Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(55,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.55");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.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: | \(64.5408271670\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.12 | ||
Character | \(\chi\) | \(=\) | 84.55 |
Dual form | 84.12.b.a.55.11 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32.5648 | + | 31.4250i | −0.719587 | + | 0.694402i | ||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 72.9330 | − | 2046.70i | 0.0356118 | − | 0.999366i | ||||
\(5\) | 4483.20i | 0.641583i | 0.947150 | + | 0.320792i | \(0.103949\pi\) | ||||
−0.947150 | + | 0.320792i | \(0.896051\pi\) | |||||||
\(6\) | 7913.25 | − | 7636.29i | 0.415454 | − | 0.400913i | ||||
\(7\) | 44244.4 | − | 4445.20i | 0.994991 | − | 0.0999660i | ||||
\(8\) | 61942.6 | + | 68942.3i | 0.668336 | + | 0.743860i | ||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −140885. | − | 145994.i | −0.445516 | − | 0.461675i | ||||
\(11\) | 407222.i | 0.762380i | 0.924497 | + | 0.381190i | \(0.124486\pi\) | ||||
−0.924497 | + | 0.381190i | \(0.875514\pi\) | |||||||
\(12\) | −17722.7 | + | 497348.i | −0.0205605 | + | 0.576984i | ||||
\(13\) | 1.73481e6i | 1.29588i | 0.761693 | + | 0.647938i | \(0.224368\pi\) | ||||
−0.761693 | + | 0.647938i | \(0.775632\pi\) | |||||||
\(14\) | −1.30112e6 | + | 1.53514e6i | −0.646566 | + | 0.762858i | ||||
\(15\) | − | 1.08942e6i | − | 0.370418i | ||||||
\(16\) | −4.18367e6 | − | 298544.i | −0.997464 | − | 0.0711785i | ||||
\(17\) | − | 5.93548e6i | − | 1.01388i | −0.861981 | − | 0.506940i | \(-0.830776\pi\) | ||
0.861981 | − | 0.506940i | \(-0.169224\pi\) | |||||||
\(18\) | −1.92292e6 | + | 1.85562e6i | −0.239862 | + | 0.231467i | ||||
\(19\) | 1.52535e7 | 1.41327 | 0.706636 | − | 0.707577i | \(-0.250212\pi\) | ||||
0.706636 | + | 0.707577i | \(0.250212\pi\) | |||||||
\(20\) | 9.17576e6 | + | 326973.i | 0.641176 | + | 0.0228479i | ||||
\(21\) | −1.07514e7 | + | 1.08018e6i | −0.574458 | + | 0.0577154i | ||||
\(22\) | −1.27970e7 | − | 1.32611e7i | −0.529398 | − | 0.548599i | ||||
\(23\) | − | 2.31359e6i | − | 0.0749519i | −0.999298 | − | 0.0374760i | \(-0.988068\pi\) | ||
0.999298 | − | 0.0374760i | \(-0.0119318\pi\) | |||||||
\(24\) | −1.50521e7 | − | 1.67530e7i | −0.385864 | − | 0.429468i | ||||
\(25\) | 2.87291e7 | 0.588371 | ||||||||
\(26\) | −5.45165e7 | − | 5.64937e7i | −0.899859 | − | 0.932496i | ||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −5.87113e6 | − | 9.08793e7i | −0.0644692 | − | 0.997920i | ||||
\(29\) | −1.10429e8 | −0.999753 | −0.499877 | − | 0.866097i | \(-0.666621\pi\) | ||||
−0.499877 | + | 0.866097i | \(0.666621\pi\) | |||||||
\(30\) | 3.42350e7 | + | 3.54767e7i | 0.257219 | + | 0.266548i | ||||
\(31\) | 9.60969e7 | 0.602865 | 0.301433 | − | 0.953487i | \(-0.402535\pi\) | ||||
0.301433 | + | 0.953487i | \(0.402535\pi\) | |||||||
\(32\) | 1.45622e8 | − | 1.21750e8i | 0.767189 | − | 0.641422i | ||||
\(33\) | − | 9.89550e7i | − | 0.440160i | ||||||
\(34\) | 1.86523e8 | + | 1.93288e8i | 0.704041 | + | 0.729576i | ||||
\(35\) | 1.99287e7 | + | 1.98356e8i | 0.0641365 | + | 0.638369i | ||||
\(36\) | 4.30662e6 | − | 1.20856e8i | 0.0118706 | − | 0.333122i | ||||
\(37\) | 6.26376e8 | 1.48500 | 0.742499 | − | 0.669848i | \(-0.233641\pi\) | ||||
0.742499 | + | 0.669848i | \(0.233641\pi\) | |||||||
\(38\) | −4.96729e8 | + | 4.79343e8i | −1.01697 | + | 0.981379i | ||||
\(39\) | − | 4.21559e8i | − | 0.748174i | ||||||
\(40\) | −3.09082e8 | + | 2.77701e8i | −0.477248 | + | 0.428793i | ||||
\(41\) | − | 9.25635e8i | − | 1.24775i | −0.781523 | − | 0.623876i | \(-0.785557\pi\) | ||
0.781523 | − | 0.623876i | \(-0.214443\pi\) | |||||||
\(42\) | 3.16172e8 | − | 3.73039e8i | 0.373295 | − | 0.440436i | ||||
\(43\) | − | 1.26922e9i | − | 1.31662i | −0.752748 | − | 0.658309i | \(-0.771272\pi\) | ||
0.752748 | − | 0.658309i | \(-0.228728\pi\) | |||||||
\(44\) | 8.33462e8 | + | 2.96999e7i | 0.761897 | + | 0.0271497i | ||||
\(45\) | 2.64728e8i | 0.213861i | ||||||||
\(46\) | 7.27046e7 | + | 7.53415e7i | 0.0520468 | + | 0.0539345i | ||||
\(47\) | −3.43921e8 | −0.218736 | −0.109368 | − | 0.994001i | \(-0.534883\pi\) | ||||
−0.109368 | + | 0.994001i | \(0.534883\pi\) | |||||||
\(48\) | 1.01663e9 | + | 7.25462e7i | 0.575886 | + | 0.0410949i | ||||
\(49\) | 1.93781e9 | − | 3.93351e8i | 0.980014 | − | 0.198931i | ||||
\(50\) | −9.35556e8 | + | 9.02812e8i | −0.423384 | + | 0.408566i | ||||
\(51\) | 1.44232e9i | 0.585364i | ||||||||
\(52\) | 3.55064e9 | + | 1.26525e8i | 1.29505 | + | 0.0461485i | ||||
\(53\) | 3.23392e9 | 1.06222 | 0.531108 | − | 0.847304i | \(-0.321776\pi\) | ||||
0.531108 | + | 0.847304i | \(0.321776\pi\) | |||||||
\(54\) | 4.67269e8 | − | 4.50915e8i | 0.138485 | − | 0.133638i | ||||
\(55\) | −1.82566e9 | −0.489130 | ||||||||
\(56\) | 3.04708e9 | + | 2.77496e9i | 0.739349 | + | 0.673323i | ||||
\(57\) | −3.70661e9 | −0.815953 | ||||||||
\(58\) | 3.59609e9 | − | 3.47023e9i | 0.719410 | − | 0.694231i | ||||
\(59\) | −4.88844e9 | −0.890194 | −0.445097 | − | 0.895482i | \(-0.646831\pi\) | ||||
−0.445097 | + | 0.895482i | \(0.646831\pi\) | |||||||
\(60\) | −2.22971e9 | − | 7.94545e7i | −0.370183 | − | 0.0131913i | ||||
\(61\) | 1.28488e9i | 0.194781i | 0.995246 | + | 0.0973906i | \(0.0310496\pi\) | ||||
−0.995246 | + | 0.0973906i | \(0.968950\pi\) | |||||||
\(62\) | −3.12938e9 | + | 3.01985e9i | −0.433814 | + | 0.418631i | ||||
\(63\) | 2.61259e9 | − | 2.62485e8i | 0.331664 | − | 0.0333220i | ||||
\(64\) | −9.16158e8 | + | 8.54094e9i | −0.106655 | + | 0.994296i | ||||
\(65\) | −7.77750e9 | −0.831412 | ||||||||
\(66\) | 3.10966e9 | + | 3.22245e9i | 0.305648 | + | 0.316734i | ||||
\(67\) | 1.47138e10i | 1.33141i | 0.746214 | + | 0.665706i | \(0.231870\pi\) | ||||
−0.746214 | + | 0.665706i | \(0.768130\pi\) | |||||||
\(68\) | −1.21482e10 | − | 4.32893e8i | −1.01324 | − | 0.0361061i | ||||
\(69\) | 5.62202e8i | 0.0432735i | ||||||||
\(70\) | −6.88233e9 | − | 5.83318e9i | −0.489437 | − | 0.414826i | ||||
\(71\) | − | 6.23819e9i | − | 0.410334i | −0.978727 | − | 0.205167i | \(-0.934226\pi\) | ||
0.978727 | − | 0.205167i | \(-0.0657738\pi\) | |||||||
\(72\) | 3.65765e9 | + | 4.07098e9i | 0.222779 | + | 0.247953i | ||||
\(73\) | − | 7.64640e9i | − | 0.431699i | −0.976427 | − | 0.215850i | \(-0.930748\pi\) | ||
0.976427 | − | 0.215850i | \(-0.0692521\pi\) | |||||||
\(74\) | −2.03978e10 | + | 1.96839e10i | −1.06859 | + | 1.03118i | ||||
\(75\) | −6.98116e9 | −0.339696 | ||||||||
\(76\) | 1.11249e9 | − | 3.12194e10i | 0.0503292 | − | 1.41238i | ||||
\(77\) | 1.81019e9 | + | 1.80173e10i | 0.0762121 | + | 0.758561i | ||||
\(78\) | 1.32475e10 | + | 1.37280e10i | 0.519534 | + | 0.538377i | ||||
\(79\) | 5.20281e10i | 1.90234i | 0.308661 | + | 0.951172i | \(0.400119\pi\) | ||||
−0.308661 | + | 0.951172i | \(0.599881\pi\) | |||||||
\(80\) | 1.33843e9 | − | 1.87562e10i | 0.0456669 | − | 0.639956i | ||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 2.90881e10 | + | 3.01431e10i | 0.866442 | + | 0.897867i | ||||
\(83\) | −3.89227e10 | −1.08461 | −0.542304 | − | 0.840182i | \(-0.682448\pi\) | ||||
−0.542304 | + | 0.840182i | \(0.682448\pi\) | |||||||
\(84\) | 1.42668e9 | + | 2.20837e10i | 0.0372213 | + | 0.576149i | ||||
\(85\) | 2.66099e10 | 0.650489 | ||||||||
\(86\) | 3.98852e10 | + | 4.13318e10i | 0.914262 | + | 0.947421i | ||||
\(87\) | 2.68342e10 | 0.577208 | ||||||||
\(88\) | −2.80748e10 | + | 2.52244e10i | −0.567104 | + | 0.509526i | ||||
\(89\) | − | 6.32910e10i | − | 1.20143i | −0.799465 | − | 0.600713i | \(-0.794883\pi\) | ||
0.799465 | − | 0.600713i | \(-0.205117\pi\) | |||||||
\(90\) | −8.31910e9 | − | 8.62083e9i | −0.148505 | − | 0.153892i | ||||
\(91\) | 7.71158e9 | + | 7.67556e10i | 0.129544 | + | 1.28938i | ||||
\(92\) | −4.73522e9 | − | 1.68737e8i | −0.0749044 | − | 0.00266917i | ||||
\(93\) | −2.33516e10 | −0.348064 | ||||||||
\(94\) | 1.11997e10 | − | 1.08077e10i | 0.157400 | − | 0.151891i | ||||
\(95\) | 6.83846e10i | 0.906731i | ||||||||
\(96\) | −3.53861e10 | + | 2.95852e10i | −0.442937 | + | 0.370325i | ||||
\(97\) | − | 5.71799e10i | − | 0.676081i | −0.941132 | − | 0.338040i | \(-0.890236\pi\) | ||
0.941132 | − | 0.338040i | \(-0.109764\pi\) | |||||||
\(98\) | −5.07432e10 | + | 7.37051e10i | −0.567068 | + | 0.823671i | ||||
\(99\) | 2.40461e10i | 0.254127i | ||||||||
\(100\) | 2.09530e9 | − | 5.87998e10i | 0.0209530 | − | 0.587998i | ||||
\(101\) | 1.30879e11i | 1.23909i | 0.784962 | + | 0.619544i | \(0.212682\pi\) | ||||
−0.784962 | + | 0.619544i | \(0.787318\pi\) | |||||||
\(102\) | −4.53250e10 | − | 4.69689e10i | −0.406478 | − | 0.421221i | ||||
\(103\) | 1.08228e11 | 0.919884 | 0.459942 | − | 0.887949i | \(-0.347870\pi\) | ||||
0.459942 | + | 0.887949i | \(0.347870\pi\) | |||||||
\(104\) | −1.19602e11 | + | 1.07459e11i | −0.963950 | + | 0.866080i | ||||
\(105\) | −4.84268e9 | − | 4.82006e10i | −0.0370292 | − | 0.368563i | ||||
\(106\) | −1.05312e11 | + | 1.01626e11i | −0.764357 | + | 0.737604i | ||||
\(107\) | 2.22083e11i | 1.53075i | 0.643584 | + | 0.765376i | \(0.277447\pi\) | ||||
−0.643584 | + | 0.765376i | \(0.722553\pi\) | |||||||
\(108\) | −1.04651e9 | + | 2.93679e10i | −0.00685350 | + | 0.192328i | ||||
\(109\) | −1.37011e11 | −0.852923 | −0.426461 | − | 0.904506i | \(-0.640240\pi\) | ||||
−0.426461 | + | 0.904506i | \(0.640240\pi\) | |||||||
\(110\) | 5.94522e10 | − | 5.73714e10i | 0.351972 | − | 0.339653i | ||||
\(111\) | −1.52209e11 | −0.857363 | ||||||||
\(112\) | −1.86431e11 | + | 5.38834e9i | −0.999583 | + | 0.0288906i | ||||
\(113\) | 2.93672e11 | 1.49945 | 0.749723 | − | 0.661752i | \(-0.230187\pi\) | ||||
0.749723 | + | 0.661752i | \(0.230187\pi\) | |||||||
\(114\) | 1.20705e11 | − | 1.16480e11i | 0.587149 | − | 0.566599i | ||||
\(115\) | 1.03723e10 | 0.0480879 | ||||||||
