | ||||||||
\(197\) | 1.17597e10 | 0.556286 | 0.278143 | − | 0.960540i | \(-0.410281\pi\) | ||||
0.278143 | + | 0.960540i | \(0.410281\pi\) | |||||||
\(198\) | −5.74805e10 | −2.65783 | ||||||||
\(199\) | 3.85010e10 | 1.74034 | 0.870169 | − | 0.492754i | \(-0.164010\pi\) | ||||
0.870169 | + | 0.492754i | \(0.164010\pi\) | |||||||
\(200\) | − | 1.01469e10i | − | 0.448433i | ||||||
\(201\) | 4.24716e9i | 0.183534i | ||||||||
\(202\) | −8.38363e9 | −0.354284 | ||||||||
\(203\) | 1.05790e10 | − | 2.21954e10i | 0.437231 | − | 0.917340i | ||||
\(204\) | 1.71273e9 | 0.0692393 | ||||||||
\(205\) | 4.17271e9i | 0.165016i | ||||||||
\(206\) | 2.47186e9i | 0.0956360i | ||||||||
\(207\) | 3.71994e10 | 1.40822 | ||||||||
\(208\) | 5.92892e10 | 2.19630 | ||||||||
\(209\) | −3.78241e10 | −1.37123 | ||||||||
\(210\) | −3.51992e10 | −1.24895 | ||||||||
\(211\) | − | 2.80121e10i | − | 0.972914i | −0.873704 | − | 0.486457i | \(-0.838289\pi\) | ||
0.873704 | − | 0.486457i | \(-0.161711\pi\) | |||||||
\(212\) | −3.83928e8 | −0.0130538 | ||||||||
\(213\) | − | 5.87531e10i | − | 1.95579i | ||||||
\(214\) | − | 2.86513e10i | − | 0.933862i | ||||||
\(215\) | 3.77262e9i | 0.120412i | ||||||||
\(216\) | −2.58568e10 | −0.808225 | ||||||||
\(217\) | 5.62555e10i | 1.72225i | ||||||||
\(218\) | 1.22539e10i | 0.367469i | ||||||||
\(219\) | 6.92208e10 | 2.03347 | ||||||||
\(220\) | − | 8.86255e9i | − | 0.255068i | ||||||
\(221\) | 1.11679e10i | 0.314925i | ||||||||
\(222\) | − | 3.18903e10i | − | 0.881190i | ||||||
\(223\) | 3.01274e10 | 0.815813 | 0.407906 | − | 0.913024i | \(-0.366259\pi\) | ||||
0.407906 | + | 0.913024i | \(0.366259\pi\) | |||||||
\(224\) | − | 1.88744e10i | − | 0.500907i | ||||||
\(225\) | 3.29362e10 | 0.856745 | ||||||||
\(226\) | 3.37620e10 | 0.860874 | ||||||||
\(227\) | −2.86557e9 | −0.0716300 | −0.0358150 | − | 0.999358i | \(-0.511403\pi\) | ||||
−0.0358150 | + | 0.999358i | \(0.511403\pi\) | |||||||
\(228\) | 1.53032e10 | 0.375037 | ||||||||
\(229\) | 6.63138e10i | 1.59347i | 0.604329 | + | 0.796735i | \(0.293441\pi\) | ||||
−0.604329 | + | 0.796735i | \(0.706559\pi\) | |||||||
\(230\) | 2.84940e10i | 0.671394i | ||||||||
\(231\) | −1.05320e11 | −2.43365 | ||||||||
\(232\) | 3.33380e10 | + | 1.58899e10i | 0.755515 | + | 0.360101i | ||||
\(233\) | −6.93682e10 | −1.54191 | −0.770955 | − | 0.636890i | \(-0.780220\pi\) | ||||
−0.770955 | + | 0.636890i | \(0.780220\pi\) | |||||||
\(234\) | 1.51641e11i | 3.30633i | ||||||||
\(235\) | 1.54292e10i | 0.330018i | ||||||||
\(236\) | −2.15295e10 | −0.451784 | ||||||||
\(237\) | 6.99147e9 | 0.143947 | ||||||||
\(238\) | 9.59185e9 | 0.193779 | ||||||||
\(239\) | 7.80502e10 | 1.54733 | 0.773666 | − | 0.633593i | \(-0.218421\pi\) | ||||
0.773666 | + | 0.633593i | \(0.218421\pi\) | |||||||
\(240\) | − | 6.70979e10i | − | 1.30544i | ||||||
\(241\) | −6.98133e10 | −1.33310 | −0.666548 | − | 0.745462i | \(-0.732229\pi\) | ||||
−0.666548 | + | 0.745462i | \(0.732229\pi\) | |||||||
\(242\) | − | 7.20399e10i | − | 1.35022i | ||||||
\(243\) | 5.61848e10i | 1.03369i | ||||||||
\(244\) | 2.10704e10i | 0.380555i | ||||||||
\(245\) | −1.25581e9 | −0.0222678 | ||||||||
\(246\) | − | 2.50951e10i | − | 0.436899i | ||||||
\(247\) | 9.97850e10i | 1.70580i | ||||||||
\(248\) | −8.44971e10 | −1.41843 | ||||||||
\(249\) | − | 1.70587e11i | − | 2.81222i | ||||||
\(250\) | 7.23141e10i | 1.17083i | ||||||||
\(251\) | − | 5.01403e10i | − | 0.797362i | −0.917090 | − | 0.398681i | \(-0.869468\pi\) | ||
0.917090 | − | 0.398681i | \(-0.130532\pi\) | |||||||
\(252\) | 2.62161e10 | 0.409511 | ||||||||
\(253\) | 8.52575e10i | 1.30825i | ||||||||
\(254\) | 6.51308e10 | 0.981826 | ||||||||
\(255\) | 1.26388e10 | 0.187186 | ||||||||
\(256\) | 4.89330e10 | 0.712069 | ||||||||
\(257\) | 2.20462e10 | 0.315235 | 0.157617 | − | 0.987500i | \(-0.449619\pi\) | ||||
0.157617 | + | 0.987500i | \(0.449619\pi\) | |||||||
\(258\) | − | 2.26890e10i | − | 0.318806i | ||||||
\(259\) | − | 3.59495e10i | − | 0.496414i | ||||||
\(260\) | −2.33806e10 | −0.317303 | ||||||||
\(261\) | −5.15775e10 | + | 1.08213e11i | −0.687983 | + | 1.44343i | ||||
\(262\) | 9.79294e9 | 0.128398 | ||||||||
\(263\) | 6.96042e10i | 0.897086i | 0.893761 | + | 0.448543i | \(0.148057\pi\) | ||||
−0.893761 | + | 0.448543i | \(0.851943\pi\) | |||||||
\(264\) | − | 1.58194e11i | − | 2.00434i | ||||||
\(265\) | −2.83313e9 | −0.0352907 | ||||||||
\(266\) | 8.57029e10 | 1.04961 | ||||||||
\(267\) | −7.65841e10 | −0.922227 | ||||||||
\(268\) | 2.42298e9 | 0.0286909 | ||||||||
\(269\) | 4.96041e10i | 0.577607i | 0.957388 | + | 0.288803i | \(0.0932574\pi\) | ||||
−0.957388 | + | 0.288803i | \(0.906743\pi\) | |||||||
\(270\) | 6.42882e10 | 0.736198 | ||||||||
\(271\) | − | 1.72902e11i | − | 1.94733i | −0.227994 | − | 0.973663i | \(-0.573217\pi\) | ||
0.227994 | − | 0.973663i | \(-0.426783\pi\) | |||||||
\(272\) | 1.82843e10i | 0.202543i | ||||||||
\(273\) | 2.77849e11i | 3.02745i | ||||||||
\(274\) | 8.47339e10 | 0.908196 | ||||||||
\(275\) | 7.54866e10i | 0.795926i | ||||||||
\(276\) | − | 3.44941e10i | − | 0.357811i | ||||||
\(277\) | 2.11540e10 | 0.215890 | 0.107945 | − | 0.994157i | \(-0.465573\pi\) | ||||
0.107945 | + | 0.994157i | \(0.465573\pi\) | |||||||
\(278\) | − | 1.71851e11i | − | 1.72564i | ||||||
\(279\) | − | 2.74272e11i | − | 2.70996i | ||||||
\(280\) | − | 5.95998e10i | − | 0.579473i | ||||||
\(281\) | −1.07209e11 | −1.02578 | −0.512890 | − | 0.858454i | \(-0.671425\pi\) | ||||
−0.512890 | + | 0.858454i | \(0.671425\pi\) | |||||||
\(282\) | − | 9.27927e10i | − | 0.873761i | ||||||
\(283\) | −1.74342e11 | −1.61571 | −0.807854 | − | 0.589383i | \(-0.799371\pi\) | ||||
−0.807854 | + | 0.589383i | \(0.799371\pi\) | |||||||
\(284\) | −3.35184e10 | −0.305739 | ||||||||
\(285\) | 1.12927e11 | 1.01390 | ||||||||
\(286\) | −3.47547e11 | −3.07161 | ||||||||
\(287\) | − | 2.82895e10i | − | 0.246125i | ||||||
\(288\) | 9.20217e10i | 0.788178i | ||||||||
\(289\) | 1.15144e11 | 0.970957 | ||||||||
\(290\) | −8.28889e10 | − | 3.95073e10i | −0.688185 | − | 0.328009i | ||||
\(291\) | 8.60291e10 | 0.703278 | ||||||||
\(292\) | − | 3.94902e10i | − | 0.317882i | ||||||
\(293\) | 2.26140e10i | 0.179255i | 0.995975 | + | 0.0896277i | \(0.0285677\pi\) | ||||