\(116\) | −8.05389e9 | + | 2.26014e11i | −0.0356030 | + | 0.999119i | ||||
\(117\) | 1.02439e11i | 0.431959i | ||||||||
\(118\) | 1.59191e11 | − | 1.53620e11i | 0.640572 | − | 0.618152i | ||||
\(119\) | −2.63844e10 | − | 2.62612e11i | −0.101354 | − | 1.00880i | ||||
\(120\) | 7.51070e10 | − | 6.74813e10i | 0.275539 | − | 0.247564i | ||||
\(121\) | 1.19482e11 | 0.418777 | ||||||||
\(122\) | −4.03773e10 | − | 4.18417e10i | −0.135256 | − | 0.140162i | ||||
\(123\) | 2.24929e11i | 0.720390i | ||||||||
\(124\) | 7.00864e9 | − | 1.96682e11i | 0.0214691 | − | 0.602483i | ||||
\(125\) | 3.47704e11i | 1.01907i | ||||||||
\(126\) | −7.68298e10 | + | 9.06485e10i | −0.215522 | + | 0.254286i | ||||
\(127\) | 1.57348e11i | 0.422612i | 0.977420 | + | 0.211306i | \(0.0677716\pi\) | ||||
−0.977420 | + | 0.211306i | \(0.932228\pi\) | |||||||
\(128\) | −2.38565e11 | − | 3.06924e11i | −0.613694 | − | 0.789544i | ||||
\(129\) | 3.08420e11i | 0.760150i | ||||||||
\(130\) | 2.53273e11 | − | 2.44408e11i | 0.598274 | − | 0.577334i | ||||
\(131\) | 7.46145e11 | 1.68978 | 0.844892 | − | 0.534938i | \(-0.179665\pi\) | ||||
0.844892 | + | 0.534938i | \(0.179665\pi\) | |||||||
\(132\) | −2.02531e11 | − | 7.21708e9i | −0.439881 | − | 0.0156749i | ||||
\(133\) | 6.74884e11 | − | 6.78051e10i | 1.40619 | − | 0.141279i | ||||
\(134\) | −4.62381e11 | − | 4.79151e11i | −0.924535 | − | 0.958067i | ||||
\(135\) | − | 6.43290e10i | − | 0.123473i | ||||||
\(136\) | 4.09206e11 | − | 3.67659e11i | 0.754185 | − | 0.677613i | ||||
\(137\) | −6.37133e10 | −0.112789 | −0.0563946 | − | 0.998409i | \(-0.517960\pi\) | ||||
−0.0563946 | + | 0.998409i | \(0.517960\pi\) | |||||||
\(138\) | −1.76672e10 | − | 1.83080e10i | −0.0300492 | − | 0.0311391i | ||||
\(139\) | 6.10597e10 | 0.0998099 | 0.0499049 | − | 0.998754i | \(-0.484108\pi\) | ||||
0.0499049 | + | 0.998754i | \(0.484108\pi\) | |||||||
\(140\) | 4.07430e11 | − | 2.63214e10i | 0.640248 | − | 0.0413623i | ||||
\(141\) | 8.35728e10 | 0.126287 | ||||||||
\(142\) | 1.96035e11 | + | 2.03145e11i | 0.284937 | + | 0.295271i | ||||
\(143\) | −7.06453e11 | −0.987950 | ||||||||
\(144\) | −2.47041e11 | − | 1.76287e10i | −0.332488 | − | 0.0237262i | ||||
\(145\) | − | 4.95074e11i | − | 0.641425i | ||||||
\(146\) | 2.40289e11 | + | 2.49004e11i | 0.299773 | + | 0.310645i | ||||
\(147\) | −4.70887e11 | + | 9.55842e10i | −0.565811 | + | 0.114853i | ||||
\(148\) | 4.56835e10 | − | 1.28200e12i | 0.0528834 | − | 1.48406i | ||||
\(149\) | 1.20132e12 | 1.34009 | 0.670045 | − | 0.742321i | \(-0.266275\pi\) | ||||
0.670045 | + | 0.742321i | \(0.266275\pi\) | |||||||
\(150\) | 2.27340e11 | − | 2.19383e11i | 0.244441 | − | 0.235886i | ||||
\(151\) | 1.22900e11i | 0.127403i | 0.997969 | + | 0.0637015i | \(0.0202906\pi\) | ||||
−0.997969 | + | 0.0637015i | \(0.979709\pi\) | |||||||
\(152\) | 9.44844e11 | + | 1.05161e12i | 0.944540 | + | 1.05128i | ||||
\(153\) | − | 3.50484e11i | − | 0.337960i | ||||||
\(154\) | −6.25143e11 | − | 5.29845e11i | −0.581588 | − | 0.492929i | ||||
\(155\) | 4.30822e11i | 0.386788i | ||||||||
\(156\) | −8.62805e11 | − | 3.07455e10i | −0.747700 | − | 0.0266438i | ||||
\(157\) | − | 9.32421e11i | − | 0.780124i | −0.920789 | − | 0.390062i | \(-0.872454\pi\) | ||
0.920789 | − | 0.390062i | \(-0.127546\pi\) | |||||||
\(158\) | −1.63499e12 | − | 1.69429e12i | −1.32099 | − | 1.36890i | ||||
\(159\) | −7.85844e11 | −0.613270 | ||||||||
\(160\) | 5.45829e11 | + | 6.52852e11i | 0.411525 | + | 0.492215i | ||||
\(161\) | −1.02844e10 | − | 1.02363e11i | −0.00749265 | − | 0.0745765i | ||||
\(162\) | −1.13546e11 | + | 1.09572e11i | −0.0799541 | + | 0.0771558i | ||||
\(163\) | 3.01539e11i | 0.205263i | 0.994719 | + | 0.102632i | \(0.0327263\pi\) | ||||
−0.994719 | + | 0.102632i | \(0.967274\pi\) | |||||||
\(164\) | −1.89450e12 | − | 6.75093e10i | −1.24696 | − | 0.0444347i | ||||
\(165\) | 4.43635e11 | 0.282399 | ||||||||
\(166\) | 1.26751e12 | − | 1.22315e12i | 0.780471 | − | 0.753154i | ||||
\(167\) | −1.81605e12 | −1.08190 | −0.540951 | − | 0.841054i | \(-0.681935\pi\) | ||||
−0.540951 | + | 0.841054i | \(0.681935\pi\) | |||||||
\(168\) | −7.40440e11 | − | 6.74316e11i | −0.426863 | − | 0.388743i | ||||
\(169\) | −1.21740e12 | −0.679294 | ||||||||
\(170\) | −8.66547e11 | + | 8.36219e11i | −0.468083 | + | 0.451701i | ||||
\(171\) | 9.00706e11 | 0.471091 | ||||||||
\(172\) | −2.59771e12 | − | 9.25679e10i | −1.31578 | − | 0.0468872i | ||||
\(173\) | 7.08521e11i | 0.347616i | 0.984780 | + | 0.173808i | \(0.0556072\pi\) | ||||
−0.984780 | + | 0.173808i | \(0.944393\pi\) | |||||||
\(174\) | −8.73849e11 | + | 8.43265e11i | −0.415351 | + | 0.400814i | ||||
\(175\) | 1.27110e12 | − | 1.27707e11i | 0.585424 | − | 0.0588171i | ||||
\(176\) | 1.21574e11 | − | 1.70368e12i | 0.0542650 | − | 0.760446i | ||||
\(177\) | 1.18789e12 | 0.513954 | ||||||||
\(178\) | 1.98892e12 | + | 2.06106e12i | 0.834273 | + | 0.864531i | ||||
\(179\) | 6.20432e11i | 0.252350i | 0.992008 | + | 0.126175i | \(0.0402700\pi\) | ||||
−0.992008 | + | 0.126175i | \(0.959730\pi\) | |||||||
\(180\) | 5.41820e11 | + | 1.93074e10i | 0.213725 | + | 0.00761598i | ||||
\(181\) | − | 1.37684e12i | − | 0.526806i | −0.964686 | − | 0.263403i | \(-0.915155\pi\) | ||
0.964686 | − | 0.263403i | \(-0.0848449\pi\) | |||||||
\(182\) | −2.66318e12 | − | 2.25719e12i | −0.988569 | − | 0.837870i | ||||
\(183\) | − | 3.12225e11i | − | 0.112457i | ||||||
\(184\) | 1.59504e11 | − | 1.43310e11i | 0.0557537 | − | 0.0500931i | ||||
\(185\) | 2.80817e12i | 0.952749i | ||||||||
\(186\) | 7.60439e11 | − | 7.33824e11i | 0.250463 | − | 0.241697i | ||||
\(187\) | 2.41706e12 | 0.772963 | ||||||||
\(188\) | −2.50832e10 | + | 7.03903e11i | −0.00778959 | + | 0.218597i | ||||
\(189\) | −6.34859e11 | + | 6.37838e10i | −0.191486 | + | 0.0192385i | ||||
\(190\) | −2.14899e12 | − | 2.22693e12i | −0.629636 | − | 0.652472i | ||||
\(191\) | 3.17158e12i | 0.902801i | 0.892321 | + | 0.451400i | \(0.149075\pi\) | ||||
−0.892321 | + | 0.451400i | \(0.850925\pi\) | |||||||
\(192\) | 2.22626e11 | − | 2.07545e12i | 0.0615772 | − | 0.574057i | ||||
\(193\) | 6.82500e12 | 1.83458 | 0.917291 | − | 0.398217i | \(-0.130371\pi\) | ||||
0.917291 | + | 0.398217i | \(0.130371\pi\) | |||||||
\(194\) | 1.79688e12 | + | 1.86205e12i | 0.469472 | + | 0.486499i | ||||
\(195\) | 1.88993e12 | 0.480016 | ||||||||
\(196\) | −6.63741e11 | − | 3.99480e12i | −0.163904 | − | 0.986476i | ||||
\(197\) | 7.97874e11 | 0.191589 | 0.0957944 | − | 0.995401i | \(-0.469461\pi\) | ||||
0.0957944 | + | 0.995401i | \(0.469461\pi\) | |||||||
\(198\) | −7.55648e11 | − | 7.83055e11i | −0.176466 | − | 0.182866i | ||||
\(199\) | 1.81743e11 | 0.0412826 | 0.0206413 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206413 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(200\) | 1.77955e12 | + | 1.98065e12i | 0.393230 | + | 0.437666i | ||||
\(201\) | − | 3.57545e12i | − | 0.768691i | ||||||
\(202\) | −4.11287e12 | − | 4.26204e12i | −0.860425 | − | 0.891631i | ||||
\(203\) | −4.88585e12 | + | 4.90878e11i | −0.994745 | + | 0.0999414i | ||||
\(204\) | 2.95200e12 | + | 1.05193e11i | 0.584993 | + | 0.0208459i | ||||
\(205\) | 4.14980e12 | 0.800537 | ||||||||
\(206\) | −3.52441e12 | + | 3.40105e12i | −0.661937 | + | 0.638769i | ||||
\(207\) | − | 1.36615e11i | − | 0.0249840i | ||||||
\(208\) | 5.17917e11 | − | 7.25786e12i | 0.0922385 | − | 1.29259i | ||||
\(209\) | 6.21158e12i | 1.07745i | ||||||||
\(210\) | 1.67241e12 | + | 1.41746e12i | 0.282576 | + | 0.239500i | ||||
\(211\) | 5.60576e12i | 0.922743i | 0.887207 | + | 0.461371i | \(0.152642\pi\) | ||||
−0.887207 | + | 0.461371i | \(0.847358\pi\) | |||||||
\(212\) | 2.35860e11 | − | 6.61888e12i | 0.0378274 | − | 1.06154i | ||||
\(213\) | 1.51588e12i | 0.236906i | ||||||||
\(214\) | −6.97897e12 | − | 7.23209e12i | −1.06296 | − | 1.10151i | ||||
\(215\) | 5.69016e12 | 0.844720 | ||||||||
\(216\) | −8.88809e11 | − | 9.89247e11i | −0.128621 | − | 0.143156i | ||||
\(217\) | 4.25175e12 | − | 4.27170e11i | 0.599845 | − | 0.0602660i | ||||
\(218\) | 4.46174e12 | − | 4.30558e12i | 0.613752 | − | 0.592271i | ||||
\(219\) | 1.85808e12i | 0.249242i | ||||||||
\(220\) | −1.33151e11 | + | 3.73657e12i | −0.0174188 | + | 0.488820i | ||||
\(221\) | 1.02969e13 | 1.31386 | ||||||||
\(222\) | 4.95667e12 | − | 4.78319e12i | 0.616948 | − | 0.595355i | ||||
\(223\) | −1.41028e13 | −1.71249 | −0.856247 | − | 0.516567i | \(-0.827210\pi\) | ||||
−0.856247 | + | 0.516567i | \(0.827210\pi\) | |||||||
\(224\) | 5.90176e12 | − | 6.03407e12i | 0.699225 | − | 0.714901i | ||||
\(225\) | 1.69642e12 | 0.196124 | ||||||||
\(226\) | −9.56336e12 | + | 9.22865e12i | −1.07898 | + | 1.04122i | ||||
\(227\) | 1.45948e12 | 0.160715 | 0.0803574 | − | 0.996766i | \(-0.474394\pi\) | ||||
0.0803574 | + | 0.996766i | \(0.474394\pi\) | |||||||
\(228\) | −2.70334e11 | + | 7.58632e12i | −0.0290576 | + | 0.815435i | ||||
\(229\) | 9.59476e12i | 1.00679i | 0.864056 | + | 0.503395i | \(0.167916\pi\) | ||||
−0.864056 | + | 0.503395i | \(0.832084\pi\) | |||||||
\(230\) | −3.37771e11 | + | 3.25949e11i | −0.0346034 | + | 0.0333923i | ||||
\(231\) | −4.39875e11 | − | 4.37820e12i | −0.0440011 | − | 0.437956i | ||||
\(232\) | −6.84024e12 | − | 7.61321e12i | −0.668171 | − | 0.743676i | ||||
\(233\) | −1.11640e13 | −1.06503 | −0.532515 | − | 0.846420i | \(-0.678753\pi\) | ||||
−0.532515 | + | 0.846420i | \(0.678753\pi\) | |||||||
\(234\) | −3.21914e12 | − | 3.33590e12i | −0.299953 | − | 0.310832i | ||||
\(235\) | − | 1.54186e12i | − | 0.140337i | ||||||
\(236\) | −3.56529e11 | + | 1.00052e13i | −0.0317014 | + | 0.889629i | ||||
\(237\) | − | 1.26428e13i | − | 1.09832i | ||||||
\(238\) | 9.11179e12 | + | 7.72277e12i | 0.773447 | + | 0.655541i | ||||
\(239\) | 9.38444e12i | 0.778431i | 0.921147 | + | 0.389215i | \(0.127254\pi\) | ||||
−0.921147 | + | 0.389215i | \(0.872746\pi\) | |||||||
\(240\) | −3.25239e11 | + | 4.55776e12i | −0.0263658 | + | 0.369479i | ||||
\(241\) | − | 6.47684e12i | − | 0.513179i | −0.966520 | − | 0.256590i | \(-0.917401\pi\) | ||
0.966520 | − | 0.256590i | \(-0.0825989\pi\) | |||||||
\(242\) | −3.89090e12 | + | 3.75472e12i | −0.301346 | + | 0.290799i | ||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 2.62976e12 | + | 9.37099e10i | 0.194658 | + | 0.00693651i | ||||
\(245\) | 1.76347e12 | + | 8.68757e12i | 0.127630 | + | 0.628760i | ||||
\(246\) | −7.06841e12 | − | 7.32478e12i | −0.500241 | − | 0.518384i | ||||
\(247\) | 2.64620e13i | 1.83143i | ||||||||
\(248\) | 5.95250e12 | + | 6.62515e12i | 0.402916 | + | 0.448447i | ||||
\(249\) | 9.45821e12 | 0.626199 | ||||||||
\(250\) | −1.09266e13 | − | 1.13229e13i | −0.707646 | − | 0.733311i | ||||
\(251\) | 1.68995e13 | 1.07070 | 0.535350 | − | 0.844630i | \(-0.320180\pi\) | ||||
0.535350 | + | 0.844630i | \(0.320180\pi\) | |||||||
\(252\) | −3.46684e11 | − | 5.36633e12i | −0.0214897 | − | 0.332640i | ||||
\(253\) | 9.42144e11 | 0.0571419 | ||||||||
\(254\) | −4.94468e12 | − | 5.12402e12i | −0.293463 | − | 0.304106i | ||||
\(255\) | −6.46622e12 | −0.375560 | ||||||||
\(256\) | 1.74139e13 | + | 2.49802e12i | 0.989867 | + | 0.141996i | ||||
\(257\) | − | 1.83480e13i | − | 1.02084i | −0.859926 | − | 0.510418i | \(-0.829491\pi\) | ||
0.859926 | − | 0.510418i | \(-0.170509\pi\) | |||||||
\(258\) | −9.69211e12 | − | 1.00436e13i | −0.527849 | − | 0.546994i | ||||
\(259\) | 2.77136e13 | − | 2.78437e12i | 1.47756 | − | 0.148449i | ||||
\(260\) | −5.67236e11 | + | 1.59182e13i | −0.0296081 | + | 0.830885i | ||||
\(261\) | −6.52070e12 | −0.333251 | ||||||||
\(262\) | −2.42981e13 | + | 2.34476e13i | −1.21595 | + | 1.17339i | ||||
\(263\) | 2.32492e13i | 1.13934i | 0.821875 | + | 0.569668i | \(0.192928\pi\) | ||||
−0.821875 | + | 0.569668i | \(0.807072\pi\) | |||||||
\(264\) | 6.82219e12 | − | 6.12953e12i | 0.327418 | − | 0.294175i | ||||
\(265\) | 1.44983e13i | 0.681499i | ||||||||
\(266\) | −1.98467e13 | + | 2.34163e13i | −0.913774 | + | 1.07813i | ||||
\(267\) | 1.53797e13i | 0.693644i | ||||||||
\(268\) | 3.01147e13 | + | 1.07312e12i | 1.33057 | + | 0.0474140i | ||||
\(269\) | 3.93209e13i | 1.70210i | 0.525084 | + | 0.851051i | \(0.324034\pi\) | ||||
−0.525084 | + | 0.851051i | \(0.675966\pi\) | |||||||
\(270\) | 2.02154e12 | + | 2.09486e12i | 0.0857397 | + | 0.0888494i | ||||
\(271\) | −1.91685e13 | −0.796633 | −0.398316 | − | 0.917248i | \(-0.630405\pi\) | ||||
−0.398316 | + | 0.917248i | \(0.630405\pi\) | |||||||
\(272\) | −1.77200e12 | + | 2.48321e13i | −0.0721665 | + | 1.01131i | ||||
\(273\) | −1.87391e12 | − | 1.86516e13i | −0.0747920 | − | 0.744427i | ||||
\(274\) | 2.07481e12 | − | 2.00219e12i | 0.0811616 | − | 0.0783210i | ||||
\(275\) | 1.16991e13i | 0.448563i | ||||||||
\(276\) | 1.15066e12 | + | 4.10031e10i | 0.0432461 | + | 0.00154105i | ||||
\(277\) | −3.04162e13 | −1.12064 | −0.560320 | − | 0.828276i | \(-0.689322\pi\) | ||||
−0.560320 | + | 0.828276i | \(0.689322\pi\) | |||||||
\(278\) | −1.98840e12 | + | 1.91880e12i | −0.0718219 | + | 0.0693082i | ||||
\(279\) | 5.67443e12 | 0.200955 | ||||||||
\(280\) | −1.24407e13 | + | 1.36606e13i | −0.431992 | + | 0.474354i | ||||
\(281\) | 9.27444e12 | 0.315793 | 0.157897 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157897 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(282\) | −2.72153e12 | + | 2.62628e12i | −0.0908747 | + | 0.0876941i | ||||
\(283\) | −4.46834e13 | −1.46326 | −0.731628 | − | 0.681704i | \(-0.761239\pi\) | ||||
−0.731628 | + | 0.681704i | \(0.761239\pi\) | |||||||
\(284\) | −1.27677e13 | − | 4.54970e11i | −0.410074 | − | 0.0146127i | ||||
\(285\) | − | 1.66175e13i | − | 0.523502i | ||||||
\(286\) | 2.30055e13 | − | 2.22003e13i | 0.710916 | − | 0.686034i | ||||
\(287\) | −4.11464e12 | − | 4.09542e13i | −0.124733 | − | 1.24150i | ||||
\(288\) | 8.59883e12 | − | 7.18921e12i | 0.255730 | − | 0.213807i | ||||
\(289\) | −9.58052e11 | −0.0279544 | ||||||||
\(290\) | 1.55577e13 | + | 1.61220e13i | 0.445407 | + | 0.461561i | ||||
\(291\) | 1.38947e13i | 0.390335i | ||||||||
\(292\) | −1.56499e13 | − | 5.57675e11i | −0.431426 | − | 0.0153736i | ||||
\(293\) | 2.42007e13i | 0.654721i | 0.944900 | + | 0.327360i | \(0.106159\pi\) | ||||
−0.944900 | + | 0.327360i | \(0.893841\pi\) | |||||||
\(294\) | 1.23306e13 | − | 1.79103e13i | 0.327397 | − | 0.475547i | ||||
\(295\) | − | 2.19159e13i | − | 0.571133i | ||||||
\(296\) | 3.87994e13 | + | 4.31838e13i | 0.992477 | + | 1.10463i | ||||
\(297\) | − | 5.84319e12i | − | 0.146720i | ||||||
\(298\) | −3.91207e13 | + | 3.77515e13i | −0.964311 | + | 0.930561i | ||||
\(299\) | 4.01363e12 | 0.0971284 | ||||||||
\(300\) | −5.09157e11 | + | 1.42884e13i | −0.0120972 | + | 0.339481i | ||||
\(301\) | −5.64193e12 | − | 5.61558e13i | −0.131617 | − | 1.31002i | ||||
\(302\) | −3.86215e12 | − | 4.00222e12i | −0.0884689 | − | 0.0916776i | ||||
\(303\) | − | 3.18036e13i | − | 0.715387i | ||||||
\(304\) | −6.38157e13 | − | 4.55385e12i | −1.40969 | − | 0.100595i | ||||
\(305\) | −5.76035e12 | −0.124968 | ||||||||
\(306\) | 1.10140e13 | + | 1.14135e13i | 0.234680 | + | 0.243192i | ||||
\(307\) | 5.66237e13 | 1.18505 | 0.592526 | − | 0.805552i | \(-0.298131\pi\) | ||||
0.592526 | + | 0.805552i | \(0.298131\pi\) | |||||||
\(308\) | 3.70080e13 | − | 2.39085e12i | 0.760794 | − | 0.0491500i | ||||
\(309\) | −2.62993e13 | −0.531095 | ||||||||
\(310\) | −1.35386e13 | − | 1.40296e13i | −0.268586 | − | 0.278328i | ||||
\(311\) | −4.87454e13 | −0.950062 | −0.475031 | − | 0.879969i | \(-0.657563\pi\) | ||||
−0.475031 | + | 0.879969i | \(0.657563\pi\) | |||||||
\(312\) | 2.90632e13 | − | 2.61125e13i | 0.556537 | − | 0.500032i | ||||
\(313\) | − | 4.59284e13i | − | 0.864147i | −0.901838 | − | 0.432074i | \(-0.857782\pi\) | ||
0.901838 | − | 0.432074i | \(-0.142218\pi\) | |||||||
\(314\) | 2.93014e13 | + | 3.03641e13i | 0.541720 | + | 0.561368i | ||||
\(315\) | 1.17677e12 | + | 1.17127e13i | 0.0213788 | + | 0.212790i | ||||
\(316\) | 1.06486e14 | + | 3.79457e12i | 1.90114 | + | 0.0677459i | ||||
\(317\) | −4.78681e13 | −0.839886 | −0.419943 | − | 0.907550i | \(-0.637950\pi\) | ||||
−0.419943 | + | 0.907550i | \(0.637950\pi\) | |||||||
\(318\) | 2.55908e13 | − | 2.46952e13i | 0.441302 | − | 0.425856i | ||||
\(319\) | − | 4.49690e13i | − | 0.762192i | ||||||
\(320\) | −3.82907e13 | − | 4.10732e12i | −0.637923 | − | 0.0684279i | ||||
\(321\) | − | 5.39662e13i | − | 0.883780i | ||||||
\(322\) | 3.55168e12 | + | 3.01025e12i | 0.0571777 | + | 0.0484614i | ||||
\(323\) | − | 9.05371e13i | − | 1.43289i | ||||||
\(324\) | 2.54302e11 | − | 7.13640e12i | 0.00395687 | − | 0.111041i | ||||
\(325\) | 4.98395e13i | 0.762456i | ||||||||
\(326\) | −9.47588e12 | − | 9.81956e12i | −0.142535 | − | 0.147705i | ||||
\(327\) | 3.32937e13 | 0.492435 | ||||||||
\(328\) | 6.38154e13 | − | 5.73363e13i | 0.928153 | − | 0.833918i | ||||
\(329\) | −1.52166e13 | + | 1.52880e12i | −0.217640 | + | 0.0218662i | ||||
\(330\) | −1.44469e13 | + | 1.39412e13i | −0.203211 | + | 0.196099i | ||||
\(331\) | − | 1.26897e14i | − | 1.75548i | −0.479133 | − | 0.877742i | \(-0.659049\pi\) | ||
0.479133 | − | 0.877742i | \(-0.340951\pi\) | |||||||
\(332\) | −2.83875e12 | + | 7.96631e13i | −0.0386249 | + | 1.08392i | ||||
\(333\) | 3.69869e13 | 0.494999 | ||||||||
\(334\) | 5.91394e13 | − | 5.70695e13i | 0.778522 | − | 0.751274i | ||||
\(335\) | −6.59647e13 | −0.854211 | ||||||||
\(336\) | 4.53027e13 | − | 1.30937e12i | 0.577109 | − | 0.0166800i | ||||
\(337\) | −1.28175e14 | −1.60635 | −0.803175 | − | 0.595743i | \(-0.796858\pi\) | ||||
−0.803175 | + | 0.595743i | \(0.796858\pi\) | |||||||
\(338\) | 3.96445e13 | − | 3.82570e13i | 0.488812 | − | 0.471703i | ||||
\(339\) | −7.13622e13 | −0.865705 | ||||||||
\(340\) | 1.94074e12 | − | 5.44626e13i | 0.0231651 | − | 0.650076i | ||||
\(341\) | 3.91328e13i | 0.459612i | ||||||||
\(342\) | −2.93313e13 | + | 2.83047e13i | −0.338991 | + | 0.327126i | ||||
\(343\) | 8.39886e13 | − | 2.60175e13i | 0.955218 | − | 0.295902i | ||||
\(344\) | 8.75029e13 | − | 7.86187e13i | 0.979379 | − | 0.879943i | ||||
\(345\) | −2.52046e12 | −0.0277636 | ||||||||
\(346\) | −2.22653e13 | − | 2.30729e13i | −0.241385 | − | 0.250140i | ||||
\(347\) | − | 1.11509e14i | − | 1.18986i | −0.803777 | − | 0.594931i | \(-0.797179\pi\) | ||
0.803777 | − | 0.594931i | \(-0.202821\pi\) | |||||||
\(348\) | 1.95710e12 | − | 5.49215e13i | 0.0205554 | − | 0.576842i | ||||
\(349\) | 4.63058e13i | 0.478735i | 0.970929 | + | 0.239367i | \(0.0769401\pi\) | ||||
−0.970929 | + | 0.239367i | \(0.923060\pi\) | |||||||
\(350\) | −3.73799e13 | + | 4.41031e13i | −0.380421 | + | 0.448844i | ||||
\(351\) | − | 2.48926e13i | − | 0.249391i | ||||||
\(352\) | 4.95792e13 | + | 5.93005e13i | 0.489007 | + | 0.584889i | ||||
\(353\) | 1.52616e14i | 1.48197i | 0.671524 | + | 0.740983i | \(0.265640\pi\) | ||||
−0.671524 | + | 0.740983i | \(0.734360\pi\) | |||||||
\(354\) | −3.86835e13 | + | 3.73295e13i | −0.369834 | + | 0.356890i | ||||
\(355\) | 2.79670e13 | 0.263263 | ||||||||
\(356\) | −1.29538e14 | − | 4.61601e12i | −1.20066 | − | 0.0427850i | ||||
\(357\) | 6.41142e12 | + | 6.38147e13i | 0.0585166 | + | 0.582432i | ||||
\(358\) | −1.94971e13 | − | 2.02042e13i | −0.175232 | − | 0.181588i | ||||
\(359\) | − | 1.12167e14i | − | 0.992762i | −0.868105 | − | 0.496381i | \(-0.834662\pi\) | ||
0.868105 | − | 0.496381i | \(-0.165338\pi\) | |||||||
\(360\) | −1.82510e13 | + | 1.63980e13i | −0.159083 | + | 0.142931i | ||||
\(361\) | 1.16180e14 | 0.997338 | ||||||||
\(362\) | 4.32672e13 | + | 4.48365e13i | 0.365815 | + | 0.379083i | ||||
\(363\) | −2.90341e13 | −0.241781 | ||||||||
\(364\) | 1.57658e14 | − | 1.01853e13i | 1.29318 | − | 0.0835441i | ||||
\(365\) | 3.42803e13 | 0.276971 | ||||||||
\(366\) | 9.81168e12 | + | 1.01675e13i | 0.0780904 | + | 0.0809226i | ||||