−0.995975 | + | 0.0896277i | \(0.971432\pi\) | |||||||
\(294\) | 7.55260e9 | 0.0589567 | ||||||||
\(295\) | −1.58874e11 | −1.22139 | ||||||||
\(296\) | 5.39970e10 | 0.408844 | ||||||||
\(297\) | 1.92358e11 | 1.43452 | ||||||||
\(298\) | − | 1.12793e11i | − | 0.828529i | ||||||
\(299\) | 2.24921e11 | 1.62745 | ||||||||
\(300\) | − | 3.05409e10i | − | 0.217689i | ||||||
\(301\) | − | 2.55770e10i | − | 0.179598i | ||||||
\(302\) | 6.26350e10i | 0.433297i | ||||||||
\(303\) | 7.48930e10 | 0.510446 | ||||||||
\(304\) | 1.63370e11i | 1.09708i | ||||||||
\(305\) | 1.55485e11i | 1.02882i | ||||||||
\(306\) | −4.67648e10 | −0.304911 | ||||||||
\(307\) | 2.82124e11i | 1.81267i | 0.422563 | + | 0.906334i | \(0.361131\pi\) | ||||
−0.422563 | + | 0.906334i | \(0.638869\pi\) | |||||||
\(308\) | 6.00848e10i | 0.380440i | ||||||||
\(309\) | − | 2.20817e10i | − | 0.137791i | ||||||
\(310\) | 2.10087e11 | 1.29203 | ||||||||
\(311\) | − | 2.72890e11i | − | 1.65412i | −0.562117 | − | 0.827058i | \(-0.690013\pi\) | ||
0.562117 | − | 0.827058i | \(-0.309987\pi\) | |||||||
\(312\) | −4.17336e11 | −2.49339 | ||||||||
\(313\) | −3.46295e10 | −0.203937 | −0.101969 | − | 0.994788i | \(-0.532514\pi\) | ||||
−0.101969 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(314\) | −2.03488e11 | −1.18129 | ||||||||
\(315\) | 1.93457e11 | 1.10710 | ||||||||
\(316\) | − | 3.98860e9i | − | 0.0225024i | ||||||
\(317\) | − | 1.89960e11i | − | 1.05656i | −0.849070 | − | 0.528281i | \(-0.822837\pi\) | ||
0.849070 | − | 0.528281i | \(-0.177163\pi\) | |||||||
\(318\) | 1.70388e10 | 0.0934364 | ||||||||
\(319\) | −2.48014e11 | − | 1.18211e11i | −1.34097 | − | 0.639144i | ||||
\(320\) | 8.14033e10 | 0.433977 | ||||||||
\(321\) | 2.55949e11i | 1.34549i | ||||||||
\(322\) | − | 1.93179e11i | − | 1.00140i | ||||||
\(323\) | −3.07729e10 | −0.157310 | ||||||||
\(324\) | 2.10873e9 | 0.0106309 | ||||||||
\(325\) | 1.99144e11 | 0.990128 | ||||||||
\(326\) | 2.05230e11 | 1.00638 | ||||||||
\(327\) | − | 1.09467e11i | − | 0.529443i | ||||||
\(328\) | 4.24914e10 | 0.202707 | ||||||||
\(329\) | − | 1.04604e11i | − | 0.492229i | ||||||
\(330\) | 3.93321e11i | 1.82572i | ||||||||
\(331\) | 8.66640e9i | 0.0396837i | 0.999803 | + | 0.0198419i | \(0.00631628\pi\) | ||||
−0.999803 | + | 0.0198419i | \(0.993684\pi\) | |||||||
\(332\) | −9.73193e10 | −0.439620 | ||||||||
\(333\) | 1.75271e11i | 0.781108i | ||||||||
\(334\) | 9.32638e10i | 0.410066i | ||||||||
\(335\) | 1.78800e10 | 0.0775650 | ||||||||
\(336\) | 4.54899e11i | 1.94710i | ||||||||
\(337\) | − | 8.34807e9i | − | 0.0352575i | −0.999845 | − | 0.0176288i | \(-0.994388\pi\) | ||
0.999845 | − | 0.0176288i | \(-0.00561170\pi\) | |||||||
\(338\) | 6.48384e11i | 2.70214i | ||||||||
\(339\) | −3.01604e11 | −1.24033 | ||||||||
\(340\) | − | 7.21037e9i | − | 0.0292619i | ||||||
\(341\) | 6.28607e11 | 2.51759 | ||||||||
\(342\) | −4.17842e11 | −1.65156 | ||||||||
\(343\) | −2.51986e11 | −0.982997 | ||||||||
\(344\) | 3.84173e10 | 0.147915 | ||||||||
\(345\) | − | 2.54543e11i | − | 0.967333i | ||||||
\(346\) | − | 2.78567e10i | − | 0.104493i | ||||||
\(347\) | 2.46570e11 | 0.912974 | 0.456487 | − | 0.889730i | \(-0.349107\pi\) | ||||
0.456487 | + | 0.889730i | \(0.349107\pi\) | |||||||
\(348\) | 1.00343e11 | + | 4.78266e10i | 0.366760 | + | 0.174809i | ||||
\(349\) | 8.56684e10 | 0.309105 | 0.154553 | − | 0.987985i | \(-0.450606\pi\) | ||||
0.154553 | + | 0.987985i | \(0.450606\pi\) | |||||||
\(350\) | − | 1.71039e11i | − | 0.609242i | ||||||
\(351\) | − | 5.07467e11i | − | 1.78454i | ||||||
\(352\) | −2.10905e11 | −0.732226 | ||||||||
\(353\) | −1.96746e11 | −0.674404 | −0.337202 | − | 0.941432i | \(-0.609481\pi\) | ||||
−0.337202 | + | 0.941432i | \(0.609481\pi\) | |||||||
\(354\) | 9.55483e11 | 3.23376 | ||||||||
\(355\) | −2.47343e11 | −0.826556 | ||||||||
\(356\) | 4.36909e10i | 0.144167i | ||||||||
\(357\) | −8.56863e10 | −0.279193 | ||||||||
\(358\) | − | 4.16283e11i | − | 1.33941i | ||||||
\(359\) | 1.70052e11i | 0.540326i | 0.962815 | + | 0.270163i | \(0.0870776\pi\) | ||||
−0.962815 | + | 0.270163i | \(0.912922\pi\) | |||||||
\(360\) | 2.90577e11i | 0.911801i | ||||||||
\(361\) | 4.77334e10 | 0.147924 | ||||||||
\(362\) | − | 4.22219e11i | − | 1.29226i | ||||||
\(363\) | 6.43550e11i | 1.94537i | ||||||||
\(364\) | 1.58512e11 | 0.473266 | ||||||||
\(365\) | − | 2.91411e11i | − | 0.859385i | ||||||
\(366\) | − | 9.35105e11i | − | 2.72393i | ||||||
\(367\) | 1.08673e11i | 0.312698i | 0.987702 | + | 0.156349i | \(0.0499725\pi\) | ||||
−0.987702 | + | 0.156349i | \(0.950028\pi\) | |||||||
\(368\) | 3.68244e11 | 1.04669 | ||||||||
\(369\) | 1.37925e11i | 0.387278i | ||||||||
\(370\) | −1.34254e11 | −0.372408 | ||||||||
\(371\) | 1.92076e10 | 0.0526369 | ||||||||
\(372\) | −2.54326e11 | −0.688570 | ||||||||
\(373\) | 6.34254e11 | 1.69658 | 0.848288 | − | 0.529535i | \(-0.177634\pi\) | ||||
0.848288 | + | 0.529535i | \(0.177634\pi\) | |||||||
\(374\) | − | 1.07181e11i | − | 0.283266i | ||||||
\(375\) | − | 6.45999e11i | − | 1.68691i | ||||||
\(376\) | 1.57118e11 | 0.405397 | ||||||||
\(377\) | −3.11856e11 | + | 6.54294e11i | −0.795092 | + | 1.66816i | ||||
\(378\) | −4.35851e11 | −1.09806 | ||||||||
\(379\) | − | 3.44954e10i | − | 0.0858785i | −0.999078 | − | 0.0429392i | \(-0.986328\pi\) | ||
0.999078 | − | 0.0429392i | \(-0.0136722\pi\) | |||||||
\(380\) | − | 6.44244e10i | − | 0.158498i | ||||||
\(381\) | −5.81829e11 | −1.41460 | ||||||||
\(382\) | 4.06998e11 | 0.977928 | ||||||||
\(383\) | −6.39905e11 | −1.51957 | −0.759786 | − | 0.650173i | \(-0.774696\pi\) | ||||
−0.759786 | + | 0.650173i | \(0.774696\pi\) | |||||||
\(384\) | −8.28154e11 | −1.94366 | ||||||||
\(385\) | 4.43386e11i | 1.02851i | ||||||||
\(386\) | −1.95046e11 | −0.447191 | ||||||||
\(387\) | 1.24700e11i | 0.282597i | ||||||||
\(388\) | − | 4.90792e10i | − | 0.109940i | ||||||
\(389\) | − | 5.67805e11i | − | 1.25726i | −0.777704 | − | 0.628631i | \(-0.783616\pi\) | ||
0.777704 | − | 0.628631i | \(-0.216384\pi\) | |||||||
\(390\) | 1.03763e12 | 2.27118 | ||||||||
\(391\) | 6.93636e10i | 0.150085i | ||||||||
\(392\) | 1.27882e10i | 0.0273540i | ||||||||
\(393\) | −8.74827e10 | −0.184993 | ||||||||
\(394\) | 2.97739e11i | 0.622448i | ||||||||