\(367\) | 2.01020e14 | 1.57607 | 0.788036 | − | 0.615630i | \(-0.211098\pi\) | ||||
0.788036 | + | 0.615630i | \(0.211098\pi\) | |||||||
\(368\) | −6.90708e11 | + | 9.67928e12i | −0.00533496 | + | 0.0747618i | ||||
\(369\) | − | 5.46578e13i | − | 0.415918i | ||||||
\(370\) | −8.82468e13 | − | 9.14474e13i | −0.661591 | − | 0.685586i | ||||
\(371\) | 1.43083e14 | − | 1.43755e13i | 1.05689 | − | 0.106185i | ||||
\(372\) | −1.70310e12 | + | 4.77936e13i | −0.0123952 | + | 0.347844i | ||||
\(373\) | −6.67376e13 | −0.478599 | −0.239299 | − | 0.970946i | \(-0.576918\pi\) | ||||
−0.239299 | + | 0.970946i | \(0.576918\pi\) | |||||||
\(374\) | −7.87111e13 | + | 7.59562e13i | −0.556214 | + | 0.536747i | ||||
\(375\) | − | 8.44921e13i | − | 0.588361i | ||||||
\(376\) | −2.13034e13 | − | 2.37107e13i | −0.146189 | − | 0.162709i | ||||
\(377\) | − | 1.91573e14i | − | 1.29556i | ||||||
\(378\) | 1.86696e13 | − | 2.20276e13i | 0.124432 | − | 0.146812i | ||||
\(379\) | 1.48535e14i | 0.975696i | 0.872929 | + | 0.487848i | \(0.162218\pi\) | ||||
−0.872929 | + | 0.487848i | \(0.837782\pi\) | |||||||
\(380\) | 1.39963e14 | + | 4.98750e12i | 0.906156 | + | 0.0322904i | ||||
\(381\) | − | 3.82356e13i | − | 0.243995i | ||||||
\(382\) | −9.96670e13 | − | 1.03282e14i | −0.626907 | − | 0.649644i | ||||
\(383\) | 1.16834e14 | 0.724394 | 0.362197 | − | 0.932101i | \(-0.382027\pi\) | ||||
0.362197 | + | 0.932101i | \(0.382027\pi\) | |||||||
\(384\) | 5.79713e13 | + | 7.45826e13i | 0.354316 | + | 0.455844i | ||||
\(385\) | −8.07751e13 | + | 8.11542e12i | −0.486680 | + | 0.0488964i | ||||
\(386\) | −2.22255e14 | + | 2.14476e14i | −1.32014 | + | 1.27394i | ||||
\(387\) | − | 7.49461e13i | − | 0.438873i | ||||||
\(388\) | −1.17030e14 | − | 4.17030e12i | −0.675652 | − | 0.0240765i | ||||
\(389\) | −2.51101e14 | −1.42931 | −0.714654 | − | 0.699478i | \(-0.753416\pi\) | ||||
−0.714654 | + | 0.699478i | \(0.753416\pi\) | |||||||
\(390\) | −6.15452e13 | + | 5.93912e13i | −0.345413 | + | 0.333324i | ||||
\(391\) | −1.37323e13 | −0.0759923 | ||||||||
\(392\) | 1.47151e14 | + | 1.09232e14i | 0.802955 | + | 0.596040i | ||||
\(393\) | −1.81313e14 | −0.975597 | ||||||||
\(394\) | −2.59826e13 | + | 2.50732e13i | −0.137865 | + | 0.133040i | ||||
\(395\) | −2.33252e14 | −1.22051 | ||||||||
\(396\) | 4.92151e13 | + | 1.75375e12i | 0.253966 | + | 0.00904991i | ||||
\(397\) | − | 1.93283e14i | − | 0.983662i | −0.870691 | − | 0.491831i | \(-0.836328\pi\) | ||
0.870691 | − | 0.491831i | \(-0.163672\pi\) | |||||||
\(398\) | −5.91844e12 | + | 5.71129e12i | −0.0297064 | + | 0.0286667i | ||||
\(399\) | −1.63997e14 | + | 1.64766e13i | −0.811866 | + | 0.0815676i | ||||
\(400\) | −1.20193e14 | − | 8.57689e12i | −0.586879 | − | 0.0418794i | ||||
\(401\) | −5.07447e13 | −0.244398 | −0.122199 | − | 0.992506i | \(-0.538995\pi\) | ||||
−0.122199 | + | 0.992506i | \(0.538995\pi\) | |||||||
\(402\) | 1.12359e14 | + | 1.16434e14i | 0.533781 | + | 0.553140i | ||||
\(403\) | 1.66710e14i | 0.781238i | ||||||||
\(404\) | 2.67870e14 | + | 9.54539e12i | 1.23830 | + | 0.0441261i | ||||
\(405\) | 1.56319e13i | 0.0712870i | ||||||||
\(406\) | 1.43681e14 | − | 1.69523e14i | 0.646407 | − | 0.762670i | ||||
\(407\) | 2.55074e14i | 1.13213i | ||||||||
\(408\) | −9.94371e13 | + | 8.93412e13i | −0.435429 | + | 0.391220i | ||||
\(409\) | 2.92527e14i | 1.26383i | 0.775039 | + | 0.631913i | \(0.217730\pi\) | ||||
−0.775039 | + | 0.631913i | \(0.782270\pi\) | |||||||
\(410\) | −1.35138e14 | + | 1.30408e14i | −0.576056 | + | 0.555894i | ||||
\(411\) | 1.54823e13 | 0.0651188 | ||||||||
\(412\) | 7.89336e12 | − | 2.21509e14i | 0.0327587 | − | 0.919300i | ||||
\(413\) | −2.16286e14 | + | 2.17301e13i | −0.885735 | + | 0.0889891i | ||||
\(414\) | 4.29313e12 | + | 4.44884e12i | 0.0173489 | + | 0.0179782i | ||||
\(415\) | − | 1.74498e14i | − | 0.695867i | ||||||
\(416\) | 2.11213e14 | + | 2.52626e14i | 0.831203 | + | 0.994181i | ||||
\(417\) | −1.48375e13 | −0.0576253 | ||||||||
\(418\) | −1.95199e14 | − | 2.02279e14i | −0.748184 | − | 0.775320i | ||||
\(419\) | −1.59383e14 | −0.602925 | −0.301463 | − | 0.953478i | \(-0.597475\pi\) | ||||
−0.301463 | + | 0.953478i | \(0.597475\pi\) | |||||||
\(420\) | −9.90054e13 | + | 6.39611e12i | −0.369648 | + | 0.0238806i | ||||
\(421\) | 2.67679e14 | 0.986423 | 0.493212 | − | 0.869909i | \(-0.335823\pi\) | ||||
0.493212 | + | 0.869909i | \(0.335823\pi\) | |||||||
\(422\) | −1.76161e14 | − | 1.82550e14i | −0.640754 | − | 0.663994i | ||||
\(423\) | −2.03082e13 | −0.0729120 | ||||||||
\(424\) | 2.00318e14 | + | 2.22954e14i | 0.709916 | + | 0.790139i | ||||
\(425\) | − | 1.70521e14i | − | 0.596538i | ||||||
\(426\) | −4.76366e13 | − | 4.93643e13i | −0.164508 | − | 0.170475i | ||||
\(427\) | 5.71154e12 | + | 5.68486e13i | 0.0194715 | + | 0.193806i | ||||
\(428\) | 4.54538e14 | + | 1.61972e13i | 1.52978 | + | 0.0545128i | ||||
\(429\) | 1.71668e14 | 0.570393 | ||||||||
\(430\) | −1.85299e14 | + | 1.78813e14i | −0.607850 | + | 0.586575i | ||||
\(431\) | 4.08490e14i | 1.32299i | 0.749950 | + | 0.661494i | \(0.230077\pi\) | ||||
−0.749950 | + | 0.661494i | \(0.769923\pi\) | |||||||
\(432\) | 6.00310e13 | + | 4.28378e12i | 0.191962 | + | 0.0136983i | ||||
\(433\) | 3.45919e13i | 0.109217i | 0.998508 | + | 0.0546085i | \(0.0173911\pi\) | ||||
−0.998508 | + | 0.0546085i | \(0.982609\pi\) | |||||||
\(434\) | −1.25034e14 | + | 1.47522e14i | −0.389792 | + | 0.459900i | ||||
\(435\) | 1.20303e14i | 0.370327i | ||||||||
\(436\) | −9.99262e12 | + | 2.80421e14i | −0.0303741 | + | 0.852382i | ||||
\(437\) | − | 3.52904e13i | − | 0.105927i | ||||||
\(438\) | −5.83901e13 | − | 6.05079e13i | −0.173074 | − | 0.179351i | ||||
\(439\) | 9.72822e12 | 0.0284760 | 0.0142380 | − | 0.999899i | \(-0.495468\pi\) | ||||
0.0142380 | + | 0.999899i | \(0.495468\pi\) | |||||||
\(440\) | −1.13086e14 | − | 1.25865e14i | −0.326903 | − | 0.363844i | ||||
\(441\) | 1.14426e14 | − | 2.32270e13i | 0.326671 | − | 0.0663102i | ||||
\(442\) | −3.35318e14 | + | 3.23582e14i | −0.945440 | + | 0.912350i | ||||
\(443\) | 2.37670e14i | 0.661840i | 0.943659 | + | 0.330920i | \(0.107359\pi\) | ||||
−0.943659 | + | 0.330920i | \(0.892641\pi\) | |||||||
\(444\) | −1.11011e13 | + | 3.11527e14i | −0.0305323 | + | 0.856820i | ||||
\(445\) | 2.83746e14 | 0.770815 | ||||||||
\(446\) | 4.59255e14 | − | 4.43182e14i | 1.23229 | − | 1.18916i | ||||
\(447\) | −2.91920e14 | −0.773701 | ||||||||
\(448\) | −2.56864e12 | + | 3.81961e14i | −0.00672471 | + | 0.999977i | ||||
\(449\) | 6.77274e14 | 1.75150 | 0.875748 | − | 0.482768i | \(-0.160369\pi\) | ||||
0.875748 | + | 0.482768i | \(0.160369\pi\) | |||||||
\(450\) | −5.52437e13 | + | 5.33102e13i | −0.141128 | + | 0.136189i | ||||
\(451\) | 3.76939e14 | 0.951262 | ||||||||
\(452\) | 2.14184e13 | − | 6.01058e14i | 0.0533980 | − | 1.49849i | ||||
\(453\) | − | 2.98648e13i | − | 0.0735561i | ||||||
\(454\) | −4.75277e13 | + | 4.58642e13i | −0.115648 | + | 0.111601i | ||||
\(455\) | −3.44111e14 | + | 3.45726e13i | −0.827247 | + | 0.0831130i | ||||
\(456\) | −2.29597e14 | − | 2.55542e14i | −0.545331 | − | 0.606955i | ||||
\(457\) | −4.00602e14 | −0.940099 | −0.470050 | − | 0.882640i | \(-0.655764\pi\) | ||||
−0.470050 | + | 0.882640i | \(0.655764\pi\) | |||||||
\(458\) | −3.01516e14 | − | 3.12451e14i | −0.699117 | − | 0.724473i | ||||
\(459\) | 8.51677e13i | 0.195121i | ||||||||
\(460\) | 7.56481e11 | − | 2.12289e13i | 0.00171250 | − | 0.0480574i | ||||
\(461\) | − | 6.40102e14i | − | 1.43184i | −0.698183 | − | 0.715919i | \(-0.746008\pi\) | ||
0.698183 | − | 0.715919i | \(-0.253992\pi\) | |||||||
\(462\) | 1.51910e14 | + | 1.28752e14i | 0.335780 | + | 0.284593i | ||||
\(463\) | − | 1.45973e14i | − | 0.318843i | −0.987211 | − | 0.159422i | \(-0.949037\pi\) | ||
0.987211 | − | 0.159422i | \(-0.0509630\pi\) | |||||||
\(464\) | 4.61997e14 | + | 3.29678e13i | 0.997218 | + | 0.0711609i | ||||
\(465\) | − | 1.04690e14i | − | 0.223312i | ||||||
\(466\) | 3.63553e14 | − | 3.50829e14i | 0.766383 | − | 0.739559i | ||||
\(467\) | 4.94883e11 | 0.00103100 | 0.000515501 | − | 1.00000i | \(-0.499836\pi\) | ||||
0.000515501 | 1.00000i | \(0.499836\pi\) | ||||||||
\(468\) | 2.09662e14 | + | 7.47117e12i | 0.431685 | + | 0.0153828i | ||||
\(469\) | 6.54057e13 | + | 6.51002e14i | 0.133096 | + | 1.32474i | ||||
\(470\) | 4.84532e13 | + | 5.02105e13i | 0.0974505 | + | 0.100985i | ||||
\(471\) | 2.26578e14i | 0.450405i | ||||||||
\(472\) | −3.02803e14 | − | 3.37021e14i | −0.594948 | − | 0.662179i | ||||
\(473\) | 5.16854e14 | 1.00376 | ||||||||
\(474\) | 3.97302e14 | + | 4.11711e14i | 0.762675 | + | 0.790336i | ||||
\(475\) | 4.38220e14 | 0.831529 | ||||||||
\(476\) | −5.39412e14 | + | 3.48480e13i | −1.01177 | + | 0.0653641i | ||||
\(477\) | 1.90960e14 | 0.354072 | ||||||||
\(478\) | −2.94907e14 | − | 3.05603e14i | −0.540544 | − | 0.560149i | ||||
\(479\) | −2.28739e14 | −0.414472 | −0.207236 | − | 0.978291i | \(-0.566447\pi\) | ||||
−0.207236 | + | 0.978291i | \(0.566447\pi\) | |||||||
\(480\) | −1.32636e14 | − | 1.58643e14i | −0.237594 | − | 0.284181i | ||||
\(481\) | 1.08664e15i | 1.92437i | ||||||||
\(482\) | 2.03535e14 | + | 2.10917e14i | 0.356353 | + | 0.369277i | ||||
\(483\) | 2.49910e12 | + | 2.48743e13i | 0.00432588 | + | 0.0430568i | ||||
\(484\) | 8.71417e12 | − | 2.44544e14i | 0.0149134 | − | 0.418511i | ||||
\(485\) | 2.56349e14 | 0.433762 | ||||||||
\(486\) | 2.75918e13 | − | 2.66261e13i | 0.0461615 | − | 0.0445459i | ||||
\(487\) | 1.05789e15i | 1.74998i | 0.484142 | + | 0.874990i | \(0.339132\pi\) | ||||
−0.484142 | + | 0.874990i | \(0.660868\pi\) | |||||||
\(488\) | −8.85824e13 | + | 7.95886e13i | −0.144890 | + | 0.130179i | ||||
\(489\) | − | 7.32740e13i | − | 0.118509i | ||||||
\(490\) | −3.30434e14 | − | 2.27492e14i | −0.528453 | − | 0.363821i | ||||
\(491\) | − | 6.23073e14i | − | 0.985350i | −0.870213 | − | 0.492675i | \(-0.836019\pi\) | ||