\(395\) | − | 2.94332e10i | − | 0.0608346i | ||||||
\(396\) | − | 2.92942e11i | − | 0.598623i | ||||||
\(397\) | −7.35961e11 | −1.48695 | −0.743477 | − | 0.668762i | \(-0.766825\pi\) | ||||
−0.743477 | + | 0.668762i | \(0.766825\pi\) | |||||||
\(398\) | 9.74794e11i | 1.94733i | ||||||||
\(399\) | −7.65604e11 | −1.51226 | ||||||||
\(400\) | 3.26041e11 | 0.636799 | ||||||||
\(401\) | −1.23592e11 | −0.238694 | −0.119347 | − | 0.992853i | \(-0.538080\pi\) | ||||
−0.119347 | + | 0.992853i | \(0.538080\pi\) | |||||||
\(402\) | −1.07532e11 | −0.205363 | ||||||||
\(403\) | − | 1.65835e12i | − | 3.13186i | ||||||
\(404\) | − | 4.27261e10i | − | 0.0797953i | ||||||
\(405\) | 1.55610e10 | 0.0287403 | ||||||||
\(406\) | 5.61956e11 | + | 2.67845e11i | 1.02644 | + | 0.489234i | ||||
\(407\) | −4.01705e11 | −0.725658 | ||||||||
\(408\) | − | 1.28703e11i | − | 0.229942i | ||||||
\(409\) | − | 6.27607e11i | − | 1.10900i | −0.832183 | − | 0.554502i | \(-0.812909\pi\) | ||
0.832183 | − | 0.554502i | \(-0.187091\pi\) | |||||||
\(410\) | −1.05647e11 | −0.184642 | ||||||||
\(411\) | −7.56948e11 | −1.30851 | ||||||||
\(412\) | −1.25975e10 | −0.0215401 | ||||||||
\(413\) | 1.07710e12 | 1.82172 | ||||||||
\(414\) | 9.41838e11i | 1.57570i | ||||||||
\(415\) | −7.18151e11 | −1.18850 | ||||||||
\(416\) | 5.56396e11i | 0.910885i | ||||||||
\(417\) | 1.53519e12i | 2.48627i | ||||||||
\(418\) | − | 9.57655e11i | − | 1.53432i | ||||||
\(419\) | −5.64770e11 | −0.895176 | −0.447588 | − | 0.894240i | \(-0.647717\pi\) | ||||
−0.447588 | + | 0.894240i | \(0.647717\pi\) | |||||||
\(420\) | − | 1.79388e11i | − | 0.281302i | ||||||
\(421\) | − | 9.40828e11i | − | 1.45962i | −0.683649 | − | 0.729811i | \(-0.739608\pi\) | ||
0.683649 | − | 0.729811i | \(-0.260392\pi\) | |||||||
\(422\) | 7.09228e11 | 1.08863 | ||||||||
\(423\) | 5.09995e11i | 0.774523i | ||||||||
\(424\) | 2.88503e10i | 0.0433514i | ||||||||
\(425\) | 6.14142e10i | 0.0913101i | ||||||||
\(426\) | 1.48755e12 | 2.18841 | ||||||||
\(427\) | − | 1.05413e12i | − | 1.53451i | ||||||
\(428\) | 1.46018e11 | 0.210334 | ||||||||
\(429\) | 3.10472e12 | 4.42553 | ||||||||
\(430\) | −9.55177e10 | −0.134734 | ||||||||
\(431\) | 1.30054e12 | 1.81542 | 0.907708 | − | 0.419602i | \(-0.137830\pi\) | ||||
0.907708 | + | 0.419602i | \(0.137830\pi\) | |||||||
\(432\) | − | 8.30833e11i | − | 1.14772i | ||||||
\(433\) | 1.41146e11i | 0.192962i | 0.995335 | + | 0.0964810i | \(0.0307587\pi\) | ||||
−0.995335 | + | 0.0964810i | \(0.969241\pi\) | |||||||
\(434\) | −1.42431e12 | −1.92709 | ||||||||
\(435\) | 7.40466e11 | + | 3.52928e11i | 0.991525 | + | 0.472590i | ||||
\(436\) | −6.24505e10 | −0.0827650 | ||||||||
\(437\) | 6.19761e11i | 0.812939i | ||||||||
\(438\) | 1.75258e12i | 2.27533i | ||||||||
\(439\) | 3.05187e11 | 0.392171 | 0.196086 | − | 0.980587i | \(-0.437177\pi\) | ||||
0.196086 | + | 0.980587i | \(0.437177\pi\) | |||||||
\(440\) | −6.65976e11 | −0.847074 | ||||||||
\(441\) | −4.15096e10 | −0.0522607 | ||||||||
\(442\) | −2.82757e11 | −0.352381 | ||||||||
\(443\) | − | 8.29399e11i | − | 1.02317i | −0.859233 | − | 0.511584i | \(-0.829059\pi\) | ||
0.859233 | − | 0.511584i | \(-0.170941\pi\) | |||||||
\(444\) | 1.62525e11 | 0.198471 | ||||||||
\(445\) | 3.22409e11i | 0.389751i | ||||||||
\(446\) | 7.62786e11i | 0.912842i | ||||||||
\(447\) | 1.00760e12i | 1.19373i | ||||||||
\(448\) | −5.51885e11 | −0.647288 | ||||||||
\(449\) | 6.65860e11i | 0.773169i | 0.922254 | + | 0.386585i | \(0.126345\pi\) | ||||
−0.922254 | + | 0.386585i | \(0.873655\pi\) | |||||||
\(450\) | 8.33899e11i | 0.958643i | ||||||||
\(451\) | −3.16110e11 | −0.359786 | ||||||||
\(452\) | 1.72064e11i | 0.193895i | ||||||||
\(453\) | − | 5.59534e11i | − | 0.624287i | ||||||
\(454\) | − | 7.25524e10i | − | 0.0801494i | ||||||
\(455\) | 1.16971e12 | 1.27946 | ||||||||
\(456\) | − | 1.14996e12i | − | 1.24549i | ||||||
\(457\) | −9.89473e11 | −1.06116 | −0.530580 | − | 0.847635i | \(-0.678026\pi\) | ||||
−0.530580 | + | 0.847635i | \(0.678026\pi\) | |||||||
\(458\) | −1.67897e12 | −1.78299 | ||||||||
\(459\) | 1.56499e11 | 0.164571 | ||||||||
\(460\) | −1.45216e11 | −0.151218 | ||||||||
\(461\) | 4.27395e11i | 0.440733i | 0.975417 | + | 0.220366i | \(0.0707253\pi\) | ||||
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(462\) | − | 2.66657e12i | − | 2.72310i | ||||||
\(463\) | −5.62508e11 | −0.568871 | −0.284436 | − | 0.958695i | \(-0.591806\pi\) | ||||
−0.284436 | + | 0.958695i | \(0.591806\pi\) | |||||||
\(464\) | −5.10575e11 | + | 1.07122e12i | −0.511362 | + | 1.07287i | ||||
\(465\) | −1.87676e12 | −1.86153 | ||||||||
\(466\) | − | 1.75631e12i | − | 1.72530i | ||||||
\(467\) | 9.75663e11i | 0.949235i | 0.880192 | + | 0.474617i | \(0.157414\pi\) | ||||
−0.880192 | + | 0.474617i | \(0.842586\pi\) | |||||||
\(468\) | −7.72820e11 | −0.744684 | ||||||||
\(469\) | −1.21220e11 | −0.115690 | ||||||||
\(470\) | −3.90645e11 | −0.369269 | ||||||||
\(471\) | 1.81781e12 | 1.70198 | ||||||||
\(472\) | 1.61784e12i | 1.50036i | ||||||||
\(473\) | −2.85801e11 | −0.262536 | ||||||||
\(474\) | 1.77015e11i | 0.161067i | ||||||||
\(475\) | 5.48734e11i | 0.494584i | ||||||||
\(476\) | 4.88837e10i | 0.0436448i | ||||||||
\(477\) | −9.36462e10 | −0.0828242 | ||||||||
\(478\) | 1.97613e12i | 1.73137i | ||||||||
\(479\) | − | 8.35058e11i | − | 0.724781i | −0.932026 | − | 0.362391i | \(-0.881961\pi\) | ||
0.932026 | − | 0.362391i | \(-0.118039\pi\) | |||||||
\(480\) | 6.29675e11 | 0.541416 | ||||||||
\(481\) | 1.05975e12i | 0.902715i | ||||||||
\(482\) | − | 1.76758e12i | − | 1.49165i | ||||||
\(483\) | 1.72571e12i | 1.44280i | ||||||||
\(484\) | 3.67142e11 | 0.304110 | ||||||||
\(485\) | − | 3.62171e11i | − | 0.297219i | ||||||
\(486\) | −1.42252e12 | −1.15663 | ||||||||
\(487\) | 1.57701e12 | 1.27044 | 0.635219 | − | 0.772332i | \(-0.280910\pi\) | ||||
0.635219 | + | 0.772332i | \(0.280910\pi\) | |||||||
\(488\) | 1.58333e12 | 1.26381 | ||||||||
\(489\) | −1.83336e12 | −1.44997 | ||||||||
\(490\) | − | 3.17955e10i | − | 0.0249163i | ||||||
\(491\) | − | 1.15196e12i | − | 0.894477i | −0.894415 | − | 0.447239i | \(-0.852407\pi\) | ||
0.894415 | − | 0.447239i | \(-0.147593\pi\) | |||||||
\(492\) | 1.27894e11 | 0.0984029 | ||||||||
\(493\) | −2.01779e11 | − | 9.61736e10i | −0.153838 | − | 0.0733238i | ||||
\(494\) | −2.52642e12 | −1.90869 | ||||||||
\(495\) | − | 2.16172e12i | − | 1.61836i | ||||||
\(496\) | − | 2.71507e12i | − | 2.01425i | ||||||
\(497\) | 1.67690e12 | 1.23283 | ||||||||
\(498\) | 4.31904e12 | 3.14670 | ||||||||
\(499\) | 4.80672e11 | 0.347054 | 0.173527 | − | 0.984829i | \(-0.444484\pi\) | ||||
0.173527 | + | 0.984829i | \(0.444484\pi\) | |||||||
\(500\) | −3.68540e11 | −0.263705 | ||||||||
\(501\) | − | 8.33148e11i | − | 0.590816i | ||||||
\(502\) | 1.26949e12 | 0.892197 | ||||||||
\(503\) | 1.70492e12i | 1.18754i | 0.804634 | + | 0.593771i | \(0.202361\pi\) | ||||
−0.804634 | + | 0.593771i | \(0.797639\pi\) | |||||||
\(504\) | − | 1.97001e12i | − | 1.35997i | ||||||
\(505\) | − | 3.15290e11i | − | 0.215724i | ||||||
\(506\) | −2.15860e12 | −1.46385 | ||||||||
\(507\) | − | 5.79217e12i | − | 3.89319i | ||||||
\(508\) | 3.31931e11i | 0.221137i | ||||||||
\(509\) | −3.58315e11 | −0.236611 | −0.118305 | − | 0.992977i | \(-0.537746\pi\) | ||||
−0.118305 | + | 0.992977i | \(0.537746\pi\) | |||||||
\(510\) | 3.19997e11i | 0.209450i | ||||||||
\(511\) | 1.97566e12i | 1.28179i | ||||||||
\(512\) | − | 6.35782e11i | − | 0.408878i | ||||||
\(513\) | 1.39831e12 | 0.891405 | ||||||||
\(514\) | 5.58178e11i | 0.352727i | ||||||||
\(515\) | −9.29613e10 | −0.0582331 | ||||||||
\(516\) | 1.15631e11 | 0.0718046 | ||||||||
\(517\) | −1.16886e12 | −0.719540 | ||||||||
\(518\) | 9.10193e11 | 0.555456 | ||||||||
\(519\) | 2.48851e11i | 0.150552i | ||||||||
\(520\) | 1.75693e12i | 1.05376i | ||||||||
\(521\) | −1.26025e12 | −0.749356 | −0.374678 | − | 0.927155i | \(-0.622247\pi\) | ||||
−0.374678 | + | 0.927155i | \(0.622247\pi\) | |||||||
\(522\) | −2.73980e12 | − | 1.30587e12i | −1.61511 | − | 0.769810i | ||||
\(523\) | 2.47350e12 | 1.44562 | 0.722809 | − | 0.691048i | \(-0.242851\pi\) | ||||
0.722809 | + | 0.691048i | \(0.242851\pi\) | |||||||
\(524\) | 4.99085e10i | 0.0289190i | ||||||||
\(525\) | 1.52794e12i | 0.877786i | ||||||||
\(526\) | −1.76228e12 | −1.00378 | ||||||||
\(527\) | 5.11420e11 | 0.288822 | ||||||||
\(528\) | 5.08310e12 | 2.84627 | ||||||||
\(529\) | −4.04178e11 | −0.224400 | ||||||||
\(530\) | − | 7.17310e10i | − | 0.0394880i | ||||||
\(531\) | −5.25140e12 | −2.86648 | ||||||||
\(532\) | 4.36774e11i | 0.236404i | ||||||||
\(533\) | 8.33940e11i | 0.447571i | ||||||||
\(534\) | − | 1.93900e12i | − | 1.03191i | ||||||
\(535\) | 1.07751e12 | 0.568631 | ||||||||
\(536\) | − | 1.82075e11i | − | 0.0952816i | ||||||
\(537\) | 3.71876e12i | 1.92981i | ||||||||
\(538\) | −1.25591e12 | −0.646305 | ||||||||
\(539\) | − | 9.51361e10i | − | 0.0485508i | ||||||
\(540\) | 3.27637e11i | 0.165814i | ||||||||
\(541\) | − | 2.21016e12i | − | 1.10927i | −0.832094 | − | 0.554634i | \(-0.812858\pi\) | ||
0.832094 | − | 0.554634i | \(-0.187142\pi\) | |||||||
\(542\) | 4.37764e12 | 2.17893 | ||||||||
\(543\) | 3.77178e12i | 1.86186i | ||||||||
\(544\) | −1.71588e11 | −0.0840023 | ||||||||
\(545\) | −4.60843e11 | −0.223753 | ||||||||
\(546\) | −7.03476e12 | −3.38753 | ||||||||
\(547\) | −1.24567e12 | −0.594921 | −0.297460 | − | 0.954734i | \(-0.596140\pi\) | ||||
−0.297460 | + | 0.954734i | \(0.596140\pi\) | |||||||
\(548\) | 4.31835e11i | 0.204553i | ||||||||
\(549\) | 5.13940e12i | 2.41455i | ||||||||
\(550\) | −1.91122e12 | −0.890591 | ||||||||
\(551\) | −1.80288e12 | − | 8.59308e11i | −0.833270 | − | 0.397161i | ||||
\(552\) | −2.59206e12 | −1.18828 | ||||||||
\(553\) | 1.99546e11i | 0.0907363i | ||||||||
\(554\) | 5.35590e11i | 0.241568i | ||||||||
\(555\) | 1.19932e12 | 0.536559 | ||||||||
\(556\) | 8.75817e11 | 0.388666 | ||||||||
\(557\) | 2.69656e12 | 1.18703 | 0.593516 | − | 0.804822i | \(-0.297739\pi\) | ||||
0.593516 | + | 0.804822i | \(0.297739\pi\) | |||||||
\(558\) | 6.94420e12 | 3.03228 | ||||||||
\(559\) | 7.53980e11i | 0.326593i | ||||||||
\(560\) | 1.91507e12 | 0.822883 | ||||||||
\(561\) | 9.57471e11i | 0.408124i | ||||||||
\(562\) | − | 2.71440e12i | − | 1.14778i | ||||||
\(563\) | − | 1.78577e12i | − | 0.749098i | −0.927207 | − | 0.374549i | \(-0.877797\pi\) | ||
0.927207 | − | 0.374549i | \(-0.122203\pi\) | |||||||
\(564\) | 4.72906e11 | 0.196797 | ||||||||
\(565\) | 1.26971e12i | 0.524189i | ||||||||
\(566\) | − | 4.41410e12i | − | 1.80787i | ||||||
\(567\) | −1.05498e11 | −0.0428668 | ||||||||
\(568\) | 2.51874e12i | 1.01535i | ||||||||
\(569\) | − | 2.11081e12i | − | 0.844197i | −0.906550 | − | 0.422099i | \(-0.861294\pi\) | ||
0.906550 | − | 0.422099i | \(-0.138706\pi\) | |||||||
\(570\) | 2.85916e12i | 1.13449i | ||||||||
\(571\) | −7.30451e11 | −0.287560 | −0.143780 | − | 0.989610i | \(-0.545926\pi\) | ||||
−0.143780 | + | 0.989610i | \(0.545926\pi\) | |||||||
\(572\) | − | 1.77123e12i | − | 0.691820i | ||||||
\(573\) | −3.63581e12 | −1.40898 | ||||||||
\(574\) | 7.16250e11 | 0.275398 | ||||||||
\(575\) | 1.23687e12 | 0.471868 | ||||||||
\(576\) | 2.69070e12 | 1.01851 | ||||||||
\(577\) | 2.07846e12i | 0.780638i | 0.920680 | + | 0.390319i | \(0.127635\pi\) | ||||
−0.920680 | + | 0.390319i | \(0.872365\pi\) | |||||||
\(578\) | 2.91528e12i | 1.08644i | ||||||||
\(579\) | 1.74239e12 | 0.644306 | ||||||||
\(580\) | 2.01344e11 | − | 4.22433e11i | 0.0738775 | − | 0.155000i | ||||
\(581\) | 4.86880e12 | 1.77268 | ||||||||
\(582\) | 2.17814e12i | 0.786923i | ||||||||
\(583\) | − | 2.14628e11i | − | 0.0769446i | ||||||
\(584\) | −2.96749e12 | −1.05568 | ||||||||
\(585\) | −5.70289e12 | −2.01323 | ||||||||
\(586\) | −5.72555e11 | −0.200575 | ||||||||
\(587\) | 1.22754e12 | 0.426740 | 0.213370 | − | 0.976971i | \(-0.431556\pi\) | ||||
0.213370 | + | 0.976971i | \(0.431556\pi\) | |||||||
\(588\) | 3.84909e10i | 0.0132788i | ||||||||
\(589\) | 4.56952e12 | 1.56441 | ||||||||
\(590\) | − | 4.02246e12i | − | 1.36665i | ||||||
\(591\) | − | 2.65978e12i | − | 0.896813i | ||||||
\(592\) | 1.73504e12i | 0.580579i | ||||||||
\(593\) | 3.59477e12 | 1.19378 | 0.596890 | − | 0.802323i | \(-0.296403\pi\) | ||||
0.596890 | + | 0.802323i | \(0.296403\pi\) | |||||||
\(594\) | 4.87025e12i | 1.60514i | ||||||||
\(595\) | 3.60729e11i | 0.117992i | ||||||||
\(596\) | 5.74833e11 | 0.186610 | ||||||||
\(597\) | − | 8.70807e12i | − | 2.80567i | ||||||