0.870213 | − | 0.492675i | \(-0.163981\pi\) | |||||||
\(492\) | 4.60363e14 | + | 1.64048e13i | 0.719934 | + | 0.0256544i | ||||
\(493\) | 6.55447e14i | 1.01363i | ||||||||
\(494\) | −8.31569e14 | − | 8.61729e14i | −1.27175 | − | 1.31787i | ||||
\(495\) | −1.07803e14 | −0.163043 | ||||||||
\(496\) | −4.02037e14 | − | 2.86892e13i | −0.601336 | − | 0.0429110i | ||||
\(497\) | −2.77300e13 | − | 2.76005e14i | −0.0410195 | − | 0.408279i | ||||
\(498\) | −3.08005e14 | + | 2.97225e14i | −0.450605 | + | 0.434834i | ||||
\(499\) | 4.39882e14i | 0.636477i | 0.948011 | + | 0.318239i | \(0.103091\pi\) | ||||
−0.948011 | + | 0.318239i | \(0.896909\pi\) | |||||||
\(500\) | 7.11647e14 | + | 2.53591e13i | 1.01843 | + | 0.0362910i | ||||
\(501\) | 4.41301e14 | 0.624636 | ||||||||
\(502\) | −5.50328e14 | + | 5.31067e14i | −0.770462 | + | 0.743496i | ||||
\(503\) | −1.26286e13 | −0.0174876 | −0.00874381 | − | 0.999962i | \(-0.502783\pi\) | ||||
−0.00874381 | + | 0.999962i | \(0.502783\pi\) | |||||||
\(504\) | 1.79927e14 | + | 1.63859e14i | 0.246450 | + | 0.224441i | ||||
\(505\) | −5.86756e14 | −0.794977 | ||||||||
\(506\) | −3.06807e13 | + | 2.96069e13i | −0.0411186 | + | 0.0396794i | ||||
\(507\) | 2.95829e14 | 0.392191 | ||||||||
\(508\) | 3.22045e14 | + | 1.14759e13i | 0.422344 | + | 0.0150500i | ||||
\(509\) | − | 1.30789e15i | − | 1.69678i | −0.529374 | − | 0.848389i | \(-0.677573\pi\) | ||
0.529374 | − | 0.848389i | \(-0.322427\pi\) | |||||||
\(510\) | 2.10571e14 | − | 2.03201e14i | 0.270248 | − | 0.260789i | ||||
\(511\) | −3.39898e13 | − | 3.38311e14i | −0.0431553 | − | 0.429537i | ||||
\(512\) | −6.45581e14 | + | 4.65886e14i | −0.810898 | + | 0.585187i | ||||
\(513\) | −2.18872e14 | −0.271984 | ||||||||
\(514\) | 5.76586e14 | + | 5.97499e14i | 0.708871 | + | 0.734581i | ||||
\(515\) | 4.85205e14i | 0.590182i | ||||||||
\(516\) | 6.31243e14 | + | 2.24940e13i | 0.759667 | + | 0.0270703i | ||||
\(517\) | − | 1.40052e14i | − | 0.166760i | ||||||
\(518\) | −8.14990e14 | + | 9.61575e14i | −0.960149 | + | 1.13284i | ||||
\(519\) | − | 1.72171e14i | − | 0.200696i | ||||||
\(520\) | −4.81758e14 | − | 5.36199e14i | −0.555662 | − | 0.618454i | ||||
\(521\) | − | 8.44201e14i | − | 0.963470i | −0.876317 | − | 0.481735i | \(-0.840007\pi\) | ||
0.876317 | − | 0.481735i | \(-0.159993\pi\) | |||||||
\(522\) | 2.12345e14 | − | 2.04913e14i | 0.239803 | − | 0.231410i | ||||
\(523\) | 9.87674e14 | 1.10371 | 0.551854 | − | 0.833940i | \(-0.313920\pi\) | ||||
0.551854 | + | 0.833940i | \(0.313920\pi\) | |||||||
\(524\) | 5.44186e13 | − | 1.52714e15i | 0.0601763 | − | 1.68871i | ||||
\(525\) | −3.08877e14 | + | 3.10327e13i | −0.337995 | + | 0.0339581i | ||||
\(526\) | −7.30608e14 | − | 7.57107e14i | −0.791158 | − | 0.819852i | ||||
\(527\) | − | 5.70382e14i | − | 0.611233i | ||||||
\(528\) | −2.95424e13 | + | 4.13994e14i | −0.0313299 | + | 0.439044i | ||||
\(529\) | 9.47457e14 | 0.994382 | ||||||||
\(530\) | −4.55610e14 | − | 4.72135e14i | −0.473234 | − | 0.490398i | ||||
\(531\) | −2.88658e14 | −0.296731 | ||||||||
\(532\) | −8.95555e13 | − | 1.38623e15i | −0.0911125 | − | 1.41033i | ||||
\(533\) | 1.60580e15 | 1.61693 | ||||||||
\(534\) | −4.83309e14 | − | 5.00838e14i | −0.481668 | − | 0.499137i | ||||
\(535\) | −9.95642e14 | −0.982104 | ||||||||
\(536\) | −1.01440e15 | + | 9.11409e14i | −0.990384 | + | 0.889830i | ||||
\(537\) | − | 1.50765e14i | − | 0.145694i | ||||||
\(538\) | −1.23566e15 | − | 1.28048e15i | −1.18194 | − | 1.22481i | ||||
\(539\) | 1.60181e14 | + | 7.89118e14i | 0.151661 | + | 0.747143i | ||||
\(540\) | −1.31662e14 | − | 4.69171e12i | −0.123394 | − | 0.00439709i | ||||
\(541\) | −4.87158e13 | −0.0451944 | −0.0225972 | − | 0.999745i | \(-0.507194\pi\) | ||||
−0.0225972 | + | 0.999745i | \(0.507194\pi\) | |||||||
\(542\) | 6.24220e14 | − | 6.02372e14i | 0.573247 | − | 0.553183i | ||||
\(543\) | 3.34572e14i | 0.304152i | ||||||||
\(544\) | −7.22644e14 | − | 8.64337e14i | −0.650325 | − | 0.777838i | ||||
\(545\) | − | 6.14247e14i | − | 0.547221i | ||||||
\(546\) | 6.47152e14 | + | 5.48498e14i | 0.570751 | + | 0.483744i | ||||
\(547\) | 2.49278e14i | 0.217647i | 0.994061 | + | 0.108824i | \(0.0347084\pi\) | ||||
−0.994061 | + | 0.108824i | \(0.965292\pi\) | |||||||
\(548\) | −4.64681e12 | + | 1.30402e14i | −0.00401663 | + | 0.112718i | ||||
\(549\) | 7.58706e13i | 0.0649271i | ||||||||
\(550\) | −3.67645e14 | − | 3.80979e14i | −0.311483 | − | 0.322780i | ||||
\(551\) | −1.68443e15 | −1.41292 | ||||||||
\(552\) | −3.87595e13 | + | 3.48243e13i | −0.0321894 | + | 0.0289212i | ||||
\(553\) | 2.31276e14 | + | 2.30195e15i | 0.190170 | + | 1.89281i | ||||
\(554\) | 9.90498e14 | − | 9.55831e14i | 0.806399 | − | 0.778175i | ||||
\(555\) | − | 6.82385e14i | − | 0.550070i | ||||||
\(556\) | 4.45327e12 | − | 1.24971e14i | 0.00355441 | − | 0.0997466i | ||||
\(557\) | −1.07858e15 | −0.852414 | −0.426207 | − | 0.904626i | \(-0.640150\pi\) | ||||
−0.426207 | + | 0.904626i | \(0.640150\pi\) | |||||||
\(558\) | −1.84787e14 | + | 1.78319e14i | −0.144605 | + | 0.139544i | ||||
\(559\) | 2.20185e15 | 1.70617 | ||||||||
\(560\) | −2.41570e13 | − | 8.35806e14i | −0.0185357 | − | 0.641315i | ||||
\(561\) | −5.87345e14 | −0.446270 | ||||||||
\(562\) | −3.02020e14 | + | 2.91450e14i | −0.227241 | + | 0.219288i | ||||
\(563\) | 1.47824e15 | 1.10141 | 0.550706 | − | 0.834699i | \(-0.314358\pi\) | ||||
0.550706 | + | 0.834699i | \(0.314358\pi\) | |||||||
\(564\) | 6.09521e12 | − | 1.71048e14i | 0.00449732 | − | 0.126207i | ||||
\(565\) | 1.31659e15i | 0.962019i | ||||||||
\(566\) | 1.45511e15 | − | 1.40418e15i | 1.05294 | − | 1.01609i | ||||
\(567\) | 1.54271e14 | − | 1.54995e13i | 0.110555 | − | 0.0111073i | ||||
\(568\) | 4.30075e14 | − | 3.86410e14i | 0.305231 | − | 0.274241i | ||||
\(569\) | 1.04040e15 | 0.731276 | 0.365638 | − | 0.930757i | \(-0.380851\pi\) | ||||
0.365638 | + | 0.930757i | \(0.380851\pi\) | |||||||
\(570\) | 5.22205e14 | + | 5.41144e14i | 0.363521 | + | 0.376705i | ||||
\(571\) | − | 1.47971e15i | − | 1.02018i | −0.860120 | − | 0.510091i | \(-0.829612\pi\) | ||
0.860120 | − | 0.510091i | \(-0.170388\pi\) | |||||||
\(572\) | −5.15237e13 | + | 1.44590e15i | −0.0351827 | + | 0.987323i | ||||
\(573\) | − | 7.70694e14i | − | 0.521232i | ||||||
\(574\) | 1.42098e15 | + | 1.20436e15i | 0.951858 | + | 0.806755i | ||||
\(575\) | − | 6.64672e13i | − | 0.0440996i | ||||||
\(576\) | −5.40982e13 | + | 5.04334e14i | −0.0355516 | + | 0.331432i | ||||
\(577\) | 2.78366e15i | 1.81196i | 0.423320 | + | 0.905980i | \(0.360865\pi\) | ||||
−0.423320 | + | 0.905980i | \(0.639135\pi\) | |||||||
\(578\) | 3.11988e13 | − | 3.01068e13i | 0.0201157 | − | 0.0194116i | ||||
\(579\) | −1.65847e15 | −1.05920 | ||||||||
\(580\) | −1.01327e15 | − | 3.61072e13i | −0.641018 | − | 0.0228423i | ||||
\(581\) | −1.72211e15 | + | 1.73019e14i | −1.07918 | + | 0.108424i | ||||
\(582\) | −4.36642e14 | − | 4.52478e14i | −0.271050 | − | 0.280880i | ||||
\(583\) | 1.31693e15i | 0.809812i | ||||||||
\(584\) | 5.27161e14 | − | 4.73638e14i | 0.321124 | − | 0.288520i | ||||
\(585\) | −4.59253e14 | −0.277137 | ||||||||
\(586\) | −7.60508e14 | − | 7.88091e14i | −0.454639 | − | 0.471129i | ||||
\(587\) | −8.72225e14 | −0.516558 | −0.258279 | − | 0.966070i | \(-0.583155\pi\) | ||||
−0.258279 | + | 0.966070i | \(0.583155\pi\) | |||||||
\(588\) | 1.61289e14 | + | 9.70736e14i | 0.0946302 | + | 0.569542i | ||||
\(589\) | 1.46582e15 | 0.852013 | ||||||||
\(590\) | 6.88707e14 | + | 7.13686e14i | 0.396596 | + | 0.410980i | ||||
\(591\) | −1.93883e14 | −0.110614 | ||||||||
\(592\) | −2.62055e15 | − | 1.87001e14i | −1.48123 | − | 0.105700i | ||||
\(593\) | − | 9.68246e14i | − | 0.542232i | −0.962547 | − | 0.271116i | \(-0.912607\pi\) | ||
0.962547 | − | 0.271116i | \(-0.0873926\pi\) | |||||||
\(594\) | 1.83623e14 | + | 1.90282e14i | 0.101883 | + | 0.105578i | ||||
\(595\) | 1.17734e15 | − | 1.18287e14i | 0.647230 | − | 0.0650268i | ||||
\(596\) | 8.76158e13 | − | 2.45874e15i | 0.0477230 | − | 1.33924i | ||||
\(597\) | −4.41636e13 | −0.0238345 | ||||||||
\(598\) | −1.30703e14 | + | 1.26129e14i | −0.0698924 | + | 0.0674462i | ||||
\(599\) | − | 1.22290e15i | − | 0.647952i | −0.946065 | − | 0.323976i | \(-0.894980\pi\) | ||
0.946065 | − | 0.323976i | \(-0.105020\pi\) | |||||||
\(600\) | −4.32432e14 | − | 4.81298e14i | −0.227031 | − | 0.252686i | ||||
\(601\) | − | 2.89149e15i | − | 1.50422i | −0.659037 | − | 0.752111i | \(-0.729036\pi\) | ||
0.659037 | − | 0.752111i | \(-0.270964\pi\) | |||||||
\(602\) | 1.94843e15 | + | 1.65140e15i | 1.00439 | + | 0.851281i | ||||
\(603\) | 8.68833e14i | 0.443804i | ||||||||
\(604\) | 2.51540e14 | + | 8.96348e12i | 0.127322 | + | 0.00453705i | ||||
\(605\) | 5.35661e14i | 0.268680i | ||||||||
\(606\) | 9.99428e14 | + | 1.03568e15i | 0.496766 | + | 0.514784i | ||||
\(607\) | −1.35219e15 | −0.666041 | −0.333021 | − | 0.942920i | \(-0.608068\pi\) | ||||
−0.333021 | + | 0.942920i | \(0.608068\pi\) | |||||||
\(608\) | 2.22125e15 | − | 1.85712e15i | 1.08425 | − | 0.906503i | ||||
\(609\) | 1.18726e15 | − | 1.19283e14i | 0.574317 | − | 0.0577012i | ||||
\(610\) | 1.87585e14 | − | 1.81019e14i | 0.0899256 | − | 0.0867783i | ||||
\(611\) | − | 5.96637e14i | − | 0.283455i | ||||||
\(612\) | −7.17337e14 | − | 2.55619e13i | −0.337746 | − | 0.0120354i | ||||
\(613\) | −1.65146e15 | −0.770610 | −0.385305 | − | 0.922789i | \(-0.625904\pi\) | ||||
−0.385305 | + | 0.922789i | \(0.625904\pi\) | |||||||
\(614\) | −1.84394e15 | + | 1.77940e15i | −0.852748 | + | 0.822902i | ||||
\(615\) | −1.00840e15 | −0.462190 | ||||||||
\(616\) | −1.13003e15 | + | 1.24084e15i | −0.513328 | + | 0.563665i | ||||
\(617\) | −1.85421e15 | −0.834815 | −0.417408 | − | 0.908719i | \(-0.637061\pi\) | ||||
−0.417408 | + | 0.908719i | \(0.637061\pi\) | |||||||
\(618\) | 8.56431e14 | − | 8.26456e14i | 0.382169 | − | 0.368794i | ||||
\(619\) | 2.67968e15 | 1.18518 | 0.592590 | − | 0.805504i | \(-0.298105\pi\) | ||||
0.592590 | + | 0.805504i | \(0.298105\pi\) | |||||||
\(620\) | 8.81763e14 | + | 3.14211e13i | 0.386543 | + | 0.0137742i | ||||
\(621\) | 3.31975e13i | 0.0144245i | ||||||||
\(622\) | 1.58739e15 | − | 1.53183e15i | 0.683652 | − | 0.659725i | ||||
\(623\) | −2.81342e14 | − | 2.80027e15i | −0.120102 | − | 1.19541i | ||||
\(624\) | −1.25854e14 | + | 1.76366e15i | −0.0532539 | + | 0.746277i | ||||
\(625\) | −1.56040e14 | −0.0654480 | ||||||||
\(626\) | 1.44330e15 | + | 1.49565e15i | 0.600065 | + | 0.621829i | ||||
\(627\) | − | 1.50941e15i | − | 0.622066i | ||||||
\(628\) | −1.90839e15 | − | 6.80042e13i | −0.779629 | − | 0.0277816i | ||||
\(629\) | − | 3.71784e15i | − | 1.50561i | ||||||
\(630\) | −4.06395e14 | − | 3.44443e14i | −0.163146 | − | 0.138275i | ||||
\(631\) | − | 1.95571e15i | − | 0.778293i | −0.921176 | − | 0.389146i | \(-0.872770\pi\) | ||
0.921176 | − | 0.389146i | \(-0.127230\pi\) | |||||||
\(632\) | −3.58694e15 | + | 3.22276e15i | −1.41508 | + | 1.27140i | ||||
\(633\) | − | 1.36220e15i | − | 0.532746i | ||||||
\(634\) | 1.55882e15 | − | 1.50426e15i | 0.604371 | − | 0.583219i | ||||
\(635\) | −7.05424e14 | −0.271141 | ||||||||
\(636\) | −5.73139e13 | + | 1.60839e15i | −0.0218397 | + | 0.612881i | ||||
\(637\) | 6.82389e14 | + | 3.36173e15i | 0.257789 | + | 1.26998i | ||||
\(638\) | 1.41315e15 | + | 1.46441e15i | 0.529268 | + | 0.548464i | ||||
\(639\) | − | 3.68359e14i | − | 0.136778i | ||||||
\(640\) | 1.37600e15 | − | 1.06953e15i | 0.506558 | − | 0.393735i | ||||
\(641\) | 7.90913e14 | 0.288675 | 0.144338 | − | 0.989528i | \(-0.453895\pi\) | ||||
0.144338 | + | 0.989528i | \(0.453895\pi\) | |||||||
\(642\) | 1.69589e15 | + | 1.75740e15i | 0.613698 | + | 0.635957i | ||||
\(643\) | 2.36334e15 | 0.847943 | 0.423972 | − | 0.905675i | \(-0.360636\pi\) | ||||
0.423972 | + | 0.905675i | \(0.360636\pi\) | |||||||
\(644\) | −2.10257e14 | + | 1.35834e13i | −0.0747960 | + | 0.00483209i | ||||
\(645\) | −1.38271e15 | −0.487699 | ||||||||
\(646\) | 2.84513e15 | + | 2.94832e15i | 0.995001 | + | 1.03109i | ||||
\(647\) | −2.45880e15 | −0.852608 | −0.426304 | − | 0.904580i | \(-0.640185\pi\) | ||||
−0.426304 | + | 0.904580i | \(0.640185\pi\) | |||||||
\(648\) | 2.15981e14 | + | 2.40387e14i | 0.0742595 | + | 0.0826511i | ||||
\(649\) | − | 1.99068e15i | − | 0.678666i | ||||||
\(650\) | −1.56621e15 | − | 1.62301e15i | −0.529451 | − | 0.548654i | ||||
\(651\) | −1.03318e15 | + | 1.03802e14i | −0.346321 | + | 0.0347946i | ||||
\(652\) | 6.17160e14 | + | 2.19921e13i | 0.205133 | + | 0.00730980i | ||||
\(653\) | 1.51415e15 | 0.499053 | 0.249526 | − | 0.968368i | \(-0.419725\pi\) | ||||
0.249526 | + | 0.968368i | \(0.419725\pi\) | |||||||
\(654\) | −1.08420e15 | + | 1.04626e15i | −0.354350 | + | 0.341948i | ||||
\(655\) | 3.34511e15i | 1.08414i | ||||||||
\(656\) | −2.76343e14 | + | 3.87255e15i | −0.0888131 | + | 1.24459i | ||||
\(657\) | − | 4.51513e14i | − | 0.143900i | ||||||
\(658\) | 4.47482e14 | − | 5.27966e14i | 0.141427 | − | 0.166864i | ||||
\(659\) | 4.30335e15i | 1.34877i | 0.738381 | + | 0.674384i | \(0.235591\pi\) | ||||
−0.738381 | + | 0.674384i | \(0.764409\pi\) | |||||||
\(660\) | 3.23556e13 | − | 9.07987e14i | 0.0100568 | − | 0.282220i | ||||
\(661\) | − | 3.33418e15i | − | 1.02774i | −0.857869 | − | 0.513868i | \(-0.828212\pi\) | ||
0.857869 | − | 0.513868i | \(-0.171788\pi\) | |||||||
\(662\) | 3.98774e15 | + | 4.13237e15i | 1.21901 | + | 1.26322i | ||||
\(663\) | −2.50215e15 | −0.758560 | ||||||||
\(664\) | −2.41097e15 | − | 2.68342e15i | −0.724883 | − | 0.806797i | ||||
\(665\) | 3.03984e14 | + | 3.02564e15i | 0.0906423 | + | 0.902189i | ||||
\(666\) | −1.20447e15 | + | 1.16231e15i | −0.356195 | + | 0.343728i | ||||
\(667\) | 2.55486e14i | 0.0749335i | ||||||||
\(668\) | −1.32450e14 | + | 3.71691e15i | −0.0385285 | + | 1.08122i | ||||
\(669\) | 3.42698e15 | 0.988709 | ||||||||
\(670\) | 2.14813e15 | − | 2.07294e15i | 0.614680 | − | 0.593166i | ||||
\(671\) | −5.23230e14 | −0.148497 | ||||||||
\(672\) | −1.43413e15 | + | 1.46628e15i | −0.403698 | + | 0.412749i | ||||
\(673\) | −5.15623e15 | −1.43963 | −0.719813 | − | 0.694168i | \(-0.755773\pi\) | ||||
−0.719813 | + | 0.694168i | \(0.755773\pi\) | |||||||
\(674\) | 4.17401e15 | − | 4.02792e15i | 1.15591 | − | 1.11545i | ||||
\(675\) | −4.12231e14 | −0.113232 | ||||||||
\(676\) | −8.87890e13 | + | 2.49166e15i | −0.0241909 | + | 0.678864i | ||||
\(677\) | − | 1.76720e15i | − | 0.477581i | −0.971071 | − | 0.238791i | \(-0.923249\pi\) | ||
0.971071 | − | 0.238791i | \(-0.0767509\pi\) | |||||||
\(678\) | 2.32390e15 | − | 2.24256e15i | 0.622951 | − | 0.601148i | ||||
\(679\) | −2.54176e14 | − | 2.52989e15i | −0.0675851 | − | 0.672694i | ||||
\(680\) | 1.64829e15 | + | 1.83455e15i | 0.434745 | + | 0.483872i | ||||
\(681\) | −3.54653e14 | −0.0927887 | ||||||||
\(682\) | −1.22975e15 | − | 1.27435e15i | −0.319156 | − | 0.330731i | ||||
\(683\) | − | 5.30298e14i | − | 0.136523i | −0.997667 | − | 0.0682616i | \(-0.978255\pi\) | ||
0.997667 | − | 0.0682616i | \(-0.0217452\pi\) | |||||||
\(684\) | 6.56912e13 | − | 1.84348e15i | 0.0167764 | − | 0.470792i | ||||
\(685\) | − | 2.85639e14i | − | 0.0723636i | ||||||
\(686\) | −1.91747e15 | + | 3.48660e15i | −0.481888 | + | 0.876233i | ||||
\(687\) | − | 2.33153e15i | − | 0.581271i | ||||||
\(688\) | −3.78918e14 | + | 5.30998e15i | −0.0937148 | + | 1.31328i | ||||
\(689\) | 5.61024e15i | 1.37650i | ||||||||
\(690\) | 8.20784e13 | − | 7.92056e13i | 0.0199783 | − | 0.0192791i | ||||
\(691\) | 1.60339e15 | 0.387177 | 0.193589 | − | 0.981083i | \(-0.437987\pi\) | ||||
0.193589 | + | 0.981083i | \(0.437987\pi\) | |||||||
\(692\) | 1.45013e15 | + | 5.16746e13i | 0.347395 | + | 0.0123792i | ||||
\(693\) | 1.06890e14 | + | 1.06390e15i | 0.0254040 | + | 0.252854i | ||||
\(694\) | 3.50416e15 | + | 3.63126e15i | 0.826242 | + | 0.856209i | ||||
\(695\) | 2.73743e14i | 0.0640363i | ||||||||
\(696\) | 1.66218e15 | + | 1.85001e15i | 0.385769 | + | 0.429362i | ||||
\(697\) | −5.49409e15 | −1.26507 | ||||||||
\(698\) | −1.45516e15 | − | 1.50794e15i | −0.332434 | − | 0.344492i | ||||
\(699\) | 2.71285e15 | 0.614896 | ||||||||
\(700\) | −1.68672e14 | − | 2.61088e15i | −0.0379318 | − | 0.587147i | ||||
\(701\) | −6.57181e15 | −1.46634 | −0.733172 | − | 0.680043i | \(-0.761961\pi\) | ||||
−0.733172 | + | 0.680043i | \(0.761961\pi\) | |||||||
\(702\) | 7.82252e14 | + | 8.10623e14i | 0.173178 | + | 0.179459i | ||||
\(703\) | 9.55445e15 | 2.09871 | ||||||||
\(704\) | −3.47806e15 | − | 3.73080e14i | −0.758032 | − | 0.0813115i | ||||
\(705\) | 3.74673e14i | 0.0810238i | ||||||||
\(706\) | −4.79595e15 | − | 4.96990e15i | −1.02908 | − | 1.06640i | ||||
\(707\) | 5.81783e14 | + | 5.79066e15i | 0.123867 | + | 1.23288i | ||||
\(708\) | 8.66365e13 | − | 2.43126e15i | 0.0183028 | − | 0.513628i | ||||
\(709\) | −5.81764e15 | −1.21953 | −0.609765 | − | 0.792582i | \(-0.708736\pi\) | ||||
−0.609765 | + | 0.792582i | \(0.708736\pi\) | |||||||
\(710\) | −9.10741e14 | + | 8.78865e14i | −0.189441 | + | 0.182811i | ||||
\(711\) | 3.07221e15i | 0.634115i | ||||||||
\(712\) | 4.36343e15 | − | 3.92041e15i | 0.893693 | − | 0.802956i | ||||
\(713\) | − | 2.22329e14i | − | 0.0451859i | ||||||
\(714\) | −2.21417e15 | − | 1.87663e15i | −0.446550 | − | 0.378477i | ||||
\(715\) | − | 3.16717e15i | − | 0.633852i | ||||||
\(716\) | 1.26984e15 | + | 4.52500e13i | 0.252189 | + | 0.00898663i | ||||
\(717\) | − | 2.28042e15i | − | 0.449427i | ||||||
\(718\) | 3.52485e15 | + | 3.65269e15i | 0.689376 | + | 0.714379i | ||||
\(719\) | 6.95565e14 | 0.134998 | 0.0674992 | − | 0.997719i | \(-0.478498\pi\) | ||||
0.0674992 | + | 0.997719i | \(0.478498\pi\) | |||||||
\(720\) | 7.90331e13 | − | 1.10753e15i | 0.0152223 | − | 0.213319i | ||||
\(721\) | 4.78846e15 | − | 4.81093e14i | 0.915276 | − | 0.0919571i | ||||
\(722\) | −3.78338e15 | + | 3.65097e15i | −0.717672 | + | 0.692554i | ||||
\(723\) | 1.57387e15i | 0.296284i | ||||||||
\(724\) | −2.81798e15 | − | 1.00417e14i | −0.526472 | − | 0.0187605i | ||||
\(725\) | −3.17251e15 | −0.588226 | ||||||||
\(726\) | 9.45489e14 | − | 9.12398e14i | 0.173982 | − | 0.167893i | ||||
\(727\) | −1.04179e15 | −0.190257 | −0.0951287 | − | 0.995465i | \(-0.530326\pi\) | ||||
−0.0951287 | + | 0.995465i | \(0.530326\pi\) | |||||||
\(728\) | −4.81404e15 | + | 5.28610e15i | −0.872543 | + | 0.958104i | ||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −1.11633e15 | + | 1.07726e15i | −0.199305 | + | 0.192329i | ||||
\(731\) | −7.53342e15 | −1.33489 | ||||||||
\(732\) | −6.39031e14 | − | 2.27715e13i | −0.112386 | − | 0.00400480i | ||||
\(733\) | 4.26471e15i | 0.744420i | 0.928149 | + | 0.372210i | \(0.121400\pi\) | ||||
−0.928149 | + | 0.372210i | \(0.878600\pi\) | |||||||
\(734\) | −6.54618e15 | + | 6.31706e15i | −1.13412 | + | 1.09443i | ||||
\(735\) | −4.28523e14 | − | 2.11108e15i | −0.0736875 | − | 0.363015i | ||||
\(736\) | −2.81679e14 | − | 3.36909e14i | −0.0480758 | − | 0.0575023i | ||||
\(737\) | −5.99177e15 | −1.01504 | ||||||||
\(738\) | 1.71762e15 | + | 1.77992e15i | 0.288814 | + | 0.299289i | ||||
\(739\) | − | 1.18750e16i | − | 1.98193i | −0.134124 | − | 0.990965i | \(-0.542822\pi\) | ||
0.134124 | − | 0.990965i | \(-0.457178\pi\) | |||||||
\(740\) | 5.74748e15 | + | 2.04808e14i | 0.952145 | + | 0.0339291i | ||||
\(741\) | − | 6.43026e15i | − | 1.05737i | ||||||
\(742\) | −4.20772e15 | + | 4.96452e15i | −0.686792 | + | 0.810319i | ||||
\(743\) | − | 2.39150e15i | − | 0.387464i | −0.981054 | − | 0.193732i | \(-0.937941\pi\) | ||
0.981054 | − | 0.193732i | \(-0.0620593\pi\) | |||||||
\(744\) | −1.44646e15 | − | 1.60991e15i | −0.232624 | − | 0.258911i | ||||
\(745\) | 5.38575e15i | 0.859778i | ||||||||
\(746\) | 2.17330e15 | − | 2.09723e15i | 0.344394 | − | 0.332340i | ||||