\(598\) | 5.69468e12i | 1.82102i | ||||||||
\(599\) | 5.88884e11i | 0.186900i | 0.995624 | + | 0.0934499i | \(0.0297895\pi\) | ||||
−0.995624 | + | 0.0934499i | \(0.970210\pi\) | |||||||
\(600\) | −2.29500e12 | −0.722939 | ||||||||
\(601\) | − | 6.43152e11i | − | 0.201084i | −0.994933 | − | 0.100542i | \(-0.967942\pi\) | ||
0.994933 | − | 0.100542i | \(-0.0320577\pi\) | |||||||
\(602\) | 6.47575e11 | 0.200958 | ||||||||
\(603\) | 5.91005e11 | 0.182038 | ||||||||
\(604\) | −3.19211e11 | −0.0975915 | ||||||||
\(605\) | 2.70926e12 | 0.822152 | ||||||||
\(606\) | 1.89619e12i | 0.571156i | ||||||||
\(607\) | − | 3.88974e12i | − | 1.16298i | −0.813555 | − | 0.581488i | \(-0.802471\pi\) | ||
0.813555 | − | 0.581488i | \(-0.197529\pi\) | |||||||
\(608\) | −1.53313e12 | −0.455002 | ||||||||
\(609\) | −5.02009e12 | − | 2.39272e12i | −1.47888 | − | 0.704879i | ||||
\(610\) | −3.93667e12 | −1.15118 | ||||||||
\(611\) | 3.08361e12i | 0.895104i | ||||||||
\(612\) | − | 2.38331e11i | − | 0.0686751i | ||||||
\(613\) | −3.06172e12 | −0.875778 | −0.437889 | − | 0.899029i | \(-0.644274\pi\) | ||||
−0.437889 | + | 0.899029i | \(0.644274\pi\) | |||||||
\(614\) | −7.14301e12 | −2.02826 | ||||||||
\(615\) | 9.43773e11 | 0.266029 | ||||||||
\(616\) | 4.51507e12 | 1.26343 | ||||||||
\(617\) | − | 4.30208e12i | − | 1.19507i | −0.801841 | − | 0.597537i | \(-0.796146\pi\) | ||
0.801841 | − | 0.597537i | \(-0.203854\pi\) | |||||||
\(618\) | 5.59079e11 | 0.154179 | ||||||||
\(619\) | 1.75113e12i | 0.479413i | 0.970845 | + | 0.239706i | \(0.0770512\pi\) | ||||
−0.970845 | + | 0.239706i | \(0.922949\pi\) | |||||||
\(620\) | 1.07068e12i | 0.291003i | ||||||||
\(621\) | − | 3.15186e12i | − | 0.850462i | ||||||
\(622\) | 6.90920e12 | 1.85085 | ||||||||
\(623\) | − | 2.18582e12i | − | 0.581323i | ||||||
\(624\) | − | 1.34099e13i | − | 3.54075i | ||||||
\(625\) | −6.75667e11 | −0.177122 | ||||||||
\(626\) | − | 8.76772e11i | − | 0.228193i | ||||||
\(627\) | 8.55497e12i | 2.21062i | ||||||||
\(628\) | − | 1.03705e12i | − | 0.266061i | ||||||
\(629\) | −3.26818e11 | −0.0832488 | ||||||||
\(630\) | 4.89807e12i | 1.23878i | ||||||||
\(631\) | −4.19856e12 | −1.05431 | −0.527155 | − | 0.849769i | \(-0.676741\pi\) | ||||
−0.527155 | + | 0.849769i | \(0.676741\pi\) | |||||||
\(632\) | −2.99723e11 | −0.0747298 | ||||||||
\(633\) | −6.33571e12 | −1.56848 | ||||||||
\(634\) | 4.80952e12 | 1.18223 | ||||||||
\(635\) | 2.44943e12i | 0.597837i | ||||||||
\(636\) | 8.68359e10i | 0.0210447i | ||||||||
\(637\) | −2.50982e11 | −0.0603969 | ||||||||
\(638\) | 2.99294e12 | − | 6.27938e12i | 0.715162 | − | 1.50046i | ||||
\(639\) | −8.17566e12 | −1.93985 | ||||||||
\(640\) | 3.48642e12i | 0.821429i | ||||||||
\(641\) | 5.18483e12i | 1.21303i | 0.795070 | + | 0.606517i | \(0.207434\pi\) | ||||
−0.795070 | + | 0.606517i | \(0.792566\pi\) | |||||||
\(642\) | −6.48028e12 | −1.50552 | ||||||||
\(643\) | 4.08571e12 | 0.942579 | 0.471289 | − | 0.881979i | \(-0.343789\pi\) | ||||
0.471289 | + | 0.881979i | \(0.343789\pi\) | |||||||
\(644\) | 9.84511e11 | 0.225545 | ||||||||
\(645\) | 8.53283e11 | 0.194122 | ||||||||
\(646\) | − | 7.79127e11i | − | 0.176020i | ||||||
\(647\) | −5.24754e12 | −1.17730 | −0.588649 | − | 0.808389i | \(-0.700340\pi\) | ||||
−0.588649 | + | 0.808389i | \(0.700340\pi\) | |||||||
\(648\) | − | 1.58461e11i | − | 0.0353048i | ||||||
\(649\) | − | 1.20357e13i | − | 2.66300i | ||||||
\(650\) | 5.04204e12i | 1.10789i | ||||||||
\(651\) | 1.27237e13 | 2.77652 | ||||||||
\(652\) | 1.04593e12i | 0.226666i | ||||||||
\(653\) | − | 4.07319e12i | − | 0.876648i | −0.898817 | − | 0.438324i | \(-0.855572\pi\) | ||
0.898817 | − | 0.438324i | \(-0.144428\pi\) | |||||||
\(654\) | 2.77156e12 | 0.592413 | ||||||||
\(655\) | 3.68291e11i | 0.0781817i | ||||||||
\(656\) | 1.36534e12i | 0.287855i | ||||||||
\(657\) | − | 9.63228e12i | − | 2.01690i | ||||||
\(658\) | 2.64843e12 | 0.550773 | ||||||||
\(659\) | 1.31285e12i | 0.271164i | 0.990766 | + | 0.135582i | \(0.0432904\pi\) | ||||
−0.990766 | + | 0.135582i | \(0.956710\pi\) | |||||||
\(660\) | −2.00451e12 | −0.411207 | ||||||||
\(661\) | 3.98945e12 | 0.812842 | 0.406421 | − | 0.913686i | \(-0.366777\pi\) | ||||
0.406421 | + | 0.913686i | \(0.366777\pi\) | |||||||
\(662\) | −2.19421e11 | −0.0444036 | ||||||||
\(663\) | 2.52593e12 | 0.507704 | ||||||||
\(664\) | 7.31306e12i | 1.45997i | ||||||||
\(665\) | 3.22310e12i | 0.639111i | ||||||||
\(666\) | −4.43762e12 | −0.874010 | ||||||||
\(667\) | −1.93692e12 | + | 4.06380e12i | −0.378919 | + | 0.794997i | ||||
\(668\) | −4.75307e11 | −0.0923592 | ||||||||
\(669\) | − | 6.81415e12i | − | 1.31521i | ||||||
\(670\) | 4.52697e11i | 0.0867903i | ||||||||
\(671\) | −1.17790e13 | −2.24315 | ||||||||
\(672\) | −4.26897e12 | −0.807534 | ||||||||
\(673\) | 4.19198e12 | 0.787683 | 0.393842 | − | 0.919178i | \(-0.371146\pi\) | ||||
0.393842 | + | 0.919178i | \(0.371146\pi\) | |||||||
\(674\) | 2.11362e11 | 0.0394509 | ||||||||
\(675\) | − | 2.79064e12i | − | 0.517413i | ||||||
\(676\) | −3.30441e12 | −0.608602 | ||||||||
\(677\) | 1.73512e12i | 0.317454i | 0.987322 | + | 0.158727i | \(0.0507390\pi\) | ||||
−0.987322 | + | 0.158727i | \(0.949261\pi\) | |||||||
\(678\) | − | 7.63620e12i | − | 1.38785i | ||||||
\(679\) | 2.45539e12i | 0.443309i | ||||||||
\(680\) | −5.41823e11 | −0.0971778 | ||||||||
\(681\) | 6.48128e11i | 0.115478i | ||||||||
\(682\) | 1.59155e13i | 2.81702i | ||||||||
\(683\) | −4.07075e12 | −0.715783 | −0.357891 | − | 0.933763i | \(-0.616504\pi\) | ||||
−0.357891 | + | 0.933763i | \(0.616504\pi\) | |||||||
\(684\) | − | 2.12948e12i | − | 0.371981i | ||||||
\(685\) | 3.18666e12i | 0.553003i | ||||||||
\(686\) | − | 6.37993e12i | − | 1.09991i | ||||||
\(687\) | 1.49987e13 | 2.56890 | ||||||||
\(688\) | 1.23443e12i | 0.210048i | ||||||||
\(689\) | −5.66218e11 | −0.0957187 | ||||||||
\(690\) | 6.44469e12 | 1.08238 | ||||||||
\(691\) | −5.33558e12 | −0.890288 | −0.445144 | − | 0.895459i | \(-0.646847\pi\) | ||||
−0.445144 | + | 0.895459i | \(0.646847\pi\) | |||||||
\(692\) | 1.41968e11 | 0.0235350 | ||||||||
\(693\) | 1.46556e13i | 2.41382i | ||||||||
\(694\) | 6.24283e12i | 1.02156i | ||||||||
\(695\) | 6.46294e12 | 1.05075 | ||||||||
\(696\) | 3.59393e12 | − | 7.54030e12i | 0.580534 | − | 1.21800i | ||||
\(697\) | −2.57180e11 | −0.0412753 | ||||||||
\(698\) | 2.16901e12i | 0.345869i | ||||||||
\(699\) | 1.56895e13i | 2.48578i | ||||||||
\(700\) | 8.71681e11 | 0.137220 | ||||||||
\(701\) | −2.30002e12 | −0.359750 | −0.179875 | − | 0.983689i | \(-0.557569\pi\) | ||||
−0.179875 | + | 0.983689i | \(0.557569\pi\) | |||||||
\(702\) | 1.28484e13 | 1.99678 | ||||||||
\(703\) | −2.92011e12 | −0.450920 | ||||||||
\(704\) | 6.16683e12i | 0.946205i | ||||||||
\(705\) | 3.48973e12 | 0.532036 | ||||||||
\(706\) | − | 4.98134e12i | − | 0.754615i | ||||||
\(707\) | 2.13755e12i | 0.321758i | ||||||||
\(708\) | 4.86950e12i | 0.728341i | ||||||||
\(709\) | −7.74840e12 | −1.15161 | −0.575803 | − | 0.817588i | \(-0.695310\pi\) | ||||
−0.575803 | + | 0.817588i | \(0.695310\pi\) | |||||||
\(710\) | − | 6.26239e12i | − | 0.924863i | ||||||
\(711\) | − | 9.72884e11i | − | 0.142774i | ||||||
\(712\) | 3.28315e12 | 0.478774 | ||||||||
\(713\) | − | 1.02999e13i | − | 1.49256i | ||||||
\(714\) | − | 2.16946e12i | − | 0.312399i | ||||||
\(715\) | − | 1.30705e13i | − | 1.87032i | ||||||
\(716\) | 2.12153e12 | 0.301676 | ||||||||
\(717\) | − | 1.76532e13i | − | 2.49452i | ||||||
\(718\) | −4.30548e12 | −0.604590 | ||||||||
\(719\) | 6.49943e12 | 0.906975 | 0.453487 | − | 0.891263i | \(-0.350180\pi\) | ||||
0.453487 | + | 0.891263i | \(0.350180\pi\) | |||||||
\(720\) | −9.33686e12 | −1.29481 | ||||||||
\(721\) | 6.30244e11 | 0.0868560 | ||||||||
\(722\) | 1.20854e12i | 0.165518i | ||||||||
\(723\) | 1.57902e13i | 2.14914i | ||||||||
\(724\) | 2.15179e12 | 0.291055 | ||||||||
\(725\) | −1.71494e12 | + | 3.59806e12i | −0.230531 | + | 0.483669i | ||||
\(726\) | −1.62938e13 | −2.17675 | ||||||||
\(727\) | 2.92436e12i | 0.388262i | 0.980976 | + | 0.194131i | \(0.0621887\pi\) | ||||
−0.980976 | + | 0.194131i | \(0.937811\pi\) | |||||||
\(728\) | − | 1.19114e13i | − | 1.57170i | ||||||
\(729\) | 1.23861e13 | 1.62428 | ||||||||
\(730\) | 7.37813e12 | 0.961597 | ||||||||
\(731\) | −2.32521e11 | −0.0301186 | ||||||||
\(732\) | 4.76564e12 | 0.613510 | ||||||||
\(733\) | − | 2.47043e12i | − | 0.316086i | −0.987432 | − | 0.158043i | \(-0.949482\pi\) | ||
0.987432 | − | 0.158043i | \(-0.0505185\pi\) | |||||||
\(734\) | −2.75146e12 | −0.349889 | ||||||||
\(735\) | 2.84037e11i | 0.0358989i | ||||||||
\(736\) | 3.45575e12i | 0.434103i | ||||||||
\(737\) | 1.35453e12i | 0.169116i | ||||||||
\(738\) | −3.49206e12 | −0.433339 | ||||||||
\(739\) | − | 4.97944e12i | − | 0.614159i | −0.951684 | − | 0.307080i | \(-0.900648\pi\) | ||
0.951684 | − | 0.307080i | \(-0.0993518\pi\) | |||||||
\(740\) | − | 6.84208e11i | − | 0.0838775i | ||||||
\(741\) | 2.25691e13 | 2.75000 | ||||||||
\(742\) | 4.86310e11i | 0.0588973i | ||||||||
\(743\) | 6.90155e12i | 0.830801i | 0.909639 | + | 0.415401i | \(0.136359\pi\) | ||||
−0.909639 | + | 0.415401i | \(0.863641\pi\) | |||||||
\(744\) | 1.91113e13i | 2.28672i | ||||||||
\(745\) | 4.24189e12 | 0.504494 | ||||||||
\(746\) | 1.60584e13i | 1.89836i | ||||||||
\(747\) | −2.37377e13 | −2.78931 | ||||||||
\(748\) | 5.46232e11 | 0.0637999 | ||||||||
\(749\) | −7.30515e12 | −0.848127 | ||||||||
\(750\) | 1.63558e13 | 1.88754 | ||||||||
\(751\) | − | 3.12113e12i | − | 0.358040i | −0.983845 | − | 0.179020i | \(-0.942707\pi\) | ||
0.983845 | − | 0.179020i | \(-0.0572927\pi\) | |||||||
\(752\) | 5.04853e12i | 0.575685i | ||||||||
\(753\) | −1.13406e13 | −1.28546 | ||||||||
\(754\) | −1.65658e13 | − | 7.89576e12i | −1.86656 | − | 0.889657i | ||||
\(755\) | −2.35557e12 | −0.263836 | ||||||||
\(756\) | − | 2.22126e12i | − | 0.247315i | ||||||
\(757\) | − | 2.84714e12i | − | 0.315121i | −0.987509 | − | 0.157560i | \(-0.949637\pi\) | ||
0.987509 | − | 0.157560i | \(-0.0503629\pi\) | |||||||
\(758\) | 8.73376e11 | 0.0960925 | ||||||||
\(759\) | 1.92833e13 | 2.10909 | ||||||||
\(760\) | −4.84117e12 | −0.526367 | ||||||||
\(761\) | −8.50265e12 | −0.919017 | −0.459508 | − | 0.888173i | \(-0.651974\pi\) | ||||
−0.459508 | + | 0.888173i | \(0.651974\pi\) | |||||||
\(762\) | − | 1.47311e13i | − | 1.58284i | ||||||
\(763\) | 3.12435e12 | 0.333733 | ||||||||
\(764\) | 2.07421e12i | 0.220259i | ||||||||
\(765\) | − | 1.75872e12i | − | 0.185661i | ||||||
\(766\) | − | 1.62015e13i | − | 1.70030i | ||||||
\(767\) | −3.17518e13 | −3.31275 | ||||||||
\(768\) | − | 1.10675e13i | − | 1.14796i | ||||||
\(769\) | 2.79377e12i | 0.288086i | 0.989571 | + | 0.144043i | \(0.0460104\pi\) | ||||
−0.989571 | + | 0.144043i | \(0.953990\pi\) | |||||||
\(770\) | −1.12259e13 | −1.15084 | ||||||||
\(771\) | − | 4.98634e12i | − | 0.508203i | ||||||
\(772\) | − | 9.94026e11i | − | 0.100721i | ||||||
\(773\) | 1.50515e13i | 1.51626i | 0.652104 | + | 0.758129i | \(0.273886\pi\) | ||||
−0.652104 | + | 0.758129i | \(0.726114\pi\) | |||||||
\(774\) | −3.15724e12 | −0.316208 | ||||||||
\(775\) | − | 9.11952e12i | − | 0.908059i | ||||||
\(776\) | −3.68805e12 | −0.365106 | ||||||||
\(777\) | −8.13097e12 | −0.800291 | ||||||||
\(778\) | 1.43760e13 | 1.40680 | ||||||||
\(779\) | −2.29789e12 | −0.223569 | ||||||||
\(780\) | 5.28816e12i | 0.511539i | ||||||||
\(781\) | − | 1.87379e13i | − | 1.80215i | ||||||
\(782\) | −1.75619e12 | −0.167935 | ||||||||
\(783\) | 9.16876e12 | + | 4.37010e12i | 0.871731 | + | 0.415493i | ||||
\(784\) | −4.10911e11 | −0.0388441 | ||||||||
\(785\) | − | 7.65274e12i | − | 0.719289i | ||||||
\(786\) | − | 2.21494e12i | − | 0.206996i | ||||||
\(787\) | 3.12979e12 | 0.290823 | 0.145412 | − | 0.989371i | \(-0.453549\pi\) | ||||
0.145412 | + | 0.989371i | \(0.453549\pi\) | |||||||
\(788\) | −1.51739e12 | −0.140194 | ||||||||
\(789\) | 1.57429e13 | 1.44623 | ||||||||
\(790\) | 7.45209e11 | 0.0680700 | ||||||||
\(791\) | − | 8.60820e12i | − | 0.781840i | ||||||
\(792\) | −2.20131e13 | −1.98801 | ||||||||
\(793\) | 3.10746e13i | 2.79046i | ||||||||
\(794\) | − | 1.86335e13i | − | 1.66381i | ||||||
\(795\) | 6.40791e11i | 0.0568937i | ||||||||
\(796\) | −4.96791e12 | −0.438596 | ||||||||
\(797\) | 1.67045e13i | 1.46646i | 0.679978 | + | 0.733232i | \(0.261989\pi\) | ||||
−0.679978 | + | 0.733232i | \(0.738011\pi\) | |||||||
\(798\) | − | 1.93841e13i | − | 1.69212i | ||||||
\(799\) | −9.50958e11 | −0.0825470 | ||||||||
\(800\) | 3.05971e12i | 0.264104i | ||||||||