\(747\) | −2.29834e15 | −0.361536 | ||||||||
\(748\) | 1.76283e14 | − | 4.94700e15i | 0.0275266 | − | 0.772472i | ||||
\(749\) | 9.87205e14 | + | 9.82593e15i | 0.153023 | + | 1.52308i | ||||
\(750\) | 2.65517e15 | + | 2.75147e15i | 0.408559 | + | 0.423377i | ||||
\(751\) | 1.10256e16i | 1.68415i | 0.539359 | + | 0.842076i | \(0.318666\pi\) | ||||
−0.539359 | + | 0.842076i | \(0.681334\pi\) | |||||||
\(752\) | 1.43885e15 | + | 1.02676e14i | 0.218181 | + | 0.0155693i | ||||
\(753\) | −4.10657e15 | −0.618169 | ||||||||
\(754\) | 6.02018e15 | + | 6.23853e15i | 0.899637 | + | 0.932266i | ||||
\(755\) | −5.50986e14 | −0.0817396 | ||||||||
\(756\) | 8.42442e13 | + | 1.30402e15i | 0.0124071 | + | 0.192050i | ||||
\(757\) | 1.11914e16 | 1.63628 | 0.818139 | − | 0.575021i | \(-0.195006\pi\) | ||||
0.818139 | + | 0.575021i | \(0.195006\pi\) | |||||||
\(758\) | −4.66773e15 | − | 4.83703e15i | −0.677525 | − | 0.702098i | ||||
\(759\) | −2.28941e14 | −0.0329909 | ||||||||
\(760\) | −4.71460e15 | + | 4.23592e15i | −0.674481 | + | 0.606001i | ||||
\(761\) | − | 3.49689e15i | − | 0.496668i | −0.968674 | − | 0.248334i | \(-0.920117\pi\) | ||
0.968674 | − | 0.248334i | \(-0.0798831\pi\) | |||||||
\(762\) | 1.20156e15 | + | 1.24514e15i | 0.169431 | + | 0.175576i | ||||
\(763\) | −6.06197e15 | + | 6.09042e14i | −0.848650 | + | 0.0852633i | ||||
\(764\) | 6.49127e15 | + | 2.31313e14i | 0.902228 | + | 0.0321504i | ||||
\(765\) | 1.57129e15 | 0.216830 | ||||||||
\(766\) | −3.80467e15 | + | 3.67151e15i | −0.521265 | + | 0.503021i | ||||
\(767\) | − | 8.48052e15i | − | 1.15358i | ||||||
\(768\) | −4.23158e15 | − | 6.07018e14i | −0.571500 | − | 0.0819813i | ||||
\(769\) | − | 6.15624e15i | − | 0.825507i | −0.910843 | − | 0.412753i | \(-0.864567\pi\) | ||
0.910843 | − | 0.412753i | \(-0.135433\pi\) | |||||||
\(770\) | 2.37540e15 | − | 2.80264e15i | 0.316255 | − | 0.373137i | ||||
\(771\) | 4.45856e15i | 0.589380i | ||||||||
\(772\) | 4.97768e14 | − | 1.39687e16i | 0.0653328 | − | 1.83342i | ||||
\(773\) | 6.51219e15i | 0.848673i | 0.905505 | + | 0.424336i | \(0.139493\pi\) | ||||
−0.905505 | + | 0.424336i | \(0.860507\pi\) | |||||||
\(774\) | 2.35518e15 | + | 2.44060e15i | 0.304754 | + | 0.315807i | ||||
\(775\) | 2.76077e15 | 0.354709 | ||||||||
\(776\) | 3.94211e15 | − | 3.54187e15i | 0.502909 | − | 0.451849i | ||||
\(777\) | −6.73441e15 | + | 6.76602e14i | −0.853069 | + | 0.0857072i | ||||
\(778\) | 8.17706e15 | − | 7.89087e15i | 1.02851 | − | 0.992515i | ||||
\(779\) | − | 1.41192e16i | − | 1.76341i | ||||||
\(780\) | 1.37838e14 | − | 3.86812e15i | 0.0170942 | − | 0.479711i | ||||
\(781\) | 2.54033e15 | 0.312831 | ||||||||
\(782\) | 4.47188e14 | − | 4.31537e14i | 0.0546831 | − | 0.0527692i | ||||
\(783\) | 1.58453e15 | 0.192403 | ||||||||
\(784\) | −8.22457e15 | + | 1.06713e15i | −0.991687 | + | 0.128670i | ||||
\(785\) | 4.18023e15 | 0.500514 | ||||||||
\(786\) | 5.90443e15 | − | 5.69778e15i | 0.702027 | − | 0.677456i | ||||
\(787\) | 8.41526e14 | 0.0993588 | 0.0496794 | − | 0.998765i | \(-0.484180\pi\) | ||||
0.0496794 | + | 0.998765i | \(0.484180\pi\) | |||||||
\(788\) | 5.81913e13 | − | 1.63301e15i | 0.00682282 | − | 0.191467i | ||||
\(789\) | − | 5.64957e15i | − | 0.657796i | ||||||
\(790\) | 7.59582e15 | − | 7.32996e15i | 0.878265 | − | 0.847526i | ||||
\(791\) | 1.29933e16 | − | 1.30543e15i | 1.49193 | − | 0.149894i | ||||
\(792\) | −1.65779e15 | + | 1.48948e15i | −0.189035 | + | 0.169842i | ||||
\(793\) | −2.22902e15 | −0.252412 | ||||||||
\(794\) | 6.07392e15 | + | 6.29422e15i | 0.683057 | + | 0.707830i | ||||
\(795\) | − | 3.52309e15i | − | 0.393464i | ||||||
\(796\) | 1.32551e13 | − | 3.71974e14i | 0.00147015 | − | 0.0412564i | ||||
\(797\) | 2.83110e14i | 0.0311842i | 0.999878 | + | 0.0155921i | \(0.00496331\pi\) | ||||
−0.999878 | + | 0.0155921i | \(0.995037\pi\) | |||||||
\(798\) | 4.82274e15 | − | 5.69016e15i | 0.527568 | − | 0.622456i | ||||
\(799\) | 2.04134e15i | 0.221772i | ||||||||
\(800\) | 4.18358e15 | − | 3.49776e15i | 0.451392 | − | 0.377394i | ||||
\(801\) | − | 3.73727e15i | − | 0.400476i | ||||||
\(802\) | 1.65249e15 | − | 1.59466e15i | 0.175865 | − | 0.169710i | ||||
\(803\) | 3.11378e15 | 0.329119 | ||||||||
\(804\) | −7.31787e15 | − | 2.60768e14i | −0.768204 | − | 0.0273745i | ||||
\(805\) | 4.58915e14 | − | 4.61069e13i | 0.0478470 | − | 0.00480716i | ||||
\(806\) | −5.23887e15 | − | 5.42888e15i | −0.542494 | − | 0.562169i | ||||
\(807\) | − | 9.55497e15i | − | 0.982709i | ||||||
\(808\) | −9.02309e15 | + | 8.10698e15i | −0.921707 | + | 0.828126i | ||||
\(809\) | 1.24272e16 | 1.26083 | 0.630416 | − | 0.776258i | \(-0.282884\pi\) | ||||
0.630416 | + | 0.776258i | \(0.282884\pi\) | |||||||
\(810\) | −4.91235e14 | − | 5.09051e14i | −0.0495018 | − | 0.0512972i | ||||
\(811\) | −1.07557e16 | −1.07653 | −0.538263 | − | 0.842777i | \(-0.680919\pi\) | ||||
−0.538263 | + | 0.842777i | \(0.680919\pi\) | |||||||
\(812\) | 6.48341e14 | + | 1.00357e16i | 0.0644533 | + | 0.997674i | ||||
\(813\) | 4.65796e15 | 0.459936 | ||||||||
\(814\) | −8.01572e15 | − | 8.30644e15i | −0.786155 | − | 0.814668i | ||||
\(815\) | −1.35186e15 | −0.131694 | ||||||||
\(816\) | 4.30597e14 | − | 6.03419e15i | 0.0416653 | − | 0.583880i | ||||
\(817\) | − | 1.93601e16i | − | 1.86074i | ||||||
\(818\) | −9.19267e15 | − | 9.52608e15i | −0.877604 | − | 0.909434i | ||||
\(819\) | 4.55361e14 | + | 4.53234e15i | 0.0431812 | + | 0.429795i | ||||
\(820\) | 3.02658e14 | − | 8.49341e15i | 0.0285086 | − | 0.800029i | ||||
\(821\) | 1.66989e16 | 1.56243 | 0.781214 | − | 0.624263i | \(-0.214601\pi\) | ||||
0.781214 | + | 0.624263i | \(0.214601\pi\) | |||||||
\(822\) | −5.04179e14 | + | 4.86533e14i | −0.0468587 | + | 0.0452186i | ||||
\(823\) | 4.63913e15i | 0.428289i | 0.976802 | + | 0.214145i | \(0.0686964\pi\) | ||||
−0.976802 | + | 0.214145i | \(0.931304\pi\) | |||||||
\(824\) | 6.70390e15 | + | 7.46146e15i | 0.614791 | + | 0.684265i | ||||
\(825\) | − | 2.84288e15i | − | 0.258978i | ||||||
\(826\) | 6.36045e15 | − | 7.50444e15i | 0.575569 | − | 0.679091i | ||||
\(827\) | − | 2.17176e15i | − | 0.195223i | −0.995225 | − | 0.0976117i | \(-0.968880\pi\) | ||
0.995225 | − | 0.0976117i | \(-0.0311203\pi\) | |||||||
\(828\) | −2.79610e14 | − | 9.96375e12i | −0.0249681 | − | 0.000889725i | ||||
\(829\) | 6.24017e15i | 0.553537i | 0.960937 | + | 0.276768i | \(0.0892635\pi\) | ||||
−0.960937 | + | 0.276768i | \(0.910737\pi\) | |||||||
\(830\) | 5.48361e15 | + | 5.68249e15i | 0.483211 | + | 0.500737i | ||||
\(831\) | 7.39114e15 | 0.647002 | ||||||||
\(832\) | −1.48169e16 | − | 1.58936e15i | −1.28848 | − | 0.138211i | ||||
\(833\) | −2.33473e15 | − | 1.15018e16i | −0.201692 | − | 0.993617i | ||||
\(834\) | 4.83181e14 | − | 4.66270e14i | 0.0414664 | − | 0.0400151i | ||||
\(835\) | − | 8.14172e15i | − | 0.694129i | ||||||
\(836\) | 1.27132e16 | + | 4.53029e14i | 1.07677 | + | 0.0383700i | ||||
\(837\) | −1.37889e15 | −0.116021 | ||||||||
\(838\) | 5.19026e15 | − | 5.00860e15i | 0.433857 | − | 0.418673i | ||||
\(839\) | 9.67165e15 | 0.803175 | 0.401587 | − | 0.915821i | \(-0.368459\pi\) | ||||
0.401587 | + | 0.915821i | \(0.368459\pi\) | |||||||
\(840\) | 3.02309e15 | − | 3.31954e15i | 0.249411 | − | 0.273868i | ||||
\(841\) | −6.01842e12 | −0.000493293 | ||||||||
\(842\) | −8.71693e15 | + | 8.41184e15i | −0.709818 | + | 0.684974i | ||||
\(843\) | −2.25369e15 | −0.182323 | ||||||||
\(844\) | 1.14733e16 | + | 4.08845e14i | 0.922158 | + | 0.0328606i | ||||
\(845\) | − | 5.45787e15i | − | 0.435824i | ||||||
\(846\) | 6.61332e14 | − | 6.38186e14i | 0.0524665 | − | 0.0506302i | ||||
\(847\) | 5.28640e15 | − | 5.31121e14i | 0.416679 | − | 0.0418634i | ||||
\(848\) | −1.35297e16 | − | 9.65469e14i | −1.05952 | − | 0.0756068i | ||||
\(849\) | 1.08581e16 | 0.844812 | ||||||||
\(850\) | 5.35863e15 | + | 5.55298e15i | 0.414237 | + | 0.429261i | ||||
\(851\) | − | 1.44918e15i | − | 0.111303i | ||||||
\(852\) | 3.10255e15 | + | 1.10558e14i | 0.236756 | + | 0.00843667i | ||||
\(853\) | 1.74669e16i | 1.32433i | 0.749358 | + | 0.662165i | \(0.230362\pi\) | ||||
−0.749358 | + | 0.662165i | \(0.769638\pi\) | |||||||
\(854\) | −1.97246e15 | − | 1.67178e15i | −0.148590 | − | 0.125939i | ||||
\(855\) | 4.03804e15i | 0.302244i | ||||||||
\(856\) | −1.53109e16 | + | 1.37564e16i | −1.13866 | + | 1.02306i | ||||
\(857\) | 2.51032e16i | 1.85496i | 0.373873 | + | 0.927480i | \(0.378029\pi\) | ||||
−0.373873 | + | 0.927480i | \(0.621971\pi\) | |||||||
\(858\) | −5.59034e15 | + | 5.39468e15i | −0.410448 | + | 0.396082i | ||||
\(859\) | −1.76987e16 | −1.29115 | −0.645577 | − | 0.763695i | \(-0.723383\pi\) | ||||
−0.645577 | + | 0.763695i | \(0.723383\pi\) | |||||||
\(860\) | 4.15000e14 | − | 1.16460e16i | 0.0300820 | − | 0.844184i | ||||
\(861\) | 9.99857e14 | + | 9.95186e15i | 0.0720146 | + | 0.716782i | ||||
\(862\) | −1.28368e16 | − | 1.33024e16i | −0.918686 | − | 0.952006i | ||||
\(863\) | 2.26334e16i | 1.60950i | 0.593615 | + | 0.804749i | \(0.297700\pi\) | ||||
−0.593615 | + | 0.804749i | \(0.702300\pi\) | |||||||
\(864\) | −2.08952e15 | + | 1.74698e15i | −0.147646 | + | 0.123442i | ||||
\(865\) | −3.17644e15 | −0.223024 | ||||||||
\(866\) | −1.08705e15 | − | 1.12648e15i | −0.0758405 | − | 0.0785912i | ||||
\(867\) | 2.32807e14 | 0.0161395 | ||||||||
\(868\) | −5.64197e14 | − | 8.73322e15i | −0.0388662 | − | 0.601611i | ||||
\(869\) | −2.11870e16 | −1.45031 | ||||||||
\(870\) | −3.78052e15 | − | 3.91764e15i | −0.257156 | − | 0.266482i | ||||
\(871\) | −2.55256e16 | −1.72534 | ||||||||
\(872\) | −8.48682e15 | − | 9.44586e15i | −0.570039 | − | 0.634455i | ||||
\(873\) | − | 3.37641e15i | − | 0.225360i | ||||||
\(874\) | 1.10900e15 | + | 1.14923e15i | 0.0735563 | + | 0.0762241i | ||||
\(875\) | 1.54562e15 | + | 1.53840e16i | 0.101873 | + | 1.01397i | ||||
\(876\) | 3.80293e15 | + | 1.35515e14i | 0.249084 | + | 0.00887595i | ||||