\(801\) | 1.06569e13i | 0.914713i | ||||||||
\(802\) | − | 3.12919e12i | − | 0.267084i | ||||||
\(803\) | 2.20763e13 | 1.87373 | ||||||||
\(804\) | − | 5.48024e11i | − | 0.0462538i | ||||||
\(805\) | 7.26503e12 | 0.609756 | ||||||||
\(806\) | 4.19871e13 | 3.50436 | ||||||||
\(807\) | 1.12193e13 | 0.931185 | ||||||||
\(808\) | −3.21065e12 | −0.264998 | ||||||||
\(809\) | − | 6.04286e12i | − | 0.495992i | −0.968761 | − | 0.247996i | \(-0.920228\pi\) | ||
0.968761 | − | 0.247996i | \(-0.0797719\pi\) | |||||||
\(810\) | 3.93984e11i | 0.0321586i | ||||||||
\(811\) | −5.01698e12 | −0.407238 | −0.203619 | − | 0.979050i | \(-0.565270\pi\) | ||||
−0.203619 | + | 0.979050i | \(0.565270\pi\) | |||||||
\(812\) | −1.36504e12 | + | 2.86394e12i | −0.110190 | + | 0.231186i | ||||
\(813\) | −3.91066e13 | −3.13937 | ||||||||
\(814\) | − | 1.01706e13i | − | 0.811965i | ||||||
\(815\) | 7.71823e12i | 0.612786i | ||||||||
\(816\) | 4.13550e12 | 0.326529 | ||||||||
\(817\) | −2.07757e12 | −0.163138 | ||||||||
\(818\) | 1.58902e13 | 1.24090 | ||||||||
\(819\) | 3.86635e13 | 3.00278 | ||||||||
\(820\) | − | 5.38418e11i | − | 0.0415870i | ||||||
\(821\) | 6.56513e12 | 0.504312 | 0.252156 | − | 0.967687i | \(-0.418860\pi\) | ||||
0.252156 | + | 0.967687i | \(0.418860\pi\) | |||||||
\(822\) | − | 1.91649e13i | − | 1.46414i | ||||||
\(823\) | 1.95790e13i | 1.48761i | 0.668395 | + | 0.743807i | \(0.266982\pi\) | ||||
−0.668395 | + | 0.743807i | \(0.733018\pi\) | |||||||
\(824\) | 9.46641e11i | 0.0715340i | ||||||||
\(825\) | 1.70734e13 | 1.28315 | ||||||||
\(826\) | 2.72708e13i | 2.03839i | ||||||||
\(827\) | 6.26218e12i | 0.465533i | 0.972533 | + | 0.232767i | \(0.0747778\pi\) | ||||
−0.972533 | + | 0.232767i | \(0.925222\pi\) | |||||||
\(828\) | −4.79996e12 | −0.354896 | ||||||||
\(829\) | − | 1.97426e13i | − | 1.45181i | −0.687796 | − | 0.725904i | \(-0.741421\pi\) | ||
0.687796 | − | 0.725904i | \(-0.258579\pi\) | |||||||
\(830\) | − | 1.81826e13i | − | 1.32986i | ||||||
\(831\) | − | 4.78456e12i | − | 0.348046i | ||||||
\(832\) | 1.62689e13 | 1.17707 | ||||||||
\(833\) | − | 7.74006e10i | − | 0.00556983i | ||||||
\(834\) | −3.88688e13 | −2.78198 | ||||||||
\(835\) | −3.50745e12 | −0.249690 | ||||||||
\(836\) | 4.88057e12 | 0.345575 | ||||||||
\(837\) | −2.32388e13 | −1.63662 | ||||||||
\(838\) | − | 1.42992e13i | − | 1.00164i | ||||||
\(839\) | 2.37593e12i | 0.165541i | 0.996569 | + | 0.0827704i | \(0.0263768\pi\) | ||||
−0.996569 | + | 0.0827704i | \(0.973623\pi\) | |||||||
\(840\) | −1.34801e13 | −0.934194 | ||||||||
\(841\) | −9.13600e12 | − | 1.12690e13i | −0.629759 | − | 0.776791i | ||||
\(842\) | 2.38205e13 | 1.63322 | ||||||||
\(843\) | 2.42484e13i | 1.65371i | ||||||||
\(844\) | 3.61449e12i | 0.245192i | ||||||||
\(845\) | −2.43843e13 | −1.64534 | ||||||||
\(846\) | −1.29124e13 | −0.866641 | ||||||||
\(847\) | −1.83678e13 | −1.22626 | ||||||||
\(848\) | −9.27020e11 | −0.0615613 | ||||||||
\(849\) | 3.94322e13i | 2.60475i | ||||||||
\(850\) | −1.55492e12 | −0.102170 | ||||||||
\(851\) | 6.58207e12i | 0.430209i | ||||||||
\(852\) | 7.58110e12i | 0.492895i | ||||||||
\(853\) | − | 4.09727e12i | − | 0.264987i | −0.991184 | − | 0.132493i | \(-0.957702\pi\) | ||
0.991184 | − | 0.132493i | \(-0.0422983\pi\) | |||||||
\(854\) | 2.66892e13 | 1.71702 | ||||||||
\(855\) | − | 1.57141e13i | − | 1.00564i | ||||||
\(856\) | − | 1.09725e13i | − | 0.698512i | ||||||
\(857\) | −9.58984e12 | −0.607292 | −0.303646 | − | 0.952785i | \(-0.598204\pi\) | ||||
−0.303646 | + | 0.952785i | \(0.598204\pi\) | |||||||
\(858\) | 7.86074e13i | 4.95188i | ||||||||
\(859\) | − | 1.27198e13i | − | 0.797100i | −0.917147 | − | 0.398550i | \(-0.869514\pi\) | ||
0.917147 | − | 0.398550i | \(-0.130486\pi\) | |||||||
\(860\) | − | 4.86794e11i | − | 0.0303460i | ||||||
\(861\) | −6.39844e12 | −0.396789 | ||||||||
\(862\) | 3.29279e13i | 2.03133i | ||||||||
\(863\) | 1.55064e13 | 0.951619 | 0.475810 | − | 0.879548i | \(-0.342155\pi\) | ||||
0.475810 | + | 0.879548i | \(0.342155\pi\) | |||||||
\(864\) | 7.79689e12 | 0.476003 | ||||||||
\(865\) | 1.04763e12 | 0.0636261 | ||||||||
\(866\) | −3.57361e12 | −0.215912 | ||||||||
\(867\) | − | 2.60429e13i | − | 1.56532i | ||||||
\(868\) | − | 7.25883e12i | − | 0.434038i | ||||||
\(869\) | 2.22976e12 | 0.132638 | ||||||||
\(870\) | −8.93566e12 | + | 1.87476e13i | −0.528798 | + | 1.10945i | ||||
\(871\) | 3.57342e12 | 0.210379 | ||||||||
\(872\) | 4.69284e12i | 0.274860i | ||||||||
\(873\) | − | 1.19712e13i | − | 0.697547i | ||||||
\(874\) | −1.56915e13 | −0.909627 | ||||||||
\(875\) | 1.84377e13 | 1.06334 | ||||||||
\(876\) | −8.93179e12 | −0.512472 | ||||||||
\(877\) | −3.32840e11 | −0.0189993 | −0.00949966 | − | 0.999955i | \(-0.503024\pi\) | ||||
−0.00949966 | + | 0.999955i | \(0.503024\pi\) | |||||||
\(878\) | 7.72692e12i | 0.438814i | ||||||||
\(879\) | 5.11477e12 | 0.288986 | ||||||||
\(880\) | − | 2.13992e13i | − | 1.20289i | ||||||
\(881\) | 1.80700e13i | 1.01057i | 0.862953 | + | 0.505285i | \(0.168613\pi\) | ||||
−0.862953 | + | 0.505285i | \(0.831387\pi\) | |||||||
\(882\) | − | 1.05097e12i | − | 0.0584763i | ||||||
\(883\) | −1.58747e13 | −0.878782 | −0.439391 | − | 0.898296i | \(-0.644806\pi\) | ||||
−0.439391 | + | 0.898296i | \(0.644806\pi\) | |||||||
\(884\) | − | 1.44103e12i | − | 0.0793668i | ||||||
\(885\) | 3.59336e13i | 1.96905i | ||||||||
\(886\) | 2.09992e13 | 1.14486 | ||||||||
\(887\) | 5.24376e12i | 0.284437i | 0.989835 | + | 0.142219i | \(0.0454236\pi\) | ||||
−0.989835 | + | 0.142219i | \(0.954576\pi\) | |||||||
\(888\) | − | 1.22129e13i | − | 0.659114i | ||||||
\(889\) | − | 1.66062e13i | − | 0.891688i | ||||||
\(890\) | −8.16296e12 | −0.436107 | ||||||||
\(891\) | 1.17885e12i | 0.0626627i | ||||||||
\(892\) | −3.88744e12 | −0.205599 | ||||||||
\(893\) | −8.49678e12 | −0.447119 | ||||||||
\(894\) | −2.55112e13 | −1.33571 | ||||||||
\(895\) | 1.56555e13 | 0.815574 | ||||||||
\(896\) | − | 2.36367e13i | − | 1.22518i | ||||||
\(897\) | − | 5.08720e13i | − | 2.62369i | ||||||
\(898\) | −1.68587e13 | −0.865127 | ||||||||
\(899\) | 2.99625e13 | + | 1.42810e13i | 1.52989 | + | 0.729190i | ||||
\(900\) | −4.24986e12 | −0.215915 | ||||||||
\(901\) | − | 1.74617e11i | − | 0.00882722i | ||||||
\(902\) | − | 8.00348e12i | − | 0.402577i | ||||||
\(903\) | −5.78494e12 | −0.289537 | ||||||||
\(904\) | 1.29297e13 | 0.643918 | ||||||||
\(905\) | 1.58787e13 | 0.786859 | ||||||||
\(906\) | 1.41666e13 | 0.698537 | ||||||||
\(907\) | − | 7.51886e12i | − | 0.368909i | −0.982841 | − | 0.184454i | \(-0.940948\pi\) | ||
0.982841 | − | 0.184454i | \(-0.0590518\pi\) | |||||||
\(908\) | 3.69754e11 | 0.0180520 | ||||||||
\(909\) | − | 1.04216e13i | − | 0.506286i | ||||||
\(910\) | 2.96155e13i | 1.43163i | ||||||||
\(911\) | − | 9.98249e12i | − | 0.480182i | −0.970750 | − | 0.240091i | \(-0.922823\pi\) | ||
0.970750 | − | 0.240091i | \(-0.0771774\pi\) | |||||||
\(912\) | 3.69505e13 | 1.76866 | ||||||||
\(913\) | − | 5.44047e13i | − | 2.59130i | ||||||
\(914\) | − | 2.50521e13i | − | 1.18737i | ||||||
\(915\) | 3.51672e13 | 1.65861 | ||||||||
\(916\) | − | 8.55668e12i | − | 0.401583i | ||||||
\(917\) | − | 2.49688e12i | − | 0.116610i | ||||||
\(918\) | 3.96233e12i | 0.184144i | ||||||||
\(919\) | −1.87276e13 | −0.866087 | −0.433044 | − | 0.901373i | \(-0.642560\pi\) | ||||
−0.433044 | + | 0.901373i | \(0.642560\pi\) | |||||||
\(920\) | 1.09122e13i | 0.502191i | ||||||||
\(921\) | 6.38102e13 | 2.92228 | ||||||||
\(922\) | −1.08211e13 | −0.493152 | ||||||||
\(923\) | −4.94329e13 | −2.24186 | ||||||||
\(924\) | 1.35898e13 | 0.613325 | ||||||||
\(925\) | 5.82773e12i | 0.261735i | ||||||||
\(926\) | − | 1.42419e13i | − | 0.636531i | ||||||
\(927\) | −3.07274e12 | −0.136668 | ||||||||
\(928\) | −1.00528e13 | − | 4.79145e12i | −0.444959 | − | 0.212081i | ||||
\(929\) | 2.14483e13 | 0.944763 | 0.472381 | − | 0.881394i | \(-0.343395\pi\) | ||||
0.472381 | + | 0.881394i | \(0.343395\pi\) | |||||||
\(930\) | − | 4.75170e13i | − | 2.08293i | ||||||
\(931\) | − | 6.91572e11i | − | 0.0301692i | ||||||
\(932\) | 8.95080e12 | 0.388589 | ||||||||
\(933\) | −6.17216e13 | −2.66667 | ||||||||
\(934\) | −2.47024e13 | −1.06213 | ||||||||
\(935\) | 4.03083e12 | 0.172481 | ||||||||
\(936\) | 5.80735e13i | 2.47307i | ||||||||
\(937\) | 3.63793e13 | 1.54179 | 0.770896 | − | 0.636961i | \(-0.219809\pi\) | ||||
0.770896 | + | 0.636961i | \(0.219809\pi\) | |||||||
\(938\) | − | 3.06912e12i | − | 0.129450i | ||||||
\(939\) | 7.83241e12i | 0.328776i | ||||||||
\(940\) | − | 1.99087e12i | − | 0.0831704i | ||||||
\(941\) | 1.40415e13 | 0.583797 | 0.291898 | − | 0.956449i | \(-0.405713\pi\) | ||||
0.291898 | + | 0.956449i | \(0.405713\pi\) | |||||||
\(942\) | 4.60244e13i | 1.90440i | ||||||||
\(943\) | 5.17957e12i | 0.213300i | ||||||||
\(944\) | −5.19845e13 | −2.13059 | ||||||||
\(945\) | − | 1.63914e13i | − | 0.668610i | ||||||
\(946\) | − | 7.23609e12i | − | 0.293761i | ||||||
\(947\) | 4.21219e13i | 1.70190i | 0.525249 | + | 0.850949i | \(0.323972\pi\) | ||||
−0.525249 | + | 0.850949i | \(0.676028\pi\) | |||||||
\(948\) | −9.02132e11 | −0.0362771 | ||||||||
\(949\) | − | 5.82402e13i | − | 2.33090i | ||||||
\(950\) | −1.38932e13 | −0.553408 | ||||||||
\(951\) | −4.29646e13 | −1.70333 | ||||||||
\(952\) | 3.67336e12 | 0.144943 | ||||||||
\(953\) | 2.27280e13 | 0.892574 | 0.446287 | − | 0.894890i | \(-0.352746\pi\) | ||||
0.446287 | + | 0.894890i | \(0.352746\pi\) | |||||||
\(954\) | − | 2.37099e12i | − | 0.0926750i | ||||||
\(955\) | 1.53063e13i | 0.595463i | ||||||||
\(956\) | −1.00711e13 | −0.389956 | ||||||||
\(957\) | −2.67366e13 | + | 5.60952e13i | −1.03039 | + | 2.16183i | ||||
\(958\) | 2.11425e13 | 0.810984 | ||||||||
\(959\) | − | 2.16044e13i | − | 0.824817i | ||||||
\(960\) | − | 1.84116e13i | − | 0.699634i | ||||||
\(961\) | −4.95022e13 | −1.87227 | ||||||||
\(962\) | −2.68314e13 | −1.01008 | ||||||||
\(963\) | 3.56161e13 | 1.33453 | ||||||||
\(964\) | 9.00823e12 | 0.335964 | ||||||||
\(965\) | − | 7.33524e12i | − | 0.272296i | ||||||
\(966\) | −4.36927e13 | −1.61440 | ||||||||
\(967\) | 1.66954e13i | 0.614015i | 0.951707 | + | 0.307007i | \(0.0993276\pi\) | ||||
−0.951707 | + | 0.307007i | \(0.900672\pi\) | |||||||
\(968\) | − | 2.75889e13i | − | 1.00994i | ||||||
\(969\) | 6.96013e12i | 0.253606i | ||||||||
\(970\) | 9.16969e12 | 0.332569 | ||||||||
\(971\) | − | 2.72129e13i | − | 0.982401i | −0.871047 | − | 0.491200i | \(-0.836558\pi\) | ||
0.871047 | − | 0.491200i | \(-0.163442\pi\) | |||||||
\(972\) | − | 7.24971e12i | − | 0.260509i | ||||||
\(973\) | −4.38164e13 | −1.56722 | ||||||||
\(974\) | 3.99277e13i | 1.42154i | ||||||||
\(975\) | − | 4.50418e13i | − | 1.59623i | ||||||
\(976\) | 5.08758e13i | 1.79468i | ||||||||
\(977\) | 4.08459e13 | 1.43424 | 0.717121 | − | 0.696949i | \(-0.245459\pi\) | ||||
0.717121 | + | 0.696949i | \(0.245459\pi\) | |||||||
\(978\) | − | 4.64183e13i | − | 1.62242i | ||||||
\(979\) | −2.44246e13 | −0.849778 | ||||||||
\(980\) | 1.62042e11 | 0.00561189 | ||||||||
\(981\) | −1.52327e13 | −0.525129 | ||||||||
\(982\) | 2.91660e13 | 1.00086 | ||||||||
\(983\) | − | 4.68988e13i | − | 1.60203i | −0.598644 | − | 0.801015i | \(-0.704294\pi\) | ||
0.598644 | − | 0.801015i | \(-0.295706\pi\) | |||||||
\(984\) | − | 9.61060e12i | − | 0.326793i | ||||||
\(985\) | −1.11973e13 | −0.379011 | ||||||||
\(986\) | 2.43498e12 | − | 5.10876e12i | 0.0820446 | − | 0.172135i | ||||
\(987\) | −2.36591e13 | −0.793544 | ||||||||
\(988\) | − | 1.28756e13i | − | 0.429893i | ||||||
\(989\) | 4.68295e12i | 0.155645i | ||||||||
\(990\) | 5.47317e13 | 1.81084 | ||||||||
\(991\) | 2.09390e13 | 0.689643 | 0.344822 | − | 0.938668i | \(-0.387939\pi\) | ||||
0.344822 | + | 0.938668i | \(0.387939\pi\) | |||||||
\(992\) | 2.54794e13 | 0.835385 | ||||||||
\(993\) | 1.96014e12 | 0.0639759 | ||||||||
\(994\) | 4.24567e13i | 1.37946i | ||||||||
\(995\) | −3.66599e13 | −1.18573 | ||||||||
\(996\) | 2.20114e13i | 0.708731i | ||||||||
\(997\) | 5.13175e13i | 1.64489i | 0.568843 | + | 0.822446i | \(0.307391\pi\) | ||||
−0.568843 | + | 0.822446i | \(0.692609\pi\) | |||||||
\(998\) | 1.21700e13i | 0.388331i | ||||||||
\(999\) | 1.48505e13 | 0.471733 |
(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 | 29.10.b.a.28.17 | yes | 22 | |
29.28 | even | 2 | inner | 29.10.b.a.28.6 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.10.b.a.28.6 | ✓ | 22 | 29.28 | even | 2 | inner | |
29.10.b.a.28.17 | yes | 22 | 1.1 | even | 1 | trivial |