\(877\) | 7.99857e15 | 0.520612 | 0.260306 | − | 0.965526i | \(-0.416177\pi\) | ||||
0.260306 | + | 0.965526i | \(0.416177\pi\) | |||||||
\(878\) | −3.16798e14 | + | 3.05710e14i | −0.0204910 | + | 0.0197738i | ||||
\(879\) | − | 5.88077e15i | − | 0.378003i | ||||||
\(880\) | 7.63794e15 | + | 5.45039e14i | 0.487889 | + | 0.0348155i | ||||
\(881\) | − | 4.50306e15i | − | 0.285851i | −0.989733 | − | 0.142926i | \(-0.954349\pi\) | ||
0.989733 | − | 0.142926i | \(-0.0456510\pi\) | |||||||
\(882\) | −2.99634e15 | + | 4.35221e15i | −0.189023 | + | 0.274557i | ||||
\(883\) | 3.45453e15i | 0.216573i | 0.994120 | + | 0.108287i | \(0.0345364\pi\) | ||||
−0.994120 | + | 0.108287i | \(0.965464\pi\) | |||||||
\(884\) | 7.50986e14 | − | 2.10747e16i | 0.0467891 | − | 1.31303i | ||||
\(885\) | 5.32555e15i | 0.329744i | ||||||||
\(886\) | −7.46878e15 | − | 7.73966e15i | −0.459583 | − | 0.476252i | ||||
\(887\) | −4.50027e15 | −0.275207 | −0.137603 | − | 0.990487i | \(-0.543940\pi\) | ||||
−0.137603 | + | 0.990487i | \(0.543940\pi\) | |||||||
\(888\) | −9.42825e15 | − | 1.04937e16i | −0.573007 | − | 0.637758i | ||||
\(889\) | 6.99445e14 | + | 6.96178e15i | 0.0422468 | + | 0.420495i | ||||
\(890\) | −9.24014e15 | + | 8.91674e15i | −0.554669 | + | 0.535255i | ||||
\(891\) | 1.41990e15i | 0.0847089i | ||||||||
\(892\) | −1.02856e15 | + | 2.88642e16i | −0.0609850 | + | 1.71141i | ||||
\(893\) | −5.24601e15 | −0.309133 | ||||||||
\(894\) | 9.50633e15 | − | 9.17361e15i | 0.556745 | − | 0.537259i | ||||
\(895\) | −2.78152e15 | −0.161903 | ||||||||
\(896\) | −1.19195e16 | − | 1.25192e16i | −0.689547 | − | 0.724241i | ||||
\(897\) | −9.75313e14 | −0.0560771 | ||||||||
\(898\) | −2.20553e16 | + | 2.12834e16i | −1.26035 | + | 1.21624i | ||||
\(899\) | −1.06119e16 | −0.602716 | ||||||||
\(900\) | 1.23725e14 | − | 3.47207e15i | 0.00698432 | − | 0.195999i | ||||
\(901\) | − | 1.91949e16i | − | 1.07696i | ||||||
\(902\) | −1.22749e16 | + | 1.18453e16i | −0.684516 | + | 0.660558i | ||||
\(903\) | 1.37099e15 | + | 1.36459e16i | 0.0759892 | + | 0.756342i | ||||
\(904\) | 1.81908e16 | + | 2.02464e16i | 1.00213 | + | 1.11538i | ||||
\(905\) | 6.17264e15 | 0.337990 | ||||||||
\(906\) | 9.38502e14 | + | 9.72540e14i | 0.0510775 | + | 0.0529301i | ||||
\(907\) | 3.48914e16i | 1.88746i | 0.330716 | + | 0.943730i | \(0.392710\pi\) | ||||
−0.330716 | + | 0.943730i | \(0.607290\pi\) | |||||||
\(908\) | 1.06444e14 | − | 2.98712e15i | 0.00572334 | − | 0.160613i | ||||
\(909\) | 7.72826e15i | 0.413029i | ||||||||
\(910\) | 1.01195e16 | − | 1.19395e16i | 0.537563 | − | 0.634249i | ||||
\(911\) | 1.76541e16i | 0.932167i | 0.884741 | + | 0.466084i | \(0.154335\pi\) | ||||
−0.884741 | + | 0.466084i | \(0.845665\pi\) | |||||||
\(912\) | 1.55072e16 | + | 1.10659e15i | 0.813883 | + | 0.0580783i | ||||
\(913\) | − | 1.58502e16i | − | 0.826884i | ||||||
\(914\) | 1.30455e16 | − | 1.25889e16i | 0.676483 | − | 0.652807i | ||||
\(915\) | 1.39977e15 | 0.0721505 | ||||||||
\(916\) | 1.96376e16 | + | 6.99775e14i | 1.00615 | + | 0.0358536i | ||||
\(917\) | 3.30127e16 | − | 3.31677e15i | 1.68132 | − | 0.168921i | ||||
\(918\) | −2.67640e15 | − | 2.77347e15i | −0.135493 | − | 0.140407i | ||||
\(919\) | 1.41179e16i | 0.710451i | 0.934781 | + | 0.355226i | \(0.115596\pi\) | ||||
−0.934781 | + | 0.355226i | \(0.884404\pi\) | |||||||
\(920\) | 6.42486e14 | + | 7.15089e14i | 0.0321389 | + | 0.0357707i | ||||
\(921\) | −1.37596e16 | −0.684190 | ||||||||
\(922\) | 2.01152e16 | + | 2.08448e16i | 0.994272 | + | 1.03033i | ||||
\(923\) | 1.08221e16 | 0.531742 | ||||||||
\(924\) | −8.99295e15 | + | 5.80977e14i | −0.439245 | + | 0.0283768i | ||||
\(925\) | 1.79952e16 | 0.873730 | ||||||||
\(926\) | 4.58721e15 | + | 4.75359e15i | 0.221406 | + | 0.229436i | ||||
\(927\) | 6.39073e15 | 0.306628 | ||||||||
\(928\) | −1.60808e16 | + | 1.34447e16i | −0.766999 | + | 0.641263i | ||||
\(929\) | − | 9.39791e15i | − | 0.445600i | −0.974864 | − | 0.222800i | \(-0.928480\pi\) | ||
0.974864 | − | 0.222800i | \(-0.0715197\pi\) | |||||||
\(930\) | 3.28988e15 | + | 3.40920e15i | 0.155068 | + | 0.160693i | ||||
\(931\) | 2.95584e16 | − | 5.99999e15i | 1.38503 | − | 0.281143i | ||||
\(932\) | −8.14224e14 | + | 2.28494e16i | −0.0379277 | + | 1.06436i | ||||
\(933\) | 1.18451e16 | 0.548518 | ||||||||
\(934\) | −1.61158e13 | + | 1.55517e13i | −0.000741896 | + | 0.000715930i | ||||
\(935\) | 1.08362e16i | 0.495920i | ||||||||
\(936\) | −7.06237e15 | + | 6.34533e15i | −0.321317 | + | 0.288693i | ||||
\(937\) | 6.83842e15i | 0.309306i | 0.987969 | + | 0.154653i | \(0.0494260\pi\) | ||||
−0.987969 | + | 0.154653i | \(0.950574\pi\) | |||||||
\(938\) | −2.25877e16 | − | 1.91444e16i | −1.01568 | − | 0.860846i | ||||
\(939\) | 1.11606e16i | 0.498916i | ||||||||
\(940\) | −3.15574e15 | − | 1.12453e14i | −0.140248 | − | 0.00499767i | ||||
\(941\) | − | 1.73416e15i | − | 0.0766205i | −0.999266 | − | 0.0383103i | \(-0.987802\pi\) | ||
0.999266 | − | 0.0383103i | \(-0.0121975\pi\) | |||||||
\(942\) | −7.12023e15 | − | 7.37848e15i | −0.312762 | − | 0.324106i | ||||
\(943\) | −2.14154e15 | −0.0935215 | ||||||||
\(944\) | 2.04516e16 | + | 1.45942e15i | 0.887936 | + | 0.0633626i | ||||
\(945\) | −2.85955e14 | − | 2.84620e15i | −0.0123431 | − | 0.122854i | ||||
\(946\) | −1.68312e16 | + | 1.62421e16i | −0.722295 | + | 0.697015i | ||||
\(947\) | 1.15888e16i | 0.494439i | 0.968960 | + | 0.247219i | \(0.0795168\pi\) | ||||
−0.968960 | + | 0.247219i | \(0.920483\pi\) | |||||||
\(948\) | −2.58761e16 | − | 9.22080e14i | −1.09762 | − | 0.0391131i | ||||
\(949\) | 1.32651e16 | 0.559429 | ||||||||
\(950\) | −1.42705e16 | + | 1.37711e16i | −0.598358 | + | 0.577415i | ||||
\(951\) | 1.16320e16 | 0.484909 | ||||||||
\(952\) | 1.64708e16 | − | 1.80859e16i | 0.682669 | − | 0.749611i | ||||
\(953\) | 8.72826e15 | 0.359680 | 0.179840 | − | 0.983696i | \(-0.442442\pi\) | ||||
0.179840 | + | 0.983696i | \(0.442442\pi\) | |||||||
\(954\) | −6.21857e15 | + | 6.00093e15i | −0.254786 | + | 0.245868i | ||||
\(955\) | −1.42188e16 | −0.579222 | ||||||||
\(956\) | 1.92071e16 | + | 6.84436e14i | 0.777937 | + | 0.0277213i | ||||
\(957\) | 1.09275e16i | 0.440052i | ||||||||
\(958\) | 7.44885e15 | − | 7.18814e15i | 0.298249 | − | 0.287810i | ||||
\(959\) | −2.81896e15 | + | 2.83219e14i | −0.112224 | + | 0.0112751i | ||||
\(960\) | 9.30464e15 | + | 9.98078e14i | 0.368305 | + | 0.0395069i | ||||
\(961\) | −1.61739e16 | −0.636554 | ||||||||
\(962\) | −3.41478e16 | − | 3.53863e16i | −1.33629 | − | 1.38475i | ||||
\(963\) | 1.31138e16i | 0.510250i | ||||||||
\(964\) | −1.32561e16 | − | 4.72375e14i | −0.512854 | − | 0.0182753i | ||||
\(965\) | 3.05978e16i | 1.17704i | ||||||||
\(966\) | −8.63058e14 | − | 7.31492e14i | −0.0330115 | − | 0.0279792i | ||||
\(967\) | − | 3.48013e16i | − | 1.32358i | −0.749690 | − | 0.661790i | \(-0.769797\pi\) | ||
0.749690 | − | 0.661790i | \(-0.230203\pi\) | |||||||
\(968\) | 7.40102e15 | + | 8.23736e15i | 0.279883 | + | 0.311511i | ||||
\(969\) | 2.20005e16i | 0.827279i | ||||||||
\(970\) | −8.34794e15 | + | 8.05577e15i | −0.312130 | + | 0.301205i | ||||
\(971\) | −1.59839e16 | −0.594262 | −0.297131 | − | 0.954837i | \(-0.596030\pi\) | ||||
−0.297131 | + | 0.954837i | \(0.596030\pi\) | |||||||
\(972\) | −6.17953e13 | + | 1.73415e15i | −0.00228450 | + | 0.0641093i | ||||
\(973\) | 2.70155e15 | − | 2.71423e14i | 0.0993099 | − | 0.00997760i | ||||
\(974\) | −3.32444e16 | − | 3.44501e16i | −1.21519 | − | 1.25926i | ||||
\(975\) | − | 1.21110e16i | − | 0.440204i | ||||||
\(976\) | 3.83592e14 | − | 5.37549e15i | 0.0138642 | − | 0.194287i | ||||
\(977\) | −1.92350e16 | −0.691310 | −0.345655 | − | 0.938362i | \(-0.612343\pi\) | ||||
−0.345655 | + | 0.938362i | \(0.612343\pi\) | |||||||
\(978\) | 2.30264e15 | + | 2.38615e15i | 0.0822928 | + | 0.0852775i | ||||
\(979\) | 2.57735e16 | 0.915944 | ||||||||
\(980\) | 1.79095e16 | − | 2.97568e15i | 0.632906 | − | 0.105158i | ||||
\(981\) | −8.09036e15 | −0.284308 | ||||||||
\(982\) | 1.95801e16 | + | 2.02902e16i | 0.684229 | + | 0.709045i | ||||
\(983\) | −1.79838e16 | −0.624937 | −0.312469 | − | 0.949928i | \(-0.601156\pi\) | ||||
−0.312469 | + | 0.949928i | \(0.601156\pi\) | |||||||
\(984\) | −1.55072e16 | + | 1.39327e16i | −0.535870 | + | 0.481463i | ||||
\(985\) | 3.57703e15i | 0.122920i | ||||||||
\(986\) | −2.05975e16 | − | 2.13445e16i | −0.703867 | − | 0.729396i | ||||
\(987\) | 3.69763e15 | − | 3.71498e14i | 0.125655 | − | 0.0126244i | ||||
\(988\) | 5.41598e16 | + | 1.92995e15i | 1.83026 | + | 0.0652204i | ||||
\(989\) | −2.93645e15 | −0.0986831 | ||||||||
\(990\) | 3.51059e15 | − | 3.38772e15i | 0.117324 | − | 0.113218i | ||||
\(991\) | 1.42077e15i | 0.0472193i | 0.999721 | + | 0.0236097i | \(0.00751588\pi\) | ||||
−0.999721 | + | 0.0236097i | \(0.992484\pi\) | |||||||
\(992\) | 1.39938e16 | − | 1.16998e16i | 0.462511 | − | 0.386691i | ||||
\(993\) | 3.08359e16i | 1.01353i | ||||||||
\(994\) | 9.57649e15 | + | 8.11663e15i | 0.313027 | + | 0.265308i | ||||
\(995\) | 8.14791e14i | 0.0264862i | ||||||||
\(996\) | 6.89816e14 | − | 1.93581e16i | 0.0223001 | − | 0.625802i | ||||
\(997\) | − | 5.05628e16i | − | 1.62558i | −0.582558 | − | 0.812789i | \(-0.697948\pi\) | ||
0.582558 | − | 0.812789i | \(-0.302052\pi\) | |||||||
\(998\) | −1.38233e16 | − | 1.43247e16i | −0.441971 | − | 0.458001i | ||||
\(999\) | −8.98781e15 | −0.285788 |
(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 | 84.12.b.a.55.12 | yes | 44 | |
4.3 | odd | 2 | 84.12.b.b.55.11 | yes | 44 | ||
7.6 | odd | 2 | 84.12.b.b.55.12 | yes | 44 | ||
28.27 | even | 2 | inner | 84.12.b.a.55.11 | ✓ | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.b.a.55.11 | ✓ | 44 | 28.27 | even | 2 | inner | |
84.12.b.a.55.12 | yes | 44 | 1.1 | even | 1 | trivial | |
84.12.b.b.55.11 | yes | 44 | 4.3 | odd | 2 | ||
84.12.b.b.55.12 | yes | 44 | 7.6 | odd | 2 |